LMFDB - Embedded newform 162.2.e.b.37.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [162,2,Mod(19,162)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(162, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([16]))

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

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

chi := DirichletCharacter("162.19");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 162 = 2 \cdot 3^{4} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	162.e (of order $9$, degree $6$, 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:	$1.29357651274$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$2$ over $\Q(\zeta_{9})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 6 x^{11} + 33 x^{10} - 110 x^{9} + 318 x^{8} - 678 x^{7} + 1225 x^{6} - 1698 x^{5} + 1905 x^{4} + \cdots + 57 $ x^12 - 6x^11 + 33x^10 - 110x^9 + 318x^8 - 678x^7 + 1225x^6 - 1698x^5 + 1905x^4 - 1584x^3 + 936x^2 - 342*x + 57
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 3^{3} $
Twist minimal:	no (minimal twist has level 54)
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			37.2
Root			$0.500000 + 1.80139i$ of defining polynomial
Character	$\chi$	$=$	162.37
Dual form			162.2.e.b.127.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.766044 + 0.642788i) q^{2} +(0.173648 - 0.984808i) q^{4} +(1.96209 - 0.714144i) q^{5} +(-0.696712 - 3.95125i) q^{7} +(0.500000 + 0.866025i) q^{8} +O(q^{10})$	\(q+(-0.766044 + 0.642788i) q^{2} +(0.173648 - 0.984808i) q^{4} +(1.96209 - 0.714144i) q^{5} +(-0.696712 - 3.95125i) q^{7} +(0.500000 + 0.866025i) q^{8} +(-1.04401 + 1.80828i) q^{10} +(0.199635 + 0.0726611i) q^{11} +(3.98269 + 3.34187i) q^{13} +(3.07353 + 2.57900i) q^{14} +(-0.939693 - 0.342020i) q^{16} +(1.89276 - 3.27836i) q^{17} +(0.636405 + 1.10229i) q^{19} +(-0.362580 - 2.05630i) q^{20} +(-0.199635 + 0.0726611i) q^{22} +(-0.144031 + 0.816841i) q^{23} +(-0.490411 + 0.411503i) q^{25} -5.19903 q^{26} -4.01220 q^{28} +(-7.05621 + 5.92087i) q^{29} +(0.614003 - 3.48219i) q^{31} +(0.939693 - 0.342020i) q^{32} +(0.657349 + 3.72801i) q^{34} +(-4.18878 - 7.25517i) q^{35} +(-1.77730 + 3.07838i) q^{37} +(-1.19605 - 0.435326i) q^{38} +(1.59951 + 1.34215i) q^{40} +(-2.09850 - 1.76085i) q^{41} +(-6.48062 - 2.35875i) q^{43} +(0.106223 - 0.183984i) q^{44} +(-0.414721 - 0.718318i) q^{46} +(0.221796 + 1.25787i) q^{47} +(-8.54912 + 3.11163i) q^{49} +(0.111167 - 0.630460i) q^{50} +(3.98269 - 3.34187i) q^{52} +11.2992 q^{53} +0.443592 q^{55} +(3.07353 - 2.57900i) q^{56} +(1.59951 - 9.07129i) q^{58} +(-8.04363 + 2.92764i) q^{59} +(0.492064 + 2.79063i) q^{61} +(1.76795 + 3.06218i) q^{62} +(-0.500000 + 0.866025i) q^{64} +(10.2010 + 3.71285i) q^{65} +(7.47702 + 6.27396i) q^{67} +(-2.89988 - 2.43329i) q^{68} +(7.87232 + 2.86529i) q^{70} +(-5.86207 + 10.1534i) q^{71} +(-0.375162 - 0.649800i) q^{73} +(-0.617250 - 3.50060i) q^{74} +(1.19605 - 0.435326i) q^{76} +(0.148014 - 0.839430i) q^{77} +(-1.81383 + 1.52198i) q^{79} -2.08802 q^{80} +2.73940 q^{82} +(8.73328 - 7.32809i) q^{83} +(1.37256 - 7.78415i) q^{85} +(6.48062 - 2.35875i) q^{86} +(0.0368910 + 0.209219i) q^{88} +(2.69813 + 4.67329i) q^{89} +(10.4298 - 18.0649i) q^{91} +(0.779421 + 0.283686i) q^{92} +(-0.978448 - 0.821016i) q^{94} +(2.03588 + 1.70830i) q^{95} +(11.8055 + 4.29685i) q^{97} +(4.54889 - 7.87892i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 3 q^{5} - 3 q^{7} + 6 q^{8}+O(q^{10}) $ 12 * q + 3 * q^5 - 3 * q^7 + 6 * q^8	$ 12 q + 3 q^{5} - 3 q^{7} + 6 q^{8} - 3 q^{10} + 12 q^{11} + 12 q^{13} + 3 q^{14} + 6 q^{17} - 9 q^{19} - 6 q^{20} - 12 q^{22} - 30 q^{23} - 9 q^{25} - 18 q^{26} + 12 q^{28} - 15 q^{29} - 15 q^{34} - 3 q^{35} - 15 q^{37} - 3 q^{38} - 3 q^{40} + 12 q^{41} + 9 q^{43} + 3 q^{44} + 3 q^{46} + 9 q^{47} - 39 q^{49} + 27 q^{50} + 12 q^{52} + 12 q^{53} + 18 q^{55} + 3 q^{56} - 3 q^{58} - 12 q^{59} - 36 q^{61} + 12 q^{62} - 6 q^{64} + 15 q^{65} + 36 q^{67} - 3 q^{68} + 39 q^{70} - 12 q^{71} - 21 q^{73} - 33 q^{74} + 3 q^{76} - 3 q^{77} + 39 q^{79} - 6 q^{80} + 6 q^{82} - 18 q^{83} + 45 q^{85} - 9 q^{86} + 6 q^{88} - 12 q^{89} - 6 q^{91} + 6 q^{92} + 36 q^{94} + 15 q^{95} + 39 q^{97} + 12 q^{98}+O(q^{100}) $ 12 * q + 3 * q^5 - 3 * q^7 + 6 * q^8 - 3 * q^10 + 12 * q^11 + 12 * q^13 + 3 * q^14 + 6 * q^17 - 9 * q^19 - 6 * q^20 - 12 * q^22 - 30 * q^23 - 9 * q^25 - 18 * q^26 + 12 * q^28 - 15 * q^29 - 15 * q^34 - 3 * q^35 - 15 * q^37 - 3 * q^38 - 3 * q^40 + 12 * q^41 + 9 * q^43 + 3 * q^44 + 3 * q^46 + 9 * q^47 - 39 * q^49 + 27 * q^50 + 12 * q^52 + 12 * q^53 + 18 * q^55 + 3 * q^56 - 3 * q^58 - 12 * q^59 - 36 * q^61 + 12 * q^62 - 6 * q^64 + 15 * q^65 + 36 * q^67 - 3 * q^68 + 39 * q^70 - 12 * q^71 - 21 * q^73 - 33 * q^74 + 3 * q^76 - 3 * q^77 + 39 * q^79 - 6 * q^80 + 6 * q^82 - 18 * q^83 + 45 * q^85 - 9 * q^86 + 6 * q^88 - 12 * q^89 - 6 * q^91 + 6 * q^92 + 36 * q^94 + 15 * q^95 + 39 * q^97 + 12 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/162\mathbb{Z}\right)^\times$.

$n$	$83$
$\chi(n)$	$e\left(\frac{7}{9}\right)$

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 $

$2$	−0.766044	+	0.642788i	−0.541675	+	0.454519i
$2$	−0.766044	+	0.642788i	−0.541675	+	0.454519i
$3$		0			0
$3$		0			0
$4$	0.173648	−	0.984808i	0.0868241	−	0.492404i
$5$	1.96209	−	0.714144i	0.877475	−	0.319375i	0.136285	−	0.990670i	$-0.456484\pi$
$5$	1.96209	−	0.714144i	0.877475	−	0.319375i	0.741190	+	0.671295i	$0.234262\pi$
$6$		0			0
$7$	−0.696712	−	3.95125i	−0.263332	−	1.49343i	−0.773742	−	0.633501i	$-0.781617\pi$
$7$	−0.696712	−	3.95125i	−0.263332	−	1.49343i	0.510410	−	0.859931i	$-0.329494\pi$
$8$	0.500000	+	0.866025i	0.176777	+	0.306186i
$9$		0			0
$10$	−1.04401	+	1.80828i	−0.330144	+	0.571827i
$11$	0.199635	+	0.0726611i	0.0601921	+	0.0219081i	0.371941	−	0.928256i	$-0.378692\pi$
$11$	0.199635	+	0.0726611i	0.0601921	+	0.0219081i	−0.311749	+	0.950165i	$0.600915\pi$
$12$		0			0
$13$	3.98269	+	3.34187i	1.10460	+	0.926868i	0.997726	−	0.0674046i	$-0.0214718\pi$
$13$	3.98269	+	3.34187i	1.10460	+	0.926868i	0.106873	+	0.994273i	$0.465916\pi$
$14$	3.07353	+	2.57900i	0.821435	+	0.689266i
$15$		0			0
$16$	−0.939693	−	0.342020i	−0.234923	−	0.0855050i
$17$	1.89276	−	3.27836i	0.459062	−	0.795119i	−0.539850	−	0.841762i	$-0.681519\pi$
$17$	1.89276	−	3.27836i	0.459062	−	0.795119i	0.998912	+	0.0466426i	$0.0148522\pi$
$18$		0			0
$19$	0.636405	+	1.10229i	0.146001	+	0.252882i	0.929746	−	0.368201i	$-0.120026\pi$
$19$	0.636405	+	1.10229i	0.146001	+	0.252882i	−0.783745	+	0.621083i	$0.786693\pi$
$20$	−0.362580	−	2.05630i	−0.0810754	−	0.459802i
$21$		0			0
$22$	−0.199635	+	0.0726611i	−0.0425622	+	0.0154914i
$23$	−0.144031	+	0.816841i	−0.0300326	+	0.170323i	−0.996135	−	0.0878361i	$-0.972005\pi$
$23$	−0.144031	+	0.816841i	−0.0300326	+	0.170323i	0.966102	+	0.258159i	$0.0831159\pi$
$24$		0			0
$25$	−0.490411	+	0.411503i	−0.0980821	+	0.0823007i
$26$	−5.19903			−1.01961
$27$		0			0
$28$	−4.01220			−0.758235
$29$	−7.05621	+	5.92087i	−1.31031	+	1.09948i	−0.322041	+	0.946726i	$0.604369\pi$
$29$	−7.05621	+	5.92087i	−1.31031	+	1.09948i	−0.988265	+	0.152752i	$0.951187\pi$
$30$		0			0
$31$	0.614003	−	3.48219i	0.110278	−	0.625419i	−0.878702	−	0.477371i	$-0.841590\pi$
$31$	0.614003	−	3.48219i	0.110278	−	0.625419i	0.988980	−	0.148048i	$-0.0472991\pi$
$32$	0.939693	−	0.342020i	0.166116	−	0.0604612i
$33$		0			0
$34$	0.657349	+	3.72801i	0.112734	+	0.639349i
$35$	−4.18878	−	7.25517i	−0.708032	−	1.22635i
$36$		0			0
$37$	−1.77730	+	3.07838i	−0.292187	+	0.506082i	−0.974326	−	0.225140i	$-0.927716\pi$
$37$	−1.77730	+	3.07838i	−0.292187	+	0.506082i	0.682140	+	0.731222i	$0.261049\pi$
$38$	−1.19605	−	0.435326i	−0.194025	−	0.0706193i
$39$		0			0
$40$	1.59951	+	1.34215i	0.252905	+	0.212213i
$41$	−2.09850	−	1.76085i	−0.327730	−	0.274998i	0.464044	−	0.885812i	$-0.346398\pi$
$41$	−2.09850	−	1.76085i	−0.327730	−	0.274998i	−0.791774	+	0.610814i	$0.790842\pi$
$42$		0			0
$43$	−6.48062	−	2.35875i	−0.988286	−	0.359707i	−0.203229	−	0.979131i	$-0.565144\pi$
$43$	−6.48062	−	2.35875i	−0.988286	−	0.359707i	−0.785056	+	0.619425i	$0.787366\pi$
$44$	0.106223	−	0.183984i	0.0160138	−	0.0277367i
$45$		0			0
$46$	−0.414721	−	0.718318i	−0.0611473	−	0.105910i
$47$	0.221796	+	1.25787i	0.0323523	+	0.183479i	0.996702	−	0.0811536i	$-0.0258604\pi$
$47$	0.221796	+	1.25787i	0.0323523	+	0.183479i	−0.964349	+	0.264633i	$0.914749\pi$
$48$		0			0
$49$	−8.54912	+	3.11163i	−1.22130	+	0.444518i
$50$	0.111167	−	0.630460i	0.0157214	−	0.0891605i
$51$		0			0
$52$	3.98269	−	3.34187i	0.552299	−	0.463434i
$53$	11.2992			1.55207			0.776036	−	0.630689i	$-0.217228\pi$
$53$	11.2992			1.55207			0.776036	+	0.630689i	$0.217228\pi$
$54$		0			0
$55$	0.443592			0.0598140
$56$	3.07353	−	2.57900i	0.410717	−	0.344633i
$57$		0			0
$58$	1.59951	−	9.07129i	0.210026	−	1.19112i
$59$	−8.04363	+	2.92764i	−1.04719	+	0.381147i	−0.807602	−	0.589728i	$-0.799235\pi$
$59$	−8.04363	+	2.92764i	−1.04719	+	0.381147i	−0.239589	+	0.970874i	$0.577013\pi$
$60$		0			0
$61$	0.492064	+	2.79063i	0.0630023	+	0.357304i	0.999969	+	0.00788485i	$0.00250985\pi$
$61$	0.492064	+	2.79063i	0.0630023	+	0.357304i	−0.936967	+	0.349419i	$0.886379\pi$
$62$	1.76795	+	3.06218i	0.224530	+	0.388898i
$63$		0			0
$64$	−0.500000	+	0.866025i	−0.0625000	+	0.108253i
$65$	10.2010	+	3.71285i	1.26528	+	0.460523i
$66$		0			0
$67$	7.47702	+	6.27396i	0.913463	+	0.766487i	0.972775	−	0.231753i	$-0.0744460\pi$
$67$	7.47702	+	6.27396i	0.913463	+	0.766487i	−0.0593114	+	0.998240i	$0.518890\pi$
$68$	−2.89988	−	2.43329i	−0.351662	−	0.295079i
$69$		0			0
$70$	7.87232	+	2.86529i	0.940923	+	0.342468i
$71$	−5.86207	+	10.1534i	−0.695700	+	1.20499i	0.274244	+	0.961660i	$0.411572\pi$
$71$	−5.86207	+	10.1534i	−0.695700	+	1.20499i	−0.969944	+	0.243327i	$0.921761\pi$
$72$		0			0
$73$	−0.375162	−	0.649800i	−0.0439094	−	0.0760534i	0.843235	−	0.537544i	$-0.180648\pi$
$73$	−0.375162	−	0.649800i	−0.0439094	−	0.0760534i	−0.887145	+	0.461491i	$0.847315\pi$
$74$	−0.617250	−	3.50060i	−0.0717539	−	0.406937i
$75$		0			0
$76$	1.19605	−	0.435326i	0.137196	−	0.0499354i
$77$	0.148014	−	0.839430i	0.0168678	−	0.0956620i
$78$		0			0
$79$	−1.81383	+	1.52198i	−0.204071	+	0.171236i	−0.739096	−	0.673600i	$-0.764747\pi$
$79$	−1.81383	+	1.52198i	−0.204071	+	0.171236i	0.535024	+	0.844837i	$0.320302\pi$
$80$	−2.08802			−0.233447
$81$		0			0
$82$	2.73940			0.302516
$83$	8.73328	−	7.32809i	0.958602	−	0.804363i	−0.0221230	−	0.999755i	$-0.507043\pi$
$83$	8.73328	−	7.32809i	0.958602	−	0.804363i	0.980725	+	0.195393i	$0.0625981\pi$
$84$		0			0
$85$	1.37256	−	7.78415i	0.148875	−	0.844310i
$86$	6.48062	−	2.35875i	0.698823	−	0.254351i
$87$		0			0
$88$	0.0368910	+	0.209219i	0.00393259	+	0.0223028i
$89$	2.69813	+	4.67329i	0.286001	+	0.495368i	0.972851	−	0.231431i	$-0.0743407\pi$
$89$	2.69813	+	4.67329i	0.286001	+	0.495368i	−0.686851	+	0.726799i	$0.741007\pi$
$90$		0			0
$91$	10.4298	−	18.0649i	1.09334	−	1.89372i
$92$	0.779421	+	0.283686i	0.0812602	+	0.0295763i
$93$		0			0
$94$	−0.978448	−	0.821016i	−0.100919	−	0.0846813i
$95$	2.03588	+	1.70830i	0.208876	+	0.175268i
$96$		0			0
$97$	11.8055	+	4.29685i	1.19867	+	0.436279i	0.862759	−	0.505615i	$-0.168734\pi$
$97$	11.8055	+	4.29685i	1.19867	+	0.436279i	0.335909	+	0.941895i	$0.390957\pi$
$98$	4.54889	−	7.87892i	0.459508	−	0.795891i
$99$		0			0
$100$	0.320093	+	0.554417i	0.0320093	+	0.0554417i
$101$	0.502628	+	2.85055i	0.0500134	+	0.283640i	0.999549	−	0.0300181i	$-0.00955651\pi$
$101$	0.502628	+	2.85055i	0.0500134	+	0.283640i	−0.949536	+	0.313658i	$0.898445\pi$
$102$		0			0
$103$	−15.6835	+	5.70832i	−1.54534	+	0.562458i	−0.967319	−	0.253564i	$-0.918397\pi$
$103$	−15.6835	+	5.70832i	−1.54534	+	0.562458i	−0.578022	+	0.816021i	$0.696175\pi$
$104$	−0.902802	+	5.12004i	−0.0885270	+	0.502061i
$105$		0			0
$106$	−8.65573	+	7.26302i	−0.840719	+	0.705447i
$107$	−0.321371			−0.0310681			−0.0155341	−	0.999879i	$-0.504945\pi$
$107$	−0.321371			−0.0310681			−0.0155341	+	0.999879i	$0.504945\pi$
$108$		0			0
$109$	0.568378			0.0544407			0.0272204	−	0.999629i	$-0.491334\pi$
$109$	0.568378			0.0544407			0.0272204	+	0.999629i	$0.491334\pi$
$110$	−0.339811	+	0.285136i	−0.0323998	+	0.0271866i
$111$		0			0
$112$	−0.696712	+	3.95125i	−0.0658331	+	0.373358i
$113$	−1.27781	+	0.465084i	−0.120206	+	0.0437514i	−0.401423	−	0.915893i	$-0.631484\pi$
$113$	−1.27781	+	0.465084i	−0.120206	+	0.0437514i	0.281217	+	0.959644i	$0.409262\pi$
$114$		0			0
$115$	0.300739	+	1.70558i	0.0280441	+	0.159046i
$116$	4.60562	+	7.97716i	0.427621	+	0.740661i
$117$		0			0
$118$	4.27993	−	7.41305i	0.393999	−	0.682427i
$119$	−14.2723	−	5.19470i	−1.30834	−	0.476198i
$120$		0			0
$121$	−8.39191	−	7.04165i	−0.762901	−	0.640150i
$122$	−2.17073	−	1.82146i	−0.196528	−	0.164907i
$123$		0			0
$124$	−3.32266	−	1.20935i	−0.298384	−	0.108603i
$125$	−5.88840	+	10.1990i	−0.526675	+	0.912227i
$126$		0			0
$127$	−0.902007	−	1.56232i	−0.0800402	−	0.138634i	0.823227	−	0.567713i	$-0.192172\pi$
$127$	−0.902007	−	1.56232i	−0.0800402	−	0.138634i	−0.903267	+	0.429079i	$0.858838\pi$
$128$	−0.173648	−	0.984808i	−0.0153485	−	0.0870455i
$129$		0			0
$130$	−10.2010	+	3.71285i	−0.894685	+	0.325639i
$131$	1.68689	−	9.56684i	0.147384	−	0.835859i	−0.818037	−	0.575165i	$-0.804938\pi$
$131$	1.68689	−	9.56684i	0.147384	−	0.835859i	0.965422	−	0.260694i	$-0.0839512\pi$
$132$		0			0
$133$	3.91201	−	3.28257i	0.339215	−	0.284635i
$134$	−9.76056			−0.843184
$135$		0			0
$136$	3.78552			0.324606
$137$	6.94643	−	5.82875i	0.593474	−	0.497984i	−0.295867	−	0.955229i	$-0.595608\pi$
$137$	6.94643	−	5.82875i	0.593474	−	0.497984i	0.889340	+	0.457246i	$0.151164\pi$
$138$		0			0
$139$	−1.74358	+	9.88833i	−0.147888	+	0.838717i	0.817114	+	0.576476i	$0.195573\pi$
$139$	−1.74358	+	9.88833i	−0.147888	+	0.838717i	−0.965002	+	0.262241i	$0.915538\pi$
$140$	−7.87232	+	2.86529i	−0.665333	+	0.242161i
$141$		0			0
$142$	−2.03588	−	11.5460i	−0.170847	−	0.968921i
$143$	0.552258	+	0.956539i	0.0461822	+	0.0799898i
$144$		0			0
$145$	−9.61660	+	16.6564i	−0.798615	+	1.38324i
$146$	0.705075	+	0.256626i	0.0583524	+	0.0212385i
$147$		0			0
$148$	2.72298	+	2.28485i	0.223828	+	0.187814i
$149$	−12.1360	−	10.1833i	−0.994221	−	0.834250i	−0.00804728	−	0.999968i	$-0.502562\pi$
$149$	−12.1360	−	10.1833i	−0.994221	−	0.834250i	−0.986173	+	0.165718i	$0.947006\pi$
$150$		0			0
$151$	−4.98746	−	1.81529i	−0.405874	−	0.147726i	0.131012	−	0.991381i	$-0.458177\pi$
$151$	−4.98746	−	1.81529i	−0.405874	−	0.147726i	−0.536886	+	0.843655i	$0.680400\pi$
$152$	−0.636405	+	1.10229i	−0.0516192	+	0.0894071i
$153$		0			0
$154$	0.426190	+	0.738183i	0.0343434	+	0.0594845i
$155$	−1.28205	−	7.27086i	−0.102977	−	0.584010i
$156$		0			0
$157$	10.8225	−	3.93906i	0.863727	−	0.314371i	0.128103	−	0.991761i	$-0.459111\pi$
$157$	10.8225	−	3.93906i	0.863727	−	0.314371i	0.735624	+	0.677390i	$0.236889\pi$
$158$	0.411161	−	2.33181i	0.0327102	−	0.185509i
$159$		0			0
$160$	1.59951	−	1.34215i	0.126453	−	0.106106i
$161$	3.32789			0.262275
$162$		0			0
$163$	7.66336			0.600241			0.300120	−	0.953901i	$-0.402973\pi$
$163$	7.66336			0.600241			0.300120	+	0.953901i	$0.402973\pi$
$164$	−2.09850	+	1.76085i	−0.163865	+	0.137499i
$165$		0			0
$166$	−1.97967	+	11.2273i	−0.153653	+	0.871407i
$167$	5.74151	−	2.08974i	0.444292	−	0.161709i	−0.110180	−	0.993912i	$-0.535143\pi$
$167$	5.74151	−	2.08974i	0.444292	−	0.161709i	0.554472	+	0.832203i	$0.312920\pi$
$168$		0			0
$169$	2.43626	+	13.8167i	0.187405	+	1.06283i
$170$	3.95212	+	6.84527i	0.303114	+	0.525008i
$171$		0			0
$172$	−3.44827	+	5.97257i	−0.262928	+	0.455404i
$173$	−10.6218	−	3.86602i	−0.807561	−	0.293928i	−0.0949449	−	0.995483i	$-0.530268\pi$
$173$	−10.6218	−	3.86602i	−0.807561	−	0.293928i	−0.712616	+	0.701554i	$0.752490\pi$
$174$		0			0
$175$	1.96763	+	1.65104i	0.148739	+	0.124807i
$176$	−0.162744	−	0.136558i	−0.0122673	−	0.0102935i
$177$		0			0
$178$	−5.07082	−	1.84563i	−0.380074	−	0.138336i
$179$	3.46495	−	6.00147i	0.258982	−	0.448571i	−0.706987	−	0.707226i	$-0.749946\pi$
$179$	3.46495	−	6.00147i	0.258982	−	0.448571i	0.965970	+	0.258656i	$0.0832795\pi$
$180$		0			0
$181$	−1.51882	−	2.63067i	−0.112893	−	0.195536i	0.804043	−	0.594572i	$-0.202678\pi$
$181$	−1.51882	−	2.63067i	−0.112893	−	0.195536i	−0.916935	+	0.399036i	$0.869345\pi$
$182$	3.62223	+	20.5427i	0.268497	+	1.52272i
$183$		0			0
$184$	−0.779421	+	0.283686i	−0.0574597	+	0.0209136i
$185$	−1.28883	+	7.30931i	−0.0947566	+	0.537391i
$186$		0			0
$187$	0.616070	−	0.516944i	0.0450515	−	0.0378027i
$188$	1.27727			0.0931547
$189$		0			0
$190$	−2.65765			−0.192806
$191$	3.90467	−	3.27640i	0.282532	−	0.237072i	−0.490498	−	0.871443i	$-0.663185\pi$
$191$	3.90467	−	3.27640i	0.282532	−	0.237072i	0.773029	+	0.634370i	$0.218741\pi$
$192$		0			0
$193$	3.27644	−	18.5816i	0.235843	−	1.33753i	−0.604987	−	0.796235i	$-0.706822\pi$
$193$	3.27644	−	18.5816i	0.235843	−	1.33753i	0.840830	−	0.541299i	$-0.182067\pi$
$194$	−11.8055	+	4.29685i	−0.847586	+	0.308496i
$195$		0			0
$196$	1.57981	+	8.95957i	0.112844	+	0.639969i
$197$	−10.0220	−	17.3586i	−0.714036	−	1.23675i	−0.963330	−	0.268319i	$-0.913532\pi$
$197$	−10.0220	−	17.3586i	−0.714036	−	1.23675i	0.249294	−	0.968428i	$-0.419801\pi$
$198$		0			0
$199$	−2.75106	+	4.76498i	−0.195018	+	0.337780i	−0.946906	−	0.321510i	$-0.895810\pi$
$199$	−2.75106	+	4.76498i	−0.195018	+	0.337780i	0.751889	+	0.659290i	$0.229143\pi$
$200$	−0.601578	−	0.218956i	−0.0425380	−	0.0154826i
$201$		0			0
$202$	−2.21733	−	1.86056i	−0.156011	−	0.130909i
$203$	28.3110	+	23.7557i	1.98704	+	1.66733i
$204$		0			0
$205$	−5.37495	−	1.95632i	−0.375403	−	0.136635i
$206$	8.34501	−	14.4540i	0.581425	−	1.00706i
$207$		0			0
$208$	−2.59951	−	4.50249i	−0.180244	−	0.312191i
$209$	0.0469552	+	0.266296i	0.00324796	+	0.0184201i
$210$		0			0
$211$	23.6287	−	8.60014i	1.62667	−	0.592058i	0.642031	−	0.766679i	$-0.278092\pi$
$211$	23.6287	−	8.60014i	1.62667	−	0.592058i	0.984636	+	0.174621i	$0.0558699\pi$
$212$	1.96209	−	11.1276i	0.134757	−	0.764246i
$213$		0			0
$214$	0.246185	−	0.206573i	0.0168288	−	0.0141211i
$215$	−14.4001			−0.982077
$216$		0			0
$217$	−14.1868			−0.963061
$218$	−0.435403	+	0.365346i	−0.0294892	+	0.0247444i
$219$		0			0
$220$	0.0770290	−	0.436853i	0.00519329	−	0.0294526i
$221$	18.4941	−	6.73131i	1.24405	−	0.452797i
$222$		0			0
$223$	−0.651596	−	3.69539i	−0.0436341	−	0.247461i	0.955187	−	0.296003i	$-0.0956538\pi$
$223$	−0.651596	−	3.69539i	−0.0436341	−	0.247461i	−0.998821	+	0.0485415i	$0.984543\pi$
$224$	−2.00610	−	3.47467i	−0.134038	−	0.232161i
$225$		0			0
$226$	0.679907	−	1.17763i	0.0452267	−	0.0783350i
$227$	17.5983	+	6.40524i	1.16804	+	0.425131i	0.851962	−	0.523603i	$-0.175412\pi$
$227$	17.5983	+	6.40524i	1.16804	+	0.425131i	0.316076	+	0.948734i	$0.397635\pi$
$228$		0			0
$229$	−3.17397	−	2.66328i	−0.209742	−	0.175994i	0.531865	−	0.846829i	$-0.321491\pi$
$229$	−3.17397	−	2.66328i	−0.209742	−	0.175994i	−0.741607	+	0.670835i	$0.765936\pi$
$230$	−1.32670	−	1.11324i	−0.0874803	−	0.0734047i
$231$		0			0
$232$	−8.65573	−	3.15043i	−0.568276	−	0.206836i
$233$	−0.958556	+	1.66027i	−0.0627971	+	0.108768i	−0.895715	−	0.444629i	$-0.853335\pi$
$233$	−0.958556	+	1.66027i	−0.0627971	+	0.108768i	0.832918	+	0.553397i	$0.186669\pi$
$234$		0			0
$235$	1.33348	+	2.30966i	0.0869869	+	0.150666i
$236$	1.48640	+	8.42981i	0.0967566	+	0.548734i
$237$		0			0
$238$	14.2723	−	5.19470i	0.925138	−	0.336723i
$239$	−4.20216	+	23.8316i	−0.271815	+	1.54154i	0.477085	+	0.878857i	$0.341693\pi$
$239$	−4.20216	+	23.8316i	−0.271815	+	1.54154i	−0.748900	+	0.662683i	$0.769418\pi$
$240$		0			0
$241$	10.1156	−	8.48797i	0.651601	−	0.546758i	−0.255955	−	0.966689i	$-0.582390\pi$
$241$	10.1156	−	8.48797i	0.651601	−	0.546758i	0.907556	+	0.419931i	$0.137946\pi$
$242$	10.9549			0.704205
$243$		0			0
$244$	2.83368			0.181408
$245$	−14.5520	+	12.2106i	−0.929695	+	0.780107i
$246$		0			0
$247$	−1.14909	+	6.51684i	−0.0731151	+	0.414656i
$248$	3.32266	−	1.20935i	0.210989	−	0.0767938i
$249$		0			0
$250$	−2.04502	−	11.5979i	−0.129338	−	0.733515i
$251$	−4.32994	−	7.49967i	−0.273303	−	0.473375i	0.696402	−	0.717652i	$-0.254783\pi$
$251$	−4.32994	−	7.49967i	−0.273303	−	0.473375i	−0.969706	+	0.244276i	$0.921450\pi$
$252$		0			0
$253$	−0.0881062	+	0.152604i	−0.00553919	+	0.00959415i
$254$	1.69522	+	0.617009i	0.106368	+	0.0387146i
$255$		0			0
$256$	0.766044	+	0.642788i	0.0478778	+	0.0401742i
$257$	−16.7233	−	14.0326i	−1.04317	−	0.875326i	−0.0508142	−	0.998708i	$-0.516182\pi$
$257$	−16.7233	−	14.0326i	−1.04317	−	0.875326i	−0.992359	+	0.123382i	$0.960626\pi$
$258$		0			0
$259$	13.4017	+	4.87782i	0.832741	+	0.303093i
$260$	5.42783	−	9.40127i	0.336620	−	0.583042i
$261$		0			0
$262$	4.85721	+	8.41294i	0.300080	+	0.519753i
$263$	0.987629	+	5.60112i	0.0608998	+	0.345380i	0.999998	+	0.00173240i	$0.000551441\pi$
$263$	0.987629	+	5.60112i	0.0608998	+	0.345380i	−0.939099	+	0.343648i	$0.888337\pi$
$264$		0			0
$265$	22.1702	−	8.06929i	1.36190	−	0.495692i
$266$	−0.886782	+	5.02919i	−0.0543721	+	0.308359i
$267$		0			0
$268$	7.47702	−	6.27396i	0.456732	−	0.383243i
$269$	22.7662			1.38808			0.694041	−	0.719936i	$-0.255829\pi$
$269$	22.7662			1.38808			0.694041	+	0.719936i	$0.255829\pi$
$270$		0			0
$271$	−19.8340			−1.20483			−0.602414	−	0.798184i	$-0.705794\pi$
$271$	−19.8340			−1.20483			−0.602414	+	0.798184i	$0.705794\pi$
$272$	−2.89988	+	2.43329i	−0.175831	+	0.147540i
$273$		0			0
$274$	−1.57463	+	8.93016i	−0.0951268	+	0.539491i
$275$	−0.127803	+	0.0465166i	−0.00770683	+	0.00280506i
$276$		0			0
$277$	−4.19132	−	23.7701i	−0.251832	−	1.42821i	−0.804076	−	0.594527i	$-0.797339\pi$
$277$	−4.19132	−	23.7701i	−0.251832	−	1.42821i	0.552244	−	0.833683i	$-0.313772\pi$
$278$	−5.02044	−	8.69565i	−0.301106	−	0.521530i
$279$		0			0
$280$	4.18878	−	7.25517i	0.250327	−	0.433579i
$281$	−22.2287	−	8.09058i	−1.32605	−	0.482644i	−0.420660	−	0.907219i	$-0.638201\pi$
$281$	−22.2287	−	8.09058i	−1.32605	−	0.482644i	−0.905393	+	0.424575i	$0.860424\pi$
$282$		0			0
$283$	−8.90462	−	7.47186i	−0.529325	−	0.444156i	0.338543	−	0.940951i	$-0.390066\pi$
$283$	−8.90462	−	7.47186i	−0.529325	−	0.444156i	−0.867868	+	0.496795i	$0.834510\pi$
$284$	8.98121	+	7.53613i	0.532937	+	0.447187i
$285$		0			0
$286$	−1.03791	−	0.377767i	−0.0613727	−	0.0223378i
$287$	−5.49551	+	9.51850i	−0.324390	+	0.561859i
$288$		0			0
$289$	1.33491	+	2.31213i	0.0785239	+	0.136007i
$290$	−3.33981	−	18.9410i	−0.196120	−	1.11225i
$291$		0			0
$292$	−0.705075	+	0.256626i	−0.0412614	+	0.0150179i
$293$	1.85993	−	10.5482i	0.108658	−	0.616232i	−0.881037	−	0.473046i	$-0.843154\pi$
$293$	1.85993	−	10.5482i	0.108658	−	0.616232i	0.989696	−	0.143186i	$-0.0457346\pi$
$294$		0			0
$295$	−13.6916	+	11.4886i	−0.797156	+	0.668893i
$296$	−3.55460			−0.206607
$297$		0			0
$298$	15.8424			0.917728
$299$	−3.30341	+	2.77189i	−0.191041	+	0.160302i
$300$		0			0
$301$	−4.80490	+	27.2499i	−0.276950	+	1.57066i
$302$	4.98746	−	1.81529i	0.286996	−	0.104458i
$303$		0			0
$304$	−0.221021	−	1.25347i	−0.0126764	−	0.0718916i
$305$	2.95839	+	5.12408i	0.169397	+	0.293404i
$306$		0			0
$307$	−12.3938	+	21.4667i	−0.707351	+	1.22517i	0.258485	+	0.966015i	$0.416777\pi$
$307$	−12.3938	+	21.4667i	−0.707351	+	1.22517i	−0.965836	+	0.259153i	$0.916557\pi$
$308$	−0.800975	−	0.291531i	−0.0456398	−	0.0166115i
$309$		0			0
$310$	5.65573	+	4.74572i	0.321224	+	0.269539i
$311$	16.6871	+	14.0022i	0.946241	+	0.793990i	0.978660	−	0.205484i	$-0.0658768\pi$
$311$	16.6871	+	14.0022i	0.946241	+	0.793990i	−0.0324195	+	0.999474i	$0.510321\pi$
$312$		0			0
$313$	8.83542	+	3.21583i	0.499408	+	0.181770i	0.579428	−	0.815024i	$-0.303276\pi$
$313$	8.83542	+	3.21583i	0.499408	+	0.181770i	−0.0800199	+	0.996793i	$0.525498\pi$
$314$	−5.75852	+	9.97404i	−0.324972	+	0.562868i
$315$		0			0
$316$	1.18389	+	2.05056i	0.0665990	+	0.115353i
$317$	2.51892	+	14.2855i	0.141477	+	0.802353i	0.970129	+	0.242590i	$0.0779969\pi$
$317$	2.51892	+	14.2855i	0.141477	+	0.802353i	−0.828652	+	0.559763i	$0.810892\pi$
$318$		0			0
$319$	−1.83888	+	0.669298i	−0.102958	+	0.0374735i
$320$	−0.362580	+	2.05630i	−0.0202689	+	0.114950i
$321$		0			0
$322$	−2.54931	+	2.13913i	−0.142068	+	0.119209i
$323$	4.81825			0.268095
$324$		0			0
$325$	−3.32834			−0.184623
$326$	−5.87047	+	4.92591i	−0.325135	+	0.272821i
$327$		0			0
$328$	0.475691	−	2.69778i	0.0262656	−	0.148960i
$329$	4.81563	−	1.75274i	0.265494	−	0.0966319i
$330$		0			0
$331$	0.140089	+	0.794483i	0.00769998	+	0.0436688i	0.988416	−	0.151771i	$-0.0484977\pi$
$331$	0.140089	+	0.794483i	0.00769998	+	0.0436688i	−0.980716	+	0.195440i	$0.937387\pi$
$332$	−5.70024	−	9.87311i	−0.312842	−	0.541857i
$333$		0			0
$334$	−3.05500	+	5.29141i	−0.167162	+	0.289533i
$335$	19.1511	+	6.97044i	1.04634	+	0.380836i
$336$		0			0
$337$	−20.4272	−	17.1404i	−1.11274	−	0.933700i	−0.114525	−	0.993420i	$-0.536535\pi$
$337$	−20.4272	−	17.1404i	−1.11274	−	0.933700i	−0.998215	+	0.0597207i	$0.980979\pi$
$338$	−10.7475	−	9.01824i	−0.584588	−	0.490527i
$339$		0			0
$340$	−7.42755	−	2.70341i	−0.402816	−	0.146613i
$341$	0.375596	−	0.650551i	0.0203396	−	0.0352293i
$342$		0			0
$343$	4.20838	+	7.28912i	0.227231	+	0.393576i
$344$	−1.19757	−	6.79176i	−0.0645687	−	0.366187i
$345$		0			0
$346$	10.6218	−	3.86602i	0.571032	−	0.207839i
$347$	5.05391	−	28.6621i	0.271308	−	1.53866i	−0.479142	−	0.877737i	$-0.659052\pi$
$347$	5.05391	−	28.6621i	0.271308	−	1.53866i	0.750450	−	0.660927i	$-0.229837\pi$
$348$		0			0
$349$	−22.6355	+	18.9934i	−1.21165	+	1.01669i	−0.212430	+	0.977176i	$0.568138\pi$
$349$	−22.6355	+	18.9934i	−1.21165	+	1.01669i	−0.999219	+	0.0395179i	$0.987418\pi$
$350$	−2.56856			−0.137295
$351$		0			0
$352$	0.212447			0.0113235
$353$	−4.78974	+	4.01907i	−0.254932	+	0.213913i	−0.761293	−	0.648408i	$-0.775435\pi$
$353$	−4.78974	+	4.01907i	−0.254932	+	0.213913i	0.506361	+	0.862322i	$0.330990\pi$
$354$		0			0
$355$	−4.25094	+	24.1083i	−0.225617	+	1.27954i
$356$	5.07082	−	1.84563i	0.268753	−	0.0978180i
$357$		0			0
$358$	1.20336	+	6.82462i	0.0635998	+	0.360692i
$359$	−1.29314	−	2.23979i	−0.0682495	−	0.118212i	0.829881	−	0.557940i	$-0.188408\pi$
$359$	−1.29314	−	2.23979i	−0.0682495	−	0.118212i	−0.898131	+	0.439728i	$0.855075\pi$
$360$		0			0
$361$	8.68998	−	15.0515i	0.457367	−	0.792183i
$362$	2.85444	+	1.03893i	0.150026	+	0.0546050i
$363$		0			0
$364$	−15.9794	−	13.4083i	−0.837546	−	0.702784i
$365$	−1.20015	−	1.00705i	−0.0628190	−	0.0527114i
$366$		0			0
$367$	−17.5546	−	6.38935i	−0.916342	−	0.333521i	−0.159560	−	0.987188i	$-0.551007\pi$
$367$	−17.5546	−	6.38935i	−0.916342	−	0.333521i	−0.756782	+	0.653667i	$0.773230\pi$
$368$	0.414721	−	0.718318i	0.0216188	−	0.0374449i
$369$		0			0
$370$	−3.71104	−	6.42770i	−0.192928	−	0.334160i
$371$	−7.87232	−	44.6462i	−0.408711	−	2.31791i
$372$		0			0
$373$	−12.7104	+	4.62621i	−0.658120	+	0.239536i	−0.649425	−	0.760426i	$-0.724990\pi$
$373$	−12.7104	+	4.62621i	−0.658120	+	0.239536i	−0.00869564	+	0.999962i	$0.502768\pi$
$374$	−0.139652	+	0.792004i	−0.00722122	+	0.0409536i
$375$		0			0
$376$	−0.978448	+	0.821016i	−0.0504596	+	0.0423406i
$377$	−47.8894			−2.46643
$378$		0			0
$379$	30.2178			1.55218			0.776092	−	0.630620i	$-0.217199\pi$
$379$	30.2178			1.55218			0.776092	+	0.630620i	$0.217199\pi$
$380$	2.03588	−	1.70830i	0.104438	−	0.0876341i
$381$		0			0
$382$	−0.885116	+	5.01974i	−0.0452865	+	0.256832i
$383$	−36.2619	+	13.1982i	−1.85289	+	0.674398i	−0.869224	+	0.494419i	$0.835381\pi$
$383$	−36.2619	+	13.1982i	−1.85289	+	0.674398i	−0.983670	+	0.179980i	$0.942397\pi$
$384$		0			0
$385$	−0.309056	−	1.75274i	−0.0157510	−	0.0893281i
$386$	9.43413	+	16.3404i	0.480185	+	0.831704i
$387$		0			0
$388$	6.28158	−	10.8800i	0.318899	−	0.552349i
$389$	−5.28688	−	1.92427i	−0.268056	−	0.0975642i	0.204496	−	0.978867i	$-0.434445\pi$
$389$	−5.28688	−	1.92427i	−0.268056	−	0.0975642i	−0.472551	+	0.881303i	$0.656667\pi$
$390$		0			0
$391$	2.40528	+	2.01827i	0.121640	+	0.102068i
$392$	−6.96931	−	5.84795i	−0.352003	−	0.295366i
$393$		0			0
$394$	18.8352	+	6.85544i	0.948901	+	0.345372i
$395$	−2.47198	+	4.28160i	−0.124379	+	0.215431i
$396$		0			0
$397$	−3.85809	−	6.68240i	−0.193632	−	0.335380i	0.752819	−	0.658227i	$-0.228693\pi$
$397$	−3.85809	−	6.68240i	−0.193632	−	0.335380i	−0.946451	+	0.322847i	$0.895360\pi$
$398$	−0.955433	−	5.41853i	−0.0478915	−	0.271606i
$399$		0			0
$400$	0.601578	−	0.218956i	0.0300789	−	0.0109478i
$401$	−6.31721	+	35.8267i	−0.315466	+	1.78910i	0.254126	+	0.967171i	$0.418212\pi$
$401$	−6.31721	+	35.8267i	−0.315466	+	1.78910i	−0.569593	+	0.821927i	$0.692899\pi$
$402$		0			0
$403$	14.0824	−	11.8165i	0.701494	−	0.588623i
$404$	2.89452			0.144008
$405$		0			0
$406$	−36.9574			−1.83416
$407$	−0.578489	+	0.485410i	−0.0286746	+	0.0240609i
$408$		0			0
$409$	1.01891	−	5.77853i	0.0503819	−	0.285730i	−0.949199	−	0.314676i	$-0.898104\pi$
$409$	1.01891	−	5.77853i	0.0503819	−	0.285730i	0.999581	+	0.0289462i	$0.00921516\pi$
$410$	5.37495	−	1.95632i	0.265450	−	0.0966159i
$411$		0			0
$412$	2.89819	+	16.4365i	0.142784	+	0.809766i
$413$	17.1719	+	29.7427i	0.844976	+	1.46354i
$414$		0			0
$415$	11.9022	−	20.6152i	0.584256	−	1.01196i
$416$	4.88549	+	1.77817i	0.239531	+	0.0871821i
$417$		0			0
$418$	−0.207142	−	0.173812i	−0.0101316	−	0.00850145i
$419$	−16.1908	−	13.5857i	−0.790972	−	0.663704i	0.155014	−	0.987912i	$-0.450458\pi$
$419$	−16.1908	−	13.5857i	−0.790972	−	0.663704i	−0.945986	+	0.324208i	$0.894902\pi$
$420$		0			0
$421$	−6.99405	−	2.54563i	−0.340869	−	0.124066i	0.165913	−	0.986140i	$-0.446943\pi$
$421$	−6.99405	−	2.54563i	−0.340869	−	0.124066i	−0.506782	+	0.862074i	$0.669165\pi$
$422$	−12.5726	+	21.7763i	−0.612023	+	1.06005i
$423$		0			0
$424$	5.64962	+	9.78544i	0.274370	+	0.475223i
$425$	0.420826	+	2.38662i	0.0204130	+	0.115768i
$426$		0			0
$427$	10.6837	−	3.88853i	0.517018	−	0.188179i
$428$	−0.0558055	+	0.316489i	−0.00269746	+	0.0152981i
$429$		0			0
$430$	11.0311	−	9.25619i	0.531967	−	0.446373i
$431$	13.0502			0.628607			0.314303	−	0.949323i	$-0.398229\pi$
$431$	13.0502			0.628607			0.314303	+	0.949323i	$0.398229\pi$
$432$		0			0
$433$	0.143533			0.00689775			0.00344887	−	0.999994i	$-0.498902\pi$
$433$	0.143533			0.00689775			0.00344887	+	0.999994i	$0.498902\pi$
$434$	10.8677	−	9.11908i	0.521666	−	0.437730i
$435$		0			0
$436$	0.0986977	−	0.559743i	0.00472676	−	0.0268068i
$437$	−0.992054	+	0.361078i	−0.0474564	+	0.0172727i
$438$		0			0
$439$	2.35406	+	13.3506i	0.112353	+	0.637187i	0.988027	+	0.154283i	$0.0493069\pi$
$439$	2.35406	+	13.3506i	0.112353	+	0.637187i	−0.875673	+	0.482904i	$0.839582\pi$
$440$	0.221796	+	0.384162i	0.0105737	+	0.0183142i
$441$		0			0
$442$	−9.84052	+	17.0443i	−0.468066	+	0.810714i
$443$	11.5406	+	4.20044i	0.548311	+	0.199569i	0.601296	−	0.799026i	$-0.294651\pi$
$443$	11.5406	+	4.20044i	0.548311	+	0.199569i	−0.0529847	+	0.998595i	$0.516873\pi$
$444$		0			0
$445$	8.63138	+	7.24258i	0.409166	+	0.343331i
$446$	2.87450	+	2.41199i	0.136112	+	0.114211i
$447$		0			0
$448$	3.77024	+	1.37225i	0.178127	+	0.0648329i
$449$	20.3323	−	35.2165i	0.959540	−	1.66197i	0.235920	−	0.971772i	$-0.424190\pi$
$449$	20.3323	−	35.2165i	0.959540	−	1.66197i	0.723620	−	0.690199i	$-0.242477\pi$
$450$		0			0
$451$	−0.290988	−	0.504006i	−0.0137021	−	0.0237327i
$452$	0.236129	+	1.33916i	0.0111066	+	0.0629886i
$453$		0			0
$454$	−17.5983	+	6.40524i	−0.825928	+	0.300613i
$455$	7.56327	−	42.8934i	0.354571	−	2.01087i
$456$		0			0
$457$	24.9661	−	20.9491i	1.16787	−	0.979956i	0.167884	−	0.985807i	$-0.446307\pi$
$457$	24.9661	−	20.9491i	1.16787	−	0.979956i	0.999983	+	0.00585037i	$0.00186224\pi$
$458$	4.14333			0.193605
$459$		0			0
$460$	1.73189			0.0807498
$461$	20.9287	−	17.5612i	0.974745	−	0.817909i	−0.00854291	−	0.999964i	$-0.502719\pi$
$461$	20.9287	−	17.5612i	0.974745	−	0.817909i	0.983288	+	0.182055i	$0.0582749\pi$
$462$		0			0
$463$	−0.590262	+	3.34754i	−0.0274318	+	0.155574i	−0.995447	−	0.0953189i	$-0.969613\pi$
$463$	−0.590262	+	3.34754i	−0.0274318	+	0.155574i	0.968015	+	0.250892i	$0.0807240\pi$
$464$	8.65573	−	3.15043i	0.401832	−	0.146255i
$465$		0			0
$466$	−0.332903	−	1.88799i	−0.0154214	−	0.0874593i
$467$	16.4988	+	28.5767i	0.763473	+	1.32237i	0.941050	+	0.338267i	$0.109841\pi$
$467$	16.4988	+	28.5767i	0.763473	+	1.32237i	−0.177577	+	0.984107i	$0.556826\pi$
$468$		0			0
$469$	19.5807	−	33.9147i	0.904152	−	1.56604i
$470$	−2.50613	−	0.912157i	−0.115599	−	0.0420747i
$471$		0			0
$472$	−6.55723	−	5.50217i	−0.301821	−	0.253258i
$473$	−1.12237	−	0.941778i	−0.0516065	−	0.0433030i
$474$		0			0
$475$	−0.765694	−	0.278690i	−0.0351324	−	0.0127872i
$476$	−7.59415	+	13.1534i	−0.348077	+	0.602887i
$477$		0			0
$478$	−12.0996	−	20.9572i	−0.553424	−	0.958559i
$479$	4.00142	+	22.6932i	0.182830	+	1.03688i	0.928712	+	0.370801i	$0.120917\pi$
$479$	4.00142	+	22.6932i	0.182830	+	1.03688i	−0.745883	+	0.666077i	$0.767972\pi$
$480$		0			0
$481$	−17.3660	+	6.32070i	−0.791820	+	0.288199i
$482$	−2.29301	+	13.0043i	−0.104444	+	0.592331i
$483$		0			0
$484$	−8.39191	+	7.04165i	−0.381451	+	0.320075i
$485$	26.2321			1.19114
$486$		0			0
$487$	26.9315			1.22038			0.610192	−	0.792254i	$-0.291092\pi$
$487$	26.9315			1.22038			0.610192	+	0.792254i	$0.291092\pi$
$488$	−2.17073	+	1.82146i	−0.0982641	+	0.0824534i
$489$		0			0
$490$	3.29868	−	18.7077i	0.149019	−	0.845129i
$491$	−0.233037	+	0.0848187i	−0.0105168	+	0.00382781i	−0.347273	−	0.937764i	$-0.612892\pi$
$491$	−0.233037	+	0.0848187i	−0.0105168	+	0.00382781i	0.336756	+	0.941592i	$0.390670\pi$
$492$		0			0
$493$	6.05500	+	34.3396i	0.272703	+	1.54658i
$494$	−3.30869	−	5.73081i	−0.148865	−	0.257841i
$495$		0			0
$496$	−1.76795	+	3.06218i	−0.0793834	+	0.137496i
$497$	44.2028	+	16.0885i	1.98277	+	0.721668i
$498$		0			0
$499$	−20.4674	−	17.1742i	−0.916247	−	0.768822i	0.0570505	−	0.998371i	$-0.481830\pi$
$499$	−20.4674	−	17.1742i	−0.916247	−	0.768822i	−0.973297	+	0.229549i	$0.926275\pi$
$500$	9.02155	+	7.56998i	0.403456	+	0.338540i
$501$		0			0
$502$	8.13762	+	2.96185i	0.363200	+	0.132194i
$503$	13.0871	−	22.6676i	0.583527	−	1.01070i	−0.411530	−	0.911396i	$-0.635006\pi$
$503$	13.0871	−	22.6676i	0.583527	−	1.01070i	0.995057	−	0.0993022i	$-0.0316611\pi$
$504$		0			0
$505$	3.02190	+	5.23409i	0.134473	+	0.232914i
$506$	−0.0305989	−	0.173535i	−0.00136029	−	0.00771458i
$507$		0			0
$508$	−1.69522	+	0.617009i	−0.0752132	+	0.0273754i
$509$	−0.947739	+	5.37490i	−0.0420078	+	0.238238i	−0.998581	−	0.0532542i	$-0.983041\pi$
$509$	−0.947739	+	5.37490i	−0.0420078	+	0.238238i	0.956573	+	0.291492i	$0.0941518\pi$
$510$		0			0
$511$	−2.30614	+	1.93508i	−0.102018	+	0.0856031i
$512$	−1.00000			−0.0441942
$513$		0			0
$514$	21.8308			0.962914
$515$	−26.6959	+	22.4005i	−1.17636	+	0.987086i
$516$		0			0
$517$	−0.0471199	+	0.267230i	−0.00207233	+	0.0117528i
$518$	−13.4017	+	4.87782i	−0.588837	+	0.214319i
$519$		0			0
$520$	1.88506	+	10.6907i	0.0826656	+	0.468820i
$521$	−13.0596	−	22.6199i	−0.572151	−	0.990995i	−0.996345	−	0.0854234i	$-0.972776\pi$
$521$	−13.0596	−	22.6199i	−0.572151	−	0.990995i	0.424194	−	0.905572i	$-0.360558\pi$
$522$		0			0
$523$	−3.70382	+	6.41521i	−0.161957	+	0.280518i	−0.935570	−	0.353140i	$-0.885114\pi$
$523$	−3.70382	+	6.41521i	−0.161957	+	0.280518i	0.773614	+	0.633658i	$0.218447\pi$
$524$	−9.12858	−	3.32253i	−0.398784	−	0.145145i
$525$		0			0
$526$	−4.35690	−	3.65587i	−0.189970	−	0.159404i
$527$	−10.2537	−	8.60387i	−0.446658	−	0.374791i
$528$		0			0
$529$	20.9664	+	7.63116i	0.911585	+	0.331790i
$530$	−11.7965	+	20.4322i	−0.512408	+	0.887516i
$531$		0			0
$532$	−2.55339	−	4.42259i	−0.110703	−	0.191744i
$533$	−2.47313	−	14.0258i	−0.107123	−	0.607526i
$534$		0			0
$535$	−0.630560	+	0.229505i	−0.0272615	+	0.00992238i
$536$	−1.69490	+	9.61227i	−0.0732086	+	0.415187i
$537$		0			0
$538$	−17.4399	+	14.6339i	−0.751889	+	0.630910i
$539$	−1.93280			−0.0832514
$540$		0			0
$541$	11.3209			0.486725			0.243362	−	0.969935i	$-0.421750\pi$
$541$	11.3209			0.486725			0.243362	+	0.969935i	$0.421750\pi$
$542$	15.1937	−	12.7490i	0.652625	−	0.547617i
$543$		0			0
$544$	0.657349	−	3.72801i	0.0281836	−	0.159837i
$545$	1.11521	−	0.405903i	0.0477704	−	0.0173870i
$546$		0			0
$547$	−1.84721	−	10.4761i	−0.0789811	−	0.447924i	−0.998494	−	0.0548639i	$-0.982528\pi$
$547$	−1.84721	−	10.4761i	−0.0789811	−	0.447924i	0.919513	−	0.393060i	$-0.128584\pi$
$548$	−4.53396	−	7.85305i	−0.193681	−	0.335466i
$549$		0			0
$550$	0.0680027	−	0.117784i	0.00289964	−	0.00502233i
$551$	−11.0171	−	4.00989i	−0.469344	−	0.170827i
$552$		0			0
$553$	7.27744	+	6.10650i	0.309468	+	0.259675i
$554$	18.4899	+	15.5149i	0.785560	+	0.659163i
$555$		0			0
$556$	9.43533	+	3.43418i	0.400147	+	0.145642i
$557$	−5.92385	+	10.2604i	−0.251001	+	0.434747i	−0.963802	−	0.266620i	$-0.914093\pi$
$557$	−5.92385	+	10.2604i	−0.251001	+	0.434747i	0.712800	+	0.701367i	$0.247427\pi$
$558$		0			0
$559$	−17.9276	−	31.0516i	−0.758258	−	1.31334i
$560$	1.45475	+	8.25028i	0.0614743	+	0.348638i
$561$		0			0
$562$	22.2287	−	8.09058i	0.937661	−	0.341281i
$563$	−1.04327	+	5.91667i	−0.0439686	+	0.249358i	−0.998868	−	0.0475719i	$-0.984852\pi$
$563$	−1.04327	+	5.91667i	−0.0439686	+	0.249358i	0.954899	+	0.296930i	$0.0959628\pi$
$564$		0			0
$565$	−2.17504	+	1.82508i	−0.0915047	+	0.0767815i
$566$	11.6242			0.488600
$567$		0			0
$568$	−11.7241			−0.491934
$569$	22.3596	−	18.7619i	0.937363	−	0.786541i	−0.0397618	−	0.999209i	$-0.512660\pi$
$569$	22.3596	−	18.7619i	0.937363	−	0.786541i	0.977124	+	0.212669i	$0.0682155\pi$
$570$		0			0
$571$	3.78797	−	21.4826i	0.158522	−	0.899021i	−0.796974	−	0.604014i	$-0.793567\pi$
$571$	3.78797	−	21.4826i	0.158522	−	0.899021i	0.955495	−	0.295007i	$-0.0953219\pi$
$572$	1.03791	−	0.377767i	0.0433970	−	0.0157952i
$573$		0			0
$574$	−1.90857	−	10.8240i	−0.0796622	−	0.451787i
$575$	−0.265499	−	0.459857i	−0.0110721	−	0.0191774i
$576$		0			0
$577$	−20.0399	+	34.7102i	−0.834273	+	1.44500i	0.0603476	+	0.998177i	$0.480779\pi$
$577$	−20.0399	+	34.7102i	−0.834273	+	1.44500i	−0.894621	+	0.446826i	$0.852554\pi$
$578$	−2.50880	−	0.913130i	−0.104353	−	0.0379812i
$579$		0			0
$580$	14.7335	+	12.3629i	0.611775	+	0.513340i
$581$	−35.0397	−	29.4018i	−1.45369	−	1.21979i
$582$		0			0
$583$	2.25572	+	0.821016i	0.0934224	+	0.0340030i
$584$	0.375162	−	0.649800i	0.0155243	−	0.0268889i
$585$		0			0
$586$	5.35546	+	9.27593i	0.221232	+	0.383185i
$587$	4.66518	+	26.4576i	0.192553	+	1.09202i	0.915861	+	0.401495i	$0.131509\pi$
$587$	4.66518	+	26.4576i	0.192553	+	1.09202i	−0.723309	+	0.690525i	$0.757380\pi$
$588$		0			0
$589$	4.22912	−	1.53927i	0.174258	−	0.0634246i
$590$	3.10363	−	17.6016i	0.127775	−	0.724646i
$591$		0			0
$592$	2.72298	−	2.28485i	0.111914	−	0.0939070i
$593$	−30.4609			−1.25088			−0.625440	−	0.780272i	$-0.715081\pi$
$593$	−30.4609			−1.25088			−0.625440	+	0.780272i	$0.715081\pi$
$594$		0			0
$595$	−31.7134			−1.30012
$596$	−12.1360	+	10.1833i	−0.497110	+	0.417125i
$597$		0			0
$598$	0.748822	−	4.24678i	0.0306216	−	0.173664i
$599$	−27.4285	+	9.98317i	−1.12070	+	0.407901i	−0.834908	−	0.550390i	$-0.814479\pi$
$599$	−27.4285	+	9.98317i	−1.12070	+	0.407901i	−0.285792	+	0.958292i	$0.592257\pi$
$600$		0			0
$601$	−4.03243	−	22.8690i	−0.164486	−	0.932847i	−0.949593	−	0.313487i	$-0.898503\pi$
$601$	−4.03243	−	22.8690i	−0.164486	−	0.932847i	0.785106	−	0.619361i	$-0.212608\pi$
$602$	−13.8352	−	23.9632i	−0.563879	−	0.976667i
$603$		0			0
$604$	−2.65377	+	4.59647i	−0.107981	+	0.187028i
$605$	−21.4945	−	7.82335i	−0.873875	−	0.318064i
$606$		0			0
$607$	32.6881	+	27.4286i	1.32677	+	1.11329i	0.984821	+	0.173574i	$0.0555317\pi$
$607$	32.6881	+	27.4286i	1.32677	+	1.11329i	0.341950	+	0.939718i	$0.388913\pi$
$608$	0.975029	+	0.818146i	0.0395426	+	0.0331802i
$609$		0			0
$610$	−5.55995	−	2.02366i	−0.225116	−	0.0819354i
$611$	−3.32029	+	5.75091i	−0.134325	+	0.232657i
$612$		0			0
$613$	6.80411	+	11.7851i	0.274815	+	0.475994i	0.970089	−	0.242752i	$-0.0780500\pi$
$613$	6.80411	+	11.7851i	0.274815	+	0.475994i	−0.695273	+	0.718746i	$0.744717\pi$
$614$	−4.30432	−	24.4110i	−0.173708	−	0.985148i
$615$		0			0
$616$	0.800975	−	0.291531i	0.0322722	−	0.0117461i
$617$	−4.88447	+	27.7012i	−0.196641	+	1.11521i	0.713421	+	0.700736i	$0.247145\pi$
$617$	−4.88447	+	27.7012i	−0.196641	+	1.11521i	−0.910062	+	0.414472i	$0.863966\pi$
$618$		0			0
$619$	−14.9355	+	12.5323i	−0.600307	+	0.503717i	−0.891544	−	0.452934i	$-0.850377\pi$
$619$	−14.9355	+	12.5323i	−0.600307	+	0.503717i	0.291237	+	0.956651i	$0.405933\pi$
$620$	−7.38303			−0.296510
$621$		0			0
$622$	−21.7835			−0.873439
$623$	16.5855	−	13.9169i	0.664485	−	0.557569i
$624$		0			0
$625$	−3.71420	+	21.0643i	−0.148568	+	0.842571i
$626$	−8.83542	+	3.21583i	−0.353135	+	0.128530i
$627$		0			0
$628$	−1.99991	−	11.3421i	−0.0798052	−	0.452598i
$629$	6.72802	+	11.6533i	0.268264	+	0.464646i
$630$		0			0
$631$	−6.27471	+	10.8681i	−0.249792	+	0.432653i	−0.963468	−	0.267823i	$-0.913696\pi$
$631$	−6.27471	+	10.8681i	−0.249792	+	0.432653i	0.713676	+	0.700476i	$0.247029\pi$
$632$	−2.22499	−	0.809829i	−0.0885052	−	0.0322133i
$633$		0			0
$634$	−11.1121	−	9.32419i	−0.441319	−	0.370311i
$635$	−2.88555	−	2.42126i	−0.114509	−	0.0960848i
$636$		0			0
$637$	−44.4471	−	16.1774i	−1.76106	−	0.640973i
$638$	0.978448	−	1.69472i	0.0387371	−	0.0670947i
$639$		0			0
$640$	−1.04401	−	1.80828i	−0.0412681	−	0.0714784i
$641$	2.42288	+	13.7409i	0.0956981	+	0.542731i	0.994531	+	0.104440i	$0.0333050\pi$
$641$	2.42288	+	13.7409i	0.0956981	+	0.542731i	−0.898833	+	0.438291i	$0.855584\pi$
$642$		0			0
$643$	−38.5754	+	14.0403i	−1.52127	+	0.553695i	−0.961464	−	0.274931i	$-0.911345\pi$
$643$	−38.5754	+	14.0403i	−1.52127	+	0.553695i	−0.559802	+	0.828627i	$0.689123\pi$
$644$	0.577882	−	3.27733i	0.0227718	−	0.129145i
$645$		0			0
$646$	−3.69099	+	3.09711i	−0.145220	+	0.121854i
$647$	−0.303995			−0.0119513			−0.00597563	−	0.999982i	$-0.501902\pi$
$647$	−0.303995			−0.0119513			−0.00597563	+	0.999982i	$0.501902\pi$
$648$		0			0
$649$	−1.81851			−0.0713829
$650$	2.54966	−	2.13942i	0.100006	−	0.0839149i
$651$		0			0
$652$	1.33073	−	7.54693i	0.0521153	−	0.295561i
$653$	44.2755	−	16.1150i	1.73263	−	0.630627i	0.733820	−	0.679344i	$-0.237735\pi$
$653$	44.2755	−	16.1150i	1.73263	−	0.630627i	0.998813	+	0.0487170i	$0.0155132\pi$
$654$		0			0
$655$	−3.52226	−	19.9757i	−0.137626	−	0.780516i
$656$	1.36970	+	2.37239i	0.0534777	+	0.0926261i
$657$		0			0
$658$	−2.56234	+	4.43811i	−0.0998905	+	0.173015i
$659$	−40.3746	−	14.6952i	−1.57277	−	0.572442i	−0.599156	−	0.800633i	$-0.704497\pi$
$659$	−40.3746	−	14.6952i	−1.57277	−	0.572442i	−0.973617	+	0.228190i	$0.926719\pi$
$660$		0			0
$661$	21.0863	+	17.6935i	0.820161	+	0.688197i	0.953010	−	0.302939i	$-0.0979680\pi$
$661$	21.0863	+	17.6935i	0.820161	+	0.688197i	−0.132849	+	0.991136i	$0.542412\pi$
$662$	−0.617998	−	0.518562i	−0.0240192	−	0.0201545i
$663$		0			0
$664$	10.7130	+	3.89920i	0.415743	+	0.151318i
$665$	5.33151	−	9.23445i	0.206747	−	0.358097i
$666$		0			0
$667$	−3.82009	−	6.61659i	−0.147915	−	0.256196i
$668$	−1.06099	−	6.01717i	−0.0410509	−	0.232811i
$669$		0			0
$670$	−19.1511	+	6.97044i	−0.739873	+	0.269292i
$671$	−0.104537	+	0.592861i	−0.00403562	+	0.0228871i
$672$		0			0
$673$	−25.7719	+	21.6252i	−0.993433	+	0.833589i	−0.986061	−	0.166384i	$-0.946791\pi$
$673$	−25.7719	+	21.6252i	−0.993433	+	0.833589i	−0.00737169	+	0.999973i	$0.502347\pi$
$674$	26.6658			1.02713
$675$		0			0
$676$	14.0299			0.539611
$677$	−26.1138	+	21.9120i	−1.00363	+	0.842148i	−0.987484	−	0.157721i	$-0.949585\pi$
$677$	−26.1138	+	21.9120i	−1.00363	+	0.842148i	−0.0161497	+	0.999870i	$0.505141\pi$
$678$		0			0
$679$	8.75290	−	49.6402i	0.335906	−	1.90502i
$680$	7.42755	−	2.70341i	0.284834	−	0.103671i
$681$		0			0
$682$	0.130443	+	0.739779i	0.00499492	+	0.0283276i
$683$	−8.22650	−	14.2487i	−0.314778	−	0.545212i	0.664612	−	0.747189i	$-0.268597\pi$
$683$	−8.22650	−	14.2487i	−0.314778	−	0.545212i	−0.979390	+	0.201976i	$0.935264\pi$
$684$		0			0
$685$	9.46699	−	16.3973i	0.361715	−	0.626509i
$686$	−7.90916	−	2.87870i	−0.301973	−	0.109909i
$687$		0			0
$688$	5.28305	+	4.43301i	0.201414	+	0.169007i
$689$	45.0014	+	37.7606i	1.71442	+	1.43857i
$690$		0			0
$691$	13.4086	+	4.88033i	0.510087	+	0.185657i	0.584225	−	0.811591i	$-0.301398\pi$
$691$	13.4086	+	4.88033i	0.510087	+	0.185657i	−0.0741383	+	0.997248i	$0.523621\pi$
$692$	−5.65174	+	9.78911i	−0.214847	+	0.372126i
$693$		0			0
$694$	14.5521	+	25.2051i	0.552392	+	0.956771i
$695$	3.64062	+	20.6470i	0.138097	+	0.783185i
$696$		0			0
$697$	−9.74465	+	3.54676i	−0.369105	+	0.134343i
$698$	5.13104	−	29.0996i	0.194213	−	1.10144i
$699$		0			0
$700$	1.96763	−	1.65104i	0.0743694	−	0.0624033i
$701$	−15.8891			−0.600123			−0.300062	−	0.953920i	$-0.597007\pi$
$701$	−15.8891			−0.600123			−0.300062	+	0.953920i	$0.597007\pi$
$702$		0			0
$703$	−4.52433			−0.170638
$704$	−0.162744	+	0.136558i	−0.00613363	+	0.00514673i
$705$		0			0
$706$	1.08575	−	6.15757i	0.0408626	−	0.231743i
$707$	10.9130	−	3.97202i	0.410427	−	0.149383i
$708$		0			0
$709$	−1.43117	−	8.11659i	−0.0537488	−	0.304825i	0.946068	−	0.323968i	$-0.105017\pi$
$709$	−1.43117	−	8.11659i	−0.0537488	−	0.304825i	−0.999817	+	0.0191436i	$0.993906\pi$
$710$	−12.2401	−	21.2005i	−0.459363	−	0.795640i
$711$		0			0
$712$	−2.69813	+	4.67329i	−0.101117	+	0.175139i
$713$	2.75596	+	1.00309i	0.103211	+	0.0375659i
$714$		0			0
$715$	1.76669	+	1.48243i	0.0660704	+	0.0554397i
$716$	−5.30861	−	4.45445i	−0.198392	−	0.166471i
$717$		0			0
$718$	2.43032	+	0.884563i	0.0906986	+	0.0330116i
$719$	10.9348	−	18.9397i	0.407801	−	0.706331i	−0.586842	−	0.809701i	$-0.699629\pi$
$719$	10.9348	−	18.9397i	0.407801	−	0.706331i	0.994643	+	0.103370i	$0.0329625\pi$
$720$		0			0
$721$	33.4819	+	57.9923i	1.24693	+	2.15975i
$722$	3.01800	+	17.1159i	0.112318	+	0.636988i
$723$		0			0
$724$	−2.85444	+	1.03893i	−0.106084	+	0.0386116i
$725$	1.02399	−	5.80731i	0.0380299	−	0.215678i
$726$		0			0
$727$	37.2742	−	31.2768i	1.38242	−	1.15999i	0.414119	−	0.910223i	$-0.364090\pi$
$727$	37.2742	−	31.2768i	1.38242	−	1.15999i	0.968305	−	0.249769i	$-0.0803548\pi$
$728$	20.8596			0.773107
$729$		0			0
$730$	1.56669			0.0579858
$731$	−19.9991	+	16.7812i	−0.739694	+	0.620677i
$732$		0			0
$733$	−4.54580	+	25.7805i	−0.167903	+	0.952226i	0.778117	+	0.628119i	$0.216175\pi$
$733$	−4.54580	+	25.7805i	−0.167903	+	0.952226i	−0.946020	+	0.324107i	$0.894936\pi$
$734$	17.5546	−	6.38935i	0.647951	−	0.235835i
$735$		0			0
$736$	0.144031	+	0.816841i	0.00530906	+	0.0301092i
$737$	1.03680	+	1.79579i	0.0381910	+	0.0661487i
$738$		0			0
$739$	−1.28655	+	2.22838i	−0.0473267	+	0.0819722i	−0.888718	−	0.458454i	$-0.848404\pi$
$739$	−1.28655	+	2.22838i	−0.0473267	+	0.0819722i	0.841392	+	0.540426i	$0.181737\pi$
$740$	6.97447	+	2.53850i	0.256386	+	0.0933170i
$741$		0			0
$742$	34.7285	+	29.1407i	1.27493	+	1.06979i
$743$	37.5339	+	31.4947i	1.37699	+	1.15543i	0.970313	+	0.241854i	$0.0777555\pi$
$743$	37.5339	+	31.4947i	1.37699	+	1.15543i	0.406673	+	0.913574i	$0.366689\pi$
$744$		0			0
$745$	−31.0843	−	11.3138i	−1.13884	−	0.414505i
$746$	6.76307	−	11.7140i	0.247614	−	0.428879i
$747$		0			0
$748$	−0.402111	−	0.696477i	−0.0147026	−	0.0254657i
$749$	0.223903	+	1.26982i	0.00818124	+	0.0463981i
$750$		0			0
$751$	−7.99761	+	2.91089i	−0.291837	+	0.106220i	−0.483790	−	0.875184i	$-0.660740\pi$
$751$	−7.99761	+	2.91089i	−0.291837	+	0.106220i	0.191953	+	0.981404i	$0.438518\pi$
$752$	0.221796	−	1.25787i	0.00808808	−	0.0458698i
$753$		0			0
$754$	36.6854	−	30.7827i	1.33601	−	1.12104i
$755$	−11.0822			−0.403324
$756$		0			0
$757$	17.3242			0.629658			0.314829	−	0.949148i	$-0.398053\pi$
$757$	17.3242			0.629658			0.314829	+	0.949148i	$0.398053\pi$
$758$	−23.1482	+	19.4236i	−0.840779	+	0.705497i
$759$		0			0
$760$	−0.461496	+	2.61727i	−0.0167402	+	0.0949384i
$761$	9.81674	−	3.57300i	0.355856	−	0.129521i	−0.157905	−	0.987454i	$-0.550474\pi$
$761$	9.81674	−	3.57300i	0.355856	−	0.129521i	0.513761	+	0.857933i	$0.328252\pi$
$762$		0			0
$763$	−0.395996	−	2.24580i	−0.0143360	−	0.0813035i
$764$	−2.54859	−	4.41429i	−0.0922047	−	0.159703i
$765$		0			0
$766$	19.2945	−	33.4191i	0.697140	−	1.20748i
$767$	−41.8191	−	15.2209i	−1.51000	−	0.549595i
$768$		0			0
$769$	30.2202	+	25.3577i	1.08977	+	0.914423i	0.996695	−	0.0812363i	$-0.0258868\pi$
$769$	30.2202	+	25.3577i	1.08977	+	0.914423i	0.0930721	+	0.995659i	$0.470331\pi$
$770$	1.36339	+	1.14402i	0.0491333	+	0.0412277i
$771$		0			0
$772$	−17.7304	−	6.45333i	−0.638130	−	0.232260i
$773$	−11.6713	+	20.2152i	−0.419786	+	0.727091i	−0.995918	−	0.0902659i	$-0.971228\pi$
$773$	−11.6713	+	20.2152i	−0.419786	+	0.727091i	0.576131	+	0.817357i	$0.304562\pi$
$774$		0			0
$775$	1.13182	+	1.96037i	0.0406561	+	0.0704184i
$776$	2.18157	+	12.3723i	0.0783138	+	0.444140i
$777$		0			0
$778$	5.28688	−	1.92427i	0.189544	−	0.0689883i
$779$	0.605464	−	3.43376i	0.0216930	−	0.123027i
$780$		0			0
$781$	−1.90803	+	1.60103i	−0.0682747	+	0.0572893i
$782$	−3.13987			−0.112282
$783$		0			0
$784$	9.09779			0.324921
$785$	18.4216	−	15.4576i	0.657497	−	0.551705i
$786$		0			0
$787$	6.57945	−	37.3139i	0.234532	−	1.33010i	−0.609065	−	0.793120i	$-0.708455\pi$
$787$	6.57945	−	37.3139i	0.234532	−	1.33010i	0.843597	−	0.536977i	$-0.180434\pi$
$788$	−18.8352	+	6.85544i	−0.670975	+	0.244215i
$789$		0			0
$790$	−0.858511	−	4.86886i	−0.0305444	−	0.173226i
$791$	2.72793	+	4.72491i	0.0969939	+	0.167998i
$792$		0			0
$793$	−7.36619	+	12.7586i	−0.261581	+	0.453072i
$794$	7.25083	+	2.63909i	0.257322	+	0.0936577i
$795$		0			0
$796$	4.21487	+	3.53670i	0.149392	+	0.125355i
$797$	2.07175	+	1.73841i	0.0733853	+	0.0615776i	0.678742	−	0.734376i	$-0.262525\pi$
$797$	2.07175	+	1.73841i	0.0733853	+	0.0615776i	−0.605357	+	0.795954i	$0.706970\pi$
$798$		0			0
$799$	4.54355	+	1.65372i	0.160739	+	0.0585043i
$800$	−0.320093	+	0.554417i	−0.0113170	+	0.0196016i
$801$		0			0
$802$	−18.1897	−	31.5054i	−0.642300	−	1.11250i
$803$	−0.0276802	−	0.156982i	−0.000976814	−	0.00553979i
$804$		0			0
$805$	6.52964	−	2.37659i	0.230139	−	0.0837639i
$806$	−3.19222	+	18.1040i	−0.112441	+	0.637685i
$807$		0			0
$808$	−2.21733	+	1.86056i	−0.0780055	+	0.0654544i
$809$	22.3977			0.787460			0.393730	−	0.919226i	$-0.371185\pi$
$809$	22.3977			0.787460			0.393730	+	0.919226i	$0.371185\pi$
$810$		0			0
$811$	−35.0916			−1.23223			−0.616117	−	0.787655i	$-0.711295\pi$
$811$	−35.0916			−1.23223			−0.616117	+	0.787655i	$0.711295\pi$
$812$	28.3110	−	23.7557i	0.993520	−	0.833663i
$813$		0			0
$814$	0.131133	−	0.743691i	0.00459620	−	0.0260664i
$815$	15.0362	−	5.47274i	0.526696	−	0.191702i
$816$		0			0
$817$	−1.52428	−	8.64462i	−0.0533278	−	0.302437i
$818$	2.93384	+	5.08156i	0.102579	+	0.177672i
$819$		0			0
$820$	−2.85995	+	4.95358i	−0.0998739	+	0.172987i
$821$	13.3135	+	4.84571i	0.464644	+	0.169117i	0.563724	−	0.825963i	$-0.309368\pi$
$821$	13.3135	+	4.84571i	0.464644	+	0.169117i	−0.0990807	+	0.995079i	$0.531590\pi$
$822$		0			0
$823$	−26.5050	−	22.2404i	−0.923907	−	0.775250i	0.0508063	−	0.998709i	$-0.483821\pi$
$823$	−26.5050	−	22.2404i	−0.923907	−	0.775250i	−0.974713	+	0.223458i	$0.928265\pi$
$824$	−12.7853	−	10.7281i	−0.445397	−	0.373732i
$825$		0			0
$826$	−32.2727	−	11.7463i	−1.12291	−	0.408706i
$827$	25.3847	−	43.9676i	0.882713	−	1.52890i	0.0344011	−	0.999408i	$-0.489048\pi$
$827$	25.3847	−	43.9676i	0.882713	−	1.52890i	0.848312	−	0.529496i	$-0.177619\pi$
$828$		0			0
$829$	−27.2911	−	47.2695i	−0.947859	−	1.64174i	−0.749924	−	0.661524i	$-0.769910\pi$
$829$	−27.2911	−	47.2695i	−0.947859	−	1.64174i	−0.197935	−	0.980215i	$-0.563423\pi$
$830$	4.13359	+	23.4428i	0.143479	+	0.813710i
$831$		0			0
$832$	−4.88549	+	1.77817i	−0.169374	+	0.0616470i
$833$	−5.98042	+	33.9167i	−0.207209	+	1.17514i
$834$		0			0
$835$	9.77302	−	8.20053i	0.338209	−	0.283791i
$836$	0.270404			0.00935213
$837$		0			0
$838$	21.1356			0.730117
$839$	8.48661	−	7.12111i	0.292990	−	0.245848i	−0.484429	−	0.874830i	$-0.660973\pi$
$839$	8.48661	−	7.12111i	0.292990	−	0.245848i	0.777420	+	0.628982i	$0.216528\pi$
$840$		0			0
$841$	9.69769	−	54.9984i	0.334403	−	1.89650i
$842$	6.99405	−	2.54563i	0.241031	−	0.0877281i
$843$		0			0
$844$	−4.36641	−	24.7631i	−0.150298	−	0.852382i
$845$	14.6473	+	25.3699i	0.503883	+	0.872751i
$846$		0			0
$847$	−21.9766	+	38.0646i	−0.755124	+	1.30791i
$848$	−10.6178	−	3.86457i	−0.364617	−	0.132710i
$849$		0			0
$850$	−1.85646	−	1.55776i	−0.0636761	−	0.0534306i
$851$	−2.25856	−	1.89516i	−0.0774224	−	0.0649651i
$852$		0			0
$853$	23.9039	+	8.70031i	0.818454	+	0.297893i	0.717111	−	0.696959i	$-0.245464\pi$
$853$	23.9039	+	8.70031i	0.818454	+	0.297893i	0.101343	+	0.994852i	$0.467686\pi$
$854$	−5.68465	+	9.84611i	−0.194525	+	0.336927i
$855$		0			0
$856$	−0.160686	−	0.278316i	−0.00549212	−	0.00951263i
$857$	−8.19583	−	46.4809i	−0.279964	−	1.58776i	−0.722738	−	0.691123i	$-0.757116\pi$
$857$	−8.19583	−	46.4809i	−0.279964	−	1.58776i	0.442773	−	0.896634i	$-0.353995\pi$
$858$		0			0
$859$	23.0571	−	8.39211i	0.786699	−	0.286335i	0.0827360	−	0.996571i	$-0.473634\pi$
$859$	23.0571	−	8.39211i	0.786699	−	0.286335i	0.703963	+	0.710236i	$0.251412\pi$
$860$	−2.50055	+	14.1813i	−0.0852680	+	0.483579i
$861$		0			0
$862$	−9.99704	+	8.38851i	−0.340501	+	0.285714i
$863$	−28.4215			−0.967479			−0.483740	−	0.875212i	$-0.660722\pi$
$863$	−28.4215			−0.967479			−0.483740	+	0.875212i	$0.660722\pi$
$864$		0			0
$865$	−23.6019			−0.802488
$866$	−0.109953	+	0.0922611i	−0.00373634	+	0.00313516i
$867$		0			0
$868$	−2.46351	+	13.9712i	−0.0836169	+	0.474215i
$869$	−0.472691	+	0.172045i	−0.0160349	+	0.00583624i
$870$		0			0
$871$	8.81185	+	49.9745i	0.298578	+	1.69332i
$872$	0.284189	+	0.492229i	0.00962385	+	0.0166690i
$873$		0			0
$874$	0.527861	−	0.914282i	0.0178552	−	0.0309261i
$875$	44.4014	+	16.1608i	1.50104	+	0.546334i
$876$		0			0
$877$	33.1323	+	27.8013i	1.11880	+	0.938784i	0.998543	−	0.0539587i	$-0.0171839\pi$
$877$	33.1323	+	27.8013i	1.11880	+	0.938784i	0.120256	+	0.992743i	$0.461628\pi$
$878$	−10.3849	−	8.71396i	−0.350473	−	0.294082i
$879$		0			0
$880$	−0.416841	−	0.151718i	−0.0140517	−	0.00511440i
$881$	−10.2218	+	17.7047i	−0.344381	+	0.596485i	−0.985241	−	0.171173i	$-0.945244\pi$
$881$	−10.2218	+	17.7047i	−0.344381	+	0.596485i	0.640860	+	0.767658i	$0.278578\pi$
$882$		0			0
$883$	14.1469	+	24.5031i	0.476080	+	0.824595i	0.999624	−	0.0274033i	$-0.00872385\pi$
$883$	14.1469	+	24.5031i	0.476080	+	0.824595i	−0.523544	+	0.851999i	$0.675391\pi$
$884$	−3.41758	−	19.3820i	−0.114946	−	0.651889i
$885$		0			0
$886$	−11.5406	+	4.20044i	−0.387715	+	0.141117i
$887$	9.97456	−	56.5686i	0.334913	−	1.89939i	−0.0931752	−	0.995650i	$-0.529702\pi$
$887$	9.97456	−	56.5686i	0.334913	−	1.89939i	0.428088	−	0.903737i	$-0.359187\pi$
$888$		0			0
$889$	−5.54469	+	4.65255i	−0.185963	+	0.156041i
$890$	−11.2675			−0.377686
$891$		0			0
$892$	−3.75239			−0.125639
$893$	−1.24538	+	1.04500i	−0.0416750	+	0.0349695i
$894$		0			0
$895$	2.51264	−	14.2499i	0.0839885	−	0.476322i
$896$	−3.77024	+	1.37225i	−0.125955	+	0.0458438i
$897$		0			0
$898$	7.06133	+	40.0468i	0.235640	+	1.33638i
$899$	16.2850	+	28.2065i	0.543136	+	0.940739i
$900$		0			0
$901$	21.3868	−	37.0430i	0.712497	−	1.23408i
$902$	0.546878	+	0.199047i	0.0182091	+	0.00662755i
$903$		0			0
$904$	−1.04168	−	0.874072i	−0.0346457	−	0.0290712i
$905$	−4.85873	−	4.07696i	−0.161510	−	0.135523i
$906$		0			0
$907$	26.7707	+	9.74375i	0.888908	+	0.323536i	0.745799	−	0.666171i	$-0.232068\pi$
$907$	26.7707	+	9.74375i	0.888908	+	0.323536i	0.143109	+	0.989707i	$0.454290\pi$
$908$	9.36384	−	16.2186i	0.310750	−	0.538235i
$909$		0			0
$910$	21.7776	+	37.7198i	0.721919	+	1.25040i
$911$	3.29560	+	18.6903i	0.109188	+	0.619236i	0.989465	+	0.144775i	$0.0462459\pi$
$911$	3.29560	+	18.6903i	0.109188	+	0.619236i	−0.880277	+	0.474461i	$0.842643\pi$
$912$		0			0
$913$	2.27593	−	0.828372i	0.0753224	−	0.0274151i
$914$	−5.65936	+	32.0958i	−0.187195	+	1.06164i
$915$		0			0
$916$	−3.17397	+	2.66328i	−0.104871	+	0.0879972i
$917$	−38.9763			−1.28711
$918$		0			0
$919$	−13.1481			−0.433715			−0.216857	−	0.976203i	$-0.569581\pi$
$919$	−13.1481			−0.433715			−0.216857	+	0.976203i	$0.569581\pi$
$920$	−1.32670	+	1.11324i	−0.0437401	+	0.0367023i
$921$		0			0
$922$	−4.74414	+	26.9054i	−0.156240	+	0.886082i
$923$	−57.2782	+	20.8475i	−1.88533	+	0.686205i
$924$		0			0
$925$	−0.395155	−	2.24103i	−0.0129926	−	0.0736848i
$926$	−1.69959	−	2.94378i	−0.0558521	−	0.0967386i
$927$		0			0
$928$	−4.60562	+	7.97716i	−0.151187	+	0.261863i
$929$	25.7306	+	9.36519i	0.844195	+	0.307262i	0.727671	−	0.685926i	$-0.240603\pi$
$929$	25.7306	+	9.36519i	0.844195	+	0.307262i	0.116524	+	0.993188i	$0.462825\pi$
$930$		0			0
$931$	−8.87060	−	7.44332i	−0.290722	−	0.243945i
$932$	1.46859	+	1.23230i	0.0481053	+	0.0403652i
$933$		0			0
$934$	−31.0076	−	11.2858i	−1.01460	−	0.369284i
$935$	0.839615	−	1.45426i	0.0274583	−	0.0475592i
$936$		0			0
$937$	−20.0466	−	34.7218i	−0.654895	−	1.13431i	−0.981920	−	0.189296i	$-0.939380\pi$
$937$	−20.0466	−	34.7218i	−0.654895	−	1.13431i	0.327025	−	0.945016i	$-0.393954\pi$
$938$	6.80030	+	38.5664i	0.222038	+	1.25924i
$939$		0			0
$940$	2.50613	−	0.912157i	0.0817410	−	0.0297513i
$941$	0.591978	−	3.35727i	0.0192979	−	0.109444i	−0.973637	−	0.228102i	$-0.926748\pi$
$941$	0.591978	−	3.35727i	0.0192979	−	0.109444i	0.992935	+	0.118658i	$0.0378592\pi$
$942$		0			0
$943$	1.74058	−	1.46052i	0.0566812	−	0.0475612i
$944$	8.55985			0.278600
$945$		0			0
$946$	1.46515			0.0476360
$947$	−2.93783	+	2.46513i	−0.0954666	+	0.0801060i	−0.689272	−	0.724503i	$-0.742069\pi$
$947$	−2.93783	+	2.46513i	−0.0954666	+	0.0801060i	0.593805	+	0.804609i	$0.297625\pi$
$948$		0			0
$949$	0.677394	−	3.84169i	0.0219892	−	0.124707i
$950$	0.765694	−	0.278690i	0.0248424	−	0.00904189i
$951$		0			0
$952$	−2.63742	−	14.9576i	−0.0854793	−	0.484777i
$953$	−26.3964	−	45.7200i	−0.855065	−	1.48102i	−0.876585	−	0.481247i	$-0.840184\pi$
$953$	−26.3964	−	45.7200i	−0.855065	−	1.48102i	0.0215205	−	0.999768i	$-0.493149\pi$
$954$		0			0
$955$	5.32150	−	9.21711i	0.172200	−	0.298259i
$956$	22.7399	+	8.27664i	0.735460	+	0.267686i
$957$		0			0
$958$	−17.6522	−	14.8119i	−0.570316	−	0.478552i
$959$	−27.8705	−	23.3861i	−0.899986	−	0.755178i
$960$		0			0
$961$	17.3819	+	6.32648i	0.560705	+	0.204080i
$962$	9.24024	−	16.0046i	0.297917	−	0.516008i
$963$		0			0
$964$	−6.60247	−	11.4358i	−0.212651	−	0.368323i
$965$	−6.84126	−	38.7987i	−0.220228	−	1.24898i
$966$		0			0
$967$	−9.43802	+	3.43516i	−0.303506	+	0.110467i	−0.489284	−	0.872125i	$-0.662742\pi$
$967$	−9.43802	+	3.43516i	−0.303506	+	0.110467i	0.185778	+	0.982592i	$0.440520\pi$
$968$	1.90229	−	10.7884i	0.0611420	−	0.346754i
$969$		0			0
$970$	−20.0949	+	16.8617i	−0.645210	+	0.541395i
$971$	−4.06174			−0.130348			−0.0651738	−	0.997874i	$-0.520760\pi$
$971$	−4.06174			−0.130348			−0.0651738	+	0.997874i	$0.520760\pi$
$972$		0			0
$973$	40.2860			1.29151
$974$	−20.6307	+	17.3113i	−0.661052	+	0.554688i
$975$		0			0
$976$	0.492064	−	2.79063i	0.0157506	−	0.0893259i
$977$	17.1297	−	6.23470i	0.548027	−	0.199466i	−0.0531425	−	0.998587i	$-0.516924\pi$
$977$	17.1297	−	6.23470i	0.548027	−	0.199466i	0.601170	+	0.799121i	$0.294702\pi$
$978$		0			0
$979$	0.199073	+	1.12900i	0.00636240	+	0.0360830i
$980$	9.49817	+	16.4513i	0.303408	+	0.525518i
$981$		0			0
$982$	0.123997	−	0.214768i	0.00395689	−	0.00685354i
$983$	−39.5076	−	14.3796i	−1.26010	−	0.458638i	−0.376296	−	0.926500i	$-0.622802\pi$
$983$	−39.5076	−	14.3796i	−1.26010	−	0.458638i	−0.883802	+	0.467862i	$0.845025\pi$
$984$		0			0
$985$	−32.0606	−	26.9020i	−1.02153	−	0.857170i
$986$	−26.7115	−	22.4136i	−0.850666	−	0.713794i
$987$		0			0
$988$	6.21829	+	2.26327i	0.197830	+	0.0720043i
$989$	2.86014	−	4.95391i	0.0909471	−	0.157525i
$990$		0			0
$991$	15.9365	+	27.6029i	0.506241	+	0.876834i	0.999974	+	0.00722097i	$0.00229853\pi$
$991$	15.9365	+	27.6029i	0.506241	+	0.876834i	−0.493733	+	0.869613i	$0.664368\pi$
$992$	−0.614003	−	3.48219i	−0.0194946	−	0.110560i
$993$		0			0
$994$	−44.2028	+	16.0885i	−1.40203	+	0.510297i
$995$	−1.99496	+	11.3140i	−0.0632445	+	0.358677i
$996$		0			0
$997$	−24.5132	+	20.5690i	−0.776342	+	0.651428i	−0.942324	−	0.334701i	$-0.891365\pi$
$997$	−24.5132	+	20.5690i	−0.776342	+	0.651428i	0.165983	+	0.986129i	$0.446920\pi$
$998$	26.7183			0.845753
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	162.2.e.b.37.2		12
3.2	odd	2		54.2.e.b.49.2	yes	12
9.2	odd	6		486.2.e.h.433.2		12
9.4	even	3		486.2.e.g.271.1		12
9.5	odd	6		486.2.e.f.271.2		12
9.7	even	3		486.2.e.e.433.1		12
12.11	even	2		432.2.u.b.49.1		12
27.2	odd	18		486.2.e.h.55.2		12
27.4	even	9		1458.2.a.f.1.3		6
27.5	odd	18		1458.2.c.f.973.3		12
27.7	even	9		486.2.e.g.217.1		12
27.11	odd	18		54.2.e.b.43.2	✓	12
27.13	even	9		1458.2.c.g.487.4		12
27.14	odd	18		1458.2.c.f.487.3		12
27.16	even	9	inner	162.2.e.b.127.2		12
27.20	odd	18		486.2.e.f.217.2		12
27.22	even	9		1458.2.c.g.973.4		12
27.23	odd	18		1458.2.a.g.1.4		6
27.25	even	9		486.2.e.e.55.1		12
108.11	even	18		432.2.u.b.97.1		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
54.2.e.b.43.2	✓	12	27.11	odd	18
54.2.e.b.49.2	yes	12	3.2	odd	2
162.2.e.b.37.2		12	1.1	even	1	trivial
162.2.e.b.127.2		12	27.16	even	9	inner
432.2.u.b.49.1		12	12.11	even	2
432.2.u.b.97.1		12	108.11	even	18
486.2.e.e.55.1		12	27.25	even	9
486.2.e.e.433.1		12	9.7	even	3
486.2.e.f.217.2		12	27.20	odd	18
486.2.e.f.271.2		12	9.5	odd	6
486.2.e.g.217.1		12	27.7	even	9
486.2.e.g.271.1		12	9.4	even	3
486.2.e.h.55.2		12	27.2	odd	18
486.2.e.h.433.2		12	9.2	odd	6
1458.2.a.f.1.3		6	27.4	even	9
1458.2.a.g.1.4		6	27.23	odd	18
1458.2.c.f.487.3		12	27.14	odd	18
1458.2.c.f.973.3		12	27.5	odd	18
1458.2.c.g.487.4		12	27.13	even	9
1458.2.c.g.973.4		12	27.22	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:	\( N \)	\(=\)	\( 162 = 2 \cdot 3^{4} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	162.e (of order \(9\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.766044 + 0.642788i) q^{2} +(0.173648 - 0.984808i) q^{4} +(1.96209 - 0.714144i) q^{5} +(-0.696712 - 3.95125i) q^{7} +(0.500000 + 0.866025i) q^{8} +O(q^{10})\)	\(q+(-0.766044 + 0.642788i) q^{2} +(0.173648 - 0.984808i) q^{4} +(1.96209 - 0.714144i) q^{5} +(-0.696712 - 3.95125i) q^{7} +(0.500000 + 0.866025i) q^{8} +(-1.04401 + 1.80828i) q^{10} +(0.199635 + 0.0726611i) q^{11} +(3.98269 + 3.34187i) q^{13} +(3.07353 + 2.57900i) q^{14} +(-0.939693 - 0.342020i) q^{16} +(1.89276 - 3.27836i) q^{17} +(0.636405 + 1.10229i) q^{19} +(-0.362580 - 2.05630i) q^{20} +(-0.199635 + 0.0726611i) q^{22} +(-0.144031 + 0.816841i) q^{23} +(-0.490411 + 0.411503i) q^{25} -5.19903 q^{26} -4.01220 q^{28} +(-7.05621 + 5.92087i) q^{29} +(0.614003 - 3.48219i) q^{31} +(0.939693 - 0.342020i) q^{32} +(0.657349 + 3.72801i) q^{34} +(-4.18878 - 7.25517i) q^{35} +(-1.77730 + 3.07838i) q^{37} +(-1.19605 - 0.435326i) q^{38} +(1.59951 + 1.34215i) q^{40} +(-2.09850 - 1.76085i) q^{41} +(-6.48062 - 2.35875i) q^{43} +(0.106223 - 0.183984i) q^{44} +(-0.414721 - 0.718318i) q^{46} +(0.221796 + 1.25787i) q^{47} +(-8.54912 + 3.11163i) q^{49} +(0.111167 - 0.630460i) q^{50} +(3.98269 - 3.34187i) q^{52} +11.2992 q^{53} +0.443592 q^{55} +(3.07353 - 2.57900i) q^{56} +(1.59951 - 9.07129i) q^{58} +(-8.04363 + 2.92764i) q^{59} +(0.492064 + 2.79063i) q^{61} +(1.76795 + 3.06218i) q^{62} +(-0.500000 + 0.866025i) q^{64} +(10.2010 + 3.71285i) q^{65} +(7.47702 + 6.27396i) q^{67} +(-2.89988 - 2.43329i) q^{68} +(7.87232 + 2.86529i) q^{70} +(-5.86207 + 10.1534i) q^{71} +(-0.375162 - 0.649800i) q^{73} +(-0.617250 - 3.50060i) q^{74} +(1.19605 - 0.435326i) q^{76} +(0.148014 - 0.839430i) q^{77} +(-1.81383 + 1.52198i) q^{79} -2.08802 q^{80} +2.73940 q^{82} +(8.73328 - 7.32809i) q^{83} +(1.37256 - 7.78415i) q^{85} +(6.48062 - 2.35875i) q^{86} +(0.0368910 + 0.209219i) q^{88} +(2.69813 + 4.67329i) q^{89} +(10.4298 - 18.0649i) q^{91} +(0.779421 + 0.283686i) q^{92} +(-0.978448 - 0.821016i) q^{94} +(2.03588 + 1.70830i) q^{95} +(11.8055 + 4.29685i) q^{97} +(4.54889 - 7.87892i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 3 q^{5} - 3 q^{7} + 6 q^{8}+O(q^{10}) \) 12 * q + 3 * q^5 - 3 * q^7 + 6 * q^8	\( 12 q + 3 q^{5} - 3 q^{7} + 6 q^{8} - 3 q^{10} + 12 q^{11} + 12 q^{13} + 3 q^{14} + 6 q^{17} - 9 q^{19} - 6 q^{20} - 12 q^{22} - 30 q^{23} - 9 q^{25} - 18 q^{26} + 12 q^{28} - 15 q^{29} - 15 q^{34} - 3 q^{35} - 15 q^{37} - 3 q^{38} - 3 q^{40} + 12 q^{41} + 9 q^{43} + 3 q^{44} + 3 q^{46} + 9 q^{47} - 39 q^{49} + 27 q^{50} + 12 q^{52} + 12 q^{53} + 18 q^{55} + 3 q^{56} - 3 q^{58} - 12 q^{59} - 36 q^{61} + 12 q^{62} - 6 q^{64} + 15 q^{65} + 36 q^{67} - 3 q^{68} + 39 q^{70} - 12 q^{71} - 21 q^{73} - 33 q^{74} + 3 q^{76} - 3 q^{77} + 39 q^{79} - 6 q^{80} + 6 q^{82} - 18 q^{83} + 45 q^{85} - 9 q^{86} + 6 q^{88} - 12 q^{89} - 6 q^{91} + 6 q^{92} + 36 q^{94} + 15 q^{95} + 39 q^{97} + 12 q^{98}+O(q^{100}) \) 12 * q + 3 * q^5 - 3 * q^7 + 6 * q^8 - 3 * q^10 + 12 * q^11 + 12 * q^13 + 3 * q^14 + 6 * q^17 - 9 * q^19 - 6 * q^20 - 12 * q^22 - 30 * q^23 - 9 * q^25 - 18 * q^26 + 12 * q^28 - 15 * q^29 - 15 * q^34 - 3 * q^35 - 15 * q^37 - 3 * q^38 - 3 * q^40 + 12 * q^41 + 9 * q^43 + 3 * q^44 + 3 * q^46 + 9 * q^47 - 39 * q^49 + 27 * q^50 + 12 * q^52 + 12 * q^53 + 18 * q^55 + 3 * q^56 - 3 * q^58 - 12 * q^59 - 36 * q^61 + 12 * q^62 - 6 * q^64 + 15 * q^65 + 36 * q^67 - 3 * q^68 + 39 * q^70 - 12 * q^71 - 21 * q^73 - 33 * q^74 + 3 * q^76 - 3 * q^77 + 39 * q^79 - 6 * q^80 + 6 * q^82 - 18 * q^83 + 45 * q^85 - 9 * q^86 + 6 * q^88 - 12 * q^89 - 6 * q^91 + 6 * q^92 + 36 * q^94 + 15 * q^95 + 39 * q^97 + 12 * q^98

Introduction

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