LMFDB - Embedded newform 162.2.e.b.127.2

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} - 1584 x^{3} + 936 x^{2} - 342 x + 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			127.2
Root			$0.500000 - 1.80139i$ of defining polynomial
Character	$\chi$	$=$	162.127
Dual form			162.2.e.b.37.2

$q$-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 $\left(\mathbb{Z}/162\mathbb{Z}\right)^\times$.

$n$	$83$
$\chi(n)$	$e\left(\frac{2}{9}\right)$

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	0.741190	−	0.671295i	$-0.234262\pi$
$5$	1.96209	+	0.714144i	0.877475	+	0.319375i	0.136285	+	0.990670i	$0.456484\pi$
$6$		0			0
$7$	−0.696712	+	3.95125i	−0.263332	+	1.49343i	0.510410	+	0.859931i	$0.329494\pi$
$7$	−0.696712	+	3.95125i	−0.263332	+	1.49343i	−0.773742	+	0.633501i	$0.781617\pi$
$8$	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	−0.311749	−	0.950165i	$-0.600915\pi$
$11$	0.199635	−	0.0726611i	0.0601921	−	0.0219081i	0.371941	+	0.928256i	$0.378692\pi$
$12$		0			0
$13$	3.98269	−	3.34187i	1.10460	−	0.926868i	0.106873	−	0.994273i	$-0.465916\pi$
$13$	3.98269	−	3.34187i	1.10460	−	0.926868i	0.997726	+	0.0674046i	$0.0214718\pi$
$14$	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	0.998912	−	0.0466426i	$-0.0148522\pi$
$17$	1.89276	+	3.27836i	0.459062	+	0.795119i	−0.539850	+	0.841762i	$0.681519\pi$
$18$		0			0
$19$	0.636405	−	1.10229i	0.146001	−	0.252882i	−0.783745	−	0.621083i	$-0.786693\pi$
$19$	0.636405	−	1.10229i	0.146001	−	0.252882i	0.929746	+	0.368201i	$0.120026\pi$
$20$	−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	0.966102	−	0.258159i	$-0.0831159\pi$
$23$	−0.144031	−	0.816841i	−0.0300326	−	0.170323i	−0.996135	+	0.0878361i	$0.972005\pi$
$24$		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	−0.988265	−	0.152752i	$-0.951187\pi$
$29$	−7.05621	−	5.92087i	−1.31031	−	1.09948i	−0.322041	−	0.946726i	$-0.604369\pi$
$30$		0			0
$31$	0.614003	+	3.48219i	0.110278	+	0.625419i	0.988980	+	0.148048i	$0.0472991\pi$
$31$	0.614003	+	3.48219i	0.110278	+	0.625419i	−0.878702	+	0.477371i	$0.841590\pi$
$32$	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	0.682140	−	0.731222i	$-0.261049\pi$
$37$	−1.77730	−	3.07838i	−0.292187	−	0.506082i	−0.974326	+	0.225140i	$0.927716\pi$
$38$	−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	−0.791774	−	0.610814i	$-0.790842\pi$
$41$	−2.09850	+	1.76085i	−0.327730	+	0.274998i	0.464044	+	0.885812i	$0.346398\pi$
$42$		0			0
$43$	−6.48062	+	2.35875i	−0.988286	+	0.359707i	−0.785056	−	0.619425i	$-0.787366\pi$
$43$	−6.48062	+	2.35875i	−0.988286	+	0.359707i	−0.203229	+	0.979131i	$0.565144\pi$
$44$	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	−0.964349	−	0.264633i	$-0.914749\pi$
$47$	0.221796	−	1.25787i	0.0323523	−	0.183479i	0.996702	+	0.0811536i	$0.0258604\pi$
$48$		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	−0.239589	−	0.970874i	$-0.577013\pi$
$59$	−8.04363	−	2.92764i	−1.04719	−	0.381147i	−0.807602	+	0.589728i	$0.799235\pi$
$60$		0			0
$61$	0.492064	−	2.79063i	0.0630023	−	0.357304i	−0.936967	−	0.349419i	$-0.886379\pi$
$61$	0.492064	−	2.79063i	0.0630023	−	0.357304i	0.999969	−	0.00788485i	$-0.00250985\pi$
$62$	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	−0.0593114	−	0.998240i	$-0.518890\pi$
$67$	7.47702	−	6.27396i	0.913463	−	0.766487i	0.972775	+	0.231753i	$0.0744460\pi$
$68$	−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	−0.969944	−	0.243327i	$-0.921761\pi$
$71$	−5.86207	−	10.1534i	−0.695700	−	1.20499i	0.274244	−	0.961660i	$-0.411572\pi$
$72$		0			0
$73$	−0.375162	+	0.649800i	−0.0439094	+	0.0760534i	−0.887145	−	0.461491i	$-0.847315\pi$
$73$	−0.375162	+	0.649800i	−0.0439094	+	0.0760534i	0.843235	+	0.537544i	$0.180648\pi$
$74$	−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	0.535024	−	0.844837i	$-0.320302\pi$
$79$	−1.81383	−	1.52198i	−0.204071	−	0.171236i	−0.739096	+	0.673600i	$0.764747\pi$
$80$	−2.08802			−0.233447
$81$		0			0
$82$	2.73940			0.302516
$83$	8.73328	+	7.32809i	0.958602	+	0.804363i	0.980725	−	0.195393i	$-0.0625981\pi$
$83$	8.73328	+	7.32809i	0.958602	+	0.804363i	−0.0221230	+	0.999755i	$0.507043\pi$
$84$		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	−0.686851	−	0.726799i	$-0.741007\pi$
$89$	2.69813	−	4.67329i	0.286001	−	0.495368i	0.972851	+	0.231431i	$0.0743407\pi$
$90$		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	0.335909	−	0.941895i	$-0.390957\pi$
$97$	11.8055	−	4.29685i	1.19867	−	0.436279i	0.862759	+	0.505615i	$0.168734\pi$
$98$	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	−0.949536	−	0.313658i	$-0.898445\pi$
$101$	0.502628	−	2.85055i	0.0500134	−	0.283640i	0.999549	+	0.0300181i	$0.00955651\pi$
$102$		0			0
$103$	−15.6835	−	5.70832i	−1.54534	−	0.562458i	−0.578022	−	0.816021i	$-0.696175\pi$
$103$	−15.6835	−	5.70832i	−1.54534	−	0.562458i	−0.967319	+	0.253564i	$0.918397\pi$
$104$	−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	0.281217	−	0.959644i	$-0.409262\pi$
$113$	−1.27781	−	0.465084i	−0.120206	−	0.0437514i	−0.401423	+	0.915893i	$0.631484\pi$
$114$		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	−0.903267	−	0.429079i	$-0.858838\pi$
$127$	−0.902007	+	1.56232i	−0.0800402	+	0.138634i	0.823227	+	0.567713i	$0.192172\pi$
$128$	−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	0.965422	+	0.260694i	$0.0839512\pi$
$131$	1.68689	+	9.56684i	0.147384	+	0.835859i	−0.818037	+	0.575165i	$0.804938\pi$
$132$		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	0.889340	−	0.457246i	$-0.151164\pi$
$137$	6.94643	+	5.82875i	0.593474	+	0.497984i	−0.295867	+	0.955229i	$0.595608\pi$
$138$		0			0
$139$	−1.74358	−	9.88833i	−0.147888	−	0.838717i	−0.965002	−	0.262241i	$-0.915538\pi$
$139$	−1.74358	−	9.88833i	−0.147888	−	0.838717i	0.817114	−	0.576476i	$-0.195573\pi$
$140$	−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	−0.986173	−	0.165718i	$-0.947006\pi$
$149$	−12.1360	+	10.1833i	−0.994221	+	0.834250i	−0.00804728	+	0.999968i	$0.502562\pi$
$150$		0			0
$151$	−4.98746	+	1.81529i	−0.405874	+	0.147726i	−0.536886	−	0.843655i	$-0.680400\pi$
$151$	−4.98746	+	1.81529i	−0.405874	+	0.147726i	0.131012	+	0.991381i	$0.458177\pi$
$152$	−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	0.735624	−	0.677390i	$-0.236889\pi$
$157$	10.8225	+	3.93906i	0.863727	+	0.314371i	0.128103	+	0.991761i	$0.459111\pi$
$158$	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	0.554472	−	0.832203i	$-0.312920\pi$
$167$	5.74151	+	2.08974i	0.444292	+	0.161709i	−0.110180	+	0.993912i	$0.535143\pi$
$168$		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	−0.712616	−	0.701554i	$-0.752490\pi$
$173$	−10.6218	+	3.86602i	−0.807561	+	0.293928i	−0.0949449	+	0.995483i	$0.530268\pi$
$174$		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	0.965970	−	0.258656i	$-0.0832795\pi$
$179$	3.46495	+	6.00147i	0.258982	+	0.448571i	−0.706987	+	0.707226i	$0.749946\pi$
$180$		0			0
$181$	−1.51882	+	2.63067i	−0.112893	+	0.195536i	−0.916935	−	0.399036i	$-0.869345\pi$
$181$	−1.51882	+	2.63067i	−0.112893	+	0.195536i	0.804043	+	0.594572i	$0.202678\pi$
$182$	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	0.773029	−	0.634370i	$-0.218741\pi$
$191$	3.90467	+	3.27640i	0.282532	+	0.237072i	−0.490498	+	0.871443i	$0.663185\pi$
$192$		0			0
$193$	3.27644	+	18.5816i	0.235843	+	1.33753i	0.840830	+	0.541299i	$0.182067\pi$
$193$	3.27644	+	18.5816i	0.235843	+	1.33753i	−0.604987	+	0.796235i	$0.706822\pi$
$194$	−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	0.249294	+	0.968428i	$0.419801\pi$
$197$	−10.0220	+	17.3586i	−0.714036	+	1.23675i	−0.963330	+	0.268319i	$0.913532\pi$
$198$		0			0
$199$	−2.75106	−	4.76498i	−0.195018	−	0.337780i	0.751889	−	0.659290i	$-0.229143\pi$
$199$	−2.75106	−	4.76498i	−0.195018	−	0.337780i	−0.946906	+	0.321510i	$0.895810\pi$
$200$	−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	0.984636	−	0.174621i	$-0.0558699\pi$
$211$	23.6287	+	8.60014i	1.62667	+	0.592058i	0.642031	+	0.766679i	$0.278092\pi$
$212$	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	−0.998821	−	0.0485415i	$-0.984543\pi$
$223$	−0.651596	+	3.69539i	−0.0436341	+	0.247461i	0.955187	+	0.296003i	$0.0956538\pi$
$224$	−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	0.316076	−	0.948734i	$-0.397635\pi$
$227$	17.5983	−	6.40524i	1.16804	−	0.425131i	0.851962	+	0.523603i	$0.175412\pi$
$228$		0			0
$229$	−3.17397	+	2.66328i	−0.209742	+	0.175994i	−0.741607	−	0.670835i	$-0.765936\pi$
$229$	−3.17397	+	2.66328i	−0.209742	+	0.175994i	0.531865	+	0.846829i	$0.321491\pi$
$230$	−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	0.832918	−	0.553397i	$-0.186669\pi$
$233$	−0.958556	−	1.66027i	−0.0627971	−	0.108768i	−0.895715	+	0.444629i	$0.853335\pi$
$234$		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	−0.748900	−	0.662683i	$-0.769418\pi$
$239$	−4.20216	−	23.8316i	−0.271815	−	1.54154i	0.477085	−	0.878857i	$-0.341693\pi$
$240$		0			0
$241$	10.1156	+	8.48797i	0.651601	+	0.546758i	0.907556	−	0.419931i	$-0.137946\pi$
$241$	10.1156	+	8.48797i	0.651601	+	0.546758i	−0.255955	+	0.966689i	$0.582390\pi$
$242$	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	−0.969706	−	0.244276i	$-0.921450\pi$
$251$	−4.32994	+	7.49967i	−0.273303	+	0.473375i	0.696402	+	0.717652i	$0.254783\pi$
$252$		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	−0.992359	−	0.123382i	$-0.960626\pi$
$257$	−16.7233	+	14.0326i	−1.04317	+	0.875326i	−0.0508142	+	0.998708i	$0.516182\pi$
$258$		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	−0.939099	−	0.343648i	$-0.888337\pi$
$263$	0.987629	−	5.60112i	0.0608998	−	0.345380i	0.999998	−	0.00173240i	$-0.000551441\pi$
$264$		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	0.552244	+	0.833683i	$0.313772\pi$
$277$	−4.19132	+	23.7701i	−0.251832	+	1.42821i	−0.804076	+	0.594527i	$0.797339\pi$
$278$	−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	−0.905393	−	0.424575i	$-0.860424\pi$
$281$	−22.2287	+	8.09058i	−1.32605	+	0.482644i	−0.420660	+	0.907219i	$0.638201\pi$
$282$		0			0
$283$	−8.90462	+	7.47186i	−0.529325	+	0.444156i	−0.867868	−	0.496795i	$-0.834510\pi$
$283$	−8.90462	+	7.47186i	−0.529325	+	0.444156i	0.338543	+	0.940951i	$0.390066\pi$
$284$	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	0.989696	+	0.143186i	$0.0457346\pi$
$293$	1.85993	+	10.5482i	0.108658	+	0.616232i	−0.881037	+	0.473046i	$0.843154\pi$
$294$		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	−0.965836	−	0.259153i	$-0.916557\pi$
$307$	−12.3938	−	21.4667i	−0.707351	−	1.22517i	0.258485	−	0.966015i	$-0.416777\pi$
$308$	−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	−0.0324195	−	0.999474i	$-0.510321\pi$
$311$	16.6871	−	14.0022i	0.946241	−	0.793990i	0.978660	+	0.205484i	$0.0658768\pi$
$312$		0			0
$313$	8.83542	−	3.21583i	0.499408	−	0.181770i	−0.0800199	−	0.996793i	$-0.525498\pi$
$313$	8.83542	−	3.21583i	0.499408	−	0.181770i	0.579428	+	0.815024i	$0.303276\pi$
$314$	−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	−0.828652	−	0.559763i	$-0.810892\pi$
$317$	2.51892	−	14.2855i	0.141477	−	0.802353i	0.970129	−	0.242590i	$-0.0779969\pi$
$318$		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	−0.980716	−	0.195440i	$-0.937387\pi$
$331$	0.140089	−	0.794483i	0.00769998	−	0.0436688i	0.988416	+	0.151771i	$0.0484977\pi$
$332$	−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	−0.998215	−	0.0597207i	$-0.980979\pi$
$337$	−20.4272	+	17.1404i	−1.11274	+	0.933700i	−0.114525	+	0.993420i	$0.536535\pi$
$338$	−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	0.750450	+	0.660927i	$0.229837\pi$
$347$	5.05391	+	28.6621i	0.271308	+	1.53866i	−0.479142	+	0.877737i	$0.659052\pi$
$348$		0			0
$349$	−22.6355	−	18.9934i	−1.21165	−	1.01669i	−0.999219	−	0.0395179i	$-0.987418\pi$
$349$	−22.6355	−	18.9934i	−1.21165	−	1.01669i	−0.212430	−	0.977176i	$-0.568138\pi$
$350$	−2.56856			−0.137295
$351$		0			0
$352$	0.212447			0.0113235
$353$	−4.78974	−	4.01907i	−0.254932	−	0.213913i	0.506361	−	0.862322i	$-0.330990\pi$
$353$	−4.78974	−	4.01907i	−0.254932	−	0.213913i	−0.761293	+	0.648408i	$0.775435\pi$
$354$		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	−0.898131	−	0.439728i	$-0.855075\pi$
$359$	−1.29314	+	2.23979i	−0.0682495	+	0.118212i	0.829881	+	0.557940i	$0.188408\pi$
$360$		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	−0.756782	−	0.653667i	$-0.773230\pi$
$367$	−17.5546	+	6.38935i	−0.916342	+	0.333521i	−0.159560	+	0.987188i	$0.551007\pi$
$368$	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	−0.00869564	−	0.999962i	$-0.502768\pi$
$373$	−12.7104	−	4.62621i	−0.658120	−	0.239536i	−0.649425	+	0.760426i	$0.724990\pi$
$374$	−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	−0.983670	−	0.179980i	$-0.942397\pi$
$383$	−36.2619	−	13.1982i	−1.85289	−	0.674398i	−0.869224	−	0.494419i	$-0.835381\pi$
$384$		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	−0.472551	−	0.881303i	$-0.656667\pi$
$389$	−5.28688	+	1.92427i	−0.268056	+	0.0975642i	0.204496	+	0.978867i	$0.434445\pi$
$390$		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	−0.946451	−	0.322847i	$-0.895360\pi$
$397$	−3.85809	+	6.68240i	−0.193632	+	0.335380i	0.752819	+	0.658227i	$0.228693\pi$
$398$	−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	−0.569593	−	0.821927i	$-0.692899\pi$
$401$	−6.31721	−	35.8267i	−0.315466	−	1.78910i	0.254126	−	0.967171i	$-0.418212\pi$
$402$		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	0.999581	−	0.0289462i	$-0.00921516\pi$
$409$	1.01891	+	5.77853i	0.0503819	+	0.285730i	−0.949199	+	0.314676i	$0.898104\pi$
$410$	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	−0.945986	−	0.324208i	$-0.894902\pi$
$419$	−16.1908	+	13.5857i	−0.790972	+	0.663704i	0.155014	+	0.987912i	$0.450458\pi$
$420$		0			0
$421$	−6.99405	+	2.54563i	−0.340869	+	0.124066i	−0.506782	−	0.862074i	$-0.669165\pi$
$421$	−6.99405	+	2.54563i	−0.340869	+	0.124066i	0.165913	+	0.986140i	$0.446943\pi$
$422$	−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	−0.875673	−	0.482904i	$-0.839582\pi$
$439$	2.35406	−	13.3506i	0.112353	−	0.637187i	0.988027	−	0.154283i	$-0.0493069\pi$
$440$	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	−0.0529847	−	0.998595i	$-0.516873\pi$
$443$	11.5406	−	4.20044i	0.548311	−	0.199569i	0.601296	+	0.799026i	$0.294651\pi$
$444$		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	0.723620	+	0.690199i	$0.242477\pi$
$449$	20.3323	+	35.2165i	0.959540	+	1.66197i	0.235920	+	0.971772i	$0.424190\pi$
$450$		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	0.999983	−	0.00585037i	$-0.00186224\pi$
$457$	24.9661	+	20.9491i	1.16787	+	0.979956i	0.167884	+	0.985807i	$0.446307\pi$
$458$	4.14333			0.193605
$459$		0			0
$460$	1.73189			0.0807498
$461$	20.9287	+	17.5612i	0.974745	+	0.817909i	0.983288	−	0.182055i	$-0.0582749\pi$
$461$	20.9287	+	17.5612i	0.974745	+	0.817909i	−0.00854291	+	0.999964i	$0.502719\pi$
$462$		0			0
$463$	−0.590262	−	3.34754i	−0.0274318	−	0.155574i	0.968015	−	0.250892i	$-0.0807240\pi$
$463$	−0.590262	−	3.34754i	−0.0274318	−	0.155574i	−0.995447	+	0.0953189i	$0.969613\pi$
$464$	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	−0.177577	−	0.984107i	$-0.556826\pi$
$467$	16.4988	−	28.5767i	0.763473	−	1.32237i	0.941050	−	0.338267i	$-0.109841\pi$
$468$		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	−0.745883	−	0.666077i	$-0.767972\pi$
$479$	4.00142	−	22.6932i	0.182830	−	1.03688i	0.928712	−	0.370801i	$-0.120917\pi$
$480$		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	0.336756	−	0.941592i	$-0.390670\pi$
$491$	−0.233037	−	0.0848187i	−0.0105168	−	0.00382781i	−0.347273	+	0.937764i	$0.612892\pi$
$492$		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	−0.973297	−	0.229549i	$-0.926275\pi$
$499$	−20.4674	+	17.1742i	−0.916247	+	0.768822i	0.0570505	+	0.998371i	$0.481830\pi$
$500$	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	0.995057	+	0.0993022i	$0.0316611\pi$
$503$	13.0871	+	22.6676i	0.583527	+	1.01070i	−0.411530	+	0.911396i	$0.635006\pi$
$504$		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	0.956573	−	0.291492i	$-0.0941518\pi$
$509$	−0.947739	−	5.37490i	−0.0420078	−	0.238238i	−0.998581	+	0.0532542i	$0.983041\pi$
$510$		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	0.424194	+	0.905572i	$0.360558\pi$
$521$	−13.0596	+	22.6199i	−0.572151	+	0.990995i	−0.996345	+	0.0854234i	$0.972776\pi$
$522$		0			0
$523$	−3.70382	−	6.41521i	−0.161957	−	0.280518i	0.773614	−	0.633658i	$-0.218447\pi$
$523$	−3.70382	−	6.41521i	−0.161957	−	0.280518i	−0.935570	+	0.353140i	$0.885114\pi$
$524$	−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	0.919513	+	0.393060i	$0.128584\pi$
$547$	−1.84721	+	10.4761i	−0.0789811	+	0.447924i	−0.998494	+	0.0548639i	$0.982528\pi$
$548$	−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	0.712800	−	0.701367i	$-0.247427\pi$
$557$	−5.92385	−	10.2604i	−0.251001	−	0.434747i	−0.963802	+	0.266620i	$0.914093\pi$
$558$		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	0.954899	−	0.296930i	$-0.0959628\pi$
$563$	−1.04327	−	5.91667i	−0.0439686	−	0.249358i	−0.998868	+	0.0475719i	$0.984852\pi$
$564$		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	0.977124	−	0.212669i	$-0.0682155\pi$
$569$	22.3596	+	18.7619i	0.937363	+	0.786541i	−0.0397618	+	0.999209i	$0.512660\pi$
$570$		0			0
$571$	3.78797	+	21.4826i	0.158522	+	0.899021i	0.955495	+	0.295007i	$0.0953219\pi$
$571$	3.78797	+	21.4826i	0.158522	+	0.899021i	−0.796974	+	0.604014i	$0.793567\pi$
$572$	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	−0.894621	−	0.446826i	$-0.852554\pi$
$577$	−20.0399	−	34.7102i	−0.834273	−	1.44500i	0.0603476	−	0.998177i	$-0.480779\pi$
$578$	−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	−0.723309	−	0.690525i	$-0.757380\pi$
$587$	4.66518	−	26.4576i	0.192553	−	1.09202i	0.915861	−	0.401495i	$-0.131509\pi$
$588$		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	−0.285792	−	0.958292i	$-0.592257\pi$
$599$	−27.4285	−	9.98317i	−1.12070	−	0.407901i	−0.834908	+	0.550390i	$0.814479\pi$
$600$		0			0
$601$	−4.03243	+	22.8690i	−0.164486	+	0.932847i	0.785106	+	0.619361i	$0.212608\pi$
$601$	−4.03243	+	22.8690i	−0.164486	+	0.932847i	−0.949593	+	0.313487i	$0.898503\pi$
$602$	−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	0.341950	−	0.939718i	$-0.388913\pi$
$607$	32.6881	−	27.4286i	1.32677	−	1.11329i	0.984821	−	0.173574i	$-0.0555317\pi$
$608$	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	−0.695273	−	0.718746i	$-0.744717\pi$
$613$	6.80411	−	11.7851i	0.274815	−	0.475994i	0.970089	+	0.242752i	$0.0780500\pi$
$614$	−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	−0.910062	−	0.414472i	$-0.863966\pi$
$617$	−4.88447	−	27.7012i	−0.196641	−	1.11521i	0.713421	−	0.700736i	$-0.247145\pi$
$618$		0			0
$619$	−14.9355	−	12.5323i	−0.600307	−	0.503717i	0.291237	−	0.956651i	$-0.405933\pi$
$619$	−14.9355	−	12.5323i	−0.600307	−	0.503717i	−0.891544	+	0.452934i	$0.850377\pi$
$620$	−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	0.713676	−	0.700476i	$-0.247029\pi$
$631$	−6.27471	−	10.8681i	−0.249792	−	0.432653i	−0.963468	+	0.267823i	$0.913696\pi$
$632$	−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	−0.898833	−	0.438291i	$-0.855584\pi$
$641$	2.42288	−	13.7409i	0.0956981	−	0.542731i	0.994531	−	0.104440i	$-0.0333050\pi$
$642$		0			0
$643$	−38.5754	−	14.0403i	−1.52127	−	0.553695i	−0.559802	−	0.828627i	$-0.689123\pi$
$643$	−38.5754	−	14.0403i	−1.52127	−	0.553695i	−0.961464	+	0.274931i	$0.911345\pi$
$644$	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	0.998813	−	0.0487170i	$-0.0155132\pi$
$653$	44.2755	+	16.1150i	1.73263	+	0.630627i	0.733820	+	0.679344i	$0.237735\pi$
$654$		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	−0.973617	−	0.228190i	$-0.926719\pi$
$659$	−40.3746	+	14.6952i	−1.57277	+	0.572442i	−0.599156	+	0.800633i	$0.704497\pi$
$660$		0			0
$661$	21.0863	−	17.6935i	0.820161	−	0.688197i	−0.132849	−	0.991136i	$-0.542412\pi$
$661$	21.0863	−	17.6935i	0.820161	−	0.688197i	0.953010	+	0.302939i	$0.0979680\pi$
$662$	−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	−0.00737169	−	0.999973i	$-0.502347\pi$
$673$	−25.7719	−	21.6252i	−0.993433	−	0.833589i	−0.986061	+	0.166384i	$0.946791\pi$
$674$	26.6658			1.02713
$675$		0			0
$676$	14.0299			0.539611
$677$	−26.1138	−	21.9120i	−1.00363	−	0.842148i	−0.0161497	−	0.999870i	$-0.505141\pi$
$677$	−26.1138	−	21.9120i	−1.00363	−	0.842148i	−0.987484	+	0.157721i	$0.949585\pi$
$678$		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	−0.979390	−	0.201976i	$-0.935264\pi$
$683$	−8.22650	+	14.2487i	−0.314778	+	0.545212i	0.664612	+	0.747189i	$0.268597\pi$
$684$		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	−0.0741383	−	0.997248i	$-0.523621\pi$
$691$	13.4086	−	4.88033i	0.510087	−	0.185657i	0.584225	+	0.811591i	$0.301398\pi$
$692$	−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	−0.999817	−	0.0191436i	$-0.993906\pi$
$709$	−1.43117	+	8.11659i	−0.0537488	+	0.304825i	0.946068	+	0.323968i	$0.105017\pi$
$710$	−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	0.994643	−	0.103370i	$-0.0329625\pi$
$719$	10.9348	+	18.9397i	0.407801	+	0.706331i	−0.586842	+	0.809701i	$0.699629\pi$
$720$		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	0.968305	+	0.249769i	$0.0803548\pi$
$727$	37.2742	+	31.2768i	1.38242	+	1.15999i	0.414119	+	0.910223i	$0.364090\pi$
$728$	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	−0.946020	−	0.324107i	$-0.894936\pi$
$733$	−4.54580	−	25.7805i	−0.167903	−	0.952226i	0.778117	−	0.628119i	$-0.216175\pi$
$734$	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	0.841392	−	0.540426i	$-0.181737\pi$
$739$	−1.28655	−	2.22838i	−0.0473267	−	0.0819722i	−0.888718	+	0.458454i	$0.848404\pi$
$740$	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	0.406673	−	0.913574i	$-0.366689\pi$
$743$	37.5339	−	31.4947i	1.37699	−	1.15543i	0.970313	−	0.241854i	$-0.0777555\pi$
$744$		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	0.191953	−	0.981404i	$-0.438518\pi$
$751$	−7.99761	−	2.91089i	−0.291837	−	0.106220i	−0.483790	+	0.875184i	$0.660740\pi$
$752$	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	0.513761	−	0.857933i	$-0.328252\pi$
$761$	9.81674	+	3.57300i	0.355856	+	0.129521i	−0.157905	+	0.987454i	$0.550474\pi$
$762$		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	0.0930721	−	0.995659i	$-0.470331\pi$
$769$	30.2202	−	25.3577i	1.08977	−	0.914423i	0.996695	+	0.0812363i	$0.0258868\pi$
$770$	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	0.576131	−	0.817357i	$-0.304562\pi$
$773$	−11.6713	−	20.2152i	−0.419786	−	0.727091i	−0.995918	+	0.0902659i	$0.971228\pi$
$774$		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

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

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