LMFDB - Embedded newform 114.2.l.b.89.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [114,2,Mod(29,114)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(114, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([9, 17]))

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

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

chi := DirichletCharacter("114.29");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 114 = 2 \cdot 3 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	114.l (of order $18$, degree $6$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$0.910294583043$
Analytic rank:	$0$
Dimension:	$18$
Relative dimension:	$3$ over $\Q(\zeta_{18})$
Coefficient field:	$\mathbb{Q}[x]/(x^{18} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{18} - x^{15} - 18 x^{14} + 36 x^{13} + 10 x^{12} + 18 x^{11} + 90 x^{10} - 567 x^{9} + 270 x^{8} + \cdots + 19683 $ x^18 - x^15 - 18x^14 + 36x^13 + 10x^12 + 18x^11 + 90x^10 - 567x^9 + 270x^8 + 162x^7 + 270x^6 + 2916x^5 - 4374x^4 - 729x^3 + 19683
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			89.1
Root			$1.40849 - 1.00804i$ of defining polynomial
Character	$\chi$	$=$	114.89
Dual form			114.2.l.b.41.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.766044 - 0.642788i) q^{2} +(-0.748148 - 1.56214i) q^{3} +(0.173648 - 0.984808i) q^{4} +(-0.262261 + 0.0462437i) q^{5} +(-1.57724 - 0.715766i) q^{6} +(0.604656 - 1.04730i) q^{7} +(-0.500000 - 0.866025i) q^{8} +(-1.88055 + 2.33742i) q^{9} +O(q^{10})$	\(q+(0.766044 - 0.642788i) q^{2} +(-0.748148 - 1.56214i) q^{3} +(0.173648 - 0.984808i) q^{4} +(-0.262261 + 0.0462437i) q^{5} +(-1.57724 - 0.715766i) q^{6} +(0.604656 - 1.04730i) q^{7} +(-0.500000 - 0.866025i) q^{8} +(-1.88055 + 2.33742i) q^{9} +(-0.171179 + 0.204003i) q^{10} +(2.03630 - 1.17566i) q^{11} +(-1.66832 + 0.465520i) q^{12} +(1.01749 + 2.79553i) q^{13} +(-0.209995 - 1.19094i) q^{14} +(0.268449 + 0.375091i) q^{15} +(-0.939693 - 0.342020i) q^{16} +(0.576470 + 0.687011i) q^{17} +(0.0618817 + 2.99936i) q^{18} +(1.97979 + 3.88335i) q^{19} +0.266307i q^{20} +(-2.08839 - 0.161024i) q^{21} +(0.804198 - 2.20952i) q^{22} +(5.53770 + 0.976446i) q^{23} +(-0.978777 + 1.42898i) q^{24} +(-4.63182 + 1.68584i) q^{25} +(2.57637 + 1.48747i) q^{26} +(5.05830 + 1.18894i) q^{27} +(-0.926387 - 0.777331i) q^{28} +(1.92487 + 1.61516i) q^{29} +(0.446748 + 0.114780i) q^{30} +(-8.98131 - 5.18536i) q^{31} +(-0.939693 + 0.342020i) q^{32} +(-3.36000 - 2.30141i) q^{33} +(0.883204 + 0.155733i) q^{34} +(-0.110147 + 0.302626i) q^{35} +(1.97536 + 2.25787i) q^{36} +3.95916i q^{37} +(4.01278 + 1.70224i) q^{38} +(3.60577 - 3.68093i) q^{39} +(0.171179 + 0.204003i) q^{40} +(-10.4227 - 3.79356i) q^{41} +(-1.70331 + 1.21904i) q^{42} +(-0.834031 - 4.73003i) q^{43} +(-0.804198 - 2.20952i) q^{44} +(0.385104 - 0.699978i) q^{45} +(4.86977 - 2.81156i) q^{46} +(1.24341 - 1.48183i) q^{47} +(0.168747 + 1.72381i) q^{48} +(2.76878 + 4.79567i) q^{49} +(-2.46454 + 4.26871i) q^{50} +(0.641920 - 1.41451i) q^{51} +(2.92974 - 0.516593i) q^{52} +(0.998339 - 5.66186i) q^{53} +(4.63912 - 2.34063i) q^{54} +(-0.479676 + 0.402496i) q^{55} -1.20931 q^{56} +(4.58516 - 5.99803i) q^{57} +2.51274 q^{58} +(-9.78136 + 8.20754i) q^{59} +(0.416008 - 0.199237i) q^{60} +(-0.153642 + 0.871345i) q^{61} +(-10.2132 + 1.80086i) q^{62} +(1.31088 + 3.38283i) q^{63} +(-0.500000 + 0.866025i) q^{64} +(-0.396123 - 0.686106i) q^{65} +(-4.05323 + 0.396777i) q^{66} +(3.28864 - 3.91925i) q^{67} +(0.776676 - 0.448414i) q^{68} +(-2.61768 - 9.38117i) q^{69} +(0.110147 + 0.302626i) q^{70} +(-1.64669 - 9.33885i) q^{71} +(2.96454 + 0.459892i) q^{72} +(0.320853 + 0.116781i) q^{73} +(2.54490 + 3.03289i) q^{74} +(6.09881 + 5.97428i) q^{75} +(4.16814 - 1.27537i) q^{76} -2.84348i q^{77} +(0.396123 - 5.13750i) q^{78} +(2.33914 - 6.42674i) q^{79} +(0.262261 + 0.0462437i) q^{80} +(-1.92708 - 8.79127i) q^{81} +(-10.4227 + 3.79356i) q^{82} +(12.2240 + 7.05752i) q^{83} +(-0.521223 + 2.02870i) q^{84} +(-0.182956 - 0.153518i) q^{85} +(-3.67931 - 3.08731i) q^{86} +(1.08301 - 4.21529i) q^{87} +(-2.03630 - 1.17566i) q^{88} +(-11.5580 + 4.20677i) q^{89} +(-0.154931 - 0.783754i) q^{90} +(3.54297 + 0.624722i) q^{91} +(1.92322 - 5.28401i) q^{92} +(-1.38090 + 17.9095i) q^{93} -1.93440i q^{94} +(-0.698802 - 0.926900i) q^{95} +(1.23731 + 1.21205i) q^{96} +(3.88456 + 4.62944i) q^{97} +(5.20361 + 1.89396i) q^{98} +(-1.08135 + 6.97057i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 18 q + 3 q^{3} - 9 q^{8} - 3 q^{9}+O(q^{10}) $ 18 * q + 3 * q^3 - 9 * q^8 - 3 * q^9	$ 18 q + 3 q^{3} - 9 q^{8} - 3 q^{9} - 12 q^{13} - 12 q^{14} + 18 q^{15} + 6 q^{17} - 6 q^{19} - 24 q^{22} + 3 q^{24} - 18 q^{25} + 18 q^{26} - 6 q^{27} + 6 q^{28} - 6 q^{29} - 24 q^{33} - 6 q^{34} - 24 q^{35} + 3 q^{38} + 6 q^{39} + 3 q^{41} - 6 q^{43} + 24 q^{44} - 54 q^{45} + 18 q^{46} + 30 q^{47} + 21 q^{49} + 3 q^{50} + 42 q^{51} - 6 q^{52} - 60 q^{53} + 54 q^{54} + 30 q^{55} + 12 q^{57} + 12 q^{58} + 3 q^{59} + 24 q^{60} + 54 q^{61} + 6 q^{62} - 18 q^{63} - 9 q^{64} + 24 q^{65} - 27 q^{66} - 15 q^{67} - 27 q^{68} + 30 q^{69} + 24 q^{70} + 36 q^{71} + 6 q^{72} - 42 q^{73} + 6 q^{74} - 24 q^{78} - 6 q^{79} - 3 q^{81} + 3 q^{82} + 36 q^{83} - 30 q^{84} - 6 q^{86} - 60 q^{89} - 18 q^{91} - 66 q^{93} + 6 q^{95} + 9 q^{97} + 12 q^{98} - 102 q^{99}+O(q^{100}) $ 18 * q + 3 * q^3 - 9 * q^8 - 3 * q^9 - 12 * q^13 - 12 * q^14 + 18 * q^15 + 6 * q^17 - 6 * q^19 - 24 * q^22 + 3 * q^24 - 18 * q^25 + 18 * q^26 - 6 * q^27 + 6 * q^28 - 6 * q^29 - 24 * q^33 - 6 * q^34 - 24 * q^35 + 3 * q^38 + 6 * q^39 + 3 * q^41 - 6 * q^43 + 24 * q^44 - 54 * q^45 + 18 * q^46 + 30 * q^47 + 21 * q^49 + 3 * q^50 + 42 * q^51 - 6 * q^52 - 60 * q^53 + 54 * q^54 + 30 * q^55 + 12 * q^57 + 12 * q^58 + 3 * q^59 + 24 * q^60 + 54 * q^61 + 6 * q^62 - 18 * q^63 - 9 * q^64 + 24 * q^65 - 27 * q^66 - 15 * q^67 - 27 * q^68 + 30 * q^69 + 24 * q^70 + 36 * q^71 + 6 * q^72 - 42 * q^73 + 6 * q^74 - 24 * q^78 - 6 * q^79 - 3 * q^81 + 3 * q^82 + 36 * q^83 - 30 * q^84 - 6 * q^86 - 60 * q^89 - 18 * q^91 - 66 * q^93 + 6 * q^95 + 9 * q^97 + 12 * q^98 - 102 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/114\mathbb{Z}\right)^\times$.

$n$	$77$	$97$
$\chi(n)$	$-1$	$e\left(\frac{5}{18}\right)$

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
$3$	−0.748148	−	1.56214i	−0.431944	−	0.901901i
$3$	−0.748148	−	1.56214i	−0.431944	−	0.901901i
$4$	0.173648	−	0.984808i	0.0868241	−	0.492404i
$5$	−0.262261	+	0.0462437i	−0.117287	+	0.0206808i	−0.231983	−	0.972720i	$-0.574522\pi$
$5$	−0.262261	+	0.0462437i	−0.117287	+	0.0206808i	0.114697	+	0.993401i	$0.463410\pi$
$6$	−1.57724	−	0.715766i	−0.643905	−	0.292210i
$7$	0.604656	−	1.04730i	0.228539	−	0.395840i	−0.728837	−	0.684688i	$-0.759939\pi$
$7$	0.604656	−	1.04730i	0.228539	−	0.395840i	0.957375	+	0.288847i	$0.0932720\pi$
$8$	−0.500000	−	0.866025i	−0.176777	−	0.306186i
$9$	−1.88055	+	2.33742i	−0.626849	+	0.779140i
$10$	−0.171179	+	0.204003i	−0.0541315	+	0.0645114i
$11$	2.03630	−	1.17566i	0.613968	−	0.354474i	−0.160549	−	0.987028i	$-0.551326\pi$
$11$	2.03630	−	1.17566i	0.613968	−	0.354474i	0.774517	+	0.632553i	$0.217993\pi$
$12$	−1.66832	+	0.465520i	−0.481602	+	0.134384i
$13$	1.01749	+	2.79553i	0.282201	+	0.775340i	0.997099	+	0.0761119i	$0.0242506\pi$
$13$	1.01749	+	2.79553i	0.282201	+	0.775340i	−0.714899	+	0.699228i	$0.753527\pi$
$14$	−0.209995	−	1.19094i	−0.0561235	−	0.318292i
$15$	0.268449	+	0.375091i	0.0693133	+	0.0968480i
$16$	−0.939693	−	0.342020i	−0.234923	−	0.0855050i
$17$	0.576470	+	0.687011i	0.139815	+	0.166625i	0.831408	−	0.555663i	$-0.187535\pi$
$17$	0.576470	+	0.687011i	0.139815	+	0.166625i	−0.691593	+	0.722287i	$0.743091\pi$
$18$	0.0618817	+	2.99936i	0.0145857	+	0.706956i
$19$	1.97979	+	3.88335i	0.454194	+	0.890903i
$19$	1.97979	+	3.88335i	0.454194	+	0.890903i
$20$			0.266307i			0.0595480i
$21$	−2.08839	−	0.161024i	−0.455724	−	0.0351383i
$22$	0.804198	−	2.20952i	0.171456	−	0.471070i
$23$	5.53770	+	0.976446i	1.15469	+	0.203603i	0.718022	−	0.696020i	$-0.245048\pi$
$23$	5.53770	+	0.976446i	1.15469	+	0.203603i	0.436668	+	0.899623i	$0.356159\pi$
$24$	−0.978777	+	1.42898i	−0.199792	+	0.291690i
$25$	−4.63182	+	1.68584i	−0.926364	+	0.337169i
$26$	2.57637	+	1.48747i	0.505268	+	0.291717i
$27$	5.05830	+	1.18894i	0.973471	+	0.228811i
$28$	−0.926387	−	0.777331i	−0.175071	−	0.146902i
$29$	1.92487	+	1.61516i	0.357440	+	0.299928i	0.803769	−	0.594941i	$-0.202825\pi$
$29$	1.92487	+	1.61516i	0.357440	+	0.299928i	−0.446329	+	0.894869i	$0.647269\pi$
$30$	0.446748	+	0.114780i	0.0815646	+	0.0209559i
$31$	−8.98131	−	5.18536i	−1.61309	−	0.931319i	−0.988648	−	0.150249i	$-0.951993\pi$
$31$	−8.98131	−	5.18536i	−1.61309	−	0.931319i	−0.624443	−	0.781070i	$-0.714674\pi$
$32$	−0.939693	+	0.342020i	−0.166116	+	0.0604612i
$33$	−3.36000	−	2.30141i	−0.584900	−	0.400625i
$34$	0.883204	+	0.155733i	0.151468	+	0.0267079i
$35$	−0.110147	+	0.302626i	−0.0186182	+	0.0511532i
$36$	1.97536	+	2.25787i	0.329226	+	0.376311i
$37$			3.95916i			0.650882i	0.945562	+	0.325441i	$0.105513\pi$
$37$			3.95916i			0.650882i	−0.945562	+	0.325441i	$0.894487\pi$
$38$	4.01278	+	1.70224i	0.650958	+	0.276140i
$39$	3.60577	−	3.68093i	0.577385	−	0.589420i
$40$	0.171179	+	0.204003i	0.0270657	+	0.0322557i
$41$	−10.4227	−	3.79356i	−1.62776	−	0.592455i	−0.642920	−	0.765934i	$-0.722277\pi$
$41$	−10.4227	−	3.79356i	−1.62776	−	0.592455i	−0.984838	+	0.173479i	$0.944499\pi$
$42$	−1.70331	+	1.21904i	−0.262826	+	0.188102i
$43$	−0.834031	−	4.73003i	−0.127189	−	0.721322i	−0.979984	−	0.199077i	$-0.936206\pi$
$43$	−0.834031	−	4.73003i	−0.127189	−	0.721322i	0.852795	−	0.522245i	$-0.174905\pi$
$44$	−0.804198	−	2.20952i	−0.121237	−	0.333097i
$45$	0.385104	−	0.699978i	0.0574079	−	0.104347i
$46$	4.86977	−	2.81156i	0.718008	−	0.414542i
$47$	1.24341	−	1.48183i	0.181369	−	0.216147i	−0.667698	−	0.744432i	$-0.732720\pi$
$47$	1.24341	−	1.48183i	0.181369	−	0.216147i	0.849067	+	0.528285i	$0.177165\pi$
$48$	0.168747	+	1.72381i	0.0243565	+	0.248811i
$49$	2.76878	+	4.79567i	0.395540	+	0.685096i
$50$	−2.46454	+	4.26871i	−0.348539	+	0.603687i
$51$	0.641920	−	1.41451i	0.0898868	−	0.198071i
$52$	2.92974	−	0.516593i	0.406282	−	0.0716385i
$53$	0.998339	−	5.66186i	0.137132	−	0.777717i	−0.836219	−	0.548396i	$-0.815239\pi$
$53$	0.998339	−	5.66186i	0.137132	−	0.777717i	0.973351	−	0.229320i	$-0.0736504\pi$
$54$	4.63912	−	2.34063i	0.631304	−	0.318520i
$55$	−0.479676	+	0.402496i	−0.0646794	+	0.0542725i
$56$	−1.20931			−0.161601
$57$	4.58516	−	5.99803i	0.607319	−	0.794458i
$58$	2.51274			0.329939
$59$	−9.78136	+	8.20754i	−1.27342	+	1.06853i	−0.279310	+	0.960201i	$0.590106\pi$
$59$	−9.78136	+	8.20754i	−1.27342	+	1.06853i	−0.994115	+	0.108329i	$0.965450\pi$
$60$	0.416008	−	0.199237i	0.0537064	−	0.0257214i
$61$	−0.153642	+	0.871345i	−0.0196718	+	0.111564i	−0.993063	−	0.117587i	$-0.962484\pi$
$61$	−0.153642	+	0.871345i	−0.0196718	+	0.111564i	0.973391	+	0.229152i	$0.0735951\pi$
$62$	−10.2132	+	1.80086i	−1.29707	+	0.228709i
$63$	1.31088	+	3.38283i	0.165156	+	0.426196i
$64$	−0.500000	+	0.866025i	−0.0625000	+	0.108253i
$65$	−0.396123	−	0.686106i	−0.0491331	−	0.0851010i
$66$	−4.05323	+	0.396777i	−0.498918	+	0.0488399i
$67$	3.28864	−	3.91925i	0.401771	−	0.478812i	−0.526788	−	0.849997i	$-0.676604\pi$
$67$	3.28864	−	3.91925i	0.401771	−	0.478812i	0.928559	+	0.371184i	$0.121048\pi$
$68$	0.776676	−	0.448414i	0.0941859	−	0.0543782i
$69$	−2.61768	−	9.38117i	−0.315131	−	1.12936i
$70$	0.110147	+	0.302626i	0.0131651	+	0.0361708i
$71$	−1.64669	−	9.33885i	−0.195426	−	1.10832i	−0.911810	−	0.410612i	$-0.865315\pi$
$71$	−1.64669	−	9.33885i	−0.195426	−	1.10832i	0.716384	−	0.697706i	$-0.245796\pi$
$72$	2.96454	+	0.459892i	0.349374	+	0.0541988i
$73$	0.320853	+	0.116781i	0.0375530	+	0.0136682i	0.360728	−	0.932671i	$-0.382528\pi$
$73$	0.320853	+	0.116781i	0.0375530	+	0.0136682i	−0.323175	+	0.946339i	$0.604750\pi$
$74$	2.54490	+	3.03289i	0.295838	+	0.352566i
$75$	6.09881	+	5.97428i	0.704230	+	0.689850i
$76$	4.16814	−	1.27537i	0.478119	−	0.146295i
$77$		−	2.84348i		−	0.324044i
$78$	0.396123	−	5.13750i	0.0448522	−	0.581707i
$79$	2.33914	−	6.42674i	0.263174	−	0.723064i	−0.735775	−	0.677226i	$-0.763182\pi$
$79$	2.33914	−	6.42674i	0.263174	−	0.723064i	0.998949	−	0.0458383i	$-0.0145959\pi$
$80$	0.262261	+	0.0462437i	0.0293217	+	0.00517020i
$81$	−1.92708	−	8.79127i	−0.214120	−	0.976807i
$82$	−10.4227	+	3.79356i	−1.15100	+	0.418929i
$83$	12.2240	+	7.05752i	1.34176	+	0.774663i	0.987065	−	0.160320i	$-0.0512527\pi$
$83$	12.2240	+	7.05752i	1.34176	+	0.774663i	0.354691	+	0.934984i	$0.384586\pi$
$84$	−0.521223	+	2.02870i	−0.0568701	+	0.221350i
$85$	−0.182956	−	0.153518i	−0.0198443	−	0.0166514i
$86$	−3.67931	−	3.08731i	−0.396750	−	0.332913i
$87$	1.08301	−	4.21529i	0.116111	−	0.451927i
$88$	−2.03630	−	1.17566i	−0.217070	−	0.125326i
$89$	−11.5580	+	4.20677i	−1.22515	+	0.445917i	−0.871933	−	0.489626i	$-0.837133\pi$
$89$	−11.5580	+	4.20677i	−1.22515	+	0.445917i	−0.353213	+	0.935543i	$0.614911\pi$
$90$	−0.154931	−	0.783754i	−0.0163311	−	0.0826150i
$91$	3.54297	+	0.624722i	0.371405	+	0.0654887i
$92$	1.92322	−	5.28401i	0.200510	−	0.550896i
$93$	−1.38090	+	17.9095i	−0.143192	+	1.85713i
$94$		−	1.93440i		−	0.199518i
$95$	−0.698802	−	0.926900i	−0.0716956	−	0.0950979i
$96$	1.23731	+	1.21205i	0.126283	+	0.123704i
$97$	3.88456	+	4.62944i	0.394418	+	0.470049i	0.926309	−	0.376764i	$-0.122963\pi$
$97$	3.88456	+	4.62944i	0.394418	+	0.470049i	−0.531892	+	0.846812i	$0.678519\pi$
$98$	5.20361	+	1.89396i	0.525644	+	0.191319i
$99$	−1.08135	+	6.97057i	−0.108680	+	0.700569i
$100$	0.855926	+	4.85420i	0.0855926	+	0.485420i
$101$	3.54557	+	9.74137i	0.352797	+	0.969302i	0.981467	+	0.191630i	$0.0613774\pi$
$101$	3.54557	+	9.74137i	0.352797	+	0.969302i	−0.628670	+	0.777672i	$0.716400\pi$
$102$	−0.417492	−	1.49620i	−0.0413378	−	0.148146i
$103$	−12.7994	+	7.38973i	−1.26116	+	0.728131i	−0.973299	−	0.229541i	$-0.926278\pi$
$103$	−12.7994	+	7.38973i	−1.26116	+	0.728131i	−0.287861	+	0.957672i	$0.592944\pi$
$104$	1.91225	−	2.27894i	0.187512	−	0.223468i
$105$	0.555150	−	0.0543446i	0.0541771	−	0.00530349i
$106$	−2.87460	−	4.97896i	−0.279206	−	0.483599i
$107$	−8.08439	+	14.0026i	−0.781547	+	1.35368i	0.149493	+	0.988763i	$0.452236\pi$
$107$	−8.08439	+	14.0026i	−0.781547	+	1.35368i	−0.931040	+	0.364917i	$0.881097\pi$
$108$	2.04924	−	4.77500i	0.197188	−	0.459474i
$109$	17.9876	−	3.17170i	1.72290	−	0.303794i	0.777302	−	0.629128i	$-0.216588\pi$
$109$	17.9876	−	3.17170i	1.72290	−	0.303794i	0.945599	+	0.325334i	$0.105477\pi$
$110$	−0.108734	+	0.616659i	−0.0103673	+	0.0587961i
$111$	6.18475	−	2.96204i	0.587030	−	0.281144i
$112$	−0.926387	+	0.777331i	−0.0875353	+	0.0734509i
$113$	2.40020			0.225792			0.112896	−	0.993607i	$-0.463987\pi$
$113$	2.40020			0.225792			0.112896	+	0.993607i	$0.463987\pi$
$114$	−0.343020	−	7.54204i	−0.0321268	−	0.706377i
$115$	−1.49748			−0.139640
$116$	1.92487	−	1.61516i	0.178720	−	0.149964i
$117$	−8.44777	−	2.87883i	−0.780996	−	0.266148i
$118$	−2.21725	+	12.5747i	−0.204115	+	1.15759i
$119$	1.06807	−	0.188329i	0.0979098	−	0.0172641i
$120$	0.190614	−	0.420029i	0.0174006	−	0.0383433i
$121$	−2.73565	+	4.73829i	−0.248696	+	0.430754i
$122$	0.442393	+	0.766248i	0.0400524	+	0.0693728i
$123$	1.87168	+	19.1199i	0.168764	+	1.72398i
$124$	−6.66618	+	7.94444i	−0.598640	+	0.713432i
$125$	2.28993	−	1.32209i	0.204818	−	0.118251i
$126$	3.17863	+	1.74877i	0.283175	+	0.155793i
$127$	−2.02408	−	5.56112i	−0.179608	−	0.493470i	0.816918	−	0.576754i	$-0.195681\pi$
$127$	−2.02408	−	5.56112i	−0.179608	−	0.493470i	−0.996526	+	0.0832849i	$0.973459\pi$
$128$	0.173648	+	0.984808i	0.0153485	+	0.0870455i
$129$	−6.76497	+	4.84163i	−0.595623	+	0.426282i
$130$	−0.744469	−	0.270964i	−0.0652942	−	0.0237652i
$131$	−11.1080	−	13.2379i	−0.970506	−	1.15660i	−0.987638	−	0.156751i	$-0.949898\pi$
$131$	−11.1080	−	13.2379i	−0.970506	−	1.15660i	0.0171319	−	0.999853i	$-0.494546\pi$
$132$	−2.84991	+	2.90931i	−0.248053	+	0.253223i
$133$	5.26411	+	0.274672i	0.456456	+	0.0238171i
$134$		−	5.11622i		−	0.441974i
$135$	−1.38158	−	0.0778975i	−0.118907	−	0.00670435i
$136$	0.306733	−	0.842743i	0.0263022	−	0.0722646i
$137$	18.0150	+	3.17653i	1.53912	+	0.271389i	0.877917	−	0.478813i	$-0.158933\pi$
$137$	18.0150	+	3.17653i	1.53912	+	0.271389i	0.661208	+	0.750203i	$0.270044\pi$
$138$	−8.03536	−	5.50379i	−0.684015	−	0.468513i
$139$	−2.16057	+	0.786381i	−0.183257	+	0.0667000i	−0.432019	−	0.901865i	$-0.642199\pi$
$139$	−2.16057	+	0.786381i	−0.183257	+	0.0667000i	0.248762	+	0.968565i	$0.419976\pi$
$140$	0.278902	+	0.161024i	0.0235715	+	0.0136090i
$141$	−3.24508	−	0.833740i	−0.273285	−	0.0702135i
$142$	−7.26434	−	6.09550i	−0.609610	−	0.511523i
$143$	5.35850	+	4.49632i	0.448100	+	0.376001i
$144$	2.56658	−	1.55327i	0.213882	−	0.129439i
$145$	−0.579510	−	0.334580i	−0.0481257	−	0.0277854i
$146$	0.320853	−	0.116781i	0.0265540	−	0.00966485i
$147$	5.42004	−	7.91309i	0.447037	−	0.652661i
$148$	3.89901	+	0.687501i	0.320497	+	0.0565122i
$149$	−2.67853	+	7.35921i	−0.219434	+	0.602890i	−0.999747	−	0.0224995i	$-0.992838\pi$
$149$	−2.67853	+	7.35921i	−0.219434	+	0.602890i	0.780313	+	0.625389i	$0.215060\pi$
$150$	8.51215	+	0.656324i	0.695014	+	0.0535886i
$151$		−	11.1343i		−	0.906098i	−0.891486	−	0.453049i	$-0.850336\pi$
$151$		−	11.1343i		−	0.906098i	0.891486	−	0.453049i	$-0.149664\pi$
$152$	2.37319	−	3.65622i	0.192491	−	0.296559i
$153$	−2.68991	+	0.0554973i	−0.217467	+	0.00448669i
$154$	−1.82775	−	2.17823i	−0.147284	−	0.175527i
$155$	2.59524	+	0.944590i	0.208455	+	0.0758713i
$156$	−2.99887	−	4.19017i	−0.240102	−	0.335482i
$157$	−3.68519	−	20.8997i	−0.294110	−	1.66798i	−0.670798	−	0.741640i	$-0.734048\pi$
$157$	−3.68519	−	20.8997i	−0.294110	−	1.66798i	0.376688	−	0.926340i	$-0.377063\pi$
$158$	−2.33914	−	6.42674i	−0.186092	−	0.511284i
$159$	−9.59152	+	2.67637i	−0.760657	+	0.212250i
$160$	0.230629	−	0.133153i	0.0182328	−	0.0105267i
$161$	4.37103	−	5.20919i	0.344485	−	0.410542i
$162$	−7.12714	−	5.49580i	−0.559961	−	0.431791i
$163$	1.74061	+	3.01482i	0.136335	+	0.236139i	0.926107	−	0.377262i	$-0.123134\pi$
$163$	1.74061	+	3.01482i	0.136335	+	0.236139i	−0.789772	+	0.613401i	$0.789801\pi$
$164$	−5.54582	+	9.60564i	−0.433056	+	0.750075i
$165$	0.987622	+	0.448193i	0.0768863	+	0.0348918i
$166$	13.9006	−	2.45105i	1.07890	−	0.190238i
$167$	3.56671	−	20.2278i	0.276000	−	1.56527i	−0.459767	−	0.888040i	$-0.652067\pi$
$167$	3.56671	−	20.2278i	0.276000	−	1.56527i	0.735767	−	0.677235i	$-0.236822\pi$
$168$	0.904745	+	1.88911i	0.0698026	+	0.145748i
$169$	3.17888	−	2.66740i	0.244529	−	0.205185i
$170$	−0.238832			−0.0183176
$171$	−12.8001	−	2.67524i	−0.978850	−	0.204581i
$172$	−4.80300			−0.366225
$173$	6.38346	−	5.35636i	0.485326	−	0.407237i	−0.367022	−	0.930212i	$-0.619623\pi$
$173$	6.38346	−	5.35636i	0.485326	−	0.407237i	0.852348	+	0.522976i	$0.175178\pi$
$174$	−1.87990	−	3.92525i	−0.142515	−	0.297572i
$175$	−1.03508	+	5.87024i	−0.0782448	+	0.443748i
$176$	−2.31560	+	0.408302i	−0.174545	+	0.0307769i
$177$	20.1392	+	9.13938i	1.51376	+	0.686958i
$178$	−6.14989	+	10.6519i	−0.460953	+	0.798395i
$179$	−4.51280	−	7.81640i	−0.337302	−	0.584225i	0.646622	−	0.762811i	$-0.276181\pi$
$179$	−4.51280	−	7.81640i	−0.337302	−	0.584225i	−0.983924	+	0.178586i	$0.942848\pi$
$180$	−0.622471	−	0.500803i	−0.0463963	−	0.0373277i
$181$	5.90976	−	7.04297i	0.439269	−	0.523500i	−0.500304	−	0.865850i	$-0.666778\pi$
$181$	5.90976	−	7.04297i	0.439269	−	0.523500i	0.939573	+	0.342350i	$0.111223\pi$
$182$	3.11564	−	1.79882i	0.230947	−	0.133337i
$183$	1.47611	−	0.411886i	0.109117	−	0.0304475i
$184$	−1.92322	−	5.28401i	−0.141782	−	0.389542i
$185$	−0.183086	−	1.03833i	−0.0134608	−	0.0763398i
$186$	10.4542	+	14.6071i	0.766536	+	1.07104i
$187$	1.98156	+	0.721228i	0.144906	+	0.0527414i
$188$	−1.24341	−	1.48183i	−0.0906846	−	0.108074i
$189$	4.30370	−	4.57864i	0.313048	−	0.333047i
$190$	−1.13111	−	0.260865i	−0.0820596	−	0.0189252i
$191$		−	7.33252i		−	0.530562i	−0.964171	−	0.265281i	$-0.914535\pi$
$191$		−	7.33252i		−	0.530562i	0.964171	−	0.265281i	$-0.0854648\pi$
$192$	1.72693	+	0.133153i	0.124630	+	0.00960952i
$193$	0.613121	−	1.68453i	0.0441334	−	0.121255i	−0.915668	−	0.401935i	$-0.868338\pi$
$193$	0.613121	−	1.68453i	0.0441334	−	0.121255i	0.959801	+	0.280680i	$0.0905599\pi$
$194$	5.95150	+	1.04941i	0.427293	+	0.0753432i
$195$	−0.775433	+	1.13211i	−0.0555299	+	0.0810720i
$196$	5.20361	−	1.89396i	0.371686	−	0.135283i
$197$	−6.85271	−	3.95642i	−0.488236	−	0.281883i	0.235607	−	0.971849i	$-0.424292\pi$
$197$	−6.85271	−	3.95642i	−0.488236	−	0.281883i	−0.723842	+	0.689966i	$0.757626\pi$
$198$	3.65224	+	6.03485i	0.259553	+	0.428878i
$199$	−8.01318	−	6.72386i	−0.568039	−	0.476642i	0.312955	−	0.949768i	$-0.398681\pi$
$199$	−8.01318	−	6.72386i	−0.568039	−	0.476642i	−0.880995	+	0.473126i	$0.843125\pi$
$200$	3.77589	+	3.16835i	0.266996	+	0.224036i
$201$	−8.58280	−	2.20513i	−0.605384	−	0.155538i
$202$	8.97769	+	5.18327i	0.631668	+	0.364694i
$203$	2.85543	−	1.03929i	0.200412	−	0.0729441i
$204$	−1.28155	−	0.877795i	−0.0897267	−	0.0614580i
$205$	2.90891	+	0.512919i	0.203167	+	0.0358238i
$206$	−5.05487	+	13.8881i	−0.352189	+	0.967633i
$207$	−12.6963	+	11.1077i	−0.882452	+	0.772037i
$208$		−	2.97494i		−	0.206275i
$209$	8.59694	+	5.58012i	0.594663	+	0.385985i
$210$	0.390338	−	0.398474i	0.0269359	−	0.0274973i
$211$	8.93046	+	10.6429i	0.614799	+	0.732688i	0.980167	−	0.198175i	$-0.0635013\pi$
$211$	8.93046	+	10.6429i	0.614799	+	0.732688i	−0.365368	+	0.930863i	$0.619057\pi$
$212$	−5.40249	−	1.96634i	−0.371044	−	0.135049i
$213$	−13.3566	+	9.55921i	−0.915180	+	0.654986i
$214$	2.80768	+	15.9231i	0.191929	+	1.08848i
$215$	0.437468	+	1.20193i	0.0298351	+	0.0819712i
$216$	−1.49950	−	4.97509i	−0.102028	−	0.338512i
$217$	−10.8612	+	6.27072i	−0.737307	+	0.425684i
$218$	11.7406	−	13.9919i	0.795172	−	0.947650i
$219$	−0.0576176	−	0.588585i	−0.00389344	−	0.0397729i
$220$	0.313086	+	0.542281i	0.0211083	+	0.0365606i
$221$	−1.33401	+	2.31057i	−0.0897349	+	0.155425i
$222$	2.83383	−	6.24453i	0.190194	−	0.419106i
$223$	−12.2714	+	2.16379i	−0.821757	+	0.144898i	−0.568691	−	0.822551i	$-0.692550\pi$
$223$	−12.2714	+	2.16379i	−0.821757	+	0.144898i	−0.253066	+	0.967449i	$0.581439\pi$
$224$	−0.209995	+	1.19094i	−0.0140309	+	0.0795730i
$225$	4.76983	−	13.9968i	0.317989	−	0.933122i
$226$	1.83866	−	1.54282i	0.122306	−	0.102627i
$227$	1.63948			0.108816			0.0544081	−	0.998519i	$-0.482673\pi$
$227$	1.63948			0.108816			0.0544081	+	0.998519i	$0.482673\pi$
$228$	−5.11070	−	5.55705i	−0.338464	−	0.368024i
$229$	−12.1547			−0.803204			−0.401602	−	0.915814i	$-0.631546\pi$
$229$	−12.1547			−0.803204			−0.401602	+	0.915814i	$0.631546\pi$
$230$	−1.14713	+	0.962560i	−0.0756398	+	0.0634693i
$231$	−4.44190	+	2.12734i	−0.292256	+	0.139969i
$232$	0.436333	−	2.47457i	0.0286467	−	0.162463i
$233$	2.37239	−	0.418316i	0.155420	−	0.0274048i	−0.0953966	−	0.995439i	$-0.530412\pi$
$233$	2.37239	−	0.418316i	0.155420	−	0.0274048i	0.250817	+	0.968035i	$0.419301\pi$
$234$	−8.32184	+	3.22481i	−0.544016	+	0.210812i
$235$	−0.257571	+	0.446127i	−0.0168021	+	0.0291021i
$236$	6.38433	+	11.0580i	0.415585	+	0.719814i
$237$	−11.7895	+	1.15409i	−0.765809	+	0.0749663i
$238$	0.697133	−	0.830810i	0.0451884	−	0.0538534i
$239$	−16.5806	+	9.57284i	−1.07251	+	0.619215i	−0.928867	−	0.370414i	$-0.879216\pi$
$239$	−16.5806	+	9.57284i	−1.07251	+	0.619215i	−0.143646	+	0.989629i	$0.545883\pi$
$240$	−0.123971	−	0.444285i	−0.00800230	−	0.0286785i
$241$	1.43503	+	3.94271i	0.0924383	+	0.253972i	0.977292	−	0.211897i	$-0.0679641\pi$
$241$	1.43503	+	3.94271i	0.0924383	+	0.253972i	−0.884854	+	0.465869i	$0.845742\pi$
$242$	0.950083	+	5.38819i	0.0610736	+	0.346366i
$243$	−12.2914	+	9.58753i	−0.788496	+	0.615040i
$244$	0.831427	+	0.302615i	0.0532267	+	0.0193729i
$245$	−0.947913	−	1.12968i	−0.0605600	−	0.0721726i
$246$	13.7238	+	13.4436i	0.874999	+	0.857132i
$247$	−8.84162	+	9.48582i	−0.562579	+	0.603568i
$248$			10.3707i			0.658542i
$249$	1.87947	−	24.3756i	0.119106	−	1.54474i
$250$	0.904364	−	2.48472i	0.0571970	−	0.157147i
$251$	4.15098	+	0.731929i	0.262007	+	0.0461990i	0.303109	−	0.952956i	$-0.401976\pi$
$251$	4.15098	+	0.731929i	0.262007	+	0.0461990i	−0.0411012	+	0.999155i	$0.513087\pi$
$252$	3.55907	−	0.703548i	0.224200	−	0.0443194i
$253$	12.4244	−	4.52211i	0.781114	−	0.284302i
$254$	−5.12516	−	2.95901i	−0.321581	−	0.185665i
$255$	−0.102938	+	0.400656i	−0.00644625	+	0.0250901i
$256$	0.766044	+	0.642788i	0.0478778	+	0.0401742i
$257$	13.6150	+	11.4244i	0.849282	+	0.712632i	0.959631	−	0.281260i	$-0.0907525\pi$
$257$	13.6150	+	11.4244i	0.849282	+	0.712632i	−0.110349	+	0.993893i	$0.535197\pi$
$258$	−2.07013	+	8.05735i	−0.128881	+	0.501629i
$259$	4.14641	+	2.39393i	0.257645	+	0.148752i
$260$	−0.744469	+	0.270964i	−0.0461700	+	0.0168045i
$261$	−7.39512	+	1.46185i	−0.457747	+	0.0904863i
$262$	−17.0184	−	3.00080i	−1.05140	−	0.185390i
$263$	0.383160	−	1.05272i	0.0236267	−	0.0649138i	−0.927319	−	0.374273i	$-0.877892\pi$
$263$	0.383160	−	1.05272i	0.0236267	−	0.0649138i	0.950945	+	0.309359i	$0.100115\pi$
$264$	−0.313086	+	4.06055i	−0.0192691	+	0.249909i
$265$			1.53105i			0.0940519i
$266$	4.20910	−	3.17329i	0.258076	−	0.194567i
$267$	15.2187	+	14.9079i	0.931366	+	0.912349i
$268$	−3.28864	−	3.91925i	−0.200886	−	0.239406i
$269$	18.2909	+	6.65734i	1.11522	+	0.405905i	0.832904	−	0.553418i	$-0.186677\pi$
$269$	18.2909	+	6.65734i	1.11522	+	0.405905i	0.282311	+	0.959323i	$0.408899\pi$
$270$	−1.10842	+	0.828388i	−0.0674564	+	0.0504141i
$271$	−0.0552285	−	0.313217i	−0.00335489	−	0.0190266i	0.983084	−	0.183153i	$-0.0586305\pi$
$271$	−0.0552285	−	0.313217i	−0.00335489	−	0.0190266i	−0.986439	+	0.164127i	$0.947519\pi$
$272$	−0.306733	−	0.842743i	−0.0185984	−	0.0510988i
$273$	−1.67477	−	6.00200i	−0.101362	−	0.363257i
$274$	15.8421	−	9.14645i	0.957057	−	0.552557i
$275$	−7.44980	+	8.87833i	−0.449240	+	0.535383i
$276$	−9.69321	+	0.948885i	−0.583463	+	0.0571162i
$277$	10.9678	+	18.9968i	0.658993	+	1.14141i	0.980877	+	0.194630i	$0.0623506\pi$
$277$	10.9678	+	18.9968i	0.658993	+	1.14141i	−0.321884	+	0.946779i	$0.604316\pi$
$278$	−1.14961	+	1.99119i	−0.0689492	+	0.119424i
$279$	29.0102	−	11.2418i	1.73679	−	0.673028i
$280$	0.317156	−	0.0559231i	0.0189537	−	0.00334204i
$281$	2.62001	−	14.8588i	0.156297	−	0.886403i	−0.801294	−	0.598271i	$-0.795855\pi$
$281$	2.62001	−	14.8588i	0.156297	−	0.886403i	0.957591	−	0.288132i	$-0.0930342\pi$
$282$	−3.02179	+	1.44721i	−0.179945	+	0.0861804i
$283$	−5.08697	+	4.26848i	−0.302389	+	0.253735i	−0.781338	−	0.624108i	$-0.785462\pi$
$283$	−5.08697	+	4.26848i	−0.302389	+	0.253735i	0.478949	+	0.877843i	$0.341018\pi$
$284$	−9.48292			−0.562708
$285$	−0.925138	+	1.78508i	−0.0548005	+	0.105739i
$286$	6.99503			0.413625
$287$	−10.2751	+	8.62187i	−0.606523	+	0.508933i
$288$	0.967692	−	2.83964i	0.0570218	−	0.167328i
$289$	2.81235	−	15.9496i	0.165433	−	0.938215i
$290$	−0.658995	+	0.116199i	−0.0386975	+	0.00682341i
$291$	4.32560	−	9.53173i	0.253571	−	0.558760i
$292$	0.170722	−	0.295699i	0.00999076	−	0.0173045i
$293$	−14.2028	−	24.5999i	−0.829735	−	1.43714i	−0.898246	−	0.439493i	$-0.855158\pi$
$293$	−14.2028	−	24.5999i	−0.829735	−	1.43714i	0.0685112	−	0.997650i	$-0.478175\pi$
$294$	−0.934446	−	9.54571i	−0.0544980	−	0.556717i
$295$	2.18572	−	2.60484i	0.127258	−	0.151660i
$296$	3.42873	−	1.97958i	0.199291	−	0.115061i
$297$	11.6980	−	3.52580i	0.678787	−	0.204588i
$298$	2.67853	+	7.35921i	0.155163	+	0.426307i
$299$	2.90487	+	16.4743i	0.167993	+	0.952734i
$300$	6.94256	−	4.96873i	0.400829	−	0.286870i
$301$	−5.45804	−	1.98656i	−0.314596	−	0.114504i
$302$	−7.15700	−	8.52938i	−0.411839	−	0.490811i
$303$	12.5647	−	12.8266i	0.721826	−	0.736872i
$304$	−0.532206	−	4.32629i	−0.0305241	−	0.248130i
$305$		−	0.235625i		−	0.0134918i
$306$	−2.02492	+	1.77156i	−0.115757	+	0.101273i
$307$	1.49097	−	4.09641i	0.0850942	−	0.233794i	−0.889846	−	0.456261i	$-0.849188\pi$
$307$	1.49097	−	4.09641i	0.0850942	−	0.233794i	0.974940	+	0.222466i	$0.0714107\pi$
$308$	−2.80028	−	0.493765i	−0.159561	−	0.0281348i
$309$	21.1196	+	14.4658i	1.20145	+	0.822930i
$310$	2.59524	−	0.944590i	0.147400	−	0.0536491i
$311$	4.11082	+	2.37338i	0.233103	+	0.134582i	0.612003	−	0.790856i	$-0.290364\pi$
$311$	4.11082	+	2.37338i	0.233103	+	0.134582i	−0.378900	+	0.925438i	$0.623697\pi$
$312$	−4.99066	−	1.28222i	−0.282541	−	0.0725916i
$313$	14.5023	+	12.1689i	0.819718	+	0.687825i	0.952906	−	0.303265i	$-0.0980769\pi$
$313$	14.5023	+	12.1689i	0.819718	+	0.687825i	−0.133188	+	0.991091i	$0.542521\pi$
$314$	−16.2571	−	13.6413i	−0.917442	−	0.769825i
$315$	−0.500228	−	0.826563i	−0.0281847	−	0.0465716i
$316$	−5.92291	−	3.41960i	−0.333190	−	0.192367i
$317$	−29.4488	+	10.7185i	−1.65401	+	0.602010i	−0.989404	−	0.145186i	$-0.953622\pi$
$317$	−29.4488	+	10.7185i	−1.65401	+	0.602010i	−0.664604	+	0.747196i	$0.731400\pi$
$318$	−5.62719	+	8.21553i	−0.315557	+	0.460704i
$319$	5.81850	+	1.02596i	0.325773	+	0.0574426i
$320$	0.0910823	−	0.250247i	0.00509166	−	0.0139892i
$321$	27.9223	+	2.15293i	1.55847	+	0.120165i
$322$		−	6.80012i		−	0.378956i
$323$	−1.52662	+	3.59877i	−0.0849432	+	0.200241i
$324$	−8.99234	+	0.371211i	−0.499575	+	0.0206229i
$325$	−9.42565	−	11.2331i	−0.522841	−	0.623098i
$326$	3.27128	+	1.19065i	0.181179	+	0.0659438i
$327$	−18.4120	−	25.7262i	−1.01819	−	1.42266i
$328$	1.92604	+	10.9231i	0.106348	+	0.603129i
$329$	−0.800083	−	2.19821i	−0.0441100	−	0.121191i
$330$	1.04466	−	0.291495i	0.0575064	−	0.0160463i
$331$	−3.20610	+	1.85104i	−0.176223	+	0.101742i	−0.585517	−	0.810660i	$-0.699108\pi$
$331$	−3.20610	+	1.85104i	−0.176223	+	0.101742i	0.409294	+	0.912403i	$0.365775\pi$
$332$	9.07297	−	10.8127i	0.497944	−	0.593426i
$333$	−9.25422	−	7.44539i	−0.507128	−	0.408005i
$334$	−10.2699	−	17.7880i	−0.561945	−	0.973318i
$335$	−0.681242	+	1.17995i	−0.0372202	+	0.0644673i
$336$	1.90737	+	0.865585i	0.104056	+	0.0472215i
$337$	−19.7344	+	3.47971i	−1.07500	+	0.189552i	−0.683004	−	0.730415i	$-0.739327\pi$
$337$	−19.7344	+	3.47971i	−1.07500	+	0.189552i	−0.391997	+	0.919967i	$0.628216\pi$
$338$	0.720594	−	4.08669i	0.0391952	−	0.222287i
$339$	−1.79570	−	3.74944i	−0.0975292	−	0.203642i
$340$	−0.182956	+	0.153518i	−0.00992217	+	0.00832569i
$341$	−24.3849			−1.32051
$342$	−11.5251	+	6.17841i	−0.623205	+	0.334090i
$343$	15.1618			0.818662
$344$	−3.67931	+	3.08731i	−0.198375	+	0.166456i
$345$	1.12034	+	2.33927i	0.0603168	+	0.125942i
$346$	1.44701	−	8.20642i	0.0777919	−	0.441180i
$347$	0.281016	−	0.0495507i	0.0150857	−	0.00266002i	−0.166100	−	0.986109i	$-0.553118\pi$
$347$	0.281016	−	0.0495507i	0.0150857	−	0.00266002i	0.181186	+	0.983449i	$0.442006\pi$
$348$	−3.96319	−	1.79854i	−0.212449	−	0.0964117i
$349$	6.98873	−	12.1048i	0.374098	−	0.647957i	−0.616093	−	0.787673i	$-0.711286\pi$
$349$	6.98873	−	12.1048i	0.374098	−	0.647957i	0.990192	+	0.139716i	$0.0446190\pi$
$350$	2.98040	+	5.16220i	0.159309	+	0.275931i
$351$	1.82306	+	15.3504i	0.0973077	+	0.819342i
$352$	−1.51140	+	1.80121i	−0.0805578	+	0.0960050i
$353$	−17.7647	+	10.2564i	−0.945519	+	0.545895i	−0.891686	−	0.452654i	$-0.850477\pi$
$353$	−17.7647	+	10.2564i	−0.945519	+	0.545895i	−0.0538327	+	0.998550i	$0.517144\pi$
$354$	21.3022	−	5.94407i	1.13220	−	0.315924i
$355$	0.863726	+	2.37307i	0.0458418	+	0.125949i
$356$	2.13583	+	12.1129i	0.113199	+	0.641983i
$357$	−1.09327	−	1.52757i	−0.0578620	−	0.0808477i
$358$	−8.48129	−	3.08694i	−0.448250	−	0.163150i
$359$	−17.9876	−	21.4368i	−0.949348	−	1.13139i	−0.991214	−	0.132266i	$-0.957775\pi$
$359$	−17.9876	−	21.4368i	−0.949348	−	1.13139i	0.0418658	−	0.999123i	$-0.486670\pi$
$360$	−0.798751	+	0.0164795i	−0.0420979	+	0.000868548i
$361$	−11.1609	+	15.3764i	−0.587415	+	0.809286i
$362$		−	9.19395i		−	0.483223i
$363$	9.44854	+	0.728524i	0.495920	+	0.0382376i
$364$	1.23046	−	3.38067i	0.0644937	−	0.177195i
$365$	−0.0895476	−	0.0157897i	−0.00468713	−	0.000826468i
$366$	0.866009	−	1.26435i	0.0452670	−	0.0660884i
$367$	1.43051	−	0.520662i	0.0746719	−	0.0271783i	−0.304414	−	0.952540i	$-0.598461\pi$
$367$	1.43051	−	0.520662i	0.0746719	−	0.0271783i	0.379086	+	0.925361i	$0.376238\pi$
$368$	−4.86977	−	2.81156i	−0.253854	−	0.146563i
$369$	28.4676	−	17.2283i	1.48196	−	0.896871i
$370$	−0.807680	−	0.677724i	−0.0419893	−	0.0352332i
$371$	−5.32599	−	4.46904i	−0.276512	−	0.232021i
$372$	17.3976	+	4.46987i	0.902023	+	0.231752i
$373$	4.13495	+	2.38731i	0.214100	+	0.123610i	0.603215	−	0.797578i	$-0.293886\pi$
$373$	4.13495	+	2.38731i	0.214100	+	0.123610i	−0.389116	+	0.921189i	$0.627219\pi$
$374$	1.98156	−	0.721228i	0.102464	−	0.0372938i
$375$	−3.77850	−	2.58806i	−0.195121	−	0.133647i
$376$	−1.90501	−	0.335904i	−0.0982432	−	0.0173229i
$377$	−2.55669	+	7.02444i	−0.131676	+	0.361777i
$378$	0.353736	−	6.27381i	0.0181942	−	0.322690i
$379$			13.4129i			0.688972i	0.938791	+	0.344486i	$0.111947\pi$
$379$			13.4129i			0.688972i	−0.938791	+	0.344486i	$0.888053\pi$
$380$	−1.03416	+	0.527231i	−0.0530515	+	0.0270464i
$381$	−7.17292	+	7.32244i	−0.367480	+	0.375140i
$382$	−4.71325	−	5.61704i	−0.241151	−	0.287393i
$383$	30.5956	+	11.1359i	1.56336	+	0.569017i	0.971503	−	0.237026i	$-0.0761727\pi$
$383$	30.5956	+	11.1359i	1.56336	+	0.569017i	0.591857	+	0.806043i	$0.298395\pi$
$384$	1.40849	−	1.00804i	0.0718767	−	0.0514416i
$385$	0.131493	+	0.745733i	0.00670150	+	0.0380061i
$386$	−0.613121	−	1.68453i	−0.0312070	−	0.0857406i
$387$	12.6245	+	6.94556i	0.641739	+	0.353063i
$388$	5.23366	−	3.02165i	0.265699	−	0.153401i
$389$	8.33624	−	9.93474i	0.422664	−	0.503711i	−0.512127	−	0.858910i	$-0.671142\pi$
$389$	8.33624	−	9.93474i	0.422664	−	0.503711i	0.934791	+	0.355199i	$0.115587\pi$
$390$	0.133689	+	1.36568i	0.00676961	+	0.0691541i
$391$	2.52149	+	4.36735i	0.127517	+	0.220866i
$392$	2.76878	−	4.79567i	0.139845	−	0.242218i
$393$	−12.3691	+	27.2561i	−0.623938	+	1.37489i
$394$	−7.79262	+	1.37405i	−0.392586	+	0.0692236i
$395$	−0.316270	+	1.79365i	−0.0159132	+	0.0902485i
$396$	6.67690	+	2.27535i	0.335527	+	0.114341i
$397$	18.9635	−	15.9123i	0.951752	−	0.798615i	−0.0278396	−	0.999612i	$-0.508863\pi$
$397$	18.9635	−	15.9123i	0.951752	−	0.798615i	0.979592	+	0.200997i	$0.0644183\pi$
$398$	−10.4605			−0.524336
$399$	−3.50926	−	8.42876i	−0.175683	−	0.421966i
$400$	4.92908			0.246454
$401$	4.89417	−	4.10670i	0.244403	−	0.205079i	−0.512354	−	0.858774i	$-0.671227\pi$
$401$	4.89417	−	4.10670i	0.244403	−	0.205079i	0.756758	+	0.653695i	$0.226782\pi$
$402$	−7.99223	+	3.82769i	−0.398616	+	0.190908i
$403$	5.35744	−	30.3836i	0.266873	−	1.51351i
$404$	10.2091	−	1.80013i	0.507919	−	0.0895599i
$405$	0.911938	+	2.21649i	0.0453146	+	0.110138i
$406$	1.51935	−	2.63158i	0.0754038	−	0.130603i
$407$	4.65462	+	8.06204i	0.230721	+	0.399620i
$408$	−1.54596	+	0.151337i	−0.0765366	+	0.00749230i
$409$	−18.5835	+	22.1469i	−0.918894	+	1.09510i	0.0762911	+	0.997086i	$0.475692\pi$
$409$	−18.5835	+	22.1469i	−0.918894	+	1.09510i	−0.995185	+	0.0980100i	$0.968752\pi$
$410$	2.55805	−	1.47689i	0.126333	−	0.0729384i
$411$	−8.51571	−	30.5184i	−0.420049	−	1.50536i
$412$	5.05487	+	13.8881i	0.249036	+	0.684220i
$413$	2.68135	+	15.2067i	0.131941	+	0.748273i
$414$	−2.58603	+	16.6700i	−0.127097	+	0.819285i
$415$	−3.53224	−	1.28563i	−0.173391	−	0.0631091i
$416$	−1.91225	−	2.27894i	−0.0937560	−	0.111734i
$417$	2.84486	+	2.78677i	0.139313	+	0.136469i
$418$	10.1725	−	1.25139i	0.497552	−	0.0612073i
$419$			19.2304i			0.939467i	0.882808	+	0.469733i	$0.155650\pi$
$419$			19.2304i			0.939467i	−0.882808	+	0.469733i	$0.844350\pi$
$420$	0.0428818	−	0.556153i	0.00209242	−	0.0271375i
$421$	−11.8370	+	32.5219i	−0.576900	+	1.58502i	0.216476	+	0.976288i	$0.430544\pi$
$421$	−11.8370	+	32.5219i	−0.576900	+	1.58502i	−0.793376	+	0.608732i	$0.791678\pi$
$422$	13.6823	+	2.41255i	0.666042	+	0.117441i
$423$	1.12538	+	5.69302i	0.0547180	+	0.276804i
$424$	−5.40249	+	1.96634i	−0.262368	+	0.0954941i
$425$	−3.82830	−	2.21027i	−0.185700	−	0.107214i
$426$	−4.08721	+	15.9082i	−0.198026	+	0.770757i
$427$	0.819655	+	0.687772i	0.0396659	+	0.0332836i
$428$	12.3860	+	10.3931i	0.598700	+	0.502369i
$429$	3.01491	−	11.7346i	0.145561	−	0.566553i
$430$	1.10771	+	0.639535i	0.0534184	+	0.0308411i
$431$	30.2120	−	10.9963i	1.45526	−	0.529671i	0.511205	−	0.859459i	$-0.329199\pi$
$431$	30.2120	−	10.9963i	1.45526	−	0.529671i	0.944055	+	0.329788i	$0.106977\pi$
$432$	−4.34661	−	2.84728i	−0.209126	−	0.136990i
$433$	−22.7212	−	4.00636i	−1.09191	−	0.192534i	−0.401435	−	0.915888i	$-0.631488\pi$
$433$	−22.7212	−	4.00636i	−1.09191	−	0.192534i	−0.690477	+	0.723354i	$0.742599\pi$
$434$	−4.28943	+	11.7851i	−0.205899	+	0.565703i
$435$	−0.0891011	+	1.15559i	−0.00427207	+	0.0554063i
$436$		−	18.2651i		−	0.874740i
$437$	7.17158	+	23.4380i	0.343063	+	1.12119i
$438$	−0.422473	−	0.413847i	−0.0201865	−	0.0197744i
$439$	7.57338	+	9.02561i	0.361458	+	0.430769i	0.915871	−	0.401473i	$-0.131502\pi$
$439$	7.57338	+	9.02561i	0.361458	+	0.430769i	−0.554413	+	0.832242i	$0.687057\pi$
$440$	0.588409	+	0.214163i	0.0280513	+	0.0102098i
$441$	−16.4163	−	2.54668i	−0.781730	−	0.121271i
$442$	0.463295	+	2.62748i	0.0220367	+	0.124976i
$443$	−7.28357	−	20.0114i	−0.346053	−	0.950772i	−0.983600	−	0.180361i	$-0.942273\pi$
$443$	−7.28357	−	20.0114i	−0.346053	−	0.950772i	0.637548	−	0.770411i	$-0.279949\pi$
$444$	−1.84307	−	6.60514i	−0.0874681	−	0.313466i
$445$	2.83668	−	1.63776i	0.134471	−	0.0776371i
$446$	−8.00962	+	9.54549i	−0.379266	+	0.451992i
$447$	13.5000	−	1.32154i	0.638530	−	0.0625068i
$448$	0.604656	+	1.04730i	0.0285673	+	0.0494800i
$449$	5.96300	−	10.3282i	0.281411	−	0.487419i	−0.690321	−	0.723503i	$-0.742531\pi$
$449$	5.96300	−	10.3282i	0.281411	−	0.487419i	0.971733	+	0.236084i	$0.0758641\pi$
$450$	−5.34308	−	13.7882i	−0.251875	−	0.649981i
$451$	−25.6837	+	4.52874i	−1.20940	+	0.213250i
$452$	0.416790	−	2.36373i	0.0196041	−	0.111181i
$453$	−17.3933	+	8.33012i	−0.817211	+	0.391383i
$454$	1.25592	−	1.05384i	0.0589431	−	0.0494591i
$455$	−0.958074			−0.0449152
$456$	−7.48702	−	0.971852i	−0.350612	−	0.0455111i
$457$	−19.1338			−0.895044			−0.447522	−	0.894273i	$-0.647693\pi$
$457$	−19.1338			−0.895044			−0.447522	+	0.894273i	$0.647693\pi$
$458$	−9.31102	+	7.81288i	−0.435076	+	0.365072i
$459$	2.09915	+	4.16050i	0.0979799	+	0.194195i
$460$	−0.260034	+	1.47473i	−0.0121242	+	0.0687595i
$461$	29.6765	−	5.23277i	1.38217	−	0.243715i	0.567376	−	0.823459i	$-0.307959\pi$
$461$	29.6765	−	5.23277i	1.38217	−	0.243715i	0.814798	+	0.579744i	$0.196848\pi$
$462$	−2.03527	+	4.48484i	−0.0946891	+	0.208654i
$463$	12.7896	−	22.1523i	0.594385	−	1.02950i	−0.399248	−	0.916843i	$-0.630729\pi$
$463$	12.7896	−	22.1523i	0.594385	−	1.02950i	0.993633	−	0.112662i	$-0.0359378\pi$
$464$	−1.25637	−	2.17610i	−0.0583256	−	0.101023i
$465$	−0.466044	−	4.76082i	−0.0216123	−	0.220778i
$466$	1.54847	−	1.84539i	0.0717313	−	0.0854860i
$467$	24.6450	−	14.2288i	1.14044	−	0.658431i	0.193898	−	0.981022i	$-0.437887\pi$
$467$	24.6450	−	14.2288i	1.14044	−	0.658431i	0.946539	+	0.322591i	$0.104554\pi$
$468$	−4.30203	+	7.81952i	−0.198861	+	0.361458i
$469$	−2.11611	−	5.81397i	−0.0977131	−	0.268464i
$470$	0.0894536	+	0.507317i	0.00412619	+	0.0234008i
$471$	−29.8912	+	21.3929i	−1.37731	+	0.985732i
$472$	11.9986	+	4.36714i	0.552281	+	0.201014i
$473$	−7.25924	−	8.65122i	−0.333780	−	0.397784i
$474$	−8.28942	+	8.46221i	−0.380746	+	0.388682i
$475$	−15.7168	−	14.6494i	−0.721134	−	0.672160i
$476$		−	1.08455i		−	0.0497101i
$477$	11.3567	+	12.9809i	0.519989	+	0.594357i
$478$	−6.54821	+	17.9910i	−0.299508	+	0.822891i
$479$	−12.1691	−	2.14575i	−0.556022	−	0.0980417i	−0.111426	−	0.993773i	$-0.535542\pi$
$479$	−12.1691	−	2.14575i	−0.556022	−	0.0980417i	−0.444596	+	0.895731i	$0.646653\pi$
$480$	−0.380548	−	0.260655i	−0.0173696	−	0.0118972i
$481$	−11.0679	+	4.02840i	−0.504655	+	0.183679i
$482$	3.63362	+	2.09787i	0.165507	+	0.0955554i
$483$	−11.4077	−	2.93090i	−0.519066	−	0.133361i
$484$	4.19126	+	3.51689i	0.190512	+	0.159859i
$485$	−1.23285	−	1.03449i	−0.0559810	−	0.0469736i
$486$	−3.25304	+	15.2453i	−0.147561	+	0.691539i
$487$	24.3442	+	14.0551i	1.10314	+	0.636899i	0.937044	−	0.349210i	$-0.113550\pi$
$487$	24.3442	+	14.0551i	1.10314	+	0.636899i	0.166097	+	0.986109i	$0.446883\pi$
$488$	0.831427	−	0.302615i	0.0376369	−	0.0136987i
$489$	3.40734	−	4.97461i	0.154085	−	0.224959i
$490$	−1.45229	−	0.256078i	−0.0656077	−	0.0115684i
$491$	1.17147	−	3.21859i	0.0528678	−	0.145253i	−0.910448	−	0.413624i	$-0.864263\pi$
$491$	1.17147	−	3.21859i	0.0528678	−	0.145253i	0.963316	+	0.268371i	$0.0864852\pi$
$492$	19.1544	+	1.47689i	0.863548	+	0.0665833i
$493$			2.25350i			0.101493i
$494$	−0.675701	+	12.9498i	−0.0304012	+	0.582641i
$495$	−0.0387486	−	1.87812i	−0.00174162	−	0.0844151i
$496$	6.66618	+	7.94444i	0.299320	+	0.356716i
$497$	−10.7762	−	3.92222i	−0.483379	−	0.175936i
$498$	−14.2286	−	19.8809i	−0.637598	−	0.890884i
$499$	6.64566	+	37.6894i	0.297500	+	1.68721i	0.656862	+	0.754010i	$0.271883\pi$
$499$	6.64566	+	37.6894i	0.297500	+	1.68721i	−0.359362	+	0.933198i	$0.617006\pi$
$500$	−0.904364	−	2.48472i	−0.0404444	−	0.111120i
$501$	−34.2670	+	9.56171i	−1.53094	+	0.427186i
$502$	3.65031	−	2.10751i	0.162921	−	0.0940626i
$503$	10.1578	−	12.1056i	0.452916	−	0.539764i	−0.490472	−	0.871457i	$-0.663175\pi$
$503$	10.1578	−	12.1056i	0.452916	−	0.539764i	0.943387	+	0.331693i	$0.107620\pi$
$504$	2.27417	−	2.82667i	0.101300	−	0.125910i
$505$	−1.38034	−	2.39082i	−0.0614244	−	0.106390i
$506$	6.61088	−	11.4504i	0.293889	−	0.509031i
$507$	−6.54512	−	2.97024i	−0.290679	−	0.131913i
$508$	−5.82811	+	1.02765i	−0.258581	+	0.0455947i
$509$	−1.72136	+	9.76234i	−0.0762981	+	0.432708i	0.922599	+	0.385760i	$0.126061\pi$
$509$	−1.72136	+	9.76234i	−0.0762981	+	0.432708i	−0.998897	+	0.0469483i	$0.985050\pi$
$510$	0.178682	+	0.373088i	0.00791215	+	0.0165206i
$511$	0.316310	−	0.265415i	0.0139927	−	0.0117413i
$512$	1.00000			0.0441942
$513$	5.39730	+	21.9970i	0.238296	+	0.971192i
$514$	17.7732			0.783941
$515$	3.01505	−	2.52993i	0.132859	−	0.111482i
$516$	3.59335	+	7.50294i	0.158189	+	0.330299i
$517$	0.789817	−	4.47928i	0.0347361	−	0.196998i
$518$	4.71512	−	0.831403i	0.207170	−	0.0365297i
$519$	−13.1431	−	5.96449i	−0.576920	−	0.261812i
$520$	−0.396123	+	0.686106i	−0.0173712	+	0.0300877i
$521$	6.93036	+	12.0037i	0.303625	+	0.525894i	0.976954	−	0.213449i	$-0.0684697\pi$
$521$	6.93036	+	12.0037i	0.303625	+	0.525894i	−0.673329	+	0.739343i	$0.735136\pi$
$522$	−4.72533	+	5.87334i	−0.206822	+	0.257069i
$523$	24.0581	−	28.6713i	1.05199	−	1.25371i	0.0856778	−	0.996323i	$-0.472694\pi$
$523$	24.0581	−	28.6713i	1.05199	−	1.25371i	0.966309	−	0.257386i	$-0.0828611\pi$
$524$	−14.9657	+	8.64045i	−0.653780	+	0.377460i
$525$	9.94452	−	2.77487i	0.434014	−	0.121105i
$526$	−0.383160	−	1.05272i	−0.0167066	−	0.0459010i
$527$	−1.61506	−	9.15947i	−0.0703532	−	0.398993i
$528$	2.37023	+	3.31181i	0.103151	+	0.144128i
$529$	8.09973	+	2.94806i	0.352162	+	0.128177i
$530$	0.984142	+	1.17286i	0.0427484	+	0.0509456i
$531$	−0.790147	−	38.2978i	−0.0342895	−	1.66198i
$532$	1.18460	−	5.13644i	0.0513590	−	0.222693i
$533$		−	32.9970i		−	1.42926i
$534$	21.2408	+	1.63776i	0.919179	+	0.0708727i
$535$	1.47269	−	4.04618i	0.0636699	−	0.174932i
$536$	−5.03849	−	0.888422i	−0.217630	−	0.0383740i
$537$	−8.83404	+	12.8974i	−0.381217	+	0.556565i
$538$	18.2909	−	6.65734i	0.788576	−	0.287018i
$539$	11.2761	+	6.51028i	0.485698	+	0.280418i
$540$	−0.316622	+	1.34706i	−0.0136253	+	0.0579683i
$541$	6.17119	+	5.17824i	0.265320	+	0.222630i	0.765736	−	0.643155i	$-0.222375\pi$
$541$	6.17119	+	5.17824i	0.265320	+	0.222630i	−0.500416	+	0.865785i	$0.666819\pi$
$542$	−0.243639	−	0.204438i	−0.0104652	−	0.00878135i
$543$	−15.4235	−	3.96266i	−0.661884	−	0.170054i
$544$	−0.776676	−	0.448414i	−0.0332997	−	0.0192256i
$545$	−4.57078	+	1.66363i	−0.195791	+	0.0712620i
$546$	−5.14096	−	3.52128i	−0.220013	−	0.150697i
$547$	25.2004	+	4.44352i	1.07749	+	0.189991i	0.684106	−	0.729382i	$-0.260192\pi$
$547$	25.2004	+	4.44352i	1.07749	+	0.189991i	0.393386	+	0.919373i	$0.371303\pi$
$548$	6.25654	−	17.1897i	0.267266	−	0.734308i
$549$	−1.74777	−	1.99773i	−0.0745930	−	0.0852611i
$550$			11.5898i			0.494192i
$551$	−2.46140	+	10.6726i	−0.104859	+	0.454670i
$552$	−6.81550	+	6.95756i	−0.290087	+	0.296133i
$553$	−5.31631	−	6.33574i	−0.226073	−	0.269423i
$554$	20.6128	+	7.50244i	0.875753	+	0.318748i
$555$	−1.48504	+	1.06283i	−0.0630366	+	0.0451147i
$556$	0.399256	+	2.26430i	0.0169322	+	0.0960275i
$557$	−4.99606	−	13.7266i	−0.211690	−	0.581613i	0.787718	−	0.616037i	$-0.211263\pi$
$557$	−4.99606	−	13.7266i	−0.211690	−	0.581613i	−0.999407	+	0.0344238i	$0.989040\pi$
$558$	14.9970	−	27.2591i	0.634874	−	1.15397i
$559$	12.3743	−	7.14431i	0.523377	−	0.302172i
$560$	0.207009	−	0.246703i	0.00874771	−	0.0104251i
$561$	−0.355841	−	3.63505i	−0.0150236	−	0.153472i
$562$	−7.54402	−	13.0666i	−0.318225	−	0.551182i
$563$	12.5968	−	21.8184i	0.530893	−	0.919534i	−0.468457	−	0.883486i	$-0.655190\pi$
$563$	12.5968	−	21.8184i	0.530893	−	0.919534i	0.999350	−	0.0360479i	$-0.0114769\pi$
$564$	−1.38458	+	3.05100i	−0.0583011	+	0.128470i
$565$	−0.629478	+	0.110994i	−0.0264824	+	0.00466955i
$566$	−1.15312	+	6.53969i	−0.0484694	+	0.274884i
$567$	−10.3723	−	3.29748i	−0.435594	−	0.138481i
$568$	−7.26434	+	6.09550i	−0.304805	+	0.255762i
$569$	−42.1013			−1.76498			−0.882490	−	0.470332i	$-0.844134\pi$
$569$	−42.1013			−1.76498			−0.882490	+	0.470332i	$0.844134\pi$
$570$	0.438733	+	1.96212i	0.0183765	+	0.0821842i
$571$	−12.9487			−0.541887			−0.270944	−	0.962595i	$-0.587336\pi$
$571$	−12.9487			−0.541887			−0.270944	+	0.962595i	$0.587336\pi$
$572$	5.35850	−	4.49632i	0.224050	−	0.188000i
$573$	−11.4544	+	5.48581i	−0.478515	+	0.229173i
$574$	−2.32919	+	13.2095i	−0.0972184	+	0.551353i
$575$	−27.2958	+	4.81298i	−1.13831	+	0.200715i
$576$	−1.08399	−	2.79731i	−0.0451663	−	0.116555i
$577$	6.43762	−	11.1503i	0.268002	−	0.464192i	−0.700344	−	0.713805i	$-0.746970\pi$
$577$	6.43762	−	11.1503i	0.268002	−	0.464192i	0.968346	+	0.249613i	$0.0803034\pi$
$578$	−8.09785	−	14.0259i	−0.336826	−	0.583400i
$579$	−3.09018	+	0.302503i	−0.128424	+	0.0125716i
$580$	−0.430128	+	0.512607i	−0.0178601	+	0.0212848i
$581$	14.7826	−	8.53474i	0.613286	−	0.354081i
$582$	−2.81328	−	10.0822i	−0.116614	−	0.417920i
$583$	−4.62350	−	12.7030i	−0.191486	−	0.526103i
$584$	−0.0592912	−	0.336257i	−0.00245349	−	0.0139144i
$585$	2.34865	+	0.364348i	0.0971046	+	0.0150639i
$586$	−26.6925	−	9.71527i	−1.10266	−	0.401334i
$587$	−11.6998	−	13.9432i	−0.482900	−	0.575498i	0.468497	−	0.883465i	$-0.344796\pi$
$587$	−11.6998	−	13.9432i	−0.482900	−	0.575498i	−0.951397	+	0.307967i	$0.900351\pi$
$588$	−6.85169	−	6.71179i	−0.282559	−	0.276790i
$589$	2.35551	−	45.1435i	0.0970573	−	1.86011i
$590$		−	3.40038i		−	0.139992i
$591$	−1.05362	+	13.6649i	−0.0433402	+	0.562098i
$592$	1.35411	−	3.72039i	0.0556537	−	0.152907i
$593$	6.08719	+	1.07334i	0.249971	+	0.0440766i	0.297230	−	0.954806i	$-0.403937\pi$
$593$	6.08719	+	1.07334i	0.249971	+	0.0440766i	−0.0472585	+	0.998883i	$0.515048\pi$
$594$	6.69485	−	10.2203i	0.274693	−	0.419342i
$595$	−0.271404	+	0.0987830i	−0.0111265	+	0.00404971i
$596$	6.78228	+	3.91575i	0.277813	+	0.160395i
$597$	−4.50854	+	17.5481i	−0.184522	+	0.718197i
$598$	12.8147	+	10.7528i	0.524034	+	0.439717i
$599$	27.9659	+	23.4662i	1.14266	+	0.958803i	0.999522	−	0.0308999i	$-0.00983730\pi$
$599$	27.9659	+	23.4662i	1.14266	+	0.958803i	0.143135	+	0.989703i	$0.454282\pi$
$600$	2.12447	−	8.26886i	0.0867312	−	0.337575i
$601$	2.01662	+	1.16430i	0.0822597	+	0.0474927i	0.540566	−	0.841302i	$-0.318210\pi$
$601$	2.01662	+	1.16430i	0.0822597	+	0.0474927i	−0.458306	+	0.888795i	$0.651544\pi$
$602$	−5.45804	+	1.98656i	−0.222453	+	0.0809663i
$603$	2.97649	+	15.0573i	0.121212	+	0.613180i
$604$	−10.9652	−	1.93345i	−0.446166	−	0.0786712i
$605$	0.498339	−	1.36918i	0.0202604	−	0.0556649i
$606$	1.38034	−	17.9022i	0.0560725	−	0.727229i
$607$			24.4621i			0.992887i	0.868069	+	0.496443i	$0.165361\pi$
$607$			24.4621i			0.992887i	−0.868069	+	0.496443i	$0.834639\pi$
$608$	−3.18858	−	2.97203i	−0.129314	−	0.120532i
$609$	−3.75981	−	3.68304i	−0.152355	−	0.149244i
$610$	−0.151457	−	0.180499i	−0.00613230	−	0.00730819i
$611$	5.40766	+	1.96823i	0.218770	+	0.0796259i
$612$	−0.412444	+	2.65868i	−0.0166721	+	0.107471i
$613$	−6.30039	−	35.7313i	−0.254470	−	1.44317i	−0.797428	−	0.603414i	$-0.793807\pi$
$613$	−6.30039	−	35.7313i	−0.254470	−	1.44317i	0.542958	−	0.839760i	$-0.317304\pi$
$614$	−1.49097	−	4.09641i	−0.0601707	−	0.165318i
$615$	−1.37504	−	4.92785i	−0.0554471	−	0.198710i
$616$	−2.46252	+	1.42174i	−0.0992179	+	0.0572835i
$617$	10.3830	−	12.3740i	0.418006	−	0.498160i	−0.515416	−	0.856940i	$-0.672363\pi$
$617$	10.3830	−	12.3740i	0.418006	−	0.498160i	0.933422	+	0.358780i	$0.116807\pi$
$618$	25.4770	−	2.49399i	1.02483	−	0.100323i
$619$	−15.2492	−	26.4123i	−0.612916	−	1.06160i	−0.990746	−	0.135726i	$-0.956663\pi$
$619$	−15.2492	−	26.4123i	−0.612916	−	1.06160i	0.377831	−	0.925875i	$-0.376670\pi$
$620$	1.38090	−	2.39179i	0.0554582	−	0.0960564i
$621$	26.8504	+	11.5231i	1.07747	+	0.462408i
$622$	4.67465	−	0.824268i	0.187437	−	0.0330501i
$623$	−2.58289	+	14.6483i	−0.103481	+	0.586871i
$624$	−4.64726	+	2.22570i	−0.186039	+	0.0890991i
$625$	18.3401	−	15.3891i	0.733602	−	0.615565i
$626$	18.9314			0.756651
$627$	2.28513	−	17.6044i	0.0912594	−	0.703051i
$628$	−21.2221			−0.846856
$629$	−2.71998	+	2.28234i	−0.108453	+	0.0910028i
$630$	−0.914502	−	0.311644i	−0.0364346	−	0.0124162i
$631$	−5.03370	+	28.5475i	−0.200388	+	1.13646i	0.704145	+	0.710056i	$0.251330\pi$
$631$	−5.03370	+	28.5475i	−0.200388	+	1.13646i	−0.904533	+	0.426403i	$0.859781\pi$
$632$	−6.73529	+	1.18761i	−0.267915	+	0.0472407i
$633$	9.94438	−	21.9131i	0.395254	−	0.870967i
$634$	−15.6694	+	27.1401i	−0.622310	+	1.07787i
$635$	0.788005	+	1.36486i	0.0312710	+	0.0541630i
$636$	0.970161	+	9.91055i	0.0384694	+	0.392979i
$637$	−10.5892	+	12.6198i	−0.419561	+	0.500013i
$638$	5.11670	−	2.95413i	0.202572	−	0.116955i
$639$	24.9255	+	13.7132i	0.986038	+	0.542484i
$640$	−0.0910823	−	0.250247i	−0.00360035	−	0.00989187i
$641$	4.38869	+	24.8895i	0.173343	+	0.983076i	0.940039	+	0.341066i	$0.110788\pi$
$641$	4.38869	+	24.8895i	0.173343	+	0.983076i	−0.766696	+	0.642010i	$0.778101\pi$
$642$	22.7736	−	16.2988i	0.898801	−	0.643264i
$643$	11.3227	+	4.12111i	0.446522	+	0.162521i	0.555488	−	0.831525i	$-0.312532\pi$
$643$	11.3227	+	4.12111i	0.446522	+	0.162521i	−0.108966	+	0.994046i	$0.534754\pi$
$644$	−4.37103	−	5.20919i	−0.172243	−	0.205271i
$645$	1.55029	−	1.58261i	0.0610428	−	0.0623152i
$646$	1.14379	+	3.73811i	0.0450018	+	0.147074i
$647$			27.8093i			1.09330i	0.837362	+	0.546649i	$0.184097\pi$
$647$			27.8093i			1.09330i	−0.837362	+	0.546649i	$0.815903\pi$
$648$	−6.64992	+	6.06453i	−0.261234	+	0.238237i
$649$	−10.2685	+	28.2126i	−0.403075	+	1.10744i
$650$	−14.4409	−	2.54633i	−0.566420	−	0.0998752i
$651$	17.9215	+	12.2753i	0.702400	+	0.481106i
$652$	3.27128	−	1.19065i	0.128113	−	0.0466293i
$653$	2.53710	+	1.46480i	0.0992846	+	0.0573220i	0.548820	−	0.835940i	$-0.315077\pi$
$653$	2.53710	+	1.46480i	0.0992846	+	0.0573220i	−0.449536	+	0.893262i	$0.648411\pi$
$654$	−30.6409	−	7.87240i	−1.19816	−	0.307835i
$655$	3.52536	+	2.95812i	0.137747	+	0.115583i
$656$	8.49669	+	7.12957i	0.331740	+	0.278363i
$657$	−0.876345	+	0.530356i	−0.0341895	+	0.0206912i
$658$	−2.02588	−	1.16964i	−0.0789771	−	0.0455975i
$659$	−25.4128	+	9.24952i	−0.989944	+	0.360310i	−0.785699	−	0.618610i	$-0.787696\pi$
$659$	−25.4128	+	9.24952i	−0.989944	+	0.360310i	−0.204245	+	0.978920i	$0.565474\pi$
$660$	0.612883	−	0.894790i	0.0238564	−	0.0348297i
$661$	13.9832	+	2.46561i	0.543883	+	0.0959013i	0.438838	−	0.898566i	$-0.355390\pi$
$661$	13.9832	+	2.46561i	0.543883	+	0.0959013i	0.105045	+	0.994467i	$0.466501\pi$
$662$	−1.26619	+	3.47882i	−0.0492118	+	0.135208i
$663$	4.60746	+	0.355255i	0.178939	+	0.0137970i
$664$		−	14.1150i		−	0.547770i
$665$	−1.39327	+	0.171396i	−0.0540288	+	0.00664645i
$666$	−11.8749	+	0.245000i	−0.460145	+	0.00949354i
$667$	9.08225	+	10.8238i	0.351666	+	0.419099i
$668$	−19.3011	−	7.02504i	−0.746784	−	0.271807i
$669$	12.5610	+	17.5509i	0.485636	+	0.678555i
$670$	0.236593	+	1.34178i	0.00914038	+	0.0518377i
$671$	0.711543	+	1.95495i	0.0274688	+	0.0754700i
$672$	2.01752	−	0.562959i	0.0778275	−	0.0217166i
$673$	−4.68491	+	2.70483i	−0.180590	+	0.104264i	−0.587570	−	0.809173i	$-0.699915\pi$
$673$	−4.68491	+	2.70483i	−0.180590	+	0.104264i	0.406980	+	0.913437i	$0.366582\pi$
$674$	−12.8807	+	15.3506i	−0.496146	+	0.591284i
$675$	−25.4335	+	3.02057i	−0.978936	+	0.116262i
$676$	−2.07487	−	3.59378i	−0.0798026	−	0.138222i
$677$	−11.2154	+	19.4256i	−0.431043	+	0.746588i	−0.996963	−	0.0778720i	$-0.975187\pi$
$677$	−11.2154	+	19.4256i	−0.431043	+	0.746588i	0.565921	+	0.824460i	$0.308521\pi$
$678$	−3.78568	−	1.71798i	−0.145388	−	0.0659787i
$679$	7.19722	−	1.26906i	0.276204	−	0.0487022i
$680$	−0.0414727	+	0.235203i	−0.00159041	+	0.00901964i
$681$	−1.22658	−	2.56110i	−0.0470025	−	0.0981414i
$682$	−18.6799	+	15.6743i	−0.715290	+	0.600200i
$683$	5.63051			0.215446			0.107723	−	0.994181i	$-0.465644\pi$
$683$	5.63051			0.215446			0.107723	+	0.994181i	$0.465644\pi$
$684$	−4.85731	+	12.1411i	−0.185724	+	0.464227i
$685$	−4.87153			−0.186131
$686$	11.6146	−	9.74584i	0.443449	−	0.372098i
$687$	9.09350	+	18.9873i	0.346939	+	0.724410i
$688$	−0.834031	+	4.73003i	−0.0317971	+	0.180331i
$689$	16.8437	−	2.97000i	0.641694	−	0.113148i
$690$	2.36188	+	1.07184i	0.0899151	+	0.0408044i
$691$	8.10408	−	14.0367i	0.308294	−	0.533980i	−0.669696	−	0.742636i	$-0.733575\pi$
$691$	8.10408	−	14.0367i	0.308294	−	0.533980i	0.977989	+	0.208655i	$0.0669087\pi$
$692$	−4.16651	−	7.21660i	−0.158387	−	0.274334i
$693$	6.64640	+	5.34730i	0.252476	+	0.203127i
$694$	0.183420	−	0.218592i	0.00696254	−	0.00829763i
$695$	0.530267	−	0.306150i	0.0201142	−	0.0116129i
$696$	−4.19206	+	1.16973i	−0.158900	+	0.0443386i
$697$	−3.40218	−	9.34740i	−0.128867	−	0.354058i
$698$	−2.42716	−	13.7651i	−0.0918694	−	0.521017i
$699$	−2.42836	−	3.39303i	−0.0918491	−	0.128336i
$700$	5.60132	+	2.03871i	0.211710	+	0.0770561i
$701$	25.1621	+	29.9870i	0.950360	+	1.13260i	0.991059	+	0.133424i	$0.0425971\pi$
$701$	25.1621	+	29.9870i	0.950360	+	1.13260i	−0.0406990	+	0.999171i	$0.512958\pi$
$702$	11.2636	+	10.5872i	0.425116	+	0.399589i
$703$	−15.3748	+	7.83829i	−0.579872	+	0.295627i
$704$			2.35132i			0.0886186i
$705$	0.889613	+	0.0685930i	0.0335048	+	0.00258336i
$706$	−7.01582	+	19.2758i	−0.264044	+	0.725455i
$707$	12.3459	+	2.17692i	0.464317	+	0.0818715i
$708$	12.4977	−	18.2462i	0.469691	−	0.685735i
$709$	−0.294067	+	0.107032i	−0.0110439	+	0.00401966i	−0.347536	−	0.937667i	$-0.612982\pi$
$709$	−0.294067	+	0.107032i	−0.0110439	+	0.00401966i	0.336492	+	0.941686i	$0.390759\pi$
$710$	2.18703	+	1.26268i	0.0820779	+	0.0473877i
$711$	10.6231	+	17.5533i	0.398398	+	0.658302i
$712$	9.42217	+	7.90614i	0.353111	+	0.296295i
$713$	−44.6726	−	37.4847i	−1.67300	−	1.40381i
$714$	−1.81940	−	0.467448i	−0.0680893	−	0.0174938i
$715$	−1.61325	−	0.931412i	−0.0603322	−	0.0348328i
$716$	−8.48129	+	3.08694i	−0.316961	+	0.115364i
$717$	27.3589	+	18.7393i	1.02174	+	0.699833i
$718$	−27.5586	−	4.85932i	−1.02848	−	0.181348i
$719$	−9.97683	+	27.4111i	−0.372073	+	1.02226i	0.602486	+	0.798130i	$0.294177\pi$
$719$	−9.97683	+	27.4111i	−0.372073	+	1.02226i	−0.974559	+	0.224132i	$0.928045\pi$
$720$	−0.601286	+	0.526051i	−0.0224086	+	0.0196048i
$721$			17.8730i			0.665624i
$722$	1.33405	+	18.9531i	0.0496481	+	0.705362i
$723$	5.08544	−	5.19144i	0.189129	−	0.193072i
$724$	−5.90976	−	7.04297i	−0.219634	−	0.261750i
$725$	−11.6386	−	4.23609i	−0.432246	−	0.157325i
$726$	7.70629	−	5.51532i	0.286007	−	0.204693i
$727$	1.39364	+	7.90374i	0.0516873	+	0.293133i	0.999684	−	0.0251476i	$-0.00800557\pi$
$727$	1.39364	+	7.90374i	0.0516873	+	0.293133i	−0.947996	+	0.318281i	$0.896894\pi$
$728$	−1.23046	−	3.38067i	−0.0456040	−	0.125296i
$729$	24.1729	+	12.0280i	0.895291	+	0.445482i
$730$	−0.0787468	+	0.0454645i	−0.00291455	+	0.00168272i
$731$	2.76878	−	3.29971i	0.102407	−	0.122044i
$732$	−0.149305	−	1.52520i	−0.00551847	−	0.0563732i
$733$	−8.60205	−	14.8992i	−0.317724	−	0.550314i	0.662289	−	0.749249i	$-0.269585\pi$
$733$	−8.60205	−	14.8992i	−0.317724	−	0.550314i	−0.980013	+	0.198935i	$0.936252\pi$
$734$	0.761157	−	1.31836i	0.0280948	−	0.0486617i
$735$	−1.05553	+	2.32594i	−0.0389340	+	0.0857936i
$736$	−5.53770	+	0.976446i	−0.204122	+	0.0359923i
$737$	2.08896	−	11.8471i	0.0769479	−	0.436393i
$738$	10.7333	−	31.4963i	0.395098	−	1.15939i
$739$	−19.8776	+	16.6793i	−0.731210	+	0.613558i	−0.930461	−	0.366390i	$-0.880593\pi$
$739$	−19.8776	+	16.6793i	−0.731210	+	0.613558i	0.199251	+	0.979948i	$0.436149\pi$
$740$	−1.05435			−0.0387587
$741$	21.4330	+	6.71502i	0.787361	+	0.246682i
$742$	−6.95259			−0.255237
$743$	−35.8677	+	30.0966i	−1.31586	+	1.10414i	−0.328693	+	0.944437i	$0.606608\pi$
$743$	−35.8677	+	30.0966i	−1.31586	+	1.10414i	−0.987166	+	0.159700i	$0.948947\pi$
$744$	16.2005	−	7.75884i	0.593939	−	0.284453i
$745$	0.362158	−	2.05390i	0.0132684	−	0.0752491i
$746$	4.70209	−	0.829106i	0.172156	−	0.0303557i
$747$	−39.4842	+	15.3006i	−1.44465	+	0.559819i
$748$	1.05436	−	1.82621i	0.0385514	−	0.0667729i
$749$	9.77655	+	16.9335i	0.357227	+	0.618736i
$750$	−4.55807	+	0.446197i	−0.166437	+	0.0162928i
$751$	−1.93570	+	2.30687i	−0.0706346	+	0.0841791i	−0.800205	−	0.599727i	$-0.795276\pi$
$751$	−1.93570	+	2.30687i	−0.0706346	+	0.0841791i	0.729570	+	0.683906i	$0.239720\pi$
$752$	−1.67524	+	0.967198i	−0.0610895	+	0.0352701i
$753$	−1.96217	−	7.03199i	−0.0715055	−	0.256260i
$754$	2.55669	+	7.02444i	0.0931091	+	0.255815i
$755$	0.514892	+	2.92010i	0.0187389	+	0.106273i
$756$	−3.76175	−	5.03339i	−0.136813	−	0.183063i
$757$	6.18347	+	2.25060i	0.224742	+	0.0817994i	0.451937	−	0.892050i	$-0.350733\pi$
$757$	6.18347	+	2.25060i	0.224742	+	0.0817994i	−0.227195	+	0.973849i	$0.572955\pi$
$758$	8.62162	+	10.2748i	0.313151	+	0.373199i
$759$	−16.3594	−	16.0254i	−0.593810	−	0.581685i
$760$	−0.453318	+	1.06863i	−0.0164436	+	0.0387633i
$761$			12.0756i			0.437741i	0.975754	+	0.218870i	$0.0702372\pi$
$761$			12.0756i			0.437741i	−0.975754	+	0.218870i	$0.929763\pi$
$762$	−0.788005	+	10.2200i	−0.0285464	+	0.370231i
$763$	7.55461	−	20.7561i	0.273495	−	0.751422i
$764$	−7.22112	−	1.27328i	−0.261251	−	0.0460656i
$765$	0.702893	−	0.138946i	0.0254132	−	0.00502362i
$766$	30.5956	−	11.1359i	1.10546	−	0.402356i
$767$	−32.8968	−	18.9930i	−1.18784	−	0.685797i
$768$	0.431008	−	1.67757i	0.0155527	−	0.0605340i
$769$	−28.1846	−	23.6497i	−1.01636	−	0.852830i	−0.0271972	−	0.999630i	$-0.508658\pi$
$769$	−28.1846	−	23.6497i	−1.01636	−	0.852830i	−0.989166	+	0.146800i	$0.953103\pi$
$770$	0.580078	+	0.486743i	0.0209045	+	0.0175410i
$771$	7.66037	−	29.8157i	0.275882	−	1.07379i
$772$	−1.55248	−	0.896322i	−0.0558748	−	0.0322593i
$773$	15.8791	−	5.77952i	0.571132	−	0.207875i	−0.0402788	−	0.999188i	$-0.512825\pi$
$773$	15.8791	−	5.77952i	0.571132	−	0.207875i	0.611411	+	0.791314i	$0.290602\pi$
$774$	14.1355	−	2.79426i	0.508088	−	0.100438i
$775$	50.3416	+	8.87657i	1.80832	+	0.318856i
$776$	2.06693	−	5.67885i	0.0741986	−	0.203859i
$777$	0.637520	−	8.26827i	0.0228709	−	0.296623i
$778$		−	12.9689i		−	0.464957i
$779$	−5.90304	−	47.9856i	−0.211498	−	1.71926i
$780$	0.980257	+	0.960241i	0.0350988	+	0.0343821i
$781$	−14.3325	−	17.0808i	−0.512856	−	0.611198i
$782$	4.73885	+	1.72480i	0.169461	+	0.0616788i
$783$	7.81626	+	10.4585i	0.279330	+	0.373757i
$784$	−0.961588	−	5.45344i	−0.0343424	−	0.194766i
$785$	1.93296	+	5.31077i	0.0689904	+	0.189550i
$786$	8.04460	+	28.8301i	0.286942	+	1.02833i
$787$	−19.2256	+	11.0999i	−0.685319	+	0.395669i	−0.801856	−	0.597517i	$-0.796154\pi$
$787$	−19.2256	+	11.0999i	−0.685319	+	0.395669i	0.116537	+	0.993186i	$0.462821\pi$
$788$	−5.08627	+	6.06158i	−0.181191	+	0.215935i
$789$	−1.93116	+	0.189045i	−0.0687512	+	0.00673017i
$790$	0.910662	+	1.57731i	0.0323999	+	0.0561183i
$791$	1.45129	−	2.51372i	0.0516021	−	0.0893774i
$792$	6.57737	−	2.54881i	0.233717	−	0.0905680i
$793$	−2.59220	+	0.457074i	−0.0920516	+	0.0162312i
$794$	4.29868	−	24.3790i	0.152555	−	0.865180i
$795$	2.39172	−	1.14546i	0.0848255	−	0.0406251i
$796$	−8.01318	+	6.72386i	−0.284020	+	0.238321i
$797$	34.5294			1.22309			0.611547	−	0.791208i	$-0.290547\pi$
$797$	34.5294			1.22309			0.611547	+	0.791208i	$0.290547\pi$
$798$	−8.10615	−	4.20110i	−0.286955	−	0.148717i
$799$	1.73482			0.0613736
$800$	3.77589	−	3.16835i	0.133498	−	0.112018i
$801$	11.9024	−	34.9270i	0.420550	−	1.23408i
$802$	1.10942	−	6.29183i	0.0391750	−	0.222172i
$803$	0.790647	−	0.139412i	0.0279013	−	0.00491976i
$804$	−3.66202	+	8.06949i	−0.129149	+	0.284589i
$805$	−0.905459	+	1.56830i	−0.0319132	+	0.0552753i
$806$	−15.4261	−	26.7189i	−0.543363	−	0.941132i
$807$	−3.28462	−	33.5536i	−0.115624	−	1.18114i
$808$	6.66349	−	7.94123i	0.234421	−	0.279372i
$809$	−19.0821	+	11.0171i	−0.670892	+	0.387340i	−0.796415	−	0.604751i	$-0.793273\pi$
$809$	−19.0821	+	11.0171i	−0.670892	+	0.387340i	0.125523	+	0.992091i	$0.459939\pi$
$810$	2.12332	+	1.11175i	0.0746058	+	0.0390629i
$811$	−3.43077	−	9.42596i	−0.120471	−	0.330990i	0.864769	−	0.502169i	$-0.167465\pi$
$811$	−3.43077	−	9.42596i	−0.120471	−	0.330990i	−0.985240	+	0.171179i	$0.945242\pi$
$812$	−0.527663	−	2.99253i	−0.0185173	−	0.105017i
$813$	−0.447968	+	0.320607i	−0.0157109	+	0.0112442i
$814$	8.74782	+	3.18395i	0.306611	+	0.111597i
$815$	−0.595911	−	0.710179i	−0.0208738	−	0.0248765i
$816$	−1.08700	+	1.10966i	−0.0380526	+	0.0388458i
$817$	16.7172	−	12.6033i	0.584860	−	0.440933i
$818$			28.9108i			1.01084i
$819$	−8.12297	+	7.10660i	−0.283840	+	0.248325i
$820$	1.01025	−	2.77565i	0.0352795	−	0.0969297i
$821$	−38.9746	−	6.87227i	−1.36022	−	0.239844i	−0.554523	−	0.832169i	$-0.687099\pi$
$821$	−38.9746	−	6.87227i	−1.36022	−	0.239844i	−0.805699	+	0.592325i	$0.798210\pi$
$822$	−26.1403	−	17.9047i	−0.911747	−	0.624497i
$823$	35.1506	−	12.7938i	1.22527	−	0.445963i	0.353297	−	0.935511i	$-0.385061\pi$
$823$	35.1506	−	12.7938i	1.22527	−	0.445963i	0.871976	+	0.489548i	$0.162838\pi$
$824$	12.7994	+	7.38973i	0.445888	+	0.257433i
$825$	19.4427	+	4.99531i	0.676909	+	0.173914i
$826$	11.8287	+	9.92548i	0.411574	+	0.345351i
$827$	−12.2053	−	10.2415i	−0.424421	−	0.356132i	0.405421	−	0.914130i	$-0.367125\pi$
$827$	−12.2053	−	10.2415i	−0.424421	−	0.356132i	−0.829842	+	0.557998i	$0.811570\pi$
$828$	8.73424	+	14.4322i	0.303536	+	0.501554i
$829$	34.9707	+	20.1903i	1.21458	+	0.701239i	0.963754	−	0.266793i	$-0.0859639\pi$
$829$	34.9707	+	20.1903i	1.21458	+	0.701239i	0.250828	+	0.968032i	$0.419297\pi$
$830$	−3.53224	+	1.28563i	−0.122606	+	0.0446249i
$831$	21.4701	−	31.3457i	0.744790	−	1.08737i
$832$	−2.92974	−	0.516593i	−0.101571	−	0.0179096i
$833$	−1.69856	+	4.66675i	−0.0588515	+	0.161693i
$834$	3.97059	+	0.306150i	0.137490	+	0.0106011i
$835$			5.46991i			0.189294i
$836$	6.98819	−	7.49736i	0.241692	−	0.259301i
$837$	−39.2651	−	36.9074i	−1.35720	−	1.27571i
$838$	12.3611	+	14.7313i	0.427006	+	0.508886i
$839$	−34.2630	−	12.4707i	−1.18289	−	0.430537i	−0.325669	−	0.945484i	$-0.605589\pi$
$839$	−34.2630	−	12.4707i	−1.18289	−	0.430537i	−0.857222	+	0.514947i	$0.827812\pi$
$840$	−0.324639	−	0.453602i	−0.0112011	−	0.0156508i
$841$	−3.93940	−	22.3415i	−0.135842	−	0.770396i
$842$	11.8370	+	32.5219i	0.407930	+	1.12078i
$843$	−25.1717	+	7.02378i	−0.866959	+	0.241912i
$844$	12.0320	−	6.94667i	0.414158	−	0.239114i
$845$	−0.710347	+	0.846558i	−0.0244367	+	0.0291225i
$846$	4.52150	+	3.63772i	0.155452	+	0.125068i
$847$	3.30826	+	5.73007i	0.113673	+	0.196888i
$848$	−2.87460	+	4.97896i	−0.0987143	+	0.170978i
$849$	10.4738	+	4.75310i	0.359459	+	0.163126i
$850$	−4.35338	+	0.767619i	−0.149320	+	0.0263291i
$851$	−3.86590	+	21.9246i	−0.132521	+	0.751566i
$852$	7.09463	+	14.8136i	0.243058	+	0.507507i
$853$	−1.13152	+	0.949455i	−0.0387424	+	0.0325087i	−0.661953	−	0.749545i	$-0.730272\pi$
$853$	−1.13152	+	0.949455i	−0.0387424	+	0.0325087i	0.623211	+	0.782054i	$0.285828\pi$
$854$	1.06998			0.0366141
$855$	3.48069	+	0.109686i	0.119037	+	0.00375118i
$856$	16.1688			0.552637
$857$	33.3088	−	27.9494i	1.13781	−	0.954734i	0.138443	−	0.990370i	$-0.455790\pi$
$857$	33.3088	−	27.9494i	1.13781	−	0.954734i	0.999365	+	0.0356363i	$0.0113458\pi$
$858$	−5.23332	−	10.9272i	−0.178662	−	0.373048i
$859$	−3.97170	+	22.5246i	−0.135513	+	0.768530i	0.838989	+	0.544149i	$0.183147\pi$
$859$	−3.97170	+	22.5246i	−0.135513	+	0.768530i	−0.974501	+	0.224381i	$0.927964\pi$
$860$	1.25964	−	0.222108i	0.0429533	−	0.00757383i
$861$	21.1559	+	9.60076i	0.720991	+	0.327193i
$862$	16.0755	−	27.8435i	0.547532	−	0.948354i
$863$	−2.34962	−	4.06966i	−0.0799820	−	0.138533i	0.823260	−	0.567665i	$-0.192153\pi$
$863$	−2.34962	−	4.06966i	−0.0799820	−	0.138533i	−0.903242	+	0.429132i	$0.858820\pi$
$864$	−5.15989	+	0.612805i	−0.175543	+	0.0208481i
$865$	−1.42644	+	1.69996i	−0.0485003	+	0.0578004i
$866$	−19.9807	+	11.5359i	−0.678972	+	0.392005i
$867$	−27.0196	+	7.53942i	−0.917634	+	0.256052i
$868$	4.28943	+	11.7851i	0.145593	+	0.400013i
$869$	−2.79245	−	15.8368i	−0.0947275	−	0.537227i
$870$	0.674544	+	0.942507i	0.0228692	+	0.0319540i
$871$	14.3025	+	5.20569i	0.484623	+	0.176388i
$872$	−11.7406	−	13.9919i	−0.397586	−	0.473825i
$873$	−18.1261	+	0.373970i	−0.613475	+	0.0126570i
$874$	20.5594	+	13.3447i	0.695432	+	0.451393i
$875$		−	3.19764i		−	0.108100i
$876$	−0.589649	−	0.0454645i	−0.0199224	−	0.00153610i
$877$	5.78823	−	15.9030i	0.195455	−	0.537007i	−0.802788	−	0.596264i	$-0.796651\pi$
$877$	5.78823	−	15.9030i	0.195455	−	0.537007i	0.998243	+	0.0592572i	$0.0188732\pi$
$878$	11.6031	+	2.04594i	0.391586	+	0.0690471i
$879$	−27.8027	+	40.5911i	−0.937762	+	1.36910i
$880$	0.588409	−	0.214163i	0.0198353	−	0.00721945i
$881$	8.11257	+	4.68379i	0.273319	+	0.157801i	0.630395	−	0.776274i	$-0.282893\pi$
$881$	8.11257	+	4.68379i	0.273319	+	0.157801i	−0.357076	+	0.934075i	$0.616226\pi$
$882$	−14.2126	+	8.60134i	−0.478564	+	0.289622i
$883$	−9.97646	−	8.37124i	−0.335735	−	0.281715i	0.459297	−	0.888283i	$-0.348101\pi$
$883$	−9.97646	−	8.37124i	−0.335735	−	0.281715i	−0.795032	+	0.606568i	$0.792546\pi$
$884$	2.04382	+	1.71496i	0.0687409	+	0.0576805i
$885$	−5.70437	−	1.46559i	−0.191750	−	0.0492653i
$886$	−18.4426	−	10.6479i	−0.619593	−	0.357722i
$887$	19.4826	−	7.09109i	0.654162	−	0.238095i	0.00644793	−	0.999979i	$-0.497948\pi$
$887$	19.4826	−	7.09109i	0.654162	−	0.238095i	0.647714	+	0.761884i	$0.275725\pi$
$888$	−5.65757	−	3.87513i	−0.189856	−	0.130041i
$889$	−7.04801	−	1.24275i	−0.236383	−	0.0416806i
$890$	1.12029	−	3.07798i	0.0375523	−	0.103174i
$891$	−14.2596	−	15.6361i	−0.477716	−	0.523828i
$892$			12.4608i			0.417217i
$893$	8.21616	+	1.89487i	0.274943	+	0.0634094i
$894$	9.49216	−	9.69002i	0.317465	−	0.324083i
$895$	1.54499	+	1.84125i	0.0516433	+	0.0615461i
$896$	1.13638	+	0.413609i	0.0379639	+	0.0138177i
$897$	23.5619	−	16.8630i	0.786708	−	0.563040i
$898$	−2.07093	−	11.7448i	−0.0691078	−	0.391930i
$899$	−8.91269	−	24.4874i	−0.297255	−	0.816701i
$900$	−12.9559	−	7.12789i	−0.431864	−	0.237596i
$901$	4.46527	−	2.57803i	0.148760	−	0.0858865i
$902$	−16.7639	+	19.9784i	−0.558176	+	0.665208i
$903$	0.980136	+	10.0124i	0.0326169	+	0.333193i
$904$	−1.20010	−	2.07863i	−0.0399147	−	0.0691343i
$905$	−1.22421	+	2.12039i	−0.0406940	+	0.0704840i
$906$	−7.96957	+	17.5615i	−0.264771	+	0.583441i
$907$	−13.6673	+	2.40991i	−0.453815	+	0.0800198i	−0.395883	−	0.918301i	$-0.629562\pi$
$907$	−13.6673	+	2.40991i	−0.453815	+	0.0800198i	−0.0579313	+	0.998321i	$0.518450\pi$
$908$	0.284693	−	1.61457i	0.00944787	−	0.0535815i
$909$	−29.4373	−	10.0316i	−0.976373	−	0.332728i
$910$	−0.733927	+	0.615838i	−0.0243294	+	0.0204148i
$911$	16.4560			0.545212			0.272606	−	0.962126i	$-0.412115\pi$
$911$	16.4560			0.545212			0.272606	+	0.962126i	$0.412115\pi$
$912$	−6.36009	+	4.06808i	−0.210604	+	0.134708i
$913$	33.1889			1.09839
$914$	−14.6574	+	12.2990i	−0.484823	+	0.406815i
$915$	−0.368078	+	0.176282i	−0.0121683	+	0.00582771i
$916$	−2.11064	+	11.9700i	−0.0697374	+	0.395501i
$917$	−20.5805	+	3.62890i	−0.679629	+	0.119837i
$918$	4.28236	+	1.83782i	0.141339	+	0.0606570i
$919$	−26.4636	+	45.8364i	−0.872955	+	1.51200i	−0.0140292	+	0.999902i	$0.504466\pi$
$919$	−26.4636	+	45.8364i	−0.872955	+	1.51200i	−0.858926	+	0.512100i	$0.828868\pi$
$920$	0.748739	+	1.29685i	0.0246852	+	0.0427560i
$921$	−7.51462	+	0.735619i	−0.247615	+	0.0242395i
$922$	19.3700	−	23.0842i	0.637916	−	0.760239i
$923$	24.4315	−	14.1056i	0.804174	−	0.464290i
$924$	1.32369	+	4.74383i	0.0435464	+	0.156061i
$925$	−6.67453	−	18.3381i	−0.219457	−	0.602953i
$926$	−4.44179	−	25.1907i	−0.145966	−	0.827817i
$927$	6.79695	−	43.8143i	0.223241	−	1.43905i
$928$	−2.36121	−	0.859409i	−0.0775104	−	0.0282115i
$929$	35.2607	+	42.0221i	1.15687	+	1.37870i	0.912530	+	0.409010i	$0.134126\pi$
$929$	35.2607	+	42.0221i	1.15687	+	1.37870i	0.244337	+	0.969690i	$0.421430\pi$
$930$	−3.41720	−	3.34743i	−0.112055	−	0.109767i
$931$	−13.1417	+	20.2466i	−0.430702	+	0.663555i
$932$		−	2.40898i		−	0.0789089i
$933$	0.632049	−	8.19731i	0.0206923	−	0.268368i
$934$	9.73308	−	26.7414i	0.318476	−	0.875006i
$935$	−0.553038	−	0.0975154i	−0.0180863	−	0.00318910i
$936$	1.73075	+	8.75539i	0.0565712	+	0.286179i
$937$	−50.8597	+	18.5114i	−1.66151	+	0.604741i	−0.990599	−	0.136794i	$-0.956320\pi$
$937$	−50.8597	+	18.5114i	−1.66151	+	0.604741i	−0.670914	+	0.741536i	$0.734098\pi$
$938$	−5.35819	−	3.09355i	−0.174951	−	0.101008i
$939$	8.15959	−	31.7587i	0.266278	−	1.03641i
$940$	0.394622	+	0.331127i	0.0128712	+	0.0108002i
$941$	−3.61129	−	3.03024i	−0.117725	−	0.0987829i	0.582025	−	0.813171i	$-0.302261\pi$
$941$	−3.61129	−	3.03024i	−0.117725	−	0.0987829i	−0.699750	+	0.714388i	$0.746705\pi$
$942$	−9.14692	+	35.6016i	−0.298023	+	1.15996i
$943$	−54.0137	−	31.1848i	−1.75893	−	1.01552i
$944$	11.9986	−	4.36714i	0.390522	−	0.142138i
$945$	−0.916961	+	1.39982i	−0.0298287	+	0.0455361i
$946$	−11.1218	−	1.96107i	−0.361601	−	0.0637600i
$947$	3.75659	−	10.3211i	0.122073	−	0.335392i	−0.863572	−	0.504226i	$-0.831778\pi$
$947$	3.75659	−	10.3211i	0.122073	−	0.335392i	0.985645	+	0.168834i	$0.0540002\pi$
$948$	−0.910662	+	11.8108i	−0.0295769	+	0.383596i
$949$			1.01578i			0.0329735i
$950$	−21.4562	−	1.11955i	−0.696130	−	0.0363229i
$951$	38.7758	+	37.9840i	1.25739	+	1.23172i
$952$	−0.697133	−	0.830810i	−0.0225942	−	0.0269267i
$953$	−3.15832	−	1.14953i	−0.102308	−	0.0372371i	0.290359	−	0.956918i	$-0.406225\pi$
$953$	−3.15832	−	1.14953i	−0.102308	−	0.0372371i	−0.392667	+	0.919681i	$0.628448\pi$
$954$	17.0438	+	2.64402i	0.551812	+	0.0856031i
$955$	0.339083	+	1.92303i	0.0109725	+	0.0622279i
$956$	6.54821	+	17.9910i	0.211784	+	0.581872i
$957$	−2.75041	−	9.85686i	−0.0889081	−	0.318627i
$958$	−10.7014	+	6.17844i	−0.345745	+	0.199616i
$959$	14.2196	−	16.9463i	0.459176	−	0.547225i
$960$	−0.459063	+	0.0449384i	−0.0148162	+	0.00145038i
$961$	38.2760	+	66.2960i	1.23471	+	2.13858i
$962$	−5.88913	+	10.2003i	−0.189873	+	0.328870i
$963$	−17.5268	−	45.2291i	−0.564794	−	1.45749i
$964$	4.13200	−	0.728583i	0.133083	−	0.0234661i
$965$	−0.0828985	+	0.470141i	−0.00266860	+	0.0151344i
$966$	−10.6227	+	5.08749i	−0.341780	+	0.163687i
$967$	−14.0085	+	11.7545i	−0.450482	+	0.377999i	−0.839615	−	0.543183i	$-0.817219\pi$
$967$	−14.0085	+	11.7545i	−0.450482	+	0.377999i	0.389133	+	0.921182i	$0.372775\pi$
$968$	5.47131			0.175854
$969$	6.76392	−	0.307630i	0.217288	−	0.00988251i
$970$	−1.60938			−0.0516739
$971$	24.2199	−	20.3229i	0.777254	−	0.652193i	−0.165302	−	0.986243i	$-0.552860\pi$
$971$	24.2199	−	20.3229i	0.777254	−	0.652193i	0.942555	+	0.334050i	$0.108415\pi$
$972$	7.30749	+	13.7696i	0.234388	+	0.441659i
$973$	−0.482826	+	2.73824i	−0.0154787	+	0.0877839i
$974$	27.6832	−	4.88130i	0.887028	−	0.156407i
$975$	−10.4958	+	23.1282i	−0.336134	+	0.740694i
$976$	0.442393	−	0.766248i	0.0141607	−	0.0245270i
$977$	24.2192	+	41.9488i	0.774839	+	1.34206i	0.934885	+	0.354952i	$0.115503\pi$
$977$	24.2192	+	41.9488i	0.774839	+	1.34206i	−0.160045	+	0.987110i	$0.551164\pi$
$978$	−0.587445	−	6.00096i	−0.0187844	−	0.191890i
$979$	−18.5898	+	22.1545i	−0.594134	+	0.708061i
$980$	−1.27712	+	0.737346i	−0.0407961	+	0.0235536i
$981$	−26.4130	+	48.0092i	−0.843301	+	1.53281i
$982$	−1.17147	−	3.21859i	−0.0373832	−	0.102709i
$983$	−4.70703	−	26.6949i	−0.150131	−	0.851435i	−0.963103	−	0.269133i	$-0.913263\pi$
$983$	−4.70703	−	26.6949i	−0.150131	−	0.851435i	0.812972	−	0.582303i	$-0.197848\pi$
$984$	15.6225	−	11.1809i	0.498026	−	0.356433i
$985$	1.98016	+	0.720719i	0.0630931	+	0.0229640i
$986$	1.44852	+	1.72628i	0.0461303	+	0.0549760i
$987$	−2.83533	+	2.89443i	−0.0902495	+	0.0921307i
$988$	7.80638	+	10.3545i	0.248354	+	0.329420i
$989$		−	27.0079i		−	0.858800i
$990$	−1.23691	−	1.41381i	−0.0393117	−	0.0449339i
$991$	16.6261	−	45.6797i	0.528144	−	1.45106i	−0.333109	−	0.942888i	$-0.608098\pi$
$991$	16.6261	−	45.6797i	0.528144	−	1.45106i	0.861253	−	0.508176i	$-0.169680\pi$
$992$	10.2132	+	1.80086i	0.324269	+	0.0571773i
$993$	5.29022	+	3.62351i	0.167880	+	0.114989i
$994$	−10.7762	+	3.92222i	−0.341801	+	0.124405i
$995$	2.41248	+	1.39285i	0.0764808	+	0.0441562i
$996$	−23.6789	−	6.08369i	−0.750295	−	0.192769i
$997$	−7.46423	−	6.26323i	−0.236394	−	0.198358i	0.516893	−	0.856050i	$-0.327089\pi$
$997$	−7.46423	−	6.26323i	−0.236394	−	0.198358i	−0.753287	+	0.657692i	$0.771533\pi$
$998$	29.3171	+	24.6000i	0.928018	+	0.778699i
$999$	−4.70719	+	20.0266i	−0.148929	+	0.633614i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	114.2.l.b.89.1	yes	18
3.2	odd	2		114.2.l.a.89.3	yes	18
4.3	odd	2		912.2.cc.c.545.3		18
12.11	even	2		912.2.cc.d.545.1		18
19.3	odd	18		114.2.l.a.41.3	✓	18
57.41	even	18	inner	114.2.l.b.41.1	yes	18
76.3	even	18		912.2.cc.d.497.1		18
228.155	odd	18		912.2.cc.c.497.3		18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
114.2.l.a.41.3	✓	18	19.3	odd	18
114.2.l.a.89.3	yes	18	3.2	odd	2
114.2.l.b.41.1	yes	18	57.41	even	18	inner
114.2.l.b.89.1	yes	18	1.1	even	1	trivial
912.2.cc.c.497.3		18	228.155	odd	18
912.2.cc.c.545.3		18	4.3	odd	2
912.2.cc.d.497.1		18	76.3	even	18
912.2.cc.d.545.1		18	12.11	even	2

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:	\( N \)	\(=\)	\( 114 = 2 \cdot 3 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	114.l (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(0.766044 - 0.642788i) q^{2} +(-0.748148 - 1.56214i) q^{3} +(0.173648 - 0.984808i) q^{4} +(-0.262261 + 0.0462437i) q^{5} +(-1.57724 - 0.715766i) q^{6} +(0.604656 - 1.04730i) q^{7} +(-0.500000 - 0.866025i) q^{8} +(-1.88055 + 2.33742i) q^{9} +O(q^{10})\)	\(q+(0.766044 - 0.642788i) q^{2} +(-0.748148 - 1.56214i) q^{3} +(0.173648 - 0.984808i) q^{4} +(-0.262261 + 0.0462437i) q^{5} +(-1.57724 - 0.715766i) q^{6} +(0.604656 - 1.04730i) q^{7} +(-0.500000 - 0.866025i) q^{8} +(-1.88055 + 2.33742i) q^{9} +(-0.171179 + 0.204003i) q^{10} +(2.03630 - 1.17566i) q^{11} +(-1.66832 + 0.465520i) q^{12} +(1.01749 + 2.79553i) q^{13} +(-0.209995 - 1.19094i) q^{14} +(0.268449 + 0.375091i) q^{15} +(-0.939693 - 0.342020i) q^{16} +(0.576470 + 0.687011i) q^{17} +(0.0618817 + 2.99936i) q^{18} +(1.97979 + 3.88335i) q^{19} +0.266307i q^{20} +(-2.08839 - 0.161024i) q^{21} +(0.804198 - 2.20952i) q^{22} +(5.53770 + 0.976446i) q^{23} +(-0.978777 + 1.42898i) q^{24} +(-4.63182 + 1.68584i) q^{25} +(2.57637 + 1.48747i) q^{26} +(5.05830 + 1.18894i) q^{27} +(-0.926387 - 0.777331i) q^{28} +(1.92487 + 1.61516i) q^{29} +(0.446748 + 0.114780i) q^{30} +(-8.98131 - 5.18536i) q^{31} +(-0.939693 + 0.342020i) q^{32} +(-3.36000 - 2.30141i) q^{33} +(0.883204 + 0.155733i) q^{34} +(-0.110147 + 0.302626i) q^{35} +(1.97536 + 2.25787i) q^{36} +3.95916i q^{37} +(4.01278 + 1.70224i) q^{38} +(3.60577 - 3.68093i) q^{39} +(0.171179 + 0.204003i) q^{40} +(-10.4227 - 3.79356i) q^{41} +(-1.70331 + 1.21904i) q^{42} +(-0.834031 - 4.73003i) q^{43} +(-0.804198 - 2.20952i) q^{44} +(0.385104 - 0.699978i) q^{45} +(4.86977 - 2.81156i) q^{46} +(1.24341 - 1.48183i) q^{47} +(0.168747 + 1.72381i) q^{48} +(2.76878 + 4.79567i) q^{49} +(-2.46454 + 4.26871i) q^{50} +(0.641920 - 1.41451i) q^{51} +(2.92974 - 0.516593i) q^{52} +(0.998339 - 5.66186i) q^{53} +(4.63912 - 2.34063i) q^{54} +(-0.479676 + 0.402496i) q^{55} -1.20931 q^{56} +(4.58516 - 5.99803i) q^{57} +2.51274 q^{58} +(-9.78136 + 8.20754i) q^{59} +(0.416008 - 0.199237i) q^{60} +(-0.153642 + 0.871345i) q^{61} +(-10.2132 + 1.80086i) q^{62} +(1.31088 + 3.38283i) q^{63} +(-0.500000 + 0.866025i) q^{64} +(-0.396123 - 0.686106i) q^{65} +(-4.05323 + 0.396777i) q^{66} +(3.28864 - 3.91925i) q^{67} +(0.776676 - 0.448414i) q^{68} +(-2.61768 - 9.38117i) q^{69} +(0.110147 + 0.302626i) q^{70} +(-1.64669 - 9.33885i) q^{71} +(2.96454 + 0.459892i) q^{72} +(0.320853 + 0.116781i) q^{73} +(2.54490 + 3.03289i) q^{74} +(6.09881 + 5.97428i) q^{75} +(4.16814 - 1.27537i) q^{76} -2.84348i q^{77} +(0.396123 - 5.13750i) q^{78} +(2.33914 - 6.42674i) q^{79} +(0.262261 + 0.0462437i) q^{80} +(-1.92708 - 8.79127i) q^{81} +(-10.4227 + 3.79356i) q^{82} +(12.2240 + 7.05752i) q^{83} +(-0.521223 + 2.02870i) q^{84} +(-0.182956 - 0.153518i) q^{85} +(-3.67931 - 3.08731i) q^{86} +(1.08301 - 4.21529i) q^{87} +(-2.03630 - 1.17566i) q^{88} +(-11.5580 + 4.20677i) q^{89} +(-0.154931 - 0.783754i) q^{90} +(3.54297 + 0.624722i) q^{91} +(1.92322 - 5.28401i) q^{92} +(-1.38090 + 17.9095i) q^{93} -1.93440i q^{94} +(-0.698802 - 0.926900i) q^{95} +(1.23731 + 1.21205i) q^{96} +(3.88456 + 4.62944i) q^{97} +(5.20361 + 1.89396i) q^{98} +(-1.08135 + 6.97057i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q + 3 q^{3} - 9 q^{8} - 3 q^{9}+O(q^{10}) \) 18 * q + 3 * q^3 - 9 * q^8 - 3 * q^9	\( 18 q + 3 q^{3} - 9 q^{8} - 3 q^{9} - 12 q^{13} - 12 q^{14} + 18 q^{15} + 6 q^{17} - 6 q^{19} - 24 q^{22} + 3 q^{24} - 18 q^{25} + 18 q^{26} - 6 q^{27} + 6 q^{28} - 6 q^{29} - 24 q^{33} - 6 q^{34} - 24 q^{35} + 3 q^{38} + 6 q^{39} + 3 q^{41} - 6 q^{43} + 24 q^{44} - 54 q^{45} + 18 q^{46} + 30 q^{47} + 21 q^{49} + 3 q^{50} + 42 q^{51} - 6 q^{52} - 60 q^{53} + 54 q^{54} + 30 q^{55} + 12 q^{57} + 12 q^{58} + 3 q^{59} + 24 q^{60} + 54 q^{61} + 6 q^{62} - 18 q^{63} - 9 q^{64} + 24 q^{65} - 27 q^{66} - 15 q^{67} - 27 q^{68} + 30 q^{69} + 24 q^{70} + 36 q^{71} + 6 q^{72} - 42 q^{73} + 6 q^{74} - 24 q^{78} - 6 q^{79} - 3 q^{81} + 3 q^{82} + 36 q^{83} - 30 q^{84} - 6 q^{86} - 60 q^{89} - 18 q^{91} - 66 q^{93} + 6 q^{95} + 9 q^{97} + 12 q^{98} - 102 q^{99}+O(q^{100}) \) 18 * q + 3 * q^3 - 9 * q^8 - 3 * q^9 - 12 * q^13 - 12 * q^14 + 18 * q^15 + 6 * q^17 - 6 * q^19 - 24 * q^22 + 3 * q^24 - 18 * q^25 + 18 * q^26 - 6 * q^27 + 6 * q^28 - 6 * q^29 - 24 * q^33 - 6 * q^34 - 24 * q^35 + 3 * q^38 + 6 * q^39 + 3 * q^41 - 6 * q^43 + 24 * q^44 - 54 * q^45 + 18 * q^46 + 30 * q^47 + 21 * q^49 + 3 * q^50 + 42 * q^51 - 6 * q^52 - 60 * q^53 + 54 * q^54 + 30 * q^55 + 12 * q^57 + 12 * q^58 + 3 * q^59 + 24 * q^60 + 54 * q^61 + 6 * q^62 - 18 * q^63 - 9 * q^64 + 24 * q^65 - 27 * q^66 - 15 * q^67 - 27 * q^68 + 30 * q^69 + 24 * q^70 + 36 * q^71 + 6 * q^72 - 42 * q^73 + 6 * q^74 - 24 * q^78 - 6 * q^79 - 3 * q^81 + 3 * q^82 + 36 * q^83 - 30 * q^84 - 6 * q^86 - 60 * q^89 - 18 * q^91 - 66 * q^93 + 6 * q^95 + 9 * q^97 + 12 * q^98 - 102 * q^99

Introduction

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