LMFDB - Embedded newform 114.2.l.a.41.3

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			41.3
Root			$1.40849 - 1.00804i$ of defining polynomial
Character	$\chi$	$=$	114.41
Dual form			114.2.l.a.89.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.766044 - 0.642788i) q^{2} +(1.57724 + 0.715766i) q^{3} +(0.173648 + 0.984808i) q^{4} +(0.262261 + 0.0462437i) q^{5} +(-0.748148 - 1.56214i) q^{6} +(0.604656 + 1.04730i) q^{7} +(0.500000 - 0.866025i) q^{8} +(1.97536 + 2.25787i) q^{9} +O(q^{10})$	\(q+(-0.766044 - 0.642788i) q^{2} +(1.57724 + 0.715766i) q^{3} +(0.173648 + 0.984808i) q^{4} +(0.262261 + 0.0462437i) q^{5} +(-0.748148 - 1.56214i) q^{6} +(0.604656 + 1.04730i) q^{7} +(0.500000 - 0.866025i) q^{8} +(1.97536 + 2.25787i) q^{9} +(-0.171179 - 0.204003i) q^{10} +(-2.03630 - 1.17566i) q^{11} +(-0.431008 + 1.67757i) q^{12} +(1.01749 - 2.79553i) q^{13} +(0.209995 - 1.19094i) q^{14} +(0.380548 + 0.260655i) 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} +(0.204068 + 2.08463i) q^{21} +(0.804198 + 2.20952i) q^{22} +(-5.53770 + 0.976446i) q^{23} +(1.40849 - 1.00804i) q^{24} +(-4.63182 - 1.68584i) q^{25} +(-2.57637 + 1.48747i) q^{26} +(1.49950 + 4.97509i) q^{27} +(-0.926387 + 0.777331i) q^{28} +(-1.92487 + 1.61516i) q^{29} +(-0.123971 - 0.444285i) q^{30} +(-8.98131 + 5.18536i) q^{31} +(0.939693 + 0.342020i) q^{32} +(-2.37023 - 3.31181i) q^{33} +(0.883204 - 0.155733i) q^{34} +(0.110147 + 0.302626i) q^{35} +(-1.88055 + 2.33742i) 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} +(1.18365 - 1.72809i) q^{42} +(-0.834031 + 4.73003i) q^{43} +(0.804198 - 2.20952i) q^{44} +(0.413647 + 0.683499i) q^{45} +(4.86977 + 2.81156i) q^{46} +(-1.24341 - 1.48183i) q^{47} +(-1.72693 - 0.133153i) q^{48} +(2.76878 - 4.79567i) q^{49} +(2.46454 + 4.26871i) q^{50} +(-1.40097 + 0.670961i) q^{51} +(2.92974 + 0.516593i) q^{52} +(-0.998339 - 5.66186i) q^{53} +(2.04924 - 4.77500i) q^{54} +(-0.479676 - 0.402496i) q^{55} +1.20931 q^{56} +(5.90217 - 4.70791i) q^{57} +2.51274 q^{58} +(9.78136 + 8.20754i) q^{59} +(-0.190614 + 0.420029i) q^{60} +(-0.153642 - 0.871345i) q^{61} +(10.2132 + 1.80086i) q^{62} +(-1.17024 + 3.43401i) q^{63} +(-0.500000 - 0.866025i) q^{64} +(0.396123 - 0.686106i) q^{65} +(-0.313086 + 4.06055i) q^{66} +(3.28864 + 3.91925i) q^{67} +(-0.776676 - 0.448414i) q^{68} +(-9.43317 - 2.42361i) q^{69} +(0.110147 - 0.302626i) q^{70} +(1.64669 - 9.33885i) q^{71} +(2.94305 - 0.581775i) 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} +(-5.12823 + 0.502012i) q^{78} +(2.33914 + 6.42674i) q^{79} +(-0.262261 + 0.0462437i) q^{80} +(-1.19593 + 8.92019i) q^{81} +(-10.4227 - 3.79356i) q^{82} +(-12.2240 + 7.05752i) q^{83} +(-2.01752 + 0.562959i) q^{84} +(-0.182956 + 0.153518i) q^{85} +(3.67931 - 3.08731i) q^{86} +(-4.19206 + 1.16973i) q^{87} +(-2.03630 + 1.17566i) q^{88} +(11.5580 + 4.20677i) q^{89} +(0.122472 - 0.789478i) q^{90} +(3.54297 - 0.624722i) q^{91} +(-1.92322 - 5.28401i) q^{92} +(-17.8772 + 1.75003i) 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} +(-1.36794 - 6.92004i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 18 q + 3 q^{6} + 9 q^{8}+O(q^{10}) $ 18 * q + 3 * q^6 + 9 * q^8	$ 18 q + 3 q^{6} + 9 q^{8} - 12 q^{13} + 12 q^{14} - 24 q^{15} - 6 q^{17} - 6 q^{19} - 24 q^{22} - 18 q^{25} - 18 q^{26} - 3 q^{27} + 6 q^{28} + 6 q^{29} - 27 q^{33} - 6 q^{34} + 24 q^{35} - 3 q^{36} - 3 q^{38} + 6 q^{39} - 3 q^{41} - 6 q^{43} - 24 q^{44} + 54 q^{45} + 18 q^{46} - 30 q^{47} + 6 q^{48} + 21 q^{49} - 3 q^{50} - 33 q^{51} - 6 q^{52} + 60 q^{53} + 30 q^{55} + 12 q^{57} + 12 q^{58} - 3 q^{59} + 18 q^{60} + 54 q^{61} - 6 q^{62} + 84 q^{63} - 9 q^{64} - 24 q^{65} + 30 q^{66} - 15 q^{67} + 27 q^{68} + 24 q^{69} + 24 q^{70} - 36 q^{71} - 42 q^{73} - 6 q^{74} - 18 q^{78} - 6 q^{79} + 3 q^{82} - 36 q^{83} - 24 q^{84} + 6 q^{86} - 54 q^{87} + 60 q^{89} - 12 q^{90} - 18 q^{91} - 84 q^{93} - 6 q^{95} + 9 q^{97} - 12 q^{98} - 30 q^{99}+O(q^{100}) $ 18 * q + 3 * q^6 + 9 * q^8 - 12 * q^13 + 12 * q^14 - 24 * q^15 - 6 * q^17 - 6 * q^19 - 24 * q^22 - 18 * q^25 - 18 * q^26 - 3 * q^27 + 6 * q^28 + 6 * q^29 - 27 * q^33 - 6 * q^34 + 24 * q^35 - 3 * q^36 - 3 * q^38 + 6 * q^39 - 3 * q^41 - 6 * q^43 - 24 * q^44 + 54 * q^45 + 18 * q^46 - 30 * q^47 + 6 * q^48 + 21 * q^49 - 3 * q^50 - 33 * q^51 - 6 * q^52 + 60 * q^53 + 30 * q^55 + 12 * q^57 + 12 * q^58 - 3 * q^59 + 18 * q^60 + 54 * q^61 - 6 * q^62 + 84 * q^63 - 9 * q^64 - 24 * q^65 + 30 * q^66 - 15 * q^67 + 27 * q^68 + 24 * q^69 + 24 * q^70 - 36 * q^71 - 42 * q^73 - 6 * q^74 - 18 * q^78 - 6 * q^79 + 3 * q^82 - 36 * q^83 - 24 * q^84 + 6 * q^86 - 54 * q^87 + 60 * q^89 - 12 * q^90 - 18 * q^91 - 84 * q^93 - 6 * q^95 + 9 * q^97 - 12 * q^98 - 30 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$77$	$97$
$\chi(n)$	$-1$	$e\left(\frac{13}{18}\right)$

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
$3$	1.57724	+	0.715766i	0.910619	+	0.413248i
$3$	1.57724	+	0.715766i	0.910619	+	0.413248i
$4$	0.173648	+	0.984808i	0.0868241	+	0.492404i
$5$	0.262261	+	0.0462437i	0.117287	+	0.0206808i	0.231983	−	0.972720i	$-0.425478\pi$
$5$	0.262261	+	0.0462437i	0.117287	+	0.0206808i	−0.114697	+	0.993401i	$0.536590\pi$
$6$	−0.748148	−	1.56214i	−0.305430	−	0.637740i
$7$	0.604656	+	1.04730i	0.228539	+	0.395840i	0.957375	−	0.288847i	$-0.0932720\pi$
$7$	0.604656	+	1.04730i	0.228539	+	0.395840i	−0.728837	+	0.684688i	$0.759939\pi$
$8$	0.500000	−	0.866025i	0.176777	−	0.306186i
$9$	1.97536	+	2.25787i	0.658452	+	0.752623i
$10$	−0.171179	−	0.204003i	−0.0541315	−	0.0645114i
$11$	−2.03630	−	1.17566i	−0.613968	−	0.354474i	0.160549	−	0.987028i	$-0.448674\pi$
$11$	−2.03630	−	1.17566i	−0.613968	−	0.354474i	−0.774517	+	0.632553i	$0.782007\pi$
$12$	−0.431008	+	1.67757i	−0.124421	+	0.484272i
$13$	1.01749	−	2.79553i	0.282201	−	0.775340i	−0.714899	−	0.699228i	$-0.753527\pi$
$13$	1.01749	−	2.79553i	0.282201	−	0.775340i	0.997099	−	0.0761119i	$-0.0242506\pi$
$14$	0.209995	−	1.19094i	0.0561235	−	0.318292i
$15$	0.380548	+	0.260655i	0.0982572	+	0.0673008i
$16$	−0.939693	+	0.342020i	−0.234923	+	0.0855050i
$17$	−0.576470	+	0.687011i	−0.139815	+	0.166625i	−0.831408	−	0.555663i	$-0.812465\pi$
$17$	−0.576470	+	0.687011i	−0.139815	+	0.166625i	0.691593	+	0.722287i	$0.256909\pi$
$18$	−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
$21$	0.204068	+	2.08463i	0.0445312	+	0.454903i
$22$	0.804198	+	2.20952i	0.171456	+	0.471070i
$23$	−5.53770	+	0.976446i	−1.15469	+	0.203603i	−0.718022	−	0.696020i	$-0.754952\pi$
$23$	−5.53770	+	0.976446i	−1.15469	+	0.203603i	−0.436668	+	0.899623i	$0.643841\pi$
$24$	1.40849	−	1.00804i	0.287507	−	0.205766i
$25$	−4.63182	−	1.68584i	−0.926364	−	0.337169i
$26$	−2.57637	+	1.48747i	−0.505268	+	0.291717i
$27$	1.49950	+	4.97509i	0.288579	+	0.957456i
$28$	−0.926387	+	0.777331i	−0.175071	+	0.146902i
$29$	−1.92487	+	1.61516i	−0.357440	+	0.299928i	−0.803769	−	0.594941i	$-0.797175\pi$
$29$	−1.92487	+	1.61516i	−0.357440	+	0.299928i	0.446329	+	0.894869i	$0.352731\pi$
$30$	−0.123971	−	0.444285i	−0.0226339	−	0.0811150i
$31$	−8.98131	+	5.18536i	−1.61309	+	0.931319i	−0.624443	+	0.781070i	$0.714674\pi$
$31$	−8.98131	+	5.18536i	−1.61309	+	0.931319i	−0.988648	+	0.150249i	$0.951993\pi$
$32$	0.939693	+	0.342020i	0.166116	+	0.0604612i
$33$	−2.37023	−	3.31181i	−0.412605	−	0.576512i
$34$	0.883204	−	0.155733i	0.151468	−	0.0267079i
$35$	0.110147	+	0.302626i	0.0186182	+	0.0511532i
$36$	−1.88055	+	2.33742i	−0.313425	+	0.389570i
$37$		−	3.95916i		−	0.650882i	−0.945562	−	0.325441i	$-0.894487\pi$
$37$		−	3.95916i		−	0.650882i	0.945562	−	0.325441i	$-0.105513\pi$
$38$	−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	$-0.277723\pi$
$41$	10.4227	−	3.79356i	1.62776	−	0.592455i	0.984838	+	0.173479i	$0.0555007\pi$
$42$	1.18365	−	1.72809i	0.182641	−	0.266650i
$43$	−0.834031	+	4.73003i	−0.127189	+	0.721322i	0.852795	+	0.522245i	$0.174905\pi$
$43$	−0.834031	+	4.73003i	−0.127189	+	0.721322i	−0.979984	+	0.199077i	$0.936206\pi$
$44$	0.804198	−	2.20952i	0.121237	−	0.333097i
$45$	0.413647	+	0.683499i	0.0616629	+	0.101890i
$46$	4.86977	+	2.81156i	0.718008	+	0.414542i
$47$	−1.24341	−	1.48183i	−0.181369	−	0.216147i	0.667698	−	0.744432i	$-0.267280\pi$
$47$	−1.24341	−	1.48183i	−0.181369	−	0.216147i	−0.849067	+	0.528285i	$0.822835\pi$
$48$	−1.72693	−	0.133153i	−0.249260	−	0.0192190i
$49$	2.76878	−	4.79567i	0.395540	−	0.685096i
$50$	2.46454	+	4.26871i	0.348539	+	0.603687i
$51$	−1.40097	+	0.670961i	−0.196175	+	0.0939533i
$52$	2.92974	+	0.516593i	0.406282	+	0.0716385i
$53$	−0.998339	−	5.66186i	−0.137132	−	0.777717i	−0.973351	−	0.229320i	$-0.926350\pi$
$53$	−0.998339	−	5.66186i	−0.137132	−	0.777717i	0.836219	−	0.548396i	$-0.184761\pi$
$54$	2.04924	−	4.77500i	0.278866	−	0.649795i
$55$	−0.479676	−	0.402496i	−0.0646794	−	0.0542725i
$56$	1.20931			0.161601
$57$	5.90217	−	4.70791i	0.781762	−	0.623578i
$58$	2.51274			0.329939
$59$	9.78136	+	8.20754i	1.27342	+	1.06853i	0.994115	+	0.108329i	$0.0345501\pi$
$59$	9.78136	+	8.20754i	1.27342	+	1.06853i	0.279310	+	0.960201i	$0.409894\pi$
$60$	−0.190614	+	0.420029i	−0.0246081	+	0.0542255i
$61$	−0.153642	−	0.871345i	−0.0196718	−	0.111564i	0.973391	−	0.229152i	$-0.0735951\pi$
$61$	−0.153642	−	0.871345i	−0.0196718	−	0.111564i	−0.993063	+	0.117587i	$0.962484\pi$
$62$	10.2132	+	1.80086i	1.29707	+	0.228709i
$63$	−1.17024	+	3.43401i	−0.147437	+	0.432645i
$64$	−0.500000	−	0.866025i	−0.0625000	−	0.108253i
$65$	0.396123	−	0.686106i	0.0491331	−	0.0851010i
$66$	−0.313086	+	4.06055i	−0.0385382	+	0.499819i
$67$	3.28864	+	3.91925i	0.401771	+	0.478812i	0.928559	−	0.371184i	$-0.121048\pi$
$67$	3.28864	+	3.91925i	0.401771	+	0.478812i	−0.526788	+	0.849997i	$0.676604\pi$
$68$	−0.776676	−	0.448414i	−0.0941859	−	0.0543782i
$69$	−9.43317	−	2.42361i	−1.13562	−	0.291769i
$70$	0.110147	−	0.302626i	0.0131651	−	0.0361708i
$71$	1.64669	−	9.33885i	0.195426	−	1.10832i	−0.716384	−	0.697706i	$-0.754204\pi$
$71$	1.64669	−	9.33885i	0.195426	−	1.10832i	0.911810	−	0.410612i	$-0.134685\pi$
$72$	2.94305	−	0.581775i	0.346842	−	0.0685629i
$73$	0.320853	−	0.116781i	0.0375530	−	0.0136682i	−0.323175	−	0.946339i	$-0.604750\pi$
$73$	0.320853	−	0.116781i	0.0375530	−	0.0136682i	0.360728	+	0.932671i	$0.382528\pi$
$74$	−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
$78$	−5.12823	+	0.502012i	−0.580658	+	0.0568416i
$79$	2.33914	+	6.42674i	0.263174	+	0.723064i	0.998949	+	0.0458383i	$0.0145959\pi$
$79$	2.33914	+	6.42674i	0.263174	+	0.723064i	−0.735775	+	0.677226i	$0.763182\pi$
$80$	−0.262261	+	0.0462437i	−0.0293217	+	0.00517020i
$81$	−1.19593	+	8.92019i	−0.132881	+	0.991132i
$82$	−10.4227	−	3.79356i	−1.15100	−	0.418929i
$83$	−12.2240	+	7.05752i	−1.34176	+	0.774663i	−0.987065	−	0.160320i	$-0.948747\pi$
$83$	−12.2240	+	7.05752i	−1.34176	+	0.774663i	−0.354691	+	0.934984i	$0.615414\pi$
$84$	−2.01752	+	0.562959i	−0.220129	+	0.0614238i
$85$	−0.182956	+	0.153518i	−0.0198443	+	0.0166514i
$86$	3.67931	−	3.08731i	0.396750	−	0.332913i
$87$	−4.19206	+	1.16973i	−0.449436	+	0.125408i
$88$	−2.03630	+	1.17566i	−0.217070	+	0.125326i
$89$	11.5580	+	4.20677i	1.22515	+	0.445917i	0.871933	−	0.489626i	$-0.162867\pi$
$89$	11.5580	+	4.20677i	1.22515	+	0.445917i	0.353213	+	0.935543i	$0.385089\pi$
$90$	0.122472	−	0.789478i	0.0129097	−	0.0832182i
$91$	3.54297	−	0.624722i	0.371405	−	0.0654887i
$92$	−1.92322	−	5.28401i	−0.200510	−	0.550896i
$93$	−17.8772	+	1.75003i	−1.85378	+	0.181469i
$94$			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	−0.531892	−	0.846812i	$-0.678519\pi$
$97$	3.88456	−	4.62944i	0.394418	−	0.470049i	0.926309	+	0.376764i	$0.122963\pi$
$98$	−5.20361	+	1.89396i	−0.525644	+	0.191319i
$99$	−1.36794	−	6.92004i	−0.137483	−	0.695490i
$100$	0.855926	−	4.85420i	0.0855926	−	0.485420i
$101$	−3.54557	+	9.74137i	−0.352797	+	0.969302i	0.628670	+	0.777672i	$0.283600\pi$
$101$	−3.54557	+	9.74137i	−0.352797	+	0.969302i	−0.981467	+	0.191630i	$0.938623\pi$
$102$	1.50449	+	0.386540i	0.148967	+	0.0382732i
$103$	−12.7994	−	7.38973i	−1.26116	−	0.728131i	−0.287861	−	0.957672i	$-0.592944\pi$
$103$	−12.7994	−	7.38973i	−1.26116	−	0.728131i	−0.973299	+	0.229541i	$0.926278\pi$
$104$	−1.91225	−	2.27894i	−0.187512	−	0.223468i
$105$	−0.0428818	+	0.556153i	−0.00418484	+	0.0542750i
$106$	−2.87460	+	4.97896i	−0.279206	+	0.483599i
$107$	8.08439	+	14.0026i	0.781547	+	1.35368i	0.931040	+	0.364917i	$0.118903\pi$
$107$	8.08439	+	14.0026i	0.781547	+	1.35368i	−0.149493	+	0.988763i	$0.547764\pi$
$108$	−4.63912	+	2.34063i	−0.446399	+	0.225228i
$109$	17.9876	+	3.17170i	1.72290	+	0.303794i	0.945599	−	0.325334i	$-0.105477\pi$
$109$	17.9876	+	3.17170i	1.72290	+	0.303794i	0.777302	+	0.629128i	$0.216588\pi$
$110$	0.108734	+	0.616659i	0.0103673	+	0.0587961i
$111$	2.83383	−	6.24453i	0.268975	−	0.592705i
$112$	−0.926387	−	0.777331i	−0.0875353	−	0.0734509i
$113$	−2.40020			−0.225792			−0.112896	−	0.993607i	$-0.536013\pi$
$113$	−2.40020			−0.225792			−0.112896	+	0.993607i	$0.536013\pi$
$114$	−7.54751	−	0.187376i	−0.706889	−	0.0175493i
$115$	−1.49748			−0.139640
$116$	−1.92487	−	1.61516i	−0.178720	−	0.149964i
$117$	8.32184	−	3.22481i	0.769354	−	0.298134i
$118$	−2.21725	−	12.5747i	−0.204115	−	1.15759i
$119$	−1.06807	−	0.188329i	−0.0979098	−	0.0172641i
$120$	0.416008	−	0.199237i	0.0379762	−	0.0181878i
$121$	−2.73565	−	4.73829i	−0.248696	−	0.430754i
$122$	−0.442393	+	0.766248i	−0.0400524	+	0.0693728i
$123$	19.1544	+	1.47689i	1.72710	+	0.133167i
$124$	−6.66618	−	7.94444i	−0.598640	−	0.713432i
$125$	−2.28993	−	1.32209i	−0.204818	−	0.118251i
$126$	3.10380	−	1.87839i	0.276508	−	0.167340i
$127$	−2.02408	+	5.56112i	−0.179608	+	0.493470i	−0.996526	−	0.0832849i	$-0.973459\pi$
$127$	−2.02408	+	5.56112i	−0.179608	+	0.493470i	0.816918	+	0.576754i	$0.195681\pi$
$128$	−0.173648	+	0.984808i	−0.0153485	+	0.0870455i
$129$	−4.70106	+	6.86340i	−0.413905	+	0.604289i
$130$	−0.744469	+	0.270964i	−0.0652942	+	0.0237652i
$131$	11.1080	−	13.2379i	0.970506	−	1.15660i	−0.0171319	−	0.999853i	$-0.505454\pi$
$131$	11.1080	−	13.2379i	0.970506	−	1.15660i	0.987638	−	0.156751i	$-0.0501020\pi$
$132$	2.84991	−	2.90931i	0.248053	−	0.253223i
$133$	5.26411	−	0.274672i	0.456456	−	0.0238171i
$134$		−	5.11622i		−	0.441974i
$135$	0.163194	+	1.37411i	0.0140455	+	0.118265i
$136$	0.306733	+	0.842743i	0.0263022	+	0.0722646i
$137$	−18.0150	+	3.17653i	−1.53912	+	0.271389i	−0.877917	−	0.478813i	$-0.841067\pi$
$137$	−18.0150	+	3.17653i	−1.53912	+	0.271389i	−0.661208	+	0.750203i	$0.729956\pi$
$138$	5.66836	+	7.92012i	0.482523	+	0.674206i
$139$	−2.16057	−	0.786381i	−0.183257	−	0.0667000i	0.248762	−	0.968565i	$-0.419976\pi$
$139$	−2.16057	−	0.786381i	−0.183257	−	0.0667000i	−0.432019	+	0.901865i	$0.642199\pi$
$140$	−0.278902	+	0.161024i	−0.0235715	+	0.0136090i
$141$	−0.900499	−	3.22719i	−0.0758357	−	0.271778i
$142$	−7.26434	+	6.09550i	−0.609610	+	0.511523i
$143$	−5.35850	+	4.49632i	−0.448100	+	0.376001i
$144$	−2.62846	−	1.44609i	−0.219039	−	0.120507i
$145$	−0.579510	+	0.334580i	−0.0481257	+	0.0277854i
$146$	−0.320853	−	0.116781i	−0.0265540	−	0.00966485i
$147$	7.79961	−	5.58211i	0.643301	−	0.460405i
$148$	3.89901	−	0.687501i	0.320497	−	0.0565122i
$149$	2.67853	+	7.35921i	0.219434	+	0.602890i	0.999747	−	0.0224995i	$-0.00716240\pi$
$149$	2.67853	+	7.35921i	0.219434	+	0.602890i	−0.780313	+	0.625389i	$0.784940\pi$
$150$	0.831767	+	8.49680i	0.0679135	+	0.693761i
$151$			11.1343i			0.906098i	0.891486	+	0.453049i	$0.149664\pi$
$151$			11.1343i			0.906098i	−0.891486	+	0.453049i	$0.850336\pi$
$152$	−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
$156$	4.25114	+	2.91180i	0.340364	+	0.233131i
$157$	−3.68519	+	20.8997i	−0.294110	+	1.66798i	0.376688	+	0.926340i	$0.377063\pi$
$157$	−3.68519	+	20.8997i	−0.294110	+	1.66798i	−0.670798	+	0.741640i	$0.734048\pi$
$158$	2.33914	−	6.42674i	0.186092	−	0.511284i
$159$	2.47795	−	9.64468i	0.196515	−	0.764873i
$160$	0.230629	+	0.133153i	0.0182328	+	0.0105267i
$161$	−4.37103	−	5.20919i	−0.344485	−	0.410542i
$162$	6.64992	−	6.06453i	0.522467	−	0.476474i
$163$	1.74061	−	3.01482i	0.136335	−	0.236139i	−0.789772	−	0.613401i	$-0.789801\pi$
$163$	1.74061	−	3.01482i	0.136335	−	0.236139i	0.926107	+	0.377262i	$0.123134\pi$
$164$	5.54582	+	9.60564i	0.433056	+	0.750075i
$165$	−0.468470	−	0.978167i	−0.0364703	−	0.0761502i
$166$	13.9006	+	2.45105i	1.07890	+	0.190238i
$167$	−3.56671	−	20.2278i	−0.276000	−	1.56527i	−0.735767	−	0.677235i	$-0.763178\pi$
$167$	−3.56671	−	20.2278i	−0.276000	−	1.56527i	0.459767	−	0.888040i	$-0.347933\pi$
$168$	1.90737	+	0.865585i	0.147157	+	0.0667813i
$169$	3.17888	+	2.66740i	0.244529	+	0.205185i
$170$	0.238832			0.0183176
$171$	12.6789	−	3.20091i	0.969579	−	0.244780i
$172$	−4.80300			−0.366225
$173$	−6.38346	−	5.35636i	−0.485326	−	0.407237i	0.367022	−	0.930212i	$-0.380377\pi$
$173$	−6.38346	−	5.35636i	−0.485326	−	0.407237i	−0.852348	+	0.522976i	$0.824822\pi$
$174$	3.96319	+	1.79854i	0.300449	+	0.136347i
$175$	−1.03508	−	5.87024i	−0.0782448	−	0.443748i
$176$	2.31560	+	0.408302i	0.174545	+	0.0307769i
$177$	9.55285	+	19.9464i	0.718036	+	1.49926i
$178$	−6.14989	−	10.6519i	−0.460953	−	0.798395i
$179$	4.51280	−	7.81640i	0.337302	−	0.584225i	−0.646622	−	0.762811i	$-0.723819\pi$
$179$	4.51280	−	7.81640i	0.337302	−	0.584225i	0.983924	+	0.178586i	$0.0571522\pi$
$180$	−0.601286	+	0.526051i	−0.0448172	+	0.0392095i
$181$	5.90976	+	7.04297i	0.439269	+	0.523500i	0.939573	−	0.342350i	$-0.111223\pi$
$181$	5.90976	+	7.04297i	0.439269	+	0.523500i	−0.500304	+	0.865850i	$0.666778\pi$
$182$	−3.11564	−	1.79882i	−0.230947	−	0.133337i
$183$	0.381350	−	1.48429i	0.0281902	−	0.109722i
$184$	−1.92322	+	5.28401i	−0.141782	+	0.389542i
$185$	0.183086	−	1.03833i	0.0134608	−	0.0763398i
$186$	14.8196	+	10.1506i	1.08663	+	0.744280i
$187$	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	$-0.0854648\pi$
$192$	−0.168747	−	1.72381i	−0.0121783	−	0.124405i
$193$	0.613121	+	1.68453i	0.0441334	+	0.121255i	0.959801	−	0.280680i	$-0.0905599\pi$
$193$	0.613121	+	1.68453i	0.0441334	+	0.121255i	−0.915668	+	0.401935i	$0.868338\pi$
$194$	−5.95150	+	1.04941i	−0.427293	+	0.0753432i
$195$	1.11587	−	0.798620i	0.0799093	−	0.0571904i
$196$	5.20361	+	1.89396i	0.371686	+	0.135283i
$197$	6.85271	−	3.95642i	0.488236	−	0.281883i	−0.235607	−	0.971849i	$-0.575708\pi$
$197$	6.85271	−	3.95642i	0.488236	−	0.281883i	0.723842	+	0.689966i	$0.242374\pi$
$198$	−3.40022	+	6.18035i	−0.241643	+	0.439219i
$199$	−8.01318	+	6.72386i	−0.568039	+	0.476642i	−0.880995	−	0.473126i	$-0.843125\pi$
$199$	−8.01318	+	6.72386i	−0.568039	+	0.476642i	0.312955	+	0.949768i	$0.398681\pi$
$200$	−3.77589	+	3.16835i	−0.266996	+	0.224036i
$201$	2.38170	+	8.53548i	0.167992	+	0.602047i
$202$	8.97769	−	5.18327i	0.631668	−	0.364694i
$203$	−2.85543	−	1.03929i	−0.200412	−	0.0729441i
$204$	−0.904043	−	1.26317i	−0.0632957	−	0.0884399i
$205$	2.90891	−	0.512919i	0.203167	−	0.0358238i
$206$	5.05487	+	13.8881i	0.352189	+	0.967633i
$207$	−13.1436	−	10.5746i	−0.913544	−	0.734983i
$208$			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	−0.365368	−	0.930863i	$-0.619057\pi$
$211$	8.93046	−	10.6429i	0.614799	−	0.732688i	0.980167	+	0.198175i	$0.0635013\pi$
$212$	5.40249	−	1.96634i	0.371044	−	0.135049i
$213$	9.28166	−	13.5509i	0.635969	−	0.928495i
$214$	2.80768	−	15.9231i	0.191929	−	1.08848i
$215$	−0.437468	+	1.20193i	−0.0298351	+	0.0819712i
$216$	5.05830	+	1.18894i	0.344174	+	0.0808970i
$217$	−10.8612	−	6.27072i	−0.737307	−	0.425684i
$218$	−11.7406	−	13.9919i	−0.795172	−	0.947650i
$219$	0.589649	+	0.0454645i	0.0398448	+	0.00307221i
$220$	0.313086	−	0.542281i	0.0211083	−	0.0365606i
$221$	1.33401	+	2.31057i	0.0897349	+	0.155425i
$222$	−6.18475	+	2.96204i	−0.415093	+	0.198799i
$223$	−12.2714	−	2.16379i	−0.821757	−	0.144898i	−0.253066	−	0.967449i	$-0.581439\pi$
$223$	−12.2714	−	2.16379i	−0.821757	−	0.144898i	−0.568691	+	0.822551i	$0.692550\pi$
$224$	0.209995	+	1.19094i	0.0140309	+	0.0795730i
$225$	−5.34308	−	13.7882i	−0.356206	−	0.919212i
$226$	1.83866	+	1.54282i	0.122306	+	0.102627i
$227$	−1.63948			−0.108816			−0.0544081	−	0.998519i	$-0.517327\pi$
$227$	−1.63948			−0.108816			−0.0544081	+	0.998519i	$0.517327\pi$
$228$	5.66128	+	4.99498i	0.374928	+	0.330801i
$229$	−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
$231$	2.03527	−	4.48484i	0.133911	−	0.295081i
$232$	0.436333	+	2.47457i	0.0286467	+	0.162463i
$233$	−2.37239	−	0.418316i	−0.155420	−	0.0274048i	0.0953966	−	0.995439i	$-0.469588\pi$
$233$	−2.37239	−	0.418316i	−0.155420	−	0.0274048i	−0.250817	+	0.968035i	$0.580699\pi$
$234$	−8.44777	−	2.87883i	−0.552248	−	0.188195i
$235$	−0.257571	−	0.446127i	−0.0168021	−	0.0291021i
$236$	−6.38433	+	11.0580i	−0.415585	+	0.719814i
$237$	−0.910662	+	11.8108i	−0.0591538	+	0.767192i
$238$	0.697133	+	0.830810i	0.0451884	+	0.0538534i
$239$	16.5806	+	9.57284i	1.07251	+	0.619215i	0.928867	−	0.370414i	$-0.120784\pi$
$239$	16.5806	+	9.57284i	1.07251	+	0.619215i	0.143646	+	0.989629i	$0.454117\pi$
$240$	−0.446748	−	0.114780i	−0.0288374	−	0.00740904i
$241$	1.43503	−	3.94271i	0.0924383	−	0.253972i	−0.884854	−	0.465869i	$-0.845742\pi$
$241$	1.43503	−	3.94271i	0.0924383	−	0.253972i	0.977292	+	0.211897i	$0.0679641\pi$
$242$	−0.950083	+	5.38819i	−0.0610736	+	0.346366i
$243$	−8.27104	+	13.2132i	−0.530587	+	0.847630i
$244$	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
$249$	−24.3317	+	2.38187i	−1.54196	+	0.150945i
$250$	0.904364	+	2.48472i	0.0571970	+	0.157147i
$251$	−4.15098	+	0.731929i	−0.262007	+	0.0461990i	−0.303109	−	0.952956i	$-0.598024\pi$
$251$	−4.15098	+	0.731929i	−0.262007	+	0.0461990i	0.0411012	+	0.999155i	$0.486913\pi$
$252$	−3.58505	−	0.556153i	−0.225837	−	0.0350344i
$253$	12.4244	+	4.52211i	0.781114	+	0.284302i
$254$	5.12516	−	2.95901i	0.321581	−	0.185665i
$255$	−0.398448	+	0.111181i	−0.0249518	+	0.00696242i
$256$	0.766044	−	0.642788i	0.0478778	−	0.0401742i
$257$	−13.6150	+	11.4244i	−0.849282	+	0.712632i	−0.959631	−	0.281260i	$-0.909248\pi$
$257$	−13.6150	+	11.4244i	−0.849282	+	0.712632i	0.110349	+	0.993893i	$0.464803\pi$
$258$	8.01293	−	2.23589i	0.498863	−	0.139200i
$259$	4.14641	−	2.39393i	0.257645	−	0.148752i
$260$	0.744469	+	0.270964i	0.0461700	+	0.0168045i
$261$	−7.44913	−	1.15559i	−0.461089	−	0.0715293i
$262$	−17.0184	+	3.00080i	−1.05140	+	0.185390i
$263$	−0.383160	−	1.05272i	−0.0236267	−	0.0649138i	0.927319	−	0.374273i	$-0.122108\pi$
$263$	−0.383160	−	1.05272i	−0.0236267	−	0.0649138i	−0.950945	+	0.309359i	$0.899885\pi$
$264$	−4.05323	+	0.396777i	−0.249459	+	0.0244200i
$265$		−	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	$-0.813323\pi$
$269$	−18.2909	+	6.65734i	−1.11522	+	0.405905i	−0.282311	+	0.959323i	$0.591101\pi$
$270$	0.758250	−	1.15753i	0.0461456	−	0.0704452i
$271$	−0.0552285	+	0.313217i	−0.00335489	+	0.0190266i	−0.986439	−	0.164127i	$-0.947519\pi$
$271$	−0.0552285	+	0.313217i	−0.00335489	+	0.0190266i	0.983084	+	0.183153i	$0.0586305\pi$
$272$	0.306733	−	0.842743i	0.0185984	−	0.0510988i
$273$	6.03527	+	1.55061i	0.365271	+	0.0938470i
$274$	15.8421	+	9.14645i	0.957057	+	0.552557i
$275$	7.44980	+	8.87833i	0.449240	+	0.535383i
$276$	0.748739	−	9.71072i	0.0450688	−	0.584517i
$277$	10.9678	−	18.9968i	0.658993	−	1.14141i	−0.321884	−	0.946779i	$-0.604316\pi$
$277$	10.9678	−	18.9968i	0.658993	−	1.14141i	0.980877	−	0.194630i	$-0.0623506\pi$
$278$	1.14961	+	1.99119i	0.0689492	+	0.119424i
$279$	−29.4492	−	10.0357i	−1.76308	−	0.600820i
$280$	0.317156	+	0.0559231i	0.0189537	+	0.00334204i
$281$	−2.62001	−	14.8588i	−0.156297	−	0.886403i	−0.957591	−	0.288132i	$-0.906966\pi$
$281$	−2.62001	−	14.8588i	−0.156297	−	0.886403i	0.801294	−	0.598271i	$-0.204145\pi$
$282$	−1.38458	+	3.05100i	−0.0824502	+	0.181684i
$283$	−5.08697	−	4.26848i	−0.302389	−	0.253735i	0.478949	−	0.877843i	$-0.341018\pi$
$283$	−5.08697	−	4.26848i	−0.302389	−	0.253735i	−0.781338	+	0.624108i	$0.785462\pi$
$284$	9.48292			0.562708
$285$	1.76562	−	0.961763i	0.104586	−	0.0569699i
$286$	6.99503			0.413625
$287$	10.2751	+	8.62187i	0.606523	+	0.508933i
$288$	1.08399	+	2.79731i	0.0638748	+	0.164833i
$289$	2.81235	+	15.9496i	0.165433	+	0.938215i
$290$	0.658995	+	0.116199i	0.0386975	+	0.00682341i
$291$	9.44048	−	4.52129i	0.553411	−	0.265043i
$292$	0.170722	+	0.295699i	0.00999076	+	0.0173045i
$293$	14.2028	−	24.5999i	0.829735	−	1.43714i	−0.0685112	−	0.997650i	$-0.521825\pi$
$293$	14.2028	−	24.5999i	0.829735	−	1.43714i	0.898246	−	0.439493i	$-0.144842\pi$
$294$	−9.56296	−	0.737346i	−0.557723	−	0.0430029i
$295$	2.18572	+	2.60484i	0.127258	+	0.151660i
$296$	−3.42873	−	1.97958i	−0.199291	−	0.115061i
$297$	2.79557	−	11.8937i	0.162215	−	0.690141i
$298$	2.67853	−	7.35921i	0.155163	−	0.426307i
$299$	−2.90487	+	16.4743i	−0.167993	+	0.952734i
$300$	4.82447	−	7.04358i	0.278541	−	0.406661i
$301$	−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
$306$	2.09627	+	1.68653i	0.119836	+	0.0964125i
$307$	1.49097	+	4.09641i	0.0850942	+	0.233794i	0.974940	−	0.222466i	$-0.0714107\pi$
$307$	1.49097	+	4.09641i	0.0850942	+	0.233794i	−0.889846	+	0.456261i	$0.849188\pi$
$308$	2.80028	−	0.493765i	0.159561	−	0.0281348i
$309$	−14.8983	−	20.8167i	−0.847537	−	1.18422i
$310$	2.59524	+	0.944590i	0.147400	+	0.0536491i
$311$	−4.11082	+	2.37338i	−0.233103	+	0.134582i	−0.612003	−	0.790856i	$-0.709636\pi$
$311$	−4.11082	+	2.37338i	−0.233103	+	0.134582i	0.378900	+	0.925438i	$0.376303\pi$
$312$	−1.38489	−	4.96315i	−0.0784041	−	0.280983i
$313$	14.5023	−	12.1689i	0.819718	−	0.687825i	−0.133188	−	0.991091i	$-0.542521\pi$
$313$	14.5023	−	12.1689i	0.819718	−	0.687825i	0.952906	+	0.303265i	$0.0980769\pi$
$314$	16.2571	−	13.6413i	0.917442	−	0.769825i
$315$	−0.465711	+	0.846492i	−0.0262398	+	0.0476944i
$316$	−5.92291	+	3.41960i	−0.333190	+	0.192367i
$317$	29.4488	+	10.7185i	1.65401	+	0.602010i	0.989404	−	0.145186i	$-0.0463782\pi$
$317$	29.4488	+	10.7185i	1.65401	+	0.602010i	0.664604	+	0.747196i	$0.268600\pi$
$318$	−8.09771	+	5.79546i	−0.454097	+	0.324993i
$319$	5.81850	−	1.02596i	0.325773	−	0.0574426i
$320$	−0.0910823	−	0.250247i	−0.00509166	−	0.0139892i
$321$	2.72843	+	27.8719i	0.152286	+	1.55566i
$322$			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
$327$	26.1005	+	17.8775i	1.44336	+	0.988626i
$328$	1.92604	−	10.9231i	0.106348	−	0.603129i
$329$	0.800083	−	2.19821i	0.0441100	−	0.121191i
$330$	−0.269885	+	1.05045i	−0.0148567	+	0.0578251i
$331$	−3.20610	−	1.85104i	−0.176223	−	0.101742i	0.409294	−	0.912403i	$-0.365775\pi$
$331$	−3.20610	−	1.85104i	−0.176223	−	0.101742i	−0.585517	+	0.810660i	$0.699108\pi$
$332$	−9.07297	−	10.8127i	−0.497944	−	0.593426i
$333$	8.93925	−	7.82075i	0.489868	−	0.428574i
$334$	−10.2699	+	17.7880i	−0.561945	+	0.973318i
$335$	0.681242	+	1.17995i	0.0372202	+	0.0644673i
$336$	−0.904745	−	1.88911i	−0.0493579	−	0.103060i
$337$	−19.7344	−	3.47971i	−1.07500	−	0.189552i	−0.391997	−	0.919967i	$-0.628216\pi$
$337$	−19.7344	−	3.47971i	−1.07500	−	0.189552i	−0.683004	+	0.730415i	$0.739327\pi$
$338$	−0.720594	−	4.08669i	−0.0391952	−	0.222287i
$339$	−3.78568	−	1.71798i	−0.205610	−	0.0933079i
$340$	−0.182956	−	0.153518i	−0.00992217	−	0.00832569i
$341$	24.3849			1.32051
$342$	−11.7701	−	5.69779i	−0.636454	−	0.308101i
$343$	15.1618			0.818662
$344$	3.67931	+	3.08731i	0.198375	+	0.166456i
$345$	−2.36188	−	1.07184i	−0.127159	−	0.0577062i
$346$	1.44701	+	8.20642i	0.0777919	+	0.441180i
$347$	−0.281016	−	0.0495507i	−0.0150857	−	0.00266002i	0.166100	−	0.986109i	$-0.446882\pi$
$347$	−0.281016	−	0.0495507i	−0.0150857	−	0.00266002i	−0.181186	+	0.983449i	$0.557994\pi$
$348$	−1.87990	−	3.92525i	−0.100773	−	0.210415i
$349$	6.98873	+	12.1048i	0.374098	+	0.647957i	0.990192	−	0.139716i	$-0.0446190\pi$
$349$	6.98873	+	12.1048i	0.374098	+	0.647957i	−0.616093	+	0.787673i	$0.711286\pi$
$350$	−2.98040	+	5.16220i	−0.159309	+	0.275931i
$351$	15.4337	+	0.870200i	0.823791	+	0.0464479i
$352$	−1.51140	−	1.80121i	−0.0805578	−	0.0960050i
$353$	17.7647	+	10.2564i	0.945519	+	0.545895i	0.891686	−	0.452654i	$-0.149523\pi$
$353$	17.7647	+	10.2564i	0.945519	+	0.545895i	0.0538327	+	0.998550i	$0.482856\pi$
$354$	5.50339	−	21.4203i	0.292502	−	1.13848i
$355$	0.863726	−	2.37307i	0.0458418	−	0.125949i
$356$	−2.13583	+	12.1129i	−0.113199	+	0.641983i
$357$	−1.54980	−	1.06153i	−0.0820241	−	0.0561820i
$358$	−8.48129	+	3.08694i	−0.448250	+	0.163150i
$359$	17.9876	−	21.4368i	0.949348	−	1.13139i	−0.0418658	−	0.999123i	$-0.513330\pi$
$359$	17.9876	−	21.4368i	0.949348	−	1.13139i	0.991214	−	0.132266i	$-0.0422254\pi$
$360$	0.798751	−	0.0164795i	0.0420979	−	0.000868548i
$361$	−11.1609	−	15.3764i	−0.587415	−	0.809286i
$362$		−	9.19395i		−	0.483223i
$363$	−0.923266	−	9.43150i	−0.0484589	−	0.495025i
$364$	1.23046	+	3.38067i	0.0644937	+	0.177195i
$365$	0.0895476	−	0.0157897i	0.00468713	−	0.000826468i
$366$	−1.24621	+	0.891904i	−0.0651406	+	0.0466206i
$367$	1.43051	+	0.520662i	0.0746719	+	0.0271783i	0.379086	−	0.925361i	$-0.376238\pi$
$367$	1.43051	+	0.520662i	0.0746719	+	0.0271783i	−0.304414	+	0.952540i	$0.598461\pi$
$368$	4.86977	−	2.81156i	0.253854	−	0.146563i
$369$	29.1540	+	16.0395i	1.51770	+	0.834983i
$370$	−0.807680	+	0.677724i	−0.0419893	+	0.0352332i
$371$	5.32599	−	4.46904i	0.276512	−	0.232021i
$372$	−4.82778	−	17.3017i	−0.250309	−	0.897051i
$373$	4.13495	−	2.38731i	0.214100	−	0.123610i	−0.389116	−	0.921189i	$-0.627219\pi$
$373$	4.13495	−	2.38731i	0.214100	−	0.123610i	0.603215	+	0.797578i	$0.293886\pi$
$374$	−1.98156	−	0.721228i	−0.102464	−	0.0372938i
$375$	−2.66545	−	3.72431i	−0.137643	−	0.192322i
$376$	−1.90501	+	0.335904i	−0.0982432	+	0.0173229i
$377$	2.55669	+	7.02444i	0.131676	+	0.361777i
$378$	6.23992	−	0.741073i	0.320947	−	0.0381167i
$379$		−	13.4129i		−	0.688972i	−0.938791	−	0.344486i	$-0.888053\pi$
$379$		−	13.4129i		−	0.688972i	0.938791	−	0.344486i	$-0.111947\pi$
$380$	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	$-0.923827\pi$
$383$	−30.5956	+	11.1359i	−1.56336	+	0.569017i	−0.591857	+	0.806043i	$0.701605\pi$
$384$	−0.978777	+	1.42898i	−0.0499480	+	0.0729225i
$385$	0.131493	−	0.745733i	0.00670150	−	0.0380061i
$386$	0.613121	−	1.68453i	0.0312070	−	0.0857406i
$387$	−12.3273	+	7.46036i	−0.626631	+	0.379231i
$388$	5.23366	+	3.02165i	0.265699	+	0.153401i
$389$	−8.33624	−	9.93474i	−0.422664	−	0.503711i	0.512127	−	0.858910i	$-0.328858\pi$
$389$	−8.33624	−	9.93474i	−0.422664	−	0.503711i	−0.934791	+	0.355199i	$0.884413\pi$
$390$	−1.36815	−	0.105490i	−0.0692790	−	0.00534172i
$391$	2.52149	−	4.36735i	0.127517	−	0.220866i
$392$	−2.76878	−	4.79567i	−0.139845	−	0.242218i
$393$	26.9952	−	12.9287i	1.36173	−	0.652166i
$394$	−7.79262	−	1.37405i	−0.392586	−	0.0692236i
$395$	0.316270	+	1.79365i	0.0159132	+	0.0902485i
$396$	6.57737	−	2.54881i	0.330525	−	0.128082i
$397$	18.9635	+	15.9123i	0.951752	+	0.798615i	0.979592	−	0.200997i	$-0.0644183\pi$
$397$	18.9635	+	15.9123i	0.951752	+	0.798615i	−0.0278396	+	0.999612i	$0.508863\pi$
$398$	10.4605			0.524336
$399$	8.49935	+	3.33465i	0.425500	+	0.166941i
$400$	4.92908			0.246454
$401$	−4.89417	−	4.10670i	−0.244403	−	0.205079i	0.512354	−	0.858774i	$-0.328773\pi$
$401$	−4.89417	−	4.10670i	−0.244403	−	0.205079i	−0.756758	+	0.653695i	$0.773218\pi$
$402$	3.66202	−	8.06949i	0.182645	−	0.402469i
$403$	5.35744	+	30.3836i	0.266873	+	1.51351i
$404$	−10.2091	−	1.80013i	−0.507919	−	0.0895599i
$405$	−0.726149	+	2.28411i	−0.0360826	+	0.113499i
$406$	1.51935	+	2.63158i	0.0754038	+	0.130603i
$407$	−4.65462	+	8.06204i	−0.230721	+	0.399620i
$408$	−0.119416	+	1.54876i	−0.00591197	+	0.0766748i
$409$	−18.5835	−	22.1469i	−0.918894	−	1.09510i	−0.995185	−	0.0980100i	$-0.968752\pi$
$409$	−18.5835	−	22.1469i	−0.918894	−	1.09510i	0.0762911	−	0.997086i	$-0.475692\pi$
$410$	−2.55805	−	1.47689i	−0.126333	−	0.0729384i
$411$	−30.6876	−	7.88439i	−1.51371	−	0.388908i
$412$	5.05487	−	13.8881i	0.249036	−	0.684220i
$413$	−2.68135	+	15.2067i	−0.131941	+	0.748273i
$414$	3.27140	+	16.5491i	0.160780	+	0.813346i
$415$	−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	$0.844350\pi$
$420$	−0.555150	+	0.0543446i	−0.0270886	+	0.00265175i
$421$	−11.8370	−	32.5219i	−0.576900	−	1.58502i	−0.793376	−	0.608732i	$-0.791678\pi$
$421$	−11.8370	−	32.5219i	−0.576900	−	1.58502i	0.216476	−	0.976288i	$-0.430544\pi$
$422$	−13.6823	+	2.41255i	−0.666042	+	0.117441i
$423$	0.889613	−	5.73459i	0.0432545	−	0.278825i
$424$	−5.40249	−	1.96634i	−0.262368	−	0.0954941i
$425$	3.82830	−	2.21027i	0.185700	−	0.107214i
$426$	−15.8205	+	4.41449i	−0.766508	+	0.213883i
$427$	0.819655	−	0.687772i	0.0396659	−	0.0332836i
$428$	−12.3860	+	10.3931i	−0.598700	+	0.502369i
$429$	−11.6699	+	3.25632i	−0.563430	+	0.157217i
$430$	1.10771	−	0.639535i	0.0534184	−	0.0308411i
$431$	−30.2120	−	10.9963i	−1.45526	−	0.529671i	−0.511205	−	0.859459i	$-0.670801\pi$
$431$	−30.2120	−	10.9963i	−1.45526	−	0.529671i	−0.944055	+	0.329788i	$0.893023\pi$
$432$	−3.11065	−	4.16219i	−0.149661	−	0.200254i
$433$	−22.7212	+	4.00636i	−1.09191	+	0.192534i	−0.690477	−	0.723354i	$-0.742599\pi$
$433$	−22.7212	+	4.00636i	−1.09191	+	0.192534i	−0.401435	+	0.915888i	$0.631488\pi$
$434$	4.28943	+	11.7851i	0.205899	+	0.565703i
$435$	−1.15351	+	0.112919i	−0.0553064	+	0.00541404i
$436$			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	−0.554413	−	0.832242i	$-0.687057\pi$
$439$	7.57338	−	9.02561i	0.361458	−	0.430769i	0.915871	+	0.401473i	$0.131502\pi$
$440$	−0.588409	+	0.214163i	−0.0280513	+	0.0102098i
$441$	16.2973	−	3.22162i	0.776063	−	0.153410i
$442$	0.463295	−	2.62748i	0.0220367	−	0.124976i
$443$	7.28357	−	20.0114i	0.346053	−	0.950772i	−0.637548	−	0.770411i	$-0.720051\pi$
$443$	7.28357	−	20.0114i	0.346053	−	0.950772i	0.983600	−	0.180361i	$-0.0577267\pi$
$444$	6.64175	+	1.70643i	0.315204	+	0.0809835i
$445$	2.83668	+	1.63776i	0.134471	+	0.0776371i
$446$	8.00962	+	9.54549i	0.379266	+	0.451992i
$447$	−1.04279	+	13.5244i	−0.0493224	+	0.639683i
$448$	0.604656	−	1.04730i	0.0285673	−	0.0494800i
$449$	−5.96300	−	10.3282i	−0.281411	−	0.487419i	0.690321	−	0.723503i	$-0.257469\pi$
$449$	−5.96300	−	10.3282i	−0.281411	−	0.487419i	−0.971733	+	0.236084i	$0.924136\pi$
$450$	−4.76983	+	13.9968i	−0.224852	+	0.659817i
$451$	−25.6837	−	4.52874i	−1.20940	−	0.213250i
$452$	−0.416790	−	2.36373i	−0.0196041	−	0.111181i
$453$	−7.96957	+	17.5615i	−0.374443	+	0.825110i
$454$	1.25592	+	1.05384i	0.0589431	+	0.0494591i
$455$	0.958074			0.0449152
$456$	−1.12608	−	7.46538i	−0.0527336	−	0.349599i
$457$	−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
$459$	−4.28236	−	1.83782i	−0.199883	−	0.0857820i
$460$	−0.260034	−	1.47473i	−0.0121242	−	0.0687595i
$461$	−29.6765	−	5.23277i	−1.38217	−	0.243715i	−0.567376	−	0.823459i	$-0.692041\pi$
$461$	−29.6765	−	5.23277i	−1.38217	−	0.243715i	−0.814798	+	0.579744i	$0.803152\pi$
$462$	−4.44190	+	2.12734i	−0.206656	+	0.0989729i
$463$	12.7896	+	22.1523i	0.594385	+	1.02950i	0.993633	+	0.112662i	$0.0359378\pi$
$463$	12.7896	+	22.1523i	0.594385	+	1.02950i	−0.399248	+	0.916843i	$0.630729\pi$
$464$	1.25637	−	2.17610i	0.0583256	−	0.101023i
$465$	−4.76942	−	0.367743i	−0.221176	−	0.0170537i
$466$	1.54847	+	1.84539i	0.0717313	+	0.0854860i
$467$	−24.6450	−	14.2288i	−1.14044	−	0.658431i	−0.193898	−	0.981022i	$-0.562113\pi$
$467$	−24.6450	−	14.2288i	−1.14044	−	0.658431i	−0.946539	+	0.322591i	$0.895446\pi$
$468$	4.62089	+	7.63543i	0.213601	+	0.352948i
$469$	−2.11611	+	5.81397i	−0.0977131	+	0.268464i
$470$	−0.0894536	+	0.507317i	−0.00412619	+	0.0234008i
$471$	−20.7717	+	30.3261i	−0.957112	+	1.39735i
$472$	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
$477$	10.8117	−	13.4383i	0.495032	−	0.615298i
$478$	−6.54821	−	17.9910i	−0.299508	−	0.822891i
$479$	12.1691	−	2.14575i	0.556022	−	0.0980417i	0.111426	−	0.993773i	$-0.464458\pi$
$479$	12.1691	−	2.14575i	0.556022	−	0.0980417i	0.444596	+	0.895731i	$0.353347\pi$
$480$	0.268449	+	0.375091i	0.0122530	+	0.0171205i
$481$	−11.0679	−	4.02840i	−0.504655	−	0.183679i
$482$	−3.63362	+	2.09787i	−0.165507	+	0.0955554i
$483$	−3.16559	−	11.3448i	−0.144039	−	0.516205i
$484$	4.19126	−	3.51689i	0.190512	−	0.159859i
$485$	1.23285	−	1.03449i	0.0559810	−	0.0469736i
$486$	14.8293	−	4.80541i	0.672671	−	0.217978i
$487$	24.3442	−	14.0551i	1.10314	−	0.636899i	0.166097	−	0.986109i	$-0.446883\pi$
$487$	24.3442	−	14.0551i	1.10314	−	0.636899i	0.937044	+	0.349210i	$0.113550\pi$
$488$	−0.831427	−	0.302615i	−0.0376369	−	0.0136987i
$489$	4.90326	−	3.50922i	0.221733	−	0.158693i
$490$	−1.45229	+	0.256078i	−0.0656077	+	0.0115684i
$491$	−1.17147	−	3.21859i	−0.0528678	−	0.145253i	0.910448	−	0.413624i	$-0.135737\pi$
$491$	−1.17147	−	3.21859i	−0.0528678	−	0.145253i	−0.963316	+	0.268371i	$0.913515\pi$
$492$	1.87168	+	19.1199i	0.0843818	+	0.861991i
$493$		−	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
$498$	20.1702	+	13.8155i	0.903847	+	0.619086i
$499$	6.64566	−	37.6894i	0.297500	−	1.68721i	−0.359362	−	0.933198i	$-0.617006\pi$
$499$	6.64566	−	37.6894i	0.297500	−	1.68721i	0.656862	−	0.754010i	$-0.271883\pi$
$500$	0.904364	−	2.48472i	0.0404444	−	0.111120i
$501$	8.85284	−	34.4570i	0.395516	−	1.53942i
$502$	3.65031	+	2.10751i	0.162921	+	0.0940626i
$503$	−10.1578	−	12.1056i	−0.452916	−	0.539764i	0.490472	−	0.871457i	$-0.336825\pi$
$503$	−10.1578	−	12.1056i	−0.452916	−	0.539764i	−0.943387	+	0.331693i	$0.892380\pi$
$504$	2.38882	+	2.73047i	0.106407	+	0.121625i
$505$	−1.38034	+	2.39082i	−0.0614244	+	0.106390i
$506$	−6.61088	−	11.4504i	−0.293889	−	0.509031i
$507$	3.10462	+	6.48246i	0.137881	+	0.287896i
$508$	−5.82811	−	1.02765i	−0.258581	−	0.0455947i
$509$	1.72136	+	9.76234i	0.0762981	+	0.432708i	0.998897	+	0.0469483i	$0.0149496\pi$
$509$	1.72136	+	9.76234i	0.0762981	+	0.432708i	−0.922599	+	0.385760i	$0.873939\pi$
$510$	0.376694	+	0.170948i	0.0166803	+	0.00756969i
$511$	0.316310	+	0.265415i	0.0139927	+	0.0117413i
$512$	−1.00000			−0.0441942
$513$	22.2887	+	4.02652i	0.984071	+	0.177775i
$514$	17.7732			0.783941
$515$	−3.01505	−	2.52993i	−0.132859	−	0.111482i
$516$	−7.57546	−	3.43782i	−0.333491	−	0.151342i
$517$	0.789817	+	4.47928i	0.0347361	+	0.196998i
$518$	−4.71512	−	0.831403i	−0.207170	−	0.0365297i
$519$	−6.23433	−	13.0173i	−0.273657	−	0.571397i
$520$	−0.396123	−	0.686106i	−0.0173712	−	0.0300877i
$521$	−6.93036	+	12.0037i	−0.303625	+	0.525894i	−0.976954	−	0.213449i	$-0.931530\pi$
$521$	−6.93036	+	12.0037i	−0.303625	+	0.525894i	0.673329	+	0.739343i	$0.264864\pi$
$522$	4.96356	+	5.67344i	0.217249	+	0.248320i
$523$	24.0581	+	28.6713i	1.05199	+	1.25371i	0.966309	+	0.257386i	$0.0828611\pi$
$523$	24.0581	+	28.6713i	1.05199	+	1.25371i	0.0856778	+	0.996323i	$0.472694\pi$
$524$	14.9657	+	8.64045i	0.653780	+	0.377460i
$525$	2.56915	−	9.99964i	0.112127	−	0.436420i
$526$	−0.383160	+	1.05272i	−0.0167066	+	0.0459010i
$527$	1.61506	−	9.15947i	0.0703532	−	0.398993i
$528$	3.36000	+	2.30141i	0.146225	+	0.100156i
$529$	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
$534$	−2.07555	−	21.2025i	−0.0898177	−	0.917521i
$535$	1.47269	+	4.04618i	0.0636699	+	0.174932i
$536$	5.03849	−	0.888422i	0.217630	−	0.0383740i
$537$	12.7125	−	9.09820i	0.548584	−	0.392616i
$538$	18.2909	+	6.65734i	0.788576	+	0.287018i
$539$	−11.2761	+	6.51028i	−0.485698	+	0.280418i
$540$	−1.32490	+	0.399327i	−0.0570146	+	0.0171843i
$541$	6.17119	−	5.17824i	0.265320	−	0.222630i	−0.500416	−	0.865785i	$-0.666819\pi$
$541$	6.17119	−	5.17824i	0.265320	−	0.222630i	0.765736	+	0.643155i	$0.222375\pi$
$542$	0.243639	−	0.204438i	0.0104652	−	0.00878135i
$543$	4.27996	+	15.3384i	0.183671	+	0.658236i
$544$	−0.776676	+	0.448414i	−0.0332997	+	0.0192256i
$545$	4.57078	+	1.66363i	0.195791	+	0.0712620i
$546$	−3.62657	−	5.06723i	−0.155203	−	0.216857i
$547$	25.2004	−	4.44352i	1.07749	−	0.189991i	0.393386	−	0.919373i	$-0.371303\pi$
$547$	25.2004	−	4.44352i	1.07749	−	0.189991i	0.684106	+	0.729382i	$0.260192\pi$
$548$	−6.25654	−	17.1897i	−0.267266	−	0.734308i
$549$	1.66388	−	2.06812i	0.0710128	−	0.0882652i
$550$		−	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
$555$	1.03197	−	1.50665i	0.0438049	−	0.0639538i
$556$	0.399256	−	2.26430i	0.0169322	−	0.0960275i
$557$	4.99606	−	13.7266i	0.211690	−	0.581613i	−0.787718	−	0.616037i	$-0.788737\pi$
$557$	4.99606	−	13.7266i	0.211690	−	0.581613i	0.999407	+	0.0344238i	$0.0109596\pi$
$558$	16.1086	+	26.6173i	0.681930	+	1.12680i
$559$	12.3743	+	7.14431i	0.523377	+	0.302172i
$560$	−0.207009	−	0.246703i	−0.00874771	−	0.0104251i
$561$	3.64162	+	0.280785i	0.153749	+	0.0118547i
$562$	−7.54402	+	13.0666i	−0.318225	+	0.551182i
$563$	−12.5968	−	21.8184i	−0.530893	−	0.919534i	−0.999350	−	0.0360479i	$-0.988523\pi$
$563$	−12.5968	−	21.8184i	−0.530893	−	0.919534i	0.468457	−	0.883486i	$-0.344810\pi$
$564$	3.02179	−	1.44721i	0.127240	−	0.0609387i
$565$	−0.629478	−	0.110994i	−0.0264824	−	0.00466955i
$566$	1.15312	+	6.53969i	0.0484694	+	0.274884i
$567$	−10.0652	+	4.14115i	−0.422699	+	0.173912i
$568$	−7.26434	−	6.09550i	−0.304805	−	0.255762i
$569$	42.1013			1.76498			0.882490	−	0.470332i	$-0.155866\pi$
$569$	42.1013			1.76498			0.882490	+	0.470332i	$0.155866\pi$
$570$	−1.97075	−	0.398166i	−0.0825458	−	0.0166773i
$571$	−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
$573$	5.24837	−	11.5651i	0.219254	−	0.483140i
$574$	−2.32919	−	13.2095i	−0.0972184	−	0.551353i
$575$	27.2958	+	4.81298i	1.13831	+	0.200715i
$576$	0.967692	−	2.83964i	0.0403205	−	0.118318i
$577$	6.43762	+	11.1503i	0.268002	+	0.464192i	0.968346	−	0.249613i	$-0.0803034\pi$
$577$	6.43762	+	11.1503i	0.268002	+	0.464192i	−0.700344	+	0.713805i	$0.746970\pi$
$578$	8.09785	−	14.0259i	0.336826	−	0.583400i
$579$	−0.238697	+	3.09576i	−0.00991990	+	0.128656i
$580$	−0.430128	−	0.512607i	−0.0178601	−	0.0212848i
$581$	−14.7826	−	8.53474i	−0.613286	−	0.354081i
$582$	−10.1381	−	2.60471i	−0.420236	−	0.107969i
$583$	−4.62350	+	12.7030i	−0.191486	+	0.526103i
$584$	0.0592912	−	0.336257i	0.00245349	−	0.0139144i
$585$	2.33162	−	0.460910i	0.0964007	−	0.0190563i
$586$	−26.6925	+	9.71527i	−1.10266	+	0.401334i
$587$	11.6998	−	13.9432i	0.482900	−	0.575498i	−0.468497	−	0.883465i	$-0.655204\pi$
$587$	11.6998	−	13.9432i	0.482900	−	0.575498i	0.951397	+	0.307967i	$0.0996486\pi$
$588$	6.85169	+	6.71179i	0.282559	+	0.276790i
$589$	2.35551	+	45.1435i	0.0970573	+	1.86011i
$590$		−	3.40038i		−	0.139992i
$591$	13.6402	−	1.33527i	0.561084	−	0.0549255i
$592$	1.35411	+	3.72039i	0.0556537	+	0.152907i
$593$	−6.08719	+	1.07334i	−0.249971	+	0.0440766i	−0.297230	−	0.954806i	$-0.596063\pi$
$593$	−6.08719	+	1.07334i	−0.249971	+	0.0440766i	0.0472585	+	0.998883i	$0.484952\pi$
$594$	−9.78664	+	7.31412i	−0.401551	+	0.300102i
$595$	−0.271404	−	0.0987830i	−0.0111265	−	0.00404971i
$596$	−6.78228	+	3.91575i	−0.277813	+	0.160395i
$597$	−17.4514	+	4.86955i	−0.714238	+	0.199298i
$598$	12.8147	−	10.7528i	0.524034	−	0.439717i
$599$	−27.9659	+	23.4662i	−1.14266	+	0.958803i	−0.999522	−	0.0308999i	$-0.990163\pi$
$599$	−27.9659	+	23.4662i	−1.14266	+	0.958803i	−0.143135	+	0.989703i	$0.545718\pi$
$600$	−8.22328	+	2.29458i	−0.335714	+	0.0936760i
$601$	2.01662	−	1.16430i	0.0822597	−	0.0474927i	−0.458306	−	0.888795i	$-0.651544\pi$
$601$	2.01662	−	1.16430i	0.0822597	−	0.0474927i	0.540566	+	0.841302i	$0.318210\pi$
$602$	5.45804	+	1.98656i	0.222453	+	0.0809663i
$603$	−2.35291	+	15.1672i	−0.0958178	+	0.617657i
$604$	−10.9652	+	1.93345i	−0.446166	+	0.0786712i
$605$	−0.498339	−	1.36918i	−0.0202604	−	0.0556649i
$606$	17.8700	−	1.74932i	0.725918	−	0.0710613i
$607$		−	24.4621i		−	0.992887i	−0.868069	−	0.496443i	$-0.834639\pi$
$607$		−	24.4621i		−	0.992887i	0.868069	−	0.496443i	$-0.165361\pi$
$608$	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
$612$	−0.521753	−	2.63941i	−0.0210906	−	0.106692i
$613$	−6.30039	+	35.7313i	−0.254470	+	1.44317i	0.542958	+	0.839760i	$0.317304\pi$
$613$	−6.30039	+	35.7313i	−0.254470	+	1.44317i	−0.797428	+	0.603414i	$0.793807\pi$
$614$	1.49097	−	4.09641i	0.0601707	−	0.165318i
$615$	4.95517	+	1.27310i	0.199812	+	0.0513365i
$616$	−2.46252	−	1.42174i	−0.0992179	−	0.0572835i
$617$	−10.3830	−	12.3740i	−0.418006	−	0.498160i	0.515416	−	0.856940i	$-0.327637\pi$
$617$	−10.3830	−	12.3740i	−0.418006	−	0.498160i	−0.933422	+	0.358780i	$0.883193\pi$
$618$	−1.96794	+	25.5230i	−0.0791620	+	1.02669i
$619$	−15.2492	+	26.4123i	−0.612916	+	1.06160i	0.377831	+	0.925875i	$0.376670\pi$
$619$	−15.2492	+	26.4123i	−0.612916	+	1.06160i	−0.990746	+	0.135726i	$0.956663\pi$
$620$	−1.38090	−	2.39179i	−0.0554582	−	0.0960564i
$621$	−13.1617	−	26.0864i	−0.528160	−	1.04681i
$622$	4.67465	+	0.824268i	0.187437	+	0.0330501i
$623$	2.58289	+	14.6483i	0.103481	+	0.586871i
$624$	−2.12936	+	4.69219i	−0.0852427	+	0.187838i
$625$	18.3401	+	15.3891i	0.733602	+	0.615565i
$626$	−18.9314			−0.756651
$627$	−17.5535	+	2.64778i	−0.701019	+	0.105742i
$628$	−21.2221			−0.846856
$629$	2.71998	+	2.28234i	0.108453	+	0.0910028i
$630$	0.900870	−	0.349098i	0.0358915	−	0.0139084i
$631$	−5.03370	−	28.5475i	−0.200388	−	1.13646i	−0.904533	−	0.426403i	$-0.859781\pi$
$631$	−5.03370	−	28.5475i	−0.200388	−	1.13646i	0.704145	−	0.710056i	$-0.251330\pi$
$632$	6.73529	+	1.18761i	0.267915	+	0.0472407i
$633$	21.7033	−	10.3943i	0.862629	−	0.413135i
$634$	−15.6694	−	27.1401i	−0.622310	−	1.07787i
$635$	−0.788005	+	1.36486i	−0.0312710	+	0.0541630i
$636$	9.92845	+	0.765527i	0.393689	+	0.0303551i
$637$	−10.5892	−	12.6198i	−0.419561	−	0.500013i
$638$	−5.11670	−	2.95413i	−0.202572	−	0.116955i
$639$	24.3387	−	14.7296i	0.962824	−	0.582692i
$640$	−0.0910823	+	0.250247i	−0.00360035	+	0.00989187i
$641$	−4.38869	+	24.8895i	−0.173343	+	0.983076i	0.766696	+	0.642010i	$0.221899\pi$
$641$	−4.38869	+	24.8895i	−0.173343	+	0.983076i	−0.940039	+	0.341066i	$0.889212\pi$
$642$	15.8256	−	23.1049i	0.624587	−	0.911879i
$643$	11.3227	−	4.12111i	0.446522	−	0.162521i	−0.108966	−	0.994046i	$-0.534754\pi$
$643$	11.3227	−	4.12111i	0.446522	−	0.162521i	0.555488	+	0.831525i	$0.312532\pi$
$644$	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	$0.815903\pi$
$648$	7.12714	+	5.49580i	0.279981	+	0.215895i
$649$	−10.2685	−	28.2126i	−0.403075	−	1.10744i
$650$	14.4409	−	2.54633i	0.566420	−	0.0998752i
$651$	−12.6423	−	17.6645i	−0.495492	−	0.692327i
$652$	3.27128	+	1.19065i	0.128113	+	0.0466293i
$653$	−2.53710	+	1.46480i	−0.0992846	+	0.0573220i	−0.548820	−	0.835940i	$-0.684923\pi$
$653$	−2.53710	+	1.46480i	−0.0992846	+	0.0573220i	0.449536	+	0.893262i	$0.351589\pi$
$654$	−8.50277	−	30.4720i	−0.332484	−	1.19155i
$655$	3.52536	−	2.95812i	0.137747	−	0.115583i
$656$	−8.49669	+	7.12957i	−0.331740	+	0.278363i
$657$	0.897474	+	0.493759i	0.0350138	+	0.0192634i
$658$	−2.02588	+	1.16964i	−0.0789771	+	0.0455975i
$659$	25.4128	+	9.24952i	0.989944	+	0.360310i	0.785699	−	0.618610i	$-0.212304\pi$
$659$	25.4128	+	9.24952i	0.989944	+	0.360310i	0.204245	+	0.978920i	$0.434526\pi$
$660$	0.881957	−	0.631209i	0.0343301	−	0.0245698i
$661$	13.9832	−	2.46561i	0.543883	−	0.0959013i	0.105045	−	0.994467i	$-0.466501\pi$
$661$	13.9832	−	2.46561i	0.543883	−	0.0959013i	0.438838	+	0.898566i	$0.355390\pi$
$662$	1.26619	+	3.47882i	0.0492118	+	0.135208i
$663$	0.450218	+	4.59915i	0.0174850	+	0.178616i
$664$			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
$669$	−17.8062	−	12.1963i	−0.688428	−	0.471536i
$670$	0.236593	−	1.34178i	0.00914038	−	0.0518377i
$671$	−0.711543	+	1.95495i	−0.0274688	+	0.0754700i
$672$	−0.521223	+	2.02870i	−0.0201066	+	0.0782589i
$673$	−4.68491	−	2.70483i	−0.180590	−	0.104264i	0.406980	−	0.913437i	$-0.366582\pi$
$673$	−4.68491	−	2.70483i	−0.180590	−	0.104264i	−0.587570	+	0.809173i	$0.699915\pi$
$674$	12.8807	+	15.3506i	0.496146	+	0.591284i
$675$	1.44181	−	25.5716i	0.0554952	−	0.984253i
$676$	−2.07487	+	3.59378i	−0.0798026	+	0.138222i
$677$	11.2154	+	19.4256i	0.431043	+	0.746588i	0.996963	−	0.0778720i	$-0.0248125\pi$
$677$	11.2154	+	19.4256i	0.431043	+	0.746588i	−0.565921	+	0.824460i	$0.691479\pi$
$678$	1.79570	+	3.74944i	0.0689636	+	0.143996i
$679$	7.19722	+	1.26906i	0.276204	+	0.0487022i
$680$	0.0414727	+	0.235203i	0.00159041	+	0.00901964i
$681$	−2.58585	−	1.17349i	−0.0990901	−	0.0449681i
$682$	−18.6799	−	15.6743i	−0.715290	−	0.600200i
$683$	−5.63051			−0.215446			−0.107723	−	0.994181i	$-0.534356\pi$
$683$	−5.63051			−0.215446			−0.107723	+	0.994181i	$0.534356\pi$
$684$	5.35395	+	11.9304i	0.204713	+	0.456172i
$685$	−4.87153			−0.186131
$686$	−11.6146	−	9.74584i	−0.443449	−	0.372098i
$687$	−19.1708	−	8.69991i	−0.731412	−	0.331922i
$688$	−0.834031	−	4.73003i	−0.0317971	−	0.180331i
$689$	−16.8437	−	2.97000i	−0.641694	−	0.113148i
$690$	1.12034	+	2.33927i	0.0426504	+	0.0890543i
$691$	8.10408	+	14.0367i	0.308294	+	0.533980i	0.977989	−	0.208655i	$-0.0669087\pi$
$691$	8.10408	+	14.0367i	0.308294	+	0.533980i	−0.669696	+	0.742636i	$0.733575\pi$
$692$	4.16651	−	7.21660i	0.158387	−	0.274334i
$693$	6.42019	−	5.61688i	0.243883	−	0.213368i
$694$	0.183420	+	0.218592i	0.00696254	+	0.00829763i
$695$	−0.530267	−	0.306150i	−0.0201142	−	0.0116129i
$696$	−1.08301	+	4.21529i	−0.0410515	+	0.159780i
$697$	−3.40218	+	9.34740i	−0.128867	+	0.354058i
$698$	2.42716	−	13.7651i	0.0918694	−	0.521017i
$699$	−3.44240	−	2.35786i	−0.130204	−	0.0891824i
$700$	5.60132	−	2.03871i	0.211710	−	0.0770561i
$701$	−25.1621	+	29.9870i	−0.950360	+	1.13260i	0.0406990	+	0.999171i	$0.487042\pi$
$701$	−25.1621	+	29.9870i	−0.950360	+	1.13260i	−0.991059	+	0.133424i	$0.957403\pi$
$702$	−11.2636	−	10.5872i	−0.425116	−	0.399589i
$703$	−15.3748	−	7.83829i	−0.579872	−	0.295627i
$704$			2.35132i			0.0886186i
$705$	−0.0869287	−	0.888009i	−0.00327392	−	0.0334443i
$706$	−7.01582	−	19.2758i	−0.264044	−	0.725455i
$707$	−12.3459	+	2.17692i	−0.464317	+	0.0818715i
$708$	−17.9845	+	12.8714i	−0.675901	+	0.483736i
$709$	−0.294067	−	0.107032i	−0.0110439	−	0.00401966i	0.336492	−	0.941686i	$-0.390759\pi$
$709$	−0.294067	−	0.107032i	−0.0110439	−	0.00401966i	−0.347536	+	0.937667i	$0.612982\pi$
$710$	−2.18703	+	1.26268i	−0.0820779	+	0.0473877i
$711$	−9.89008	+	17.9766i	−0.370907	+	0.674174i
$712$	9.42217	−	7.90614i	0.353111	−	0.296295i
$713$	44.6726	−	37.4847i	1.67300	−	1.40381i
$714$	0.504878	+	1.80937i	0.0188946	+	0.0677140i
$715$	−1.61325	+	0.931412i	−0.0603322	+	0.0348328i
$716$	8.48129	+	3.08694i	0.316961	+	0.115364i
$717$	19.2997	+	26.9665i	0.720760	+	1.00708i
$718$	−27.5586	+	4.85932i	−1.02848	+	0.181348i
$719$	9.97683	+	27.4111i	0.372073	+	1.02226i	0.974559	+	0.224132i	$0.0719548\pi$
$719$	9.97683	+	27.4111i	0.372073	+	1.02226i	−0.602486	+	0.798130i	$0.705823\pi$
$720$	−0.622471	−	0.500803i	−0.0231981	−	0.0186638i
$721$		−	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
$726$	−5.35519	+	7.81841i	−0.198750	+	0.290169i
$727$	1.39364	−	7.90374i	0.0516873	−	0.293133i	−0.947996	−	0.318281i	$-0.896894\pi$
$727$	1.39364	−	7.90374i	0.0516873	−	0.293133i	0.999684	+	0.0251476i	$0.00800557\pi$
$728$	1.23046	−	3.38067i	0.0456040	−	0.125296i
$729$	−22.5030	+	14.9203i	−0.833444	+	0.552604i
$730$	−0.0787468	−	0.0454645i	−0.00291455	−	0.00168272i
$731$	−2.76878	−	3.29971i	−0.102407	−	0.122044i
$732$	1.52796	+	0.117812i	0.0564750	+	0.00435447i
$733$	−8.60205	+	14.8992i	−0.317724	+	0.550314i	−0.980013	−	0.198935i	$-0.936252\pi$
$733$	−8.60205	+	14.8992i	−0.317724	+	0.550314i	0.662289	+	0.749249i	$0.269585\pi$
$734$	−0.761157	−	1.31836i	−0.0280948	−	0.0486617i
$735$	2.30367	−	1.10329i	0.0849722	−	0.0406954i
$736$	−5.53770	−	0.976446i	−0.204122	−	0.0359923i
$737$	−2.08896	−	11.8471i	−0.0769479	−	0.436393i
$738$	−12.0232	−	31.0268i	−0.442582	−	1.14211i
$739$	−19.8776	−	16.6793i	−0.731210	−	0.613558i	0.199251	−	0.979948i	$-0.436149\pi$
$739$	−19.8776	−	16.6793i	−0.731210	−	0.613558i	−0.930461	+	0.366390i	$0.880593\pi$
$740$	1.05435			0.0387587
$741$	−7.15569	−	21.2899i	−0.262871	−	0.782105i
$742$	−6.95259			−0.255237
$743$	35.8677	+	30.0966i	1.31586	+	1.10414i	0.987166	+	0.159700i	$0.0510527\pi$
$743$	35.8677	+	30.0966i	1.31586	+	1.10414i	0.328693	+	0.944437i	$0.393392\pi$
$744$	−7.42302	+	16.3571i	−0.272141	+	0.599680i
$745$	0.362158	+	2.05390i	0.0132684	+	0.0752491i
$746$	−4.70209	−	0.829106i	−0.172156	−	0.0303557i
$747$	−40.0817	−	13.6590i	−1.46651	−	0.499757i
$748$	1.05436	+	1.82621i	0.0385514	+	0.0667729i
$749$	−9.77655	+	16.9335i	−0.357227	+	0.618736i
$750$	−0.352082	+	4.56631i	−0.0128562	+	0.166738i
$751$	−1.93570	−	2.30687i	−0.0706346	−	0.0841791i	0.729570	−	0.683906i	$-0.239720\pi$
$751$	−1.93570	−	2.30687i	−0.0706346	−	0.0841791i	−0.800205	+	0.599727i	$0.795276\pi$
$752$	1.67524	+	0.967198i	0.0610895	+	0.0352701i
$753$	−7.07097	−	1.81670i	−0.257680	−	0.0662044i
$754$	2.55669	−	7.02444i	0.0931091	−	0.255815i
$755$	−0.514892	+	2.92010i	−0.0187389	+	0.106273i
$756$	−5.25641	−	3.44325i	−0.191174	−	0.125230i
$757$	6.18347	−	2.25060i	0.224742	−	0.0817994i	−0.227195	−	0.973849i	$-0.572955\pi$
$757$	6.18347	−	2.25060i	0.224742	−	0.0817994i	0.451937	+	0.892050i	$0.350733\pi$
$758$	−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	$0.929763\pi$
$762$	10.2015	−	0.998647i	0.369563	−	0.0361772i
$763$	7.55461	+	20.7561i	0.273495	+	0.751422i
$764$	7.22112	−	1.27328i	0.261251	−	0.0460656i
$765$	−0.708026	−	0.109837i	−0.0255987	−	0.00397116i
$766$	30.5956	+	11.1359i	1.10546	+	0.402356i
$767$	32.8968	−	18.9930i	1.18784	−	0.685797i
$768$	1.66832	−	0.465520i	0.0602003	−	0.0167980i
$769$	−28.1846	+	23.6497i	−1.01636	+	0.852830i	−0.989166	−	0.146800i	$-0.953103\pi$
$769$	−28.1846	+	23.6497i	−1.01636	+	0.852830i	−0.0271972	+	0.999630i	$0.508658\pi$
$770$	−0.580078	+	0.486743i	−0.0209045	+	0.0175410i
$771$	−29.6513	+	8.27376i	−1.06787	+	0.297972i
$772$	−1.55248	+	0.896322i	−0.0558748	+	0.0322593i
$773$	−15.8791	−	5.77952i	−0.571132	−	0.207875i	0.0402788	−	0.999188i	$-0.487175\pi$
$773$	−15.8791	−	5.77952i	−0.571132	−	0.207875i	−0.611411	+	0.791314i	$0.709398\pi$
$774$	14.2387	+	2.20886i	0.511799	+	0.0793958i
$775$	50.3416	−	8.87657i	1.80832	−	0.318856i
$776$	−2.06693	−	5.67885i	−0.0741986	−	0.203859i
$777$	8.25336	−	0.807936i	0.296088	−	0.0289845i
$778$			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
$783$	−10.9219	−	7.15448i	−0.390317	−	0.255680i
$784$	−0.961588	+	5.45344i	−0.0343424	+	0.194766i
$785$	−1.93296	+	5.31077i	−0.0689904	+	0.189550i
$786$	−28.9899	−	7.44821i	−1.03403	−	0.265669i
$787$	−19.2256	−	11.0999i	−0.685319	−	0.395669i	0.116537	−	0.993186i	$-0.462821\pi$
$787$	−19.2256	−	11.0999i	−0.685319	−	0.395669i	−0.801856	+	0.597517i	$0.796154\pi$
$788$	5.08627	+	6.06158i	0.181191	+	0.215935i
$789$	0.149170	−	1.93465i	0.00531059	−	0.0688754i
$790$	0.910662	−	1.57731i	0.0323999	−	0.0561183i
$791$	−1.45129	−	2.51372i	−0.0516021	−	0.0893774i
$792$	−6.67690	−	2.27535i	−0.237253	−	0.0808511i
$793$	−2.59220	−	0.457074i	−0.0920516	−	0.0162312i
$794$	−4.29868	−	24.3790i	−0.152555	−	0.865180i
$795$	1.09588	−	2.41484i	0.0388667	−	0.0856454i
$796$	−8.01318	−	6.72386i	−0.284020	−	0.238321i
$797$	−34.5294			−1.22309			−0.611547	−	0.791208i	$-0.709453\pi$
$797$	−34.5294			−1.22309			−0.611547	+	0.791208i	$0.709453\pi$
$798$	−4.36741	−	8.01777i	−0.154605	−	0.283826i
$799$	1.73482			0.0613736
$800$	−3.77589	−	3.16835i	−0.133498	−	0.112018i
$801$	13.3329	+	34.4063i	0.471093	+	1.21569i
$802$	1.10942	+	6.29183i	0.0391750	+	0.222172i
$803$	−0.790647	−	0.139412i	−0.0279013	−	0.00491976i
$804$	−7.99223	+	3.82769i	−0.281864	+	0.134992i
$805$	−0.905459	−	1.56830i	−0.0319132	−	0.0552753i
$806$	15.4261	−	26.7189i	0.543363	−	0.941132i
$807$	−33.6142	−	2.59180i	−1.18328	−	0.0912357i
$808$	6.66349	+	7.94123i	0.234421	+	0.279372i
$809$	19.0821	+	11.0171i	0.670892	+	0.387340i	0.796415	−	0.604751i	$-0.206727\pi$
$809$	19.0821	+	11.0171i	0.670892	+	0.387340i	−0.125523	+	0.992091i	$0.540061\pi$
$810$	2.02446	−	1.28297i	0.0711324	−	0.0450791i
$811$	−3.43077	+	9.42596i	−0.120471	+	0.330990i	−0.985240	−	0.171179i	$-0.945242\pi$
$811$	−3.43077	+	9.42596i	−0.120471	+	0.330990i	0.864769	+	0.502169i	$0.167465\pi$
$812$	0.527663	−	2.99253i	0.0185173	−	0.105017i
$813$	−0.311298	+	0.454486i	−0.0109177	+	0.0159395i
$814$	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
$819$	8.40918	+	6.76552i	0.293840	+	0.236406i
$820$	1.01025	+	2.77565i	0.0352795	+	0.0969297i
$821$	38.9746	−	6.87227i	1.36022	−	0.239844i	0.554523	−	0.832169i	$-0.312901\pi$
$821$	38.9746	−	6.87227i	1.36022	−	0.239844i	0.805699	+	0.592325i	$0.201790\pi$
$822$	18.4401	+	25.7654i	0.643171	+	0.898671i
$823$	35.1506	+	12.7938i	1.22527	+	0.445963i	0.871976	−	0.489548i	$-0.162838\pi$
$823$	35.1506	+	12.7938i	1.22527	+	0.445963i	0.353297	+	0.935511i	$0.385061\pi$
$824$	−12.7994	+	7.38973i	−0.445888	+	0.257433i
$825$	5.39530	+	19.3355i	0.187840	+	0.673177i
$826$	11.8287	−	9.92548i	0.411574	−	0.345351i
$827$	12.2053	−	10.2415i	0.424421	−	0.356132i	−0.405421	−	0.914130i	$-0.632875\pi$
$827$	12.2053	−	10.2415i	0.424421	−	0.356132i	0.829842	+	0.557998i	$0.188430\pi$
$828$	8.13155	−	14.7802i	0.282591	−	0.513647i
$829$	34.9707	−	20.1903i	1.21458	−	0.701239i	0.250828	−	0.968032i	$-0.419297\pi$
$829$	34.9707	−	20.1903i	1.21458	−	0.701239i	0.963754	+	0.266793i	$0.0859639\pi$
$830$	3.53224	+	1.28563i	0.122606	+	0.0446249i
$831$	30.8962	−	22.1121i	1.07178	−	0.767061i
$832$	−2.92974	+	0.516593i	−0.101571	+	0.0179096i
$833$	1.69856	+	4.66675i	0.0588515	+	0.161693i
$834$	0.387987	+	3.96343i	0.0134349	+	0.137242i
$835$		−	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	$-0.394411\pi$
$839$	34.2630	−	12.4707i	1.18289	−	0.430537i	0.857222	+	0.514947i	$0.172188\pi$
$840$	0.460202	+	0.315213i	0.0158785	+	0.0108759i
$841$	−3.93940	+	22.3415i	−0.135842	+	0.770396i
$842$	−11.8370	+	32.5219i	−0.407930	+	1.12078i
$843$	6.50306	−	25.3112i	0.223977	−	0.871764i
$844$	12.0320	+	6.94667i	0.414158	+	0.239114i
$845$	0.710347	+	0.846558i	0.0244367	+	0.0291225i
$846$	−4.36761	+	3.82112i	−0.150161	+	0.131373i
$847$	3.30826	−	5.73007i	0.113673	−	0.196888i
$848$	2.87460	+	4.97896i	0.0987143	+	0.170978i
$849$	−4.96813	−	10.3735i	−0.170506	−	0.356017i
$850$	−4.35338	−	0.767619i	−0.149320	−	0.0263291i
$851$	3.86590	+	21.9246i	0.132521	+	0.751566i
$852$	14.9568	+	6.78756i	0.512412	+	0.232538i
$853$	−1.13152	−	0.949455i	−0.0387424	−	0.0325087i	0.623211	−	0.782054i	$-0.285828\pi$
$853$	−1.13152	−	0.949455i	−0.0387424	−	0.0325087i	−0.661953	+	0.749545i	$0.730272\pi$
$854$	−1.06998			−0.0366141
$855$	3.47320	−	0.253156i	0.118781	−	0.00865776i
$856$	16.1688			0.552637
$857$	−33.3088	−	27.9494i	−1.13781	−	0.954734i	−0.138443	−	0.990370i	$-0.544210\pi$
$857$	−33.3088	−	27.9494i	−1.13781	−	0.954734i	−0.999365	+	0.0356363i	$0.988654\pi$
$858$	11.0328	+	5.00681i	0.376654	+	0.170930i
$859$	−3.97170	−	22.5246i	−0.135513	−	0.768530i	−0.974501	−	0.224381i	$-0.927964\pi$
$859$	−3.97170	−	22.5246i	−0.135513	−	0.768530i	0.838989	−	0.544149i	$-0.183147\pi$
$860$	−1.25964	−	0.222108i	−0.0429533	−	0.00757383i
$861$	10.0351	+	20.9534i	0.341995	+	0.714088i
$862$	16.0755	+	27.8435i	0.547532	+	0.948354i
$863$	2.34962	−	4.06966i	0.0799820	−	0.138533i	−0.823260	−	0.567665i	$-0.807847\pi$
$863$	2.34962	−	4.06966i	0.0799820	−	0.138533i	0.903242	+	0.429132i	$0.141180\pi$
$864$	−0.292510	+	5.18791i	−0.00995140	+	0.176496i
$865$	−1.42644	−	1.69996i	−0.0485003	−	0.0578004i
$866$	19.9807	+	11.5359i	0.678972	+	0.392005i
$867$	−6.98047	+	27.1694i	−0.237069	+	0.922720i
$868$	4.28943	−	11.7851i	0.145593	−	0.400013i
$869$	2.79245	−	15.8368i	0.0947275	−	0.537227i
$870$	0.956220	+	0.654959i	0.0324189	+	0.0222052i
$871$	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
$876$	0.0576176	+	0.588585i	0.00194672	+	0.0198865i
$877$	5.78823	+	15.9030i	0.195455	+	0.537007i	0.998243	−	0.0592572i	$-0.0188732\pi$
$877$	5.78823	+	15.9030i	0.195455	+	0.537007i	−0.802788	+	0.596264i	$0.796651\pi$
$878$	−11.6031	+	2.04594i	−0.391586	+	0.0690471i
$879$	40.0090	−	28.6341i	1.34947	−	0.965803i
$880$	0.588409	+	0.214163i	0.0198353	+	0.00721945i
$881$	−8.11257	+	4.68379i	−0.273319	+	0.157801i	−0.630395	−	0.776274i	$-0.717107\pi$
$881$	−8.11257	+	4.68379i	−0.273319	+	0.157801i	0.357076	+	0.934075i	$0.383774\pi$
$882$	−14.5553	−	8.00781i	−0.490102	−	0.269637i
$883$	−9.97646	+	8.37124i	−0.335735	+	0.281715i	−0.795032	−	0.606568i	$-0.792546\pi$
$883$	−9.97646	+	8.37124i	−0.335735	+	0.281715i	0.459297	+	0.888283i	$0.348101\pi$
$884$	−2.04382	+	1.71496i	−0.0687409	+	0.0576805i
$885$	1.58295	+	5.67293i	0.0532101	+	0.190693i
$886$	−18.4426	+	10.6479i	−0.619593	+	0.357722i
$887$	−19.4826	−	7.09109i	−0.654162	−	0.238095i	−0.00644793	−	0.999979i	$-0.502052\pi$
$887$	−19.4826	−	7.09109i	−0.654162	−	0.238095i	−0.647714	+	0.761884i	$0.724275\pi$
$888$	−3.99101	−	5.57644i	−0.133929	−	0.187133i
$889$	−7.04801	+	1.24275i	−0.236383	+	0.0416806i
$890$	−1.12029	−	3.07798i	−0.0375523	−	0.103174i
$891$	12.9224	−	16.7582i	0.432916	−	0.561420i
$892$		−	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
$897$	−16.3734	+	23.9047i	−0.546693	+	0.798155i
$898$	−2.07093	+	11.7448i	−0.0691078	+	0.391930i
$899$	8.91269	−	24.4874i	0.297255	−	0.816701i
$900$	12.6509	−	7.65620i	0.421696	−	0.255207i
$901$	4.46527	+	2.57803i	0.148760	+	0.0858865i
$902$	16.7639	+	19.9784i	0.558176	+	0.665208i
$903$	−10.0305	−	0.773398i	−0.333795	−	0.0257371i
$904$	−1.20010	+	2.07863i	−0.0399147	+	0.0691343i
$905$	1.22421	+	2.12039i	0.0406940	+	0.0704840i
$906$	17.3933	−	8.33012i	0.577855	−	0.276750i
$907$	−13.6673	−	2.40991i	−0.453815	−	0.0800198i	−0.0579313	−	0.998321i	$-0.518450\pi$
$907$	−13.6673	−	2.40991i	−0.453815	−	0.0800198i	−0.395883	+	0.918301i	$0.629562\pi$
$908$	−0.284693	−	1.61457i	−0.00944787	−	0.0535815i
$909$	−28.9985	+	11.2373i	−0.961819	+	0.372716i
$910$	−0.733927	−	0.615838i	−0.0243294	−	0.0204148i
$911$	−16.4560			−0.545212			−0.272606	−	0.962126i	$-0.587885\pi$
$911$	−16.4560			−0.545212			−0.272606	+	0.962126i	$0.587885\pi$
$912$	−3.93603	+	6.44265i	−0.130335	+	0.213337i
$913$	33.1889			1.09839
$914$	14.6574	+	12.2990i	0.484823	+	0.406815i
$915$	0.168652	−	0.371636i	0.00557547	−	0.0122859i
$916$	−2.11064	−	11.9700i	−0.0697374	−	0.395501i
$917$	20.5805	+	3.62890i	0.679629	+	0.119837i
$918$	2.09915	+	4.16050i	0.0692822	+	0.137317i
$919$	−26.4636	−	45.8364i	−0.872955	−	1.51200i	−0.858926	−	0.512100i	$-0.828868\pi$
$919$	−26.4636	−	45.8364i	−0.872955	−	1.51200i	−0.0140292	−	0.999902i	$-0.504466\pi$
$920$	−0.748739	+	1.29685i	−0.0246852	+	0.0427560i
$921$	−0.580457	+	7.52819i	−0.0191267	+	0.248062i
$922$	19.3700	+	23.0842i	0.637916	+	0.760239i
$923$	−24.4315	−	14.1056i	−0.804174	−	0.464290i
$924$	4.77012	+	1.22556i	0.156926	+	0.0403180i
$925$	−6.67453	+	18.3381i	−0.219457	+	0.602953i
$926$	4.44179	−	25.1907i	0.145966	−	0.827817i
$927$	−8.59832	−	43.4966i	−0.282406	−	1.42862i
$928$	−2.36121	+	0.859409i	−0.0775104	+	0.0282115i
$929$	−35.2607	+	42.0221i	−1.15687	+	1.37870i	−0.244337	+	0.969690i	$0.578570\pi$
$929$	−35.2607	+	42.0221i	−1.15687	+	1.37870i	−0.912530	+	0.409010i	$0.865874\pi$
$930$	3.41720	+	3.34743i	0.112055	+	0.109767i
$931$	−13.1417	−	20.2466i	−0.430702	−	0.663555i
$932$		−	2.40898i		−	0.0789089i
$933$	−8.18253	+	0.801002i	−0.267884	+	0.0262236i
$934$	9.73308	+	26.7414i	0.318476	+	0.875006i
$935$	0.553038	−	0.0975154i	0.0180863	−	0.00318910i
$936$	1.36815	−	8.81933i	0.0447194	−	0.288269i
$937$	−50.8597	−	18.5114i	−1.66151	−	0.604741i	−0.670914	−	0.741536i	$-0.734098\pi$
$937$	−50.8597	−	18.5114i	−1.66151	−	0.604741i	−0.990599	+	0.136794i	$0.956320\pi$
$938$	5.35819	−	3.09355i	0.174951	−	0.101008i
$939$	31.5836	−	8.81294i	1.03069	−	0.287600i
$940$	0.394622	−	0.331127i	0.0128712	−	0.0108002i
$941$	3.61129	−	3.03024i	0.117725	−	0.0987829i	−0.582025	−	0.813171i	$-0.697739\pi$
$941$	3.61129	−	3.03024i	0.117725	−	0.0987829i	0.699750	+	0.714388i	$0.253295\pi$
$942$	35.4053	−	9.87933i	1.15357	−	0.321886i
$943$	−54.0137	+	31.1848i	−1.75893	+	1.01552i
$944$	−11.9986	−	4.36714i	−0.390522	−	0.142138i
$945$	−1.34043	+	1.00178i	−0.0436041	+	0.0325879i
$946$	−11.1218	+	1.96107i	−0.361601	+	0.0637600i
$947$	−3.75659	−	10.3211i	−0.122073	−	0.335392i	0.863572	−	0.504226i	$-0.168222\pi$
$947$	−3.75659	−	10.3211i	−0.122073	−	0.335392i	−0.985645	+	0.168834i	$0.946000\pi$
$948$	−11.7895	+	1.15409i	−0.382904	+	0.0374832i
$949$		−	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	$-0.593775\pi$
$953$	3.15832	−	1.14953i	0.102308	−	0.0372371i	0.392667	+	0.919681i	$0.371552\pi$
$954$	−16.9202	+	3.34475i	−0.547812	+	0.108290i
$955$	0.339083	−	1.92303i	0.0109725	−	0.0622279i
$956$	−6.54821	+	17.9910i	−0.211784	+	0.581872i
$957$	9.91150	+	2.54650i	0.320393	+	0.0823168i
$958$	−10.7014	−	6.17844i	−0.345745	−	0.199616i
$959$	−14.2196	−	16.9463i	−0.459176	−	0.547225i
$960$	0.0354597	−	0.459892i	0.00114446	−	0.0148430i
$961$	38.2760	−	66.2960i	1.23471	−	2.13858i
$962$	5.88913	+	10.2003i	0.189873	+	0.328870i
$963$	−15.6464	+	45.9135i	−0.504198	+	1.47954i
$964$	4.13200	+	0.728583i	0.133083	+	0.0234661i
$965$	0.0828985	+	0.470141i	0.00266860	+	0.0151344i
$966$	−4.86729	+	10.7254i	−0.156603	+	0.345084i
$967$	−14.0085	−	11.7545i	−0.450482	−	0.377999i	0.389133	−	0.921182i	$-0.372775\pi$
$967$	−14.0085	−	11.7545i	−0.450482	−	0.377999i	−0.839615	+	0.543183i	$0.817219\pi$
$968$	−5.47131			−0.175854
$969$	−0.168044	+	6.76882i	−0.00539835	+	0.217446i
$970$	−1.60938			−0.0516739
$971$	−24.2199	−	20.3229i	−0.777254	−	0.652193i	0.165302	−	0.986243i	$-0.447140\pi$
$971$	−24.2199	−	20.3229i	−0.777254	−	0.652193i	−0.942555	+	0.334050i	$0.891585\pi$
$972$	−14.4488	−	5.85093i	−0.463444	−	0.187669i
$973$	−0.482826	−	2.73824i	−0.0154787	−	0.0877839i
$974$	−27.6832	−	4.88130i	−0.887028	−	0.156407i
$975$	−22.9067	+	10.9706i	−0.733603	+	0.351341i
$976$	0.442393	+	0.766248i	0.0141607	+	0.0245270i
$977$	−24.2192	+	41.9488i	−0.774839	+	1.34206i	0.160045	+	0.987110i	$0.448836\pi$
$977$	−24.2192	+	41.9488i	−0.774839	+	1.34206i	−0.934885	+	0.354952i	$0.884497\pi$
$978$	−6.01180	−	0.463536i	−0.192236	−	0.0148223i
$979$	−18.5898	−	22.1545i	−0.594134	−	0.708061i
$980$	1.27712	+	0.737346i	0.0407961	+	0.0235536i
$981$	28.3707	+	46.8789i	0.905806	+	1.49673i
$982$	−1.17147	+	3.21859i	−0.0373832	+	0.102709i
$983$	4.70703	−	26.6949i	0.150131	−	0.851435i	−0.812972	−	0.582303i	$-0.802152\pi$
$983$	4.70703	−	26.6949i	0.150131	−	0.851435i	0.963103	−	0.269133i	$-0.0867370\pi$
$984$	10.8562	−	15.8498i	0.346084	−	0.505272i
$985$	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
$990$	−1.17755	+	1.46363i	−0.0374249	+	0.0465171i
$991$	16.6261	+	45.6797i	0.528144	+	1.45106i	0.861253	+	0.508176i	$0.169680\pi$
$991$	16.6261	+	45.6797i	0.528144	+	1.45106i	−0.333109	+	0.942888i	$0.608098\pi$
$992$	−10.2132	+	1.80086i	−0.324269	+	0.0571773i
$993$	−3.73186	−	5.21435i	−0.118427	−	0.165472i
$994$	−10.7762	−	3.92222i	−0.341801	−	0.124405i
$995$	−2.41248	+	1.39285i	−0.0764808	+	0.0441562i
$996$	−6.57083	−	23.5484i	−0.208205	−	0.746159i
$997$	−7.46423	+	6.26323i	−0.236394	+	0.198358i	−0.753287	−	0.657692i	$-0.771533\pi$
$997$	−7.46423	+	6.26323i	−0.236394	+	0.198358i	0.516893	+	0.856050i	$0.327089\pi$
$998$	−29.3171	+	24.6000i	−0.928018	+	0.778699i
$999$	19.6972	−	5.93676i	0.623191	−	0.187831i

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
114.2.l.a.41.3	✓	18	1.1	even	1	trivial
114.2.l.a.89.3	yes	18	57.32	even	18	inner
114.2.l.b.41.1	yes	18	3.2	odd	2
114.2.l.b.89.1	yes	18	19.13	odd	18
912.2.cc.c.497.3		18	12.11	even	2
912.2.cc.c.545.3		18	76.51	even	18
912.2.cc.d.497.1		18	4.3	odd	2
912.2.cc.d.545.1		18	228.203	odd	18

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)

\(f(q)\)	\(=\)	\(q+(-0.766044 - 0.642788i) q^{2} +(1.57724 + 0.715766i) q^{3} +(0.173648 + 0.984808i) q^{4} +(0.262261 + 0.0462437i) q^{5} +(-0.748148 - 1.56214i) q^{6} +(0.604656 + 1.04730i) q^{7} +(0.500000 - 0.866025i) q^{8} +(1.97536 + 2.25787i) q^{9} +O(q^{10})\)	\(q+(-0.766044 - 0.642788i) q^{2} +(1.57724 + 0.715766i) q^{3} +(0.173648 + 0.984808i) q^{4} +(0.262261 + 0.0462437i) q^{5} +(-0.748148 - 1.56214i) q^{6} +(0.604656 + 1.04730i) q^{7} +(0.500000 - 0.866025i) q^{8} +(1.97536 + 2.25787i) q^{9} +(-0.171179 - 0.204003i) q^{10} +(-2.03630 - 1.17566i) q^{11} +(-0.431008 + 1.67757i) q^{12} +(1.01749 - 2.79553i) q^{13} +(0.209995 - 1.19094i) q^{14} +(0.380548 + 0.260655i) 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} +(0.204068 + 2.08463i) q^{21} +(0.804198 + 2.20952i) q^{22} +(-5.53770 + 0.976446i) q^{23} +(1.40849 - 1.00804i) q^{24} +(-4.63182 - 1.68584i) q^{25} +(-2.57637 + 1.48747i) q^{26} +(1.49950 + 4.97509i) q^{27} +(-0.926387 + 0.777331i) q^{28} +(-1.92487 + 1.61516i) q^{29} +(-0.123971 - 0.444285i) q^{30} +(-8.98131 + 5.18536i) q^{31} +(0.939693 + 0.342020i) q^{32} +(-2.37023 - 3.31181i) q^{33} +(0.883204 - 0.155733i) q^{34} +(0.110147 + 0.302626i) q^{35} +(-1.88055 + 2.33742i) 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} +(1.18365 - 1.72809i) q^{42} +(-0.834031 + 4.73003i) q^{43} +(0.804198 - 2.20952i) q^{44} +(0.413647 + 0.683499i) q^{45} +(4.86977 + 2.81156i) q^{46} +(-1.24341 - 1.48183i) q^{47} +(-1.72693 - 0.133153i) q^{48} +(2.76878 - 4.79567i) q^{49} +(2.46454 + 4.26871i) q^{50} +(-1.40097 + 0.670961i) q^{51} +(2.92974 + 0.516593i) q^{52} +(-0.998339 - 5.66186i) q^{53} +(2.04924 - 4.77500i) q^{54} +(-0.479676 - 0.402496i) q^{55} +1.20931 q^{56} +(5.90217 - 4.70791i) q^{57} +2.51274 q^{58} +(9.78136 + 8.20754i) q^{59} +(-0.190614 + 0.420029i) q^{60} +(-0.153642 - 0.871345i) q^{61} +(10.2132 + 1.80086i) q^{62} +(-1.17024 + 3.43401i) q^{63} +(-0.500000 - 0.866025i) q^{64} +(0.396123 - 0.686106i) q^{65} +(-0.313086 + 4.06055i) q^{66} +(3.28864 + 3.91925i) q^{67} +(-0.776676 - 0.448414i) q^{68} +(-9.43317 - 2.42361i) q^{69} +(0.110147 - 0.302626i) q^{70} +(1.64669 - 9.33885i) q^{71} +(2.94305 - 0.581775i) 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} +(-5.12823 + 0.502012i) q^{78} +(2.33914 + 6.42674i) q^{79} +(-0.262261 + 0.0462437i) q^{80} +(-1.19593 + 8.92019i) q^{81} +(-10.4227 - 3.79356i) q^{82} +(-12.2240 + 7.05752i) q^{83} +(-2.01752 + 0.562959i) q^{84} +(-0.182956 + 0.153518i) q^{85} +(3.67931 - 3.08731i) q^{86} +(-4.19206 + 1.16973i) q^{87} +(-2.03630 + 1.17566i) q^{88} +(11.5580 + 4.20677i) q^{89} +(0.122472 - 0.789478i) q^{90} +(3.54297 - 0.624722i) q^{91} +(-1.92322 - 5.28401i) q^{92} +(-17.8772 + 1.75003i) 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} +(-1.36794 - 6.92004i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q + 3 q^{6} + 9 q^{8}+O(q^{10}) \) 18 * q + 3 * q^6 + 9 * q^8	\( 18 q + 3 q^{6} + 9 q^{8} - 12 q^{13} + 12 q^{14} - 24 q^{15} - 6 q^{17} - 6 q^{19} - 24 q^{22} - 18 q^{25} - 18 q^{26} - 3 q^{27} + 6 q^{28} + 6 q^{29} - 27 q^{33} - 6 q^{34} + 24 q^{35} - 3 q^{36} - 3 q^{38} + 6 q^{39} - 3 q^{41} - 6 q^{43} - 24 q^{44} + 54 q^{45} + 18 q^{46} - 30 q^{47} + 6 q^{48} + 21 q^{49} - 3 q^{50} - 33 q^{51} - 6 q^{52} + 60 q^{53} + 30 q^{55} + 12 q^{57} + 12 q^{58} - 3 q^{59} + 18 q^{60} + 54 q^{61} - 6 q^{62} + 84 q^{63} - 9 q^{64} - 24 q^{65} + 30 q^{66} - 15 q^{67} + 27 q^{68} + 24 q^{69} + 24 q^{70} - 36 q^{71} - 42 q^{73} - 6 q^{74} - 18 q^{78} - 6 q^{79} + 3 q^{82} - 36 q^{83} - 24 q^{84} + 6 q^{86} - 54 q^{87} + 60 q^{89} - 12 q^{90} - 18 q^{91} - 84 q^{93} - 6 q^{95} + 9 q^{97} - 12 q^{98} - 30 q^{99}+O(q^{100}) \) 18 * q + 3 * q^6 + 9 * q^8 - 12 * q^13 + 12 * q^14 - 24 * q^15 - 6 * q^17 - 6 * q^19 - 24 * q^22 - 18 * q^25 - 18 * q^26 - 3 * q^27 + 6 * q^28 + 6 * q^29 - 27 * q^33 - 6 * q^34 + 24 * q^35 - 3 * q^36 - 3 * q^38 + 6 * q^39 - 3 * q^41 - 6 * q^43 - 24 * q^44 + 54 * q^45 + 18 * q^46 - 30 * q^47 + 6 * q^48 + 21 * q^49 - 3 * q^50 - 33 * q^51 - 6 * q^52 + 60 * q^53 + 30 * q^55 + 12 * q^57 + 12 * q^58 - 3 * q^59 + 18 * q^60 + 54 * q^61 - 6 * q^62 + 84 * q^63 - 9 * q^64 - 24 * q^65 + 30 * q^66 - 15 * q^67 + 27 * q^68 + 24 * q^69 + 24 * q^70 - 36 * q^71 - 42 * q^73 - 6 * q^74 - 18 * q^78 - 6 * q^79 + 3 * q^82 - 36 * q^83 - 24 * q^84 + 6 * q^86 - 54 * q^87 + 60 * q^89 - 12 * q^90 - 18 * q^91 - 84 * q^93 - 6 * q^95 + 9 * q^97 - 12 * q^98 - 30 * q^99

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