LMFDB - Embedded newform 162.2.g.a.31.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [162,2,Mod(7,162)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(162, base_ring=CyclotomicField(54))

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

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

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

chi := DirichletCharacter("162.7");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 162 = 2 \cdot 3^{4} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	162.g (of order $27$, degree $18$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$1.29357651274$
Analytic rank:	$0$
Dimension:	$72$
Relative dimension:	$4$ over $\Q(\zeta_{27})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{27}]$

Embedding invariants

Embedding label			31.3
Character	$\chi$	$=$	162.31
Dual form			162.2.g.a.115.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.396080 - 0.918216i) q^{2} +(1.05738 + 1.37184i) q^{3} +(-0.686242 + 0.727374i) q^{4} +(-0.141847 + 2.43542i) q^{5} +(0.840836 - 1.51426i) q^{6} +(-0.675743 + 0.160154i) q^{7} +(0.939693 + 0.342020i) q^{8} +(-0.763881 + 2.90112i) q^{9} +O(q^{10})$	\(q+(-0.396080 - 0.918216i) q^{2} +(1.05738 + 1.37184i) q^{3} +(-0.686242 + 0.727374i) q^{4} +(-0.141847 + 2.43542i) q^{5} +(0.840836 - 1.51426i) q^{6} +(-0.675743 + 0.160154i) q^{7} +(0.939693 + 0.342020i) q^{8} +(-0.763881 + 2.90112i) q^{9} +(2.29243 - 0.834375i) q^{10} +(-1.56143 + 1.02697i) q^{11} +(-1.72346 - 0.172300i) q^{12} +(4.35581 - 0.509122i) q^{13} +(0.414704 + 0.557045i) q^{14} +(-3.49099 + 2.38058i) q^{15} +(-0.0581448 - 0.998308i) q^{16} +(-3.09677 - 2.59850i) q^{17} +(2.96641 - 0.447666i) q^{18} +(6.05044 - 5.07693i) q^{19} +(-1.67412 - 1.77446i) q^{20} +(-0.934225 - 0.757666i) q^{21} +(1.56143 + 1.02697i) q^{22} +(2.63822 + 0.625269i) q^{23} +(0.524419 + 1.65075i) q^{24} +(-0.944964 - 0.110450i) q^{25} +(-2.19273 - 3.79792i) q^{26} +(-4.78758 + 2.01967i) q^{27} +(0.347231 - 0.601422i) q^{28} +(0.986496 - 1.32509i) q^{29} +(3.56860 + 2.26258i) q^{30} +(-2.29559 - 7.66782i) q^{31} +(-0.893633 + 0.448799i) q^{32} +(-3.05986 - 1.05613i) q^{33} +(-1.15942 + 3.87272i) q^{34} +(-0.294190 - 1.66844i) q^{35} +(-1.58599 - 2.54650i) q^{36} +(-1.07416 + 6.09184i) q^{37} +(-7.05817 - 3.54475i) q^{38} +(5.30420 + 5.43713i) q^{39} +(-0.966256 + 2.24003i) q^{40} +(-2.57993 + 5.98096i) q^{41} +(-0.325674 + 1.15792i) q^{42} +(-3.81384 - 1.91538i) q^{43} +(0.324528 - 1.84049i) q^{44} +(-6.95709 - 2.27189i) q^{45} +(-0.470813 - 2.67011i) q^{46} +(0.986899 - 3.29647i) q^{47} +(1.30804 - 1.13536i) q^{48} +(-5.82445 + 2.92515i) q^{49} +(0.272864 + 0.911429i) q^{50} +(0.290247 - 6.99588i) q^{51} +(-2.61882 + 3.51768i) q^{52} +(5.32106 - 9.21634i) q^{53} +(3.75076 + 3.59608i) q^{54} +(-2.27961 - 3.94840i) q^{55} +(-0.689767 - 0.0806222i) q^{56} +(13.3624 + 2.93198i) q^{57} +(-1.60745 - 0.380973i) q^{58} +(-5.75027 - 3.78201i) q^{59} +(0.664091 - 4.17291i) q^{60} +(7.31570 + 7.75419i) q^{61} +(-6.13147 + 5.14492i) q^{62} +(0.0515617 - 2.08275i) q^{63} +(0.766044 + 0.642788i) q^{64} +(0.622066 + 10.6805i) q^{65} +(0.242194 + 3.22792i) q^{66} +(-6.33676 - 8.51174i) q^{67} +(4.01521 - 0.469311i) q^{68} +(1.93184 + 4.28036i) q^{69} +(-1.41546 + 0.930964i) q^{70} +(7.97798 - 2.90375i) q^{71} +(-1.71005 + 2.46490i) q^{72} +(2.86854 + 1.04406i) q^{73} +(6.01908 - 1.42655i) q^{74} +(-0.847669 - 1.41313i) q^{75} +(-0.459245 + 7.88493i) q^{76} +(0.890651 - 0.944035i) q^{77} +(2.89158 - 7.02394i) q^{78} +(3.88894 + 9.01558i) q^{79} +2.43955 q^{80} +(-7.83297 - 4.43222i) q^{81} +6.51367 q^{82} +(2.85728 + 6.62392i) q^{83} +(1.19221 - 0.159589i) q^{84} +(6.76771 - 7.17335i) q^{85} +(-0.248150 + 4.26057i) q^{86} +(2.86092 - 0.0478192i) q^{87} +(-1.81850 + 0.430993i) q^{88} +(17.4051 + 6.33493i) q^{89} +(0.669479 + 7.28796i) q^{90} +(-2.86187 + 1.04164i) q^{91} +(-2.26526 + 1.48989i) q^{92} +(8.09168 - 11.2570i) q^{93} +(-3.41776 + 0.399479i) q^{94} +(11.5062 + 15.4555i) q^{95} +(-1.56059 - 0.751367i) q^{96} +(-0.260900 - 4.47948i) q^{97} +(4.99286 + 4.18951i) q^{98} +(-1.78661 - 5.31436i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 72 q + 9 q^{6}+O(q^{10}) $ 72 * q + 9 * q^6	$ 72 q + 9 q^{6} + 18 q^{13} - 9 q^{20} - 81 q^{23} + 18 q^{25} - 27 q^{26} - 27 q^{27} + 18 q^{28} - 27 q^{29} - 63 q^{30} - 54 q^{31} + 9 q^{33} - 27 q^{35} - 9 q^{36} + 9 q^{38} - 9 q^{41} + 9 q^{42} + 36 q^{43} - 117 q^{45} - 18 q^{46} - 27 q^{47} + 9 q^{48} - 27 q^{51} - 36 q^{52} - 27 q^{53} + 54 q^{55} + 27 q^{57} + 9 q^{58} - 18 q^{59} + 9 q^{63} + 9 q^{65} + 36 q^{66} - 135 q^{67} - 18 q^{68} + 108 q^{69} + 18 q^{70} + 72 q^{71} + 54 q^{72} + 36 q^{73} + 99 q^{74} - 36 q^{75} - 9 q^{76} + 144 q^{77} + 90 q^{78} - 9 q^{79} + 18 q^{80} - 72 q^{82} + 99 q^{83} + 18 q^{84} + 9 q^{85} + 72 q^{86} + 207 q^{87} - 9 q^{88} + 126 q^{89} - 18 q^{90} + 63 q^{91} + 36 q^{92} + 81 q^{93} + 18 q^{94} + 45 q^{95} - 171 q^{97} + 36 q^{98} + 99 q^{99}+O(q^{100}) $ 72 * q + 9 * q^6 + 18 * q^13 - 9 * q^20 - 81 * q^23 + 18 * q^25 - 27 * q^26 - 27 * q^27 + 18 * q^28 - 27 * q^29 - 63 * q^30 - 54 * q^31 + 9 * q^33 - 27 * q^35 - 9 * q^36 + 9 * q^38 - 9 * q^41 + 9 * q^42 + 36 * q^43 - 117 * q^45 - 18 * q^46 - 27 * q^47 + 9 * q^48 - 27 * q^51 - 36 * q^52 - 27 * q^53 + 54 * q^55 + 27 * q^57 + 9 * q^58 - 18 * q^59 + 9 * q^63 + 9 * q^65 + 36 * q^66 - 135 * q^67 - 18 * q^68 + 108 * q^69 + 18 * q^70 + 72 * q^71 + 54 * q^72 + 36 * q^73 + 99 * q^74 - 36 * q^75 - 9 * q^76 + 144 * q^77 + 90 * q^78 - 9 * q^79 + 18 * q^80 - 72 * q^82 + 99 * q^83 + 18 * q^84 + 9 * q^85 + 72 * q^86 + 207 * q^87 - 9 * q^88 + 126 * q^89 - 18 * q^90 + 63 * q^91 + 36 * q^92 + 81 * q^93 + 18 * q^94 + 45 * q^95 - 171 * q^97 + 36 * q^98 + 99 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$83$
$\chi(n)$	$e\left(\frac{10}{27}\right)$

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 $

$2$	−0.396080	−	0.918216i	−0.280071	−	0.649277i
$2$	−0.396080	−	0.918216i	−0.280071	−	0.649277i
$3$	1.05738	+	1.37184i	0.610481	+	0.792031i
$3$	1.05738	+	1.37184i	0.610481	+	0.792031i
$4$	−0.686242	+	0.727374i	−0.343121	+	0.363687i
$5$	−0.141847	+	2.43542i	−0.0634360	+	1.08915i	0.804975	+	0.593309i	$0.202179\pi$
$5$	−0.141847	+	2.43542i	−0.0634360	+	1.08915i	−0.868411	+	0.495845i	$0.834858\pi$
$6$	0.840836	−	1.51426i	0.343270	−	0.618196i
$7$	−0.675743	+	0.160154i	−0.255407	+	0.0605326i	−0.356325	−	0.934362i	$-0.615970\pi$
$7$	−0.675743	+	0.160154i	−0.255407	+	0.0605326i	0.100918	+	0.994895i	$0.467822\pi$
$8$	0.939693	+	0.342020i	0.332232	+	0.120922i
$9$	−0.763881	+	2.90112i	−0.254627	+	0.967039i
$10$	2.29243	−	0.834375i	0.724929	−	0.263852i
$11$	−1.56143	+	1.02697i	−0.470788	+	0.309642i	−0.762642	−	0.646821i	$-0.776098\pi$
$11$	−1.56143	+	1.02697i	−0.470788	+	0.309642i	0.291854	+	0.956463i	$0.405728\pi$
$12$	−1.72346	−	0.172300i	−0.497520	−	0.0497387i
$13$	4.35581	−	0.509122i	1.20809	−	0.141205i	0.511886	−	0.859053i	$-0.328947\pi$
$13$	4.35581	−	0.509122i	1.20809	−	0.141205i	0.696199	+	0.717849i	$0.254873\pi$
$14$	0.414704	+	0.557045i	0.110834	+	0.148876i
$15$	−3.49099	+	2.38058i	−0.901370	+	0.614664i
$16$	−0.0581448	−	0.998308i	−0.0145362	−	0.249577i
$17$	−3.09677	−	2.59850i	−0.751077	−	0.630228i	0.184711	−	0.982793i	$-0.440865\pi$
$17$	−3.09677	−	2.59850i	−0.751077	−	0.630228i	−0.935787	+	0.352565i	$0.885310\pi$
$18$	2.96641	−	0.447666i	0.699190	−	0.105516i
$19$	6.05044	−	5.07693i	1.38807	−	1.16473i	0.421951	−	0.906619i	$-0.361345\pi$
$19$	6.05044	−	5.07693i	1.38807	−	1.16473i	0.966116	−	0.258108i	$-0.0830991\pi$
$20$	−1.67412	−	1.77446i	−0.374345	−	0.396782i
$21$	−0.934225	−	0.757666i	−0.203865	−	0.165336i
$22$	1.56143	+	1.02697i	0.332897	+	0.218950i
$23$	2.63822	+	0.625269i	0.550107	+	0.130378i	0.496264	−	0.868172i	$-0.334705\pi$
$23$	2.63822	+	0.625269i	0.550107	+	0.130378i	0.0538429	+	0.998549i	$0.482853\pi$
$24$	0.524419	+	1.65075i	0.107047	+	0.336959i
$25$	−0.944964	−	0.110450i	−0.188993	−	0.0220901i
$26$	−2.19273	−	3.79792i	−0.430030	−	0.744834i
$27$	−4.78758	+	2.01967i	−0.921370	+	0.388686i
$28$	0.347231	−	0.601422i	0.0656205	−	0.113658i
$29$	0.986496	−	1.32509i	0.183188	−	0.246064i	−0.701038	−	0.713124i	$-0.747280\pi$
$29$	0.986496	−	1.32509i	0.183188	−	0.246064i	0.884225	+	0.467060i	$0.154687\pi$
$30$	3.56860	+	2.26258i	0.651534	+	0.413089i
$31$	−2.29559	−	7.66782i	−0.412301	−	1.37718i	−0.872174	−	0.489196i	$-0.837290\pi$
$31$	−2.29559	−	7.66782i	−0.412301	−	1.37718i	0.459873	−	0.887985i	$-0.347895\pi$
$32$	−0.893633	+	0.448799i	−0.157973	+	0.0793372i
$33$	−3.05986	−	1.05613i	−0.532653	−	0.183848i
$34$	−1.15942	+	3.87272i	−0.198838	+	0.664165i
$35$	−0.294190	−	1.66844i	−0.0497273	−	0.282017i
$36$	−1.58599	−	2.54650i	−0.264332	−	0.424416i
$37$	−1.07416	+	6.09184i	−0.176590	+	1.00149i	0.759702	+	0.650271i	$0.225345\pi$
$37$	−1.07416	+	6.09184i	−0.176590	+	1.00149i	−0.936292	+	0.351222i	$0.885766\pi$
$38$	−7.05817	−	3.54475i	−1.14499	−	0.575034i
$39$	5.30420	+	5.43713i	0.849351	+	0.870638i
$40$	−0.966256	+	2.24003i	−0.152778	+	0.354180i
$41$	−2.57993	+	5.98096i	−0.402918	+	0.934069i	0.589110	+	0.808053i	$0.299478\pi$
$41$	−2.57993	+	5.98096i	−0.402918	+	0.934069i	−0.992028	+	0.126016i	$0.959781\pi$
$42$	−0.325674	+	1.15792i	−0.0502525	+	0.178670i
$43$	−3.81384	−	1.91538i	−0.581605	−	0.292093i	0.133569	−	0.991040i	$-0.457356\pi$
$43$	−3.81384	−	1.91538i	−0.581605	−	0.292093i	−0.715174	+	0.698946i	$0.753653\pi$
$44$	0.324528	−	1.84049i	0.0489244	−	0.277464i
$45$	−6.95709	−	2.27189i	−1.03710	−	0.338673i
$46$	−0.470813	−	2.67011i	−0.0694176	−	0.393687i
$47$	0.986899	−	3.29647i	0.143954	−	0.480840i	−0.855354	−	0.518044i	$-0.826660\pi$
$47$	0.986899	−	3.29647i	0.143954	−	0.480840i	0.999308	+	0.0372047i	$0.0118454\pi$
$48$	1.30804	−	1.13536i	0.188799	−	0.163875i
$49$	−5.82445	+	2.92515i	−0.832064	+	0.417878i
$50$	0.272864	+	0.911429i	0.0385888	+	0.128895i
$51$	0.290247	−	6.99588i	0.0406427	−	0.979619i
$52$	−2.61882	+	3.51768i	−0.363165	+	0.487815i
$53$	5.32106	−	9.21634i	0.730903	−	1.26596i	−0.225594	−	0.974221i	$-0.572432\pi$
$53$	5.32106	−	9.21634i	0.730903	−	1.26596i	0.956497	−	0.291741i	$-0.0942344\pi$
$54$	3.75076	+	3.59608i	0.510414	+	0.489365i
$55$	−2.27961	−	3.94840i	−0.307383	−	0.532403i
$56$	−0.689767	−	0.0806222i	−0.0921740	−	0.0107736i
$57$	13.3624	+	2.93198i	1.76989	+	0.388350i
$58$	−1.60745	−	0.380973i	−0.211069	−	0.0500243i
$59$	−5.75027	−	3.78201i	−0.748621	−	0.492376i	0.116965	−	0.993136i	$-0.462683\pi$
$59$	−5.75027	−	3.78201i	−0.748621	−	0.492376i	−0.865586	+	0.500760i	$0.833054\pi$
$60$	0.664091	−	4.17291i	0.0857337	−	0.538720i
$61$	7.31570	+	7.75419i	0.936680	+	0.992822i	0.999987	−	0.00517165i	$-0.00164619\pi$
$61$	7.31570	+	7.75419i	0.936680	+	0.992822i	−0.0633069	+	0.997994i	$0.520165\pi$
$62$	−6.13147	+	5.14492i	−0.778698	+	0.653405i
$63$	0.0515617	−	2.08275i	0.00649616	−	0.262402i
$64$	0.766044	+	0.642788i	0.0957556	+	0.0803485i
$65$	0.622066	+	10.6805i	0.0771578	+	1.32475i
$66$	0.242194	+	3.22792i	0.0298121	+	0.397330i
$67$	−6.33676	−	8.51174i	−0.774158	−	1.03987i	−0.997871	−	0.0652194i	$-0.979225\pi$
$67$	−6.33676	−	8.51174i	−0.774158	−	1.03987i	0.223713	−	0.974655i	$-0.428182\pi$
$68$	4.01521	−	0.469311i	0.486916	−	0.0569123i
$69$	1.93184	+	4.28036i	0.232566	+	0.515295i
$70$	−1.41546	+	0.930964i	−0.169180	+	0.111272i
$71$	7.97798	−	2.90375i	0.946812	−	0.344612i	0.177960	−	0.984038i	$-0.443050\pi$
$71$	7.97798	−	2.90375i	0.946812	−	0.344612i	0.768852	+	0.639426i	$0.220828\pi$
$72$	−1.71005	+	2.46490i	−0.201532	+	0.290491i
$73$	2.86854	+	1.04406i	0.335737	+	0.122198i	0.504387	−	0.863478i	$-0.331719\pi$
$73$	2.86854	+	1.04406i	0.335737	+	0.122198i	−0.168650	+	0.985676i	$0.553941\pi$
$74$	6.01908	−	1.42655i	0.699704	−	0.165833i
$75$	−0.847669	−	1.41313i	−0.0978804	−	0.163174i
$76$	−0.459245	+	7.88493i	−0.0526790	+	0.904464i
$77$	0.890651	−	0.944035i	0.101499	−	0.107583i
$78$	2.89158	−	7.02394i	0.327407	−	0.795304i
$79$	3.88894	+	9.01558i	0.437540	+	1.01433i	0.984213	+	0.176986i	$0.0566348\pi$
$79$	3.88894	+	9.01558i	0.437540	+	1.01433i	−0.546673	+	0.837346i	$0.684106\pi$
$80$	2.43955			0.272750
$81$	−7.83297	−	4.43222i	−0.870330	−	0.492469i
$82$	6.51367			0.719315
$83$	2.85728	+	6.62392i	0.313627	+	0.727070i	1.00000		0.000180023i	$-5.73031e-5\pi$
$83$	2.85728	+	6.62392i	0.313627	+	0.727070i	−0.686373	+	0.727250i	$0.740798\pi$
$84$	1.19221	−	0.159589i	0.130081	−	0.0174125i
$85$	6.76771	−	7.17335i	0.734061	−	0.778059i
$86$	−0.248150	+	4.26057i	−0.0267587	+	0.459429i
$87$	2.86092	−	0.0478192i	0.306723	−	0.00512676i
$88$	−1.81850	+	0.430993i	−0.193853	+	0.0459441i
$89$	17.4051	+	6.33493i	1.84493	+	0.671501i	0.987655	+	0.156648i	$0.0500688\pi$
$89$	17.4051	+	6.33493i	1.84493	+	0.671501i	0.857279	+	0.514853i	$0.172153\pi$
$90$	0.669479	+	7.28796i	0.0705692	+	0.768219i
$91$	−2.86187	+	1.04164i	−0.300006	+	0.109193i
$92$	−2.26526	+	1.48989i	−0.236170	+	0.155331i
$93$	8.09168	−	11.2570i	0.839068	−	1.16730i
$94$	−3.41776	+	0.399479i	−0.352515	+	0.0412031i
$95$	11.5062	+	15.4555i	1.18051	+	1.58570i
$96$	−1.56059	−	0.751367i	−0.159277	−	0.0766861i
$97$	−0.260900	−	4.47948i	−0.0264904	−	0.454822i	−0.985307	−	0.170795i	$-0.945366\pi$
$97$	−0.260900	−	4.47948i	−0.0264904	−	0.454822i	0.958816	−	0.284027i	$-0.0916706\pi$
$98$	4.99286	+	4.18951i	0.504355	+	0.423204i
$99$	−1.78661	−	5.31436i	−0.179561	−	0.534114i
$100$	0.728813	−	0.611546i	0.0728813	−	0.0611546i
$101$	−4.70033	−	4.98206i	−0.467701	−	0.495734i	0.449988	−	0.893035i	$-0.351428\pi$
$101$	−4.70033	−	4.98206i	−0.467701	−	0.495734i	−0.917688	+	0.397301i	$0.869947\pi$
$102$	−6.53869	+	2.50442i	−0.647426	+	0.247974i
$103$	−8.80772	−	5.79293i	−0.867851	−	0.570794i	0.0356581	−	0.999364i	$-0.488647\pi$
$103$	−8.80772	−	5.79293i	−0.867851	−	0.570794i	−0.903509	+	0.428570i	$0.859018\pi$
$104$	4.26726	+	1.01136i	0.418439	+	0.0991718i
$105$	1.97775	−	2.16776i	0.193009	−	0.211552i
$106$	−10.5702	−	1.23547i	−1.02666	−	0.120000i
$107$	−7.99271	−	13.8438i	−0.772685	−	1.33833i	−0.936087	−	0.351770i	$-0.885580\pi$
$107$	−7.99271	−	13.8438i	−0.772685	−	1.33833i	0.163402	−	0.986560i	$-0.447753\pi$
$108$	1.81638	−	4.86834i	0.174781	−	0.468456i
$109$	2.49832	−	4.32722i	0.239296	−	0.414473i	−0.721216	−	0.692710i	$-0.756417\pi$
$109$	2.49832	−	4.32722i	0.239296	−	0.414473i	0.960513	+	0.278237i	$0.0897500\pi$
$110$	−2.72258	+	3.65706i	−0.259588	+	0.348687i
$111$	−9.49282	+	4.96784i	−0.901019	+	0.471527i
$112$	0.199174	+	0.665288i	0.0188202	+	0.0628638i
$113$	−8.68926	+	4.36391i	−0.817417	+	0.410522i	−0.807818	−	0.589432i	$-0.799352\pi$
$113$	−8.68926	+	4.36391i	−0.817417	+	0.410522i	−0.00959849	+	0.999954i	$0.503055\pi$
$114$	−2.60037	−	13.4308i	−0.243547	−	1.25791i
$115$	−1.89702	+	6.33648i	−0.176898	+	0.590880i
$116$	0.286864	+	1.62689i	0.0266346	+	0.151053i
$117$	−1.85030	+	13.0256i	−0.171060	+	1.20422i
$118$	−1.19514	+	6.77797i	−0.110021	+	0.623962i
$119$	2.50878	+	1.25996i	0.229980	+	0.115500i
$120$	−4.09467	+	1.04303i	−0.373790	+	0.0952148i
$121$	−2.97348	+	6.89331i	−0.270317	+	0.626665i
$122$	4.22242	−	9.78867i	0.382280	−	0.886225i
$123$	−10.9329	+	2.78491i	−0.985786	+	0.251107i
$124$	7.15270	+	3.59222i	0.642331	+	0.322591i
$125$	−1.71508	+	9.72671i	−0.153402	+	0.869984i
$126$	−1.93284	+	0.777590i	−0.172191	+	0.0692732i
$127$	0.799789	+	4.53583i	0.0709698	+	0.402490i	0.999511	+	0.0312611i	$0.00995234\pi$
$127$	0.799789	+	4.53583i	0.0709698	+	0.402490i	−0.928541	+	0.371229i	$0.878937\pi$
$128$	0.286803	−	0.957990i	0.0253501	−	0.0846751i
$129$	−1.40510	−	7.25727i	−0.123712	−	0.638967i
$130$	9.56058	−	4.80150i	0.838518	−	0.421120i
$131$	−0.842729	−	2.81491i	−0.0736296	−	0.245940i	0.913250	−	0.407401i	$-0.133565\pi$
$131$	−0.842729	−	2.81491i	−0.0736296	−	0.245940i	−0.986879	+	0.161461i	$0.948380\pi$
$132$	2.86800	−	1.50090i	0.249628	−	0.130637i
$133$	−3.27546	+	4.39970i	−0.284018	+	0.381503i
$134$	−5.30576	+	9.18984i	−0.458347	+	0.793881i
$135$	−4.23965	−	11.9463i	−0.364891	−	1.02817i
$136$	−2.02127	−	3.50095i	−0.173323	−	0.300204i
$137$	−22.4321	−	2.62193i	−1.91650	−	0.224007i	−0.927708	−	0.373307i	$-0.878224\pi$
$137$	−22.4321	−	2.62193i	−1.91650	−	0.224007i	−0.988792	+	0.149300i	$0.952298\pi$
$138$	3.16513	−	3.46921i	0.269434	−	0.295319i
$139$	−9.55124	−	2.26369i	−0.810126	−	0.192003i	−0.195379	−	0.980728i	$-0.562594\pi$
$139$	−9.55124	−	2.26369i	−0.810126	−	0.192003i	−0.614747	+	0.788725i	$0.710742\pi$
$140$	1.41546	+	0.930964i	0.119628	+	0.0786809i
$141$	5.56576	−	2.13177i	0.468721	−	0.179527i
$142$	−5.82619	−	6.17540i	−0.488923	−	0.518228i
$143$	−6.27843	+	5.26823i	−0.525029	+	0.440552i
$144$	2.94063	+	0.593904i	0.245052	+	0.0494920i
$145$	3.08723	+	2.59049i	0.256380	+	0.215129i
$146$	−0.177495	−	3.04747i	−0.0146896	−	0.252210i
$147$	−10.1715	−	4.89720i	−0.838932	−	0.403914i
$148$	−3.69392	−	4.96179i	−0.303638	−	0.407857i
$149$	8.85502	−	1.03500i	0.725431	−	0.0847908i	0.254641	−	0.967036i	$-0.418043\pi$
$149$	8.85502	−	1.03500i	0.725431	−	0.0847908i	0.470791	+	0.882245i	$0.343969\pi$
$150$	−0.961811	+	1.33805i	−0.0785316	+	0.109252i
$151$	11.4929	−	7.55897i	0.935275	−	0.615140i	0.0122686	−	0.999925i	$-0.496095\pi$
$151$	11.4929	−	7.55897i	0.935275	−	0.615140i	0.923006	+	0.384785i	$0.125724\pi$
$152$	7.42197	−	2.70138i	0.602001	−	0.219111i
$153$	9.90411	−	6.99915i	0.800700	−	0.565848i
$154$	−1.21960	−	0.443897i	−0.0982779	−	0.0357702i
$155$	19.0000	−	4.50308i	1.52612	−	0.361696i
$156$	−7.59479	+	0.126944i	−0.608070	+	0.0101637i
$157$	−1.03391	+	17.7515i	−0.0825149	+	1.41673i	0.662192	+	0.749334i	$0.269626\pi$
$157$	−1.03391	+	17.7515i	−0.0825149	+	1.41673i	−0.744707	+	0.667392i	$0.767411\pi$
$158$	6.73792	−	7.14178i	0.536040	−	0.568170i
$159$	18.2697	−	2.44557i	1.44888	−	0.193947i
$160$	−0.966256	−	2.24003i	−0.0763892	−	0.177090i
$161$	−1.88290			−0.148393
$162$	−0.967254	+	8.94787i	−0.0759946	+	0.703011i
$163$	−21.3005			−1.66839			−0.834193	−	0.551472i	$-0.814066\pi$
$163$	−21.3005			−1.66839			−0.834193	+	0.551472i	$0.814066\pi$
$164$	−2.57993	−	5.98096i	−0.201459	−	0.467035i
$165$	3.00615	−	7.30224i	0.234028	−	0.568478i
$166$	4.95048	−	5.24720i	0.384232	−	0.407262i
$167$	0.529121	−	9.08466i	0.0409446	−	0.702992i	−0.913910	−	0.405917i	$-0.866952\pi$
$167$	0.529121	−	9.08466i	0.0409446	−	0.702992i	0.954854	−	0.297074i	$-0.0960109\pi$
$168$	−0.618747	−	1.03150i	−0.0477374	−	0.0795817i
$169$	6.06432	−	1.43727i	0.466486	−	0.110559i
$170$	−9.26724	−	3.37300i	−0.710765	−	0.258697i
$171$	10.1069	+	21.4312i	0.772897	+	1.63889i
$172$	4.01041	−	1.45967i	0.305791	−	0.111299i
$173$	−8.41308	+	5.53337i	−0.639635	+	0.420694i	−0.827473	−	0.561506i	$-0.810222\pi$
$173$	−8.41308	+	5.53337i	−0.639635	+	0.420694i	0.187838	+	0.982200i	$0.439852\pi$
$174$	−1.17706	−	2.60800i	−0.0892327	−	0.197712i
$175$	0.656242	−	0.0767037i	0.0496073	−	0.00579826i
$176$	1.11602	+	1.49907i	0.0841230	+	0.112997i
$177$	−0.891930	−	11.8875i	−0.0670415	−	0.893517i
$178$	−1.07696	−	18.4907i	−0.0807218	−	1.38594i
$179$	9.72888	+	8.16350i	0.727171	+	0.610169i	0.929359	−	0.369178i	$-0.120361\pi$
$179$	9.72888	+	8.16350i	0.727171	+	0.610169i	−0.202188	+	0.979347i	$0.564805\pi$
$180$	6.42676	−	3.50134i	0.479022	−	0.260974i
$181$	−2.29087	+	1.92227i	−0.170279	+	0.142881i	−0.723945	−	0.689858i	$-0.757673\pi$
$181$	−2.29087	+	1.92227i	−0.170279	+	0.142881i	0.553666	+	0.832739i	$0.313229\pi$
$182$	2.08998	+	2.21525i	0.154919	+	0.164205i
$183$	−2.90200	+	18.2351i	−0.214522	+	1.34798i
$184$	2.26526	+	1.48989i	0.166997	+	0.109836i
$185$	−14.6838	−	3.48013i	−1.07958	−	0.255865i
$186$	−13.5413	−	2.97124i	−0.992897	−	0.217862i
$187$	7.50395	+	0.877086i	0.548743	+	0.0641389i
$188$	1.72052	+	2.98002i	0.125481	+	0.217340i
$189$	2.91172	−	2.13153i	0.211796	−	0.155046i
$190$	9.63414	−	16.6868i	0.698934	−	1.21059i
$191$	5.32394	−	7.15129i	0.385227	−	0.517449i	−0.566638	−	0.823967i	$-0.691756\pi$
$191$	5.32394	−	7.15129i	0.385227	−	0.517449i	0.951865	+	0.306517i	$0.0991637\pi$
$192$	−0.0717982	+	1.73056i	−0.00518159	+	0.124893i
$193$	−0.525396	−	1.75494i	−0.0378188	−	0.126324i	0.936996	−	0.349341i	$-0.113595\pi$
$193$	−0.525396	−	1.75494i	−0.0378188	−	0.126324i	−0.974814	+	0.223017i	$0.928409\pi$
$194$	−4.00979	+	2.01379i	−0.287886	+	0.144582i
$195$	−13.9941	+	12.1467i	−1.00214	+	0.869844i
$196$	1.86930	−	6.24391i	0.133522	−	0.445994i
$197$	−2.56216	−	14.5308i	−0.182547	−	1.03527i	−0.929067	−	0.369911i	$-0.879388\pi$
$197$	−2.56216	−	14.5308i	−0.182547	−	1.03527i	0.746520	−	0.665362i	$-0.231723\pi$
$198$	−4.17210	+	3.74540i	−0.296498	+	0.266174i
$199$	−4.46744	+	25.3361i	−0.316688	+	1.79603i	0.245903	+	0.969294i	$0.420916\pi$
$199$	−4.46744	+	25.3361i	−0.316688	+	1.79603i	−0.562591	+	0.826735i	$0.690196\pi$
$200$	−0.850200	−	0.426986i	−0.0601182	−	0.0301925i
$201$	4.97635	−	17.6932i	0.351005	−	1.24798i
$202$	−2.71290	+	6.28922i	−0.190879	+	0.442508i
$203$	−0.454399	+	1.05341i	−0.0318925	+	0.0739352i
$204$	4.88944	+	5.01198i	0.342329	+	0.350909i
$205$	−14.2002	−	7.13161i	−0.991785	−	0.498093i
$206$	−1.83060	+	10.3819i	−0.127544	+	0.723338i
$207$	−3.82927	+	7.17615i	−0.266152	+	0.498777i
$208$	−0.761528	−	4.31884i	−0.0528025	−	0.299458i
$209$	−4.23349	+	14.1409i	−0.292837	+	0.978143i
$210$	−2.77382	−	0.957400i	−0.191412	−	0.0660669i
$211$	11.2716	−	5.66079i	0.775966	−	0.389705i	−0.0163104	−	0.999867i	$-0.505192\pi$
$211$	11.2716	−	5.66079i	0.775966	−	0.389705i	0.792277	+	0.610162i	$0.208896\pi$
$212$	3.05219	+	10.1950i	0.209625	+	0.700198i
$213$	12.4193	+	7.87413i	0.850954	+	0.539526i
$214$	−9.54583	+	12.8223i	−0.652540	+	0.876513i
$215$	5.20575	−	9.01662i	0.355029	−	0.614928i
$216$	−5.18962	+	0.260422i	−0.353109	+	0.0177195i
$217$	2.77926	+	4.81383i	0.188669	+	0.326784i
$218$	−4.96286	−	0.580076i	−0.336128	−	0.0392877i
$219$	1.60086	+	5.03914i	0.108176	+	0.340514i
$220$	4.43633	+	1.05143i	0.299097	+	0.0708874i
$221$	−14.8119	−	9.74194i	−0.996356	−	0.655314i
$222$	8.32147	+	6.74880i	0.558500	+	0.452950i
$223$	8.54564	+	9.05785i	0.572258	+	0.606558i	0.947260	−	0.320466i	$-0.103839\pi$
$223$	8.54564	+	9.05785i	0.572258	+	0.606558i	−0.375002	+	0.927024i	$0.622358\pi$
$224$	0.531989	−	0.446392i	0.0355450	−	0.0298258i
$225$	1.04227	−	2.65708i	0.0694847	−	0.177139i
$226$	7.44865	+	6.25016i	0.495477	+	0.415754i
$227$	0.712321	+	12.2301i	0.0472784	+	0.811738i	0.935719	+	0.352747i	$0.114752\pi$
$227$	0.712321	+	12.2301i	0.0472784	+	0.811738i	−0.888441	+	0.458992i	$0.848211\pi$
$228$	−11.3024	+	7.70738i	−0.748523	+	0.510434i
$229$	−7.98067	−	10.7199i	−0.527378	−	0.708391i	0.455997	−	0.889982i	$-0.349283\pi$
$229$	−7.98067	−	10.7199i	−0.527378	−	0.708391i	−0.983374	+	0.181590i	$0.941876\pi$
$230$	6.56963	−	0.767880i	0.433189	−	0.0506325i
$231$	2.23682	+	0.223622i	0.147172	+	0.0147133i
$232$	1.38021	−	0.907779i	0.0906153	−	0.0595986i
$233$	−5.09727	+	1.85525i	−0.333933	+	0.121542i	−0.503545	−	0.863969i	$-0.667971\pi$
$233$	−5.09727	+	1.85525i	−0.333933	+	0.121542i	0.169611	+	0.985511i	$0.445749\pi$
$234$	12.6932	−	3.46021i	0.829781	−	0.226201i
$235$	7.88831	+	2.87111i	0.514576	+	0.187291i
$236$	6.69701	−	1.58722i	0.435938	−	0.103319i
$237$	−8.25582	+	14.8679i	−0.536273	+	0.965776i
$238$	0.163236	−	2.80265i	0.0105810	−	0.181669i
$239$	1.31200	−	1.39064i	0.0848662	−	0.0899529i	−0.683549	−	0.729905i	$-0.739564\pi$
$239$	1.31200	−	1.39064i	0.0848662	−	0.0899529i	0.768415	+	0.639952i	$0.221046\pi$
$240$	2.57954	+	3.34667i	0.166508	+	0.216026i
$241$	2.53579	+	5.87863i	0.163345	+	0.378676i	0.980156	−	0.198230i	$-0.0635193\pi$
$241$	2.53579	+	5.87863i	0.163345	+	0.378676i	−0.816811	+	0.576906i	$0.804260\pi$
$242$	7.50729			0.482587
$243$	−2.20216	−	15.4321i	−0.141269	−	0.989971i
$244$	−10.6605			−0.682471
$245$	−6.29779	−	14.5999i	−0.402351	−	0.932754i
$246$	6.88745	+	8.93571i	0.439128	+	0.569720i
$247$	23.7698	−	25.1945i	1.51244	−	1.60309i
$248$	0.465395	−	7.99053i	0.0295526	−	0.507399i
$249$	−6.06571	+	10.9238i	−0.384399	+	0.692265i
$250$	9.61053	−	2.27774i	0.607824	−	0.144057i
$251$	−9.84637	−	3.58379i	−0.621497	−	0.226207i	0.0120290	−	0.999928i	$-0.496171\pi$
$251$	−9.84637	−	3.58379i	−0.621497	−	0.226207i	−0.633526	+	0.773721i	$0.718393\pi$
$252$	1.47955	+	1.46677i	0.0932031	+	0.0923981i
$253$	−4.76152	+	1.73305i	−0.299354	+	0.108956i
$254$	3.84809	−	2.53093i	0.241451	−	0.158805i
$255$	16.9967	+	1.69922i	1.06438	+	0.106409i
$256$	−0.993238	+	0.116093i	−0.0620774	+	0.00725581i
$257$	−11.4029	−	15.3168i	−0.711295	−	0.955435i	0.288703	−	0.957419i	$-0.406776\pi$
$257$	−11.4029	−	15.3168i	−0.711295	−	0.955435i	−0.999998	+	0.00198350i	$0.999369\pi$
$258$	−6.10721	+	4.16464i	−0.380218	+	0.259279i
$259$	−0.249780	−	4.28855i	−0.0155206	−	0.266478i
$260$	−8.19557	−	6.87690i	−0.508268	−	0.426487i
$261$	3.09069	+	3.87415i	0.191309	+	0.239804i
$262$	−2.25091	+	1.88874i	−0.139062	+	0.116687i
$263$	−6.90162	−	7.31529i	−0.425572	−	0.451080i	0.478737	−	0.877958i	$-0.341095\pi$
$263$	−6.90162	−	7.31529i	−0.425572	−	0.451080i	−0.904309	+	0.426878i	$0.859613\pi$
$264$	−2.51411	−	2.03897i	−0.154733	−	0.125490i
$265$	21.6909	+	14.2663i	1.33246	+	0.876374i
$266$	5.33722	+	1.26494i	0.327246	+	0.0775587i
$267$	9.71333	+	30.5754i	0.594446	+	1.87118i
$268$	10.5398	+	1.23192i	0.643818	+	0.0752516i
$269$	−3.94610	−	6.83484i	−0.240598	−	0.416728i	0.720287	−	0.693676i	$-0.244010\pi$
$269$	−3.94610	−	6.83484i	−0.240598	−	0.416728i	−0.960885	+	0.276949i	$0.910677\pi$
$270$	−9.29001	+	8.62458i	−0.565372	+	0.524875i
$271$	−3.22186	+	5.58042i	−0.195714	+	0.338986i	−0.947134	−	0.320837i	$-0.896036\pi$
$271$	−3.22186	+	5.58042i	−0.195714	+	0.338986i	0.751421	+	0.659824i	$0.229369\pi$
$272$	−2.41404	+	3.24262i	−0.146373	+	0.196613i
$273$	−4.45505	−	2.82462i	−0.269632	−	0.170954i
$274$	6.47738	+	21.6360i	0.391313	+	1.30708i
$275$	1.58892	−	0.797986i	0.0958156	−	0.0481204i
$276$	−4.43913	−	1.53219i	−0.267204	−	0.0922271i
$277$	3.97545	−	13.2789i	0.238862	−	0.797854i	−0.751546	−	0.659680i	$-0.770692\pi$
$277$	3.97545	−	13.2789i	0.238862	−	0.797854i	0.990408	−	0.138173i	$-0.0441231\pi$
$278$	1.70450	+	9.66670i	0.102229	+	0.579770i
$279$	23.9988	−	0.802487i	1.43677	−	0.0480436i
$280$	0.294190	−	1.66844i	0.0175812	−	0.0997082i
$281$	18.2744	+	9.17775i	1.09016	+	0.547498i	0.900723	−	0.434395i	$-0.143038\pi$
$281$	18.2744	+	9.17775i	1.09016	+	0.547498i	0.189436	+	0.981893i	$0.439334\pi$
$282$	−4.16191	−	4.26622i	−0.247838	−	0.254050i
$283$	−11.0299	+	25.5703i	−0.655662	+	1.52000i	0.187459	+	0.982272i	$0.439975\pi$
$283$	−11.0299	+	25.5703i	−0.655662	+	1.52000i	−0.843121	+	0.537724i	$0.819284\pi$
$284$	−3.36271	+	7.79565i	−0.199540	+	0.462587i
$285$	−9.03601	+	32.1271i	−0.535247	+	1.90304i
$286$	7.32413	+	3.67832i	0.433085	+	0.217504i
$287$	0.785498	−	4.45478i	0.0463665	−	0.262957i
$288$	−0.619390	−	2.93536i	−0.0364979	−	0.172968i
$289$	−0.114230	−	0.647833i	−0.00671944	−	0.0381078i
$290$	1.15584	−	3.86079i	0.0678735	−	0.226713i
$291$	5.86925	−	5.09444i	0.344062	−	0.298641i
$292$	−2.72793	+	1.37002i	−0.159640	+	0.0801743i
$293$	−8.85324	−	29.5719i	−0.517212	−	1.72761i	−0.672837	−	0.739791i	$-0.734924\pi$
$293$	−8.85324	−	29.5719i	−0.517212	−	1.72761i	0.155625	−	0.987816i	$-0.450261\pi$
$294$	−0.467960	+	11.2793i	−0.0272920	+	0.657823i
$295$	10.0264	−	13.4679i	0.583762	−	0.784129i
$296$	−3.09291	+	5.35708i	−0.179772	+	0.311374i
$297$	5.40132	−	8.07025i	0.313416	−	0.468284i
$298$	−4.45765	−	7.72088i	−0.258225	−	0.447258i
$299$	11.8099	+	1.38038i	0.682986	+	0.0798296i
$300$	1.60958	+	0.353174i	0.0929290	+	0.0203905i
$301$	2.88393	+	0.683505i	0.166227	+	0.0393966i
$302$	−11.4929	−	7.55897i	−0.661339	−	0.434970i
$303$	1.86453	−	11.7160i	0.107115	−	0.673069i
$304$	−5.42014	−	5.74501i	−0.310866	−	0.329499i
$305$	−19.9224	+	16.7169i	−1.14076	+	0.957207i
$306$	−10.3496	−	6.32189i	−0.591644	−	0.361399i
$307$	−22.0435	−	18.4967i	−1.25809	−	1.05566i	−0.995883	−	0.0906508i	$-0.971105\pi$
$307$	−22.0435	−	18.4967i	−1.25809	−	1.05566i	−0.262207	−	0.965012i	$-0.584450\pi$
$308$	0.0754643	+	1.29567i	0.00429998	+	0.0738277i
$309$	−1.36617	−	18.2081i	−0.0777189	−	1.03582i
$310$	−11.6603	−	15.6625i	−0.662261	−	0.889571i
$311$	−12.5663	+	1.46879i	−0.712569	+	0.0832873i	−0.464651	−	0.885494i	$-0.653820\pi$
$311$	−12.5663	+	1.46879i	−0.712569	+	0.0832873i	−0.247918	+	0.968781i	$0.579746\pi$
$312$	3.12470	+	6.92338i	0.176902	+	0.391959i
$313$	5.31511	−	3.49580i	0.300428	−	0.197594i	−0.390341	−	0.920670i	$-0.627643\pi$
$313$	5.31511	−	3.49580i	0.300428	−	0.197594i	0.690768	+	0.723076i	$0.257272\pi$
$314$	16.7093	−	6.08167i	0.942958	−	0.343209i
$315$	5.06506	+	0.421006i	0.285384	+	0.0237210i
$316$	−9.22645	−	3.35815i	−0.519029	−	0.188911i
$317$	18.6880	−	4.42915i	1.04963	−	0.248766i	0.330615	−	0.943766i	$-0.392744\pi$
$317$	18.6880	−	4.42915i	1.04963	−	0.248766i	0.719010	+	0.695000i	$0.244596\pi$
$318$	−9.48184	−	15.8069i	−0.531715	−	0.886408i
$319$	−0.179514	+	3.08213i	−0.0100508	+	0.172566i
$320$	−1.67412	+	1.77446i	−0.0935861	+	0.0991955i
$321$	10.5401	−	25.6029i	0.588290	−	1.42901i
$322$	0.745778	+	1.72891i	0.0415606	+	0.0963483i
$323$	−31.9292			−1.77659
$324$	8.59919	−	2.65592i	0.477733	−	0.147551i
$325$	−4.17232			−0.231439
$326$	8.43671	+	19.5585i	0.467266	+	1.08324i
$327$	8.57794	−	1.14824i	0.474361	−	0.0634977i
$328$	−4.46995	+	4.73787i	−0.246812	+	0.261605i
$329$	−0.138947	+	2.38562i	−0.00766038	+	0.131524i
$330$	−7.89571	+	0.131974i	−0.434644	+	0.00726492i
$331$	5.03636	−	1.19364i	0.276823	−	0.0656083i	−0.0898592	−	0.995954i	$-0.528642\pi$
$331$	5.03636	−	1.19364i	0.276823	−	0.0656083i	0.366682	+	0.930346i	$0.380494\pi$
$332$	−6.77885	−	2.46730i	−0.372038	−	0.135411i
$333$	−16.8526	−	7.76970i	−0.923518	−	0.425777i
$334$	−8.55125	+	3.11240i	−0.467904	+	0.170303i
$335$	21.6285	−	14.2253i	1.18169	−	0.777211i
$336$	−0.702064	+	0.976699i	−0.0383007	+	0.0532833i
$337$	26.2604	−	3.06940i	1.43049	−	0.167201i	0.634696	−	0.772762i	$-0.281125\pi$
$337$	26.2604	−	3.06940i	1.43049	−	0.167201i	0.795799	+	0.605561i	$0.207051\pi$
$338$	−3.72168	−	4.99908i	−0.202433	−	0.271914i
$339$	−15.1745	−	7.30593i	−0.824163	−	0.396804i
$340$	0.573423	+	9.84530i	0.0310983	+	0.533936i
$341$	11.4590	+	9.61524i	0.620539	+	0.520694i
$342$	15.6753	−	17.7688i	0.847625	−	0.960828i
$343$	7.19128	−	6.03420i	0.388293	−	0.325816i
$344$	−2.92874	−	3.10428i	−0.157907	−	0.167372i
$345$	−10.6985	+	4.09769i	−0.575988	+	0.220612i
$346$	8.41308	+	5.53337i	0.452290	+	0.297476i
$347$	−3.41862	−	0.810228i	−0.183521	−	0.0434953i	0.137828	−	0.990456i	$-0.455988\pi$
$347$	−3.41862	−	0.810228i	−0.183521	−	0.0434953i	−0.321349	+	0.946961i	$0.604136\pi$
$348$	−1.92850	+	2.11377i	−0.103378	+	0.113310i
$349$	−22.8121	−	2.66635i	−1.22110	−	0.142726i	−0.518982	−	0.854785i	$-0.673689\pi$
$349$	−22.8121	−	2.66635i	−1.22110	−	0.142726i	−0.702120	+	0.712059i	$0.747763\pi$
$350$	−0.330355	−	0.572192i	−0.0176582	−	0.0305849i
$351$	−19.8255	+	11.2348i	−1.05821	+	0.599668i
$352$	0.934440	−	1.61850i	0.0498058	−	0.0862662i
$353$	6.39081	−	8.58435i	0.340149	−	0.456899i	−0.598829	−	0.800877i	$-0.704367\pi$
$353$	6.39081	−	8.58435i	0.340149	−	0.456899i	0.938978	+	0.343978i	$0.111775\pi$
$354$	−10.5620	+	5.52737i	−0.561364	+	0.293777i
$355$	5.94020	+	19.8416i	0.315273	+	1.05308i
$356$	−16.5519	+	8.31270i	−0.877251	+	0.440572i
$357$	0.924285	+	4.77390i	0.0489184	+	0.252662i
$358$	3.64244	−	12.1666i	0.192509	−	0.643025i
$359$	5.49988	+	31.1914i	0.290273	+	1.64622i	0.685818	+	0.727773i	$0.259444\pi$
$359$	5.49988	+	31.1914i	0.290273	+	1.64622i	−0.395546	+	0.918446i	$0.629444\pi$
$360$	−5.76049	−	4.51434i	−0.303605	−	0.237927i
$361$	7.53339	−	42.7240i	0.396494	−	2.24863i
$362$	2.67243	+	1.34214i	0.140460	+	0.0705415i
$363$	−12.6006	+	3.20973i	−0.661361	+	0.168467i
$364$	1.20628	−	2.79647i	0.0632261	−	0.146575i
$365$	−2.94962	+	6.83799i	−0.154390	+	0.357917i
$366$	17.8932	−	4.55790i	0.935292	−	0.238245i
$367$	−11.4005	−	5.72555i	−0.595102	−	0.298872i	0.125639	−	0.992076i	$-0.459902\pi$
$367$	−11.4005	−	5.72555i	−0.595102	−	0.298872i	−0.720741	+	0.693205i	$0.756198\pi$
$368$	0.470813	−	2.67011i	0.0245428	−	0.139189i
$369$	−15.3807	−	12.0534i	−0.800688	−	0.627477i
$370$	2.62046	+	14.8613i	0.136231	+	0.772605i
$371$	−2.11963	+	7.08007i	−0.110046	+	0.367579i
$372$	2.63520	+	13.6107i	0.136629	+	0.705682i
$373$	−21.4099	+	10.7525i	−1.10856	+	0.556742i	−0.906319	−	0.422593i	$-0.861120\pi$
$373$	−21.4099	+	10.7525i	−1.10856	+	0.556742i	−0.202244	+	0.979335i	$0.564824\pi$
$374$	−2.16681	−	7.23764i	−0.112043	−	0.374250i
$375$	−15.1570	+	7.93205i	−0.782703	+	0.409609i
$376$	2.05484	−	2.76013i	0.105970	−	0.142343i
$377$	3.62236	−	6.27411i	0.186561	−	0.323133i
$378$	−3.11048	−	1.82933i	−0.159986	−	0.0940905i
$379$	0.540044	+	0.935384i	0.0277402	+	0.0480475i	0.879562	−	0.475784i	$-0.157836\pi$
$379$	0.540044	+	0.935384i	0.0277402	+	0.0480475i	−0.851822	+	0.523831i	$0.824502\pi$
$380$	−19.1380	−	2.23691i	−0.981758	−	0.114751i
$381$	−5.37674	+	5.89329i	−0.275459	+	0.301923i
$382$	−8.67514	−	2.05605i	−0.443859	−	0.105196i
$383$	31.4543	+	20.6878i	1.60724	+	1.05710i	0.953938	+	0.300003i	$0.0969877\pi$
$383$	31.4543	+	20.6878i	1.60724	+	1.05710i	0.653303	+	0.757096i	$0.273383\pi$
$384$	1.61747	−	0.619514i	0.0825411	−	0.0316145i
$385$	2.17279	+	2.30302i	0.110735	+	0.117373i
$386$	−1.40332	+	1.17753i	−0.0714271	+	0.0599344i
$387$	8.47007	−	9.60128i	0.430558	−	0.488060i
$388$	3.43730	+	2.88423i	0.174502	+	0.146425i
$389$	1.28739	+	22.1036i	0.0652733	+	1.12070i	0.858849	+	0.512228i	$0.171180\pi$
$389$	1.28739	+	22.1036i	0.0652733	+	1.12070i	−0.793576	+	0.608471i	$0.791783\pi$
$390$	16.6961	+	8.03854i	0.845439	+	0.407047i
$391$	−6.54520	−	8.79172i	−0.331005	−	0.444617i
$392$	−6.47365	+	0.756661i	−0.326969	+	0.0382172i
$393$	2.97052	−	4.13253i	0.149843	−	0.208458i
$394$	−12.3276	+	8.10796i	−0.621053	+	0.408473i
$395$	−22.5084	+	8.19238i	−1.13252	+	0.412203i
$396$	5.09157	+	2.34741i	0.255861	+	0.117962i
$397$	23.9869	+	8.73052i	1.20387	+	0.438172i	0.864573	−	0.502508i	$-0.167589\pi$
$397$	23.9869	+	8.73052i	1.20387	+	0.438172i	0.339296	+	0.940680i	$0.389811\pi$
$398$	25.0335	−	5.93305i	1.25482	−	0.297397i
$399$	−9.49909	+	0.158774i	−0.475549	+	0.00794864i
$400$	−0.0553188	+	0.949788i	−0.00276594	+	0.0474894i
$401$	4.28696	−	4.54392i	0.214081	−	0.226912i	−0.611430	−	0.791298i	$-0.709406\pi$
$401$	4.28696	−	4.54392i	0.214081	−	0.226912i	0.825511	+	0.564386i	$0.190887\pi$
$402$	−18.2172	+	2.43854i	−0.908591	+	0.121623i
$403$	−13.9030	−	32.2308i	−0.692559	−	1.60553i
$404$	6.84939			0.340770
$405$	11.9054	−	18.4479i	0.591584	−	0.916683i
$406$	1.14724			0.0569366
$407$	−4.57890	−	10.6151i	−0.226968	−	0.526171i
$408$	2.66547	−	6.47470i	0.131961	−	0.320546i
$409$	9.66974	−	10.2493i	0.478138	−	0.506797i	−0.442739	−	0.896651i	$-0.645993\pi$
$409$	9.66974	−	10.2493i	0.478138	−	0.506797i	0.920877	+	0.389854i	$0.127475\pi$
$410$	−0.923946	+	15.8635i	−0.0456304	+	0.783444i
$411$	−20.1224	−	33.5455i	−0.992565	−	1.65468i
$412$	10.2578	−	2.43115i	0.505368	−	0.119774i
$413$	4.49141	+	1.63474i	0.221008	+	0.0804403i
$414$	8.10595	+	0.673765i	0.398386	+	0.0331137i
$415$	−16.5373	+	6.01910i	−0.811786	+	0.295466i
$416$	−3.66400	+	2.40985i	−0.179643	+	0.118153i
$417$	−6.99391	−	15.4963i	−0.342493	−	0.758859i
$418$	14.6612	−	1.71364i	0.717101	−	0.0838171i
$419$	14.8608	+	19.9615i	0.725995	+	0.975181i	0.999910	+	0.0134268i	$0.00427400\pi$
$419$	14.8608	+	19.9615i	0.725995	+	0.975181i	−0.273915	+	0.961754i	$0.588319\pi$
$420$	0.219554	+	2.92617i	0.0107131	+	0.142783i
$421$	−0.276523	−	4.74771i	−0.0134769	−	0.231389i	−0.998320	−	0.0579415i	$-0.981546\pi$
$421$	−0.276523	−	4.74771i	−0.0134769	−	0.231389i	0.984843	−	0.173448i	$-0.0554907\pi$
$422$	−9.66227	−	8.10760i	−0.470352	−	0.394672i
$423$	8.80958	+	5.38122i	0.428336	+	0.261644i
$424$	8.15233	−	6.84062i	0.395912	−	0.332210i
$425$	2.63933	+	2.79753i	0.128026	+	0.135700i
$426$	2.31113	−	14.5223i	0.111975	−	0.703610i
$427$	−6.18540	−	4.06820i	−0.299333	−	0.196874i
$428$	15.5545	+	3.68649i	0.751857	+	0.178193i
$429$	−13.8659	−	3.04246i	−0.669451	−	0.146891i
$430$	−10.3411	−	1.20870i	−0.498692	−	0.0582887i
$431$	9.13866	+	15.8286i	0.440194	+	0.762438i	0.997704	−	0.0677322i	$-0.0215763\pi$
$431$	9.13866	+	15.8286i	0.440194	+	0.762438i	−0.557510	+	0.830171i	$0.688243\pi$
$432$	2.29463	+	4.66205i	0.110400	+	0.224303i
$433$	−16.0854	+	27.8607i	−0.773015	+	1.33890i	0.162889	+	0.986644i	$0.447919\pi$
$433$	−16.0854	+	27.8607i	−0.773015	+	1.33890i	−0.935904	+	0.352256i	$0.885415\pi$
$434$	3.31932	−	4.45862i	0.159333	−	0.214021i
$435$	−0.289353	+	6.97432i	−0.0138734	+	0.334393i
$436$	1.43306	+	4.78674i	0.0686309	+	0.229243i
$437$	19.1368	−	9.61089i	0.915439	−	0.459751i
$438$	3.99295	−	3.46583i	0.190791	−	0.165604i
$439$	−7.21221	+	24.0905i	−0.344220	+	1.14978i	0.594211	+	0.804309i	$0.297464\pi$
$439$	−7.21221	+	24.0905i	−0.344220	+	1.14978i	−0.938431	+	0.345466i	$0.887721\pi$
$440$	−0.791701	−	4.48996i	−0.0377429	−	0.214050i
$441$	−4.03701	−	19.1319i	−0.192239	−	0.911042i
$442$	−3.07851	+	17.4591i	−0.146430	+	0.830445i
$443$	−5.57999	−	2.80237i	−0.265113	−	0.133145i	0.311278	−	0.950319i	$-0.399243\pi$
$443$	−5.57999	−	2.80237i	−0.265113	−	0.133145i	−0.576391	+	0.817174i	$0.695539\pi$
$444$	2.90089	−	10.3140i	0.137670	−	0.489479i
$445$	−17.8971	+	41.4901i	−0.848402	+	1.96682i
$446$	4.93231	−	11.4344i	0.233551	−	0.541433i
$447$	10.7830	+	11.0533i	0.510019	+	0.522801i
$448$	−0.620594	−	0.311674i	−0.0293203	−	0.0147252i
$449$	1.31051	−	7.43224i	0.0618466	−	0.350749i	−0.938143	−	0.346247i	$-0.887456\pi$
$449$	1.31051	−	7.43224i	0.0618466	−	0.350749i	0.999990	−	0.00450206i	$-0.00143305\pi$
$450$	−2.85260	+	0.0953869i	−0.134473	+	0.00449658i
$451$	−2.11387	−	11.9883i	−0.0995381	−	0.564509i
$452$	2.78874	−	9.31503i	0.131171	−	0.438142i
$453$	22.5220	+	7.77361i	1.05818	+	0.365236i
$454$	10.9477	−	5.49815i	0.513802	−	0.258041i
$455$	−2.13088	−	7.11762i	−0.0998970	−	0.333679i
$456$	11.5537	+	7.32535i	0.541052	+	0.343041i
$457$	−5.43504	+	7.30053i	−0.254240	+	0.341504i	−0.910858	−	0.412719i	$-0.864579\pi$
$457$	−5.43504	+	7.30053i	−0.254240	+	0.341504i	0.656618	+	0.754223i	$0.271986\pi$
$458$	−6.68221	+	11.5739i	−0.312239	+	0.540814i
$459$	20.0741	+	6.18606i	0.936981	+	0.288741i
$460$	−3.30718	−	5.72820i	−0.154198	−	0.267079i
$461$	19.3563	+	2.26243i	0.901515	+	0.105372i	0.554207	−	0.832379i	$-0.313022\pi$
$461$	19.3563	+	2.26243i	0.901515	+	0.105372i	0.347308	+	0.937751i	$0.387096\pi$
$462$	−0.680626	−	2.14246i	−0.0316656	−	0.0996762i
$463$	−9.69976	−	2.29889i	−0.450786	−	0.106838i	−0.00104939	−	0.999999i	$-0.500334\pi$
$463$	−9.69976	−	2.29889i	−0.450786	−	0.106838i	−0.449737	+	0.893161i	$0.648482\pi$
$464$	−1.38021	−	0.907779i	−0.0640747	−	0.0421426i
$465$	26.2678	+	21.3034i	1.21814	+	0.987923i
$466$	3.72245	+	3.94557i	0.172439	+	0.182775i
$467$	11.9126	−	9.99582i	0.551247	−	0.462551i	−0.324116	−	0.946017i	$-0.605067\pi$
$467$	11.9126	−	9.99582i	0.551247	−	0.462551i	0.875363	+	0.483466i	$0.160622\pi$
$468$	−8.20475	−	10.2846i	−0.379265	−	0.475406i
$469$	5.64521	+	4.73689i	0.260672	+	0.218729i
$470$	−0.488100	−	8.38036i	−0.0225144	−	0.386557i
$471$	−25.4455	+	17.3518i	−1.17247	+	0.799529i
$472$	−4.10996	−	5.52064i	−0.189176	−	0.254108i
$473$	7.92207	−	0.925957i	0.364257	−	0.0425755i
$474$	16.9219	+	1.69174i	0.777250	+	0.0777043i
$475$	−6.27820	+	4.12924i	−0.288064	+	0.189462i
$476$	−2.63809	+	0.960186i	−0.120917	+	0.0440101i
$477$	22.6730	+	22.4772i	1.03813	+	1.02916i
$478$	−1.79656	−	0.653895i	−0.0821729	−	0.0299085i
$479$	−18.9679	+	4.49547i	−0.866665	+	0.205403i	−0.639817	−	0.768527i	$-0.720990\pi$
$479$	−18.9679	+	4.49547i	−0.866665	+	0.205403i	−0.226847	+	0.973930i	$0.572842\pi$
$480$	2.05126	−	3.69412i	0.0936268	−	0.168613i
$481$	−1.57734	+	27.0818i	−0.0719203	+	1.23482i
$482$	4.39347	−	4.65681i	0.200117	−	0.212112i
$483$	−1.99095	−	2.58303i	−0.0905911	−	0.117532i
$484$	−2.97348	−	6.89331i	−0.135158	−	0.313332i
$485$	10.9464			0.497052
$486$	−13.2978	+	8.13441i	−0.603200	+	0.368985i
$487$	8.28387			0.375378			0.187689	−	0.982229i	$-0.439900\pi$
$487$	8.28387			0.375378			0.187689	+	0.982229i	$0.439900\pi$
$488$	4.22242	+	9.78867i	0.191140	+	0.443112i
$489$	−22.5228	−	29.2209i	−1.01852	−	1.32141i
$490$	−10.9114	+	11.5655i	−0.492929	+	0.522474i
$491$	−0.250629	+	4.30314i	−0.0113108	+	0.194198i	0.987919	+	0.154968i	$0.0495275\pi$
$491$	−0.250629	+	4.30314i	−0.0113108	+	0.194198i	−0.999230	+	0.0392299i	$0.987510\pi$
$492$	5.47693	−	9.86342i	0.246919	−	0.444677i
$493$	−6.49820	+	1.54010i	−0.292664	+	0.0693627i
$494$	−32.5488	−	11.8468i	−1.46444	−	0.533012i
$495$	13.1961	−	3.59731i	0.593122	−	0.161687i
$496$	−7.52137	+	2.73755i	−0.337719	+	0.122920i
$497$	−4.92602	+	3.23989i	−0.220962	+	0.145329i
$498$	12.4329	+	1.24296i	0.557130	+	0.0556982i
$499$	20.6040	−	2.40826i	0.922362	−	0.107809i	0.358362	−	0.933583i	$-0.383336\pi$
$499$	20.6040	−	2.40826i	0.922362	−	0.107809i	0.564001	+	0.825774i	$0.309261\pi$
$500$	−5.89799	−	7.92238i	−0.263766	−	0.354300i
$501$	13.0222	−	8.88010i	0.581787	−	0.396733i
$502$	0.609258	+	10.4606i	0.0271925	+	0.466878i
$503$	10.7596	+	9.02839i	0.479747	+	0.402556i	0.850335	−	0.526242i	$-0.176399\pi$
$503$	10.7596	+	9.02839i	0.479747	+	0.402556i	−0.370588	+	0.928798i	$0.620844\pi$
$504$	0.760794	−	1.93951i	0.0338885	−	0.0863926i
$505$	12.8002	−	10.7406i	0.569599	−	0.477951i
$506$	3.47726	+	3.68568i	0.154583	+	0.163848i
$507$	8.38401	+	6.79952i	0.372347	+	0.301977i
$508$	−3.84809	−	2.53093i	−0.170732	−	0.112292i
$509$	12.8694	+	3.05011i	0.570428	+	0.135194i	0.505700	−	0.862709i	$-0.331234\pi$
$509$	12.8694	+	3.05011i	0.570428	+	0.135194i	0.0647272	+	0.997903i	$0.479382\pi$
$510$	−5.17181	−	16.2797i	−0.229012	−	0.720877i
$511$	−2.10560	−	0.246110i	−0.0931464	−	0.0108873i
$512$	0.500000	+	0.866025i	0.0220971	+	0.0382733i
$513$	−18.7133	+	36.5261i	−0.826211	+	1.61267i
$514$	−9.54766	+	16.5370i	−0.421129	+	0.729417i
$515$	15.3576	−	20.6288i	0.676736	−	0.909014i
$516$	6.24298	+	3.95821i	0.274832	+	0.174250i
$517$	1.84440	+	6.16071i	0.0811164	+	0.270948i
$518$	−3.83889	+	1.92796i	−0.168671	+	0.0847097i
$519$	−16.4867	−	5.69049i	−0.723688	−	0.249785i
$520$	−3.06838	+	10.2491i	−0.134557	+	0.449453i
$521$	2.42643	+	13.7610i	0.106304	+	0.602878i	0.990692	+	0.136126i	$0.0434651\pi$
$521$	2.42643	+	13.7610i	0.106304	+	0.602878i	−0.884388	+	0.466753i	$0.845424\pi$
$522$	2.33315	−	4.37239i	0.102119	−	0.191374i
$523$	−1.99108	+	11.2920i	−0.0870639	+	0.493764i	0.909828	+	0.414985i	$0.136213\pi$
$523$	−1.99108	+	11.2920i	−0.0870639	+	0.493764i	−0.996892	+	0.0787788i	$0.974898\pi$
$524$	2.62581	+	1.31873i	0.114709	+	0.0576090i
$525$	0.799125	+	0.819153i	0.0348767	+	0.0357508i
$526$	−3.98343	+	9.23462i	−0.173686	+	0.402649i
$527$	−12.8159	+	29.7106i	−0.558269	+	1.29421i
$528$	−0.876426	+	3.11609i	−0.0381416	+	0.135610i
$529$	−13.9843	−	7.02319i	−0.608014	−	0.305356i
$530$	4.50825	−	25.5675i	0.195826	−	1.11058i
$531$	15.3646	−	13.7932i	0.666766	−	0.598574i
$532$	−0.952472	−	5.40174i	−0.0412949	−	0.234195i
$533$	−8.19268	+	27.3654i	−0.354864	+	1.18533i
$534$	24.2276	−	21.0292i	1.04843	−	0.910024i
$535$	34.8492	−	17.5019i	1.50666	−	0.756674i
$536$	−3.04342	−	10.1657i	−0.131456	−	0.439092i
$537$	−0.911847	+	21.9784i	−0.0393491	+	0.948438i
$538$	−4.71289	+	6.33051i	−0.203187	+	0.272928i
$539$	6.09042	−	10.5489i	0.262333	−	0.454374i
$540$	11.5988	+	5.11421i	0.499134	+	0.220081i
$541$	−13.0207	−	22.5525i	−0.559802	−	0.969606i	−0.997513	−	0.0704897i	$-0.977544\pi$
$541$	−13.0207	−	22.5525i	−0.559802	−	0.969606i	0.437710	−	0.899116i	$-0.355790\pi$
$542$	6.40014	+	0.748069i	0.274910	+	0.0321323i
$543$	−5.05937	−	1.11013i	−0.217118	−	0.0476402i
$544$	3.93358	+	0.932275i	0.168651	+	0.0399710i
$545$	10.1842	+	6.69828i	0.436245	+	0.286923i
$546$	−0.829053	+	5.20948i	−0.0354802	+	0.222945i
$547$	17.6538	+	18.7119i	0.754822	+	0.800065i	0.984903	−	0.173107i	$-0.0553806\pi$
$547$	17.6538	+	18.7119i	0.754822	+	0.800065i	−0.230081	+	0.973171i	$0.573899\pi$
$548$	17.3009	−	14.5172i	0.739059	−	0.620144i
$549$	−28.0842	+	15.3004i	−1.19860	+	0.653007i
$550$	−1.36206	−	1.14291i	−0.0580786	−	0.0487337i
$551$	−0.758665	−	13.0258i	−0.0323202	−	0.554916i
$552$	0.351367	+	4.68295i	0.0149552	+	0.199320i
$553$	−4.07181	−	5.46939i	−0.173151	−	0.232582i
$554$	−13.7675	+	1.60919i	−0.584926	+	0.0683681i
$555$	−10.7523	−	23.8237i	−0.456408	−	1.01126i
$556$	8.20100	−	5.39389i	0.347800	−	0.228752i
$557$	1.13016	−	0.411346i	0.0478866	−	0.0174293i	−0.317966	−	0.948102i	$-0.603000\pi$
$557$	1.13016	−	0.411346i	0.0478866	−	0.0174293i	0.365852	+	0.930673i	$0.380777\pi$
$558$	−10.2423	−	21.7182i	−0.433591	−	0.919406i
$559$	−17.5875	−	6.40134i	−0.743874	−	0.270748i
$560$	−1.64851	+	0.390704i	−0.0696622	+	0.0165102i
$561$	6.73133	+	11.2216i	0.284197	+	0.473777i
$562$	1.18904	−	20.4150i	0.0501565	−	0.861153i
$563$	2.95231	−	3.12926i	0.124425	−	0.131883i	−0.662166	−	0.749357i	$-0.730363\pi$
$563$	2.95231	−	3.12926i	0.124425	−	0.131883i	0.786591	+	0.617474i	$0.211844\pi$
$564$	−2.26886	+	5.51129i	−0.0955363	+	0.232067i
$565$	−9.39541	−	21.7810i	−0.395268	−	0.916334i
$566$	27.8478			1.17053
$567$	6.00292	+	1.74056i	0.252099	+	0.0730966i
$568$	8.48999			0.356232
$569$	−0.154573	−	0.358340i	−0.00648003	−	0.0150224i	0.914945	−	0.403578i	$-0.132234\pi$
$569$	−0.154573	−	0.358340i	−0.00648003	−	0.0150224i	−0.921425	+	0.388555i	$0.872974\pi$
$570$	33.0786	−	4.42788i	1.38551	−	0.185463i
$571$	−8.72547	+	9.24845i	−0.365149	+	0.387036i	−0.883733	−	0.467991i	$-0.844978\pi$
$571$	−8.72547	+	9.24845i	−0.365149	+	0.387036i	0.518584	+	0.855027i	$0.326459\pi$
$572$	0.476550	−	8.18205i	0.0199256	−	0.342108i
$573$	15.4399	−	0.258072i	0.645010	−	0.0107811i
$574$	−4.40157	+	1.04319i	−0.183718	+	0.0435420i
$575$	−2.42396	−	0.882250i	−0.101086	−	0.0367924i
$576$	−2.44997	+	1.73137i	−0.102082	+	0.0721405i
$577$	38.3069	−	13.9426i	1.59474	−	0.580436i	0.616395	−	0.787437i	$-0.288593\pi$
$577$	38.3069	−	13.9426i	1.59474	−	0.580436i	0.978341	+	0.207001i	$0.0663703\pi$
$578$	−0.549607	+	0.361482i	−0.0228606	+	0.0150357i
$579$	1.85196	−	2.57641i	0.0769646	−	0.107072i
$580$	−4.00284	+	0.467865i	−0.166209	+	0.0194270i
$581$	−2.99164	−	4.01847i	−0.124114	−	0.166714i
$582$	−7.00249	−	3.37144i	−0.290262	−	0.139751i
$583$	1.15643	+	19.8552i	0.0478946	+	0.822318i
$584$	2.33845	+	1.96219i	0.0967658	+	0.0811961i
$585$	−31.4604	−	6.35391i	−1.30073	−	0.262702i
$586$	−23.6468	+	19.8420i	−0.976839	+	0.819666i
$587$	−23.3798	−	24.7811i	−0.964987	−	1.02283i	−0.999725	−	0.0234303i	$-0.992541\pi$
$587$	−23.3798	−	24.7811i	−0.964987	−	1.02283i	0.0347382	−	0.999396i	$-0.488940\pi$
$588$	10.5422	−	4.03782i	0.434753	−	0.166517i
$589$	−52.8183	−	34.7391i	−2.17634	−	1.43140i
$590$	−16.3377	−	3.87210i	−0.672612	−	0.159412i
$591$	17.2247	−	18.8795i	0.708528	−	0.776597i
$592$	6.14399	+	0.718130i	0.252517	+	0.0295150i
$593$	19.6691	+	34.0678i	0.807712	+	1.39900i	0.914445	+	0.404711i	$0.132628\pi$
$593$	19.6691	+	34.0678i	0.807712	+	1.39900i	−0.106732	+	0.994288i	$0.534039\pi$
$594$	−9.54959	−	1.76311i	−0.391824	−	0.0723415i
$595$	−3.42439	+	5.93122i	−0.140386	+	0.243156i
$596$	−5.32385	+	7.15117i	−0.218073	+	0.292923i
$597$	−39.4809	+	20.6614i	−1.61584	+	0.845614i
$598$	−3.41018	−	11.3908i	−0.139453	−	0.465805i
$599$	7.65216	−	3.84306i	0.312659	−	0.157023i	−0.285549	−	0.958364i	$-0.592176\pi$
$599$	7.65216	−	3.84306i	0.312659	−	0.157023i	0.598208	+	0.801341i	$0.295880\pi$
$600$	−0.313231	−	1.61782i	−0.0127876	−	0.0660474i
$601$	1.76835	−	5.90669i	0.0721324	−	0.240939i	−0.914318	−	0.404996i	$-0.867273\pi$
$601$	1.76835	−	5.90669i	0.0721324	−	0.240939i	0.986451	+	0.164057i	$0.0524581\pi$
$602$	−0.514663	−	2.91880i	−0.0209761	−	0.118961i
$603$	29.5341	−	11.8817i	1.20272	−	0.483861i
$604$	−2.38868	+	13.5469i	−0.0971940	+	0.551215i
$605$	−16.3663	−	8.21948i	−0.665386	−	0.334169i
$606$	−11.4964	+	2.92845i	−0.467008	+	0.118960i
$607$	5.15898	−	11.9599i	0.209397	−	0.485436i	−0.780857	−	0.624709i	$-0.785217\pi$
$607$	5.15898	−	11.9599i	0.209397	−	0.485436i	0.990254	+	0.139273i	$0.0444767\pi$
$608$	−3.12835	+	7.25234i	−0.126872	+	0.294121i
$609$	−1.92559	+	0.490501i	−0.0780288	+	0.0198761i
$610$	23.2406	+	11.6719i	0.940985	+	0.472580i
$611$	2.62044	−	14.8613i	0.106012	−	0.601222i
$612$	−1.70562	+	12.0071i	−0.0689455	+	0.485358i
$613$	1.57852	+	8.95223i	0.0637558	+	0.361577i	0.999949	+	0.0100916i	$0.00321230\pi$
$613$	1.57852	+	8.95223i	0.0637558	+	0.361577i	−0.936193	+	0.351486i	$0.885677\pi$
$614$	−8.25298	+	27.5669i	−0.333063	+	1.11251i
$615$	−5.23164	−	27.0212i	−0.210960	−	1.08960i
$616$	1.15982	−	0.582482i	0.0467303	−	0.0234689i
$617$	3.53554	+	11.8095i	0.142335	+	0.475434i	0.999195	−	0.0401163i	$-0.0127729\pi$
$617$	3.53554	+	11.8095i	0.142335	+	0.475434i	−0.856860	+	0.515550i	$0.827588\pi$
$618$	−16.1779	+	8.46631i	−0.650769	+	0.340565i
$619$	18.3546	−	24.6545i	0.737733	−	0.990947i	−0.261933	−	0.965086i	$-0.584360\pi$
$619$	18.3546	−	24.6545i	0.737733	−	0.990947i	0.999666	−	0.0258608i	$-0.00823267\pi$
$620$	−9.76316	+	16.9103i	−0.392098	+	0.679134i
$621$	−13.8935	+	2.33481i	−0.557528	+	0.0936927i
$622$	6.32592	+	10.9568i	0.253646	+	0.439328i
$623$	−12.7759	−	1.49329i	−0.511856	−	0.0598274i
$624$	5.11952	−	5.61136i	0.204945	−	0.224634i
$625$	−28.0741	−	6.65369i	−1.12297	−	0.266148i
$626$	−5.31511	−	3.49580i	−0.212434	−	0.139720i
$627$	−23.8754	+	9.14463i	−0.953491	+	0.365201i
$628$	−12.2025	−	12.9339i	−0.486932	−	0.516118i
$629$	19.1561	−	16.0738i	0.763802	−	0.640906i
$630$	−1.61959	−	4.81757i	−0.0645261	−	0.191937i
$631$	−14.1277	−	11.8545i	−0.562415	−	0.471922i	0.316704	−	0.948524i	$-0.397424\pi$
$631$	−14.1277	−	11.8545i	−0.562415	−	0.471922i	−0.879119	+	0.476602i	$0.841868\pi$
$632$	0.570900	+	9.80197i	0.0227092	+	0.389902i
$633$	19.6840	+	9.47713i	0.782371	+	0.376682i
$634$	−11.4689	−	15.4054i	−0.455487	−	0.611825i
$635$	−11.1601	+	1.30443i	−0.442875	+	0.0517647i
$636$	−10.7586	+	14.9672i	−0.426606	+	0.593487i
$637$	−23.8810	+	15.7068i	−0.946198	+	0.622324i
$638$	2.90117	−	1.05594i	0.114858	−	0.0418050i
$639$	2.32988	+	25.3632i	0.0921688	+	1.00335i
$640$	2.29243	+	0.834375i	0.0906161	+	0.0329816i
$641$	−45.1789	+	10.7076i	−1.78446	+	0.422924i	−0.984248	−	0.176796i	$-0.943427\pi$
$641$	−45.1789	+	10.7076i	−1.78446	+	0.422924i	−0.800210	+	0.599720i	$0.795279\pi$
$642$	−27.6837	+	0.462723i	−1.09259	+	0.0182622i
$643$	0.394719	−	6.77706i	0.0155662	−	0.267261i	−0.981541	−	0.191252i	$-0.938745\pi$
$643$	0.394719	−	6.77706i	0.0155662	−	0.267261i	0.997107	−	0.0760090i	$-0.0242178\pi$
$644$	1.29212	−	1.36957i	0.0509168	−	0.0539686i
$645$	17.8738	−	2.39258i	0.703781	−	0.0942076i
$646$	12.6465	+	29.3179i	0.497570	+	1.15350i
$647$	−39.2378			−1.54260			−0.771298	−	0.636474i	$-0.780392\pi$
$647$	−39.2378			−1.54260			−0.771298	+	0.636474i	$0.780392\pi$
$648$	−5.84468	−	6.84396i	−0.229601	−	0.268856i
$649$	12.8626			0.504902
$650$	1.65257	+	3.83109i	0.0648192	+	0.150268i
$651$	−3.66504	+	8.90276i	−0.143644	+	0.348927i
$652$	14.6173	−	15.4934i	0.572458	−	0.606770i
$653$	−0.545832	+	9.37158i	−0.0213601	+	0.366738i	0.970643	+	0.240525i	$0.0773195\pi$
$653$	−0.545832	+	9.37158i	−0.0213601	+	0.366738i	−0.992003	+	0.126214i	$0.959718\pi$
$654$	−4.45188	−	7.42161i	−0.174082	−	0.290208i
$655$	6.97503	−	1.65311i	0.272537	−	0.0645925i
$656$	6.12085	+	2.22781i	0.238979	+	0.0869813i
$657$	−5.22017	+	7.52442i	−0.203658	+	0.293556i
$658$	2.24555	−	0.817314i	0.0875407	−	0.0318622i
$659$	1.56937	−	1.03219i	0.0611340	−	0.0402085i	−0.518574	−	0.855033i	$-0.673537\pi$
$659$	1.56937	−	1.03219i	0.0611340	−	0.0402085i	0.579708	+	0.814824i	$0.303167\pi$
$660$	3.24851	+	7.19769i	0.126448	+	0.280170i
$661$	32.4822	−	3.79662i	1.26341	−	0.147671i	0.542118	−	0.840302i	$-0.317623\pi$
$661$	32.4822	−	3.79662i	1.26341	−	0.147671i	0.721292	+	0.692631i	$0.243549\pi$
$662$	−3.09082	−	4.15169i	−0.120128	−	0.161360i
$663$	−2.29749	−	30.6205i	−0.0892270	−	1.18920i
$664$	0.419451	+	7.20170i	0.0162779	+	0.279480i
$665$	−10.2505	−	8.60120i	−0.397498	−	0.333540i
$666$	−0.459278	+	18.5518i	−0.0177967	+	0.718867i
$667$	3.43113	−	2.87906i	0.132854	−	0.111478i
$668$	6.24483	+	6.61914i	0.241620	+	0.256102i
$669$	−3.38989	+	21.3008i	−0.131061	+	0.823538i
$670$	−21.6285	−	14.2253i	−0.835583	−	0.549571i
$671$	−19.3862	−	4.59462i	−0.748397	−	0.177373i
$672$	1.17489	+	0.257796i	0.0453225	+	0.00994469i
$673$	30.3981	+	3.55302i	1.17176	+	0.136959i	0.679625	−	0.733560i	$-0.262143\pi$
$673$	30.3981	+	3.55302i	1.17176	+	0.136959i	0.492135	+	0.870519i	$0.336217\pi$
$674$	−13.2196	−	22.8970i	−0.509199	−	0.881959i
$675$	4.74717	−	1.37973i	0.182719	−	0.0531057i
$676$	−3.11616	+	5.39734i	−0.119852	+	0.207590i
$677$	−11.1166	+	14.9322i	−0.427245	+	0.573889i	−0.962665	−	0.270697i	$-0.912746\pi$
$677$	−11.1166	+	14.9322i	−0.427245	+	0.573889i	0.535420	+	0.844586i	$0.320153\pi$
$678$	−0.698131	+	16.8272i	−0.0268116	+	0.646243i
$679$	0.893708	+	2.98519i	0.0342974	+	0.114561i
$680$	8.81299	−	4.42605i	0.337963	−	0.169731i
$681$	−16.0245	+	13.9091i	−0.614060	+	0.532996i
$682$	4.29019	−	14.3302i	0.164280	−	0.548733i
$683$	−5.67430	−	32.1806i	−0.217121	−	1.23135i	−0.877188	−	0.480148i	$-0.840583\pi$
$683$	−5.67430	−	32.1806i	−0.217121	−	1.23135i	0.660067	−	0.751207i	$-0.270528\pi$
$684$	−22.5243	−	7.35548i	−0.861238	−	0.281244i
$685$	9.56743	−	54.2596i	0.365553	−	2.07315i
$686$	−8.38902	−	4.21313i	−0.320294	−	0.160858i
$687$	6.26735	−	22.2832i	0.239114	−	0.850159i
$688$	−1.69039	+	3.91876i	−0.0644454	+	0.149401i
$689$	18.4853	−	42.8537i	0.704234	−	1.63260i
$690$	8.00002	+	8.20053i	0.304556	+	0.312189i
$691$	19.4419	+	9.76411i	0.739606	+	0.371444i	0.778371	−	0.627804i	$-0.216046\pi$
$691$	19.4419	+	9.76411i	0.739606	+	0.371444i	−0.0387652	+	0.999248i	$0.512342\pi$
$692$	1.74858	−	9.91668i	0.0664710	−	0.376976i
$693$	2.05840	+	3.30501i	0.0781923	+	0.125547i
$694$	0.610082	+	3.45995i	0.0231584	+	0.131338i
$695$	6.86784	−	22.9402i	0.260512	−	0.870171i
$696$	2.70474	+	0.933556i	0.102523	+	0.0353864i
$697$	23.5310	−	11.8177i	0.891299	−	0.447627i
$698$	6.58711	+	22.0025i	0.249326	+	0.832806i
$699$	−7.93488	−	5.03092i	−0.300125	−	0.190287i
$700$	−0.394549	+	0.529971i	−0.0149125	+	0.0200310i
$701$	15.0925	−	26.1410i	0.570036	−	0.987332i	−0.426525	−	0.904476i	$-0.640263\pi$
$701$	15.0925	−	26.1410i	0.570036	−	0.987332i	0.996562	−	0.0828560i	$-0.0264042\pi$
$702$	18.1684	+	13.7543i	0.685724	+	0.519121i
$703$	24.4287	+	42.3118i	0.921346	+	1.59582i
$704$	−1.85624	−	0.216964i	−0.0699598	−	0.00817713i
$705$	4.40227	+	13.8573i	0.165799	+	0.521898i
$706$	−10.4136	−	2.46806i	−0.391920	−	0.0928867i
$707$	3.97412	+	2.61382i	0.149462	+	0.0983027i
$708$	9.25871	+	7.50891i	0.347964	+	0.282202i
$709$	−19.3256	−	20.4840i	−0.725789	−	0.769291i	0.254455	−	0.967085i	$-0.418104\pi$
$709$	−19.3256	−	20.4840i	−0.725789	−	0.769291i	−0.980244	+	0.197793i	$0.936623\pi$
$710$	15.8661	−	13.3133i	0.595445	−	0.499638i
$711$	−29.1260	+	4.39545i	−1.09231	+	0.164842i
$712$	14.1887	+	11.9058i	0.531745	+	0.446187i
$713$	−1.26183	−	21.6647i	−0.0472558	−	0.811351i
$714$	4.01738	−	2.73954i	0.150347	−	0.102525i
$715$	−11.9398	−	16.0379i	−0.446523	−	0.599784i
$716$	−12.6143	+	1.47440i	−0.471418	+	0.0551008i
$717$	3.29502	+	0.329414i	0.123055	+	0.0123022i
$718$	26.4621	−	17.4044i	0.987555	−	0.649525i
$719$	−3.87526	+	1.41048i	−0.144523	+	0.0526020i	−0.413269	−	0.910609i	$-0.635613\pi$
$719$	−3.87526	+	1.41048i	−0.144523	+	0.0526020i	0.268746	+	0.963211i	$0.413391\pi$
$720$	−1.86353	+	7.07742i	−0.0694495	+	0.263760i
$721$	6.87952	+	2.50394i	0.256207	+	0.0932516i
$722$	−42.2137	+	10.0048i	−1.57103	+	0.372341i
$723$	−5.38322	+	9.69466i	−0.200204	+	0.360548i
$724$	0.173883	−	2.98546i	0.00646232	−	0.110954i
$725$	−1.07856	+	1.14321i	−0.0400567	+	0.0424577i
$726$	7.93808	+	10.2988i	0.294610	+	0.382224i
$727$	15.8886	+	36.8340i	0.589277	+	1.36610i	0.908288	+	0.418346i	$0.137390\pi$
$727$	15.8886	+	36.8340i	0.589277	+	1.36610i	−0.319011	+	0.947751i	$0.603351\pi$
$728$	−3.04554			−0.112875
$729$	18.8419	−	19.3387i	0.697846	−	0.716248i
$730$	7.44704			0.275627
$731$	6.83347	+	15.8418i	0.252745	+	0.585928i
$732$	−11.2723	−	14.6245i	−0.416635	−	0.540538i
$733$	3.92057	−	4.15556i	0.144809	−	0.153489i	−0.650909	−	0.759156i	$-0.725612\pi$
$733$	3.92057	−	4.15556i	0.144809	−	0.153489i	0.795718	+	0.605667i	$0.207094\pi$
$734$	−0.741783	+	12.7359i	−0.0273797	+	0.470091i
$735$	13.3695	−	24.0772i	0.493143	−	0.888103i
$736$	−2.63822	+	0.625269i	−0.0972461	+	0.0230477i
$737$	18.6357	+	6.78282i	0.686453	+	0.249848i
$738$	−4.97567	+	18.8969i	−0.183157	+	0.695606i
$739$	11.1409	−	4.05496i	0.409825	−	0.149164i	−0.128877	−	0.991661i	$-0.541137\pi$
$739$	11.1409	−	4.05496i	0.409825	−	0.149164i	0.538702	+	0.842496i	$0.318915\pi$
$740$	12.6080	−	8.29243i	0.463480	−	0.304836i
$741$	59.6967	+	5.96807i	2.19301	+	0.219243i
$742$	7.34058	−	0.857991i	0.269481	−	0.0314978i
$743$	−0.164744	−	0.221290i	−0.00604388	−	0.00811834i	0.799091	−	0.601210i	$-0.205315\pi$
$743$	−0.164744	−	0.221290i	−0.00604388	−	0.00811834i	−0.805135	+	0.593092i	$0.797907\pi$
$744$	11.4538	−	7.81060i	0.419917	−	0.286351i
$745$	1.26461	+	21.7125i	0.0463317	+	0.795485i
$746$	18.3531	+	15.4001i	0.671956	+	0.563838i
$747$	−21.3994	+	3.22942i	−0.782963	+	0.118158i
$748$	−5.78749	+	4.85628i	−0.211612	+	0.177563i
$749$	7.61816	+	8.07478i	0.278362	+	0.295046i
$750$	13.2867	+	10.7757i	0.485162	+	0.393471i
$751$	−8.35010	−	5.49195i	−0.304700	−	0.200404i	0.387946	−	0.921682i	$-0.373185\pi$
$751$	−8.35010	−	5.49195i	−0.304700	−	0.200404i	−0.692646	+	0.721278i	$0.743555\pi$
$752$	−3.34828	−	0.793556i	−0.122099	−	0.0289380i
$753$	−5.49501	−	17.2971i	−0.200249	−	0.630340i
$754$	−7.19573	−	0.841060i	−0.262053	−	0.0306296i
$755$	16.7790	+	29.0622i	0.610652	+	1.05768i
$756$	−0.447722	+	3.58065i	−0.0162835	+	0.130227i
$757$	13.4452	−	23.2877i	0.488672	−	0.846405i	−0.511243	−	0.859436i	$-0.670815\pi$
$757$	13.4452	−	23.2877i	0.488672	−	0.846405i	0.999915	+	0.0130311i	$0.00414804\pi$
$758$	0.644984	−	0.866364i	0.0234269	−	0.0314678i
$759$	−7.41221	−	4.69953i	−0.269046	−	0.170582i
$760$	5.52620	+	18.4588i	0.200456	+	0.669571i
$761$	2.86608	−	1.43940i	0.103895	−	0.0521782i	−0.396093	−	0.918211i	$-0.629634\pi$
$761$	2.86608	−	1.43940i	0.103895	−	0.0521782i	0.499988	+	0.866032i	$0.333338\pi$
$762$	7.54094	+	2.60280i	0.273179	+	0.0942894i
$763$	−0.995203	+	3.32421i	−0.0360288	+	0.120344i
$764$	1.54815	+	8.78001i	0.0560102	+	0.317650i
$765$	15.6410	+	25.1135i	0.565502	+	0.907980i
$766$	6.53748	−	37.0759i	0.236209	−	1.33961i
$767$	−26.9726	−	13.5461i	−0.973924

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 162 = 2 \cdot 3^{4} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	162.g (of order \(27\), degree \(18\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.396080 - 0.918216i) q^{2} +(1.05738 + 1.37184i) q^{3} +(-0.686242 + 0.727374i) q^{4} +(-0.141847 + 2.43542i) q^{5} +(0.840836 - 1.51426i) q^{6} +(-0.675743 + 0.160154i) q^{7} +(0.939693 + 0.342020i) q^{8} +(-0.763881 + 2.90112i) q^{9} +O(q^{10})\)	\(q+(-0.396080 - 0.918216i) q^{2} +(1.05738 + 1.37184i) q^{3} +(-0.686242 + 0.727374i) q^{4} +(-0.141847 + 2.43542i) q^{5} +(0.840836 - 1.51426i) q^{6} +(-0.675743 + 0.160154i) q^{7} +(0.939693 + 0.342020i) q^{8} +(-0.763881 + 2.90112i) q^{9} +(2.29243 - 0.834375i) q^{10} +(-1.56143 + 1.02697i) q^{11} +(-1.72346 - 0.172300i) q^{12} +(4.35581 - 0.509122i) q^{13} +(0.414704 + 0.557045i) q^{14} +(-3.49099 + 2.38058i) q^{15} +(-0.0581448 - 0.998308i) q^{16} +(-3.09677 - 2.59850i) q^{17} +(2.96641 - 0.447666i) q^{18} +(6.05044 - 5.07693i) q^{19} +(-1.67412 - 1.77446i) q^{20} +(-0.934225 - 0.757666i) q^{21} +(1.56143 + 1.02697i) q^{22} +(2.63822 + 0.625269i) q^{23} +(0.524419 + 1.65075i) q^{24} +(-0.944964 - 0.110450i) q^{25} +(-2.19273 - 3.79792i) q^{26} +(-4.78758 + 2.01967i) q^{27} +(0.347231 - 0.601422i) q^{28} +(0.986496 - 1.32509i) q^{29} +(3.56860 + 2.26258i) q^{30} +(-2.29559 - 7.66782i) q^{31} +(-0.893633 + 0.448799i) q^{32} +(-3.05986 - 1.05613i) q^{33} +(-1.15942 + 3.87272i) q^{34} +(-0.294190 - 1.66844i) q^{35} +(-1.58599 - 2.54650i) q^{36} +(-1.07416 + 6.09184i) q^{37} +(-7.05817 - 3.54475i) q^{38} +(5.30420 + 5.43713i) q^{39} +(-0.966256 + 2.24003i) q^{40} +(-2.57993 + 5.98096i) q^{41} +(-0.325674 + 1.15792i) q^{42} +(-3.81384 - 1.91538i) q^{43} +(0.324528 - 1.84049i) q^{44} +(-6.95709 - 2.27189i) q^{45} +(-0.470813 - 2.67011i) q^{46} +(0.986899 - 3.29647i) q^{47} +(1.30804 - 1.13536i) q^{48} +(-5.82445 + 2.92515i) q^{49} +(0.272864 + 0.911429i) q^{50} +(0.290247 - 6.99588i) q^{51} +(-2.61882 + 3.51768i) q^{52} +(5.32106 - 9.21634i) q^{53} +(3.75076 + 3.59608i) q^{54} +(-2.27961 - 3.94840i) q^{55} +(-0.689767 - 0.0806222i) q^{56} +(13.3624 + 2.93198i) q^{57} +(-1.60745 - 0.380973i) q^{58} +(-5.75027 - 3.78201i) q^{59} +(0.664091 - 4.17291i) q^{60} +(7.31570 + 7.75419i) q^{61} +(-6.13147 + 5.14492i) q^{62} +(0.0515617 - 2.08275i) q^{63} +(0.766044 + 0.642788i) q^{64} +(0.622066 + 10.6805i) q^{65} +(0.242194 + 3.22792i) q^{66} +(-6.33676 - 8.51174i) q^{67} +(4.01521 - 0.469311i) q^{68} +(1.93184 + 4.28036i) q^{69} +(-1.41546 + 0.930964i) q^{70} +(7.97798 - 2.90375i) q^{71} +(-1.71005 + 2.46490i) q^{72} +(2.86854 + 1.04406i) q^{73} +(6.01908 - 1.42655i) q^{74} +(-0.847669 - 1.41313i) q^{75} +(-0.459245 + 7.88493i) q^{76} +(0.890651 - 0.944035i) q^{77} +(2.89158 - 7.02394i) q^{78} +(3.88894 + 9.01558i) q^{79} +2.43955 q^{80} +(-7.83297 - 4.43222i) q^{81} +6.51367 q^{82} +(2.85728 + 6.62392i) q^{83} +(1.19221 - 0.159589i) q^{84} +(6.76771 - 7.17335i) q^{85} +(-0.248150 + 4.26057i) q^{86} +(2.86092 - 0.0478192i) q^{87} +(-1.81850 + 0.430993i) q^{88} +(17.4051 + 6.33493i) q^{89} +(0.669479 + 7.28796i) q^{90} +(-2.86187 + 1.04164i) q^{91} +(-2.26526 + 1.48989i) q^{92} +(8.09168 - 11.2570i) q^{93} +(-3.41776 + 0.399479i) q^{94} +(11.5062 + 15.4555i) q^{95} +(-1.56059 - 0.751367i) q^{96} +(-0.260900 - 4.47948i) q^{97} +(4.99286 + 4.18951i) q^{98} +(-1.78661 - 5.31436i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 72 q + 9 q^{6}+O(q^{10}) \) 72 * q + 9 * q^6	\( 72 q + 9 q^{6} + 18 q^{13} - 9 q^{20} - 81 q^{23} + 18 q^{25} - 27 q^{26} - 27 q^{27} + 18 q^{28} - 27 q^{29} - 63 q^{30} - 54 q^{31} + 9 q^{33} - 27 q^{35} - 9 q^{36} + 9 q^{38} - 9 q^{41} + 9 q^{42} + 36 q^{43} - 117 q^{45} - 18 q^{46} - 27 q^{47} + 9 q^{48} - 27 q^{51} - 36 q^{52} - 27 q^{53} + 54 q^{55} + 27 q^{57} + 9 q^{58} - 18 q^{59} + 9 q^{63} + 9 q^{65} + 36 q^{66} - 135 q^{67} - 18 q^{68} + 108 q^{69} + 18 q^{70} + 72 q^{71} + 54 q^{72} + 36 q^{73} + 99 q^{74} - 36 q^{75} - 9 q^{76} + 144 q^{77} + 90 q^{78} - 9 q^{79} + 18 q^{80} - 72 q^{82} + 99 q^{83} + 18 q^{84} + 9 q^{85} + 72 q^{86} + 207 q^{87} - 9 q^{88} + 126 q^{89} - 18 q^{90} + 63 q^{91} + 36 q^{92} + 81 q^{93} + 18 q^{94} + 45 q^{95} - 171 q^{97} + 36 q^{98} + 99 q^{99}+O(q^{100}) \) 72 * q + 9 * q^6 + 18 * q^13 - 9 * q^20 - 81 * q^23 + 18 * q^25 - 27 * q^26 - 27 * q^27 + 18 * q^28 - 27 * q^29 - 63 * q^30 - 54 * q^31 + 9 * q^33 - 27 * q^35 - 9 * q^36 + 9 * q^38 - 9 * q^41 + 9 * q^42 + 36 * q^43 - 117 * q^45 - 18 * q^46 - 27 * q^47 + 9 * q^48 - 27 * q^51 - 36 * q^52 - 27 * q^53 + 54 * q^55 + 27 * q^57 + 9 * q^58 - 18 * q^59 + 9 * q^63 + 9 * q^65 + 36 * q^66 - 135 * q^67 - 18 * q^68 + 108 * q^69 + 18 * q^70 + 72 * q^71 + 54 * q^72 + 36 * q^73 + 99 * q^74 - 36 * q^75 - 9 * q^76 + 144 * q^77 + 90 * q^78 - 9 * q^79 + 18 * q^80 - 72 * q^82 + 99 * q^83 + 18 * q^84 + 9 * q^85 + 72 * q^86 + 207 * q^87 - 9 * q^88 + 126 * q^89 - 18 * q^90 + 63 * q^91 + 36 * q^92 + 81 * q^93 + 18 * q^94 + 45 * q^95 - 171 * q^97 + 36 * q^98 + 99 * q^99

Introduction

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