LMFDB - Embedded newform 162.2.g.a.7.1

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			7.1
Character	$\chi$	$=$	162.7
Dual form			162.2.g.a.139.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.597159 - 0.802123i) q^{2} +(-1.65406 + 0.513880i) q^{3} +(-0.286803 + 0.957990i) q^{4} +(2.13228 - 1.40243i) q^{5} +(1.39993 + 1.01990i) q^{6} +(-0.606844 + 0.643217i) q^{7} +(0.939693 - 0.342020i) q^{8} +(2.47185 - 1.69998i) q^{9} +O(q^{10})$	\(q+(-0.597159 - 0.802123i) q^{2} +(-1.65406 + 0.513880i) q^{3} +(-0.286803 + 0.957990i) q^{4} +(2.13228 - 1.40243i) q^{5} +(1.39993 + 1.01990i) q^{6} +(-0.606844 + 0.643217i) q^{7} +(0.939693 - 0.342020i) q^{8} +(2.47185 - 1.69998i) q^{9} +(-2.39823 - 0.872884i) q^{10} +(4.06416 - 2.04110i) q^{11} +(-0.0179009 - 1.73196i) q^{12} +(-2.69275 - 6.24250i) q^{13} +(0.878322 + 0.102661i) q^{14} +(-2.80626 + 3.41544i) q^{15} +(-0.835488 - 0.549509i) q^{16} +(1.89618 - 1.59109i) q^{17} +(-2.83968 - 0.967574i) q^{18} +(4.81115 + 4.03704i) q^{19} +(0.731963 + 2.44493i) q^{20} +(0.673223 - 1.37577i) q^{21} +(-4.06416 - 2.04110i) q^{22} +(0.808531 + 0.856993i) q^{23} +(-1.37855 + 1.04861i) q^{24} +(0.599441 - 1.38966i) q^{25} +(-3.39926 + 5.88769i) q^{26} +(-3.21502 + 4.08211i) q^{27} +(-0.442151 - 0.765827i) q^{28} +(-0.855129 + 0.0999503i) q^{29} +(4.41538 + 0.211404i) q^{30} +(-7.52782 + 1.78413i) q^{31} +(0.0581448 + 0.998308i) q^{32} +(-5.67350 + 5.46460i) q^{33} +(-2.40857 - 0.570841i) q^{34} +(-0.391900 + 2.22258i) q^{35} +(0.919628 + 2.85557i) q^{36} +(1.51717 + 8.60431i) q^{37} +(0.365179 - 6.26989i) q^{38} +(7.66188 + 8.94175i) q^{39} +(1.52403 - 2.04713i) q^{40} +(4.25521 - 5.71574i) q^{41} +(-1.50556 + 0.281544i) q^{42} +(0.375968 - 6.45512i) q^{43} +(0.789737 + 4.47882i) q^{44} +(2.88660 - 7.09144i) q^{45} +(0.204593 - 1.16030i) q^{46} +(-4.65668 - 1.10365i) q^{47} +(1.66433 + 0.479582i) q^{48} +(0.361545 + 6.20749i) q^{49} +(-1.47264 + 0.349022i) q^{50} +(-2.31878 + 3.60617i) q^{51} +(6.75254 - 0.789259i) q^{52} +(2.47156 + 4.28086i) q^{53} +(5.19423 + 0.141172i) q^{54} +(5.80346 - 10.0519i) q^{55} +(-0.350254 + 0.811980i) q^{56} +(-10.0325 - 4.20516i) q^{57} +(0.590820 + 0.626233i) q^{58} +(-4.45417 - 2.23697i) q^{59} +(-2.46711 - 3.66792i) q^{60} +(0.694103 + 2.31847i) q^{61} +(5.92639 + 4.97283i) q^{62} +(-0.406574 + 2.62156i) q^{63} +(0.766044 - 0.642788i) q^{64} +(-14.4964 - 9.53441i) q^{65} +(7.77127 + 1.28762i) q^{66} +(2.81724 + 0.329288i) q^{67} +(0.980412 + 2.27285i) q^{68} +(-1.77775 - 1.00203i) q^{69} +(2.01681 - 1.01288i) q^{70} +(-10.2786 - 3.74111i) q^{71} +(1.74136 - 2.44288i) q^{72} +(-5.92032 + 2.15482i) q^{73} +(5.99572 - 6.35510i) q^{74} +(-0.277395 + 2.60663i) q^{75} +(-5.24729 + 3.45120i) q^{76} +(-1.15344 + 3.85277i) q^{77} +(2.59702 - 11.4854i) q^{78} +(1.95423 + 2.62498i) q^{79} -2.55214 q^{80} +(3.22013 - 8.40421i) q^{81} -7.12577 q^{82} +(-1.88641 - 2.53389i) q^{83} +(1.12489 + 1.03952i) q^{84} +(1.81182 - 6.05190i) q^{85} +(-5.40232 + 3.55316i) q^{86} +(1.36308 - 0.604758i) q^{87} +(3.12097 - 3.30803i) q^{88} +(5.44891 - 1.98324i) q^{89} +(-7.41196 + 1.91930i) q^{90} +(5.64937 + 2.05620i) q^{91} +(-1.05288 + 0.528776i) q^{92} +(11.5347 - 6.81946i) q^{93} +(1.89551 + 4.39429i) q^{94} +(15.9204 + 1.86083i) q^{95} +(-0.609186 - 1.62139i) q^{96} +(0.222871 + 0.146585i) q^{97} +(4.76327 - 3.99686i) q^{98} +(6.57619 - 11.9543i) 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 $\left(\mathbb{Z}/162\mathbb{Z}\right)^\times$.

$n$	$83$
$\chi(n)$	$e\left(\frac{8}{27}\right)$

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 $

$2$	−0.597159	−	0.802123i	−0.422255	−	0.567187i
$2$	−0.597159	−	0.802123i	−0.422255	−	0.567187i
$3$	−1.65406	+	0.513880i	−0.954974	+	0.296689i
$3$	−1.65406	+	0.513880i	−0.954974	+	0.296689i
$4$	−0.286803	+	0.957990i	−0.143402	+	0.478995i
$5$	2.13228	−	1.40243i	0.953587	−	0.627184i	0.0255503	−	0.999674i	$-0.491866\pi$
$5$	2.13228	−	1.40243i	0.953587	−	0.627184i	0.928036	+	0.372490i	$0.121496\pi$
$6$	1.39993	+	1.01990i	0.571520	+	0.416370i
$7$	−0.606844	+	0.643217i	−0.229366	+	0.243113i	−0.831827	−	0.555034i	$-0.812705\pi$
$7$	−0.606844	+	0.643217i	−0.229366	+	0.243113i	0.602462	+	0.798148i	$0.294187\pi$
$8$	0.939693	−	0.342020i	0.332232	−	0.120922i
$9$	2.47185	−	1.69998i	0.823952	−	0.566660i
$10$	−2.39823	−	0.872884i	−0.758387	−	0.276030i
$11$	4.06416	−	2.04110i	1.22539	−	0.615415i	0.285989	−	0.958233i	$-0.407678\pi$
$11$	4.06416	−	2.04110i	1.22539	−	0.615415i	0.939402	+	0.342818i	$0.111381\pi$
$12$	−0.0179009	−	1.73196i	−0.00516754	−	0.499973i
$13$	−2.69275	−	6.24250i	−0.746835	−	1.73136i	−0.679554	−	0.733625i	$-0.737827\pi$
$13$	−2.69275	−	6.24250i	−0.746835	−	1.73136i	−0.0672811	−	0.997734i	$-0.521432\pi$
$14$	0.878322	+	0.102661i	0.234741	+	0.0274373i
$15$	−2.80626	+	3.41544i	−0.724572	+	0.881863i
$16$	−0.835488	−	0.549509i	−0.208872	−	0.137377i
$17$	1.89618	−	1.59109i	0.459892	−	0.385895i	−0.383199	−	0.923666i	$-0.625178\pi$
$17$	1.89618	−	1.59109i	0.459892	−	0.385895i	0.843091	+	0.537771i	$0.180733\pi$
$18$	−2.83968	−	0.967574i	−0.669320	−	0.228059i
$19$	4.81115	+	4.03704i	1.10375	+	0.926160i	0.997672	−	0.0681975i	$-0.0217248\pi$
$19$	4.81115	+	4.03704i	1.10375	+	0.926160i	0.106083	+	0.994357i	$0.466169\pi$
$20$	0.731963	+	2.44493i	0.163672	+	0.546702i
$21$	0.673223	−	1.37577i	0.146909	−	0.300217i
$22$	−4.06416	−	2.04110i	−0.866482	−	0.435164i
$23$	0.808531	+	0.856993i	0.168590	+	0.178695i	0.806160	−	0.591697i	$-0.201542\pi$
$23$	0.808531	+	0.856993i	0.168590	+	0.178695i	−0.637570	+	0.770392i	$0.720060\pi$
$24$	−1.37855	+	1.04861i	−0.281396	+	0.214047i
$25$	0.599441	−	1.38966i	0.119888	−	0.277932i
$26$	−3.39926	+	5.88769i	−0.666649	+	1.15467i
$27$	−3.21502	+	4.08211i	−0.618731	+	0.785603i
$28$	−0.442151	−	0.765827i	−0.0835586	−	0.144728i
$29$	−0.855129	+	0.0999503i	−0.158794	+	0.0185603i	−0.195118	−	0.980780i	$-0.562509\pi$
$29$	−0.855129	+	0.0999503i	−0.158794	+	0.0185603i	0.0363247	+	0.999340i	$0.488435\pi$
$30$	4.41538	+	0.211404i	0.806135	+	0.0385969i
$31$	−7.52782	+	1.78413i	−1.35204	+	0.320439i	−0.841890	−	0.539649i	$-0.818557\pi$
$31$	−7.52782	+	1.78413i	−1.35204	+	0.320439i	−0.510146	+	0.860088i	$0.670409\pi$
$32$	0.0581448	+	0.998308i	0.0102787	+	0.176478i
$33$	−5.67350	+	5.46460i	−0.987630	+	0.951265i
$34$	−2.40857	−	0.570841i	−0.413066	−	0.0978985i
$35$	−0.391900	+	2.22258i	−0.0662432	+	0.375684i
$36$	0.919628	+	2.85557i	0.153271	+	0.475928i
$37$	1.51717	+	8.60431i	0.249421	+	1.41454i	0.809996	+	0.586435i	$0.199469\pi$
$37$	1.51717	+	8.60431i	0.249421	+	1.41454i	−0.560574	+	0.828104i	$0.689420\pi$
$38$	0.365179	−	6.26989i	0.0592399	−	1.01711i
$39$	7.66188	+	8.94175i	1.22688	+	1.43183i
$40$	1.52403	−	2.04713i	0.240971	−	0.323680i
$41$	4.25521	−	5.71574i	0.664552	−	0.892649i	−0.334204	−	0.942501i	$-0.608467\pi$
$41$	4.25521	−	5.71574i	0.664552	−	0.892649i	0.998757	+	0.0498518i	$0.0158749\pi$
$42$	−1.50556	+	0.281544i	−0.232312	+	0.0434432i
$43$	0.375968	−	6.45512i	0.0573346	−	0.984397i	−0.839871	−	0.542785i	$-0.817370\pi$
$43$	0.375968	−	6.45512i	0.0573346	−	0.984397i	0.897206	−	0.441612i	$-0.145593\pi$
$44$	0.789737	+	4.47882i	0.119057	+	0.675207i
$45$	2.88660	−	7.09144i	0.430309	−	1.05713i
$46$	0.204593	−	1.16030i	0.0301655	−	0.171077i
$47$	−4.65668	−	1.10365i	−0.679247	−	0.160985i	−0.123511	−	0.992343i	$-0.539415\pi$
$47$	−4.65668	−	1.10365i	−0.679247	−	0.160985i	−0.555736	+	0.831359i	$0.687564\pi$
$48$	1.66433	+	0.479582i	0.240226	+	0.0692218i
$49$	0.361545	+	6.20749i	0.0516493	+	0.886784i
$50$	−1.47264	+	0.349022i	−0.208263	+	0.0493592i
$51$	−2.31878	+	3.60617i	−0.324694	+	0.504964i
$52$	6.75254	−	0.789259i	0.936409	−	0.109451i
$53$	2.47156	+	4.28086i	0.339494	+	0.588021i	0.984338	−	0.176293i	$-0.0564108\pi$
$53$	2.47156	+	4.28086i	0.339494	+	0.588021i	−0.644843	+	0.764315i	$0.723077\pi$
$54$	5.19423	+	0.141172i	0.706846	+	0.0192110i
$55$	5.80346	−	10.0519i	0.782539	−	1.35540i
$56$	−0.350254	+	0.811980i	−0.0468046	+	0.108505i
$57$	−10.0325	−	4.20516i	−1.32884	−	0.556987i
$58$	0.590820	+	0.626233i	0.0775785	+	0.0822284i
$59$	−4.45417	−	2.23697i	−0.579884	−	0.291229i	0.134578	−	0.990903i	$-0.457032\pi$
$59$	−4.45417	−	2.23697i	−0.579884	−	0.291229i	−0.714462	+	0.699674i	$0.753328\pi$
$60$	−2.46711	−	3.66792i	−0.318503	−	0.473527i
$61$	0.694103	+	2.31847i	0.0888708	+	0.296849i	0.990857	−	0.134916i	$-0.0430763\pi$
$61$	0.694103	+	2.31847i	0.0888708	+	0.296849i	−0.901986	+	0.431765i	$0.857891\pi$
$62$	5.92639	+	4.97283i	0.752653	+	0.631550i
$63$	−0.406574	+	2.62156i	−0.0512235	+	0.330286i
$64$	0.766044	−	0.642788i	0.0957556	−	0.0803485i
$65$	−14.4964	−	9.53441i	−1.79805	−	1.18260i
$66$	7.77127	+	1.28762i	0.956577	+	0.158495i
$67$	2.81724	+	0.329288i	0.344181	+	0.0402289i	0.286427	−	0.958102i	$-0.407532\pi$
$67$	2.81724	+	0.329288i	0.344181	+	0.0402289i	0.0577532	+	0.998331i	$0.481606\pi$
$68$	0.980412	+	2.27285i	0.118892	+	0.275624i
$69$	−1.77775	−	1.00203i	−0.214016	−	0.120631i
$70$	2.01681	−	1.01288i	0.241055	−	0.121062i
$71$	−10.2786	−	3.74111i	−1.21985	−	0.443988i	−0.349738	−	0.936848i	$-0.613729\pi$
$71$	−10.2786	−	3.74111i	−1.21985	−	0.443988i	−0.870109	+	0.492860i	$0.835952\pi$
$72$	1.74136	−	2.44288i	0.205221	−	0.287897i
$73$	−5.92032	+	2.15482i	−0.692921	+	0.252202i	−0.664385	−	0.747390i	$-0.731307\pi$
$73$	−5.92032	+	2.15482i	−0.692921	+	0.252202i	−0.0285354	+	0.999593i	$0.509084\pi$
$74$	5.99572	−	6.35510i	0.696989	−	0.738765i
$75$	−0.277395	+	2.60663i	−0.0320308	+	0.300987i
$76$	−5.24729	+	3.45120i	−0.601906	+	0.395880i
$77$	−1.15344	+	3.85277i	−0.131447	+	0.439064i
$78$	2.59702	−	11.4854i	0.294055	−	1.30047i
$79$	1.95423	+	2.62498i	0.219868	+	0.295334i	0.898348	−	0.439285i	$-0.144768\pi$
$79$	1.95423	+	2.62498i	0.219868	+	0.295334i	−0.678480	+	0.734619i	$0.737361\pi$
$80$	−2.55214			−0.285338
$81$	3.22013	−	8.40421i	0.357792	−	0.933801i
$82$	−7.12577			−0.786909
$83$	−1.88641	−	2.53389i	−0.207061	−	0.278131i	0.686446	−	0.727181i	$-0.259170\pi$
$83$	−1.88641	−	2.53389i	−0.207061	−	0.278131i	−0.893507	+	0.449050i	$0.851762\pi$
$84$	1.12489	+	1.03952i	0.122735	+	0.113420i
$85$	1.81182	−	6.05190i	0.196520	−	0.656421i
$86$	−5.40232	+	3.55316i	−0.582547	+	0.383147i
$87$	1.36308	−	0.604758i	0.146137	−	0.0648369i
$88$	3.12097	−	3.30803i	0.332696	−	0.352637i
$89$	5.44891	−	1.98324i	0.577583	−	0.210223i	−0.0366764	−	0.999327i	$-0.511677\pi$
$89$	5.44891	−	1.98324i	0.577583	−	0.210223i	0.614259	+	0.789104i	$0.289455\pi$
$90$	−7.41196	+	1.91930i	−0.781289	+	0.202312i
$91$	5.64937	+	2.05620i	0.592215	+	0.215549i
$92$	−1.05288	+	0.528776i	−0.109770	+	0.0551287i
$93$	11.5347	−	6.81946i	1.19609	−	0.707145i
$94$	1.89551	+	4.39429i	0.195507	+	0.453236i
$95$	15.9204	+	1.86083i	1.63340	+	0.190917i
$96$	−0.609186	−	1.62139i	−0.0621748	−	0.165482i
$97$	0.222871	+	0.146585i	0.0226292	+	0.0148834i	0.560773	−	0.827969i	$-0.310504\pi$
$97$	0.222871	+	0.146585i	0.0226292	+	0.0148834i	−0.538144	+	0.842853i	$0.680874\pi$
$98$	4.76327	−	3.99686i	0.481163	−	0.403744i
$99$	6.57619	−	11.9543i	0.660932	−	1.20145i
$100$	1.15936	+	0.972817i	0.115936	+	0.0972817i
$101$	4.91049	+	16.4022i	0.488612	+	1.63208i	0.746128	+	0.665803i	$0.231911\pi$
$101$	4.91049	+	16.4022i	0.488612	+	1.63208i	−0.257516	+	0.966274i	$0.582904\pi$
$102$	4.27727	−	0.293508i	0.423513	−	0.0290616i
$103$	−1.71448	−	0.861043i	−0.168933	−	0.0848411i	0.362324	−	0.932052i	$-0.381984\pi$
$103$	−1.71448	−	0.861043i	−0.168933	−	0.0848411i	−0.531256	+	0.847211i	$0.678280\pi$
$104$	−4.66542	−	4.94506i	−0.457482	−	0.484903i
$105$	−0.493910	−	3.87767i	−0.0482007	−	0.378422i
$106$	1.95787	−	4.53884i	0.190165	−	0.440851i
$107$	−9.11205	+	15.7825i	−0.880895	+	1.52575i	−0.0305470	+	0.999533i	$0.509725\pi$
$107$	−9.11205	+	15.7825i	−0.880895	+	1.52575i	−0.850348	+	0.526221i	$0.823608\pi$
$108$	−2.98854	−	4.25072i	−0.287573	−	0.409026i
$109$	5.96993	+	10.3402i	0.571816	+	0.990414i	0.996380	+	0.0850161i	$0.0270942\pi$
$109$	5.96993	+	10.3402i	0.571816	+	0.990414i	−0.424564	+	0.905398i	$0.639572\pi$
$110$	−11.5284	+	1.34748i	−1.09919	+	0.128477i
$111$	−6.93108	−	13.4524i	−0.657869	−	1.27685i
$112$	0.860465	−	0.203934i	0.0813063	−	0.0192699i
$113$	−0.522123	−	8.96451i	−0.0491172	−	0.843310i	−0.929449	−	0.368951i	$-0.879717\pi$
$113$	−0.522123	−	8.96451i	−0.0491172	−	0.843310i	0.880332	−	0.474359i	$-0.157320\pi$
$114$	2.61794	+	10.5585i	0.245193	+	0.988890i
$115$	2.92589	+	0.693448i	0.272840	+	0.0646643i
$116$	0.149503	−	0.847871i	0.0138810	−	0.0787228i
$117$	−17.2682	−	10.8529i	−1.59645	−	1.00335i
$118$	0.865522	+	4.90862i	0.0796778	+	0.451875i
$119$	−0.127273	+	2.18520i	−0.0116671	+	0.200317i
$120$	−1.46887	+	4.16926i	−0.134089	+	0.380600i
$121$	5.78259	−	7.76737i	0.525690	−	0.706124i
$122$	1.44521	−	1.94125i	0.130843	−	0.175752i
$123$	−4.10119	+	11.6409i	−0.369792	+	1.04962i
$124$	0.449829	−	7.72327i	0.0403958	−	0.693570i
$125$	1.54516	+	8.76303i	0.138203	+	0.783789i
$126$	2.34561	−	1.23937i	0.208963	−	0.110412i
$127$	−3.15631	+	17.9003i	−0.280077	+	1.58840i	0.442281	+	0.896876i	$0.354169\pi$
$127$	−3.15631	+	17.9003i	−0.280077	+	1.58840i	−0.722358	+	0.691519i	$0.756942\pi$
$128$	−0.973045	−	0.230616i	−0.0860058	−	0.0203838i
$129$	2.69528	+	10.8704i	0.237307	+	0.957085i
$130$	1.00886	+	17.3214i	0.0884827	+	1.51919i
$131$	12.9101	−	3.05976i	1.12796	−	0.267332i	0.376054	−	0.926598i	$-0.377281\pi$
$131$	12.9101	−	3.05976i	1.12796	−	0.267332i	0.751910	+	0.659265i	$0.229133\pi$
$132$	−3.60785	−	7.00242i	−0.314023	−	0.609483i
$133$	−5.51631	+	0.644765i	−0.478325	+	0.0559082i
$134$	−1.41821	−	2.45641i	−0.122515	−	0.212202i
$135$	−1.13047	+	13.2131i	−0.0972957	+	1.13720i
$136$	1.23765	−	2.14366i	0.106127	−	0.183818i
$137$	3.45487	−	8.00929i	0.295170	−	0.684280i	−0.704507	−	0.709697i	$-0.748832\pi$
$137$	3.45487	−	8.00929i	0.295170	−	0.684280i	0.999677	+	0.0254168i	$0.00809128\pi$
$138$	0.257847	+	2.02435i	0.0219494	+	0.172324i
$139$	−0.0882163	−	0.0935038i	−0.00748241	−	0.00793089i	0.723622	−	0.690197i	$-0.242476\pi$
$139$	−0.0882163	−	0.0935038i	−0.00748241	−	0.00793089i	−0.731104	+	0.682266i	$0.760995\pi$
$140$	−2.01681	−	1.01288i	−0.170451	−	0.0856039i
$141$	8.26960	−	0.567462i	0.696426	−	0.0477890i
$142$	3.13713	+	10.4787i	0.263262	+	0.879357i
$143$	−23.6854	−	19.8744i	−1.98067	−	1.66198i
$144$	−2.99936	+	0.0620071i	−0.249947	+	0.00516726i
$145$	−1.68321	+	1.41238i	−0.139783	+	0.117292i
$146$	5.26380	+	3.46205i	0.435635	+	0.286522i
$147$	−3.78793	−	10.0818i	−0.312423	−	0.831533i
$148$	−8.67797	−	1.01431i	−0.713324	−	0.0833757i
$149$	4.30950	+	9.99055i	0.353048	+	0.818458i	0.998505	+	0.0546609i	$0.0174078\pi$
$149$	4.30950	+	9.99055i	0.353048	+	0.818458i	−0.645457	+	0.763797i	$0.723333\pi$
$150$	2.25649	−	1.33407i	0.184241	−	0.108926i
$151$	7.03070	−	3.53095i	0.572150	−	0.287344i	−0.139106	−	0.990277i	$-0.544423\pi$
$151$	7.03070	−	3.53095i	0.572150	−	0.287344i	0.711256	+	0.702933i	$0.248127\pi$
$152$	5.90175	+	2.14806i	0.478695	+	0.174231i
$153$	1.98227	−	7.15641i	0.160257	−	0.578561i
$154$	3.77919	−	1.37551i	0.304535	−	0.110842i
$155$	−13.5494	+	14.3615i	−1.08831	+	1.15354i
$156$	−10.7636	+	4.77548i	−0.861774	+	0.382345i
$157$	8.24535	−	5.42305i	0.658051	−	0.432807i	−0.176078	−	0.984376i	$-0.556341\pi$
$157$	8.24535	−	5.42305i	0.658051	−	0.432807i	0.834129	+	0.551569i	$0.185971\pi$
$158$	0.938576	−	3.13506i	0.0746691	−	0.249412i
$159$	−6.28796	−	5.81073i	−0.498668	−	0.460821i
$160$	1.52403	+	2.04713i	0.120485	+	0.161840i
$161$	−1.04189			−0.0821121
$162$	−8.66414	+	2.43571i	−0.680719	+	0.191367i
$163$	10.5493			0.826288			0.413144	−	0.910666i	$-0.364431\pi$
$163$	10.5493			0.826288			0.413144	+	0.910666i	$0.364431\pi$
$164$	4.25521	+	5.71574i	0.332276	+	0.446324i
$165$	−4.43383	+	19.6088i	−0.345173	+	1.52654i
$166$	−0.906005	+	3.02627i	−0.0703197	+	0.234884i
$167$	−3.55094	+	2.33549i	−0.274780	+	0.180726i	−0.679418	−	0.733751i	$-0.737768\pi$
$167$	−3.55094	+	2.33549i	−0.274780	+	0.180726i	0.404638	+	0.914477i	$0.367397\pi$
$168$	0.162082	−	1.52305i	0.0125049	−	0.117506i
$169$	−22.7968	+	24.1632i	−1.75360	+	1.85871i
$170$	−5.93632	+	2.16064i	−0.455295	+	0.165714i
$171$	18.7554	+	1.80010i	1.43426	+	0.137657i
$172$	6.07611	+	2.21152i	0.463299	+	0.168627i
$173$	0.254068	−	0.127598i	0.0193165	−	0.00970110i	−0.439115	−	0.898431i	$-0.644708\pi$
$173$	0.254068	−	0.127598i	0.0193165	−	0.00970110i	0.458431	+	0.888730i	$0.348412\pi$
$174$	−1.29906	−	0.732218i	−0.0984817	−	0.0555093i
$175$	0.530086	+	1.22888i	0.0400708	+	0.0928945i
$176$	−4.51716	−	0.527980i	−0.340494	−	0.0397980i
$177$	8.51702	+	1.41118i	0.640178	+	0.106071i
$178$	−4.84466	−	3.18639i	−0.363123	−	0.238830i
$179$	11.8953	−	9.98138i	0.889100	−	0.746043i	−0.0789297	−	0.996880i	$-0.525150\pi$
$179$	11.8953	−	9.98138i	0.889100	−	0.746043i	0.968029	+	0.250837i	$0.0807058\pi$
$180$	5.96563	+	4.79918i	0.444652	+	0.357710i
$181$	−18.1872	−	15.2608i	−1.35184	−	1.13433i	−0.978410	−	0.206671i	$-0.933737\pi$
$181$	−18.1872	−	15.2608i	−1.35184	−	1.13433i	−0.373431	−	0.927658i	$-0.621819\pi$
$182$	−1.72424	−	5.75937i	−0.127809	−	0.426913i
$183$	−2.33950	−	3.47820i	−0.172941	−	0.257116i
$184$	1.05288	+	0.528776i	0.0776193	+	0.0389819i
$185$	15.3019	+	16.2191i	1.12502	+	1.19245i
$186$	−12.3581	−	5.17993i	−0.906138	−	0.379811i
$187$	4.45883	−	10.3367i	0.326062	−	0.755896i
$188$	2.39284	−	4.14452i	0.174516	−	0.302270i
$189$	−0.674671	−	4.54516i	−0.0490751	−	0.330612i
$190$	−8.01439	−	13.8813i	−0.581425	−	1.00706i
$191$	−19.2480	+	2.24976i	−1.39273	+	0.162787i	−0.779147	−	0.626841i	$-0.784348\pi$
$191$	−19.2480	+	2.24976i	−1.39273	+	0.162787i	−0.613586	+	0.789628i	$0.710273\pi$
$192$	−0.936771	+	1.45687i	−0.0676056	+	0.105140i
$193$	−19.7857	+	4.68929i	−1.42420	+	0.337543i	−0.869264	−	0.494348i	$-0.835407\pi$
$193$	−19.7857	+	4.68929i	−1.42420	+	0.337543i	−0.554940	+	0.831891i	$0.687259\pi$
$194$	−0.0155105	−	0.266305i	−0.00111359	−	0.0191196i
$195$	28.8775	+	8.32113i	2.06796	+	0.595888i
$196$	−6.05040	−	1.43397i	−0.432172	−	0.102427i
$197$	2.52128	−	14.2989i	0.179634	−	1.01875i	−0.753024	−	0.657993i	$-0.771406\pi$
$197$	2.52128	−	14.2989i	0.179634	−	1.01875i	0.932658	−	0.360761i	$-0.117483\pi$
$198$	−13.5158	+	1.86370i	−0.960530	+	0.132447i
$199$	−2.76820	−	15.6993i	−0.196233	−	1.11289i	−0.910652	−	0.413173i	$-0.864420\pi$
$199$	−2.76820	−	15.6993i	−0.196233	−	1.11289i	0.714420	−	0.699717i	$-0.246691\pi$
$200$	0.0879984	−	1.51087i	0.00622243	−	0.106835i
$201$	−4.82911	+	0.903060i	−0.340619	+	0.0636969i
$202$	10.2242	−	13.7335i	0.719374	−	0.966287i
$203$	0.454641	−	0.610688i	0.0319095	−	0.0428619i
$204$	−2.78964	−	3.25563i	−0.195314	−	0.227939i
$205$	1.05742	−	18.1552i	0.0738534	−	1.26801i
$206$	0.333152	+	1.88940i	0.0232118	+	0.131641i
$207$	3.45544	+	0.743874i	0.240170	+	0.0517028i
$208$	−1.18055	+	6.69523i	−0.0818564	+	0.464231i
$209$	27.7933	+	6.58713i	1.92250	+	0.455642i
$210$	−2.81543	+	2.71176i	−0.194283	+	0.187129i
$211$	0.804379	+	13.8107i	0.0553757	+	0.950765i	0.905544	+	0.424253i	$0.139463\pi$
$211$	0.804379	+	13.8107i	0.0553757	+	0.950765i	−0.850168	+	0.526512i	$0.823500\pi$
$212$	−4.80987	+	1.13996i	−0.330343	+	0.0782928i
$213$	18.9240	+	0.906059i	1.29665	+	0.0620821i
$214$	18.1009	−	2.11569i	1.23735	−	0.144625i
$215$	−8.25116	−	14.2914i	−0.562725	−	0.974667i
$216$	−1.62496	+	4.93553i	−0.110565	+	0.335821i
$217$	3.42063	−	5.92471i	0.232208	−	0.402196i
$218$	4.72914	−	10.9634i	0.320298	−	0.742534i
$219$	8.68526	−	6.60654i	0.586896	−	0.446429i
$220$	7.96515	+	8.44257i	0.537011	+	0.569198i
$221$	−15.0383	−	7.55252i	−1.01159	−	0.508038i
$222$	−6.65155	+	13.5928i	−0.446423	+	0.912290i
$223$	2.07404	+	6.92777i	0.138888	+	0.463918i	0.998927	−	0.0463101i	$-0.0147462\pi$
$223$	2.07404	+	6.92777i	0.138888	+	0.463918i	−0.860039	+	0.510228i	$0.829561\pi$
$224$	−0.677414	−	0.568418i	−0.0452616	−	0.0379790i
$225$	−0.880665	−	4.45408i	−0.0587110	−	0.296938i
$226$	−6.87885	+	5.77204i	−0.457574	+	0.383950i
$227$	4.75675	+	3.12856i	0.315716	+	0.207650i	0.697470	−	0.716614i	$-0.254309\pi$
$227$	4.75675	+	3.12856i	0.315716	+	0.207650i	−0.381753	+	0.924264i	$0.624680\pi$
$228$	6.90586	−	8.40498i	0.457352	−	0.556634i
$229$	−3.67805	−	0.429902i	−0.243052	−	0.0284087i	−0.00630543	−	0.999980i	$-0.502007\pi$
$229$	−3.67805	−	0.429902i	−0.243052	−	0.0284087i	−0.236747	+	0.971571i	$0.576081\pi$
$230$	−1.19099	−	2.76102i	−0.0785314	−	0.182056i
$231$	−0.0719924	−	6.96546i	−0.00473675	−	0.458294i
$232$	−0.769374	+	0.386394i	−0.0505119	+	0.0253680i
$233$	22.6677	+	8.25035i	1.48501	+	0.540499i	0.952130	−	0.305694i	$-0.0988883\pi$
$233$	22.6677	+	8.25035i	1.48501	+	0.540499i	0.532878	+	0.846192i	$0.321111\pi$
$234$	1.60648	+	20.3322i	0.105019	+	1.32916i
$235$	−11.4772	+	4.17735i	−0.748688	+	0.272500i
$236$	3.42046	−	3.62548i	0.222653	−	0.235999i
$237$	−4.58135	−	3.33765i	−0.297590	−	0.216804i
$238$	1.82880	−	1.20282i	0.118544	−	0.0779673i
$239$	−3.68585	+	12.3116i	−0.238418	+	0.796371i	0.752107	+	0.659040i	$0.229037\pi$
$239$	−3.68585	+	12.3116i	−0.238418	+	0.796371i	−0.990525	+	0.137330i	$0.956148\pi$
$240$	4.22141	−	1.31150i	0.272491	−	0.0846567i
$241$	−10.1786	−	13.6722i	−0.655660	−	0.880704i	0.342611	−	0.939477i	$-0.388689\pi$
$241$	−10.1786	−	13.6722i	−0.655660	−	0.880704i	−0.998271	+	0.0587730i	$0.981281\pi$
$242$	−9.68351			−0.622479
$243$	−1.00754	+	15.5559i	−0.0646339	+	0.997909i
$244$	−2.42014			−0.154933
$245$	9.47646	+	12.7291i	0.605429	+	0.813232i
$246$	11.7865	−	3.66179i	0.751478	−	0.233467i
$247$	12.2460	−	40.9044i	0.779193	−	2.60268i
$248$	−6.46363	+	4.25120i	−0.410441	+	0.269951i
$249$	4.42236	+	3.22183i	0.280256	+	0.204175i
$250$	6.10632	−	6.47233i	0.386198	−	0.409346i
$251$	10.1177	−	3.68253i	0.638622	−	0.232439i	−0.00235792	−	0.999997i	$-0.500751\pi$
$251$	10.1177	−	3.68253i	0.638622	−	0.232439i	0.640980	+	0.767558i	$0.278528\pi$
$252$	−2.39482	−	1.14137i	−0.150860	−	0.0718993i
$253$	5.03521	+	1.83267i	0.316561	+	0.115219i
$254$	16.2431	−	8.15757i	1.01918	−	0.511852i
$255$	0.113085	+	10.9413i	0.00708166	+	0.685170i
$256$	0.396080	+	0.918216i	0.0247550	+	0.0573885i
$257$	−10.7548	−	1.25705i	−0.670865	−	0.0784129i	−0.226160	−	0.974090i	$-0.572617\pi$
$257$	−10.7548	−	1.25705i	−0.670865	−	0.0784129i	−0.444705	+	0.895677i	$0.646691\pi$
$258$	7.10988	−	8.65330i	0.442642	−	0.538731i
$259$	−6.45513	−	4.24560i	−0.401102	−	0.263809i
$260$	13.2915	−	11.1529i	0.824302	−	0.691671i
$261$	−1.94384	+	1.70077i	−0.120321	+	0.105275i
$262$	−10.1637	−	8.52836i	−0.627916	−	0.526884i
$263$	4.10800	+	13.7217i	0.253310	+	0.846114i	0.986170	+	0.165735i	$0.0529996\pi$
$263$	4.10800	+	13.7217i	0.253310	+	0.846114i	−0.732860	+	0.680379i	$0.761815\pi$
$264$	−3.46235	+	7.07550i	−0.213093	+	0.435467i
$265$	11.2736	+	5.66184i	0.692535	+	0.347804i
$266$	3.81130	+	4.03974i	0.233686	+	0.247692i
$267$	−7.99369	+	6.08049i	−0.489206	+	0.372120i
$268$	−1.12345	+	2.60445i	−0.0686255	+	0.159092i
$269$	0.700424	−	1.21317i	0.0427056	−	0.0739682i	−0.843883	−	0.536528i	$-0.819736\pi$
$269$	0.700424	−	1.21317i	0.0427056	−	0.0739682i	0.886588	+	0.462560i	$0.153069\pi$
$270$	11.2736	−	6.98351i	0.686088	−	0.425003i
$271$	−13.5650	−	23.4952i	−0.824013	−	1.42723i	−0.902671	−	0.430330i	$-0.858397\pi$
$271$	−13.5650	−	23.4952i	−0.824013	−	1.42723i	0.0786586	−	0.996902i	$-0.474936\pi$
$272$	−2.45855	+	0.287364i	−0.149072	+	0.0174240i
$273$	−10.4011	−	0.497992i	−0.629501	−	0.0301398i
$274$	−8.48754	+	2.01158i	−0.512751	+	0.121524i
$275$	−0.400209	−	6.87132i	−0.0241335	−	0.414356i
$276$	1.46980	−	1.41568i	0.0884717	−	0.0852141i
$277$	5.89811	+	1.39788i	0.354383	+	0.0839903i	0.403951	−	0.914780i	$-0.367636\pi$
$277$	5.89811	+	1.39788i	0.354383	+	0.0839903i	−0.0495685	+	0.998771i	$0.515785\pi$
$278$	−0.0223225	+	0.126597i	−0.00133881	+	0.00759278i
$279$	−15.5747	+	17.2073i	−0.932433	+	1.03017i
$280$	0.391900	+	2.22258i	0.0234205	+	0.132824i
$281$	0.366850	−	6.29857i	0.0218844	−	0.375741i	−0.969529	−	0.244977i	$-0.921220\pi$
$281$	0.366850	−	6.29857i	0.0218844	−	0.375741i	0.991413	−	0.130765i	$-0.0417432\pi$
$282$	−5.39344	−	6.29437i	−0.321174	−	0.374824i
$283$	1.91231	−	2.56868i	0.113675	−	0.152692i	−0.741644	−	0.670794i	$-0.765954\pi$
$283$	1.91231	−	2.56868i	0.113675	−	0.152692i	0.855319	+	0.518101i	$0.173361\pi$
$284$	6.53188	−	8.77384i	0.387596	−	0.520632i
$285$	−27.2896	+	5.10325i	−1.61650	+	0.302290i
$286$	−1.79778	+	30.8667i	−0.106305	+	1.82519i
$287$	1.09421	+	6.20559i	0.0645894	+	0.366305i
$288$	1.84083	+	2.36883i	0.108472	+	0.139584i
$289$	−1.88807	+	10.7078i	−0.111063	+	0.629868i
$290$	2.13804	+	0.506725i	0.125550	+	0.0297559i
$291$	−0.443971	−	0.127931i	−0.0260260	−	0.00749948i
$292$	−0.366328	−	6.28961i	−0.0214377	−	0.368072i
$293$	−22.2902	+	5.28286i	−1.30221	+	0.308628i	−0.822482	−	0.568792i	$-0.807411\pi$
$293$	−22.2902	+	5.28286i	−1.30221	+	0.308628i	−0.479723	+	0.877420i	$0.659263\pi$
$294$	−5.82485	+	9.05881i	−0.339712	+	0.528321i
$295$	−12.6347	+	1.47679i	−0.735623	+	0.0859820i
$296$	4.36852	+	7.56650i	0.253915	+	0.439794i
$297$	−4.73436	+	23.1525i	−0.274715	+	1.34345i
$298$	5.44020	−	9.42269i	0.315142	−	0.545842i
$299$	3.17261	−	7.35493i	0.183477	−	0.425346i
$300$	−2.41756	−	1.01333i	−0.139578	−	0.0585047i
$301$	3.92389	+	4.15909i	0.226170	+	0.239726i
$302$	−7.03070	−	3.53095i	−0.404571	−	0.203183i
$303$	−16.5510	−	24.6068i	−0.950831	−	1.41363i
$304$	−1.80127	−	6.01667i	−0.103310	−	0.345080i
$305$	4.73150	+	3.97020i	0.270925	+	0.227333i
$306$	−6.92405	+	2.68348i	−0.395822	+	0.153405i
$307$	20.9420	−	17.5724i	1.19522	−	1.00291i	0.195468	−	0.980710i	$-0.437377\pi$
$307$	20.9420	−	17.5724i	1.19522	−	1.00291i	0.999754	−	0.0222000i	$-0.00706707\pi$
$308$	−3.36010	−	2.20997i	−0.191460	−	0.125925i
$309$	3.27833	+	0.543184i	0.186498	+	0.0309007i
$310$	19.6108	+	2.29217i	1.11382	+	0.130187i
$311$	−9.40973	−	21.8142i	−0.533577	−	1.23697i	−0.945461	−	0.325734i	$-0.894389\pi$
$311$	−9.40973	−	21.8142i	−0.533577	−	1.23697i	0.411884	−	0.911236i	$-0.364871\pi$
$312$	10.2581	+	5.78198i	0.580749	+	0.327340i
$313$	−19.0791	+	9.58190i	−1.07842	+	0.541601i	−0.897102	−	0.441824i	$-0.854332\pi$
$313$	−19.0791	+	9.58190i	−1.07842	+	0.541601i	−0.181315	+	0.983425i	$0.558035\pi$
$314$	−9.27374	−	3.37537i	−0.523348	−	0.190483i
$315$	2.80962	+	6.16011i	0.158304	+	0.347083i
$316$	−3.07519	+	1.11928i	−0.172993	+	0.0629642i
$317$	10.0762	−	10.6802i	0.565938	−	0.599859i	−0.379688	−	0.925115i	$-0.623969\pi$
$317$	10.0762	−	10.6802i	0.565938	−	0.599859i	0.945626	+	0.325255i	$0.105450\pi$
$318$	−0.906014	+	8.51365i	−0.0508067	+	0.477422i
$319$	−3.27138	+	2.15162i	−0.183162	+	0.120467i
$320$	0.731963	−	2.44493i	0.0409180	−	0.136676i
$321$	6.96158	−	30.7878i	0.388557	−	1.71841i
$322$	0.622171	+	0.835720i	0.0346722	+	0.0465729i
$323$	15.5461			0.865008
$324$	7.12760	+	5.49521i	0.395978	+	0.305289i
$325$	−10.2891			−0.570737
$326$	−6.29963	−	8.46187i	−0.348904	−	0.468659i
$327$	−15.1883	−	14.0356i	−0.839914	−	0.776169i
$328$	2.04369	−	6.82641i	0.112844	−	0.376925i
$329$	3.53577	−	2.32551i	0.194933	−	0.128210i
$330$	18.3763	−	8.15306i	1.01158	−	0.448811i
$331$	−0.958085	+	1.01551i	−0.0526611	+	0.0558175i	−0.753169	−	0.657828i	$-0.771476\pi$
$331$	−0.958085	+	1.01551i	−0.0526611	+	0.0558175i	0.700507	+	0.713645i	$0.252957\pi$
$332$	2.96847	−	1.08043i	0.162916	−	0.0592965i
$333$	18.3774	+	18.6894i	1.00707	+	1.02417i
$334$	3.99382	+	1.45363i	0.218532	+	0.0795392i
$335$	6.46896	−	3.24883i	0.353437	−	0.177503i
$336$	−1.31847	+	0.779495i	−0.0719282	+	0.0425250i
$337$	13.5371	+	31.3824i	0.737410	+	1.70951i	0.704138	+	0.710063i	$0.251333\pi$
$337$	13.5371	+	31.3824i	0.737410	+	1.70951i	0.0332717	+	0.999446i	$0.489407\pi$
$338$	32.9952	+	3.85658i	1.79470	+	0.209770i
$339$	5.47031	+	14.5596i	0.297106	+	0.790767i
$340$	5.27802	+	3.47141i	0.286241	+	0.188264i
$341$	−26.9527	+	22.6160i	−1.45957	+	1.22473i
$342$	−9.75602	−	16.1191i	−0.527545	−	0.871619i
$343$	−8.95407	−	7.51335i	−0.483474	−	0.405683i
$344$	−1.85449	−	6.19442i	−0.0999873	−	0.333981i
$345$	−5.19595	+	0.356548i	−0.279741	+	0.0191959i
$346$	−0.254068	−	0.127598i	−0.0136588	−	0.00685971i
$347$	−1.49937	−	1.58924i	−0.0804902	−	0.0853146i	0.685877	−	0.727718i	$-0.259419\pi$
$347$	−1.49937	−	1.58924i	−0.0804902	−	0.0853146i	−0.766367	+	0.642403i	$0.777937\pi$
$348$	0.188417	+	1.47926i	0.0101002	+	0.0792966i
$349$	−8.22188	+	19.0605i	−0.440107	+	1.02028i	0.543410	+	0.839467i	$0.317133\pi$
$349$	−8.22188	+	19.0605i	−0.440107	+	1.02028i	−0.983517	+	0.180815i	$0.942126\pi$
$350$	0.669166	−	1.15903i	0.0357684	−	0.0619528i
$351$	34.1399	+	9.07764i	1.82225	+	0.484529i
$352$	2.27396	+	3.93861i	0.121202	+	0.209928i
$353$	−8.52487	+	0.996414i	−0.453733	+	0.0530338i	−0.339890	−	0.940465i	$-0.610390\pi$
$353$	−8.52487	+	0.996414i	−0.453733	+	0.0530338i	−0.113842	+	0.993499i	$0.536316\pi$
$354$	−3.95407	−	7.67440i	−0.210157	−	0.407890i
$355$	−27.1636	+	6.43788i	−1.44169	+	0.341687i
$356$	0.337159	+	5.78879i	0.0178694	+	0.306806i
$357$	−0.912412	−	3.67986i	−0.0482900	−	0.194759i
$358$	−15.1097	−	3.58106i	−0.798573	−	0.189265i
$359$	3.02344	−	17.1468i	0.159571	−	0.904974i	−0.794915	−	0.606720i	$-0.792485\pi$
$359$	3.02344	−	17.1468i	0.159571	−	0.904974i	0.954487	−	0.298254i	$-0.0964041\pi$
$360$	0.287103	−	7.65104i	0.0151317	−	0.403245i
$361$	3.55021	+	20.1343i	0.186853	+	1.05970i
$362$	−1.38045	+	23.7015i	−0.0725551	+	1.24572i
$363$	−5.57328	+	15.8193i	−0.292521	+	0.830297i
$364$	−3.59008	+	4.82231i	−0.188171	+	0.252758i
$365$	−9.60182	+	12.8975i	−0.502582	+	0.675085i
$366$	−1.39289	+	3.95361i	−0.0728077	+	0.206658i
$367$	−0.654713	+	11.2410i	−0.0341757	+	0.586775i	0.937136	+	0.348965i	$0.113467\pi$
$367$	−0.654713	+	11.2410i	−0.0341757	+	0.586775i	−0.971312	+	0.237810i	$0.923570\pi$
$368$	−0.204593	−	1.16030i	−0.0106651	−	0.0604849i
$369$	0.801613	−	21.3623i	0.0417303	−	1.11207i
$370$	3.87204	−	21.9594i	0.201298	−	1.14162i
$371$	−4.25337	−	1.00807i	−0.220824	−	0.0523363i
$372$	3.22479	+	13.0059i	0.167197	+	0.674326i
$373$	−0.429192	−	7.36894i	−0.0222227	−	0.381549i	−0.991022	−	0.133701i	$-0.957314\pi$
$373$	−0.429192	−	7.36894i	−0.0222227	−	0.381549i	0.968799	−	0.247848i	$-0.0797234\pi$
$374$	−10.9540	+	2.59614i	−0.566416	+	0.134243i
$375$	−7.05894	−	13.7006i	−0.364522	−	0.707495i
$376$	−4.75332	+	0.555584i	−0.245134	+	0.0286520i
$377$	2.92659	+	5.06901i	0.150727	+	0.261067i
$378$	−3.24290	+	3.25535i	−0.166797	+	0.167437i
$379$	−1.15880	+	2.00709i	−0.0595233	+	0.103097i	−0.894252	−	0.447565i	$-0.852291\pi$
$379$	−1.15880	+	2.00709i	−0.0595233	+	0.103097i	0.834728	+	0.550662i	$0.185625\pi$
$380$	−6.34867	+	14.7179i	−0.325680	+	0.755011i
$381$	−3.97788	−	31.2302i	−0.203793	−	1.59997i
$382$	13.2987	+	14.0958i	0.680419	+	0.721202i
$383$	5.28873	+	2.65610i	0.270241	+	0.135720i	0.578760	−	0.815498i	$-0.303537\pi$
$383$	5.28873	+	2.65610i	0.270241	+	0.135720i	−0.308518	+	0.951218i	$0.599833\pi$
$384$	1.72799	−	0.118575i	0.0881810	−	0.00605101i
$385$	2.94375	+	9.83282i	0.150028	+	0.501127i
$386$	15.5766	+	13.0703i	0.792827	+	0.665261i
$387$	−10.0443	−	16.5953i	−0.510578	−	0.843585i
$388$	−0.204347	+	0.171467i	−0.0103741	+	0.00870494i
$389$	−3.04831	−	2.00490i	−0.154555	−	0.101653i	0.469876	−	0.882733i	$-0.344299\pi$
$389$	−3.04831	−	2.00490i	−0.154555	−	0.101653i	−0.624431	+	0.781080i	$0.714669\pi$
$390$	−10.5699	−	28.1323i	−0.535225	−	1.42453i
$391$	2.89667	+	0.338572i	0.146491	+	0.0171223i
$392$	2.46283	+	5.70948i	0.124392	+	0.288372i
$393$	−19.7819	+	11.6953i	−0.997862	+	0.589950i
$394$	−12.9751	+	6.51633i	−0.653675	+	0.328288i
$395$	7.84832	+	2.85655i	0.394892	+	0.143729i
$396$	9.56602	+	9.72845i	0.480711	+	0.488873i
$397$	11.1881	−	4.07213i	0.561514	−	0.204375i	−0.0456407	−	0.998958i	$-0.514533\pi$
$397$	11.1881	−	4.07213i	0.561514	−	0.204375i	0.607155	+	0.794583i	$0.292311\pi$
$398$	−10.9397	+	11.5954i	−0.548357	+	0.581224i
$399$	8.79300	−	3.90121i	0.440201	−	0.195305i
$400$	−1.26446	+	0.831646i	−0.0632228	+	0.0415823i
$401$	−5.36480	+	17.9197i	−0.267905	+	0.894866i	0.713129	+	0.701033i	$0.247277\pi$
$401$	−5.36480	+	17.9197i	−0.267905	+	0.894866i	−0.981034	+	0.193833i	$0.937908\pi$
$402$	3.60811	+	3.33427i	0.179956	+	0.166298i
$403$	31.4080	+	42.1882i	1.56454	+	2.10155i
$404$	−17.1214			−0.851824
$405$	−4.92005	−	22.4362i	−0.244479	−	1.11486i
$406$	−0.761340			−0.0377847
$407$	23.7283	+	31.8726i	1.17617	+	1.57987i
$408$	−0.945558	+	4.18176i	−0.0468121	+	0.207028i
$409$	2.77586	−	9.27201i	0.137257	−	0.458471i	−0.861530	−	0.507707i	$-0.830493\pi$
$409$	2.77586	−	9.27201i	0.137257	−	0.458471i	0.998787	+	0.0492356i	$0.0156785\pi$
$410$	−15.1942	+	9.99336i	−0.750386	+	0.493537i
$411$	−1.59876	+	15.0233i	−0.0788611	+	0.741043i
$412$	1.31659	−	1.39550i	0.0648636	−	0.0687514i
$413$	4.14185	−	1.50751i	0.203807	−	0.0741797i
$414$	−1.46677	−	3.21590i	−0.0720877	−	0.158053i
$415$	−7.57596	−	2.75742i	−0.371889	−	0.135357i
$416$	6.07537	−	3.05117i	0.297870	−	0.149596i
$417$	0.193965	+	0.109329i	0.00949851	+	0.00535385i
$418$	−11.3133	−	26.2272i	−0.553353	−	1.28282i
$419$	−33.6890	−	3.93767i	−1.64581	−	0.192368i	−0.757897	−	0.652374i	$-0.773773\pi$
$419$	−33.6890	−	3.93767i	−1.64581	−	0.192368i	−0.887916	+	0.460006i	$0.847847\pi$
$420$	3.85643	+	0.638969i	0.188174	+	0.0311785i
$421$	−20.1800	−	13.2726i	−0.983515	−	0.646868i	−0.0475156	−	0.998870i	$-0.515130\pi$
$421$	−20.1800	−	13.2726i	−0.983515	−	0.646868i	−0.935999	+	0.352003i	$0.885501\pi$
$422$	10.5975	−	8.89236i	0.515879	−	0.432874i
$423$	−13.3868	+	5.18820i	−0.650890	+	0.252259i
$424$	3.78664	+	3.17737i	0.183896	+	0.154307i
$425$	−1.07442	−	3.58881i	−0.0521170	−	0.174083i
$426$	−10.5738	−	15.7204i	−0.512304	−	0.761656i
$427$	−1.91249	−	0.960488i	−0.0925519	−	0.0464813i
$428$	−12.5061	−	13.2557i	−0.604507	−	0.640740i
$429$	49.3901	+	20.7021i	2.38458	+	0.999505i
$430$	−6.53624	+	15.1527i	−0.315205	+	0.730728i
$431$	4.49405	−	7.78392i	0.216471	−	0.374938i	−0.737256	−	0.675614i	$-0.763879\pi$
$431$	4.49405	−	7.78392i	0.216471	−	0.374938i	0.953726	+	0.300676i	$0.0972121\pi$
$432$	4.92927	−	1.64387i	0.237159	−	0.0790910i
$433$	10.4614	+	18.1197i	0.502742	+	0.870775i	0.999995	+	0.00316933i	$0.00100883\pi$
$433$	10.4614	+	18.1197i	0.502742	+	0.870775i	−0.497253	+	0.867606i	$0.665658\pi$
$434$	−6.79501	+	0.794223i	−0.326171	+	0.0381239i
$435$	2.05834	−	3.20113i	0.0986897	−	0.153482i
$436$	−11.6180	+	2.75352i	−0.556403	+	0.131870i
$437$	0.430255	+	7.38719i	0.0205819	+	0.353377i
$438$	−10.4857	−	3.02150i	−0.501028	−	0.144373i
$439$	19.5922	+	4.64343i	0.935084	+	0.221619i	0.669792	−	0.742549i	$-0.266383\pi$
$439$	19.5922	+	4.64343i	0.935084	+	0.221619i	0.265292	+	0.964168i	$0.414531\pi$
$440$	2.01552	−	11.4306i	0.0960862	−	0.544932i
$441$	11.4463	+	14.7294i	0.545062	+	0.701400i
$442$	2.92220	+	16.5726i	0.138995	+	0.788280i
$443$	0.627345	−	10.7711i	0.0298061	−	0.511750i	−0.950057	−	0.312078i	$-0.898975\pi$
$443$	0.627345	−	10.7711i	0.0298061	−	0.511750i	0.979863	−	0.199673i	$-0.0639879\pi$
$444$	14.8751	−	2.78170i	0.705943	−	0.132014i
$445$	8.83727	−	11.8705i	0.418927	−	0.562717i
$446$	4.31840	−	5.80061i	0.204482	−	0.274667i
$447$	−12.2621	−	14.3104i	−0.579979	−	0.676861i
$448$	−0.0514175	+	0.882805i	−0.00242925	+	0.0417086i
$449$	−7.05769	−	40.0261i	−0.333073	−	1.88895i	−0.445487	−	0.895289i	$-0.646969\pi$
$449$	−7.05769	−	40.0261i	−0.333073	−	1.88895i	0.112414	−	0.993661i	$-0.464142\pi$
$450$	−3.04682	+	3.36619i	−0.143629	+	0.158684i
$451$	5.62748	−	31.9150i	0.264988	−	1.50282i
$452$	8.73765	+	2.07086i	0.410985	+	0.0974051i
$453$	−9.81474	+	9.45335i	−0.461137	+	0.444157i
$454$	−0.331040	−	5.68375i	−0.0155365	−	0.266751i
$455$	14.9297	−	3.53841i	0.699917	−	0.165883i
$456$	−10.8657	−	0.520239i	−0.508834	−	0.0243624i
$457$	31.1797	−	3.64439i	1.45853	−	0.170477i	0.650447	−	0.759552i	$-0.274582\pi$
$457$	31.1797	−	3.64439i	1.45853	−	0.170477i	0.808079	+	0.589074i	$0.200508\pi$
$458$	1.85154	+	3.20697i	0.0865169	+	0.149852i
$459$	0.398732	+	12.8558i	0.0186112	+	0.600057i
$460$	−1.50347	+	2.60409i	−0.0700996	+	0.121416i
$461$	5.57032	−	12.9135i	0.259436	−	0.601440i	−0.737858	−	0.674956i	$-0.764163\pi$
$461$	5.57032	−	12.9135i	0.259436	−	0.601440i	0.997294	+	0.0735160i	$0.0234220\pi$
$462$	−5.54417	+	4.21723i	−0.257938	+	0.196203i
$463$	12.4631	+	13.2101i	0.579209	+	0.613926i	0.949033	−	0.315176i	$-0.102064\pi$
$463$	12.4631	+	13.2101i	0.579209	+	0.613926i	−0.369824	+	0.929102i	$0.620582\pi$
$464$	0.769374	+	0.386394i	0.0357173	+	0.0179379i
$465$	15.0314	−	30.7175i	0.697065	−	1.42449i
$466$	−6.91839	−	23.1090i	−0.320488	−	1.07050i
$467$	−29.1271	−	24.4405i	−1.34784	−	1.13097i	−0.979536	−	0.201268i	$-0.935494\pi$
$467$	−29.1271	−	24.4405i	−1.34784	−	1.13097i	−0.368305	−	0.929705i	$-0.620062\pi$
$468$	15.3496	−	13.4301i	0.709535	−	0.620808i
$469$	−1.92143	+	1.61227i	−0.0887234	+	0.0744478i
$470$	10.2044	+	6.71156i	0.470696	+	0.309581i
$471$	−10.8515	+	13.2072i	−0.500013	+	0.608556i
$472$	−4.95064	−	0.578647i	−0.227872	−	0.0266344i
$473$	−11.6476	−	27.0021i	−0.535555	−	1.24156i
$474$	0.0585814	+	5.66791i	0.00269073	+	0.260336i
$475$	8.49411	−	4.26590i	0.389737	−	0.195733i
$476$	−2.05690	−	0.748649i	−0.0942776	−	0.0343143i
$477$	13.3867	+	6.38006i	0.612935	+	0.292123i
$478$	12.0765	−	4.39547i	0.552364	−	0.201044i
$479$	8.05347	−	8.53618i	0.367973	−	0.390028i	−0.516758	−	0.856132i	$-0.672861\pi$
$479$	8.05347	−	8.53618i	0.367973	−	0.390028i	0.884730	+	0.466104i	$0.154343\pi$
$480$	−3.57283	−	2.60292i	−0.163077	−	0.118806i
$481$	49.6271	−	32.6402i	2.26280	−	1.48827i
$482$	−4.88857	+	16.3290i	−0.222668	+	0.743763i
$483$	1.72334	−	0.535404i	0.0784149	−	0.0243617i
$484$	5.78259	+	7.76737i	0.262845	+	0.353062i
$485$	0.680800			0.0309135
$486$	13.0794	−	8.48114i	0.593293	−	0.384712i
$487$	13.6206			0.617210			0.308605	−	0.951190i	$-0.400138\pi$
$487$	13.6206			0.617210			0.308605	+	0.951190i	$0.400138\pi$
$488$	1.44521	+	1.94125i	0.0654214	+	0.0878761i
$489$	−17.4493	+	5.42109i	−0.789084	+	0.245150i
$490$	4.55135	−	15.2026i	0.205609	−	0.686783i
$491$	17.4899	−	11.5033i	0.789309	−	0.519137i	−0.0896845	−	0.995970i	$-0.528586\pi$
$491$	17.4899	−	11.5033i	0.789309	−	0.519137i	0.878994	+	0.476833i	$0.158215\pi$
$492$	−9.97560	−	7.26753i	−0.449735	−	0.327646i
$493$	−1.46245	+	1.55011i	−0.0658655	+	0.0698133i
$494$	−40.1232	+	14.6036i	−1.80523	+	0.657048i
$495$	−2.74271	−	34.7126i	−0.123276	−	1.56021i
$496$	7.26980	+	2.64599i	0.326423	+	0.118808i
$497$	8.64386	−	4.34111i	0.387730	−	0.194725i
$498$	−0.0565485	−	5.47122i	−0.00253400	−	0.245171i
$499$	7.15992	+	16.5986i	0.320522	+	0.743054i	0.999957	+	0.00931768i	$0.00296595\pi$
$499$	7.15992	+	16.5986i	0.320522	+	0.743054i	−0.679434	+	0.733736i	$0.737775\pi$
$500$	−8.83805	−	1.03302i	−0.395249	−	0.0461980i
$501$	4.67332	−	5.68780i	0.208788	−	0.254112i
$502$	−8.99570	−	5.91656i	−0.401498	−	0.264069i
$503$	−21.1388	+	17.7376i	−0.942534	+	0.790880i	−0.978024	−	0.208490i	$-0.933145\pi$
$503$	−21.1388	+	17.7376i	−0.942534	+	0.790880i	0.0354905	+	0.999370i	$0.488701\pi$
$504$	0.514573	+	2.60252i	0.0229209	+	0.115925i
$505$	33.4734	+	28.0875i	1.48955	+	1.24988i
$506$	−1.53679	−	5.13325i	−0.0683188	−	0.228201i
$507$	25.2904	−	51.6823i	1.12318	−	2.29529i
$508$	−16.2431	−	8.15757i	−0.720670	−	0.361934i
$509$	−7.85731	−	8.32827i	−0.348269	−	0.369144i	0.529432	−	0.848353i	$-0.322405\pi$
$509$	−7.85731	−	8.32827i	−0.348269	−	0.369144i	−0.877701	+	0.479209i	$0.840924\pi$
$510$	8.70873	−	6.62439i	0.385629	−	0.293333i
$511$	2.20669	−	5.11569i	0.0976184	−	0.226305i
$512$	0.500000	−	0.866025i	0.0220971	−	0.0382733i
$513$	−31.9476	+	6.66053i	−1.41052	+	0.294069i
$514$	5.41400	+	9.37732i	0.238801	+	0.413616i
$515$	−4.86330	+	0.568439i	−0.214303	+	0.0250484i
$516$	−11.1867	−	0.535609i	−0.492469	−	0.0235789i
$517$	−21.1782	+	5.01932i	−0.931416	+	0.220750i
$518$	0.449237	+	7.71311i	0.0197384	+	0.338894i
$519$	−0.354675	+	0.341616i	−0.0155685	+	0.0149953i
$520$	−16.8831	−	4.00137i	−0.740372	−	0.175471i
$521$	−6.83079	+	38.7393i	−0.299262	+	1.69720i	0.350092	+	0.936715i	$0.386150\pi$
$521$	−6.83079	+	38.7393i	−0.299262	+	1.69720i	−0.649355	+	0.760486i	$0.724961\pi$
$522$	2.52501	+	0.543573i	0.110516	+	0.0237916i
$523$	−5.54442	−	31.4440i	−0.242441	−	1.37495i	−0.826362	−	0.563139i	$-0.809593\pi$
$523$	−5.54442	−	31.4440i	−0.242441	−	1.37495i	0.583921	−	0.811810i	$-0.301518\pi$
$524$	−0.771453	+	13.2453i	−0.0337011	+	0.578625i
$525$	−1.50829	−	1.76024i	−0.0658273	−	0.0768233i
$526$	8.55334	−	11.4891i	0.372943	−	0.500950i
$527$	−11.4354	+	15.3604i	−0.498135	+	0.669111i
$528$	7.74299	−	1.44797i	0.336970	−	0.0630146i
$529$	1.25662	−	21.5753i	0.0546355	−	0.938056i
$530$	−2.19066	−	12.4239i	−0.0951563	−	0.539658i
$531$	−14.8129	+	2.04255i	−0.642824	+	0.0886389i
$532$	0.964419	−	5.46949i	0.0418129	−	0.237133i
$533$	−47.1388	−	11.1721i	−2.04181	−	0.483917i
$534$	9.65080	+	2.78091i	0.417631	+	0.120342i
$535$	2.70434	+	46.4318i	0.116919	+	2.00742i
$536$	2.75996	−	0.654123i	0.119212	−	0.0282538i
$537$	−14.5464	+	22.6226i	−0.627725	+	0.976238i
$538$	−1.39138	+	0.162628i	−0.0599865	+	0.00701141i
$539$	14.1395	+	24.4903i	0.609031	+	1.05487i
$540$	−12.3337	−	4.87253i	−0.530760	−	0.209680i
$541$	−2.43494	+	4.21744i	−0.104686	+	0.181322i	−0.913610	−	0.406592i	$-0.866717\pi$
$541$	−2.43494	+	4.21744i	−0.104686	+	0.181322i	0.808924	+	0.587914i	$0.200051\pi$
$542$	−10.7456	+	24.9111i	−0.461564	+	1.07002i
$543$	37.9250	+	15.8964i	1.62752	+	0.682179i
$544$	1.69865	+	1.80046i	0.0728289	+	0.0771941i
$545$	27.2310	+	13.6759i	1.16645	+	0.585812i
$546$	5.81163	+	8.64031i	0.248715	+	0.369771i
$547$	−2.70344	−	9.03013i	−0.115591	−	0.386101i	0.880541	−	0.473970i	$-0.157179\pi$
$547$	−2.70344	−	9.03013i	−0.115591	−	0.386101i	−0.996132	+	0.0878692i	$0.971994\pi$
$548$	6.68195	+	5.60682i	0.285439	+	0.239511i
$549$	5.65707	+	4.55095i	0.241438	+	0.194230i
$550$	−5.27266	+	4.42429i	−0.224827	+	0.188652i
$551$	−4.51766	−	2.97131i	−0.192459	−	0.126582i
$552$	−2.01326	−	0.333575i	−0.0856899	−	0.0141979i
$553$	−2.87435	−	0.335963i	−0.122230	−	0.0142866i
$554$	−2.40084	−	5.56576i	−0.102002	−	0.236467i
$555$	−33.6451	−	18.9641i	−1.42815	−	0.804981i
$556$	0.114876	−	0.0576931i	0.00487184	−	0.00244673i
$557$	22.5380	+	8.20316i	0.954965	+	0.347579i	0.772059	−	0.635551i	$-0.219227\pi$
$557$	22.5380	+	8.20316i	0.954965	+	0.347579i	0.182907	+	0.983130i	$0.441449\pi$
$558$	23.1029	+	2.21737i	0.978024	+	0.0938686i
$559$	−41.3085	+	15.0351i	−1.74716	+	0.635916i
$560$	1.54875	−	1.64158i	0.0654468	−	0.0693695i
$561$	−2.06335	+	19.3889i	−0.0871147	+	0.818601i
$562$	−5.27130	+	3.46699i	−0.222356	+	0.146246i
$563$	5.83501	−	19.4903i	0.245916	−	0.821418i	−0.742526	−	0.669818i	$-0.766372\pi$
$563$	5.83501	−	19.4903i	0.245916	−	0.821418i	0.988442	−	0.151600i	$-0.0484425\pi$
$564$	−1.82812	+	8.08494i	−0.0769779	+	0.340437i
$565$	−13.6854	−	18.3826i	−0.575748	−	0.773364i
$566$	−3.20236			−0.134605
$567$	3.45162	+	7.17129i	0.144954	+	0.301166i
$568$	−10.9383			−0.458960
$569$	−18.5307	−	24.8910i	−0.776847	−	1.04349i	−0.997674	−	0.0681730i	$-0.978283\pi$
$569$	−18.5307	−	24.8910i	−0.776847	−	1.04349i	0.220827	−	0.975313i	$-0.429124\pi$
$570$	20.3896	+	18.8422i	0.854028	+	0.789211i
$571$	−3.45648	+	11.5454i	−0.144649	+	0.483161i	−0.999353	−	0.0359536i	$-0.988553\pi$
$571$	−3.45648	+	11.5454i	−0.144649	+	0.483161i	0.854704	+	0.519115i	$0.173738\pi$
$572$	25.8325	−	16.9903i	1.08011	−	0.710400i
$573$	30.6812	−	13.6124i	1.28173	−	0.568666i
$574$	4.32423	−	4.58342i	0.180490	−	0.191308i
$575$	1.67560	−	0.609867i	0.0698772	−	0.0254332i
$576$	0.800824	−	2.89114i	0.0333677	−	0.120464i
$577$	−6.57434	−	2.39287i	−0.273694	−	0.0996163i	0.201527	−	0.979483i	$-0.435410\pi$
$577$	−6.57434	−	2.39287i	−0.273694	−	0.0996163i	−0.475221	+	0.879867i	$0.657632\pi$
$578$	9.71641	−	4.87977i	0.404150	−	0.202972i
$579$	30.3170	−	17.9238i	1.25993	−	0.744890i
$580$	−0.870294	−	2.01757i	−0.0361370	−	0.0837750i
$581$	2.77460	+	0.324304i	0.115110	+	0.0134544i
$582$	0.162504	+	0.432515i	0.00673601	+	0.0179283i
$583$	18.7825	+	12.3534i	0.777890	+	0.511626i
$584$	−4.82629	+	4.04973i	−0.199713	+	0.167579i
$585$	−52.0412	+	1.07587i	−2.15164	+	0.0444818i
$586$	17.5483	+	14.7247i	0.724912	+	0.608274i
$587$	4.21156	+	14.0676i	0.173830	+	0.580631i	0.999856	+	0.0169992i	$0.00541129\pi$
$587$	4.21156	+	14.0676i	0.173830	+	0.580631i	−0.826026	+	0.563632i	$0.809404\pi$
$588$	10.7446	−	0.737301i	0.443102	−	0.0304058i
$589$	−43.4201	−	21.8064i	−1.78909	−	0.898517i
$590$	8.72952	+	9.25275i	0.359388	+	0.380929i
$591$	3.17756	+	24.9469i	0.130707	+	1.02618i
$592$	3.46057	−	8.02249i	0.142228	−	0.329722i
$593$	6.72451	−	11.6472i	0.276142	−	0.478293i	−0.694280	−	0.719705i	$-0.744277\pi$
$593$	6.72451	−	11.6472i	0.276142	−	0.478293i	0.970423	+	0.241412i	$0.0776105\pi$
$594$	21.3984	−	10.0282i	0.877985	−	0.411462i
$595$	2.79320	+	4.83796i	0.114510	+	0.198337i
$596$	−10.8068	+	1.26314i	−0.442665	+	0.0517401i
$597$	12.6463	+	24.5450i	0.517579	+	1.00456i
$598$	−7.79411	+	1.84724i	−0.318725	+	0.0755392i
$599$	−0.630836	−	10.8310i	−0.0257753	−	0.442544i	−0.986365	−	0.164573i	$-0.947375\pi$
$599$	−0.630836	−	10.8310i	−0.0257753	−	0.442544i	0.960590	−	0.277971i	$-0.0896618\pi$
$600$	0.630853	+	2.54430i	0.0257545	+	0.103871i
$601$	−5.29117	−	1.25403i	−0.215831	−	0.0511530i	0.121278	−	0.992619i	$-0.461301\pi$
$601$	−5.29117	−	1.25403i	−0.215831	−	0.0511530i	−0.337109	+	0.941466i	$0.609449\pi$
$602$	0.992911	−	5.63108i	0.0404681	−	0.229506i
$603$	7.52359	−	3.97530i	0.306384	−	0.161887i
$604$	1.36619	+	7.74802i	0.0555893	+	0.315262i
$605$	1.43697	−	24.6719i	0.0584213	−	1.00305i
$606$	−9.85414	+	27.9701i	−0.400297	+	1.13621i
$607$	−8.92745	+	11.9916i	−0.362354	+	0.486726i	−0.945491	−	0.325648i	$-0.894418\pi$
$607$	−8.92745	+	11.9916i	−0.362354	+	0.486726i	0.583137	+	0.812374i	$0.301825\pi$
$608$	−3.75046	+	5.03775i	−0.152101	+	0.204308i
$609$	−0.438184	+	1.24375i	−0.0177561	+	0.0503992i
$610$	0.359134	−	6.16608i	0.0145409	−	0.249657i
$611$	5.64973	+	32.0412i	0.228564	+	1.29625i
$612$	6.28724	+	3.95148i	0.254147	+	0.159729i
$613$	1.49965	−	8.50493i	0.0605702	−	0.343511i	−0.939429	−	0.342742i	$-0.888644\pi$
$613$	1.49965	−	8.50493i	0.0605702	−	0.343511i	1.00000		0.000768585i	$-0.000244648\pi$
$614$	−26.6009	−	6.30453i	−1.07353	−	0.254430i
$615$	7.58056	+	30.5733i	0.305678	+	1.23283i
$616$	0.233843	+	4.01492i	0.00942178	+	0.161766i
$617$	−33.0572	+	7.83469i	−1.33083	+	0.315413i	−0.833679	−	0.552250i	$-0.813769\pi$
$617$	−33.0572	+	7.83469i	−1.33083	+	0.315413i	−0.497153	+	0.867663i	$0.665621\pi$
$618$	−1.52198	−	2.95399i	−0.0612231	−	0.118827i
$619$	−0.273547	+	0.0319731i	−0.0109948	+	0.00128511i	−0.121589	−	0.992581i	$-0.538799\pi$
$619$	−0.273547	+	0.0319731i	−0.0109948	+	0.00128511i	0.110594	+	0.993866i	$0.464725\pi$
$620$	−9.87214	−	17.0991i	−0.396475	−	0.686715i
$621$	−6.09778	+	0.545268i	−0.244696	+	0.0218808i
$622$	−11.8786	+	20.5743i	−0.476288	+	0.824955i
$623$	−2.03098	+	4.70835i	−0.0813696	+	0.188636i
$624$	−1.48784	−	11.6810i	−0.0595613	−	0.467614i
$625$	20.7771	+	22.0225i	0.831085	+	0.880899i
$626$	19.0791	+	9.58190i	0.762556	+	0.382970i
$627$	−49.3569	+	3.38689i	−1.97112	+	0.135259i
$628$	2.83044	+	9.45431i	0.112947	+	0.377268i
$629$	16.5670	+	13.9014i	0.660571	+	0.554285i
$630$	3.26338	−	5.93222i	0.130016	−	0.236345i
$631$	−11.3712	+	9.54158i	−0.452681	+	0.379844i	−0.840430	−	0.541921i	$-0.817697\pi$
$631$	−11.3712	+	9.54158i	−0.452681	+	0.379844i	0.387749	+	0.921765i	$0.373253\pi$
$632$	2.73417	+	1.79829i	0.108759	+	0.0715322i
$633$	−8.42752	−	22.4304i	−0.334964	−	0.891527i
$634$	−14.5839	−	1.70462i	−0.579202	−	0.0676990i
$635$	18.3737	+	42.5950i	0.729138	+	1.69033i
$636$	7.37003	−	4.35726i	0.292241	−	0.172777i
$637$	37.7767	−	18.9722i	1.49677	−	0.751706i
$638$	3.67939	+	1.33919i	0.145669	+	0.0530190i
$639$	−31.7670	+	8.22597i	−1.25669	+	0.325414i
$640$	−2.39823	+	0.872884i	−0.0947984	+	0.0345038i
$641$	25.3341	−	26.8526i	1.00064	−	1.06061i	0.00247661	−	0.999997i	$-0.499212\pi$
$641$	25.3341	−	26.8526i	1.00064	−	1.06061i	0.998161	−	0.0606171i	$-0.0193068\pi$
$642$	−28.8528	+	12.8012i	−1.13873	+	0.505221i
$643$	4.81729	−	3.16838i	0.189975	−	0.124949i	−0.450958	−	0.892545i	$-0.648918\pi$
$643$	4.81729	−	3.16838i	0.189975	−	0.124949i	0.640934	+	0.767596i	$0.278547\pi$
$644$	0.298816	−	0.998115i	0.0117750	−	0.0393312i
$645$	20.9920	+	19.3988i	0.826560	+	0.763828i
$646$	−9.28349	−	12.4699i	−0.365254	−	0.490621i
$647$	8.03991			0.316082			0.158041	−	0.987433i	$-0.449482\pi$
$647$	8.03991			0.316082			0.158041	+	0.987433i	$0.449482\pi$
$648$	0.151522	−	8.99872i	0.00595236	−	0.353503i
$649$	−22.6684			−0.889811
$650$	6.14423	+	8.25313i	0.240996	+	0.323714i
$651$	−2.61336	+	11.5576i	−0.102425	+	0.452980i
$652$	−3.02558	+	10.1062i	−0.118491	+	0.395788i
$653$	−7.40917	+	4.87309i	−0.289943	+	0.190699i	−0.686145	−	0.727465i	$-0.740698\pi$
$653$	−7.40917	+	4.87309i	−0.289943	+	0.190699i	0.396202	+	0.918163i	$0.370328\pi$
$654$	−2.18844	+	20.5643i	−0.0855747	+	0.804129i
$655$	23.2370	−	24.6298i	0.907945	−	0.962366i
$656$	−6.69603	+	2.43716i	−0.261436	+	0.0951549i
$657$	−10.9710	+	15.3908i	−0.428020	+	0.600453i
$658$	−3.97677	−	1.44742i	−0.155030	−	0.0564265i
$659$	−11.4692	+	5.76003i	−0.446775	+	0.224379i	−0.657938	−	0.753072i	$-0.728571\pi$
$659$	−11.4692	+	5.76003i	−0.446775	+	0.224379i	0.211163	+	0.977451i	$0.432275\pi$
$660$	−17.5133	−	9.87142i	−0.681706	−	0.384244i
$661$	10.6938	+	24.7909i	0.415939	+	0.964255i	0.989426	+	0.145040i	$0.0463312\pi$
$661$	10.6938	+	24.7909i	0.415939	+	0.964255i	−0.573487	+	0.819215i	$0.694410\pi$
$662$	1.38669	+	0.162081i	0.0538954	+	0.00629947i
$663$	28.7554	+	4.76447i	1.11677	+	0.185037i
$664$	−2.63929	−	1.73589i	−0.102424	−	0.0673655i
$665$	−10.8581	+	9.11104i	−0.421060	+	0.353311i
$666$	4.01701	−	25.9015i	0.155656	−	1.00366i
$667$	−0.777055	−	0.652027i	−0.0300877	−	0.0252466i
$668$	−1.21895	−	4.07159i	−0.0471627	−	0.157534i
$669$	−6.99063	−	10.3932i	−0.270274	−	0.401823i
$670$	−6.46896	−	3.24883i	−0.249918	−	0.125513i
$671$	7.55317	+	8.00589i	0.291587	+	0.309064i
$672$	1.41258	+	0.592090i	0.0544916	+	0.0228404i
$673$	9.47018	−	21.9544i	0.365049	−	0.846278i	−0.632383	−	0.774656i	$-0.717923\pi$
$673$	9.47018	−	21.9544i	0.365049	−	0.846278i	0.997432	−	0.0716223i	$-0.0228176\pi$
$674$	17.0888	−	29.5987i	0.658236	−	1.14010i
$675$	3.74554	+	6.91477i	0.144166	+	0.266150i
$676$	−16.6099	−	28.7692i	−0.638842	−	1.10651i
$677$	27.6660	−	3.23370i	1.06329	−	0.124281i	0.433584	−	0.901113i	$-0.357249\pi$
$677$	27.6660	−	3.23370i	1.06329	−	0.124281i	0.629708	+	0.776832i	$0.283175\pi$
$678$	8.41192	−	13.0822i	0.323058	−	0.502420i
$679$	−0.229534	+	0.0544006i	−0.00880871	+	0.00208770i
$680$	−0.367318	−	6.30661i	−0.0140860	−	0.241847i
$681$	−9.47567	−	2.73044i	−0.363108	−	0.104631i
$682$	34.2359	+	8.11405i	1.31096	+	0.310703i
$683$	1.17701	−	6.67515i	0.0450370	−	0.255418i	−0.953974	−	0.299891i	$-0.903050\pi$
$683$	1.17701	−	6.67515i	0.0450370	−	0.255418i	0.999011	+	0.0444731i	$0.0141609\pi$
$684$	−7.10357	+	17.4512i	−0.271612	+	0.667262i
$685$	−3.86567	−	21.9233i	−0.147700	−	0.837646i
$686$	−0.679638	+	11.6689i	−0.0259487	+	0.445522i
$687$	6.30464	−	1.17899i	0.240537	−	0.0449813i
$688$	−3.86127	+	5.18658i	−0.147209	+	0.197737i
$689$	20.0680	−	26.9560i	0.764530	−	1.02694i
$690$	3.38880	+	3.95488i	0.129010	+	0.150560i
$691$	−2.37423	+	40.7639i	−0.0903199	+	1.55073i	0.583669	+	0.811992i	$0.301617\pi$
$691$	−2.37423	+	40.7639i	−0.0903199	+	1.55073i	−0.673989	+	0.738741i	$0.735421\pi$
$692$	0.0493699	+	0.279990i	0.00187676	+	0.0106436i
$693$	3.69849	+	11.4843i	0.140494	+	0.436253i
$694$	−0.379403	+	2.15170i	−0.0144019	+	0.0816775i
$695$	−0.319234	−	0.0756599i	−0.0121093	−	0.00286995i
$696$	1.07403	−	1.03449i	0.0407111	−	0.0392121i
$697$	−1.02558	−	17.6085i	−0.0388465	−	0.666969i
$698$	20.1986	−	4.78715i	0.764528	−	0.181196i
$699$	−41.7335	−	1.99815i	−1.57850	−	0.0755771i
$700$	−1.32928	+	0.155371i	−0.0502422	+	0.00587247i
$701$	−2.50398	−	4.33703i	−0.0945742	−	0.163807i	0.814857	−	0.579663i	$-0.196816\pi$
$701$	−2.50398	−	4.33703i	−0.0945742	−	0.163807i	−0.909431	+	0.415855i	$0.863482\pi$
$702$	−13.1055	−	32.8052i	−0.494636	−	1.23815i
$703$	−27.4366	+	47.5215i	−1.03479	+	1.79231i
$704$	1.80134	−	4.17597i	0.0678904	−	0.157388i
$705$	16.8373	−	12.8075i	0.634130	−	0.482358i
$706$	5.88994	+	6.24298i	0.221671	+	0.234958i
$707$	−13.5301	−	6.79505i	−0.508850	−	0.255554i
$708$	−3.79460	+	7.75448i	−0.142610	+	0.291431i
$709$	−5.91270	−	19.7498i	−0.222056	−	0.741719i	−0.994321	−	0.106419i	$-0.966062\pi$
$709$	−5.91270	−	19.7498i	−0.222056	−	0.741719i	0.772265	−	0.635300i	$-0.219124\pi$
$710$	21.3849	+	17.9441i	0.802562	+	0.673429i
$711$	9.29299	+	3.16643i	0.348514	+	0.118750i
$712$	4.44199	−	3.72727i	0.166471	−	0.139685i
$713$	−7.61546	−	5.00877i	−0.285201	−	0.187580i
$714$	−2.40685	+	2.92933i	−0.0900740	+	0.109627i
$715$	−78.3763	−	9.16087i	−2.93111	−	0.342597i
$716$	6.15043	+	14.2583i	0.229852	+	0.532858i
$717$	−0.230053	−	22.2583i	−0.00859149	−	0.831250i
$718$	−15.5593	+	7.81419i	−0.580669	+	0.291623i
$719$	−13.9245	−	5.06812i	−0.519298	−	0.189009i	0.0690555	−	0.997613i	$-0.478001\pi$
$719$	−13.9245	−	5.06812i	−0.519298	−	0.189009i	−0.588354	+	0.808604i	$0.700224\pi$
$720$	−6.30853	+	4.33859i	−0.235105	+	0.161690i
$721$	1.59426	−	0.580263i	0.0593733	−	0.0216101i
$722$	14.0301	−	14.8711i	0.522147	−	0.553444i
$723$	23.8619	+	17.3841i	0.887433	+	0.646523i
$724$	19.8359	−	13.0463i	0.737194	−	0.484860i
$725$	−0.373703	+	1.24825i	−0.0138790	+	0.0463590i
$726$	16.0171	−	4.97616i	0.594452	−	0.184683i
$727$	−23.5747	−	31.6664i	−0.874339	−	1.17444i	−0.983588	−	0.180427i	$-0.942252\pi$
$727$	−23.5747	−	31.6664i	−0.874339	−	1.17444i	0.109249	−	0.994014i	$-0.465155\pi$
$728$	6.01193			0.222817
$729$	−6.32731	−	26.2481i	−0.234345	−	0.972154i
$730$	16.0792			0.595117
$731$	−9.55775	−	12.8383i	−0.353506	−	0.474841i
$732$	4.00306	−	1.24366i	0.147957	−	0.0459670i
$733$	6.27529	−	20.9609i	0.231783	−	0.774209i	−0.760404	−	0.649450i	$-0.774999\pi$
$733$	6.27529	−	20.9609i	0.231783	−	0.774209i	0.992187	−	0.124759i	$-0.0398158\pi$
$734$	9.40762	−	6.18749i	0.347242	−	0.228384i
$735$	−22.2159	−	16.1850i	−0.819446	−	0.596992i
$736$	−0.808531	+	0.856993i	−0.0298028	+	0.0315892i
$737$	12.1218	−	4.41199i	0.446513	−	0.162518i
$738$	−17.6139	+	12.1137i	−0.648375	+	0.445910i
$739$	−19.9756	−	7.27052i	−0.734814	−	0.267450i	−0.0526126	−	0.998615i	$-0.516755\pi$
$739$	−19.9756	−	7.27052i	−0.734814	−	0.267450i	−0.682201	+	0.731165i	$0.738977\pi$
$740$	−19.9264	+	10.0074i	−0.732509	+	0.367880i
$741$	0.764335	+	73.9514i	0.0280785	+	2.71667i
$742$	1.73134	+	4.01371i	0.0635596	+	0.147348i
$743$	29.2201	+	3.41534i	1.07198	+	0.125297i	0.633729	−	0.773555i	$-0.281523\pi$
$743$	29.2201	+	3.41534i	1.07198	+	0.125297i	0.438253	+	0.898852i	$0.355597\pi$
$744$	8.50665	−	10.3533i	0.311869	−	0.379570i
$745$	23.2001	+	15.2589i	0.849985	+	0.559044i
$746$	−5.65450	+	4.74469i	−0.207026	+	0.173716i
$747$	−8.97050	−	3.05654i	−0.328213	−	0.111833i
$748$	8.62367	+	7.23612i	0.315313	+	0.264579i
$749$	−4.62200	−	15.4386i	−0.168884	−	0.564113i
$750$	−6.77425	+	13.8436i	−0.247361	+	0.505495i
$751$	0.669138	+	0.336054i	0.0244172	+	0.0122628i	0.460966	−	0.887418i	$-0.347503\pi$
$751$	0.669138	+	0.336054i	0.0244172	+	0.0122628i	−0.436549	+	0.899681i	$0.643799\pi$
$752$	3.28413	+	3.48098i	0.119760	+	0.126938i
$753$	−14.8429	+	11.2904i	−0.540905	+	0.411445i
$754$	2.31833	−	5.37449i	0.0844285	−	0.195727i
$755$	10.0396	−	17.3890i	0.365377	−	0.632851i
$756$	4.54772	+	0.657240i	0.165399	+	0.0239036i
$757$	7.72635	+	13.3824i	0.280819	+	0.486393i	0.971587	−	0.236684i	$-0.0760606\pi$
$757$	7.72635	+	13.3824i	0.280819	+	0.486393i	−0.690768	+	0.723077i	$0.742727\pi$
$758$	2.30192	−	0.269056i	0.0836095	−	0.00977255i
$759$	−9.27033	−	0.443853i	−0.336492	−	0.0161109i
$760$	15.5967	−	3.69649i	0.565752	−	0.134086i
$761$	−2.23822	−	38.4287i	−0.0811354	−	1.39304i	−0.755745	−	0.654866i	$-0.772725\pi$
$761$	−2.23822	−	38.4287i	−0.0811354	−	1.39304i	0.674610	−	0.738175i	$-0.264312\pi$
$762$	−22.6751	+	21.8401i	−0.821431	+	0.791185i
$763$	−10.2738	−	2.43494i	−0.371938	−	0.0881509i
$764$	3.36513	−	19.0846i	0.121746	−	0.690456i
$765$	−5.80956	−	18.0395i	−0.210045	−	0.652219i
$766$	−1.02769	−	5.82832i	−0.0371320	−	0.210586i
$767$	−1.97030	+	33.8288i	−0.0711435	+

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)

\(f(q)\)	\(=\)	\(q+(-0.597159 - 0.802123i) q^{2} +(-1.65406 + 0.513880i) q^{3} +(-0.286803 + 0.957990i) q^{4} +(2.13228 - 1.40243i) q^{5} +(1.39993 + 1.01990i) q^{6} +(-0.606844 + 0.643217i) q^{7} +(0.939693 - 0.342020i) q^{8} +(2.47185 - 1.69998i) q^{9} +O(q^{10})\)	\(q+(-0.597159 - 0.802123i) q^{2} +(-1.65406 + 0.513880i) q^{3} +(-0.286803 + 0.957990i) q^{4} +(2.13228 - 1.40243i) q^{5} +(1.39993 + 1.01990i) q^{6} +(-0.606844 + 0.643217i) q^{7} +(0.939693 - 0.342020i) q^{8} +(2.47185 - 1.69998i) q^{9} +(-2.39823 - 0.872884i) q^{10} +(4.06416 - 2.04110i) q^{11} +(-0.0179009 - 1.73196i) q^{12} +(-2.69275 - 6.24250i) q^{13} +(0.878322 + 0.102661i) q^{14} +(-2.80626 + 3.41544i) q^{15} +(-0.835488 - 0.549509i) q^{16} +(1.89618 - 1.59109i) q^{17} +(-2.83968 - 0.967574i) q^{18} +(4.81115 + 4.03704i) q^{19} +(0.731963 + 2.44493i) q^{20} +(0.673223 - 1.37577i) q^{21} +(-4.06416 - 2.04110i) q^{22} +(0.808531 + 0.856993i) q^{23} +(-1.37855 + 1.04861i) q^{24} +(0.599441 - 1.38966i) q^{25} +(-3.39926 + 5.88769i) q^{26} +(-3.21502 + 4.08211i) q^{27} +(-0.442151 - 0.765827i) q^{28} +(-0.855129 + 0.0999503i) q^{29} +(4.41538 + 0.211404i) q^{30} +(-7.52782 + 1.78413i) q^{31} +(0.0581448 + 0.998308i) q^{32} +(-5.67350 + 5.46460i) q^{33} +(-2.40857 - 0.570841i) q^{34} +(-0.391900 + 2.22258i) q^{35} +(0.919628 + 2.85557i) q^{36} +(1.51717 + 8.60431i) q^{37} +(0.365179 - 6.26989i) q^{38} +(7.66188 + 8.94175i) q^{39} +(1.52403 - 2.04713i) q^{40} +(4.25521 - 5.71574i) q^{41} +(-1.50556 + 0.281544i) q^{42} +(0.375968 - 6.45512i) q^{43} +(0.789737 + 4.47882i) q^{44} +(2.88660 - 7.09144i) q^{45} +(0.204593 - 1.16030i) q^{46} +(-4.65668 - 1.10365i) q^{47} +(1.66433 + 0.479582i) q^{48} +(0.361545 + 6.20749i) q^{49} +(-1.47264 + 0.349022i) q^{50} +(-2.31878 + 3.60617i) q^{51} +(6.75254 - 0.789259i) q^{52} +(2.47156 + 4.28086i) q^{53} +(5.19423 + 0.141172i) q^{54} +(5.80346 - 10.0519i) q^{55} +(-0.350254 + 0.811980i) q^{56} +(-10.0325 - 4.20516i) q^{57} +(0.590820 + 0.626233i) q^{58} +(-4.45417 - 2.23697i) q^{59} +(-2.46711 - 3.66792i) q^{60} +(0.694103 + 2.31847i) q^{61} +(5.92639 + 4.97283i) q^{62} +(-0.406574 + 2.62156i) q^{63} +(0.766044 - 0.642788i) q^{64} +(-14.4964 - 9.53441i) q^{65} +(7.77127 + 1.28762i) q^{66} +(2.81724 + 0.329288i) q^{67} +(0.980412 + 2.27285i) q^{68} +(-1.77775 - 1.00203i) q^{69} +(2.01681 - 1.01288i) q^{70} +(-10.2786 - 3.74111i) q^{71} +(1.74136 - 2.44288i) q^{72} +(-5.92032 + 2.15482i) q^{73} +(5.99572 - 6.35510i) q^{74} +(-0.277395 + 2.60663i) q^{75} +(-5.24729 + 3.45120i) q^{76} +(-1.15344 + 3.85277i) q^{77} +(2.59702 - 11.4854i) q^{78} +(1.95423 + 2.62498i) q^{79} -2.55214 q^{80} +(3.22013 - 8.40421i) q^{81} -7.12577 q^{82} +(-1.88641 - 2.53389i) q^{83} +(1.12489 + 1.03952i) q^{84} +(1.81182 - 6.05190i) q^{85} +(-5.40232 + 3.55316i) q^{86} +(1.36308 - 0.604758i) q^{87} +(3.12097 - 3.30803i) q^{88} +(5.44891 - 1.98324i) q^{89} +(-7.41196 + 1.91930i) q^{90} +(5.64937 + 2.05620i) q^{91} +(-1.05288 + 0.528776i) q^{92} +(11.5347 - 6.81946i) q^{93} +(1.89551 + 4.39429i) q^{94} +(15.9204 + 1.86083i) q^{95} +(-0.609186 - 1.62139i) q^{96} +(0.222871 + 0.146585i) q^{97} +(4.76327 - 3.99686i) q^{98} +(6.57619 - 11.9543i) 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

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