LMFDB - Embedded newform 162.2.g.b.25.3

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:	$90$
Relative dimension:	$5$ over $\Q(\zeta_{27})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{27}]$

Embedding invariants

Embedding label			25.3
Character	$\chi$	$=$	162.25
Dual form			162.2.g.b.13.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.893633 - 0.448799i) q^{2} +(-0.530234 - 1.64889i) q^{3} +(0.597159 - 0.802123i) q^{4} +(-0.536865 + 1.79325i) q^{5} +(-1.21386 - 1.23554i) q^{6} +(1.99514 - 4.62524i) q^{7} +(0.173648 - 0.984808i) q^{8} +(-2.43770 + 1.74860i) q^{9} +O(q^{10})$	\(q+(0.893633 - 0.448799i) q^{2} +(-0.530234 - 1.64889i) q^{3} +(0.597159 - 0.802123i) q^{4} +(-0.536865 + 1.79325i) q^{5} +(-1.21386 - 1.23554i) q^{6} +(1.99514 - 4.62524i) q^{7} +(0.173648 - 0.984808i) q^{8} +(-2.43770 + 1.74860i) q^{9} +(0.325051 + 1.84346i) q^{10} +(1.04359 + 0.247336i) q^{11} +(-1.63925 - 0.559338i) q^{12} +(-2.13082 + 1.40147i) q^{13} +(-0.292887 - 5.02868i) q^{14} +(3.24155 - 0.0656115i) q^{15} +(-0.286803 - 0.957990i) q^{16} +(5.49113 + 1.99861i) q^{17} +(-1.39364 + 2.65665i) q^{18} +(-5.64228 + 2.05362i) q^{19} +(1.11782 + 1.50149i) q^{20} +(-8.68443 - 0.837303i) q^{21} +(1.04359 - 0.247336i) q^{22} +(1.77254 + 4.10922i) q^{23} +(-1.71592 + 0.235852i) q^{24} +(1.24990 + 0.822072i) q^{25} +(-1.27520 + 2.20871i) q^{26} +(4.17581 + 3.09235i) q^{27} +(-2.51860 - 4.36235i) q^{28} +(-0.0699925 + 1.20173i) q^{29} +(2.86731 - 1.51344i) q^{30} +(6.69052 + 0.782010i) q^{31} +(-0.686242 - 0.727374i) q^{32} +(-0.145518 - 1.85192i) q^{33} +(5.80403 - 0.678393i) q^{34} +(7.22312 + 6.06092i) q^{35} +(-0.0531021 + 2.99953i) q^{36} +(1.39018 - 1.16650i) q^{37} +(-4.12046 + 4.36743i) q^{38} +(3.44070 + 2.77040i) q^{39} +(1.67279 + 0.840105i) q^{40} +(-5.78256 - 2.90411i) q^{41} +(-8.13647 + 3.14932i) q^{42} +(-1.11720 + 1.18417i) q^{43} +(0.821586 - 0.689392i) q^{44} +(-1.82697 - 5.31019i) q^{45} +(3.42822 + 2.87662i) q^{46} +(-11.9271 + 1.39408i) q^{47} +(-1.42755 + 0.980867i) q^{48} +(-12.6086 - 13.3644i) q^{49} +(1.48590 + 0.173676i) q^{50} +(0.383906 - 10.1140i) q^{51} +(-0.148292 + 2.54608i) q^{52} +(2.50648 + 4.34135i) q^{53} +(5.11948 + 0.889320i) q^{54} +(-1.00381 + 1.73864i) q^{55} +(-4.20852 - 2.76799i) q^{56} +(6.37794 + 8.21462i) q^{57} +(0.476786 + 1.10531i) q^{58} +(-2.74121 + 0.649679i) q^{59} +(1.88309 - 2.63930i) q^{60} +(-2.62080 - 3.52034i) q^{61} +(6.32983 - 2.30387i) q^{62} +(3.22416 + 14.7637i) q^{63} +(-0.939693 - 0.342020i) q^{64} +(-1.36922 - 4.57351i) q^{65} +(-0.961181 - 1.58963i) q^{66} +(-0.636693 - 10.9316i) q^{67} +(4.88220 - 3.21108i) q^{68} +(5.83580 - 5.10159i) q^{69} +(9.17495 + 2.17450i) q^{70} +(-1.51839 - 8.61121i) q^{71} +(1.29873 + 2.70431i) q^{72} +(-1.22998 + 6.97557i) q^{73} +(0.718785 - 1.66633i) q^{74} +(0.692770 - 2.49684i) q^{75} +(-1.72208 + 5.75214i) q^{76} +(3.22610 - 4.33341i) q^{77} +(4.31808 + 0.931533i) q^{78} +(5.34642 - 2.68507i) q^{79} +1.87189 q^{80} +(2.88479 - 8.52514i) q^{81} -6.47084 q^{82} +(-8.01224 + 4.02390i) q^{83} +(-5.85760 + 6.46598i) q^{84} +(-6.53201 + 8.77401i) q^{85} +(-0.466916 + 1.55961i) q^{86} +(2.01863 - 0.521786i) q^{87} +(0.424797 - 0.984790i) q^{88} +(-1.24608 + 7.06686i) q^{89} +(-4.01585 - 3.92541i) q^{90} +(2.23084 + 12.6517i) q^{91} +(4.35459 + 1.03206i) q^{92} +(-2.25809 - 11.4466i) q^{93} +(-10.0328 + 6.59869i) q^{94} +(-0.653523 - 11.2206i) q^{95} +(-0.835493 + 1.51722i) q^{96} +(-2.10743 - 7.03931i) q^{97} +(-17.2654 - 6.28409i) q^{98} +(-2.97647 + 1.22190i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 90 q - 9 q^{6}+O(q^{10}) $ 90 * q - 9 * q^6	$ 90 q - 9 q^{6} - 18 q^{13} - 9 q^{18} - 9 q^{20} - 54 q^{21} + 27 q^{23} - 18 q^{25} - 27 q^{26} - 27 q^{27} - 18 q^{28} - 27 q^{29} + 9 q^{30} + 54 q^{31} - 63 q^{33} - 27 q^{35} - 9 q^{36} - 18 q^{38} - 9 q^{41} - 9 q^{42} - 36 q^{43} + 63 q^{45} + 18 q^{46} - 27 q^{47} - 9 q^{48} - 36 q^{51} + 36 q^{52} - 27 q^{53} - 54 q^{55} - 81 q^{57} - 9 q^{58} - 45 q^{59} - 63 q^{63} + 9 q^{65} + 36 q^{66} + 81 q^{67} + 36 q^{68} + 18 q^{69} - 72 q^{70} + 72 q^{71} + 18 q^{72} - 36 q^{73} + 45 q^{74} + 216 q^{75} - 18 q^{76} + 144 q^{77} + 54 q^{78} - 99 q^{79} + 18 q^{80} + 144 q^{81} + 72 q^{82} + 45 q^{83} + 18 q^{84} - 117 q^{85} + 72 q^{86} + 81 q^{87} - 18 q^{88} + 45 q^{89} + 162 q^{90} - 63 q^{91} + 36 q^{92} + 45 q^{93} - 72 q^{94} + 45 q^{95} + 18 q^{96} + 117 q^{97} + 36 q^{98} - 81 q^{99}+O(q^{100}) $ 90 * q - 9 * q^6 - 18 * q^13 - 9 * q^18 - 9 * q^20 - 54 * q^21 + 27 * q^23 - 18 * q^25 - 27 * q^26 - 27 * q^27 - 18 * q^28 - 27 * q^29 + 9 * q^30 + 54 * q^31 - 63 * q^33 - 27 * q^35 - 9 * q^36 - 18 * q^38 - 9 * q^41 - 9 * q^42 - 36 * q^43 + 63 * q^45 + 18 * q^46 - 27 * q^47 - 9 * q^48 - 36 * q^51 + 36 * q^52 - 27 * q^53 - 54 * q^55 - 81 * q^57 - 9 * q^58 - 45 * q^59 - 63 * q^63 + 9 * q^65 + 36 * q^66 + 81 * q^67 + 36 * q^68 + 18 * q^69 - 72 * q^70 + 72 * q^71 + 18 * q^72 - 36 * q^73 + 45 * q^74 + 216 * q^75 - 18 * q^76 + 144 * q^77 + 54 * q^78 - 99 * q^79 + 18 * q^80 + 144 * q^81 + 72 * q^82 + 45 * q^83 + 18 * q^84 - 117 * q^85 + 72 * q^86 + 81 * q^87 - 18 * q^88 + 45 * q^89 + 162 * q^90 - 63 * q^91 + 36 * q^92 + 45 * q^93 - 72 * q^94 + 45 * q^95 + 18 * q^96 + 117 * q^97 + 36 * q^98 - 81 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$83$
$\chi(n)$	$e\left(\frac{23}{27}\right)$

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 $

$2$	0.893633	−	0.448799i	0.631894	−	0.317349i
$2$	0.893633	−	0.448799i	0.631894	−	0.317349i
$3$	−0.530234	−	1.64889i	−0.306131	−	0.951989i
$3$	−0.530234	−	1.64889i	−0.306131	−	0.951989i
$4$	0.597159	−	0.802123i	0.298579	−	0.401062i
$5$	−0.536865	+	1.79325i	−0.240093	+	0.801968i	0.749985	+	0.661454i	$0.230061\pi$
$5$	−0.536865	+	1.79325i	−0.240093	+	0.801968i	−0.990079	+	0.140514i	$0.955125\pi$
$6$	−1.21386	−	1.23554i	−0.495555	−	0.504406i
$7$	1.99514	−	4.62524i	0.754090	−	1.74818i	0.0958168	−	0.995399i	$-0.469454\pi$
$7$	1.99514	−	4.62524i	0.754090	−	1.74818i	0.658274	−	0.752779i	$-0.271287\pi$
$8$	0.173648	−	0.984808i	0.0613939	−	0.348182i
$9$	−2.43770	+	1.74860i	−0.812568	+	0.582867i
$10$	0.325051	+	1.84346i	0.102790	+	0.582952i
$11$	1.04359	+	0.247336i	0.314656	+	0.0745747i	0.384909	−	0.922954i	$-0.374233\pi$
$11$	1.04359	+	0.247336i	0.314656	+	0.0745747i	−0.0702537	+	0.997529i	$0.522381\pi$
$12$	−1.63925	−	0.559338i	−0.473211	−	0.161467i
$13$	−2.13082	+	1.40147i	−0.590984	+	0.388697i	−0.809485	−	0.587140i	$-0.800254\pi$
$13$	−2.13082	+	1.40147i	−0.590984	+	0.388697i	0.218501	+	0.975837i	$0.429883\pi$
$14$	−0.292887	−	5.02868i	−0.0782775	−	1.34397i
$15$	3.24155	−	0.0656115i	0.836965	−	0.0169408i
$16$	−0.286803	−	0.957990i	−0.0717008	−	0.239497i
$17$	5.49113	+	1.99861i	1.33179	+	0.484734i	0.907219	−	0.420659i	$-0.138201\pi$
$17$	5.49113	+	1.99861i	1.33179	+	0.484734i	0.424576	+	0.905392i	$0.360423\pi$
$18$	−1.39364	+	2.65665i	−0.328484	+	0.626177i
$19$	−5.64228	+	2.05362i	−1.29443	+	0.471133i	−0.895178	−	0.445709i	$-0.852952\pi$
$19$	−5.64228	+	2.05362i	−1.29443	+	0.471133i	−0.399250	+	0.916842i	$0.630729\pi$
$20$	1.11782	+	1.50149i	0.249952	+	0.335743i
$21$	−8.68443	−	0.837303i	−1.89510	−	0.182715i
$22$	1.04359	−	0.247336i	0.222495	−	0.0527323i
$23$	1.77254	+	4.10922i	0.369601	+	0.856831i	0.996946	+	0.0780902i	$0.0248822\pi$
$23$	1.77254	+	4.10922i	0.369601	+	0.856831i	−0.627345	+	0.778741i	$0.715859\pi$
$24$	−1.71592	+	0.235852i	−0.350260	+	0.0481430i
$25$	1.24990	+	0.822072i	0.249980	+	0.164414i
$26$	−1.27520	+	2.20871i	−0.250087	+	0.433163i
$27$	4.17581	+	3.09235i	0.803635	+	0.595122i
$28$	−2.51860	−	4.36235i	−0.475971	−	0.824406i
$29$	−0.0699925	+	1.20173i	−0.0129973	+	0.223155i	0.985555	+	0.169358i	$0.0541694\pi$
$29$	−0.0699925	+	1.20173i	−0.0129973	+	0.223155i	−0.998552	+	0.0537969i	$0.982868\pi$
$30$	2.86731	−	1.51344i	0.523497	−	0.276315i
$31$	6.69052	+	0.782010i	1.20165	+	0.140453i	0.693270	−	0.720678i	$-0.256169\pi$
$31$	6.69052	+	0.782010i	1.20165	+	0.140453i	0.508383	+	0.861131i	$0.330243\pi$
$32$	−0.686242	−	0.727374i	−0.121312	−	0.128583i
$33$	−0.145518	−	1.85192i	−0.0253314	−	0.322378i
$34$	5.80403	−	0.678393i	0.995382	−	0.116343i
$35$	7.22312	+	6.06092i	1.22093	+	1.02448i
$36$	−0.0531021	+	2.99953i	−0.00885035	+	0.499922i
$37$	1.39018	−	1.16650i	0.228544	−	0.191771i	−0.521324	−	0.853359i	$-0.674562\pi$
$37$	1.39018	−	1.16650i	0.228544	−	0.191771i	0.749868	+	0.661588i	$0.230117\pi$
$38$	−4.12046	+	4.36743i	−0.668427	+	0.708491i
$39$	3.44070	+	2.77040i	0.550954	+	0.443619i
$40$	1.67279	+	0.840105i	0.264491	+	0.132832i
$41$	−5.78256	−	2.90411i	−0.903084	−	0.453546i	−0.0642502	−	0.997934i	$-0.520466\pi$
$41$	−5.78256	−	2.90411i	−0.903084	−	0.453546i	−0.838833	+	0.544388i	$0.816762\pi$
$42$	−8.13647	+	3.14932i	−1.25548	+	0.485951i
$43$	−1.11720	+	1.18417i	−0.170372	+	0.180584i	−0.806934	−	0.590642i	$-0.798875\pi$
$43$	−1.11720	+	1.18417i	−0.170372	+	0.180584i	0.636562	+	0.771226i	$0.280356\pi$
$44$	0.821586	−	0.689392i	0.123859	−	0.103930i
$45$	−1.82697	−	5.31019i	−0.272348	−	0.791596i
$46$	3.42822	+	2.87662i	0.505463	+	0.424134i
$47$	−11.9271	+	1.39408i	−1.73975	+	0.203348i	−0.925911	−	0.377741i	$-0.876701\pi$
$47$	−11.9271	+	1.39408i	−1.73975	+	0.203348i	−0.813840	+	0.581088i	$0.802627\pi$
$48$	−1.42755	+	0.980867i	−0.206049	+	0.141576i
$49$	−12.6086	−	13.3644i	−1.80123	−	1.90919i
$50$	1.48590	+	0.173676i	0.210138	+	0.0245616i
$51$	0.383906	−	10.1140i	0.0537577	−	1.41625i
$52$	−0.148292	+	2.54608i	−0.0205644	+	0.353078i
$53$	2.50648	+	4.34135i	0.344291	+	0.596330i	0.985225	−	0.171266i	$-0.0547858\pi$
$53$	2.50648	+	4.34135i	0.344291	+	0.596330i	−0.640933	+	0.767597i	$0.721452\pi$
$54$	5.11948	+	0.889320i	0.696673	+	0.121021i
$55$	−1.00381	+	1.73864i	−0.135353	+	0.234439i
$56$	−4.20852	−	2.76799i	−0.562388	−	0.369888i
$57$	6.37794	+	8.21462i	0.844778	+	1.08805i
$58$	0.476786	+	1.10531i	0.0626050	+	0.145135i
$59$	−2.74121	+	0.649679i	−0.356875	+	0.0845810i	−0.405143	−	0.914253i	$-0.632778\pi$
$59$	−2.74121	+	0.649679i	−0.356875	+	0.0845810i	0.0482675	+	0.998834i	$0.484630\pi$
$60$	1.88309	−	2.63930i	0.243106	−	0.340733i
$61$	−2.62080	−	3.52034i	−0.335559	−	0.450734i	0.602033	−	0.798471i	$-0.294358\pi$
$61$	−2.62080	−	3.52034i	−0.335559	−	0.450734i	−0.937592	+	0.347737i	$0.886950\pi$
$62$	6.32983	−	2.30387i	0.803890	−	0.292592i
$63$	3.22416	+	14.7637i	0.406206	+	1.86005i
$64$	−0.939693	−	0.342020i	−0.117462	−	0.0427525i
$65$	−1.36922	−	4.57351i	−0.169831	−	0.567274i
$66$	−0.961181	−	1.58963i	−0.118313	−	0.195670i
$67$	−0.636693	−	10.9316i	−0.0777844	−	1.33551i	−0.781001	−	0.624530i	$-0.785290\pi$
$67$	−0.636693	−	10.9316i	−0.0777844	−	1.33551i	0.703216	−	0.710976i	$-0.251747\pi$
$68$	4.88220	−	3.21108i	0.592054	−	0.389400i
$69$	5.83580	−	5.10159i	0.702548	−	0.614159i
$70$	9.17495	+	2.17450i	1.09662	+	0.259903i
$71$	−1.51839	−	8.61121i	−0.180200	−	1.02196i	−0.931969	−	0.362537i	$-0.881911\pi$
$71$	−1.51839	−	8.61121i	−0.180200	−	1.02196i	0.751770	−	0.659426i	$-0.229200\pi$
$72$	1.29873	+	2.70431i	0.153057	+	0.318706i
$73$	−1.22998	+	6.97557i	−0.143958	+	0.816429i	0.824239	+	0.566242i	$0.191603\pi$
$73$	−1.22998	+	6.97557i	−0.143958	+	0.816429i	−0.968198	+	0.250187i	$0.919508\pi$
$74$	0.718785	−	1.66633i	0.0835570	−	0.193707i
$75$	0.692770	−	2.49684i	0.0799942	−	0.288311i
$76$	−1.72208	+	5.75214i	−0.197536	+	0.659816i
$77$	3.22610	−	4.33341i	0.367649	−	0.493838i
$78$	4.31808	+	0.931533i	0.488926	+	0.105475i
$79$	5.34642	−	2.68507i	0.601519	−	0.302094i	−0.121858	−	0.992548i	$-0.538885\pi$
$79$	5.34642	−	2.68507i	0.601519	−	0.302094i	0.723377	+	0.690453i	$0.242589\pi$
$80$	1.87189			0.209284
$81$	2.88479	−	8.52514i	0.320532	−	0.947238i
$82$	−6.47084			−0.714585
$83$	−8.01224	+	4.02390i	−0.879457	+	0.441680i	−0.830434	−	0.557117i	$-0.811907\pi$
$83$	−8.01224	+	4.02390i	−0.879457	+	0.441680i	−0.0490238	+	0.998798i	$0.515611\pi$
$84$	−5.85760	+	6.46598i	−0.639117	+	0.705496i
$85$	−6.53201	+	8.77401i	−0.708496	+	0.951675i
$86$	−0.466916	+	1.55961i	−0.0503489	+	0.168177i
$87$	2.01863	−	0.521786i	0.216420	−	0.0559413i
$88$	0.424797	−	0.984790i	0.0452835	−	0.104979i
$89$	−1.24608	+	7.06686i	−0.132084	+	0.749086i	0.844762	+	0.535142i	$0.179742\pi$
$89$	−1.24608	+	7.06686i	−0.132084	+	0.749086i	−0.976846	+	0.213944i	$0.931369\pi$
$90$	−4.01585	−	3.92541i	−0.423307	−	0.413775i
$91$	2.23084	+	12.6517i	0.233855	+	1.32626i
$92$	4.35459	+	1.03206i	0.453997	+	0.107599i
$93$	−2.25809	−	11.4466i	−0.234153	−	1.18696i
$94$	−10.0328	+	6.59869i	−1.03481	+	0.680603i
$95$	−0.653523	−	11.2206i	−0.0670501	−	1.15121i
$96$	−0.835493	+	1.51722i	−0.0852722	+	0.154850i
$97$	−2.10743	−	7.03931i	−0.213977	−	0.714733i	−0.995827	−	0.0912660i	$-0.970909\pi$
$97$	−2.10743	−	7.03931i	−0.213977	−	0.714733i	0.781849	−	0.623467i	$-0.214277\pi$
$98$	−17.2654	−	6.28409i	−1.74407	−	0.634789i
$99$	−2.97647	+	1.22190i	−0.299146	+	0.122805i
$100$	1.40579	−	0.511666i	0.140579	−	0.0511666i
$101$	5.43054	+	7.29449i	0.540359	+	0.725829i	0.985508	−	0.169628i	$-0.0542566\pi$
$101$	5.43054	+	7.29449i	0.540359	+	0.725829i	−0.445149	+	0.895457i	$0.646849\pi$
$102$	−4.19609	−	9.21052i	−0.415475	−	0.911977i
$103$	13.8032	−	3.27141i	1.36007	−	0.322342i	0.515087	−	0.857138i	$-0.327760\pi$
$103$	13.8032	−	3.27141i	1.36007	−	0.322342i	0.844981	+	0.534796i	$0.179612\pi$
$104$	1.01016	+	2.34181i	0.0990543	+	0.229634i
$105$	6.16387	−	15.1239i	0.601532	−	1.47594i
$106$	4.18827	+	2.75467i	0.406800	+	0.267557i
$107$	5.56989	−	9.64733i	0.538461	−	0.932642i	−0.460526	−	0.887646i	$-0.652339\pi$
$107$	5.56989	−	9.64733i	0.538461	−	0.932642i	0.998987	−	0.0449960i	$-0.0143275\pi$
$108$	4.97406	−	1.50289i	0.478629	−	0.144616i
$109$	3.29673	+	5.71010i	0.315769	+	0.546928i	0.979601	−	0.200954i	$-0.0644041\pi$
$109$	3.29673	+	5.71010i	0.315769	+	0.546928i	−0.663831	+	0.747882i	$0.731071\pi$
$110$	−0.116732	+	2.00422i	−0.0111300	+	0.191095i
$111$	−2.66055	−	1.67374i	−0.252528	−	0.158864i
$112$	−5.00315	−	0.584784i	−0.472753	−	0.0552569i
$113$	−0.570269	−	0.604449i	−0.0536464	−	0.0568618i	0.699995	−	0.714148i	$-0.253186\pi$
$113$	−0.570269	−	0.604449i	−0.0536464	−	0.0568618i	−0.753641	+	0.657286i	$0.771704\pi$
$114$	9.38625	+	4.47844i	0.879102	+	0.419444i
$115$	−8.32049	+	0.972526i	−0.775890	+	0.0906886i
$116$	0.922135	+	0.773763i	0.0856181	+	0.0718421i
$117$	2.74371	−	7.14232i	0.253656	−	0.660307i
$118$	−2.15806	+	1.81083i	−0.198666	+	0.166700i
$119$	20.1996	−	21.4103i	1.85169	−	1.96268i
$120$	0.498275	−	3.20370i	0.0454861	−	0.292456i
$121$	−8.80205	−	4.42055i	−0.800186	−	0.401868i
$122$	−3.92196	−	1.96968i	−0.355078	−	0.178327i
$123$	−1.72246	+	11.0747i	−0.155309	+	0.998570i
$124$	4.62257	−	4.89964i	0.415119	−	0.440001i
$125$	−9.31498	+	7.81620i	−0.833157	+	0.699102i
$126$	9.50713	+	11.7463i	0.846963	+	1.04644i
$127$	10.7630	+	9.03120i	0.955058	+	0.801389i	0.980142	−	0.198296i	$-0.0635408\pi$
$127$	10.7630	+	9.03120i	0.955058	+	0.801389i	−0.0250838	+	0.999685i	$0.507985\pi$
$128$	−0.993238	+	0.116093i	−0.0877907	+	0.0102613i
$129$	2.54494	+	1.21426i	0.224070	+	0.106910i
$130$	−3.27617	−	3.47253i	−0.287339	−	0.304561i
$131$	−14.9995	−	1.75319i	−1.31052	−	0.153177i	−0.568013	−	0.823020i	$-0.692288\pi$
$131$	−14.9995	−	1.75319i	−1.31052	−	0.153177i	−0.742503	+	0.669843i	$0.766362\pi$
$132$	−1.57237	−	0.989168i	−0.136857	−	0.0860960i
$133$	−1.75861	+	30.1942i	−0.152491	+	2.61817i
$134$	−5.47506	−	9.48308i	−0.472973	−	0.819213i
$135$	−7.78721	+	5.82812i	−0.670217	+	0.501605i
$136$	2.92177	−	5.06065i	0.250540	−	0.433947i
$137$	−9.13015	−	6.00500i	−0.780042	−	0.513041i	0.0959394	−	0.995387i	$-0.469415\pi$
$137$	−9.13015	−	6.00500i	−0.780042	−	0.513041i	−0.875981	+	0.482346i	$0.839785\pi$
$138$	2.92548	−	7.17805i	0.249033	−	0.611036i
$139$	3.28755	+	7.62139i	0.278846	+	0.646438i	0.998871	−	0.0475106i	$-0.0151288\pi$
$139$	3.28755	+	7.62139i	0.278846	+	0.646438i	−0.720025	+	0.693949i	$0.755870\pi$
$140$	9.17495	−	2.17450i	0.775425	−	0.183779i
$141$	8.62287	+	18.9274i	0.726177	+	1.59397i
$142$	−5.22158	−	7.01381i	−0.438186	−	0.588585i
$143$	−2.57035	+	0.935531i	−0.214943	+	0.0782330i
$144$	2.37428	+	1.83379i	0.197857	+	0.152816i
$145$	−2.11742	−	0.770679i	−0.175842	−	0.0640014i
$146$	2.03148	+	6.78561i	0.168126	+	0.561581i
$147$	−15.3509	+	27.8765i	−1.26612	+	2.29922i
$148$	−0.105518	−	1.81168i	−0.00867354	−	0.148919i
$149$	10.8825	−	7.15754i	0.891530	−	0.586369i	−0.0189963	−	0.999820i	$-0.506047\pi$
$149$	10.8825	−	7.15754i	0.891530	−	0.586369i	0.910526	+	0.413451i	$0.135677\pi$
$150$	−0.501500	−	2.54218i	−0.0409473	−	0.207568i
$151$	−0.857201	−	0.203160i	−0.0697580	−	0.0165329i	0.195589	−	0.980686i	$-0.437338\pi$
$151$	−0.857201	−	0.203160i	−0.0697580	−	0.0165329i	−0.265347	+	0.964153i	$0.585486\pi$
$152$	1.04265	+	5.91317i	0.0845702	+	0.479621i
$153$	−16.8805	+	4.72978i	−1.36471	+	0.382380i
$154$	0.938121	−	5.32035i	0.0755959	−	0.428726i
$155$	−4.99425	+	11.5780i	−0.401148	+	0.929966i
$156$	4.27685	−	1.10550i	0.342422	−	0.0885109i
$157$	0.988610	−	3.30219i	0.0788997	−	0.263543i	−0.909434	−	0.415849i	$-0.863485\pi$
$157$	0.988610	−	3.30219i	0.0788997	−	0.263543i	0.988333	+	0.152305i	$0.0486697\pi$
$158$	3.57268	−	4.79894i	0.284227	−	0.381783i
$159$	5.82941	−	6.43485i	0.462302	−	0.510317i
$160$	1.67279	−	0.840105i	0.132245	−	0.0664161i
$161$	22.5426			1.77661
$162$	−1.24813	−	8.91303i	−0.0980625	−	0.700274i
$163$	−9.35157			−0.732472			−0.366236	−	0.930522i	$-0.619354\pi$
$163$	−9.35157			−0.732472			−0.366236	+	0.930522i	$0.619354\pi$
$164$	−5.78256	+	2.90411i	−0.451542	+	0.226773i
$165$	3.39909	+	0.733282i	0.264619	+	0.0570859i
$166$	−5.35408	+	7.19177i	−0.415557	+	0.558190i
$167$	−3.28860	+	10.9847i	−0.254480	+	0.850021i	0.731311	+	0.682044i	$0.238909\pi$
$167$	−3.28860	+	10.9847i	−0.254480	+	0.850021i	−0.985791	+	0.167977i	$0.946276\pi$
$168$	−2.33262	+	8.40709i	−0.179965	+	0.648621i
$169$	−2.57273	+	5.96426i	−0.197902	+	0.458789i
$170$	−1.89945	+	10.7723i	−0.145681	+	0.826198i
$171$	10.1632	−	14.8722i	0.777202	−	1.13731i
$172$	0.282700	+	1.60327i	0.0215556	+	0.122248i
$173$	−5.93149	−	1.40579i	−0.450963	−	0.106880i	−0.00114272	−	0.999999i	$-0.500364\pi$
$173$	−5.93149	−	1.40579i	−0.450963	−	0.106880i	−0.449820	+	0.893119i	$0.648512\pi$
$174$	1.56974	−	1.37224i	0.119001	−	0.104030i
$175$	6.29600	−	4.14095i	0.475933	−	0.313026i
$176$	−0.0623605	−	1.07069i	−0.00470060	−	0.0807062i
$177$	2.52474	+	4.17548i	0.189771	+	0.313849i
$178$	2.05806	+	6.87442i	0.154258	+	0.515259i
$179$	−10.5797	−	3.85070i	−0.790764	−	0.287815i	−0.0851106	−	0.996372i	$-0.527124\pi$
$179$	−10.5797	−	3.85070i	−0.790764	−	0.287815i	−0.705654	+	0.708557i	$0.749347\pi$
$180$	−5.35041	−	1.70557i	−0.398796	−	0.127126i
$181$	−11.5465	+	4.20258i	−0.858244	+	0.312375i	−0.733397	−	0.679801i	$-0.762066\pi$
$181$	−11.5465	+	4.20258i	−0.858244	+	0.312375i	−0.124847	+	0.992176i	$0.539844\pi$
$182$	7.67162	+	10.3048i	0.568658	+	0.763840i
$183$	−4.41504	+	6.18803i	−0.326369	+	0.457432i
$184$	4.35459	−	1.03206i	0.321025	−	0.0760842i
$185$	1.34549	+	3.11919i	0.0989223	+	0.229328i
$186$	−7.15514	−	9.21563i	−0.524640	−	0.675723i
$187$	5.23618	+	3.44389i	0.382908	+	0.251842i
$188$	−6.00417	+	10.3995i	−0.437899	+	0.758463i
$189$	22.6342	−	13.1445i	1.64639	−	0.956121i
$190$	−5.61979	−	9.73376i	−0.407702	−	0.706161i
$191$	−0.477753	+	8.20270i	−0.0345690	+	0.593526i	0.935895	+	0.352279i	$0.114593\pi$
$191$	−0.477753	+	8.20270i	−0.0345690	+	0.593526i	−0.970464	+	0.241247i	$0.922444\pi$
$192$	−0.0656976	+	1.73080i	−0.00474132	+	0.124910i
$193$	13.7338	+	1.60525i	0.988579	+	0.115548i	0.594986	−	0.803736i	$-0.297158\pi$
$193$	13.7338	+	1.60525i	0.988579	+	0.115548i	0.393593	+	0.919285i	$0.371232\pi$
$194$	−5.04250	−	5.34474i	−0.362031	−	0.383730i
$195$	−6.81523	+	4.68273i	−0.488048	+	0.335337i
$196$	−18.2492	+	2.13303i	−1.30352	+	0.152359i
$197$	2.18860	+	1.83645i	0.155931	+	0.130842i	0.717415	−	0.696646i	$-0.245325\pi$
$197$	2.18860	+	1.83645i	0.155931	+	0.130842i	−0.561484	+	0.827487i	$0.689770\pi$
$198$	−2.11148	+	2.42776i	−0.150056	+	0.172534i
$199$	15.5073	−	13.0122i	1.09929	−	0.922411i	0.101909	−	0.994794i	$-0.467505\pi$
$199$	15.5073	−	13.0122i	1.09929	−	0.922411i	0.997377	+	0.0723832i	$0.0230605\pi$
$200$	1.02663	−	1.08816i	0.0725934	−	0.0769445i
$201$	−17.6874	+	6.84614i	−1.24758	+	0.482890i
$202$	8.12667	+	4.08137i	0.571791	+	0.287164i
$203$	5.41863	+	2.72134i	0.380313	+	0.191000i
$204$	−7.88344	−	6.34761i	−0.551951	−	0.444422i
$205$	8.31226	−	8.81048i	0.580554	−	0.615351i
$206$	10.8668	−	9.11830i	0.757123	−	0.635302i
$207$	−11.5063	−	6.91758i	−0.799744	−	0.480805i
$208$	1.95372	+	1.63936i	0.135466	+	0.113669i
$209$	−6.39619	+	0.747607i	−0.442433	+	0.0517131i
$210$	−1.27935	−	16.2815i	−0.0882835	−	1.12353i
$211$	2.94231	+	3.11867i	0.202557	+	0.214698i	0.820687	−	0.571378i	$-0.193591\pi$
$211$	2.94231	+	3.11867i	0.202557	+	0.214698i	−0.618130	+	0.786076i	$0.712109\pi$
$212$	4.97906	+	0.581969i	0.341964	+	0.0399698i
$213$	−13.3939	+	7.06962i	−0.917733	+	0.484402i
$214$	0.647720	−	11.1209i	0.0442772	−	0.760211i
$215$	−1.52372	−	2.63917i	−0.103917	−	0.179990i
$216$	3.77049	−	3.57539i	0.256549	−	0.243275i
$217$	16.9655	−	29.3851i	1.15169	−	1.99479i
$218$	5.50875	+	3.62316i	0.373100	+	0.245392i
$219$	12.1542	−	1.67058i	0.821302	−	0.112887i
$220$	0.795175	+	1.84342i	0.0536107	+	0.124284i
$221$	−14.5016	+	3.43694i	−0.975484	+	0.231194i
$222$	−3.12873	−	0.301654i	−0.209986	−	0.0202457i
$223$	−9.37331	−	12.5905i	−0.627684	−	0.843125i	0.368571	−	0.929600i	$-0.379847\pi$
$223$	−9.37331	−	12.5905i	−0.627684	−	0.843125i	−0.996254	+	0.0864745i	$0.972440\pi$
$224$	−4.73343	+	1.72283i	−0.316265	+	0.115111i
$225$	−4.48436	+	0.181608i	−0.298957	+	0.0121072i
$226$	−0.780887	−	0.284220i	−0.0519438	−	0.0189060i
$227$	3.74342	+	12.5039i	0.248459	+	0.829912i	0.987685	+	0.156455i	$0.0500065\pi$
$227$	3.74342	+	12.5039i	0.248459	+	0.829912i	−0.739226	+	0.673458i	$0.764808\pi$
$228$	10.3978	−	0.210459i	0.688610	−	0.0139380i
$229$	0.594069	+	10.1998i	0.0392572	+	0.674020i	0.959333	+	0.282278i	$0.0910902\pi$
$229$	0.594069	+	10.1998i	0.0392572	+	0.674020i	−0.920075	+	0.391741i	$0.871873\pi$
$230$	−6.99900	+	4.60331i	−0.461500	+	0.303533i
$231$	−8.85592	−	3.02178i	−0.582677	−	0.198819i
$232$	1.17131	+	0.277607i	0.0769006	+	0.0182258i
$233$	0.481261	+	2.72937i	0.0315284	+	0.178807i	0.996505	−	0.0835278i	$-0.0266187\pi$
$233$	0.481261	+	2.72937i	0.0315284	+	0.178807i	−0.964977	+	0.262334i	$0.915508\pi$
$234$	−0.753594	−	7.61398i	−0.0492640	−	0.497742i
$235$	3.90332	−	22.1368i	0.254625	−	1.44405i
$236$	−1.11582	+	2.58675i	−0.0726334	+	0.168383i
$237$	−7.26226	−	7.39196i	−0.471734	−	0.480160i
$238$	8.44208	−	28.1985i	0.547219	−	1.82784i
$239$	6.77718	−	9.10334i	0.438380	−	0.588846i	−0.526945	−	0.849900i	$-0.676663\pi$
$239$	6.77718	−	9.10334i	0.438380	−	0.588846i	0.965324	+	0.261054i	$0.0840699\pi$
$240$	−0.992543	−	3.08656i	−0.0640684	−	0.199236i
$241$	−18.1734	+	9.12700i	−1.17065	+	0.587922i	−0.924452	−	0.381298i	$-0.875477\pi$
$241$	−18.1734	+	9.12700i	−1.17065	+	0.587922i	−0.246196	+	0.969220i	$0.579181\pi$
$242$	−9.84974			−0.633165
$243$	−15.5867	−	0.236394i	−0.999885	−	0.0151647i
$244$	−4.38878			−0.280963
$245$	30.7348	−	15.4356i	1.96358	−	0.986145i
$246$	3.43106	+	10.6697i	0.218757	+	0.680277i
$247$	9.14463	−	12.2834i	0.581859	−	0.781572i
$248$	1.93193	−	6.45308i	0.122677	−	0.409771i
$249$	10.8833	+	11.0777i	0.689704	+	0.702022i
$250$	−4.81627	+	11.1654i	−0.304608	+	0.706160i
$251$	2.70424	−	15.3365i	0.170690	−	0.968031i	−0.772312	−	0.635244i	$-0.780900\pi$
$251$	2.70424	−	15.3365i	0.170690	−	0.968031i	0.943002	−	0.332788i	$-0.107989\pi$
$252$	13.7676	+	6.23008i	0.867278	+	0.392458i
$253$	0.833457	+	4.72677i	0.0523990	+	0.297170i
$254$	13.6713	+	3.24016i	0.857815	+	0.203306i
$255$	17.9309	+	6.11831i	1.12288	+	0.383143i
$256$	−0.835488	+	0.549509i	−0.0522180	+	0.0343443i
$257$	1.48001	+	25.4107i	0.0923203	+	1.58508i	0.653203	+	0.757183i	$0.273425\pi$
$257$	1.48001	+	25.4107i	0.0923203	+	1.58508i	−0.560883	+	0.827895i	$0.689538\pi$
$258$	2.81921	−	0.0570629i	0.175516	−	0.00355258i
$259$	−2.62174	−	8.75723i	−0.162907	−	0.544148i
$260$	−4.48616	−	1.63283i	−0.278220	−	0.101264i
$261$	−1.93072	−	3.05184i	−0.119508	−	0.188904i
$262$	−14.1909	+	5.16507i	−0.876717	+	0.319099i
$263$	−13.5174	−	18.1571i	−0.833520	−	1.11961i	−0.991233	−	0.132127i	$-0.957819\pi$
$263$	−13.5174	−	18.1571i	−0.833520	−	1.11961i	0.157713	−	0.987485i	$-0.449588\pi$
$264$	−1.84906	−	0.178276i	−0.113802	−	0.0109721i
$265$	−9.13079	+	2.16404i	−0.560900	+	0.132936i
$266$	11.9796	+	27.7718i	0.734514	+	1.70280i
$267$	12.3132	−	1.69244i	0.753557	−	0.103576i
$268$	−9.14869	−	6.01719i	−0.558845	−	0.367558i
$269$	12.0247	−	20.8273i	0.733157	−	1.26987i	−0.222370	−	0.974962i	$-0.571379\pi$
$269$	12.0247	−	20.8273i	0.733157	−	1.26987i	0.955527	−	0.294903i	$-0.0952874\pi$
$270$	−4.34325	+	8.70309i	−0.264322	+	0.529653i
$271$	−5.59596	−	9.69249i	−0.339930	−	0.588777i	0.644489	−	0.764614i	$-0.277070\pi$
$271$	−5.59596	−	9.69249i	−0.339930	−	0.588777i	−0.984419	+	0.175837i	$0.943737\pi$
$272$	0.339772	−	5.83365i	0.0206017	−	0.353717i
$273$	19.6784	−	10.3868i	1.19099	−	0.628636i
$274$	−10.8540	−	1.26866i	−0.655716	−	0.0766423i
$275$	1.10106	+	1.16706i	0.0663964	+	0.0703761i
$276$	−0.607201	−	7.72749i	−0.0365492	−	0.465140i
$277$	17.0390	−	1.99157i	1.02377	−	0.119662i	0.412399	−	0.911003i	$-0.364691\pi$
$277$	17.0390	−	1.99157i	1.02377	−	0.119662i	0.611375	+	0.791341i	$0.290617\pi$
$278$	6.35833	+	5.33528i	0.381348	+	0.319989i
$279$	−17.6769	+	9.79274i	−1.05829	+	0.586276i
$280$	7.22312	−	6.06092i	0.431664	−	0.362209i
$281$	7.44382	−	7.88999i	0.444061	−	0.470677i	−0.466220	−	0.884669i	$-0.654384\pi$
$281$	7.44382	−	7.88999i	0.444061	−	0.470677i	0.910281	+	0.413992i	$0.135866\pi$
$282$	16.2003	+	13.0442i	0.964713	+	0.776771i
$283$	−14.3469	−	7.20529i	−0.852836	−	0.428310i	−0.0320092	−	0.999488i	$-0.510191\pi$
$283$	−14.3469	−	7.20529i	−0.852836	−	0.428310i	−0.820827	+	0.571177i	$0.806487\pi$
$284$	−7.81397	−	3.92432i	−0.463674	−	0.232866i
$285$	−18.1550	+	7.02712i	−1.07541	+	0.416251i
$286$	−1.87708	+	1.98959i	−0.110994	+	0.117647i
$287$	−24.9692	+	20.9516i	−1.47389	+	1.23674i
$288$	2.94474	+	0.573158i	0.173520	+	0.0337737i
$289$	13.1353	+	11.0218i	0.772666	+	0.648343i
$290$	−2.23808	+	0.261594i	−0.131425	+	0.0153613i
$291$	−10.4896	+	7.20741i	−0.614913	+	0.422506i
$292$	4.86077	+	5.15212i	0.284455	+	0.301505i
$293$	15.1195	+	1.76722i	0.883292	+	0.103242i	0.545631	−	0.838026i	$-0.316290\pi$
$293$	15.1195	+	1.76722i	0.883292	+	0.103242i	0.337661	+	0.941268i	$0.390364\pi$
$294$	−1.20709	+	31.8008i	−0.0703990	+	1.85466i
$295$	0.306621	−	5.26448i	0.0178522	−	0.306510i
$296$	−0.907374	−	1.57162i	−0.0527400	−	0.0913484i
$297$	3.59300	+	4.25998i	0.208487	+	0.247189i
$298$	6.51267	−	11.2803i	0.377269	−	0.653449i
$299$	−9.53591	−	6.27187i	−0.551476	−	0.362711i
$300$	−1.58908	−	2.04670i	−0.0917457	−	0.118166i
$301$	3.24809	+	7.52991i	0.187217	+	0.434017i
$302$	−0.857201	+	0.203160i	−0.0493263	+	0.0116906i
$303$	9.14837	−	12.8222i	0.525560	−	0.736615i
$304$	3.58557	+	4.81626i	0.205647	+	0.276231i
$305$	7.71989	−	2.80981i	0.442040	−	0.160889i
$306$	−12.9623	+	11.8026i	−0.741003	+	0.674712i
$307$	32.4411	+	11.8076i	1.85151	+	0.673895i	0.984443	+	0.175703i	$0.0562197\pi$
$307$	32.4411	+	11.8076i	1.85151	+	0.673895i	0.867067	+	0.498192i	$0.166002\pi$
$308$	−1.54943	−	5.17546i	−0.0882871	−	0.294899i
$309$	−12.7131	−	21.0254i	−0.723225	−	1.19609i
$310$	0.733160	+	12.5879i	0.0416407	+	0.714943i
$311$	11.1339	−	7.32288i	0.631345	−	0.415242i	−0.193104	−	0.981178i	$-0.561855\pi$
$311$	11.1339	−	7.32288i	0.631345	−	0.415242i	0.824449	+	0.565936i	$0.191485\pi$
$312$	3.32578	−	2.90736i	0.188285	−	0.164597i
$313$	−2.13146	−	0.505166i	−0.120477	−	0.0285537i	0.169935	−	0.985455i	$-0.445644\pi$
$313$	−2.13146	−	0.505166i	−0.120477	−	0.0285537i	−0.290412	+	0.956902i	$0.593792\pi$
$314$	−0.598565	−	3.39463i	−0.0337790	−	0.191570i
$315$	−28.2060	−	2.14436i	−1.58923	−	0.120821i
$316$	1.03890	−	5.89190i	0.0584428	−	0.331445i
$317$	−0.244657	+	0.567178i	−0.0137413	+	0.0318559i	−0.924949	−	0.380092i	$-0.875892\pi$
$317$	−0.244657	+	0.567178i	−0.0137413	+	0.0318559i	0.911207	+	0.411948i	$0.135152\pi$
$318$	2.32139	−	8.36663i	0.130177	−	0.469177i
$319$	−0.370274	+	1.23680i	−0.0207314	+	0.0692476i
$320$	1.11782	−	1.50149i	0.0624879	−	0.0839358i
$321$	−18.8608	−	4.06881i	−1.05271	−	0.227099i
$322$	20.1448	−	10.1171i	1.12263	−	0.563804i
$323$	−35.0869			−1.95229
$324$	−5.11553	−	7.40482i	−0.284196	−	0.411379i
$325$	−3.81542			−0.211642
$326$	−8.35687	+	4.19698i	−0.462844	+	0.232449i
$327$	7.66731	−	8.46365i	0.424003	−	0.468041i
$328$	−3.86412	+	5.19041i	−0.213360	+	0.286593i
$329$	−17.3483	+	57.9473i	−0.956442	+	3.19474i
$330$	3.36664	−	0.870225i	0.185327	−	0.0479043i
$331$	2.89932	−	6.72139i	0.159361	−	0.369441i	−0.819763	−	0.572703i	$-0.805895\pi$
$331$	2.89932	−	6.72139i	0.159361	−	0.369441i	0.979124	+	0.203262i	$0.0651542\pi$
$332$	−1.55692	+	8.82971i	−0.0854468	+	0.484593i
$333$	−1.34910	+	5.27444i	−0.0739303	+	0.289037i
$334$	1.99112	+	11.2922i	0.108949	+	0.617882i
$335$	19.9449	+	4.72704i	1.08971	+	0.258266i
$336$	1.68859	+	8.55973i	0.0921203	+	0.466972i
$337$	−4.06934	+	2.67645i	−0.221671	+	0.145795i	−0.655488	−	0.755206i	$-0.727537\pi$
$337$	−4.06934	+	2.67645i	−0.221671	+	0.145795i	0.433817	+	0.901001i	$0.357167\pi$
$338$	0.377679	+	6.48449i	0.0205430	+	0.352710i
$339$	−0.694297	+	1.26081i	−0.0377090	+	0.0684779i
$340$	3.13719	+	10.4790i	0.170138	+	0.568301i
$341$	6.78877	+	2.47091i	0.367633	+	0.133807i
$342$	2.40756	−	17.8515i	0.130186	−	0.965301i
$343$	−53.8354	+	19.5945i	−2.90684	+	1.05800i
$344$	0.972176	+	1.30586i	0.0524162	+	0.0704072i
$345$	6.01541	+	13.2039i	0.323859	+	0.710877i
$346$	−5.93149	+	1.40579i	−0.318879	+	0.0755757i
$347$	7.33642	+	17.0077i	0.393840	+	0.913023i	0.993612	+	0.112852i	$0.0359986\pi$
$347$	7.33642	+	17.0077i	0.393840	+	0.913023i	−0.599772	+	0.800171i	$0.704742\pi$
$348$	0.786906	−	1.93078i	0.0421826	−	0.103501i
$349$	−16.5633	−	10.8939i	−0.886614	−	0.583135i	0.0224706	−	0.999748i	$-0.492847\pi$
$349$	−16.5633	−	10.8939i	−0.886614	−	0.583135i	−0.909084	+	0.416613i	$0.863217\pi$
$350$	3.76786	−	6.52613i	0.201401	−	0.348836i
$351$	−13.2317	−	0.736991i	−0.706258	−	0.0393377i
$352$	−0.536252	−	0.928815i	−0.0285823	−	0.0495060i
$353$	1.72791	−	29.6671i	0.0919676	−	1.57902i	−0.564992	−	0.825096i	$-0.691121\pi$
$353$	1.72791	−	29.6671i	0.0919676	−	1.57902i	0.656960	−	0.753926i	$-0.271842\pi$
$354$	4.13014	+	2.59825i	0.219514	+	0.138095i
$355$	16.2573	+	1.90020i	0.862846	+	0.100852i
$356$	4.92439	+	5.21954i	0.260992	+	0.276635i
$357$	−46.0139	−	21.9545i	−2.43531	−	1.16196i
$358$	−11.1826	+	1.30705i	−0.591017	+	0.0690799i
$359$	−11.3334	−	9.50989i	−0.598156	−	0.501913i	0.292696	−	0.956205i	$-0.405448\pi$
$359$	−11.3334	−	9.50989i	−0.598156	−	0.501913i	−0.890852	+	0.454293i	$0.849892\pi$
$360$	−5.54676	+	0.877109i	−0.292340	+	0.0462277i
$361$	13.0631	−	10.9613i	0.687532	−	0.576908i
$362$	−8.43220	+	8.93762i	−0.443187	+	0.469751i
$363$	−2.62188	+	16.8576i	−0.137613	+	0.884793i
$364$	11.4804	+	5.76566i	0.601735	+	0.302203i
$365$	−11.8486	−	5.95061i	−0.620186	−	0.311469i
$366$	−1.16824	+	7.51129i	−0.0610648	+	0.392621i
$367$	−4.57859	+	4.85302i	−0.239001	+	0.253326i	−0.835761	−	0.549094i	$-0.814973\pi$
$367$	−4.57859	+	4.85302i	−0.239001	+	0.253326i	0.596760	+	0.802420i	$0.296454\pi$
$368$	3.42822	−	2.87662i	0.178708	−	0.149954i
$369$	19.1743	−	3.03203i	0.998173	−	0.157841i
$370$	2.60226	+	2.18356i	0.135285	+	0.113518i
$371$	25.0806	−	2.93150i	1.30212	−	0.152196i
$372$	−10.5300	−	5.02417i	−0.545957	−	0.260491i
$373$	25.1298	+	26.6360i	1.30117	+	1.37916i	0.881996	+	0.471257i	$0.156200\pi$
$373$	25.1298	+	26.6360i	1.30117	+	1.37916i	0.419177	+	0.907905i	$0.362319\pi$
$374$	6.22484	+	0.727579i	0.321879	+	0.0376222i
$375$	17.8272	+	11.2150i	0.920593	+	0.579140i
$376$	−0.698223	+	11.9880i	−0.0360081	+	0.618235i
$377$	−1.53503	−	2.65876i	−0.0790583	−	0.136933i
$378$	14.3274	−	21.9045i	0.736921	−	1.12665i
$379$	−12.2441	+	21.2074i	−0.628937	+	1.08935i	0.358828	+	0.933404i	$0.383176\pi$
$379$	−12.2441	+	21.2074i	−0.628937	+	1.08935i	−0.987765	+	0.155948i	$0.950157\pi$
$380$	−9.39053	−	6.17625i	−0.481724	−	0.316835i
$381$	9.18459	−	22.5356i	0.470541	−	1.15454i
$382$	3.25443	+	7.54461i	0.166511	+	0.386016i
$383$	8.10990	−	1.92208i	0.414396	−	0.0982138i	−0.0181286	−	0.999836i	$-0.505771\pi$
$383$	8.10990	−	1.92208i	0.414396	−	0.0982138i	0.432525	+	0.901622i	$0.357623\pi$
$384$	0.718074	+	1.57619i	0.0366441	+	0.0804345i
$385$	6.03892	+	8.11168i	0.307772	+	0.413410i
$386$	12.9934	−	4.72921i	0.661346	−	0.240710i
$387$	0.652776	−	4.84019i	0.0331825	−	0.246041i
$388$	−6.90486	−	2.51316i	−0.350541	−	0.127587i
$389$	−1.19298	−	3.98483i	−0.0604865	−	0.202039i	0.922405	−	0.386224i	$-0.126221\pi$
$389$	−1.19298	−	3.98483i	−0.0604865	−	0.202039i	−0.982892	+	0.184185i	$0.941036\pi$
$390$	−3.98870	+	7.24331i	−0.201976	+	0.366779i
$391$	1.52055	+	26.1069i	0.0768976	+	1.32028i
$392$	−15.3508	+	10.0964i	−0.775332	+	0.509944i
$393$	5.06244	+	25.6623i	0.255366	+	1.29449i
$394$	2.78000	+	0.658871i	0.140054	+	0.0331935i
$395$	1.94471	+	11.0290i	0.0978492	+	0.554930i
$396$	−0.797310	+	3.11716i	−0.0400663	+	0.156643i
$397$	2.96473	−	16.8138i	0.148795	−	0.843861i	−0.815446	−	0.578834i	$-0.803508\pi$
$397$	2.96473	−	16.8138i	0.148795	−	0.843861i	0.964241	−	0.265027i	$-0.0853809\pi$
$398$	8.01800	−	18.5878i	0.401906	−	0.931723i
$399$	50.7195	−	13.1102i	2.53915	−	0.656332i
$400$	0.429061	−	1.43316i	0.0214531	−	0.0716582i
$401$	5.56884	−	7.48025i	0.278095	−	0.373546i	−0.641028	−	0.767518i	$-0.721492\pi$
$401$	5.56884	−	7.48025i	0.278095	−	0.373546i	0.919123	+	0.393972i	$0.128899\pi$
$402$	−12.7335	+	14.0560i	−0.635091	+	0.701052i
$403$	−15.3523	+	7.71021i	−0.764752	+	0.384073i
$404$	9.09397			0.452442
$405$	13.7390	+	9.75002i	0.682696	+	0.484482i
$406$	6.06360			0.300931
$407$	1.73930	−	0.873508i	0.0862138	−	0.0432982i
$408$	−9.89370	−	2.13436i	−0.489811	−	0.105666i
$409$	12.5707	−	16.8854i	0.621582	−	0.834929i	−0.374136	−	0.927374i	$-0.622061\pi$
$409$	12.5707	−	16.8854i	0.621582	−	0.834929i	0.995718	+	0.0924446i	$0.0294681\pi$
$410$	3.47397	−	11.6039i	0.171567	−	0.573074i
$411$	−5.06048	+	18.2387i	−0.249615	+	0.899649i
$412$	5.61861	−	13.0254i	0.276809	−	0.641716i
$413$	−2.46416	+	13.9750i	−0.121254	+	0.687663i
$414$	−13.3870	−	1.01775i	−0.657937	−	0.0500198i
$415$	−2.91438	−	16.5283i	−0.143061	−	0.811341i
$416$	2.48165	+	0.588162i	0.121673	+	0.0288370i
$417$	10.8237	−	9.46194i	0.530039	−	0.463353i
$418$	−5.38032	+	3.53869i	−0.263160	+	0.173083i
$419$	−2.33696	−	40.1241i	−0.114168	−	1.96019i	−0.246909	−	0.969039i	$-0.579415\pi$
$419$	−2.33696	−	40.1241i	−0.114168	−	1.96019i	0.132741	−	0.991151i	$-0.457622\pi$
$420$	−8.45040	−	13.9755i	−0.412337	−	0.681936i
$421$	−1.37580	−	4.59550i	−0.0670524	−	0.223971i	0.917895	−	0.396822i	$-0.129887\pi$
$421$	−1.37580	−	4.59550i	−0.0670524	−	0.223971i	−0.984948	+	0.172852i	$0.944702\pi$
$422$	4.02900	+	1.46644i	0.196129	+	0.0713850i
$423$	26.6371	−	24.2542i	1.29514	−	1.17928i
$424$	4.71064	−	1.71453i	0.228769	−	0.0832651i
$425$	5.22036	+	7.01216i	0.253225	+	0.340140i
$426$	−8.79636	+	12.3288i	−0.426185	+	0.597332i
$427$	−21.5113	+	5.09827i	−1.04100	+	0.246723i
$428$	−4.41224	−	10.2287i	−0.213274	−	0.494424i
$429$	2.90548	+	3.74218i	0.140278	+	0.180674i
$430$	−2.54611	−	1.67460i	−0.122784	−	0.0807564i
$431$	5.09865	−	8.83111i	0.245593	−	0.425380i	−0.716705	−	0.697376i	$-0.754351\pi$
$431$	5.09865	−	8.83111i	0.245593	−	0.425380i	0.962298	+	0.271997i	$0.0876840\pi$
$432$	1.76480	−	4.88728i	0.0849089	−	0.235139i
$433$	4.56740	+	7.91097i	0.219495	+	0.380177i	0.954654	−	0.297718i	$-0.0962256\pi$
$433$	4.56740	+	7.91097i	0.219495	+	0.380177i	−0.735158	+	0.677895i	$0.762892\pi$
$434$	1.97291	−	33.8736i	0.0947027	−	1.62598i
$435$	−0.148037	+	3.90005i	−0.00709785	+	0.186993i
$436$	6.54887	+	0.765453i	0.313634	+	0.0366586i
$437$	−18.4400	−	19.5452i	−0.882103	−	0.934975i
$438$	10.1116	−	6.94766i	0.483151	−	0.331972i
$439$	−6.06428	+	0.708813i	−0.289433	+	0.0338298i	−0.259570	−	0.965724i	$-0.583581\pi$
$439$	−6.06428	+	0.708813i	−0.289433	+	0.0338298i	−0.0298622	+	0.999554i	$0.509507\pi$
$440$	1.53792	+	1.29047i	0.0733175	+	0.0615207i
$441$	54.1050	+	10.5309i	2.57643	+	0.501471i
$442$	−11.4166	+	9.57968i	−0.543033	+	0.455659i
$443$	−14.5831	+	15.4572i	−0.692866	+	0.734395i	−0.974317	−	0.225181i	$-0.927703\pi$
$443$	−14.5831	+	15.4572i	−0.692866	+	0.734395i	0.281451	+	0.959576i	$0.409184\pi$
$444$	−2.93131	+	1.13460i	−0.139114	+	0.0538458i
$445$	−12.0037	−	6.02849i	−0.569030	−	0.285778i
$446$	−14.0269	−	7.04459i	−0.664194	−	0.333571i
$447$	−17.5723	−	14.1489i	−0.831142	−	0.669222i
$448$	−3.45674	+	3.66393i	−0.163316	+	0.173104i
$449$	8.46436	−	7.10244i	0.399458	−	0.335185i	−0.420826	−	0.907141i	$-0.638260\pi$
$449$	8.46436	−	7.10244i	0.399458	−	0.335185i	0.820284	+	0.571956i	$0.193815\pi$
$450$	−3.92587	+	2.17487i	−0.185067	+	0.102524i
$451$	−5.31635	−	4.46095i	−0.250337	−	0.210058i
$452$	−0.825384	+	0.0964735i	−0.0388228	+	0.00453773i
$453$	0.119527	+	1.52116i	0.00561589	+	0.0714701i
$454$	8.95698	+	9.49384i	0.420372	+	0.445568i
$455$	−23.8854	−	2.79180i	−1.11976	−	0.130882i
$456$	9.19734	−	4.85459i	0.430705	−	0.227337i
$457$	−0.353765	+	6.07391i	−0.0165484	+	0.284126i	0.979874	+	0.199616i	$0.0639694\pi$
$457$	−0.353765	+	6.07391i	−0.0165484	+	0.284126i	−0.996423	+	0.0845097i	$0.973068\pi$
$458$	5.10853	+	8.84823i	0.238706	+	0.413451i
$459$	16.7495	+	25.3263i	0.781801	+	1.18213i
$460$	−4.18857	+	7.25481i	−0.195293	+	0.338257i
$461$	14.5760	+	9.58681i	0.678874	+	0.446502i	0.841551	−	0.540177i	$-0.181643\pi$
$461$	14.5760	+	9.58681i	0.678874	+	0.446502i	−0.162678	+	0.986679i	$0.552013\pi$
$462$	−9.27011	+	1.27417i	−0.431285	+	0.0592797i
$463$	5.39732	+	12.5124i	0.250835	+	0.581500i	0.996385	−	0.0849490i	$-0.0270727\pi$
$463$	5.39732	+	12.5124i	0.250835	+	0.581500i	−0.745551	+	0.666449i	$0.767813\pi$
$464$	1.17131	−	0.277607i	0.0543769	−	0.0128876i
$465$	21.7390	+	2.09595i	1.00812	+	0.0971974i
$466$	1.65501	+	2.22306i	0.0766667	+	0.102981i
$467$	−38.3864	+	13.9715i	−1.77631	+	0.646523i	−0.776442	+	0.630189i	$0.782978\pi$
$467$	−38.3864	+	13.9715i	−1.77631	+	0.646523i	−0.999867	+	0.0163348i	$0.994800\pi$
$468$	−4.09059	−	6.46589i	−0.189087	−	0.298886i
$469$	−51.8316	−	18.8651i	−2.39336	−	0.871111i
$470$	−6.44686	−	21.5340i	−0.297371	−	0.993290i
$471$	−5.96915	+	0.120820i	−0.275044	+	0.00556710i
$472$	0.163803	+	2.81238i	0.00753962	+	0.129450i
$473$	−1.45879	+	0.959464i	−0.0670754	+	0.0441162i
$474$	−9.80730	−	3.34640i	−0.450464	−	0.153705i
$475$	−8.74051	−	2.07154i	−0.401042	−	0.0950487i
$476$	−5.11135	−	28.9879i	−0.234278	−	1.32866i
$477$	−13.7013	−	6.20009i	−0.627341	−	0.283883i
$478$	1.97074	−	11.1766i	0.0901397	−	0.511207i
$479$	−11.1002	+	25.7330i	−0.507179	+	1.17577i	0.451755	+	0.892142i	$0.350798\pi$
$479$	−11.1002	+	25.7330i	−0.507179	+	1.17577i	−0.958934	+	0.283631i	$0.908461\pi$
$480$	−2.27221	−	2.31279i	−0.103712	−	0.105564i
$481$	−1.32742	+	4.43389i	−0.0605251	+	0.202168i
$482$	−12.1441	+	16.3124i	−0.553149	+	0.743008i
$483$	−11.9529	−	37.1704i	−0.543874	−	1.69131i
$484$	−8.80205	+	4.42055i	−0.400093	+	0.200934i
$485$	13.7547			0.624568
$486$	−14.0348	+	6.78403i	−0.636634	+	0.307730i
$487$	2.97604			0.134857			0.0674287	−	0.997724i	$-0.478520\pi$
$487$	2.97604			0.134857			0.0674287	+	0.997724i	$0.478520\pi$
$488$	−3.92196	+	1.96968i	−0.177539	+	0.0891633i
$489$	4.95852	+	15.4197i	0.224232	+	0.697305i
$490$	20.5382	−	27.5875i	0.927820	−	1.24628i
$491$	9.76652	−	32.6224i	0.440757	−	1.47223i	−0.392711	−	0.919662i	$-0.628463\pi$
$491$	9.76652	−	32.6224i	0.440757	−	1.47223i	0.833468	−	0.552568i	$-0.186352\pi$
$492$	7.85468	+	7.99496i	0.354116	+	0.360441i
$493$	−2.78612	+	6.45894i	−0.125480	+	0.290896i
$494$	2.65917	−	15.0809i	0.119642	−	0.678523i
$495$	−0.593212	−	5.99356i	−0.0266629	−	0.269390i
$496$	−1.16971	−	6.63373i	−0.0525214	−	0.297863i
$497$	−42.8583	−	10.1576i	−1.92246	−	0.455631i
$498$	14.6974	+	5.01498i	0.658606	+	0.224727i
$499$	12.3610	−	8.12994i	0.553353	−	0.363946i	−0.241827	−	0.970319i	$-0.577747\pi$
$499$	12.3610	−	8.12994i	0.553353	−	0.363946i	0.795180	+	0.606373i	$0.207376\pi$
$500$	0.707032	+	12.1393i	0.0316194	+	0.542885i
$501$	19.8563	−	0.401907i	0.887115	−	0.0179559i
$502$	−4.46641	−	14.9189i	−0.199346	−	0.665861i
$503$	25.3285	+	9.21882i	1.12934	+	0.411047i	0.838053	−	0.545588i	$-0.183694\pi$
$503$	25.3285	+	9.21882i	1.12934	+	0.411047i	0.291288	+	0.956635i	$0.405916\pi$
$504$	15.0992	−	0.611491i	0.672574	−	0.0272380i
$505$	−15.9963	+	5.82219i	−0.711828	+	0.259084i
$506$	2.86618	+	3.84994i	0.127417	+	0.171151i
$507$	11.1986	+	1.07970i	0.497346	+	0.0479513i
$508$	13.6713	−	3.24016i	0.606567	−	0.143759i
$509$	1.71839	+	3.98368i	0.0761663	+	0.176573i	0.952045	−	0.305958i	$-0.0989767\pi$
$509$	1.71839	+	3.98368i	0.0761663	+	0.176573i	−0.875879	+	0.482531i	$0.839717\pi$
$510$	18.7695	−	2.57986i	0.831129	−	0.114238i
$511$	29.8097	+	19.6062i	1.31871	+	0.867326i
$512$	−0.500000	+	0.866025i	−0.0220971	+	0.0382733i
$513$	−29.9116	−	8.87234i	−1.32063	−	0.391723i
$514$	12.7269	+	22.0436i	0.561360	+	0.972303i
$515$	−1.54397	+	26.5089i	−0.0680354	+	1.16812i
$516$	2.49372	−	1.31625i	0.109780	−	0.0579447i
$517$	−12.7919	−	1.49516i	−0.562587	−	0.0657570i
$518$	−6.27311	−	6.64911i	−0.275625	−	0.292145i
$519$	0.827083	+	10.5258i	0.0363049	+	0.462031i
$520$	−4.74179	+	0.554236i	−0.207941	+	0.0243048i
$521$	−8.49590	−	7.12891i	−0.372212	−	0.312323i	0.437424	−	0.899256i	$-0.355891\pi$
$521$	−8.49590	−	7.12891i	−0.372212	−	0.312323i	−0.809636	+	0.586932i	$0.800335\pi$
$522$	−3.09501	−	1.86072i	−0.135465	−	0.0814414i
$523$	26.9661	−	22.6273i	1.17915	−	0.989421i	0.179162	−	0.983820i	$-0.442661\pi$
$523$	26.9661	−	22.6273i	1.17915	−	0.989421i	0.999984	−	0.00560136i	$-0.00178298\pi$
$524$	−10.3634	+	10.9845i	−0.452726	+	0.479862i
$525$	−10.1663	−	8.18577i	−0.443696	−	0.357256i
$526$	−20.2285	−	10.1591i	−0.882004	−	0.442959i
$527$	35.1756	+	17.6658i	1.53227	+	0.769536i
$528$	−1.73239	+	0.670542i	−0.0753925	+	0.0291816i
$529$	2.03979	−	2.16205i	0.0886865	−	0.0940022i
$530$	−7.18835	+	6.03175i	−0.312242	+	0.262002i
$531$	5.54623	−	6.37701i	0.240686	−	0.276739i
$532$	23.1693	+	19.4413i	1.00452	+	0.842889i
$533$	16.3916	−	1.91591i	0.710000	−	0.0829871i
$534$	10.2439	−	7.03858i	0.443298	−	0.304589i
$535$	14.3098	+	15.1675i	0.618668	+	0.655750i
$536$	−10.8761	−	1.27123i	−0.469775	−	0.0549088i
$537$	−0.739669	+	19.4866i	−0.0319191	+	0.840908i
$538$	1.39834	−	24.0087i	0.0602869	−	1.03509i
$539$	−9.85279	−	17.0655i	−0.424390	−	0.735065i
$540$	0.0246705	+	9.72662i	0.00106165	+	0.418567i
$541$	2.34850	−	4.06772i	0.100970	−	0.174885i	−0.811115	−	0.584887i	$-0.801139\pi$
$541$	2.34850	−	4.06772i	0.100970	−	0.174885i	0.912085	+	0.410002i	$0.134472\pi$
$542$	−9.35072	−	6.15006i	−0.401648	−	0.264168i
$543$	13.0520	+	16.8106i	0.560113	+	0.721411i
$544$	−2.31451	−	5.36563i	−0.0992337	−	0.230050i
$545$	−12.0096	+	2.84632i	−0.514433	+	0.121923i
$546$	12.9237	−	18.1136i	0.553084	−	0.775192i
$547$	−3.87036	−	5.19879i	−0.165485	−	0.222284i	0.711644	−	0.702541i	$-0.247951\pi$
$547$	−3.87036	−	5.19879i	−0.165485	−	0.222284i	−0.877128	+	0.480256i	$0.840544\pi$
$548$	−10.2689	+	3.73757i	−0.438665	+	0.159661i
$549$	12.5444	+	3.99882i	0.535382	+	0.170666i
$550$	1.50772	+	0.548764i	0.0642893	+	0.0233994i
$551$	−2.07297	−	6.92421i	−0.0883116	−	0.294981i
$552$	−4.01071	−	6.63303i	−0.170707	−	0.282320i
$553$	−1.75229	−	30.0856i	−0.0745148	−	1.27937i
$554$	14.3328	−	9.42682i	0.608942	−	0.400507i
$555$	4.42980	−	3.87247i	0.188034	−	0.164377i
$556$	8.07648	+	1.91416i	0.342519	+	0.0811785i
$557$	0.496060	+	2.81330i	0.0210187	+	0.119203i	0.993512	−	0.113728i	$-0.0362793\pi$
$557$	0.496060	+	2.81330i	0.0210187	+	0.119203i	−0.972493	+	0.232931i	$0.925168\pi$
$558$	−11.4017	+	16.6845i	−0.482673	+	0.706312i
$559$	0.720996	−	4.08897i	0.0304949	−	0.172945i
$560$	3.73468	−	8.65797i	0.157819	−	0.365866i
$561$	2.90221	−	10.4600i	0.122531	−	0.441621i
$562$	3.11102	−	10.3915i	0.131230	−	0.438340i
$563$	13.5371	−	18.1835i	0.570521	−	0.766343i	−0.419425	−	0.907790i	$-0.637768\pi$
$563$	13.5371	−	18.1835i	0.570521	−	0.766343i	0.989946	+	0.141447i	$0.0451756\pi$
$564$	20.3313	+	4.38605i	0.856103	+	0.184686i
$565$	1.39009	−	0.698129i	0.0584815	−	0.0293705i
$566$	−16.0546			−0.674826
$567$	−33.6753	−	30.3517i	−1.41423	−	1.27465i
$568$	−8.74405			−0.366892
$569$	−37.9767	+	19.0726i	−1.59206	+	0.799565i	−0.999980	−	0.00631157i	$-0.997991\pi$
$569$	−37.9767	+	19.0726i	−1.59206	+	0.799565i	−0.592084	+	0.805876i	$0.701695\pi$
$570$	−13.0701	+	14.4276i	−0.547448	+	0.604306i
$571$	−21.1902	+	28.4633i	−0.886780	+	1.19115i	0.0939089	+	0.995581i	$0.470064\pi$
$571$	−21.1902	+	28.4633i	−0.886780	+	1.19115i	−0.980689	+	0.195572i	$0.937344\pi$
$572$	−0.784495	+	2.62040i	−0.0328014	+	0.109564i
$573$	13.7787	−	3.56159i	0.575613	−	0.148787i
$574$	−12.9102	+	29.9292i	−0.538862	+	1.24922i
$575$	−1.16257	+	6.59327i	−0.0484826	+	0.274958i
$576$	2.88875	−	0.809404i	0.120365	−	0.0337252i
$577$	−1.40717	−	7.98046i	−0.0585813	−	0.332231i	0.941406	−	0.337276i	$-0.109505\pi$
$577$	−1.40717	−	7.98046i	−0.0585813	−	0.332231i	−0.999987	+	0.00504446i	$0.998394\pi$
$578$	16.6847	+	3.95436i	0.693994	+	0.164479i
$579$	−4.63524	−	23.4967i	−0.192634	−	0.976490i
$580$	−1.88262	+	1.23822i	−0.0781714	+	0.0514142i
$581$	2.62601	+	45.0868i	0.108945	+	1.87051i
$582$	−6.13920	+	11.1485i	−0.254478	+	0.462121i
$583$	1.54197	+	5.15055i	0.0638620	+	0.213314i
$584$	6.65601	+	2.42259i	0.275428	+	0.100248i
$585$	11.3350	+	8.75464i	0.468644	+	0.361960i
$586$	14.3044	−	5.20639i	0.590910	−	0.215074i
$587$	5.99154	+	8.04803i	0.247297	+	0.332178i	0.908388	−	0.418128i	$-0.137314\pi$
$587$	5.99154	+	8.04803i	0.247297	+	0.332178i	−0.661091	+	0.750306i	$0.729906\pi$
$588$	13.1935	+	28.9600i	0.544091	+	1.19429i
$589$	−39.3558	+	9.32748i	−1.62163	+	0.384332i
$590$	−2.08869	−	4.84212i	−0.0859899	−	0.199347i
$591$	1.86764	−	4.58251i	0.0768245	−	0.188499i
$592$	−1.51620	−	0.997220i	−0.0623154	−	0.0409855i
$593$	−12.9045	+	22.3512i	−0.529924	+	0.917855i	0.469467	+	0.882950i	$0.344446\pi$
$593$	−12.9045	+	22.3512i	−0.529924	+	0.917855i	−0.999391	+	0.0349048i	$0.988887\pi$
$594$	5.12270	+	2.19432i	0.210187	+	0.0900342i
$595$	27.5497	+	47.7175i	1.12943	+	1.95623i
$596$	0.757356	−	13.0033i	0.0310225	−	0.532636i
$597$	−29.6783	−	18.6704i	−1.21465	−	0.764130i
$598$	−11.3364	−	1.32504i	−0.463580	−	0.0541847i
$599$	9.22767	+	9.78076i	0.377032	+	0.399631i	0.887906	−	0.460025i	$-0.152159\pi$
$599$	9.22767	+	9.78076i	0.377032	+	0.399631i	−0.510874	+	0.859656i	$0.670678\pi$
$600$	−2.33861	−	1.11582i	−0.0954735	−	0.0455531i
$601$	−1.37064	+	0.160205i	−0.0559095	+	0.00653488i	−0.144002	−	0.989577i	$-0.545997\pi$
$601$	−1.37064	+	0.160205i	−0.0559095	+	0.00653488i	0.0880922	+	0.996112i	$0.471923\pi$
$602$	6.28201	+	5.27123i	0.256036	+	0.214839i
$603$	20.6671	+	25.5346i	0.841627	+	1.03985i
$604$	−0.674844	+	0.566262i	−0.0274590	+	0.0230409i
$605$	12.6527	−	13.4111i	0.514405	−	0.545238i
$606$	2.42070	−	15.5641i	0.0983343	−	0.632248i
$607$	−6.86975	−	3.45012i	−0.278834	−	0.140036i	0.303886	−	0.952708i	$-0.401716\pi$
$607$	−6.86975	−	3.45012i	−0.278834	−	0.140036i	−0.582721	+	0.812672i	$0.698012\pi$
$608$	5.36572	+	2.69476i	0.217609	+	0.109287i
$609$	1.61405	−	10.3777i	0.0654048	−	0.420525i
$610$	5.63771	−	5.97562i	0.228264	−	0.241946i
$611$	23.4609	−	19.6860i	0.949126	−	0.796411i
$612$	−6.28647	+	16.3647i	−0.254116	+	0.661503i
$613$	13.7738	+	11.5576i	0.556320	+	0.466808i	0.877074	−	0.480354i	$-0.159492\pi$
$613$	13.7738	+	11.5576i	0.556320	+	0.466808i	−0.320754	+	0.947162i	$0.603936\pi$
$614$	34.2896	−	4.00788i	1.38382	−	0.161745i
$615$	−18.9350	−	9.03442i	−0.763533	−	0.364303i
$616$	−3.70737	−	3.92958i	−0.149374	−	0.158327i
$617$	−4.50402	−	0.526445i	−0.181325	−	0.0211939i	0.0249457	−	0.999689i	$-0.492059\pi$
$617$	−4.50402	−	0.526445i	−0.181325	−	0.0211939i	−0.206271	+	0.978495i	$0.566133\pi$
$618$	−20.7970	−	13.0833i	−0.836580	−	0.526288i
$619$	1.45338	−	24.9535i	0.0584161	−	1.00297i	−0.834003	−	0.551759i	$-0.813957\pi$
$619$	1.45338	−	24.9535i	0.0584161	−	1.00297i	0.892419	−	0.451207i	$-0.149006\pi$
$620$	6.30460	+	10.9199i	0.253199	+	0.438554i
$621$	−5.30532	+	22.6406i	−0.212895	+	0.908538i
$622$	6.66311	−	11.5408i	0.267166	−	0.462746i
$623$	30.1999	+	19.8628i	1.20993	+	0.795785i
$624$	1.66721	−	4.09072i	0.0667417	−	0.163760i
$625$	−6.05285	−	14.0321i	−0.242114	−	0.561283i
$626$	−2.13146	+	0.505166i	−0.0851904	+	0.0201905i
$627$	4.62420	+	10.1502i	0.184673	+	0.405361i
$628$	−2.05840	−	2.76492i	−0.0821393	−	0.110332i
$629$	9.96501	−	3.62697i	0.397331	−	0.144617i
$630$	−26.1682	+	10.7425i	−1.04256	+	0.427993i
$631$	−43.9175	−	15.9847i	−1.74833	−	0.636340i	−0.748683	−	0.662928i	$-0.769314\pi$
$631$	−43.9175	−	15.9847i	−1.74833	−	0.636340i	−0.999646	+	0.0265877i	$0.991536\pi$
$632$	−1.71589	−	5.73146i	−0.0682542	−	0.227985i
$633$	3.58224	−	6.50519i	0.142381	−	0.258558i
$634$	0.0359158	+	0.616651i	0.00142640	+	0.0244903i
$635$	−21.9735	+	14.4522i	−0.871992	+	0.573518i
$636$	−1.68047	−	8.51853i	−0.0666348	−	0.337782i
$637$	45.5964	+	10.8066i	1.80660	+	0.428171i
$638$	0.224187	+	1.27143i	0.00887563	+	0.0503362i
$639$	18.7589	+	18.3365i	0.742092	+	0.725381i
$640$	0.325051	−	1.84346i	0.0128488	−	0.0728690i
$641$	−4.96994	+	11.5216i	−0.196301	+	0.455076i	−0.987727	−	0.156188i	$-0.950079\pi$
$641$	−4.96994	+	11.5216i	−0.196301	+	0.455076i	0.791427	+	0.611264i	$0.209339\pi$
$642$	−18.6807	+	4.82868i	−0.737267	+	0.190573i
$643$	5.98110	−	19.9783i	0.235872	−	0.787866i	−0.755311	−	0.655366i	$-0.772514\pi$
$643$	5.98110	−	19.9783i	0.235872	−	0.787866i	0.991183	−	0.132500i	$-0.0423004\pi$
$644$	13.4615	−	18.0819i	0.530458	−	0.712529i
$645$	−3.54378	+	3.91184i	−0.139536	+	0.154028i
$646$	−31.3548	+	15.7470i	−1.23364	+	0.619556i
$647$	47.1984			1.85556			0.927779	−	0.373129i	$-0.121715\pi$
$647$	47.1984			1.85556			0.927779	+	0.373129i	$0.121715\pi$
$648$	−7.89468	−	4.32134i	−0.310132	−	0.169758i
$649$	−3.02140			−0.118600
$650$	−3.40959	+	1.71236i	−0.133735	+	0.0671642i
$651$	−57.4486	−	12.3933i	−2.25159	−	0.485732i
$652$	−5.58437	+	7.50111i	−0.218701	+	0.293766i
$653$	11.9824	−	40.0239i	0.468906	−	1.56625i	−0.317322	−	0.948318i	$-0.602784\pi$
$653$	11.9824	−	40.0239i	0.468906	−	1.56625i	0.786228	−	0.617937i	$-0.212031\pi$
$654$	3.05328	−	11.0045i	0.119393	−	0.430309i
$655$	11.1967	−	25.9568i	0.437490	−	1.01421i
$656$	−1.12365	+	6.37254i	−0.0438712	+	0.248806i
$657$	−9.19916	−	19.1551i	−0.358893	−	0.747312i
$658$	10.5037	+	59.5695i	0.409477	+	2.32226i
$659$	−2.25604	−	0.534692i	−0.0878830	−	0.0208287i	0.186439	−	0.982467i	$-0.440305\pi$
$659$	−2.25604	−	0.534692i	−0.0878830	−	0.0208287i	−0.274322	+	0.961638i	$0.588453\pi$
$660$	2.61798	−	2.28861i	0.101905	−	0.0890839i
$661$	−0.641914	+	0.422194i	−0.0249676	+	0.0164214i	−0.561931	−	0.827184i	$-0.689942\pi$
$661$	−0.641914	+	0.422194i	−0.0249676	+	0.0164214i	0.536964	+	0.843605i	$0.319571\pi$
$662$	−0.425623	−	7.30767i	−0.0165423	−	0.284021i
$663$	13.3564	+	22.0892i	0.518720	+	0.857875i
$664$	2.57145	+	8.58926i	0.0997918	+	0.333328i
$665$	−53.2017	−	19.3638i	−2.06307	−	0.750897i
$666$	1.16156	+	5.31889i	0.0450096	+	0.206103i
$667$	−5.06222	+	1.84250i	−0.196010	+	0.0713418i
$668$	6.84726	+	9.19747i	0.264928	+	0.355861i
$669$	−15.7904	+	22.1315i	−0.610493	+	0.855655i
$670$	19.9449	−	4.72704i	0.770540	−	0.182621i
$671$	−1.86434	−	4.32203i	−0.0719721	−	0.166850i
$672$	5.35058	+	6.89142i	0.206403	+	0.265842i
$673$	4.16034	+	2.73630i	0.160369	+	0.105476i	0.627157	−	0.778893i	$-0.284218\pi$
$673$	4.16034	+	2.73630i	0.160369	+	0.105476i	−0.466788	+	0.884369i	$0.654589\pi$
$674$	−2.43531	+	4.21808i	−0.0938045	+	0.162474i
$675$	2.67722	+	7.29794i	0.103046	+	0.280898i
$676$	3.24774	+	5.62525i	0.124913	+	0.216356i
$677$	−1.76839	+	30.3621i	−0.0679648	+	1.16691i	0.776079	+	0.630636i	$0.217206\pi$
$677$	−1.76839	+	30.3621i	−0.0679648	+	1.16691i	−0.844044	+	0.536274i	$0.819831\pi$
$678$	−0.0545949	+	1.43830i	−0.00209670	+	0.0552377i
$679$	−36.7631	−	4.29699i	−1.41084	−	0.164903i
$680$	7.50644	+	7.95637i	0.287859	+	0.305113i
$681$	18.6327	−	12.8025i	0.714007	−	0.490593i
$682$	7.17561	−	0.838709i	0.274768	−	0.0321158i
$683$	−16.3627	−	13.7299i	−0.626101	−	0.525361i	0.273614	−	0.961840i	$-0.411781\pi$
$683$	−16.3627	−	13.7299i	−0.626101	−	0.525361i	−0.899715	+	0.436479i	$0.856225\pi$
$684$	−5.86028	−	17.0332i	−0.224074	−	0.651282i
$685$	15.6701	−	13.1488i	0.598726	−	0.502390i
$686$	−39.3151	+	41.6715i	−1.50106	+	1.59103i
$687$	16.5033	−	6.38783i	0.629642	−	0.243711i
$688$	1.45484	+	0.730646i	0.0554651	+	0.0278556i
$689$	−11.4251	−	5.73791i	−0.435262	−	0.218597i
$690$	11.3015	+	9.09977i	0.430240	+	0.346422i
$691$	10.2908	−	10.9076i	0.391481	−	0.414946i	−0.501416	−	0.865206i	$-0.667187\pi$
$691$	10.2908	−	10.9076i	0.391481	−	0.414946i	0.892897	+	0.450261i	$0.148669\pi$
$692$	−4.66966	+	3.91831i	−0.177514	+	0.148952i
$693$	−0.286880	+	16.2047i	−0.0108977	+	0.615567i
$694$	14.1891	+	11.9061i	0.538612	+	0.451949i
$695$	−15.4321	+	1.80375i	−0.585372	+	0.0684201i
$696$	−0.163327	−	2.07857i	−0.00619091	−	0.0787880i
$697$	−25.9486	−	27.5039i	−0.982873	−	1.04178i
$698$	−19.6907	−	2.30151i	−0.745303	−	0.0871134i
$699$	4.24525	−	2.24075i	0.160570	−	0.0847530i
$700$	0.438163	−	7.52297i	0.0165610	−	0.284342i
$701$	5.88669	+	10.1961i	0.222337	+	0.385100i	0.955517	−	0.294935i	$-0.0952980\pi$
$701$	5.88669	+	10.1961i	0.222337	+	0.385100i	−0.733180	+	0.680035i	$0.761965\pi$
$702$	−12.1551	+	5.27979i	−0.458764	+	0.199273i
$703$	−5.44822	+	9.43660i	−0.205484	+	0.355908i
$704$	−0.896064	−	0.589350i	−0.0337717	−	0.0222120i
$705$	−38.5710	+	5.30155i	−1.45267	+	0.199668i
$706$	−11.7705	−	27.2870i	−0.442987	−	1.02696i
$707$	44.5735	−	10.5641i	1.67636	−	0.397304i
$708$	4.85692	+	0.468277i	0.182534	+	0.0175989i
$709$	26.4532	+	35.5328i	0.993472	+	1.33446i	0.941936	+	0.335793i	$0.109004\pi$
$709$	26.4532	+	35.5328i	0.993472	+	1.33446i	0.0515358	+	0.998671i	$0.483588\pi$
$710$	15.3808	−	5.59816i	0.577232	−	0.210095i
$711$	−8.33786	+	15.8942i	−0.312694	+	0.596078i
$712$	6.74312	+	2.45429i	0.252709	+	0.0919786i
$713$	8.64580	+	28.8790i	0.323788	+	1.08153i
$714$	−50.9727	+	1.03173i	−1.90760	+	0.0386114i
$715$	−0.297714	−	5.11155i	−0.0111339	−	0.191161i
$716$	−9.40650	+	6.18675i	−0.351537	+	0.231210i
$717$	−18.6039	−	6.34796i	−0.694777	−	0.237069i
$718$	−14.3960	−	3.41191i	−0.537253	−	0.127331i
$719$	8.01362	+	45.4475i	0.298858	+	1.69491i	0.651095	+	0.758996i	$0.274310\pi$
$719$	8.01362	+	45.4475i	0.298858	+	1.69491i	−0.352237	+	0.935911i	$0.614579\pi$
$720$	−4.56312	+	3.27320i	−0.170058	+	0.121985i
$721$	12.4081	−	70.3700i	0.462103	−	2.62071i
$722$	6.75422	−	15.6580i	0.251366	−	0.582732i
$723$	24.6856	+	25.1265i	0.918067	+	0.934464i
$724$	−3.52410	+	11.7713i	−0.130972	+	0.437477i
$725$	−1.07539	+	1.44450i	−0.0399389	+	0.0536473i
$726$	5.22267	+	16.2412i	0.193831	+	0.602766i
$727$	21.1662	−	10.6301i	0.785011	−	0.394247i	−0.0106855	−	0.999943i	$-0.503401\pi$
$727$	21.1662	−	10.6301i	0.785011	−	0.394247i	0.795696	+	0.605696i	$0.207105\pi$
$728$	12.8469			0.476137
$729$	7.87480	+	25.8261i	0.291659	+	0.956522i
$730$	−13.2590			−0.490736
$731$	−8.50139	+	4.26956i	−0.314435	+	0.157915i
$732$	2.32708	+	7.23664i	0.0860115	+	0.267474i
$733$	−1.43809	+	1.93169i	−0.0531170	+	0.0713484i	−0.827888	−	0.560893i	$-0.810458\pi$
$733$	−1.43809	+	1.93169i	−0.0531170	+	0.0713484i	0.774771	+	0.632242i	$0.217865\pi$
$734$	−1.91355	+	6.39169i	−0.0706303	+	0.235922i
$735$	−41.7484	−	42.4940i	−1.53991	−	1.56741i
$736$	1.77254	−	4.10922i	0.0653368	−	0.151468i
$737$	2.03933	−	11.5656i	0.0751197	−	0.426025i
$738$	15.7740	−	11.3149i	0.580649	−	0.416508i
$739$	4.07653	+	23.1191i	0.149957	+	0.850451i	0.963252	+	0.268599i	$0.0865606\pi$
$739$	4.07653	+	23.1191i	0.149957	+	0.850451i	−0.813295	+	0.581852i	$0.802328\pi$
$740$	3.30545	+	0.783406i	0.121511	+	0.0287986i
$741$	−25.1028	−	8.56546i	−0.922173	−	0.314660i
$742$	21.0972	−	13.8758i	0.774501	−	0.509397i
$743$	0.475483	+	8.16373i	0.0174438	+	0.299498i	0.995735	+	0.0922622i	$0.0294098\pi$
$743$	0.475483	+	8.16373i	0.0174438	+	0.299498i	−0.978291	+	0.207236i	$0.933553\pi$
$744$	−11.6648	+	0.236105i	−0.427653	+	0.00865603i
$745$	6.99285	+	23.3578i	0.256198	+	0.855762i
$746$	34.4111	+	12.5246i	1.25988	+	0.458558i
$747$	12.4953	−	23.8193i	0.457178	−	0.871502i
$748$	5.88926	−	2.14351i	0.215333	−	0.0783746i
$749$	−33.5086	−	45.0098i	−1.22438	−	1.64462i
$750$	20.9643	+	2.02126i	0.765507	+	0.0738058i
$751$	47.6064	−	11.2829i	1.73718	−	0.411720i	0.764643	−	0.644454i	$-0.222915\pi$
$751$	47.6064	−	11.2829i	1.73718	−	0.411720i	0.972540	+	0.232734i	$0.0747672\pi$
$752$	4.75626	+	11.0262i	0.173443	+	0.402086i
$753$	−26.7221	+	3.67294i	−0.973809	+	0.133849i
$754$	−2.56501	−	1.68703i	−0.0934120	−	0.0614380i
$755$	0.824519	−	1.42811i	0.0300073	−	0.0519742i
$756$	2.97268	−	26.0047i	0.108115	−	0.945783i
$757$	6.74727	+	11.6866i	0.245234	+	0.424757i	0.962197	−	0.272353i	$-0.0878019\pi$
$757$	6.74727	+	11.6866i	0.245234	+	0.424757i	−0.716963	+	0.697111i	$0.754469\pi$
$758$	−1.42386	+	24.4468i	−0.0517170	+	0.887947i
$759$	7.35202	−	3.88058i	0.266861	−	0.140856i
$760$	−11.1636	−	1.30484i	−0.404946	−	0.0473314i
$761$	−16.9998	−	18.0187i	−0.616243	−	0.653179i	0.341811	−	0.939769i	$-0.388960\pi$
$761$	−16.9998	−	18.0187i	−0.616243	−	0.653179i	−0.958053	+	0.286590i	$0.907478\pi$
$762$	−1.90632	−	24.2606i	−0.0690587	−	0.878869i
$763$	32.9880	−	3.85575i	1.19425	−	0.139587i
$764$	6.29428	+	5.28153i	0.227719	+	0.191079i
$765$	0.580857	−	32.8103i	0.0210009	−	1.18626i
$766$	6.38464	−	5.35735i	0.230686	−	0.193569i
$767$	4.93054	−	5.22606i	0.178031	−	0.188702i

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)

\(f(q)\)	\(=\)	\(q+(0.893633 - 0.448799i) q^{2} +(-0.530234 - 1.64889i) q^{3} +(0.597159 - 0.802123i) q^{4} +(-0.536865 + 1.79325i) q^{5} +(-1.21386 - 1.23554i) q^{6} +(1.99514 - 4.62524i) q^{7} +(0.173648 - 0.984808i) q^{8} +(-2.43770 + 1.74860i) q^{9} +O(q^{10})\)	\(q+(0.893633 - 0.448799i) q^{2} +(-0.530234 - 1.64889i) q^{3} +(0.597159 - 0.802123i) q^{4} +(-0.536865 + 1.79325i) q^{5} +(-1.21386 - 1.23554i) q^{6} +(1.99514 - 4.62524i) q^{7} +(0.173648 - 0.984808i) q^{8} +(-2.43770 + 1.74860i) q^{9} +(0.325051 + 1.84346i) q^{10} +(1.04359 + 0.247336i) q^{11} +(-1.63925 - 0.559338i) q^{12} +(-2.13082 + 1.40147i) q^{13} +(-0.292887 - 5.02868i) q^{14} +(3.24155 - 0.0656115i) q^{15} +(-0.286803 - 0.957990i) q^{16} +(5.49113 + 1.99861i) q^{17} +(-1.39364 + 2.65665i) q^{18} +(-5.64228 + 2.05362i) q^{19} +(1.11782 + 1.50149i) q^{20} +(-8.68443 - 0.837303i) q^{21} +(1.04359 - 0.247336i) q^{22} +(1.77254 + 4.10922i) q^{23} +(-1.71592 + 0.235852i) q^{24} +(1.24990 + 0.822072i) q^{25} +(-1.27520 + 2.20871i) q^{26} +(4.17581 + 3.09235i) q^{27} +(-2.51860 - 4.36235i) q^{28} +(-0.0699925 + 1.20173i) q^{29} +(2.86731 - 1.51344i) q^{30} +(6.69052 + 0.782010i) q^{31} +(-0.686242 - 0.727374i) q^{32} +(-0.145518 - 1.85192i) q^{33} +(5.80403 - 0.678393i) q^{34} +(7.22312 + 6.06092i) q^{35} +(-0.0531021 + 2.99953i) q^{36} +(1.39018 - 1.16650i) q^{37} +(-4.12046 + 4.36743i) q^{38} +(3.44070 + 2.77040i) q^{39} +(1.67279 + 0.840105i) q^{40} +(-5.78256 - 2.90411i) q^{41} +(-8.13647 + 3.14932i) q^{42} +(-1.11720 + 1.18417i) q^{43} +(0.821586 - 0.689392i) q^{44} +(-1.82697 - 5.31019i) q^{45} +(3.42822 + 2.87662i) q^{46} +(-11.9271 + 1.39408i) q^{47} +(-1.42755 + 0.980867i) q^{48} +(-12.6086 - 13.3644i) q^{49} +(1.48590 + 0.173676i) q^{50} +(0.383906 - 10.1140i) q^{51} +(-0.148292 + 2.54608i) q^{52} +(2.50648 + 4.34135i) q^{53} +(5.11948 + 0.889320i) q^{54} +(-1.00381 + 1.73864i) q^{55} +(-4.20852 - 2.76799i) q^{56} +(6.37794 + 8.21462i) q^{57} +(0.476786 + 1.10531i) q^{58} +(-2.74121 + 0.649679i) q^{59} +(1.88309 - 2.63930i) q^{60} +(-2.62080 - 3.52034i) q^{61} +(6.32983 - 2.30387i) q^{62} +(3.22416 + 14.7637i) q^{63} +(-0.939693 - 0.342020i) q^{64} +(-1.36922 - 4.57351i) q^{65} +(-0.961181 - 1.58963i) q^{66} +(-0.636693 - 10.9316i) q^{67} +(4.88220 - 3.21108i) q^{68} +(5.83580 - 5.10159i) q^{69} +(9.17495 + 2.17450i) q^{70} +(-1.51839 - 8.61121i) q^{71} +(1.29873 + 2.70431i) q^{72} +(-1.22998 + 6.97557i) q^{73} +(0.718785 - 1.66633i) q^{74} +(0.692770 - 2.49684i) q^{75} +(-1.72208 + 5.75214i) q^{76} +(3.22610 - 4.33341i) q^{77} +(4.31808 + 0.931533i) q^{78} +(5.34642 - 2.68507i) q^{79} +1.87189 q^{80} +(2.88479 - 8.52514i) q^{81} -6.47084 q^{82} +(-8.01224 + 4.02390i) q^{83} +(-5.85760 + 6.46598i) q^{84} +(-6.53201 + 8.77401i) q^{85} +(-0.466916 + 1.55961i) q^{86} +(2.01863 - 0.521786i) q^{87} +(0.424797 - 0.984790i) q^{88} +(-1.24608 + 7.06686i) q^{89} +(-4.01585 - 3.92541i) q^{90} +(2.23084 + 12.6517i) q^{91} +(4.35459 + 1.03206i) q^{92} +(-2.25809 - 11.4466i) q^{93} +(-10.0328 + 6.59869i) q^{94} +(-0.653523 - 11.2206i) q^{95} +(-0.835493 + 1.51722i) q^{96} +(-2.10743 - 7.03931i) q^{97} +(-17.2654 - 6.28409i) q^{98} +(-2.97647 + 1.22190i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 90 q - 9 q^{6}+O(q^{10}) \) 90 * q - 9 * q^6	\( 90 q - 9 q^{6} - 18 q^{13} - 9 q^{18} - 9 q^{20} - 54 q^{21} + 27 q^{23} - 18 q^{25} - 27 q^{26} - 27 q^{27} - 18 q^{28} - 27 q^{29} + 9 q^{30} + 54 q^{31} - 63 q^{33} - 27 q^{35} - 9 q^{36} - 18 q^{38} - 9 q^{41} - 9 q^{42} - 36 q^{43} + 63 q^{45} + 18 q^{46} - 27 q^{47} - 9 q^{48} - 36 q^{51} + 36 q^{52} - 27 q^{53} - 54 q^{55} - 81 q^{57} - 9 q^{58} - 45 q^{59} - 63 q^{63} + 9 q^{65} + 36 q^{66} + 81 q^{67} + 36 q^{68} + 18 q^{69} - 72 q^{70} + 72 q^{71} + 18 q^{72} - 36 q^{73} + 45 q^{74} + 216 q^{75} - 18 q^{76} + 144 q^{77} + 54 q^{78} - 99 q^{79} + 18 q^{80} + 144 q^{81} + 72 q^{82} + 45 q^{83} + 18 q^{84} - 117 q^{85} + 72 q^{86} + 81 q^{87} - 18 q^{88} + 45 q^{89} + 162 q^{90} - 63 q^{91} + 36 q^{92} + 45 q^{93} - 72 q^{94} + 45 q^{95} + 18 q^{96} + 117 q^{97} + 36 q^{98} - 81 q^{99}+O(q^{100}) \) 90 * q - 9 * q^6 - 18 * q^13 - 9 * q^18 - 9 * q^20 - 54 * q^21 + 27 * q^23 - 18 * q^25 - 27 * q^26 - 27 * q^27 - 18 * q^28 - 27 * q^29 + 9 * q^30 + 54 * q^31 - 63 * q^33 - 27 * q^35 - 9 * q^36 - 18 * q^38 - 9 * q^41 - 9 * q^42 - 36 * q^43 + 63 * q^45 + 18 * q^46 - 27 * q^47 - 9 * q^48 - 36 * q^51 + 36 * q^52 - 27 * q^53 - 54 * q^55 - 81 * q^57 - 9 * q^58 - 45 * q^59 - 63 * q^63 + 9 * q^65 + 36 * q^66 + 81 * q^67 + 36 * q^68 + 18 * q^69 - 72 * q^70 + 72 * q^71 + 18 * q^72 - 36 * q^73 + 45 * q^74 + 216 * q^75 - 18 * q^76 + 144 * q^77 + 54 * q^78 - 99 * q^79 + 18 * q^80 + 144 * q^81 + 72 * q^82 + 45 * q^83 + 18 * q^84 - 117 * q^85 + 72 * q^86 + 81 * q^87 - 18 * q^88 + 45 * q^89 + 162 * q^90 - 63 * q^91 + 36 * q^92 + 45 * q^93 - 72 * q^94 + 45 * q^95 + 18 * q^96 + 117 * q^97 + 36 * q^98 - 81 * q^99

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