LMFDB - Embedded newform 225.2.q.a.211.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [225,2,Mod(16,225)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(225, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([20, 6]))

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

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

chi := DirichletCharacter("225.16");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 225 = 3^{2} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	225.q (of order $15$, degree $8$, 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:	$1.79663404548$
Analytic rank:	$0$
Dimension:	$224$
Relative dimension:	$28$ over $\Q(\zeta_{15})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			211.6
Character	$\chi$	$=$	225.211
Dual form			225.2.q.a.16.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.76509 - 0.785867i) q^{2} +(-1.27173 + 1.17589i) q^{3} +(1.15968 + 1.28795i) q^{4} +(-0.197349 - 2.22734i) q^{5} +(3.16880 - 1.07614i) q^{6} +(1.35187 + 2.34151i) q^{7} +(0.159347 + 0.490420i) q^{8} +(0.234573 - 2.99082i) q^{9} +O(q^{10})$	\(q+(-1.76509 - 0.785867i) q^{2} +(-1.27173 + 1.17589i) q^{3} +(1.15968 + 1.28795i) q^{4} +(-0.197349 - 2.22734i) q^{5} +(3.16880 - 1.07614i) q^{6} +(1.35187 + 2.34151i) q^{7} +(0.159347 + 0.490420i) q^{8} +(0.234573 - 2.99082i) q^{9} +(-1.40206 + 4.08654i) q^{10} +(-0.748543 - 0.333273i) q^{11} +(-2.98929 - 0.274272i) q^{12} +(-2.49560 + 1.11111i) q^{13} +(-0.546054 - 5.19535i) q^{14} +(2.87008 + 2.60051i) q^{15} +(0.466463 - 4.43810i) q^{16} +(-2.45676 - 7.56113i) q^{17} +(-2.76442 + 5.09470i) q^{18} +(-2.21677 - 6.82252i) q^{19} +(2.63985 - 2.83718i) q^{20} +(-4.47256 - 1.38811i) q^{21} +(1.05934 + 1.17651i) q^{22} +(-0.215497 - 2.05032i) q^{23} +(-0.779325 - 0.436305i) q^{24} +(-4.92211 + 0.879126i) q^{25} +5.27814 q^{26} +(3.21855 + 4.07933i) q^{27} +(-1.44802 + 4.45655i) q^{28} +(-5.45784 + 1.16010i) q^{29} +(-3.02228 - 6.84562i) q^{30} +(6.92035 + 1.47097i) q^{31} +(-3.79544 + 6.57390i) q^{32} +(1.34383 - 0.456372i) q^{33} +(-1.60565 + 15.2767i) q^{34} +(4.94855 - 3.47317i) q^{35} +(4.12406 - 3.16627i) q^{36} +(-1.38079 - 1.00320i) q^{37} +(-1.44880 + 13.7844i) q^{38} +(1.86718 - 4.34758i) q^{39} +(1.06089 - 0.451704i) q^{40} +(1.64566 - 0.732693i) q^{41} +(6.80359 + 5.96497i) q^{42} +(-4.43594 - 7.68327i) q^{43} +(-0.438830 - 1.35058i) q^{44} +(-6.70786 + 0.0677586i) q^{45} +(-1.23091 + 3.78834i) q^{46} +(-3.05932 + 0.650279i) q^{47} +(4.62549 + 6.19255i) q^{48} +(-0.155110 + 0.268659i) q^{49} +(9.37882 + 2.31639i) q^{50} +(12.0154 + 6.72681i) q^{51} +(-4.32516 - 1.92569i) q^{52} +(0.613099 - 1.88692i) q^{53} +(-2.47521 - 9.72972i) q^{54} +(-0.594589 + 1.73303i) q^{55} +(-0.932906 + 1.03610i) q^{56} +(10.8416 + 6.06970i) q^{57} +(10.5452 + 2.24146i) q^{58} +(3.67181 - 1.63480i) q^{59} +(-0.0209650 + 6.71229i) q^{60} +(2.29219 + 1.02055i) q^{61} +(-11.0590 - 8.03486i) q^{62} +(7.32013 - 3.49394i) q^{63} +(4.64494 - 3.37475i) q^{64} +(2.96733 + 5.33928i) q^{65} +(-2.73063 - 0.250539i) q^{66} +(-5.67625 - 1.20652i) q^{67} +(6.88934 - 11.9327i) q^{68} +(2.68500 + 2.35404i) q^{69} +(-11.4641 + 2.24155i) q^{70} +(-3.34762 + 10.3029i) q^{71} +(1.50413 - 0.361538i) q^{72} +(12.1616 - 8.83593i) q^{73} +(1.64883 + 2.85586i) q^{74} +(5.22582 - 6.90586i) q^{75} +(6.21635 - 10.7670i) q^{76} +(-0.231572 - 2.20326i) q^{77} +(-6.71234 + 6.20650i) q^{78} +(6.97559 - 1.48271i) q^{79} +(-9.97722 - 0.163120i) q^{80} +(-8.88995 - 1.40313i) q^{81} -3.48052 q^{82} +(1.78998 - 1.98798i) q^{83} +(-3.39892 - 7.37022i) q^{84} +(-16.3564 + 6.96422i) q^{85} +(1.79178 + 17.0477i) q^{86} +(5.57673 - 7.89315i) q^{87} +(0.0441655 - 0.420207i) q^{88} +(-8.19461 + 5.95373i) q^{89} +(11.8932 + 5.15189i) q^{90} +(-5.97541 - 4.34139i) q^{91} +(2.39081 - 2.65526i) q^{92} +(-10.5305 + 6.26690i) q^{93} +(5.91100 + 1.25642i) q^{94} +(-14.7586 + 6.28392i) q^{95} +(-2.90341 - 12.8232i) q^{96} +(-5.78117 + 1.22883i) q^{97} +(0.484914 - 0.352310i) q^{98} +(-1.17235 + 2.16058i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 224 q - 3 q^{2} - 8 q^{3} + 23 q^{4} - 8 q^{5} - 10 q^{6} - 8 q^{7} - 20 q^{8} - 8 q^{9}+O(q^{10}) $ 224 * q - 3 * q^2 - 8 * q^3 + 23 * q^4 - 8 * q^5 - 10 * q^6 - 8 * q^7 - 20 * q^8 - 8 * q^9	\( 224 q - 3 q^{2} - 8 q^{3} + 23 q^{4} - 8 q^{5} - 10 q^{6} - 8 q^{7} - 20 q^{8} - 8 q^{9} - 20 q^{10} - 11 q^{11} - 4 q^{12} - 3 q^{13} + q^{14} - 48 q^{15} + 23 q^{16} - 24 q^{17} - 12 q^{19} + q^{20} + 15 q^{21} - 11 q^{22} + q^{23} - 30 q^{24} - 16 q^{25} - 136 q^{26} + 7 q^{27} + 4 q^{28} - 15 q^{29} - 24 q^{30} + 3 q^{31} + 12 q^{32} - 5 q^{33} + q^{34} + 14 q^{35} + 38 q^{36} - 24 q^{37} + 55 q^{38} + 20 q^{39} + q^{40} - 19 q^{41} - 38 q^{42} - 8 q^{43} + 4 q^{44} - 38 q^{45} - 20 q^{46} - 10 q^{47} - 25 q^{48} - 72 q^{49} - 3 q^{50} - 26 q^{51} - 25 q^{52} - 12 q^{53} + 53 q^{54} - 20 q^{55} - 60 q^{56} + 38 q^{57} - 23 q^{58} - 30 q^{59} - 33 q^{60} - 3 q^{61} - 44 q^{62} + 46 q^{63} - 44 q^{64} + 51 q^{65} - 134 q^{66} - 12 q^{67} - 156 q^{68} + 4 q^{69} - 16 q^{70} + 42 q^{71} + 74 q^{72} - 12 q^{73} + 90 q^{74} + 67 q^{75} - 8 q^{76} + 31 q^{77} - 92 q^{78} - 15 q^{79} + 298 q^{80} - 104 q^{81} + 8 q^{82} + 59 q^{83} + 115 q^{84} - 11 q^{85} + 9 q^{86} - 59 q^{87} - 23 q^{88} + 106 q^{89} + 107 q^{90} + 30 q^{91} + 11 q^{92} + 32 q^{93} + 25 q^{94} + 7 q^{95} + 35 q^{96} - 21 q^{97} + 146 q^{98} - 20 q^{99}+O(q^{100}) \) 224 * q - 3 * q^2 - 8 * q^3 + 23 * q^4 - 8 * q^5 - 10 * q^6 - 8 * q^7 - 20 * q^8 - 8 * q^9 - 20 * q^10 - 11 * q^11 - 4 * q^12 - 3 * q^13 + q^14 - 48 * q^15 + 23 * q^16 - 24 * q^17 - 12 * q^19 + q^20 + 15 * q^21 - 11 * q^22 + q^23 - 30 * q^24 - 16 * q^25 - 136 * q^26 + 7 * q^27 + 4 * q^28 - 15 * q^29 - 24 * q^30 + 3 * q^31 + 12 * q^32 - 5 * q^33 + q^34 + 14 * q^35 + 38 * q^36 - 24 * q^37 + 55 * q^38 + 20 * q^39 + q^40 - 19 * q^41 - 38 * q^42 - 8 * q^43 + 4 * q^44 - 38 * q^45 - 20 * q^46 - 10 * q^47 - 25 * q^48 - 72 * q^49 - 3 * q^50 - 26 * q^51 - 25 * q^52 - 12 * q^53 + 53 * q^54 - 20 * q^55 - 60 * q^56 + 38 * q^57 - 23 * q^58 - 30 * q^59 - 33 * q^60 - 3 * q^61 - 44 * q^62 + 46 * q^63 - 44 * q^64 + 51 * q^65 - 134 * q^66 - 12 * q^67 - 156 * q^68 + 4 * q^69 - 16 * q^70 + 42 * q^71 + 74 * q^72 - 12 * q^73 + 90 * q^74 + 67 * q^75 - 8 * q^76 + 31 * q^77 - 92 * q^78 - 15 * q^79 + 298 * q^80 - 104 * q^81 + 8 * q^82 + 59 * q^83 + 115 * q^84 - 11 * q^85 + 9 * q^86 - 59 * q^87 - 23 * q^88 + 106 * q^89 + 107 * q^90 + 30 * q^91 + 11 * q^92 + 32 * q^93 + 25 * q^94 + 7 * q^95 + 35 * q^96 - 21 * q^97 + 146 * q^98 - 20 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/225\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{4}{5}\right)$

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 $

$2$	−1.76509	−	0.785867i	−1.24810	−	0.555692i	−0.327006	−	0.945022i	$-0.606040\pi$
$2$	−1.76509	−	0.785867i	−1.24810	−	0.555692i	−0.921098	+	0.389331i	$0.872706\pi$
$3$	−1.27173	+	1.17589i	−0.734231	+	0.678899i
$3$	−1.27173	+	1.17589i	−0.734231	+	0.678899i
$4$	1.15968	+	1.28795i	0.579840	+	0.643977i
$5$	−0.197349	−	2.22734i	−0.0882570	−	0.996098i
$5$	−0.197349	−	2.22734i	−0.0882570	−	0.996098i
$6$	3.16880	−	1.07614i	1.29366	−	0.439331i
$7$	1.35187	+	2.34151i	0.510959	+	0.885007i	0.999919	+	0.0127012i	$0.00404302\pi$
$7$	1.35187	+	2.34151i	0.510959	+	0.885007i	−0.488960	+	0.872306i	$0.662624\pi$
$8$	0.159347	+	0.490420i	0.0563377	+	0.173390i
$9$	0.234573	−	2.99082i	0.0781911	−	0.996938i
$10$	−1.40206	+	4.08654i	−0.443369	+	1.29228i
$11$	−0.748543	−	0.333273i	−0.225694	−	0.100486i	0.290774	−	0.956792i	$-0.406087\pi$
$11$	−0.748543	−	0.333273i	−0.225694	−	0.100486i	−0.516469	+	0.856306i	$0.672754\pi$
$12$	−2.98929	−	0.274272i	−0.862932	−	0.0791754i
$13$	−2.49560	+	1.11111i	−0.692155	+	0.308167i	−0.722499	−	0.691372i	$-0.757007\pi$
$13$	−2.49560	+	1.11111i	−0.692155	+	0.308167i	0.0303436	+	0.999540i	$0.490340\pi$
$14$	−0.546054	−	5.19535i	−0.145939	−	1.38852i
$15$	2.87008	+	2.60051i	0.741051	+	0.671448i
$16$	0.466463	−	4.43810i	0.116616	−	1.10952i
$17$	−2.45676	−	7.56113i	−0.595852	−	1.83384i	−0.550440	−	0.834875i	$-0.685540\pi$
$17$	−2.45676	−	7.56113i	−0.595852	−	1.83384i	−0.0454115	−	0.998968i	$-0.514460\pi$
$18$	−2.76442	+	5.09470i	−0.651581	+	1.20083i
$19$	−2.21677	−	6.82252i	−0.508562	−	1.56519i	−0.794698	−	0.607005i	$-0.792371\pi$
$19$	−2.21677	−	6.82252i	−0.508562	−	1.56519i	0.286136	−	0.958189i	$-0.407629\pi$
$20$	2.63985	−	2.83718i	0.590289	−	0.634413i
$21$	−4.47256	−	1.38811i	−0.975993	−	0.302910i
$22$	1.05934	+	1.17651i	0.225851	+	0.250833i
$23$	−0.215497	−	2.05032i	−0.0449343	−	0.427521i	−0.993745	−	0.111675i	$-0.964378\pi$
$23$	−0.215497	−	2.05032i	−0.0449343	−	0.427521i	0.948811	−	0.315846i	$-0.102288\pi$
$24$	−0.779325	−	0.436305i	−0.159079	−	0.0890604i
$25$	−4.92211	+	0.879126i	−0.984421	+	0.175825i
$26$	5.27814			1.03513
$27$	3.21855	+	4.07933i	0.619411	+	0.785067i
$28$	−1.44802	+	4.45655i	−0.273650	+	0.842209i
$29$	−5.45784	+	1.16010i	−1.01350	+	0.215425i	−0.684583	−	0.728935i	$-0.740016\pi$
$29$	−5.45784	+	1.16010i	−1.01350	+	0.215425i	−0.328913	+	0.944360i	$0.606682\pi$
$30$	−3.02228	−	6.84562i	−0.551791	−	1.24983i
$31$	6.92035	+	1.47097i	1.24293	+	0.264193i	0.782021	−	0.623253i	$-0.214189\pi$
$31$	6.92035	+	1.47097i	1.24293	+	0.264193i	0.460912	+	0.887446i	$0.347523\pi$
$32$	−3.79544	+	6.57390i	−0.670946	+	1.16211i
$33$	1.34383	−	0.456372i	0.233931	−	0.0794441i
$34$	−1.60565	+	15.2767i	−0.275366	+	2.61994i
$35$	4.94855	−	3.47317i	0.836458	−	0.587073i
$36$	4.12406	−	3.16627i	0.687344	−	0.527711i
$37$	−1.38079	−	1.00320i	−0.227001	−	0.164926i	0.468472	−	0.883479i	$-0.344805\pi$
$37$	−1.38079	−	1.00320i	−0.227001	−	0.164926i	−0.695472	+	0.718553i	$0.744805\pi$
$38$	−1.44880	+	13.7844i	−0.235027	+	2.23613i
$39$	1.86718	−	4.34758i	0.298987	−	0.696170i
$40$	1.06089	−	0.451704i	0.167741	−	0.0714207i
$41$	1.64566	−	0.732693i	0.257008	−	0.114427i	−0.274188	−	0.961676i	$-0.588409\pi$
$41$	1.64566	−	0.732693i	0.257008	−	0.114427i	0.531197	+	0.847249i	$0.321743\pi$
$42$	6.80359	+	5.96497i	1.04982	+	0.920415i
$43$	−4.43594	−	7.68327i	−0.676474	−	1.17169i	−0.976036	−	0.217611i	$-0.930174\pi$
$43$	−4.43594	−	7.68327i	−0.676474	−	1.17169i	0.299562	−	0.954077i	$-0.403160\pi$
$44$	−0.438830	−	1.35058i	−0.0661561	−	0.203608i
$45$	−6.70786	+	0.0677586i	−0.999949	+	0.0101009i
$46$	−1.23091	+	3.78834i	−0.181487	+	0.558560i
$47$	−3.05932	+	0.650279i	−0.446248	+	0.0948529i	−0.425554	−	0.904933i	$-0.639921\pi$
$47$	−3.05932	+	0.650279i	−0.446248	+	0.0948529i	−0.0206937	+	0.999786i	$0.506587\pi$
$48$	4.62549	+	6.19255i	0.667633	+	0.893818i
$49$	−0.155110	+	0.268659i	−0.0221586	+	0.0383799i
$50$	9.37882	+	2.31639i	1.32636	+	0.327587i
$51$	12.0154	+	6.72681i	1.68249	+	0.941941i
$52$	−4.32516	−	1.92569i	−0.599792	−	0.267045i
$53$	0.613099	−	1.88692i	0.0842156	−	0.259189i	−0.900078	−	0.435729i	$-0.856491\pi$
$53$	0.613099	−	1.88692i	0.0842156	−	0.259189i	0.984293	+	0.176540i	$0.0564906\pi$
$54$	−2.47521	−	9.72972i	−0.336833	−	1.32405i
$55$	−0.594589	+	1.73303i	−0.0801744	+	0.233682i
$56$	−0.932906	+	1.03610i	−0.124665	+	0.138454i
$57$	10.8416	+	6.06970i	1.43601	+	0.803951i
$58$	10.5452	+	2.24146i	1.38466	+	0.294318i
$59$	3.67181	−	1.63480i	0.478029	−	0.212832i	−0.153554	−	0.988140i	$-0.549072\pi$
$59$	3.67181	−	1.63480i	0.478029	−	0.212832i	0.631584	+	0.775308i	$0.282405\pi$
$60$	−0.0209650	+	6.71229i	−0.00270657	+	0.866553i
$61$	2.29219	+	1.02055i	0.293485	+	0.130668i	0.548198	−	0.836349i	$-0.315314\pi$
$61$	2.29219	+	1.02055i	0.293485	+	0.130668i	−0.254712	+	0.967017i	$0.581981\pi$
$62$	−11.0590	−	8.03486i	−1.40450	−	1.02043i
$63$	7.32013	−	3.49394i	0.922250	−	0.440195i
$64$	4.64494	−	3.37475i	0.580618	−	0.421843i
$65$	2.96733	+	5.33928i	0.368052	+	0.662256i
$66$	−2.73063	−	0.250539i	−0.336117	−	0.0308393i
$67$	−5.67625	−	1.20652i	−0.693465	−	0.147400i	−0.152322	−	0.988331i	$-0.548675\pi$
$67$	−5.67625	−	1.20652i	−0.693465	−	0.147400i	−0.541143	+	0.840931i	$0.682008\pi$
$68$	6.88934	−	11.9327i	0.835455	−	1.44705i
$69$	2.68500	+	2.35404i	0.323236	+	0.283393i
$70$	−11.4641	+	2.24155i	−1.37022	+	0.267916i
$71$	−3.34762	+	10.3029i	−0.397290	+	1.22273i	0.529874	+	0.848076i	$0.322239\pi$
$71$	−3.34762	+	10.3029i	−0.397290	+	1.22273i	−0.927164	+	0.374656i	$0.877761\pi$
$72$	1.50413	−	0.361538i	0.177264	−	0.0426077i
$73$	12.1616	−	8.83593i	1.42341	−	1.03417i	0.432213	−	0.901771i	$-0.357733\pi$
$73$	12.1616	−	8.83593i	1.42341	−	1.03417i	0.991197	−	0.132396i	$-0.0422672\pi$
$74$	1.64883	+	2.85586i	0.191673	+	0.331987i
$75$	5.22582	−	6.90586i	0.603425	−	0.797420i
$76$	6.21635	−	10.7670i	0.713065	−	1.23506i
$77$	−0.231572	−	2.20326i	−0.0263901	−	0.251085i
$78$	−6.71234	+	6.20650i	−0.760023	+	0.702748i
$79$	6.97559	−	1.48271i	0.784815	−	0.166818i	0.201960	−	0.979394i	$-0.435269\pi$
$79$	6.97559	−	1.48271i	0.784815	−	0.166818i	0.582855	+	0.812576i	$0.301936\pi$
$80$	−9.97722	−	0.163120i	−1.11549	−	0.0182373i
$81$	−8.88995	−	1.40313i	−0.987772	−	0.155903i
$82$	−3.48052			−0.384359
$83$	1.78998	−	1.98798i	0.196476	−	0.218209i	−0.636854	−	0.770984i	$-0.719765\pi$
$83$	1.78998	−	1.98798i	0.196476	−	0.218209i	0.833330	+	0.552775i	$0.186431\pi$
$84$	−3.39892	−	7.37022i	−0.370852	−	0.804157i
$85$	−16.3564	+	6.96422i	−1.77410	+	0.755376i
$86$	1.79178	+	17.0477i	0.193213	+	1.83830i
$87$	5.57673	−	7.89315i	0.597889	−	0.846234i
$88$	0.0441655	−	0.420207i	0.00470806	−	0.0447942i
$89$	−8.19461	+	5.95373i	−0.868627	+	0.631094i	−0.930218	−	0.367007i	$-0.880382\pi$
$89$	−8.19461	+	5.95373i	−0.868627	+	0.631094i	0.0615912	+	0.998101i	$0.480382\pi$
$90$	11.8932	+	5.15189i	1.25365	+	0.543056i
$91$	−5.97541	−	4.34139i	−0.626393	−	0.455101i
$92$	2.39081	−	2.65526i	0.249259	−	0.276830i
$93$	−10.5305	+	6.26690i	−1.09196	+	0.649847i
$94$	5.91100	+	1.25642i	0.609673	+	0.129590i
$95$	−14.7586	+	6.28392i	−1.51420	+	0.644717i
$96$	−2.90341	−	12.8232i	−0.296328	−	1.30876i
$97$	−5.78117	+	1.22883i	−0.586989	+	0.124768i	−0.491826	−	0.870693i	$-0.663670\pi$
$97$	−5.78117	+	1.22883i	−0.586989	+	0.124768i	−0.0951626	+	0.995462i	$0.530337\pi$
$98$	0.484914	−	0.352310i	0.0489837	−	0.0355887i
$99$	−1.17235	+	2.16058i	−0.117825	+	0.217146i
$100$	−6.84034	−	5.31995i	−0.684034	−	0.531995i
$101$	4.27666	+	7.40739i	0.425544	+	0.737063i	0.996471	−	0.0839375i	$-0.0267496\pi$
$101$	4.27666	+	7.40739i	0.425544	+	0.737063i	−0.570927	+	0.821000i	$0.693416\pi$
$102$	−15.9218	−	21.3159i	−1.57649	−	2.11059i
$103$	0.723748	+	0.803804i	0.0713130	+	0.0792011i	0.777745	−	0.628579i	$-0.216363\pi$
$103$	0.723748	+	0.803804i	0.0713130	+	0.0792011i	−0.706432	+	0.707780i	$0.749697\pi$
$104$	−0.942578	−	1.04684i	−0.0924274	−	0.102651i
$105$	−2.20914	+	10.2359i	−0.215590	+	0.998919i
$106$	−2.56504	+	2.84877i	−0.249139	+	0.276697i
$107$	−11.2196			−1.08464			−0.542321	−	0.840171i	$-0.682455\pi$
$107$	−11.2196			−1.08464			−0.542321	+	0.840171i	$0.682455\pi$
$108$	−1.52150	+	8.87606i	−0.146407	+	0.854100i
$109$	−5.51708	−	4.00840i	−0.528441	−	0.383935i	0.291333	−	0.956622i	$-0.405901\pi$
$109$	−5.51708	−	4.00840i	−0.528441	−	0.383935i	−0.819774	+	0.572687i	$0.805901\pi$
$110$	2.41143	−	2.59168i	0.229921	−	0.247107i
$111$	2.93565	−	0.347857i	0.278639	−	0.0330171i
$112$	11.0224	−	4.90751i	1.04152	−	0.463716i
$113$	10.0257	−	4.46373i	0.943139	−	0.419912i	0.123212	−	0.992380i	$-0.460681\pi$
$113$	10.0257	−	4.46373i	0.943139	−	0.419912i	0.819927	+	0.572468i	$0.194014\pi$
$114$	−14.3665	−	19.2336i	−1.34554	−	1.80139i
$115$	−4.52423	+	0.884614i	−0.421887	+	0.0824907i
$116$	−7.82351	−	5.68411i	−0.726394	−	0.527756i
$117$	2.73773	+	7.72452i	0.253103	+	0.714132i
$118$	−7.76580			−0.714900
$119$	14.3832	−	15.9742i	1.31851	−	1.46435i
$120$	−0.818002	+	1.82193i	−0.0746730	+	0.166318i
$121$	−6.91119	−	7.67565i	−0.628290	−	0.697787i
$122$	−3.24390	−	3.60272i	−0.293689	−	0.326175i
$123$	−1.23126	+	2.86689i	−0.111019	+	0.258499i
$124$	6.13085	+	10.6190i	0.550567	+	0.953610i
$125$	2.92949	+	10.7897i	0.262021	+	0.965062i
$126$	−15.6664	+	0.414455i	−1.39568	+	0.0369226i
$127$	3.49392	−	2.53848i	0.310035	−	0.225254i	−0.421876	−	0.906653i	$-0.638628\pi$
$127$	3.49392	−	2.53848i	0.310035	−	0.225254i	0.731912	+	0.681400i	$0.238628\pi$
$128$	3.99919	−	0.850054i	0.353482	−	0.0751349i
$129$	14.6760	+	4.55484i	1.29215	+	0.401032i
$130$	−1.04163	−	11.7562i	−0.0913573	−	1.03109i
$131$	9.77474	+	2.07769i	0.854023	+	0.181528i	0.614065	−	0.789255i	$-0.289533\pi$
$131$	9.77474	+	2.07769i	0.854023	+	0.181528i	0.239958	+	0.970783i	$0.422866\pi$
$132$	2.14620	+	1.20155i	0.186803	+	0.104582i
$133$	12.9782	−	14.4138i	1.12535	−	1.24983i
$134$	9.07090	+	6.59040i	0.783607	+	0.569324i
$135$	8.45088	−	7.97387i	0.727336	−	0.686281i
$136$	3.31665	−	2.40969i	0.284400	−	0.206629i
$137$	−1.57702	+	15.0043i	−0.134734	+	1.28190i	0.693064	+	0.720876i	$0.256260\pi$
$137$	−1.57702	+	15.0043i	−0.134734	+	1.28190i	−0.827797	+	0.561027i	$0.810406\pi$
$138$	−2.88929	−	6.26514i	−0.245953	−	0.533324i
$139$	1.95191	+	18.5712i	0.165559	+	1.57519i	0.690045	+	0.723766i	$0.257591\pi$
$139$	1.95191	+	18.5712i	0.165559	+	1.57519i	−0.524486	+	0.851419i	$0.675743\pi$
$140$	10.2120	+	2.34574i	0.863074	+	0.198251i
$141$	3.12596	−	4.42440i	0.263253	−	0.372601i
$142$	14.0056	−	15.5548i	1.17532	−	1.30533i
$143$	2.23837			0.187182
$144$	−13.1641	−	2.43616i	−1.09701	−	0.203014i
$145$	3.66104	+	11.9275i	0.304033	+	0.990529i
$146$	−28.4102	+	6.03877i	−2.35124	+	0.499772i
$147$	−0.118655	−	0.524054i	−0.00978652	−	0.0432232i
$148$	−0.309195	−	2.94179i	−0.0254157	−	0.241814i
$149$	4.15919	−	7.20392i	0.340734	−	0.590168i	−0.643835	−	0.765164i	$-0.722658\pi$
$149$	4.15919	−	7.20392i	0.340734	−	0.590168i	0.984569	+	0.174996i	$0.0559912\pi$
$150$	−14.6511	+	8.08263i	−1.19626	+	0.659944i
$151$	−4.97506	−	8.61706i	−0.404865	−	0.701247i	0.589441	−	0.807812i	$-0.299348\pi$
$151$	−4.97506	−	8.61706i	−0.404865	−	0.701247i	−0.994306	+	0.106565i	$0.966015\pi$
$152$	2.99266	−	2.17430i	0.242737	−	0.176359i
$153$	−23.1902	+	5.57408i	−1.87482	+	0.450637i
$154$	−1.32273	+	4.07093i	−0.106588	+	0.328045i
$155$	1.91062	−	15.7043i	0.153465	−	1.26140i
$156$	7.76481	−	2.63696i	0.621682	−	0.211126i
$157$	−8.25724	+	14.3020i	−0.658999	+	1.14142i	0.321876	+	0.946782i	$0.395687\pi$
$157$	−8.25724	+	14.3020i	−0.658999	+	1.14142i	−0.980875	+	0.194638i	$0.937647\pi$
$158$	−13.4777	−	2.86478i	−1.07223	−	0.227909i
$159$	1.43912	+	3.12058i	0.114129	+	0.247478i
$160$	15.3913	+	7.15640i	1.21679	+	0.565763i
$161$	4.50952	−	3.27636i	0.355400	−	0.258213i
$162$	14.5889	+	9.46296i	1.14621	+	0.743481i
$163$	4.87852	+	3.54446i	0.382115	+	0.277623i	0.762217	−	0.647322i	$-0.224111\pi$
$163$	4.87852	+	3.54446i	0.382115	+	0.277623i	−0.380101	+	0.924945i	$0.624111\pi$
$164$	2.85211	+	1.26984i	0.222712	+	0.0991579i
$165$	−1.28170	−	2.90311i	−0.0997802	−	0.226007i
$166$	−4.72176	+	2.10226i	−0.366480	+	0.163167i
$167$	8.11680	+	1.72528i	0.628097	+	0.133506i	0.510953	−	0.859609i	$-0.329293\pi$
$167$	8.11680	+	1.72528i	0.628097	+	0.133506i	0.117144	+	0.993115i	$0.462626\pi$
$168$	−0.0319338	−	2.41462i	−0.00246375	−	0.186292i
$169$	−3.70525	+	4.11509i	−0.285019	+	0.316546i
$170$	34.3434	+	0.561487i	2.63402	+	0.0430641i
$171$	−20.9249	+	5.02957i	−1.60017	+	0.384621i
$172$	4.75144	−	14.6234i	0.362294	−	1.11503i
$173$	−5.37441	−	2.39284i	−0.408609	−	0.181924i	0.192131	−	0.981369i	$-0.438460\pi$
$173$	−5.37441	−	2.39284i	−0.408609	−	0.181924i	−0.600739	+	0.799445i	$0.705127\pi$
$174$	−16.0464	+	9.54951i	−1.21647	+	0.723946i
$175$	−8.71254	−	10.3367i	−0.658606	−	0.781381i
$176$	−1.82827	+	3.16665i	−0.137811	+	0.238695i
$177$	−2.74720	+	6.39666i	−0.206492	+	0.480802i
$178$	19.1430	−	4.06898i	1.43483	−	0.304983i
$179$	−2.86737	+	8.82487i	−0.214318	+	0.659602i	0.784884	+	0.619643i	$0.212723\pi$
$179$	−2.86737	+	8.82487i	−0.214318	+	0.659602i	−0.999201	+	0.0399587i	$0.987277\pi$
$180$	−7.86624	−	8.56084i	−0.586315	−	0.638088i
$181$	−1.70671	−	5.25272i	−0.126859	−	0.390432i	0.867376	−	0.497653i	$-0.165805\pi$
$181$	−1.70671	−	5.25272i	−0.126859	−	0.390432i	−0.994235	+	0.107221i	$0.965805\pi$
$182$	7.13536	+	12.3588i	0.528908	+	0.916096i
$183$	−4.11509	+	1.39750i	−0.304197	+	0.103306i
$184$	0.971178	−	0.432396i	0.0715962	−	0.0318767i
$185$	−1.96198	+	3.27348i	−0.144248	+	0.240671i
$186$	23.5122	−	2.78605i	1.72399	−	0.204283i
$187$	−0.680929	+	6.47860i	−0.0497944	+	0.473763i
$188$	−4.38536	−	3.18615i	−0.319835	−	0.232374i
$189$	−5.20072	+	13.0510i	−0.378297	+	0.949320i
$190$	30.9885	+	0.506638i	2.24814	+	0.0367554i
$191$	0.674771	−	6.42002i	0.0488247	−	0.464536i	−0.942606	−	0.333906i	$-0.891633\pi$
$191$	0.674771	−	6.42002i	0.0488247	−	0.464536i	0.991431	−	0.130630i	$-0.0417001\pi$
$192$	−1.93877	+	9.75369i	−0.139918	+	0.703912i
$193$	−1.85003	+	3.20434i	−0.133168	+	0.230653i	−0.924896	−	0.380220i	$-0.875848\pi$
$193$	−1.85003	+	3.20434i	−0.133168	+	0.230653i	0.791728	+	0.610873i	$0.209182\pi$
$194$	11.1700	+	2.37425i	0.801956	+	0.170461i
$195$	−10.0520	−	3.30085i	−0.719841	−	0.236379i
$196$	−0.525899	+	0.111783i	−0.0375642	+	0.00798453i
$197$	6.74729	−	20.7660i	0.480724	−	1.47952i	−0.357355	−	0.933969i	$-0.616321\pi$
$197$	6.74729	−	20.7660i	0.480724	−	1.47952i	0.838079	−	0.545549i	$-0.183679\pi$
$198$	3.76722	−	2.89230i	0.267725	−	0.205547i
$199$	16.3004			1.15550			0.577752	−	0.816212i	$-0.303930\pi$
$199$	16.3004			1.15550			0.577752	+	0.816212i	$0.303930\pi$
$200$	−1.21546	−	2.27381i	−0.0859463	−	0.160783i
$201$	8.63737	−	5.14027i	0.609233	−	0.362567i
$202$	−1.72745	−	16.4356i	−0.121543	−	1.15640i
$203$	−10.0947	−	11.2113i	−0.708508	−	0.786878i
$204$	5.27015	+	23.2762i	0.368984	+	1.62966i
$205$	−1.95673	−	3.52084i	−0.136664	−	0.245906i
$206$	−0.645795	−	1.98755i	−0.0449947	−	0.138479i
$207$	−6.18267	+	0.163562i	−0.429726	+	0.0113684i
$208$	3.76712	+	11.5940i	0.261203	+	0.803900i
$209$	−0.614412	+	5.84574i	−0.0424998	+	0.404359i
$210$	11.9433	−	16.3311i	0.824169	−	1.12695i
$211$	0.324720	+	3.08951i	0.0223547	+	0.212691i	0.999997	+	0.00241612i	$0.000769075\pi$
$211$	0.324720	+	3.08951i	0.0223547	+	0.212691i	−0.977642	+	0.210274i	$0.932564\pi$
$212$	3.14127	−	1.39858i	0.215743	−	0.0960551i
$213$	−7.85783	−	17.0389i	−0.538410	−	1.16749i
$214$	19.8036	+	8.81714i	1.35375	+	0.602727i
$215$	−16.2378	+	11.3966i	−1.10741	+	0.777244i
$216$	−1.48772	+	2.22847i	−0.101226	+	0.151628i
$217$	5.91114	+	18.1926i	0.401275	+	1.23500i
$218$	6.58806	+	11.4109i	0.446200	+	0.772841i
$219$	−5.07617	+	25.5376i	−0.343016	+	1.72567i
$220$	−2.92160	+	1.24396i	−0.196974	+	0.0838678i
$221$	14.5324	+	16.1398i	0.977552	+	1.08568i
$222$	−5.45504	−	1.69303i	−0.366118	−	0.113629i
$223$	14.8973	+	6.63273i	0.997600	+	0.444160i	0.839557	−	0.543272i	$-0.182815\pi$
$223$	14.8973	+	6.63273i	0.997600	+	0.444160i	0.158043	+	0.987432i	$0.449481\pi$
$224$	−20.5238			−1.37130
$225$	1.47471	+	14.9273i	0.0983140	+	0.995155i
$226$	−21.2041			−1.41048
$227$	−6.12578	−	2.72737i	−0.406583	−	0.181022i	0.193247	−	0.981150i	$-0.438098\pi$
$227$	−6.12578	−	2.72737i	−0.406583	−	0.181022i	−0.599829	+	0.800128i	$0.704765\pi$
$228$	4.75534	+	21.0025i	0.314930	+	1.39092i
$229$	−8.22313	−	9.13271i	−0.543400	−	0.603507i	0.407424	−	0.913239i	$-0.366427\pi$
$229$	−8.22313	−	9.13271i	−0.543400	−	0.603507i	−0.950824	+	0.309732i	$0.899761\pi$
$230$	8.68085	+	1.99403i	0.572398	+	0.131482i
$231$	2.88529	+	2.52964i	0.189838	+	0.166438i
$232$	−1.43863	−	2.49178i	−0.0944505	−	0.163593i
$233$	−7.56793	−	23.2917i	−0.495791	−	1.52589i	−0.815720	−	0.578447i	$-0.803659\pi$
$233$	−7.56793	−	23.2917i	−0.495791	−	1.52589i	0.319929	−	0.947442i	$-0.396341\pi$
$234$	1.23811	−	15.7859i	0.0809378	−	1.03196i
$235$	2.05215	+	6.68582i	0.133867	+	0.436135i
$236$	6.36367	+	2.83329i	0.414240	+	0.184431i
$237$	−7.12754	+	10.0881i	−0.462983	+	0.655293i
$238$	−37.9412	+	16.8925i	−2.45936	+	1.09498i
$239$	−2.76725	−	26.3287i	−0.178999	−	1.70306i	−0.603280	−	0.797529i	$-0.706140\pi$
$239$	−2.76725	−	26.3287i	−0.178999	−	1.70306i	0.424282	−	0.905530i	$-0.360527\pi$
$240$	12.8801	−	11.5247i	0.831407	−	0.743913i
$241$	−0.625085	+	5.94729i	−0.0402653	+	0.383098i	0.955768	+	0.294121i	$0.0950267\pi$
$241$	−0.625085	+	5.94729i	−0.0402653	+	0.383098i	−0.996034	+	0.0889779i	$0.971640\pi$
$242$	6.16680	+	18.9795i	0.396417	+	1.22005i
$243$	12.9555	−	8.66919i	0.831096	−	0.556129i
$244$	1.34379	+	4.13575i	0.0860272	+	0.264764i
$245$	0.629007	+	0.292465i	0.0401858	+	0.0186849i
$246$	4.42627	−	4.09270i	0.282209	−	0.260941i
$247$	13.1128	+	14.5632i	0.834345	+	0.926635i
$248$	0.381347	+	3.62827i	0.0242155	+	0.230396i
$249$	0.0612719	+	4.63298i	0.00388295	+	0.293603i
$250$	3.30849	−	21.3470i	0.209247	−	1.35010i
$251$	5.15329			0.325273			0.162636	−	0.986686i	$-0.448000\pi$
$251$	5.15329			0.325273			0.162636	+	0.986686i	$0.448000\pi$
$252$	12.9890	+	5.37615i	0.818233	+	0.338666i
$253$	−0.522007	+	1.60657i	−0.0328183	+	0.101004i
$254$	−8.16198	+	1.73488i	−0.512128	+	0.108856i
$255$	12.6117	−	28.0899i	0.789774	−	1.75906i
$256$	−18.9589	−	4.02985i	−1.18493	−	0.251865i
$257$	2.34536	−	4.06228i	0.146300	−	0.253398i	−0.783558	−	0.621319i	$-0.786597\pi$
$257$	2.34536	−	4.06228i	0.146300	−	0.253398i	0.929857	+	0.367921i	$0.119930\pi$
$258$	−22.3248	−	19.5730i	−1.38988	−	1.21856i
$259$	0.482359	−	4.58934i	0.0299723	−	0.285168i
$260$	−3.43560	+	10.0136i	−0.213067	+	0.621020i
$261$	2.18938	+	16.5955i	0.135519	+	1.02724i
$262$	−15.6205	−	11.3489i	−0.965036	−	0.701140i
$263$	−1.16975	+	11.1294i	−0.0721298	+	0.686269i	0.897387	+	0.441244i	$0.145463\pi$
$263$	−1.16975	+	11.1294i	−0.0721298	+	0.686269i	−0.969517	+	0.245025i	$0.921204\pi$
$264$	0.437950	+	0.586321i	0.0269539	+	0.0360856i
$265$	−4.32382	−	0.993198i	−0.265610	−	0.0610117i
$266$	−34.2349	+	15.2424i	−2.09908	+	0.934570i
$267$	3.42037	−	17.2075i	0.209323	−	1.05308i
$268$	−5.02868	−	8.70994i	−0.307176	−	0.532044i
$269$	1.35264	+	4.16300i	0.0824720	+	0.253823i	0.983787	−	0.179342i	$-0.0573969\pi$
$269$	1.35264	+	4.16300i	0.0824720	+	0.253823i	−0.901315	+	0.433165i	$0.857397\pi$
$270$	−21.1829	+	7.43329i	−1.28915	+	0.452376i
$271$	−2.71988	+	8.37092i	−0.165221	+	0.508497i	−0.999052	−	0.0435216i	$-0.986142\pi$
$271$	−2.71988	+	8.37092i	−0.165221	+	0.508497i	0.833832	+	0.552019i	$0.186142\pi$
$272$	−34.7030	+	7.37635i	−2.10418	+	0.447257i
$273$	12.7041	−	1.50536i	0.768886	−	0.0911084i
$274$	14.5749	−	25.2446i	0.880505	−	1.52508i
$275$	3.97740	+	0.982341i	0.239846	+	0.0592374i
$276$	0.0818385	+	6.18809i	0.00492610	+	0.372479i
$277$	−9.68902	−	4.31383i	−0.582157	−	0.259193i	0.0944594	−	0.995529i	$-0.469888\pi$
$277$	−9.68902	−	4.31383i	−0.582157	−	0.259193i	−0.676616	+	0.736336i	$0.736554\pi$
$278$	11.1492	−	34.3136i	0.668683	−	2.05799i
$279$	6.02272	−	20.3524i	0.360571	−	1.21847i
$280$	2.49185	+	1.87343i	0.148917	+	0.111959i
$281$	19.5667	−	21.7310i	1.16725	−	1.29636i	0.220135	−	0.975470i	$-0.429350\pi$
$281$	19.5667	−	21.7310i	1.16725	−	1.29636i	0.947115	−	0.320893i	$-0.103983\pi$
$282$	−8.99458	+	5.35285i	−0.535619	+	0.318757i
$283$	−5.64494	−	1.19987i	−0.335557	−	0.0713248i	0.0370520	−	0.999313i	$-0.488203\pi$
$283$	−5.64494	−	1.19987i	−0.335557	−	0.0713248i	−0.372609	+	0.927989i	$0.621537\pi$
$284$	−17.1519	+	7.63651i	−1.01778	+	0.453143i
$285$	11.3797	−	25.3459i	0.674076	−	1.50136i
$286$	−3.95091	−	1.75906i	−0.233622	−	0.104015i
$287$	3.94032	+	2.86281i	0.232590	+	0.168986i
$288$	18.7710	+	12.8935i	1.10609	+	0.759758i
$289$	−37.3817	+	27.1594i	−2.19892	+	1.59761i
$290$	2.91141	−	23.9302i	0.170964	−	1.40523i
$291$	5.90710	−	8.36074i	0.346280	−	0.490115i
$292$	25.4839	+	5.41676i	1.49133	+	0.316992i
$293$	−2.64859	+	4.58748i	−0.154732	+	0.268004i	−0.932961	−	0.359976i	$-0.882785\pi$
$293$	−2.64859	+	4.58748i	−0.154732	+	0.268004i	0.778229	+	0.627980i	$0.216118\pi$
$294$	−0.202400	+	1.01825i	−0.0118042	+	0.0593853i
$295$	−4.36588	−	7.85576i	−0.254191	−	0.457380i
$296$	0.271966	−	0.837026i	0.0158077	−	0.0486511i
$297$	−1.04970	−	4.12621i	−0.0609095	−	0.239427i
$298$	−13.0026	+	9.44697i	−0.753223	+	0.547248i
$299$	2.81593	+	4.87734i	0.162849	+	0.282064i
$300$	14.9547	−	1.27797i	0.863410	−	0.0737834i
$301$	11.9936	−	20.7736i	0.691301	−	1.19737i
$302$	2.00955	+	19.1196i	0.115637	+	1.10021i
$303$	−14.1490	−	4.39130i	−0.812839	−	0.252273i
$304$	−31.3131	+	6.65580i	−1.79593	+	0.381736i
$305$	1.82075	−	5.30690i	0.104256	−	0.303872i
$306$	45.3132	+	8.38571i	2.59038	+	0.479379i
$307$	1.36470			0.0778874			0.0389437	−	0.999241i	$-0.487601\pi$
$307$	1.36470			0.0778874			0.0389437	+	0.999241i	$0.487601\pi$
$308$	2.56915	−	2.85333i	0.146391	−	0.162584i
$309$	−1.86559	−	0.171171i	−0.106130	−	0.00973758i
$310$	−15.7139	+	26.2179i	−0.892489	+	1.48908i
$311$	1.02447	+	9.74719i	0.0580924	+	0.552712i	0.984400	+	0.175944i	$0.0562979\pi$
$311$	1.02447	+	9.74719i	0.0580924	+	0.552712i	−0.926308	+	0.376768i	$0.877035\pi$
$312$	2.42967	+	0.222926i	0.137553	+	0.0126207i
$313$	−2.64290	+	25.1455i	−0.149385	+	1.42131i	0.621041	+	0.783778i	$0.286710\pi$
$313$	−2.64290	+	25.1455i	−0.149385	+	1.42131i	−0.770427	+	0.637529i	$0.779957\pi$
$314$	25.8142	−	18.7551i	1.45678	−	1.05841i
$315$	−9.22682	−	15.6149i	−0.519872	−	0.879801i
$316$	9.99910	+	7.26477i	0.562494	+	0.408675i
$317$	10.9212	−	12.1292i	0.613393	−	0.681242i	−0.353789	−	0.935325i	$-0.615107\pi$
$317$	10.9212	−	12.1292i	0.613393	−	0.681242i	0.967182	+	0.254083i	$0.0817736\pi$
$318$	−0.0878025	−	6.63905i	−0.00492372	−	0.372300i
$319$	4.47206	+	0.950567i	0.250388	+	0.0532215i
$320$	−8.43339	−	9.67987i	−0.471441	−	0.541121i
$321$	14.2683	−	13.1930i	0.796379	−	0.736364i
$322$	−10.5345	+	2.23917i	−0.587063	+	0.124784i
$323$	−46.1399	+	33.5226i	−2.56729	+	1.86525i
$324$	−8.50233	−	13.0770i	−0.472351	−	0.726502i
$325$	11.3068	−	7.66297i	0.627189	−	0.425065i
$326$	−5.82554	−	10.0901i	−0.322647	−	0.558841i
$327$	11.7296	−	1.38989i	0.648651	−	0.0768613i
$328$	0.621557	+	0.690309i	0.0343198	+	0.0381160i
$329$	−5.65844	−	6.28433i	−0.311960	−	0.346467i
$330$	−0.0191509	+	6.13149i	−0.00105422	+	0.337527i
$331$	−1.81538	+	2.01618i	−0.0997823	+	0.110820i	−0.790967	−	0.611858i	$-0.790422\pi$
$331$	−1.81538	+	2.01618i	−0.0997823	+	0.110820i	0.691185	+	0.722678i	$0.257089\pi$
$332$	4.63623			0.254446
$333$	−3.32430	+	3.89437i	−0.182170	+	0.213410i
$334$	−12.9710	−	9.42398i	−0.709742	−	0.515657i
$335$	−1.56714	+	12.8811i	−0.0856221	+	0.703768i
$336$	−8.24685	+	19.2022i	−0.449902	+	1.04756i
$337$	31.5207	−	14.0339i	1.71704	−	0.764477i	0.719494	−	0.694499i	$-0.244374\pi$
$337$	31.5207	−	14.0339i	1.71704	−	0.764477i	0.997549	−	0.0699777i	$-0.0222928\pi$
$338$	9.77399	−	4.35166i	0.531635	−	0.236699i
$339$	−7.50110	+	17.4657i	−0.407404	+	0.948609i
$340$	−27.9378	−	12.9900i	−1.51514	−	0.704482i
$341$	−4.68995	−	3.40745i	−0.253975	−	0.184524i
$342$	40.8868	+	7.56655i	2.21091	+	0.409152i
$343$	18.0874			0.976630
$344$	3.06117	−	3.39978i	0.165047	−	0.183304i
$345$	4.71338	−	6.44498i	0.253760	−	0.346986i
$346$	7.60584	+	8.44714i	0.408892	+	0.454121i
$347$	15.2132	+	16.8960i	0.816688	+	0.907024i	0.997064	−	0.0765735i	$-0.0243980\pi$
$347$	15.2132	+	16.8960i	0.816688	+	0.907024i	−0.180376	+	0.983598i	$0.557731\pi$
$348$	16.6332	−	1.97094i	0.891635	−	0.105653i
$349$	−16.7926	−	29.0857i	−0.898890	−	1.55692i	−0.828915	−	0.559374i	$-0.811042\pi$
$349$	−16.7926	−	29.0857i	−0.898890	−	1.55692i	−0.0699744	−	0.997549i	$-0.522292\pi$
$350$	7.25511	+	25.0920i	0.387802	+	1.34123i
$351$	−12.5648	−	6.60420i	−0.670660	−	0.352506i
$352$	5.03196	−	3.65593i	0.268204	−	0.194862i
$353$	7.10339	−	1.50987i	0.378075	−	0.0803623i	−0.0149545	−	0.999888i	$-0.504760\pi$
$353$	7.10339	−	1.50987i	0.378075	−	0.0803623i	0.393030	+	0.919526i	$0.371427\pi$
$354$	9.87596	−	9.13171i	0.524902	−	0.485345i
$355$	23.6088	+	5.42303i	1.25302	+	0.287825i
$356$	−17.1713	−	3.64986i	−0.910075	−	0.193442i
$357$	0.492344	+	37.2279i	0.0260576	+	1.97031i
$358$	11.9963	−	13.3233i	0.634026	−	0.704157i
$359$	28.1506	+	20.4526i	1.48573	+	1.07945i	0.975653	+	0.219320i	$0.0703837\pi$
$359$	28.1506	+	20.4526i	1.48573	+	1.07945i	0.510079	+	0.860128i	$0.329616\pi$
$360$	−1.10211	−	3.27887i	−0.0580862	−	0.172812i
$361$	−26.2614	+	19.0800i	−1.38218	+	1.00421i
$362$	−1.11544	+	10.6127i	−0.0586265	+	0.557794i
$363$	17.8149	+	1.63454i	0.935037	+	0.0857911i
$364$	−1.33805	−	12.7307i	−0.0701328	−	0.667269i
$365$	−22.0807	−	25.3443i	−1.15576	−	1.32658i
$366$	8.36175	+	0.767203i	0.437075	+	0.0401023i
$367$	0.958614	−	1.06465i	0.0500392	−	0.0555742i	−0.717606	−	0.696450i	$-0.754762\pi$
$367$	0.958614	−	1.06465i	0.0500392	−	0.0555742i	0.767645	+	0.640876i	$0.221429\pi$
$368$	−9.20004			−0.479585
$369$	−1.80532	−	5.09372i	−0.0939813	−	0.265168i
$370$	6.03558	−	4.23611i	0.313775	−	0.220225i
$371$	5.24708	−	1.11530i	0.272415	−	0.0579035i
$372$	−20.2835	−	6.29519i	−1.05165	−	0.326391i
$373$	−3.21995	−	30.6357i	−0.166722	−	1.58626i	−0.683378	−	0.730065i	$-0.739490\pi$
$373$	−3.21995	−	30.6357i	−0.166722	−	1.58626i	0.516655	−	0.856194i	$-0.327177\pi$
$374$	6.29322	−	10.9002i	0.325415	−	0.563635i
$375$	−16.4130	−	10.2768i	−0.847564	−	0.530693i
$376$	−0.806403	−	1.39673i	−0.0415871	−	0.0720309i
$377$	12.3316	−	8.95943i	0.635110	−	0.461434i
$378$	19.4361	−	18.9491i	0.999683	−	0.974634i
$379$	7.87727	−	24.2437i	0.404628	−	1.24532i	−0.516577	−	0.856241i	$-0.672794\pi$
$379$	7.87727	−	24.2437i	0.404628	−	1.24532i	0.921205	−	0.389077i	$-0.127206\pi$
$380$	−25.2087	−	11.7211i	−1.29318	−	0.601279i
$381$	−1.45834	+	7.33671i	−0.0747129	+	0.375871i
$382$	−6.23631	+	10.8016i	−0.319077	+	0.552658i
$383$	2.68451	+	0.570611i	0.137172	+	0.0291568i	0.275986	−	0.961162i	$-0.410996\pi$
$383$	2.68451	+	0.570611i	0.137172	+	0.0291568i	−0.138814	+	0.990318i	$0.544329\pi$
$384$	−4.08630	+	5.78364i	−0.208528	+	0.295145i
$385$	−4.86172	+	0.950602i	−0.247776	+	0.0484472i
$386$	5.78364	−	4.20206i	0.294380	−	0.213879i
$387$	−24.0198	+	11.4648i	−1.22099	+	0.582788i
$388$	−8.28697	−	6.02084i	−0.420707	−	0.305662i
$389$	23.8712	+	10.6282i	1.21032	+	0.538869i	0.909856	−	0.414924i	$-0.136192\pi$
$389$	23.8712	+	10.6282i	1.21032	+	0.538869i	0.300463	+	0.953793i	$0.402859\pi$
$390$	15.1487	+	13.7258i	0.767083	+	0.695035i
$391$	−14.9733	+	6.66654i	−0.757232	+	0.337142i
$392$	−0.156472	−	0.0332592i	−0.00790304	−	0.00167984i
$393$	−14.8739	+	8.85176i	−0.750290	+	0.446512i
$394$	−28.2289	+	31.3513i	−1.42215	+	1.57946i
$395$	−4.67912	−	15.2444i	−0.235432	−	0.767029i
$396$	−4.14227	+	0.995650i	−0.208157	+	0.0500333i
$397$	0.161451	−	0.496896i	0.00810301	−	0.0249385i	−0.946923	−	0.321460i	$-0.895827\pi$
$397$	0.161451	−	0.496896i	0.00810301	−	0.0249385i	0.955026	+	0.296521i	$0.0958265\pi$
$398$	−28.7716	−	12.8099i	−1.44219	−	0.642104i
$399$	0.444250	+	33.5913i	0.0222403	+	1.68167i
$400$	1.60567	+	22.2549i	0.0802834	+	1.11274i
$401$	6.86560	−	11.8916i	0.342852	−	0.593837i	−0.642109	−	0.766613i	$-0.721940\pi$
$401$	6.86560	−	11.8916i	0.342852	−	0.593837i	0.984961	+	0.172776i	$0.0552738\pi$
$402$	−19.2853	+	2.28519i	−0.961862	+	0.113975i
$403$	−18.9049	+	4.01835i	−0.941718	+	0.200168i
$404$	−4.58083	+	14.0983i	−0.227905	+	0.701419i
$405$	−1.37083	+	20.0779i	−0.0681172	+	0.997677i
$406$	9.00741	+	27.7220i	0.447030	+	1.37582i
$407$	0.699242	+	1.21112i	0.0346601	+	0.0600331i
$408$	−1.38435	+	6.96447i	−0.0685353	+	0.344793i
$409$	−18.6309	+	8.29503i	−0.921240	+	0.410163i	−0.811870	−	0.583838i	$-0.801550\pi$
$409$	−18.6309	+	8.29503i	−0.921240	+	0.410163i	−0.109371	+	0.994001i	$0.534884\pi$
$410$	0.686876	+	7.75231i	0.0339224	+	0.382859i
$411$	−15.6379	−	20.9358i	−0.771358	−	1.03268i
$412$	−0.195947	+	1.86431i	−0.00965361	+	0.0918479i
$413$	8.79171	+	6.38755i	0.432612	+	0.314311i
$414$	11.0415	+	4.57006i	0.542660	+	0.224606i
$415$	−4.78116	−	3.59458i	−0.234698	−	0.176451i
$416$	2.16756	−	20.6230i	0.106274	−	1.01113i
$417$	−24.3199	−	21.3222i	−1.19095	−	1.04415i
$418$	5.67847	−	9.83539i	0.277743	−	0.481065i
$419$	−31.4528	−	6.68550i	−1.53657	−	0.326608i	−0.639603	−	0.768705i	$-0.720901\pi$
$419$	−31.4528	−	6.68550i	−1.53657	−	0.326608i	−0.896967	+	0.442097i	$0.854235\pi$
$420$	−15.7452	+	9.02506i	−0.768288	+	0.440378i
$421$	7.32382	−	1.55673i	0.356941	−	0.0758702i	−0.0259510	−	0.999663i	$-0.508261\pi$
$421$	7.32382	−	1.55673i	0.356941	−	0.0758702i	0.382892	+	0.923793i	$0.374928\pi$
$422$	1.85478	−	5.70843i	0.0902894	−	0.277882i
$423$	1.22723	+	9.30240i	0.0596699	+	0.452298i
$424$	1.02308			0.0496852
$425$	18.7396	+	35.0569i	0.909005	+	1.70051i
$426$	0.479417	+	36.2504i	0.0232278	+	1.75634i
$427$	0.709122	+	6.74684i	0.0343168	+	0.326503i
$428$	−13.0112	−	14.4504i	−0.628919	−	0.698485i
$429$	−2.84659	+	2.63207i	−0.137435	+	0.127078i
$430$	37.6174	−	7.35525i	1.81407	−	0.354702i
$431$	−10.7714	−	33.1508i	−0.518838	−	1.59682i	−0.776188	−	0.630501i	$-0.782849\pi$
$431$	−10.7714	−	33.1508i	−0.518838	−	1.59682i	0.257350	−	0.966318i	$-0.417151\pi$
$432$	19.6058	−	12.3814i	0.943284	−	0.595700i
$433$	−0.450743	−	1.38724i	−0.0216613	−	0.0666667i	0.939642	−	0.342160i	$-0.111159\pi$
$433$	−0.450743	−	1.38724i	−0.0216613	−	0.0666667i	−0.961303	+	0.275494i	$0.911159\pi$
$434$	3.86331	−	36.7569i	0.185445	−	1.76439i
$435$	−18.6813	−	10.8636i	−0.895700	−	0.520869i
$436$	−1.23542	−	11.7542i	−0.0591658	−	0.562925i
$437$	−13.5106	+	6.01532i	−0.646301	+	0.287752i
$438$	29.0290	−	41.0868i	1.38706	−	1.96321i
$439$	16.2351	+	7.22832i	0.774858	+	0.344989i	0.755777	−	0.654829i	$-0.227259\pi$
$439$	16.2351	+	7.22832i	0.774858	+	0.344989i	0.0190810	+	0.999818i	$0.493926\pi$
$440$	−0.944660	−	0.0154444i	−0.0450349	−	0.000736285i
$441$	0.767125	+	0.526927i	0.0365298	+	0.0250918i
$442$	−12.9671	−	39.9087i	−0.616783	−	1.89826i
$443$	−9.45458	−	16.3758i	−0.449201	−	0.778038i	0.549134	−	0.835735i	$-0.314958\pi$
$443$	−9.45458	−	16.3758i	−0.449201	−	0.778038i	−0.998334	+	0.0576964i	$0.981624\pi$
$444$	3.85243	+	3.37758i	0.182828	+	0.160293i
$445$	14.8782	+	17.0772i	0.705294	+	0.809539i
$446$	−21.0827	−	23.4147i	−0.998293	−	1.10872i
$447$	3.18166	+	14.0521i	0.150487	+	0.664644i
$448$	14.1814	+	6.31395i	0.670007	+	0.298306i
$449$	15.8263			0.746890			0.373445	−	0.927652i	$-0.378177\pi$
$449$	15.8263			0.746890			0.373445	+	0.927652i	$0.378177\pi$
$450$	9.12791	−	27.5069i	0.430294	−	1.29669i
$451$	−1.47603			−0.0695036
$452$	17.3757	+	7.73615i	0.817283	+	0.363878i
$453$	16.4596	+	5.10842i	0.773340	+	0.240015i
$454$	8.66918	+	9.62810i	0.406865	+	0.451869i
$455$	−8.49052	+	14.1661i	−0.398042	+	0.664115i
$456$	−1.24912	+	6.28415i	−0.0584952	+	0.294282i
$457$	−11.0341	−	19.1116i	−0.516152	−	0.894001i	−0.999824	−	0.0187518i	$-0.994031\pi$
$457$	−11.0341	−	19.1116i	−0.516152	−	0.894001i	0.483673	−	0.875249i	$-0.339303\pi$
$458$	7.33744	+	22.5823i	0.342856	+	1.05520i
$459$	22.9371	−	34.3578i	1.07061	−	1.60369i
$460$	−6.38600	−	4.80114i	−0.297749	−	0.223854i
$461$	−20.8135	−	9.26675i	−0.969380	−	0.431596i	−0.139920	−	0.990163i	$-0.544685\pi$
$461$	−20.8135	−	9.26675i	−0.969380	−	0.431596i	−0.829459	+	0.558567i	$0.811351\pi$
$462$	−3.10482	−	6.73249i	−0.144449	−	0.313224i
$463$	−7.78195	+	3.46475i	−0.361658	+	0.161020i	−0.579518	−	0.814960i	$-0.696759\pi$
$463$	−7.78195	+	3.46475i	−0.361658	+	0.161020i	0.217860	+	0.975980i	$0.430092\pi$
$464$	2.60276	+	24.7636i	0.120830	+	1.14962i
$465$	16.0367	+	22.2182i	0.743684	+	1.03035i
$466$	−4.94612	+	47.0592i	−0.229125	+	2.17997i
$467$	0.960766	+	2.95693i	0.0444590	+	0.136831i	0.970822	−	0.239801i	$-0.0770822\pi$
$467$	0.960766	+	2.95693i	0.0444590	+	0.136831i	−0.926363	+	0.376632i	$0.877082\pi$
$468$	−6.77394	+	12.4840i	−0.313125	+	0.577075i
$469$	−4.84847	−	14.9221i	−0.223882	−	0.689037i
$470$	1.63195	−	13.4138i	0.0752763	−	0.618731i
$471$	−6.31656	−	27.8978i	−0.291052	−	1.28546i
$472$	1.38683	+	1.54023i	0.0638340	+	0.0708948i
$473$	0.759866	+	7.22964i	0.0349387	+	0.332419i
$474$	20.5086	−	12.2051i	0.941992	−	0.560598i
$475$	16.9090	+	31.6324i	0.775840	+	1.45139i
$476$	37.2540			1.70753
$477$	−5.49962	−	2.27629i	−0.251810	−	0.104224i
$478$	−15.8064	+	48.6470i	−0.722967	+	2.22506i
$479$	17.1529	−	3.64596i	0.783735	−	0.166588i	0.201370	−	0.979515i	$-0.435461\pi$
$479$	17.1529	−	3.64596i	0.783735	−	0.166588i	0.582365	+	0.812927i	$0.302127\pi$
$480$	−27.9887	+	8.99753i	−1.27750	+	0.410679i
$481$	4.56058	+	0.969381i	0.207945	+	0.0442000i
$482$	5.77710	−	10.0062i	0.263140	−	0.455772i
$483$	−1.88224	+	9.46931i	−0.0856449	+	0.430869i
$484$	1.87113	−	17.8026i	0.0850513	−	0.809209i
$485$	3.87792	+	12.6341i	0.176087	+	0.573686i
$486$	−29.6804	+	5.12057i	−1.34633	+	0.232274i
$487$	4.18121	+	3.03782i	0.189469	+	0.137657i	0.678476	−	0.734623i	$-0.262641\pi$
$487$	4.18121	+	3.03782i	0.189469	+	0.137657i	−0.489007	+	0.872280i	$0.662641\pi$
$488$	−0.135244	+	1.28676i	−0.00612220	+	0.0582488i
$489$	−10.3720	+	1.22902i	−0.469039	+	0.0555784i
$490$	−0.880413	−	1.01054i	−0.0397730	−	0.0456516i
$491$	15.4984	−	6.90033i	0.699433	−	0.311408i	−0.0260375	−	0.999661i	$-0.508289\pi$
$491$	15.4984	−	6.90033i	0.699433	−	0.311408i	0.725470	+	0.688253i	$0.241622\pi$
$492$	−5.12029	+	1.73887i	−0.230840	+	0.0783944i
$493$	22.1803	+	38.4174i	0.998950	+	1.73023i
$494$	−11.7004	−	36.0102i	−0.526427	−	1.62018i
$495$	5.04371	+	2.18483i	0.226698	+	0.0982008i
$496$	9.75638	−	30.0271i	0.438074	−	1.34825i
$497$	−28.6500	+	6.08974i	−1.28513	+	0.273162i
$498$	3.53276	−	8.22576i	0.158307	−	0.368605i
$499$	−4.22329	+	7.31496i	−0.189061	+	0.327463i	−0.944937	−	0.327251i	$-0.893878\pi$
$499$	−4.22329	+	7.31496i	−0.189061	+	0.327463i	0.755877	+	0.654714i	$0.227211\pi$
$500$	−10.4994	+	16.2857i	−0.469548	+	0.728317i
$501$	−12.3511	+	7.35036i	−0.551805	+	0.328390i
$502$	−9.09600	−	4.04980i	−0.405974	−	0.180751i
$503$	−6.58427	+	20.2643i	−0.293578	+	0.903541i	0.690117	+	0.723698i	$0.257559\pi$
$503$	−6.58427	+	20.2643i	−0.293578	+	0.903541i	−0.983695	+	0.179843i	$0.942441\pi$
$504$	2.87994	+	3.03319i	0.128283	+	0.135109i
$505$	15.6548	−	10.9874i	0.696630	−	0.488934i
$506$	2.18394	−	2.42551i	0.0970879	−	0.107827i
$507$	−0.126832	−	9.59023i	−0.00563282	−	0.425917i
$508$	7.32128	+	1.55619i	0.324829	+	0.0690446i
$509$	5.25717	−	2.34064i	0.233020	−	0.103747i	−0.286905	−	0.957959i	$-0.592626\pi$
$509$	5.25717	−	2.34064i	0.233020	−	0.103747i	0.519925	+	0.854212i	$0.325960\pi$
$510$	−44.3356	+	39.6699i	−1.96321	+	1.75661i
$511$	37.1304	+	16.5315i	1.64255	+	0.731311i
$512$	23.6818	+	17.2059i	1.04660	+	0.760399i
$513$	20.6965	−	31.0016i	0.913773	−	1.36875i
$514$	−7.33217	+	5.32714i	−0.323408	+	0.234970i
$515$	1.64752	−	1.77066i	0.0725982	−	0.0780248i
$516$	11.1530	+	24.1841i	0.490983	+	1.06465i
$517$	2.50675	+	0.532827i	0.110247	+	0.0234337i
$518$	−4.45802	+	7.72151i	−0.195874	+	0.339264i
$519$	9.64849	−	3.27667i	0.423522	−	0.143830i
$520$	−2.14565	+	2.30604i	−0.0940931	+	0.101126i
$521$	−1.60876	+	4.95126i	−0.0704811	+	0.216918i	−0.980092	−	0.198542i	$-0.936379\pi$
$521$	−1.60876	+	4.95126i	−0.0704811	+	0.216918i	0.909611	+	0.415460i	$0.136379\pi$
$522$	9.17743	−	31.0131i	0.401685	−	1.35741i
$523$	31.9268	−	23.1962i	1.39606	−	1.01430i	0.400893	−	0.916125i	$-0.368700\pi$
$523$	31.9268	−	23.1962i	1.39606	−	1.01430i	0.995169	−	0.0981735i	$-0.0313000\pi$
$524$	8.65960	+	14.9989i	0.378296	+	0.655229i
$525$	23.2348	+	2.90047i	1.01405	+	0.126587i
$526$	10.8109	−	18.7251i	0.471379	−	0.816453i
$527$	−5.87948	−	55.9395i	−0.256114	−	2.43676i
$528$	−1.39857	−	6.17695i	−0.0608651	−	0.268817i
$529$	18.3400	−	3.89829i	0.797392	−	0.169491i
$530$	6.85139	+	5.15103i	0.297605	+	0.223746i
$531$	−4.02807	−	11.3652i	−0.174803	−	0.493207i
$532$	33.6148			1.45739
$533$	−3.29279	+	3.65702i	−0.142627	+	0.158403i
$534$	−19.5600	+	27.6847i	−0.846445	+	1.19803i
$535$	2.21418	+	24.9900i	0.0957274	+	1.08041i
$536$	−0.312790	−	2.97600i	−0.0135105	−	0.128544i
$537$	−6.73055	−	14.5945i	−0.290445	−	0.629800i
$538$	0.884037	−	8.41105i	0.0381135	−	0.362626i
$539$	0.205644	−	0.149409i	0.00885771	−	0.00643550i
$540$	20.0703	+	1.63723i	0.863688	+	0.0704550i
$541$	3.83727	+	2.78794i	0.164977	+	0.119863i	0.667211	−	0.744869i	$-0.267488\pi$
$541$	3.83727	+	2.78794i	0.164977	+	0.119863i	−0.502233	+	0.864732i	$0.667488\pi$
$542$	11.3792	−	12.6379i	0.488780	−	0.542845i
$543$	8.34708	+	4.67312i	0.358208	+	0.200543i
$544$	59.0306	+	12.5473i	2.53092	+	0.537963i
$545$	−7.83928	+	13.0795i	−0.335798	+	0.560264i
$546$	−23.6068	−	7.32663i	−1.01028	−	0.313551i
$547$	−35.7135	+	7.59114i	−1.52700	+	0.324574i	−0.893462	−	0.449139i	$-0.851731\pi$
$547$	−35.7135	+	7.59114i	−1.52700	+	0.324574i	−0.633537	+	0.773713i	$0.718397\pi$
$548$	−21.1537	+	15.3691i	−0.903641	+	0.656534i
$549$	3.58996	−	6.61613i	0.153216	−	0.282370i
$550$	−6.24846	−	4.85962i	−0.266435	−	0.207215i
$551$	20.0136	+	34.6646i	0.852608	+	1.47676i
$552$	−0.726622	+	1.69189i	−0.0309271	+	0.0720115i
$553$	12.9019	+	14.3290i	0.548643	+	0.609330i
$554$	13.7119	+	15.2286i	0.582561	+	0.647000i
$555$	−1.35414	−	6.47004i	−0.0574801	−	0.274638i
$556$	−21.6552	+	24.0506i	−0.918386	+	1.01997i
$557$	−17.5287			−0.742714			−0.371357	−	0.928490i	$-0.621107\pi$
$557$	−17.5287			−0.742714			−0.371357	+	0.928490i	$0.621107\pi$
$558$	−26.6249	+	31.1908i	−1.12712	+	1.32041i
$559$	19.6073	+	14.2455i	0.829301	+	0.602522i
$560$	−13.1060	−	23.5823i	−0.553828	−	0.996533i
$561$	−6.75216	−	9.03971i	−0.285076	−	0.381657i
$562$	−51.6145	+	22.9803i	−2.17723	+	0.969364i
$563$	−4.44867	+	1.98067i	−0.187489	+	0.0834755i	−0.498334	−	0.866985i	$-0.666055\pi$
$563$	−4.44867	+	1.98067i	−0.187489	+	0.0834755i	0.310845	+	0.950461i	$0.399388\pi$
$564$	9.32353	−	1.10478i	0.392592	−	0.0465198i
$565$	−11.9208	−	21.4498i	−0.501512	−	0.902398i
$566$	9.02086	+	6.55404i	0.379175	+	0.275487i
$567$	−8.73262	−	22.7128i	−0.366736	−	0.953846i
$568$	−5.58619			−0.234391
$569$	−25.0518	+	27.8228i	−1.05023	+	1.16639i	−0.0645199	+	0.997916i	$0.520552\pi$
$569$	−25.0518	+	27.8228i	−1.05023	+	1.16639i	−0.985706	+	0.168477i	$0.946115\pi$
$570$	−40.0047	+	35.7948i	−1.67561	+	1.49928i
$571$	0.660086	+	0.733100i	0.0276237	+	0.0306793i	0.756798	−	0.653648i	$-0.226762\pi$
$571$	0.660086	+	0.733100i	0.0276237	+	0.0306793i	−0.729175	+	0.684328i	$0.760096\pi$
$572$	2.59579	+	2.88292i	0.108535	+	0.120541i
$573$	6.69110	+	8.95796i	0.279525	+	0.374224i
$574$	−4.70522	−	8.14967i	−0.196392	−	0.340161i
$575$	2.86319	+	9.90244i	0.119403	+	0.412960i
$576$	−9.00367	−	14.6838i	−0.375153	−	0.611825i
$577$	5.32656	−	3.86997i	0.221747	−	0.161109i	−0.471365	−	0.881938i	$-0.656239\pi$
$577$	5.32656	−	3.86997i	0.221747	−	0.161109i	0.693113	+	0.720829i	$0.256239\pi$
$578$	87.3256	−	18.5616i	3.63227	−	0.772062i
$579$	−1.41522	−	6.25047i	−0.0588145	−	0.259761i
$580$	−11.1165	+	18.5474i	−0.461588	+	0.770138i
$581$	7.07469	+	1.50377i	0.293508	+	0.0623870i
$582$	−16.9970	+	10.1152i	−0.704547	+	0.419290i
$583$	−1.08779	+	1.20811i	−0.0450517	+	0.0500350i
$584$	6.27124	+	4.55632i	0.259506	+	0.188542i
$585$	16.6649	−	7.62229i	0.689007	−	0.315143i
$586$	8.28013	−	6.01587i	0.342049	−	0.248513i
$587$	4.07528	−	38.7737i	0.168205	−	1.60036i	−0.506477	−	0.862253i	$-0.669053\pi$
$587$	4.07528	−	38.7737i	0.168205	−	1.60036i	0.674682	−	0.738108i	$-0.264281\pi$
$588$	0.537355	−	0.760557i	0.0221601	−	0.0313648i
$589$	−5.30514	−	50.4751i	−0.218595	−	2.07979i
$590$	1.53257	+	17.2971i	0.0630949	+	0.712110i
$591$	15.8378	+	34.3427i	0.651481	+	1.41267i
$592$	−5.09641	+	5.66013i	−0.209461	+	0.232630i
$593$	40.1968			1.65068			0.825342	−	0.564633i	$-0.190982\pi$
$593$	40.1968			1.65068			0.825342	+	0.564633i	$0.190982\pi$
$594$	−1.38985	+	8.10804i	−0.0570262	+	0.332677i
$595$	−38.4185	−	28.8839i	−1.57501	−	1.18412i
$596$	14.1016	−	2.99740i	0.577626	−	0.122778i
$597$	−20.7296	+	19.1674i	−0.848407	+	0.784471i
$598$	−1.13742	−	10.8219i	−0.0465127	−	0.442539i
$599$	−16.0097	+	27.7297i	−0.654140	+	1.13300i	0.327968	+	0.944689i	$0.393636\pi$
$599$	−16.0097	+	27.7297i	−0.654140	+	1.13300i	−0.982109	+	0.188316i	$0.939697\pi$
$600$	4.21949	+	1.46242i	0.172260	+	0.0597029i
$601$	−19.3911	−	33.5864i	−0.790981	−	1.37002i	−0.925360	−	0.379089i	$-0.876237\pi$
$601$	−19.3911	−	33.5864i	−0.790981	−	1.37002i	0.134379	−	0.990930i	$-0.457096\pi$
$602$	−37.4951	+	27.2417i	−1.52818	+	1.11029i
$603$	−4.93999	+	16.6936i	−0.201172	+	0.679816i
$604$	5.32891	−	16.4007i	0.216830	−	0.667334i
$605$	−15.7324	+	16.9084i	−0.639613	+	0.687423i
$606$	21.5232	+	18.8702i	0.874321	+	0.766551i
$607$	−4.75715	+	8.23963i	−0.193087	+	0.334436i	−0.946272	−	0.323373i	$-0.895183\pi$
$607$	−4.75715	+	8.23963i	−0.193087	+	0.334436i	0.753185	+	0.657809i	$0.228517\pi$
$608$	53.2642	+	11.3217i	2.16015	+	0.459154i
$609$	26.0209	+	2.38746i	1.05442	+	0.0967447i
$610$	−7.38430	+	7.93627i	−0.298982	+	0.321330i
$611$	6.91231	−	5.02209i	0.279642	−	0.203172i
$612$	−34.0724	−	23.4038i	−1.37729	−	0.946043i
$613$	−30.1095	−	21.8759i	−1.21611	−	0.883558i	−0.220342	−	0.975423i	$-0.570717\pi$
$613$	−30.1095	−	21.8759i	−1.21611	−	0.883558i	−0.995771	+	0.0918649i	$0.970717\pi$
$614$	−2.40881	−	1.07247i	−0.0972116	−	0.0432814i
$615$	6.62853	+	2.17665i	0.267288	+	0.0877712i
$616$	1.04362	−	0.464651i	0.0420488	−	0.0187213i
$617$	−1.01266	−	0.215248i	−0.0407683	−	0.00866558i	0.187482	−	0.982268i	$-0.439967\pi$
$617$	−1.01266	−	0.215248i	−0.0407683	−	0.00866558i	−0.228251	+	0.973602i	$0.573301\pi$
$618$	3.15841	+	1.76824i	0.127050	+	0.0711290i
$619$	8.59371	−	9.54428i	0.345410	−	0.383617i	−0.545260	−	0.838267i	$-0.683569\pi$
$619$	8.59371	−	9.54428i	0.345410	−	0.383617i	0.890670	+	0.454650i	$0.150236\pi$
$620$	22.4421	−	15.7511i	0.901297	−	0.632581i
$621$	7.67034	−	7.47814i	0.307800	−	0.300087i
$622$	5.85171	−	18.0097i	0.234632	−	0.722124i
$623$	−25.0188	−	11.1391i	−1.00236	−	0.446278i
$624$	−18.4240	−	10.3147i	−0.737551	−	0.412918i
$625$	23.4543	−	8.65431i	0.938171	−	0.346172i
$626$	24.4259	−	42.3070i	0.976257	−	1.69093i
$627$	−6.09258	−	8.15666i	−0.243314	−	0.325746i
$628$	−27.9960	+	5.95074i	−1.11716	+	0.237460i
$629$	−4.19308	+	12.9050i	−0.167189	+	0.514555i
$630$	4.01488	+	34.8127i	0.159957	+	1.38697i
$631$	−1.15787	−	3.56357i	−0.0460943	−	0.141864i	0.925361	−	0.379088i	$-0.123762\pi$
$631$	−1.15787	−	3.56357i	−0.0460943	−	0.141864i	−0.971455	+	0.237225i	$0.923762\pi$
$632$	1.83869	+	3.18470i	0.0731391	+	0.126681i
$633$	−4.04587	−	3.54717i	−0.160809	−	0.140987i
$634$	−28.8087	+	12.8265i	−1.14414	+	0.509404i
$635$	−6.34359	−	7.28119i	−0.251738	−	0.288945i
$636$	−2.35026	+	5.47240i	−0.0931937	+	0.216995i
$637$	0.0885831	−	0.842812i	0.00350979	−	0.0333934i
$638$	−7.14656	−	5.19228i	−0.282935	−	0.205564i
$639$	30.0289	+	12.4289i	1.18792	+	0.491680i
$640$	−2.68260	−	8.73981i	−0.106039	−	0.345471i
$641$	−0.782463	+	7.44463i	−0.0309054	+	0.294045i	0.968142	+	0.250403i	$0.0805630\pi$
$641$	−0.782463	+	7.44463i	−0.0309054	+	0.294045i	−0.999047	+	0.0436428i	$0.986104\pi$
$642$	−35.5527	+	12.0739i	−1.40315	+	0.476517i
$643$	19.9559	−	34.5645i	0.786982	−	1.36309i	−0.140826	−	0.990034i	$-0.544976\pi$
$643$	19.9559	−	34.5645i	0.786982	−	1.36309i	0.927808	−	0.373058i	$-0.121691\pi$
$644$	9.44939	+	2.00853i	0.372358	+	0.0791472i
$645$	7.24892	−	33.5873i	0.285426	−	1.32250i
$646$	107.785	−	22.9104i	4.24075	−	0.901399i
$647$	−1.26863	+	3.90445i	−0.0498751	+	0.153500i	−0.972892	−	0.231259i	$-0.925715\pi$
$647$	−1.26863	+	3.90445i	−0.0498751	+	0.153500i	0.923017	+	0.384759i	$0.125715\pi$
$648$	−0.728464	−	4.58339i	−0.0286168	−	0.180053i
$649$	−3.29335			−0.129275
$650$	−25.9796	+	4.64015i	−1.01900	+	0.182002i
$651$	−28.9099	−	16.1852i	−1.13307	−	0.634348i
$652$	1.09243	+	10.3937i	0.0427827	+	0.407051i
$653$	−3.68589	−	4.09359i	−0.144240	−	0.160195i	0.666696	−	0.745330i	$-0.267708\pi$
$653$	−3.68589	−	4.09359i	−0.144240	−	0.160195i	−0.810936	+	0.585135i	$0.801041\pi$
$654$	−21.7961	−	6.76466i	−0.852295	−	0.264519i
$655$	2.69868	−	22.1817i	0.105446	−	0.866712i
$656$	−2.48413	−	7.64535i	−0.0969888	−	0.298501i
$657$	−23.5739	−	38.4458i	−0.919704	−	1.49991i
$658$	5.04898	+	15.5392i	0.196830	+	0.605780i
$659$	−0.740780	+	7.04805i	−0.0288567	+	0.274553i	0.970574	+	0.240804i	$0.0774112\pi$
$659$	−0.740780	+	7.04805i	−0.0288567	+	0.274553i	−0.999430	+	0.0337487i	$0.989255\pi$
$660$	2.25272	−	5.01745i	0.0876869	−	0.195304i
$661$	−3.60565	−	34.3055i	−0.140243	−	1.33433i	−0.807662	−	0.589645i	$-0.799268\pi$
$661$	−3.60565	−	34.3055i	−0.140243	−	1.33433i	0.667419	−	0.744682i	$-0.267399\pi$
$662$	4.78875	−	2.13209i	0.186120	−	0.0828661i
$663$	−37.4598	−	3.43699i	−1.45482	−	0.133482i
$664$	1.26017	+	0.561065i	0.0489042	+	0.0217735i
$665$	−34.6656	−	26.0624i	−1.34427	−	1.01066i
$666$	8.92812	−	4.26144i	0.345958	−	0.165128i
$667$	3.55473	+	10.9403i	0.137640	+	0.423611i
$668$	7.19080	+	12.4548i	0.278220	+	0.481892i
$669$	−26.7447	+	9.08261i	−1.03401	+	0.351154i
$670$	12.8889	−	21.5046i	0.497943	−	0.830796i
$671$	−1.37568	−	1.52785i	−0.0531077	−	0.0589821i
$672$	26.1006	−	24.1337i	1.00685	−	0.930977i
$673$	−27.8887	−	12.4169i	−1.07503	−	0.478634i	−0.208635	−	0.977993i	$-0.566902\pi$
$673$	−27.8887	−	12.4169i	−1.07503	−	0.478634i	−0.866395	+	0.499359i	$0.833569\pi$
$674$	−66.6655			−2.56786
$675$	−19.4283	−	17.2494i	−0.747796	−	0.663929i
$676$	−9.59695			−0.369114
$677$	−8.96654	−	3.99216i	−0.344612	−	0.153431i	0.227130	−	0.973864i	$-0.427066\pi$
$677$	−8.96654	−	3.99216i	−0.344612	−	0.153431i	−0.571742	+	0.820433i	$0.693732\pi$
$678$	26.9658	−	24.9337i	1.03562	−	0.957572i
$679$	−10.6927	−	11.8754i	−0.410348	−	0.455738i
$680$	−6.02173	−	6.91177i	−0.230923	−	0.265054i
$681$	10.9974	−	3.73477i	0.421422	−	0.143117i
$682$	5.60037	+	9.70012i	0.214449	+	0.371437i
$683$	9.67861	+	29.7877i	0.370342	+	1.13979i	0.946568	+	0.322504i	$0.104525\pi$
$683$	9.67861	+	29.7877i	0.370342	+	1.13979i	−0.576226	+	0.817290i	$0.695475\pi$
$684$	−30.7440	−	21.1176i	−1.17553	−	0.807452i
$685$	33.7309	+	0.551474i	1.28879	+	0.0210707i
$686$	−31.9259	−	14.2143i	−1.21894	−	0.542705i
$687$	21.1966	+	1.94482i	0.808702	+	0.0741996i
$688$	−36.1683	+	16.1032i	−1.37890	+	0.613927i
$689$	0.566536	+	5.39023i	0.0215833	+	0.205351i
$690$	−13.3844	+	7.67185i	−0.509536	+	0.292062i
$691$	−2.65596	+	25.2698i	−0.101037	+	0.961307i	0.820140	+	0.572164i	$0.193896\pi$
$691$	−2.65596	+	25.2698i	−0.101037	+	0.961307i	−0.921177	+	0.389144i	$0.872771\pi$
$692$	−3.15072	−	9.69692i	−0.119772	−	0.368622i
$693$	−6.64387	+	0.175763i	−0.252380	+	0.00667670i
$694$	−13.5746	−	41.7784i	−0.515286	−	1.58589i
$695$	40.9791	−	8.01256i	1.55443	−	0.303934i
$696$	4.75959	+	1.47719i	0.180412	+	0.0559928i
$697$	−9.58296	−	10.6430i	−0.362981	−	0.403131i
$698$	6.78296	+	64.5356i	0.256739	+	2.44271i
$699$	37.0127	+	20.7216i	1.39995	+	0.783763i
$700$	3.20944	−	23.2086i	0.121306	−	0.877203i
$701$	−6.16132			−0.232710			−0.116355	−	0.993208i	$-0.537121\pi$
$701$	−6.16132			−0.232710			−0.116355	+	0.993208i	$0.537121\pi$
$702$	16.9880	+	21.5313i	0.641169	+	0.812645i
$703$	−3.78348	+	11.6444i	−0.142697	+	0.439175i
$704$	−4.60165	+	0.978112i	−0.173431	+	0.0368640i
$705$	−10.4715	−	6.08944i	−0.394381	−	0.229342i
$706$	−13.7246	−	2.91726i	−0.516534	−	0.109793i
$707$	−11.5630	+	20.0277i	−0.434871	+	0.753218i
$708$	−11.4245	+	3.87980i	−0.429358	+	0.145812i
$709$	1.87963	−	17.8835i	0.0705912	−	0.671630i	−0.900814	−	0.434204i	$-0.857030\pi$
$709$	1.87963	−	17.8835i	0.0705912	−	0.671630i	0.971406	−	0.237426i	$-0.0763037\pi$
$710$	−37.4098	−	28.1255i	−1.40396	−	1.05553i
$711$	−2.79822	−	21.2105i	−0.104941	−	0.795456i
$712$	−4.22562	−	3.07009i	−0.158362	−	0.115056i
$713$	1.52463	−	14.5059i	0.0570980	−	0.543251i
$714$	28.3871	−	66.0973i	1.06236	−	2.47363i
$715$	−0.441739	−	4.98562i	−0.0165201	−	0.186451i
$716$	−14.6913	+	6.54097i	−0.549038	+	0.244448i
$717$	34.4788	+	30.2289i	1.28763	+	1.12892i
$718$	−33.6152	−	58.2232i	−1.25451	−	2.17287i
$719$	−3.67562	−	11.3124i	−0.137078	−	0.421881i	0.858830	−	0.512261i	$-0.171192\pi$
$719$	−3.67562	−	11.3124i	−0.137078	−	0.421881i	−0.995907	+	0.0903796i	$0.971192\pi$
$720$	−2.82825	+	29.8018i	−0.105403	+	1.11065i
$721$	−0.903700	+	2.78130i	−0.0336555	+	0.103581i
$722$	61.3480	−	13.0399i	2.28313	−	0.485295i
$723$	−6.19841	−	8.29835i	−0.230521	−	0.308619i
$724$	4.78603	−	8.28964i	0.177871	−	0.308082i
$725$	25.8442	−	10.5083i	0.959830	−	0.390267i
$726$	−30.1602	−	16.8852i	−1.11935	−	0.626669i
$727$	40.7090	+	18.1248i	1.50981	+	0.672212i	0.983964	−	0.178366i	$-0.0570813\pi$
$727$	40.7090	+	18.1248i	1.50981	+	0.672212i	0.525848	+	0.850578i	$0.323748\pi$
$728$	1.17694	−	3.62225i	0.0436203	−	0.134249i
$729$	−6.28185	+	26.2591i	−0.232661	+	0.972558i
$730$	19.0571	+	62.0874i	0.705335	+	2.29796i
$731$	−47.1962	+	52.4166i	−1.74561	+	1.93870i
$732$	−6.57211	−	3.67940i	−0.242912	−	0.135995i
$733$	30.5184	+	6.48688i	1.12722	+	0.239598i	0.733539	−	0.679648i	$-0.237867\pi$
$733$	30.5184	+	6.48688i	1.12722	+	0.239598i	0.393683	+	0.919246i	$0.371201\pi$
$734$	−2.52871	+	1.12585i	−0.0933363	+	0.0415560i
$735$	−1.14383	+	0.367707i	−0.0421908	+	0.0135631i
$736$	14.2965	+	6.36521i	0.526976	+	0.234625i
$737$	3.84682	+	2.79488i	0.141699	+	0.102951i
$738$	−0.816437	+	10.4096i	−0.0300535	+	0.383183i
$739$	−18.8750	+	13.7135i	−0.694328	+	0.504459i	−0.878080	−	0.478514i	$-0.841176\pi$
$739$	−18.8750	+	13.7135i	−0.694328	+	0.504459i	0.183752	+	0.982973i	$0.441176\pi$
$740$	−6.49136	+	1.26924i	−0.238627	+	0.0466583i
$741$	−33.8005	−	3.10125i	−1.24169	−	0.113927i
$742$	−10.1380	−	2.15490i	−0.372178	−	0.0791090i
$743$	−27.0017	+	46.7683i	−0.990597	+	1.71576i	−0.376814	+	0.926289i	$0.622980\pi$
$743$	−27.0017	+	46.7683i	−0.990597	+	1.71576i	−0.613783	+	0.789475i	$0.710353\pi$
$744$	−4.75141	−	4.16575i	−0.174195	−	0.152724i
$745$	−16.8664	−	7.84224i	−0.617937	−	0.287318i
$746$	−18.3921	+	56.6052i	−0.673384	+	2.07246i
$747$	−5.52579	−	5.81983i	−0.202178	−	0.212937i
$748$	−9.13381	+	6.63610i	−0.333965	+	0.242640i
$749$	−15.1675	−	26.2709i	−0.554208	−	0.959917i
$750$	20.8942	+	31.0379i	0.762947	+	1.13334i
$751$	−9.85880	+	17.0759i	−0.359753	+	0.623110i	−0.987919	−	0.154969i	$-0.950472\pi$
$751$	−9.85880	+	17.0759i	−0.359753	+	0.623110i	0.628167	+	0.778079i	$0.283806\pi$
$752$	1.45894	+	13.8809i	0.0532021	+	0.506184i
$753$	−6.55357	+	6.05969i	−0.238825	+	0.220828i
$754$	−28.8072	+	6.12317i	−1.04910	+	0.222993i
$755$	−18.2113	+	12.7817i	−0.662778	+	0.465175i
$756$	−22.8403	+	8.43668i	−0.830692	+	0.306839i
$757$	15.3080			0.556380			0.278190	−	0.960526i	$-0.410265\pi$
$757$	15.3080			0.556380			0.278190	+	0.960526i	$0.410265\pi$
$758$	−32.9564	+	36.6018i	−1.19703	+	1.32944i
$759$	−1.22530	−	2.65694i	−0.0444756	−	0.0964409i
$760$	−5.43350	−	6.23659i	−0.197094	−	0.226225i
$761$	0.560352	+	5.33140i	0.0203128	+	0.193263i	0.999973	−	0.00740241i	$-0.00235628\pi$
$761$	0.560352	+	5.33140i	0.0203128	+	0.193263i	−0.979660	+	0.200665i	$0.935690\pi$
$762$	8.33977	−	11.8039i	0.302118	−	0.427609i
$763$	1.92731	−	18.3371i	0.0697733	−	0.663849i
$764$	9.05121	−	6.57609i	0.327461	−	0.237915i
$765$	16.9919	+	50.5525i	0.614345	+	1.82773i
$766$	−4.28997	−	3.11685i	−0.155003	−	0.112616i
$767$	−7.34694	+	8.15960i	−0.265282	+	0.294626i
$768$	28.8492	−	17.1687i	1.04101

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:	\( N \)	\(=\)	\( 225 = 3^{2} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	225.q (of order \(15\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.76509 - 0.785867i) q^{2} +(-1.27173 + 1.17589i) q^{3} +(1.15968 + 1.28795i) q^{4} +(-0.197349 - 2.22734i) q^{5} +(3.16880 - 1.07614i) q^{6} +(1.35187 + 2.34151i) q^{7} +(0.159347 + 0.490420i) q^{8} +(0.234573 - 2.99082i) q^{9} +O(q^{10})\)	\(q+(-1.76509 - 0.785867i) q^{2} +(-1.27173 + 1.17589i) q^{3} +(1.15968 + 1.28795i) q^{4} +(-0.197349 - 2.22734i) q^{5} +(3.16880 - 1.07614i) q^{6} +(1.35187 + 2.34151i) q^{7} +(0.159347 + 0.490420i) q^{8} +(0.234573 - 2.99082i) q^{9} +(-1.40206 + 4.08654i) q^{10} +(-0.748543 - 0.333273i) q^{11} +(-2.98929 - 0.274272i) q^{12} +(-2.49560 + 1.11111i) q^{13} +(-0.546054 - 5.19535i) q^{14} +(2.87008 + 2.60051i) q^{15} +(0.466463 - 4.43810i) q^{16} +(-2.45676 - 7.56113i) q^{17} +(-2.76442 + 5.09470i) q^{18} +(-2.21677 - 6.82252i) q^{19} +(2.63985 - 2.83718i) q^{20} +(-4.47256 - 1.38811i) q^{21} +(1.05934 + 1.17651i) q^{22} +(-0.215497 - 2.05032i) q^{23} +(-0.779325 - 0.436305i) q^{24} +(-4.92211 + 0.879126i) q^{25} +5.27814 q^{26} +(3.21855 + 4.07933i) q^{27} +(-1.44802 + 4.45655i) q^{28} +(-5.45784 + 1.16010i) q^{29} +(-3.02228 - 6.84562i) q^{30} +(6.92035 + 1.47097i) q^{31} +(-3.79544 + 6.57390i) q^{32} +(1.34383 - 0.456372i) q^{33} +(-1.60565 + 15.2767i) q^{34} +(4.94855 - 3.47317i) q^{35} +(4.12406 - 3.16627i) q^{36} +(-1.38079 - 1.00320i) q^{37} +(-1.44880 + 13.7844i) q^{38} +(1.86718 - 4.34758i) q^{39} +(1.06089 - 0.451704i) q^{40} +(1.64566 - 0.732693i) q^{41} +(6.80359 + 5.96497i) q^{42} +(-4.43594 - 7.68327i) q^{43} +(-0.438830 - 1.35058i) q^{44} +(-6.70786 + 0.0677586i) q^{45} +(-1.23091 + 3.78834i) q^{46} +(-3.05932 + 0.650279i) q^{47} +(4.62549 + 6.19255i) q^{48} +(-0.155110 + 0.268659i) q^{49} +(9.37882 + 2.31639i) q^{50} +(12.0154 + 6.72681i) q^{51} +(-4.32516 - 1.92569i) q^{52} +(0.613099 - 1.88692i) q^{53} +(-2.47521 - 9.72972i) q^{54} +(-0.594589 + 1.73303i) q^{55} +(-0.932906 + 1.03610i) q^{56} +(10.8416 + 6.06970i) q^{57} +(10.5452 + 2.24146i) q^{58} +(3.67181 - 1.63480i) q^{59} +(-0.0209650 + 6.71229i) q^{60} +(2.29219 + 1.02055i) q^{61} +(-11.0590 - 8.03486i) q^{62} +(7.32013 - 3.49394i) q^{63} +(4.64494 - 3.37475i) q^{64} +(2.96733 + 5.33928i) q^{65} +(-2.73063 - 0.250539i) q^{66} +(-5.67625 - 1.20652i) q^{67} +(6.88934 - 11.9327i) q^{68} +(2.68500 + 2.35404i) q^{69} +(-11.4641 + 2.24155i) q^{70} +(-3.34762 + 10.3029i) q^{71} +(1.50413 - 0.361538i) q^{72} +(12.1616 - 8.83593i) q^{73} +(1.64883 + 2.85586i) q^{74} +(5.22582 - 6.90586i) q^{75} +(6.21635 - 10.7670i) q^{76} +(-0.231572 - 2.20326i) q^{77} +(-6.71234 + 6.20650i) q^{78} +(6.97559 - 1.48271i) q^{79} +(-9.97722 - 0.163120i) q^{80} +(-8.88995 - 1.40313i) q^{81} -3.48052 q^{82} +(1.78998 - 1.98798i) q^{83} +(-3.39892 - 7.37022i) q^{84} +(-16.3564 + 6.96422i) q^{85} +(1.79178 + 17.0477i) q^{86} +(5.57673 - 7.89315i) q^{87} +(0.0441655 - 0.420207i) q^{88} +(-8.19461 + 5.95373i) q^{89} +(11.8932 + 5.15189i) q^{90} +(-5.97541 - 4.34139i) q^{91} +(2.39081 - 2.65526i) q^{92} +(-10.5305 + 6.26690i) q^{93} +(5.91100 + 1.25642i) q^{94} +(-14.7586 + 6.28392i) q^{95} +(-2.90341 - 12.8232i) q^{96} +(-5.78117 + 1.22883i) q^{97} +(0.484914 - 0.352310i) q^{98} +(-1.17235 + 2.16058i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 224 q - 3 q^{2} - 8 q^{3} + 23 q^{4} - 8 q^{5} - 10 q^{6} - 8 q^{7} - 20 q^{8} - 8 q^{9}+O(q^{10}) \) 224 * q - 3 * q^2 - 8 * q^3 + 23 * q^4 - 8 * q^5 - 10 * q^6 - 8 * q^7 - 20 * q^8 - 8 * q^9	\( 224 q - 3 q^{2} - 8 q^{3} + 23 q^{4} - 8 q^{5} - 10 q^{6} - 8 q^{7} - 20 q^{8} - 8 q^{9} - 20 q^{10} - 11 q^{11} - 4 q^{12} - 3 q^{13} + q^{14} - 48 q^{15} + 23 q^{16} - 24 q^{17} - 12 q^{19} + q^{20} + 15 q^{21} - 11 q^{22} + q^{23} - 30 q^{24} - 16 q^{25} - 136 q^{26} + 7 q^{27} + 4 q^{28} - 15 q^{29} - 24 q^{30} + 3 q^{31} + 12 q^{32} - 5 q^{33} + q^{34} + 14 q^{35} + 38 q^{36} - 24 q^{37} + 55 q^{38} + 20 q^{39} + q^{40} - 19 q^{41} - 38 q^{42} - 8 q^{43} + 4 q^{44} - 38 q^{45} - 20 q^{46} - 10 q^{47} - 25 q^{48} - 72 q^{49} - 3 q^{50} - 26 q^{51} - 25 q^{52} - 12 q^{53} + 53 q^{54} - 20 q^{55} - 60 q^{56} + 38 q^{57} - 23 q^{58} - 30 q^{59} - 33 q^{60} - 3 q^{61} - 44 q^{62} + 46 q^{63} - 44 q^{64} + 51 q^{65} - 134 q^{66} - 12 q^{67} - 156 q^{68} + 4 q^{69} - 16 q^{70} + 42 q^{71} + 74 q^{72} - 12 q^{73} + 90 q^{74} + 67 q^{75} - 8 q^{76} + 31 q^{77} - 92 q^{78} - 15 q^{79} + 298 q^{80} - 104 q^{81} + 8 q^{82} + 59 q^{83} + 115 q^{84} - 11 q^{85} + 9 q^{86} - 59 q^{87} - 23 q^{88} + 106 q^{89} + 107 q^{90} + 30 q^{91} + 11 q^{92} + 32 q^{93} + 25 q^{94} + 7 q^{95} + 35 q^{96} - 21 q^{97} + 146 q^{98} - 20 q^{99}+O(q^{100}) \) 224 * q - 3 * q^2 - 8 * q^3 + 23 * q^4 - 8 * q^5 - 10 * q^6 - 8 * q^7 - 20 * q^8 - 8 * q^9 - 20 * q^10 - 11 * q^11 - 4 * q^12 - 3 * q^13 + q^14 - 48 * q^15 + 23 * q^16 - 24 * q^17 - 12 * q^19 + q^20 + 15 * q^21 - 11 * q^22 + q^23 - 30 * q^24 - 16 * q^25 - 136 * q^26 + 7 * q^27 + 4 * q^28 - 15 * q^29 - 24 * q^30 + 3 * q^31 + 12 * q^32 - 5 * q^33 + q^34 + 14 * q^35 + 38 * q^36 - 24 * q^37 + 55 * q^38 + 20 * q^39 + q^40 - 19 * q^41 - 38 * q^42 - 8 * q^43 + 4 * q^44 - 38 * q^45 - 20 * q^46 - 10 * q^47 - 25 * q^48 - 72 * q^49 - 3 * q^50 - 26 * q^51 - 25 * q^52 - 12 * q^53 + 53 * q^54 - 20 * q^55 - 60 * q^56 + 38 * q^57 - 23 * q^58 - 30 * q^59 - 33 * q^60 - 3 * q^61 - 44 * q^62 + 46 * q^63 - 44 * q^64 + 51 * q^65 - 134 * q^66 - 12 * q^67 - 156 * q^68 + 4 * q^69 - 16 * q^70 + 42 * q^71 + 74 * q^72 - 12 * q^73 + 90 * q^74 + 67 * q^75 - 8 * q^76 + 31 * q^77 - 92 * q^78 - 15 * q^79 + 298 * q^80 - 104 * q^81 + 8 * q^82 + 59 * q^83 + 115 * q^84 - 11 * q^85 + 9 * q^86 - 59 * q^87 - 23 * q^88 + 106 * q^89 + 107 * q^90 + 30 * q^91 + 11 * q^92 + 32 * q^93 + 25 * q^94 + 7 * q^95 + 35 * q^96 - 21 * q^97 + 146 * q^98 - 20 * q^99

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