LMFDB - Embedded newform 225.2.q.a.16.6

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			16.6
Character	$\chi$	$=$	225.16
Dual form			225.2.q.a.211.6

$q$-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 $\left(\mathbb{Z}/225\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{5}\right)$

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	−0.921098	−	0.389331i	$-0.872706\pi$
$2$	−1.76509	+	0.785867i	−1.24810	+	0.555692i	−0.327006	+	0.945022i	$0.606040\pi$
$3$	−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	−0.488960	−	0.872306i	$-0.662624\pi$
$7$	1.35187	−	2.34151i	0.510959	−	0.885007i	0.999919	−	0.0127012i	$-0.00404302\pi$
$8$	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	−0.516469	−	0.856306i	$-0.672754\pi$
$11$	−0.748543	+	0.333273i	−0.225694	+	0.100486i	0.290774	+	0.956792i	$0.406087\pi$
$12$	−2.98929	+	0.274272i	−0.862932	+	0.0791754i
$13$	−2.49560	−	1.11111i	−0.692155	−	0.308167i	0.0303436	−	0.999540i	$-0.490340\pi$
$13$	−2.49560	−	1.11111i	−0.692155	−	0.308167i	−0.722499	+	0.691372i	$0.757007\pi$
$14$	−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	−0.0454115	+	0.998968i	$0.514460\pi$
$17$	−2.45676	+	7.56113i	−0.595852	+	1.83384i	−0.550440	+	0.834875i	$0.685540\pi$
$18$	−2.76442	−	5.09470i	−0.651581	−	1.20083i
$19$	−2.21677	+	6.82252i	−0.508562	+	1.56519i	0.286136	+	0.958189i	$0.407629\pi$
$19$	−2.21677	+	6.82252i	−0.508562	+	1.56519i	−0.794698	+	0.607005i	$0.792371\pi$
$20$	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	0.948811	+	0.315846i	$0.102288\pi$
$23$	−0.215497	+	2.05032i	−0.0449343	+	0.427521i	−0.993745	+	0.111675i	$0.964378\pi$
$24$	−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	−0.328913	−	0.944360i	$-0.606682\pi$
$29$	−5.45784	−	1.16010i	−1.01350	−	0.215425i	−0.684583	+	0.728935i	$0.740016\pi$
$30$	−3.02228	+	6.84562i	−0.551791	+	1.24983i
$31$	6.92035	−	1.47097i	1.24293	−	0.264193i	0.460912	−	0.887446i	$-0.347523\pi$
$31$	6.92035	−	1.47097i	1.24293	−	0.264193i	0.782021	+	0.623253i	$0.214189\pi$
$32$	−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	−0.695472	−	0.718553i	$-0.744805\pi$
$37$	−1.38079	+	1.00320i	−0.227001	+	0.164926i	0.468472	+	0.883479i	$0.344805\pi$
$38$	−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	0.531197	−	0.847249i	$-0.321743\pi$
$41$	1.64566	+	0.732693i	0.257008	+	0.114427i	−0.274188	+	0.961676i	$0.588409\pi$
$42$	6.80359	−	5.96497i	1.04982	−	0.920415i
$43$	−4.43594	+	7.68327i	−0.676474	+	1.17169i	0.299562	+	0.954077i	$0.403160\pi$
$43$	−4.43594	+	7.68327i	−0.676474	+	1.17169i	−0.976036	+	0.217611i	$0.930174\pi$
$44$	−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	−0.0206937	−	0.999786i	$-0.506587\pi$
$47$	−3.05932	−	0.650279i	−0.446248	−	0.0948529i	−0.425554	+	0.904933i	$0.639921\pi$
$48$	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	0.984293	−	0.176540i	$-0.0564906\pi$
$53$	0.613099	+	1.88692i	0.0842156	+	0.259189i	−0.900078	+	0.435729i	$0.856491\pi$
$54$	−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	0.631584	−	0.775308i	$-0.282405\pi$
$59$	3.67181	+	1.63480i	0.478029	+	0.212832i	−0.153554	+	0.988140i	$0.549072\pi$
$60$	−0.0209650	−	6.71229i	−0.00270657	−	0.866553i
$61$	2.29219	−	1.02055i	0.293485	−	0.130668i	−0.254712	−	0.967017i	$-0.581981\pi$
$61$	2.29219	−	1.02055i	0.293485	−	0.130668i	0.548198	+	0.836349i	$0.315314\pi$
$62$	−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	−0.541143	−	0.840931i	$-0.682008\pi$
$67$	−5.67625	+	1.20652i	−0.693465	+	0.147400i	−0.152322	+	0.988331i	$0.548675\pi$
$68$	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	−0.927164	−	0.374656i	$-0.877761\pi$
$71$	−3.34762	−	10.3029i	−0.397290	−	1.22273i	0.529874	−	0.848076i	$-0.322239\pi$
$72$	1.50413	+	0.361538i	0.177264	+	0.0426077i
$73$	12.1616	+	8.83593i	1.42341	+	1.03417i	0.991197	+	0.132396i	$0.0422672\pi$
$73$	12.1616	+	8.83593i	1.42341	+	1.03417i	0.432213	+	0.901771i	$0.357733\pi$
$74$	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	0.582855	−	0.812576i	$-0.301936\pi$
$79$	6.97559	+	1.48271i	0.784815	+	0.166818i	0.201960	+	0.979394i	$0.435269\pi$
$80$	−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	0.833330	−	0.552775i	$-0.186431\pi$
$83$	1.78998	+	1.98798i	0.196476	+	0.218209i	−0.636854	+	0.770984i	$0.719765\pi$
$84$	−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	0.0615912	−	0.998101i	$-0.480382\pi$
$89$	−8.19461	−	5.95373i	−0.868627	−	0.631094i	−0.930218	+	0.367007i	$0.880382\pi$
$90$	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	−0.0951626	−	0.995462i	$-0.530337\pi$
$97$	−5.78117	−	1.22883i	−0.586989	−	0.124768i	−0.491826	+	0.870693i	$0.663670\pi$
$98$	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	−0.570927	−	0.821000i	$-0.693416\pi$
$101$	4.27666	−	7.40739i	0.425544	−	0.737063i	0.996471	+	0.0839375i	$0.0267496\pi$
$102$	−15.9218	+	21.3159i	−1.57649	+	2.11059i
$103$	0.723748	−	0.803804i	0.0713130	−	0.0792011i	−0.706432	−	0.707780i	$-0.749697\pi$
$103$	0.723748	−	0.803804i	0.0713130	−	0.0792011i	0.777745	+	0.628579i	$0.216363\pi$
$104$	−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	−0.819774	−	0.572687i	$-0.805901\pi$
$109$	−5.51708	+	4.00840i	−0.528441	+	0.383935i	0.291333	+	0.956622i	$0.405901\pi$
$110$	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	0.819927	−	0.572468i	$-0.194014\pi$
$113$	10.0257	+	4.46373i	0.943139	+	0.419912i	0.123212	+	0.992380i	$0.460681\pi$
$114$	−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	0.731912	−	0.681400i	$-0.238628\pi$
$127$	3.49392	+	2.53848i	0.310035	+	0.225254i	−0.421876	+	0.906653i	$0.638628\pi$
$128$	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	0.239958	−	0.970783i	$-0.422866\pi$
$131$	9.77474	−	2.07769i	0.854023	−	0.181528i	0.614065	+	0.789255i	$0.289533\pi$
$132$	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	−0.827797	−	0.561027i	$-0.810406\pi$
$137$	−1.57702	−	15.0043i	−0.134734	−	1.28190i	0.693064	−	0.720876i	$-0.256260\pi$
$138$	−2.88929	+	6.26514i	−0.245953	+	0.533324i
$139$	1.95191	−	18.5712i	0.165559	−	1.57519i	−0.524486	−	0.851419i	$-0.675743\pi$
$139$	1.95191	−	18.5712i	0.165559	−	1.57519i	0.690045	−	0.723766i	$-0.257591\pi$
$140$	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	0.984569	−	0.174996i	$-0.0559912\pi$
$149$	4.15919	+	7.20392i	0.340734	+	0.590168i	−0.643835	+	0.765164i	$0.722658\pi$
$150$	−14.6511	−	8.08263i	−1.19626	−	0.659944i
$151$	−4.97506	+	8.61706i	−0.404865	+	0.701247i	−0.994306	−	0.106565i	$-0.966015\pi$
$151$	−4.97506	+	8.61706i	−0.404865	+	0.701247i	0.589441	+	0.807812i	$0.299348\pi$
$152$	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	−0.980875	−	0.194638i	$-0.937647\pi$
$157$	−8.25724	−	14.3020i	−0.658999	−	1.14142i	0.321876	−	0.946782i	$-0.395687\pi$
$158$	−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	−0.380101	−	0.924945i	$-0.624111\pi$
$163$	4.87852	−	3.54446i	0.382115	−	0.277623i	0.762217	+	0.647322i	$0.224111\pi$
$164$	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	0.117144	−	0.993115i	$-0.462626\pi$
$167$	8.11680	−	1.72528i	0.628097	−	0.133506i	0.510953	+	0.859609i	$0.329293\pi$
$168$	−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	−0.600739	−	0.799445i	$-0.705127\pi$
$173$	−5.37441	+	2.39284i	−0.408609	+	0.181924i	0.192131	+	0.981369i	$0.438460\pi$
$174$	−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	−0.999201	−	0.0399587i	$-0.987277\pi$
$179$	−2.86737	−	8.82487i	−0.214318	−	0.659602i	0.784884	−	0.619643i	$-0.212723\pi$
$180$	−7.86624	+	8.56084i	−0.586315	+	0.638088i
$181$	−1.70671	+	5.25272i	−0.126859	+	0.390432i	−0.994235	−	0.107221i	$-0.965805\pi$
$181$	−1.70671	+	5.25272i	−0.126859	+	0.390432i	0.867376	+	0.497653i	$0.165805\pi$
$182$	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	0.991431	+	0.130630i	$0.0417001\pi$
$191$	0.674771	+	6.42002i	0.0488247	+	0.464536i	−0.942606	+	0.333906i	$0.891633\pi$
$192$	−1.93877	−	9.75369i	−0.139918	−	0.703912i
$193$	−1.85003	−	3.20434i	−0.133168	−	0.230653i	0.791728	−	0.610873i	$-0.209182\pi$
$193$	−1.85003	−	3.20434i	−0.133168	−	0.230653i	−0.924896	+	0.380220i	$0.875848\pi$
$194$	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	0.838079	+	0.545549i	$0.183679\pi$
$197$	6.74729	+	20.7660i	0.480724	+	1.47952i	−0.357355	+	0.933969i	$0.616321\pi$
$198$	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	−0.977642	−	0.210274i	$-0.932564\pi$
$211$	0.324720	−	3.08951i	0.0223547	−	0.212691i	0.999997	−	0.00241612i	$-0.000769075\pi$
$212$	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	0.158043	−	0.987432i	$-0.449481\pi$
$223$	14.8973	−	6.63273i	0.997600	−	0.444160i	0.839557	+	0.543272i	$0.182815\pi$
$224$	−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	−0.599829	−	0.800128i	$-0.704765\pi$
$227$	−6.12578	+	2.72737i	−0.406583	+	0.181022i	0.193247	+	0.981150i	$0.438098\pi$
$228$	4.75534	−	21.0025i	0.314930	−	1.39092i
$229$	−8.22313	+	9.13271i	−0.543400	+	0.603507i	−0.950824	−	0.309732i	$-0.899761\pi$
$229$	−8.22313	+	9.13271i	−0.543400	+	0.603507i	0.407424	+	0.913239i	$0.366427\pi$
$230$	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	0.319929	+	0.947442i	$0.396341\pi$
$233$	−7.56793	+	23.2917i	−0.495791	+	1.52589i	−0.815720	+	0.578447i	$0.803659\pi$
$234$	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	0.424282	+	0.905530i	$0.360527\pi$
$239$	−2.76725	+	26.3287i	−0.178999	+	1.70306i	−0.603280	+	0.797529i	$0.706140\pi$
$240$	12.8801	+	11.5247i	0.831407	+	0.743913i
$241$	−0.625085	−	5.94729i	−0.0402653	−	0.383098i	−0.996034	−	0.0889779i	$-0.971640\pi$
$241$	−0.625085	−	5.94729i	−0.0402653	−	0.383098i	0.955768	−	0.294121i	$-0.0950267\pi$
$242$	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	0.929857	−	0.367921i	$-0.119930\pi$
$257$	2.34536	+	4.06228i	0.146300	+	0.253398i	−0.783558	+	0.621319i	$0.786597\pi$
$258$	−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	−0.969517	−	0.245025i	$-0.921204\pi$
$263$	−1.16975	−	11.1294i	−0.0721298	−	0.686269i	0.897387	−	0.441244i	$-0.145463\pi$
$264$	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	−0.901315	−	0.433165i	$-0.857397\pi$
$269$	1.35264	−	4.16300i	0.0824720	−	0.253823i	0.983787	+	0.179342i	$0.0573969\pi$
$270$	−21.1829	−	7.43329i	−1.28915	−	0.452376i
$271$	−2.71988	−	8.37092i	−0.165221	−	0.508497i	0.833832	−	0.552019i	$-0.186142\pi$
$271$	−2.71988	−	8.37092i	−0.165221	−	0.508497i	−0.999052	+	0.0435216i	$0.986142\pi$
$272$	−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	−0.676616	−	0.736336i	$-0.736554\pi$
$277$	−9.68902	+	4.31383i	−0.582157	+	0.259193i	0.0944594	+	0.995529i	$0.469888\pi$
$278$	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	0.947115	+	0.320893i	$0.103983\pi$
$281$	19.5667	+	21.7310i	1.16725	+	1.29636i	0.220135	+	0.975470i	$0.429350\pi$
$282$	−8.99458	−	5.35285i	−0.535619	−	0.318757i
$283$	−5.64494	+	1.19987i	−0.335557	+	0.0713248i	−0.372609	−	0.927989i	$-0.621537\pi$
$283$	−5.64494	+	1.19987i	−0.335557	+	0.0713248i	0.0370520	+	0.999313i	$0.488203\pi$
$284$	−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	0.778229	−	0.627980i	$-0.216118\pi$
$293$	−2.64859	−	4.58748i	−0.154732	−	0.268004i	−0.932961	+	0.359976i	$0.882785\pi$
$294$	−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	−0.926308	−	0.376768i	$-0.877035\pi$
$311$	1.02447	−	9.74719i	0.0580924	−	0.552712i	0.984400	−	0.175944i	$-0.0562979\pi$
$312$	2.42967	−	0.222926i	0.137553	−	0.0126207i
$313$	−2.64290	−	25.1455i	−0.149385	−	1.42131i	−0.770427	−	0.637529i	$-0.779957\pi$
$313$	−2.64290	−	25.1455i	−0.149385	−	1.42131i	0.621041	−	0.783778i	$-0.286710\pi$
$314$	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	0.967182	−	0.254083i	$-0.0817736\pi$
$317$	10.9212	+	12.1292i	0.613393	+	0.681242i	−0.353789	+	0.935325i	$0.615107\pi$
$318$	−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	0.691185	−	0.722678i	$-0.257089\pi$
$331$	−1.81538	−	2.01618i	−0.0997823	−	0.110820i	−0.790967	+	0.611858i	$0.790422\pi$
$332$	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	0.997549	+	0.0699777i	$0.0222928\pi$
$337$	31.5207	+	14.0339i	1.71704	+	0.764477i	0.719494	+	0.694499i	$0.244374\pi$
$338$	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	−0.180376	−	0.983598i	$-0.557731\pi$
$347$	15.2132	−	16.8960i	0.816688	−	0.907024i	0.997064	+	0.0765735i	$0.0243980\pi$
$348$	16.6332	+	1.97094i	0.891635	+	0.105653i
$349$	−16.7926	+	29.0857i	−0.898890	+	1.55692i	−0.0699744	+	0.997549i	$0.522292\pi$
$349$	−16.7926	+	29.0857i	−0.898890	+	1.55692i	−0.828915	+	0.559374i	$0.811042\pi$
$350$	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	0.393030	−	0.919526i	$-0.371427\pi$
$353$	7.10339	+	1.50987i	0.378075	+	0.0803623i	−0.0149545	+	0.999888i	$0.504760\pi$
$354$	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	0.510079	−	0.860128i	$-0.329616\pi$
$359$	28.1506	−	20.4526i	1.48573	−	1.07945i	0.975653	−	0.219320i	$-0.0703837\pi$
$360$	−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	0.767645	−	0.640876i	$-0.221429\pi$
$367$	0.958614	+	1.06465i	0.0500392	+	0.0555742i	−0.717606	+	0.696450i	$0.754762\pi$
$368$	−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	0.516655	+	0.856194i	$0.327177\pi$
$373$	−3.21995	+	30.6357i	−0.166722	+	1.58626i	−0.683378	+	0.730065i	$0.739490\pi$
$374$	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	0.921205	+	0.389077i	$0.127206\pi$
$379$	7.87727	+	24.2437i	0.404628	+	1.24532i	−0.516577	+	0.856241i	$0.672794\pi$
$380$	−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	−0.138814	−	0.990318i	$-0.544329\pi$
$383$	2.68451	−	0.570611i	0.137172	−	0.0291568i	0.275986	+	0.961162i	$0.410996\pi$
$384$	−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	0.300463	−	0.953793i	$-0.402859\pi$
$389$	23.8712	−	10.6282i	1.21032	−	0.538869i	0.909856	+	0.414924i	$0.136192\pi$
$390$	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	0.955026	−	0.296521i	$-0.0958265\pi$
$397$	0.161451	+	0.496896i	0.00810301	+	0.0249385i	−0.946923	+	0.321460i	$0.895827\pi$
$398$	−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	0.984961	−	0.172776i	$-0.0552738\pi$
$401$	6.86560	+	11.8916i	0.342852	+	0.593837i	−0.642109	+	0.766613i	$0.721940\pi$
$402$	−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	−0.109371	−	0.994001i	$-0.534884\pi$
$409$	−18.6309	−	8.29503i	−0.921240	−	0.410163i	−0.811870	+	0.583838i	$0.801550\pi$
$410$	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	−0.896967	−	0.442097i	$-0.854235\pi$
$419$	−31.4528	+	6.68550i	−1.53657	+	0.326608i	−0.639603	+	0.768705i	$0.720901\pi$
$420$	−15.7452	−	9.02506i	−0.768288	−	0.440378i
$421$	7.32382	+	1.55673i	0.356941	+	0.0758702i	0.382892	−	0.923793i	$-0.374928\pi$
$421$	7.32382	+	1.55673i	0.356941	+	0.0758702i	−0.0259510	+	0.999663i	$0.508261\pi$
$422$	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	0.257350	+	0.966318i	$0.417151\pi$
$431$	−10.7714	+	33.1508i	−0.518838	+	1.59682i	−0.776188	+	0.630501i	$0.782849\pi$
$432$	19.6058	+	12.3814i	0.943284	+	0.595700i
$433$	−0.450743	+	1.38724i	−0.0216613	+	0.0666667i	−0.961303	−	0.275494i	$-0.911159\pi$
$433$	−0.450743	+	1.38724i	−0.0216613	+	0.0666667i	0.939642	+	0.342160i	$0.111159\pi$
$434$	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	0.0190810	−	0.999818i	$-0.493926\pi$
$439$	16.2351	−	7.22832i	0.774858	−	0.344989i	0.755777	+	0.654829i	$0.227259\pi$
$440$	−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	−0.998334	−	0.0576964i	$-0.981624\pi$
$443$	−9.45458	+	16.3758i	−0.449201	+	0.778038i	0.549134	+	0.835735i	$0.314958\pi$
$444$	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	0.483673	+	0.875249i	$0.339303\pi$
$457$	−11.0341	+	19.1116i	−0.516152	+	0.894001i	−0.999824	+	0.0187518i	$0.994031\pi$
$458$	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	−0.829459	−	0.558567i	$-0.811351\pi$
$461$	−20.8135	+	9.26675i	−0.969380	+	0.431596i	−0.139920	+	0.990163i	$0.544685\pi$
$462$	−3.10482	+	6.73249i	−0.144449	+	0.313224i
$463$	−7.78195	−	3.46475i	−0.361658	−	0.161020i	0.217860	−	0.975980i	$-0.430092\pi$
$463$	−7.78195	−	3.46475i	−0.361658	−	0.161020i	−0.579518	+	0.814960i	$0.696759\pi$
$464$	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	−0.926363	−	0.376632i	$-0.877082\pi$
$467$	0.960766	−	2.95693i	0.0444590	−	0.136831i	0.970822	+	0.239801i	$0.0770822\pi$
$468$	−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	0.582365	−	0.812927i	$-0.302127\pi$
$479$	17.1529	+	3.64596i	0.783735	+	0.166588i	0.201370	+	0.979515i	$0.435461\pi$
$480$	−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	−0.489007	−	0.872280i	$-0.662641\pi$
$487$	4.18121	−	3.03782i	0.189469	−	0.137657i	0.678476	+	0.734623i	$0.262641\pi$
$488$	−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	0.725470	−	0.688253i	$-0.241622\pi$
$491$	15.4984	+	6.90033i	0.699433	+	0.311408i	−0.0260375	+	0.999661i	$0.508289\pi$
$492$	−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	0.755877	−	0.654714i	$-0.227211\pi$
$499$	−4.22329	−	7.31496i	−0.189061	−	0.327463i	−0.944937	+	0.327251i	$0.893878\pi$
$500$	−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	−0.983695	−	0.179843i	$-0.942441\pi$
$503$	−6.58427	−	20.2643i	−0.293578	−	0.903541i	0.690117	−	0.723698i	$-0.257559\pi$
$504$	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	0.519925	−	0.854212i	$-0.325960\pi$
$509$	5.25717	+	2.34064i	0.233020	+	0.103747i	−0.286905	+	0.957959i	$0.592626\pi$
$510$	−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	0.909611	−	0.415460i	$-0.136379\pi$
$521$	−1.60876	−	4.95126i	−0.0704811	−	0.216918i	−0.980092	+	0.198542i	$0.936379\pi$
$522$	9.17743	+	31.0131i	0.401685	+	1.35741i
$523$	31.9268	+	23.1962i	1.39606	+	1.01430i	0.995169	+	0.0981735i	$0.0313000\pi$
$523$	31.9268	+	23.1962i	1.39606	+	1.01430i	0.400893	+	0.916125i	$0.368700\pi$
$524$	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	−0.502233	−	0.864732i	$-0.667488\pi$
$541$	3.83727	−	2.78794i	0.164977	−	0.119863i	0.667211	+	0.744869i	$0.267488\pi$
$542$	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	−0.633537	−	0.773713i	$-0.718397\pi$
$547$	−35.7135	−	7.59114i	−1.52700	−	0.324574i	−0.893462	+	0.449139i	$0.851731\pi$
$548$	−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	0.310845	−	0.950461i	$-0.399388\pi$
$563$	−4.44867	−	1.98067i	−0.187489	−	0.0834755i	−0.498334	+	0.866985i	$0.666055\pi$
$564$	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	−0.985706	−	0.168477i	$-0.946115\pi$
$569$	−25.0518	−	27.8228i	−1.05023	−	1.16639i	−0.0645199	−	0.997916i	$-0.520552\pi$
$570$	−40.0047	−	35.7948i	−1.67561	−	1.49928i
$571$	0.660086	−	0.733100i	0.0276237	−	0.0306793i	−0.729175	−	0.684328i	$-0.760096\pi$
$571$	0.660086	−	0.733100i	0.0276237	−	0.0306793i	0.756798	+	0.653648i	$0.226762\pi$
$572$	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	0.693113	−	0.720829i	$-0.256239\pi$
$577$	5.32656	+	3.86997i	0.221747	+	0.161109i	−0.471365	+	0.881938i	$0.656239\pi$
$578$	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	0.674682	+	0.738108i	$0.264281\pi$
$587$	4.07528	+	38.7737i	0.168205	+	1.60036i	−0.506477	+	0.862253i	$0.669053\pi$
$588$	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	−0.982109	−	0.188316i	$-0.939697\pi$
$599$	−16.0097	−	27.7297i	−0.654140	−	1.13300i	0.327968	−	0.944689i	$-0.393636\pi$
$600$	4.21949	−	1.46242i	0.172260	−	0.0597029i
$601$	−19.3911	+	33.5864i	−0.790981	+	1.37002i	0.134379	+	0.990930i	$0.457096\pi$
$601$	−19.3911	+	33.5864i	−0.790981	+	1.37002i	−0.925360	+	0.379089i	$0.876237\pi$
$602$	−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	0.753185	−	0.657809i	$-0.228517\pi$
$607$	−4.75715	−	8.23963i	−0.193087	−	0.334436i	−0.946272	+	0.323373i	$0.895183\pi$
$608$	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	−0.995771	−	0.0918649i	$-0.970717\pi$
$613$	−30.1095	+	21.8759i	−1.21611	+	0.883558i	−0.220342	+	0.975423i	$0.570717\pi$
$614$	−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	−0.228251	−	0.973602i	$-0.573301\pi$
$617$	−1.01266	+	0.215248i	−0.0407683	+	0.00866558i	0.187482	+	0.982268i	$0.439967\pi$
$618$	3.15841	−	1.76824i	0.127050	−	0.0711290i
$619$	8.59371	+	9.54428i	0.345410	+	0.383617i	0.890670	−	0.454650i	$-0.150236\pi$
$619$	8.59371	+	9.54428i	0.345410	+	0.383617i	−0.545260	+	0.838267i	$0.683569\pi$
$620$	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	−0.971455	−	0.237225i	$-0.923762\pi$
$631$	−1.15787	+	3.56357i	−0.0460943	+	0.141864i	0.925361	+	0.379088i	$0.123762\pi$
$632$	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	−0.999047	−	0.0436428i	$-0.986104\pi$
$641$	−0.782463	−	7.44463i	−0.0309054	−	0.294045i	0.968142	−	0.250403i	$-0.0805630\pi$
$642$	−35.5527	−	12.0739i	−1.40315	−	0.476517i
$643$	19.9559	+	34.5645i	0.786982	+	1.36309i	0.927808	+	0.373058i	$0.121691\pi$
$643$	19.9559	+	34.5645i	0.786982	+	1.36309i	−0.140826	+	0.990034i	$0.544976\pi$
$644$	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	0.923017	−	0.384759i	$-0.125715\pi$
$647$	−1.26863	−	3.90445i	−0.0498751	−	0.153500i	−0.972892	+	0.231259i	$0.925715\pi$
$648$	−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	−0.810936	−	0.585135i	$-0.801041\pi$
$653$	−3.68589	+	4.09359i	−0.144240	+	0.160195i	0.666696	+	0.745330i	$0.267708\pi$
$654$	−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	−0.999430	−	0.0337487i	$-0.989255\pi$
$659$	−0.740780	−	7.04805i	−0.0288567	−	0.274553i	0.970574	−	0.240804i	$-0.0774112\pi$
$660$	2.25272	+	5.01745i	0.0876869	+	0.195304i
$661$	−3.60565	+	34.3055i	−0.140243	+	1.33433i	0.667419	+	0.744682i	$0.267399\pi$
$661$	−3.60565	+	34.3055i	−0.140243	+	1.33433i	−0.807662	+	0.589645i	$0.799268\pi$
$662$	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	−0.866395	−	0.499359i	$-0.833569\pi$
$673$	−27.8887	+	12.4169i	−1.07503	+	0.478634i	−0.208635	+	0.977993i	$0.566902\pi$
$674$	−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	−0.571742	−	0.820433i	$-0.693732\pi$
$677$	−8.96654	+	3.99216i	−0.344612	+	0.153431i	0.227130	+	0.973864i	$0.427066\pi$
$678$	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	−0.576226	−	0.817290i	$-0.695475\pi$
$683$	9.67861	−	29.7877i	0.370342	−	1.13979i	0.946568	−	0.322504i	$-0.104525\pi$
$684$	−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	−0.921177	−	0.389144i	$-0.872771\pi$
$691$	−2.65596	−	25.2698i	−0.101037	−	0.961307i	0.820140	−	0.572164i	$-0.193896\pi$
$692$	−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	0.971406	+	0.237426i	$0.0763037\pi$
$709$	1.87963	+	17.8835i	0.0705912	+	0.671630i	−0.900814	+	0.434204i	$0.857030\pi$
$710$	−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	−0.995907	−	0.0903796i	$-0.971192\pi$
$719$	−3.67562	+	11.3124i	−0.137078	+	0.421881i	0.858830	+	0.512261i	$0.171192\pi$
$720$	−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	0.525848	−	0.850578i	$-0.323748\pi$
$727$	40.7090	−	18.1248i	1.50981	−	0.672212i	0.983964	+	0.178366i	$0.0570813\pi$
$728$	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	0.393683	−	0.919246i	$-0.371201\pi$
$733$	30.5184	−	6.48688i	1.12722	−	0.239598i	0.733539	+	0.679648i	$0.237867\pi$
$734$	−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	0.183752	−	0.982973i	$-0.441176\pi$
$739$	−18.8750	−	13.7135i	−0.694328	−	0.504459i	−0.878080	+	0.478514i	$0.841176\pi$
$740$	−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	−0.613783	−	0.789475i	$-0.710353\pi$
$743$	−27.0017	−	46.7683i	−0.990597	−	1.71576i	−0.376814	−	0.926289i	$-0.622980\pi$
$744$	−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	0.628167	−	0.778079i	$-0.283806\pi$
$751$	−9.85880	−	17.0759i	−0.359753	−	0.623110i	−0.987919	+	0.154969i	$0.950472\pi$
$752$	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	−0.979660	−	0.200665i	$-0.935690\pi$
$761$	0.560352	−	5.33140i	0.0203128	−	0.193263i	0.999973	+	0.00740241i	$0.00235628\pi$
$762$	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	+	0.619523i
$769$	27.7808	−	5.90499i	1.00180	−	0.212939i	0.322319	−	0.946631i	$-0.395538\pi$
$769$	27.7808	−	5.90499i	1.00180	−	0.212939i	0.679482	+	0.733692i	$0.262204\pi$
$770$	9.32840	−	2.14277i	0.336172	−	0.0772201i
$771$	1.79414	−	7.92399i	0.0646142	−	0.285376i
$772$	−6.27248	−	1.33326i	−0.225752	−	0.0479850i
$773$	29.0303	+	21.0917i	1.04415	+	0.758617i	0.971091	−	0.238711i	$-0.0767248\pi$
$773$	29.0303	+	21.0917i	1.04415	+	0.758617i	0.0730562	+	0.997328i	$0.476725\pi$
$774$	51.4068	+	1.35996i	1.84778	+	0.0488829i
$775$	−35.3559	+	1.15639i	−1.27002	+	0.0415388i
$776$	−1.52385	+	2.63939i	−0.0547031	+	0.0947486i
$777$	4.78312	−	6.40358i	0.171594	−	0.229727i
$778$	−33.7824	+	37.5192i	−1.21116	+	1.34513i
$779$	−8.64685	+	9.60330i	−0.309806	+	0.344074i
$780$	−7.40579	+	16.7745i	−0.265170	+	0.600623i
$781$	5.93953	+	6.59652i	0.212533	+	0.236042i
$782$	31.6682			1.13245
$783$	−22.2988	+	18.5305i	−0.796894	+	0.662226i
$784$	1.11998	−	0.813715i	0.0399994	−	0.0290613i
$785$	33.4849	−	15.5692i	1.19513	−	0.555689i
$786$	33.2100	+	3.93519i	1.18456	+	0.140364i
$787$	−2.73474	−	1.21759i	−0.0974830	−	0.0434022i	0.357416	−	0.933945i	$-0.383658\pi$
$787$	−2.73474	−	1.21759i	−0.0974830	−	0.0434022i	−0.454899	+	0.890543i	$0.650325\pi$
$788$	34.5704	+	15.3917i	1.23152	+	0.548307i
$789$	−11.5993	+	15.5291i	−0.412948	+	0.552849i
$790$	−3.72103	−	30.5849i	−0.132388	−	1.08816i
$791$	24.0053	−	17.4409i	0.853531	−	0.620126i
$792$	−1.24640	+	0.230660i	−0.0442889	+	0.00819615i
$793$	−6.85435			−0.243405
$794$	−0.675470	−	0.750185i	−0.0239715	−	0.0266231i
$795$	6.66660	+	3.82125i	0.236440	+	0.135526i
$796$	18.9032	−	20.9942i	0.670007	−	0.744118i
$797$	32.2463	−	35.8132i	1.14222	−	1.26857i	0.183879	−	0.982949i	$-0.441134\pi$
$797$	32.2463	−	35.8132i	1.14222	−	1.26857i	0.958344	−	0.285618i	$-0.0921989\pi$
$798$	25.6141	+	59.6406i	0.906730	+	2.11125i
$799$	12.4329	−	21.5343i	0.439843	−	0.761830i
$800$	12.9023	+	35.6941i	0.456165	+	1.26198i
$801$	15.8843	−	25.9052i	0.561243	−	0.915313i
$802$	−21.4636	−	15.5942i	−0.757905	−	0.550650i
$803$	−12.0483	−	2.56094i	−0.425175	−	0.0903736i
$804$	16.6370	−	5.16348i	0.586742	−	0.182102i
$805$	−8.18751	+	9.39765i	−0.288572	+	0.331224i
$806$	36.5266	−	7.76396i	1.28659	−	0.273474i
$807$	−6.61541	+	3.70364i	−0.232874	+	0.130374i
$808$	−2.95126	−	3.27770i	−0.103825	−	0.115309i
$809$	−10.6882	+	7.76542i	−0.375776	+	0.273018i	−0.759602	−	0.650388i	$-0.774606\pi$
$809$	−10.6882	+	7.76542i	−0.375776	+	0.273018i	0.383826	+	0.923406i	$0.374606\pi$
$810$	18.1982	+	34.3619i	0.639418	+	1.20735i
$811$	−19.9495	−	14.4942i	−0.700522	−	0.508959i	0.179581	−	0.983743i	$-0.442526\pi$
$811$	−19.9495	−	14.4942i	−0.700522	−	0.508959i	−0.880102	+	0.474785i	$0.842526\pi$
$812$	2.73303	+	26.0030i	0.0959104	+	0.912526i
$813$	−6.38433	+	13.8438i	−0.223908	+	0.485523i
$814$	−0.282441	+	2.68725i	−0.00989955	+	0.0941880i
$815$	6.93194	+	11.5656i	0.242815	+	0.405127i
$816$	35.4590	+	50.1876i	1.24131	+	1.75692i
$817$	−42.5858	−	47.2963i	−1.48989	−	1.65469i
$818$	39.4040			1.37773
$819$	−14.3860	−	16.8530i	−0.502686	−	0.588891i
$820$	2.26551	+	6.60322i	0.0791150	+	0.230594i
$821$	37.2526	+	7.91828i	1.30012	+	0.276350i	0.805416	−	0.592709i	$-0.201942\pi$
$821$	37.2526	+	7.91828i	1.30012	+	0.276350i	0.494708	+	0.869059i	$0.335275\pi$
$822$	11.1494	−	49.2427i	0.388881	−	1.71754i
$823$	1.35340	−	12.8767i	0.0471765	−	0.448854i	−0.945280	−	0.326259i	$-0.894212\pi$
$823$	1.35340	−	12.8767i	0.0471765	−	0.448854i	0.992457	−	0.122595i	$-0.0391216\pi$
$824$	−0.278874	−	0.483024i	−0.00971504	−	0.0168269i
$825$	−6.21329	−	3.42771i	−0.216319	−	0.119338i
$826$	−10.4984	+	18.1837i	−0.365285	+	0.632691i
$827$	12.8319	+	9.32289i	0.446207	+	0.324189i	0.788097	−	0.615552i	$-0.211067\pi$
$827$	12.8319	+	9.32289i	0.446207	+	0.324189i	−0.341889	+	0.939740i	$0.611067\pi$
$828$	−7.38058	+	7.77332i	−0.256493	+	0.270142i
$829$	11.3136	+	34.8198i	0.392939	+	1.20934i	0.930555	+	0.366151i	$0.119325\pi$
$829$	11.3136	+	34.8198i	0.392939	+	1.20934i	−0.537617	+	0.843189i	$0.680675\pi$
$830$	5.61429	−	10.1021i	0.194875	−	0.350649i
$831$	17.3944	+	5.90720i	0.603404	+	0.204918i
$832$	−7.84219	−	13.5831i	−0.271879	−	0.470909i
$833$	2.41244	−	0.512779i	0.0835860	−	0.0177667i
$834$	26.1703	−	56.7477i	0.906203	−	1.96501i
$835$	2.24095	+	18.4194i	0.0775511	+	0.637428i
$836$	−8.24157	−	5.98785i	−0.285041	−	0.207094i
$837$	16.2730	−	32.9648i	0.562476	−	1.13943i
$838$	50.2630	−	36.5182i	1.73631	−	1.26150i
$839$	−44.1950	+	19.6769i	−1.52578	+	0.679322i	−0.986643	−	0.162895i	$-0.947917\pi$
$839$	−44.1950	+	19.6769i	−1.52578	+	0.679322i	−0.539139	+	0.842217i	$0.681250\pi$
$840$	−5.37189	−	0.547650i	−0.185348	−	0.0188957i
$841$	1.94941	+	0.867935i	0.0672211	+	0.0299288i
$842$	−14.1505	+	3.00779i	−0.487660	+	0.103655i
$843$	0.669776	−	50.6441i	0.0230683	−	1.74428i
$844$	−3.60257	−	4.00106i	−0.124006	−	0.137722i
$845$	9.89695	−	7.44074i	0.340465	−	0.255969i
$846$	5.14428	+	17.3840i	0.176864	+	0.597673i
$847$	8.62958	+	26.5591i	0.296516	+	0.912582i
$848$	−8.08836	+	3.60117i	−0.277756	+	0.123665i
$849$	8.58973	+	5.11191i	0.294799	+	0.175440i
$850$	−5.52700	+	76.6052i	−0.189574	+	2.62754i
$851$	−1.75933	−	3.04725i	−0.0603091	−	0.104458i
$852$	12.8328	+	29.8802i	0.439645	+	1.02368i
$853$	28.6661	+	6.09317i	0.981510	+	0.208626i	0.670605	−	0.741815i	$-0.266035\pi$
$853$	28.6661	+	6.09317i	0.981510	+	0.208626i	0.310905	+	0.950441i	$0.399368\pi$
$854$	4.05046	+	12.4660i	0.138604	+	0.426579i
$855$	15.3321	−	45.6143i	0.524346	−	1.55998i
$856$	−1.78782	+	5.50233i	−0.0611063	+	0.188066i
$857$	−2.37131	+	4.10724i	−0.0810025	+	0.140300i	−0.903681	−	0.428207i	$-0.859146\pi$
$857$	−2.37131	+	4.10724i	−0.0810025	+	0.140300i	0.822678	+	0.568507i	$0.192479\pi$
$858$	7.09294	+	2.40879i	0.242149	+	0.0822348i
$859$	25.3873	+	11.3031i	0.866202	+	0.385658i	0.791224	−	0.611527i	$-0.209444\pi$
$859$	25.3873	+	11.3031i	0.866202	+	0.385658i	0.0749788	+	0.997185i	$0.476111\pi$
$860$	−33.5090	+	7.69716i	−1.14265	+	0.262471i
$861$	−8.37735	−	0.992667i	−0.285499	−	0.0338300i
$862$	−7.03977	−	66.9789i	−0.239775	−	2.28131i
$863$	−14.3996	+	10.4619i	−0.490167	+	0.356127i	−0.805249	−	0.592937i	$-0.797968\pi$
$863$	−14.3996	+	10.4619i	−0.490167	+	0.356127i	0.315081	+	0.949065i	$0.397968\pi$
$864$	−39.0329	−	5.67558i	−1.32793	−	0.193087i
$865$	−4.26904	−	12.4429i	−0.145152	−	0.423070i
$866$	−0.294589	−	2.80283i	−0.0100105	−	0.0952440i
$867$	15.6029	+	78.4960i	0.529901	+	2.66586i
$868$	−16.5762	−	28.7109i	−0.562635	−	0.974512i
$869$	−5.71568	+	1.21490i	−0.193891	+	0.0412128i
$870$	24.4368	−	33.8562i	0.828484	−	1.14783i
$871$	15.5062	+	3.29595i	0.525409	+	0.111679i
$872$	1.08667	+	3.34441i	0.0367992	+	0.113256i
$873$	2.31908	−	17.5787i	0.0784890	−	0.594947i
$874$	28.5747			0.966553
$875$	−21.3039	−	21.4457i	−0.720205	−	0.724998i
$876$	−38.7780	−	23.0775i	−1.31019	−	0.779718i
$877$	5.05264	−	48.0727i	0.170616	−	1.62330i	−0.489409	−	0.872054i	$-0.662787\pi$
$877$	5.05264	−	48.0727i	0.170616	−	1.62330i	0.660024	−	0.751244i	$-0.270546\pi$
$878$	−22.9758	+	25.5172i	−0.775396	+	0.861165i
$879$	−2.02609	+	8.94846i	−0.0683385	+	0.301824i
$880$	7.41402	−	3.44724i	0.249927	−	0.116206i
$881$	−5.26492	+	16.2037i	−0.177380	+	0.545918i	−0.999734	−	0.0230573i	$-0.992660\pi$
$881$	−5.26492	+	16.2037i	−0.177380	+	0.545918i	0.822355	+	0.568975i	$0.192660\pi$
$882$	−0.939947	+	1.53293i	−0.0316497	+	0.0516164i
$883$	7.62570	−	23.4695i	0.256625	−	0.789811i	−0.736880	−	0.676024i	$-0.763702\pi$
$883$	7.62570	−	23.4695i	0.256625	−	0.789811i	0.993505	−	0.113788i	$-0.0362984\pi$
$884$	−3.93448	−	37.4340i	−0.132331	−	1.25904i
$885$	14.7897	−	4.85659i	0.497150	−	0.163252i
$886$	3.81894	−	36.3347i	0.128300	−	1.22069i
$887$	11.6952	+	5.20706i	0.392688	+	0.174836i	0.593575	−	0.804778i	$-0.297716\pi$
$887$	11.6952	+	5.20706i	0.392688	+	0.174836i	−0.200887	+	0.979614i	$0.564383\pi$
$888$	0.638382	−	1.38427i	0.0214227	−	0.0464530i
$889$	10.6672	−	4.74935i	0.357767	−	0.159288i
$890$	−12.8409	+	41.8351i	−0.430426	+	1.40231i
$891$	6.18689	−	4.01308i	0.207269	−	0.134443i
$892$	8.73350	−	26.8789i	0.292419	−	0.899973i
$893$	11.2184	−	19.4308i	0.375408	−	0.650226i
$894$	5.42721	+	27.3036i	0.181513	+	0.913169i
$895$	20.2219	−	4.64505i	0.675943	−	0.155267i
$896$	7.39680	−	8.21498i	0.247110	−	0.274443i
$897$	−9.31629	+	2.89141i	−0.311062	+	0.0965415i
$898$	−27.9348	+	12.4374i	−0.932196	+	0.415040i
$899$	−39.4767			−1.31662
$900$	−17.5155	−	19.2103i	−0.583851	−	0.640343i
$901$	−15.7735			−0.525492
$902$	2.60532	−	1.15996i	0.0867477	−	0.0386226i
$903$	9.17480	−	40.5215i	0.305318	−	1.34847i
$904$	3.78667	−	4.20552i	0.125943	−	0.139874i
$905$	−11.3628	−	4.83805i	−0.377712	−	0.160822i
$906$	−25.0381	+	21.9519i	−0.831835	+	0.729302i
$907$	−7.73118	+	13.3908i	−0.256710	+	0.444634i	−0.965358	−	0.260927i	$-0.915972\pi$
$907$	−7.73118	+	13.3908i	−0.256710	+	0.444634i	0.708649	+	0.705561i	$0.249305\pi$
$908$	−3.59121	+	11.0526i	−0.119179	+	0.366794i
$909$	23.1573	+	11.0531i	0.768080	+	0.366609i
$910$	26.1191	+	18.3319i	0.865841	+	0.607696i
$911$	16.7164	−	7.44262i	0.553839	−	0.246585i	−0.110680	−	0.993856i	$-0.535303\pi$
$911$	16.7164	−	7.44262i	0.553839	−	0.246585i	0.664519	+	0.747271i	$0.268636\pi$
$912$	31.9951	+	45.2850i	1.05947	+	1.49954i
$913$	−2.00242	−	0.891535i	−0.0662704	−	0.0295055i
$914$	4.45693	−	42.4048i	0.147422	−	1.40263i
$915$	3.92483	−	8.88993i	0.129751	−	0.293892i
$916$	2.22632	+	21.1820i	0.0735598	+	0.699874i
$917$	8.34927	−	25.6964i	0.275717	−	0.848570i
$918$	−67.4866	−	42.6190i	−2.22739	−	1.40664i
$919$	1.81787	−	5.59482i	0.0599659	−	0.184556i	−0.916586	−	0.399837i	$-0.869067\pi$
$919$	1.81787	−	5.59482i	0.0599659	−	0.184556i	0.976552	+	0.215281i	$0.0690667\pi$
$920$	−1.15476	+	2.07781i	−0.0380712	+	0.0685035i
$921$	−1.73552	−	1.60473i	−0.0571874	−	0.0528777i
$922$	29.4551	−	32.7132i	0.970052	−	1.07735i
$923$	−3.09338	+	29.4316i	−0.101820	+	0.968752i
$924$	0.0879433	−	6.64970i	0.00289312	−	0.218759i
$925$	7.67835	−	3.72399i	0.252463	−	0.122444i
$926$	16.4586			0.540864
$927$	2.57380	+	1.97605i	0.0845347	+	0.0649019i
$928$	13.0885	+	40.2824i	0.429653	+	1.32234i
$929$	1.18051	+	0.250926i	0.0387314	+	0.00823262i	0.227237	−	0.973840i	$-0.427031\pi$
$929$	1.18051	+	0.250926i	0.0387314	+	0.00823262i	−0.188505	+	0.982072i	$0.560364\pi$
$930$	−10.8456	+	51.8198i	−0.355641	+	1.69924i
$931$	2.17678	−	0.462688i	0.0713410	−	0.0151640i
$932$	21.2223	+	36.7580i	0.695158	+	1.20405i
$933$	−12.7644	+	11.1911i	−0.417889	+	0.366380i
$934$	0.627922	+	5.97428i	0.0205462	+	0.195484i
$935$	14.5645	−	0.238117i	0.476308	−	0.00778727i
$936$	−3.35201	−	2.57352i	−0.109564	−	0.0841181i
$937$	35.0428	−	25.4601i	1.14480	−	0.831745i	0.157018	−	0.987596i	$-0.449812\pi$
$937$	35.0428	−	25.4601i	1.14480	−	0.831745i	0.987781	+	0.155851i	$0.0498120\pi$
$938$	−3.16878	−	30.1490i	−0.103464	−	0.984399i
$939$	−26.2072	+	35.0859i	−0.855241	+	1.14499i
$940$	−6.23120	−	10.3965i	−0.203239	−	0.339096i
$941$	17.6872	+	7.87485i	0.576586	+	0.256713i	0.674246	−	0.738507i	$-0.264469\pi$
$941$	17.6872	+	7.87485i	0.576586	+	0.256713i	−0.0976595	+	0.995220i	$0.531136\pi$
$942$	−10.7746	−	54.2059i	−0.351057	−	1.76612i
$943$	−1.85689	+	3.21622i	−0.0604686	+	0.104735i
$944$	−5.54262	+	17.0584i	−0.180397	+	0.555205i
$945$	30.0954	−	9.00819i	0.979003	−	0.293036i
$946$	4.34031	+	13.3581i	0.141115	+	0.434309i
$947$	25.9173	+	5.50890i	0.842200	+	0.179015i	0.608758	−	0.793356i	$-0.291668\pi$
$947$	25.9173	+	5.50890i	0.842200	+	0.179015i	0.233442	+	0.972371i	$0.425001\pi$
$948$	−21.2587	−	2.51903i	−0.690450	−	0.0818142i
$949$	−20.5328	−	35.5639i	−0.666524	−	1.15445i
$950$	−4.98709	+	69.1221i	−0.161803	+	2.24262i
$951$	0.373836	−	28.2670i	0.0121225	−	0.916622i
$952$	10.1260	−	4.50838i	0.328185	−	0.146117i
$953$	7.07575	+	21.7769i	0.229206	+	0.705424i	0.997837	+	0.0657319i	$0.0209382\pi$
$953$	7.07575	+	21.7769i	0.229206	+	0.705424i	−0.768631	+	0.639692i	$0.779062\pi$
$954$	7.91845	−	8.33981i	0.256369	−	0.270011i
$955$	−14.4327	+	0.235964i	−0.467033	+	0.00763562i
$956$	30.7010	+	34.0969i	0.992941	+	1.10277i
$957$	−6.80500	−	4.04979i	−0.219974	−	0.130911i
$958$	−33.1415	+	7.04445i	−1.07075	+	0.227596i
$959$	−37.2646	−	16.5913i	−1.20334	−	0.535760i
$960$	22.1074	−	2.39342i	0.713514	−	0.0772472i
$961$	17.4076	−	7.75038i	0.561537	−	0.250012i
$962$	−7.28801	+	5.29505i	−0.234975	+	0.170719i
$963$	−2.63183	−	33.5559i	−0.0848094	−	1.08132i
$964$	−8.38474	−	6.09187i	−0.270054	−	0.196206i
$965$	7.50226	−	3.48827i	0.241506	−	0.112291i
$966$	10.7639	+	15.2350i	0.346324	+	0.490177i
$967$	−56.6305	+	12.0372i	−1.82111	+	0.387090i	−0.986502	−	0.163749i	$-0.947641\pi$
$967$	−56.6305	+	12.0372i	−1.82111	+	0.387090i	−0.834612	+	0.550839i	$0.814308\pi$
$968$	2.66302	+	4.61248i	0.0855925	+	0.148251i
$969$	19.2585	+	96.8869i	0.618671	+	3.11246i
$970$	3.08388	+	25.3479i	0.0990175	+	0.813871i
$971$	−11.4709	−	35.3038i	−0.368119	−	1.13295i	−0.948005	−	0.318255i	$-0.896903\pi$
$971$	−11.4709	−	35.3038i	−0.368119	−	1.13295i	0.579886	−	0.814697i	$-0.303097\pi$
$972$	26.1898	−	6.63262i	0.840037	−	0.212741i
$973$	−40.8458	−	29.6762i	−1.30946	−	0.951376i
$974$	−4.99286	+	8.64789i	−0.159982	+	0.277096i
$975$	−5.36837	−	23.0407i	−0.171925	−	0.737894i
$976$	5.59853	+	9.69693i	0.179204	+	0.310391i
$977$	−1.59806	+	15.2045i	−0.0511264	+	0.486436i	0.938760	+	0.344572i	$0.111976\pi$
$977$	−1.59806	+	15.2045i	−0.0511264	+	0.486436i	−0.989886	+	0.141863i	$0.954691\pi$
$978$	19.2734	−	5.98170i	0.616294	−	0.191274i
$979$	8.11824	+	1.72559i	0.259460	+	0.0551499i
$980$	0.352765	−	1.14930i	0.0112687	−	0.0367130i
$981$	−13.2825	−	15.5603i	−0.424079	−	0.496803i
$982$	−32.7787			−1.04601
$983$	17.4517	+	19.3821i	0.556623	+	0.618192i	0.954125	−	0.299409i	$-0.0967896\pi$
$983$	17.4517	+	19.3821i	0.556623	+	0.618192i	−0.397502	+	0.917601i	$0.630123\pi$
$984$	−1.60218	+	0.147002i	−0.0510755	+	0.00468626i
$985$	−47.5846	+	10.9304i	−1.51617	+	0.348271i
$986$	−8.95916	+	85.2407i	−0.285318	+	2.71462i
$987$	14.5857	−	1.33826i	0.464267	−	0.0425972i
$988$	−3.55014	−	33.7773i	−0.112945	−	1.07460i
$989$	−14.7972	−	10.7508i	−0.470524	−	0.341856i
$990$	−7.18559	+	7.82009i	−0.228373	+	0.248539i
$991$	23.1924	−	16.8503i	0.736731	−	0.535266i	−0.154955	−	0.987922i	$-0.549523\pi$
$991$	23.1924	−	16.8503i	0.736731	−	0.535266i	0.891686	+	0.452655i	$0.149523\pi$
$992$	−35.9358	−	39.9107i	−1.14096	−	1.26717i
$993$	−0.0621413	+	4.69872i	−0.00197199	+	0.149109i
$994$	55.3553	−	11.7661i	1.75576	−	0.373199i
$995$	−3.21686	+	36.3066i	−0.101981	+	1.15100i
$996$	−5.89602	−	5.45169i	−0.186822	−	0.172743i
$997$	16.9658	+	3.60618i	0.537311	+	0.114209i	0.468571	−	0.883426i	$-0.344769\pi$
$997$	16.9658	+	3.60618i	0.537311	+	0.114209i	0.0687396	+	0.997635i	$0.478102\pi$
$998$	13.2031	+	9.59259i	0.417936	+	0.303648i
$999$	−0.351751	+	8.86157i	−0.0111289	+	0.280368i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	225.2.q.a.16.6	✓	224
3.2	odd	2		675.2.r.a.316.23		224
9.4	even	3	inner	225.2.q.a.166.23	yes	224
9.5	odd	6		675.2.r.a.91.6		224
25.11	even	5	inner	225.2.q.a.61.23	yes	224
75.11	odd	10		675.2.r.a.586.6		224
225.86	odd	30		675.2.r.a.361.23		224
225.211	even	15	inner	225.2.q.a.211.6	yes	224

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
225.2.q.a.16.6	✓	224	1.1	even	1	trivial
225.2.q.a.61.23	yes	224	25.11	even	5	inner
225.2.q.a.166.23	yes	224	9.4	even	3	inner
225.2.q.a.211.6	yes	224	225.211	even	15	inner
675.2.r.a.91.6		224	9.5	odd	6
675.2.r.a.316.23		224	3.2	odd	2
675.2.r.a.361.23		224	225.86	odd	30
675.2.r.a.586.6		224	75.11	odd	10

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

Introduction

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