LMFDB - Embedded newform 462.2.g.a.419.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [462,2,Mod(419,462)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(462, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 1, 0]))

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

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

chi := DirichletCharacter("462.419");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 462 = 2 \cdot 3 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	462.g (of order $2$, degree $1$, 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:	$3.68908857338$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(i, \sqrt{5})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 3x^{2} + 1 $ x^4 + 3*x^2 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			419.1
Root			$-0.618034i$ of defining polynomial
Character	$\chi$	$=$	462.419
Dual form			462.2.g.a.419.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000i q^{2} +(-1.61803 + 0.618034i) q^{3} -1.00000 q^{4} -3.23607 q^{5} +(0.618034 + 1.61803i) q^{6} +(0.381966 + 2.61803i) q^{7} +1.00000i q^{8} +(2.23607 - 2.00000i) q^{9} +O(q^{10})$	\(q-1.00000i q^{2} +(-1.61803 + 0.618034i) q^{3} -1.00000 q^{4} -3.23607 q^{5} +(0.618034 + 1.61803i) q^{6} +(0.381966 + 2.61803i) q^{7} +1.00000i q^{8} +(2.23607 - 2.00000i) q^{9} +3.23607i q^{10} +1.00000i q^{11} +(1.61803 - 0.618034i) q^{12} -6.00000i q^{13} +(2.61803 - 0.381966i) q^{14} +(5.23607 - 2.00000i) q^{15} +1.00000 q^{16} +7.23607 q^{17} +(-2.00000 - 2.23607i) q^{18} -2.00000i q^{19} +3.23607 q^{20} +(-2.23607 - 4.00000i) q^{21} +1.00000 q^{22} -1.23607i q^{23} +(-0.618034 - 1.61803i) q^{24} +5.47214 q^{25} -6.00000 q^{26} +(-2.38197 + 4.61803i) q^{27} +(-0.381966 - 2.61803i) q^{28} -0.472136i q^{29} +(-2.00000 - 5.23607i) q^{30} -0.763932i q^{31} -1.00000i q^{32} +(-0.618034 - 1.61803i) q^{33} -7.23607i q^{34} +(-1.23607 - 8.47214i) q^{35} +(-2.23607 + 2.00000i) q^{36} -4.47214 q^{37} -2.00000 q^{38} +(3.70820 + 9.70820i) q^{39} -3.23607i q^{40} +12.1803 q^{41} +(-4.00000 + 2.23607i) q^{42} +10.9443 q^{43} -1.00000i q^{44} +(-7.23607 + 6.47214i) q^{45} -1.23607 q^{46} +1.52786 q^{47} +(-1.61803 + 0.618034i) q^{48} +(-6.70820 + 2.00000i) q^{49} -5.47214i q^{50} +(-11.7082 + 4.47214i) q^{51} +6.00000i q^{52} -7.70820i q^{53} +(4.61803 + 2.38197i) q^{54} -3.23607i q^{55} +(-2.61803 + 0.381966i) q^{56} +(1.23607 + 3.23607i) q^{57} -0.472136 q^{58} +3.23607 q^{59} +(-5.23607 + 2.00000i) q^{60} +3.52786i q^{61} -0.763932 q^{62} +(6.09017 + 5.09017i) q^{63} -1.00000 q^{64} +19.4164i q^{65} +(-1.61803 + 0.618034i) q^{66} +1.52786 q^{67} -7.23607 q^{68} +(0.763932 + 2.00000i) q^{69} +(-8.47214 + 1.23607i) q^{70} +6.18034i q^{71} +(2.00000 + 2.23607i) q^{72} -14.1803i q^{73} +4.47214i q^{74} +(-8.85410 + 3.38197i) q^{75} +2.00000i q^{76} +(-2.61803 + 0.381966i) q^{77} +(9.70820 - 3.70820i) q^{78} +7.23607 q^{79} -3.23607 q^{80} +(1.00000 - 8.94427i) q^{81} -12.1803i q^{82} +6.00000 q^{83} +(2.23607 + 4.00000i) q^{84} -23.4164 q^{85} -10.9443i q^{86} +(0.291796 + 0.763932i) q^{87} -1.00000 q^{88} -12.9443 q^{89} +(6.47214 + 7.23607i) q^{90} +(15.7082 - 2.29180i) q^{91} +1.23607i q^{92} +(0.472136 + 1.23607i) q^{93} -1.52786i q^{94} +6.47214i q^{95} +(0.618034 + 1.61803i) q^{96} +2.47214i q^{97} +(2.00000 + 6.70820i) q^{98} +(2.00000 + 2.23607i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 2 q^{3} - 4 q^{4} - 4 q^{5} - 2 q^{6} + 6 q^{7}+O(q^{10}) $ 4 * q - 2 * q^3 - 4 * q^4 - 4 * q^5 - 2 * q^6 + 6 * q^7	$ 4 q - 2 q^{3} - 4 q^{4} - 4 q^{5} - 2 q^{6} + 6 q^{7} + 2 q^{12} + 6 q^{14} + 12 q^{15} + 4 q^{16} + 20 q^{17} - 8 q^{18} + 4 q^{20} + 4 q^{22} + 2 q^{24} + 4 q^{25} - 24 q^{26} - 14 q^{27} - 6 q^{28} - 8 q^{30} + 2 q^{33} + 4 q^{35} - 8 q^{38} - 12 q^{39} + 4 q^{41} - 16 q^{42} + 8 q^{43} - 20 q^{45} + 4 q^{46} + 24 q^{47} - 2 q^{48} - 20 q^{51} + 14 q^{54} - 6 q^{56} - 4 q^{57} + 16 q^{58} + 4 q^{59} - 12 q^{60} - 12 q^{62} + 2 q^{63} - 4 q^{64} - 2 q^{66} + 24 q^{67} - 20 q^{68} + 12 q^{69} - 16 q^{70} + 8 q^{72} - 22 q^{75} - 6 q^{77} + 12 q^{78} + 20 q^{79} - 4 q^{80} + 4 q^{81} + 24 q^{83} - 40 q^{85} + 28 q^{87} - 4 q^{88} - 16 q^{89} + 8 q^{90} + 36 q^{91} - 16 q^{93} - 2 q^{96} + 8 q^{98} + 8 q^{99}+O(q^{100}) $ 4 * q - 2 * q^3 - 4 * q^4 - 4 * q^5 - 2 * q^6 + 6 * q^7 + 2 * q^12 + 6 * q^14 + 12 * q^15 + 4 * q^16 + 20 * q^17 - 8 * q^18 + 4 * q^20 + 4 * q^22 + 2 * q^24 + 4 * q^25 - 24 * q^26 - 14 * q^27 - 6 * q^28 - 8 * q^30 + 2 * q^33 + 4 * q^35 - 8 * q^38 - 12 * q^39 + 4 * q^41 - 16 * q^42 + 8 * q^43 - 20 * q^45 + 4 * q^46 + 24 * q^47 - 2 * q^48 - 20 * q^51 + 14 * q^54 - 6 * q^56 - 4 * q^57 + 16 * q^58 + 4 * q^59 - 12 * q^60 - 12 * q^62 + 2 * q^63 - 4 * q^64 - 2 * q^66 + 24 * q^67 - 20 * q^68 + 12 * q^69 - 16 * q^70 + 8 * q^72 - 22 * q^75 - 6 * q^77 + 12 * q^78 + 20 * q^79 - 4 * q^80 + 4 * q^81 + 24 * q^83 - 40 * q^85 + 28 * q^87 - 4 * q^88 - 16 * q^89 + 8 * q^90 + 36 * q^91 - 16 * q^93 - 2 * q^96 + 8 * q^98 + 8 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/462\mathbb{Z}\right)^\times$.

$n$	$155$	$199$	$211$
$\chi(n)$	$-1$	$-1$	$1$

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 $

$2$		−	1.00000i		−	0.707107i
$2$		−	1.00000i		−	0.707107i
$3$	−1.61803	+	0.618034i	−0.934172	+	0.356822i
$3$	−1.61803	+	0.618034i	−0.934172	+	0.356822i
$4$	−1.00000			−0.500000
$5$	−3.23607			−1.44721			−0.723607	−	0.690212i	$-0.757517\pi$
$5$	−3.23607			−1.44721			−0.723607	+	0.690212i	$0.757517\pi$
$6$	0.618034	+	1.61803i	0.252311	+	0.660560i
$7$	0.381966	+	2.61803i	0.144370	+	0.989524i
$7$	0.381966	+	2.61803i	0.144370	+	0.989524i
$8$			1.00000i			0.353553i
$9$	2.23607	−	2.00000i	0.745356	−	0.666667i
$10$			3.23607i			1.02333i
$11$			1.00000i			0.301511i
$11$			1.00000i			0.301511i
$12$	1.61803	−	0.618034i	0.467086	−	0.178411i
$13$		−	6.00000i		−	1.66410i	−0.554700	−	0.832050i	$-0.687167\pi$
$13$		−	6.00000i		−	1.66410i	0.554700	−	0.832050i	$-0.312833\pi$
$14$	2.61803	−	0.381966i	0.699699	−	0.102085i
$15$	5.23607	−	2.00000i	1.35195	−	0.516398i
$16$	1.00000			0.250000
$17$	7.23607			1.75500			0.877502	−	0.479573i	$-0.159208\pi$
$17$	7.23607			1.75500			0.877502	+	0.479573i	$0.159208\pi$
$18$	−2.00000	−	2.23607i	−0.471405	−	0.527046i
$19$		−	2.00000i		−	0.458831i	−0.973329	−	0.229416i	$-0.926318\pi$
$19$		−	2.00000i		−	0.458831i	0.973329	−	0.229416i	$-0.0736815\pi$
$20$	3.23607			0.723607
$21$	−2.23607	−	4.00000i	−0.487950	−	0.872872i
$22$	1.00000			0.213201
$23$		−	1.23607i		−	0.257738i	−0.991662	−	0.128869i	$-0.958865\pi$
$23$		−	1.23607i		−	0.257738i	0.991662	−	0.128869i	$-0.0411347\pi$
$24$	−0.618034	−	1.61803i	−0.126156	−	0.330280i
$25$	5.47214			1.09443
$26$	−6.00000			−1.17670
$27$	−2.38197	+	4.61803i	−0.458410	+	0.888741i
$28$	−0.381966	−	2.61803i	−0.0721848	−	0.494762i
$29$		−	0.472136i		−	0.0876734i	−0.999039	−	0.0438367i	$-0.986042\pi$
$29$		−	0.472136i		−	0.0876734i	0.999039	−	0.0438367i	$-0.0139581\pi$
$30$	−2.00000	−	5.23607i	−0.365148	−	0.955971i
$31$		−	0.763932i		−	0.137206i	−0.997644	−	0.0686031i	$-0.978146\pi$
$31$		−	0.763932i		−	0.137206i	0.997644	−	0.0686031i	$-0.0218542\pi$
$32$		−	1.00000i		−	0.176777i
$33$	−0.618034	−	1.61803i	−0.107586	−	0.281664i
$34$		−	7.23607i		−	1.24098i
$35$	−1.23607	−	8.47214i	−0.208934	−	1.43205i
$36$	−2.23607	+	2.00000i	−0.372678	+	0.333333i
$37$	−4.47214			−0.735215			−0.367607	−	0.929981i	$-0.619823\pi$
$37$	−4.47214			−0.735215			−0.367607	+	0.929981i	$0.619823\pi$
$38$	−2.00000			−0.324443
$39$	3.70820	+	9.70820i	0.593788	+	1.55456i
$40$		−	3.23607i		−	0.511667i
$41$	12.1803			1.90225			0.951125	−	0.308807i	$-0.0999297\pi$
$41$	12.1803			1.90225			0.951125	+	0.308807i	$0.0999297\pi$
$42$	−4.00000	+	2.23607i	−0.617213	+	0.345033i
$43$	10.9443			1.66899			0.834493	−	0.551019i	$-0.185761\pi$
$43$	10.9443			1.66899			0.834493	+	0.551019i	$0.185761\pi$
$44$		−	1.00000i		−	0.150756i
$45$	−7.23607	+	6.47214i	−1.07869	+	0.964809i
$46$	−1.23607			−0.182248
$47$	1.52786			0.222862			0.111431	−	0.993772i	$-0.464457\pi$
$47$	1.52786			0.222862			0.111431	+	0.993772i	$0.464457\pi$
$48$	−1.61803	+	0.618034i	−0.233543	+	0.0892055i
$49$	−6.70820	+	2.00000i	−0.958315	+	0.285714i
$50$		−	5.47214i		−	0.773877i
$51$	−11.7082	+	4.47214i	−1.63948	+	0.626224i
$52$			6.00000i			0.832050i
$53$		−	7.70820i		−	1.05880i	−0.848371	−	0.529402i	$-0.822416\pi$
$53$		−	7.70820i		−	1.05880i	0.848371	−	0.529402i	$-0.177584\pi$
$54$	4.61803	+	2.38197i	0.628435	+	0.324145i
$55$		−	3.23607i		−	0.436351i
$56$	−2.61803	+	0.381966i	−0.349850	+	0.0510424i
$57$	1.23607	+	3.23607i	0.163721	+	0.428628i
$58$	−0.472136			−0.0619945
$59$	3.23607			0.421300			0.210650	−	0.977562i	$-0.432442\pi$
$59$	3.23607			0.421300			0.210650	+	0.977562i	$0.432442\pi$
$60$	−5.23607	+	2.00000i	−0.675973	+	0.258199i
$61$			3.52786i			0.451697i	0.974162	+	0.225848i	$0.0725154\pi$
$61$			3.52786i			0.451697i	−0.974162	+	0.225848i	$0.927485\pi$
$62$	−0.763932			−0.0970195
$63$	6.09017	+	5.09017i	0.767289	+	0.641301i
$64$	−1.00000			−0.125000
$65$			19.4164i			2.40831i
$66$	−1.61803	+	0.618034i	−0.199166	+	0.0760747i
$67$	1.52786			0.186658			0.0933292	−	0.995635i	$-0.470249\pi$
$67$	1.52786			0.186658			0.0933292	+	0.995635i	$0.470249\pi$
$68$	−7.23607			−0.877502
$69$	0.763932	+	2.00000i	0.0919666	+	0.240772i
$70$	−8.47214	+	1.23607i	−1.01261	+	0.147738i
$71$			6.18034i			0.733471i	0.930325	+	0.366736i	$0.119525\pi$
$71$			6.18034i			0.733471i	−0.930325	+	0.366736i	$0.880475\pi$
$72$	2.00000	+	2.23607i	0.235702	+	0.263523i
$73$		−	14.1803i		−	1.65968i	−0.557999	−	0.829842i	$-0.688431\pi$
$73$		−	14.1803i		−	1.65968i	0.557999	−	0.829842i	$-0.311569\pi$
$74$			4.47214i			0.519875i
$75$	−8.85410	+	3.38197i	−1.02238	+	0.390516i
$76$			2.00000i			0.229416i
$77$	−2.61803	+	0.381966i	−0.298353	+	0.0435291i
$78$	9.70820	−	3.70820i	1.09924	−	0.419871i
$79$	7.23607			0.814121			0.407061	−	0.913401i	$-0.366554\pi$
$79$	7.23607			0.814121			0.407061	+	0.913401i	$0.366554\pi$
$80$	−3.23607			−0.361803
$81$	1.00000	−	8.94427i	0.111111	−	0.993808i
$82$		−	12.1803i		−	1.34509i
$83$	6.00000			0.658586			0.329293	−	0.944228i	$-0.393190\pi$
$83$	6.00000			0.658586			0.329293	+	0.944228i	$0.393190\pi$
$84$	2.23607	+	4.00000i	0.243975	+	0.436436i
$85$	−23.4164			−2.53987
$86$		−	10.9443i		−	1.18015i
$87$	0.291796	+	0.763932i	0.0312838	+	0.0819021i
$88$	−1.00000			−0.106600
$89$	−12.9443			−1.37209			−0.686045	−	0.727559i	$-0.740655\pi$
$89$	−12.9443			−1.37209			−0.686045	+	0.727559i	$0.740655\pi$
$90$	6.47214	+	7.23607i	0.682223	+	0.762749i
$91$	15.7082	−	2.29180i	1.64667	−	0.240246i
$92$			1.23607i			0.128869i
$93$	0.472136	+	1.23607i	0.0489582	+	0.128174i
$94$		−	1.52786i		−	0.157587i
$95$			6.47214i			0.664027i
$96$	0.618034	+	1.61803i	0.0630778	+	0.165140i
$97$			2.47214i			0.251007i	0.992093	+	0.125504i	$0.0400547\pi$
$97$			2.47214i			0.251007i	−0.992093	+	0.125504i	$0.959945\pi$
$98$	2.00000	+	6.70820i	0.202031	+	0.677631i
$99$	2.00000	+	2.23607i	0.201008	+	0.224733i
$100$	−5.47214			−0.547214
$101$	−6.76393			−0.673036			−0.336518	−	0.941677i	$-0.609249\pi$
$101$	−6.76393			−0.673036			−0.336518	+	0.941677i	$0.609249\pi$
$102$	4.47214	+	11.7082i	0.442807	+	1.15928i
$103$		−	9.70820i		−	0.956578i	−0.878203	−	0.478289i	$-0.841257\pi$
$103$		−	9.70820i		−	0.956578i	0.878203	−	0.478289i	$-0.158743\pi$
$104$	6.00000			0.588348
$105$	7.23607	+	12.9443i	0.706168	+	1.26323i
$106$	−7.70820			−0.748687
$107$		−	8.94427i		−	0.864675i	−0.901712	−	0.432338i	$-0.857689\pi$
$107$		−	8.94427i		−	0.864675i	0.901712	−	0.432338i	$-0.142311\pi$
$108$	2.38197	−	4.61803i	0.229205	−	0.444371i
$109$	8.76393			0.839432			0.419716	−	0.907655i	$-0.362130\pi$
$109$	8.76393			0.839432			0.419716	+	0.907655i	$0.362130\pi$
$110$	−3.23607			−0.308547
$111$	7.23607	−	2.76393i	0.686817	−	0.262341i
$112$	0.381966	+	2.61803i	0.0360924	+	0.247381i
$113$			8.00000i			0.752577i	0.926503	+	0.376288i	$0.122800\pi$
$113$			8.00000i			0.752577i	−0.926503	+	0.376288i	$0.877200\pi$
$114$	3.23607	−	1.23607i	0.303086	−	0.115768i
$115$			4.00000i			0.373002i
$116$			0.472136i			0.0438367i
$117$	−12.0000	−	13.4164i	−1.10940	−	1.24035i
$118$		−	3.23607i		−	0.297904i
$119$	2.76393	+	18.9443i	0.253369	+	1.73662i
$120$	2.00000	+	5.23607i	0.182574	+	0.477985i
$121$	−1.00000			−0.0909091
$122$	3.52786			0.319398
$123$	−19.7082	+	7.52786i	−1.77703	+	0.678765i
$124$			0.763932i			0.0686031i
$125$	−1.52786			−0.136656
$126$	5.09017	−	6.09017i	0.453468	−	0.542555i
$127$	−17.7082			−1.57135			−0.785675	−	0.618640i	$-0.787684\pi$
$127$	−17.7082			−1.57135			−0.785675	+	0.618640i	$0.787684\pi$
$128$			1.00000i			0.0883883i
$129$	−17.7082	+	6.76393i	−1.55912	+	0.595531i
$130$	19.4164			1.70293
$131$	−9.41641			−0.822715			−0.411358	−	0.911474i	$-0.634945\pi$
$131$	−9.41641			−0.822715			−0.411358	+	0.911474i	$0.634945\pi$
$132$	0.618034	+	1.61803i	0.0537930	+	0.140832i
$133$	5.23607	−	0.763932i	0.454025	−	0.0662413i
$134$		−	1.52786i		−	0.131987i
$135$	7.70820	−	14.9443i	0.663417	−	1.28620i
$136$			7.23607i			0.620488i
$137$		−	6.47214i		−	0.552952i	−0.961021	−	0.276476i	$-0.910833\pi$
$137$		−	6.47214i		−	0.552952i	0.961021	−	0.276476i	$-0.0891666\pi$
$138$	2.00000	−	0.763932i	0.170251	−	0.0650302i
$139$			10.0000i			0.848189i	0.905618	+	0.424094i	$0.139408\pi$
$139$			10.0000i			0.848189i	−0.905618	+	0.424094i	$0.860592\pi$
$140$	1.23607	+	8.47214i	0.104467	+	0.716026i
$141$	−2.47214	+	0.944272i	−0.208191	+	0.0795220i
$142$	6.18034			0.518643
$143$	6.00000			0.501745
$144$	2.23607	−	2.00000i	0.186339	−	0.166667i
$145$			1.52786i			0.126882i
$146$	−14.1803			−1.17357
$147$	9.61803	−	7.38197i	0.793282	−	0.608854i
$148$	4.47214			0.367607
$149$			2.00000i			0.163846i	0.996639	+	0.0819232i	$0.0261062\pi$
$149$			2.00000i			0.163846i	−0.996639	+	0.0819232i	$0.973894\pi$
$150$	3.38197	+	8.85410i	0.276136	+	0.722934i
$151$	12.1803			0.991222			0.495611	−	0.868545i	$-0.334944\pi$
$151$	12.1803			0.991222			0.495611	+	0.868545i	$0.334944\pi$
$152$	2.00000			0.162221
$153$	16.1803	−	14.4721i	1.30810	−	1.17000i
$154$	0.381966	+	2.61803i	0.0307797	+	0.210967i
$155$			2.47214i			0.198567i
$156$	−3.70820	−	9.70820i	−0.296894	−	0.777278i
$157$		−	13.4164i		−	1.07075i	−0.844616	−	0.535373i	$-0.820171\pi$
$157$		−	13.4164i		−	1.07075i	0.844616	−	0.535373i	$-0.179829\pi$
$158$		−	7.23607i		−	0.575671i
$159$	4.76393	+	12.4721i	0.377804	+	0.989105i
$160$			3.23607i			0.255834i
$161$	3.23607	−	0.472136i	0.255038	−	0.0372095i
$162$	−8.94427	−	1.00000i	−0.702728	−	0.0785674i
$163$	18.4721			1.44685			0.723425	−	0.690403i	$-0.242567\pi$
$163$	18.4721			1.44685			0.723425	+	0.690403i	$0.242567\pi$
$164$	−12.1803			−0.951125
$165$	2.00000	+	5.23607i	0.155700	+	0.407627i
$166$		−	6.00000i		−	0.465690i
$167$	13.8885			1.07473			0.537364	−	0.843350i	$-0.319420\pi$
$167$	13.8885			1.07473			0.537364	+	0.843350i	$0.319420\pi$
$168$	4.00000	−	2.23607i	0.308607	−	0.172516i
$169$	−23.0000			−1.76923
$170$			23.4164i			1.79596i
$171$	−4.00000	−	4.47214i	−0.305888	−	0.341993i
$172$	−10.9443			−0.834493
$173$	7.70820			0.586044			0.293022	−	0.956106i	$-0.405339\pi$
$173$	7.70820			0.586044			0.293022	+	0.956106i	$0.405339\pi$
$174$	0.763932	−	0.291796i	0.0579135	−	0.0221210i
$175$	2.09017	+	14.3262i	0.158002	+	1.08296i
$176$			1.00000i			0.0753778i
$177$	−5.23607	+	2.00000i	−0.393567	+	0.150329i
$178$			12.9443i			0.970214i
$179$			12.9443i			0.967500i	0.875206	+	0.483750i	$0.160726\pi$
$179$			12.9443i			0.967500i	−0.875206	+	0.483750i	$0.839274\pi$
$180$	7.23607	−	6.47214i	0.539345	−	0.482405i
$181$		−	3.52786i		−	0.262224i	−0.991368	−	0.131112i	$-0.958145\pi$
$181$		−	3.52786i		−	0.262224i	0.991368	−	0.131112i	$-0.0418548\pi$
$182$	−2.29180	−	15.7082i	−0.169879	−	1.16437i
$183$	−2.18034	−	5.70820i	−0.161175	−	0.421963i
$184$	1.23607			0.0911241
$185$	14.4721			1.06401
$186$	1.23607	−	0.472136i	0.0906329	−	0.0346187i
$187$			7.23607i			0.529154i
$188$	−1.52786			−0.111431
$189$	−13.0000	−	4.47214i	−0.945611	−	0.325300i
$190$	6.47214			0.469538
$191$		−	11.7082i		−	0.847176i	−0.905855	−	0.423588i	$-0.860770\pi$
$191$		−	11.7082i		−	0.847176i	0.905855	−	0.423588i	$-0.139230\pi$
$192$	1.61803	−	0.618034i	0.116772	−	0.0446028i
$193$	−2.94427			−0.211933			−0.105967	−	0.994370i	$-0.533794\pi$
$193$	−2.94427			−0.211933			−0.105967	+	0.994370i	$0.533794\pi$
$194$	2.47214			0.177489
$195$	−12.0000	−	31.4164i	−0.859338	−	2.24978i
$196$	6.70820	−	2.00000i	0.479157	−	0.142857i
$197$		−	14.9443i		−	1.06474i	−0.846513	−	0.532368i	$-0.821302\pi$
$197$		−	14.9443i		−	1.06474i	0.846513	−	0.532368i	$-0.178698\pi$
$198$	2.23607	−	2.00000i	0.158910	−	0.142134i
$199$		−	20.1803i		−	1.43055i	−0.698845	−	0.715273i	$-0.746302\pi$
$199$		−	20.1803i		−	1.43055i	0.698845	−	0.715273i	$-0.253698\pi$
$200$			5.47214i			0.386938i
$201$	−2.47214	+	0.944272i	−0.174371	+	0.0666038i
$202$			6.76393i			0.475909i
$203$	1.23607	−	0.180340i	0.0867550	−	0.0126574i
$204$	11.7082	−	4.47214i	0.819738	−	0.313112i
$205$	−39.4164			−2.75296
$206$	−9.70820			−0.676403
$207$	−2.47214	−	2.76393i	−0.171825	−	0.192107i
$208$		−	6.00000i		−	0.416025i
$209$	2.00000			0.138343
$210$	12.9443	−	7.23607i	0.893240	−	0.499336i
$211$	9.41641			0.648252			0.324126	−	0.946014i	$-0.394930\pi$
$211$	9.41641			0.648252			0.324126	+	0.946014i	$0.394930\pi$
$212$			7.70820i			0.529402i
$213$	−3.81966	−	10.0000i	−0.261719	−	0.685189i
$214$	−8.94427			−0.611418
$215$	−35.4164			−2.41538
$216$	−4.61803	−	2.38197i	−0.314217	−	0.162072i
$217$	2.00000	−	0.291796i	0.135769	−	0.0198084i
$218$		−	8.76393i		−	0.593568i
$219$	8.76393	+	22.9443i	0.592212	+	1.55043i
$220$			3.23607i			0.218176i
$221$		−	43.4164i		−	2.92050i
$222$	−2.76393	−	7.23607i	−0.185503	−	0.485653i
$223$			23.5967i			1.58016i	0.613007	+	0.790078i	$0.289960\pi$
$223$			23.5967i			1.58016i	−0.613007	+	0.790078i	$0.710040\pi$
$224$	2.61803	−	0.381966i	0.174925	−	0.0255212i
$225$	12.2361	−	10.9443i	0.815738	−	0.729618i
$226$	8.00000			0.532152
$227$	−22.0000			−1.46019			−0.730096	−	0.683345i	$-0.760525\pi$
$227$	−22.0000			−1.46019			−0.730096	+	0.683345i	$0.760525\pi$
$228$	−1.23607	−	3.23607i	−0.0818606	−	0.214314i
$229$			2.00000i			0.132164i	0.997814	+	0.0660819i	$0.0210498\pi$
$229$			2.00000i			0.132164i	−0.997814	+	0.0660819i	$0.978950\pi$
$230$	4.00000			0.263752
$231$	4.00000	−	2.23607i	0.263181	−	0.147122i
$232$	0.472136			0.0309972
$233$		−	25.4164i		−	1.66508i	−0.553962	−	0.832542i	$-0.686885\pi$
$233$		−	25.4164i		−	1.66508i	0.553962	−	0.832542i	$-0.313115\pi$
$234$	−13.4164	+	12.0000i	−0.877058	+	0.784465i
$235$	−4.94427			−0.322529
$236$	−3.23607			−0.210650
$237$	−11.7082	+	4.47214i	−0.760530	+	0.290496i
$238$	18.9443	−	2.76393i	1.22797	−	0.179159i
$239$		−	21.8885i		−	1.41585i	−0.706287	−	0.707926i	$-0.749631\pi$
$239$		−	21.8885i		−	1.41585i	0.706287	−	0.707926i	$-0.250369\pi$
$240$	5.23607	−	2.00000i	0.337987	−	0.129099i
$241$			18.1803i			1.17110i	0.810637	+	0.585549i	$0.199121\pi$
$241$			18.1803i			1.17110i	−0.810637	+	0.585549i	$0.800879\pi$
$242$			1.00000i			0.0642824i
$243$	3.90983	+	15.0902i	0.250816	+	0.968035i
$244$		−	3.52786i		−	0.225848i
$245$	21.7082	−	6.47214i	1.38689	−	0.413490i
$246$	7.52786	+	19.7082i	0.479959	+	1.25655i
$247$	−12.0000			−0.763542
$248$	0.763932			0.0485097
$249$	−9.70820	+	3.70820i	−0.615232	+	0.234998i
$250$			1.52786i			0.0966306i
$251$	−1.70820			−0.107821			−0.0539104	−	0.998546i	$-0.517169\pi$
$251$	−1.70820			−0.107821			−0.0539104	+	0.998546i	$0.517169\pi$
$252$	−6.09017	−	5.09017i	−0.383645	−	0.320651i
$253$	1.23607			0.0777109
$254$			17.7082i			1.11111i
$255$	37.8885	−	14.4721i	2.37267	−	0.906280i
$256$	1.00000			0.0625000
$257$	0.944272			0.0589021			0.0294510	−	0.999566i	$-0.490624\pi$
$257$	0.944272			0.0589021			0.0294510	+	0.999566i	$0.490624\pi$
$258$	6.76393	+	17.7082i	0.421104	+	1.10246i
$259$	−1.70820	−	11.7082i	−0.106143	−	0.727512i
$260$		−	19.4164i		−	1.20415i
$261$	−0.944272	−	1.05573i	−0.0584490	−	0.0653479i
$262$			9.41641i			0.581748i
$263$		−	21.5279i		−	1.32746i	−0.747970	−	0.663732i	$-0.768971\pi$
$263$		−	21.5279i		−	1.32746i	0.747970	−	0.663732i	$-0.231029\pi$
$264$	1.61803	−	0.618034i	0.0995831	−	0.0380374i
$265$			24.9443i			1.53231i
$266$	−0.763932	−	5.23607i	−0.0468397	−	0.321044i
$267$	20.9443	−	8.00000i	1.28177	−	0.489592i
$268$	−1.52786			−0.0933292
$269$	23.5967			1.43872			0.719360	−	0.694638i	$-0.244435\pi$
$269$	23.5967			1.43872			0.719360	+	0.694638i	$0.244435\pi$
$270$	−14.9443	−	7.70820i	−0.909479	−	0.469106i
$271$			23.7082i			1.44017i	0.693885	+	0.720085i	$0.255897\pi$
$271$			23.7082i			1.44017i	−0.693885	+	0.720085i	$0.744103\pi$
$272$	7.23607			0.438751
$273$	−24.0000	+	13.4164i	−1.45255	+	0.811998i
$274$	−6.47214			−0.390996
$275$			5.47214i			0.329982i
$276$	−0.763932	−	2.00000i	−0.0459833	−	0.120386i
$277$	−24.1803			−1.45286			−0.726428	−	0.687243i	$-0.758821\pi$
$277$	−24.1803			−1.45286			−0.726428	+	0.687243i	$0.758821\pi$
$278$	10.0000			0.599760
$279$	−1.52786	−	1.70820i	−0.0914708	−	0.102267i
$280$	8.47214	−	1.23607i	0.506307	−	0.0738692i
$281$			25.4164i			1.51622i	0.652129	+	0.758108i	$0.273876\pi$
$281$			25.4164i			1.51622i	−0.652129	+	0.758108i	$0.726124\pi$
$282$	0.944272	+	2.47214i	0.0562306	+	0.147214i
$283$		−	14.9443i		−	0.888345i	−0.895941	−	0.444172i	$-0.853498\pi$
$283$		−	14.9443i		−	0.888345i	0.895941	−	0.444172i	$-0.146502\pi$
$284$		−	6.18034i		−	0.366736i
$285$	−4.00000	−	10.4721i	−0.236940	−	0.620316i
$286$		−	6.00000i		−	0.354787i
$287$	4.65248	+	31.8885i	0.274627	+	1.88232i
$288$	−2.00000	−	2.23607i	−0.117851	−	0.131762i
$289$	35.3607			2.08004
$290$	1.52786			0.0897193
$291$	−1.52786	−	4.00000i	−0.0895650	−	0.234484i
$292$			14.1803i			0.829842i
$293$	18.1803			1.06211			0.531053	−	0.847338i	$-0.321796\pi$
$293$	18.1803			1.06211			0.531053	+	0.847338i	$0.321796\pi$
$294$	−7.38197	−	9.61803i	−0.430525	−	0.560935i
$295$	−10.4721			−0.609711
$296$		−	4.47214i		−	0.259938i
$297$	−4.61803	−	2.38197i	−0.267966	−	0.138216i
$298$	2.00000			0.115857
$299$	−7.41641			−0.428902
$300$	8.85410	−	3.38197i	0.511192	−	0.195258i
$301$	4.18034	+	28.6525i	0.240951	+	1.65150i
$302$		−	12.1803i		−	0.700900i
$303$	10.9443	−	4.18034i	0.628732	−	0.240154i
$304$		−	2.00000i		−	0.114708i
$305$		−	11.4164i		−	0.653702i
$306$	−14.4721	−	16.1803i	−0.827317	−	0.924968i
$307$		−	3.52786i		−	0.201346i	−0.994920	−	0.100673i	$-0.967900\pi$
$307$		−	3.52786i		−	0.201346i	0.994920	−	0.100673i	$-0.0320996\pi$
$308$	2.61803	−	0.381966i	0.149176	−	0.0217645i
$309$	6.00000	+	15.7082i	0.341328	+	0.893609i
$310$	2.47214			0.140408
$311$	−10.4721			−0.593820			−0.296910	−	0.954905i	$-0.595956\pi$
$311$	−10.4721			−0.593820			−0.296910	+	0.954905i	$0.595956\pi$
$312$	−9.70820	+	3.70820i	−0.549619	+	0.209936i
$313$		−	8.00000i		−	0.452187i	−0.974106	−	0.226093i	$-0.927405\pi$
$313$		−	8.00000i		−	0.452187i	0.974106	−	0.226093i	$-0.0725954\pi$
$314$	−13.4164			−0.757132
$315$	−19.7082	−	16.4721i	−1.11043	−	0.928100i
$316$	−7.23607			−0.407061
$317$			12.2918i			0.690376i	0.938534	+	0.345188i	$0.112185\pi$
$317$			12.2918i			0.690376i	−0.938534	+	0.345188i	$0.887815\pi$
$318$	12.4721	−	4.76393i	0.699403	−	0.267148i
$319$	0.472136			0.0264345
$320$	3.23607			0.180902
$321$	5.52786	+	14.4721i	0.308535	+	0.807756i
$322$	−0.472136	−	3.23607i	−0.0263111	−	0.180339i
$323$		−	14.4721i		−	0.805251i
$324$	−1.00000	+	8.94427i	−0.0555556	+	0.496904i
$325$		−	32.8328i		−	1.82124i
$326$		−	18.4721i		−	1.02308i
$327$	−14.1803	+	5.41641i	−0.784175	+	0.299528i
$328$			12.1803i			0.672547i
$329$	0.583592	+	4.00000i	0.0321745	+	0.220527i
$330$	5.23607	−	2.00000i	0.288236	−	0.110096i
$331$	8.94427			0.491622			0.245811	−	0.969318i	$-0.420946\pi$
$331$	8.94427			0.491622			0.245811	+	0.969318i	$0.420946\pi$
$332$	−6.00000			−0.329293
$333$	−10.0000	+	8.94427i	−0.547997	+	0.490143i
$334$		−	13.8885i		−	0.759947i
$335$	−4.94427			−0.270134
$336$	−2.23607	−	4.00000i	−0.121988	−	0.218218i
$337$	13.4164			0.730838			0.365419	−	0.930843i	$-0.380926\pi$
$337$	13.4164			0.730838			0.365419	+	0.930843i	$0.380926\pi$
$338$			23.0000i			1.25104i
$339$	−4.94427	−	12.9443i	−0.268536	−	0.703036i
$340$	23.4164			1.26993
$341$	0.763932			0.0413692
$342$	−4.47214	+	4.00000i	−0.241825	+	0.216295i
$343$	−7.79837	−	16.7984i	−0.421073	−	0.907027i
$344$			10.9443i			0.590076i
$345$	−2.47214	−	6.47214i	−0.133095	−	0.348448i
$346$		−	7.70820i		−	0.414396i
$347$			16.9443i			0.909616i	0.890589	+	0.454808i	$0.150292\pi$
$347$			16.9443i			0.909616i	−0.890589	+	0.454808i	$0.849708\pi$
$348$	−0.291796	−	0.763932i	−0.0156419	−	0.0409511i
$349$			22.0000i			1.17763i	0.808267	+	0.588817i	$0.200406\pi$
$349$			22.0000i			1.17763i	−0.808267	+	0.588817i	$0.799594\pi$
$350$	14.3262	−	2.09017i	0.765770	−	0.111724i
$351$	27.7082	+	14.2918i	1.47895	+	0.762840i
$352$	1.00000			0.0533002
$353$	0.944272			0.0502585			0.0251293	−	0.999684i	$-0.492000\pi$
$353$	0.944272			0.0502585			0.0251293	+	0.999684i	$0.492000\pi$
$354$	2.00000	+	5.23607i	0.106299	+	0.278294i
$355$		−	20.0000i		−	1.06149i
$356$	12.9443			0.686045
$357$	−16.1803	−	28.9443i	−0.856354	−	1.53189i
$358$	12.9443			0.684126
$359$			18.8328i			0.993958i	0.867763	+	0.496979i	$0.165557\pi$
$359$			18.8328i			0.993958i	−0.867763	+	0.496979i	$0.834443\pi$
$360$	−6.47214	−	7.23607i	−0.341112	−	0.381374i
$361$	15.0000			0.789474
$362$	−3.52786			−0.185420
$363$	1.61803	−	0.618034i	0.0849248	−	0.0324384i
$364$	−15.7082	+	2.29180i	−0.823334	+	0.120123i
$365$			45.8885i			2.40192i
$366$	−5.70820	+	2.18034i	−0.298373	+	0.113968i
$367$			26.6525i			1.39125i	0.718406	+	0.695624i	$0.244872\pi$
$367$			26.6525i			1.39125i	−0.718406	+	0.695624i	$0.755128\pi$
$368$		−	1.23607i		−	0.0644345i
$369$	27.2361	−	24.3607i	1.41785	−	1.26817i
$370$		−	14.4721i		−	0.752371i
$371$	20.1803	−	2.94427i	1.04771	−	0.152859i
$372$	−0.472136	−	1.23607i	−0.0244791	−	0.0640871i
$373$	−7.81966			−0.404887			−0.202443	−	0.979294i	$-0.564888\pi$
$373$	−7.81966			−0.404887			−0.202443	+	0.979294i	$0.564888\pi$
$374$	7.23607			0.374168
$375$	2.47214	−	0.944272i	0.127661	−	0.0487620i
$376$			1.52786i			0.0787936i
$377$	−2.83282			−0.145897
$378$	−4.47214	+	13.0000i	−0.230022	+	0.668648i
$379$	−12.3607			−0.634925			−0.317463	−	0.948271i	$-0.602831\pi$
$379$	−12.3607			−0.634925			−0.317463	+	0.948271i	$0.602831\pi$
$380$		−	6.47214i		−	0.332014i
$381$	28.6525	−	10.9443i	1.46791	−	0.560692i
$382$	−11.7082			−0.599044
$383$	20.0000			1.02195			0.510976	−	0.859595i	$-0.329284\pi$
$383$	20.0000			1.02195			0.510976	+	0.859595i	$0.329284\pi$
$384$	−0.618034	−	1.61803i	−0.0315389	−	0.0825700i
$385$	8.47214	−	1.23607i	0.431780	−	0.0629959i
$386$			2.94427i			0.149859i
$387$	24.4721	−	21.8885i	1.24399	−	1.11266i
$388$		−	2.47214i		−	0.125504i
$389$			17.2361i			0.873903i	0.899485	+	0.436952i	$0.143942\pi$
$389$			17.2361i			0.873903i	−0.899485	+	0.436952i	$0.856058\pi$
$390$	−31.4164	+	12.0000i	−1.59083	+	0.607644i
$391$		−	8.94427i		−	0.452331i
$392$	−2.00000	−	6.70820i	−0.101015	−	0.338815i
$393$	15.2361	−	5.81966i	0.768558	−	0.293563i
$394$	−14.9443			−0.752882
$395$	−23.4164			−1.17821
$396$	−2.00000	−	2.23607i	−0.100504	−	0.112367i
$397$			14.9443i			0.750032i	0.927018	+	0.375016i	$0.122363\pi$
$397$			14.9443i			0.750032i	−0.927018	+	0.375016i	$0.877637\pi$
$398$	−20.1803			−1.01155
$399$	−8.00000	+	4.47214i	−0.400501	+	0.223887i
$400$	5.47214			0.273607
$401$			2.47214i			0.123453i	0.998093	+	0.0617263i	$0.0196606\pi$
$401$			2.47214i			0.123453i	−0.998093	+	0.0617263i	$0.980339\pi$
$402$	0.944272	+	2.47214i	0.0470960	+	0.123299i
$403$	−4.58359			−0.228325
$404$	6.76393			0.336518
$405$	−3.23607	+	28.9443i	−0.160802	+	1.43825i
$406$	−0.180340	−	1.23607i	−0.00895012	−	0.0613450i
$407$		−	4.47214i		−	0.221676i
$408$	−4.47214	−	11.7082i	−0.221404	−	0.579642i
$409$			5.23607i			0.258907i	0.991586	+	0.129453i	$0.0413223\pi$
$409$			5.23607i			0.258907i	−0.991586	+	0.129453i	$0.958678\pi$
$410$			39.4164i			1.94664i
$411$	4.00000	+	10.4721i	0.197305	+	0.516552i
$412$			9.70820i			0.478289i
$413$	1.23607	+	8.47214i	0.0608229	+	0.416887i
$414$	−2.76393	+	2.47214i	−0.135840	+	0.121499i
$415$	−19.4164			−0.953114
$416$	−6.00000			−0.294174
$417$	−6.18034	−	16.1803i	−0.302653	−	0.792355i
$418$		−	2.00000i		−	0.0978232i
$419$	−9.12461			−0.445766			−0.222883	−	0.974845i	$-0.571547\pi$
$419$	−9.12461			−0.445766			−0.222883	+	0.974845i	$0.571547\pi$
$420$	−7.23607	−	12.9443i	−0.353084	−	0.631616i
$421$	4.47214			0.217959			0.108979	−	0.994044i	$-0.465242\pi$
$421$	4.47214			0.217959			0.108979	+	0.994044i	$0.465242\pi$
$422$		−	9.41641i		−	0.458384i
$423$	3.41641	−	3.05573i	0.166111	−	0.148575i
$424$	7.70820			0.374343
$425$	39.5967			1.92072
$426$	−10.0000	+	3.81966i	−0.484502	+	0.185063i
$427$	−9.23607	+	1.34752i	−0.446965	+	0.0652113i
$428$			8.94427i			0.432338i
$429$	−9.70820	+	3.70820i	−0.468717	+	0.179034i
$430$			35.4164i			1.70793i
$431$			5.88854i			0.283641i	0.989892	+	0.141821i	$0.0452956\pi$
$431$			5.88854i			0.283641i	−0.989892	+	0.141821i	$0.954704\pi$
$432$	−2.38197	+	4.61803i	−0.114602	+	0.222185i
$433$		−	26.4721i		−	1.27217i	−0.771619	−	0.636085i	$-0.780553\pi$
$433$		−	26.4721i		−	1.27217i	0.771619	−	0.636085i	$-0.219447\pi$
$434$	−0.291796	−	2.00000i	−0.0140067	−	0.0960031i
$435$	−0.944272	−	2.47214i	−0.0452744	−	0.118530i
$436$	−8.76393			−0.419716
$437$	−2.47214			−0.118258
$438$	22.9443	−	8.76393i	1.09632	−	0.418757i
$439$			17.2361i			0.822633i	0.911493	+	0.411316i	$0.134931\pi$
$439$			17.2361i			0.822633i	−0.911493	+	0.411316i	$0.865069\pi$
$440$	3.23607			0.154273
$441$	−11.0000	+	17.8885i	−0.523810	+	0.851835i
$442$	−43.4164			−2.06511
$443$		−	29.8885i		−	1.42005i	−0.704178	−	0.710024i	$-0.748684\pi$
$443$		−	29.8885i		−	1.42005i	0.704178	−	0.710024i	$-0.251316\pi$
$444$	−7.23607	+	2.76393i	−0.343409	+	0.131170i
$445$	41.8885			1.98571
$446$	23.5967			1.11734
$447$	−1.23607	−	3.23607i	−0.0584640	−	0.153061i
$448$	−0.381966	−	2.61803i	−0.0180462	−	0.123690i
$449$			31.4164i			1.48263i	0.671156	+	0.741316i	$0.265798\pi$
$449$			31.4164i			1.48263i	−0.671156	+	0.741316i	$0.734202\pi$
$450$	−10.9443	−	12.2361i	−0.515918	−	0.576814i
$451$			12.1803i			0.573550i
$452$		−	8.00000i		−	0.376288i
$453$	−19.7082	+	7.52786i	−0.925972	+	0.353690i
$454$			22.0000i			1.03251i
$455$	−50.8328	+	7.41641i	−2.38308	+	0.347687i
$456$	−3.23607	+	1.23607i	−0.151543	+	0.0578842i
$457$	−2.00000			−0.0935561			−0.0467780	−	0.998905i	$-0.514895\pi$
$457$	−2.00000			−0.0935561			−0.0467780	+	0.998905i	$0.514895\pi$
$458$	2.00000			0.0934539
$459$	−17.2361	+	33.4164i	−0.804511	+	1.55974i
$460$		−	4.00000i		−	0.186501i
$461$	−41.2361			−1.92056			−0.960278	−	0.279047i	$-0.909982\pi$
$461$	−41.2361			−1.92056			−0.960278	+	0.279047i	$0.909982\pi$
$462$	−2.23607	−	4.00000i	−0.104031	−	0.186097i
$463$	−26.4721			−1.23026			−0.615132	−	0.788424i	$-0.710897\pi$
$463$	−26.4721			−1.23026			−0.615132	+	0.788424i	$0.710897\pi$
$464$		−	0.472136i		−	0.0219184i
$465$	−1.52786	−	4.00000i	−0.0708530	−	0.185496i
$466$	−25.4164			−1.17739
$467$	−22.6525			−1.04823			−0.524116	−	0.851647i	$-0.675604\pi$
$467$	−22.6525			−1.04823			−0.524116	+	0.851647i	$0.675604\pi$
$468$	12.0000	+	13.4164i	0.554700	+	0.620174i
$469$	0.583592	+	4.00000i	0.0269478	+	0.184703i
$470$			4.94427i			0.228062i
$471$	8.29180	+	21.7082i	0.382066	+	1.00026i
$472$			3.23607i			0.148952i
$473$			10.9443i			0.503218i
$474$	4.47214	+	11.7082i	0.205412	+	0.537776i
$475$		−	10.9443i		−	0.502158i
$476$	−2.76393	−	18.9443i	−0.126685	−	0.868309i
$477$	−15.4164	−	17.2361i	−0.705869	−	0.789185i
$478$	−21.8885			−1.00116
$479$	−0.944272			−0.0431449			−0.0215724	−	0.999767i	$-0.506867\pi$
$479$	−0.944272			−0.0431449			−0.0215724	+	0.999767i	$0.506867\pi$
$480$	−2.00000	−	5.23607i	−0.0912871	−	0.238993i
$481$			26.8328i			1.22347i
$482$	18.1803			0.828092
$483$	−4.94427	+	2.76393i	−0.224972	+	0.125763i
$484$	1.00000			0.0454545
$485$		−	8.00000i		−	0.363261i
$486$	15.0902	−	3.90983i	0.684504	−	0.177353i
$487$	1.52786			0.0692341			0.0346171	−	0.999401i	$-0.488979\pi$
$487$	1.52786			0.0692341			0.0346171	+	0.999401i	$0.488979\pi$
$488$	−3.52786			−0.159699
$489$	−29.8885	+	11.4164i	−1.35161	+	0.516268i
$490$	−6.47214	−	21.7082i	−0.292381	−	0.980677i
$491$		0			0		1.00000			$0$
$491$		0			0		−1.00000			$\pi$
$492$	19.7082	−	7.52786i	0.888514	−	0.339382i
$493$		−	3.41641i		−	0.153867i
$494$			12.0000i			0.539906i
$495$	−6.47214	−	7.23607i	−0.290901	−	0.325237i
$496$		−	0.763932i		−	0.0343016i
$497$	−16.1803	+	2.36068i	−0.725787	+	0.105891i
$498$	3.70820	+	9.70820i	0.166169	+	0.435035i
$499$	19.0557			0.853052			0.426526	−	0.904475i	$-0.359737\pi$
$499$	19.0557			0.853052			0.426526	+	0.904475i	$0.359737\pi$
$500$	1.52786			0.0683282
$501$	−22.4721	+	8.58359i	−1.00398	+	0.383487i
$502$			1.70820i			0.0762409i
$503$	−4.58359			−0.204372			−0.102186	−	0.994765i	$-0.532584\pi$
$503$	−4.58359			−0.204372			−0.102186	+	0.994765i	$0.532584\pi$
$504$	−5.09017	+	6.09017i	−0.226734	+	0.271278i
$505$	21.8885			0.974027
$506$		−	1.23607i		−	0.0549499i
$507$	37.2148	−	14.2148i	1.65277	−	0.631301i
$508$	17.7082			0.785675
$509$	17.1246			0.759035			0.379518	−	0.925185i	$-0.376090\pi$
$509$	17.1246			0.759035			0.379518	+	0.925185i	$0.376090\pi$
$510$	−14.4721	−	37.8885i	−0.640837	−	1.67773i
$511$	37.1246	−	5.41641i	1.64230	−	0.239608i
$512$		−	1.00000i		−	0.0441942i
$513$	9.23607	+	4.76393i	0.407782	+	0.210333i
$514$		−	0.944272i		−	0.0416500i
$515$			31.4164i			1.38437i
$516$	17.7082	−	6.76393i	0.779560	−	0.297766i
$517$			1.52786i			0.0671954i
$518$	−11.7082	+	1.70820i	−0.514429	+	0.0750542i
$519$	−12.4721	+	4.76393i	−0.547466	+	0.209113i
$520$	−19.4164			−0.851466
$521$	19.0557			0.834847			0.417423	−	0.908712i	$-0.362933\pi$
$521$	19.0557			0.834847			0.417423	+	0.908712i	$0.362933\pi$
$522$	−1.05573	+	0.944272i	−0.0462080	+	0.0413297i
$523$			29.7771i			1.30206i	0.759052	+	0.651031i	$0.225663\pi$
$523$			29.7771i			1.30206i	−0.759052	+	0.651031i	$0.774337\pi$
$524$	9.41641			0.411358
$525$	−12.2361	−	21.8885i	−0.534026	−	0.955294i
$526$	−21.5279			−0.938659
$527$		−	5.52786i		−	0.240798i
$528$	−0.618034	−	1.61803i	−0.0268965	−	0.0704159i
$529$	21.4721			0.933571
$530$	24.9443			1.08351
$531$	7.23607	−	6.47214i	0.314019	−	0.280867i
$532$	−5.23607	+	0.763932i	−0.227012	+	0.0331207i
$533$		−	73.0820i		−	3.16553i
$534$	−8.00000	−	20.9443i	−0.346194	−	0.906347i
$535$			28.9443i			1.25137i
$536$			1.52786i			0.0659937i
$537$	−8.00000	−	20.9443i	−0.345225	−	0.903812i
$538$		−	23.5967i		−	1.01733i
$539$	−2.00000	−	6.70820i	−0.0861461	−	0.288943i
$540$	−7.70820	+	14.9443i	−0.331708	+	0.643099i
$541$	−23.5967			−1.01450			−0.507252	−	0.861798i	$-0.669339\pi$
$541$	−23.5967			−1.01450			−0.507252	+	0.861798i	$0.669339\pi$
$542$	23.7082			1.01835
$543$	2.18034	+	5.70820i	0.0935673	+	0.244962i
$544$		−	7.23607i		−	0.310244i
$545$	−28.3607			−1.21484
$546$	13.4164	+	24.0000i	0.574169	+	1.02711i
$547$	24.8328			1.06177			0.530887	−	0.847442i	$-0.321859\pi$
$547$	24.8328			1.06177			0.530887	+	0.847442i	$0.321859\pi$
$548$			6.47214i			0.276476i
$549$	7.05573	+	7.88854i	0.301131	+	0.336675i
$550$	5.47214			0.233333
$551$	−0.944272			−0.0402273
$552$	−2.00000	+	0.763932i	−0.0851257	+	0.0325151i
$553$	2.76393	+	18.9443i	0.117534	+	0.805592i
$554$			24.1803i			1.02732i
$555$	−23.4164	+	8.94427i	−0.993971	+	0.379663i
$556$		−	10.0000i		−	0.424094i
$557$			9.05573i			0.383704i	0.981424	+	0.191852i	$0.0614493\pi$
$557$			9.05573i			0.383704i	−0.981424	+	0.191852i	$0.938551\pi$
$558$	−1.70820	+	1.52786i	−0.0723140	+	0.0646796i
$559$		−	65.6656i		−	2.77736i
$560$	−1.23607	−	8.47214i	−0.0522334	−	0.358013i
$561$	−4.47214	−	11.7082i	−0.188814	−	0.494321i
$562$	25.4164			1.07213
$563$	−23.5279			−0.991581			−0.495791	−	0.868442i	$-0.665122\pi$
$563$	−23.5279			−0.991581			−0.495791	+	0.868442i	$0.665122\pi$
$564$	2.47214	−	0.944272i	0.104096	−	0.0397610i
$565$		−	25.8885i		−	1.08914i
$566$	−14.9443			−0.628155
$567$	23.7984	−	0.798374i	0.999438	−	0.0335286i
$568$	−6.18034			−0.259321
$569$			6.00000i			0.251533i	0.992060	+	0.125767i	$0.0401390\pi$
$569$			6.00000i			0.251533i	−0.992060	+	0.125767i	$0.959861\pi$
$570$	−10.4721	+	4.00000i	−0.438630	+	0.167542i
$571$	−26.9443			−1.12758			−0.563791	−	0.825917i	$-0.690658\pi$
$571$	−26.9443			−1.12758			−0.563791	+	0.825917i	$0.690658\pi$
$572$	−6.00000			−0.250873
$573$	7.23607	+	18.9443i	0.302291	+	0.791408i
$574$	31.8885	−	4.65248i	1.33100	−	0.194191i
$575$		−	6.76393i		−	0.282075i
$576$	−2.23607	+	2.00000i	−0.0931695	+	0.0833333i
$577$		−	37.5279i		−	1.56231i	−0.624340	−	0.781153i	$-0.714632\pi$
$577$		−	37.5279i		−	1.56231i	0.624340	−	0.781153i	$-0.285368\pi$
$578$		−	35.3607i		−	1.47081i
$579$	4.76393	−	1.81966i	0.197982	−	0.0756225i
$580$		−	1.52786i		−	0.0634411i
$581$	2.29180	+	15.7082i	0.0950797	+	0.651686i
$582$	−4.00000	+	1.52786i	−0.165805	+	0.0633320i
$583$	7.70820			0.319241
$584$	14.1803			0.586787
$585$	38.8328	+	43.4164i	1.60554	+	1.79505i
$586$		−	18.1803i		−	0.751023i
$587$	27.5967			1.13904			0.569520	−	0.821978i	$-0.307129\pi$
$587$	27.5967			1.13904			0.569520	+	0.821978i	$0.307129\pi$
$588$	−9.61803	+	7.38197i	−0.396641	+	0.304427i
$589$	−1.52786			−0.0629545
$590$			10.4721i			0.431131i
$591$	9.23607	+	24.1803i	0.379921	+	0.994646i
$592$	−4.47214			−0.183804
$593$	1.70820			0.0701475			0.0350738	−	0.999385i	$-0.488833\pi$
$593$	1.70820			0.0701475			0.0350738	+	0.999385i	$0.488833\pi$
$594$	−2.38197	+	4.61803i	−0.0977332	+	0.189480i
$595$	−8.94427	−	61.3050i	−0.366679	−	2.51326i
$596$		−	2.00000i		−	0.0819232i
$597$	12.4721	+	32.6525i	0.510451	+	1.33638i
$598$			7.41641i			0.303279i
$599$		−	15.7082i		−	0.641820i	−0.947110	−	0.320910i	$-0.896011\pi$
$599$		−	15.7082i		−	0.641820i	0.947110	−	0.320910i	$-0.103989\pi$
$600$	−3.38197	−	8.85410i	−0.138068	−	0.361467i
$601$		−	9.23607i		−	0.376747i	−0.982097	−	0.188374i	$-0.939678\pi$
$601$		−	9.23607i		−	0.376747i	0.982097	−	0.188374i	$-0.0603216\pi$
$602$	28.6525	−	4.18034i	1.16779	−	0.170378i
$603$	3.41641	−	3.05573i	0.139127	−	0.124439i
$604$	−12.1803			−0.495611
$605$	3.23607			0.131565
$606$	−4.18034	−	10.9443i	−0.169815	−	0.444581i
$607$			1.23607i			0.0501705i	0.999685	+	0.0250852i	$0.00798571\pi$
$607$			1.23607i			0.0501705i	−0.999685	+	0.0250852i	$0.992014\pi$
$608$	−2.00000			−0.0811107
$609$	−1.88854	+	1.05573i	−0.0765277	+	0.0427803i
$610$	−11.4164			−0.462237
$611$		−	9.16718i		−	0.370865i
$612$	−16.1803	+	14.4721i	−0.654051	+	0.585001i
$613$	−4.18034			−0.168842			−0.0844212	−	0.996430i	$-0.526904\pi$
$613$	−4.18034			−0.168842			−0.0844212	+	0.996430i	$0.526904\pi$
$614$	−3.52786			−0.142373
$615$	63.7771	−	24.3607i	2.57174	−	0.982317i
$616$	−0.381966	−	2.61803i	−0.0153898	−	0.105484i
$617$		−	11.0557i		−	0.445087i	−0.974923	−	0.222543i	$-0.928564\pi$
$617$		−	11.0557i		−	0.445087i	0.974923	−	0.222543i	$-0.0714359\pi$
$618$	15.7082	−	6.00000i	0.631877	−	0.241355i
$619$		−	21.2361i		−	0.853550i	−0.904358	−	0.426775i	$-0.859650\pi$
$619$		−	21.2361i		−	0.853550i	0.904358	−	0.426775i	$-0.140350\pi$
$620$		−	2.47214i		−	0.0992834i
$621$	5.70820	+	2.94427i	0.229062	+	0.118150i
$622$			10.4721i			0.419894i
$623$	−4.94427	−	33.8885i	−0.198088	−	1.35772i
$624$	3.70820	+	9.70820i	0.148447	+	0.388639i
$625$	−22.4164			−0.896656
$626$	−8.00000			−0.319744
$627$	−3.23607	+	1.23607i	−0.129236	+	0.0493638i
$628$			13.4164i			0.535373i
$629$	−32.3607			−1.29030
$630$	−16.4721	+	19.7082i	−0.656266	+	0.785194i
$631$	−32.9443			−1.31149			−0.655745	−	0.754982i	$-0.727646\pi$
$631$	−32.9443			−1.31149			−0.655745	+	0.754982i	$0.727646\pi$
$632$			7.23607i			0.287835i
$633$	−15.2361	+	5.81966i	−0.605579	+	0.231311i
$634$	12.2918			0.488170
$635$	57.3050			2.27408
$636$	−4.76393	−	12.4721i	−0.188902	−	0.494552i
$637$	12.0000	+	40.2492i	0.475457	+	1.59473i
$638$		−	0.472136i		−	0.0186920i
$639$	12.3607	+	13.8197i	0.488981	+	0.546697i
$640$		−	3.23607i		−	0.127917i
$641$		−	32.3607i		−	1.27817i	−0.769136	−	0.639085i	$-0.779313\pi$
$641$		−	32.3607i		−	1.27817i	0.769136	−	0.639085i	$-0.220687\pi$
$642$	14.4721	−	5.52786i	0.571170	−	0.218167i
$643$			32.0689i			1.26467i	0.774694	+	0.632337i	$0.217904\pi$
$643$			32.0689i			1.26467i	−0.774694	+	0.632337i	$0.782096\pi$
$644$	−3.23607	+	0.472136i	−0.127519	+	0.0186048i
$645$	57.3050	−	21.8885i	2.25638	−	0.861861i
$646$	−14.4721			−0.569399
$647$	5.88854			0.231503			0.115751	−	0.993278i	$-0.463072\pi$
$647$	5.88854			0.231503			0.115751	+	0.993278i	$0.463072\pi$
$648$	8.94427	+	1.00000i	0.351364	+	0.0392837i
$649$			3.23607i			0.127027i
$650$	−32.8328			−1.28781
$651$	−3.05573	+	1.70820i	−0.119763	+	0.0669498i
$652$	−18.4721			−0.723425
$653$		−	21.2361i		−	0.831032i	−0.909586	−	0.415516i	$-0.863601\pi$
$653$		−	21.2361i		−	0.831032i	0.909586	−	0.415516i	$-0.136399\pi$
$654$	5.41641	+	14.1803i	0.211798	+	0.554495i
$655$	30.4721			1.19064
$656$	12.1803			0.475562
$657$	−28.3607	−	31.7082i	−1.10646	−	1.23705i
$658$	4.00000	−	0.583592i	0.155936	−	0.0227508i
$659$			9.88854i			0.385203i	0.981277	+	0.192601i	$0.0616925\pi$
$659$			9.88854i			0.385203i	−0.981277	+	0.192601i	$0.938308\pi$
$660$	−2.00000	−	5.23607i	−0.0778499	−	0.203814i
$661$		−	44.4721i		−	1.72977i	−0.501974	−	0.864883i	$-0.667393\pi$
$661$		−	44.4721i		−	1.72977i	0.501974	−	0.864883i	$-0.332607\pi$
$662$		−	8.94427i		−	0.347629i
$663$	26.8328	+	70.2492i	1.04210	+	2.72825i
$664$			6.00000i			0.232845i
$665$	−16.9443	+	2.47214i	−0.657071	+	0.0958653i
$666$	8.94427	+	10.0000i	0.346583	+	0.387492i
$667$	−0.583592			−0.0225968
$668$	−13.8885			−0.537364
$669$	−14.5836	−	38.1803i	−0.563834	−	1.47614i
$670$			4.94427i			0.191014i
$671$	−3.52786			−0.136192
$672$	−4.00000	+	2.23607i	−0.154303	+	0.0862582i
$673$	−11.3050			−0.435774			−0.217887	−	0.975974i	$-0.569916\pi$
$673$	−11.3050			−0.435774			−0.217887	+	0.975974i	$0.569916\pi$
$674$		−	13.4164i		−	0.516781i
$675$	−13.0344	+	25.2705i	−0.501696	+	0.972662i
$676$	23.0000			0.884615
$677$	2.76393			0.106227			0.0531133	−	0.998588i	$-0.483086\pi$
$677$	2.76393			0.106227			0.0531133	+	0.998588i	$0.483086\pi$
$678$	−12.9443	+	4.94427i	−0.497122	+	0.189884i
$679$	−6.47214	+	0.944272i	−0.248378	+	0.0362378i
$680$		−	23.4164i		−	0.897978i
$681$	35.5967	−	13.5967i	1.36407	−	0.521029i
$682$		−	0.763932i		−	0.0292525i
$683$			33.8885i			1.29671i	0.761339	+	0.648355i	$0.224543\pi$
$683$			33.8885i			1.29671i	−0.761339	+	0.648355i	$0.775457\pi$
$684$	4.00000	+	4.47214i	0.152944	+	0.170996i
$685$			20.9443i			0.800239i
$686$	−16.7984	+	7.79837i	−0.641365	+	0.297743i
$687$	−1.23607	−	3.23607i	−0.0471589	−	0.123464i
$688$	10.9443			0.417246
$689$	−46.2492			−1.76196
$690$	−6.47214	+	2.47214i	−0.246390	+	0.0941126i
$691$			29.5967i			1.12591i	0.826486	+	0.562957i	$0.190336\pi$
$691$			29.5967i			1.12591i	−0.826486	+	0.562957i	$0.809664\pi$
$692$	−7.70820			−0.293022
$693$	−5.09017	+	6.09017i	−0.193360	+	0.231346i
$694$	16.9443			0.643196
$695$		−	32.3607i		−	1.22751i
$696$	−0.763932	+	0.291796i	−0.0289568	+	0.0110605i
$697$	88.1378			3.33846
$698$	22.0000			0.832712
$699$	15.7082	+	41.1246i	0.594139	+	1.55548i
$700$	−2.09017	−	14.3262i	−0.0790010	−	0.541481i
$701$			17.4164i			0.657809i	0.944363	+	0.328904i	$0.106679\pi$
$701$			17.4164i			0.657809i	−0.944363	+	0.328904i	$0.893321\pi$
$702$	14.2918	−	27.7082i	0.539409	−	1.04578i
$703$			8.94427i			0.337340i
$704$		−	1.00000i		−	0.0376889i
$705$	8.00000	−	3.05573i	0.301297	−	0.115085i
$706$		−	0.944272i		−	0.0355381i
$707$	−2.58359	−	17.7082i	−0.0971660	−	0.665986i
$708$	5.23607	−	2.00000i	0.196783	−	0.0751646i
$709$	−22.5836			−0.848145			−0.424072	−	0.905628i	$-0.639400\pi$
$709$	−22.5836			−0.848145			−0.424072	+	0.905628i	$0.639400\pi$
$710$	−20.0000			−0.750587
$711$	16.1803	−	14.4721i	0.606810	−	0.542748i
$712$		−	12.9443i		−	0.485107i
$713$	−0.944272			−0.0353633
$714$	−28.9443	+	16.1803i	−1.08321	+	0.605534i
$715$	−19.4164			−0.726132
$716$		−	12.9443i		−	0.483750i
$717$	13.5279	+	35.4164i	0.505207	+	1.32265i
$718$	18.8328			0.702834
$719$	−17.5279			−0.653679			−0.326840	−	0.945080i	$-0.605984\pi$
$719$	−17.5279			−0.653679			−0.326840	+	0.945080i	$0.605984\pi$
$720$	−7.23607	+	6.47214i	−0.269672	+	0.241202i
$721$	25.4164	−	3.70820i	0.946556	−	0.138101i
$722$		−	15.0000i		−	0.558242i
$723$	−11.2361	−	29.4164i	−0.417874	−	1.09401i
$724$			3.52786i			0.131112i
$725$		−	2.58359i		−	0.0959522i
$726$	−0.618034	−	1.61803i	−0.0229374	−	0.0600509i
$727$			2.29180i			0.0849980i	0.999097	+	0.0424990i	$0.0135319\pi$
$727$			2.29180i			0.0849980i	−0.999097	+	0.0424990i	$0.986468\pi$
$728$	2.29180	+	15.7082i	0.0849396	+	0.582185i
$729$	−15.6525	−	22.0000i	−0.579721	−	0.814815i
$730$	45.8885			1.69841
$731$	79.1935			2.92908
$732$	2.18034	+	5.70820i	0.0805877	+	0.210981i
$733$		−	26.5836i		−	0.981887i	−0.871191	−	0.490944i	$-0.836652\pi$
$733$		−	26.5836i		−	0.981887i	0.871191	−	0.490944i	$-0.163348\pi$
$734$	26.6525			0.983761
$735$	−31.1246	+	23.8885i	−1.14805	+	0.881142i
$736$	−1.23607			−0.0455621
$737$			1.52786i			0.0562796i
$738$	−24.3607	−	27.2361i	−0.896729	−	1.00257i
$739$	9.41641			0.346388			0.173194	−	0.984888i	$-0.444591\pi$
$739$	9.41641			0.346388			0.173194	+	0.984888i	$0.444591\pi$
$740$	−14.4721			−0.532006
$741$	19.4164	−	7.41641i	0.713280	−	0.272449i
$742$	−2.94427	−	20.1803i	−0.108088	−	0.740844i
$743$		−	1.52786i		−	0.0560519i	−0.999607	−	0.0280259i	$-0.991078\pi$
$743$		−	1.52786i		−	0.0560519i	0.999607	−	0.0280259i	$-0.00892210\pi$
$744$	−1.23607	+	0.472136i	−0.0453165	+	0.0173093i
$745$		−	6.47214i		−	0.237121i
$746$			7.81966i			0.286298i
$747$	13.4164	−	12.0000i	0.490881	−	0.439057i
$748$		−	7.23607i		−	0.264577i
$749$	23.4164	−	3.41641i	0.855617	−	0.124833i
$750$	−0.944272	−	2.47214i	−0.0344799	−	0.0902696i
$751$	−32.3607			−1.18086			−0.590429	−	0.807090i	$-0.701041\pi$
$751$	−32.3607			−1.18086			−0.590429	+	0.807090i	$0.701041\pi$
$752$	1.52786			0.0557155
$753$	2.76393	−	1.05573i	0.100723	−	0.0384729i
$754$			2.83282i			0.103165i
$755$	−39.4164			−1.43451
$756$	13.0000	+	4.47214i	0.472805	+	0.162650i
$757$	−1.41641			−0.0514802			−0.0257401	−	0.999669i	$-0.508194\pi$
$757$	−1.41641			−0.0514802			−0.0257401	+	0.999669i	$0.508194\pi$
$758$			12.3607i			0.448960i
$759$	−2.00000	+	0.763932i	−0.0725954	+	0.0277290i
$760$	−6.47214			−0.234769
$761$	−33.1246			−1.20077			−0.600383	−	0.799713i	$-0.704985\pi$
$761$	−33.1246			−1.20077			−0.600383	+	0.799713i	$0.704985\pi$
$762$	−10.9443	−	28.6525i	−0.396469	−	1.03797i
$763$	3.34752	+	22.9443i	0.121189	+	0.830638i
$764$			11.7082i			0.423588i
$765$	−52.3607	+	46.8328i	−1.89310	+	1.69324i
$766$		−	20.0000i		−	0.722629i
$767$		−	19.4164i		−	0.701086i
$768$	−1.61803	+	0.618034i	−0.0583858	+	0.0223014i
$769$		−	51.4853i		−	1.85661i	−0.371823	−	0.928304i	$-0.621267\pi$
$769$		−	51.4853i		−	1.85661i	0.371823	−	0.928304i	$-0.378733\pi$
$770$	−1.23607	−	8.47214i	−0.0445448	−	0.305315i
$771$	−1.52786	+	0.583592i	−0.0550247	+	0.0210176i
$772$	2.94427			0.105967
$773$	1.12461			0.0404495			0.0202247	−	0.999795i	$-0.493562\pi$
$773$	1.12461			0.0404495			0.0202247	+	0.999795i	$0.493562\pi$
$774$	−21.8885	−	24.4721i	−0.786767	−	0.879633i
$775$		−	4.18034i		−	0.150162i
$776$	−2.47214			−0.0887445
$777$	10.0000	+	17.8885i	0.358748	+	0.641748i
$778$	17.2361			0.617943
$779$		−	24.3607i		−	0.872812i
$780$	12.0000	+	31.4164i	0.429669	+	1.12489i
$781$	−6.18034			−0.221150
$782$	−8.94427			−0.319847
$783$	2.18034	+	1.12461i	0.0779190	+	0.0401903i
$784$	−6.70820	+	2.00000i	−0.239579	+	0.0714286i
$785$			43.4164i			1.54960i
$786$	−5.81966	−	15.2361i	−0.207580	−	0.543453i
$787$			43.5279i			1.55160i	0.630978	+	0.775800i	$0.282654\pi$
$787$			43.5279i			1.55160i	−0.630978	+	0.775800i	$0.717346\pi$
$788$			14.9443i			0.532368i
$789$	13.3050	+	34.8328i	0.473669	+	1.24008i
$790$			23.4164i			0.833118i
$791$	−20.9443	+	3.05573i	−0.744693	+	0.108649i
$792$	−2.23607	+	2.00000i	−0.0794552	+	0.0710669i
$793$	21.1672			0.751669
$794$	14.9443			0.530352
$795$	−15.4164	−	40.3607i	−0.546764	−	1.43145i
$796$			20.1803i			0.715273i
$797$	49.7082			1.76075			0.880377	−	0.474274i	$-0.157289\pi$
$797$	49.7082			1.76075			0.880377	+	0.474274i	$0.157289\pi$
$798$	4.47214	+	8.00000i	0.158312	+	0.283197i
$799$	11.0557			0.391124
$800$		−	5.47214i		−	0.193469i
$801$	−28.9443	+	25.8885i	−1.02270	+	0.914727i
$802$	2.47214			0.0872942
$803$	14.1803			0.500413
$804$	2.47214	−	0.944272i	0.0871855	−	0.0333019i
$805$	−10.4721	+	1.52786i	−0.369094	+	0.0538501i
$806$			4.58359i			0.161450i
$807$	−38.1803	+	14.5836i	−1.34401	+	0.513367i
$808$		−	6.76393i		−	0.237954i
$809$			16.8328i			0.591810i	0.955217	+	0.295905i	$0.0956212\pi$
$809$			16.8328i			0.591810i	−0.955217	+	0.295905i	$0.904379\pi$
$810$	28.9443	+	3.23607i	1.01700	+	0.113704i
$811$		−	46.7214i		−	1.64061i	−0.571927	−	0.820304i	$-0.693804\pi$
$811$		−	46.7214i		−	1.64061i	0.571927	−	0.820304i	$-0.306196\pi$
$812$	−1.23607	+	0.180340i	−0.0433775	+	0.00632869i
$813$	−14.6525	−	38.3607i	−0.513885	−	1.34537i
$814$	−4.47214			−0.156748
$815$	−59.7771			−2.09390
$816$	−11.7082	+	4.47214i	−0.409869	+	0.156556i
$817$		−	21.8885i		−	0.765783i
$818$	5.23607			0.183075
$819$	30.5410	−	36.5410i	1.06719	−	1.27685i
$820$	39.4164			1.37648
$821$		−	1.63932i		−	0.0572127i	−0.999591	−	0.0286063i	$-0.990893\pi$
$821$		−	1.63932i		−	0.0572127i	0.999591	−	0.0286063i	$-0.00910692\pi$
$822$	10.4721	−	4.00000i	0.365258	−	0.139516i
$823$	−38.2492			−1.33328			−0.666642	−	0.745378i	$-0.732269\pi$
$823$	−38.2492			−1.33328			−0.666642	+	0.745378i	$0.732269\pi$
$824$	9.70820			0.338201
$825$	−3.38197	−	8.85410i	−0.117745	−	0.308260i
$826$	8.47214	−	1.23607i	0.294783	−	0.0430083i
$827$		−	16.9443i		−	0.589210i	−0.955619	−	0.294605i	$-0.904812\pi$
$827$		−	16.9443i		−	0.589210i	0.955619	−	0.294605i	$-0.0951881\pi$
$828$	2.47214	+	2.76393i	0.0859127	+	0.0960533i
$829$			23.8885i			0.829683i	0.909894	+	0.414842i	$0.136163\pi$
$829$			23.8885i			0.829683i	−0.909894	+	0.414842i	$0.863837\pi$
$830$			19.4164i			0.673953i
$831$	39.1246	−	14.9443i	1.35722	−	0.518411i
$832$			6.00000i			0.208013i
$833$	−48.5410	+	14.4721i	−1.68185	+	0.501430i
$834$	−16.1803	+	6.18034i	−0.560279	+	0.214008i
$835$	−44.9443			−1.55536
$836$	−2.00000			−0.0691714
$837$	3.52786	+	1.81966i	0.121941	+	0.0628967i
$838$			9.12461i			0.315204i
$839$	−48.9443			−1.68974			−0.844872	−	0.534969i	$-0.820323\pi$
$839$	−48.9443			−1.68974			−0.844872	+	0.534969i	$0.820323\pi$
$840$	−12.9443	+	7.23607i	−0.446620	+	0.249668i
$841$	28.7771			0.992313
$842$		−	4.47214i		−	0.154120i
$843$	−15.7082	−	41.1246i	−0.541019	−	1.41641i
$844$	−9.41641			−0.324126
$845$	74.4296			2.56045
$846$	−3.05573	−	3.41641i	−0.105058	−	0.117459i
$847$	−0.381966	−	2.61803i	−0.0131245	−	0.0899567i
$848$		−	7.70820i		−	0.264701i
$849$	9.23607	+	24.1803i	0.316981	+	0.829867i
$850$		−	39.5967i		−	1.35816i
$851$			5.52786i			0.189493i
$852$	3.81966	+	10.0000i	0.130859	+	0.342594i
$853$		−	6.94427i		−	0.237767i	−0.992908	−	0.118884i	$-0.962068\pi$
$853$		−	6.94427i		−	0.237767i	0.992908	−	0.118884i	$-0.0379316\pi$
$854$	1.34752	+	9.23607i	0.0461113	+	0.316052i
$855$	12.9443	+	14.4721i	0.442685	+	0.494937i
$856$	8.94427			0.305709
$857$	18.2918			0.624836			0.312418	−	0.949945i	$-0.398861\pi$
$857$	18.2918			0.624836			0.312418	+	0.949945i	$0.398861\pi$
$858$	3.70820	+	9.70820i	0.126596	+	0.331433i
$859$		−	4.65248i		−	0.158740i	−0.996845	−	0.0793702i	$-0.974709\pi$
$859$		−	4.65248i		−	0.158740i	0.996845	−	0.0793702i	$-0.0252909\pi$
$860$	35.4164			1.20769
$861$	−27.2361	−	48.7214i	−0.928203	−	1.66042i
$862$	5.88854			0.200565
$863$			25.5967i			0.871323i	0.900110	+	0.435662i	$0.143486\pi$
$863$			25.5967i			0.871323i	−0.900110	+	0.435662i	$0.856514\pi$
$864$	4.61803	+	2.38197i	0.157109	+	0.0810361i
$865$	−24.9443			−0.848131
$866$	−26.4721			−0.899560
$867$	−57.2148	+	21.8541i	−1.94312	+	0.742204i
$868$	−2.00000	+	0.291796i	−0.0678844	+	0.00990420i
$869$			7.23607i			0.245467i
$870$	−2.47214	+	0.944272i	−0.0838133	+	0.0320138i
$871$		−	9.16718i		−	0.310618i
$872$			8.76393i			0.296784i
$873$	4.94427	+	5.52786i	0.167338	+	0.187090i
$874$			2.47214i			0.0836212i
$875$	−0.583592	−	4.00000i	−0.0197290	−	0.135225i
$876$	−8.76393	−	22.9443i	−0.296106	−	0.775215i
$877$	55.0132			1.85766			0.928831	−	0.370503i	$-0.120815\pi$
$877$	55.0132			1.85766			0.928831	+	0.370503i	$0.120815\pi$
$878$	17.2361			0.581689
$879$	−29.4164	+	11.2361i	−0.992191	+	0.378983i
$880$		−	3.23607i		−	0.109088i
$881$	−23.4164			−0.788919			−0.394459	−	0.918913i	$-0.629068\pi$
$881$	−23.4164			−0.788919			−0.394459	+	0.918913i	$0.629068\pi$
$882$	17.8885	+	11.0000i	0.602339	+	0.370389i
$883$	−12.9443			−0.435609			−0.217805	−	0.975992i	$-0.569890\pi$
$883$	−12.9443			−0.435609			−0.217805	+	0.975992i	$0.569890\pi$
$884$			43.4164i			1.46025i
$885$	16.9443	−	6.47214i	0.569575	−	0.217558i
$886$	−29.8885			−1.00413
$887$	−0.944272			−0.0317055			−0.0158528	−	0.999874i	$-0.505046\pi$
$887$	−0.944272			−0.0317055			−0.0158528	+	0.999874i	$0.505046\pi$
$888$	2.76393	+	7.23607i	0.0927515	+	0.242827i
$889$	−6.76393	−	46.3607i	−0.226855	−	1.55489i
$890$		−	41.8885i		−	1.40411i
$891$	8.94427	+	1.00000i	0.299644	+	0.0335013i
$892$		−	23.5967i		−	0.790078i
$893$		−	3.05573i		−	0.102256i
$894$	−3.23607	+	1.23607i	−0.108230	+	0.0413403i
$895$		−	41.8885i		−	1.40018i
$896$	−2.61803	+	0.381966i	−0.0874624	+	0.0127606i
$897$	12.0000	−	4.58359i	0.400668	−	0.153042i
$898$	31.4164			1.04838
$899$	−0.360680			−0.0120293
$900$	−12.2361	+	10.9443i	−0.407869	+	0.364809i
$901$		−	55.7771i		−	1.85820i
$902$	12.1803			0.405561
$903$	−24.4721	−	43.7771i	−0.814382	−	1.45681i
$904$	−8.00000			−0.266076
$905$			11.4164i			0.379494i
$906$	7.52786	+	19.7082i	0.250097	+	0.654761i
$907$	−55.4164			−1.84007			−0.920036	−	0.391834i	$-0.871841\pi$
$907$	−55.4164			−1.84007			−0.920036	+	0.391834i	$0.871841\pi$
$908$	22.0000			0.730096
$909$	−15.1246	+	13.5279i	−0.501652	+	0.448691i
$910$	7.41641	+	50.8328i	0.245852	+	1.68509i
$911$			16.2918i			0.539771i	0.962892	+	0.269886i	$0.0869859\pi$
$911$			16.2918i			0.539771i	−0.962892	+	0.269886i	$0.913014\pi$
$912$	1.23607	+	3.23607i	0.0409303	+	0.107157i
$913$			6.00000i			0.198571i
$914$			2.00000i			0.0661541i
$915$	7.05573	+	18.4721i	0.233255	+	0.610670i
$916$		−	2.00000i		−	0.0660819i
$917$	−3.59675	−	24.6525i	−0.118775	−	0.814096i
$918$	33.4164	+	17.2361i	1.10291	+	0.568875i
$919$	−21.1246			−0.696837			−0.348418	−	0.937339i	$-0.613281\pi$
$919$	−21.1246			−0.696837			−0.348418	+	0.937339i	$0.613281\pi$
$920$	−4.00000			−0.131876
$921$	2.18034	+	5.70820i	0.0718446	+	0.188092i
$922$			41.2361i			1.35804i
$923$	37.0820			1.22057
$924$	−4.00000	+	2.23607i	−0.131590	+	0.0735612i
$925$	−24.4721			−0.804639
$926$			26.4721i			0.869928i
$927$	−19.4164	−	21.7082i	−0.637719	−	0.712991i
$928$	−0.472136			−0.0154986
$929$	0.944272			0.0309806			0.0154903	−	0.999880i	$-0.495069\pi$
$929$	0.944272			0.0309806			0.0154903	+	0.999880i	$0.495069\pi$
$930$	−4.00000	+	1.52786i	−0.131165	+	0.0501006i
$931$	4.00000	+	13.4164i	0.131095	+	0.439705i
$932$			25.4164i			0.832542i
$933$	16.9443	−	6.47214i	0.554731	−	0.211888i
$934$			22.6525i			0.741212i
$935$		−	23.4164i		−	0.765798i
$936$	13.4164	−	12.0000i	0.438529	−	0.392232i
$937$			46.1803i			1.50865i	0.656504	+	0.754323i	$0.272035\pi$
$937$			46.1803i			1.50865i	−0.656504	+	0.754323i	$0.727965\pi$
$938$	4.00000	−	0.583592i	0.130605	−	0.0190550i
$939$	4.94427	+	12.9443i	0.161350	+	0.422420i
$940$	4.94427			0.161264
$941$	−32.2918			−1.05268			−0.526341	−	0.850273i	$-0.676437\pi$
$941$	−32.2918			−1.05268			−0.526341	+	0.850273i	$0.676437\pi$
$942$	21.7082	−	8.29180i	0.707292	−	0.270161i
$943$		−	15.0557i		−	0.490282i
$944$	3.23607			0.105325
$945$	42.0689	+	14.4721i	1.36850	+	0.470779i
$946$	10.9443			0.355829
$947$			32.0000i			1.03986i	0.854209	+	0.519930i	$0.174042\pi$
$947$			32.0000i			1.03986i	−0.854209	+	0.519930i	$0.825958\pi$
$948$	11.7082	−	4.47214i	0.380265	−	0.145248i
$949$	−85.0820			−2.76188
$950$	−10.9443			−0.355079
$951$	−7.59675	−	19.8885i	−0.246341	−	0.644930i
$952$	−18.9443	+	2.76393i	−0.613987	+	0.0895796i
$953$		−	2.36068i		−	0.0764699i	−0.999269	−	0.0382350i	$-0.987826\pi$
$953$		−	2.36068i		−	0.0764699i	0.999269	−	0.0382350i	$-0.0121735\pi$
$954$	−17.2361	+	15.4164i	−0.558038	+	0.499125i
$955$			37.8885i			1.22604i
$956$			21.8885i			0.707926i
$957$	−0.763932	+	0.291796i	−0.0246944	+	0.00943243i
$958$			0.944272i			0.0305080i
$959$	16.9443	−	2.47214i	0.547159	−	0.0798294i
$960$	−5.23607	+	2.00000i	−0.168993	+	0.0645497i
$961$	30.4164			0.981174
$962$	26.8328			0.865125
$963$	−17.8885	−	20.0000i	−0.576450	−	0.644491i
$964$		−	18.1803i		−	0.585549i
$965$	9.52786			0.306713
$966$	2.76393	+	4.94427i	0.0889281	+	0.159079i
$967$	−38.0689			−1.22421			−0.612106	−	0.790775i	$-0.709678\pi$
$967$	−38.0689			−1.22421			−0.612106	+	0.790775i	$0.709678\pi$
$968$		−	1.00000i		−	0.0321412i
$969$	8.94427	+	23.4164i	0.287331	+	0.752243i
$970$	−8.00000			−0.256865
$971$	−8.76393			−0.281248			−0.140624	−	0.990063i	$-0.544911\pi$
$971$	−8.76393			−0.281248			−0.140624	+	0.990063i	$0.544911\pi$
$972$	−3.90983	−	15.0902i	−0.125408	−	0.484017i
$973$	−26.1803	+	3.81966i	−0.839303	+	0.122453i
$974$		−	1.52786i		−	0.0489559i
$975$	20.2918	+	53.1246i	0.649858	+	1.70135i
$976$			3.52786i			0.112924i
$977$		−	21.3050i		−	0.681606i	−0.940135	−	0.340803i	$-0.889301\pi$
$977$		−	21.3050i		−	0.681606i	0.940135	−	0.340803i	$-0.110699\pi$
$978$	11.4164	+	29.8885i	0.365056	+	0.955730i
$979$		−	12.9443i		−	0.413701i
$980$	−21.7082	+	6.47214i	−0.693443	+	0.206745i
$981$	19.5967	−	17.5279i	0.625676	−	0.559622i
$982$		0			0
$983$	15.0557			0.480203			0.240102	−	0.970748i	$-0.422819\pi$
$983$	15.0557			0.480203			0.240102	+	0.970748i	$0.422819\pi$
$984$	−7.52786	−	19.7082i	−0.239980	−	0.628275i
$985$			48.3607i			1.54090i
$986$	−3.41641			−0.108801
$987$	−3.41641	−	6.11146i	−0.108745	−	0.194530i
$988$	12.0000			0.381771
$989$		−	13.5279i		−	0.430161i
$990$	−7.23607	+	6.47214i	−0.229977	+	0.205698i
$991$	−0.944272			−0.0299958			−0.0149979	−	0.999888i	$-0.504774\pi$
$991$	−0.944272			−0.0299958			−0.0149979	+	0.999888i	$0.504774\pi$
$992$	−0.763932			−0.0242549
$993$	−14.4721	+	5.52786i	−0.459259	+	0.175421i
$994$	2.36068	+	16.1803i	0.0748762	+	0.513209i
$995$			65.3050i			2.07031i
$996$	9.70820	−	3.70820i	0.307616	−	0.117499i
$997$			32.4721i			1.02840i	0.857669	+	0.514201i	$0.171912\pi$
$997$			32.4721i			1.02840i	−0.857669	+	0.514201i	$0.828088\pi$
$998$		−	19.0557i		−	0.603199i
$999$	10.6525	−	20.6525i	0.337029	−	0.653415i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	462.2.g.a.419.1	✓	4
3.2	odd	2		462.2.g.d.419.4	yes	4
7.6	odd	2		462.2.g.d.419.2	yes	4
21.20	even	2	inner	462.2.g.a.419.3	yes	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
462.2.g.a.419.1	✓	4	1.1	even	1	trivial
462.2.g.a.419.3	yes	4	21.20	even	2	inner
462.2.g.d.419.2	yes	4	7.6	odd	2
462.2.g.d.419.4	yes	4	3.2	odd	2

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:	\( N \)	\(=\)	\( 462 = 2 \cdot 3 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	462.g (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-1.00000i q^{2} +(-1.61803 + 0.618034i) q^{3} -1.00000 q^{4} -3.23607 q^{5} +(0.618034 + 1.61803i) q^{6} +(0.381966 + 2.61803i) q^{7} +1.00000i q^{8} +(2.23607 - 2.00000i) q^{9} +O(q^{10})\)	\(q-1.00000i q^{2} +(-1.61803 + 0.618034i) q^{3} -1.00000 q^{4} -3.23607 q^{5} +(0.618034 + 1.61803i) q^{6} +(0.381966 + 2.61803i) q^{7} +1.00000i q^{8} +(2.23607 - 2.00000i) q^{9} +3.23607i q^{10} +1.00000i q^{11} +(1.61803 - 0.618034i) q^{12} -6.00000i q^{13} +(2.61803 - 0.381966i) q^{14} +(5.23607 - 2.00000i) q^{15} +1.00000 q^{16} +7.23607 q^{17} +(-2.00000 - 2.23607i) q^{18} -2.00000i q^{19} +3.23607 q^{20} +(-2.23607 - 4.00000i) q^{21} +1.00000 q^{22} -1.23607i q^{23} +(-0.618034 - 1.61803i) q^{24} +5.47214 q^{25} -6.00000 q^{26} +(-2.38197 + 4.61803i) q^{27} +(-0.381966 - 2.61803i) q^{28} -0.472136i q^{29} +(-2.00000 - 5.23607i) q^{30} -0.763932i q^{31} -1.00000i q^{32} +(-0.618034 - 1.61803i) q^{33} -7.23607i q^{34} +(-1.23607 - 8.47214i) q^{35} +(-2.23607 + 2.00000i) q^{36} -4.47214 q^{37} -2.00000 q^{38} +(3.70820 + 9.70820i) q^{39} -3.23607i q^{40} +12.1803 q^{41} +(-4.00000 + 2.23607i) q^{42} +10.9443 q^{43} -1.00000i q^{44} +(-7.23607 + 6.47214i) q^{45} -1.23607 q^{46} +1.52786 q^{47} +(-1.61803 + 0.618034i) q^{48} +(-6.70820 + 2.00000i) q^{49} -5.47214i q^{50} +(-11.7082 + 4.47214i) q^{51} +6.00000i q^{52} -7.70820i q^{53} +(4.61803 + 2.38197i) q^{54} -3.23607i q^{55} +(-2.61803 + 0.381966i) q^{56} +(1.23607 + 3.23607i) q^{57} -0.472136 q^{58} +3.23607 q^{59} +(-5.23607 + 2.00000i) q^{60} +3.52786i q^{61} -0.763932 q^{62} +(6.09017 + 5.09017i) q^{63} -1.00000 q^{64} +19.4164i q^{65} +(-1.61803 + 0.618034i) q^{66} +1.52786 q^{67} -7.23607 q^{68} +(0.763932 + 2.00000i) q^{69} +(-8.47214 + 1.23607i) q^{70} +6.18034i q^{71} +(2.00000 + 2.23607i) q^{72} -14.1803i q^{73} +4.47214i q^{74} +(-8.85410 + 3.38197i) q^{75} +2.00000i q^{76} +(-2.61803 + 0.381966i) q^{77} +(9.70820 - 3.70820i) q^{78} +7.23607 q^{79} -3.23607 q^{80} +(1.00000 - 8.94427i) q^{81} -12.1803i q^{82} +6.00000 q^{83} +(2.23607 + 4.00000i) q^{84} -23.4164 q^{85} -10.9443i q^{86} +(0.291796 + 0.763932i) q^{87} -1.00000 q^{88} -12.9443 q^{89} +(6.47214 + 7.23607i) q^{90} +(15.7082 - 2.29180i) q^{91} +1.23607i q^{92} +(0.472136 + 1.23607i) q^{93} -1.52786i q^{94} +6.47214i q^{95} +(0.618034 + 1.61803i) q^{96} +2.47214i q^{97} +(2.00000 + 6.70820i) q^{98} +(2.00000 + 2.23607i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 2 q^{3} - 4 q^{4} - 4 q^{5} - 2 q^{6} + 6 q^{7}+O(q^{10}) \) 4 * q - 2 * q^3 - 4 * q^4 - 4 * q^5 - 2 * q^6 + 6 * q^7	\( 4 q - 2 q^{3} - 4 q^{4} - 4 q^{5} - 2 q^{6} + 6 q^{7} + 2 q^{12} + 6 q^{14} + 12 q^{15} + 4 q^{16} + 20 q^{17} - 8 q^{18} + 4 q^{20} + 4 q^{22} + 2 q^{24} + 4 q^{25} - 24 q^{26} - 14 q^{27} - 6 q^{28} - 8 q^{30} + 2 q^{33} + 4 q^{35} - 8 q^{38} - 12 q^{39} + 4 q^{41} - 16 q^{42} + 8 q^{43} - 20 q^{45} + 4 q^{46} + 24 q^{47} - 2 q^{48} - 20 q^{51} + 14 q^{54} - 6 q^{56} - 4 q^{57} + 16 q^{58} + 4 q^{59} - 12 q^{60} - 12 q^{62} + 2 q^{63} - 4 q^{64} - 2 q^{66} + 24 q^{67} - 20 q^{68} + 12 q^{69} - 16 q^{70} + 8 q^{72} - 22 q^{75} - 6 q^{77} + 12 q^{78} + 20 q^{79} - 4 q^{80} + 4 q^{81} + 24 q^{83} - 40 q^{85} + 28 q^{87} - 4 q^{88} - 16 q^{89} + 8 q^{90} + 36 q^{91} - 16 q^{93} - 2 q^{96} + 8 q^{98} + 8 q^{99}+O(q^{100}) \) 4 * q - 2 * q^3 - 4 * q^4 - 4 * q^5 - 2 * q^6 + 6 * q^7 + 2 * q^12 + 6 * q^14 + 12 * q^15 + 4 * q^16 + 20 * q^17 - 8 * q^18 + 4 * q^20 + 4 * q^22 + 2 * q^24 + 4 * q^25 - 24 * q^26 - 14 * q^27 - 6 * q^28 - 8 * q^30 + 2 * q^33 + 4 * q^35 - 8 * q^38 - 12 * q^39 + 4 * q^41 - 16 * q^42 + 8 * q^43 - 20 * q^45 + 4 * q^46 + 24 * q^47 - 2 * q^48 - 20 * q^51 + 14 * q^54 - 6 * q^56 - 4 * q^57 + 16 * q^58 + 4 * q^59 - 12 * q^60 - 12 * q^62 + 2 * q^63 - 4 * q^64 - 2 * q^66 + 24 * q^67 - 20 * q^68 + 12 * q^69 - 16 * q^70 + 8 * q^72 - 22 * q^75 - 6 * q^77 + 12 * q^78 + 20 * q^79 - 4 * q^80 + 4 * q^81 + 24 * q^83 - 40 * q^85 + 28 * q^87 - 4 * q^88 - 16 * q^89 + 8 * q^90 + 36 * q^91 - 16 * q^93 - 2 * q^96 + 8 * q^98 + 8 * q^99

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