LMFDB - Embedded newform 950.2.j.g.49.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [950,2,Mod(49,950)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(950, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 4]))

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

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

chi := DirichletCharacter("950.49");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 950 = 2 \cdot 5^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	950.j (of order $6$, degree $2$, not 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:	$7.58578819202$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
Coefficient field:	8.0.49787136.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 3x^{6} + 5x^{4} + 12x^{2} + 16 $ x^8 + 3x^6 + 5x^4 + 12*x^2 + 16
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	no (minimal twist has level 38)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			49.2
Root			$1.09445 - 0.895644i$ of defining polynomial
Character	$\chi$	$=$	950.49
Dual form			950.2.j.g.349.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.866025 - 0.500000i) q^{2} +(2.29129 + 1.32288i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-1.32288 - 2.29129i) q^{6} +3.64575i q^{7} -1.00000i q^{8} +(2.00000 + 3.46410i) q^{9} +O(q^{10})$	\(q+(-0.866025 - 0.500000i) q^{2} +(2.29129 + 1.32288i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-1.32288 - 2.29129i) q^{6} +3.64575i q^{7} -1.00000i q^{8} +(2.00000 + 3.46410i) q^{9} -4.64575 q^{11} +2.64575i q^{12} +(-1.73205 + 1.00000i) q^{13} +(1.82288 - 3.15731i) q^{14} +(-0.500000 + 0.866025i) q^{16} -4.00000i q^{18} +(-1.67712 + 4.02334i) q^{19} +(-4.82288 + 8.35347i) q^{21} +(4.02334 + 2.32288i) q^{22} +(1.42526 - 0.822876i) q^{23} +(1.32288 - 2.29129i) q^{24} +2.00000 q^{26} +2.64575i q^{27} +(-3.15731 + 1.82288i) q^{28} +(0.822876 + 1.42526i) q^{29} -5.64575 q^{31} +(0.866025 - 0.500000i) q^{32} +(-10.6448 - 6.14575i) q^{33} +(-2.00000 + 3.46410i) q^{36} +0.354249i q^{37} +(3.46410 - 2.64575i) q^{38} -5.29150 q^{39} +(0.145751 - 0.252449i) q^{41} +(8.35347 - 4.82288i) q^{42} +(9.77873 + 5.64575i) q^{43} +(-2.32288 - 4.02334i) q^{44} -1.64575 q^{46} +(3.77089 - 2.17712i) q^{47} +(-2.29129 + 1.32288i) q^{48} -6.29150 q^{49} +(-1.73205 - 1.00000i) q^{52} +(10.8972 - 6.29150i) q^{53} +(1.32288 - 2.29129i) q^{54} +3.64575 q^{56} +(-9.16515 + 7.00000i) q^{57} -1.64575i q^{58} +(-3.96863 + 6.87386i) q^{59} +(-0.468627 - 0.811686i) q^{61} +(4.88936 + 2.82288i) q^{62} +(-12.6293 + 7.29150i) q^{63} -1.00000 q^{64} +(6.14575 + 10.6448i) q^{66} +(0.559237 - 0.322876i) q^{67} +4.35425 q^{69} +(1.35425 - 2.34563i) q^{71} +(3.46410 - 2.00000i) q^{72} +(1.47960 + 0.854249i) q^{73} +(0.177124 - 0.306788i) q^{74} +(-4.32288 + 0.559237i) q^{76} -16.9373i q^{77} +(4.58258 + 2.64575i) q^{78} +(-2.00000 + 3.46410i) q^{79} +(2.50000 - 4.33013i) q^{81} +(-0.252449 + 0.145751i) q^{82} -7.93725i q^{83} -9.64575 q^{84} +(-5.64575 - 9.77873i) q^{86} +4.35425i q^{87} +4.64575i q^{88} +(-3.64575 - 6.31463i) q^{91} +(1.42526 + 0.822876i) q^{92} +(-12.9360 - 7.46863i) q^{93} -4.35425 q^{94} +2.64575 q^{96} +(3.21165 + 1.85425i) q^{97} +(5.44860 + 3.14575i) q^{98} +(-9.29150 - 16.0934i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 4 q^{4} + 16 q^{9}+O(q^{10}) $ 8 * q + 4 * q^4 + 16 * q^9	$ 8 q + 4 q^{4} + 16 q^{9} - 16 q^{11} + 4 q^{14} - 4 q^{16} - 24 q^{19} - 28 q^{21} + 16 q^{26} - 4 q^{29} - 24 q^{31} - 16 q^{36} - 20 q^{41} - 8 q^{44} + 8 q^{46} - 8 q^{49} + 8 q^{56} + 28 q^{61} - 8 q^{64} + 28 q^{66} + 56 q^{69} + 32 q^{71} + 12 q^{74} - 24 q^{76} - 16 q^{79} + 20 q^{81} - 56 q^{84} - 24 q^{86} - 8 q^{91} - 56 q^{94} - 32 q^{99}+O(q^{100}) $ 8 * q + 4 * q^4 + 16 * q^9 - 16 * q^11 + 4 * q^14 - 4 * q^16 - 24 * q^19 - 28 * q^21 + 16 * q^26 - 4 * q^29 - 24 * q^31 - 16 * q^36 - 20 * q^41 - 8 * q^44 + 8 * q^46 - 8 * q^49 + 8 * q^56 + 28 * q^61 - 8 * q^64 + 28 * q^66 + 56 * q^69 + 32 * q^71 + 12 * q^74 - 24 * q^76 - 16 * q^79 + 20 * q^81 - 56 * q^84 - 24 * q^86 - 8 * q^91 - 56 * q^94 - 32 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/950\mathbb{Z}\right)^\times$.

$n$	$77$	$401$
$\chi(n)$	$-1$	$e\left(\frac{2}{3}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−0.866025	−	0.500000i	−0.612372	−	0.353553i
$2$	−0.866025	−	0.500000i	−0.612372	−	0.353553i
$3$	2.29129	+	1.32288i	1.32288	+	0.763763i	0.984186	−	0.177136i	$-0.0566831\pi$
$3$	2.29129	+	1.32288i	1.32288	+	0.763763i	0.338689	+	0.940898i	$0.390016\pi$
$4$	0.500000	+	0.866025i	0.250000	+	0.433013i
$5$		0			0
$5$		0			0
$6$	−1.32288	−	2.29129i	−0.540062	−	0.935414i
$7$			3.64575i			1.37796i	0.724778	+	0.688982i	$0.241942\pi$
$7$			3.64575i			1.37796i	−0.724778	+	0.688982i	$0.758058\pi$
$8$		−	1.00000i		−	0.353553i
$9$	2.00000	+	3.46410i	0.666667	+	1.15470i
$10$		0			0
$11$	−4.64575			−1.40075			−0.700373	−	0.713777i	$-0.746983\pi$
$11$	−4.64575			−1.40075			−0.700373	+	0.713777i	$0.746983\pi$
$12$			2.64575i			0.763763i
$13$	−1.73205	+	1.00000i	−0.480384	+	0.277350i	−0.720577	−	0.693375i	$-0.756123\pi$
$13$	−1.73205	+	1.00000i	−0.480384	+	0.277350i	0.240192	+	0.970725i	$0.422790\pi$
$14$	1.82288	−	3.15731i	0.487184	−	0.843827i
$15$		0			0
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$17$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$18$		−	4.00000i		−	0.942809i
$19$	−1.67712	+	4.02334i	−0.384759	+	0.923017i
$19$	−1.67712	+	4.02334i	−0.384759	+	0.923017i
$20$		0			0
$21$	−4.82288	+	8.35347i	−1.05244	+	1.82288i
$22$	4.02334	+	2.32288i	0.857779	+	0.495239i
$23$	1.42526	−	0.822876i	0.297188	−	0.171581i	−0.343991	−	0.938973i	$-0.611779\pi$
$23$	1.42526	−	0.822876i	0.297188	−	0.171581i	0.641179	+	0.767391i	$0.278446\pi$
$24$	1.32288	−	2.29129i	0.270031	−	0.467707i
$25$		0			0
$26$	2.00000			0.392232
$27$			2.64575i			0.509175i
$28$	−3.15731	+	1.82288i	−0.596676	+	0.344491i
$29$	0.822876	+	1.42526i	0.152804	+	0.264665i	0.932257	−	0.361796i	$-0.117836\pi$
$29$	0.822876	+	1.42526i	0.152804	+	0.264665i	−0.779453	+	0.626461i	$0.784503\pi$
$30$		0			0
$31$	−5.64575			−1.01401			−0.507003	−	0.861944i	$-0.669247\pi$
$31$	−5.64575			−1.01401			−0.507003	+	0.861944i	$0.669247\pi$
$32$	0.866025	−	0.500000i	0.153093	−	0.0883883i
$33$	−10.6448	−	6.14575i	−1.85301	−	1.06984i
$34$		0			0
$35$		0			0
$36$	−2.00000	+	3.46410i	−0.333333	+	0.577350i
$37$			0.354249i			0.0582381i	0.999576	+	0.0291191i	$0.00927020\pi$
$37$			0.354249i			0.0582381i	−0.999576	+	0.0291191i	$0.990730\pi$
$38$	3.46410	−	2.64575i	0.561951	−	0.429198i
$39$	−5.29150			−0.847319
$40$		0			0
$41$	0.145751	−	0.252449i	0.0227625	−	0.0394259i	−0.854420	−	0.519583i	$-0.826087\pi$
$41$	0.145751	−	0.252449i	0.0227625	−	0.0394259i	0.877182	+	0.480158i	$0.159421\pi$
$42$	8.35347	−	4.82288i	1.28897	−	0.744186i
$43$	9.77873	+	5.64575i	1.49124	+	0.860969i	0.999950	−	0.0100257i	$-0.00319135\pi$
$43$	9.77873	+	5.64575i	1.49124	+	0.860969i	0.491292	+	0.870995i	$0.336525\pi$
$44$	−2.32288	−	4.02334i	−0.350187	−	0.606541i
$45$		0			0
$46$	−1.64575			−0.242653
$47$	3.77089	−	2.17712i	0.550041	−	0.317566i	−0.199098	−	0.979980i	$-0.563801\pi$
$47$	3.77089	−	2.17712i	0.550041	−	0.317566i	0.749138	+	0.662413i	$0.230468\pi$
$48$	−2.29129	+	1.32288i	−0.330719	+	0.190941i
$49$	−6.29150			−0.898786
$50$		0			0
$51$		0			0
$52$	−1.73205	−	1.00000i	−0.240192	−	0.138675i
$53$	10.8972	−	6.29150i	1.49685	−	0.864204i	0.496852	−	0.867835i	$-0.334489\pi$
$53$	10.8972	−	6.29150i	1.49685	−	0.864204i	0.999993	+	0.00363070i	$0.00115569\pi$
$54$	1.32288	−	2.29129i	0.180021	−	0.311805i
$55$		0			0
$56$	3.64575			0.487184
$57$	−9.16515	+	7.00000i	−1.21395	+	0.927173i
$58$		−	1.64575i		−	0.216098i
$59$	−3.96863	+	6.87386i	−0.516671	+	0.894901i	0.483141	+	0.875542i	$0.339496\pi$
$59$	−3.96863	+	6.87386i	−0.516671	+	0.894901i	−0.999813	+	0.0193585i	$0.993838\pi$
$60$		0			0
$61$	−0.468627	−	0.811686i	−0.0600015	−	0.103926i	0.834464	−	0.551062i	$-0.185777\pi$
$61$	−0.468627	−	0.811686i	−0.0600015	−	0.103926i	−0.894466	+	0.447136i	$0.852444\pi$
$62$	4.88936	+	2.82288i	0.620950	+	0.358506i
$63$	−12.6293	+	7.29150i	−1.59114	+	0.918643i
$64$	−1.00000			−0.125000
$65$		0			0
$66$	6.14575	+	10.6448i	0.756490	+	1.31028i
$67$	0.559237	−	0.322876i	0.0683217	−	0.0394455i	−0.465450	−	0.885074i	$-0.654108\pi$
$67$	0.559237	−	0.322876i	0.0683217	−	0.0394455i	0.533772	+	0.845629i	$0.320774\pi$
$68$		0			0
$69$	4.35425			0.524190
$70$		0			0
$71$	1.35425	−	2.34563i	0.160720	−	0.278375i	−0.774407	−	0.632687i	$-0.781952\pi$
$71$	1.35425	−	2.34563i	0.160720	−	0.278375i	0.935127	+	0.354313i	$0.115285\pi$
$72$	3.46410	−	2.00000i	0.408248	−	0.235702i
$73$	1.47960	+	0.854249i	0.173174	+	0.0999822i	0.584082	−	0.811695i	$-0.301455\pi$
$73$	1.47960	+	0.854249i	0.173174	+	0.0999822i	−0.410907	+	0.911677i	$0.634788\pi$
$74$	0.177124	−	0.306788i	0.0205903	−	0.0356634i
$75$		0			0
$76$	−4.32288	+	0.559237i	−0.495868	+	0.0641489i
$77$		−	16.9373i		−	1.93018i
$78$	4.58258	+	2.64575i	0.518875	+	0.299572i
$79$	−2.00000	+	3.46410i	−0.225018	+	0.389742i	−0.956325	−	0.292306i	$-0.905577\pi$
$79$	−2.00000	+	3.46410i	−0.225018	+	0.389742i	0.731307	+	0.682048i	$0.238911\pi$
$80$		0			0
$81$	2.50000	−	4.33013i	0.277778	−	0.481125i
$82$	−0.252449	+	0.145751i	−0.0278783	+	0.0160955i
$83$		−	7.93725i		−	0.871227i	−0.900134	−	0.435613i	$-0.856531\pi$
$83$		−	7.93725i		−	0.871227i	0.900134	−	0.435613i	$-0.143469\pi$
$84$	−9.64575			−1.05244
$85$		0			0
$86$	−5.64575	−	9.77873i	−0.608797	−	1.05447i
$87$			4.35425i			0.466824i
$88$			4.64575i			0.495239i
$89$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$89$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$90$		0			0
$91$	−3.64575	−	6.31463i	−0.382179	−	0.661953i
$92$	1.42526	+	0.822876i	0.148594	+	0.0857907i
$93$	−12.9360	−	7.46863i	−1.34141	−	0.774461i
$94$	−4.35425			−0.449106
$95$		0			0
$96$	2.64575			0.270031
$97$	3.21165	+	1.85425i	0.326094	+	0.188270i	0.654106	−	0.756403i	$-0.273045\pi$
$97$	3.21165	+	1.85425i	0.326094	+	0.188270i	−0.328012	+	0.944674i	$0.606379\pi$
$98$	5.44860	+	3.14575i	0.550392	+	0.317769i
$99$	−9.29150	−	16.0934i	−0.933831	−	1.61744i
$100$		0			0
$101$	6.82288	+	11.8176i	0.678902	+	1.17589i	0.975312	+	0.220831i	$0.0708770\pi$
$101$	6.82288	+	11.8176i	0.678902	+	1.17589i	−0.296411	+	0.955061i	$0.595790\pi$
$102$		0			0
$103$			13.2915i			1.30965i	0.755780	+	0.654825i	$0.227258\pi$
$103$			13.2915i			1.30965i	−0.755780	+	0.654825i	$0.772742\pi$
$104$	1.00000	+	1.73205i	0.0980581	+	0.169842i
$105$		0			0
$106$	−12.5830			−1.22217
$107$			15.2915i			1.47829i	0.673549	+	0.739143i	$0.264769\pi$
$107$			15.2915i			1.47829i	−0.673549	+	0.739143i	$0.735231\pi$
$108$	−2.29129	+	1.32288i	−0.220479	+	0.127294i
$109$	7.29150	−	12.6293i	0.698399	−	1.20966i	−0.270622	−	0.962686i	$-0.587229\pi$
$109$	7.29150	−	12.6293i	0.698399	−	1.20966i	0.969021	−	0.246977i	$-0.0794373\pi$
$110$		0			0
$111$	−0.468627	+	0.811686i	−0.0444801	+	0.0770418i
$112$	−3.15731	−	1.82288i	−0.298338	−	0.172246i
$113$			15.5830i			1.46593i	0.680269	+	0.732963i	$0.261863\pi$
$113$			15.5830i			1.46593i	−0.680269	+	0.732963i	$0.738137\pi$
$114$	11.4373	−	1.47960i	1.07120	−	0.138577i
$115$		0			0
$116$	−0.822876	+	1.42526i	−0.0764021	+	0.132332i
$117$	−6.92820	−	4.00000i	−0.640513	−	0.369800i
$118$	6.87386	−	3.96863i	0.632790	−	0.365342i
$119$		0			0
$120$		0			0
$121$	10.5830			0.962091
$122$			0.937254i			0.0848550i
$123$	0.667916	−	0.385622i	0.0602240	−	0.0347703i
$124$	−2.82288	−	4.88936i	−0.253502	−	0.439078i
$125$		0			0
$126$	14.5830			1.29916
$127$	−11.5108	+	6.64575i	−1.02142	+	0.589715i	−0.914514	−	0.404554i	$-0.867427\pi$
$127$	−11.5108	+	6.64575i	−1.02142	+	0.589715i	−0.106903	+	0.994270i	$0.534093\pi$
$128$	0.866025	+	0.500000i	0.0765466	+	0.0441942i
$129$	14.9373	+	25.8721i	1.31515	+	2.27791i
$130$		0			0
$131$	−0.968627	+	1.67771i	−0.0846293	+	0.146582i	−0.905233	−	0.424915i	$-0.860304\pi$
$131$	−0.968627	+	1.67771i	−0.0846293	+	0.146582i	0.820604	+	0.571497i	$0.193637\pi$
$132$		−	12.2915i		−	1.06984i
$133$	−14.6681	−	6.11438i	−1.27188	−	0.530184i
$134$	−0.645751			−0.0557844
$135$		0			0
$136$		0			0
$137$	13.4953	−	7.79150i	1.15298	−	0.665673i	0.203368	−	0.979102i	$-0.434811\pi$
$137$	13.4953	−	7.79150i	1.15298	−	0.665673i	0.949612	+	0.313429i	$0.101478\pi$
$138$	−3.77089	−	2.17712i	−0.320999	−	0.185329i
$139$	9.32288	+	16.1477i	0.790756	+	1.36963i	0.925499	+	0.378749i	$0.123646\pi$
$139$	9.32288	+	16.1477i	0.790756	+	1.36963i	−0.134743	+	0.990881i	$0.543021\pi$
$140$		0			0
$141$	11.5203			0.970181
$142$	−2.34563	+	1.35425i	−0.196841	+	0.113646i
$143$	8.04668	−	4.64575i	0.672897	−	0.388497i
$144$	−4.00000			−0.333333
$145$		0			0
$146$	−0.854249	−	1.47960i	−0.0706981	−	0.122453i
$147$	−14.4156	−	8.32288i	−1.18898	−	0.686459i
$148$	−0.306788	+	0.177124i	−0.0252178	+	0.0145595i
$149$	5.46863	−	9.47194i	0.448007	−	0.775972i	−0.550249	−	0.835001i	$-0.685467\pi$
$149$	5.46863	−	9.47194i	0.448007	−	0.775972i	0.998256	+	0.0590292i	$0.0188005\pi$
$150$		0			0
$151$	12.9373			1.05282			0.526409	−	0.850231i	$-0.323538\pi$
$151$	12.9373			1.05282			0.526409	+	0.850231i	$0.323538\pi$
$152$	4.02334	+	1.67712i	0.326336	+	0.136033i
$153$		0			0
$154$	−8.46863	+	14.6681i	−0.682421	+	1.18199i
$155$		0			0
$156$	−2.64575	−	4.58258i	−0.211830	−	0.366900i
$157$	9.16515	+	5.29150i	0.731459	+	0.422308i	0.818956	−	0.573857i	$-0.194553\pi$
$157$	9.16515	+	5.29150i	0.731459	+	0.422308i	−0.0874969	+	0.996165i	$0.527887\pi$
$158$	3.46410	−	2.00000i	0.275589	−	0.159111i
$159$	33.2915			2.64019
$160$		0			0
$161$	3.00000	+	5.19615i	0.236433	+	0.409514i
$162$	−4.33013	+	2.50000i	−0.340207	+	0.196419i
$163$		−	3.93725i		−	0.308390i	−0.988040	−	0.154195i	$-0.950722\pi$
$163$		−	3.93725i		−	0.308390i	0.988040	−	0.154195i	$-0.0492783\pi$
$164$	0.291503			0.0227625
$165$		0			0
$166$	−3.96863	+	6.87386i	−0.308025	+	0.533515i
$167$	−10.3923	+	6.00000i	−0.804181	+	0.464294i	−0.844931	−	0.534875i	$-0.820359\pi$
$167$	−10.3923	+	6.00000i	−0.804181	+	0.464294i	0.0407502	+	0.999169i	$0.487025\pi$
$168$	8.35347	+	4.82288i	0.644484	+	0.372093i
$169$	−4.50000	+	7.79423i	−0.346154	+	0.599556i
$170$		0			0
$171$	−17.2915	+	2.23695i	−1.32231	+	0.171064i
$172$			11.2915i			0.860969i
$173$	−5.19615	−	3.00000i	−0.395056	−	0.228086i	0.289292	−	0.957241i	$-0.406580\pi$
$173$	−5.19615	−	3.00000i	−0.395056	−	0.228086i	−0.684349	+	0.729155i	$0.739913\pi$
$174$	2.17712	−	3.77089i	0.165047	−	0.285870i
$175$		0			0
$176$	2.32288	−	4.02334i	0.175093	−	0.303271i
$177$	−18.1865	+	10.5000i	−1.36698	+	0.789228i
$178$		0			0
$179$	−4.06275			−0.303664			−0.151832	−	0.988406i	$-0.548517\pi$
$179$	−4.06275			−0.303664			−0.151832	+	0.988406i	$0.548517\pi$
$180$		0			0
$181$	−11.1144	−	19.2507i	−0.826125	−	1.43089i	−0.901056	−	0.433702i	$-0.857207\pi$
$181$	−11.1144	−	19.2507i	−0.826125	−	1.43089i	0.0749311	−	0.997189i	$-0.476126\pi$
$182$			7.29150i			0.540482i
$183$		−	2.47974i		−	0.183308i
$184$	−0.822876	−	1.42526i	−0.0606632	−	0.105072i
$185$		0			0
$186$	7.46863	+	12.9360i	0.547626	+	0.948517i
$187$		0			0
$188$	3.77089	+	2.17712i	0.275020	+	0.158783i
$189$	−9.64575			−0.701625
$190$		0			0
$191$	6.58301			0.476330			0.238165	−	0.971225i	$-0.423454\pi$
$191$	6.58301			0.476330			0.238165	+	0.971225i	$0.423454\pi$
$192$	−2.29129	−	1.32288i	−0.165359	−	0.0954703i
$193$	12.6293	+	7.29150i	0.909074	+	0.524854i	0.880133	−	0.474727i	$-0.157453\pi$
$193$	12.6293	+	7.29150i	0.909074	+	0.524854i	0.0289406	+	0.999581i	$0.490787\pi$
$194$	−1.85425	−	3.21165i	−0.133127	−	0.230583i
$195$		0			0
$196$	−3.14575	−	5.44860i	−0.224697	−	0.389186i
$197$		−	7.64575i		−	0.544737i	−0.962193	−	0.272369i	$-0.912193\pi$
$197$		−	7.64575i		−	0.544737i	0.962193	−	0.272369i	$-0.0878070\pi$
$198$			18.5830i			1.32064i
$199$	−9.93725	−	17.2118i	−0.704433	−	1.22011i	−0.966896	−	0.255172i	$-0.917868\pi$
$199$	−9.93725	−	17.2118i	−0.704433	−	1.22011i	0.262462	−	0.964942i	$-0.415465\pi$
$200$		0			0
$201$	1.70850			0.120508
$202$		−	13.6458i		−	0.960112i
$203$	−5.19615	+	3.00000i	−0.364698	+	0.210559i
$204$		0			0
$205$		0			0
$206$	6.64575	−	11.5108i	0.463031	−	0.801994i
$207$	5.70105	+	3.29150i	0.396250	+	0.228775i
$208$		−	2.00000i		−	0.138675i
$209$	7.79150	−	18.6914i	0.538950	−	1.29291i
$210$		0			0
$211$	6.64575	−	11.5108i	0.457512	−	0.792435i	−0.541316	−	0.840819i	$-0.682074\pi$
$211$	6.64575	−	11.5108i	0.457512	−	0.792435i	0.998829	+	0.0483843i	$0.0154072\pi$
$212$	10.8972	+	6.29150i	0.748423	+	0.432102i
$213$	6.20595	−	3.58301i	0.425224	−	0.245503i
$214$	7.64575	−	13.2428i	0.522653	−	0.905261i
$215$		0			0
$216$	2.64575			0.180021
$217$		−	20.5830i		−	1.39727i
$218$	−12.6293	+	7.29150i	−0.855361	+	0.493843i
$219$	2.26013	+	3.91466i	0.152725	+	0.264528i
$220$		0			0
$221$		0			0
$222$	0.811686	−	0.468627i	0.0544768	−	0.0314522i
$223$	−16.2915	−	9.40588i	−1.09096	−	0.629864i	−0.157126	−	0.987579i	$-0.550223\pi$
$223$	−16.2915	−	9.40588i	−1.09096	−	0.629864i	−0.933831	+	0.357714i	$0.883556\pi$
$224$	1.82288	+	3.15731i	0.121796	+	0.210957i
$225$		0			0
$226$	7.79150	−	13.4953i	0.518283	−	0.897693i
$227$		−	7.35425i		−	0.488119i	−0.969760	−	0.244059i	$-0.921521\pi$
$227$		−	7.35425i		−	0.488119i	0.969760	−	0.244059i	$-0.0784792\pi$
$228$	−10.6448	−	4.43725i	−0.704966	−	0.293864i
$229$	−20.0000			−1.32164			−0.660819	−	0.750546i	$-0.729791\pi$
$229$	−20.0000			−1.32164			−0.660819	+	0.750546i	$0.729791\pi$
$230$		0			0
$231$	22.4059	−	38.8081i	1.47420	−	2.55339i
$232$	1.42526	−	0.822876i	0.0935731	−	0.0540244i
$233$	16.3458	+	9.43725i	1.07085	+	0.618255i	0.928413	−	0.371549i	$-0.121173\pi$
$233$	16.3458	+	9.43725i	1.07085	+	0.618255i	0.142436	+	0.989804i	$0.454507\pi$
$234$	4.00000	+	6.92820i	0.261488	+	0.452911i
$235$		0			0
$236$	−7.93725			−0.516671
$237$	−9.16515	+	5.29150i	−0.595341	+	0.343720i
$238$		0			0
$239$	12.0000			0.776215			0.388108	−	0.921614i	$-0.373129\pi$
$239$	12.0000			0.776215			0.388108	+	0.921614i	$0.373129\pi$
$240$		0			0
$241$	3.79150	+	6.56708i	0.244232	+	0.423022i	0.961915	−	0.273347i	$-0.0881308\pi$
$241$	3.79150	+	6.56708i	0.244232	+	0.423022i	−0.717683	+	0.696370i	$0.754797\pi$
$242$	−9.16515	−	5.29150i	−0.589158	−	0.340151i
$243$	18.3303	−	10.5830i	1.17589	−	0.678900i
$244$	0.468627	−	0.811686i	0.0300008	−	0.0519629i
$245$		0			0
$246$	−0.771243			−0.0491727
$247$	−1.11847	−	8.64575i	−0.0711668	−	0.550116i
$248$			5.64575i			0.358506i
$249$	10.5000	−	18.1865i	0.665410	−	1.15252i
$250$		0			0
$251$	−14.6144	−	25.3128i	−0.922451	−	1.59773i	−0.795610	−	0.605810i	$-0.792849\pi$
$251$	−14.6144	−	25.3128i	−0.922451	−	1.59773i	−0.126842	−	0.991923i	$-0.540484\pi$
$252$	−12.6293	−	7.29150i	−0.795568	−	0.459321i
$253$	−6.62141	+	3.82288i	−0.416285	+	0.240342i
$254$	13.2915			0.833983
$255$		0			0
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	10.6448	−	6.14575i	0.664001	−	0.383361i	−0.129798	−	0.991540i	$-0.541433\pi$
$257$	10.6448	−	6.14575i	0.664001	−	0.383361i	0.793800	+	0.608179i	$0.208100\pi$
$258$		−	29.8745i		−	1.85991i
$259$	−1.29150			−0.0802501
$260$		0			0
$261$	−3.29150	+	5.70105i	−0.203739	+	0.352886i
$262$	1.67771	−	0.968627i	0.103649	−	0.0598420i
$263$	−9.47194	−	5.46863i	−0.584065	−	0.337210i	0.178682	−	0.983907i	$-0.442817\pi$
$263$	−9.47194	−	5.46863i	−0.584065	−	0.337210i	−0.762747	+	0.646697i	$0.776150\pi$
$264$	−6.14575	+	10.6448i	−0.378245	+	0.655139i
$265$		0			0
$266$	9.64575	+	12.6293i	0.591419	+	0.774349i
$267$		0			0
$268$	0.559237	+	0.322876i	0.0341608	+	0.0197228i
$269$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$269$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$270$		0			0
$271$	−6.17712	+	10.6991i	−0.375234	+	0.649924i	−0.990362	−	0.138503i	$-0.955771\pi$
$271$	−6.17712	+	10.6991i	−0.375234	+	0.649924i	0.615128	+	0.788427i	$0.289104\pi$
$272$		0			0
$273$		−	19.2915i		−	1.16757i
$274$	−15.5830			−0.941404
$275$		0			0
$276$	2.17712	+	3.77089i	0.131047	+	0.226981i
$277$		−	27.5203i		−	1.65353i	−0.562546	−	0.826766i	$-0.690178\pi$
$277$		−	27.5203i		−	1.65353i	0.562546	−	0.826766i	$-0.309822\pi$
$278$		−	18.6458i		−	1.11830i
$279$	−11.2915	−	19.5575i	−0.676005	−	1.17087i
$280$		0			0
$281$	−12.7288	−	22.0469i	−0.759334	−	1.31520i	−0.943191	−	0.332252i	$-0.892192\pi$
$281$	−12.7288	−	22.0469i	−0.759334	−	1.31520i	0.183857	−	0.982953i	$-0.441142\pi$
$282$	−9.97684	−	5.76013i	−0.594112	−	0.343011i
$283$	26.5400	+	15.3229i	1.57764	+	0.910850i	0.995188	+	0.0979848i	$0.0312397\pi$
$283$	26.5400	+	15.3229i	1.57764	+	0.910850i	0.582451	+	0.812866i	$0.302094\pi$
$284$	2.70850			0.160720
$285$		0			0
$286$	−9.29150			−0.549418
$287$	0.920365	+	0.531373i	0.0543274	+	0.0313660i
$288$	3.46410	+	2.00000i	0.204124	+	0.117851i
$289$	−8.50000	−	14.7224i	−0.500000	−	0.866025i
$290$		0			0
$291$	4.90588	+	8.49723i	0.287588	+	0.498117i
$292$			1.70850i			0.0999822i
$293$		−	28.9373i		−	1.69053i	−0.534345	−	0.845266i	$-0.679442\pi$
$293$		−	28.9373i		−	1.69053i	0.534345	−	0.845266i	$-0.320558\pi$
$294$	8.32288	+	14.4156i	0.485400	+	0.840737i
$295$		0			0
$296$	0.354249			0.0205903
$297$		−	12.2915i		−	0.713225i
$298$	−9.47194	+	5.46863i	−0.548695	+	0.316789i
$299$	−1.64575	+	2.85052i	−0.0951763	+	0.164850i
$300$		0			0
$301$	−20.5830	+	35.6508i	−1.18638	+	2.05488i
$302$	−11.2040	−	6.46863i	−0.644717	−	0.372228i
$303$			36.1033i			2.07408i
$304$	−2.64575	−	3.46410i	−0.151744	−	0.198680i
$305$		0			0
$306$		0			0
$307$	−0.559237	−	0.322876i	−0.0319173	−	0.0184275i	0.483956	−	0.875092i	$-0.339199\pi$
$307$	−0.559237	−	0.322876i	−0.0319173	−	0.0184275i	−0.515874	+	0.856665i	$0.672533\pi$
$308$	14.6681	−	8.46863i	0.835792	−	0.482545i
$309$	−17.5830	+	30.4547i	−1.00026	+	1.73250i
$310$		0			0
$311$	13.6458			0.773780			0.386890	−	0.922126i	$-0.373549\pi$
$311$	13.6458			0.773780			0.386890	+	0.922126i	$0.373549\pi$
$312$			5.29150i			0.299572i
$313$	−7.68555	+	4.43725i	−0.434413	+	0.250808i	−0.701225	−	0.712940i	$-0.747363\pi$
$313$	−7.68555	+	4.43725i	−0.434413	+	0.250808i	0.266812	+	0.963749i	$0.414030\pi$
$314$	−5.29150	−	9.16515i	−0.298617	−	0.517219i
$315$		0			0
$316$	−4.00000			−0.225018
$317$	−5.19615	+	3.00000i	−0.291845	+	0.168497i	−0.638774	−	0.769395i	$-0.720558\pi$
$317$	−5.19615	+	3.00000i	−0.291845	+	0.168497i	0.346929	+	0.937892i	$0.387225\pi$
$318$	−28.8313	−	16.6458i	−1.61678	−	0.933447i
$319$	−3.82288	−	6.62141i	−0.214040	−	0.370728i
$320$		0			0
$321$	−20.2288	+	35.0372i	−1.12906	+	1.95559i
$322$		−	6.00000i		−	0.334367i
$323$		0			0
$324$	5.00000			0.277778
$325$		0			0
$326$	−1.96863	+	3.40976i	−0.109032	+	0.188849i
$327$	33.4139	−	19.2915i	1.84779	−	1.06682i
$328$	−0.252449	−	0.145751i	−0.0139391	−	0.00804777i
$329$	7.93725	+	13.7477i	0.437595	+	0.757937i
$330$		0			0
$331$	19.8118			1.08895			0.544476	−	0.838776i	$-0.316728\pi$
$331$	19.8118			1.08895			0.544476	+	0.838776i	$0.316728\pi$
$332$	6.87386	−	3.96863i	0.377252	−	0.217807i
$333$	−1.22715	+	0.708497i	−0.0672476	+	0.0388254i
$334$	12.0000			0.656611
$335$		0			0
$336$	−4.82288	−	8.35347i	−0.263109	−	0.455719i
$337$	8.40781	+	4.85425i	0.458002	+	0.264428i	0.711204	−	0.702986i	$-0.248150\pi$
$337$	8.40781	+	4.85425i	0.458002	+	0.264428i	−0.253202	+	0.967414i	$0.581484\pi$
$338$	7.79423	−	4.50000i	0.423950	−	0.244768i
$339$	−20.6144	+	35.7052i	−1.11962	+	1.93924i
$340$		0			0
$341$	26.2288			1.42037
$342$	16.0934	+	6.70850i	0.870229	+	0.362754i
$343$			2.58301i			0.139469i
$344$	5.64575	−	9.77873i	0.304399	−	0.527234i
$345$		0			0
$346$	3.00000	+	5.19615i	0.161281	+	0.279347i
$347$	20.1167	+	11.6144i	1.07992	+	0.623492i	0.930875	−	0.365338i	$-0.119047\pi$
$347$	20.1167	+	11.6144i	1.07992	+	0.623492i	0.149046	+	0.988830i	$0.452380\pi$
$348$	−3.77089	+	2.17712i	−0.202141	+	0.116706i
$349$	−21.1660			−1.13299			−0.566495	−	0.824065i	$-0.691701\pi$
$349$	−21.1660			−1.13299			−0.566495	+	0.824065i	$0.691701\pi$
$350$		0			0
$351$	−2.64575	−	4.58258i	−0.141220	−	0.244600i
$352$	−4.02334	+	2.32288i	−0.214445	+	0.123810i
$353$		−	12.8745i		−	0.685241i	−0.939474	−	0.342620i	$-0.888686\pi$
$353$		−	12.8745i		−	0.685241i	0.939474	−	0.342620i	$-0.111314\pi$
$354$	21.0000			1.11614
$355$		0			0
$356$		0			0
$357$		0			0
$358$	3.51844	+	2.03137i	0.185955	+	0.107361i
$359$	−2.46863	+	4.27579i	−0.130289	+	0.225667i	−0.923788	−	0.382904i	$-0.874924\pi$
$359$	−2.46863	+	4.27579i	−0.130289	+	0.225667i	0.793499	+	0.608572i	$0.208257\pi$
$360$		0			0
$361$	−13.3745	−	13.4953i	−0.703921	−	0.710278i
$362$			22.2288i			1.16832i
$363$	24.2487	+	14.0000i	1.27273	+	0.734809i
$364$	3.64575	−	6.31463i	0.191089	−	0.330976i
$365$		0			0
$366$	−1.23987	+	2.14752i	−0.0648091	+	0.112253i
$367$	14.0545	−	8.11438i	0.733640	−	0.423567i	−0.0861125	−	0.996285i	$-0.527444\pi$
$367$	14.0545	−	8.11438i	0.733640	−	0.423567i	0.819752	+	0.572718i	$0.194111\pi$
$368$			1.64575i			0.0857907i
$369$	1.16601			0.0607001
$370$		0			0
$371$	22.9373	+	39.7285i	1.19084	+	2.06260i
$372$		−	14.9373i		−	0.774461i
$373$			4.00000i			0.207112i	0.994624	+	0.103556i	$0.0330221\pi$
$373$			4.00000i			0.207112i	−0.994624	+	0.103556i	$0.966978\pi$
$374$		0			0
$375$		0			0
$376$	−2.17712	−	3.77089i	−0.112277	−	0.194469i
$377$	−2.85052	−	1.64575i	−0.146810	−	0.0847605i
$378$	8.35347	+	4.82288i	0.429656	+	0.248062i
$379$	−10.7085			−0.550059			−0.275029	−	0.961436i	$-0.588688\pi$
$379$	−10.7085			−0.550059			−0.275029	+	0.961436i	$0.588688\pi$
$380$		0			0
$381$	−35.1660			−1.80161
$382$	−5.70105	−	3.29150i	−0.291691	−	0.168408i
$383$	4.78068	+	2.76013i	0.244282	+	0.141036i	0.617143	−	0.786851i	$-0.288290\pi$
$383$	4.78068	+	2.76013i	0.244282	+	0.141036i	−0.372861	+	0.927887i	$0.621623\pi$
$384$	1.32288	+	2.29129i	0.0675077	+	0.116927i
$385$		0			0
$386$	−7.29150	−	12.6293i	−0.371128	−	0.642812i
$387$			45.1660i			2.29592i
$388$			3.70850i			0.188270i
$389$	6.00000	+	10.3923i	0.304212	+	0.526911i	0.977086	−	0.212847i	$-0.0682735\pi$
$389$	6.00000	+	10.3923i	0.304212	+	0.526911i	−0.672874	+	0.739758i	$0.734940\pi$
$390$		0			0
$391$		0			0
$392$			6.29150i			0.317769i
$393$	−4.43881	+	2.56275i	−0.223908	+	0.129273i
$394$	−3.82288	+	6.62141i	−0.192594	+	0.333582i
$395$		0			0
$396$	9.29150	−	16.0934i	0.466916	−	0.808721i
$397$	−18.2409	−	10.5314i	−0.915483	−	0.528554i	−0.0332919	−	0.999446i	$-0.510599\pi$
$397$	−18.2409	−	10.5314i	−0.915483	−	0.528554i	−0.882191	+	0.470891i	$0.843932\pi$
$398$			19.8745i			0.996219i
$399$	−25.5203	−	33.4139i	−1.27761	−	1.67279i
$400$		0			0
$401$	−13.7915	+	23.8876i	−0.688715	+	1.19289i	0.283539	+	0.958961i	$0.408491\pi$
$401$	−13.7915	+	23.8876i	−0.688715	+	1.19289i	−0.972254	+	0.233928i	$0.924842\pi$
$402$	−1.47960	−	0.854249i	−0.0737958	−	0.0426061i
$403$	9.77873	−	5.64575i	0.487113	−	0.281235i
$404$	−6.82288	+	11.8176i	−0.339451	+	0.587946i
$405$		0			0
$406$	6.00000			0.297775
$407$		−	1.64575i		−	0.0815769i
$408$		0			0
$409$	−3.79150	−	6.56708i	−0.187478	−	0.324721i	0.756931	−	0.653495i	$-0.226698\pi$
$409$	−3.79150	−	6.56708i	−0.187478	−	0.324721i	−0.944409	+	0.328774i	$0.893365\pi$
$410$		0			0
$411$	41.2288			2.03366
$412$	−11.5108	+	6.64575i	−0.567095	+	0.327413i
$413$	−25.0604	−	14.4686i	−1.23314	−	0.711955i
$414$	−3.29150	−	5.70105i	−0.161769	−	0.280191i
$415$		0			0
$416$	−1.00000	+	1.73205i	−0.0490290	+	0.0849208i
$417$			49.3320i			2.41580i
$418$	−16.0934	+	12.2915i	−0.787152	+	0.601197i
$419$	31.7490			1.55104			0.775520	−	0.631322i	$-0.217488\pi$
$419$	31.7490			1.55104			0.775520	+	0.631322i	$0.217488\pi$
$420$		0			0
$421$	12.4059	−	21.4876i	0.604626	−	1.04724i	−0.387485	−	0.921876i	$-0.626656\pi$
$421$	12.4059	−	21.4876i	0.604626	−	1.04724i	0.992111	−	0.125366i	$-0.0400106\pi$
$422$	−11.5108	+	6.64575i	−0.560336	+	0.323510i
$423$	15.0836	+	8.70850i	0.733388	+	0.423422i
$424$	−6.29150	−	10.8972i	−0.305542	−	0.529215i
$425$		0			0
$426$	−7.16601			−0.347194
$427$	2.95920	−	1.70850i	0.143206	−	0.0826800i
$428$	−13.2428	+	7.64575i	−0.640116	+	0.369571i
$429$	24.5830			1.18688
$430$		0			0
$431$	−13.9373	−	24.1400i	−0.671334	−	1.16278i	−0.977526	−	0.210815i	$-0.932388\pi$
$431$	−13.9373	−	24.1400i	−0.671334	−	1.16278i	0.306192	−	0.951970i	$-0.400945\pi$
$432$	−2.29129	−	1.32288i	−0.110240	−	0.0636469i
$433$	−15.4798	+	8.93725i	−0.743911	+	0.429497i	−0.823489	−	0.567332i	$-0.807976\pi$
$433$	−15.4798	+	8.93725i	−0.743911	+	0.429497i	0.0795788	+	0.996829i	$0.474642\pi$
$434$	−10.2915	+	17.8254i	−0.494008	+	0.855647i
$435$		0			0
$436$	14.5830			0.698399
$437$	0.920365	+	7.11438i	0.0440270	+	0.340327i
$438$		−	4.52026i		−	0.215986i
$439$	5.40588	−	9.36326i	0.258009	−	0.446884i	−0.707700	−	0.706513i	$-0.750267\pi$
$439$	5.40588	−	9.36326i	0.258009	−	0.446884i	0.965708	+	0.259629i	$0.0836004\pi$
$440$		0			0
$441$	−12.5830	−	21.7944i	−0.599191	−	1.03783i
$442$		0			0
$443$	−9.21949	+	5.32288i	−0.438031	+	0.252897i	−0.702762	−	0.711425i	$-0.748050\pi$
$443$	−9.21949	+	5.32288i	−0.438031	+	0.252897i	0.264731	+	0.964322i	$0.414717\pi$
$444$	−0.937254			−0.0444801
$445$		0			0
$446$	9.40588	+	16.2915i	0.445381	+	0.771423i
$447$	25.0604	−	14.4686i	1.18532	−	0.684343i
$448$		−	3.64575i		−	0.172246i
$449$	24.2915			1.14639			0.573193	−	0.819420i	$-0.305704\pi$
$449$	24.2915			1.14639			0.573193	+	0.819420i	$0.305704\pi$
$450$		0			0
$451$	−0.677124	+	1.17281i	−0.0318845	+	0.0552256i
$452$	−13.4953	+	7.79150i	−0.634765	+	0.366481i
$453$	29.6430	+	17.1144i	1.39275	+	0.804104i
$454$	−3.67712	+	6.36897i	−0.172576	+	0.298910i
$455$		0			0
$456$	7.00000	+	9.16515i	0.327805	+	0.429198i
$457$			32.8745i			1.53780i	0.639366	+	0.768902i	$0.279197\pi$
$457$			32.8745i			1.53780i	−0.639366	+	0.768902i	$0.720803\pi$
$458$	17.3205	+	10.0000i	0.809334	+	0.467269i
$459$		0			0
$460$		0			0
$461$	−9.58301	+	16.5983i	−0.446325	+	0.773058i	−0.998143	−	0.0609066i	$-0.980601\pi$
$461$	−9.58301	+	16.5983i	−0.446325	+	0.773058i	0.551818	+	0.833964i	$0.313934\pi$
$462$	−38.8081	+	22.4059i	−1.80552	+	1.04242i
$463$			38.4575i			1.78727i	0.448792	+	0.893636i	$0.351854\pi$
$463$			38.4575i			1.78727i	−0.448792	+	0.893636i	$0.648146\pi$
$464$	−1.64575			−0.0764021
$465$		0			0
$466$	−9.43725	−	16.3458i	−0.437172	−	0.757205i
$467$		−	19.3542i		−	0.895608i	−0.894132	−	0.447804i	$-0.852206\pi$
$467$		−	19.3542i		−	0.895608i	0.894132	−	0.447804i	$-0.147794\pi$
$468$		−	8.00000i		−	0.369800i
$469$	1.17712	+	2.03884i	0.0543546	+	0.0941448i
$470$		0			0
$471$	14.0000	+	24.2487i	0.645086	+	1.11732i
$472$	6.87386	+	3.96863i	0.316395	+	0.182671i
$473$	−45.4295	−	26.2288i	−2.08885	−	1.20600i
$474$	10.5830			0.486094
$475$		0			0
$476$		0			0
$477$	43.5888	+	25.1660i	1.99579	+	1.15227i
$478$	−10.3923	−	6.00000i	−0.475333	−	0.274434i
$479$	3.29150	+	5.70105i	0.150393	+	0.260488i	0.931372	−	0.364069i	$-0.118613\pi$
$479$	3.29150	+	5.70105i	0.150393	+	0.260488i	−0.780979	+	0.624557i	$0.785280\pi$
$480$		0			0
$481$	−0.354249	−	0.613577i	−0.0161523	−	0.0279767i
$482$		−	7.58301i		−	0.345396i
$483$			15.8745i			0.722315i
$484$	5.29150	+	9.16515i	0.240523	+	0.416598i
$485$		0			0
$486$	−21.1660			−0.960110
$487$			4.22876i			0.191623i	0.995399	+	0.0958116i	$0.0305446\pi$
$487$			4.22876i			0.191623i	−0.995399	+	0.0958116i	$0.969455\pi$
$488$	−0.811686	+	0.468627i	−0.0367433	+	0.0212137i
$489$	5.20850	−	9.02138i	0.235536	−	0.407961i
$490$		0			0
$491$	−19.6458	+	34.0274i	−0.886600	+	1.53564i	−0.0427320	+	0.999087i	$0.513606\pi$
$491$	−19.6458	+	34.0274i	−0.886600	+	1.53564i	−0.843868	+	0.536550i	$0.819727\pi$
$492$	0.667916	+	0.385622i	0.0301120	+	0.0173852i
$493$		0			0
$494$	−3.35425	+	8.04668i	−0.150915	+	0.362037i
$495$		0			0
$496$	2.82288	−	4.88936i	0.126751	−	0.219539i
$497$	8.55157	+	4.93725i	0.383591	+	0.221466i
$498$	−18.1865	+	10.5000i	−0.814958	+	0.470516i
$499$	−2.38562	+	4.13202i	−0.106795	+	0.184975i	−0.914470	−	0.404653i	$-0.867392\pi$
$499$	−2.38562	+	4.13202i	−0.106795	+	0.184975i	0.807675	+	0.589628i	$0.200726\pi$
$500$		0			0
$501$	−31.7490			−1.41844
$502$			29.2288i			1.30454i
$503$	35.4527	−	20.4686i	1.58076	−	0.912651i	0.586009	−	0.810305i	$-0.300698\pi$
$503$	35.4527	−	20.4686i	1.58076	−	0.912651i	0.994749	−	0.102346i	$-0.0326350\pi$
$504$	7.29150	+	12.6293i	0.324789	+	0.562552i
$505$		0			0
$506$	7.64575			0.339895
$507$	−20.6216	+	11.9059i	−0.915837	+	0.528759i
$508$	−11.5108	−	6.64575i	−0.510708	−	0.294858i
$509$	−15.8745	−	27.4955i	−0.703625	−	1.21871i	−0.967185	−	0.254072i	$-0.918230\pi$
$509$	−15.8745	−	27.4955i	−0.703625	−	1.21871i	0.263560	−	0.964643i	$-0.415103\pi$
$510$		0			0
$511$	−3.11438	+	5.39426i	−0.137772	+	0.238628i
$512$			1.00000i			0.0441942i
$513$	−10.6448	−	4.43725i	−0.469977	−	0.195910i
$514$	−12.2915			−0.542155
$515$		0			0
$516$	−14.9373	+	25.8721i	−0.657576	+	1.13895i
$517$	−17.5186	+	10.1144i	−0.770468	+	0.444830i
$518$	1.11847	+	0.645751i	0.0491429	+	0.0283727i
$519$	−7.93725	−	13.7477i	−0.348407	−	0.603458i
$520$		0			0
$521$	−11.7085			−0.512959			−0.256479	−	0.966550i	$-0.582563\pi$
$521$	−11.7085			−0.512959			−0.256479	+	0.966550i	$0.582563\pi$
$522$	5.70105	−	3.29150i	0.249528	−	0.144065i
$523$	1.62337	−	0.937254i	0.0709851	−	0.0409833i	−0.464087	−	0.885789i	$-0.653618\pi$
$523$	1.62337	−	0.937254i	0.0709851	−	0.0409833i	0.535072	+	0.844806i	$0.320284\pi$
$524$	−1.93725			−0.0846293
$525$		0			0
$526$	5.46863	+	9.47194i	0.238443	+	0.412996i
$527$		0			0
$528$	10.6448	−	6.14575i	0.463253	−	0.267459i
$529$	−10.1458	+	17.5730i	−0.441120	+	0.764042i
$530$		0			0
$531$	−31.7490			−1.37779
$532$	−2.03884	−	15.7601i	−0.0883949	−	0.683288i
$533$			0.583005i			0.0252528i
$534$		0			0
$535$		0			0
$536$	−0.322876	−	0.559237i	−0.0139461	−	0.0241554i
$537$	−9.30892	−	5.37451i	−0.401710	−	0.231927i
$538$		0			0
$539$	29.2288			1.25897
$540$		0			0
$541$	−4.00000	−	6.92820i	−0.171973	−	0.297867i	0.767136	−	0.641484i	$-0.221681\pi$
$541$	−4.00000	−	6.92820i	−0.171973	−	0.297867i	−0.939110	+	0.343617i	$0.888348\pi$
$542$	10.6991	−	6.17712i	0.459565	−	0.265330i
$543$		−	58.8118i		−	2.52385i
$544$		0			0
$545$		0			0
$546$	−9.64575	+	16.7069i	−0.412800	+	0.714991i
$547$	9.77873	−	5.64575i	0.418108	−	0.241395i	−0.276159	−	0.961112i	$-0.589062\pi$
$547$	9.77873	−	5.64575i	0.418108	−	0.241395i	0.694268	+	0.719717i	$0.255728\pi$
$548$	13.4953	+	7.79150i	0.576490	+	0.332836i
$549$	1.87451	−	3.24674i	0.0800020	−	0.138568i
$550$		0			0
$551$	−7.11438	+	0.920365i	−0.303083	+	0.0392089i
$552$		−	4.35425i		−	0.185329i
$553$	−12.6293	−	7.29150i	−0.537050	−	0.310066i
$554$	−13.7601	+	23.8332i	−0.584612	+	1.01258i
$555$		0			0
$556$	−9.32288	+	16.1477i	−0.395378	+	0.684815i
$557$	−4.69126	+	2.70850i	−0.198775	+	0.114763i	−0.596084	−	0.802922i	$-0.703277\pi$
$557$	−4.69126	+	2.70850i	−0.198775	+	0.114763i	0.397309	+	0.917685i	$0.369944\pi$
$558$			22.5830i			0.956015i
$559$	−22.5830			−0.955159
$560$		0			0
$561$		0			0
$562$			25.4575i			1.07386i
$563$		−	10.0627i		−	0.424094i	−0.977259	−	0.212047i	$-0.931987\pi$
$563$		−	10.0627i		−	0.424094i	0.977259	−	0.212047i	$-0.0680130\pi$
$564$	5.76013	+	9.97684i	0.242545	+	0.420101i
$565$		0			0
$566$	−15.3229	−	26.5400i	−0.644069	−	1.11556i
$567$	15.7866	+	9.11438i	0.662973	+	0.382768i
$568$	−2.34563	−	1.35425i	−0.0984203	−	0.0568230i
$569$	−6.58301			−0.275974			−0.137987	−	0.990434i	$-0.544063\pi$
$569$	−6.58301			−0.275974			−0.137987	+	0.990434i	$0.544063\pi$
$570$		0			0
$571$	7.81176			0.326912			0.163456	−	0.986551i	$-0.447736\pi$
$571$	7.81176			0.326912			0.163456	+	0.986551i	$0.447736\pi$
$572$	8.04668	+	4.64575i	0.336448	+	0.194249i
$573$	15.0836	+	8.70850i	0.630125	+	0.363803i
$574$	−0.531373	−	0.920365i	−0.0221791	−	0.0384153i
$575$		0			0
$576$	−2.00000	−	3.46410i	−0.0833333	−	0.144338i
$577$			11.0000i			0.457936i	0.973434	+	0.228968i	$0.0735351\pi$
$577$			11.0000i			0.457936i	−0.973434	+	0.228968i	$0.926465\pi$
$578$			17.0000i			0.707107i
$579$	19.2915	+	33.4139i	0.801727	+	1.38863i
$580$		0			0
$581$	28.9373			1.20052
$582$		−	9.81176i		−	0.406711i
$583$	−50.6257	+	29.2288i	−2.09670	+	1.21053i
$584$	0.854249	−	1.47960i	0.0353491	−	0.0612264i
$585$		0			0
$586$	−14.4686	+	25.0604i	−0.597693	+	1.03524i
$587$	12.2330	+	7.06275i	0.504911	+	0.291511i	0.730739	−	0.682656i	$-0.239175\pi$
$587$	12.2330	+	7.06275i	0.504911	+	0.291511i	−0.225828	+	0.974167i	$0.572509\pi$
$588$		−	16.6458i		−	0.686459i
$589$	9.46863	−	22.7148i	0.390148	−	0.935946i
$590$		0			0
$591$	10.1144	−	17.5186i	0.416050	−	0.720620i
$592$	−0.306788	−	0.177124i	−0.0126089	−	0.00727977i
$593$	−25.7283	+	14.8542i	−1.05654	+	0.609991i	−0.924472	−	0.381250i	$-0.875494\pi$
$593$	−25.7283	+	14.8542i	−1.05654	+	0.609991i	−0.132063	+	0.991241i	$0.542160\pi$
$594$	−6.14575	+	10.6448i	−0.252163	+	0.436760i
$595$		0			0
$596$	10.9373			0.448007
$597$		−	52.5830i		−	2.15208i
$598$	2.85052	−	1.64575i	0.116567	−	0.0672998i
$599$	−8.46863	−	14.6681i	−0.346019	−	0.599322i	0.639520	−	0.768775i	$-0.279133\pi$
$599$	−8.46863	−	14.6681i	−0.346019	−	0.599322i	−0.985538	+	0.169453i	$0.945800\pi$
$600$		0			0
$601$	10.4170			0.424918			0.212459	−	0.977170i	$-0.431853\pi$
$601$	10.4170			0.424918			0.212459	+	0.977170i	$0.431853\pi$
$602$	35.6508	−	20.5830i	1.45302	−	0.838901i
$603$	2.23695	+	1.29150i	0.0910956	+	0.0525941i
$604$	6.46863	+	11.2040i	0.263205	+	0.455884i
$605$		0			0
$606$	18.0516	−	31.2663i	0.733297	−	1.27011i
$607$			6.93725i			0.281574i	0.990040	+	0.140787i	$0.0449633\pi$
$607$			6.93725i			0.281574i	−0.990040	+	0.140787i	$0.955037\pi$
$608$	0.559237	+	4.32288i	0.0226801	+	0.175316i
$609$	−15.8745			−0.643268
$610$		0			0
$611$	−4.35425	+	7.54178i	−0.176154	+	0.305108i
$612$		0			0
$613$	6.42331	+	3.70850i	0.259435	+	0.149785i	0.624077	−	0.781363i	$-0.285475\pi$
$613$	6.42331	+	3.70850i	0.259435	+	0.149785i	−0.364642	+	0.931148i	$0.618809\pi$
$614$	0.322876	+	0.559237i	0.0130302	+	0.0225690i
$615$		0			0
$616$	−16.9373			−0.682421
$617$	−26.7381	+	15.4373i	−1.07644	+	0.621480i	−0.929933	−	0.367730i	$-0.880135\pi$
$617$	−26.7381	+	15.4373i	−1.07644	+	0.621480i	−0.146503	+	0.989210i	$0.546802\pi$
$618$	30.4547	−	17.5830i	1.22507	−	0.707292i
$619$	8.45751			0.339936			0.169968	−	0.985450i	$-0.445634\pi$
$619$	8.45751			0.339936			0.169968	+	0.985450i	$0.445634\pi$
$620$		0			0
$621$	2.17712	+	3.77089i	0.0873650	+	0.151321i
$622$	−11.8176	−	6.82288i	−0.473841	−	0.273572i
$623$		0			0
$624$	2.64575	−	4.58258i	0.105915	−	0.183450i
$625$		0			0
$626$	8.87451			0.354697
$627$	42.5790	−	32.5203i	1.70044	−	1.29873i
$628$			10.5830i			0.422308i
$629$		0			0
$630$		0			0
$631$	12.4059	+	21.4876i	0.493870	+	0.855408i	0.999975	−	0.00706354i	$-0.00224841\pi$
$631$	12.4059	+	21.4876i	0.493870	+	0.855408i	−0.506105	+	0.862472i	$0.668915\pi$
$632$	3.46410	+	2.00000i	0.137795	+	0.0795557i
$633$	30.4547	−	17.5830i	1.21046	−	0.698862i
$634$	6.00000			0.238290
$635$		0			0
$636$	16.6458	+	28.8313i	0.660047	+	1.14323i
$637$	10.8972	−	6.29150i	0.431763	−	0.249278i
$638$			7.64575i			0.302698i
$639$	10.8340			0.428586
$640$		0			0
$641$	−6.43725	+	11.1497i	−0.254256	+	0.440385i	−0.964693	−	0.263376i	$-0.915164\pi$
$641$	−6.43725	+	11.1497i	−0.254256	+	0.440385i	0.710437	+	0.703761i	$0.248497\pi$
$642$	35.0372	−	20.2288i	1.38281	−	0.798365i
$643$	−5.64671	−	3.26013i	−0.222685	−	0.128567i	0.384508	−	0.923122i	$-0.374371\pi$
$643$	−5.64671	−	3.26013i	−0.222685	−	0.128567i	−0.607193	+	0.794555i	$0.707704\pi$
$644$	−3.00000	+	5.19615i	−0.118217	+	0.204757i
$645$		0			0
$646$		0			0
$647$		−	22.4575i		−	0.882896i	−0.897287	−	0.441448i	$-0.854465\pi$
$647$		−	22.4575i		−	0.882896i	0.897287	−	0.441448i	$-0.145535\pi$
$648$	−4.33013	−	2.50000i	−0.170103	−	0.0982093i
$649$	18.4373	−	31.9343i	0.723726	−	1.25353i
$650$		0			0
$651$	27.2288	−	47.1616i	1.06718	−	1.84841i
$652$	3.40976	−	1.96863i	0.133537	−	0.0770974i
$653$		−	24.0000i		−	0.939193i	−0.882881	−	0.469596i	$-0.844399\pi$
$653$		−	24.0000i		−	0.939193i	0.882881	−	0.469596i	$-0.155601\pi$
$654$	−38.5830			−1.50871
$655$		0			0
$656$	0.145751	+	0.252449i	0.00569063	+	0.00985646i
$657$			6.83399i			0.266619i
$658$		−	15.8745i		−	0.618853i
$659$	−9.29150	−	16.0934i	−0.361946	−	0.626908i	0.626335	−	0.779554i	$-0.284554\pi$
$659$	−9.29150	−	16.0934i	−0.361946	−	0.626908i	−0.988281	+	0.152646i	$0.951221\pi$
$660$		0			0
$661$	−8.11438	−	14.0545i	−0.315613	−	0.546657i	0.663955	−	0.747773i	$-0.268877\pi$
$661$	−8.11438	−	14.0545i	−0.315613	−	0.546657i	−0.979568	+	0.201115i	$0.935543\pi$
$662$	−17.1575	−	9.90588i	−0.666845	−	0.385003i
$663$		0			0
$664$	−7.93725			−0.308025
$665$		0			0
$666$	1.41699			0.0549074
$667$	2.34563	+	1.35425i	0.0908231	+	0.0524367i
$668$	−10.3923	−	6.00000i	−0.402090	−	0.232147i
$669$	−24.8856	−	43.1032i	−0.962134	−	1.66646i
$670$		0			0
$671$	2.17712	+	3.77089i	0.0840470	+	0.145574i
$672$			9.64575i			0.372093i
$673$			13.8745i			0.534823i	0.963582	+	0.267411i	$0.0861683\pi$
$673$			13.8745i			0.534823i	−0.963582	+	0.267411i	$0.913832\pi$
$674$	−4.85425	−	8.40781i	−0.186979	−	0.323857i
$675$		0			0
$676$	−9.00000			−0.346154
$677$		−	11.4170i		−	0.438791i	−0.975636	−	0.219395i	$-0.929592\pi$
$677$		−	11.4170i		−	0.438791i	0.975636	−	0.219395i	$-0.0704085\pi$
$678$	35.7052	−	20.6144i	1.37125	−	0.791690i
$679$	−6.76013	+	11.7089i	−0.259430	+	0.449346i
$680$		0			0
$681$	9.72876	−	16.8507i	0.372807	−	0.645720i
$682$	−22.7148	−	13.1144i	−0.869793	−	0.502175i
$683$			5.41699i			0.207276i	0.994615	+	0.103638i	$0.0330483\pi$
$683$			5.41699i			0.207276i	−0.994615	+	0.103638i	$0.966952\pi$
$684$	−10.5830	−	13.8564i	−0.404651	−	0.529813i
$685$		0			0
$686$	1.29150	−	2.23695i	0.0493098	−	0.0854071i
$687$	−45.8258	−	26.4575i	−1.74836	−	1.00942i
$688$	−9.77873	+	5.64575i	−0.372811	+	0.215242i
$689$	−12.5830	+	21.7944i	−0.479374	+	0.830301i
$690$		0			0
$691$	2.58301			0.0982622			0.0491311	−	0.998792i	$-0.484355\pi$
$691$	2.58301			0.0982622			0.0491311	+	0.998792i	$0.484355\pi$
$692$		−	6.00000i		−	0.228086i
$693$	58.6724	−	33.8745i	2.22878	−	1.28679i
$694$	−11.6144	−	20.1167i	−0.440876	−	0.763619i
$695$		0			0
$696$	4.35425			0.165047
$697$		0			0
$698$	18.3303	+	10.5830i	0.693812	+	0.400573i
$699$	24.9686	+	43.2469i	0.944400	+	1.63575i
$700$		0			0
$701$	−5.17712	+	8.96704i	−0.195537	+	0.338681i	−0.947077	−	0.321008i	$-0.895978\pi$
$701$	−5.17712	+	8.96704i	−0.195537	+	0.338681i	0.751539	+	0.659688i	$0.229312\pi$
$702$			5.29150i			0.199715i
$703$	−1.42526	−	0.594119i	−0.0537548	−	0.0224076i
$704$	4.64575			0.175093
$705$		0			0
$706$	−6.43725	+	11.1497i	−0.242269	+	0.419623i
$707$	−43.0839	+	24.8745i	−1.62034	+	0.935502i
$708$	−18.1865	−	10.5000i	−0.683492	−	0.394614i
$709$	1.82288	+	3.15731i	0.0684595	+	0.118575i	0.898223	−	0.439539i	$-0.144858\pi$
$709$	1.82288	+	3.15731i	0.0684595	+	0.118575i	−0.829764	+	0.558115i	$0.811525\pi$
$710$		0			0
$711$	−16.0000			−0.600047
$712$		0			0
$713$	−8.04668	+	4.64575i	−0.301350	+	0.173985i
$714$		0			0
$715$		0			0
$716$	−2.03137	−	3.51844i	−0.0759160	−	0.131490i
$717$	27.4955	+	15.8745i	1.02684	+	0.592844i
$718$	4.27579	−	2.46863i	0.159571	−	0.0921283i
$719$	1.35425	−	2.34563i	0.0505050	−	0.0874771i	−0.839668	−	0.543100i	$-0.817250\pi$
$719$	1.35425	−	2.34563i	0.0505050	−	0.0874771i	0.890173	+	0.455623i	$0.150584\pi$
$720$		0			0
$721$	−48.4575			−1.80465
$722$	4.83502	+	18.3745i	0.179941	+	0.683828i
$723$			20.0627i			0.746142i
$724$	11.1144	−	19.2507i	0.413063	−	0.715445i
$725$		0			0
$726$	−14.0000	−	24.2487i	−0.519589	−	0.899954i
$727$	−1.22715	−	0.708497i	−0.0455126	−	0.0262767i	0.477071	−	0.878865i	$-0.341698\pi$
$727$	−1.22715	−	0.708497i	−0.0455126	−	0.0262767i	−0.522584	+	0.852588i	$0.675032\pi$
$728$	−6.31463	+	3.64575i	−0.234036	+	0.135121i
$729$	41.0000			1.51852
$730$		0			0
$731$		0			0
$732$	2.14752	−	1.23987i	0.0793746	−	0.0458269i
$733$			16.1033i			0.594788i	0.954755	+	0.297394i	$0.0961174\pi$
$733$			16.1033i			0.594788i	−0.954755	+	0.297394i	$0.903883\pi$
$734$	−16.2288			−0.599014
$735$		0			0
$736$	0.822876	−	1.42526i	0.0303316	−	0.0525359i
$737$	−2.59808	+	1.50000i	−0.0957014	+	0.0552532i
$738$	−1.00979	−	0.583005i	−0.0371711	−	0.0214607i
$739$	−16.9059	+	29.2818i	−0.621893	+	1.07715i	0.367240	+	0.930126i	$0.380303\pi$
$739$	−16.9059	+	29.2818i	−0.621893	+	1.07715i	−0.989133	+	0.147024i	$0.953031\pi$
$740$		0			0
$741$	8.87451	−	21.2895i	0.326013	−	0.782090i
$742$		−	45.8745i		−	1.68411i
$743$	−41.1538	−	23.7601i	−1.50978	−	0.871675i	−0.999935	−	0.0114112i	$-0.996368\pi$
$743$	−41.1538	−	23.7601i	−1.50978	−	0.871675i	−0.509850	−	0.860263i	$-0.670299\pi$
$744$	−7.46863	+	12.9360i	−0.273813	+	0.474258i
$745$		0			0
$746$	2.00000	−	3.46410i	0.0732252	−	0.126830i
$747$	27.4955	−	15.8745i	1.00601	−	0.580818i
$748$		0			0
$749$	−55.7490			−2.03702
$750$		0			0
$751$	3.93725	+	6.81952i	0.143672	+	0.248848i	0.928877	−	0.370389i	$-0.120775\pi$
$751$	3.93725	+	6.81952i	0.143672	+	0.248848i	−0.785204	+	0.619237i	$0.787442\pi$
$752$			4.35425i			0.158783i
$753$		−	77.3320i		−	2.81814i
$754$	1.64575	+	2.85052i	0.0599347	+	0.103810i
$755$		0			0
$756$	−4.82288	−	8.35347i	−0.175406	−	0.303813i
$757$	3.96900	+	2.29150i	0.144256	+	0.0832861i	0.570391	−	0.821374i	$-0.306792\pi$
$757$	3.96900	+	2.29150i	0.144256	+	0.0832861i	−0.426135	+	0.904660i	$0.640125\pi$
$758$	9.27383	+	5.35425i	0.336841	+	0.194475i
$759$	−20.2288			−0.734257
$760$		0			0
$761$	42.8745			1.55420			0.777100	−	0.629377i	$-0.216690\pi$
$761$	42.8745			1.55420			0.777100	+	0.629377i	$0.216690\pi$
$762$	30.4547	+	17.5830i	1.10326	+	0.636965i
$763$	46.0431	+	26.5830i	1.66687	+	0.962369i
$764$	3.29150	+	5.70105i	0.119082	+	0.206257i
$765$		0			0
$766$	−2.76013	−	4.78068i	−0.0997275	−	0.172733i
$767$		−	15.8745i		−	0.573195i
$768$		−	2.64575i		−	0.0954703i
$769$	17.6458	+	30.5633i	0.636322	+	1.10214i	0.986233	+	0.165359i	$0.0528784\pi$
$769$	17.6458	+	30.5633i	0.636322	+	1.10214i	−0.349911	+	0.936783i	$0.613788\pi$
$770$		0			0
$771$	32.5203			1.17119
$772$			14.5830i			0.524854i
$773$	4.27579	−	2.46863i	0.153789	−	0.0887903i	−0.421130	−	0.907000i	$-0.638367\pi$
$773$	4.27579	−	2.46863i	0.153789	−	0.0887903i	0.574920	+	0.818210i	$0.305033\pi$
$774$	22.5830	−	39.1149i	0.811729	−	1.40596i
$775$		0			0
$776$	1.85425	−	3.21165i	0.0665636	−	0.115292i
$777$	−2.95920	−	1.70850i	−0.106161	−	0.0612920i
$778$		−	12.0000i		−	0.430221i
$779$	0.771243	+	1.00979i	0.0276327	+	0.0361796i
$780$		0			0
$781$	−6.29150	+	10.8972i	−0.225128	+	0.389933i
$782$		0			0
$783$	−3.77089	+	2.17712i	−0.134761	+	0.0778041i
$784$	3.14575	−	5.44860i	0.112348	−	0.194593i
$785$		0			0
$786$	5.12549			0.182820
$787$		−	42.5203i		−	1.51568i	−0.652438	−	0.757842i	$-0.726254\pi$
$787$		−	42.5203i		−	1.51568i	0.652438	−	0.757842i	$-0.273746\pi$
$788$	6.62141	−	3.82288i	0.235878	−	0.136184i
$789$	−14.4686	−	25.0604i	−0.515097	−	0.892174i
$790$		0			0
$791$	−56.8118			−2.01999
$792$	−16.0934	+	9.29150i	−0.571852	+	0.330159i
$793$	1.62337	+	0.937254i	0.0576476	+	0.0332829i
$794$	10.5314	+	18.2409i	0.373744	+	0.647344i
$795$		0			0
$796$	9.93725	−	17.2118i	0.352217	−	0.610057i
$797$		−	44.8118i		−	1.58731i	−0.608365	−	0.793657i	$-0.708174\pi$
$797$		−	44.8118i		−	1.58731i	0.608365	−	0.793657i	$-0.291826\pi$
$798$	5.39426	+	41.6974i	0.190955	+	1.47607i
$799$		0			0
$800$		0			0
$801$		0			0
$802$	23.8876	−	13.7915i	0.843500	−	0.486995i
$803$	−6.87386	−	3.96863i	−0.242573	−	0.140050i
$804$	0.854249	+	1.47960i	0.0301270	+	0.0521815i
$805$		0			0
$806$	−11.2915			−0.397726
$807$		0			0
$808$	11.8176	−	6.82288i	0.415741	−	0.240028i
$809$	9.00000			0.316423			0.158212	−	0.987405i	$-0.449427\pi$
$809$	9.00000			0.316423			0.158212	+	0.987405i	$0.449427\pi$
$810$		0			0
$811$	15.6458	+	27.0992i	0.549397	+	0.951583i	0.998316	+	0.0580106i	$0.0184757\pi$
$811$	15.6458	+	27.0992i	0.549397	+	0.951583i	−0.448919	+	0.893572i	$0.648191\pi$
$812$	−5.19615	−	3.00000i	−0.182349	−	0.105279i
$813$	−28.3071	+	16.3431i	−0.992775	+	0.573179i
$814$	−0.822876	+	1.42526i	−0.0288418	+	0.0499554i
$815$		0			0
$816$		0			0
$817$	−39.1149	+	29.8745i	−1.36846	+	1.04518i
$818$			7.58301i			0.265134i
$819$	14.5830	−	25.2585i	0.509571	−	0.882604i
$820$		0			0
$821$	3.00000	+	5.19615i	0.104701	+	0.181347i	0.913616	−	0.406578i	$-0.133278\pi$
$821$	3.00000	+	5.19615i	0.104701	+	0.181347i	−0.808915	+	0.587925i	$0.799945\pi$
$822$	−35.7052	−	20.6144i	−1.24536	−	0.719009i
$823$	27.6041	−	15.9373i	0.962220	−	0.555538i	0.0653641	−	0.997861i	$-0.479179\pi$
$823$	27.6041	−	15.9373i	0.962220	−	0.555538i	0.896855	+	0.442324i	$0.145846\pi$
$824$	13.2915			0.463031
$825$		0			0
$826$	14.4686	+	25.0604i	0.503428	+	0.871963i
$827$	−45.5926	+	26.3229i	−1.58541	+	0.915336i	−0.591359	+	0.806408i	$0.701408\pi$
$827$	−45.5926	+	26.3229i	−1.58541	+	0.915336i	−0.994050	+	0.108928i	$0.965258\pi$
$828$			6.58301i			0.228775i
$829$	17.1660			0.596200			0.298100	−	0.954535i	$-0.403647\pi$
$829$	17.1660			0.596200			0.298100	+	0.954535i	$0.403647\pi$
$830$		0			0
$831$	36.4059	−	63.0568i	1.26291	−	2.18742i
$832$	1.73205	−	1.00000i	0.0600481	−	0.0346688i
$833$		0			0
$834$	24.6660	−	42.7228i	0.854114	−	1.47937i
$835$		0			0
$836$	20.0830	−	2.59808i	0.694585	−	0.0898563i
$837$		−	14.9373i		−	0.516307i
$838$	−27.4955	−	15.8745i	−0.949815	−	0.548376i
$839$	−20.7601	+	35.9576i	−0.716719	+	1.24139i	0.245573	+	0.969378i	$0.421024\pi$
$839$	−20.7601	+	35.9576i	−0.716719	+	1.24139i	−0.962293	+	0.272016i	$0.912310\pi$
$840$		0			0
$841$	13.1458	−	22.7691i	0.453302	−	0.785142i
$842$	−21.4876	+	12.4059i	−0.740512	+	0.427535i
$843$		−	67.3542i		−	2.31980i
$844$	13.2915			0.457512
$845$		0			0
$846$	−8.70850	−	15.0836i	−0.299404	−	0.518583i
$847$			38.5830i			1.32573i
$848$			12.5830i			0.432102i
$849$	40.5405	+	70.2182i	1.39135	+	2.40988i
$850$		0			0
$851$	0.291503	+	0.504897i	0.00999258	+	0.0173077i
$852$	6.20595	+	3.58301i	0.212612	+	0.122752i
$853$	7.43310	+	4.29150i	0.254505	+	0.146938i	0.621825	−	0.783156i	$-0.286391\pi$
$853$	7.43310	+	4.29150i	0.254505	+	0.146938i	−0.367321	+	0.930094i	$0.619725\pi$
$854$	−3.41699			−0.116927
$855$		0			0
$856$	15.2915			0.522653
$857$	−18.1865	−	10.5000i	−0.621240	−	0.358673i	0.156112	−	0.987739i	$-0.450104\pi$
$857$	−18.1865	−	10.5000i	−0.621240	−	0.358673i	−0.777352	+	0.629066i	$0.783437\pi$
$858$	−21.2895	−	12.2915i	−0.726812	−	0.419625i
$859$	6.61438	+	11.4564i	0.225680	+	0.390889i	0.956523	−	0.291656i	$-0.0942064\pi$
$859$	6.61438	+	11.4564i	0.225680	+	0.390889i	−0.730843	+	0.682545i	$0.760873\pi$
$860$		0			0
$861$	1.40588	+	2.43506i	0.0479123	+	0.0829865i
$862$			27.8745i			0.949410i
$863$			31.0627i			1.05739i	0.848812	+	0.528694i	$0.177318\pi$
$863$			31.0627i			1.05739i	−0.848812	+	0.528694i	$0.822682\pi$
$864$	1.32288	+	2.29129i	0.0450051	+	0.0779512i
$865$		0			0
$866$	17.8745			0.607401
$867$		−	44.9778i		−	1.52753i
$868$	17.8254	−	10.2915i	0.605034	−	0.349316i
$869$	9.29150	−	16.0934i	0.315193	−	0.545930i
$870$		0			0
$871$	−0.645751	+	1.11847i	−0.0218804	+	0.0378980i
$872$	−12.6293	−	7.29150i	−0.427680	−	0.246921i
$873$			14.8340i			0.502054i
$874$	2.76013	−	6.62141i	0.0933628	−	0.223973i
$875$		0			0
$876$	−2.26013	+	3.91466i	−0.0763627	+	0.132264i
$877$	36.0663	+	20.8229i	1.21787	+	0.703139i	0.964462	−	0.264221i	$-0.0851147\pi$
$877$	36.0663	+	20.8229i	1.21787	+	0.703139i	0.253409	+	0.967359i	$0.418448\pi$
$878$	−9.36326	+	5.40588i	−0.315995	+	0.182440i
$879$	38.2804	−	66.3036i	1.29117	−	2.23636i
$880$		0			0
$881$	−36.8745			−1.24233			−0.621167	−	0.783678i	$-0.713341\pi$
$881$	−36.8745			−1.24233			−0.621167	+	0.783678i	$0.713341\pi$
$882$			25.1660i			0.847384i
$883$	24.5906	−	14.1974i	0.827539	−	0.477780i	−0.0254701	−	0.999676i	$-0.508108\pi$
$883$	24.5906	−	14.1974i	0.827539	−	0.477780i	0.853009	+	0.521896i	$0.174775\pi$
$884$		0			0
$885$		0			0
$886$	10.6458			0.357651
$887$	−15.0836	+	8.70850i	−0.506456	+	0.292403i	−0.731376	−	0.681975i	$-0.761121\pi$
$887$	−15.0836	+	8.70850i	−0.506456	+	0.292403i	0.224919	+	0.974377i	$0.427788\pi$
$888$	0.811686	+	0.468627i	0.0272384	+	0.0157261i
$889$	−24.2288	−	41.9654i	−0.812606	−	1.40748i
$890$		0			0
$891$	−11.6144	+	20.1167i	−0.389096	+	0.673935i
$892$		−	18.8118i		−	0.629864i
$893$	2.43506	+	18.8229i	0.0814861	+	0.629884i
$894$	−28.9373			−0.967807
$895$		0			0
$896$	−1.82288	+	3.15731i	−0.0608980	+	0.105478i
$897$	−7.54178	+	4.35425i	−0.251813	+	0.145384i
$898$	−21.0371	−	12.1458i	−0.702016	−	0.405309i
$899$	−4.64575	−	8.04668i	−0.154944	−	0.268372i
$900$		0			0
$901$		0			0
$902$	1.17281	−	0.677124i	0.0390504	−	0.0225458i
$903$	−94.3232	+	54.4575i	−3.13888	+	1.81223i
$904$	15.5830			0.518283
$905$		0			0
$906$	−17.1144	−	29.6430i	−0.568587	−	0.984822i
$907$	−34.5867	−	19.9686i	−1.14843	−	0.663047i	−0.199927	−	0.979811i	$-0.564071\pi$
$907$	−34.5867	−	19.9686i	−1.14843	−	0.663047i	−0.948505	+	0.316763i	$0.897404\pi$
$908$	6.36897	−	3.67712i	0.211362	−	0.122030i
$909$	−27.2915	+	47.2703i	−0.905202	+	1.56786i
$910$		0			0
$911$	16.9373			0.561156			0.280578	−	0.959831i	$-0.409474\pi$
$911$	16.9373			0.561156			0.280578	+	0.959831i	$0.409474\pi$
$912$	−1.47960	−	11.4373i	−0.0489945	−	0.378725i
$913$			36.8745i			1.22037i
$914$	16.4373	−	28.4702i	0.543696	−	0.941709i
$915$		0			0
$916$	−10.0000	−	17.3205i	−0.330409	−	0.572286i
$917$	−6.11652	−	3.53137i	−0.201985	−	0.116616i
$918$		0			0
$919$	19.8745			0.655600			0.327800	−	0.944747i	$-0.393693\pi$
$919$	19.8745			0.655600			0.327800	+	0.944747i	$0.393693\pi$
$920$		0			0
$921$	−0.854249	−	1.47960i	−0.0281485	−	0.0487545i
$922$	16.5983	−	9.58301i	0.546634	−	0.315599i
$923$			5.41699i			0.178303i
$924$	44.8118			1.47420
$925$		0			0
$926$	19.2288	−	33.3052i	0.631896	−	1.09448i
$927$	−46.0431	+	26.5830i	−1.51225	+	0.873100i
$928$	1.42526	+	0.822876i	0.0467865	+	0.0270122i
$929$	−4.79150	+	8.29913i	−0.157204	+	0.272285i	−0.933859	−	0.357640i	$-0.883581\pi$
$929$	−4.79150	+	8.29913i	−0.157204	+	0.272285i	0.776655	+	0.629926i	$0.216915\pi$
$930$		0			0
$931$	10.5516	−	25.3128i	0.345816	−	0.829595i
$932$			18.8745i			0.618255i
$933$	31.2663	+	18.0516i	1.02361	+	0.590984i
$934$	−9.67712	+	16.7613i	−0.316645	+	0.548446i
$935$		0			0
$936$	−4.00000	+	6.92820i	−0.130744	+	0.226455i
$937$	6.17086	−	3.56275i	0.201593	−	0.116390i	−0.395805	−	0.918334i	$-0.629534\pi$
$937$	6.17086	−	3.56275i	0.201593	−	0.116390i	0.597398	+	0.801945i	$0.296201\pi$
$938$		−	2.35425i		−	0.0768689i
$939$	−23.4797			−0.766232
$940$		0			0
$941$	−8.41699	−	14.5787i	−0.274386	−	0.475251i	0.695594	−	0.718435i	$-0.255141\pi$
$941$	−8.41699	−	14.5787i	−0.274386	−	0.475251i	−0.969980	+	0.243184i	$0.921808\pi$
$942$		−	28.0000i		−	0.912289i
$943$		−	0.479741i		−	0.0156225i
$944$	−3.96863	−	6.87386i	−0.129168	−	0.223725i
$945$		0			0
$946$	26.2288	+	45.4295i	0.852770	+	1.47704i
$947$	6.71084	+	3.87451i	0.218073	+	0.125905i	0.605058	−	0.796182i	$-0.293150\pi$
$947$	6.71084	+	3.87451i	0.218073	+	0.125905i	−0.386985	+	0.922086i	$0.626483\pi$
$948$	−9.16515	−	5.29150i	−0.297670	−	0.171860i
$949$	−3.41699			−0.110920
$950$		0			0
$951$	−15.8745			−0.514766
$952$		0			0
$953$	−11.6545	−	6.72876i	−0.377528	−	0.217966i	0.299214	−	0.954186i	$-0.403275\pi$
$953$	−11.6545	−	6.72876i	−0.377528	−	0.217966i	−0.676742	+	0.736220i	$0.736609\pi$
$954$	−25.1660	−	43.5888i	−0.814780	−	1.41124i
$955$		0			0
$956$	6.00000	+	10.3923i	0.194054	+	0.336111i
$957$		−	20.2288i		−	0.653903i
$958$		−	6.58301i		−	0.212687i
$959$	28.4059	+	49.2004i	0.917274	+	1.58876i
$960$		0			0
$961$	0.874508			0.0282099
$962$			0.708497i			0.0228429i
$963$	−52.9713	+	30.5830i	−1.70698	+	0.985524i
$964$	−3.79150	+	6.56708i	−0.122116	+	0.211511i
$965$		0			0
$966$	7.93725	−	13.7477i	0.255377	−	0.442326i
$967$	11.5108	+	6.64575i	0.370162	+	0.213713i	0.673529	−	0.739161i	$-0.264778\pi$
$967$	11.5108	+	6.64575i	0.370162	+	0.213713i	−0.303367	+	0.952874i	$0.598111\pi$
$968$		−	10.5830i		−	0.340151i
$969$		0			0
$970$		0			0
$971$	27.1974	−	47.1073i	0.872806	−	1.51174i	0.0137234	−	0.999906i	$-0.495632\pi$
$971$	27.1974	−	47.1073i	0.872806	−	1.51174i	0.859082	−	0.511838i	$-0.171035\pi$
$972$	18.3303	+	10.5830i	0.587945	+	0.339450i
$973$	−58.8705	+	33.9889i	−1.88730	+	1.08963i
$974$	2.11438	−	3.66221i	0.0677491	−	0.117345i
$975$		0			0
$976$	0.937254			0.0300008
$977$		−	7.45751i		−	0.238587i	−0.992859	−	0.119293i	$-0.961937\pi$
$977$		−	7.45751i		−	0.238587i	0.992859	−	0.119293i	$-0.0380629\pi$
$978$	−9.02138	+	5.20850i	−0.288472	+	0.166549i
$979$		0			0
$980$		0			0
$981$	58.3320			1.86240
$982$	34.0274	−	19.6458i	1.08586	−	0.626921i
$983$	27.4955	+	15.8745i	0.876969	+	0.506318i	0.869658	−	0.493655i	$-0.164339\pi$
$983$	27.4955	+	15.8745i	0.876969	+	0.506318i	0.00731102	+	0.999973i	$0.497673\pi$
$984$	−0.385622	−	0.667916i	−0.0122932	−	0.0212924i
$985$		0			0
$986$		0			0
$987$			42.0000i			1.33687i
$988$	6.92820	−	5.29150i	0.220416	−	0.168345i
$989$	18.5830			0.590905
$990$		0			0
$991$	1.41699	−	2.45431i	0.0450123	−	0.0779636i	−0.842641	−	0.538475i	$-0.819001\pi$
$991$	1.41699	−	2.45431i	0.0450123	−	0.0779636i	0.887654	+	0.460511i	$0.152334\pi$
$992$	−4.88936	+	2.82288i	−0.155237	+	0.0896264i
$993$	45.3944	+	26.2085i	1.44055	+	0.831702i
$994$	−4.93725	−	8.55157i	−0.156600	−	0.271239i
$995$		0			0
$996$	21.0000			0.665410
$997$	14.0545	−	8.11438i	0.445111	−	0.256985i	−0.260652	−	0.965433i	$-0.583938\pi$
$997$	14.0545	−	8.11438i	0.445111	−	0.256985i	0.705763	+	0.708448i	$0.250604\pi$
$998$	4.13202	−	2.38562i	0.130797	−	0.0755155i
$999$	−0.937254			−0.0296534

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	950.2.j.g.49.2		8
5.2	odd	4		950.2.e.k.201.2		4
5.3	odd	4		38.2.c.b.11.1	yes	4
5.4	even	2	inner	950.2.j.g.49.3		8
15.8	even	4		342.2.g.f.163.1		4
19.7	even	3	inner	950.2.j.g.349.3		8
20.3	even	4		304.2.i.e.49.2		4
40.3	even	4		1216.2.i.k.961.1		4
40.13	odd	4		1216.2.i.l.961.2		4
60.23	odd	4		2736.2.s.v.1873.1		4
95.3	even	36		722.2.e.o.99.1		12
95.7	odd	12		950.2.e.k.501.2		4
95.8	even	12		722.2.a.g.1.1		2
95.13	even	36		722.2.e.o.415.2		12
95.18	even	4		722.2.c.j.429.2		4
95.23	odd	36		722.2.e.n.423.2		12
95.28	odd	36		722.2.e.n.245.2		12
95.33	even	36		722.2.e.o.389.1		12
95.43	odd	36		722.2.e.n.389.2		12
95.48	even	36		722.2.e.o.245.1		12
95.53	even	36		722.2.e.o.423.1		12
95.63	odd	36		722.2.e.n.415.1		12
95.64	even	6	inner	950.2.j.g.349.2		8
95.68	odd	12		722.2.a.j.1.2		2
95.73	odd	36		722.2.e.n.99.2		12
95.78	even	36		722.2.e.o.595.2		12
95.83	odd	12		38.2.c.b.7.1	✓	4
95.88	even	12		722.2.c.j.653.2		4
95.93	odd	36		722.2.e.n.595.1		12
285.8	odd	12		6498.2.a.bg.1.2		2
285.68	even	12		6498.2.a.ba.1.2		2
285.83	even	12		342.2.g.f.235.1		4
380.83	even	12		304.2.i.e.273.2		4
380.103	odd	12		5776.2.a.z.1.2		2
380.163	even	12		5776.2.a.ba.1.1		2
760.83	even	12		1216.2.i.k.577.1		4
760.653	odd	12		1216.2.i.l.577.2		4
1140.83	odd	12		2736.2.s.v.577.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
38.2.c.b.7.1	✓	4	95.83	odd	12
38.2.c.b.11.1	yes	4	5.3	odd	4
304.2.i.e.49.2		4	20.3	even	4
304.2.i.e.273.2		4	380.83	even	12
342.2.g.f.163.1		4	15.8	even	4
342.2.g.f.235.1		4	285.83	even	12
722.2.a.g.1.1		2	95.8	even	12
722.2.a.j.1.2		2	95.68	odd	12
722.2.c.j.429.2		4	95.18	even	4
722.2.c.j.653.2		4	95.88	even	12
722.2.e.n.99.2		12	95.73	odd	36
722.2.e.n.245.2		12	95.28	odd	36
722.2.e.n.389.2		12	95.43	odd	36
722.2.e.n.415.1		12	95.63	odd	36
722.2.e.n.423.2		12	95.23	odd	36
722.2.e.n.595.1		12	95.93	odd	36
722.2.e.o.99.1		12	95.3	even	36
722.2.e.o.245.1		12	95.48	even	36
722.2.e.o.389.1		12	95.33	even	36
722.2.e.o.415.2		12	95.13	even	36
722.2.e.o.423.1		12	95.53	even	36
722.2.e.o.595.2		12	95.78	even	36
950.2.e.k.201.2		4	5.2	odd	4
950.2.e.k.501.2		4	95.7	odd	12
950.2.j.g.49.2		8	1.1	even	1	trivial
950.2.j.g.49.3		8	5.4	even	2	inner
950.2.j.g.349.2		8	95.64	even	6	inner
950.2.j.g.349.3		8	19.7	even	3	inner
1216.2.i.k.577.1		4	760.83	even	12
1216.2.i.k.961.1		4	40.3	even	4
1216.2.i.l.577.2		4	760.653	odd	12
1216.2.i.l.961.2		4	40.13	odd	4
2736.2.s.v.577.1		4	1140.83	odd	12
2736.2.s.v.1873.1		4	60.23	odd	4
5776.2.a.z.1.2		2	380.103	odd	12
5776.2.a.ba.1.1		2	380.163	even	12
6498.2.a.ba.1.2		2	285.68	even	12
6498.2.a.bg.1.2		2	285.8	odd	12

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:	\( N \)	\(=\)	\( 950 = 2 \cdot 5^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	950.j (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.866025 - 0.500000i) q^{2} +(2.29129 + 1.32288i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-1.32288 - 2.29129i) q^{6} +3.64575i q^{7} -1.00000i q^{8} +(2.00000 + 3.46410i) q^{9} +O(q^{10})\)	\(q+(-0.866025 - 0.500000i) q^{2} +(2.29129 + 1.32288i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-1.32288 - 2.29129i) q^{6} +3.64575i q^{7} -1.00000i q^{8} +(2.00000 + 3.46410i) q^{9} -4.64575 q^{11} +2.64575i q^{12} +(-1.73205 + 1.00000i) q^{13} +(1.82288 - 3.15731i) q^{14} +(-0.500000 + 0.866025i) q^{16} -4.00000i q^{18} +(-1.67712 + 4.02334i) q^{19} +(-4.82288 + 8.35347i) q^{21} +(4.02334 + 2.32288i) q^{22} +(1.42526 - 0.822876i) q^{23} +(1.32288 - 2.29129i) q^{24} +2.00000 q^{26} +2.64575i q^{27} +(-3.15731 + 1.82288i) q^{28} +(0.822876 + 1.42526i) q^{29} -5.64575 q^{31} +(0.866025 - 0.500000i) q^{32} +(-10.6448 - 6.14575i) q^{33} +(-2.00000 + 3.46410i) q^{36} +0.354249i q^{37} +(3.46410 - 2.64575i) q^{38} -5.29150 q^{39} +(0.145751 - 0.252449i) q^{41} +(8.35347 - 4.82288i) q^{42} +(9.77873 + 5.64575i) q^{43} +(-2.32288 - 4.02334i) q^{44} -1.64575 q^{46} +(3.77089 - 2.17712i) q^{47} +(-2.29129 + 1.32288i) q^{48} -6.29150 q^{49} +(-1.73205 - 1.00000i) q^{52} +(10.8972 - 6.29150i) q^{53} +(1.32288 - 2.29129i) q^{54} +3.64575 q^{56} +(-9.16515 + 7.00000i) q^{57} -1.64575i q^{58} +(-3.96863 + 6.87386i) q^{59} +(-0.468627 - 0.811686i) q^{61} +(4.88936 + 2.82288i) q^{62} +(-12.6293 + 7.29150i) q^{63} -1.00000 q^{64} +(6.14575 + 10.6448i) q^{66} +(0.559237 - 0.322876i) q^{67} +4.35425 q^{69} +(1.35425 - 2.34563i) q^{71} +(3.46410 - 2.00000i) q^{72} +(1.47960 + 0.854249i) q^{73} +(0.177124 - 0.306788i) q^{74} +(-4.32288 + 0.559237i) q^{76} -16.9373i q^{77} +(4.58258 + 2.64575i) q^{78} +(-2.00000 + 3.46410i) q^{79} +(2.50000 - 4.33013i) q^{81} +(-0.252449 + 0.145751i) q^{82} -7.93725i q^{83} -9.64575 q^{84} +(-5.64575 - 9.77873i) q^{86} +4.35425i q^{87} +4.64575i q^{88} +(-3.64575 - 6.31463i) q^{91} +(1.42526 + 0.822876i) q^{92} +(-12.9360 - 7.46863i) q^{93} -4.35425 q^{94} +2.64575 q^{96} +(3.21165 + 1.85425i) q^{97} +(5.44860 + 3.14575i) q^{98} +(-9.29150 - 16.0934i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 4 q^{4} + 16 q^{9}+O(q^{10}) \) 8 * q + 4 * q^4 + 16 * q^9	\( 8 q + 4 q^{4} + 16 q^{9} - 16 q^{11} + 4 q^{14} - 4 q^{16} - 24 q^{19} - 28 q^{21} + 16 q^{26} - 4 q^{29} - 24 q^{31} - 16 q^{36} - 20 q^{41} - 8 q^{44} + 8 q^{46} - 8 q^{49} + 8 q^{56} + 28 q^{61} - 8 q^{64} + 28 q^{66} + 56 q^{69} + 32 q^{71} + 12 q^{74} - 24 q^{76} - 16 q^{79} + 20 q^{81} - 56 q^{84} - 24 q^{86} - 8 q^{91} - 56 q^{94} - 32 q^{99}+O(q^{100}) \) 8 * q + 4 * q^4 + 16 * q^9 - 16 * q^11 + 4 * q^14 - 4 * q^16 - 24 * q^19 - 28 * q^21 + 16 * q^26 - 4 * q^29 - 24 * q^31 - 16 * q^36 - 20 * q^41 - 8 * q^44 + 8 * q^46 - 8 * q^49 + 8 * q^56 + 28 * q^61 - 8 * q^64 + 28 * q^66 + 56 * q^69 + 32 * q^71 + 12 * q^74 - 24 * q^76 - 16 * q^79 + 20 * q^81 - 56 * q^84 - 24 * q^86 - 8 * q^91 - 56 * q^94 - 32 * q^99

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