LMFDB - Embedded newform 950.2.e.k.501.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [950,2,Mod(201,950)]

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([0, 4]))

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

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

chi := DirichletCharacter("950.201");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 950 = 2 \cdot 5^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	950.e (of order $3$, degree $2$, 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:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\sqrt{-3}, \sqrt{7})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 7x^{2} + 49 $ x^4 + 7*x^2 + 49
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 38)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			501.2
Root			$1.32288 + 2.29129i$ of defining polynomial
Character	$\chi$	$=$	950.501
Dual form			950.2.e.k.201.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

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

Display 100 coefficients 10 coefficients

Character values

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

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

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 $

$2$	0.500000	+	0.866025i	0.353553	+	0.612372i
$2$	0.500000	+	0.866025i	0.353553	+	0.612372i
$3$	1.32288	+	2.29129i	0.763763	+	1.32288i	0.940898	+	0.338689i	$0.109984\pi$
$3$	1.32288	+	2.29129i	0.763763	+	1.32288i	−0.177136	+	0.984186i	$0.556683\pi$
$4$	−0.500000	+	0.866025i	−0.250000	+	0.433013i
$5$		0			0
$5$		0			0
$6$	−1.32288	+	2.29129i	−0.540062	+	0.935414i
$7$	−3.64575			−1.37796			−0.688982	−	0.724778i	$-0.741942\pi$
$7$	−3.64575			−1.37796			−0.688982	+	0.724778i	$0.741942\pi$
$8$	−1.00000			−0.353553
$9$	−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	$0.746983\pi$
$12$	−2.64575			−0.763763
$13$	1.00000	−	1.73205i	0.277350	−	0.480384i	−0.693375	−	0.720577i	$-0.743877\pi$
$13$	1.00000	−	1.73205i	0.277350	−	0.480384i	0.970725	+	0.240192i	$0.0772105\pi$
$14$	−1.82288	−	3.15731i	−0.487184	−	0.843827i
$15$		0			0
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$17$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$18$	−4.00000			−0.942809
$19$	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
$22$	−2.32288	−	4.02334i	−0.495239	−	0.857779i
$23$	−0.822876	+	1.42526i	−0.171581	+	0.297188i	−0.938973	−	0.343991i	$-0.888221\pi$
$23$	−0.822876	+	1.42526i	−0.171581	+	0.297188i	0.767391	+	0.641179i	$0.221554\pi$
$24$	−1.32288	−	2.29129i	−0.270031	−	0.467707i
$25$		0			0
$26$	2.00000			0.392232
$27$	−2.64575			−0.509175
$28$	1.82288	−	3.15731i	0.344491	−	0.596676i
$29$	−0.822876	+	1.42526i	−0.152804	+	0.264665i	−0.932257	−	0.361796i	$-0.882164\pi$
$29$	−0.822876	+	1.42526i	−0.152804	+	0.264665i	0.779453	+	0.626461i	$0.215497\pi$
$30$		0			0
$31$	−5.64575			−1.01401			−0.507003	−	0.861944i	$-0.669247\pi$
$31$	−5.64575			−1.01401			−0.507003	+	0.861944i	$0.669247\pi$
$32$	0.500000	−	0.866025i	0.0883883	−	0.153093i
$33$	−6.14575	−	10.6448i	−1.06984	−	1.85301i
$34$		0			0
$35$		0			0
$36$	−2.00000	−	3.46410i	−0.333333	−	0.577350i
$37$	−0.354249			−0.0582381			−0.0291191	−	0.999576i	$-0.509270\pi$
$37$	−0.354249			−0.0582381			−0.0291191	+	0.999576i	$0.509270\pi$
$38$	−2.64575	+	3.46410i	−0.429198	+	0.561951i
$39$	5.29150			0.847319
$40$		0			0
$41$	0.145751	+	0.252449i	0.0227625	+	0.0394259i	0.877182	−	0.480158i	$-0.159421\pi$
$41$	0.145751	+	0.252449i	0.0227625	+	0.0394259i	−0.854420	+	0.519583i	$0.826087\pi$
$42$	4.82288	−	8.35347i	0.744186	−	1.28897i
$43$	5.64575	+	9.77873i	0.860969	+	1.49124i	0.870995	+	0.491292i	$0.163475\pi$
$43$	5.64575	+	9.77873i	0.860969	+	1.49124i	−0.0100257	+	0.999950i	$0.503191\pi$
$44$	2.32288	−	4.02334i	0.350187	−	0.606541i
$45$		0			0
$46$	−1.64575			−0.242653
$47$	2.17712	−	3.77089i	0.317566	−	0.550041i	−0.662413	−	0.749138i	$-0.730468\pi$
$47$	2.17712	−	3.77089i	0.317566	−	0.550041i	0.979980	+	0.199098i	$0.0638011\pi$
$48$	1.32288	−	2.29129i	0.190941	−	0.330719i
$49$	6.29150			0.898786
$50$		0			0
$51$		0			0
$52$	1.00000	+	1.73205i	0.138675	+	0.240192i
$53$	−6.29150	+	10.8972i	−0.864204	+	1.49685i	0.00363070	+	0.999993i	$0.498844\pi$
$53$	−6.29150	+	10.8972i	−0.864204	+	1.49685i	−0.867835	+	0.496852i	$0.834489\pi$
$54$	−1.32288	−	2.29129i	−0.180021	−	0.311805i
$55$		0			0
$56$	3.64575			0.487184
$57$	−7.00000	+	9.16515i	−0.927173	+	1.21395i
$58$	−1.64575			−0.216098
$59$	3.96863	+	6.87386i	0.516671	+	0.894901i	0.999813	+	0.0193585i	$0.00616237\pi$
$59$	3.96863	+	6.87386i	0.516671	+	0.894901i	−0.483141	+	0.875542i	$0.660504\pi$
$60$		0			0
$61$	−0.468627	+	0.811686i	−0.0600015	+	0.103926i	−0.894466	−	0.447136i	$-0.852444\pi$
$61$	−0.468627	+	0.811686i	−0.0600015	+	0.103926i	0.834464	+	0.551062i	$0.185777\pi$
$62$	−2.82288	−	4.88936i	−0.358506	−	0.620950i
$63$	7.29150	−	12.6293i	0.918643	−	1.59114i
$64$	1.00000			0.125000
$65$		0			0
$66$	6.14575	−	10.6448i	0.756490	−	1.31028i
$67$	0.322876	−	0.559237i	0.0394455	−	0.0683217i	−0.845629	−	0.533772i	$-0.820774\pi$
$67$	0.322876	−	0.559237i	0.0394455	−	0.0683217i	0.885074	+	0.465450i	$0.154108\pi$
$68$		0			0
$69$	−4.35425			−0.524190
$70$		0			0
$71$	1.35425	+	2.34563i	0.160720	+	0.278375i	0.935127	−	0.354313i	$-0.115285\pi$
$71$	1.35425	+	2.34563i	0.160720	+	0.278375i	−0.774407	+	0.632687i	$0.781952\pi$
$72$	2.00000	−	3.46410i	0.235702	−	0.408248i
$73$	0.854249	+	1.47960i	0.0999822	+	0.173174i	0.911677	−	0.410907i	$-0.134788\pi$
$73$	0.854249	+	1.47960i	0.0999822	+	0.173174i	−0.811695	+	0.584082i	$0.801455\pi$
$74$	−0.177124	−	0.306788i	−0.0205903	−	0.0356634i
$75$		0			0
$76$	−4.32288	−	0.559237i	−0.495868	−	0.0641489i
$77$	16.9373			1.93018
$78$	2.64575	+	4.58258i	0.299572	+	0.518875i
$79$	2.00000	+	3.46410i	0.225018	+	0.389742i	0.956325	−	0.292306i	$-0.0944227\pi$
$79$	2.00000	+	3.46410i	0.225018	+	0.389742i	−0.731307	+	0.682048i	$0.761089\pi$
$80$		0			0
$81$	2.50000	+	4.33013i	0.277778	+	0.481125i
$82$	−0.145751	+	0.252449i	−0.0160955	+	0.0278783i
$83$	−7.93725			−0.871227			−0.435613	−	0.900134i	$-0.643469\pi$
$83$	−7.93725			−0.871227			−0.435613	+	0.900134i	$0.643469\pi$
$84$	9.64575			1.05244
$85$		0			0
$86$	−5.64575	+	9.77873i	−0.608797	+	1.05447i
$87$	−4.35425			−0.466824
$88$	4.64575			0.495239
$89$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$89$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$90$		0			0
$91$	−3.64575	+	6.31463i	−0.382179	+	0.661953i
$92$	−0.822876	−	1.42526i	−0.0857907	−	0.148594i
$93$	−7.46863	−	12.9360i	−0.774461	−	1.34141i
$94$	4.35425			0.449106
$95$		0			0
$96$	2.64575			0.270031
$97$	−1.85425	−	3.21165i	−0.188270	−	0.326094i	0.756403	−	0.654106i	$-0.226955\pi$
$97$	−1.85425	−	3.21165i	−0.188270	−	0.326094i	−0.944674	+	0.328012i	$0.893621\pi$
$98$	3.14575	+	5.44860i	0.317769	+	0.550392i
$99$	9.29150	−	16.0934i	0.933831	−	1.61744i
$100$		0			0
$101$	6.82288	−	11.8176i	0.678902	−	1.17589i	−0.296411	−	0.955061i	$-0.595790\pi$
$101$	6.82288	−	11.8176i	0.678902	−	1.17589i	0.975312	−	0.220831i	$-0.0708770\pi$
$102$		0			0
$103$	13.2915			1.30965			0.654825	−	0.755780i	$-0.272742\pi$
$103$	13.2915			1.30965			0.654825	+	0.755780i	$0.272742\pi$
$104$	−1.00000	+	1.73205i	−0.0980581	+	0.169842i
$105$		0			0
$106$	−12.5830			−1.22217
$107$	−15.2915			−1.47829			−0.739143	−	0.673549i	$-0.764769\pi$
$107$	−15.2915			−1.47829			−0.739143	+	0.673549i	$0.764769\pi$
$108$	1.32288	−	2.29129i	0.127294	−	0.220479i
$109$	−7.29150	−	12.6293i	−0.698399	−	1.20966i	−0.969021	−	0.246977i	$-0.920563\pi$
$109$	−7.29150	−	12.6293i	−0.698399	−	1.20966i	0.270622	−	0.962686i	$-0.412771\pi$
$110$		0			0
$111$	−0.468627	−	0.811686i	−0.0444801	−	0.0770418i
$112$	1.82288	+	3.15731i	0.172246	+	0.298338i
$113$	15.5830			1.46593			0.732963	−	0.680269i	$-0.238137\pi$
$113$	15.5830			1.46593			0.732963	+	0.680269i	$0.238137\pi$
$114$	−11.4373	−	1.47960i	−1.07120	−	0.138577i
$115$		0			0
$116$	−0.822876	−	1.42526i	−0.0764021	−	0.132332i
$117$	4.00000	+	6.92820i	0.369800	+	0.640513i
$118$	−3.96863	+	6.87386i	−0.365342	+	0.632790i
$119$		0			0
$120$		0			0
$121$	10.5830			0.962091
$122$	−0.937254			−0.0848550
$123$	−0.385622	+	0.667916i	−0.0347703	+	0.0602240i
$124$	2.82288	−	4.88936i	0.253502	−	0.439078i
$125$		0			0
$126$	14.5830			1.29916
$127$	−6.64575	+	11.5108i	−0.589715	+	1.02142i	0.404554	+	0.914514i	$0.367427\pi$
$127$	−6.64575	+	11.5108i	−0.589715	+	1.02142i	−0.994270	+	0.106903i	$0.965907\pi$
$128$	0.500000	+	0.866025i	0.0441942	+	0.0765466i
$129$	−14.9373	+	25.8721i	−1.31515	+	2.27791i
$130$		0			0
$131$	−0.968627	−	1.67771i	−0.0846293	−	0.146582i	0.820604	−	0.571497i	$-0.193637\pi$
$131$	−0.968627	−	1.67771i	−0.0846293	−	0.146582i	−0.905233	+	0.424915i	$0.860304\pi$
$132$	12.2915			1.06984
$133$	−6.11438	−	14.6681i	−0.530184	−	1.27188i
$134$	0.645751			0.0557844
$135$		0			0
$136$		0			0
$137$	7.79150	−	13.4953i	0.665673	−	1.15298i	−0.313429	−	0.949612i	$-0.601478\pi$
$137$	7.79150	−	13.4953i	0.665673	−	1.15298i	0.979102	−	0.203368i	$-0.0651888\pi$
$138$	−2.17712	−	3.77089i	−0.185329	−	0.320999i
$139$	−9.32288	+	16.1477i	−0.790756	+	1.36963i	0.134743	+	0.990881i	$0.456979\pi$
$139$	−9.32288	+	16.1477i	−0.790756	+	1.36963i	−0.925499	+	0.378749i	$0.876354\pi$
$140$		0			0
$141$	11.5203			0.970181
$142$	−1.35425	+	2.34563i	−0.113646	+	0.196841i
$143$	−4.64575	+	8.04668i	−0.388497	+	0.672897i
$144$	4.00000			0.333333
$145$		0			0
$146$	−0.854249	+	1.47960i	−0.0706981	+	0.122453i
$147$	8.32288	+	14.4156i	0.686459	+	1.18898i
$148$	0.177124	−	0.306788i	0.0145595	−	0.0252178i
$149$	−5.46863	−	9.47194i	−0.448007	−	0.775972i	0.550249	−	0.835001i	$-0.314533\pi$
$149$	−5.46863	−	9.47194i	−0.448007	−	0.775972i	−0.998256	+	0.0590292i	$0.981200\pi$
$150$		0			0
$151$	12.9373			1.05282			0.526409	−	0.850231i	$-0.323538\pi$
$151$	12.9373			1.05282			0.526409	+	0.850231i	$0.323538\pi$
$152$	−1.67712	−	4.02334i	−0.136033	−	0.326336i
$153$		0			0
$154$	8.46863	+	14.6681i	0.682421	+	1.18199i
$155$		0			0
$156$	−2.64575	+	4.58258i	−0.211830	+	0.366900i
$157$	−5.29150	−	9.16515i	−0.422308	−	0.731459i	0.573857	−	0.818956i	$-0.305447\pi$
$157$	−5.29150	−	9.16515i	−0.422308	−	0.731459i	−0.996165	+	0.0874969i	$0.972113\pi$
$158$	−2.00000	+	3.46410i	−0.159111	+	0.275589i
$159$	−33.2915			−2.64019
$160$		0			0
$161$	3.00000	−	5.19615i	0.236433	−	0.409514i
$162$	−2.50000	+	4.33013i	−0.196419	+	0.340207i
$163$	−3.93725			−0.308390			−0.154195	−	0.988040i	$-0.549278\pi$
$163$	−3.93725			−0.308390			−0.154195	+	0.988040i	$0.549278\pi$
$164$	−0.291503			−0.0227625
$165$		0			0
$166$	−3.96863	−	6.87386i	−0.308025	−	0.533515i
$167$	−6.00000	+	10.3923i	−0.464294	+	0.804181i	−0.999169	−	0.0407502i	$-0.987025\pi$
$167$	−6.00000	+	10.3923i	−0.464294	+	0.804181i	0.534875	+	0.844931i	$0.320359\pi$
$168$	4.82288	+	8.35347i	0.372093	+	0.644484i
$169$	4.50000	+	7.79423i	0.346154	+	0.599556i
$170$		0			0
$171$	−17.2915	−	2.23695i	−1.32231	−	0.171064i
$172$	−11.2915			−0.860969
$173$	−3.00000	−	5.19615i	−0.228086	−	0.395056i	0.729155	−	0.684349i	$-0.239913\pi$
$173$	−3.00000	−	5.19615i	−0.228086	−	0.395056i	−0.957241	+	0.289292i	$0.906580\pi$
$174$	−2.17712	−	3.77089i	−0.165047	−	0.285870i
$175$		0			0
$176$	2.32288	+	4.02334i	0.175093	+	0.303271i
$177$	−10.5000	+	18.1865i	−0.789228	+	1.36698i
$178$		0			0
$179$	4.06275			0.303664			0.151832	−	0.988406i	$-0.451483\pi$
$179$	4.06275			0.303664			0.151832	+	0.988406i	$0.451483\pi$
$180$		0			0
$181$	−11.1144	+	19.2507i	−0.826125	+	1.43089i	0.0749311	+	0.997189i	$0.476126\pi$
$181$	−11.1144	+	19.2507i	−0.826125	+	1.43089i	−0.901056	+	0.433702i	$0.857207\pi$
$182$	−7.29150			−0.540482
$183$	−2.47974			−0.183308
$184$	0.822876	−	1.42526i	0.0606632	−	0.105072i
$185$		0			0
$186$	7.46863	−	12.9360i	0.547626	−	0.948517i
$187$		0			0
$188$	2.17712	+	3.77089i	0.158783	+	0.275020i
$189$	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	$0.423454\pi$
$192$	1.32288	+	2.29129i	0.0954703	+	0.165359i
$193$	7.29150	+	12.6293i	0.524854	+	0.909074i	0.999581	+	0.0289406i	$0.00921336\pi$
$193$	7.29150	+	12.6293i	0.524854	+	0.909074i	−0.474727	+	0.880133i	$0.657453\pi$
$194$	1.85425	−	3.21165i	0.133127	−	0.230583i
$195$		0			0
$196$	−3.14575	+	5.44860i	−0.224697	+	0.389186i
$197$	7.64575			0.544737			0.272369	−	0.962193i	$-0.412193\pi$
$197$	7.64575			0.544737			0.272369	+	0.962193i	$0.412193\pi$
$198$	18.5830			1.32064
$199$	9.93725	−	17.2118i	0.704433	−	1.22011i	−0.262462	−	0.964942i	$-0.584535\pi$
$199$	9.93725	−	17.2118i	0.704433	−	1.22011i	0.966896	−	0.255172i	$-0.0821321\pi$
$200$		0			0
$201$	1.70850			0.120508
$202$	13.6458			0.960112
$203$	3.00000	−	5.19615i	0.210559	−	0.364698i
$204$		0			0
$205$		0			0
$206$	6.64575	+	11.5108i	0.463031	+	0.801994i
$207$	−3.29150	−	5.70105i	−0.228775	−	0.396250i
$208$	−2.00000			−0.138675
$209$	−7.79150	−	18.6914i	−0.538950	−	1.29291i
$210$		0			0
$211$	6.64575	+	11.5108i	0.457512	+	0.792435i	0.998829	−	0.0483843i	$-0.0154072\pi$
$211$	6.64575	+	11.5108i	0.457512	+	0.792435i	−0.541316	+	0.840819i	$0.682074\pi$
$212$	−6.29150	−	10.8972i	−0.432102	−	0.748423i
$213$	−3.58301	+	6.20595i	−0.245503	+	0.425224i
$214$	−7.64575	−	13.2428i	−0.522653	−	0.905261i
$215$		0			0
$216$	2.64575			0.180021
$217$	20.5830			1.39727
$218$	7.29150	−	12.6293i	0.493843	−	0.855361i
$219$	−2.26013	+	3.91466i	−0.152725	+	0.264528i
$220$		0			0
$221$		0			0
$222$	0.468627	−	0.811686i	0.0314522	−	0.0544768i
$223$	−9.40588	−	16.2915i	−0.629864	−	1.09096i	−0.987579	−	0.157126i	$-0.949777\pi$
$223$	−9.40588	−	16.2915i	−0.629864	−	1.09096i	0.357714	−	0.933831i	$-0.383556\pi$
$224$	−1.82288	+	3.15731i	−0.121796	+	0.210957i
$225$		0			0
$226$	7.79150	+	13.4953i	0.518283	+	0.897693i
$227$	7.35425			0.488119			0.244059	−	0.969760i	$-0.421521\pi$
$227$	7.35425			0.488119			0.244059	+	0.969760i	$0.421521\pi$
$228$	−4.43725	−	10.6448i	−0.293864	−	0.704966i
$229$	20.0000			1.32164			0.660819	−	0.750546i	$-0.270209\pi$
$229$	20.0000			1.32164			0.660819	+	0.750546i	$0.270209\pi$
$230$		0			0
$231$	22.4059	+	38.8081i	1.47420	+	2.55339i
$232$	0.822876	−	1.42526i	0.0540244	−	0.0935731i
$233$	9.43725	+	16.3458i	0.618255	+	1.07085i	0.989804	+	0.142436i	$0.0454935\pi$
$233$	9.43725	+	16.3458i	0.618255	+	1.07085i	−0.371549	+	0.928413i	$0.621173\pi$
$234$	−4.00000	+	6.92820i	−0.261488	+	0.452911i
$235$		0			0
$236$	−7.93725			−0.516671
$237$	−5.29150	+	9.16515i	−0.343720	+	0.595341i
$238$		0			0
$239$	−12.0000			−0.776215			−0.388108	−	0.921614i	$-0.626871\pi$
$239$	−12.0000			−0.776215			−0.388108	+	0.921614i	$0.626871\pi$
$240$		0			0
$241$	3.79150	−	6.56708i	0.244232	−	0.423022i	−0.717683	−	0.696370i	$-0.754797\pi$
$241$	3.79150	−	6.56708i	0.244232	−	0.423022i	0.961915	+	0.273347i	$0.0881308\pi$
$242$	5.29150	+	9.16515i	0.340151	+	0.589158i
$243$	−10.5830	+	18.3303i	−0.678900	+	1.17589i
$244$	−0.468627	−	0.811686i	−0.0300008	−	0.0519629i
$245$		0			0
$246$	−0.771243			−0.0491727
$247$	8.64575	+	1.11847i	0.550116	+	0.0711668i
$248$	5.64575			0.358506
$249$	−10.5000	−	18.1865i	−0.665410	−	1.15252i
$250$		0			0
$251$	−14.6144	+	25.3128i	−0.922451	+	1.59773i	−0.126842	+	0.991923i	$0.540484\pi$
$251$	−14.6144	+	25.3128i	−0.922451	+	1.59773i	−0.795610	+	0.605810i	$0.792849\pi$
$252$	7.29150	+	12.6293i	0.459321	+	0.795568i
$253$	3.82288	−	6.62141i	0.240342	−	0.416285i
$254$	−13.2915			−0.833983
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	6.14575	−	10.6448i	0.383361	−	0.664001i	−0.608179	−	0.793800i	$-0.708100\pi$
$257$	6.14575	−	10.6448i	0.383361	−	0.664001i	0.991540	+	0.129798i	$0.0414330\pi$
$258$	−29.8745			−1.85991
$259$	1.29150			0.0802501
$260$		0			0
$261$	−3.29150	−	5.70105i	−0.203739	−	0.352886i
$262$	0.968627	−	1.67771i	0.0598420	−	0.103649i
$263$	−5.46863	−	9.47194i	−0.337210	−	0.584065i	0.646697	−	0.762747i	$-0.276150\pi$
$263$	−5.46863	−	9.47194i	−0.337210	−	0.584065i	−0.983907	+	0.178682i	$0.942817\pi$
$264$	6.14575	+	10.6448i	0.378245	+	0.655139i
$265$		0			0
$266$	9.64575	−	12.6293i	0.591419	−	0.774349i
$267$		0			0
$268$	0.322876	+	0.559237i	0.0197228	+	0.0341608i
$269$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$269$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$270$		0			0
$271$	−6.17712	−	10.6991i	−0.375234	−	0.649924i	0.615128	−	0.788427i	$-0.289104\pi$
$271$	−6.17712	−	10.6991i	−0.375234	−	0.649924i	−0.990362	+	0.138503i	$0.955771\pi$
$272$		0			0
$273$	−19.2915			−1.16757
$274$	15.5830			0.941404
$275$		0			0
$276$	2.17712	−	3.77089i	0.131047	−	0.226981i
$277$	27.5203			1.65353			0.826766	−	0.562546i	$-0.190178\pi$
$277$	27.5203			1.65353			0.826766	+	0.562546i	$0.190178\pi$
$278$	−18.6458			−1.11830
$279$	11.2915	−	19.5575i	0.676005	−	1.17087i
$280$		0			0
$281$	−12.7288	+	22.0469i	−0.759334	+	1.31520i	0.183857	+	0.982953i	$0.441142\pi$
$281$	−12.7288	+	22.0469i	−0.759334	+	1.31520i	−0.943191	+	0.332252i	$0.892192\pi$
$282$	5.76013	+	9.97684i	0.343011	+	0.594112i
$283$	15.3229	+	26.5400i	0.910850	+	1.57764i	0.812866	+	0.582451i	$0.197906\pi$
$283$	15.3229	+	26.5400i	0.910850	+	1.57764i	0.0979848	+	0.995188i	$0.468760\pi$
$284$	−2.70850			−0.160720
$285$		0			0
$286$	−9.29150			−0.549418
$287$	−0.531373	−	0.920365i	−0.0313660	−	0.0543274i
$288$	2.00000	+	3.46410i	0.117851	+	0.204124i
$289$	8.50000	−	14.7224i	0.500000	−	0.866025i
$290$		0			0
$291$	4.90588	−	8.49723i	0.287588	−	0.498117i
$292$	−1.70850			−0.0999822
$293$	−28.9373			−1.69053			−0.845266	−	0.534345i	$-0.820558\pi$
$293$	−28.9373			−1.69053			−0.845266	+	0.534345i	$0.820558\pi$
$294$	−8.32288	+	14.4156i	−0.485400	+	0.840737i
$295$		0			0
$296$	0.354249			0.0205903
$297$	12.2915			0.713225
$298$	5.46863	−	9.47194i	0.316789	−	0.548695i
$299$	1.64575	+	2.85052i	0.0951763	+	0.164850i
$300$		0			0
$301$	−20.5830	−	35.6508i	−1.18638	−	2.05488i
$302$	6.46863	+	11.2040i	0.372228	+	0.644717i
$303$	36.1033			2.07408
$304$	2.64575	−	3.46410i	0.151744	−	0.198680i
$305$		0			0
$306$		0			0
$307$	0.322876	+	0.559237i	0.0184275	+	0.0319173i	0.875092	−	0.483956i	$-0.160801\pi$
$307$	0.322876	+	0.559237i	0.0184275	+	0.0319173i	−0.856665	+	0.515874i	$0.827467\pi$
$308$	−8.46863	+	14.6681i	−0.482545	+	0.835792i
$309$	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	$0.373549\pi$
$312$	−5.29150			−0.299572
$313$	4.43725	−	7.68555i	0.250808	−	0.434413i	−0.712940	−	0.701225i	$-0.752637\pi$
$313$	4.43725	−	7.68555i	0.250808	−	0.434413i	0.963749	+	0.266812i	$0.0859702\pi$
$314$	5.29150	−	9.16515i	0.298617	−	0.517219i
$315$		0			0
$316$	−4.00000			−0.225018
$317$	−3.00000	+	5.19615i	−0.168497	+	0.291845i	−0.937892	−	0.346929i	$-0.887225\pi$
$317$	−3.00000	+	5.19615i	−0.168497	+	0.291845i	0.769395	+	0.638774i	$0.220558\pi$
$318$	−16.6458	−	28.8313i	−0.933447	−	1.61678i
$319$	3.82288	−	6.62141i	0.214040	−	0.370728i
$320$		0			0
$321$	−20.2288	−	35.0372i	−1.12906	−	1.95559i
$322$	6.00000			0.334367
$323$		0			0
$324$	−5.00000			−0.277778
$325$		0			0
$326$	−1.96863	−	3.40976i	−0.109032	−	0.188849i
$327$	19.2915	−	33.4139i	1.06682	−	1.84779i
$328$	−0.145751	−	0.252449i	−0.00804777	−	0.0139391i
$329$	−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	$0.316728\pi$
$332$	3.96863	−	6.87386i	0.217807	−	0.377252i
$333$	0.708497	−	1.22715i	0.0388254	−	0.0672476i
$334$	−12.0000			−0.656611
$335$		0			0
$336$	−4.82288	+	8.35347i	−0.263109	+	0.455719i
$337$	−4.85425	−	8.40781i	−0.264428	−	0.458002i	0.702986	−	0.711204i	$-0.251850\pi$
$337$	−4.85425	−	8.40781i	−0.264428	−	0.458002i	−0.967414	+	0.253202i	$0.918516\pi$
$338$	−4.50000	+	7.79423i	−0.244768	+	0.423950i
$339$	20.6144	+	35.7052i	1.11962	+	1.93924i
$340$		0			0
$341$	26.2288			1.42037
$342$	−6.70850	−	16.0934i	−0.362754	−	0.870229i
$343$	2.58301			0.139469
$344$	−5.64575	−	9.77873i	−0.304399	−	0.527234i
$345$		0			0
$346$	3.00000	−	5.19615i	0.161281	−	0.279347i
$347$	−11.6144	−	20.1167i	−0.623492	−	1.07992i	−0.988830	−	0.149046i	$-0.952380\pi$
$347$	−11.6144	−	20.1167i	−0.623492	−	1.07992i	0.365338	−	0.930875i	$-0.380953\pi$
$348$	2.17712	−	3.77089i	0.116706	−	0.202141i
$349$	21.1660			1.13299			0.566495	−	0.824065i	$-0.308299\pi$
$349$	21.1660			1.13299			0.566495	+	0.824065i	$0.308299\pi$
$350$		0			0
$351$	−2.64575	+	4.58258i	−0.141220	+	0.244600i
$352$	−2.32288	+	4.02334i	−0.123810	+	0.214445i
$353$	−12.8745			−0.685241			−0.342620	−	0.939474i	$-0.611314\pi$
$353$	−12.8745			−0.685241			−0.342620	+	0.939474i	$0.611314\pi$
$354$	−21.0000			−1.11614
$355$		0			0
$356$		0			0
$357$		0			0
$358$	2.03137	+	3.51844i	0.107361	+	0.185955i
$359$	2.46863	+	4.27579i	0.130289	+	0.225667i	0.923788	−	0.382904i	$-0.125076\pi$
$359$	2.46863	+	4.27579i	0.130289	+	0.225667i	−0.793499	+	0.608572i	$0.791743\pi$
$360$		0			0
$361$	−13.3745	+	13.4953i	−0.703921	+	0.710278i
$362$	−22.2288			−1.16832
$363$	14.0000	+	24.2487i	0.734809	+	1.27273i
$364$	−3.64575	−	6.31463i	−0.191089	−	0.330976i
$365$		0			0
$366$	−1.23987	−	2.14752i	−0.0648091	−	0.112253i
$367$	8.11438	−	14.0545i	0.423567	−	0.733640i	−0.572718	−	0.819752i	$-0.694111\pi$
$367$	8.11438	−	14.0545i	0.423567	−	0.733640i	0.996285	+	0.0861125i	$0.0274444\pi$
$368$	1.64575			0.0857907
$369$	−1.16601			−0.0607001
$370$		0			0
$371$	22.9373	−	39.7285i	1.19084	−	2.06260i
$372$	14.9373			0.774461
$373$	4.00000			0.207112			0.103556	−	0.994624i	$-0.466978\pi$
$373$	4.00000			0.207112			0.103556	+	0.994624i	$0.466978\pi$
$374$		0			0
$375$		0			0
$376$	−2.17712	+	3.77089i	−0.112277	+	0.194469i
$377$	1.64575	+	2.85052i	0.0847605	+	0.146810i
$378$	4.82288	+	8.35347i	0.248062	+	0.429656i
$379$	10.7085			0.550059			0.275029	−	0.961436i	$-0.411312\pi$
$379$	10.7085			0.550059			0.275029	+	0.961436i	$0.411312\pi$
$380$		0			0
$381$	−35.1660			−1.80161
$382$	3.29150	+	5.70105i	0.168408	+	0.291691i
$383$	2.76013	+	4.78068i	0.141036	+	0.244282i	0.927887	−	0.372861i	$-0.121623\pi$
$383$	2.76013	+	4.78068i	0.141036	+	0.244282i	−0.786851	+	0.617143i	$0.788290\pi$
$384$	−1.32288	+	2.29129i	−0.0675077	+	0.116927i
$385$		0			0
$386$	−7.29150	+	12.6293i	−0.371128	+	0.642812i
$387$	−45.1660			−2.29592
$388$	3.70850			0.188270
$389$	−6.00000	+	10.3923i	−0.304212	+	0.526911i	−0.977086	−	0.212847i	$-0.931726\pi$
$389$	−6.00000	+	10.3923i	−0.304212	+	0.526911i	0.672874	+	0.739758i	$0.265060\pi$
$390$		0			0
$391$		0			0
$392$	−6.29150			−0.317769
$393$	2.56275	−	4.43881i	0.129273	−	0.223908i
$394$	3.82288	+	6.62141i	0.192594	+	0.333582i
$395$		0			0
$396$	9.29150	+	16.0934i	0.466916	+	0.808721i
$397$	10.5314	+	18.2409i	0.528554	+	0.915483i	0.999446	+	0.0332919i	$0.0105991\pi$
$397$	10.5314	+	18.2409i	0.528554	+	0.915483i	−0.470891	+	0.882191i	$0.656068\pi$
$398$	19.8745			0.996219
$399$	25.5203	−	33.4139i	1.27761	−	1.67279i
$400$		0			0
$401$	−13.7915	−	23.8876i	−0.688715	−	1.19289i	−0.972254	−	0.233928i	$-0.924842\pi$
$401$	−13.7915	−	23.8876i	−0.688715	−	1.19289i	0.283539	−	0.958961i	$-0.408491\pi$
$402$	0.854249	+	1.47960i	0.0426061	+	0.0737958i
$403$	−5.64575	+	9.77873i	−0.281235	+	0.487113i
$404$	6.82288	+	11.8176i	0.339451	+	0.587946i
$405$		0			0
$406$	6.00000			0.297775
$407$	1.64575			0.0815769
$408$		0			0
$409$	3.79150	−	6.56708i	0.187478	−	0.324721i	−0.756931	−	0.653495i	$-0.773302\pi$
$409$	3.79150	−	6.56708i	0.187478	−	0.324721i	0.944409	+	0.328774i	$0.106635\pi$
$410$		0			0
$411$	41.2288			2.03366
$412$	−6.64575	+	11.5108i	−0.327413	+	0.567095i
$413$	−14.4686	−	25.0604i	−0.711955	−	1.23314i
$414$	3.29150	−	5.70105i	0.161769	−	0.280191i
$415$		0			0
$416$	−1.00000	−	1.73205i	−0.0490290	−	0.0849208i
$417$	−49.3320			−2.41580
$418$	12.2915	−	16.0934i	0.601197	−	0.787152i
$419$	−31.7490			−1.55104			−0.775520	−	0.631322i	$-0.782512\pi$
$419$	−31.7490			−1.55104			−0.775520	+	0.631322i	$0.782512\pi$
$420$		0			0
$421$	12.4059	+	21.4876i	0.604626	+	1.04724i	0.992111	+	0.125366i	$0.0400106\pi$
$421$	12.4059	+	21.4876i	0.604626	+	1.04724i	−0.387485	+	0.921876i	$0.626656\pi$
$422$	−6.64575	+	11.5108i	−0.323510	+	0.560336i
$423$	8.70850	+	15.0836i	0.423422	+	0.733388i
$424$	6.29150	−	10.8972i	0.305542	−	0.529215i
$425$		0			0
$426$	−7.16601			−0.347194
$427$	1.70850	−	2.95920i	0.0826800	−	0.143206i
$428$	7.64575	−	13.2428i	0.369571	−	0.640116i
$429$	−24.5830			−1.18688
$430$		0			0
$431$	−13.9373	+	24.1400i	−0.671334	+	1.16278i	0.306192	+	0.951970i	$0.400945\pi$
$431$	−13.9373	+	24.1400i	−0.671334	+	1.16278i	−0.977526	+	0.210815i	$0.932388\pi$
$432$	1.32288	+	2.29129i	0.0636469	+	0.110240i
$433$	8.93725	−	15.4798i	0.429497	−	0.743911i	−0.567332	−	0.823489i	$-0.692024\pi$
$433$	8.93725	−	15.4798i	0.429497	−	0.743911i	0.996829	+	0.0795788i	$0.0253575\pi$
$434$	10.2915	+	17.8254i	0.494008	+	0.855647i
$435$		0			0
$436$	14.5830			0.698399
$437$	−7.11438	−	0.920365i	−0.340327	−	0.0440270i
$438$	−4.52026			−0.215986
$439$	−5.40588	−	9.36326i	−0.258009	−	0.446884i	0.707700	−	0.706513i	$-0.249733\pi$
$439$	−5.40588	−	9.36326i	−0.258009	−	0.446884i	−0.965708	+	0.259629i	$0.916400\pi$
$440$		0			0
$441$	−12.5830	+	21.7944i	−0.599191	+	1.03783i
$442$		0			0
$443$	5.32288	−	9.21949i	0.252897	−	0.438031i	−0.711425	−	0.702762i	$-0.751950\pi$
$443$	5.32288	−	9.21949i	0.252897	−	0.438031i	0.964322	+	0.264731i	$0.0852831\pi$
$444$	0.937254			0.0444801
$445$		0			0
$446$	9.40588	−	16.2915i	0.445381	−	0.771423i
$447$	14.4686	−	25.0604i	0.684343	−	1.18532i
$448$	−3.64575			−0.172246
$449$	−24.2915			−1.14639			−0.573193	−	0.819420i	$-0.694296\pi$
$449$	−24.2915			−1.14639			−0.573193	+	0.819420i	$0.694296\pi$
$450$		0			0
$451$	−0.677124	−	1.17281i	−0.0318845	−	0.0552256i
$452$	−7.79150	+	13.4953i	−0.366481	+	0.634765i
$453$	17.1144	+	29.6430i	0.804104	+	1.39275i
$454$	3.67712	+	6.36897i	0.172576	+	0.298910i
$455$		0			0
$456$	7.00000	−	9.16515i	0.327805	−	0.429198i
$457$	−32.8745			−1.53780			−0.768902	−	0.639366i	$-0.779197\pi$
$457$	−32.8745			−1.53780			−0.768902	+	0.639366i	$0.779197\pi$
$458$	10.0000	+	17.3205i	0.467269	+	0.809334i
$459$		0			0
$460$		0			0
$461$	−9.58301	−	16.5983i	−0.446325	−	0.773058i	0.551818	−	0.833964i	$-0.313934\pi$
$461$	−9.58301	−	16.5983i	−0.446325	−	0.773058i	−0.998143	+	0.0609066i	$0.980601\pi$
$462$	−22.4059	+	38.8081i	−1.04242	+	1.80552i
$463$	38.4575			1.78727			0.893636	−	0.448792i	$-0.148146\pi$
$463$	38.4575			1.78727			0.893636	+	0.448792i	$0.148146\pi$
$464$	1.64575			0.0764021
$465$		0			0
$466$	−9.43725	+	16.3458i	−0.437172	+	0.757205i
$467$	19.3542			0.895608			0.447804	−	0.894132i	$-0.352206\pi$
$467$	19.3542			0.895608			0.447804	+	0.894132i	$0.352206\pi$
$468$	−8.00000			−0.369800
$469$	−1.17712	+	2.03884i	−0.0543546	+	0.0941448i
$470$		0			0
$471$	14.0000	−	24.2487i	0.645086	−	1.11732i
$472$	−3.96863	−	6.87386i	−0.182671	−	0.316395i
$473$	−26.2288	−	45.4295i	−1.20600	−	2.08885i
$474$	−10.5830			−0.486094
$475$		0			0
$476$		0			0
$477$	−25.1660	−	43.5888i	−1.15227	−	1.99579i
$478$	−6.00000	−	10.3923i	−0.274434	−	0.475333i
$479$	−3.29150	+	5.70105i	−0.150393	+	0.260488i	−0.931372	−	0.364069i	$-0.881387\pi$
$479$	−3.29150	+	5.70105i	−0.150393	+	0.260488i	0.780979	+	0.624557i	$0.214720\pi$
$480$		0			0
$481$	−0.354249	+	0.613577i	−0.0161523	+	0.0279767i
$482$	7.58301			0.345396
$483$	15.8745			0.722315
$484$	−5.29150	+	9.16515i	−0.240523	+	0.416598i
$485$		0			0
$486$	−21.1660			−0.960110
$487$	−4.22876			−0.191623			−0.0958116	−	0.995399i	$-0.530545\pi$
$487$	−4.22876			−0.191623			−0.0958116	+	0.995399i	$0.530545\pi$
$488$	0.468627	−	0.811686i	0.0212137	−	0.0367433i
$489$	−5.20850	−	9.02138i	−0.235536	−	0.407961i
$490$		0			0
$491$	−19.6458	−	34.0274i	−0.886600	−	1.53564i	−0.843868	−	0.536550i	$-0.819727\pi$
$491$	−19.6458	−	34.0274i	−0.886600	−	1.53564i	−0.0427320	−	0.999087i	$-0.513606\pi$
$492$	−0.385622	−	0.667916i	−0.0173852	−	0.0301120i
$493$		0			0
$494$	3.35425	+	8.04668i	0.150915	+	0.362037i
$495$		0			0
$496$	2.82288	+	4.88936i	0.126751	+	0.219539i
$497$	−4.93725	−	8.55157i	−0.221466	−	0.383591i
$498$	10.5000	−	18.1865i	0.470516	−	0.814958i
$499$	2.38562	+	4.13202i	0.106795	+	0.184975i	0.914470	−	0.404653i	$-0.132608\pi$
$499$	2.38562	+	4.13202i	0.106795	+	0.184975i	−0.807675	+	0.589628i	$0.799274\pi$
$500$		0			0
$501$	−31.7490			−1.41844
$502$	−29.2288			−1.30454
$503$	−20.4686	+	35.4527i	−0.912651	+	1.58076i	−0.102346	+	0.994749i	$0.532635\pi$
$503$	−20.4686	+	35.4527i	−0.912651	+	1.58076i	−0.810305	+	0.586009i	$0.800698\pi$
$504$	−7.29150	+	12.6293i	−0.324789	+	0.562552i
$505$		0			0
$506$	7.64575			0.339895
$507$	−11.9059	+	20.6216i	−0.528759	+	0.915837i
$508$	−6.64575	−	11.5108i	−0.294858	−	0.510708i
$509$	15.8745	−	27.4955i	0.703625	−	1.21871i	−0.263560	−	0.964643i	$-0.584897\pi$
$509$	15.8745	−	27.4955i	0.703625	−	1.21871i	0.967185	−	0.254072i	$-0.0817699\pi$
$510$		0			0
$511$	−3.11438	−	5.39426i	−0.137772	−	0.238628i
$512$	−1.00000			−0.0441942
$513$	−4.43725	−	10.6448i	−0.195910	−	0.469977i
$514$	12.2915			0.542155
$515$		0			0
$516$	−14.9373	−	25.8721i	−0.657576	−	1.13895i
$517$	−10.1144	+	17.5186i	−0.444830	+	0.770468i
$518$	0.645751	+	1.11847i	0.0283727	+	0.0491429i
$519$	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	$0.582563\pi$
$522$	3.29150	−	5.70105i	0.144065	−	0.249528i
$523$	−0.937254	+	1.62337i	−0.0409833	+	0.0709851i	−0.885789	−	0.464087i	$-0.846382\pi$
$523$	−0.937254	+	1.62337i	−0.0409833	+	0.0709851i	0.844806	+	0.535072i	$0.179716\pi$
$524$	1.93725			0.0846293
$525$		0			0
$526$	5.46863	−	9.47194i	0.238443	−	0.412996i
$527$		0			0
$528$	−6.14575	+	10.6448i	−0.267459	+	0.463253i
$529$	10.1458	+	17.5730i	0.441120	+	0.764042i
$530$		0			0
$531$	−31.7490			−1.37779
$532$	15.7601	+	2.03884i	0.683288	+	0.0883949i
$533$	0.583005			0.0252528
$534$		0			0
$535$		0			0
$536$	−0.322876	+	0.559237i	−0.0139461	+	0.0241554i
$537$	5.37451	+	9.30892i	0.231927	+	0.401710i
$538$		0			0
$539$	−29.2288			−1.25897
$540$		0			0
$541$	−4.00000	+	6.92820i	−0.171973	+	0.297867i	−0.939110	−	0.343617i	$-0.888348\pi$
$541$	−4.00000	+	6.92820i	−0.171973	+	0.297867i	0.767136	+	0.641484i	$0.221681\pi$
$542$	6.17712	−	10.6991i	0.265330	−	0.459565i
$543$	−58.8118			−2.52385
$544$		0			0
$545$		0			0
$546$	−9.64575	−	16.7069i	−0.412800	−	0.714991i
$547$	5.64575	−	9.77873i	0.241395	−	0.418108i	−0.719717	−	0.694268i	$-0.755728\pi$
$547$	5.64575	−	9.77873i	0.241395	−	0.418108i	0.961112	+	0.276159i	$0.0890618\pi$
$548$	7.79150	+	13.4953i	0.332836	+	0.576490i
$549$	−1.87451	−	3.24674i	−0.0800020	−	0.138568i
$550$		0			0
$551$	−7.11438	−	0.920365i	−0.303083	−	0.0392089i
$552$	4.35425			0.185329
$553$	−7.29150	−	12.6293i	−0.310066	−	0.537050i
$554$	13.7601	+	23.8332i	0.584612	+	1.01258i
$555$		0			0
$556$	−9.32288	−	16.1477i	−0.395378	−	0.684815i
$557$	−2.70850	+	4.69126i	−0.114763	+	0.198775i	−0.917685	−	0.397309i	$-0.869944\pi$
$557$	−2.70850	+	4.69126i	−0.114763	+	0.198775i	0.802922	+	0.596084i	$0.203277\pi$
$558$	22.5830			0.956015
$559$	22.5830			0.955159
$560$		0			0
$561$		0			0
$562$	−25.4575			−1.07386
$563$	−10.0627			−0.424094			−0.212047	−	0.977259i	$-0.568013\pi$
$563$	−10.0627			−0.424094			−0.212047	+	0.977259i	$0.568013\pi$
$564$	−5.76013	+	9.97684i	−0.242545	+	0.420101i
$565$		0			0
$566$	−15.3229	+	26.5400i	−0.644069	+	1.11556i
$567$	−9.11438	−	15.7866i	−0.382768	−	0.662973i
$568$	−1.35425	−	2.34563i	−0.0568230	−	0.0984203i
$569$	6.58301			0.275974			0.137987	−	0.990434i	$-0.455937\pi$
$569$	6.58301			0.275974			0.137987	+	0.990434i	$0.455937\pi$
$570$		0			0
$571$	7.81176			0.326912			0.163456	−	0.986551i	$-0.447736\pi$
$571$	7.81176			0.326912			0.163456	+	0.986551i	$0.447736\pi$
$572$	−4.64575	−	8.04668i	−0.194249	−	0.336448i
$573$	8.70850	+	15.0836i	0.363803	+	0.630125i
$574$	0.531373	−	0.920365i	0.0221791	−	0.0384153i
$575$		0			0
$576$	−2.00000	+	3.46410i	−0.0833333	+	0.144338i
$577$	−11.0000			−0.457936			−0.228968	−	0.973434i	$-0.573535\pi$
$577$	−11.0000			−0.457936			−0.228968	+	0.973434i	$0.573535\pi$
$578$	17.0000			0.707107
$579$	−19.2915	+	33.4139i	−0.801727	+	1.38863i
$580$		0			0
$581$	28.9373			1.20052
$582$	9.81176			0.406711
$583$	29.2288	−	50.6257i	1.21053	−	2.09670i
$584$	−0.854249	−	1.47960i	−0.0353491	−	0.0612264i
$585$		0			0
$586$	−14.4686	−	25.0604i	−0.597693	−	1.03524i
$587$	−7.06275	−	12.2330i	−0.291511	−	0.504911i	0.682656	−	0.730739i	$-0.260825\pi$
$587$	−7.06275	−	12.2330i	−0.291511	−	0.504911i	−0.974167	+	0.225828i	$0.927491\pi$
$588$	−16.6458			−0.686459
$589$	−9.46863	−	22.7148i	−0.390148	−	0.935946i
$590$		0			0
$591$	10.1144	+	17.5186i	0.416050	+	0.720620i
$592$	0.177124	+	0.306788i	0.00727977	+	0.0126089i
$593$	14.8542	−	25.7283i	0.609991	−	1.05654i	−0.381250	−	0.924472i	$-0.624506\pi$
$593$	14.8542	−	25.7283i	0.609991	−	1.05654i	0.991241	−	0.132063i	$-0.0421602\pi$
$594$	6.14575	+	10.6448i	0.252163	+	0.436760i
$595$		0			0
$596$	10.9373			0.448007
$597$	52.5830			2.15208
$598$	−1.64575	+	2.85052i	−0.0672998	+	0.116567i
$599$	8.46863	−	14.6681i	0.346019	−	0.599322i	−0.639520	−	0.768775i	$-0.720867\pi$
$599$	8.46863	−	14.6681i	0.346019	−	0.599322i	0.985538	+	0.169453i	$0.0542000\pi$
$600$		0			0
$601$	10.4170			0.424918			0.212459	−	0.977170i	$-0.431853\pi$
$601$	10.4170			0.424918			0.212459	+	0.977170i	$0.431853\pi$
$602$	20.5830	−	35.6508i	0.838901	−	1.45302i
$603$	1.29150	+	2.23695i	0.0525941	+	0.0910956i
$604$	−6.46863	+	11.2040i	−0.263205	+	0.455884i
$605$		0			0
$606$	18.0516	+	31.2663i	0.733297	+	1.27011i
$607$	−6.93725			−0.281574			−0.140787	−	0.990040i	$-0.544963\pi$
$607$	−6.93725			−0.281574			−0.140787	+	0.990040i	$0.544963\pi$
$608$	4.32288	+	0.559237i	0.175316	+	0.0226801i
$609$	15.8745			0.643268
$610$		0			0
$611$	−4.35425	−	7.54178i	−0.176154	−	0.305108i
$612$		0			0
$613$	3.70850	+	6.42331i	0.149785	+	0.259435i	0.931148	−	0.364642i	$-0.118809\pi$
$613$	3.70850	+	6.42331i	0.149785	+	0.259435i	−0.781363	+	0.624077i	$0.785475\pi$
$614$	−0.322876	+	0.559237i	−0.0130302	+	0.0225690i
$615$		0			0
$616$	−16.9373			−0.682421
$617$	−15.4373	+	26.7381i	−0.621480	+	1.07644i	0.367730	+	0.929933i	$0.380135\pi$
$617$	−15.4373	+	26.7381i	−0.621480	+	1.07644i	−0.989210	+	0.146503i	$0.953198\pi$
$618$	−17.5830	+	30.4547i	−0.707292	+	1.22507i
$619$	−8.45751			−0.339936			−0.169968	−	0.985450i	$-0.554366\pi$
$619$	−8.45751			−0.339936			−0.169968	+	0.985450i	$0.554366\pi$
$620$		0			0
$621$	2.17712	−	3.77089i	0.0873650	−	0.151321i
$622$	6.82288	+	11.8176i	0.273572	+	0.473841i
$623$		0			0
$624$	−2.64575	−	4.58258i	−0.105915	−	0.183450i
$625$		0			0
$626$	8.87451			0.354697
$627$	32.5203	−	42.5790i	1.29873	−	1.70044i
$628$	10.5830			0.422308
$629$		0			0
$630$		0			0
$631$	12.4059	−	21.4876i	0.493870	−	0.855408i	−0.506105	−	0.862472i	$-0.668915\pi$
$631$	12.4059	−	21.4876i	0.493870	−	0.855408i	0.999975	+	0.00706354i	$0.00224841\pi$
$632$	−2.00000	−	3.46410i	−0.0795557	−	0.137795i
$633$	−17.5830	+	30.4547i	−0.698862	+	1.21046i
$634$	−6.00000			−0.238290
$635$		0			0
$636$	16.6458	−	28.8313i	0.660047	−	1.14323i
$637$	6.29150	−	10.8972i	0.249278	−	0.431763i
$638$	7.64575			0.302698
$639$	−10.8340			−0.428586
$640$		0			0
$641$	−6.43725	−	11.1497i	−0.254256	−	0.440385i	0.710437	−	0.703761i	$-0.248497\pi$
$641$	−6.43725	−	11.1497i	−0.254256	−	0.440385i	−0.964693	+	0.263376i	$0.915164\pi$
$642$	20.2288	−	35.0372i	0.798365	−	1.38281i
$643$	−3.26013	−	5.64671i	−0.128567	−	0.222685i	0.794555	−	0.607193i	$-0.207704\pi$
$643$	−3.26013	−	5.64671i	−0.128567	−	0.222685i	−0.923122	+	0.384508i	$0.874371\pi$
$644$	3.00000	+	5.19615i	0.118217	+	0.204757i
$645$		0			0
$646$		0			0
$647$	22.4575			0.882896			0.441448	−	0.897287i	$-0.354465\pi$
$647$	22.4575			0.882896			0.441448	+	0.897287i	$0.354465\pi$
$648$	−2.50000	−	4.33013i	−0.0982093	−	0.170103i
$649$	−18.4373	−	31.9343i	−0.723726	−	1.25353i
$650$		0			0
$651$	27.2288	+	47.1616i	1.06718	+	1.84841i
$652$	1.96863	−	3.40976i	0.0770974	−	0.133537i
$653$	−24.0000			−0.939193			−0.469596	−	0.882881i	$-0.655601\pi$
$653$	−24.0000			−0.939193			−0.469596	+	0.882881i	$0.655601\pi$
$654$	38.5830			1.50871
$655$		0			0
$656$	0.145751	−	0.252449i	0.00569063	−	0.00985646i
$657$	−6.83399			−0.266619
$658$	−15.8745			−0.618853
$659$	9.29150	−	16.0934i	0.361946	−	0.626908i	−0.626335	−	0.779554i	$-0.715446\pi$
$659$	9.29150	−	16.0934i	0.361946	−	0.626908i	0.988281	+	0.152646i	$0.0487793\pi$
$660$		0			0
$661$	−8.11438	+	14.0545i	−0.315613	+	0.546657i	−0.979568	−	0.201115i	$-0.935543\pi$
$661$	−8.11438	+	14.0545i	−0.315613	+	0.546657i	0.663955	+	0.747773i	$0.268877\pi$
$662$	9.90588	+	17.1575i	0.385003	+	0.666845i
$663$		0			0
$664$	7.93725			0.308025
$665$		0			0
$666$	1.41699			0.0549074
$667$	−1.35425	−	2.34563i	−0.0524367	−	0.0908231i
$668$	−6.00000	−	10.3923i	−0.232147	−	0.402090i
$669$	24.8856	−	43.1032i	0.962134	−	1.66646i
$670$		0			0
$671$	2.17712	−	3.77089i	0.0840470	−	0.145574i
$672$	−9.64575			−0.372093
$673$	13.8745			0.534823			0.267411	−	0.963582i	$-0.413832\pi$
$673$	13.8745			0.534823			0.267411	+	0.963582i	$0.413832\pi$
$674$	4.85425	−	8.40781i	0.186979	−	0.323857i
$675$		0			0
$676$	−9.00000			−0.346154
$677$	11.4170			0.438791			0.219395	−	0.975636i	$-0.429592\pi$
$677$	11.4170			0.438791			0.219395	+	0.975636i	$0.429592\pi$
$678$	−20.6144	+	35.7052i	−0.791690	+	1.37125i
$679$	6.76013	+	11.7089i	0.259430	+	0.449346i
$680$		0			0
$681$	9.72876	+	16.8507i	0.372807	+	0.645720i
$682$	13.1144	+	22.7148i	0.502175	+	0.869793i
$683$	5.41699			0.207276			0.103638	−	0.994615i	$-0.466952\pi$
$683$	5.41699			0.207276			0.103638	+	0.994615i	$0.466952\pi$
$684$	10.5830	−	13.8564i	0.404651	−	0.529813i
$685$		0			0
$686$	1.29150	+	2.23695i	0.0493098	+	0.0854071i
$687$	26.4575	+	45.8258i	1.00942	+	1.74836i
$688$	5.64575	−	9.77873i	0.215242	−	0.372811i
$689$	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	$0.484355\pi$
$692$	6.00000			0.228086
$693$	−33.8745	+	58.6724i	−1.28679	+	2.22878i
$694$	11.6144	−	20.1167i	0.440876	−	0.763619i
$695$		0			0
$696$	4.35425			0.165047
$697$		0			0
$698$	10.5830	+	18.3303i	0.400573	+	0.693812i
$699$	−24.9686	+	43.2469i	−0.944400	+	1.63575i
$700$		0			0
$701$	−5.17712	−	8.96704i	−0.195537	−	0.338681i	0.751539	−	0.659688i	$-0.229312\pi$
$701$	−5.17712	−	8.96704i	−0.195537	−	0.338681i	−0.947077	+	0.321008i	$0.895978\pi$
$702$	−5.29150			−0.199715
$703$	−0.594119	−	1.42526i	−0.0224076	−	0.0537548i
$704$	−4.64575			−0.175093
$705$		0			0
$706$	−6.43725	−	11.1497i	−0.242269	−	0.419623i
$707$	−24.8745	+	43.0839i	−0.935502	+	1.62034i
$708$	−10.5000	−	18.1865i	−0.394614	−	0.683492i
$709$	−1.82288	+	3.15731i	−0.0684595	+	0.118575i	−0.898223	−	0.439539i	$-0.855142\pi$
$709$	−1.82288	+	3.15731i	−0.0684595	+	0.118575i	0.829764	+	0.558115i	$0.188475\pi$
$710$		0			0
$711$	−16.0000			−0.600047
$712$		0			0
$713$	4.64575	−	8.04668i	0.173985	−	0.301350i
$714$		0			0
$715$		0			0
$716$	−2.03137	+	3.51844i	−0.0759160	+	0.131490i
$717$	−15.8745	−	27.4955i	−0.592844	−	1.02684i
$718$	−2.46863	+	4.27579i	−0.0921283	+	0.159571i
$719$	−1.35425	−	2.34563i	−0.0505050	−	0.0874771i	0.839668	−	0.543100i	$-0.182750\pi$
$719$	−1.35425	−	2.34563i	−0.0505050	−	0.0874771i	−0.890173	+	0.455623i	$0.849416\pi$
$720$		0			0
$721$	−48.4575			−1.80465
$722$	−18.3745	−	4.83502i	−0.683828	−	0.179941i
$723$	20.0627			0.746142
$724$	−11.1144	−	19.2507i	−0.413063	−	0.715445i
$725$		0			0
$726$	−14.0000	+	24.2487i	−0.519589	+	0.899954i
$727$	0.708497	+	1.22715i	0.0262767	+	0.0455126i	0.878865	−	0.477071i	$-0.158302\pi$
$727$	0.708497	+	1.22715i	0.0262767	+	0.0455126i	−0.852588	+	0.522584i	$0.824968\pi$
$728$	3.64575	−	6.31463i	0.135121	−	0.234036i
$729$	−41.0000			−1.51852
$730$		0			0
$731$		0			0
$732$	1.23987	−	2.14752i	0.0458269	−	0.0793746i
$733$	16.1033			0.594788			0.297394	−	0.954755i	$-0.403883\pi$
$733$	16.1033			0.594788			0.297394	+	0.954755i	$0.403883\pi$
$734$	16.2288			0.599014
$735$		0			0
$736$	0.822876	+	1.42526i	0.0303316	+	0.0525359i
$737$	−1.50000	+	2.59808i	−0.0552532	+	0.0957014i
$738$	−0.583005	−	1.00979i	−0.0214607	−	0.0371711i
$739$	16.9059	+	29.2818i	0.621893	+	1.07715i	0.989133	+	0.147024i	$0.0469694\pi$
$739$	16.9059	+	29.2818i	0.621893	+	1.07715i	−0.367240	+	0.930126i	$0.619697\pi$
$740$		0			0
$741$	8.87451	+	21.2895i	0.326013	+	0.782090i
$742$	45.8745			1.68411
$743$	−23.7601	−	41.1538i	−0.871675	−	1.50978i	−0.860263	−	0.509850i	$-0.829701\pi$
$743$	−23.7601	−	41.1538i	−0.871675	−	1.50978i	−0.0114112	−	0.999935i	$-0.503632\pi$
$744$	7.46863	+	12.9360i	0.273813	+	0.474258i
$745$		0			0
$746$	2.00000	+	3.46410i	0.0732252	+	0.126830i
$747$	15.8745	−	27.4955i	0.580818	−	1.00601i
$748$		0			0
$749$	55.7490			2.03702
$750$		0			0
$751$	3.93725	−	6.81952i	0.143672	−	0.248848i	−0.785204	−	0.619237i	$-0.787442\pi$
$751$	3.93725	−	6.81952i	0.143672	−	0.248848i	0.928877	+	0.370389i	$0.120775\pi$
$752$	−4.35425			−0.158783
$753$	−77.3320			−2.81814
$754$	−1.64575	+	2.85052i	−0.0599347	+	0.103810i
$755$		0			0
$756$	−4.82288	+	8.35347i	−0.175406	+	0.303813i
$757$	−2.29150	−	3.96900i	−0.0832861	−	0.144256i	0.821374	−	0.570391i	$-0.193208\pi$
$757$	−2.29150	−	3.96900i	−0.0832861	−	0.144256i	−0.904660	+	0.426135i	$0.859875\pi$
$758$	5.35425	+	9.27383i	0.194475	+	0.336841i
$759$	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	$0.216690\pi$
$762$	−17.5830	−	30.4547i	−0.636965	−	1.10326i
$763$	26.5830	+	46.0431i	0.962369	+	1.66687i
$764$	−3.29150	+	5.70105i	−0.119082	+	0.206257i
$765$		0			0
$766$	−2.76013	+	4.78068i	−0.0997275	+	0.172733i
$767$	15.8745			0.573195
$768$	−2.64575			−0.0954703
$769$	−17.6458	+	30.5633i	−0.636322	+	1.10214i	0.349911	+	0.936783i	$0.386212\pi$
$769$	−17.6458	+	30.5633i	−0.636322	+	1.10214i	−0.986233	+	0.165359i	$0.947122\pi$
$770$		0			0
$771$	32.5203			1.17119
$772$	−14.5830			−0.524854
$773$	−2.46863	+	4.27579i	−0.0887903	+	0.153789i	−0.907000	−	0.421130i	$-0.861633\pi$
$773$	−2.46863	+	4.27579i	−0.0887903	+	0.153789i	0.818210	+	0.574920i	$0.194967\pi$
$774$	−22.5830	−	39.1149i	−0.811729	−	1.40596i
$775$		0			0
$776$	1.85425	+	3.21165i	0.0665636	+	0.115292i
$777$	1.70850	+	2.95920i	0.0612920	+	0.106161i
$778$	−12.0000			−0.430221
$779$	−0.771243	+	1.00979i	−0.0276327	+	0.0361796i
$780$		0			0
$781$	−6.29150	−	10.8972i	−0.225128	−	0.389933i
$782$		0			0
$783$	2.17712	−	3.77089i	0.0778041	−	0.134761i
$784$	−3.14575	−	5.44860i	−0.112348	−	0.194593i
$785$		0			0
$786$	5.12549			0.182820
$787$	42.5203			1.51568			0.757842	−	0.652438i	$-0.226254\pi$
$787$	42.5203			1.51568			0.757842	+	0.652438i	$0.226254\pi$
$788$	−3.82288	+	6.62141i	−0.136184	+	0.235878i
$789$	14.4686	−	25.0604i	0.515097	−	0.892174i
$790$		0			0
$791$	−56.8118			−2.01999
$792$	−9.29150	+	16.0934i	−0.330159	+	0.571852i
$793$	0.937254	+	1.62337i	0.0332829	+	0.0576476i
$794$	−10.5314	+	18.2409i	−0.373744	+	0.647344i
$795$		0			0
$796$	9.93725	+	17.2118i	0.352217	+	0.610057i
$797$	44.8118			1.58731			0.793657	−	0.608365i	$-0.208174\pi$
$797$	44.8118			1.58731			0.793657	+	0.608365i	$0.208174\pi$
$798$	41.6974	+	5.39426i	1.47607	+	0.190955i
$799$		0			0
$800$		0			0
$801$		0			0
$802$	13.7915	−	23.8876i	0.486995	−	0.843500i
$803$	−3.96863	−	6.87386i	−0.140050	−	0.242573i
$804$	−0.854249	+	1.47960i	−0.0301270	+	0.0521815i
$805$		0			0
$806$	−11.2915			−0.397726
$807$		0			0
$808$	−6.82288	+	11.8176i	−0.240028	+	0.415741i
$809$	−9.00000			−0.316423			−0.158212	−	0.987405i	$-0.550573\pi$
$809$	−9.00000			−0.316423			−0.158212	+	0.987405i	$0.550573\pi$
$810$		0			0
$811$	15.6458	−	27.0992i	0.549397	−	0.951583i	−0.448919	−	0.893572i	$-0.648191\pi$
$811$	15.6458	−	27.0992i	0.549397	−	0.951583i	0.998316	−	0.0580106i	$-0.0184757\pi$
$812$	3.00000	+	5.19615i	0.105279	+	0.182349i
$813$	16.3431	−	28.3071i	0.573179	−	0.992775i
$814$	0.822876	+	1.42526i	0.0288418	+	0.0499554i
$815$		0			0
$816$		0			0
$817$	−29.8745	+	39.1149i	−1.04518	+	1.36846i
$818$	7.58301			0.265134
$819$	−14.5830	−	25.2585i	−0.509571	−	0.882604i
$820$		0			0
$821$	3.00000	−	5.19615i	0.104701	−	0.181347i	−0.808915	−	0.587925i	$-0.799945\pi$
$821$	3.00000	−	5.19615i	0.104701	−	0.181347i	0.913616	+	0.406578i	$0.133278\pi$
$822$	20.6144	+	35.7052i	0.719009	+	1.24536i
$823$	−15.9373	+	27.6041i	−0.555538	+	0.962220i	0.442324	+	0.896855i	$0.354154\pi$
$823$	−15.9373	+	27.6041i	−0.555538	+	0.962220i	−0.997861	+	0.0653641i	$0.979179\pi$
$824$	−13.2915			−0.463031
$825$		0			0
$826$	14.4686	−	25.0604i	0.503428	−	0.871963i
$827$	−26.3229	+	45.5926i	−0.915336	+	1.58541i	−0.108928	+	0.994050i	$0.534742\pi$
$827$	−26.3229	+	45.5926i	−0.915336	+	1.58541i	−0.806408	+	0.591359i	$0.798592\pi$
$828$	6.58301			0.228775
$829$	−17.1660			−0.596200			−0.298100	−	0.954535i	$-0.596353\pi$
$829$	−17.1660			−0.596200			−0.298100	+	0.954535i	$0.596353\pi$
$830$		0			0
$831$	36.4059	+	63.0568i	1.26291	+	2.18742i
$832$	1.00000	−	1.73205i	0.0346688	−	0.0600481i
$833$		0			0
$834$	−24.6660	−	42.7228i	−0.854114	−	1.47937i
$835$		0			0
$836$	20.0830	+	2.59808i	0.694585	+	0.0898563i
$837$	14.9373			0.516307
$838$	−15.8745	−	27.4955i	−0.548376	−	0.949815i
$839$	20.7601	+	35.9576i	0.716719	+	1.24139i	0.962293	+	0.272016i	$0.0876904\pi$
$839$	20.7601	+	35.9576i	0.716719	+	1.24139i	−0.245573	+	0.969378i	$0.578976\pi$
$840$		0			0
$841$	13.1458	+	22.7691i	0.453302	+	0.785142i
$842$	−12.4059	+	21.4876i	−0.427535	+	0.740512i
$843$	−67.3542			−2.31980
$844$	−13.2915			−0.457512
$845$		0			0
$846$	−8.70850	+	15.0836i	−0.299404	+	0.518583i
$847$	−38.5830			−1.32573
$848$	12.5830			0.432102
$849$	−40.5405	+	70.2182i	−1.39135	+	2.40988i
$850$		0			0
$851$	0.291503	−	0.504897i	0.00999258	−	0.0173077i
$852$	−3.58301	−	6.20595i	−0.122752	−	0.212612i
$853$	4.29150	+	7.43310i	0.146938	+	0.254505i	0.930094	−	0.367321i	$-0.119725\pi$
$853$	4.29150	+	7.43310i	0.146938	+	0.254505i	−0.783156	+	0.621825i	$0.786391\pi$
$854$	3.41699			0.116927
$855$		0			0
$856$	15.2915			0.522653
$857$	10.5000	+	18.1865i	0.358673	+	0.621240i	0.987739	−	0.156112i	$-0.0498959\pi$
$857$	10.5000	+	18.1865i	0.358673	+	0.621240i	−0.629066	+	0.777352i	$0.716563\pi$
$858$	−12.2915	−	21.2895i	−0.419625	−	0.726812i
$859$	−6.61438	+	11.4564i	−0.225680	+	0.390889i	−0.956523	−	0.291656i	$-0.905794\pi$
$859$	−6.61438	+	11.4564i	−0.225680	+	0.390889i	0.730843	+	0.682545i	$0.239127\pi$
$860$		0			0
$861$	1.40588	−	2.43506i	0.0479123	−	0.0829865i
$862$	−27.8745			−0.949410
$863$	31.0627			1.05739			0.528694	−	0.848812i	$-0.322682\pi$
$863$	31.0627			1.05739			0.528694	+	0.848812i	$0.322682\pi$
$864$	−1.32288	+	2.29129i	−0.0450051	+	0.0779512i
$865$		0			0
$866$	17.8745			0.607401
$867$	44.9778			1.52753
$868$	−10.2915	+	17.8254i	−0.349316	+	0.605034i
$869$	−9.29150	−	16.0934i	−0.315193	−	0.545930i
$870$		0			0
$871$	−0.645751	−	1.11847i	−0.0218804	−	0.0378980i
$872$	7.29150	+	12.6293i	0.246921	+	0.427680i
$873$	14.8340			0.502054
$874$	−2.76013	−	6.62141i	−0.0933628	−	0.223973i
$875$		0			0
$876$	−2.26013	−	3.91466i	−0.0763627	−	0.132264i
$877$	−20.8229	−	36.0663i	−0.703139	−	1.21787i	−0.967359	−	0.253409i	$-0.918448\pi$
$877$	−20.8229	−	36.0663i	−0.703139	−	1.21787i	0.264221	−	0.964462i	$-0.414885\pi$
$878$	5.40588	−	9.36326i	0.182440	−	0.315995i
$879$	−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	$0.713341\pi$
$882$	−25.1660			−0.847384
$883$	−14.1974	+	24.5906i	−0.477780	+	0.827539i	−0.999676	−	0.0254701i	$-0.991892\pi$
$883$	−14.1974	+	24.5906i	−0.477780	+	0.827539i	0.521896	+	0.853009i	$0.325225\pi$
$884$		0			0
$885$		0			0
$886$	10.6458			0.357651
$887$	−8.70850	+	15.0836i	−0.292403	+	0.506456i	−0.974377	−	0.224919i	$-0.927788\pi$
$887$	−8.70850	+	15.0836i	−0.292403	+	0.506456i	0.681975	+	0.731376i	$0.261121\pi$
$888$	0.468627	+	0.811686i	0.0157261	+	0.0272384i
$889$	24.2288	−	41.9654i	0.812606	−	1.40748i
$890$		0			0
$891$	−11.6144	−	20.1167i	−0.389096	−	0.673935i
$892$	18.8118			0.629864
$893$	18.8229	+	2.43506i	0.629884	+	0.0814861i
$894$	28.9373			0.967807
$895$		0			0
$896$	−1.82288	−	3.15731i	−0.0608980	−	0.105478i
$897$	−4.35425	+	7.54178i	−0.145384	+	0.251813i
$898$	−12.1458	−	21.0371i	−0.405309	−	0.702016i
$899$	4.64575	−	8.04668i	0.154944	−	0.268372i
$900$		0			0
$901$		0			0
$902$	0.677124	−	1.17281i	0.0225458	−	0.0390504i
$903$	54.4575	−	94.3232i	1.81223	−	3.13888i
$904$	−15.5830			−0.518283
$905$		0			0
$906$	−17.1144	+	29.6430i	−0.568587	+	0.984822i
$907$	19.9686	+	34.5867i	0.663047	+	1.14843i	0.979811	+	0.199927i	$0.0640706\pi$
$907$	19.9686	+	34.5867i	0.663047	+	1.14843i	−0.316763	+	0.948505i	$0.602596\pi$
$908$	−3.67712	+	6.36897i	−0.122030	+	0.211362i
$909$	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	$0.409474\pi$
$912$	11.4373	+	1.47960i	0.378725	+	0.0489945i
$913$	36.8745			1.22037
$914$	−16.4373	−	28.4702i	−0.543696	−	0.941709i
$915$		0			0
$916$	−10.0000	+	17.3205i	−0.330409	+	0.572286i
$917$	3.53137	+	6.11652i	0.116616	+	0.201985i
$918$		0			0
$919$	−19.8745			−0.655600			−0.327800	−	0.944747i	$-0.606307\pi$
$919$	−19.8745			−0.655600			−0.327800	+	0.944747i	$0.606307\pi$
$920$		0			0
$921$	−0.854249	+	1.47960i	−0.0281485	+	0.0487545i
$922$	9.58301	−	16.5983i	0.315599	−	0.546634i
$923$	5.41699			0.178303
$924$	−44.8118			−1.47420
$925$		0			0
$926$	19.2288	+	33.3052i	0.631896	+	1.09448i
$927$	−26.5830	+	46.0431i	−0.873100	+	1.51225i
$928$	0.822876	+	1.42526i	0.0270122	+	0.0467865i
$929$	4.79150	+	8.29913i	0.157204	+	0.272285i	0.933859	−	0.357640i	$-0.116419\pi$
$929$	4.79150	+	8.29913i	0.157204	+	0.272285i	−0.776655	+	0.629926i	$0.783085\pi$
$930$		0			0
$931$	10.5516	+	25.3128i	0.345816	+	0.829595i
$932$	−18.8745			−0.618255
$933$	18.0516	+	31.2663i	0.590984	+	1.02361i
$934$	9.67712	+	16.7613i	0.316645	+	0.548446i
$935$		0			0
$936$	−4.00000	−	6.92820i	−0.130744	−	0.226455i
$937$	3.56275	−	6.17086i	0.116390	−	0.201593i	−0.801945	−	0.597398i	$-0.796201\pi$
$937$	3.56275	−	6.17086i	0.116390	−	0.201593i	0.918334	+	0.395805i	$0.129534\pi$
$938$	−2.35425			−0.0768689
$939$	23.4797			0.766232
$940$		0			0
$941$	−8.41699	+	14.5787i	−0.274386	+	0.475251i	−0.969980	−	0.243184i	$-0.921808\pi$
$941$	−8.41699	+	14.5787i	−0.274386	+	0.475251i	0.695594	+	0.718435i	$0.255141\pi$
$942$	28.0000			0.912289
$943$	−0.479741			−0.0156225
$944$	3.96863	−	6.87386i	0.129168	−	0.223725i
$945$		0			0
$946$	26.2288	−	45.4295i	0.852770	−	1.47704i
$947$	−3.87451	−	6.71084i	−0.125905	−	0.218073i	0.796182	−	0.605058i	$-0.206850\pi$
$947$	−3.87451	−	6.71084i	−0.125905	−	0.218073i	−0.922086	+	0.386985i	$0.873517\pi$
$948$	−5.29150	−	9.16515i	−0.171860	−	0.297670i
$949$	3.41699			0.110920
$950$		0			0
$951$	−15.8745			−0.514766
$952$		0			0
$953$	−6.72876	−	11.6545i	−0.217966	−	0.377528i	0.736220	−	0.676742i	$-0.236609\pi$
$953$	−6.72876	−	11.6545i	−0.217966	−	0.377528i	−0.954186	+	0.299214i	$0.903275\pi$
$954$	25.1660	−	43.5888i	0.814780	−	1.41124i
$955$		0			0
$956$	6.00000	−	10.3923i	0.194054	−	0.336111i
$957$	20.2288			0.653903
$958$	−6.58301			−0.212687
$959$	−28.4059	+	49.2004i	−0.917274	+	1.58876i
$960$		0			0
$961$	0.874508			0.0282099
$962$	−0.708497			−0.0228429
$963$	30.5830	−	52.9713i	0.985524	−	1.70698i
$964$	3.79150	+	6.56708i	0.122116	+	0.211511i
$965$		0			0
$966$	7.93725	+	13.7477i	0.255377	+	0.442326i
$967$	−6.64575	−	11.5108i	−0.213713	−	0.370162i	0.739161	−	0.673529i	$-0.235222\pi$
$967$	−6.64575	−	11.5108i	−0.213713	−	0.370162i	−0.952874	+	0.303367i	$0.901889\pi$
$968$	−10.5830			−0.340151
$969$		0			0
$970$		0			0
$971$	27.1974	+	47.1073i	0.872806	+	1.51174i	0.859082	+	0.511838i	$0.171035\pi$
$971$	27.1974	+	47.1073i	0.872806	+	1.51174i	0.0137234	+	0.999906i	$0.495632\pi$
$972$	−10.5830	−	18.3303i	−0.339450	−	0.587945i
$973$	33.9889	−	58.8705i	1.08963	−	1.88730i
$974$	−2.11438	−	3.66221i	−0.0677491	−	0.117345i
$975$		0			0
$976$	0.937254			0.0300008
$977$	7.45751			0.238587			0.119293	−	0.992859i	$-0.461937\pi$
$977$	7.45751			0.238587			0.119293	+	0.992859i	$0.461937\pi$
$978$	5.20850	−	9.02138i	0.166549	−	0.288472i
$979$		0			0
$980$		0			0
$981$	58.3320			1.86240
$982$	19.6458	−	34.0274i	0.626921	−	1.08586i
$983$	15.8745	+	27.4955i	0.506318	+	0.876969i	0.999973	+	0.00731102i	$0.00232719\pi$
$983$	15.8745	+	27.4955i	0.506318	+	0.876969i	−0.493655	+	0.869658i	$0.664339\pi$
$984$	0.385622	−	0.667916i	0.0122932	−	0.0212924i
$985$		0			0
$986$		0			0
$987$	−42.0000			−1.33687
$988$	−5.29150	+	6.92820i	−0.168345	+	0.220416i
$989$	−18.5830			−0.590905
$990$		0			0
$991$	1.41699	+	2.45431i	0.0450123	+	0.0779636i	0.887654	−	0.460511i	$-0.152334\pi$
$991$	1.41699	+	2.45431i	0.0450123	+	0.0779636i	−0.842641	+	0.538475i	$0.819001\pi$
$992$	−2.82288	+	4.88936i	−0.0896264	+	0.155237i
$993$	26.2085	+	45.3944i	0.831702	+	1.44055i
$994$	4.93725	−	8.55157i	0.156600	−	0.271239i
$995$		0			0
$996$	21.0000			0.665410
$997$	8.11438	−	14.0545i	0.256985	−	0.445111i	−0.708448	−	0.705763i	$-0.750604\pi$
$997$	8.11438	−	14.0545i	0.256985	−	0.445111i	0.965433	+	0.260652i	$0.0839376\pi$
$998$	−2.38562	+	4.13202i	−0.0755155	+	0.130797i
$999$	0.937254			0.0296534

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	950.2.e.k.501.2		4
5.2	odd	4		950.2.j.g.349.2		8
5.3	odd	4		950.2.j.g.349.3		8
5.4	even	2		38.2.c.b.7.1	✓	4
15.14	odd	2		342.2.g.f.235.1		4
19.11	even	3	inner	950.2.e.k.201.2		4
20.19	odd	2		304.2.i.e.273.2		4
40.19	odd	2		1216.2.i.k.577.1		4
40.29	even	2		1216.2.i.l.577.2		4
60.59	even	2		2736.2.s.v.577.1		4
95.4	even	18		722.2.e.n.245.2		12
95.9	even	18		722.2.e.n.415.1		12
95.14	odd	18		722.2.e.o.99.1		12
95.24	even	18		722.2.e.n.99.2		12
95.29	odd	18		722.2.e.o.415.2		12
95.34	odd	18		722.2.e.o.245.1		12
95.44	even	18		722.2.e.n.423.2		12
95.49	even	6		38.2.c.b.11.1	yes	4
95.54	even	18		722.2.e.n.595.1		12
95.59	odd	18		722.2.e.o.389.1		12
95.64	even	6		722.2.a.j.1.2		2
95.68	odd	12		950.2.j.g.49.2		8
95.69	odd	6		722.2.a.g.1.1		2
95.74	even	18		722.2.e.n.389.2		12
95.79	odd	18		722.2.e.o.595.2		12
95.84	odd	6		722.2.c.j.429.2		4
95.87	odd	12		950.2.j.g.49.3		8
95.89	odd	18		722.2.e.o.423.1		12
95.94	odd	2		722.2.c.j.653.2		4
285.164	even	6		6498.2.a.bg.1.2		2
285.239	odd	6		342.2.g.f.163.1		4
285.254	odd	6		6498.2.a.ba.1.2		2
380.159	odd	6		5776.2.a.ba.1.1		2
380.239	odd	6		304.2.i.e.49.2		4
380.259	even	6		5776.2.a.z.1.2		2
760.429	even	6		1216.2.i.l.961.2		4
760.619	odd	6		1216.2.i.k.961.1		4
1140.239	even	6		2736.2.s.v.1873.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
38.2.c.b.7.1	✓	4	5.4	even	2
38.2.c.b.11.1	yes	4	95.49	even	6
304.2.i.e.49.2		4	380.239	odd	6
304.2.i.e.273.2		4	20.19	odd	2
342.2.g.f.163.1		4	285.239	odd	6
342.2.g.f.235.1		4	15.14	odd	2
722.2.a.g.1.1		2	95.69	odd	6
722.2.a.j.1.2		2	95.64	even	6
722.2.c.j.429.2		4	95.84	odd	6
722.2.c.j.653.2		4	95.94	odd	2
722.2.e.n.99.2		12	95.24	even	18
722.2.e.n.245.2		12	95.4	even	18
722.2.e.n.389.2		12	95.74	even	18
722.2.e.n.415.1		12	95.9	even	18
722.2.e.n.423.2		12	95.44	even	18
722.2.e.n.595.1		12	95.54	even	18
722.2.e.o.99.1		12	95.14	odd	18
722.2.e.o.245.1		12	95.34	odd	18
722.2.e.o.389.1		12	95.59	odd	18
722.2.e.o.415.2		12	95.29	odd	18
722.2.e.o.423.1		12	95.89	odd	18
722.2.e.o.595.2		12	95.79	odd	18
950.2.e.k.201.2		4	19.11	even	3	inner
950.2.e.k.501.2		4	1.1	even	1	trivial
950.2.j.g.49.2		8	95.68	odd	12
950.2.j.g.49.3		8	95.87	odd	12
950.2.j.g.349.2		8	5.2	odd	4
950.2.j.g.349.3		8	5.3	odd	4
1216.2.i.k.577.1		4	40.19	odd	2
1216.2.i.k.961.1		4	760.619	odd	6
1216.2.i.l.577.2		4	40.29	even	2
1216.2.i.l.961.2		4	760.429	even	6
2736.2.s.v.577.1		4	60.59	even	2
2736.2.s.v.1873.1		4	1140.239	even	6
5776.2.a.z.1.2		2	380.259	even	6
5776.2.a.ba.1.1		2	380.159	odd	6
6498.2.a.ba.1.2		2	285.254	odd	6
6498.2.a.bg.1.2		2	285.164	even	6

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.e (of order \(3\), degree \(2\), minimal)

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

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