LMFDB - Embedded newform 8034.2.a.s.1.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8034,2,Mod(1,8034)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8034, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("8034.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8034 = 2 \cdot 3 \cdot 13 \cdot 103 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8034.a (trivial)

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:	yes
Analytic conductor:	$64.1518129839$
Analytic rank:	$1$
Dimension:	$10$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - 4x^{9} - 15x^{8} + 72x^{7} - 27x^{6} - 115x^{5} + 54x^{4} + 68x^{3} - 15x^{2} - 15x - 2 $ x^10 - 4x^9 - 15x^8 + 72x^7 - 27x^6 - 115x^5 + 54x^4 + 68x^3 - 15x^2 - 15*x - 2
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.6
Root			$1.27214$ of defining polynomial
Character	$\chi$	$=$	8034.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +1.40775 q^{5} +1.00000 q^{6} -4.52824 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +1.40775 q^{5} +1.00000 q^{6} -4.52824 q^{7} -1.00000 q^{8} +1.00000 q^{9} -1.40775 q^{10} -2.48891 q^{11} -1.00000 q^{12} -1.00000 q^{13} +4.52824 q^{14} -1.40775 q^{15} +1.00000 q^{16} +3.25610 q^{17} -1.00000 q^{18} +2.32675 q^{19} +1.40775 q^{20} +4.52824 q^{21} +2.48891 q^{22} +7.94245 q^{23} +1.00000 q^{24} -3.01825 q^{25} +1.00000 q^{26} -1.00000 q^{27} -4.52824 q^{28} -6.13450 q^{29} +1.40775 q^{30} +4.13377 q^{31} -1.00000 q^{32} +2.48891 q^{33} -3.25610 q^{34} -6.37461 q^{35} +1.00000 q^{36} +9.38272 q^{37} -2.32675 q^{38} +1.00000 q^{39} -1.40775 q^{40} -10.4366 q^{41} -4.52824 q^{42} -11.2716 q^{43} -2.48891 q^{44} +1.40775 q^{45} -7.94245 q^{46} -11.8439 q^{47} -1.00000 q^{48} +13.5049 q^{49} +3.01825 q^{50} -3.25610 q^{51} -1.00000 q^{52} +8.80361 q^{53} +1.00000 q^{54} -3.50375 q^{55} +4.52824 q^{56} -2.32675 q^{57} +6.13450 q^{58} -1.56533 q^{59} -1.40775 q^{60} +9.79962 q^{61} -4.13377 q^{62} -4.52824 q^{63} +1.00000 q^{64} -1.40775 q^{65} -2.48891 q^{66} -1.67018 q^{67} +3.25610 q^{68} -7.94245 q^{69} +6.37461 q^{70} +8.11876 q^{71} -1.00000 q^{72} +8.24122 q^{73} -9.38272 q^{74} +3.01825 q^{75} +2.32675 q^{76} +11.2704 q^{77} -1.00000 q^{78} -1.00405 q^{79} +1.40775 q^{80} +1.00000 q^{81} +10.4366 q^{82} -2.03579 q^{83} +4.52824 q^{84} +4.58377 q^{85} +11.2716 q^{86} +6.13450 q^{87} +2.48891 q^{88} +8.03751 q^{89} -1.40775 q^{90} +4.52824 q^{91} +7.94245 q^{92} -4.13377 q^{93} +11.8439 q^{94} +3.27548 q^{95} +1.00000 q^{96} +9.30986 q^{97} -13.5049 q^{98} -2.48891 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q - 10 q^{2} - 10 q^{3} + 10 q^{4} + 6 q^{5} + 10 q^{6} - 9 q^{7} - 10 q^{8} + 10 q^{9}+O(q^{10}) $ 10 * q - 10 * q^2 - 10 * q^3 + 10 * q^4 + 6 * q^5 + 10 * q^6 - 9 * q^7 - 10 * q^8 + 10 * q^9	\( 10 q - 10 q^{2} - 10 q^{3} + 10 q^{4} + 6 q^{5} + 10 q^{6} - 9 q^{7} - 10 q^{8} + 10 q^{9} - 6 q^{10} - q^{11} - 10 q^{12} - 10 q^{13} + 9 q^{14} - 6 q^{15} + 10 q^{16} + 5 q^{17} - 10 q^{18} - 9 q^{19} + 6 q^{20} + 9 q^{21} + q^{22} + q^{23} + 10 q^{24} + 20 q^{25} + 10 q^{26} - 10 q^{27} - 9 q^{28} - 22 q^{29} + 6 q^{30} - 13 q^{31} - 10 q^{32} + q^{33} - 5 q^{34} + 14 q^{35} + 10 q^{36} + 10 q^{37} + 9 q^{38} + 10 q^{39} - 6 q^{40} - 18 q^{41} - 9 q^{42} + 10 q^{43} - q^{44} + 6 q^{45} - q^{46} + 28 q^{47} - 10 q^{48} + 11 q^{49} - 20 q^{50} - 5 q^{51} - 10 q^{52} + 6 q^{53} + 10 q^{54} - 26 q^{55} + 9 q^{56} + 9 q^{57} + 22 q^{58} + 7 q^{59} - 6 q^{60} - 20 q^{61} + 13 q^{62} - 9 q^{63} + 10 q^{64} - 6 q^{65} - q^{66} - 21 q^{67} + 5 q^{68} - q^{69} - 14 q^{70} - 19 q^{71} - 10 q^{72} + 3 q^{73} - 10 q^{74} - 20 q^{75} - 9 q^{76} + 28 q^{77} - 10 q^{78} - 11 q^{79} + 6 q^{80} + 10 q^{81} + 18 q^{82} + 20 q^{83} + 9 q^{84} - q^{85} - 10 q^{86} + 22 q^{87} + q^{88} + 22 q^{89} - 6 q^{90} + 9 q^{91} + q^{92} + 13 q^{93} - 28 q^{94} + 10 q^{96} - 10 q^{97} - 11 q^{98} - q^{99}+O(q^{100}) \) 10 * q - 10 * q^2 - 10 * q^3 + 10 * q^4 + 6 * q^5 + 10 * q^6 - 9 * q^7 - 10 * q^8 + 10 * q^9 - 6 * q^10 - q^11 - 10 * q^12 - 10 * q^13 + 9 * q^14 - 6 * q^15 + 10 * q^16 + 5 * q^17 - 10 * q^18 - 9 * q^19 + 6 * q^20 + 9 * q^21 + q^22 + q^23 + 10 * q^24 + 20 * q^25 + 10 * q^26 - 10 * q^27 - 9 * q^28 - 22 * q^29 + 6 * q^30 - 13 * q^31 - 10 * q^32 + q^33 - 5 * q^34 + 14 * q^35 + 10 * q^36 + 10 * q^37 + 9 * q^38 + 10 * q^39 - 6 * q^40 - 18 * q^41 - 9 * q^42 + 10 * q^43 - q^44 + 6 * q^45 - q^46 + 28 * q^47 - 10 * q^48 + 11 * q^49 - 20 * q^50 - 5 * q^51 - 10 * q^52 + 6 * q^53 + 10 * q^54 - 26 * q^55 + 9 * q^56 + 9 * q^57 + 22 * q^58 + 7 * q^59 - 6 * q^60 - 20 * q^61 + 13 * q^62 - 9 * q^63 + 10 * q^64 - 6 * q^65 - q^66 - 21 * q^67 + 5 * q^68 - q^69 - 14 * q^70 - 19 * q^71 - 10 * q^72 + 3 * q^73 - 10 * q^74 - 20 * q^75 - 9 * q^76 + 28 * q^77 - 10 * q^78 - 11 * q^79 + 6 * q^80 + 10 * q^81 + 18 * q^82 + 20 * q^83 + 9 * q^84 - q^85 - 10 * q^86 + 22 * q^87 + q^88 + 22 * q^89 - 6 * q^90 + 9 * q^91 + q^92 + 13 * q^93 - 28 * q^94 + 10 * q^96 - 10 * q^97 - 11 * q^98 - q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	1.00000	0.500000
$5$	1.40775	0.629563	0.314782	−	0.949164i	$-0.398069\pi$
$5$	1.40775	0.629563	0.314782	+	0.949164i	$0.398069\pi$
$6$	1.00000	0.408248
$7$	−4.52824	−1.71151	−0.855756	−	0.517379i	$-0.826908\pi$
$7$	−4.52824	−1.71151	−0.855756	+	0.517379i	$0.826908\pi$
$8$	−1.00000	−0.353553
$9$	1.00000	0.333333
$10$	−1.40775	−0.445168
$11$	−2.48891	−0.750433	−0.375217	−	0.926937i	$-0.622432\pi$
$11$	−2.48891	−0.750433	−0.375217	+	0.926937i	$0.622432\pi$
$12$	−1.00000	−0.288675
$13$	−1.00000	−0.277350
$13$	−1.00000	−0.277350
$14$	4.52824	1.21022
$15$	−1.40775	−0.363478
$16$	1.00000	0.250000
$17$	3.25610	0.789721	0.394860	−	0.918741i	$-0.370793\pi$
$17$	3.25610	0.789721	0.394860	+	0.918741i	$0.370793\pi$
$18$	−1.00000	−0.235702
$19$	2.32675	0.533794	0.266897	−	0.963725i	$-0.414002\pi$
$19$	2.32675	0.533794	0.266897	+	0.963725i	$0.414002\pi$
$20$	1.40775	0.314782
$21$	4.52824	0.988142
$22$	2.48891	0.530637
$23$	7.94245	1.65611	0.828057	−	0.560643i	$-0.189446\pi$
$23$	7.94245	1.65611	0.828057	+	0.560643i	$0.189446\pi$
$24$	1.00000	0.204124
$25$	−3.01825	−0.603650
$26$	1.00000	0.196116
$27$	−1.00000	−0.192450
$28$	−4.52824	−0.855756
$29$	−6.13450	−1.13915	−0.569574	−	0.821940i	$-0.692892\pi$
$29$	−6.13450	−1.13915	−0.569574	+	0.821940i	$0.692892\pi$
$30$	1.40775	0.257018
$31$	4.13377	0.742448	0.371224	−	0.928543i	$-0.378938\pi$
$31$	4.13377	0.742448	0.371224	+	0.928543i	$0.378938\pi$
$32$	−1.00000	−0.176777
$33$	2.48891	0.433263
$34$	−3.25610	−0.558417
$35$	−6.37461	−1.07751
$36$	1.00000	0.166667
$37$	9.38272	1.54251	0.771255	−	0.636526i	$-0.219629\pi$
$37$	9.38272	1.54251	0.771255	+	0.636526i	$0.219629\pi$
$38$	−2.32675	−0.377449
$39$	1.00000	0.160128
$40$	−1.40775	−0.222584
$41$	−10.4366	−1.62992	−0.814962	−	0.579514i	$-0.803243\pi$
$41$	−10.4366	−1.62992	−0.814962	+	0.579514i	$0.803243\pi$
$42$	−4.52824	−0.698722
$43$	−11.2716	−1.71890	−0.859452	−	0.511217i	$-0.829195\pi$
$43$	−11.2716	−1.71890	−0.859452	+	0.511217i	$0.829195\pi$
$44$	−2.48891	−0.375217
$45$	1.40775	0.209854
$46$	−7.94245	−1.17105
$47$	−11.8439	−1.72762	−0.863808	−	0.503822i	$-0.831927\pi$
$47$	−11.8439	−1.72762	−0.863808	+	0.503822i	$0.831927\pi$
$48$	−1.00000	−0.144338
$49$	13.5049	1.92928
$50$	3.01825	0.426845
$51$	−3.25610	−0.455946
$52$	−1.00000	−0.138675
$53$	8.80361	1.20927	0.604635	−	0.796503i	$-0.293319\pi$
$53$	8.80361	1.20927	0.604635	+	0.796503i	$0.293319\pi$
$54$	1.00000	0.136083
$55$	−3.50375	−0.472445
$56$	4.52824	0.605111
$57$	−2.32675	−0.308186
$58$	6.13450	0.805499
$59$	−1.56533	−0.203789	−0.101895	−	0.994795i	$-0.532490\pi$
$59$	−1.56533	−0.203789	−0.101895	+	0.994795i	$0.532490\pi$
$60$	−1.40775	−0.181739
$61$	9.79962	1.25471	0.627357	−	0.778732i	$-0.284137\pi$
$61$	9.79962	1.25471	0.627357	+	0.778732i	$0.284137\pi$
$62$	−4.13377	−0.524990
$63$	−4.52824	−0.570504
$64$	1.00000	0.125000
$65$	−1.40775	−0.174609
$66$	−2.48891	−0.306363
$67$	−1.67018	−0.204045	−0.102023	−	0.994782i	$-0.532531\pi$
$67$	−1.67018	−0.204045	−0.102023	+	0.994782i	$0.532531\pi$
$68$	3.25610	0.394860
$69$	−7.94245	−0.956158
$70$	6.37461	0.761911
$71$	8.11876	0.963519	0.481760	−	0.876303i	$-0.339998\pi$
$71$	8.11876	0.963519	0.481760	+	0.876303i	$0.339998\pi$
$72$	−1.00000	−0.117851
$73$	8.24122	0.964562	0.482281	−	0.876017i	$-0.339808\pi$
$73$	8.24122	0.964562	0.482281	+	0.876017i	$0.339808\pi$
$74$	−9.38272	−1.09072
$75$	3.01825	0.348518
$76$	2.32675	0.266897
$77$	11.2704	1.28438
$78$	−1.00000	−0.113228
$79$	−1.00405	−0.112964	−0.0564821	−	0.998404i	$-0.517988\pi$
$79$	−1.00405	−0.112964	−0.0564821	+	0.998404i	$0.517988\pi$
$80$	1.40775	0.157391
$81$	1.00000	0.111111
$82$	10.4366	1.15253
$83$	−2.03579	−0.223457	−0.111729	−	0.993739i	$-0.535639\pi$
$83$	−2.03579	−0.223457	−0.111729	+	0.993739i	$0.535639\pi$
$84$	4.52824	0.494071
$85$	4.58377	0.497179
$86$	11.2716	1.21545
$87$	6.13450	0.657687
$88$	2.48891	0.265318
$89$	8.03751	0.851974	0.425987	−	0.904729i	$-0.359927\pi$
$89$	8.03751	0.851974	0.425987	+	0.904729i	$0.359927\pi$
$90$	−1.40775	−0.148389
$91$	4.52824	0.474688
$92$	7.94245	0.828057
$93$	−4.13377	−0.428652
$94$	11.8439	1.22161
$95$	3.27548	0.336057
$96$	1.00000	0.102062
$97$	9.30986	0.945273	0.472637	−	0.881257i	$-0.343302\pi$
$97$	9.30986	0.945273	0.472637	+	0.881257i	$0.343302\pi$
$98$	−13.5049	−1.36420
$99$	−2.48891	−0.250144
$100$	−3.01825	−0.301825
$101$	9.65272	0.960482	0.480241	−	0.877137i	$-0.340549\pi$
$101$	9.65272	0.960482	0.480241	+	0.877137i	$0.340549\pi$
$102$	3.25610	0.322402
$103$	−1.00000	−0.0985329
$103$	−1.00000	−0.0985329
$104$	1.00000	0.0980581
$105$	6.37461	0.622098
$106$	−8.80361	−0.855083
$107$	6.32459	0.611422	0.305711	−	0.952124i	$-0.401106\pi$
$107$	6.32459	0.611422	0.305711	+	0.952124i	$0.401106\pi$
$108$	−1.00000	−0.0962250
$109$	−3.42711	−0.328258	−0.164129	−	0.986439i	$-0.552481\pi$
$109$	−3.42711	−0.328258	−0.164129	+	0.986439i	$0.552481\pi$
$110$	3.50375	0.334069
$111$	−9.38272	−0.890569
$112$	−4.52824	−0.427878
$113$	15.7386	1.48057	0.740284	−	0.672295i	$-0.234691\pi$
$113$	15.7386	1.48057	0.740284	+	0.672295i	$0.234691\pi$
$114$	2.32675	0.217920
$115$	11.1809	1.04263
$116$	−6.13450	−0.569574
$117$	−1.00000	−0.0924500
$118$	1.56533	0.144101
$119$	−14.7444	−1.35162
$120$	1.40775	0.128509
$121$	−4.80535	−0.436850
$122$	−9.79962	−0.887216
$123$	10.4366	0.941038
$124$	4.13377	0.371224
$125$	−11.2877	−1.00960
$126$	4.52824	0.403407
$127$	−16.5723	−1.47055	−0.735275	−	0.677769i	$-0.762947\pi$
$127$	−16.5723	−1.47055	−0.735275	+	0.677769i	$0.762947\pi$
$128$	−1.00000	−0.0883883
$129$	11.2716	0.992409
$130$	1.40775	0.123467
$131$	−17.0821	−1.49247	−0.746233	−	0.665685i	$-0.768139\pi$
$131$	−17.0821	−1.49247	−0.746233	+	0.665685i	$0.768139\pi$
$132$	2.48891	0.216631
$133$	−10.5361	−0.913595
$134$	1.67018	0.144282
$135$	−1.40775	−0.121159
$136$	−3.25610	−0.279208
$137$	−11.6264	−0.993309	−0.496655	−	0.867948i	$-0.665438\pi$
$137$	−11.6264	−0.993309	−0.496655	+	0.867948i	$0.665438\pi$
$138$	7.94245	0.676106
$139$	−8.47436	−0.718786	−0.359393	−	0.933186i	$-0.617016\pi$
$139$	−8.47436	−0.718786	−0.359393	+	0.933186i	$0.617016\pi$
$140$	−6.37461	−0.538753
$141$	11.8439	0.997439
$142$	−8.11876	−0.681311
$143$	2.48891	0.208133
$144$	1.00000	0.0833333
$145$	−8.63581	−0.717165
$146$	−8.24122	−0.682048
$147$	−13.5049	−1.11387
$148$	9.38272	0.771255
$149$	−17.4106	−1.42633	−0.713165	−	0.700996i	$-0.752739\pi$
$149$	−17.4106	−1.42633	−0.713165	+	0.700996i	$0.752739\pi$
$150$	−3.01825	−0.246439
$151$	9.64889	0.785216	0.392608	−	0.919706i	$-0.371573\pi$
$151$	9.64889	0.785216	0.392608	+	0.919706i	$0.371573\pi$
$152$	−2.32675	−0.188725
$153$	3.25610	0.263240
$154$	−11.2704	−0.908191
$155$	5.81930	0.467418
$156$	1.00000	0.0800641
$157$	18.8897	1.50756	0.753782	−	0.657124i	$-0.228227\pi$
$157$	18.8897	1.50756	0.753782	+	0.657124i	$0.228227\pi$
$158$	1.00405	0.0798778
$159$	−8.80361	−0.698172
$160$	−1.40775	−0.111292
$161$	−35.9653	−2.83446
$162$	−1.00000	−0.0785674
$163$	16.1378	1.26401	0.632006	−	0.774963i	$-0.282232\pi$
$163$	16.1378	1.26401	0.632006	+	0.774963i	$0.282232\pi$
$164$	−10.4366	−0.814962
$165$	3.50375	0.272766
$166$	2.03579	0.158008
$167$	8.93841	0.691675	0.345838	−	0.938294i	$-0.387595\pi$
$167$	8.93841	0.691675	0.345838	+	0.938294i	$0.387595\pi$
$168$	−4.52824	−0.349361
$169$	1.00000	0.0769231
$170$	−4.58377	−0.351559
$171$	2.32675	0.177931
$172$	−11.2716	−0.859452
$173$	10.2742	0.781134	0.390567	−	0.920575i	$-0.372279\pi$
$173$	10.2742	0.781134	0.390567	+	0.920575i	$0.372279\pi$
$174$	−6.13450	−0.465055
$175$	13.6674	1.03316
$176$	−2.48891	−0.187608
$177$	1.56533	0.117658
$178$	−8.03751	−0.602436
$179$	−1.84948	−0.138237	−0.0691184	−	0.997608i	$-0.522019\pi$
$179$	−1.84948	−0.138237	−0.0691184	+	0.997608i	$0.522019\pi$
$180$	1.40775	0.104927
$181$	−13.1117	−0.974584	−0.487292	−	0.873239i	$-0.662015\pi$
$181$	−13.1117	−0.974584	−0.487292	+	0.873239i	$0.662015\pi$
$182$	−4.52824	−0.335655
$183$	−9.79962	−0.724409
$184$	−7.94245	−0.585525
$185$	13.2085	0.971108
$186$	4.13377	0.303103
$187$	−8.10413	−0.592633
$188$	−11.8439	−0.863808
$189$	4.52824	0.329381
$190$	−3.27548	−0.237628
$191$	13.6919	0.990715	0.495357	−	0.868689i	$-0.335037\pi$
$191$	13.6919	0.990715	0.495357	+	0.868689i	$0.335037\pi$
$192$	−1.00000	−0.0721688
$193$	−26.3563	−1.89717	−0.948584	−	0.316527i	$-0.897483\pi$
$193$	−26.3563	−1.89717	−0.948584	+	0.316527i	$0.897483\pi$
$194$	−9.30986	−0.668409
$195$	1.40775	0.100811
$196$	13.5049	0.964638
$197$	−15.1038	−1.07610	−0.538051	−	0.842912i	$-0.680839\pi$
$197$	−15.1038	−1.07610	−0.538051	+	0.842912i	$0.680839\pi$
$198$	2.48891	0.176879
$199$	−6.34126	−0.449520	−0.224760	−	0.974414i	$-0.572160\pi$
$199$	−6.34126	−0.449520	−0.224760	+	0.974414i	$0.572160\pi$
$200$	3.01825	0.213423
$201$	1.67018	0.117806
$202$	−9.65272	−0.679163
$203$	27.7785	1.94966
$204$	−3.25610	−0.227973
$205$	−14.6921	−1.02614
$206$	1.00000	0.0696733
$207$	7.94245	0.552038
$208$	−1.00000	−0.0693375
$209$	−5.79107	−0.400577
$210$	−6.37461	−0.439890
$211$	0.649989	0.0447471	0.0223736	−	0.999750i	$-0.492878\pi$
$211$	0.649989	0.0447471	0.0223736	+	0.999750i	$0.492878\pi$
$212$	8.80361	0.604635
$213$	−8.11876	−0.556288
$214$	−6.32459	−0.432340
$215$	−15.8676	−1.08216
$216$	1.00000	0.0680414
$217$	−18.7187	−1.27071
$218$	3.42711	0.232113
$219$	−8.24122	−0.556890
$220$	−3.50375	−0.236223
$221$	−3.25610	−0.219029
$222$	9.38272	0.629727
$223$	−7.48778	−0.501419	−0.250709	−	0.968062i	$-0.580664\pi$
$223$	−7.48778	−0.501419	−0.250709	+	0.968062i	$0.580664\pi$
$224$	4.52824	0.302556
$225$	−3.01825	−0.201217
$226$	−15.7386	−1.04692
$227$	27.4371	1.82106	0.910531	−	0.413441i	$-0.135673\pi$
$227$	27.4371	1.82106	0.910531	+	0.413441i	$0.135673\pi$
$228$	−2.32675	−0.154093
$229$	−0.703845	−0.0465114	−0.0232557	−	0.999730i	$-0.507403\pi$
$229$	−0.703845	−0.0465114	−0.0232557	+	0.999730i	$0.507403\pi$
$230$	−11.1809	−0.737250
$231$	−11.2704	−0.741535
$232$	6.13450	0.402749
$233$	15.8083	1.03564	0.517819	−	0.855490i	$-0.326744\pi$
$233$	15.8083	1.03564	0.517819	+	0.855490i	$0.326744\pi$
$234$	1.00000	0.0653720
$235$	−16.6733	−1.08764
$236$	−1.56533	−0.101895
$237$	1.00405	0.0652199
$238$	14.7444	0.955738
$239$	5.54584	0.358730	0.179365	−	0.983783i	$-0.442596\pi$
$239$	5.54584	0.358730	0.179365	+	0.983783i	$0.442596\pi$
$240$	−1.40775	−0.0908696
$241$	−0.771368	−0.0496882	−0.0248441	−	0.999691i	$-0.507909\pi$
$241$	−0.771368	−0.0496882	−0.0248441	+	0.999691i	$0.507909\pi$
$242$	4.80535	0.308899
$243$	−1.00000	−0.0641500
$244$	9.79962	0.627357
$245$	19.0115	1.21460
$246$	−10.4366	−0.665414
$247$	−2.32675	−0.148048
$248$	−4.13377	−0.262495
$249$	2.03579	0.129013
$250$	11.2877	0.713894
$251$	−20.9345	−1.32137	−0.660686	−	0.750663i	$-0.729734\pi$
$251$	−20.9345	−1.32137	−0.660686	+	0.750663i	$0.729734\pi$
$252$	−4.52824	−0.285252
$253$	−19.7680	−1.24280
$254$	16.5723	1.03984
$255$	−4.58377	−0.287047
$256$	1.00000	0.0625000
$257$	−10.1729	−0.634567	−0.317284	−	0.948331i	$-0.602771\pi$
$257$	−10.1729	−0.634567	−0.317284	+	0.948331i	$0.602771\pi$
$258$	−11.2716	−0.701739
$259$	−42.4872	−2.64003
$260$	−1.40775	−0.0873047
$261$	−6.13450	−0.379716
$262$	17.0821	1.05533
$263$	−19.5965	−1.20837	−0.604185	−	0.796844i	$-0.706501\pi$
$263$	−19.5965	−1.20837	−0.604185	+	0.796844i	$0.706501\pi$
$264$	−2.48891	−0.153182
$265$	12.3933	0.761311
$266$	10.5361	0.646009
$267$	−8.03751	−0.491887
$268$	−1.67018	−0.102023
$269$	4.11436	0.250857	0.125428	−	0.992103i	$-0.459969\pi$
$269$	4.11436	0.250857	0.125428	+	0.992103i	$0.459969\pi$
$270$	1.40775	0.0856727
$271$	−19.0088	−1.15470	−0.577351	−	0.816496i	$-0.695914\pi$
$271$	−19.0088	−1.15470	−0.577351	+	0.816496i	$0.695914\pi$
$272$	3.25610	0.197430
$273$	−4.52824	−0.274061
$274$	11.6264	0.702376
$275$	7.51214	0.452999
$276$	−7.94245	−0.478079
$277$	3.88739	0.233570	0.116785	−	0.993157i	$-0.462741\pi$
$277$	3.88739	0.233570	0.116785	+	0.993157i	$0.462741\pi$
$278$	8.47436	0.508258
$279$	4.13377	0.247483
$280$	6.37461	0.380956
$281$	−7.84531	−0.468012	−0.234006	−	0.972235i	$-0.575184\pi$
$281$	−7.84531	−0.468012	−0.234006	+	0.972235i	$0.575184\pi$
$282$	−11.8439	−0.705296
$283$	−19.6759	−1.16961	−0.584805	−	0.811174i	$-0.698829\pi$
$283$	−19.6759	−1.16961	−0.584805	+	0.811174i	$0.698829\pi$
$284$	8.11876	0.481760
$285$	−3.27548	−0.194023
$286$	−2.48891	−0.147172
$287$	47.2595	2.78964
$288$	−1.00000	−0.0589256
$289$	−6.39780	−0.376341
$290$	8.63581	0.507112
$291$	−9.30986	−0.545754
$292$	8.24122	0.482281
$293$	−3.18381	−0.186000	−0.0930002	−	0.995666i	$-0.529646\pi$
$293$	−3.18381	−0.186000	−0.0930002	+	0.995666i	$0.529646\pi$
$294$	13.5049	0.787624
$295$	−2.20359	−0.128298
$296$	−9.38272	−0.545360
$297$	2.48891	0.144421
$298$	17.4106	1.00857
$299$	−7.94245	−0.459324
$300$	3.01825	0.174259
$301$	51.0405	2.94192
$302$	−9.64889	−0.555231
$303$	−9.65272	−0.554534
$304$	2.32675	0.133448
$305$	13.7954	0.789921
$306$	−3.25610	−0.186139
$307$	−33.2438	−1.89733	−0.948663	−	0.316290i	$-0.897563\pi$
$307$	−33.2438	−1.89733	−0.948663	+	0.316290i	$0.897563\pi$
$308$	11.2704	0.642188
$309$	1.00000	0.0568880
$310$	−5.81930	−0.330514
$311$	26.9328	1.52722	0.763609	−	0.645679i	$-0.223426\pi$
$311$	26.9328	1.52722	0.763609	+	0.645679i	$0.223426\pi$
$312$	−1.00000	−0.0566139
$313$	−11.8809	−0.671550	−0.335775	−	0.941942i	$-0.608998\pi$
$313$	−11.8809	−0.671550	−0.335775	+	0.941942i	$0.608998\pi$
$314$	−18.8897	−1.06601
$315$	−6.37461	−0.359168
$316$	−1.00405	−0.0564821
$317$	18.5287	1.04067	0.520337	−	0.853961i	$-0.325806\pi$
$317$	18.5287	1.04067	0.520337	+	0.853961i	$0.325806\pi$
$318$	8.80361	0.493682
$319$	15.2682	0.854854
$320$	1.40775	0.0786954
$321$	−6.32459	−0.353004
$322$	35.9653	2.00427
$323$	7.57615	0.421548
$324$	1.00000	0.0555556
$325$	3.01825	0.167422
$326$	−16.1378	−0.893791
$327$	3.42711	0.189520
$328$	10.4366	0.576265
$329$	53.6322	2.95684
$330$	−3.50375	−0.192875
$331$	10.0084	0.550112	0.275056	−	0.961428i	$-0.411304\pi$
$331$	10.0084	0.550112	0.275056	+	0.961428i	$0.411304\pi$
$332$	−2.03579	−0.111729
$333$	9.38272	0.514170
$334$	−8.93841	−0.489088
$335$	−2.35119	−0.128459
$336$	4.52824	0.247036
$337$	5.00785	0.272795	0.136398	−	0.990654i	$-0.456448\pi$
$337$	5.00785	0.272795	0.136398	+	0.990654i	$0.456448\pi$
$338$	−1.00000	−0.0543928
$339$	−15.7386	−0.854806
$340$	4.58377	0.248590
$341$	−10.2886	−0.557157
$342$	−2.32675	−0.125816
$343$	−29.4559	−1.59047
$344$	11.2716	0.607724
$345$	−11.1809	−0.601962
$346$	−10.2742	−0.552345
$347$	27.8817	1.49677	0.748384	−	0.663266i	$-0.230830\pi$
$347$	27.8817	1.49677	0.748384	+	0.663266i	$0.230830\pi$
$348$	6.13450	0.328843
$349$	−26.4066	−1.41351	−0.706756	−	0.707458i	$-0.749842\pi$
$349$	−26.4066	−1.41351	−0.706756	+	0.707458i	$0.749842\pi$
$350$	−13.6674	−0.730551
$351$	1.00000	0.0533761
$352$	2.48891	0.132659
$353$	−22.6228	−1.20409	−0.602044	−	0.798463i	$-0.705647\pi$
$353$	−22.6228	−1.20409	−0.602044	+	0.798463i	$0.705647\pi$
$354$	−1.56533	−0.0831965
$355$	11.4291	0.606596
$356$	8.03751	0.425987
$357$	14.7444	0.780357
$358$	1.84948	0.0977482
$359$	−32.4794	−1.71420	−0.857099	−	0.515152i	$-0.827735\pi$
$359$	−32.4794	−1.71420	−0.857099	+	0.515152i	$0.827735\pi$
$360$	−1.40775	−0.0741947
$361$	−13.5862	−0.715064
$362$	13.1117	0.689135
$363$	4.80535	0.252215
$364$	4.52824	0.237344
$365$	11.6015	0.607253
$366$	9.79962	0.512235
$367$	0.603926	0.0315247	0.0157624	−	0.999876i	$-0.494982\pi$
$367$	0.603926	0.0315247	0.0157624	+	0.999876i	$0.494982\pi$
$368$	7.94245	0.414029
$369$	−10.4366	−0.543308
$370$	−13.2085	−0.686677
$371$	−39.8649	−2.06968
$372$	−4.13377	−0.214326
$373$	24.4688	1.26694	0.633472	−	0.773765i	$-0.281629\pi$
$373$	24.4688	1.26694	0.633472	+	0.773765i	$0.281629\pi$
$374$	8.10413	0.419055
$375$	11.2877	0.582892
$376$	11.8439	0.610804
$377$	6.13450	0.315943
$378$	−4.52824	−0.232907
$379$	−18.5001	−0.950287	−0.475143	−	0.879908i	$-0.657604\pi$
$379$	−18.5001	−0.950287	−0.475143	+	0.879908i	$0.657604\pi$
$380$	3.27548	0.168028
$381$	16.5723	0.849023
$382$	−13.6919	−0.700541
$383$	−19.7840	−1.01091	−0.505457	−	0.862852i	$-0.668676\pi$
$383$	−19.7840	−1.01091	−0.505457	+	0.862852i	$0.668676\pi$
$384$	1.00000	0.0510310
$385$	15.8658	0.808596
$386$	26.3563	1.34150
$387$	−11.2716	−0.572968
$388$	9.30986	0.472637
$389$	6.49170	0.329142	0.164571	−	0.986365i	$-0.447376\pi$
$389$	6.49170	0.329142	0.164571	+	0.986365i	$0.447376\pi$
$390$	−1.40775	−0.0712840
$391$	25.8614	1.30787
$392$	−13.5049	−0.682102
$393$	17.0821	0.861676
$394$	15.1038	0.760919
$395$	−1.41344	−0.0711181
$396$	−2.48891	−0.125072
$397$	18.6334	0.935185	0.467592	−	0.883944i	$-0.345122\pi$
$397$	18.6334	0.935185	0.467592	+	0.883944i	$0.345122\pi$
$398$	6.34126	0.317859
$399$	10.5361	0.527464
$400$	−3.01825	−0.150913
$401$	−12.8013	−0.639265	−0.319633	−	0.947542i	$-0.603560\pi$
$401$	−12.8013	−0.639265	−0.319633	+	0.947542i	$0.603560\pi$
$402$	−1.67018	−0.0833011
$403$	−4.13377	−0.205918
$404$	9.65272	0.480241
$405$	1.40775	0.0699515
$406$	−27.7785	−1.37862
$407$	−23.3527	−1.15755
$408$	3.25610	0.161201
$409$	−19.2507	−0.951886	−0.475943	−	0.879476i	$-0.657893\pi$
$409$	−19.2507	−0.951886	−0.475943	+	0.879476i	$0.657893\pi$
$410$	14.6921	0.725591
$411$	11.6264	0.573487
$412$	−1.00000	−0.0492665
$413$	7.08820	0.348788
$414$	−7.94245	−0.390350
$415$	−2.86588	−0.140680
$416$	1.00000	0.0490290
$417$	8.47436	0.414991
$418$	5.79107	0.283251
$419$	14.1482	0.691186	0.345593	−	0.938385i	$-0.387678\pi$
$419$	14.1482	0.691186	0.345593	+	0.938385i	$0.387678\pi$
$420$	6.37461	0.311049
$421$	−37.4109	−1.82330	−0.911648	−	0.410971i	$-0.865190\pi$
$421$	−37.4109	−1.82330	−0.911648	+	0.410971i	$0.865190\pi$
$422$	−0.649989	−0.0316410
$423$	−11.8439	−0.575872
$424$	−8.80361	−0.427541
$425$	−9.82773	−0.476715
$426$	8.11876	0.393355
$427$	−44.3750	−2.14746
$428$	6.32459	0.305711
$429$	−2.48891	−0.120166
$430$	15.8676	0.765201
$431$	−16.0642	−0.773787	−0.386893	−	0.922124i	$-0.626452\pi$
$431$	−16.0642	−0.773787	−0.386893	+	0.922124i	$0.626452\pi$
$432$	−1.00000	−0.0481125
$433$	4.44935	0.213822	0.106911	−	0.994269i	$-0.465904\pi$
$433$	4.44935	0.213822	0.106911	+	0.994269i	$0.465904\pi$
$434$	18.7187	0.898527
$435$	8.63581	0.414055
$436$	−3.42711	−0.164129
$437$	18.4801	0.884024
$438$	8.24122	0.393781
$439$	−24.6863	−1.17821	−0.589106	−	0.808056i	$-0.700520\pi$
$439$	−24.6863	−1.17821	−0.589106	+	0.808056i	$0.700520\pi$
$440$	3.50375	0.167035
$441$	13.5049	0.643092
$442$	3.25610	0.154877
$443$	30.5010	1.44915	0.724573	−	0.689198i	$-0.242037\pi$
$443$	30.5010	1.44915	0.724573	+	0.689198i	$0.242037\pi$
$444$	−9.38272	−0.445284
$445$	11.3148	0.536371
$446$	7.48778	0.354557
$447$	17.4106	0.823492
$448$	−4.52824	−0.213939
$449$	−5.26344	−0.248397	−0.124198	−	0.992257i	$-0.539636\pi$
$449$	−5.26344	−0.248397	−0.124198	+	0.992257i	$0.539636\pi$
$450$	3.01825	0.142282
$451$	25.9757	1.22315
$452$	15.7386	0.740284
$453$	−9.64889	−0.453344
$454$	−27.4371	−1.28769
$455$	6.37461	0.298846
$456$	2.32675	0.108960
$457$	−36.3597	−1.70084	−0.850418	−	0.526108i	$-0.823651\pi$
$457$	−36.3597	−1.70084	−0.850418	+	0.526108i	$0.823651\pi$
$458$	0.703845	0.0328885
$459$	−3.25610	−0.151982
$460$	11.1809	0.521314
$461$	−33.4847	−1.55954	−0.779768	−	0.626068i	$-0.784663\pi$
$461$	−33.4847	−1.55954	−0.779768	+	0.626068i	$0.784663\pi$
$462$	11.2704	0.524344
$463$	−35.4150	−1.64587	−0.822937	−	0.568133i	$-0.807666\pi$
$463$	−35.4150	−1.64587	−0.822937	+	0.568133i	$0.807666\pi$
$464$	−6.13450	−0.284787
$465$	−5.81930	−0.269864
$466$	−15.8083	−0.732307
$467$	−26.2721	−1.21573	−0.607863	−	0.794042i	$-0.707973\pi$
$467$	−26.2721	−1.21573	−0.607863	+	0.794042i	$0.707973\pi$
$468$	−1.00000	−0.0462250
$469$	7.56298	0.349226
$470$	16.6733	0.769080
$471$	−18.8897	−0.870393
$472$	1.56533	0.0720503
$473$	28.0540	1.28992
$474$	−1.00405	−0.0461175
$475$	−7.02273	−0.322225
$476$	−14.7444	−0.675809
$477$	8.80361	0.403090
$478$	−5.54584	−0.253661
$479$	21.9505	1.00294	0.501471	−	0.865174i	$-0.332792\pi$
$479$	21.9505	1.00294	0.501471	+	0.865174i	$0.332792\pi$
$480$	1.40775	0.0642545
$481$	−9.38272	−0.427815
$482$	0.771368	0.0351349
$483$	35.9653	1.63648
$484$	−4.80535	−0.218425
$485$	13.1059	0.595109
$486$	1.00000	0.0453609
$487$	1.20736	0.0547107	0.0273553	−	0.999626i	$-0.491291\pi$
$487$	1.20736	0.0547107	0.0273553	+	0.999626i	$0.491291\pi$
$488$	−9.79962	−0.443608
$489$	−16.1378	−0.729778
$490$	−19.0115	−0.858853
$491$	−15.6642	−0.706915	−0.353458	−	0.935451i	$-0.614994\pi$
$491$	−15.6642	−0.706915	−0.353458	+	0.935451i	$0.614994\pi$
$492$	10.4366	0.470519
$493$	−19.9745	−0.899608
$494$	2.32675	0.104686
$495$	−3.50375	−0.157482
$496$	4.13377	0.185612
$497$	−36.7637	−1.64908
$498$	−2.03579	−0.0912260
$499$	−19.8922	−0.890497	−0.445248	−	0.895407i	$-0.646885\pi$
$499$	−19.8922	−0.890497	−0.445248	+	0.895407i	$0.646885\pi$
$500$	−11.2877	−0.504800
$501$	−8.93841	−0.399339
$502$	20.9345	0.934351
$503$	−2.52100	−0.112406	−0.0562029	−	0.998419i	$-0.517899\pi$
$503$	−2.52100	−0.112406	−0.0562029	+	0.998419i	$0.517899\pi$
$504$	4.52824	0.201704
$505$	13.5886	0.604684
$506$	19.7680	0.878795
$507$	−1.00000	−0.0444116
$508$	−16.5723	−0.735275
$509$	9.02532	0.400040	0.200020	−	0.979792i	$-0.435899\pi$
$509$	9.02532	0.400040	0.200020	+	0.979792i	$0.435899\pi$
$510$	4.58377	0.202973
$511$	−37.3182	−1.65086
$512$	−1.00000	−0.0441942
$513$	−2.32675	−0.102729
$514$	10.1729	0.448707
$515$	−1.40775	−0.0620327
$516$	11.2716	0.496205
$517$	29.4784	1.29646
$518$	42.4872	1.86678
$519$	−10.2742	−0.450988
$520$	1.40775	0.0617337
$521$	14.8107	0.648868	0.324434	−	0.945908i	$-0.394826\pi$
$521$	14.8107	0.648868	0.324434	+	0.945908i	$0.394826\pi$
$522$	6.13450	0.268500
$523$	−4.76291	−0.208268	−0.104134	−	0.994563i	$-0.533207\pi$
$523$	−4.76291	−0.208268	−0.104134	+	0.994563i	$0.533207\pi$
$524$	−17.0821	−0.746233
$525$	−13.6674	−0.596492
$526$	19.5965	0.854446
$527$	13.4600	0.586326
$528$	2.48891	0.108316
$529$	40.0825	1.74272
$530$	−12.3933	−0.538328
$531$	−1.56533	−0.0679297
$532$	−10.5361	−0.456798
$533$	10.4366	0.452060
$534$	8.03751	0.347817
$535$	8.90342	0.384928
$536$	1.67018	0.0721409
$537$	1.84948	0.0798111
$538$	−4.11436	−0.177383
$539$	−33.6125	−1.44779
$540$	−1.40775	−0.0605797
$541$	9.70902	0.417423	0.208712	−	0.977977i	$-0.433073\pi$
$541$	9.70902	0.417423	0.208712	+	0.977977i	$0.433073\pi$
$542$	19.0088	0.816498
$543$	13.1117	0.562676
$544$	−3.25610	−0.139604
$545$	−4.82450	−0.206659
$546$	4.52824	0.193791
$547$	23.1259	0.988794	0.494397	−	0.869236i	$-0.335389\pi$
$547$	23.1259	0.988794	0.494397	+	0.869236i	$0.335389\pi$
$548$	−11.6264	−0.496655
$549$	9.79962	0.418238
$550$	−7.51214	−0.320319
$551$	−14.2735	−0.608070
$552$	7.94245	0.338053
$553$	4.54657	0.193340
$554$	−3.88739	−0.165159
$555$	−13.2085	−0.560669
$556$	−8.47436	−0.359393
$557$	11.2656	0.477341	0.238670	−	0.971101i	$-0.423288\pi$
$557$	11.2656	0.477341	0.238670	+	0.971101i	$0.423288\pi$
$558$	−4.13377	−0.174997
$559$	11.2716	0.476738
$560$	−6.37461	−0.269376
$561$	8.10413	0.342157
$562$	7.84531	0.330935
$563$	−0.244770	−0.0103158	−0.00515792	−	0.999987i	$-0.501642\pi$
$563$	−0.244770	−0.0103158	−0.00515792	+	0.999987i	$0.501642\pi$
$564$	11.8439	0.498720
$565$	22.1560	0.932111
$566$	19.6759	0.827040
$567$	−4.52824	−0.190168
$568$	−8.11876	−0.340655
$569$	−26.9097	−1.12811	−0.564057	−	0.825736i	$-0.690760\pi$
$569$	−26.9097	−1.12811	−0.564057	+	0.825736i	$0.690760\pi$
$570$	3.27548	0.137195
$571$	−23.8899	−0.999759	−0.499880	−	0.866095i	$-0.666622\pi$
$571$	−23.8899	−0.999759	−0.499880	+	0.866095i	$0.666622\pi$
$572$	2.48891	0.104066
$573$	−13.6919	−0.571989
$574$	−47.2595	−1.97257
$575$	−23.9723	−0.999714
$576$	1.00000	0.0416667
$577$	−20.0899	−0.836353	−0.418177	−	0.908366i	$-0.637331\pi$
$577$	−20.0899	−0.836353	−0.418177	+	0.908366i	$0.637331\pi$
$578$	6.39780	0.266113
$579$	26.3563	1.09533
$580$	−8.63581	−0.358583
$581$	9.21855	0.382450
$582$	9.30986	0.385906
$583$	−21.9114	−0.907476
$584$	−8.24122	−0.341024
$585$	−1.40775	−0.0582031
$586$	3.18381	0.131522
$587$	−10.8666	−0.448513	−0.224257	−	0.974530i	$-0.571995\pi$
$587$	−10.8666	−0.448513	−0.224257	+	0.974530i	$0.571995\pi$
$588$	−13.5049	−0.556934
$589$	9.61827	0.396314
$590$	2.20359	0.0907205
$591$	15.1038	0.621288
$592$	9.38272	0.385628
$593$	33.6570	1.38213	0.691065	−	0.722793i	$-0.257142\pi$
$593$	33.6570	1.38213	0.691065	+	0.722793i	$0.257142\pi$
$594$	−2.48891	−0.102121
$595$	−20.7564	−0.850928
$596$	−17.4106	−0.713165
$597$	6.34126	0.259531
$598$	7.94245	0.324791
$599$	−8.18411	−0.334394	−0.167197	−	0.985924i	$-0.553472\pi$
$599$	−8.18411	−0.334394	−0.167197	+	0.985924i	$0.553472\pi$
$600$	−3.01825	−0.123220
$601$	12.9740	0.529221	0.264610	−	0.964355i	$-0.414757\pi$
$601$	12.9740	0.529221	0.264610	+	0.964355i	$0.414757\pi$
$602$	−51.0405	−2.08026
$603$	−1.67018	−0.0680151
$604$	9.64889	0.392608
$605$	−6.76471	−0.275025
$606$	9.65272	0.392115
$607$	35.0313	1.42188	0.710939	−	0.703254i	$-0.248270\pi$
$607$	35.0313	1.42188	0.710939	+	0.703254i	$0.248270\pi$
$608$	−2.32675	−0.0943623
$609$	−27.7785	−1.12564
$610$	−13.7954	−0.558559
$611$	11.8439	0.479154
$612$	3.25610	0.131620
$613$	36.7852	1.48574	0.742870	−	0.669435i	$-0.233464\pi$
$613$	36.7852	1.48574	0.742870	+	0.669435i	$0.233464\pi$
$614$	33.2438	1.34161
$615$	14.6921	0.592443
$616$	−11.2704	−0.454096
$617$	−35.3306	−1.42236	−0.711178	−	0.703012i	$-0.751838\pi$
$617$	−35.3306	−1.42236	−0.711178	+	0.703012i	$0.751838\pi$
$618$	−1.00000	−0.0402259
$619$	−19.7354	−0.793232	−0.396616	−	0.917985i	$-0.629815\pi$
$619$	−19.7354	−0.793232	−0.396616	+	0.917985i	$0.629815\pi$
$620$	5.81930	0.233709
$621$	−7.94245	−0.318719
$622$	−26.9328	−1.07991
$623$	−36.3957	−1.45816
$624$	1.00000	0.0400320
$625$	−0.798906	−0.0319562
$626$	11.8809	0.474858
$627$	5.79107	0.231273
$628$	18.8897	0.753782
$629$	30.5511	1.21815
$630$	6.37461	0.253970
$631$	46.1023	1.83530	0.917652	−	0.397385i	$-0.130082\pi$
$631$	46.1023	1.83530	0.917652	+	0.397385i	$0.130082\pi$
$632$	1.00405	0.0399389
$633$	−0.649989	−0.0258348
$634$	−18.5287	−0.735868
$635$	−23.3295	−0.925804
$636$	−8.80361	−0.349086
$637$	−13.5049	−0.535085
$638$	−15.2682	−0.604473
$639$	8.11876	0.321173
$640$	−1.40775	−0.0556460
$641$	44.6536	1.76371	0.881855	−	0.471521i	$-0.156295\pi$
$641$	44.6536	1.76371	0.881855	+	0.471521i	$0.156295\pi$
$642$	6.32459	0.249612
$643$	−24.6802	−0.973294	−0.486647	−	0.873599i	$-0.661780\pi$
$643$	−24.6802	−0.973294	−0.486647	+	0.873599i	$0.661780\pi$
$644$	−35.9653	−1.41723
$645$	15.8676	0.624784
$646$	−7.57615	−0.298080
$647$	−13.7435	−0.540311	−0.270156	−	0.962817i	$-0.587075\pi$
$647$	−13.7435	−0.540311	−0.270156	+	0.962817i	$0.587075\pi$
$648$	−1.00000	−0.0392837
$649$	3.89597	0.152930
$650$	−3.01825	−0.118386
$651$	18.7187	0.733644
$652$	16.1378	0.632006
$653$	−17.5295	−0.685981	−0.342991	−	0.939339i	$-0.611440\pi$
$653$	−17.5295	−0.685981	−0.342991	+	0.939339i	$0.611440\pi$
$654$	−3.42711	−0.134011
$655$	−24.0472	−0.939602
$656$	−10.4366	−0.407481
$657$	8.24122	0.321521
$658$	−53.6322	−2.09080
$659$	−9.68344	−0.377213	−0.188607	−	0.982053i	$-0.560397\pi$
$659$	−9.68344	−0.377213	−0.188607	+	0.982053i	$0.560397\pi$
$660$	3.50375	0.136383
$661$	35.5720	1.38359	0.691795	−	0.722094i	$-0.256820\pi$
$661$	35.5720	1.38359	0.691795	+	0.722094i	$0.256820\pi$
$662$	−10.0084	−0.388988
$663$	3.25610	0.126457
$664$	2.03579	0.0790040
$665$	−14.8321	−0.575166
$666$	−9.38272	−0.363573
$667$	−48.7229	−1.88656
$668$	8.93841	0.345838
$669$	7.48778	0.289494
$670$	2.35119	0.0908345
$671$	−24.3903	−0.941579
$672$	−4.52824	−0.174681
$673$	−30.1525	−1.16229	−0.581146	−	0.813799i	$-0.697396\pi$
$673$	−30.1525	−1.16229	−0.581146	+	0.813799i	$0.697396\pi$
$674$	−5.00785	−0.192895
$675$	3.01825	0.116173
$676$	1.00000	0.0384615
$677$	31.3430	1.20461	0.602305	−	0.798266i	$-0.294249\pi$
$677$	31.3430	1.20461	0.602305	+	0.798266i	$0.294249\pi$
$678$	15.7386	0.604439
$679$	−42.1573	−1.61785
$680$	−4.58377	−0.175779
$681$	−27.4371	−1.05139
$682$	10.2886	0.393970
$683$	−33.3095	−1.27455	−0.637276	−	0.770635i	$-0.719939\pi$
$683$	−33.3095	−1.27455	−0.637276	+	0.770635i	$0.719939\pi$
$684$	2.32675	0.0889656
$685$	−16.3670	−0.625351
$686$	29.4559	1.12463
$687$	0.703845	0.0268534
$688$	−11.2716	−0.429726
$689$	−8.80361	−0.335391
$690$	11.1809	0.425651
$691$	−37.7872	−1.43749	−0.718747	−	0.695272i	$-0.755284\pi$
$691$	−37.7872	−1.43749	−0.718747	+	0.695272i	$0.755284\pi$
$692$	10.2742	0.390567
$693$	11.2704	0.428125
$694$	−27.8817	−1.05837
$695$	−11.9297	−0.452521
$696$	−6.13450	−0.232527
$697$	−33.9827	−1.28719
$698$	26.4066	0.999504
$699$	−15.8083	−0.597926
$700$	13.6674	0.516578
$701$	−14.8434	−0.560628	−0.280314	−	0.959908i	$-0.590439\pi$
$701$	−14.8434	−0.560628	−0.280314	+	0.959908i	$0.590439\pi$
$702$	−1.00000	−0.0377426
$703$	21.8313	0.823383
$704$	−2.48891	−0.0938042
$705$	16.6733	0.627951
$706$	22.6228	0.851419
$707$	−43.7098	−1.64388
$708$	1.56533	0.0588288
$709$	−30.4942	−1.14523	−0.572617	−	0.819823i	$-0.694072\pi$
$709$	−30.4942	−1.14523	−0.572617	+	0.819823i	$0.694072\pi$
$710$	−11.4291	−0.428928
$711$	−1.00405	−0.0376547
$712$	−8.03751	−0.301218
$713$	32.8323	1.22958
$714$	−14.7444	−0.551795
$715$	3.50375	0.131033
$716$	−1.84948	−0.0691184
$717$	−5.54584	−0.207113
$718$	32.4794	1.21212
$719$	−9.22692	−0.344106	−0.172053	−	0.985088i	$-0.555040\pi$
$719$	−9.22692	−0.344106	−0.172053	+	0.985088i	$0.555040\pi$
$720$	1.40775	0.0524636
$721$	4.52824	0.168640
$722$	13.5862	0.505627
$723$	0.771368	0.0286875
$724$	−13.1117	−0.487292
$725$	18.5154	0.687646
$726$	−4.80535	−0.178343
$727$	−50.5766	−1.87578	−0.937891	−	0.346931i	$-0.887224\pi$
$727$	−50.5766	−1.87578	−0.937891	+	0.346931i	$0.887224\pi$
$728$	−4.52824	−0.167828
$729$	1.00000	0.0370370
$730$	−11.6015	−0.429393
$731$	−36.7015	−1.35745
$732$	−9.79962	−0.362204
$733$	−19.6855	−0.727101	−0.363550	−	0.931575i	$-0.618436\pi$
$733$	−19.6855	−0.727101	−0.363550	+	0.931575i	$0.618436\pi$
$734$	−0.603926	−0.0222913
$735$	−19.0115	−0.701250
$736$	−7.94245	−0.292763
$737$	4.15693	0.153122
$738$	10.4366	0.384177
$739$	−52.6776	−1.93778	−0.968888	−	0.247501i	$-0.920391\pi$
$739$	−52.6776	−1.93778	−0.968888	+	0.247501i	$0.920391\pi$
$740$	13.2085	0.485554
$741$	2.32675	0.0854754
$742$	39.8649	1.46348
$743$	−8.50526	−0.312028	−0.156014	−	0.987755i	$-0.549864\pi$
$743$	−8.50526	−0.312028	−0.156014	+	0.987755i	$0.549864\pi$
$744$	4.13377	0.151551
$745$	−24.5097	−0.897965
$746$	−24.4688	−0.895865
$747$	−2.03579	−0.0744857
$748$	−8.10413	−0.296316
$749$	−28.6393	−1.04646
$750$	−11.2877	−0.412167
$751$	20.3327	0.741950	0.370975	−	0.928643i	$-0.379024\pi$
$751$	20.3327	0.741950	0.370975	+	0.928643i	$0.379024\pi$
$752$	−11.8439	−0.431904
$753$	20.9345	0.762894
$754$	−6.13450	−0.223405
$755$	13.5832	0.494343
$756$	4.52824	0.164690
$757$	21.5319	0.782591	0.391295	−	0.920265i	$-0.372027\pi$
$757$	21.5319	0.782591	0.391295	+	0.920265i	$0.372027\pi$
$758$	18.5001	0.671954
$759$	19.7680	0.717533
$760$	−3.27548	−0.118814
$761$	42.2202	1.53048	0.765241	−	0.643744i	$-0.222620\pi$
$761$	42.2202	1.53048	0.765241	+	0.643744i	$0.222620\pi$
$762$	−16.5723	−0.600350
$763$	15.5188	0.561818
$764$	13.6919	0.495357
$765$	4.58377	0.165726
$766$	19.7840	0.714824
$767$	1.56533	0.0565209
$768$	−1.00000	−0.0360844
$769$	17.5221	0.631862	0.315931	−	0.948782i	$-0.397683\pi$
$769$	17.5221	0.631862	0.315931	+	0.948782i	$0.397683\pi$
$770$	−15.8658	−0.571764
$771$	10.1729	0.366367
$772$	−26.3563	−0.948584
$773$	6.40003	0.230193	0.115097	−	0.993354i	$-0.463282\pi$
$773$	6.40003	0.230193	0.115097	+	0.993354i	$0.463282\pi$
$774$	11.2716	0.405149
$775$	−12.4768	−0.448179
$776$	−9.30986	−0.334205
$777$	42.4872	1.52422
$778$	−6.49170	−0.232739
$779$	−24.2834	−0.870044
$780$	1.40775	0.0504054
$781$	−20.2068	−0.723057
$782$	−25.8614	−0.924803
$783$	6.13450	0.219229
$784$	13.5049	0.482319
$785$	26.5919	0.949107
$786$	−17.0821	−0.609297
$787$	24.0855	0.858557	0.429278	−	0.903172i	$-0.358768\pi$
$787$	24.0855	0.858557	0.429278	+	0.903172i	$0.358768\pi$
$788$	−15.1038	−0.538051
$789$	19.5965	0.697653
$790$	1.41344	0.0502881
$791$	−71.2683	−2.53401
$792$	2.48891	0.0884394
$793$	−9.79962	−0.347995
$794$	−18.6334	−0.661275
$795$	−12.3933	−0.439543
$796$	−6.34126	−0.224760
$797$	−52.7915	−1.86997	−0.934986	−	0.354686i	$-0.884588\pi$
$797$	−52.7915	−1.86997	−0.934986	+	0.354686i	$0.884588\pi$
$798$	−10.5361	−0.372974
$799$	−38.5651	−1.36433
$800$	3.01825	0.106711
$801$	8.03751	0.283991
$802$	12.8013	0.452029
$803$	−20.5116	−0.723840
$804$	1.67018	0.0589028
$805$	−50.6300	−1.78447
$806$	4.13377	0.145606
$807$	−4.11436	−0.144832
$808$	−9.65272	−0.339582
$809$	23.8079	0.837040	0.418520	−	0.908208i	$-0.362549\pi$
$809$	23.8079	0.837040	0.418520	+	0.908208i	$0.362549\pi$
$810$	−1.40775	−0.0494632
$811$	0.309763	0.0108773	0.00543863	−	0.999985i	$-0.498269\pi$
$811$	0.309763	0.0108773	0.00543863	+	0.999985i	$0.498269\pi$
$812$	27.7785	0.974832
$813$	19.0088	0.666668
$814$	23.3527	0.818512
$815$	22.7180	0.795775
$816$	−3.25610	−0.113986
$817$	−26.2262	−0.917540
$818$	19.2507	0.673085
$819$	4.52824	0.158229
$820$	−14.6921	−0.513070
$821$	41.7038	1.45547	0.727737	−	0.685856i	$-0.240572\pi$
$821$	41.7038	1.45547	0.727737	+	0.685856i	$0.240572\pi$
$822$	−11.6264	−0.405517
$823$	32.7698	1.14228	0.571141	−	0.820852i	$-0.306501\pi$
$823$	32.7698	1.14228	0.571141	+	0.820852i	$0.306501\pi$
$824$	1.00000	0.0348367
$825$	−7.51214	−0.261539
$826$	−7.08820	−0.246630
$827$	36.1626	1.25750	0.628748	−	0.777609i	$-0.283568\pi$
$827$	36.1626	1.25750	0.628748	+	0.777609i	$0.283568\pi$
$828$	7.94245	0.276019
$829$	−43.2159	−1.50095	−0.750476	−	0.660898i	$-0.770176\pi$
$829$	−43.2159	−1.50095	−0.750476	+	0.660898i	$0.770176\pi$
$830$	2.86588	0.0994760
$831$	−3.88739	−0.134852
$832$	−1.00000	−0.0346688
$833$	43.9734	1.52359
$834$	−8.47436	−0.293443
$835$	12.5830	0.435453
$836$	−5.79107	−0.200288
$837$	−4.13377	−0.142884
$838$	−14.1482	−0.488742
$839$	−31.4362	−1.08530	−0.542649	−	0.839960i	$-0.682579\pi$
$839$	−31.4362	−1.08530	−0.542649	+	0.839960i	$0.682579\pi$
$840$	−6.37461	−0.219945
$841$	8.63203	0.297656
$842$	37.4109	1.28927
$843$	7.84531	0.270207
$844$	0.649989	0.0223736
$845$	1.40775	0.0484279
$846$	11.8439	0.407203
$847$	21.7598	0.747674
$848$	8.80361	0.302317
$849$	19.6759	0.675275
$850$	9.82773	0.337088
$851$	74.5218	2.55457
$852$	−8.11876	−0.278144
$853$	21.1280	0.723410	0.361705	−	0.932293i	$-0.382195\pi$
$853$	21.1280	0.723410	0.361705	+	0.932293i	$0.382195\pi$
$854$	44.3750	1.51848
$855$	3.27548	0.112019
$856$	−6.32459	−0.216170
$857$	36.1033	1.23327	0.616633	−	0.787251i	$-0.288496\pi$
$857$	36.1033	1.23327	0.616633	+	0.787251i	$0.288496\pi$
$858$	2.48891	0.0849698
$859$	12.7114	0.433706	0.216853	−	0.976204i	$-0.430421\pi$
$859$	12.7114	0.433706	0.216853	+	0.976204i	$0.430421\pi$
$860$	−15.8676	−0.541079
$861$	−47.2595	−1.61060
$862$	16.0642	0.547150
$863$	3.80459	0.129510	0.0647548	−	0.997901i	$-0.479373\pi$
$863$	3.80459	0.129510	0.0647548	+	0.997901i	$0.479373\pi$
$864$	1.00000	0.0340207
$865$	14.4635	0.491773
$866$	−4.44935	−0.151195
$867$	6.39780	0.217281
$868$	−18.7187	−0.635354
$869$	2.49898	0.0847721
$870$	−8.63581	−0.292781
$871$	1.67018	0.0565920
$872$	3.42711	0.116057
$873$	9.30986	0.315091
$874$	−18.4801	−0.625099
$875$	51.1132	1.72794
$876$	−8.24122	−0.278445
$877$	−36.9952	−1.24924	−0.624619	−	0.780930i	$-0.714746\pi$
$877$	−36.9952	−1.24924	−0.624619	+	0.780930i	$0.714746\pi$
$878$	24.6863	0.833121
$879$	3.18381	0.107387
$880$	−3.50375	−0.118111
$881$	−2.10383	−0.0708797	−0.0354398	−	0.999372i	$-0.511283\pi$
$881$	−2.10383	−0.0708797	−0.0354398	+	0.999372i	$0.511283\pi$
$882$	−13.5049	−0.454735
$883$	2.67144	0.0899011	0.0449506	−	0.998989i	$-0.485687\pi$
$883$	2.67144	0.0899011	0.0449506	+	0.998989i	$0.485687\pi$
$884$	−3.25610	−0.109515
$885$	2.20359	0.0740729
$886$	−30.5010	−1.02470
$887$	−18.8854	−0.634109	−0.317054	−	0.948407i	$-0.602694\pi$
$887$	−18.8854	−0.634109	−0.317054	+	0.948407i	$0.602694\pi$
$888$	9.38272	0.314864
$889$	75.0431	2.51687
$890$	−11.3148	−0.379272
$891$	−2.48891	−0.0833815
$892$	−7.48778	−0.250709
$893$	−27.5579	−0.922191
$894$	−17.4106	−0.582297
$895$	−2.60360	−0.0870288
$896$	4.52824	0.151278
$897$	7.94245	0.265191
$898$	5.26344	0.175643
$899$	−25.3586	−0.845757
$900$	−3.01825	−0.100608
$901$	28.6655	0.954985
$902$	−25.9757	−0.864898
$903$	−51.0405	−1.69852
$904$	−15.7386	−0.523460
$905$	−18.4579	−0.613562
$906$	9.64889	0.320563
$907$	−28.1875	−0.935951	−0.467975	−	0.883742i	$-0.655016\pi$
$907$	−28.1875	−0.935951	−0.467975	+	0.883742i	$0.655016\pi$
$908$	27.4371	0.910531
$909$	9.65272	0.320161
$910$	−6.37461	−0.211316
$911$	−46.2895	−1.53364	−0.766820	−	0.641862i	$-0.778162\pi$
$911$	−46.2895	−1.53364	−0.766820	+	0.641862i	$0.778162\pi$
$912$	−2.32675	−0.0770465
$913$	5.06689	0.167690
$914$	36.3597	1.20267
$915$	−13.7954	−0.456061
$916$	−0.703845	−0.0232557
$917$	77.3516	2.55437
$918$	3.25610	0.107467
$919$	0.734715	0.0242360	0.0121180	−	0.999927i	$-0.496143\pi$
$919$	0.734715	0.0242360	0.0121180	+	0.999927i	$0.496143\pi$
$920$	−11.1809	−0.368625
$921$	33.2438	1.09542
$922$	33.4847	1.10276
$923$	−8.11876	−0.267232
$924$	−11.2704	−0.370768
$925$	−28.3194	−0.931137
$926$	35.4150	1.16381
$927$	−1.00000	−0.0328443
$928$	6.13450	0.201375
$929$	−42.9635	−1.40959	−0.704793	−	0.709413i	$-0.748960\pi$
$929$	−42.9635	−1.40959	−0.704793	+	0.709413i	$0.748960\pi$
$930$	5.81930	0.190822
$931$	31.4227	1.02984
$932$	15.8083	0.517819
$933$	−26.9328	−0.881739
$934$	26.2721	0.859649
$935$	−11.4086	−0.373100
$936$	1.00000	0.0326860
$937$	24.7032	0.807018	0.403509	−	0.914976i	$-0.367790\pi$
$937$	24.7032	0.807018	0.403509	+	0.914976i	$0.367790\pi$
$938$	−7.56298	−0.246940
$939$	11.8809	0.387720
$940$	−16.6733	−0.543822
$941$	−29.5958	−0.964795	−0.482398	−	0.875952i	$-0.660234\pi$
$941$	−29.5958	−0.964795	−0.482398	+	0.875952i	$0.660234\pi$
$942$	18.8897	0.615461
$943$	−82.8922	−2.69934
$944$	−1.56533	−0.0509473
$945$	6.37461	0.207366
$946$	−28.0540	−0.912113
$947$	6.81104	0.221329	0.110665	−	0.993858i	$-0.464702\pi$
$947$	6.81104	0.221329	0.110665	+	0.993858i	$0.464702\pi$
$948$	1.00405	0.0326100
$949$	−8.24122	−0.267521
$950$	7.02273	0.227847
$951$	−18.5287	−0.600833
$952$	14.7444	0.477869
$953$	−11.4702	−0.371556	−0.185778	−	0.982592i	$-0.559480\pi$
$953$	−11.4702	−0.371556	−0.185778	+	0.982592i	$0.559480\pi$
$954$	−8.80361	−0.285028
$955$	19.2748	0.623718
$956$	5.54584	0.179365
$957$	−15.2682	−0.493550
$958$	−21.9505	−0.709187
$959$	52.6470	1.70006
$960$	−1.40775	−0.0454348
$961$	−13.9119	−0.448772
$962$	9.38272	0.302511
$963$	6.32459	0.203807
$964$	−0.771368	−0.0248441
$965$	−37.1030	−1.19439
$966$	−35.9653	−1.15716
$967$	39.6882	1.27629	0.638143	−	0.769918i	$-0.279703\pi$
$967$	39.6882	1.27629	0.638143	+	0.769918i	$0.279703\pi$
$968$	4.80535	0.154450
$969$	−7.57615	−0.243381
$970$	−13.1059	−0.420806
$971$	27.7101	0.889258	0.444629	−	0.895715i	$-0.353336\pi$
$971$	27.7101	0.889258	0.444629	+	0.895715i	$0.353336\pi$
$972$	−1.00000	−0.0320750
$973$	38.3739	1.23021
$974$	−1.20736	−0.0386863
$975$	−3.01825	−0.0966614
$976$	9.79962	0.313678
$977$	−6.58047	−0.210528	−0.105264	−	0.994444i	$-0.533569\pi$
$977$	−6.58047	−0.210528	−0.105264	+	0.994444i	$0.533569\pi$
$978$	16.1378	0.516031
$979$	−20.0046	−0.639350
$980$	19.0115	0.607301
$981$	−3.42711	−0.109419
$982$	15.6642	0.499865
$983$	42.6736	1.36108	0.680539	−	0.732712i	$-0.261746\pi$
$983$	42.6736	1.36108	0.680539	+	0.732712i	$0.261746\pi$
$984$	−10.4366	−0.332707
$985$	−21.2623	−0.677474
$986$	19.9745	0.636119
$987$	−53.6322	−1.70713
$988$	−2.32675	−0.0740239
$989$	−89.5241	−2.84670
$990$	3.50375	0.111356
$991$	3.90624	0.124086	0.0620429	−	0.998073i	$-0.480238\pi$
$991$	3.90624	0.124086	0.0620429	+	0.998073i	$0.480238\pi$
$992$	−4.13377	−0.131247
$993$	−10.0084	−0.317607
$994$	36.7637	1.16607
$995$	−8.92689	−0.283001
$996$	2.03579	0.0645065
$997$	−19.2076	−0.608311	−0.304156	−	0.952622i	$-0.598374\pi$
$997$	−19.2076	−0.608311	−0.304156	+	0.952622i	$0.598374\pi$
$998$	19.8922	0.629676
$999$	−9.38272	−0.296856

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8034.2.a.s.1.6	✓	10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8034.2.a.s.1.6	✓	10	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 8034 = 2 \cdot 3 \cdot 13 \cdot 103 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8034.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +1.40775 q^{5} +1.00000 q^{6} -4.52824 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +1.40775 q^{5} +1.00000 q^{6} -4.52824 q^{7} -1.00000 q^{8} +1.00000 q^{9} -1.40775 q^{10} -2.48891 q^{11} -1.00000 q^{12} -1.00000 q^{13} +4.52824 q^{14} -1.40775 q^{15} +1.00000 q^{16} +3.25610 q^{17} -1.00000 q^{18} +2.32675 q^{19} +1.40775 q^{20} +4.52824 q^{21} +2.48891 q^{22} +7.94245 q^{23} +1.00000 q^{24} -3.01825 q^{25} +1.00000 q^{26} -1.00000 q^{27} -4.52824 q^{28} -6.13450 q^{29} +1.40775 q^{30} +4.13377 q^{31} -1.00000 q^{32} +2.48891 q^{33} -3.25610 q^{34} -6.37461 q^{35} +1.00000 q^{36} +9.38272 q^{37} -2.32675 q^{38} +1.00000 q^{39} -1.40775 q^{40} -10.4366 q^{41} -4.52824 q^{42} -11.2716 q^{43} -2.48891 q^{44} +1.40775 q^{45} -7.94245 q^{46} -11.8439 q^{47} -1.00000 q^{48} +13.5049 q^{49} +3.01825 q^{50} -3.25610 q^{51} -1.00000 q^{52} +8.80361 q^{53} +1.00000 q^{54} -3.50375 q^{55} +4.52824 q^{56} -2.32675 q^{57} +6.13450 q^{58} -1.56533 q^{59} -1.40775 q^{60} +9.79962 q^{61} -4.13377 q^{62} -4.52824 q^{63} +1.00000 q^{64} -1.40775 q^{65} -2.48891 q^{66} -1.67018 q^{67} +3.25610 q^{68} -7.94245 q^{69} +6.37461 q^{70} +8.11876 q^{71} -1.00000 q^{72} +8.24122 q^{73} -9.38272 q^{74} +3.01825 q^{75} +2.32675 q^{76} +11.2704 q^{77} -1.00000 q^{78} -1.00405 q^{79} +1.40775 q^{80} +1.00000 q^{81} +10.4366 q^{82} -2.03579 q^{83} +4.52824 q^{84} +4.58377 q^{85} +11.2716 q^{86} +6.13450 q^{87} +2.48891 q^{88} +8.03751 q^{89} -1.40775 q^{90} +4.52824 q^{91} +7.94245 q^{92} -4.13377 q^{93} +11.8439 q^{94} +3.27548 q^{95} +1.00000 q^{96} +9.30986 q^{97} -13.5049 q^{98} -2.48891 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - 10 q^{2} - 10 q^{3} + 10 q^{4} + 6 q^{5} + 10 q^{6} - 9 q^{7} - 10 q^{8} + 10 q^{9}+O(q^{10}) \) 10 * q - 10 * q^2 - 10 * q^3 + 10 * q^4 + 6 * q^5 + 10 * q^6 - 9 * q^7 - 10 * q^8 + 10 * q^9	\( 10 q - 10 q^{2} - 10 q^{3} + 10 q^{4} + 6 q^{5} + 10 q^{6} - 9 q^{7} - 10 q^{8} + 10 q^{9} - 6 q^{10} - q^{11} - 10 q^{12} - 10 q^{13} + 9 q^{14} - 6 q^{15} + 10 q^{16} + 5 q^{17} - 10 q^{18} - 9 q^{19} + 6 q^{20} + 9 q^{21} + q^{22} + q^{23} + 10 q^{24} + 20 q^{25} + 10 q^{26} - 10 q^{27} - 9 q^{28} - 22 q^{29} + 6 q^{30} - 13 q^{31} - 10 q^{32} + q^{33} - 5 q^{34} + 14 q^{35} + 10 q^{36} + 10 q^{37} + 9 q^{38} + 10 q^{39} - 6 q^{40} - 18 q^{41} - 9 q^{42} + 10 q^{43} - q^{44} + 6 q^{45} - q^{46} + 28 q^{47} - 10 q^{48} + 11 q^{49} - 20 q^{50} - 5 q^{51} - 10 q^{52} + 6 q^{53} + 10 q^{54} - 26 q^{55} + 9 q^{56} + 9 q^{57} + 22 q^{58} + 7 q^{59} - 6 q^{60} - 20 q^{61} + 13 q^{62} - 9 q^{63} + 10 q^{64} - 6 q^{65} - q^{66} - 21 q^{67} + 5 q^{68} - q^{69} - 14 q^{70} - 19 q^{71} - 10 q^{72} + 3 q^{73} - 10 q^{74} - 20 q^{75} - 9 q^{76} + 28 q^{77} - 10 q^{78} - 11 q^{79} + 6 q^{80} + 10 q^{81} + 18 q^{82} + 20 q^{83} + 9 q^{84} - q^{85} - 10 q^{86} + 22 q^{87} + q^{88} + 22 q^{89} - 6 q^{90} + 9 q^{91} + q^{92} + 13 q^{93} - 28 q^{94} + 10 q^{96} - 10 q^{97} - 11 q^{98} - q^{99}+O(q^{100}) \) 10 * q - 10 * q^2 - 10 * q^3 + 10 * q^4 + 6 * q^5 + 10 * q^6 - 9 * q^7 - 10 * q^8 + 10 * q^9 - 6 * q^10 - q^11 - 10 * q^12 - 10 * q^13 + 9 * q^14 - 6 * q^15 + 10 * q^16 + 5 * q^17 - 10 * q^18 - 9 * q^19 + 6 * q^20 + 9 * q^21 + q^22 + q^23 + 10 * q^24 + 20 * q^25 + 10 * q^26 - 10 * q^27 - 9 * q^28 - 22 * q^29 + 6 * q^30 - 13 * q^31 - 10 * q^32 + q^33 - 5 * q^34 + 14 * q^35 + 10 * q^36 + 10 * q^37 + 9 * q^38 + 10 * q^39 - 6 * q^40 - 18 * q^41 - 9 * q^42 + 10 * q^43 - q^44 + 6 * q^45 - q^46 + 28 * q^47 - 10 * q^48 + 11 * q^49 - 20 * q^50 - 5 * q^51 - 10 * q^52 + 6 * q^53 + 10 * q^54 - 26 * q^55 + 9 * q^56 + 9 * q^57 + 22 * q^58 + 7 * q^59 - 6 * q^60 - 20 * q^61 + 13 * q^62 - 9 * q^63 + 10 * q^64 - 6 * q^65 - q^66 - 21 * q^67 + 5 * q^68 - q^69 - 14 * q^70 - 19 * q^71 - 10 * q^72 + 3 * q^73 - 10 * q^74 - 20 * q^75 - 9 * q^76 + 28 * q^77 - 10 * q^78 - 11 * q^79 + 6 * q^80 + 10 * q^81 + 18 * q^82 + 20 * q^83 + 9 * q^84 - q^85 - 10 * q^86 + 22 * q^87 + q^88 + 22 * q^89 - 6 * q^90 + 9 * q^91 + q^92 + 13 * q^93 - 28 * q^94 + 10 * q^96 - 10 * q^97 - 11 * q^98 - q^99

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