LMFDB - Embedded newform 8042.2.a.c.1.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8042,2,Mod(1,8042)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8042, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("8042.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8042 = 2 \cdot 4021 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8042.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:	$64.2156933055$
Analytic rank:	$0$
Dimension:	$86$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.9
Character	$\chi$	$=$	8042.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -2.54862 q^{3} +1.00000 q^{4} -1.05969 q^{5} +2.54862 q^{6} -0.366146 q^{7} -1.00000 q^{8} +3.49545 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -2.54862 q^{3} +1.00000 q^{4} -1.05969 q^{5} +2.54862 q^{6} -0.366146 q^{7} -1.00000 q^{8} +3.49545 q^{9} +1.05969 q^{10} -0.330498 q^{11} -2.54862 q^{12} -2.15141 q^{13} +0.366146 q^{14} +2.70075 q^{15} +1.00000 q^{16} +2.98970 q^{17} -3.49545 q^{18} -8.00967 q^{19} -1.05969 q^{20} +0.933166 q^{21} +0.330498 q^{22} -7.06260 q^{23} +2.54862 q^{24} -3.87705 q^{25} +2.15141 q^{26} -1.26271 q^{27} -0.366146 q^{28} -2.43858 q^{29} -2.70075 q^{30} -8.65756 q^{31} -1.00000 q^{32} +0.842314 q^{33} -2.98970 q^{34} +0.388002 q^{35} +3.49545 q^{36} -6.23500 q^{37} +8.00967 q^{38} +5.48312 q^{39} +1.05969 q^{40} +5.24599 q^{41} -0.933166 q^{42} +8.94270 q^{43} -0.330498 q^{44} -3.70410 q^{45} +7.06260 q^{46} -2.67032 q^{47} -2.54862 q^{48} -6.86594 q^{49} +3.87705 q^{50} -7.61961 q^{51} -2.15141 q^{52} -9.83026 q^{53} +1.26271 q^{54} +0.350226 q^{55} +0.366146 q^{56} +20.4136 q^{57} +2.43858 q^{58} +8.95349 q^{59} +2.70075 q^{60} -3.72746 q^{61} +8.65756 q^{62} -1.27985 q^{63} +1.00000 q^{64} +2.27983 q^{65} -0.842314 q^{66} +13.8648 q^{67} +2.98970 q^{68} +17.9999 q^{69} -0.388002 q^{70} -6.95344 q^{71} -3.49545 q^{72} -15.4340 q^{73} +6.23500 q^{74} +9.88112 q^{75} -8.00967 q^{76} +0.121011 q^{77} -5.48312 q^{78} +5.74110 q^{79} -1.05969 q^{80} -7.26818 q^{81} -5.24599 q^{82} -4.36949 q^{83} +0.933166 q^{84} -3.16817 q^{85} -8.94270 q^{86} +6.21500 q^{87} +0.330498 q^{88} -0.774967 q^{89} +3.70410 q^{90} +0.787730 q^{91} -7.06260 q^{92} +22.0648 q^{93} +2.67032 q^{94} +8.48779 q^{95} +2.54862 q^{96} -6.51475 q^{97} +6.86594 q^{98} -1.15524 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 86 q - 86 q^{2} + 12 q^{3} + 86 q^{4} - 4 q^{5} - 12 q^{6} + 35 q^{7} - 86 q^{8} + 72 q^{9}+O(q^{10}) $ 86 * q - 86 * q^2 + 12 * q^3 + 86 * q^4 - 4 * q^5 - 12 * q^6 + 35 * q^7 - 86 * q^8 + 72 * q^9	\( 86 q - 86 q^{2} + 12 q^{3} + 86 q^{4} - 4 q^{5} - 12 q^{6} + 35 q^{7} - 86 q^{8} + 72 q^{9} + 4 q^{10} + 13 q^{11} + 12 q^{12} + 45 q^{13} - 35 q^{14} + 17 q^{15} + 86 q^{16} + 5 q^{17} - 72 q^{18} + 47 q^{19} - 4 q^{20} + 15 q^{21} - 13 q^{22} + 6 q^{23} - 12 q^{24} + 112 q^{25} - 45 q^{26} + 51 q^{27} + 35 q^{28} - 14 q^{29} - 17 q^{30} + 24 q^{31} - 86 q^{32} + 43 q^{33} - 5 q^{34} + 42 q^{35} + 72 q^{36} + 61 q^{37} - 47 q^{38} + 20 q^{39} + 4 q^{40} - 16 q^{41} - 15 q^{42} + 72 q^{43} + 13 q^{44} + 6 q^{45} - 6 q^{46} + 11 q^{47} + 12 q^{48} + 89 q^{49} - 112 q^{50} + 56 q^{51} + 45 q^{52} - 7 q^{53} - 51 q^{54} + 48 q^{55} - 35 q^{56} + 65 q^{57} + 14 q^{58} + 24 q^{59} + 17 q^{60} + 31 q^{61} - 24 q^{62} + 98 q^{63} + 86 q^{64} - 9 q^{65} - 43 q^{66} + 157 q^{67} + 5 q^{68} + q^{69} - 42 q^{70} - 11 q^{71} - 72 q^{72} + 74 q^{73} - 61 q^{74} + 76 q^{75} + 47 q^{76} - 13 q^{77} - 20 q^{78} + 57 q^{79} - 4 q^{80} + 34 q^{81} + 16 q^{82} + 65 q^{83} + 15 q^{84} + 102 q^{85} - 72 q^{86} + 49 q^{87} - 13 q^{88} - 34 q^{89} - 6 q^{90} + 91 q^{91} + 6 q^{92} + 57 q^{93} - 11 q^{94} - 13 q^{95} - 12 q^{96} + 64 q^{97} - 89 q^{98} + 56 q^{99}+O(q^{100}) \) 86 * q - 86 * q^2 + 12 * q^3 + 86 * q^4 - 4 * q^5 - 12 * q^6 + 35 * q^7 - 86 * q^8 + 72 * q^9 + 4 * q^10 + 13 * q^11 + 12 * q^12 + 45 * q^13 - 35 * q^14 + 17 * q^15 + 86 * q^16 + 5 * q^17 - 72 * q^18 + 47 * q^19 - 4 * q^20 + 15 * q^21 - 13 * q^22 + 6 * q^23 - 12 * q^24 + 112 * q^25 - 45 * q^26 + 51 * q^27 + 35 * q^28 - 14 * q^29 - 17 * q^30 + 24 * q^31 - 86 * q^32 + 43 * q^33 - 5 * q^34 + 42 * q^35 + 72 * q^36 + 61 * q^37 - 47 * q^38 + 20 * q^39 + 4 * q^40 - 16 * q^41 - 15 * q^42 + 72 * q^43 + 13 * q^44 + 6 * q^45 - 6 * q^46 + 11 * q^47 + 12 * q^48 + 89 * q^49 - 112 * q^50 + 56 * q^51 + 45 * q^52 - 7 * q^53 - 51 * q^54 + 48 * q^55 - 35 * q^56 + 65 * q^57 + 14 * q^58 + 24 * q^59 + 17 * q^60 + 31 * q^61 - 24 * q^62 + 98 * q^63 + 86 * q^64 - 9 * q^65 - 43 * q^66 + 157 * q^67 + 5 * q^68 + q^69 - 42 * q^70 - 11 * q^71 - 72 * q^72 + 74 * q^73 - 61 * q^74 + 76 * q^75 + 47 * q^76 - 13 * q^77 - 20 * q^78 + 57 * q^79 - 4 * q^80 + 34 * q^81 + 16 * q^82 + 65 * q^83 + 15 * q^84 + 102 * q^85 - 72 * q^86 + 49 * q^87 - 13 * q^88 - 34 * q^89 - 6 * q^90 + 91 * q^91 + 6 * q^92 + 57 * q^93 - 11 * q^94 - 13 * q^95 - 12 * q^96 + 64 * q^97 - 89 * q^98 + 56 * 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
$3$	−2.54862	−1.47144	−0.735722	−	0.677283i	$-0.763157\pi$
$3$	−2.54862	−1.47144	−0.735722	+	0.677283i	$0.763157\pi$
$4$	1.00000	0.500000
$5$	−1.05969	−0.473909	−0.236954	−	0.971521i	$-0.576149\pi$
$5$	−1.05969	−0.473909	−0.236954	+	0.971521i	$0.576149\pi$
$6$	2.54862	1.04047
$7$	−0.366146	−0.138390	−0.0691951	−	0.997603i	$-0.522043\pi$
$7$	−0.366146	−0.138390	−0.0691951	+	0.997603i	$0.522043\pi$
$8$	−1.00000	−0.353553
$9$	3.49545	1.16515
$10$	1.05969	0.335104
$11$	−0.330498	−0.0996490	−0.0498245	−	0.998758i	$-0.515866\pi$
$11$	−0.330498	−0.0996490	−0.0498245	+	0.998758i	$0.515866\pi$
$12$	−2.54862	−0.735722
$13$	−2.15141	−0.596694	−0.298347	−	0.954458i	$-0.596435\pi$
$13$	−2.15141	−0.596694	−0.298347	+	0.954458i	$0.596435\pi$
$14$	0.366146	0.0978567
$15$	2.70075	0.697331
$16$	1.00000	0.250000
$17$	2.98970	0.725109	0.362555	−	0.931962i	$-0.381905\pi$
$17$	2.98970	0.725109	0.362555	+	0.931962i	$0.381905\pi$
$18$	−3.49545	−0.823886
$19$	−8.00967	−1.83754	−0.918772	−	0.394788i	$-0.870818\pi$
$19$	−8.00967	−1.83754	−0.918772	+	0.394788i	$0.870818\pi$
$20$	−1.05969	−0.236954
$21$	0.933166	0.203634
$22$	0.330498	0.0704625
$23$	−7.06260	−1.47265	−0.736327	−	0.676626i	$-0.763441\pi$
$23$	−7.06260	−1.47265	−0.736327	+	0.676626i	$0.763441\pi$
$24$	2.54862	0.520234
$25$	−3.87705	−0.775410
$26$	2.15141	0.421926
$27$	−1.26271	−0.243009
$28$	−0.366146	−0.0691951
$29$	−2.43858	−0.452832	−0.226416	−	0.974031i	$-0.572701\pi$
$29$	−2.43858	−0.452832	−0.226416	+	0.974031i	$0.572701\pi$
$30$	−2.70075	−0.493087
$31$	−8.65756	−1.55494	−0.777472	−	0.628917i	$-0.783498\pi$
$31$	−8.65756	−1.55494	−0.777472	+	0.628917i	$0.783498\pi$
$32$	−1.00000	−0.176777
$33$	0.842314	0.146628
$34$	−2.98970	−0.512730
$35$	0.388002	0.0655843
$36$	3.49545	0.582575
$37$	−6.23500	−1.02503	−0.512514	−	0.858679i	$-0.671286\pi$
$37$	−6.23500	−1.02503	−0.512514	+	0.858679i	$0.671286\pi$
$38$	8.00967	1.29934
$39$	5.48312	0.878002
$40$	1.05969	0.167552
$41$	5.24599	0.819286	0.409643	−	0.912246i	$-0.365653\pi$
$41$	5.24599	0.819286	0.409643	+	0.912246i	$0.365653\pi$
$42$	−0.933166	−0.143991
$43$	8.94270	1.36375	0.681874	−	0.731469i	$-0.261165\pi$
$43$	8.94270	1.36375	0.681874	+	0.731469i	$0.261165\pi$
$44$	−0.330498	−0.0498245
$45$	−3.70410	−0.552175
$46$	7.06260	1.04132
$47$	−2.67032	−0.389506	−0.194753	−	0.980852i	$-0.562391\pi$
$47$	−2.67032	−0.389506	−0.194753	+	0.980852i	$0.562391\pi$
$48$	−2.54862	−0.367861
$49$	−6.86594	−0.980848
$50$	3.87705	0.548298
$51$	−7.61961	−1.06696
$52$	−2.15141	−0.298347
$53$	−9.83026	−1.35029	−0.675145	−	0.737685i	$-0.735919\pi$
$53$	−9.83026	−1.35029	−0.675145	+	0.737685i	$0.735919\pi$
$54$	1.26271	0.171834
$55$	0.350226	0.0472245
$56$	0.366146	0.0489283
$57$	20.4136	2.70385
$58$	2.43858	0.320201
$59$	8.95349	1.16565	0.582823	−	0.812599i	$-0.301948\pi$
$59$	8.95349	1.16565	0.582823	+	0.812599i	$0.301948\pi$
$60$	2.70075	0.348665
$61$	−3.72746	−0.477252	−0.238626	−	0.971112i	$-0.576697\pi$
$61$	−3.72746	−0.477252	−0.238626	+	0.971112i	$0.576697\pi$
$62$	8.65756	1.09951
$63$	−1.27985	−0.161245
$64$	1.00000	0.125000
$65$	2.27983	0.282778
$66$	−0.842314	−0.103682
$67$	13.8648	1.69385	0.846926	−	0.531711i	$-0.178451\pi$
$67$	13.8648	1.69385	0.846926	+	0.531711i	$0.178451\pi$
$68$	2.98970	0.362555
$69$	17.9999	2.16693
$70$	−0.388002	−0.0463751
$71$	−6.95344	−0.825221	−0.412610	−	0.910908i	$-0.635383\pi$
$71$	−6.95344	−0.825221	−0.412610	+	0.910908i	$0.635383\pi$
$72$	−3.49545	−0.411943
$73$	−15.4340	−1.80641	−0.903207	−	0.429205i	$-0.858794\pi$
$73$	−15.4340	−1.80641	−0.903207	+	0.429205i	$0.858794\pi$
$74$	6.23500	0.724804
$75$	9.88112	1.14097
$76$	−8.00967	−0.918772
$77$	0.121011	0.0137904
$78$	−5.48312	−0.620841
$79$	5.74110	0.645924	0.322962	−	0.946412i	$-0.395321\pi$
$79$	5.74110	0.645924	0.322962	+	0.946412i	$0.395321\pi$
$80$	−1.05969	−0.118477
$81$	−7.26818	−0.807575
$82$	−5.24599	−0.579323
$83$	−4.36949	−0.479614	−0.239807	−	0.970821i	$-0.577084\pi$
$83$	−4.36949	−0.479614	−0.239807	+	0.970821i	$0.577084\pi$
$84$	0.933166	0.101817
$85$	−3.16817	−0.343636
$86$	−8.94270	−0.964316
$87$	6.21500	0.666318
$88$	0.330498	0.0352312
$89$	−0.774967	−0.0821464	−0.0410732	−	0.999156i	$-0.513078\pi$
$89$	−0.774967	−0.0821464	−0.0410732	+	0.999156i	$0.513078\pi$
$90$	3.70410	0.390447
$91$	0.787730	0.0825766
$92$	−7.06260	−0.736327
$93$	22.0648	2.28802
$94$	2.67032	0.275423
$95$	8.48779	0.870829
$96$	2.54862	0.260117
$97$	−6.51475	−0.661473	−0.330736	−	0.943723i	$-0.607297\pi$
$97$	−6.51475	−0.661473	−0.330736	+	0.943723i	$0.607297\pi$
$98$	6.86594	0.693564
$99$	−1.15524	−0.116106
$100$	−3.87705	−0.387705
$101$	−10.3298	−1.02786	−0.513929	−	0.857833i	$-0.671810\pi$
$101$	−10.3298	−1.02786	−0.513929	+	0.857833i	$0.671810\pi$
$102$	7.61961	0.754454
$103$	17.2839	1.70304	0.851518	−	0.524326i	$-0.175683\pi$
$103$	17.2839	1.70304	0.851518	+	0.524326i	$0.175683\pi$
$104$	2.15141	0.210963
$105$	−0.988869	−0.0965037
$106$	9.83026	0.954800
$107$	−8.50588	−0.822294	−0.411147	−	0.911569i	$-0.634872\pi$
$107$	−8.50588	−0.822294	−0.411147	+	0.911569i	$0.634872\pi$
$108$	−1.26271	−0.121505
$109$	−10.8442	−1.03869	−0.519345	−	0.854565i	$-0.673824\pi$
$109$	−10.8442	−1.03869	−0.519345	+	0.854565i	$0.673824\pi$
$110$	−0.350226	−0.0333928
$111$	15.8906	1.50827
$112$	−0.366146	−0.0345976
$113$	−5.24240	−0.493163	−0.246582	−	0.969122i	$-0.579307\pi$
$113$	−5.24240	−0.493163	−0.246582	+	0.969122i	$0.579307\pi$
$114$	−20.4136	−1.91191
$115$	7.48418	0.697904
$116$	−2.43858	−0.226416
$117$	−7.52015	−0.695238
$118$	−8.95349	−0.824236
$119$	−1.09467	−0.100348
$120$	−2.70075	−0.246544
$121$	−10.8908	−0.990070
$122$	3.72746	0.337468
$123$	−13.3700	−1.20553
$124$	−8.65756	−0.777472
$125$	9.40694	0.841383
$126$	1.27985	0.114018
$127$	−17.7420	−1.57435	−0.787176	−	0.616729i	$-0.788458\pi$
$127$	−17.7420	−1.57435	−0.787176	+	0.616729i	$0.788458\pi$
$128$	−1.00000	−0.0883883
$129$	−22.7915	−2.00668
$130$	−2.27983	−0.199955
$131$	−2.76252	−0.241362	−0.120681	−	0.992691i	$-0.538508\pi$
$131$	−2.76252	−0.241362	−0.120681	+	0.992691i	$0.538508\pi$
$132$	0.842314	0.0733140
$133$	2.93271	0.254298
$134$	−13.8648	−1.19773
$135$	1.33809	0.115164
$136$	−2.98970	−0.256365
$137$	−3.43082	−0.293114	−0.146557	−	0.989202i	$-0.546819\pi$
$137$	−3.43082	−0.293114	−0.146557	+	0.989202i	$0.546819\pi$
$138$	−17.9999	−1.53225
$139$	2.55804	0.216970	0.108485	−	0.994098i	$-0.465400\pi$
$139$	2.55804	0.216970	0.108485	+	0.994098i	$0.465400\pi$
$140$	0.388002	0.0327922
$141$	6.80563	0.573137
$142$	6.95344	0.583519
$143$	0.711037	0.0594599
$144$	3.49545	0.291288
$145$	2.58414	0.214601
$146$	15.4340	1.27733
$147$	17.4986	1.44326
$148$	−6.23500	−0.512514
$149$	−8.31160	−0.680913	−0.340456	−	0.940260i	$-0.610582\pi$
$149$	−8.31160	−0.680913	−0.340456	+	0.940260i	$0.610582\pi$
$150$	−9.88112	−0.806790
$151$	14.9476	1.21642	0.608209	−	0.793777i	$-0.291888\pi$
$151$	14.9476	1.21642	0.608209	+	0.793777i	$0.291888\pi$
$152$	8.00967	0.649670
$153$	10.4504	0.844861
$154$	−0.121011	−0.00975131
$155$	9.17436	0.736902
$156$	5.48312	0.439001
$157$	−16.7138	−1.33390	−0.666952	−	0.745100i	$-0.732401\pi$
$157$	−16.7138	−1.33390	−0.666952	+	0.745100i	$0.732401\pi$
$158$	−5.74110	−0.456738
$159$	25.0536	1.98688
$160$	1.05969	0.0837760
$161$	2.58594	0.203801
$162$	7.26818	0.571042
$163$	18.4268	1.44330	0.721649	−	0.692259i	$-0.243385\pi$
$163$	18.4268	1.44330	0.721649	+	0.692259i	$0.243385\pi$
$164$	5.24599	0.409643
$165$	−0.892593	−0.0694883
$166$	4.36949	0.339138
$167$	−20.2855	−1.56974	−0.784869	−	0.619662i	$-0.787270\pi$
$167$	−20.2855	−1.56974	−0.784869	+	0.619662i	$0.787270\pi$
$168$	−0.933166	−0.0719953
$169$	−8.37144	−0.643957
$170$	3.16817	0.242987
$171$	−27.9974	−2.14102
$172$	8.94270	0.681874
$173$	13.6654	1.03896	0.519479	−	0.854483i	$-0.326126\pi$
$173$	13.6654	1.03896	0.519479	+	0.854483i	$0.326126\pi$
$174$	−6.21500	−0.471158
$175$	1.41957	0.107309
$176$	−0.330498	−0.0249122
$177$	−22.8190	−1.71518
$178$	0.774967	0.0580862
$179$	−22.8049	−1.70452	−0.852260	−	0.523118i	$-0.824769\pi$
$179$	−22.8049	−1.70452	−0.852260	+	0.523118i	$0.824769\pi$
$180$	−3.70410	−0.276087
$181$	−14.7165	−1.09387	−0.546935	−	0.837175i	$-0.684205\pi$
$181$	−14.7165	−1.09387	−0.546935	+	0.837175i	$0.684205\pi$
$182$	−0.787730	−0.0583904
$183$	9.49986	0.702250
$184$	7.06260	0.520662
$185$	6.60718	0.485769
$186$	−22.0648	−1.61787
$187$	−0.988092	−0.0722564
$188$	−2.67032	−0.194753
$189$	0.462338	0.0336301
$190$	−8.48779	−0.615769
$191$	3.37278	0.244046	0.122023	−	0.992527i	$-0.461062\pi$
$191$	3.37278	0.244046	0.122023	+	0.992527i	$0.461062\pi$
$192$	−2.54862	−0.183931
$193$	−2.70698	−0.194853	−0.0974265	−	0.995243i	$-0.531061\pi$
$193$	−2.70698	−0.194853	−0.0974265	+	0.995243i	$0.531061\pi$
$194$	6.51475	0.467732
$195$	−5.81042	−0.416093
$196$	−6.86594	−0.490424
$197$	−8.37524	−0.596711	−0.298356	−	0.954455i	$-0.596438\pi$
$197$	−8.37524	−0.596711	−0.298356	+	0.954455i	$0.596438\pi$
$198$	1.15524	0.0820993
$199$	−17.8799	−1.26747	−0.633737	−	0.773549i	$-0.718480\pi$
$199$	−17.8799	−1.26747	−0.633737	+	0.773549i	$0.718480\pi$
$200$	3.87705	0.274149
$201$	−35.3360	−2.49241
$202$	10.3298	0.726805
$203$	0.892875	0.0626676
$204$	−7.61961	−0.533479
$205$	−5.55913	−0.388267
$206$	−17.2839	−1.20423
$207$	−24.6870	−1.71586
$208$	−2.15141	−0.149173
$209$	2.64718	0.183109
$210$	0.988869	0.0682385
$211$	12.1439	0.836019	0.418009	−	0.908443i	$-0.362728\pi$
$211$	12.1439	0.836019	0.418009	+	0.908443i	$0.362728\pi$
$212$	−9.83026	−0.675145
$213$	17.7216	1.21427
$214$	8.50588	0.581450
$215$	−9.47651	−0.646293
$216$	1.26271	0.0859168
$217$	3.16993	0.215189
$218$	10.8442	0.734464
$219$	39.3354	2.65804
$220$	0.350226	0.0236123
$221$	−6.43208	−0.432668
$222$	−15.8906	−1.06651
$223$	−19.6029	−1.31271	−0.656355	−	0.754452i	$-0.727903\pi$
$223$	−19.6029	−1.31271	−0.656355	+	0.754452i	$0.727903\pi$
$224$	0.366146	0.0244642
$225$	−13.5520	−0.903470
$226$	5.24240	0.348719
$227$	−14.7189	−0.976925	−0.488463	−	0.872585i	$-0.662442\pi$
$227$	−14.7189	−0.976925	−0.488463	+	0.872585i	$0.662442\pi$
$228$	20.4136	1.35192
$229$	25.3893	1.67777	0.838887	−	0.544305i	$-0.183207\pi$
$229$	25.3893	1.67777	0.838887	+	0.544305i	$0.183207\pi$
$230$	−7.48418	−0.493492
$231$	−0.308410	−0.0202919
$232$	2.43858	0.160100
$233$	21.4986	1.40842	0.704210	−	0.709992i	$-0.251302\pi$
$233$	21.4986	1.40842	0.704210	+	0.709992i	$0.251302\pi$
$234$	7.52015	0.491607
$235$	2.82972	0.184590
$236$	8.95349	0.582823
$237$	−14.6319	−0.950442
$238$	1.09467	0.0709568
$239$	14.2698	0.923034	0.461517	−	0.887131i	$-0.347305\pi$
$239$	14.2698	0.923034	0.461517	+	0.887131i	$0.347305\pi$
$240$	2.70075	0.174333
$241$	−15.4480	−0.995093	−0.497547	−	0.867437i	$-0.665766\pi$
$241$	−15.4480	−0.995093	−0.497547	+	0.867437i	$0.665766\pi$
$242$	10.8908	0.700085
$243$	22.3119	1.43131
$244$	−3.72746	−0.238626
$245$	7.27578	0.464833
$246$	13.3700	0.852441
$247$	17.2321	1.09645
$248$	8.65756	0.549756
$249$	11.1362	0.705726
$250$	−9.40694	−0.594947
$251$	−16.6366	−1.05009	−0.525047	−	0.851073i	$-0.675952\pi$
$251$	−16.6366	−1.05009	−0.525047	+	0.851073i	$0.675952\pi$
$252$	−1.27985	−0.0806227
$253$	2.33418	0.146748
$254$	17.7420	1.11323
$255$	8.07444	0.505641
$256$	1.00000	0.0625000
$257$	1.42749	0.0890445	0.0445222	−	0.999008i	$-0.485823\pi$
$257$	1.42749	0.0890445	0.0445222	+	0.999008i	$0.485823\pi$
$258$	22.7915	1.41894
$259$	2.28292	0.141854
$260$	2.27983	0.141389
$261$	−8.52392	−0.527618
$262$	2.76252	0.170669
$263$	5.94040	0.366301	0.183150	−	0.983085i	$-0.441370\pi$
$263$	5.94040	0.366301	0.183150	+	0.983085i	$0.441370\pi$
$264$	−0.842314	−0.0518408
$265$	10.4171	0.639915
$266$	−2.93271	−0.179816
$267$	1.97509	0.120874
$268$	13.8648	0.846926
$269$	−20.6741	−1.26052	−0.630260	−	0.776384i	$-0.717052\pi$
$269$	−20.6741	−1.26052	−0.630260	+	0.776384i	$0.717052\pi$
$270$	−1.33809	−0.0814334
$271$	−0.938906	−0.0570345	−0.0285172	−	0.999593i	$-0.509079\pi$
$271$	−0.938906	−0.0570345	−0.0285172	+	0.999593i	$0.509079\pi$
$272$	2.98970	0.181277
$273$	−2.00762	−0.121507
$274$	3.43082	0.207263
$275$	1.28136	0.0772688
$276$	17.9999	1.08346
$277$	−12.3029	−0.739210	−0.369605	−	0.929189i	$-0.620507\pi$
$277$	−12.3029	−0.739210	−0.369605	+	0.929189i	$0.620507\pi$
$278$	−2.55804	−0.153421
$279$	−30.2621	−1.81174
$280$	−0.388002	−0.0231876
$281$	5.33996	0.318555	0.159278	−	0.987234i	$-0.449083\pi$
$281$	5.33996	0.318555	0.159278	+	0.987234i	$0.449083\pi$
$282$	−6.80563	−0.405269
$283$	13.5917	0.807943	0.403971	−	0.914772i	$-0.367630\pi$
$283$	13.5917	0.807943	0.403971	+	0.914772i	$0.367630\pi$
$284$	−6.95344	−0.412610
$285$	−21.6321	−1.28138
$286$	−0.711037	−0.0420445
$287$	−1.92080	−0.113381
$288$	−3.49545	−0.205971
$289$	−8.06168	−0.474216
$290$	−2.58414	−0.151746
$291$	16.6036	0.973320
$292$	−15.4340	−0.903207
$293$	−25.0194	−1.46165	−0.730823	−	0.682567i	$-0.760864\pi$
$293$	−25.0194	−1.46165	−0.730823	+	0.682567i	$0.760864\pi$
$294$	−17.4986	−1.02054
$295$	−9.48795	−0.552410
$296$	6.23500	0.362402
$297$	0.417325	0.0242156
$298$	8.31160	0.481478
$299$	15.1945	0.878723
$300$	9.88112	0.570487
$301$	−3.27433	−0.188729
$302$	−14.9476	−0.860137
$303$	26.3268	1.51244
$304$	−8.00967	−0.459386
$305$	3.94996	0.226174
$306$	−10.4504	−0.597407
$307$	13.4626	0.768353	0.384177	−	0.923260i	$-0.374485\pi$
$307$	13.4626	0.768353	0.384177	+	0.923260i	$0.374485\pi$
$308$	0.121011	0.00689522
$309$	−44.0501	−2.50592
$310$	−9.17436	−0.521068
$311$	−26.4013	−1.49708	−0.748541	−	0.663088i	$-0.769245\pi$
$311$	−26.4013	−1.49708	−0.748541	+	0.663088i	$0.769245\pi$
$312$	−5.48312	−0.310421
$313$	22.3747	1.26469	0.632347	−	0.774686i	$-0.282092\pi$
$313$	22.3747	1.26469	0.632347	+	0.774686i	$0.282092\pi$
$314$	16.7138	0.943213
$315$	1.35624	0.0764156
$316$	5.74110	0.322962
$317$	20.0705	1.12727	0.563636	−	0.826023i	$-0.309402\pi$
$317$	20.0705	1.12727	0.563636	+	0.826023i	$0.309402\pi$
$318$	−25.0536	−1.40493
$319$	0.805945	0.0451243
$320$	−1.05969	−0.0592386
$321$	21.6782	1.20996
$322$	−2.58594	−0.144109
$323$	−23.9465	−1.33242
$324$	−7.26818	−0.403788
$325$	8.34113	0.462682
$326$	−18.4268	−1.02057
$327$	27.6378	1.52837
$328$	−5.24599	−0.289661
$329$	0.977727	0.0539039
$330$	0.892593	0.0491356
$331$	1.67062	0.0918257	0.0459129	−	0.998945i	$-0.485380\pi$
$331$	1.67062	0.0918257	0.0459129	+	0.998945i	$0.485380\pi$
$332$	−4.36949	−0.239807
$333$	−21.7941	−1.19431
$334$	20.2855	1.10997
$335$	−14.6924	−0.802732
$336$	0.933166	0.0509084
$337$	7.19091	0.391714	0.195857	−	0.980633i	$-0.437251\pi$
$337$	7.19091	0.391714	0.195857	+	0.980633i	$0.437251\pi$
$338$	8.37144	0.455346
$339$	13.3609	0.725662
$340$	−3.16817	−0.171818
$341$	2.86131	0.154949
$342$	27.9974	1.51393
$343$	5.07696	0.274130
$344$	−8.94270	−0.482158
$345$	−19.0743	−1.02693
$346$	−13.6654	−0.734655
$347$	−19.6921	−1.05713	−0.528565	−	0.848893i	$-0.677270\pi$
$347$	−19.6921	−1.05713	−0.528565	+	0.848893i	$0.677270\pi$
$348$	6.21500	0.333159
$349$	23.1445	1.23890	0.619448	−	0.785038i	$-0.287357\pi$
$349$	23.1445	1.23890	0.619448	+	0.785038i	$0.287357\pi$
$350$	−1.41957	−0.0758791
$351$	2.71661	0.145002
$352$	0.330498	0.0176156
$353$	−1.35810	−0.0722842	−0.0361421	−	0.999347i	$-0.511507\pi$
$353$	−1.35810	−0.0722842	−0.0361421	+	0.999347i	$0.511507\pi$
$354$	22.8190	1.21282
$355$	7.36850	0.391080
$356$	−0.774967	−0.0410732
$357$	2.78989	0.147657
$358$	22.8049	1.20528
$359$	−10.7991	−0.569954	−0.284977	−	0.958534i	$-0.591986\pi$
$359$	−10.7991	−0.569954	−0.284977	+	0.958534i	$0.591986\pi$
$360$	3.70410	0.195223
$361$	45.1548	2.37657
$362$	14.7165	0.773482
$363$	27.7564	1.45683
$364$	0.787730	0.0412883
$365$	16.3553	0.856076
$366$	−9.49986	−0.496566
$367$	−11.8639	−0.619290	−0.309645	−	0.950852i	$-0.600210\pi$
$367$	−11.8639	−0.619290	−0.309645	+	0.950852i	$0.600210\pi$
$368$	−7.06260	−0.368163
$369$	18.3371	0.954591
$370$	−6.60718	−0.343491
$371$	3.59931	0.186867
$372$	22.0648	1.14401
$373$	6.60210	0.341844	0.170922	−	0.985285i	$-0.445325\pi$
$373$	6.60210	0.341844	0.170922	+	0.985285i	$0.445325\pi$
$374$	0.988092	0.0510930
$375$	−23.9747	−1.23805
$376$	2.67032	0.137711
$377$	5.24638	0.270202
$378$	−0.462338	−0.0237801
$379$	9.40309	0.483004	0.241502	−	0.970400i	$-0.422360\pi$
$379$	9.40309	0.483004	0.241502	+	0.970400i	$0.422360\pi$
$380$	8.48779	0.435414
$381$	45.2177	2.31657
$382$	−3.37278	−0.172566
$383$	−2.72237	−0.139106	−0.0695532	−	0.997578i	$-0.522157\pi$
$383$	−2.72237	−0.139106	−0.0695532	+	0.997578i	$0.522157\pi$
$384$	2.54862	0.130059
$385$	−0.128234	−0.00653541
$386$	2.70698	0.137782
$387$	31.2588	1.58897
$388$	−6.51475	−0.330736
$389$	−15.1828	−0.769799	−0.384899	−	0.922959i	$-0.625764\pi$
$389$	−15.1828	−0.769799	−0.384899	+	0.922959i	$0.625764\pi$
$390$	5.81042	0.294222
$391$	−21.1151	−1.06784
$392$	6.86594	0.346782
$393$	7.04060	0.355152
$394$	8.37524	0.421939
$395$	−6.08380	−0.306109
$396$	−1.15524	−0.0580530
$397$	3.09801	0.155485	0.0777424	−	0.996973i	$-0.475229\pi$
$397$	3.09801	0.155485	0.0777424	+	0.996973i	$0.475229\pi$
$398$	17.8799	0.896239
$399$	−7.47436	−0.374186
$400$	−3.87705	−0.193853
$401$	2.08597	0.104169	0.0520843	−	0.998643i	$-0.483414\pi$
$401$	2.08597	0.104169	0.0520843	+	0.998643i	$0.483414\pi$
$402$	35.3360	1.76240
$403$	18.6260	0.927825
$404$	−10.3298	−0.513929
$405$	7.70203	0.382717
$406$	−0.892875	−0.0443127
$407$	2.06066	0.102143
$408$	7.61961	0.377227
$409$	−13.4996	−0.667514	−0.333757	−	0.942659i	$-0.608316\pi$
$409$	−13.4996	−0.667514	−0.333757	+	0.942659i	$0.608316\pi$
$410$	5.55913	0.274546
$411$	8.74384	0.431302
$412$	17.2839	0.851518
$413$	−3.27829	−0.161314
$414$	24.6870	1.21330
$415$	4.63032	0.227293
$416$	2.15141	0.105482
$417$	−6.51946	−0.319259
$418$	−2.64718	−0.129478
$419$	12.6852	0.619714	0.309857	−	0.950783i	$-0.399719\pi$
$419$	12.6852	0.619714	0.309857	+	0.950783i	$0.399719\pi$
$420$	−0.988869	−0.0482519
$421$	−25.0748	−1.22207	−0.611035	−	0.791604i	$-0.709247\pi$
$421$	−25.0748	−1.22207	−0.611035	+	0.791604i	$0.709247\pi$
$422$	−12.1439	−0.591155
$423$	−9.33397	−0.453833
$424$	9.83026	0.477400
$425$	−11.5912	−0.562257
$426$	−17.7216	−0.858617
$427$	1.36479	0.0660470
$428$	−8.50588	−0.411147
$429$	−1.81216	−0.0874920
$430$	9.47651	0.456998
$431$	−22.5872	−1.08799	−0.543993	−	0.839090i	$-0.683088\pi$
$431$	−22.5872	−1.08799	−0.543993	+	0.839090i	$0.683088\pi$
$432$	−1.26271	−0.0607523
$433$	7.18379	0.345231	0.172615	−	0.984989i	$-0.444778\pi$
$433$	7.18379	0.345231	0.172615	+	0.984989i	$0.444778\pi$
$434$	−3.16993	−0.152162
$435$	−6.58599	−0.315774
$436$	−10.8442	−0.519345
$437$	56.5691	2.70607
$438$	−39.3354	−1.87952
$439$	−15.5591	−0.742596	−0.371298	−	0.928514i	$-0.621087\pi$
$439$	−15.5591	−0.742596	−0.371298	+	0.928514i	$0.621087\pi$
$440$	−0.350226	−0.0166964
$441$	−23.9995	−1.14284
$442$	6.43208	0.305943
$443$	11.8115	0.561180	0.280590	−	0.959828i	$-0.409470\pi$
$443$	11.8115	0.561180	0.280590	+	0.959828i	$0.409470\pi$
$444$	15.8906	0.754136
$445$	0.821227	0.0389299
$446$	19.6029	0.928226
$447$	21.1831	1.00193
$448$	−0.366146	−0.0172988
$449$	−39.4386	−1.86122	−0.930611	−	0.366010i	$-0.880724\pi$
$449$	−39.4386	−1.86122	−0.930611	+	0.366010i	$0.880724\pi$
$450$	13.5520	0.638849
$451$	−1.73379	−0.0816410
$452$	−5.24240	−0.246582
$453$	−38.0957	−1.78989
$454$	14.7189	0.690791
$455$	−0.834752	−0.0391338
$456$	−20.4136	−0.955954
$457$	−8.03841	−0.376021	−0.188010	−	0.982167i	$-0.560204\pi$
$457$	−8.03841	−0.376021	−0.188010	+	0.982167i	$0.560204\pi$
$458$	−25.3893	−1.18637
$459$	−3.77514	−0.176208
$460$	7.48418	0.348952
$461$	1.68334	0.0784008	0.0392004	−	0.999231i	$-0.487519\pi$
$461$	1.68334	0.0784008	0.0392004	+	0.999231i	$0.487519\pi$
$462$	0.308410	0.0143485
$463$	15.6386	0.726786	0.363393	−	0.931636i	$-0.381618\pi$
$463$	15.6386	0.726786	0.363393	+	0.931636i	$0.381618\pi$
$464$	−2.43858	−0.113208
$465$	−23.3819	−1.08431
$466$	−21.4986	−0.995903
$467$	27.6720	1.28051	0.640255	−	0.768163i	$-0.278829\pi$
$467$	27.6720	1.28051	0.640255	+	0.768163i	$0.278829\pi$
$468$	−7.52015	−0.347619
$469$	−5.07653	−0.234413
$470$	−2.82972	−0.130525
$471$	42.5970	1.96277
$472$	−8.95349	−0.412118
$473$	−2.95555	−0.135896
$474$	14.6319	0.672064
$475$	31.0539	1.42485
$476$	−1.09467	−0.0501740
$477$	−34.3612	−1.57329
$478$	−14.2698	−0.652684
$479$	−31.5909	−1.44342	−0.721712	−	0.692194i	$-0.756644\pi$
$479$	−31.5909	−1.44342	−0.721712	+	0.692194i	$0.756644\pi$
$480$	−2.70075	−0.123272
$481$	13.4140	0.611627
$482$	15.4480	0.703637
$483$	−6.59058	−0.299882
$484$	−10.8908	−0.495035
$485$	6.90363	0.313478
$486$	−22.3119	−1.01209
$487$	−4.10339	−0.185942	−0.0929712	−	0.995669i	$-0.529636\pi$
$487$	−4.10339	−0.185942	−0.0929712	+	0.995669i	$0.529636\pi$
$488$	3.72746	0.168734
$489$	−46.9628	−2.12373
$490$	−7.27578	−0.328686
$491$	−4.83659	−0.218272	−0.109136	−	0.994027i	$-0.534808\pi$
$491$	−4.83659	−0.218272	−0.109136	+	0.994027i	$0.534808\pi$
$492$	−13.3700	−0.602767
$493$	−7.29062	−0.328353
$494$	−17.2321	−0.775308
$495$	1.22420	0.0550237
$496$	−8.65756	−0.388736
$497$	2.54597	0.114202
$498$	−11.1362	−0.499023
$499$	7.24316	0.324248	0.162124	−	0.986770i	$-0.448166\pi$
$499$	7.24316	0.324248	0.162124	+	0.986770i	$0.448166\pi$
$500$	9.40694	0.420691
$501$	51.6999	2.30978
$502$	16.6366	0.742529
$503$	7.47134	0.333130	0.166565	−	0.986030i	$-0.446732\pi$
$503$	7.47134	0.333130	0.166565	+	0.986030i	$0.446732\pi$
$504$	1.27985	0.0570088
$505$	10.9464	0.487111
$506$	−2.33418	−0.103767
$507$	21.3356	0.947547
$508$	−17.7420	−0.787176
$509$	−43.1162	−1.91109	−0.955546	−	0.294844i	$-0.904732\pi$
$509$	−43.1162	−1.91109	−0.955546	+	0.294844i	$0.904732\pi$
$510$	−8.07444	−0.357542
$511$	5.65110	0.249990
$512$	−1.00000	−0.0441942
$513$	10.1139	0.446541
$514$	−1.42749	−0.0629640
$515$	−18.3156	−0.807084
$516$	−22.7915	−1.00334
$517$	0.882536	0.0388139
$518$	−2.28292	−0.100306
$519$	−34.8278	−1.52877
$520$	−2.27983	−0.0999773
$521$	30.9573	1.35626	0.678132	−	0.734940i	$-0.262790\pi$
$521$	30.9573	1.35626	0.678132	+	0.734940i	$0.262790\pi$
$522$	8.52392	0.373082
$523$	36.1888	1.58243	0.791213	−	0.611540i	$-0.209450\pi$
$523$	36.1888	1.58243	0.791213	+	0.611540i	$0.209450\pi$
$524$	−2.76252	−0.120681
$525$	−3.61793	−0.157900
$526$	−5.94040	−0.259014
$527$	−25.8835	−1.12750
$528$	0.842314	0.0366570
$529$	26.8803	1.16871
$530$	−10.4171	−0.452488
$531$	31.2965	1.35815
$532$	2.93271	0.127149
$533$	−11.2863	−0.488863
$534$	−1.97509	−0.0854707
$535$	9.01361	0.389693
$536$	−13.8648	−0.598867
$537$	58.1210	2.50811
$538$	20.6741	0.891322
$539$	2.26918	0.0977405
$540$	1.33809	0.0575821
$541$	34.8984	1.50040	0.750200	−	0.661211i	$-0.229957\pi$
$541$	34.8984	1.50040	0.750200	+	0.661211i	$0.229957\pi$
$542$	0.938906	0.0403295
$543$	37.5067	1.60957
$544$	−2.98970	−0.128182
$545$	11.4916	0.492244
$546$	2.00762	0.0859183
$547$	34.3162	1.46725	0.733627	−	0.679553i	$-0.237826\pi$
$547$	34.3162	1.46725	0.733627	+	0.679553i	$0.237826\pi$
$548$	−3.43082	−0.146557
$549$	−13.0291	−0.556070
$550$	−1.28136	−0.0546373
$551$	19.5322	0.832100
$552$	−17.9999	−0.766125
$553$	−2.10208	−0.0893896
$554$	12.3029	0.522700
$555$	−16.8392	−0.714783
$556$	2.55804	0.108485
$557$	−32.5766	−1.38031	−0.690157	−	0.723660i	$-0.742459\pi$
$557$	−32.5766	−1.38031	−0.690157	+	0.723660i	$0.742459\pi$
$558$	30.2621	1.28110
$559$	−19.2394	−0.813740
$560$	0.388002	0.0163961
$561$	2.51827	0.106321
$562$	−5.33996	−0.225253
$563$	38.8319	1.63657	0.818284	−	0.574814i	$-0.194925\pi$
$563$	38.8319	1.63657	0.818284	+	0.574814i	$0.194925\pi$
$564$	6.80563	0.286569
$565$	5.55533	0.233714
$566$	−13.5917	−0.571302
$567$	2.66121	0.111761
$568$	6.95344	0.291760
$569$	6.29532	0.263913	0.131957	−	0.991255i	$-0.457874\pi$
$569$	6.29532	0.263913	0.131957	+	0.991255i	$0.457874\pi$
$570$	21.6321	0.906070
$571$	−14.9014	−0.623606	−0.311803	−	0.950147i	$-0.600933\pi$
$571$	−14.9014	−0.623606	−0.311803	+	0.950147i	$0.600933\pi$
$572$	0.711037	0.0297300
$573$	−8.59592	−0.359100
$574$	1.92080	0.0801726
$575$	27.3821	1.14191
$576$	3.49545	0.145644
$577$	4.65194	0.193663	0.0968315	−	0.995301i	$-0.469129\pi$
$577$	4.65194	0.193663	0.0968315	+	0.995301i	$0.469129\pi$
$578$	8.06168	0.335322
$579$	6.89907	0.286715
$580$	2.58414	0.107301
$581$	1.59987	0.0663739
$582$	−16.6036	−0.688241
$583$	3.24888	0.134555
$584$	15.4340	0.638664
$585$	7.96904	0.329479
$586$	25.0194	1.03354
$587$	23.8958	0.986284	0.493142	−	0.869949i	$-0.335848\pi$
$587$	23.8958	0.986284	0.493142	+	0.869949i	$0.335848\pi$
$588$	17.4986	0.721632
$589$	69.3442	2.85728
$590$	9.48795	0.390613
$591$	21.3453	0.878028
$592$	−6.23500	−0.256257
$593$	14.2096	0.583520	0.291760	−	0.956492i	$-0.405759\pi$
$593$	14.2096	0.583520	0.291760	+	0.956492i	$0.405759\pi$
$594$	−0.417325	−0.0171230
$595$	1.16001	0.0475558
$596$	−8.31160	−0.340456
$597$	45.5690	1.86502
$598$	−15.1945	−0.621351
$599$	−16.9127	−0.691035	−0.345517	−	0.938412i	$-0.612297\pi$
$599$	−16.9127	−0.691035	−0.345517	+	0.938412i	$0.612297\pi$
$600$	−9.88112	−0.403395
$601$	−23.6271	−0.963769	−0.481884	−	0.876235i	$-0.660048\pi$
$601$	−23.6271	−0.963769	−0.481884	+	0.876235i	$0.660048\pi$
$602$	3.27433	0.133452
$603$	48.4636	1.97359
$604$	14.9476	0.608209
$605$	11.5409	0.469203
$606$	−26.3268	−1.06945
$607$	−2.82393	−0.114620	−0.0573099	−	0.998356i	$-0.518252\pi$
$607$	−2.82393	−0.114620	−0.0573099	+	0.998356i	$0.518252\pi$
$608$	8.00967	0.324835
$609$	−2.27560	−0.0922119
$610$	−3.94996	−0.159929
$611$	5.74495	0.232416
$612$	10.4504	0.422431
$613$	−21.5454	−0.870210	−0.435105	−	0.900380i	$-0.643289\pi$
$613$	−21.5454	−0.870210	−0.435105	+	0.900380i	$0.643289\pi$
$614$	−13.4626	−0.543308
$615$	14.1681	0.571313
$616$	−0.121011	−0.00487566
$617$	31.3867	1.26358	0.631791	−	0.775139i	$-0.282320\pi$
$617$	31.3867	1.26358	0.631791	+	0.775139i	$0.282320\pi$
$618$	44.0501	1.77196
$619$	21.5477	0.866075	0.433038	−	0.901376i	$-0.357442\pi$
$619$	21.5477	0.866075	0.433038	+	0.901376i	$0.357442\pi$
$620$	9.17436	0.368451
$621$	8.91804	0.357869
$622$	26.4013	1.05860
$623$	0.283751	0.0113683
$624$	5.48312	0.219500
$625$	9.41679	0.376672
$626$	−22.3747	−0.894273
$627$	−6.74665	−0.269435
$628$	−16.7138	−0.666952
$629$	−18.6408	−0.743257
$630$	−1.35624	−0.0540340
$631$	29.5610	1.17680	0.588402	−	0.808568i	$-0.299757\pi$
$631$	29.5610	1.17680	0.588402	+	0.808568i	$0.299757\pi$
$632$	−5.74110	−0.228369
$633$	−30.9501	−1.23016
$634$	−20.0705	−0.797101
$635$	18.8011	0.746099
$636$	25.0536	0.993439
$637$	14.7714	0.585266
$638$	−0.805945	−0.0319077
$639$	−24.3054	−0.961506
$640$	1.05969	0.0418880
$641$	−3.11296	−0.122955	−0.0614774	−	0.998108i	$-0.519581\pi$
$641$	−3.11296	−0.122955	−0.0614774	+	0.998108i	$0.519581\pi$
$642$	−21.6782	−0.855571
$643$	−29.9587	−1.18146	−0.590728	−	0.806871i	$-0.701159\pi$
$643$	−29.9587	−1.18146	−0.590728	+	0.806871i	$0.701159\pi$
$644$	2.58594	0.101900
$645$	24.1520	0.950984
$646$	23.9465	0.942164
$647$	−48.0370	−1.88853	−0.944265	−	0.329188i	$-0.893225\pi$
$647$	−48.0370	−1.88853	−0.944265	+	0.329188i	$0.893225\pi$
$648$	7.26818	0.285521
$649$	−2.95911	−0.116155
$650$	−8.34113	−0.327166
$651$	−8.07895	−0.316639
$652$	18.4268	0.721649
$653$	46.6806	1.82675	0.913376	−	0.407118i	$-0.133466\pi$
$653$	46.6806	1.82675	0.913376	+	0.407118i	$0.133466\pi$
$654$	−27.6378	−1.08072
$655$	2.92742	0.114384
$656$	5.24599	0.204821
$657$	−53.9488	−2.10474
$658$	−0.977727	−0.0381158
$659$	−13.1787	−0.513370	−0.256685	−	0.966495i	$-0.582630\pi$
$659$	−13.1787	−0.513370	−0.256685	+	0.966495i	$0.582630\pi$
$660$	−0.892593	−0.0347441
$661$	15.8645	0.617057	0.308528	−	0.951215i	$-0.400164\pi$
$661$	15.8645	0.617057	0.308528	+	0.951215i	$0.400164\pi$
$662$	−1.67062	−0.0649306
$663$	16.3929	0.636647
$664$	4.36949	0.169569
$665$	−3.10777	−0.120514
$666$	21.7941	0.844505
$667$	17.2227	0.666865
$668$	−20.2855	−0.784869
$669$	49.9604	1.93158
$670$	14.6924	0.567617
$671$	1.23192	0.0475577
$672$	−0.933166	−0.0359977
$673$	16.8205	0.648384	0.324192	−	0.945991i	$-0.394908\pi$
$673$	16.8205	0.648384	0.324192	+	0.945991i	$0.394908\pi$
$674$	−7.19091	−0.276983
$675$	4.89561	0.188432
$676$	−8.37144	−0.321978
$677$	−24.3155	−0.934519	−0.467260	−	0.884120i	$-0.654759\pi$
$677$	−24.3155	−0.934519	−0.467260	+	0.884120i	$0.654759\pi$
$678$	−13.3609	−0.513121
$679$	2.38535	0.0915413
$680$	3.16817	0.121494
$681$	37.5128	1.43749
$682$	−2.86131	−0.109565
$683$	36.1274	1.38238	0.691188	−	0.722675i	$-0.257087\pi$
$683$	36.1274	1.38238	0.691188	+	0.722675i	$0.257087\pi$
$684$	−27.9974	−1.07051
$685$	3.63561	0.138909
$686$	−5.07696	−0.193839
$687$	−64.7077	−2.46875
$688$	8.94270	0.340937
$689$	21.1489	0.805710
$690$	19.0743	0.726147
$691$	8.41715	0.320204	0.160102	−	0.987101i	$-0.448818\pi$
$691$	8.41715	0.320204	0.160102	+	0.987101i	$0.448818\pi$
$692$	13.6654	0.519479
$693$	0.422987	0.0160679
$694$	19.6921	0.747504
$695$	−2.71073	−0.102824
$696$	−6.21500	−0.235579
$697$	15.6839	0.594072
$698$	−23.1445	−0.876031
$699$	−54.7917	−2.07241
$700$	1.41957	0.0536546
$701$	−33.3448	−1.25942	−0.629708	−	0.776832i	$-0.716825\pi$
$701$	−33.3448	−1.25942	−0.629708	+	0.776832i	$0.716825\pi$
$702$	−2.71661	−0.102532
$703$	49.9403	1.88353
$704$	−0.330498	−0.0124561
$705$	−7.21187	−0.271615
$706$	1.35810	0.0511126
$707$	3.78223	0.142245
$708$	−22.8190	−0.857592
$709$	38.4715	1.44483	0.722413	−	0.691462i	$-0.243033\pi$
$709$	38.4715	1.44483	0.722413	+	0.691462i	$0.243033\pi$
$710$	−7.36850	−0.276535
$711$	20.0677	0.752599
$712$	0.774967	0.0290431
$713$	61.1449	2.28989
$714$	−2.78989	−0.104409
$715$	−0.753481	−0.0281786
$716$	−22.8049	−0.852260
$717$	−36.3682	−1.35819
$718$	10.7991	0.403018
$719$	20.5776	0.767416	0.383708	−	0.923454i	$-0.374647\pi$
$719$	20.5776	0.767416	0.383708	+	0.923454i	$0.374647\pi$
$720$	−3.70410	−0.138044
$721$	−6.32844	−0.235683
$722$	−45.1548	−1.68049
$723$	39.3710	1.46422
$724$	−14.7165	−0.546935
$725$	9.45449	0.351131
$726$	−27.7564	−1.03014
$727$	−9.44500	−0.350296	−0.175148	−	0.984542i	$-0.556040\pi$
$727$	−9.44500	−0.350296	−0.175148	+	0.984542i	$0.556040\pi$
$728$	−0.787730	−0.0291952
$729$	−35.0601	−1.29852
$730$	−16.3553	−0.605337
$731$	26.7360	0.988867
$732$	9.49986	0.351125
$733$	8.98357	0.331816	0.165908	−	0.986141i	$-0.446945\pi$
$733$	8.98357	0.331816	0.165908	+	0.986141i	$0.446945\pi$
$734$	11.8639	0.437905
$735$	−18.5432	−0.683976
$736$	7.06260	0.260331
$737$	−4.58228	−0.168791
$738$	−18.3371	−0.674998
$739$	−12.5226	−0.460651	−0.230326	−	0.973114i	$-0.573979\pi$
$739$	−12.5226	−0.460651	−0.230326	+	0.973114i	$0.573979\pi$
$740$	6.60718	0.242885
$741$	−43.9180	−1.61337
$742$	−3.59931	−0.132135
$743$	31.5382	1.15703	0.578513	−	0.815674i	$-0.303633\pi$
$743$	31.5382	1.15703	0.578513	+	0.815674i	$0.303633\pi$
$744$	−22.0648	−0.808936
$745$	8.80774	0.322691
$746$	−6.60210	−0.241720
$747$	−15.2733	−0.558822
$748$	−0.988092	−0.0361282
$749$	3.11439	0.113797
$750$	23.9747	0.875432
$751$	−29.9161	−1.09165	−0.545826	−	0.837898i	$-0.683784\pi$
$751$	−29.9161	−1.09165	−0.545826	+	0.837898i	$0.683784\pi$
$752$	−2.67032	−0.0973766
$753$	42.4004	1.54516
$754$	−5.24638	−0.191062
$755$	−15.8399	−0.576471
$756$	0.462338	0.0168151
$757$	51.6813	1.87839	0.939195	−	0.343385i	$-0.111573\pi$
$757$	51.6813	1.87839	0.939195	+	0.343385i	$0.111573\pi$
$758$	−9.40309	−0.341536
$759$	−5.94892	−0.215932
$760$	−8.48779	−0.307884
$761$	−17.0393	−0.617673	−0.308837	−	0.951115i	$-0.599940\pi$
$761$	−17.0393	−0.617673	−0.308837	+	0.951115i	$0.599940\pi$
$762$	−45.2177	−1.63806
$763$	3.97057	0.143744
$764$	3.37278	0.122023
$765$	−11.0742	−0.400387
$766$	2.72237	0.0983631
$767$	−19.2626	−0.695533
$768$	−2.54862	−0.0919653
$769$	9.90111	0.357043	0.178522	−	0.983936i	$-0.442869\pi$
$769$	9.90111	0.357043	0.178522	+	0.983936i	$0.442869\pi$
$770$	0.128234	0.00462123
$771$	−3.63813	−0.131024
$772$	−2.70698	−0.0974265
$773$	−2.81430	−0.101224	−0.0506118	−	0.998718i	$-0.516117\pi$
$773$	−2.81430	−0.101224	−0.0506118	+	0.998718i	$0.516117\pi$
$774$	−31.2588	−1.12357
$775$	33.5658	1.20572
$776$	6.51475	0.233866
$777$	−5.81829	−0.208730
$778$	15.1828	0.544330
$779$	−42.0186	−1.50547
$780$	−5.81042	−0.208046
$781$	2.29810	0.0822324
$782$	21.1151	0.755073
$783$	3.07922	0.110043
$784$	−6.86594	−0.245212
$785$	17.7115	0.632149
$786$	−7.04060	−0.251130
$787$	15.1718	0.540815	0.270408	−	0.962746i	$-0.412842\pi$
$787$	15.1718	0.540815	0.270408	+	0.962746i	$0.412842\pi$
$788$	−8.37524	−0.298356
$789$	−15.1398	−0.538991
$790$	6.08380	0.216452
$791$	1.91948	0.0682490
$792$	1.15524	0.0410497
$793$	8.01929	0.284773
$794$	−3.09801	−0.109944
$795$	−26.5491	−0.941599
$796$	−17.8799	−0.633737
$797$	41.2589	1.46146	0.730732	−	0.682664i	$-0.239179\pi$
$797$	41.2589	1.46146	0.730732	+	0.682664i	$0.239179\pi$
$798$	7.47436	0.264589
$799$	−7.98347	−0.282435
$800$	3.87705	0.137074
$801$	−2.70886	−0.0957128
$802$	−2.08597	−0.0736583
$803$	5.10091	0.180007
$804$	−35.3360	−1.24621
$805$	−2.74030	−0.0965830
$806$	−18.6260	−0.656072
$807$	52.6903	1.85479
$808$	10.3298	0.363402
$809$	28.6529	1.00738	0.503691	−	0.863884i	$-0.331975\pi$
$809$	28.6529	1.00738	0.503691	+	0.863884i	$0.331975\pi$
$810$	−7.70203	−0.270622
$811$	24.5042	0.860457	0.430229	−	0.902720i	$-0.358433\pi$
$811$	24.5042	0.860457	0.430229	+	0.902720i	$0.358433\pi$
$812$	0.892875	0.0313338
$813$	2.39291	0.0839231
$814$	−2.06066	−0.0722259
$815$	−19.5267	−0.683992
$816$	−7.61961	−0.266740
$817$	−71.6281	−2.50595
$818$	13.4996	0.472003
$819$	2.75347	0.0962141
$820$	−5.55913	−0.194133
$821$	11.0710	0.386381	0.193191	−	0.981161i	$-0.438116\pi$
$821$	11.0710	0.386381	0.193191	+	0.981161i	$0.438116\pi$
$822$	−8.74384	−0.304976
$823$	−36.2138	−1.26233	−0.631167	−	0.775647i	$-0.717424\pi$
$823$	−36.2138	−1.26233	−0.631167	+	0.775647i	$0.717424\pi$
$824$	−17.2839	−0.602114
$825$	−3.26569	−0.113697
$826$	3.27829	0.114066
$827$	−34.5386	−1.20103	−0.600513	−	0.799615i	$-0.705037\pi$
$827$	−34.5386	−1.20103	−0.600513	+	0.799615i	$0.705037\pi$
$828$	−24.6870	−0.857931
$829$	25.0908	0.871439	0.435720	−	0.900082i	$-0.356494\pi$
$829$	25.0908	0.871439	0.435720	+	0.900082i	$0.356494\pi$
$830$	−4.63032	−0.160721
$831$	31.3554	1.08771
$832$	−2.15141	−0.0745867
$833$	−20.5271	−0.711222
$834$	6.51946	0.225750
$835$	21.4964	0.743913
$836$	2.64718	0.0915547
$837$	10.9320	0.377866
$838$	−12.6852	−0.438204
$839$	−22.6697	−0.782645	−0.391323	−	0.920254i	$-0.627982\pi$
$839$	−22.6697	−0.782645	−0.391323	+	0.920254i	$0.627982\pi$
$840$	0.988869	0.0341192
$841$	−23.0533	−0.794943
$842$	25.0748	0.864134
$843$	−13.6095	−0.468737
$844$	12.1439	0.418009
$845$	8.87115	0.305177
$846$	9.33397	0.320909
$847$	3.98761	0.137016
$848$	−9.83026	−0.337573
$849$	−34.6400	−1.18884
$850$	11.5912	0.397576
$851$	44.0353	1.50951
$852$	17.7216	0.607134
$853$	−26.4036	−0.904042	−0.452021	−	0.892007i	$-0.649297\pi$
$853$	−26.4036	−0.904042	−0.452021	+	0.892007i	$0.649297\pi$
$854$	−1.36479	−0.0467023
$855$	29.6686	1.01465
$856$	8.50588	0.290725
$857$	−43.9697	−1.50198	−0.750988	−	0.660316i	$-0.770423\pi$
$857$	−43.9697	−1.50198	−0.750988	+	0.660316i	$0.770423\pi$
$858$	1.81216	0.0618662
$859$	−42.2380	−1.44114	−0.720571	−	0.693381i	$-0.756120\pi$
$859$	−42.2380	−1.44114	−0.720571	+	0.693381i	$0.756120\pi$
$860$	−9.47651	−0.323146
$861$	4.89538	0.166834
$862$	22.5872	0.769322
$863$	43.1074	1.46739	0.733696	−	0.679477i	$-0.237793\pi$
$863$	43.1074	1.46739	0.733696	+	0.679477i	$0.237793\pi$
$864$	1.26271	0.0429584
$865$	−14.4811	−0.492372
$866$	−7.18379	−0.244115
$867$	20.5461	0.697783
$868$	3.16993	0.107595
$869$	−1.89742	−0.0643657
$870$	6.58599	0.223286
$871$	−29.8288	−1.01071
$872$	10.8442	0.367232
$873$	−22.7720	−0.770715
$874$	−56.5691	−1.91348
$875$	−3.44432	−0.116439
$876$	39.3354	1.32902
$877$	27.8161	0.939284	0.469642	−	0.882857i	$-0.344383\pi$
$877$	27.8161	0.939284	0.469642	+	0.882857i	$0.344383\pi$
$878$	15.5591	0.525095
$879$	63.7648	2.15073
$880$	0.350226	0.0118061
$881$	−24.6494	−0.830460	−0.415230	−	0.909716i	$-0.636299\pi$
$881$	−24.6494	−0.830460	−0.415230	+	0.909716i	$0.636299\pi$
$882$	23.9995	0.808107
$883$	58.3109	1.96232	0.981159	−	0.193204i	$-0.0618880\pi$
$883$	58.3109	1.96232	0.981159	+	0.193204i	$0.0618880\pi$
$884$	−6.43208	−0.216334
$885$	24.1811	0.812840
$886$	−11.8115	−0.396814
$887$	13.8987	0.466672	0.233336	−	0.972396i	$-0.425036\pi$
$887$	13.8987	0.466672	0.233336	+	0.972396i	$0.425036\pi$
$888$	−15.8906	−0.533254
$889$	6.49618	0.217875
$890$	−0.821227	−0.0275276
$891$	2.40212	0.0804740
$892$	−19.6029	−0.656355
$893$	21.3884	0.715735
$894$	−21.1831	−0.708468
$895$	24.1662	0.807787
$896$	0.366146	0.0122321
$897$	−38.7251	−1.29299
$898$	39.4386	1.31608
$899$	21.1121	0.704129
$900$	−13.5520	−0.451735
$901$	−29.3896	−0.979108
$902$	1.73379	0.0577289
$903$	8.34502	0.277705
$904$	5.24240	0.174360
$905$	15.5950	0.518394
$906$	38.0957	1.26564
$907$	−27.5844	−0.915924	−0.457962	−	0.888972i	$-0.651420\pi$
$907$	−27.5844	−0.915924	−0.457962	+	0.888972i	$0.651420\pi$
$908$	−14.7189	−0.488463
$909$	−36.1074	−1.19761
$910$	0.834752	0.0276717
$911$	35.3576	1.17145	0.585725	−	0.810510i	$-0.300810\pi$
$911$	35.3576	1.17145	0.585725	+	0.810510i	$0.300810\pi$
$912$	20.4136	0.675961
$913$	1.44411	0.0477930
$914$	8.03841	0.265887
$915$	−10.0669	−0.332803
$916$	25.3893	0.838887
$917$	1.01149	0.0334022
$918$	3.77514	0.124598
$919$	18.8639	0.622262	0.311131	−	0.950367i	$-0.399292\pi$
$919$	18.8639	0.622262	0.311131	+	0.950367i	$0.399292\pi$
$920$	−7.48418	−0.246746
$921$	−34.3111	−1.13059
$922$	−1.68334	−0.0554377
$923$	14.9597	0.492404
$924$	−0.308410	−0.0101459
$925$	24.1734	0.794817
$926$	−15.6386	−0.513915
$927$	60.4151	1.98429
$928$	2.43858	0.0800502
$929$	−46.8990	−1.53871	−0.769353	−	0.638824i	$-0.779421\pi$
$929$	−46.8990	−1.53871	−0.769353	+	0.638824i	$0.779421\pi$
$930$	23.3819	0.766723
$931$	54.9939	1.80235
$932$	21.4986	0.704210
$933$	67.2869	2.20287
$934$	−27.6720	−0.905457
$935$	1.04707	0.0342430
$936$	7.52015	0.245804
$937$	−39.5010	−1.29044	−0.645221	−	0.763996i	$-0.723235\pi$
$937$	−39.5010	−1.29044	−0.645221	+	0.763996i	$0.723235\pi$
$938$	5.07653	0.165755
$939$	−57.0246	−1.86093
$940$	2.82972	0.0922952
$941$	−2.64668	−0.0862791	−0.0431396	−	0.999069i	$-0.513736\pi$
$941$	−2.64668	−0.0862791	−0.0431396	+	0.999069i	$0.513736\pi$
$942$	−42.5970	−1.38789
$943$	−37.0503	−1.20652
$944$	8.95349	0.291411
$945$	−0.489936	−0.0159376
$946$	2.95555	0.0960931
$947$	3.22084	0.104663	0.0523316	−	0.998630i	$-0.483335\pi$
$947$	3.22084	0.104663	0.0523316	+	0.998630i	$0.483335\pi$
$948$	−14.6319	−0.475221
$949$	33.2049	1.07788
$950$	−31.0539	−1.00752
$951$	−51.1520	−1.65872
$952$	1.09467	0.0354784
$953$	9.36133	0.303243	0.151622	−	0.988439i	$-0.451550\pi$
$953$	9.36133	0.303243	0.151622	+	0.988439i	$0.451550\pi$
$954$	34.3612	1.11248
$955$	−3.57411	−0.115655
$956$	14.2698	0.461517
$957$	−2.05405	−0.0663979
$958$	31.5909	1.02065
$959$	1.25618	0.0405642
$960$	2.70075	0.0871663
$961$	43.9534	1.41785
$962$	−13.4140	−0.432486
$963$	−29.7319	−0.958096
$964$	−15.4480	−0.497547
$965$	2.86857	0.0923426
$966$	6.59058	0.212048
$967$	19.8715	0.639025	0.319512	−	0.947582i	$-0.396481\pi$
$967$	19.8715	0.639025	0.319512	+	0.947582i	$0.396481\pi$
$968$	10.8908	0.350043
$969$	61.0306	1.96058
$970$	−6.90363	−0.221662
$971$	12.4048	0.398090	0.199045	−	0.979990i	$-0.436216\pi$
$971$	12.4048	0.398090	0.199045	+	0.979990i	$0.436216\pi$
$972$	22.3119	0.715656
$973$	−0.936616	−0.0300265
$974$	4.10339	0.131481
$975$	−21.2583	−0.680812
$976$	−3.72746	−0.119313
$977$	28.0136	0.896235	0.448117	−	0.893975i	$-0.352095\pi$
$977$	28.0136	0.896235	0.448117	+	0.893975i	$0.352095\pi$
$978$	46.9628	1.50171
$979$	0.256125	0.00818580
$980$	7.27578	0.232416
$981$	−37.9055	−1.21023
$982$	4.83659	0.154342
$983$	−58.1407	−1.85440	−0.927200	−	0.374568i	$-0.877791\pi$
$983$	−58.1407	−1.85440	−0.927200	+	0.374568i	$0.877791\pi$
$984$	13.3700	0.426221
$985$	8.87518	0.282787
$986$	7.29062	0.232181
$987$	−2.49185	−0.0793166
$988$	17.2321	0.548226
$989$	−63.1587	−2.00833
$990$	−1.22420	−0.0389076
$991$	−37.1599	−1.18042	−0.590212	−	0.807249i	$-0.700956\pi$
$991$	−37.1599	−1.18042	−0.590212	+	0.807249i	$0.700956\pi$
$992$	8.65756	0.274878
$993$	−4.25778	−0.135116
$994$	−2.54597	−0.0807534
$995$	18.9472	0.600667
$996$	11.1362	0.352863
$997$	53.1299	1.68264	0.841321	−	0.540537i	$-0.181779\pi$
$997$	53.1299	1.68264	0.841321	+	0.540537i	$0.181779\pi$
$998$	−7.24316	−0.229278
$999$	7.87302	0.249091

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8042.2.a.c.1.9	✓	86

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8042.2.a.c.1.9	✓	86	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:	\( N \)	\(=\)	\( 8042 = 2 \cdot 4021 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8042.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -2.54862 q^{3} +1.00000 q^{4} -1.05969 q^{5} +2.54862 q^{6} -0.366146 q^{7} -1.00000 q^{8} +3.49545 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -2.54862 q^{3} +1.00000 q^{4} -1.05969 q^{5} +2.54862 q^{6} -0.366146 q^{7} -1.00000 q^{8} +3.49545 q^{9} +1.05969 q^{10} -0.330498 q^{11} -2.54862 q^{12} -2.15141 q^{13} +0.366146 q^{14} +2.70075 q^{15} +1.00000 q^{16} +2.98970 q^{17} -3.49545 q^{18} -8.00967 q^{19} -1.05969 q^{20} +0.933166 q^{21} +0.330498 q^{22} -7.06260 q^{23} +2.54862 q^{24} -3.87705 q^{25} +2.15141 q^{26} -1.26271 q^{27} -0.366146 q^{28} -2.43858 q^{29} -2.70075 q^{30} -8.65756 q^{31} -1.00000 q^{32} +0.842314 q^{33} -2.98970 q^{34} +0.388002 q^{35} +3.49545 q^{36} -6.23500 q^{37} +8.00967 q^{38} +5.48312 q^{39} +1.05969 q^{40} +5.24599 q^{41} -0.933166 q^{42} +8.94270 q^{43} -0.330498 q^{44} -3.70410 q^{45} +7.06260 q^{46} -2.67032 q^{47} -2.54862 q^{48} -6.86594 q^{49} +3.87705 q^{50} -7.61961 q^{51} -2.15141 q^{52} -9.83026 q^{53} +1.26271 q^{54} +0.350226 q^{55} +0.366146 q^{56} +20.4136 q^{57} +2.43858 q^{58} +8.95349 q^{59} +2.70075 q^{60} -3.72746 q^{61} +8.65756 q^{62} -1.27985 q^{63} +1.00000 q^{64} +2.27983 q^{65} -0.842314 q^{66} +13.8648 q^{67} +2.98970 q^{68} +17.9999 q^{69} -0.388002 q^{70} -6.95344 q^{71} -3.49545 q^{72} -15.4340 q^{73} +6.23500 q^{74} +9.88112 q^{75} -8.00967 q^{76} +0.121011 q^{77} -5.48312 q^{78} +5.74110 q^{79} -1.05969 q^{80} -7.26818 q^{81} -5.24599 q^{82} -4.36949 q^{83} +0.933166 q^{84} -3.16817 q^{85} -8.94270 q^{86} +6.21500 q^{87} +0.330498 q^{88} -0.774967 q^{89} +3.70410 q^{90} +0.787730 q^{91} -7.06260 q^{92} +22.0648 q^{93} +2.67032 q^{94} +8.48779 q^{95} +2.54862 q^{96} -6.51475 q^{97} +6.86594 q^{98} -1.15524 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 86 q - 86 q^{2} + 12 q^{3} + 86 q^{4} - 4 q^{5} - 12 q^{6} + 35 q^{7} - 86 q^{8} + 72 q^{9}+O(q^{10}) \) 86 * q - 86 * q^2 + 12 * q^3 + 86 * q^4 - 4 * q^5 - 12 * q^6 + 35 * q^7 - 86 * q^8 + 72 * q^9	\( 86 q - 86 q^{2} + 12 q^{3} + 86 q^{4} - 4 q^{5} - 12 q^{6} + 35 q^{7} - 86 q^{8} + 72 q^{9} + 4 q^{10} + 13 q^{11} + 12 q^{12} + 45 q^{13} - 35 q^{14} + 17 q^{15} + 86 q^{16} + 5 q^{17} - 72 q^{18} + 47 q^{19} - 4 q^{20} + 15 q^{21} - 13 q^{22} + 6 q^{23} - 12 q^{24} + 112 q^{25} - 45 q^{26} + 51 q^{27} + 35 q^{28} - 14 q^{29} - 17 q^{30} + 24 q^{31} - 86 q^{32} + 43 q^{33} - 5 q^{34} + 42 q^{35} + 72 q^{36} + 61 q^{37} - 47 q^{38} + 20 q^{39} + 4 q^{40} - 16 q^{41} - 15 q^{42} + 72 q^{43} + 13 q^{44} + 6 q^{45} - 6 q^{46} + 11 q^{47} + 12 q^{48} + 89 q^{49} - 112 q^{50} + 56 q^{51} + 45 q^{52} - 7 q^{53} - 51 q^{54} + 48 q^{55} - 35 q^{56} + 65 q^{57} + 14 q^{58} + 24 q^{59} + 17 q^{60} + 31 q^{61} - 24 q^{62} + 98 q^{63} + 86 q^{64} - 9 q^{65} - 43 q^{66} + 157 q^{67} + 5 q^{68} + q^{69} - 42 q^{70} - 11 q^{71} - 72 q^{72} + 74 q^{73} - 61 q^{74} + 76 q^{75} + 47 q^{76} - 13 q^{77} - 20 q^{78} + 57 q^{79} - 4 q^{80} + 34 q^{81} + 16 q^{82} + 65 q^{83} + 15 q^{84} + 102 q^{85} - 72 q^{86} + 49 q^{87} - 13 q^{88} - 34 q^{89} - 6 q^{90} + 91 q^{91} + 6 q^{92} + 57 q^{93} - 11 q^{94} - 13 q^{95} - 12 q^{96} + 64 q^{97} - 89 q^{98} + 56 q^{99}+O(q^{100}) \) 86 * q - 86 * q^2 + 12 * q^3 + 86 * q^4 - 4 * q^5 - 12 * q^6 + 35 * q^7 - 86 * q^8 + 72 * q^9 + 4 * q^10 + 13 * q^11 + 12 * q^12 + 45 * q^13 - 35 * q^14 + 17 * q^15 + 86 * q^16 + 5 * q^17 - 72 * q^18 + 47 * q^19 - 4 * q^20 + 15 * q^21 - 13 * q^22 + 6 * q^23 - 12 * q^24 + 112 * q^25 - 45 * q^26 + 51 * q^27 + 35 * q^28 - 14 * q^29 - 17 * q^30 + 24 * q^31 - 86 * q^32 + 43 * q^33 - 5 * q^34 + 42 * q^35 + 72 * q^36 + 61 * q^37 - 47 * q^38 + 20 * q^39 + 4 * q^40 - 16 * q^41 - 15 * q^42 + 72 * q^43 + 13 * q^44 + 6 * q^45 - 6 * q^46 + 11 * q^47 + 12 * q^48 + 89 * q^49 - 112 * q^50 + 56 * q^51 + 45 * q^52 - 7 * q^53 - 51 * q^54 + 48 * q^55 - 35 * q^56 + 65 * q^57 + 14 * q^58 + 24 * q^59 + 17 * q^60 + 31 * q^61 - 24 * q^62 + 98 * q^63 + 86 * q^64 - 9 * q^65 - 43 * q^66 + 157 * q^67 + 5 * q^68 + q^69 - 42 * q^70 - 11 * q^71 - 72 * q^72 + 74 * q^73 - 61 * q^74 + 76 * q^75 + 47 * q^76 - 13 * q^77 - 20 * q^78 + 57 * q^79 - 4 * q^80 + 34 * q^81 + 16 * q^82 + 65 * q^83 + 15 * q^84 + 102 * q^85 - 72 * q^86 + 49 * q^87 - 13 * q^88 - 34 * q^89 - 6 * q^90 + 91 * q^91 + 6 * q^92 + 57 * q^93 - 11 * q^94 - 13 * q^95 - 12 * q^96 + 64 * q^97 - 89 * q^98 + 56 * q^99

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