LMFDB - Embedded newform 8039.2.a.b.1.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8039,2,Mod(1,8039)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8039, 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("8039.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8039 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8039.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:	$64.1917381849$
Analytic rank:	$0$
Dimension:	$391$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.16
Character	$\chi$	$=$	8039.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.64673 q^{2} -3.15136 q^{3} +5.00518 q^{4} +2.70892 q^{5} +8.34080 q^{6} -2.33255 q^{7} -7.95389 q^{8} +6.93109 q^{9} +O(q^{10})$	\(q-2.64673 q^{2} -3.15136 q^{3} +5.00518 q^{4} +2.70892 q^{5} +8.34080 q^{6} -2.33255 q^{7} -7.95389 q^{8} +6.93109 q^{9} -7.16979 q^{10} +5.07906 q^{11} -15.7731 q^{12} -5.63175 q^{13} +6.17363 q^{14} -8.53680 q^{15} +11.0414 q^{16} +3.44159 q^{17} -18.3447 q^{18} -1.62224 q^{19} +13.5586 q^{20} +7.35072 q^{21} -13.4429 q^{22} +4.60394 q^{23} +25.0656 q^{24} +2.33827 q^{25} +14.9057 q^{26} -12.3883 q^{27} -11.6748 q^{28} -2.56214 q^{29} +22.5946 q^{30} -7.10645 q^{31} -13.3159 q^{32} -16.0060 q^{33} -9.10896 q^{34} -6.31871 q^{35} +34.6913 q^{36} -2.56590 q^{37} +4.29362 q^{38} +17.7477 q^{39} -21.5465 q^{40} +10.1927 q^{41} -19.4554 q^{42} +7.54657 q^{43} +25.4216 q^{44} +18.7758 q^{45} -12.1854 q^{46} -8.81470 q^{47} -34.7956 q^{48} -1.55920 q^{49} -6.18876 q^{50} -10.8457 q^{51} -28.1879 q^{52} -1.27267 q^{53} +32.7884 q^{54} +13.7588 q^{55} +18.5529 q^{56} +5.11225 q^{57} +6.78130 q^{58} -4.13805 q^{59} -42.7282 q^{60} -4.41716 q^{61} +18.8088 q^{62} -16.1671 q^{63} +13.1608 q^{64} -15.2560 q^{65} +42.3635 q^{66} -2.83265 q^{67} +17.2258 q^{68} -14.5087 q^{69} +16.7239 q^{70} +5.08293 q^{71} -55.1291 q^{72} -9.73281 q^{73} +6.79125 q^{74} -7.36872 q^{75} -8.11958 q^{76} -11.8472 q^{77} -46.9734 q^{78} -10.8214 q^{79} +29.9104 q^{80} +18.2467 q^{81} -26.9773 q^{82} -10.6173 q^{83} +36.7916 q^{84} +9.32300 q^{85} -19.9737 q^{86} +8.07424 q^{87} -40.3983 q^{88} +16.3182 q^{89} -49.6944 q^{90} +13.1364 q^{91} +23.0435 q^{92} +22.3950 q^{93} +23.3301 q^{94} -4.39451 q^{95} +41.9633 q^{96} -4.21927 q^{97} +4.12678 q^{98} +35.2034 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 391 q + 14 q^{2} + 12 q^{3} + 446 q^{4} + 22 q^{5} + 40 q^{6} + 63 q^{7} + 36 q^{8} + 501 q^{9}+O(q^{10}) $ 391 * q + 14 * q^2 + 12 * q^3 + 446 * q^4 + 22 * q^5 + 40 * q^6 + 63 * q^7 + 36 * q^8 + 501 * q^9	\( 391 q + 14 q^{2} + 12 q^{3} + 446 q^{4} + 22 q^{5} + 40 q^{6} + 63 q^{7} + 36 q^{8} + 501 q^{9} + 40 q^{10} + 57 q^{11} + 20 q^{12} + 83 q^{13} + 21 q^{14} + 60 q^{15} + 548 q^{16} + 59 q^{17} + 54 q^{18} + 131 q^{19} + 35 q^{20} + 121 q^{21} + 89 q^{22} + 34 q^{23} + 110 q^{24} + 609 q^{25} + 54 q^{26} + 27 q^{27} + 182 q^{28} + 102 q^{29} + 92 q^{30} + 88 q^{31} + 76 q^{32} + 131 q^{33} + 128 q^{34} + 31 q^{35} + 654 q^{36} + 135 q^{37} + 23 q^{38} + 96 q^{39} + 113 q^{40} + 128 q^{41} + 45 q^{42} + 140 q^{43} + 151 q^{44} + 77 q^{45} + 245 q^{46} + 22 q^{47} + 25 q^{48} + 712 q^{49} + 53 q^{50} + 102 q^{51} + 174 q^{52} + 54 q^{53} + 131 q^{54} + 101 q^{55} + 43 q^{56} + 226 q^{57} + 109 q^{58} + 40 q^{59} + 123 q^{60} + 249 q^{61} + 28 q^{62} + 139 q^{63} + 730 q^{64} + 227 q^{65} + 55 q^{66} + 169 q^{67} + 48 q^{68} + 89 q^{69} + 98 q^{70} + 66 q^{71} + 120 q^{72} + 324 q^{73} + 60 q^{74} + 19 q^{75} + 356 q^{76} + 83 q^{77} - 11 q^{78} + 195 q^{79} + 26 q^{80} + 807 q^{81} + 49 q^{82} + 74 q^{83} + 252 q^{84} + 373 q^{85} + 100 q^{86} + 43 q^{87} + 211 q^{88} + 207 q^{89} + 10 q^{90} + 189 q^{91} + 30 q^{92} + 172 q^{93} + 130 q^{94} + 43 q^{95} + 203 q^{96} + 254 q^{97} + 26 q^{98} + 273 q^{99}+O(q^{100}) \) 391 * q + 14 * q^2 + 12 * q^3 + 446 * q^4 + 22 * q^5 + 40 * q^6 + 63 * q^7 + 36 * q^8 + 501 * q^9 + 40 * q^10 + 57 * q^11 + 20 * q^12 + 83 * q^13 + 21 * q^14 + 60 * q^15 + 548 * q^16 + 59 * q^17 + 54 * q^18 + 131 * q^19 + 35 * q^20 + 121 * q^21 + 89 * q^22 + 34 * q^23 + 110 * q^24 + 609 * q^25 + 54 * q^26 + 27 * q^27 + 182 * q^28 + 102 * q^29 + 92 * q^30 + 88 * q^31 + 76 * q^32 + 131 * q^33 + 128 * q^34 + 31 * q^35 + 654 * q^36 + 135 * q^37 + 23 * q^38 + 96 * q^39 + 113 * q^40 + 128 * q^41 + 45 * q^42 + 140 * q^43 + 151 * q^44 + 77 * q^45 + 245 * q^46 + 22 * q^47 + 25 * q^48 + 712 * q^49 + 53 * q^50 + 102 * q^51 + 174 * q^52 + 54 * q^53 + 131 * q^54 + 101 * q^55 + 43 * q^56 + 226 * q^57 + 109 * q^58 + 40 * q^59 + 123 * q^60 + 249 * q^61 + 28 * q^62 + 139 * q^63 + 730 * q^64 + 227 * q^65 + 55 * q^66 + 169 * q^67 + 48 * q^68 + 89 * q^69 + 98 * q^70 + 66 * q^71 + 120 * q^72 + 324 * q^73 + 60 * q^74 + 19 * q^75 + 356 * q^76 + 83 * q^77 - 11 * q^78 + 195 * q^79 + 26 * q^80 + 807 * q^81 + 49 * q^82 + 74 * q^83 + 252 * q^84 + 373 * q^85 + 100 * q^86 + 43 * q^87 + 211 * q^88 + 207 * q^89 + 10 * q^90 + 189 * q^91 + 30 * q^92 + 172 * q^93 + 130 * q^94 + 43 * q^95 + 203 * q^96 + 254 * q^97 + 26 * q^98 + 273 * 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 $

$2$	−2.64673	−1.87152	−0.935760	−	0.352637i	$-0.885285\pi$
$2$	−2.64673	−1.87152	−0.935760	+	0.352637i	$0.885285\pi$
$3$	−3.15136	−1.81944	−0.909720	−	0.415222i	$-0.863704\pi$
$3$	−3.15136	−1.81944	−0.909720	+	0.415222i	$0.863704\pi$
$4$	5.00518	2.50259
$5$	2.70892	1.21147	0.605734	−	0.795667i	$-0.292880\pi$
$5$	2.70892	1.21147	0.605734	+	0.795667i	$0.292880\pi$
$6$	8.34080	3.40512
$7$	−2.33255	−0.881622	−0.440811	−	0.897600i	$-0.645309\pi$
$7$	−2.33255	−0.881622	−0.440811	+	0.897600i	$0.645309\pi$
$8$	−7.95389	−2.81212
$9$	6.93109	2.31036
$10$	−7.16979	−2.26729
$11$	5.07906	1.53140	0.765698	−	0.643200i	$-0.222394\pi$
$11$	5.07906	1.53140	0.765698	+	0.643200i	$0.222394\pi$
$12$	−15.7731	−4.55331
$13$	−5.63175	−1.56197	−0.780984	−	0.624551i	$-0.785282\pi$
$13$	−5.63175	−1.56197	−0.780984	+	0.624551i	$0.785282\pi$
$14$	6.17363	1.64997
$15$	−8.53680	−2.20419
$16$	11.0414	2.76036
$17$	3.44159	0.834708	0.417354	−	0.908744i	$-0.362958\pi$
$17$	3.44159	0.834708	0.417354	+	0.908744i	$0.362958\pi$
$18$	−18.3447	−4.32389
$19$	−1.62224	−0.372166	−0.186083	−	0.982534i	$-0.559579\pi$
$19$	−1.62224	−0.372166	−0.186083	+	0.982534i	$0.559579\pi$
$20$	13.5586	3.03180
$21$	7.35072	1.60406
$22$	−13.4429	−2.86604
$23$	4.60394	0.959987	0.479994	−	0.877272i	$-0.340639\pi$
$23$	4.60394	0.959987	0.479994	+	0.877272i	$0.340639\pi$
$24$	25.0656	5.11649
$25$	2.33827	0.467653
$26$	14.9057	2.92325
$27$	−12.3883	−2.38412
$28$	−11.6748	−2.20634
$29$	−2.56214	−0.475778	−0.237889	−	0.971292i	$-0.576455\pi$
$29$	−2.56214	−0.475778	−0.237889	+	0.971292i	$0.576455\pi$
$30$	22.5946	4.12519
$31$	−7.10645	−1.27636	−0.638178	−	0.769889i	$-0.720312\pi$
$31$	−7.10645	−1.27636	−0.638178	+	0.769889i	$0.720312\pi$
$32$	−13.3159	−2.35395
$33$	−16.0060	−2.78628
$34$	−9.10896	−1.56217
$35$	−6.31871	−1.06806
$36$	34.6913	5.78188
$37$	−2.56590	−0.421832	−0.210916	−	0.977504i	$-0.567645\pi$
$37$	−2.56590	−0.421832	−0.210916	+	0.977504i	$0.567645\pi$
$38$	4.29362	0.696517
$39$	17.7477	2.84191
$40$	−21.5465	−3.40680
$41$	10.1927	1.59183	0.795916	−	0.605407i	$-0.206990\pi$
$41$	10.1927	1.59183	0.795916	+	0.605407i	$0.206990\pi$
$42$	−19.4554	−3.00203
$43$	7.54657	1.15084	0.575421	−	0.817857i	$-0.304838\pi$
$43$	7.54657	1.15084	0.575421	+	0.817857i	$0.304838\pi$
$44$	25.4216	3.83245
$45$	18.7758	2.79893
$46$	−12.1854	−1.79664
$47$	−8.81470	−1.28576	−0.642878	−	0.765968i	$-0.722260\pi$
$47$	−8.81470	−1.28576	−0.642878	+	0.765968i	$0.722260\pi$
$48$	−34.7956	−5.02231
$49$	−1.55920	−0.222743
$50$	−6.18876	−0.875222
$51$	−10.8457	−1.51870
$52$	−28.1879	−3.90896
$53$	−1.27267	−0.174815	−0.0874073	−	0.996173i	$-0.527858\pi$
$53$	−1.27267	−0.174815	−0.0874073	+	0.996173i	$0.527858\pi$
$54$	32.7884	4.46194
$55$	13.7588	1.85524
$56$	18.5529	2.47923
$57$	5.11225	0.677134
$58$	6.78130	0.890428
$59$	−4.13805	−0.538728	−0.269364	−	0.963038i	$-0.586813\pi$
$59$	−4.13805	−0.538728	−0.269364	+	0.963038i	$0.586813\pi$
$60$	−42.7282	−5.51619
$61$	−4.41716	−0.565559	−0.282780	−	0.959185i	$-0.591257\pi$
$61$	−4.41716	−0.565559	−0.282780	+	0.959185i	$0.591257\pi$
$62$	18.8088	2.38873
$63$	−16.1671	−2.03687
$64$	13.1608	1.64510
$65$	−15.2560	−1.89227
$66$	42.3635	5.21458
$67$	−2.83265	−0.346063	−0.173032	−	0.984916i	$-0.555356\pi$
$67$	−2.83265	−0.346063	−0.173032	+	0.984916i	$0.555356\pi$
$68$	17.2258	2.08893
$69$	−14.5087	−1.74664
$70$	16.7239	1.99889
$71$	5.08293	0.603233	0.301617	−	0.953429i	$-0.402474\pi$
$71$	5.08293	0.603233	0.301617	+	0.953429i	$0.402474\pi$
$72$	−55.1291	−6.49703
$73$	−9.73281	−1.13914	−0.569570	−	0.821943i	$-0.692890\pi$
$73$	−9.73281	−1.13914	−0.569570	+	0.821943i	$0.692890\pi$
$74$	6.79125	0.789466
$75$	−7.36872	−0.850867
$76$	−8.11958	−0.931379
$77$	−11.8472	−1.35011
$78$	−46.9734	−5.31869
$79$	−10.8214	−1.21750	−0.608750	−	0.793362i	$-0.708329\pi$
$79$	−10.8214	−1.21750	−0.608750	+	0.793362i	$0.708329\pi$
$80$	29.9104	3.34409
$81$	18.2467	2.02741
$82$	−26.9773	−2.97915
$83$	−10.6173	−1.16540	−0.582702	−	0.812686i	$-0.698005\pi$
$83$	−10.6173	−1.16540	−0.582702	+	0.812686i	$0.698005\pi$
$84$	36.7916	4.01430
$85$	9.32300	1.01122
$86$	−19.9737	−2.15382
$87$	8.07424	0.865650
$88$	−40.3983	−4.30648
$89$	16.3182	1.72973	0.864865	−	0.502004i	$-0.167404\pi$
$89$	16.3182	1.72973	0.864865	+	0.502004i	$0.167404\pi$
$90$	−49.6944	−5.23825
$91$	13.1364	1.37706
$92$	23.0435	2.40245
$93$	22.3950	2.32225
$94$	23.3301	2.40632
$95$	−4.39451	−0.450867
$96$	41.9633	4.28286
$97$	−4.21927	−0.428402	−0.214201	−	0.976790i	$-0.568715\pi$
$97$	−4.21927	−0.428402	−0.214201	+	0.976790i	$0.568715\pi$
$98$	4.12678	0.416868
$99$	35.2034	3.53808
$100$	11.7034	1.17034
$101$	12.3608	1.22994	0.614971	−	0.788549i	$-0.289168\pi$
$101$	12.3608	1.22994	0.614971	+	0.788549i	$0.289168\pi$
$102$	28.7056	2.84228
$103$	−1.19064	−0.117318	−0.0586588	−	0.998278i	$-0.518682\pi$
$103$	−1.19064	−0.117318	−0.0586588	+	0.998278i	$0.518682\pi$
$104$	44.7944	4.39245
$105$	19.9125	1.94326
$106$	3.36841	0.327169
$107$	18.7130	1.80905	0.904527	−	0.426417i	$-0.140224\pi$
$107$	18.7130	1.80905	0.904527	+	0.426417i	$0.140224\pi$
$108$	−62.0055	−5.96648
$109$	3.88559	0.372172	0.186086	−	0.982533i	$-0.440420\pi$
$109$	3.88559	0.372172	0.186086	+	0.982533i	$0.440420\pi$
$110$	−36.4158	−3.47211
$111$	8.08608	0.767497
$112$	−25.7547	−2.43359
$113$	3.32818	0.313089	0.156544	−	0.987671i	$-0.449965\pi$
$113$	3.32818	0.313089	0.156544	+	0.987671i	$0.449965\pi$
$114$	−13.5308	−1.26727
$115$	12.4717	1.16299
$116$	−12.8240	−1.19068
$117$	−39.0342	−3.60871
$118$	10.9523	1.00824
$119$	−8.02769	−0.735897
$120$	67.9008	6.19846
$121$	14.7969	1.34517
$122$	11.6910	1.05846
$123$	−32.1209	−2.89624
$124$	−35.5690	−3.19419
$125$	−7.21044	−0.644921
$126$	42.7900	3.81204
$127$	17.5790	1.55988	0.779942	−	0.625852i	$-0.215248\pi$
$127$	17.5790	1.55988	0.779942	+	0.625852i	$0.215248\pi$
$128$	−8.20117	−0.724888
$129$	−23.7820	−2.09389
$130$	40.3785	3.54143
$131$	8.80768	0.769531	0.384765	−	0.923014i	$-0.374282\pi$
$131$	8.80768	0.769531	0.384765	+	0.923014i	$0.374282\pi$
$132$	−80.1127	−6.97292
$133$	3.78395	0.328110
$134$	7.49726	0.647664
$135$	−33.5589	−2.88829
$136$	−27.3740	−2.34730
$137$	19.3286	1.65135	0.825677	−	0.564143i	$-0.190793\pi$
$137$	19.3286	1.65135	0.825677	+	0.564143i	$0.190793\pi$
$138$	38.4005	3.26887
$139$	−7.38335	−0.626248	−0.313124	−	0.949712i	$-0.601376\pi$
$139$	−7.38335	−0.626248	−0.313124	+	0.949712i	$0.601376\pi$
$140$	−31.6262	−2.67290
$141$	27.7783	2.33936
$142$	−13.4531	−1.12896
$143$	−28.6040	−2.39199
$144$	76.5292	6.37743
$145$	−6.94065	−0.576390
$146$	25.7601	2.13192
$147$	4.91360	0.405267
$148$	−12.8428	−1.05567
$149$	5.27626	0.432248	0.216124	−	0.976366i	$-0.430658\pi$
$149$	5.27626	0.432248	0.216124	+	0.976366i	$0.430658\pi$
$150$	19.5030	1.59241
$151$	−15.4388	−1.25639	−0.628195	−	0.778056i	$-0.716206\pi$
$151$	−15.4388	−1.25639	−0.628195	+	0.778056i	$0.716206\pi$
$152$	12.9031	1.04658
$153$	23.8540	1.92848
$154$	31.3563	2.52676
$155$	−19.2508	−1.54626
$156$	88.8304	7.11212
$157$	6.03509	0.481653	0.240826	−	0.970568i	$-0.422582\pi$
$157$	6.03509	0.481653	0.240826	+	0.970568i	$0.422582\pi$
$158$	28.6412	2.27858
$159$	4.01064	0.318065
$160$	−36.0718	−2.85173
$161$	−10.7389	−0.846346
$162$	−48.2940	−3.79434
$163$	10.0012	0.783357	0.391678	−	0.920102i	$-0.371895\pi$
$163$	10.0012	0.783357	0.391678	+	0.920102i	$0.371895\pi$
$164$	51.0162	3.98370
$165$	−43.3590	−3.37549
$166$	28.1012	2.18108
$167$	−15.3771	−1.18991	−0.594956	−	0.803758i	$-0.702831\pi$
$167$	−15.3771	−1.18991	−0.594956	+	0.803758i	$0.702831\pi$
$168$	−58.4668	−4.51081
$169$	18.7167	1.43974
$170$	−24.6755	−1.89252
$171$	−11.2439	−0.859839
$172$	37.7719	2.88008
$173$	22.8996	1.74103	0.870513	−	0.492146i	$-0.163787\pi$
$173$	22.8996	1.74103	0.870513	+	0.492146i	$0.163787\pi$
$174$	−21.3703	−1.62008
$175$	−5.45413	−0.412293
$176$	56.0802	4.22720
$177$	13.0405	0.980183
$178$	−43.1900	−3.23723
$179$	−0.238348	−0.0178150	−0.00890748	−	0.999960i	$-0.502835\pi$
$179$	−0.238348	−0.0178150	−0.00890748	+	0.999960i	$0.502835\pi$
$180$	93.9761	7.00456
$181$	−17.2790	−1.28434	−0.642168	−	0.766564i	$-0.721965\pi$
$181$	−17.2790	−1.28434	−0.642168	+	0.766564i	$0.721965\pi$
$182$	−34.7684	−2.57721
$183$	13.9201	1.02900
$184$	−36.6192	−2.69960
$185$	−6.95083	−0.511035
$186$	−59.2735	−4.34614
$187$	17.4801	1.27827
$188$	−44.1192	−3.21772
$189$	28.8963	2.10190
$190$	11.6311	0.843808
$191$	−3.26014	−0.235895	−0.117948	−	0.993020i	$-0.537631\pi$
$191$	−3.26014	−0.235895	−0.117948	+	0.993020i	$0.537631\pi$
$192$	−41.4744	−2.99316
$193$	20.1875	1.45313	0.726563	−	0.687100i	$-0.241117\pi$
$193$	20.1875	1.45313	0.726563	+	0.687100i	$0.241117\pi$
$194$	11.1673	0.801763
$195$	48.0772	3.44288
$196$	−7.80407	−0.557434
$197$	−19.0915	−1.36021	−0.680107	−	0.733113i	$-0.738067\pi$
$197$	−19.0915	−1.36021	−0.680107	+	0.733113i	$0.738067\pi$
$198$	−93.1740	−6.62159
$199$	7.11073	0.504066	0.252033	−	0.967719i	$-0.418901\pi$
$199$	7.11073	0.504066	0.252033	+	0.967719i	$0.418901\pi$
$200$	−18.5983	−1.31510
$201$	8.92670	0.629641
$202$	−32.7156	−2.30186
$203$	5.97633	0.419456
$204$	−54.2846	−3.80068
$205$	27.6112	1.92845
$206$	3.15131	0.219562
$207$	31.9103	2.21792
$208$	−62.1827	−4.31159
$209$	−8.23944	−0.569934
$210$	−52.7031	−3.63686
$211$	−22.4019	−1.54221	−0.771104	−	0.636709i	$-0.780295\pi$
$211$	−22.4019	−1.54221	−0.771104	+	0.636709i	$0.780295\pi$
$212$	−6.36994	−0.437489
$213$	−16.0182	−1.09755
$214$	−49.5282	−3.38568
$215$	20.4431	1.39421
$216$	98.5350	6.70446
$217$	16.5762	1.12526
$218$	−10.2841	−0.696528
$219$	30.6716	2.07260
$220$	68.8652	4.64289
$221$	−19.3822	−1.30379
$222$	−21.4017	−1.43639
$223$	−4.96264	−0.332323	−0.166161	−	0.986099i	$-0.553137\pi$
$223$	−4.96264	−0.332323	−0.166161	+	0.986099i	$0.553137\pi$
$224$	31.0601	2.07529
$225$	16.2067	1.08045
$226$	−8.80878	−0.585952
$227$	21.8180	1.44811	0.724056	−	0.689742i	$-0.242276\pi$
$227$	21.8180	1.44811	0.724056	+	0.689742i	$0.242276\pi$
$228$	25.5877	1.69459
$229$	18.8800	1.24763	0.623814	−	0.781573i	$-0.285582\pi$
$229$	18.8800	1.24763	0.623814	+	0.781573i	$0.285582\pi$
$230$	−33.0093	−2.17657
$231$	37.3348	2.45645
$232$	20.3790	1.33795
$233$	18.3460	1.20188	0.600942	−	0.799292i	$-0.294792\pi$
$233$	18.3460	1.20188	0.600942	+	0.799292i	$0.294792\pi$
$234$	103.313	6.75378
$235$	−23.8784	−1.55765
$236$	−20.7117	−1.34821
$237$	34.1021	2.21517
$238$	21.2471	1.37725
$239$	14.7027	0.951038	0.475519	−	0.879706i	$-0.342260\pi$
$239$	14.7027	0.951038	0.475519	+	0.879706i	$0.342260\pi$
$240$	−94.2586	−6.08436
$241$	6.85937	0.441851	0.220926	−	0.975291i	$-0.429092\pi$
$241$	6.85937	0.441851	0.220926	+	0.975291i	$0.429092\pi$
$242$	−39.1634	−2.51752
$243$	−20.3371	−1.30463
$244$	−22.1087	−1.41536
$245$	−4.22375	−0.269846
$246$	85.0153	5.42038
$247$	9.13603	0.581312
$248$	56.5239	3.58927
$249$	33.4591	2.12038
$250$	19.0841	1.20698
$251$	−20.7372	−1.30892	−0.654460	−	0.756097i	$-0.727104\pi$
$251$	−20.7372	−1.30892	−0.654460	+	0.756097i	$0.727104\pi$
$252$	−80.9193	−5.09744
$253$	23.3837	1.47012
$254$	−46.5269	−2.91936
$255$	−29.3802	−1.83986
$256$	−4.61529	−0.288456
$257$	−12.5341	−0.781856	−0.390928	−	0.920421i	$-0.627846\pi$
$257$	−12.5341	−0.781856	−0.390928	+	0.920421i	$0.627846\pi$
$258$	62.9445	3.91875
$259$	5.98510	0.371896
$260$	−76.3589	−4.73558
$261$	−17.7584	−1.09922
$262$	−23.3115	−1.44019
$263$	−8.10510	−0.499782	−0.249891	−	0.968274i	$-0.580395\pi$
$263$	−8.10510	−0.499782	−0.249891	+	0.968274i	$0.580395\pi$
$264$	127.310	7.83537
$265$	−3.44757	−0.211782
$266$	−10.0151	−0.614065
$267$	−51.4247	−3.14714
$268$	−14.1779	−0.866054
$269$	0.138037	0.00841625	0.00420813	−	0.999991i	$-0.498661\pi$
$269$	0.138037	0.00841625	0.00420813	+	0.999991i	$0.498661\pi$
$270$	88.8213	5.40549
$271$	−12.3273	−0.748833	−0.374416	−	0.927261i	$-0.622157\pi$
$271$	−12.3273	−0.748833	−0.374416	+	0.927261i	$0.622157\pi$
$272$	38.0001	2.30410
$273$	−41.3974	−2.50549
$274$	−51.1576	−3.09054
$275$	11.8762	0.716162
$276$	−72.6185	−4.37112
$277$	27.7058	1.66468	0.832341	−	0.554264i	$-0.187000\pi$
$277$	27.7058	1.66468	0.832341	+	0.554264i	$0.187000\pi$
$278$	19.5417	1.17204
$279$	−49.2554	−2.94884
$280$	50.2583	3.00351
$281$	22.6880	1.35345	0.676727	−	0.736234i	$-0.263398\pi$
$281$	22.6880	1.35345	0.676727	+	0.736234i	$0.263398\pi$
$282$	−73.5217	−4.37815
$283$	−14.8078	−0.880234	−0.440117	−	0.897940i	$-0.645063\pi$
$283$	−14.8078	−0.880234	−0.440117	+	0.897940i	$0.645063\pi$
$284$	25.4410	1.50964
$285$	13.8487	0.820326
$286$	75.7072	4.47666
$287$	−23.7750	−1.40339
$288$	−92.2939	−5.43847
$289$	−5.15546	−0.303262
$290$	18.3700	1.07872
$291$	13.2964	0.779451
$292$	−48.7144	−2.85080
$293$	−20.5973	−1.20331	−0.601653	−	0.798758i	$-0.705491\pi$
$293$	−20.5973	−1.20331	−0.601653	+	0.798758i	$0.705491\pi$
$294$	−13.0050	−0.758466
$295$	−11.2097	−0.652651
$296$	20.4089	1.18624
$297$	−62.9209	−3.65104
$298$	−13.9648	−0.808961
$299$	−25.9282	−1.49947
$300$	−36.8818	−2.12937
$301$	−17.6028	−1.01461
$302$	40.8623	2.35136
$303$	−38.9533	−2.23781
$304$	−17.9118	−1.02731
$305$	−11.9657	−0.685157
$306$	−63.1350	−3.60919
$307$	14.6758	0.837595	0.418797	−	0.908080i	$-0.362452\pi$
$307$	14.6758	0.837595	0.418797	+	0.908080i	$0.362452\pi$
$308$	−59.2973	−3.37877
$309$	3.75215	0.213452
$310$	50.9517	2.89386
$311$	−16.8921	−0.957863	−0.478932	−	0.877852i	$-0.658976\pi$
$311$	−16.8921	−0.957863	−0.478932	+	0.877852i	$0.658976\pi$
$312$	−141.163	−7.99180
$313$	−4.97216	−0.281043	−0.140522	−	0.990078i	$-0.544878\pi$
$313$	−4.97216	−0.281043	−0.140522	+	0.990078i	$0.544878\pi$
$314$	−15.9733	−0.901423
$315$	−43.7955	−2.46760
$316$	−54.1629	−3.04690
$317$	−29.9091	−1.67986	−0.839931	−	0.542694i	$-0.817404\pi$
$317$	−29.9091	−1.67986	−0.839931	+	0.542694i	$0.817404\pi$
$318$	−10.6151	−0.595265
$319$	−13.0133	−0.728604
$320$	35.6515	1.99298
$321$	−58.9714	−3.29146
$322$	28.4230	1.58395
$323$	−5.58307	−0.310650
$324$	91.3279	5.07377
$325$	−13.1685	−0.730459
$326$	−26.4706	−1.46607
$327$	−12.2449	−0.677145
$328$	−81.0716	−4.47643
$329$	20.5608	1.13355
$330$	114.759	6.31730
$331$	−24.8180	−1.36412	−0.682060	−	0.731296i	$-0.738916\pi$
$331$	−24.8180	−1.36412	−0.682060	+	0.731296i	$0.738916\pi$
$332$	−53.1417	−2.91653
$333$	−17.7845	−0.974583
$334$	40.6989	2.22694
$335$	−7.67343	−0.419244
$336$	81.1625	4.42778
$337$	19.4039	1.05700	0.528500	−	0.848933i	$-0.322755\pi$
$337$	19.4039	1.05700	0.528500	+	0.848933i	$0.322755\pi$
$338$	−49.5379	−2.69451
$339$	−10.4883	−0.569646
$340$	46.6633	2.53067
$341$	−36.0941	−1.95461
$342$	29.7594	1.60921
$343$	19.9648	1.07800
$344$	−60.0246	−3.23631
$345$	−39.3029	−2.11600
$346$	−60.6091	−3.25836
$347$	9.37399	0.503222	0.251611	−	0.967828i	$-0.419040\pi$
$347$	9.37399	0.503222	0.251611	+	0.967828i	$0.419040\pi$
$348$	40.4130	2.16636
$349$	11.9547	0.639923	0.319961	−	0.947431i	$-0.396330\pi$
$349$	11.9547	0.639923	0.319961	+	0.947431i	$0.396330\pi$
$350$	14.4356	0.771615
$351$	69.7677	3.72393
$352$	−67.6325	−3.60482
$353$	17.8987	0.952650	0.476325	−	0.879269i	$-0.341969\pi$
$353$	17.8987	0.952650	0.476325	+	0.879269i	$0.341969\pi$
$354$	−34.5147	−1.83443
$355$	13.7693	0.730797
$356$	81.6757	4.32880
$357$	25.2982	1.33892
$358$	0.630843	0.0333411
$359$	−12.3340	−0.650963	−0.325481	−	0.945548i	$-0.605526\pi$
$359$	−12.3340	−0.650963	−0.325481	+	0.945548i	$0.605526\pi$
$360$	−149.340	−7.87093
$361$	−16.3684	−0.861492
$362$	45.7328	2.40366
$363$	−46.6304	−2.44746
$364$	65.7498	3.44623
$365$	−26.3654	−1.38003
$366$	−36.8427	−1.92580
$367$	−25.5384	−1.33309	−0.666546	−	0.745463i	$-0.732228\pi$
$367$	−25.5384	−1.33309	−0.666546	+	0.745463i	$0.732228\pi$
$368$	50.8341	2.64991
$369$	70.6464	3.67771
$370$	18.3970	0.956413
$371$	2.96857	0.154120
$372$	112.091	5.81164
$373$	10.3828	0.537603	0.268802	−	0.963196i	$-0.413372\pi$
$373$	10.3828	0.537603	0.268802	+	0.963196i	$0.413372\pi$
$374$	−46.2650	−2.39231
$375$	22.7227	1.17339
$376$	70.1112	3.61571
$377$	14.4294	0.743150
$378$	−76.4807	−3.93374
$379$	−10.0302	−0.515216	−0.257608	−	0.966249i	$-0.582934\pi$
$379$	−10.0302	−0.515216	−0.257608	+	0.966249i	$0.582934\pi$
$380$	−21.9953	−1.12834
$381$	−55.3978	−2.83812
$382$	8.62870	0.441483
$383$	13.7696	0.703593	0.351797	−	0.936076i	$-0.385571\pi$
$383$	13.7696	0.703593	0.351797	+	0.936076i	$0.385571\pi$
$384$	25.8448	1.31889
$385$	−32.0931	−1.63562
$386$	−53.4307	−2.71955
$387$	52.3059	2.65886
$388$	−21.1182	−1.07211
$389$	−20.9810	−1.06378	−0.531890	−	0.846814i	$-0.678518\pi$
$389$	−20.9810	−1.06378	−0.531890	+	0.846814i	$0.678518\pi$
$390$	−127.247	−6.44341
$391$	15.8449	0.801309
$392$	12.4017	0.626381
$393$	−27.7562	−1.40011
$394$	50.5301	2.54567
$395$	−29.3143	−1.47496
$396$	176.199	8.85435
$397$	−21.5630	−1.08222	−0.541108	−	0.840953i	$-0.681995\pi$
$397$	−21.5630	−1.08222	−0.541108	+	0.840953i	$0.681995\pi$
$398$	−18.8202	−0.943370
$399$	−11.9246	−0.596977
$400$	25.8178	1.29089
$401$	−2.88469	−0.144055	−0.0720273	−	0.997403i	$-0.522947\pi$
$401$	−2.88469	−0.144055	−0.0720273	+	0.997403i	$0.522947\pi$
$402$	−23.6266	−1.17839
$403$	40.0218	1.99363
$404$	61.8678	3.07804
$405$	49.4289	2.45614
$406$	−15.8177	−0.785021
$407$	−13.0324	−0.645991
$408$	86.2655	4.27078
$409$	23.8718	1.18038	0.590191	−	0.807263i	$-0.299052\pi$
$409$	23.8718	1.18038	0.590191	+	0.807263i	$0.299052\pi$
$410$	−73.0795	−3.60914
$411$	−60.9115	−3.00454
$412$	−5.95938	−0.293598
$413$	9.65221	0.474954
$414$	−84.4579	−4.15088
$415$	−28.7616	−1.41185
$416$	74.9921	3.67679
$417$	23.2676	1.13942
$418$	21.8076	1.06664
$419$	−30.6975	−1.49967	−0.749836	−	0.661624i	$-0.769868\pi$
$419$	−30.6975	−1.49967	−0.749836	+	0.661624i	$0.769868\pi$
$420$	99.6657	4.86319
$421$	23.0696	1.12434	0.562171	−	0.827021i	$-0.309966\pi$
$421$	23.0696	1.12434	0.562171	+	0.827021i	$0.309966\pi$
$422$	59.2917	2.88627
$423$	−61.0955	−2.97056
$424$	10.1227	0.491601
$425$	8.04735	0.390354
$426$	42.3957	2.05408
$427$	10.3033	0.498609
$428$	93.6618	4.52732
$429$	90.1417	4.35208
$430$	−54.1073	−2.60929
$431$	−1.48043	−0.0713097	−0.0356548	−	0.999364i	$-0.511352\pi$
$431$	−1.48043	−0.0713097	−0.0356548	+	0.999364i	$0.511352\pi$
$432$	−136.784	−6.58104
$433$	−25.9592	−1.24752	−0.623761	−	0.781615i	$-0.714396\pi$
$433$	−25.9592	−1.24752	−0.623761	+	0.781615i	$0.714396\pi$
$434$	−43.8726	−2.10595
$435$	21.8725	1.04871
$436$	19.4481	0.931394
$437$	−7.46867	−0.357275
$438$	−81.1795	−3.87891
$439$	−29.8687	−1.42555	−0.712776	−	0.701391i	$-0.752563\pi$
$439$	−29.8687	−1.42555	−0.712776	+	0.701391i	$0.752563\pi$
$440$	−109.436	−5.21715
$441$	−10.8069	−0.514617
$442$	51.2994	2.44006
$443$	−29.2208	−1.38832	−0.694161	−	0.719820i	$-0.744225\pi$
$443$	−29.2208	−1.38832	−0.694161	+	0.719820i	$0.744225\pi$
$444$	40.4723	1.92073
$445$	44.2049	2.09551
$446$	13.1348	0.621949
$447$	−16.6274	−0.786450
$448$	−30.6982	−1.45035
$449$	30.5920	1.44373	0.721864	−	0.692035i	$-0.243286\pi$
$449$	30.5920	1.44373	0.721864	+	0.692035i	$0.243286\pi$
$450$	−42.8948	−2.02208
$451$	51.7694	2.43772
$452$	16.6581	0.783532
$453$	48.6532	2.28593
$454$	−57.7463	−2.71017
$455$	35.5854	1.66827
$456$	−40.6623	−1.90419
$457$	40.8767	1.91213	0.956065	−	0.293155i	$-0.0947052\pi$
$457$	40.8767	1.91213	0.956065	+	0.293155i	$0.0947052\pi$
$458$	−49.9704	−2.33496
$459$	−42.6354	−1.99005
$460$	62.4231	2.91049
$461$	3.49778	0.162908	0.0814539	−	0.996677i	$-0.474044\pi$
$461$	3.49778	0.162908	0.0814539	+	0.996677i	$0.474044\pi$
$462$	−98.8150	−4.59729
$463$	8.01063	0.372285	0.186143	−	0.982523i	$-0.440401\pi$
$463$	8.01063	0.372285	0.186143	+	0.982523i	$0.440401\pi$
$464$	−28.2898	−1.31332
$465$	60.6663	2.81333
$466$	−48.5568	−2.24935
$467$	−12.9604	−0.599734	−0.299867	−	0.953981i	$-0.596942\pi$
$467$	−12.9604	−0.599734	−0.299867	+	0.953981i	$0.596942\pi$
$468$	−195.373	−9.03112
$469$	6.60730	0.305097
$470$	63.1996	2.91518
$471$	−19.0188	−0.876338
$472$	32.9136	1.51497
$473$	38.3295	1.76239
$474$	−90.2589	−4.14573
$475$	−3.79322	−0.174045
$476$	−40.1800	−1.84165
$477$	−8.82098	−0.403885
$478$	−38.9140	−1.77989
$479$	29.8990	1.36612	0.683059	−	0.730363i	$-0.260649\pi$
$479$	29.8990	1.36612	0.683059	+	0.730363i	$0.260649\pi$
$480$	113.675	5.18855
$481$	14.4505	0.658887
$482$	−18.1549	−0.826933
$483$	33.8422	1.53988
$484$	74.0611	3.36641
$485$	−11.4297	−0.518995
$486$	53.8268	2.44163
$487$	−14.6893	−0.665634	−0.332817	−	0.942991i	$-0.607999\pi$
$487$	−14.6893	−0.665634	−0.332817	+	0.942991i	$0.607999\pi$
$488$	35.1336	1.59042
$489$	−31.5175	−1.42527
$490$	11.1791	0.505022
$491$	−8.49352	−0.383307	−0.191654	−	0.981463i	$-0.561385\pi$
$491$	−8.49352	−0.383307	−0.191654	+	0.981463i	$0.561385\pi$
$492$	−160.771	−7.24810
$493$	−8.81784	−0.397136
$494$	−24.1806	−1.08794
$495$	95.3634	4.28627
$496$	−78.4654	−3.52320
$497$	−11.8562	−0.531824
$498$	−88.5572	−3.96834
$499$	3.12788	0.140023	0.0700116	−	0.997546i	$-0.477696\pi$
$499$	3.12788	0.140023	0.0700116	+	0.997546i	$0.477696\pi$
$500$	−36.0895	−1.61397
$501$	48.4587	2.16497
$502$	54.8857	2.44967
$503$	−21.7556	−0.970035	−0.485017	−	0.874504i	$-0.661187\pi$
$503$	−21.7556	−0.970035	−0.485017	+	0.874504i	$0.661187\pi$
$504$	128.591	5.72792
$505$	33.4844	1.49004
$506$	−61.8903	−2.75136
$507$	−58.9830	−2.61953
$508$	87.9860	3.90375
$509$	31.4673	1.39477	0.697383	−	0.716699i	$-0.254348\pi$
$509$	31.4673	1.39477	0.697383	+	0.716699i	$0.254348\pi$
$510$	77.7613	3.44333
$511$	22.7023	1.00429
$512$	28.6178	1.26474
$513$	20.0967	0.887291
$514$	33.1744	1.46326
$515$	−3.22536	−0.142126
$516$	−119.033	−5.24014
$517$	−44.7705	−1.96900
$518$	−15.8409	−0.696011
$519$	−72.1650	−3.16769
$520$	121.344	5.32131
$521$	31.7048	1.38901	0.694507	−	0.719486i	$-0.255623\pi$
$521$	31.7048	1.38901	0.694507	+	0.719486i	$0.255623\pi$
$522$	47.0018	2.05721
$523$	31.1680	1.36288	0.681441	−	0.731873i	$-0.261353\pi$
$523$	31.1680	1.36288	0.681441	+	0.731873i	$0.261353\pi$
$524$	44.0840	1.92582
$525$	17.1879	0.750143
$526$	21.4520	0.935352
$527$	−24.4575	−1.06538
$528$	−176.729	−7.69114
$529$	−1.80375	−0.0784241
$530$	9.12477	0.396355
$531$	−28.6812	−1.24466
$532$	18.9393	0.821124
$533$	−57.4028	−2.48639
$534$	136.107	5.88994
$535$	50.6921	2.19161
$536$	22.5306	0.973173
$537$	0.751121	0.0324133
$538$	−0.365346	−0.0157512
$539$	−7.91928	−0.341107
$540$	−167.968	−7.22820
$541$	−5.17850	−0.222641	−0.111321	−	0.993785i	$-0.535508\pi$
$541$	−5.17850	−0.222641	−0.111321	+	0.993785i	$0.535508\pi$
$542$	32.6271	1.40146
$543$	54.4523	2.33677
$544$	−45.8280	−1.96486
$545$	10.5258	0.450875
$546$	109.568	4.68907
$547$	3.36987	0.144085	0.0720426	−	0.997402i	$-0.477048\pi$
$547$	3.36987	0.144085	0.0720426	+	0.997402i	$0.477048\pi$
$548$	96.7431	4.13266
$549$	−30.6157	−1.30665
$550$	−31.4331	−1.34031
$551$	4.15640	0.177069
$552$	115.400	4.91177
$553$	25.2414	1.07337
$554$	−73.3298	−3.11549
$555$	21.9046	0.929798
$556$	−36.9550	−1.56724
$557$	26.9568	1.14220	0.571099	−	0.820881i	$-0.306517\pi$
$557$	26.9568	1.14220	0.571099	+	0.820881i	$0.306517\pi$
$558$	130.366	5.51882
$559$	−42.5005	−1.79758
$560$	−69.7676	−2.94822
$561$	−55.0860	−2.32573
$562$	−60.0491	−2.53302
$563$	−38.6513	−1.62896	−0.814479	−	0.580193i	$-0.802977\pi$
$563$	−38.6513	−1.62896	−0.814479	+	0.580193i	$0.802977\pi$
$564$	139.035	5.85445
$565$	9.01578	0.379297
$566$	39.1923	1.64738
$567$	−42.5614	−1.78741
$568$	−40.4291	−1.69637
$569$	23.8139	0.998331	0.499166	−	0.866507i	$-0.333640\pi$
$569$	23.8139	0.998331	0.499166	+	0.866507i	$0.333640\pi$
$570$	−36.6538	−1.53526
$571$	42.3837	1.77370	0.886851	−	0.462056i	$-0.152888\pi$
$571$	42.3837	1.77370	0.886851	+	0.462056i	$0.152888\pi$
$572$	−143.168	−5.98617
$573$	10.2739	0.429197
$574$	62.9260	2.62648
$575$	10.7652	0.448941
$576$	91.2185	3.80077
$577$	−14.8969	−0.620165	−0.310082	−	0.950710i	$-0.600357\pi$
$577$	−14.8969	−0.620165	−0.310082	+	0.950710i	$0.600357\pi$
$578$	13.6451	0.567562
$579$	−63.6180	−2.64387
$580$	−34.7392	−1.44247
$581$	24.7655	1.02745
$582$	−35.1921	−1.45876
$583$	−6.46397	−0.267710
$584$	77.4137	3.20340
$585$	−105.741	−4.37183
$586$	54.5154	2.25201
$587$	13.6506	0.563420	0.281710	−	0.959500i	$-0.409098\pi$
$587$	13.6506	0.563420	0.281710	+	0.959500i	$0.409098\pi$
$588$	24.5935	1.01422
$589$	11.5283	0.475017
$590$	29.6689	1.22145
$591$	60.1643	2.47483
$592$	−28.3312	−1.16441
$593$	−1.43226	−0.0588161	−0.0294080	−	0.999567i	$-0.509362\pi$
$593$	−1.43226	−0.0588161	−0.0294080	+	0.999567i	$0.509362\pi$
$594$	166.534	6.83299
$595$	−21.7464	−0.891515
$596$	26.4086	1.08174
$597$	−22.4085	−0.917118
$598$	68.6251	2.80629
$599$	8.10127	0.331009	0.165504	−	0.986209i	$-0.447075\pi$
$599$	8.10127	0.331009	0.165504	+	0.986209i	$0.447075\pi$
$600$	58.6100	2.39274
$601$	−30.3978	−1.23995	−0.619975	−	0.784621i	$-0.712857\pi$
$601$	−30.3978	−1.23995	−0.619975	+	0.784621i	$0.712857\pi$
$602$	46.5898	1.89886
$603$	−19.6333	−0.799531
$604$	−77.2738	−3.14423
$605$	40.0837	1.62963
$606$	103.099	4.18810
$607$	35.3861	1.43628	0.718139	−	0.695900i	$-0.244994\pi$
$607$	35.3861	1.43628	0.718139	+	0.695900i	$0.244994\pi$
$608$	21.6016	0.876060
$609$	−18.8336	−0.763176
$610$	31.6701	1.28228
$611$	49.6423	2.00831
$612$	119.393	4.82619
$613$	−31.8392	−1.28597	−0.642986	−	0.765878i	$-0.722305\pi$
$613$	−31.8392	−1.28597	−0.642986	+	0.765878i	$0.722305\pi$
$614$	−38.8430	−1.56758
$615$	−87.0130	−3.50870
$616$	94.2312	3.79668
$617$	−27.0190	−1.08774	−0.543871	−	0.839169i	$-0.683042\pi$
$617$	−27.0190	−1.08774	−0.543871	+	0.839169i	$0.683042\pi$
$618$	−9.93092	−0.399480
$619$	10.6908	0.429700	0.214850	−	0.976647i	$-0.431074\pi$
$619$	10.6908	0.429700	0.214850	+	0.976647i	$0.431074\pi$
$620$	−96.3538	−3.86966
$621$	−57.0348	−2.28873
$622$	44.7088	1.79266
$623$	−38.0632	−1.52497
$624$	195.960	7.84469
$625$	−31.2238	−1.24895
$626$	13.1600	0.525978
$627$	25.9655	1.03696
$628$	30.2067	1.20538
$629$	−8.83078	−0.352106
$630$	115.915	4.61816
$631$	−14.9586	−0.595491	−0.297746	−	0.954645i	$-0.596235\pi$
$631$	−14.9586	−0.595491	−0.297746	+	0.954645i	$0.596235\pi$
$632$	86.0720	3.42376
$633$	70.5964	2.80595
$634$	79.1613	3.14389
$635$	47.6202	1.88975
$636$	20.0740	0.795985
$637$	8.78103	0.347917
$638$	34.4427	1.36360
$639$	35.2302	1.39369
$640$	−22.2163	−0.878178
$641$	16.4121	0.648239	0.324119	−	0.946016i	$-0.394932\pi$
$641$	16.4121	0.648239	0.324119	+	0.946016i	$0.394932\pi$
$642$	156.081	6.16004
$643$	7.81623	0.308242	0.154121	−	0.988052i	$-0.450745\pi$
$643$	7.81623	0.308242	0.154121	+	0.988052i	$0.450745\pi$
$644$	−53.7502	−2.11806
$645$	−64.4236	−2.53668
$646$	14.7769	0.581388
$647$	34.4596	1.35475	0.677373	−	0.735640i	$-0.263118\pi$
$647$	34.4596	1.35475	0.677373	+	0.735640i	$0.263118\pi$
$648$	−145.132	−5.70133
$649$	−21.0174	−0.825006
$650$	34.8536	1.36707
$651$	−52.2375	−2.04735
$652$	50.0579	1.96042
$653$	33.5961	1.31472	0.657358	−	0.753579i	$-0.271674\pi$
$653$	33.5961	1.31472	0.657358	+	0.753579i	$0.271674\pi$
$654$	32.4090	1.26729
$655$	23.8593	0.932261
$656$	112.542	4.39403
$657$	−67.4589	−2.63182
$658$	−54.4188	−2.12146
$659$	−20.3881	−0.794209	−0.397105	−	0.917773i	$-0.629985\pi$
$659$	−20.3881	−0.794209	−0.397105	+	0.917773i	$0.629985\pi$
$660$	−217.019	−8.44746
$661$	46.0221	1.79005	0.895027	−	0.446012i	$-0.147156\pi$
$661$	46.0221	1.79005	0.895027	+	0.446012i	$0.147156\pi$
$662$	65.6865	2.55298
$663$	61.0803	2.37216
$664$	84.4492	3.27726
$665$	10.2504	0.397495
$666$	47.0707	1.82395
$667$	−11.7959	−0.456741
$668$	−76.9649	−2.97786
$669$	15.6391	0.604641
$670$	20.3095	0.784624
$671$	−22.4350	−0.866095
$672$	−97.8816	−3.77587
$673$	−1.06335	−0.0409891	−0.0204945	−	0.999790i	$-0.506524\pi$
$673$	−1.06335	−0.0409891	−0.0204945	+	0.999790i	$0.506524\pi$
$674$	−51.3570	−1.97820
$675$	−28.9671	−1.11494
$676$	93.6802	3.60308
$677$	48.1693	1.85130	0.925648	−	0.378386i	$-0.123521\pi$
$677$	48.1693	1.85130	0.925648	+	0.378386i	$0.123521\pi$
$678$	27.7597	1.06610
$679$	9.84166	0.377688
$680$	−74.1541	−2.84368
$681$	−68.7564	−2.63475
$682$	95.5313	3.65808
$683$	−24.0321	−0.919563	−0.459781	−	0.888032i	$-0.652072\pi$
$683$	−24.0321	−0.919563	−0.459781	+	0.888032i	$0.652072\pi$
$684$	−56.2775	−2.15182
$685$	52.3597	2.00056
$686$	−52.8414	−2.01749
$687$	−59.4979	−2.26999
$688$	83.3251	3.17674
$689$	7.16737	0.273055
$690$	104.024	3.96013
$691$	26.8971	1.02321	0.511607	−	0.859219i	$-0.329050\pi$
$691$	26.8971	1.02321	0.511607	+	0.859219i	$0.329050\pi$
$692$	114.617	4.35707
$693$	−82.1138	−3.11925
$694$	−24.8104	−0.941790
$695$	−20.0009	−0.758679
$696$	−64.2216	−2.43431
$697$	35.0791	1.32871
$698$	−31.6410	−1.19763
$699$	−57.8148	−2.18676
$700$	−27.2989	−1.03180
$701$	−14.4907	−0.547307	−0.273654	−	0.961828i	$-0.588232\pi$
$701$	−14.4907	−0.547307	−0.273654	+	0.961828i	$0.588232\pi$
$702$	−184.656	−6.96940
$703$	4.16250	0.156992
$704$	66.8445	2.51930
$705$	75.2494	2.83405
$706$	−47.3729	−1.78290
$707$	−28.8321	−1.08434
$708$	65.2700	2.45300
$709$	12.5039	0.469593	0.234797	−	0.972045i	$-0.424558\pi$
$709$	12.5039	0.469593	0.234797	+	0.972045i	$0.424558\pi$
$710$	−36.4435	−1.36770
$711$	−75.0039	−2.81286
$712$	−129.794	−4.86422
$713$	−32.7176	−1.22529
$714$	−66.9574	−2.50582
$715$	−77.4862	−2.89782
$716$	−1.19297	−0.0445835
$717$	−46.3335	−1.73036
$718$	32.6447	1.21829
$719$	26.4586	0.986738	0.493369	−	0.869820i	$-0.335765\pi$
$719$	26.4586	0.986738	0.493369	+	0.869820i	$0.335765\pi$
$720$	207.312	7.72605
$721$	2.77724	0.103430
$722$	43.3226	1.61230
$723$	−21.6164	−0.803922
$724$	−86.4844	−3.21417
$725$	−5.99097	−0.222499
$726$	123.418	4.58047
$727$	48.8575	1.81203	0.906013	−	0.423250i	$-0.139111\pi$
$727$	48.8575	1.81203	0.906013	+	0.423250i	$0.139111\pi$
$728$	−104.485	−3.87248
$729$	9.34952	0.346278
$730$	69.7822	2.58275
$731$	25.9722	0.960617
$732$	69.6724	2.57517
$733$	−31.2761	−1.15521	−0.577604	−	0.816317i	$-0.696012\pi$
$733$	−31.2761	−1.15521	−0.577604	+	0.816317i	$0.696012\pi$
$734$	67.5932	2.49491
$735$	13.3106	0.490968
$736$	−61.3057	−2.25976
$737$	−14.3872	−0.529960
$738$	−186.982	−6.88290
$739$	32.1337	1.18206	0.591028	−	0.806651i	$-0.298722\pi$
$739$	32.1337	1.18206	0.591028	+	0.806651i	$0.298722\pi$
$740$	−34.7901	−1.27891
$741$	−28.7910	−1.05766
$742$	−7.85700	−0.288440
$743$	−36.8277	−1.35108	−0.675539	−	0.737324i	$-0.736089\pi$
$743$	−36.8277	−1.35108	−0.675539	+	0.737324i	$0.736089\pi$
$744$	−178.127	−6.53046
$745$	14.2930	0.523655
$746$	−27.4806	−1.00614
$747$	−73.5897	−2.69251
$748$	87.4908	3.19898
$749$	−43.6490	−1.59490
$750$	−60.1408	−2.19603
$751$	24.2386	0.884480	0.442240	−	0.896897i	$-0.354184\pi$
$751$	24.2386	0.884480	0.442240	+	0.896897i	$0.354184\pi$
$752$	−97.3271	−3.54915
$753$	65.3504	2.38150
$754$	−38.1906	−1.39082
$755$	−41.8225	−1.52208
$756$	144.631	5.26018
$757$	20.8047	0.756160	0.378080	−	0.925773i	$-0.376584\pi$
$757$	20.8047	0.756160	0.378080	+	0.925773i	$0.376584\pi$
$758$	26.5472	0.964238
$759$	−73.6905	−2.67480
$760$	34.9535	1.26790
$761$	9.72273	0.352449	0.176224	−	0.984350i	$-0.443612\pi$
$761$	9.72273	0.352449	0.176224	+	0.984350i	$0.443612\pi$
$762$	146.623	5.31159
$763$	−9.06335	−0.328115
$764$	−16.3176	−0.590349
$765$	64.6185	2.33629
$766$	−36.4444	−1.31679
$767$	23.3045	0.841476
$768$	14.5445	0.524828
$769$	−3.95861	−0.142751	−0.0713755	−	0.997450i	$-0.522739\pi$
$769$	−3.95861	−0.142751	−0.0713755	+	0.997450i	$0.522739\pi$
$770$	84.9418	3.06109
$771$	39.4995	1.42254
$772$	101.042	3.63657
$773$	−25.1380	−0.904149	−0.452075	−	0.891980i	$-0.649316\pi$
$773$	−25.1380	−0.904149	−0.452075	+	0.891980i	$0.649316\pi$
$774$	−138.440	−4.97611
$775$	−16.6168	−0.596892
$776$	33.5596	1.20472
$777$	−18.8612	−0.676642
$778$	55.5310	1.99088
$779$	−16.5350	−0.592426
$780$	240.635	8.61610
$781$	25.8165	0.923789
$782$	−41.9371	−1.49967
$783$	31.7405	1.13431
$784$	−17.2158	−0.614851
$785$	16.3486	0.583506
$786$	73.4631	2.62034
$787$	−10.3485	−0.368885	−0.184442	−	0.982843i	$-0.559048\pi$
$787$	−10.3485	−0.368885	−0.184442	+	0.982843i	$0.559048\pi$
$788$	−95.5564	−3.40406
$789$	25.5421	0.909323
$790$	77.5869	2.76042
$791$	−7.76315	−0.276026
$792$	−280.004	−9.94952
$793$	24.8764	0.883385
$794$	57.0714	2.02539
$795$	10.8645	0.385325
$796$	35.5904	1.26147
$797$	23.1342	0.819455	0.409728	−	0.912208i	$-0.365624\pi$
$797$	23.1342	0.819455	0.409728	+	0.912208i	$0.365624\pi$
$798$	31.5612	1.11725
$799$	−30.3366	−1.07323
$800$	−31.1362	−1.10083
$801$	113.103	3.99630
$802$	7.63500	0.269601
$803$	−49.4336	−1.74447
$804$	44.6797	1.57573
$805$	−29.0909	−1.02532
$806$	−105.927	−3.73111
$807$	−0.435004	−0.0153129
$808$	−98.3162	−3.45875
$809$	−28.0436	−0.985959	−0.492979	−	0.870041i	$-0.664092\pi$
$809$	−28.0436	−0.985959	−0.492979	+	0.870041i	$0.664092\pi$
$810$	−130.825	−4.59672
$811$	34.5613	1.21361	0.606806	−	0.794850i	$-0.292450\pi$
$811$	34.5613	1.21361	0.606806	+	0.794850i	$0.292450\pi$
$812$	29.9126	1.04973
$813$	38.8479	1.36246
$814$	34.4932	1.20899
$815$	27.0926	0.949011
$816$	−119.752	−4.19216
$817$	−12.2423	−0.428305
$818$	−63.1821	−2.20911
$819$	91.0492	3.18152
$820$	138.199	4.82612
$821$	−17.0436	−0.594827	−0.297414	−	0.954749i	$-0.596124\pi$
$821$	−17.0436	−0.594827	−0.297414	+	0.954749i	$0.596124\pi$
$822$	161.216	5.62306
$823$	28.6587	0.998979	0.499489	−	0.866320i	$-0.333521\pi$
$823$	28.6587	0.998979	0.499489	+	0.866320i	$0.333521\pi$
$824$	9.47025	0.329912
$825$	−37.4262	−1.30301
$826$	−25.5468	−0.888887
$827$	16.3082	0.567091	0.283545	−	0.958959i	$-0.408489\pi$
$827$	16.3082	0.567091	0.283545	+	0.958959i	$0.408489\pi$
$828$	159.717	5.55054
$829$	7.65519	0.265876	0.132938	−	0.991124i	$-0.457559\pi$
$829$	7.65519	0.265876	0.132938	+	0.991124i	$0.457559\pi$
$830$	76.1241	2.64231
$831$	−87.3111	−3.02879
$832$	−74.1183	−2.56959
$833$	−5.36613	−0.185925
$834$	−61.5831	−2.13245
$835$	−41.6553	−1.44154
$836$	−41.2399	−1.42631
$837$	88.0366	3.04299
$838$	81.2480	2.80667
$839$	18.6349	0.643350	0.321675	−	0.946850i	$-0.395754\pi$
$839$	18.6349	0.643350	0.321675	+	0.946850i	$0.395754\pi$
$840$	−158.382	−5.46470
$841$	−22.4354	−0.773635
$842$	−61.0589	−2.10423
$843$	−71.4982	−2.46253
$844$	−112.125	−3.85951
$845$	50.7020	1.74420
$846$	161.703	5.55947
$847$	−34.5145	−1.18593
$848$	−14.0521	−0.482552
$849$	46.6648	1.60153
$850$	−21.2992	−0.730555
$851$	−11.8132	−0.404953
$852$	−80.1737	−2.74671
$853$	−33.2897	−1.13982	−0.569909	−	0.821708i	$-0.693021\pi$
$853$	−33.2897	−1.13982	−0.569909	+	0.821708i	$0.693021\pi$
$854$	−27.2699	−0.933158
$855$	−30.4587	−1.04167
$856$	−148.841	−5.08728
$857$	9.85363	0.336594	0.168297	−	0.985736i	$-0.446173\pi$
$857$	9.85363	0.336594	0.168297	+	0.985736i	$0.446173\pi$
$858$	−238.581	−8.14501
$859$	−30.9312	−1.05536	−0.527680	−	0.849443i	$-0.676938\pi$
$859$	−30.9312	−1.05536	−0.527680	+	0.849443i	$0.676938\pi$
$860$	102.321	3.48913
$861$	74.9236	2.55339
$862$	3.91829	0.133458
$863$	45.6915	1.55536	0.777679	−	0.628662i	$-0.216397\pi$
$863$	45.6915	1.55536	0.777679	+	0.628662i	$0.216397\pi$
$864$	164.961	5.61210
$865$	62.0333	2.10920
$866$	68.7071	2.33476
$867$	16.2467	0.551768
$868$	82.9666	2.81607
$869$	−54.9625	−1.86447
$870$	−57.8906	−1.96267
$871$	15.9528	0.540539
$872$	−30.9056	−1.04660
$873$	−29.2441	−0.989763
$874$	19.7676	0.668648
$875$	16.8187	0.568576
$876$	153.517	5.18685
$877$	0.781045	0.0263740	0.0131870	−	0.999913i	$-0.495802\pi$
$877$	0.781045	0.0263740	0.0131870	+	0.999913i	$0.495802\pi$
$878$	79.0542	2.66795
$879$	64.9095	2.18934
$880$	151.917	5.12112
$881$	19.4238	0.654405	0.327203	−	0.944954i	$-0.393894\pi$
$881$	19.4238	0.654405	0.327203	+	0.944954i	$0.393894\pi$
$882$	28.6031	0.963115
$883$	−1.24183	−0.0417910	−0.0208955	−	0.999782i	$-0.506652\pi$
$883$	−1.24183	−0.0417910	−0.0208955	+	0.999782i	$0.506652\pi$
$884$	−97.0113	−3.26284
$885$	35.3257	1.18746
$886$	77.3396	2.59827
$887$	−6.19538	−0.208021	−0.104010	−	0.994576i	$-0.533167\pi$
$887$	−6.19538	−0.208021	−0.104010	+	0.994576i	$0.533167\pi$
$888$	−64.3158	−2.15830
$889$	−41.0039	−1.37523
$890$	−116.998	−3.92179
$891$	92.6761	3.10477
$892$	−24.8389	−0.831667
$893$	14.2995	0.478516
$894$	44.0083	1.47186
$895$	−0.645666	−0.0215822
$896$	19.1297	0.639077
$897$	81.7093	2.72819
$898$	−80.9689	−2.70197
$899$	18.2077	0.607262
$900$	81.1175	2.70392
$901$	−4.38001	−0.145919
$902$	−137.019	−4.56225
$903$	55.4727	1.84602
$904$	−26.4720	−0.880444
$905$	−46.8074	−1.55593
$906$	−128.772	−4.27816
$907$	−30.7913	−1.02241	−0.511205	−	0.859459i	$-0.670801\pi$
$907$	−30.7913	−1.02241	−0.511205	+	0.859459i	$0.670801\pi$
$908$	109.203	3.62403
$909$	85.6736	2.84161
$910$	−94.1849	−3.12220
$911$	−23.9811	−0.794529	−0.397264	−	0.917704i	$-0.630040\pi$
$911$	−23.9811	−0.794529	−0.397264	+	0.917704i	$0.630040\pi$
$912$	56.4466	1.86914
$913$	−53.9262	−1.78470
$914$	−108.189	−3.57859
$915$	37.7084	1.24660
$916$	94.4980	3.12230
$917$	−20.5444	−0.678435
$918$	112.844	3.72442
$919$	0.121011	0.00399180	0.00199590	−	0.999998i	$-0.499365\pi$
$919$	0.121011	0.00399180	0.00199590	+	0.999998i	$0.499365\pi$
$920$	−99.1987	−3.27048
$921$	−46.2489	−1.52395
$922$	−9.25767	−0.304885
$923$	−28.6258	−0.942231
$924$	186.867	6.14748
$925$	−5.99976	−0.197271
$926$	−21.2020	−0.696740
$927$	−8.25245	−0.271046
$928$	34.1173	1.11996
$929$	−18.8954	−0.619938	−0.309969	−	0.950747i	$-0.600319\pi$
$929$	−18.8954	−0.619938	−0.309969	+	0.950747i	$0.600319\pi$
$930$	−160.567	−5.26521
$931$	2.52939	0.0828974
$932$	91.8248	3.00782
$933$	53.2331	1.74277
$934$	34.3026	1.12242
$935$	47.3521	1.54858
$936$	310.474	10.1481
$937$	−14.2161	−0.464420	−0.232210	−	0.972666i	$-0.574596\pi$
$937$	−14.2161	−0.464420	−0.232210	+	0.972666i	$0.574596\pi$
$938$	−17.4877	−0.570995
$939$	15.6691	0.511341
$940$	−119.515	−3.89816
$941$	2.07639	0.0676883	0.0338441	−	0.999427i	$-0.489225\pi$
$941$	2.07639	0.0676883	0.0338441	+	0.999427i	$0.489225\pi$
$942$	50.3375	1.64008
$943$	46.9265	1.52814
$944$	−45.6900	−1.48708
$945$	78.2779	2.54638
$946$	−101.448	−3.29836
$947$	4.31162	0.140109	0.0700543	−	0.997543i	$-0.477683\pi$
$947$	4.31162	0.140109	0.0700543	+	0.997543i	$0.477683\pi$
$948$	170.687	5.54365
$949$	54.8128	1.77930
$950$	10.0396	0.325728
$951$	94.2544	3.05641
$952$	63.8513	2.06943
$953$	20.9058	0.677205	0.338603	−	0.940929i	$-0.390046\pi$
$953$	20.9058	0.677205	0.338603	+	0.940929i	$0.390046\pi$
$954$	23.3468	0.755879
$955$	−8.83146	−0.285779
$956$	73.5895	2.38006
$957$	41.0096	1.32565
$958$	−79.1345	−2.55672
$959$	−45.0850	−1.45587
$960$	−112.351	−3.62611
$961$	19.5016	0.629083
$962$	−38.2466	−1.23312
$963$	129.701	4.17957
$964$	34.3324	1.10577
$965$	54.6863	1.76041
$966$	−89.5713	−2.88191
$967$	21.8521	0.702716	0.351358	−	0.936241i	$-0.385720\pi$
$967$	21.8521	0.702716	0.351358	+	0.936241i	$0.385720\pi$
$968$	−117.693	−3.78279
$969$	17.5943	0.565210
$970$	30.2512	0.971309
$971$	3.63813	0.116753	0.0583765	−	0.998295i	$-0.481408\pi$
$971$	3.63813	0.116753	0.0583765	+	0.998295i	$0.481408\pi$
$972$	−101.791	−3.26494
$973$	17.2221	0.552114
$974$	38.8785	1.24575
$975$	41.4988	1.32903
$976$	−48.7718	−1.56115
$977$	−43.4449	−1.38992	−0.694962	−	0.719046i	$-0.744579\pi$
$977$	−43.4449	−1.38992	−0.694962	+	0.719046i	$0.744579\pi$
$978$	83.4183	2.66742
$979$	82.8814	2.64890
$980$	−21.1406	−0.675313
$981$	26.9314	0.859853
$982$	22.4800	0.717367
$983$	−0.835037	−0.0266335	−0.0133168	−	0.999911i	$-0.504239\pi$
$983$	−0.835037	−0.0266335	−0.0133168	+	0.999911i	$0.504239\pi$
$984$	255.486	8.14459
$985$	−51.7174	−1.64785
$986$	23.3384	0.743248
$987$	−64.7944	−2.06243
$988$	45.7275	1.45478
$989$	34.7440	1.10479
$990$	−252.401	−8.02183
$991$	4.92074	0.156312	0.0781562	−	0.996941i	$-0.475097\pi$
$991$	4.92074	0.156312	0.0781562	+	0.996941i	$0.475097\pi$
$992$	94.6290	3.00447
$993$	78.2105	2.48193
$994$	31.3802	0.995319
$995$	19.2624	0.610659
$996$	167.469	5.30645
$997$	−34.3062	−1.08649	−0.543244	−	0.839575i	$-0.682804\pi$
$997$	−34.3062	−1.08649	−0.543244	+	0.839575i	$0.682804\pi$
$998$	−8.27866	−0.262056
$999$	31.7871	1.00570

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8039.2.a.b.1.16	✓	391

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8039.2.a.b.1.16	✓	391	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:	\( N \)	\(=\)	\( 8039 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8039.a (trivial)

\(f(q)\)	\(=\)	\(q-2.64673 q^{2} -3.15136 q^{3} +5.00518 q^{4} +2.70892 q^{5} +8.34080 q^{6} -2.33255 q^{7} -7.95389 q^{8} +6.93109 q^{9} +O(q^{10})\)	\(q-2.64673 q^{2} -3.15136 q^{3} +5.00518 q^{4} +2.70892 q^{5} +8.34080 q^{6} -2.33255 q^{7} -7.95389 q^{8} +6.93109 q^{9} -7.16979 q^{10} +5.07906 q^{11} -15.7731 q^{12} -5.63175 q^{13} +6.17363 q^{14} -8.53680 q^{15} +11.0414 q^{16} +3.44159 q^{17} -18.3447 q^{18} -1.62224 q^{19} +13.5586 q^{20} +7.35072 q^{21} -13.4429 q^{22} +4.60394 q^{23} +25.0656 q^{24} +2.33827 q^{25} +14.9057 q^{26} -12.3883 q^{27} -11.6748 q^{28} -2.56214 q^{29} +22.5946 q^{30} -7.10645 q^{31} -13.3159 q^{32} -16.0060 q^{33} -9.10896 q^{34} -6.31871 q^{35} +34.6913 q^{36} -2.56590 q^{37} +4.29362 q^{38} +17.7477 q^{39} -21.5465 q^{40} +10.1927 q^{41} -19.4554 q^{42} +7.54657 q^{43} +25.4216 q^{44} +18.7758 q^{45} -12.1854 q^{46} -8.81470 q^{47} -34.7956 q^{48} -1.55920 q^{49} -6.18876 q^{50} -10.8457 q^{51} -28.1879 q^{52} -1.27267 q^{53} +32.7884 q^{54} +13.7588 q^{55} +18.5529 q^{56} +5.11225 q^{57} +6.78130 q^{58} -4.13805 q^{59} -42.7282 q^{60} -4.41716 q^{61} +18.8088 q^{62} -16.1671 q^{63} +13.1608 q^{64} -15.2560 q^{65} +42.3635 q^{66} -2.83265 q^{67} +17.2258 q^{68} -14.5087 q^{69} +16.7239 q^{70} +5.08293 q^{71} -55.1291 q^{72} -9.73281 q^{73} +6.79125 q^{74} -7.36872 q^{75} -8.11958 q^{76} -11.8472 q^{77} -46.9734 q^{78} -10.8214 q^{79} +29.9104 q^{80} +18.2467 q^{81} -26.9773 q^{82} -10.6173 q^{83} +36.7916 q^{84} +9.32300 q^{85} -19.9737 q^{86} +8.07424 q^{87} -40.3983 q^{88} +16.3182 q^{89} -49.6944 q^{90} +13.1364 q^{91} +23.0435 q^{92} +22.3950 q^{93} +23.3301 q^{94} -4.39451 q^{95} +41.9633 q^{96} -4.21927 q^{97} +4.12678 q^{98} +35.2034 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 391 q + 14 q^{2} + 12 q^{3} + 446 q^{4} + 22 q^{5} + 40 q^{6} + 63 q^{7} + 36 q^{8} + 501 q^{9}+O(q^{10}) \) 391 * q + 14 * q^2 + 12 * q^3 + 446 * q^4 + 22 * q^5 + 40 * q^6 + 63 * q^7 + 36 * q^8 + 501 * q^9	\( 391 q + 14 q^{2} + 12 q^{3} + 446 q^{4} + 22 q^{5} + 40 q^{6} + 63 q^{7} + 36 q^{8} + 501 q^{9} + 40 q^{10} + 57 q^{11} + 20 q^{12} + 83 q^{13} + 21 q^{14} + 60 q^{15} + 548 q^{16} + 59 q^{17} + 54 q^{18} + 131 q^{19} + 35 q^{20} + 121 q^{21} + 89 q^{22} + 34 q^{23} + 110 q^{24} + 609 q^{25} + 54 q^{26} + 27 q^{27} + 182 q^{28} + 102 q^{29} + 92 q^{30} + 88 q^{31} + 76 q^{32} + 131 q^{33} + 128 q^{34} + 31 q^{35} + 654 q^{36} + 135 q^{37} + 23 q^{38} + 96 q^{39} + 113 q^{40} + 128 q^{41} + 45 q^{42} + 140 q^{43} + 151 q^{44} + 77 q^{45} + 245 q^{46} + 22 q^{47} + 25 q^{48} + 712 q^{49} + 53 q^{50} + 102 q^{51} + 174 q^{52} + 54 q^{53} + 131 q^{54} + 101 q^{55} + 43 q^{56} + 226 q^{57} + 109 q^{58} + 40 q^{59} + 123 q^{60} + 249 q^{61} + 28 q^{62} + 139 q^{63} + 730 q^{64} + 227 q^{65} + 55 q^{66} + 169 q^{67} + 48 q^{68} + 89 q^{69} + 98 q^{70} + 66 q^{71} + 120 q^{72} + 324 q^{73} + 60 q^{74} + 19 q^{75} + 356 q^{76} + 83 q^{77} - 11 q^{78} + 195 q^{79} + 26 q^{80} + 807 q^{81} + 49 q^{82} + 74 q^{83} + 252 q^{84} + 373 q^{85} + 100 q^{86} + 43 q^{87} + 211 q^{88} + 207 q^{89} + 10 q^{90} + 189 q^{91} + 30 q^{92} + 172 q^{93} + 130 q^{94} + 43 q^{95} + 203 q^{96} + 254 q^{97} + 26 q^{98} + 273 q^{99}+O(q^{100}) \) 391 * q + 14 * q^2 + 12 * q^3 + 446 * q^4 + 22 * q^5 + 40 * q^6 + 63 * q^7 + 36 * q^8 + 501 * q^9 + 40 * q^10 + 57 * q^11 + 20 * q^12 + 83 * q^13 + 21 * q^14 + 60 * q^15 + 548 * q^16 + 59 * q^17 + 54 * q^18 + 131 * q^19 + 35 * q^20 + 121 * q^21 + 89 * q^22 + 34 * q^23 + 110 * q^24 + 609 * q^25 + 54 * q^26 + 27 * q^27 + 182 * q^28 + 102 * q^29 + 92 * q^30 + 88 * q^31 + 76 * q^32 + 131 * q^33 + 128 * q^34 + 31 * q^35 + 654 * q^36 + 135 * q^37 + 23 * q^38 + 96 * q^39 + 113 * q^40 + 128 * q^41 + 45 * q^42 + 140 * q^43 + 151 * q^44 + 77 * q^45 + 245 * q^46 + 22 * q^47 + 25 * q^48 + 712 * q^49 + 53 * q^50 + 102 * q^51 + 174 * q^52 + 54 * q^53 + 131 * q^54 + 101 * q^55 + 43 * q^56 + 226 * q^57 + 109 * q^58 + 40 * q^59 + 123 * q^60 + 249 * q^61 + 28 * q^62 + 139 * q^63 + 730 * q^64 + 227 * q^65 + 55 * q^66 + 169 * q^67 + 48 * q^68 + 89 * q^69 + 98 * q^70 + 66 * q^71 + 120 * q^72 + 324 * q^73 + 60 * q^74 + 19 * q^75 + 356 * q^76 + 83 * q^77 - 11 * q^78 + 195 * q^79 + 26 * q^80 + 807 * q^81 + 49 * q^82 + 74 * q^83 + 252 * q^84 + 373 * q^85 + 100 * q^86 + 43 * q^87 + 211 * q^88 + 207 * q^89 + 10 * q^90 + 189 * q^91 + 30 * q^92 + 172 * q^93 + 130 * q^94 + 43 * q^95 + 203 * q^96 + 254 * q^97 + 26 * q^98 + 273 * q^99

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