LMFDB - Embedded newform 8021.2.a.d.1.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8021,2,Mod(1,8021)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8021, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("8021.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8021 = 13 \cdot 617 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8021.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:	$64.0480074613$
Analytic rank:	$0$
Dimension:	$174$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.11
Character	$\chi$	$=$	8021.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.64300 q^{2} -0.434399 q^{3} +4.98547 q^{4} -0.633166 q^{5} +1.14812 q^{6} +1.76480 q^{7} -7.89059 q^{8} -2.81130 q^{9} +O(q^{10})$	\(q-2.64300 q^{2} -0.434399 q^{3} +4.98547 q^{4} -0.633166 q^{5} +1.14812 q^{6} +1.76480 q^{7} -7.89059 q^{8} -2.81130 q^{9} +1.67346 q^{10} +3.07168 q^{11} -2.16568 q^{12} +1.00000 q^{13} -4.66436 q^{14} +0.275047 q^{15} +10.8839 q^{16} -5.17211 q^{17} +7.43027 q^{18} +5.55084 q^{19} -3.15663 q^{20} -0.766625 q^{21} -8.11847 q^{22} -8.80013 q^{23} +3.42766 q^{24} -4.59910 q^{25} -2.64300 q^{26} +2.52442 q^{27} +8.79833 q^{28} -2.96717 q^{29} -0.726949 q^{30} +5.05817 q^{31} -12.9851 q^{32} -1.33434 q^{33} +13.6699 q^{34} -1.11741 q^{35} -14.0156 q^{36} +4.73590 q^{37} -14.6709 q^{38} -0.434399 q^{39} +4.99606 q^{40} -4.72173 q^{41} +2.02619 q^{42} -0.539613 q^{43} +15.3138 q^{44} +1.78002 q^{45} +23.2588 q^{46} -8.74542 q^{47} -4.72797 q^{48} -3.88549 q^{49} +12.1554 q^{50} +2.24676 q^{51} +4.98547 q^{52} +4.12133 q^{53} -6.67205 q^{54} -1.94489 q^{55} -13.9253 q^{56} -2.41128 q^{57} +7.84224 q^{58} +1.01484 q^{59} +1.37124 q^{60} -7.93769 q^{61} -13.3687 q^{62} -4.96137 q^{63} +12.5517 q^{64} -0.633166 q^{65} +3.52665 q^{66} -5.28468 q^{67} -25.7854 q^{68} +3.82277 q^{69} +2.95332 q^{70} +12.6904 q^{71} +22.1828 q^{72} +9.28736 q^{73} -12.5170 q^{74} +1.99784 q^{75} +27.6735 q^{76} +5.42090 q^{77} +1.14812 q^{78} +13.4798 q^{79} -6.89134 q^{80} +7.33729 q^{81} +12.4795 q^{82} -8.94575 q^{83} -3.82198 q^{84} +3.27481 q^{85} +1.42620 q^{86} +1.28893 q^{87} -24.2374 q^{88} -7.05729 q^{89} -4.70460 q^{90} +1.76480 q^{91} -43.8727 q^{92} -2.19726 q^{93} +23.1142 q^{94} -3.51460 q^{95} +5.64070 q^{96} -7.34317 q^{97} +10.2694 q^{98} -8.63542 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 174 q + 6 q^{2} + 37 q^{3} + 214 q^{4} + 10 q^{5} + 12 q^{6} + 28 q^{7} + 15 q^{8} + 211 q^{9}+O(q^{10}) $ 174 * q + 6 * q^2 + 37 * q^3 + 214 * q^4 + 10 * q^5 + 12 * q^6 + 28 * q^7 + 15 * q^8 + 211 * q^9	\( 174 q + 6 q^{2} + 37 q^{3} + 214 q^{4} + 10 q^{5} + 12 q^{6} + 28 q^{7} + 15 q^{8} + 211 q^{9} + 47 q^{10} + 47 q^{11} + 81 q^{12} + 174 q^{13} + 22 q^{14} + 26 q^{15} + 286 q^{16} + 27 q^{17} + 22 q^{18} + 91 q^{19} + 18 q^{20} + 8 q^{21} + 58 q^{22} + 62 q^{23} + 24 q^{24} + 244 q^{25} + 6 q^{26} + 139 q^{27} + 43 q^{28} + 42 q^{29} + 31 q^{30} + 82 q^{31} + 11 q^{32} + 12 q^{33} + 50 q^{34} + 74 q^{35} + 310 q^{36} + 47 q^{37} + 10 q^{38} + 37 q^{39} + 118 q^{40} + 16 q^{41} + 26 q^{42} + 136 q^{43} + 74 q^{44} + 18 q^{45} + 53 q^{46} + 15 q^{47} + 132 q^{48} + 254 q^{49} - 5 q^{50} + 121 q^{51} + 214 q^{52} + 39 q^{53} + 30 q^{54} + 188 q^{55} + 55 q^{56} + 11 q^{57} + 32 q^{58} + 58 q^{59} + 16 q^{60} + 128 q^{61} + 27 q^{62} + 42 q^{63} + 423 q^{64} + 10 q^{65} + 4 q^{66} + 132 q^{67} + 52 q^{68} + 63 q^{69} - 8 q^{70} + 78 q^{71} + 2 q^{72} + 21 q^{73} - 16 q^{74} + 188 q^{75} + 160 q^{76} + 20 q^{77} + 12 q^{78} + 232 q^{79} + 2 q^{80} + 302 q^{81} + 115 q^{82} + 18 q^{83} - 26 q^{84} + 47 q^{85} + 27 q^{86} + 127 q^{87} + 163 q^{88} + 14 q^{90} + 28 q^{91} + 68 q^{92} + 15 q^{93} + 91 q^{94} + 75 q^{95} - 26 q^{96} + 34 q^{97} - 60 q^{98} + 181 q^{99}+O(q^{100}) \) 174 * q + 6 * q^2 + 37 * q^3 + 214 * q^4 + 10 * q^5 + 12 * q^6 + 28 * q^7 + 15 * q^8 + 211 * q^9 + 47 * q^10 + 47 * q^11 + 81 * q^12 + 174 * q^13 + 22 * q^14 + 26 * q^15 + 286 * q^16 + 27 * q^17 + 22 * q^18 + 91 * q^19 + 18 * q^20 + 8 * q^21 + 58 * q^22 + 62 * q^23 + 24 * q^24 + 244 * q^25 + 6 * q^26 + 139 * q^27 + 43 * q^28 + 42 * q^29 + 31 * q^30 + 82 * q^31 + 11 * q^32 + 12 * q^33 + 50 * q^34 + 74 * q^35 + 310 * q^36 + 47 * q^37 + 10 * q^38 + 37 * q^39 + 118 * q^40 + 16 * q^41 + 26 * q^42 + 136 * q^43 + 74 * q^44 + 18 * q^45 + 53 * q^46 + 15 * q^47 + 132 * q^48 + 254 * q^49 - 5 * q^50 + 121 * q^51 + 214 * q^52 + 39 * q^53 + 30 * q^54 + 188 * q^55 + 55 * q^56 + 11 * q^57 + 32 * q^58 + 58 * q^59 + 16 * q^60 + 128 * q^61 + 27 * q^62 + 42 * q^63 + 423 * q^64 + 10 * q^65 + 4 * q^66 + 132 * q^67 + 52 * q^68 + 63 * q^69 - 8 * q^70 + 78 * q^71 + 2 * q^72 + 21 * q^73 - 16 * q^74 + 188 * q^75 + 160 * q^76 + 20 * q^77 + 12 * q^78 + 232 * q^79 + 2 * q^80 + 302 * q^81 + 115 * q^82 + 18 * q^83 - 26 * q^84 + 47 * q^85 + 27 * q^86 + 127 * q^87 + 163 * q^88 + 14 * q^90 + 28 * q^91 + 68 * q^92 + 15 * q^93 + 91 * q^94 + 75 * q^95 - 26 * q^96 + 34 * q^97 - 60 * q^98 + 181 * 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 $

$2$	−2.64300	−1.86889	−0.934443	−	0.356114i	$-0.884102\pi$
$2$	−2.64300	−1.86889	−0.934443	+	0.356114i	$0.884102\pi$
$3$	−0.434399	−0.250800	−0.125400	−	0.992106i	$-0.540021\pi$
$3$	−0.434399	−0.250800	−0.125400	+	0.992106i	$0.540021\pi$
$4$	4.98547	2.49273
$5$	−0.633166	−0.283161	−0.141580	−	0.989927i	$-0.545218\pi$
$5$	−0.633166	−0.283161	−0.141580	+	0.989927i	$0.545218\pi$
$6$	1.14812	0.468717
$7$	1.76480	0.667030	0.333515	−	0.942745i	$-0.391765\pi$
$7$	1.76480	0.667030	0.333515	+	0.942745i	$0.391765\pi$
$8$	−7.89059	−2.78975
$9$	−2.81130	−0.937099
$10$	1.67346	0.529195
$11$	3.07168	0.926148	0.463074	−	0.886320i	$-0.346746\pi$
$11$	3.07168	0.926148	0.463074	+	0.886320i	$0.346746\pi$
$12$	−2.16568	−0.625178
$13$	1.00000	0.277350
$13$	1.00000	0.277350
$14$	−4.66436	−1.24660
$15$	0.275047	0.0710167
$16$	10.8839	2.72098
$17$	−5.17211	−1.25442	−0.627211	−	0.778849i	$-0.715804\pi$
$17$	−5.17211	−1.25442	−0.627211	+	0.778849i	$0.715804\pi$
$18$	7.43027	1.75133
$19$	5.55084	1.27345	0.636725	−	0.771091i	$-0.280289\pi$
$19$	5.55084	1.27345	0.636725	+	0.771091i	$0.280289\pi$
$20$	−3.15663	−0.705844
$21$	−0.766625	−0.167291
$22$	−8.11847	−1.73086
$23$	−8.80013	−1.83495	−0.917477	−	0.397789i	$-0.869778\pi$
$23$	−8.80013	−1.83495	−0.917477	+	0.397789i	$0.869778\pi$
$24$	3.42766	0.699669
$25$	−4.59910	−0.919820
$26$	−2.64300	−0.518336
$27$	2.52442	0.485825
$28$	8.79833	1.66273
$29$	−2.96717	−0.550990	−0.275495	−	0.961303i	$-0.588842\pi$
$29$	−2.96717	−0.550990	−0.275495	+	0.961303i	$0.588842\pi$
$30$	−0.726949	−0.132722
$31$	5.05817	0.908473	0.454237	−	0.890881i	$-0.349912\pi$
$31$	5.05817	0.908473	0.454237	+	0.890881i	$0.349912\pi$
$32$	−12.9851	−2.29546
$33$	−1.33434	−0.232278
$34$	13.6699	2.34437
$35$	−1.11741	−0.188877
$36$	−14.0156	−2.33594
$37$	4.73590	0.778578	0.389289	−	0.921116i	$-0.372721\pi$
$37$	4.73590	0.778578	0.389289	+	0.921116i	$0.372721\pi$
$38$	−14.6709	−2.37993
$39$	−0.434399	−0.0695595
$40$	4.99606	0.789946
$41$	−4.72173	−0.737410	−0.368705	−	0.929546i	$-0.620199\pi$
$41$	−4.72173	−0.737410	−0.368705	+	0.929546i	$0.620199\pi$
$42$	2.02619	0.312648
$43$	−0.539613	−0.0822902	−0.0411451	−	0.999153i	$-0.513101\pi$
$43$	−0.539613	−0.0822902	−0.0411451	+	0.999153i	$0.513101\pi$
$44$	15.3138	2.30864
$45$	1.78002	0.265350
$46$	23.2588	3.42932
$47$	−8.74542	−1.27565	−0.637825	−	0.770181i	$-0.720166\pi$
$47$	−8.74542	−1.27565	−0.637825	+	0.770181i	$0.720166\pi$
$48$	−4.72797	−0.682423
$49$	−3.88549	−0.555071
$50$	12.1554	1.71904
$51$	2.24676	0.314609
$52$	4.98547	0.691360
$53$	4.12133	0.566109	0.283054	−	0.959104i	$-0.408652\pi$
$53$	4.12133	0.566109	0.283054	+	0.959104i	$0.408652\pi$
$54$	−6.67205	−0.907951
$55$	−1.94489	−0.262248
$56$	−13.9253	−1.86085
$57$	−2.41128	−0.319381
$58$	7.84224	1.02974
$59$	1.01484	0.132121	0.0660604	−	0.997816i	$-0.478957\pi$
$59$	1.01484	0.132121	0.0660604	+	0.997816i	$0.478957\pi$
$60$	1.37124	0.177026
$61$	−7.93769	−1.01632	−0.508159	−	0.861263i	$-0.669674\pi$
$61$	−7.93769	−1.01632	−0.508159	+	0.861263i	$0.669674\pi$
$62$	−13.3687	−1.69783
$63$	−4.96137	−0.625074
$64$	12.5517	1.56897
$65$	−0.633166	−0.0785346
$66$	3.52665	0.434101
$67$	−5.28468	−0.645627	−0.322814	−	0.946463i	$-0.604629\pi$
$67$	−5.28468	−0.645627	−0.322814	+	0.946463i	$0.604629\pi$
$68$	−25.7854	−3.12694
$69$	3.82277	0.460207
$70$	2.95332	0.352989
$71$	12.6904	1.50607	0.753037	−	0.657979i	$-0.228588\pi$
$71$	12.6904	1.50607	0.753037	+	0.657979i	$0.228588\pi$
$72$	22.1828	2.61427
$73$	9.28736	1.08700	0.543502	−	0.839408i	$-0.317098\pi$
$73$	9.28736	1.08700	0.543502	+	0.839408i	$0.317098\pi$
$74$	−12.5170	−1.45507
$75$	1.99784	0.230691
$76$	27.6735	3.17437
$77$	5.42090	0.617769
$78$	1.14812	0.129999
$79$	13.4798	1.51659	0.758296	−	0.651911i	$-0.226032\pi$
$79$	13.4798	1.51659	0.758296	+	0.651911i	$0.226032\pi$
$80$	−6.89134	−0.770475
$81$	7.33729	0.815254
$82$	12.4795	1.37814
$83$	−8.94575	−0.981923	−0.490962	−	0.871181i	$-0.663354\pi$
$83$	−8.94575	−0.981923	−0.490962	+	0.871181i	$0.663354\pi$
$84$	−3.82198	−0.417013
$85$	3.27481	0.355203
$86$	1.42620	0.153791
$87$	1.28893	0.138188
$88$	−24.2374	−2.58372
$89$	−7.05729	−0.748071	−0.374035	−	0.927414i	$-0.622026\pi$
$89$	−7.05729	−0.748071	−0.374035	+	0.927414i	$0.622026\pi$
$90$	−4.70460	−0.495908
$91$	1.76480	0.185001
$92$	−43.8727	−4.57405
$93$	−2.19726	−0.227845
$94$	23.1142	2.38405
$95$	−3.51460	−0.360591
$96$	5.64070	0.575702
$97$	−7.34317	−0.745586	−0.372793	−	0.927915i	$-0.621600\pi$
$97$	−7.34317	−0.745586	−0.372793	+	0.927915i	$0.621600\pi$
$98$	10.2694	1.03736
$99$	−8.63542	−0.867892
$100$	−22.9287	−2.29287
$101$	7.23742	0.720150	0.360075	−	0.932923i	$-0.382751\pi$
$101$	7.23742	0.720150	0.360075	+	0.932923i	$0.382751\pi$
$102$	−5.93819	−0.587969
$103$	−13.9396	−1.37351	−0.686755	−	0.726889i	$-0.740965\pi$
$103$	−13.9396	−1.37351	−0.686755	+	0.726889i	$0.740965\pi$
$104$	−7.89059	−0.773736
$105$	0.485401	0.0473703
$106$	−10.8927	−1.05799
$107$	12.4102	1.19974	0.599872	−	0.800096i	$-0.295218\pi$
$107$	12.4102	1.19974	0.599872	+	0.800096i	$0.295218\pi$
$108$	12.5854	1.21103
$109$	5.84996	0.560325	0.280162	−	0.959953i	$-0.409612\pi$
$109$	5.84996	0.560325	0.280162	+	0.959953i	$0.409612\pi$
$110$	5.14034	0.490112
$111$	−2.05727	−0.195267
$112$	19.2079	1.81498
$113$	16.0106	1.50615	0.753074	−	0.657936i	$-0.228570\pi$
$113$	16.0106	1.50615	0.753074	+	0.657936i	$0.228570\pi$
$114$	6.37301	0.596887
$115$	5.57195	0.519587
$116$	−14.7927	−1.37347
$117$	−2.81130	−0.259905
$118$	−2.68222	−0.246919
$119$	−9.12773	−0.836738
$120$	−2.17028	−0.198119
$121$	−1.56476	−0.142251
$122$	20.9793	1.89938
$123$	2.05111	0.184943
$124$	25.2173	2.26458
$125$	6.07783	0.543617
$126$	13.1129	1.16819
$127$	4.33202	0.384405	0.192202	−	0.981355i	$-0.438437\pi$
$127$	4.33202	0.384405	0.192202	+	0.981355i	$0.438437\pi$
$128$	−7.20413	−0.636761
$129$	0.234407	0.0206384
$130$	1.67346	0.146772
$131$	−0.919865	−0.0803690	−0.0401845	−	0.999192i	$-0.512795\pi$
$131$	−0.919865	−0.0803690	−0.0401845	+	0.999192i	$0.512795\pi$
$132$	−6.65228	−0.579007
$133$	9.79610	0.849430
$134$	13.9674	1.20660
$135$	−1.59838	−0.137566
$136$	40.8111	3.49952
$137$	−18.8288	−1.60865	−0.804325	−	0.594190i	$-0.797473\pi$
$137$	−18.8288	−1.60865	−0.804325	+	0.594190i	$0.797473\pi$
$138$	−10.1036	−0.860074
$139$	−20.4680	−1.73607	−0.868037	−	0.496499i	$-0.834619\pi$
$139$	−20.4680	−1.73607	−0.868037	+	0.496499i	$0.834619\pi$
$140$	−5.57081	−0.470819
$141$	3.79900	0.319934
$142$	−33.5408	−2.81468
$143$	3.07168	0.256867
$144$	−30.5980	−2.54983
$145$	1.87871	0.156019
$146$	−24.5465	−2.03148
$147$	1.68785	0.139212
$148$	23.6107	1.94079
$149$	13.5668	1.11143	0.555717	−	0.831371i	$-0.312444\pi$
$149$	13.5668	1.11143	0.555717	+	0.831371i	$0.312444\pi$
$150$	−5.28031	−0.431135
$151$	3.72987	0.303532	0.151766	−	0.988416i	$-0.451504\pi$
$151$	3.72987	0.303532	0.151766	+	0.988416i	$0.451504\pi$
$152$	−43.7994	−3.55260
$153$	14.5404	1.17552
$154$	−14.3274	−1.15454
$155$	−3.20266	−0.257244
$156$	−2.16568	−0.173393
$157$	8.17248	0.652235	0.326118	−	0.945329i	$-0.394259\pi$
$157$	8.17248	0.652235	0.326118	+	0.945329i	$0.394259\pi$
$158$	−35.6271	−2.83434
$159$	−1.79030	−0.141980
$160$	8.22171	0.649984
$161$	−15.5304	−1.22397
$162$	−19.3925	−1.52362
$163$	−19.8146	−1.55200	−0.775999	−	0.630735i	$-0.782754\pi$
$163$	−19.8146	−1.55200	−0.775999	+	0.630735i	$0.782754\pi$
$164$	−23.5400	−1.83817
$165$	0.844856	0.0657720
$166$	23.6436	1.83510
$167$	10.9889	0.850347	0.425173	−	0.905112i	$-0.360213\pi$
$167$	10.9889	0.850347	0.425173	+	0.905112i	$0.360213\pi$
$168$	6.04913	0.466700
$169$	1.00000	0.0769231
$170$	−8.65533	−0.663833
$171$	−15.6051	−1.19335
$172$	−2.69022	−0.205128
$173$	−10.7514	−0.817416	−0.408708	−	0.912665i	$-0.634021\pi$
$173$	−10.7514	−0.817416	−0.408708	+	0.912665i	$0.634021\pi$
$174$	−3.40666	−0.258258
$175$	−8.11648	−0.613548
$176$	33.4320	2.52003
$177$	−0.440845	−0.0331359
$178$	18.6524	1.39806
$179$	13.3431	0.997308	0.498654	−	0.866801i	$-0.333828\pi$
$179$	13.3431	0.997308	0.498654	+	0.866801i	$0.333828\pi$
$180$	8.87422	0.661445
$181$	25.5657	1.90029	0.950143	−	0.311814i	$-0.100937\pi$
$181$	25.5657	1.90029	0.950143	+	0.311814i	$0.100937\pi$
$182$	−4.66436	−0.345746
$183$	3.44812	0.254893
$184$	69.4383	5.11906
$185$	−2.99861	−0.220463
$186$	5.80737	0.425817
$187$	−15.8871	−1.16178
$188$	−43.6000	−3.17986
$189$	4.45509	0.324060
$190$	9.28911	0.673903
$191$	−1.83851	−0.133030	−0.0665150	−	0.997785i	$-0.521188\pi$
$191$	−1.83851	−0.133030	−0.0665150	+	0.997785i	$0.521188\pi$
$192$	−5.45246	−0.393497
$193$	19.3897	1.39570	0.697852	−	0.716242i	$-0.254139\pi$
$193$	19.3897	1.39570	0.697852	+	0.716242i	$0.254139\pi$
$194$	19.4080	1.39341
$195$	0.275047	0.0196965
$196$	−19.3710	−1.38364
$197$	25.3145	1.80358	0.901790	−	0.432174i	$-0.142253\pi$
$197$	25.3145	1.80358	0.901790	+	0.432174i	$0.142253\pi$
$198$	22.8234	1.62199
$199$	11.3018	0.801167	0.400583	−	0.916260i	$-0.368808\pi$
$199$	11.3018	0.801167	0.400583	+	0.916260i	$0.368808\pi$
$200$	36.2896	2.56606
$201$	2.29566	0.161923
$202$	−19.1285	−1.34588
$203$	−5.23645	−0.367527
$204$	11.2011	0.784237
$205$	2.98964	0.208805
$206$	36.8424	2.56693
$207$	24.7398	1.71953
$208$	10.8839	0.754665
$209$	17.0504	1.17940
$210$	−1.28292	−0.0885297
$211$	2.46574	0.169749	0.0848744	−	0.996392i	$-0.472951\pi$
$211$	2.46574	0.169749	0.0848744	+	0.996392i	$0.472951\pi$
$212$	20.5468	1.41116
$213$	−5.51269	−0.377723
$214$	−32.8003	−2.24218
$215$	0.341665	0.0233014
$216$	−19.9192	−1.35533
$217$	8.92663	0.605979
$218$	−15.4615	−1.04718
$219$	−4.03442	−0.272621
$220$	−9.69616	−0.653715
$221$	−5.17211	−0.347914
$222$	5.43737	0.364933
$223$	−3.47759	−0.232877	−0.116438	−	0.993198i	$-0.537148\pi$
$223$	−3.47759	−0.232877	−0.116438	+	0.993198i	$0.537148\pi$
$224$	−22.9160	−1.53114
$225$	12.9294	0.861963
$226$	−42.3160	−2.81482
$227$	−26.9642	−1.78968	−0.894839	−	0.446389i	$-0.852710\pi$
$227$	−26.9642	−1.78968	−0.894839	+	0.446389i	$0.852710\pi$
$228$	−12.0213	−0.796133
$229$	5.55591	0.367145	0.183572	−	0.983006i	$-0.441234\pi$
$229$	5.55591	0.367145	0.183572	+	0.983006i	$0.441234\pi$
$230$	−14.7267	−0.971048
$231$	−2.35483	−0.154936
$232$	23.4127	1.53712
$233$	2.36654	0.155037	0.0775186	−	0.996991i	$-0.475300\pi$
$233$	2.36654	0.155037	0.0775186	+	0.996991i	$0.475300\pi$
$234$	7.43027	0.485732
$235$	5.53731	0.361214
$236$	5.05945	0.329342
$237$	−5.85559	−0.380361
$238$	24.1246	1.56377
$239$	18.5594	1.20051	0.600255	−	0.799809i	$-0.295066\pi$
$239$	18.5594	1.20051	0.600255	+	0.799809i	$0.295066\pi$
$240$	2.99359	0.193235
$241$	11.2106	0.722139	0.361070	−	0.932539i	$-0.382412\pi$
$241$	11.2106	0.722139	0.361070	+	0.932539i	$0.382412\pi$
$242$	4.13566	0.265850
$243$	−10.7606	−0.690291
$244$	−39.5731	−2.53341
$245$	2.46016	0.157174
$246$	−5.42110	−0.345637
$247$	5.55084	0.353191
$248$	−39.9119	−2.53441
$249$	3.88602	0.246267
$250$	−16.0637	−1.01596
$251$	−27.1164	−1.71157	−0.855786	−	0.517330i	$-0.826926\pi$
$251$	−27.1164	−1.71157	−0.855786	+	0.517330i	$0.826926\pi$
$252$	−24.7347	−1.55814
$253$	−27.0312	−1.69944
$254$	−11.4496	−0.718409
$255$	−1.42257	−0.0890849
$256$	−6.06294	−0.378934
$257$	8.04665	0.501936	0.250968	−	0.967995i	$-0.419251\pi$
$257$	8.04665	0.501936	0.250968	+	0.967995i	$0.419251\pi$
$258$	−0.619539	−0.0385708
$259$	8.35791	0.519335
$260$	−3.15663	−0.195766
$261$	8.34160	0.516332
$262$	2.43121	0.150200
$263$	26.0469	1.60612	0.803060	−	0.595899i	$-0.203204\pi$
$263$	26.0469	1.60612	0.803060	+	0.595899i	$0.203204\pi$
$264$	10.5287	0.647997
$265$	−2.60949	−0.160300
$266$	−25.8911	−1.58749
$267$	3.06568	0.187616
$268$	−26.3466	−1.60938
$269$	10.9453	0.667345	0.333673	−	0.942689i	$-0.391712\pi$
$269$	10.9453	0.667345	0.333673	+	0.942689i	$0.391712\pi$
$270$	4.22452	0.257096
$271$	7.08936	0.430648	0.215324	−	0.976543i	$-0.430919\pi$
$271$	7.08936	0.430648	0.215324	+	0.976543i	$0.430919\pi$
$272$	−56.2929	−3.41326
$273$	−0.766625	−0.0463983
$274$	49.7645	3.00638
$275$	−14.1270	−0.851889
$276$	19.0583	1.14717
$277$	−22.4542	−1.34914	−0.674572	−	0.738209i	$-0.735672\pi$
$277$	−22.4542	−1.34914	−0.674572	+	0.738209i	$0.735672\pi$
$278$	54.0970	3.24453
$279$	−14.2200	−0.851330
$280$	8.81702	0.526918
$281$	7.94040	0.473685	0.236842	−	0.971548i	$-0.423888\pi$
$281$	7.94040	0.473685	0.236842	+	0.971548i	$0.423888\pi$
$282$	−10.0408	−0.597919
$283$	20.1500	1.19779	0.598896	−	0.800827i	$-0.295606\pi$
$283$	20.1500	1.19779	0.598896	+	0.800827i	$0.295606\pi$
$284$	63.2675	3.75424
$285$	1.52674	0.0904362
$286$	−8.11847	−0.480055
$287$	−8.33289	−0.491875
$288$	36.5049	2.15107
$289$	9.75077	0.573575
$290$	−4.96544	−0.291581
$291$	3.18986	0.186993
$292$	46.3018	2.70961
$293$	−1.77067	−0.103443	−0.0517217	−	0.998662i	$-0.516471\pi$
$293$	−1.77067	−0.103443	−0.0517217	+	0.998662i	$0.516471\pi$
$294$	−4.46100	−0.260171
$295$	−0.642562	−0.0374114
$296$	−37.3691	−2.17203
$297$	7.75422	0.449946
$298$	−35.8570	−2.07714
$299$	−8.80013	−0.508925
$300$	9.96018	0.575051
$301$	−0.952307	−0.0548901
$302$	−9.85805	−0.567267
$303$	−3.14392	−0.180614
$304$	60.4150	3.46504
$305$	5.02588	0.287781
$306$	−38.4302	−2.19691
$307$	4.23763	0.241855	0.120927	−	0.992661i	$-0.461413\pi$
$307$	4.23763	0.241855	0.120927	+	0.992661i	$0.461413\pi$
$308$	27.0257	1.53993
$309$	6.05534	0.344476
$310$	8.46464	0.480759
$311$	11.1010	0.629479	0.314740	−	0.949178i	$-0.398083\pi$
$311$	11.1010	0.629479	0.314740	+	0.949178i	$0.398083\pi$
$312$	3.42766	0.194053
$313$	−3.49925	−0.197789	−0.0988947	−	0.995098i	$-0.531531\pi$
$313$	−3.49925	−0.197789	−0.0988947	+	0.995098i	$0.531531\pi$
$314$	−21.5999	−1.21895
$315$	3.14137	0.176996
$316$	67.2029	3.78046
$317$	12.5594	0.705405	0.352702	−	0.935736i	$-0.385263\pi$
$317$	12.5594	0.705405	0.352702	+	0.935736i	$0.385263\pi$
$318$	4.73177	0.265345
$319$	−9.11421	−0.510298
$320$	−7.94734	−0.444270
$321$	−5.39099	−0.300896
$322$	41.0470	2.28746
$323$	−28.7096	−1.59744
$324$	36.5798	2.03221
$325$	−4.59910	−0.255112
$326$	52.3700	2.90050
$327$	−2.54122	−0.140530
$328$	37.2572	2.05719
$329$	−15.4339	−0.850898
$330$	−2.23296	−0.122920
$331$	18.7974	1.03320	0.516600	−	0.856227i	$-0.327197\pi$
$331$	18.7974	1.03320	0.516600	+	0.856227i	$0.327197\pi$
$332$	−44.5987	−2.44767
$333$	−13.3140	−0.729605
$334$	−29.0437	−1.58920
$335$	3.34608	0.182816
$336$	−8.34390	−0.455197
$337$	23.9379	1.30398	0.651990	−	0.758227i	$-0.273934\pi$
$337$	23.9379	1.30398	0.651990	+	0.758227i	$0.273934\pi$
$338$	−2.64300	−0.143760
$339$	−6.95497	−0.377742
$340$	16.3264	0.885426
$341$	15.5371	0.841380
$342$	41.2442	2.23023
$343$	−19.2107	−1.03728
$344$	4.25787	0.229569
$345$	−2.42045	−0.130312
$346$	28.4161	1.52766
$347$	−0.849796	−0.0456194	−0.0228097	−	0.999740i	$-0.507261\pi$
$347$	−0.849796	−0.0456194	−0.0228097	+	0.999740i	$0.507261\pi$
$348$	6.42594	0.344466
$349$	−35.6315	−1.90731	−0.953656	−	0.300898i	$-0.902714\pi$
$349$	−35.6315	−1.90731	−0.953656	+	0.300898i	$0.902714\pi$
$350$	21.4519	1.14665
$351$	2.52442	0.134744
$352$	−39.8861	−2.12593
$353$	3.78446	0.201426	0.100713	−	0.994915i	$-0.467888\pi$
$353$	3.78446	0.201426	0.100713	+	0.994915i	$0.467888\pi$
$354$	1.16515	0.0619273
$355$	−8.03513	−0.426460
$356$	−35.1839	−1.86474
$357$	3.96507	0.209854
$358$	−35.2658	−1.86385
$359$	−22.5568	−1.19050	−0.595252	−	0.803539i	$-0.702948\pi$
$359$	−22.5568	−1.19050	−0.595252	+	0.803539i	$0.702948\pi$
$360$	−14.0454	−0.740258
$361$	11.8118	0.621674
$362$	−67.5703	−3.55142
$363$	0.679728	0.0356765
$364$	8.79833	0.461158
$365$	−5.88044	−0.307796
$366$	−9.11340	−0.476365
$367$	−16.6651	−0.869912	−0.434956	−	0.900452i	$-0.643236\pi$
$367$	−16.6651	−0.869912	−0.434956	+	0.900452i	$0.643236\pi$
$368$	−95.7800	−4.99288
$369$	13.2742	0.691027
$370$	7.92535	0.412019
$371$	7.27332	0.377612
$372$	−10.9544	−0.567957
$373$	−25.7017	−1.33079	−0.665393	−	0.746494i	$-0.731736\pi$
$373$	−25.7017	−1.33079	−0.665393	+	0.746494i	$0.731736\pi$
$374$	41.9897	2.17123
$375$	−2.64020	−0.136339
$376$	69.0066	3.55874
$377$	−2.96717	−0.152817
$378$	−11.7748	−0.605631
$379$	−34.8531	−1.79028	−0.895141	−	0.445783i	$-0.852925\pi$
$379$	−34.8531	−1.79028	−0.895141	+	0.445783i	$0.852925\pi$
$380$	−17.5219	−0.898856
$381$	−1.88183	−0.0964088
$382$	4.85919	0.248618
$383$	30.0844	1.53724	0.768621	−	0.639705i	$-0.220943\pi$
$383$	30.0844	1.53724	0.768621	+	0.639705i	$0.220943\pi$
$384$	3.12947	0.159700
$385$	−3.43233	−0.174928
$386$	−51.2471	−2.60841
$387$	1.51701	0.0771141
$388$	−36.6091	−1.85855
$389$	−24.3363	−1.23390	−0.616949	−	0.787003i	$-0.711632\pi$
$389$	−24.3363	−1.23390	−0.616949	+	0.787003i	$0.711632\pi$
$390$	−0.726949	−0.0368105
$391$	45.5153	2.30181
$392$	30.6589	1.54851
$393$	0.399588	0.0201566
$394$	−66.9062	−3.37068
$395$	−8.53493	−0.429439
$396$	−43.0516	−2.16342
$397$	−7.48508	−0.375665	−0.187833	−	0.982201i	$-0.560146\pi$
$397$	−7.48508	−0.375665	−0.187833	+	0.982201i	$0.560146\pi$
$398$	−29.8708	−1.49729
$399$	−4.25541	−0.213037
$400$	−50.0563	−2.50282
$401$	−33.7406	−1.68493	−0.842464	−	0.538753i	$-0.818896\pi$
$401$	−33.7406	−1.68493	−0.842464	+	0.538753i	$0.818896\pi$
$402$	−6.06744	−0.302616
$403$	5.05817	0.251965
$404$	36.0819	1.79514
$405$	−4.64572	−0.230848
$406$	13.8400	0.686865
$407$	14.5472	0.721078
$408$	−17.7283	−0.877680
$409$	−4.52369	−0.223682	−0.111841	−	0.993726i	$-0.535675\pi$
$409$	−4.52369	−0.223682	−0.111841	+	0.993726i	$0.535675\pi$
$410$	−7.90163	−0.390233
$411$	8.17919	0.403450
$412$	−69.4954	−3.42379
$413$	1.79098	0.0881286
$414$	−65.3873	−3.21361
$415$	5.66415	0.278042
$416$	−12.9851	−0.636646
$417$	8.89128	0.435408
$418$	−45.0643	−2.20417
$419$	0.666418	0.0325566	0.0162783	−	0.999867i	$-0.494818\pi$
$419$	0.666418	0.0325566	0.0162783	+	0.999867i	$0.494818\pi$
$420$	2.41995	0.118082
$421$	3.91818	0.190960	0.0954802	−	0.995431i	$-0.469561\pi$
$421$	3.91818	0.190960	0.0954802	+	0.995431i	$0.469561\pi$
$422$	−6.51697	−0.317241
$423$	24.5860	1.19541
$424$	−32.5198	−1.57930
$425$	23.7871	1.15384
$426$	14.5701	0.705922
$427$	−14.0084	−0.677915
$428$	61.8708	2.99064
$429$	−1.33434	−0.0644223
$430$	−0.903021	−0.0435476
$431$	41.4268	1.99546	0.997728	−	0.0673646i	$-0.0214591\pi$
$431$	41.4268	1.99546	0.997728	+	0.0673646i	$0.0214591\pi$
$432$	27.4756	1.32192
$433$	29.5960	1.42229	0.711147	−	0.703043i	$-0.248176\pi$
$433$	29.5960	1.42229	0.711147	+	0.703043i	$0.248176\pi$
$434$	−23.5931	−1.13251
$435$	−0.816110	−0.0391295
$436$	29.1648	1.39674
$437$	−48.8481	−2.33672
$438$	10.6630	0.509497
$439$	−34.3959	−1.64163	−0.820814	−	0.571195i	$-0.806480\pi$
$439$	−34.3959	−1.64163	−0.820814	+	0.571195i	$0.806480\pi$
$440$	15.3463	0.731607
$441$	10.9233	0.520156
$442$	13.6699	0.650212
$443$	−33.6454	−1.59854	−0.799270	−	0.600972i	$-0.794780\pi$
$443$	−33.6454	−1.59854	−0.799270	+	0.600972i	$0.794780\pi$
$444$	−10.2564	−0.486750
$445$	4.46844	0.211824
$446$	9.19128	0.435220
$447$	−5.89339	−0.278748
$448$	22.1513	1.04655
$449$	−3.88460	−0.183325	−0.0916627	−	0.995790i	$-0.529218\pi$
$449$	−3.88460	−0.183325	−0.0916627	+	0.995790i	$0.529218\pi$
$450$	−34.1726	−1.61091
$451$	−14.5037	−0.682951
$452$	79.8201	3.75442
$453$	−1.62025	−0.0761259
$454$	71.2665	3.34470
$455$	−1.11741	−0.0523850
$456$	19.0264	0.890993
$457$	−31.2359	−1.46115	−0.730577	−	0.682830i	$-0.760749\pi$
$457$	−31.2359	−1.46115	−0.730577	+	0.682830i	$0.760749\pi$
$458$	−14.6843	−0.686152
$459$	−13.0566	−0.609429
$460$	27.7787	1.29519
$461$	32.5097	1.51413	0.757064	−	0.653341i	$-0.226633\pi$
$461$	32.5097	1.51413	0.757064	+	0.653341i	$0.226633\pi$
$462$	6.22382	0.289559
$463$	−20.0958	−0.933933	−0.466967	−	0.884275i	$-0.654653\pi$
$463$	−20.0958	−0.933933	−0.466967	+	0.884275i	$0.654653\pi$
$464$	−32.2945	−1.49923
$465$	1.39123	0.0645168
$466$	−6.25477	−0.289747
$467$	−33.0335	−1.52861	−0.764305	−	0.644855i	$-0.776918\pi$
$467$	−33.0335	−1.52861	−0.764305	+	0.644855i	$0.776918\pi$
$468$	−14.0156	−0.647873
$469$	−9.32639	−0.430653
$470$	−14.6351	−0.675068
$471$	−3.55012	−0.163581
$472$	−8.00769	−0.368584
$473$	−1.65752	−0.0762129
$474$	15.4763	0.710852
$475$	−25.5289	−1.17134
$476$	−45.5060	−2.08576
$477$	−11.5863	−0.530500
$478$	−49.0526	−2.24362
$479$	−26.0137	−1.18860	−0.594299	−	0.804244i	$-0.702570\pi$
$479$	−26.0137	−1.18860	−0.594299	+	0.804244i	$0.702570\pi$
$480$	−3.57150	−0.163016
$481$	4.73590	0.215939
$482$	−29.6297	−1.34960
$483$	6.74640	0.306972
$484$	−7.80104	−0.354593
$485$	4.64945	0.211121
$486$	28.4402	1.29007
$487$	−10.9872	−0.497878	−0.248939	−	0.968519i	$-0.580082\pi$
$487$	−10.9872	−0.497878	−0.248939	+	0.968519i	$0.580082\pi$
$488$	62.6331	2.83527
$489$	8.60742	0.389241
$490$	−6.50222	−0.293740
$491$	−28.5913	−1.29031	−0.645154	−	0.764052i	$-0.723207\pi$
$491$	−28.5913	−1.29031	−0.645154	+	0.764052i	$0.723207\pi$
$492$	10.2258	0.461012
$493$	15.3465	0.691173
$494$	−14.6709	−0.660074
$495$	5.46766	0.245753
$496$	55.0527	2.47194
$497$	22.3960	1.00460
$498$	−10.2708	−0.460244
$499$	26.4785	1.18534	0.592670	−	0.805445i	$-0.298074\pi$
$499$	26.4785	1.18534	0.592670	+	0.805445i	$0.298074\pi$
$500$	30.3008	1.35509
$501$	−4.77357	−0.213267
$502$	71.6687	3.19873
$503$	33.8836	1.51080	0.755398	−	0.655266i	$-0.227443\pi$
$503$	33.8836	1.51080	0.755398	+	0.655266i	$0.227443\pi$
$504$	39.1481	1.74380
$505$	−4.58249	−0.203918
$506$	71.4436	3.17606
$507$	−0.434399	−0.0192923
$508$	21.5972	0.958219
$509$	−1.16913	−0.0518206	−0.0259103	−	0.999664i	$-0.508248\pi$
$509$	−1.16913	−0.0518206	−0.0259103	+	0.999664i	$0.508248\pi$
$510$	3.75986	0.166490
$511$	16.3903	0.725064
$512$	30.4326	1.34495
$513$	14.0126	0.618674
$514$	−21.2673	−0.938062
$515$	8.82608	0.388924
$516$	1.16863	0.0514460
$517$	−26.8632	−1.18144
$518$	−22.0900	−0.970578
$519$	4.67041	0.205008
$520$	4.99606	0.219092
$521$	−16.6477	−0.729348	−0.364674	−	0.931135i	$-0.618820\pi$
$521$	−16.6477	−0.729348	−0.364674	+	0.931135i	$0.618820\pi$
$522$	−22.0469	−0.964965
$523$	23.2907	1.01843	0.509216	−	0.860638i	$-0.329935\pi$
$523$	23.2907	1.01843	0.509216	+	0.860638i	$0.329935\pi$
$524$	−4.58596	−0.200338
$525$	3.52579	0.153878
$526$	−68.8420	−3.00165
$527$	−26.1614	−1.13961
$528$	−14.5228	−0.632025
$529$	54.4423	2.36706
$530$	6.89689	0.299582
$531$	−2.85302	−0.123810
$532$	48.8381	2.11740
$533$	−4.72173	−0.204521
$534$	−8.10259	−0.350633
$535$	−7.85775	−0.339720
$536$	41.6993	1.80114
$537$	−5.79621	−0.250125
$538$	−28.9284	−1.24719
$539$	−11.9350	−0.514077
$540$	−7.96866	−0.342916
$541$	−14.6658	−0.630531	−0.315265	−	0.949004i	$-0.602094\pi$
$541$	−14.6658	−0.630531	−0.315265	+	0.949004i	$0.602094\pi$
$542$	−18.7372	−0.804832
$543$	−11.1057	−0.476592
$544$	67.1603	2.87948
$545$	−3.70400	−0.158662
$546$	2.02619	0.0867130
$547$	36.0048	1.53945	0.769726	−	0.638374i	$-0.220393\pi$
$547$	36.0048	1.53945	0.769726	+	0.638374i	$0.220393\pi$
$548$	−93.8701	−4.00993
$549$	22.3152	0.952390
$550$	37.3377	1.59208
$551$	−16.4703	−0.701658
$552$	−30.1639	−1.28386
$553$	23.7890	1.01161
$554$	59.3466	2.52139
$555$	1.30259	0.0552920
$556$	−102.043	−4.32757
$557$	27.4710	1.16398	0.581992	−	0.813195i	$-0.302273\pi$
$557$	27.4710	1.16398	0.581992	+	0.813195i	$0.302273\pi$
$558$	37.5835	1.59104
$559$	−0.539613	−0.0228232
$560$	−12.1618	−0.513930
$561$	6.90134	0.291375
$562$	−20.9865	−0.885262
$563$	−23.2321	−0.979118	−0.489559	−	0.871970i	$-0.662842\pi$
$563$	−23.2321	−0.979118	−0.489559	+	0.871970i	$0.662842\pi$
$564$	18.9398	0.797509
$565$	−10.1374	−0.426482
$566$	−53.2565	−2.23854
$567$	12.9488	0.543799
$568$	−100.135	−4.20156
$569$	1.72772	0.0724299	0.0362149	−	0.999344i	$-0.488470\pi$
$569$	1.72772	0.0724299	0.0362149	+	0.999344i	$0.488470\pi$
$570$	−4.03518	−0.169015
$571$	−2.82267	−0.118125	−0.0590625	−	0.998254i	$-0.518811\pi$
$571$	−2.82267	−0.118125	−0.0590625	+	0.998254i	$0.518811\pi$
$572$	15.3138	0.640301
$573$	0.798646	0.0333639
$574$	22.0239	0.919258
$575$	40.4727	1.68783
$576$	−35.2867	−1.47028
$577$	27.3306	1.13779	0.568895	−	0.822410i	$-0.307371\pi$
$577$	27.3306	1.13779	0.568895	+	0.822410i	$0.307371\pi$
$578$	−25.7713	−1.07195
$579$	−8.42287	−0.350043
$580$	9.36625	0.388912
$581$	−15.7874	−0.654973
$582$	−8.43082	−0.349469
$583$	12.6594	0.524300
$584$	−73.2828	−3.03246
$585$	1.78002	0.0735947
$586$	4.67988	0.193324
$587$	29.6529	1.22391	0.611953	−	0.790894i	$-0.290384\pi$
$587$	29.6529	1.22391	0.611953	+	0.790894i	$0.290384\pi$
$588$	8.41473	0.347018
$589$	28.0771	1.15690
$590$	1.69829	0.0699176
$591$	−10.9966	−0.452338
$592$	51.5453	2.11850
$593$	35.8882	1.47375	0.736877	−	0.676027i	$-0.236300\pi$
$593$	35.8882	1.47375	0.736877	+	0.676027i	$0.236300\pi$
$594$	−20.4944	−0.840897
$595$	5.77937	0.236931
$596$	67.6367	2.77051
$597$	−4.90951	−0.200933
$598$	23.2588	0.951122
$599$	12.3318	0.503862	0.251931	−	0.967745i	$-0.418934\pi$
$599$	12.3318	0.503862	0.251931	+	0.967745i	$0.418934\pi$
$600$	−15.7642	−0.643569
$601$	6.73469	0.274714	0.137357	−	0.990522i	$-0.456139\pi$
$601$	6.73469	0.274714	0.137357	+	0.990522i	$0.456139\pi$
$602$	2.51695	0.102583
$603$	14.8568	0.605017
$604$	18.5951	0.756625
$605$	0.990752	0.0402798
$606$	8.30940	0.337546
$607$	−44.3447	−1.79990	−0.899948	−	0.435998i	$-0.856395\pi$
$607$	−44.3447	−1.79990	−0.899948	+	0.435998i	$0.856395\pi$
$608$	−72.0781	−2.92315
$609$	2.27471	0.0921758
$610$	−13.2834	−0.537830
$611$	−8.74542	−0.353802
$612$	72.4904	2.93025
$613$	5.17209	0.208899	0.104449	−	0.994530i	$-0.466692\pi$
$613$	5.17209	0.208899	0.104449	+	0.994530i	$0.466692\pi$
$614$	−11.2001	−0.451998
$615$	−1.29870	−0.0523685
$616$	−42.7741	−1.72342
$617$	−1.00000	−0.0402585
$617$	−1.00000	−0.0402585
$618$	−16.0043	−0.643787
$619$	21.6966	0.872061	0.436031	−	0.899932i	$-0.356384\pi$
$619$	21.6966	0.872061	0.436031	+	0.899932i	$0.356384\pi$
$620$	−15.9667	−0.641240
$621$	−22.2152	−0.891466
$622$	−29.3400	−1.17642
$623$	−12.4547	−0.498986
$624$	−4.72797	−0.189270
$625$	19.1472	0.765889
$626$	9.24853	0.369646
$627$	−7.40668	−0.295794
$628$	40.7436	1.62585
$629$	−24.4946	−0.976665
$630$	−8.30265	−0.330786
$631$	39.4099	1.56888	0.784441	−	0.620203i	$-0.212950\pi$
$631$	39.4099	1.56888	0.784441	+	0.620203i	$0.212950\pi$
$632$	−106.363	−4.23091
$633$	−1.07112	−0.0425730
$634$	−33.1945	−1.31832
$635$	−2.74289	−0.108848
$636$	−8.92549	−0.353919
$637$	−3.88549	−0.153949
$638$	24.0889	0.953688
$639$	−35.6765	−1.41134
$640$	4.56141	0.180306
$641$	27.0581	1.06873	0.534366	−	0.845253i	$-0.320550\pi$
$641$	27.0581	1.06873	0.534366	+	0.845253i	$0.320550\pi$
$642$	14.2484	0.562340
$643$	42.5580	1.67832	0.839162	−	0.543882i	$-0.183046\pi$
$643$	42.5580	1.67832	0.839162	+	0.543882i	$0.183046\pi$
$644$	−77.4265	−3.05103
$645$	−0.148419	−0.00584398
$646$	75.8795	2.98544
$647$	1.61519	0.0634997	0.0317498	−	0.999496i	$-0.489892\pi$
$647$	1.61519	0.0634997	0.0317498	+	0.999496i	$0.489892\pi$
$648$	−57.8956	−2.27435
$649$	3.11727	0.122363
$650$	12.1554	0.476775
$651$	−3.87772	−0.151980
$652$	−98.7849	−3.86871
$653$	38.2027	1.49499	0.747493	−	0.664270i	$-0.231257\pi$
$653$	38.2027	1.49499	0.747493	+	0.664270i	$0.231257\pi$
$654$	6.71644	0.262634
$655$	0.582428	0.0227573
$656$	−51.3910	−2.00648
$657$	−26.1095	−1.01863
$658$	40.7918	1.59023
$659$	10.1845	0.396732	0.198366	−	0.980128i	$-0.436437\pi$
$659$	10.1845	0.396732	0.198366	+	0.980128i	$0.436437\pi$
$660$	4.21200	0.163952
$661$	4.36037	0.169599	0.0847994	−	0.996398i	$-0.472975\pi$
$661$	4.36037	0.169599	0.0847994	+	0.996398i	$0.472975\pi$
$662$	−49.6817	−1.93093
$663$	2.24676	0.0872569
$664$	70.5873	2.73932
$665$	−6.20256	−0.240525
$666$	35.1890	1.36355
$667$	26.1115	1.01104
$668$	54.7848	2.11969
$669$	1.51066	0.0584055
$670$	−8.84371	−0.341662
$671$	−24.3821	−0.941260
$672$	9.95469	0.384011
$673$	20.8763	0.804724	0.402362	−	0.915481i	$-0.368189\pi$
$673$	20.8763	0.804724	0.402362	+	0.915481i	$0.368189\pi$
$674$	−63.2679	−2.43699
$675$	−11.6101	−0.446871
$676$	4.98547	0.191749
$677$	−27.8937	−1.07204	−0.536022	−	0.844204i	$-0.680073\pi$
$677$	−27.8937	−1.07204	−0.536022	+	0.844204i	$0.680073\pi$
$678$	18.3820	0.705957
$679$	−12.9592	−0.497329
$680$	−25.8402	−0.990926
$681$	11.7132	0.448852
$682$	−41.0646	−1.57244
$683$	16.9758	0.649562	0.324781	−	0.945789i	$-0.394709\pi$
$683$	16.9758	0.649562	0.324781	+	0.945789i	$0.394709\pi$
$684$	−77.7985	−2.97470
$685$	11.9217	0.455506
$686$	50.7739	1.93856
$687$	−2.41348	−0.0920800
$688$	−5.87311	−0.223910
$689$	4.12133	0.157010
$690$	6.39725	0.243539
$691$	42.3138	1.60969	0.804846	−	0.593483i	$-0.202248\pi$
$691$	42.3138	1.60969	0.804846	+	0.593483i	$0.202248\pi$
$692$	−53.6009	−2.03760
$693$	−15.2398	−0.578910
$694$	2.24601	0.0852575
$695$	12.9597	0.491588
$696$	−10.1705	−0.385510
$697$	24.4213	0.925024
$698$	94.1743	3.56455
$699$	−1.02802	−0.0388834
$700$	−40.4644	−1.52941
$701$	34.9480	1.31997	0.659983	−	0.751280i	$-0.270563\pi$
$701$	34.9480	1.31997	0.659983	+	0.751280i	$0.270563\pi$
$702$	−6.67205	−0.251820
$703$	26.2882	0.991480
$704$	38.5550	1.45310
$705$	−2.40540	−0.0905926
$706$	−10.0023	−0.376443
$707$	12.7726	0.480362
$708$	−2.19782	−0.0825990
$709$	22.2825	0.836836	0.418418	−	0.908255i	$-0.362585\pi$
$709$	22.2825	0.836836	0.418418	+	0.908255i	$0.362585\pi$
$710$	21.2369	0.797006
$711$	−37.8956	−1.42120
$712$	55.6862	2.08693
$713$	−44.5125	−1.66701
$714$	−10.4797	−0.392193
$715$	−1.94489	−0.0727346
$716$	66.5214	2.48602
$717$	−8.06219	−0.301088
$718$	59.6178	2.22492
$719$	20.4327	0.762012	0.381006	−	0.924573i	$-0.375578\pi$
$719$	20.4327	0.762012	0.381006	+	0.924573i	$0.375578\pi$
$720$	19.3736	0.722012
$721$	−24.6005	−0.916172
$722$	−31.2187	−1.16184
$723$	−4.86988	−0.181113
$724$	127.457	4.73691
$725$	13.6463	0.506811
$726$	−1.79652	−0.0666753
$727$	−27.7060	−1.02756	−0.513780	−	0.857922i	$-0.671755\pi$
$727$	−27.7060	−1.02756	−0.513780	+	0.857922i	$0.671755\pi$
$728$	−13.9253	−0.516106
$729$	−17.3375	−0.642129
$730$	15.5420	0.575236
$731$	2.79094	0.103227
$732$	17.1905	0.635379
$733$	11.4974	0.424667	0.212334	−	0.977197i	$-0.431894\pi$
$733$	11.4974	0.424667	0.212334	+	0.977197i	$0.431894\pi$
$734$	44.0460	1.62577
$735$	−1.06869	−0.0394193
$736$	114.270	4.21206
$737$	−16.2329	−0.597946
$738$	−35.0837	−1.29145
$739$	15.6940	0.577312	0.288656	−	0.957433i	$-0.406792\pi$
$739$	15.6940	0.577312	0.288656	+	0.957433i	$0.406792\pi$
$740$	−14.9495	−0.549554
$741$	−2.41128	−0.0885805
$742$	−19.2234	−0.705713
$743$	−50.6508	−1.85820	−0.929098	−	0.369834i	$-0.879415\pi$
$743$	−50.6508	−1.85820	−0.929098	+	0.369834i	$0.879415\pi$
$744$	17.3377	0.635630
$745$	−8.59003	−0.314714
$746$	67.9298	2.48709
$747$	25.1492	0.920160
$748$	−79.2046	−2.89601
$749$	21.9016	0.800265
$750$	6.97806	0.254803
$751$	36.4925	1.33163	0.665815	−	0.746117i	$-0.268084\pi$
$751$	36.4925	1.33163	0.665815	+	0.746117i	$0.268084\pi$
$752$	−95.1846	−3.47102
$753$	11.7793	0.429263
$754$	7.84224	0.285597
$755$	−2.36163	−0.0859483
$756$	22.2107	0.807795
$757$	7.04040	0.255888	0.127944	−	0.991781i	$-0.459162\pi$
$757$	7.04040	0.255888	0.127944	+	0.991781i	$0.459162\pi$
$758$	92.1168	3.34583
$759$	11.7423	0.426219
$760$	27.7323	1.00596
$761$	−27.5238	−0.997737	−0.498868	−	0.866678i	$-0.666251\pi$
$761$	−27.5238	−0.997737	−0.498868	+	0.866678i	$0.666251\pi$
$762$	4.97367	0.180177
$763$	10.3240	0.373754
$764$	−9.16583	−0.331608
$765$	−9.20646	−0.332860
$766$	−79.5132	−2.87293
$767$	1.01484	0.0366437
$768$	2.63373	0.0950367
$769$	30.4745	1.09894	0.549469	−	0.835514i	$-0.314830\pi$
$769$	30.4745	1.09894	0.549469	+	0.835514i	$0.314830\pi$
$770$	9.07166	0.326920
$771$	−3.49545	−0.125886
$772$	96.6668	3.47912
$773$	−50.2666	−1.80797	−0.903983	−	0.427569i	$-0.859370\pi$
$773$	−50.2666	−1.80797	−0.903983	+	0.427569i	$0.859370\pi$
$774$	−4.00947	−0.144117
$775$	−23.2630	−0.835632
$776$	57.9420	2.08000
$777$	−3.63066	−0.130249
$778$	64.3209	2.30601
$779$	−26.2096	−0.939055
$780$	1.37124	0.0490981
$781$	38.9809	1.39485
$782$	−120.297	−4.30181
$783$	−7.49038	−0.267684
$784$	−42.2895	−1.51034
$785$	−5.17454	−0.184687
$786$	−1.05611	−0.0376703
$787$	35.7570	1.27460	0.637300	−	0.770616i	$-0.280051\pi$
$787$	35.7570	1.27460	0.637300	+	0.770616i	$0.280051\pi$
$788$	126.204	4.49584
$789$	−11.3147	−0.402815
$790$	22.5578	0.802572
$791$	28.2554	1.00465
$792$	68.1386	2.42120
$793$	−7.93769	−0.281876
$794$	19.7831	0.702076
$795$	1.13356	0.0402032
$796$	56.3450	1.99709
$797$	10.6945	0.378820	0.189410	−	0.981898i	$-0.439343\pi$
$797$	10.6945	0.378820	0.189410	+	0.981898i	$0.439343\pi$
$798$	11.2471	0.398142
$799$	45.2323	1.60020
$800$	59.7197	2.11141
$801$	19.8401	0.701017
$802$	89.1766	3.14894
$803$	28.5278	1.00673
$804$	11.4449	0.403632
$805$	9.83335	0.346580
$806$	−13.3687	−0.470894
$807$	−4.75461	−0.167370
$808$	−57.1075	−2.00903
$809$	30.5093	1.07265	0.536325	−	0.844011i	$-0.319812\pi$
$809$	30.5093	1.07265	0.536325	+	0.844011i	$0.319812\pi$
$810$	12.2787	0.431428
$811$	−44.5973	−1.56602	−0.783012	−	0.622006i	$-0.786318\pi$
$811$	−44.5973	−1.56602	−0.783012	+	0.622006i	$0.786318\pi$
$812$	−26.1061	−0.916146
$813$	−3.07961	−0.108007
$814$	−38.4483	−1.34761
$815$	12.5459	0.439464
$816$	24.4536	0.856047
$817$	−2.99531	−0.104792
$818$	11.9561	0.418037
$819$	−4.96137	−0.173364
$820$	14.9047	0.520496
$821$	28.6750	1.00076	0.500382	−	0.865805i	$-0.333193\pi$
$821$	28.6750	1.00076	0.500382	+	0.865805i	$0.333193\pi$
$822$	−21.6176	−0.754001
$823$	29.5734	1.03086	0.515431	−	0.856931i	$-0.327632\pi$
$823$	29.5734	1.03086	0.515431	+	0.856931i	$0.327632\pi$
$824$	109.992	3.83174
$825$	6.13674	0.213654
$826$	−4.73358	−0.164702
$827$	24.9384	0.867193	0.433597	−	0.901107i	$-0.357244\pi$
$827$	24.9384	0.867193	0.433597	+	0.901107i	$0.357244\pi$
$828$	123.339	4.28634
$829$	43.2718	1.50289	0.751445	−	0.659795i	$-0.229357\pi$
$829$	43.2718	1.50289	0.751445	+	0.659795i	$0.229357\pi$
$830$	−14.9704	−0.519629
$831$	9.75408	0.338365
$832$	12.5517	0.435153
$833$	20.0962	0.696293
$834$	−23.4997	−0.813727
$835$	−6.95780	−0.240785
$836$	85.0043	2.93993
$837$	12.7689	0.441359
$838$	−1.76134	−0.0608446
$839$	−28.8447	−0.995831	−0.497916	−	0.867226i	$-0.665901\pi$
$839$	−28.8447	−0.995831	−0.497916	+	0.867226i	$0.665901\pi$
$840$	−3.83010	−0.132151
$841$	−20.1959	−0.696411
$842$	−10.3558	−0.356883
$843$	−3.44930	−0.118800
$844$	12.2929	0.423139
$845$	−0.633166	−0.0217816
$846$	−64.9808	−2.23409
$847$	−2.76148	−0.0948855
$848$	44.8563	1.54037
$849$	−8.75313	−0.300406
$850$	−62.8693	−2.15640
$851$	−41.6766	−1.42865
$852$	−27.4833	−0.941563
$853$	−30.3469	−1.03906	−0.519530	−	0.854452i	$-0.673893\pi$
$853$	−30.3469	−1.03906	−0.519530	+	0.854452i	$0.673893\pi$
$854$	37.0243	1.26694
$855$	9.88060	0.337909
$856$	−97.9242	−3.34698
$857$	40.9766	1.39973	0.699867	−	0.714273i	$-0.253242\pi$
$857$	40.9766	1.39973	0.699867	+	0.714273i	$0.253242\pi$
$858$	3.52665	0.120398
$859$	46.6656	1.59221	0.796105	−	0.605158i	$-0.206890\pi$
$859$	46.6656	1.59221	0.796105	+	0.605158i	$0.206890\pi$
$860$	1.70336	0.0580840
$861$	3.61980	0.123362
$862$	−109.491	−3.72928
$863$	34.1753	1.16334	0.581670	−	0.813425i	$-0.302399\pi$
$863$	34.1753	1.16334	0.581670	+	0.813425i	$0.302399\pi$
$864$	−32.7798	−1.11519
$865$	6.80744	0.231460
$866$	−78.2224	−2.65811
$867$	−4.23572	−0.143853
$868$	44.5034	1.51054
$869$	41.4056	1.40459
$870$	2.15698	0.0731285
$871$	−5.28468	−0.179065
$872$	−46.1597	−1.56316
$873$	20.6438	0.698688
$874$	129.106	4.36707
$875$	10.7261	0.362609
$876$	−20.1134	−0.679570
$877$	52.8504	1.78463	0.892316	−	0.451412i	$-0.149080\pi$
$877$	52.8504	1.78463	0.892316	+	0.451412i	$0.149080\pi$
$878$	90.9085	3.06801
$879$	0.769175	0.0259436
$880$	−21.1680	−0.713574
$881$	−27.8299	−0.937612	−0.468806	−	0.883301i	$-0.655316\pi$
$881$	−27.8299	−0.937612	−0.468806	+	0.883301i	$0.655316\pi$
$882$	−28.8703	−0.972112
$883$	−21.2950	−0.716635	−0.358318	−	0.933600i	$-0.616650\pi$
$883$	−21.2950	−0.716635	−0.358318	+	0.933600i	$0.616650\pi$
$884$	−25.7854	−0.867257
$885$	0.279128	0.00938279
$886$	88.9248	2.98749
$887$	−6.79910	−0.228291	−0.114146	−	0.993464i	$-0.536413\pi$
$887$	−6.79910	−0.228291	−0.114146	+	0.993464i	$0.536413\pi$
$888$	16.2331	0.544747
$889$	7.64514	0.256410
$890$	−11.8101	−0.395875
$891$	22.5378	0.755046
$892$	−17.3374	−0.580499
$893$	−48.5444	−1.62448
$894$	15.5763	0.520948
$895$	−8.44838	−0.282398
$896$	−12.7138	−0.424739
$897$	3.82277	0.127638
$898$	10.2670	0.342614
$899$	−15.0084	−0.500559
$900$	64.4593	2.14864
$901$	−21.3160	−0.710139
$902$	38.3332	1.27636
$903$	0.413681	0.0137664
$904$	−126.333	−4.20177
$905$	−16.1874	−0.538086
$906$	4.28232	0.142271
$907$	−50.3221	−1.67092	−0.835459	−	0.549552i	$-0.814798\pi$
$907$	−50.3221	−1.67092	−0.835459	+	0.549552i	$0.814798\pi$
$908$	−134.429	−4.46119
$909$	−20.3465	−0.674852
$910$	2.95332	0.0979015
$911$	55.7771	1.84798	0.923990	−	0.382417i	$-0.124908\pi$
$911$	55.7771	1.84798	0.923990	+	0.382417i	$0.124908\pi$
$912$	−26.2442	−0.869032
$913$	−27.4785	−0.909406
$914$	82.5566	2.73073
$915$	−2.18324	−0.0721755
$916$	27.6988	0.915194
$917$	−1.62337	−0.0536086
$918$	34.5086	1.13895
$919$	−52.1512	−1.72031	−0.860155	−	0.510032i	$-0.829633\pi$
$919$	−52.1512	−1.72031	−0.860155	+	0.510032i	$0.829633\pi$
$920$	−43.9660	−1.44951
$921$	−1.84082	−0.0606572
$922$	−85.9233	−2.82973
$923$	12.6904	0.417710
$924$	−11.7399	−0.386215
$925$	−21.7809	−0.716152
$926$	53.1134	1.74541
$927$	39.1883	1.28711
$928$	38.5289	1.26477
$929$	18.1194	0.594480	0.297240	−	0.954803i	$-0.403934\pi$
$929$	18.1194	0.594480	0.297240	+	0.954803i	$0.403934\pi$
$930$	−3.67703	−0.120574
$931$	−21.5677	−0.706854
$932$	11.7983	0.386466
$933$	−4.82226	−0.157874
$934$	87.3077	2.85680
$935$	10.0592	0.328970
$936$	22.1828	0.725068
$937$	−22.4254	−0.732606	−0.366303	−	0.930496i	$-0.619377\pi$
$937$	−22.4254	−0.732606	−0.366303	+	0.930496i	$0.619377\pi$
$938$	24.6497	0.804841
$939$	1.52007	0.0496056
$940$	27.6060	0.900410
$941$	1.09152	0.0355826	0.0177913	−	0.999842i	$-0.494337\pi$
$941$	1.09152	0.0355826	0.0177913	+	0.999842i	$0.494337\pi$
$942$	9.38297	0.305714
$943$	41.5518	1.35311
$944$	11.0454	0.359499
$945$	−2.82081	−0.0917610
$946$	4.38083	0.142433
$947$	−35.2062	−1.14405	−0.572024	−	0.820237i	$-0.693842\pi$
$947$	−35.2062	−1.14405	−0.572024	+	0.820237i	$0.693842\pi$
$948$	−29.1928	−0.948139
$949$	9.28736	0.301481
$950$	67.4729	2.18911
$951$	−5.45577	−0.176916
$952$	72.0232	2.33429
$953$	0.253995	0.00822770	0.00411385	−	0.999992i	$-0.498691\pi$
$953$	0.253995	0.00822770	0.00411385	+	0.999992i	$0.498691\pi$
$954$	30.6226	0.991444
$955$	1.16408	0.0376688
$956$	92.5274	2.99255
$957$	3.95920	0.127983
$958$	68.7544	2.22135
$959$	−33.2289	−1.07302
$960$	3.45231	0.111423
$961$	−5.41496	−0.174676
$962$	−12.5170	−0.403565
$963$	−34.8889	−1.12428
$964$	55.8901	1.80010
$965$	−12.2769	−0.395208
$966$	−17.8308	−0.573695
$967$	4.95287	0.159273	0.0796367	−	0.996824i	$-0.474624\pi$
$967$	4.95287	0.159273	0.0796367	+	0.996824i	$0.474624\pi$
$968$	12.3469	0.396843
$969$	12.4714	0.400639
$970$	−12.2885	−0.394560
$971$	14.7777	0.474238	0.237119	−	0.971481i	$-0.423797\pi$
$971$	14.7777	0.474238	0.237119	+	0.971481i	$0.423797\pi$
$972$	−53.6464	−1.72071
$973$	−36.1219	−1.15801
$974$	29.0392	0.930476
$975$	1.99784	0.0639822
$976$	−86.3933	−2.76538
$977$	10.9733	0.351067	0.175534	−	0.984473i	$-0.443835\pi$
$977$	10.9733	0.351067	0.175534	+	0.984473i	$0.443835\pi$
$978$	−22.7494	−0.727447
$979$	−21.6778	−0.692824
$980$	12.2651	0.391793
$981$	−16.4460	−0.525080
$982$	75.5670	2.41144
$983$	−8.14686	−0.259844	−0.129922	−	0.991524i	$-0.541473\pi$
$983$	−8.14686	−0.259844	−0.129922	+	0.991524i	$0.541473\pi$
$984$	−16.1845	−0.515943
$985$	−16.0283	−0.510703
$986$	−40.5610	−1.29172
$987$	6.70446	0.213405
$988$	27.6735	0.880412
$989$	4.74867	0.150999
$990$	−14.4510	−0.459284
$991$	−13.8365	−0.439530	−0.219765	−	0.975553i	$-0.570529\pi$
$991$	−13.8365	−0.439530	−0.219765	+	0.975553i	$0.570529\pi$
$992$	−65.6807	−2.08536
$993$	−8.16558	−0.259127
$994$	−59.1926	−1.87748
$995$	−7.15595	−0.226859
$996$	19.3736	0.613877
$997$	16.6816	0.528310	0.264155	−	0.964480i	$-0.414907\pi$
$997$	16.6816	0.528310	0.264155	+	0.964480i	$0.414907\pi$
$998$	−69.9828	−2.21527
$999$	11.9554	0.378252

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8021.2.a.d.1.11	✓	174

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8021.2.a.d.1.11	✓	174	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:	\( N \)	\(=\)	\( 8021 = 13 \cdot 617 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8021.a (trivial)

\(f(q)\)	\(=\)	\(q-2.64300 q^{2} -0.434399 q^{3} +4.98547 q^{4} -0.633166 q^{5} +1.14812 q^{6} +1.76480 q^{7} -7.89059 q^{8} -2.81130 q^{9} +O(q^{10})\)	\(q-2.64300 q^{2} -0.434399 q^{3} +4.98547 q^{4} -0.633166 q^{5} +1.14812 q^{6} +1.76480 q^{7} -7.89059 q^{8} -2.81130 q^{9} +1.67346 q^{10} +3.07168 q^{11} -2.16568 q^{12} +1.00000 q^{13} -4.66436 q^{14} +0.275047 q^{15} +10.8839 q^{16} -5.17211 q^{17} +7.43027 q^{18} +5.55084 q^{19} -3.15663 q^{20} -0.766625 q^{21} -8.11847 q^{22} -8.80013 q^{23} +3.42766 q^{24} -4.59910 q^{25} -2.64300 q^{26} +2.52442 q^{27} +8.79833 q^{28} -2.96717 q^{29} -0.726949 q^{30} +5.05817 q^{31} -12.9851 q^{32} -1.33434 q^{33} +13.6699 q^{34} -1.11741 q^{35} -14.0156 q^{36} +4.73590 q^{37} -14.6709 q^{38} -0.434399 q^{39} +4.99606 q^{40} -4.72173 q^{41} +2.02619 q^{42} -0.539613 q^{43} +15.3138 q^{44} +1.78002 q^{45} +23.2588 q^{46} -8.74542 q^{47} -4.72797 q^{48} -3.88549 q^{49} +12.1554 q^{50} +2.24676 q^{51} +4.98547 q^{52} +4.12133 q^{53} -6.67205 q^{54} -1.94489 q^{55} -13.9253 q^{56} -2.41128 q^{57} +7.84224 q^{58} +1.01484 q^{59} +1.37124 q^{60} -7.93769 q^{61} -13.3687 q^{62} -4.96137 q^{63} +12.5517 q^{64} -0.633166 q^{65} +3.52665 q^{66} -5.28468 q^{67} -25.7854 q^{68} +3.82277 q^{69} +2.95332 q^{70} +12.6904 q^{71} +22.1828 q^{72} +9.28736 q^{73} -12.5170 q^{74} +1.99784 q^{75} +27.6735 q^{76} +5.42090 q^{77} +1.14812 q^{78} +13.4798 q^{79} -6.89134 q^{80} +7.33729 q^{81} +12.4795 q^{82} -8.94575 q^{83} -3.82198 q^{84} +3.27481 q^{85} +1.42620 q^{86} +1.28893 q^{87} -24.2374 q^{88} -7.05729 q^{89} -4.70460 q^{90} +1.76480 q^{91} -43.8727 q^{92} -2.19726 q^{93} +23.1142 q^{94} -3.51460 q^{95} +5.64070 q^{96} -7.34317 q^{97} +10.2694 q^{98} -8.63542 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 174 q + 6 q^{2} + 37 q^{3} + 214 q^{4} + 10 q^{5} + 12 q^{6} + 28 q^{7} + 15 q^{8} + 211 q^{9}+O(q^{10}) \) 174 * q + 6 * q^2 + 37 * q^3 + 214 * q^4 + 10 * q^5 + 12 * q^6 + 28 * q^7 + 15 * q^8 + 211 * q^9	\( 174 q + 6 q^{2} + 37 q^{3} + 214 q^{4} + 10 q^{5} + 12 q^{6} + 28 q^{7} + 15 q^{8} + 211 q^{9} + 47 q^{10} + 47 q^{11} + 81 q^{12} + 174 q^{13} + 22 q^{14} + 26 q^{15} + 286 q^{16} + 27 q^{17} + 22 q^{18} + 91 q^{19} + 18 q^{20} + 8 q^{21} + 58 q^{22} + 62 q^{23} + 24 q^{24} + 244 q^{25} + 6 q^{26} + 139 q^{27} + 43 q^{28} + 42 q^{29} + 31 q^{30} + 82 q^{31} + 11 q^{32} + 12 q^{33} + 50 q^{34} + 74 q^{35} + 310 q^{36} + 47 q^{37} + 10 q^{38} + 37 q^{39} + 118 q^{40} + 16 q^{41} + 26 q^{42} + 136 q^{43} + 74 q^{44} + 18 q^{45} + 53 q^{46} + 15 q^{47} + 132 q^{48} + 254 q^{49} - 5 q^{50} + 121 q^{51} + 214 q^{52} + 39 q^{53} + 30 q^{54} + 188 q^{55} + 55 q^{56} + 11 q^{57} + 32 q^{58} + 58 q^{59} + 16 q^{60} + 128 q^{61} + 27 q^{62} + 42 q^{63} + 423 q^{64} + 10 q^{65} + 4 q^{66} + 132 q^{67} + 52 q^{68} + 63 q^{69} - 8 q^{70} + 78 q^{71} + 2 q^{72} + 21 q^{73} - 16 q^{74} + 188 q^{75} + 160 q^{76} + 20 q^{77} + 12 q^{78} + 232 q^{79} + 2 q^{80} + 302 q^{81} + 115 q^{82} + 18 q^{83} - 26 q^{84} + 47 q^{85} + 27 q^{86} + 127 q^{87} + 163 q^{88} + 14 q^{90} + 28 q^{91} + 68 q^{92} + 15 q^{93} + 91 q^{94} + 75 q^{95} - 26 q^{96} + 34 q^{97} - 60 q^{98} + 181 q^{99}+O(q^{100}) \) 174 * q + 6 * q^2 + 37 * q^3 + 214 * q^4 + 10 * q^5 + 12 * q^6 + 28 * q^7 + 15 * q^8 + 211 * q^9 + 47 * q^10 + 47 * q^11 + 81 * q^12 + 174 * q^13 + 22 * q^14 + 26 * q^15 + 286 * q^16 + 27 * q^17 + 22 * q^18 + 91 * q^19 + 18 * q^20 + 8 * q^21 + 58 * q^22 + 62 * q^23 + 24 * q^24 + 244 * q^25 + 6 * q^26 + 139 * q^27 + 43 * q^28 + 42 * q^29 + 31 * q^30 + 82 * q^31 + 11 * q^32 + 12 * q^33 + 50 * q^34 + 74 * q^35 + 310 * q^36 + 47 * q^37 + 10 * q^38 + 37 * q^39 + 118 * q^40 + 16 * q^41 + 26 * q^42 + 136 * q^43 + 74 * q^44 + 18 * q^45 + 53 * q^46 + 15 * q^47 + 132 * q^48 + 254 * q^49 - 5 * q^50 + 121 * q^51 + 214 * q^52 + 39 * q^53 + 30 * q^54 + 188 * q^55 + 55 * q^56 + 11 * q^57 + 32 * q^58 + 58 * q^59 + 16 * q^60 + 128 * q^61 + 27 * q^62 + 42 * q^63 + 423 * q^64 + 10 * q^65 + 4 * q^66 + 132 * q^67 + 52 * q^68 + 63 * q^69 - 8 * q^70 + 78 * q^71 + 2 * q^72 + 21 * q^73 - 16 * q^74 + 188 * q^75 + 160 * q^76 + 20 * q^77 + 12 * q^78 + 232 * q^79 + 2 * q^80 + 302 * q^81 + 115 * q^82 + 18 * q^83 - 26 * q^84 + 47 * q^85 + 27 * q^86 + 127 * q^87 + 163 * q^88 + 14 * q^90 + 28 * q^91 + 68 * q^92 + 15 * q^93 + 91 * q^94 + 75 * q^95 - 26 * q^96 + 34 * q^97 - 60 * q^98 + 181 * q^99

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