LMFDB - Embedded newform 8007.2.a.j.1.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8007,2,Mod(1,8007)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8007, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("8007.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8007 = 3 \cdot 17 \cdot 157 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8007.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:	$63.9362168984$
Analytic rank:	$0$
Dimension:	$64$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.6
Character	$\chi$	$=$	8007.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.38697 q^{2} -1.00000 q^{3} +3.69761 q^{4} +2.25593 q^{5} +2.38697 q^{6} -4.86795 q^{7} -4.05215 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-2.38697 q^{2} -1.00000 q^{3} +3.69761 q^{4} +2.25593 q^{5} +2.38697 q^{6} -4.86795 q^{7} -4.05215 q^{8} +1.00000 q^{9} -5.38482 q^{10} +1.03520 q^{11} -3.69761 q^{12} -0.688087 q^{13} +11.6196 q^{14} -2.25593 q^{15} +2.27712 q^{16} +1.00000 q^{17} -2.38697 q^{18} -8.17166 q^{19} +8.34155 q^{20} +4.86795 q^{21} -2.47100 q^{22} +7.38826 q^{23} +4.05215 q^{24} +0.0892066 q^{25} +1.64244 q^{26} -1.00000 q^{27} -17.9998 q^{28} +2.85376 q^{29} +5.38482 q^{30} -10.3049 q^{31} +2.66889 q^{32} -1.03520 q^{33} -2.38697 q^{34} -10.9817 q^{35} +3.69761 q^{36} +1.32195 q^{37} +19.5055 q^{38} +0.688087 q^{39} -9.14135 q^{40} +8.69790 q^{41} -11.6196 q^{42} +4.03880 q^{43} +3.82779 q^{44} +2.25593 q^{45} -17.6355 q^{46} -12.0312 q^{47} -2.27712 q^{48} +16.6969 q^{49} -0.212933 q^{50} -1.00000 q^{51} -2.54428 q^{52} -8.62613 q^{53} +2.38697 q^{54} +2.33535 q^{55} +19.7256 q^{56} +8.17166 q^{57} -6.81184 q^{58} -2.74590 q^{59} -8.34155 q^{60} -10.2874 q^{61} +24.5974 q^{62} -4.86795 q^{63} -10.9248 q^{64} -1.55227 q^{65} +2.47100 q^{66} +15.1775 q^{67} +3.69761 q^{68} -7.38826 q^{69} +26.2130 q^{70} -3.50593 q^{71} -4.05215 q^{72} +5.22796 q^{73} -3.15545 q^{74} -0.0892066 q^{75} -30.2156 q^{76} -5.03932 q^{77} -1.64244 q^{78} +4.50555 q^{79} +5.13702 q^{80} +1.00000 q^{81} -20.7616 q^{82} -7.62159 q^{83} +17.9998 q^{84} +2.25593 q^{85} -9.64049 q^{86} -2.85376 q^{87} -4.19480 q^{88} -3.63646 q^{89} -5.38482 q^{90} +3.34957 q^{91} +27.3189 q^{92} +10.3049 q^{93} +28.7180 q^{94} -18.4347 q^{95} -2.66889 q^{96} -4.49489 q^{97} -39.8550 q^{98} +1.03520 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q + 5 q^{2} - 64 q^{3} + 77 q^{4} - 3 q^{5} - 5 q^{6} + 5 q^{7} + 18 q^{8} + 64 q^{9}+O(q^{10}) $ 64 * q + 5 * q^2 - 64 * q^3 + 77 * q^4 - 3 * q^5 - 5 * q^6 + 5 * q^7 + 18 * q^8 + 64 * q^9	\( 64 q + 5 q^{2} - 64 q^{3} + 77 q^{4} - 3 q^{5} - 5 q^{6} + 5 q^{7} + 18 q^{8} + 64 q^{9} + 12 q^{10} - 7 q^{11} - 77 q^{12} + 24 q^{13} - 14 q^{14} + 3 q^{15} + 103 q^{16} + 64 q^{17} + 5 q^{18} + 26 q^{19} - 24 q^{20} - 5 q^{21} + 25 q^{22} + 20 q^{23} - 18 q^{24} + 141 q^{25} + 9 q^{26} - 64 q^{27} + 14 q^{28} + 5 q^{29} - 12 q^{30} + 11 q^{31} + 31 q^{32} + 7 q^{33} + 5 q^{34} - 3 q^{35} + 77 q^{36} + 50 q^{37} + 8 q^{38} - 24 q^{39} + 28 q^{40} - 9 q^{41} + 14 q^{42} + 59 q^{43} - 6 q^{44} - 3 q^{45} + 11 q^{47} - 103 q^{48} + 163 q^{49} + 20 q^{50} - 64 q^{51} + 65 q^{52} + 39 q^{53} - 5 q^{54} + 35 q^{55} - 34 q^{56} - 26 q^{57} - 27 q^{58} - 65 q^{59} + 24 q^{60} + 15 q^{61} + 18 q^{62} + 5 q^{63} + 152 q^{64} + 49 q^{65} - 25 q^{66} + 56 q^{67} + 77 q^{68} - 20 q^{69} + 28 q^{70} - 18 q^{71} + 18 q^{72} + 37 q^{73} - 76 q^{74} - 141 q^{75} + 30 q^{76} + 80 q^{77} - 9 q^{78} + 20 q^{79} - 144 q^{80} + 64 q^{81} + 27 q^{82} + 3 q^{83} - 14 q^{84} - 3 q^{85} + 12 q^{86} - 5 q^{87} + 108 q^{88} + 42 q^{89} + 12 q^{90} + 25 q^{91} + 18 q^{92} - 11 q^{93} + 60 q^{94} + 42 q^{95} - 31 q^{96} + 72 q^{97} + 18 q^{98} - 7 q^{99}+O(q^{100}) \) 64 * q + 5 * q^2 - 64 * q^3 + 77 * q^4 - 3 * q^5 - 5 * q^6 + 5 * q^7 + 18 * q^8 + 64 * q^9 + 12 * q^10 - 7 * q^11 - 77 * q^12 + 24 * q^13 - 14 * q^14 + 3 * q^15 + 103 * q^16 + 64 * q^17 + 5 * q^18 + 26 * q^19 - 24 * q^20 - 5 * q^21 + 25 * q^22 + 20 * q^23 - 18 * q^24 + 141 * q^25 + 9 * q^26 - 64 * q^27 + 14 * q^28 + 5 * q^29 - 12 * q^30 + 11 * q^31 + 31 * q^32 + 7 * q^33 + 5 * q^34 - 3 * q^35 + 77 * q^36 + 50 * q^37 + 8 * q^38 - 24 * q^39 + 28 * q^40 - 9 * q^41 + 14 * q^42 + 59 * q^43 - 6 * q^44 - 3 * q^45 + 11 * q^47 - 103 * q^48 + 163 * q^49 + 20 * q^50 - 64 * q^51 + 65 * q^52 + 39 * q^53 - 5 * q^54 + 35 * q^55 - 34 * q^56 - 26 * q^57 - 27 * q^58 - 65 * q^59 + 24 * q^60 + 15 * q^61 + 18 * q^62 + 5 * q^63 + 152 * q^64 + 49 * q^65 - 25 * q^66 + 56 * q^67 + 77 * q^68 - 20 * q^69 + 28 * q^70 - 18 * q^71 + 18 * q^72 + 37 * q^73 - 76 * q^74 - 141 * q^75 + 30 * q^76 + 80 * q^77 - 9 * q^78 + 20 * q^79 - 144 * q^80 + 64 * q^81 + 27 * q^82 + 3 * q^83 - 14 * q^84 - 3 * q^85 + 12 * q^86 - 5 * q^87 + 108 * q^88 + 42 * q^89 + 12 * q^90 + 25 * q^91 + 18 * q^92 - 11 * q^93 + 60 * q^94 + 42 * q^95 - 31 * q^96 + 72 * q^97 + 18 * q^98 - 7 * 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 $

$2$	−2.38697	−1.68784	−0.843920	−	0.536468i	$-0.819758\pi$
$2$	−2.38697	−1.68784	−0.843920	+	0.536468i	$0.819758\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	3.69761	1.84881
$5$	2.25593	1.00888	0.504441	−	0.863446i	$-0.331699\pi$
$5$	2.25593	1.00888	0.504441	+	0.863446i	$0.331699\pi$
$6$	2.38697	0.974475
$7$	−4.86795	−1.83991	−0.919956	−	0.392022i	$-0.871776\pi$
$7$	−4.86795	−1.83991	−0.919956	+	0.392022i	$0.871776\pi$
$8$	−4.05215	−1.43265
$9$	1.00000	0.333333
$10$	−5.38482	−1.70283
$11$	1.03520	0.312126	0.156063	−	0.987747i	$-0.450120\pi$
$11$	1.03520	0.312126	0.156063	+	0.987747i	$0.450120\pi$
$12$	−3.69761	−1.06741
$13$	−0.688087	−0.190841	−0.0954205	−	0.995437i	$-0.530420\pi$
$13$	−0.688087	−0.190841	−0.0954205	+	0.995437i	$0.530420\pi$
$14$	11.6196	3.10548
$15$	−2.25593	−0.582478
$16$	2.27712	0.569280
$17$	1.00000	0.242536
$17$	1.00000	0.242536
$18$	−2.38697	−0.562614
$19$	−8.17166	−1.87471	−0.937354	−	0.348379i	$-0.886732\pi$
$19$	−8.17166	−1.87471	−0.937354	+	0.348379i	$0.886732\pi$
$20$	8.34155	1.86523
$21$	4.86795	1.06227
$22$	−2.47100	−0.526819
$23$	7.38826	1.54056	0.770280	−	0.637706i	$-0.220117\pi$
$23$	7.38826	1.54056	0.770280	+	0.637706i	$0.220117\pi$
$24$	4.05215	0.827141
$25$	0.0892066	0.0178413
$26$	1.64244	0.322109
$27$	−1.00000	−0.192450
$28$	−17.9998	−3.40164
$29$	2.85376	0.529930	0.264965	−	0.964258i	$-0.414640\pi$
$29$	2.85376	0.529930	0.264965	+	0.964258i	$0.414640\pi$
$30$	5.38482	0.983130
$31$	−10.3049	−1.85081	−0.925406	−	0.378978i	$-0.876276\pi$
$31$	−10.3049	−1.85081	−0.925406	+	0.378978i	$0.876276\pi$
$32$	2.66889	0.471797
$33$	−1.03520	−0.180206
$34$	−2.38697	−0.409362
$35$	−10.9817	−1.85625
$36$	3.69761	0.616269
$37$	1.32195	0.217327	0.108664	−	0.994079i	$-0.465343\pi$
$37$	1.32195	0.217327	0.108664	+	0.994079i	$0.465343\pi$
$38$	19.5055	3.16421
$39$	0.688087	0.110182
$40$	−9.14135	−1.44537
$41$	8.69790	1.35838	0.679192	−	0.733961i	$-0.262330\pi$
$41$	8.69790	1.35838	0.679192	+	0.733961i	$0.262330\pi$
$42$	−11.6196	−1.79295
$43$	4.03880	0.615912	0.307956	−	0.951401i	$-0.400355\pi$
$43$	4.03880	0.615912	0.307956	+	0.951401i	$0.400355\pi$
$44$	3.82779	0.577061
$45$	2.25593	0.336294
$46$	−17.6355	−2.60022
$47$	−12.0312	−1.75493	−0.877464	−	0.479643i	$-0.840766\pi$
$47$	−12.0312	−1.75493	−0.877464	+	0.479643i	$0.840766\pi$
$48$	−2.27712	−0.328674
$49$	16.6969	2.38527
$50$	−0.212933	−0.0301133
$51$	−1.00000	−0.140028
$52$	−2.54428	−0.352828
$53$	−8.62613	−1.18489	−0.592445	−	0.805611i	$-0.701837\pi$
$53$	−8.62613	−1.18489	−0.592445	+	0.805611i	$0.701837\pi$
$54$	2.38697	0.324825
$55$	2.33535	0.314898
$56$	19.7256	2.63595
$57$	8.17166	1.08236
$58$	−6.81184	−0.894438
$59$	−2.74590	−0.357486	−0.178743	−	0.983896i	$-0.557203\pi$
$59$	−2.74590	−0.357486	−0.178743	+	0.983896i	$0.557203\pi$
$60$	−8.34155	−1.07689
$61$	−10.2874	−1.31717	−0.658586	−	0.752505i	$-0.728845\pi$
$61$	−10.2874	−1.31717	−0.658586	+	0.752505i	$0.728845\pi$
$62$	24.5974	3.12387
$63$	−4.86795	−0.613304
$64$	−10.9248	−1.36560
$65$	−1.55227	−0.192536
$66$	2.47100	0.304159
$67$	15.1775	1.85423	0.927114	−	0.374780i	$-0.122282\pi$
$67$	15.1775	1.85423	0.927114	+	0.374780i	$0.122282\pi$
$68$	3.69761	0.448402
$69$	−7.38826	−0.889443
$70$	26.2130	3.13306
$71$	−3.50593	−0.416078	−0.208039	−	0.978121i	$-0.566708\pi$
$71$	−3.50593	−0.416078	−0.208039	+	0.978121i	$0.566708\pi$
$72$	−4.05215	−0.477550
$73$	5.22796	0.611886	0.305943	−	0.952050i	$-0.401028\pi$
$73$	5.22796	0.611886	0.305943	+	0.952050i	$0.401028\pi$
$74$	−3.15545	−0.366814
$75$	−0.0892066	−0.0103007
$76$	−30.2156	−3.46597
$77$	−5.03932	−0.574284
$78$	−1.64244	−0.185970
$79$	4.50555	0.506914	0.253457	−	0.967347i	$-0.418432\pi$
$79$	4.50555	0.506914	0.253457	+	0.967347i	$0.418432\pi$
$80$	5.13702	0.574336
$81$	1.00000	0.111111
$82$	−20.7616	−2.29274
$83$	−7.62159	−0.836578	−0.418289	−	0.908314i	$-0.637370\pi$
$83$	−7.62159	−0.836578	−0.418289	+	0.908314i	$0.637370\pi$
$84$	17.9998	1.96394
$85$	2.25593	0.244690
$86$	−9.64049	−1.03956
$87$	−2.85376	−0.305955
$88$	−4.19480	−0.447168
$89$	−3.63646	−0.385464	−0.192732	−	0.981251i	$-0.561735\pi$
$89$	−3.63646	−0.385464	−0.192732	+	0.981251i	$0.561735\pi$
$90$	−5.38482	−0.567610
$91$	3.34957	0.351131
$92$	27.3189	2.84820
$93$	10.3049	1.06857
$94$	28.7180	2.96204
$95$	−18.4347	−1.89136
$96$	−2.66889	−0.272392
$97$	−4.49489	−0.456387	−0.228194	−	0.973616i	$-0.573282\pi$
$97$	−4.49489	−0.456387	−0.228194	+	0.973616i	$0.573282\pi$
$98$	−39.8550	−4.02596
$99$	1.03520	0.104042
$100$	0.329852	0.0329852
$101$	−14.1289	−1.40588	−0.702938	−	0.711251i	$-0.748129\pi$
$101$	−14.1289	−1.40588	−0.702938	+	0.711251i	$0.748129\pi$
$102$	2.38697	0.236345
$103$	2.40939	0.237404	0.118702	−	0.992930i	$-0.462127\pi$
$103$	2.40939	0.237404	0.118702	+	0.992930i	$0.462127\pi$
$104$	2.78823	0.273409
$105$	10.9817	1.07171
$106$	20.5903	1.99991
$107$	7.48379	0.723486	0.361743	−	0.932278i	$-0.382182\pi$
$107$	7.48379	0.723486	0.361743	+	0.932278i	$0.382182\pi$
$108$	−3.69761	−0.355803
$109$	−8.01499	−0.767697	−0.383848	−	0.923396i	$-0.625401\pi$
$109$	−8.01499	−0.767697	−0.383848	+	0.923396i	$0.625401\pi$
$110$	−5.57439	−0.531498
$111$	−1.32195	−0.125474
$112$	−11.0849	−1.04742
$113$	6.04782	0.568931	0.284465	−	0.958686i	$-0.408184\pi$
$113$	6.04782	0.568931	0.284465	+	0.958686i	$0.408184\pi$
$114$	−19.5055	−1.82686
$115$	16.6674	1.55424
$116$	10.5521	0.979739
$117$	−0.688087	−0.0636137
$118$	6.55437	0.603379
$119$	−4.86795	−0.446244
$120$	9.14135	0.834487
$121$	−9.92835	−0.902577
$122$	24.5558	2.22318
$123$	−8.69790	−0.784263
$124$	−38.1035	−3.42179
$125$	−11.0784	−0.990881
$126$	11.6196	1.03516
$127$	−15.1142	−1.34117	−0.670585	−	0.741833i	$-0.733957\pi$
$127$	−15.1142	−1.34117	−0.670585	+	0.741833i	$0.733957\pi$
$128$	20.7393	1.83312
$129$	−4.03880	−0.355597
$130$	3.70523	0.324970
$131$	−3.12398	−0.272943	−0.136471	−	0.990644i	$-0.543576\pi$
$131$	−3.12398	−0.272943	−0.136471	+	0.990644i	$0.543576\pi$
$132$	−3.82779	−0.333166
$133$	39.7792	3.44930
$134$	−36.2282	−3.12964
$135$	−2.25593	−0.194159
$136$	−4.05215	−0.347469
$137$	14.0665	1.20179	0.600893	−	0.799329i	$-0.294812\pi$
$137$	14.0665	1.20179	0.600893	+	0.799329i	$0.294812\pi$
$138$	17.6355	1.50124
$139$	1.39970	0.118721	0.0593603	−	0.998237i	$-0.481094\pi$
$139$	1.39970	0.118721	0.0593603	+	0.998237i	$0.481094\pi$
$140$	−40.6062	−3.43185
$141$	12.0312	1.01321
$142$	8.36855	0.702273
$143$	−0.712311	−0.0595664
$144$	2.27712	0.189760
$145$	6.43788	0.534637
$146$	−12.4790	−1.03277
$147$	−16.6969	−1.37714
$148$	4.88806	0.401796
$149$	23.2464	1.90442	0.952208	−	0.305451i	$-0.0988071\pi$
$149$	23.2464	1.90442	0.952208	+	0.305451i	$0.0988071\pi$
$150$	0.212933	0.0173859
$151$	−18.3008	−1.48930	−0.744650	−	0.667456i	$-0.767383\pi$
$151$	−18.3008	−1.48930	−0.744650	+	0.667456i	$0.767383\pi$
$152$	33.1128	2.68580
$153$	1.00000	0.0808452
$154$	12.0287	0.969300
$155$	−23.2471	−1.86725
$156$	2.54428	0.203705
$157$	−1.00000	−0.0798087
$157$	−1.00000	−0.0798087
$158$	−10.7546	−0.855590
$159$	8.62613	0.684096
$160$	6.02081	0.475987
$161$	−35.9657	−2.83449
$162$	−2.38697	−0.187538
$163$	23.0881	1.80840	0.904201	−	0.427107i	$-0.140467\pi$
$163$	23.0881	1.80840	0.904201	+	0.427107i	$0.140467\pi$
$164$	32.1615	2.51139
$165$	−2.33535	−0.181806
$166$	18.1925	1.41201
$167$	−5.92527	−0.458511	−0.229255	−	0.973366i	$-0.573629\pi$
$167$	−5.92527	−0.458511	−0.229255	+	0.973366i	$0.573629\pi$
$168$	−19.7256	−1.52187
$169$	−12.5265	−0.963580
$170$	−5.38482	−0.412997
$171$	−8.17166	−0.624903
$172$	14.9339	1.13870
$173$	9.10713	0.692402	0.346201	−	0.938160i	$-0.387472\pi$
$173$	9.10713	0.692402	0.346201	+	0.938160i	$0.387472\pi$
$174$	6.81184	0.516404
$175$	−0.434253	−0.0328265
$176$	2.35729	0.177687
$177$	2.74590	0.206394
$178$	8.68011	0.650602
$179$	8.84444	0.661064	0.330532	−	0.943795i	$-0.392772\pi$
$179$	8.84444	0.661064	0.330532	+	0.943795i	$0.392772\pi$
$180$	8.34155	0.621742
$181$	4.37866	0.325463	0.162732	−	0.986670i	$-0.447970\pi$
$181$	4.37866	0.325463	0.162732	+	0.986670i	$0.447970\pi$
$182$	−7.99532	−0.592653
$183$	10.2874	0.760470
$184$	−29.9383	−2.20708
$185$	2.98222	0.219257
$186$	−24.5974	−1.80357
$187$	1.03520	0.0757017
$188$	−44.4866	−3.24452
$189$	4.86795	0.354091
$190$	44.0030	3.19231
$191$	23.8655	1.72684	0.863422	−	0.504483i	$-0.168317\pi$
$191$	23.8655	1.72684	0.863422	+	0.504483i	$0.168317\pi$
$192$	10.9248	0.788428
$193$	25.8382	1.85987	0.929936	−	0.367722i	$-0.119862\pi$
$193$	25.8382	1.85987	0.929936	+	0.367722i	$0.119862\pi$
$194$	10.7292	0.770309
$195$	1.55227	0.111161
$196$	61.7388	4.40991
$197$	−11.8190	−0.842072	−0.421036	−	0.907044i	$-0.638333\pi$
$197$	−11.8190	−0.842072	−0.421036	+	0.907044i	$0.638333\pi$
$198$	−2.47100	−0.175606
$199$	−8.56448	−0.607120	−0.303560	−	0.952812i	$-0.598175\pi$
$199$	−8.56448	−0.607120	−0.303560	+	0.952812i	$0.598175\pi$
$200$	−0.361478	−0.0255604
$201$	−15.1775	−1.07054
$202$	33.7252	2.37290
$203$	−13.8920	−0.975025
$204$	−3.69761	−0.258885
$205$	19.6218	1.37045
$206$	−5.75112	−0.400700
$207$	7.38826	0.513520
$208$	−1.56686	−0.108642
$209$	−8.45934	−0.585145
$210$	−26.2130	−1.80887
$211$	−19.5382	−1.34506	−0.672532	−	0.740068i	$-0.734793\pi$
$211$	−19.5382	−1.34506	−0.672532	+	0.740068i	$0.734793\pi$
$212$	−31.8961	−2.19063
$213$	3.50593	0.240223
$214$	−17.8636	−1.22113
$215$	9.11125	0.621382
$216$	4.05215	0.275714
$217$	50.1636	3.40533
$218$	19.1315	1.29575
$219$	−5.22796	−0.353273
$220$	8.63521	0.582186
$221$	−0.688087	−0.0462858
$222$	3.15545	0.211780
$223$	16.2790	1.09012	0.545060	−	0.838397i	$-0.316507\pi$
$223$	16.2790	1.09012	0.545060	+	0.838397i	$0.316507\pi$
$224$	−12.9920	−0.868064
$225$	0.0892066	0.00594711
$226$	−14.4359	−0.960265
$227$	1.57421	0.104484	0.0522420	−	0.998634i	$-0.483363\pi$
$227$	1.57421	0.104484	0.0522420	+	0.998634i	$0.483363\pi$
$228$	30.2156	2.00108
$229$	1.72625	0.114074	0.0570368	−	0.998372i	$-0.481835\pi$
$229$	1.72625	0.114074	0.0570368	+	0.998372i	$0.481835\pi$
$230$	−39.7845	−2.62331
$231$	5.03932	0.331563
$232$	−11.5639	−0.759205
$233$	8.90826	0.583600	0.291800	−	0.956479i	$-0.405746\pi$
$233$	8.90826	0.583600	0.291800	+	0.956479i	$0.405746\pi$
$234$	1.64244	0.107370
$235$	−27.1415	−1.77051
$236$	−10.1533	−0.660922
$237$	−4.50555	−0.292667
$238$	11.6196	0.753189
$239$	12.7409	0.824140	0.412070	−	0.911152i	$-0.364806\pi$
$239$	12.7409	0.824140	0.412070	+	0.911152i	$0.364806\pi$
$240$	−5.13702	−0.331593
$241$	−5.25252	−0.338344	−0.169172	−	0.985587i	$-0.554109\pi$
$241$	−5.25252	−0.338344	−0.169172	+	0.985587i	$0.554109\pi$
$242$	23.6987	1.52341
$243$	−1.00000	−0.0641500
$244$	−38.0390	−2.43520
$245$	37.6670	2.40646
$246$	20.7616	1.32371
$247$	5.62282	0.357771
$248$	41.7569	2.65157
$249$	7.62159	0.482999
$250$	26.4438	1.67245
$251$	−0.517752	−0.0326802	−0.0163401	−	0.999866i	$-0.505201\pi$
$251$	−0.517752	−0.0326802	−0.0163401	+	0.999866i	$0.505201\pi$
$252$	−17.9998	−1.13388
$253$	7.64837	0.480849
$254$	36.0771	2.26368
$255$	−2.25593	−0.141272
$256$	−27.6545	−1.72841
$257$	23.9250	1.49240	0.746200	−	0.665722i	$-0.231876\pi$
$257$	23.9250	1.49240	0.746200	+	0.665722i	$0.231876\pi$
$258$	9.64049	0.600191
$259$	−6.43518	−0.399863
$260$	−5.73971	−0.355962
$261$	2.85376	0.176643
$262$	7.45683	0.460684
$263$	−24.0357	−1.48211	−0.741053	−	0.671447i	$-0.765673\pi$
$263$	−24.0357	−1.48211	−0.741053	+	0.671447i	$0.765673\pi$
$264$	4.19480	0.258172
$265$	−19.4599	−1.19541
$266$	−94.9517	−5.82186
$267$	3.63646	0.222548
$268$	56.1206	3.42811
$269$	1.15181	0.0702268	0.0351134	−	0.999383i	$-0.488821\pi$
$269$	1.15181	0.0702268	0.0351134	+	0.999383i	$0.488821\pi$
$270$	5.38482	0.327710
$271$	6.73126	0.408895	0.204447	−	0.978878i	$-0.434460\pi$
$271$	6.73126	0.408895	0.204447	+	0.978878i	$0.434460\pi$
$272$	2.27712	0.138071
$273$	−3.34957	−0.202725
$274$	−33.5764	−2.02842
$275$	0.0923471	0.00556874
$276$	−27.3189	−1.64441
$277$	−19.6709	−1.18191	−0.590955	−	0.806705i	$-0.701249\pi$
$277$	−19.6709	−1.18191	−0.590955	+	0.806705i	$0.701249\pi$
$278$	−3.34103	−0.200382
$279$	−10.3049	−0.616937
$280$	44.4996	2.65936
$281$	14.5307	0.866831	0.433415	−	0.901194i	$-0.357308\pi$
$281$	14.5307	0.866831	0.433415	+	0.901194i	$0.357308\pi$
$282$	−28.7180	−1.71013
$283$	1.06397	0.0632463	0.0316232	−	0.999500i	$-0.489932\pi$
$283$	1.06397	0.0632463	0.0316232	+	0.999500i	$0.489932\pi$
$284$	−12.9636	−0.769247
$285$	18.4347	1.09198
$286$	1.70026	0.100539
$287$	−42.3409	−2.49931
$288$	2.66889	0.157266
$289$	1.00000	0.0588235
$290$	−15.3670	−0.902382
$291$	4.49489	0.263495
$292$	19.3310	1.13126
$293$	−16.5473	−0.966706	−0.483353	−	0.875426i	$-0.660581\pi$
$293$	−16.5473	−0.966706	−0.483353	+	0.875426i	$0.660581\pi$
$294$	39.8550	2.32439
$295$	−6.19455	−0.360661
$296$	−5.35674	−0.311354
$297$	−1.03520	−0.0600687
$298$	−55.4883	−3.21435
$299$	−5.08377	−0.294002
$300$	−0.329852	−0.0190440
$301$	−19.6607	−1.13322
$302$	43.6834	2.51370
$303$	14.1289	0.811683
$304$	−18.6079	−1.06723
$305$	−23.2077	−1.32887
$306$	−2.38697	−0.136454
$307$	−12.0964	−0.690377	−0.345188	−	0.938533i	$-0.612185\pi$
$307$	−12.0964	−0.690377	−0.345188	+	0.938533i	$0.612185\pi$
$308$	−18.6335	−1.06174
$309$	−2.40939	−0.137065
$310$	55.4900	3.15162
$311$	−20.6007	−1.16816	−0.584079	−	0.811697i	$-0.698544\pi$
$311$	−20.6007	−1.16816	−0.584079	+	0.811697i	$0.698544\pi$
$312$	−2.78823	−0.157853
$313$	19.8787	1.12361	0.561804	−	0.827270i	$-0.310108\pi$
$313$	19.8787	1.12361	0.561804	+	0.827270i	$0.310108\pi$
$314$	2.38697	0.134704
$315$	−10.9817	−0.618751
$316$	16.6598	0.937186
$317$	12.4872	0.701351	0.350676	−	0.936497i	$-0.385952\pi$
$317$	12.4872	0.701351	0.350676	+	0.936497i	$0.385952\pi$
$318$	−20.5903	−1.15465
$319$	2.95423	0.165405
$320$	−24.6455	−1.37773
$321$	−7.48379	−0.417705
$322$	85.8489	4.78417
$323$	−8.17166	−0.454683
$324$	3.69761	0.205423
$325$	−0.0613819	−0.00340486
$326$	−55.1106	−3.05230
$327$	8.01499	0.443230
$328$	−35.2452	−1.94609
$329$	58.5671	3.22891
$330$	5.57439	0.306860
$331$	−32.9406	−1.81058	−0.905291	−	0.424792i	$-0.860347\pi$
$331$	−32.9406	−1.81058	−0.905291	+	0.424792i	$0.860347\pi$
$332$	−28.1817	−1.54667
$333$	1.32195	0.0724424
$334$	14.1434	0.773893
$335$	34.2393	1.87070
$336$	11.0849	0.604731
$337$	30.3454	1.65302	0.826510	−	0.562922i	$-0.190323\pi$
$337$	30.3454	1.65302	0.826510	+	0.562922i	$0.190323\pi$
$338$	29.9004	1.62637
$339$	−6.04782	−0.328472
$340$	8.34155	0.452384
$341$	−10.6677	−0.577686
$342$	19.5055	1.05474
$343$	−47.2041	−2.54878
$344$	−16.3658	−0.882387
$345$	−16.6674	−0.897342
$346$	−21.7384	−1.16866
$347$	−4.53769	−0.243596	−0.121798	−	0.992555i	$-0.538866\pi$
$347$	−4.53769	−0.243596	−0.121798	+	0.992555i	$0.538866\pi$
$348$	−10.5521	−0.565653
$349$	−23.4313	−1.25425	−0.627126	−	0.778918i	$-0.715769\pi$
$349$	−23.4313	−1.25425	−0.627126	+	0.778918i	$0.715769\pi$
$350$	1.03655	0.0554058
$351$	0.688087	0.0367274
$352$	2.76284	0.147260
$353$	−24.5331	−1.30577	−0.652883	−	0.757458i	$-0.726441\pi$
$353$	−24.5331	−1.30577	−0.652883	+	0.757458i	$0.726441\pi$
$354$	−6.55437	−0.348361
$355$	−7.90913	−0.419773
$356$	−13.4462	−0.712648
$357$	4.86795	0.257639
$358$	−21.1114	−1.11577
$359$	−16.6243	−0.877399	−0.438700	−	0.898634i	$-0.644561\pi$
$359$	−16.6243	−0.877399	−0.438700	+	0.898634i	$0.644561\pi$
$360$	−9.14135	−0.481792
$361$	47.7760	2.51453
$362$	−10.4517	−0.549330
$363$	9.92835	0.521103
$364$	12.3854	0.649173
$365$	11.7939	0.617320
$366$	−24.5558	−1.28355
$367$	30.8098	1.60826	0.804129	−	0.594455i	$-0.202632\pi$
$367$	30.8098	1.60826	0.804129	+	0.594455i	$0.202632\pi$
$368$	16.8240	0.877010
$369$	8.69790	0.452795
$370$	−7.11846	−0.370071
$371$	41.9915	2.18009
$372$	38.1035	1.97557
$373$	−27.8694	−1.44302	−0.721510	−	0.692404i	$-0.756552\pi$
$373$	−27.8694	−1.44302	−0.721510	+	0.692404i	$0.756552\pi$
$374$	−2.47100	−0.127772
$375$	11.0784	0.572086
$376$	48.7521	2.51420
$377$	−1.96364	−0.101132
$378$	−11.6196	−0.597649
$379$	0.141939	0.00729092	0.00364546	−	0.999993i	$-0.498840\pi$
$379$	0.141939	0.00729092	0.00364546	+	0.999993i	$0.498840\pi$
$380$	−68.1643	−3.49675
$381$	15.1142	0.774325
$382$	−56.9661	−2.91464
$383$	−18.9612	−0.968872	−0.484436	−	0.874827i	$-0.660975\pi$
$383$	−18.9612	−0.968872	−0.484436	+	0.874827i	$0.660975\pi$
$384$	−20.7393	−1.05835
$385$	−11.3683	−0.579384
$386$	−61.6748	−3.13917
$387$	4.03880	0.205304
$388$	−16.6204	−0.843772
$389$	14.6757	0.744086	0.372043	−	0.928216i	$-0.378657\pi$
$389$	14.6757	0.744086	0.372043	+	0.928216i	$0.378657\pi$
$390$	−3.70523	−0.187622
$391$	7.38826	0.373641
$392$	−67.6584	−3.41727
$393$	3.12398	0.157584
$394$	28.2117	1.42128
$395$	10.1642	0.511416
$396$	3.82779	0.192354
$397$	−6.47396	−0.324919	−0.162459	−	0.986715i	$-0.551943\pi$
$397$	−6.47396	−0.324919	−0.162459	+	0.986715i	$0.551943\pi$
$398$	20.4431	1.02472
$399$	−39.7792	−1.99145
$400$	0.203134	0.0101567
$401$	26.7107	1.33387	0.666934	−	0.745117i	$-0.267606\pi$
$401$	26.7107	1.33387	0.666934	+	0.745117i	$0.267606\pi$
$402$	36.2282	1.80690
$403$	7.09066	0.353211
$404$	−52.2432	−2.59919
$405$	2.25593	0.112098
$406$	33.1597	1.64569
$407$	1.36849	0.0678334
$408$	4.05215	0.200611
$409$	−4.47245	−0.221148	−0.110574	−	0.993868i	$-0.535269\pi$
$409$	−4.47245	−0.221148	−0.110574	+	0.993868i	$0.535269\pi$
$410$	−46.8367	−2.31310
$411$	−14.0665	−0.693852
$412$	8.90898	0.438914
$413$	13.3669	0.657742
$414$	−17.6355	−0.866740
$415$	−17.1938	−0.844008
$416$	−1.83643	−0.0900382
$417$	−1.39970	−0.0685434
$418$	20.1922	0.987631
$419$	−4.70265	−0.229739	−0.114870	−	0.993381i	$-0.536645\pi$
$419$	−4.70265	−0.229739	−0.114870	+	0.993381i	$0.536645\pi$
$420$	40.6062	1.98138
$421$	23.6631	1.15327	0.576633	−	0.817003i	$-0.304366\pi$
$421$	23.6631	1.15327	0.576633	+	0.817003i	$0.304366\pi$
$422$	46.6370	2.27025
$423$	−12.0312	−0.584976
$424$	34.9544	1.69753
$425$	0.0892066	0.00432716
$426$	−8.36855	−0.405458
$427$	50.0788	2.42348
$428$	27.6722	1.33759
$429$	0.712311	0.0343907
$430$	−21.7482	−1.04879
$431$	−16.0270	−0.771992	−0.385996	−	0.922501i	$-0.626142\pi$
$431$	−16.0270	−0.771992	−0.385996	+	0.922501i	$0.626142\pi$
$432$	−2.27712	−0.109558
$433$	8.77716	0.421803	0.210902	−	0.977507i	$-0.432360\pi$
$433$	8.77716	0.421803	0.210902	+	0.977507i	$0.432360\pi$
$434$	−119.739	−5.74765
$435$	−6.43788	−0.308673
$436$	−29.6363	−1.41932
$437$	−60.3744	−2.88810
$438$	12.4790	0.596268
$439$	−32.1966	−1.53666	−0.768330	−	0.640054i	$-0.778912\pi$
$439$	−32.1966	−1.53666	−0.768330	+	0.640054i	$0.778912\pi$
$440$	−9.46317	−0.451139
$441$	16.6969	0.795091
$442$	1.64244	0.0781230
$443$	28.9989	1.37778	0.688890	−	0.724866i	$-0.258098\pi$
$443$	28.9989	1.37778	0.688890	+	0.724866i	$0.258098\pi$
$444$	−4.88806	−0.231977
$445$	−8.20359	−0.388887
$446$	−38.8574	−1.83995
$447$	−23.2464	−1.09951
$448$	53.1813	2.51258
$449$	6.15803	0.290615	0.145308	−	0.989387i	$-0.453583\pi$
$449$	6.15803	0.290615	0.145308	+	0.989387i	$0.453583\pi$
$450$	−0.212933	−0.0100378
$451$	9.00410	0.423987
$452$	22.3625	1.05184
$453$	18.3008	0.859847
$454$	−3.75759	−0.176352
$455$	7.55639	0.354249
$456$	−33.1128	−1.55065
$457$	−4.17338	−0.195222	−0.0976112	−	0.995225i	$-0.531120\pi$
$457$	−4.17338	−0.195222	−0.0976112	+	0.995225i	$0.531120\pi$
$458$	−4.12050	−0.192538
$459$	−1.00000	−0.0466760
$460$	61.6296	2.87349
$461$	13.6076	0.633770	0.316885	−	0.948464i	$-0.397363\pi$
$461$	13.6076	0.633770	0.316885	+	0.948464i	$0.397363\pi$
$462$	−12.0287	−0.559626
$463$	−17.9595	−0.834648	−0.417324	−	0.908758i	$-0.637032\pi$
$463$	−17.9595	−0.834648	−0.417324	+	0.908758i	$0.637032\pi$
$464$	6.49836	0.301679
$465$	23.2471	1.07806
$466$	−21.2637	−0.985023
$467$	−20.2696	−0.937963	−0.468982	−	0.883208i	$-0.655379\pi$
$467$	−20.2696	−0.937963	−0.468982	+	0.883208i	$0.655379\pi$
$468$	−2.54428	−0.117609
$469$	−73.8833	−3.41161
$470$	64.7858	2.98835
$471$	1.00000	0.0460776
$472$	11.1268	0.512152
$473$	4.18099	0.192242
$474$	10.7546	0.493975
$475$	−0.728966	−0.0334473
$476$	−17.9998	−0.825019
$477$	−8.62613	−0.394963
$478$	−30.4121	−1.39102
$479$	29.2474	1.33635	0.668175	−	0.744004i	$-0.267076\pi$
$479$	29.2474	1.33635	0.668175	+	0.744004i	$0.267076\pi$
$480$	−6.02081	−0.274811
$481$	−0.909616	−0.0414749
$482$	12.5376	0.571071
$483$	35.9657	1.63650
$484$	−36.7112	−1.66869
$485$	−10.1401	−0.460440
$486$	2.38697	0.108275
$487$	−27.1984	−1.23248	−0.616239	−	0.787559i	$-0.711345\pi$
$487$	−27.1984	−1.23248	−0.616239	+	0.787559i	$0.711345\pi$
$488$	41.6863	1.88705
$489$	−23.0881	−1.04408
$490$	−89.9100	−4.06172
$491$	18.3532	0.828270	0.414135	−	0.910215i	$-0.364084\pi$
$491$	18.3532	0.828270	0.414135	+	0.910215i	$0.364084\pi$
$492$	−32.1615	−1.44995
$493$	2.85376	0.128527
$494$	−13.4215	−0.603861
$495$	2.33535	0.104966
$496$	−23.4654	−1.05363
$497$	17.0667	0.765546
$498$	−18.1925	−0.815225
$499$	38.9303	1.74276	0.871381	−	0.490608i	$-0.163225\pi$
$499$	38.9303	1.74276	0.871381	+	0.490608i	$0.163225\pi$
$500$	−40.9636	−1.83195
$501$	5.92527	0.264721
$502$	1.23586	0.0551590
$503$	−16.4097	−0.731671	−0.365835	−	0.930680i	$-0.619217\pi$
$503$	−16.4097	−0.731671	−0.365835	+	0.930680i	$0.619217\pi$
$504$	19.7256	0.878650
$505$	−31.8737	−1.41836
$506$	−18.2564	−0.811596
$507$	12.5265	0.556323
$508$	−55.8865	−2.47956
$509$	29.0100	1.28585	0.642923	−	0.765931i	$-0.277722\pi$
$509$	29.0100	1.28585	0.642923	+	0.765931i	$0.277722\pi$
$510$	5.38482	0.238444
$511$	−25.4494	−1.12582
$512$	24.5318	1.08416
$513$	8.17166	0.360788
$514$	−57.1082	−2.51893
$515$	5.43540	0.239512
$516$	−14.9339	−0.657430
$517$	−12.4547	−0.547758
$518$	15.3606	0.674905
$519$	−9.10713	−0.399758
$520$	6.29005	0.275837
$521$	−26.2257	−1.14897	−0.574485	−	0.818515i	$-0.694798\pi$
$521$	−26.2257	−1.14897	−0.574485	+	0.818515i	$0.694798\pi$
$522$	−6.81184	−0.298146
$523$	−15.9597	−0.697868	−0.348934	−	0.937147i	$-0.613456\pi$
$523$	−15.9597	−0.697868	−0.348934	+	0.937147i	$0.613456\pi$
$524$	−11.5513	−0.504619
$525$	0.434253	0.0189524
$526$	57.3725	2.50156
$527$	−10.3049	−0.448888
$528$	−2.35729	−0.102588
$529$	31.5865	1.37332
$530$	46.4502	2.01767
$531$	−2.74590	−0.119162
$532$	147.088	6.37708
$533$	−5.98491	−0.259235
$534$	−8.68011	−0.375625
$535$	16.8829	0.729911
$536$	−61.5015	−2.65646
$537$	−8.84444	−0.381666
$538$	−2.74932	−0.118532
$539$	17.2847	0.744506
$540$	−8.34155	−0.358963
$541$	−18.9157	−0.813251	−0.406626	−	0.913595i	$-0.633295\pi$
$541$	−18.9157	−0.813251	−0.406626	+	0.913595i	$0.633295\pi$
$542$	−16.0673	−0.690150
$543$	−4.37866	−0.187906
$544$	2.66889	0.114428
$545$	−18.0812	−0.774515
$546$	7.99532	0.342168
$547$	−14.0848	−0.602225	−0.301112	−	0.953589i	$-0.597358\pi$
$547$	−14.0848	−0.602225	−0.301112	+	0.953589i	$0.597358\pi$
$548$	52.0127	2.22187
$549$	−10.2874	−0.439058
$550$	−0.220430	−0.00939915
$551$	−23.3200	−0.993465
$552$	29.9383	1.27426
$553$	−21.9328	−0.932677
$554$	46.9538	1.99488
$555$	−2.98222	−0.126588
$556$	5.17553	0.219492
$557$	25.0666	1.06210	0.531052	−	0.847339i	$-0.321797\pi$
$557$	25.0666	1.06210	0.531052	+	0.847339i	$0.321797\pi$
$558$	24.5974	1.04129
$559$	−2.77905	−0.117541
$560$	−25.0067	−1.05673
$561$	−1.03520	−0.0437064
$562$	−34.6844	−1.46307
$563$	20.9268	0.881961	0.440980	−	0.897517i	$-0.354631\pi$
$563$	20.9268	0.881961	0.440980	+	0.897517i	$0.354631\pi$
$564$	44.4866	1.87323
$565$	13.6434	0.573984
$566$	−2.53966	−0.106750
$567$	−4.86795	−0.204435
$568$	14.2066	0.596094
$569$	−20.2596	−0.849328	−0.424664	−	0.905351i	$-0.639608\pi$
$569$	−20.2596	−0.849328	−0.424664	+	0.905351i	$0.639608\pi$
$570$	−44.0030	−1.84308
$571$	−11.9229	−0.498958	−0.249479	−	0.968380i	$-0.580259\pi$
$571$	−11.9229	−0.498958	−0.249479	+	0.968380i	$0.580259\pi$
$572$	−2.63385	−0.110127
$573$	−23.8655	−0.996994
$574$	101.066	4.21843
$575$	0.659082	0.0274856
$576$	−10.9248	−0.455199
$577$	24.8018	1.03251	0.516256	−	0.856434i	$-0.327325\pi$
$577$	24.8018	1.03251	0.516256	+	0.856434i	$0.327325\pi$
$578$	−2.38697	−0.0992848
$579$	−25.8382	−1.07380
$580$	23.8048	0.988440
$581$	37.1015	1.53923
$582$	−10.7292	−0.444738
$583$	−8.92981	−0.369835
$584$	−21.1845	−0.876619
$585$	−1.55227	−0.0641786
$586$	39.4980	1.63165
$587$	−42.9454	−1.77255	−0.886273	−	0.463163i	$-0.846714\pi$
$587$	−42.9454	−1.77255	−0.886273	+	0.463163i	$0.846714\pi$
$588$	−61.7388	−2.54606
$589$	84.2080	3.46973
$590$	14.7862	0.608738
$591$	11.8190	0.486171
$592$	3.01024	0.123720
$593$	4.33274	0.177924	0.0889621	−	0.996035i	$-0.471645\pi$
$593$	4.33274	0.177924	0.0889621	+	0.996035i	$0.471645\pi$
$594$	2.47100	0.101386
$595$	−10.9817	−0.450207
$596$	85.9560	3.52090
$597$	8.56448	0.350521
$598$	12.1348	0.496229
$599$	−2.55928	−0.104569	−0.0522847	−	0.998632i	$-0.516650\pi$
$599$	−2.55928	−0.104569	−0.0522847	+	0.998632i	$0.516650\pi$
$600$	0.361478	0.0147573
$601$	48.9485	1.99665	0.998325	−	0.0578602i	$-0.0184278\pi$
$601$	48.9485	1.99665	0.998325	+	0.0578602i	$0.0184278\pi$
$602$	46.9294	1.91270
$603$	15.1775	0.618076
$604$	−67.6693	−2.75343
$605$	−22.3976	−0.910593
$606$	−33.7252	−1.36999
$607$	12.1269	0.492217	0.246109	−	0.969242i	$-0.420848\pi$
$607$	12.1269	0.492217	0.246109	+	0.969242i	$0.420848\pi$
$608$	−21.8092	−0.884481
$609$	13.8920	0.562931
$610$	55.3961	2.24292
$611$	8.27850	0.334912
$612$	3.69761	0.149467
$613$	44.0029	1.77726	0.888631	−	0.458623i	$-0.151657\pi$
$613$	44.0029	1.77726	0.888631	+	0.458623i	$0.151657\pi$
$614$	28.8737	1.16525
$615$	−19.6218	−0.791228
$616$	20.4201	0.822749
$617$	20.8755	0.840416	0.420208	−	0.907428i	$-0.361957\pi$
$617$	20.8755	0.840416	0.420208	+	0.907428i	$0.361957\pi$
$618$	5.75112	0.231344
$619$	−0.996380	−0.0400479	−0.0200239	−	0.999800i	$-0.506374\pi$
$619$	−0.996380	−0.0400479	−0.0200239	+	0.999800i	$0.506374\pi$
$620$	−85.9586	−3.45218
$621$	−7.38826	−0.296481
$622$	49.1731	1.97166
$623$	17.7021	0.709219
$624$	1.56686	0.0627245
$625$	−25.4381	−1.01752
$626$	−47.4497	−1.89647
$627$	8.45934	0.337834
$628$	−3.69761	−0.147551
$629$	1.32195	0.0527096
$630$	26.2130	1.04435
$631$	8.38733	0.333894	0.166947	−	0.985966i	$-0.446609\pi$
$631$	8.38733	0.333894	0.166947	+	0.985966i	$0.446609\pi$
$632$	−18.2572	−0.726231
$633$	19.5382	0.776573
$634$	−29.8065	−1.18377
$635$	−34.0966	−1.35308
$636$	31.8961	1.26476
$637$	−11.4889	−0.455208
$638$	−7.05165	−0.279177
$639$	−3.50593	−0.138693
$640$	46.7864	1.84940
$641$	35.4979	1.40208	0.701042	−	0.713120i	$-0.252719\pi$
$641$	35.4979	1.40208	0.701042	+	0.713120i	$0.252719\pi$
$642$	17.8636	0.705019
$643$	21.1198	0.832883	0.416442	−	0.909162i	$-0.363277\pi$
$643$	21.1198	0.832883	0.416442	+	0.909162i	$0.363277\pi$
$644$	−132.987	−5.24043
$645$	−9.11125	−0.358755
$646$	19.5055	0.767433
$647$	21.1705	0.832297	0.416148	−	0.909297i	$-0.363380\pi$
$647$	21.1705	0.832297	0.416148	+	0.909297i	$0.363380\pi$
$648$	−4.05215	−0.159183
$649$	−2.84257	−0.111581
$650$	0.146517	0.00574686
$651$	−50.1636	−1.96607
$652$	85.3710	3.34339
$653$	28.6436	1.12091	0.560456	−	0.828185i	$-0.310626\pi$
$653$	28.6436	1.12091	0.560456	+	0.828185i	$0.310626\pi$
$654$	−19.1315	−0.748101
$655$	−7.04746	−0.275367
$656$	19.8062	0.773301
$657$	5.22796	0.203962
$658$	−139.798	−5.44989
$659$	5.58343	0.217499	0.108750	−	0.994069i	$-0.465315\pi$
$659$	5.58343	0.217499	0.108750	+	0.994069i	$0.465315\pi$
$660$	−8.63521	−0.336125
$661$	−25.2857	−0.983499	−0.491749	−	0.870737i	$-0.663642\pi$
$661$	−25.2857	−0.983499	−0.491749	+	0.870737i	$0.663642\pi$
$662$	78.6283	3.05597
$663$	0.688087	0.0267231
$664$	30.8838	1.19852
$665$	89.7390	3.47993
$666$	−3.15545	−0.122271
$667$	21.0844	0.816389
$668$	−21.9093	−0.847698
$669$	−16.2790	−0.629381
$670$	−81.7282	−3.15744
$671$	−10.6496	−0.411124
$672$	12.9920	0.501177
$673$	−6.22366	−0.239904	−0.119952	−	0.992780i	$-0.538274\pi$
$673$	−6.22366	−0.239904	−0.119952	+	0.992780i	$0.538274\pi$
$674$	−72.4335	−2.79003
$675$	−0.0892066	−0.00343356
$676$	−46.3183	−1.78147
$677$	24.4292	0.938890	0.469445	−	0.882962i	$-0.344454\pi$
$677$	24.4292	0.938890	0.469445	+	0.882962i	$0.344454\pi$
$678$	14.4359	0.554409
$679$	21.8809	0.839712
$680$	−9.14135	−0.350555
$681$	−1.57421	−0.0603238
$682$	25.4634	0.975042
$683$	50.5092	1.93268	0.966340	−	0.257268i	$-0.0828222\pi$
$683$	50.5092	1.93268	0.966340	+	0.257268i	$0.0828222\pi$
$684$	−30.2156	−1.15532
$685$	31.7331	1.21246
$686$	112.675	4.30194
$687$	−1.72625	−0.0658605
$688$	9.19684	0.350626
$689$	5.93553	0.226126
$690$	39.7845	1.51457
$691$	16.7000	0.635298	0.317649	−	0.948208i	$-0.397107\pi$
$691$	16.7000	0.635298	0.317649	+	0.948208i	$0.397107\pi$
$692$	33.6746	1.28012
$693$	−5.03932	−0.191428
$694$	10.8313	0.411151
$695$	3.15761	0.119775
$696$	11.5639	0.438327
$697$	8.69790	0.329456
$698$	55.9299	2.11698
$699$	−8.90826	−0.336941
$700$	−1.60570	−0.0606898
$701$	−11.9214	−0.450265	−0.225133	−	0.974328i	$-0.572282\pi$
$701$	−11.9214	−0.450265	−0.225133	+	0.974328i	$0.572282\pi$
$702$	−1.64244	−0.0619900
$703$	−10.8025	−0.407425
$704$	−11.3094	−0.426239
$705$	27.1415	1.02221
$706$	58.5598	2.20393
$707$	68.7787	2.58669
$708$	10.1533	0.381584
$709$	−3.68560	−0.138416	−0.0692078	−	0.997602i	$-0.522047\pi$
$709$	−3.68560	−0.138416	−0.0692078	+	0.997602i	$0.522047\pi$
$710$	18.8788	0.708510
$711$	4.50555	0.168971
$712$	14.7355	0.552235
$713$	−76.1352	−2.85129
$714$	−11.6196	−0.434854
$715$	−1.60692	−0.0600955
$716$	32.7033	1.22218
$717$	−12.7409	−0.475818
$718$	39.6818	1.48091
$719$	19.9854	0.745330	0.372665	−	0.927966i	$-0.378444\pi$
$719$	19.9854	0.745330	0.372665	+	0.927966i	$0.378444\pi$
$720$	5.13702	0.191445
$721$	−11.7288	−0.436802
$722$	−114.040	−4.24412
$723$	5.25252	0.195343
$724$	16.1906	0.601718
$725$	0.254574	0.00945466
$726$	−23.6987	−0.879539
$727$	48.8817	1.81292	0.906460	−	0.422291i	$-0.138774\pi$
$727$	48.8817	1.81292	0.906460	+	0.422291i	$0.138774\pi$
$728$	−13.5730	−0.503048
$729$	1.00000	0.0370370
$730$	−28.1516	−1.04194
$731$	4.03880	0.149381
$732$	38.0390	1.40596
$733$	−48.1988	−1.78026	−0.890132	−	0.455704i	$-0.849388\pi$
$733$	−48.1988	−1.78026	−0.890132	+	0.455704i	$0.849388\pi$
$734$	−73.5420	−2.71448
$735$	−37.6670	−1.38937
$736$	19.7184	0.726831
$737$	15.7118	0.578752
$738$	−20.7616	−0.764245
$739$	10.8723	0.399944	0.199972	−	0.979802i	$-0.435915\pi$
$739$	10.8723	0.399944	0.199972	+	0.979802i	$0.435915\pi$
$740$	11.0271	0.405364
$741$	−5.62282	−0.206559
$742$	−100.232	−3.67965
$743$	−4.04041	−0.148228	−0.0741141	−	0.997250i	$-0.523613\pi$
$743$	−4.04041	−0.148228	−0.0741141	+	0.997250i	$0.523613\pi$
$744$	−41.7569	−1.53088
$745$	52.4421	1.92133
$746$	66.5233	2.43559
$747$	−7.62159	−0.278859
$748$	3.82779	0.139958
$749$	−36.4307	−1.33115
$750$	−26.4438	−0.965590
$751$	50.6975	1.84998	0.924989	−	0.379993i	$-0.124074\pi$
$751$	50.6975	1.84998	0.924989	+	0.379993i	$0.124074\pi$
$752$	−27.3964	−0.999045
$753$	0.517752	0.0188679
$754$	4.68714	0.170696
$755$	−41.2853	−1.50253
$756$	17.9998	0.654646
$757$	15.8022	0.574340	0.287170	−	0.957880i	$-0.407286\pi$
$757$	15.8022	0.574340	0.287170	+	0.957880i	$0.407286\pi$
$758$	−0.338804	−0.0123059
$759$	−7.64837	−0.277618
$760$	74.7000	2.70965
$761$	32.2278	1.16826	0.584129	−	0.811661i	$-0.301436\pi$
$761$	32.2278	1.16826	0.584129	+	0.811661i	$0.301436\pi$
$762$	−36.0771	−1.30694
$763$	39.0165	1.41249
$764$	88.2452	3.19260
$765$	2.25593	0.0815632
$766$	45.2598	1.63530
$767$	1.88942	0.0682229
$768$	27.6545	0.997897
$769$	0.0266519	0.000961094 0	0.000480547	−	1.00000i	$-0.499847\pi$
$769$	0.0266519	0.000961094 0	0.000480547		1.00000i	$0.499847\pi$
$770$	27.1359	0.977909
$771$	−23.9250	−0.861637
$772$	95.5395	3.43854
$773$	8.33097	0.299644	0.149822	−	0.988713i	$-0.452130\pi$
$773$	8.33097	0.299644	0.149822	+	0.988713i	$0.452130\pi$
$774$	−9.64049	−0.346520
$775$	−0.919263	−0.0330209
$776$	18.2140	0.653844
$777$	6.43518	0.230861
$778$	−35.0303	−1.25590
$779$	−71.0763	−2.54657
$780$	5.73971	0.205515
$781$	−3.62936	−0.129869
$782$	−17.6355	−0.630646
$783$	−2.85376	−0.101985
$784$	38.0209	1.35789
$785$	−2.25593	−0.0805175
$786$	−7.45683	−0.265976
$787$	6.96595	0.248309	0.124155	−	0.992263i	$-0.460378\pi$
$787$	6.96595	0.248309	0.124155	+	0.992263i	$0.460378\pi$
$788$	−43.7023	−1.55683
$789$	24.0357	0.855694
$790$	−24.2616	−0.863189
$791$	−29.4405	−1.04678
$792$	−4.19480	−0.149056
$793$	7.07866	0.251371
$794$	15.4531	0.548411
$795$	19.4599	0.690172
$796$	−31.6681	−1.12245
$797$	−50.1632	−1.77687	−0.888436	−	0.459001i	$-0.848207\pi$
$797$	−50.1632	−1.77687	−0.888436	+	0.459001i	$0.848207\pi$
$798$	94.9517	3.36125
$799$	−12.0312	−0.425632
$800$	0.238082	0.00841748
$801$	−3.63646	−0.128488
$802$	−63.7576	−2.25136
$803$	5.41201	0.190986
$804$	−56.1206	−1.97922
$805$	−81.1360	−2.85967
$806$	−16.9252	−0.596164
$807$	−1.15181	−0.0405455
$808$	57.2523	2.01413
$809$	22.7875	0.801165	0.400583	−	0.916261i	$-0.368808\pi$
$809$	22.7875	0.801165	0.400583	+	0.916261i	$0.368808\pi$
$810$	−5.38482	−0.189203
$811$	22.7928	0.800363	0.400181	−	0.916436i	$-0.368947\pi$
$811$	22.7928	0.800363	0.400181	+	0.916436i	$0.368947\pi$
$812$	−51.3671	−1.80263
$813$	−6.73126	−0.236076
$814$	−3.26654	−0.114492
$815$	52.0852	1.82446
$816$	−2.27712	−0.0797151
$817$	−33.0037	−1.15465
$818$	10.6756	0.373263
$819$	3.34957	0.117044
$820$	72.5539	2.53369
$821$	−31.5337	−1.10053	−0.550266	−	0.834989i	$-0.685474\pi$
$821$	−31.5337	−1.10053	−0.550266	+	0.834989i	$0.685474\pi$
$822$	33.5764	1.17111
$823$	48.0071	1.67342	0.836712	−	0.547643i	$-0.184475\pi$
$823$	48.0071	1.67342	0.836712	+	0.547643i	$0.184475\pi$
$824$	−9.76319	−0.340117
$825$	−0.0923471	−0.00321511
$826$	−31.9063	−1.11016
$827$	33.5928	1.16814	0.584068	−	0.811705i	$-0.301460\pi$
$827$	33.5928	1.16814	0.584068	+	0.811705i	$0.301460\pi$
$828$	27.3189	0.949399
$829$	−44.4695	−1.54449	−0.772245	−	0.635325i	$-0.780866\pi$
$829$	−44.4695	−1.54449	−0.772245	+	0.635325i	$0.780866\pi$
$830$	41.0409	1.42455
$831$	19.6709	0.682376
$832$	7.51720	0.260612
$833$	16.6969	0.578514
$834$	3.34103	0.115690
$835$	−13.3670	−0.462583
$836$	−31.2794	−1.08182
$837$	10.3049	0.356189
$838$	11.2251	0.387763
$839$	7.51957	0.259604	0.129802	−	0.991540i	$-0.458566\pi$
$839$	7.51957	0.259604	0.129802	+	0.991540i	$0.458566\pi$
$840$	−44.4996	−1.53538
$841$	−20.8560	−0.719174
$842$	−56.4829	−1.94653
$843$	−14.5307	−0.500465
$844$	−72.2446	−2.48676
$845$	−28.2590	−0.972137
$846$	28.7180	0.987346
$847$	48.3307	1.66066
$848$	−19.6427	−0.674534
$849$	−1.06397	−0.0365153
$850$	−0.212933	−0.00730355
$851$	9.76691	0.334805
$852$	12.9636	0.444125
$853$	−11.9113	−0.407834	−0.203917	−	0.978988i	$-0.565367\pi$
$853$	−11.9113	−0.407834	−0.203917	+	0.978988i	$0.565367\pi$
$854$	−119.536	−4.09045
$855$	−18.4347	−0.630452
$856$	−30.3254	−1.03650
$857$	−25.0072	−0.854230	−0.427115	−	0.904197i	$-0.640470\pi$
$857$	−25.0072	−0.854230	−0.427115	+	0.904197i	$0.640470\pi$
$858$	−1.70026	−0.0580460
$859$	40.2573	1.37356	0.686780	−	0.726865i	$-0.259023\pi$
$859$	40.2573	1.37356	0.686780	+	0.726865i	$0.259023\pi$
$860$	33.6899	1.14882
$861$	42.3409	1.44297
$862$	38.2558	1.30300
$863$	11.4655	0.390291	0.195146	−	0.980774i	$-0.437482\pi$
$863$	11.4655	0.390291	0.195146	+	0.980774i	$0.437482\pi$
$864$	−2.66889	−0.0907974
$865$	20.5450	0.698551
$866$	−20.9508	−0.711937
$867$	−1.00000	−0.0339618
$868$	185.486	6.29579
$869$	4.66417	0.158221
$870$	15.3670	0.520990
$871$	−10.4434	−0.353863
$872$	32.4779	1.09984
$873$	−4.49489	−0.152129
$874$	144.112	4.87465
$875$	53.9290	1.82313
$876$	−19.3310	−0.653133
$877$	−8.02608	−0.271022	−0.135511	−	0.990776i	$-0.543268\pi$
$877$	−8.02608	−0.271022	−0.135511	+	0.990776i	$0.543268\pi$
$878$	76.8523	2.59364
$879$	16.5473	0.558128
$880$	5.31786	0.179265
$881$	−1.37081	−0.0461836	−0.0230918	−	0.999733i	$-0.507351\pi$
$881$	−1.37081	−0.0461836	−0.0230918	+	0.999733i	$0.507351\pi$
$882$	−39.8550	−1.34199
$883$	46.8654	1.57715	0.788573	−	0.614941i	$-0.210820\pi$
$883$	46.8654	1.57715	0.788573	+	0.614941i	$0.210820\pi$
$884$	−2.54428	−0.0855734
$885$	6.19455	0.208228
$886$	−69.2194	−2.32547
$887$	44.6925	1.50063	0.750314	−	0.661082i	$-0.229902\pi$
$887$	44.6925	1.50063	0.750314	+	0.661082i	$0.229902\pi$
$888$	5.35674	0.179760
$889$	73.5752	2.46763
$890$	19.5817	0.656380
$891$	1.03520	0.0346807
$892$	60.1933	2.01542
$893$	98.3147	3.28998
$894$	55.4883	1.85581
$895$	19.9524	0.666935
$896$	−100.958	−3.37277
$897$	5.08377	0.169742
$898$	−14.6990	−0.490512
$899$	−29.4077	−0.980801
$900$	0.329852	0.0109951
$901$	−8.62613	−0.287378
$902$	−21.4925	−0.715622
$903$	19.6607	0.654267
$904$	−24.5067	−0.815079
$905$	9.87793	0.328354
$906$	−43.6834	−1.45129
$907$	16.8013	0.557877	0.278939	−	0.960309i	$-0.410017\pi$
$907$	16.8013	0.557877	0.278939	+	0.960309i	$0.410017\pi$
$908$	5.82082	0.193171
$909$	−14.1289	−0.468626
$910$	−18.0369	−0.597916
$911$	−25.4071	−0.841774	−0.420887	−	0.907113i	$-0.638281\pi$
$911$	−25.4071	−0.841774	−0.420887	+	0.907113i	$0.638281\pi$
$912$	18.6079	0.616168
$913$	−7.88991	−0.261118
$914$	9.96172	0.329504
$915$	23.2077	0.767224
$916$	6.38300	0.210900
$917$	15.2073	0.502191
$918$	2.38697	0.0787817
$919$	3.57057	0.117782	0.0588912	−	0.998264i	$-0.481244\pi$
$919$	3.57057	0.117782	0.0588912	+	0.998264i	$0.481244\pi$
$920$	−67.5387	−2.22669
$921$	12.0964	0.398589
$922$	−32.4809	−1.06970
$923$	2.41239	0.0794047
$924$	18.6335	0.612996
$925$	0.117927	0.00387740
$926$	42.8687	1.40875
$927$	2.40939	0.0791346
$928$	7.61637	0.250020
$929$	−0.00949945	−0.000311667 0	−0.000155833	−	1.00000i	$-0.500050\pi$
$929$	−0.00949945	−0.000311667 0	−0.000155833		1.00000i	$0.500050\pi$
$930$	−55.4900	−1.81959
$931$	−136.442	−4.47169
$932$	32.9393	1.07896
$933$	20.6007	0.674436
$934$	48.3828	1.58313
$935$	2.33535	0.0763740
$936$	2.78823	0.0911362
$937$	11.8867	0.388320	0.194160	−	0.980970i	$-0.437802\pi$
$937$	11.8867	0.388320	0.194160	+	0.980970i	$0.437802\pi$
$938$	176.357	5.75826
$939$	−19.8787	−0.648715
$940$	−100.359	−3.27334
$941$	1.27612	0.0416005	0.0208002	−	0.999784i	$-0.493379\pi$
$941$	1.27612	0.0416005	0.0208002	+	0.999784i	$0.493379\pi$
$942$	−2.38697	−0.0777716
$943$	64.2624	2.09267
$944$	−6.25274	−0.203509
$945$	10.9817	0.357236
$946$	−9.97988	−0.324474
$947$	−14.2844	−0.464180	−0.232090	−	0.972694i	$-0.574556\pi$
$947$	−14.2844	−0.464180	−0.232090	+	0.972694i	$0.574556\pi$
$948$	−16.6598	−0.541085
$949$	−3.59729	−0.116773
$950$	1.74002	0.0564537
$951$	−12.4872	−0.404925
$952$	19.7256	0.639312
$953$	1.39435	0.0451674	0.0225837	−	0.999745i	$-0.492811\pi$
$953$	1.39435	0.0451674	0.0225837	+	0.999745i	$0.492811\pi$
$954$	20.5903	0.666635
$955$	53.8387	1.74218
$956$	47.1109	1.52368
$957$	−2.95423	−0.0954966
$958$	−69.8127	−2.25555
$959$	−68.4752	−2.21118
$960$	24.6455	0.795431
$961$	75.1906	2.42550
$962$	2.17122	0.0700031
$963$	7.48379	0.241162
$964$	−19.4218	−0.625533
$965$	58.2890	1.87639
$966$	−85.8489	−2.76214
$967$	32.5456	1.04660	0.523298	−	0.852150i	$-0.324702\pi$
$967$	32.5456	1.04660	0.523298	+	0.852150i	$0.324702\pi$
$968$	40.2312	1.29308
$969$	8.17166	0.262512
$970$	24.2042	0.777150
$971$	23.2256	0.745346	0.372673	−	0.927963i	$-0.378441\pi$
$971$	23.2256	0.745346	0.372673	+	0.927963i	$0.378441\pi$
$972$	−3.69761	−0.118601
$973$	−6.81364	−0.218435
$974$	64.9218	2.08023
$975$	0.0613819	0.00196579
$976$	−23.4258	−0.749840
$977$	−50.8529	−1.62693	−0.813465	−	0.581614i	$-0.802421\pi$
$977$	−50.8529	−1.62693	−0.813465	+	0.581614i	$0.802421\pi$
$978$	55.1106	1.76224
$979$	−3.76448	−0.120313
$980$	139.278	4.44908
$981$	−8.01499	−0.255899
$982$	−43.8086	−1.39799
$983$	0.196709	0.00627403	0.00313702	−	0.999995i	$-0.499001\pi$
$983$	0.196709	0.00627403	0.00313702	+	0.999995i	$0.499001\pi$
$984$	35.2452	1.12358
$985$	−26.6629	−0.849551
$986$	−6.81184	−0.216933
$987$	−58.5671	−1.86421
$988$	20.7910	0.661450
$989$	29.8398	0.948849
$990$	−5.57439	−0.177166
$991$	42.1068	1.33757	0.668784	−	0.743457i	$-0.266815\pi$
$991$	42.1068	1.33757	0.668784	+	0.743457i	$0.266815\pi$
$992$	−27.5026	−0.873207
$993$	32.9406	1.04534
$994$	−40.7377	−1.29212
$995$	−19.3208	−0.612512
$996$	28.1817	0.892971
$997$	43.7861	1.38672	0.693360	−	0.720592i	$-0.256130\pi$
$997$	43.7861	1.38672	0.693360	+	0.720592i	$0.256130\pi$
$998$	−92.9255	−2.94150
$999$	−1.32195	−0.0418246

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8007.2.a.j.1.6	✓	64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8007.2.a.j.1.6	✓	64	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:	\( N \)	\(=\)	\( 8007 = 3 \cdot 17 \cdot 157 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8007.a (trivial)

\(f(q)\)	\(=\)	\(q-2.38697 q^{2} -1.00000 q^{3} +3.69761 q^{4} +2.25593 q^{5} +2.38697 q^{6} -4.86795 q^{7} -4.05215 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-2.38697 q^{2} -1.00000 q^{3} +3.69761 q^{4} +2.25593 q^{5} +2.38697 q^{6} -4.86795 q^{7} -4.05215 q^{8} +1.00000 q^{9} -5.38482 q^{10} +1.03520 q^{11} -3.69761 q^{12} -0.688087 q^{13} +11.6196 q^{14} -2.25593 q^{15} +2.27712 q^{16} +1.00000 q^{17} -2.38697 q^{18} -8.17166 q^{19} +8.34155 q^{20} +4.86795 q^{21} -2.47100 q^{22} +7.38826 q^{23} +4.05215 q^{24} +0.0892066 q^{25} +1.64244 q^{26} -1.00000 q^{27} -17.9998 q^{28} +2.85376 q^{29} +5.38482 q^{30} -10.3049 q^{31} +2.66889 q^{32} -1.03520 q^{33} -2.38697 q^{34} -10.9817 q^{35} +3.69761 q^{36} +1.32195 q^{37} +19.5055 q^{38} +0.688087 q^{39} -9.14135 q^{40} +8.69790 q^{41} -11.6196 q^{42} +4.03880 q^{43} +3.82779 q^{44} +2.25593 q^{45} -17.6355 q^{46} -12.0312 q^{47} -2.27712 q^{48} +16.6969 q^{49} -0.212933 q^{50} -1.00000 q^{51} -2.54428 q^{52} -8.62613 q^{53} +2.38697 q^{54} +2.33535 q^{55} +19.7256 q^{56} +8.17166 q^{57} -6.81184 q^{58} -2.74590 q^{59} -8.34155 q^{60} -10.2874 q^{61} +24.5974 q^{62} -4.86795 q^{63} -10.9248 q^{64} -1.55227 q^{65} +2.47100 q^{66} +15.1775 q^{67} +3.69761 q^{68} -7.38826 q^{69} +26.2130 q^{70} -3.50593 q^{71} -4.05215 q^{72} +5.22796 q^{73} -3.15545 q^{74} -0.0892066 q^{75} -30.2156 q^{76} -5.03932 q^{77} -1.64244 q^{78} +4.50555 q^{79} +5.13702 q^{80} +1.00000 q^{81} -20.7616 q^{82} -7.62159 q^{83} +17.9998 q^{84} +2.25593 q^{85} -9.64049 q^{86} -2.85376 q^{87} -4.19480 q^{88} -3.63646 q^{89} -5.38482 q^{90} +3.34957 q^{91} +27.3189 q^{92} +10.3049 q^{93} +28.7180 q^{94} -18.4347 q^{95} -2.66889 q^{96} -4.49489 q^{97} -39.8550 q^{98} +1.03520 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q + 5 q^{2} - 64 q^{3} + 77 q^{4} - 3 q^{5} - 5 q^{6} + 5 q^{7} + 18 q^{8} + 64 q^{9}+O(q^{10}) \) 64 * q + 5 * q^2 - 64 * q^3 + 77 * q^4 - 3 * q^5 - 5 * q^6 + 5 * q^7 + 18 * q^8 + 64 * q^9	\( 64 q + 5 q^{2} - 64 q^{3} + 77 q^{4} - 3 q^{5} - 5 q^{6} + 5 q^{7} + 18 q^{8} + 64 q^{9} + 12 q^{10} - 7 q^{11} - 77 q^{12} + 24 q^{13} - 14 q^{14} + 3 q^{15} + 103 q^{16} + 64 q^{17} + 5 q^{18} + 26 q^{19} - 24 q^{20} - 5 q^{21} + 25 q^{22} + 20 q^{23} - 18 q^{24} + 141 q^{25} + 9 q^{26} - 64 q^{27} + 14 q^{28} + 5 q^{29} - 12 q^{30} + 11 q^{31} + 31 q^{32} + 7 q^{33} + 5 q^{34} - 3 q^{35} + 77 q^{36} + 50 q^{37} + 8 q^{38} - 24 q^{39} + 28 q^{40} - 9 q^{41} + 14 q^{42} + 59 q^{43} - 6 q^{44} - 3 q^{45} + 11 q^{47} - 103 q^{48} + 163 q^{49} + 20 q^{50} - 64 q^{51} + 65 q^{52} + 39 q^{53} - 5 q^{54} + 35 q^{55} - 34 q^{56} - 26 q^{57} - 27 q^{58} - 65 q^{59} + 24 q^{60} + 15 q^{61} + 18 q^{62} + 5 q^{63} + 152 q^{64} + 49 q^{65} - 25 q^{66} + 56 q^{67} + 77 q^{68} - 20 q^{69} + 28 q^{70} - 18 q^{71} + 18 q^{72} + 37 q^{73} - 76 q^{74} - 141 q^{75} + 30 q^{76} + 80 q^{77} - 9 q^{78} + 20 q^{79} - 144 q^{80} + 64 q^{81} + 27 q^{82} + 3 q^{83} - 14 q^{84} - 3 q^{85} + 12 q^{86} - 5 q^{87} + 108 q^{88} + 42 q^{89} + 12 q^{90} + 25 q^{91} + 18 q^{92} - 11 q^{93} + 60 q^{94} + 42 q^{95} - 31 q^{96} + 72 q^{97} + 18 q^{98} - 7 q^{99}+O(q^{100}) \) 64 * q + 5 * q^2 - 64 * q^3 + 77 * q^4 - 3 * q^5 - 5 * q^6 + 5 * q^7 + 18 * q^8 + 64 * q^9 + 12 * q^10 - 7 * q^11 - 77 * q^12 + 24 * q^13 - 14 * q^14 + 3 * q^15 + 103 * q^16 + 64 * q^17 + 5 * q^18 + 26 * q^19 - 24 * q^20 - 5 * q^21 + 25 * q^22 + 20 * q^23 - 18 * q^24 + 141 * q^25 + 9 * q^26 - 64 * q^27 + 14 * q^28 + 5 * q^29 - 12 * q^30 + 11 * q^31 + 31 * q^32 + 7 * q^33 + 5 * q^34 - 3 * q^35 + 77 * q^36 + 50 * q^37 + 8 * q^38 - 24 * q^39 + 28 * q^40 - 9 * q^41 + 14 * q^42 + 59 * q^43 - 6 * q^44 - 3 * q^45 + 11 * q^47 - 103 * q^48 + 163 * q^49 + 20 * q^50 - 64 * q^51 + 65 * q^52 + 39 * q^53 - 5 * q^54 + 35 * q^55 - 34 * q^56 - 26 * q^57 - 27 * q^58 - 65 * q^59 + 24 * q^60 + 15 * q^61 + 18 * q^62 + 5 * q^63 + 152 * q^64 + 49 * q^65 - 25 * q^66 + 56 * q^67 + 77 * q^68 - 20 * q^69 + 28 * q^70 - 18 * q^71 + 18 * q^72 + 37 * q^73 - 76 * q^74 - 141 * q^75 + 30 * q^76 + 80 * q^77 - 9 * q^78 + 20 * q^79 - 144 * q^80 + 64 * q^81 + 27 * q^82 + 3 * q^83 - 14 * q^84 - 3 * q^85 + 12 * q^86 - 5 * q^87 + 108 * q^88 + 42 * q^89 + 12 * q^90 + 25 * q^91 + 18 * q^92 - 11 * q^93 + 60 * q^94 + 42 * q^95 - 31 * q^96 + 72 * q^97 + 18 * q^98 - 7 * q^99

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