LMFDB - Embedded newform 8007.2.a.h.1.12

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:	$56$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.12
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)

$f(q)$	$=$	$q-1.81301 q^{2} +1.00000 q^{3} +1.28701 q^{4} +1.68912 q^{5} -1.81301 q^{6} +2.36168 q^{7} +1.29265 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.81301 q^{2} +1.00000 q^{3} +1.28701 q^{4} +1.68912 q^{5} -1.81301 q^{6} +2.36168 q^{7} +1.29265 q^{8} +1.00000 q^{9} -3.06240 q^{10} -6.20367 q^{11} +1.28701 q^{12} -0.435340 q^{13} -4.28175 q^{14} +1.68912 q^{15} -4.91762 q^{16} -1.00000 q^{17} -1.81301 q^{18} +3.20833 q^{19} +2.17392 q^{20} +2.36168 q^{21} +11.2473 q^{22} +7.21657 q^{23} +1.29265 q^{24} -2.14687 q^{25} +0.789277 q^{26} +1.00000 q^{27} +3.03951 q^{28} -3.18093 q^{29} -3.06240 q^{30} +4.00056 q^{31} +6.33040 q^{32} -6.20367 q^{33} +1.81301 q^{34} +3.98917 q^{35} +1.28701 q^{36} -2.98067 q^{37} -5.81675 q^{38} -0.435340 q^{39} +2.18345 q^{40} +8.05809 q^{41} -4.28175 q^{42} -5.68730 q^{43} -7.98421 q^{44} +1.68912 q^{45} -13.0837 q^{46} +10.1846 q^{47} -4.91762 q^{48} -1.42247 q^{49} +3.89229 q^{50} -1.00000 q^{51} -0.560288 q^{52} -0.902444 q^{53} -1.81301 q^{54} -10.4788 q^{55} +3.05283 q^{56} +3.20833 q^{57} +5.76706 q^{58} -4.48291 q^{59} +2.17392 q^{60} -3.75865 q^{61} -7.25307 q^{62} +2.36168 q^{63} -1.64186 q^{64} -0.735343 q^{65} +11.2473 q^{66} -7.17864 q^{67} -1.28701 q^{68} +7.21657 q^{69} -7.23241 q^{70} +10.7654 q^{71} +1.29265 q^{72} +4.49662 q^{73} +5.40398 q^{74} -2.14687 q^{75} +4.12917 q^{76} -14.6511 q^{77} +0.789277 q^{78} -6.14671 q^{79} -8.30647 q^{80} +1.00000 q^{81} -14.6094 q^{82} +11.9599 q^{83} +3.03951 q^{84} -1.68912 q^{85} +10.3111 q^{86} -3.18093 q^{87} -8.01920 q^{88} +5.84912 q^{89} -3.06240 q^{90} -1.02813 q^{91} +9.28783 q^{92} +4.00056 q^{93} -18.4648 q^{94} +5.41927 q^{95} +6.33040 q^{96} +6.74716 q^{97} +2.57895 q^{98} -6.20367 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q + 7 q^{2} + 56 q^{3} + 61 q^{4} + 17 q^{5} + 7 q^{6} + 5 q^{7} + 18 q^{8} + 56 q^{9}+O(q^{10}) $ 56 * q + 7 * q^2 + 56 * q^3 + 61 * q^4 + 17 * q^5 + 7 * q^6 + 5 * q^7 + 18 * q^8 + 56 * q^9	\( 56 q + 7 q^{2} + 56 q^{3} + 61 q^{4} + 17 q^{5} + 7 q^{6} + 5 q^{7} + 18 q^{8} + 56 q^{9} - 2 q^{10} + 35 q^{11} + 61 q^{12} + 8 q^{13} + 36 q^{14} + 17 q^{15} + 71 q^{16} - 56 q^{17} + 7 q^{18} - 2 q^{19} + 58 q^{20} + 5 q^{21} + 27 q^{22} + 40 q^{23} + 18 q^{24} + 85 q^{25} + 15 q^{26} + 56 q^{27} - 4 q^{28} + 41 q^{29} - 2 q^{30} + q^{31} + 43 q^{32} + 35 q^{33} - 7 q^{34} + 57 q^{35} + 61 q^{36} + 34 q^{37} + 52 q^{38} + 8 q^{39} + 14 q^{40} + 49 q^{41} + 36 q^{42} + 27 q^{43} + 66 q^{44} + 17 q^{45} + 10 q^{46} + 43 q^{47} + 71 q^{48} + 51 q^{49} + 30 q^{50} - 56 q^{51} - 7 q^{52} + 73 q^{53} + 7 q^{54} + 15 q^{55} + 118 q^{56} - 2 q^{57} - q^{58} + 53 q^{59} + 58 q^{60} + 15 q^{61} + 16 q^{62} + 5 q^{63} + 124 q^{64} + 107 q^{65} + 27 q^{66} + 20 q^{67} - 61 q^{68} + 40 q^{69} + 16 q^{70} + 56 q^{71} + 18 q^{72} + 49 q^{73} + 28 q^{74} + 85 q^{75} - 38 q^{76} + 50 q^{77} + 15 q^{78} - 4 q^{79} + 74 q^{80} + 56 q^{81} + 59 q^{82} + 35 q^{83} - 4 q^{84} - 17 q^{85} + 38 q^{86} + 41 q^{87} + 64 q^{88} + 66 q^{89} - 2 q^{90} + 5 q^{91} + 96 q^{92} + q^{93} - 12 q^{94} + 70 q^{95} + 43 q^{96} + 60 q^{97} + 26 q^{98} + 35 q^{99}+O(q^{100}) \) 56 * q + 7 * q^2 + 56 * q^3 + 61 * q^4 + 17 * q^5 + 7 * q^6 + 5 * q^7 + 18 * q^8 + 56 * q^9 - 2 * q^10 + 35 * q^11 + 61 * q^12 + 8 * q^13 + 36 * q^14 + 17 * q^15 + 71 * q^16 - 56 * q^17 + 7 * q^18 - 2 * q^19 + 58 * q^20 + 5 * q^21 + 27 * q^22 + 40 * q^23 + 18 * q^24 + 85 * q^25 + 15 * q^26 + 56 * q^27 - 4 * q^28 + 41 * q^29 - 2 * q^30 + q^31 + 43 * q^32 + 35 * q^33 - 7 * q^34 + 57 * q^35 + 61 * q^36 + 34 * q^37 + 52 * q^38 + 8 * q^39 + 14 * q^40 + 49 * q^41 + 36 * q^42 + 27 * q^43 + 66 * q^44 + 17 * q^45 + 10 * q^46 + 43 * q^47 + 71 * q^48 + 51 * q^49 + 30 * q^50 - 56 * q^51 - 7 * q^52 + 73 * q^53 + 7 * q^54 + 15 * q^55 + 118 * q^56 - 2 * q^57 - q^58 + 53 * q^59 + 58 * q^60 + 15 * q^61 + 16 * q^62 + 5 * q^63 + 124 * q^64 + 107 * q^65 + 27 * q^66 + 20 * q^67 - 61 * q^68 + 40 * q^69 + 16 * q^70 + 56 * q^71 + 18 * q^72 + 49 * q^73 + 28 * q^74 + 85 * q^75 - 38 * q^76 + 50 * q^77 + 15 * q^78 - 4 * q^79 + 74 * q^80 + 56 * q^81 + 59 * q^82 + 35 * q^83 - 4 * q^84 - 17 * q^85 + 38 * q^86 + 41 * q^87 + 64 * q^88 + 66 * q^89 - 2 * q^90 + 5 * q^91 + 96 * q^92 + q^93 - 12 * q^94 + 70 * q^95 + 43 * q^96 + 60 * q^97 + 26 * q^98 + 35 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−1.81301	−1.28199	−0.640997	−	0.767544i	$-0.721479\pi$
$2$	−1.81301	−1.28199	−0.640997	+	0.767544i	$0.721479\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	1.28701	0.643507
$5$	1.68912	0.755399	0.377699	−	0.925928i	$-0.376715\pi$
$5$	1.68912	0.755399	0.377699	+	0.925928i	$0.376715\pi$
$6$	−1.81301	−0.740159
$7$	2.36168	0.892631	0.446316	−	0.894876i	$-0.352736\pi$
$7$	2.36168	0.892631	0.446316	+	0.894876i	$0.352736\pi$
$8$	1.29265	0.457022
$9$	1.00000	0.333333
$10$	−3.06240	−0.968416
$11$	−6.20367	−1.87048	−0.935239	−	0.354017i	$-0.884816\pi$
$11$	−6.20367	−1.87048	−0.935239	+	0.354017i	$0.884816\pi$
$12$	1.28701	0.371529
$13$	−0.435340	−0.120742	−0.0603708	−	0.998176i	$-0.519228\pi$
$13$	−0.435340	−0.120742	−0.0603708	+	0.998176i	$0.519228\pi$
$14$	−4.28175	−1.14435
$15$	1.68912	0.436130
$16$	−4.91762	−1.22941
$17$	−1.00000	−0.242536
$17$	−1.00000	−0.242536
$18$	−1.81301	−0.427331
$19$	3.20833	0.736042	0.368021	−	0.929817i	$-0.380035\pi$
$19$	3.20833	0.736042	0.368021	+	0.929817i	$0.380035\pi$
$20$	2.17392	0.486104
$21$	2.36168	0.515361
$22$	11.2473	2.39794
$23$	7.21657	1.50476	0.752380	−	0.658729i	$-0.228906\pi$
$23$	7.21657	1.50476	0.752380	+	0.658729i	$0.228906\pi$
$24$	1.29265	0.263862
$25$	−2.14687	−0.429373
$26$	0.789277	0.154790
$27$	1.00000	0.192450
$28$	3.03951	0.574414
$29$	−3.18093	−0.590684	−0.295342	−	0.955392i	$-0.595434\pi$
$29$	−3.18093	−0.590684	−0.295342	+	0.955392i	$0.595434\pi$
$30$	−3.06240	−0.559115
$31$	4.00056	0.718522	0.359261	−	0.933237i	$-0.383029\pi$
$31$	4.00056	0.718522	0.359261	+	0.933237i	$0.383029\pi$
$32$	6.33040	1.11907
$33$	−6.20367	−1.07992
$34$	1.81301	0.310929
$35$	3.98917	0.674292
$36$	1.28701	0.214502
$37$	−2.98067	−0.490019	−0.245009	−	0.969521i	$-0.578791\pi$
$37$	−2.98067	−0.490019	−0.245009	+	0.969521i	$0.578791\pi$
$38$	−5.81675	−0.943601
$39$	−0.435340	−0.0697102
$40$	2.18345	0.345234
$41$	8.05809	1.25846	0.629231	−	0.777218i	$-0.283370\pi$
$41$	8.05809	1.25846	0.629231	+	0.777218i	$0.283370\pi$
$42$	−4.28175	−0.660689
$43$	−5.68730	−0.867305	−0.433653	−	0.901080i	$-0.642776\pi$
$43$	−5.68730	−0.867305	−0.433653	+	0.901080i	$0.642776\pi$
$44$	−7.98421	−1.20367
$45$	1.68912	0.251800
$46$	−13.0837	−1.92909
$47$	10.1846	1.48558	0.742788	−	0.669527i	$-0.233503\pi$
$47$	10.1846	1.48558	0.742788	+	0.669527i	$0.233503\pi$
$48$	−4.91762	−0.709798
$49$	−1.42247	−0.203210
$50$	3.89229	0.550453
$51$	−1.00000	−0.140028
$52$	−0.560288	−0.0776980
$53$	−0.902444	−0.123960	−0.0619801	−	0.998077i	$-0.519742\pi$
$53$	−0.902444	−0.123960	−0.0619801	+	0.998077i	$0.519742\pi$
$54$	−1.81301	−0.246720
$55$	−10.4788	−1.41296
$56$	3.05283	0.407952
$57$	3.20833	0.424954
$58$	5.76706	0.757253
$59$	−4.48291	−0.583625	−0.291812	−	0.956476i	$-0.594258\pi$
$59$	−4.48291	−0.583625	−0.291812	+	0.956476i	$0.594258\pi$
$60$	2.17392	0.280652
$61$	−3.75865	−0.481246	−0.240623	−	0.970619i	$-0.577352\pi$
$61$	−3.75865	−0.481246	−0.240623	+	0.970619i	$0.577352\pi$
$62$	−7.25307	−0.921140
$63$	2.36168	0.297544
$64$	−1.64186	−0.205232
$65$	−0.735343	−0.0912080
$66$	11.2473	1.38445
$67$	−7.17864	−0.877010	−0.438505	−	0.898729i	$-0.644492\pi$
$67$	−7.17864	−0.877010	−0.438505	+	0.898729i	$0.644492\pi$
$68$	−1.28701	−0.156073
$69$	7.21657	0.868773
$70$	−7.23241	−0.864438
$71$	10.7654	1.27762	0.638811	−	0.769364i	$-0.279426\pi$
$71$	10.7654	1.27762	0.638811	+	0.769364i	$0.279426\pi$
$72$	1.29265	0.152341
$73$	4.49662	0.526289	0.263145	−	0.964756i	$-0.415240\pi$
$73$	4.49662	0.526289	0.263145	+	0.964756i	$0.415240\pi$
$74$	5.40398	0.628200
$75$	−2.14687	−0.247899
$76$	4.12917	0.473648
$77$	−14.6511	−1.66965
$78$	0.789277	0.0893680
$79$	−6.14671	−0.691559	−0.345780	−	0.938316i	$-0.612386\pi$
$79$	−6.14671	−0.691559	−0.345780	+	0.938316i	$0.612386\pi$
$80$	−8.30647	−0.928691
$81$	1.00000	0.111111
$82$	−14.6094	−1.61334
$83$	11.9599	1.31277	0.656385	−	0.754426i	$-0.272085\pi$
$83$	11.9599	1.31277	0.656385	+	0.754426i	$0.272085\pi$
$84$	3.03951	0.331638
$85$	−1.68912	−0.183211
$86$	10.3111	1.11188
$87$	−3.18093	−0.341031
$88$	−8.01920	−0.854849
$89$	5.84912	0.620005	0.310002	−	0.950736i	$-0.399670\pi$
$89$	5.84912	0.620005	0.310002	+	0.950736i	$0.399670\pi$
$90$	−3.06240	−0.322805
$91$	−1.02813	−0.107778
$92$	9.28783	0.968323
$93$	4.00056	0.414839
$94$	−18.4648	−1.90450
$95$	5.41927	0.556005
$96$	6.33040	0.646094
$97$	6.74716	0.685071	0.342535	−	0.939505i	$-0.388714\pi$
$97$	6.74716	0.685071	0.342535	+	0.939505i	$0.388714\pi$
$98$	2.57895	0.260514
$99$	−6.20367	−0.623493
$100$	−2.76304	−0.276304
$101$	−17.3624	−1.72762	−0.863811	−	0.503817i	$-0.831929\pi$
$101$	−17.3624	−1.72762	−0.863811	+	0.503817i	$0.831929\pi$
$102$	1.81301	0.179515
$103$	−0.489124	−0.0481948	−0.0240974	−	0.999710i	$-0.507671\pi$
$103$	−0.489124	−0.0481948	−0.0240974	+	0.999710i	$0.507671\pi$
$104$	−0.562744	−0.0551815
$105$	3.98917	0.389303
$106$	1.63614	0.158916
$107$	0.439465	0.0424847	0.0212424	−	0.999774i	$-0.493238\pi$
$107$	0.439465	0.0424847	0.0212424	+	0.999774i	$0.493238\pi$
$108$	1.28701	0.123843
$109$	7.55340	0.723484	0.361742	−	0.932278i	$-0.382182\pi$
$109$	7.55340	0.723484	0.361742	+	0.932278i	$0.382182\pi$
$110$	18.9981	1.81140
$111$	−2.98067	−0.282912
$112$	−11.6139	−1.09741
$113$	1.95525	0.183934	0.0919672	−	0.995762i	$-0.470685\pi$
$113$	1.95525	0.183934	0.0919672	+	0.995762i	$0.470685\pi$
$114$	−5.81675	−0.544788
$115$	12.1897	1.13669
$116$	−4.09390	−0.380109
$117$	−0.435340	−0.0402472
$118$	8.12757	0.748203
$119$	−2.36168	−0.216495
$120$	2.18345	0.199321
$121$	27.4856	2.49869
$122$	6.81449	0.616955
$123$	8.05809	0.726574
$124$	5.14878	0.462374
$125$	−12.0719	−1.07975
$126$	−4.28175	−0.381449
$127$	10.3428	0.917772	0.458886	−	0.888495i	$-0.348249\pi$
$127$	10.3428	0.917772	0.458886	+	0.888495i	$0.348249\pi$
$128$	−9.68411	−0.855962
$129$	−5.68730	−0.500739
$130$	1.33319	0.116928
$131$	16.1908	1.41460	0.707298	−	0.706916i	$-0.249914\pi$
$131$	16.1908	1.41460	0.707298	+	0.706916i	$0.249914\pi$
$132$	−7.98421	−0.694937
$133$	7.57706	0.657014
$134$	13.0150	1.12432
$135$	1.68912	0.145377
$136$	−1.29265	−0.110844
$137$	15.0781	1.28821	0.644105	−	0.764937i	$-0.277230\pi$
$137$	15.0781	1.28821	0.644105	+	0.764937i	$0.277230\pi$
$138$	−13.0837	−1.11376
$139$	5.92376	0.502447	0.251223	−	0.967929i	$-0.419167\pi$
$139$	5.92376	0.502447	0.251223	+	0.967929i	$0.419167\pi$
$140$	5.13411	0.433912
$141$	10.1846	0.857697
$142$	−19.5179	−1.63790
$143$	2.70071	0.225844
$144$	−4.91762	−0.409802
$145$	−5.37298	−0.446202
$146$	−8.15243	−0.674699
$147$	−1.42247	−0.117323
$148$	−3.83616	−0.315330
$149$	9.41137	0.771009	0.385505	−	0.922706i	$-0.374027\pi$
$149$	9.41137	0.771009	0.385505	+	0.922706i	$0.374027\pi$
$150$	3.89229	0.317804
$151$	−15.6927	−1.27706	−0.638529	−	0.769598i	$-0.720457\pi$
$151$	−15.6927	−1.27706	−0.638529	+	0.769598i	$0.720457\pi$
$152$	4.14726	0.336387
$153$	−1.00000	−0.0808452
$154$	26.5626	2.14048
$155$	6.75744	0.542770
$156$	−0.560288	−0.0448590
$157$	−1.00000	−0.0798087
$157$	−1.00000	−0.0798087
$158$	11.1441	0.886574
$159$	−0.902444	−0.0715685
$160$	10.6928	0.845342
$161$	17.0432	1.34320
$162$	−1.81301	−0.142444
$163$	15.9548	1.24968	0.624838	−	0.780755i	$-0.285165\pi$
$163$	15.9548	1.24968	0.624838	+	0.780755i	$0.285165\pi$
$164$	10.3709	0.809829
$165$	−10.4788	−0.815771
$166$	−21.6835	−1.68296
$167$	8.40679	0.650537	0.325268	−	0.945622i	$-0.394545\pi$
$167$	8.40679	0.650537	0.325268	+	0.945622i	$0.394545\pi$
$168$	3.05283	0.235531
$169$	−12.8105	−0.985421
$170$	3.06240	0.234875
$171$	3.20833	0.245347
$172$	−7.31963	−0.558117
$173$	−14.8399	−1.12825	−0.564127	−	0.825688i	$-0.690787\pi$
$173$	−14.8399	−1.12825	−0.564127	+	0.825688i	$0.690787\pi$
$174$	5.76706	0.437200
$175$	−5.07021	−0.383272
$176$	30.5073	2.29958
$177$	−4.48291	−0.336956
$178$	−10.6045	−0.794842
$179$	12.2076	0.912435	0.456218	−	0.889868i	$-0.349204\pi$
$179$	12.2076	0.912435	0.456218	+	0.889868i	$0.349204\pi$
$180$	2.17392	0.162035
$181$	22.3017	1.65767	0.828836	−	0.559492i	$-0.189004\pi$
$181$	22.3017	1.65767	0.828836	+	0.559492i	$0.189004\pi$
$182$	1.86402	0.138170
$183$	−3.75865	−0.277848
$184$	9.32853	0.687708
$185$	−5.03471	−0.370159
$186$	−7.25307	−0.531821
$187$	6.20367	0.453658
$188$	13.1077	0.955978
$189$	2.36168	0.171787
$190$	−9.82520	−0.712795
$191$	11.1309	0.805407	0.402704	−	0.915330i	$-0.368071\pi$
$191$	11.1309	0.805407	0.402704	+	0.915330i	$0.368071\pi$
$192$	−1.64186	−0.118491
$193$	14.5269	1.04567	0.522833	−	0.852435i	$-0.324875\pi$
$193$	14.5269	1.04567	0.522833	+	0.852435i	$0.324875\pi$
$194$	−12.2327	−0.878256
$195$	−0.735343	−0.0526590
$196$	−1.83074	−0.130767
$197$	9.27140	0.660560	0.330280	−	0.943883i	$-0.392857\pi$
$197$	9.27140	0.660560	0.330280	+	0.943883i	$0.392857\pi$
$198$	11.2473	0.799313
$199$	11.2479	0.797342	0.398671	−	0.917094i	$-0.369472\pi$
$199$	11.2479	0.797342	0.398671	+	0.917094i	$0.369472\pi$
$200$	−2.77515	−0.196233
$201$	−7.17864	−0.506342
$202$	31.4782	2.21480
$203$	−7.51234	−0.527263
$204$	−1.28701	−0.0901090
$205$	13.6111	0.950641
$206$	0.886788	0.0617855
$207$	7.21657	0.501587
$208$	2.14084	0.148440
$209$	−19.9035	−1.37675
$210$	−7.23241	−0.499084
$211$	−19.9685	−1.37469	−0.687344	−	0.726332i	$-0.741224\pi$
$211$	−19.9685	−1.37469	−0.687344	+	0.726332i	$0.741224\pi$
$212$	−1.16146	−0.0797692
$213$	10.7654	0.737636
$214$	−0.796756	−0.0544651
$215$	−9.60655	−0.655161
$216$	1.29265	0.0879539
$217$	9.44804	0.641375
$218$	−13.6944	−0.927502
$219$	4.49662	0.303853
$220$	−13.4863	−0.909247
$221$	0.435340	0.0292841
$222$	5.40398	0.362692
$223$	20.8958	1.39929	0.699643	−	0.714492i	$-0.253342\pi$
$223$	20.8958	1.39929	0.699643	+	0.714492i	$0.253342\pi$
$224$	14.9504	0.998915
$225$	−2.14687	−0.143124
$226$	−3.54489	−0.235803
$227$	−22.2653	−1.47780	−0.738899	−	0.673817i	$-0.764654\pi$
$227$	−22.2653	−1.47780	−0.738899	+	0.673817i	$0.764654\pi$
$228$	4.12917	0.273461
$229$	−4.05286	−0.267820	−0.133910	−	0.990993i	$-0.542753\pi$
$229$	−4.05286	−0.267820	−0.133910	+	0.990993i	$0.542753\pi$
$230$	−22.1000	−1.45723
$231$	−14.6511	−0.963971
$232$	−4.11184	−0.269955
$233$	6.87955	0.450695	0.225347	−	0.974278i	$-0.427648\pi$
$233$	6.87955	0.450695	0.225347	+	0.974278i	$0.427648\pi$
$234$	0.789277	0.0515966
$235$	17.2030	1.12220
$236$	−5.76956	−0.375567
$237$	−6.14671	−0.399272
$238$	4.28175	0.277545
$239$	26.8217	1.73495	0.867475	−	0.497481i	$-0.165742\pi$
$239$	26.8217	1.73495	0.867475	+	0.497481i	$0.165742\pi$
$240$	−8.30647	−0.536180
$241$	−1.70159	−0.109609	−0.0548046	−	0.998497i	$-0.517454\pi$
$241$	−1.70159	−0.109609	−0.0548046	+	0.998497i	$0.517454\pi$
$242$	−49.8317	−3.20330
$243$	1.00000	0.0641500
$244$	−4.83744	−0.309685
$245$	−2.40272	−0.153504
$246$	−14.6094	−0.931463
$247$	−1.39672	−0.0888709
$248$	5.17134	0.328380
$249$	11.9599	0.757929
$250$	21.8866	1.38423
$251$	15.9979	1.00978	0.504888	−	0.863185i	$-0.331534\pi$
$251$	15.9979	1.00978	0.504888	+	0.863185i	$0.331534\pi$
$252$	3.03951	0.191471
$253$	−44.7693	−2.81462
$254$	−18.7516	−1.17658
$255$	−1.68912	−0.105777
$256$	20.8411	1.30257
$257$	−12.5797	−0.784702	−0.392351	−	0.919816i	$-0.628338\pi$
$257$	−12.5797	−0.784702	−0.392351	+	0.919816i	$0.628338\pi$
$258$	10.3111	0.641944
$259$	−7.03938	−0.437406
$260$	−0.946396	−0.0586930
$261$	−3.18093	−0.196895
$262$	−29.3541	−1.81350
$263$	−15.3369	−0.945711	−0.472856	−	0.881140i	$-0.656777\pi$
$263$	−15.3369	−0.945711	−0.472856	+	0.881140i	$0.656777\pi$
$264$	−8.01920	−0.493548
$265$	−1.52434	−0.0936394
$266$	−13.7373	−0.842288
$267$	5.84912	0.357960
$268$	−9.23900	−0.564362
$269$	−19.8589	−1.21082	−0.605409	−	0.795915i	$-0.706990\pi$
$269$	−19.8589	−1.21082	−0.605409	+	0.795915i	$0.706990\pi$
$270$	−3.06240	−0.186372
$271$	−5.57613	−0.338725	−0.169363	−	0.985554i	$-0.554171\pi$
$271$	−5.57613	−0.338725	−0.169363	+	0.985554i	$0.554171\pi$
$272$	4.91762	0.298175
$273$	−1.02813	−0.0622255
$274$	−27.3368	−1.65148
$275$	13.3185	0.803133
$276$	9.28783	0.559062
$277$	−7.37334	−0.443021	−0.221510	−	0.975158i	$-0.571099\pi$
$277$	−7.37334	−0.443021	−0.221510	+	0.975158i	$0.571099\pi$
$278$	−10.7399	−0.644134
$279$	4.00056	0.239507
$280$	5.15661	0.308166
$281$	3.15015	0.187922	0.0939612	−	0.995576i	$-0.470047\pi$
$281$	3.15015	0.187922	0.0939612	+	0.995576i	$0.470047\pi$
$282$	−18.4648	−1.09956
$283$	−27.2726	−1.62119	−0.810594	−	0.585609i	$-0.800855\pi$
$283$	−27.2726	−1.62119	−0.810594	+	0.585609i	$0.800855\pi$
$284$	13.8553	0.822159
$285$	5.41927	0.321010
$286$	−4.89642	−0.289531
$287$	19.0306	1.12334
$288$	6.33040	0.373023
$289$	1.00000	0.0588235
$290$	9.74128	0.572028
$291$	6.74716	0.395526
$292$	5.78721	0.338671
$293$	25.5914	1.49507	0.747534	−	0.664223i	$-0.231238\pi$
$293$	25.5914	1.49507	0.747534	+	0.664223i	$0.231238\pi$
$294$	2.57895	0.150408
$295$	−7.57218	−0.440869
$296$	−3.85297	−0.223949
$297$	−6.20367	−0.359974
$298$	−17.0629	−0.988429
$299$	−3.14166	−0.181687
$300$	−2.76304	−0.159524
$301$	−13.4316	−0.774184
$302$	28.4511	1.63718
$303$	−17.3624	−0.997443
$304$	−15.7774	−0.904894
$305$	−6.34883	−0.363533
$306$	1.81301	0.103643
$307$	−13.7890	−0.786981	−0.393491	−	0.919329i	$-0.628733\pi$
$307$	−13.7890	−0.786981	−0.393491	+	0.919329i	$0.628733\pi$
$308$	−18.8562	−1.07443
$309$	−0.489124	−0.0278253
$310$	−12.2513	−0.695828
$311$	3.07139	0.174163	0.0870813	−	0.996201i	$-0.472246\pi$
$311$	3.07139	0.174163	0.0870813	+	0.996201i	$0.472246\pi$
$312$	−0.562744	−0.0318591
$313$	−27.4529	−1.55173	−0.775865	−	0.630898i	$-0.782686\pi$
$313$	−27.4529	−1.55173	−0.775865	+	0.630898i	$0.782686\pi$
$314$	1.81301	0.102314
$315$	3.98917	0.224764
$316$	−7.91090	−0.445023
$317$	2.54043	0.142685	0.0713424	−	0.997452i	$-0.477272\pi$
$317$	2.54043	0.142685	0.0713424	+	0.997452i	$0.477272\pi$
$318$	1.63614	0.0917503
$319$	19.7335	1.10486
$320$	−2.77330	−0.155032
$321$	0.439465	0.0245286
$322$	−30.8996	−1.72197
$323$	−3.20833	−0.178516
$324$	1.28701	0.0715008
$325$	0.934616	0.0518432
$326$	−28.9262	−1.60208
$327$	7.55340	0.417704
$328$	10.4163	0.575145
$329$	24.0527	1.32607
$330$	18.9981	1.04581
$331$	4.65560	0.255895	0.127948	−	0.991781i	$-0.459161\pi$
$331$	4.65560	0.255895	0.127948	+	0.991781i	$0.459161\pi$
$332$	15.3926	0.844777
$333$	−2.98067	−0.163340
$334$	−15.2416	−0.833984
$335$	−12.1256	−0.662492
$336$	−11.6139	−0.633588
$337$	2.77333	0.151073	0.0755365	−	0.997143i	$-0.475933\pi$
$337$	2.77333	0.151073	0.0755365	+	0.997143i	$0.475933\pi$
$338$	23.2256	1.26330
$339$	1.95525	0.106195
$340$	−2.17392	−0.117898
$341$	−24.8182	−1.34398
$342$	−5.81675	−0.314534
$343$	−19.8912	−1.07402
$344$	−7.35171	−0.396378
$345$	12.1897	0.656270
$346$	26.9048	1.44641
$347$	−21.3879	−1.14816	−0.574082	−	0.818798i	$-0.694641\pi$
$347$	−21.3879	−1.14816	−0.574082	+	0.818798i	$0.694641\pi$
$348$	−4.09390	−0.219456
$349$	26.4099	1.41369	0.706845	−	0.707369i	$-0.250118\pi$
$349$	26.4099	1.41369	0.706845	+	0.707369i	$0.250118\pi$
$350$	9.19235	0.491352
$351$	−0.435340	−0.0232367
$352$	−39.2718	−2.09319
$353$	7.26229	0.386533	0.193266	−	0.981146i	$-0.438092\pi$
$353$	7.26229	0.386533	0.193266	+	0.981146i	$0.438092\pi$
$354$	8.12757	0.431975
$355$	18.1841	0.965114
$356$	7.52789	0.398977
$357$	−2.36168	−0.124993
$358$	−22.1324	−1.16974
$359$	34.1313	1.80138	0.900690	−	0.434461i	$-0.143061\pi$
$359$	34.1313	1.80138	0.900690	+	0.434461i	$0.143061\pi$
$360$	2.18345	0.115078
$361$	−8.70660	−0.458242
$362$	−40.4332	−2.12512
$363$	27.4856	1.44262
$364$	−1.32322	−0.0693557
$365$	7.59534	0.397558
$366$	6.81449	0.356199
$367$	−35.2173	−1.83833	−0.919163	−	0.393877i	$-0.871134\pi$
$367$	−35.2173	−1.83833	−0.919163	+	0.393877i	$0.871134\pi$
$368$	−35.4884	−1.84996
$369$	8.05809	0.419488
$370$	9.12799	0.474542
$371$	−2.13128	−0.110651
$372$	5.14878	0.266952
$373$	24.0681	1.24620	0.623101	−	0.782142i	$-0.285873\pi$
$373$	24.0681	1.24620	0.623101	+	0.782142i	$0.285873\pi$
$374$	−11.2473	−0.581586
$375$	−12.0719	−0.623392
$376$	13.1651	0.678941
$377$	1.38479	0.0713201
$378$	−4.28175	−0.220230
$379$	9.18168	0.471631	0.235816	−	0.971798i	$-0.424224\pi$
$379$	9.18168	0.471631	0.235816	+	0.971798i	$0.424224\pi$
$380$	6.97467	0.357793
$381$	10.3428	0.529876
$382$	−20.1805	−1.03253
$383$	21.7432	1.11103	0.555513	−	0.831508i	$-0.312522\pi$
$383$	21.7432	1.11103	0.555513	+	0.831508i	$0.312522\pi$
$384$	−9.68411	−0.494190
$385$	−24.7475	−1.26125
$386$	−26.3374	−1.34054
$387$	−5.68730	−0.289102
$388$	8.68369	0.440848
$389$	6.62279	0.335789	0.167894	−	0.985805i	$-0.446303\pi$
$389$	6.62279	0.335789	0.167894	+	0.985805i	$0.446303\pi$
$390$	1.33319	0.0675084
$391$	−7.21657	−0.364958
$392$	−1.83876	−0.0928713
$393$	16.1908	0.816717
$394$	−16.8092	−0.846834
$395$	−10.3826	−0.522403
$396$	−7.98421	−0.401222
$397$	−18.1439	−0.910616	−0.455308	−	0.890334i	$-0.650471\pi$
$397$	−18.1439	−0.910616	−0.455308	+	0.890334i	$0.650471\pi$
$398$	−20.3926	−1.02219
$399$	7.57706	0.379327
$400$	10.5575	0.527874
$401$	−5.33152	−0.266243	−0.133122	−	0.991100i	$-0.542500\pi$
$401$	−5.33152	−0.266243	−0.133122	+	0.991100i	$0.542500\pi$
$402$	13.0150	0.649127
$403$	−1.74160	−0.0867555
$404$	−22.3456	−1.11174
$405$	1.68912	0.0839332
$406$	13.6200	0.675947
$407$	18.4911	0.916569
$408$	−1.29265	−0.0639959
$409$	15.5200	0.767415	0.383708	−	0.923455i	$-0.374647\pi$
$409$	15.5200	0.767415	0.383708	+	0.923455i	$0.374647\pi$
$410$	−24.6771	−1.21872
$411$	15.0781	0.743748
$412$	−0.629510	−0.0310137
$413$	−10.5872	−0.520962
$414$	−13.0837	−0.643031
$415$	20.2018	0.991665
$416$	−2.75588	−0.135118
$417$	5.92376	0.290088
$418$	36.0852	1.76499
$419$	2.60819	0.127419	0.0637093	−	0.997969i	$-0.479707\pi$
$419$	2.60819	0.127419	0.0637093	+	0.997969i	$0.479707\pi$
$420$	5.13411	0.250519
$421$	−10.9463	−0.533491	−0.266745	−	0.963767i	$-0.585948\pi$
$421$	−10.9463	−0.533491	−0.266745	+	0.963767i	$0.585948\pi$
$422$	36.2031	1.76234
$423$	10.1846	0.495192
$424$	−1.16655	−0.0566525
$425$	2.14687	0.104138
$426$	−19.5179	−0.945644
$427$	−8.87674	−0.429576
$428$	0.565598	0.0273392
$429$	2.70071	0.130391
$430$	17.4168	0.839912
$431$	13.7213	0.660929	0.330465	−	0.943818i	$-0.392795\pi$
$431$	13.7213	0.660929	0.330465	+	0.943818i	$0.392795\pi$
$432$	−4.91762	−0.236599
$433$	1.19462	0.0574098	0.0287049	−	0.999588i	$-0.490862\pi$
$433$	1.19462	0.0574098	0.0287049	+	0.999588i	$0.490862\pi$
$434$	−17.1294	−0.822238
$435$	−5.37298	−0.257615
$436$	9.72133	0.465567
$437$	23.1532	1.10757
$438$	−8.15243	−0.389538
$439$	22.6893	1.08290	0.541450	−	0.840733i	$-0.317876\pi$
$439$	22.6893	1.08290	0.541450	+	0.840733i	$0.317876\pi$
$440$	−13.5454	−0.645752
$441$	−1.42247	−0.0677366
$442$	−0.789277	−0.0375421
$443$	−24.5746	−1.16757	−0.583787	−	0.811907i	$-0.698430\pi$
$443$	−24.5746	−1.16757	−0.583787	+	0.811907i	$0.698430\pi$
$444$	−3.83616	−0.182056
$445$	9.87987	0.468351
$446$	−37.8844	−1.79388
$447$	9.41137	0.445142
$448$	−3.87754	−0.183196
$449$	−9.27282	−0.437611	−0.218806	−	0.975768i	$-0.570216\pi$
$449$	−9.27282	−0.437611	−0.218806	+	0.975768i	$0.570216\pi$
$450$	3.89229	0.183484
$451$	−49.9898	−2.35393
$452$	2.51643	0.118363
$453$	−15.6927	−0.737310
$454$	40.3672	1.89453
$455$	−1.73664	−0.0814151
$456$	4.14726	0.194213
$457$	−10.5220	−0.492198	−0.246099	−	0.969245i	$-0.579149\pi$
$457$	−10.5220	−0.492198	−0.246099	+	0.969245i	$0.579149\pi$
$458$	7.34788	0.343344
$459$	−1.00000	−0.0466760
$460$	15.6883	0.731470
$461$	−4.89350	−0.227913	−0.113956	−	0.993486i	$-0.536352\pi$
$461$	−4.89350	−0.227913	−0.113956	+	0.993486i	$0.536352\pi$
$462$	26.5626	1.23580
$463$	−10.0498	−0.467052	−0.233526	−	0.972351i	$-0.575026\pi$
$463$	−10.0498	−0.467052	−0.233526	+	0.972351i	$0.575026\pi$
$464$	15.6426	0.726190
$465$	6.75744	0.313369
$466$	−12.4727	−0.577787
$467$	22.8881	1.05913	0.529567	−	0.848268i	$-0.322354\pi$
$467$	22.8881	1.05913	0.529567	+	0.848268i	$0.322354\pi$
$468$	−0.560288	−0.0258993
$469$	−16.9536	−0.782846
$470$	−31.1893	−1.43866
$471$	−1.00000	−0.0460776
$472$	−5.79485	−0.266729
$473$	35.2822	1.62228
$474$	11.1441	0.511864
$475$	−6.88786	−0.316037
$476$	−3.03951	−0.139316
$477$	−0.902444	−0.0413201
$478$	−48.6280	−2.22419
$479$	42.0743	1.92242	0.961212	−	0.275811i	$-0.0889463\pi$
$479$	42.0743	1.92242	0.961212	+	0.275811i	$0.0889463\pi$
$480$	10.6928	0.488059
$481$	1.29760	0.0591656
$482$	3.08501	0.140518
$483$	17.0432	0.775494
$484$	35.3743	1.60792
$485$	11.3968	0.517501
$486$	−1.81301	−0.0822399
$487$	34.7372	1.57409	0.787047	−	0.616893i	$-0.211609\pi$
$487$	34.7372	1.57409	0.787047	+	0.616893i	$0.211609\pi$
$488$	−4.85864	−0.219940
$489$	15.9548	0.721501
$490$	4.35617	0.196792
$491$	−0.453529	−0.0204675	−0.0102337	−	0.999948i	$-0.503258\pi$
$491$	−0.453529	−0.0204675	−0.0102337	+	0.999948i	$0.503258\pi$
$492$	10.3709	0.467555
$493$	3.18093	0.143262
$494$	2.53226	0.113932
$495$	−10.4788	−0.470985
$496$	−19.6732	−0.883355
$497$	25.4245	1.14045
$498$	−21.6835	−0.971659
$499$	−5.43453	−0.243283	−0.121642	−	0.992574i	$-0.538816\pi$
$499$	−5.43453	−0.243283	−0.121642	+	0.992574i	$0.538816\pi$
$500$	−15.5367	−0.694824
$501$	8.40679	0.375588
$502$	−29.0043	−1.29453
$503$	13.7820	0.614508	0.307254	−	0.951628i	$-0.400590\pi$
$503$	13.7820	0.614508	0.307254	+	0.951628i	$0.400590\pi$
$504$	3.05283	0.135984
$505$	−29.3272	−1.30504
$506$	81.1672	3.60832
$507$	−12.8105	−0.568933
$508$	13.3113	0.590593
$509$	19.5883	0.868238	0.434119	−	0.900855i	$-0.357060\pi$
$509$	19.5883	0.868238	0.434119	+	0.900855i	$0.357060\pi$
$510$	3.06240	0.135605
$511$	10.6196	0.469782
$512$	−18.4170	−0.813923
$513$	3.20833	0.141651
$514$	22.8072	1.00598
$515$	−0.826191	−0.0364063
$516$	−7.31963	−0.322229
$517$	−63.1819	−2.77874
$518$	12.7625	0.560751
$519$	−14.8399	−0.651398
$520$	−0.950543	−0.0416841
$521$	30.9068	1.35405	0.677026	−	0.735959i	$-0.263269\pi$
$521$	30.9068	1.35405	0.677026	+	0.735959i	$0.263269\pi$
$522$	5.76706	0.252418
$523$	−21.8651	−0.956092	−0.478046	−	0.878335i	$-0.658655\pi$
$523$	−21.8651	−0.956092	−0.478046	+	0.878335i	$0.658655\pi$
$524$	20.8378	0.910301
$525$	−5.07021	−0.221282
$526$	27.8059	1.21240
$527$	−4.00056	−0.174267
$528$	30.5073	1.32766
$529$	29.0789	1.26430
$530$	2.76364	0.120045
$531$	−4.48291	−0.194542
$532$	9.75177	0.422793
$533$	−3.50801	−0.151949
$534$	−10.6045	−0.458902
$535$	0.742311	0.0320929
$536$	−9.27949	−0.400813
$537$	12.2076	0.526795
$538$	36.0044	1.55226
$539$	8.82453	0.380099
$540$	2.17392	0.0935508
$541$	−3.37057	−0.144912	−0.0724561	−	0.997372i	$-0.523084\pi$
$541$	−3.37057	−0.144912	−0.0724561	+	0.997372i	$0.523084\pi$
$542$	10.1096	0.434244
$543$	22.3017	0.957057
$544$	−6.33040	−0.271414
$545$	12.7586	0.546519
$546$	1.86402	0.0797726
$547$	6.94781	0.297067	0.148533	−	0.988907i	$-0.452545\pi$
$547$	6.94781	0.297067	0.148533	+	0.988907i	$0.452545\pi$
$548$	19.4057	0.828971
$549$	−3.75865	−0.160415
$550$	−24.1465	−1.02961
$551$	−10.2055	−0.434768
$552$	9.32853	0.397049
$553$	−14.5166	−0.617307
$554$	13.3679	0.567950
$555$	−5.03471	−0.213712
$556$	7.62396	0.323328
$557$	−3.48023	−0.147462	−0.0737310	−	0.997278i	$-0.523491\pi$
$557$	−3.48023	−0.147462	−0.0737310	+	0.997278i	$0.523491\pi$
$558$	−7.25307	−0.307047
$559$	2.47591	0.104720
$560$	−19.6172	−0.828979
$561$	6.20367	0.261919
$562$	−5.71127	−0.240915
$563$	−39.6364	−1.67048	−0.835238	−	0.549888i	$-0.814670\pi$
$563$	−39.6364	−1.67048	−0.835238	+	0.549888i	$0.814670\pi$
$564$	13.1077	0.551934
$565$	3.30266	0.138944
$566$	49.4456	2.07835
$567$	2.36168	0.0991812
$568$	13.9160	0.583901
$569$	17.3154	0.725901	0.362951	−	0.931808i	$-0.381769\pi$
$569$	17.3154	0.725901	0.362951	+	0.931808i	$0.381769\pi$
$570$	−9.82520	−0.411532
$571$	−29.1142	−1.21839	−0.609196	−	0.793020i	$-0.708508\pi$
$571$	−29.1142	−1.21839	−0.609196	+	0.793020i	$0.708508\pi$
$572$	3.47585	0.145332
$573$	11.1309	0.465002
$574$	−34.5028	−1.44012
$575$	−15.4930	−0.646103
$576$	−1.64186	−0.0684106
$577$	−28.3167	−1.17884	−0.589419	−	0.807827i	$-0.700643\pi$
$577$	−28.3167	−1.17884	−0.589419	+	0.807827i	$0.700643\pi$
$578$	−1.81301	−0.0754114
$579$	14.5269	0.603716
$580$	−6.91510	−0.287134
$581$	28.2455	1.17182
$582$	−12.2327	−0.507061
$583$	5.59847	0.231865
$584$	5.81257	0.240526
$585$	−0.735343	−0.0304027
$586$	−46.3976	−1.91667
$587$	2.53907	0.104799	0.0523993	−	0.998626i	$-0.483313\pi$
$587$	2.53907	0.104799	0.0523993	+	0.998626i	$0.483313\pi$
$588$	−1.83074	−0.0754983
$589$	12.8351	0.528862
$590$	13.7285	0.565192
$591$	9.27140	0.381375
$592$	14.6578	0.602432
$593$	22.4538	0.922068	0.461034	−	0.887382i	$-0.347479\pi$
$593$	22.4538	0.922068	0.461034	+	0.887382i	$0.347479\pi$
$594$	11.2473	0.461484
$595$	−3.98917	−0.163540
$596$	12.1126	0.496150
$597$	11.2479	0.460346
$598$	5.69587	0.232922
$599$	−16.2938	−0.665746	−0.332873	−	0.942972i	$-0.608018\pi$
$599$	−16.2938	−0.665746	−0.332873	+	0.942972i	$0.608018\pi$
$600$	−2.77515	−0.113295
$601$	15.3188	0.624865	0.312433	−	0.949940i	$-0.398856\pi$
$601$	15.3188	0.624865	0.312433	+	0.949940i	$0.398856\pi$
$602$	24.3516	0.992498
$603$	−7.17864	−0.292337
$604$	−20.1968	−0.821795
$605$	46.4265	1.88751
$606$	31.4782	1.27871
$607$	16.6630	0.676328	0.338164	−	0.941087i	$-0.390194\pi$
$607$	16.6630	0.676328	0.338164	+	0.941087i	$0.390194\pi$
$608$	20.3100	0.823681
$609$	−7.51234	−0.304415
$610$	11.5105	0.466047
$611$	−4.43376	−0.179371
$612$	−1.28701	−0.0520244
$613$	12.2508	0.494805	0.247403	−	0.968913i	$-0.420423\pi$
$613$	12.2508	0.494805	0.247403	+	0.968913i	$0.420423\pi$
$614$	24.9997	1.00890
$615$	13.6111	0.548853
$616$	−18.9388	−0.763065
$617$	−0.245963	−0.00990210	−0.00495105	−	0.999988i	$-0.501576\pi$
$617$	−0.245963	−0.00990210	−0.00495105	+	0.999988i	$0.501576\pi$
$618$	0.886788	0.0356719
$619$	−1.30902	−0.0526139	−0.0263070	−	0.999654i	$-0.508375\pi$
$619$	−1.30902	−0.0526139	−0.0263070	+	0.999654i	$0.508375\pi$
$620$	8.69691	0.349276
$621$	7.21657	0.289591
$622$	−5.56847	−0.223275
$623$	13.8137	0.553436
$624$	2.14084	0.0857021
$625$	−9.65664	−0.386266
$626$	49.7725	1.98931
$627$	−19.9035	−0.794867
$628$	−1.28701	−0.0513574
$629$	2.98067	0.118847
$630$	−7.23241	−0.288146
$631$	−17.3911	−0.692327	−0.346164	−	0.938174i	$-0.612516\pi$
$631$	−17.3911	−0.692327	−0.346164	+	0.938174i	$0.612516\pi$
$632$	−7.94557	−0.316058
$633$	−19.9685	−0.793677
$634$	−4.60584	−0.182921
$635$	17.4702	0.693284
$636$	−1.16146	−0.0460548
$637$	0.619257	0.0245359
$638$	−35.7770	−1.41642
$639$	10.7654	0.425874
$640$	−16.3576	−0.646593
$641$	−16.1341	−0.637259	−0.318630	−	0.947879i	$-0.603223\pi$
$641$	−16.1341	−0.637259	−0.318630	+	0.947879i	$0.603223\pi$
$642$	−0.796756	−0.0314455
$643$	33.4928	1.32083	0.660414	−	0.750901i	$-0.270381\pi$
$643$	33.4928	1.32083	0.660414	+	0.750901i	$0.270381\pi$
$644$	21.9349	0.864355
$645$	−9.60655	−0.378257
$646$	5.81675	0.228857
$647$	13.8592	0.544863	0.272431	−	0.962175i	$-0.412172\pi$
$647$	13.8592	0.544863	0.272431	+	0.962175i	$0.412172\pi$
$648$	1.29265	0.0507802
$649$	27.8105	1.09166
$650$	−1.69447	−0.0664626
$651$	9.44804	0.370298
$652$	20.5340	0.804175
$653$	−34.9125	−1.36623	−0.683117	−	0.730309i	$-0.739376\pi$
$653$	−34.9125	−1.36623	−0.683117	+	0.730309i	$0.739376\pi$
$654$	−13.6944	−0.535494
$655$	27.3482	1.06858
$656$	−39.6267	−1.54716
$657$	4.49662	0.175430
$658$	−43.6079	−1.70001
$659$	33.2033	1.29342	0.646709	−	0.762736i	$-0.276145\pi$
$659$	33.2033	1.29342	0.646709	+	0.762736i	$0.276145\pi$
$660$	−13.4863	−0.524954
$661$	0.912043	0.0354744	0.0177372	−	0.999843i	$-0.494354\pi$
$661$	0.912043	0.0354744	0.0177372	+	0.999843i	$0.494354\pi$
$662$	−8.44066	−0.328056
$663$	0.435340	0.0169072
$664$	15.4600	0.599965
$665$	12.7986	0.496307
$666$	5.40398	0.209400
$667$	−22.9554	−0.888837
$668$	10.8197	0.418625
$669$	20.8958	0.807879
$670$	21.9839	0.849310
$671$	23.3175	0.900161
$672$	14.9504	0.576724
$673$	−12.7975	−0.493309	−0.246655	−	0.969103i	$-0.579331\pi$
$673$	−12.7975	−0.493309	−0.246655	+	0.969103i	$0.579331\pi$
$674$	−5.02809	−0.193675
$675$	−2.14687	−0.0826329
$676$	−16.4873	−0.634125
$677$	−40.0839	−1.54055	−0.770274	−	0.637713i	$-0.779881\pi$
$677$	−40.0839	−1.54055	−0.770274	+	0.637713i	$0.779881\pi$
$678$	−3.54489	−0.136141
$679$	15.9346	0.611515
$680$	−2.18345	−0.0837315
$681$	−22.2653	−0.853207
$682$	44.9957	1.72297
$683$	−31.3932	−1.20123	−0.600614	−	0.799539i	$-0.705077\pi$
$683$	−31.3932	−1.20123	−0.600614	+	0.799539i	$0.705077\pi$
$684$	4.12917	0.157883
$685$	25.4688	0.973111
$686$	36.0629	1.37689
$687$	−4.05286	−0.154626
$688$	27.9680	1.06627
$689$	0.392870	0.0149672
$690$	−22.1000	−0.841334
$691$	14.0581	0.534796	0.267398	−	0.963586i	$-0.413836\pi$
$691$	14.0581	0.534796	0.267398	+	0.963586i	$0.413836\pi$
$692$	−19.0991	−0.726039
$693$	−14.6511	−0.556549
$694$	38.7766	1.47194
$695$	10.0060	0.379548
$696$	−4.11184	−0.155859
$697$	−8.05809	−0.305222
$698$	−47.8815	−1.81234
$699$	6.87955	0.260209
$700$	−6.52543	−0.246638
$701$	22.4115	0.846471	0.423236	−	0.906020i	$-0.360894\pi$
$701$	22.4115	0.846471	0.423236	+	0.906020i	$0.360894\pi$
$702$	0.789277	0.0297893
$703$	−9.56297	−0.360674
$704$	10.1855	0.383882
$705$	17.2030	0.647903
$706$	−13.1666	−0.495533
$707$	−41.0044	−1.54213
$708$	−5.76956	−0.216833
$709$	−23.1686	−0.870114	−0.435057	−	0.900403i	$-0.643272\pi$
$709$	−23.1686	−0.870114	−0.435057	+	0.900403i	$0.643272\pi$
$710$	−32.9681	−1.23727
$711$	−6.14671	−0.230520
$712$	7.56088	0.283356
$713$	28.8703	1.08120
$714$	4.28175	0.160241
$715$	4.56183	0.170603
$716$	15.7113	0.587158
$717$	26.8217	1.00167
$718$	−61.8805	−2.30936
$719$	30.6361	1.14253	0.571267	−	0.820764i	$-0.306452\pi$
$719$	30.6361	1.14253	0.571267	+	0.820764i	$0.306452\pi$
$720$	−8.30647	−0.309564
$721$	−1.15515	−0.0430202
$722$	15.7852	0.587463
$723$	−1.70159	−0.0632829
$724$	28.7026	1.06672
$725$	6.82903	0.253624
$726$	−49.8317	−1.84943
$727$	−31.0050	−1.14991	−0.574957	−	0.818184i	$-0.694981\pi$
$727$	−31.0050	−1.14991	−0.574957	+	0.818184i	$0.694981\pi$
$728$	−1.32902	−0.0492568
$729$	1.00000	0.0370370
$730$	−13.7704	−0.509667
$731$	5.68730	0.210352
$732$	−4.83744	−0.178797
$733$	48.0312	1.77407	0.887037	−	0.461698i	$-0.152760\pi$
$733$	48.0312	1.77407	0.887037	+	0.461698i	$0.152760\pi$
$734$	63.8493	2.35672
$735$	−2.40272	−0.0886258
$736$	45.6838	1.68393
$737$	44.5339	1.64043
$738$	−14.6094	−0.537780
$739$	4.09642	0.150689	0.0753447	−	0.997158i	$-0.475994\pi$
$739$	4.09642	0.150689	0.0753447	+	0.997158i	$0.475994\pi$
$740$	−6.47974	−0.238200
$741$	−1.39672	−0.0513096
$742$	3.86404	0.141853
$743$	−30.0944	−1.10406	−0.552028	−	0.833825i	$-0.686146\pi$
$743$	−30.0944	−1.10406	−0.552028	+	0.833825i	$0.686146\pi$
$744$	5.17134	0.189590
$745$	15.8970	0.582419
$746$	−43.6358	−1.59762
$747$	11.9599	0.437590
$748$	7.98421	0.291932
$749$	1.03788	0.0379232
$750$	21.8866	0.799184
$751$	8.90380	0.324904	0.162452	−	0.986716i	$-0.448060\pi$
$751$	8.90380	0.324904	0.162452	+	0.986716i	$0.448060\pi$
$752$	−50.0840	−1.82638
$753$	15.9979	0.582995
$754$	−2.51063	−0.0914319
$755$	−26.5070	−0.964688
$756$	3.03951	0.110546
$757$	22.9007	0.832340	0.416170	−	0.909287i	$-0.363372\pi$
$757$	22.9007	0.832340	0.416170	+	0.909287i	$0.363372\pi$
$758$	−16.6465	−0.604628
$759$	−44.7693	−1.62502
$760$	7.00523	0.254107
$761$	−27.7246	−1.00501	−0.502507	−	0.864573i	$-0.667589\pi$
$761$	−27.7246	−1.00501	−0.502507	+	0.864573i	$0.667589\pi$
$762$	−18.7516	−0.679298
$763$	17.8387	0.645805
$764$	14.3257	0.518285
$765$	−1.68912	−0.0610704
$766$	−39.4207	−1.42433
$767$	1.95159	0.0704678
$768$	20.8411	0.752039
$769$	11.4164	0.411687	0.205844	−	0.978585i	$-0.434006\pi$
$769$	11.4164	0.411687	0.205844	+	0.978585i	$0.434006\pi$
$770$	44.8675	1.61691
$771$	−12.5797	−0.453048
$772$	18.6963	0.672894
$773$	5.22466	0.187918	0.0939589	−	0.995576i	$-0.470048\pi$
$773$	5.22466	0.187918	0.0939589	+	0.995576i	$0.470048\pi$
$774$	10.3111	0.370627
$775$	−8.58866	−0.308514
$776$	8.72174	0.313092
$777$	−7.03938	−0.252536
$778$	−12.0072	−0.430479
$779$	25.8531	0.926282
$780$	−0.946396	−0.0338864
$781$	−66.7853	−2.38976
$782$	13.0837	0.467874
$783$	−3.18093	−0.113677
$784$	6.99516	0.249827
$785$	−1.68912	−0.0602874
$786$	−29.3541	−1.04703
$787$	−13.2429	−0.472059	−0.236029	−	0.971746i	$-0.575846\pi$
$787$	−13.2429	−0.472059	−0.236029	+	0.971746i	$0.575846\pi$
$788$	11.9324	0.425075
$789$	−15.3369	−0.546007
$790$	18.8237	0.669717
$791$	4.61767	0.164186
$792$	−8.01920	−0.284950
$793$	1.63629	0.0581065
$794$	32.8951	1.16740
$795$	−1.52434	−0.0540627
$796$	14.4762	0.513095
$797$	29.7622	1.05423	0.527115	−	0.849794i	$-0.323274\pi$
$797$	29.7622	1.05423	0.527115	+	0.849794i	$0.323274\pi$
$798$	−13.7373	−0.486295
$799$	−10.1846	−0.360305
$800$	−13.5905	−0.480498
$801$	5.84912	0.206668
$802$	9.66611	0.341322
$803$	−27.8956	−0.984413
$804$	−9.23900	−0.325834
$805$	28.7881	1.01465
$806$	3.15755	0.111220
$807$	−19.8589	−0.699066
$808$	−22.4435	−0.789561
$809$	−44.2883	−1.55709	−0.778546	−	0.627587i	$-0.784043\pi$
$809$	−44.2883	−1.55709	−0.778546	+	0.627587i	$0.784043\pi$
$810$	−3.06240	−0.107602
$811$	−26.2630	−0.922219	−0.461109	−	0.887343i	$-0.652548\pi$
$811$	−26.2630	−0.922219	−0.461109	+	0.887343i	$0.652548\pi$
$812$	−9.66848	−0.339297
$813$	−5.57613	−0.195563
$814$	−33.5246	−1.17504
$815$	26.9496	0.944003
$816$	4.91762	0.172151
$817$	−18.2468	−0.638373
$818$	−28.1380	−0.983821
$819$	−1.02813	−0.0359259
$820$	17.5177	0.611744
$821$	−6.43439	−0.224562	−0.112281	−	0.993677i	$-0.535816\pi$
$821$	−6.43439	−0.224562	−0.112281	+	0.993677i	$0.535816\pi$
$822$	−27.3368	−0.953480
$823$	−19.2389	−0.670626	−0.335313	−	0.942107i	$-0.608842\pi$
$823$	−19.2389	−0.670626	−0.335313	+	0.942107i	$0.608842\pi$
$824$	−0.632268	−0.0220261
$825$	13.3185	0.463689
$826$	19.1947	0.667869
$827$	−28.7321	−0.999113	−0.499556	−	0.866281i	$-0.666504\pi$
$827$	−28.7321	−0.999113	−0.499556	+	0.866281i	$0.666504\pi$
$828$	9.28783	0.322774
$829$	−34.6285	−1.20270	−0.601348	−	0.798987i	$-0.705370\pi$
$829$	−34.6285	−1.20270	−0.601348	+	0.798987i	$0.705370\pi$
$830$	−36.6260	−1.27131
$831$	−7.37334	−0.255778
$832$	0.714765	0.0247800
$833$	1.42247	0.0492856
$834$	−10.7399	−0.371891
$835$	14.2001	0.491415
$836$	−25.6160	−0.885948
$837$	4.00056	0.138280
$838$	−4.72869	−0.163350
$839$	19.9491	0.688720	0.344360	−	0.938838i	$-0.388096\pi$
$839$	19.9491	0.688720	0.344360	+	0.938838i	$0.388096\pi$
$840$	5.15661	0.177920
$841$	−18.8817	−0.651093
$842$	19.8458	0.683932
$843$	3.15015	0.108497
$844$	−25.6997	−0.884621
$845$	−21.6385	−0.744386
$846$	−18.4648	−0.634833
$847$	64.9121	2.23041
$848$	4.43788	0.152397
$849$	−27.2726	−0.935993
$850$	−3.89229	−0.133505
$851$	−21.5102	−0.737360
$852$	13.8553	0.474674
$853$	47.7424	1.63467	0.817334	−	0.576164i	$-0.195451\pi$
$853$	47.7424	1.63467	0.817334	+	0.576164i	$0.195451\pi$
$854$	16.0936	0.550713
$855$	5.41927	0.185335
$856$	0.568076	0.0194164
$857$	−11.5932	−0.396015	−0.198007	−	0.980201i	$-0.563447\pi$
$857$	−11.5932	−0.396015	−0.198007	+	0.980201i	$0.563447\pi$
$858$	−4.89642	−0.167161
$859$	15.1060	0.515410	0.257705	−	0.966224i	$-0.417034\pi$
$859$	15.1060	0.515410	0.257705	+	0.966224i	$0.417034\pi$
$860$	−12.3638	−0.421601
$861$	19.0306	0.648562
$862$	−24.8768	−0.847307
$863$	−10.1091	−0.344119	−0.172059	−	0.985087i	$-0.555042\pi$
$863$	−10.1091	−0.344119	−0.172059	+	0.985087i	$0.555042\pi$
$864$	6.33040	0.215365
$865$	−25.0663	−0.852281
$866$	−2.16586	−0.0735990
$867$	1.00000	0.0339618
$868$	12.1598	0.412729
$869$	38.1322	1.29355
$870$	9.74128	0.330260
$871$	3.12515	0.105892
$872$	9.76392	0.330648
$873$	6.74716	0.228357
$874$	−41.9770	−1.41989
$875$	−28.5100	−0.963815
$876$	5.78721	0.195532
$877$	50.6302	1.70966	0.854831	−	0.518907i	$-0.173661\pi$
$877$	50.6302	1.70966	0.854831	+	0.518907i	$0.173661\pi$
$878$	−41.1359	−1.38827
$879$	25.5914	0.863178
$880$	51.5306	1.73710
$881$	29.0294	0.978025	0.489013	−	0.872277i	$-0.337357\pi$
$881$	29.0294	0.978025	0.489013	+	0.872277i	$0.337357\pi$
$882$	2.57895	0.0868379
$883$	16.0566	0.540347	0.270173	−	0.962812i	$-0.412919\pi$
$883$	16.0566	0.540347	0.270173	+	0.962812i	$0.412919\pi$
$884$	0.560288	0.0188445
$885$	−7.57218	−0.254536
$886$	44.5541	1.49682
$887$	−7.91952	−0.265912	−0.132956	−	0.991122i	$-0.542447\pi$
$887$	−7.91952	−0.265912	−0.132956	+	0.991122i	$0.542447\pi$
$888$	−3.85297	−0.129297
$889$	24.4263	0.819232
$890$	−17.9123	−0.600423
$891$	−6.20367	−0.207831
$892$	26.8932	0.900451
$893$	32.6756	1.09345
$894$	−17.0629	−0.570670
$895$	20.6201	0.689252
$896$	−22.8708	−0.764058
$897$	−3.14166	−0.104897
$898$	16.8117	0.561015
$899$	−12.7255	−0.424419
$900$	−2.76304	−0.0921015
$901$	0.902444	0.0300648
$902$	90.6321	3.01772
$903$	−13.4316	−0.446975
$904$	2.52746	0.0840621
$905$	37.6703	1.25220
$906$	28.4511	0.945226
$907$	−21.6702	−0.719548	−0.359774	−	0.933040i	$-0.617146\pi$
$907$	−21.6702	−0.719548	−0.359774	+	0.933040i	$0.617146\pi$
$908$	−28.6557	−0.950972
$909$	−17.3624	−0.575874
$910$	3.14856	0.104374
$911$	24.6941	0.818153	0.409077	−	0.912500i	$-0.365851\pi$
$911$	24.6941	0.818153	0.409077	+	0.912500i	$0.365851\pi$
$912$	−15.7774	−0.522441
$913$	−74.1954	−2.45551
$914$	19.0765	0.630994
$915$	−6.34883	−0.209886
$916$	−5.21608	−0.172344
$917$	38.2374	1.26271
$918$	1.81301	0.0598383
$919$	−16.2225	−0.535132	−0.267566	−	0.963539i	$-0.586219\pi$
$919$	−16.2225	−0.535132	−0.267566	+	0.963539i	$0.586219\pi$
$920$	15.7570	0.519494
$921$	−13.7890	−0.454364
$922$	8.87197	0.292183
$923$	−4.68663	−0.154262
$924$	−18.8562	−0.620322
$925$	6.39909	0.210401
$926$	18.2203	0.598757
$927$	−0.489124	−0.0160649
$928$	−20.1366	−0.661015
$929$	11.8506	0.388807	0.194403	−	0.980922i	$-0.437723\pi$
$929$	11.8506	0.388807	0.194403	+	0.980922i	$0.437723\pi$
$930$	−12.2513	−0.401736
$931$	−4.56375	−0.149571
$932$	8.85408	0.290025
$933$	3.07139	0.100553
$934$	−41.4964	−1.35780
$935$	10.4788	0.342692
$936$	−0.562744	−0.0183938
$937$	−29.7770	−0.972773	−0.486386	−	0.873744i	$-0.661685\pi$
$937$	−29.7770	−0.972773	−0.486386	+	0.873744i	$0.661685\pi$
$938$	30.7372	1.00360
$939$	−27.4529	−0.895892
$940$	22.1405	0.722144
$941$	18.5025	0.603164	0.301582	−	0.953440i	$-0.402485\pi$
$941$	18.5025	0.603164	0.301582	+	0.953440i	$0.402485\pi$
$942$	1.81301	0.0590711
$943$	58.1518	1.89368
$944$	22.0453	0.717512
$945$	3.98917	0.129768
$946$	−63.9670	−2.07975
$947$	−44.3703	−1.44184	−0.720920	−	0.693018i	$-0.756281\pi$
$947$	−44.3703	−1.44184	−0.720920	+	0.693018i	$0.756281\pi$
$948$	−7.91090	−0.256934
$949$	−1.95756	−0.0635450
$950$	12.4878	0.405157
$951$	2.54043	0.0823792
$952$	−3.05283	−0.0989429
$953$	−3.21558	−0.104163	−0.0520814	−	0.998643i	$-0.516586\pi$
$953$	−3.21558	−0.104163	−0.0520814	+	0.998643i	$0.516586\pi$
$954$	1.63614	0.0529720
$955$	18.8015	0.608403
$956$	34.5199	1.11645
$957$	19.7335	0.637892
$958$	−76.2812	−2.46453
$959$	35.6096	1.14990
$960$	−2.77330	−0.0895077
$961$	−14.9955	−0.483726
$962$	−2.35257	−0.0758499
$963$	0.439465	0.0141616
$964$	−2.18997	−0.0705343
$965$	24.5377	0.789895
$966$	−30.8996	−0.994178
$967$	33.1268	1.06529	0.532643	−	0.846340i	$-0.321199\pi$
$967$	33.1268	1.06529	0.532643	+	0.846340i	$0.321199\pi$
$968$	35.5293	1.14196
$969$	−3.20833	−0.103067
$970$	−20.6625	−0.663433
$971$	−25.0481	−0.803833	−0.401917	−	0.915676i	$-0.631656\pi$
$971$	−25.0481	−0.803833	−0.401917	+	0.915676i	$0.631656\pi$
$972$	1.28701	0.0412810
$973$	13.9900	0.448500
$974$	−62.9790	−2.01798
$975$	0.934616	0.0299317
$976$	18.4836	0.591647
$977$	30.1996	0.966170	0.483085	−	0.875574i	$-0.339516\pi$
$977$	30.1996	0.966170	0.483085	+	0.875574i	$0.339516\pi$
$978$	−28.9262	−0.924959
$979$	−36.2860	−1.15971
$980$	−3.09234	−0.0987811
$981$	7.55340	0.241161
$982$	0.822253	0.0262392
$983$	−22.4588	−0.716324	−0.358162	−	0.933659i	$-0.616596\pi$
$983$	−22.4588	−0.716324	−0.358162	+	0.933659i	$0.616596\pi$
$984$	10.4163	0.332060
$985$	15.6605	0.498986
$986$	−5.76706	−0.183661
$987$	24.0527	0.765607
$988$	−1.79759	−0.0571890
$989$	−41.0428	−1.30509
$990$	18.9981	0.603800
$991$	17.7942	0.565253	0.282626	−	0.959230i	$-0.408794\pi$
$991$	17.7942	0.565253	0.282626	+	0.959230i	$0.408794\pi$
$992$	25.3252	0.804075
$993$	4.65560	0.147741
$994$	−46.0950	−1.46204
$995$	18.9991	0.602311
$996$	15.3926	0.487732
$997$	40.5617	1.28460	0.642301	−	0.766452i	$-0.277980\pi$
$997$	40.5617	1.28460	0.642301	+	0.766452i	$0.277980\pi$
$998$	9.85287	0.311887
$999$	−2.98067	−0.0943041

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8007.2.a.h.1.12	✓	56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8007.2.a.h.1.12	✓	56	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)

\(f(q)\)	\(=\)	\(q-1.81301 q^{2} +1.00000 q^{3} +1.28701 q^{4} +1.68912 q^{5} -1.81301 q^{6} +2.36168 q^{7} +1.29265 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.81301 q^{2} +1.00000 q^{3} +1.28701 q^{4} +1.68912 q^{5} -1.81301 q^{6} +2.36168 q^{7} +1.29265 q^{8} +1.00000 q^{9} -3.06240 q^{10} -6.20367 q^{11} +1.28701 q^{12} -0.435340 q^{13} -4.28175 q^{14} +1.68912 q^{15} -4.91762 q^{16} -1.00000 q^{17} -1.81301 q^{18} +3.20833 q^{19} +2.17392 q^{20} +2.36168 q^{21} +11.2473 q^{22} +7.21657 q^{23} +1.29265 q^{24} -2.14687 q^{25} +0.789277 q^{26} +1.00000 q^{27} +3.03951 q^{28} -3.18093 q^{29} -3.06240 q^{30} +4.00056 q^{31} +6.33040 q^{32} -6.20367 q^{33} +1.81301 q^{34} +3.98917 q^{35} +1.28701 q^{36} -2.98067 q^{37} -5.81675 q^{38} -0.435340 q^{39} +2.18345 q^{40} +8.05809 q^{41} -4.28175 q^{42} -5.68730 q^{43} -7.98421 q^{44} +1.68912 q^{45} -13.0837 q^{46} +10.1846 q^{47} -4.91762 q^{48} -1.42247 q^{49} +3.89229 q^{50} -1.00000 q^{51} -0.560288 q^{52} -0.902444 q^{53} -1.81301 q^{54} -10.4788 q^{55} +3.05283 q^{56} +3.20833 q^{57} +5.76706 q^{58} -4.48291 q^{59} +2.17392 q^{60} -3.75865 q^{61} -7.25307 q^{62} +2.36168 q^{63} -1.64186 q^{64} -0.735343 q^{65} +11.2473 q^{66} -7.17864 q^{67} -1.28701 q^{68} +7.21657 q^{69} -7.23241 q^{70} +10.7654 q^{71} +1.29265 q^{72} +4.49662 q^{73} +5.40398 q^{74} -2.14687 q^{75} +4.12917 q^{76} -14.6511 q^{77} +0.789277 q^{78} -6.14671 q^{79} -8.30647 q^{80} +1.00000 q^{81} -14.6094 q^{82} +11.9599 q^{83} +3.03951 q^{84} -1.68912 q^{85} +10.3111 q^{86} -3.18093 q^{87} -8.01920 q^{88} +5.84912 q^{89} -3.06240 q^{90} -1.02813 q^{91} +9.28783 q^{92} +4.00056 q^{93} -18.4648 q^{94} +5.41927 q^{95} +6.33040 q^{96} +6.74716 q^{97} +2.57895 q^{98} -6.20367 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q + 7 q^{2} + 56 q^{3} + 61 q^{4} + 17 q^{5} + 7 q^{6} + 5 q^{7} + 18 q^{8} + 56 q^{9}+O(q^{10}) \) 56 * q + 7 * q^2 + 56 * q^3 + 61 * q^4 + 17 * q^5 + 7 * q^6 + 5 * q^7 + 18 * q^8 + 56 * q^9	\( 56 q + 7 q^{2} + 56 q^{3} + 61 q^{4} + 17 q^{5} + 7 q^{6} + 5 q^{7} + 18 q^{8} + 56 q^{9} - 2 q^{10} + 35 q^{11} + 61 q^{12} + 8 q^{13} + 36 q^{14} + 17 q^{15} + 71 q^{16} - 56 q^{17} + 7 q^{18} - 2 q^{19} + 58 q^{20} + 5 q^{21} + 27 q^{22} + 40 q^{23} + 18 q^{24} + 85 q^{25} + 15 q^{26} + 56 q^{27} - 4 q^{28} + 41 q^{29} - 2 q^{30} + q^{31} + 43 q^{32} + 35 q^{33} - 7 q^{34} + 57 q^{35} + 61 q^{36} + 34 q^{37} + 52 q^{38} + 8 q^{39} + 14 q^{40} + 49 q^{41} + 36 q^{42} + 27 q^{43} + 66 q^{44} + 17 q^{45} + 10 q^{46} + 43 q^{47} + 71 q^{48} + 51 q^{49} + 30 q^{50} - 56 q^{51} - 7 q^{52} + 73 q^{53} + 7 q^{54} + 15 q^{55} + 118 q^{56} - 2 q^{57} - q^{58} + 53 q^{59} + 58 q^{60} + 15 q^{61} + 16 q^{62} + 5 q^{63} + 124 q^{64} + 107 q^{65} + 27 q^{66} + 20 q^{67} - 61 q^{68} + 40 q^{69} + 16 q^{70} + 56 q^{71} + 18 q^{72} + 49 q^{73} + 28 q^{74} + 85 q^{75} - 38 q^{76} + 50 q^{77} + 15 q^{78} - 4 q^{79} + 74 q^{80} + 56 q^{81} + 59 q^{82} + 35 q^{83} - 4 q^{84} - 17 q^{85} + 38 q^{86} + 41 q^{87} + 64 q^{88} + 66 q^{89} - 2 q^{90} + 5 q^{91} + 96 q^{92} + q^{93} - 12 q^{94} + 70 q^{95} + 43 q^{96} + 60 q^{97} + 26 q^{98} + 35 q^{99}+O(q^{100}) \) 56 * q + 7 * q^2 + 56 * q^3 + 61 * q^4 + 17 * q^5 + 7 * q^6 + 5 * q^7 + 18 * q^8 + 56 * q^9 - 2 * q^10 + 35 * q^11 + 61 * q^12 + 8 * q^13 + 36 * q^14 + 17 * q^15 + 71 * q^16 - 56 * q^17 + 7 * q^18 - 2 * q^19 + 58 * q^20 + 5 * q^21 + 27 * q^22 + 40 * q^23 + 18 * q^24 + 85 * q^25 + 15 * q^26 + 56 * q^27 - 4 * q^28 + 41 * q^29 - 2 * q^30 + q^31 + 43 * q^32 + 35 * q^33 - 7 * q^34 + 57 * q^35 + 61 * q^36 + 34 * q^37 + 52 * q^38 + 8 * q^39 + 14 * q^40 + 49 * q^41 + 36 * q^42 + 27 * q^43 + 66 * q^44 + 17 * q^45 + 10 * q^46 + 43 * q^47 + 71 * q^48 + 51 * q^49 + 30 * q^50 - 56 * q^51 - 7 * q^52 + 73 * q^53 + 7 * q^54 + 15 * q^55 + 118 * q^56 - 2 * q^57 - q^58 + 53 * q^59 + 58 * q^60 + 15 * q^61 + 16 * q^62 + 5 * q^63 + 124 * q^64 + 107 * q^65 + 27 * q^66 + 20 * q^67 - 61 * q^68 + 40 * q^69 + 16 * q^70 + 56 * q^71 + 18 * q^72 + 49 * q^73 + 28 * q^74 + 85 * q^75 - 38 * q^76 + 50 * q^77 + 15 * q^78 - 4 * q^79 + 74 * q^80 + 56 * q^81 + 59 * q^82 + 35 * q^83 - 4 * q^84 - 17 * q^85 + 38 * q^86 + 41 * q^87 + 64 * q^88 + 66 * q^89 - 2 * q^90 + 5 * q^91 + 96 * q^92 + q^93 - 12 * q^94 + 70 * q^95 + 43 * q^96 + 60 * q^97 + 26 * q^98 + 35 * q^99

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