LMFDB - Embedded newform 8007.2.a.c.1.16

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:	$1$
Dimension:	$39$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.16
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)

$f(q)$	$=$	$q-0.744255 q^{2} -1.00000 q^{3} -1.44608 q^{4} +1.71466 q^{5} +0.744255 q^{6} -3.69118 q^{7} +2.56477 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-0.744255 q^{2} -1.00000 q^{3} -1.44608 q^{4} +1.71466 q^{5} +0.744255 q^{6} -3.69118 q^{7} +2.56477 q^{8} +1.00000 q^{9} -1.27614 q^{10} -0.320749 q^{11} +1.44608 q^{12} -1.38308 q^{13} +2.74718 q^{14} -1.71466 q^{15} +0.983327 q^{16} +1.00000 q^{17} -0.744255 q^{18} -1.35980 q^{19} -2.47954 q^{20} +3.69118 q^{21} +0.238719 q^{22} +3.98938 q^{23} -2.56477 q^{24} -2.05994 q^{25} +1.02936 q^{26} -1.00000 q^{27} +5.33776 q^{28} +3.50363 q^{29} +1.27614 q^{30} +4.07488 q^{31} -5.86138 q^{32} +0.320749 q^{33} -0.744255 q^{34} -6.32912 q^{35} -1.44608 q^{36} -7.33472 q^{37} +1.01204 q^{38} +1.38308 q^{39} +4.39770 q^{40} -7.61449 q^{41} -2.74718 q^{42} +3.57511 q^{43} +0.463830 q^{44} +1.71466 q^{45} -2.96912 q^{46} -0.864286 q^{47} -0.983327 q^{48} +6.62484 q^{49} +1.53312 q^{50} -1.00000 q^{51} +2.00005 q^{52} -4.84145 q^{53} +0.744255 q^{54} -0.549975 q^{55} -9.46703 q^{56} +1.35980 q^{57} -2.60760 q^{58} +2.86767 q^{59} +2.47954 q^{60} +8.17485 q^{61} -3.03275 q^{62} -3.69118 q^{63} +2.39571 q^{64} -2.37151 q^{65} -0.238719 q^{66} +6.80250 q^{67} -1.44608 q^{68} -3.98938 q^{69} +4.71048 q^{70} -1.78505 q^{71} +2.56477 q^{72} +11.6859 q^{73} +5.45890 q^{74} +2.05994 q^{75} +1.96638 q^{76} +1.18394 q^{77} -1.02936 q^{78} -9.39936 q^{79} +1.68607 q^{80} +1.00000 q^{81} +5.66712 q^{82} +6.30017 q^{83} -5.33776 q^{84} +1.71466 q^{85} -2.66080 q^{86} -3.50363 q^{87} -0.822646 q^{88} +3.25502 q^{89} -1.27614 q^{90} +5.10520 q^{91} -5.76898 q^{92} -4.07488 q^{93} +0.643250 q^{94} -2.33159 q^{95} +5.86138 q^{96} +4.97859 q^{97} -4.93057 q^{98} -0.320749 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 39 q - 4 q^{2} - 39 q^{3} + 30 q^{4} - 3 q^{5} + 4 q^{6} - 5 q^{7} - 3 q^{8} + 39 q^{9}+O(q^{10}) $ 39 * q - 4 * q^2 - 39 * q^3 + 30 * q^4 - 3 * q^5 + 4 * q^6 - 5 * q^7 - 3 * q^8 + 39 * q^9	\( 39 q - 4 q^{2} - 39 q^{3} + 30 q^{4} - 3 q^{5} + 4 q^{6} - 5 q^{7} - 3 q^{8} + 39 q^{9} + 4 q^{10} + q^{11} - 30 q^{12} - 26 q^{13} - 4 q^{14} + 3 q^{15} + 8 q^{16} + 39 q^{17} - 4 q^{18} - 14 q^{19} - 14 q^{20} + 5 q^{21} - 17 q^{22} + 2 q^{23} + 3 q^{24} - 6 q^{25} - 17 q^{26} - 39 q^{27} - 14 q^{28} - 7 q^{29} - 4 q^{30} - q^{31} - 30 q^{32} - q^{33} - 4 q^{34} + q^{35} + 30 q^{36} - 24 q^{37} - 20 q^{38} + 26 q^{39} + 12 q^{40} + q^{41} + 4 q^{42} - 41 q^{43} - 2 q^{44} - 3 q^{45} - 6 q^{46} - 9 q^{47} - 8 q^{48} - 10 q^{49} - 9 q^{50} - 39 q^{51} - 37 q^{52} - 47 q^{53} + 4 q^{54} - 39 q^{55} + 8 q^{56} + 14 q^{57} - 27 q^{58} + 41 q^{59} + 14 q^{60} - 41 q^{61} + 36 q^{62} - 5 q^{63} - 47 q^{64} - 39 q^{65} + 17 q^{66} - 36 q^{67} + 30 q^{68} - 2 q^{69} - 52 q^{70} - 2 q^{71} - 3 q^{72} - 63 q^{73} - 6 q^{74} + 6 q^{75} - 34 q^{76} - 64 q^{77} + 17 q^{78} + 20 q^{79} - 28 q^{80} + 39 q^{81} - 37 q^{82} + 45 q^{83} + 14 q^{84} - 3 q^{85} + 32 q^{86} + 7 q^{87} + 6 q^{88} - 32 q^{89} + 4 q^{90} - 11 q^{91} + 28 q^{92} + q^{93} - 44 q^{94} + 22 q^{95} + 30 q^{96} - 20 q^{97} + 63 q^{98} + q^{99}+O(q^{100}) \) 39 * q - 4 * q^2 - 39 * q^3 + 30 * q^4 - 3 * q^5 + 4 * q^6 - 5 * q^7 - 3 * q^8 + 39 * q^9 + 4 * q^10 + q^11 - 30 * q^12 - 26 * q^13 - 4 * q^14 + 3 * q^15 + 8 * q^16 + 39 * q^17 - 4 * q^18 - 14 * q^19 - 14 * q^20 + 5 * q^21 - 17 * q^22 + 2 * q^23 + 3 * q^24 - 6 * q^25 - 17 * q^26 - 39 * q^27 - 14 * q^28 - 7 * q^29 - 4 * q^30 - q^31 - 30 * q^32 - q^33 - 4 * q^34 + q^35 + 30 * q^36 - 24 * q^37 - 20 * q^38 + 26 * q^39 + 12 * q^40 + q^41 + 4 * q^42 - 41 * q^43 - 2 * q^44 - 3 * q^45 - 6 * q^46 - 9 * q^47 - 8 * q^48 - 10 * q^49 - 9 * q^50 - 39 * q^51 - 37 * q^52 - 47 * q^53 + 4 * q^54 - 39 * q^55 + 8 * q^56 + 14 * q^57 - 27 * q^58 + 41 * q^59 + 14 * q^60 - 41 * q^61 + 36 * q^62 - 5 * q^63 - 47 * q^64 - 39 * q^65 + 17 * q^66 - 36 * q^67 + 30 * q^68 - 2 * q^69 - 52 * q^70 - 2 * q^71 - 3 * q^72 - 63 * q^73 - 6 * q^74 + 6 * q^75 - 34 * q^76 - 64 * q^77 + 17 * q^78 + 20 * q^79 - 28 * q^80 + 39 * q^81 - 37 * q^82 + 45 * q^83 + 14 * q^84 - 3 * q^85 + 32 * q^86 + 7 * q^87 + 6 * q^88 - 32 * q^89 + 4 * q^90 - 11 * q^91 + 28 * q^92 + q^93 - 44 * q^94 + 22 * q^95 + 30 * q^96 - 20 * q^97 + 63 * q^98 + 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 $

$2$	−0.744255	−0.526268	−0.263134	−	0.964759i	$-0.584756\pi$
$2$	−0.744255	−0.526268	−0.263134	+	0.964759i	$0.584756\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	−1.44608	−0.723042
$5$	1.71466	0.766819	0.383409	−	0.923578i	$-0.374750\pi$
$5$	1.71466	0.766819	0.383409	+	0.923578i	$0.374750\pi$
$6$	0.744255	0.303841
$7$	−3.69118	−1.39514	−0.697568	−	0.716518i	$-0.745735\pi$
$7$	−3.69118	−1.39514	−0.697568	+	0.716518i	$0.745735\pi$
$8$	2.56477	0.906782
$9$	1.00000	0.333333
$10$	−1.27614	−0.403552
$11$	−0.320749	−0.0967094	−0.0483547	−	0.998830i	$-0.515398\pi$
$11$	−0.320749	−0.0967094	−0.0483547	+	0.998830i	$0.515398\pi$
$12$	1.44608	0.417449
$13$	−1.38308	−0.383597	−0.191798	−	0.981434i	$-0.561432\pi$
$13$	−1.38308	−0.383597	−0.191798	+	0.981434i	$0.561432\pi$
$14$	2.74718	0.734216
$15$	−1.71466	−0.442723
$16$	0.983327	0.245832
$17$	1.00000	0.242536
$17$	1.00000	0.242536
$18$	−0.744255	−0.175423
$19$	−1.35980	−0.311959	−0.155980	−	0.987760i	$-0.549853\pi$
$19$	−1.35980	−0.311959	−0.155980	+	0.987760i	$0.549853\pi$
$20$	−2.47954	−0.554442
$21$	3.69118	0.805482
$22$	0.238719	0.0508951
$23$	3.98938	0.831843	0.415921	−	0.909401i	$-0.363459\pi$
$23$	3.98938	0.831843	0.415921	+	0.909401i	$0.363459\pi$
$24$	−2.56477	−0.523531
$25$	−2.05994	−0.411989
$26$	1.02936	0.201875
$27$	−1.00000	−0.192450
$28$	5.33776	1.00874
$29$	3.50363	0.650608	0.325304	−	0.945609i	$-0.394533\pi$
$29$	3.50363	0.650608	0.325304	+	0.945609i	$0.394533\pi$
$30$	1.27614	0.232991
$31$	4.07488	0.731871	0.365935	−	0.930640i	$-0.380749\pi$
$31$	4.07488	0.731871	0.365935	+	0.930640i	$0.380749\pi$
$32$	−5.86138	−1.03616
$33$	0.320749	0.0558352
$34$	−0.744255	−0.127639
$35$	−6.32912	−1.06982
$36$	−1.44608	−0.241014
$37$	−7.33472	−1.20582	−0.602910	−	0.797809i	$-0.705992\pi$
$37$	−7.33472	−1.20582	−0.602910	+	0.797809i	$0.705992\pi$
$38$	1.01204	0.164174
$39$	1.38308	0.221470
$40$	4.39770	0.695337
$41$	−7.61449	−1.18918	−0.594591	−	0.804028i	$-0.702686\pi$
$41$	−7.61449	−1.18918	−0.594591	+	0.804028i	$0.702686\pi$
$42$	−2.74718	−0.423900
$43$	3.57511	0.545200	0.272600	−	0.962128i	$-0.412117\pi$
$43$	3.57511	0.545200	0.272600	+	0.962128i	$0.412117\pi$
$44$	0.463830	0.0699250
$45$	1.71466	0.255606
$46$	−2.96912	−0.437772
$47$	−0.864286	−0.126069	−0.0630345	−	0.998011i	$-0.520078\pi$
$47$	−0.864286	−0.126069	−0.0630345	+	0.998011i	$0.520078\pi$
$48$	−0.983327	−0.141931
$49$	6.62484	0.946406
$50$	1.53312	0.216816
$51$	−1.00000	−0.140028
$52$	2.00005	0.277357
$53$	−4.84145	−0.665025	−0.332512	−	0.943099i	$-0.607896\pi$
$53$	−4.84145	−0.665025	−0.332512	+	0.943099i	$0.607896\pi$
$54$	0.744255	0.101280
$55$	−0.549975	−0.0741586
$56$	−9.46703	−1.26508
$57$	1.35980	0.180110
$58$	−2.60760	−0.342394
$59$	2.86767	0.373339	0.186670	−	0.982423i	$-0.440231\pi$
$59$	2.86767	0.373339	0.186670	+	0.982423i	$0.440231\pi$
$60$	2.47954	0.320107
$61$	8.17485	1.04668	0.523341	−	0.852123i	$-0.324685\pi$
$61$	8.17485	1.04668	0.523341	+	0.852123i	$0.324685\pi$
$62$	−3.03275	−0.385160
$63$	−3.69118	−0.465046
$64$	2.39571	0.299464
$65$	−2.37151	−0.294149
$66$	−0.238719	−0.0293843
$67$	6.80250	0.831058	0.415529	−	0.909580i	$-0.363596\pi$
$67$	6.80250	0.831058	0.415529	+	0.909580i	$0.363596\pi$
$68$	−1.44608	−0.175363
$69$	−3.98938	−0.480265
$70$	4.71048	0.563010
$71$	−1.78505	−0.211847	−0.105923	−	0.994374i	$-0.533780\pi$
$71$	−1.78505	−0.211847	−0.105923	+	0.994374i	$0.533780\pi$
$72$	2.56477	0.302261
$73$	11.6859	1.36773	0.683867	−	0.729606i	$-0.260297\pi$
$73$	11.6859	1.36773	0.683867	+	0.729606i	$0.260297\pi$
$74$	5.45890	0.634584
$75$	2.05994	0.237862
$76$	1.96638	0.225560
$77$	1.18394	0.134923
$78$	−1.02936	−0.116552
$79$	−9.39936	−1.05751	−0.528755	−	0.848774i	$-0.677341\pi$
$79$	−9.39936	−1.05751	−0.528755	+	0.848774i	$0.677341\pi$
$80$	1.68607	0.188508
$81$	1.00000	0.111111
$82$	5.66712	0.625829
$83$	6.30017	0.691534	0.345767	−	0.938320i	$-0.387619\pi$
$83$	6.30017	0.691534	0.345767	+	0.938320i	$0.387619\pi$
$84$	−5.33776	−0.582398
$85$	1.71466	0.185981
$86$	−2.66080	−0.286921
$87$	−3.50363	−0.375629
$88$	−0.822646	−0.0876943
$89$	3.25502	0.345032	0.172516	−	0.985007i	$-0.444810\pi$
$89$	3.25502	0.345032	0.172516	+	0.985007i	$0.444810\pi$
$90$	−1.27614	−0.134517
$91$	5.10520	0.535170
$92$	−5.76898	−0.601457
$93$	−4.07488	−0.422546
$94$	0.643250	0.0663461
$95$	−2.33159	−0.239216
$96$	5.86138	0.598224
$97$	4.97859	0.505500	0.252750	−	0.967532i	$-0.418665\pi$
$97$	4.97859	0.505500	0.252750	+	0.967532i	$0.418665\pi$
$98$	−4.93057	−0.498063
$99$	−0.320749	−0.0322365
$100$	2.97885	0.297885
$101$	−14.7721	−1.46988	−0.734940	−	0.678132i	$-0.762790\pi$
$101$	−14.7721	−1.46988	−0.734940	+	0.678132i	$0.762790\pi$
$102$	0.744255	0.0736923
$103$	18.4532	1.81825	0.909124	−	0.416526i	$-0.136753\pi$
$103$	18.4532	1.81825	0.909124	+	0.416526i	$0.136753\pi$
$104$	−3.54727	−0.347839
$105$	6.32912	0.617659
$106$	3.60328	0.349981
$107$	−10.6947	−1.03389	−0.516946	−	0.856018i	$-0.672931\pi$
$107$	−10.6947	−1.03389	−0.516946	+	0.856018i	$0.672931\pi$
$108$	1.44608	0.139150
$109$	3.92761	0.376197	0.188098	−	0.982150i	$-0.439768\pi$
$109$	3.92761	0.376197	0.188098	+	0.982150i	$0.439768\pi$
$110$	0.409322	0.0390273
$111$	7.33472	0.696181
$112$	−3.62964	−0.342969
$113$	17.1216	1.61066	0.805330	−	0.592826i	$-0.201988\pi$
$113$	17.1216	1.61066	0.805330	+	0.592826i	$0.201988\pi$
$114$	−1.01204	−0.0947859
$115$	6.84042	0.637873
$116$	−5.06655	−0.470417
$117$	−1.38308	−0.127866
$118$	−2.13428	−0.196476
$119$	−3.69118	−0.338370
$120$	−4.39770	−0.401453
$121$	−10.8971	−0.990647
$122$	−6.08418	−0.550835
$123$	7.61449	0.686575
$124$	−5.89262	−0.529173
$125$	−12.1054	−1.08274
$126$	2.74718	0.244739
$127$	6.11175	0.542330	0.271165	−	0.962533i	$-0.412591\pi$
$127$	6.11175	0.542330	0.271165	+	0.962533i	$0.412591\pi$
$128$	9.93974	0.878557
$129$	−3.57511	−0.314771
$130$	1.76501	0.154801
$131$	21.1575	1.84854	0.924271	−	0.381737i	$-0.124674\pi$
$131$	21.1575	1.84854	0.924271	+	0.381737i	$0.124674\pi$
$132$	−0.463830	−0.0403712
$133$	5.01927	0.435226
$134$	−5.06280	−0.437359
$135$	−1.71466	−0.147574
$136$	2.56477	0.219927
$137$	−9.47488	−0.809494	−0.404747	−	0.914429i	$-0.632640\pi$
$137$	−9.47488	−0.809494	−0.404747	+	0.914429i	$0.632640\pi$
$138$	2.96912	0.252748
$139$	−6.59053	−0.559002	−0.279501	−	0.960145i	$-0.590169\pi$
$139$	−6.59053	−0.559002	−0.279501	+	0.960145i	$0.590169\pi$
$140$	9.15244	0.773523
$141$	0.864286	0.0727860
$142$	1.32853	0.111488
$143$	0.443621	0.0370974
$144$	0.983327	0.0819439
$145$	6.00753	0.498899
$146$	−8.69731	−0.719795
$147$	−6.62484	−0.546408
$148$	10.6066	0.871859
$149$	0.0784364	0.00642576	0.00321288	−	0.999995i	$-0.498977\pi$
$149$	0.0784364	0.00642576	0.00321288	+	0.999995i	$0.498977\pi$
$150$	−1.53312	−0.125179
$151$	−13.1851	−1.07298	−0.536492	−	0.843905i	$-0.680251\pi$
$151$	−13.1851	−1.07298	−0.536492	+	0.843905i	$0.680251\pi$
$152$	−3.48756	−0.282879
$153$	1.00000	0.0808452
$154$	−0.881156	−0.0710056
$155$	6.98704	0.561212
$156$	−2.00005	−0.160132
$157$	1.00000	0.0798087
$157$	1.00000	0.0798087
$158$	6.99552	0.556534
$159$	4.84145	0.383952
$160$	−10.0503	−0.794543
$161$	−14.7255	−1.16053
$162$	−0.744255	−0.0584742
$163$	2.87636	0.225294	0.112647	−	0.993635i	$-0.464067\pi$
$163$	2.87636	0.225294	0.112647	+	0.993635i	$0.464067\pi$
$164$	11.0112	0.859829
$165$	0.549975	0.0428155
$166$	−4.68894	−0.363932
$167$	−19.5257	−1.51094	−0.755471	−	0.655182i	$-0.772592\pi$
$167$	−19.5257	−1.51094	−0.755471	+	0.655182i	$0.772592\pi$
$168$	9.46703	0.730397
$169$	−11.0871	−0.852853
$170$	−1.27614	−0.0978758
$171$	−1.35980	−0.103986
$172$	−5.16991	−0.394202
$173$	−20.6292	−1.56841	−0.784205	−	0.620502i	$-0.786929\pi$
$173$	−20.6292	−1.56841	−0.784205	+	0.620502i	$0.786929\pi$
$174$	2.60760	0.197681
$175$	7.60363	0.574781
$176$	−0.315401	−0.0237742
$177$	−2.86767	−0.215547
$178$	−2.42257	−0.181579
$179$	10.9564	0.818916	0.409458	−	0.912329i	$-0.365718\pi$
$179$	10.9564	0.818916	0.409458	+	0.912329i	$0.365718\pi$
$180$	−2.47954	−0.184814
$181$	−6.13996	−0.456379	−0.228190	−	0.973617i	$-0.573281\pi$
$181$	−6.13996	−0.456379	−0.228190	+	0.973617i	$0.573281\pi$
$182$	−3.79957	−0.281643
$183$	−8.17485	−0.604302
$184$	10.2318	0.754300
$185$	−12.5765	−0.924646
$186$	3.03275	0.222372
$187$	−0.320749	−0.0234555
$188$	1.24983	0.0911532
$189$	3.69118	0.268494
$190$	1.73530	0.125892
$191$	18.9399	1.37044	0.685220	−	0.728336i	$-0.259706\pi$
$191$	18.9399	1.37044	0.685220	+	0.728336i	$0.259706\pi$
$192$	−2.39571	−0.172895
$193$	−12.8537	−0.925229	−0.462615	−	0.886559i	$-0.653089\pi$
$193$	−12.8537	−0.925229	−0.462615	+	0.886559i	$0.653089\pi$
$194$	−3.70535	−0.266028
$195$	2.37151	0.169827
$196$	−9.58008	−0.684291
$197$	15.9657	1.13751	0.568753	−	0.822508i	$-0.307426\pi$
$197$	15.9657	1.13751	0.568753	+	0.822508i	$0.307426\pi$
$198$	0.238719	0.0169650
$199$	12.7837	0.906213	0.453107	−	0.891456i	$-0.350316\pi$
$199$	12.7837	0.906213	0.453107	+	0.891456i	$0.350316\pi$
$200$	−5.28327	−0.373584
$201$	−6.80250	−0.479811
$202$	10.9942	0.773551
$203$	−12.9325	−0.907687
$204$	1.44608	0.101246
$205$	−13.0562	−0.911888
$206$	−13.7339	−0.956885
$207$	3.98938	0.277281
$208$	−1.36002	−0.0943003
$209$	0.436154	0.0301694
$210$	−4.71048	−0.325054
$211$	22.7342	1.56509	0.782545	−	0.622594i	$-0.213921\pi$
$211$	22.7342	1.56509	0.782545	+	0.622594i	$0.213921\pi$
$212$	7.00115	0.480841
$213$	1.78505	0.122310
$214$	7.95956	0.544104
$215$	6.13010	0.418069
$216$	−2.56477	−0.174510
$217$	−15.0411	−1.02106
$218$	−2.92314	−0.197980
$219$	−11.6859	−0.789662
$220$	0.795310	0.0536198
$221$	−1.38308	−0.0930359
$222$	−5.45890	−0.366378
$223$	−15.1816	−1.01664	−0.508318	−	0.861169i	$-0.669733\pi$
$223$	−15.1816	−1.01664	−0.508318	+	0.861169i	$0.669733\pi$
$224$	21.6354	1.44558
$225$	−2.05994	−0.137330
$226$	−12.7428	−0.847639
$227$	−15.1853	−1.00788	−0.503940	−	0.863738i	$-0.668117\pi$
$227$	−15.1853	−1.00788	−0.503940	+	0.863738i	$0.668117\pi$
$228$	−1.96638	−0.130227
$229$	21.5195	1.42205	0.711023	−	0.703169i	$-0.248232\pi$
$229$	21.5195	1.42205	0.711023	+	0.703169i	$0.248232\pi$
$230$	−5.09102	−0.335692
$231$	−1.18394	−0.0778977
$232$	8.98600	0.589960
$233$	−3.04734	−0.199638	−0.0998188	−	0.995006i	$-0.531826\pi$
$233$	−3.04734	−0.199638	−0.0998188	+	0.995006i	$0.531826\pi$
$234$	1.02936	0.0672916
$235$	−1.48196	−0.0966722
$236$	−4.14689	−0.269940
$237$	9.39936	0.610554
$238$	2.74718	0.178073
$239$	−3.15119	−0.203834	−0.101917	−	0.994793i	$-0.532498\pi$
$239$	−3.15119	−0.203834	−0.101917	+	0.994793i	$0.532498\pi$
$240$	−1.68607	−0.108835
$241$	18.9980	1.22377	0.611883	−	0.790948i	$-0.290412\pi$
$241$	18.9980	1.22377	0.611883	+	0.790948i	$0.290412\pi$
$242$	8.11024	0.521346
$243$	−1.00000	−0.0641500
$244$	−11.8215	−0.756795
$245$	11.3593	0.725722
$246$	−5.66712	−0.361322
$247$	1.88071	0.119667
$248$	10.4511	0.663647
$249$	−6.30017	−0.399257
$250$	9.00951	0.569811
$251$	−14.4324	−0.910967	−0.455483	−	0.890244i	$-0.650534\pi$
$251$	−14.4324	−0.910967	−0.455483	+	0.890244i	$0.650534\pi$
$252$	5.33776	0.336247
$253$	−1.27959	−0.0804470
$254$	−4.54870	−0.285411
$255$	−1.71466	−0.107376
$256$	−12.1891	−0.761820
$257$	−15.1466	−0.944820	−0.472410	−	0.881379i	$-0.656616\pi$
$257$	−15.1466	−0.944820	−0.472410	+	0.881379i	$0.656616\pi$
$258$	2.66080	0.165654
$259$	27.0738	1.68228
$260$	3.42940	0.212682
$261$	3.50363	0.216869
$262$	−15.7466	−0.972828
$263$	17.3972	1.07276	0.536379	−	0.843977i	$-0.319792\pi$
$263$	17.3972	1.07276	0.536379	+	0.843977i	$0.319792\pi$
$264$	0.822646	0.0506303
$265$	−8.30144	−0.509954
$266$	−3.73562	−0.229045
$267$	−3.25502	−0.199204
$268$	−9.83699	−0.600890
$269$	−6.67835	−0.407186	−0.203593	−	0.979056i	$-0.565262\pi$
$269$	−6.67835	−0.407186	−0.203593	+	0.979056i	$0.565262\pi$
$270$	1.27614	0.0776637
$271$	16.5230	1.00370	0.501851	−	0.864954i	$-0.332653\pi$
$271$	16.5230	1.00370	0.501851	+	0.864954i	$0.332653\pi$
$272$	0.983327	0.0596230
$273$	−5.10520	−0.308981
$274$	7.05173	0.426011
$275$	0.660724	0.0398432
$276$	5.76898	0.347252
$277$	12.6815	0.761957	0.380978	−	0.924584i	$-0.375587\pi$
$277$	12.6815	0.761957	0.380978	+	0.924584i	$0.375587\pi$
$278$	4.90504	0.294185
$279$	4.07488	0.243957
$280$	−16.2327	−0.970091
$281$	14.0116	0.835862	0.417931	−	0.908479i	$-0.362755\pi$
$281$	14.0116	0.835862	0.417931	+	0.908479i	$0.362755\pi$
$282$	−0.643250	−0.0383050
$283$	−22.3767	−1.33015	−0.665077	−	0.746774i	$-0.731601\pi$
$283$	−22.3767	−1.33015	−0.665077	+	0.746774i	$0.731601\pi$
$284$	2.58133	0.153174
$285$	2.33159	0.138112
$286$	−0.330167	−0.0195232
$287$	28.1065	1.65907
$288$	−5.86138	−0.345385
$289$	1.00000	0.0588235
$290$	−4.47114	−0.262554
$291$	−4.97859	−0.291850
$292$	−16.8988	−0.988930
$293$	16.8674	0.985403	0.492701	−	0.870198i	$-0.336010\pi$
$293$	16.8674	0.985403	0.492701	+	0.870198i	$0.336010\pi$
$294$	4.93057	0.287557
$295$	4.91708	0.286283
$296$	−18.8118	−1.09342
$297$	0.320749	0.0186117
$298$	−0.0583767	−0.00338167
$299$	−5.51762	−0.319092
$300$	−2.97885	−0.171984
$301$	−13.1964	−0.760628
$302$	9.81305	0.564678
$303$	14.7721	0.848636
$304$	−1.33713	−0.0766895
$305$	14.0171	0.802616
$306$	−0.744255	−0.0425462
$307$	−16.2702	−0.928591	−0.464295	−	0.885680i	$-0.653692\pi$
$307$	−16.2702	−0.928591	−0.464295	+	0.885680i	$0.653692\pi$
$308$	−1.71208	−0.0975549
$309$	−18.4532	−1.04977
$310$	−5.20014	−0.295348
$311$	−19.9919	−1.13364	−0.566818	−	0.823843i	$-0.691826\pi$
$311$	−19.9919	−1.13364	−0.566818	+	0.823843i	$0.691826\pi$
$312$	3.54727	0.200825
$313$	−30.4542	−1.72137	−0.860687	−	0.509134i	$-0.829966\pi$
$313$	−30.4542	−1.72137	−0.860687	+	0.509134i	$0.829966\pi$
$314$	−0.744255	−0.0420008
$315$	−6.32912	−0.356606
$316$	13.5923	0.764624
$317$	−9.80999	−0.550984	−0.275492	−	0.961303i	$-0.588841\pi$
$317$	−9.80999	−0.550984	−0.275492	+	0.961303i	$0.588841\pi$
$318$	−3.60328	−0.202062
$319$	−1.12379	−0.0629199
$320$	4.10782	0.229634
$321$	10.6947	0.596918
$322$	10.9596	0.610752
$323$	−1.35980	−0.0756612
$324$	−1.44608	−0.0803380
$325$	2.84906	0.158038
$326$	−2.14075	−0.118565
$327$	−3.92761	−0.217197
$328$	−19.5294	−1.07833
$329$	3.19024	0.175884
$330$	−0.409322	−0.0225324
$331$	10.5896	0.582059	0.291029	−	0.956714i	$-0.406002\pi$
$331$	10.5896	0.582059	0.291029	+	0.956714i	$0.406002\pi$
$332$	−9.11058	−0.500008
$333$	−7.33472	−0.401940
$334$	14.5321	0.795160
$335$	11.6640	0.637271
$336$	3.62964	0.198013
$337$	1.56532	0.0852684	0.0426342	−	0.999091i	$-0.486425\pi$
$337$	1.56532	0.0852684	0.0426342	+	0.999091i	$0.486425\pi$
$338$	8.25163	0.448829
$339$	−17.1216	−0.929915
$340$	−2.47954	−0.134472
$341$	−1.30701	−0.0707788
$342$	1.01204	0.0547247
$343$	1.38478	0.0747710
$344$	9.16933	0.494377
$345$	−6.84042	−0.368276
$346$	15.3534	0.825404
$347$	−25.7013	−1.37972	−0.689859	−	0.723943i	$-0.742328\pi$
$347$	−25.7013	−1.37972	−0.689859	+	0.723943i	$0.742328\pi$
$348$	5.06655	0.271595
$349$	−7.30932	−0.391259	−0.195630	−	0.980678i	$-0.562675\pi$
$349$	−7.30932	−0.391259	−0.195630	+	0.980678i	$0.562675\pi$
$350$	−5.65904	−0.302489
$351$	1.38308	0.0738233
$352$	1.88003	0.100206
$353$	−3.17562	−0.169021	−0.0845107	−	0.996423i	$-0.526933\pi$
$353$	−3.17562	−0.169021	−0.0845107	+	0.996423i	$0.526933\pi$
$354$	2.13428	0.113436
$355$	−3.06075	−0.162448
$356$	−4.70703	−0.249472
$357$	3.69118	0.195358
$358$	−8.15432	−0.430969
$359$	37.5536	1.98200	0.991001	−	0.133858i	$-0.0427365\pi$
$359$	37.5536	1.98200	0.991001	+	0.133858i	$0.0427365\pi$
$360$	4.39770	0.231779
$361$	−17.1509	−0.902682
$362$	4.56969	0.240178
$363$	10.8971	0.571950
$364$	−7.38254	−0.386950
$365$	20.0374	1.04880
$366$	6.08418	0.318025
$367$	−15.9710	−0.833678	−0.416839	−	0.908980i	$-0.636862\pi$
$367$	−15.9710	−0.833678	−0.416839	+	0.908980i	$0.636862\pi$
$368$	3.92286	0.204493
$369$	−7.61449	−0.396394
$370$	9.36016	0.486611
$371$	17.8707	0.927800
$372$	5.89262	0.305518
$373$	5.80175	0.300403	0.150202	−	0.988655i	$-0.452008\pi$
$373$	5.80175	0.300403	0.150202	+	0.988655i	$0.452008\pi$
$374$	0.238719	0.0123439
$375$	12.1054	0.625120
$376$	−2.21669	−0.114317
$377$	−4.84580	−0.249571
$378$	−2.74718	−0.141300
$379$	−20.1699	−1.03606	−0.518029	−	0.855363i	$-0.673334\pi$
$379$	−20.1699	−1.03606	−0.518029	+	0.855363i	$0.673334\pi$
$380$	3.37168	0.172963
$381$	−6.11175	−0.313114
$382$	−14.0961	−0.721218
$383$	−14.5498	−0.743461	−0.371730	−	0.928341i	$-0.621235\pi$
$383$	−14.5498	−0.743461	−0.371730	+	0.928341i	$0.621235\pi$
$384$	−9.93974	−0.507235
$385$	2.03006	0.103461
$386$	9.56643	0.486918
$387$	3.57511	0.181733
$388$	−7.19947	−0.365497
$389$	−36.6981	−1.86067	−0.930334	−	0.366713i	$-0.880483\pi$
$389$	−36.6981	−1.86067	−0.930334	+	0.366713i	$0.880483\pi$
$390$	−1.76501	−0.0893746
$391$	3.98938	0.201752
$392$	16.9912	0.858184
$393$	−21.1575	−1.06726
$394$	−11.8825	−0.598633
$395$	−16.1167	−0.810919
$396$	0.463830	0.0233083
$397$	−1.75791	−0.0882268	−0.0441134	−	0.999027i	$-0.514046\pi$
$397$	−1.75791	−0.0882268	−0.0441134	+	0.999027i	$0.514046\pi$
$398$	−9.51434	−0.476911
$399$	−5.01927	−0.251278
$400$	−2.02560	−0.101280
$401$	−23.1855	−1.15783	−0.578914	−	0.815389i	$-0.696523\pi$
$401$	−23.1855	−1.15783	−0.578914	+	0.815389i	$0.696523\pi$
$402$	5.06280	0.252509
$403$	−5.63588	−0.280743
$404$	21.3617	1.06279
$405$	1.71466	0.0852021
$406$	9.62512	0.477687
$407$	2.35260	0.116614
$408$	−2.56477	−0.126975
$409$	−16.0371	−0.792984	−0.396492	−	0.918038i	$-0.629772\pi$
$409$	−16.0371	−0.792984	−0.396492	+	0.918038i	$0.629772\pi$
$410$	9.71718	0.479897
$411$	9.47488	0.467361
$412$	−26.6849	−1.31467
$413$	−10.5851	−0.520859
$414$	−2.96912	−0.145924
$415$	10.8027	0.530281
$416$	8.10675	0.397466
$417$	6.59053	0.322740
$418$	−0.324610	−0.0158772
$419$	10.3183	0.504084	0.252042	−	0.967716i	$-0.418898\pi$
$419$	10.3183	0.504084	0.252042	+	0.967716i	$0.418898\pi$
$420$	−9.15244	−0.446594
$421$	27.1867	1.32500	0.662500	−	0.749062i	$-0.269496\pi$
$421$	27.1867	1.32500	0.662500	+	0.749062i	$0.269496\pi$
$422$	−16.9201	−0.823657
$423$	−0.864286	−0.0420230
$424$	−12.4172	−0.603032
$425$	−2.05994	−0.0999219
$426$	−1.32853	−0.0643677
$427$	−30.1749	−1.46027
$428$	15.4654	0.747547
$429$	−0.443621	−0.0214182
$430$	−4.56236	−0.220017
$431$	6.15689	0.296567	0.148284	−	0.988945i	$-0.452625\pi$
$431$	6.15689	0.296567	0.148284	+	0.988945i	$0.452625\pi$
$432$	−0.983327	−0.0473103
$433$	−17.4130	−0.836813	−0.418407	−	0.908260i	$-0.637411\pi$
$433$	−17.4130	−0.836813	−0.418407	+	0.908260i	$0.637411\pi$
$434$	11.1945	0.537351
$435$	−6.00753	−0.288039
$436$	−5.67965	−0.272006
$437$	−5.42475	−0.259501
$438$	8.69731	0.415574
$439$	24.1836	1.15422	0.577111	−	0.816666i	$-0.304180\pi$
$439$	24.1836	1.15422	0.577111	+	0.816666i	$0.304180\pi$
$440$	−1.41056	−0.0672457
$441$	6.62484	0.315469
$442$	1.02936	0.0489618
$443$	−17.4856	−0.830765	−0.415383	−	0.909647i	$-0.636352\pi$
$443$	−17.4856	−0.830765	−0.415383	+	0.909647i	$0.636352\pi$
$444$	−10.6066	−0.503368
$445$	5.58125	0.264577
$446$	11.2990	0.535023
$447$	−0.0784364	−0.00370992
$448$	−8.84300	−0.417793
$449$	−11.1172	−0.524653	−0.262327	−	0.964979i	$-0.584490\pi$
$449$	−11.1172	−0.524653	−0.262327	+	0.964979i	$0.584490\pi$
$450$	1.53312	0.0722722
$451$	2.44234	0.115005
$452$	−24.7592	−1.16458
$453$	13.1851	0.619488
$454$	11.3017	0.530415
$455$	8.75367	0.410378
$456$	3.48756	0.163320
$457$	27.0208	1.26398	0.631990	−	0.774976i	$-0.282238\pi$
$457$	27.0208	1.26398	0.631990	+	0.774976i	$0.282238\pi$
$458$	−16.0160	−0.748377
$459$	−1.00000	−0.0466760
$460$	−9.89183	−0.461209
$461$	−13.5111	−0.629274	−0.314637	−	0.949212i	$-0.601883\pi$
$461$	−13.5111	−0.629274	−0.314637	+	0.949212i	$0.601883\pi$
$462$	0.881156	0.0409951
$463$	−29.9108	−1.39007	−0.695036	−	0.718975i	$-0.744612\pi$
$463$	−29.9108	−1.39007	−0.695036	+	0.718975i	$0.744612\pi$
$464$	3.44522	0.159940
$465$	−6.98704	−0.324016
$466$	2.26800	0.105063
$467$	−18.6187	−0.861572	−0.430786	−	0.902454i	$-0.641764\pi$
$467$	−18.6187	−0.861572	−0.430786	+	0.902454i	$0.641764\pi$
$468$	2.00005	0.0924522
$469$	−25.1093	−1.15944
$470$	1.10295	0.0508755
$471$	−1.00000	−0.0460776
$472$	7.35491	0.338537
$473$	−1.14671	−0.0527259
$474$	−6.99552	−0.321315
$475$	2.80111	0.128524
$476$	5.33776	0.244656
$477$	−4.84145	−0.221675
$478$	2.34529	0.107271
$479$	1.66357	0.0760105	0.0380053	−	0.999278i	$-0.487900\pi$
$479$	1.66357	0.0760105	0.0380053	+	0.999278i	$0.487900\pi$
$480$	10.0503	0.458730
$481$	10.1445	0.462549
$482$	−14.1393	−0.644029
$483$	14.7255	0.670035
$484$	15.7582	0.716280
$485$	8.53659	0.387627
$486$	0.744255	0.0337601
$487$	−18.7027	−0.847500	−0.423750	−	0.905779i	$-0.639287\pi$
$487$	−18.7027	−0.847500	−0.423750	+	0.905779i	$0.639287\pi$
$488$	20.9666	0.949113
$489$	−2.87636	−0.130074
$490$	−8.45425	−0.381924
$491$	−5.93865	−0.268008	−0.134004	−	0.990981i	$-0.542783\pi$
$491$	−5.93865	−0.268008	−0.134004	+	0.990981i	$0.542783\pi$
$492$	−11.0112	−0.496423
$493$	3.50363	0.157796
$494$	−1.39973	−0.0629767
$495$	−0.549975	−0.0247195
$496$	4.00694	0.179917
$497$	6.58895	0.295555
$498$	4.68894	0.210116
$499$	−20.1550	−0.902262	−0.451131	−	0.892458i	$-0.648979\pi$
$499$	−20.1550	−0.902262	−0.451131	+	0.892458i	$0.648979\pi$
$500$	17.5054	0.782866
$501$	19.5257	0.872343
$502$	10.7414	0.479413
$503$	−14.1382	−0.630389	−0.315195	−	0.949027i	$-0.602070\pi$
$503$	−14.1382	−0.630389	−0.315195	+	0.949027i	$0.602070\pi$
$504$	−9.46703	−0.421695
$505$	−25.3291	−1.12713
$506$	0.952340	0.0423367
$507$	11.0871	0.492395
$508$	−8.83810	−0.392127
$509$	−18.8463	−0.835350	−0.417675	−	0.908597i	$-0.637155\pi$
$509$	−18.8463	−0.835350	−0.417675	+	0.908597i	$0.637155\pi$
$510$	1.27614	0.0565086
$511$	−43.1349	−1.90818
$512$	−10.8077	−0.477636
$513$	1.35980	0.0600366
$514$	11.2729	0.497228
$515$	31.6409	1.39427
$516$	5.16991	0.227593
$517$	0.277219	0.0121921
$518$	−20.1498	−0.885332
$519$	20.6292	0.905522
$520$	−6.08236	−0.266729
$521$	−16.7394	−0.733365	−0.366682	−	0.930346i	$-0.619506\pi$
$521$	−16.7394	−0.733365	−0.366682	+	0.930346i	$0.619506\pi$
$522$	−2.60760	−0.114131
$523$	−22.5553	−0.986273	−0.493136	−	0.869952i	$-0.664150\pi$
$523$	−22.5553	−0.986273	−0.493136	+	0.869952i	$0.664150\pi$
$524$	−30.5956	−1.33657
$525$	−7.60363	−0.331850
$526$	−12.9480	−0.564558
$527$	4.07488	0.177505
$528$	0.315401	0.0137261
$529$	−7.08487	−0.308038
$530$	6.17839	0.268372
$531$	2.86767	0.124446
$532$	−7.25828	−0.314686
$533$	10.5314	0.456167
$534$	2.42257	0.104835
$535$	−18.3377	−0.792808
$536$	17.4468	0.753588
$537$	−10.9564	−0.472802
$538$	4.97040	0.214289
$539$	−2.12491	−0.0915264
$540$	2.47954	0.106702
$541$	−24.6653	−1.06044	−0.530222	−	0.847859i	$-0.677891\pi$
$541$	−24.6653	−1.06044	−0.530222	+	0.847859i	$0.677891\pi$
$542$	−12.2973	−0.528216
$543$	6.13996	0.263491
$544$	−5.86138	−0.251305
$545$	6.73451	0.288475
$546$	3.79957	0.162607
$547$	−24.6731	−1.05495	−0.527473	−	0.849572i	$-0.676860\pi$
$547$	−24.6731	−1.05495	−0.527473	+	0.849572i	$0.676860\pi$
$548$	13.7015	0.585298
$549$	8.17485	0.348894
$550$	−0.491748	−0.0209682
$551$	−4.76423	−0.202963
$552$	−10.2318	−0.435495
$553$	34.6948	1.47537
$554$	−9.43826	−0.400993
$555$	12.5765	0.533844
$556$	9.53047	0.404182
$557$	11.8383	0.501607	0.250803	−	0.968038i	$-0.419305\pi$
$557$	11.8383	0.501607	0.250803	+	0.968038i	$0.419305\pi$
$558$	−3.03275	−0.128387
$559$	−4.94466	−0.209137
$560$	−6.22360	−0.262995
$561$	0.320749	0.0135420
$562$	−10.4282	−0.439888
$563$	21.5636	0.908798	0.454399	−	0.890798i	$-0.349854\pi$
$563$	21.5636	0.908798	0.454399	+	0.890798i	$0.349854\pi$
$564$	−1.24983	−0.0526274
$565$	29.3576	1.23509
$566$	16.6540	0.700018
$567$	−3.69118	−0.155015
$568$	−4.57824	−0.192099
$569$	−24.7560	−1.03783	−0.518913	−	0.854827i	$-0.673663\pi$
$569$	−24.7560	−1.03783	−0.518913	+	0.854827i	$0.673663\pi$
$570$	−1.73530	−0.0726837
$571$	2.88137	0.120582	0.0602909	−	0.998181i	$-0.480797\pi$
$571$	2.88137	0.120582	0.0602909	+	0.998181i	$0.480797\pi$
$572$	−0.641513	−0.0268230
$573$	−18.9399	−0.791224
$574$	−20.9184	−0.873117
$575$	−8.21789	−0.342710
$576$	2.39571	0.0998212
$577$	−15.2973	−0.636837	−0.318418	−	0.947950i	$-0.603152\pi$
$577$	−15.2973	−0.636837	−0.318418	+	0.947950i	$0.603152\pi$
$578$	−0.744255	−0.0309569
$579$	12.8537	0.534181
$580$	−8.68740	−0.360725
$581$	−23.2551	−0.964784
$582$	3.70535	0.153591
$583$	1.55289	0.0643141
$584$	29.9717	1.24024
$585$	−2.37151	−0.0980498
$586$	−12.5536	−0.518586
$587$	−27.4012	−1.13097	−0.565484	−	0.824760i	$-0.691310\pi$
$587$	−27.4012	−1.13097	−0.565484	+	0.824760i	$0.691310\pi$
$588$	9.58008	0.395076
$589$	−5.54102	−0.228314
$590$	−3.65956	−0.150662
$591$	−15.9657	−0.656739
$592$	−7.21243	−0.296429
$593$	11.0375	0.453256	0.226628	−	0.973981i	$-0.427230\pi$
$593$	11.0375	0.453256	0.226628	+	0.973981i	$0.427230\pi$
$594$	−0.238719	−0.00979476
$595$	−6.32912	−0.259469
$596$	−0.113426	−0.00464610
$597$	−12.7837	−0.523202
$598$	4.10652	0.167928
$599$	39.4727	1.61281	0.806406	−	0.591362i	$-0.201410\pi$
$599$	39.4727	1.61281	0.806406	+	0.591362i	$0.201410\pi$
$600$	5.28327	0.215689
$601$	−43.3359	−1.76771	−0.883854	−	0.467763i	$-0.845060\pi$
$601$	−43.3359	−1.76771	−0.883854	+	0.467763i	$0.845060\pi$
$602$	9.82149	0.400294
$603$	6.80250	0.277019
$604$	19.0667	0.775813
$605$	−18.6848	−0.759647
$606$	−10.9942	−0.446610
$607$	43.8475	1.77972	0.889858	−	0.456238i	$-0.150803\pi$
$607$	43.8475	1.77972	0.889858	+	0.456238i	$0.150803\pi$
$608$	7.97029	0.323238
$609$	12.9325	0.524053
$610$	−10.4323	−0.422391
$611$	1.19538	0.0483597
$612$	−1.44608	−0.0584545
$613$	−37.2813	−1.50578	−0.752889	−	0.658147i	$-0.771340\pi$
$613$	−37.2813	−1.50578	−0.752889	+	0.658147i	$0.771340\pi$
$614$	12.1092	0.488688
$615$	13.0562	0.526479
$616$	3.03654	0.122346
$617$	−11.4117	−0.459417	−0.229709	−	0.973259i	$-0.573777\pi$
$617$	−11.4117	−0.459417	−0.229709	+	0.973259i	$0.573777\pi$
$618$	13.7339	0.552458
$619$	35.1526	1.41290	0.706452	−	0.707761i	$-0.250295\pi$
$619$	35.1526	1.41290	0.706452	+	0.707761i	$0.250295\pi$
$620$	−10.1038	−0.405780
$621$	−3.98938	−0.160088
$622$	14.8791	0.596596
$623$	−12.0149	−0.481366
$624$	1.36002	0.0544443
$625$	−10.4569	−0.418277
$626$	22.6657	0.905904
$627$	−0.436154	−0.0174183
$628$	−1.44608	−0.0577050
$629$	−7.33472	−0.292454
$630$	4.71048	0.187670
$631$	−45.8685	−1.82599	−0.912997	−	0.407966i	$-0.866238\pi$
$631$	−45.8685	−1.82599	−0.912997	+	0.407966i	$0.866238\pi$
$632$	−24.1072	−0.958931
$633$	−22.7342	−0.903605
$634$	7.30114	0.289965
$635$	10.4796	0.415869
$636$	−7.00115	−0.277614
$637$	−9.16267	−0.363038
$638$	0.836383	0.0331127
$639$	−1.78505	−0.0706155
$640$	17.0433	0.673694
$641$	17.1447	0.677174	0.338587	−	0.940935i	$-0.390051\pi$
$641$	17.1447	0.677174	0.338587	+	0.940935i	$0.390051\pi$
$642$	−7.95956	−0.314139
$643$	8.45311	0.333358	0.166679	−	0.986011i	$-0.446696\pi$
$643$	8.45311	0.333358	0.166679	+	0.986011i	$0.446696\pi$
$644$	21.2944	0.839115
$645$	−6.13010	−0.241372
$646$	1.01204	0.0398181
$647$	−42.7402	−1.68029	−0.840145	−	0.542361i	$-0.817530\pi$
$647$	−42.7402	−1.68029	−0.840145	+	0.542361i	$0.817530\pi$
$648$	2.56477	0.100754
$649$	−0.919802	−0.0361054
$650$	−2.12043	−0.0831701
$651$	15.0411	0.589509
$652$	−4.15946	−0.162897
$653$	14.5625	0.569876	0.284938	−	0.958546i	$-0.408027\pi$
$653$	14.5625	0.569876	0.284938	+	0.958546i	$0.408027\pi$
$654$	2.92314	0.114304
$655$	36.2780	1.41750
$656$	−7.48753	−0.292339
$657$	11.6859	0.455911
$658$	−2.37435	−0.0925619
$659$	39.0927	1.52284	0.761418	−	0.648261i	$-0.224504\pi$
$659$	39.0927	1.52284	0.761418	+	0.648261i	$0.224504\pi$
$660$	−0.795310	−0.0309574
$661$	10.8956	0.423789	0.211894	−	0.977293i	$-0.432037\pi$
$661$	10.8956	0.423789	0.211894	+	0.977293i	$0.432037\pi$
$662$	−7.88139	−0.306319
$663$	1.38308	0.0537143
$664$	16.1585	0.627070
$665$	8.60633	0.333739
$666$	5.45890	0.211528
$667$	13.9773	0.541204
$668$	28.2358	1.09247
$669$	15.1816	0.586956
$670$	−8.68097	−0.335375
$671$	−2.62207	−0.101224
$672$	−21.6354	−0.834605
$673$	−35.9620	−1.38623	−0.693116	−	0.720826i	$-0.743763\pi$
$673$	−35.9620	−1.38623	−0.693116	+	0.720826i	$0.743763\pi$
$674$	−1.16500	−0.0448740
$675$	2.05994	0.0792873
$676$	16.0329	0.616649
$677$	28.8740	1.10972	0.554859	−	0.831944i	$-0.312772\pi$
$677$	28.8740	1.10972	0.554859	+	0.831944i	$0.312772\pi$
$678$	12.7428	0.489385
$679$	−18.3769	−0.705241
$680$	4.39770	0.168644
$681$	15.1853	0.581900
$682$	0.972752	0.0372486
$683$	33.4523	1.28002	0.640008	−	0.768368i	$-0.278931\pi$
$683$	33.4523	1.28002	0.640008	+	0.768368i	$0.278931\pi$
$684$	1.96638	0.0751865
$685$	−16.2462	−0.620735
$686$	−1.03063	−0.0393496
$687$	−21.5195	−0.821019
$688$	3.51551	0.134027
$689$	6.69611	0.255101
$690$	5.09102	0.193812
$691$	−10.8958	−0.414495	−0.207248	−	0.978288i	$-0.566451\pi$
$691$	−10.8958	−0.414495	−0.207248	+	0.978288i	$0.566451\pi$
$692$	29.8316	1.13403
$693$	1.18394	0.0449743
$694$	19.1283	0.726102
$695$	−11.3005	−0.428653
$696$	−8.98600	−0.340613
$697$	−7.61449	−0.288419
$698$	5.44000	0.205907
$699$	3.04734	0.115261
$700$	−10.9955	−0.415590
$701$	−0.392709	−0.0148324	−0.00741621	−	0.999972i	$-0.502361\pi$
$701$	−0.392709	−0.0148324	−0.00741621	+	0.999972i	$0.502361\pi$
$702$	−1.02936	−0.0388508
$703$	9.97373	0.376167
$704$	−0.768421	−0.0289609
$705$	1.48196	0.0558137
$706$	2.36347	0.0889505
$707$	54.5266	2.05068
$708$	4.14689	0.155850
$709$	−30.0613	−1.12898	−0.564489	−	0.825441i	$-0.690927\pi$
$709$	−30.0613	−1.12898	−0.564489	+	0.825441i	$0.690927\pi$
$710$	2.27798	0.0854912
$711$	−9.39936	−0.352503
$712$	8.34837	0.312868
$713$	16.2562	0.608801
$714$	−2.74718	−0.102811
$715$	0.760658	0.0284470
$716$	−15.8438	−0.592111
$717$	3.15119	0.117683
$718$	−27.9494	−1.04306
$719$	7.75698	0.289287	0.144643	−	0.989484i	$-0.453797\pi$
$719$	7.75698	0.289287	0.144643	+	0.989484i	$0.453797\pi$
$720$	1.68607	0.0628362
$721$	−68.1141	−2.53670
$722$	12.7647	0.475052
$723$	−18.9980	−0.706542
$724$	8.87889	0.329981
$725$	−7.21728	−0.268043
$726$	−8.11024	−0.300999
$727$	−19.4006	−0.719528	−0.359764	−	0.933043i	$-0.617143\pi$
$727$	−19.4006	−0.719528	−0.359764	+	0.933043i	$0.617143\pi$
$728$	13.0936	0.485282
$729$	1.00000	0.0370370
$730$	−14.9129	−0.551952
$731$	3.57511	0.132230
$732$	11.8215	0.436936
$733$	−38.9368	−1.43816	−0.719082	−	0.694925i	$-0.755437\pi$
$733$	−38.9368	−1.43816	−0.719082	+	0.694925i	$0.755437\pi$
$734$	11.8865	0.438738
$735$	−11.3593	−0.418996
$736$	−23.3833	−0.861918
$737$	−2.18189	−0.0803711
$738$	5.66712	0.208610
$739$	28.7702	1.05833	0.529165	−	0.848519i	$-0.322505\pi$
$739$	28.7702	1.05833	0.529165	+	0.848519i	$0.322505\pi$
$740$	18.1867	0.668558
$741$	−1.88071	−0.0690895
$742$	−13.3004	−0.488272
$743$	−34.4039	−1.26216	−0.631078	−	0.775720i	$-0.717387\pi$
$743$	−34.4039	−1.26216	−0.631078	+	0.775720i	$0.717387\pi$
$744$	−10.4511	−0.383157
$745$	0.134492	0.00492740
$746$	−4.31799	−0.158093
$747$	6.30017	0.230511
$748$	0.463830	0.0169593
$749$	39.4760	1.44242
$750$	−9.00951	−0.328981
$751$	34.6949	1.26604	0.633018	−	0.774137i	$-0.281816\pi$
$751$	34.6949	1.26604	0.633018	+	0.774137i	$0.281816\pi$
$752$	−0.849876	−0.0309918
$753$	14.4324	0.525947
$754$	3.60651	0.131341
$755$	−22.6079	−0.822785
$756$	−5.33776	−0.194133
$757$	−51.1770	−1.86006	−0.930029	−	0.367486i	$-0.880219\pi$
$757$	−51.1770	−1.86006	−0.930029	+	0.367486i	$0.880219\pi$
$758$	15.0115	0.545244
$759$	1.27959	0.0464461
$760$	−5.97998	−0.216917
$761$	−23.6654	−0.857872	−0.428936	−	0.903335i	$-0.641111\pi$
$761$	−23.6654	−0.857872	−0.428936	+	0.903335i	$0.641111\pi$
$762$	4.54870	0.164782
$763$	−14.4975	−0.524846
$764$	−27.3886	−0.990885
$765$	1.71466	0.0619936
$766$	10.8288	0.391260
$767$	−3.96621	−0.143212
$768$	12.1891	0.439837
$769$	−27.8573	−1.00456	−0.502280	−	0.864705i	$-0.667505\pi$
$769$	−27.8573	−1.00456	−0.502280	+	0.864705i	$0.667505\pi$
$770$	−1.51088	−0.0544484
$771$	15.1466	0.545492
$772$	18.5875	0.668980
$773$	−44.4665	−1.59935	−0.799674	−	0.600434i	$-0.794995\pi$
$773$	−44.4665	−1.59935	−0.799674	+	0.600434i	$0.794995\pi$
$774$	−2.66080	−0.0956404
$775$	−8.39403	−0.301522
$776$	12.7689	0.458378
$777$	−27.0738	−0.971267
$778$	27.3128	0.979210
$779$	10.3542	0.370976
$780$	−3.42940	−0.122792
$781$	0.572553	0.0204876
$782$	−2.96912	−0.106175
$783$	−3.50363	−0.125210
$784$	6.51439	0.232657
$785$	1.71466	0.0611988
$786$	15.7466	0.561663
$787$	−0.738702	−0.0263319	−0.0131659	−	0.999913i	$-0.504191\pi$
$787$	−0.738702	−0.0263319	−0.0131659	+	0.999913i	$0.504191\pi$
$788$	−23.0877	−0.822464
$789$	−17.3972	−0.619357
$790$	11.9949	0.426761
$791$	−63.1988	−2.24709
$792$	−0.822646	−0.0292314
$793$	−11.3065	−0.401504
$794$	1.30833	0.0464310
$795$	8.30144	0.294422
$796$	−18.4863	−0.655230
$797$	29.7820	1.05493	0.527465	−	0.849576i	$-0.323142\pi$
$797$	29.7820	1.05493	0.527465	+	0.849576i	$0.323142\pi$
$798$	3.73562	0.132239
$799$	−0.864286	−0.0305762
$800$	12.0741	0.426884
$801$	3.25502	0.115011
$802$	17.2559	0.609328
$803$	−3.74825	−0.132273
$804$	9.83699	0.346924
$805$	−25.2493	−0.889920
$806$	4.19454	0.147746
$807$	6.67835	0.235089
$808$	−37.8870	−1.33286
$809$	−26.5338	−0.932878	−0.466439	−	0.884553i	$-0.654463\pi$
$809$	−26.5338	−0.932878	−0.466439	+	0.884553i	$0.654463\pi$
$810$	−1.27614	−0.0448391
$811$	6.23412	0.218909	0.109455	−	0.993992i	$-0.465090\pi$
$811$	6.23412	0.218909	0.109455	+	0.993992i	$0.465090\pi$
$812$	18.7016	0.656296
$813$	−16.5230	−0.579487
$814$	−1.75094	−0.0613703
$815$	4.93199	0.172760
$816$	−0.983327	−0.0344233
$817$	−4.86143	−0.170080
$818$	11.9357	0.417322
$819$	5.10520	0.178390
$820$	18.8804	0.659333
$821$	18.9852	0.662588	0.331294	−	0.943528i	$-0.392515\pi$
$821$	18.9852	0.662588	0.331294	+	0.943528i	$0.392515\pi$
$822$	−7.05173	−0.245957
$823$	49.4324	1.72310	0.861552	−	0.507669i	$-0.169493\pi$
$823$	49.4324	1.72310	0.861552	+	0.507669i	$0.169493\pi$
$824$	47.3281	1.64875
$825$	−0.660724	−0.0230035
$826$	7.87802	0.274111
$827$	−39.7750	−1.38311	−0.691557	−	0.722322i	$-0.743075\pi$
$827$	−39.7750	−1.38311	−0.691557	+	0.722322i	$0.743075\pi$
$828$	−5.76898	−0.200486
$829$	−49.2152	−1.70932	−0.854658	−	0.519192i	$-0.826233\pi$
$829$	−49.2152	−1.70932	−0.854658	+	0.519192i	$0.826233\pi$
$830$	−8.03993	−0.279070
$831$	−12.6815	−0.439916
$832$	−3.31345	−0.114873
$833$	6.62484	0.229537
$834$	−4.90504	−0.169848
$835$	−33.4799	−1.15862
$836$	−0.630715	−0.0218137
$837$	−4.07488	−0.140849
$838$	−7.67949	−0.265283
$839$	26.2036	0.904647	0.452324	−	0.891854i	$-0.350595\pi$
$839$	26.2036	0.904647	0.452324	+	0.891854i	$0.350595\pi$
$840$	16.2327	0.560082
$841$	−16.7246	−0.576709
$842$	−20.2339	−0.697305
$843$	−14.0116	−0.482585
$844$	−32.8756	−1.13163
$845$	−19.0106	−0.653984
$846$	0.643250	0.0221154
$847$	40.2233	1.38209
$848$	−4.76073	−0.163484
$849$	22.3767	0.767965
$850$	1.53312	0.0525857
$851$	−29.2610	−1.00305
$852$	−2.58133	−0.0884350
$853$	−10.4992	−0.359485	−0.179742	−	0.983714i	$-0.557526\pi$
$853$	−10.4992	−0.359485	−0.179742	+	0.983714i	$0.557526\pi$
$854$	22.4578	0.768491
$855$	−2.33159	−0.0797387
$856$	−27.4293	−0.937514
$857$	−7.87374	−0.268962	−0.134481	−	0.990916i	$-0.542937\pi$
$857$	−7.87374	−0.268962	−0.134481	+	0.990916i	$0.542937\pi$
$858$	0.330167	0.0112717
$859$	45.5746	1.55499	0.777493	−	0.628891i	$-0.216491\pi$
$859$	45.5746	1.55499	0.777493	+	0.628891i	$0.216491\pi$
$860$	−8.86464	−0.302282
$861$	−28.1065	−0.957866
$862$	−4.58230	−0.156074
$863$	−19.5935	−0.666969	−0.333484	−	0.942756i	$-0.608224\pi$
$863$	−19.5935	−0.666969	−0.333484	+	0.942756i	$0.608224\pi$
$864$	5.86138	0.199408
$865$	−35.3721	−1.20269
$866$	12.9597	0.440388
$867$	−1.00000	−0.0339618
$868$	21.7508	0.738269
$869$	3.01483	0.102271
$870$	4.47114	0.151586
$871$	−9.40839	−0.318791
$872$	10.0734	0.341128
$873$	4.97859	0.168500
$874$	4.03740	0.136567
$875$	44.6833	1.51057
$876$	16.8988	0.570959
$877$	−24.4618	−0.826017	−0.413009	−	0.910727i	$-0.635522\pi$
$877$	−24.4618	−0.826017	−0.413009	+	0.910727i	$0.635522\pi$
$878$	−17.9988	−0.607430
$879$	−16.8674	−0.568923
$880$	−0.540805	−0.0182305
$881$	−10.5833	−0.356561	−0.178280	−	0.983980i	$-0.557053\pi$
$881$	−10.5833	−0.356561	−0.178280	+	0.983980i	$0.557053\pi$
$882$	−4.93057	−0.166021
$883$	−23.0248	−0.774845	−0.387422	−	0.921902i	$-0.626635\pi$
$883$	−23.0248	−0.774845	−0.387422	+	0.921902i	$0.626635\pi$
$884$	2.00005	0.0672689
$885$	−4.91708	−0.165286
$886$	13.0137	0.437205
$887$	−13.3238	−0.447369	−0.223685	−	0.974662i	$-0.571809\pi$
$887$	−13.3238	−0.447369	−0.223685	+	0.974662i	$0.571809\pi$
$888$	18.8118	0.631284
$889$	−22.5596	−0.756624
$890$	−4.15388	−0.139238
$891$	−0.320749	−0.0107455
$892$	21.9539	0.735071
$893$	1.17525	0.0393284
$894$	0.0583767	0.00195241
$895$	18.7864	0.627961
$896$	−36.6894	−1.22571
$897$	5.51762	0.184228
$898$	8.27403	0.276108
$899$	14.2769	0.476161
$900$	2.97885	0.0992951
$901$	−4.84145	−0.161292
$902$	−1.81772	−0.0605235
$903$	13.1964	0.439149
$904$	43.9128	1.46052
$905$	−10.5279	−0.349960
$906$	−9.81305	−0.326017
$907$	42.9131	1.42491	0.712453	−	0.701720i	$-0.247584\pi$
$907$	42.9131	1.42491	0.712453	+	0.701720i	$0.247584\pi$
$908$	21.9592	0.728740
$909$	−14.7721	−0.489960
$910$	−6.51497	−0.215969
$911$	−22.2589	−0.737469	−0.368734	−	0.929535i	$-0.620209\pi$
$911$	−22.2589	−0.737469	−0.368734	+	0.929535i	$0.620209\pi$
$912$	1.33713	0.0442767
$913$	−2.02077	−0.0668778
$914$	−20.1104	−0.665193
$915$	−14.0171	−0.463391
$916$	−31.1190	−1.02820
$917$	−78.0963	−2.57897
$918$	0.744255	0.0245641
$919$	−25.7392	−0.849058	−0.424529	−	0.905414i	$-0.639560\pi$
$919$	−25.7392	−0.849058	−0.424529	+	0.905414i	$0.639560\pi$
$920$	17.5441	0.578411
$921$	16.2702	0.536122
$922$	10.0557	0.331167
$923$	2.46887	0.0812637
$924$	1.71208	0.0563233
$925$	15.1091	0.496784
$926$	22.2613	0.731551
$927$	18.4532	0.606082
$928$	−20.5361	−0.674131
$929$	−14.1960	−0.465757	−0.232879	−	0.972506i	$-0.574814\pi$
$929$	−14.1960	−0.465757	−0.232879	+	0.972506i	$0.574814\pi$
$930$	5.20014	0.170519
$931$	−9.00845	−0.295240
$932$	4.40670	0.144346
$933$	19.9919	0.654505
$934$	13.8571	0.453418
$935$	−0.549975	−0.0179861
$936$	−3.54727	−0.115946
$937$	56.6365	1.85023	0.925117	−	0.379683i	$-0.123967\pi$
$937$	56.6365	1.85023	0.925117	+	0.379683i	$0.123967\pi$
$938$	18.6877	0.610176
$939$	30.4542	0.993836
$940$	2.14303	0.0698980
$941$	0.522603	0.0170364	0.00851818	−	0.999964i	$-0.497289\pi$
$941$	0.522603	0.0170364	0.00851818	+	0.999964i	$0.497289\pi$
$942$	0.744255	0.0242491
$943$	−30.3771	−0.989213
$944$	2.81986	0.0917786
$945$	6.32912	0.205886
$946$	0.853447	0.0277480
$947$	6.05503	0.196762	0.0983811	−	0.995149i	$-0.468634\pi$
$947$	6.05503	0.196762	0.0983811	+	0.995149i	$0.468634\pi$
$948$	−13.5923	−0.441456
$949$	−16.1626	−0.524659
$950$	−2.08474	−0.0676379
$951$	9.80999	0.318111
$952$	−9.46703	−0.306828
$953$	48.0870	1.55769	0.778846	−	0.627215i	$-0.215805\pi$
$953$	48.0870	1.55769	0.778846	+	0.627215i	$0.215805\pi$
$954$	3.60328	0.116660
$955$	32.4754	1.05088
$956$	4.55689	0.147380
$957$	1.12379	0.0363268
$958$	−1.23812	−0.0400019
$959$	34.9735	1.12935
$960$	−4.10782	−0.132579
$961$	−14.3953	−0.464365
$962$	−7.55009	−0.243425
$963$	−10.6947	−0.344631
$964$	−27.4726	−0.884834
$965$	−22.0397	−0.709483
$966$	−10.9596	−0.352618
$967$	−42.3090	−1.36056	−0.680282	−	0.732950i	$-0.738143\pi$
$967$	−42.3090	−1.36056	−0.680282	+	0.732950i	$0.738143\pi$
$968$	−27.9486	−0.898301
$969$	1.35980	0.0436830
$970$	−6.35340	−0.203996
$971$	−2.71306	−0.0870664	−0.0435332	−	0.999052i	$-0.513861\pi$
$971$	−2.71306	−0.0870664	−0.0435332	+	0.999052i	$0.513861\pi$
$972$	1.44608	0.0463832
$973$	24.3269	0.779884
$974$	13.9196	0.446012
$975$	−2.84906	−0.0912430
$976$	8.03855	0.257308
$977$	−23.0592	−0.737730	−0.368865	−	0.929483i	$-0.620253\pi$
$977$	−23.0592	−0.737730	−0.368865	+	0.929483i	$0.620253\pi$
$978$	2.14075	0.0684536
$979$	−1.04404	−0.0333678
$980$	−16.4266	−0.524728
$981$	3.92761	0.125399
$982$	4.41987	0.141044
$983$	57.5285	1.83487	0.917437	−	0.397881i	$-0.130254\pi$
$983$	57.5285	1.83487	0.917437	+	0.397881i	$0.130254\pi$
$984$	19.5294	0.622574
$985$	27.3757	0.872261
$986$	−2.60760	−0.0830428
$987$	−3.19024	−0.101546
$988$	−2.71966	−0.0865239
$989$	14.2625	0.453520
$990$	0.409322	0.0130091
$991$	−46.1072	−1.46464	−0.732321	−	0.680959i	$-0.761563\pi$
$991$	−46.1072	−1.46464	−0.732321	+	0.680959i	$0.761563\pi$
$992$	−23.8844	−0.758332
$993$	−10.5896	−0.336052
$994$	−4.90386	−0.155541
$995$	21.9197	0.694901
$996$	9.11058	0.288680
$997$	−38.7607	−1.22756	−0.613781	−	0.789476i	$-0.710352\pi$
$997$	−38.7607	−1.22756	−0.613781	+	0.789476i	$0.710352\pi$
$998$	15.0005	0.474831
$999$	7.33472	0.232060

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8007.2.a.c.1.16	✓	39

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8007.2.a.c.1.16	✓	39	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)

\(f(q)\)	\(=\)	\(q-0.744255 q^{2} -1.00000 q^{3} -1.44608 q^{4} +1.71466 q^{5} +0.744255 q^{6} -3.69118 q^{7} +2.56477 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-0.744255 q^{2} -1.00000 q^{3} -1.44608 q^{4} +1.71466 q^{5} +0.744255 q^{6} -3.69118 q^{7} +2.56477 q^{8} +1.00000 q^{9} -1.27614 q^{10} -0.320749 q^{11} +1.44608 q^{12} -1.38308 q^{13} +2.74718 q^{14} -1.71466 q^{15} +0.983327 q^{16} +1.00000 q^{17} -0.744255 q^{18} -1.35980 q^{19} -2.47954 q^{20} +3.69118 q^{21} +0.238719 q^{22} +3.98938 q^{23} -2.56477 q^{24} -2.05994 q^{25} +1.02936 q^{26} -1.00000 q^{27} +5.33776 q^{28} +3.50363 q^{29} +1.27614 q^{30} +4.07488 q^{31} -5.86138 q^{32} +0.320749 q^{33} -0.744255 q^{34} -6.32912 q^{35} -1.44608 q^{36} -7.33472 q^{37} +1.01204 q^{38} +1.38308 q^{39} +4.39770 q^{40} -7.61449 q^{41} -2.74718 q^{42} +3.57511 q^{43} +0.463830 q^{44} +1.71466 q^{45} -2.96912 q^{46} -0.864286 q^{47} -0.983327 q^{48} +6.62484 q^{49} +1.53312 q^{50} -1.00000 q^{51} +2.00005 q^{52} -4.84145 q^{53} +0.744255 q^{54} -0.549975 q^{55} -9.46703 q^{56} +1.35980 q^{57} -2.60760 q^{58} +2.86767 q^{59} +2.47954 q^{60} +8.17485 q^{61} -3.03275 q^{62} -3.69118 q^{63} +2.39571 q^{64} -2.37151 q^{65} -0.238719 q^{66} +6.80250 q^{67} -1.44608 q^{68} -3.98938 q^{69} +4.71048 q^{70} -1.78505 q^{71} +2.56477 q^{72} +11.6859 q^{73} +5.45890 q^{74} +2.05994 q^{75} +1.96638 q^{76} +1.18394 q^{77} -1.02936 q^{78} -9.39936 q^{79} +1.68607 q^{80} +1.00000 q^{81} +5.66712 q^{82} +6.30017 q^{83} -5.33776 q^{84} +1.71466 q^{85} -2.66080 q^{86} -3.50363 q^{87} -0.822646 q^{88} +3.25502 q^{89} -1.27614 q^{90} +5.10520 q^{91} -5.76898 q^{92} -4.07488 q^{93} +0.643250 q^{94} -2.33159 q^{95} +5.86138 q^{96} +4.97859 q^{97} -4.93057 q^{98} -0.320749 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 39 q - 4 q^{2} - 39 q^{3} + 30 q^{4} - 3 q^{5} + 4 q^{6} - 5 q^{7} - 3 q^{8} + 39 q^{9}+O(q^{10}) \) 39 * q - 4 * q^2 - 39 * q^3 + 30 * q^4 - 3 * q^5 + 4 * q^6 - 5 * q^7 - 3 * q^8 + 39 * q^9	\( 39 q - 4 q^{2} - 39 q^{3} + 30 q^{4} - 3 q^{5} + 4 q^{6} - 5 q^{7} - 3 q^{8} + 39 q^{9} + 4 q^{10} + q^{11} - 30 q^{12} - 26 q^{13} - 4 q^{14} + 3 q^{15} + 8 q^{16} + 39 q^{17} - 4 q^{18} - 14 q^{19} - 14 q^{20} + 5 q^{21} - 17 q^{22} + 2 q^{23} + 3 q^{24} - 6 q^{25} - 17 q^{26} - 39 q^{27} - 14 q^{28} - 7 q^{29} - 4 q^{30} - q^{31} - 30 q^{32} - q^{33} - 4 q^{34} + q^{35} + 30 q^{36} - 24 q^{37} - 20 q^{38} + 26 q^{39} + 12 q^{40} + q^{41} + 4 q^{42} - 41 q^{43} - 2 q^{44} - 3 q^{45} - 6 q^{46} - 9 q^{47} - 8 q^{48} - 10 q^{49} - 9 q^{50} - 39 q^{51} - 37 q^{52} - 47 q^{53} + 4 q^{54} - 39 q^{55} + 8 q^{56} + 14 q^{57} - 27 q^{58} + 41 q^{59} + 14 q^{60} - 41 q^{61} + 36 q^{62} - 5 q^{63} - 47 q^{64} - 39 q^{65} + 17 q^{66} - 36 q^{67} + 30 q^{68} - 2 q^{69} - 52 q^{70} - 2 q^{71} - 3 q^{72} - 63 q^{73} - 6 q^{74} + 6 q^{75} - 34 q^{76} - 64 q^{77} + 17 q^{78} + 20 q^{79} - 28 q^{80} + 39 q^{81} - 37 q^{82} + 45 q^{83} + 14 q^{84} - 3 q^{85} + 32 q^{86} + 7 q^{87} + 6 q^{88} - 32 q^{89} + 4 q^{90} - 11 q^{91} + 28 q^{92} + q^{93} - 44 q^{94} + 22 q^{95} + 30 q^{96} - 20 q^{97} + 63 q^{98} + q^{99}+O(q^{100}) \) 39 * q - 4 * q^2 - 39 * q^3 + 30 * q^4 - 3 * q^5 + 4 * q^6 - 5 * q^7 - 3 * q^8 + 39 * q^9 + 4 * q^10 + q^11 - 30 * q^12 - 26 * q^13 - 4 * q^14 + 3 * q^15 + 8 * q^16 + 39 * q^17 - 4 * q^18 - 14 * q^19 - 14 * q^20 + 5 * q^21 - 17 * q^22 + 2 * q^23 + 3 * q^24 - 6 * q^25 - 17 * q^26 - 39 * q^27 - 14 * q^28 - 7 * q^29 - 4 * q^30 - q^31 - 30 * q^32 - q^33 - 4 * q^34 + q^35 + 30 * q^36 - 24 * q^37 - 20 * q^38 + 26 * q^39 + 12 * q^40 + q^41 + 4 * q^42 - 41 * q^43 - 2 * q^44 - 3 * q^45 - 6 * q^46 - 9 * q^47 - 8 * q^48 - 10 * q^49 - 9 * q^50 - 39 * q^51 - 37 * q^52 - 47 * q^53 + 4 * q^54 - 39 * q^55 + 8 * q^56 + 14 * q^57 - 27 * q^58 + 41 * q^59 + 14 * q^60 - 41 * q^61 + 36 * q^62 - 5 * q^63 - 47 * q^64 - 39 * q^65 + 17 * q^66 - 36 * q^67 + 30 * q^68 - 2 * q^69 - 52 * q^70 - 2 * q^71 - 3 * q^72 - 63 * q^73 - 6 * q^74 + 6 * q^75 - 34 * q^76 - 64 * q^77 + 17 * q^78 + 20 * q^79 - 28 * q^80 + 39 * q^81 - 37 * q^82 + 45 * q^83 + 14 * q^84 - 3 * q^85 + 32 * q^86 + 7 * q^87 + 6 * q^88 - 32 * q^89 + 4 * q^90 - 11 * q^91 + 28 * q^92 + q^93 - 44 * q^94 + 22 * q^95 + 30 * q^96 - 20 * q^97 + 63 * q^98 + q^99

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