LMFDB - Embedded newform 8007.2.a.c.1.19

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			1.19
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)

$f(q)$	$=$	$q-0.554461 q^{2} -1.00000 q^{3} -1.69257 q^{4} -2.60082 q^{5} +0.554461 q^{6} +2.71630 q^{7} +2.04739 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-0.554461 q^{2} -1.00000 q^{3} -1.69257 q^{4} -2.60082 q^{5} +0.554461 q^{6} +2.71630 q^{7} +2.04739 q^{8} +1.00000 q^{9} +1.44205 q^{10} +3.78169 q^{11} +1.69257 q^{12} -2.37483 q^{13} -1.50608 q^{14} +2.60082 q^{15} +2.24995 q^{16} +1.00000 q^{17} -0.554461 q^{18} +5.06564 q^{19} +4.40207 q^{20} -2.71630 q^{21} -2.09680 q^{22} -4.47742 q^{23} -2.04739 q^{24} +1.76425 q^{25} +1.31675 q^{26} -1.00000 q^{27} -4.59754 q^{28} -7.08839 q^{29} -1.44205 q^{30} -6.71511 q^{31} -5.34229 q^{32} -3.78169 q^{33} -0.554461 q^{34} -7.06460 q^{35} -1.69257 q^{36} +8.80443 q^{37} -2.80870 q^{38} +2.37483 q^{39} -5.32488 q^{40} +4.09058 q^{41} +1.50608 q^{42} -10.4995 q^{43} -6.40078 q^{44} -2.60082 q^{45} +2.48256 q^{46} +11.0837 q^{47} -2.24995 q^{48} +0.378292 q^{49} -0.978208 q^{50} -1.00000 q^{51} +4.01958 q^{52} -2.56188 q^{53} +0.554461 q^{54} -9.83547 q^{55} +5.56133 q^{56} -5.06564 q^{57} +3.93024 q^{58} +1.26655 q^{59} -4.40207 q^{60} -13.0027 q^{61} +3.72327 q^{62} +2.71630 q^{63} -1.53780 q^{64} +6.17651 q^{65} +2.09680 q^{66} +1.50891 q^{67} -1.69257 q^{68} +4.47742 q^{69} +3.91705 q^{70} +15.6673 q^{71} +2.04739 q^{72} +0.155659 q^{73} -4.88171 q^{74} -1.76425 q^{75} -8.57397 q^{76} +10.2722 q^{77} -1.31675 q^{78} -9.11742 q^{79} -5.85170 q^{80} +1.00000 q^{81} -2.26807 q^{82} -0.232204 q^{83} +4.59754 q^{84} -2.60082 q^{85} +5.82158 q^{86} +7.08839 q^{87} +7.74258 q^{88} -9.44493 q^{89} +1.44205 q^{90} -6.45076 q^{91} +7.57836 q^{92} +6.71511 q^{93} -6.14546 q^{94} -13.1748 q^{95} +5.34229 q^{96} +1.00603 q^{97} -0.209748 q^{98} +3.78169 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−0.554461	−0.392063	−0.196032	−	0.980598i	$-0.562806\pi$
$2$	−0.554461	−0.392063	−0.196032	+	0.980598i	$0.562806\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	−1.69257	−0.846286
$5$	−2.60082	−1.16312	−0.581560	−	0.813503i	$-0.697558\pi$
$5$	−2.60082	−1.16312	−0.581560	+	0.813503i	$0.697558\pi$
$6$	0.554461	0.226358
$7$	2.71630	1.02667	0.513333	−	0.858190i	$-0.328411\pi$
$7$	2.71630	1.02667	0.513333	+	0.858190i	$0.328411\pi$
$8$	2.04739	0.723861
$9$	1.00000	0.333333
$10$	1.44205	0.456017
$11$	3.78169	1.14022	0.570111	−	0.821568i	$-0.306900\pi$
$11$	3.78169	1.14022	0.570111	+	0.821568i	$0.306900\pi$
$12$	1.69257	0.488604
$13$	−2.37483	−0.658660	−0.329330	−	0.944215i	$-0.606823\pi$
$13$	−2.37483	−0.658660	−0.329330	+	0.944215i	$0.606823\pi$
$14$	−1.50608	−0.402518
$15$	2.60082	0.671528
$16$	2.24995	0.562487
$17$	1.00000	0.242536
$17$	1.00000	0.242536
$18$	−0.554461	−0.130688
$19$	5.06564	1.16214	0.581069	−	0.813854i	$-0.302635\pi$
$19$	5.06564	1.16214	0.581069	+	0.813854i	$0.302635\pi$
$20$	4.40207	0.984333
$21$	−2.71630	−0.592746
$22$	−2.09680	−0.447039
$23$	−4.47742	−0.933607	−0.466803	−	0.884361i	$-0.654594\pi$
$23$	−4.47742	−0.933607	−0.466803	+	0.884361i	$0.654594\pi$
$24$	−2.04739	−0.417922
$25$	1.76425	0.352850
$26$	1.31675	0.258237
$27$	−1.00000	−0.192450
$28$	−4.59754	−0.868853
$29$	−7.08839	−1.31628	−0.658140	−	0.752895i	$-0.728657\pi$
$29$	−7.08839	−1.31628	−0.658140	+	0.752895i	$0.728657\pi$
$30$	−1.44205	−0.263282
$31$	−6.71511	−1.20607	−0.603035	−	0.797715i	$-0.706042\pi$
$31$	−6.71511	−1.20607	−0.603035	+	0.797715i	$0.706042\pi$
$32$	−5.34229	−0.944392
$33$	−3.78169	−0.658307
$34$	−0.554461	−0.0950894
$35$	−7.06460	−1.19414
$36$	−1.69257	−0.282095
$37$	8.80443	1.44744	0.723719	−	0.690094i	$-0.242431\pi$
$37$	8.80443	1.44744	0.723719	+	0.690094i	$0.242431\pi$
$38$	−2.80870	−0.455632
$39$	2.37483	0.380278
$40$	−5.32488	−0.841938
$41$	4.09058	0.638842	0.319421	−	0.947613i	$-0.396512\pi$
$41$	4.09058	0.638842	0.319421	+	0.947613i	$0.396512\pi$
$42$	1.50608	0.232394
$43$	−10.4995	−1.60116	−0.800581	−	0.599224i	$-0.795476\pi$
$43$	−10.4995	−1.60116	−0.800581	+	0.599224i	$0.795476\pi$
$44$	−6.40078	−0.964954
$45$	−2.60082	−0.387707
$46$	2.48256	0.366033
$47$	11.0837	1.61672	0.808359	−	0.588690i	$-0.200356\pi$
$47$	11.0837	1.61672	0.808359	+	0.588690i	$0.200356\pi$
$48$	−2.24995	−0.324752
$49$	0.378292	0.0540417
$50$	−0.978208	−0.138340
$51$	−1.00000	−0.140028
$52$	4.01958	0.557415
$53$	−2.56188	−0.351901	−0.175951	−	0.984399i	$-0.556300\pi$
$53$	−2.56188	−0.351901	−0.175951	+	0.984399i	$0.556300\pi$
$54$	0.554461	0.0754527
$55$	−9.83547	−1.32622
$56$	5.56133	0.743163
$57$	−5.06564	−0.670961
$58$	3.93024	0.516066
$59$	1.26655	0.164891	0.0824453	−	0.996596i	$-0.473727\pi$
$59$	1.26655	0.164891	0.0824453	+	0.996596i	$0.473727\pi$
$60$	−4.40207	−0.568305
$61$	−13.0027	−1.66483	−0.832414	−	0.554154i	$-0.813042\pi$
$61$	−13.0027	−1.66483	−0.832414	+	0.554154i	$0.813042\pi$
$62$	3.72327	0.472856
$63$	2.71630	0.342222
$64$	−1.53780	−0.192225
$65$	6.17651	0.766102
$66$	2.09680	0.258098
$67$	1.50891	0.184343	0.0921713	−	0.995743i	$-0.470619\pi$
$67$	1.50891	0.184343	0.0921713	+	0.995743i	$0.470619\pi$
$68$	−1.69257	−0.205255
$69$	4.47742	0.539018
$70$	3.91705	0.468177
$71$	15.6673	1.85937	0.929686	−	0.368353i	$-0.120078\pi$
$71$	15.6673	1.85937	0.929686	+	0.368353i	$0.120078\pi$
$72$	2.04739	0.241287
$73$	0.155659	0.0182185	0.00910924	−	0.999959i	$-0.497100\pi$
$73$	0.155659	0.0182185	0.00910924	+	0.999959i	$0.497100\pi$
$74$	−4.88171	−0.567488
$75$	−1.76425	−0.203718
$76$	−8.57397	−0.983501
$77$	10.2722	1.17063
$78$	−1.31675	−0.149093
$79$	−9.11742	−1.02579	−0.512895	−	0.858451i	$-0.671427\pi$
$79$	−9.11742	−1.02579	−0.512895	+	0.858451i	$0.671427\pi$
$80$	−5.85170	−0.654240
$81$	1.00000	0.111111
$82$	−2.26807	−0.250467
$83$	−0.232204	−0.0254877	−0.0127438	−	0.999919i	$-0.504057\pi$
$83$	−0.232204	−0.0254877	−0.0127438	+	0.999919i	$0.504057\pi$
$84$	4.59754	0.501632
$85$	−2.60082	−0.282098
$86$	5.82158	0.627757
$87$	7.08839	0.759955
$88$	7.74258	0.825362
$89$	−9.44493	−1.00116	−0.500580	−	0.865690i	$-0.666880\pi$
$89$	−9.44493	−1.00116	−0.500580	+	0.865690i	$0.666880\pi$
$90$	1.44205	0.152006
$91$	−6.45076	−0.676224
$92$	7.57836	0.790098
$93$	6.71511	0.696324
$94$	−6.14546	−0.633856
$95$	−13.1748	−1.35171
$96$	5.34229	0.545245
$97$	1.00603	0.102147	0.0510736	−	0.998695i	$-0.483736\pi$
$97$	1.00603	0.102147	0.0510736	+	0.998695i	$0.483736\pi$
$98$	−0.209748	−0.0211878
$99$	3.78169	0.380074
$100$	−2.98612	−0.298612
$101$	0.865332	0.0861037	0.0430519	−	0.999073i	$-0.486292\pi$
$101$	0.865332	0.0861037	0.0430519	+	0.999073i	$0.486292\pi$
$102$	0.554461	0.0548999
$103$	2.02414	0.199445	0.0997224	−	0.995015i	$-0.468205\pi$
$103$	2.02414	0.199445	0.0997224	+	0.995015i	$0.468205\pi$
$104$	−4.86221	−0.476779
$105$	7.06460	0.689435
$106$	1.42046	0.137968
$107$	9.38943	0.907710	0.453855	−	0.891076i	$-0.350048\pi$
$107$	9.38943	0.907710	0.453855	+	0.891076i	$0.350048\pi$
$108$	1.69257	0.162868
$109$	17.9710	1.72131	0.860654	−	0.509191i	$-0.170055\pi$
$109$	17.9710	1.72131	0.860654	+	0.509191i	$0.170055\pi$
$110$	5.45339	0.519961
$111$	−8.80443	−0.835679
$112$	6.11153	0.577486
$113$	−14.4400	−1.35840	−0.679201	−	0.733952i	$-0.737673\pi$
$113$	−14.4400	−1.35840	−0.679201	+	0.733952i	$0.737673\pi$
$114$	2.80870	0.263059
$115$	11.6449	1.08590
$116$	11.9976	1.11395
$117$	−2.37483	−0.219553
$118$	−0.702253	−0.0646476
$119$	2.71630	0.249003
$120$	5.32488	0.486093
$121$	3.30115	0.300105
$122$	7.20951	0.652718
$123$	−4.09058	−0.368835
$124$	11.3658	1.02068
$125$	8.41560	0.752714
$126$	−1.50608	−0.134173
$127$	5.75778	0.510921	0.255460	−	0.966820i	$-0.417773\pi$
$127$	5.75778	0.510921	0.255460	+	0.966820i	$0.417773\pi$
$128$	11.5372	1.01976
$129$	10.4995	0.924432
$130$	−3.42464	−0.300360
$131$	1.80061	0.157320	0.0786600	−	0.996901i	$-0.474936\pi$
$131$	1.80061	0.157320	0.0786600	+	0.996901i	$0.474936\pi$
$132$	6.40078	0.557116
$133$	13.7598	1.19313
$134$	−0.836632	−0.0722740
$135$	2.60082	0.223843
$136$	2.04739	0.175562
$137$	15.0439	1.28528	0.642642	−	0.766166i	$-0.277838\pi$
$137$	15.0439	1.28528	0.642642	+	0.766166i	$0.277838\pi$
$138$	−2.48256	−0.211329
$139$	−6.45182	−0.547236	−0.273618	−	0.961838i	$-0.588220\pi$
$139$	−6.45182	−0.547236	−0.273618	+	0.961838i	$0.588220\pi$
$140$	11.9574	1.01058
$141$	−11.0837	−0.933412
$142$	−8.68694	−0.728992
$143$	−8.98088	−0.751019
$144$	2.24995	0.187496
$145$	18.4356	1.53099
$146$	−0.0863068	−0.00714280
$147$	−0.378292	−0.0312010
$148$	−14.9021	−1.22495
$149$	−0.0972045	−0.00796330	−0.00398165	−	0.999992i	$-0.501267\pi$
$149$	−0.0972045	−0.00796330	−0.00398165	+	0.999992i	$0.501267\pi$
$150$	0.978208	0.0798704
$151$	−17.7438	−1.44397	−0.721984	−	0.691909i	$-0.756770\pi$
$151$	−17.7438	−1.44397	−0.721984	+	0.691909i	$0.756770\pi$
$152$	10.3713	0.841227
$153$	1.00000	0.0808452
$154$	−5.69554	−0.458960
$155$	17.4648	1.40280
$156$	−4.01958	−0.321824
$157$	1.00000	0.0798087
$157$	1.00000	0.0798087
$158$	5.05526	0.402175
$159$	2.56188	0.203170
$160$	13.8943	1.09844
$161$	−12.1620	−0.958501
$162$	−0.554461	−0.0435626
$163$	20.0255	1.56851	0.784257	−	0.620436i	$-0.213044\pi$
$163$	20.0255	1.56851	0.784257	+	0.620436i	$0.213044\pi$
$164$	−6.92361	−0.540643
$165$	9.83547	0.765691
$166$	0.128748	0.00999278
$167$	−0.191219	−0.0147970	−0.00739848	−	0.999973i	$-0.502355\pi$
$167$	−0.191219	−0.0147970	−0.00739848	+	0.999973i	$0.502355\pi$
$168$	−5.56133	−0.429066
$169$	−7.36016	−0.566166
$170$	1.44205	0.110600
$171$	5.06564	0.387379
$172$	17.7712	1.35504
$173$	−10.0438	−0.763617	−0.381809	−	0.924241i	$-0.624699\pi$
$173$	−10.0438	−0.763617	−0.381809	+	0.924241i	$0.624699\pi$
$174$	−3.93024	−0.297951
$175$	4.79223	0.362259
$176$	8.50859	0.641359
$177$	−1.26655	−0.0951996
$178$	5.23685	0.392519
$179$	−14.9109	−1.11449	−0.557245	−	0.830348i	$-0.688142\pi$
$179$	−14.9109	−1.11449	−0.557245	+	0.830348i	$0.688142\pi$
$180$	4.40207	0.328111
$181$	16.5249	1.22828	0.614142	−	0.789195i	$-0.289502\pi$
$181$	16.5249	1.22828	0.614142	+	0.789195i	$0.289502\pi$
$182$	3.57670	0.265123
$183$	13.0027	0.961189
$184$	−9.16702	−0.675802
$185$	−22.8987	−1.68355
$186$	−3.72327	−0.273003
$187$	3.78169	0.276544
$188$	−18.7599	−1.36821
$189$	−2.71630	−0.197582
$190$	7.30492	0.529955
$191$	11.8044	0.854140	0.427070	−	0.904219i	$-0.359546\pi$
$191$	11.8044	0.854140	0.427070	+	0.904219i	$0.359546\pi$
$192$	1.53780	0.110981
$193$	−27.2324	−1.96023	−0.980115	−	0.198428i	$-0.936416\pi$
$193$	−27.2324	−1.96023	−0.980115	+	0.198428i	$0.936416\pi$
$194$	−0.557807	−0.0400482
$195$	−6.17651	−0.442309
$196$	−0.640286	−0.0457347
$197$	−3.15468	−0.224762	−0.112381	−	0.993665i	$-0.535848\pi$
$197$	−3.15468	−0.224762	−0.112381	+	0.993665i	$0.535848\pi$
$198$	−2.09680	−0.149013
$199$	−12.3656	−0.876577	−0.438288	−	0.898834i	$-0.644415\pi$
$199$	−12.3656	−0.876577	−0.438288	+	0.898834i	$0.644415\pi$
$200$	3.61210	0.255414
$201$	−1.50891	−0.106430
$202$	−0.479793	−0.0337581
$203$	−19.2542	−1.35138
$204$	1.69257	0.118504
$205$	−10.6389	−0.743050
$206$	−1.12231	−0.0781950
$207$	−4.47742	−0.311202
$208$	−5.34325	−0.370488
$209$	19.1567	1.32509
$210$	−3.91705	−0.270302
$211$	5.60876	0.386123	0.193061	−	0.981187i	$-0.438158\pi$
$211$	5.60876	0.386123	0.193061	+	0.981187i	$0.438158\pi$
$212$	4.33617	0.297809
$213$	−15.6673	−1.07351
$214$	−5.20608	−0.355880
$215$	27.3073	1.86235
$216$	−2.04739	−0.139307
$217$	−18.2403	−1.23823
$218$	−9.96421	−0.674862
$219$	−0.155659	−0.0105184
$220$	16.6473	1.12236
$221$	−2.37483	−0.159749
$222$	4.88171	0.327639
$223$	3.51649	0.235482	0.117741	−	0.993044i	$-0.462435\pi$
$223$	3.51649	0.235482	0.117741	+	0.993044i	$0.462435\pi$
$224$	−14.5113	−0.969574
$225$	1.76425	0.117617
$226$	8.00643	0.532580
$227$	−11.5171	−0.764415	−0.382207	−	0.924077i	$-0.624836\pi$
$227$	−11.5171	−0.764415	−0.382207	+	0.924077i	$0.624836\pi$
$228$	8.57397	0.567825
$229$	28.1045	1.85719	0.928597	−	0.371089i	$-0.121016\pi$
$229$	28.1045	1.85719	0.928597	+	0.371089i	$0.121016\pi$
$230$	−6.45668	−0.425741
$231$	−10.2722	−0.675861
$232$	−14.5127	−0.952805
$233$	2.98103	0.195294	0.0976470	−	0.995221i	$-0.468868\pi$
$233$	2.98103	0.195294	0.0976470	+	0.995221i	$0.468868\pi$
$234$	1.31675	0.0860789
$235$	−28.8266	−1.88044
$236$	−2.14373	−0.139545
$237$	9.11742	0.592240
$238$	−1.50608	−0.0976249
$239$	3.71433	0.240260	0.120130	−	0.992758i	$-0.461669\pi$
$239$	3.71433	0.240260	0.120130	+	0.992758i	$0.461669\pi$
$240$	5.85170	0.377726
$241$	13.4848	0.868633	0.434317	−	0.900760i	$-0.356990\pi$
$241$	13.4848	0.868633	0.434317	+	0.900760i	$0.356990\pi$
$242$	−1.83036	−0.117660
$243$	−1.00000	−0.0641500
$244$	22.0081	1.40892
$245$	−0.983868	−0.0628570
$246$	2.26807	0.144607
$247$	−12.0301	−0.765454
$248$	−13.7484	−0.873027
$249$	0.232204	0.0147153
$250$	−4.66612	−0.295112
$251$	1.14811	0.0724681	0.0362341	−	0.999343i	$-0.488464\pi$
$251$	1.14811	0.0724681	0.0362341	+	0.999343i	$0.488464\pi$
$252$	−4.59754	−0.289618
$253$	−16.9322	−1.06452
$254$	−3.19247	−0.200313
$255$	2.60082	0.162869
$256$	−3.32135	−0.207584
$257$	−3.85389	−0.240399	−0.120200	−	0.992750i	$-0.538353\pi$
$257$	−3.85389	−0.240399	−0.120200	+	0.992750i	$0.538353\pi$
$258$	−5.82158	−0.362436
$259$	23.9155	1.48603
$260$	−10.4542	−0.648341
$261$	−7.08839	−0.438760
$262$	−0.998369	−0.0616795
$263$	−11.1982	−0.690513	−0.345256	−	0.938508i	$-0.612208\pi$
$263$	−11.1982	−0.690513	−0.345256	+	0.938508i	$0.612208\pi$
$264$	−7.74258	−0.476523
$265$	6.66298	0.409304
$266$	−7.62928	−0.467781
$267$	9.44493	0.578021
$268$	−2.55394	−0.156007
$269$	−0.513140	−0.0312867	−0.0156433	−	0.999878i	$-0.504980\pi$
$269$	−0.513140	−0.0312867	−0.0156433	+	0.999878i	$0.504980\pi$
$270$	−1.44205	−0.0877605
$271$	−17.5029	−1.06323	−0.531614	−	0.846987i	$-0.678414\pi$
$271$	−17.5029	−1.06323	−0.531614	+	0.846987i	$0.678414\pi$
$272$	2.24995	0.136423
$273$	6.45076	0.390418
$274$	−8.34125	−0.503913
$275$	6.67184	0.402327
$276$	−7.57836	−0.456163
$277$	−17.4892	−1.05082	−0.525411	−	0.850849i	$-0.676088\pi$
$277$	−17.4892	−1.05082	−0.525411	+	0.850849i	$0.676088\pi$
$278$	3.57729	0.214551
$279$	−6.71511	−0.402023
$280$	−14.4640	−0.864389
$281$	−5.22220	−0.311531	−0.155765	−	0.987794i	$-0.549784\pi$
$281$	−5.22220	−0.311531	−0.155765	+	0.987794i	$0.549784\pi$
$282$	6.14546	0.365957
$283$	−14.8911	−0.885185	−0.442593	−	0.896723i	$-0.645941\pi$
$283$	−14.8911	−0.885185	−0.442593	+	0.896723i	$0.645941\pi$
$284$	−26.5181	−1.57356
$285$	13.1748	0.780408
$286$	4.97955	0.294447
$287$	11.1113	0.655877
$288$	−5.34229	−0.314797
$289$	1.00000	0.0588235
$290$	−10.2218	−0.600247
$291$	−1.00603	−0.0589747
$292$	−0.263464	−0.0154181
$293$	11.2595	0.657786	0.328893	−	0.944367i	$-0.393324\pi$
$293$	11.2595	0.657786	0.328893	+	0.944367i	$0.393324\pi$
$294$	0.209748	0.0122328
$295$	−3.29406	−0.191788
$296$	18.0261	1.04774
$297$	−3.78169	−0.219436
$298$	0.0538961	0.00312212
$299$	10.6331	0.614930
$300$	2.98612	0.172404
$301$	−28.5199	−1.64386
$302$	9.83825	0.566127
$303$	−0.865332	−0.0497120
$304$	11.3974	0.653687
$305$	33.8177	1.93640
$306$	−0.554461	−0.0316965
$307$	−13.3312	−0.760853	−0.380427	−	0.924811i	$-0.624223\pi$
$307$	−13.3312	−0.760853	−0.380427	+	0.924811i	$0.624223\pi$
$308$	−17.3864	−0.990685
$309$	−2.02414	−0.115149
$310$	−9.68354	−0.549988
$311$	−6.35767	−0.360511	−0.180255	−	0.983620i	$-0.557692\pi$
$311$	−6.35767	−0.360511	−0.180255	+	0.983620i	$0.557692\pi$
$312$	4.86221	0.275268
$313$	−10.4893	−0.592889	−0.296445	−	0.955050i	$-0.595801\pi$
$313$	−10.4893	−0.592889	−0.296445	+	0.955050i	$0.595801\pi$
$314$	−0.554461	−0.0312901
$315$	−7.06460	−0.398045
$316$	15.4319	0.868112
$317$	24.2585	1.36249	0.681247	−	0.732054i	$-0.261438\pi$
$317$	24.2585	1.36249	0.681247	+	0.732054i	$0.261438\pi$
$318$	−1.42046	−0.0796557
$319$	−26.8061	−1.50085
$320$	3.99954	0.223581
$321$	−9.38943	−0.524067
$322$	6.74337	0.375793
$323$	5.06564	0.281860
$324$	−1.69257	−0.0940318
$325$	−4.18980	−0.232408
$326$	−11.1033	−0.614957
$327$	−17.9710	−0.993797
$328$	8.37502	0.462433
$329$	30.1065	1.65983
$330$	−5.45339	−0.300199
$331$	−26.4465	−1.45363	−0.726814	−	0.686834i	$-0.759000\pi$
$331$	−26.4465	−1.45363	−0.726814	+	0.686834i	$0.759000\pi$
$332$	0.393021	0.0215699
$333$	8.80443	0.482480
$334$	0.106023	0.00580134
$335$	−3.92440	−0.214413
$336$	−6.11153	−0.333411
$337$	5.10263	0.277958	0.138979	−	0.990295i	$-0.455618\pi$
$337$	5.10263	0.277958	0.138979	+	0.990295i	$0.455618\pi$
$338$	4.08093	0.221973
$339$	14.4400	0.784274
$340$	4.40207	0.238736
$341$	−25.3944	−1.37519
$342$	−2.80870	−0.151877
$343$	−17.9866	−0.971183
$344$	−21.4966	−1.15902
$345$	−11.6449	−0.626943
$346$	5.56891	0.299386
$347$	−22.2219	−1.19293	−0.596466	−	0.802638i	$-0.703429\pi$
$347$	−22.2219	−1.19293	−0.596466	+	0.802638i	$0.703429\pi$
$348$	−11.9976	−0.643139
$349$	−21.4996	−1.15085	−0.575424	−	0.817855i	$-0.695163\pi$
$349$	−21.4996	−1.15085	−0.575424	+	0.817855i	$0.695163\pi$
$350$	−2.65711	−0.142028
$351$	2.37483	0.126759
$352$	−20.2029	−1.07682
$353$	23.4806	1.24975	0.624873	−	0.780727i	$-0.285151\pi$
$353$	23.4806	1.24975	0.624873	+	0.780727i	$0.285151\pi$
$354$	0.702253	0.0373243
$355$	−40.7479	−2.16267
$356$	15.9862	0.847269
$357$	−2.71630	−0.143762
$358$	8.26750	0.436951
$359$	−20.8843	−1.10223	−0.551115	−	0.834429i	$-0.685798\pi$
$359$	−20.8843	−1.10223	−0.551115	+	0.834429i	$0.685798\pi$
$360$	−5.32488	−0.280646
$361$	6.66073	0.350565
$362$	−9.16241	−0.481565
$363$	−3.30115	−0.173266
$364$	10.9184	0.572279
$365$	−0.404840	−0.0211903
$366$	−7.20951	−0.376847
$367$	−18.7707	−0.979823	−0.489912	−	0.871772i	$-0.662971\pi$
$367$	−18.7707	−0.979823	−0.489912	+	0.871772i	$0.662971\pi$
$368$	−10.0740	−0.525141
$369$	4.09058	0.212947
$370$	12.6964	0.660057
$371$	−6.95884	−0.361285
$372$	−11.3658	−0.589290
$373$	17.5331	0.907831	0.453916	−	0.891045i	$-0.350027\pi$
$373$	17.5331	0.907831	0.453916	+	0.891045i	$0.350027\pi$
$374$	−2.09680	−0.108423
$375$	−8.41560	−0.434580
$376$	22.6926	1.17028
$377$	16.8337	0.866982
$378$	1.50608	0.0774646
$379$	−15.7861	−0.810880	−0.405440	−	0.914122i	$-0.632882\pi$
$379$	−15.7861	−0.810880	−0.405440	+	0.914122i	$0.632882\pi$
$380$	22.2993	1.14393
$381$	−5.75778	−0.294980
$382$	−6.54511	−0.334877
$383$	2.09154	0.106873	0.0534364	−	0.998571i	$-0.482983\pi$
$383$	2.09154	0.106873	0.0534364	+	0.998571i	$0.482983\pi$
$384$	−11.5372	−0.588757
$385$	−26.7161	−1.36158
$386$	15.0993	0.768535
$387$	−10.4995	−0.533721
$388$	−1.70279	−0.0864458
$389$	17.2226	0.873222	0.436611	−	0.899650i	$-0.356179\pi$
$389$	17.2226	0.873222	0.436611	+	0.899650i	$0.356179\pi$
$390$	3.42464	0.173413
$391$	−4.47742	−0.226433
$392$	0.774511	0.0391187
$393$	−1.80061	−0.0908288
$394$	1.74915	0.0881209
$395$	23.7127	1.19312
$396$	−6.40078	−0.321651
$397$	6.44185	0.323307	0.161654	−	0.986848i	$-0.448317\pi$
$397$	6.44185	0.323307	0.161654	+	0.986848i	$0.448317\pi$
$398$	6.85627	0.343674
$399$	−13.7598	−0.688852
$400$	3.96947	0.198473
$401$	9.08832	0.453849	0.226924	−	0.973912i	$-0.427133\pi$
$401$	9.08832	0.453849	0.226924	+	0.973912i	$0.427133\pi$
$402$	0.836632	0.0417274
$403$	15.9473	0.794390
$404$	−1.46464	−0.0728684
$405$	−2.60082	−0.129236
$406$	10.6757	0.529827
$407$	33.2956	1.65040
$408$	−2.04739	−0.101361
$409$	27.5664	1.36307	0.681535	−	0.731786i	$-0.261313\pi$
$409$	27.5664	1.36307	0.681535	+	0.731786i	$0.261313\pi$
$410$	5.89884	0.291323
$411$	−15.0439	−0.742059
$412$	−3.42601	−0.168787
$413$	3.44033	0.169287
$414$	2.48256	0.122011
$415$	0.603919	0.0296452
$416$	12.6870	0.622034
$417$	6.45182	0.315947
$418$	−10.6216	−0.519521
$419$	26.9489	1.31654	0.658270	−	0.752782i	$-0.271288\pi$
$419$	26.9489	1.31654	0.658270	+	0.752782i	$0.271288\pi$
$420$	−11.9574	−0.583459
$421$	36.1631	1.76248	0.881242	−	0.472666i	$-0.156708\pi$
$421$	36.1631	1.76248	0.881242	+	0.472666i	$0.156708\pi$
$422$	−3.10984	−0.151385
$423$	11.0837	0.538906
$424$	−5.24517	−0.254728
$425$	1.76425	0.0855787
$426$	8.68694	0.420884
$427$	−35.3193	−1.70922
$428$	−15.8923	−0.768183
$429$	8.98088	0.433601
$430$	−15.1409	−0.730158
$431$	25.5781	1.23206	0.616028	−	0.787724i	$-0.288741\pi$
$431$	25.5781	1.23206	0.616028	+	0.787724i	$0.288741\pi$
$432$	−2.24995	−0.108251
$433$	−31.0373	−1.49156	−0.745778	−	0.666194i	$-0.767922\pi$
$433$	−31.0373	−1.49156	−0.745778	+	0.666194i	$0.767922\pi$
$434$	10.1135	0.485464
$435$	−18.4356	−0.883919
$436$	−30.4172	−1.45672
$437$	−22.6810	−1.08498
$438$	0.0863068	0.00412390
$439$	25.1093	1.19840	0.599201	−	0.800598i	$-0.295485\pi$
$439$	25.1093	1.19840	0.599201	+	0.800598i	$0.295485\pi$
$440$	−20.1370	−0.959996
$441$	0.378292	0.0180139
$442$	1.31675	0.0626316
$443$	−33.3677	−1.58535	−0.792675	−	0.609645i	$-0.791312\pi$
$443$	−33.3677	−1.58535	−0.792675	+	0.609645i	$0.791312\pi$
$444$	14.9021	0.707224
$445$	24.5645	1.16447
$446$	−1.94976	−0.0923237
$447$	0.0972045	0.00459761
$448$	−4.17713	−0.197351
$449$	−32.4797	−1.53281	−0.766407	−	0.642355i	$-0.777957\pi$
$449$	−32.4797	−1.53281	−0.766407	+	0.642355i	$0.777957\pi$
$450$	−0.978208	−0.0461132
$451$	15.4693	0.728421
$452$	24.4408	1.14960
$453$	17.7438	0.833676
$454$	6.38577	0.299699
$455$	16.7773	0.786530
$456$	−10.3713	−0.485682
$457$	−40.6688	−1.90241	−0.951203	−	0.308565i	$-0.900151\pi$
$457$	−40.6688	−1.90241	−0.951203	+	0.308565i	$0.900151\pi$
$458$	−15.5828	−0.728138
$459$	−1.00000	−0.0466760
$460$	−19.7099	−0.918980
$461$	−2.47067	−0.115071	−0.0575353	−	0.998343i	$-0.518324\pi$
$461$	−2.47067	−0.115071	−0.0575353	+	0.998343i	$0.518324\pi$
$462$	5.69554	0.264980
$463$	−17.0426	−0.792036	−0.396018	−	0.918243i	$-0.629608\pi$
$463$	−17.0426	−0.792036	−0.396018	+	0.918243i	$0.629608\pi$
$464$	−15.9485	−0.740390
$465$	−17.4648	−0.809909
$466$	−1.65287	−0.0765676
$467$	−6.02951	−0.279012	−0.139506	−	0.990221i	$-0.544552\pi$
$467$	−6.02951	−0.279012	−0.139506	+	0.990221i	$0.544552\pi$
$468$	4.01958	0.185805
$469$	4.09865	0.189258
$470$	15.9832	0.737251
$471$	−1.00000	−0.0460776
$472$	2.59312	0.119358
$473$	−39.7059	−1.82568
$474$	−5.05526	−0.232196
$475$	8.93705	0.410060
$476$	−4.59754	−0.210728
$477$	−2.56188	−0.117300
$478$	−2.05945	−0.0941971
$479$	−10.5290	−0.481082	−0.240541	−	0.970639i	$-0.577325\pi$
$479$	−10.5290	−0.481082	−0.240541	+	0.970639i	$0.577325\pi$
$480$	−13.8943	−0.634186
$481$	−20.9090	−0.953371
$482$	−7.47681	−0.340559
$483$	12.1620	0.553391
$484$	−5.58744	−0.253975
$485$	−2.61651	−0.118810
$486$	0.554461	0.0251509
$487$	2.35242	0.106598	0.0532992	−	0.998579i	$-0.483026\pi$
$487$	2.35242	0.106598	0.0532992	+	0.998579i	$0.483026\pi$
$488$	−26.6216	−1.20510
$489$	−20.0255	−0.905582
$490$	0.545517	0.0246439
$491$	10.0484	0.453477	0.226739	−	0.973956i	$-0.427194\pi$
$491$	10.0484	0.453477	0.226739	+	0.973956i	$0.427194\pi$
$492$	6.92361	0.312140
$493$	−7.08839	−0.319245
$494$	6.67020	0.300107
$495$	−9.83547	−0.442072
$496$	−15.1086	−0.678398
$497$	42.5572	1.90895
$498$	−0.128748	−0.00576933
$499$	−14.4630	−0.647454	−0.323727	−	0.946150i	$-0.604936\pi$
$499$	−14.4630	−0.647454	−0.323727	+	0.946150i	$0.604936\pi$
$500$	−14.2440	−0.637011
$501$	0.191219	0.00854302
$502$	−0.636583	−0.0284121
$503$	18.1815	0.810673	0.405336	−	0.914168i	$-0.367154\pi$
$503$	18.1815	0.810673	0.405336	+	0.914168i	$0.367154\pi$
$504$	5.56133	0.247721
$505$	−2.25057	−0.100149
$506$	9.38825	0.417359
$507$	7.36016	0.326876
$508$	−9.74547	−0.432385
$509$	−33.6925	−1.49340	−0.746698	−	0.665164i	$-0.768362\pi$
$509$	−33.6925	−1.49340	−0.746698	+	0.665164i	$0.768362\pi$
$510$	−1.44205	−0.0638552
$511$	0.422816	0.0187043
$512$	−21.2329	−0.938370
$513$	−5.06564	−0.223654
$514$	2.13684	0.0942518
$515$	−5.26443	−0.231978
$516$	−17.7712	−0.782334
$517$	41.9149	1.84342
$518$	−13.2602	−0.582620
$519$	10.0438	0.440875
$520$	12.6457	0.554551
$521$	29.0702	1.27359	0.636795	−	0.771033i	$-0.280260\pi$
$521$	29.0702	1.27359	0.636795	+	0.771033i	$0.280260\pi$
$522$	3.93024	0.172022
$523$	−37.9108	−1.65773	−0.828863	−	0.559452i	$-0.811012\pi$
$523$	−37.9108	−1.65773	−0.828863	+	0.559452i	$0.811012\pi$
$524$	−3.04766	−0.133138
$525$	−4.79223	−0.209150
$526$	6.20899	0.270725
$527$	−6.71511	−0.292515
$528$	−8.50859	−0.370289
$529$	−2.95271	−0.128379
$530$	−3.69437	−0.160473
$531$	1.26655	0.0549635
$532$	−23.2895	−1.00973
$533$	−9.71446	−0.420780
$534$	−5.23685	−0.226621
$535$	−24.4202	−1.05578
$536$	3.08932	0.133439
$537$	14.9109	0.643451
$538$	0.284516	0.0122664
$539$	1.43058	0.0616195
$540$	−4.40207	−0.189435
$541$	7.08702	0.304695	0.152347	−	0.988327i	$-0.451317\pi$
$541$	7.08702	0.304695	0.152347	+	0.988327i	$0.451317\pi$
$542$	9.70471	0.416853
$543$	−16.5249	−0.709150
$544$	−5.34229	−0.229049
$545$	−46.7392	−2.00209
$546$	−3.57670	−0.153069
$547$	−29.2633	−1.25121	−0.625603	−	0.780141i	$-0.715147\pi$
$547$	−29.2633	−1.25121	−0.625603	+	0.780141i	$0.715147\pi$
$548$	−25.4628	−1.08772
$549$	−13.0027	−0.554943
$550$	−3.69928	−0.157738
$551$	−35.9072	−1.52970
$552$	9.16702	0.390174
$553$	−24.7657	−1.05314
$554$	9.69706	0.411989
$555$	22.8987	0.971996
$556$	10.9202	0.463118
$557$	−27.2907	−1.15634	−0.578172	−	0.815915i	$-0.696234\pi$
$557$	−27.2907	−1.15634	−0.578172	+	0.815915i	$0.696234\pi$
$558$	3.72327	0.157619
$559$	24.9346	1.05462
$560$	−15.8950	−0.671685
$561$	−3.78169	−0.159663
$562$	2.89551	0.122140
$563$	−17.7877	−0.749663	−0.374832	−	0.927093i	$-0.622299\pi$
$563$	−17.7877	−0.749663	−0.374832	+	0.927093i	$0.622299\pi$
$564$	18.7599	0.789934
$565$	37.5558	1.57999
$566$	8.25655	0.347049
$567$	2.71630	0.114074
$568$	32.0772	1.34593
$569$	1.41111	0.0591568	0.0295784	−	0.999562i	$-0.490584\pi$
$569$	1.41111	0.0591568	0.0295784	+	0.999562i	$0.490584\pi$
$570$	−7.30492	−0.305970
$571$	25.5886	1.07085	0.535424	−	0.844583i	$-0.320152\pi$
$571$	25.5886	1.07085	0.535424	+	0.844583i	$0.320152\pi$
$572$	15.2008	0.635577
$573$	−11.8044	−0.493138
$574$	−6.16076	−0.257145
$575$	−7.89928	−0.329423
$576$	−1.53780	−0.0640750
$577$	−17.6300	−0.733946	−0.366973	−	0.930232i	$-0.619606\pi$
$577$	−17.6300	−0.733946	−0.366973	+	0.930232i	$0.619606\pi$
$578$	−0.554461	−0.0230626
$579$	27.2324	1.13174
$580$	−31.2036	−1.29566
$581$	−0.630735	−0.0261673
$582$	0.557807	0.0231218
$583$	−9.68823	−0.401246
$584$	0.318694	0.0131877
$585$	6.17651	0.255367
$586$	−6.24295	−0.257894
$587$	28.9192	1.19362	0.596812	−	0.802381i	$-0.296434\pi$
$587$	28.9192	1.19362	0.596812	+	0.802381i	$0.296434\pi$
$588$	0.640286	0.0264050
$589$	−34.0163	−1.40162
$590$	1.82643	0.0751930
$591$	3.15468	0.129766
$592$	19.8095	0.814165
$593$	9.66403	0.396854	0.198427	−	0.980116i	$-0.436417\pi$
$593$	9.66403	0.396854	0.198427	+	0.980116i	$0.436417\pi$
$594$	2.09680	0.0860327
$595$	−7.06460	−0.289620
$596$	0.164526	0.00673923
$597$	12.3656	0.506092
$598$	−5.89566	−0.241091
$599$	−35.9718	−1.46977	−0.734883	−	0.678194i	$-0.762763\pi$
$599$	−35.9718	−1.46977	−0.734883	+	0.678194i	$0.762763\pi$
$600$	−3.61210	−0.147464
$601$	−16.9273	−0.690481	−0.345240	−	0.938514i	$-0.612203\pi$
$601$	−16.9273	−0.690481	−0.345240	+	0.938514i	$0.612203\pi$
$602$	15.8132	0.644497
$603$	1.50891	0.0614475
$604$	30.0326	1.22201
$605$	−8.58570	−0.349058
$606$	0.479793	0.0194903
$607$	−38.2651	−1.55313	−0.776567	−	0.630035i	$-0.783041\pi$
$607$	−38.2651	−1.55313	−0.776567	+	0.630035i	$0.783041\pi$
$608$	−27.0621	−1.09751
$609$	19.2542	0.780219
$610$	−18.7506	−0.759190
$611$	−26.3218	−1.06487
$612$	−1.69257	−0.0684182
$613$	−1.04225	−0.0420963	−0.0210481	−	0.999778i	$-0.506700\pi$
$613$	−1.04225	−0.0420963	−0.0210481	+	0.999778i	$0.506700\pi$
$614$	7.39165	0.298303
$615$	10.6389	0.429000
$616$	21.0312	0.847371
$617$	−23.9533	−0.964322	−0.482161	−	0.876083i	$-0.660148\pi$
$617$	−23.9533	−0.964322	−0.482161	+	0.876083i	$0.660148\pi$
$618$	1.12231	0.0451459
$619$	−11.6995	−0.470241	−0.235121	−	0.971966i	$-0.575548\pi$
$619$	−11.6995	−0.470241	−0.235121	+	0.971966i	$0.575548\pi$
$620$	−29.5604	−1.18717
$621$	4.47742	0.179673
$622$	3.52508	0.141343
$623$	−25.6553	−1.02786
$624$	5.34325	0.213901
$625$	−30.7087	−1.22835
$626$	5.81590	0.232450
$627$	−19.1567	−0.765044
$628$	−1.69257	−0.0675410
$629$	8.80443	0.351055
$630$	3.91705	0.156059
$631$	−17.2015	−0.684780	−0.342390	−	0.939558i	$-0.611236\pi$
$631$	−17.2015	−0.684780	−0.342390	+	0.939558i	$0.611236\pi$
$632$	−18.6669	−0.742530
$633$	−5.60876	−0.222928
$634$	−13.4504	−0.534184
$635$	−14.9749	−0.594262
$636$	−4.33617	−0.171940
$637$	−0.898380	−0.0355951
$638$	14.8629	0.588429
$639$	15.6673	0.619791
$640$	−30.0062	−1.18610
$641$	−0.923545	−0.0364778	−0.0182389	−	0.999834i	$-0.505806\pi$
$641$	−0.923545	−0.0364778	−0.0182389	+	0.999834i	$0.505806\pi$
$642$	5.20608	0.205467
$643$	31.2442	1.23215	0.616075	−	0.787688i	$-0.288722\pi$
$643$	31.2442	1.23215	0.616075	+	0.787688i	$0.288722\pi$
$644$	20.5851	0.811167
$645$	−27.3073	−1.07523
$646$	−2.80870	−0.110507
$647$	21.4912	0.844907	0.422453	−	0.906385i	$-0.361169\pi$
$647$	21.4912	0.844907	0.422453	+	0.906385i	$0.361169\pi$
$648$	2.04739	0.0804290
$649$	4.78969	0.188012
$650$	2.32308	0.0911188
$651$	18.2403	0.714892
$652$	−33.8945	−1.32741
$653$	33.1099	1.29569	0.647846	−	0.761771i	$-0.275670\pi$
$653$	33.1099	1.29569	0.647846	+	0.761771i	$0.275670\pi$
$654$	9.96421	0.389632
$655$	−4.68306	−0.182982
$656$	9.20359	0.359340
$657$	0.155659	0.00607283
$658$	−16.6929	−0.650758
$659$	50.0613	1.95011	0.975055	−	0.221963i	$-0.0712464\pi$
$659$	50.0613	1.95011	0.975055	+	0.221963i	$0.0712464\pi$
$660$	−16.6473	−0.647993
$661$	−29.6208	−1.15211	−0.576057	−	0.817409i	$-0.695410\pi$
$661$	−29.6208	−1.15211	−0.576057	+	0.817409i	$0.695410\pi$
$662$	14.6635	0.569915
$663$	2.37483	0.0922309
$664$	−0.475411	−0.0184495
$665$	−35.7867	−1.38775
$666$	−4.88171	−0.189163
$667$	31.7377	1.22889
$668$	0.323652	0.0125225
$669$	−3.51649	−0.135955
$670$	2.17593	0.0840634
$671$	−49.1722	−1.89827
$672$	14.5113	0.559784
$673$	29.8555	1.15085	0.575423	−	0.817856i	$-0.304837\pi$
$673$	29.8555	1.15085	0.575423	+	0.817856i	$0.304837\pi$
$674$	−2.82921	−0.108977
$675$	−1.76425	−0.0679060
$676$	12.4576	0.479139
$677$	33.0687	1.27093	0.635467	−	0.772128i	$-0.280808\pi$
$677$	33.0687	1.27093	0.635467	+	0.772128i	$0.280808\pi$
$678$	−8.00643	−0.307485
$679$	2.73269	0.104871
$680$	−5.32488	−0.204200
$681$	11.5171	0.441335
$682$	14.0802	0.539160
$683$	−27.8323	−1.06497	−0.532486	−	0.846439i	$-0.678742\pi$
$683$	−27.8323	−1.06497	−0.532486	+	0.846439i	$0.678742\pi$
$684$	−8.57397	−0.327834
$685$	−39.1264	−1.49494
$686$	9.97285	0.380765
$687$	−28.1045	−1.07225
$688$	−23.6234	−0.900633
$689$	6.08404	0.231784
$690$	6.45668	0.245801
$691$	−42.1285	−1.60264	−0.801321	−	0.598234i	$-0.795869\pi$
$691$	−42.1285	−1.60264	−0.801321	+	0.598234i	$0.795869\pi$
$692$	16.9999	0.646239
$693$	10.2722	0.390209
$694$	12.3212	0.467705
$695$	16.7800	0.636502
$696$	14.5127	0.550102
$697$	4.09058	0.154942
$698$	11.9207	0.451205
$699$	−2.98103	−0.112753
$700$	−8.11120	−0.306575
$701$	24.0482	0.908290	0.454145	−	0.890928i	$-0.349945\pi$
$701$	24.0482	0.908290	0.454145	+	0.890928i	$0.349945\pi$
$702$	−1.31675	−0.0496977
$703$	44.6001	1.68212
$704$	−5.81548	−0.219179
$705$	28.8266	1.08567
$706$	−13.0191	−0.489979
$707$	2.35050	0.0883997
$708$	2.14373	0.0805662
$709$	−30.0213	−1.12748	−0.563738	−	0.825954i	$-0.690637\pi$
$709$	−30.0213	−1.12748	−0.563738	+	0.825954i	$0.690637\pi$
$710$	22.5931	0.847905
$711$	−9.11742	−0.341930
$712$	−19.3375	−0.724702
$713$	30.0664	1.12599
$714$	1.50608	0.0563638
$715$	23.3576	0.873525
$716$	25.2377	0.943178
$717$	−3.71433	−0.138714
$718$	11.5795	0.432144
$719$	8.04703	0.300104	0.150052	−	0.988678i	$-0.452056\pi$
$719$	8.04703	0.300104	0.150052	+	0.988678i	$0.452056\pi$
$720$	−5.85170	−0.218080
$721$	5.49818	0.204763
$722$	−3.69312	−0.137444
$723$	−13.4848	−0.501506
$724$	−27.9696	−1.03948
$725$	−12.5057	−0.464449
$726$	1.83036	0.0679311
$727$	−7.69002	−0.285207	−0.142604	−	0.989780i	$-0.545547\pi$
$727$	−7.69002	−0.285207	−0.142604	+	0.989780i	$0.545547\pi$
$728$	−13.2072	−0.489492
$729$	1.00000	0.0370370
$730$	0.224468	0.00830794
$731$	−10.4995	−0.388339
$732$	−22.0081	−0.813441
$733$	5.60496	0.207024	0.103512	−	0.994628i	$-0.466992\pi$
$733$	5.60496	0.207024	0.103512	+	0.994628i	$0.466992\pi$
$734$	10.4076	0.384153
$735$	0.983868	0.0362905
$736$	23.9197	0.881690
$737$	5.70622	0.210191
$738$	−2.26807	−0.0834888
$739$	41.3238	1.52012	0.760060	−	0.649853i	$-0.225170\pi$
$739$	41.3238	1.52012	0.760060	+	0.649853i	$0.225170\pi$
$740$	38.7577	1.42476
$741$	12.0301	0.441935
$742$	3.85841	0.141647
$743$	−26.1875	−0.960727	−0.480363	−	0.877070i	$-0.659495\pi$
$743$	−26.1875	−0.960727	−0.480363	+	0.877070i	$0.659495\pi$
$744$	13.7484	0.504042
$745$	0.252811	0.00926228
$746$	−9.72145	−0.355928
$747$	−0.232204	−0.00849589
$748$	−6.40078	−0.234036
$749$	25.5045	0.931915
$750$	4.66612	0.170383
$751$	−37.7562	−1.37774	−0.688872	−	0.724883i	$-0.741894\pi$
$751$	−37.7562	−1.37774	−0.688872	+	0.724883i	$0.741894\pi$
$752$	24.9376	0.909382
$753$	−1.14811	−0.0418395
$754$	−9.33366	−0.339912
$755$	46.1483	1.67951
$756$	4.59754	0.167211
$757$	1.07473	0.0390616	0.0195308	−	0.999809i	$-0.493783\pi$
$757$	1.07473	0.0390616	0.0195308	+	0.999809i	$0.493783\pi$
$758$	8.75281	0.317916
$759$	16.9322	0.614600
$760$	−26.9740	−0.978448
$761$	13.4425	0.487289	0.243644	−	0.969865i	$-0.421657\pi$
$761$	13.4425	0.487289	0.243644	+	0.969865i	$0.421657\pi$
$762$	3.19247	0.115651
$763$	48.8146	1.76721
$764$	−19.9799	−0.722847
$765$	−2.60082	−0.0940327
$766$	−1.15968	−0.0419009
$767$	−3.00784	−0.108607
$768$	3.32135	0.119849
$769$	−18.2948	−0.659726	−0.329863	−	0.944029i	$-0.607003\pi$
$769$	−18.2948	−0.659726	−0.329863	+	0.944029i	$0.607003\pi$
$770$	14.8131	0.533825
$771$	3.85389	0.138795
$772$	46.0928	1.65892
$773$	2.89632	0.104173	0.0520867	−	0.998643i	$-0.483413\pi$
$773$	2.89632	0.104173	0.0520867	+	0.998643i	$0.483413\pi$
$774$	5.82158	0.209252
$775$	−11.8471	−0.425561
$776$	2.05974	0.0739405
$777$	−23.9155	−0.857963
$778$	−9.54928	−0.342358
$779$	20.7214	0.742422
$780$	10.4542	0.374320
$781$	59.2490	2.12010
$782$	2.48256	0.0887760
$783$	7.08839	0.253318
$784$	0.851136	0.0303977
$785$	−2.60082	−0.0928271
$786$	0.998369	0.0356107
$787$	20.9002	0.745013	0.372506	−	0.928030i	$-0.378498\pi$
$787$	20.9002	0.745013	0.372506	+	0.928030i	$0.378498\pi$
$788$	5.33953	0.190213
$789$	11.1982	0.398668
$790$	−13.1478	−0.467778
$791$	−39.2234	−1.39462
$792$	7.74258	0.275121
$793$	30.8793	1.09656
$794$	−3.57176	−0.126757
$795$	−6.66298	−0.236312
$796$	20.9297	0.741835
$797$	−40.5713	−1.43711	−0.718555	−	0.695471i	$-0.755196\pi$
$797$	−40.5713	−1.43711	−0.718555	+	0.695471i	$0.755196\pi$
$798$	7.62928	0.270074
$799$	11.0837	0.392112
$800$	−9.42513	−0.333228
$801$	−9.44493	−0.333720
$802$	−5.03912	−0.177938
$803$	0.588653	0.0207731
$804$	2.55394	0.0900705
$805$	31.6312	1.11485
$806$	−8.84215	−0.311451
$807$	0.513140	0.0180634
$808$	1.77167	0.0623271
$809$	−19.5167	−0.686170	−0.343085	−	0.939304i	$-0.611472\pi$
$809$	−19.5167	−0.686170	−0.343085	+	0.939304i	$0.611472\pi$
$810$	1.44205	0.0506686
$811$	−27.1240	−0.952452	−0.476226	−	0.879323i	$-0.657996\pi$
$811$	−27.1240	−0.952452	−0.476226	+	0.879323i	$0.657996\pi$
$812$	32.5891	1.14365
$813$	17.5029	0.613855
$814$	−18.4611	−0.647062
$815$	−52.0825	−1.82437
$816$	−2.24995	−0.0787639
$817$	−53.1868	−1.86077
$818$	−15.2845	−0.534410
$819$	−6.45076	−0.225408
$820$	18.0070	0.628833
$821$	37.2420	1.29975	0.649877	−	0.760040i	$-0.274821\pi$
$821$	37.2420	1.29975	0.649877	+	0.760040i	$0.274821\pi$
$822$	8.34125	0.290934
$823$	1.71377	0.0597382	0.0298691	−	0.999554i	$-0.490491\pi$
$823$	1.71377	0.0597382	0.0298691	+	0.999554i	$0.490491\pi$
$824$	4.14421	0.144370
$825$	−6.67184	−0.232284
$826$	−1.90753	−0.0663714
$827$	−2.64640	−0.0920243	−0.0460121	−	0.998941i	$-0.514651\pi$
$827$	−2.64640	−0.0920243	−0.0460121	+	0.998941i	$0.514651\pi$
$828$	7.57836	0.263366
$829$	50.7190	1.76154	0.880772	−	0.473541i	$-0.157024\pi$
$829$	50.7190	1.76154	0.880772	+	0.473541i	$0.157024\pi$
$830$	−0.334850	−0.0116228
$831$	17.4892	0.606692
$832$	3.65202	0.126611
$833$	0.378292	0.0131070
$834$	−3.57729	−0.123871
$835$	0.497325	0.0172106
$836$	−32.4241	−1.12141
$837$	6.71511	0.232108
$838$	−14.9421	−0.516168
$839$	−54.3243	−1.87548	−0.937742	−	0.347334i	$-0.887087\pi$
$839$	−54.3243	−1.87548	−0.937742	+	0.347334i	$0.887087\pi$
$840$	14.4640	0.499055
$841$	21.2453	0.732595
$842$	−20.0511	−0.691005
$843$	5.22220	0.179862
$844$	−9.49323	−0.326770
$845$	19.1424	0.658520
$846$	−6.14546	−0.211285
$847$	8.96693	0.308107
$848$	−5.76409	−0.197940
$849$	14.8911	0.511062
$850$	−0.978208	−0.0335523
$851$	−39.4211	−1.35134
$852$	26.5181	0.908496
$853$	49.5721	1.69732	0.848658	−	0.528942i	$-0.177411\pi$
$853$	49.5721	1.69732	0.848658	+	0.528942i	$0.177411\pi$
$854$	19.5832	0.670123
$855$	−13.1748	−0.450569
$856$	19.2238	0.657056
$857$	−2.78102	−0.0949979	−0.0474990	−	0.998871i	$-0.515125\pi$
$857$	−2.78102	−0.0949979	−0.0474990	+	0.998871i	$0.515125\pi$
$858$	−4.97955	−0.169999
$859$	−55.5600	−1.89568	−0.947842	−	0.318740i	$-0.896740\pi$
$859$	−55.5600	−1.89568	−0.947842	+	0.318740i	$0.896740\pi$
$860$	−46.2197	−1.57608
$861$	−11.1113	−0.378671
$862$	−14.1821	−0.483044
$863$	19.1941	0.653373	0.326687	−	0.945133i	$-0.394068\pi$
$863$	19.1941	0.653373	0.326687	+	0.945133i	$0.394068\pi$
$864$	5.34229	0.181748
$865$	26.1221	0.888179
$866$	17.2090	0.584785
$867$	−1.00000	−0.0339618
$868$	30.8730	1.04790
$869$	−34.4792	−1.16963
$870$	10.2218	0.346553
$871$	−3.58341	−0.121419
$872$	36.7936	1.24599
$873$	1.00603	0.0340491
$874$	12.5757	0.425381
$875$	22.8593	0.772785
$876$	0.263464	0.00890162
$877$	31.9395	1.07852	0.539260	−	0.842139i	$-0.318704\pi$
$877$	31.9395	1.07852	0.539260	+	0.842139i	$0.318704\pi$
$878$	−13.9222	−0.469850
$879$	−11.2595	−0.379773
$880$	−22.1293	−0.745978
$881$	0.737808	0.0248574	0.0124287	−	0.999923i	$-0.496044\pi$
$881$	0.737808	0.0248574	0.0124287	+	0.999923i	$0.496044\pi$
$882$	−0.209748	−0.00706259
$883$	−48.4596	−1.63079	−0.815397	−	0.578902i	$-0.803482\pi$
$883$	−48.4596	−1.63079	−0.815397	+	0.578902i	$0.803482\pi$
$884$	4.01958	0.135193
$885$	3.29406	0.110729
$886$	18.5011	0.621558
$887$	1.40366	0.0471303	0.0235652	−	0.999722i	$-0.492498\pi$
$887$	1.40366	0.0471303	0.0235652	+	0.999722i	$0.492498\pi$
$888$	−18.0261	−0.604916
$889$	15.6399	0.524545
$890$	−13.6201	−0.456547
$891$	3.78169	0.126691
$892$	−5.95191	−0.199285
$893$	56.1458	1.87885
$894$	−0.0538961	−0.00180256
$895$	38.7804	1.29629
$896$	31.3386	1.04695
$897$	−10.6331	−0.355030
$898$	18.0088	0.600960
$899$	47.5993	1.58753
$900$	−2.98612	−0.0995373
$901$	−2.56188	−0.0853486
$902$	−8.57713	−0.285587
$903$	28.5199	0.949082
$904$	−29.5643	−0.983294
$905$	−42.9782	−1.42864
$906$	−9.83825	−0.326854
$907$	29.0855	0.965769	0.482884	−	0.875684i	$-0.339589\pi$
$907$	29.0855	0.965769	0.482884	+	0.875684i	$0.339589\pi$
$908$	19.4935	0.646914
$909$	0.865332	0.0287012
$910$	−9.30234	−0.308370
$911$	−38.8095	−1.28582	−0.642909	−	0.765943i	$-0.722273\pi$
$911$	−38.8095	−1.28582	−0.642909	+	0.765943i	$0.722273\pi$
$912$	−11.3974	−0.377406
$913$	−0.878121	−0.0290616
$914$	22.5493	0.745864
$915$	−33.8177	−1.11798
$916$	−47.5688	−1.57172
$917$	4.89100	0.161515
$918$	0.554461	0.0183000
$919$	29.3793	0.969132	0.484566	−	0.874755i	$-0.338978\pi$
$919$	29.3793	0.969132	0.484566	+	0.874755i	$0.338978\pi$
$920$	23.8417	0.786039
$921$	13.3312	0.439279
$922$	1.36989	0.0451150
$923$	−37.2073	−1.22469
$924$	17.3864	0.571972
$925$	15.5332	0.510728
$926$	9.44946	0.310528
$927$	2.02414	0.0664816
$928$	37.8682	1.24308
$929$	25.1209	0.824190	0.412095	−	0.911141i	$-0.364797\pi$
$929$	25.1209	0.824190	0.412095	+	0.911141i	$0.364797\pi$
$930$	9.68354	0.317536
$931$	1.91629	0.0628039
$932$	−5.04561	−0.165275
$933$	6.35767	0.208141
$934$	3.34313	0.109391
$935$	−9.83547	−0.321654
$936$	−4.86221	−0.158926
$937$	−46.6740	−1.52477	−0.762386	−	0.647123i	$-0.775972\pi$
$937$	−46.6740	−1.52477	−0.762386	+	0.647123i	$0.775972\pi$
$938$	−2.27254	−0.0742012
$939$	10.4893	0.342305
$940$	48.7910	1.59139
$941$	−1.80408	−0.0588112	−0.0294056	−	0.999568i	$-0.509361\pi$
$941$	−1.80408	−0.0588112	−0.0294056	+	0.999568i	$0.509361\pi$
$942$	0.554461	0.0180653
$943$	−18.3153	−0.596427
$944$	2.84967	0.0927488
$945$	7.06460	0.229812
$946$	22.0154	0.715782
$947$	−12.7285	−0.413620	−0.206810	−	0.978381i	$-0.566308\pi$
$947$	−12.7285	−0.413620	−0.206810	+	0.978381i	$0.566308\pi$
$948$	−15.4319	−0.501205
$949$	−0.369664	−0.0119998
$950$	−4.95525	−0.160770
$951$	−24.2585	−0.786636
$952$	5.56133	0.180244
$953$	11.0318	0.357354	0.178677	−	0.983908i	$-0.442818\pi$
$953$	11.0318	0.357354	0.178677	+	0.983908i	$0.442818\pi$
$954$	1.42046	0.0459892
$955$	−30.7012	−0.993468
$956$	−6.28677	−0.203329
$957$	26.8061	0.866517
$958$	5.83792	0.188615
$959$	40.8637	1.31956
$960$	−3.99954	−0.129085
$961$	14.0927	0.454603
$962$	11.5933	0.373782
$963$	9.38943	0.302570
$964$	−22.8240	−0.735112
$965$	70.8265	2.27999
$966$	−6.74337	−0.216964
$967$	−19.5555	−0.628862	−0.314431	−	0.949280i	$-0.601814\pi$
$967$	−19.5555	−0.628862	−0.314431	+	0.949280i	$0.601814\pi$
$968$	6.75875	0.217234
$969$	−5.06564	−0.162732
$970$	1.45075	0.0465809
$971$	29.4854	0.946231	0.473116	−	0.881000i	$-0.343129\pi$
$971$	29.4854	0.946231	0.473116	+	0.881000i	$0.343129\pi$
$972$	1.69257	0.0542893
$973$	−17.5251	−0.561828
$974$	−1.30433	−0.0417933
$975$	4.18980	0.134181
$976$	−29.2554	−0.936444
$977$	10.5611	0.337881	0.168940	−	0.985626i	$-0.445965\pi$
$977$	10.5611	0.337881	0.168940	+	0.985626i	$0.445965\pi$
$978$	11.1033	0.355046
$979$	−35.7178	−1.14155
$980$	1.66527	0.0531950
$981$	17.9710	0.573769
$982$	−5.57144	−0.177792
$983$	56.9571	1.81665	0.908324	−	0.418267i	$-0.137362\pi$
$983$	56.9571	1.81665	0.908324	+	0.418267i	$0.137362\pi$
$984$	−8.37502	−0.266986
$985$	8.20475	0.261425
$986$	3.93024	0.125164
$987$	−30.1065	−0.958302
$988$	20.3617	0.647793
$989$	47.0108	1.49486
$990$	5.45339	0.173320
$991$	28.4047	0.902305	0.451152	−	0.892447i	$-0.351013\pi$
$991$	28.4047	0.902305	0.451152	+	0.892447i	$0.351013\pi$
$992$	35.8740	1.13900
$993$	26.4465	0.839253
$994$	−23.5963	−0.748431
$995$	32.1608	1.01956
$996$	−0.393021	−0.0124534
$997$	−1.06020	−0.0335768	−0.0167884	−	0.999859i	$-0.505344\pi$
$997$	−1.06020	−0.0335768	−0.0167884	+	0.999859i	$0.505344\pi$
$998$	8.01920	0.253843
$999$	−8.80443	−0.278560

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8007.2.a.c.1.19	✓	39

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8007.2.a.c.1.19	✓	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)

\(f(q)\)	\(=\)	\(q-0.554461 q^{2} -1.00000 q^{3} -1.69257 q^{4} -2.60082 q^{5} +0.554461 q^{6} +2.71630 q^{7} +2.04739 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-0.554461 q^{2} -1.00000 q^{3} -1.69257 q^{4} -2.60082 q^{5} +0.554461 q^{6} +2.71630 q^{7} +2.04739 q^{8} +1.00000 q^{9} +1.44205 q^{10} +3.78169 q^{11} +1.69257 q^{12} -2.37483 q^{13} -1.50608 q^{14} +2.60082 q^{15} +2.24995 q^{16} +1.00000 q^{17} -0.554461 q^{18} +5.06564 q^{19} +4.40207 q^{20} -2.71630 q^{21} -2.09680 q^{22} -4.47742 q^{23} -2.04739 q^{24} +1.76425 q^{25} +1.31675 q^{26} -1.00000 q^{27} -4.59754 q^{28} -7.08839 q^{29} -1.44205 q^{30} -6.71511 q^{31} -5.34229 q^{32} -3.78169 q^{33} -0.554461 q^{34} -7.06460 q^{35} -1.69257 q^{36} +8.80443 q^{37} -2.80870 q^{38} +2.37483 q^{39} -5.32488 q^{40} +4.09058 q^{41} +1.50608 q^{42} -10.4995 q^{43} -6.40078 q^{44} -2.60082 q^{45} +2.48256 q^{46} +11.0837 q^{47} -2.24995 q^{48} +0.378292 q^{49} -0.978208 q^{50} -1.00000 q^{51} +4.01958 q^{52} -2.56188 q^{53} +0.554461 q^{54} -9.83547 q^{55} +5.56133 q^{56} -5.06564 q^{57} +3.93024 q^{58} +1.26655 q^{59} -4.40207 q^{60} -13.0027 q^{61} +3.72327 q^{62} +2.71630 q^{63} -1.53780 q^{64} +6.17651 q^{65} +2.09680 q^{66} +1.50891 q^{67} -1.69257 q^{68} +4.47742 q^{69} +3.91705 q^{70} +15.6673 q^{71} +2.04739 q^{72} +0.155659 q^{73} -4.88171 q^{74} -1.76425 q^{75} -8.57397 q^{76} +10.2722 q^{77} -1.31675 q^{78} -9.11742 q^{79} -5.85170 q^{80} +1.00000 q^{81} -2.26807 q^{82} -0.232204 q^{83} +4.59754 q^{84} -2.60082 q^{85} +5.82158 q^{86} +7.08839 q^{87} +7.74258 q^{88} -9.44493 q^{89} +1.44205 q^{90} -6.45076 q^{91} +7.57836 q^{92} +6.71511 q^{93} -6.14546 q^{94} -13.1748 q^{95} +5.34229 q^{96} +1.00603 q^{97} -0.209748 q^{98} +3.78169 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 39 q - 4 q^{2} - 39 q^{3} + 30 q^{4} - 3 q^{5} + 4 q^{6} - 5 q^{7} - 3 q^{8} + 39 q^{9}+O(q^{10}) \) 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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