LMFDB - Embedded newform 8007.2.a.d.1.4

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:	$40$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Character	$\chi$	$=$	8007.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.49435 q^{2} +1.00000 q^{3} +4.22179 q^{4} -2.73091 q^{5} -2.49435 q^{6} +0.916542 q^{7} -5.54193 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-2.49435 q^{2} +1.00000 q^{3} +4.22179 q^{4} -2.73091 q^{5} -2.49435 q^{6} +0.916542 q^{7} -5.54193 q^{8} +1.00000 q^{9} +6.81185 q^{10} +0.721969 q^{11} +4.22179 q^{12} +1.85370 q^{13} -2.28618 q^{14} -2.73091 q^{15} +5.37995 q^{16} +1.00000 q^{17} -2.49435 q^{18} +2.15393 q^{19} -11.5293 q^{20} +0.916542 q^{21} -1.80084 q^{22} +1.69376 q^{23} -5.54193 q^{24} +2.45786 q^{25} -4.62377 q^{26} +1.00000 q^{27} +3.86945 q^{28} -5.62666 q^{29} +6.81185 q^{30} -6.54084 q^{31} -2.33562 q^{32} +0.721969 q^{33} -2.49435 q^{34} -2.50299 q^{35} +4.22179 q^{36} +5.31996 q^{37} -5.37266 q^{38} +1.85370 q^{39} +15.1345 q^{40} -3.49038 q^{41} -2.28618 q^{42} +10.3048 q^{43} +3.04800 q^{44} -2.73091 q^{45} -4.22483 q^{46} -4.09151 q^{47} +5.37995 q^{48} -6.15995 q^{49} -6.13077 q^{50} +1.00000 q^{51} +7.82592 q^{52} -3.50839 q^{53} -2.49435 q^{54} -1.97163 q^{55} -5.07941 q^{56} +2.15393 q^{57} +14.0349 q^{58} -1.16660 q^{59} -11.5293 q^{60} -6.54237 q^{61} +16.3152 q^{62} +0.916542 q^{63} -4.93404 q^{64} -5.06227 q^{65} -1.80084 q^{66} -4.44386 q^{67} +4.22179 q^{68} +1.69376 q^{69} +6.24334 q^{70} -2.13225 q^{71} -5.54193 q^{72} +9.40170 q^{73} -13.2699 q^{74} +2.45786 q^{75} +9.09345 q^{76} +0.661715 q^{77} -4.62377 q^{78} +6.74838 q^{79} -14.6921 q^{80} +1.00000 q^{81} +8.70623 q^{82} -12.7635 q^{83} +3.86945 q^{84} -2.73091 q^{85} -25.7038 q^{86} -5.62666 q^{87} -4.00110 q^{88} -6.74930 q^{89} +6.81185 q^{90} +1.69899 q^{91} +7.15070 q^{92} -6.54084 q^{93} +10.2057 q^{94} -5.88219 q^{95} -2.33562 q^{96} +1.08957 q^{97} +15.3651 q^{98} +0.721969 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q - 7 q^{2} + 40 q^{3} + 29 q^{4} - 15 q^{5} - 7 q^{6} - 13 q^{7} - 18 q^{8} + 40 q^{9}+O(q^{10}) $ 40 * q - 7 * q^2 + 40 * q^3 + 29 * q^4 - 15 * q^5 - 7 * q^6 - 13 * q^7 - 18 * q^8 + 40 * q^9	\( 40 q - 7 q^{2} + 40 q^{3} + 29 q^{4} - 15 q^{5} - 7 q^{6} - 13 q^{7} - 18 q^{8} + 40 q^{9} - 6 q^{10} - 25 q^{11} + 29 q^{12} - 24 q^{13} - 22 q^{14} - 15 q^{15} + 7 q^{16} + 40 q^{17} - 7 q^{18} - 18 q^{19} - 20 q^{20} - 13 q^{21} - 25 q^{22} - 28 q^{23} - 18 q^{24} - 11 q^{25} - 13 q^{26} + 40 q^{27} - 8 q^{28} - 23 q^{29} - 6 q^{30} - 11 q^{31} - 23 q^{32} - 25 q^{33} - 7 q^{34} - 45 q^{35} + 29 q^{36} - 38 q^{37} - 30 q^{38} - 24 q^{39} - 12 q^{40} - 33 q^{41} - 22 q^{42} - 25 q^{43} - 14 q^{44} - 15 q^{45} + 8 q^{46} - 55 q^{47} + 7 q^{48} - 21 q^{49} + 2 q^{50} + 40 q^{51} - 39 q^{52} - 39 q^{53} - 7 q^{54} - 9 q^{55} - 48 q^{56} - 18 q^{57} - 13 q^{58} - 81 q^{59} - 20 q^{60} - 9 q^{61} - 16 q^{62} - 13 q^{63} - 4 q^{64} - 43 q^{65} - 25 q^{66} - 24 q^{67} + 29 q^{68} - 28 q^{69} + 48 q^{70} - 32 q^{71} - 18 q^{72} - 43 q^{73} - 20 q^{74} - 11 q^{75} - 58 q^{76} - 32 q^{77} - 13 q^{78} - 22 q^{79} - 48 q^{80} + 40 q^{81} - 11 q^{82} - 45 q^{83} - 8 q^{84} - 15 q^{85} - 30 q^{86} - 23 q^{87} - 48 q^{88} - 94 q^{89} - 6 q^{90} - 7 q^{91} - 98 q^{92} - 11 q^{93} + 32 q^{94} - 23 q^{96} - 28 q^{97} - 46 q^{98} - 25 q^{99}+O(q^{100}) \) 40 * q - 7 * q^2 + 40 * q^3 + 29 * q^4 - 15 * q^5 - 7 * q^6 - 13 * q^7 - 18 * q^8 + 40 * q^9 - 6 * q^10 - 25 * q^11 + 29 * q^12 - 24 * q^13 - 22 * q^14 - 15 * q^15 + 7 * q^16 + 40 * q^17 - 7 * q^18 - 18 * q^19 - 20 * q^20 - 13 * q^21 - 25 * q^22 - 28 * q^23 - 18 * q^24 - 11 * q^25 - 13 * q^26 + 40 * q^27 - 8 * q^28 - 23 * q^29 - 6 * q^30 - 11 * q^31 - 23 * q^32 - 25 * q^33 - 7 * q^34 - 45 * q^35 + 29 * q^36 - 38 * q^37 - 30 * q^38 - 24 * q^39 - 12 * q^40 - 33 * q^41 - 22 * q^42 - 25 * q^43 - 14 * q^44 - 15 * q^45 + 8 * q^46 - 55 * q^47 + 7 * q^48 - 21 * q^49 + 2 * q^50 + 40 * q^51 - 39 * q^52 - 39 * q^53 - 7 * q^54 - 9 * q^55 - 48 * q^56 - 18 * q^57 - 13 * q^58 - 81 * q^59 - 20 * q^60 - 9 * q^61 - 16 * q^62 - 13 * q^63 - 4 * q^64 - 43 * q^65 - 25 * q^66 - 24 * q^67 + 29 * q^68 - 28 * q^69 + 48 * q^70 - 32 * q^71 - 18 * q^72 - 43 * q^73 - 20 * q^74 - 11 * q^75 - 58 * q^76 - 32 * q^77 - 13 * q^78 - 22 * q^79 - 48 * q^80 + 40 * q^81 - 11 * q^82 - 45 * q^83 - 8 * q^84 - 15 * q^85 - 30 * q^86 - 23 * q^87 - 48 * q^88 - 94 * q^89 - 6 * q^90 - 7 * q^91 - 98 * q^92 - 11 * q^93 + 32 * q^94 - 23 * q^96 - 28 * q^97 - 46 * q^98 - 25 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−2.49435	−1.76377	−0.881887	−	0.471461i	$-0.843727\pi$
$2$	−2.49435	−1.76377	−0.881887	+	0.471461i	$0.843727\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	4.22179	2.11090
$5$	−2.73091	−1.22130	−0.610650	−	0.791901i	$-0.709092\pi$
$5$	−2.73091	−1.22130	−0.610650	+	0.791901i	$0.709092\pi$
$6$	−2.49435	−1.01832
$7$	0.916542	0.346420	0.173210	−	0.984885i	$-0.444586\pi$
$7$	0.916542	0.346420	0.173210	+	0.984885i	$0.444586\pi$
$8$	−5.54193	−1.95937
$9$	1.00000	0.333333
$10$	6.81185	2.15410
$11$	0.721969	0.217682	0.108841	−	0.994059i	$-0.465286\pi$
$11$	0.721969	0.217682	0.108841	+	0.994059i	$0.465286\pi$
$12$	4.22179	1.21873
$13$	1.85370	0.514123	0.257061	−	0.966395i	$-0.417246\pi$
$13$	1.85370	0.514123	0.257061	+	0.966395i	$0.417246\pi$
$14$	−2.28618	−0.611007
$15$	−2.73091	−0.705117
$16$	5.37995	1.34499
$17$	1.00000	0.242536
$17$	1.00000	0.242536
$18$	−2.49435	−0.587924
$19$	2.15393	0.494145	0.247073	−	0.968997i	$-0.420531\pi$
$19$	2.15393	0.494145	0.247073	+	0.968997i	$0.420531\pi$
$20$	−11.5293	−2.57804
$21$	0.916542	0.200006
$22$	−1.80084	−0.383941
$23$	1.69376	0.353173	0.176587	−	0.984285i	$-0.443494\pi$
$23$	1.69376	0.353173	0.176587	+	0.984285i	$0.443494\pi$
$24$	−5.54193	−1.13124
$25$	2.45786	0.491572
$26$	−4.62377	−0.906796
$27$	1.00000	0.192450
$28$	3.86945	0.731257
$29$	−5.62666	−1.04484	−0.522422	−	0.852687i	$-0.674971\pi$
$29$	−5.62666	−1.04484	−0.522422	+	0.852687i	$0.674971\pi$
$30$	6.81185	1.24367
$31$	−6.54084	−1.17477	−0.587385	−	0.809308i	$-0.699843\pi$
$31$	−6.54084	−1.17477	−0.587385	+	0.809308i	$0.699843\pi$
$32$	−2.33562	−0.412883
$33$	0.721969	0.125679
$34$	−2.49435	−0.427778
$35$	−2.50299	−0.423083
$36$	4.22179	0.703632
$37$	5.31996	0.874597	0.437298	−	0.899316i	$-0.355935\pi$
$37$	5.31996	0.874597	0.437298	+	0.899316i	$0.355935\pi$
$38$	−5.37266	−0.871561
$39$	1.85370	0.296829
$40$	15.1345	2.39298
$41$	−3.49038	−0.545105	−0.272553	−	0.962141i	$-0.587868\pi$
$41$	−3.49038	−0.545105	−0.272553	+	0.962141i	$0.587868\pi$
$42$	−2.28618	−0.352765
$43$	10.3048	1.57147	0.785734	−	0.618565i	$-0.212286\pi$
$43$	10.3048	1.57147	0.785734	+	0.618565i	$0.212286\pi$
$44$	3.04800	0.459504
$45$	−2.73091	−0.407100
$46$	−4.22483	−0.622918
$47$	−4.09151	−0.596808	−0.298404	−	0.954440i	$-0.596454\pi$
$47$	−4.09151	−0.596808	−0.298404	+	0.954440i	$0.596454\pi$
$48$	5.37995	0.776529
$49$	−6.15995	−0.879993
$50$	−6.13077	−0.867022
$51$	1.00000	0.140028
$52$	7.82592	1.08526
$53$	−3.50839	−0.481914	−0.240957	−	0.970536i	$-0.577461\pi$
$53$	−3.50839	−0.481914	−0.240957	+	0.970536i	$0.577461\pi$
$54$	−2.49435	−0.339438
$55$	−1.97163	−0.265855
$56$	−5.07941	−0.678765
$57$	2.15393	0.285295
$58$	14.0349	1.84287
$59$	−1.16660	−0.151879	−0.0759393	−	0.997112i	$-0.524196\pi$
$59$	−1.16660	−0.151879	−0.0759393	+	0.997112i	$0.524196\pi$
$60$	−11.5293	−1.48843
$61$	−6.54237	−0.837665	−0.418833	−	0.908063i	$-0.637561\pi$
$61$	−6.54237	−0.837665	−0.418833	+	0.908063i	$0.637561\pi$
$62$	16.3152	2.07203
$63$	0.916542	0.115473
$64$	−4.93404	−0.616755
$65$	−5.06227	−0.627898
$66$	−1.80084	−0.221669
$67$	−4.44386	−0.542904	−0.271452	−	0.962452i	$-0.587504\pi$
$67$	−4.44386	−0.542904	−0.271452	+	0.962452i	$0.587504\pi$
$68$	4.22179	0.511968
$69$	1.69376	0.203905
$70$	6.24334	0.746222
$71$	−2.13225	−0.253052	−0.126526	−	0.991963i	$-0.540383\pi$
$71$	−2.13225	−0.253052	−0.126526	+	0.991963i	$0.540383\pi$
$72$	−5.54193	−0.653123
$73$	9.40170	1.10039	0.550193	−	0.835038i	$-0.314554\pi$
$73$	9.40170	1.10039	0.550193	+	0.835038i	$0.314554\pi$
$74$	−13.2699	−1.54259
$75$	2.45786	0.283809
$76$	9.09345	1.04309
$77$	0.661715	0.0754094
$78$	−4.62377	−0.523539
$79$	6.74838	0.759252	0.379626	−	0.925140i	$-0.376053\pi$
$79$	6.74838	0.759252	0.379626	+	0.925140i	$0.376053\pi$
$80$	−14.6921	−1.64263
$81$	1.00000	0.111111
$82$	8.70623	0.961442
$83$	−12.7635	−1.40097	−0.700487	−	0.713665i	$-0.747034\pi$
$83$	−12.7635	−1.40097	−0.700487	+	0.713665i	$0.747034\pi$
$84$	3.86945	0.422192
$85$	−2.73091	−0.296209
$86$	−25.7038	−2.77171
$87$	−5.62666	−0.603241
$88$	−4.00110	−0.426519
$89$	−6.74930	−0.715425	−0.357712	−	0.933832i	$-0.616443\pi$
$89$	−6.74930	−0.715425	−0.357712	+	0.933832i	$0.616443\pi$
$90$	6.81185	0.718032
$91$	1.69899	0.178102
$92$	7.15070	0.745512
$93$	−6.54084	−0.678254
$94$	10.2057	1.05263
$95$	−5.88219	−0.603499
$96$	−2.33562	−0.238378
$97$	1.08957	0.110629	0.0553145	−	0.998469i	$-0.482384\pi$
$97$	1.08957	0.110629	0.0553145	+	0.998469i	$0.482384\pi$
$98$	15.3651	1.55211
$99$	0.721969	0.0725606
$100$	10.3766	1.03766
$101$	−1.01965	−0.101459	−0.0507293	−	0.998712i	$-0.516155\pi$
$101$	−1.01965	−0.101459	−0.0507293	+	0.998712i	$0.516155\pi$
$102$	−2.49435	−0.246978
$103$	1.04852	0.103314	0.0516568	−	0.998665i	$-0.483550\pi$
$103$	1.04852	0.103314	0.0516568	+	0.998665i	$0.483550\pi$
$104$	−10.2731	−1.00736
$105$	−2.50299	−0.244267
$106$	8.75116	0.849988
$107$	−13.9445	−1.34806	−0.674032	−	0.738702i	$-0.735439\pi$
$107$	−13.9445	−1.34806	−0.674032	+	0.738702i	$0.735439\pi$
$108$	4.22179	0.406242
$109$	4.94437	0.473585	0.236792	−	0.971560i	$-0.423904\pi$
$109$	4.94437	0.473585	0.236792	+	0.971560i	$0.423904\pi$
$110$	4.91794	0.468907
$111$	5.31996	0.504949
$112$	4.93095	0.465931
$113$	2.00801	0.188897	0.0944487	−	0.995530i	$-0.469891\pi$
$113$	2.00801	0.188897	0.0944487	+	0.995530i	$0.469891\pi$
$114$	−5.37266	−0.503196
$115$	−4.62550	−0.431330
$116$	−23.7546	−2.20556
$117$	1.85370	0.171374
$118$	2.90991	0.267879
$119$	0.916542	0.0840192
$120$	15.1345	1.38159
$121$	−10.4788	−0.952615
$122$	16.3190	1.47745
$123$	−3.49038	−0.314717
$124$	−27.6141	−2.47982
$125$	6.94235	0.620943
$126$	−2.28618	−0.203669
$127$	−10.6177	−0.942170	−0.471085	−	0.882088i	$-0.656137\pi$
$127$	−10.6177	−0.942170	−0.471085	+	0.882088i	$0.656137\pi$
$128$	16.9785	1.50070
$129$	10.3048	0.907287
$130$	12.6271	1.10747
$131$	18.8239	1.64465	0.822325	−	0.569018i	$-0.192677\pi$
$131$	18.8239	1.64465	0.822325	+	0.569018i	$0.192677\pi$
$132$	3.04800	0.265295
$133$	1.97417	0.171182
$134$	11.0845	0.957559
$135$	−2.73091	−0.235039
$136$	−5.54193	−0.475217
$137$	21.3145	1.82102	0.910511	−	0.413485i	$-0.135689\pi$
$137$	21.3145	1.82102	0.910511	+	0.413485i	$0.135689\pi$
$138$	−4.22483	−0.359642
$139$	−16.1540	−1.37016	−0.685081	−	0.728467i	$-0.740233\pi$
$139$	−16.1540	−1.37016	−0.685081	+	0.728467i	$0.740233\pi$
$140$	−10.5671	−0.893084
$141$	−4.09151	−0.344567
$142$	5.31859	0.446326
$143$	1.33831	0.111915
$144$	5.37995	0.448329
$145$	15.3659	1.27607
$146$	−23.4512	−1.94083
$147$	−6.15995	−0.508064
$148$	22.4598	1.84618
$149$	−13.5549	−1.11046	−0.555228	−	0.831698i	$-0.687369\pi$
$149$	−13.5549	−1.11046	−0.555228	+	0.831698i	$0.687369\pi$
$150$	−6.13077	−0.500575
$151$	21.0440	1.71253	0.856267	−	0.516533i	$-0.172778\pi$
$151$	21.0440	1.71253	0.856267	+	0.516533i	$0.172778\pi$
$152$	−11.9369	−0.968214
$153$	1.00000	0.0808452
$154$	−1.65055	−0.133005
$155$	17.8624	1.43475
$156$	7.82592	0.626575
$157$	−1.00000	−0.0798087
$157$	−1.00000	−0.0798087
$158$	−16.8328	−1.33915
$159$	−3.50839	−0.278233
$160$	6.37837	0.504254
$161$	1.55240	0.122346
$162$	−2.49435	−0.195975
$163$	5.41301	0.423980	0.211990	−	0.977272i	$-0.432006\pi$
$163$	5.41301	0.423980	0.211990	+	0.977272i	$0.432006\pi$
$164$	−14.7356	−1.15066
$165$	−1.97163	−0.153491
$166$	31.8366	2.47100
$167$	−7.18847	−0.556260	−0.278130	−	0.960543i	$-0.589715\pi$
$167$	−7.18847	−0.556260	−0.278130	+	0.960543i	$0.589715\pi$
$168$	−5.07941	−0.391885
$169$	−9.56381	−0.735678
$170$	6.81185	0.522445
$171$	2.15393	0.164715
$172$	43.5047	3.31721
$173$	−17.4443	−1.32627	−0.663134	−	0.748501i	$-0.730774\pi$
$173$	−17.4443	−1.32627	−0.663134	+	0.748501i	$0.730774\pi$
$174$	14.0349	1.06398
$175$	2.25273	0.170290
$176$	3.88416	0.292779
$177$	−1.16660	−0.0876871
$178$	16.8351	1.26185
$179$	−3.22913	−0.241357	−0.120678	−	0.992692i	$-0.538507\pi$
$179$	−3.22913	−0.241357	−0.120678	+	0.992692i	$0.538507\pi$
$180$	−11.5293	−0.859345
$181$	21.2441	1.57906	0.789530	−	0.613711i	$-0.210324\pi$
$181$	21.2441	1.57906	0.789530	+	0.613711i	$0.210324\pi$
$182$	−4.23788	−0.314132
$183$	−6.54237	−0.483626
$184$	−9.38670	−0.691997
$185$	−14.5283	−1.06814
$186$	16.3152	1.19629
$187$	0.721969	0.0527956
$188$	−17.2735	−1.25980
$189$	0.916542	0.0666686
$190$	14.6722	1.06444
$191$	5.23585	0.378852	0.189426	−	0.981895i	$-0.439337\pi$
$191$	5.23585	0.378852	0.189426	+	0.981895i	$0.439337\pi$
$192$	−4.93404	−0.356083
$193$	−5.27029	−0.379364	−0.189682	−	0.981846i	$-0.560746\pi$
$193$	−5.27029	−0.379364	−0.189682	+	0.981846i	$0.560746\pi$
$194$	−2.71777	−0.195124
$195$	−5.06227	−0.362517
$196$	−26.0060	−1.85757
$197$	−1.86044	−0.132551	−0.0662755	−	0.997801i	$-0.521112\pi$
$197$	−1.86044	−0.132551	−0.0662755	+	0.997801i	$0.521112\pi$
$198$	−1.80084	−0.127980
$199$	24.5221	1.73832	0.869162	−	0.494528i	$-0.164659\pi$
$199$	24.5221	1.73832	0.869162	+	0.494528i	$0.164659\pi$
$200$	−13.6213	−0.963171
$201$	−4.44386	−0.313446
$202$	2.54336	0.178950
$203$	−5.15707	−0.361955
$204$	4.22179	0.295585
$205$	9.53190	0.665737
$206$	−2.61538	−0.182222
$207$	1.69376	0.117724
$208$	9.97279	0.691489
$209$	1.55507	0.107566
$210$	6.24334	0.430832
$211$	−14.5837	−1.00398	−0.501990	−	0.864873i	$-0.667399\pi$
$211$	−14.5837	−1.00398	−0.501990	+	0.864873i	$0.667399\pi$
$212$	−14.8117	−1.01727
$213$	−2.13225	−0.146100
$214$	34.7824	2.37768
$215$	−28.1415	−1.91923
$216$	−5.54193	−0.377081
$217$	−5.99495	−0.406964
$218$	−12.3330	−0.835296
$219$	9.40170	0.635308
$220$	−8.32382	−0.561192
$221$	1.85370	0.124693
$222$	−13.2699	−0.890615
$223$	14.3616	0.961721	0.480860	−	0.876797i	$-0.340324\pi$
$223$	14.3616	0.961721	0.480860	+	0.876797i	$0.340324\pi$
$224$	−2.14069	−0.143031
$225$	2.45786	0.163857
$226$	−5.00867	−0.333172
$227$	19.4957	1.29398	0.646988	−	0.762500i	$-0.276028\pi$
$227$	19.4957	1.29398	0.646988	+	0.762500i	$0.276028\pi$
$228$	9.09345	0.602228
$229$	21.7676	1.43845	0.719223	−	0.694780i	$-0.244498\pi$
$229$	21.7676	1.43845	0.719223	+	0.694780i	$0.244498\pi$
$230$	11.5376	0.760769
$231$	0.661715	0.0435376
$232$	31.1826	2.04724
$233$	−15.4421	−1.01165	−0.505824	−	0.862636i	$-0.668812\pi$
$233$	−15.4421	−1.01165	−0.505824	+	0.862636i	$0.668812\pi$
$234$	−4.62377	−0.302265
$235$	11.1735	0.728881
$236$	−4.92515	−0.320600
$237$	6.74838	0.438354
$238$	−2.28618	−0.148191
$239$	−15.8064	−1.02243	−0.511215	−	0.859453i	$-0.670805\pi$
$239$	−15.8064	−1.02243	−0.511215	+	0.859453i	$0.670805\pi$
$240$	−14.6921	−0.948374
$241$	−24.8605	−1.60141	−0.800703	−	0.599062i	$-0.795540\pi$
$241$	−24.8605	−1.60141	−0.800703	+	0.599062i	$0.795540\pi$
$242$	26.1377	1.68020
$243$	1.00000	0.0641500
$244$	−27.6205	−1.76822
$245$	16.8223	1.07473
$246$	8.70623	0.555089
$247$	3.99273	0.254051
$248$	36.2489	2.30181
$249$	−12.7635	−0.808853
$250$	−17.3167	−1.09520
$251$	−25.3494	−1.60004	−0.800020	−	0.599974i	$-0.795178\pi$
$251$	−25.3494	−1.60004	−0.800020	+	0.599974i	$0.795178\pi$
$252$	3.86945	0.243752
$253$	1.22284	0.0768794
$254$	26.4843	1.66177
$255$	−2.73091	−0.171016
$256$	−32.4822	−2.03014
$257$	25.2344	1.57408	0.787041	−	0.616901i	$-0.211612\pi$
$257$	25.2344	1.57408	0.787041	+	0.616901i	$0.211612\pi$
$258$	−25.7038	−1.60025
$259$	4.87597	0.302978
$260$	−21.3719	−1.32543
$261$	−5.62666	−0.348281
$262$	−46.9534	−2.90079
$263$	−11.8831	−0.732743	−0.366372	−	0.930469i	$-0.619400\pi$
$263$	−11.8831	−0.732743	−0.366372	+	0.930469i	$0.619400\pi$
$264$	−4.00110	−0.246251
$265$	9.58109	0.588562
$266$	−4.92427	−0.301926
$267$	−6.74930	−0.413051
$268$	−18.7611	−1.14601
$269$	0.468808	0.0285837	0.0142919	−	0.999898i	$-0.495451\pi$
$269$	0.468808	0.0285837	0.0142919	+	0.999898i	$0.495451\pi$
$270$	6.81185	0.414556
$271$	18.3768	1.11631	0.558155	−	0.829737i	$-0.311509\pi$
$271$	18.3768	1.11631	0.558155	+	0.829737i	$0.311509\pi$
$272$	5.37995	0.326207
$273$	1.69899	0.102828
$274$	−53.1659	−3.21187
$275$	1.77450	0.107006
$276$	7.15070	0.430422
$277$	−27.0614	−1.62596	−0.812980	−	0.582292i	$-0.802156\pi$
$277$	−27.0614	−1.62596	−0.812980	+	0.582292i	$0.802156\pi$
$278$	40.2937	2.41666
$279$	−6.54084	−0.391590
$280$	13.8714	0.828975
$281$	2.23006	0.133034	0.0665171	−	0.997785i	$-0.478811\pi$
$281$	2.23006	0.133034	0.0665171	+	0.997785i	$0.478811\pi$
$282$	10.2057	0.607739
$283$	−21.4421	−1.27460	−0.637300	−	0.770616i	$-0.719949\pi$
$283$	−21.4421	−1.27460	−0.637300	+	0.770616i	$0.719949\pi$
$284$	−9.00194	−0.534167
$285$	−5.88219	−0.348431
$286$	−3.33822	−0.197393
$287$	−3.19908	−0.188835
$288$	−2.33562	−0.137628
$289$	1.00000	0.0588235
$290$	−38.3279	−2.25069
$291$	1.08957	0.0638716
$292$	39.6920	2.32280
$293$	19.5071	1.13961	0.569807	−	0.821778i	$-0.307018\pi$
$293$	19.5071	1.13961	0.569807	+	0.821778i	$0.307018\pi$
$294$	15.3651	0.896110
$295$	3.18588	0.185489
$296$	−29.4829	−1.71366
$297$	0.721969	0.0418929
$298$	33.8106	1.95859
$299$	3.13971	0.181574
$300$	10.3766	0.599092
$301$	9.44478	0.544388
$302$	−52.4911	−3.02052
$303$	−1.01965	−0.0585771
$304$	11.5880	0.664619
$305$	17.8666	1.02304
$306$	−2.49435	−0.142593
$307$	−21.3888	−1.22072	−0.610361	−	0.792124i	$-0.708975\pi$
$307$	−21.3888	−1.22072	−0.610361	+	0.792124i	$0.708975\pi$
$308$	2.79362	0.159181
$309$	1.04852	0.0596482
$310$	−44.5552	−2.53057
$311$	11.7401	0.665722	0.332861	−	0.942976i	$-0.391986\pi$
$311$	11.7401	0.665722	0.332861	+	0.942976i	$0.391986\pi$
$312$	−10.2731	−0.581597
$313$	−11.1290	−0.629046	−0.314523	−	0.949250i	$-0.601845\pi$
$313$	−11.1290	−0.629046	−0.314523	+	0.949250i	$0.601845\pi$
$314$	2.49435	0.140764
$315$	−2.50299	−0.141028
$316$	28.4902	1.60270
$317$	15.9572	0.896246	0.448123	−	0.893972i	$-0.352093\pi$
$317$	15.9572	0.896246	0.448123	+	0.893972i	$0.352093\pi$
$318$	8.75116	0.490741
$319$	−4.06227	−0.227444
$320$	13.4744	0.753242
$321$	−13.9445	−0.778305
$322$	−3.87224	−0.215791
$323$	2.15393	0.119848
$324$	4.22179	0.234544
$325$	4.55612	0.252728
$326$	−13.5020	−0.747804
$327$	4.94437	0.273424
$328$	19.3434	1.06806
$329$	−3.75004	−0.206746
$330$	4.91794	0.270724
$331$	−31.4462	−1.72844	−0.864219	−	0.503116i	$-0.832187\pi$
$331$	−31.4462	−1.72844	−0.864219	+	0.503116i	$0.832187\pi$
$332$	−53.8848	−2.95731
$333$	5.31996	0.291532
$334$	17.9306	0.981117
$335$	12.1358	0.663048
$336$	4.93095	0.269005
$337$	−28.0495	−1.52795	−0.763977	−	0.645244i	$-0.776756\pi$
$337$	−28.0495	−1.52795	−0.763977	+	0.645244i	$0.776756\pi$
$338$	23.8555	1.29757
$339$	2.00801	0.109060
$340$	−11.5293	−0.625266
$341$	−4.72228	−0.255726
$342$	−5.37266	−0.290520
$343$	−12.0616	−0.651268
$344$	−57.1085	−3.07909
$345$	−4.62550	−0.249029
$346$	43.5123	2.33924
$347$	−24.3090	−1.30497	−0.652487	−	0.757800i	$-0.726274\pi$
$347$	−24.3090	−1.30497	−0.652487	+	0.757800i	$0.726274\pi$
$348$	−23.7546	−1.27338
$349$	6.55970	0.351133	0.175566	−	0.984468i	$-0.443824\pi$
$349$	6.55970	0.351133	0.175566	+	0.984468i	$0.443824\pi$
$350$	−5.61910	−0.300354
$351$	1.85370	0.0989430
$352$	−1.68625	−0.0898772
$353$	−30.7423	−1.63625	−0.818123	−	0.575043i	$-0.804985\pi$
$353$	−30.7423	−1.63625	−0.818123	+	0.575043i	$0.804985\pi$
$354$	2.90991	0.154660
$355$	5.82299	0.309052
$356$	−28.4942	−1.51019
$357$	0.916542	0.0485085
$358$	8.05459	0.425698
$359$	14.6939	0.775515	0.387757	−	0.921761i	$-0.373250\pi$
$359$	14.6939	0.775515	0.387757	+	0.921761i	$0.373250\pi$
$360$	15.1345	0.797659
$361$	−14.3606	−0.755820
$362$	−52.9902	−2.78511
$363$	−10.4788	−0.549992
$364$	7.17278	0.375956
$365$	−25.6752	−1.34390
$366$	16.3190	0.853007
$367$	−35.9045	−1.87420	−0.937100	−	0.349061i	$-0.886501\pi$
$367$	−35.9045	−1.87420	−0.937100	+	0.349061i	$0.886501\pi$
$368$	9.11234	0.475014
$369$	−3.49038	−0.181702
$370$	36.2388	1.88396
$371$	−3.21558	−0.166945
$372$	−27.6141	−1.43172
$373$	6.88526	0.356505	0.178253	−	0.983985i	$-0.442956\pi$
$373$	6.88526	0.356505	0.178253	+	0.983985i	$0.442956\pi$
$374$	−1.80084	−0.0931195
$375$	6.94235	0.358501
$376$	22.6749	1.16937
$377$	−10.4301	−0.537178
$378$	−2.28618	−0.117588
$379$	7.96952	0.409367	0.204683	−	0.978828i	$-0.434384\pi$
$379$	7.96952	0.409367	0.204683	+	0.978828i	$0.434384\pi$
$380$	−24.8334	−1.27392
$381$	−10.6177	−0.543962
$382$	−13.0600	−0.668210
$383$	−12.5725	−0.642423	−0.321211	−	0.947008i	$-0.604090\pi$
$383$	−12.5725	−0.642423	−0.321211	+	0.947008i	$0.604090\pi$
$384$	16.9785	0.866429
$385$	−1.80708	−0.0920974
$386$	13.1460	0.669111
$387$	10.3048	0.523822
$388$	4.59993	0.233526
$389$	14.9613	0.758570	0.379285	−	0.925280i	$-0.376170\pi$
$389$	14.9613	0.758570	0.379285	+	0.925280i	$0.376170\pi$
$390$	12.6271	0.639398
$391$	1.69376	0.0856571
$392$	34.1380	1.72423
$393$	18.8239	0.949539
$394$	4.64060	0.233790
$395$	−18.4292	−0.927274
$396$	3.04800	0.153168
$397$	21.0022	1.05407	0.527036	−	0.849843i	$-0.323303\pi$
$397$	21.0022	1.05407	0.527036	+	0.849843i	$0.323303\pi$
$398$	−61.1667	−3.06601
$399$	1.97417	0.0988320
$400$	13.2232	0.661158
$401$	29.2485	1.46060	0.730301	−	0.683126i	$-0.239380\pi$
$401$	29.2485	1.46060	0.730301	+	0.683126i	$0.239380\pi$
$402$	11.0845	0.552847
$403$	−12.1247	−0.603976
$404$	−4.30473	−0.214168
$405$	−2.73091	−0.135700
$406$	12.8635	0.638407
$407$	3.84085	0.190384
$408$	−5.54193	−0.274367
$409$	−36.8892	−1.82405	−0.912026	−	0.410133i	$-0.865482\pi$
$409$	−36.8892	−1.82405	−0.912026	+	0.410133i	$0.865482\pi$
$410$	−23.7759	−1.17421
$411$	21.3145	1.05137
$412$	4.42663	0.218084
$413$	−1.06924	−0.0526138
$414$	−4.22483	−0.207639
$415$	34.8559	1.71101
$416$	−4.32953	−0.212273
$417$	−16.1540	−0.791063
$418$	−3.87889	−0.189723
$419$	9.63923	0.470907	0.235454	−	0.971886i	$-0.424342\pi$
$419$	9.63923	0.470907	0.235454	+	0.971886i	$0.424342\pi$
$420$	−10.5671	−0.515622
$421$	3.07760	0.149993	0.0749965	−	0.997184i	$-0.476105\pi$
$421$	3.07760	0.149993	0.0749965	+	0.997184i	$0.476105\pi$
$422$	36.3768	1.77079
$423$	−4.09151	−0.198936
$424$	19.4433	0.944248
$425$	2.45786	0.119224
$426$	5.31859	0.257687
$427$	−5.99636	−0.290184
$428$	−58.8707	−2.84562
$429$	1.33831	0.0646142
$430$	70.1947	3.38509
$431$	10.2043	0.491525	0.245763	−	0.969330i	$-0.420962\pi$
$431$	10.2043	0.491525	0.245763	+	0.969330i	$0.420962\pi$
$432$	5.37995	0.258843
$433$	−20.2518	−0.973238	−0.486619	−	0.873614i	$-0.661770\pi$
$433$	−20.2518	−0.973238	−0.486619	+	0.873614i	$0.661770\pi$
$434$	14.9535	0.717792
$435$	15.3659	0.736738
$436$	20.8741	0.999688
$437$	3.64824	0.174519
$438$	−23.4512	−1.12054
$439$	12.0287	0.574098	0.287049	−	0.957916i	$-0.407326\pi$
$439$	12.0287	0.574098	0.287049	+	0.957916i	$0.407326\pi$
$440$	10.9266	0.520908
$441$	−6.15995	−0.293331
$442$	−4.62377	−0.219930
$443$	25.8916	1.23015	0.615073	−	0.788470i	$-0.289127\pi$
$443$	25.8916	1.23015	0.615073	+	0.788470i	$0.289127\pi$
$444$	22.4598	1.06589
$445$	18.4317	0.873748
$446$	−35.8228	−1.69626
$447$	−13.5549	−0.641122
$448$	−4.52225	−0.213656
$449$	−6.40188	−0.302123	−0.151062	−	0.988524i	$-0.548269\pi$
$449$	−6.40188	−0.302123	−0.151062	+	0.988524i	$0.548269\pi$
$450$	−6.13077	−0.289007
$451$	−2.51994	−0.118659
$452$	8.47739	0.398743
$453$	21.0440	0.988732
$454$	−48.6292	−2.28228
$455$	−4.63978	−0.217516
$456$	−11.9369	−0.558998
$457$	36.0712	1.68734	0.843669	−	0.536863i	$-0.180391\pi$
$457$	36.0712	1.68734	0.843669	+	0.536863i	$0.180391\pi$
$458$	−54.2961	−2.53709
$459$	1.00000	0.0466760
$460$	−19.5279	−0.910493
$461$	29.1871	1.35938	0.679689	−	0.733500i	$-0.262115\pi$
$461$	29.1871	1.35938	0.679689	+	0.733500i	$0.262115\pi$
$462$	−1.65055	−0.0767905
$463$	−6.88463	−0.319956	−0.159978	−	0.987121i	$-0.551142\pi$
$463$	−6.88463	−0.319956	−0.159978	+	0.987121i	$0.551142\pi$
$464$	−30.2711	−1.40530
$465$	17.8624	0.828351
$466$	38.5182	1.78432
$467$	−6.19455	−0.286650	−0.143325	−	0.989676i	$-0.545779\pi$
$467$	−6.19455	−0.286650	−0.143325	+	0.989676i	$0.545779\pi$
$468$	7.82592	0.361753
$469$	−4.07298	−0.188073
$470$	−27.8707	−1.28558
$471$	−1.00000	−0.0460776
$472$	6.46523	0.297586
$473$	7.43975	0.342080
$474$	−16.8328	−0.773157
$475$	5.29406	0.242908
$476$	3.86945	0.177356
$477$	−3.50839	−0.160638
$478$	39.4267	1.80334
$479$	6.68675	0.305526	0.152763	−	0.988263i	$-0.451183\pi$
$479$	6.68675	0.305526	0.152763	+	0.988263i	$0.451183\pi$
$480$	6.37837	0.291131
$481$	9.86159	0.449650
$482$	62.0108	2.82452
$483$	1.55240	0.0706367
$484$	−44.2392	−2.01087
$485$	−2.97551	−0.135111
$486$	−2.49435	−0.113146
$487$	−24.4207	−1.10661	−0.553304	−	0.832979i	$-0.686633\pi$
$487$	−24.4207	−1.10661	−0.553304	+	0.832979i	$0.686633\pi$
$488$	36.2574	1.64130
$489$	5.41301	0.244785
$490$	−41.9606	−1.89559
$491$	26.4880	1.19539	0.597694	−	0.801724i	$-0.296084\pi$
$491$	26.4880	1.19539	0.597694	+	0.801724i	$0.296084\pi$
$492$	−14.7356	−0.664334
$493$	−5.62666	−0.253412
$494$	−9.95928	−0.448089
$495$	−1.97163	−0.0886182
$496$	−35.1894	−1.58005
$497$	−1.95430	−0.0876623
$498$	31.8366	1.42663
$499$	−10.0666	−0.450642	−0.225321	−	0.974285i	$-0.572343\pi$
$499$	−10.0666	−0.450642	−0.225321	+	0.974285i	$0.572343\pi$
$500$	29.3092	1.31075
$501$	−7.18847	−0.321157
$502$	63.2303	2.82211
$503$	−8.63787	−0.385143	−0.192572	−	0.981283i	$-0.561683\pi$
$503$	−8.63787	−0.385143	−0.192572	+	0.981283i	$0.561683\pi$
$504$	−5.07941	−0.226255
$505$	2.78456	0.123911
$506$	−3.05020	−0.135598
$507$	−9.56381	−0.424744
$508$	−44.8258	−1.98882
$509$	−24.4546	−1.08393	−0.541966	−	0.840401i	$-0.682320\pi$
$509$	−24.4546	−1.08393	−0.541966	+	0.840401i	$0.682320\pi$
$510$	6.81185	0.301634
$511$	8.61705	0.381196
$512$	47.0651	2.08000
$513$	2.15393	0.0950983
$514$	−62.9436	−2.77632
$515$	−2.86341	−0.126177
$516$	43.5047	1.91519
$517$	−2.95394	−0.129914
$518$	−12.1624	−0.534384
$519$	−17.4443	−0.765721
$520$	28.0548	1.23028
$521$	2.43061	0.106487	0.0532434	−	0.998582i	$-0.483044\pi$
$521$	2.43061	0.106487	0.0532434	+	0.998582i	$0.483044\pi$
$522$	14.0349	0.614290
$523$	−5.97608	−0.261316	−0.130658	−	0.991428i	$-0.541709\pi$
$523$	−5.97608	−0.261316	−0.130658	+	0.991428i	$0.541709\pi$
$524$	79.4705	3.47169
$525$	2.25273	0.0983172
$526$	29.6406	1.29239
$527$	−6.54084	−0.284924
$528$	3.88416	0.169036
$529$	−20.1312	−0.875269
$530$	−23.8986	−1.03809
$531$	−1.16660	−0.0506262
$532$	8.33452	0.361347
$533$	−6.47009	−0.280251
$534$	16.8351	0.728528
$535$	38.0811	1.64639
$536$	24.6276	1.06375
$537$	−3.22913	−0.139347
$538$	−1.16937	−0.0504152
$539$	−4.44729	−0.191558
$540$	−11.5293	−0.496143
$541$	24.0308	1.03316	0.516582	−	0.856238i	$-0.327204\pi$
$541$	24.0308	1.03316	0.516582	+	0.856238i	$0.327204\pi$
$542$	−45.8382	−1.96892
$543$	21.2441	0.911671
$544$	−2.33562	−0.100139
$545$	−13.5026	−0.578388
$546$	−4.23788	−0.181364
$547$	28.9447	1.23759	0.618794	−	0.785553i	$-0.287622\pi$
$547$	28.9447	1.23759	0.618794	+	0.785553i	$0.287622\pi$
$548$	89.9854	3.84399
$549$	−6.54237	−0.279222
$550$	−4.42622	−0.188735
$551$	−12.1194	−0.516305
$552$	−9.38670	−0.399525
$553$	6.18517	0.263020
$554$	67.5006	2.86782
$555$	−14.5283	−0.616693
$556$	−68.1987	−2.89227
$557$	−6.82269	−0.289087	−0.144543	−	0.989498i	$-0.546171\pi$
$557$	−6.82269	−0.289087	−0.144543	+	0.989498i	$0.546171\pi$
$558$	16.3152	0.690676
$559$	19.1020	0.807927
$560$	−13.4660	−0.569041
$561$	0.721969	0.0304816
$562$	−5.56255	−0.234642
$563$	−10.0006	−0.421476	−0.210738	−	0.977543i	$-0.567587\pi$
$563$	−10.0006	−0.421476	−0.210738	+	0.977543i	$0.567587\pi$
$564$	−17.2735	−0.727346
$565$	−5.48368	−0.230700
$566$	53.4841	2.24810
$567$	0.916542	0.0384911
$568$	11.8168	0.495823
$569$	−1.28743	−0.0539718	−0.0269859	−	0.999636i	$-0.508591\pi$
$569$	−1.28743	−0.0539718	−0.0269859	+	0.999636i	$0.508591\pi$
$570$	14.6722	0.614553
$571$	−18.3329	−0.767210	−0.383605	−	0.923497i	$-0.625318\pi$
$571$	−18.3329	−0.767210	−0.383605	+	0.923497i	$0.625318\pi$
$572$	5.65007	0.236241
$573$	5.23585	0.218731
$574$	7.97962	0.333063
$575$	4.16302	0.173610
$576$	−4.93404	−0.205585
$577$	−45.3881	−1.88953	−0.944766	−	0.327747i	$-0.893711\pi$
$577$	−45.3881	−1.88953	−0.944766	+	0.327747i	$0.893711\pi$
$578$	−2.49435	−0.103751
$579$	−5.27029	−0.219026
$580$	64.8716	2.69365
$581$	−11.6983	−0.485326
$582$	−2.71777	−0.112655
$583$	−2.53295	−0.104904
$584$	−52.1036	−2.15606
$585$	−5.06227	−0.209299
$586$	−48.6575	−2.01002
$587$	−23.1011	−0.953483	−0.476741	−	0.879044i	$-0.658182\pi$
$587$	−23.1011	−0.953483	−0.476741	+	0.879044i	$0.658182\pi$
$588$	−26.0060	−1.07247
$589$	−14.0885	−0.580507
$590$	−7.94671	−0.327161
$591$	−1.86044	−0.0765284
$592$	28.6211	1.17632
$593$	−32.7054	−1.34305	−0.671525	−	0.740982i	$-0.734360\pi$
$593$	−32.7054	−1.34305	−0.671525	+	0.740982i	$0.734360\pi$
$594$	−1.80084	−0.0738896
$595$	−2.50299	−0.102613
$596$	−57.2258	−2.34406
$597$	24.5221	1.00362
$598$	−7.83155	−0.320256
$599$	−24.0437	−0.982400	−0.491200	−	0.871047i	$-0.663442\pi$
$599$	−24.0437	−0.982400	−0.491200	+	0.871047i	$0.663442\pi$
$600$	−13.6213	−0.556087
$601$	5.20530	0.212329	0.106164	−	0.994349i	$-0.466143\pi$
$601$	5.20530	0.212329	0.106164	+	0.994349i	$0.466143\pi$
$602$	−23.5586	−0.960177
$603$	−4.44386	−0.180968
$604$	88.8433	3.61498
$605$	28.6165	1.16343
$606$	2.54336	0.103317
$607$	31.1199	1.26312	0.631558	−	0.775328i	$-0.282416\pi$
$607$	31.1199	1.26312	0.631558	+	0.775328i	$0.282416\pi$
$608$	−5.03077	−0.204025
$609$	−5.15707	−0.208975
$610$	−44.5656	−1.80441
$611$	−7.58442	−0.306833
$612$	4.22179	0.170656
$613$	−24.9119	−1.00618	−0.503090	−	0.864234i	$-0.667804\pi$
$613$	−24.9119	−1.00618	−0.503090	+	0.864234i	$0.667804\pi$
$614$	53.3511	2.15308
$615$	9.53190	0.384363
$616$	−3.66718	−0.147755
$617$	26.6923	1.07459	0.537295	−	0.843394i	$-0.319446\pi$
$617$	26.6923	1.07459	0.537295	+	0.843394i	$0.319446\pi$
$618$	−2.61538	−0.105206
$619$	16.7621	0.673725	0.336862	−	0.941554i	$-0.390634\pi$
$619$	16.7621	0.673725	0.336862	+	0.941554i	$0.390634\pi$
$620$	75.4115	3.02860
$621$	1.69376	0.0679682
$622$	−29.2840	−1.17418
$623$	−6.18602	−0.247838
$624$	9.97279	0.399231
$625$	−31.2482	−1.24993
$626$	27.7596	1.10949
$627$	1.55507	0.0621035
$628$	−4.22179	−0.168468
$629$	5.31996	0.212121
$630$	6.24334	0.248741
$631$	28.9040	1.15065	0.575324	−	0.817925i	$-0.304876\pi$
$631$	28.9040	1.15065	0.575324	+	0.817925i	$0.304876\pi$
$632$	−37.3991	−1.48765
$633$	−14.5837	−0.579649
$634$	−39.8029	−1.58077
$635$	28.9960	1.15067
$636$	−14.8117	−0.587322
$637$	−11.4187	−0.452424
$638$	10.1327	0.401159
$639$	−2.13225	−0.0843507
$640$	−46.3666	−1.83280
$641$	20.6683	0.816348	0.408174	−	0.912904i	$-0.366166\pi$
$641$	20.6683	0.816348	0.408174	+	0.912904i	$0.366166\pi$
$642$	34.7824	1.37275
$643$	−11.9464	−0.471121	−0.235561	−	0.971860i	$-0.575693\pi$
$643$	−11.9464	−0.471121	−0.235561	+	0.971860i	$0.575693\pi$
$644$	6.55392	0.258260
$645$	−28.1415	−1.10807
$646$	−5.37266	−0.211384
$647$	21.3009	0.837426	0.418713	−	0.908119i	$-0.362481\pi$
$647$	21.3009	0.837426	0.418713	+	0.908119i	$0.362481\pi$
$648$	−5.54193	−0.217708
$649$	−0.842250	−0.0330612
$650$	−11.3646	−0.445755
$651$	−5.99495	−0.234961
$652$	22.8526	0.894977
$653$	−43.5119	−1.70275	−0.851375	−	0.524557i	$-0.824231\pi$
$653$	−43.5119	−1.70275	−0.851375	+	0.524557i	$0.824231\pi$
$654$	−12.3330	−0.482258
$655$	−51.4063	−2.00861
$656$	−18.7780	−0.733160
$657$	9.40170	0.366795
$658$	9.35392	0.364654
$659$	−18.8647	−0.734866	−0.367433	−	0.930050i	$-0.619763\pi$
$659$	−18.8647	−0.734866	−0.367433	+	0.930050i	$0.619763\pi$
$660$	−8.32382	−0.324004
$661$	−6.53733	−0.254273	−0.127136	−	0.991885i	$-0.540579\pi$
$661$	−6.53733	−0.254273	−0.127136	+	0.991885i	$0.540579\pi$
$662$	78.4378	3.04857
$663$	1.85370	0.0719916
$664$	70.7344	2.74503
$665$	−5.39127	−0.209064
$666$	−13.2699	−0.514197
$667$	−9.53021	−0.369011
$668$	−30.3482	−1.17421
$669$	14.3616	0.555250
$670$	−30.2709	−1.16947
$671$	−4.72339	−0.182344
$672$	−2.14069	−0.0825791
$673$	21.8268	0.841361	0.420681	−	0.907209i	$-0.361791\pi$
$673$	21.8268	0.841361	0.420681	+	0.907209i	$0.361791\pi$
$674$	69.9653	2.69496
$675$	2.45786	0.0946031
$676$	−40.3764	−1.55294
$677$	40.7507	1.56618	0.783088	−	0.621910i	$-0.213643\pi$
$677$	40.7507	1.56618	0.783088	+	0.621910i	$0.213643\pi$
$678$	−5.00867	−0.192357
$679$	0.998635	0.0383241
$680$	15.1345	0.580382
$681$	19.4957	0.747077
$682$	11.7790	0.451043
$683$	−37.4611	−1.43341	−0.716704	−	0.697378i	$-0.754350\pi$
$683$	−37.4611	−1.43341	−0.716704	+	0.697378i	$0.754350\pi$
$684$	9.09345	0.347697
$685$	−58.2080	−2.22401
$686$	30.0860	1.14869
$687$	21.7676	0.830487
$688$	55.4393	2.11360
$689$	−6.50349	−0.247763
$690$	11.5376	0.439230
$691$	−13.5115	−0.514003	−0.257002	−	0.966411i	$-0.582735\pi$
$691$	−13.5115	−0.514003	−0.257002	+	0.966411i	$0.582735\pi$
$692$	−73.6463	−2.79961
$693$	0.661715	0.0251365
$694$	60.6351	2.30168
$695$	44.1150	1.67338
$696$	31.1826	1.18197
$697$	−3.49038	−0.132207
$698$	−16.3622	−0.619318
$699$	−15.4421	−0.584076
$700$	9.51056	0.359466
$701$	−11.2252	−0.423969	−0.211985	−	0.977273i	$-0.567993\pi$
$701$	−11.2252	−0.423969	−0.211985	+	0.977273i	$0.567993\pi$
$702$	−4.62377	−0.174513
$703$	11.4588	0.432178
$704$	−3.56222	−0.134256
$705$	11.1735	0.420820
$706$	76.6821	2.88597
$707$	−0.934548	−0.0351473
$708$	−4.92515	−0.185098
$709$	−14.7893	−0.555425	−0.277713	−	0.960664i	$-0.589576\pi$
$709$	−14.7893	−0.555425	−0.277713	+	0.960664i	$0.589576\pi$
$710$	−14.5246	−0.545098
$711$	6.74838	0.253084
$712$	37.4042	1.40178
$713$	−11.0786	−0.414897
$714$	−2.28618	−0.0855581
$715$	−3.65480	−0.136682
$716$	−13.6327	−0.509479
$717$	−15.8064	−0.590301
$718$	−36.6518	−1.36783
$719$	7.17684	0.267651	0.133826	−	0.991005i	$-0.457274\pi$
$719$	7.17684	0.267651	0.133826	+	0.991005i	$0.457274\pi$
$720$	−14.6921	−0.547544
$721$	0.961011	0.0357899
$722$	35.8204	1.33310
$723$	−24.8605	−0.924572
$724$	89.6881	3.33323
$725$	−13.8295	−0.513616
$726$	26.1377	0.970062
$727$	−15.4470	−0.572898	−0.286449	−	0.958095i	$-0.592475\pi$
$727$	−15.4470	−0.572898	−0.286449	+	0.958095i	$0.592475\pi$
$728$	−9.41569	−0.348969
$729$	1.00000	0.0370370
$730$	64.0430	2.37034
$731$	10.3048	0.381137
$732$	−27.6205	−1.02088
$733$	−13.6753	−0.505110	−0.252555	−	0.967583i	$-0.581271\pi$
$733$	−13.6753	−0.505110	−0.252555	+	0.967583i	$0.581271\pi$
$734$	89.5585	3.30566
$735$	16.8223	0.620498
$736$	−3.95598	−0.145819
$737$	−3.20833	−0.118180
$738$	8.70623	0.320481
$739$	38.6856	1.42307	0.711537	−	0.702649i	$-0.247999\pi$
$739$	38.6856	1.42307	0.711537	+	0.702649i	$0.247999\pi$
$740$	−61.3356	−2.25474
$741$	3.99273	0.146677
$742$	8.02080	0.294453
$743$	−28.9920	−1.06361	−0.531807	−	0.846866i	$-0.678487\pi$
$743$	−28.9920	−1.06361	−0.531807	+	0.846866i	$0.678487\pi$
$744$	36.2489	1.32895
$745$	37.0171	1.35620
$746$	−17.1743	−0.628794
$747$	−12.7635	−0.466991
$748$	3.04800	0.111446
$749$	−12.7807	−0.466996
$750$	−17.3167	−0.632315
$751$	−5.05181	−0.184343	−0.0921716	−	0.995743i	$-0.529381\pi$
$751$	−5.05181	−0.184343	−0.0921716	+	0.995743i	$0.529381\pi$
$752$	−22.0121	−0.802700
$753$	−25.3494	−0.923783
$754$	26.0164	0.947461
$755$	−57.4692	−2.09152
$756$	3.86945	0.140731
$757$	−8.76606	−0.318608	−0.159304	−	0.987230i	$-0.550925\pi$
$757$	−8.76606	−0.318608	−0.159304	+	0.987230i	$0.550925\pi$
$758$	−19.8788	−0.722030
$759$	1.22284	0.0443863
$760$	32.5987	1.18248
$761$	−3.53688	−0.128212	−0.0641058	−	0.997943i	$-0.520420\pi$
$761$	−3.53688	−0.128212	−0.0641058	+	0.997943i	$0.520420\pi$
$762$	26.4843	0.959426
$763$	4.53172	0.164059
$764$	22.1047	0.799718
$765$	−2.73091	−0.0987362
$766$	31.3601	1.13309
$767$	−2.16252	−0.0780842
$768$	−32.4822	−1.17210
$769$	2.53290	0.0913386	0.0456693	−	0.998957i	$-0.485458\pi$
$769$	2.53290	0.0913386	0.0456693	+	0.998957i	$0.485458\pi$
$770$	4.50750	0.162439
$771$	25.2344	0.908796
$772$	−22.2501	−0.800797
$773$	−18.6166	−0.669594	−0.334797	−	0.942290i	$-0.608668\pi$
$773$	−18.6166	−0.669594	−0.334797	+	0.942290i	$0.608668\pi$
$774$	−25.7038	−0.923904
$775$	−16.0765	−0.577484
$776$	−6.03832	−0.216763
$777$	4.87597	0.174924
$778$	−37.3189	−1.33795
$779$	−7.51803	−0.269361
$780$	−21.3719	−0.765236
$781$	−1.53942	−0.0550848
$782$	−4.22483	−0.151080
$783$	−5.62666	−0.201080
$784$	−33.1402	−1.18358
$785$	2.73091	0.0974703
$786$	−46.9534	−1.67477
$787$	3.35190	0.119482	0.0597411	−	0.998214i	$-0.480972\pi$
$787$	3.35190	0.119482	0.0597411	+	0.998214i	$0.480972\pi$
$788$	−7.85440	−0.279801
$789$	−11.8831	−0.423049
$790$	45.9689	1.63550
$791$	1.84042	0.0654378
$792$	−4.00110	−0.142173
$793$	−12.1276	−0.430663
$794$	−52.3870	−1.85914
$795$	9.58109	0.339806
$796$	103.527	3.66942
$797$	−6.62933	−0.234823	−0.117411	−	0.993083i	$-0.537460\pi$
$797$	−6.62933	−0.234823	−0.117411	+	0.993083i	$0.537460\pi$
$798$	−4.92427	−0.174317
$799$	−4.09151	−0.144747
$800$	−5.74063	−0.202962
$801$	−6.74930	−0.238475
$802$	−72.9561	−2.57617
$803$	6.78774	0.239534
$804$	−18.7611	−0.661651
$805$	−4.23946	−0.149422
$806$	30.2433	1.06528
$807$	0.468808	0.0165028
$808$	5.65081	0.198795
$809$	38.6876	1.36018	0.680092	−	0.733126i	$-0.261940\pi$
$809$	38.6876	1.36018	0.680092	+	0.733126i	$0.261940\pi$
$810$	6.81185	0.239344
$811$	−10.2246	−0.359033	−0.179517	−	0.983755i	$-0.557453\pi$
$811$	−10.2246	−0.359033	−0.179517	+	0.983755i	$0.557453\pi$
$812$	−21.7721	−0.764050
$813$	18.3768	0.644502
$814$	−9.58043	−0.335794
$815$	−14.7824	−0.517806
$816$	5.37995	0.188336
$817$	22.1958	0.776533
$818$	92.0146	3.21721
$819$	1.69899	0.0593675
$820$	40.2417	1.40530
$821$	−49.3826	−1.72347	−0.861733	−	0.507363i	$-0.830620\pi$
$821$	−49.3826	−1.72347	−0.861733	+	0.507363i	$0.830620\pi$
$822$	−53.1659	−1.85437
$823$	−32.2981	−1.12584	−0.562921	−	0.826510i	$-0.690323\pi$
$823$	−32.2981	−1.12584	−0.562921	+	0.826510i	$0.690323\pi$
$824$	−5.81082	−0.202430
$825$	1.77450	0.0617801
$826$	2.66706	0.0927988
$827$	11.3393	0.394307	0.197154	−	0.980373i	$-0.436830\pi$
$827$	11.3393	0.394307	0.197154	+	0.980373i	$0.436830\pi$
$828$	7.15070	0.248504
$829$	−41.3818	−1.43725	−0.718625	−	0.695397i	$-0.755228\pi$
$829$	−41.3818	−1.43725	−0.718625	+	0.695397i	$0.755228\pi$
$830$	−86.9429	−3.01783
$831$	−27.0614	−0.938748
$832$	−9.14620	−0.317088
$833$	−6.15995	−0.213430
$834$	40.2937	1.39526
$835$	19.6311	0.679361
$836$	6.56519	0.227062
$837$	−6.54084	−0.226085
$838$	−24.0436	−0.830573
$839$	28.1219	0.970874	0.485437	−	0.874272i	$-0.338660\pi$
$839$	28.1219	0.970874	0.485437	+	0.874272i	$0.338660\pi$
$840$	13.8714	0.478609
$841$	2.65929	0.0916997
$842$	−7.67662	−0.264554
$843$	2.23006	0.0768073
$844$	−61.5692	−2.11930
$845$	26.1179	0.898483
$846$	10.2057	0.350878
$847$	−9.60422	−0.330005
$848$	−18.8750	−0.648169
$849$	−21.4421	−0.735890
$850$	−6.13077	−0.210284
$851$	9.01074	0.308884
$852$	−9.00194	−0.308401
$853$	−13.7255	−0.469953	−0.234977	−	0.972001i	$-0.575501\pi$
$853$	−13.7255	−0.469953	−0.234977	+	0.972001i	$0.575501\pi$
$854$	14.9570	0.511819
$855$	−5.88219	−0.201166
$856$	77.2794	2.64136
$857$	−48.4926	−1.65648	−0.828239	−	0.560376i	$-0.810657\pi$
$857$	−48.4926	−1.65648	−0.828239	+	0.560376i	$0.810657\pi$
$858$	−3.33822	−0.113965
$859$	−34.5219	−1.17787	−0.588936	−	0.808180i	$-0.700453\pi$
$859$	−34.5219	−1.17787	−0.588936	+	0.808180i	$0.700453\pi$
$860$	−118.807	−4.05130
$861$	−3.19908	−0.109024
$862$	−25.4532	−0.866939
$863$	−26.1201	−0.889138	−0.444569	−	0.895745i	$-0.646643\pi$
$863$	−26.1201	−0.889138	−0.444569	+	0.895745i	$0.646643\pi$
$864$	−2.33562	−0.0794595
$865$	47.6389	1.61977
$866$	50.5151	1.71657
$867$	1.00000	0.0339618
$868$	−25.3095	−0.859059
$869$	4.87212	0.165275
$870$	−38.3279	−1.29944
$871$	−8.23756	−0.279119
$872$	−27.4014	−0.927927
$873$	1.08957	0.0368763
$874$	−9.09999	−0.307812
$875$	6.36295	0.215107
$876$	39.6920	1.34107
$877$	16.9626	0.572785	0.286393	−	0.958112i	$-0.407544\pi$
$877$	16.9626	0.572785	0.286393	+	0.958112i	$0.407544\pi$
$878$	−30.0038	−1.01258
$879$	19.5071	0.657957
$880$	−10.6073	−0.357571
$881$	38.7715	1.30624	0.653122	−	0.757253i	$-0.273459\pi$
$881$	38.7715	1.30624	0.653122	+	0.757253i	$0.273459\pi$
$882$	15.3651	0.517369
$883$	−33.3835	−1.12344	−0.561721	−	0.827326i	$-0.689861\pi$
$883$	−33.3835	−1.12344	−0.561721	+	0.827326i	$0.689861\pi$
$884$	7.82592	0.263214
$885$	3.18588	0.107092
$886$	−64.5827	−2.16970
$887$	−24.8868	−0.835618	−0.417809	−	0.908535i	$-0.637202\pi$
$887$	−24.8868	−0.835618	−0.417809	+	0.908535i	$0.637202\pi$
$888$	−29.4829	−0.989381
$889$	−9.73158	−0.326387
$890$	−45.9752	−1.54109
$891$	0.721969	0.0241869
$892$	60.6315	2.03009
$893$	−8.81283	−0.294910
$894$	33.8106	1.13079
$895$	8.81846	0.294769
$896$	15.5615	0.519872
$897$	3.13971	0.104832
$898$	15.9685	0.532877
$899$	36.8031	1.22745
$900$	10.3766	0.345886
$901$	−3.50839	−0.116881
$902$	6.28563	0.209288
$903$	9.44478	0.314303
$904$	−11.1282	−0.370120
$905$	−58.0157	−1.92851
$906$	−52.4911	−1.74390
$907$	−57.1886	−1.89892	−0.949458	−	0.313893i	$-0.898367\pi$
$907$	−57.1886	−1.89892	−0.949458	+	0.313893i	$0.898367\pi$
$908$	82.3069	2.73145
$909$	−1.01965	−0.0338195
$910$	11.5733	0.383650
$911$	−10.9312	−0.362166	−0.181083	−	0.983468i	$-0.557960\pi$
$911$	−10.9312	−0.362166	−0.181083	+	0.983468i	$0.557960\pi$
$912$	11.5880	0.383718
$913$	−9.21484	−0.304967
$914$	−89.9742	−2.97608
$915$	17.8666	0.590652
$916$	91.8984	3.03641
$917$	17.2529	0.569740
$918$	−2.49435	−0.0823259
$919$	−41.2369	−1.36028	−0.680140	−	0.733082i	$-0.738081\pi$
$919$	−41.2369	−1.36028	−0.680140	+	0.733082i	$0.738081\pi$
$920$	25.6342	0.845135
$921$	−21.3888	−0.704784
$922$	−72.8029	−2.39763
$923$	−3.95255	−0.130100
$924$	2.79362	0.0919034
$925$	13.0757	0.429927
$926$	17.1727	0.564330
$927$	1.04852	0.0344379
$928$	13.1417	0.431399
$929$	−43.3891	−1.42355	−0.711775	−	0.702407i	$-0.752109\pi$
$929$	−43.3891	−1.42355	−0.711775	+	0.702407i	$0.752109\pi$
$930$	−44.5552	−1.46102
$931$	−13.2681	−0.434845
$932$	−65.1936	−2.13549
$933$	11.7401	0.384355
$934$	15.4514	0.505585
$935$	−1.97163	−0.0644792
$936$	−10.2731	−0.335785
$937$	−2.68087	−0.0875803	−0.0437901	−	0.999041i	$-0.513943\pi$
$937$	−2.68087	−0.0875803	−0.0437901	+	0.999041i	$0.513943\pi$
$938$	10.1595	0.331718
$939$	−11.1290	−0.363180
$940$	47.1724	1.53859
$941$	55.5400	1.81055	0.905276	−	0.424824i	$-0.139664\pi$
$941$	55.5400	1.81055	0.905276	+	0.424824i	$0.139664\pi$
$942$	2.49435	0.0812704
$943$	−5.91186	−0.192517
$944$	−6.27626	−0.204275
$945$	−2.50299	−0.0814223
$946$	−18.5573	−0.603351
$947$	0.0792329	0.00257472	0.00128736	−	0.999999i	$-0.499590\pi$
$947$	0.0792329	0.00257472	0.00128736	+	0.999999i	$0.499590\pi$
$948$	28.4902	0.925320
$949$	17.4279	0.565733
$950$	−13.2052	−0.428435
$951$	15.9572	0.517448
$952$	−5.07941	−0.164625
$953$	16.1127	0.521942	0.260971	−	0.965347i	$-0.415957\pi$
$953$	16.1127	0.521942	0.260971	+	0.965347i	$0.415957\pi$
$954$	8.75116	0.283329
$955$	−14.2986	−0.462692
$956$	−66.7313	−2.15825
$957$	−4.06227	−0.131315
$958$	−16.6791	−0.538878
$959$	19.5356	0.630839
$960$	13.4744	0.434884
$961$	11.7826	0.380084
$962$	−24.5983	−0.793081
$963$	−13.9445	−0.449355
$964$	−104.956	−3.38040
$965$	14.3927	0.463317
$966$	−3.87224	−0.124587
$967$	−32.8573	−1.05662	−0.528310	−	0.849052i	$-0.677174\pi$
$967$	−32.8573	−1.05662	−0.528310	+	0.849052i	$0.677174\pi$
$968$	58.0726	1.86652
$969$	2.15393	0.0691942
$970$	7.42198	0.238305
$971$	−27.7445	−0.890362	−0.445181	−	0.895441i	$-0.646861\pi$
$971$	−27.7445	−0.890362	−0.445181	+	0.895441i	$0.646861\pi$
$972$	4.22179	0.135414
$973$	−14.8058	−0.474652
$974$	60.9138	1.95181
$975$	4.55612	0.145913
$976$	−35.1976	−1.12665
$977$	2.34099	0.0748948	0.0374474	−	0.999299i	$-0.488077\pi$
$977$	2.34099	0.0748948	0.0374474	+	0.999299i	$0.488077\pi$
$978$	−13.5020	−0.431745
$979$	−4.87279	−0.155735
$980$	71.0201	2.26865
$981$	4.94437	0.157862
$982$	−66.0705	−2.10839
$983$	12.5995	0.401863	0.200932	−	0.979605i	$-0.435603\pi$
$983$	12.5995	0.401863	0.200932	+	0.979605i	$0.435603\pi$
$984$	19.3434	0.616646
$985$	5.08070	0.161884
$986$	14.0349	0.446961
$987$	−3.75004	−0.119365
$988$	16.8565	0.536276
$989$	17.4539	0.555000
$990$	4.91794	0.156302
$991$	−13.7841	−0.437867	−0.218934	−	0.975740i	$-0.570258\pi$
$991$	−13.7841	−0.437867	−0.218934	+	0.975740i	$0.570258\pi$
$992$	15.2769	0.485043
$993$	−31.4462	−0.997914
$994$	4.87471	0.154617
$995$	−66.9675	−2.12301
$996$	−53.8848	−1.70740
$997$	−15.4688	−0.489901	−0.244950	−	0.969536i	$-0.578772\pi$
$997$	−15.4688	−0.489901	−0.244950	+	0.969536i	$0.578772\pi$
$998$	25.1096	0.794830
$999$	5.31996	0.168316

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8007.2.a.d.1.4	✓	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8007.2.a.d.1.4	✓	40	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 8007 = 3 \cdot 17 \cdot 157 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8007.a (trivial)

\(f(q)\)	\(=\)	\(q-2.49435 q^{2} +1.00000 q^{3} +4.22179 q^{4} -2.73091 q^{5} -2.49435 q^{6} +0.916542 q^{7} -5.54193 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-2.49435 q^{2} +1.00000 q^{3} +4.22179 q^{4} -2.73091 q^{5} -2.49435 q^{6} +0.916542 q^{7} -5.54193 q^{8} +1.00000 q^{9} +6.81185 q^{10} +0.721969 q^{11} +4.22179 q^{12} +1.85370 q^{13} -2.28618 q^{14} -2.73091 q^{15} +5.37995 q^{16} +1.00000 q^{17} -2.49435 q^{18} +2.15393 q^{19} -11.5293 q^{20} +0.916542 q^{21} -1.80084 q^{22} +1.69376 q^{23} -5.54193 q^{24} +2.45786 q^{25} -4.62377 q^{26} +1.00000 q^{27} +3.86945 q^{28} -5.62666 q^{29} +6.81185 q^{30} -6.54084 q^{31} -2.33562 q^{32} +0.721969 q^{33} -2.49435 q^{34} -2.50299 q^{35} +4.22179 q^{36} +5.31996 q^{37} -5.37266 q^{38} +1.85370 q^{39} +15.1345 q^{40} -3.49038 q^{41} -2.28618 q^{42} +10.3048 q^{43} +3.04800 q^{44} -2.73091 q^{45} -4.22483 q^{46} -4.09151 q^{47} +5.37995 q^{48} -6.15995 q^{49} -6.13077 q^{50} +1.00000 q^{51} +7.82592 q^{52} -3.50839 q^{53} -2.49435 q^{54} -1.97163 q^{55} -5.07941 q^{56} +2.15393 q^{57} +14.0349 q^{58} -1.16660 q^{59} -11.5293 q^{60} -6.54237 q^{61} +16.3152 q^{62} +0.916542 q^{63} -4.93404 q^{64} -5.06227 q^{65} -1.80084 q^{66} -4.44386 q^{67} +4.22179 q^{68} +1.69376 q^{69} +6.24334 q^{70} -2.13225 q^{71} -5.54193 q^{72} +9.40170 q^{73} -13.2699 q^{74} +2.45786 q^{75} +9.09345 q^{76} +0.661715 q^{77} -4.62377 q^{78} +6.74838 q^{79} -14.6921 q^{80} +1.00000 q^{81} +8.70623 q^{82} -12.7635 q^{83} +3.86945 q^{84} -2.73091 q^{85} -25.7038 q^{86} -5.62666 q^{87} -4.00110 q^{88} -6.74930 q^{89} +6.81185 q^{90} +1.69899 q^{91} +7.15070 q^{92} -6.54084 q^{93} +10.2057 q^{94} -5.88219 q^{95} -2.33562 q^{96} +1.08957 q^{97} +15.3651 q^{98} +0.721969 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 7 q^{2} + 40 q^{3} + 29 q^{4} - 15 q^{5} - 7 q^{6} - 13 q^{7} - 18 q^{8} + 40 q^{9}+O(q^{10}) \) 40 * q - 7 * q^2 + 40 * q^3 + 29 * q^4 - 15 * q^5 - 7 * q^6 - 13 * q^7 - 18 * q^8 + 40 * q^9	\( 40 q - 7 q^{2} + 40 q^{3} + 29 q^{4} - 15 q^{5} - 7 q^{6} - 13 q^{7} - 18 q^{8} + 40 q^{9} - 6 q^{10} - 25 q^{11} + 29 q^{12} - 24 q^{13} - 22 q^{14} - 15 q^{15} + 7 q^{16} + 40 q^{17} - 7 q^{18} - 18 q^{19} - 20 q^{20} - 13 q^{21} - 25 q^{22} - 28 q^{23} - 18 q^{24} - 11 q^{25} - 13 q^{26} + 40 q^{27} - 8 q^{28} - 23 q^{29} - 6 q^{30} - 11 q^{31} - 23 q^{32} - 25 q^{33} - 7 q^{34} - 45 q^{35} + 29 q^{36} - 38 q^{37} - 30 q^{38} - 24 q^{39} - 12 q^{40} - 33 q^{41} - 22 q^{42} - 25 q^{43} - 14 q^{44} - 15 q^{45} + 8 q^{46} - 55 q^{47} + 7 q^{48} - 21 q^{49} + 2 q^{50} + 40 q^{51} - 39 q^{52} - 39 q^{53} - 7 q^{54} - 9 q^{55} - 48 q^{56} - 18 q^{57} - 13 q^{58} - 81 q^{59} - 20 q^{60} - 9 q^{61} - 16 q^{62} - 13 q^{63} - 4 q^{64} - 43 q^{65} - 25 q^{66} - 24 q^{67} + 29 q^{68} - 28 q^{69} + 48 q^{70} - 32 q^{71} - 18 q^{72} - 43 q^{73} - 20 q^{74} - 11 q^{75} - 58 q^{76} - 32 q^{77} - 13 q^{78} - 22 q^{79} - 48 q^{80} + 40 q^{81} - 11 q^{82} - 45 q^{83} - 8 q^{84} - 15 q^{85} - 30 q^{86} - 23 q^{87} - 48 q^{88} - 94 q^{89} - 6 q^{90} - 7 q^{91} - 98 q^{92} - 11 q^{93} + 32 q^{94} - 23 q^{96} - 28 q^{97} - 46 q^{98} - 25 q^{99}+O(q^{100}) \) 40 * q - 7 * q^2 + 40 * q^3 + 29 * q^4 - 15 * q^5 - 7 * q^6 - 13 * q^7 - 18 * q^8 + 40 * q^9 - 6 * q^10 - 25 * q^11 + 29 * q^12 - 24 * q^13 - 22 * q^14 - 15 * q^15 + 7 * q^16 + 40 * q^17 - 7 * q^18 - 18 * q^19 - 20 * q^20 - 13 * q^21 - 25 * q^22 - 28 * q^23 - 18 * q^24 - 11 * q^25 - 13 * q^26 + 40 * q^27 - 8 * q^28 - 23 * q^29 - 6 * q^30 - 11 * q^31 - 23 * q^32 - 25 * q^33 - 7 * q^34 - 45 * q^35 + 29 * q^36 - 38 * q^37 - 30 * q^38 - 24 * q^39 - 12 * q^40 - 33 * q^41 - 22 * q^42 - 25 * q^43 - 14 * q^44 - 15 * q^45 + 8 * q^46 - 55 * q^47 + 7 * q^48 - 21 * q^49 + 2 * q^50 + 40 * q^51 - 39 * q^52 - 39 * q^53 - 7 * q^54 - 9 * q^55 - 48 * q^56 - 18 * q^57 - 13 * q^58 - 81 * q^59 - 20 * q^60 - 9 * q^61 - 16 * q^62 - 13 * q^63 - 4 * q^64 - 43 * q^65 - 25 * q^66 - 24 * q^67 + 29 * q^68 - 28 * q^69 + 48 * q^70 - 32 * q^71 - 18 * q^72 - 43 * q^73 - 20 * q^74 - 11 * q^75 - 58 * q^76 - 32 * q^77 - 13 * q^78 - 22 * q^79 - 48 * q^80 + 40 * q^81 - 11 * q^82 - 45 * q^83 - 8 * q^84 - 15 * q^85 - 30 * q^86 - 23 * q^87 - 48 * q^88 - 94 * q^89 - 6 * q^90 - 7 * q^91 - 98 * q^92 - 11 * q^93 + 32 * q^94 - 23 * q^96 - 28 * q^97 - 46 * q^98 - 25 * q^99

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