LMFDB - Embedded newform 8007.2.a.c.1.2

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			1.2
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)

$f(q)$	$=$	$q-2.62708 q^{2} -1.00000 q^{3} +4.90155 q^{4} +1.61007 q^{5} +2.62708 q^{6} -0.284525 q^{7} -7.62261 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-2.62708 q^{2} -1.00000 q^{3} +4.90155 q^{4} +1.61007 q^{5} +2.62708 q^{6} -0.284525 q^{7} -7.62261 q^{8} +1.00000 q^{9} -4.22979 q^{10} -2.96263 q^{11} -4.90155 q^{12} -0.885389 q^{13} +0.747471 q^{14} -1.61007 q^{15} +10.2221 q^{16} +1.00000 q^{17} -2.62708 q^{18} +3.78346 q^{19} +7.89185 q^{20} +0.284525 q^{21} +7.78307 q^{22} +7.24585 q^{23} +7.62261 q^{24} -2.40767 q^{25} +2.32599 q^{26} -1.00000 q^{27} -1.39462 q^{28} -0.699776 q^{29} +4.22979 q^{30} -9.02793 q^{31} -11.6091 q^{32} +2.96263 q^{33} -2.62708 q^{34} -0.458106 q^{35} +4.90155 q^{36} -2.17399 q^{37} -9.93945 q^{38} +0.885389 q^{39} -12.2729 q^{40} +0.732601 q^{41} -0.747471 q^{42} -7.42289 q^{43} -14.5215 q^{44} +1.61007 q^{45} -19.0354 q^{46} +0.637422 q^{47} -10.2221 q^{48} -6.91905 q^{49} +6.32514 q^{50} -1.00000 q^{51} -4.33978 q^{52} +13.1503 q^{53} +2.62708 q^{54} -4.77005 q^{55} +2.16882 q^{56} -3.78346 q^{57} +1.83837 q^{58} +2.66276 q^{59} -7.89185 q^{60} +3.73679 q^{61} +23.7171 q^{62} -0.284525 q^{63} +10.0537 q^{64} -1.42554 q^{65} -7.78307 q^{66} -7.48744 q^{67} +4.90155 q^{68} -7.24585 q^{69} +1.20348 q^{70} +11.3882 q^{71} -7.62261 q^{72} +5.02906 q^{73} +5.71125 q^{74} +2.40767 q^{75} +18.5448 q^{76} +0.842944 q^{77} -2.32599 q^{78} +11.4430 q^{79} +16.4583 q^{80} +1.00000 q^{81} -1.92460 q^{82} +4.39773 q^{83} +1.39462 q^{84} +1.61007 q^{85} +19.5005 q^{86} +0.699776 q^{87} +22.5830 q^{88} -2.96141 q^{89} -4.22979 q^{90} +0.251915 q^{91} +35.5159 q^{92} +9.02793 q^{93} -1.67456 q^{94} +6.09164 q^{95} +11.6091 q^{96} +4.79840 q^{97} +18.1769 q^{98} -2.96263 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−2.62708	−1.85763	−0.928813	−	0.370548i	$-0.879170\pi$
$2$	−2.62708	−1.85763	−0.928813	+	0.370548i	$0.879170\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	4.90155	2.45078
$5$	1.61007	0.720046	0.360023	−	0.932943i	$-0.382769\pi$
$5$	1.61007	0.720046	0.360023	+	0.932943i	$0.382769\pi$
$6$	2.62708	1.07250
$7$	−0.284525	−0.107540	−0.0537702	−	0.998553i	$-0.517124\pi$
$7$	−0.284525	−0.107540	−0.0537702	+	0.998553i	$0.517124\pi$
$8$	−7.62261	−2.69500
$9$	1.00000	0.333333
$10$	−4.22979	−1.33758
$11$	−2.96263	−0.893267	−0.446634	−	0.894717i	$-0.647377\pi$
$11$	−2.96263	−0.893267	−0.446634	+	0.894717i	$0.647377\pi$
$12$	−4.90155	−1.41496
$13$	−0.885389	−0.245563	−0.122781	−	0.992434i	$-0.539181\pi$
$13$	−0.885389	−0.245563	−0.122781	+	0.992434i	$0.539181\pi$
$14$	0.747471	0.199770
$15$	−1.61007	−0.415719
$16$	10.2221	2.55552
$17$	1.00000	0.242536
$17$	1.00000	0.242536
$18$	−2.62708	−0.619209
$19$	3.78346	0.867985	0.433992	−	0.900917i	$-0.357105\pi$
$19$	3.78346	0.867985	0.433992	+	0.900917i	$0.357105\pi$
$20$	7.89185	1.76467
$21$	0.284525	0.0620885
$22$	7.78307	1.65936
$23$	7.24585	1.51086	0.755432	−	0.655227i	$-0.227427\pi$
$23$	7.24585	1.51086	0.755432	+	0.655227i	$0.227427\pi$
$24$	7.62261	1.55596
$25$	−2.40767	−0.481534
$26$	2.32599	0.456164
$27$	−1.00000	−0.192450
$28$	−1.39462	−0.263557
$29$	−0.699776	−0.129945	−0.0649726	−	0.997887i	$-0.520696\pi$
$29$	−0.699776	−0.129945	−0.0649726	+	0.997887i	$0.520696\pi$
$30$	4.22979	0.772250
$31$	−9.02793	−1.62146	−0.810732	−	0.585417i	$-0.800931\pi$
$31$	−9.02793	−1.62146	−0.810732	+	0.585417i	$0.800931\pi$
$32$	−11.6091	−2.05221
$33$	2.96263	0.515728
$34$	−2.62708	−0.450541
$35$	−0.458106	−0.0774341
$36$	4.90155	0.816925
$37$	−2.17399	−0.357402	−0.178701	−	0.983903i	$-0.557189\pi$
$37$	−2.17399	−0.357402	−0.178701	+	0.983903i	$0.557189\pi$
$38$	−9.93945	−1.61239
$39$	0.885389	0.141776
$40$	−12.2729	−1.94052
$41$	0.732601	0.114413	0.0572065	−	0.998362i	$-0.481781\pi$
$41$	0.732601	0.114413	0.0572065	+	0.998362i	$0.481781\pi$
$42$	−0.747471	−0.115337
$43$	−7.42289	−1.13198	−0.565990	−	0.824412i	$-0.691506\pi$
$43$	−7.42289	−1.13198	−0.565990	+	0.824412i	$0.691506\pi$
$44$	−14.5215	−2.18920
$45$	1.61007	0.240015
$46$	−19.0354	−2.80662
$47$	0.637422	0.0929775	0.0464888	−	0.998919i	$-0.485197\pi$
$47$	0.637422	0.0929775	0.0464888	+	0.998919i	$0.485197\pi$
$48$	−10.2221	−1.47543
$49$	−6.91905	−0.988435
$50$	6.32514	0.894510
$51$	−1.00000	−0.140028
$52$	−4.33978	−0.601819
$53$	13.1503	1.80633	0.903166	−	0.429292i	$-0.141237\pi$
$53$	13.1503	1.80633	0.903166	+	0.429292i	$0.141237\pi$
$54$	2.62708	0.357500
$55$	−4.77005	−0.643193
$56$	2.16882	0.289821
$57$	−3.78346	−0.501131
$58$	1.83837	0.241390
$59$	2.66276	0.346662	0.173331	−	0.984864i	$-0.444547\pi$
$59$	2.66276	0.346662	0.173331	+	0.984864i	$0.444547\pi$
$60$	−7.89185	−1.01883
$61$	3.73679	0.478447	0.239224	−	0.970964i	$-0.423107\pi$
$61$	3.73679	0.478447	0.239224	+	0.970964i	$0.423107\pi$
$62$	23.7171	3.01207
$63$	−0.284525	−0.0358468
$64$	10.0537	1.25672
$65$	−1.42554	−0.176816
$66$	−7.78307	−0.958030
$67$	−7.48744	−0.914736	−0.457368	−	0.889277i	$-0.651208\pi$
$67$	−7.48744	−0.914736	−0.457368	+	0.889277i	$0.651208\pi$
$68$	4.90155	0.594400
$69$	−7.24585	−0.872298
$70$	1.20348	0.143844
$71$	11.3882	1.35153	0.675763	−	0.737119i	$-0.263814\pi$
$71$	11.3882	1.35153	0.675763	+	0.737119i	$0.263814\pi$
$72$	−7.62261	−0.898333
$73$	5.02906	0.588607	0.294303	−	0.955712i	$-0.404912\pi$
$73$	5.02906	0.588607	0.294303	+	0.955712i	$0.404912\pi$
$74$	5.71125	0.663919
$75$	2.40767	0.278014
$76$	18.5448	2.12724
$77$	0.842944	0.0960624
$78$	−2.32599	−0.263366
$79$	11.4430	1.28744	0.643719	−	0.765262i	$-0.277391\pi$
$79$	11.4430	1.28744	0.643719	+	0.765262i	$0.277391\pi$
$80$	16.4583	1.84010
$81$	1.00000	0.111111
$82$	−1.92460	−0.212537
$83$	4.39773	0.482714	0.241357	−	0.970436i	$-0.422408\pi$
$83$	4.39773	0.482714	0.241357	+	0.970436i	$0.422408\pi$
$84$	1.39462	0.152165
$85$	1.61007	0.174637
$86$	19.5005	2.10280
$87$	0.699776	0.0750239
$88$	22.5830	2.40735
$89$	−2.96141	−0.313909	−0.156954	−	0.987606i	$-0.550168\pi$
$89$	−2.96141	−0.313909	−0.156954	+	0.987606i	$0.550168\pi$
$90$	−4.22979	−0.445859
$91$	0.251915	0.0264079
$92$	35.5159	3.70279
$93$	9.02793	0.936153
$94$	−1.67456	−0.172717
$95$	6.09164	0.624989
$96$	11.6091	1.18484
$97$	4.79840	0.487203	0.243602	−	0.969875i	$-0.421671\pi$
$97$	4.79840	0.487203	0.243602	+	0.969875i	$0.421671\pi$
$98$	18.1769	1.83614
$99$	−2.96263	−0.297756
$100$	−11.8013	−1.18013
$101$	−9.24915	−0.920325	−0.460163	−	0.887835i	$-0.652209\pi$
$101$	−9.24915	−0.920325	−0.460163	+	0.887835i	$0.652209\pi$
$102$	2.62708	0.260120
$103$	−13.1086	−1.29163	−0.645813	−	0.763495i	$-0.723482\pi$
$103$	−13.1086	−1.29163	−0.645813	+	0.763495i	$0.723482\pi$
$104$	6.74897	0.661791
$105$	0.458106	0.0447066
$106$	−34.5469	−3.35549
$107$	−7.68927	−0.743349	−0.371675	−	0.928363i	$-0.621216\pi$
$107$	−7.68927	−0.743349	−0.371675	+	0.928363i	$0.621216\pi$
$108$	−4.90155	−0.471652
$109$	5.76019	0.551726	0.275863	−	0.961197i	$-0.411036\pi$
$109$	5.76019	0.551726	0.275863	+	0.961197i	$0.411036\pi$
$110$	12.5313	1.19481
$111$	2.17399	0.206346
$112$	−2.90845	−0.274822
$113$	−16.7942	−1.57986	−0.789931	−	0.613195i	$-0.789884\pi$
$113$	−16.7942	−1.57986	−0.789931	+	0.613195i	$0.789884\pi$
$114$	9.93945	0.930914
$115$	11.6663	1.08789
$116$	−3.42999	−0.318466
$117$	−0.885389	−0.0818542
$118$	−6.99528	−0.643968
$119$	−0.284525	−0.0260824
$120$	12.2729	1.12036
$121$	−2.22281	−0.202074
$122$	−9.81686	−0.888776
$123$	−0.732601	−0.0660564
$124$	−44.2509	−3.97385
$125$	−11.9269	−1.06677
$126$	0.747471	0.0665900
$127$	−2.11820	−0.187960	−0.0939799	−	0.995574i	$-0.529959\pi$
$127$	−2.11820	−0.187960	−0.0939799	+	0.995574i	$0.529959\pi$
$128$	−3.19386	−0.282300
$129$	7.42289	0.653549
$130$	3.74501	0.328459
$131$	20.0492	1.75171	0.875853	−	0.482578i	$-0.160300\pi$
$131$	20.0492	1.75171	0.875853	+	0.482578i	$0.160300\pi$
$132$	14.5215	1.26393
$133$	−1.07649	−0.0933434
$134$	19.6701	1.69924
$135$	−1.61007	−0.138573
$136$	−7.62261	−0.653633
$137$	−10.9224	−0.933160	−0.466580	−	0.884479i	$-0.654514\pi$
$137$	−10.9224	−0.933160	−0.466580	+	0.884479i	$0.654514\pi$
$138$	19.0354	1.62040
$139$	−7.53654	−0.639241	−0.319620	−	0.947546i	$-0.603555\pi$
$139$	−7.53654	−0.639241	−0.319620	+	0.947546i	$0.603555\pi$
$140$	−2.24543	−0.189774
$141$	−0.637422	−0.0536806
$142$	−29.9176	−2.51063
$143$	2.62308	0.219353
$144$	10.2221	0.851842
$145$	−1.12669	−0.0935665
$146$	−13.2117	−1.09341
$147$	6.91905	0.570673
$148$	−10.6559	−0.875912
$149$	−7.84584	−0.642756	−0.321378	−	0.946951i	$-0.604146\pi$
$149$	−7.84584	−0.642756	−0.321378	+	0.946951i	$0.604146\pi$
$150$	−6.32514	−0.516445
$151$	20.0746	1.63365	0.816824	−	0.576887i	$-0.195733\pi$
$151$	20.0746	1.63365	0.816824	+	0.576887i	$0.195733\pi$
$152$	−28.8398	−2.33922
$153$	1.00000	0.0808452
$154$	−2.21448	−0.178448
$155$	−14.5356	−1.16753
$156$	4.33978	0.347460
$157$	1.00000	0.0798087
$157$	1.00000	0.0798087
$158$	−30.0617	−2.39158
$159$	−13.1503	−1.04289
$160$	−18.6914	−1.47769
$161$	−2.06163	−0.162479
$162$	−2.62708	−0.206403
$163$	−10.0582	−0.787816	−0.393908	−	0.919150i	$-0.628877\pi$
$163$	−10.0582	−0.787816	−0.393908	+	0.919150i	$0.628877\pi$
$164$	3.59088	0.280401
$165$	4.77005	0.371348
$166$	−11.5532	−0.896702
$167$	−14.4882	−1.12113	−0.560564	−	0.828111i	$-0.689416\pi$
$167$	−14.4882	−1.12113	−0.560564	+	0.828111i	$0.689416\pi$
$168$	−2.16882	−0.167328
$169$	−12.2161	−0.939699
$170$	−4.22979	−0.324410
$171$	3.78346	0.289328
$172$	−36.3837	−2.77423
$173$	−15.1318	−1.15045	−0.575223	−	0.817996i	$-0.695085\pi$
$173$	−15.1318	−1.15045	−0.575223	+	0.817996i	$0.695085\pi$
$174$	−1.83837	−0.139366
$175$	0.685043	0.0517844
$176$	−30.2843	−2.28277
$177$	−2.66276	−0.200145
$178$	7.77986	0.583125
$179$	25.3465	1.89448	0.947242	−	0.320519i	$-0.103857\pi$
$179$	25.3465	1.89448	0.947242	+	0.320519i	$0.103857\pi$
$180$	7.89185	0.588224
$181$	−17.5200	−1.30225	−0.651124	−	0.758971i	$-0.725702\pi$
$181$	−17.5200	−1.30225	−0.651124	+	0.758971i	$0.725702\pi$
$182$	−0.661802	−0.0490560
$183$	−3.73679	−0.276232
$184$	−55.2323	−4.07178
$185$	−3.50028	−0.257346
$186$	−23.7171	−1.73902
$187$	−2.96263	−0.216649
$188$	3.12435	0.227867
$189$	0.284525	0.0206962
$190$	−16.0032	−1.16100
$191$	12.7841	0.925024	0.462512	−	0.886613i	$-0.346948\pi$
$191$	12.7841	0.925024	0.462512	+	0.886613i	$0.346948\pi$
$192$	−10.0537	−0.725566
$193$	6.02354	0.433584	0.216792	−	0.976218i	$-0.430441\pi$
$193$	6.02354	0.433584	0.216792	+	0.976218i	$0.430441\pi$
$194$	−12.6058	−0.905042
$195$	1.42554	0.102085
$196$	−33.9141	−2.42243
$197$	−10.3601	−0.738129	−0.369065	−	0.929404i	$-0.620322\pi$
$197$	−10.3601	−0.738129	−0.369065	+	0.929404i	$0.620322\pi$
$198$	7.78307	0.553119
$199$	5.21661	0.369796	0.184898	−	0.982758i	$-0.440805\pi$
$199$	5.21661	0.369796	0.184898	+	0.982758i	$0.440805\pi$
$200$	18.3527	1.29773
$201$	7.48744	0.528123
$202$	24.2983	1.70962
$203$	0.199104	0.0139744
$204$	−4.90155	−0.343177
$205$	1.17954	0.0823826
$206$	34.4373	2.39936
$207$	7.24585	0.503622
$208$	−9.05053	−0.627541
$209$	−11.2090	−0.775342
$210$	−1.20348	−0.0830481
$211$	−5.05852	−0.348243	−0.174121	−	0.984724i	$-0.555709\pi$
$211$	−5.05852	−0.348243	−0.174121	+	0.984724i	$0.555709\pi$
$212$	64.4568	4.42691
$213$	−11.3882	−0.780304
$214$	20.2003	1.38087
$215$	−11.9514	−0.815078
$216$	7.62261	0.518653
$217$	2.56867	0.174373
$218$	−15.1325	−1.02490
$219$	−5.02906	−0.339832
$220$	−23.3806	−1.57632
$221$	−0.885389	−0.0595577
$222$	−5.71125	−0.383314
$223$	1.03456	0.0692794	0.0346397	−	0.999400i	$-0.488972\pi$
$223$	1.03456	0.0692794	0.0346397	+	0.999400i	$0.488972\pi$
$224$	3.30307	0.220696
$225$	−2.40767	−0.160511
$226$	44.1196	2.93479
$227$	−3.04932	−0.202391	−0.101195	−	0.994867i	$-0.532267\pi$
$227$	−3.04932	−0.202391	−0.101195	+	0.994867i	$0.532267\pi$
$228$	−18.5448	−1.22816
$229$	25.2830	1.67075	0.835373	−	0.549683i	$-0.185251\pi$
$229$	25.2830	1.67075	0.835373	+	0.549683i	$0.185251\pi$
$230$	−30.6484	−2.02090
$231$	−0.842944	−0.0554616
$232$	5.33412	0.350202
$233$	−30.5059	−1.99851	−0.999255	−	0.0385864i	$-0.987715\pi$
$233$	−30.5059	−1.99851	−0.999255	+	0.0385864i	$0.987715\pi$
$234$	2.32599	0.152055
$235$	1.02629	0.0669481
$236$	13.0516	0.849590
$237$	−11.4430	−0.743303
$238$	0.747471	0.0484513
$239$	0.421924	0.0272920	0.0136460	−	0.999907i	$-0.495656\pi$
$239$	0.421924	0.0272920	0.0136460	+	0.999907i	$0.495656\pi$
$240$	−16.4583	−1.06238
$241$	7.11438	0.458277	0.229139	−	0.973394i	$-0.426409\pi$
$241$	7.11438	0.458277	0.229139	+	0.973394i	$0.426409\pi$
$242$	5.83950	0.375377
$243$	−1.00000	−0.0641500
$244$	18.3161	1.17257
$245$	−11.1402	−0.711719
$246$	1.92460	0.122708
$247$	−3.34983	−0.213145
$248$	68.8164	4.36984
$249$	−4.39773	−0.278695
$250$	31.3329	1.98166
$251$	25.7289	1.62399	0.811996	−	0.583663i	$-0.198381\pi$
$251$	25.7289	1.62399	0.811996	+	0.583663i	$0.198381\pi$
$252$	−1.39462	−0.0878525
$253$	−21.4668	−1.34961
$254$	5.56468	0.349159
$255$	−1.61007	−0.100827
$256$	−11.7170	−0.732310
$257$	14.6336	0.912818	0.456409	−	0.889770i	$-0.349135\pi$
$257$	14.6336	0.912818	0.456409	+	0.889770i	$0.349135\pi$
$258$	−19.5005	−1.21405
$259$	0.618555	0.0384352
$260$	−6.98735	−0.433337
$261$	−0.699776	−0.0433150
$262$	−52.6708	−3.25401
$263$	8.47505	0.522594	0.261297	−	0.965258i	$-0.415850\pi$
$263$	8.47505	0.522594	0.261297	+	0.965258i	$0.415850\pi$
$264$	−22.5830	−1.38989
$265$	21.1729	1.30064
$266$	2.82802	0.173397
$267$	2.96141	0.181235
$268$	−36.7001	−2.24181
$269$	16.8168	1.02534	0.512668	−	0.858587i	$-0.328657\pi$
$269$	16.8168	1.02534	0.512668	+	0.858587i	$0.328657\pi$
$270$	4.22979	0.257417
$271$	−15.7009	−0.953765	−0.476882	−	0.878967i	$-0.658233\pi$
$271$	−15.7009	−0.953765	−0.476882	+	0.878967i	$0.658233\pi$
$272$	10.2221	0.619806
$273$	−0.251915	−0.0152466
$274$	28.6939	1.73346
$275$	7.13304	0.430138
$276$	−35.5159	−2.13781
$277$	−0.0815824	−0.00490181	−0.00245090	−	0.999997i	$-0.500780\pi$
$277$	−0.0815824	−0.00490181	−0.00245090	+	0.999997i	$0.500780\pi$
$278$	19.7991	1.18747
$279$	−9.02793	−0.540488
$280$	3.49196	0.208685
$281$	11.9894	0.715225	0.357613	−	0.933870i	$-0.383591\pi$
$281$	11.9894	0.715225	0.357613	+	0.933870i	$0.383591\pi$
$282$	1.67456	0.0997185
$283$	−20.3274	−1.20834	−0.604168	−	0.796857i	$-0.706494\pi$
$283$	−20.3274	−1.20834	−0.604168	+	0.796857i	$0.706494\pi$
$284$	55.8197	3.31229
$285$	−6.09164	−0.360837
$286$	−6.89104	−0.407476
$287$	−0.208443	−0.0123040
$288$	−11.6091	−0.684071
$289$	1.00000	0.0588235
$290$	2.95990	0.173812
$291$	−4.79840	−0.281287
$292$	24.6502	1.44254
$293$	−12.9094	−0.754176	−0.377088	−	0.926178i	$-0.623075\pi$
$293$	−12.9094	−0.754176	−0.377088	+	0.926178i	$0.623075\pi$
$294$	−18.1769	−1.06010
$295$	4.28723	0.249612
$296$	16.5715	0.963197
$297$	2.96263	0.171909
$298$	20.6117	1.19400
$299$	−6.41540	−0.371012
$300$	11.8013	0.681349
$301$	2.11200	0.121734
$302$	−52.7376	−3.03471
$303$	9.24915	0.531350
$304$	38.6749	2.21816
$305$	6.01650	0.344504
$306$	−2.62708	−0.150180
$307$	−0.788898	−0.0450248	−0.0225124	−	0.999747i	$-0.507167\pi$
$307$	−0.788898	−0.0450248	−0.0225124	+	0.999747i	$0.507167\pi$
$308$	4.13173	0.235427
$309$	13.1086	0.745721
$310$	38.1862	2.16883
$311$	−24.0276	−1.36248	−0.681240	−	0.732060i	$-0.738559\pi$
$311$	−24.0276	−1.36248	−0.681240	+	0.732060i	$0.738559\pi$
$312$	−6.74897	−0.382085
$313$	−9.60388	−0.542844	−0.271422	−	0.962460i	$-0.587494\pi$
$313$	−9.60388	−0.542844	−0.271422	+	0.962460i	$0.587494\pi$
$314$	−2.62708	−0.148255
$315$	−0.458106	−0.0258114
$316$	56.0884	3.15522
$317$	−29.1664	−1.63815	−0.819075	−	0.573686i	$-0.805513\pi$
$317$	−29.1664	−1.63815	−0.819075	+	0.573686i	$0.805513\pi$
$318$	34.5469	1.93729
$319$	2.07318	0.116076
$320$	16.1872	0.904894
$321$	7.68927	0.429173
$322$	5.41606	0.301825
$323$	3.78346	0.210517
$324$	4.90155	0.272308
$325$	2.13172	0.118247
$326$	26.4236	1.46347
$327$	−5.76019	−0.318539
$328$	−5.58433	−0.308343
$329$	−0.181363	−0.00999884
$330$	−12.5313	−0.689826
$331$	15.2948	0.840679	0.420340	−	0.907367i	$-0.361911\pi$
$331$	15.2948	0.840679	0.420340	+	0.907367i	$0.361911\pi$
$332$	21.5557	1.18302
$333$	−2.17399	−0.119134
$334$	38.0616	2.08264
$335$	−12.0553	−0.658652
$336$	2.90845	0.158669
$337$	3.15065	0.171627	0.0858135	−	0.996311i	$-0.472651\pi$
$337$	3.15065	0.171627	0.0858135	+	0.996311i	$0.472651\pi$
$338$	32.0926	1.74561
$339$	16.7942	0.912134
$340$	7.89185	0.427996
$341$	26.7464	1.44840
$342$	−9.93945	−0.537464
$343$	3.96032	0.213837
$344$	56.5818	3.05069
$345$	−11.6663	−0.628095
$346$	39.7524	2.13710
$347$	10.4790	0.562544	0.281272	−	0.959628i	$-0.409244\pi$
$347$	10.4790	0.562544	0.281272	+	0.959628i	$0.409244\pi$
$348$	3.42999	0.183867
$349$	−25.0785	−1.34242	−0.671210	−	0.741267i	$-0.734225\pi$
$349$	−25.0785	−1.34242	−0.671210	+	0.741267i	$0.734225\pi$
$350$	−1.79966	−0.0961960
$351$	0.885389	0.0472586
$352$	34.3934	1.83317
$353$	24.5341	1.30582	0.652909	−	0.757437i	$-0.273549\pi$
$353$	24.5341	1.30582	0.652909	+	0.757437i	$0.273549\pi$
$354$	6.99528	0.371795
$355$	18.3358	0.973161
$356$	−14.5155	−0.769320
$357$	0.284525	0.0150587
$358$	−66.5872	−3.51924
$359$	−33.7201	−1.77968	−0.889840	−	0.456273i	$-0.849184\pi$
$359$	−33.7201	−1.77968	−0.889840	+	0.456273i	$0.849184\pi$
$360$	−12.2729	−0.646841
$361$	−4.68545	−0.246603
$362$	46.0263	2.41909
$363$	2.22281	0.116667
$364$	1.23478	0.0647199
$365$	8.09714	0.423824
$366$	9.81686	0.513135
$367$	1.33357	0.0696118	0.0348059	−	0.999394i	$-0.488919\pi$
$367$	1.33357	0.0696118	0.0348059	+	0.999394i	$0.488919\pi$
$368$	74.0678	3.86105
$369$	0.732601	0.0381377
$370$	9.19552	0.478052
$371$	−3.74159	−0.194254
$372$	44.2509	2.29430
$373$	−1.54396	−0.0799431	−0.0399716	−	0.999201i	$-0.512727\pi$
$373$	−1.54396	−0.0799431	−0.0399716	+	0.999201i	$0.512727\pi$
$374$	7.78307	0.402453
$375$	11.9269	0.615901
$376$	−4.85882	−0.250574
$377$	0.619574	0.0319097
$378$	−0.747471	−0.0384457
$379$	17.3321	0.890290	0.445145	−	0.895459i	$-0.353152\pi$
$379$	17.3321	0.890290	0.445145	+	0.895459i	$0.353152\pi$
$380$	29.8585	1.53171
$381$	2.11820	0.108519
$382$	−33.5848	−1.71835
$383$	10.5789	0.540558	0.270279	−	0.962782i	$-0.412884\pi$
$383$	10.5789	0.540558	0.270279	+	0.962782i	$0.412884\pi$
$384$	3.19386	0.162986
$385$	1.35720	0.0691693
$386$	−15.8243	−0.805436
$387$	−7.42289	−0.377327
$388$	23.5196	1.19403
$389$	−30.7733	−1.56027	−0.780134	−	0.625612i	$-0.784849\pi$
$389$	−30.7733	−1.56027	−0.780134	+	0.625612i	$0.784849\pi$
$390$	−3.74501	−0.189636
$391$	7.24585	0.366439
$392$	52.7412	2.66383
$393$	−20.0492	−1.01135
$394$	27.2169	1.37117
$395$	18.4241	0.927015
$396$	−14.5215	−0.729732
$397$	−22.2668	−1.11754	−0.558770	−	0.829322i	$-0.688727\pi$
$397$	−22.2668	−1.11754	−0.558770	+	0.829322i	$0.688727\pi$
$398$	−13.7045	−0.686943
$399$	1.07649	0.0538919
$400$	−24.6114	−1.23057
$401$	24.6794	1.23243	0.616216	−	0.787577i	$-0.288665\pi$
$401$	24.6794	1.23243	0.616216	+	0.787577i	$0.288665\pi$
$402$	−19.6701	−0.981056
$403$	7.99323	0.398171
$404$	−45.3352	−2.25551
$405$	1.61007	0.0800051
$406$	−0.523062	−0.0259591
$407$	6.44073	0.319255
$408$	7.62261	0.377375
$409$	7.98565	0.394865	0.197433	−	0.980316i	$-0.436740\pi$
$409$	7.98565	0.394865	0.197433	+	0.980316i	$0.436740\pi$
$410$	−3.09874	−0.153036
$411$	10.9224	0.538760
$412$	−64.2524	−3.16549
$413$	−0.757622	−0.0372802
$414$	−19.0354	−0.935541
$415$	7.08067	0.347576
$416$	10.2785	0.503946
$417$	7.53654	0.369066
$418$	29.4469	1.44030
$419$	−3.06393	−0.149683	−0.0748414	−	0.997195i	$-0.523845\pi$
$419$	−3.06393	−0.149683	−0.0748414	+	0.997195i	$0.523845\pi$
$420$	2.24543	0.109566
$421$	−21.3923	−1.04260	−0.521300	−	0.853374i	$-0.674553\pi$
$421$	−21.3923	−1.04260	−0.521300	+	0.853374i	$0.674553\pi$
$422$	13.2891	0.646905
$423$	0.637422	0.0309925
$424$	−100.240	−4.86806
$425$	−2.40767	−0.116789
$426$	29.9176	1.44951
$427$	−1.06321	−0.0514524
$428$	−37.6893	−1.82178
$429$	−2.62308	−0.126644
$430$	31.3973	1.51411
$431$	34.0163	1.63851	0.819254	−	0.573431i	$-0.194388\pi$
$431$	34.0163	1.63851	0.819254	+	0.573431i	$0.194388\pi$
$432$	−10.2221	−0.491811
$433$	−13.3429	−0.641220	−0.320610	−	0.947211i	$-0.603888\pi$
$433$	−13.3429	−0.641220	−0.320610	+	0.947211i	$0.603888\pi$
$434$	−6.74811	−0.323920
$435$	1.12669	0.0540206
$436$	28.2339	1.35216
$437$	27.4144	1.31141
$438$	13.2117	0.631281
$439$	−33.8771	−1.61687	−0.808434	−	0.588587i	$-0.799684\pi$
$439$	−33.8771	−1.61687	−0.808434	+	0.588587i	$0.799684\pi$
$440$	36.3602	1.73341
$441$	−6.91905	−0.329478
$442$	2.32599	0.110636
$443$	−36.8307	−1.74988	−0.874940	−	0.484231i	$-0.839099\pi$
$443$	−36.8307	−1.74988	−0.874940	+	0.484231i	$0.839099\pi$
$444$	10.6559	0.505708
$445$	−4.76808	−0.226029
$446$	−2.71788	−0.128695
$447$	7.84584	0.371096
$448$	−2.86054	−0.135148
$449$	25.6586	1.21090	0.605452	−	0.795882i	$-0.292992\pi$
$449$	25.6586	1.21090	0.605452	+	0.795882i	$0.292992\pi$
$450$	6.32514	0.298170
$451$	−2.17043	−0.102201
$452$	−82.3175	−3.87189
$453$	−20.0746	−0.943187
$454$	8.01082	0.375966
$455$	0.405602	0.0190149
$456$	28.8398	1.35055
$457$	−20.1767	−0.943827	−0.471914	−	0.881645i	$-0.656437\pi$
$457$	−20.1767	−0.943827	−0.471914	+	0.881645i	$0.656437\pi$
$458$	−66.4204	−3.10362
$459$	−1.00000	−0.0466760
$460$	57.1832	2.66618
$461$	20.1378	0.937912	0.468956	−	0.883222i	$-0.344630\pi$
$461$	20.1378	0.937912	0.468956	+	0.883222i	$0.344630\pi$
$462$	2.21448	0.103027
$463$	−35.0808	−1.63034	−0.815171	−	0.579221i	$-0.803357\pi$
$463$	−35.0808	−1.63034	−0.815171	+	0.579221i	$0.803357\pi$
$464$	−7.15318	−0.332078
$465$	14.5356	0.674073
$466$	80.1416	3.71249
$467$	25.4730	1.17875	0.589375	−	0.807860i	$-0.299374\pi$
$467$	25.4730	1.17875	0.589375	+	0.807860i	$0.299374\pi$
$468$	−4.33978	−0.200606
$469$	2.13037	0.0983712
$470$	−2.69616	−0.124365
$471$	−1.00000	−0.0460776
$472$	−20.2972	−0.934253
$473$	21.9913	1.01116
$474$	30.0617	1.38078
$475$	−9.10931	−0.417964
$476$	−1.39462	−0.0639221
$477$	13.1503	0.602110
$478$	−1.10843	−0.0506983
$479$	−30.0816	−1.37446	−0.687231	−	0.726439i	$-0.741174\pi$
$479$	−30.0816	−1.37446	−0.687231	+	0.726439i	$0.741174\pi$
$480$	18.6914	0.853143
$481$	1.92483	0.0877645
$482$	−18.6900	−0.851308
$483$	2.06163	0.0938073
$484$	−10.8952	−0.495237
$485$	7.72576	0.350809
$486$	2.62708	0.119167
$487$	−5.33825	−0.241899	−0.120950	−	0.992659i	$-0.538594\pi$
$487$	−5.33825	−0.241899	−0.120950	+	0.992659i	$0.538594\pi$
$488$	−28.4841	−1.28941
$489$	10.0582	0.454846
$490$	29.2661	1.32211
$491$	−30.8545	−1.39245	−0.696223	−	0.717826i	$-0.745137\pi$
$491$	−30.8545	−1.39245	−0.696223	+	0.717826i	$0.745137\pi$
$492$	−3.59088	−0.161889
$493$	−0.699776	−0.0315163
$494$	8.80027	0.395943
$495$	−4.77005	−0.214398
$496$	−92.2844	−4.14369
$497$	−3.24022	−0.145344
$498$	11.5532	0.517711
$499$	33.8201	1.51400	0.756998	−	0.653418i	$-0.226665\pi$
$499$	33.8201	1.51400	0.756998	+	0.653418i	$0.226665\pi$
$500$	−58.4602	−2.61442
$501$	14.4882	0.647284
$502$	−67.5918	−3.01677
$503$	37.0697	1.65286	0.826429	−	0.563042i	$-0.190369\pi$
$503$	37.0697	1.65286	0.826429	+	0.563042i	$0.190369\pi$
$504$	2.16882	0.0966071
$505$	−14.8918	−0.662676
$506$	56.3950	2.50706
$507$	12.2161	0.542535
$508$	−10.3825	−0.460647
$509$	29.6957	1.31624	0.658119	−	0.752914i	$-0.271353\pi$
$509$	29.6957	1.31624	0.658119	+	0.752914i	$0.271353\pi$
$510$	4.22979	0.187298
$511$	−1.43089	−0.0632990
$512$	37.1691	1.64266
$513$	−3.78346	−0.167044
$514$	−38.4436	−1.69567
$515$	−21.1058	−0.930031
$516$	36.3837	1.60170
$517$	−1.88845	−0.0830538
$518$	−1.62499	−0.0713982
$519$	15.1318	0.664211
$520$	10.8663	0.476520
$521$	22.5690	0.988766	0.494383	−	0.869244i	$-0.335394\pi$
$521$	22.5690	0.988766	0.494383	+	0.869244i	$0.335394\pi$
$522$	1.83837	0.0804632
$523$	8.08889	0.353703	0.176851	−	0.984238i	$-0.443409\pi$
$523$	8.08889	0.353703	0.176851	+	0.984238i	$0.443409\pi$
$524$	98.2721	4.29304
$525$	−0.685043	−0.0298977
$526$	−22.2646	−0.970784
$527$	−9.02793	−0.393263
$528$	30.2843	1.31796
$529$	29.5024	1.28271
$530$	−55.6229	−2.41611
$531$	2.66276	0.115554
$532$	−5.27647	−0.228764
$533$	−0.648636	−0.0280956
$534$	−7.77986	−0.336667
$535$	−12.3803	−0.535246
$536$	57.0738	2.46521
$537$	−25.3465	−1.09378
$538$	−44.1790	−1.90469
$539$	20.4986	0.882937
$540$	−7.89185	−0.339611
$541$	6.99339	0.300669	0.150335	−	0.988635i	$-0.451965\pi$
$541$	6.99339	0.300669	0.150335	+	0.988635i	$0.451965\pi$
$542$	41.2476	1.77174
$543$	17.5200	0.751853
$544$	−11.6091	−0.497734
$545$	9.27432	0.397268
$546$	0.661802	0.0283225
$547$	−30.5055	−1.30432	−0.652161	−	0.758081i	$-0.726137\pi$
$547$	−30.5055	−1.30432	−0.652161	+	0.758081i	$0.726137\pi$
$548$	−53.5365	−2.28697
$549$	3.73679	0.159482
$550$	−18.7391	−0.799036
$551$	−2.64757	−0.112790
$552$	55.2323	2.35084
$553$	−3.25582	−0.138452
$554$	0.214323	0.00910573
$555$	3.50028	0.148579
$556$	−36.9407	−1.56664
$557$	−5.24525	−0.222248	−0.111124	−	0.993807i	$-0.535445\pi$
$557$	−5.24525	−0.222248	−0.111124	+	0.993807i	$0.535445\pi$
$558$	23.7171	1.00402
$559$	6.57214	0.277972
$560$	−4.68281	−0.197885
$561$	2.96263	0.125082
$562$	−31.4970	−1.32862
$563$	−23.4638	−0.988881	−0.494441	−	0.869211i	$-0.664627\pi$
$563$	−23.4638	−0.988881	−0.494441	+	0.869211i	$0.664627\pi$
$564$	−3.12435	−0.131559
$565$	−27.0398	−1.13757
$566$	53.4016	2.24464
$567$	−0.284525	−0.0119489
$568$	−86.8075	−3.64236
$569$	1.37492	0.0576396	0.0288198	−	0.999585i	$-0.490825\pi$
$569$	1.37492	0.0576396	0.0288198	+	0.999585i	$0.490825\pi$
$570$	16.0032	0.670301
$571$	33.4602	1.40026	0.700132	−	0.714013i	$-0.253124\pi$
$571$	33.4602	1.40026	0.700132	+	0.714013i	$0.253124\pi$
$572$	12.8572	0.537585
$573$	−12.7841	−0.534063
$574$	0.547597	0.0228563
$575$	−17.4456	−0.727532
$576$	10.0537	0.418906
$577$	−24.6510	−1.02624	−0.513118	−	0.858318i	$-0.671510\pi$
$577$	−24.6510	−1.02624	−0.513118	+	0.858318i	$0.671510\pi$
$578$	−2.62708	−0.109272
$579$	−6.02354	−0.250330
$580$	−5.52253	−0.229310
$581$	−1.25127	−0.0519113
$582$	12.6058	0.522526
$583$	−38.9595	−1.61354
$584$	−38.3345	−1.58629
$585$	−1.42554	−0.0589388
$586$	33.9141	1.40098
$587$	−6.79371	−0.280406	−0.140203	−	0.990123i	$-0.544776\pi$
$587$	−6.79371	−0.280406	−0.140203	+	0.990123i	$0.544776\pi$
$588$	33.9141	1.39859
$589$	−34.1568	−1.40741
$590$	−11.2629	−0.463686
$591$	10.3601	0.426159
$592$	−22.2227	−0.913349
$593$	−7.08909	−0.291114	−0.145557	−	0.989350i	$-0.546497\pi$
$593$	−7.08909	−0.291114	−0.145557	+	0.989350i	$0.546497\pi$
$594$	−7.78307	−0.319343
$595$	−0.458106	−0.0187805
$596$	−38.4568	−1.57525
$597$	−5.21661	−0.213502
$598$	16.8538	0.689202
$599$	−40.5876	−1.65836	−0.829182	−	0.558978i	$-0.811193\pi$
$599$	−40.5876	−1.65836	−0.829182	+	0.558978i	$0.811193\pi$
$600$	−18.3527	−0.749246
$601$	3.17450	0.129491	0.0647453	−	0.997902i	$-0.479377\pi$
$601$	3.17450	0.129491	0.0647453	+	0.997902i	$0.479377\pi$
$602$	−5.54839	−0.226136
$603$	−7.48744	−0.304912
$604$	98.3967	4.00370
$605$	−3.57888	−0.145502
$606$	−24.2983	−0.987050
$607$	27.6709	1.12313	0.561565	−	0.827433i	$-0.310200\pi$
$607$	27.6709	1.12313	0.561565	+	0.827433i	$0.310200\pi$
$608$	−43.9224	−1.78129
$609$	−0.199104	−0.00806810
$610$	−15.8058	−0.639960
$611$	−0.564366	−0.0228318
$612$	4.90155	0.198133
$613$	32.6584	1.31906	0.659530	−	0.751678i	$-0.270755\pi$
$613$	32.6584	1.31906	0.659530	+	0.751678i	$0.270755\pi$
$614$	2.07250	0.0836392
$615$	−1.17954	−0.0475636
$616$	−6.42543	−0.258888
$617$	−28.7467	−1.15730	−0.578650	−	0.815576i	$-0.696420\pi$
$617$	−28.7467	−1.15730	−0.578650	+	0.815576i	$0.696420\pi$
$618$	−34.4373	−1.38527
$619$	−10.8935	−0.437846	−0.218923	−	0.975742i	$-0.570254\pi$
$619$	−10.8935	−0.437846	−0.218923	+	0.975742i	$0.570254\pi$
$620$	−71.2471	−2.86135
$621$	−7.24585	−0.290766
$622$	63.1225	2.53098
$623$	0.842596	0.0337579
$624$	9.05053	0.362311
$625$	−7.16479	−0.286591
$626$	25.2302	1.00840
$627$	11.2090	0.447644
$628$	4.90155	0.195593
$629$	−2.17399	−0.0866827
$630$	1.20348	0.0479479
$631$	3.63940	0.144882	0.0724411	−	0.997373i	$-0.476921\pi$
$631$	3.63940	0.144882	0.0724411	+	0.997373i	$0.476921\pi$
$632$	−87.2255	−3.46964
$633$	5.05852	0.201058
$634$	76.6226	3.04307
$635$	−3.41045	−0.135340
$636$	−64.4568	−2.55588
$637$	6.12604	0.242723
$638$	−5.44641	−0.215625
$639$	11.3882	0.450509
$640$	−5.14234	−0.203269
$641$	−37.3779	−1.47634	−0.738169	−	0.674615i	$-0.764310\pi$
$641$	−37.3779	−1.47634	−0.738169	+	0.674615i	$0.764310\pi$
$642$	−20.2003	−0.797243
$643$	−17.0644	−0.672953	−0.336477	−	0.941692i	$-0.609235\pi$
$643$	−17.0644	−0.672953	−0.336477	+	0.941692i	$0.609235\pi$
$644$	−10.1052	−0.398200
$645$	11.9514	0.470585
$646$	−9.93945	−0.391062
$647$	22.0478	0.866787	0.433394	−	0.901205i	$-0.357316\pi$
$647$	22.0478	0.866787	0.433394	+	0.901205i	$0.357316\pi$
$648$	−7.62261	−0.299444
$649$	−7.88878	−0.309662
$650$	−5.60021	−0.219658
$651$	−2.56867	−0.100674
$652$	−49.3006	−1.93076
$653$	−30.6924	−1.20109	−0.600543	−	0.799592i	$-0.705049\pi$
$653$	−30.6924	−1.20109	−0.600543	+	0.799592i	$0.705049\pi$
$654$	15.1325	0.591727
$655$	32.2806	1.26131
$656$	7.48872	0.292385
$657$	5.02906	0.196202
$658$	0.476454	0.0185741
$659$	−8.10238	−0.315624	−0.157812	−	0.987469i	$-0.550444\pi$
$659$	−8.10238	−0.315624	−0.157812	+	0.987469i	$0.550444\pi$
$660$	23.3806	0.910090
$661$	−19.8638	−0.772611	−0.386306	−	0.922371i	$-0.626249\pi$
$661$	−19.8638	−0.772611	−0.386306	+	0.922371i	$0.626249\pi$
$662$	−40.1807	−1.56167
$663$	0.885389	0.0343856
$664$	−33.5222	−1.30091
$665$	−1.73322	−0.0672116
$666$	5.71125	0.221306
$667$	−5.07047	−0.196330
$668$	−71.0145	−2.74763
$669$	−1.03456	−0.0399985
$670$	31.6703	1.22353
$671$	−11.0707	−0.427381
$672$	−3.30307	−0.127419
$673$	27.0963	1.04448	0.522242	−	0.852797i	$-0.325096\pi$
$673$	27.0963	1.04448	0.522242	+	0.852797i	$0.325096\pi$
$674$	−8.27702	−0.318819
$675$	2.40767	0.0926712
$676$	−59.8778	−2.30299
$677$	−15.1605	−0.582667	−0.291333	−	0.956622i	$-0.594099\pi$
$677$	−15.1605	−0.582667	−0.291333	+	0.956622i	$0.594099\pi$
$678$	−44.1196	−1.69440
$679$	−1.36527	−0.0523941
$680$	−12.2729	−0.470646
$681$	3.04932	0.116850
$682$	−70.2650	−2.69059
$683$	11.5930	0.443594	0.221797	−	0.975093i	$-0.428808\pi$
$683$	11.5930	0.443594	0.221797	+	0.975093i	$0.428808\pi$
$684$	18.5448	0.709078
$685$	−17.5858	−0.671918
$686$	−10.4041	−0.397230
$687$	−25.2830	−0.964606
$688$	−75.8775	−2.89280
$689$	−11.6431	−0.443568
$690$	30.6484	1.16677
$691$	−29.5444	−1.12392	−0.561961	−	0.827164i	$-0.689953\pi$
$691$	−29.5444	−1.12392	−0.561961	+	0.827164i	$0.689953\pi$
$692$	−74.1691	−2.81949
$693$	0.842944	0.0320208
$694$	−27.5293	−1.04500
$695$	−12.1344	−0.460283
$696$	−5.33412	−0.202189
$697$	0.732601	0.0277492
$698$	65.8832	2.49371
$699$	30.5059	1.15384
$700$	3.35777	0.126912
$701$	−11.2717	−0.425728	−0.212864	−	0.977082i	$-0.568279\pi$
$701$	−11.2717	−0.425728	−0.212864	+	0.977082i	$0.568279\pi$
$702$	−2.32599	−0.0877887
$703$	−8.22520	−0.310219
$704$	−29.7855	−1.12258
$705$	−1.02629	−0.0386525
$706$	−64.4530	−2.42572
$707$	2.63162	0.0989722
$708$	−13.0516	−0.490511
$709$	20.0379	0.752537	0.376269	−	0.926511i	$-0.377207\pi$
$709$	20.0379	0.752537	0.376269	+	0.926511i	$0.377207\pi$
$710$	−48.1695	−1.80777
$711$	11.4430	0.429146
$712$	22.5737	0.845984
$713$	−65.4151	−2.44981
$714$	−0.747471	−0.0279734
$715$	4.22335	0.157944
$716$	124.237	4.64296
$717$	−0.421924	−0.0157570
$718$	88.5855	3.30598
$719$	26.5702	0.990901	0.495451	−	0.868636i	$-0.335003\pi$
$719$	26.5702	0.990901	0.495451	+	0.868636i	$0.335003\pi$
$720$	16.4583	0.613365
$721$	3.72972	0.138902
$722$	12.3091	0.458096
$723$	−7.11438	−0.264586
$724$	−85.8750	−3.19152
$725$	1.68483	0.0625730
$726$	−5.83950	−0.216724
$727$	17.6283	0.653796	0.326898	−	0.945060i	$-0.393997\pi$
$727$	17.6283	0.653796	0.326898	+	0.945060i	$0.393997\pi$
$728$	−1.92025	−0.0711693
$729$	1.00000	0.0370370
$730$	−21.2718	−0.787306
$731$	−7.42289	−0.274546
$732$	−18.3161	−0.676982
$733$	−10.8290	−0.399978	−0.199989	−	0.979798i	$-0.564091\pi$
$733$	−10.8290	−0.399978	−0.199989	+	0.979798i	$0.564091\pi$
$734$	−3.50339	−0.129313
$735$	11.1402	0.410911
$736$	−84.1176	−3.10061
$737$	22.1825	0.817104
$738$	−1.92460	−0.0708455
$739$	42.2632	1.55468	0.777339	−	0.629082i	$-0.216569\pi$
$739$	42.2632	1.55468	0.777339	+	0.629082i	$0.216569\pi$
$740$	−17.1568	−0.630697
$741$	3.34983	0.123059
$742$	9.82946	0.360851
$743$	16.4517	0.603555	0.301777	−	0.953378i	$-0.402420\pi$
$743$	16.4517	0.603555	0.301777	+	0.953378i	$0.402420\pi$
$744$	−68.8164	−2.52293
$745$	−12.6324	−0.462814
$746$	4.05610	0.148504
$747$	4.39773	0.160905
$748$	−14.5215	−0.530958
$749$	2.18779	0.0799401
$750$	−31.3329	−1.14411
$751$	1.82050	0.0664310	0.0332155	−	0.999448i	$-0.489425\pi$
$751$	1.82050	0.0664310	0.0332155	+	0.999448i	$0.489425\pi$
$752$	6.51579	0.237606
$753$	−25.7289	−0.937612
$754$	−1.62767	−0.0592762
$755$	32.3216	1.17630
$756$	1.39462	0.0507217
$757$	50.3452	1.82983	0.914913	−	0.403651i	$-0.132259\pi$
$757$	50.3452	1.82983	0.914913	+	0.403651i	$0.132259\pi$
$758$	−45.5328	−1.65383
$759$	21.4668	0.779195
$760$	−46.4342	−1.68434
$761$	47.2922	1.71434	0.857170	−	0.515034i	$-0.172221\pi$
$761$	47.2922	1.71434	0.857170	+	0.515034i	$0.172221\pi$
$762$	−5.56468	−0.201587
$763$	−1.63892	−0.0593329
$764$	62.6618	2.26703
$765$	1.61007	0.0582123
$766$	−27.7917	−1.00415
$767$	−2.35758	−0.0851272
$768$	11.7170	0.422800
$769$	−38.4740	−1.38741	−0.693704	−	0.720261i	$-0.744022\pi$
$769$	−38.4740	−1.38741	−0.693704	+	0.720261i	$0.744022\pi$
$770$	−3.56547	−0.128491
$771$	−14.6336	−0.527016
$772$	29.5247	1.06262
$773$	−9.33809	−0.335868	−0.167934	−	0.985798i	$-0.553710\pi$
$773$	−9.33809	−0.335868	−0.167934	+	0.985798i	$0.553710\pi$
$774$	19.5005	0.700932
$775$	21.7363	0.780790
$776$	−36.5763	−1.31301
$777$	−0.618555	−0.0221905
$778$	80.8439	2.89840
$779$	2.77176	0.0993087
$780$	6.98735	0.250187
$781$	−33.7389	−1.20727
$782$	−19.0354	−0.680706
$783$	0.699776	0.0250080
$784$	−70.7272	−2.52597
$785$	1.61007	0.0574659
$786$	52.6708	1.87871
$787$	26.8790	0.958132	0.479066	−	0.877779i	$-0.340976\pi$
$787$	26.8790	0.958132	0.479066	+	0.877779i	$0.340976\pi$
$788$	−50.7808	−1.80899
$789$	−8.47505	−0.301720
$790$	−48.4015	−1.72205
$791$	4.77837	0.169899
$792$	22.5830	0.802451
$793$	−3.30851	−0.117489
$794$	58.4968	2.07597
$795$	−21.1729	−0.750926
$796$	25.5695	0.906287
$797$	−8.89506	−0.315079	−0.157540	−	0.987513i	$-0.550356\pi$
$797$	−8.89506	−0.315079	−0.157540	+	0.987513i	$0.550356\pi$
$798$	−2.82802	−0.100111
$799$	0.637422	0.0225504
$800$	27.9508	0.988209
$801$	−2.96141	−0.104636
$802$	−64.8348	−2.28940
$803$	−14.8992	−0.525783
$804$	36.7001	1.29431
$805$	−3.31937	−0.116992
$806$	−20.9989	−0.739653
$807$	−16.8168	−0.591978
$808$	70.5027	2.48027
$809$	−41.1758	−1.44766	−0.723832	−	0.689977i	$-0.757621\pi$
$809$	−41.1758	−1.44766	−0.723832	+	0.689977i	$0.757621\pi$
$810$	−4.22979	−0.148620
$811$	18.0014	0.632116	0.316058	−	0.948740i	$-0.397641\pi$
$811$	18.0014	0.632116	0.316058	+	0.948740i	$0.397641\pi$
$812$	0.975918	0.0342480
$813$	15.7009	0.550656
$814$	−16.9203	−0.593057
$815$	−16.1944	−0.567263
$816$	−10.2221	−0.357845
$817$	−28.0842	−0.982541
$818$	−20.9789	−0.733512
$819$	0.251915	0.00880264
$820$	5.78157	0.201901
$821$	46.9456	1.63841	0.819206	−	0.573499i	$-0.194415\pi$
$821$	46.9456	1.63841	0.819206	+	0.573499i	$0.194415\pi$
$822$	−28.6939	−1.00082
$823$	−33.7240	−1.17555	−0.587773	−	0.809026i	$-0.699995\pi$
$823$	−33.7240	−1.17555	−0.587773	+	0.809026i	$0.699995\pi$
$824$	99.9216	3.48093
$825$	−7.13304	−0.248340
$826$	1.99033	0.0692526
$827$	32.3216	1.12393	0.561966	−	0.827160i	$-0.310045\pi$
$827$	32.3216	1.12393	0.561966	+	0.827160i	$0.310045\pi$
$828$	35.5159	1.23426
$829$	−27.6503	−0.960335	−0.480167	−	0.877177i	$-0.659424\pi$
$829$	−27.6503	−0.960335	−0.480167	+	0.877177i	$0.659424\pi$
$830$	−18.6015	−0.645667
$831$	0.0815824	0.00283006
$832$	−8.90147	−0.308603
$833$	−6.91905	−0.239731
$834$	−19.7991	−0.685587
$835$	−23.3270	−0.807264
$836$	−54.9414	−1.90019
$837$	9.02793	0.312051
$838$	8.04919	0.278055
$839$	3.46179	0.119514	0.0597571	−	0.998213i	$-0.480967\pi$
$839$	3.46179	0.119514	0.0597571	+	0.998213i	$0.480967\pi$
$840$	−3.49196	−0.120484
$841$	−28.5103	−0.983114
$842$	56.1994	1.93676
$843$	−11.9894	−0.412936
$844$	−24.7946	−0.853465
$845$	−19.6688	−0.676626
$846$	−1.67456	−0.0575725
$847$	0.632446	0.0217311
$848$	134.424	4.61612
$849$	20.3274	0.697633
$850$	6.32514	0.216951
$851$	−15.7524	−0.539986
$852$	−55.8197	−1.91235
$853$	−16.5612	−0.567045	−0.283522	−	0.958966i	$-0.591503\pi$
$853$	−16.5612	−0.567045	−0.283522	+	0.958966i	$0.591503\pi$
$854$	2.79314	0.0955794
$855$	6.09164	0.208330
$856$	58.6123	2.00333
$857$	30.3308	1.03608	0.518040	−	0.855356i	$-0.326662\pi$
$857$	30.3308	1.03608	0.518040	+	0.855356i	$0.326662\pi$
$858$	6.89104	0.235256
$859$	−32.7517	−1.11747	−0.558737	−	0.829345i	$-0.688714\pi$
$859$	−32.7517	−1.11747	−0.558737	+	0.829345i	$0.688714\pi$
$860$	−58.5803	−1.99757
$861$	0.208443	0.00710373
$862$	−89.3636	−3.04373
$863$	−36.9849	−1.25898	−0.629490	−	0.777009i	$-0.716736\pi$
$863$	−36.9849	−1.25898	−0.629490	+	0.777009i	$0.716736\pi$
$864$	11.6091	0.394948
$865$	−24.3632	−0.828375
$866$	35.0530	1.19115
$867$	−1.00000	−0.0339618
$868$	12.5905	0.427349
$869$	−33.9014	−1.15003
$870$	−2.95990	−0.100350
$871$	6.62930	0.224625
$872$	−43.9077	−1.48690
$873$	4.79840	0.162401
$874$	−72.0198	−2.43610
$875$	3.39350	0.114721
$876$	−24.6502	−0.832852
$877$	19.2913	0.651420	0.325710	−	0.945470i	$-0.394397\pi$
$877$	19.2913	0.651420	0.325710	+	0.945470i	$0.394397\pi$
$878$	88.9979	3.00353
$879$	12.9094	0.435424
$880$	−48.7599	−1.64370
$881$	−46.9912	−1.58318	−0.791588	−	0.611056i	$-0.790745\pi$
$881$	−46.9912	−1.58318	−0.791588	+	0.611056i	$0.790745\pi$
$882$	18.1769	0.612048
$883$	−26.5778	−0.894414	−0.447207	−	0.894431i	$-0.647581\pi$
$883$	−26.5778	−0.894414	−0.447207	+	0.894431i	$0.647581\pi$
$884$	−4.33978	−0.145963
$885$	−4.28723	−0.144114
$886$	96.7573	3.25062
$887$	−35.7772	−1.20128	−0.600640	−	0.799519i	$-0.705088\pi$
$887$	−35.7772	−1.20128	−0.600640	+	0.799519i	$0.705088\pi$
$888$	−16.5715	−0.556102
$889$	0.602681	0.0202133
$890$	12.5261	0.419877
$891$	−2.96263	−0.0992519
$892$	5.07096	0.169788
$893$	2.41166	0.0807030
$894$	−20.6117	−0.689357
$895$	40.8096	1.36412
$896$	0.908732	0.0303586
$897$	6.41540	0.214204
$898$	−67.4072	−2.24941
$899$	6.31753	0.210701
$900$	−11.8013	−0.393377
$901$	13.1503	0.438100
$902$	5.70188	0.189852
$903$	−2.11200	−0.0702830
$904$	128.015	4.25773
$905$	−28.2084	−0.937679
$906$	52.7376	1.75209
$907$	−33.5702	−1.11468	−0.557340	−	0.830285i	$-0.688178\pi$
$907$	−33.5702	−1.11468	−0.557340	+	0.830285i	$0.688178\pi$
$908$	−14.9464	−0.496014
$909$	−9.24915	−0.306775
$910$	−1.06555	−0.0353226
$911$	−46.1003	−1.52737	−0.763685	−	0.645589i	$-0.776612\pi$
$911$	−46.1003	−1.52737	−0.763685	+	0.645589i	$0.776612\pi$
$912$	−38.6749	−1.28065
$913$	−13.0289	−0.431193
$914$	53.0059	1.75328
$915$	−6.01650	−0.198900
$916$	123.926	4.09463
$917$	−5.70450	−0.188379
$918$	2.62708	0.0867066
$919$	−28.1940	−0.930034	−0.465017	−	0.885302i	$-0.653952\pi$
$919$	−28.1940	−0.930034	−0.465017	+	0.885302i	$0.653952\pi$
$920$	−88.9280	−2.93187
$921$	0.788898	0.0259951
$922$	−52.9037	−1.74229
$923$	−10.0830	−0.331884
$924$	−4.13173	−0.135924
$925$	5.23425	0.172101
$926$	92.1600	3.02857
$927$	−13.1086	−0.430542
$928$	8.12374	0.266675
$929$	−16.7732	−0.550312	−0.275156	−	0.961400i	$-0.588730\pi$
$929$	−16.7732	−0.550312	−0.275156	+	0.961400i	$0.588730\pi$
$930$	−38.1862	−1.25218
$931$	−26.1779	−0.857946
$932$	−149.526	−4.89790
$933$	24.0276	0.786629
$934$	−66.9196	−2.18968
$935$	−4.77005	−0.155997
$936$	6.74897	0.220597
$937$	51.8408	1.69357	0.846783	−	0.531938i	$-0.178536\pi$
$937$	51.8408	1.69357	0.846783	+	0.531938i	$0.178536\pi$
$938$	−5.59664	−0.182737
$939$	9.60388	0.313411
$940$	5.03044	0.164075
$941$	−13.8930	−0.452900	−0.226450	−	0.974023i	$-0.572712\pi$
$941$	−13.8930	−0.452900	−0.226450	+	0.974023i	$0.572712\pi$
$942$	2.62708	0.0855949
$943$	5.30832	0.172863
$944$	27.2190	0.885903
$945$	0.458106	0.0149022
$946$	−57.7729	−1.87836
$947$	−13.1243	−0.426483	−0.213242	−	0.976999i	$-0.568402\pi$
$947$	−13.1243	−0.426483	−0.213242	+	0.976999i	$0.568402\pi$
$948$	−56.0884	−1.82167
$949$	−4.45267	−0.144540
$950$	23.9309	0.776421
$951$	29.1664	0.945786
$952$	2.16882	0.0702920
$953$	−11.9964	−0.388601	−0.194300	−	0.980942i	$-0.562244\pi$
$953$	−11.9964	−0.388601	−0.194300	+	0.980942i	$0.562244\pi$
$954$	−34.5469	−1.11850
$955$	20.5833	0.666060
$956$	2.06808	0.0668865
$957$	−2.07318	−0.0670164
$958$	79.0267	2.55324
$959$	3.10769	0.100352
$960$	−16.1872	−0.522441
$961$	50.5036	1.62915
$962$	−5.05667	−0.163034
$963$	−7.68927	−0.247783
$964$	34.8715	1.12313
$965$	9.69832	0.312200
$966$	−5.41606	−0.174259
$967$	−7.13739	−0.229523	−0.114762	−	0.993393i	$-0.536610\pi$
$967$	−7.13739	−0.229523	−0.114762	+	0.993393i	$0.536610\pi$
$968$	16.9436	0.544588
$969$	−3.78346	−0.121542
$970$	−20.2962	−0.651672
$971$	19.4148	0.623052	0.311526	−	0.950238i	$-0.399160\pi$
$971$	19.4148	0.623052	0.311526	+	0.950238i	$0.399160\pi$
$972$	−4.90155	−0.157217
$973$	2.14434	0.0687443
$974$	14.0240	0.449358
$975$	−2.13172	−0.0682698
$976$	38.1979	1.22268
$977$	4.80125	0.153606	0.0768029	−	0.997046i	$-0.475529\pi$
$977$	4.80125	0.153606	0.0768029	+	0.997046i	$0.475529\pi$
$978$	−26.4236	−0.844933
$979$	8.77357	0.280404
$980$	−54.6041	−1.74426
$981$	5.76019	0.183909
$982$	81.0573	2.58664
$983$	−43.9311	−1.40119	−0.700593	−	0.713561i	$-0.747081\pi$
$983$	−43.9311	−1.40119	−0.700593	+	0.713561i	$0.747081\pi$
$984$	5.58433	0.178022
$985$	−16.6806	−0.531487
$986$	1.83837	0.0585456
$987$	0.181363	0.00577283
$988$	−16.4194	−0.522370
$989$	−53.7852	−1.71027
$990$	12.5313	0.398271
$991$	−18.5564	−0.589464	−0.294732	−	0.955580i	$-0.595230\pi$
$991$	−18.5564	−0.589464	−0.294732	+	0.955580i	$0.595230\pi$
$992$	104.806	3.32759
$993$	−15.2948	−0.485366
$994$	8.51232	0.269994
$995$	8.39912	0.266270
$996$	−21.5557	−0.683019
$997$	23.1100	0.731901	0.365951	−	0.930634i	$-0.380744\pi$
$997$	23.1100	0.731901	0.365951	+	0.930634i	$0.380744\pi$
$998$	−88.8481	−2.81244
$999$	2.17399	0.0687820

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8007.2.a.c.1.2	✓	39

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8007.2.a.c.1.2	✓	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)

\(f(q)\)	\(=\)	\(q-2.62708 q^{2} -1.00000 q^{3} +4.90155 q^{4} +1.61007 q^{5} +2.62708 q^{6} -0.284525 q^{7} -7.62261 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-2.62708 q^{2} -1.00000 q^{3} +4.90155 q^{4} +1.61007 q^{5} +2.62708 q^{6} -0.284525 q^{7} -7.62261 q^{8} +1.00000 q^{9} -4.22979 q^{10} -2.96263 q^{11} -4.90155 q^{12} -0.885389 q^{13} +0.747471 q^{14} -1.61007 q^{15} +10.2221 q^{16} +1.00000 q^{17} -2.62708 q^{18} +3.78346 q^{19} +7.89185 q^{20} +0.284525 q^{21} +7.78307 q^{22} +7.24585 q^{23} +7.62261 q^{24} -2.40767 q^{25} +2.32599 q^{26} -1.00000 q^{27} -1.39462 q^{28} -0.699776 q^{29} +4.22979 q^{30} -9.02793 q^{31} -11.6091 q^{32} +2.96263 q^{33} -2.62708 q^{34} -0.458106 q^{35} +4.90155 q^{36} -2.17399 q^{37} -9.93945 q^{38} +0.885389 q^{39} -12.2729 q^{40} +0.732601 q^{41} -0.747471 q^{42} -7.42289 q^{43} -14.5215 q^{44} +1.61007 q^{45} -19.0354 q^{46} +0.637422 q^{47} -10.2221 q^{48} -6.91905 q^{49} +6.32514 q^{50} -1.00000 q^{51} -4.33978 q^{52} +13.1503 q^{53} +2.62708 q^{54} -4.77005 q^{55} +2.16882 q^{56} -3.78346 q^{57} +1.83837 q^{58} +2.66276 q^{59} -7.89185 q^{60} +3.73679 q^{61} +23.7171 q^{62} -0.284525 q^{63} +10.0537 q^{64} -1.42554 q^{65} -7.78307 q^{66} -7.48744 q^{67} +4.90155 q^{68} -7.24585 q^{69} +1.20348 q^{70} +11.3882 q^{71} -7.62261 q^{72} +5.02906 q^{73} +5.71125 q^{74} +2.40767 q^{75} +18.5448 q^{76} +0.842944 q^{77} -2.32599 q^{78} +11.4430 q^{79} +16.4583 q^{80} +1.00000 q^{81} -1.92460 q^{82} +4.39773 q^{83} +1.39462 q^{84} +1.61007 q^{85} +19.5005 q^{86} +0.699776 q^{87} +22.5830 q^{88} -2.96141 q^{89} -4.22979 q^{90} +0.251915 q^{91} +35.5159 q^{92} +9.02793 q^{93} -1.67456 q^{94} +6.09164 q^{95} +11.6091 q^{96} +4.79840 q^{97} +18.1769 q^{98} -2.96263 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 39 q - 4 q^{2} - 39 q^{3} + 30 q^{4} - 3 q^{5} + 4 q^{6} - 5 q^{7} - 3 q^{8} + 39 q^{9}+O(q^{10}) \) 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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