LMFDB - Embedded newform 8007.2.a.i.1.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8007,2,Mod(1,8007)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8007, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0, 0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("8007.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$63.9362168984$
Analytic rank:	$0$
Dimension:	$63$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.10
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)

$f(q)$	$=$	$q-2.11232 q^{2} +1.00000 q^{3} +2.46191 q^{4} -3.85779 q^{5} -2.11232 q^{6} +0.0837724 q^{7} -0.975695 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-2.11232 q^{2} +1.00000 q^{3} +2.46191 q^{4} -3.85779 q^{5} -2.11232 q^{6} +0.0837724 q^{7} -0.975695 q^{8} +1.00000 q^{9} +8.14890 q^{10} +3.28960 q^{11} +2.46191 q^{12} -3.49121 q^{13} -0.176954 q^{14} -3.85779 q^{15} -2.86283 q^{16} +1.00000 q^{17} -2.11232 q^{18} +4.74031 q^{19} -9.49752 q^{20} +0.0837724 q^{21} -6.94869 q^{22} +0.819634 q^{23} -0.975695 q^{24} +9.88256 q^{25} +7.37456 q^{26} +1.00000 q^{27} +0.206240 q^{28} +8.30917 q^{29} +8.14890 q^{30} +1.21037 q^{31} +7.99861 q^{32} +3.28960 q^{33} -2.11232 q^{34} -0.323176 q^{35} +2.46191 q^{36} -0.312542 q^{37} -10.0131 q^{38} -3.49121 q^{39} +3.76403 q^{40} +7.40198 q^{41} -0.176954 q^{42} +7.91175 q^{43} +8.09869 q^{44} -3.85779 q^{45} -1.73133 q^{46} +9.53497 q^{47} -2.86283 q^{48} -6.99298 q^{49} -20.8751 q^{50} +1.00000 q^{51} -8.59503 q^{52} -1.20268 q^{53} -2.11232 q^{54} -12.6906 q^{55} -0.0817363 q^{56} +4.74031 q^{57} -17.5517 q^{58} +1.03027 q^{59} -9.49752 q^{60} -13.1488 q^{61} -2.55669 q^{62} +0.0837724 q^{63} -11.1700 q^{64} +13.4684 q^{65} -6.94869 q^{66} -13.9564 q^{67} +2.46191 q^{68} +0.819634 q^{69} +0.682653 q^{70} -6.92804 q^{71} -0.975695 q^{72} -9.27996 q^{73} +0.660190 q^{74} +9.88256 q^{75} +11.6702 q^{76} +0.275578 q^{77} +7.37456 q^{78} -8.39490 q^{79} +11.0442 q^{80} +1.00000 q^{81} -15.6354 q^{82} +15.5618 q^{83} +0.206240 q^{84} -3.85779 q^{85} -16.7122 q^{86} +8.30917 q^{87} -3.20965 q^{88} -11.1482 q^{89} +8.14890 q^{90} -0.292467 q^{91} +2.01786 q^{92} +1.21037 q^{93} -20.1409 q^{94} -18.2871 q^{95} +7.99861 q^{96} +6.83225 q^{97} +14.7714 q^{98} +3.28960 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 63 q + 10 q^{2} + 63 q^{3} + 70 q^{4} + 19 q^{5} + 10 q^{6} + 11 q^{7} + 27 q^{8} + 63 q^{9}+O(q^{10}) $ 63 * q + 10 * q^2 + 63 * q^3 + 70 * q^4 + 19 * q^5 + 10 * q^6 + 11 * q^7 + 27 * q^8 + 63 * q^9	\( 63 q + 10 q^{2} + 63 q^{3} + 70 q^{4} + 19 q^{5} + 10 q^{6} + 11 q^{7} + 27 q^{8} + 63 q^{9} + 4 q^{10} + 23 q^{11} + 70 q^{12} + 10 q^{13} + 18 q^{14} + 19 q^{15} + 72 q^{16} + 63 q^{17} + 10 q^{18} + 6 q^{19} + 48 q^{20} + 11 q^{21} + 21 q^{22} + 44 q^{23} + 27 q^{24} + 110 q^{25} + 41 q^{26} + 63 q^{27} + 26 q^{28} + 35 q^{29} + 4 q^{30} + q^{31} + 54 q^{32} + 23 q^{33} + 10 q^{34} + 47 q^{35} + 70 q^{36} + 40 q^{37} + 38 q^{38} + 10 q^{39} - 10 q^{40} + 35 q^{41} + 18 q^{42} + 27 q^{43} + 46 q^{44} + 19 q^{45} + 8 q^{46} + 29 q^{47} + 72 q^{48} + 114 q^{49} + 27 q^{50} + 63 q^{51} - q^{52} + 75 q^{53} + 10 q^{54} + 5 q^{55} + 24 q^{56} + 6 q^{57} + 41 q^{58} + 105 q^{59} + 48 q^{60} + 5 q^{61} + 22 q^{62} + 11 q^{63} + 61 q^{64} + 49 q^{65} + 21 q^{66} + 4 q^{67} + 70 q^{68} + 44 q^{69} - 16 q^{70} + 16 q^{71} + 27 q^{72} + 39 q^{73} + 54 q^{74} + 110 q^{75} + 6 q^{76} + 88 q^{77} + 41 q^{78} + 16 q^{79} + 102 q^{80} + 63 q^{81} - 29 q^{82} + 73 q^{83} + 26 q^{84} + 19 q^{85} + 46 q^{86} + 35 q^{87} + 18 q^{88} + 88 q^{89} + 4 q^{90} - 15 q^{91} + 110 q^{92} + q^{93} - 8 q^{94} + 28 q^{95} + 54 q^{96} + 70 q^{97} + 33 q^{98} + 23 q^{99}+O(q^{100}) \) 63 * q + 10 * q^2 + 63 * q^3 + 70 * q^4 + 19 * q^5 + 10 * q^6 + 11 * q^7 + 27 * q^8 + 63 * q^9 + 4 * q^10 + 23 * q^11 + 70 * q^12 + 10 * q^13 + 18 * q^14 + 19 * q^15 + 72 * q^16 + 63 * q^17 + 10 * q^18 + 6 * q^19 + 48 * q^20 + 11 * q^21 + 21 * q^22 + 44 * q^23 + 27 * q^24 + 110 * q^25 + 41 * q^26 + 63 * q^27 + 26 * q^28 + 35 * q^29 + 4 * q^30 + q^31 + 54 * q^32 + 23 * q^33 + 10 * q^34 + 47 * q^35 + 70 * q^36 + 40 * q^37 + 38 * q^38 + 10 * q^39 - 10 * q^40 + 35 * q^41 + 18 * q^42 + 27 * q^43 + 46 * q^44 + 19 * q^45 + 8 * q^46 + 29 * q^47 + 72 * q^48 + 114 * q^49 + 27 * q^50 + 63 * q^51 - q^52 + 75 * q^53 + 10 * q^54 + 5 * q^55 + 24 * q^56 + 6 * q^57 + 41 * q^58 + 105 * q^59 + 48 * q^60 + 5 * q^61 + 22 * q^62 + 11 * q^63 + 61 * q^64 + 49 * q^65 + 21 * q^66 + 4 * q^67 + 70 * q^68 + 44 * q^69 - 16 * q^70 + 16 * q^71 + 27 * q^72 + 39 * q^73 + 54 * q^74 + 110 * q^75 + 6 * q^76 + 88 * q^77 + 41 * q^78 + 16 * q^79 + 102 * q^80 + 63 * q^81 - 29 * q^82 + 73 * q^83 + 26 * q^84 + 19 * q^85 + 46 * q^86 + 35 * q^87 + 18 * q^88 + 88 * q^89 + 4 * q^90 - 15 * q^91 + 110 * q^92 + q^93 - 8 * q^94 + 28 * q^95 + 54 * q^96 + 70 * q^97 + 33 * q^98 + 23 * 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 $

$2$	−2.11232	−1.49364	−0.746819	−	0.665028i	$-0.768420\pi$
$2$	−2.11232	−1.49364	−0.746819	+	0.665028i	$0.768420\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	2.46191	1.23095
$5$	−3.85779	−1.72526	−0.862628	−	0.505838i	$-0.831183\pi$
$5$	−3.85779	−1.72526	−0.862628	+	0.505838i	$0.831183\pi$
$6$	−2.11232	−0.862352
$7$	0.0837724	0.0316630	0.0158315	−	0.999875i	$-0.494960\pi$
$7$	0.0837724	0.0316630	0.0158315	+	0.999875i	$0.494960\pi$
$8$	−0.975695	−0.344960
$9$	1.00000	0.333333
$10$	8.14890	2.57691
$11$	3.28960	0.991852	0.495926	−	0.868365i	$-0.334829\pi$
$11$	3.28960	0.991852	0.495926	+	0.868365i	$0.334829\pi$
$12$	2.46191	0.710691
$13$	−3.49121	−0.968288	−0.484144	−	0.874988i	$-0.660869\pi$
$13$	−3.49121	−0.968288	−0.484144	+	0.874988i	$0.660869\pi$
$14$	−0.176954	−0.0472930
$15$	−3.85779	−0.996077
$16$	−2.86283	−0.715707
$17$	1.00000	0.242536
$17$	1.00000	0.242536
$18$	−2.11232	−0.497879
$19$	4.74031	1.08750	0.543751	−	0.839247i	$-0.317004\pi$
$19$	4.74031	1.08750	0.543751	+	0.839247i	$0.317004\pi$
$20$	−9.49752	−2.12371
$21$	0.0837724	0.0182806
$22$	−6.94869	−1.48147
$23$	0.819634	0.170906	0.0854528	−	0.996342i	$-0.472766\pi$
$23$	0.819634	0.170906	0.0854528	+	0.996342i	$0.472766\pi$
$24$	−0.975695	−0.199163
$25$	9.88256	1.97651
$26$	7.37456	1.44627
$27$	1.00000	0.192450
$28$	0.206240	0.0389756
$29$	8.30917	1.54297	0.771487	−	0.636245i	$-0.219513\pi$
$29$	8.30917	1.54297	0.771487	+	0.636245i	$0.219513\pi$
$30$	8.14890	1.48778
$31$	1.21037	0.217388	0.108694	−	0.994075i	$-0.465333\pi$
$31$	1.21037	0.217388	0.108694	+	0.994075i	$0.465333\pi$
$32$	7.99861	1.41397
$33$	3.28960	0.572646
$34$	−2.11232	−0.362260
$35$	−0.323176	−0.0546268
$36$	2.46191	0.410318
$37$	−0.312542	−0.0513816	−0.0256908	−	0.999670i	$-0.508179\pi$
$37$	−0.312542	−0.0513816	−0.0256908	+	0.999670i	$0.508179\pi$
$38$	−10.0131	−1.62433
$39$	−3.49121	−0.559041
$40$	3.76403	0.595145
$41$	7.40198	1.15600	0.577998	−	0.816038i	$-0.303834\pi$
$41$	7.40198	1.15600	0.577998	+	0.816038i	$0.303834\pi$
$42$	−0.176954	−0.0273046
$43$	7.91175	1.20653	0.603266	−	0.797540i	$-0.293866\pi$
$43$	7.91175	1.20653	0.603266	+	0.797540i	$0.293866\pi$
$44$	8.09869	1.22092
$45$	−3.85779	−0.575086
$46$	−1.73133	−0.255271
$47$	9.53497	1.39082	0.695409	−	0.718614i	$-0.255223\pi$
$47$	9.53497	1.39082	0.695409	+	0.718614i	$0.255223\pi$
$48$	−2.86283	−0.413214
$49$	−6.99298	−0.998997
$50$	−20.8751	−2.95219
$51$	1.00000	0.140028
$52$	−8.59503	−1.19192
$53$	−1.20268	−0.165200	−0.0826001	−	0.996583i	$-0.526322\pi$
$53$	−1.20268	−0.165200	−0.0826001	+	0.996583i	$0.526322\pi$
$54$	−2.11232	−0.287451
$55$	−12.6906	−1.71120
$56$	−0.0817363	−0.0109225
$57$	4.74031	0.627869
$58$	−17.5517	−2.30464
$59$	1.03027	0.134129	0.0670646	−	0.997749i	$-0.478637\pi$
$59$	1.03027	0.134129	0.0670646	+	0.997749i	$0.478637\pi$
$60$	−9.49752	−1.22612
$61$	−13.1488	−1.68353	−0.841766	−	0.539842i	$-0.818484\pi$
$61$	−13.1488	−1.68353	−0.841766	+	0.539842i	$0.818484\pi$
$62$	−2.55669	−0.324700
$63$	0.0837724	0.0105543
$64$	−11.1700	−1.39625
$65$	13.4684	1.67054
$66$	−6.94869	−0.855325
$67$	−13.9564	−1.70504	−0.852521	−	0.522693i	$-0.824927\pi$
$67$	−13.9564	−1.70504	−0.852521	+	0.522693i	$0.824927\pi$
$68$	2.46191	0.298550
$69$	0.819634	0.0986724
$70$	0.682653	0.0815926
$71$	−6.92804	−0.822208	−0.411104	−	0.911589i	$-0.634857\pi$
$71$	−6.92804	−0.822208	−0.411104	+	0.911589i	$0.634857\pi$
$72$	−0.975695	−0.114987
$73$	−9.27996	−1.08614	−0.543069	−	0.839688i	$-0.682738\pi$
$73$	−9.27996	−1.08614	−0.543069	+	0.839688i	$0.682738\pi$
$74$	0.660190	0.0767455
$75$	9.88256	1.14114
$76$	11.6702	1.33866
$77$	0.275578	0.0314050
$78$	7.37456	0.835005
$79$	−8.39490	−0.944500	−0.472250	−	0.881465i	$-0.656558\pi$
$79$	−8.39490	−0.944500	−0.472250	+	0.881465i	$0.656558\pi$
$80$	11.0442	1.23478
$81$	1.00000	0.111111
$82$	−15.6354	−1.72664
$83$	15.5618	1.70813	0.854064	−	0.520168i	$-0.174131\pi$
$83$	15.5618	1.70813	0.854064	+	0.520168i	$0.174131\pi$
$84$	0.206240	0.0225026
$85$	−3.85779	−0.418436
$86$	−16.7122	−1.80212
$87$	8.30917	0.890837
$88$	−3.20965	−0.342149
$89$	−11.1482	−1.18171	−0.590854	−	0.806778i	$-0.701209\pi$
$89$	−11.1482	−1.18171	−0.590854	+	0.806778i	$0.701209\pi$
$90$	8.14890	0.858969
$91$	−0.292467	−0.0306589
$92$	2.01786	0.210377
$93$	1.21037	0.125509
$94$	−20.1409	−2.07738
$95$	−18.2871	−1.87622
$96$	7.99861	0.816355
$97$	6.83225	0.693710	0.346855	−	0.937919i	$-0.387250\pi$
$97$	6.83225	0.693710	0.346855	+	0.937919i	$0.387250\pi$
$98$	14.7714	1.49214
$99$	3.28960	0.330617
$100$	24.3299	2.43299
$101$	10.2117	1.01610	0.508050	−	0.861328i	$-0.330367\pi$
$101$	10.2117	1.01610	0.508050	+	0.861328i	$0.330367\pi$
$102$	−2.11232	−0.209151
$103$	3.79265	0.373701	0.186850	−	0.982388i	$-0.440172\pi$
$103$	3.79265	0.373701	0.186850	+	0.982388i	$0.440172\pi$
$104$	3.40636	0.334021
$105$	−0.323176	−0.0315388
$106$	2.54044	0.246749
$107$	−7.53774	−0.728701	−0.364351	−	0.931262i	$-0.618709\pi$
$107$	−7.53774	−0.728701	−0.364351	+	0.931262i	$0.618709\pi$
$108$	2.46191	0.236897
$109$	13.4909	1.29220	0.646098	−	0.763255i	$-0.276400\pi$
$109$	13.4909	1.29220	0.646098	+	0.763255i	$0.276400\pi$
$110$	26.8066	2.55591
$111$	−0.312542	−0.0296652
$112$	−0.239826	−0.0226614
$113$	−1.78842	−0.168241	−0.0841204	−	0.996456i	$-0.526808\pi$
$113$	−1.78842	−0.168241	−0.0841204	+	0.996456i	$0.526808\pi$
$114$	−10.0131	−0.937809
$115$	−3.16198	−0.294856
$116$	20.4564	1.89933
$117$	−3.49121	−0.322763
$118$	−2.17626	−0.200341
$119$	0.0837724	0.00767940
$120$	3.76403	0.343607
$121$	−0.178535	−0.0162305
$122$	27.7745	2.51459
$123$	7.40198	0.667414
$124$	2.97981	0.267595
$125$	−18.8359	−1.68473
$126$	−0.176954	−0.0157643
$127$	14.2397	1.26357	0.631784	−	0.775144i	$-0.282323\pi$
$127$	14.2397	1.26357	0.631784	+	0.775144i	$0.282323\pi$
$128$	7.59739	0.671521
$129$	7.91175	0.696591
$130$	−28.4495	−2.49519
$131$	0.0964608	0.00842782	0.00421391	−	0.999991i	$-0.498659\pi$
$131$	0.0964608	0.00842782	0.00421391	+	0.999991i	$0.498659\pi$
$132$	8.09869	0.704900
$133$	0.397107	0.0344336
$134$	29.4803	2.54671
$135$	−3.85779	−0.332026
$136$	−0.975695	−0.0836652
$137$	1.54857	0.132303	0.0661516	−	0.997810i	$-0.478928\pi$
$137$	1.54857	0.132303	0.0661516	+	0.997810i	$0.478928\pi$
$138$	−1.73133	−0.147381
$139$	12.0571	1.02267	0.511335	−	0.859381i	$-0.329151\pi$
$139$	12.0571	1.02267	0.511335	+	0.859381i	$0.329151\pi$
$140$	−0.795630	−0.0672430
$141$	9.53497	0.802989
$142$	14.6343	1.22808
$143$	−11.4847	−0.960398
$144$	−2.86283	−0.238569
$145$	−32.0551	−2.66203
$146$	19.6023	1.62230
$147$	−6.99298	−0.576771
$148$	−0.769449	−0.0632483
$149$	7.97528	0.653360	0.326680	−	0.945135i	$-0.394070\pi$
$149$	7.97528	0.653360	0.326680	+	0.945135i	$0.394070\pi$
$150$	−20.8751	−1.70445
$151$	−1.43329	−0.116640	−0.0583198	−	0.998298i	$-0.518574\pi$
$151$	−1.43329	−0.116640	−0.0583198	+	0.998298i	$0.518574\pi$
$152$	−4.62510	−0.375145
$153$	1.00000	0.0808452
$154$	−0.582109	−0.0469077
$155$	−4.66935	−0.375051
$156$	−8.59503	−0.688153
$157$	1.00000	0.0798087
$157$	1.00000	0.0798087
$158$	17.7327	1.41074
$159$	−1.20268	−0.0953784
$160$	−30.8570	−2.43946
$161$	0.0686627	0.00541138
$162$	−2.11232	−0.165960
$163$	9.76673	0.764990	0.382495	−	0.923958i	$-0.375065\pi$
$163$	9.76673	0.764990	0.382495	+	0.923958i	$0.375065\pi$
$164$	18.2230	1.42298
$165$	−12.6906	−0.987961
$166$	−32.8715	−2.55132
$167$	3.52868	0.273058	0.136529	−	0.990636i	$-0.456405\pi$
$167$	3.52868	0.273058	0.136529	+	0.990636i	$0.456405\pi$
$168$	−0.0817363	−0.00630609
$169$	−0.811446	−0.0624189
$170$	8.14890	0.624992
$171$	4.74031	0.362501
$172$	19.4780	1.48518
$173$	5.11778	0.389097	0.194549	−	0.980893i	$-0.437676\pi$
$173$	5.11778	0.389097	0.194549	+	0.980893i	$0.437676\pi$
$174$	−17.5517	−1.33059
$175$	0.827885	0.0625822
$176$	−9.41756	−0.709876
$177$	1.03027	0.0774396
$178$	23.5486	1.76504
$179$	−9.15852	−0.684540	−0.342270	−	0.939602i	$-0.611196\pi$
$179$	−9.15852	−0.684540	−0.342270	+	0.939602i	$0.611196\pi$
$180$	−9.49752	−0.707903
$181$	−21.4494	−1.59432	−0.797161	−	0.603767i	$-0.793666\pi$
$181$	−21.4494	−1.59432	−0.797161	+	0.603767i	$0.793666\pi$
$182$	0.617785	0.0457932
$183$	−13.1488	−0.971988
$184$	−0.799713	−0.0589556
$185$	1.20572	0.0886465
$186$	−2.55669	−0.187465
$187$	3.28960	0.240559
$188$	23.4742	1.71203
$189$	0.0837724	0.00609354
$190$	38.6283	2.80239
$191$	−1.23719	−0.0895197	−0.0447598	−	0.998998i	$-0.514252\pi$
$191$	−1.23719	−0.0895197	−0.0447598	+	0.998998i	$0.514252\pi$
$192$	−11.1700	−0.806124
$193$	1.58559	0.114133	0.0570665	−	0.998370i	$-0.481825\pi$
$193$	1.58559	0.114133	0.0570665	+	0.998370i	$0.481825\pi$
$194$	−14.4319	−1.03615
$195$	13.4684	0.964490
$196$	−17.2161	−1.22972
$197$	−14.2162	−1.01286	−0.506432	−	0.862280i	$-0.669036\pi$
$197$	−14.2162	−1.01286	−0.506432	+	0.862280i	$0.669036\pi$
$198$	−6.94869	−0.493822
$199$	−16.6082	−1.17732	−0.588662	−	0.808379i	$-0.700345\pi$
$199$	−16.6082	−1.17732	−0.588662	+	0.808379i	$0.700345\pi$
$200$	−9.64236	−0.681818
$201$	−13.9564	−0.984406
$202$	−21.5704	−1.51768
$203$	0.696079	0.0488552
$204$	2.46191	0.172368
$205$	−28.5553	−1.99439
$206$	−8.01129	−0.558173
$207$	0.819634	0.0569685
$208$	9.99474	0.693011
$209$	15.5937	1.07864
$210$	0.682653	0.0471075
$211$	18.2578	1.25692	0.628458	−	0.777843i	$-0.283686\pi$
$211$	18.2578	1.25692	0.628458	+	0.777843i	$0.283686\pi$
$212$	−2.96087	−0.203354
$213$	−6.92804	−0.474702
$214$	15.9221	1.08842
$215$	−30.5219	−2.08158
$216$	−0.975695	−0.0663877
$217$	0.101395	0.00688317
$218$	−28.4972	−1.93007
$219$	−9.27996	−0.627082
$220$	−31.2430	−2.10641
$221$	−3.49121	−0.234844
$222$	0.660190	0.0443090
$223$	7.91171	0.529807	0.264904	−	0.964275i	$-0.414660\pi$
$223$	7.91171	0.529807	0.264904	+	0.964275i	$0.414660\pi$
$224$	0.670063	0.0447704
$225$	9.88256	0.658837
$226$	3.77773	0.251291
$227$	−7.91386	−0.525261	−0.262631	−	0.964896i	$-0.584590\pi$
$227$	−7.91386	−0.525261	−0.262631	+	0.964896i	$0.584590\pi$
$228$	11.6702	0.772878
$229$	19.5929	1.29474	0.647369	−	0.762177i	$-0.275869\pi$
$229$	19.5929	1.29474	0.647369	+	0.762177i	$0.275869\pi$
$230$	6.67912	0.440408
$231$	0.275578	0.0181317
$232$	−8.10722	−0.532265
$233$	24.0682	1.57676	0.788379	−	0.615190i	$-0.210921\pi$
$233$	24.0682	1.57676	0.788379	+	0.615190i	$0.210921\pi$
$234$	7.37456	0.482090
$235$	−36.7839	−2.39952
$236$	2.53642	0.165107
$237$	−8.39490	−0.545308
$238$	−0.176954	−0.0114702
$239$	−29.0671	−1.88019	−0.940096	−	0.340909i	$-0.889265\pi$
$239$	−29.0671	−1.88019	−0.940096	+	0.340909i	$0.889265\pi$
$240$	11.0442	0.712900
$241$	−12.7214	−0.819460	−0.409730	−	0.912207i	$-0.634377\pi$
$241$	−12.7214	−0.819460	−0.409730	+	0.912207i	$0.634377\pi$
$242$	0.377124	0.0242425
$243$	1.00000	0.0641500
$244$	−32.3711	−2.07235
$245$	26.9775	1.72353
$246$	−15.6354	−0.996875
$247$	−16.5494	−1.05301
$248$	−1.18095	−0.0749904
$249$	15.5618	0.986188
$250$	39.7875	2.51638
$251$	18.9280	1.19472	0.597361	−	0.801972i	$-0.296216\pi$
$251$	18.9280	1.19472	0.597361	+	0.801972i	$0.296216\pi$
$252$	0.206240	0.0129919
$253$	2.69627	0.169513
$254$	−30.0788	−1.88731
$255$	−3.85779	−0.241584
$256$	6.29183	0.393240
$257$	−16.0993	−1.00425	−0.502123	−	0.864796i	$-0.667448\pi$
$257$	−16.0993	−1.00425	−0.502123	+	0.864796i	$0.667448\pi$
$258$	−16.7122	−1.04045
$259$	−0.0261824	−0.00162689
$260$	33.1579	2.05636
$261$	8.30917	0.514325
$262$	−0.203756	−0.0125881
$263$	−3.74690	−0.231044	−0.115522	−	0.993305i	$-0.536854\pi$
$263$	−3.74690	−0.231044	−0.115522	+	0.993305i	$0.536854\pi$
$264$	−3.20965	−0.197540
$265$	4.63967	0.285013
$266$	−0.838818	−0.0514312
$267$	−11.1482	−0.682260
$268$	−34.3593	−2.09883
$269$	−19.3314	−1.17866	−0.589329	−	0.807893i	$-0.700608\pi$
$269$	−19.3314	−1.17866	−0.589329	+	0.807893i	$0.700608\pi$
$270$	8.14890	0.495926
$271$	−4.22295	−0.256526	−0.128263	−	0.991740i	$-0.540940\pi$
$271$	−4.22295	−0.256526	−0.128263	+	0.991740i	$0.540940\pi$
$272$	−2.86283	−0.173585
$273$	−0.292467	−0.0177009
$274$	−3.27108	−0.197613
$275$	32.5096	1.96041
$276$	2.01786	0.121461
$277$	18.2497	1.09652	0.548260	−	0.836308i	$-0.315290\pi$
$277$	18.2497	1.09652	0.548260	+	0.836308i	$0.315290\pi$
$278$	−25.4685	−1.52750
$279$	1.21037	0.0724628
$280$	0.315322	0.0188441
$281$	−24.6776	−1.47214	−0.736072	−	0.676903i	$-0.763322\pi$
$281$	−24.6776	−1.47214	−0.736072	+	0.676903i	$0.763322\pi$
$282$	−20.1409	−1.19937
$283$	7.23941	0.430339	0.215169	−	0.976577i	$-0.430970\pi$
$283$	7.23941	0.430339	0.215169	+	0.976577i	$0.430970\pi$
$284$	−17.0562	−1.01210
$285$	−18.2871	−1.08324
$286$	24.2594	1.43449
$287$	0.620082	0.0366023
$288$	7.99861	0.471323
$289$	1.00000	0.0588235
$290$	67.7106	3.97610
$291$	6.83225	0.400514
$292$	−22.8464	−1.33698
$293$	22.0683	1.28924	0.644621	−	0.764502i	$-0.277015\pi$
$293$	22.0683	1.28924	0.644621	+	0.764502i	$0.277015\pi$
$294$	14.7714	0.861488
$295$	−3.97455	−0.231407
$296$	0.304946	0.0177246
$297$	3.28960	0.190882
$298$	−16.8464	−0.975883
$299$	−2.86152	−0.165486
$300$	24.3299	1.40469
$301$	0.662786	0.0382024
$302$	3.02757	0.174217
$303$	10.2117	0.586645
$304$	−13.5707	−0.778333
$305$	50.7254	2.90453
$306$	−2.11232	−0.120753
$307$	−9.48581	−0.541384	−0.270692	−	0.962666i	$-0.587252\pi$
$307$	−9.48581	−0.541384	−0.270692	+	0.962666i	$0.587252\pi$
$308$	0.678446	0.0386581
$309$	3.79265	0.215756
$310$	9.86317	0.560190
$311$	6.78881	0.384958	0.192479	−	0.981301i	$-0.438347\pi$
$311$	6.78881	0.384958	0.192479	+	0.981301i	$0.438347\pi$
$312$	3.40636	0.192847
$313$	9.41729	0.532296	0.266148	−	0.963932i	$-0.414249\pi$
$313$	9.41729	0.532296	0.266148	+	0.963932i	$0.414249\pi$
$314$	−2.11232	−0.119205
$315$	−0.323176	−0.0182089
$316$	−20.6675	−1.16264
$317$	−8.95658	−0.503052	−0.251526	−	0.967851i	$-0.580932\pi$
$317$	−8.95658	−0.503052	−0.251526	+	0.967851i	$0.580932\pi$
$318$	2.54044	0.142461
$319$	27.3339	1.53040
$320$	43.0915	2.40889
$321$	−7.53774	−0.420716
$322$	−0.145038	−0.00808264
$323$	4.74031	0.263758
$324$	2.46191	0.136773
$325$	−34.5021	−1.91383
$326$	−20.6305	−1.14262
$327$	13.4909	0.746050
$328$	−7.22208	−0.398773
$329$	0.798767	0.0440374
$330$	26.8066	1.47566
$331$	0.761518	0.0418568	0.0209284	−	0.999781i	$-0.493338\pi$
$331$	0.761518	0.0418568	0.0209284	+	0.999781i	$0.493338\pi$
$332$	38.3117	2.10263
$333$	−0.312542	−0.0171272
$334$	−7.45372	−0.407849
$335$	53.8407	2.94163
$336$	−0.239826	−0.0130836
$337$	35.2617	1.92083	0.960413	−	0.278581i	$-0.0898640\pi$
$337$	35.2617	1.92083	0.960413	+	0.278581i	$0.0898640\pi$
$338$	1.71404	0.0932313
$339$	−1.78842	−0.0971339
$340$	−9.49752	−0.515075
$341$	3.98163	0.215617
$342$	−10.0131	−0.541445
$343$	−1.17223	−0.0632942
$344$	−7.71946	−0.416205
$345$	−3.16198	−0.170235
$346$	−10.8104	−0.581171
$347$	30.0431	1.61280	0.806398	−	0.591373i	$-0.201414\pi$
$347$	30.0431	1.61280	0.806398	+	0.591373i	$0.201414\pi$
$348$	20.4564	1.09658
$349$	−18.8364	−1.00829	−0.504144	−	0.863620i	$-0.668192\pi$
$349$	−18.8364	−1.00829	−0.504144	+	0.863620i	$0.668192\pi$
$350$	−1.74876	−0.0934752
$351$	−3.49121	−0.186347
$352$	26.3122	1.40245
$353$	21.5124	1.14499	0.572495	−	0.819908i	$-0.305976\pi$
$353$	21.5124	1.14499	0.572495	+	0.819908i	$0.305976\pi$
$354$	−2.17626	−0.115667
$355$	26.7269	1.41852
$356$	−27.4459	−1.45463
$357$	0.0837724	0.00443370
$358$	19.3457	1.02245
$359$	7.54776	0.398355	0.199178	−	0.979963i	$-0.436173\pi$
$359$	7.54776	0.398355	0.199178	+	0.979963i	$0.436173\pi$
$360$	3.76403	0.198382
$361$	3.47054	0.182660
$362$	45.3081	2.38134
$363$	−0.178535	−0.00937068
$364$	−0.720026	−0.0377396
$365$	35.8002	1.87387
$366$	27.7745	1.45180
$367$	−16.9178	−0.883103	−0.441551	−	0.897236i	$-0.645572\pi$
$367$	−16.9178	−0.883103	−0.441551	+	0.897236i	$0.645572\pi$
$368$	−2.34647	−0.122318
$369$	7.40198	0.385332
$370$	−2.54687	−0.132406
$371$	−0.100751	−0.00523073
$372$	2.97981	0.154496
$373$	−12.5433	−0.649467	−0.324734	−	0.945806i	$-0.605275\pi$
$373$	−12.5433	−0.649467	−0.324734	+	0.945806i	$0.605275\pi$
$374$	−6.94869	−0.359308
$375$	−18.8359	−0.972681
$376$	−9.30322	−0.479777
$377$	−29.0091	−1.49404
$378$	−0.176954	−0.00910155
$379$	−32.6144	−1.67529	−0.837646	−	0.546214i	$-0.816069\pi$
$379$	−32.6144	−1.67529	−0.837646	+	0.546214i	$0.816069\pi$
$380$	−45.0212	−2.30954
$381$	14.2397	0.729521
$382$	2.61334	0.133710
$383$	32.2739	1.64912	0.824559	−	0.565776i	$-0.191423\pi$
$383$	32.2739	1.64912	0.824559	+	0.565776i	$0.191423\pi$
$384$	7.59739	0.387703
$385$	−1.06312	−0.0541817
$386$	−3.34927	−0.170473
$387$	7.91175	0.402177
$388$	16.8204	0.853925
$389$	7.31594	0.370933	0.185467	−	0.982651i	$-0.440620\pi$
$389$	7.31594	0.370933	0.185467	+	0.982651i	$0.440620\pi$
$390$	−28.4495	−1.44060
$391$	0.819634	0.0414507
$392$	6.82302	0.344615
$393$	0.0964608	0.00486580
$394$	30.0292	1.51285
$395$	32.3858	1.62951
$396$	8.09869	0.406974
$397$	−22.9548	−1.15207	−0.576035	−	0.817425i	$-0.695401\pi$
$397$	−22.9548	−1.15207	−0.576035	+	0.817425i	$0.695401\pi$
$398$	35.0819	1.75850
$399$	0.397107	0.0198802
$400$	−28.2921	−1.41460
$401$	−26.6492	−1.33080	−0.665399	−	0.746487i	$-0.731739\pi$
$401$	−26.6492	−1.33080	−0.665399	+	0.746487i	$0.731739\pi$
$402$	29.4803	1.47035
$403$	−4.22565	−0.210495
$404$	25.1402	1.25077
$405$	−3.85779	−0.191695
$406$	−1.47034	−0.0729719
$407$	−1.02814	−0.0509629
$408$	−0.975695	−0.0483041
$409$	25.2943	1.25072	0.625361	−	0.780335i	$-0.284952\pi$
$409$	25.2943	1.25072	0.625361	+	0.780335i	$0.284952\pi$
$410$	60.3180	2.97889
$411$	1.54857	0.0763853
$412$	9.33714	0.460008
$413$	0.0863079	0.00424693
$414$	−1.73133	−0.0850903
$415$	−60.0341	−2.94696
$416$	−27.9248	−1.36913
$417$	12.0571	0.590439
$418$	−32.9390	−1.61110
$419$	−12.2950	−0.600651	−0.300325	−	0.953837i	$-0.597095\pi$
$419$	−12.2950	−0.600651	−0.300325	+	0.953837i	$0.597095\pi$
$420$	−0.795630	−0.0388228
$421$	−21.7221	−1.05867	−0.529335	−	0.848413i	$-0.677559\pi$
$421$	−21.7221	−1.05867	−0.529335	+	0.848413i	$0.677559\pi$
$422$	−38.5663	−1.87738
$423$	9.53497	0.463606
$424$	1.17344	0.0569875
$425$	9.88256	0.479374
$426$	14.6343	0.709032
$427$	−1.10151	−0.0533057
$428$	−18.5572	−0.896997
$429$	−11.4847	−0.554486
$430$	64.4721	3.10912
$431$	21.4619	1.03378	0.516891	−	0.856051i	$-0.327089\pi$
$431$	21.4619	1.03378	0.516891	+	0.856051i	$0.327089\pi$
$432$	−2.86283	−0.137738
$433$	−28.4746	−1.36840	−0.684202	−	0.729293i	$-0.739849\pi$
$433$	−28.4746	−1.36840	−0.684202	+	0.729293i	$0.739849\pi$
$434$	−0.214180	−0.0102810
$435$	−32.0551	−1.53692
$436$	33.2134	1.59063
$437$	3.88532	0.185860
$438$	19.6023	0.936633
$439$	3.93877	0.187987	0.0939937	−	0.995573i	$-0.470037\pi$
$439$	3.93877	0.187987	0.0939937	+	0.995573i	$0.470037\pi$
$440$	12.3821	0.590296
$441$	−6.99298	−0.332999
$442$	7.37456	0.350772
$443$	20.9465	0.995198	0.497599	−	0.867407i	$-0.334215\pi$
$443$	20.9465	0.995198	0.497599	+	0.867407i	$0.334215\pi$
$444$	−0.769449	−0.0365165
$445$	43.0075	2.03875
$446$	−16.7121	−0.791340
$447$	7.97528	0.377218
$448$	−0.935736	−0.0442094
$449$	0.922103	0.0435167	0.0217584	−	0.999763i	$-0.493074\pi$
$449$	0.922103	0.0435167	0.0217584	+	0.999763i	$0.493074\pi$
$450$	−20.8751	−0.984064
$451$	24.3496	1.14658
$452$	−4.40293	−0.207097
$453$	−1.43329	−0.0673419
$454$	16.7166	0.784550
$455$	1.12828	0.0528944
$456$	−4.62510	−0.216590
$457$	28.1637	1.31744	0.658722	−	0.752386i	$-0.271097\pi$
$457$	28.1637	1.31744	0.658722	+	0.752386i	$0.271097\pi$
$458$	−41.3866	−1.93387
$459$	1.00000	0.0466760
$460$	−7.78449	−0.362954
$461$	−7.31400	−0.340647	−0.170323	−	0.985388i	$-0.554481\pi$
$461$	−7.31400	−0.340647	−0.170323	+	0.985388i	$0.554481\pi$
$462$	−0.582109	−0.0270821
$463$	−15.5195	−0.721253	−0.360626	−	0.932710i	$-0.617437\pi$
$463$	−15.5195	−0.721253	−0.360626	+	0.932710i	$0.617437\pi$
$464$	−23.7877	−1.10432
$465$	−4.66935	−0.216536
$466$	−50.8397	−2.35510
$467$	35.8519	1.65903	0.829514	−	0.558486i	$-0.188618\pi$
$467$	35.8519	1.65903	0.829514	+	0.558486i	$0.188618\pi$
$468$	−8.59503	−0.397306
$469$	−1.16916	−0.0539867
$470$	77.6995	3.58401
$471$	1.00000	0.0460776
$472$	−1.00523	−0.0462693
$473$	26.0265	1.19670
$474$	17.7327	0.814492
$475$	46.8464	2.14946
$476$	0.206240	0.00945298
$477$	−1.20268	−0.0550667
$478$	61.3990	2.80833
$479$	12.2746	0.560841	0.280421	−	0.959877i	$-0.409526\pi$
$479$	12.2746	0.560841	0.280421	+	0.959877i	$0.409526\pi$
$480$	−30.8570	−1.40842
$481$	1.09115	0.0497522
$482$	26.8718	1.22398
$483$	0.0686627	0.00312426
$484$	−0.439538	−0.0199790
$485$	−26.3574	−1.19683
$486$	−2.11232	−0.0958169
$487$	25.5448	1.15755	0.578773	−	0.815489i	$-0.303532\pi$
$487$	25.5448	1.15755	0.578773	+	0.815489i	$0.303532\pi$
$488$	12.8292	0.580752
$489$	9.76673	0.441667
$490$	−56.9851	−2.57432
$491$	18.7433	0.845872	0.422936	−	0.906160i	$-0.361000\pi$
$491$	18.7433	0.845872	0.422936	+	0.906160i	$0.361000\pi$
$492$	18.2230	0.821556
$493$	8.30917	0.374226
$494$	34.9577	1.57282
$495$	−12.6906	−0.570400
$496$	−3.46508	−0.155587
$497$	−0.580379	−0.0260335
$498$	−32.8715	−1.47301
$499$	12.4105	0.555570	0.277785	−	0.960643i	$-0.410400\pi$
$499$	12.4105	0.555570	0.277785	+	0.960643i	$0.410400\pi$
$500$	−46.3722	−2.07383
$501$	3.52868	0.157650
$502$	−39.9820	−1.78448
$503$	27.6254	1.23175	0.615877	−	0.787842i	$-0.288802\pi$
$503$	27.6254	1.23175	0.615877	+	0.787842i	$0.288802\pi$
$504$	−0.0817363	−0.00364082
$505$	−39.3945	−1.75303
$506$	−5.69539	−0.253191
$507$	−0.811446	−0.0360376
$508$	35.0568	1.55539
$509$	−22.0597	−0.977779	−0.488889	−	0.872346i	$-0.662598\pi$
$509$	−22.0597	−0.977779	−0.488889	+	0.872346i	$0.662598\pi$
$510$	8.14890	0.360839
$511$	−0.777405	−0.0343904
$512$	−28.4852	−1.25888
$513$	4.74031	0.209290
$514$	34.0069	1.49998
$515$	−14.6312	−0.644729
$516$	19.4780	0.857471
$517$	31.3662	1.37948
$518$	0.0553057	0.00242999
$519$	5.11778	0.224646
$520$	−13.1410	−0.576272
$521$	3.00735	0.131755	0.0658773	−	0.997828i	$-0.479015\pi$
$521$	3.00735	0.131755	0.0658773	+	0.997828i	$0.479015\pi$
$522$	−17.5517	−0.768215
$523$	25.3845	1.10999	0.554993	−	0.831855i	$-0.312721\pi$
$523$	25.3845	1.10999	0.554993	+	0.831855i	$0.312721\pi$
$524$	0.237477	0.0103743
$525$	0.827885	0.0361319
$526$	7.91465	0.345095
$527$	1.21037	0.0527245
$528$	−9.41756	−0.409847
$529$	−22.3282	−0.970791
$530$	−9.80048	−0.425706
$531$	1.03027	0.0447098
$532$	0.977640	0.0423861
$533$	−25.8419	−1.11934
$534$	23.5486	1.01905
$535$	29.0790	1.25720
$536$	13.6172	0.588172
$537$	−9.15852	−0.395219
$538$	40.8342	1.76049
$539$	−23.0041	−0.990857
$540$	−9.49752	−0.408708
$541$	−9.81458	−0.421962	−0.210981	−	0.977490i	$-0.567666\pi$
$541$	−9.81458	−0.421962	−0.210981	+	0.977490i	$0.567666\pi$
$542$	8.92023	0.383157
$543$	−21.4494	−0.920482
$544$	7.99861	0.342938
$545$	−52.0452	−2.22937
$546$	0.617785	0.0264387
$547$	−13.4096	−0.573352	−0.286676	−	0.958028i	$-0.592550\pi$
$547$	−13.4096	−0.573352	−0.286676	+	0.958028i	$0.592550\pi$
$548$	3.81243	0.162859
$549$	−13.1488	−0.561178
$550$	−68.6709	−2.92814
$551$	39.3881	1.67799
$552$	−0.799713	−0.0340381
$553$	−0.703261	−0.0299057
$554$	−38.5493	−1.63780
$555$	1.20572	0.0511801
$556$	29.6835	1.25886
$557$	26.4273	1.11976	0.559881	−	0.828573i	$-0.310847\pi$
$557$	26.4273	1.11976	0.559881	+	0.828573i	$0.310847\pi$
$558$	−2.55669	−0.108233
$559$	−27.6216	−1.16827
$560$	0.925199	0.0390968
$561$	3.28960	0.138887
$562$	52.1271	2.19885
$563$	26.4686	1.11552	0.557758	−	0.830003i	$-0.311662\pi$
$563$	26.4686	1.11552	0.557758	+	0.830003i	$0.311662\pi$
$564$	23.4742	0.988442
$565$	6.89937	0.290259
$566$	−15.2920	−0.642770
$567$	0.0837724	0.00351811
$568$	6.75966	0.283629
$569$	9.36662	0.392669	0.196335	−	0.980537i	$-0.437096\pi$
$569$	9.36662	0.392669	0.196335	+	0.980537i	$0.437096\pi$
$570$	38.6283	1.61796
$571$	22.7683	0.952825	0.476413	−	0.879222i	$-0.341937\pi$
$571$	22.7683	0.952825	0.476413	+	0.879222i	$0.341937\pi$
$572$	−28.2742	−1.18220
$573$	−1.23719	−0.0516842
$574$	−1.30981	−0.0546705
$575$	8.10008	0.337797
$576$	−11.1700	−0.465416
$577$	33.7123	1.40346	0.701731	−	0.712442i	$-0.252411\pi$
$577$	33.7123	1.40346	0.701731	+	0.712442i	$0.252411\pi$
$578$	−2.11232	−0.0878610
$579$	1.58559	0.0658947
$580$	−78.9165	−3.27683
$581$	1.30365	0.0540844
$582$	−14.4319	−0.598222
$583$	−3.95632	−0.163854
$584$	9.05441	0.374674
$585$	13.4684	0.556848
$586$	−46.6153	−1.92566
$587$	7.90311	0.326196	0.163098	−	0.986610i	$-0.447851\pi$
$587$	7.90311	0.326196	0.163098	+	0.986610i	$0.447851\pi$
$588$	−17.2161	−0.709979
$589$	5.73752	0.236410
$590$	8.39554	0.345639
$591$	−14.2162	−0.584777
$592$	0.894755	0.0367742
$593$	−41.3715	−1.69892	−0.849462	−	0.527650i	$-0.823073\pi$
$593$	−41.3715	−1.69892	−0.849462	+	0.527650i	$0.823073\pi$
$594$	−6.94869	−0.285108
$595$	−0.323176	−0.0132489
$596$	19.6344	0.804256
$597$	−16.6082	−0.679728
$598$	6.04444	0.247176
$599$	12.7615	0.521420	0.260710	−	0.965417i	$-0.416043\pi$
$599$	12.7615	0.521420	0.260710	+	0.965417i	$0.416043\pi$
$600$	−9.64236	−0.393648
$601$	7.56493	0.308580	0.154290	−	0.988026i	$-0.450691\pi$
$601$	7.56493	0.308580	0.154290	+	0.988026i	$0.450691\pi$
$602$	−1.40002	−0.0570605
$603$	−13.9564	−0.568347
$604$	−3.52863	−0.143578
$605$	0.688753	0.0280018
$606$	−21.5704	−0.876236
$607$	6.53133	0.265099	0.132549	−	0.991176i	$-0.457684\pi$
$607$	6.53133	0.265099	0.132549	+	0.991176i	$0.457684\pi$
$608$	37.9159	1.53769
$609$	0.696079	0.0282066
$610$	−107.148	−4.33831
$611$	−33.2886	−1.34671
$612$	2.46191	0.0995167
$613$	17.0046	0.686810	0.343405	−	0.939187i	$-0.388420\pi$
$613$	17.0046	0.686810	0.343405	+	0.939187i	$0.388420\pi$
$614$	20.0371	0.808631
$615$	−28.5553	−1.15146
$616$	−0.268880	−0.0108335
$617$	31.1825	1.25536	0.627681	−	0.778471i	$-0.284004\pi$
$617$	31.1825	1.25536	0.627681	+	0.778471i	$0.284004\pi$
$618$	−8.01129	−0.322261
$619$	36.1570	1.45327	0.726637	−	0.687022i	$-0.241082\pi$
$619$	36.1570	1.45327	0.726637	+	0.687022i	$0.241082\pi$
$620$	−11.4955	−0.461670
$621$	0.819634	0.0328908
$622$	−14.3402	−0.574988
$623$	−0.933913	−0.0374164
$624$	9.99474	0.400110
$625$	23.2521	0.930085
$626$	−19.8923	−0.795058
$627$	15.5937	0.622753
$628$	2.46191	0.0982408
$629$	−0.312542	−0.0124619
$630$	0.682653	0.0271975
$631$	−11.8536	−0.471886	−0.235943	−	0.971767i	$-0.575818\pi$
$631$	−11.8536	−0.471886	−0.235943	+	0.971767i	$0.575818\pi$
$632$	8.19087	0.325815
$633$	18.2578	0.725681
$634$	18.9192	0.751377
$635$	−54.9337	−2.17998
$636$	−2.96087	−0.117406
$637$	24.4140	0.967317
$638$	−57.7379	−2.28587
$639$	−6.92804	−0.274069
$640$	−29.3091	−1.15855
$641$	23.5467	0.930039	0.465020	−	0.885300i	$-0.346047\pi$
$641$	23.5467	0.930039	0.465020	+	0.885300i	$0.346047\pi$
$642$	15.9221	0.628397
$643$	−47.6515	−1.87919	−0.939596	−	0.342284i	$-0.888799\pi$
$643$	−47.6515	−1.87919	−0.939596	+	0.342284i	$0.888799\pi$
$644$	0.169041	0.00666115
$645$	−30.5219	−1.20180
$646$	−10.0131	−0.393959
$647$	−4.36478	−0.171597	−0.0857987	−	0.996312i	$-0.527344\pi$
$647$	−4.36478	−0.171597	−0.0857987	+	0.996312i	$0.527344\pi$
$648$	−0.975695	−0.0383289
$649$	3.38916	0.133036
$650$	72.8795	2.85857
$651$	0.101395	0.00397400
$652$	24.0448	0.941666
$653$	−36.8843	−1.44339	−0.721697	−	0.692209i	$-0.756638\pi$
$653$	−36.8843	−1.44339	−0.721697	+	0.692209i	$0.756638\pi$
$654$	−28.4972	−1.11433
$655$	−0.372126	−0.0145402
$656$	−21.1906	−0.827355
$657$	−9.27996	−0.362046
$658$	−1.68725	−0.0657760
$659$	14.1194	0.550012	0.275006	−	0.961442i	$-0.411320\pi$
$659$	14.1194	0.550012	0.275006	+	0.961442i	$0.411320\pi$
$660$	−31.2430	−1.21613
$661$	−24.8128	−0.965108	−0.482554	−	0.875866i	$-0.660291\pi$
$661$	−24.8128	−0.965108	−0.482554	+	0.875866i	$0.660291\pi$
$662$	−1.60857	−0.0625189
$663$	−3.49121	−0.135587
$664$	−15.1836	−0.589236
$665$	−1.53196	−0.0594067
$666$	0.660190	0.0255818
$667$	6.81048	0.263703
$668$	8.68729	0.336121
$669$	7.91171	0.305884
$670$	−113.729	−4.39374
$671$	−43.2543	−1.66981
$672$	0.670063	0.0258482
$673$	7.18553	0.276982	0.138491	−	0.990364i	$-0.455775\pi$
$673$	7.18553	0.276982	0.138491	+	0.990364i	$0.455775\pi$
$674$	−74.4840	−2.86902
$675$	9.88256	0.380380
$676$	−1.99770	−0.0768348
$677$	−40.9665	−1.57447	−0.787235	−	0.616653i	$-0.788488\pi$
$677$	−40.9665	−1.57447	−0.787235	+	0.616653i	$0.788488\pi$
$678$	3.77773	0.145083
$679$	0.572354	0.0219649
$680$	3.76403	0.144344
$681$	−7.91386	−0.303260
$682$	−8.41048	−0.322054
$683$	45.2067	1.72979	0.864894	−	0.501955i	$-0.167386\pi$
$683$	45.2067	1.72979	0.864894	+	0.501955i	$0.167386\pi$
$684$	11.6702	0.446221
$685$	−5.97406	−0.228257
$686$	2.47612	0.0945386
$687$	19.5929	0.747517
$688$	−22.6500	−0.863523
$689$	4.19879	0.159961
$690$	6.67912	0.254270
$691$	−16.9414	−0.644482	−0.322241	−	0.946658i	$-0.604436\pi$
$691$	−16.9414	−0.644482	−0.322241	+	0.946658i	$0.604436\pi$
$692$	12.5995	0.478961
$693$	0.275578	0.0104683
$694$	−63.4607	−2.40893
$695$	−46.5138	−1.76437
$696$	−8.10722	−0.307303
$697$	7.40198	0.280370
$698$	39.7885	1.50602
$699$	24.0682	0.910341
$700$	2.03818	0.0770358
$701$	−11.8484	−0.447507	−0.223754	−	0.974646i	$-0.571831\pi$
$701$	−11.8484	−0.447507	−0.223754	+	0.974646i	$0.571831\pi$
$702$	7.37456	0.278335
$703$	−1.48155	−0.0558776
$704$	−36.7448	−1.38487
$705$	−36.7839	−1.38536
$706$	−45.4411	−1.71020
$707$	0.855456	0.0321727
$708$	2.53642	0.0953245
$709$	10.0177	0.376223	0.188111	−	0.982148i	$-0.439763\pi$
$709$	10.0177	0.376223	0.188111	+	0.982148i	$0.439763\pi$
$710$	−56.4559	−2.11875
$711$	−8.39490	−0.314833
$712$	10.8773	0.407643
$713$	0.992059	0.0371529
$714$	−0.176954	−0.00662235
$715$	44.3055	1.65693
$716$	−22.5474	−0.842636
$717$	−29.0671	−1.08553
$718$	−15.9433	−0.594999
$719$	−5.05620	−0.188564	−0.0942822	−	0.995546i	$-0.530056\pi$
$719$	−5.05620	−0.188564	−0.0942822	+	0.995546i	$0.530056\pi$
$720$	11.0442	0.411593
$721$	0.317719	0.0118325
$722$	−7.33091	−0.272828
$723$	−12.7214	−0.473115
$724$	−52.8064	−1.96254
$725$	82.1159	3.04971
$726$	0.377124	0.0139964
$727$	9.64578	0.357742	0.178871	−	0.983873i	$-0.442755\pi$
$727$	9.64578	0.357742	0.178871	+	0.983873i	$0.442755\pi$
$728$	0.285359	0.0105761
$729$	1.00000	0.0370370
$730$	−75.6215	−2.79888
$731$	7.91175	0.292627
$732$	−32.3711	−1.19647
$733$	−3.85024	−0.142212	−0.0711059	−	0.997469i	$-0.522653\pi$
$733$	−3.85024	−0.142212	−0.0711059	+	0.997469i	$0.522653\pi$
$734$	35.7359	1.31904
$735$	26.9775	0.995079
$736$	6.55593	0.241655
$737$	−45.9109	−1.69115
$738$	−15.6354	−0.575546
$739$	35.6039	1.30971	0.654855	−	0.755755i	$-0.272730\pi$
$739$	35.6039	1.30971	0.654855	+	0.755755i	$0.272730\pi$
$740$	2.96838	0.109120
$741$	−16.5494	−0.607958
$742$	0.212819	0.00781281
$743$	−15.1966	−0.557510	−0.278755	−	0.960362i	$-0.589922\pi$
$743$	−15.1966	−0.557510	−0.278755	+	0.960362i	$0.589922\pi$
$744$	−1.18095	−0.0432957
$745$	−30.7670	−1.12721
$746$	26.4955	0.970068
$747$	15.5618	0.569376
$748$	8.09869	0.296117
$749$	−0.631455	−0.0230729
$750$	39.7875	1.45283
$751$	48.7581	1.77921	0.889604	−	0.456733i	$-0.150980\pi$
$751$	48.7581	1.77921	0.889604	+	0.456733i	$0.150980\pi$
$752$	−27.2970	−0.995419
$753$	18.9280	0.689774
$754$	61.2765	2.23156
$755$	5.52934	0.201233
$756$	0.206240	0.00750087
$757$	46.4489	1.68821	0.844106	−	0.536176i	$-0.180132\pi$
$757$	46.4489	1.68821	0.844106	+	0.536176i	$0.180132\pi$
$758$	68.8922	2.50228
$759$	2.69627	0.0978683
$760$	17.8427	0.647221
$761$	28.1943	1.02204	0.511022	−	0.859568i	$-0.329267\pi$
$761$	28.1943	1.02204	0.511022	+	0.859568i	$0.329267\pi$
$762$	−30.0788	−1.08964
$763$	1.13017	0.0409148
$764$	−3.04584	−0.110195
$765$	−3.85779	−0.139479
$766$	−68.1728	−2.46318
$767$	−3.59688	−0.129876
$768$	6.29183	0.227037
$769$	48.1225	1.73534	0.867672	−	0.497138i	$-0.165616\pi$
$769$	48.1225	1.73534	0.867672	+	0.497138i	$0.165616\pi$
$770$	2.24565	0.0809278
$771$	−16.0993	−0.579802
$772$	3.90357	0.140492
$773$	−15.7830	−0.567675	−0.283838	−	0.958872i	$-0.591608\pi$
$773$	−15.7830	−0.567675	−0.283838	+	0.958872i	$0.591608\pi$
$774$	−16.7122	−0.600707
$775$	11.9615	0.429671
$776$	−6.66620	−0.239303
$777$	−0.0261824	−0.000939288 0
$778$	−15.4536	−0.554040
$779$	35.0877	1.25715
$780$	33.1579	1.18724
$781$	−22.7905	−0.815508
$782$	−1.73133	−0.0619123
$783$	8.30917	0.296946
$784$	20.0197	0.714990
$785$	−3.85779	−0.137690
$786$	−0.203756	−0.00726775
$787$	−1.51220	−0.0539042	−0.0269521	−	0.999637i	$-0.508580\pi$
$787$	−1.51220	−0.0539042	−0.0269521	+	0.999637i	$0.508580\pi$
$788$	−34.9990	−1.24679
$789$	−3.74690	−0.133393
$790$	−68.4092	−2.43389
$791$	−0.149821	−0.00532701
$792$	−3.20965	−0.114050
$793$	45.9053	1.63014
$794$	48.4880	1.72078
$795$	4.63967	0.164552
$796$	−40.8878	−1.44923
$797$	−7.59320	−0.268965	−0.134482	−	0.990916i	$-0.542937\pi$
$797$	−7.59320	−0.268965	−0.134482	+	0.990916i	$0.542937\pi$
$798$	−0.838818	−0.0296938
$799$	9.53497	0.337323
$800$	79.0467	2.79472
$801$	−11.1482	−0.393903
$802$	56.2918	1.98773
$803$	−30.5274	−1.07729
$804$	−34.3593	−1.21176
$805$	−0.264886	−0.00933602
$806$	8.92593	0.314403
$807$	−19.3314	−0.680498
$808$	−9.96348	−0.350514
$809$	33.2929	1.17052	0.585258	−	0.810847i	$-0.300993\pi$
$809$	33.2929	1.17052	0.585258	+	0.810847i	$0.300993\pi$
$810$	8.14890	0.286323
$811$	34.8871	1.22505	0.612526	−	0.790450i	$-0.290153\pi$
$811$	34.8871	1.22505	0.612526	+	0.790450i	$0.290153\pi$
$812$	1.71368	0.0601384
$813$	−4.22295	−0.148105
$814$	2.17176	0.0761201
$815$	−37.6780	−1.31980
$816$	−2.86283	−0.100219
$817$	37.5042	1.31210
$818$	−53.4297	−1.86813
$819$	−0.292467	−0.0102196
$820$	−70.3005	−2.45500
$821$	−24.5704	−0.857514	−0.428757	−	0.903420i	$-0.641048\pi$
$821$	−24.5704	−0.857514	−0.428757	+	0.903420i	$0.641048\pi$
$822$	−3.27108	−0.114092
$823$	43.1170	1.50296	0.751482	−	0.659753i	$-0.229339\pi$
$823$	43.1170	1.50296	0.751482	+	0.659753i	$0.229339\pi$
$824$	−3.70047	−0.128912
$825$	32.5096	1.13184
$826$	−0.182310	−0.00634338
$827$	−22.3819	−0.778295	−0.389147	−	0.921176i	$-0.627230\pi$
$827$	−22.3819	−0.778295	−0.389147	+	0.921176i	$0.627230\pi$
$828$	2.01786	0.0701256
$829$	−18.1372	−0.629933	−0.314966	−	0.949103i	$-0.601993\pi$
$829$	−18.1372	−0.629933	−0.314966	+	0.949103i	$0.601993\pi$
$830$	126.811	4.40169
$831$	18.2497	0.633077
$832$	38.9968	1.35197
$833$	−6.99298	−0.242292
$834$	−25.4685	−0.881902
$835$	−13.6129	−0.471095
$836$	38.3903	1.32776
$837$	1.21037	0.0418364
$838$	25.9710	0.897154
$839$	55.1696	1.90467	0.952333	−	0.305060i	$-0.0986765\pi$
$839$	55.1696	1.90467	0.952333	+	0.305060i	$0.0986765\pi$
$840$	0.315322	0.0108796
$841$	40.0424	1.38077
$842$	45.8841	1.58127
$843$	−24.6776	−0.849943
$844$	44.9489	1.54720
$845$	3.13039	0.107689
$846$	−20.1409	−0.692459
$847$	−0.0149563	−0.000513906 0
$848$	3.44305	0.118235
$849$	7.23941	0.248456
$850$	−20.8751	−0.716012
$851$	−0.256170	−0.00878140
$852$	−17.0562	−0.584336
$853$	−50.7648	−1.73816	−0.869078	−	0.494676i	$-0.835287\pi$
$853$	−50.7648	−1.73816	−0.869078	+	0.494676i	$0.835287\pi$
$854$	2.32674	0.0796193
$855$	−18.2871	−0.625407
$856$	7.35454	0.251373
$857$	28.9427	0.988664	0.494332	−	0.869273i	$-0.335413\pi$
$857$	28.9427	0.988664	0.494332	+	0.869273i	$0.335413\pi$
$858$	24.2594	0.828201
$859$	13.5767	0.463232	0.231616	−	0.972807i	$-0.425599\pi$
$859$	13.5767	0.463232	0.231616	+	0.972807i	$0.425599\pi$
$860$	−75.1420	−2.56232
$861$	0.620082	0.0211323
$862$	−45.3344	−1.54410
$863$	25.2055	0.858004	0.429002	−	0.903304i	$-0.358865\pi$
$863$	25.2055	0.858004	0.429002	+	0.903304i	$0.358865\pi$
$864$	7.99861	0.272118
$865$	−19.7433	−0.671293
$866$	60.1476	2.04390
$867$	1.00000	0.0339618
$868$	0.249626	0.00847286
$869$	−27.6159	−0.936804
$870$	67.7106	2.29560
$871$	48.7246	1.65097
$872$	−13.1630	−0.445756
$873$	6.83225	0.231237
$874$	−8.20705	−0.277608
$875$	−1.57793	−0.0533436
$876$	−22.8464	−0.771908
$877$	−42.3697	−1.43072	−0.715362	−	0.698754i	$-0.753738\pi$
$877$	−42.3697	−1.43072	−0.715362	+	0.698754i	$0.753738\pi$
$878$	−8.31996	−0.280785
$879$	22.0683	0.744344
$880$	36.3310	1.22472
$881$	14.0307	0.472707	0.236354	−	0.971667i	$-0.424048\pi$
$881$	14.0307	0.472707	0.236354	+	0.971667i	$0.424048\pi$
$882$	14.7714	0.497380
$883$	−34.1366	−1.14879	−0.574395	−	0.818579i	$-0.694762\pi$
$883$	−34.1366	−1.14879	−0.574395	+	0.818579i	$0.694762\pi$
$884$	−8.59503	−0.289082
$885$	−3.97455	−0.133603
$886$	−44.2458	−1.48647
$887$	−6.24853	−0.209805	−0.104903	−	0.994483i	$-0.533453\pi$
$887$	−6.24853	−0.209805	−0.104903	+	0.994483i	$0.533453\pi$
$888$	0.304946	0.0102333
$889$	1.19289	0.0400083
$890$	−90.8457	−3.04515
$891$	3.28960	0.110206
$892$	19.4779	0.652168
$893$	45.1987	1.51252
$894$	−16.8464	−0.563427
$895$	35.3316	1.18101
$896$	0.636451	0.0212623
$897$	−2.86152	−0.0955432
$898$	−1.94778	−0.0649982
$899$	10.0572	0.335425
$900$	24.3299	0.810998
$901$	−1.20268	−0.0400669
$902$	−51.4341	−1.71257
$903$	0.662786	0.0220562
$904$	1.74496	0.0580364
$905$	82.7473	2.75061
$906$	3.02757	0.100584
$907$	−26.5967	−0.883127	−0.441564	−	0.897230i	$-0.645576\pi$
$907$	−26.5967	−0.883127	−0.441564	+	0.897230i	$0.645576\pi$
$908$	−19.4832	−0.646572
$909$	10.2117	0.338700
$910$	−2.38328	−0.0790051
$911$	40.9867	1.35795	0.678975	−	0.734161i	$-0.262424\pi$
$911$	40.9867	1.35795	0.678975	+	0.734161i	$0.262424\pi$
$912$	−13.5707	−0.449371
$913$	51.1920	1.69421
$914$	−59.4909	−1.96778
$915$	50.7254	1.67693
$916$	48.2360	1.59376
$917$	0.00808075	0.000266850 0
$918$	−2.11232	−0.0697170
$919$	35.2733	1.16356	0.581780	−	0.813346i	$-0.302357\pi$
$919$	35.2733	1.16356	0.581780	+	0.813346i	$0.302357\pi$
$920$	3.08513	0.101714
$921$	−9.48581	−0.312568
$922$	15.4495	0.508803
$923$	24.1873	0.796133
$924$	0.678446	0.0223192
$925$	−3.08871	−0.101556
$926$	32.7822	1.07729
$927$	3.79265	0.124567
$928$	66.4618	2.18172
$929$	−5.27974	−0.173223	−0.0866114	−	0.996242i	$-0.527604\pi$
$929$	−5.27974	−0.173223	−0.0866114	+	0.996242i	$0.527604\pi$
$930$	9.86317	0.323426
$931$	−33.1489	−1.08641
$932$	59.2535	1.94091
$933$	6.78881	0.222256
$934$	−75.7307	−2.47799
$935$	−12.6906	−0.415027
$936$	3.40636	0.111340
$937$	9.85356	0.321902	0.160951	−	0.986962i	$-0.448544\pi$
$937$	9.85356	0.321902	0.160951	+	0.986962i	$0.448544\pi$
$938$	2.46964	0.0806366
$939$	9.41729	0.307321
$940$	−90.5585	−2.95369
$941$	3.03598	0.0989701	0.0494851	−	0.998775i	$-0.484242\pi$
$941$	3.03598	0.0989701	0.0494851	+	0.998775i	$0.484242\pi$
$942$	−2.11232	−0.0688232
$943$	6.06692	0.197566
$944$	−2.94948	−0.0959973
$945$	−0.323176	−0.0105129
$946$	−54.9764	−1.78744
$947$	−2.51612	−0.0817630	−0.0408815	−	0.999164i	$-0.513017\pi$
$947$	−2.51612	−0.0817630	−0.0408815	+	0.999164i	$0.513017\pi$
$948$	−20.6675	−0.671248
$949$	32.3983	1.05169
$950$	−98.9547	−3.21051
$951$	−8.95658	−0.290437
$952$	−0.0817363	−0.00264909
$953$	−20.7319	−0.671571	−0.335785	−	0.941939i	$-0.609002\pi$
$953$	−20.7319	−0.671571	−0.335785	+	0.941939i	$0.609002\pi$
$954$	2.54044	0.0822497
$955$	4.77281	0.154444
$956$	−71.5604	−2.31443
$957$	27.3339	0.883578
$958$	−25.9279	−0.837693
$959$	0.129727	0.00418912
$960$	43.0915	1.39077
$961$	−29.5350	−0.952742
$962$	−2.30486	−0.0743117
$963$	−7.53774	−0.242900
$964$	−31.3190	−1.00872
$965$	−6.11686	−0.196909
$966$	−0.145038	−0.00466651
$967$	6.62227	0.212958	0.106479	−	0.994315i	$-0.466042\pi$
$967$	6.62227	0.212958	0.106479	+	0.994315i	$0.466042\pi$
$968$	0.174196	0.00559888
$969$	4.74031	0.152281
$970$	55.6753	1.78763
$971$	16.2706	0.522148	0.261074	−	0.965319i	$-0.415923\pi$
$971$	16.2706	0.522148	0.261074	+	0.965319i	$0.415923\pi$
$972$	2.46191	0.0789657
$973$	1.01005	0.0323808
$974$	−53.9589	−1.72895
$975$	−34.5021	−1.10495
$976$	37.6428	1.20492
$977$	−13.0246	−0.416694	−0.208347	−	0.978055i	$-0.566808\pi$
$977$	−13.0246	−0.416694	−0.208347	+	0.978055i	$0.566808\pi$
$978$	−20.6305	−0.659690
$979$	−36.6732	−1.17208
$980$	66.4160	2.12158
$981$	13.4909	0.430732
$982$	−39.5918	−1.26343
$983$	30.6327	0.977030	0.488515	−	0.872555i	$-0.337539\pi$
$983$	30.6327	0.977030	0.488515	+	0.872555i	$0.337539\pi$
$984$	−7.22208	−0.230231
$985$	54.8432	1.74745
$986$	−17.5517	−0.558959
$987$	0.798767	0.0254250
$988$	−40.7431	−1.29621
$989$	6.48474	0.206203
$990$	26.8066	0.851970
$991$	23.0228	0.731344	0.365672	−	0.930744i	$-0.380839\pi$
$991$	23.0228	0.731344	0.365672	+	0.930744i	$0.380839\pi$
$992$	9.68126	0.307380
$993$	0.761518	0.0241660
$994$	1.22595	0.0388847
$995$	64.0710	2.03119
$996$	38.3117	1.21395
$997$	40.2870	1.27590	0.637951	−	0.770077i	$-0.279782\pi$
$997$	40.2870	1.27590	0.637951	+	0.770077i	$0.279782\pi$
$998$	−26.2150	−0.829820
$999$	−0.312542	−0.00988839

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8007.2.a.i.1.10	✓	63

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8007.2.a.i.1.10	✓	63	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)

\(f(q)\)	\(=\)	\(q-2.11232 q^{2} +1.00000 q^{3} +2.46191 q^{4} -3.85779 q^{5} -2.11232 q^{6} +0.0837724 q^{7} -0.975695 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-2.11232 q^{2} +1.00000 q^{3} +2.46191 q^{4} -3.85779 q^{5} -2.11232 q^{6} +0.0837724 q^{7} -0.975695 q^{8} +1.00000 q^{9} +8.14890 q^{10} +3.28960 q^{11} +2.46191 q^{12} -3.49121 q^{13} -0.176954 q^{14} -3.85779 q^{15} -2.86283 q^{16} +1.00000 q^{17} -2.11232 q^{18} +4.74031 q^{19} -9.49752 q^{20} +0.0837724 q^{21} -6.94869 q^{22} +0.819634 q^{23} -0.975695 q^{24} +9.88256 q^{25} +7.37456 q^{26} +1.00000 q^{27} +0.206240 q^{28} +8.30917 q^{29} +8.14890 q^{30} +1.21037 q^{31} +7.99861 q^{32} +3.28960 q^{33} -2.11232 q^{34} -0.323176 q^{35} +2.46191 q^{36} -0.312542 q^{37} -10.0131 q^{38} -3.49121 q^{39} +3.76403 q^{40} +7.40198 q^{41} -0.176954 q^{42} +7.91175 q^{43} +8.09869 q^{44} -3.85779 q^{45} -1.73133 q^{46} +9.53497 q^{47} -2.86283 q^{48} -6.99298 q^{49} -20.8751 q^{50} +1.00000 q^{51} -8.59503 q^{52} -1.20268 q^{53} -2.11232 q^{54} -12.6906 q^{55} -0.0817363 q^{56} +4.74031 q^{57} -17.5517 q^{58} +1.03027 q^{59} -9.49752 q^{60} -13.1488 q^{61} -2.55669 q^{62} +0.0837724 q^{63} -11.1700 q^{64} +13.4684 q^{65} -6.94869 q^{66} -13.9564 q^{67} +2.46191 q^{68} +0.819634 q^{69} +0.682653 q^{70} -6.92804 q^{71} -0.975695 q^{72} -9.27996 q^{73} +0.660190 q^{74} +9.88256 q^{75} +11.6702 q^{76} +0.275578 q^{77} +7.37456 q^{78} -8.39490 q^{79} +11.0442 q^{80} +1.00000 q^{81} -15.6354 q^{82} +15.5618 q^{83} +0.206240 q^{84} -3.85779 q^{85} -16.7122 q^{86} +8.30917 q^{87} -3.20965 q^{88} -11.1482 q^{89} +8.14890 q^{90} -0.292467 q^{91} +2.01786 q^{92} +1.21037 q^{93} -20.1409 q^{94} -18.2871 q^{95} +7.99861 q^{96} +6.83225 q^{97} +14.7714 q^{98} +3.28960 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 63 q + 10 q^{2} + 63 q^{3} + 70 q^{4} + 19 q^{5} + 10 q^{6} + 11 q^{7} + 27 q^{8} + 63 q^{9}+O(q^{10}) \) 63 * q + 10 * q^2 + 63 * q^3 + 70 * q^4 + 19 * q^5 + 10 * q^6 + 11 * q^7 + 27 * q^8 + 63 * q^9	\( 63 q + 10 q^{2} + 63 q^{3} + 70 q^{4} + 19 q^{5} + 10 q^{6} + 11 q^{7} + 27 q^{8} + 63 q^{9} + 4 q^{10} + 23 q^{11} + 70 q^{12} + 10 q^{13} + 18 q^{14} + 19 q^{15} + 72 q^{16} + 63 q^{17} + 10 q^{18} + 6 q^{19} + 48 q^{20} + 11 q^{21} + 21 q^{22} + 44 q^{23} + 27 q^{24} + 110 q^{25} + 41 q^{26} + 63 q^{27} + 26 q^{28} + 35 q^{29} + 4 q^{30} + q^{31} + 54 q^{32} + 23 q^{33} + 10 q^{34} + 47 q^{35} + 70 q^{36} + 40 q^{37} + 38 q^{38} + 10 q^{39} - 10 q^{40} + 35 q^{41} + 18 q^{42} + 27 q^{43} + 46 q^{44} + 19 q^{45} + 8 q^{46} + 29 q^{47} + 72 q^{48} + 114 q^{49} + 27 q^{50} + 63 q^{51} - q^{52} + 75 q^{53} + 10 q^{54} + 5 q^{55} + 24 q^{56} + 6 q^{57} + 41 q^{58} + 105 q^{59} + 48 q^{60} + 5 q^{61} + 22 q^{62} + 11 q^{63} + 61 q^{64} + 49 q^{65} + 21 q^{66} + 4 q^{67} + 70 q^{68} + 44 q^{69} - 16 q^{70} + 16 q^{71} + 27 q^{72} + 39 q^{73} + 54 q^{74} + 110 q^{75} + 6 q^{76} + 88 q^{77} + 41 q^{78} + 16 q^{79} + 102 q^{80} + 63 q^{81} - 29 q^{82} + 73 q^{83} + 26 q^{84} + 19 q^{85} + 46 q^{86} + 35 q^{87} + 18 q^{88} + 88 q^{89} + 4 q^{90} - 15 q^{91} + 110 q^{92} + q^{93} - 8 q^{94} + 28 q^{95} + 54 q^{96} + 70 q^{97} + 33 q^{98} + 23 q^{99}+O(q^{100}) \) 63 * q + 10 * q^2 + 63 * q^3 + 70 * q^4 + 19 * q^5 + 10 * q^6 + 11 * q^7 + 27 * q^8 + 63 * q^9 + 4 * q^10 + 23 * q^11 + 70 * q^12 + 10 * q^13 + 18 * q^14 + 19 * q^15 + 72 * q^16 + 63 * q^17 + 10 * q^18 + 6 * q^19 + 48 * q^20 + 11 * q^21 + 21 * q^22 + 44 * q^23 + 27 * q^24 + 110 * q^25 + 41 * q^26 + 63 * q^27 + 26 * q^28 + 35 * q^29 + 4 * q^30 + q^31 + 54 * q^32 + 23 * q^33 + 10 * q^34 + 47 * q^35 + 70 * q^36 + 40 * q^37 + 38 * q^38 + 10 * q^39 - 10 * q^40 + 35 * q^41 + 18 * q^42 + 27 * q^43 + 46 * q^44 + 19 * q^45 + 8 * q^46 + 29 * q^47 + 72 * q^48 + 114 * q^49 + 27 * q^50 + 63 * q^51 - q^52 + 75 * q^53 + 10 * q^54 + 5 * q^55 + 24 * q^56 + 6 * q^57 + 41 * q^58 + 105 * q^59 + 48 * q^60 + 5 * q^61 + 22 * q^62 + 11 * q^63 + 61 * q^64 + 49 * q^65 + 21 * q^66 + 4 * q^67 + 70 * q^68 + 44 * q^69 - 16 * q^70 + 16 * q^71 + 27 * q^72 + 39 * q^73 + 54 * q^74 + 110 * q^75 + 6 * q^76 + 88 * q^77 + 41 * q^78 + 16 * q^79 + 102 * q^80 + 63 * q^81 - 29 * q^82 + 73 * q^83 + 26 * q^84 + 19 * q^85 + 46 * q^86 + 35 * q^87 + 18 * q^88 + 88 * q^89 + 4 * q^90 - 15 * q^91 + 110 * q^92 + q^93 - 8 * q^94 + 28 * q^95 + 54 * q^96 + 70 * q^97 + 33 * q^98 + 23 * q^99

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