LMFDB - Embedded newform 8007.2.a.j.1.38

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:	$64$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.38
Character	$\chi$	$=$	8007.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.613812 q^{2} -1.00000 q^{3} -1.62323 q^{4} -0.298819 q^{5} -0.613812 q^{6} -1.36057 q^{7} -2.22399 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+0.613812 q^{2} -1.00000 q^{3} -1.62323 q^{4} -0.298819 q^{5} -0.613812 q^{6} -1.36057 q^{7} -2.22399 q^{8} +1.00000 q^{9} -0.183419 q^{10} -3.42125 q^{11} +1.62323 q^{12} +5.58826 q^{13} -0.835137 q^{14} +0.298819 q^{15} +1.88136 q^{16} +1.00000 q^{17} +0.613812 q^{18} -6.24580 q^{19} +0.485053 q^{20} +1.36057 q^{21} -2.10000 q^{22} -0.595546 q^{23} +2.22399 q^{24} -4.91071 q^{25} +3.43015 q^{26} -1.00000 q^{27} +2.20853 q^{28} +7.05022 q^{29} +0.183419 q^{30} -8.38741 q^{31} +5.60277 q^{32} +3.42125 q^{33} +0.613812 q^{34} +0.406565 q^{35} -1.62323 q^{36} -5.81955 q^{37} -3.83375 q^{38} -5.58826 q^{39} +0.664570 q^{40} -0.519006 q^{41} +0.835137 q^{42} -0.288070 q^{43} +5.55349 q^{44} -0.298819 q^{45} -0.365554 q^{46} -2.20010 q^{47} -1.88136 q^{48} -5.14884 q^{49} -3.01425 q^{50} -1.00000 q^{51} -9.07106 q^{52} +1.17528 q^{53} -0.613812 q^{54} +1.02233 q^{55} +3.02590 q^{56} +6.24580 q^{57} +4.32751 q^{58} +2.57801 q^{59} -0.485053 q^{60} -3.34313 q^{61} -5.14830 q^{62} -1.36057 q^{63} -0.323664 q^{64} -1.66988 q^{65} +2.10000 q^{66} +12.1355 q^{67} -1.62323 q^{68} +0.595546 q^{69} +0.249555 q^{70} +1.21772 q^{71} -2.22399 q^{72} +0.366026 q^{73} -3.57211 q^{74} +4.91071 q^{75} +10.1384 q^{76} +4.65486 q^{77} -3.43015 q^{78} -11.2704 q^{79} -0.562186 q^{80} +1.00000 q^{81} -0.318572 q^{82} -3.58341 q^{83} -2.20853 q^{84} -0.298819 q^{85} -0.176821 q^{86} -7.05022 q^{87} +7.60881 q^{88} +0.160193 q^{89} -0.183419 q^{90} -7.60324 q^{91} +0.966711 q^{92} +8.38741 q^{93} -1.35045 q^{94} +1.86637 q^{95} -5.60277 q^{96} +4.26862 q^{97} -3.16042 q^{98} -3.42125 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q + 5 q^{2} - 64 q^{3} + 77 q^{4} - 3 q^{5} - 5 q^{6} + 5 q^{7} + 18 q^{8} + 64 q^{9}+O(q^{10}) $ 64 * q + 5 * q^2 - 64 * q^3 + 77 * q^4 - 3 * q^5 - 5 * q^6 + 5 * q^7 + 18 * q^8 + 64 * q^9	\( 64 q + 5 q^{2} - 64 q^{3} + 77 q^{4} - 3 q^{5} - 5 q^{6} + 5 q^{7} + 18 q^{8} + 64 q^{9} + 12 q^{10} - 7 q^{11} - 77 q^{12} + 24 q^{13} - 14 q^{14} + 3 q^{15} + 103 q^{16} + 64 q^{17} + 5 q^{18} + 26 q^{19} - 24 q^{20} - 5 q^{21} + 25 q^{22} + 20 q^{23} - 18 q^{24} + 141 q^{25} + 9 q^{26} - 64 q^{27} + 14 q^{28} + 5 q^{29} - 12 q^{30} + 11 q^{31} + 31 q^{32} + 7 q^{33} + 5 q^{34} - 3 q^{35} + 77 q^{36} + 50 q^{37} + 8 q^{38} - 24 q^{39} + 28 q^{40} - 9 q^{41} + 14 q^{42} + 59 q^{43} - 6 q^{44} - 3 q^{45} + 11 q^{47} - 103 q^{48} + 163 q^{49} + 20 q^{50} - 64 q^{51} + 65 q^{52} + 39 q^{53} - 5 q^{54} + 35 q^{55} - 34 q^{56} - 26 q^{57} - 27 q^{58} - 65 q^{59} + 24 q^{60} + 15 q^{61} + 18 q^{62} + 5 q^{63} + 152 q^{64} + 49 q^{65} - 25 q^{66} + 56 q^{67} + 77 q^{68} - 20 q^{69} + 28 q^{70} - 18 q^{71} + 18 q^{72} + 37 q^{73} - 76 q^{74} - 141 q^{75} + 30 q^{76} + 80 q^{77} - 9 q^{78} + 20 q^{79} - 144 q^{80} + 64 q^{81} + 27 q^{82} + 3 q^{83} - 14 q^{84} - 3 q^{85} + 12 q^{86} - 5 q^{87} + 108 q^{88} + 42 q^{89} + 12 q^{90} + 25 q^{91} + 18 q^{92} - 11 q^{93} + 60 q^{94} + 42 q^{95} - 31 q^{96} + 72 q^{97} + 18 q^{98} - 7 q^{99}+O(q^{100}) \) 64 * q + 5 * q^2 - 64 * q^3 + 77 * q^4 - 3 * q^5 - 5 * q^6 + 5 * q^7 + 18 * q^8 + 64 * q^9 + 12 * q^10 - 7 * q^11 - 77 * q^12 + 24 * q^13 - 14 * q^14 + 3 * q^15 + 103 * q^16 + 64 * q^17 + 5 * q^18 + 26 * q^19 - 24 * q^20 - 5 * q^21 + 25 * q^22 + 20 * q^23 - 18 * q^24 + 141 * q^25 + 9 * q^26 - 64 * q^27 + 14 * q^28 + 5 * q^29 - 12 * q^30 + 11 * q^31 + 31 * q^32 + 7 * q^33 + 5 * q^34 - 3 * q^35 + 77 * q^36 + 50 * q^37 + 8 * q^38 - 24 * q^39 + 28 * q^40 - 9 * q^41 + 14 * q^42 + 59 * q^43 - 6 * q^44 - 3 * q^45 + 11 * q^47 - 103 * q^48 + 163 * q^49 + 20 * q^50 - 64 * q^51 + 65 * q^52 + 39 * q^53 - 5 * q^54 + 35 * q^55 - 34 * q^56 - 26 * q^57 - 27 * q^58 - 65 * q^59 + 24 * q^60 + 15 * q^61 + 18 * q^62 + 5 * q^63 + 152 * q^64 + 49 * q^65 - 25 * q^66 + 56 * q^67 + 77 * q^68 - 20 * q^69 + 28 * q^70 - 18 * q^71 + 18 * q^72 + 37 * q^73 - 76 * q^74 - 141 * q^75 + 30 * q^76 + 80 * q^77 - 9 * q^78 + 20 * q^79 - 144 * q^80 + 64 * q^81 + 27 * q^82 + 3 * q^83 - 14 * q^84 - 3 * q^85 + 12 * q^86 - 5 * q^87 + 108 * q^88 + 42 * q^89 + 12 * q^90 + 25 * q^91 + 18 * q^92 - 11 * q^93 + 60 * q^94 + 42 * q^95 - 31 * q^96 + 72 * q^97 + 18 * q^98 - 7 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	0.613812	0.434031	0.217015	−	0.976168i	$-0.430368\pi$
$2$	0.613812	0.434031	0.217015	+	0.976168i	$0.430368\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	−1.62323	−0.811617
$5$	−0.298819	−0.133636	−0.0668180	−	0.997765i	$-0.521285\pi$
$5$	−0.298819	−0.133636	−0.0668180	+	0.997765i	$0.521285\pi$
$6$	−0.613812	−0.250588
$7$	−1.36057	−0.514248	−0.257124	−	0.966378i	$-0.582775\pi$
$7$	−1.36057	−0.514248	−0.257124	+	0.966378i	$0.582775\pi$
$8$	−2.22399	−0.786298
$9$	1.00000	0.333333
$10$	−0.183419	−0.0580021
$11$	−3.42125	−1.03154	−0.515772	−	0.856726i	$-0.672495\pi$
$11$	−3.42125	−1.03154	−0.515772	+	0.856726i	$0.672495\pi$
$12$	1.62323	0.468587
$13$	5.58826	1.54991	0.774953	−	0.632019i	$-0.217774\pi$
$13$	5.58826	1.54991	0.774953	+	0.632019i	$0.217774\pi$
$14$	−0.835137	−0.223200
$15$	0.298819	0.0771548
$16$	1.88136	0.470340
$17$	1.00000	0.242536
$17$	1.00000	0.242536
$18$	0.613812	0.144677
$19$	−6.24580	−1.43289	−0.716443	−	0.697646i	$-0.754231\pi$
$19$	−6.24580	−1.43289	−0.716443	+	0.697646i	$0.754231\pi$
$20$	0.485053	0.108461
$21$	1.36057	0.296901
$22$	−2.10000	−0.447722
$23$	−0.595546	−0.124180	−0.0620900	−	0.998071i	$-0.519777\pi$
$23$	−0.595546	−0.124180	−0.0620900	+	0.998071i	$0.519777\pi$
$24$	2.22399	0.453969
$25$	−4.91071	−0.982141
$26$	3.43015	0.672707
$27$	−1.00000	−0.192450
$28$	2.20853	0.417373
$29$	7.05022	1.30919	0.654596	−	0.755979i	$-0.272839\pi$
$29$	7.05022	1.30919	0.654596	+	0.755979i	$0.272839\pi$
$30$	0.183419	0.0334876
$31$	−8.38741	−1.50642	−0.753212	−	0.657778i	$-0.771497\pi$
$31$	−8.38741	−1.50642	−0.753212	+	0.657778i	$0.771497\pi$
$32$	5.60277	0.990440
$33$	3.42125	0.595563
$34$	0.613812	0.105268
$35$	0.406565	0.0687221
$36$	−1.62323	−0.270539
$37$	−5.81955	−0.956728	−0.478364	−	0.878162i	$-0.658770\pi$
$37$	−5.81955	−0.956728	−0.478364	+	0.878162i	$0.658770\pi$
$38$	−3.83375	−0.621917
$39$	−5.58826	−0.894838
$40$	0.664570	0.105078
$41$	−0.519006	−0.0810551	−0.0405275	−	0.999178i	$-0.512904\pi$
$41$	−0.519006	−0.0810551	−0.0405275	+	0.999178i	$0.512904\pi$
$42$	0.835137	0.128864
$43$	−0.288070	−0.0439303	−0.0219652	−	0.999759i	$-0.506992\pi$
$43$	−0.288070	−0.0439303	−0.0219652	+	0.999759i	$0.506992\pi$
$44$	5.55349	0.837219
$45$	−0.298819	−0.0445453
$46$	−0.365554	−0.0538980
$47$	−2.20010	−0.320918	−0.160459	−	0.987043i	$-0.551297\pi$
$47$	−2.20010	−0.320918	−0.160459	+	0.987043i	$0.551297\pi$
$48$	−1.88136	−0.271551
$49$	−5.14884	−0.735549
$50$	−3.01425	−0.426280
$51$	−1.00000	−0.140028
$52$	−9.07106	−1.25793
$53$	1.17528	0.161437	0.0807185	−	0.996737i	$-0.474279\pi$
$53$	1.17528	0.161437	0.0807185	+	0.996737i	$0.474279\pi$
$54$	−0.613812	−0.0835293
$55$	1.02233	0.137852
$56$	3.02590	0.404352
$57$	6.24580	0.827277
$58$	4.32751	0.568230
$59$	2.57801	0.335629	0.167814	−	0.985819i	$-0.446329\pi$
$59$	2.57801	0.335629	0.167814	+	0.985819i	$0.446329\pi$
$60$	−0.485053	−0.0626201
$61$	−3.34313	−0.428043	−0.214022	−	0.976829i	$-0.568656\pi$
$61$	−3.34313	−0.428043	−0.214022	+	0.976829i	$0.568656\pi$
$62$	−5.14830	−0.653835
$63$	−1.36057	−0.171416
$64$	−0.323664	−0.0404581
$65$	−1.66988	−0.207123
$66$	2.10000	0.258493
$67$	12.1355	1.48259	0.741296	−	0.671178i	$-0.234211\pi$
$67$	12.1355	1.48259	0.741296	+	0.671178i	$0.234211\pi$
$68$	−1.62323	−0.196846
$69$	0.595546	0.0716954
$70$	0.249555	0.0298275
$71$	1.21772	0.144517	0.0722583	−	0.997386i	$-0.476979\pi$
$71$	1.21772	0.144517	0.0722583	+	0.997386i	$0.476979\pi$
$72$	−2.22399	−0.262099
$73$	0.366026	0.0428401	0.0214201	−	0.999771i	$-0.493181\pi$
$73$	0.366026	0.0428401	0.0214201	+	0.999771i	$0.493181\pi$
$74$	−3.57211	−0.415250
$75$	4.91071	0.567040
$76$	10.1384	1.16295
$77$	4.65486	0.530470
$78$	−3.43015	−0.388388
$79$	−11.2704	−1.26802	−0.634012	−	0.773323i	$-0.718593\pi$
$79$	−11.2704	−1.26802	−0.634012	+	0.773323i	$0.718593\pi$
$80$	−0.562186	−0.0628543
$81$	1.00000	0.111111
$82$	−0.318572	−0.0351804
$83$	−3.58341	−0.393330	−0.196665	−	0.980471i	$-0.563011\pi$
$83$	−3.58341	−0.393330	−0.196665	+	0.980471i	$0.563011\pi$
$84$	−2.20853	−0.240970
$85$	−0.298819	−0.0324115
$86$	−0.176821	−0.0190671
$87$	−7.05022	−0.755862
$88$	7.60881	0.811102
$89$	0.160193	0.0169804	0.00849020	−	0.999964i	$-0.497297\pi$
$89$	0.160193	0.0169804	0.00849020	+	0.999964i	$0.497297\pi$
$90$	−0.183419	−0.0193340
$91$	−7.60324	−0.797036
$92$	0.966711	0.100787
$93$	8.38741	0.869734
$94$	−1.35045	−0.139288
$95$	1.86637	0.191485
$96$	−5.60277	−0.571831
$97$	4.26862	0.433413	0.216706	−	0.976237i	$-0.430469\pi$
$97$	4.26862	0.433413	0.216706	+	0.976237i	$0.430469\pi$
$98$	−3.16042	−0.319251
$99$	−3.42125	−0.343848
$100$	7.97123	0.797123
$101$	−13.3910	−1.33246	−0.666229	−	0.745748i	$-0.732093\pi$
$101$	−13.3910	−1.33246	−0.666229	+	0.745748i	$0.732093\pi$
$102$	−0.613812	−0.0607765
$103$	−13.5499	−1.33511	−0.667554	−	0.744561i	$-0.732659\pi$
$103$	−13.5499	−1.33511	−0.667554	+	0.744561i	$0.732659\pi$
$104$	−12.4282	−1.21869
$105$	−0.406565	−0.0396767
$106$	0.721401	0.0700686
$107$	−10.1373	−0.980011	−0.490005	−	0.871719i	$-0.663005\pi$
$107$	−10.1373	−0.980011	−0.490005	+	0.871719i	$0.663005\pi$
$108$	1.62323	0.156196
$109$	11.1864	1.07146	0.535731	−	0.844389i	$-0.320036\pi$
$109$	11.1864	1.07146	0.535731	+	0.844389i	$0.320036\pi$
$110$	0.627521	0.0598318
$111$	5.81955	0.552367
$112$	−2.55973	−0.241871
$113$	−11.2084	−1.05440	−0.527198	−	0.849743i	$-0.676757\pi$
$113$	−11.2084	−1.05440	−0.527198	+	0.849743i	$0.676757\pi$
$114$	3.83375	0.359064
$115$	0.177961	0.0165949
$116$	−11.4442	−1.06256
$117$	5.58826	0.516635
$118$	1.58242	0.145673
$119$	−1.36057	−0.124724
$120$	−0.664570	−0.0606666
$121$	0.704932	0.0640847
$122$	−2.05205	−0.185784
$123$	0.519006	0.0467972
$124$	13.6147	1.22264
$125$	2.96151	0.264885
$126$	−0.835137	−0.0743999
$127$	3.16937	0.281236	0.140618	−	0.990064i	$-0.455091\pi$
$127$	3.16937	0.281236	0.140618	+	0.990064i	$0.455091\pi$
$128$	−11.4042	−1.00800
$129$	0.288070	0.0253632
$130$	−1.02499	−0.0898978
$131$	0.442638	0.0386735	0.0193367	−	0.999813i	$-0.493845\pi$
$131$	0.442638	0.0386735	0.0193367	+	0.999813i	$0.493845\pi$
$132$	−5.55349	−0.483369
$133$	8.49787	0.736859
$134$	7.44895	0.643491
$135$	0.298819	0.0257183
$136$	−2.22399	−0.190705
$137$	14.2155	1.21451	0.607256	−	0.794507i	$-0.292270\pi$
$137$	14.2155	1.21451	0.607256	+	0.794507i	$0.292270\pi$
$138$	0.365554	0.0311180
$139$	−6.78299	−0.575326	−0.287663	−	0.957732i	$-0.592878\pi$
$139$	−6.78299	−0.575326	−0.287663	+	0.957732i	$0.592878\pi$
$140$	−0.659951	−0.0557760
$141$	2.20010	0.185282
$142$	0.747451	0.0627247
$143$	−19.1188	−1.59880
$144$	1.88136	0.156780
$145$	−2.10674	−0.174955
$146$	0.224671	0.0185939
$147$	5.14884	0.424669
$148$	9.44649	0.776497
$149$	6.53198	0.535121	0.267560	−	0.963541i	$-0.413783\pi$
$149$	6.53198	0.535121	0.267560	+	0.963541i	$0.413783\pi$
$150$	3.01425	0.246113
$151$	16.8971	1.37506	0.687532	−	0.726154i	$-0.258694\pi$
$151$	16.8971	1.37506	0.687532	+	0.726154i	$0.258694\pi$
$152$	13.8906	1.12668
$153$	1.00000	0.0808452
$154$	2.85721	0.230240
$155$	2.50632	0.201312
$156$	9.07106	0.726266
$157$	−1.00000	−0.0798087
$157$	−1.00000	−0.0798087
$158$	−6.91794	−0.550362
$159$	−1.17528	−0.0932056
$160$	−1.67422	−0.132358
$161$	0.810284	0.0638594
$162$	0.613812	0.0482257
$163$	−6.04172	−0.473224	−0.236612	−	0.971604i	$-0.576037\pi$
$163$	−6.04172	−0.473224	−0.236612	+	0.971604i	$0.576037\pi$
$164$	0.842468	0.0657857
$165$	−1.02233	−0.0795886
$166$	−2.19954	−0.170717
$167$	−5.38633	−0.416807	−0.208403	−	0.978043i	$-0.566827\pi$
$167$	−5.38633	−0.416807	−0.208403	+	0.978043i	$0.566827\pi$
$168$	−3.02590	−0.233453
$169$	18.2287	1.40221
$170$	−0.183419	−0.0140676
$171$	−6.24580	−0.477629
$172$	0.467606	0.0356546
$173$	7.51730	0.571529	0.285765	−	0.958300i	$-0.407752\pi$
$173$	7.51730	0.571529	0.285765	+	0.958300i	$0.407752\pi$
$174$	−4.32751	−0.328068
$175$	6.68138	0.505065
$176$	−6.43659	−0.485176
$177$	−2.57801	−0.193775
$178$	0.0983283	0.00737002
$179$	5.84744	0.437058	0.218529	−	0.975830i	$-0.429874\pi$
$179$	5.84744	0.437058	0.218529	+	0.975830i	$0.429874\pi$
$180$	0.485053	0.0361538
$181$	7.62500	0.566762	0.283381	−	0.959007i	$-0.408544\pi$
$181$	7.62500	0.566762	0.283381	+	0.959007i	$0.408544\pi$
$182$	−4.66696	−0.345938
$183$	3.34313	0.247131
$184$	1.32449	0.0976425
$185$	1.73899	0.127853
$186$	5.14830	0.377492
$187$	−3.42125	−0.250186
$188$	3.57128	0.260462
$189$	1.36057	0.0989671
$190$	1.14560	0.0831105
$191$	15.6080	1.12935	0.564676	−	0.825312i	$-0.309001\pi$
$191$	15.6080	1.12935	0.564676	+	0.825312i	$0.309001\pi$
$192$	0.323664	0.0233585
$193$	11.8956	0.856262	0.428131	−	0.903717i	$-0.359172\pi$
$193$	11.8956	0.856262	0.428131	+	0.903717i	$0.359172\pi$
$194$	2.62013	0.188114
$195$	1.66988	0.119583
$196$	8.35777	0.596984
$197$	−2.59316	−0.184755	−0.0923777	−	0.995724i	$-0.529447\pi$
$197$	−2.59316	−0.184755	−0.0923777	+	0.995724i	$0.529447\pi$
$198$	−2.10000	−0.149241
$199$	12.5930	0.892697	0.446348	−	0.894859i	$-0.352724\pi$
$199$	12.5930	0.892697	0.446348	+	0.894859i	$0.352724\pi$
$200$	10.9213	0.772256
$201$	−12.1355	−0.855975
$202$	−8.21958	−0.578328
$203$	−9.59233	−0.673250
$204$	1.62323	0.113649
$205$	0.155089	0.0108319
$206$	−8.31708	−0.579478
$207$	−0.595546	−0.0413933
$208$	10.5135	0.728982
$209$	21.3684	1.47809
$210$	−0.249555	−0.0172209
$211$	27.4150	1.88733	0.943663	−	0.330907i	$-0.107355\pi$
$211$	27.4150	1.88733	0.943663	+	0.330907i	$0.107355\pi$
$212$	−1.90775	−0.131025
$213$	−1.21772	−0.0834367
$214$	−6.22241	−0.425355
$215$	0.0860809	0.00587067
$216$	2.22399	0.151323
$217$	11.4117	0.774676
$218$	6.86634	0.465048
$219$	−0.366026	−0.0247338
$220$	−1.65949	−0.111883
$221$	5.58826	0.375907
$222$	3.57211	0.239744
$223$	−4.47356	−0.299572	−0.149786	−	0.988718i	$-0.547858\pi$
$223$	−4.47356	−0.299572	−0.149786	+	0.988718i	$0.547858\pi$
$224$	−7.62298	−0.509332
$225$	−4.91071	−0.327380
$226$	−6.87984	−0.457640
$227$	−20.2353	−1.34307	−0.671534	−	0.740974i	$-0.734364\pi$
$227$	−20.2353	−1.34307	−0.671534	+	0.740974i	$0.734364\pi$
$228$	−10.1384	−0.671432
$229$	2.40649	0.159025	0.0795127	−	0.996834i	$-0.474664\pi$
$229$	2.40649	0.159025	0.0795127	+	0.996834i	$0.474664\pi$
$230$	0.109234	0.00720271
$231$	−4.65486	−0.306267
$232$	−15.6796	−1.02942
$233$	−1.57721	−0.103326	−0.0516631	−	0.998665i	$-0.516452\pi$
$233$	−1.57721	−0.103326	−0.0516631	+	0.998665i	$0.516452\pi$
$234$	3.43015	0.224236
$235$	0.657432	0.0428862
$236$	−4.18472	−0.272402
$237$	11.2704	0.732094
$238$	−0.835137	−0.0541339
$239$	−11.2427	−0.727233	−0.363616	−	0.931549i	$-0.618458\pi$
$239$	−11.2427	−0.727233	−0.363616	+	0.931549i	$0.618458\pi$
$240$	0.562186	0.0362889
$241$	−0.135953	−0.00875750	−0.00437875	−	0.999990i	$-0.501394\pi$
$241$	−0.135953	−0.00875750	−0.00437875	+	0.999990i	$0.501394\pi$
$242$	0.432696	0.0278148
$243$	−1.00000	−0.0641500
$244$	5.42668	0.347407
$245$	1.53857	0.0982958
$246$	0.318572	0.0203114
$247$	−34.9032	−2.22084
$248$	18.6535	1.18450
$249$	3.58341	0.227089
$250$	1.81781	0.114968
$251$	16.8998	1.06671	0.533354	−	0.845892i	$-0.320932\pi$
$251$	16.8998	1.06671	0.533354	+	0.845892i	$0.320932\pi$
$252$	2.20853	0.139124
$253$	2.03751	0.128097
$254$	1.94540	0.122065
$255$	0.298819	0.0187128
$256$	−6.35272	−0.397045
$257$	−17.8296	−1.11218	−0.556090	−	0.831122i	$-0.687699\pi$
$257$	−17.8296	−1.11218	−0.556090	+	0.831122i	$0.687699\pi$
$258$	0.176821	0.0110084
$259$	7.91792	0.491996
$260$	2.71061	0.168105
$261$	7.05022	0.436397
$262$	0.271697	0.0167855
$263$	18.7908	1.15869	0.579344	−	0.815083i	$-0.303309\pi$
$263$	18.7908	1.15869	0.579344	+	0.815083i	$0.303309\pi$
$264$	−7.60881	−0.468290
$265$	−0.351196	−0.0215738
$266$	5.21610	0.319820
$267$	−0.160193	−0.00980364
$268$	−19.6988	−1.20330
$269$	17.3736	1.05928	0.529642	−	0.848221i	$-0.322326\pi$
$269$	17.3736	1.05928	0.529642	+	0.848221i	$0.322326\pi$
$270$	0.183419	0.0111625
$271$	22.7824	1.38393	0.691967	−	0.721929i	$-0.256744\pi$
$271$	22.7824	1.38393	0.691967	+	0.721929i	$0.256744\pi$
$272$	1.88136	0.114074
$273$	7.60324	0.460169
$274$	8.72564	0.527135
$275$	16.8007	1.01312
$276$	−0.966711	−0.0581892
$277$	14.8232	0.890640	0.445320	−	0.895371i	$-0.353090\pi$
$277$	14.8232	0.890640	0.445320	+	0.895371i	$0.353090\pi$
$278$	−4.16348	−0.249709
$279$	−8.38741	−0.502141
$280$	−0.904196	−0.0540360
$281$	−3.12110	−0.186189	−0.0930945	−	0.995657i	$-0.529676\pi$
$281$	−3.12110	−0.186189	−0.0930945	+	0.995657i	$0.529676\pi$
$282$	1.35045	0.0804181
$283$	5.03458	0.299275	0.149637	−	0.988741i	$-0.452189\pi$
$283$	5.03458	0.299275	0.149637	+	0.988741i	$0.452189\pi$
$284$	−1.97664	−0.117292
$285$	−1.86637	−0.110554
$286$	−11.7354	−0.693927
$287$	0.706145	0.0416824
$288$	5.60277	0.330147
$289$	1.00000	0.0588235
$290$	−1.29314	−0.0759360
$291$	−4.26862	−0.250231
$292$	−0.594146	−0.0347698
$293$	−5.43694	−0.317629	−0.158815	−	0.987308i	$-0.550767\pi$
$293$	−5.43694	−0.317629	−0.158815	+	0.987308i	$0.550767\pi$
$294$	3.16042	0.184320
$295$	−0.770360	−0.0448521
$296$	12.9426	0.752273
$297$	3.42125	0.198521
$298$	4.00941	0.232259
$299$	−3.32807	−0.192467
$300$	−7.97123	−0.460219
$301$	0.391941	0.0225911
$302$	10.3716	0.596821
$303$	13.3910	0.769295
$304$	−11.7506	−0.673943
$305$	0.998990	0.0572020
$306$	0.613812	0.0350893
$307$	33.8884	1.93412	0.967058	−	0.254557i	$-0.0819296\pi$
$307$	33.8884	1.93412	0.967058	+	0.254557i	$0.0819296\pi$
$308$	−7.55592	−0.430539
$309$	13.5499	0.770825
$310$	1.53841	0.0873758
$311$	25.9832	1.47337	0.736687	−	0.676234i	$-0.236389\pi$
$311$	25.9832	1.47337	0.736687	+	0.676234i	$0.236389\pi$
$312$	12.4282	0.703610
$313$	2.57629	0.145621	0.0728104	−	0.997346i	$-0.476803\pi$
$313$	2.57629	0.145621	0.0728104	+	0.997346i	$0.476803\pi$
$314$	−0.613812	−0.0346394
$315$	0.406565	0.0229074
$316$	18.2946	1.02915
$317$	26.0064	1.46066	0.730332	−	0.683093i	$-0.239366\pi$
$317$	26.0064	1.46066	0.730332	+	0.683093i	$0.239366\pi$
$318$	−0.721401	−0.0404541
$319$	−24.1205	−1.35049
$320$	0.0967171	0.00540665
$321$	10.1373	0.565810
$322$	0.497363	0.0277169
$323$	−6.24580	−0.347526
$324$	−1.62323	−0.0901797
$325$	−27.4423	−1.52223
$326$	−3.70848	−0.205394
$327$	−11.1864	−0.618609
$328$	1.15426	0.0637334
$329$	2.99340	0.165031
$330$	−0.627521	−0.0345439
$331$	13.9238	0.765322	0.382661	−	0.923889i	$-0.375008\pi$
$331$	13.9238	0.765322	0.382661	+	0.923889i	$0.375008\pi$
$332$	5.81671	0.319233
$333$	−5.81955	−0.318909
$334$	−3.30620	−0.180907
$335$	−3.62633	−0.198128
$336$	2.55973	0.139644
$337$	15.0475	0.819690	0.409845	−	0.912155i	$-0.365583\pi$
$337$	15.0475	0.819690	0.409845	+	0.912155i	$0.365583\pi$
$338$	11.1890	0.608601
$339$	11.2084	0.608755
$340$	0.485053	0.0263057
$341$	28.6954	1.55394
$342$	−3.83375	−0.207306
$343$	16.5294	0.892503
$344$	0.640664	0.0345423
$345$	−0.177961	−0.00958108
$346$	4.61421	0.248061
$347$	−28.5689	−1.53366	−0.766830	−	0.641850i	$-0.778167\pi$
$347$	−28.5689	−1.53366	−0.766830	+	0.641850i	$0.778167\pi$
$348$	11.4442	0.613471
$349$	−9.17373	−0.491059	−0.245529	−	0.969389i	$-0.578962\pi$
$349$	−9.17373	−0.491059	−0.245529	+	0.969389i	$0.578962\pi$
$350$	4.10111	0.219214
$351$	−5.58826	−0.298279
$352$	−19.1685	−1.02168
$353$	−4.73786	−0.252171	−0.126085	−	0.992019i	$-0.540241\pi$
$353$	−4.73786	−0.252171	−0.126085	+	0.992019i	$0.540241\pi$
$354$	−1.58242	−0.0841045
$355$	−0.363878	−0.0193126
$356$	−0.260030	−0.0137816
$357$	1.36057	0.0720092
$358$	3.58923	0.189697
$359$	−13.9671	−0.737158	−0.368579	−	0.929596i	$-0.620156\pi$
$359$	−13.9671	−0.737158	−0.368579	+	0.929596i	$0.620156\pi$
$360$	0.664570	0.0350259
$361$	20.0101	1.05316
$362$	4.68032	0.245992
$363$	−0.704932	−0.0369993
$364$	12.3418	0.646888
$365$	−0.109376	−0.00572498
$366$	2.05205	0.107262
$367$	12.4589	0.650350	0.325175	−	0.945654i	$-0.394577\pi$
$367$	12.4589	0.650350	0.325175	+	0.945654i	$0.394577\pi$
$368$	−1.12044	−0.0584068
$369$	−0.519006	−0.0270184
$370$	1.06742	0.0554923
$371$	−1.59905	−0.0830187
$372$	−13.6147	−0.705891
$373$	16.3707	0.847645	0.423822	−	0.905745i	$-0.360688\pi$
$373$	16.3707	0.847645	0.423822	+	0.905745i	$0.360688\pi$
$374$	−2.10000	−0.108589
$375$	−2.96151	−0.152932
$376$	4.89299	0.252337
$377$	39.3985	2.02912
$378$	0.835137	0.0429548
$379$	−28.2508	−1.45115	−0.725574	−	0.688144i	$-0.758426\pi$
$379$	−28.2508	−1.45115	−0.725574	+	0.688144i	$0.758426\pi$
$380$	−3.02955	−0.155413
$381$	−3.16937	−0.162372
$382$	9.58037	0.490174
$383$	−4.70747	−0.240540	−0.120270	−	0.992741i	$-0.538376\pi$
$383$	−4.70747	−0.240540	−0.120270	+	0.992741i	$0.538376\pi$
$384$	11.4042	0.581969
$385$	−1.39096	−0.0708899
$386$	7.30165	0.371644
$387$	−0.288070	−0.0146434
$388$	−6.92897	−0.351765
$389$	38.6909	1.96171	0.980854	−	0.194744i	$-0.0623875\pi$
$389$	38.6909	1.96171	0.980854	+	0.194744i	$0.0623875\pi$
$390$	1.02499	0.0519025
$391$	−0.595546	−0.0301181
$392$	11.4510	0.578360
$393$	−0.442638	−0.0223281
$394$	−1.59172	−0.0801895
$395$	3.36783	0.169454
$396$	5.55349	0.279073
$397$	−6.71759	−0.337146	−0.168573	−	0.985689i	$-0.553916\pi$
$397$	−6.71759	−0.337146	−0.168573	+	0.985689i	$0.553916\pi$
$398$	7.72976	0.387458
$399$	−8.49787	−0.425426
$400$	−9.23880	−0.461940
$401$	−20.1977	−1.00863	−0.504314	−	0.863521i	$-0.668254\pi$
$401$	−20.1977	−1.00863	−0.504314	+	0.863521i	$0.668254\pi$
$402$	−7.44895	−0.371520
$403$	−46.8711	−2.33481
$404$	21.7368	1.08145
$405$	−0.298819	−0.0148484
$406$	−5.88789	−0.292211
$407$	19.9101	0.986908
$408$	2.22399	0.110104
$409$	13.4454	0.664832	0.332416	−	0.943133i	$-0.392136\pi$
$409$	13.4454	0.664832	0.332416	+	0.943133i	$0.392136\pi$
$410$	0.0951954	0.00470137
$411$	−14.2155	−0.701198
$412$	21.9946	1.08360
$413$	−3.50758	−0.172597
$414$	−0.365554	−0.0179660
$415$	1.07079	0.0525630
$416$	31.3098	1.53509
$417$	6.78299	0.332164
$418$	13.1162	0.641535
$419$	12.6399	0.617500	0.308750	−	0.951143i	$-0.400089\pi$
$419$	12.6399	0.617500	0.308750	+	0.951143i	$0.400089\pi$
$420$	0.659951	0.0322023
$421$	28.4270	1.38545	0.692723	−	0.721204i	$-0.256411\pi$
$421$	28.4270	1.38545	0.692723	+	0.721204i	$0.256411\pi$
$422$	16.8277	0.819158
$423$	−2.20010	−0.106973
$424$	−2.61380	−0.126937
$425$	−4.91071	−0.238204
$426$	−0.747451	−0.0362141
$427$	4.54857	0.220121
$428$	16.4552	0.795394
$429$	19.1188	0.923066
$430$	0.0528375	0.00254805
$431$	8.25242	0.397505	0.198753	−	0.980050i	$-0.436311\pi$
$431$	8.25242	0.397505	0.198753	+	0.980050i	$0.436311\pi$
$432$	−1.88136	−0.0905169
$433$	3.78492	0.181892	0.0909458	−	0.995856i	$-0.471011\pi$
$433$	3.78492	0.181892	0.0909458	+	0.995856i	$0.471011\pi$
$434$	7.00464	0.336233
$435$	2.10674	0.101010
$436$	−18.1581	−0.869617
$437$	3.71967	0.177936
$438$	−0.224671	−0.0107352
$439$	−29.7149	−1.41821	−0.709107	−	0.705101i	$-0.750902\pi$
$439$	−29.7149	−1.41821	−0.709107	+	0.705101i	$0.750902\pi$
$440$	−2.27366	−0.108392
$441$	−5.14884	−0.245183
$442$	3.43015	0.163155
$443$	−22.8014	−1.08333	−0.541664	−	0.840595i	$-0.682206\pi$
$443$	−22.8014	−1.08333	−0.541664	+	0.840595i	$0.682206\pi$
$444$	−9.44649	−0.448311
$445$	−0.0478687	−0.00226919
$446$	−2.74593	−0.130023
$447$	−6.53198	−0.308952
$448$	0.440369	0.0208055
$449$	15.6611	0.739095	0.369548	−	0.929212i	$-0.379513\pi$
$449$	15.6611	0.739095	0.369548	+	0.929212i	$0.379513\pi$
$450$	−3.01425	−0.142093
$451$	1.77565	0.0836119
$452$	18.1938	0.855765
$453$	−16.8971	−0.793894
$454$	−12.4207	−0.582933
$455$	2.27199	0.106513
$456$	−13.8906	−0.650486
$457$	9.69641	0.453579	0.226789	−	0.973944i	$-0.427177\pi$
$457$	9.69641	0.453579	0.226789	+	0.973944i	$0.427177\pi$
$458$	1.47713	0.0690219
$459$	−1.00000	−0.0466760
$460$	−0.288872	−0.0134687
$461$	−11.9916	−0.558503	−0.279252	−	0.960218i	$-0.590086\pi$
$461$	−11.9916	−0.558503	−0.279252	+	0.960218i	$0.590086\pi$
$462$	−2.85721	−0.132929
$463$	8.50727	0.395366	0.197683	−	0.980266i	$-0.436658\pi$
$463$	8.50727	0.395366	0.197683	+	0.980266i	$0.436658\pi$
$464$	13.2640	0.615765
$465$	−2.50632	−0.116228
$466$	−0.968109	−0.0448468
$467$	30.7040	1.42081	0.710405	−	0.703793i	$-0.248512\pi$
$467$	30.7040	1.42081	0.710405	+	0.703793i	$0.248512\pi$
$468$	−9.07106	−0.419310
$469$	−16.5113	−0.762421
$470$	0.403540	0.0186139
$471$	1.00000	0.0460776
$472$	−5.73347	−0.263904
$473$	0.985560	0.0453161
$474$	6.91794	0.317752
$475$	30.6713	1.40730
$476$	2.20853	0.101228
$477$	1.17528	0.0538123
$478$	−6.90094	−0.315641
$479$	−25.7458	−1.17635	−0.588177	−	0.808732i	$-0.700154\pi$
$479$	−25.7458	−1.17635	−0.588177	+	0.808732i	$0.700154\pi$
$480$	1.67422	0.0764172
$481$	−32.5212	−1.48284
$482$	−0.0834496	−0.00380103
$483$	−0.810284	−0.0368692
$484$	−1.14427	−0.0520123
$485$	−1.27555	−0.0579195
$486$	−0.613812	−0.0278431
$487$	−22.4976	−1.01947	−0.509733	−	0.860333i	$-0.670256\pi$
$487$	−22.4976	−1.01947	−0.509733	+	0.860333i	$0.670256\pi$
$488$	7.43507	0.336570
$489$	6.04172	0.273216
$490$	0.944395	0.0426634
$491$	3.19570	0.144220	0.0721099	−	0.997397i	$-0.477027\pi$
$491$	3.19570	0.144220	0.0721099	+	0.997397i	$0.477027\pi$
$492$	−0.842468	−0.0379814
$493$	7.05022	0.317526
$494$	−21.4240	−0.963912
$495$	1.02233	0.0459505
$496$	−15.7797	−0.708531
$497$	−1.65680	−0.0743175
$498$	2.19954	0.0985637
$499$	−37.3550	−1.67224	−0.836121	−	0.548545i	$-0.815182\pi$
$499$	−37.3550	−1.67224	−0.836121	+	0.548545i	$0.815182\pi$
$500$	−4.80722	−0.214986
$501$	5.38633	0.240643
$502$	10.3733	0.462984
$503$	−30.0753	−1.34099	−0.670496	−	0.741913i	$-0.733919\pi$
$503$	−30.0753	−1.34099	−0.670496	+	0.741913i	$0.733919\pi$
$504$	3.02590	0.134784
$505$	4.00150	0.178064
$506$	1.25065	0.0555982
$507$	−18.2287	−0.809565
$508$	−5.14463	−0.228256
$509$	22.7128	1.00672	0.503362	−	0.864075i	$-0.332096\pi$
$509$	22.7128	1.00672	0.503362	+	0.864075i	$0.332096\pi$
$510$	0.183419	0.00812193
$511$	−0.498006	−0.0220305
$512$	18.9091	0.835670
$513$	6.24580	0.275759
$514$	−10.9440	−0.482721
$515$	4.04896	0.178419
$516$	−0.467606	−0.0205852
$517$	7.52709	0.331041
$518$	4.86012	0.213541
$519$	−7.51730	−0.329973
$520$	3.71379	0.162860
$521$	32.4648	1.42231	0.711155	−	0.703035i	$-0.248172\pi$
$521$	32.4648	1.42231	0.711155	+	0.703035i	$0.248172\pi$
$522$	4.32751	0.189410
$523$	36.7522	1.60706	0.803530	−	0.595265i	$-0.202953\pi$
$523$	36.7522	1.60706	0.803530	+	0.595265i	$0.202953\pi$
$524$	−0.718505	−0.0313880
$525$	−6.68138	−0.291599
$526$	11.5340	0.502906
$527$	−8.38741	−0.365361
$528$	6.43659	0.280117
$529$	−22.6453	−0.984579
$530$	−0.215568	−0.00936369
$531$	2.57801	0.111876
$532$	−13.7940	−0.598048
$533$	−2.90034	−0.125628
$534$	−0.0983283	−0.00425508
$535$	3.02922	0.130965
$536$	−26.9893	−1.16576
$537$	−5.84744	−0.252336
$538$	10.6641	0.459762
$539$	17.6155	0.758751
$540$	−0.485053	−0.0208734
$541$	4.44171	0.190964	0.0954821	−	0.995431i	$-0.469561\pi$
$541$	4.44171	0.190964	0.0954821	+	0.995431i	$0.469561\pi$
$542$	13.9841	0.600670
$543$	−7.62500	−0.327220
$544$	5.60277	0.240217
$545$	−3.34271	−0.143186
$546$	4.66696	0.199728
$547$	−18.5852	−0.794644	−0.397322	−	0.917679i	$-0.630060\pi$
$547$	−18.5852	−0.794644	−0.397322	+	0.917679i	$0.630060\pi$
$548$	−23.0751	−0.985718
$549$	−3.34313	−0.142681
$550$	10.3125	0.439727
$551$	−44.0343	−1.87592
$552$	−1.32449	−0.0563739
$553$	15.3343	0.652079
$554$	9.09867	0.386565
$555$	−1.73899	−0.0738161
$556$	11.0104	0.466944
$557$	−17.0164	−0.721007	−0.360504	−	0.932758i	$-0.617395\pi$
$557$	−17.0164	−0.721007	−0.360504	+	0.932758i	$0.617395\pi$
$558$	−5.14830	−0.217945
$559$	−1.60981	−0.0680878
$560$	0.764895	0.0323227
$561$	3.42125	0.144445
$562$	−1.91577	−0.0808118
$563$	6.78966	0.286150	0.143075	−	0.989712i	$-0.454301\pi$
$563$	6.78966	0.286150	0.143075	+	0.989712i	$0.454301\pi$
$564$	−3.57128	−0.150378
$565$	3.34928	0.140905
$566$	3.09029	0.129895
$567$	−1.36057	−0.0571387
$568$	−2.70819	−0.113633
$569$	2.55445	0.107088	0.0535441	−	0.998565i	$-0.482948\pi$
$569$	2.55445	0.107088	0.0535441	+	0.998565i	$0.482948\pi$
$570$	−1.14560	−0.0479838
$571$	−20.9365	−0.876166	−0.438083	−	0.898935i	$-0.644342\pi$
$571$	−20.9365	−0.876166	−0.438083	+	0.898935i	$0.644342\pi$
$572$	31.0343	1.29761
$573$	−15.6080	−0.652032
$574$	0.433441	0.0180915
$575$	2.92455	0.121962
$576$	−0.323664	−0.0134860
$577$	15.0162	0.625131	0.312566	−	0.949896i	$-0.398812\pi$
$577$	15.0162	0.625131	0.312566	+	0.949896i	$0.398812\pi$
$578$	0.613812	0.0255312
$579$	−11.8956	−0.494363
$580$	3.41973	0.141997
$581$	4.87549	0.202269
$582$	−2.62013	−0.108608
$583$	−4.02092	−0.166529
$584$	−0.814037	−0.0336851
$585$	−1.66988	−0.0690410
$586$	−3.33726	−0.137861
$587$	−9.11905	−0.376383	−0.188192	−	0.982132i	$-0.560263\pi$
$587$	−9.11905	−0.376383	−0.188192	+	0.982132i	$0.560263\pi$
$588$	−8.35777	−0.344669
$589$	52.3861	2.15853
$590$	−0.472856	−0.0194672
$591$	2.59316	0.106669
$592$	−10.9487	−0.449987
$593$	−27.5219	−1.13019	−0.565095	−	0.825026i	$-0.691161\pi$
$593$	−27.5219	−1.13019	−0.565095	+	0.825026i	$0.691161\pi$
$594$	2.10000	0.0861642
$595$	0.406565	0.0166676
$596$	−10.6029	−0.434313
$597$	−12.5930	−0.515399
$598$	−2.04281	−0.0835368
$599$	13.1615	0.537765	0.268882	−	0.963173i	$-0.413346\pi$
$599$	13.1615	0.537765	0.268882	+	0.963173i	$0.413346\pi$
$600$	−10.9213	−0.445862
$601$	−15.6389	−0.637923	−0.318962	−	0.947768i	$-0.603334\pi$
$601$	−15.6389	−0.637923	−0.318962	+	0.947768i	$0.603334\pi$
$602$	0.240578	0.00980523
$603$	12.1355	0.494197
$604$	−27.4279	−1.11603
$605$	−0.210647	−0.00856403
$606$	8.21958	0.333898
$607$	−13.9535	−0.566355	−0.283177	−	0.959068i	$-0.591388\pi$
$607$	−13.9535	−0.566355	−0.283177	+	0.959068i	$0.591388\pi$
$608$	−34.9938	−1.41919
$609$	9.59233	0.388701
$610$	0.613192	0.0248274
$611$	−12.2947	−0.497392
$612$	−1.62323	−0.0656154
$613$	20.8188	0.840863	0.420432	−	0.907324i	$-0.361879\pi$
$613$	20.8188	0.840863	0.420432	+	0.907324i	$0.361879\pi$
$614$	20.8011	0.839466
$615$	−0.155089	−0.00625378
$616$	−10.3523	−0.417108
$617$	1.91968	0.0772835	0.0386417	−	0.999253i	$-0.487697\pi$
$617$	1.91968	0.0772835	0.0386417	+	0.999253i	$0.487697\pi$
$618$	8.31708	0.334562
$619$	−13.8152	−0.555280	−0.277640	−	0.960685i	$-0.589552\pi$
$619$	−13.8152	−0.555280	−0.277640	+	0.960685i	$0.589552\pi$
$620$	−4.06834	−0.163389
$621$	0.595546	0.0238985
$622$	15.9488	0.639490
$623$	−0.217954	−0.00873214
$624$	−10.5135	−0.420878
$625$	23.6686	0.946743
$626$	1.58136	0.0632039
$627$	−21.3684	−0.853373
$628$	1.62323	0.0647741
$629$	−5.81955	−0.232041
$630$	0.249555	0.00994250
$631$	−16.4965	−0.656717	−0.328358	−	0.944553i	$-0.606495\pi$
$631$	−16.4965	−0.656717	−0.328358	+	0.944553i	$0.606495\pi$
$632$	25.0653	0.997045
$633$	−27.4150	−1.08965
$634$	15.9630	0.633973
$635$	−0.947068	−0.0375832
$636$	1.90775	0.0756473
$637$	−28.7731	−1.14003
$638$	−14.8055	−0.586155
$639$	1.21772	0.0481722
$640$	3.40780	0.134705
$641$	−13.5931	−0.536895	−0.268447	−	0.963294i	$-0.586511\pi$
$641$	−13.5931	−0.536895	−0.268447	+	0.963294i	$0.586511\pi$
$642$	6.22241	0.245579
$643$	24.6506	0.972125	0.486062	−	0.873924i	$-0.338433\pi$
$643$	24.6506	0.972125	0.486062	+	0.873924i	$0.338433\pi$
$644$	−1.31528	−0.0518294
$645$	−0.0860809	−0.00338943
$646$	−3.83375	−0.150837
$647$	−39.4563	−1.55119	−0.775593	−	0.631233i	$-0.782549\pi$
$647$	−39.4563	−1.55119	−0.775593	+	0.631233i	$0.782549\pi$
$648$	−2.22399	−0.0873664
$649$	−8.82002	−0.346216
$650$	−16.8444	−0.660693
$651$	−11.4117	−0.447259
$652$	9.80712	0.384076
$653$	12.5390	0.490689	0.245345	−	0.969436i	$-0.421099\pi$
$653$	12.5390	0.490689	0.245345	+	0.969436i	$0.421099\pi$
$654$	−6.86634	−0.268495
$655$	−0.132269	−0.00516816
$656$	−0.976436	−0.0381234
$657$	0.366026	0.0142800
$658$	1.83739	0.0716287
$659$	9.73909	0.379381	0.189690	−	0.981844i	$-0.439252\pi$
$659$	9.73909	0.379381	0.189690	+	0.981844i	$0.439252\pi$
$660$	1.65949	0.0645955
$661$	2.51861	0.0979624	0.0489812	−	0.998800i	$-0.484403\pi$
$661$	2.51861	0.0979624	0.0489812	+	0.998800i	$0.484403\pi$
$662$	8.54661	0.332173
$663$	−5.58826	−0.217030
$664$	7.96945	0.309275
$665$	−2.53933	−0.0984709
$666$	−3.57211	−0.138417
$667$	−4.19873	−0.162575
$668$	8.74328	0.338287
$669$	4.47356	0.172958
$670$	−2.22589	−0.0859935
$671$	11.4377	0.441546
$672$	7.62298	0.294063
$673$	28.1771	1.08615	0.543074	−	0.839685i	$-0.317260\pi$
$673$	28.1771	1.08615	0.543074	+	0.839685i	$0.317260\pi$
$674$	9.23635	0.355771
$675$	4.91071	0.189013
$676$	−29.5894	−1.13806
$677$	−25.9407	−0.996983	−0.498492	−	0.866895i	$-0.666113\pi$
$677$	−25.9407	−0.996983	−0.498492	+	0.866895i	$0.666113\pi$
$678$	6.87984	0.264219
$679$	−5.80777	−0.222882
$680$	0.664570	0.0254851
$681$	20.2353	0.775420
$682$	17.6136	0.674460
$683$	−26.1130	−0.999185	−0.499593	−	0.866261i	$-0.666517\pi$
$683$	−26.1130	−0.999185	−0.499593	+	0.866261i	$0.666517\pi$
$684$	10.1384	0.387652
$685$	−4.24786	−0.162302
$686$	10.1459	0.387374
$687$	−2.40649	−0.0918134
$688$	−0.541963	−0.0206622
$689$	6.56777	0.250212
$690$	−0.109234	−0.00415848
$691$	32.6711	1.24287	0.621433	−	0.783467i	$-0.286551\pi$
$691$	32.6711	1.24287	0.621433	+	0.783467i	$0.286551\pi$
$692$	−12.2023	−0.463863
$693$	4.65486	0.176823
$694$	−17.5360	−0.665656
$695$	2.02689	0.0768842
$696$	15.6796	0.594333
$697$	−0.519006	−0.0196587
$698$	−5.63095	−0.213135
$699$	1.57721	0.0596555
$700$	−10.8454	−0.409919
$701$	8.78320	0.331737	0.165868	−	0.986148i	$-0.446957\pi$
$701$	8.78320	0.331737	0.165868	+	0.986148i	$0.446957\pi$
$702$	−3.43015	−0.129463
$703$	36.3478	1.37088
$704$	1.10734	0.0417343
$705$	−0.657432	−0.0247603
$706$	−2.90816	−0.109450
$707$	18.2195	0.685214
$708$	4.18472	0.157271
$709$	35.1657	1.32068	0.660338	−	0.750968i	$-0.270413\pi$
$709$	35.1657	1.32068	0.660338	+	0.750968i	$0.270413\pi$
$710$	−0.223353	−0.00838228
$711$	−11.2704	−0.422675
$712$	−0.356267	−0.0133517
$713$	4.99509	0.187068
$714$	0.835137	0.0312542
$715$	5.71307	0.213657
$716$	−9.49176	−0.354724
$717$	11.2427	0.419868
$718$	−8.57321	−0.319949
$719$	−0.442769	−0.0165125	−0.00825625	−	0.999966i	$-0.502628\pi$
$719$	−0.442769	−0.0165125	−0.00825625	+	0.999966i	$0.502628\pi$
$720$	−0.562186	−0.0209514
$721$	18.4356	0.686577
$722$	12.2824	0.457105
$723$	0.135953	0.00505615
$724$	−12.3772	−0.459994
$725$	−34.6215	−1.28581
$726$	−0.432696	−0.0160589
$727$	1.31955	0.0489396	0.0244698	−	0.999701i	$-0.492210\pi$
$727$	1.31955	0.0489396	0.0244698	+	0.999701i	$0.492210\pi$
$728$	16.9095	0.626708
$729$	1.00000	0.0370370
$730$	−0.0671361	−0.00248482
$731$	−0.288070	−0.0106547
$732$	−5.42668	−0.200576
$733$	8.38757	0.309802	0.154901	−	0.987930i	$-0.450494\pi$
$733$	8.38757	0.309802	0.154901	+	0.987930i	$0.450494\pi$
$734$	7.64743	0.282272
$735$	−1.53857	−0.0567511
$736$	−3.33671	−0.122993
$737$	−41.5187	−1.52936
$738$	−0.318572	−0.0117268
$739$	−5.36576	−0.197383	−0.0986914	−	0.995118i	$-0.531466\pi$
$739$	−5.36576	−0.197383	−0.0986914	+	0.995118i	$0.531466\pi$
$740$	−2.82279	−0.103768
$741$	34.9032	1.28220
$742$	−0.981518	−0.0360327
$743$	8.81001	0.323208	0.161604	−	0.986856i	$-0.448333\pi$
$743$	8.81001	0.323208	0.161604	+	0.986856i	$0.448333\pi$
$744$	−18.6535	−0.683870
$745$	−1.95188	−0.0715114
$746$	10.0486	0.367904
$747$	−3.58341	−0.131110
$748$	5.55349	0.203056
$749$	13.7926	0.503969
$750$	−1.81781	−0.0663771
$751$	−40.1188	−1.46396	−0.731978	−	0.681328i	$-0.761403\pi$
$751$	−40.1188	−1.46396	−0.731978	+	0.681328i	$0.761403\pi$
$752$	−4.13918	−0.150940
$753$	−16.8998	−0.615864
$754$	24.1833	0.880703
$755$	−5.04917	−0.183758
$756$	−2.20853	−0.0803234
$757$	−32.4342	−1.17884	−0.589421	−	0.807826i	$-0.700644\pi$
$757$	−32.4342	−1.17884	−0.589421	+	0.807826i	$0.700644\pi$
$758$	−17.3407	−0.629843
$759$	−2.03751	−0.0739570
$760$	−4.15077	−0.150564
$761$	7.22973	0.262077	0.131039	−	0.991377i	$-0.458169\pi$
$761$	7.22973	0.262077	0.131039	+	0.991377i	$0.458169\pi$
$762$	−1.94540	−0.0704743
$763$	−15.2199	−0.550997
$764$	−25.3354	−0.916602
$765$	−0.298819	−0.0108038
$766$	−2.88950	−0.104402
$767$	14.4066	0.520193
$768$	6.35272	0.229234
$769$	33.2489	1.19899	0.599493	−	0.800380i	$-0.295369\pi$
$769$	33.2489	1.19899	0.599493	+	0.800380i	$0.295369\pi$
$770$	−0.853789	−0.0307684
$771$	17.8296	0.642118
$772$	−19.3093	−0.694957
$773$	15.1294	0.544165	0.272083	−	0.962274i	$-0.412288\pi$
$773$	15.1294	0.544165	0.272083	+	0.962274i	$0.412288\pi$
$774$	−0.176821	−0.00635570
$775$	41.1881	1.47952
$776$	−9.49335	−0.340791
$777$	−7.91792	−0.284054
$778$	23.7490	0.851442
$779$	3.24161	0.116143
$780$	−2.71061	−0.0970553
$781$	−4.16612	−0.149075
$782$	−0.365554	−0.0130722
$783$	−7.05022	−0.251954
$784$	−9.68681	−0.345958
$785$	0.298819	0.0106653
$786$	−0.271697	−0.00969110
$787$	34.8486	1.24222	0.621109	−	0.783724i	$-0.286682\pi$
$787$	34.8486	1.24222	0.621109	+	0.783724i	$0.286682\pi$
$788$	4.20931	0.149951
$789$	−18.7908	−0.668969
$790$	2.06721	0.0735481
$791$	15.2498	0.542221
$792$	7.60881	0.270367
$793$	−18.6823	−0.663427
$794$	−4.12334	−0.146332
$795$	0.351196	0.0124556
$796$	−20.4414	−0.724528
$797$	4.01903	0.142361	0.0711807	−	0.997463i	$-0.477323\pi$
$797$	4.01903	0.142361	0.0711807	+	0.997463i	$0.477323\pi$
$798$	−5.21610	−0.184648
$799$	−2.20010	−0.0778340
$800$	−27.5136	−0.972752
$801$	0.160193	0.00566013
$802$	−12.3976	−0.437775
$803$	−1.25227	−0.0441915
$804$	19.6988	0.694724
$805$	−0.242128	−0.00853391
$806$	−28.7701	−1.01338
$807$	−17.3736	−0.611578
$808$	29.7815	1.04771
$809$	3.97641	0.139803	0.0699016	−	0.997554i	$-0.477731\pi$
$809$	3.97641	0.139803	0.0699016	+	0.997554i	$0.477731\pi$
$810$	−0.183419	−0.00644468
$811$	8.51174	0.298888	0.149444	−	0.988770i	$-0.452252\pi$
$811$	8.51174	0.298888	0.149444	+	0.988770i	$0.452252\pi$
$812$	15.5706	0.546421
$813$	−22.7824	−0.799015
$814$	12.2211	0.428349
$815$	1.80538	0.0632397
$816$	−1.88136	−0.0658607
$817$	1.79923	0.0629471
$818$	8.25295	0.288558
$819$	−7.60324	−0.265679
$820$	−0.251745	−0.00879133
$821$	−10.3462	−0.361083	−0.180542	−	0.983567i	$-0.557785\pi$
$821$	−10.3462	−0.361083	−0.180542	+	0.983567i	$0.557785\pi$
$822$	−8.72564	−0.304342
$823$	55.0815	1.92002	0.960010	−	0.279965i	$-0.0903227\pi$
$823$	55.0815	1.92002	0.960010	+	0.279965i	$0.0903227\pi$
$824$	30.1347	1.04979
$825$	−16.8007	−0.584927
$826$	−2.15299	−0.0749122
$827$	−15.1083	−0.525367	−0.262683	−	0.964882i	$-0.584607\pi$
$827$	−15.1083	−0.525367	−0.262683	+	0.964882i	$0.584607\pi$
$828$	0.966711	0.0335955
$829$	30.8933	1.07297	0.536484	−	0.843911i	$-0.319752\pi$
$829$	30.8933	1.07297	0.536484	+	0.843911i	$0.319752\pi$
$830$	0.657265	0.0228140
$831$	−14.8232	−0.514211
$832$	−1.80872	−0.0627062
$833$	−5.14884	−0.178397
$834$	4.16348	0.144170
$835$	1.60954	0.0557004
$836$	−34.6860	−1.19964
$837$	8.38741	0.289911
$838$	7.75853	0.268014
$839$	37.3262	1.28864	0.644322	−	0.764754i	$-0.277140\pi$
$839$	37.3262	1.28864	0.644322	+	0.764754i	$0.277140\pi$
$840$	0.904196	0.0311977
$841$	20.7055	0.713984
$842$	17.4488	0.601327
$843$	3.12110	0.107496
$844$	−44.5010	−1.53179
$845$	−5.44708	−0.187385
$846$	−1.35045	−0.0464294
$847$	−0.959112	−0.0329555
$848$	2.21112	0.0759302
$849$	−5.03458	−0.172786
$850$	−3.01425	−0.103388
$851$	3.46581	0.118806
$852$	1.97664	0.0677187
$853$	−14.9741	−0.512705	−0.256353	−	0.966583i	$-0.582521\pi$
$853$	−14.9741	−0.512705	−0.256353	+	0.966583i	$0.582521\pi$
$854$	2.79197	0.0955391
$855$	1.86637	0.0638284
$856$	22.5452	0.770580
$857$	−7.83519	−0.267645	−0.133823	−	0.991005i	$-0.542725\pi$
$857$	−7.83519	−0.267645	−0.133823	+	0.991005i	$0.542725\pi$
$858$	11.7354	0.400639
$859$	−20.5634	−0.701615	−0.350807	−	0.936448i	$-0.614093\pi$
$859$	−20.5634	−0.701615	−0.350807	+	0.936448i	$0.614093\pi$
$860$	−0.139729	−0.00476474
$861$	−0.706145	−0.0240654
$862$	5.06544	0.172530
$863$	29.1753	0.993140	0.496570	−	0.867997i	$-0.334593\pi$
$863$	29.1753	0.993140	0.496570	+	0.867997i	$0.334593\pi$
$864$	−5.60277	−0.190610
$865$	−2.24631	−0.0763769
$866$	2.32323	0.0789466
$867$	−1.00000	−0.0339618
$868$	−18.5238	−0.628740
$869$	38.5590	1.30802
$870$	1.29314	0.0438416
$871$	67.8166	2.29788
$872$	−24.8784	−0.842488
$873$	4.26862	0.144471
$874$	2.28318	0.0772296
$875$	−4.02935	−0.136217
$876$	0.594146	0.0200743
$877$	36.7791	1.24194	0.620971	−	0.783834i	$-0.286739\pi$
$877$	36.7791	1.24194	0.620971	+	0.783834i	$0.286739\pi$
$878$	−18.2394	−0.615549
$879$	5.43694	0.183383
$880$	1.92338	0.0648370
$881$	30.4828	1.02699	0.513496	−	0.858092i	$-0.328350\pi$
$881$	30.4828	1.02699	0.513496	+	0.858092i	$0.328350\pi$
$882$	−3.16042	−0.106417
$883$	25.1571	0.846604	0.423302	−	0.905989i	$-0.360871\pi$
$883$	25.1571	0.846604	0.423302	+	0.905989i	$0.360871\pi$
$884$	−9.07106	−0.305093
$885$	0.770360	0.0258954
$886$	−13.9958	−0.470198
$887$	−17.8353	−0.598852	−0.299426	−	0.954120i	$-0.596795\pi$
$887$	−17.8353	−0.598852	−0.299426	+	0.954120i	$0.596795\pi$
$888$	−12.9426	−0.434325
$889$	−4.31216	−0.144625
$890$	−0.0293824	−0.000984900 0
$891$	−3.42125	−0.114616
$892$	7.26163	0.243137
$893$	13.7414	0.459838
$894$	−4.00941	−0.134095
$895$	−1.74733	−0.0584067
$896$	15.5163	0.518362
$897$	3.32807	0.111121
$898$	9.61301	0.320790
$899$	−59.1331	−1.97220
$900$	7.97123	0.265708
$901$	1.17528	0.0391542
$902$	1.08991	0.0362902
$903$	−0.391941	−0.0130430
$904$	24.9273	0.829069
$905$	−2.27850	−0.0757398
$906$	−10.3716	−0.344575
$907$	−42.4472	−1.40943	−0.704717	−	0.709488i	$-0.748926\pi$
$907$	−42.4472	−1.40943	−0.704717	+	0.709488i	$0.748926\pi$
$908$	32.8467	1.09006
$909$	−13.3910	−0.444152
$910$	1.39458	0.0462298
$911$	−52.0508	−1.72452	−0.862259	−	0.506467i	$-0.830951\pi$
$911$	−52.0508	−1.72452	−0.862259	+	0.506467i	$0.830951\pi$
$912$	11.7506	0.389101
$913$	12.2597	0.405738
$914$	5.95177	0.196867
$915$	−0.998990	−0.0330256
$916$	−3.90630	−0.129068
$917$	−0.602241	−0.0198878
$918$	−0.613812	−0.0202588
$919$	14.7616	0.486940	0.243470	−	0.969908i	$-0.421714\pi$
$919$	14.7616	0.486940	0.243470	+	0.969908i	$0.421714\pi$
$920$	−0.395782	−0.0130485
$921$	−33.8884	−1.11666
$922$	−7.36058	−0.242408
$923$	6.80494	0.223987
$924$	7.55592	0.248572
$925$	28.5781	0.939642
$926$	5.22187	0.171601
$927$	−13.5499	−0.445036
$928$	39.5008	1.29668
$929$	−2.00927	−0.0659221	−0.0329610	−	0.999457i	$-0.510494\pi$
$929$	−2.00927	−0.0659221	−0.0329610	+	0.999457i	$0.510494\pi$
$930$	−1.53841	−0.0504465
$931$	32.1587	1.05396
$932$	2.56018	0.0838614
$933$	−25.9832	−0.850653
$934$	18.8465	0.616676
$935$	1.02233	0.0334339
$936$	−12.4282	−0.406229
$937$	−15.2478	−0.498123	−0.249062	−	0.968488i	$-0.580122\pi$
$937$	−15.2478	−0.498123	−0.249062	+	0.968488i	$0.580122\pi$
$938$	−10.1348	−0.330914
$939$	−2.57629	−0.0840742
$940$	−1.06717	−0.0348071
$941$	12.0815	0.393845	0.196922	−	0.980419i	$-0.436905\pi$
$941$	12.0815	0.393845	0.196922	+	0.980419i	$0.436905\pi$
$942$	0.613812	0.0199991
$943$	0.309092	0.0100654
$944$	4.85017	0.157859
$945$	−0.406565	−0.0132256
$946$	0.604949	0.0196686
$947$	−38.5001	−1.25108	−0.625542	−	0.780190i	$-0.715122\pi$
$947$	−38.5001	−1.25108	−0.625542	+	0.780190i	$0.715122\pi$
$948$	−18.2946	−0.594180
$949$	2.04545	0.0663982
$950$	18.8264	0.610810
$951$	−26.0064	−0.843314
$952$	3.02590	0.0980699
$953$	−32.2307	−1.04405	−0.522027	−	0.852929i	$-0.674824\pi$
$953$	−32.2307	−1.04405	−0.522027	+	0.852929i	$0.674824\pi$
$954$	0.721401	0.0233562
$955$	−4.66396	−0.150922
$956$	18.2496	0.590234
$957$	24.1205	0.779706
$958$	−15.8031	−0.510574
$959$	−19.3412	−0.624560
$960$	−0.0967171	−0.00312153
$961$	39.3487	1.26931
$962$	−19.9619	−0.643598
$963$	−10.1373	−0.326670
$964$	0.220684	0.00710774
$965$	−3.55463	−0.114427
$966$	−0.497363	−0.0160024
$967$	37.7890	1.21521	0.607607	−	0.794238i	$-0.292130\pi$
$967$	37.7890	1.21521	0.607607	+	0.794238i	$0.292130\pi$
$968$	−1.56776	−0.0503897
$969$	6.24580	0.200644
$970$	−0.782945	−0.0251389
$971$	6.65485	0.213564	0.106782	−	0.994282i	$-0.465945\pi$
$971$	6.65485	0.213564	0.106782	+	0.994282i	$0.465945\pi$
$972$	1.62323	0.0520653
$973$	9.22875	0.295860
$974$	−13.8093	−0.442479
$975$	27.4423	0.878858
$976$	−6.28962	−0.201326
$977$	−10.3989	−0.332689	−0.166344	−	0.986068i	$-0.553196\pi$
$977$	−10.3989	−0.332689	−0.166344	+	0.986068i	$0.553196\pi$
$978$	3.70848	0.118584
$979$	−0.548059	−0.0175160
$980$	−2.49746	−0.0797785
$981$	11.1864	0.357154
$982$	1.96156	0.0625958
$983$	25.4502	0.811736	0.405868	−	0.913932i	$-0.366969\pi$
$983$	25.4502	0.811736	0.405868	+	0.913932i	$0.366969\pi$
$984$	−1.15426	−0.0367965
$985$	0.774887	0.0246900
$986$	4.32751	0.137816
$987$	−2.99340	−0.0952809
$988$	56.6561	1.80247
$989$	0.171559	0.00545527
$990$	0.627521	0.0199439
$991$	20.4521	0.649682	0.324841	−	0.945769i	$-0.394689\pi$
$991$	20.4521	0.649682	0.324841	+	0.945769i	$0.394689\pi$
$992$	−46.9928	−1.49202
$993$	−13.9238	−0.441859
$994$	−1.01696	−0.0322561
$995$	−3.76304	−0.119296
$996$	−5.81671	−0.184309
$997$	−13.5556	−0.429311	−0.214656	−	0.976690i	$-0.568863\pi$
$997$	−13.5556	−0.429311	−0.214656	+	0.976690i	$0.568863\pi$
$998$	−22.9290	−0.725805
$999$	5.81955	0.184122

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8007.2.a.j.1.38	✓	64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8007.2.a.j.1.38	✓	64	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+0.613812 q^{2} -1.00000 q^{3} -1.62323 q^{4} -0.298819 q^{5} -0.613812 q^{6} -1.36057 q^{7} -2.22399 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+0.613812 q^{2} -1.00000 q^{3} -1.62323 q^{4} -0.298819 q^{5} -0.613812 q^{6} -1.36057 q^{7} -2.22399 q^{8} +1.00000 q^{9} -0.183419 q^{10} -3.42125 q^{11} +1.62323 q^{12} +5.58826 q^{13} -0.835137 q^{14} +0.298819 q^{15} +1.88136 q^{16} +1.00000 q^{17} +0.613812 q^{18} -6.24580 q^{19} +0.485053 q^{20} +1.36057 q^{21} -2.10000 q^{22} -0.595546 q^{23} +2.22399 q^{24} -4.91071 q^{25} +3.43015 q^{26} -1.00000 q^{27} +2.20853 q^{28} +7.05022 q^{29} +0.183419 q^{30} -8.38741 q^{31} +5.60277 q^{32} +3.42125 q^{33} +0.613812 q^{34} +0.406565 q^{35} -1.62323 q^{36} -5.81955 q^{37} -3.83375 q^{38} -5.58826 q^{39} +0.664570 q^{40} -0.519006 q^{41} +0.835137 q^{42} -0.288070 q^{43} +5.55349 q^{44} -0.298819 q^{45} -0.365554 q^{46} -2.20010 q^{47} -1.88136 q^{48} -5.14884 q^{49} -3.01425 q^{50} -1.00000 q^{51} -9.07106 q^{52} +1.17528 q^{53} -0.613812 q^{54} +1.02233 q^{55} +3.02590 q^{56} +6.24580 q^{57} +4.32751 q^{58} +2.57801 q^{59} -0.485053 q^{60} -3.34313 q^{61} -5.14830 q^{62} -1.36057 q^{63} -0.323664 q^{64} -1.66988 q^{65} +2.10000 q^{66} +12.1355 q^{67} -1.62323 q^{68} +0.595546 q^{69} +0.249555 q^{70} +1.21772 q^{71} -2.22399 q^{72} +0.366026 q^{73} -3.57211 q^{74} +4.91071 q^{75} +10.1384 q^{76} +4.65486 q^{77} -3.43015 q^{78} -11.2704 q^{79} -0.562186 q^{80} +1.00000 q^{81} -0.318572 q^{82} -3.58341 q^{83} -2.20853 q^{84} -0.298819 q^{85} -0.176821 q^{86} -7.05022 q^{87} +7.60881 q^{88} +0.160193 q^{89} -0.183419 q^{90} -7.60324 q^{91} +0.966711 q^{92} +8.38741 q^{93} -1.35045 q^{94} +1.86637 q^{95} -5.60277 q^{96} +4.26862 q^{97} -3.16042 q^{98} -3.42125 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q + 5 q^{2} - 64 q^{3} + 77 q^{4} - 3 q^{5} - 5 q^{6} + 5 q^{7} + 18 q^{8} + 64 q^{9}+O(q^{10}) \) 64 * q + 5 * q^2 - 64 * q^3 + 77 * q^4 - 3 * q^5 - 5 * q^6 + 5 * q^7 + 18 * q^8 + 64 * q^9	\( 64 q + 5 q^{2} - 64 q^{3} + 77 q^{4} - 3 q^{5} - 5 q^{6} + 5 q^{7} + 18 q^{8} + 64 q^{9} + 12 q^{10} - 7 q^{11} - 77 q^{12} + 24 q^{13} - 14 q^{14} + 3 q^{15} + 103 q^{16} + 64 q^{17} + 5 q^{18} + 26 q^{19} - 24 q^{20} - 5 q^{21} + 25 q^{22} + 20 q^{23} - 18 q^{24} + 141 q^{25} + 9 q^{26} - 64 q^{27} + 14 q^{28} + 5 q^{29} - 12 q^{30} + 11 q^{31} + 31 q^{32} + 7 q^{33} + 5 q^{34} - 3 q^{35} + 77 q^{36} + 50 q^{37} + 8 q^{38} - 24 q^{39} + 28 q^{40} - 9 q^{41} + 14 q^{42} + 59 q^{43} - 6 q^{44} - 3 q^{45} + 11 q^{47} - 103 q^{48} + 163 q^{49} + 20 q^{50} - 64 q^{51} + 65 q^{52} + 39 q^{53} - 5 q^{54} + 35 q^{55} - 34 q^{56} - 26 q^{57} - 27 q^{58} - 65 q^{59} + 24 q^{60} + 15 q^{61} + 18 q^{62} + 5 q^{63} + 152 q^{64} + 49 q^{65} - 25 q^{66} + 56 q^{67} + 77 q^{68} - 20 q^{69} + 28 q^{70} - 18 q^{71} + 18 q^{72} + 37 q^{73} - 76 q^{74} - 141 q^{75} + 30 q^{76} + 80 q^{77} - 9 q^{78} + 20 q^{79} - 144 q^{80} + 64 q^{81} + 27 q^{82} + 3 q^{83} - 14 q^{84} - 3 q^{85} + 12 q^{86} - 5 q^{87} + 108 q^{88} + 42 q^{89} + 12 q^{90} + 25 q^{91} + 18 q^{92} - 11 q^{93} + 60 q^{94} + 42 q^{95} - 31 q^{96} + 72 q^{97} + 18 q^{98} - 7 q^{99}+O(q^{100}) \) 64 * q + 5 * q^2 - 64 * q^3 + 77 * q^4 - 3 * q^5 - 5 * q^6 + 5 * q^7 + 18 * q^8 + 64 * q^9 + 12 * q^10 - 7 * q^11 - 77 * q^12 + 24 * q^13 - 14 * q^14 + 3 * q^15 + 103 * q^16 + 64 * q^17 + 5 * q^18 + 26 * q^19 - 24 * q^20 - 5 * q^21 + 25 * q^22 + 20 * q^23 - 18 * q^24 + 141 * q^25 + 9 * q^26 - 64 * q^27 + 14 * q^28 + 5 * q^29 - 12 * q^30 + 11 * q^31 + 31 * q^32 + 7 * q^33 + 5 * q^34 - 3 * q^35 + 77 * q^36 + 50 * q^37 + 8 * q^38 - 24 * q^39 + 28 * q^40 - 9 * q^41 + 14 * q^42 + 59 * q^43 - 6 * q^44 - 3 * q^45 + 11 * q^47 - 103 * q^48 + 163 * q^49 + 20 * q^50 - 64 * q^51 + 65 * q^52 + 39 * q^53 - 5 * q^54 + 35 * q^55 - 34 * q^56 - 26 * q^57 - 27 * q^58 - 65 * q^59 + 24 * q^60 + 15 * q^61 + 18 * q^62 + 5 * q^63 + 152 * q^64 + 49 * q^65 - 25 * q^66 + 56 * q^67 + 77 * q^68 - 20 * q^69 + 28 * q^70 - 18 * q^71 + 18 * q^72 + 37 * q^73 - 76 * q^74 - 141 * q^75 + 30 * q^76 + 80 * q^77 - 9 * q^78 + 20 * q^79 - 144 * q^80 + 64 * q^81 + 27 * q^82 + 3 * q^83 - 14 * q^84 - 3 * q^85 + 12 * q^86 - 5 * q^87 + 108 * q^88 + 42 * q^89 + 12 * q^90 + 25 * q^91 + 18 * q^92 - 11 * q^93 + 60 * q^94 + 42 * q^95 - 31 * q^96 + 72 * q^97 + 18 * q^98 - 7 * q^99

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