LMFDB - Embedded newform 6002.2.a.c.1.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6002,2,Mod(1,6002)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6002, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("6002.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6002 = 2 \cdot 3001 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6002.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:	$47.9262112932$
Analytic rank:	$0$
Dimension:	$69$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.12
Character	$\chi$	$=$	6002.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -2.31615 q^{3} +1.00000 q^{4} +2.10238 q^{5} +2.31615 q^{6} -3.46770 q^{7} -1.00000 q^{8} +2.36454 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -2.31615 q^{3} +1.00000 q^{4} +2.10238 q^{5} +2.31615 q^{6} -3.46770 q^{7} -1.00000 q^{8} +2.36454 q^{9} -2.10238 q^{10} -4.91782 q^{11} -2.31615 q^{12} -2.17593 q^{13} +3.46770 q^{14} -4.86942 q^{15} +1.00000 q^{16} -4.15234 q^{17} -2.36454 q^{18} +8.15841 q^{19} +2.10238 q^{20} +8.03169 q^{21} +4.91782 q^{22} +4.01851 q^{23} +2.31615 q^{24} -0.580000 q^{25} +2.17593 q^{26} +1.47183 q^{27} -3.46770 q^{28} -10.2466 q^{29} +4.86942 q^{30} -8.27632 q^{31} -1.00000 q^{32} +11.3904 q^{33} +4.15234 q^{34} -7.29041 q^{35} +2.36454 q^{36} +3.50759 q^{37} -8.15841 q^{38} +5.03978 q^{39} -2.10238 q^{40} -11.7871 q^{41} -8.03169 q^{42} +9.37123 q^{43} -4.91782 q^{44} +4.97115 q^{45} -4.01851 q^{46} -8.93292 q^{47} -2.31615 q^{48} +5.02492 q^{49} +0.580000 q^{50} +9.61744 q^{51} -2.17593 q^{52} -5.18743 q^{53} -1.47183 q^{54} -10.3391 q^{55} +3.46770 q^{56} -18.8961 q^{57} +10.2466 q^{58} -8.13173 q^{59} -4.86942 q^{60} -6.87505 q^{61} +8.27632 q^{62} -8.19949 q^{63} +1.00000 q^{64} -4.57464 q^{65} -11.3904 q^{66} +13.4320 q^{67} -4.15234 q^{68} -9.30745 q^{69} +7.29041 q^{70} +10.1292 q^{71} -2.36454 q^{72} -12.0318 q^{73} -3.50759 q^{74} +1.34336 q^{75} +8.15841 q^{76} +17.0535 q^{77} -5.03978 q^{78} -1.44676 q^{79} +2.10238 q^{80} -10.5026 q^{81} +11.7871 q^{82} -4.19355 q^{83} +8.03169 q^{84} -8.72980 q^{85} -9.37123 q^{86} +23.7327 q^{87} +4.91782 q^{88} -10.3682 q^{89} -4.97115 q^{90} +7.54547 q^{91} +4.01851 q^{92} +19.1692 q^{93} +8.93292 q^{94} +17.1521 q^{95} +2.31615 q^{96} +4.82288 q^{97} -5.02492 q^{98} -11.6284 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 69 q - 69 q^{2} + 11 q^{3} + 69 q^{4} - 2 q^{5} - 11 q^{6} + 23 q^{7} - 69 q^{8} + 72 q^{9}+O(q^{10}) $ 69 * q - 69 * q^2 + 11 * q^3 + 69 * q^4 - 2 * q^5 - 11 * q^6 + 23 * q^7 - 69 * q^8 + 72 * q^9	\( 69 q - 69 q^{2} + 11 q^{3} + 69 q^{4} - 2 q^{5} - 11 q^{6} + 23 q^{7} - 69 q^{8} + 72 q^{9} + 2 q^{10} - 14 q^{11} + 11 q^{12} + 31 q^{13} - 23 q^{14} + 34 q^{15} + 69 q^{16} - 4 q^{17} - 72 q^{18} + 17 q^{19} - 2 q^{20} - 11 q^{21} + 14 q^{22} + 33 q^{23} - 11 q^{24} + 119 q^{25} - 31 q^{26} + 44 q^{27} + 23 q^{28} - 25 q^{29} - 34 q^{30} + 49 q^{31} - 69 q^{32} + 10 q^{33} + 4 q^{34} - 11 q^{35} + 72 q^{36} + 73 q^{37} - 17 q^{38} + 31 q^{39} + 2 q^{40} - 46 q^{41} + 11 q^{42} + 76 q^{43} - 14 q^{44} + 9 q^{45} - 33 q^{46} + 23 q^{47} + 11 q^{48} + 100 q^{49} - 119 q^{50} + 25 q^{51} + 31 q^{52} + 30 q^{53} - 44 q^{54} + 81 q^{55} - 23 q^{56} + 12 q^{57} + 25 q^{58} - 3 q^{59} + 34 q^{60} + 13 q^{61} - 49 q^{62} + 65 q^{63} + 69 q^{64} - 27 q^{65} - 10 q^{66} + 105 q^{67} - 4 q^{68} + 19 q^{69} + 11 q^{70} + 51 q^{71} - 72 q^{72} + 43 q^{73} - 73 q^{74} + 77 q^{75} + 17 q^{76} - 19 q^{77} - 31 q^{78} + 89 q^{79} - 2 q^{80} + 73 q^{81} + 46 q^{82} - 10 q^{83} - 11 q^{84} + 44 q^{85} - 76 q^{86} + 57 q^{87} + 14 q^{88} - 28 q^{89} - 9 q^{90} + 76 q^{91} + 33 q^{92} + 59 q^{93} - 23 q^{94} + 72 q^{95} - 11 q^{96} + 89 q^{97} - 100 q^{98} - 17 q^{99}+O(q^{100}) \) 69 * q - 69 * q^2 + 11 * q^3 + 69 * q^4 - 2 * q^5 - 11 * q^6 + 23 * q^7 - 69 * q^8 + 72 * q^9 + 2 * q^10 - 14 * q^11 + 11 * q^12 + 31 * q^13 - 23 * q^14 + 34 * q^15 + 69 * q^16 - 4 * q^17 - 72 * q^18 + 17 * q^19 - 2 * q^20 - 11 * q^21 + 14 * q^22 + 33 * q^23 - 11 * q^24 + 119 * q^25 - 31 * q^26 + 44 * q^27 + 23 * q^28 - 25 * q^29 - 34 * q^30 + 49 * q^31 - 69 * q^32 + 10 * q^33 + 4 * q^34 - 11 * q^35 + 72 * q^36 + 73 * q^37 - 17 * q^38 + 31 * q^39 + 2 * q^40 - 46 * q^41 + 11 * q^42 + 76 * q^43 - 14 * q^44 + 9 * q^45 - 33 * q^46 + 23 * q^47 + 11 * q^48 + 100 * q^49 - 119 * q^50 + 25 * q^51 + 31 * q^52 + 30 * q^53 - 44 * q^54 + 81 * q^55 - 23 * q^56 + 12 * q^57 + 25 * q^58 - 3 * q^59 + 34 * q^60 + 13 * q^61 - 49 * q^62 + 65 * q^63 + 69 * q^64 - 27 * q^65 - 10 * q^66 + 105 * q^67 - 4 * q^68 + 19 * q^69 + 11 * q^70 + 51 * q^71 - 72 * q^72 + 43 * q^73 - 73 * q^74 + 77 * q^75 + 17 * q^76 - 19 * q^77 - 31 * q^78 + 89 * q^79 - 2 * q^80 + 73 * q^81 + 46 * q^82 - 10 * q^83 - 11 * q^84 + 44 * q^85 - 76 * q^86 + 57 * q^87 + 14 * q^88 - 28 * q^89 - 9 * q^90 + 76 * q^91 + 33 * q^92 + 59 * q^93 - 23 * q^94 + 72 * q^95 - 11 * q^96 + 89 * q^97 - 100 * q^98 - 17 * 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 $

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	−2.31615	−1.33723	−0.668614	−	0.743610i	$-0.733112\pi$
$3$	−2.31615	−1.33723	−0.668614	+	0.743610i	$0.733112\pi$
$4$	1.00000	0.500000
$5$	2.10238	0.940213	0.470106	−	0.882610i	$-0.344216\pi$
$5$	2.10238	0.940213	0.470106	+	0.882610i	$0.344216\pi$
$6$	2.31615	0.945563
$7$	−3.46770	−1.31067	−0.655333	−	0.755340i	$-0.727472\pi$
$7$	−3.46770	−1.31067	−0.655333	+	0.755340i	$0.727472\pi$
$8$	−1.00000	−0.353553
$9$	2.36454	0.788179
$10$	−2.10238	−0.664831
$11$	−4.91782	−1.48278	−0.741389	−	0.671076i	$-0.765833\pi$
$11$	−4.91782	−1.48278	−0.741389	+	0.671076i	$0.765833\pi$
$12$	−2.31615	−0.668614
$13$	−2.17593	−0.603495	−0.301748	−	0.953388i	$-0.597570\pi$
$13$	−2.17593	−0.603495	−0.301748	+	0.953388i	$0.597570\pi$
$14$	3.46770	0.926781
$15$	−4.86942	−1.25728
$16$	1.00000	0.250000
$17$	−4.15234	−1.00709	−0.503546	−	0.863969i	$-0.667971\pi$
$17$	−4.15234	−1.00709	−0.503546	+	0.863969i	$0.667971\pi$
$18$	−2.36454	−0.557327
$19$	8.15841	1.87167	0.935834	−	0.352441i	$-0.114648\pi$
$19$	8.15841	1.87167	0.935834	+	0.352441i	$0.114648\pi$
$20$	2.10238	0.470106
$21$	8.03169	1.75266
$22$	4.91782	1.04848
$23$	4.01851	0.837917	0.418958	−	0.908005i	$-0.362395\pi$
$23$	4.01851	0.837917	0.418958	+	0.908005i	$0.362395\pi$
$24$	2.31615	0.472782
$25$	−0.580000	−0.116000
$26$	2.17593	0.426735
$27$	1.47183	0.283253
$28$	−3.46770	−0.655333
$29$	−10.2466	−1.90275	−0.951376	−	0.308031i	$-0.900330\pi$
$29$	−10.2466	−1.90275	−0.951376	+	0.308031i	$0.900330\pi$
$30$	4.86942	0.889030
$31$	−8.27632	−1.48647	−0.743235	−	0.669030i	$-0.766710\pi$
$31$	−8.27632	−1.48647	−0.743235	+	0.669030i	$0.766710\pi$
$32$	−1.00000	−0.176777
$33$	11.3904	1.98281
$34$	4.15234	0.712121
$35$	−7.29041	−1.23230
$36$	2.36454	0.394089
$37$	3.50759	0.576645	0.288322	−	0.957533i	$-0.406903\pi$
$37$	3.50759	0.576645	0.288322	+	0.957533i	$0.406903\pi$
$38$	−8.15841	−1.32347
$39$	5.03978	0.807011
$40$	−2.10238	−0.332415
$41$	−11.7871	−1.84084	−0.920419	−	0.390934i	$-0.872152\pi$
$41$	−11.7871	−1.84084	−0.920419	+	0.390934i	$0.872152\pi$
$42$	−8.03169	−1.23932
$43$	9.37123	1.42910	0.714549	−	0.699585i	$-0.246632\pi$
$43$	9.37123	1.42910	0.714549	+	0.699585i	$0.246632\pi$
$44$	−4.91782	−0.741389
$45$	4.97115	0.741056
$46$	−4.01851	−0.592497
$47$	−8.93292	−1.30300	−0.651500	−	0.758648i	$-0.725860\pi$
$47$	−8.93292	−1.30300	−0.651500	+	0.758648i	$0.725860\pi$
$48$	−2.31615	−0.334307
$49$	5.02492	0.717845
$50$	0.580000	0.0820244
$51$	9.61744	1.34671
$52$	−2.17593	−0.301748
$53$	−5.18743	−0.712549	−0.356274	−	0.934381i	$-0.615953\pi$
$53$	−5.18743	−0.712549	−0.356274	+	0.934381i	$0.615953\pi$
$54$	−1.47183	−0.200290
$55$	−10.3391	−1.39413
$56$	3.46770	0.463390
$57$	−18.8961	−2.50285
$58$	10.2466	1.34545
$59$	−8.13173	−1.05866	−0.529330	−	0.848416i	$-0.677557\pi$
$59$	−8.13173	−1.05866	−0.529330	+	0.848416i	$0.677557\pi$
$60$	−4.86942	−0.628639
$61$	−6.87505	−0.880261	−0.440130	−	0.897934i	$-0.645068\pi$
$61$	−6.87505	−0.880261	−0.440130	+	0.897934i	$0.645068\pi$
$62$	8.27632	1.05109
$63$	−8.19949	−1.03304
$64$	1.00000	0.125000
$65$	−4.57464	−0.567414
$66$	−11.3904	−1.40206
$67$	13.4320	1.64098	0.820492	−	0.571657i	$-0.193699\pi$
$67$	13.4320	1.64098	0.820492	+	0.571657i	$0.193699\pi$
$68$	−4.15234	−0.503546
$69$	−9.30745	−1.12049
$70$	7.29041	0.871371
$71$	10.1292	1.20212	0.601060	−	0.799204i	$-0.294745\pi$
$71$	10.1292	1.20212	0.601060	+	0.799204i	$0.294745\pi$
$72$	−2.36454	−0.278663
$73$	−12.0318	−1.40821	−0.704106	−	0.710094i	$-0.748652\pi$
$73$	−12.0318	−1.40821	−0.704106	+	0.710094i	$0.748652\pi$
$74$	−3.50759	−0.407749
$75$	1.34336	0.155118
$76$	8.15841	0.935834
$77$	17.0535	1.94343
$78$	−5.03978	−0.570643
$79$	−1.44676	−0.162773	−0.0813865	−	0.996683i	$-0.525935\pi$
$79$	−1.44676	−0.162773	−0.0813865	+	0.996683i	$0.525935\pi$
$80$	2.10238	0.235053
$81$	−10.5026	−1.16695
$82$	11.7871	1.30167
$83$	−4.19355	−0.460302	−0.230151	−	0.973155i	$-0.573922\pi$
$83$	−4.19355	−0.460302	−0.230151	+	0.973155i	$0.573922\pi$
$84$	8.03169	0.876330
$85$	−8.72980	−0.946880
$86$	−9.37123	−1.01053
$87$	23.7327	2.54441
$88$	4.91782	0.524241
$89$	−10.3682	−1.09903	−0.549516	−	0.835483i	$-0.685188\pi$
$89$	−10.3682	−1.09903	−0.549516	+	0.835483i	$0.685188\pi$
$90$	−4.97115	−0.524006
$91$	7.54547	0.790980
$92$	4.01851	0.418958
$93$	19.1692	1.98775
$94$	8.93292	0.921361
$95$	17.1521	1.75977
$96$	2.31615	0.236391
$97$	4.82288	0.489689	0.244844	−	0.969562i	$-0.421263\pi$
$97$	4.82288	0.489689	0.244844	+	0.969562i	$0.421263\pi$
$98$	−5.02492	−0.507593
$99$	−11.6284	−1.16869
$100$	−0.580000	−0.0580000
$101$	1.32031	0.131376	0.0656879	−	0.997840i	$-0.479076\pi$
$101$	1.32031	0.131376	0.0656879	+	0.997840i	$0.479076\pi$
$102$	−9.61744	−0.952268
$103$	−4.44825	−0.438299	−0.219150	−	0.975691i	$-0.570328\pi$
$103$	−4.44825	−0.438299	−0.219150	+	0.975691i	$0.570328\pi$
$104$	2.17593	0.213368
$105$	16.8857	1.64787
$106$	5.18743	0.503848
$107$	−8.39902	−0.811964	−0.405982	−	0.913881i	$-0.633070\pi$
$107$	−8.39902	−0.811964	−0.405982	+	0.913881i	$0.633070\pi$
$108$	1.47183	0.141627
$109$	−7.71089	−0.738569	−0.369284	−	0.929316i	$-0.620397\pi$
$109$	−7.71089	−0.738569	−0.369284	+	0.929316i	$0.620397\pi$
$110$	10.3391	0.985796
$111$	−8.12410	−0.771105
$112$	−3.46770	−0.327666
$113$	3.89485	0.366397	0.183198	−	0.983076i	$-0.441355\pi$
$113$	3.89485	0.366397	0.183198	+	0.983076i	$0.441355\pi$
$114$	18.8961	1.76978
$115$	8.44843	0.787820
$116$	−10.2466	−0.951376
$117$	−5.14507	−0.475662
$118$	8.13173	0.748586
$119$	14.3991	1.31996
$120$	4.86942	0.444515
$121$	13.1849	1.19863
$122$	6.87505	0.622438
$123$	27.3007	2.46162
$124$	−8.27632	−0.743235
$125$	−11.7313	−1.04928
$126$	8.19949	0.730469
$127$	−15.2406	−1.35238	−0.676190	−	0.736727i	$-0.736370\pi$
$127$	−15.2406	−1.35238	−0.676190	+	0.736727i	$0.736370\pi$
$128$	−1.00000	−0.0883883
$129$	−21.7051	−1.91103
$130$	4.57464	0.401222
$131$	2.00121	0.174846	0.0874231	−	0.996171i	$-0.472137\pi$
$131$	2.00121	0.174846	0.0874231	+	0.996171i	$0.472137\pi$
$132$	11.3904	0.991406
$133$	−28.2909	−2.45313
$134$	−13.4320	−1.16035
$135$	3.09434	0.266318
$136$	4.15234	0.356061
$137$	7.71384	0.659038	0.329519	−	0.944149i	$-0.393113\pi$
$137$	7.71384	0.659038	0.329519	+	0.944149i	$0.393113\pi$
$138$	9.30745	0.792303
$139$	19.5535	1.65851	0.829253	−	0.558874i	$-0.188766\pi$
$139$	19.5535	1.65851	0.829253	+	0.558874i	$0.188766\pi$
$140$	−7.29041	−0.616152
$141$	20.6900	1.74241
$142$	−10.1292	−0.850028
$143$	10.7008	0.894849
$144$	2.36454	0.197045
$145$	−21.5423	−1.78899
$146$	12.0318	0.995757
$147$	−11.6384	−0.959923
$148$	3.50759	0.288322
$149$	19.0181	1.55803	0.779013	−	0.627008i	$-0.215721\pi$
$149$	19.0181	1.55803	0.779013	+	0.627008i	$0.215721\pi$
$150$	−1.34336	−0.109685
$151$	10.0600	0.818673	0.409336	−	0.912384i	$-0.365760\pi$
$151$	10.0600	0.818673	0.409336	+	0.912384i	$0.365760\pi$
$152$	−8.15841	−0.661735
$153$	−9.81837	−0.793768
$154$	−17.0535	−1.37421
$155$	−17.4000	−1.39760
$156$	5.03978	0.403505
$157$	6.80837	0.543367	0.271683	−	0.962387i	$-0.412420\pi$
$157$	6.80837	0.543367	0.271683	+	0.962387i	$0.412420\pi$
$158$	1.44676	0.115098
$159$	12.0149	0.952840
$160$	−2.10238	−0.166208
$161$	−13.9350	−1.09823
$162$	10.5026	0.825160
$163$	−9.50229	−0.744277	−0.372139	−	0.928177i	$-0.621375\pi$
$163$	−9.50229	−0.744277	−0.372139	+	0.928177i	$0.621375\pi$
$164$	−11.7871	−0.920419
$165$	23.9469	1.86427
$166$	4.19355	0.325483
$167$	−5.68905	−0.440232	−0.220116	−	0.975474i	$-0.570644\pi$
$167$	−5.68905	−0.440232	−0.220116	+	0.975474i	$0.570644\pi$
$168$	−8.03169	−0.619659
$169$	−8.26532	−0.635794
$170$	8.72980	0.669545
$171$	19.2909	1.47521
$172$	9.37123	0.714549
$173$	−0.209300	−0.0159128	−0.00795641	−	0.999968i	$-0.502533\pi$
$173$	−0.209300	−0.0159128	−0.00795641	+	0.999968i	$0.502533\pi$
$174$	−23.7327	−1.79917
$175$	2.01126	0.152037
$176$	−4.91782	−0.370694
$177$	18.8343	1.41567
$178$	10.3682	0.777133
$179$	22.8047	1.70450	0.852251	−	0.523134i	$-0.175237\pi$
$179$	22.8047	1.70450	0.852251	+	0.523134i	$0.175237\pi$
$180$	4.97115	0.370528
$181$	−5.81168	−0.431979	−0.215990	−	0.976396i	$-0.569298\pi$
$181$	−5.81168	−0.431979	−0.215990	+	0.976396i	$0.569298\pi$
$182$	−7.54547	−0.559308
$183$	15.9236	1.17711
$184$	−4.01851	−0.296248
$185$	7.37429	0.542169
$186$	−19.1692	−1.40555
$187$	20.4205	1.49329
$188$	−8.93292	−0.651500
$189$	−5.10385	−0.371250
$190$	−17.1521	−1.24434
$191$	−24.0551	−1.74057	−0.870285	−	0.492549i	$-0.836065\pi$
$191$	−24.0551	−1.74057	−0.870285	+	0.492549i	$0.836065\pi$
$192$	−2.31615	−0.167154
$193$	15.4880	1.11485	0.557427	−	0.830226i	$-0.311789\pi$
$193$	15.4880	1.11485	0.557427	+	0.830226i	$0.311789\pi$
$194$	−4.82288	−0.346262
$195$	10.5955	0.758762
$196$	5.02492	0.358923
$197$	−0.0137024	−0.000976255 0	−0.000488127	−	1.00000i	$-0.500155\pi$
$197$	−0.0137024	−0.000976255 0	−0.000488127		1.00000i	$0.500155\pi$
$198$	11.6284	0.826391
$199$	−27.5803	−1.95511	−0.977557	−	0.210673i	$-0.932434\pi$
$199$	−27.5803	−1.95511	−0.977557	+	0.210673i	$0.932434\pi$
$200$	0.580000	0.0410122
$201$	−31.1106	−2.19437
$202$	−1.32031	−0.0928967
$203$	35.5322	2.49387
$204$	9.61744	0.673355
$205$	−24.7810	−1.73078
$206$	4.44825	0.309924
$207$	9.50191	0.660428
$208$	−2.17593	−0.150874
$209$	−40.1216	−2.77527
$210$	−16.8857	−1.16522
$211$	−14.9119	−1.02658	−0.513290	−	0.858215i	$-0.671573\pi$
$211$	−14.9119	−1.02658	−0.513290	+	0.858215i	$0.671573\pi$
$212$	−5.18743	−0.356274
$213$	−23.4608	−1.60751
$214$	8.39902	0.574145
$215$	19.7019	1.34366
$216$	−1.47183	−0.100145
$217$	28.6998	1.94827
$218$	7.71089	0.522247
$219$	27.8674	1.88310
$220$	−10.3391	−0.697063
$221$	9.03522	0.607775
$222$	8.12410	0.545254
$223$	21.3181	1.42757	0.713784	−	0.700366i	$-0.246980\pi$
$223$	21.3181	1.42757	0.713784	+	0.700366i	$0.246980\pi$
$224$	3.46770	0.231695
$225$	−1.37143	−0.0914287
$226$	−3.89485	−0.259082
$227$	0.921110	0.0611362	0.0305681	−	0.999533i	$-0.490268\pi$
$227$	0.921110	0.0611362	0.0305681	+	0.999533i	$0.490268\pi$
$228$	−18.8961	−1.25142
$229$	6.49312	0.429078	0.214539	−	0.976715i	$-0.431175\pi$
$229$	6.49312	0.429078	0.214539	+	0.976715i	$0.431175\pi$
$230$	−8.44843	−0.557073
$231$	−39.4984	−2.59880
$232$	10.2466	0.672725
$233$	−10.2872	−0.673939	−0.336969	−	0.941516i	$-0.609402\pi$
$233$	−10.2872	−0.673939	−0.336969	+	0.941516i	$0.609402\pi$
$234$	5.14507	0.336344
$235$	−18.7804	−1.22510
$236$	−8.13173	−0.529330
$237$	3.35090	0.217665
$238$	−14.3991	−0.933353
$239$	12.4974	0.808389	0.404195	−	0.914673i	$-0.367552\pi$
$239$	12.4974	0.808389	0.404195	+	0.914673i	$0.367552\pi$
$240$	−4.86942	−0.314320
$241$	−15.9351	−1.02647	−0.513235	−	0.858248i	$-0.671553\pi$
$241$	−15.9351	−1.02647	−0.513235	+	0.858248i	$0.671553\pi$
$242$	−13.1849	−0.847559
$243$	19.9100	1.27723
$244$	−6.87505	−0.440130
$245$	10.5643	0.674927
$246$	−27.3007	−1.74063
$247$	−17.7522	−1.12954
$248$	8.27632	0.525547
$249$	9.71289	0.615529
$250$	11.7313	0.741951
$251$	−29.4714	−1.86022	−0.930111	−	0.367280i	$-0.880289\pi$
$251$	−29.4714	−1.86022	−0.930111	+	0.367280i	$0.880289\pi$
$252$	−8.19949	−0.516520
$253$	−19.7623	−1.24244
$254$	15.2406	0.956277
$255$	20.2195	1.26619
$256$	1.00000	0.0625000
$257$	1.18726	0.0740591	0.0370296	−	0.999314i	$-0.488210\pi$
$257$	1.18726	0.0740591	0.0370296	+	0.999314i	$0.488210\pi$
$258$	21.7051	1.35130
$259$	−12.1633	−0.755788
$260$	−4.57464	−0.283707
$261$	−24.2285	−1.49971
$262$	−2.00121	−0.123635
$263$	−4.96863	−0.306379	−0.153189	−	0.988197i	$-0.548954\pi$
$263$	−4.96863	−0.306379	−0.153189	+	0.988197i	$0.548954\pi$
$264$	−11.3904	−0.701030
$265$	−10.9060	−0.669947
$266$	28.2909	1.73463
$267$	24.0144	1.46966
$268$	13.4320	0.820492
$269$	23.2144	1.41541	0.707704	−	0.706509i	$-0.249731\pi$
$269$	23.2144	1.41541	0.707704	+	0.706509i	$0.249731\pi$
$270$	−3.09434	−0.188315
$271$	2.30904	0.140264	0.0701321	−	0.997538i	$-0.477658\pi$
$271$	2.30904	0.140264	0.0701321	+	0.997538i	$0.477658\pi$
$272$	−4.15234	−0.251773
$273$	−17.4764	−1.05772
$274$	−7.71384	−0.466010
$275$	2.85233	0.172002
$276$	−9.30745	−0.560243
$277$	23.7682	1.42809	0.714045	−	0.700100i	$-0.246861\pi$
$277$	23.7682	1.42809	0.714045	+	0.700100i	$0.246861\pi$
$278$	−19.5535	−1.17274
$279$	−19.5697	−1.17160
$280$	7.29041	0.435686
$281$	−7.78709	−0.464539	−0.232269	−	0.972652i	$-0.574615\pi$
$281$	−7.78709	−0.464539	−0.232269	+	0.972652i	$0.574615\pi$
$282$	−20.6900	−1.23207
$283$	−26.0414	−1.54800	−0.774001	−	0.633184i	$-0.781748\pi$
$283$	−26.0414	−1.54800	−0.774001	+	0.633184i	$0.781748\pi$
$284$	10.1292	0.601060
$285$	−39.7267	−2.35321
$286$	−10.7008	−0.632754
$287$	40.8741	2.41272
$288$	−2.36454	−0.139332
$289$	0.241958	0.0142328
$290$	21.5423	1.26501
$291$	−11.1705	−0.654826
$292$	−12.0318	−0.704106
$293$	−14.9148	−0.871335	−0.435667	−	0.900108i	$-0.643488\pi$
$293$	−14.9148	−0.871335	−0.435667	+	0.900108i	$0.643488\pi$
$294$	11.6384	0.678768
$295$	−17.0960	−0.995366
$296$	−3.50759	−0.203875
$297$	−7.23818	−0.420002
$298$	−19.0181	−1.10169
$299$	−8.74400	−0.505679
$300$	1.34336	0.0775592
$301$	−32.4966	−1.87307
$302$	−10.0600	−0.578889
$303$	−3.05803	−0.175679
$304$	8.15841	0.467917
$305$	−14.4540	−0.827632
$306$	9.81837	0.561279
$307$	17.7360	1.01225	0.506125	−	0.862460i	$-0.331077\pi$
$307$	17.7360	1.01225	0.506125	+	0.862460i	$0.331077\pi$
$308$	17.0535	0.971713
$309$	10.3028	0.586106
$310$	17.4000	0.988251
$311$	−2.72467	−0.154502	−0.0772509	−	0.997012i	$-0.524614\pi$
$311$	−2.72467	−0.154502	−0.0772509	+	0.997012i	$0.524614\pi$
$312$	−5.03978	−0.285321
$313$	−28.2908	−1.59909	−0.799546	−	0.600605i	$-0.794927\pi$
$313$	−28.2908	−1.59909	−0.799546	+	0.600605i	$0.794927\pi$
$314$	−6.80837	−0.384218
$315$	−17.2384	−0.971277
$316$	−1.44676	−0.0813865
$317$	19.9123	1.11839	0.559193	−	0.829037i	$-0.311111\pi$
$317$	19.9123	1.11839	0.559193	+	0.829037i	$0.311111\pi$
$318$	−12.0149	−0.673760
$319$	50.3911	2.82136
$320$	2.10238	0.117527
$321$	19.4534	1.08578
$322$	13.9350	0.776565
$323$	−33.8765	−1.88494
$324$	−10.5026	−0.583476
$325$	1.26204	0.0700054
$326$	9.50229	0.526283
$327$	17.8595	0.987635
$328$	11.7871	0.650834
$329$	30.9767	1.70780
$330$	−23.9469	−1.31823
$331$	−12.0593	−0.662837	−0.331419	−	0.943484i	$-0.607527\pi$
$331$	−12.0593	−0.662837	−0.331419	+	0.943484i	$0.607527\pi$
$332$	−4.19355	−0.230151
$333$	8.29383	0.454499
$334$	5.68905	0.311291
$335$	28.2392	1.54287
$336$	8.03169	0.438165
$337$	0.371395	0.0202312	0.0101156	−	0.999949i	$-0.496780\pi$
$337$	0.371395	0.0202312	0.0101156	+	0.999949i	$0.496780\pi$
$338$	8.26532	0.449574
$339$	−9.02105	−0.489956
$340$	−8.72980	−0.473440
$341$	40.7014	2.20411
$342$	−19.2909	−1.04313
$343$	6.84899	0.369811
$344$	−9.37123	−0.505263
$345$	−19.5678	−1.05349
$346$	0.209300	0.0112521
$347$	9.95564	0.534447	0.267223	−	0.963635i	$-0.413894\pi$
$347$	9.95564	0.534447	0.267223	+	0.963635i	$0.413894\pi$
$348$	23.7327	1.27221
$349$	4.86417	0.260373	0.130186	−	0.991490i	$-0.458442\pi$
$349$	4.86417	0.260373	0.130186	+	0.991490i	$0.458442\pi$
$350$	−2.01126	−0.107507
$351$	−3.20260	−0.170942
$352$	4.91782	0.262121
$353$	33.6949	1.79340	0.896698	−	0.442642i	$-0.145959\pi$
$353$	33.6949	1.79340	0.896698	+	0.442642i	$0.145959\pi$
$354$	−18.8343	−1.00103
$355$	21.2955	1.13025
$356$	−10.3682	−0.549516
$357$	−33.3504	−1.76509
$358$	−22.8047	−1.20526
$359$	−3.81653	−0.201429	−0.100714	−	0.994915i	$-0.532113\pi$
$359$	−3.81653	−0.201429	−0.100714	+	0.994915i	$0.532113\pi$
$360$	−4.97115	−0.262003
$361$	47.5597	2.50314
$362$	5.81168	0.305455
$363$	−30.5382	−1.60284
$364$	7.54547	0.395490
$365$	−25.2954	−1.32402
$366$	−15.9236	−0.832342
$367$	16.2238	0.846875	0.423437	−	0.905925i	$-0.360823\pi$
$367$	16.2238	0.846875	0.423437	+	0.905925i	$0.360823\pi$
$368$	4.01851	0.209479
$369$	−27.8710	−1.45091
$370$	−7.37429	−0.383371
$371$	17.9884	0.933913
$372$	19.1692	0.993875
$373$	36.7865	1.90473	0.952365	−	0.304960i	$-0.0986430\pi$
$373$	36.7865	1.90473	0.952365	+	0.304960i	$0.0986430\pi$
$374$	−20.4205	−1.05592
$375$	27.1714	1.40312
$376$	8.93292	0.460680
$377$	22.2960	1.14830
$378$	5.10385	0.262514
$379$	−12.9035	−0.662810	−0.331405	−	0.943489i	$-0.607523\pi$
$379$	−12.9035	−0.662810	−0.331405	+	0.943489i	$0.607523\pi$
$380$	17.1521	0.879883
$381$	35.2994	1.80844
$382$	24.0551	1.23077
$383$	17.9236	0.915851	0.457926	−	0.888991i	$-0.348593\pi$
$383$	17.9236	0.915851	0.457926	+	0.888991i	$0.348593\pi$
$384$	2.31615	0.118195
$385$	35.8529	1.82723
$386$	−15.4880	−0.788321
$387$	22.1586	1.12639
$388$	4.82288	0.244844
$389$	−6.86522	−0.348080	−0.174040	−	0.984739i	$-0.555682\pi$
$389$	−6.86522	−0.348080	−0.174040	+	0.984739i	$0.555682\pi$
$390$	−10.5955	−0.536525
$391$	−16.6862	−0.843859
$392$	−5.02492	−0.253797
$393$	−4.63509	−0.233809
$394$	0.0137024	0.000690316 0
$395$	−3.04164	−0.153041
$396$	−11.6284	−0.584347
$397$	11.6356	0.583974	0.291987	−	0.956422i	$-0.405684\pi$
$397$	11.6356	0.583974	0.291987	+	0.956422i	$0.405684\pi$
$398$	27.5803	1.38247
$399$	65.5259	3.28040
$400$	−0.580000	−0.0290000
$401$	−34.4396	−1.71983	−0.859916	−	0.510436i	$-0.829484\pi$
$401$	−34.4396	−1.71983	−0.859916	+	0.510436i	$0.829484\pi$
$402$	31.1106	1.55165
$403$	18.0087	0.897078
$404$	1.32031	0.0656879
$405$	−22.0804	−1.09718
$406$	−35.5322	−1.76343
$407$	−17.2497	−0.855036
$408$	−9.61744	−0.476134
$409$	10.4726	0.517838	0.258919	−	0.965899i	$-0.416634\pi$
$409$	10.4726	0.517838	0.258919	+	0.965899i	$0.416634\pi$
$410$	24.7810	1.22385
$411$	−17.8664	−0.881284
$412$	−4.44825	−0.219150
$413$	28.1984	1.38755
$414$	−9.50191	−0.466993
$415$	−8.81644	−0.432782
$416$	2.17593	0.106684
$417$	−45.2888	−2.21780
$418$	40.1216	1.96241
$419$	25.9632	1.26839	0.634194	−	0.773174i	$-0.281332\pi$
$419$	25.9632	1.26839	0.634194	+	0.773174i	$0.281332\pi$
$420$	16.8857	0.823936
$421$	10.2328	0.498715	0.249358	−	0.968411i	$-0.419781\pi$
$421$	10.2328	0.498715	0.249358	+	0.968411i	$0.419781\pi$
$422$	14.9119	0.725902
$423$	−21.1222	−1.02700
$424$	5.18743	0.251924
$425$	2.40836	0.116823
$426$	23.4608	1.13668
$427$	23.8406	1.15373
$428$	−8.39902	−0.405982
$429$	−24.7847	−1.19662
$430$	−19.7019	−0.950109
$431$	24.5095	1.18058	0.590291	−	0.807191i	$-0.299013\pi$
$431$	24.5095	1.18058	0.590291	+	0.807191i	$0.299013\pi$
$432$	1.47183	0.0708133
$433$	2.24526	0.107900	0.0539502	−	0.998544i	$-0.482819\pi$
$433$	2.24526	0.107900	0.0539502	+	0.998544i	$0.482819\pi$
$434$	−28.6998	−1.37763
$435$	49.8952	2.39229
$436$	−7.71089	−0.369284
$437$	32.7846	1.56830
$438$	−27.8674	−1.33155
$439$	3.69514	0.176359	0.0881796	−	0.996105i	$-0.471895\pi$
$439$	3.69514	0.176359	0.0881796	+	0.996105i	$0.471895\pi$
$440$	10.3391	0.492898
$441$	11.8816	0.565790
$442$	−9.03522	−0.429762
$443$	26.1312	1.24153	0.620765	−	0.783996i	$-0.286822\pi$
$443$	26.1312	1.24153	0.620765	+	0.783996i	$0.286822\pi$
$444$	−8.12410	−0.385553
$445$	−21.7980	−1.03332
$446$	−21.3181	−1.00944
$447$	−44.0488	−2.08343
$448$	−3.46770	−0.163833
$449$	14.6645	0.692062	0.346031	−	0.938223i	$-0.387529\pi$
$449$	14.6645	0.692062	0.346031	+	0.938223i	$0.387529\pi$
$450$	1.37143	0.0646499
$451$	57.9668	2.72955
$452$	3.89485	0.183198
$453$	−23.3005	−1.09475
$454$	−0.921110	−0.0432298
$455$	15.8634	0.743690
$456$	18.8961	0.884890
$457$	1.92383	0.0899929	0.0449965	−	0.998987i	$-0.485672\pi$
$457$	1.92383	0.0899929	0.0449965	+	0.998987i	$0.485672\pi$
$458$	−6.49312	−0.303404
$459$	−6.11153	−0.285262
$460$	8.44843	0.393910
$461$	−15.6590	−0.729312	−0.364656	−	0.931142i	$-0.618813\pi$
$461$	−15.6590	−0.729312	−0.364656	+	0.931142i	$0.618813\pi$
$462$	39.4984	1.83763
$463$	21.0365	0.977648	0.488824	−	0.872382i	$-0.337426\pi$
$463$	21.0365	0.977648	0.488824	+	0.872382i	$0.337426\pi$
$464$	−10.2466	−0.475688
$465$	40.3009	1.86891
$466$	10.2872	0.476546
$467$	15.0908	0.698318	0.349159	−	0.937063i	$-0.386467\pi$
$467$	15.0908	0.698318	0.349159	+	0.937063i	$0.386467\pi$
$468$	−5.14507	−0.237831
$469$	−46.5782	−2.15078
$470$	18.7804	0.866275
$471$	−15.7692	−0.726605
$472$	8.13173	0.374293
$473$	−46.0860	−2.11904
$474$	−3.35090	−0.153912
$475$	−4.73188	−0.217113
$476$	14.3991	0.659980
$477$	−12.2659	−0.561616
$478$	−12.4974	−0.571618
$479$	7.63864	0.349018	0.174509	−	0.984656i	$-0.444166\pi$
$479$	7.63864	0.349018	0.174509	+	0.984656i	$0.444166\pi$
$480$	4.86942	0.222258
$481$	−7.63228	−0.348002
$482$	15.9351	0.725824
$483$	32.2754	1.46858
$484$	13.1849	0.599315
$485$	10.1395	0.460412
$486$	−19.9100	−0.903137
$487$	23.1875	1.05073	0.525364	−	0.850878i	$-0.323929\pi$
$487$	23.1875	1.05073	0.525364	+	0.850878i	$0.323929\pi$
$488$	6.87505	0.311219
$489$	22.0087	0.995268
$490$	−10.5643	−0.477246
$491$	−2.49274	−0.112496	−0.0562479	−	0.998417i	$-0.517914\pi$
$491$	−2.49274	−0.112496	−0.0562479	+	0.998417i	$0.517914\pi$
$492$	27.3007	1.23081
$493$	42.5476	1.91625
$494$	17.7522	0.798707
$495$	−24.4472	−1.09882
$496$	−8.27632	−0.371618
$497$	−35.1252	−1.57558
$498$	−9.71289	−0.435245
$499$	16.1401	0.722528	0.361264	−	0.932464i	$-0.382345\pi$
$499$	16.1401	0.722528	0.361264	+	0.932464i	$0.382345\pi$
$500$	−11.7313	−0.524639
$501$	13.1767	0.588690
$502$	29.4714	1.31538
$503$	−34.0573	−1.51854	−0.759270	−	0.650776i	$-0.774444\pi$
$503$	−34.0573	−1.51854	−0.759270	+	0.650776i	$0.774444\pi$
$504$	8.19949	0.365234
$505$	2.77579	0.123521
$506$	19.7623	0.878541
$507$	19.1437	0.850201
$508$	−15.2406	−0.676190
$509$	23.2855	1.03211	0.516056	−	0.856555i	$-0.327400\pi$
$509$	23.2855	1.03211	0.516056	+	0.856555i	$0.327400\pi$
$510$	−20.2195	−0.895335
$511$	41.7225	1.84570
$512$	−1.00000	−0.0441942
$513$	12.0078	0.530156
$514$	−1.18726	−0.0523677
$515$	−9.35191	−0.412095
$516$	−21.7051	−0.955515
$517$	43.9305	1.93206
$518$	12.1633	0.534423
$519$	0.484770	0.0212791
$520$	4.57464	0.200611
$521$	18.8190	0.824474	0.412237	−	0.911077i	$-0.364748\pi$
$521$	18.8190	0.824474	0.412237	+	0.911077i	$0.364748\pi$
$522$	24.2285	1.06045
$523$	32.9625	1.44135	0.720675	−	0.693273i	$-0.243832\pi$
$523$	32.9625	1.44135	0.720675	+	0.693273i	$0.243832\pi$
$524$	2.00121	0.0874231
$525$	−4.65838	−0.203308
$526$	4.96863	0.216642
$527$	34.3661	1.49701
$528$	11.3904	0.495703
$529$	−6.85160	−0.297896
$530$	10.9060	0.473724
$531$	−19.2278	−0.834414
$532$	−28.2909	−1.22657
$533$	25.6480	1.11094
$534$	−24.0144	−1.03920
$535$	−17.6579	−0.763419
$536$	−13.4320	−0.580176
$537$	−52.8190	−2.27931
$538$	−23.2144	−1.00084
$539$	−24.7116	−1.06441
$540$	3.09434	0.133159
$541$	−9.79422	−0.421087	−0.210543	−	0.977585i	$-0.567523\pi$
$541$	−9.79422	−0.421087	−0.210543	+	0.977585i	$0.567523\pi$
$542$	−2.30904	−0.0991817
$543$	13.4607	0.577654
$544$	4.15234	0.178030
$545$	−16.2112	−0.694412
$546$	17.4764	0.747922
$547$	0.268842	0.0114949	0.00574743	−	0.999983i	$-0.498171\pi$
$547$	0.268842	0.0114949	0.00574743	+	0.999983i	$0.498171\pi$
$548$	7.71384	0.329519
$549$	−16.2563	−0.693803
$550$	−2.85233	−0.121624
$551$	−83.5963	−3.56132
$552$	9.30745	0.396152
$553$	5.01692	0.213341
$554$	−23.7682	−1.00981
$555$	−17.0799	−0.725003
$556$	19.5535	0.829253
$557$	−10.1087	−0.428320	−0.214160	−	0.976799i	$-0.568701\pi$
$557$	−10.1087	−0.428320	−0.214160	+	0.976799i	$0.568701\pi$
$558$	19.5697	0.828449
$559$	−20.3912	−0.862454
$560$	−7.29041	−0.308076
$561$	−47.2968	−1.99687
$562$	7.78709	0.328478
$563$	−9.50869	−0.400744	−0.200372	−	0.979720i	$-0.564215\pi$
$563$	−9.50869	−0.400744	−0.200372	+	0.979720i	$0.564215\pi$
$564$	20.6900	0.871204
$565$	8.18846	0.344491
$566$	26.0414	1.09460
$567$	36.4197	1.52949
$568$	−10.1292	−0.425014
$569$	23.8450	0.999633	0.499816	−	0.866131i	$-0.333401\pi$
$569$	23.8450	0.999633	0.499816	+	0.866131i	$0.333401\pi$
$570$	39.7267	1.66397
$571$	−10.9387	−0.457771	−0.228885	−	0.973453i	$-0.573508\pi$
$571$	−10.9387	−0.457771	−0.228885	+	0.973453i	$0.573508\pi$
$572$	10.7008	0.447425
$573$	55.7153	2.32754
$574$	−40.8741	−1.70605
$575$	−2.33073	−0.0971983
$576$	2.36454	0.0985224
$577$	7.88869	0.328411	0.164205	−	0.986426i	$-0.447494\pi$
$577$	7.88869	0.328411	0.164205	+	0.986426i	$0.447494\pi$
$578$	−0.241958	−0.0100641
$579$	−35.8726	−1.49081
$580$	−21.5423	−0.894496
$581$	14.5420	0.603303
$582$	11.1705	0.463032
$583$	25.5108	1.05655
$584$	12.0318	0.497878
$585$	−10.8169	−0.447224
$586$	14.9148	0.616127
$587$	−23.9040	−0.986623	−0.493312	−	0.869853i	$-0.664214\pi$
$587$	−23.9040	−0.986623	−0.493312	+	0.869853i	$0.664214\pi$
$588$	−11.6384	−0.479961
$589$	−67.5216	−2.78218
$590$	17.0960	0.703830
$591$	0.0317367	0.00130548
$592$	3.50759	0.144161
$593$	−30.5457	−1.25436	−0.627181	−	0.778874i	$-0.715791\pi$
$593$	−30.5457	−1.25436	−0.627181	+	0.778874i	$0.715791\pi$
$594$	7.23818	0.296986
$595$	30.2723	1.24104
$596$	19.0181	0.779013
$597$	63.8799	2.61443
$598$	8.74400	0.357569
$599$	−15.0967	−0.616836	−0.308418	−	0.951251i	$-0.599799\pi$
$599$	−15.0967	−0.616836	−0.308418	+	0.951251i	$0.599799\pi$
$600$	−1.34336	−0.0548426
$601$	−40.0431	−1.63339	−0.816695	−	0.577069i	$-0.804196\pi$
$601$	−40.0431	−1.63339	−0.816695	+	0.577069i	$0.804196\pi$
$602$	32.4966	1.32446
$603$	31.7605	1.29339
$604$	10.0600	0.409336
$605$	27.7197	1.12697
$606$	3.05803	0.124224
$607$	−17.1920	−0.697804	−0.348902	−	0.937159i	$-0.613445\pi$
$607$	−17.1920	−0.697804	−0.348902	+	0.937159i	$0.613445\pi$
$608$	−8.15841	−0.330867
$609$	−82.2978	−3.33488
$610$	14.4540	0.585224
$611$	19.4374	0.786354
$612$	−9.81837	−0.396884
$613$	3.66839	0.148165	0.0740824	−	0.997252i	$-0.476397\pi$
$613$	3.66839	0.148165	0.0740824	+	0.997252i	$0.476397\pi$
$614$	−17.7360	−0.715769
$615$	57.3964	2.31445
$616$	−17.0535	−0.687105
$617$	−41.1736	−1.65759	−0.828793	−	0.559556i	$-0.810972\pi$
$617$	−41.1736	−1.65759	−0.828793	+	0.559556i	$0.810972\pi$
$618$	−10.3028	−0.414440
$619$	29.2025	1.17375	0.586874	−	0.809678i	$-0.300358\pi$
$619$	29.2025	1.17375	0.586874	+	0.809678i	$0.300358\pi$
$620$	−17.4000	−0.698799
$621$	5.91455	0.237343
$622$	2.72467	0.109249
$623$	35.9539	1.44046
$624$	5.03978	0.201753
$625$	−21.7636	−0.870544
$626$	28.2908	1.13073
$627$	92.9275	3.71117
$628$	6.80837	0.271683
$629$	−14.5647	−0.580734
$630$	17.2384	0.686796
$631$	8.65893	0.344706	0.172353	−	0.985035i	$-0.444863\pi$
$631$	8.65893	0.344706	0.172353	+	0.985035i	$0.444863\pi$
$632$	1.44676	0.0575490
$633$	34.5382	1.37277
$634$	−19.9123	−0.790818
$635$	−32.0414	−1.27153
$636$	12.0149	0.476420
$637$	−10.9339	−0.433216
$638$	−50.3911	−1.99500
$639$	23.9510	0.947486
$640$	−2.10238	−0.0831039
$641$	19.8235	0.782981	0.391490	−	0.920182i	$-0.371960\pi$
$641$	19.8235	0.782981	0.391490	+	0.920182i	$0.371960\pi$
$642$	−19.4534	−0.767763
$643$	−25.0443	−0.987650	−0.493825	−	0.869561i	$-0.664402\pi$
$643$	−25.0443	−0.987650	−0.493825	+	0.869561i	$0.664402\pi$
$644$	−13.9350	−0.549114
$645$	−45.6324	−1.79678
$646$	33.8765	1.33285
$647$	45.5815	1.79199	0.895997	−	0.444059i	$-0.146462\pi$
$647$	45.5815	1.79199	0.895997	+	0.444059i	$0.146462\pi$
$648$	10.5026	0.412580
$649$	39.9903	1.56976
$650$	−1.26204	−0.0495013
$651$	−66.4728	−2.60528
$652$	−9.50229	−0.372139
$653$	−16.4512	−0.643784	−0.321892	−	0.946776i	$-0.604319\pi$
$653$	−16.4512	−0.643784	−0.321892	+	0.946776i	$0.604319\pi$
$654$	−17.8595	−0.698363
$655$	4.20730	0.164393
$656$	−11.7871	−0.460209
$657$	−28.4496	−1.10992
$658$	−30.9767	−1.20760
$659$	−18.2266	−0.710008	−0.355004	−	0.934865i	$-0.615520\pi$
$659$	−18.2266	−0.710008	−0.355004	+	0.934865i	$0.615520\pi$
$660$	23.9469	0.932133
$661$	−15.7218	−0.611507	−0.305754	−	0.952111i	$-0.598908\pi$
$661$	−15.7218	−0.611507	−0.305754	+	0.952111i	$0.598908\pi$
$662$	12.0593	0.468697
$663$	−20.9269	−0.812733
$664$	4.19355	0.162741
$665$	−59.4782	−2.30647
$666$	−8.29383	−0.321379
$667$	−41.1762	−1.59435
$668$	−5.68905	−0.220116
$669$	−49.3760	−1.90898
$670$	−28.2392	−1.09098
$671$	33.8103	1.30523
$672$	−8.03169	−0.309829
$673$	3.36224	0.129605	0.0648025	−	0.997898i	$-0.479358\pi$
$673$	3.36224	0.129605	0.0648025	+	0.997898i	$0.479358\pi$
$674$	−0.371395	−0.0143056
$675$	−0.853660	−0.0328574
$676$	−8.26532	−0.317897
$677$	−5.31209	−0.204160	−0.102080	−	0.994776i	$-0.532550\pi$
$677$	−5.31209	−0.204160	−0.102080	+	0.994776i	$0.532550\pi$
$678$	9.02105	0.346451
$679$	−16.7243	−0.641818
$680$	8.72980	0.334773
$681$	−2.13343	−0.0817531
$682$	−40.7014	−1.55854
$683$	5.38963	0.206229	0.103114	−	0.994670i	$-0.467119\pi$
$683$	5.38963	0.206229	0.103114	+	0.994670i	$0.467119\pi$
$684$	19.2909	0.737605
$685$	16.2174	0.619636
$686$	−6.84899	−0.261496
$687$	−15.0390	−0.573775
$688$	9.37123	0.357275
$689$	11.2875	0.430020
$690$	19.5678	0.744933
$691$	14.6764	0.558317	0.279159	−	0.960245i	$-0.409944\pi$
$691$	14.6764	0.558317	0.279159	+	0.960245i	$0.409944\pi$
$692$	−0.209300	−0.00795641
$693$	40.3236	1.53177
$694$	−9.95564	−0.377911
$695$	41.1089	1.55935
$696$	−23.7327	−0.899586
$697$	48.9441	1.85389
$698$	−4.86417	−0.184111
$699$	23.8267	0.901209
$700$	2.01126	0.0760186
$701$	−24.3057	−0.918014	−0.459007	−	0.888433i	$-0.651795\pi$
$701$	−24.3057	−0.918014	−0.459007	+	0.888433i	$0.651795\pi$
$702$	3.20260	0.120874
$703$	28.6164	1.07929
$704$	−4.91782	−0.185347
$705$	43.4981	1.63823
$706$	−33.6949	−1.26812
$707$	−4.57843	−0.172190
$708$	18.8343	0.707835
$709$	−29.9603	−1.12518	−0.562592	−	0.826735i	$-0.690196\pi$
$709$	−29.9603	−1.12518	−0.562592	+	0.826735i	$0.690196\pi$
$710$	−21.2955	−0.799207
$711$	−3.42091	−0.128294
$712$	10.3682	0.388566
$713$	−33.2584	−1.24554
$714$	33.3504	1.24811
$715$	22.4972	0.841349
$716$	22.8047	0.852251
$717$	−28.9458	−1.08100
$718$	3.81653	0.142432
$719$	36.6276	1.36598	0.682990	−	0.730428i	$-0.260679\pi$
$719$	36.6276	1.36598	0.682990	+	0.730428i	$0.260679\pi$
$720$	4.97115	0.185264
$721$	15.4252	0.574464
$722$	−47.5597	−1.76999
$723$	36.9081	1.37263
$724$	−5.81168	−0.215990
$725$	5.94305	0.220719
$726$	30.5382	1.13338
$727$	11.9540	0.443347	0.221674	−	0.975121i	$-0.428848\pi$
$727$	11.9540	0.443347	0.221674	+	0.975121i	$0.428848\pi$
$728$	−7.54547	−0.279654
$729$	−14.6068	−0.540993
$730$	25.2954	0.936223
$731$	−38.9126	−1.43923
$732$	15.9236	0.588555
$733$	34.7698	1.28425	0.642126	−	0.766599i	$-0.278053\pi$
$733$	34.7698	1.28425	0.642126	+	0.766599i	$0.278053\pi$
$734$	−16.2238	−0.598831
$735$	−24.4684	−0.902532
$736$	−4.01851	−0.148124
$737$	−66.0563	−2.43322
$738$	27.8710	1.02595
$739$	−21.4987	−0.790842	−0.395421	−	0.918500i	$-0.629401\pi$
$739$	−21.4987	−0.790842	−0.395421	+	0.918500i	$0.629401\pi$
$740$	7.37429	0.271084
$741$	41.1166	1.51046
$742$	−17.9884	−0.660376
$743$	29.4074	1.07885	0.539427	−	0.842032i	$-0.318641\pi$
$743$	29.4074	1.07885	0.539427	+	0.842032i	$0.318641\pi$
$744$	−19.1692	−0.702776
$745$	39.9833	1.46488
$746$	−36.7865	−1.34685
$747$	−9.91581	−0.362801
$748$	20.4205	0.746646
$749$	29.1252	1.06421
$750$	−27.1714	−0.992158
$751$	17.6482	0.643992	0.321996	−	0.946741i	$-0.395646\pi$
$751$	17.6482	0.643992	0.321996	+	0.946741i	$0.395646\pi$
$752$	−8.93292	−0.325750
$753$	68.2602	2.48754
$754$	−22.2960	−0.811972
$755$	21.1500	0.769727
$756$	−5.10385	−0.185625
$757$	48.3630	1.75778	0.878892	−	0.477021i	$-0.158283\pi$
$757$	48.3630	1.75778	0.878892	+	0.477021i	$0.158283\pi$
$758$	12.9035	0.468677
$759$	45.7724	1.66143
$760$	−17.1521	−0.622171
$761$	−35.4822	−1.28623	−0.643114	−	0.765771i	$-0.722358\pi$
$761$	−35.4822	−1.28623	−0.643114	+	0.765771i	$0.722358\pi$
$762$	−35.2994	−1.27876
$763$	26.7390	0.968017
$764$	−24.0551	−0.870285
$765$	−20.6419	−0.746311
$766$	−17.9236	−0.647605
$767$	17.6941	0.638896
$768$	−2.31615	−0.0835768
$769$	26.4921	0.955330	0.477665	−	0.878542i	$-0.341483\pi$
$769$	26.4921	0.955330	0.477665	+	0.878542i	$0.341483\pi$
$770$	−35.8529	−1.29205
$771$	−2.74986	−0.0990340
$772$	15.4880	0.557427
$773$	−45.5379	−1.63789	−0.818943	−	0.573875i	$-0.805439\pi$
$773$	−45.5379	−1.63789	−0.818943	+	0.573875i	$0.805439\pi$
$774$	−22.1586	−0.796475
$775$	4.80026	0.172431
$776$	−4.82288	−0.173131
$777$	28.1719	1.01066
$778$	6.86522	0.246130
$779$	−96.1641	−3.44544
$780$	10.5955	0.379381
$781$	−49.8138	−1.78248
$782$	16.6862	0.596698
$783$	−15.0813	−0.538961
$784$	5.02492	0.179461
$785$	14.3138	0.510880
$786$	4.63509	0.165328
$787$	13.5629	0.483465	0.241732	−	0.970343i	$-0.422284\pi$
$787$	13.5629	0.483465	0.241732	+	0.970343i	$0.422284\pi$
$788$	−0.0137024	−0.000488127 0
$789$	11.5081	0.409698
$790$	3.04164	0.108217
$791$	−13.5062	−0.480224
$792$	11.6284	0.413196
$793$	14.9597	0.531233
$794$	−11.6356	−0.412932
$795$	25.2598	0.895872
$796$	−27.5803	−0.977557
$797$	13.4096	0.474993	0.237496	−	0.971388i	$-0.423673\pi$
$797$	13.4096	0.474993	0.237496	+	0.971388i	$0.423673\pi$
$798$	−65.5259	−2.31959
$799$	37.0926	1.31224
$800$	0.580000	0.0205061
$801$	−24.5161	−0.866234
$802$	34.4396	1.21610
$803$	59.1701	2.08807
$804$	−31.1106	−1.09719
$805$	−29.2966	−1.03257
$806$	−18.0087	−0.634330
$807$	−53.7680	−1.89272
$808$	−1.32031	−0.0464483
$809$	35.0601	1.23265	0.616323	−	0.787493i	$-0.288621\pi$
$809$	35.0601	1.23265	0.616323	+	0.787493i	$0.288621\pi$
$810$	22.0804	0.775826
$811$	−33.7481	−1.18506	−0.592528	−	0.805550i	$-0.701870\pi$
$811$	−33.7481	−1.18506	−0.592528	+	0.805550i	$0.701870\pi$
$812$	35.5322	1.24694
$813$	−5.34807	−0.187565
$814$	17.2497	0.604602
$815$	−19.9774	−0.699779
$816$	9.61744	0.336678
$817$	76.4543	2.67480
$818$	−10.4726	−0.366167
$819$	17.8415	0.623434
$820$	−24.7810	−0.865389
$821$	−33.7979	−1.17956	−0.589778	−	0.807566i	$-0.700785\pi$
$821$	−33.7979	−1.17956	−0.589778	+	0.807566i	$0.700785\pi$
$822$	17.8664	0.623162
$823$	51.3114	1.78860	0.894302	−	0.447465i	$-0.147673\pi$
$823$	51.3114	1.78860	0.894302	+	0.447465i	$0.147673\pi$
$824$	4.44825	0.154962
$825$	−6.60642	−0.230006
$826$	−28.1984	−0.981146
$827$	15.9673	0.555237	0.277619	−	0.960691i	$-0.410455\pi$
$827$	15.9673	0.555237	0.277619	+	0.960691i	$0.410455\pi$
$828$	9.50191	0.330214
$829$	3.53114	0.122641	0.0613207	−	0.998118i	$-0.480469\pi$
$829$	3.53114	0.122641	0.0613207	+	0.998118i	$0.480469\pi$
$830$	8.81644	0.306023
$831$	−55.0506	−1.90968
$832$	−2.17593	−0.0754369
$833$	−20.8652	−0.722936
$834$	45.2888	1.56822
$835$	−11.9605	−0.413911
$836$	−40.1216	−1.38763
$837$	−12.1813	−0.421048
$838$	−25.9632	−0.896885
$839$	−32.2496	−1.11338	−0.556690	−	0.830721i	$-0.687929\pi$
$839$	−32.2496	−1.11338	−0.556690	+	0.830721i	$0.687929\pi$
$840$	−16.8857	−0.582611
$841$	75.9935	2.62047
$842$	−10.2328	−0.352645
$843$	18.0360	0.621194
$844$	−14.9119	−0.513290
$845$	−17.3768	−0.597781
$846$	21.1222	0.726197
$847$	−45.7213	−1.57100
$848$	−5.18743	−0.178137
$849$	60.3158	2.07003
$850$	−2.40836	−0.0826060
$851$	14.0953	0.483180
$852$	−23.4608	−0.803755
$853$	−18.1634	−0.621904	−0.310952	−	0.950426i	$-0.600648\pi$
$853$	−18.1634	−0.621904	−0.310952	+	0.950426i	$0.600648\pi$
$854$	−23.8406	−0.815809
$855$	40.5567	1.38701
$856$	8.39902	0.287073
$857$	42.9476	1.46706	0.733531	−	0.679657i	$-0.237871\pi$
$857$	42.9476	1.46706	0.733531	+	0.679657i	$0.237871\pi$
$858$	24.7847	0.846136
$859$	−20.5485	−0.701106	−0.350553	−	0.936543i	$-0.614006\pi$
$859$	−20.5485	−0.701106	−0.350553	+	0.936543i	$0.614006\pi$
$860$	19.7019	0.671828
$861$	−94.6704	−3.22636
$862$	−24.5095	−0.834797
$863$	51.3368	1.74753	0.873763	−	0.486353i	$-0.161673\pi$
$863$	51.3368	1.74753	0.873763	+	0.486353i	$0.161673\pi$
$864$	−1.47183	−0.0500726
$865$	−0.440029	−0.0149614
$866$	−2.24526	−0.0762971
$867$	−0.560411	−0.0190326
$868$	28.6998	0.974133
$869$	7.11489	0.241356
$870$	−49.8952	−1.69160
$871$	−29.2272	−0.990326
$872$	7.71089	0.261124
$873$	11.4039	0.385962
$874$	−32.7846	−1.10896
$875$	40.6805	1.37525
$876$	27.8674	0.941551
$877$	6.76401	0.228404	0.114202	−	0.993458i	$-0.463569\pi$
$877$	6.76401	0.228404	0.114202	+	0.993458i	$0.463569\pi$
$878$	−3.69514	−0.124705
$879$	34.5450	1.16517
$880$	−10.3391	−0.348532
$881$	45.6982	1.53961	0.769806	−	0.638278i	$-0.220353\pi$
$881$	45.6982	1.53961	0.769806	+	0.638278i	$0.220353\pi$
$882$	−11.8816	−0.400074
$883$	−46.4321	−1.56256	−0.781282	−	0.624178i	$-0.785434\pi$
$883$	−46.4321	−1.56256	−0.781282	+	0.624178i	$0.785434\pi$
$884$	9.03522	0.303887
$885$	39.5968	1.33103
$886$	−26.1312	−0.877895
$887$	20.6604	0.693709	0.346855	−	0.937919i	$-0.387250\pi$
$887$	20.6604	0.693709	0.346855	+	0.937919i	$0.387250\pi$
$888$	8.12410	0.272627
$889$	52.8496	1.77252
$890$	21.7980	0.730670
$891$	51.6498	1.73033
$892$	21.3181	0.713784
$893$	−72.8784	−2.43878
$894$	44.0488	1.47321
$895$	47.9441	1.60259
$896$	3.46770	0.115848
$897$	20.2524	0.676208
$898$	−14.6645	−0.489361
$899$	84.8044	2.82839
$900$	−1.37143	−0.0457144
$901$	21.5400	0.717602
$902$	−57.9668	−1.93008
$903$	75.2668	2.50472
$904$	−3.89485	−0.129541
$905$	−12.2184	−0.406152
$906$	23.3005	0.774107
$907$	34.0550	1.13078	0.565389	−	0.824825i	$-0.308726\pi$
$907$	34.0550	1.13078	0.565389	+	0.824825i	$0.308726\pi$
$908$	0.921110	0.0305681
$909$	3.12192	0.103548
$910$	−15.8634	−0.525868
$911$	−29.3758	−0.973264	−0.486632	−	0.873607i	$-0.661775\pi$
$911$	−29.3758	−0.973264	−0.486632	+	0.873607i	$0.661775\pi$
$912$	−18.8961	−0.625712
$913$	20.6231	0.682526
$914$	−1.92383	−0.0636346
$915$	33.4775	1.10673
$916$	6.49312	0.214539
$917$	−6.93958	−0.229165
$918$	6.11153	0.201711
$919$	−27.2588	−0.899185	−0.449593	−	0.893234i	$-0.648431\pi$
$919$	−27.2588	−0.899185	−0.449593	+	0.893234i	$0.648431\pi$
$920$	−8.44843	−0.278536
$921$	−41.0793	−1.35361
$922$	15.6590	0.515702
$923$	−22.0406	−0.725474
$924$	−39.4984	−1.29940
$925$	−2.03440	−0.0668907
$926$	−21.0365	−0.691302
$927$	−10.5181	−0.345458
$928$	10.2466	0.336362
$929$	−28.9024	−0.948256	−0.474128	−	0.880456i	$-0.657237\pi$
$929$	−28.9024	−0.948256	−0.474128	+	0.880456i	$0.657237\pi$
$930$	−40.3009	−1.32152
$931$	40.9953	1.34357
$932$	−10.2872	−0.336969
$933$	6.31073	0.206604
$934$	−15.0908	−0.493786
$935$	42.9316	1.40401
$936$	5.14507	0.168172
$937$	−17.5979	−0.574897	−0.287449	−	0.957796i	$-0.592807\pi$
$937$	−17.5979	−0.574897	−0.287449	+	0.957796i	$0.592807\pi$
$938$	46.5782	1.52083
$939$	65.5257	2.13835
$940$	−18.7804	−0.612549
$941$	22.7436	0.741419	0.370709	−	0.928749i	$-0.379115\pi$
$941$	22.7436	0.741419	0.370709	+	0.928749i	$0.379115\pi$
$942$	15.7692	0.513788
$943$	−47.3666	−1.54247
$944$	−8.13173	−0.264665
$945$	−10.7302	−0.349054
$946$	46.0860	1.49838
$947$	−22.6347	−0.735530	−0.367765	−	0.929919i	$-0.619877\pi$
$947$	−22.6347	−0.735530	−0.367765	+	0.929919i	$0.619877\pi$
$948$	3.35090	0.108832
$949$	26.1803	0.849850
$950$	4.73188	0.153522
$951$	−46.1198	−1.49554
$952$	−14.3991	−0.466676
$953$	6.69397	0.216839	0.108420	−	0.994105i	$-0.465421\pi$
$953$	6.69397	0.216839	0.108420	+	0.994105i	$0.465421\pi$
$954$	12.2659	0.397122
$955$	−50.5731	−1.63651
$956$	12.4974	0.404195
$957$	−116.713	−3.77280
$958$	−7.63864	−0.246793
$959$	−26.7492	−0.863778
$960$	−4.86942	−0.157160
$961$	37.4974	1.20959
$962$	7.63228	0.246075
$963$	−19.8598	−0.639973
$964$	−15.9351	−0.513235
$965$	32.5617	1.04820
$966$	−32.2754	−1.03844
$967$	−20.9810	−0.674702	−0.337351	−	0.941379i	$-0.609531\pi$
$967$	−20.9810	−0.674702	−0.337351	+	0.941379i	$0.609531\pi$
$968$	−13.1849	−0.423780
$969$	78.4630	2.52060
$970$	−10.1395	−0.325560
$971$	−26.3694	−0.846234	−0.423117	−	0.906075i	$-0.639064\pi$
$971$	−26.3694	−0.846234	−0.423117	+	0.906075i	$0.639064\pi$
$972$	19.9100	0.638614
$973$	−67.8056	−2.17375
$974$	−23.1875	−0.742977
$975$	−2.92307	−0.0936132
$976$	−6.87505	−0.220065
$977$	−40.1491	−1.28448	−0.642242	−	0.766502i	$-0.721996\pi$
$977$	−40.1491	−1.28448	−0.642242	+	0.766502i	$0.721996\pi$
$978$	−22.0087	−0.703761
$979$	50.9891	1.62962
$980$	10.5643	0.337464
$981$	−18.2327	−0.582124
$982$	2.49274	0.0795465
$983$	−22.5351	−0.718758	−0.359379	−	0.933192i	$-0.617012\pi$
$983$	−22.5351	−0.718758	−0.359379	+	0.933192i	$0.617012\pi$
$984$	−27.3007	−0.870314
$985$	−0.0288076	−0.000917887 0
$986$	−42.5476	−1.35499
$987$	−71.7465	−2.28372
$988$	−17.7522	−0.564771
$989$	37.6583	1.19747
$990$	24.4472	0.776984
$991$	−22.5169	−0.715273	−0.357637	−	0.933861i	$-0.616417\pi$
$991$	−22.5169	−0.715273	−0.357637	+	0.933861i	$0.616417\pi$
$992$	8.27632	0.262773
$993$	27.9310	0.886365
$994$	35.1252	1.11410
$995$	−57.9842	−1.83822
$996$	9.71289	0.307765
$997$	−49.4247	−1.56530	−0.782648	−	0.622464i	$-0.786132\pi$
$997$	−49.4247	−1.56530	−0.782648	+	0.622464i	$0.786132\pi$
$998$	−16.1401	−0.510905
$999$	5.16257	0.163336

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6002.2.a.c.1.12	✓	69

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6002.2.a.c.1.12	✓	69	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:	\( N \)	\(=\)	\( 6002 = 2 \cdot 3001 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6002.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -2.31615 q^{3} +1.00000 q^{4} +2.10238 q^{5} +2.31615 q^{6} -3.46770 q^{7} -1.00000 q^{8} +2.36454 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -2.31615 q^{3} +1.00000 q^{4} +2.10238 q^{5} +2.31615 q^{6} -3.46770 q^{7} -1.00000 q^{8} +2.36454 q^{9} -2.10238 q^{10} -4.91782 q^{11} -2.31615 q^{12} -2.17593 q^{13} +3.46770 q^{14} -4.86942 q^{15} +1.00000 q^{16} -4.15234 q^{17} -2.36454 q^{18} +8.15841 q^{19} +2.10238 q^{20} +8.03169 q^{21} +4.91782 q^{22} +4.01851 q^{23} +2.31615 q^{24} -0.580000 q^{25} +2.17593 q^{26} +1.47183 q^{27} -3.46770 q^{28} -10.2466 q^{29} +4.86942 q^{30} -8.27632 q^{31} -1.00000 q^{32} +11.3904 q^{33} +4.15234 q^{34} -7.29041 q^{35} +2.36454 q^{36} +3.50759 q^{37} -8.15841 q^{38} +5.03978 q^{39} -2.10238 q^{40} -11.7871 q^{41} -8.03169 q^{42} +9.37123 q^{43} -4.91782 q^{44} +4.97115 q^{45} -4.01851 q^{46} -8.93292 q^{47} -2.31615 q^{48} +5.02492 q^{49} +0.580000 q^{50} +9.61744 q^{51} -2.17593 q^{52} -5.18743 q^{53} -1.47183 q^{54} -10.3391 q^{55} +3.46770 q^{56} -18.8961 q^{57} +10.2466 q^{58} -8.13173 q^{59} -4.86942 q^{60} -6.87505 q^{61} +8.27632 q^{62} -8.19949 q^{63} +1.00000 q^{64} -4.57464 q^{65} -11.3904 q^{66} +13.4320 q^{67} -4.15234 q^{68} -9.30745 q^{69} +7.29041 q^{70} +10.1292 q^{71} -2.36454 q^{72} -12.0318 q^{73} -3.50759 q^{74} +1.34336 q^{75} +8.15841 q^{76} +17.0535 q^{77} -5.03978 q^{78} -1.44676 q^{79} +2.10238 q^{80} -10.5026 q^{81} +11.7871 q^{82} -4.19355 q^{83} +8.03169 q^{84} -8.72980 q^{85} -9.37123 q^{86} +23.7327 q^{87} +4.91782 q^{88} -10.3682 q^{89} -4.97115 q^{90} +7.54547 q^{91} +4.01851 q^{92} +19.1692 q^{93} +8.93292 q^{94} +17.1521 q^{95} +2.31615 q^{96} +4.82288 q^{97} -5.02492 q^{98} -11.6284 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 69 q - 69 q^{2} + 11 q^{3} + 69 q^{4} - 2 q^{5} - 11 q^{6} + 23 q^{7} - 69 q^{8} + 72 q^{9}+O(q^{10}) \) 69 * q - 69 * q^2 + 11 * q^3 + 69 * q^4 - 2 * q^5 - 11 * q^6 + 23 * q^7 - 69 * q^8 + 72 * q^9	\( 69 q - 69 q^{2} + 11 q^{3} + 69 q^{4} - 2 q^{5} - 11 q^{6} + 23 q^{7} - 69 q^{8} + 72 q^{9} + 2 q^{10} - 14 q^{11} + 11 q^{12} + 31 q^{13} - 23 q^{14} + 34 q^{15} + 69 q^{16} - 4 q^{17} - 72 q^{18} + 17 q^{19} - 2 q^{20} - 11 q^{21} + 14 q^{22} + 33 q^{23} - 11 q^{24} + 119 q^{25} - 31 q^{26} + 44 q^{27} + 23 q^{28} - 25 q^{29} - 34 q^{30} + 49 q^{31} - 69 q^{32} + 10 q^{33} + 4 q^{34} - 11 q^{35} + 72 q^{36} + 73 q^{37} - 17 q^{38} + 31 q^{39} + 2 q^{40} - 46 q^{41} + 11 q^{42} + 76 q^{43} - 14 q^{44} + 9 q^{45} - 33 q^{46} + 23 q^{47} + 11 q^{48} + 100 q^{49} - 119 q^{50} + 25 q^{51} + 31 q^{52} + 30 q^{53} - 44 q^{54} + 81 q^{55} - 23 q^{56} + 12 q^{57} + 25 q^{58} - 3 q^{59} + 34 q^{60} + 13 q^{61} - 49 q^{62} + 65 q^{63} + 69 q^{64} - 27 q^{65} - 10 q^{66} + 105 q^{67} - 4 q^{68} + 19 q^{69} + 11 q^{70} + 51 q^{71} - 72 q^{72} + 43 q^{73} - 73 q^{74} + 77 q^{75} + 17 q^{76} - 19 q^{77} - 31 q^{78} + 89 q^{79} - 2 q^{80} + 73 q^{81} + 46 q^{82} - 10 q^{83} - 11 q^{84} + 44 q^{85} - 76 q^{86} + 57 q^{87} + 14 q^{88} - 28 q^{89} - 9 q^{90} + 76 q^{91} + 33 q^{92} + 59 q^{93} - 23 q^{94} + 72 q^{95} - 11 q^{96} + 89 q^{97} - 100 q^{98} - 17 q^{99}+O(q^{100}) \) 69 * q - 69 * q^2 + 11 * q^3 + 69 * q^4 - 2 * q^5 - 11 * q^6 + 23 * q^7 - 69 * q^8 + 72 * q^9 + 2 * q^10 - 14 * q^11 + 11 * q^12 + 31 * q^13 - 23 * q^14 + 34 * q^15 + 69 * q^16 - 4 * q^17 - 72 * q^18 + 17 * q^19 - 2 * q^20 - 11 * q^21 + 14 * q^22 + 33 * q^23 - 11 * q^24 + 119 * q^25 - 31 * q^26 + 44 * q^27 + 23 * q^28 - 25 * q^29 - 34 * q^30 + 49 * q^31 - 69 * q^32 + 10 * q^33 + 4 * q^34 - 11 * q^35 + 72 * q^36 + 73 * q^37 - 17 * q^38 + 31 * q^39 + 2 * q^40 - 46 * q^41 + 11 * q^42 + 76 * q^43 - 14 * q^44 + 9 * q^45 - 33 * q^46 + 23 * q^47 + 11 * q^48 + 100 * q^49 - 119 * q^50 + 25 * q^51 + 31 * q^52 + 30 * q^53 - 44 * q^54 + 81 * q^55 - 23 * q^56 + 12 * q^57 + 25 * q^58 - 3 * q^59 + 34 * q^60 + 13 * q^61 - 49 * q^62 + 65 * q^63 + 69 * q^64 - 27 * q^65 - 10 * q^66 + 105 * q^67 - 4 * q^68 + 19 * q^69 + 11 * q^70 + 51 * q^71 - 72 * q^72 + 43 * q^73 - 73 * q^74 + 77 * q^75 + 17 * q^76 - 19 * q^77 - 31 * q^78 + 89 * q^79 - 2 * q^80 + 73 * q^81 + 46 * q^82 - 10 * q^83 - 11 * q^84 + 44 * q^85 - 76 * q^86 + 57 * q^87 + 14 * q^88 - 28 * q^89 - 9 * q^90 + 76 * q^91 + 33 * q^92 + 59 * q^93 - 23 * q^94 + 72 * q^95 - 11 * q^96 + 89 * q^97 - 100 * q^98 - 17 * q^99

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