LMFDB - Embedded newform 6034.2.a.n.1.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6034,2,Mod(1,6034)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6034, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([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("6034.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6034 = 2 \cdot 7 \cdot 431 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6034.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:	$48.1817325796$
Analytic rank:	$0$
Dimension:	$24$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Character	$\chi$	$=$	6034.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -1.92027 q^{3} +1.00000 q^{4} -2.53143 q^{5} +1.92027 q^{6} -1.00000 q^{7} -1.00000 q^{8} +0.687441 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -1.92027 q^{3} +1.00000 q^{4} -2.53143 q^{5} +1.92027 q^{6} -1.00000 q^{7} -1.00000 q^{8} +0.687441 q^{9} +2.53143 q^{10} -3.57947 q^{11} -1.92027 q^{12} +3.61870 q^{13} +1.00000 q^{14} +4.86104 q^{15} +1.00000 q^{16} -0.257224 q^{17} -0.687441 q^{18} +0.598623 q^{19} -2.53143 q^{20} +1.92027 q^{21} +3.57947 q^{22} +8.37463 q^{23} +1.92027 q^{24} +1.40815 q^{25} -3.61870 q^{26} +4.44074 q^{27} -1.00000 q^{28} -4.10604 q^{29} -4.86104 q^{30} -10.1150 q^{31} -1.00000 q^{32} +6.87354 q^{33} +0.257224 q^{34} +2.53143 q^{35} +0.687441 q^{36} -4.11862 q^{37} -0.598623 q^{38} -6.94889 q^{39} +2.53143 q^{40} +2.61524 q^{41} -1.92027 q^{42} -2.17771 q^{43} -3.57947 q^{44} -1.74021 q^{45} -8.37463 q^{46} +4.93647 q^{47} -1.92027 q^{48} +1.00000 q^{49} -1.40815 q^{50} +0.493939 q^{51} +3.61870 q^{52} +1.94415 q^{53} -4.44074 q^{54} +9.06118 q^{55} +1.00000 q^{56} -1.14952 q^{57} +4.10604 q^{58} -8.21369 q^{59} +4.86104 q^{60} -15.5521 q^{61} +10.1150 q^{62} -0.687441 q^{63} +1.00000 q^{64} -9.16050 q^{65} -6.87354 q^{66} -8.51172 q^{67} -0.257224 q^{68} -16.0816 q^{69} -2.53143 q^{70} -4.42305 q^{71} -0.687441 q^{72} -9.04366 q^{73} +4.11862 q^{74} -2.70403 q^{75} +0.598623 q^{76} +3.57947 q^{77} +6.94889 q^{78} -2.43578 q^{79} -2.53143 q^{80} -10.5897 q^{81} -2.61524 q^{82} +1.85571 q^{83} +1.92027 q^{84} +0.651144 q^{85} +2.17771 q^{86} +7.88471 q^{87} +3.57947 q^{88} +15.7350 q^{89} +1.74021 q^{90} -3.61870 q^{91} +8.37463 q^{92} +19.4235 q^{93} -4.93647 q^{94} -1.51537 q^{95} +1.92027 q^{96} -11.1596 q^{97} -1.00000 q^{98} -2.46067 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 24 q^{2} + 7 q^{3} + 24 q^{4} + 8 q^{5} - 7 q^{6} - 24 q^{7} - 24 q^{8} + 19 q^{9}+O(q^{10}) $ 24 * q - 24 * q^2 + 7 * q^3 + 24 * q^4 + 8 * q^5 - 7 * q^6 - 24 * q^7 - 24 * q^8 + 19 * q^9	\( 24 q - 24 q^{2} + 7 q^{3} + 24 q^{4} + 8 q^{5} - 7 q^{6} - 24 q^{7} - 24 q^{8} + 19 q^{9} - 8 q^{10} + 15 q^{11} + 7 q^{12} - 7 q^{13} + 24 q^{14} + 13 q^{15} + 24 q^{16} - 5 q^{17} - 19 q^{18} + 6 q^{19} + 8 q^{20} - 7 q^{21} - 15 q^{22} + 3 q^{23} - 7 q^{24} + 12 q^{25} + 7 q^{26} + 22 q^{27} - 24 q^{28} + 5 q^{29} - 13 q^{30} + 13 q^{31} - 24 q^{32} - 8 q^{33} + 5 q^{34} - 8 q^{35} + 19 q^{36} + 2 q^{37} - 6 q^{38} + 7 q^{39} - 8 q^{40} + 25 q^{41} + 7 q^{42} - 15 q^{43} + 15 q^{44} + 41 q^{45} - 3 q^{46} + 35 q^{47} + 7 q^{48} + 24 q^{49} - 12 q^{50} + 31 q^{51} - 7 q^{52} + 2 q^{53} - 22 q^{54} + 14 q^{55} + 24 q^{56} - 13 q^{57} - 5 q^{58} + 35 q^{59} + 13 q^{60} - 7 q^{61} - 13 q^{62} - 19 q^{63} + 24 q^{64} - 4 q^{65} + 8 q^{66} + 10 q^{67} - 5 q^{68} + 6 q^{69} + 8 q^{70} + 58 q^{71} - 19 q^{72} + 9 q^{73} - 2 q^{74} + 7 q^{75} + 6 q^{76} - 15 q^{77} - 7 q^{78} + 31 q^{79} + 8 q^{80} + 16 q^{81} - 25 q^{82} - q^{83} - 7 q^{84} - 4 q^{85} + 15 q^{86} + 30 q^{87} - 15 q^{88} + 45 q^{89} - 41 q^{90} + 7 q^{91} + 3 q^{92} + 25 q^{93} - 35 q^{94} - 10 q^{95} - 7 q^{96} - 9 q^{97} - 24 q^{98} + 64 q^{99}+O(q^{100}) \) 24 * q - 24 * q^2 + 7 * q^3 + 24 * q^4 + 8 * q^5 - 7 * q^6 - 24 * q^7 - 24 * q^8 + 19 * q^9 - 8 * q^10 + 15 * q^11 + 7 * q^12 - 7 * q^13 + 24 * q^14 + 13 * q^15 + 24 * q^16 - 5 * q^17 - 19 * q^18 + 6 * q^19 + 8 * q^20 - 7 * q^21 - 15 * q^22 + 3 * q^23 - 7 * q^24 + 12 * q^25 + 7 * q^26 + 22 * q^27 - 24 * q^28 + 5 * q^29 - 13 * q^30 + 13 * q^31 - 24 * q^32 - 8 * q^33 + 5 * q^34 - 8 * q^35 + 19 * q^36 + 2 * q^37 - 6 * q^38 + 7 * q^39 - 8 * q^40 + 25 * q^41 + 7 * q^42 - 15 * q^43 + 15 * q^44 + 41 * q^45 - 3 * q^46 + 35 * q^47 + 7 * q^48 + 24 * q^49 - 12 * q^50 + 31 * q^51 - 7 * q^52 + 2 * q^53 - 22 * q^54 + 14 * q^55 + 24 * q^56 - 13 * q^57 - 5 * q^58 + 35 * q^59 + 13 * q^60 - 7 * q^61 - 13 * q^62 - 19 * q^63 + 24 * q^64 - 4 * q^65 + 8 * q^66 + 10 * q^67 - 5 * q^68 + 6 * q^69 + 8 * q^70 + 58 * q^71 - 19 * q^72 + 9 * q^73 - 2 * q^74 + 7 * q^75 + 6 * q^76 - 15 * q^77 - 7 * q^78 + 31 * q^79 + 8 * q^80 + 16 * q^81 - 25 * q^82 - q^83 - 7 * q^84 - 4 * q^85 + 15 * q^86 + 30 * q^87 - 15 * q^88 + 45 * q^89 - 41 * q^90 + 7 * q^91 + 3 * q^92 + 25 * q^93 - 35 * q^94 - 10 * q^95 - 7 * q^96 - 9 * q^97 - 24 * q^98 + 64 * 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
$3$	−1.92027	−1.10867	−0.554334	−	0.832294i	$-0.687027\pi$
$3$	−1.92027	−1.10867	−0.554334	+	0.832294i	$0.687027\pi$
$4$	1.00000	0.500000
$5$	−2.53143	−1.13209	−0.566046	−	0.824374i	$-0.691527\pi$
$5$	−2.53143	−1.13209	−0.566046	+	0.824374i	$0.691527\pi$
$6$	1.92027	0.783947
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	−1.00000	−0.353553
$9$	0.687441	0.229147
$10$	2.53143	0.800509
$11$	−3.57947	−1.07925	−0.539625	−	0.841906i	$-0.681434\pi$
$11$	−3.57947	−1.07925	−0.539625	+	0.841906i	$0.681434\pi$
$12$	−1.92027	−0.554334
$13$	3.61870	1.00365	0.501824	−	0.864970i	$-0.332663\pi$
$13$	3.61870	1.00365	0.501824	+	0.864970i	$0.332663\pi$
$14$	1.00000	0.267261
$15$	4.86104	1.25511
$16$	1.00000	0.250000
$17$	−0.257224	−0.0623859	−0.0311929	−	0.999513i	$-0.509931\pi$
$17$	−0.257224	−0.0623859	−0.0311929	+	0.999513i	$0.509931\pi$
$18$	−0.687441	−0.162031
$19$	0.598623	0.137333	0.0686667	−	0.997640i	$-0.478125\pi$
$19$	0.598623	0.137333	0.0686667	+	0.997640i	$0.478125\pi$
$20$	−2.53143	−0.566046
$21$	1.92027	0.419037
$22$	3.57947	0.763145
$23$	8.37463	1.74623	0.873116	−	0.487513i	$-0.162096\pi$
$23$	8.37463	1.74623	0.873116	+	0.487513i	$0.162096\pi$
$24$	1.92027	0.391974
$25$	1.40815	0.281630
$26$	−3.61870	−0.709686
$27$	4.44074	0.854621
$28$	−1.00000	−0.188982
$29$	−4.10604	−0.762472	−0.381236	−	0.924478i	$-0.624502\pi$
$29$	−4.10604	−0.762472	−0.381236	+	0.924478i	$0.624502\pi$
$30$	−4.86104	−0.887500
$31$	−10.1150	−1.81671	−0.908353	−	0.418204i	$-0.862660\pi$
$31$	−10.1150	−1.81671	−0.908353	+	0.418204i	$0.862660\pi$
$32$	−1.00000	−0.176777
$33$	6.87354	1.19653
$34$	0.257224	0.0441135
$35$	2.53143	0.427890
$36$	0.687441	0.114573
$37$	−4.11862	−0.677096	−0.338548	−	0.940949i	$-0.609936\pi$
$37$	−4.11862	−0.677096	−0.338548	+	0.940949i	$0.609936\pi$
$38$	−0.598623	−0.0971094
$39$	−6.94889	−1.11271
$40$	2.53143	0.400255
$41$	2.61524	0.408432	0.204216	−	0.978926i	$-0.434535\pi$
$41$	2.61524	0.408432	0.204216	+	0.978926i	$0.434535\pi$
$42$	−1.92027	−0.296304
$43$	−2.17771	−0.332098	−0.166049	−	0.986118i	$-0.553101\pi$
$43$	−2.17771	−0.332098	−0.166049	+	0.986118i	$0.553101\pi$
$44$	−3.57947	−0.539625
$45$	−1.74021	−0.259415
$46$	−8.37463	−1.23477
$47$	4.93647	0.720058	0.360029	−	0.932941i	$-0.382767\pi$
$47$	4.93647	0.720058	0.360029	+	0.932941i	$0.382767\pi$
$48$	−1.92027	−0.277167
$49$	1.00000	0.142857
$50$	−1.40815	−0.199143
$51$	0.493939	0.0691653
$52$	3.61870	0.501824
$53$	1.94415	0.267049	0.133525	−	0.991046i	$-0.457371\pi$
$53$	1.94415	0.267049	0.133525	+	0.991046i	$0.457371\pi$
$54$	−4.44074	−0.604308
$55$	9.06118	1.22181
$56$	1.00000	0.133631
$57$	−1.14952	−0.152257
$58$	4.10604	0.539149
$59$	−8.21369	−1.06933	−0.534666	−	0.845064i	$-0.679563\pi$
$59$	−8.21369	−1.06933	−0.534666	+	0.845064i	$0.679563\pi$
$60$	4.86104	0.627557
$61$	−15.5521	−1.99124	−0.995621	−	0.0934776i	$-0.970202\pi$
$61$	−15.5521	−1.99124	−0.995621	+	0.0934776i	$0.970202\pi$
$62$	10.1150	1.28461
$63$	−0.687441	−0.0866094
$64$	1.00000	0.125000
$65$	−9.16050	−1.13622
$66$	−6.87354	−0.846075
$67$	−8.51172	−1.03987	−0.519936	−	0.854205i	$-0.674044\pi$
$67$	−8.51172	−1.03987	−0.519936	+	0.854205i	$0.674044\pi$
$68$	−0.257224	−0.0311929
$69$	−16.0816	−1.93599
$70$	−2.53143	−0.302564
$71$	−4.42305	−0.524919	−0.262460	−	0.964943i	$-0.584534\pi$
$71$	−4.42305	−0.524919	−0.262460	+	0.964943i	$0.584534\pi$
$72$	−0.687441	−0.0810157
$73$	−9.04366	−1.05848	−0.529240	−	0.848472i	$-0.677523\pi$
$73$	−9.04366	−1.05848	−0.529240	+	0.848472i	$0.677523\pi$
$74$	4.11862	0.478779
$75$	−2.70403	−0.312235
$76$	0.598623	0.0686667
$77$	3.57947	0.407918
$78$	6.94889	0.786807
$79$	−2.43578	−0.274047	−0.137023	−	0.990568i	$-0.543754\pi$
$79$	−2.43578	−0.274047	−0.137023	+	0.990568i	$0.543754\pi$
$80$	−2.53143	−0.283023
$81$	−10.5897	−1.17664
$82$	−2.61524	−0.288805
$83$	1.85571	0.203691	0.101845	−	0.994800i	$-0.467525\pi$
$83$	1.85571	0.203691	0.101845	+	0.994800i	$0.467525\pi$
$84$	1.92027	0.209519
$85$	0.651144	0.0706265
$86$	2.17771	0.234828
$87$	7.88471	0.845329
$88$	3.57947	0.381572
$89$	15.7350	1.66790	0.833952	−	0.551838i	$-0.186073\pi$
$89$	15.7350	1.66790	0.833952	+	0.551838i	$0.186073\pi$
$90$	1.74021	0.183434
$91$	−3.61870	−0.379343
$92$	8.37463	0.873116
$93$	19.4235	2.01413
$94$	−4.93647	−0.509158
$95$	−1.51537	−0.155474
$96$	1.92027	0.195987
$97$	−11.1596	−1.13309	−0.566545	−	0.824031i	$-0.691720\pi$
$97$	−11.1596	−1.13309	−0.566545	+	0.824031i	$0.691720\pi$
$98$	−1.00000	−0.101015
$99$	−2.46067	−0.247307
$100$	1.40815	0.140815
$101$	−4.51337	−0.449097	−0.224548	−	0.974463i	$-0.572091\pi$
$101$	−4.51337	−0.449097	−0.224548	+	0.974463i	$0.572091\pi$
$102$	−0.493939	−0.0489072
$103$	−6.56636	−0.647003	−0.323502	−	0.946228i	$-0.604860\pi$
$103$	−6.56636	−0.647003	−0.323502	+	0.946228i	$0.604860\pi$
$104$	−3.61870	−0.354843
$105$	−4.86104	−0.474389
$106$	−1.94415	−0.188832
$107$	−8.62604	−0.833911	−0.416956	−	0.908927i	$-0.636903\pi$
$107$	−8.62604	−0.833911	−0.416956	+	0.908927i	$0.636903\pi$
$108$	4.44074	0.427310
$109$	9.73455	0.932400	0.466200	−	0.884679i	$-0.345623\pi$
$109$	9.73455	0.932400	0.466200	+	0.884679i	$0.345623\pi$
$110$	−9.06118	−0.863949
$111$	7.90886	0.750676
$112$	−1.00000	−0.0944911
$113$	−12.9385	−1.21715	−0.608574	−	0.793497i	$-0.708258\pi$
$113$	−12.9385	−1.21715	−0.608574	+	0.793497i	$0.708258\pi$
$114$	1.14952	0.107662
$115$	−21.1998	−1.97689
$116$	−4.10604	−0.381236
$117$	2.48764	0.229983
$118$	8.21369	0.756132
$119$	0.257224	0.0235796
$120$	−4.86104	−0.443750
$121$	1.81257	0.164779
$122$	15.5521	1.40802
$123$	−5.02197	−0.452816
$124$	−10.1150	−0.908353
$125$	9.09252	0.813260
$126$	0.687441	0.0612421
$127$	−10.1471	−0.900411	−0.450206	−	0.892925i	$-0.648649\pi$
$127$	−10.1471	−0.900411	−0.450206	+	0.892925i	$0.648649\pi$
$128$	−1.00000	−0.0883883
$129$	4.18179	0.368186
$130$	9.16050	0.803429
$131$	11.9416	1.04334	0.521672	−	0.853146i	$-0.325309\pi$
$131$	11.9416	1.04334	0.521672	+	0.853146i	$0.325309\pi$
$132$	6.87354	0.598265
$133$	−0.598623	−0.0519072
$134$	8.51172	0.735300
$135$	−11.2414	−0.967509
$136$	0.257224	0.0220567
$137$	9.15383	0.782064	0.391032	−	0.920377i	$-0.372118\pi$
$137$	9.15383	0.782064	0.391032	+	0.920377i	$0.372118\pi$
$138$	16.0816	1.36895
$139$	−0.332567	−0.0282079	−0.0141040	−	0.999901i	$-0.504490\pi$
$139$	−0.332567	−0.0282079	−0.0141040	+	0.999901i	$0.504490\pi$
$140$	2.53143	0.213945
$141$	−9.47935	−0.798306
$142$	4.42305	0.371174
$143$	−12.9530	−1.08319
$144$	0.687441	0.0572867
$145$	10.3942	0.863188
$146$	9.04366	0.748459
$147$	−1.92027	−0.158381
$148$	−4.11862	−0.338548
$149$	−6.88464	−0.564012	−0.282006	−	0.959413i	$-0.591000\pi$
$149$	−6.88464	−0.564012	−0.282006	+	0.959413i	$0.591000\pi$
$150$	2.70403	0.220783
$151$	−1.65194	−0.134433	−0.0672165	−	0.997738i	$-0.521412\pi$
$151$	−1.65194	−0.134433	−0.0672165	+	0.997738i	$0.521412\pi$
$152$	−0.598623	−0.0485547
$153$	−0.176826	−0.0142955
$154$	−3.57947	−0.288442
$155$	25.6054	2.05668
$156$	−6.94889	−0.556357
$157$	−8.97337	−0.716153	−0.358076	−	0.933692i	$-0.616567\pi$
$157$	−8.97337	−0.716153	−0.358076	+	0.933692i	$0.616567\pi$
$158$	2.43578	0.193780
$159$	−3.73329	−0.296069
$160$	2.53143	0.200127
$161$	−8.37463	−0.660013
$162$	10.5897	0.832009
$163$	12.9833	1.01693	0.508465	−	0.861083i	$-0.330213\pi$
$163$	12.9833	1.01693	0.508465	+	0.861083i	$0.330213\pi$
$164$	2.61524	0.204216
$165$	−17.3999	−1.35458
$166$	−1.85571	−0.144031
$167$	4.34910	0.336543	0.168272	−	0.985741i	$-0.446181\pi$
$167$	4.34910	0.336543	0.168272	+	0.985741i	$0.446181\pi$
$168$	−1.92027	−0.148152
$169$	0.0950129	0.00730869
$170$	−0.651144	−0.0499405
$171$	0.411518	0.0314695
$172$	−2.17771	−0.166049
$173$	19.2037	1.46003	0.730013	−	0.683433i	$-0.239514\pi$
$173$	19.2037	1.46003	0.730013	+	0.683433i	$0.239514\pi$
$174$	−7.88471	−0.597738
$175$	−1.40815	−0.106446
$176$	−3.57947	−0.269812
$177$	15.7725	1.18553
$178$	−15.7350	−1.17939
$179$	12.8897	0.963424	0.481712	−	0.876330i	$-0.340015\pi$
$179$	12.8897	0.963424	0.481712	+	0.876330i	$0.340015\pi$
$180$	−1.74021	−0.129708
$181$	−19.4900	−1.44868	−0.724340	−	0.689443i	$-0.757855\pi$
$181$	−19.4900	−1.44868	−0.724340	+	0.689443i	$0.757855\pi$
$182$	3.61870	0.268236
$183$	29.8643	2.20763
$184$	−8.37463	−0.617386
$185$	10.4260	0.766535
$186$	−19.4235	−1.42420
$187$	0.920723	0.0673299
$188$	4.93647	0.360029
$189$	−4.44074	−0.323016
$190$	1.51537	0.109937
$191$	21.3778	1.54684	0.773422	−	0.633891i	$-0.218543\pi$
$191$	21.3778	1.54684	0.773422	+	0.633891i	$0.218543\pi$
$192$	−1.92027	−0.138584
$193$	−3.51896	−0.253300	−0.126650	−	0.991947i	$-0.540423\pi$
$193$	−3.51896	−0.253300	−0.126650	+	0.991947i	$0.540423\pi$
$194$	11.1596	0.801216
$195$	17.5906	1.25969
$196$	1.00000	0.0714286
$197$	−12.9752	−0.924443	−0.462222	−	0.886764i	$-0.652948\pi$
$197$	−12.9752	−0.924443	−0.462222	+	0.886764i	$0.652948\pi$
$198$	2.46067	0.174872
$199$	24.2163	1.71665	0.858325	−	0.513107i	$-0.171505\pi$
$199$	24.2163	1.71665	0.858325	+	0.513107i	$0.171505\pi$
$200$	−1.40815	−0.0995714
$201$	16.3448	1.15287
$202$	4.51337	0.317559
$203$	4.10604	0.288187
$204$	0.493939	0.0345826
$205$	−6.62031	−0.462383
$206$	6.56636	0.457500
$207$	5.75706	0.400143
$208$	3.61870	0.250912
$209$	−2.14275	−0.148217
$210$	4.86104	0.335443
$211$	−17.3419	−1.19387	−0.596933	−	0.802291i	$-0.703614\pi$
$211$	−17.3419	−1.19387	−0.596933	+	0.802291i	$0.703614\pi$
$212$	1.94415	0.133525
$213$	8.49345	0.581962
$214$	8.62604	0.589664
$215$	5.51272	0.375965
$216$	−4.44074	−0.302154
$217$	10.1150	0.686650
$218$	−9.73455	−0.659307
$219$	17.3663	1.17350
$220$	9.06118	0.610904
$221$	−0.930816	−0.0626134
$222$	−7.90886	−0.530808
$223$	16.5519	1.10840	0.554199	−	0.832384i	$-0.313025\pi$
$223$	16.5519	1.10840	0.554199	+	0.832384i	$0.313025\pi$
$224$	1.00000	0.0668153
$225$	0.968021	0.0645347
$226$	12.9385	0.860653
$227$	−4.67367	−0.310203	−0.155101	−	0.987899i	$-0.549570\pi$
$227$	−4.67367	−0.310203	−0.155101	+	0.987899i	$0.549570\pi$
$228$	−1.14952	−0.0761287
$229$	−22.0926	−1.45992	−0.729959	−	0.683491i	$-0.760461\pi$
$229$	−22.0926	−1.45992	−0.729959	+	0.683491i	$0.760461\pi$
$230$	21.1998	1.39787
$231$	−6.87354	−0.452246
$232$	4.10604	0.269575
$233$	−18.0457	−1.18221	−0.591106	−	0.806594i	$-0.701308\pi$
$233$	−18.0457	−1.18221	−0.591106	+	0.806594i	$0.701308\pi$
$234$	−2.48764	−0.162622
$235$	−12.4963	−0.815171
$236$	−8.21369	−0.534666
$237$	4.67736	0.303827
$238$	−0.257224	−0.0166733
$239$	−22.6294	−1.46377	−0.731887	−	0.681426i	$-0.761360\pi$
$239$	−22.6294	−1.46377	−0.731887	+	0.681426i	$0.761360\pi$
$240$	4.86104	0.313779
$241$	−4.88488	−0.314663	−0.157331	−	0.987546i	$-0.550289\pi$
$241$	−4.88488	−0.314663	−0.157331	+	0.987546i	$0.550289\pi$
$242$	−1.81257	−0.116517
$243$	7.01296	0.449882
$244$	−15.5521	−0.995621
$245$	−2.53143	−0.161727
$246$	5.02197	0.320189
$247$	2.16624	0.137834
$248$	10.1150	0.642303
$249$	−3.56347	−0.225826
$250$	−9.09252	−0.575062
$251$	5.84078	0.368667	0.184333	−	0.982864i	$-0.440987\pi$
$251$	5.84078	0.368667	0.184333	+	0.982864i	$0.440987\pi$
$252$	−0.687441	−0.0433047
$253$	−29.9767	−1.88462
$254$	10.1471	0.636687
$255$	−1.25037	−0.0783014
$256$	1.00000	0.0625000
$257$	5.57160	0.347547	0.173773	−	0.984786i	$-0.444404\pi$
$257$	5.57160	0.347547	0.173773	+	0.984786i	$0.444404\pi$
$258$	−4.18179	−0.260347
$259$	4.11862	0.255918
$260$	−9.16050	−0.568110
$261$	−2.82266	−0.174718
$262$	−11.9416	−0.737755
$263$	−21.9048	−1.35071	−0.675353	−	0.737495i	$-0.736009\pi$
$263$	−21.9048	−1.35071	−0.675353	+	0.737495i	$0.736009\pi$
$264$	−6.87354	−0.423037
$265$	−4.92148	−0.302324
$266$	0.598623	0.0367039
$267$	−30.2154	−1.84915
$268$	−8.51172	−0.519936
$269$	15.3493	0.935866	0.467933	−	0.883764i	$-0.344999\pi$
$269$	15.3493	0.935866	0.467933	+	0.883764i	$0.344999\pi$
$270$	11.2414	0.684132
$271$	29.7738	1.80863	0.904315	−	0.426866i	$-0.140382\pi$
$271$	29.7738	1.80863	0.904315	+	0.426866i	$0.140382\pi$
$272$	−0.257224	−0.0155965
$273$	6.94889	0.420566
$274$	−9.15383	−0.553003
$275$	−5.04043	−0.303949
$276$	−16.0816	−0.967996
$277$	−23.7870	−1.42922	−0.714610	−	0.699523i	$-0.753396\pi$
$277$	−23.7870	−1.42922	−0.714610	+	0.699523i	$0.753396\pi$
$278$	0.332567	0.0199460
$279$	−6.95346	−0.416293
$280$	−2.53143	−0.151282
$281$	1.87745	0.112000	0.0559998	−	0.998431i	$-0.482165\pi$
$281$	1.87745	0.112000	0.0559998	+	0.998431i	$0.482165\pi$
$282$	9.47935	0.564487
$283$	−15.9527	−0.948290	−0.474145	−	0.880447i	$-0.657243\pi$
$283$	−15.9527	−0.948290	−0.474145	+	0.880447i	$0.657243\pi$
$284$	−4.42305	−0.262460
$285$	2.90993	0.172369
$286$	12.9530	0.765928
$287$	−2.61524	−0.154373
$288$	−0.687441	−0.0405078
$289$	−16.9338	−0.996108
$290$	−10.3942	−0.610366
$291$	21.4295	1.25622
$292$	−9.04366	−0.529240
$293$	−6.31742	−0.369067	−0.184534	−	0.982826i	$-0.559077\pi$
$293$	−6.31742	−0.369067	−0.184534	+	0.982826i	$0.559077\pi$
$294$	1.92027	0.111992
$295$	20.7924	1.21058
$296$	4.11862	0.239390
$297$	−15.8955	−0.922349
$298$	6.88464	0.398817
$299$	30.3053	1.75260
$300$	−2.70403	−0.156117
$301$	2.17771	0.125521
$302$	1.65194	0.0950585
$303$	8.66689	0.497900
$304$	0.598623	0.0343334
$305$	39.3691	2.25427
$306$	0.176826	0.0101085
$307$	12.5877	0.718415	0.359208	−	0.933258i	$-0.383047\pi$
$307$	12.5877	0.718415	0.359208	+	0.933258i	$0.383047\pi$
$308$	3.57947	0.203959
$309$	12.6092	0.717312
$310$	−25.6054	−1.45429
$311$	−25.4835	−1.44504	−0.722519	−	0.691351i	$-0.757016\pi$
$311$	−25.4835	−1.44504	−0.722519	+	0.691351i	$0.757016\pi$
$312$	6.94889	0.393403
$313$	14.0108	0.791940	0.395970	−	0.918263i	$-0.370408\pi$
$313$	14.0108	0.791940	0.395970	+	0.918263i	$0.370408\pi$
$314$	8.97337	0.506397
$315$	1.74021	0.0980497
$316$	−2.43578	−0.137023
$317$	30.6658	1.72236	0.861181	−	0.508299i	$-0.169726\pi$
$317$	30.6658	1.72236	0.861181	+	0.508299i	$0.169726\pi$
$318$	3.73329	0.209352
$319$	14.6974	0.822898
$320$	−2.53143	−0.141511
$321$	16.5643	0.924531
$322$	8.37463	0.466700
$323$	−0.153980	−0.00856767
$324$	−10.5897	−0.588319
$325$	5.09568	0.282658
$326$	−12.9833	−0.719078
$327$	−18.6930	−1.03372
$328$	−2.61524	−0.144403
$329$	−4.93647	−0.272156
$330$	17.3999	0.957834
$331$	−17.5804	−0.966306	−0.483153	−	0.875536i	$-0.660508\pi$
$331$	−17.5804	−0.966306	−0.483153	+	0.875536i	$0.660508\pi$
$332$	1.85571	0.101845
$333$	−2.83130	−0.155155
$334$	−4.34910	−0.237972
$335$	21.5468	1.17723
$336$	1.92027	0.104759
$337$	2.39027	0.130206	0.0651031	−	0.997879i	$-0.479262\pi$
$337$	2.39027	0.130206	0.0651031	+	0.997879i	$0.479262\pi$
$338$	−0.0950129	−0.00516802
$339$	24.8453	1.34941
$340$	0.651144	0.0353132
$341$	36.2063	1.96068
$342$	−0.411518	−0.0222523
$343$	−1.00000	−0.0539949
$344$	2.17771	0.117414
$345$	40.7094	2.19172
$346$	−19.2037	−1.03239
$347$	−0.211265	−0.0113413	−0.00567064	−	0.999984i	$-0.501805\pi$
$347$	−0.211265	−0.0113413	−0.00567064	+	0.999984i	$0.501805\pi$
$348$	7.88471	0.422665
$349$	3.91333	0.209476	0.104738	−	0.994500i	$-0.466600\pi$
$349$	3.91333	0.209476	0.104738	+	0.994500i	$0.466600\pi$
$350$	1.40815	0.0752689
$351$	16.0697	0.857738
$352$	3.57947	0.190786
$353$	9.57877	0.509827	0.254913	−	0.966964i	$-0.417953\pi$
$353$	9.57877	0.509827	0.254913	+	0.966964i	$0.417953\pi$
$354$	−15.7725	−0.838300
$355$	11.1967	0.594257
$356$	15.7350	0.833952
$357$	−0.493939	−0.0261420
$358$	−12.8897	−0.681244
$359$	28.8694	1.52367	0.761834	−	0.647772i	$-0.224299\pi$
$359$	28.8694	1.52367	0.761834	+	0.647772i	$0.224299\pi$
$360$	1.74021	0.0917171
$361$	−18.6417	−0.981140
$362$	19.4900	1.02437
$363$	−3.48063	−0.182686
$364$	−3.61870	−0.189672
$365$	22.8934	1.19830
$366$	−29.8643	−1.56103
$367$	2.06116	0.107591	0.0537957	−	0.998552i	$-0.482868\pi$
$367$	2.06116	0.107591	0.0537957	+	0.998552i	$0.482868\pi$
$368$	8.37463	0.436558
$369$	1.79782	0.0935910
$370$	−10.4260	−0.542022
$371$	−1.94415	−0.100935
$372$	19.4235	1.00706
$373$	−9.76150	−0.505431	−0.252716	−	0.967541i	$-0.581324\pi$
$373$	−9.76150	−0.505431	−0.252716	+	0.967541i	$0.581324\pi$
$374$	−0.920723	−0.0476094
$375$	−17.4601	−0.901636
$376$	−4.93647	−0.254579
$377$	−14.8585	−0.765253
$378$	4.44074	0.228407
$379$	36.6366	1.88189	0.940947	−	0.338554i	$-0.109938\pi$
$379$	36.6366	1.88189	0.940947	+	0.338554i	$0.109938\pi$
$380$	−1.51537	−0.0777370
$381$	19.4852	0.998258
$382$	−21.3778	−1.09378
$383$	11.9608	0.611166	0.305583	−	0.952165i	$-0.401149\pi$
$383$	11.9608	0.611166	0.305583	+	0.952165i	$0.401149\pi$
$384$	1.92027	0.0979934
$385$	−9.06118	−0.461800
$386$	3.51896	0.179110
$387$	−1.49705	−0.0760991
$388$	−11.1596	−0.566545
$389$	−19.3100	−0.979054	−0.489527	−	0.871988i	$-0.662831\pi$
$389$	−19.3100	−0.979054	−0.489527	+	0.871988i	$0.662831\pi$
$390$	−17.5906	−0.890737
$391$	−2.15415	−0.108940
$392$	−1.00000	−0.0505076
$393$	−22.9311	−1.15672
$394$	12.9752	0.653680
$395$	6.16601	0.310246
$396$	−2.46067	−0.123653
$397$	21.5798	1.08306	0.541528	−	0.840683i	$-0.317846\pi$
$397$	21.5798	1.08306	0.541528	+	0.840683i	$0.317846\pi$
$398$	−24.2163	−1.21385
$399$	1.14952	0.0575479
$400$	1.40815	0.0704076
$401$	17.0332	0.850598	0.425299	−	0.905053i	$-0.360169\pi$
$401$	17.0332	0.850598	0.425299	+	0.905053i	$0.360169\pi$
$402$	−16.3448	−0.815205
$403$	−36.6032	−1.82333
$404$	−4.51337	−0.224548
$405$	26.8072	1.33206
$406$	−4.10604	−0.203779
$407$	14.7424	0.730756
$408$	−0.493939	−0.0244536
$409$	36.8660	1.82290	0.911452	−	0.411406i	$-0.134962\pi$
$409$	36.8660	1.82290	0.911452	+	0.411406i	$0.134962\pi$
$410$	6.62031	0.326954
$411$	−17.5778	−0.867051
$412$	−6.56636	−0.323502
$413$	8.21369	0.404169
$414$	−5.75706	−0.282944
$415$	−4.69761	−0.230596
$416$	−3.61870	−0.177422
$417$	0.638618	0.0312733
$418$	2.14275	0.104805
$419$	−36.8813	−1.80177	−0.900884	−	0.434060i	$-0.857081\pi$
$419$	−36.8813	−1.80177	−0.900884	+	0.434060i	$0.857081\pi$
$420$	−4.86104	−0.237194
$421$	−8.50994	−0.414749	−0.207375	−	0.978262i	$-0.566492\pi$
$421$	−8.50994	−0.414749	−0.207375	+	0.978262i	$0.566492\pi$
$422$	17.3419	0.844190
$423$	3.39353	0.164999
$424$	−1.94415	−0.0944161
$425$	−0.362210	−0.0175698
$426$	−8.49345	−0.411509
$427$	15.5521	0.752619
$428$	−8.62604	−0.416956
$429$	24.8733	1.20089
$430$	−5.51272	−0.265847
$431$	1.00000	0.0481683
$431$	1.00000	0.0481683
$432$	4.44074	0.213655
$433$	26.8256	1.28916	0.644578	−	0.764539i	$-0.277033\pi$
$433$	26.8256	1.28916	0.644578	+	0.764539i	$0.277033\pi$
$434$	−10.1150	−0.485535
$435$	−19.9596	−0.956990
$436$	9.73455	0.466200
$437$	5.01324	0.239816
$438$	−17.3663	−0.829793
$439$	29.2805	1.39748	0.698741	−	0.715375i	$-0.253744\pi$
$439$	29.2805	1.39748	0.698741	+	0.715375i	$0.253744\pi$
$440$	−9.06118	−0.431975
$441$	0.687441	0.0327353
$442$	0.930816	0.0442744
$443$	−27.1409	−1.28950	−0.644752	−	0.764392i	$-0.723039\pi$
$443$	−27.1409	−1.28950	−0.644752	+	0.764392i	$0.723039\pi$
$444$	7.90886	0.375338
$445$	−39.8320	−1.88822
$446$	−16.5519	−0.783755
$447$	13.2204	0.625303
$448$	−1.00000	−0.0472456
$449$	−4.32527	−0.204122	−0.102061	−	0.994778i	$-0.532544\pi$
$449$	−4.32527	−0.204122	−0.102061	+	0.994778i	$0.532544\pi$
$450$	−0.968021	−0.0456329
$451$	−9.36117	−0.440800
$452$	−12.9385	−0.608574
$453$	3.17217	0.149042
$454$	4.67367	0.219346
$455$	9.16050	0.429451
$456$	1.14952	0.0538311
$457$	28.1770	1.31806	0.659032	−	0.752115i	$-0.270966\pi$
$457$	28.1770	1.31806	0.659032	+	0.752115i	$0.270966\pi$
$458$	22.0926	1.03232
$459$	−1.14226	−0.0533163
$460$	−21.1998	−0.988446
$461$	11.8908	0.553808	0.276904	−	0.960898i	$-0.410692\pi$
$461$	11.8908	0.553808	0.276904	+	0.960898i	$0.410692\pi$
$462$	6.87354	0.319786
$463$	19.8802	0.923910	0.461955	−	0.886903i	$-0.347148\pi$
$463$	19.8802	0.923910	0.461955	+	0.886903i	$0.347148\pi$
$464$	−4.10604	−0.190618
$465$	−49.1694	−2.28017
$466$	18.0457	0.835949
$467$	−18.2222	−0.843222	−0.421611	−	0.906777i	$-0.638535\pi$
$467$	−18.2222	−0.843222	−0.421611	+	0.906777i	$0.638535\pi$
$468$	2.48764	0.114991
$469$	8.51172	0.393035
$470$	12.4963	0.576413
$471$	17.2313	0.793976
$472$	8.21369	0.378066
$473$	7.79504	0.358416
$474$	−4.67736	−0.214838
$475$	0.842951	0.0386773
$476$	0.257224	0.0117898
$477$	1.33649	0.0611935
$478$	22.6294	1.03504
$479$	33.3364	1.52318	0.761590	−	0.648059i	$-0.224419\pi$
$479$	33.3364	1.52318	0.761590	+	0.648059i	$0.224419\pi$
$480$	−4.86104	−0.221875
$481$	−14.9040	−0.679566
$482$	4.88488	0.222500
$483$	16.0816	0.731736
$484$	1.81257	0.0823896
$485$	28.2499	1.28276
$486$	−7.01296	−0.318114
$487$	23.6231	1.07047	0.535233	−	0.844704i	$-0.320224\pi$
$487$	23.6231	1.07047	0.535233	+	0.844704i	$0.320224\pi$
$488$	15.5521	0.704011
$489$	−24.9314	−1.12744
$490$	2.53143	0.114358
$491$	25.5752	1.15419	0.577097	−	0.816676i	$-0.304186\pi$
$491$	25.5752	1.15419	0.577097	+	0.816676i	$0.304186\pi$
$492$	−5.02197	−0.226408
$493$	1.05617	0.0475675
$494$	−2.16624	−0.0974636
$495$	6.22902	0.279974
$496$	−10.1150	−0.454177
$497$	4.42305	0.198401
$498$	3.56347	0.159683
$499$	7.94164	0.355517	0.177758	−	0.984074i	$-0.443115\pi$
$499$	7.94164	0.355517	0.177758	+	0.984074i	$0.443115\pi$
$500$	9.09252	0.406630
$501$	−8.35145	−0.373115
$502$	−5.84078	−0.260687
$503$	13.3794	0.596558	0.298279	−	0.954479i	$-0.403587\pi$
$503$	13.3794	0.596558	0.298279	+	0.954479i	$0.403587\pi$
$504$	0.687441	0.0306210
$505$	11.4253	0.508418
$506$	29.9767	1.33263
$507$	−0.182451	−0.00810292
$508$	−10.1471	−0.450206
$509$	−29.4965	−1.30741	−0.653705	−	0.756750i	$-0.726786\pi$
$509$	−29.4965	−1.30741	−0.653705	+	0.756750i	$0.726786\pi$
$510$	1.25037	0.0553675
$511$	9.04366	0.400068
$512$	−1.00000	−0.0441942
$513$	2.65833	0.117368
$514$	−5.57160	−0.245753
$515$	16.6223	0.732466
$516$	4.18179	0.184093
$517$	−17.6699	−0.777122
$518$	−4.11862	−0.180962
$519$	−36.8762	−1.61869
$520$	9.16050	0.401715
$521$	−3.49588	−0.153157	−0.0765787	−	0.997064i	$-0.524400\pi$
$521$	−3.49588	−0.153157	−0.0765787	+	0.997064i	$0.524400\pi$
$522$	2.82266	0.123544
$523$	−37.7659	−1.65139	−0.825693	−	0.564120i	$-0.809216\pi$
$523$	−37.7659	−1.65139	−0.825693	+	0.564120i	$0.809216\pi$
$524$	11.9416	0.521672
$525$	2.70403	0.118014
$526$	21.9048	0.955093
$527$	2.60181	0.113337
$528$	6.87354	0.299133
$529$	47.1344	2.04932
$530$	4.92148	0.213775
$531$	−5.64643	−0.245034
$532$	−0.598623	−0.0259536
$533$	9.46379	0.409922
$534$	30.2154	1.30755
$535$	21.8362	0.944063
$536$	8.51172	0.367650
$537$	−24.7518	−1.06812
$538$	−15.3493	−0.661757
$539$	−3.57947	−0.154178
$540$	−11.2414	−0.483754
$541$	−4.69716	−0.201947	−0.100973	−	0.994889i	$-0.532196\pi$
$541$	−4.69716	−0.201947	−0.100973	+	0.994889i	$0.532196\pi$
$542$	−29.7738	−1.27889
$543$	37.4260	1.60611
$544$	0.257224	0.0110284
$545$	−24.6423	−1.05556
$546$	−6.94889	−0.297385
$547$	26.8344	1.14736	0.573679	−	0.819081i	$-0.305516\pi$
$547$	26.8344	1.14736	0.573679	+	0.819081i	$0.305516\pi$
$548$	9.15383	0.391032
$549$	−10.6911	−0.456287
$550$	5.04043	0.214925
$551$	−2.45797	−0.104713
$552$	16.0816	0.684477
$553$	2.43578	0.103580
$554$	23.7870	1.01061
$555$	−20.0207	−0.849833
$556$	−0.332567	−0.0141040
$557$	−37.7660	−1.60020	−0.800098	−	0.599869i	$-0.795219\pi$
$557$	−37.7660	−1.60020	−0.800098	+	0.599869i	$0.795219\pi$
$558$	6.95346	0.294363
$559$	−7.88048	−0.333309
$560$	2.53143	0.106973
$561$	−1.76804	−0.0746466
$562$	−1.87745	−0.0791956
$563$	44.6848	1.88324	0.941621	−	0.336676i	$-0.109303\pi$
$563$	44.6848	1.88324	0.941621	+	0.336676i	$0.109303\pi$
$564$	−9.47935	−0.399153
$565$	32.7528	1.37792
$566$	15.9527	0.670543
$567$	10.5897	0.444728
$568$	4.42305	0.185587
$569$	44.7601	1.87644	0.938221	−	0.346037i	$-0.112473\pi$
$569$	44.7601	1.87644	0.938221	+	0.346037i	$0.112473\pi$
$570$	−2.90993	−0.121883
$571$	−12.0269	−0.503310	−0.251655	−	0.967817i	$-0.580975\pi$
$571$	−12.0269	−0.503310	−0.251655	+	0.967817i	$0.580975\pi$
$572$	−12.9530	−0.541593
$573$	−41.0512	−1.71494
$574$	2.61524	0.109158
$575$	11.7927	0.491792
$576$	0.687441	0.0286434
$577$	−35.1423	−1.46299	−0.731497	−	0.681845i	$-0.761178\pi$
$577$	−35.1423	−1.46299	−0.731497	+	0.681845i	$0.761178\pi$
$578$	16.9338	0.704355
$579$	6.75736	0.280826
$580$	10.3942	0.431594
$581$	−1.85571	−0.0769879
$582$	−21.4295	−0.888283
$583$	−6.95900	−0.288212
$584$	9.04366	0.374229
$585$	−6.29730	−0.260361
$586$	6.31742	0.260970
$587$	−29.4813	−1.21682	−0.608412	−	0.793621i	$-0.708193\pi$
$587$	−29.4813	−1.21682	−0.608412	+	0.793621i	$0.708193\pi$
$588$	−1.92027	−0.0791906
$589$	−6.05506	−0.249495
$590$	−20.7924	−0.856010
$591$	24.9159	1.02490
$592$	−4.11862	−0.169274
$593$	21.0135	0.862919	0.431460	−	0.902132i	$-0.357999\pi$
$593$	21.0135	0.862919	0.431460	+	0.902132i	$0.357999\pi$
$594$	15.8955	0.652199
$595$	−0.651144	−0.0266943
$596$	−6.88464	−0.282006
$597$	−46.5019	−1.90320
$598$	−30.3053	−1.23928
$599$	−26.3189	−1.07536	−0.537680	−	0.843149i	$-0.680699\pi$
$599$	−26.3189	−1.07536	−0.537680	+	0.843149i	$0.680699\pi$
$600$	2.70403	0.110392
$601$	−12.3216	−0.502610	−0.251305	−	0.967908i	$-0.580860\pi$
$601$	−12.3216	−0.502610	−0.251305	+	0.967908i	$0.580860\pi$
$602$	−2.17771	−0.0887568
$603$	−5.85130	−0.238283
$604$	−1.65194	−0.0672165
$605$	−4.58840	−0.186545
$606$	−8.66689	−0.352068
$607$	−16.6222	−0.674673	−0.337336	−	0.941384i	$-0.609526\pi$
$607$	−16.6222	−0.674673	−0.337336	+	0.941384i	$0.609526\pi$
$608$	−0.598623	−0.0242774
$609$	−7.88471	−0.319504
$610$	−39.3691	−1.59401
$611$	17.8636	0.722684
$612$	−0.176826	−0.00714776
$613$	−44.6724	−1.80430	−0.902151	−	0.431420i	$-0.858013\pi$
$613$	−44.6724	−1.80430	−0.902151	+	0.431420i	$0.858013\pi$
$614$	−12.5877	−0.507996
$615$	12.7128	0.512629
$616$	−3.57947	−0.144221
$617$	−19.8383	−0.798662	−0.399331	−	0.916807i	$-0.630758\pi$
$617$	−19.8383	−0.798662	−0.399331	+	0.916807i	$0.630758\pi$
$618$	−12.6092	−0.507216
$619$	33.1395	1.33199	0.665994	−	0.745958i	$-0.268008\pi$
$619$	33.1395	1.33199	0.665994	+	0.745958i	$0.268008\pi$
$620$	25.6054	1.02834
$621$	37.1896	1.49237
$622$	25.4835	1.02180
$623$	−15.7350	−0.630408
$624$	−6.94889	−0.278178
$625$	−30.0579	−1.20231
$626$	−14.0108	−0.559986
$627$	4.11466	0.164324
$628$	−8.97337	−0.358076
$629$	1.05941	0.0422412
$630$	−1.74021	−0.0693316
$631$	35.8455	1.42699	0.713493	−	0.700662i	$-0.247112\pi$
$631$	35.8455	1.42699	0.713493	+	0.700662i	$0.247112\pi$
$632$	2.43578	0.0968901
$633$	33.3011	1.32360
$634$	−30.6658	−1.21789
$635$	25.6867	1.01935
$636$	−3.73329	−0.148034
$637$	3.61870	0.143378
$638$	−14.6974	−0.581877
$639$	−3.04058	−0.120284
$640$	2.53143	0.100064
$641$	23.4067	0.924508	0.462254	−	0.886748i	$-0.347041\pi$
$641$	23.4067	0.924508	0.462254	+	0.886748i	$0.347041\pi$
$642$	−16.5643	−0.653742
$643$	28.1021	1.10824	0.554119	−	0.832437i	$-0.313055\pi$
$643$	28.1021	1.10824	0.554119	+	0.832437i	$0.313055\pi$
$644$	−8.37463	−0.330007
$645$	−10.5859	−0.416820
$646$	0.153980	0.00605825
$647$	28.8652	1.13481	0.567404	−	0.823440i	$-0.307948\pi$
$647$	28.8652	1.13481	0.567404	+	0.823440i	$0.307948\pi$
$648$	10.5897	0.416005
$649$	29.4006	1.15408
$650$	−5.09568	−0.199869
$651$	−19.4235	−0.761268
$652$	12.9833	0.508465
$653$	17.7438	0.694368	0.347184	−	0.937797i	$-0.387138\pi$
$653$	17.7438	0.694368	0.347184	+	0.937797i	$0.387138\pi$
$654$	18.6930	0.730953
$655$	−30.2294	−1.18116
$656$	2.61524	0.102108
$657$	−6.21698	−0.242548
$658$	4.93647	0.192443
$659$	27.0341	1.05310	0.526550	−	0.850144i	$-0.323485\pi$
$659$	27.0341	1.05310	0.526550	+	0.850144i	$0.323485\pi$
$660$	−17.3999	−0.677291
$661$	11.8516	0.460973	0.230486	−	0.973076i	$-0.425968\pi$
$661$	11.8516	0.460973	0.230486	+	0.973076i	$0.425968\pi$
$662$	17.5804	0.683281
$663$	1.78742	0.0694176
$664$	−1.85571	−0.0720156
$665$	1.51537	0.0587636
$666$	2.83130	0.109711
$667$	−34.3866	−1.33145
$668$	4.34910	0.168272
$669$	−31.7841	−1.22885
$670$	−21.5468	−0.832427
$671$	55.6682	2.14905
$672$	−1.92027	−0.0740761
$673$	3.23045	0.124525	0.0622624	−	0.998060i	$-0.480168\pi$
$673$	3.23045	0.124525	0.0622624	+	0.998060i	$0.480168\pi$
$674$	−2.39027	−0.0920697
$675$	6.25324	0.240687
$676$	0.0950129	0.00365434
$677$	−42.4144	−1.63012	−0.815059	−	0.579378i	$-0.803295\pi$
$677$	−42.4144	−1.63012	−0.815059	+	0.579378i	$0.803295\pi$
$678$	−24.8453	−0.954180
$679$	11.1596	0.428268
$680$	−0.651144	−0.0249702
$681$	8.97472	0.343912
$682$	−36.2063	−1.38641
$683$	−15.5111	−0.593514	−0.296757	−	0.954953i	$-0.595905\pi$
$683$	−15.5111	−0.593514	−0.296757	+	0.954953i	$0.595905\pi$
$684$	0.411518	0.0157348
$685$	−23.1723	−0.885368
$686$	1.00000	0.0381802
$687$	42.4237	1.61857
$688$	−2.17771	−0.0830244
$689$	7.03529	0.268023
$690$	−40.7094	−1.54978
$691$	19.0728	0.725565	0.362782	−	0.931874i	$-0.381827\pi$
$691$	19.0728	0.725565	0.362782	+	0.931874i	$0.381827\pi$
$692$	19.2037	0.730013
$693$	2.46067	0.0934731
$694$	0.211265	0.00801949
$695$	0.841870	0.0319339
$696$	−7.88471	−0.298869
$697$	−0.672702	−0.0254804
$698$	−3.91333	−0.148122
$699$	34.6526	1.31068
$700$	−1.40815	−0.0532231
$701$	10.1492	0.383330	0.191665	−	0.981460i	$-0.438611\pi$
$701$	10.1492	0.383330	0.191665	+	0.981460i	$0.438611\pi$
$702$	−16.0697	−0.606513
$703$	−2.46550	−0.0929880
$704$	−3.57947	−0.134906
$705$	23.9963	0.903755
$706$	−9.57877	−0.360502
$707$	4.51337	0.169743
$708$	15.7725	0.592767
$709$	−4.71016	−0.176894	−0.0884469	−	0.996081i	$-0.528190\pi$
$709$	−4.71016	−0.176894	−0.0884469	+	0.996081i	$0.528190\pi$
$710$	−11.1967	−0.420203
$711$	−1.67445	−0.0627969
$712$	−15.7350	−0.589693
$713$	−84.7093	−3.17239
$714$	0.493939	0.0184852
$715$	32.7897	1.22627
$716$	12.8897	0.481712
$717$	43.4546	1.62284
$718$	−28.8694	−1.07740
$719$	−27.4159	−1.02244	−0.511220	−	0.859450i	$-0.670806\pi$
$719$	−27.4159	−1.02244	−0.511220	+	0.859450i	$0.670806\pi$
$720$	−1.74021	−0.0648538
$721$	6.56636	0.244544
$722$	18.6417	0.693770
$723$	9.38029	0.348857
$724$	−19.4900	−0.724340
$725$	−5.78193	−0.214735
$726$	3.48063	0.129178
$727$	12.8952	0.478256	0.239128	−	0.970988i	$-0.423139\pi$
$727$	12.8952	0.478256	0.239128	+	0.970988i	$0.423139\pi$
$728$	3.61870	0.134118
$729$	18.3025	0.677869
$730$	−22.8934	−0.847324
$731$	0.560158	0.0207182
$732$	29.8643	1.10381
$733$	36.0673	1.33217	0.666087	−	0.745874i	$-0.267968\pi$
$733$	36.0673	1.33217	0.666087	+	0.745874i	$0.267968\pi$
$734$	−2.06116	−0.0760787
$735$	4.86104	0.179302
$736$	−8.37463	−0.308693
$737$	30.4674	1.12228
$738$	−1.79782	−0.0661788
$739$	23.6268	0.869124	0.434562	−	0.900642i	$-0.356903\pi$
$739$	23.6268	0.869124	0.434562	+	0.900642i	$0.356903\pi$
$740$	10.4260	0.383267
$741$	−4.15976	−0.152813
$742$	1.94415	0.0713719
$743$	−47.4064	−1.73917	−0.869586	−	0.493782i	$-0.835614\pi$
$743$	−47.4064	−1.73917	−0.869586	+	0.493782i	$0.835614\pi$
$744$	−19.4235	−0.712101
$745$	17.4280	0.638513
$746$	9.76150	0.357394
$747$	1.27569	0.0466751
$748$	0.920723	0.0336650
$749$	8.62604	0.315189
$750$	17.4601	0.637553
$751$	−47.1565	−1.72076	−0.860382	−	0.509650i	$-0.829775\pi$
$751$	−47.1565	−1.72076	−0.860382	+	0.509650i	$0.829775\pi$
$752$	4.93647	0.180014
$753$	−11.2159	−0.408730
$754$	14.8585	0.541116
$755$	4.18178	0.152190
$756$	−4.44074	−0.161508
$757$	33.2278	1.20769	0.603843	−	0.797103i	$-0.293635\pi$
$757$	33.2278	1.20769	0.603843	+	0.797103i	$0.293635\pi$
$758$	−36.6366	−1.33070
$759$	57.5634	2.08942
$760$	1.51537	0.0549683
$761$	−24.4532	−0.886427	−0.443214	−	0.896416i	$-0.646162\pi$
$761$	−24.4532	−0.886427	−0.443214	+	0.896416i	$0.646162\pi$
$762$	−19.4852	−0.705875
$763$	−9.73455	−0.352414
$764$	21.3778	0.773422
$765$	0.447623	0.0161838
$766$	−11.9608	−0.432160
$767$	−29.7229	−1.07323
$768$	−1.92027	−0.0692918
$769$	7.81428	0.281790	0.140895	−	0.990025i	$-0.455002\pi$
$769$	7.81428	0.281790	0.140895	+	0.990025i	$0.455002\pi$
$770$	9.06118	0.326542
$771$	−10.6990	−0.385315
$772$	−3.51896	−0.126650
$773$	50.5238	1.81721	0.908607	−	0.417653i	$-0.137147\pi$
$773$	50.5238	1.81721	0.908607	+	0.417653i	$0.137147\pi$
$774$	1.49705	0.0538102
$775$	−14.2434	−0.511640
$776$	11.1596	0.400608
$777$	−7.90886	−0.283729
$778$	19.3100	0.692296
$779$	1.56554	0.0560914
$780$	17.5906	0.629846
$781$	15.8322	0.566519
$782$	2.15415	0.0770323
$783$	−18.2339	−0.651625
$784$	1.00000	0.0357143
$785$	22.7155	0.810750
$786$	22.9311	0.817926
$787$	23.8235	0.849217	0.424608	−	0.905377i	$-0.360412\pi$
$787$	23.8235	0.849217	0.424608	+	0.905377i	$0.360412\pi$
$788$	−12.9752	−0.462222
$789$	42.0631	1.49749
$790$	−6.16601	−0.219377
$791$	12.9385	0.460039
$792$	2.46067	0.0874361
$793$	−56.2784	−1.99851
$794$	−21.5798	−0.765837
$795$	9.45057	0.335177
$796$	24.2163	0.858325
$797$	−6.73393	−0.238528	−0.119264	−	0.992863i	$-0.538054\pi$
$797$	−6.73393	−0.238528	−0.119264	+	0.992863i	$0.538054\pi$
$798$	−1.14952	−0.0406925
$799$	−1.26978	−0.0449214
$800$	−1.40815	−0.0497857
$801$	10.8169	0.382195
$802$	−17.0332	−0.601464
$803$	32.3715	1.14236
$804$	16.3448	0.576437
$805$	21.1998	0.747195
$806$	36.6032	1.28929
$807$	−29.4749	−1.03757
$808$	4.51337	0.158780
$809$	11.4594	0.402892	0.201446	−	0.979500i	$-0.435436\pi$
$809$	11.4594	0.402892	0.201446	+	0.979500i	$0.435436\pi$
$810$	−26.8072	−0.941910
$811$	42.2035	1.48196	0.740982	−	0.671525i	$-0.234360\pi$
$811$	42.2035	1.48196	0.740982	+	0.671525i	$0.234360\pi$
$812$	4.10604	0.144094
$813$	−57.1738	−2.00517
$814$	−14.7424	−0.516722
$815$	−32.8663	−1.15126
$816$	0.493939	0.0172913
$817$	−1.30363	−0.0456081
$818$	−36.8660	−1.28899
$819$	−2.48764	−0.0869253
$820$	−6.62031	−0.231191
$821$	−41.7478	−1.45701	−0.728504	−	0.685042i	$-0.759784\pi$
$821$	−41.7478	−1.45701	−0.728504	+	0.685042i	$0.759784\pi$
$822$	17.5778	0.613097
$823$	−31.4625	−1.09671	−0.548357	−	0.836244i	$-0.684747\pi$
$823$	−31.4625	−1.09671	−0.548357	+	0.836244i	$0.684747\pi$
$824$	6.56636	0.228750
$825$	9.67899	0.336979
$826$	−8.21369	−0.285791
$827$	−31.4249	−1.09275	−0.546376	−	0.837540i	$-0.683993\pi$
$827$	−31.4249	−1.09275	−0.546376	+	0.837540i	$0.683993\pi$
$828$	5.75706	0.200072
$829$	28.0892	0.975580	0.487790	−	0.872961i	$-0.337803\pi$
$829$	28.0892	0.975580	0.487790	+	0.872961i	$0.337803\pi$
$830$	4.69761	0.163056
$831$	45.6774	1.58453
$832$	3.61870	0.125456
$833$	−0.257224	−0.00891227
$834$	−0.638618	−0.0221135
$835$	−11.0094	−0.380998
$836$	−2.14275	−0.0741085
$837$	−44.9181	−1.55260
$838$	36.8813	1.27404
$839$	35.5109	1.22597	0.612987	−	0.790093i	$-0.289968\pi$
$839$	35.5109	1.22597	0.612987	+	0.790093i	$0.289968\pi$
$840$	4.86104	0.167722
$841$	−12.1404	−0.418636
$842$	8.50994	0.293272
$843$	−3.60522	−0.124170
$844$	−17.3419	−0.596933
$845$	−0.240519	−0.00827410
$846$	−3.39353	−0.116672
$847$	−1.81257	−0.0622807
$848$	1.94415	0.0667623
$849$	30.6335	1.05134
$850$	0.362210	0.0124237
$851$	−34.4919	−1.18237
$852$	8.49345	0.290981
$853$	14.4060	0.493252	0.246626	−	0.969111i	$-0.420678\pi$
$853$	14.4060	0.493252	0.246626	+	0.969111i	$0.420678\pi$
$854$	−15.5521	−0.532182
$855$	−1.04173	−0.0356264
$856$	8.62604	0.294832
$857$	−18.5416	−0.633370	−0.316685	−	0.948531i	$-0.602570\pi$
$857$	−18.5416	−0.633370	−0.316685	+	0.948531i	$0.602570\pi$
$858$	−24.8733	−0.849161
$859$	47.9436	1.63582	0.817908	−	0.575349i	$-0.195134\pi$
$859$	47.9436	1.63582	0.817908	+	0.575349i	$0.195134\pi$
$860$	5.51272	0.187982
$861$	5.02197	0.171148
$862$	−1.00000	−0.0340601
$863$	−26.2151	−0.892371	−0.446185	−	0.894941i	$-0.647218\pi$
$863$	−26.2151	−0.892371	−0.446185	+	0.894941i	$0.647218\pi$
$864$	−4.44074	−0.151077
$865$	−48.6128	−1.65288
$866$	−26.8256	−0.911571
$867$	32.5176	1.10435
$868$	10.1150	0.343325
$869$	8.71879	0.295765
$870$	19.9596	0.676694
$871$	−30.8014	−1.04366
$872$	−9.73455	−0.329653
$873$	−7.67160	−0.259644
$874$	−5.01324	−0.169575
$875$	−9.09252	−0.307383
$876$	17.3663	0.586752
$877$	−27.4345	−0.926396	−0.463198	−	0.886255i	$-0.653298\pi$
$877$	−27.4345	−0.926396	−0.463198	+	0.886255i	$0.653298\pi$
$878$	−29.2805	−0.988169
$879$	12.1312	0.409174
$880$	9.06118	0.305452
$881$	19.5667	0.659218	0.329609	−	0.944118i	$-0.393083\pi$
$881$	19.5667	0.659218	0.329609	+	0.944118i	$0.393083\pi$
$882$	−0.687441	−0.0231473
$883$	−15.4238	−0.519054	−0.259527	−	0.965736i	$-0.583567\pi$
$883$	−15.4238	−0.519054	−0.259527	+	0.965736i	$0.583567\pi$
$884$	−0.930816	−0.0313067
$885$	−39.9271	−1.34213
$886$	27.1409	0.911817
$887$	−24.2448	−0.814061	−0.407030	−	0.913415i	$-0.633436\pi$
$887$	−24.2448	−0.814061	−0.407030	+	0.913415i	$0.633436\pi$
$888$	−7.90886	−0.265404
$889$	10.1471	0.340323
$890$	39.8320	1.33517
$891$	37.9056	1.26989
$892$	16.5519	0.554199
$893$	2.95508	0.0988880
$894$	−13.2204	−0.442156
$895$	−32.6295	−1.09068
$896$	1.00000	0.0334077
$897$	−58.1944	−1.94305
$898$	4.32527	0.144336
$899$	41.5325	1.38519
$900$	0.968021	0.0322674
$901$	−0.500080	−0.0166601
$902$	9.36117	0.311693
$903$	−4.18179	−0.139161
$904$	12.9385	0.430327
$905$	49.3376	1.64004
$906$	−3.17217	−0.105388
$907$	32.7706	1.08813	0.544066	−	0.839043i	$-0.316884\pi$
$907$	32.7706	1.08813	0.544066	+	0.839043i	$0.316884\pi$
$908$	−4.67367	−0.155101
$909$	−3.10267	−0.102909
$910$	−9.16050	−0.303668
$911$	−3.32266	−0.110085	−0.0550423	−	0.998484i	$-0.517529\pi$
$911$	−3.32266	−0.110085	−0.0550423	+	0.998484i	$0.517529\pi$
$912$	−1.14952	−0.0380643
$913$	−6.64245	−0.219833
$914$	−28.1770	−0.932012
$915$	−75.5993	−2.49924
$916$	−22.0926	−0.729959
$917$	−11.9416	−0.394347
$918$	1.14226	0.0377003
$919$	7.20609	0.237707	0.118853	−	0.992912i	$-0.462078\pi$
$919$	7.20609	0.237707	0.118853	+	0.992912i	$0.462078\pi$
$920$	21.1998	0.698937
$921$	−24.1717	−0.796485
$922$	−11.8908	−0.391602
$923$	−16.0057	−0.526834
$924$	−6.87354	−0.226123
$925$	−5.79964	−0.190691
$926$	−19.8802	−0.653303
$927$	−4.51399	−0.148259
$928$	4.10604	0.134787
$929$	−10.7846	−0.353832	−0.176916	−	0.984226i	$-0.556612\pi$
$929$	−10.7846	−0.353832	−0.176916	+	0.984226i	$0.556612\pi$
$930$	49.1694	1.61233
$931$	0.598623	0.0196191
$932$	−18.0457	−0.591106
$933$	48.9353	1.60207
$934$	18.2222	0.596248
$935$	−2.33075	−0.0762236
$936$	−2.48764	−0.0813112
$937$	−34.5629	−1.12912	−0.564560	−	0.825392i	$-0.690954\pi$
$937$	−34.5629	−1.12912	−0.564560	+	0.825392i	$0.690954\pi$
$938$	−8.51172	−0.277917
$939$	−26.9046	−0.877999
$940$	−12.4963	−0.407585
$941$	−38.3022	−1.24862	−0.624308	−	0.781179i	$-0.714619\pi$
$941$	−38.3022	−1.24862	−0.624308	+	0.781179i	$0.714619\pi$
$942$	−17.2313	−0.561426
$943$	21.9017	0.713217
$944$	−8.21369	−0.267333
$945$	11.2414	0.365684
$946$	−7.79504	−0.253438
$947$	−10.4257	−0.338789	−0.169395	−	0.985548i	$-0.554181\pi$
$947$	−10.4257	−0.338789	−0.169395	+	0.985548i	$0.554181\pi$
$948$	4.67736	0.151914
$949$	−32.7263	−1.06234
$950$	−0.842951	−0.0273490
$951$	−58.8866	−1.90953
$952$	−0.257224	−0.00833666
$953$	−24.3620	−0.789162	−0.394581	−	0.918861i	$-0.629110\pi$
$953$	−24.3620	−0.789162	−0.394581	+	0.918861i	$0.629110\pi$
$954$	−1.33649	−0.0432703
$955$	−54.1165	−1.75117
$956$	−22.6294	−0.731887
$957$	−28.2230	−0.912321
$958$	−33.3364	−1.07705
$959$	−9.15383	−0.295593
$960$	4.86104	0.156889
$961$	71.3131	2.30042
$962$	14.9040	0.480526
$963$	−5.92989	−0.191088
$964$	−4.88488	−0.157331
$965$	8.90802	0.286759
$966$	−16.0816	−0.517416
$967$	26.6509	0.857034	0.428517	−	0.903534i	$-0.359036\pi$
$967$	26.6509	0.857034	0.428517	+	0.903534i	$0.359036\pi$
$968$	−1.81257	−0.0582583
$969$	0.295683	0.00949871
$970$	−28.2499	−0.907050
$971$	39.9077	1.28070	0.640349	−	0.768084i	$-0.278790\pi$
$971$	39.9077	1.28070	0.640349	+	0.768084i	$0.278790\pi$
$972$	7.01296	0.224941
$973$	0.332567	0.0106616
$974$	−23.6231	−0.756934
$975$	−9.78509	−0.313374
$976$	−15.5521	−0.497811
$977$	8.73674	0.279513	0.139757	−	0.990186i	$-0.455368\pi$
$977$	8.73674	0.279513	0.139757	+	0.990186i	$0.455368\pi$
$978$	24.9314	0.797219
$979$	−56.3228	−1.80008
$980$	−2.53143	−0.0808637
$981$	6.69192	0.213657
$982$	−25.5752	−0.816138
$983$	22.3321	0.712283	0.356141	−	0.934432i	$-0.384092\pi$
$983$	22.3321	0.712283	0.356141	+	0.934432i	$0.384092\pi$
$984$	5.02197	0.160095
$985$	32.8458	1.04655
$986$	−1.05617	−0.0336353
$987$	9.47935	0.301731
$988$	2.16624	0.0689172
$989$	−18.2375	−0.579919
$990$	−6.22902	−0.197971
$991$	0.307369	0.00976388	0.00488194	−	0.999988i	$-0.498446\pi$
$991$	0.307369	0.00976388	0.00488194	+	0.999988i	$0.498446\pi$
$992$	10.1150	0.321151
$993$	33.7591	1.07131
$994$	−4.42305	−0.140291
$995$	−61.3020	−1.94340
$996$	−3.56347	−0.112913
$997$	−2.36172	−0.0747963	−0.0373982	−	0.999300i	$-0.511907\pi$
$997$	−2.36172	−0.0747963	−0.0373982	+	0.999300i	$0.511907\pi$
$998$	−7.94164	−0.251388
$999$	−18.2897	−0.578661

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6034.2.a.n.1.4	✓	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6034.2.a.n.1.4	✓	24	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:	\( N \)	\(=\)	\( 6034 = 2 \cdot 7 \cdot 431 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6034.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -1.92027 q^{3} +1.00000 q^{4} -2.53143 q^{5} +1.92027 q^{6} -1.00000 q^{7} -1.00000 q^{8} +0.687441 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -1.92027 q^{3} +1.00000 q^{4} -2.53143 q^{5} +1.92027 q^{6} -1.00000 q^{7} -1.00000 q^{8} +0.687441 q^{9} +2.53143 q^{10} -3.57947 q^{11} -1.92027 q^{12} +3.61870 q^{13} +1.00000 q^{14} +4.86104 q^{15} +1.00000 q^{16} -0.257224 q^{17} -0.687441 q^{18} +0.598623 q^{19} -2.53143 q^{20} +1.92027 q^{21} +3.57947 q^{22} +8.37463 q^{23} +1.92027 q^{24} +1.40815 q^{25} -3.61870 q^{26} +4.44074 q^{27} -1.00000 q^{28} -4.10604 q^{29} -4.86104 q^{30} -10.1150 q^{31} -1.00000 q^{32} +6.87354 q^{33} +0.257224 q^{34} +2.53143 q^{35} +0.687441 q^{36} -4.11862 q^{37} -0.598623 q^{38} -6.94889 q^{39} +2.53143 q^{40} +2.61524 q^{41} -1.92027 q^{42} -2.17771 q^{43} -3.57947 q^{44} -1.74021 q^{45} -8.37463 q^{46} +4.93647 q^{47} -1.92027 q^{48} +1.00000 q^{49} -1.40815 q^{50} +0.493939 q^{51} +3.61870 q^{52} +1.94415 q^{53} -4.44074 q^{54} +9.06118 q^{55} +1.00000 q^{56} -1.14952 q^{57} +4.10604 q^{58} -8.21369 q^{59} +4.86104 q^{60} -15.5521 q^{61} +10.1150 q^{62} -0.687441 q^{63} +1.00000 q^{64} -9.16050 q^{65} -6.87354 q^{66} -8.51172 q^{67} -0.257224 q^{68} -16.0816 q^{69} -2.53143 q^{70} -4.42305 q^{71} -0.687441 q^{72} -9.04366 q^{73} +4.11862 q^{74} -2.70403 q^{75} +0.598623 q^{76} +3.57947 q^{77} +6.94889 q^{78} -2.43578 q^{79} -2.53143 q^{80} -10.5897 q^{81} -2.61524 q^{82} +1.85571 q^{83} +1.92027 q^{84} +0.651144 q^{85} +2.17771 q^{86} +7.88471 q^{87} +3.57947 q^{88} +15.7350 q^{89} +1.74021 q^{90} -3.61870 q^{91} +8.37463 q^{92} +19.4235 q^{93} -4.93647 q^{94} -1.51537 q^{95} +1.92027 q^{96} -11.1596 q^{97} -1.00000 q^{98} -2.46067 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 24 q^{2} + 7 q^{3} + 24 q^{4} + 8 q^{5} - 7 q^{6} - 24 q^{7} - 24 q^{8} + 19 q^{9}+O(q^{10}) \) 24 * q - 24 * q^2 + 7 * q^3 + 24 * q^4 + 8 * q^5 - 7 * q^6 - 24 * q^7 - 24 * q^8 + 19 * q^9	\( 24 q - 24 q^{2} + 7 q^{3} + 24 q^{4} + 8 q^{5} - 7 q^{6} - 24 q^{7} - 24 q^{8} + 19 q^{9} - 8 q^{10} + 15 q^{11} + 7 q^{12} - 7 q^{13} + 24 q^{14} + 13 q^{15} + 24 q^{16} - 5 q^{17} - 19 q^{18} + 6 q^{19} + 8 q^{20} - 7 q^{21} - 15 q^{22} + 3 q^{23} - 7 q^{24} + 12 q^{25} + 7 q^{26} + 22 q^{27} - 24 q^{28} + 5 q^{29} - 13 q^{30} + 13 q^{31} - 24 q^{32} - 8 q^{33} + 5 q^{34} - 8 q^{35} + 19 q^{36} + 2 q^{37} - 6 q^{38} + 7 q^{39} - 8 q^{40} + 25 q^{41} + 7 q^{42} - 15 q^{43} + 15 q^{44} + 41 q^{45} - 3 q^{46} + 35 q^{47} + 7 q^{48} + 24 q^{49} - 12 q^{50} + 31 q^{51} - 7 q^{52} + 2 q^{53} - 22 q^{54} + 14 q^{55} + 24 q^{56} - 13 q^{57} - 5 q^{58} + 35 q^{59} + 13 q^{60} - 7 q^{61} - 13 q^{62} - 19 q^{63} + 24 q^{64} - 4 q^{65} + 8 q^{66} + 10 q^{67} - 5 q^{68} + 6 q^{69} + 8 q^{70} + 58 q^{71} - 19 q^{72} + 9 q^{73} - 2 q^{74} + 7 q^{75} + 6 q^{76} - 15 q^{77} - 7 q^{78} + 31 q^{79} + 8 q^{80} + 16 q^{81} - 25 q^{82} - q^{83} - 7 q^{84} - 4 q^{85} + 15 q^{86} + 30 q^{87} - 15 q^{88} + 45 q^{89} - 41 q^{90} + 7 q^{91} + 3 q^{92} + 25 q^{93} - 35 q^{94} - 10 q^{95} - 7 q^{96} - 9 q^{97} - 24 q^{98} + 64 q^{99}+O(q^{100}) \) 24 * q - 24 * q^2 + 7 * q^3 + 24 * q^4 + 8 * q^5 - 7 * q^6 - 24 * q^7 - 24 * q^8 + 19 * q^9 - 8 * q^10 + 15 * q^11 + 7 * q^12 - 7 * q^13 + 24 * q^14 + 13 * q^15 + 24 * q^16 - 5 * q^17 - 19 * q^18 + 6 * q^19 + 8 * q^20 - 7 * q^21 - 15 * q^22 + 3 * q^23 - 7 * q^24 + 12 * q^25 + 7 * q^26 + 22 * q^27 - 24 * q^28 + 5 * q^29 - 13 * q^30 + 13 * q^31 - 24 * q^32 - 8 * q^33 + 5 * q^34 - 8 * q^35 + 19 * q^36 + 2 * q^37 - 6 * q^38 + 7 * q^39 - 8 * q^40 + 25 * q^41 + 7 * q^42 - 15 * q^43 + 15 * q^44 + 41 * q^45 - 3 * q^46 + 35 * q^47 + 7 * q^48 + 24 * q^49 - 12 * q^50 + 31 * q^51 - 7 * q^52 + 2 * q^53 - 22 * q^54 + 14 * q^55 + 24 * q^56 - 13 * q^57 - 5 * q^58 + 35 * q^59 + 13 * q^60 - 7 * q^61 - 13 * q^62 - 19 * q^63 + 24 * q^64 - 4 * q^65 + 8 * q^66 + 10 * q^67 - 5 * q^68 + 6 * q^69 + 8 * q^70 + 58 * q^71 - 19 * q^72 + 9 * q^73 - 2 * q^74 + 7 * q^75 + 6 * q^76 - 15 * q^77 - 7 * q^78 + 31 * q^79 + 8 * q^80 + 16 * q^81 - 25 * q^82 - q^83 - 7 * q^84 - 4 * q^85 + 15 * q^86 + 30 * q^87 - 15 * q^88 + 45 * q^89 - 41 * q^90 + 7 * q^91 + 3 * q^92 + 25 * q^93 - 35 * q^94 - 10 * q^95 - 7 * q^96 - 9 * q^97 - 24 * q^98 + 64 * q^99

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