LMFDB - Embedded newform 6026.2.a.k.1.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6026,2,Mod(1,6026)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6026, 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("6026.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6026 = 2 \cdot 23 \cdot 131 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6026.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:	$48.1178522580$
Analytic rank:	$0$
Dimension:	$35$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.6
Character	$\chi$	$=$	6026.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -2.77524 q^{3} +1.00000 q^{4} -2.60760 q^{5} -2.77524 q^{6} -2.68280 q^{7} +1.00000 q^{8} +4.70196 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -2.77524 q^{3} +1.00000 q^{4} -2.60760 q^{5} -2.77524 q^{6} -2.68280 q^{7} +1.00000 q^{8} +4.70196 q^{9} -2.60760 q^{10} -4.62485 q^{11} -2.77524 q^{12} +3.73467 q^{13} -2.68280 q^{14} +7.23673 q^{15} +1.00000 q^{16} +6.00283 q^{17} +4.70196 q^{18} -6.31185 q^{19} -2.60760 q^{20} +7.44540 q^{21} -4.62485 q^{22} -1.00000 q^{23} -2.77524 q^{24} +1.79960 q^{25} +3.73467 q^{26} -4.72335 q^{27} -2.68280 q^{28} -8.79796 q^{29} +7.23673 q^{30} -3.27132 q^{31} +1.00000 q^{32} +12.8351 q^{33} +6.00283 q^{34} +6.99567 q^{35} +4.70196 q^{36} -0.593078 q^{37} -6.31185 q^{38} -10.3646 q^{39} -2.60760 q^{40} -10.0465 q^{41} +7.44540 q^{42} -4.66799 q^{43} -4.62485 q^{44} -12.2608 q^{45} -1.00000 q^{46} -12.7017 q^{47} -2.77524 q^{48} +0.197394 q^{49} +1.79960 q^{50} -16.6593 q^{51} +3.73467 q^{52} +1.91560 q^{53} -4.72335 q^{54} +12.0598 q^{55} -2.68280 q^{56} +17.5169 q^{57} -8.79796 q^{58} -4.31508 q^{59} +7.23673 q^{60} -0.465995 q^{61} -3.27132 q^{62} -12.6144 q^{63} +1.00000 q^{64} -9.73855 q^{65} +12.8351 q^{66} -3.37661 q^{67} +6.00283 q^{68} +2.77524 q^{69} +6.99567 q^{70} +7.48886 q^{71} +4.70196 q^{72} -3.88577 q^{73} -0.593078 q^{74} -4.99431 q^{75} -6.31185 q^{76} +12.4075 q^{77} -10.3646 q^{78} -10.8761 q^{79} -2.60760 q^{80} -0.997447 q^{81} -10.0465 q^{82} +4.30768 q^{83} +7.44540 q^{84} -15.6530 q^{85} -4.66799 q^{86} +24.4164 q^{87} -4.62485 q^{88} +6.17007 q^{89} -12.2608 q^{90} -10.0194 q^{91} -1.00000 q^{92} +9.07870 q^{93} -12.7017 q^{94} +16.4588 q^{95} -2.77524 q^{96} +7.79337 q^{97} +0.197394 q^{98} -21.7459 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 35 q + 35 q^{2} - 3 q^{3} + 35 q^{4} + 10 q^{5} - 3 q^{6} + 14 q^{7} + 35 q^{8} + 54 q^{9}+O(q^{10}) $ 35 * q + 35 * q^2 - 3 * q^3 + 35 * q^4 + 10 * q^5 - 3 * q^6 + 14 * q^7 + 35 * q^8 + 54 * q^9	\( 35 q + 35 q^{2} - 3 q^{3} + 35 q^{4} + 10 q^{5} - 3 q^{6} + 14 q^{7} + 35 q^{8} + 54 q^{9} + 10 q^{10} + 9 q^{11} - 3 q^{12} + 19 q^{13} + 14 q^{14} + 14 q^{15} + 35 q^{16} + 28 q^{17} + 54 q^{18} + 21 q^{19} + 10 q^{20} + 28 q^{21} + 9 q^{22} - 35 q^{23} - 3 q^{24} + 81 q^{25} + 19 q^{26} - 21 q^{27} + 14 q^{28} + 35 q^{29} + 14 q^{30} + 5 q^{31} + 35 q^{32} + 26 q^{33} + 28 q^{34} - 7 q^{35} + 54 q^{36} + 51 q^{37} + 21 q^{38} + 21 q^{39} + 10 q^{40} + 3 q^{41} + 28 q^{42} + 43 q^{43} + 9 q^{44} + 2 q^{45} - 35 q^{46} + 10 q^{47} - 3 q^{48} + 85 q^{49} + 81 q^{50} + 26 q^{51} + 19 q^{52} + 39 q^{53} - 21 q^{54} + 2 q^{55} + 14 q^{56} + 50 q^{57} + 35 q^{58} - 42 q^{59} + 14 q^{60} + 47 q^{61} + 5 q^{62} + 23 q^{63} + 35 q^{64} + 61 q^{65} + 26 q^{66} + 22 q^{67} + 28 q^{68} + 3 q^{69} - 7 q^{70} + 54 q^{72} + 30 q^{73} + 51 q^{74} - 26 q^{75} + 21 q^{76} + 2 q^{77} + 21 q^{78} + 55 q^{79} + 10 q^{80} + 67 q^{81} + 3 q^{82} + 20 q^{83} + 28 q^{84} + 28 q^{85} + 43 q^{86} + 29 q^{87} + 9 q^{88} - 31 q^{89} + 2 q^{90} + 32 q^{91} - 35 q^{92} + 11 q^{93} + 10 q^{94} + 16 q^{95} - 3 q^{96} + 36 q^{97} + 85 q^{98} - 9 q^{99}+O(q^{100}) \) 35 * q + 35 * q^2 - 3 * q^3 + 35 * q^4 + 10 * q^5 - 3 * q^6 + 14 * q^7 + 35 * q^8 + 54 * q^9 + 10 * q^10 + 9 * q^11 - 3 * q^12 + 19 * q^13 + 14 * q^14 + 14 * q^15 + 35 * q^16 + 28 * q^17 + 54 * q^18 + 21 * q^19 + 10 * q^20 + 28 * q^21 + 9 * q^22 - 35 * q^23 - 3 * q^24 + 81 * q^25 + 19 * q^26 - 21 * q^27 + 14 * q^28 + 35 * q^29 + 14 * q^30 + 5 * q^31 + 35 * q^32 + 26 * q^33 + 28 * q^34 - 7 * q^35 + 54 * q^36 + 51 * q^37 + 21 * q^38 + 21 * q^39 + 10 * q^40 + 3 * q^41 + 28 * q^42 + 43 * q^43 + 9 * q^44 + 2 * q^45 - 35 * q^46 + 10 * q^47 - 3 * q^48 + 85 * q^49 + 81 * q^50 + 26 * q^51 + 19 * q^52 + 39 * q^53 - 21 * q^54 + 2 * q^55 + 14 * q^56 + 50 * q^57 + 35 * q^58 - 42 * q^59 + 14 * q^60 + 47 * q^61 + 5 * q^62 + 23 * q^63 + 35 * q^64 + 61 * q^65 + 26 * q^66 + 22 * q^67 + 28 * q^68 + 3 * q^69 - 7 * q^70 + 54 * q^72 + 30 * q^73 + 51 * q^74 - 26 * q^75 + 21 * q^76 + 2 * q^77 + 21 * q^78 + 55 * q^79 + 10 * q^80 + 67 * q^81 + 3 * q^82 + 20 * q^83 + 28 * q^84 + 28 * q^85 + 43 * q^86 + 29 * q^87 + 9 * q^88 - 31 * q^89 + 2 * q^90 + 32 * q^91 - 35 * q^92 + 11 * q^93 + 10 * q^94 + 16 * q^95 - 3 * q^96 + 36 * q^97 + 85 * q^98 - 9 * 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
$3$	−2.77524	−1.60229	−0.801143	−	0.598473i	$-0.795774\pi$
$3$	−2.77524	−1.60229	−0.801143	+	0.598473i	$0.795774\pi$
$4$	1.00000	0.500000
$5$	−2.60760	−1.16616	−0.583078	−	0.812416i	$-0.698152\pi$
$5$	−2.60760	−1.16616	−0.583078	+	0.812416i	$0.698152\pi$
$6$	−2.77524	−1.13299
$7$	−2.68280	−1.01400	−0.507001	−	0.861946i	$-0.669246\pi$
$7$	−2.68280	−1.01400	−0.507001	+	0.861946i	$0.669246\pi$
$8$	1.00000	0.353553
$9$	4.70196	1.56732
$10$	−2.60760	−0.824597
$11$	−4.62485	−1.39444	−0.697222	−	0.716855i	$-0.745581\pi$
$11$	−4.62485	−1.39444	−0.697222	+	0.716855i	$0.745581\pi$
$12$	−2.77524	−0.801143
$13$	3.73467	1.03581	0.517906	−	0.855438i	$-0.326712\pi$
$13$	3.73467	1.03581	0.517906	+	0.855438i	$0.326712\pi$
$14$	−2.68280	−0.717007
$15$	7.23673	1.86851
$16$	1.00000	0.250000
$17$	6.00283	1.45590	0.727950	−	0.685630i	$-0.240473\pi$
$17$	6.00283	1.45590	0.727950	+	0.685630i	$0.240473\pi$
$18$	4.70196	1.10826
$19$	−6.31185	−1.44804	−0.724019	−	0.689780i	$-0.757707\pi$
$19$	−6.31185	−1.44804	−0.724019	+	0.689780i	$0.757707\pi$
$20$	−2.60760	−0.583078
$21$	7.44540	1.62472
$22$	−4.62485	−0.986021
$23$	−1.00000	−0.208514
$23$	−1.00000	−0.208514
$24$	−2.77524	−0.566494
$25$	1.79960	0.359919
$26$	3.73467	0.732430
$27$	−4.72335	−0.909009
$28$	−2.68280	−0.507001
$29$	−8.79796	−1.63374	−0.816870	−	0.576822i	$-0.804293\pi$
$29$	−8.79796	−1.63374	−0.816870	+	0.576822i	$0.804293\pi$
$30$	7.23673	1.32124
$31$	−3.27132	−0.587546	−0.293773	−	0.955875i	$-0.594911\pi$
$31$	−3.27132	−0.587546	−0.293773	+	0.955875i	$0.594911\pi$
$32$	1.00000	0.176777
$33$	12.8351	2.23430
$34$	6.00283	1.02948
$35$	6.99567	1.18248
$36$	4.70196	0.783660
$37$	−0.593078	−0.0975015	−0.0487507	−	0.998811i	$-0.515524\pi$
$37$	−0.593078	−0.0975015	−0.0487507	+	0.998811i	$0.515524\pi$
$38$	−6.31185	−1.02392
$39$	−10.3646	−1.65967
$40$	−2.60760	−0.412298
$41$	−10.0465	−1.56900	−0.784501	−	0.620127i	$-0.787081\pi$
$41$	−10.0465	−1.56900	−0.784501	+	0.620127i	$0.787081\pi$
$42$	7.44540	1.14885
$43$	−4.66799	−0.711861	−0.355931	−	0.934512i	$-0.615836\pi$
$43$	−4.66799	−0.711861	−0.355931	+	0.934512i	$0.615836\pi$
$44$	−4.62485	−0.697222
$45$	−12.2608	−1.82774
$46$	−1.00000	−0.147442
$47$	−12.7017	−1.85274	−0.926370	−	0.376614i	$-0.877088\pi$
$47$	−12.7017	−1.85274	−0.926370	+	0.376614i	$0.877088\pi$
$48$	−2.77524	−0.400571
$49$	0.197394	0.0281992
$50$	1.79960	0.254501
$51$	−16.6593	−2.33277
$52$	3.73467	0.517906
$53$	1.91560	0.263128	0.131564	−	0.991308i	$-0.458000\pi$
$53$	1.91560	0.263128	0.131564	+	0.991308i	$0.458000\pi$
$54$	−4.72335	−0.642767
$55$	12.0598	1.62614
$56$	−2.68280	−0.358504
$57$	17.5169	2.32017
$58$	−8.79796	−1.15523
$59$	−4.31508	−0.561775	−0.280887	−	0.959741i	$-0.590629\pi$
$59$	−4.31508	−0.561775	−0.280887	+	0.959741i	$0.590629\pi$
$60$	7.23673	0.934257
$61$	−0.465995	−0.0596645	−0.0298323	−	0.999555i	$-0.509497\pi$
$61$	−0.465995	−0.0596645	−0.0298323	+	0.999555i	$0.509497\pi$
$62$	−3.27132	−0.415458
$63$	−12.6144	−1.58927
$64$	1.00000	0.125000
$65$	−9.73855	−1.20792
$66$	12.8351	1.57989
$67$	−3.37661	−0.412519	−0.206259	−	0.978497i	$-0.566129\pi$
$67$	−3.37661	−0.412519	−0.206259	+	0.978497i	$0.566129\pi$
$68$	6.00283	0.727950
$69$	2.77524	0.334100
$70$	6.99567	0.836142
$71$	7.48886	0.888764	0.444382	−	0.895837i	$-0.353423\pi$
$71$	7.48886	0.888764	0.444382	+	0.895837i	$0.353423\pi$
$72$	4.70196	0.554131
$73$	−3.88577	−0.454795	−0.227397	−	0.973802i	$-0.573022\pi$
$73$	−3.88577	−0.454795	−0.227397	+	0.973802i	$0.573022\pi$
$74$	−0.593078	−0.0689440
$75$	−4.99431	−0.576694
$76$	−6.31185	−0.724019
$77$	12.4075	1.41397
$78$	−10.3646	−1.17356
$79$	−10.8761	−1.22366	−0.611830	−	0.790989i	$-0.709566\pi$
$79$	−10.8761	−1.22366	−0.611830	+	0.790989i	$0.709566\pi$
$80$	−2.60760	−0.291539
$81$	−0.997447	−0.110827
$82$	−10.0465	−1.10945
$83$	4.30768	0.472830	0.236415	−	0.971652i	$-0.424028\pi$
$83$	4.30768	0.472830	0.236415	+	0.971652i	$0.424028\pi$
$84$	7.44540	0.812360
$85$	−15.6530	−1.69781
$86$	−4.66799	−0.503362
$87$	24.4164	2.61772
$88$	−4.62485	−0.493011
$89$	6.17007	0.654026	0.327013	−	0.945020i	$-0.393958\pi$
$89$	6.17007	0.654026	0.327013	+	0.945020i	$0.393958\pi$
$90$	−12.2608	−1.29241
$91$	−10.0194	−1.05031
$92$	−1.00000	−0.104257
$93$	9.07870	0.941417
$94$	−12.7017	−1.31009
$95$	16.4588	1.68864
$96$	−2.77524	−0.283247
$97$	7.79337	0.791296	0.395648	−	0.918402i	$-0.370520\pi$
$97$	7.79337	0.791296	0.395648	+	0.918402i	$0.370520\pi$
$98$	0.197394	0.0199398
$99$	−21.7459	−2.18554
$100$	1.79960	0.179960
$101$	−16.9911	−1.69067	−0.845337	−	0.534233i	$-0.820600\pi$
$101$	−16.9911	−1.69067	−0.845337	+	0.534233i	$0.820600\pi$
$102$	−16.6593	−1.64952
$103$	18.4041	1.81341	0.906703	−	0.421769i	$-0.138591\pi$
$103$	18.4041	1.81341	0.906703	+	0.421769i	$0.138591\pi$
$104$	3.73467	0.366215
$105$	−19.4147	−1.89468
$106$	1.91560	0.186059
$107$	−9.36482	−0.905331	−0.452666	−	0.891680i	$-0.649527\pi$
$107$	−9.36482	−0.905331	−0.452666	+	0.891680i	$0.649527\pi$
$108$	−4.72335	−0.454505
$109$	12.5704	1.20402	0.602012	−	0.798487i	$-0.294366\pi$
$109$	12.5704	1.20402	0.602012	+	0.798487i	$0.294366\pi$
$110$	12.0598	1.14985
$111$	1.64594	0.156225
$112$	−2.68280	−0.253500
$113$	9.63110	0.906018	0.453009	−	0.891506i	$-0.350351\pi$
$113$	9.63110	0.906018	0.453009	+	0.891506i	$0.350351\pi$
$114$	17.5169	1.64061
$115$	2.60760	0.243160
$116$	−8.79796	−0.816870
$117$	17.5603	1.62345
$118$	−4.31508	−0.397235
$119$	−16.1044	−1.47629
$120$	7.23673	0.660620
$121$	10.3892	0.944475
$122$	−0.465995	−0.0421892
$123$	27.8815	2.51399
$124$	−3.27132	−0.293773
$125$	8.34538	0.746434
$126$	−12.6144	−1.12378
$127$	−2.22462	−0.197403	−0.0987015	−	0.995117i	$-0.531469\pi$
$127$	−2.22462	−0.197403	−0.0987015	+	0.995117i	$0.531469\pi$
$128$	1.00000	0.0883883
$129$	12.9548	1.14061
$130$	−9.73855	−0.854127
$131$	−1.00000	−0.0873704
$131$	−1.00000	−0.0873704
$132$	12.8351	1.11715
$133$	16.9334	1.46831
$134$	−3.37661	−0.291695
$135$	12.3166	1.06005
$136$	6.00283	0.514739
$137$	9.39924	0.803031	0.401515	−	0.915852i	$-0.368484\pi$
$137$	9.39924	0.803031	0.401515	+	0.915852i	$0.368484\pi$
$138$	2.77524	0.236244
$139$	5.11864	0.434157	0.217079	−	0.976154i	$-0.430347\pi$
$139$	5.11864	0.434157	0.217079	+	0.976154i	$0.430347\pi$
$140$	6.99567	0.591242
$141$	35.2504	2.96862
$142$	7.48886	0.628451
$143$	−17.2723	−1.44438
$144$	4.70196	0.391830
$145$	22.9416	1.90519
$146$	−3.88577	−0.321589
$147$	−0.547816	−0.0451831
$148$	−0.593078	−0.0487507
$149$	14.6115	1.19702	0.598510	−	0.801115i	$-0.295760\pi$
$149$	14.6115	1.19702	0.598510	+	0.801115i	$0.295760\pi$
$150$	−4.99431	−0.407784
$151$	−9.69632	−0.789076	−0.394538	−	0.918880i	$-0.629095\pi$
$151$	−9.69632	−0.789076	−0.394538	+	0.918880i	$0.629095\pi$
$152$	−6.31185	−0.511959
$153$	28.2251	2.28186
$154$	12.4075	0.999827
$155$	8.53030	0.685171
$156$	−10.3646	−0.829834
$157$	3.45816	0.275992	0.137996	−	0.990433i	$-0.455934\pi$
$157$	3.45816	0.275992	0.137996	+	0.990433i	$0.455934\pi$
$158$	−10.8761	−0.865258
$159$	−5.31625	−0.421606
$160$	−2.60760	−0.206149
$161$	2.68280	0.211434
$162$	−0.997447	−0.0783668
$163$	20.2399	1.58531	0.792657	−	0.609667i	$-0.208697\pi$
$163$	20.2399	1.58531	0.792657	+	0.609667i	$0.208697\pi$
$164$	−10.0465	−0.784501
$165$	−33.4688	−2.60554
$166$	4.30768	0.334341
$167$	−18.7131	−1.44806	−0.724030	−	0.689768i	$-0.757712\pi$
$167$	−18.7131	−1.44806	−0.724030	+	0.689768i	$0.757712\pi$
$168$	7.44540	0.574425
$169$	0.947785	0.0729065
$170$	−15.6530	−1.20053
$171$	−29.6781	−2.26954
$172$	−4.66799	−0.355931
$173$	−11.4779	−0.872648	−0.436324	−	0.899790i	$-0.643720\pi$
$173$	−11.4779	−0.872648	−0.436324	+	0.899790i	$0.643720\pi$
$174$	24.4164	1.85101
$175$	−4.82795	−0.364959
$176$	−4.62485	−0.348611
$177$	11.9754	0.900124
$178$	6.17007	0.462467
$179$	−3.69849	−0.276438	−0.138219	−	0.990402i	$-0.544138\pi$
$179$	−3.69849	−0.276438	−0.138219	+	0.990402i	$0.544138\pi$
$180$	−12.2608	−0.913870
$181$	−17.9340	−1.33302	−0.666511	−	0.745496i	$-0.732213\pi$
$181$	−17.9340	−1.33302	−0.666511	+	0.745496i	$0.732213\pi$
$182$	−10.0194	−0.742685
$183$	1.29325	0.0955996
$184$	−1.00000	−0.0737210
$185$	1.54651	0.113702
$186$	9.07870	0.665683
$187$	−27.7622	−2.03017
$188$	−12.7017	−0.926370
$189$	12.6718	0.921737
$190$	16.4588	1.19405
$191$	−8.03408	−0.581326	−0.290663	−	0.956826i	$-0.593876\pi$
$191$	−8.03408	−0.581326	−0.290663	+	0.956826i	$0.593876\pi$
$192$	−2.77524	−0.200286
$193$	8.54723	0.615243	0.307622	−	0.951509i	$-0.400467\pi$
$193$	8.54723	0.615243	0.307622	+	0.951509i	$0.400467\pi$
$194$	7.79337	0.559531
$195$	27.0268	1.93543
$196$	0.197394	0.0140996
$197$	22.4868	1.60212	0.801058	−	0.598587i	$-0.204271\pi$
$197$	22.4868	1.60212	0.801058	+	0.598587i	$0.204271\pi$
$198$	−21.7459	−1.54541
$199$	10.8157	0.766702	0.383351	−	0.923603i	$-0.374770\pi$
$199$	10.8157	0.766702	0.383351	+	0.923603i	$0.374770\pi$
$200$	1.79960	0.127251
$201$	9.37090	0.660973
$202$	−16.9911	−1.19549
$203$	23.6031	1.65661
$204$	−16.6593	−1.16638
$205$	26.1973	1.82970
$206$	18.4041	1.28227
$207$	−4.70196	−0.326809
$208$	3.73467	0.258953
$209$	29.1913	2.01921
$210$	−19.4147	−1.33974
$211$	0.707666	0.0487178	0.0243589	−	0.999703i	$-0.492246\pi$
$211$	0.707666	0.0487178	0.0243589	+	0.999703i	$0.492246\pi$
$212$	1.91560	0.131564
$213$	−20.7834	−1.42405
$214$	−9.36482	−0.640166
$215$	12.1723	0.830141
$216$	−4.72335	−0.321383
$217$	8.77628	0.595773
$218$	12.5704	0.851374
$219$	10.7839	0.728711
$220$	12.0598	0.813070
$221$	22.4186	1.50804
$222$	1.64594	0.110468
$223$	22.1444	1.48290	0.741450	−	0.671008i	$-0.234138\pi$
$223$	22.1444	1.48290	0.741450	+	0.671008i	$0.234138\pi$
$224$	−2.68280	−0.179252
$225$	8.46163	0.564109
$226$	9.63110	0.640651
$227$	−25.8400	−1.71506	−0.857529	−	0.514435i	$-0.828002\pi$
$227$	−25.8400	−1.71506	−0.857529	+	0.514435i	$0.828002\pi$
$228$	17.5169	1.16009
$229$	−13.6931	−0.904869	−0.452434	−	0.891798i	$-0.649444\pi$
$229$	−13.6931	−0.904869	−0.452434	+	0.891798i	$0.649444\pi$
$230$	2.60760	0.171940
$231$	−34.4339	−2.26558
$232$	−8.79796	−0.577614
$233$	−15.5958	−1.02172	−0.510858	−	0.859665i	$-0.670672\pi$
$233$	−15.5958	−1.02172	−0.510858	+	0.859665i	$0.670672\pi$
$234$	17.5603	1.14795
$235$	33.1211	2.16058
$236$	−4.31508	−0.280887
$237$	30.1839	1.96065
$238$	−16.1044	−1.04389
$239$	12.9018	0.834547	0.417274	−	0.908781i	$-0.362986\pi$
$239$	12.9018	0.834547	0.417274	+	0.908781i	$0.362986\pi$
$240$	7.23673	0.467129
$241$	−11.8769	−0.765057	−0.382528	−	0.923944i	$-0.624947\pi$
$241$	−11.8769	−0.765057	−0.382528	+	0.923944i	$0.624947\pi$
$242$	10.3892	0.667845
$243$	16.9382	1.08659
$244$	−0.465995	−0.0298323
$245$	−0.514726	−0.0328846
$246$	27.8815	1.77766
$247$	−23.5727	−1.49989
$248$	−3.27132	−0.207729
$249$	−11.9549	−0.757608
$250$	8.34538	0.527808
$251$	1.52760	0.0964210	0.0482105	−	0.998837i	$-0.484648\pi$
$251$	1.52760	0.0964210	0.0482105	+	0.998837i	$0.484648\pi$
$252$	−12.6144	−0.794633
$253$	4.62485	0.290762
$254$	−2.22462	−0.139585
$255$	43.4409	2.72037
$256$	1.00000	0.0625000
$257$	6.40903	0.399784	0.199892	−	0.979818i	$-0.435941\pi$
$257$	6.40903	0.399784	0.199892	+	0.979818i	$0.435941\pi$
$258$	12.9548	0.806530
$259$	1.59111	0.0988667
$260$	−9.73855	−0.603959
$261$	−41.3676	−2.56059
$262$	−1.00000	−0.0617802
$263$	10.5118	0.648187	0.324093	−	0.946025i	$-0.394941\pi$
$263$	10.5118	0.648187	0.324093	+	0.946025i	$0.394941\pi$
$264$	12.8351	0.789944
$265$	−4.99512	−0.306848
$266$	16.9334	1.03825
$267$	−17.1234	−1.04794
$268$	−3.37661	−0.206259
$269$	−22.2313	−1.35547	−0.677733	−	0.735308i	$-0.737037\pi$
$269$	−22.2313	−1.35547	−0.677733	+	0.735308i	$0.737037\pi$
$270$	12.3166	0.749566
$271$	21.0130	1.27645	0.638224	−	0.769851i	$-0.279669\pi$
$271$	21.0130	1.27645	0.638224	+	0.769851i	$0.279669\pi$
$272$	6.00283	0.363975
$273$	27.8062	1.68290
$274$	9.39924	0.567829
$275$	−8.32286	−0.501887
$276$	2.77524	0.167050
$277$	−9.22892	−0.554512	−0.277256	−	0.960796i	$-0.589425\pi$
$277$	−9.22892	−0.554512	−0.277256	+	0.960796i	$0.589425\pi$
$278$	5.11864	0.306995
$279$	−15.3816	−0.920873
$280$	6.99567	0.418071
$281$	31.7421	1.89358	0.946788	−	0.321859i	$-0.104308\pi$
$281$	31.7421	1.89358	0.946788	+	0.321859i	$0.104308\pi$
$282$	35.2504	2.09913
$283$	−26.1732	−1.55583	−0.777916	−	0.628368i	$-0.783723\pi$
$283$	−26.1732	−1.55583	−0.777916	+	0.628368i	$0.783723\pi$
$284$	7.48886	0.444382
$285$	−45.6771	−2.70568
$286$	−17.2723	−1.02133
$287$	26.9528	1.59097
$288$	4.70196	0.277066
$289$	19.0340	1.11965
$290$	22.9416	1.34718
$291$	−21.6285	−1.26788
$292$	−3.88577	−0.227397
$293$	−25.9156	−1.51400	−0.757002	−	0.653412i	$-0.773337\pi$
$293$	−25.9156	−1.51400	−0.757002	+	0.653412i	$0.773337\pi$
$294$	−0.547816	−0.0319493
$295$	11.2520	0.655117
$296$	−0.593078	−0.0344720
$297$	21.8448	1.26756
$298$	14.6115	0.846421
$299$	−3.73467	−0.215982
$300$	−4.99431	−0.288347
$301$	12.5233	0.721828
$302$	−9.69632	−0.557961
$303$	47.1543	2.70894
$304$	−6.31185	−0.362009
$305$	1.21513	0.0695781
$306$	28.2251	1.61352
$307$	25.3638	1.44759	0.723793	−	0.690017i	$-0.242397\pi$
$307$	25.3638	1.44759	0.723793	+	0.690017i	$0.242397\pi$
$308$	12.4075	0.706984
$309$	−51.0757	−2.90560
$310$	8.53030	0.484489
$311$	23.3767	1.32557	0.662786	−	0.748809i	$-0.269374\pi$
$311$	23.3767	1.32557	0.662786	+	0.748809i	$0.269374\pi$
$312$	−10.3646	−0.586781
$313$	−34.9497	−1.97548	−0.987738	−	0.156122i	$-0.950101\pi$
$313$	−34.9497	−1.97548	−0.987738	+	0.156122i	$0.950101\pi$
$314$	3.45816	0.195155
$315$	32.8934	1.85333
$316$	−10.8761	−0.611830
$317$	13.4297	0.754289	0.377145	−	0.926154i	$-0.376906\pi$
$317$	13.4297	0.754289	0.377145	+	0.926154i	$0.376906\pi$
$318$	−5.31625	−0.298120
$319$	40.6892	2.27816
$320$	−2.60760	−0.145769
$321$	25.9896	1.45060
$322$	2.68280	0.149506
$323$	−37.8890	−2.10820
$324$	−0.997447	−0.0554137
$325$	6.72090	0.372809
$326$	20.2399	1.12099
$327$	−34.8858	−1.92919
$328$	−10.0465	−0.554726
$329$	34.0762	1.87868
$330$	−33.4688	−1.84240
$331$	−23.5201	−1.29278	−0.646391	−	0.763007i	$-0.723722\pi$
$331$	−23.5201	−1.29278	−0.646391	+	0.763007i	$0.723722\pi$
$332$	4.30768	0.236415
$333$	−2.78863	−0.152816
$334$	−18.7131	−1.02393
$335$	8.80486	0.481061
$336$	7.44540	0.406180
$337$	−13.0306	−0.709820	−0.354910	−	0.934901i	$-0.615488\pi$
$337$	−13.0306	−0.709820	−0.354910	+	0.934901i	$0.615488\pi$
$338$	0.947785	0.0515527
$339$	−26.7286	−1.45170
$340$	−15.6530	−0.848904
$341$	15.1294	0.819301
$342$	−29.6781	−1.60481
$343$	18.2500	0.985408
$344$	−4.66799	−0.251681
$345$	−7.23673	−0.389612
$346$	−11.4779	−0.617055
$347$	−25.9719	−1.39424	−0.697122	−	0.716953i	$-0.745536\pi$
$347$	−25.9719	−1.39424	−0.697122	+	0.716953i	$0.745536\pi$
$348$	24.4164	1.30886
$349$	0.169106	0.00905202	0.00452601	−	0.999990i	$-0.498559\pi$
$349$	0.169106	0.00905202	0.00452601	+	0.999990i	$0.498559\pi$
$350$	−4.82795	−0.258065
$351$	−17.6402	−0.941563
$352$	−4.62485	−0.246505
$353$	28.7080	1.52797	0.763987	−	0.645232i	$-0.223239\pi$
$353$	28.7080	1.52797	0.763987	+	0.645232i	$0.223239\pi$
$354$	11.9754	0.636484
$355$	−19.5280	−1.03644
$356$	6.17007	0.327013
$357$	44.6935	2.36543
$358$	−3.69849	−0.195471
$359$	4.25407	0.224521	0.112261	−	0.993679i	$-0.464191\pi$
$359$	4.25407	0.224521	0.112261	+	0.993679i	$0.464191\pi$
$360$	−12.2608	−0.646204
$361$	20.8394	1.09681
$362$	−17.9340	−0.942588
$363$	−28.8326	−1.51332
$364$	−10.0194	−0.525157
$365$	10.1325	0.530362
$366$	1.29325	0.0675991
$367$	26.5075	1.38368	0.691840	−	0.722051i	$-0.256800\pi$
$367$	26.5075	1.38368	0.691840	+	0.722051i	$0.256800\pi$
$368$	−1.00000	−0.0521286
$369$	−47.2383	−2.45913
$370$	1.54651	0.0803994
$371$	−5.13916	−0.266812
$372$	9.07870	0.470709
$373$	−26.8126	−1.38830	−0.694151	−	0.719829i	$-0.744220\pi$
$373$	−26.8126	−1.38830	−0.694151	+	0.719829i	$0.744220\pi$
$374$	−27.7622	−1.43555
$375$	−23.1604	−1.19600
$376$	−12.7017	−0.655043
$377$	−32.8575	−1.69225
$378$	12.6718	0.651766
$379$	11.2331	0.577007	0.288503	−	0.957479i	$-0.406842\pi$
$379$	11.2331	0.577007	0.288503	+	0.957479i	$0.406842\pi$
$380$	16.4588	0.844319
$381$	6.17386	0.316296
$382$	−8.03408	−0.411060
$383$	−17.4332	−0.890797	−0.445399	−	0.895332i	$-0.646938\pi$
$383$	−17.4332	−0.890797	−0.445399	+	0.895332i	$0.646938\pi$
$384$	−2.77524	−0.141623
$385$	−32.3539	−1.64891
$386$	8.54723	0.435043
$387$	−21.9487	−1.11571
$388$	7.79337	0.395648
$389$	−2.47985	−0.125733	−0.0628667	−	0.998022i	$-0.520024\pi$
$389$	−2.47985	−0.125733	−0.0628667	+	0.998022i	$0.520024\pi$
$390$	27.0268	1.36856
$391$	−6.00283	−0.303576
$392$	0.197394	0.00996991
$393$	2.77524	0.139992
$394$	22.4868	1.13287
$395$	28.3606	1.42698
$396$	−21.7459	−1.09277
$397$	−36.4896	−1.83136	−0.915679	−	0.401910i	$-0.868347\pi$
$397$	−36.4896	−1.83136	−0.915679	+	0.401910i	$0.868347\pi$
$398$	10.8157	0.542140
$399$	−46.9943	−2.35266
$400$	1.79960	0.0899798
$401$	3.79285	0.189406	0.0947029	−	0.995506i	$-0.469810\pi$
$401$	3.79285	0.189406	0.0947029	+	0.995506i	$0.469810\pi$
$402$	9.37090	0.467378
$403$	−12.2173	−0.608588
$404$	−16.9911	−0.845337
$405$	2.60095	0.129242
$406$	23.6031	1.17140
$407$	2.74290	0.135960
$408$	−16.6593	−0.824758
$409$	10.4167	0.515071	0.257535	−	0.966269i	$-0.417090\pi$
$409$	10.4167	0.515071	0.257535	+	0.966269i	$0.417090\pi$
$410$	26.1973	1.29379
$411$	−26.0851	−1.28669
$412$	18.4041	0.906703
$413$	11.5765	0.569641
$414$	−4.70196	−0.231089
$415$	−11.2327	−0.551393
$416$	3.73467	0.183107
$417$	−14.2054	−0.695644
$418$	29.1913	1.42780
$419$	−8.83280	−0.431511	−0.215755	−	0.976447i	$-0.569221\pi$
$419$	−8.83280	−0.431511	−0.215755	+	0.976447i	$0.569221\pi$
$420$	−19.4147	−0.947339
$421$	26.5564	1.29428	0.647140	−	0.762372i	$-0.275965\pi$
$421$	26.5564	1.29428	0.647140	+	0.762372i	$0.275965\pi$
$422$	0.707666	0.0344487
$423$	−59.7231	−2.90384
$424$	1.91560	0.0930297
$425$	10.8027	0.524007
$426$	−20.7834	−1.00696
$427$	1.25017	0.0604999
$428$	−9.36482	−0.452666
$429$	47.9348	2.31431
$430$	12.1723	0.586998
$431$	17.1515	0.826158	0.413079	−	0.910695i	$-0.364453\pi$
$431$	17.1515	0.826158	0.413079	+	0.910695i	$0.364453\pi$
$432$	−4.72335	−0.227252
$433$	−3.66321	−0.176042	−0.0880212	−	0.996119i	$-0.528054\pi$
$433$	−3.66321	−0.176042	−0.0880212	+	0.996119i	$0.528054\pi$
$434$	8.77628	0.421275
$435$	−63.6684	−3.05267
$436$	12.5704	0.602012
$437$	6.31185	0.301937
$438$	10.7839	0.515277
$439$	40.0518	1.91157	0.955783	−	0.294072i	$-0.0950104\pi$
$439$	40.0518	1.91157	0.955783	+	0.294072i	$0.0950104\pi$
$440$	12.0598	0.574927
$441$	0.928140	0.0441971
$442$	22.4186	1.06634
$443$	14.9416	0.709898	0.354949	−	0.934886i	$-0.384498\pi$
$443$	14.9416	0.709898	0.354949	+	0.934886i	$0.384498\pi$
$444$	1.64594	0.0781126
$445$	−16.0891	−0.762697
$446$	22.1444	1.04857
$447$	−40.5504	−1.91797
$448$	−2.68280	−0.126750
$449$	−24.2545	−1.14464	−0.572321	−	0.820030i	$-0.693957\pi$
$449$	−24.2545	−1.14464	−0.572321	+	0.820030i	$0.693957\pi$
$450$	8.46163	0.398885
$451$	46.4636	2.18789
$452$	9.63110	0.453009
$453$	26.9096	1.26432
$454$	−25.8400	−1.21273
$455$	26.1265	1.22483
$456$	17.5169	0.820304
$457$	23.3404	1.09182	0.545909	−	0.837844i	$-0.316184\pi$
$457$	23.3404	1.09182	0.545909	+	0.837844i	$0.316184\pi$
$458$	−13.6931	−0.639839
$459$	−28.3535	−1.32343
$460$	2.60760	0.121580
$461$	−14.7458	−0.686782	−0.343391	−	0.939193i	$-0.611576\pi$
$461$	−14.7458	−0.686782	−0.343391	+	0.939193i	$0.611576\pi$
$462$	−34.4339	−1.60201
$463$	−16.5235	−0.767914	−0.383957	−	0.923351i	$-0.625439\pi$
$463$	−16.5235	−0.767914	−0.383957	+	0.923351i	$0.625439\pi$
$464$	−8.79796	−0.408435
$465$	−23.6736	−1.09784
$466$	−15.5958	−0.722462
$467$	2.67443	0.123758	0.0618790	−	0.998084i	$-0.480291\pi$
$467$	2.67443	0.123758	0.0618790	+	0.998084i	$0.480291\pi$
$468$	17.5603	0.811725
$469$	9.05875	0.418294
$470$	33.1211	1.52776
$471$	−9.59724	−0.442217
$472$	−4.31508	−0.198617
$473$	21.5887	0.992651
$474$	30.1839	1.38639
$475$	−11.3588	−0.521177
$476$	−16.1044	−0.738143
$477$	9.00707	0.412406
$478$	12.9018	0.590114
$479$	4.49613	0.205433	0.102717	−	0.994711i	$-0.467247\pi$
$479$	4.49613	0.205433	0.102717	+	0.994711i	$0.467247\pi$
$480$	7.23673	0.330310
$481$	−2.21495	−0.100993
$482$	−11.8769	−0.540977
$483$	−7.44540	−0.338778
$484$	10.3892	0.472238
$485$	−20.3220	−0.922775
$486$	16.9382	0.768333
$487$	28.3239	1.28348	0.641739	−	0.766923i	$-0.278213\pi$
$487$	28.3239	1.28348	0.641739	+	0.766923i	$0.278213\pi$
$488$	−0.465995	−0.0210946
$489$	−56.1707	−2.54013
$490$	−0.514726	−0.0232529
$491$	14.8750	0.671299	0.335649	−	0.941987i	$-0.391044\pi$
$491$	14.8750	0.671299	0.335649	+	0.941987i	$0.391044\pi$
$492$	27.8815	1.25700
$493$	−52.8127	−2.37856
$494$	−23.5727	−1.06059
$495$	56.7046	2.54868
$496$	−3.27132	−0.146887
$497$	−20.0911	−0.901208
$498$	−11.9549	−0.535710
$499$	29.6232	1.32612	0.663059	−	0.748567i	$-0.269258\pi$
$499$	29.6232	1.32612	0.663059	+	0.748567i	$0.269258\pi$
$500$	8.34538	0.373217
$501$	51.9333	2.32021
$502$	1.52760	0.0681799
$503$	−35.2192	−1.57035	−0.785174	−	0.619275i	$-0.787427\pi$
$503$	−35.2192	−1.57035	−0.785174	+	0.619275i	$0.787427\pi$
$504$	−12.6144	−0.561890
$505$	44.3060	1.97159
$506$	4.62485	0.205600
$507$	−2.63033	−0.116817
$508$	−2.22462	−0.0987015
$509$	−20.0469	−0.888565	−0.444283	−	0.895887i	$-0.646541\pi$
$509$	−20.0469	−0.888565	−0.444283	+	0.895887i	$0.646541\pi$
$510$	43.4409	1.92359
$511$	10.4247	0.461163
$512$	1.00000	0.0441942
$513$	29.8131	1.31628
$514$	6.40903	0.282690
$515$	−47.9905	−2.11471
$516$	12.9548	0.570303
$517$	58.7437	2.58354
$518$	1.59111	0.0699093
$519$	31.8539	1.39823
$520$	−9.73855	−0.427064
$521$	6.31636	0.276725	0.138362	−	0.990382i	$-0.455816\pi$
$521$	6.31636	0.276725	0.138362	+	0.990382i	$0.455816\pi$
$522$	−41.3676	−1.81061
$523$	24.8142	1.08505	0.542524	−	0.840040i	$-0.317469\pi$
$523$	24.8142	1.08505	0.542524	+	0.840040i	$0.317469\pi$
$524$	−1.00000	−0.0436852
$525$	13.3987	0.584768
$526$	10.5118	0.458337
$527$	−19.6372	−0.855409
$528$	12.8351	0.558575
$529$	1.00000	0.0434783
$530$	−4.99512	−0.216974
$531$	−20.2893	−0.880481
$532$	16.9334	0.734156
$533$	−37.5205	−1.62519
$534$	−17.1234	−0.741004
$535$	24.4197	1.05576
$536$	−3.37661	−0.145847
$537$	10.2642	0.442933
$538$	−22.2313	−0.958459
$539$	−0.912918	−0.0393222
$540$	12.3166	0.530023
$541$	5.24765	0.225614	0.112807	−	0.993617i	$-0.464016\pi$
$541$	5.24765	0.225614	0.112807	+	0.993617i	$0.464016\pi$
$542$	21.0130	0.902585
$543$	49.7711	2.13588
$544$	6.00283	0.257369
$545$	−32.7786	−1.40408
$546$	27.8062	1.18999
$547$	−9.32339	−0.398639	−0.199320	−	0.979935i	$-0.563873\pi$
$547$	−9.32339	−0.398639	−0.199320	+	0.979935i	$0.563873\pi$
$548$	9.39924	0.401515
$549$	−2.19109	−0.0935134
$550$	−8.32286	−0.354888
$551$	55.5314	2.36572
$552$	2.77524	0.118122
$553$	29.1784	1.24079
$554$	−9.22892	−0.392099
$555$	−4.29195	−0.182183
$556$	5.11864	0.217079
$557$	36.2387	1.53548	0.767742	−	0.640759i	$-0.221380\pi$
$557$	36.2387	1.53548	0.767742	+	0.640759i	$0.221380\pi$
$558$	−15.3816	−0.651156
$559$	−17.4334	−0.737354
$560$	6.99567	0.295621
$561$	77.0468	3.25292
$562$	31.7421	1.33896
$563$	5.66842	0.238895	0.119448	−	0.992841i	$-0.461888\pi$
$563$	5.66842	0.238895	0.119448	+	0.992841i	$0.461888\pi$
$564$	35.2504	1.48431
$565$	−25.1141	−1.05656
$566$	−26.1732	−1.10014
$567$	2.67595	0.112379
$568$	7.48886	0.314226
$569$	−6.16475	−0.258440	−0.129220	−	0.991616i	$-0.541247\pi$
$569$	−6.16475	−0.258440	−0.129220	+	0.991616i	$0.541247\pi$
$570$	−45.6771	−1.91320
$571$	24.6254	1.03054	0.515271	−	0.857027i	$-0.327691\pi$
$571$	24.6254	1.03054	0.515271	+	0.857027i	$0.327691\pi$
$572$	−17.2723	−0.722191
$573$	22.2965	0.931450
$574$	26.9528	1.12499
$575$	−1.79960	−0.0750484
$576$	4.70196	0.195915
$577$	−23.0459	−0.959414	−0.479707	−	0.877429i	$-0.659257\pi$
$577$	−23.0459	−0.959414	−0.479707	+	0.877429i	$0.659257\pi$
$578$	19.0340	0.791710
$579$	−23.7206	−0.985795
$580$	22.9416	0.952597
$581$	−11.5566	−0.479450
$582$	−21.6285	−0.896529
$583$	−8.85936	−0.366917
$584$	−3.88577	−0.160794
$585$	−45.7903	−1.89319
$586$	−25.9156	−1.07056
$587$	−27.4422	−1.13266	−0.566330	−	0.824179i	$-0.691637\pi$
$587$	−27.4422	−1.13266	−0.566330	+	0.824179i	$0.691637\pi$
$588$	−0.547816	−0.0225916
$589$	20.6481	0.850789
$590$	11.2520	0.463238
$591$	−62.4062	−2.56705
$592$	−0.593078	−0.0243754
$593$	5.91277	0.242808	0.121404	−	0.992603i	$-0.461260\pi$
$593$	5.91277	0.242808	0.121404	+	0.992603i	$0.461260\pi$
$594$	21.8448	0.896302
$595$	41.9938	1.72158
$596$	14.6115	0.598510
$597$	−30.0161	−1.22848
$598$	−3.73467	−0.152722
$599$	−38.7235	−1.58220	−0.791100	−	0.611687i	$-0.790491\pi$
$599$	−38.7235	−1.58220	−0.791100	+	0.611687i	$0.790491\pi$
$600$	−4.99431	−0.203892
$601$	−6.07090	−0.247637	−0.123819	−	0.992305i	$-0.539514\pi$
$601$	−6.07090	−0.247637	−0.123819	+	0.992305i	$0.539514\pi$
$602$	12.5233	0.510410
$603$	−15.8767	−0.646549
$604$	−9.69632	−0.394538
$605$	−27.0910	−1.10141
$606$	47.1543	1.91551
$607$	10.8626	0.440898	0.220449	−	0.975399i	$-0.429248\pi$
$607$	10.8626	0.440898	0.220449	+	0.975399i	$0.429248\pi$
$608$	−6.31185	−0.255979
$609$	−65.5043	−2.65437
$610$	1.21513	0.0491992
$611$	−47.4369	−1.91909
$612$	28.2251	1.14093
$613$	37.5496	1.51661	0.758307	−	0.651898i	$-0.226027\pi$
$613$	37.5496	1.51661	0.758307	+	0.651898i	$0.226027\pi$
$614$	25.3638	1.02360
$615$	−72.7039	−2.93170
$616$	12.4075	0.499913
$617$	46.5628	1.87455	0.937274	−	0.348593i	$-0.113341\pi$
$617$	46.5628	1.87455	0.937274	+	0.348593i	$0.113341\pi$
$618$	−51.0757	−2.05457
$619$	4.12268	0.165705	0.0828523	−	0.996562i	$-0.473597\pi$
$619$	4.12268	0.165705	0.0828523	+	0.996562i	$0.473597\pi$
$620$	8.53030	0.342585
$621$	4.72335	0.189542
$622$	23.3767	0.937321
$623$	−16.5530	−0.663184
$624$	−10.3646	−0.414917
$625$	−30.7594	−1.23038
$626$	−34.9497	−1.39687
$627$	−81.0130	−3.23535
$628$	3.45816	0.137996
$629$	−3.56015	−0.141952
$630$	32.8934	1.31050
$631$	1.63218	0.0649760	0.0324880	−	0.999472i	$-0.489657\pi$
$631$	1.63218	0.0649760	0.0324880	+	0.999472i	$0.489657\pi$
$632$	−10.8761	−0.432629
$633$	−1.96394	−0.0780598
$634$	13.4297	0.533363
$635$	5.80093	0.230203
$636$	−5.31625	−0.210803
$637$	0.737203	0.0292090
$638$	40.6892	1.61090
$639$	35.2123	1.39298
$640$	−2.60760	−0.103075
$641$	5.21406	0.205943	0.102971	−	0.994684i	$-0.467165\pi$
$641$	5.21406	0.205943	0.102971	+	0.994684i	$0.467165\pi$
$642$	25.9896	1.02573
$643$	3.17969	0.125395	0.0626974	−	0.998033i	$-0.480030\pi$
$643$	3.17969	0.125395	0.0626974	+	0.998033i	$0.480030\pi$
$644$	2.68280	0.105717
$645$	−33.7809	−1.33012
$646$	−37.8890	−1.49072
$647$	30.7303	1.20813	0.604067	−	0.796934i	$-0.293546\pi$
$647$	30.7303	1.20813	0.604067	+	0.796934i	$0.293546\pi$
$648$	−0.997447	−0.0391834
$649$	19.9566	0.783364
$650$	6.72090	0.263616
$651$	−24.3563	−0.954599
$652$	20.2399	0.792657
$653$	−24.7526	−0.968646	−0.484323	−	0.874889i	$-0.660934\pi$
$653$	−24.7526	−0.968646	−0.484323	+	0.874889i	$0.660934\pi$
$654$	−34.8858	−1.36414
$655$	2.60760	0.101888
$656$	−10.0465	−0.392251
$657$	−18.2707	−0.712809
$658$	34.0762	1.32843
$659$	17.3792	0.676997	0.338499	−	0.940967i	$-0.390081\pi$
$659$	17.3792	0.676997	0.338499	+	0.940967i	$0.390081\pi$
$660$	−33.4688	−1.30277
$661$	25.8137	1.00404	0.502019	−	0.864857i	$-0.332591\pi$
$661$	25.8137	1.00404	0.502019	+	0.864857i	$0.332591\pi$
$662$	−23.5201	−0.914134
$663$	−62.2171	−2.41631
$664$	4.30768	0.167170
$665$	−44.1556	−1.71228
$666$	−2.78863	−0.108057
$667$	8.79796	0.340658
$668$	−18.7131	−0.724030
$669$	−61.4561	−2.37603
$670$	8.80486	0.340161
$671$	2.15516	0.0831989
$672$	7.44540	0.287213
$673$	2.00751	0.0773839	0.0386920	−	0.999251i	$-0.487681\pi$
$673$	2.00751	0.0773839	0.0386920	+	0.999251i	$0.487681\pi$
$674$	−13.0306	−0.501918
$675$	−8.50012	−0.327170
$676$	0.947785	0.0364533
$677$	−42.4568	−1.63175	−0.815874	−	0.578229i	$-0.803744\pi$
$677$	−42.4568	−1.63175	−0.815874	+	0.578229i	$0.803744\pi$
$678$	−26.7286	−1.02651
$679$	−20.9080	−0.802376
$680$	−15.6530	−0.600265
$681$	71.7121	2.74801
$682$	15.1294	0.579333
$683$	−17.5714	−0.672352	−0.336176	−	0.941799i	$-0.609134\pi$
$683$	−17.5714	−0.672352	−0.336176	+	0.941799i	$0.609134\pi$
$684$	−29.6781	−1.13477
$685$	−24.5095	−0.936459
$686$	18.2500	0.696788
$687$	38.0018	1.44986
$688$	−4.66799	−0.177965
$689$	7.15414	0.272551
$690$	−7.23673	−0.275498
$691$	−30.1051	−1.14525	−0.572625	−	0.819817i	$-0.694075\pi$
$691$	−30.1051	−1.14525	−0.572625	+	0.819817i	$0.694075\pi$
$692$	−11.4779	−0.436324
$693$	58.3397	2.21614
$694$	−25.9719	−0.985879
$695$	−13.3474	−0.506295
$696$	24.4164	0.925503
$697$	−60.3076	−2.28431
$698$	0.169106	0.00640074
$699$	43.2821	1.63708
$700$	−4.82795	−0.182479
$701$	−18.7328	−0.707528	−0.353764	−	0.935335i	$-0.615098\pi$
$701$	−18.7328	−0.707528	−0.353764	+	0.935335i	$0.615098\pi$
$702$	−17.6402	−0.665785
$703$	3.74342	0.141186
$704$	−4.62485	−0.174306
$705$	−91.9191	−3.46187
$706$	28.7080	1.08044
$707$	45.5836	1.71435
$708$	11.9754	0.450062
$709$	26.1526	0.982183	0.491091	−	0.871108i	$-0.336598\pi$
$709$	26.1526	0.982183	0.491091	+	0.871108i	$0.336598\pi$
$710$	−19.5280	−0.732872
$711$	−51.1391	−1.91787
$712$	6.17007	0.231233
$713$	3.27132	0.122512
$714$	44.6935	1.67261
$715$	45.0393	1.68437
$716$	−3.69849	−0.138219
$717$	−35.8056	−1.33718
$718$	4.25407	0.158761
$719$	−24.6274	−0.918447	−0.459224	−	0.888321i	$-0.651872\pi$
$719$	−24.6274	−0.918447	−0.459224	+	0.888321i	$0.651872\pi$
$720$	−12.2608	−0.456935
$721$	−49.3744	−1.83880
$722$	20.8394	0.775563
$723$	32.9612	1.22584
$724$	−17.9340	−0.666511
$725$	−15.8328	−0.588014
$726$	−28.8326	−1.07008
$727$	−5.73424	−0.212671	−0.106336	−	0.994330i	$-0.533912\pi$
$727$	−5.73424	−0.212671	−0.106336	+	0.994330i	$0.533912\pi$
$728$	−10.0194	−0.371342
$729$	−44.0153	−1.63019
$730$	10.1325	0.375022
$731$	−28.0211	−1.03640
$732$	1.29325	0.0477998
$733$	2.11331	0.0780570	0.0390285	−	0.999238i	$-0.487574\pi$
$733$	2.11331	0.0780570	0.0390285	+	0.999238i	$0.487574\pi$
$734$	26.5075	0.978410
$735$	1.42849	0.0526906
$736$	−1.00000	−0.0368605
$737$	15.6163	0.575234
$738$	−47.2383	−1.73887
$739$	7.65336	0.281533	0.140767	−	0.990043i	$-0.455043\pi$
$739$	7.65336	0.281533	0.140767	+	0.990043i	$0.455043\pi$
$740$	1.54651	0.0568510
$741$	65.4199	2.40326
$742$	−5.13916	−0.188665
$743$	42.6775	1.56569	0.782843	−	0.622220i	$-0.213769\pi$
$743$	42.6775	1.56569	0.782843	+	0.622220i	$0.213769\pi$
$744$	9.07870	0.332841
$745$	−38.1010	−1.39591
$746$	−26.8126	−0.981678
$747$	20.2546	0.741075
$748$	−27.7622	−1.01509
$749$	25.1239	0.918007
$750$	−23.1604	−0.845700
$751$	50.2590	1.83398	0.916989	−	0.398912i	$-0.130612\pi$
$751$	50.2590	1.83398	0.916989	+	0.398912i	$0.130612\pi$
$752$	−12.7017	−0.463185
$753$	−4.23945	−0.154494
$754$	−32.8575	−1.19660
$755$	25.2842	0.920185
$756$	12.6718	0.460868
$757$	16.3535	0.594380	0.297190	−	0.954818i	$-0.403951\pi$
$757$	16.3535	0.594380	0.297190	+	0.954818i	$0.403951\pi$
$758$	11.2331	0.408005
$759$	−12.8351	−0.465883
$760$	16.4588	0.597023
$761$	−14.8552	−0.538502	−0.269251	−	0.963070i	$-0.586776\pi$
$761$	−14.8552	−0.538502	−0.269251	+	0.963070i	$0.586776\pi$
$762$	6.17386	0.223655
$763$	−33.7238	−1.22088
$764$	−8.03408	−0.290663
$765$	−73.5998	−2.66101
$766$	−17.4332	−0.629889
$767$	−16.1154	−0.581893
$768$	−2.77524	−0.100143
$769$	−6.05376	−0.218304	−0.109152	−	0.994025i	$-0.534814\pi$
$769$	−6.05376	−0.218304	−0.109152	+	0.994025i	$0.534814\pi$
$770$	−32.3539	−1.16595
$771$	−17.7866	−0.640568
$772$	8.54723	0.307622
$773$	19.7286	0.709588	0.354794	−	0.934945i	$-0.384551\pi$
$773$	19.7286	0.709588	0.354794	+	0.934945i	$0.384551\pi$
$774$	−21.9487	−0.788929
$775$	−5.88705	−0.211469
$776$	7.79337	0.279766
$777$	−4.41571	−0.158413
$778$	−2.47985	−0.0889069
$779$	63.4121	2.27197
$780$	27.0268	0.967715
$781$	−34.6348	−1.23933
$782$	−6.00283	−0.214661
$783$	41.5558	1.48508
$784$	0.197394	0.00704979
$785$	−9.01752	−0.321849
$786$	2.77524	0.0989896
$787$	−27.8766	−0.993693	−0.496846	−	0.867839i	$-0.665509\pi$
$787$	−27.8766	−0.993693	−0.496846	+	0.867839i	$0.665509\pi$
$788$	22.4868	0.801058
$789$	−29.1728	−1.03858
$790$	28.3606	1.00903
$791$	−25.8383	−0.918703
$792$	−21.7459	−0.772705
$793$	−1.74034	−0.0618012
$794$	−36.4896	−1.29497
$795$	13.8627	0.491658
$796$	10.8157	0.383351
$797$	16.5880	0.587576	0.293788	−	0.955871i	$-0.405084\pi$
$797$	16.5880	0.587576	0.293788	+	0.955871i	$0.405084\pi$
$798$	−46.9943	−1.66358
$799$	−76.2465	−2.69741
$800$	1.79960	0.0636253
$801$	29.0114	1.02507
$802$	3.79285	0.133930
$803$	17.9711	0.634186
$804$	9.37090	0.330486
$805$	−6.99567	−0.246565
$806$	−12.2173	−0.430336
$807$	61.6972	2.17184
$808$	−16.9911	−0.597744
$809$	51.0717	1.79558	0.897792	−	0.440419i	$-0.145170\pi$
$809$	51.0717	1.79558	0.897792	+	0.440419i	$0.145170\pi$
$810$	2.60095	0.0913879
$811$	50.2803	1.76558	0.882791	−	0.469766i	$-0.155662\pi$
$811$	50.2803	1.76558	0.882791	+	0.469766i	$0.155662\pi$
$812$	23.6031	0.828307
$813$	−58.3161	−2.04523
$814$	2.74290	0.0961385
$815$	−52.7778	−1.84872
$816$	−16.6593	−0.583192
$817$	29.4636	1.03080
$818$	10.4167	0.364210
$819$	−47.1107	−1.64618
$820$	26.1973	0.914850
$821$	−45.0457	−1.57211	−0.786054	−	0.618158i	$-0.787879\pi$
$821$	−45.0457	−1.57211	−0.786054	+	0.618158i	$0.787879\pi$
$822$	−26.0851	−0.909824
$823$	−53.7092	−1.87219	−0.936093	−	0.351753i	$-0.885586\pi$
$823$	−53.7092	−1.87219	−0.936093	+	0.351753i	$0.885586\pi$
$824$	18.4041	0.641136
$825$	23.0979	0.804167
$826$	11.5765	0.402797
$827$	13.0886	0.455136	0.227568	−	0.973762i	$-0.426923\pi$
$827$	13.0886	0.455136	0.227568	+	0.973762i	$0.426923\pi$
$828$	−4.70196	−0.163404
$829$	41.4324	1.43901	0.719503	−	0.694489i	$-0.244369\pi$
$829$	41.4324	1.43901	0.719503	+	0.694489i	$0.244369\pi$
$830$	−11.2327	−0.389894
$831$	25.6125	0.888486
$832$	3.73467	0.129477
$833$	1.18492	0.0410552
$834$	−14.2054	−0.491894
$835$	48.7963	1.68866
$836$	29.1913	1.00960
$837$	15.4516	0.534085
$838$	−8.83280	−0.305124
$839$	−53.8810	−1.86018	−0.930090	−	0.367331i	$-0.880272\pi$
$839$	−53.8810	−1.86018	−0.930090	+	0.367331i	$0.880272\pi$
$840$	−19.4147	−0.669870
$841$	48.4040	1.66910
$842$	26.5564	0.915194
$843$	−88.0920	−3.03405
$844$	0.707666	0.0243589
$845$	−2.47145	−0.0850204
$846$	−59.7231	−2.05332
$847$	−27.8722	−0.957699
$848$	1.91560	0.0657819
$849$	72.6368	2.49289
$850$	10.8027	0.370529
$851$	0.593078	0.0203305
$852$	−20.7834	−0.712027
$853$	−20.9258	−0.716485	−0.358243	−	0.933629i	$-0.616624\pi$
$853$	−20.9258	−0.716485	−0.358243	+	0.933629i	$0.616624\pi$
$854$	1.25017	0.0427799
$855$	77.3886	2.64664
$856$	−9.36482	−0.320083
$857$	−41.8316	−1.42894	−0.714470	−	0.699666i	$-0.753332\pi$
$857$	−41.8316	−1.42894	−0.714470	+	0.699666i	$0.753332\pi$
$858$	47.9348	1.63647
$859$	−34.2756	−1.16947	−0.584735	−	0.811224i	$-0.698801\pi$
$859$	−34.2756	−1.16947	−0.584735	+	0.811224i	$0.698801\pi$
$860$	12.1723	0.415071
$861$	−74.8004	−2.54919
$862$	17.1515	0.584182
$863$	−4.13138	−0.140634	−0.0703169	−	0.997525i	$-0.522401\pi$
$863$	−4.13138	−0.140634	−0.0703169	+	0.997525i	$0.522401\pi$
$864$	−4.72335	−0.160692
$865$	29.9298	1.01764
$866$	−3.66321	−0.124481
$867$	−52.8239	−1.79399
$868$	8.77628	0.297886
$869$	50.3004	1.70633
$870$	−63.6684	−2.15856
$871$	−12.6105	−0.427292
$872$	12.5704	0.425687
$873$	36.6441	1.24021
$874$	6.31185	0.213501
$875$	−22.3890	−0.756885
$876$	10.7839	0.364356
$877$	−37.0974	−1.25269	−0.626345	−	0.779546i	$-0.715450\pi$
$877$	−37.0974	−1.25269	−0.626345	+	0.779546i	$0.715450\pi$
$878$	40.0518	1.35168
$879$	71.9220	2.42587
$880$	12.0598	0.406535
$881$	29.2978	0.987069	0.493534	−	0.869726i	$-0.335705\pi$
$881$	29.2978	0.987069	0.493534	+	0.869726i	$0.335705\pi$
$882$	0.928140	0.0312521
$883$	0.274700	0.00924440	0.00462220	−	0.999989i	$-0.498529\pi$
$883$	0.274700	0.00924440	0.00462220	+	0.999989i	$0.498529\pi$
$884$	22.4186	0.754020
$885$	−31.2270	−1.04968
$886$	14.9416	0.501974
$887$	16.1053	0.540763	0.270382	−	0.962753i	$-0.412850\pi$
$887$	16.1053	0.540763	0.270382	+	0.962753i	$0.412850\pi$
$888$	1.64594	0.0552340
$889$	5.96820	0.200167
$890$	−16.0891	−0.539308
$891$	4.61304	0.154543
$892$	22.1444	0.741450
$893$	80.1715	2.68284
$894$	−40.5504	−1.35621
$895$	9.64419	0.322370
$896$	−2.68280	−0.0896259
$897$	10.3646	0.346064
$898$	−24.2545	−0.809384
$899$	28.7809	0.959898
$900$	8.46163	0.282054
$901$	11.4990	0.383088
$902$	46.4636	1.54707
$903$	−34.7550	−1.15658
$904$	9.63110	0.320326
$905$	46.7647	1.55451
$906$	26.9096	0.894013
$907$	23.6954	0.786792	0.393396	−	0.919369i	$-0.371300\pi$
$907$	23.6954	0.786792	0.393396	+	0.919369i	$0.371300\pi$
$908$	−25.8400	−0.857529
$909$	−79.8913	−2.64983
$910$	26.1265	0.866086
$911$	22.7151	0.752584	0.376292	−	0.926501i	$-0.377199\pi$
$911$	22.7151	0.752584	0.376292	+	0.926501i	$0.377199\pi$
$912$	17.5169	0.580043
$913$	−19.9224	−0.659335
$914$	23.3404	0.772032
$915$	−3.37228	−0.111484
$916$	−13.6931	−0.452434
$917$	2.68280	0.0885937
$918$	−28.3535	−0.935804
$919$	27.7894	0.916687	0.458344	−	0.888775i	$-0.348443\pi$
$919$	27.7894	0.916687	0.458344	+	0.888775i	$0.348443\pi$
$920$	2.60760	0.0859701
$921$	−70.3906	−2.31945
$922$	−14.7458	−0.485628
$923$	27.9684	0.920593
$924$	−34.4339	−1.13279
$925$	−1.06730	−0.0350927
$926$	−16.5235	−0.542997
$927$	86.5352	2.84219
$928$	−8.79796	−0.288807
$929$	−20.0565	−0.658034	−0.329017	−	0.944324i	$-0.606717\pi$
$929$	−20.0565	−0.658034	−0.329017	+	0.944324i	$0.606717\pi$
$930$	−23.6736	−0.776290
$931$	−1.24592	−0.0408334
$932$	−15.5958	−0.510858
$933$	−64.8760	−2.12395
$934$	2.67443	0.0875101
$935$	72.3928	2.36750
$936$	17.5603	0.573976
$937$	−1.65727	−0.0541405	−0.0270703	−	0.999634i	$-0.508618\pi$
$937$	−1.65727	−0.0541405	−0.0270703	+	0.999634i	$0.508618\pi$
$938$	9.05875	0.295779
$939$	96.9939	3.16528
$940$	33.1211	1.08029
$941$	−8.50221	−0.277164	−0.138582	−	0.990351i	$-0.544254\pi$
$941$	−8.50221	−0.277164	−0.138582	+	0.990351i	$0.544254\pi$
$942$	−9.59724	−0.312695
$943$	10.0465	0.327160
$944$	−4.31508	−0.140444
$945$	−33.0430	−1.07489
$946$	21.5887	0.701910
$947$	−0.774947	−0.0251824	−0.0125912	−	0.999921i	$-0.504008\pi$
$947$	−0.774947	−0.0251824	−0.0125912	+	0.999921i	$0.504008\pi$
$948$	30.1839	0.980327
$949$	−14.5121	−0.471082
$950$	−11.3588	−0.368527
$951$	−37.2708	−1.20859
$952$	−16.1044	−0.521946
$953$	5.63388	0.182499	0.0912497	−	0.995828i	$-0.470914\pi$
$953$	5.63388	0.182499	0.0912497	+	0.995828i	$0.470914\pi$
$954$	9.00707	0.291615
$955$	20.9497	0.677917
$956$	12.9018	0.417274
$957$	−112.922	−3.65026
$958$	4.49613	0.145263
$959$	−25.2162	−0.814275
$960$	7.23673	0.233564
$961$	−20.2985	−0.654789
$962$	−2.21495	−0.0714130
$963$	−44.0330	−1.41894
$964$	−11.8769	−0.382528
$965$	−22.2878	−0.717469
$966$	−7.44540	−0.239552
$967$	30.3861	0.977152	0.488576	−	0.872521i	$-0.337516\pi$
$967$	30.3861	0.977152	0.488576	+	0.872521i	$0.337516\pi$
$968$	10.3892	0.333922
$969$	105.151	3.37794
$970$	−20.3220	−0.652500
$971$	−46.1107	−1.47976	−0.739881	−	0.672737i	$-0.765118\pi$
$971$	−46.1107	−1.47976	−0.739881	+	0.672737i	$0.765118\pi$
$972$	16.9382	0.543293
$973$	−13.7323	−0.440236
$974$	28.3239	0.907556
$975$	−18.6521	−0.597346
$976$	−0.465995	−0.0149161
$977$	15.0874	0.482689	0.241345	−	0.970439i	$-0.422412\pi$
$977$	15.0874	0.482689	0.241345	+	0.970439i	$0.422412\pi$
$978$	−56.1707	−1.79614
$979$	−28.5357	−0.912003
$980$	−0.514726	−0.0164423
$981$	59.1055	1.88709
$982$	14.8750	0.474680
$983$	−18.6979	−0.596370	−0.298185	−	0.954508i	$-0.596381\pi$
$983$	−18.6979	−0.596370	−0.298185	+	0.954508i	$0.596381\pi$
$984$	27.8815	0.888830
$985$	−58.6366	−1.86832
$986$	−52.8127	−1.68190
$987$	−94.5697	−3.01019
$988$	−23.5727	−0.749947
$989$	4.66799	0.148433
$990$	56.7046	1.80219
$991$	23.8645	0.758082	0.379041	−	0.925380i	$-0.376254\pi$
$991$	23.8645	0.758082	0.379041	+	0.925380i	$0.376254\pi$
$992$	−3.27132	−0.103865
$993$	65.2739	2.07141
$994$	−20.0911	−0.637250
$995$	−28.2030	−0.894094
$996$	−11.9549	−0.378804
$997$	33.5508	1.06256	0.531282	−	0.847195i	$-0.321710\pi$
$997$	33.5508	1.06256	0.531282	+	0.847195i	$0.321710\pi$
$998$	29.6232	0.937707
$999$	2.80132	0.0886298

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6026.2.a.k.1.6	✓	35

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6026.2.a.k.1.6	✓	35	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:	\( N \)	\(=\)	\( 6026 = 2 \cdot 23 \cdot 131 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6026.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -2.77524 q^{3} +1.00000 q^{4} -2.60760 q^{5} -2.77524 q^{6} -2.68280 q^{7} +1.00000 q^{8} +4.70196 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -2.77524 q^{3} +1.00000 q^{4} -2.60760 q^{5} -2.77524 q^{6} -2.68280 q^{7} +1.00000 q^{8} +4.70196 q^{9} -2.60760 q^{10} -4.62485 q^{11} -2.77524 q^{12} +3.73467 q^{13} -2.68280 q^{14} +7.23673 q^{15} +1.00000 q^{16} +6.00283 q^{17} +4.70196 q^{18} -6.31185 q^{19} -2.60760 q^{20} +7.44540 q^{21} -4.62485 q^{22} -1.00000 q^{23} -2.77524 q^{24} +1.79960 q^{25} +3.73467 q^{26} -4.72335 q^{27} -2.68280 q^{28} -8.79796 q^{29} +7.23673 q^{30} -3.27132 q^{31} +1.00000 q^{32} +12.8351 q^{33} +6.00283 q^{34} +6.99567 q^{35} +4.70196 q^{36} -0.593078 q^{37} -6.31185 q^{38} -10.3646 q^{39} -2.60760 q^{40} -10.0465 q^{41} +7.44540 q^{42} -4.66799 q^{43} -4.62485 q^{44} -12.2608 q^{45} -1.00000 q^{46} -12.7017 q^{47} -2.77524 q^{48} +0.197394 q^{49} +1.79960 q^{50} -16.6593 q^{51} +3.73467 q^{52} +1.91560 q^{53} -4.72335 q^{54} +12.0598 q^{55} -2.68280 q^{56} +17.5169 q^{57} -8.79796 q^{58} -4.31508 q^{59} +7.23673 q^{60} -0.465995 q^{61} -3.27132 q^{62} -12.6144 q^{63} +1.00000 q^{64} -9.73855 q^{65} +12.8351 q^{66} -3.37661 q^{67} +6.00283 q^{68} +2.77524 q^{69} +6.99567 q^{70} +7.48886 q^{71} +4.70196 q^{72} -3.88577 q^{73} -0.593078 q^{74} -4.99431 q^{75} -6.31185 q^{76} +12.4075 q^{77} -10.3646 q^{78} -10.8761 q^{79} -2.60760 q^{80} -0.997447 q^{81} -10.0465 q^{82} +4.30768 q^{83} +7.44540 q^{84} -15.6530 q^{85} -4.66799 q^{86} +24.4164 q^{87} -4.62485 q^{88} +6.17007 q^{89} -12.2608 q^{90} -10.0194 q^{91} -1.00000 q^{92} +9.07870 q^{93} -12.7017 q^{94} +16.4588 q^{95} -2.77524 q^{96} +7.79337 q^{97} +0.197394 q^{98} -21.7459 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 35 q + 35 q^{2} - 3 q^{3} + 35 q^{4} + 10 q^{5} - 3 q^{6} + 14 q^{7} + 35 q^{8} + 54 q^{9}+O(q^{10}) \) 35 * q + 35 * q^2 - 3 * q^3 + 35 * q^4 + 10 * q^5 - 3 * q^6 + 14 * q^7 + 35 * q^8 + 54 * q^9	\( 35 q + 35 q^{2} - 3 q^{3} + 35 q^{4} + 10 q^{5} - 3 q^{6} + 14 q^{7} + 35 q^{8} + 54 q^{9} + 10 q^{10} + 9 q^{11} - 3 q^{12} + 19 q^{13} + 14 q^{14} + 14 q^{15} + 35 q^{16} + 28 q^{17} + 54 q^{18} + 21 q^{19} + 10 q^{20} + 28 q^{21} + 9 q^{22} - 35 q^{23} - 3 q^{24} + 81 q^{25} + 19 q^{26} - 21 q^{27} + 14 q^{28} + 35 q^{29} + 14 q^{30} + 5 q^{31} + 35 q^{32} + 26 q^{33} + 28 q^{34} - 7 q^{35} + 54 q^{36} + 51 q^{37} + 21 q^{38} + 21 q^{39} + 10 q^{40} + 3 q^{41} + 28 q^{42} + 43 q^{43} + 9 q^{44} + 2 q^{45} - 35 q^{46} + 10 q^{47} - 3 q^{48} + 85 q^{49} + 81 q^{50} + 26 q^{51} + 19 q^{52} + 39 q^{53} - 21 q^{54} + 2 q^{55} + 14 q^{56} + 50 q^{57} + 35 q^{58} - 42 q^{59} + 14 q^{60} + 47 q^{61} + 5 q^{62} + 23 q^{63} + 35 q^{64} + 61 q^{65} + 26 q^{66} + 22 q^{67} + 28 q^{68} + 3 q^{69} - 7 q^{70} + 54 q^{72} + 30 q^{73} + 51 q^{74} - 26 q^{75} + 21 q^{76} + 2 q^{77} + 21 q^{78} + 55 q^{79} + 10 q^{80} + 67 q^{81} + 3 q^{82} + 20 q^{83} + 28 q^{84} + 28 q^{85} + 43 q^{86} + 29 q^{87} + 9 q^{88} - 31 q^{89} + 2 q^{90} + 32 q^{91} - 35 q^{92} + 11 q^{93} + 10 q^{94} + 16 q^{95} - 3 q^{96} + 36 q^{97} + 85 q^{98} - 9 q^{99}+O(q^{100}) \) 35 * q + 35 * q^2 - 3 * q^3 + 35 * q^4 + 10 * q^5 - 3 * q^6 + 14 * q^7 + 35 * q^8 + 54 * q^9 + 10 * q^10 + 9 * q^11 - 3 * q^12 + 19 * q^13 + 14 * q^14 + 14 * q^15 + 35 * q^16 + 28 * q^17 + 54 * q^18 + 21 * q^19 + 10 * q^20 + 28 * q^21 + 9 * q^22 - 35 * q^23 - 3 * q^24 + 81 * q^25 + 19 * q^26 - 21 * q^27 + 14 * q^28 + 35 * q^29 + 14 * q^30 + 5 * q^31 + 35 * q^32 + 26 * q^33 + 28 * q^34 - 7 * q^35 + 54 * q^36 + 51 * q^37 + 21 * q^38 + 21 * q^39 + 10 * q^40 + 3 * q^41 + 28 * q^42 + 43 * q^43 + 9 * q^44 + 2 * q^45 - 35 * q^46 + 10 * q^47 - 3 * q^48 + 85 * q^49 + 81 * q^50 + 26 * q^51 + 19 * q^52 + 39 * q^53 - 21 * q^54 + 2 * q^55 + 14 * q^56 + 50 * q^57 + 35 * q^58 - 42 * q^59 + 14 * q^60 + 47 * q^61 + 5 * q^62 + 23 * q^63 + 35 * q^64 + 61 * q^65 + 26 * q^66 + 22 * q^67 + 28 * q^68 + 3 * q^69 - 7 * q^70 + 54 * q^72 + 30 * q^73 + 51 * q^74 - 26 * q^75 + 21 * q^76 + 2 * q^77 + 21 * q^78 + 55 * q^79 + 10 * q^80 + 67 * q^81 + 3 * q^82 + 20 * q^83 + 28 * q^84 + 28 * q^85 + 43 * q^86 + 29 * q^87 + 9 * q^88 - 31 * q^89 + 2 * q^90 + 32 * q^91 - 35 * q^92 + 11 * q^93 + 10 * q^94 + 16 * q^95 - 3 * q^96 + 36 * q^97 + 85 * q^98 - 9 * q^99

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