LMFDB - Embedded newform 5077.2.a.c.1.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [5077,2,Mod(1,5077)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(5077, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("5077.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 5077 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	5077.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:	$40.5400491062$
Analytic rank:	$0$
Dimension:	$216$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.13
Character	$\chi$	$=$	5077.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.48492 q^{2} -1.01672 q^{3} +4.17484 q^{4} +0.988176 q^{5} +2.52648 q^{6} +3.63719 q^{7} -5.40431 q^{8} -1.96628 q^{9} +O(q^{10})$	\(q-2.48492 q^{2} -1.01672 q^{3} +4.17484 q^{4} +0.988176 q^{5} +2.52648 q^{6} +3.63719 q^{7} -5.40431 q^{8} -1.96628 q^{9} -2.45554 q^{10} +0.624460 q^{11} -4.24465 q^{12} -2.18793 q^{13} -9.03814 q^{14} -1.00470 q^{15} +5.07961 q^{16} +4.02301 q^{17} +4.88604 q^{18} +2.34236 q^{19} +4.12548 q^{20} -3.69801 q^{21} -1.55173 q^{22} -1.45796 q^{23} +5.49468 q^{24} -4.02351 q^{25} +5.43684 q^{26} +5.04932 q^{27} +15.1847 q^{28} +5.68065 q^{29} +2.49660 q^{30} -1.16585 q^{31} -1.81381 q^{32} -0.634902 q^{33} -9.99687 q^{34} +3.59418 q^{35} -8.20889 q^{36} -5.24356 q^{37} -5.82058 q^{38} +2.22452 q^{39} -5.34041 q^{40} -7.68601 q^{41} +9.18927 q^{42} -8.47532 q^{43} +2.60702 q^{44} -1.94303 q^{45} +3.62291 q^{46} -4.56245 q^{47} -5.16455 q^{48} +6.22916 q^{49} +9.99811 q^{50} -4.09028 q^{51} -9.13426 q^{52} +8.31041 q^{53} -12.5472 q^{54} +0.617076 q^{55} -19.6565 q^{56} -2.38153 q^{57} -14.1160 q^{58} -3.61586 q^{59} -4.19446 q^{60} +6.45215 q^{61} +2.89704 q^{62} -7.15172 q^{63} -5.65203 q^{64} -2.16206 q^{65} +1.57768 q^{66} +0.418439 q^{67} +16.7954 q^{68} +1.48234 q^{69} -8.93127 q^{70} +14.6848 q^{71} +10.6264 q^{72} +9.87776 q^{73} +13.0298 q^{74} +4.09079 q^{75} +9.77897 q^{76} +2.27128 q^{77} -5.52775 q^{78} +8.32119 q^{79} +5.01954 q^{80} +0.765073 q^{81} +19.0991 q^{82} +15.4844 q^{83} -15.4386 q^{84} +3.97544 q^{85} +21.0605 q^{86} -5.77564 q^{87} -3.37477 q^{88} -6.49830 q^{89} +4.82827 q^{90} -7.95792 q^{91} -6.08673 q^{92} +1.18534 q^{93} +11.3373 q^{94} +2.31466 q^{95} +1.84414 q^{96} +11.5609 q^{97} -15.4790 q^{98} -1.22786 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 216 q + 25 q^{2} + 62 q^{3} + 223 q^{4} + 46 q^{5} + 26 q^{6} + 30 q^{7} + 75 q^{8} + 234 q^{9}+O(q^{10}) $ 216 * q + 25 * q^2 + 62 * q^3 + 223 * q^4 + 46 * q^5 + 26 * q^6 + 30 * q^7 + 75 * q^8 + 234 * q^9	\( 216 q + 25 q^{2} + 62 q^{3} + 223 q^{4} + 46 q^{5} + 26 q^{6} + 30 q^{7} + 75 q^{8} + 234 q^{9} + 24 q^{10} + 89 q^{11} + 114 q^{12} + 34 q^{13} + 53 q^{14} + 61 q^{15} + 229 q^{16} + 76 q^{17} + 57 q^{18} + 54 q^{19} + 118 q^{20} + 25 q^{21} + 26 q^{22} + 109 q^{23} + 65 q^{24} + 232 q^{25} + 58 q^{26} + 236 q^{27} + 57 q^{28} + 54 q^{29} + 6 q^{30} + 77 q^{31} + 155 q^{32} + 80 q^{33} + 28 q^{34} + 137 q^{35} + 257 q^{36} + 42 q^{37} + 104 q^{38} + 46 q^{39} + 47 q^{40} + 109 q^{41} + 27 q^{42} + 68 q^{43} + 145 q^{44} + 109 q^{45} - 7 q^{46} + 264 q^{47} + 198 q^{48} + 222 q^{49} + 86 q^{50} + 57 q^{51} + 68 q^{52} + 95 q^{53} + 79 q^{54} + 50 q^{55} + 108 q^{56} + 55 q^{57} + 38 q^{58} + 292 q^{59} + 91 q^{60} + 16 q^{61} + 91 q^{62} + 113 q^{63} + 231 q^{64} + 68 q^{65} - 15 q^{66} + 152 q^{67} + 199 q^{68} + 83 q^{69} + 24 q^{70} + 131 q^{71} + 162 q^{72} + 71 q^{73} + 10 q^{74} + 232 q^{75} + 60 q^{76} + 131 q^{77} + 102 q^{78} + 10 q^{79} + 236 q^{80} + 268 q^{81} + 54 q^{82} + 299 q^{83} - 9 q^{85} + 35 q^{86} + 103 q^{87} + 45 q^{88} + 134 q^{89} + 8 q^{90} + 79 q^{91} + 206 q^{92} + 95 q^{93} + 18 q^{94} + 119 q^{95} + 77 q^{96} + 129 q^{97} + 150 q^{98} + 221 q^{99}+O(q^{100}) \) 216 * q + 25 * q^2 + 62 * q^3 + 223 * q^4 + 46 * q^5 + 26 * q^6 + 30 * q^7 + 75 * q^8 + 234 * q^9 + 24 * q^10 + 89 * q^11 + 114 * q^12 + 34 * q^13 + 53 * q^14 + 61 * q^15 + 229 * q^16 + 76 * q^17 + 57 * q^18 + 54 * q^19 + 118 * q^20 + 25 * q^21 + 26 * q^22 + 109 * q^23 + 65 * q^24 + 232 * q^25 + 58 * q^26 + 236 * q^27 + 57 * q^28 + 54 * q^29 + 6 * q^30 + 77 * q^31 + 155 * q^32 + 80 * q^33 + 28 * q^34 + 137 * q^35 + 257 * q^36 + 42 * q^37 + 104 * q^38 + 46 * q^39 + 47 * q^40 + 109 * q^41 + 27 * q^42 + 68 * q^43 + 145 * q^44 + 109 * q^45 - 7 * q^46 + 264 * q^47 + 198 * q^48 + 222 * q^49 + 86 * q^50 + 57 * q^51 + 68 * q^52 + 95 * q^53 + 79 * q^54 + 50 * q^55 + 108 * q^56 + 55 * q^57 + 38 * q^58 + 292 * q^59 + 91 * q^60 + 16 * q^61 + 91 * q^62 + 113 * q^63 + 231 * q^64 + 68 * q^65 - 15 * q^66 + 152 * q^67 + 199 * q^68 + 83 * q^69 + 24 * q^70 + 131 * q^71 + 162 * q^72 + 71 * q^73 + 10 * q^74 + 232 * q^75 + 60 * q^76 + 131 * q^77 + 102 * q^78 + 10 * q^79 + 236 * q^80 + 268 * q^81 + 54 * q^82 + 299 * q^83 - 9 * q^85 + 35 * q^86 + 103 * q^87 + 45 * q^88 + 134 * q^89 + 8 * q^90 + 79 * q^91 + 206 * q^92 + 95 * q^93 + 18 * q^94 + 119 * q^95 + 77 * q^96 + 129 * q^97 + 150 * q^98 + 221 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−2.48492	−1.75711	−0.878553	−	0.477645i	$-0.841490\pi$
$2$	−2.48492	−1.75711	−0.878553	+	0.477645i	$0.841490\pi$
$3$	−1.01672	−0.587005	−0.293502	−	0.955958i	$-0.594821\pi$
$3$	−1.01672	−0.587005	−0.293502	+	0.955958i	$0.594821\pi$
$4$	4.17484	2.08742
$5$	0.988176	0.441926	0.220963	−	0.975282i	$-0.429080\pi$
$5$	0.988176	0.441926	0.220963	+	0.975282i	$0.429080\pi$
$6$	2.52648	1.03143
$7$	3.63719	1.37473	0.687364	−	0.726313i	$-0.258768\pi$
$7$	3.63719	1.37473	0.687364	+	0.726313i	$0.258768\pi$
$8$	−5.40431	−1.91071
$9$	−1.96628	−0.655426
$10$	−2.45554	−0.776510
$11$	0.624460	0.188282	0.0941408	−	0.995559i	$-0.469990\pi$
$11$	0.624460	0.188282	0.0941408	+	0.995559i	$0.469990\pi$
$12$	−4.24465	−1.22533
$13$	−2.18793	−0.606823	−0.303411	−	0.952860i	$-0.598126\pi$
$13$	−2.18793	−0.606823	−0.303411	+	0.952860i	$0.598126\pi$
$14$	−9.03814	−2.41554
$15$	−1.00470	−0.259412
$16$	5.07961	1.26990
$17$	4.02301	0.975724	0.487862	−	0.872921i	$-0.337777\pi$
$17$	4.02301	0.975724	0.487862	+	0.872921i	$0.337777\pi$
$18$	4.88604	1.15165
$19$	2.34236	0.537374	0.268687	−	0.963228i	$-0.413410\pi$
$19$	2.34236	0.537374	0.268687	+	0.963228i	$0.413410\pi$
$20$	4.12548	0.922485
$21$	−3.69801	−0.806972
$22$	−1.55173	−0.330831
$23$	−1.45796	−0.304005	−0.152002	−	0.988380i	$-0.548572\pi$
$23$	−1.45796	−0.304005	−0.152002	+	0.988380i	$0.548572\pi$
$24$	5.49468	1.12160
$25$	−4.02351	−0.804702
$26$	5.43684	1.06625
$27$	5.04932	0.971743
$28$	15.1847	2.86964
$29$	5.68065	1.05487	0.527435	−	0.849595i	$-0.323154\pi$
$29$	5.68065	1.05487	0.527435	+	0.849595i	$0.323154\pi$
$30$	2.49660	0.455815
$31$	−1.16585	−0.209392	−0.104696	−	0.994504i	$-0.533387\pi$
$31$	−1.16585	−0.209392	−0.104696	+	0.994504i	$0.533387\pi$
$32$	−1.81381	−0.320640
$33$	−0.634902	−0.110522
$34$	−9.99687	−1.71445
$35$	3.59418	0.607528
$36$	−8.20889	−1.36815
$37$	−5.24356	−0.862035	−0.431018	−	0.902344i	$-0.641845\pi$
$37$	−5.24356	−0.862035	−0.431018	+	0.902344i	$0.641845\pi$
$38$	−5.82058	−0.944223
$39$	2.22452	0.356208
$40$	−5.34041	−0.844392
$41$	−7.68601	−1.20035	−0.600176	−	0.799868i	$-0.704903\pi$
$41$	−7.68601	−1.20035	−0.600176	+	0.799868i	$0.704903\pi$
$42$	9.18927	1.41794
$43$	−8.47532	−1.29247	−0.646237	−	0.763137i	$-0.723658\pi$
$43$	−8.47532	−1.29247	−0.646237	+	0.763137i	$0.723658\pi$
$44$	2.60702	0.393023
$45$	−1.94303	−0.289649
$46$	3.62291	0.534169
$47$	−4.56245	−0.665502	−0.332751	−	0.943015i	$-0.607977\pi$
$47$	−4.56245	−0.665502	−0.332751	+	0.943015i	$0.607977\pi$
$48$	−5.16455	−0.745438
$49$	6.22916	0.889880
$50$	9.99811	1.41395
$51$	−4.09028	−0.572754
$52$	−9.13426	−1.26669
$53$	8.31041	1.14152	0.570761	−	0.821116i	$-0.306648\pi$
$53$	8.31041	1.14152	0.570761	+	0.821116i	$0.306648\pi$
$54$	−12.5472	−1.70745
$55$	0.617076	0.0832065
$56$	−19.6565	−2.62671
$57$	−2.38153	−0.315441
$58$	−14.1160	−1.85352
$59$	−3.61586	−0.470745	−0.235373	−	0.971905i	$-0.575631\pi$
$59$	−3.61586	−0.470745	−0.235373	+	0.971905i	$0.575631\pi$
$60$	−4.19446	−0.541503
$61$	6.45215	0.826114	0.413057	−	0.910705i	$-0.364461\pi$
$61$	6.45215	0.826114	0.413057	+	0.910705i	$0.364461\pi$
$62$	2.89704	0.367924
$63$	−7.15172	−0.901032
$64$	−5.65203	−0.706504
$65$	−2.16206	−0.268171
$66$	1.57768	0.194199
$67$	0.418439	0.0511205	0.0255602	−	0.999673i	$-0.491863\pi$
$67$	0.418439	0.0511205	0.0255602	+	0.999673i	$0.491863\pi$
$68$	16.7954	2.03674
$69$	1.48234	0.178452
$70$	−8.93127	−1.06749
$71$	14.6848	1.74277	0.871383	−	0.490604i	$-0.163224\pi$
$71$	14.6848	1.74277	0.871383	+	0.490604i	$0.163224\pi$
$72$	10.6264	1.25233
$73$	9.87776	1.15610	0.578052	−	0.816000i	$-0.303813\pi$
$73$	9.87776	1.15610	0.578052	+	0.816000i	$0.303813\pi$
$74$	13.0298	1.51469
$75$	4.09079	0.472364
$76$	9.77897	1.12173
$77$	2.27128	0.258836
$78$	−5.52775	−0.625895
$79$	8.32119	0.936207	0.468103	−	0.883674i	$-0.344938\pi$
$79$	8.32119	0.936207	0.468103	+	0.883674i	$0.344938\pi$
$80$	5.01954	0.561202
$81$	0.765073	0.0850081
$82$	19.0991	2.10915
$83$	15.4844	1.69964	0.849819	−	0.527074i	$-0.176711\pi$
$83$	15.4844	1.69964	0.849819	+	0.527074i	$0.176711\pi$
$84$	−15.4386	−1.68449
$85$	3.97544	0.431197
$86$	21.0605	2.27101
$87$	−5.77564	−0.619213
$88$	−3.37477	−0.359752
$89$	−6.49830	−0.688819	−0.344409	−	0.938820i	$-0.611921\pi$
$89$	−6.49830	−0.688819	−0.344409	+	0.938820i	$0.611921\pi$
$90$	4.82827	0.508945
$91$	−7.95792	−0.834217
$92$	−6.08673	−0.634586
$93$	1.18534	0.122914
$94$	11.3373	1.16936
$95$	2.31466	0.237479
$96$	1.84414	0.188217
$97$	11.5609	1.17384	0.586918	−	0.809646i	$-0.300341\pi$
$97$	11.5609	1.17384	0.586918	+	0.809646i	$0.300341\pi$
$98$	−15.4790	−1.56361
$99$	−1.22786	−0.123405
$100$	−16.7975	−1.67975
$101$	7.23075	0.719487	0.359743	−	0.933051i	$-0.382864\pi$
$101$	7.23075	0.719487	0.359743	+	0.933051i	$0.382864\pi$
$102$	10.1640	1.00639
$103$	−6.57102	−0.647462	−0.323731	−	0.946149i	$-0.604937\pi$
$103$	−6.57102	−0.647462	−0.323731	+	0.946149i	$0.604937\pi$
$104$	11.8243	1.15946
$105$	−3.65429	−0.356622
$106$	−20.6507	−2.00578
$107$	−14.5074	−1.40249	−0.701244	−	0.712921i	$-0.747372\pi$
$107$	−14.5074	−1.40249	−0.701244	+	0.712921i	$0.747372\pi$
$108$	21.0801	2.02843
$109$	6.57188	0.629472	0.314736	−	0.949179i	$-0.398084\pi$
$109$	6.57188	0.629472	0.314736	+	0.949179i	$0.398084\pi$
$110$	−1.53339	−0.146203
$111$	5.33124	0.506019
$112$	18.4755	1.74577
$113$	15.2742	1.43687	0.718437	−	0.695592i	$-0.244858\pi$
$113$	15.2742	1.43687	0.718437	+	0.695592i	$0.244858\pi$
$114$	5.91791	0.554263
$115$	−1.44072	−0.134348
$116$	23.7158	2.20196
$117$	4.30208	0.397727
$118$	8.98514	0.827149
$119$	14.6325	1.34136
$120$	5.42971	0.495662
$121$	−10.6101	−0.964550
$122$	−16.0331	−1.45157
$123$	7.81453	0.704613
$124$	−4.86722	−0.437089
$125$	−8.91681	−0.797544
$126$	17.7715	1.58321
$127$	−1.33877	−0.118797	−0.0593983	−	0.998234i	$-0.518918\pi$
$127$	−1.33877	−0.118797	−0.0593983	+	0.998234i	$0.518918\pi$
$128$	17.6725	1.56204
$129$	8.61705	0.758689
$130$	5.37255	0.471204
$131$	8.02998	0.701583	0.350791	−	0.936454i	$-0.385913\pi$
$131$	8.02998	0.701583	0.350791	+	0.936454i	$0.385913\pi$
$132$	−2.65061	−0.230706
$133$	8.51961	0.738744
$134$	−1.03979	−0.0898241
$135$	4.98962	0.429438
$136$	−21.7416	−1.86433
$137$	−0.943447	−0.0806041	−0.0403021	−	0.999188i	$-0.512832\pi$
$137$	−0.943447	−0.0806041	−0.0403021	+	0.999188i	$0.512832\pi$
$138$	−3.68349	−0.313560
$139$	2.23326	0.189423	0.0947114	−	0.995505i	$-0.469807\pi$
$139$	2.23326	0.189423	0.0947114	+	0.995505i	$0.469807\pi$
$140$	15.0051	1.26817
$141$	4.63874	0.390653
$142$	−36.4906	−3.06222
$143$	−1.36627	−0.114254
$144$	−9.98791	−0.832326
$145$	5.61348	0.466174
$146$	−24.5455	−2.03140
$147$	−6.33332	−0.522364
$148$	−21.8910	−1.79943
$149$	−10.7238	−0.878525	−0.439263	−	0.898359i	$-0.644760\pi$
$149$	−10.7238	−0.878525	−0.439263	+	0.898359i	$0.644760\pi$
$150$	−10.1653	−0.829993
$151$	5.74870	0.467823	0.233911	−	0.972258i	$-0.424847\pi$
$151$	5.74870	0.467823	0.233911	+	0.972258i	$0.424847\pi$
$152$	−12.6588	−1.02677
$153$	−7.91035	−0.639514
$154$	−5.64395	−0.454803
$155$	−1.15206	−0.0925357
$156$	9.28700	0.743555
$157$	−13.1629	−1.05051	−0.525257	−	0.850944i	$-0.676031\pi$
$157$	−13.1629	−1.05051	−0.525257	+	0.850944i	$0.676031\pi$
$158$	−20.6775	−1.64501
$159$	−8.44938	−0.670079
$160$	−1.79237	−0.141699
$161$	−5.30287	−0.417924
$162$	−1.90115	−0.149368
$163$	−8.11829	−0.635873	−0.317937	−	0.948112i	$-0.602990\pi$
$163$	−8.11829	−0.635873	−0.317937	+	0.948112i	$0.602990\pi$
$164$	−32.0879	−2.50564
$165$	−0.627395	−0.0488426
$166$	−38.4776	−2.98644
$167$	24.8440	1.92249	0.961245	−	0.275697i	$-0.0889086\pi$
$167$	24.8440	1.92249	0.961245	+	0.275697i	$0.0889086\pi$
$168$	19.9852	1.54189
$169$	−8.21296	−0.631766
$170$	−9.87867	−0.757659
$171$	−4.60573	−0.352209
$172$	−35.3831	−2.69794
$173$	17.7256	1.34765	0.673824	−	0.738892i	$-0.264650\pi$
$173$	17.7256	1.34765	0.673824	+	0.738892i	$0.264650\pi$
$174$	14.3520	1.08802
$175$	−14.6343	−1.10625
$176$	3.17201	0.239099
$177$	3.67633	0.276330
$178$	16.1478	1.21033
$179$	−17.0896	−1.27733	−0.638667	−	0.769483i	$-0.720514\pi$
$179$	−17.0896	−1.27733	−0.638667	+	0.769483i	$0.720514\pi$
$180$	−8.11183	−0.604620
$181$	15.6493	1.16321	0.581603	−	0.813473i	$-0.302426\pi$
$181$	15.6493	1.16321	0.581603	+	0.813473i	$0.302426\pi$
$182$	19.7748	1.46581
$183$	−6.56005	−0.484933
$184$	7.87925	0.580866
$185$	−5.18156	−0.380956
$186$	−2.94548	−0.215973
$187$	2.51221	0.183711
$188$	−19.0475	−1.38918
$189$	18.3653	1.33588
$190$	−5.75176	−0.417276
$191$	22.7148	1.64358	0.821791	−	0.569789i	$-0.192975\pi$
$191$	22.7148	1.64358	0.821791	+	0.569789i	$0.192975\pi$
$192$	5.74654	0.414721
$193$	−19.3702	−1.39430	−0.697149	−	0.716926i	$-0.745549\pi$
$193$	−19.3702	−1.39430	−0.697149	+	0.716926i	$0.745549\pi$
$194$	−28.7281	−2.06255
$195$	2.19822	0.157417
$196$	26.0057	1.85755
$197$	22.6028	1.61039	0.805193	−	0.593013i	$-0.202062\pi$
$197$	22.6028	1.61039	0.805193	+	0.593013i	$0.202062\pi$
$198$	3.05114	0.216835
$199$	−21.2481	−1.50624	−0.753119	−	0.657885i	$-0.771451\pi$
$199$	−21.2481	−1.50624	−0.753119	+	0.657885i	$0.771451\pi$
$200$	21.7443	1.53755
$201$	−0.425436	−0.0300080
$202$	−17.9679	−1.26421
$203$	20.6616	1.45016
$204$	−17.0763	−1.19558
$205$	−7.59513	−0.530467
$206$	16.3285	1.13766
$207$	2.86675	0.199253
$208$	−11.1138	−0.770605
$209$	1.46271	0.101178
$210$	9.08062	0.626622
$211$	10.5163	0.723970	0.361985	−	0.932184i	$-0.382099\pi$
$211$	10.5163	0.723970	0.361985	+	0.932184i	$0.382099\pi$
$212$	34.6946	2.38284
$213$	−14.9304	−1.02301
$214$	36.0499	2.46432
$215$	−8.37511	−0.571178
$216$	−27.2881	−1.85672
$217$	−4.24040	−0.287857
$218$	−16.3306	−1.10605
$219$	−10.0429	−0.678639
$220$	2.57619	0.173687
$221$	−8.80207	−0.592092
$222$	−13.2477	−0.889128
$223$	−11.1717	−0.748112	−0.374056	−	0.927406i	$-0.622033\pi$
$223$	−11.1717	−0.748112	−0.374056	+	0.927406i	$0.622033\pi$
$224$	−6.59718	−0.440793
$225$	7.91133	0.527422
$226$	−37.9552	−2.52474
$227$	−5.17318	−0.343356	−0.171678	−	0.985153i	$-0.554919\pi$
$227$	−5.17318	−0.343356	−0.171678	+	0.985153i	$0.554919\pi$
$228$	−9.94250	−0.658458
$229$	−1.19125	−0.0787200	−0.0393600	−	0.999225i	$-0.512532\pi$
$229$	−1.19125	−0.0787200	−0.0393600	+	0.999225i	$0.512532\pi$
$230$	3.58007	0.236063
$231$	−2.30926	−0.151938
$232$	−30.7000	−2.01555
$233$	−2.04746	−0.134134	−0.0670668	−	0.997748i	$-0.521364\pi$
$233$	−2.04746	−0.134134	−0.0670668	+	0.997748i	$0.521364\pi$
$234$	−10.6903	−0.698849
$235$	−4.50850	−0.294102
$236$	−15.0957	−0.982643
$237$	−8.46033	−0.549558
$238$	−36.3605	−2.35690
$239$	18.1662	1.17507	0.587536	−	0.809198i	$-0.300098\pi$
$239$	18.1662	1.17507	0.587536	+	0.809198i	$0.300098\pi$
$240$	−5.10348	−0.329428
$241$	4.54739	0.292923	0.146461	−	0.989216i	$-0.453212\pi$
$241$	4.54739	0.292923	0.146461	+	0.989216i	$0.453212\pi$
$242$	26.3652	1.69482
$243$	−15.9258	−1.02164
$244$	26.9367	1.72445
$245$	6.15551	0.393261
$246$	−19.4185	−1.23808
$247$	−5.12492	−0.326091
$248$	6.30059	0.400088
$249$	−15.7434	−0.997696
$250$	22.1576	1.40137
$251$	−19.6105	−1.23781	−0.618903	−	0.785468i	$-0.712422\pi$
$251$	−19.6105	−1.23781	−0.618903	+	0.785468i	$0.712422\pi$
$252$	−29.8573	−1.88083
$253$	−0.910435	−0.0572386
$254$	3.32674	0.208738
$255$	−4.04192	−0.253115
$256$	−32.6107	−2.03817
$257$	−0.823088	−0.0513428	−0.0256714	−	0.999670i	$-0.508172\pi$
$257$	−0.823088	−0.0513428	−0.0256714	+	0.999670i	$0.508172\pi$
$258$	−21.4127	−1.33310
$259$	−19.0718	−1.18506
$260$	−9.02626	−0.559785
$261$	−11.1697	−0.691388
$262$	−19.9539	−1.23276
$263$	25.3624	1.56391	0.781957	−	0.623332i	$-0.214221\pi$
$263$	25.3624	1.56391	0.781957	+	0.623332i	$0.214221\pi$
$264$	3.43120	0.211176
$265$	8.21215	0.504468
$266$	−21.1706	−1.29805
$267$	6.60697	0.404340
$268$	1.74692	0.106710
$269$	−3.12700	−0.190657	−0.0953283	−	0.995446i	$-0.530390\pi$
$269$	−3.12700	−0.190657	−0.0953283	+	0.995446i	$0.530390\pi$
$270$	−12.3988	−0.754568
$271$	−5.44132	−0.330537	−0.165268	−	0.986249i	$-0.552849\pi$
$271$	−5.44132	−0.330537	−0.165268	+	0.986249i	$0.552849\pi$
$272$	20.4353	1.23907
$273$	8.09100	0.489689
$274$	2.34439	0.141630
$275$	−2.51252	−0.151511
$276$	6.18852	0.372505
$277$	20.8112	1.25042	0.625212	−	0.780455i	$-0.285013\pi$
$277$	20.8112	1.25042	0.625212	+	0.780455i	$0.285013\pi$
$278$	−5.54948	−0.332836
$279$	2.29237	0.137241
$280$	−19.4241	−1.16081
$281$	23.4113	1.39660	0.698302	−	0.715803i	$-0.253939\pi$
$281$	23.4113	1.39660	0.698302	+	0.715803i	$0.253939\pi$
$282$	−11.5269	−0.686418
$283$	−16.1980	−0.962873	−0.481436	−	0.876481i	$-0.659885\pi$
$283$	−16.1980	−0.962873	−0.481436	+	0.876481i	$0.659885\pi$
$284$	61.3067	3.63788
$285$	−2.35337	−0.139402
$286$	3.39509	0.200756
$287$	−27.9555	−1.65016
$288$	3.56646	0.210155
$289$	−0.815375	−0.0479633
$290$	−13.9491	−0.819117
$291$	−11.7543	−0.689048
$292$	41.2381	2.41328
$293$	14.3088	0.835929	0.417965	−	0.908463i	$-0.362744\pi$
$293$	14.3088	0.835929	0.417965	+	0.908463i	$0.362744\pi$
$294$	15.7378	0.917848
$295$	−3.57311	−0.208035
$296$	28.3378	1.64710
$297$	3.15310	0.182961
$298$	26.6477	1.54366
$299$	3.18991	0.184477
$300$	17.0784	0.986021
$301$	−30.8264	−1.77680
$302$	−14.2851	−0.822014
$303$	−7.35166	−0.422342
$304$	11.8983	0.682412
$305$	6.37586	0.365081
$306$	19.6566	1.12369
$307$	−17.7442	−1.01272	−0.506359	−	0.862323i	$-0.669009\pi$
$307$	−17.7442	−1.01272	−0.506359	+	0.862323i	$0.669009\pi$
$308$	9.48222	0.540300
$309$	6.68090	0.380063
$310$	2.86278	0.162595
$311$	−32.1906	−1.82536	−0.912680	−	0.408675i	$-0.865991\pi$
$311$	−32.1906	−1.82536	−0.912680	+	0.408675i	$0.865991\pi$
$312$	−12.0220	−0.680610
$313$	24.5305	1.38655	0.693273	−	0.720675i	$-0.256168\pi$
$313$	24.5305	1.38655	0.693273	+	0.720675i	$0.256168\pi$
$314$	32.7088	1.84586
$315$	−7.06716	−0.398189
$316$	34.7396	1.95426
$317$	−18.4095	−1.03398	−0.516992	−	0.855991i	$-0.672948\pi$
$317$	−18.4095	−1.03398	−0.516992	+	0.855991i	$0.672948\pi$
$318$	20.9960	1.17740
$319$	3.54733	0.198613
$320$	−5.58520	−0.312222
$321$	14.7500	0.823267
$322$	13.1772	0.734337
$323$	9.42334	0.524329
$324$	3.19406	0.177448
$325$	8.80316	0.488311
$326$	20.1733	1.11730
$327$	−6.68177	−0.369503
$328$	41.5376	2.29353
$329$	−16.5945	−0.914885
$330$	1.55903	0.0858216
$331$	21.5825	1.18628	0.593140	−	0.805099i	$-0.297888\pi$
$331$	21.5825	1.18628	0.593140	+	0.805099i	$0.297888\pi$
$332$	64.6451	3.54786
$333$	10.3103	0.565000
$334$	−61.7355	−3.37802
$335$	0.413492	0.0225915
$336$	−18.7844	−1.02478
$337$	20.9053	1.13879	0.569393	−	0.822065i	$-0.307178\pi$
$337$	20.9053	1.13879	0.569393	+	0.822065i	$0.307178\pi$
$338$	20.4086	1.11008
$339$	−15.5296	−0.843452
$340$	16.5968	0.900090
$341$	−0.728023	−0.0394247
$342$	11.4449	0.618868
$343$	−2.80370	−0.151385
$344$	45.8032	2.46955
$345$	1.46481	0.0788627
$346$	−44.0466	−2.36796
$347$	5.25339	0.282017	0.141008	−	0.990008i	$-0.454966\pi$
$347$	5.25339	0.282017	0.141008	+	0.990008i	$0.454966\pi$
$348$	−24.1124	−1.29256
$349$	−25.6279	−1.37183	−0.685915	−	0.727682i	$-0.740598\pi$
$349$	−25.6279	−1.37183	−0.685915	+	0.727682i	$0.740598\pi$
$350$	36.3650	1.94379
$351$	−11.0476	−0.589676
$352$	−1.13265	−0.0603706
$353$	24.5561	1.30699	0.653495	−	0.756930i	$-0.273302\pi$
$353$	24.5561	1.30699	0.653495	+	0.756930i	$0.273302\pi$
$354$	−9.13539	−0.485541
$355$	14.5112	0.770173
$356$	−27.1294	−1.43785
$357$	−14.8771	−0.787382
$358$	42.4662	2.24441
$359$	−8.71875	−0.460158	−0.230079	−	0.973172i	$-0.573898\pi$
$359$	−8.71875	−0.460158	−0.230079	+	0.973172i	$0.573898\pi$
$360$	10.5007	0.553436
$361$	−13.5134	−0.711229
$362$	−38.8874	−2.04388
$363$	10.7875	0.566195
$364$	−33.2231	−1.74136
$365$	9.76097	0.510912
$366$	16.3012	0.852078
$367$	33.9166	1.77043	0.885217	−	0.465179i	$-0.154010\pi$
$367$	33.9166	1.77043	0.885217	+	0.465179i	$0.154010\pi$
$368$	−7.40584	−0.386056
$369$	15.1128	0.786742
$370$	12.8758	0.669379
$371$	30.2265	1.56928
$372$	4.94861	0.256573
$373$	9.18720	0.475695	0.237848	−	0.971302i	$-0.423558\pi$
$373$	9.18720	0.475695	0.237848	+	0.971302i	$0.423558\pi$
$374$	−6.24264	−0.322799
$375$	9.06592	0.468162
$376$	24.6569	1.27158
$377$	−12.4289	−0.640119
$378$	−45.6365	−2.34729
$379$	−17.3311	−0.890237	−0.445119	−	0.895472i	$-0.646839\pi$
$379$	−17.3311	−0.890237	−0.445119	+	0.895472i	$0.646839\pi$
$380$	9.66335	0.495719
$381$	1.36116	0.0697342
$382$	−56.4444	−2.88795
$383$	24.1713	1.23510	0.617548	−	0.786533i	$-0.288126\pi$
$383$	24.1713	1.23510	0.617548	+	0.786533i	$0.288126\pi$
$384$	−17.9680	−0.916926
$385$	2.24442	0.114386
$386$	48.1335	2.44993
$387$	16.6648	0.847121
$388$	48.2651	2.45029
$389$	−17.5722	−0.890946	−0.445473	−	0.895295i	$-0.646965\pi$
$389$	−17.5722	−0.890946	−0.445473	+	0.895295i	$0.646965\pi$
$390$	−5.46239	−0.276599
$391$	−5.86538	−0.296625
$392$	−33.6643	−1.70030
$393$	−8.16426	−0.411832
$394$	−56.1663	−2.82962
$395$	8.22280	0.413734
$396$	−5.12612	−0.257597
$397$	8.08127	0.405587	0.202794	−	0.979221i	$-0.434998\pi$
$397$	8.08127	0.405587	0.202794	+	0.979221i	$0.434998\pi$
$398$	52.7999	2.64662
$399$	−8.66207	−0.433646
$400$	−20.4378	−1.02189
$401$	−6.14445	−0.306839	−0.153420	−	0.988161i	$-0.549029\pi$
$401$	−6.14445	−0.306839	−0.153420	+	0.988161i	$0.549029\pi$
$402$	1.05718	0.0527272
$403$	2.55079	0.127064
$404$	30.1872	1.50187
$405$	0.756027	0.0375673
$406$	−51.3425	−2.54808
$407$	−3.27439	−0.162305
$408$	22.1052	1.09437
$409$	19.5110	0.964758	0.482379	−	0.875963i	$-0.339773\pi$
$409$	19.5110	0.964758	0.482379	+	0.875963i	$0.339773\pi$
$410$	18.8733	0.932086
$411$	0.959223	0.0473150
$412$	−27.4330	−1.35152
$413$	−13.1516	−0.647147
$414$	−7.12364	−0.350108
$415$	15.3014	0.751114
$416$	3.96850	0.194571
$417$	−2.27061	−0.111192
$418$	−3.63472	−0.177780
$419$	7.34814	0.358980	0.179490	−	0.983760i	$-0.442555\pi$
$419$	7.34814	0.358980	0.179490	+	0.983760i	$0.442555\pi$
$420$	−15.2561	−0.744420
$421$	18.7072	0.911734	0.455867	−	0.890048i	$-0.349329\pi$
$421$	18.7072	0.911734	0.455867	+	0.890048i	$0.349329\pi$
$422$	−26.1321	−1.27209
$423$	8.97104	0.436187
$424$	−44.9120	−2.18112
$425$	−16.1866	−0.785166
$426$	37.1008	1.79754
$427$	23.4677	1.13568
$428$	−60.5663	−2.92758
$429$	1.38912	0.0670674
$430$	20.8115	1.00362
$431$	−5.79410	−0.279092	−0.139546	−	0.990216i	$-0.544564\pi$
$431$	−5.79410	−0.279092	−0.139546	+	0.990216i	$0.544564\pi$
$432$	25.6486	1.23402
$433$	8.35735	0.401629	0.200814	−	0.979629i	$-0.435641\pi$
$433$	8.35735	0.401629	0.200814	+	0.979629i	$0.435641\pi$
$434$	10.5371	0.505796
$435$	−5.70735	−0.273646
$436$	27.4365	1.31397
$437$	−3.41506	−0.163364
$438$	24.9559	1.19244
$439$	12.8535	0.613463	0.306732	−	0.951796i	$-0.400765\pi$
$439$	12.8535	0.613463	0.306732	+	0.951796i	$0.400765\pi$
$440$	−3.33487	−0.158984
$441$	−12.2482	−0.583250
$442$	21.8725	1.04037
$443$	31.9042	1.51581	0.757907	−	0.652362i	$-0.226222\pi$
$443$	31.9042	1.51581	0.757907	+	0.652362i	$0.226222\pi$
$444$	22.2571	1.05627
$445$	−6.42147	−0.304407
$446$	27.7608	1.31451
$447$	10.9031	0.515698
$448$	−20.5575	−0.971251
$449$	−30.3400	−1.43183	−0.715916	−	0.698187i	$-0.753991\pi$
$449$	−30.3400	−1.43183	−0.715916	+	0.698187i	$0.753991\pi$
$450$	−19.6590	−0.926736
$451$	−4.79960	−0.226004
$452$	63.7673	2.99936
$453$	−5.84483	−0.274614
$454$	12.8549	0.603313
$455$	−7.86383	−0.368662
$456$	12.8705	0.602717
$457$	−28.2348	−1.32077	−0.660385	−	0.750927i	$-0.729607\pi$
$457$	−28.2348	−1.32077	−0.660385	+	0.750927i	$0.729607\pi$
$458$	2.96016	0.138319
$459$	20.3135	0.948152
$460$	−6.01477	−0.280440
$461$	1.33906	0.0623660	0.0311830	−	0.999514i	$-0.490073\pi$
$461$	1.33906	0.0623660	0.0311830	+	0.999514i	$0.490073\pi$
$462$	5.73833	0.266971
$463$	14.6917	0.682781	0.341391	−	0.939922i	$-0.389102\pi$
$463$	14.6917	0.682781	0.341391	+	0.939922i	$0.389102\pi$
$464$	28.8554	1.33958
$465$	1.17133	0.0543189
$466$	5.08778	0.235687
$467$	−6.83882	−0.316463	−0.158231	−	0.987402i	$-0.550579\pi$
$467$	−6.83882	−0.316463	−0.158231	+	0.987402i	$0.550579\pi$
$468$	17.9605	0.830224
$469$	1.52194	0.0702768
$470$	11.2033	0.516769
$471$	13.3830	0.616657
$472$	19.5412	0.899459
$473$	−5.29250	−0.243349
$474$	21.0233	0.965631
$475$	−9.42450	−0.432426
$476$	61.0882	2.79997
$477$	−16.3406	−0.748183
$478$	−45.1415	−2.06472
$479$	−31.4716	−1.43797	−0.718987	−	0.695023i	$-0.755394\pi$
$479$	−31.4716	−1.43797	−0.718987	+	0.695023i	$0.755394\pi$
$480$	1.82234	0.0831779
$481$	11.4725	0.523103
$482$	−11.2999	−0.514696
$483$	5.39154	0.245324
$484$	−44.2953	−2.01342
$485$	11.4243	0.518749
$486$	39.5745	1.79513
$487$	15.4593	0.700526	0.350263	−	0.936651i	$-0.386092\pi$
$487$	15.4593	0.700526	0.350263	+	0.936651i	$0.386092\pi$
$488$	−34.8694	−1.57846
$489$	8.25404	0.373261
$490$	−15.2960	−0.691001
$491$	4.05713	0.183096	0.0915478	−	0.995801i	$-0.470819\pi$
$491$	4.05713	0.183096	0.0915478	+	0.995801i	$0.470819\pi$
$492$	32.6244	1.47082
$493$	22.8533	1.02926
$494$	12.7350	0.572976
$495$	−1.21334	−0.0545357
$496$	−5.92204	−0.265907
$497$	53.4114	2.39583
$498$	39.1211	1.75306
$499$	25.9311	1.16084	0.580419	−	0.814318i	$-0.302889\pi$
$499$	25.9311	1.16084	0.580419	+	0.814318i	$0.302889\pi$
$500$	−37.2263	−1.66481
$501$	−25.2595	−1.12851
$502$	48.7306	2.17495
$503$	−4.36970	−0.194835	−0.0974176	−	0.995244i	$-0.531058\pi$
$503$	−4.36970	−0.194835	−0.0974176	+	0.995244i	$0.531058\pi$
$504$	38.6501	1.72161
$505$	7.14526	0.317960
$506$	2.26236	0.100574
$507$	8.35029	0.370850
$508$	−5.58915	−0.247979
$509$	−8.57581	−0.380116	−0.190058	−	0.981773i	$-0.560868\pi$
$509$	−8.57581	−0.380116	−0.190058	+	0.981773i	$0.560868\pi$
$510$	10.0439	0.444750
$511$	35.9273	1.58933
$512$	45.6901	2.01923
$513$	11.8273	0.522189
$514$	2.04531	0.0902148
$515$	−6.49333	−0.286130
$516$	35.9748	1.58370
$517$	−2.84907	−0.125302
$518$	47.3920	2.08228
$519$	−18.0220	−0.791076
$520$	11.6844	0.512397
$521$	35.6554	1.56209	0.781046	−	0.624474i	$-0.214686\pi$
$521$	35.6554	1.56209	0.781046	+	0.624474i	$0.214686\pi$
$522$	27.7559	1.21484
$523$	−31.8977	−1.39479	−0.697396	−	0.716686i	$-0.745658\pi$
$523$	−31.8977	−1.39479	−0.697396	+	0.716686i	$0.745658\pi$
$524$	33.5239	1.46450
$525$	14.8790	0.649372
$526$	−63.0237	−2.74796
$527$	−4.69021	−0.204309
$528$	−3.22505	−0.140352
$529$	−20.8744	−0.907581
$530$	−20.4066	−0.886404
$531$	7.10979	0.308539
$532$	35.5680	1.54207
$533$	16.8165	0.728402
$534$	−16.4178	−0.710468
$535$	−14.3359	−0.619795
$536$	−2.26137	−0.0976765
$537$	17.3753	0.749801
$538$	7.77035	0.335004
$539$	3.88986	0.167548
$540$	20.8309	0.896417
$541$	25.7069	1.10523	0.552614	−	0.833438i	$-0.313631\pi$
$541$	25.7069	1.10523	0.552614	+	0.833438i	$0.313631\pi$
$542$	13.5213	0.580788
$543$	−15.9110	−0.682807
$544$	−7.29699	−0.312856
$545$	6.49417	0.278180
$546$	−20.1055	−0.860436
$547$	34.9436	1.49408	0.747039	−	0.664780i	$-0.231475\pi$
$547$	34.9436	1.49408	0.747039	+	0.664780i	$0.231475\pi$
$548$	−3.93874	−0.168255
$549$	−12.6867	−0.541456
$550$	6.24341	0.266220
$551$	13.3061	0.566860
$552$	−8.01100	−0.340971
$553$	30.2657	1.28703
$554$	−51.7142	−2.19713
$555$	5.26820	0.223623
$556$	9.32351	0.395405
$557$	32.4500	1.37495	0.687475	−	0.726208i	$-0.258719\pi$
$557$	32.4500	1.37495	0.687475	+	0.726208i	$0.258719\pi$
$558$	−5.69637	−0.241147
$559$	18.5434	0.784303
$560$	18.2570	0.771501
$561$	−2.55422	−0.107839
$562$	−58.1754	−2.45398
$563$	29.0044	1.22239	0.611194	−	0.791481i	$-0.290689\pi$
$563$	29.0044	1.22239	0.611194	+	0.791481i	$0.290689\pi$
$564$	19.3660	0.815456
$565$	15.0936	0.634992
$566$	40.2508	1.69187
$567$	2.78272	0.116863
$568$	−79.3612	−3.32992
$569$	−43.8271	−1.83733	−0.918663	−	0.395042i	$-0.870730\pi$
$569$	−43.8271	−1.83733	−0.918663	+	0.395042i	$0.870730\pi$
$570$	5.84794	0.244943
$571$	8.87583	0.371442	0.185721	−	0.982603i	$-0.440538\pi$
$571$	8.87583	0.371442	0.185721	+	0.982603i	$0.440538\pi$
$572$	−5.70398	−0.238495
$573$	−23.0946	−0.964791
$574$	69.4672	2.89951
$575$	5.86610	0.244633
$576$	11.1135	0.463061
$577$	−5.52846	−0.230153	−0.115076	−	0.993357i	$-0.536711\pi$
$577$	−5.52846	−0.230153	−0.115076	+	0.993357i	$0.536711\pi$
$578$	2.02614	0.0842765
$579$	19.6941	0.818460
$580$	23.4354	0.973101
$581$	56.3199	2.33654
$582$	29.2084	1.21073
$583$	5.18952	0.214928
$584$	−53.3825	−2.20898
$585$	4.25121	0.175766
$586$	−35.5563	−1.46882
$587$	−21.4131	−0.883814	−0.441907	−	0.897061i	$-0.645698\pi$
$587$	−21.4131	−0.883814	−0.441907	+	0.897061i	$0.645698\pi$
$588$	−26.4406	−1.09039
$589$	−2.73083	−0.112522
$590$	8.87890	0.365539
$591$	−22.9808	−0.945304
$592$	−26.6352	−1.09470
$593$	31.5205	1.29439	0.647196	−	0.762324i	$-0.275941\pi$
$593$	31.5205	1.29439	0.647196	+	0.762324i	$0.275941\pi$
$594$	−7.83520	−0.321482
$595$	14.4594	0.592780
$596$	−44.7700	−1.83385
$597$	21.6034	0.884169
$598$	−7.92668	−0.324146
$599$	−8.82326	−0.360509	−0.180254	−	0.983620i	$-0.557692\pi$
$599$	−8.82326	−0.360509	−0.180254	+	0.983620i	$0.557692\pi$
$600$	−22.1079	−0.902550
$601$	21.1253	0.861718	0.430859	−	0.902419i	$-0.358211\pi$
$601$	21.1253	0.861718	0.430859	+	0.902419i	$0.358211\pi$
$602$	76.6011	3.12203
$603$	−0.822767	−0.0335057
$604$	23.9999	0.976543
$605$	−10.4846	−0.426259
$606$	18.2683	0.742100
$607$	−23.3445	−0.947523	−0.473762	−	0.880653i	$-0.657104\pi$
$607$	−23.3445	−0.947523	−0.473762	+	0.880653i	$0.657104\pi$
$608$	−4.24860	−0.172303
$609$	−21.0071	−0.851251
$610$	−15.8435	−0.641486
$611$	9.98233	0.403842
$612$	−33.0245	−1.33493
$613$	−10.4762	−0.423128	−0.211564	−	0.977364i	$-0.567856\pi$
$613$	−10.4762	−0.423128	−0.211564	+	0.977364i	$0.567856\pi$
$614$	44.0931	1.77945
$615$	7.72213	0.311387
$616$	−12.2747	−0.494561
$617$	−34.9105	−1.40545	−0.702723	−	0.711464i	$-0.748033\pi$
$617$	−34.9105	−1.40545	−0.702723	+	0.711464i	$0.748033\pi$
$618$	−16.6015	−0.667811
$619$	−47.1354	−1.89453	−0.947265	−	0.320451i	$-0.896165\pi$
$619$	−47.1354	−1.89453	−0.947265	+	0.320451i	$0.896165\pi$
$620$	−4.80967	−0.193161
$621$	−7.36169	−0.295415
$622$	79.9911	3.20735
$623$	−23.6356	−0.946939
$624$	11.2997	0.452349
$625$	11.3062	0.452246
$626$	−60.9564	−2.43631
$627$	−1.48717	−0.0593918
$628$	−54.9530	−2.19286
$629$	−21.0949	−0.841108
$630$	17.5613	0.699661
$631$	36.8985	1.46891	0.734453	−	0.678659i	$-0.237439\pi$
$631$	36.8985	1.46891	0.734453	+	0.678659i	$0.237439\pi$
$632$	−44.9702	−1.78882
$633$	−10.6921	−0.424974
$634$	45.7463	1.81682
$635$	−1.32294	−0.0524993
$636$	−35.2748	−1.39874
$637$	−13.6290	−0.540000
$638$	−8.81485	−0.348983
$639$	−28.8744	−1.14225
$640$	17.4635	0.690306
$641$	20.3616	0.804236	0.402118	−	0.915588i	$-0.368274\pi$
$641$	20.3616	0.804236	0.402118	+	0.915588i	$0.368274\pi$
$642$	−36.6527	−1.44657
$643$	3.16593	0.124852	0.0624261	−	0.998050i	$-0.480116\pi$
$643$	3.16593	0.124852	0.0624261	+	0.998050i	$0.480116\pi$
$644$	−22.1386	−0.872384
$645$	8.51516	0.335284
$646$	−23.4163	−0.921301
$647$	−25.5296	−1.00367	−0.501837	−	0.864962i	$-0.667342\pi$
$647$	−25.5296	−1.00367	−0.501837	+	0.864962i	$0.667342\pi$
$648$	−4.13469	−0.162426
$649$	−2.25796	−0.0886327
$650$	−21.8752	−0.858015
$651$	4.31131	0.168974
$652$	−33.8925	−1.32733
$653$	0.951977	0.0372537	0.0186269	−	0.999827i	$-0.494071\pi$
$653$	0.951977	0.0372537	0.0186269	+	0.999827i	$0.494071\pi$
$654$	16.6037	0.649255
$655$	7.93504	0.310048
$656$	−39.0419	−1.52433
$657$	−19.4224	−0.757741
$658$	41.2361	1.60755
$659$	43.3788	1.68980	0.844899	−	0.534927i	$-0.179661\pi$
$659$	43.3788	1.68980	0.844899	+	0.534927i	$0.179661\pi$
$660$	−2.61927	−0.101955
$661$	0.913915	0.0355472	0.0177736	−	0.999842i	$-0.494342\pi$
$661$	0.913915	0.0355472	0.0177736	+	0.999842i	$0.494342\pi$
$662$	−53.6308	−2.08442
$663$	8.94926	0.347561
$664$	−83.6827	−3.24752
$665$	8.41887	0.326470
$666$	−25.6202	−0.992764
$667$	−8.28214	−0.320686
$668$	103.720	4.01304
$669$	11.3585	0.439145
$670$	−1.02749	−0.0396956
$671$	4.02911	0.155542
$672$	6.70750	0.258747
$673$	−8.73710	−0.336790	−0.168395	−	0.985720i	$-0.553858\pi$
$673$	−8.73710	−0.336790	−0.168395	+	0.985720i	$0.553858\pi$
$674$	−51.9482	−2.00097
$675$	−20.3160	−0.781963
$676$	−34.2878	−1.31876
$677$	24.2923	0.933628	0.466814	−	0.884355i	$-0.345402\pi$
$677$	24.2923	0.933628	0.466814	+	0.884355i	$0.345402\pi$
$678$	38.5898	1.48203
$679$	42.0494	1.61371
$680$	−21.4845	−0.823894
$681$	5.25969	0.201552
$682$	1.80908	0.0692733
$683$	33.5716	1.28458	0.642290	−	0.766462i	$-0.277984\pi$
$683$	33.5716	1.28458	0.642290	+	0.766462i	$0.277984\pi$
$684$	−19.2282	−0.735207
$685$	−0.932292	−0.0356210
$686$	6.96697	0.266000
$687$	1.21117	0.0462090
$688$	−43.0513	−1.64132
$689$	−18.1826	−0.692702
$690$	−3.63994	−0.138570
$691$	−34.5440	−1.31411	−0.657057	−	0.753841i	$-0.728199\pi$
$691$	−34.5440	−1.31411	−0.657057	+	0.753841i	$0.728199\pi$
$692$	74.0013	2.81311
$693$	−4.46596	−0.169648
$694$	−13.0543	−0.495533
$695$	2.20686	0.0837108
$696$	31.2133	1.18314
$697$	−30.9209	−1.17121
$698$	63.6833	2.41045
$699$	2.08170	0.0787370
$700$	−61.0957	−2.30920
$701$	−39.0620	−1.47535	−0.737676	−	0.675155i	$-0.764077\pi$
$701$	−39.0620	−1.47535	−0.737676	+	0.675155i	$0.764077\pi$
$702$	27.4524	1.03612
$703$	−12.2823	−0.463235
$704$	−3.52946	−0.133022
$705$	4.58390	0.172639
$706$	−61.0201	−2.29652
$707$	26.2996	0.989099
$708$	15.3481	0.576816
$709$	−21.4201	−0.804447	−0.402224	−	0.915541i	$-0.631763\pi$
$709$	−21.4201	−0.804447	−0.402224	+	0.915541i	$0.631763\pi$
$710$	−36.0591	−1.35328
$711$	−16.3618	−0.613614
$712$	35.1188	1.31613
$713$	1.69975	0.0636562
$714$	36.9686	1.38351
$715$	−1.35012	−0.0504916
$716$	−71.3462	−2.66633
$717$	−18.4699	−0.689772
$718$	21.6654	0.808546
$719$	6.27683	0.234086	0.117043	−	0.993127i	$-0.462658\pi$
$719$	6.27683	0.234086	0.117043	+	0.993127i	$0.462658\pi$
$720$	−9.86981	−0.367826
$721$	−23.9001	−0.890085
$722$	33.5796	1.24970
$723$	−4.62343	−0.171947
$724$	65.3335	2.42810
$725$	−22.8561	−0.848855
$726$	−26.8060	−0.994865
$727$	28.5799	1.05997	0.529985	−	0.848007i	$-0.322197\pi$
$727$	28.5799	1.05997	0.529985	+	0.848007i	$0.322197\pi$
$728$	43.0071	1.59395
$729$	13.8969	0.514701
$730$	−24.2552	−0.897727
$731$	−34.0963	−1.26110
$732$	−27.3871	−1.01226
$733$	31.9135	1.17875	0.589376	−	0.807859i	$-0.299374\pi$
$733$	31.9135	1.17875	0.589376	+	0.807859i	$0.299374\pi$
$734$	−84.2802	−3.11084
$735$	−6.25844	−0.230846
$736$	2.64446	0.0974760
$737$	0.261298	0.00962505
$738$	−37.5542	−1.38239
$739$	10.0008	0.367886	0.183943	−	0.982937i	$-0.441114\pi$
$739$	10.0008	0.367886	0.183943	+	0.982937i	$0.441114\pi$
$740$	−21.6322	−0.795214
$741$	5.21062	0.191417
$742$	−75.1106	−2.75740
$743$	29.6922	1.08930	0.544651	−	0.838663i	$-0.316662\pi$
$743$	29.6922	1.08930	0.544651	+	0.838663i	$0.316662\pi$
$744$	−6.40595	−0.234853
$745$	−10.5970	−0.388243
$746$	−22.8295	−0.835847
$747$	−30.4467	−1.11399
$748$	10.4881	0.383482
$749$	−52.7664	−1.92804
$750$	−22.5281	−0.822610
$751$	41.7543	1.52364	0.761819	−	0.647790i	$-0.224307\pi$
$751$	41.7543	1.52364	0.761819	+	0.647790i	$0.224307\pi$
$752$	−23.1755	−0.845122
$753$	19.9385	0.726598
$754$	30.8848	1.12476
$755$	5.68073	0.206743
$756$	76.6724	2.78855
$757$	−14.0926	−0.512203	−0.256101	−	0.966650i	$-0.582438\pi$
$757$	−14.0926	−0.512203	−0.256101	+	0.966650i	$0.582438\pi$
$758$	43.0664	1.56424
$759$	0.925659	0.0335993
$760$	−12.5091	−0.453755
$761$	36.2927	1.31561	0.657805	−	0.753188i	$-0.271485\pi$
$761$	36.2927	1.31561	0.657805	+	0.753188i	$0.271485\pi$
$762$	−3.38237	−0.122530
$763$	23.9032	0.865353
$764$	94.8305	3.43085
$765$	−7.81682	−0.282618
$766$	−60.0638	−2.17019
$767$	7.91126	0.285659
$768$	33.1560	1.19641
$769$	−19.6555	−0.708796	−0.354398	−	0.935095i	$-0.615314\pi$
$769$	−19.6555	−0.708796	−0.354398	+	0.935095i	$0.615314\pi$
$770$	−5.57722	−0.200989
$771$	0.836852	0.0301385
$772$	−80.8675	−2.91049
$773$	21.2641	0.764815	0.382408	−	0.923994i	$-0.375095\pi$
$773$	21.2641	0.764815	0.382408	+	0.923994i	$0.375095\pi$
$774$	−41.4108	−1.48848
$775$	4.69079	0.168498
$776$	−62.4789	−2.24286
$777$	19.3907	0.695639
$778$	43.6656	1.56549
$779$	−18.0034	−0.645038
$780$	9.17720	0.328596
$781$	9.17007	0.328131
$782$	14.5750	0.521201
$783$	28.6834	1.02506
$784$	31.6417	1.13006
$785$	−13.0073	−0.464249
$786$	20.2876	0.723633
$787$	48.1034	1.71470	0.857351	−	0.514732i	$-0.172109\pi$
$787$	48.1034	1.71470	0.857351	+	0.514732i	$0.172109\pi$
$788$	94.3632	3.36155
$789$	−25.7865	−0.918025
$790$	−20.4330	−0.726974
$791$	55.5551	1.97531
$792$	6.63573	0.235791
$793$	−14.1169	−0.501305
$794$	−20.0813	−0.712660
$795$	−8.34947	−0.296125
$796$	−88.7074	−3.14415
$797$	49.7859	1.76351	0.881753	−	0.471711i	$-0.156364\pi$
$797$	49.7859	1.76351	0.881753	+	0.471711i	$0.156364\pi$
$798$	21.5246	0.761962
$799$	−18.3548	−0.649346
$800$	7.29789	0.258019
$801$	12.7775	0.451470
$802$	15.2685	0.539149
$803$	6.16826	0.217673
$804$	−1.77613	−0.0626392
$805$	−5.24017	−0.184692
$806$	−6.33852	−0.223265
$807$	3.17929	0.111916
$808$	−39.0772	−1.37473
$809$	−0.196582	−0.00691146	−0.00345573	−	0.999994i	$-0.501100\pi$
$809$	−0.196582	−0.00691146	−0.00345573	+	0.999994i	$0.501100\pi$
$810$	−1.87867	−0.0660097
$811$	50.4884	1.77289	0.886444	−	0.462835i	$-0.153168\pi$
$811$	50.4884	1.77289	0.886444	+	0.462835i	$0.153168\pi$
$812$	86.2589	3.02709
$813$	5.53231	0.194027
$814$	8.13660	0.285188
$815$	−8.02230	−0.281009
$816$	−20.7770	−0.727342
$817$	−19.8522	−0.694542
$818$	−48.4834	−1.69518
$819$	15.6475	0.546767
$820$	−31.7084	−1.10731
$821$	−5.26563	−0.183772	−0.0918858	−	0.995770i	$-0.529289\pi$
$821$	−5.26563	−0.183772	−0.0918858	+	0.995770i	$0.529289\pi$
$822$	−2.38360	−0.0831375
$823$	18.4950	0.644695	0.322347	−	0.946621i	$-0.395528\pi$
$823$	18.4950	0.644695	0.322347	+	0.946621i	$0.395528\pi$
$824$	35.5118	1.23711
$825$	2.55453	0.0889374
$826$	32.6807	1.13711
$827$	41.9103	1.45736	0.728682	−	0.684852i	$-0.240133\pi$
$827$	41.9103	1.45736	0.728682	+	0.684852i	$0.240133\pi$
$828$	11.9682	0.415924
$829$	0.892350	0.0309926	0.0154963	−	0.999880i	$-0.495067\pi$
$829$	0.892350	0.0309926	0.0154963	+	0.999880i	$0.495067\pi$
$830$	−38.0227	−1.31979
$831$	−21.1592	−0.734005
$832$	12.3663	0.428723
$833$	25.0600	0.868277
$834$	5.64228	0.195376
$835$	24.5503	0.849597
$836$	6.10657	0.211200
$837$	−5.88673	−0.203475
$838$	−18.2595	−0.630766
$839$	24.5608	0.847933	0.423967	−	0.905678i	$-0.360637\pi$
$839$	24.5608	0.847933	0.423967	+	0.905678i	$0.360637\pi$
$840$	19.7489	0.681401
$841$	3.26975	0.112750
$842$	−46.4860	−1.60201
$843$	−23.8028	−0.819813
$844$	43.9038	1.51123
$845$	−8.11585	−0.279194
$846$	−22.2923	−0.766426
$847$	−38.5908	−1.32599
$848$	42.2136	1.44962
$849$	16.4689	0.565211
$850$	40.2225	1.37962
$851$	7.64488	0.262063
$852$	−62.3319	−2.13545
$853$	37.9859	1.30061	0.650306	−	0.759672i	$-0.274641\pi$
$853$	37.9859	1.30061	0.650306	+	0.759672i	$0.274641\pi$
$854$	−58.3155	−1.99551
$855$	−4.55127	−0.155650
$856$	78.4027	2.67975
$857$	−14.9397	−0.510331	−0.255165	−	0.966897i	$-0.582130\pi$
$857$	−14.9397	−0.510331	−0.255165	+	0.966897i	$0.582130\pi$
$858$	−3.45186	−0.117845
$859$	44.0371	1.50253	0.751263	−	0.660002i	$-0.229445\pi$
$859$	44.0371	1.50253	0.751263	+	0.660002i	$0.229445\pi$
$860$	−34.9647	−1.19229
$861$	28.4230	0.968652
$862$	14.3979	0.490394
$863$	−34.6695	−1.18016	−0.590081	−	0.807344i	$-0.700904\pi$
$863$	−34.6695	−1.18016	−0.590081	+	0.807344i	$0.700904\pi$
$864$	−9.15852	−0.311579
$865$	17.5160	0.595561
$866$	−20.7674	−0.705704
$867$	0.829010	0.0281547
$868$	−17.7030	−0.600879
$869$	5.19624	0.176271
$870$	14.1823	0.480826
$871$	−0.915516	−0.0310211
$872$	−35.5164	−1.20274
$873$	−22.7320	−0.769362
$874$	8.48615	0.287048
$875$	−32.4322	−1.09641
$876$	−41.9277	−1.41660
$877$	−36.5805	−1.23523	−0.617617	−	0.786479i	$-0.711902\pi$
$877$	−36.5805	−1.23523	−0.617617	+	0.786479i	$0.711902\pi$
$878$	−31.9399	−1.07792
$879$	−14.5481	−0.490694
$880$	3.13450	0.105664
$881$	6.48790	0.218583	0.109292	−	0.994010i	$-0.465142\pi$
$881$	6.48790	0.218583	0.109292	+	0.994010i	$0.465142\pi$
$882$	30.4359	1.02483
$883$	−39.8087	−1.33967	−0.669834	−	0.742510i	$-0.733635\pi$
$883$	−39.8087	−1.33967	−0.669834	+	0.742510i	$0.733635\pi$
$884$	−36.7472	−1.23594
$885$	3.63286	0.122117
$886$	−79.2795	−2.66345
$887$	49.5576	1.66398	0.831990	−	0.554791i	$-0.187202\pi$
$887$	49.5576	1.66398	0.831990	+	0.554791i	$0.187202\pi$
$888$	−28.8116	−0.966856
$889$	−4.86936	−0.163313
$890$	15.9569	0.534875
$891$	0.477757	0.0160055
$892$	−46.6400	−1.56162
$893$	−10.6869	−0.357623
$894$	−27.0933	−0.906136
$895$	−16.8875	−0.564487
$896$	64.2782	2.14738
$897$	−3.24325	−0.108289
$898$	75.3925	2.51588
$899$	−6.62276	−0.220881
$900$	33.0285	1.10095
$901$	33.4329	1.11381
$902$	11.9266	0.397114
$903$	31.3418	1.04299
$904$	−82.5464	−2.74545
$905$	15.4643	0.514051
$906$	14.5240	0.482526
$907$	13.3321	0.442684	0.221342	−	0.975196i	$-0.428956\pi$
$907$	13.3321	0.442684	0.221342	+	0.975196i	$0.428956\pi$
$908$	−21.5972	−0.716728
$909$	−14.2177	−0.471570
$910$	19.5410	0.647778
$911$	−16.6277	−0.550901	−0.275451	−	0.961315i	$-0.588827\pi$
$911$	−16.6277	−0.550901	−0.275451	+	0.961315i	$0.588827\pi$
$912$	−12.0972	−0.400579
$913$	9.66941	0.320011
$914$	70.1614	2.32073
$915$	−6.48248	−0.214304
$916$	−4.97328	−0.164322
$917$	29.2066	0.964486
$918$	−50.4774	−1.66600
$919$	34.4272	1.13565	0.567823	−	0.823150i	$-0.307786\pi$
$919$	34.4272	1.13565	0.567823	+	0.823150i	$0.307786\pi$
$920$	7.78608	0.256700
$921$	18.0410	0.594470
$922$	−3.32745	−0.109584
$923$	−32.1293	−1.05755
$924$	−9.64079	−0.317159
$925$	21.0975	0.693681
$926$	−36.5077	−1.19972
$927$	12.9204	0.424363
$928$	−10.3036	−0.338233
$929$	−19.6997	−0.646327	−0.323163	−	0.946343i	$-0.604746\pi$
$929$	−19.6997	−0.646327	−0.323163	+	0.946343i	$0.604746\pi$
$930$	−2.91065	−0.0954441
$931$	14.5909	0.478198
$932$	−8.54782	−0.279993
$933$	32.7289	1.07149
$934$	16.9939	0.556058
$935$	2.48250	0.0811866
$936$	−23.2498	−0.759942
$937$	−3.26052	−0.106517	−0.0532583	−	0.998581i	$-0.516961\pi$
$937$	−3.26052	−0.106517	−0.0532583	+	0.998581i	$0.516961\pi$
$938$	−3.78191	−0.123484
$939$	−24.9407	−0.813909
$940$	−18.8223	−0.613915
$941$	−35.2142	−1.14795	−0.573975	−	0.818873i	$-0.694599\pi$
$941$	−35.2142	−1.14795	−0.573975	+	0.818873i	$0.694599\pi$
$942$	−33.2557	−1.08353
$943$	11.2059	0.364913
$944$	−18.3672	−0.597800
$945$	18.1482	0.590361
$946$	13.1514	0.427590
$947$	−9.72004	−0.315859	−0.157929	−	0.987450i	$-0.550482\pi$
$947$	−9.72004	−0.315859	−0.157929	+	0.987450i	$0.550482\pi$
$948$	−35.3205	−1.14716
$949$	−21.6119	−0.701551
$950$	23.4192	0.759818
$951$	18.7174	0.606953
$952$	−79.0783	−2.56294
$953$	23.6615	0.766470	0.383235	−	0.923651i	$-0.374810\pi$
$953$	23.6615	0.766470	0.383235	+	0.923651i	$0.374810\pi$
$954$	40.6050	1.31464
$955$	22.4462	0.726342
$956$	75.8408	2.45287
$957$	−3.60665	−0.116587
$958$	78.2045	2.52667
$959$	−3.43150	−0.110809
$960$	5.67860	0.183276
$961$	−29.6408	−0.956155
$962$	−28.5084	−0.919147
$963$	28.5257	0.919226
$964$	18.9846	0.611453
$965$	−19.1412	−0.616176
$966$	−13.3976	−0.431059
$967$	−21.7257	−0.698652	−0.349326	−	0.937001i	$-0.613589\pi$
$967$	−21.7257	−0.698652	−0.349326	+	0.937001i	$0.613589\pi$
$968$	57.3400	1.84298
$969$	−9.58091	−0.307783
$970$	−28.3884	−0.911496
$971$	19.2563	0.617963	0.308981	−	0.951068i	$-0.400012\pi$
$971$	19.2563	0.617963	0.308981	+	0.951068i	$0.400012\pi$
$972$	−66.4878	−2.13260
$973$	8.12280	0.260405
$974$	−38.4150	−1.23090
$975$	−8.95037	−0.286641
$976$	32.7744	1.04908
$977$	−16.3671	−0.523631	−0.261816	−	0.965118i	$-0.584321\pi$
$977$	−16.3671	−0.523631	−0.261816	+	0.965118i	$0.584321\pi$
$978$	−20.5106	−0.655858
$979$	−4.05793	−0.129692
$980$	25.6982	0.820900
$981$	−12.9221	−0.412572
$982$	−10.0817	−0.321718
$983$	37.9693	1.21103	0.605516	−	0.795833i	$-0.292967\pi$
$983$	37.9693	1.21103	0.605516	+	0.795833i	$0.292967\pi$
$984$	−42.2321	−1.34631
$985$	22.3356	0.711671
$986$	−56.7887	−1.80852
$987$	16.8720	0.537042
$988$	−21.3957	−0.680689
$989$	12.3567	0.392919
$990$	3.01506	0.0958249
$991$	15.5782	0.494858	0.247429	−	0.968906i	$-0.420414\pi$
$991$	15.5782	0.494858	0.247429	+	0.968906i	$0.420414\pi$
$992$	2.11462	0.0671394
$993$	−21.9434	−0.696352
$994$	−132.723	−4.20973
$995$	−20.9969	−0.665645
$996$	−65.7261	−2.08261
$997$	37.2630	1.18013	0.590065	−	0.807355i	$-0.299102\pi$
$997$	37.2630	1.18013	0.590065	+	0.807355i	$0.299102\pi$
$998$	−64.4369	−2.03971
$999$	−26.4764	−0.837676

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	5077.2.a.c.1.13	✓	216

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
5077.2.a.c.1.13	✓	216	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:	\( N \)	\(=\)	\( 5077 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	5077.a (trivial)

\(f(q)\)	\(=\)	\(q-2.48492 q^{2} -1.01672 q^{3} +4.17484 q^{4} +0.988176 q^{5} +2.52648 q^{6} +3.63719 q^{7} -5.40431 q^{8} -1.96628 q^{9} +O(q^{10})\)	\(q-2.48492 q^{2} -1.01672 q^{3} +4.17484 q^{4} +0.988176 q^{5} +2.52648 q^{6} +3.63719 q^{7} -5.40431 q^{8} -1.96628 q^{9} -2.45554 q^{10} +0.624460 q^{11} -4.24465 q^{12} -2.18793 q^{13} -9.03814 q^{14} -1.00470 q^{15} +5.07961 q^{16} +4.02301 q^{17} +4.88604 q^{18} +2.34236 q^{19} +4.12548 q^{20} -3.69801 q^{21} -1.55173 q^{22} -1.45796 q^{23} +5.49468 q^{24} -4.02351 q^{25} +5.43684 q^{26} +5.04932 q^{27} +15.1847 q^{28} +5.68065 q^{29} +2.49660 q^{30} -1.16585 q^{31} -1.81381 q^{32} -0.634902 q^{33} -9.99687 q^{34} +3.59418 q^{35} -8.20889 q^{36} -5.24356 q^{37} -5.82058 q^{38} +2.22452 q^{39} -5.34041 q^{40} -7.68601 q^{41} +9.18927 q^{42} -8.47532 q^{43} +2.60702 q^{44} -1.94303 q^{45} +3.62291 q^{46} -4.56245 q^{47} -5.16455 q^{48} +6.22916 q^{49} +9.99811 q^{50} -4.09028 q^{51} -9.13426 q^{52} +8.31041 q^{53} -12.5472 q^{54} +0.617076 q^{55} -19.6565 q^{56} -2.38153 q^{57} -14.1160 q^{58} -3.61586 q^{59} -4.19446 q^{60} +6.45215 q^{61} +2.89704 q^{62} -7.15172 q^{63} -5.65203 q^{64} -2.16206 q^{65} +1.57768 q^{66} +0.418439 q^{67} +16.7954 q^{68} +1.48234 q^{69} -8.93127 q^{70} +14.6848 q^{71} +10.6264 q^{72} +9.87776 q^{73} +13.0298 q^{74} +4.09079 q^{75} +9.77897 q^{76} +2.27128 q^{77} -5.52775 q^{78} +8.32119 q^{79} +5.01954 q^{80} +0.765073 q^{81} +19.0991 q^{82} +15.4844 q^{83} -15.4386 q^{84} +3.97544 q^{85} +21.0605 q^{86} -5.77564 q^{87} -3.37477 q^{88} -6.49830 q^{89} +4.82827 q^{90} -7.95792 q^{91} -6.08673 q^{92} +1.18534 q^{93} +11.3373 q^{94} +2.31466 q^{95} +1.84414 q^{96} +11.5609 q^{97} -15.4790 q^{98} -1.22786 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 216 q + 25 q^{2} + 62 q^{3} + 223 q^{4} + 46 q^{5} + 26 q^{6} + 30 q^{7} + 75 q^{8} + 234 q^{9}+O(q^{10}) \) 216 * q + 25 * q^2 + 62 * q^3 + 223 * q^4 + 46 * q^5 + 26 * q^6 + 30 * q^7 + 75 * q^8 + 234 * q^9	\( 216 q + 25 q^{2} + 62 q^{3} + 223 q^{4} + 46 q^{5} + 26 q^{6} + 30 q^{7} + 75 q^{8} + 234 q^{9} + 24 q^{10} + 89 q^{11} + 114 q^{12} + 34 q^{13} + 53 q^{14} + 61 q^{15} + 229 q^{16} + 76 q^{17} + 57 q^{18} + 54 q^{19} + 118 q^{20} + 25 q^{21} + 26 q^{22} + 109 q^{23} + 65 q^{24} + 232 q^{25} + 58 q^{26} + 236 q^{27} + 57 q^{28} + 54 q^{29} + 6 q^{30} + 77 q^{31} + 155 q^{32} + 80 q^{33} + 28 q^{34} + 137 q^{35} + 257 q^{36} + 42 q^{37} + 104 q^{38} + 46 q^{39} + 47 q^{40} + 109 q^{41} + 27 q^{42} + 68 q^{43} + 145 q^{44} + 109 q^{45} - 7 q^{46} + 264 q^{47} + 198 q^{48} + 222 q^{49} + 86 q^{50} + 57 q^{51} + 68 q^{52} + 95 q^{53} + 79 q^{54} + 50 q^{55} + 108 q^{56} + 55 q^{57} + 38 q^{58} + 292 q^{59} + 91 q^{60} + 16 q^{61} + 91 q^{62} + 113 q^{63} + 231 q^{64} + 68 q^{65} - 15 q^{66} + 152 q^{67} + 199 q^{68} + 83 q^{69} + 24 q^{70} + 131 q^{71} + 162 q^{72} + 71 q^{73} + 10 q^{74} + 232 q^{75} + 60 q^{76} + 131 q^{77} + 102 q^{78} + 10 q^{79} + 236 q^{80} + 268 q^{81} + 54 q^{82} + 299 q^{83} - 9 q^{85} + 35 q^{86} + 103 q^{87} + 45 q^{88} + 134 q^{89} + 8 q^{90} + 79 q^{91} + 206 q^{92} + 95 q^{93} + 18 q^{94} + 119 q^{95} + 77 q^{96} + 129 q^{97} + 150 q^{98} + 221 q^{99}+O(q^{100}) \) 216 * q + 25 * q^2 + 62 * q^3 + 223 * q^4 + 46 * q^5 + 26 * q^6 + 30 * q^7 + 75 * q^8 + 234 * q^9 + 24 * q^10 + 89 * q^11 + 114 * q^12 + 34 * q^13 + 53 * q^14 + 61 * q^15 + 229 * q^16 + 76 * q^17 + 57 * q^18 + 54 * q^19 + 118 * q^20 + 25 * q^21 + 26 * q^22 + 109 * q^23 + 65 * q^24 + 232 * q^25 + 58 * q^26 + 236 * q^27 + 57 * q^28 + 54 * q^29 + 6 * q^30 + 77 * q^31 + 155 * q^32 + 80 * q^33 + 28 * q^34 + 137 * q^35 + 257 * q^36 + 42 * q^37 + 104 * q^38 + 46 * q^39 + 47 * q^40 + 109 * q^41 + 27 * q^42 + 68 * q^43 + 145 * q^44 + 109 * q^45 - 7 * q^46 + 264 * q^47 + 198 * q^48 + 222 * q^49 + 86 * q^50 + 57 * q^51 + 68 * q^52 + 95 * q^53 + 79 * q^54 + 50 * q^55 + 108 * q^56 + 55 * q^57 + 38 * q^58 + 292 * q^59 + 91 * q^60 + 16 * q^61 + 91 * q^62 + 113 * q^63 + 231 * q^64 + 68 * q^65 - 15 * q^66 + 152 * q^67 + 199 * q^68 + 83 * q^69 + 24 * q^70 + 131 * q^71 + 162 * q^72 + 71 * q^73 + 10 * q^74 + 232 * q^75 + 60 * q^76 + 131 * q^77 + 102 * q^78 + 10 * q^79 + 236 * q^80 + 268 * q^81 + 54 * q^82 + 299 * q^83 - 9 * q^85 + 35 * q^86 + 103 * q^87 + 45 * q^88 + 134 * q^89 + 8 * q^90 + 79 * q^91 + 206 * q^92 + 95 * q^93 + 18 * q^94 + 119 * q^95 + 77 * q^96 + 129 * q^97 + 150 * q^98 + 221 * q^99

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