LMFDB - Embedded newform 2013.4.a.g.1.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2013,4,Mod(1,2013)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2013, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("2013.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 2013 = 3 \cdot 11 \cdot 61 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	2013.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:	$118.770844842$
Analytic rank:	$0$
Dimension:	$39$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.16
Character	$\chi$	$=$	2013.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.12400 q^{2} -3.00000 q^{3} -6.73663 q^{4} -4.49934 q^{5} +3.37199 q^{6} -12.1013 q^{7} +16.5639 q^{8} +9.00000 q^{9} +O(q^{10})$	\(q-1.12400 q^{2} -3.00000 q^{3} -6.73663 q^{4} -4.49934 q^{5} +3.37199 q^{6} -12.1013 q^{7} +16.5639 q^{8} +9.00000 q^{9} +5.05724 q^{10} +11.0000 q^{11} +20.2099 q^{12} +48.9992 q^{13} +13.6018 q^{14} +13.4980 q^{15} +35.2753 q^{16} +104.125 q^{17} -10.1160 q^{18} +123.078 q^{19} +30.3104 q^{20} +36.3039 q^{21} -12.3640 q^{22} +66.4772 q^{23} -49.6917 q^{24} -104.756 q^{25} -55.0749 q^{26} -27.0000 q^{27} +81.5221 q^{28} +189.645 q^{29} -15.1717 q^{30} +205.769 q^{31} -172.161 q^{32} -33.0000 q^{33} -117.036 q^{34} +54.4480 q^{35} -60.6297 q^{36} -232.751 q^{37} -138.339 q^{38} -146.998 q^{39} -74.5267 q^{40} +167.713 q^{41} -40.8055 q^{42} -150.105 q^{43} -74.1030 q^{44} -40.4941 q^{45} -74.7201 q^{46} +221.299 q^{47} -105.826 q^{48} -196.558 q^{49} +117.745 q^{50} -312.374 q^{51} -330.090 q^{52} +94.6410 q^{53} +30.3479 q^{54} -49.4928 q^{55} -200.445 q^{56} -369.234 q^{57} -213.160 q^{58} -356.049 q^{59} -90.9313 q^{60} +61.0000 q^{61} -231.283 q^{62} -108.912 q^{63} -88.6946 q^{64} -220.464 q^{65} +37.0919 q^{66} +1080.21 q^{67} -701.450 q^{68} -199.432 q^{69} -61.1993 q^{70} -554.127 q^{71} +149.075 q^{72} +198.531 q^{73} +261.611 q^{74} +314.268 q^{75} -829.132 q^{76} -133.114 q^{77} +165.225 q^{78} +910.924 q^{79} -158.716 q^{80} +81.0000 q^{81} -188.509 q^{82} -1071.79 q^{83} -244.566 q^{84} -468.493 q^{85} +168.717 q^{86} -568.934 q^{87} +182.203 q^{88} +740.421 q^{89} +45.5152 q^{90} -592.955 q^{91} -447.833 q^{92} -617.307 q^{93} -248.739 q^{94} -553.771 q^{95} +516.482 q^{96} -138.866 q^{97} +220.931 q^{98} +99.0000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 39 q + 4 q^{2} - 117 q^{3} + 182 q^{4} + 5 q^{5} - 12 q^{6} + 77 q^{7} + 27 q^{8} + 351 q^{9}+O(q^{10}) $ 39 * q + 4 * q^2 - 117 * q^3 + 182 * q^4 + 5 * q^5 - 12 * q^6 + 77 * q^7 + 27 * q^8 + 351 * q^9	\( 39 q + 4 q^{2} - 117 q^{3} + 182 q^{4} + 5 q^{5} - 12 q^{6} + 77 q^{7} + 27 q^{8} + 351 q^{9} + 95 q^{10} + 429 q^{11} - 546 q^{12} + 169 q^{13} + 46 q^{14} - 15 q^{15} + 822 q^{16} + 294 q^{17} + 36 q^{18} + 259 q^{19} + 426 q^{20} - 231 q^{21} + 44 q^{22} + 177 q^{23} - 81 q^{24} + 1388 q^{25} + 695 q^{26} - 1053 q^{27} + 1104 q^{28} - 18 q^{29} - 285 q^{30} + 422 q^{31} + 55 q^{32} - 1287 q^{33} + 364 q^{34} + 906 q^{35} + 1638 q^{36} + 424 q^{37} + 9 q^{38} - 507 q^{39} + 1067 q^{40} + 16 q^{41} - 138 q^{42} + 1013 q^{43} + 2002 q^{44} + 45 q^{45} + 9 q^{46} + 1615 q^{47} - 2466 q^{48} + 2024 q^{49} - 1342 q^{50} - 882 q^{51} + 1298 q^{52} - 541 q^{53} - 108 q^{54} + 55 q^{55} - 161 q^{56} - 777 q^{57} + 1061 q^{58} + 1019 q^{59} - 1278 q^{60} + 2379 q^{61} + 879 q^{62} + 693 q^{63} + 1055 q^{64} - 1134 q^{65} - 132 q^{66} + 1917 q^{67} + 3526 q^{68} - 531 q^{69} + 758 q^{70} - 479 q^{71} + 243 q^{72} + 3319 q^{73} - 332 q^{74} - 4164 q^{75} + 692 q^{76} + 847 q^{77} - 2085 q^{78} + 651 q^{79} + 2973 q^{80} + 3159 q^{81} - 826 q^{82} + 4001 q^{83} - 3312 q^{84} + 3595 q^{85} - 6247 q^{86} + 54 q^{87} + 297 q^{88} - 1625 q^{89} + 855 q^{90} + 2048 q^{91} - 507 q^{92} - 1266 q^{93} - 2436 q^{94} + 1400 q^{95} - 165 q^{96} + 2176 q^{97} - 1396 q^{98} + 3861 q^{99}+O(q^{100}) \) 39 * q + 4 * q^2 - 117 * q^3 + 182 * q^4 + 5 * q^5 - 12 * q^6 + 77 * q^7 + 27 * q^8 + 351 * q^9 + 95 * q^10 + 429 * q^11 - 546 * q^12 + 169 * q^13 + 46 * q^14 - 15 * q^15 + 822 * q^16 + 294 * q^17 + 36 * q^18 + 259 * q^19 + 426 * q^20 - 231 * q^21 + 44 * q^22 + 177 * q^23 - 81 * q^24 + 1388 * q^25 + 695 * q^26 - 1053 * q^27 + 1104 * q^28 - 18 * q^29 - 285 * q^30 + 422 * q^31 + 55 * q^32 - 1287 * q^33 + 364 * q^34 + 906 * q^35 + 1638 * q^36 + 424 * q^37 + 9 * q^38 - 507 * q^39 + 1067 * q^40 + 16 * q^41 - 138 * q^42 + 1013 * q^43 + 2002 * q^44 + 45 * q^45 + 9 * q^46 + 1615 * q^47 - 2466 * q^48 + 2024 * q^49 - 1342 * q^50 - 882 * q^51 + 1298 * q^52 - 541 * q^53 - 108 * q^54 + 55 * q^55 - 161 * q^56 - 777 * q^57 + 1061 * q^58 + 1019 * q^59 - 1278 * q^60 + 2379 * q^61 + 879 * q^62 + 693 * q^63 + 1055 * q^64 - 1134 * q^65 - 132 * q^66 + 1917 * q^67 + 3526 * q^68 - 531 * q^69 + 758 * q^70 - 479 * q^71 + 243 * q^72 + 3319 * q^73 - 332 * q^74 - 4164 * q^75 + 692 * q^76 + 847 * q^77 - 2085 * q^78 + 651 * q^79 + 2973 * q^80 + 3159 * q^81 - 826 * q^82 + 4001 * q^83 - 3312 * q^84 + 3595 * q^85 - 6247 * q^86 + 54 * q^87 + 297 * q^88 - 1625 * q^89 + 855 * q^90 + 2048 * q^91 - 507 * q^92 - 1266 * q^93 - 2436 * q^94 + 1400 * q^95 - 165 * q^96 + 2176 * q^97 - 1396 * q^98 + 3861 * 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 $

$2$	−1.12400	−0.397393	−0.198696	−	0.980061i	$-0.563671\pi$
$2$	−1.12400	−0.397393	−0.198696	+	0.980061i	$0.563671\pi$
$3$	−3.00000	−0.577350
$3$	−3.00000	−0.577350
$4$	−6.73663	−0.842079
$5$	−4.49934	−0.402434	−0.201217	−	0.979547i	$-0.564490\pi$
$5$	−4.49934	−0.402434	−0.201217	+	0.979547i	$0.564490\pi$
$6$	3.37199	0.229435
$7$	−12.1013	−0.653409	−0.326705	−	0.945126i	$-0.605938\pi$
$7$	−12.1013	−0.653409	−0.326705	+	0.945126i	$0.605938\pi$
$8$	16.5639	0.732029
$9$	9.00000	0.333333
$10$	5.05724	0.159924
$11$	11.0000	0.301511
$11$	11.0000	0.301511
$12$	20.2099	0.486175
$13$	48.9992	1.04538	0.522690	−	0.852523i	$-0.324929\pi$
$13$	48.9992	1.04538	0.522690	+	0.852523i	$0.324929\pi$
$14$	13.6018	0.259660
$15$	13.4980	0.232345
$16$	35.2753	0.551177
$17$	104.125	1.48553	0.742764	−	0.669554i	$-0.233515\pi$
$17$	104.125	1.48553	0.742764	+	0.669554i	$0.233515\pi$
$18$	−10.1160	−0.132464
$19$	123.078	1.48611	0.743054	−	0.669231i	$-0.233377\pi$
$19$	123.078	1.48611	0.743054	+	0.669231i	$0.233377\pi$
$20$	30.3104	0.338881
$21$	36.3039	0.377246
$22$	−12.3640	−0.119818
$23$	66.4772	0.602672	0.301336	−	0.953518i	$-0.402567\pi$
$23$	66.4772	0.602672	0.301336	+	0.953518i	$0.402567\pi$
$24$	−49.6917	−0.422637
$25$	−104.756	−0.838047
$26$	−55.0749	−0.415426
$27$	−27.0000	−0.192450
$28$	81.5221	0.550222
$29$	189.645	1.21435	0.607174	−	0.794569i	$-0.292303\pi$
$29$	189.645	1.21435	0.607174	+	0.794569i	$0.292303\pi$
$30$	−15.1717	−0.0923322
$31$	205.769	1.19217	0.596084	−	0.802922i	$-0.296723\pi$
$31$	205.769	1.19217	0.596084	+	0.802922i	$0.296723\pi$
$32$	−172.161	−0.951062
$33$	−33.0000	−0.174078
$34$	−117.036	−0.590337
$35$	54.4480	0.262954
$36$	−60.6297	−0.280693
$37$	−232.751	−1.03416	−0.517082	−	0.855936i	$-0.672982\pi$
$37$	−232.751	−1.03416	−0.517082	+	0.855936i	$0.672982\pi$
$38$	−138.339	−0.590568
$39$	−146.998	−0.603550
$40$	−74.5267	−0.294593
$41$	167.713	0.638840	0.319420	−	0.947613i	$-0.396512\pi$
$41$	167.713	0.638840	0.319420	+	0.947613i	$0.396512\pi$
$42$	−40.8055	−0.149915
$43$	−150.105	−0.532343	−0.266172	−	0.963926i	$-0.585759\pi$
$43$	−150.105	−0.532343	−0.266172	+	0.963926i	$0.585759\pi$
$44$	−74.1030	−0.253896
$45$	−40.4941	−0.134145
$46$	−74.7201	−0.239497
$47$	221.299	0.686804	0.343402	−	0.939189i	$-0.388421\pi$
$47$	221.299	0.686804	0.343402	+	0.939189i	$0.388421\pi$
$48$	−105.826	−0.318222
$49$	−196.558	−0.573056
$50$	117.745	0.333034
$51$	−312.374	−0.857669
$52$	−330.090	−0.880292
$53$	94.6410	0.245282	0.122641	−	0.992451i	$-0.460864\pi$
$53$	94.6410	0.245282	0.122641	+	0.992451i	$0.460864\pi$
$54$	30.3479	0.0764782
$55$	−49.4928	−0.121338
$56$	−200.445	−0.478314
$57$	−369.234	−0.858005
$58$	−213.160	−0.482573
$59$	−356.049	−0.785654	−0.392827	−	0.919612i	$-0.628503\pi$
$59$	−356.049	−0.785654	−0.392827	+	0.919612i	$0.628503\pi$
$60$	−90.9313	−0.195653
$61$	61.0000	0.128037
$61$	61.0000	0.128037
$62$	−231.283	−0.473759
$63$	−108.912	−0.217803
$64$	−88.6946	−0.173232
$65$	−220.464	−0.420696
$66$	37.0919	0.0691772
$67$	1080.21	1.96969	0.984843	−	0.173447i	$-0.0554905\pi$
$67$	1080.21	1.96969	0.984843	+	0.173447i	$0.0554905\pi$
$68$	−701.450	−1.25093
$69$	−199.432	−0.347953
$70$	−61.1993	−0.104496
$71$	−554.127	−0.926237	−0.463118	−	0.886296i	$-0.653270\pi$
$71$	−554.127	−0.926237	−0.463118	+	0.886296i	$0.653270\pi$
$72$	149.075	0.244010
$73$	198.531	0.318305	0.159153	−	0.987254i	$-0.449124\pi$
$73$	198.531	0.318305	0.159153	+	0.987254i	$0.449124\pi$
$74$	261.611	0.410969
$75$	314.268	0.483847
$76$	−829.132	−1.25142
$77$	−133.114	−0.197010
$78$	165.225	0.239846
$79$	910.924	1.29730	0.648651	−	0.761086i	$-0.275333\pi$
$79$	910.924	1.29730	0.648651	+	0.761086i	$0.275333\pi$
$80$	−158.716	−0.221812
$81$	81.0000	0.111111
$82$	−188.509	−0.253870
$83$	−1071.79	−1.41740	−0.708702	−	0.705508i	$-0.750719\pi$
$83$	−1071.79	−1.41740	−0.708702	+	0.705508i	$0.750719\pi$
$84$	−244.566	−0.317671
$85$	−468.493	−0.597826
$86$	168.717	0.211549
$87$	−568.934	−0.701105
$88$	182.203	0.220715
$89$	740.421	0.881848	0.440924	−	0.897544i	$-0.354651\pi$
$89$	740.421	0.881848	0.440924	+	0.897544i	$0.354651\pi$
$90$	45.5152	0.0533080
$91$	−592.955	−0.683061
$92$	−447.833	−0.507497
$93$	−617.307	−0.688298
$94$	−248.739	−0.272931
$95$	−553.771	−0.598060
$96$	516.482	0.549096
$97$	−138.866	−0.145358	−0.0726789	−	0.997355i	$-0.523155\pi$
$97$	−138.866	−0.145358	−0.0726789	+	0.997355i	$0.523155\pi$
$98$	220.931	0.227728
$99$	99.0000	0.100504
$100$	705.702	0.705702
$101$	1109.62	1.09318	0.546591	−	0.837400i	$-0.315925\pi$
$101$	1109.62	1.09318	0.546591	+	0.837400i	$0.315925\pi$
$102$	351.107	0.340831
$103$	−630.668	−0.603316	−0.301658	−	0.953416i	$-0.597540\pi$
$103$	−630.668	−0.603316	−0.301658	+	0.953416i	$0.597540\pi$
$104$	811.619	0.765248
$105$	−163.344	−0.151816
$106$	−106.376	−0.0974732
$107$	1250.30	1.12963	0.564817	−	0.825216i	$-0.308947\pi$
$107$	1250.30	1.12963	0.564817	+	0.825216i	$0.308947\pi$
$108$	181.889	0.162058
$109$	−1329.03	−1.16787	−0.583937	−	0.811799i	$-0.698488\pi$
$109$	−1329.03	−1.16787	−0.583937	+	0.811799i	$0.698488\pi$
$110$	55.6297	0.0482189
$111$	698.253	0.597075
$112$	−426.877	−0.360144
$113$	1871.48	1.55800	0.779000	−	0.627023i	$-0.215727\pi$
$113$	1871.48	1.55800	0.779000	+	0.627023i	$0.215727\pi$
$114$	415.018	0.340965
$115$	−299.104	−0.242535
$116$	−1277.57	−1.02258
$117$	440.993	0.348460
$118$	400.197	0.312213
$119$	−1260.05	−0.970657
$120$	223.580	0.170083
$121$	121.000	0.0909091
$122$	−68.5637	−0.0508809
$123$	−503.140	−0.368834
$124$	−1386.19	−1.00390
$125$	1033.75	0.739692
$126$	122.416	0.0865533
$127$	−1168.16	−0.816201	−0.408101	−	0.912937i	$-0.633809\pi$
$127$	−1168.16	−0.816201	−0.408101	+	0.912937i	$0.633809\pi$
$128$	1476.98	1.01990
$129$	450.314	0.307349
$130$	247.801	0.167181
$131$	294.525	0.196433	0.0982165	−	0.995165i	$-0.468686\pi$
$131$	294.525	0.196433	0.0982165	+	0.995165i	$0.468686\pi$
$132$	222.309	0.146587
$133$	−1489.41	−0.971037
$134$	−1214.15	−0.782739
$135$	121.482	0.0774484
$136$	1724.71	1.08745
$137$	1446.24	0.901901	0.450951	−	0.892549i	$-0.351085\pi$
$137$	1446.24	0.901901	0.450951	+	0.892549i	$0.351085\pi$
$138$	224.160	0.138274
$139$	−817.717	−0.498977	−0.249489	−	0.968378i	$-0.580263\pi$
$139$	−817.717	−0.498977	−0.249489	+	0.968378i	$0.580263\pi$
$140$	−366.796	−0.221428
$141$	−663.897	−0.396527
$142$	622.837	0.368080
$143$	538.991	0.315194
$144$	317.478	0.183726
$145$	−853.276	−0.488695
$146$	−223.148	−0.126492
$147$	589.675	0.330854
$148$	1567.96	0.870848
$149$	−1834.18	−1.00847	−0.504234	−	0.863567i	$-0.668225\pi$
$149$	−1834.18	−1.00847	−0.504234	+	0.863567i	$0.668225\pi$
$150$	−353.236	−0.192277
$151$	−1547.94	−0.834234	−0.417117	−	0.908853i	$-0.636960\pi$
$151$	−1547.94	−0.834234	−0.417117	+	0.908853i	$0.636960\pi$
$152$	2038.66	1.08787
$153$	937.123	0.495176
$154$	149.620	0.0782904
$155$	−925.825	−0.479768
$156$	990.269	0.508237
$157$	−104.599	−0.0531713	−0.0265857	−	0.999647i	$-0.508463\pi$
$157$	−104.599	−0.0531713	−0.0265857	+	0.999647i	$0.508463\pi$
$158$	−1023.87	−0.515538
$159$	−283.923	−0.141614
$160$	774.610	0.382739
$161$	−804.461	−0.393791
$162$	−91.0437	−0.0441547
$163$	2273.97	1.09271	0.546353	−	0.837555i	$-0.316016\pi$
$163$	2273.97	1.09271	0.546353	+	0.837555i	$0.316016\pi$
$164$	−1129.82	−0.537954
$165$	148.478	0.0700547
$166$	1204.69	0.563266
$167$	−1510.29	−0.699818	−0.349909	−	0.936784i	$-0.613788\pi$
$167$	−1510.29	−0.699818	−0.349909	+	0.936784i	$0.613788\pi$
$168$	601.335	0.276155
$169$	203.922	0.0928184
$170$	526.584	0.237572
$171$	1107.70	0.495369
$172$	1011.20	0.448275
$173$	1858.47	0.816746	0.408373	−	0.912815i	$-0.366096\pi$
$173$	1858.47	0.816746	0.408373	+	0.912815i	$0.366096\pi$
$174$	639.479	0.278614
$175$	1267.68	0.547588
$176$	388.028	0.166186
$177$	1068.15	0.453598
$178$	−832.230	−0.350440
$179$	1906.75	0.796185	0.398092	−	0.917345i	$-0.369672\pi$
$179$	1906.75	0.796185	0.398092	+	0.917345i	$0.369672\pi$
$180$	272.794	0.112960
$181$	−2896.36	−1.18942	−0.594709	−	0.803941i	$-0.702733\pi$
$181$	−2896.36	−1.18942	−0.594709	+	0.803941i	$0.702733\pi$
$182$	666.478	0.271443
$183$	−183.000	−0.0739221
$184$	1101.12	0.441173
$185$	1047.23	0.416182
$186$	693.850	0.273525
$187$	1145.37	0.447903
$188$	−1490.81	−0.578343
$189$	326.735	0.125749
$190$	622.436	0.237664
$191$	−3205.41	−1.21432	−0.607161	−	0.794579i	$-0.707692\pi$
$191$	−3205.41	−1.21432	−0.607161	+	0.794579i	$0.707692\pi$
$192$	266.084	0.100015
$193$	−1024.23	−0.381997	−0.190998	−	0.981590i	$-0.561172\pi$
$193$	−1024.23	−0.381997	−0.190998	+	0.981590i	$0.561172\pi$
$194$	156.085	0.0577641
$195$	661.393	0.242889
$196$	1324.14	0.482559
$197$	−2125.67	−0.768771	−0.384385	−	0.923173i	$-0.625587\pi$
$197$	−2125.67	−0.768771	−0.384385	+	0.923173i	$0.625587\pi$
$198$	−111.276	−0.0399395
$199$	−1473.17	−0.524776	−0.262388	−	0.964962i	$-0.584510\pi$
$199$	−1473.17	−0.524776	−0.262388	+	0.964962i	$0.584510\pi$
$200$	−1735.17	−0.613474
$201$	−3240.64	−1.13720
$202$	−1247.21	−0.434422
$203$	−2294.95	−0.793467
$204$	2104.35	0.722226
$205$	−754.600	−0.257091
$206$	708.868	0.239753
$207$	598.295	0.200891
$208$	1728.46	0.576189
$209$	1353.86	0.448078
$210$	183.598	0.0603307
$211$	38.7363	0.0126385	0.00631923	−	0.999980i	$-0.497989\pi$
$211$	38.7363	0.0126385	0.00631923	+	0.999980i	$0.497989\pi$
$212$	−637.561	−0.206547
$213$	1662.38	0.534763
$214$	−1405.33	−0.448909
$215$	675.373	0.214233
$216$	−447.226	−0.140879
$217$	−2490.07	−0.778973
$218$	1493.83	0.464104
$219$	−595.592	−0.183774
$220$	333.415	0.102176
$221$	5102.03	1.55294
$222$	−784.834	−0.237273
$223$	6167.19	1.85195	0.925976	−	0.377582i	$-0.123244\pi$
$223$	6167.19	1.85195	0.925976	+	0.377582i	$0.123244\pi$
$224$	2083.37	0.621433
$225$	−942.803	−0.279349
$226$	−2103.54	−0.619138
$227$	1640.97	0.479803	0.239902	−	0.970797i	$-0.422885\pi$
$227$	1640.97	0.479803	0.239902	+	0.970797i	$0.422885\pi$
$228$	2487.40	0.722508
$229$	5165.48	1.49059	0.745294	−	0.666736i	$-0.232309\pi$
$229$	5165.48	1.49059	0.745294	+	0.666736i	$0.232309\pi$
$230$	336.191	0.0963818
$231$	399.343	0.113744
$232$	3141.26	0.888938
$233$	3543.23	0.996244	0.498122	−	0.867107i	$-0.334023\pi$
$233$	3543.23	0.996244	0.498122	+	0.867107i	$0.334023\pi$
$234$	−495.674	−0.138475
$235$	−995.701	−0.276393
$236$	2398.57	0.661583
$237$	−2732.77	−0.748998
$238$	1416.29	0.385732
$239$	−3488.59	−0.944176	−0.472088	−	0.881552i	$-0.656499\pi$
$239$	−3488.59	−0.944176	−0.472088	+	0.881552i	$0.656499\pi$
$240$	476.147	0.128063
$241$	−2425.83	−0.648389	−0.324195	−	0.945990i	$-0.605093\pi$
$241$	−2425.83	−0.648389	−0.324195	+	0.945990i	$0.605093\pi$
$242$	−136.003	−0.0361266
$243$	−243.000	−0.0641500
$244$	−410.935	−0.107817
$245$	884.383	0.230617
$246$	565.527	0.146572
$247$	6030.73	1.55355
$248$	3408.34	0.872701
$249$	3215.38	0.818339
$250$	−1161.93	−0.293948
$251$	5689.34	1.43071	0.715355	−	0.698761i	$-0.246265\pi$
$251$	5689.34	1.43071	0.715355	+	0.698761i	$0.246265\pi$
$252$	733.699	0.183407
$253$	731.249	0.181712
$254$	1313.01	0.324352
$255$	1405.48	0.345155
$256$	−950.559	−0.232070
$257$	−6565.59	−1.59358	−0.796790	−	0.604256i	$-0.793470\pi$
$257$	−6565.59	−1.59358	−0.796790	+	0.604256i	$0.793470\pi$
$258$	−506.151	−0.122138
$259$	2816.59	0.675732
$260$	1485.19	0.354259
$261$	1706.80	0.404783
$262$	−331.044	−0.0780610
$263$	2782.22	0.652315	0.326158	−	0.945315i	$-0.394246\pi$
$263$	2782.22	0.652315	0.326158	+	0.945315i	$0.394246\pi$
$264$	−546.609	−0.127430
$265$	−425.822	−0.0987096
$266$	1674.09	0.385883
$267$	−2221.26	−0.509135
$268$	−7277.00	−1.65863
$269$	1581.24	0.358401	0.179201	−	0.983813i	$-0.442649\pi$
$269$	1581.24	0.358401	0.179201	+	0.983813i	$0.442649\pi$
$270$	−136.546	−0.0307774
$271$	3922.88	0.879329	0.439664	−	0.898162i	$-0.355097\pi$
$271$	3922.88	0.879329	0.439664	+	0.898162i	$0.355097\pi$
$272$	3673.03	0.818788
$273$	1778.86	0.394365
$274$	−1625.57	−0.358409
$275$	−1152.31	−0.252681
$276$	1343.50	0.293004
$277$	2809.99	0.609516	0.304758	−	0.952430i	$-0.401424\pi$
$277$	2809.99	0.609516	0.304758	+	0.952430i	$0.401424\pi$
$278$	919.111	0.198290
$279$	1851.92	0.397389
$280$	901.871	0.192490
$281$	−167.178	−0.0354911	−0.0177456	−	0.999843i	$-0.505649\pi$
$281$	−167.178	−0.0354911	−0.0177456	+	0.999843i	$0.505649\pi$
$282$	746.218	0.157577
$283$	−4675.52	−0.982087	−0.491043	−	0.871135i	$-0.663384\pi$
$283$	−4675.52	−0.982087	−0.491043	+	0.871135i	$0.663384\pi$
$284$	3732.95	0.779965
$285$	1661.31	0.345290
$286$	−605.824	−0.125256
$287$	−2029.55	−0.417424
$288$	−1549.45	−0.317021
$289$	5928.96	1.20679
$290$	959.079	0.194204
$291$	416.598	0.0839224
$292$	−1337.43	−0.268038
$293$	−3848.97	−0.767438	−0.383719	−	0.923450i	$-0.625357\pi$
$293$	−3848.97	−0.767438	−0.383719	+	0.923450i	$0.625357\pi$
$294$	−662.792	−0.131479
$295$	1601.99	0.316174
$296$	−3855.27	−0.757037
$297$	−297.000	−0.0580259
$298$	2061.61	0.400758
$299$	3257.33	0.630021
$300$	−2117.11	−0.407437
$301$	1816.46	0.347838
$302$	1739.88	0.331519
$303$	−3328.86	−0.631149
$304$	4341.62	0.819108
$305$	−274.460	−0.0515263
$306$	−1053.32	−0.196779
$307$	6970.45	1.29584	0.647922	−	0.761706i	$-0.275638\pi$
$307$	6970.45	1.29584	0.647922	+	0.761706i	$0.275638\pi$
$308$	896.743	0.165898
$309$	1892.00	0.348325
$310$	1040.62	0.190656
$311$	−8302.27	−1.51376	−0.756878	−	0.653556i	$-0.773276\pi$
$311$	−8302.27	−1.51376	−0.756878	+	0.653556i	$0.773276\pi$
$312$	−2434.86	−0.441816
$313$	−8630.72	−1.55858	−0.779292	−	0.626661i	$-0.784421\pi$
$313$	−8630.72	−1.55858	−0.779292	+	0.626661i	$0.784421\pi$
$314$	117.569	0.0211299
$315$	490.032	0.0876513
$316$	−6136.56	−1.09243
$317$	−10663.0	−1.88925	−0.944625	−	0.328151i	$-0.893574\pi$
$317$	−10663.0	−1.88925	−0.944625	+	0.328151i	$0.893574\pi$
$318$	319.128	0.0562761
$319$	2086.09	0.366140
$320$	399.067	0.0697142
$321$	−3750.90	−0.652195
$322$	904.211	0.156490
$323$	12815.5	2.20765
$324$	−545.667	−0.0935644
$325$	−5132.96	−0.876077
$326$	−2555.93	−0.434233
$327$	3987.10	0.674272
$328$	2777.99	0.467649
$329$	−2678.01	−0.448764
$330$	−166.889	−0.0278392
$331$	1585.40	0.263267	0.131634	−	0.991298i	$-0.457978\pi$
$331$	1585.40	0.263267	0.131634	+	0.991298i	$0.457978\pi$
$332$	7220.27	1.19357
$333$	−2094.76	−0.344721
$334$	1697.56	0.278103
$335$	−4860.25	−0.792668
$336$	1280.63	0.207929
$337$	5351.01	0.864950	0.432475	−	0.901646i	$-0.357640\pi$
$337$	5351.01	0.864950	0.432475	+	0.901646i	$0.357640\pi$
$338$	−229.207	−0.0368853
$339$	−5614.44	−0.899512
$340$	3156.07	0.503417
$341$	2263.46	0.359452
$342$	−1245.05	−0.196856
$343$	6529.36	1.02785
$344$	−2486.32	−0.389690
$345$	897.311	0.140028
$346$	−2088.91	−0.324569
$347$	−9719.12	−1.50360	−0.751801	−	0.659391i	$-0.770814\pi$
$347$	−9719.12	−1.50360	−0.751801	+	0.659391i	$0.770814\pi$
$348$	3832.70	0.590386
$349$	3420.26	0.524592	0.262296	−	0.964988i	$-0.415520\pi$
$349$	3420.26	0.524592	0.262296	+	0.964988i	$0.415520\pi$
$350$	−1424.87	−0.217607
$351$	−1322.98	−0.201183
$352$	−1893.77	−0.286756
$353$	−10831.8	−1.63320	−0.816601	−	0.577202i	$-0.804145\pi$
$353$	−10831.8	−1.63320	−0.816601	+	0.577202i	$0.804145\pi$
$354$	−1200.59	−0.180256
$355$	2493.21	0.372749
$356$	−4987.95	−0.742586
$357$	3780.14	0.560409
$358$	−2143.18	−0.316398
$359$	−3812.62	−0.560508	−0.280254	−	0.959926i	$-0.590419\pi$
$359$	−3812.62	−0.560508	−0.280254	+	0.959926i	$0.590419\pi$
$360$	−670.741	−0.0981976
$361$	8289.22	1.20852
$362$	3255.50	0.472666
$363$	−363.000	−0.0524864
$364$	3994.52	0.575191
$365$	−893.258	−0.128097
$366$	205.691	0.0293761
$367$	−2974.66	−0.423096	−0.211548	−	0.977368i	$-0.567850\pi$
$367$	−2974.66	−0.423096	−0.211548	+	0.977368i	$0.567850\pi$
$368$	2345.00	0.332179
$369$	1509.42	0.212947
$370$	−1177.08	−0.165388
$371$	−1145.28	−0.160269
$372$	4158.57	0.579602
$373$	4357.43	0.604878	0.302439	−	0.953169i	$-0.402199\pi$
$373$	4357.43	0.604878	0.302439	+	0.953169i	$0.402199\pi$
$374$	−1287.39	−0.177993
$375$	−3101.25	−0.427061
$376$	3665.58	0.502760
$377$	9292.43	1.26946
$378$	−367.249	−0.0499716
$379$	5721.86	0.775494	0.387747	−	0.921766i	$-0.373254\pi$
$379$	5721.86	0.775494	0.387747	+	0.921766i	$0.373254\pi$
$380$	3730.55	0.503614
$381$	3504.49	0.471234
$382$	3602.87	0.482563
$383$	7709.17	1.02851	0.514256	−	0.857637i	$-0.328068\pi$
$383$	7709.17	1.02851	0.514256	+	0.857637i	$0.328068\pi$
$384$	−4430.93	−0.588841
$385$	598.927	0.0792836
$386$	1151.22	0.151803
$387$	−1350.94	−0.177448
$388$	935.490	0.122403
$389$	5153.07	0.671648	0.335824	−	0.941925i	$-0.390985\pi$
$389$	5153.07	0.671648	0.335824	+	0.941925i	$0.390985\pi$
$390$	−743.403	−0.0965222
$391$	6921.92	0.895286
$392$	−3255.77	−0.419494
$393$	−883.574	−0.113411
$394$	2389.25	0.305504
$395$	−4098.56	−0.522078
$396$	−666.927	−0.0846321
$397$	−6934.78	−0.876691	−0.438346	−	0.898806i	$-0.644435\pi$
$397$	−6934.78	−0.876691	−0.438346	+	0.898806i	$0.644435\pi$
$398$	1655.84	0.208542
$399$	4468.22	0.560628
$400$	−3695.30	−0.461912
$401$	10595.2	1.31945	0.659723	−	0.751509i	$-0.270674\pi$
$401$	10595.2	1.31945	0.659723	+	0.751509i	$0.270674\pi$
$402$	3642.46	0.451914
$403$	10082.5	1.24627
$404$	−7475.11	−0.920546
$405$	−364.447	−0.0447148
$406$	2579.51	0.315318
$407$	−2560.26	−0.311812
$408$	−5174.14	−0.627839
$409$	7313.25	0.884148	0.442074	−	0.896978i	$-0.354243\pi$
$409$	7313.25	0.884148	0.442074	+	0.896978i	$0.354243\pi$
$410$	848.168	0.102166
$411$	−4338.72	−0.520713
$412$	4248.58	0.508040
$413$	4308.66	0.513354
$414$	−672.481	−0.0798324
$415$	4822.36	0.570411
$416$	−8435.73	−0.994221
$417$	2453.15	0.288085
$418$	−1521.73	−0.178063
$419$	4998.22	0.582766	0.291383	−	0.956606i	$-0.405885\pi$
$419$	4998.22	0.582766	0.291383	+	0.956606i	$0.405885\pi$
$420$	1100.39	0.127841
$421$	5357.88	0.620254	0.310127	−	0.950695i	$-0.399628\pi$
$421$	5357.88	0.620254	0.310127	+	0.950695i	$0.399628\pi$
$422$	−43.5394	−0.00502243
$423$	1991.69	0.228935
$424$	1567.62	0.179553
$425$	−10907.7	−1.24494
$426$	−1868.51	−0.212511
$427$	−738.180	−0.0836605
$428$	−8422.80	−0.951242
$429$	−1616.97	−0.181977
$430$	−759.116	−0.0851345
$431$	4607.15	0.514892	0.257446	−	0.966293i	$-0.417119\pi$
$431$	4607.15	0.514892	0.257446	+	0.966293i	$0.417119\pi$
$432$	−952.433	−0.106074
$433$	2697.96	0.299435	0.149718	−	0.988729i	$-0.452164\pi$
$433$	2697.96	0.299435	0.149718	+	0.988729i	$0.452164\pi$
$434$	2798.83	0.309558
$435$	2559.83	0.282148
$436$	8953.20	0.983442
$437$	8181.89	0.895636
$438$	669.443	0.0730302
$439$	1753.30	0.190616	0.0953081	−	0.995448i	$-0.469616\pi$
$439$	1753.30	0.190616	0.0953081	+	0.995448i	$0.469616\pi$
$440$	−819.794	−0.0888231
$441$	−1769.02	−0.191019
$442$	−5734.66	−0.617127
$443$	1796.85	0.192711	0.0963555	−	0.995347i	$-0.469281\pi$
$443$	1796.85	0.192711	0.0963555	+	0.995347i	$0.469281\pi$
$444$	−4703.88	−0.502784
$445$	−3331.41	−0.354885
$446$	−6931.89	−0.735952
$447$	5502.54	0.582240
$448$	1073.32	0.113191
$449$	13895.6	1.46052	0.730259	−	0.683171i	$-0.239400\pi$
$449$	13895.6	1.46052	0.730259	+	0.683171i	$0.239400\pi$
$450$	1059.71	0.111011
$451$	1844.85	0.192617
$452$	−12607.5	−1.31196
$453$	4643.81	0.481645
$454$	−1844.45	−0.190670
$455$	2667.91	0.274887
$456$	−6115.97	−0.628084
$457$	−10973.0	−1.12318	−0.561592	−	0.827414i	$-0.689811\pi$
$457$	−10973.0	−1.12318	−0.561592	+	0.827414i	$0.689811\pi$
$458$	−5805.98	−0.592348
$459$	−2811.37	−0.285890
$460$	2014.95	0.204234
$461$	−3139.99	−0.317232	−0.158616	−	0.987340i	$-0.550703\pi$
$461$	−3139.99	−0.317232	−0.158616	+	0.987340i	$0.550703\pi$
$462$	−448.860	−0.0452010
$463$	15062.1	1.51187	0.755935	−	0.654647i	$-0.227183\pi$
$463$	15062.1	1.51187	0.755935	+	0.654647i	$0.227183\pi$
$464$	6689.77	0.669320
$465$	2777.48	0.276994
$466$	−3982.58	−0.395900
$467$	−9716.27	−0.962774	−0.481387	−	0.876508i	$-0.659867\pi$
$467$	−9716.27	−0.962774	−0.481387	+	0.876508i	$0.659867\pi$
$468$	−2970.81	−0.293431
$469$	−13072.0	−1.28701
$470$	1119.16	0.109837
$471$	313.797	0.0306985
$472$	−5897.56	−0.575121
$473$	−1651.15	−0.160508
$474$	3071.62	0.297646
$475$	−12893.2	−1.24543
$476$	8488.47	0.817370
$477$	851.769	0.0817606
$478$	3921.16	0.375208
$479$	4094.89	0.390606	0.195303	−	0.980743i	$-0.437431\pi$
$479$	4094.89	0.390606	0.195303	+	0.980743i	$0.437431\pi$
$480$	−2323.83	−0.220975
$481$	−11404.6	−1.08109
$482$	2726.63	0.257665
$483$	2413.38	0.227356
$484$	−815.133	−0.0765527
$485$	624.806	0.0584969
$486$	273.131	0.0254927
$487$	18988.2	1.76681	0.883406	−	0.468608i	$-0.155244\pi$
$487$	18988.2	1.76681	0.883406	+	0.468608i	$0.155244\pi$
$488$	1010.40	0.0937266
$489$	−6821.91	−0.630874
$490$	−994.043	−0.0916455
$491$	−21300.1	−1.95776	−0.978880	−	0.204437i	$-0.934464\pi$
$491$	−21300.1	−1.95776	−0.978880	+	0.204437i	$0.934464\pi$
$492$	3389.47	0.310588
$493$	19746.7	1.80395
$494$	−6778.51	−0.617368
$495$	−445.435	−0.0404461
$496$	7258.56	0.657095
$497$	6705.67	0.605212
$498$	−3614.07	−0.325202
$499$	−8155.67	−0.731659	−0.365830	−	0.930682i	$-0.619215\pi$
$499$	−8155.67	−0.731659	−0.365830	+	0.930682i	$0.619215\pi$
$500$	−6964.00	−0.622879
$501$	4530.87	0.404040
$502$	−6394.80	−0.568553
$503$	5048.58	0.447525	0.223762	−	0.974644i	$-0.428166\pi$
$503$	5048.58	0.447525	0.223762	+	0.974644i	$0.428166\pi$
$504$	−1804.01	−0.159438
$505$	−4992.56	−0.439933
$506$	−821.921	−0.0722112
$507$	−611.766	−0.0535887
$508$	7869.48	0.687306
$509$	−10256.8	−0.893172	−0.446586	−	0.894741i	$-0.647360\pi$
$509$	−10256.8	−0.893172	−0.446586	+	0.894741i	$0.647360\pi$
$510$	−1579.75	−0.137162
$511$	−2402.48	−0.207984
$512$	−10747.4	−0.927680
$513$	−3323.11	−0.286002
$514$	7379.70	0.633277
$515$	2837.59	0.242795
$516$	−3033.60	−0.258812
$517$	2434.29	0.207079
$518$	−3165.84	−0.268531
$519$	−5575.42	−0.471548
$520$	−3651.75	−0.307961
$521$	−16427.3	−1.38137	−0.690683	−	0.723158i	$-0.742690\pi$
$521$	−16427.3	−1.38137	−0.690683	+	0.723158i	$0.742690\pi$
$522$	−1918.44	−0.160858
$523$	3251.21	0.271827	0.135914	−	0.990721i	$-0.456603\pi$
$523$	3251.21	0.271827	0.135914	+	0.990721i	$0.456603\pi$
$524$	−1984.10	−0.165412
$525$	−3803.05	−0.316150
$526$	−3127.20	−0.259225
$527$	21425.6	1.77100
$528$	−1164.08	−0.0959475
$529$	−7747.78	−0.636787
$530$	478.622	0.0392265
$531$	−3204.44	−0.261885
$532$	10033.6	0.817690
$533$	8217.82	0.667830
$534$	2496.69	0.202327
$535$	−5625.52	−0.454603
$536$	17892.6	1.44187
$537$	−5720.25	−0.459678
$538$	−1777.31	−0.142426
$539$	−2162.14	−0.172783
$540$	−818.382	−0.0652177
$541$	−1955.42	−0.155398	−0.0776989	−	0.996977i	$-0.524757\pi$
$541$	−1955.42	−0.155398	−0.0776989	+	0.996977i	$0.524757\pi$
$542$	−4409.30	−0.349439
$543$	8689.08	0.686711
$544$	−17926.2	−1.41283
$545$	5979.77	0.469991
$546$	−1999.44	−0.156718
$547$	12947.5	1.01205	0.506027	−	0.862517i	$-0.331113\pi$
$547$	12947.5	1.01205	0.506027	+	0.862517i	$0.331113\pi$
$548$	−9742.78	−0.759472
$549$	549.000	0.0426790
$550$	1295.20	0.100413
$551$	23341.1	1.80465
$552$	−3303.37	−0.254711
$553$	−11023.4	−0.847670
$554$	−3158.42	−0.242217
$555$	−3141.68	−0.240283
$556$	5508.66	0.420179
$557$	455.695	0.0346650	0.0173325	−	0.999850i	$-0.494483\pi$
$557$	455.695	0.0346650	0.0173325	+	0.999850i	$0.494483\pi$
$558$	−2081.55	−0.157920
$559$	−7355.01	−0.556501
$560$	1920.67	0.144934
$561$	−3436.12	−0.258597
$562$	187.907	0.0141039
$563$	151.235	0.0113211	0.00566057	−	0.999984i	$-0.498198\pi$
$563$	151.235	0.0113211	0.00566057	+	0.999984i	$0.498198\pi$
$564$	4472.43	0.333907
$565$	−8420.44	−0.626992
$566$	5255.26	0.390274
$567$	−980.206	−0.0726010
$568$	−9178.52	−0.678032
$569$	−14567.0	−1.07325	−0.536627	−	0.843820i	$-0.680302\pi$
$569$	−14567.0	−1.07325	−0.536627	+	0.843820i	$0.680302\pi$
$570$	−1867.31	−0.137216
$571$	23626.7	1.73160	0.865802	−	0.500387i	$-0.166809\pi$
$571$	23626.7	1.73160	0.865802	+	0.500387i	$0.166809\pi$
$572$	−3630.99	−0.265418
$573$	9616.24	0.701089
$574$	2281.21	0.165881
$575$	−6963.88	−0.505068
$576$	−798.251	−0.0577439
$577$	18253.6	1.31700	0.658499	−	0.752581i	$-0.271192\pi$
$577$	18253.6	1.31700	0.658499	+	0.752581i	$0.271192\pi$
$578$	−6664.13	−0.479570
$579$	3072.68	0.220546
$580$	5748.21	0.411520
$581$	12970.1	0.926145
$582$	−468.255	−0.0333501
$583$	1041.05	0.0739552
$584$	3288.45	0.233008
$585$	−1984.18	−0.140232
$586$	4326.23	0.304974
$587$	−24168.2	−1.69936	−0.849682	−	0.527295i	$-0.823206\pi$
$587$	−24168.2	−1.69936	−0.849682	+	0.527295i	$0.823206\pi$
$588$	−3972.42	−0.278605
$589$	25325.7	1.77169
$590$	−1800.63	−0.125645
$591$	6377.01	0.443850
$592$	−8210.37	−0.570007
$593$	−21690.1	−1.50204	−0.751018	−	0.660282i	$-0.770437\pi$
$593$	−21690.1	−1.50204	−0.751018	+	0.660282i	$0.770437\pi$
$594$	333.827	0.0230591
$595$	5669.38	0.390625
$596$	12356.2	0.849211
$597$	4419.52	0.302980
$598$	−3661.23	−0.250366
$599$	13481.8	0.919618	0.459809	−	0.888018i	$-0.347918\pi$
$599$	13481.8	0.919618	0.459809	+	0.888018i	$0.347918\pi$
$600$	5205.50	0.354190
$601$	15565.6	1.05646	0.528230	−	0.849101i	$-0.322856\pi$
$601$	15565.6	1.05646	0.528230	+	0.849101i	$0.322856\pi$
$602$	−2041.70	−0.138228
$603$	9721.91	0.656562
$604$	10427.9	0.702491
$605$	−544.421	−0.0365849
$606$	3741.63	0.250814
$607$	−20781.8	−1.38963	−0.694817	−	0.719186i	$-0.744515\pi$
$607$	−20781.8	−1.38963	−0.694817	+	0.719186i	$0.744515\pi$
$608$	−21189.2	−1.41338
$609$	6884.84	0.458108
$610$	308.492	0.0204762
$611$	10843.5	0.717971
$612$	−6313.05	−0.416977
$613$	−10628.1	−0.700267	−0.350133	−	0.936700i	$-0.613864\pi$
$613$	−10628.1	−0.700267	−0.350133	+	0.936700i	$0.613864\pi$
$614$	−7834.75	−0.514959
$615$	2263.80	0.148431
$616$	−2204.90	−0.144217
$617$	−13523.5	−0.882394	−0.441197	−	0.897410i	$-0.645446\pi$
$617$	−13523.5	−0.882394	−0.441197	+	0.897410i	$0.645446\pi$
$618$	−2126.60	−0.138422
$619$	6748.92	0.438226	0.219113	−	0.975699i	$-0.429684\pi$
$619$	6748.92	0.438226	0.219113	+	0.975699i	$0.429684\pi$
$620$	6236.95	0.404003
$621$	−1794.88	−0.115984
$622$	9331.71	0.601556
$623$	−8960.06	−0.576208
$624$	−5185.38	−0.332663
$625$	8443.29	0.540370
$626$	9700.89	0.619370
$627$	−4061.58	−0.258698
$628$	704.644	0.0447745
$629$	−24235.2	−1.53628
$630$	−550.793	−0.0348320
$631$	12019.3	0.758287	0.379143	−	0.925338i	$-0.376219\pi$
$631$	12019.3	0.758287	0.379143	+	0.925338i	$0.376219\pi$
$632$	15088.5	0.949663
$633$	−116.209	−0.00729682
$634$	11985.1	0.750774
$635$	5255.96	0.328467
$636$	1912.68	0.119250
$637$	−9631.20	−0.599061
$638$	−2344.76	−0.145501
$639$	−4987.15	−0.308746
$640$	−6645.43	−0.410443
$641$	−1182.76	−0.0728801	−0.0364400	−	0.999336i	$-0.511602\pi$
$641$	−1182.76	−0.0728801	−0.0364400	+	0.999336i	$0.511602\pi$
$642$	4215.99	0.259177
$643$	10026.8	0.614957	0.307479	−	0.951555i	$-0.400515\pi$
$643$	10026.8	0.614957	0.307479	+	0.951555i	$0.400515\pi$
$644$	5419.36	0.331604
$645$	−2026.12	−0.123687
$646$	−14404.5	−0.877305
$647$	14780.4	0.898111	0.449055	−	0.893504i	$-0.351761\pi$
$647$	14780.4	0.898111	0.449055	+	0.893504i	$0.351761\pi$
$648$	1341.68	0.0813365
$649$	−3916.54	−0.236884
$650$	5769.42	0.348147
$651$	7470.22	0.449741
$652$	−15318.9	−0.920145
$653$	26165.0	1.56802	0.784008	−	0.620751i	$-0.213172\pi$
$653$	26165.0	1.56802	0.784008	+	0.620751i	$0.213172\pi$
$654$	−4481.48	−0.267951
$655$	−1325.17	−0.0790513
$656$	5916.14	0.352114
$657$	1786.78	0.106102
$658$	3010.07	0.178336
$659$	−23007.2	−1.35999	−0.679994	−	0.733218i	$-0.738017\pi$
$659$	−23007.2	−1.35999	−0.679994	+	0.733218i	$0.738017\pi$
$660$	−1000.24	−0.0589916
$661$	2721.90	0.160166	0.0800828	−	0.996788i	$-0.474482\pi$
$661$	2721.90	0.160166	0.0800828	+	0.996788i	$0.474482\pi$
$662$	−1781.98	−0.104621
$663$	−15306.1	−0.896590
$664$	−17753.1	−1.03758
$665$	6701.35	0.390778
$666$	2354.50	0.136990
$667$	12607.0	0.731854
$668$	10174.3	0.589302
$669$	−18501.6	−1.06923
$670$	5462.90	0.315000
$671$	671.000	0.0386046
$672$	−6250.11	−0.358784
$673$	−14861.9	−0.851241	−0.425621	−	0.904902i	$-0.639944\pi$
$673$	−14861.9	−0.851241	−0.425621	+	0.904902i	$0.639944\pi$
$674$	−6014.52	−0.343725
$675$	2828.41	0.161282
$676$	−1373.75	−0.0781604
$677$	−24726.1	−1.40369	−0.701847	−	0.712327i	$-0.747641\pi$
$677$	−24726.1	−1.40369	−0.701847	+	0.712327i	$0.747641\pi$
$678$	6310.61	0.357459
$679$	1680.46	0.0949782
$680$	−7760.08	−0.437626
$681$	−4922.92	−0.277014
$682$	−2544.12	−0.142844
$683$	33171.5	1.85838	0.929190	−	0.369603i	$-0.120506\pi$
$683$	33171.5	1.85838	0.929190	+	0.369603i	$0.120506\pi$
$684$	−7462.19	−0.417140
$685$	−6507.12	−0.362955
$686$	−7338.98	−0.408460
$687$	−15496.4	−0.860591
$688$	−5294.99	−0.293415
$689$	4637.33	0.256413
$690$	−1008.57	−0.0556460
$691$	−34806.0	−1.91618	−0.958091	−	0.286464i	$-0.907520\pi$
$691$	−34806.0	−1.91618	−0.958091	+	0.286464i	$0.907520\pi$
$692$	−12519.8	−0.687765
$693$	−1198.03	−0.0656701
$694$	10924.2	0.597520
$695$	3679.19	0.200805
$696$	−9423.77	−0.513229
$697$	17463.1	0.949014
$698$	−3844.36	−0.208469
$699$	−10629.7	−0.575182
$700$	−8539.92	−0.461112
$701$	8218.98	0.442834	0.221417	−	0.975179i	$-0.428932\pi$
$701$	8218.98	0.442834	0.221417	+	0.975179i	$0.428932\pi$
$702$	1487.02	0.0799488
$703$	−28646.6	−1.53688
$704$	−975.640	−0.0522313
$705$	2987.10	0.159576
$706$	12174.9	0.649023
$707$	−13427.9	−0.714295
$708$	−7195.71	−0.381965
$709$	−2975.51	−0.157613	−0.0788066	−	0.996890i	$-0.525111\pi$
$709$	−2975.51	−0.157613	−0.0788066	+	0.996890i	$0.525111\pi$
$710$	−2802.36	−0.148128
$711$	8198.31	0.432434
$712$	12264.3	0.645538
$713$	13678.9	0.718486
$714$	−4248.86	−0.222702
$715$	−2425.11	−0.126845
$716$	−12845.1	−0.670451
$717$	10465.8	0.545120
$718$	4285.37	0.222742
$719$	10860.3	0.563311	0.281656	−	0.959516i	$-0.409116\pi$
$719$	10860.3	0.563311	0.281656	+	0.959516i	$0.409116\pi$
$720$	−1428.44	−0.0739373
$721$	7631.91	0.394212
$722$	−9317.05	−0.480256
$723$	7277.50	0.374348
$724$	19511.7	1.00158
$725$	−19866.4	−1.01768
$726$	408.010	0.0208577
$727$	33028.8	1.68497	0.842484	−	0.538722i	$-0.181093\pi$
$727$	33028.8	1.68497	0.842484	+	0.538722i	$0.181093\pi$
$728$	−9821.65	−0.500020
$729$	729.000	0.0370370
$730$	1004.02	0.0509047
$731$	−15629.6	−0.790810
$732$	1232.80	0.0622483
$733$	−30645.4	−1.54422	−0.772110	−	0.635489i	$-0.780798\pi$
$733$	−30645.4	−1.54422	−0.772110	+	0.635489i	$0.780798\pi$
$734$	3343.51	0.168135
$735$	−2653.15	−0.133147
$736$	−11444.8	−0.573178
$737$	11882.3	0.593883
$738$	−1696.58	−0.0846234
$739$	30750.3	1.53067	0.765336	−	0.643631i	$-0.222573\pi$
$739$	30750.3	1.53067	0.765336	+	0.643631i	$0.222573\pi$
$740$	−7054.79	−0.350458
$741$	−18092.2	−0.896941
$742$	1287.29	0.0636899
$743$	−2850.14	−0.140729	−0.0703645	−	0.997521i	$-0.522416\pi$
$743$	−2850.14	−0.140729	−0.0703645	+	0.997521i	$0.522416\pi$
$744$	−10225.0	−0.503854
$745$	8252.61	0.405842
$746$	−4897.74	−0.240374
$747$	−9646.13	−0.472468
$748$	−7715.95	−0.377170
$749$	−15130.3	−0.738114
$750$	3485.79	0.169711
$751$	4328.53	0.210320	0.105160	−	0.994455i	$-0.466465\pi$
$751$	4328.53	0.210320	0.105160	+	0.994455i	$0.466465\pi$
$752$	7806.39	0.378550
$753$	−17068.0	−0.826021
$754$	−10444.7	−0.504472
$755$	6964.70	0.335724
$756$	−2201.10	−0.105890
$757$	26270.4	1.26131	0.630656	−	0.776063i	$-0.282786\pi$
$757$	26270.4	1.26131	0.630656	+	0.776063i	$0.282786\pi$
$758$	−6431.34	−0.308175
$759$	−2193.75	−0.104912
$760$	−9172.61	−0.437797
$761$	−19741.7	−0.940390	−0.470195	−	0.882562i	$-0.655816\pi$
$761$	−19741.7	−0.940390	−0.470195	+	0.882562i	$0.655816\pi$
$762$	−3939.03	−0.187265
$763$	16083.0	0.763099
$764$	21593.7	1.02256
$765$	−4216.44	−0.199275
$766$	−8665.08	−0.408723
$767$	−17446.1	−0.821307
$768$	2851.68	0.133986
$769$	22454.9	1.05298	0.526491	−	0.850181i	$-0.323507\pi$
$769$	22454.9	1.05298	0.526491	+	0.850181i	$0.323507\pi$
$770$	−673.192	−0.0315067
$771$	19696.8	0.920054
$772$	6899.83	0.321671
$773$	−27883.7	−1.29742	−0.648711	−	0.761035i	$-0.724691\pi$
$773$	−27883.7	−1.29742	−0.648711	+	0.761035i	$0.724691\pi$
$774$	1518.45	0.0705164
$775$	−21555.5	−0.999093
$776$	−2300.17	−0.106406
$777$	−8449.78	−0.390134
$778$	−5792.03	−0.266908
$779$	20641.8	0.949385
$780$	−4455.56	−0.204532
$781$	−6095.40	−0.279271
$782$	−7780.21	−0.355780
$783$	−5120.40	−0.233702
$784$	−6933.65	−0.315855
$785$	470.626	0.0213979
$786$	993.133	0.0450686
$787$	30744.7	1.39254	0.696270	−	0.717780i	$-0.254842\pi$
$787$	30744.7	1.39254	0.696270	+	0.717780i	$0.254842\pi$
$788$	14319.9	0.647366
$789$	−8346.65	−0.376614
$790$	4606.76	0.207470
$791$	−22647.4	−1.01801
$792$	1639.83	0.0735716
$793$	2988.95	0.133847
$794$	7794.66	0.348391
$795$	1277.47	0.0569900
$796$	9924.22	0.441903
$797$	−3241.67	−0.144073	−0.0720363	−	0.997402i	$-0.522950\pi$
$797$	−3241.67	−0.144073	−0.0720363	+	0.997402i	$0.522950\pi$
$798$	−5022.26	−0.222790
$799$	23042.7	1.02027
$800$	18034.8	0.797035
$801$	6663.79	0.293949
$802$	−11908.9	−0.524338
$803$	2183.84	0.0959726
$804$	21831.0	0.957612
$805$	3619.55	0.158475
$806$	−11332.7	−0.495257
$807$	−4743.72	−0.206923
$808$	18379.7	0.800240
$809$	11540.1	0.501520	0.250760	−	0.968049i	$-0.419320\pi$
$809$	11540.1	0.501520	0.250760	+	0.968049i	$0.419320\pi$
$810$	409.637	0.0177693
$811$	−26052.2	−1.12801	−0.564006	−	0.825771i	$-0.690740\pi$
$811$	−26052.2	−1.12801	−0.564006	+	0.825771i	$0.690740\pi$
$812$	15460.2	0.668162
$813$	−11768.6	−0.507681
$814$	2877.72	0.123912
$815$	−10231.4	−0.439742
$816$	−11019.1	−0.472727
$817$	−18474.6	−0.791120
$818$	−8220.06	−0.351354
$819$	−5336.59	−0.227687
$820$	5083.47	0.216491
$821$	32786.3	1.39373	0.696863	−	0.717205i	$-0.254579\pi$
$821$	32786.3	1.39373	0.696863	+	0.717205i	$0.254579\pi$
$822$	4876.70	0.206927
$823$	−28122.4	−1.19111	−0.595555	−	0.803314i	$-0.703068\pi$
$823$	−28122.4	−1.19111	−0.595555	+	0.803314i	$0.703068\pi$
$824$	−10446.3	−0.441644
$825$	3456.94	0.145885
$826$	−4842.91	−0.204003
$827$	−27829.4	−1.17016	−0.585080	−	0.810976i	$-0.698937\pi$
$827$	−27829.4	−1.17016	−0.585080	+	0.810976i	$0.698937\pi$
$828$	−4030.49	−0.169166
$829$	44809.6	1.87732	0.938662	−	0.344840i	$-0.112067\pi$
$829$	44809.6	1.87732	0.938662	+	0.344840i	$0.112067\pi$
$830$	−5420.32	−0.226677
$831$	−8429.97	−0.351904
$832$	−4345.96	−0.181093
$833$	−20466.6	−0.851291
$834$	−2757.33	−0.114483
$835$	6795.31	0.281630
$836$	−9120.45	−0.377318
$837$	−5555.76	−0.229433
$838$	−5617.98	−0.231587
$839$	−15031.8	−0.618542	−0.309271	−	0.950974i	$-0.600085\pi$
$839$	−15031.8	−0.618542	−0.309271	+	0.950974i	$0.600085\pi$
$840$	−2705.61	−0.111134
$841$	11576.1	0.474643
$842$	−6022.23	−0.246484
$843$	501.534	0.0204908
$844$	−260.952	−0.0106426
$845$	−917.515	−0.0373532
$846$	−2238.65	−0.0909769
$847$	−1464.26	−0.0594008
$848$	3338.49	0.135194
$849$	14026.5	0.567008
$850$	12260.2	0.494731
$851$	−15472.6	−0.623261
$852$	−11198.9	−0.450313
$853$	−37070.0	−1.48799	−0.743994	−	0.668186i	$-0.767071\pi$
$853$	−37070.0	−1.48799	−0.743994	+	0.668186i	$0.767071\pi$
$854$	829.711	0.0332461
$855$	−4983.94	−0.199353
$856$	20709.8	0.826925
$857$	24595.9	0.980372	0.490186	−	0.871618i	$-0.336929\pi$
$857$	24595.9	0.980372	0.490186	+	0.871618i	$0.336929\pi$
$858$	1817.47	0.0723164
$859$	20730.0	0.823397	0.411698	−	0.911320i	$-0.364936\pi$
$859$	20730.0	0.823397	0.411698	+	0.911320i	$0.364936\pi$
$860$	−4549.74	−0.180401
$861$	6088.66	0.241000
$862$	−5178.42	−0.204614
$863$	9201.76	0.362957	0.181478	−	0.983395i	$-0.441912\pi$
$863$	9201.76	0.362957	0.181478	+	0.983395i	$0.441912\pi$
$864$	4648.34	0.183032
$865$	−8361.91	−0.328686
$866$	−3032.49	−0.118993
$867$	−17786.9	−0.696741
$868$	16774.7	0.655957
$869$	10020.2	0.391152
$870$	−2877.24	−0.112124
$871$	52929.6	2.05907
$872$	−22014.0	−0.854916
$873$	−1249.79	−0.0484526
$874$	−9196.41	−0.355919
$875$	−12509.7	−0.483322
$876$	4012.29	0.154752
$877$	−42487.8	−1.63593	−0.817966	−	0.575266i	$-0.804898\pi$
$877$	−42487.8	−1.63593	−0.817966	+	0.575266i	$0.804898\pi$
$878$	−1970.70	−0.0757495
$879$	11546.9	0.443080
$880$	−1745.87	−0.0668788
$881$	20505.8	0.784175	0.392088	−	0.919928i	$-0.371753\pi$
$881$	20505.8	0.784175	0.392088	+	0.919928i	$0.371753\pi$
$882$	1988.38	0.0759094
$883$	−6154.35	−0.234553	−0.117276	−	0.993099i	$-0.537416\pi$
$883$	−6154.35	−0.234553	−0.117276	+	0.993099i	$0.537416\pi$
$884$	−34370.5	−1.30770
$885$	−4805.96	−0.182543
$886$	−2019.65	−0.0765819
$887$	24987.5	0.945884	0.472942	−	0.881094i	$-0.343192\pi$
$887$	24987.5	0.945884	0.472942	+	0.881094i	$0.343192\pi$
$888$	11565.8	0.437076
$889$	14136.3	0.533314
$890$	3744.49	0.141029
$891$	891.000	0.0335013
$892$	−41546.1	−1.55949
$893$	27237.1	1.02067
$894$	−6184.83	−0.231378
$895$	−8579.12	−0.320412
$896$	−17873.4	−0.666414
$897$	−9771.99	−0.363743
$898$	−15618.6	−0.580399
$899$	39023.0	1.44771
$900$	6351.32	0.235234
$901$	9854.47	0.364373
$902$	−2073.60	−0.0765447
$903$	−5449.39	−0.200824
$904$	30999.0	1.14050
$905$	13031.7	0.478662
$906$	−5219.63	−0.191402
$907$	−30053.5	−1.10023	−0.550116	−	0.835088i	$-0.685416\pi$
$907$	−30053.5	−1.10023	−0.550116	+	0.835088i	$0.685416\pi$
$908$	−11054.6	−0.404032
$909$	9986.58	0.364394
$910$	−2998.72	−0.109238
$911$	−41585.3	−1.51238	−0.756192	−	0.654350i	$-0.772942\pi$
$911$	−41585.3	−1.51238	−0.756192	+	0.654350i	$0.772942\pi$
$912$	−13024.8	−0.472912
$913$	−11789.7	−0.427363
$914$	12333.6	0.446345
$915$	823.380	0.0297487
$916$	−34797.9	−1.25519
$917$	−3564.13	−0.128351
$918$	3159.97	0.113610
$919$	20076.4	0.720630	0.360315	−	0.932831i	$-0.382669\pi$
$919$	20076.4	0.720630	0.360315	+	0.932831i	$0.382669\pi$
$920$	−4954.33	−0.177543
$921$	−20911.3	−0.748156
$922$	3529.34	0.126066
$923$	−27151.8	−0.968269
$924$	−2690.23	−0.0957814
$925$	24382.1	0.866678
$926$	−16929.7	−0.600805
$927$	−5676.01	−0.201105
$928$	−32649.3	−1.15492
$929$	−16483.0	−0.582119	−0.291059	−	0.956705i	$-0.594008\pi$
$929$	−16483.0	−0.582119	−0.291059	+	0.956705i	$0.594008\pi$
$930$	−3121.87	−0.110075
$931$	−24192.0	−0.851623
$932$	−23869.5	−0.838917
$933$	24906.8	0.873968
$934$	10921.1	0.382599
$935$	−5153.42	−0.180251
$936$	7304.57	0.255083
$937$	22100.6	0.770538	0.385269	−	0.922804i	$-0.374109\pi$
$937$	22100.6	0.770538	0.385269	+	0.922804i	$0.374109\pi$
$938$	14692.9	0.511449
$939$	25892.1	0.899849
$940$	6707.67	0.232745
$941$	−36121.6	−1.25136	−0.625680	−	0.780080i	$-0.715178\pi$
$941$	−36121.6	−1.25136	−0.625680	+	0.780080i	$0.715178\pi$
$942$	−352.706	−0.0121993
$943$	11149.1	0.385011
$944$	−12559.7	−0.433034
$945$	−1470.09	−0.0506055
$946$	1855.89	0.0637845
$947$	19443.3	0.667181	0.333591	−	0.942718i	$-0.391740\pi$
$947$	19443.3	0.667181	0.333591	+	0.942718i	$0.391740\pi$
$948$	18409.7	0.630716
$949$	9727.85	0.332750
$950$	14491.9	0.494924
$951$	31988.9	1.09076
$952$	−20871.3	−0.710549
$953$	18739.7	0.636977	0.318489	−	0.947927i	$-0.396825\pi$
$953$	18739.7	0.636977	0.318489	+	0.947927i	$0.396825\pi$
$954$	−957.384	−0.0324911
$955$	14422.3	0.488684
$956$	23501.3	0.795071
$957$	−6258.27	−0.211391
$958$	−4602.64	−0.155224
$959$	−17501.4	−0.589311
$960$	−1197.20	−0.0402495
$961$	12549.9	0.421264
$962$	12818.7	0.429618
$963$	11252.7	0.376545
$964$	16342.0	0.545995
$965$	4608.34	0.153728
$966$	−2712.63	−0.0903494
$967$	−32608.4	−1.08440	−0.542201	−	0.840249i	$-0.682409\pi$
$967$	−32608.4	−1.08440	−0.542201	+	0.840249i	$0.682409\pi$
$968$	2004.23	0.0665480
$969$	−38446.4	−1.27459
$970$	−702.280	−0.0232462
$971$	−44703.5	−1.47745	−0.738725	−	0.674007i	$-0.764572\pi$
$971$	−44703.5	−1.47745	−0.738725	+	0.674007i	$0.764572\pi$
$972$	1637.00	0.0540194
$973$	9895.45	0.326037
$974$	−21342.7	−0.702118
$975$	15398.9	0.505804
$976$	2151.79	0.0705709
$977$	53062.3	1.73758	0.868789	−	0.495182i	$-0.164899\pi$
$977$	53062.3	1.73758	0.868789	+	0.495182i	$0.164899\pi$
$978$	7667.80	0.250705
$979$	8144.63	0.265887
$980$	−5957.77	−0.194198
$981$	−11961.3	−0.389291
$982$	23941.2	0.777999
$983$	18863.3	0.612050	0.306025	−	0.952023i	$-0.401001\pi$
$983$	18863.3	0.612050	0.306025	+	0.952023i	$0.401001\pi$
$984$	−8333.97	−0.269997
$985$	9564.13	0.309379
$986$	−22195.2	−0.716875
$987$	8034.03	0.259094
$988$	−40626.8	−1.30821
$989$	−9978.54	−0.320828
$990$	500.667	0.0160730
$991$	−12659.0	−0.405779	−0.202890	−	0.979202i	$-0.565033\pi$
$991$	−12659.0	−0.405779	−0.202890	+	0.979202i	$0.565033\pi$
$992$	−35425.3	−1.13383
$993$	−4756.20	−0.151998
$994$	−7537.14	−0.240507
$995$	6628.31	0.211187
$996$	−21660.8	−0.689106
$997$	−37116.8	−1.17904	−0.589518	−	0.807755i	$-0.700682\pi$
$997$	−37116.8	−1.17904	−0.589518	+	0.807755i	$0.700682\pi$
$998$	9166.94	0.290756
$999$	6284.28	0.199025

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2013.4.a.g.1.16	✓	39

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2013.4.a.g.1.16	✓	39	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:	\( N \)	\(=\)	\( 2013 = 3 \cdot 11 \cdot 61 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	2013.a (trivial)

\(f(q)\)	\(=\)	\(q-1.12400 q^{2} -3.00000 q^{3} -6.73663 q^{4} -4.49934 q^{5} +3.37199 q^{6} -12.1013 q^{7} +16.5639 q^{8} +9.00000 q^{9} +O(q^{10})\)	\(q-1.12400 q^{2} -3.00000 q^{3} -6.73663 q^{4} -4.49934 q^{5} +3.37199 q^{6} -12.1013 q^{7} +16.5639 q^{8} +9.00000 q^{9} +5.05724 q^{10} +11.0000 q^{11} +20.2099 q^{12} +48.9992 q^{13} +13.6018 q^{14} +13.4980 q^{15} +35.2753 q^{16} +104.125 q^{17} -10.1160 q^{18} +123.078 q^{19} +30.3104 q^{20} +36.3039 q^{21} -12.3640 q^{22} +66.4772 q^{23} -49.6917 q^{24} -104.756 q^{25} -55.0749 q^{26} -27.0000 q^{27} +81.5221 q^{28} +189.645 q^{29} -15.1717 q^{30} +205.769 q^{31} -172.161 q^{32} -33.0000 q^{33} -117.036 q^{34} +54.4480 q^{35} -60.6297 q^{36} -232.751 q^{37} -138.339 q^{38} -146.998 q^{39} -74.5267 q^{40} +167.713 q^{41} -40.8055 q^{42} -150.105 q^{43} -74.1030 q^{44} -40.4941 q^{45} -74.7201 q^{46} +221.299 q^{47} -105.826 q^{48} -196.558 q^{49} +117.745 q^{50} -312.374 q^{51} -330.090 q^{52} +94.6410 q^{53} +30.3479 q^{54} -49.4928 q^{55} -200.445 q^{56} -369.234 q^{57} -213.160 q^{58} -356.049 q^{59} -90.9313 q^{60} +61.0000 q^{61} -231.283 q^{62} -108.912 q^{63} -88.6946 q^{64} -220.464 q^{65} +37.0919 q^{66} +1080.21 q^{67} -701.450 q^{68} -199.432 q^{69} -61.1993 q^{70} -554.127 q^{71} +149.075 q^{72} +198.531 q^{73} +261.611 q^{74} +314.268 q^{75} -829.132 q^{76} -133.114 q^{77} +165.225 q^{78} +910.924 q^{79} -158.716 q^{80} +81.0000 q^{81} -188.509 q^{82} -1071.79 q^{83} -244.566 q^{84} -468.493 q^{85} +168.717 q^{86} -568.934 q^{87} +182.203 q^{88} +740.421 q^{89} +45.5152 q^{90} -592.955 q^{91} -447.833 q^{92} -617.307 q^{93} -248.739 q^{94} -553.771 q^{95} +516.482 q^{96} -138.866 q^{97} +220.931 q^{98} +99.0000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 39 q + 4 q^{2} - 117 q^{3} + 182 q^{4} + 5 q^{5} - 12 q^{6} + 77 q^{7} + 27 q^{8} + 351 q^{9}+O(q^{10}) \) 39 * q + 4 * q^2 - 117 * q^3 + 182 * q^4 + 5 * q^5 - 12 * q^6 + 77 * q^7 + 27 * q^8 + 351 * q^9	\( 39 q + 4 q^{2} - 117 q^{3} + 182 q^{4} + 5 q^{5} - 12 q^{6} + 77 q^{7} + 27 q^{8} + 351 q^{9} + 95 q^{10} + 429 q^{11} - 546 q^{12} + 169 q^{13} + 46 q^{14} - 15 q^{15} + 822 q^{16} + 294 q^{17} + 36 q^{18} + 259 q^{19} + 426 q^{20} - 231 q^{21} + 44 q^{22} + 177 q^{23} - 81 q^{24} + 1388 q^{25} + 695 q^{26} - 1053 q^{27} + 1104 q^{28} - 18 q^{29} - 285 q^{30} + 422 q^{31} + 55 q^{32} - 1287 q^{33} + 364 q^{34} + 906 q^{35} + 1638 q^{36} + 424 q^{37} + 9 q^{38} - 507 q^{39} + 1067 q^{40} + 16 q^{41} - 138 q^{42} + 1013 q^{43} + 2002 q^{44} + 45 q^{45} + 9 q^{46} + 1615 q^{47} - 2466 q^{48} + 2024 q^{49} - 1342 q^{50} - 882 q^{51} + 1298 q^{52} - 541 q^{53} - 108 q^{54} + 55 q^{55} - 161 q^{56} - 777 q^{57} + 1061 q^{58} + 1019 q^{59} - 1278 q^{60} + 2379 q^{61} + 879 q^{62} + 693 q^{63} + 1055 q^{64} - 1134 q^{65} - 132 q^{66} + 1917 q^{67} + 3526 q^{68} - 531 q^{69} + 758 q^{70} - 479 q^{71} + 243 q^{72} + 3319 q^{73} - 332 q^{74} - 4164 q^{75} + 692 q^{76} + 847 q^{77} - 2085 q^{78} + 651 q^{79} + 2973 q^{80} + 3159 q^{81} - 826 q^{82} + 4001 q^{83} - 3312 q^{84} + 3595 q^{85} - 6247 q^{86} + 54 q^{87} + 297 q^{88} - 1625 q^{89} + 855 q^{90} + 2048 q^{91} - 507 q^{92} - 1266 q^{93} - 2436 q^{94} + 1400 q^{95} - 165 q^{96} + 2176 q^{97} - 1396 q^{98} + 3861 q^{99}+O(q^{100}) \) 39 * q + 4 * q^2 - 117 * q^3 + 182 * q^4 + 5 * q^5 - 12 * q^6 + 77 * q^7 + 27 * q^8 + 351 * q^9 + 95 * q^10 + 429 * q^11 - 546 * q^12 + 169 * q^13 + 46 * q^14 - 15 * q^15 + 822 * q^16 + 294 * q^17 + 36 * q^18 + 259 * q^19 + 426 * q^20 - 231 * q^21 + 44 * q^22 + 177 * q^23 - 81 * q^24 + 1388 * q^25 + 695 * q^26 - 1053 * q^27 + 1104 * q^28 - 18 * q^29 - 285 * q^30 + 422 * q^31 + 55 * q^32 - 1287 * q^33 + 364 * q^34 + 906 * q^35 + 1638 * q^36 + 424 * q^37 + 9 * q^38 - 507 * q^39 + 1067 * q^40 + 16 * q^41 - 138 * q^42 + 1013 * q^43 + 2002 * q^44 + 45 * q^45 + 9 * q^46 + 1615 * q^47 - 2466 * q^48 + 2024 * q^49 - 1342 * q^50 - 882 * q^51 + 1298 * q^52 - 541 * q^53 - 108 * q^54 + 55 * q^55 - 161 * q^56 - 777 * q^57 + 1061 * q^58 + 1019 * q^59 - 1278 * q^60 + 2379 * q^61 + 879 * q^62 + 693 * q^63 + 1055 * q^64 - 1134 * q^65 - 132 * q^66 + 1917 * q^67 + 3526 * q^68 - 531 * q^69 + 758 * q^70 - 479 * q^71 + 243 * q^72 + 3319 * q^73 - 332 * q^74 - 4164 * q^75 + 692 * q^76 + 847 * q^77 - 2085 * q^78 + 651 * q^79 + 2973 * q^80 + 3159 * q^81 - 826 * q^82 + 4001 * q^83 - 3312 * q^84 + 3595 * q^85 - 6247 * q^86 + 54 * q^87 + 297 * q^88 - 1625 * q^89 + 855 * q^90 + 2048 * q^91 - 507 * q^92 - 1266 * q^93 - 2436 * q^94 + 1400 * q^95 - 165 * q^96 + 2176 * q^97 - 1396 * q^98 + 3861 * q^99

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