LMFDB - Embedded newform 2013.4.a.f.1.9

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:	$38$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.9
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)

$f(q)$	$=$	$q-3.25945 q^{2} +3.00000 q^{3} +2.62403 q^{4} +10.3368 q^{5} -9.77836 q^{6} -26.6613 q^{7} +17.5227 q^{8} +9.00000 q^{9} +O(q^{10})$	\(q-3.25945 q^{2} +3.00000 q^{3} +2.62403 q^{4} +10.3368 q^{5} -9.77836 q^{6} -26.6613 q^{7} +17.5227 q^{8} +9.00000 q^{9} -33.6924 q^{10} +11.0000 q^{11} +7.87208 q^{12} +3.76844 q^{13} +86.9013 q^{14} +31.0105 q^{15} -78.1067 q^{16} +2.59016 q^{17} -29.3351 q^{18} +116.264 q^{19} +27.1241 q^{20} -79.9840 q^{21} -35.8540 q^{22} +16.9922 q^{23} +52.5682 q^{24} -18.1499 q^{25} -12.2830 q^{26} +27.0000 q^{27} -69.9600 q^{28} -7.83254 q^{29} -101.077 q^{30} +47.9389 q^{31} +114.403 q^{32} +33.0000 q^{33} -8.44249 q^{34} -275.594 q^{35} +23.6162 q^{36} +278.565 q^{37} -378.956 q^{38} +11.3053 q^{39} +181.130 q^{40} +50.3828 q^{41} +260.704 q^{42} +145.505 q^{43} +28.8643 q^{44} +93.0315 q^{45} -55.3853 q^{46} -213.992 q^{47} -234.320 q^{48} +367.827 q^{49} +59.1586 q^{50} +7.77047 q^{51} +9.88849 q^{52} -506.509 q^{53} -88.0052 q^{54} +113.705 q^{55} -467.179 q^{56} +348.791 q^{57} +25.5298 q^{58} -861.934 q^{59} +81.3724 q^{60} -61.0000 q^{61} -156.255 q^{62} -239.952 q^{63} +251.962 q^{64} +38.9537 q^{65} -107.562 q^{66} +527.406 q^{67} +6.79664 q^{68} +50.9767 q^{69} +898.285 q^{70} +662.200 q^{71} +157.705 q^{72} -333.452 q^{73} -907.970 q^{74} -54.4496 q^{75} +305.079 q^{76} -293.275 q^{77} -36.8491 q^{78} -19.7856 q^{79} -807.376 q^{80} +81.0000 q^{81} -164.220 q^{82} +518.594 q^{83} -209.880 q^{84} +26.7740 q^{85} -474.265 q^{86} -23.4976 q^{87} +192.750 q^{88} +127.902 q^{89} -303.232 q^{90} -100.472 q^{91} +44.5880 q^{92} +143.817 q^{93} +697.497 q^{94} +1201.80 q^{95} +343.210 q^{96} -260.354 q^{97} -1198.91 q^{98} +99.0000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 38 q + 14 q^{2} + 114 q^{3} + 170 q^{4} + 35 q^{5} + 42 q^{6} + 105 q^{7} + 147 q^{8} + 342 q^{9}+O(q^{10}) $ 38 * q + 14 * q^2 + 114 * q^3 + 170 * q^4 + 35 * q^5 + 42 * q^6 + 105 * q^7 + 147 * q^8 + 342 * q^9	\( 38 q + 14 q^{2} + 114 q^{3} + 170 q^{4} + 35 q^{5} + 42 q^{6} + 105 q^{7} + 147 q^{8} + 342 q^{9} + 99 q^{10} + 418 q^{11} + 510 q^{12} + 209 q^{13} + 128 q^{14} + 105 q^{15} + 798 q^{16} + 512 q^{17} + 126 q^{18} + 487 q^{19} + 328 q^{20} + 315 q^{21} + 154 q^{22} + 417 q^{23} + 441 q^{24} + 925 q^{25} + 177 q^{26} + 1026 q^{27} + 902 q^{28} + 626 q^{29} + 297 q^{30} + 300 q^{31} + 1625 q^{32} + 1254 q^{33} - 180 q^{34} + 1086 q^{35} + 1530 q^{36} + 554 q^{37} + 845 q^{38} + 627 q^{39} + 329 q^{40} + 1378 q^{41} + 384 q^{42} + 1979 q^{43} + 1870 q^{44} + 315 q^{45} + 937 q^{46} + 1345 q^{47} + 2394 q^{48} + 2635 q^{49} + 800 q^{50} + 1536 q^{51} + 2006 q^{52} + 1497 q^{53} + 378 q^{54} + 385 q^{55} + 415 q^{56} + 1461 q^{57} + 1241 q^{58} + 2827 q^{59} + 984 q^{60} - 2318 q^{61} + 509 q^{62} + 945 q^{63} + 1003 q^{64} + 2810 q^{65} + 462 q^{66} + 369 q^{67} + 3936 q^{68} + 1251 q^{69} + 922 q^{70} + 965 q^{71} + 1323 q^{72} + 3081 q^{73} + 722 q^{74} + 2775 q^{75} + 2210 q^{76} + 1155 q^{77} + 531 q^{78} + 3795 q^{79} + 3793 q^{80} + 3078 q^{81} - 1678 q^{82} + 3869 q^{83} + 2706 q^{84} + 3553 q^{85} + 3305 q^{86} + 1878 q^{87} + 1617 q^{88} + 2849 q^{89} + 891 q^{90} + 1252 q^{91} + 4519 q^{92} + 900 q^{93} + 340 q^{94} + 1504 q^{95} + 4875 q^{96} + 2562 q^{97} + 6164 q^{98} + 3762 q^{99}+O(q^{100}) \) 38 * q + 14 * q^2 + 114 * q^3 + 170 * q^4 + 35 * q^5 + 42 * q^6 + 105 * q^7 + 147 * q^8 + 342 * q^9 + 99 * q^10 + 418 * q^11 + 510 * q^12 + 209 * q^13 + 128 * q^14 + 105 * q^15 + 798 * q^16 + 512 * q^17 + 126 * q^18 + 487 * q^19 + 328 * q^20 + 315 * q^21 + 154 * q^22 + 417 * q^23 + 441 * q^24 + 925 * q^25 + 177 * q^26 + 1026 * q^27 + 902 * q^28 + 626 * q^29 + 297 * q^30 + 300 * q^31 + 1625 * q^32 + 1254 * q^33 - 180 * q^34 + 1086 * q^35 + 1530 * q^36 + 554 * q^37 + 845 * q^38 + 627 * q^39 + 329 * q^40 + 1378 * q^41 + 384 * q^42 + 1979 * q^43 + 1870 * q^44 + 315 * q^45 + 937 * q^46 + 1345 * q^47 + 2394 * q^48 + 2635 * q^49 + 800 * q^50 + 1536 * q^51 + 2006 * q^52 + 1497 * q^53 + 378 * q^54 + 385 * q^55 + 415 * q^56 + 1461 * q^57 + 1241 * q^58 + 2827 * q^59 + 984 * q^60 - 2318 * q^61 + 509 * q^62 + 945 * q^63 + 1003 * q^64 + 2810 * q^65 + 462 * q^66 + 369 * q^67 + 3936 * q^68 + 1251 * q^69 + 922 * q^70 + 965 * q^71 + 1323 * q^72 + 3081 * q^73 + 722 * q^74 + 2775 * q^75 + 2210 * q^76 + 1155 * q^77 + 531 * q^78 + 3795 * q^79 + 3793 * q^80 + 3078 * q^81 - 1678 * q^82 + 3869 * q^83 + 2706 * q^84 + 3553 * q^85 + 3305 * q^86 + 1878 * q^87 + 1617 * q^88 + 2849 * q^89 + 891 * q^90 + 1252 * q^91 + 4519 * q^92 + 900 * q^93 + 340 * q^94 + 1504 * q^95 + 4875 * q^96 + 2562 * q^97 + 6164 * q^98 + 3762 * 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 $

$2$	−3.25945	−1.15239	−0.576195	−	0.817312i	$-0.695463\pi$
$2$	−3.25945	−1.15239	−0.576195	+	0.817312i	$0.695463\pi$
$3$	3.00000	0.577350
$3$	3.00000	0.577350
$4$	2.62403	0.328003
$5$	10.3368	0.924555	0.462277	−	0.886735i	$-0.347032\pi$
$5$	10.3368	0.924555	0.462277	+	0.886735i	$0.347032\pi$
$6$	−9.77836	−0.665333
$7$	−26.6613	−1.43958	−0.719788	−	0.694194i	$-0.755761\pi$
$7$	−26.6613	−1.43958	−0.719788	+	0.694194i	$0.755761\pi$
$8$	17.5227	0.774403
$9$	9.00000	0.333333
$10$	−33.6924	−1.06545
$11$	11.0000	0.301511
$11$	11.0000	0.301511
$12$	7.87208	0.189373
$13$	3.76844	0.0803983	0.0401991	−	0.999192i	$-0.487201\pi$
$13$	3.76844	0.0803983	0.0401991	+	0.999192i	$0.487201\pi$
$14$	86.9013	1.65895
$15$	31.0105	0.533792
$16$	−78.1067	−1.22042
$17$	2.59016	0.0369533	0.0184766	−	0.999829i	$-0.494118\pi$
$17$	2.59016	0.0369533	0.0184766	+	0.999829i	$0.494118\pi$
$18$	−29.3351	−0.384130
$19$	116.264	1.40383	0.701914	−	0.712262i	$-0.252329\pi$
$19$	116.264	1.40383	0.701914	+	0.712262i	$0.252329\pi$
$20$	27.1241	0.303257
$21$	−79.9840	−0.831140
$22$	−35.8540	−0.347459
$23$	16.9922	0.154049	0.0770244	−	0.997029i	$-0.475458\pi$
$23$	16.9922	0.154049	0.0770244	+	0.997029i	$0.475458\pi$
$24$	52.5682	0.447101
$25$	−18.1499	−0.145199
$26$	−12.2830	−0.0926502
$27$	27.0000	0.192450
$28$	−69.9600	−0.472186
$29$	−7.83254	−0.0501540	−0.0250770	−	0.999686i	$-0.507983\pi$
$29$	−7.83254	−0.0501540	−0.0250770	+	0.999686i	$0.507983\pi$
$30$	−101.077	−0.615136
$31$	47.9389	0.277745	0.138872	−	0.990310i	$-0.455652\pi$
$31$	47.9389	0.277745	0.138872	+	0.990310i	$0.455652\pi$
$32$	114.403	0.631994
$33$	33.0000	0.174078
$34$	−8.44249	−0.0425846
$35$	−275.594	−1.33097
$36$	23.6162	0.109334
$37$	278.565	1.23773	0.618863	−	0.785499i	$-0.287594\pi$
$37$	278.565	1.23773	0.618863	+	0.785499i	$0.287594\pi$
$38$	−378.956	−1.61776
$39$	11.3053	0.0464180
$40$	181.130	0.715977
$41$	50.3828	0.191914	0.0959569	−	0.995385i	$-0.469409\pi$
$41$	50.3828	0.191914	0.0959569	+	0.995385i	$0.469409\pi$
$42$	260.704	0.957797
$43$	145.505	0.516029	0.258014	−	0.966141i	$-0.416932\pi$
$43$	145.505	0.516029	0.258014	+	0.966141i	$0.416932\pi$
$44$	28.8643	0.0988967
$45$	93.0315	0.308185
$46$	−55.3853	−0.177524
$47$	−213.992	−0.664127	−0.332064	−	0.943257i	$-0.607745\pi$
$47$	−213.992	−0.664127	−0.332064	+	0.943257i	$0.607745\pi$
$48$	−234.320	−0.704608
$49$	367.827	1.07238
$50$	59.1586	0.167326
$51$	7.77047	0.0213350
$52$	9.88849	0.0263709
$53$	−506.509	−1.31273	−0.656363	−	0.754446i	$-0.727906\pi$
$53$	−506.509	−1.31273	−0.656363	+	0.754446i	$0.727906\pi$
$54$	−88.0052	−0.221778
$55$	113.705	0.278764
$56$	−467.179	−1.11481
$57$	348.791	0.810500
$58$	25.5298	0.0577970
$59$	−861.934	−1.90194	−0.950968	−	0.309289i	$-0.899909\pi$
$59$	−861.934	−1.90194	−0.950968	+	0.309289i	$0.899909\pi$
$60$	81.3724	0.175085
$61$	−61.0000	−0.128037
$61$	−61.0000	−0.128037
$62$	−156.255	−0.320070
$63$	−239.952	−0.479859
$64$	251.962	0.492113
$65$	38.9537	0.0743326
$66$	−107.562	−0.200605
$67$	527.406	0.961686	0.480843	−	0.876807i	$-0.340331\pi$
$67$	527.406	0.961686	0.480843	+	0.876807i	$0.340331\pi$
$68$	6.79664	0.0121208
$69$	50.9767	0.0889401
$70$	898.285	1.53379
$71$	662.200	1.10688	0.553441	−	0.832888i	$-0.313314\pi$
$71$	662.200	1.10688	0.553441	+	0.832888i	$0.313314\pi$
$72$	157.705	0.258134
$73$	−333.452	−0.534624	−0.267312	−	0.963610i	$-0.586136\pi$
$73$	−333.452	−0.534624	−0.267312	+	0.963610i	$0.586136\pi$
$74$	−907.970	−1.42634
$75$	−54.4496	−0.0838306
$76$	305.079	0.460460
$77$	−293.275	−0.434049
$78$	−36.8491	−0.0534916
$79$	−19.7856	−0.0281778	−0.0140889	−	0.999901i	$-0.504485\pi$
$79$	−19.7856	−0.0281778	−0.0140889	+	0.999901i	$0.504485\pi$
$80$	−807.376	−1.12834
$81$	81.0000	0.111111
$82$	−164.220	−0.221160
$83$	518.594	0.685820	0.342910	−	0.939368i	$-0.388587\pi$
$83$	518.594	0.685820	0.342910	+	0.939368i	$0.388587\pi$
$84$	−209.880	−0.272617
$85$	26.7740	0.0341653
$86$	−474.265	−0.594667
$87$	−23.4976	−0.0289564
$88$	192.750	0.233491
$89$	127.902	0.152333	0.0761663	−	0.997095i	$-0.475732\pi$
$89$	127.902	0.152333	0.0761663	+	0.997095i	$0.475732\pi$
$90$	−303.232	−0.355149
$91$	−100.472	−0.115739
$92$	44.5880	0.0505285
$93$	143.817	0.160356
$94$	697.497	0.765334
$95$	1201.80	1.29791
$96$	343.210	0.364882
$97$	−260.354	−0.272525	−0.136263	−	0.990673i	$-0.543509\pi$
$97$	−260.354	−0.272525	−0.136263	+	0.990673i	$0.543509\pi$
$98$	−1198.91	−1.23580
$99$	99.0000	0.100504
$100$	−47.6257	−0.0476257
$101$	1089.30	1.07316	0.536582	−	0.843848i	$-0.319715\pi$
$101$	1089.30	1.07316	0.536582	+	0.843848i	$0.319715\pi$
$102$	−25.3275	−0.0245862
$103$	−1281.48	−1.22590	−0.612952	−	0.790120i	$-0.710018\pi$
$103$	−1281.48	−1.22590	−0.612952	+	0.790120i	$0.710018\pi$
$104$	66.0334	0.0622606
$105$	−826.781	−0.768434
$106$	1650.94	1.51277
$107$	1953.15	1.76465	0.882326	−	0.470639i	$-0.155977\pi$
$107$	1953.15	1.76465	0.882326	+	0.470639i	$0.155977\pi$
$108$	70.8487	0.0631243
$109$	−246.040	−0.216205	−0.108103	−	0.994140i	$-0.534477\pi$
$109$	−246.040	−0.216205	−0.108103	+	0.994140i	$0.534477\pi$
$110$	−370.617	−0.321245
$111$	835.696	0.714601
$112$	2082.43	1.75688
$113$	1424.30	1.18573	0.592863	−	0.805304i	$-0.297998\pi$
$113$	1424.30	1.18573	0.592863	+	0.805304i	$0.297998\pi$
$114$	−1136.87	−0.934012
$115$	175.646	0.142427
$116$	−20.5528	−0.0164507
$117$	33.9160	0.0267994
$118$	2809.43	2.19177
$119$	−69.0570	−0.0531970
$120$	543.389	0.413370
$121$	121.000	0.0909091
$122$	198.827	0.147548
$123$	151.148	0.110801
$124$	125.793	0.0911011
$125$	−1479.72	−1.05880
$126$	782.112	0.552985
$127$	−484.526	−0.338541	−0.169270	−	0.985570i	$-0.554141\pi$
$127$	−484.526	−0.338541	−0.169270	+	0.985570i	$0.554141\pi$
$128$	−1736.48	−1.19910
$129$	436.514	0.297929
$130$	−126.968	−0.0856601
$131$	−1251.06	−0.834392	−0.417196	−	0.908817i	$-0.636987\pi$
$131$	−1251.06	−0.834392	−0.417196	+	0.908817i	$0.636987\pi$
$132$	86.5929	0.0570980
$133$	−3099.74	−2.02092
$134$	−1719.06	−1.10824
$135$	279.095	0.177931
$136$	45.3866	0.0286167
$137$	342.142	0.213366	0.106683	−	0.994293i	$-0.465977\pi$
$137$	342.142	0.213366	0.106683	+	0.994293i	$0.465977\pi$
$138$	−166.156	−0.102494
$139$	213.762	0.130439	0.0652196	−	0.997871i	$-0.479225\pi$
$139$	213.762	0.130439	0.0652196	+	0.997871i	$0.479225\pi$
$140$	−723.165	−0.436561
$141$	−641.977	−0.383434
$142$	−2158.41	−1.27556
$143$	41.4528	0.0242410
$144$	−702.960	−0.406806
$145$	−80.9637	−0.0463701
$146$	1086.87	0.616096
$147$	1103.48	0.619139
$148$	730.962	0.405978
$149$	852.150	0.468529	0.234265	−	0.972173i	$-0.424732\pi$
$149$	852.150	0.468529	0.234265	+	0.972173i	$0.424732\pi$
$150$	177.476	0.0966056
$151$	1169.42	0.630239	0.315119	−	0.949052i	$-0.397955\pi$
$151$	1169.42	0.630239	0.315119	+	0.949052i	$0.397955\pi$
$152$	2037.26	1.08713
$153$	23.3114	0.0123178
$154$	955.915	0.500193
$155$	495.537	0.256790
$156$	29.6655	0.0152252
$157$	3090.68	1.57110	0.785551	−	0.618797i	$-0.212379\pi$
$157$	3090.68	1.57110	0.785551	+	0.618797i	$0.212379\pi$
$158$	64.4901	0.0324719
$159$	−1519.53	−0.757902
$160$	1182.57	0.584313
$161$	−453.035	−0.221765
$162$	−264.016	−0.128043
$163$	−452.795	−0.217581	−0.108790	−	0.994065i	$-0.534698\pi$
$163$	−452.795	−0.217581	−0.108790	+	0.994065i	$0.534698\pi$
$164$	132.206	0.0629483
$165$	341.116	0.160944
$166$	−1690.33	−0.790332
$167$	258.658	0.119854	0.0599269	−	0.998203i	$-0.480913\pi$
$167$	258.658	0.119854	0.0599269	+	0.998203i	$0.480913\pi$
$168$	−1401.54	−0.643637
$169$	−2182.80	−0.993536
$170$	−87.2687	−0.0393718
$171$	1046.37	0.467942
$172$	381.808	0.169259
$173$	867.756	0.381354	0.190677	−	0.981653i	$-0.438932\pi$
$173$	867.756	0.381354	0.190677	+	0.981653i	$0.438932\pi$
$174$	76.5893	0.0333691
$175$	483.899	0.209025
$176$	−859.174	−0.367970
$177$	−2585.80	−1.09808
$178$	−416.891	−0.175547
$179$	3430.09	1.43227	0.716136	−	0.697960i	$-0.245909\pi$
$179$	3430.09	1.43227	0.716136	+	0.697960i	$0.245909\pi$
$180$	244.117	0.101086
$181$	1219.69	0.500877	0.250439	−	0.968132i	$-0.419425\pi$
$181$	1219.69	0.500877	0.250439	+	0.968132i	$0.419425\pi$
$182$	327.482	0.133377
$183$	−183.000	−0.0739221
$184$	297.750	0.119296
$185$	2879.48	1.14434
$186$	−468.764	−0.184793
$187$	28.4917	0.0111418
$188$	−561.521	−0.217836
$189$	−719.856	−0.277047
$190$	−3917.20	−1.49570
$191$	−4345.06	−1.64606	−0.823029	−	0.567999i	$-0.807718\pi$
$191$	−4345.06	−1.64606	−0.823029	+	0.567999i	$0.807718\pi$
$192$	755.886	0.284122
$193$	3533.49	1.31786	0.658928	−	0.752206i	$-0.271010\pi$
$193$	3533.49	1.31786	0.658928	+	0.752206i	$0.271010\pi$
$194$	848.611	0.314055
$195$	116.861	0.0429159
$196$	965.186	0.351744
$197$	−4060.26	−1.46844	−0.734218	−	0.678914i	$-0.762451\pi$
$197$	−4060.26	−1.46844	−0.734218	+	0.678914i	$0.762451\pi$
$198$	−322.686	−0.115820
$199$	−3534.69	−1.25913	−0.629567	−	0.776946i	$-0.716768\pi$
$199$	−3534.69	−1.25913	−0.629567	+	0.776946i	$0.716768\pi$
$200$	−318.035	−0.112442
$201$	1582.22	0.555230
$202$	−3550.52	−1.23670
$203$	208.826	0.0722005
$204$	20.3899	0.00699794
$205$	520.798	0.177435
$206$	4176.93	1.41272
$207$	152.930	0.0513496
$208$	−294.340	−0.0981194
$209$	1278.90	0.423270
$210$	2694.85	0.885536
$211$	902.040	0.294308	0.147154	−	0.989114i	$-0.452989\pi$
$211$	902.040	0.294308	0.147154	+	0.989114i	$0.452989\pi$
$212$	−1329.09	−0.430578
$213$	1986.60	0.639059
$214$	−6366.18	−2.03357
$215$	1504.06	0.477097
$216$	473.114	0.149034
$217$	−1278.12	−0.399835
$218$	801.956	0.249153
$219$	−1000.36	−0.308666
$220$	298.365	0.0914354
$221$	9.76085	0.00297098
$222$	−2723.91	−0.823499
$223$	464.457	0.139472	0.0697362	−	0.997565i	$-0.477784\pi$
$223$	464.457	0.139472	0.0697362	+	0.997565i	$0.477784\pi$
$224$	−3050.14	−0.909804
$225$	−163.349	−0.0483996
$226$	−4642.44	−1.36642
$227$	−161.300	−0.0471623	−0.0235812	−	0.999722i	$-0.507507\pi$
$227$	−161.300	−0.0471623	−0.0235812	+	0.999722i	$0.507507\pi$
$228$	915.237	0.265847
$229$	−1384.75	−0.399593	−0.199796	−	0.979837i	$-0.564028\pi$
$229$	−1384.75	−0.399593	−0.199796	+	0.979837i	$0.564028\pi$
$230$	−572.509	−0.164131
$231$	−879.824	−0.250598
$232$	−137.247	−0.0388394
$233$	−3480.99	−0.978744	−0.489372	−	0.872075i	$-0.662774\pi$
$233$	−3480.99	−0.978744	−0.489372	+	0.872075i	$0.662774\pi$
$234$	−110.547	−0.0308834
$235$	−2212.00	−0.614022
$236$	−2261.74	−0.623841
$237$	−59.3567	−0.0162685
$238$	225.088	0.0613038
$239$	−3797.53	−1.02779	−0.513894	−	0.857854i	$-0.671798\pi$
$239$	−3797.53	−1.02779	−0.513894	+	0.857854i	$0.671798\pi$
$240$	−2422.13	−0.651449
$241$	2696.46	0.720723	0.360361	−	0.932813i	$-0.382653\pi$
$241$	2696.46	0.720723	0.360361	+	0.932813i	$0.382653\pi$
$242$	−394.394	−0.104763
$243$	243.000	0.0641500
$244$	−160.066	−0.0419965
$245$	3802.16	0.991474
$246$	−492.661	−0.127687
$247$	438.133	0.112865
$248$	840.021	0.215086
$249$	1555.78	0.395958
$250$	4823.06	1.22015
$251$	393.584	0.0989754	0.0494877	−	0.998775i	$-0.484241\pi$
$251$	393.584	0.0989754	0.0494877	+	0.998775i	$0.484241\pi$
$252$	−629.640	−0.157395
$253$	186.914	0.0464475
$254$	1579.29	0.390131
$255$	80.3221	0.0197253
$256$	3644.29	0.889719
$257$	−1011.56	−0.245522	−0.122761	−	0.992436i	$-0.539175\pi$
$257$	−1011.56	−0.245522	−0.122761	+	0.992436i	$0.539175\pi$
$258$	−1422.80	−0.343331
$259$	−7426.92	−1.78180
$260$	102.216	0.0243813
$261$	−70.4928	−0.0167180
$262$	4077.76	0.961545
$263$	2453.05	0.575140	0.287570	−	0.957760i	$-0.407153\pi$
$263$	2453.05	0.575140	0.287570	+	0.957760i	$0.407153\pi$
$264$	578.250	0.134806
$265$	−5235.70	−1.21369
$266$	10103.5	2.32888
$267$	383.707	0.0879493
$268$	1383.93	0.315436
$269$	1997.98	0.452858	0.226429	−	0.974028i	$-0.427295\pi$
$269$	1997.98	0.452858	0.226429	+	0.974028i	$0.427295\pi$
$270$	−909.695	−0.205045
$271$	5912.34	1.32527	0.662637	−	0.748941i	$-0.269437\pi$
$271$	5912.34	1.32527	0.662637	+	0.748941i	$0.269437\pi$
$272$	−202.309	−0.0450984
$273$	−301.415	−0.0668222
$274$	−1115.19	−0.245881
$275$	−199.648	−0.0437791
$276$	133.764	0.0291726
$277$	3197.96	0.693671	0.346836	−	0.937926i	$-0.387256\pi$
$277$	3197.96	0.693671	0.346836	+	0.937926i	$0.387256\pi$
$278$	−696.747	−0.150317
$279$	431.450	0.0925815
$280$	−4829.15	−1.03070
$281$	6221.28	1.32075	0.660374	−	0.750937i	$-0.270398\pi$
$281$	6221.28	1.32075	0.660374	+	0.750937i	$0.270398\pi$
$282$	2092.49	0.441866
$283$	2395.07	0.503082	0.251541	−	0.967847i	$-0.419063\pi$
$283$	2395.07	0.503082	0.251541	+	0.967847i	$0.419063\pi$
$284$	1737.63	0.363061
$285$	3605.40	0.749352
$286$	−135.114	−0.0279351
$287$	−1343.27	−0.276275
$288$	1029.63	0.210665
$289$	−4906.29	−0.998634
$290$	263.897	0.0534365
$291$	−781.062	−0.157342
$292$	−874.986	−0.175359
$293$	8870.09	1.76859	0.884293	−	0.466932i	$-0.154641\pi$
$293$	8870.09	1.76859	0.884293	+	0.466932i	$0.154641\pi$
$294$	−3596.74	−0.713490
$295$	−8909.67	−1.75844
$296$	4881.22	0.958498
$297$	297.000	0.0580259
$298$	−2777.54	−0.539928
$299$	64.0342	0.0123853
$300$	−142.877	−0.0274967
$301$	−3879.35	−0.742863
$302$	−3811.67	−0.726281
$303$	3267.90	0.619591
$304$	−9080.97	−1.71325
$305$	−630.547	−0.118377
$306$	−75.9824	−0.0141949
$307$	922.703	0.171536	0.0857678	−	0.996315i	$-0.472666\pi$
$307$	922.703	0.171536	0.0857678	+	0.996315i	$0.472666\pi$
$308$	−769.560	−0.142369
$309$	−3844.44	−0.707776
$310$	−1615.18	−0.295922
$311$	6905.59	1.25910	0.629550	−	0.776960i	$-0.283239\pi$
$311$	6905.59	1.25910	0.629550	+	0.776960i	$0.283239\pi$
$312$	198.100	0.0359462
$313$	−249.643	−0.0450819	−0.0225410	−	0.999746i	$-0.507176\pi$
$313$	−249.643	−0.0450819	−0.0225410	+	0.999746i	$0.507176\pi$
$314$	−10073.9	−1.81052
$315$	−2480.34	−0.443656
$316$	−51.9178	−0.00924242
$317$	620.578	0.109953	0.0549766	−	0.998488i	$-0.482492\pi$
$317$	620.578	0.109953	0.0549766	+	0.998488i	$0.482492\pi$
$318$	4952.83	0.873399
$319$	−86.1579	−0.0151220
$320$	2604.49	0.454985
$321$	5859.44	1.01882
$322$	1476.65	0.255560
$323$	301.141	0.0518760
$324$	212.546	0.0364448
$325$	−68.3967	−0.0116737
$326$	1475.86	0.250738
$327$	−738.120	−0.124826
$328$	882.843	0.148619
$329$	5705.32	0.956062
$330$	−1111.85	−0.185471
$331$	−3351.82	−0.556594	−0.278297	−	0.960495i	$-0.589770\pi$
$331$	−3351.82	−0.556594	−0.278297	+	0.960495i	$0.589770\pi$
$332$	1360.80	0.224951
$333$	2507.09	0.412575
$334$	−843.085	−0.138118
$335$	5451.71	0.889131
$336$	6247.29	1.01434
$337$	11986.3	1.93750	0.968749	−	0.248045i	$-0.0797879\pi$
$337$	11986.3	1.93750	0.968749	+	0.248045i	$0.0797879\pi$
$338$	7114.73	1.14494
$339$	4272.90	0.684579
$340$	70.2557	0.0112063
$341$	527.328	0.0837432
$342$	−3410.60	−0.539252
$343$	−661.908	−0.104197
$344$	2549.64	0.399614
$345$	526.937	0.0822300
$346$	−2828.41	−0.439469
$347$	7008.39	1.08424	0.542118	−	0.840302i	$-0.317623\pi$
$347$	7008.39	1.08424	0.542118	+	0.840302i	$0.317623\pi$
$348$	−61.6584	−0.00949780
$349$	5105.50	0.783070	0.391535	−	0.920163i	$-0.371944\pi$
$349$	5105.50	0.783070	0.391535	+	0.920163i	$0.371944\pi$
$350$	−1577.25	−0.240878
$351$	101.748	0.0154727
$352$	1258.43	0.190553
$353$	−401.636	−0.0605578	−0.0302789	−	0.999541i	$-0.509640\pi$
$353$	−401.636	−0.0605578	−0.0302789	+	0.999541i	$0.509640\pi$
$354$	8428.29	1.26542
$355$	6845.05	1.02337
$356$	335.619	0.0499656
$357$	−207.171	−0.0307133
$358$	−11180.2	−1.65054
$359$	−1127.46	−0.165752	−0.0828758	−	0.996560i	$-0.526410\pi$
$359$	−1127.46	−0.165752	−0.0828758	+	0.996560i	$0.526410\pi$
$360$	1630.17	0.238659
$361$	6658.24	0.970731
$362$	−3975.52	−0.577206
$363$	363.000	0.0524864
$364$	−263.640	−0.0379629
$365$	−3446.84	−0.494289
$366$	596.480	0.0851871
$367$	−10633.6	−1.51246	−0.756228	−	0.654308i	$-0.772960\pi$
$367$	−10633.6	−1.51246	−0.756228	+	0.654308i	$0.772960\pi$
$368$	−1327.21	−0.188004
$369$	453.445	0.0639713
$370$	−9385.53	−1.31873
$371$	13504.2	1.88977
$372$	377.379	0.0525973
$373$	−2896.97	−0.402143	−0.201072	−	0.979577i	$-0.564442\pi$
$373$	−2896.97	−0.402143	−0.201072	+	0.979577i	$0.564442\pi$
$374$	−92.8674	−0.0128397
$375$	−4439.15	−0.611298
$376$	−3749.73	−0.514302
$377$	−29.5165	−0.00403229
$378$	2346.34	0.319266
$379$	3972.25	0.538366	0.269183	−	0.963089i	$-0.413246\pi$
$379$	3972.25	0.538366	0.269183	+	0.963089i	$0.413246\pi$
$380$	3153.55	0.425720
$381$	−1453.58	−0.195457
$382$	14162.5	1.89690
$383$	12957.0	1.72865	0.864325	−	0.502933i	$-0.167746\pi$
$383$	12957.0	1.72865	0.864325	+	0.502933i	$0.167746\pi$
$384$	−5209.45	−0.692301
$385$	−3031.53	−0.401302
$386$	−11517.2	−1.51869
$387$	1309.54	0.172010
$388$	−683.175	−0.0893891
$389$	14699.9	1.91597	0.957987	−	0.286812i	$-0.0925956\pi$
$389$	14699.9	1.91597	0.957987	+	0.286812i	$0.0925956\pi$
$390$	−380.904	−0.0494559
$391$	44.0125	0.00569261
$392$	6445.32	0.830454
$393$	−3753.17	−0.481736
$394$	13234.2	1.69221
$395$	−204.520	−0.0260519
$396$	259.779	0.0329656
$397$	1162.40	0.146950	0.0734749	−	0.997297i	$-0.476591\pi$
$397$	1162.40	0.146950	0.0734749	+	0.997297i	$0.476591\pi$
$398$	11521.2	1.45101
$399$	−9299.23	−1.16678
$400$	1417.63	0.177203
$401$	−12754.0	−1.58829	−0.794144	−	0.607730i	$-0.792080\pi$
$401$	−12754.0	−1.58829	−0.794144	+	0.607730i	$0.792080\pi$
$402$	−5157.17	−0.639841
$403$	180.655	0.0223302
$404$	2858.35	0.352001
$405$	837.284	0.102728
$406$	−680.658	−0.0832032
$407$	3064.22	0.373188
$408$	136.160	0.0165219
$409$	5538.56	0.669594	0.334797	−	0.942290i	$-0.391332\pi$
$409$	5538.56	0.669594	0.334797	+	0.942290i	$0.391332\pi$
$410$	−1697.52	−0.204474
$411$	1026.42	0.123187
$412$	−3362.64	−0.402100
$413$	22980.3	2.73798
$414$	−498.468	−0.0591748
$415$	5360.62	0.634078
$416$	431.122	0.0508112
$417$	641.286	0.0753091
$418$	−4168.51	−0.487772
$419$	2375.11	0.276926	0.138463	−	0.990368i	$-0.455784\pi$
$419$	2375.11	0.276926	0.138463	+	0.990368i	$0.455784\pi$
$420$	−2169.50	−0.252049
$421$	3580.97	0.414550	0.207275	−	0.978283i	$-0.433540\pi$
$421$	3580.97	0.414550	0.207275	+	0.978283i	$0.433540\pi$
$422$	−2940.16	−0.339158
$423$	−1925.93	−0.221376
$424$	−8875.43	−1.01658
$425$	−47.0110	−0.00536557
$426$	−6475.23	−0.736445
$427$	1626.34	0.184319
$428$	5125.10	0.578811
$429$	124.359	0.0139955
$430$	−4902.40	−0.549802
$431$	−5619.57	−0.628039	−0.314020	−	0.949416i	$-0.601676\pi$
$431$	−5619.57	−0.628039	−0.314020	+	0.949416i	$0.601676\pi$
$432$	−2108.88	−0.234869
$433$	8864.47	0.983832	0.491916	−	0.870643i	$-0.336297\pi$
$433$	8864.47	0.983832	0.491916	+	0.870643i	$0.336297\pi$
$434$	4165.95	0.460765
$435$	−242.891	−0.0267718
$436$	−645.615	−0.0709160
$437$	1975.58	0.216258
$438$	3260.61	0.355703
$439$	2989.25	0.324987	0.162494	−	0.986710i	$-0.448046\pi$
$439$	2989.25	0.324987	0.162494	+	0.986710i	$0.448046\pi$
$440$	1992.42	0.215875
$441$	3310.44	0.357460
$442$	−31.8150	−0.00342373
$443$	5247.41	0.562781	0.281391	−	0.959593i	$-0.409204\pi$
$443$	5247.41	0.562781	0.281391	+	0.959593i	$0.409204\pi$
$444$	2192.89	0.234391
$445$	1322.10	0.140840
$446$	−1513.88	−0.160727
$447$	2556.45	0.270505
$448$	−6717.64	−0.708434
$449$	−4202.42	−0.441703	−0.220851	−	0.975307i	$-0.570884\pi$
$449$	−4202.42	−0.441703	−0.220851	+	0.975307i	$0.570884\pi$
$450$	532.427	0.0557753
$451$	554.210	0.0578642
$452$	3737.40	0.388922
$453$	3508.26	0.363868
$454$	525.749	0.0543494
$455$	−1038.56	−0.107007
$456$	6111.77	0.627653
$457$	−1913.30	−0.195843	−0.0979215	−	0.995194i	$-0.531219\pi$
$457$	−1913.30	−0.195843	−0.0979215	+	0.995194i	$0.531219\pi$
$458$	4513.52	0.460487
$459$	69.9343	0.00711166
$460$	460.899	0.0467164
$461$	8983.07	0.907556	0.453778	−	0.891115i	$-0.350076\pi$
$461$	8983.07	0.907556	0.453778	+	0.891115i	$0.350076\pi$
$462$	2867.74	0.288787
$463$	17405.0	1.74704	0.873518	−	0.486791i	$-0.161833\pi$
$463$	17405.0	1.74704	0.873518	+	0.486791i	$0.161833\pi$
$464$	611.774	0.0612088
$465$	1486.61	0.148258
$466$	11346.1	1.12790
$467$	6872.10	0.680949	0.340474	−	0.940254i	$-0.389412\pi$
$467$	6872.10	0.680949	0.340474	+	0.940254i	$0.389412\pi$
$468$	88.9964	0.00879030
$469$	−14061.4	−1.38442
$470$	7209.91	0.707593
$471$	9272.04	0.907077
$472$	−15103.4	−1.47286
$473$	1600.55	0.155589
$474$	193.470	0.0187476
$475$	−2110.17	−0.203834
$476$	−181.207	−0.0174488
$477$	−4558.59	−0.437575
$478$	12377.8	1.18441
$479$	5192.37	0.495293	0.247647	−	0.968850i	$-0.420343\pi$
$479$	5192.37	0.495293	0.247647	+	0.968850i	$0.420343\pi$
$480$	3547.70	0.337353
$481$	1049.76	0.0995110
$482$	−8788.98	−0.830554
$483$	−1359.11	−0.128036
$484$	317.507	0.0298185
$485$	−2691.23	−0.251964
$486$	−792.047	−0.0739259
$487$	3128.97	0.291144	0.145572	−	0.989348i	$-0.453498\pi$
$487$	3128.97	0.291144	0.145572	+	0.989348i	$0.453498\pi$
$488$	−1068.89	−0.0991521
$489$	−1358.39	−0.125620
$490$	−12393.0	−1.14257
$491$	12128.8	1.11480	0.557399	−	0.830245i	$-0.311800\pi$
$491$	12128.8	1.11480	0.557399	+	0.830245i	$0.311800\pi$
$492$	396.617	0.0363432
$493$	−20.2875	−0.00185335
$494$	−1428.07	−0.130065
$495$	1023.35	0.0929212
$496$	−3744.35	−0.338964
$497$	−17655.1	−1.59344
$498$	−5070.99	−0.456298
$499$	−7596.02	−0.681452	−0.340726	−	0.940163i	$-0.610673\pi$
$499$	−7596.02	−0.681452	−0.340726	+	0.940163i	$0.610673\pi$
$500$	−3882.81	−0.347289
$501$	775.975	0.0691976
$502$	−1282.87	−0.114058
$503$	5832.80	0.517041	0.258521	−	0.966006i	$-0.416765\pi$
$503$	5832.80	0.517041	0.258521	+	0.966006i	$0.416765\pi$
$504$	−4204.61	−0.371604
$505$	11259.9	0.992198
$506$	−609.239	−0.0535256
$507$	−6548.40	−0.573618
$508$	−1271.41	−0.111043
$509$	−8902.59	−0.775246	−0.387623	−	0.921818i	$-0.626704\pi$
$509$	−8902.59	−0.775246	−0.387623	+	0.921818i	$0.626704\pi$
$510$	−261.806	−0.0227313
$511$	8890.27	0.769633
$512$	2013.48	0.173797
$513$	3139.12	0.270167
$514$	3297.12	0.282937
$515$	−13246.5	−1.13341
$516$	1145.42	0.0977218
$517$	−2353.91	−0.200242
$518$	24207.7	2.05333
$519$	2603.27	0.220175
$520$	682.576	0.0575633
$521$	6008.59	0.505262	0.252631	−	0.967563i	$-0.418704\pi$
$521$	6008.59	0.505262	0.252631	+	0.967563i	$0.418704\pi$
$522$	229.768	0.0192657
$523$	15228.1	1.27319	0.636593	−	0.771200i	$-0.280343\pi$
$523$	15228.1	1.27319	0.636593	+	0.771200i	$0.280343\pi$
$524$	−3282.80	−0.273683
$525$	1451.70	0.120681
$526$	−7995.61	−0.662785
$527$	124.169	0.0102636
$528$	−2577.52	−0.212447
$529$	−11878.3	−0.976269
$530$	17065.5	1.39864
$531$	−7757.40	−0.633979
$532$	−8133.81	−0.662867
$533$	189.864	0.0154295
$534$	−1250.67	−0.101352
$535$	20189.3	1.63152
$536$	9241.60	0.744732
$537$	10290.3	0.826923
$538$	−6512.31	−0.521870
$539$	4046.09	0.323335
$540$	732.351	0.0583618
$541$	8553.62	0.679757	0.339879	−	0.940469i	$-0.389614\pi$
$541$	8553.62	0.679757	0.339879	+	0.940469i	$0.389614\pi$
$542$	−19271.0	−1.52723
$543$	3659.07	0.289182
$544$	296.322	0.0233542
$545$	−2543.27	−0.199893
$546$	982.447	0.0770052
$547$	−2197.49	−0.171769	−0.0858847	−	0.996305i	$-0.527372\pi$
$547$	−2197.49	−0.171769	−0.0858847	+	0.996305i	$0.527372\pi$
$548$	897.788	0.0699847
$549$	−549.000	−0.0426790
$550$	650.745	0.0504506
$551$	−910.640	−0.0704076
$552$	893.250	0.0688755
$553$	527.509	0.0405641
$554$	−10423.6	−0.799380
$555$	8638.45	0.660688
$556$	560.917	0.0427845
$557$	12005.7	0.913284	0.456642	−	0.889650i	$-0.349052\pi$
$557$	12005.7	0.913284	0.456642	+	0.889650i	$0.349052\pi$
$558$	−1406.29	−0.106690
$559$	548.325	0.0414878
$560$	21525.7	1.62433
$561$	85.4752	0.00643274
$562$	−20277.9	−1.52202
$563$	21775.6	1.63007	0.815037	−	0.579408i	$-0.196716\pi$
$563$	21775.6	1.63007	0.815037	+	0.579408i	$0.196716\pi$
$564$	−1684.56	−0.125768
$565$	14722.8	1.09627
$566$	−7806.61	−0.579746
$567$	−2159.57	−0.159953
$568$	11603.6	0.857173
$569$	−1070.16	−0.0788458	−0.0394229	−	0.999223i	$-0.512552\pi$
$569$	−1070.16	−0.0788458	−0.0394229	+	0.999223i	$0.512552\pi$
$570$	−11751.6	−0.863545
$571$	14807.1	1.08522	0.542609	−	0.839986i	$-0.317437\pi$
$571$	14807.1	1.08522	0.542609	+	0.839986i	$0.317437\pi$
$572$	108.773	0.00795112
$573$	−13035.2	−0.950352
$574$	4378.33	0.318376
$575$	−308.406	−0.0223677
$576$	2267.66	0.164038
$577$	−7213.62	−0.520463	−0.260231	−	0.965546i	$-0.583799\pi$
$577$	−7213.62	−0.520463	−0.260231	+	0.965546i	$0.583799\pi$
$578$	15991.8	1.15082
$579$	10600.5	0.760865
$580$	−212.451	−0.0152095
$581$	−13826.4	−0.987290
$582$	2545.83	0.181320
$583$	−5571.60	−0.395802
$584$	−5842.99	−0.414015
$585$	350.584	0.0247775
$586$	−28911.6	−2.03810
$587$	3531.39	0.248306	0.124153	−	0.992263i	$-0.460379\pi$
$587$	3531.39	0.248306	0.124153	+	0.992263i	$0.460379\pi$
$588$	2895.56	0.203080
$589$	5573.55	0.389905
$590$	29040.6	2.02641
$591$	−12180.8	−0.847802
$592$	−21757.8	−1.51054
$593$	2990.97	0.207124	0.103562	−	0.994623i	$-0.466976\pi$
$593$	2990.97	0.207124	0.103562	+	0.994623i	$0.466976\pi$
$594$	−968.057	−0.0668685
$595$	−713.831	−0.0491836
$596$	2236.06	0.153679
$597$	−10604.1	−0.726962
$598$	−208.716	−0.0142726
$599$	13671.8	0.932581	0.466291	−	0.884632i	$-0.345590\pi$
$599$	13671.8	0.932581	0.466291	+	0.884632i	$0.345590\pi$
$600$	−954.105	−0.0649186
$601$	6852.94	0.465120	0.232560	−	0.972582i	$-0.425290\pi$
$601$	6852.94	0.465120	0.232560	+	0.972582i	$0.425290\pi$
$602$	12644.5	0.856068
$603$	4746.66	0.320562
$604$	3068.59	0.206720
$605$	1250.76	0.0840504
$606$	−10651.6	−0.714011
$607$	7839.24	0.524192	0.262096	−	0.965042i	$-0.415586\pi$
$607$	7839.24	0.524192	0.262096	+	0.965042i	$0.415586\pi$
$608$	13300.9	0.887211
$609$	626.478	0.0416850
$610$	2055.24	0.136417
$611$	−806.417	−0.0533947
$612$	61.1698	0.00404026
$613$	−22878.5	−1.50743	−0.753716	−	0.657200i	$-0.771741\pi$
$613$	−22878.5	−1.50743	−0.753716	+	0.657200i	$0.771741\pi$
$614$	−3007.51	−0.197676
$615$	1562.39	0.102442
$616$	−5138.97	−0.336128
$617$	14253.7	0.930039	0.465020	−	0.885300i	$-0.346047\pi$
$617$	14253.7	0.930039	0.465020	+	0.885300i	$0.346047\pi$
$618$	12530.8	0.815634
$619$	−24961.0	−1.62079	−0.810393	−	0.585887i	$-0.800746\pi$
$619$	−24961.0	−1.62079	−0.810393	+	0.585887i	$0.800746\pi$
$620$	1300.30	0.0842280
$621$	458.790	0.0296467
$622$	−22508.4	−1.45097
$623$	−3410.04	−0.219295
$624$	−883.021	−0.0566493
$625$	−13026.8	−0.833718
$626$	813.699	0.0519520
$627$	3836.70	0.244375
$628$	8110.02	0.515327
$629$	721.528	0.0457380
$630$	8084.56	0.511264
$631$	−3005.79	−0.189633	−0.0948167	−	0.995495i	$-0.530226\pi$
$631$	−3005.79	−0.189633	−0.0948167	+	0.995495i	$0.530226\pi$
$632$	−346.697	−0.0218210
$633$	2706.12	0.169919
$634$	−2022.75	−0.126709
$635$	−5008.46	−0.313000
$636$	−3987.28	−0.248594
$637$	1386.13	0.0862175
$638$	280.828	0.0174264
$639$	5959.80	0.368961
$640$	−17949.7	−1.10863
$641$	−14827.9	−0.913675	−0.456838	−	0.889550i	$-0.651018\pi$
$641$	−14827.9	−0.913675	−0.456838	+	0.889550i	$0.651018\pi$
$642$	−19098.6	−1.17408
$643$	21861.6	1.34080	0.670401	−	0.741999i	$-0.266122\pi$
$643$	21861.6	1.34080	0.670401	+	0.741999i	$0.266122\pi$
$644$	−1188.78	−0.0727397
$645$	4512.17	0.275452
$646$	−981.555	−0.0597814
$647$	17255.8	1.04852	0.524262	−	0.851557i	$-0.324341\pi$
$647$	17255.8	1.04852	0.524262	+	0.851557i	$0.324341\pi$
$648$	1419.34	0.0860447
$649$	−9481.27	−0.573455
$650$	222.936	0.0134527
$651$	−3834.35	−0.230845
$652$	−1188.15	−0.0713672
$653$	−21270.2	−1.27468	−0.637340	−	0.770583i	$-0.719965\pi$
$653$	−21270.2	−1.27468	−0.637340	+	0.770583i	$0.719965\pi$
$654$	2405.87	0.143848
$655$	−12932.0	−0.771441
$656$	−3935.23	−0.234215
$657$	−3001.07	−0.178208
$658$	−18596.2	−1.10176
$659$	28041.6	1.65758	0.828790	−	0.559559i	$-0.189030\pi$
$659$	28041.6	1.65758	0.828790	+	0.559559i	$0.189030\pi$
$660$	895.096	0.0527902
$661$	−26235.0	−1.54376	−0.771879	−	0.635769i	$-0.780683\pi$
$661$	−26235.0	−1.54376	−0.771879	+	0.635769i	$0.780683\pi$
$662$	10925.1	0.641413
$663$	29.2826	0.00171529
$664$	9087.17	0.531101
$665$	−32041.5	−1.86845
$666$	−8171.73	−0.475448
$667$	−133.092	−0.00772616
$668$	678.726	0.0393124
$669$	1393.37	0.0805245
$670$	−17769.6	−1.02463
$671$	−671.000	−0.0386046
$672$	−9150.42	−0.525276
$673$	−13097.2	−0.750166	−0.375083	−	0.926991i	$-0.622386\pi$
$673$	−13097.2	−0.750166	−0.375083	+	0.926991i	$0.622386\pi$
$674$	−39068.8	−2.23275
$675$	−490.046	−0.0279435
$676$	−5727.72	−0.325883
$677$	−14263.4	−0.809732	−0.404866	−	0.914376i	$-0.632682\pi$
$677$	−14263.4	−0.809732	−0.404866	+	0.914376i	$0.632682\pi$
$678$	−13927.3	−0.788902
$679$	6941.38	0.392321
$680$	469.154	0.0264577
$681$	−483.899	−0.0272292
$682$	−1718.80	−0.0965048
$683$	26813.0	1.50215	0.751076	−	0.660216i	$-0.229535\pi$
$683$	26813.0	1.50215	0.751076	+	0.660216i	$0.229535\pi$
$684$	2745.71	0.153487
$685$	3536.66	0.197268
$686$	2157.46	0.120076
$687$	−4154.24	−0.230705
$688$	−11364.9	−0.629770
$689$	−1908.75	−0.105541
$690$	−1717.53	−0.0947610
$691$	27553.9	1.51693	0.758466	−	0.651712i	$-0.225949\pi$
$691$	27553.9	1.51693	0.758466	+	0.651712i	$0.225949\pi$
$692$	2277.01	0.125085
$693$	−2639.47	−0.144683
$694$	−22843.5	−1.24946
$695$	2209.62	0.120598
$696$	−411.742	−0.0224239
$697$	130.499	0.00709184
$698$	−16641.1	−0.902402
$699$	−10443.0	−0.565078
$700$	1269.76	0.0685609
$701$	4497.74	0.242336	0.121168	−	0.992632i	$-0.461336\pi$
$701$	4497.74	0.242336	0.121168	+	0.992632i	$0.461336\pi$
$702$	−331.642	−0.0178305
$703$	32387.0	1.73755
$704$	2771.58	0.148378
$705$	−6636.01	−0.354506
$706$	1309.11	0.0697863
$707$	−29042.2	−1.54490
$708$	−6785.21	−0.360175
$709$	−5147.64	−0.272671	−0.136336	−	0.990663i	$-0.543533\pi$
$709$	−5147.64	−0.272671	−0.136336	+	0.990663i	$0.543533\pi$
$710$	−22311.1	−1.17933
$711$	−178.070	−0.00939261
$712$	2241.20	0.117967
$713$	814.589	0.0427862
$714$	675.264	0.0353937
$715$	428.491	0.0224121
$716$	9000.64	0.469790
$717$	−11392.6	−0.593394
$718$	3674.89	0.191011
$719$	−9791.94	−0.507897	−0.253948	−	0.967218i	$-0.581729\pi$
$719$	−9791.94	−0.507897	−0.253948	+	0.967218i	$0.581729\pi$
$720$	−7266.38	−0.376114
$721$	34166.0	1.76478
$722$	−21702.2	−1.11866
$723$	8089.38	0.416109
$724$	3200.50	0.164289
$725$	142.159	0.00728231
$726$	−1183.18	−0.0604848
$727$	−35491.3	−1.81059	−0.905295	−	0.424784i	$-0.860350\pi$
$727$	−35491.3	−1.81059	−0.905295	+	0.424784i	$0.860350\pi$
$728$	−1760.54	−0.0896289
$729$	729.000	0.0370370
$730$	11234.8	0.569614
$731$	376.880	0.0190689
$732$	−480.197	−0.0242467
$733$	−16685.2	−0.840764	−0.420382	−	0.907347i	$-0.638104\pi$
$733$	−16685.2	−0.840764	−0.420382	+	0.907347i	$0.638104\pi$
$734$	34659.8	1.74294
$735$	11406.5	0.572428
$736$	1943.96	0.0973580
$737$	5801.47	0.289959
$738$	−1477.98	−0.0737199
$739$	−27670.0	−1.37735	−0.688673	−	0.725072i	$-0.741806\pi$
$739$	−27670.0	−1.37735	−0.688673	+	0.725072i	$0.741806\pi$
$740$	7555.84	0.375349
$741$	1314.40	0.0651628
$742$	−44016.3	−2.17775
$743$	−21606.9	−1.06687	−0.533433	−	0.845842i	$-0.679098\pi$
$743$	−21606.9	−1.06687	−0.533433	+	0.845842i	$0.679098\pi$
$744$	2520.06	0.124180
$745$	8808.53	0.433181
$746$	9442.53	0.463426
$747$	4667.34	0.228607
$748$	74.7630	0.00365456
$749$	−52073.5	−2.54035
$750$	14469.2	0.704454
$751$	38360.2	1.86389	0.931947	−	0.362594i	$-0.118109\pi$
$751$	38360.2	1.86389	0.931947	+	0.362594i	$0.118109\pi$
$752$	16714.2	0.810512
$753$	1180.75	0.0571435
$754$	96.2075	0.00464678
$755$	12088.1	0.582690
$756$	−1888.92	−0.0908722
$757$	−17703.3	−0.849985	−0.424992	−	0.905197i	$-0.639723\pi$
$757$	−17703.3	−0.849985	−0.424992	+	0.905197i	$0.639723\pi$
$758$	−12947.4	−0.620408
$759$	560.743	0.0268165
$760$	21058.8	1.00511
$761$	14815.9	0.705748	0.352874	−	0.935671i	$-0.385204\pi$
$761$	14815.9	0.705748	0.352874	+	0.935671i	$0.385204\pi$
$762$	4737.86	0.225242
$763$	6559.75	0.311244
$764$	−11401.5	−0.539913
$765$	240.966	0.0113884
$766$	−42232.8	−1.99208
$767$	−3248.15	−0.152912
$768$	10932.9	0.513679
$769$	2504.31	0.117435	0.0587177	−	0.998275i	$-0.481299\pi$
$769$	2504.31	0.117435	0.0587177	+	0.998275i	$0.481299\pi$
$770$	9881.13	0.462456
$771$	−3034.67	−0.141752
$772$	9271.98	0.432261
$773$	−22353.8	−1.04012	−0.520059	−	0.854130i	$-0.674090\pi$
$773$	−22353.8	−1.04012	−0.520059	+	0.854130i	$0.674090\pi$
$774$	−4268.39	−0.198222
$775$	−870.085	−0.0403282
$776$	−4562.11	−0.211044
$777$	−22280.8	−1.02872
$778$	−47913.6	−2.20795
$779$	5857.69	0.269414
$780$	306.647	0.0140766
$781$	7284.20	0.333738
$782$	−143.457	−0.00656010
$783$	−211.479	−0.00965214
$784$	−28729.7	−1.30875
$785$	31947.8	1.45257
$786$	12233.3	0.555148
$787$	−11601.9	−0.525494	−0.262747	−	0.964865i	$-0.584628\pi$
$787$	−11601.9	−0.525494	−0.262747	+	0.964865i	$0.584628\pi$
$788$	−10654.2	−0.481652
$789$	7359.16	0.332057
$790$	666.623	0.0300220
$791$	−37973.8	−1.70694
$792$	1734.75	0.0778304
$793$	−229.875	−0.0102939
$794$	−3788.78	−0.169343
$795$	−15707.1	−0.700722
$796$	−9275.13	−0.413000
$797$	−17148.4	−0.762143	−0.381071	−	0.924546i	$-0.624445\pi$
$797$	−17148.4	−0.762143	−0.381071	+	0.924546i	$0.624445\pi$
$798$	30310.4	1.34458
$799$	−554.274	−0.0245417
$800$	−2076.40	−0.0917649
$801$	1151.12	0.0507776
$802$	41571.0	1.83033
$803$	−3667.97	−0.161195
$804$	4151.78	0.182117
$805$	−4682.95	−0.205034
$806$	−588.836	−0.0257331
$807$	5993.94	0.261458
$808$	19087.5	0.831060
$809$	−15845.8	−0.688640	−0.344320	−	0.938852i	$-0.611891\pi$
$809$	−15845.8	−0.688640	−0.344320	+	0.938852i	$0.611891\pi$
$810$	−2729.09	−0.118383
$811$	−11106.5	−0.480889	−0.240445	−	0.970663i	$-0.577293\pi$
$811$	−11106.5	−0.480889	−0.240445	+	0.970663i	$0.577293\pi$
$812$	547.965	0.0236820
$813$	17737.0	0.765147
$814$	−9987.67	−0.430059
$815$	−4680.47	−0.201165
$816$	−606.926	−0.0260376
$817$	16916.9	0.724415
$818$	−18052.7	−0.771634
$819$	−904.245	−0.0385798
$820$	1366.59	0.0581992
$821$	−35162.7	−1.49475	−0.747373	−	0.664404i	$-0.768685\pi$
$821$	−35162.7	−1.49475	−0.747373	+	0.664404i	$0.768685\pi$
$822$	−3345.58	−0.141959
$823$	46635.1	1.97521	0.987604	−	0.156964i	$-0.0501705\pi$
$823$	46635.1	1.97521	0.987604	+	0.156964i	$0.0501705\pi$
$824$	−22455.0	−0.949343
$825$	−598.945	−0.0252759
$826$	−74903.2	−3.15522
$827$	2925.09	0.122993	0.0614966	−	0.998107i	$-0.480413\pi$
$827$	2925.09	0.122993	0.0614966	+	0.998107i	$0.480413\pi$
$828$	401.292	0.0168428
$829$	18440.2	0.772562	0.386281	−	0.922381i	$-0.373759\pi$
$829$	18440.2	0.772562	0.386281	+	0.922381i	$0.373759\pi$
$830$	−17472.7	−0.730705
$831$	9593.89	0.400491
$832$	949.503	0.0395650
$833$	952.729	0.0396280
$834$	−2090.24	−0.0867855
$835$	2673.71	0.110811
$836$	3355.87	0.138834
$837$	1294.35	0.0534520
$838$	−7741.57	−0.319127
$839$	4912.33	0.202137	0.101068	−	0.994879i	$-0.467774\pi$
$839$	4912.33	0.202137	0.101068	+	0.994879i	$0.467774\pi$
$840$	−14487.5	−0.595077
$841$	−24327.7	−0.997485
$842$	−11672.0	−0.477723
$843$	18663.8	0.762534
$844$	2366.98	0.0965340
$845$	−22563.2	−0.918578
$846$	6277.48	0.255111
$847$	−3226.02	−0.130871
$848$	39561.8	1.60207
$849$	7185.21	0.290454
$850$	153.230	0.00618323
$851$	4733.44	0.190670
$852$	5212.89	0.209613
$853$	7605.38	0.305279	0.152640	−	0.988282i	$-0.451223\pi$
$853$	7605.38	0.305279	0.152640	+	0.988282i	$0.451223\pi$
$854$	−5300.98	−0.212407
$855$	10816.2	0.432638
$856$	34224.4	1.36655
$857$	−42921.5	−1.71082	−0.855408	−	0.517954i	$-0.826694\pi$
$857$	−42921.5	−1.71082	−0.855408	+	0.517954i	$0.826694\pi$
$858$	−405.341	−0.0161283
$859$	−6173.96	−0.245230	−0.122615	−	0.992454i	$-0.539128\pi$
$859$	−6173.96	−0.245230	−0.122615	+	0.992454i	$0.539128\pi$
$860$	3946.68	0.156489
$861$	−4029.81	−0.159507
$862$	18316.7	0.723746
$863$	−36873.4	−1.45445	−0.727223	−	0.686402i	$-0.759189\pi$
$863$	−36873.4	−1.45445	−0.727223	+	0.686402i	$0.759189\pi$
$864$	3088.89	0.121627
$865$	8969.85	0.352583
$866$	−28893.3	−1.13376
$867$	−14718.9	−0.576562
$868$	−3353.81	−0.131147
$869$	−217.641	−0.00849594
$870$	791.691	0.0308516
$871$	1987.50	0.0773179
$872$	−4311.29	−0.167430
$873$	−2343.19	−0.0908417
$874$	−6439.30	−0.249214
$875$	39451.2	1.52422
$876$	−2624.96	−0.101243
$877$	15047.3	0.579374	0.289687	−	0.957121i	$-0.406449\pi$
$877$	15047.3	0.579374	0.289687	+	0.957121i	$0.406449\pi$
$878$	−9743.33	−0.374512
$879$	26610.3	1.02109
$880$	−8881.14	−0.340208
$881$	25419.3	0.972074	0.486037	−	0.873938i	$-0.338442\pi$
$881$	25419.3	0.972074	0.486037	+	0.873938i	$0.338442\pi$
$882$	−10790.2	−0.411934
$883$	−6497.48	−0.247631	−0.123815	−	0.992305i	$-0.539513\pi$
$883$	−6497.48	−0.247631	−0.123815	+	0.992305i	$0.539513\pi$
$884$	25.6127	0.000974490 0
$885$	−26729.0	−1.01524
$886$	−17103.7	−0.648544
$887$	43590.4	1.65008	0.825040	−	0.565074i	$-0.191153\pi$
$887$	43590.4	1.65008	0.825040	+	0.565074i	$0.191153\pi$
$888$	14643.7	0.553389
$889$	12918.1	0.487356
$890$	−4309.33	−0.162302
$891$	891.000	0.0335013
$892$	1218.75	0.0457474
$893$	−24879.5	−0.932320
$894$	−8332.63	−0.311728
$895$	35456.2	1.32421
$896$	46297.0	1.72620
$897$	192.103	0.00715063
$898$	13697.6	0.509014
$899$	−375.483	−0.0139300
$900$	−428.631	−0.0158752
$901$	−1311.94	−0.0485095
$902$	−1806.42	−0.0666821
$903$	−11638.0	−0.428892
$904$	24957.6	0.918229
$905$	12607.7	0.463088
$906$	−11435.0	−0.419318
$907$	31175.5	1.14131	0.570654	−	0.821191i	$-0.306690\pi$
$907$	31175.5	1.14131	0.570654	+	0.821191i	$0.306690\pi$
$908$	−423.255	−0.0154694
$909$	9803.71	0.357721
$910$	3385.13	0.123314
$911$	−3022.55	−0.109925	−0.0549625	−	0.998488i	$-0.517504\pi$
$911$	−3022.55	−0.109925	−0.0549625	+	0.998488i	$0.517504\pi$
$912$	−27242.9	−0.989148
$913$	5704.53	0.206782
$914$	6236.30	0.225688
$915$	−1891.64	−0.0683450
$916$	−3633.61	−0.131068
$917$	33354.8	1.20117
$918$	−227.947	−0.00819541
$919$	−34644.1	−1.24353	−0.621766	−	0.783203i	$-0.713584\pi$
$919$	−34644.1	−1.24353	−0.621766	+	0.783203i	$0.713584\pi$
$920$	3077.79	0.110295
$921$	2768.11	0.0990361
$922$	−29279.9	−1.04586
$923$	2495.46	0.0889914
$924$	−2308.68	−0.0821970
$925$	−5055.92	−0.179716
$926$	−56730.7	−2.01327
$927$	−11533.3	−0.408635
$928$	−896.067	−0.0316970
$929$	1651.73	0.0583332	0.0291666	−	0.999575i	$-0.490715\pi$
$929$	1651.73	0.0583332	0.0291666	+	0.999575i	$0.490715\pi$
$930$	−4845.53	−0.170851
$931$	42764.9	1.50544
$932$	−9134.22	−0.321031
$933$	20716.8	0.726941
$934$	−22399.3	−0.784719
$935$	294.514	0.0103012
$936$	594.300	0.0207535
$937$	−13913.2	−0.485084	−0.242542	−	0.970141i	$-0.577981\pi$
$937$	−13913.2	−0.485084	−0.242542	+	0.970141i	$0.577981\pi$
$938$	45832.3	1.59539
$939$	−748.928	−0.0260281
$940$	−5804.35	−0.201401
$941$	33075.8	1.14584	0.572922	−	0.819610i	$-0.305810\pi$
$941$	33075.8	1.14584	0.572922	+	0.819610i	$0.305810\pi$
$942$	−30221.8	−1.04531
$943$	856.115	0.0295641
$944$	67322.8	2.32116
$945$	−7441.03	−0.256145
$946$	−5216.92	−0.179299
$947$	19897.7	0.682775	0.341387	−	0.939923i	$-0.389103\pi$
$947$	19897.7	0.682775	0.341387	+	0.939923i	$0.389103\pi$
$948$	−155.753	−0.00533611
$949$	−1256.59	−0.0429829
$950$	6878.00	0.234897
$951$	1861.74	0.0634815
$952$	−1210.07	−0.0411959
$953$	−10800.9	−0.367132	−0.183566	−	0.983007i	$-0.558764\pi$
$953$	−10800.9	−0.367132	−0.183566	+	0.983007i	$0.558764\pi$
$954$	14858.5	0.504257
$955$	−44914.1	−1.52187
$956$	−9964.80	−0.337118
$957$	−258.474	−0.00873069
$958$	−16924.3	−0.570771
$959$	−9121.95	−0.307156
$960$	7813.47	0.262686
$961$	−27492.9	−0.922858
$962$	−3421.63	−0.114675
$963$	17578.3	0.588217
$964$	7075.58	0.236399
$965$	36525.1	1.21843
$966$	4429.94	0.147548
$967$	37643.1	1.25183	0.625915	−	0.779891i	$-0.284726\pi$
$967$	37643.1	1.25183	0.625915	+	0.779891i	$0.284726\pi$
$968$	2120.25	0.0704002
$969$	903.424	0.0299506
$970$	8771.95	0.290361
$971$	−15133.8	−0.500172	−0.250086	−	0.968224i	$-0.580459\pi$
$971$	−15133.8	−0.500172	−0.250086	+	0.968224i	$0.580459\pi$
$972$	637.638	0.0210414
$973$	−5699.18	−0.187777
$974$	−10198.7	−0.335512
$975$	−205.190	−0.00673984
$976$	4764.51	0.156258
$977$	−12585.8	−0.412134	−0.206067	−	0.978538i	$-0.566066\pi$
$977$	−12585.8	−0.412134	−0.206067	+	0.978538i	$0.566066\pi$
$978$	4427.59	0.144764
$979$	1406.92	0.0459300
$980$	9976.97	0.325207
$981$	−2214.36	−0.0720684
$982$	−39533.3	−1.28468
$983$	−31841.8	−1.03316	−0.516580	−	0.856239i	$-0.672795\pi$
$983$	−31841.8	−1.03316	−0.516580	+	0.856239i	$0.672795\pi$
$984$	2648.53	0.0858049
$985$	−41970.3	−1.35765
$986$	66.1262	0.00213579
$987$	17116.0	0.551983
$988$	1149.67	0.0370202
$989$	2472.45	0.0794936
$990$	−3335.55	−0.107082
$991$	14579.3	0.467333	0.233666	−	0.972317i	$-0.424928\pi$
$991$	14579.3	0.467333	0.233666	+	0.972317i	$0.424928\pi$
$992$	5484.36	0.175533
$993$	−10055.5	−0.321350
$994$	57546.1	1.83627
$995$	−36537.5	−1.16414
$996$	4082.41	0.129876
$997$	−4192.20	−0.133168	−0.0665839	−	0.997781i	$-0.521210\pi$
$997$	−4192.20	−0.133168	−0.0665839	+	0.997781i	$0.521210\pi$
$998$	24758.9	0.785299
$999$	7521.26	0.238200

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2013.4.a.f.1.9	✓	38

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2013.4.a.f.1.9	✓	38	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)

\(f(q)\)	\(=\)	\(q-3.25945 q^{2} +3.00000 q^{3} +2.62403 q^{4} +10.3368 q^{5} -9.77836 q^{6} -26.6613 q^{7} +17.5227 q^{8} +9.00000 q^{9} +O(q^{10})\)	\(q-3.25945 q^{2} +3.00000 q^{3} +2.62403 q^{4} +10.3368 q^{5} -9.77836 q^{6} -26.6613 q^{7} +17.5227 q^{8} +9.00000 q^{9} -33.6924 q^{10} +11.0000 q^{11} +7.87208 q^{12} +3.76844 q^{13} +86.9013 q^{14} +31.0105 q^{15} -78.1067 q^{16} +2.59016 q^{17} -29.3351 q^{18} +116.264 q^{19} +27.1241 q^{20} -79.9840 q^{21} -35.8540 q^{22} +16.9922 q^{23} +52.5682 q^{24} -18.1499 q^{25} -12.2830 q^{26} +27.0000 q^{27} -69.9600 q^{28} -7.83254 q^{29} -101.077 q^{30} +47.9389 q^{31} +114.403 q^{32} +33.0000 q^{33} -8.44249 q^{34} -275.594 q^{35} +23.6162 q^{36} +278.565 q^{37} -378.956 q^{38} +11.3053 q^{39} +181.130 q^{40} +50.3828 q^{41} +260.704 q^{42} +145.505 q^{43} +28.8643 q^{44} +93.0315 q^{45} -55.3853 q^{46} -213.992 q^{47} -234.320 q^{48} +367.827 q^{49} +59.1586 q^{50} +7.77047 q^{51} +9.88849 q^{52} -506.509 q^{53} -88.0052 q^{54} +113.705 q^{55} -467.179 q^{56} +348.791 q^{57} +25.5298 q^{58} -861.934 q^{59} +81.3724 q^{60} -61.0000 q^{61} -156.255 q^{62} -239.952 q^{63} +251.962 q^{64} +38.9537 q^{65} -107.562 q^{66} +527.406 q^{67} +6.79664 q^{68} +50.9767 q^{69} +898.285 q^{70} +662.200 q^{71} +157.705 q^{72} -333.452 q^{73} -907.970 q^{74} -54.4496 q^{75} +305.079 q^{76} -293.275 q^{77} -36.8491 q^{78} -19.7856 q^{79} -807.376 q^{80} +81.0000 q^{81} -164.220 q^{82} +518.594 q^{83} -209.880 q^{84} +26.7740 q^{85} -474.265 q^{86} -23.4976 q^{87} +192.750 q^{88} +127.902 q^{89} -303.232 q^{90} -100.472 q^{91} +44.5880 q^{92} +143.817 q^{93} +697.497 q^{94} +1201.80 q^{95} +343.210 q^{96} -260.354 q^{97} -1198.91 q^{98} +99.0000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 38 q + 14 q^{2} + 114 q^{3} + 170 q^{4} + 35 q^{5} + 42 q^{6} + 105 q^{7} + 147 q^{8} + 342 q^{9}+O(q^{10}) \) 38 * q + 14 * q^2 + 114 * q^3 + 170 * q^4 + 35 * q^5 + 42 * q^6 + 105 * q^7 + 147 * q^8 + 342 * q^9	\( 38 q + 14 q^{2} + 114 q^{3} + 170 q^{4} + 35 q^{5} + 42 q^{6} + 105 q^{7} + 147 q^{8} + 342 q^{9} + 99 q^{10} + 418 q^{11} + 510 q^{12} + 209 q^{13} + 128 q^{14} + 105 q^{15} + 798 q^{16} + 512 q^{17} + 126 q^{18} + 487 q^{19} + 328 q^{20} + 315 q^{21} + 154 q^{22} + 417 q^{23} + 441 q^{24} + 925 q^{25} + 177 q^{26} + 1026 q^{27} + 902 q^{28} + 626 q^{29} + 297 q^{30} + 300 q^{31} + 1625 q^{32} + 1254 q^{33} - 180 q^{34} + 1086 q^{35} + 1530 q^{36} + 554 q^{37} + 845 q^{38} + 627 q^{39} + 329 q^{40} + 1378 q^{41} + 384 q^{42} + 1979 q^{43} + 1870 q^{44} + 315 q^{45} + 937 q^{46} + 1345 q^{47} + 2394 q^{48} + 2635 q^{49} + 800 q^{50} + 1536 q^{51} + 2006 q^{52} + 1497 q^{53} + 378 q^{54} + 385 q^{55} + 415 q^{56} + 1461 q^{57} + 1241 q^{58} + 2827 q^{59} + 984 q^{60} - 2318 q^{61} + 509 q^{62} + 945 q^{63} + 1003 q^{64} + 2810 q^{65} + 462 q^{66} + 369 q^{67} + 3936 q^{68} + 1251 q^{69} + 922 q^{70} + 965 q^{71} + 1323 q^{72} + 3081 q^{73} + 722 q^{74} + 2775 q^{75} + 2210 q^{76} + 1155 q^{77} + 531 q^{78} + 3795 q^{79} + 3793 q^{80} + 3078 q^{81} - 1678 q^{82} + 3869 q^{83} + 2706 q^{84} + 3553 q^{85} + 3305 q^{86} + 1878 q^{87} + 1617 q^{88} + 2849 q^{89} + 891 q^{90} + 1252 q^{91} + 4519 q^{92} + 900 q^{93} + 340 q^{94} + 1504 q^{95} + 4875 q^{96} + 2562 q^{97} + 6164 q^{98} + 3762 q^{99}+O(q^{100}) \) 38 * q + 14 * q^2 + 114 * q^3 + 170 * q^4 + 35 * q^5 + 42 * q^6 + 105 * q^7 + 147 * q^8 + 342 * q^9 + 99 * q^10 + 418 * q^11 + 510 * q^12 + 209 * q^13 + 128 * q^14 + 105 * q^15 + 798 * q^16 + 512 * q^17 + 126 * q^18 + 487 * q^19 + 328 * q^20 + 315 * q^21 + 154 * q^22 + 417 * q^23 + 441 * q^24 + 925 * q^25 + 177 * q^26 + 1026 * q^27 + 902 * q^28 + 626 * q^29 + 297 * q^30 + 300 * q^31 + 1625 * q^32 + 1254 * q^33 - 180 * q^34 + 1086 * q^35 + 1530 * q^36 + 554 * q^37 + 845 * q^38 + 627 * q^39 + 329 * q^40 + 1378 * q^41 + 384 * q^42 + 1979 * q^43 + 1870 * q^44 + 315 * q^45 + 937 * q^46 + 1345 * q^47 + 2394 * q^48 + 2635 * q^49 + 800 * q^50 + 1536 * q^51 + 2006 * q^52 + 1497 * q^53 + 378 * q^54 + 385 * q^55 + 415 * q^56 + 1461 * q^57 + 1241 * q^58 + 2827 * q^59 + 984 * q^60 - 2318 * q^61 + 509 * q^62 + 945 * q^63 + 1003 * q^64 + 2810 * q^65 + 462 * q^66 + 369 * q^67 + 3936 * q^68 + 1251 * q^69 + 922 * q^70 + 965 * q^71 + 1323 * q^72 + 3081 * q^73 + 722 * q^74 + 2775 * q^75 + 2210 * q^76 + 1155 * q^77 + 531 * q^78 + 3795 * q^79 + 3793 * q^80 + 3078 * q^81 - 1678 * q^82 + 3869 * q^83 + 2706 * q^84 + 3553 * q^85 + 3305 * q^86 + 1878 * q^87 + 1617 * q^88 + 2849 * q^89 + 891 * q^90 + 1252 * q^91 + 4519 * q^92 + 900 * q^93 + 340 * q^94 + 1504 * q^95 + 4875 * q^96 + 2562 * q^97 + 6164 * q^98 + 3762 * q^99

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