LMFDB - Embedded newform 2013.4.a.f.1.1

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			1.1
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)

$f(q)$	$=$	$q-5.20141 q^{2} +3.00000 q^{3} +19.0547 q^{4} -1.81138 q^{5} -15.6042 q^{6} +3.78751 q^{7} -57.5001 q^{8} +9.00000 q^{9} +O(q^{10})$	\(q-5.20141 q^{2} +3.00000 q^{3} +19.0547 q^{4} -1.81138 q^{5} -15.6042 q^{6} +3.78751 q^{7} -57.5001 q^{8} +9.00000 q^{9} +9.42176 q^{10} +11.0000 q^{11} +57.1641 q^{12} +26.8140 q^{13} -19.7004 q^{14} -5.43415 q^{15} +146.644 q^{16} -35.2698 q^{17} -46.8127 q^{18} -58.8048 q^{19} -34.5154 q^{20} +11.3625 q^{21} -57.2156 q^{22} +125.025 q^{23} -172.500 q^{24} -121.719 q^{25} -139.471 q^{26} +27.0000 q^{27} +72.1699 q^{28} +281.219 q^{29} +28.2653 q^{30} -175.091 q^{31} -302.757 q^{32} +33.0000 q^{33} +183.453 q^{34} -6.86063 q^{35} +171.492 q^{36} +49.4508 q^{37} +305.868 q^{38} +80.4419 q^{39} +104.155 q^{40} +395.538 q^{41} -59.1012 q^{42} -319.779 q^{43} +209.602 q^{44} -16.3024 q^{45} -650.306 q^{46} +282.134 q^{47} +439.933 q^{48} -328.655 q^{49} +633.110 q^{50} -105.809 q^{51} +510.933 q^{52} -301.073 q^{53} -140.438 q^{54} -19.9252 q^{55} -217.782 q^{56} -176.415 q^{57} -1462.74 q^{58} -312.900 q^{59} -103.546 q^{60} -61.0000 q^{61} +910.721 q^{62} +34.0876 q^{63} +401.610 q^{64} -48.5704 q^{65} -171.647 q^{66} +26.7795 q^{67} -672.055 q^{68} +375.074 q^{69} +35.6850 q^{70} +73.1574 q^{71} -517.501 q^{72} +168.531 q^{73} -257.214 q^{74} -365.157 q^{75} -1120.51 q^{76} +41.6626 q^{77} -418.412 q^{78} +612.469 q^{79} -265.629 q^{80} +81.0000 q^{81} -2057.36 q^{82} +683.013 q^{83} +216.510 q^{84} +63.8871 q^{85} +1663.30 q^{86} +843.658 q^{87} -632.502 q^{88} +1094.32 q^{89} +84.7958 q^{90} +101.558 q^{91} +2382.31 q^{92} -525.273 q^{93} -1467.50 q^{94} +106.518 q^{95} -908.271 q^{96} +236.627 q^{97} +1709.47 q^{98} +99.0000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−5.20141	−1.83898	−0.919489	−	0.393116i	$-0.871397\pi$
$2$	−5.20141	−1.83898	−0.919489	+	0.393116i	$0.871397\pi$
$3$	3.00000	0.577350
$3$	3.00000	0.577350
$4$	19.0547	2.38184
$5$	−1.81138	−0.162015	−0.0810075	−	0.996713i	$-0.525814\pi$
$5$	−1.81138	−0.162015	−0.0810075	+	0.996713i	$0.525814\pi$
$6$	−15.6042	−1.06173
$7$	3.78751	0.204506	0.102253	−	0.994758i	$-0.467395\pi$
$7$	3.78751	0.204506	0.102253	+	0.994758i	$0.467395\pi$
$8$	−57.5001	−2.54117
$9$	9.00000	0.333333
$10$	9.42176	0.297942
$11$	11.0000	0.301511
$11$	11.0000	0.301511
$12$	57.1641	1.37516
$13$	26.8140	0.572066	0.286033	−	0.958220i	$-0.407663\pi$
$13$	26.8140	0.572066	0.286033	+	0.958220i	$0.407663\pi$
$14$	−19.7004	−0.376083
$15$	−5.43415	−0.0935394
$16$	146.644	2.29132
$17$	−35.2698	−0.503187	−0.251593	−	0.967833i	$-0.580955\pi$
$17$	−35.2698	−0.503187	−0.251593	+	0.967833i	$0.580955\pi$
$18$	−46.8127	−0.612993
$19$	−58.8048	−0.710040	−0.355020	−	0.934859i	$-0.615526\pi$
$19$	−58.8048	−0.710040	−0.355020	+	0.934859i	$0.615526\pi$
$20$	−34.5154	−0.385894
$21$	11.3625	0.118072
$22$	−57.2156	−0.554473
$23$	125.025	1.13346	0.566728	−	0.823905i	$-0.308209\pi$
$23$	125.025	1.13346	0.566728	+	0.823905i	$0.308209\pi$
$24$	−172.500	−1.46715
$25$	−121.719	−0.973751
$26$	−139.471	−1.05202
$27$	27.0000	0.192450
$28$	72.1699	0.487101
$29$	281.219	1.80073	0.900364	−	0.435137i	$-0.143300\pi$
$29$	281.219	1.80073	0.900364	+	0.435137i	$0.143300\pi$
$30$	28.2653	0.172017
$31$	−175.091	−1.01443	−0.507214	−	0.861820i	$-0.669325\pi$
$31$	−175.091	−1.01443	−0.507214	+	0.861820i	$0.669325\pi$
$32$	−302.757	−1.67251
$33$	33.0000	0.174078
$34$	183.453	0.925349
$35$	−6.86063	−0.0331331
$36$	171.492	0.793946
$37$	49.4508	0.219720	0.109860	−	0.993947i	$-0.464960\pi$
$37$	49.4508	0.219720	0.109860	+	0.993947i	$0.464960\pi$
$38$	305.868	1.30575
$39$	80.4419	0.330283
$40$	104.155	0.411708
$41$	395.538	1.50665	0.753325	−	0.657648i	$-0.228449\pi$
$41$	395.538	1.50665	0.753325	+	0.657648i	$0.228449\pi$
$42$	−59.1012	−0.217131
$43$	−319.779	−1.13409	−0.567045	−	0.823687i	$-0.691913\pi$
$43$	−319.779	−1.13409	−0.567045	+	0.823687i	$0.691913\pi$
$44$	209.602	0.718151
$45$	−16.3024	−0.0540050
$46$	−650.306	−2.08440
$47$	282.134	0.875607	0.437803	−	0.899071i	$-0.355757\pi$
$47$	282.134	0.875607	0.437803	+	0.899071i	$0.355757\pi$
$48$	439.933	1.32289
$49$	−328.655	−0.958177
$50$	633.110	1.79071
$51$	−105.809	−0.290515
$52$	510.933	1.36257
$53$	−301.073	−0.780293	−0.390146	−	0.920753i	$-0.627576\pi$
$53$	−301.073	−0.780293	−0.390146	+	0.920753i	$0.627576\pi$
$54$	−140.438	−0.353911
$55$	−19.9252	−0.0488494
$56$	−217.782	−0.519685
$57$	−176.415	−0.409942
$58$	−1462.74	−3.31150
$59$	−312.900	−0.690442	−0.345221	−	0.938521i	$-0.612196\pi$
$59$	−312.900	−0.690442	−0.345221	+	0.938521i	$0.612196\pi$
$60$	−103.546	−0.222796
$61$	−61.0000	−0.128037
$61$	−61.0000	−0.128037
$62$	910.721	1.86551
$63$	34.0876	0.0681688
$64$	401.610	0.784394
$65$	−48.5704	−0.0926833
$66$	−171.647	−0.320125
$67$	26.7795	0.0488304	0.0244152	−	0.999702i	$-0.492228\pi$
$67$	26.7795	0.0488304	0.0244152	+	0.999702i	$0.492228\pi$
$68$	−672.055	−1.19851
$69$	375.074	0.654401
$70$	35.6850	0.0609310
$71$	73.1574	0.122284	0.0611422	−	0.998129i	$-0.480526\pi$
$71$	73.1574	0.122284	0.0611422	+	0.998129i	$0.480526\pi$
$72$	−517.501	−0.847057
$73$	168.531	0.270206	0.135103	−	0.990832i	$-0.456864\pi$
$73$	168.531	0.270206	0.135103	+	0.990832i	$0.456864\pi$
$74$	−257.214	−0.404061
$75$	−365.157	−0.562195
$76$	−1120.51	−1.69120
$77$	41.6626	0.0616610
$78$	−418.412	−0.607382
$79$	612.469	0.872256	0.436128	−	0.899885i	$-0.356350\pi$
$79$	612.469	0.872256	0.436128	+	0.899885i	$0.356350\pi$
$80$	−265.629	−0.371228
$81$	81.0000	0.111111
$82$	−2057.36	−2.77070
$83$	683.013	0.903258	0.451629	−	0.892206i	$-0.350843\pi$
$83$	683.013	0.903258	0.451629	+	0.892206i	$0.350843\pi$
$84$	216.510	0.281228
$85$	63.8871	0.0815238
$86$	1663.30	2.08557
$87$	843.658	1.03965
$88$	−632.502	−0.766192
$89$	1094.32	1.30334	0.651671	−	0.758501i	$-0.274068\pi$
$89$	1094.32	1.30334	0.651671	+	0.758501i	$0.274068\pi$
$90$	84.7958	0.0993140
$91$	101.558	0.116991
$92$	2382.31	2.69971
$93$	−525.273	−0.585681
$94$	−1467.50	−1.61022
$95$	106.518	0.115037
$96$	−908.271	−0.965625
$97$	236.627	0.247689	0.123845	−	0.992302i	$-0.460478\pi$
$97$	236.627	0.247689	0.123845	+	0.992302i	$0.460478\pi$
$98$	1709.47	1.76207
$99$	99.0000	0.100504
$100$	−2319.32	−2.31932
$101$	−331.370	−0.326461	−0.163231	−	0.986588i	$-0.552191\pi$
$101$	−331.370	−0.326461	−0.163231	+	0.986588i	$0.552191\pi$
$102$	550.358	0.534250
$103$	1166.25	1.11567	0.557837	−	0.829950i	$-0.311631\pi$
$103$	1166.25	1.11567	0.557837	+	0.829950i	$0.311631\pi$
$104$	−1541.81	−1.45372
$105$	−20.5819	−0.0191294
$106$	1566.00	1.43494
$107$	624.864	0.564560	0.282280	−	0.959332i	$-0.408909\pi$
$107$	624.864	0.564560	0.282280	+	0.959332i	$0.408909\pi$
$108$	514.477	0.458385
$109$	886.286	0.778815	0.389408	−	0.921066i	$-0.372680\pi$
$109$	886.286	0.778815	0.389408	+	0.921066i	$0.372680\pi$
$110$	103.639	0.0898329
$111$	148.352	0.126856
$112$	555.417	0.468589
$113$	−786.106	−0.654430	−0.327215	−	0.944950i	$-0.606110\pi$
$113$	−786.106	−0.654430	−0.327215	+	0.944950i	$0.606110\pi$
$114$	917.605	0.753874
$115$	−226.468	−0.183637
$116$	5358.55	4.28905
$117$	241.326	0.190689
$118$	1627.52	1.26971
$119$	−133.585	−0.102905
$120$	312.464	0.237700
$121$	121.000	0.0909091
$122$	317.286	0.235457
$123$	1186.61	0.869865
$124$	−3336.31	−2.41621
$125$	446.902	0.319777
$126$	−177.304	−0.125361
$127$	1019.44	0.712286	0.356143	−	0.934432i	$-0.384092\pi$
$127$	1019.44	0.712286	0.356143	+	0.934432i	$0.384092\pi$
$128$	333.117	0.230029
$129$	−959.337	−0.654767
$130$	252.635	0.170443
$131$	−901.457	−0.601226	−0.300613	−	0.953746i	$-0.597191\pi$
$131$	−901.457	−0.601226	−0.300613	+	0.953746i	$0.597191\pi$
$132$	628.806	0.414625
$133$	−222.724	−0.145208
$134$	−139.291	−0.0897980
$135$	−48.9073	−0.0311798
$136$	2028.02	1.27868
$137$	−2468.42	−1.53935	−0.769675	−	0.638436i	$-0.779582\pi$
$137$	−2468.42	−1.53935	−0.769675	+	0.638436i	$0.779582\pi$
$138$	−1950.92	−1.20343
$139$	968.800	0.591169	0.295585	−	0.955317i	$-0.404486\pi$
$139$	968.800	0.591169	0.295585	+	0.955317i	$0.404486\pi$
$140$	−130.727	−0.0789177
$141$	846.403	0.505532
$142$	−380.522	−0.224878
$143$	294.954	0.172484
$144$	1319.80	0.763773
$145$	−509.396	−0.291745
$146$	−876.597	−0.496902
$147$	−985.964	−0.553204
$148$	942.270	0.523339
$149$	−261.704	−0.143890	−0.0719451	−	0.997409i	$-0.522921\pi$
$149$	−261.704	−0.143890	−0.0719451	+	0.997409i	$0.522921\pi$
$150$	1899.33	1.03386
$151$	−65.7482	−0.0354338	−0.0177169	−	0.999843i	$-0.505640\pi$
$151$	−65.7482	−0.0354338	−0.0177169	+	0.999843i	$0.505640\pi$
$152$	3381.29	1.80433
$153$	−317.428	−0.167729
$154$	−216.704	−0.113393
$155$	317.157	0.164353
$156$	1532.80	0.786680
$157$	963.789	0.489928	0.244964	−	0.969532i	$-0.421224\pi$
$157$	963.789	0.489928	0.244964	+	0.969532i	$0.421224\pi$
$158$	−3185.71	−1.60406
$159$	−903.218	−0.450502
$160$	548.409	0.270972
$161$	473.533	0.231799
$162$	−421.315	−0.204331
$163$	−956.285	−0.459521	−0.229761	−	0.973247i	$-0.573794\pi$
$163$	−956.285	−0.459521	−0.229761	+	0.973247i	$0.573794\pi$
$164$	7536.86	3.58860
$165$	−59.7756	−0.0282032
$166$	−3552.63	−1.66107
$167$	140.975	0.0653231	0.0326615	−	0.999466i	$-0.489602\pi$
$167$	140.975	0.0653231	0.0326615	+	0.999466i	$0.489602\pi$
$168$	−653.347	−0.300041
$169$	−1478.01	−0.672740
$170$	−332.303	−0.149920
$171$	−529.244	−0.236680
$172$	−6093.30	−2.70122
$173$	1728.56	0.759654	0.379827	−	0.925058i	$-0.375984\pi$
$173$	1728.56	0.759654	0.379827	+	0.925058i	$0.375984\pi$
$174$	−4388.22	−1.91190
$175$	−461.011	−0.199138
$176$	1613.09	0.690858
$177$	−938.699	−0.398627
$178$	−5692.00	−2.39682
$179$	−1176.16	−0.491118	−0.245559	−	0.969382i	$-0.578972\pi$
$179$	−1176.16	−0.491118	−0.245559	+	0.969382i	$0.578972\pi$
$180$	−310.638	−0.128631
$181$	1673.68	0.687314	0.343657	−	0.939095i	$-0.388334\pi$
$181$	1673.68	0.687314	0.343657	+	0.939095i	$0.388334\pi$
$182$	−528.246	−0.215144
$183$	−183.000	−0.0739221
$184$	−7188.94	−2.88030
$185$	−89.5743	−0.0355980
$186$	2732.16	1.07705
$187$	−387.967	−0.151716
$188$	5375.99	2.08555
$189$	102.263	0.0393573
$190$	−554.045	−0.211551
$191$	−345.471	−0.130877	−0.0654383	−	0.997857i	$-0.520845\pi$
$191$	−345.471	−0.130877	−0.0654383	+	0.997857i	$0.520845\pi$
$192$	1204.83	0.452870
$193$	185.611	0.0692258	0.0346129	−	0.999401i	$-0.488980\pi$
$193$	185.611	0.0692258	0.0346129	+	0.999401i	$0.488980\pi$
$194$	−1230.80	−0.455495
$195$	−145.711	−0.0535107
$196$	−6262.42	−2.28222
$197$	−2140.88	−0.774270	−0.387135	−	0.922023i	$-0.626535\pi$
$197$	−2140.88	−0.774270	−0.387135	+	0.922023i	$0.626535\pi$
$198$	−514.940	−0.184824
$199$	4033.84	1.43694	0.718470	−	0.695558i	$-0.244843\pi$
$199$	4033.84	1.43694	0.718470	+	0.695558i	$0.244843\pi$
$200$	6998.85	2.47447
$201$	80.3385	0.0281922
$202$	1723.60	0.600355
$203$	1065.12	0.368260
$204$	−2016.17	−0.691960
$205$	−716.471	−0.244100
$206$	−6066.17	−2.05170
$207$	1125.22	0.377818
$208$	3932.12	1.31079
$209$	−646.853	−0.214085
$210$	107.055	0.0351785
$211$	2050.18	0.668912	0.334456	−	0.942411i	$-0.391447\pi$
$211$	2050.18	0.668912	0.334456	+	0.942411i	$0.391447\pi$
$212$	−5736.85	−1.85853
$213$	219.472	0.0706009
$214$	−3250.18	−1.03821
$215$	579.243	0.183740
$216$	−1552.50	−0.489049
$217$	−663.159	−0.207457
$218$	−4609.94	−1.43222
$219$	505.592	0.156003
$220$	−379.669	−0.116351
$221$	−945.723	−0.287856
$222$	−771.642	−0.233285
$223$	−1867.57	−0.560815	−0.280408	−	0.959881i	$-0.590470\pi$
$223$	−1867.57	−0.560815	−0.280408	+	0.959881i	$0.590470\pi$
$224$	−1146.70	−0.342039
$225$	−1095.47	−0.324584
$226$	4088.86	1.20348
$227$	464.643	0.135857	0.0679283	−	0.997690i	$-0.478361\pi$
$227$	464.643	0.135857	0.0679283	+	0.997690i	$0.478361\pi$
$228$	−3361.53	−0.976415
$229$	−5990.13	−1.72855	−0.864277	−	0.503017i	$-0.832223\pi$
$229$	−5990.13	−1.72855	−0.864277	+	0.503017i	$0.832223\pi$
$230$	1177.95	0.337704
$231$	124.988	0.0356000
$232$	−16170.2	−4.57596
$233$	−530.237	−0.149086	−0.0745429	−	0.997218i	$-0.523750\pi$
$233$	−530.237	−0.149086	−0.0745429	+	0.997218i	$0.523750\pi$
$234$	−1255.24	−0.350672
$235$	−511.053	−0.141861
$236$	−5962.21	−1.64452
$237$	1837.41	0.503597
$238$	694.829	0.189240
$239$	−593.871	−0.160729	−0.0803647	−	0.996766i	$-0.525609\pi$
$239$	−593.871	−0.160729	−0.0803647	+	0.996766i	$0.525609\pi$
$240$	−796.887	−0.214329
$241$	2801.59	0.748823	0.374412	−	0.927263i	$-0.377845\pi$
$241$	2801.59	0.748823	0.374412	+	0.927263i	$0.377845\pi$
$242$	−629.371	−0.167180
$243$	243.000	0.0641500
$244$	−1162.34	−0.304963
$245$	595.320	0.155239
$246$	−6172.07	−1.59966
$247$	−1576.79	−0.406190
$248$	10067.8	2.57784
$249$	2049.04	0.521496
$250$	−2324.53	−0.588063
$251$	−1215.15	−0.305575	−0.152788	−	0.988259i	$-0.548825\pi$
$251$	−1215.15	−0.305575	−0.152788	+	0.988259i	$0.548825\pi$
$252$	649.529	0.162367
$253$	1375.27	0.341750
$254$	−5302.51	−1.30988
$255$	191.661	0.0470678
$256$	−4945.56	−1.20741
$257$	−4299.71	−1.04361	−0.521807	−	0.853064i	$-0.674742\pi$
$257$	−4299.71	−1.04361	−0.521807	+	0.853064i	$0.674742\pi$
$258$	4989.91	1.20410
$259$	187.295	0.0449342
$260$	−925.495	−0.220757
$261$	2530.97	0.600243
$262$	4688.85	1.10564
$263$	3653.77	0.856658	0.428329	−	0.903623i	$-0.359103\pi$
$263$	3653.77	0.856658	0.428329	+	0.903623i	$0.359103\pi$
$264$	−1897.50	−0.442361
$265$	545.358	0.126419
$266$	1158.48	0.267034
$267$	3282.95	0.752485
$268$	510.276	0.116306
$269$	8421.66	1.90884	0.954420	−	0.298467i	$-0.0964754\pi$
$269$	8421.66	1.90884	0.954420	+	0.298467i	$0.0964754\pi$
$270$	254.387	0.0573390
$271$	−7552.58	−1.69294	−0.846469	−	0.532437i	$-0.821276\pi$
$271$	−7552.58	−1.69294	−0.846469	+	0.532437i	$0.821276\pi$
$272$	−5172.11	−1.15296
$273$	304.675	0.0675449
$274$	12839.3	2.83083
$275$	−1338.91	−0.293597
$276$	7146.93	1.55868
$277$	8159.59	1.76990	0.884950	−	0.465686i	$-0.154193\pi$
$277$	8159.59	1.76990	0.884950	+	0.465686i	$0.154193\pi$
$278$	−5039.13	−1.08715
$279$	−1575.82	−0.338143
$280$	394.487	0.0841969
$281$	−2789.36	−0.592167	−0.296084	−	0.955162i	$-0.595681\pi$
$281$	−2789.36	−0.592167	−0.296084	+	0.955162i	$0.595681\pi$
$282$	−4402.49	−0.929662
$283$	−6524.03	−1.37037	−0.685183	−	0.728371i	$-0.740278\pi$
$283$	−6524.03	−1.37037	−0.685183	+	0.728371i	$0.740278\pi$
$284$	1393.99	0.291262
$285$	319.554	0.0664167
$286$	−1534.18	−0.317195
$287$	1498.10	0.308120
$288$	−2724.81	−0.557504
$289$	−3669.04	−0.746803
$290$	2649.58	0.536513
$291$	709.882	0.143004
$292$	3211.30	0.643586
$293$	296.312	0.0590810	0.0295405	−	0.999564i	$-0.490596\pi$
$293$	296.312	0.0590810	0.0295405	+	0.999564i	$0.490596\pi$
$294$	5128.41	1.01733
$295$	566.781	0.111862
$296$	−2843.43	−0.558347
$297$	297.000	0.0580259
$298$	1361.23	0.264611
$299$	3352.41	0.648411
$300$	−6957.96	−1.33906
$301$	−1211.17	−0.231928
$302$	341.984	0.0651621
$303$	−994.111	−0.188483
$304$	−8623.40	−1.62693
$305$	110.494	0.0207439
$306$	1651.07	0.308450
$307$	6398.72	1.18956	0.594779	−	0.803889i	$-0.297239\pi$
$307$	6398.72	1.18956	0.594779	+	0.803889i	$0.297239\pi$
$308$	793.869	0.146866
$309$	3498.76	0.644135
$310$	−1649.67	−0.302241
$311$	−7934.00	−1.44661	−0.723306	−	0.690528i	$-0.757378\pi$
$311$	−7934.00	−1.44661	−0.723306	+	0.690528i	$0.757378\pi$
$312$	−4625.42	−0.839304
$313$	−6178.11	−1.11568	−0.557840	−	0.829949i	$-0.688370\pi$
$313$	−6178.11	−1.11568	−0.557840	+	0.829949i	$0.688370\pi$
$314$	−5013.07	−0.900967
$315$	−61.7457	−0.0110444
$316$	11670.4	2.07757
$317$	10941.2	1.93854	0.969272	−	0.245991i	$-0.0791134\pi$
$317$	10941.2	1.93854	0.969272	+	0.245991i	$0.0791134\pi$
$318$	4698.01	0.828463
$319$	3093.41	0.542940
$320$	−727.469	−0.127084
$321$	1874.59	0.325949
$322$	−2463.04	−0.426273
$323$	2074.03	0.357283
$324$	1543.43	0.264649
$325$	−3263.77	−0.557050
$326$	4974.03	0.845050
$327$	2658.86	0.449649
$328$	−22743.5	−3.82866
$329$	1068.59	0.179067
$330$	310.918	0.0518651
$331$	1527.81	0.253704	0.126852	−	0.991922i	$-0.459513\pi$
$331$	1527.81	0.253704	0.126852	+	0.991922i	$0.459513\pi$
$332$	13014.6	2.15142
$333$	445.057	0.0732402
$334$	−733.268	−0.120128
$335$	−48.5079	−0.00791126
$336$	1666.25	0.270540
$337$	3605.07	0.582732	0.291366	−	0.956612i	$-0.405890\pi$
$337$	3605.07	0.582732	0.291366	+	0.956612i	$0.405890\pi$
$338$	7687.75	1.23715
$339$	−2358.32	−0.377836
$340$	1217.35	0.194177
$341$	−1926.00	−0.305862
$342$	2752.82	0.435249
$343$	−2543.90	−0.400460
$344$	18387.3	2.88192
$345$	−679.403	−0.106023
$346$	−8990.97	−1.39699
$347$	5928.86	0.917227	0.458613	−	0.888636i	$-0.348346\pi$
$347$	5928.86	0.917227	0.458613	+	0.888636i	$0.348346\pi$
$348$	16075.7	2.47628
$349$	−5723.78	−0.877899	−0.438950	−	0.898512i	$-0.644649\pi$
$349$	−5723.78	−0.877899	−0.438950	+	0.898512i	$0.644649\pi$
$350$	2397.91	0.366211
$351$	723.977	0.110094
$352$	−3330.33	−0.504281
$353$	7280.16	1.09769	0.548844	−	0.835925i	$-0.315068\pi$
$353$	7280.16	1.09769	0.548844	+	0.835925i	$0.315068\pi$
$354$	4882.56	0.733066
$355$	−132.516	−0.0198119
$356$	20851.9	3.10435
$357$	−400.754	−0.0594121
$358$	6117.69	0.903156
$359$	10271.6	1.51007	0.755034	−	0.655686i	$-0.227620\pi$
$359$	10271.6	1.51007	0.755034	+	0.655686i	$0.227620\pi$
$360$	937.393	0.137236
$361$	−3400.99	−0.495844
$362$	−8705.52	−1.26396
$363$	363.000	0.0524864
$364$	1935.16	0.278654
$365$	−305.273	−0.0437774
$366$	951.859	0.135941
$367$	6781.99	0.964624	0.482312	−	0.875999i	$-0.339797\pi$
$367$	6781.99	0.964624	0.482312	+	0.875999i	$0.339797\pi$
$368$	18334.2	2.59711
$369$	3559.84	0.502217
$370$	465.913	0.0654640
$371$	−1140.32	−0.159575
$372$	−10008.9	−1.39500
$373$	11396.2	1.58197	0.790986	−	0.611835i	$-0.209568\pi$
$373$	11396.2	1.58197	0.790986	+	0.611835i	$0.209568\pi$
$374$	2017.98	0.279003
$375$	1340.71	0.184624
$376$	−16222.8	−2.22507
$377$	7540.61	1.03014
$378$	−531.911	−0.0723771
$379$	5921.61	0.802567	0.401284	−	0.915954i	$-0.368564\pi$
$379$	5921.61	0.802567	0.401284	+	0.915954i	$0.368564\pi$
$380$	2029.67	0.274000
$381$	3058.31	0.411238
$382$	1796.94	0.240679
$383$	−362.083	−0.0483071	−0.0241535	−	0.999708i	$-0.507689\pi$
$383$	−362.083	−0.0483071	−0.0241535	+	0.999708i	$0.507689\pi$
$384$	999.352	0.132807
$385$	−75.4669	−0.00999000
$386$	−965.441	−0.127305
$387$	−2878.01	−0.378030
$388$	4508.87	0.589956
$389$	2533.34	0.330195	0.165097	−	0.986277i	$-0.447206\pi$
$389$	2533.34	0.330195	0.165097	+	0.986277i	$0.447206\pi$
$390$	757.904	0.0984051
$391$	−4409.59	−0.570340
$392$	18897.7	2.43489
$393$	−2704.37	−0.347118
$394$	11135.6	1.42387
$395$	−1109.42	−0.141319
$396$	1886.42	0.239384
$397$	2502.33	0.316343	0.158172	−	0.987412i	$-0.449440\pi$
$397$	2502.33	0.316343	0.158172	+	0.987412i	$0.449440\pi$
$398$	−20981.7	−2.64250
$399$	−668.172	−0.0838356
$400$	−17849.4	−2.23117
$401$	6063.25	0.755073	0.377537	−	0.925995i	$-0.376771\pi$
$401$	6063.25	0.755073	0.377537	+	0.925995i	$0.376771\pi$
$402$	−417.874	−0.0518449
$403$	−4694.89	−0.580320
$404$	−6314.17	−0.777578
$405$	−146.722	−0.0180017
$406$	−5540.14	−0.677222
$407$	543.959	0.0662482
$408$	6084.05	0.738248
$409$	3848.93	0.465323	0.232662	−	0.972558i	$-0.425257\pi$
$409$	3848.93	0.465323	0.232662	+	0.972558i	$0.425257\pi$
$410$	3726.66	0.448895
$411$	−7405.25	−0.888744
$412$	22222.6	2.65736
$413$	−1185.11	−0.141200
$414$	−5852.75	−0.694800
$415$	−1237.20	−0.146341
$416$	−8118.12	−0.956787
$417$	2906.40	0.341312
$418$	3364.55	0.393698
$419$	−4784.13	−0.557804	−0.278902	−	0.960320i	$-0.589970\pi$
$419$	−4784.13	−0.557804	−0.278902	+	0.960320i	$0.589970\pi$
$420$	−392.182	−0.0455632
$421$	2463.03	0.285132	0.142566	−	0.989785i	$-0.454465\pi$
$421$	2463.03	0.285132	0.142566	+	0.989785i	$0.454465\pi$
$422$	−10663.9	−1.23012
$423$	2539.21	0.291869
$424$	17311.7	1.98286
$425$	4293.00	0.489979
$426$	−1141.57	−0.129833
$427$	−231.038	−0.0261843
$428$	11906.6	1.34469
$429$	884.861	0.0995839
$430$	−3012.88	−0.337893
$431$	15547.9	1.73762	0.868811	−	0.495143i	$-0.164884\pi$
$431$	15547.9	1.73762	0.868811	+	0.495143i	$0.164884\pi$
$432$	3959.40	0.440964
$433$	4045.17	0.448957	0.224478	−	0.974479i	$-0.427932\pi$
$433$	4045.17	0.448957	0.224478	+	0.974479i	$0.427932\pi$
$434$	3449.37	0.381509
$435$	−1528.19	−0.168439
$436$	16887.9	1.85501
$437$	−7352.06	−0.804798
$438$	−2629.79	−0.286887
$439$	1654.68	0.179894	0.0899469	−	0.995947i	$-0.471330\pi$
$439$	1654.68	0.179894	0.0899469	+	0.995947i	$0.471330\pi$
$440$	1145.70	0.124135
$441$	−2957.89	−0.319392
$442$	4919.09	0.529361
$443$	8826.77	0.946665	0.473332	−	0.880884i	$-0.343051\pi$
$443$	8826.77	0.946665	0.473332	+	0.880884i	$0.343051\pi$
$444$	2826.81	0.302150
$445$	−1982.23	−0.211161
$446$	9714.01	1.03133
$447$	−785.112	−0.0830750
$448$	1521.10	0.160413
$449$	4617.51	0.485331	0.242666	−	0.970110i	$-0.421978\pi$
$449$	4617.51	0.485331	0.242666	+	0.970110i	$0.421978\pi$
$450$	5697.99	0.596902
$451$	4350.92	0.454272
$452$	−14979.0	−1.55875
$453$	−197.245	−0.0204577
$454$	−2416.80	−0.249837
$455$	−183.961	−0.0189543
$456$	10143.9	1.04173
$457$	−8151.22	−0.834350	−0.417175	−	0.908826i	$-0.636980\pi$
$457$	−8151.22	−0.834350	−0.417175	+	0.908826i	$0.636980\pi$
$458$	31157.1	3.17877
$459$	−952.283	−0.0968383
$460$	−4315.28	−0.437393
$461$	3931.32	0.397180	0.198590	−	0.980083i	$-0.436364\pi$
$461$	3931.32	0.397180	0.198590	+	0.980083i	$0.436364\pi$
$462$	−650.113	−0.0654676
$463$	16343.9	1.64053	0.820264	−	0.571985i	$-0.193827\pi$
$463$	16343.9	1.64053	0.820264	+	0.571985i	$0.193827\pi$
$464$	41239.2	4.12604
$465$	951.471	0.0948891
$466$	2757.98	0.274165
$467$	−5148.69	−0.510177	−0.255089	−	0.966918i	$-0.582105\pi$
$467$	−5148.69	−0.510177	−0.255089	+	0.966918i	$0.582105\pi$
$468$	4598.39	0.454190
$469$	101.428	0.00998613
$470$	2658.20	0.260880
$471$	2891.37	0.282860
$472$	17991.8	1.75453
$473$	−3517.57	−0.341941
$474$	−9557.12	−0.926104
$475$	7157.66	0.691402
$476$	−2545.41	−0.245103
$477$	−2709.65	−0.260098
$478$	3088.97	0.295578
$479$	16753.8	1.59813	0.799063	−	0.601247i	$-0.205329\pi$
$479$	16753.8	1.59813	0.799063	+	0.601247i	$0.205329\pi$
$480$	1645.23	0.156446
$481$	1325.97	0.125695
$482$	−14572.2	−1.37707
$483$	1420.60	0.133829
$484$	2305.62	0.216531
$485$	−428.623	−0.0401294
$486$	−1263.94	−0.117970
$487$	−13644.0	−1.26954	−0.634772	−	0.772699i	$-0.718906\pi$
$487$	−13644.0	−1.26954	−0.634772	+	0.772699i	$0.718906\pi$
$488$	3507.51	0.325364
$489$	−2868.85	−0.265305
$490$	−3096.50	−0.285481
$491$	−2892.04	−0.265817	−0.132908	−	0.991128i	$-0.542432\pi$
$491$	−2892.04	−0.265817	−0.132908	+	0.991128i	$0.542432\pi$
$492$	22610.6	2.07188
$493$	−9918.54	−0.906102
$494$	8201.55	0.746974
$495$	−179.327	−0.0162831
$496$	−25676.1	−2.32438
$497$	277.084	0.0250079
$498$	−10657.9	−0.959020
$499$	6215.90	0.557639	0.278820	−	0.960344i	$-0.410057\pi$
$499$	6215.90	0.557639	0.278820	+	0.960344i	$0.410057\pi$
$500$	8515.60	0.761658
$501$	422.924	0.0377143
$502$	6320.49	0.561947
$503$	−9464.68	−0.838984	−0.419492	−	0.907759i	$-0.637792\pi$
$503$	−9464.68	−0.838984	−0.419492	+	0.907759i	$0.637792\pi$
$504$	−1960.04	−0.173228
$505$	600.239	0.0528916
$506$	−7153.36	−0.628470
$507$	−4434.03	−0.388407
$508$	19425.1	1.69655
$509$	1325.44	0.115421	0.0577105	−	0.998333i	$-0.481620\pi$
$509$	1325.44	0.115421	0.0577105	+	0.998333i	$0.481620\pi$
$510$	−996.909	−0.0865566
$511$	638.311	0.0552587
$512$	23059.0	1.99037
$513$	−1587.73	−0.136647
$514$	22364.6	1.91918
$515$	−2112.53	−0.180756
$516$	−18279.9	−1.55955
$517$	3103.48	0.264005
$518$	−974.200	−0.0826330
$519$	5185.69	0.438586
$520$	2792.80	0.235524
$521$	3857.66	0.324390	0.162195	−	0.986759i	$-0.448143\pi$
$521$	3857.66	0.324390	0.162195	+	0.986759i	$0.448143\pi$
$522$	−13164.6	−1.10383
$523$	7626.67	0.637650	0.318825	−	0.947814i	$-0.396712\pi$
$523$	7626.67	0.637650	0.318825	+	0.947814i	$0.396712\pi$
$524$	−17177.0	−1.43202
$525$	−1383.03	−0.114973
$526$	−19004.8	−1.57537
$527$	6175.42	0.510447
$528$	4839.26	0.398867
$529$	3464.20	0.284721
$530$	−2836.63	−0.232482
$531$	−2816.10	−0.230147
$532$	−4243.94	−0.345861
$533$	10606.0	0.861904
$534$	−17076.0	−1.38380
$535$	−1131.87	−0.0914672
$536$	−1539.83	−0.124086
$537$	−3528.48	−0.283547
$538$	−43804.6	−3.51031
$539$	−3615.20	−0.288901
$540$	−931.915	−0.0742653
$541$	19350.7	1.53780	0.768902	−	0.639367i	$-0.220803\pi$
$541$	19350.7	1.53780	0.768902	+	0.639367i	$0.220803\pi$
$542$	39284.1	3.11328
$543$	5021.05	0.396821
$544$	10678.2	0.841586
$545$	−1605.40	−0.126180
$546$	−1584.74	−0.124213
$547$	−6746.67	−0.527362	−0.263681	−	0.964610i	$-0.584937\pi$
$547$	−6746.67	−0.527362	−0.263681	+	0.964610i	$0.584937\pi$
$548$	−47035.0	−3.66649
$549$	−549.000	−0.0426790
$550$	6964.21	0.539918
$551$	−16537.1	−1.27859
$552$	−21566.8	−1.66294
$553$	2319.73	0.178382
$554$	−42441.4	−3.25481
$555$	−268.723	−0.0205525
$556$	18460.2	1.40807
$557$	11464.4	0.872102	0.436051	−	0.899922i	$-0.356377\pi$
$557$	11464.4	0.872102	0.436051	+	0.899922i	$0.356377\pi$
$558$	8196.49	0.621837
$559$	−8574.55	−0.648774
$560$	−1006.07	−0.0759185
$561$	−1163.90	−0.0875935
$562$	14508.6	1.08898
$563$	−20670.1	−1.54732	−0.773658	−	0.633604i	$-0.781575\pi$
$563$	−20670.1	−1.54732	−0.773658	+	0.633604i	$0.781575\pi$
$564$	16128.0	1.20410
$565$	1423.94	0.106028
$566$	33934.2	2.52007
$567$	306.788	0.0227229
$568$	−4206.56	−0.310746
$569$	−14987.5	−1.10423	−0.552117	−	0.833767i	$-0.686180\pi$
$569$	−14987.5	−1.10423	−0.552117	+	0.833767i	$0.686180\pi$
$570$	−1662.13	−0.122139
$571$	−5831.72	−0.427408	−0.213704	−	0.976898i	$-0.568553\pi$
$571$	−5831.72	−0.427408	−0.213704	+	0.976898i	$0.568553\pi$
$572$	5620.26	0.410830
$573$	−1036.41	−0.0755616
$574$	−7792.26	−0.566625
$575$	−15217.9	−1.10370
$576$	3614.49	0.261465
$577$	9364.22	0.675628	0.337814	−	0.941213i	$-0.390313\pi$
$577$	9364.22	0.675628	0.337814	+	0.941213i	$0.390313\pi$
$578$	19084.2	1.37335
$579$	556.834	0.0399676
$580$	−9706.40	−0.694890
$581$	2586.92	0.184722
$582$	−3692.39	−0.262980
$583$	−3311.80	−0.235267
$584$	−9690.53	−0.686639
$585$	−437.134	−0.0308944
$586$	−1541.24	−0.108649
$587$	13897.9	0.977221	0.488611	−	0.872502i	$-0.337504\pi$
$587$	13897.9	0.977221	0.488611	+	0.872502i	$0.337504\pi$
$588$	−18787.3	−1.31764
$589$	10296.2	0.720285
$590$	−2948.06	−0.205712
$591$	−6422.63	−0.447025
$592$	7251.68	0.503450
$593$	3217.08	0.222782	0.111391	−	0.993777i	$-0.464469\pi$
$593$	3217.08	0.222782	0.111391	+	0.993777i	$0.464469\pi$
$594$	−1544.82	−0.106708
$595$	241.973	0.0166721
$596$	−4986.69	−0.342723
$597$	12101.5	0.829618
$598$	−17437.3	−1.19241
$599$	−546.721	−0.0372928	−0.0186464	−	0.999826i	$-0.505936\pi$
$599$	−546.721	−0.0372928	−0.0186464	+	0.999826i	$0.505936\pi$
$600$	20996.6	1.42863
$601$	5388.84	0.365749	0.182875	−	0.983136i	$-0.441460\pi$
$601$	5388.84	0.365749	0.182875	+	0.983136i	$0.441460\pi$
$602$	6299.78	0.426511
$603$	241.016	0.0162768
$604$	−1252.81	−0.0843977
$605$	−219.177	−0.0147286
$606$	5170.79	0.346615
$607$	12550.5	0.839225	0.419613	−	0.907703i	$-0.362166\pi$
$607$	12550.5	0.839225	0.419613	+	0.907703i	$0.362166\pi$
$608$	17803.6	1.18755
$609$	3195.36	0.212615
$610$	−574.727	−0.0381476
$611$	7565.14	0.500905
$612$	−6048.50	−0.399503
$613$	23963.0	1.57888	0.789442	−	0.613825i	$-0.210370\pi$
$613$	23963.0	1.57888	0.789442	+	0.613825i	$0.210370\pi$
$614$	−33282.4	−2.18757
$615$	−2149.41	−0.140931
$616$	−2395.61	−0.156691
$617$	112.947	0.00736963	0.00368481	−	0.999993i	$-0.498827\pi$
$617$	112.947	0.00736963	0.00368481	+	0.999993i	$0.498827\pi$
$618$	−18198.5	−1.18455
$619$	−15271.2	−0.991600	−0.495800	−	0.868437i	$-0.665125\pi$
$619$	−15271.2	−0.991600	−0.495800	+	0.868437i	$0.665125\pi$
$620$	6043.34	0.391462
$621$	3375.67	0.218134
$622$	41268.0	2.66029
$623$	4144.74	0.266542
$624$	11796.4	0.756782
$625$	14405.3	0.921942
$626$	32134.9	2.05171
$627$	−1940.56	−0.123602
$628$	18364.7	1.16693
$629$	−1744.12	−0.110560
$630$	321.165	0.0203103
$631$	19141.2	1.20760	0.603802	−	0.797134i	$-0.293652\pi$
$631$	19141.2	1.20760	0.603802	+	0.797134i	$0.293652\pi$
$632$	−35217.1	−2.21655
$633$	6150.55	0.386197
$634$	−56909.7	−3.56494
$635$	−1846.59	−0.115401
$636$	−17210.6	−1.07302
$637$	−8812.54	−0.548141
$638$	−16090.1	−0.998455
$639$	658.417	0.0407615
$640$	−603.403	−0.0372681
$641$	−7299.22	−0.449769	−0.224885	−	0.974385i	$-0.572201\pi$
$641$	−7299.22	−0.449769	−0.224885	+	0.974385i	$0.572201\pi$
$642$	−9750.53	−0.599412
$643$	21779.8	1.33579	0.667894	−	0.744256i	$-0.267196\pi$
$643$	21779.8	1.33579	0.667894	+	0.744256i	$0.267196\pi$
$644$	9023.03	0.552107
$645$	1737.73	0.106082
$646$	−10787.9	−0.657035
$647$	28293.8	1.71923	0.859617	−	0.510939i	$-0.170702\pi$
$647$	28293.8	1.71923	0.859617	+	0.510939i	$0.170702\pi$
$648$	−4657.51	−0.282352
$649$	−3441.90	−0.208176
$650$	16976.2	1.02440
$651$	−1989.48	−0.119775
$652$	−18221.7	−1.09451
$653$	639.863	0.0383458	0.0191729	−	0.999816i	$-0.493897\pi$
$653$	639.863	0.0383458	0.0191729	+	0.999816i	$0.493897\pi$
$654$	−13829.8	−0.826895
$655$	1632.88	0.0974077
$656$	58003.4	3.45222
$657$	1516.77	0.0900685
$658$	−5558.16	−0.329300
$659$	−14718.1	−0.870008	−0.435004	−	0.900429i	$-0.643253\pi$
$659$	−14718.1	−0.870008	−0.435004	+	0.900429i	$0.643253\pi$
$660$	−1139.01	−0.0671755
$661$	−17373.9	−1.02234	−0.511170	−	0.859479i	$-0.670788\pi$
$661$	−17373.9	−1.02234	−0.511170	+	0.859479i	$0.670788\pi$
$662$	−7946.76	−0.466555
$663$	−2837.17	−0.166194
$664$	−39273.3	−2.29533
$665$	403.438	0.0235258
$666$	−2314.93	−0.134687
$667$	35159.4	2.04105
$668$	2686.23	0.155589
$669$	−5602.71	−0.323787
$670$	252.310	0.0145486
$671$	−671.000	−0.0386046
$672$	−3440.09	−0.197476
$673$	−13681.8	−0.783649	−0.391825	−	0.920040i	$-0.628156\pi$
$673$	−13681.8	−0.783649	−0.391825	+	0.920040i	$0.628156\pi$
$674$	−18751.5	−1.07163
$675$	−3286.41	−0.187398
$676$	−28163.1	−1.60236
$677$	30751.2	1.74574	0.872870	−	0.487953i	$-0.162256\pi$
$677$	30751.2	1.74574	0.872870	+	0.487953i	$0.162256\pi$
$678$	12266.6	0.694831
$679$	896.228	0.0506540
$680$	−3673.51	−0.207166
$681$	1393.93	0.0784368
$682$	10017.9	0.562473
$683$	9295.07	0.520741	0.260370	−	0.965509i	$-0.416155\pi$
$683$	9295.07	0.520741	0.260370	+	0.965509i	$0.416155\pi$
$684$	−10084.6	−0.563733
$685$	4471.25	0.249398
$686$	13231.9	0.736436
$687$	−17970.4	−0.997981
$688$	−46893.8	−2.59856
$689$	−8072.96	−0.446379
$690$	3533.86	0.194974
$691$	−5370.38	−0.295657	−0.147828	−	0.989013i	$-0.547228\pi$
$691$	−5370.38	−0.295657	−0.147828	+	0.989013i	$0.547228\pi$
$692$	32937.2	1.80937
$693$	374.963	0.0205537
$694$	−30838.4	−1.68676
$695$	−1754.87	−0.0957783
$696$	−48510.5	−2.64193
$697$	−13950.5	−0.758126
$698$	29771.8	1.61444
$699$	−1590.71	−0.0860747
$700$	−8784.44	−0.474315
$701$	7549.95	0.406787	0.203393	−	0.979097i	$-0.434803\pi$
$701$	7549.95	0.406787	0.203393	+	0.979097i	$0.434803\pi$
$702$	−3765.71	−0.202461
$703$	−2907.95	−0.156010
$704$	4417.71	0.236504
$705$	−1533.16	−0.0819038
$706$	−37867.1	−2.01862
$707$	−1255.07	−0.0667634
$708$	−17886.6	−0.949465
$709$	−11442.7	−0.606123	−0.303061	−	0.952971i	$-0.598009\pi$
$709$	−11442.7	−0.606123	−0.303061	+	0.952971i	$0.598009\pi$
$710$	689.271	0.0364337
$711$	5512.22	0.290752
$712$	−62923.4	−3.31202
$713$	−21890.7	−1.14981
$714$	2084.49	0.109258
$715$	−534.274	−0.0279451
$716$	−22411.4	−1.16977
$717$	−1781.61	−0.0927972
$718$	−53426.9	−2.77698
$719$	19273.5	0.999692	0.499846	−	0.866114i	$-0.333390\pi$
$719$	19273.5	0.999692	0.499846	+	0.866114i	$0.333390\pi$
$720$	−2390.66	−0.123743
$721$	4417.20	0.228162
$722$	17690.0	0.911845
$723$	8404.77	0.432333
$724$	31891.5	1.63707
$725$	−34229.7	−1.75346
$726$	−1888.11	−0.0965213
$727$	35613.4	1.81682	0.908410	−	0.418080i	$-0.137297\pi$
$727$	35613.4	1.81682	0.908410	+	0.418080i	$0.137297\pi$
$728$	−5839.61	−0.297294
$729$	729.000	0.0370370
$730$	1587.85	0.0805056
$731$	11278.5	0.570659
$732$	−3487.01	−0.176071
$733$	−1888.15	−0.0951438	−0.0475719	−	0.998868i	$-0.515148\pi$
$733$	−1888.15	−0.0951438	−0.0475719	+	0.998868i	$0.515148\pi$
$734$	−35276.0	−1.77392
$735$	1785.96	0.0896273
$736$	−37852.1	−1.89572
$737$	294.575	0.0147229
$738$	−18516.2	−0.923566
$739$	7571.76	0.376904	0.188452	−	0.982082i	$-0.439653\pi$
$739$	7571.76	0.376904	0.188452	+	0.982082i	$0.439653\pi$
$740$	−1706.81	−0.0847888
$741$	−4730.38	−0.234514
$742$	5931.25	0.293454
$743$	5007.89	0.247270	0.123635	−	0.992328i	$-0.460545\pi$
$743$	5007.89	0.247270	0.123635	+	0.992328i	$0.460545\pi$
$744$	30203.3	1.48831
$745$	474.046	0.0233124
$746$	−59276.6	−2.90921
$747$	6147.12	0.301086
$748$	−7392.61	−0.361364
$749$	2366.68	0.115456
$750$	−6973.58	−0.339519
$751$	38826.4	1.88655	0.943274	−	0.332017i	$-0.107729\pi$
$751$	38826.4	1.88655	0.943274	+	0.332017i	$0.107729\pi$
$752$	41373.4	2.00629
$753$	−3645.44	−0.176424
$754$	−39221.8	−1.89440
$755$	119.095	0.00574082
$756$	1948.59	0.0937426
$757$	−29348.5	−1.40910	−0.704550	−	0.709654i	$-0.748851\pi$
$757$	−29348.5	−1.40910	−0.704550	+	0.709654i	$0.748851\pi$
$758$	−30800.8	−1.47590
$759$	4125.82	0.197309
$760$	−6124.81	−0.292329
$761$	20173.9	0.960976	0.480488	−	0.877001i	$-0.340460\pi$
$761$	20173.9	0.960976	0.480488	+	0.877001i	$0.340460\pi$
$762$	−15907.5	−0.756258
$763$	3356.82	0.159273
$764$	−6582.85	−0.311727
$765$	574.983	0.0271746
$766$	1883.35	0.0888356
$767$	−8390.08	−0.394978
$768$	−14836.7	−0.697100
$769$	31167.0	1.46152	0.730762	−	0.682632i	$-0.239165\pi$
$769$	31167.0	1.46152	0.730762	+	0.682632i	$0.239165\pi$
$770$	392.535	0.0183714
$771$	−12899.1	−0.602531
$772$	3536.77	0.164885
$773$	16305.6	0.758695	0.379348	−	0.925254i	$-0.376148\pi$
$773$	16305.6	0.758695	0.379348	+	0.925254i	$0.376148\pi$
$774$	14969.7	0.695189
$775$	21311.9	0.987801
$776$	−13606.1	−0.629421
$777$	561.886	0.0259428
$778$	−13177.0	−0.607220
$779$	−23259.6	−1.06978
$780$	−2776.48	−0.127454
$781$	804.732	0.0368701
$782$	22936.1	1.04884
$783$	7592.92	0.346550
$784$	−48195.4	−2.19549
$785$	−1745.79	−0.0793757
$786$	14066.5	0.638342
$787$	−233.696	−0.0105850	−0.00529248	−	0.999986i	$-0.501685\pi$
$787$	−233.696	−0.0105850	−0.00529248	+	0.999986i	$0.501685\pi$
$788$	−40793.8	−1.84419
$789$	10961.3	0.494591
$790$	5770.54	0.259882
$791$	−2977.38	−0.133835
$792$	−5692.51	−0.255397
$793$	−1635.65	−0.0732456
$794$	−13015.6	−0.581748
$795$	1636.07	0.0729881
$796$	76863.6	3.42256
$797$	23231.2	1.03249	0.516244	−	0.856442i	$-0.327330\pi$
$797$	23231.2	1.03249	0.516244	+	0.856442i	$0.327330\pi$
$798$	3475.44	0.154172
$799$	−9950.81	−0.440594
$800$	36851.2	1.62861
$801$	9848.86	0.434448
$802$	−31537.5	−1.38856
$803$	1853.84	0.0814701
$804$	1530.83	0.0671494
$805$	−857.749	−0.0375549
$806$	24420.1	1.06720
$807$	25265.0	1.10207
$808$	19053.8	0.829594
$809$	−42829.6	−1.86132	−0.930661	−	0.365882i	$-0.880767\pi$
$809$	−42829.6	−1.86132	−0.930661	+	0.365882i	$0.880767\pi$
$810$	763.162	0.0331047
$811$	−32869.4	−1.42318	−0.711591	−	0.702594i	$-0.752025\pi$
$811$	−32869.4	−1.42318	−0.711591	+	0.702594i	$0.752025\pi$
$812$	20295.6	0.877137
$813$	−22657.7	−0.977419
$814$	−2829.35	−0.121829
$815$	1732.20	0.0744494
$816$	−15516.3	−0.665662
$817$	18804.6	0.805249
$818$	−20019.9	−0.855719
$819$	914.024	0.0389970
$820$	−13652.2	−0.581407
$821$	36726.5	1.56122	0.780611	−	0.625017i	$-0.214908\pi$
$821$	36726.5	1.56122	0.780611	+	0.625017i	$0.214908\pi$
$822$	38517.8	1.63438
$823$	5474.61	0.231875	0.115937	−	0.993257i	$-0.463013\pi$
$823$	5474.61	0.231875	0.115937	+	0.993257i	$0.463013\pi$
$824$	−67059.8	−2.83512
$825$	−4016.72	−0.169508
$826$	6164.25	0.259663
$827$	5849.35	0.245952	0.122976	−	0.992410i	$-0.460756\pi$
$827$	5849.35	0.245952	0.122976	+	0.992410i	$0.460756\pi$
$828$	21440.8	0.899903
$829$	−16643.6	−0.697294	−0.348647	−	0.937254i	$-0.613359\pi$
$829$	−16643.6	−0.697294	−0.348647	+	0.937254i	$0.613359\pi$
$830$	6435.18	0.269119
$831$	24478.8	1.02185
$832$	10768.8	0.448725
$833$	11591.6	0.482142
$834$	−15117.4	−0.627665
$835$	−255.359	−0.0105833
$836$	−12325.6	−0.509916
$837$	−4727.46	−0.195227
$838$	24884.2	1.02579
$839$	−38678.0	−1.59155	−0.795777	−	0.605590i	$-0.792937\pi$
$839$	−38678.0	−1.59155	−0.795777	+	0.605590i	$0.792937\pi$
$840$	1183.46	0.0486111
$841$	54695.3	2.24262
$842$	−12811.2	−0.524352
$843$	−8368.07	−0.341888
$844$	39065.7	1.59324
$845$	2677.24	0.108994
$846$	−13207.5	−0.536740
$847$	458.289	0.0185915
$848$	−44150.6	−1.78790
$849$	−19572.1	−0.791181
$850$	−22329.7	−0.901060
$851$	6182.57	0.249043
$852$	4181.98	0.168160
$853$	−25749.8	−1.03360	−0.516798	−	0.856107i	$-0.672876\pi$
$853$	−25749.8	−1.03360	−0.516798	+	0.856107i	$0.672876\pi$
$854$	1201.72	0.0481524
$855$	958.663	0.0383457
$856$	−35929.8	−1.43464
$857$	−14955.5	−0.596115	−0.298057	−	0.954548i	$-0.596339\pi$
$857$	−14955.5	−0.596115	−0.298057	+	0.954548i	$0.596339\pi$
$858$	−4602.53	−0.183133
$859$	−42919.0	−1.70475	−0.852373	−	0.522935i	$-0.824837\pi$
$859$	−42919.0	−1.70475	−0.852373	+	0.522935i	$0.824837\pi$
$860$	11037.3	0.437638
$861$	4494.31	0.177893
$862$	−80871.0	−3.19545
$863$	16487.2	0.650326	0.325163	−	0.945658i	$-0.394581\pi$
$863$	16487.2	0.650326	0.325163	+	0.945658i	$0.394581\pi$
$864$	−8174.44	−0.321875
$865$	−3131.09	−0.123075
$866$	−21040.6	−0.825622
$867$	−11007.1	−0.431167
$868$	−12636.3	−0.494129
$869$	6737.16	0.262995
$870$	7948.74	0.309756
$871$	718.065	0.0279342
$872$	−50961.6	−1.97910
$873$	2129.65	0.0825631
$874$	38241.1	1.48001
$875$	1692.65	0.0653965
$876$	9633.90	0.371575
$877$	−15032.7	−0.578812	−0.289406	−	0.957206i	$-0.593458\pi$
$877$	−15032.7	−0.578812	−0.289406	+	0.957206i	$0.593458\pi$
$878$	−8606.65	−0.330821
$879$	888.936	0.0341104
$880$	−2921.92	−0.111929
$881$	−12966.4	−0.495857	−0.247929	−	0.968778i	$-0.579750\pi$
$881$	−12966.4	−0.495857	−0.247929	+	0.968778i	$0.579750\pi$
$882$	15385.2	0.587355
$883$	−19829.1	−0.755721	−0.377860	−	0.925863i	$-0.623340\pi$
$883$	−19829.1	−0.755721	−0.377860	+	0.925863i	$0.623340\pi$
$884$	−18020.5	−0.685627
$885$	1700.34	0.0645835
$886$	−45911.7	−1.74090
$887$	22576.7	0.854624	0.427312	−	0.904104i	$-0.359461\pi$
$887$	22576.7	0.854624	0.427312	+	0.904104i	$0.359461\pi$
$888$	−8530.28	−0.322362
$889$	3861.12	0.145667
$890$	10310.4	0.388321
$891$	891.000	0.0335013
$892$	−35586.0	−1.33577
$893$	−16590.9	−0.621716
$894$	4083.69	0.152773
$895$	2130.47	0.0795686
$896$	1261.69	0.0470424
$897$	10057.2	0.374360
$898$	−24017.6	−0.892513
$899$	−49239.0	−1.82671
$900$	−20873.9	−0.773106
$901$	10618.8	0.392633
$902$	−22630.9	−0.835397
$903$	−3633.50	−0.133904
$904$	45201.2	1.66302
$905$	−3031.68	−0.111355
$906$	1025.95	0.0376213
$907$	17166.8	0.628461	0.314230	−	0.949347i	$-0.398254\pi$
$907$	17166.8	0.628461	0.314230	+	0.949347i	$0.398254\pi$
$908$	8853.64	0.323589
$909$	−2982.33	−0.108820
$910$	956.857	0.0348566
$911$	−12707.1	−0.462136	−0.231068	−	0.972938i	$-0.574222\pi$
$911$	−12707.1	−0.462136	−0.231068	+	0.972938i	$0.574222\pi$
$912$	−25870.2	−0.939307
$913$	7513.14	0.272343
$914$	42397.9	1.53435
$915$	331.483	0.0119765
$916$	−114140.	−4.11714
$917$	−3414.28	−0.122955
$918$	4953.22	0.178083
$919$	−6997.73	−0.251179	−0.125590	−	0.992082i	$-0.540082\pi$
$919$	−6997.73	−0.251179	−0.125590	+	0.992082i	$0.540082\pi$
$920$	13021.9	0.466653
$921$	19196.2	0.686792
$922$	−20448.4	−0.730405
$923$	1961.64	0.0699547
$924$	2381.61	0.0847934
$925$	−6019.09	−0.213953
$926$	−85011.3	−3.01689
$927$	10496.3	0.371891
$928$	−85141.1	−3.01174
$929$	12725.6	0.449424	0.224712	−	0.974425i	$-0.427856\pi$
$929$	12725.6	0.449424	0.224712	+	0.974425i	$0.427856\pi$
$930$	−4949.00	−0.174499
$931$	19326.5	0.680344
$932$	−10103.5	−0.355098
$933$	−23802.0	−0.835201
$934$	26780.5	0.938205
$935$	702.758	0.0245804
$936$	−13876.3	−0.484573
$937$	−34721.9	−1.21058	−0.605291	−	0.796004i	$-0.706943\pi$
$937$	−34721.9	−1.21058	−0.605291	+	0.796004i	$0.706943\pi$
$938$	−527.567	−0.0183643
$939$	−18534.3	−0.644138
$940$	−9737.98	−0.337891
$941$	4690.31	0.162487	0.0812433	−	0.996694i	$-0.474111\pi$
$941$	4690.31	0.162487	0.0812433	+	0.996694i	$0.474111\pi$
$942$	−15039.2	−0.520174
$943$	49452.1	1.70772
$944$	−45885.0	−1.58202
$945$	−185.237	−0.00637647
$946$	18296.3	0.628822
$947$	−19455.7	−0.667607	−0.333803	−	0.942643i	$-0.608332\pi$
$947$	−19455.7	−0.667607	−0.333803	+	0.942643i	$0.608332\pi$
$948$	35011.3	1.19949
$949$	4518.97	0.154575
$950$	−37230.0	−1.27147
$951$	32823.6	1.11922
$952$	7681.13	0.261499
$953$	43280.0	1.47112	0.735559	−	0.677460i	$-0.236920\pi$
$953$	43280.0	1.47112	0.735559	+	0.677460i	$0.236920\pi$
$954$	14094.0	0.478314
$955$	625.781	0.0212040
$956$	−11316.0	−0.382832
$957$	9280.24	0.313467
$958$	−87143.7	−2.93892
$959$	−9349.15	−0.314807
$960$	−2182.41	−0.0733718
$961$	865.896	0.0290657
$962$	−6896.93	−0.231150
$963$	5623.78	0.188187
$964$	53383.5	1.78358
$965$	−336.213	−0.0112156
$966$	−7389.12	−0.246109
$967$	38947.9	1.29522	0.647610	−	0.761972i	$-0.275768\pi$
$967$	38947.9	1.29522	0.647610	+	0.761972i	$0.275768\pi$
$968$	−6957.52	−0.231016
$969$	6222.10	0.206277
$970$	2229.44	0.0737971
$971$	−47573.3	−1.57230	−0.786149	−	0.618037i	$-0.787928\pi$
$971$	−47573.3	−1.57230	−0.786149	+	0.618037i	$0.787928\pi$
$972$	4630.30	0.152795
$973$	3669.34	0.120898
$974$	70968.0	2.33466
$975$	−9791.30	−0.321613
$976$	−8945.31	−0.293373
$977$	8483.42	0.277798	0.138899	−	0.990307i	$-0.455644\pi$
$977$	8483.42	0.277798	0.138899	+	0.990307i	$0.455644\pi$
$978$	14922.1	0.487890
$979$	12037.5	0.392973
$980$	11343.6	0.369755
$981$	7976.58	0.259605
$982$	15042.7	0.488831
$983$	5064.80	0.164336	0.0821679	−	0.996619i	$-0.473816\pi$
$983$	5064.80	0.164336	0.0821679	+	0.996619i	$0.473816\pi$
$984$	−68230.5	−2.21048
$985$	3877.95	0.125443
$986$	51590.4	1.66630
$987$	3205.76	0.103384
$988$	−30045.3	−0.967478
$989$	−39980.3	−1.28544
$990$	932.754	0.0299443
$991$	−39964.4	−1.28104	−0.640520	−	0.767941i	$-0.721281\pi$
$991$	−39964.4	−1.28104	−0.640520	+	0.767941i	$0.721281\pi$
$992$	53010.1	1.69664
$993$	4583.42	0.146476
$994$	−1441.23	−0.0459890
$995$	−7306.82	−0.232806
$996$	39043.8	1.24212
$997$	25759.8	0.818275	0.409138	−	0.912473i	$-0.365830\pi$
$997$	25759.8	0.818275	0.409138	+	0.912473i	$0.365830\pi$
$998$	−32331.5	−1.02549
$999$	1335.17	0.0422852

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2013.4.a.f.1.1	✓	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)

\(f(q)\)	\(=\)	\(q-5.20141 q^{2} +3.00000 q^{3} +19.0547 q^{4} -1.81138 q^{5} -15.6042 q^{6} +3.78751 q^{7} -57.5001 q^{8} +9.00000 q^{9} +O(q^{10})\)	\(q-5.20141 q^{2} +3.00000 q^{3} +19.0547 q^{4} -1.81138 q^{5} -15.6042 q^{6} +3.78751 q^{7} -57.5001 q^{8} +9.00000 q^{9} +9.42176 q^{10} +11.0000 q^{11} +57.1641 q^{12} +26.8140 q^{13} -19.7004 q^{14} -5.43415 q^{15} +146.644 q^{16} -35.2698 q^{17} -46.8127 q^{18} -58.8048 q^{19} -34.5154 q^{20} +11.3625 q^{21} -57.2156 q^{22} +125.025 q^{23} -172.500 q^{24} -121.719 q^{25} -139.471 q^{26} +27.0000 q^{27} +72.1699 q^{28} +281.219 q^{29} +28.2653 q^{30} -175.091 q^{31} -302.757 q^{32} +33.0000 q^{33} +183.453 q^{34} -6.86063 q^{35} +171.492 q^{36} +49.4508 q^{37} +305.868 q^{38} +80.4419 q^{39} +104.155 q^{40} +395.538 q^{41} -59.1012 q^{42} -319.779 q^{43} +209.602 q^{44} -16.3024 q^{45} -650.306 q^{46} +282.134 q^{47} +439.933 q^{48} -328.655 q^{49} +633.110 q^{50} -105.809 q^{51} +510.933 q^{52} -301.073 q^{53} -140.438 q^{54} -19.9252 q^{55} -217.782 q^{56} -176.415 q^{57} -1462.74 q^{58} -312.900 q^{59} -103.546 q^{60} -61.0000 q^{61} +910.721 q^{62} +34.0876 q^{63} +401.610 q^{64} -48.5704 q^{65} -171.647 q^{66} +26.7795 q^{67} -672.055 q^{68} +375.074 q^{69} +35.6850 q^{70} +73.1574 q^{71} -517.501 q^{72} +168.531 q^{73} -257.214 q^{74} -365.157 q^{75} -1120.51 q^{76} +41.6626 q^{77} -418.412 q^{78} +612.469 q^{79} -265.629 q^{80} +81.0000 q^{81} -2057.36 q^{82} +683.013 q^{83} +216.510 q^{84} +63.8871 q^{85} +1663.30 q^{86} +843.658 q^{87} -632.502 q^{88} +1094.32 q^{89} +84.7958 q^{90} +101.558 q^{91} +2382.31 q^{92} -525.273 q^{93} -1467.50 q^{94} +106.518 q^{95} -908.271 q^{96} +236.627 q^{97} +1709.47 q^{98} +99.0000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 38 q + 14 q^{2} + 114 q^{3} + 170 q^{4} + 35 q^{5} + 42 q^{6} + 105 q^{7} + 147 q^{8} + 342 q^{9}+O(q^{10}) \) 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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