LMFDB - Embedded newform 2013.4.a.c.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:	$1$
Dimension:	$37$
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)

$f(q)$	$=$	$q-5.41306 q^{2} +3.00000 q^{3} +21.3012 q^{4} -13.4657 q^{5} -16.2392 q^{6} +11.1590 q^{7} -72.0002 q^{8} +9.00000 q^{9} +O(q^{10})$	\(q-5.41306 q^{2} +3.00000 q^{3} +21.3012 q^{4} -13.4657 q^{5} -16.2392 q^{6} +11.1590 q^{7} -72.0002 q^{8} +9.00000 q^{9} +72.8907 q^{10} -11.0000 q^{11} +63.9036 q^{12} +79.3054 q^{13} -60.4043 q^{14} -40.3971 q^{15} +219.332 q^{16} +23.6113 q^{17} -48.7175 q^{18} -63.5988 q^{19} -286.836 q^{20} +33.4770 q^{21} +59.5437 q^{22} +208.787 q^{23} -216.001 q^{24} +56.3254 q^{25} -429.285 q^{26} +27.0000 q^{27} +237.700 q^{28} -264.140 q^{29} +218.672 q^{30} -217.687 q^{31} -611.255 q^{32} -33.0000 q^{33} -127.809 q^{34} -150.264 q^{35} +191.711 q^{36} -99.1882 q^{37} +344.264 q^{38} +237.916 q^{39} +969.535 q^{40} -244.032 q^{41} -181.213 q^{42} +364.385 q^{43} -234.313 q^{44} -121.191 q^{45} -1130.18 q^{46} -462.269 q^{47} +657.996 q^{48} -218.477 q^{49} -304.893 q^{50} +70.8338 q^{51} +1689.30 q^{52} +225.587 q^{53} -146.153 q^{54} +148.123 q^{55} -803.451 q^{56} -190.797 q^{57} +1429.81 q^{58} +384.110 q^{59} -860.508 q^{60} -61.0000 q^{61} +1178.35 q^{62} +100.431 q^{63} +1554.10 q^{64} -1067.90 q^{65} +178.631 q^{66} +715.248 q^{67} +502.949 q^{68} +626.361 q^{69} +813.388 q^{70} -413.856 q^{71} -648.002 q^{72} -518.368 q^{73} +536.912 q^{74} +168.976 q^{75} -1354.73 q^{76} -122.749 q^{77} -1287.85 q^{78} +656.211 q^{79} -2953.46 q^{80} +81.0000 q^{81} +1320.96 q^{82} +525.109 q^{83} +713.101 q^{84} -317.943 q^{85} -1972.44 q^{86} -792.421 q^{87} +792.003 q^{88} -1192.68 q^{89} +656.016 q^{90} +884.969 q^{91} +4447.42 q^{92} -653.060 q^{93} +2502.29 q^{94} +856.404 q^{95} -1833.76 q^{96} -207.239 q^{97} +1182.63 q^{98} -99.0000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 37 q - 8 q^{2} + 111 q^{3} + 130 q^{4} - 35 q^{5} - 24 q^{6} - 35 q^{7} - 117 q^{8} + 333 q^{9}+O(q^{10}) $ 37 * q - 8 * q^2 + 111 * q^3 + 130 * q^4 - 35 * q^5 - 24 * q^6 - 35 * q^7 - 117 * q^8 + 333 * q^9	\( 37 q - 8 q^{2} + 111 q^{3} + 130 q^{4} - 35 q^{5} - 24 q^{6} - 35 q^{7} - 117 q^{8} + 333 q^{9} - 41 q^{10} - 407 q^{11} + 390 q^{12} + 51 q^{13} - 228 q^{14} - 105 q^{15} + 462 q^{16} - 190 q^{17} - 72 q^{18} - 51 q^{19} - 720 q^{20} - 105 q^{21} + 88 q^{22} - 583 q^{23} - 351 q^{24} + 598 q^{25} - 1019 q^{26} + 999 q^{27} - 498 q^{28} - 566 q^{29} - 123 q^{30} - 696 q^{31} - 859 q^{32} - 1221 q^{33} - 348 q^{34} - 1102 q^{35} + 1170 q^{36} - 1022 q^{37} - 455 q^{38} + 153 q^{39} - 503 q^{40} - 790 q^{41} - 684 q^{42} - 87 q^{43} - 1430 q^{44} - 315 q^{45} - 303 q^{46} - 1603 q^{47} + 1386 q^{48} + 110 q^{49} - 1926 q^{50} - 570 q^{51} + 736 q^{52} - 2619 q^{53} - 216 q^{54} + 385 q^{55} - 4937 q^{56} - 153 q^{57} - 1099 q^{58} - 2471 q^{59} - 2160 q^{60} - 2257 q^{61} - 2909 q^{62} - 315 q^{63} - 265 q^{64} - 1970 q^{65} + 264 q^{66} - 3033 q^{67} - 1956 q^{68} - 1749 q^{69} + 2410 q^{70} - 3891 q^{71} - 1053 q^{72} + 391 q^{73} - 532 q^{74} + 1794 q^{75} + 1554 q^{76} + 385 q^{77} - 3057 q^{78} + 67 q^{79} - 5111 q^{80} + 2997 q^{81} - 4818 q^{82} - 5315 q^{83} - 1494 q^{84} - 2747 q^{85} - 5195 q^{86} - 1698 q^{87} + 1287 q^{88} - 8945 q^{89} - 369 q^{90} - 4432 q^{91} - 4701 q^{92} - 2088 q^{93} - 372 q^{94} - 3388 q^{95} - 2577 q^{96} - 3784 q^{97} - 4502 q^{98} - 3663 q^{99}+O(q^{100}) \) 37 * q - 8 * q^2 + 111 * q^3 + 130 * q^4 - 35 * q^5 - 24 * q^6 - 35 * q^7 - 117 * q^8 + 333 * q^9 - 41 * q^10 - 407 * q^11 + 390 * q^12 + 51 * q^13 - 228 * q^14 - 105 * q^15 + 462 * q^16 - 190 * q^17 - 72 * q^18 - 51 * q^19 - 720 * q^20 - 105 * q^21 + 88 * q^22 - 583 * q^23 - 351 * q^24 + 598 * q^25 - 1019 * q^26 + 999 * q^27 - 498 * q^28 - 566 * q^29 - 123 * q^30 - 696 * q^31 - 859 * q^32 - 1221 * q^33 - 348 * q^34 - 1102 * q^35 + 1170 * q^36 - 1022 * q^37 - 455 * q^38 + 153 * q^39 - 503 * q^40 - 790 * q^41 - 684 * q^42 - 87 * q^43 - 1430 * q^44 - 315 * q^45 - 303 * q^46 - 1603 * q^47 + 1386 * q^48 + 110 * q^49 - 1926 * q^50 - 570 * q^51 + 736 * q^52 - 2619 * q^53 - 216 * q^54 + 385 * q^55 - 4937 * q^56 - 153 * q^57 - 1099 * q^58 - 2471 * q^59 - 2160 * q^60 - 2257 * q^61 - 2909 * q^62 - 315 * q^63 - 265 * q^64 - 1970 * q^65 + 264 * q^66 - 3033 * q^67 - 1956 * q^68 - 1749 * q^69 + 2410 * q^70 - 3891 * q^71 - 1053 * q^72 + 391 * q^73 - 532 * q^74 + 1794 * q^75 + 1554 * q^76 + 385 * q^77 - 3057 * q^78 + 67 * q^79 - 5111 * q^80 + 2997 * q^81 - 4818 * q^82 - 5315 * q^83 - 1494 * q^84 - 2747 * q^85 - 5195 * q^86 - 1698 * q^87 + 1287 * q^88 - 8945 * q^89 - 369 * q^90 - 4432 * q^91 - 4701 * q^92 - 2088 * q^93 - 372 * q^94 - 3388 * q^95 - 2577 * q^96 - 3784 * q^97 - 4502 * q^98 - 3663 * 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 $

$2$	−5.41306	−1.91381	−0.956903	−	0.290409i	$-0.906209\pi$
$2$	−5.41306	−1.91381	−0.956903	+	0.290409i	$0.906209\pi$
$3$	3.00000	0.577350
$3$	3.00000	0.577350
$4$	21.3012	2.66265
$5$	−13.4657	−1.20441	−0.602205	−	0.798341i	$-0.705711\pi$
$5$	−13.4657	−1.20441	−0.602205	+	0.798341i	$0.705711\pi$
$6$	−16.2392	−1.10494
$7$	11.1590	0.602530	0.301265	−	0.953541i	$-0.402591\pi$
$7$	11.1590	0.602530	0.301265	+	0.953541i	$0.402591\pi$
$8$	−72.0002	−3.18199
$9$	9.00000	0.333333
$10$	72.8907	2.30501
$11$	−11.0000	−0.301511
$11$	−11.0000	−0.301511
$12$	63.9036	1.53728
$13$	79.3054	1.69195	0.845975	−	0.533222i	$-0.179019\pi$
$13$	79.3054	1.69195	0.845975	+	0.533222i	$0.179019\pi$
$14$	−60.4043	−1.15312
$15$	−40.3971	−0.695366
$16$	219.332	3.42706
$17$	23.6113	0.336857	0.168429	−	0.985714i	$-0.446131\pi$
$17$	23.6113	0.336857	0.168429	+	0.985714i	$0.446131\pi$
$18$	−48.7175	−0.637935
$19$	−63.5988	−0.767925	−0.383963	−	0.923349i	$-0.625441\pi$
$19$	−63.5988	−0.767925	−0.383963	+	0.923349i	$0.625441\pi$
$20$	−286.836	−3.20692
$21$	33.4770	0.347871
$22$	59.5437	0.577034
$23$	208.787	1.89283	0.946415	−	0.322952i	$-0.104675\pi$
$23$	208.787	1.89283	0.946415	+	0.322952i	$0.104675\pi$
$24$	−216.001	−1.83712
$25$	56.3254	0.450603
$26$	−429.285	−3.23806
$27$	27.0000	0.192450
$28$	237.700	1.60433
$29$	−264.140	−1.69137	−0.845683	−	0.533685i	$-0.820807\pi$
$29$	−264.140	−1.69137	−0.845683	+	0.533685i	$0.820807\pi$
$30$	218.672	1.33080
$31$	−217.687	−1.26122	−0.630608	−	0.776101i	$-0.717194\pi$
$31$	−217.687	−1.26122	−0.630608	+	0.776101i	$0.717194\pi$
$32$	−611.255	−3.37674
$33$	−33.0000	−0.174078
$34$	−127.809	−0.644679
$35$	−150.264	−0.725693
$36$	191.711	0.887550
$37$	−99.1882	−0.440715	−0.220357	−	0.975419i	$-0.570722\pi$
$37$	−99.1882	−0.440715	−0.220357	+	0.975419i	$0.570722\pi$
$38$	344.264	1.46966
$39$	237.916	0.976848
$40$	969.535	3.83242
$41$	−244.032	−0.929545	−0.464772	−	0.885430i	$-0.653864\pi$
$41$	−244.032	−0.929545	−0.464772	+	0.885430i	$0.653864\pi$
$42$	−181.213	−0.665757
$43$	364.385	1.29228	0.646141	−	0.763218i	$-0.276382\pi$
$43$	364.385	1.29228	0.646141	+	0.763218i	$0.276382\pi$
$44$	−234.313	−0.802820
$45$	−121.191	−0.401470
$46$	−1130.18	−3.62251
$47$	−462.269	−1.43466	−0.717329	−	0.696735i	$-0.754635\pi$
$47$	−462.269	−1.43466	−0.717329	+	0.696735i	$0.754635\pi$
$48$	657.996	1.97861
$49$	−218.477	−0.636958
$50$	−304.893	−0.862367
$51$	70.8338	0.194485
$52$	1689.30	4.50508
$53$	225.587	0.584655	0.292328	−	0.956318i	$-0.405570\pi$
$53$	225.587	0.584655	0.292328	+	0.956318i	$0.405570\pi$
$54$	−146.153	−0.368312
$55$	148.123	0.363143
$56$	−803.451	−1.91724
$57$	−190.797	−0.443362
$58$	1429.81	3.23695
$59$	384.110	0.847574	0.423787	−	0.905762i	$-0.360701\pi$
$59$	384.110	0.847574	0.423787	+	0.905762i	$0.360701\pi$
$60$	−860.508	−1.85152
$61$	−61.0000	−0.128037
$61$	−61.0000	−0.128037
$62$	1178.35	2.41372
$63$	100.431	0.200843
$64$	1554.10	3.03536
$65$	−1067.90	−2.03780
$66$	178.631	0.333151
$67$	715.248	1.30420	0.652100	−	0.758133i	$-0.273888\pi$
$67$	715.248	1.30420	0.652100	+	0.758133i	$0.273888\pi$
$68$	502.949	0.896933
$69$	626.361	1.09283
$70$	813.388	1.38883
$71$	−413.856	−0.691769	−0.345885	−	0.938277i	$-0.612421\pi$
$71$	−413.856	−0.691769	−0.345885	+	0.938277i	$0.612421\pi$
$72$	−648.002	−1.06066
$73$	−518.368	−0.831101	−0.415551	−	0.909570i	$-0.636411\pi$
$73$	−518.368	−0.831101	−0.415551	+	0.909570i	$0.636411\pi$
$74$	536.912	0.843442
$75$	168.976	0.260156
$76$	−1354.73	−2.04472
$77$	−122.749	−0.181669
$78$	−1287.85	−1.86950
$79$	656.211	0.934551	0.467275	−	0.884112i	$-0.345236\pi$
$79$	656.211	0.934551	0.467275	+	0.884112i	$0.345236\pi$
$80$	−2953.46	−4.12759
$81$	81.0000	0.111111
$82$	1320.96	1.77897
$83$	525.109	0.694436	0.347218	−	0.937785i	$-0.387126\pi$
$83$	525.109	0.694436	0.347218	+	0.937785i	$0.387126\pi$
$84$	713.101	0.926258
$85$	−317.943	−0.405714
$86$	−1972.44	−2.47318
$87$	−792.421	−0.976511
$88$	792.003	0.959406
$89$	−1192.68	−1.42049	−0.710245	−	0.703954i	$-0.751416\pi$
$89$	−1192.68	−1.42049	−0.710245	+	0.703954i	$0.751416\pi$
$90$	656.016	0.768335
$91$	884.969	1.01945
$92$	4447.42	5.03995
$93$	−653.060	−0.728164
$94$	2502.29	2.74565
$95$	856.404	0.924897
$96$	−1833.76	−1.94956
$97$	−207.239	−0.216927	−0.108463	−	0.994100i	$-0.534593\pi$
$97$	−207.239	−0.216927	−0.108463	+	0.994100i	$0.534593\pi$
$98$	1182.63	1.21901
$99$	−99.0000	−0.100504
$100$	1199.80	1.19980
$101$	−418.947	−0.412741	−0.206370	−	0.978474i	$-0.566165\pi$
$101$	−418.947	−0.412741	−0.206370	+	0.978474i	$0.566165\pi$
$102$	−383.428	−0.372206
$103$	1392.44	1.33205	0.666026	−	0.745929i	$-0.267994\pi$
$103$	1392.44	1.33205	0.666026	+	0.745929i	$0.267994\pi$
$104$	−5710.01	−5.38377
$105$	−450.792	−0.418979
$106$	−1221.11	−1.11892
$107$	100.041	0.0903862	0.0451931	−	0.998978i	$-0.485610\pi$
$107$	100.041	0.0903862	0.0451931	+	0.998978i	$0.485610\pi$
$108$	575.133	0.512427
$109$	−1092.20	−0.959759	−0.479879	−	0.877334i	$-0.659320\pi$
$109$	−1092.20	−0.959759	−0.479879	+	0.877334i	$0.659320\pi$
$110$	−801.798	−0.694986
$111$	−297.565	−0.254447
$112$	2447.53	2.06491
$113$	−901.639	−0.750611	−0.375305	−	0.926901i	$-0.622462\pi$
$113$	−901.639	−0.750611	−0.375305	+	0.926901i	$0.622462\pi$
$114$	1032.79	0.848508
$115$	−2811.47	−2.27974
$116$	−5626.51	−4.50352
$117$	713.749	0.563984
$118$	−2079.21	−1.62209
$119$	263.478	0.202966
$120$	2908.60	2.21265
$121$	121.000	0.0909091
$122$	330.197	0.245038
$123$	−732.095	−0.536673
$124$	−4636.99	−3.35818
$125$	924.752	0.661699
$126$	−543.639	−0.384375
$127$	1027.50	0.717922	0.358961	−	0.933353i	$-0.383131\pi$
$127$	1027.50	0.717922	0.358961	+	0.933353i	$0.383131\pi$
$128$	−3522.41	−2.43234
$129$	1093.15	0.746099
$130$	5780.63	3.89996
$131$	799.137	0.532984	0.266492	−	0.963837i	$-0.414135\pi$
$131$	799.137	0.532984	0.266492	+	0.963837i	$0.414135\pi$
$132$	−702.940	−0.463508
$133$	−709.700	−0.462698
$134$	−3871.68	−2.49599
$135$	−363.574	−0.231789
$136$	−1700.02	−1.07188
$137$	−668.594	−0.416947	−0.208474	−	0.978028i	$-0.566850\pi$
$137$	−668.594	−0.416947	−0.208474	+	0.978028i	$0.566850\pi$
$138$	−3390.53	−2.09146
$139$	−1779.33	−1.08576	−0.542879	−	0.839811i	$-0.682666\pi$
$139$	−1779.33	−1.08576	−0.542879	+	0.839811i	$0.682666\pi$
$140$	−3200.80	−1.93227
$141$	−1386.81	−0.828300
$142$	2240.22	1.32391
$143$	−872.359	−0.510142
$144$	1973.99	1.14235
$145$	3556.84	2.03710
$146$	2805.96	1.59057
$147$	−655.430	−0.367748
$148$	−2112.83	−1.17347
$149$	1441.78	0.792717	0.396358	−	0.918096i	$-0.370274\pi$
$149$	1441.78	0.792717	0.396358	+	0.918096i	$0.370274\pi$
$150$	−914.679	−0.497888
$151$	−1663.86	−0.896710	−0.448355	−	0.893856i	$-0.647990\pi$
$151$	−1663.86	−0.896710	−0.448355	+	0.893856i	$0.647990\pi$
$152$	4579.13	2.44353
$153$	212.501	0.112286
$154$	664.448	0.347680
$155$	2931.31	1.51902
$156$	5067.90	2.60101
$157$	−1992.73	−1.01297	−0.506487	−	0.862248i	$-0.669056\pi$
$157$	−1992.73	−1.01297	−0.506487	+	0.862248i	$0.669056\pi$
$158$	−3552.11	−1.78855
$159$	676.761	0.337551
$160$	8230.98	4.06698
$161$	2329.85	1.14049
$162$	−438.458	−0.212645
$163$	−1876.90	−0.901902	−0.450951	−	0.892549i	$-0.648915\pi$
$163$	−1876.90	−0.901902	−0.450951	+	0.892549i	$0.648915\pi$
$164$	−5198.17	−2.47505
$165$	444.369	0.209661
$166$	−2842.44	−1.32901
$167$	−2011.46	−0.932046	−0.466023	−	0.884773i	$-0.654314\pi$
$167$	−2011.46	−0.932046	−0.466023	+	0.884773i	$0.654314\pi$
$168$	−2410.35	−1.10692
$169$	4092.35	1.86270
$170$	1721.04	0.776458
$171$	−572.390	−0.255975
$172$	7761.83	3.44090
$173$	1038.03	0.456186	0.228093	−	0.973639i	$-0.426751\pi$
$173$	1038.03	0.456186	0.228093	+	0.973639i	$0.426751\pi$
$174$	4289.42	1.86885
$175$	628.536	0.271502
$176$	−2412.65	−1.03330
$177$	1152.33	0.489347
$178$	6456.04	2.71854
$179$	−351.436	−0.146746	−0.0733730	−	0.997305i	$-0.523376\pi$
$179$	−351.436	−0.146746	−0.0733730	+	0.997305i	$0.523376\pi$
$180$	−2581.52	−1.06897
$181$	−2487.99	−1.02172	−0.510858	−	0.859665i	$-0.670672\pi$
$181$	−2487.99	−1.02172	−0.510858	+	0.859665i	$0.670672\pi$
$182$	−4790.39	−1.95103
$183$	−183.000	−0.0739221
$184$	−15032.7	−6.02297
$185$	1335.64	0.530801
$186$	3535.06	1.39356
$187$	−259.724	−0.101566
$188$	−9846.89	−3.81999
$189$	301.293	0.115957
$190$	−4635.76	−1.77007
$191$	3230.54	1.22384	0.611920	−	0.790920i	$-0.290397\pi$
$191$	3230.54	1.22384	0.611920	+	0.790920i	$0.290397\pi$
$192$	4662.31	1.75246
$193$	746.039	0.278244	0.139122	−	0.990275i	$-0.455572\pi$
$193$	746.039	0.278244	0.139122	+	0.990275i	$0.455572\pi$
$194$	1121.79	0.415156
$195$	−3203.71	−1.17653
$196$	−4653.82	−1.69600
$197$	3619.09	1.30888	0.654440	−	0.756114i	$-0.272904\pi$
$197$	3619.09	1.30888	0.654440	+	0.756114i	$0.272904\pi$
$198$	535.893	0.192345
$199$	−2317.25	−0.825453	−0.412727	−	0.910855i	$-0.635423\pi$
$199$	−2317.25	−0.825453	−0.412727	+	0.910855i	$0.635423\pi$
$200$	−4055.44	−1.43382
$201$	2145.74	0.752980
$202$	2267.79	0.789905
$203$	−2947.54	−1.01910
$204$	1508.85	0.517845
$205$	3286.06	1.11955
$206$	−7537.37	−2.54929
$207$	1879.08	0.630943
$208$	17394.2	5.79842
$209$	699.587	0.231538
$210$	2440.16	0.801844
$211$	3204.26	1.04545	0.522726	−	0.852500i	$-0.324915\pi$
$211$	3204.26	1.04545	0.522726	+	0.852500i	$0.324915\pi$
$212$	4805.27	1.55673
$213$	−1241.57	−0.399393
$214$	−541.527	−0.172982
$215$	−4906.70	−1.55644
$216$	−1944.01	−0.612375
$217$	−2429.17	−0.759920
$218$	5912.14	1.83679
$219$	−1555.10	−0.479836
$220$	3155.20	0.966924
$221$	1872.50	0.569946
$222$	1610.73	0.486961
$223$	91.8721	0.0275884	0.0137942	−	0.999905i	$-0.495609\pi$
$223$	91.8721	0.0275884	0.0137942	+	0.999905i	$0.495609\pi$
$224$	−6820.99	−2.03458
$225$	506.929	0.150201
$226$	4880.62	1.43652
$227$	5076.24	1.48424	0.742118	−	0.670269i	$-0.233821\pi$
$227$	5076.24	1.48424	0.742118	+	0.670269i	$0.233821\pi$
$228$	−4064.20	−1.18052
$229$	2446.40	0.705952	0.352976	−	0.935632i	$-0.385170\pi$
$229$	2446.40	0.705952	0.352976	+	0.935632i	$0.385170\pi$
$230$	15218.6	4.36299
$231$	−368.247	−0.104887
$232$	19018.2	5.38191
$233$	−2634.30	−0.740680	−0.370340	−	0.928896i	$-0.620759\pi$
$233$	−2634.30	−0.740680	−0.370340	+	0.928896i	$0.620759\pi$
$234$	−3863.56	−1.07935
$235$	6224.78	1.72792
$236$	8182.01	2.25679
$237$	1968.63	0.539563
$238$	−1426.22	−0.388438
$239$	6016.88	1.62845	0.814226	−	0.580548i	$-0.197162\pi$
$239$	6016.88	1.62845	0.814226	+	0.580548i	$0.197162\pi$
$240$	−8860.38	−2.38306
$241$	1293.83	0.345822	0.172911	−	0.984937i	$-0.444683\pi$
$241$	1293.83	0.345822	0.172911	+	0.984937i	$0.444683\pi$
$242$	−654.980	−0.173982
$243$	243.000	0.0641500
$244$	−1299.37	−0.340918
$245$	2941.94	0.767159
$246$	3962.87	1.02709
$247$	−5043.73	−1.29929
$248$	15673.5	4.01318
$249$	1575.33	0.400933
$250$	−5005.74	−1.26636
$251$	−1444.41	−0.363229	−0.181614	−	0.983370i	$-0.558132\pi$
$251$	−1444.41	−0.363229	−0.181614	+	0.983370i	$0.558132\pi$
$252$	2139.30	0.534775
$253$	−2296.66	−0.570710
$254$	−5561.93	−1.37396
$255$	−953.828	−0.234239
$256$	6634.20	1.61968
$257$	−234.798	−0.0569894	−0.0284947	−	0.999594i	$-0.509071\pi$
$257$	−234.798	−0.0569894	−0.0284947	+	0.999594i	$0.509071\pi$
$258$	−5917.31	−1.42789
$259$	−1106.84	−0.265544
$260$	−22747.6	−5.42596
$261$	−2377.26	−0.563789
$262$	−4325.77	−1.02003
$263$	839.137	0.196743	0.0983715	−	0.995150i	$-0.468637\pi$
$263$	839.137	0.196743	0.0983715	+	0.995150i	$0.468637\pi$
$264$	2376.01	0.553914
$265$	−3037.69	−0.704165
$266$	3841.65	0.885513
$267$	−3578.04	−0.820121
$268$	15235.6	3.47263
$269$	−3598.24	−0.815571	−0.407786	−	0.913078i	$-0.633699\pi$
$269$	−3598.24	−0.815571	−0.407786	+	0.913078i	$0.633699\pi$
$270$	1968.05	0.443599
$271$	2927.87	0.656293	0.328146	−	0.944627i	$-0.393576\pi$
$271$	2927.87	0.656293	0.328146	+	0.944627i	$0.393576\pi$
$272$	5178.70	1.15443
$273$	2654.91	0.588580
$274$	3619.14	0.797956
$275$	−619.580	−0.135862
$276$	13342.2	2.90982
$277$	−4933.48	−1.07012	−0.535061	−	0.844813i	$-0.679711\pi$
$277$	−4933.48	−1.07012	−0.535061	+	0.844813i	$0.679711\pi$
$278$	9631.60	2.07793
$279$	−1959.18	−0.420405
$280$	10819.0	2.30915
$281$	−6792.84	−1.44209	−0.721044	−	0.692889i	$-0.756338\pi$
$281$	−6792.84	−1.44209	−0.721044	+	0.692889i	$0.756338\pi$
$282$	7506.87	1.58520
$283$	1802.28	0.378566	0.189283	−	0.981923i	$-0.439384\pi$
$283$	1802.28	0.378566	0.189283	+	0.981923i	$0.439384\pi$
$284$	−8815.63	−1.84194
$285$	2569.21	0.533989
$286$	4722.13	0.976313
$287$	−2723.15	−0.560078
$288$	−5501.29	−1.12558
$289$	−4355.51	−0.886527
$290$	−19253.4	−3.89861
$291$	−621.716	−0.125243
$292$	−11041.9	−2.21293
$293$	4974.36	0.991827	0.495913	−	0.868372i	$-0.334833\pi$
$293$	4974.36	0.991827	0.495913	+	0.868372i	$0.334833\pi$
$294$	3547.88	0.703798
$295$	−5172.31	−1.02083
$296$	7141.57	1.40235
$297$	−297.000	−0.0580259
$298$	−7804.41	−1.51711
$299$	16557.9	3.20258
$300$	3599.40	0.692705
$301$	4066.17	0.778638
$302$	9006.59	1.71613
$303$	−1256.84	−0.238296
$304$	−13949.3	−2.63173
$305$	821.408	0.154209
$306$	−1150.28	−0.214893
$307$	−1347.91	−0.250583	−0.125292	−	0.992120i	$-0.539987\pi$
$307$	−1347.91	−0.250583	−0.125292	+	0.992120i	$0.539987\pi$
$308$	−2614.70	−0.483723
$309$	4177.32	0.769061
$310$	−15867.3	−2.90711
$311$	−5958.82	−1.08648	−0.543238	−	0.839579i	$-0.682802\pi$
$311$	−5958.82	−1.08648	−0.543238	+	0.839579i	$0.682802\pi$
$312$	−17130.0	−3.10832
$313$	−4142.67	−0.748107	−0.374053	−	0.927407i	$-0.622032\pi$
$313$	−4142.67	−0.748107	−0.374053	+	0.927407i	$0.622032\pi$
$314$	10786.7	1.93864
$315$	−1352.38	−0.241898
$316$	13978.1	2.48838
$317$	−4311.78	−0.763955	−0.381978	−	0.924172i	$-0.624757\pi$
$317$	−4311.78	−0.763955	−0.381978	+	0.924172i	$0.624757\pi$
$318$	−3663.34	−0.646007
$319$	2905.54	0.509966
$320$	−20927.1	−3.65581
$321$	300.123	0.0521845
$322$	−12611.6	−2.18267
$323$	−1501.65	−0.258681
$324$	1725.40	0.295850
$325$	4466.91	0.762399
$326$	10159.8	1.72606
$327$	−3276.60	−0.554117
$328$	17570.3	2.95780
$329$	−5158.46	−0.864423
$330$	−2405.39	−0.401250
$331$	−10277.2	−1.70661	−0.853304	−	0.521414i	$-0.825405\pi$
$331$	−10277.2	−1.70661	−0.853304	+	0.521414i	$0.825405\pi$
$332$	11185.4	1.84904
$333$	−892.694	−0.146905
$334$	10888.2	1.78375
$335$	−9631.32	−1.57079
$336$	7342.58	1.19217
$337$	−1806.42	−0.291994	−0.145997	−	0.989285i	$-0.546639\pi$
$337$	−1806.42	−0.291994	−0.145997	+	0.989285i	$0.546639\pi$
$338$	−22152.1	−3.56484
$339$	−2704.92	−0.433365
$340$	−6772.56	−1.08028
$341$	2394.56	0.380271
$342$	3098.38	0.489886
$343$	−6265.52	−0.986316
$344$	−26235.8	−4.11203
$345$	−8434.40	−1.31621
$346$	−5618.93	−0.873051
$347$	−617.617	−0.0955488	−0.0477744	−	0.998858i	$-0.515213\pi$
$347$	−617.617	−0.0955488	−0.0477744	+	0.998858i	$0.515213\pi$
$348$	−16879.5	−2.60011
$349$	−3720.82	−0.570690	−0.285345	−	0.958425i	$-0.592108\pi$
$349$	−3720.82	−0.570690	−0.285345	+	0.958425i	$0.592108\pi$
$350$	−3402.30	−0.519602
$351$	2141.25	0.325616
$352$	6723.80	1.01812
$353$	−1297.37	−0.195616	−0.0978078	−	0.995205i	$-0.531183\pi$
$353$	−1297.37	−0.195616	−0.0978078	+	0.995205i	$0.531183\pi$
$354$	−6237.63	−0.936515
$355$	5572.86	0.833174
$356$	−25405.5	−3.78227
$357$	790.435	0.117183
$358$	1902.34	0.280843
$359$	−9038.30	−1.32876	−0.664378	−	0.747397i	$-0.731303\pi$
$359$	−9038.30	−1.32876	−0.664378	+	0.747397i	$0.731303\pi$
$360$	8725.81	1.27747
$361$	−2814.19	−0.410291
$362$	13467.6	1.95537
$363$	363.000	0.0524864
$364$	18850.9	2.71444
$365$	6980.19	1.00099
$366$	990.590	0.141473
$367$	−10926.2	−1.55406	−0.777031	−	0.629463i	$-0.783275\pi$
$367$	−10926.2	−1.55406	−0.777031	+	0.629463i	$0.783275\pi$
$368$	45793.7	6.48685
$369$	−2196.28	−0.309848
$370$	−7229.90	−1.01585
$371$	2517.32	0.352272
$372$	−13911.0	−1.93885
$373$	−949.537	−0.131810	−0.0659051	−	0.997826i	$-0.520993\pi$
$373$	−949.537	−0.131810	−0.0659051	+	0.997826i	$0.520993\pi$
$374$	1405.90	0.194378
$375$	2774.26	0.382032
$376$	33283.5	4.56507
$377$	−20947.8	−2.86171
$378$	−1630.92	−0.221919
$379$	12025.5	1.62983	0.814917	−	0.579578i	$-0.196783\pi$
$379$	12025.5	1.62983	0.814917	+	0.579578i	$0.196783\pi$
$380$	18242.4	2.46268
$381$	3082.51	0.414493
$382$	−17487.1	−2.34219
$383$	−7507.64	−1.00163	−0.500813	−	0.865556i	$-0.666966\pi$
$383$	−7507.64	−1.00163	−0.500813	+	0.865556i	$0.666966\pi$
$384$	−10567.2	−1.40431
$385$	1652.90	0.218805
$386$	−4038.35	−0.532505
$387$	3279.46	0.430761
$388$	−4414.43	−0.577600
$389$	5300.46	0.690859	0.345429	−	0.938445i	$-0.387733\pi$
$389$	5300.46	0.690859	0.345429	+	0.938445i	$0.387733\pi$
$390$	17341.9	2.25164
$391$	4929.72	0.637614
$392$	15730.4	2.02680
$393$	2397.41	0.307718
$394$	−19590.3	−2.50494
$395$	−8836.35	−1.12558
$396$	−2108.82	−0.267607
$397$	−12377.4	−1.56475	−0.782373	−	0.622810i	$-0.785991\pi$
$397$	−12377.4	−1.56475	−0.782373	+	0.622810i	$0.785991\pi$
$398$	12543.4	1.57976
$399$	−2129.10	−0.267139
$400$	12354.0	1.54425
$401$	1106.16	0.137753	0.0688763	−	0.997625i	$-0.478059\pi$
$401$	1106.16	0.137753	0.0688763	+	0.997625i	$0.478059\pi$
$402$	−11615.0	−1.44106
$403$	−17263.7	−2.13392
$404$	−8924.08	−1.09898
$405$	−1090.72	−0.133823
$406$	15955.2	1.95036
$407$	1091.07	0.132880
$408$	−5100.05	−0.618848
$409$	2953.66	0.357088	0.178544	−	0.983932i	$-0.442861\pi$
$409$	2953.66	0.357088	0.178544	+	0.983932i	$0.442861\pi$
$410$	−17787.6	−2.14261
$411$	−2005.78	−0.240725
$412$	29660.7	3.54679
$413$	4286.28	0.510688
$414$	−10171.6	−1.20750
$415$	−7070.96	−0.836385
$416$	−48475.8	−5.71327
$417$	−5337.98	−0.626863
$418$	−3786.91	−0.443119
$419$	−8177.10	−0.953407	−0.476703	−	0.879064i	$-0.658168\pi$
$419$	−8177.10	−0.953407	−0.476703	+	0.879064i	$0.658168\pi$
$420$	−9602.41	−1.11559
$421$	−4662.35	−0.539737	−0.269868	−	0.962897i	$-0.586980\pi$
$421$	−4662.35	−0.539737	−0.269868	+	0.962897i	$0.586980\pi$
$422$	−17344.9	−2.00079
$423$	−4160.42	−0.478219
$424$	−16242.3	−1.86037
$425$	1329.91	0.151789
$426$	6720.67	0.764361
$427$	−680.699	−0.0771460
$428$	2130.99	0.240667
$429$	−2617.08	−0.294531
$430$	26560.2	2.97872
$431$	−13781.1	−1.54017	−0.770084	−	0.637942i	$-0.779786\pi$
$431$	−13781.1	−1.54017	−0.770084	+	0.637942i	$0.779786\pi$
$432$	5921.96	0.659538
$433$	15830.7	1.75698	0.878491	−	0.477759i	$-0.158551\pi$
$433$	15830.7	1.75698	0.878491	+	0.477759i	$0.158551\pi$
$434$	13149.2	1.45434
$435$	10670.5	1.17612
$436$	−23265.2	−2.55550
$437$	−13278.6	−1.45355
$438$	8417.87	0.918314
$439$	−14739.1	−1.60241	−0.801206	−	0.598388i	$-0.795808\pi$
$439$	−14739.1	−1.60241	−0.801206	+	0.598388i	$0.795808\pi$
$440$	−10664.9	−1.15552
$441$	−1966.29	−0.212319
$442$	−10136.0	−1.09077
$443$	313.691	0.0336432	0.0168216	−	0.999859i	$-0.494645\pi$
$443$	313.691	0.0336432	0.0168216	+	0.999859i	$0.494645\pi$
$444$	−6338.49	−0.677503
$445$	16060.3	1.71085
$446$	−497.309	−0.0527988
$447$	4325.33	0.457675
$448$	17342.2	1.82889
$449$	−9226.49	−0.969766	−0.484883	−	0.874579i	$-0.661138\pi$
$449$	−9226.49	−0.969766	−0.484883	+	0.874579i	$0.661138\pi$
$450$	−2744.04	−0.287456
$451$	2684.35	0.280268
$452$	−19206.0	−1.99861
$453$	−4991.59	−0.517716
$454$	−27478.0	−2.84054
$455$	−11916.7	−1.22784
$456$	13737.4	1.41077
$457$	12109.4	1.23951	0.619755	−	0.784796i	$-0.287232\pi$
$457$	12109.4	1.23951	0.619755	+	0.784796i	$0.287232\pi$
$458$	−13242.5	−1.35105
$459$	637.504	0.0648282
$460$	−59887.6	−6.07016
$461$	−12000.4	−1.21239	−0.606196	−	0.795316i	$-0.707305\pi$
$461$	−12000.4	−1.21239	−0.606196	+	0.795316i	$0.707305\pi$
$462$	1993.34	0.200733
$463$	9370.39	0.940559	0.470280	−	0.882517i	$-0.344153\pi$
$463$	9370.39	0.940559	0.470280	+	0.882517i	$0.344153\pi$
$464$	−57934.4	−5.79642
$465$	8793.93	0.877008
$466$	14259.6	1.41752
$467$	3281.84	0.325194	0.162597	−	0.986693i	$-0.448013\pi$
$467$	3281.84	0.325194	0.162597	+	0.986693i	$0.448013\pi$
$468$	15203.7	1.50169
$469$	7981.45	0.785819
$470$	−33695.1	−3.30689
$471$	−5978.18	−0.584841
$472$	−27656.0	−2.69697
$473$	−4008.23	−0.389638
$474$	−10656.3	−1.03262
$475$	−3582.23	−0.346030
$476$	5612.40	0.540429
$477$	2030.28	0.194885
$478$	−32569.8	−3.11654
$479$	14145.2	1.34929	0.674646	−	0.738142i	$-0.264296\pi$
$479$	14145.2	1.34929	0.674646	+	0.738142i	$0.264296\pi$
$480$	24692.9	2.34807
$481$	−7866.16	−0.745667
$482$	−7003.60	−0.661837
$483$	6989.56	0.658460
$484$	2577.45	0.242059
$485$	2790.62	0.261269
$486$	−1315.37	−0.122771
$487$	−4565.67	−0.424826	−0.212413	−	0.977180i	$-0.568132\pi$
$487$	−4565.67	−0.424826	−0.212413	+	0.977180i	$0.568132\pi$
$488$	4392.01	0.407412
$489$	−5630.69	−0.520713
$490$	−15924.9	−1.46819
$491$	21051.1	1.93487	0.967435	−	0.253120i	$-0.0814568\pi$
$491$	21051.1	1.93487	0.967435	+	0.253120i	$0.0814568\pi$
$492$	−15594.5	−1.42897
$493$	−6236.69	−0.569749
$494$	27302.0	2.48659
$495$	1333.11	0.121048
$496$	−47745.7	−4.32227
$497$	−4618.22	−0.416811
$498$	−8527.33	−0.767307
$499$	−12715.5	−1.14073	−0.570365	−	0.821392i	$-0.693198\pi$
$499$	−12715.5	−1.14073	−0.570365	+	0.821392i	$0.693198\pi$
$500$	19698.3	1.76187
$501$	−6034.39	−0.538117
$502$	7818.68	0.695149
$503$	4413.34	0.391215	0.195607	−	0.980682i	$-0.437332\pi$
$503$	4413.34	0.391215	0.195607	+	0.980682i	$0.437332\pi$
$504$	−7231.06	−0.639081
$505$	5641.42	0.497109
$506$	12431.9	1.09223
$507$	12277.0	1.07543
$508$	21887.1	1.91158
$509$	6391.18	0.556550	0.278275	−	0.960501i	$-0.410237\pi$
$509$	6391.18	0.556550	0.278275	+	0.960501i	$0.410237\pi$
$510$	5163.12	0.448288
$511$	−5784.47	−0.500763
$512$	−7732.04	−0.667405
$513$	−1717.17	−0.147787
$514$	1270.97	0.109067
$515$	−18750.2	−1.60434
$516$	23285.5	1.98660
$517$	5084.96	0.432565
$518$	5991.40	0.508199
$519$	3114.10	0.263379
$520$	76889.3	6.48427
$521$	11776.9	0.990321	0.495161	−	0.868801i	$-0.335109\pi$
$521$	11776.9	0.990321	0.495161	+	0.868801i	$0.335109\pi$
$522$	12868.3	1.07898
$523$	4447.42	0.371840	0.185920	−	0.982565i	$-0.440473\pi$
$523$	4447.42	0.371840	0.185920	+	0.982565i	$0.440473\pi$
$524$	17022.6	1.41915
$525$	1885.61	0.156752
$526$	−4542.30	−0.376528
$527$	−5139.86	−0.424850
$528$	−7237.95	−0.596575
$529$	31425.0	2.58281
$530$	16443.2	1.34763
$531$	3456.99	0.282525
$532$	−15117.5	−1.23200
$533$	−19353.0	−1.57274
$534$	19368.1	1.56955
$535$	−1347.12	−0.108862
$536$	−51498.0	−4.14995
$537$	−1054.31	−0.0847239
$538$	19477.5	1.56084
$539$	2403.24	0.192050
$540$	−7744.57	−0.617173
$541$	−14698.5	−1.16809	−0.584046	−	0.811721i	$-0.698531\pi$
$541$	−14698.5	−1.16809	−0.584046	+	0.811721i	$0.698531\pi$
$542$	−15848.7	−1.25602
$543$	−7463.96	−0.589888
$544$	−14432.5	−1.13748
$545$	14707.2	1.15594
$546$	−14371.2	−1.12643
$547$	−12504.2	−0.977406	−0.488703	−	0.872450i	$-0.662530\pi$
$547$	−12504.2	−0.977406	−0.488703	+	0.872450i	$0.662530\pi$
$548$	−14241.9	−1.11019
$549$	−549.000	−0.0426790
$550$	3353.82	0.260014
$551$	16799.0	1.29884
$552$	−45098.1	−3.47736
$553$	7322.66	0.563094
$554$	26705.2	2.04801
$555$	4006.92	0.306458
$556$	−37901.8	−2.89100
$557$	22646.4	1.72273	0.861364	−	0.507988i	$-0.169611\pi$
$557$	22646.4	1.72273	0.861364	+	0.507988i	$0.169611\pi$
$558$	10605.2	0.804574
$559$	28897.7	2.18648
$560$	−32957.7	−2.48699
$561$	−779.172	−0.0586393
$562$	36770.1	2.75988
$563$	3321.94	0.248674	0.124337	−	0.992240i	$-0.460320\pi$
$563$	3321.94	0.248674	0.124337	+	0.992240i	$0.460320\pi$
$564$	−29540.7	−2.20547
$565$	12141.2	0.904043
$566$	−9755.82	−0.724501
$567$	903.879	0.0669477
$568$	29797.7	2.20120
$569$	−6614.55	−0.487340	−0.243670	−	0.969858i	$-0.578351\pi$
$569$	−6614.55	−0.487340	−0.243670	+	0.969858i	$0.578351\pi$
$570$	−13907.3	−1.02195
$571$	−15390.5	−1.12797	−0.563986	−	0.825784i	$-0.690733\pi$
$571$	−15390.5	−1.12797	−0.563986	+	0.825784i	$0.690733\pi$
$572$	−18582.3	−1.35833
$573$	9691.61	0.706584
$574$	14740.6	1.07188
$575$	11760.0	0.852916
$576$	13986.9	1.01179
$577$	−21722.1	−1.56725	−0.783625	−	0.621234i	$-0.786632\pi$
$577$	−21722.1	−1.56725	−0.783625	+	0.621234i	$0.786632\pi$
$578$	23576.6	1.69664
$579$	2238.12	0.160644
$580$	75764.9	5.42408
$581$	5859.69	0.418418
$582$	3365.38	0.239690
$583$	−2481.46	−0.176280
$584$	37322.6	2.64456
$585$	−9611.13	−0.679267
$586$	−26926.5	−1.89816
$587$	−21471.3	−1.50973	−0.754867	−	0.655878i	$-0.772298\pi$
$587$	−21471.3	−1.50973	−0.754867	+	0.655878i	$0.772298\pi$
$588$	−13961.5	−0.979185
$589$	13844.6	0.968520
$590$	27998.0	1.95366
$591$	10857.3	0.755682
$592$	−21755.1	−1.51036
$593$	−28429.8	−1.96875	−0.984376	−	0.176078i	$-0.943659\pi$
$593$	−28429.8	−1.96875	−0.984376	+	0.176078i	$0.943659\pi$
$594$	1607.68	0.111050
$595$	−3547.92	−0.244455
$596$	30711.6	2.11073
$597$	−6951.74	−0.476576
$598$	−89629.1	−6.12911
$599$	14138.6	0.964419	0.482210	−	0.876056i	$-0.339834\pi$
$599$	14138.6	0.964419	0.482210	+	0.876056i	$0.339834\pi$
$600$	−12166.3	−0.827814
$601$	3952.13	0.268237	0.134119	−	0.990965i	$-0.457180\pi$
$601$	3952.13	0.268237	0.134119	+	0.990965i	$0.457180\pi$
$602$	−22010.4	−1.49016
$603$	6437.23	0.434733
$604$	−35442.3	−2.38763
$605$	−1629.35	−0.109492
$606$	6803.36	0.456052
$607$	12960.5	0.866640	0.433320	−	0.901240i	$-0.357342\pi$
$607$	12960.5	0.866640	0.433320	+	0.901240i	$0.357342\pi$
$608$	38875.1	2.59308
$609$	−8842.63	−0.588377
$610$	−4446.33	−0.295126
$611$	−36660.4	−2.42737
$612$	4526.54	0.298978
$613$	13948.8	0.919064	0.459532	−	0.888161i	$-0.348017\pi$
$613$	13948.8	0.919064	0.459532	+	0.888161i	$0.348017\pi$
$614$	7296.30	0.479568
$615$	9858.18	0.646374
$616$	8837.96	0.578071
$617$	−26595.0	−1.73529	−0.867644	−	0.497186i	$-0.834367\pi$
$617$	−26595.0	−1.73529	−0.867644	+	0.497186i	$0.834367\pi$
$618$	−22612.1	−1.47183
$619$	−27484.0	−1.78461	−0.892305	−	0.451432i	$-0.850913\pi$
$619$	−27484.0	−1.78461	−0.892305	+	0.451432i	$0.850913\pi$
$620$	62440.4	4.04463
$621$	5637.25	0.364275
$622$	32255.5	2.07930
$623$	−13309.1	−0.855888
$624$	52182.6	3.34772
$625$	−19493.1	−1.24756
$626$	22424.5	1.43173
$627$	2098.76	0.133679
$628$	−42447.5	−2.69720
$629$	−2341.96	−0.148458
$630$	7320.49	0.462945
$631$	5764.41	0.363673	0.181836	−	0.983329i	$-0.441796\pi$
$631$	5764.41	0.363673	0.181836	+	0.983329i	$0.441796\pi$
$632$	−47247.3	−2.97373
$633$	9612.79	0.603593
$634$	23339.9	1.46206
$635$	−13836.1	−0.864673
$636$	14415.8	0.898781
$637$	−17326.4	−1.07770
$638$	−15727.9	−0.975976
$639$	−3724.70	−0.230590
$640$	47431.8	2.92954
$641$	−18671.7	−1.15052	−0.575262	−	0.817969i	$-0.695100\pi$
$641$	−18671.7	−1.15052	−0.575262	+	0.817969i	$0.695100\pi$
$642$	−1624.58	−0.0998710
$643$	3196.43	0.196042	0.0980210	−	0.995184i	$-0.468749\pi$
$643$	3196.43	0.196042	0.0980210	+	0.995184i	$0.468749\pi$
$644$	49628.7	3.03672
$645$	−14720.1	−0.898610
$646$	8128.52	0.495065
$647$	−25618.5	−1.55667	−0.778336	−	0.627847i	$-0.783936\pi$
$647$	−25618.5	−1.55667	−0.778336	+	0.627847i	$0.783936\pi$
$648$	−5832.02	−0.353555
$649$	−4225.21	−0.255553
$650$	−24179.7	−1.45908
$651$	−7287.50	−0.438740
$652$	−39980.2	−2.40145
$653$	−28804.8	−1.72622	−0.863108	−	0.505019i	$-0.831485\pi$
$653$	−28804.8	−1.72622	−0.863108	+	0.505019i	$0.831485\pi$
$654$	17736.4	1.06047
$655$	−10760.9	−0.641931
$656$	−53523.9	−3.18561
$657$	−4665.31	−0.277034
$658$	27923.1	1.65434
$659$	23244.4	1.37401	0.687006	−	0.726652i	$-0.258925\pi$
$659$	23244.4	1.37401	0.687006	+	0.726652i	$0.258925\pi$
$660$	9465.59	0.558254
$661$	−17570.4	−1.03390	−0.516950	−	0.856015i	$-0.672933\pi$
$661$	−17570.4	−1.03390	−0.516950	+	0.856015i	$0.672933\pi$
$662$	55631.2	3.26612
$663$	5617.50	0.329058
$664$	−37807.9	−2.20969
$665$	9556.61	0.557278
$666$	4832.20	0.281147
$667$	−55149.1	−3.20147
$668$	−42846.6	−2.48171
$669$	275.616	0.0159282
$670$	52134.9	3.00619
$671$	671.000	0.0386046
$672$	−20463.0	−1.17467
$673$	33244.1	1.90411	0.952056	−	0.305923i	$-0.0989649\pi$
$673$	33244.1	1.90411	0.952056	+	0.305923i	$0.0989649\pi$
$674$	9778.27	0.558820
$675$	1520.79	0.0867187
$676$	87171.9	4.95971
$677$	−23659.0	−1.34312	−0.671559	−	0.740951i	$-0.734375\pi$
$677$	−23659.0	−1.34312	−0.671559	+	0.740951i	$0.734375\pi$
$678$	14641.9	0.829377
$679$	−2312.58	−0.130705
$680$	22891.9	1.29098
$681$	15228.7	0.856924
$682$	−12961.9	−0.727765
$683$	22548.7	1.26325	0.631626	−	0.775274i	$-0.282388\pi$
$683$	22548.7	1.26325	0.631626	+	0.775274i	$0.282388\pi$
$684$	−12192.6	−0.681572
$685$	9003.09	0.502176
$686$	33915.6	1.88762
$687$	7339.21	0.407581
$688$	79921.2	4.42873
$689$	17890.3	0.989208
$690$	45655.9	2.51897
$691$	−3454.63	−0.190188	−0.0950942	−	0.995468i	$-0.530315\pi$
$691$	−3454.63	−0.190188	−0.0950942	+	0.995468i	$0.530315\pi$
$692$	22111.3	1.21466
$693$	−1104.74	−0.0605565
$694$	3343.20	0.182862
$695$	23959.9	1.30770
$696$	57054.5	3.10725
$697$	−5761.89	−0.313124
$698$	20141.0	1.09219
$699$	−7902.89	−0.427632
$700$	13388.6	0.722915
$701$	−18295.7	−0.985759	−0.492880	−	0.870097i	$-0.664056\pi$
$701$	−18295.7	−0.985759	−0.492880	+	0.870097i	$0.664056\pi$
$702$	−11590.7	−0.623166
$703$	6308.25	0.338436
$704$	−17095.1	−0.915194
$705$	18674.4	0.997612
$706$	7022.77	0.374370
$707$	−4675.03	−0.248688
$708$	24546.0	1.30296
$709$	−2527.64	−0.133889	−0.0669446	−	0.997757i	$-0.521325\pi$
$709$	−2527.64	−0.133889	−0.0669446	+	0.997757i	$0.521325\pi$
$710$	−30166.2	−1.59453
$711$	5905.90	0.311517
$712$	85873.1	4.51999
$713$	−45450.2	−2.38727
$714$	−4278.67	−0.224265
$715$	11746.9	0.614421
$716$	−7486.01	−0.390734
$717$	18050.7	0.940187
$718$	48924.9	2.54298
$719$	−3385.11	−0.175582	−0.0877909	−	0.996139i	$-0.527981\pi$
$719$	−3385.11	−0.175582	−0.0877909	+	0.996139i	$0.527981\pi$
$720$	−26581.1	−1.37586
$721$	15538.3	0.802601
$722$	15233.4	0.785217
$723$	3881.50	0.199661
$724$	−52997.1	−2.72047
$725$	−14877.8	−0.762135
$726$	−1964.94	−0.100449
$727$	4431.58	0.226077	0.113039	−	0.993591i	$-0.463942\pi$
$727$	4431.58	0.226077	0.113039	+	0.993591i	$0.463942\pi$
$728$	−63718.0	−3.24388
$729$	729.000	0.0370370
$730$	−37784.2	−1.91569
$731$	8603.58	0.435315
$732$	−3898.12	−0.196829
$733$	−34221.3	−1.72441	−0.862205	−	0.506560i	$-0.830917\pi$
$733$	−34221.3	−1.72441	−0.862205	+	0.506560i	$0.830917\pi$
$734$	59143.9	2.97417
$735$	8825.83	0.442919
$736$	−127622.	−6.39159
$737$	−7867.72	−0.393231
$738$	11888.6	0.592989
$739$	9710.62	0.483371	0.241685	−	0.970355i	$-0.422300\pi$
$739$	9710.62	0.483371	0.241685	+	0.970355i	$0.422300\pi$
$740$	28450.7	1.41334
$741$	−15131.2	−0.750146
$742$	−13626.4	−0.674180
$743$	28867.0	1.42534	0.712671	−	0.701499i	$-0.247485\pi$
$743$	28867.0	1.42534	0.712671	+	0.701499i	$0.247485\pi$
$744$	47020.5	2.31701
$745$	−19414.5	−0.954756
$746$	5139.90	0.252259
$747$	4725.98	0.231479
$748$	−5532.43	−0.270436
$749$	1116.36	0.0544603
$750$	−15017.2	−0.731135
$751$	−9400.69	−0.456772	−0.228386	−	0.973571i	$-0.573345\pi$
$751$	−9400.69	−0.456772	−0.228386	+	0.973571i	$0.573345\pi$
$752$	−101390.	−4.91666
$753$	−4333.23	−0.209710
$754$	113391.	5.47675
$755$	22405.1	1.08001
$756$	6417.91	0.308753
$757$	−89.7414	−0.00430873	−0.00215436	−	0.999998i	$-0.500686\pi$
$757$	−89.7414	−0.00430873	−0.00215436	+	0.999998i	$0.500686\pi$
$758$	−65094.6	−3.11918
$759$	−6889.97	−0.329499
$760$	−61661.3	−2.94301
$761$	−11980.6	−0.570692	−0.285346	−	0.958425i	$-0.592108\pi$
$761$	−11980.6	−0.570692	−0.285346	+	0.958425i	$0.592108\pi$
$762$	−16685.8	−0.793258
$763$	−12187.9	−0.578283
$764$	68814.3	3.25866
$765$	−2861.48	−0.135238
$766$	40639.3	1.91692
$767$	30462.0	1.43405
$768$	19902.6	0.935122
$769$	11646.9	0.546159	0.273079	−	0.961991i	$-0.411958\pi$
$769$	11646.9	0.546159	0.273079	+	0.961991i	$0.411958\pi$
$770$	−8947.26	−0.418749
$771$	−704.393	−0.0329029
$772$	15891.5	0.740866
$773$	−14728.1	−0.685295	−0.342647	−	0.939464i	$-0.611324\pi$
$773$	−14728.1	−0.685295	−0.342647	+	0.939464i	$0.611324\pi$
$774$	−17751.9	−0.824392
$775$	−12261.3	−0.568308
$776$	14921.2	0.690259
$777$	−3320.52	−0.153312
$778$	−28691.7	−1.32217
$779$	15520.1	0.713821
$780$	−68242.9	−3.13268
$781$	4552.41	0.208576
$782$	−26684.9	−1.22027
$783$	−7131.79	−0.325504
$784$	−47918.9	−2.18289
$785$	26833.5	1.22004
$786$	−12977.3	−0.588913
$787$	−34352.2	−1.55594	−0.777969	−	0.628303i	$-0.783750\pi$
$787$	−34352.2	−1.55594	−0.777969	+	0.628303i	$0.783750\pi$
$788$	77091.0	3.48509
$789$	2517.41	0.113590
$790$	47831.7	2.15415
$791$	−10061.4	−0.452265
$792$	7128.02	0.319802
$793$	−4837.63	−0.216632
$794$	66999.6	2.99462
$795$	−9113.06	−0.406550
$796$	−49360.1	−2.19789
$797$	−38209.8	−1.69819	−0.849097	−	0.528236i	$-0.822854\pi$
$797$	−38209.8	−1.69819	−0.849097	+	0.528236i	$0.822854\pi$
$798$	11524.9	0.511251
$799$	−10914.8	−0.483275
$800$	−34429.2	−1.52157
$801$	−10734.1	−0.473497
$802$	−5987.69	−0.263632
$803$	5702.05	0.250586
$804$	45706.9	2.00492
$805$	−31373.2	−1.37361
$806$	93449.7	4.08390
$807$	−10794.7	−0.470870
$808$	30164.3	1.31334
$809$	−33414.9	−1.45217	−0.726085	−	0.687605i	$-0.758662\pi$
$809$	−33414.9	−1.45217	−0.726085	+	0.687605i	$0.758662\pi$
$810$	5904.15	0.256112
$811$	−17538.8	−0.759395	−0.379697	−	0.925111i	$-0.623972\pi$
$811$	−17538.8	−0.759395	−0.379697	+	0.925111i	$0.623972\pi$
$812$	−62786.2	−2.71350
$813$	8783.61	0.378911
$814$	−5906.03	−0.254307
$815$	25273.8	1.08626
$816$	15536.1	0.666511
$817$	−23174.4	−0.992376
$818$	−15988.3	−0.683397
$819$	7964.72	0.339817
$820$	69997.0	2.98098
$821$	28492.9	1.21122	0.605608	−	0.795763i	$-0.292930\pi$
$821$	28492.9	1.21122	0.605608	+	0.795763i	$0.292930\pi$
$822$	10857.4	0.460700
$823$	−18144.7	−0.768510	−0.384255	−	0.923227i	$-0.625542\pi$
$823$	−18144.7	−0.768510	−0.384255	+	0.923227i	$0.625542\pi$
$824$	−100256.	−4.23858
$825$	−1858.74	−0.0784400
$826$	−23201.9	−0.977358
$827$	20105.7	0.845398	0.422699	−	0.906270i	$-0.361083\pi$
$827$	20105.7	0.845398	0.422699	+	0.906270i	$0.361083\pi$
$828$	40026.7	1.67998
$829$	−24558.8	−1.02890	−0.514452	−	0.857519i	$-0.672005\pi$
$829$	−24558.8	−1.02890	−0.514452	+	0.857519i	$0.672005\pi$
$830$	38275.5	1.60068
$831$	−14800.4	−0.617835
$832$	123249.	5.13567
$833$	−5158.51	−0.214564
$834$	28894.8	1.19969
$835$	27085.8	1.12257
$836$	14902.1	0.616505
$837$	−5877.54	−0.242721
$838$	44263.1	1.82463
$839$	7061.84	0.290586	0.145293	−	0.989389i	$-0.453587\pi$
$839$	7061.84	0.290586	0.145293	+	0.989389i	$0.453587\pi$
$840$	32457.1	1.33319
$841$	45381.1	1.86072
$842$	25237.6	1.03295
$843$	−20378.5	−0.832590
$844$	68254.7	2.78368
$845$	−55106.4	−2.24345
$846$	22520.6	0.915218
$847$	1350.24	0.0547754
$848$	49478.4	2.00365
$849$	5406.83	0.218565
$850$	−7198.91	−0.290495
$851$	−20709.2	−0.834198
$852$	−26446.9	−1.06344
$853$	−18003.6	−0.722662	−0.361331	−	0.932438i	$-0.617678\pi$
$853$	−18003.6	−0.722662	−0.361331	+	0.932438i	$0.617678\pi$
$854$	3684.67	0.147642
$855$	7707.63	0.308299
$856$	−7202.97	−0.287608
$857$	43900.2	1.74983	0.874914	−	0.484279i	$-0.160918\pi$
$857$	43900.2	1.74983	0.874914	+	0.484279i	$0.160918\pi$
$858$	14166.4	0.563675
$859$	23416.0	0.930085	0.465043	−	0.885288i	$-0.346039\pi$
$859$	23416.0	0.930085	0.465043	+	0.885288i	$0.346039\pi$
$860$	−104519.	−4.14425
$861$	−8169.45	−0.323361
$862$	74597.9	2.94758
$863$	37462.4	1.47768	0.738839	−	0.673882i	$-0.235374\pi$
$863$	37462.4	1.47768	0.738839	+	0.673882i	$0.235374\pi$
$864$	−16503.9	−0.649853
$865$	−13977.8	−0.549435
$866$	−85692.3	−3.36252
$867$	−13066.5	−0.511837
$868$	−51744.2	−2.02340
$869$	−7218.32	−0.281778
$870$	−57760.1	−2.25086
$871$	56723.0	2.20664
$872$	78638.6	3.05394
$873$	−1865.15	−0.0723089
$874$	71877.9	2.78182
$875$	10319.3	0.398693
$876$	−33125.6	−1.27764
$877$	25194.0	0.970057	0.485028	−	0.874498i	$-0.338809\pi$
$877$	25194.0	0.970057	0.485028	+	0.874498i	$0.338809\pi$
$878$	79783.7	3.06671
$879$	14923.1	0.572631
$880$	32488.1	1.24451
$881$	−18526.2	−0.708472	−0.354236	−	0.935156i	$-0.615259\pi$
$881$	−18526.2	−0.708472	−0.354236	+	0.935156i	$0.615259\pi$
$882$	10643.6	0.406338
$883$	−2249.75	−0.0857418	−0.0428709	−	0.999081i	$-0.513650\pi$
$883$	−2249.75	−0.0857418	−0.0428709	+	0.999081i	$0.513650\pi$
$884$	39886.5	1.51757
$885$	−15516.9	−0.589374
$886$	−1698.03	−0.0643865
$887$	−27044.1	−1.02373	−0.511867	−	0.859065i	$-0.671046\pi$
$887$	−27044.1	−1.02373	−0.511867	+	0.859065i	$0.671046\pi$
$888$	21424.7	0.809647
$889$	11465.9	0.432569
$890$	−86935.2	−3.27424
$891$	−891.000	−0.0335013
$892$	1956.99	0.0734582
$893$	29399.8	1.10171
$894$	−23413.2	−0.875902
$895$	4732.33	0.176742
$896$	−39306.6	−1.46556
$897$	49673.8	1.84901
$898$	49943.5	1.85594
$899$	57499.9	2.13318
$900$	10798.2	0.399933
$901$	5326.39	0.196945
$902$	−14530.5	−0.536379
$903$	12198.5	0.449547
$904$	64918.2	2.38844
$905$	33502.5	1.23056
$906$	27019.8	0.990807
$907$	340.244	0.0124560	0.00622801	−	0.999981i	$-0.498018\pi$
$907$	340.244	0.0124560	0.00622801	+	0.999981i	$0.498018\pi$
$908$	108130.	3.95200
$909$	−3770.52	−0.137580
$910$	64506.0	2.34984
$911$	37278.1	1.35574	0.677870	−	0.735182i	$-0.262903\pi$
$911$	37278.1	1.35574	0.677870	+	0.735182i	$0.262903\pi$
$912$	−41847.8	−1.51943
$913$	−5776.19	−0.209380
$914$	−65549.1	−2.37218
$915$	2464.23	0.0890325
$916$	52111.4	1.87970
$917$	8917.57	0.321139
$918$	−3450.85	−0.124069
$919$	−26176.9	−0.939605	−0.469802	−	0.882772i	$-0.655675\pi$
$919$	−26176.9	−0.939605	−0.469802	+	0.882772i	$0.655675\pi$
$920$	202426.	7.25413
$921$	−4043.72	−0.144674
$922$	64958.6	2.32028
$923$	−32821.0	−1.17044
$924$	−7844.11	−0.279277
$925$	−5586.82	−0.198587
$926$	−50722.5	−1.80005
$927$	12532.0	0.444017
$928$	161457.	5.71130
$929$	−18330.3	−0.647359	−0.323680	−	0.946167i	$-0.604920\pi$
$929$	−18330.3	−0.647359	−0.323680	+	0.946167i	$0.604920\pi$
$930$	−47602.0	−1.67842
$931$	13894.9	0.489136
$932$	−56113.7	−1.97217
$933$	−17876.5	−0.627277
$934$	−17764.8	−0.622358
$935$	3497.37	0.122327
$936$	−51390.1	−1.79459
$937$	9461.39	0.329872	0.164936	−	0.986304i	$-0.447258\pi$
$937$	9461.39	0.329872	0.164936	+	0.986304i	$0.447258\pi$
$938$	−43204.1	−1.50391
$939$	−12428.0	−0.431920
$940$	132595.	4.60084
$941$	−9625.59	−0.333459	−0.166730	−	0.986003i	$-0.553321\pi$
$941$	−9625.59	−0.333459	−0.166730	+	0.986003i	$0.553321\pi$
$942$	32360.2	1.11927
$943$	−50950.6	−1.75947
$944$	84247.6	2.90469
$945$	−4057.13	−0.139660
$946$	21696.8	0.745691
$947$	−22482.1	−0.771457	−0.385729	−	0.922612i	$-0.626050\pi$
$947$	−22482.1	−0.771457	−0.385729	+	0.922612i	$0.626050\pi$
$948$	41934.3	1.43667
$949$	−41109.4	−1.40618
$950$	19390.8	0.662233
$951$	−12935.3	−0.441070
$952$	−18970.5	−0.645837
$953$	23080.0	0.784506	0.392253	−	0.919857i	$-0.371696\pi$
$953$	23080.0	0.784506	0.392253	+	0.919857i	$0.371696\pi$
$954$	−10990.0	−0.372972
$955$	−43501.5	−1.47401
$956$	128167.	4.33600
$957$	8716.63	0.294429
$958$	−76568.8	−2.58228
$959$	−7460.84	−0.251223
$960$	−62781.3	−2.11068
$961$	17596.6	0.590667
$962$	42580.0	1.42706
$963$	900.368	0.0301287
$964$	27560.2	0.920805
$965$	−10045.9	−0.335120
$966$	−37834.9	−1.26016
$967$	29915.7	0.994855	0.497427	−	0.867506i	$-0.334278\pi$
$967$	29915.7	0.994855	0.497427	+	0.867506i	$0.334278\pi$
$968$	−8712.03	−0.289272
$969$	−4504.95	−0.149350
$970$	−15105.8	−0.500017
$971$	−24035.1	−0.794359	−0.397179	−	0.917741i	$-0.630011\pi$
$971$	−24035.1	−0.794359	−0.397179	+	0.917741i	$0.630011\pi$
$972$	5176.19	0.170809
$973$	−19855.5	−0.654202
$974$	24714.2	0.813034
$975$	13400.7	0.440171
$976$	−13379.2	−0.438790
$977$	9642.07	0.315739	0.157870	−	0.987460i	$-0.449537\pi$
$977$	9642.07	0.315739	0.157870	+	0.987460i	$0.449537\pi$
$978$	30479.3	0.996544
$979$	13119.5	0.428294
$980$	62667.0	2.04268
$981$	−9829.79	−0.319920
$982$	−113951.	−3.70296
$983$	38457.7	1.24782	0.623911	−	0.781495i	$-0.285543\pi$
$983$	38457.7	1.24782	0.623911	+	0.781495i	$0.285543\pi$
$984$	52711.0	1.70769
$985$	−48733.6	−1.57643
$986$	33759.6	1.09039
$987$	−15475.4	−0.499075
$988$	−107438.	−3.45956
$989$	76078.8	2.44607
$990$	−7216.18	−0.231662
$991$	−24161.6	−0.774488	−0.387244	−	0.921977i	$-0.626573\pi$
$991$	−24161.6	−0.774488	−0.387244	+	0.921977i	$0.626573\pi$
$992$	133062.	4.25880
$993$	−30831.7	−0.985311
$994$	24998.7	0.797696
$995$	31203.4	0.994184
$996$	33556.3	1.06754
$997$	254.329	0.00807893	0.00403947	−	0.999992i	$-0.498714\pi$
$997$	254.329	0.00807893	0.00403947	+	0.999992i	$0.498714\pi$
$998$	68829.7	2.18313
$999$	−2678.08	−0.0848155

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2013.4.a.c.1.1	✓	37

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2013.4.a.c.1.1	✓	37	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)

\(f(q)\)	\(=\)	\(q-5.41306 q^{2} +3.00000 q^{3} +21.3012 q^{4} -13.4657 q^{5} -16.2392 q^{6} +11.1590 q^{7} -72.0002 q^{8} +9.00000 q^{9} +O(q^{10})\)	\(q-5.41306 q^{2} +3.00000 q^{3} +21.3012 q^{4} -13.4657 q^{5} -16.2392 q^{6} +11.1590 q^{7} -72.0002 q^{8} +9.00000 q^{9} +72.8907 q^{10} -11.0000 q^{11} +63.9036 q^{12} +79.3054 q^{13} -60.4043 q^{14} -40.3971 q^{15} +219.332 q^{16} +23.6113 q^{17} -48.7175 q^{18} -63.5988 q^{19} -286.836 q^{20} +33.4770 q^{21} +59.5437 q^{22} +208.787 q^{23} -216.001 q^{24} +56.3254 q^{25} -429.285 q^{26} +27.0000 q^{27} +237.700 q^{28} -264.140 q^{29} +218.672 q^{30} -217.687 q^{31} -611.255 q^{32} -33.0000 q^{33} -127.809 q^{34} -150.264 q^{35} +191.711 q^{36} -99.1882 q^{37} +344.264 q^{38} +237.916 q^{39} +969.535 q^{40} -244.032 q^{41} -181.213 q^{42} +364.385 q^{43} -234.313 q^{44} -121.191 q^{45} -1130.18 q^{46} -462.269 q^{47} +657.996 q^{48} -218.477 q^{49} -304.893 q^{50} +70.8338 q^{51} +1689.30 q^{52} +225.587 q^{53} -146.153 q^{54} +148.123 q^{55} -803.451 q^{56} -190.797 q^{57} +1429.81 q^{58} +384.110 q^{59} -860.508 q^{60} -61.0000 q^{61} +1178.35 q^{62} +100.431 q^{63} +1554.10 q^{64} -1067.90 q^{65} +178.631 q^{66} +715.248 q^{67} +502.949 q^{68} +626.361 q^{69} +813.388 q^{70} -413.856 q^{71} -648.002 q^{72} -518.368 q^{73} +536.912 q^{74} +168.976 q^{75} -1354.73 q^{76} -122.749 q^{77} -1287.85 q^{78} +656.211 q^{79} -2953.46 q^{80} +81.0000 q^{81} +1320.96 q^{82} +525.109 q^{83} +713.101 q^{84} -317.943 q^{85} -1972.44 q^{86} -792.421 q^{87} +792.003 q^{88} -1192.68 q^{89} +656.016 q^{90} +884.969 q^{91} +4447.42 q^{92} -653.060 q^{93} +2502.29 q^{94} +856.404 q^{95} -1833.76 q^{96} -207.239 q^{97} +1182.63 q^{98} -99.0000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 37 q - 8 q^{2} + 111 q^{3} + 130 q^{4} - 35 q^{5} - 24 q^{6} - 35 q^{7} - 117 q^{8} + 333 q^{9}+O(q^{10}) \) 37 * q - 8 * q^2 + 111 * q^3 + 130 * q^4 - 35 * q^5 - 24 * q^6 - 35 * q^7 - 117 * q^8 + 333 * q^9	\( 37 q - 8 q^{2} + 111 q^{3} + 130 q^{4} - 35 q^{5} - 24 q^{6} - 35 q^{7} - 117 q^{8} + 333 q^{9} - 41 q^{10} - 407 q^{11} + 390 q^{12} + 51 q^{13} - 228 q^{14} - 105 q^{15} + 462 q^{16} - 190 q^{17} - 72 q^{18} - 51 q^{19} - 720 q^{20} - 105 q^{21} + 88 q^{22} - 583 q^{23} - 351 q^{24} + 598 q^{25} - 1019 q^{26} + 999 q^{27} - 498 q^{28} - 566 q^{29} - 123 q^{30} - 696 q^{31} - 859 q^{32} - 1221 q^{33} - 348 q^{34} - 1102 q^{35} + 1170 q^{36} - 1022 q^{37} - 455 q^{38} + 153 q^{39} - 503 q^{40} - 790 q^{41} - 684 q^{42} - 87 q^{43} - 1430 q^{44} - 315 q^{45} - 303 q^{46} - 1603 q^{47} + 1386 q^{48} + 110 q^{49} - 1926 q^{50} - 570 q^{51} + 736 q^{52} - 2619 q^{53} - 216 q^{54} + 385 q^{55} - 4937 q^{56} - 153 q^{57} - 1099 q^{58} - 2471 q^{59} - 2160 q^{60} - 2257 q^{61} - 2909 q^{62} - 315 q^{63} - 265 q^{64} - 1970 q^{65} + 264 q^{66} - 3033 q^{67} - 1956 q^{68} - 1749 q^{69} + 2410 q^{70} - 3891 q^{71} - 1053 q^{72} + 391 q^{73} - 532 q^{74} + 1794 q^{75} + 1554 q^{76} + 385 q^{77} - 3057 q^{78} + 67 q^{79} - 5111 q^{80} + 2997 q^{81} - 4818 q^{82} - 5315 q^{83} - 1494 q^{84} - 2747 q^{85} - 5195 q^{86} - 1698 q^{87} + 1287 q^{88} - 8945 q^{89} - 369 q^{90} - 4432 q^{91} - 4701 q^{92} - 2088 q^{93} - 372 q^{94} - 3388 q^{95} - 2577 q^{96} - 3784 q^{97} - 4502 q^{98} - 3663 q^{99}+O(q^{100}) \) 37 * q - 8 * q^2 + 111 * q^3 + 130 * q^4 - 35 * q^5 - 24 * q^6 - 35 * q^7 - 117 * q^8 + 333 * q^9 - 41 * q^10 - 407 * q^11 + 390 * q^12 + 51 * q^13 - 228 * q^14 - 105 * q^15 + 462 * q^16 - 190 * q^17 - 72 * q^18 - 51 * q^19 - 720 * q^20 - 105 * q^21 + 88 * q^22 - 583 * q^23 - 351 * q^24 + 598 * q^25 - 1019 * q^26 + 999 * q^27 - 498 * q^28 - 566 * q^29 - 123 * q^30 - 696 * q^31 - 859 * q^32 - 1221 * q^33 - 348 * q^34 - 1102 * q^35 + 1170 * q^36 - 1022 * q^37 - 455 * q^38 + 153 * q^39 - 503 * q^40 - 790 * q^41 - 684 * q^42 - 87 * q^43 - 1430 * q^44 - 315 * q^45 - 303 * q^46 - 1603 * q^47 + 1386 * q^48 + 110 * q^49 - 1926 * q^50 - 570 * q^51 + 736 * q^52 - 2619 * q^53 - 216 * q^54 + 385 * q^55 - 4937 * q^56 - 153 * q^57 - 1099 * q^58 - 2471 * q^59 - 2160 * q^60 - 2257 * q^61 - 2909 * q^62 - 315 * q^63 - 265 * q^64 - 1970 * q^65 + 264 * q^66 - 3033 * q^67 - 1956 * q^68 - 1749 * q^69 + 2410 * q^70 - 3891 * q^71 - 1053 * q^72 + 391 * q^73 - 532 * q^74 + 1794 * q^75 + 1554 * q^76 + 385 * q^77 - 3057 * q^78 + 67 * q^79 - 5111 * q^80 + 2997 * q^81 - 4818 * q^82 - 5315 * q^83 - 1494 * q^84 - 2747 * q^85 - 5195 * q^86 - 1698 * q^87 + 1287 * q^88 - 8945 * q^89 - 369 * q^90 - 4432 * q^91 - 4701 * q^92 - 2088 * q^93 - 372 * q^94 - 3388 * q^95 - 2577 * q^96 - 3784 * q^97 - 4502 * q^98 - 3663 * q^99

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