LMFDB - Embedded newform 2013.4.a.c.1.20

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			1.20
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)

$f(q)$	$=$	$q-0.108103 q^{2} +3.00000 q^{3} -7.98831 q^{4} -6.73266 q^{5} -0.324309 q^{6} -18.3209 q^{7} +1.72838 q^{8} +9.00000 q^{9} +O(q^{10})$	\(q-0.108103 q^{2} +3.00000 q^{3} -7.98831 q^{4} -6.73266 q^{5} -0.324309 q^{6} -18.3209 q^{7} +1.72838 q^{8} +9.00000 q^{9} +0.727821 q^{10} -11.0000 q^{11} -23.9649 q^{12} -24.3098 q^{13} +1.98054 q^{14} -20.1980 q^{15} +63.7197 q^{16} -6.64445 q^{17} -0.972927 q^{18} +52.9949 q^{19} +53.7826 q^{20} -54.9627 q^{21} +1.18913 q^{22} +68.3010 q^{23} +5.18515 q^{24} -79.6713 q^{25} +2.62796 q^{26} +27.0000 q^{27} +146.353 q^{28} +264.845 q^{29} +2.18346 q^{30} +180.147 q^{31} -20.7154 q^{32} -33.0000 q^{33} +0.718285 q^{34} +123.348 q^{35} -71.8948 q^{36} +89.4287 q^{37} -5.72891 q^{38} -72.9293 q^{39} -11.6366 q^{40} +125.161 q^{41} +5.94163 q^{42} -46.8777 q^{43} +87.8715 q^{44} -60.5939 q^{45} -7.38354 q^{46} -271.317 q^{47} +191.159 q^{48} -7.34442 q^{49} +8.61270 q^{50} -19.9333 q^{51} +194.194 q^{52} +441.412 q^{53} -2.91878 q^{54} +74.0593 q^{55} -31.6656 q^{56} +158.985 q^{57} -28.6306 q^{58} -267.139 q^{59} +161.348 q^{60} -61.0000 q^{61} -19.4744 q^{62} -164.888 q^{63} -507.518 q^{64} +163.669 q^{65} +3.56740 q^{66} +837.902 q^{67} +53.0779 q^{68} +204.903 q^{69} -13.3343 q^{70} -730.419 q^{71} +15.5555 q^{72} -703.209 q^{73} -9.66751 q^{74} -239.014 q^{75} -423.340 q^{76} +201.530 q^{77} +7.88388 q^{78} -850.697 q^{79} -429.003 q^{80} +81.0000 q^{81} -13.5303 q^{82} +198.628 q^{83} +439.059 q^{84} +44.7348 q^{85} +5.06762 q^{86} +794.536 q^{87} -19.0122 q^{88} +543.465 q^{89} +6.55039 q^{90} +445.377 q^{91} -545.610 q^{92} +540.440 q^{93} +29.3302 q^{94} -356.797 q^{95} -62.1461 q^{96} -29.3234 q^{97} +0.793954 q^{98} -99.0000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−0.108103	−0.0382202	−0.0191101	−	0.999817i	$-0.506083\pi$
$2$	−0.108103	−0.0382202	−0.0191101	+	0.999817i	$0.506083\pi$
$3$	3.00000	0.577350
$3$	3.00000	0.577350
$4$	−7.98831	−0.998539
$5$	−6.73266	−0.602187	−0.301094	−	0.953595i	$-0.597352\pi$
$5$	−6.73266	−0.602187	−0.301094	+	0.953595i	$0.597352\pi$
$6$	−0.324309	−0.0220664
$7$	−18.3209	−0.989236	−0.494618	−	0.869111i	$-0.664692\pi$
$7$	−18.3209	−0.989236	−0.494618	+	0.869111i	$0.664692\pi$
$8$	1.72838	0.0763845
$9$	9.00000	0.333333
$10$	0.727821	0.0230157
$11$	−11.0000	−0.301511
$11$	−11.0000	−0.301511
$12$	−23.9649	−0.576507
$13$	−24.3098	−0.518640	−0.259320	−	0.965791i	$-0.583498\pi$
$13$	−24.3098	−0.518640	−0.259320	+	0.965791i	$0.583498\pi$
$14$	1.98054	0.0378088
$15$	−20.1980	−0.347673
$16$	63.7197	0.995620
$17$	−6.64445	−0.0947950	−0.0473975	−	0.998876i	$-0.515093\pi$
$17$	−6.64445	−0.0947950	−0.0473975	+	0.998876i	$0.515093\pi$
$18$	−0.972927	−0.0127401
$19$	52.9949	0.639887	0.319944	−	0.947437i	$-0.396336\pi$
$19$	52.9949	0.639887	0.319944	+	0.947437i	$0.396336\pi$
$20$	53.7826	0.601308
$21$	−54.9627	−0.571136
$22$	1.18913	0.0115238
$23$	68.3010	0.619206	0.309603	−	0.950866i	$-0.399804\pi$
$23$	68.3010	0.619206	0.309603	+	0.950866i	$0.399804\pi$
$24$	5.18515	0.0441006
$25$	−79.6713	−0.637370
$26$	2.62796	0.0198225
$27$	27.0000	0.192450
$28$	146.353	0.987791
$29$	264.845	1.69588	0.847941	−	0.530091i	$-0.177842\pi$
$29$	264.845	1.69588	0.847941	+	0.530091i	$0.177842\pi$
$30$	2.18346	0.0132881
$31$	180.147	1.04372	0.521860	−	0.853031i	$-0.325238\pi$
$31$	180.147	1.04372	0.521860	+	0.853031i	$0.325238\pi$
$32$	−20.7154	−0.114437
$33$	−33.0000	−0.174078
$34$	0.718285	0.00362308
$35$	123.348	0.595705
$36$	−71.8948	−0.332846
$37$	89.4287	0.397351	0.198675	−	0.980065i	$-0.436336\pi$
$37$	89.4287	0.397351	0.198675	+	0.980065i	$0.436336\pi$
$38$	−5.72891	−0.0244566
$39$	−72.9293	−0.299437
$40$	−11.6366	−0.0459978
$41$	125.161	0.476753	0.238376	−	0.971173i	$-0.423385\pi$
$41$	125.161	0.476753	0.238376	+	0.971173i	$0.423385\pi$
$42$	5.94163	0.0218289
$43$	−46.8777	−0.166251	−0.0831253	−	0.996539i	$-0.526490\pi$
$43$	−46.8777	−0.166251	−0.0831253	+	0.996539i	$0.526490\pi$
$44$	87.8715	0.301071
$45$	−60.5939	−0.200729
$46$	−7.38354	−0.0236662
$47$	−271.317	−0.842037	−0.421018	−	0.907052i	$-0.638327\pi$
$47$	−271.317	−0.842037	−0.421018	+	0.907052i	$0.638327\pi$
$48$	191.159	0.574821
$49$	−7.34442	−0.0214123
$50$	8.61270	0.0243604
$51$	−19.9333	−0.0547299
$52$	194.194	0.517882
$53$	441.412	1.14401	0.572006	−	0.820250i	$-0.306165\pi$
$53$	441.412	1.14401	0.572006	+	0.820250i	$0.306165\pi$
$54$	−2.91878	−0.00735548
$55$	74.0593	0.181566
$56$	−31.6656	−0.0755623
$57$	158.985	0.369439
$58$	−28.6306	−0.0648169
$59$	−267.139	−0.589468	−0.294734	−	0.955579i	$-0.595231\pi$
$59$	−267.139	−0.589468	−0.294734	+	0.955579i	$0.595231\pi$
$60$	161.348	0.347165
$61$	−61.0000	−0.128037
$61$	−61.0000	−0.128037
$62$	−19.4744	−0.0398911
$63$	−164.888	−0.329745
$64$	−507.518	−0.991246
$65$	163.669	0.312318
$66$	3.56740	0.00665328
$67$	837.902	1.52785	0.763925	−	0.645305i	$-0.223270\pi$
$67$	837.902	1.52785	0.763925	+	0.645305i	$0.223270\pi$
$68$	53.0779	0.0946566
$69$	204.903	0.357499
$70$	−13.3343	−0.0227680
$71$	−730.419	−1.22091	−0.610456	−	0.792050i	$-0.709014\pi$
$71$	−730.419	−1.22091	−0.610456	+	0.792050i	$0.709014\pi$
$72$	15.5555	0.0254615
$73$	−703.209	−1.12746	−0.563729	−	0.825960i	$-0.690634\pi$
$73$	−703.209	−1.12746	−0.563729	+	0.825960i	$0.690634\pi$
$74$	−9.66751	−0.0151868
$75$	−239.014	−0.367986
$76$	−423.340	−0.638953
$77$	201.530	0.298266
$78$	7.88388	0.0114445
$79$	−850.697	−1.21153	−0.605765	−	0.795644i	$-0.707133\pi$
$79$	−850.697	−1.21153	−0.605765	+	0.795644i	$0.707133\pi$
$80$	−429.003	−0.599550
$81$	81.0000	0.111111
$82$	−13.5303	−0.0182216
$83$	198.628	0.262677	0.131339	−	0.991338i	$-0.458072\pi$
$83$	198.628	0.262677	0.131339	+	0.991338i	$0.458072\pi$
$84$	439.059	0.570301
$85$	44.7348	0.0570844
$86$	5.06762	0.00635413
$87$	794.536	0.979118
$88$	−19.0122	−0.0230308
$89$	543.465	0.647272	0.323636	−	0.946182i	$-0.395095\pi$
$89$	543.465	0.647272	0.323636	+	0.946182i	$0.395095\pi$
$90$	6.55039	0.00767190
$91$	445.377	0.513057
$92$	−545.610	−0.618302
$93$	540.440	0.602592
$94$	29.3302	0.0321828
$95$	−356.797	−0.385332
$96$	−62.1461	−0.0660704
$97$	−29.3234	−0.0306943	−0.0153471	−	0.999882i	$-0.504885\pi$
$97$	−29.3234	−0.0306943	−0.0153471	+	0.999882i	$0.504885\pi$
$98$	0.793954	0.000818382 0
$99$	−99.0000	−0.100504
$100$	636.439	0.636439
$101$	−1773.87	−1.74759	−0.873796	−	0.486292i	$-0.838349\pi$
$101$	−1773.87	−1.74759	−0.873796	+	0.486292i	$0.838349\pi$
$102$	2.15485	0.00209179
$103$	−1233.57	−1.18007	−0.590036	−	0.807377i	$-0.700886\pi$
$103$	−1233.57	−1.18007	−0.590036	+	0.807377i	$0.700886\pi$
$104$	−42.0166	−0.0396161
$105$	370.045	0.343931
$106$	−47.7180	−0.0437243
$107$	1804.61	1.63045	0.815226	−	0.579143i	$-0.196613\pi$
$107$	1804.61	1.63045	0.815226	+	0.579143i	$0.196613\pi$
$108$	−215.684	−0.192169
$109$	1575.07	1.38407	0.692036	−	0.721863i	$-0.256714\pi$
$109$	1575.07	1.38407	0.692036	+	0.721863i	$0.256714\pi$
$110$	−8.00603	−0.00693950
$111$	268.286	0.229411
$112$	−1167.40	−0.984903
$113$	1394.40	1.16083	0.580415	−	0.814321i	$-0.302891\pi$
$113$	1394.40	1.16083	0.580415	+	0.814321i	$0.302891\pi$
$114$	−17.1867	−0.0141200
$115$	−459.847	−0.372878
$116$	−2115.67	−1.69340
$117$	−218.788	−0.172880
$118$	28.8786	0.0225296
$119$	121.732	0.0937747
$120$	−34.9099	−0.0265568
$121$	121.000	0.0909091
$122$	6.59428	0.00489359
$123$	375.483	0.275253
$124$	−1439.07	−1.04220
$125$	1377.98	0.986004
$126$	17.8249	0.0126029
$127$	−687.229	−0.480171	−0.240086	−	0.970752i	$-0.577175\pi$
$127$	−687.229	−0.480171	−0.240086	+	0.970752i	$0.577175\pi$
$128$	220.587	0.152323
$129$	−140.633	−0.0959849
$130$	−17.6932	−0.0119369
$131$	−2785.70	−1.85792	−0.928962	−	0.370175i	$-0.879298\pi$
$131$	−2785.70	−1.85792	−0.928962	+	0.370175i	$0.879298\pi$
$132$	263.614	0.173823
$133$	−970.914	−0.633000
$134$	−90.5796	−0.0583947
$135$	−181.782	−0.115891
$136$	−11.4842	−0.00724087
$137$	−459.931	−0.286822	−0.143411	−	0.989663i	$-0.545807\pi$
$137$	−459.931	−0.286822	−0.143411	+	0.989663i	$0.545807\pi$
$138$	−22.1506	−0.0136637
$139$	−1068.72	−0.652141	−0.326071	−	0.945345i	$-0.605725\pi$
$139$	−1068.72	−0.652141	−0.326071	+	0.945345i	$0.605725\pi$
$140$	−985.346	−0.594835
$141$	−813.952	−0.486150
$142$	78.9605	0.0466635
$143$	267.408	0.156376
$144$	573.477	0.331873
$145$	−1783.11	−1.02124
$146$	76.0190	0.0430916
$147$	−22.0333	−0.0123624
$148$	−714.384	−0.396771
$149$	−427.288	−0.234931	−0.117466	−	0.993077i	$-0.537477\pi$
$149$	−427.288	−0.234931	−0.117466	+	0.993077i	$0.537477\pi$
$150$	25.8381	0.0140645
$151$	3234.61	1.74323	0.871617	−	0.490187i	$-0.163071\pi$
$151$	3234.61	1.74323	0.871617	+	0.490187i	$0.163071\pi$
$152$	91.5955	0.0488775
$153$	−59.8000	−0.0315983
$154$	−21.7860	−0.0113998
$155$	−1212.87	−0.628515
$156$	582.582	0.299000
$157$	−3612.89	−1.83656	−0.918280	−	0.395932i	$-0.870422\pi$
$157$	−3612.89	−1.83656	−0.918280	+	0.395932i	$0.870422\pi$
$158$	91.9629	0.0463049
$159$	1324.24	0.660495
$160$	139.469	0.0689127
$161$	−1251.34	−0.612541
$162$	−8.75634	−0.00424669
$163$	−830.262	−0.398964	−0.199482	−	0.979901i	$-0.563926\pi$
$163$	−830.262	−0.398964	−0.199482	+	0.979901i	$0.563926\pi$
$164$	−999.826	−0.476057
$165$	222.178	0.104827
$166$	−21.4723	−0.0100396
$167$	2038.03	0.944354	0.472177	−	0.881504i	$-0.343468\pi$
$167$	2038.03	0.944354	0.472177	+	0.881504i	$0.343468\pi$
$168$	−94.9967	−0.0436259
$169$	−1606.03	−0.731013
$170$	−4.83597	−0.00218177
$171$	476.954	0.213296
$172$	374.474	0.166008
$173$	1867.43	0.820680	0.410340	−	0.911933i	$-0.365410\pi$
$173$	1867.43	0.820680	0.410340	+	0.911933i	$0.365410\pi$
$174$	−85.8917	−0.0374220
$175$	1459.65	0.630510
$176$	−700.916	−0.300191
$177$	−801.418	−0.340329
$178$	−58.7502	−0.0247388
$179$	64.5737	0.0269635	0.0134818	−	0.999909i	$-0.495708\pi$
$179$	64.5737	0.0269635	0.0134818	+	0.999909i	$0.495708\pi$
$180$	484.043	0.200436
$181$	−2377.53	−0.976357	−0.488179	−	0.872744i	$-0.662339\pi$
$181$	−2377.53	−0.976357	−0.488179	+	0.872744i	$0.662339\pi$
$182$	−48.1466	−0.0196091
$183$	−183.000	−0.0739221
$184$	118.050	0.0472978
$185$	−602.093	−0.239280
$186$	−58.4232	−0.0230312
$187$	73.0889	0.0285818
$188$	2167.37	0.840807
$189$	−494.664	−0.190379
$190$	38.5708	0.0147275
$191$	3211.80	1.21674	0.608372	−	0.793652i	$-0.291823\pi$
$191$	3211.80	1.21674	0.608372	+	0.793652i	$0.291823\pi$
$192$	−1522.55	−0.572296
$193$	−2338.25	−0.872077	−0.436039	−	0.899928i	$-0.643619\pi$
$193$	−2338.25	−0.872077	−0.436039	+	0.899928i	$0.643619\pi$
$194$	3.16995	0.00117314
$195$	491.008	0.180317
$196$	58.6695	0.0213810
$197$	−2014.83	−0.728684	−0.364342	−	0.931265i	$-0.618706\pi$
$197$	−2014.83	−0.728684	−0.364342	+	0.931265i	$0.618706\pi$
$198$	10.7022	0.00384127
$199$	−3824.99	−1.36254	−0.681272	−	0.732030i	$-0.738573\pi$
$199$	−3824.99	−1.36254	−0.681272	+	0.732030i	$0.738573\pi$
$200$	−137.703	−0.0486852
$201$	2513.70	0.882105
$202$	191.761	0.0667933
$203$	−4852.21	−1.67763
$204$	159.234	0.0546500
$205$	−842.667	−0.287095
$206$	133.353	0.0451025
$207$	614.709	0.206402
$208$	−1549.01	−0.516368
$209$	−582.944	−0.192933
$210$	−40.0030	−0.0131451
$211$	5366.40	1.75089	0.875445	−	0.483317i	$-0.160568\pi$
$211$	5366.40	1.75089	0.875445	+	0.483317i	$0.160568\pi$
$212$	−3526.14	−1.14234
$213$	−2191.26	−0.704894
$214$	−195.084	−0.0623161
$215$	315.612	0.100114
$216$	46.6664	0.0147002
$217$	−3300.45	−1.03249
$218$	−170.269	−0.0528995
$219$	−2109.63	−0.650938
$220$	−591.609	−0.181301
$221$	161.525	0.0491645
$222$	−29.0025	−0.00876812
$223$	−5269.98	−1.58253	−0.791265	−	0.611474i	$-0.790577\pi$
$223$	−5269.98	−1.58253	−0.791265	+	0.611474i	$0.790577\pi$
$224$	379.524	0.113205
$225$	−717.042	−0.212457
$226$	−150.738	−0.0443671
$227$	1282.72	0.375054	0.187527	−	0.982259i	$-0.439953\pi$
$227$	1282.72	0.375054	0.187527	+	0.982259i	$0.439953\pi$
$228$	−1270.02	−0.368900
$229$	3420.56	0.987062	0.493531	−	0.869728i	$-0.335706\pi$
$229$	3420.56	0.987062	0.493531	+	0.869728i	$0.335706\pi$
$230$	49.7109	0.0142515
$231$	604.590	0.172204
$232$	457.755	0.129539
$233$	672.225	0.189008	0.0945042	−	0.995524i	$-0.469873\pi$
$233$	672.225	0.189008	0.0945042	+	0.995524i	$0.469873\pi$
$234$	23.6516	0.00660750
$235$	1826.69	0.507064
$236$	2133.99	0.588607
$237$	−2552.09	−0.699477
$238$	−13.1596	−0.00358408
$239$	−4366.81	−1.18186	−0.590932	−	0.806721i	$-0.701240\pi$
$239$	−4366.81	−1.18186	−0.590932	+	0.806721i	$0.701240\pi$
$240$	−1287.01	−0.346150
$241$	−807.418	−0.215811	−0.107905	−	0.994161i	$-0.534414\pi$
$241$	−807.418	−0.215811	−0.107905	+	0.994161i	$0.534414\pi$
$242$	−13.0805	−0.00347456
$243$	243.000	0.0641500
$244$	487.287	0.127850
$245$	49.4475	0.0128942
$246$	−40.5908	−0.0105202
$247$	−1288.29	−0.331871
$248$	311.363	0.0797240
$249$	595.883	0.151657
$250$	−148.964	−0.0376852
$251$	−4854.37	−1.22074	−0.610369	−	0.792117i	$-0.708979\pi$
$251$	−4854.37	−1.22074	−0.610369	+	0.792117i	$0.708979\pi$
$252$	1317.18	0.329264
$253$	−751.311	−0.186698
$254$	74.2915	0.0183522
$255$	134.204	0.0329577
$256$	4036.30	0.985424
$257$	−3398.75	−0.824935	−0.412468	−	0.910972i	$-0.635333\pi$
$257$	−3398.75	−0.824935	−0.412468	+	0.910972i	$0.635333\pi$
$258$	15.2029	0.00366856
$259$	−1638.41	−0.393074
$260$	−1307.44	−0.311862
$261$	2383.61	0.565294
$262$	301.143	0.0710102
$263$	−5520.29	−1.29428	−0.647140	−	0.762371i	$-0.724035\pi$
$263$	−5520.29	−1.29428	−0.647140	+	0.762371i	$0.724035\pi$
$264$	−57.0367	−0.0132968
$265$	−2971.88	−0.688909
$266$	104.959	0.0241934
$267$	1630.40	0.373702
$268$	−6693.42	−1.52562
$269$	378.813	0.0858612	0.0429306	−	0.999078i	$-0.486331\pi$
$269$	378.813	0.0858612	0.0429306	+	0.999078i	$0.486331\pi$
$270$	19.6512	0.00442938
$271$	−6304.43	−1.41316	−0.706581	−	0.707632i	$-0.749763\pi$
$271$	−6304.43	−1.41316	−0.706581	+	0.707632i	$0.749763\pi$
$272$	−423.382	−0.0943798
$273$	1336.13	0.296214
$274$	49.7199	0.0109624
$275$	876.384	0.192174
$276$	−1636.83	−0.356977
$277$	4733.17	1.02667	0.513337	−	0.858187i	$-0.328409\pi$
$277$	4733.17	1.02667	0.513337	+	0.858187i	$0.328409\pi$
$278$	115.532	0.0249249
$279$	1621.32	0.347907
$280$	213.193	0.0455027
$281$	−4942.07	−1.04918	−0.524590	−	0.851355i	$-0.675781\pi$
$281$	−4942.07	−1.04918	−0.524590	+	0.851355i	$0.675781\pi$
$282$	87.9907	0.0185807
$283$	−1078.11	−0.226455	−0.113228	−	0.993569i	$-0.536119\pi$
$283$	−1078.11	−0.226455	−0.113228	+	0.993569i	$0.536119\pi$
$284$	5834.82	1.21913
$285$	−1070.39	−0.222472
$286$	−28.9076	−0.00597671
$287$	−2293.06	−0.471621
$288$	−186.438	−0.0381458
$289$	−4868.85	−0.991014
$290$	192.760	0.0390319
$291$	−87.9703	−0.0177213
$292$	5617.46	1.12581
$293$	5957.57	1.18787	0.593933	−	0.804514i	$-0.297574\pi$
$293$	5957.57	1.18787	0.593933	+	0.804514i	$0.297574\pi$
$294$	2.38186	0.000472493 0
$295$	1798.56	0.354970
$296$	154.567	0.0303515
$297$	−297.000	−0.0580259
$298$	46.1911	0.00897912
$299$	−1660.38	−0.321145
$300$	1909.32	0.367448
$301$	858.842	0.164461
$302$	−349.670	−0.0666267
$303$	−5321.61	−1.00897
$304$	3376.82	0.637085
$305$	410.692	0.0771022
$306$	6.46456	0.00120769
$307$	5039.95	0.936955	0.468478	−	0.883475i	$-0.344803\pi$
$307$	5039.95	0.936955	0.468478	+	0.883475i	$0.344803\pi$
$308$	−1609.88	−0.297830
$309$	−3700.71	−0.681314
$310$	131.115	0.0240219
$311$	6806.89	1.24110	0.620552	−	0.784166i	$-0.286909\pi$
$311$	6806.89	1.24110	0.620552	+	0.784166i	$0.286909\pi$
$312$	−126.050	−0.0228723
$313$	−3509.68	−0.633798	−0.316899	−	0.948459i	$-0.602642\pi$
$313$	−3509.68	−0.633798	−0.316899	+	0.948459i	$0.602642\pi$
$314$	390.564	0.0701936
$315$	1110.14	0.198568
$316$	6795.63	1.20976
$317$	4399.84	0.779558	0.389779	−	0.920908i	$-0.372551\pi$
$317$	4399.84	0.779558	0.389779	+	0.920908i	$0.372551\pi$
$318$	−143.154	−0.0252442
$319$	−2913.30	−0.511328
$320$	3416.95	0.596916
$321$	5413.83	0.941342
$322$	135.273	0.0234114
$323$	−352.122	−0.0606582
$324$	−647.053	−0.110949
$325$	1936.79	0.330566
$326$	89.7538	0.0152485
$327$	4725.20	0.799094
$328$	216.326	0.0364165
$329$	4970.78	0.832973
$330$	−24.0181	−0.00400652
$331$	7285.33	1.20978	0.604891	−	0.796308i	$-0.293217\pi$
$331$	7285.33	1.20978	0.604891	+	0.796308i	$0.293217\pi$
$332$	−1586.70	−0.262294
$333$	804.858	0.132450
$334$	−220.317	−0.0360934
$335$	−5641.31	−0.920052
$336$	−3502.21	−0.568634
$337$	−1145.58	−0.185174	−0.0925869	−	0.995705i	$-0.529514\pi$
$337$	−1145.58	−0.185174	−0.0925869	+	0.995705i	$0.529514\pi$
$338$	173.617	0.0279394
$339$	4183.19	0.670205
$340$	−357.356	−0.0570010
$341$	−1981.61	−0.314693
$342$	−51.5601	−0.00815220
$343$	6418.63	1.01042
$344$	−81.0227	−0.0126990
$345$	−1379.54	−0.215281
$346$	−201.874	−0.0313665
$347$	−3452.89	−0.534181	−0.267091	−	0.963671i	$-0.586062\pi$
$347$	−3452.89	−0.534181	−0.267091	+	0.963671i	$0.586062\pi$
$348$	−6347.01	−0.977687
$349$	−2099.86	−0.322071	−0.161035	−	0.986949i	$-0.551483\pi$
$349$	−2099.86	−0.322071	−0.161035	+	0.986949i	$0.551483\pi$
$350$	−157.793	−0.0240982
$351$	−656.364	−0.0998123
$352$	227.869	0.0345041
$353$	−11889.1	−1.79261	−0.896304	−	0.443440i	$-0.853758\pi$
$353$	−11889.1	−1.79261	−0.896304	+	0.443440i	$0.853758\pi$
$354$	86.6357	0.0130074
$355$	4917.66	0.735218
$356$	−4341.37	−0.646326
$357$	365.197	0.0541408
$358$	−6.98061	−0.00103055
$359$	4626.39	0.680143	0.340071	−	0.940400i	$-0.389549\pi$
$359$	4626.39	0.680143	0.340071	+	0.940400i	$0.389549\pi$
$360$	−104.730	−0.0153326
$361$	−4050.54	−0.590544
$362$	257.018	0.0373166
$363$	363.000	0.0524864
$364$	−3557.81	−0.512308
$365$	4734.47	0.678941
$366$	19.7828	0.00282532
$367$	9649.46	1.37247	0.686236	−	0.727379i	$-0.259262\pi$
$367$	9649.46	1.37247	0.686236	+	0.727379i	$0.259262\pi$
$368$	4352.12	0.616494
$369$	1126.45	0.158918
$370$	65.0880	0.00914531
$371$	−8087.07	−1.13170
$372$	−4317.21	−0.601712
$373$	7523.66	1.04440	0.522199	−	0.852824i	$-0.325112\pi$
$373$	7523.66	1.04440	0.522199	+	0.852824i	$0.325112\pi$
$374$	−7.90113	−0.00109240
$375$	4133.95	0.569270
$376$	−468.941	−0.0643186
$377$	−6438.33	−0.879552
$378$	53.4747	0.00727630
$379$	10542.6	1.42885	0.714426	−	0.699711i	$-0.246688\pi$
$379$	10542.6	1.42885	0.714426	+	0.699711i	$0.246688\pi$
$380$	2850.20	0.384769
$381$	−2061.69	−0.277227
$382$	−347.206	−0.0465041
$383$	−4659.29	−0.621616	−0.310808	−	0.950473i	$-0.600600\pi$
$383$	−4659.29	−0.621616	−0.310808	+	0.950473i	$0.600600\pi$
$384$	661.761	0.0879437
$385$	−1356.83	−0.179612
$386$	252.772	0.0333309
$387$	−421.899	−0.0554169
$388$	234.245	0.0306494
$389$	−11058.6	−1.44137	−0.720685	−	0.693263i	$-0.756173\pi$
$389$	−11058.6	−1.44137	−0.720685	+	0.693263i	$0.756173\pi$
$390$	−53.0795	−0.00689175
$391$	−453.822	−0.0586977
$392$	−12.6940	−0.00163557
$393$	−8357.11	−1.07267
$394$	217.809	0.0278504
$395$	5727.45	0.729568
$396$	790.843	0.100357
$397$	−7104.93	−0.898202	−0.449101	−	0.893481i	$-0.648256\pi$
$397$	−7104.93	−0.898202	−0.449101	+	0.893481i	$0.648256\pi$
$398$	413.493	0.0520767
$399$	−2912.74	−0.365463
$400$	−5076.63	−0.634578
$401$	−2949.82	−0.367349	−0.183674	−	0.982987i	$-0.558799\pi$
$401$	−2949.82	−0.367349	−0.183674	+	0.982987i	$0.558799\pi$
$402$	−271.739	−0.0337142
$403$	−4379.33	−0.541315
$404$	14170.2	1.74504
$405$	−545.345	−0.0669097
$406$	524.538	0.0641192
$407$	−983.716	−0.119806
$408$	−34.4525	−0.00418052
$409$	7672.84	0.927623	0.463811	−	0.885934i	$-0.346482\pi$
$409$	7672.84	0.927623	0.463811	+	0.885934i	$0.346482\pi$
$410$	91.0948	0.0109728
$411$	−1379.79	−0.165596
$412$	9854.15	1.17835
$413$	4894.24	0.583123
$414$	−66.4519	−0.00788872
$415$	−1337.29	−0.158181
$416$	503.586	0.0593517
$417$	−3206.16	−0.376514
$418$	63.0180	0.00737395
$419$	2785.18	0.324738	0.162369	−	0.986730i	$-0.448087\pi$
$419$	2785.18	0.324738	0.162369	+	0.986730i	$0.448087\pi$
$420$	−2956.04	−0.343428
$421$	16958.5	1.96320	0.981599	−	0.190951i	$-0.0611573\pi$
$421$	16958.5	1.96320	0.981599	+	0.190951i	$0.0611573\pi$
$422$	−580.123	−0.0669194
$423$	−2441.86	−0.280679
$424$	762.930	0.0873848
$425$	529.372	0.0604195
$426$	236.881	0.0269412
$427$	1117.58	0.126659
$428$	−14415.8	−1.62807
$429$	802.223	0.0902836
$430$	−34.1185	−0.00382638
$431$	−10203.3	−1.14031	−0.570156	−	0.821536i	$-0.693117\pi$
$431$	−10203.3	−1.14031	−0.570156	+	0.821536i	$0.693117\pi$
$432$	1720.43	0.191607
$433$	−10160.6	−1.12768	−0.563840	−	0.825884i	$-0.690677\pi$
$433$	−10160.6	−1.12768	−0.563840	+	0.825884i	$0.690677\pi$
$434$	356.789	0.0394618
$435$	−5349.34	−0.589612
$436$	−12582.1	−1.38205
$437$	3619.60	0.396222
$438$	228.057	0.0248790
$439$	−13440.8	−1.46126	−0.730629	−	0.682774i	$-0.760773\pi$
$439$	−13440.8	−1.46126	−0.730629	+	0.682774i	$0.760773\pi$
$440$	128.003	0.0138689
$441$	−66.0998	−0.00713743
$442$	−17.4613	−0.00187908
$443$	−12649.6	−1.35666	−0.678330	−	0.734757i	$-0.737296\pi$
$443$	−12649.6	−1.35666	−0.678330	+	0.734757i	$0.737296\pi$
$444$	−2143.15	−0.229076
$445$	−3658.97	−0.389779
$446$	569.701	0.0604845
$447$	−1281.86	−0.135638
$448$	9298.19	0.980576
$449$	11086.7	1.16528	0.582642	−	0.812729i	$-0.302019\pi$
$449$	11086.7	1.16528	0.582642	+	0.812729i	$0.302019\pi$
$450$	77.5143	0.00812013
$451$	−1376.77	−0.143746
$452$	−11138.9	−1.15913
$453$	9703.82	1.00646
$454$	−138.666	−0.0143346
$455$	−2998.57	−0.308957
$456$	274.787	0.0282194
$457$	−11418.7	−1.16880	−0.584401	−	0.811465i	$-0.698671\pi$
$457$	−11418.7	−1.16880	−0.584401	+	0.811465i	$0.698671\pi$
$458$	−369.773	−0.0377257
$459$	−179.400	−0.0182433
$460$	3673.40	0.372333
$461$	−10413.6	−1.05208	−0.526040	−	0.850460i	$-0.676324\pi$
$461$	−10413.6	−1.05208	−0.526040	+	0.850460i	$0.676324\pi$
$462$	−65.3580	−0.00658166
$463$	602.839	0.0605103	0.0302552	−	0.999542i	$-0.490368\pi$
$463$	602.839	0.0605103	0.0302552	+	0.999542i	$0.490368\pi$
$464$	16875.9	1.68845
$465$	−3638.60	−0.362873
$466$	−72.6696	−0.00722393
$467$	2720.36	0.269557	0.134778	−	0.990876i	$-0.456968\pi$
$467$	2720.36	0.269557	0.134778	+	0.990876i	$0.456968\pi$
$468$	1747.75	0.172627
$469$	−15351.1	−1.51140
$470$	−197.470	−0.0193801
$471$	−10838.7	−1.06034
$472$	−461.720	−0.0450262
$473$	515.655	0.0501265
$474$	275.889	0.0267341
$475$	−4222.17	−0.407845
$476$	−972.436	−0.0936377
$477$	3972.71	0.381337
$478$	472.065	0.0451711
$479$	−18250.9	−1.74093	−0.870464	−	0.492233i	$-0.836181\pi$
$479$	−18250.9	−1.74093	−0.870464	+	0.492233i	$0.836181\pi$
$480$	418.408	0.0397868
$481$	−2173.99	−0.206082
$482$	87.2843	0.00824832
$483$	−3754.01	−0.353651
$484$	−966.586	−0.0907763
$485$	197.425	0.0184837
$486$	−26.2690	−0.00245183
$487$	−879.907	−0.0818735	−0.0409367	−	0.999162i	$-0.513034\pi$
$487$	−879.907	−0.0818735	−0.0409367	+	0.999162i	$0.513034\pi$
$488$	−105.431	−0.00978004
$489$	−2490.79	−0.230342
$490$	−5.34542	−0.000492819 0
$491$	8243.13	0.757652	0.378826	−	0.925468i	$-0.376328\pi$
$491$	8243.13	0.757652	0.378826	+	0.925468i	$0.376328\pi$
$492$	−2999.48	−0.274851
$493$	−1759.75	−0.160761
$494$	139.268	0.0126842
$495$	666.533	0.0605221
$496$	11478.9	1.03915
$497$	13381.9	1.20777
$498$	−64.4168	−0.00579635
$499$	12305.3	1.10393	0.551965	−	0.833867i	$-0.313878\pi$
$499$	12305.3	1.10393	0.551965	+	0.833867i	$0.313878\pi$
$500$	−11007.8	−0.984563
$501$	6114.08	0.545223
$502$	524.772	0.0466568
$503$	−12782.6	−1.13310	−0.566550	−	0.824027i	$-0.691722\pi$
$503$	−12782.6	−1.13310	−0.566550	+	0.824027i	$0.691722\pi$
$504$	−284.990	−0.0251874
$505$	11942.9	1.05238
$506$	81.2189	0.00713562
$507$	−4818.10	−0.422050
$508$	5489.80	0.479470
$509$	4967.64	0.432587	0.216293	−	0.976328i	$-0.430603\pi$
$509$	4967.64	0.432587	0.216293	+	0.976328i	$0.430603\pi$
$510$	−14.5079	−0.00125965
$511$	12883.4	1.11532
$512$	−2201.03	−0.189986
$513$	1430.86	0.123146
$514$	367.415	0.0315292
$515$	8305.21	0.710624
$516$	1123.42	0.0958447
$517$	2984.49	0.253884
$518$	177.117	0.0150234
$519$	5602.28	0.473820
$520$	282.884	0.0238563
$521$	11425.5	0.960769	0.480385	−	0.877058i	$-0.340497\pi$
$521$	11425.5	0.960769	0.480385	+	0.877058i	$0.340497\pi$
$522$	−257.675	−0.0216056
$523$	5598.23	0.468056	0.234028	−	0.972230i	$-0.424809\pi$
$523$	5598.23	0.468056	0.234028	+	0.972230i	$0.424809\pi$
$524$	22253.1	1.85521
$525$	4378.95	0.364025
$526$	596.760	0.0494676
$527$	−1196.98	−0.0989394
$528$	−2102.75	−0.173315
$529$	−7501.98	−0.616584
$530$	321.269	0.0263302
$531$	−2404.26	−0.196489
$532$	7755.97	0.632075
$533$	−3042.64	−0.247263
$534$	−176.251	−0.0142830
$535$	−12149.8	−0.981838
$536$	1448.22	0.116704
$537$	193.721	0.0155674
$538$	−40.9508	−0.00328163
$539$	80.7886	0.00645605
$540$	1452.13	0.115722
$541$	−5672.01	−0.450756	−0.225378	−	0.974271i	$-0.572362\pi$
$541$	−5672.01	−0.450756	−0.225378	+	0.974271i	$0.572362\pi$
$542$	681.528	0.0540113
$543$	−7132.60	−0.563700
$544$	137.642	0.0108481
$545$	−10604.4	−0.833471
$546$	−144.440	−0.0113213
$547$	−17253.1	−1.34861	−0.674304	−	0.738454i	$-0.735556\pi$
$547$	−17253.1	−1.34861	−0.674304	+	0.738454i	$0.735556\pi$
$548$	3674.07	0.286403
$549$	−549.000	−0.0426790
$550$	−94.7397	−0.00734494
$551$	14035.5	1.08517
$552$	354.151	0.0273074
$553$	15585.5	1.19849
$554$	−511.670	−0.0392396
$555$	−1806.28	−0.138148
$556$	8537.27	0.651188
$557$	−9773.99	−0.743514	−0.371757	−	0.928330i	$-0.621245\pi$
$557$	−9773.99	−0.743514	−0.371757	+	0.928330i	$0.621245\pi$
$558$	−175.270	−0.0132970
$559$	1139.59	0.0862243
$560$	7859.72	0.593096
$561$	219.267	0.0165017
$562$	534.253	0.0400998
$563$	−26626.4	−1.99320	−0.996599	−	0.0824015i	$-0.973741\pi$
$563$	−26626.4	−1.99320	−0.996599	+	0.0824015i	$0.973741\pi$
$564$	6502.11	0.485440
$565$	−9387.99	−0.699037
$566$	116.547	0.00865516
$567$	−1483.99	−0.109915
$568$	−1262.45	−0.0932588
$569$	−22053.3	−1.62482	−0.812411	−	0.583085i	$-0.801845\pi$
$569$	−22053.3	−1.62482	−0.812411	+	0.583085i	$0.801845\pi$
$570$	115.712	0.00850290
$571$	−6741.96	−0.494119	−0.247060	−	0.969000i	$-0.579464\pi$
$571$	−6741.96	−0.494119	−0.247060	+	0.969000i	$0.579464\pi$
$572$	−2136.14	−0.156147
$573$	9635.41	0.702487
$574$	247.887	0.0180254
$575$	−5441.63	−0.394664
$576$	−4567.66	−0.330415
$577$	−9357.79	−0.675164	−0.337582	−	0.941296i	$-0.609609\pi$
$577$	−9357.79	−0.675164	−0.337582	+	0.941296i	$0.609609\pi$
$578$	526.337	0.0378767
$579$	−7014.75	−0.503494
$580$	14244.1	1.01975
$581$	−3639.04	−0.259850
$582$	9.50985	0.000677313 0
$583$	−4855.53	−0.344932
$584$	−1215.42	−0.0861203
$585$	1473.03	0.104106
$586$	−644.031	−0.0454005
$587$	−19249.2	−1.35349	−0.676745	−	0.736217i	$-0.736610\pi$
$587$	−19249.2	−1.35349	−0.676745	+	0.736217i	$0.736610\pi$
$588$	176.009	0.0123443
$589$	9546.86	0.667863
$590$	−194.430	−0.0135670
$591$	−6044.49	−0.420706
$592$	5698.37	0.395610
$593$	2839.59	0.196641	0.0983204	−	0.995155i	$-0.468653\pi$
$593$	2839.59	0.196641	0.0983204	+	0.995155i	$0.468653\pi$
$594$	32.1066	0.00221776
$595$	−819.582	−0.0564699
$596$	3413.31	0.234588
$597$	−11475.0	−0.786665
$598$	179.492	0.0122742
$599$	3027.49	0.206511	0.103255	−	0.994655i	$-0.467074\pi$
$599$	3027.49	0.206511	0.103255	+	0.994655i	$0.467074\pi$
$600$	−413.108	−0.0281084
$601$	14331.1	0.972673	0.486336	−	0.873772i	$-0.338333\pi$
$601$	14331.1	0.972673	0.486336	+	0.873772i	$0.338333\pi$
$602$	−92.8433	−0.00628573
$603$	7541.11	0.509283
$604$	−25839.0	−1.74069
$605$	−814.652	−0.0547443
$606$	575.282	0.0385631
$607$	17683.9	1.18249	0.591243	−	0.806494i	$-0.298637\pi$
$607$	17683.9	1.18249	0.591243	+	0.806494i	$0.298637\pi$
$608$	−1097.81	−0.0732270
$609$	−14556.6	−0.968578
$610$	−44.3971	−0.00294686
$611$	6595.67	0.436714
$612$	477.702	0.0315522
$613$	11984.5	0.789643	0.394821	−	0.918758i	$-0.370806\pi$
$613$	11984.5	0.789643	0.394821	+	0.918758i	$0.370806\pi$
$614$	−544.834	−0.0358106
$615$	−2528.00	−0.165754
$616$	348.321	0.0227829
$617$	14635.5	0.954948	0.477474	−	0.878646i	$-0.341552\pi$
$617$	14635.5	0.954948	0.477474	+	0.878646i	$0.341552\pi$
$618$	400.058	0.0260400
$619$	−481.222	−0.0312471	−0.0156236	−	0.999878i	$-0.504973\pi$
$619$	−481.222	−0.0312471	−0.0156236	+	0.999878i	$0.504973\pi$
$620$	9688.76	0.627597
$621$	1844.13	0.119166
$622$	−735.845	−0.0474352
$623$	−9956.77	−0.640304
$624$	−4647.03	−0.298125
$625$	681.425	0.0436112
$626$	379.406	0.0242239
$627$	−1748.83	−0.111390
$628$	28860.9	1.83388
$629$	−594.204	−0.0376669
$630$	−120.009	−0.00758932
$631$	−28158.6	−1.77651	−0.888255	−	0.459350i	$-0.848082\pi$
$631$	−28158.6	−1.77651	−0.888255	+	0.459350i	$0.848082\pi$
$632$	−1470.33	−0.0925421
$633$	16099.2	1.01088
$634$	−475.636	−0.0297948
$635$	4626.88	0.289153
$636$	−10578.4	−0.659531
$637$	178.541	0.0111053
$638$	314.936	0.0195430
$639$	−6573.77	−0.406971
$640$	−1485.14	−0.0917269
$641$	16752.3	1.03225	0.516127	−	0.856512i	$-0.327373\pi$
$641$	16752.3	1.03225	0.516127	+	0.856512i	$0.327373\pi$
$642$	−585.251	−0.0359782
$643$	−26980.3	−1.65474	−0.827370	−	0.561657i	$-0.810164\pi$
$643$	−26980.3	−1.65474	−0.827370	+	0.561657i	$0.810164\pi$
$644$	9996.06	0.611646
$645$	946.835	0.0578009
$646$	38.0654	0.00231837
$647$	−16497.5	−1.00245	−0.501225	−	0.865317i	$-0.667117\pi$
$647$	−16497.5	−1.00245	−0.501225	+	0.865317i	$0.667117\pi$
$648$	139.999	0.00848717
$649$	2938.53	0.177731
$650$	−209.373	−0.0126343
$651$	−9901.35	−0.596105
$652$	6632.39	0.398381
$653$	21318.9	1.27760	0.638800	−	0.769373i	$-0.279431\pi$
$653$	21318.9	1.27760	0.638800	+	0.769373i	$0.279431\pi$
$654$	−510.808	−0.0305415
$655$	18755.2	1.11882
$656$	7975.22	0.474665
$657$	−6328.88	−0.375819
$658$	−537.356	−0.0318364
$659$	2488.08	0.147074	0.0735370	−	0.997292i	$-0.476571\pi$
$659$	2488.08	0.147074	0.0735370	+	0.997292i	$0.476571\pi$
$660$	−1774.83	−0.104674
$661$	−7563.53	−0.445064	−0.222532	−	0.974925i	$-0.571432\pi$
$661$	−7563.53	−0.445064	−0.222532	+	0.974925i	$0.571432\pi$
$662$	−787.565	−0.0462381
$663$	484.575	0.0283851
$664$	343.305	0.0200645
$665$	6536.84	0.381184
$666$	−87.0076	−0.00506227
$667$	18089.2	1.05010
$668$	−16280.4	−0.942975
$669$	−15809.9	−0.913674
$670$	609.842	0.0351646
$671$	671.000	0.0386046
$672$	1138.57	0.0653592
$673$	17534.8	1.00434	0.502168	−	0.864770i	$-0.332536\pi$
$673$	17534.8	1.00434	0.502168	+	0.864770i	$0.332536\pi$
$674$	123.840	0.00707738
$675$	−2151.12	−0.122662
$676$	12829.5	0.729945
$677$	6112.36	0.346997	0.173499	−	0.984834i	$-0.444493\pi$
$677$	6112.36	0.346997	0.173499	+	0.984834i	$0.444493\pi$
$678$	−452.215	−0.0256153
$679$	537.232	0.0303639
$680$	77.3190	0.00436036
$681$	3848.16	0.216537
$682$	214.218	0.0120276
$683$	−4825.79	−0.270357	−0.135179	−	0.990821i	$-0.543161\pi$
$683$	−4825.79	−0.270357	−0.135179	+	0.990821i	$0.543161\pi$
$684$	−3810.06	−0.212984
$685$	3096.56	0.172720
$686$	−693.873	−0.0386183
$687$	10261.7	0.569881
$688$	−2987.03	−0.165522
$689$	−10730.6	−0.593330
$690$	149.133	0.00822809
$691$	14195.6	0.781513	0.390756	−	0.920494i	$-0.372213\pi$
$691$	14195.6	0.781513	0.390756	+	0.920494i	$0.372213\pi$
$692$	−14917.6	−0.819482
$693$	1813.77	0.0994220
$694$	373.268	0.0204165
$695$	7195.33	0.392711
$696$	1373.26	0.0747894
$697$	−831.626	−0.0451938
$698$	227.001	0.0123096
$699$	2016.68	0.109124
$700$	−11660.1	−0.629589
$701$	−27250.6	−1.46825	−0.734124	−	0.679015i	$-0.762407\pi$
$701$	−27250.6	−1.46825	−0.734124	+	0.679015i	$0.762407\pi$
$702$	70.9549	0.00381484
$703$	4739.26	0.254260
$704$	5582.70	0.298872
$705$	5480.06	0.292753
$706$	1285.24	0.0685138
$707$	32498.9	1.72878
$708$	6401.98	0.339832
$709$	9042.85	0.479000	0.239500	−	0.970896i	$-0.423016\pi$
$709$	9042.85	0.479000	0.239500	+	0.970896i	$0.423016\pi$
$710$	−531.614	−0.0281002
$711$	−7656.27	−0.403843
$712$	939.316	0.0494415
$713$	12304.2	0.646278
$714$	−39.4789	−0.00206927
$715$	−1800.36	−0.0941676
$716$	−515.835	−0.0269241
$717$	−13100.4	−0.682350
$718$	−500.126	−0.0259952
$719$	−6380.04	−0.330925	−0.165463	−	0.986216i	$-0.552912\pi$
$719$	−6380.04	−0.330925	−0.165463	+	0.986216i	$0.552912\pi$
$720$	−3861.03	−0.199850
$721$	22600.1	1.16737
$722$	437.876	0.0225707
$723$	−2422.25	−0.124598
$724$	18992.5	0.974931
$725$	−21100.6	−1.08090
$726$	−39.2414	−0.00200604
$727$	31543.8	1.60921	0.804605	−	0.593810i	$-0.202377\pi$
$727$	31543.8	1.60921	0.804605	+	0.593810i	$0.202377\pi$
$728$	769.783	0.0391896
$729$	729.000	0.0370370
$730$	−511.810	−0.0259492
$731$	311.476	0.0157597
$732$	1461.86	0.0738141
$733$	−7090.93	−0.357312	−0.178656	−	0.983912i	$-0.557175\pi$
$733$	−7090.93	−0.357312	−0.178656	+	0.983912i	$0.557175\pi$
$734$	−1043.13	−0.0524561
$735$	148.342	0.00744448
$736$	−1414.88	−0.0708603
$737$	−9216.92	−0.460664
$738$	−121.773	−0.00607386
$739$	28990.3	1.44307	0.721534	−	0.692380i	$-0.243438\pi$
$739$	28990.3	1.44307	0.721534	+	0.692380i	$0.243438\pi$
$740$	4809.71	0.238930
$741$	−3864.88	−0.191606
$742$	874.236	0.0432537
$743$	14058.1	0.694135	0.347067	−	0.937840i	$-0.387178\pi$
$743$	14058.1	0.694135	0.347067	+	0.937840i	$0.387178\pi$
$744$	934.088	0.0460287
$745$	2876.78	0.141473
$746$	−813.330	−0.0399171
$747$	1787.65	0.0875592
$748$	−583.857	−0.0285400
$749$	−33062.1	−1.61290
$750$	−446.892	−0.0217576
$751$	−18271.2	−0.887786	−0.443893	−	0.896080i	$-0.646403\pi$
$751$	−18271.2	−0.887786	−0.443893	+	0.896080i	$0.646403\pi$
$752$	−17288.3	−0.838348
$753$	−14563.1	−0.704793
$754$	696.003	0.0336166
$755$	−21777.5	−1.04975
$756$	3951.53	0.190100
$757$	11300.3	0.542558	0.271279	−	0.962501i	$-0.412553\pi$
$757$	11300.3	0.542558	0.271279	+	0.962501i	$0.412553\pi$
$758$	−1139.68	−0.0546109
$759$	−2253.93	−0.107790
$760$	−616.682	−0.0294334
$761$	2942.39	0.140160	0.0700798	−	0.997541i	$-0.477675\pi$
$761$	2942.39	0.140160	0.0700798	+	0.997541i	$0.477675\pi$
$762$	222.875	0.0105957
$763$	−28856.6	−1.36917
$764$	−25656.9	−1.21497
$765$	402.613	0.0190281
$766$	503.684	0.0237583
$767$	6494.10	0.305722
$768$	12108.9	0.568935
$769$	9478.84	0.444494	0.222247	−	0.974990i	$-0.428661\pi$
$769$	9478.84	0.444494	0.222247	+	0.974990i	$0.428661\pi$
$770$	146.678	0.00686480
$771$	−10196.3	−0.476277
$772$	18678.7	0.870803
$773$	−11216.9	−0.521922	−0.260961	−	0.965349i	$-0.584039\pi$
$773$	−11216.9	−0.521922	−0.260961	+	0.965349i	$0.584039\pi$
$774$	45.6086	0.00211804
$775$	−14352.5	−0.665236
$776$	−50.6822	−0.00234457
$777$	−4915.24	−0.226941
$778$	1195.47	0.0550894
$779$	6632.90	0.305068
$780$	−3922.33	−0.180054
$781$	8034.61	0.368119
$782$	49.0596	0.00224343
$783$	7150.83	0.326373
$784$	−467.984	−0.0213185
$785$	24324.4	1.10595
$786$	903.428	0.0409977
$787$	−23425.2	−1.06101	−0.530506	−	0.847681i	$-0.677998\pi$
$787$	−23425.2	−1.06101	−0.530506	+	0.847681i	$0.677998\pi$
$788$	16095.1	0.727619
$789$	−16560.9	−0.747253
$790$	−619.155	−0.0278842
$791$	−25546.6	−1.14833
$792$	−171.110	−0.00767693
$793$	1482.90	0.0664050
$794$	768.064	0.0343294
$795$	−8915.63	−0.397742
$796$	30555.2	1.36055
$797$	−35582.9	−1.58144	−0.790722	−	0.612175i	$-0.790295\pi$
$797$	−35582.9	−1.58144	−0.790722	+	0.612175i	$0.790295\pi$
$798$	314.876	0.0139680
$799$	1802.76	0.0798209
$800$	1650.42	0.0729389
$801$	4891.19	0.215757
$802$	318.884	0.0140401
$803$	7735.30	0.339941
$804$	−20080.3	−0.880816
$805$	8424.82	0.368864
$806$	473.418	0.0206891
$807$	1136.44	0.0495720
$808$	−3065.93	−0.133489
$809$	10784.7	0.468691	0.234345	−	0.972153i	$-0.424705\pi$
$809$	10784.7	0.468691	0.234345	+	0.972153i	$0.424705\pi$
$810$	58.9535	0.00255730
$811$	36606.4	1.58499	0.792493	−	0.609881i	$-0.208783\pi$
$811$	36606.4	1.58499	0.792493	+	0.609881i	$0.208783\pi$
$812$	38761.0	1.67518
$813$	−18913.3	−0.815890
$814$	106.343	0.00457900
$815$	5589.87	0.240251
$816$	−1270.15	−0.0544902
$817$	−2484.28	−0.106382
$818$	−829.457	−0.0354539
$819$	4008.39	0.171019
$820$	6731.49	0.286675
$821$	−22519.4	−0.957288	−0.478644	−	0.878009i	$-0.658871\pi$
$821$	−22519.4	−0.957288	−0.478644	+	0.878009i	$0.658871\pi$
$822$	149.160	0.00632913
$823$	−2472.17	−0.104708	−0.0523539	−	0.998629i	$-0.516672\pi$
$823$	−2472.17	−0.104708	−0.0523539	+	0.998629i	$0.516672\pi$
$824$	−2132.08	−0.0901392
$825$	2629.15	0.110952
$826$	−529.082	−0.0222871
$827$	27513.1	1.15686	0.578430	−	0.815732i	$-0.303666\pi$
$827$	27513.1	1.15686	0.578430	+	0.815732i	$0.303666\pi$
$828$	−4910.49	−0.206101
$829$	4515.84	0.189194	0.0945970	−	0.995516i	$-0.469844\pi$
$829$	4515.84	0.189194	0.0945970	+	0.995516i	$0.469844\pi$
$830$	144.565	0.00604571
$831$	14199.5	0.592750
$832$	12337.6	0.514100
$833$	48.7996	0.00202978
$834$	346.595	0.0143904
$835$	−13721.3	−0.568678
$836$	4656.74	0.192651
$837$	4863.96	0.200864
$838$	−301.087	−0.0124115
$839$	−4031.37	−0.165886	−0.0829431	−	0.996554i	$-0.526432\pi$
$839$	−4031.37	−0.165886	−0.0829431	+	0.996554i	$0.526432\pi$
$840$	639.580	0.0262710
$841$	45754.1	1.87601
$842$	−1833.26	−0.0750338
$843$	−14826.2	−0.605744
$844$	−42868.5	−1.74833
$845$	10812.9	0.440207
$846$	263.972	0.0107276
$847$	−2216.83	−0.0899305
$848$	28126.6	1.13900
$849$	−3234.32	−0.130744
$850$	−57.2267	−0.00230925
$851$	6108.07	0.246042
$852$	17504.5	0.703865
$853$	3577.31	0.143593	0.0717965	−	0.997419i	$-0.477127\pi$
$853$	3577.31	0.143593	0.0717965	+	0.997419i	$0.477127\pi$
$854$	−120.813	−0.00484092
$855$	−3211.17	−0.128444
$856$	3119.06	0.124541
$857$	−41041.2	−1.63587	−0.817934	−	0.575312i	$-0.804881\pi$
$857$	−41041.2	−1.63587	−0.817934	+	0.575312i	$0.804881\pi$
$858$	−86.7227	−0.00345066
$859$	29774.8	1.18266	0.591330	−	0.806430i	$-0.298603\pi$
$859$	29774.8	1.18266	0.591330	+	0.806430i	$0.298603\pi$
$860$	−2521.20	−0.0999678
$861$	−6879.19	−0.272291
$862$	1103.01	0.0435829
$863$	−44248.4	−1.74535	−0.872673	−	0.488305i	$-0.837615\pi$
$863$	−44248.4	−1.74535	−0.872673	+	0.488305i	$0.837615\pi$
$864$	−559.315	−0.0220235
$865$	−12572.7	−0.494203
$866$	1098.39	0.0431001
$867$	−14606.6	−0.572162
$868$	26365.0	1.03098
$869$	9357.66	0.365290
$870$	578.280	0.0225351
$871$	−20369.2	−0.792404
$872$	2722.32	0.105722
$873$	−263.911	−0.0102314
$874$	−391.290	−0.0151437
$875$	−25245.9	−0.975390
$876$	16852.4	0.649987
$877$	−9159.18	−0.352661	−0.176330	−	0.984331i	$-0.556423\pi$
$877$	−9159.18	−0.352661	−0.176330	+	0.984331i	$0.556423\pi$
$878$	1452.99	0.0558496
$879$	17872.7	0.685815
$880$	4719.03	0.180771
$881$	−26.8988	−0.00102865	−0.000514327	−	1.00000i	$-0.500164\pi$
$881$	−26.8988	−0.00102865	−0.000514327		1.00000i	$0.500164\pi$
$882$	7.14558	0.000272794 0
$883$	−22771.9	−0.867879	−0.433939	−	0.900942i	$-0.642877\pi$
$883$	−22771.9	−0.867879	−0.433939	+	0.900942i	$0.642877\pi$
$884$	−1290.31	−0.0490927
$885$	5395.68	0.204942
$886$	1367.46	0.0518518
$887$	−7651.78	−0.289652	−0.144826	−	0.989457i	$-0.546262\pi$
$887$	−7651.78	−0.289652	−0.144826	+	0.989457i	$0.546262\pi$
$888$	463.701	0.0175234
$889$	12590.7	0.475002
$890$	395.545	0.0148974
$891$	−891.000	−0.0335013
$892$	42098.3	1.58022
$893$	−14378.4	−0.538809
$894$	138.573	0.00518410
$895$	−434.753	−0.0162371
$896$	−4041.36	−0.150683
$897$	−4981.15	−0.185413
$898$	−1198.50	−0.0445373
$899$	47711.0	1.77003
$900$	5727.95	0.212146
$901$	−2932.94	−0.108447
$902$	148.833	0.00549401
$903$	2576.52	0.0949517
$904$	2410.05	0.0886694
$905$	16007.1	0.587950
$906$	−1049.01	−0.0384670
$907$	−8226.55	−0.301166	−0.150583	−	0.988597i	$-0.548115\pi$
$907$	−8226.55	−0.301166	−0.150583	+	0.988597i	$0.548115\pi$
$908$	−10246.8	−0.374506
$909$	−15964.8	−0.582531
$910$	324.155	0.0118084
$911$	52415.3	1.90625	0.953126	−	0.302574i	$-0.0978461\pi$
$911$	52415.3	1.90625	0.953126	+	0.302574i	$0.0978461\pi$
$912$	10130.4	0.367821
$913$	−2184.91	−0.0792002
$914$	1234.39	0.0446718
$915$	1232.08	0.0445150
$916$	−27324.5	−0.985620
$917$	51036.6	1.83792
$918$	19.3937	0.000697263 0
$919$	9610.98	0.344980	0.172490	−	0.985011i	$-0.444819\pi$
$919$	9610.98	0.344980	0.172490	+	0.985011i	$0.444819\pi$
$920$	−794.793	−0.0284821
$921$	15119.9	0.540951
$922$	1125.74	0.0402107
$923$	17756.3	0.633214
$924$	−4829.65	−0.171952
$925$	−7124.90	−0.253260
$926$	−65.1686	−0.00231272
$927$	−11102.1	−0.393357
$928$	−5486.37	−0.194072
$929$	−45883.4	−1.62044	−0.810218	−	0.586129i	$-0.800651\pi$
$929$	−45883.4	−1.62044	−0.810218	+	0.586129i	$0.800651\pi$
$930$	393.344	0.0138691
$931$	−389.217	−0.0137015
$932$	−5369.95	−0.188732
$933$	20420.7	0.716551
$934$	−294.078	−0.0103025
$935$	−492.083	−0.0172116
$936$	−378.150	−0.0132054
$937$	17138.1	0.597521	0.298761	−	0.954328i	$-0.403427\pi$
$937$	17138.1	0.597521	0.298761	+	0.954328i	$0.403427\pi$
$938$	1659.50	0.0577661
$939$	−10529.0	−0.365923
$940$	−14592.2	−0.506323
$941$	20735.2	0.718330	0.359165	−	0.933274i	$-0.383062\pi$
$941$	20735.2	0.718330	0.359165	+	0.933274i	$0.383062\pi$
$942$	1171.69	0.0405263
$943$	8548.62	0.295208
$944$	−17022.0	−0.586886
$945$	3330.41	0.114644
$946$	−55.7438	−0.00191584
$947$	−13888.3	−0.476566	−0.238283	−	0.971196i	$-0.576585\pi$
$947$	−13888.3	−0.476566	−0.238283	+	0.971196i	$0.576585\pi$
$948$	20386.9	0.698455
$949$	17094.9	0.584745
$950$	456.429	0.0155879
$951$	13199.5	0.450078
$952$	210.400	0.00716293
$953$	47672.7	1.62043	0.810215	−	0.586133i	$-0.199350\pi$
$953$	47672.7	1.62043	0.810215	+	0.586133i	$0.199350\pi$
$954$	−429.462	−0.0145748
$955$	−21624.0	−0.732707
$956$	34883.5	1.18014
$957$	−8739.90	−0.295215
$958$	1972.97	0.0665385
$959$	8426.35	0.283734
$960$	10250.8	0.344630
$961$	2661.85	0.0893508
$962$	235.015	0.00787649
$963$	16241.5	0.543484
$964$	6449.91	0.215495
$965$	15742.6	0.525154
$966$	405.819	0.0135166
$967$	23268.1	0.773785	0.386892	−	0.922125i	$-0.373548\pi$
$967$	23268.1	0.773785	0.386892	+	0.922125i	$0.373548\pi$
$968$	209.135	0.00694405
$969$	−1056.37	−0.0350210
$970$	−21.3422	−0.000706450 0
$971$	27428.6	0.906515	0.453257	−	0.891380i	$-0.350262\pi$
$971$	27428.6	0.906515	0.453257	+	0.891380i	$0.350262\pi$
$972$	−1941.16	−0.0640563
$973$	19579.9	0.645121
$974$	95.1206	0.00312922
$975$	5810.37	0.190852
$976$	−3886.90	−0.127476
$977$	−31283.9	−1.02442	−0.512210	−	0.858860i	$-0.671173\pi$
$977$	−31283.9	−1.02442	−0.512210	+	0.858860i	$0.671173\pi$
$978$	269.261	0.00880371
$979$	−5978.12	−0.195160
$980$	−395.002	−0.0128754
$981$	14175.6	0.461357
$982$	−891.106	−0.0289576
$983$	−20569.8	−0.667421	−0.333711	−	0.942676i	$-0.608301\pi$
$983$	−20569.8	−0.667421	−0.333711	+	0.942676i	$0.608301\pi$
$984$	648.979	0.0210251
$985$	13565.2	0.438804
$986$	190.234	0.00614432
$987$	14912.3	0.480917
$988$	10291.3	0.331386
$989$	−3201.79	−0.102943
$990$	−72.0542	−0.00231317
$991$	51177.5	1.64047	0.820235	−	0.572026i	$-0.193843\pi$
$991$	51177.5	1.64047	0.820235	+	0.572026i	$0.193843\pi$
$992$	−3731.80	−0.119440
$993$	21856.0	0.698468
$994$	−1446.63	−0.0461612
$995$	25752.3	0.820507
$996$	−4760.10	−0.151435
$997$	51571.9	1.63821	0.819106	−	0.573642i	$-0.194470\pi$
$997$	51571.9	1.63821	0.819106	+	0.573642i	$0.194470\pi$
$998$	−1330.24	−0.0421924
$999$	2414.57	0.0764702

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2013.4.a.c.1.20	✓	37

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2013.4.a.c.1.20	✓	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)

\(f(q)\)	\(=\)	\(q-0.108103 q^{2} +3.00000 q^{3} -7.98831 q^{4} -6.73266 q^{5} -0.324309 q^{6} -18.3209 q^{7} +1.72838 q^{8} +9.00000 q^{9} +O(q^{10})\)	\(q-0.108103 q^{2} +3.00000 q^{3} -7.98831 q^{4} -6.73266 q^{5} -0.324309 q^{6} -18.3209 q^{7} +1.72838 q^{8} +9.00000 q^{9} +0.727821 q^{10} -11.0000 q^{11} -23.9649 q^{12} -24.3098 q^{13} +1.98054 q^{14} -20.1980 q^{15} +63.7197 q^{16} -6.64445 q^{17} -0.972927 q^{18} +52.9949 q^{19} +53.7826 q^{20} -54.9627 q^{21} +1.18913 q^{22} +68.3010 q^{23} +5.18515 q^{24} -79.6713 q^{25} +2.62796 q^{26} +27.0000 q^{27} +146.353 q^{28} +264.845 q^{29} +2.18346 q^{30} +180.147 q^{31} -20.7154 q^{32} -33.0000 q^{33} +0.718285 q^{34} +123.348 q^{35} -71.8948 q^{36} +89.4287 q^{37} -5.72891 q^{38} -72.9293 q^{39} -11.6366 q^{40} +125.161 q^{41} +5.94163 q^{42} -46.8777 q^{43} +87.8715 q^{44} -60.5939 q^{45} -7.38354 q^{46} -271.317 q^{47} +191.159 q^{48} -7.34442 q^{49} +8.61270 q^{50} -19.9333 q^{51} +194.194 q^{52} +441.412 q^{53} -2.91878 q^{54} +74.0593 q^{55} -31.6656 q^{56} +158.985 q^{57} -28.6306 q^{58} -267.139 q^{59} +161.348 q^{60} -61.0000 q^{61} -19.4744 q^{62} -164.888 q^{63} -507.518 q^{64} +163.669 q^{65} +3.56740 q^{66} +837.902 q^{67} +53.0779 q^{68} +204.903 q^{69} -13.3343 q^{70} -730.419 q^{71} +15.5555 q^{72} -703.209 q^{73} -9.66751 q^{74} -239.014 q^{75} -423.340 q^{76} +201.530 q^{77} +7.88388 q^{78} -850.697 q^{79} -429.003 q^{80} +81.0000 q^{81} -13.5303 q^{82} +198.628 q^{83} +439.059 q^{84} +44.7348 q^{85} +5.06762 q^{86} +794.536 q^{87} -19.0122 q^{88} +543.465 q^{89} +6.55039 q^{90} +445.377 q^{91} -545.610 q^{92} +540.440 q^{93} +29.3302 q^{94} -356.797 q^{95} -62.1461 q^{96} -29.3234 q^{97} +0.793954 q^{98} -99.0000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 37 q - 8 q^{2} + 111 q^{3} + 130 q^{4} - 35 q^{5} - 24 q^{6} - 35 q^{7} - 117 q^{8} + 333 q^{9}+O(q^{10}) \) 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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