LMFDB - Embedded newform 6013.2.a.f.1.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6013,2,Mod(1,6013)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6013, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("6013.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6013 = 7 \cdot 859 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6013.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:	$48.0140467354$
Analytic rank:	$0$
Dimension:	$110$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.11
Character	$\chi$	$=$	6013.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.30986 q^{2} +1.63849 q^{3} +3.33543 q^{4} -0.463511 q^{5} -3.78466 q^{6} -1.00000 q^{7} -3.08465 q^{8} -0.315366 q^{9} +O(q^{10})$	\(q-2.30986 q^{2} +1.63849 q^{3} +3.33543 q^{4} -0.463511 q^{5} -3.78466 q^{6} -1.00000 q^{7} -3.08465 q^{8} -0.315366 q^{9} +1.07064 q^{10} -3.31180 q^{11} +5.46505 q^{12} -3.00533 q^{13} +2.30986 q^{14} -0.759456 q^{15} +0.454235 q^{16} +0.112289 q^{17} +0.728449 q^{18} +1.40893 q^{19} -1.54601 q^{20} -1.63849 q^{21} +7.64978 q^{22} -6.18250 q^{23} -5.05415 q^{24} -4.78516 q^{25} +6.94187 q^{26} -5.43218 q^{27} -3.33543 q^{28} +3.55266 q^{29} +1.75423 q^{30} -2.93704 q^{31} +5.12008 q^{32} -5.42634 q^{33} -0.259372 q^{34} +0.463511 q^{35} -1.05188 q^{36} -7.33489 q^{37} -3.25443 q^{38} -4.92419 q^{39} +1.42977 q^{40} -0.531021 q^{41} +3.78466 q^{42} +7.95648 q^{43} -11.0463 q^{44} +0.146175 q^{45} +14.2807 q^{46} +11.1201 q^{47} +0.744257 q^{48} +1.00000 q^{49} +11.0530 q^{50} +0.183985 q^{51} -10.0241 q^{52} -4.39660 q^{53} +12.5475 q^{54} +1.53506 q^{55} +3.08465 q^{56} +2.30851 q^{57} -8.20614 q^{58} -3.52462 q^{59} -2.53311 q^{60} +4.54489 q^{61} +6.78414 q^{62} +0.315366 q^{63} -12.7351 q^{64} +1.39300 q^{65} +12.5341 q^{66} -1.49310 q^{67} +0.374534 q^{68} -10.1299 q^{69} -1.07064 q^{70} -7.93773 q^{71} +0.972793 q^{72} -0.359105 q^{73} +16.9425 q^{74} -7.84041 q^{75} +4.69939 q^{76} +3.31180 q^{77} +11.3742 q^{78} +8.17057 q^{79} -0.210543 q^{80} -7.95445 q^{81} +1.22658 q^{82} +2.45799 q^{83} -5.46505 q^{84} -0.0520474 q^{85} -18.3783 q^{86} +5.82099 q^{87} +10.2157 q^{88} +10.1190 q^{89} -0.337644 q^{90} +3.00533 q^{91} -20.6213 q^{92} -4.81230 q^{93} -25.6857 q^{94} -0.653055 q^{95} +8.38918 q^{96} +5.29876 q^{97} -2.30986 q^{98} +1.04443 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 110 q + 16 q^{2} + 29 q^{3} + 118 q^{4} + 12 q^{6} - 110 q^{7} + 57 q^{8} + 127 q^{9}+O(q^{10}) $ 110 * q + 16 * q^2 + 29 * q^3 + 118 * q^4 + 12 * q^6 - 110 * q^7 + 57 * q^8 + 127 * q^9	\( 110 q + 16 q^{2} + 29 q^{3} + 118 q^{4} + 12 q^{6} - 110 q^{7} + 57 q^{8} + 127 q^{9} + 3 q^{10} + 52 q^{11} + 62 q^{12} - 9 q^{13} - 16 q^{14} + 39 q^{15} + 146 q^{16} + 11 q^{17} + 60 q^{18} + 14 q^{19} + 18 q^{20} - 29 q^{21} + 32 q^{22} + 73 q^{23} + 24 q^{24} + 132 q^{25} - 7 q^{26} + 116 q^{27} - 118 q^{28} + 35 q^{29} + 18 q^{30} + 36 q^{31} + 140 q^{32} + 42 q^{33} - 7 q^{34} + 180 q^{36} + 49 q^{37} + 45 q^{39} + 6 q^{40} - 14 q^{41} - 12 q^{42} + 58 q^{43} + 92 q^{44} + 17 q^{45} + 27 q^{46} + 87 q^{47} + 98 q^{48} + 110 q^{49} + 91 q^{50} + 42 q^{51} + 16 q^{52} + 95 q^{53} + 41 q^{54} + 8 q^{55} - 57 q^{56} + 61 q^{57} + 46 q^{58} + 114 q^{59} + 81 q^{60} - 47 q^{61} + 31 q^{62} - 127 q^{63} + 199 q^{64} + 62 q^{65} + 21 q^{66} + 95 q^{67} + 60 q^{68} - 39 q^{69} - 3 q^{70} + 131 q^{71} + 186 q^{72} + 31 q^{73} + 23 q^{74} + 121 q^{75} + 14 q^{76} - 52 q^{77} + 110 q^{78} + 9 q^{79} + 61 q^{80} + 194 q^{81} + 45 q^{82} + 73 q^{83} - 62 q^{84} + 59 q^{85} + 72 q^{86} + 64 q^{87} + 100 q^{88} - 17 q^{89} + 11 q^{90} + 9 q^{91} + 192 q^{92} + 85 q^{93} - 11 q^{94} + 108 q^{95} + 68 q^{96} + 32 q^{97} + 16 q^{98} + 160 q^{99}+O(q^{100}) \) 110 * q + 16 * q^2 + 29 * q^3 + 118 * q^4 + 12 * q^6 - 110 * q^7 + 57 * q^8 + 127 * q^9 + 3 * q^10 + 52 * q^11 + 62 * q^12 - 9 * q^13 - 16 * q^14 + 39 * q^15 + 146 * q^16 + 11 * q^17 + 60 * q^18 + 14 * q^19 + 18 * q^20 - 29 * q^21 + 32 * q^22 + 73 * q^23 + 24 * q^24 + 132 * q^25 - 7 * q^26 + 116 * q^27 - 118 * q^28 + 35 * q^29 + 18 * q^30 + 36 * q^31 + 140 * q^32 + 42 * q^33 - 7 * q^34 + 180 * q^36 + 49 * q^37 + 45 * q^39 + 6 * q^40 - 14 * q^41 - 12 * q^42 + 58 * q^43 + 92 * q^44 + 17 * q^45 + 27 * q^46 + 87 * q^47 + 98 * q^48 + 110 * q^49 + 91 * q^50 + 42 * q^51 + 16 * q^52 + 95 * q^53 + 41 * q^54 + 8 * q^55 - 57 * q^56 + 61 * q^57 + 46 * q^58 + 114 * q^59 + 81 * q^60 - 47 * q^61 + 31 * q^62 - 127 * q^63 + 199 * q^64 + 62 * q^65 + 21 * q^66 + 95 * q^67 + 60 * q^68 - 39 * q^69 - 3 * q^70 + 131 * q^71 + 186 * q^72 + 31 * q^73 + 23 * q^74 + 121 * q^75 + 14 * q^76 - 52 * q^77 + 110 * q^78 + 9 * q^79 + 61 * q^80 + 194 * q^81 + 45 * q^82 + 73 * q^83 - 62 * q^84 + 59 * q^85 + 72 * q^86 + 64 * q^87 + 100 * q^88 - 17 * q^89 + 11 * q^90 + 9 * q^91 + 192 * q^92 + 85 * q^93 - 11 * q^94 + 108 * q^95 + 68 * q^96 + 32 * q^97 + 16 * q^98 + 160 * 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 $

$2$	−2.30986	−1.63331	−0.816657	−	0.577123i	$-0.804175\pi$
$2$	−2.30986	−1.63331	−0.816657	+	0.577123i	$0.804175\pi$
$3$	1.63849	0.945980	0.472990	−	0.881068i	$-0.343175\pi$
$3$	1.63849	0.945980	0.472990	+	0.881068i	$0.343175\pi$
$4$	3.33543	1.66772
$5$	−0.463511	−0.207288	−0.103644	−	0.994614i	$-0.533050\pi$
$5$	−0.463511	−0.207288	−0.103644	+	0.994614i	$0.533050\pi$
$6$	−3.78466	−1.54508
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	−3.08465	−1.09059
$9$	−0.315366	−0.105122
$10$	1.07064	0.338567
$11$	−3.31180	−0.998545	−0.499273	−	0.866445i	$-0.666399\pi$
$11$	−3.31180	−0.998545	−0.499273	+	0.866445i	$0.666399\pi$
$12$	5.46505	1.57763
$13$	−3.00533	−0.833528	−0.416764	−	0.909015i	$-0.636836\pi$
$13$	−3.00533	−0.833528	−0.416764	+	0.909015i	$0.636836\pi$
$14$	2.30986	0.617335
$15$	−0.759456	−0.196091
$16$	0.454235	0.113559
$17$	0.112289	0.0272342	0.0136171	−	0.999907i	$-0.495665\pi$
$17$	0.112289	0.0272342	0.0136171	+	0.999907i	$0.495665\pi$
$18$	0.728449	0.171697
$19$	1.40893	0.323231	0.161616	−	0.986854i	$-0.448330\pi$
$19$	1.40893	0.323231	0.161616	+	0.986854i	$0.448330\pi$
$20$	−1.54601	−0.345698
$21$	−1.63849	−0.357547
$22$	7.64978	1.63094
$23$	−6.18250	−1.28914	−0.644570	−	0.764545i	$-0.722964\pi$
$23$	−6.18250	−1.28914	−0.644570	+	0.764545i	$0.722964\pi$
$24$	−5.05415	−1.03168
$25$	−4.78516	−0.957032
$26$	6.94187	1.36141
$27$	−5.43218	−1.04542
$28$	−3.33543	−0.630337
$29$	3.55266	0.659713	0.329857	−	0.944031i	$-0.393000\pi$
$29$	3.55266	0.659713	0.329857	+	0.944031i	$0.393000\pi$
$30$	1.75423	0.320278
$31$	−2.93704	−0.527508	−0.263754	−	0.964590i	$-0.584961\pi$
$31$	−2.93704	−0.527508	−0.263754	+	0.964590i	$0.584961\pi$
$32$	5.12008	0.905112
$33$	−5.42634	−0.944604
$34$	−0.259372	−0.0444820
$35$	0.463511	0.0783477
$36$	−1.05188	−0.175313
$37$	−7.33489	−1.20585	−0.602924	−	0.797799i	$-0.705998\pi$
$37$	−7.33489	−1.20585	−0.602924	+	0.797799i	$0.705998\pi$
$38$	−3.25443	−0.527938
$39$	−4.92419	−0.788501
$40$	1.42977	0.226066
$41$	−0.531021	−0.0829316	−0.0414658	−	0.999140i	$-0.513203\pi$
$41$	−0.531021	−0.0829316	−0.0414658	+	0.999140i	$0.513203\pi$
$42$	3.78466	0.583986
$43$	7.95648	1.21335	0.606676	−	0.794949i	$-0.292503\pi$
$43$	7.95648	1.21335	0.606676	+	0.794949i	$0.292503\pi$
$44$	−11.0463	−1.66529
$45$	0.146175	0.0217905
$46$	14.2807	2.10557
$47$	11.1201	1.62203	0.811013	−	0.585028i	$-0.198916\pi$
$47$	11.1201	1.62203	0.811013	+	0.585028i	$0.198916\pi$
$48$	0.744257	0.107424
$49$	1.00000	0.142857
$50$	11.0530	1.56313
$51$	0.183985	0.0257630
$52$	−10.0241	−1.39009
$53$	−4.39660	−0.603920	−0.301960	−	0.953321i	$-0.597641\pi$
$53$	−4.39660	−0.603920	−0.301960	+	0.953321i	$0.597641\pi$
$54$	12.5475	1.70750
$55$	1.53506	0.206987
$56$	3.08465	0.412204
$57$	2.30851	0.305770
$58$	−8.20614	−1.07752
$59$	−3.52462	−0.458866	−0.229433	−	0.973324i	$-0.573687\pi$
$59$	−3.52462	−0.458866	−0.229433	+	0.973324i	$0.573687\pi$
$60$	−2.53311	−0.327023
$61$	4.54489	0.581914	0.290957	−	0.956736i	$-0.406026\pi$
$61$	4.54489	0.581914	0.290957	+	0.956736i	$0.406026\pi$
$62$	6.78414	0.861587
$63$	0.315366	0.0397323
$64$	−12.7351	−1.59189
$65$	1.39300	0.172781
$66$	12.5341	1.54284
$67$	−1.49310	−0.182411	−0.0912054	−	0.995832i	$-0.529072\pi$
$67$	−1.49310	−0.182411	−0.0912054	+	0.995832i	$0.529072\pi$
$68$	0.374534	0.0454189
$69$	−10.1299	−1.21950
$70$	−1.07064	−0.127966
$71$	−7.93773	−0.942035	−0.471018	−	0.882124i	$-0.656113\pi$
$71$	−7.93773	−0.942035	−0.471018	+	0.882124i	$0.656113\pi$
$72$	0.972793	0.114645
$73$	−0.359105	−0.0420301	−0.0210151	−	0.999779i	$-0.506690\pi$
$73$	−0.359105	−0.0420301	−0.0210151	+	0.999779i	$0.506690\pi$
$74$	16.9425	1.96953
$75$	−7.84041	−0.905333
$76$	4.69939	0.539057
$77$	3.31180	0.377415
$78$	11.3742	1.28787
$79$	8.17057	0.919261	0.459631	−	0.888110i	$-0.347982\pi$
$79$	8.17057	0.919261	0.459631	+	0.888110i	$0.347982\pi$
$80$	−0.210543	−0.0235394
$81$	−7.95445	−0.883828
$82$	1.22658	0.135453
$83$	2.45799	0.269799	0.134900	−	0.990859i	$-0.456929\pi$
$83$	2.45799	0.269799	0.134900	+	0.990859i	$0.456929\pi$
$84$	−5.46505	−0.596286
$85$	−0.0520474	−0.00564533
$86$	−18.3783	−1.98179
$87$	5.82099	0.624075
$88$	10.2157	1.08900
$89$	10.1190	1.07261	0.536305	−	0.844024i	$-0.319820\pi$
$89$	10.1190	1.07261	0.536305	+	0.844024i	$0.319820\pi$
$90$	−0.337644	−0.0355908
$91$	3.00533	0.315044
$92$	−20.6213	−2.14992
$93$	−4.81230	−0.499012
$94$	−25.6857	−2.64928
$95$	−0.653055	−0.0670020
$96$	8.38918	0.856217
$97$	5.29876	0.538008	0.269004	−	0.963139i	$-0.413306\pi$
$97$	5.29876	0.538008	0.269004	+	0.963139i	$0.413306\pi$
$98$	−2.30986	−0.233331
$99$	1.04443	0.104969
$100$	−15.9606	−1.59606
$101$	−4.47511	−0.445290	−0.222645	−	0.974900i	$-0.571469\pi$
$101$	−4.47511	−0.445290	−0.222645	+	0.974900i	$0.571469\pi$
$102$	−0.424978	−0.0420791
$103$	−5.73357	−0.564946	−0.282473	−	0.959275i	$-0.591155\pi$
$103$	−5.73357	−0.564946	−0.282473	+	0.959275i	$0.591155\pi$
$104$	9.27039	0.909036
$105$	0.759456	0.0741153
$106$	10.1555	0.986391
$107$	7.89299	0.763044	0.381522	−	0.924360i	$-0.375400\pi$
$107$	7.89299	0.763044	0.381522	+	0.924360i	$0.375400\pi$
$108$	−18.1187	−1.74347
$109$	0.486312	0.0465802	0.0232901	−	0.999729i	$-0.492586\pi$
$109$	0.486312	0.0465802	0.0232901	+	0.999729i	$0.492586\pi$
$110$	−3.54576	−0.338075
$111$	−12.0181	−1.14071
$112$	−0.454235	−0.0429212
$113$	15.7326	1.48000	0.740000	−	0.672607i	$-0.234825\pi$
$113$	15.7326	1.48000	0.740000	+	0.672607i	$0.234825\pi$
$114$	−5.33233	−0.499419
$115$	2.86566	0.267224
$116$	11.8497	1.10021
$117$	0.947777	0.0876220
$118$	8.14136	0.749473
$119$	−0.112289	−0.0102936
$120$	2.34266	0.213854
$121$	−0.0319782	−0.00290711
$122$	−10.4980	−0.950448
$123$	−0.870071	−0.0784516
$124$	−9.79630	−0.879734
$125$	4.53553	0.405670
$126$	−0.728449	−0.0648954
$127$	−9.87026	−0.875844	−0.437922	−	0.899013i	$-0.644285\pi$
$127$	−9.87026	−0.875844	−0.437922	+	0.899013i	$0.644285\pi$
$128$	19.1761	1.69495
$129$	13.0366	1.14781
$130$	−3.21763	−0.282205
$131$	−11.1886	−0.977556	−0.488778	−	0.872408i	$-0.662557\pi$
$131$	−11.1886	−0.977556	−0.488778	+	0.872408i	$0.662557\pi$
$132$	−18.0992	−1.57533
$133$	−1.40893	−0.122170
$134$	3.44884	0.297934
$135$	2.51787	0.216704
$136$	−0.346374	−0.0297013
$137$	18.9964	1.62297	0.811487	−	0.584371i	$-0.198659\pi$
$137$	18.9964	1.62297	0.811487	+	0.584371i	$0.198659\pi$
$138$	23.3987	1.99183
$139$	18.2226	1.54562	0.772810	−	0.634638i	$-0.218851\pi$
$139$	18.2226	1.54562	0.772810	+	0.634638i	$0.218851\pi$
$140$	1.54601	0.130662
$141$	18.2200	1.53440
$142$	18.3350	1.53864
$143$	9.95305	0.832315
$144$	−0.143250	−0.0119375
$145$	−1.64670	−0.136751
$146$	0.829481	0.0686484
$147$	1.63849	0.135140
$148$	−24.4650	−2.01101
$149$	0.957656	0.0784542	0.0392271	−	0.999230i	$-0.487510\pi$
$149$	0.957656	0.0784542	0.0392271	+	0.999230i	$0.487510\pi$
$150$	18.1102	1.47869
$151$	−12.1112	−0.985596	−0.492798	−	0.870144i	$-0.664026\pi$
$151$	−12.1112	−0.985596	−0.492798	+	0.870144i	$0.664026\pi$
$152$	−4.34606	−0.352512
$153$	−0.0354122	−0.00286291
$154$	−7.64978	−0.616437
$155$	1.36135	0.109346
$156$	−16.4243	−1.31499
$157$	18.6847	1.49120	0.745602	−	0.666391i	$-0.232162\pi$
$157$	18.6847	1.49120	0.745602	+	0.666391i	$0.232162\pi$
$158$	−18.8728	−1.50144
$159$	−7.20377	−0.571296
$160$	−2.37322	−0.187619
$161$	6.18250	0.487249
$162$	18.3736	1.44357
$163$	−21.3242	−1.67024	−0.835119	−	0.550069i	$-0.814601\pi$
$163$	−21.3242	−1.67024	−0.835119	+	0.550069i	$0.814601\pi$
$164$	−1.77119	−0.138306
$165$	2.51517	0.195805
$166$	−5.67759	−0.440667
$167$	21.5569	1.66812	0.834061	−	0.551672i	$-0.186010\pi$
$167$	21.5569	1.66812	0.834061	+	0.551672i	$0.186010\pi$
$168$	5.05415	0.389937
$169$	−3.96801	−0.305231
$170$	0.120222	0.00922060
$171$	−0.444329	−0.0339787
$172$	26.5383	2.02353
$173$	−11.5755	−0.880067	−0.440033	−	0.897981i	$-0.645033\pi$
$173$	−11.5755	−0.880067	−0.440033	+	0.897981i	$0.645033\pi$
$174$	−13.4456	−1.01931
$175$	4.78516	0.361724
$176$	−1.50434	−0.113394
$177$	−5.77503	−0.434078
$178$	−23.3734	−1.75191
$179$	21.9629	1.64159	0.820793	−	0.571226i	$-0.193532\pi$
$179$	21.9629	1.64159	0.820793	+	0.571226i	$0.193532\pi$
$180$	0.487558	0.0363404
$181$	0.0260766	0.00193826	0.000969128	−	1.00000i	$-0.499692\pi$
$181$	0.0260766	0.00193826	0.000969128		1.00000i	$0.499692\pi$
$182$	−6.94187	−0.514566
$183$	7.44674	0.550479
$184$	19.0709	1.40592
$185$	3.39980	0.249958
$186$	11.1157	0.815044
$187$	−0.371880	−0.0271946
$188$	37.0902	2.70508
$189$	5.43218	0.395133
$190$	1.50846	0.109435
$191$	−1.22735	−0.0888082	−0.0444041	−	0.999014i	$-0.514139\pi$
$191$	−1.22735	−0.0888082	−0.0444041	+	0.999014i	$0.514139\pi$
$192$	−20.8663	−1.50590
$193$	−12.1425	−0.874038	−0.437019	−	0.899452i	$-0.643966\pi$
$193$	−12.1425	−0.874038	−0.437019	+	0.899452i	$0.643966\pi$
$194$	−12.2394	−0.878736
$195$	2.28241	0.163447
$196$	3.33543	0.238245
$197$	18.5659	1.32276	0.661381	−	0.750050i	$-0.269970\pi$
$197$	18.5659	1.32276	0.661381	+	0.750050i	$0.269970\pi$
$198$	−2.41248	−0.171447
$199$	11.8856	0.842547	0.421274	−	0.906934i	$-0.361583\pi$
$199$	11.8856	0.842547	0.421274	+	0.906934i	$0.361583\pi$
$200$	14.7605	1.04373
$201$	−2.44642	−0.172557
$202$	10.3369	0.727298
$203$	−3.55266	−0.249348
$204$	0.613668	0.0429653
$205$	0.246134	0.0171908
$206$	13.2437	0.922734
$207$	1.94975	0.135517
$208$	−1.36513	−0.0946544
$209$	−4.66610	−0.322761
$210$	−1.75423	−0.121054
$211$	11.2167	0.772192	0.386096	−	0.922459i	$-0.373823\pi$
$211$	11.2167	0.772192	0.386096	+	0.922459i	$0.373823\pi$
$212$	−14.6646	−1.00717
$213$	−13.0059	−0.891147
$214$	−18.2317	−1.24629
$215$	−3.68792	−0.251514
$216$	16.7564	1.14013
$217$	2.93704	0.199379
$218$	−1.12331	−0.0760801
$219$	−0.588389	−0.0397596
$220$	5.12007	0.345195
$221$	−0.337467	−0.0227005
$222$	27.7601	1.86313
$223$	7.76639	0.520076	0.260038	−	0.965598i	$-0.416265\pi$
$223$	7.76639	0.520076	0.260038	+	0.965598i	$0.416265\pi$
$224$	−5.12008	−0.342100
$225$	1.50907	0.100605
$226$	−36.3401	−2.41731
$227$	−0.146557	−0.00972734	−0.00486367	−	0.999988i	$-0.501548\pi$
$227$	−0.146557	−0.00972734	−0.00486367	+	0.999988i	$0.501548\pi$
$228$	7.69989	0.509937
$229$	17.8070	1.17672	0.588360	−	0.808599i	$-0.299774\pi$
$229$	17.8070	1.17672	0.588360	+	0.808599i	$0.299774\pi$
$230$	−6.61925	−0.436460
$231$	5.42634	0.357027
$232$	−10.9587	−0.719476
$233$	14.5880	0.955692	0.477846	−	0.878444i	$-0.341418\pi$
$233$	14.5880	0.955692	0.477846	+	0.878444i	$0.341418\pi$
$234$	−2.18923	−0.143114
$235$	−5.15427	−0.336227
$236$	−11.7561	−0.765258
$237$	13.3874	0.869603
$238$	0.259372	0.0168126
$239$	0.147144	0.00951797	0.00475898	−	0.999989i	$-0.498485\pi$
$239$	0.147144	0.00951797	0.00475898	+	0.999989i	$0.498485\pi$
$240$	−0.344971	−0.0222678
$241$	1.12277	0.0723242	0.0361621	−	0.999346i	$-0.488487\pi$
$241$	1.12277	0.0723242	0.0361621	+	0.999346i	$0.488487\pi$
$242$	0.0738650	0.00474822
$243$	3.26329	0.209340
$244$	15.1592	0.970467
$245$	−0.463511	−0.0296126
$246$	2.00974	0.128136
$247$	−4.23430	−0.269422
$248$	9.05975	0.575295
$249$	4.02738	0.255225
$250$	−10.4764	−0.662586
$251$	−1.90173	−0.120036	−0.0600182	−	0.998197i	$-0.519116\pi$
$251$	−1.90173	−0.120036	−0.0600182	+	0.998197i	$0.519116\pi$
$252$	1.05188	0.0662622
$253$	20.4752	1.28727
$254$	22.7989	1.43053
$255$	−0.0852789	−0.00534037
$256$	−18.8238	−1.17649
$257$	−17.6756	−1.10258	−0.551288	−	0.834315i	$-0.685863\pi$
$257$	−17.6756	−1.10258	−0.551288	+	0.834315i	$0.685863\pi$
$258$	−30.1126	−1.87473
$259$	7.33489	0.455768
$260$	4.64626	0.288149
$261$	−1.12039	−0.0693503
$262$	25.8441	1.59666
$263$	6.93679	0.427741	0.213870	−	0.976862i	$-0.431393\pi$
$263$	6.93679	0.427741	0.213870	+	0.976862i	$0.431393\pi$
$264$	16.7384	1.03017
$265$	2.03787	0.125186
$266$	3.25443	0.199542
$267$	16.5798	1.01467
$268$	−4.98012	−0.304209
$269$	8.06976	0.492022	0.246011	−	0.969267i	$-0.420880\pi$
$269$	8.06976	0.492022	0.246011	+	0.969267i	$0.420880\pi$
$270$	−5.81592	−0.353946
$271$	−0.000584988 0	−3.55355e−5 0	−1.77678e−5	−	1.00000i	$-0.500006\pi$
$271$	−0.000584988 0	−3.55355e−5 0	−1.77678e−5		1.00000i	$0.500006\pi$
$272$	0.0510058	0.00309268
$273$	4.92419	0.298025
$274$	−43.8790	−2.65083
$275$	15.8475	0.955639
$276$	−33.7877	−2.03378
$277$	−29.4649	−1.77037	−0.885186	−	0.465238i	$-0.845969\pi$
$277$	−29.4649	−1.77037	−0.885186	+	0.465238i	$0.845969\pi$
$278$	−42.0915	−2.52448
$279$	0.926242	0.0554527
$280$	−1.42977	−0.0854451
$281$	−6.03978	−0.360303	−0.180152	−	0.983639i	$-0.557659\pi$
$281$	−6.03978	−0.360303	−0.180152	+	0.983639i	$0.557659\pi$
$282$	−42.0857	−2.50616
$283$	−26.5565	−1.57862	−0.789310	−	0.613995i	$-0.789562\pi$
$283$	−26.5565	−1.57862	−0.789310	+	0.613995i	$0.789562\pi$
$284$	−26.4758	−1.57105
$285$	−1.07002	−0.0633826
$286$	−22.9901	−1.35943
$287$	0.531021	0.0313452
$288$	−1.61470	−0.0951470
$289$	−16.9874	−0.999258
$290$	3.80364	0.223357
$291$	8.68194	0.508945
$292$	−1.19777	−0.0700942
$293$	27.6055	1.61273	0.806365	−	0.591418i	$-0.201432\pi$
$293$	27.6055	1.61273	0.806365	+	0.591418i	$0.201432\pi$
$294$	−3.78466	−0.220726
$295$	1.63370	0.0951176
$296$	22.6256	1.31508
$297$	17.9903	1.04390
$298$	−2.21205	−0.128140
$299$	18.5804	1.07453
$300$	−26.1511	−1.50984
$301$	−7.95648	−0.458604
$302$	27.9751	1.60979
$303$	−7.33240	−0.421235
$304$	0.639986	0.0367057
$305$	−2.10661	−0.120624
$306$	0.0817971	0.00467603
$307$	16.9833	0.969290	0.484645	−	0.874711i	$-0.338949\pi$
$307$	16.9833	0.969290	0.484645	+	0.874711i	$0.338949\pi$
$308$	11.0463	0.629420
$309$	−9.39437	−0.534427
$310$	−3.14452	−0.178597
$311$	−7.75071	−0.439503	−0.219751	−	0.975556i	$-0.570525\pi$
$311$	−7.75071	−0.439503	−0.219751	+	0.975556i	$0.570525\pi$
$312$	15.1894	0.859930
$313$	−13.0602	−0.738207	−0.369103	−	0.929388i	$-0.620335\pi$
$313$	−13.0602	−0.738207	−0.369103	+	0.929388i	$0.620335\pi$
$314$	−43.1590	−2.43560
$315$	−0.146175	−0.00823605
$316$	27.2524	1.53307
$317$	−28.8896	−1.62260	−0.811302	−	0.584627i	$-0.801241\pi$
$317$	−28.8896	−1.62260	−0.811302	+	0.584627i	$0.801241\pi$
$318$	16.6397	0.933106
$319$	−11.7657	−0.658753
$320$	5.90287	0.329980
$321$	12.9325	0.721824
$322$	−14.2807	−0.795831
$323$	0.158208	0.00880294
$324$	−26.5315	−1.47397
$325$	14.3810	0.797712
$326$	49.2558	2.72802
$327$	0.796815	0.0440640
$328$	1.63802	0.0904443
$329$	−11.1201	−0.613068
$330$	−5.80967	−0.319812
$331$	1.61751	0.0889063	0.0444532	−	0.999011i	$-0.485845\pi$
$331$	1.61751	0.0889063	0.0444532	+	0.999011i	$0.485845\pi$
$332$	8.19845	0.449948
$333$	2.31317	0.126761
$334$	−49.7933	−2.72457
$335$	0.692067	0.0378117
$336$	−0.744257	−0.0406026
$337$	22.5852	1.23029	0.615147	−	0.788412i	$-0.289097\pi$
$337$	22.5852	1.23029	0.615147	+	0.788412i	$0.289097\pi$
$338$	9.16552	0.498538
$339$	25.7777	1.40005
$340$	−0.173600	−0.00941481
$341$	9.72690	0.526741
$342$	1.02633	0.0554978
$343$	−1.00000	−0.0539949
$344$	−24.5430	−1.32327
$345$	4.69534	0.252788
$346$	26.7377	1.43743
$347$	−3.47771	−0.186693	−0.0933467	−	0.995634i	$-0.529756\pi$
$347$	−3.47771	−0.186693	−0.0933467	+	0.995634i	$0.529756\pi$
$348$	19.4155	1.04078
$349$	16.0357	0.858369	0.429185	−	0.903217i	$-0.358801\pi$
$349$	16.0357	0.858369	0.429185	+	0.903217i	$0.358801\pi$
$350$	−11.0530	−0.590809
$351$	16.3255	0.871389
$352$	−16.9567	−0.903795
$353$	27.9586	1.48809	0.744043	−	0.668132i	$-0.232906\pi$
$353$	27.9586	1.48809	0.744043	+	0.668132i	$0.232906\pi$
$354$	13.3395	0.708986
$355$	3.67923	0.195273
$356$	33.7511	1.78881
$357$	−0.183985	−0.00973750
$358$	−50.7311	−2.68122
$359$	−29.5567	−1.55994	−0.779971	−	0.625816i	$-0.784766\pi$
$359$	−29.5567	−1.55994	−0.779971	+	0.625816i	$0.784766\pi$
$360$	−0.450900	−0.0237645
$361$	−17.0149	−0.895522
$362$	−0.0602331	−0.00316578
$363$	−0.0523958	−0.00275007
$364$	10.0241	0.525404
$365$	0.166449	0.00871235
$366$	−17.2009	−0.899105
$367$	5.06139	0.264202	0.132101	−	0.991236i	$-0.457828\pi$
$367$	5.06139	0.264202	0.132101	+	0.991236i	$0.457828\pi$
$368$	−2.80831	−0.146393
$369$	0.167466	0.00871793
$370$	−7.85305	−0.408260
$371$	4.39660	0.228260
$372$	−16.0511	−0.832210
$373$	−16.2831	−0.843105	−0.421552	−	0.906804i	$-0.638515\pi$
$373$	−16.2831	−0.843105	−0.421552	+	0.906804i	$0.638515\pi$
$374$	0.858989	0.0444173
$375$	7.43140	0.383756
$376$	−34.3015	−1.76896
$377$	−10.6769	−0.549889
$378$	−12.5475	−0.645376
$379$	0.248217	0.0127500	0.00637502	−	0.999980i	$-0.497971\pi$
$379$	0.248217	0.0127500	0.00637502	+	0.999980i	$0.497971\pi$
$380$	−2.17822	−0.111740
$381$	−16.1723	−0.828531
$382$	2.83501	0.145052
$383$	34.9651	1.78664	0.893318	−	0.449425i	$-0.148371\pi$
$383$	34.9651	1.78664	0.893318	+	0.449425i	$0.148371\pi$
$384$	31.4198	1.60338
$385$	−1.53506	−0.0782337
$386$	28.0475	1.42758
$387$	−2.50920	−0.127550
$388$	17.6736	0.897244
$389$	−1.70763	−0.0865802	−0.0432901	−	0.999063i	$-0.513784\pi$
$389$	−1.70763	−0.0865802	−0.0432901	+	0.999063i	$0.513784\pi$
$390$	−5.27205	−0.266960
$391$	−0.694229	−0.0351087
$392$	−3.08465	−0.155798
$393$	−18.3324	−0.924749
$394$	−42.8844	−2.16049
$395$	−3.78715	−0.190552
$396$	3.48362	0.175058
$397$	−38.1548	−1.91493	−0.957467	−	0.288544i	$-0.906829\pi$
$397$	−38.1548	−1.91493	−0.957467	+	0.288544i	$0.906829\pi$
$398$	−27.4540	−1.37614
$399$	−2.30851	−0.115570
$400$	−2.17359	−0.108679
$401$	16.0923	0.803612	0.401806	−	0.915725i	$-0.368383\pi$
$401$	16.0923	0.803612	0.401806	+	0.915725i	$0.368383\pi$
$402$	5.65087	0.281840
$403$	8.82677	0.439693
$404$	−14.9264	−0.742617
$405$	3.68697	0.183207
$406$	8.20614	0.407264
$407$	24.2917	1.20409
$408$	−0.567528	−0.0280968
$409$	−10.0402	−0.496454	−0.248227	−	0.968702i	$-0.579848\pi$
$409$	−10.0402	−0.496454	−0.248227	+	0.968702i	$0.579848\pi$
$410$	−0.568534	−0.0280779
$411$	31.1254	1.53530
$412$	−19.1239	−0.942168
$413$	3.52462	0.173435
$414$	−4.50363	−0.221342
$415$	−1.13930	−0.0559262
$416$	−15.3875	−0.754436
$417$	29.8574	1.46212
$418$	10.7780	0.527170
$419$	26.4027	1.28986	0.644928	−	0.764243i	$-0.276887\pi$
$419$	26.4027	1.28986	0.644928	+	0.764243i	$0.276887\pi$
$420$	2.53311	0.123603
$421$	−6.19979	−0.302159	−0.151080	−	0.988522i	$-0.548275\pi$
$421$	−6.19979	−0.302159	−0.151080	+	0.988522i	$0.548275\pi$
$422$	−25.9091	−1.26123
$423$	−3.50688	−0.170510
$424$	13.5620	0.658628
$425$	−0.537323	−0.0260640
$426$	30.0416	1.45552
$427$	−4.54489	−0.219943
$428$	26.3265	1.27254
$429$	16.3079	0.787354
$430$	8.51855	0.410801
$431$	−1.43275	−0.0690134	−0.0345067	−	0.999404i	$-0.510986\pi$
$431$	−1.43275	−0.0690134	−0.0345067	+	0.999404i	$0.510986\pi$
$432$	−2.46749	−0.118717
$433$	−20.4985	−0.985096	−0.492548	−	0.870285i	$-0.663934\pi$
$433$	−20.4985	−0.985096	−0.492548	+	0.870285i	$0.663934\pi$
$434$	−6.78414	−0.325649
$435$	−2.69809	−0.129364
$436$	1.62206	0.0776825
$437$	−8.71072	−0.416690
$438$	1.35909	0.0649400
$439$	−34.0471	−1.62498	−0.812489	−	0.582977i	$-0.801888\pi$
$439$	−34.0471	−1.62498	−0.812489	+	0.582977i	$0.801888\pi$
$440$	−4.73511	−0.225738
$441$	−0.315366	−0.0150174
$442$	0.779499	0.0370770
$443$	7.32412	0.347980	0.173990	−	0.984747i	$-0.444334\pi$
$443$	7.32412	0.347980	0.173990	+	0.984747i	$0.444334\pi$
$444$	−40.0856	−1.90238
$445$	−4.69026	−0.222339
$446$	−17.9392	−0.849447
$447$	1.56911	0.0742161
$448$	12.7351	0.601678
$449$	11.9702	0.564909	0.282455	−	0.959281i	$-0.408851\pi$
$449$	11.9702	0.564909	0.282455	+	0.959281i	$0.408851\pi$
$450$	−3.48574	−0.164319
$451$	1.75864	0.0828110
$452$	52.4751	2.46822
$453$	−19.8440	−0.932354
$454$	0.338526	0.0158878
$455$	−1.39300	−0.0653050
$456$	−7.12096	−0.333469
$457$	1.37689	0.0644081	0.0322041	−	0.999481i	$-0.489747\pi$
$457$	1.37689	0.0644081	0.0322041	+	0.999481i	$0.489747\pi$
$458$	−41.1316	−1.92195
$459$	−0.609976	−0.0284713
$460$	9.55820	0.445653
$461$	0.456596	0.0212658	0.0106329	−	0.999943i	$-0.496615\pi$
$461$	0.456596	0.0212658	0.0106329	+	0.999943i	$0.496615\pi$
$462$	−12.5341	−0.583137
$463$	−35.2555	−1.63846	−0.819231	−	0.573464i	$-0.805599\pi$
$463$	−35.2555	−1.63846	−0.819231	+	0.573464i	$0.805599\pi$
$464$	1.61374	0.0749162
$465$	2.23055	0.103439
$466$	−33.6962	−1.56095
$467$	−5.35498	−0.247799	−0.123900	−	0.992295i	$-0.539540\pi$
$467$	−5.35498	−0.247799	−0.123900	+	0.992295i	$0.539540\pi$
$468$	3.16124	0.146129
$469$	1.49310	0.0689448
$470$	11.9056	0.549165
$471$	30.6147	1.41065
$472$	10.8722	0.500434
$473$	−26.3503	−1.21159
$474$	−30.9229	−1.42033
$475$	−6.74196	−0.309342
$476$	−0.374534	−0.0171667
$477$	1.38654	0.0634852
$478$	−0.339882	−0.0155458
$479$	−10.6913	−0.488498	−0.244249	−	0.969713i	$-0.578541\pi$
$479$	−10.6913	−0.488498	−0.244249	+	0.969713i	$0.578541\pi$
$480$	−3.88848	−0.177484
$481$	22.0437	1.00511
$482$	−2.59345	−0.118128
$483$	10.1299	0.460928
$484$	−0.106661	−0.00484823
$485$	−2.45603	−0.111523
$486$	−7.53772	−0.341918
$487$	25.2458	1.14399	0.571997	−	0.820256i	$-0.306169\pi$
$487$	25.2458	1.14399	0.571997	+	0.820256i	$0.306169\pi$
$488$	−14.0194	−0.634629
$489$	−34.9394	−1.58001
$490$	1.07064	0.0483667
$491$	−26.1240	−1.17896	−0.589479	−	0.807784i	$-0.700667\pi$
$491$	−26.1240	−1.17896	−0.589479	+	0.807784i	$0.700667\pi$
$492$	−2.90206	−0.130835
$493$	0.398927	0.0179668
$494$	9.78062	0.440051
$495$	−0.484104	−0.0217589
$496$	−1.33411	−0.0599032
$497$	7.93773	0.356056
$498$	−9.30266	−0.416862
$499$	−9.96128	−0.445928	−0.222964	−	0.974827i	$-0.571573\pi$
$499$	−9.96128	−0.445928	−0.222964	+	0.974827i	$0.571573\pi$
$500$	15.1279	0.676542
$501$	35.3206	1.57801
$502$	4.39273	0.196057
$503$	−15.1678	−0.676300	−0.338150	−	0.941092i	$-0.609801\pi$
$503$	−15.1678	−0.676300	−0.338150	+	0.941092i	$0.609801\pi$
$504$	−0.972793	−0.0433316
$505$	2.07426	0.0923034
$506$	−47.2948	−2.10251
$507$	−6.50152	−0.288743
$508$	−32.9216	−1.46066
$509$	−18.8495	−0.835489	−0.417744	−	0.908565i	$-0.637179\pi$
$509$	−18.8495	−0.835489	−0.417744	+	0.908565i	$0.637179\pi$
$510$	0.196982	0.00872250
$511$	0.359105	0.0158859
$512$	5.12803	0.226629
$513$	−7.65357	−0.337913
$514$	40.8282	1.80085
$515$	2.65757	0.117107
$516$	43.4826	1.91421
$517$	−36.8274	−1.61967
$518$	−16.9425	−0.744412
$519$	−18.9662	−0.832525
$520$	−4.29693	−0.188433
$521$	10.7834	0.472429	0.236215	−	0.971701i	$-0.424093\pi$
$521$	10.7834	0.472429	0.236215	+	0.971701i	$0.424093\pi$
$522$	2.58793	0.113271
$523$	34.3612	1.50251	0.751254	−	0.660013i	$-0.229449\pi$
$523$	34.3612	1.50251	0.751254	+	0.660013i	$0.229449\pi$
$524$	−37.3189	−1.63029
$525$	7.84041	0.342184
$526$	−16.0230	−0.698635
$527$	−0.329799	−0.0143663
$528$	−2.46483	−0.107268
$529$	15.2233	0.661883
$530$	−4.70719	−0.204467
$531$	1.11154	0.0482369
$532$	−4.69939	−0.203744
$533$	1.59589	0.0691258
$534$	−38.2969	−1.65727
$535$	−3.65849	−0.158170
$536$	4.60568	0.198935
$537$	35.9859	1.55291
$538$	−18.6400	−0.803627
$539$	−3.31180	−0.142649
$540$	8.39819	0.361401
$541$	−11.2896	−0.485376	−0.242688	−	0.970104i	$-0.578029\pi$
$541$	−11.2896	−0.485376	−0.242688	+	0.970104i	$0.578029\pi$
$542$	0.00135124	5.80407e−5 0
$543$	0.0427261	0.00183355
$544$	0.574931	0.0246500
$545$	−0.225411	−0.00965554
$546$	−11.3742	−0.486769
$547$	3.45453	0.147705	0.0738525	−	0.997269i	$-0.476471\pi$
$547$	3.45453	0.147705	0.0738525	+	0.997269i	$0.476471\pi$
$548$	63.3612	2.70666
$549$	−1.43330	−0.0611719
$550$	−36.6054	−1.56086
$551$	5.00546	0.213240
$552$	31.2473	1.32997
$553$	−8.17057	−0.347448
$554$	68.0595	2.89157
$555$	5.57052	0.236456
$556$	60.7801	2.57765
$557$	11.7768	0.498998	0.249499	−	0.968375i	$-0.419734\pi$
$557$	11.7768	0.498998	0.249499	+	0.968375i	$0.419734\pi$
$558$	−2.13949	−0.0905716
$559$	−23.9118	−1.01136
$560$	0.210543	0.00889706
$561$	−0.609320	−0.0257255
$562$	13.9510	0.588488
$563$	14.8004	0.623761	0.311881	−	0.950121i	$-0.399041\pi$
$563$	14.8004	0.623761	0.311881	+	0.950121i	$0.399041\pi$
$564$	60.7717	2.55895
$565$	−7.29224	−0.306787
$566$	61.3417	2.57838
$567$	7.95445	0.334055
$568$	24.4851	1.02737
$569$	−17.6730	−0.740893	−0.370446	−	0.928854i	$-0.620795\pi$
$569$	−17.6730	−0.740893	−0.370446	+	0.928854i	$0.620795\pi$
$570$	2.47159	0.103524
$571$	22.6576	0.948190	0.474095	−	0.880474i	$-0.342775\pi$
$571$	22.6576	0.948190	0.474095	+	0.880474i	$0.342775\pi$
$572$	33.1977	1.38807
$573$	−2.01100	−0.0840108
$574$	−1.22658	−0.0511966
$575$	29.5842	1.23375
$576$	4.01622	0.167342
$577$	−15.7199	−0.654429	−0.327214	−	0.944950i	$-0.606110\pi$
$577$	−15.7199	−0.654429	−0.327214	+	0.944950i	$0.606110\pi$
$578$	39.2384	1.63210
$579$	−19.8954	−0.826823
$580$	−5.49245	−0.228062
$581$	−2.45799	−0.101974
$582$	−20.0540	−0.831266
$583$	14.5607	0.603042
$584$	1.10771	0.0458376
$585$	−0.439305	−0.0181630
$586$	−63.7647	−2.63409
$587$	−32.3818	−1.33654	−0.668269	−	0.743919i	$-0.732965\pi$
$587$	−32.3818	−1.33654	−0.668269	+	0.743919i	$0.732965\pi$
$588$	5.46505	0.225375
$589$	−4.13809	−0.170507
$590$	−3.77361	−0.155357
$591$	30.4199	1.25131
$592$	−3.33176	−0.136935
$593$	39.4670	1.62072	0.810358	−	0.585935i	$-0.199273\pi$
$593$	39.4670	1.62072	0.810358	+	0.585935i	$0.199273\pi$
$594$	−41.5550	−1.70502
$595$	0.0520474	0.00213374
$596$	3.19420	0.130839
$597$	19.4744	0.797033
$598$	−42.9181	−1.75505
$599$	14.2349	0.581623	0.290812	−	0.956780i	$-0.406075\pi$
$599$	14.2349	0.581623	0.290812	+	0.956780i	$0.406075\pi$
$600$	24.1849	0.987346
$601$	−39.0882	−1.59444	−0.797220	−	0.603688i	$-0.793697\pi$
$601$	−39.0882	−1.59444	−0.797220	+	0.603688i	$0.793697\pi$
$602$	18.3783	0.749044
$603$	0.470872	0.0191754
$604$	−40.3961	−1.64369
$605$	0.0148223	0.000602610 0
$606$	16.9368	0.688010
$607$	30.5158	1.23860	0.619298	−	0.785156i	$-0.287417\pi$
$607$	30.5158	1.23860	0.619298	+	0.785156i	$0.287417\pi$
$608$	7.21385	0.292560
$609$	−5.82099	−0.235878
$610$	4.86596	0.197017
$611$	−33.4194	−1.35200
$612$	−0.118115	−0.00477452
$613$	−17.2507	−0.696750	−0.348375	−	0.937355i	$-0.613266\pi$
$613$	−17.2507	−0.696750	−0.348375	+	0.937355i	$0.613266\pi$
$614$	−39.2290	−1.58315
$615$	0.403287	0.0162621
$616$	−10.2157	−0.411604
$617$	2.81227	0.113218	0.0566088	−	0.998396i	$-0.481971\pi$
$617$	2.81227	0.113218	0.0566088	+	0.998396i	$0.481971\pi$
$618$	21.6996	0.872887
$619$	47.1012	1.89316	0.946578	−	0.322476i	$-0.104515\pi$
$619$	47.1012	1.89316	0.946578	+	0.322476i	$0.104515\pi$
$620$	4.54069	0.182359
$621$	33.5844	1.34770
$622$	17.9030	0.717846
$623$	−10.1190	−0.405408
$624$	−2.23674	−0.0895412
$625$	21.8235	0.872941
$626$	30.1672	1.20572
$627$	−7.64534	−0.305325
$628$	62.3216	2.48690
$629$	−0.823630	−0.0328403
$630$	0.337644	0.0134521
$631$	24.4629	0.973852	0.486926	−	0.873443i	$-0.338118\pi$
$631$	24.4629	0.973852	0.486926	+	0.873443i	$0.338118\pi$
$632$	−25.2034	−1.00254
$633$	18.3785	0.730479
$634$	66.7309	2.65022
$635$	4.57497	0.181552
$636$	−24.0277	−0.952760
$637$	−3.00533	−0.119075
$638$	27.1771	1.07595
$639$	2.50329	0.0990285
$640$	−8.88834	−0.351343
$641$	49.0353	1.93678	0.968388	−	0.249448i	$-0.0802493\pi$
$641$	49.0353	1.93678	0.968388	+	0.249448i	$0.0802493\pi$
$642$	−29.8723	−1.17897
$643$	26.8507	1.05889	0.529445	−	0.848344i	$-0.322400\pi$
$643$	26.8507	1.05889	0.529445	+	0.848344i	$0.322400\pi$
$644$	20.6213	0.812593
$645$	−6.04260	−0.237927
$646$	−0.365438	−0.0143780
$647$	−18.6730	−0.734110	−0.367055	−	0.930199i	$-0.619634\pi$
$647$	−18.6730	−0.734110	−0.367055	+	0.930199i	$0.619634\pi$
$648$	24.5367	0.963892
$649$	11.6728	0.458199
$650$	−33.2179	−1.30292
$651$	4.81230	0.188609
$652$	−71.1253	−2.78548
$653$	33.9626	1.32906	0.664531	−	0.747261i	$-0.268632\pi$
$653$	33.9626	1.32906	0.664531	+	0.747261i	$0.268632\pi$
$654$	−1.84053	−0.0719703
$655$	5.18606	0.202636
$656$	−0.241209	−0.00941761
$657$	0.113249	0.00441828
$658$	25.6857	1.00133
$659$	−26.2354	−1.02199	−0.510993	−	0.859585i	$-0.670722\pi$
$659$	−26.2354	−1.02199	−0.510993	+	0.859585i	$0.670722\pi$
$660$	8.38916	0.326548
$661$	28.3892	1.10421	0.552106	−	0.833774i	$-0.313824\pi$
$661$	28.3892	1.10421	0.552106	+	0.833774i	$0.313824\pi$
$662$	−3.73621	−0.145212
$663$	−0.552934	−0.0214742
$664$	−7.58203	−0.294240
$665$	0.653055	0.0253244
$666$	−5.34309	−0.207041
$667$	−21.9643	−0.850463
$668$	71.9015	2.78195
$669$	12.7251	0.491981
$670$	−1.59857	−0.0617583
$671$	−15.0518	−0.581068
$672$	−8.38918	−0.323620
$673$	36.4311	1.40432	0.702158	−	0.712022i	$-0.252220\pi$
$673$	36.4311	1.40432	0.702158	+	0.712022i	$0.252220\pi$
$674$	−52.1685	−2.00946
$675$	25.9938	1.00050
$676$	−13.2350	−0.509039
$677$	−30.7345	−1.18122	−0.590611	−	0.806956i	$-0.701113\pi$
$677$	−30.7345	−1.18122	−0.590611	+	0.806956i	$0.701113\pi$
$678$	−59.5427	−2.28672
$679$	−5.29876	−0.203348
$680$	0.160548	0.00615674
$681$	−0.240132	−0.00920187
$682$	−22.4677	−0.860334
$683$	−46.4985	−1.77922	−0.889608	−	0.456726i	$-0.849022\pi$
$683$	−46.4985	−1.77922	−0.889608	+	0.456726i	$0.849022\pi$
$684$	−1.48203	−0.0566667
$685$	−8.80505	−0.336424
$686$	2.30986	0.0881907
$687$	29.1765	1.11315
$688$	3.61411	0.137787
$689$	13.2132	0.503384
$690$	−10.8455	−0.412883
$691$	13.5955	0.517198	0.258599	−	0.965985i	$-0.416739\pi$
$691$	13.5955	0.517198	0.258599	+	0.965985i	$0.416739\pi$
$692$	−38.6092	−1.46770
$693$	−1.04443	−0.0396745
$694$	8.03301	0.304929
$695$	−8.44637	−0.320389
$696$	−17.9557	−0.680610
$697$	−0.0596281	−0.00225858
$698$	−37.0400	−1.40199
$699$	23.9022	0.904065
$700$	15.9606	0.603252
$701$	15.7676	0.595534	0.297767	−	0.954639i	$-0.403758\pi$
$701$	15.7676	0.595534	0.297767	+	0.954639i	$0.403758\pi$
$702$	−37.7095	−1.42325
$703$	−10.3344	−0.389767
$704$	42.1762	1.58957
$705$	−8.44519	−0.318064
$706$	−64.5803	−2.43051
$707$	4.47511	0.168304
$708$	−19.2622	−0.723919
$709$	40.7237	1.52941	0.764705	−	0.644380i	$-0.222885\pi$
$709$	40.7237	1.52941	0.764705	+	0.644380i	$0.222885\pi$
$710$	−8.49848	−0.318942
$711$	−2.57672	−0.0966344
$712$	−31.2135	−1.16978
$713$	18.1583	0.680032
$714$	0.424978	0.0159044
$715$	−4.61335	−0.172529
$716$	73.2558	2.73770
$717$	0.241094	0.00900381
$718$	68.2716	2.54787
$719$	−1.22551	−0.0457037	−0.0228519	−	0.999739i	$-0.507275\pi$
$719$	−1.22551	−0.0457037	−0.0228519	+	0.999739i	$0.507275\pi$
$720$	0.0663980	0.00247451
$721$	5.73357	0.213529
$722$	39.3020	1.46267
$723$	1.83965	0.0684173
$724$	0.0869766	0.00323246
$725$	−17.0001	−0.631366
$726$	0.121027	0.00449173
$727$	−3.36707	−0.124878	−0.0624389	−	0.998049i	$-0.519888\pi$
$727$	−3.36707	−0.124878	−0.0624389	+	0.998049i	$0.519888\pi$
$728$	−9.27039	−0.343583
$729$	29.2102	1.08186
$730$	−0.384474	−0.0142300
$731$	0.893429	0.0330447
$732$	24.8381	0.918042
$733$	−1.41424	−0.0522361	−0.0261181	−	0.999659i	$-0.508315\pi$
$733$	−1.41424	−0.0522361	−0.0261181	+	0.999659i	$0.508315\pi$
$734$	−11.6911	−0.431525
$735$	−0.759456	−0.0280130
$736$	−31.6549	−1.16682
$737$	4.94484	0.182146
$738$	−0.386822	−0.0142391
$739$	−23.9227	−0.880011	−0.440005	−	0.897995i	$-0.645023\pi$
$739$	−23.9227	−0.880011	−0.440005	+	0.897995i	$0.645023\pi$
$740$	11.3398	0.416859
$741$	−6.93784	−0.254868
$742$	−10.1555	−0.372821
$743$	42.5833	1.56223	0.781115	−	0.624387i	$-0.214651\pi$
$743$	42.5833	1.56223	0.781115	+	0.624387i	$0.214651\pi$
$744$	14.8443	0.544217
$745$	−0.443884	−0.0162627
$746$	37.6115	1.37706
$747$	−0.775165	−0.0283618
$748$	−1.24038	−0.0453528
$749$	−7.89299	−0.288403
$750$	−17.1654	−0.626794
$751$	10.1425	0.370106	0.185053	−	0.982729i	$-0.440754\pi$
$751$	10.1425	0.370106	0.185053	+	0.982729i	$0.440754\pi$
$752$	5.05112	0.184195
$753$	−3.11596	−0.113552
$754$	24.6621	0.898142
$755$	5.61368	0.204303
$756$	18.1187	0.658969
$757$	10.8065	0.392768	0.196384	−	0.980527i	$-0.437080\pi$
$757$	10.8065	0.392768	0.196384	+	0.980527i	$0.437080\pi$
$758$	−0.573344	−0.0208248
$759$	33.5483	1.21773
$760$	2.01445	0.0730717
$761$	27.9426	1.01292	0.506460	−	0.862264i	$-0.330954\pi$
$761$	27.9426	1.01292	0.506460	+	0.862264i	$0.330954\pi$
$762$	37.3556	1.35325
$763$	−0.486312	−0.0176057
$764$	−4.09375	−0.148107
$765$	0.0164140	0.000593448 0
$766$	−80.7644	−2.91814
$767$	10.5926	0.382478
$768$	−30.8425	−1.11293
$769$	8.71868	0.314404	0.157202	−	0.987566i	$-0.449753\pi$
$769$	8.71868	0.314404	0.157202	+	0.987566i	$0.449753\pi$
$770$	3.54576	0.127780
$771$	−28.9613	−1.04302
$772$	−40.5005	−1.45765
$773$	31.8830	1.14675	0.573375	−	0.819293i	$-0.305634\pi$
$773$	31.8830	1.14675	0.573375	+	0.819293i	$0.305634\pi$
$774$	5.79589	0.208329
$775$	14.0542	0.504842
$776$	−16.3448	−0.586745
$777$	12.0181	0.431147
$778$	3.94438	0.141413
$779$	−0.748173	−0.0268061
$780$	7.61283	0.272583
$781$	26.2882	0.940665
$782$	1.60357	0.0573435
$783$	−19.2987	−0.689679
$784$	0.454235	0.0162227
$785$	−8.66058	−0.309109
$786$	42.3453	1.51041
$787$	33.5360	1.19543	0.597715	−	0.801708i	$-0.296075\pi$
$787$	33.5360	1.19543	0.597715	+	0.801708i	$0.296075\pi$
$788$	61.9251	2.20599
$789$	11.3658	0.404634
$790$	8.74777	0.311232
$791$	−15.7326	−0.559388
$792$	−3.22170	−0.114478
$793$	−13.6589	−0.485042
$794$	88.1320	3.12769
$795$	3.33903	0.118423
$796$	39.6436	1.40513
$797$	36.8795	1.30634	0.653170	−	0.757211i	$-0.273439\pi$
$797$	36.8795	1.30634	0.653170	+	0.757211i	$0.273439\pi$
$798$	5.33233	0.188762
$799$	1.24866	0.0441746
$800$	−24.5004	−0.866220
$801$	−3.19118	−0.112755
$802$	−37.1709	−1.31255
$803$	1.18929	0.0419690
$804$	−8.15986	−0.287776
$805$	−2.86566	−0.101001
$806$	−20.3886	−0.718157
$807$	13.2222	0.465443
$808$	13.8041	0.485628
$809$	−33.0165	−1.16080	−0.580399	−	0.814332i	$-0.697103\pi$
$809$	−33.0165	−1.16080	−0.580399	+	0.814332i	$0.697103\pi$
$810$	−8.51638	−0.299235
$811$	21.2691	0.746859	0.373429	−	0.927659i	$-0.378182\pi$
$811$	21.2691	0.746859	0.373429	+	0.927659i	$0.378182\pi$
$812$	−11.8497	−0.415842
$813$	−0.000958495 0	−3.36159e−5 0
$814$	−56.1103	−1.96666
$815$	9.88399	0.346221
$816$	0.0835723	0.00292561
$817$	11.2101	0.392193
$818$	23.1913	0.810866
$819$	−0.947777	−0.0331180
$820$	0.820964	0.0286693
$821$	36.4194	1.27105	0.635523	−	0.772082i	$-0.280785\pi$
$821$	36.4194	1.27105	0.635523	+	0.772082i	$0.280785\pi$
$822$	−71.8951	−2.50763
$823$	24.8814	0.867312	0.433656	−	0.901078i	$-0.357223\pi$
$823$	24.8814	0.867312	0.433656	+	0.901078i	$0.357223\pi$
$824$	17.6861	0.616123
$825$	25.9659	0.904016
$826$	−8.14136	−0.283274
$827$	−10.5292	−0.366137	−0.183068	−	0.983100i	$-0.558603\pi$
$827$	−10.5292	−0.366137	−0.183068	+	0.983100i	$0.558603\pi$
$828$	6.50325	0.226003
$829$	−3.00729	−0.104447	−0.0522237	−	0.998635i	$-0.516631\pi$
$829$	−3.00729	−0.104447	−0.0522237	+	0.998635i	$0.516631\pi$
$830$	2.63163	0.0913451
$831$	−48.2777	−1.67474
$832$	38.2732	1.32689
$833$	0.112289	0.00389060
$834$	−68.9663	−2.38811
$835$	−9.99186	−0.345782
$836$	−15.5634	−0.538273
$837$	15.9545	0.551469
$838$	−60.9864	−2.10674
$839$	0.795370	0.0274592	0.0137296	−	0.999906i	$-0.495630\pi$
$839$	0.795370	0.0274592	0.0137296	+	0.999906i	$0.495630\pi$
$840$	−2.34266	−0.0808293
$841$	−16.3786	−0.564779
$842$	14.3206	0.493521
$843$	−9.89609	−0.340840
$844$	37.4127	1.28780
$845$	1.83921	0.0632709
$846$	8.10039	0.278497
$847$	0.0319782	0.00109878
$848$	−1.99709	−0.0685804
$849$	−43.5124	−1.49334
$850$	1.24114	0.0425707
$851$	45.3479	1.55451
$852$	−43.3801	−1.48618
$853$	32.3298	1.10695	0.553476	−	0.832865i	$-0.313301\pi$
$853$	32.3298	1.10695	0.553476	+	0.832865i	$0.313301\pi$
$854$	10.4980	0.359236
$855$	0.205951	0.00704338
$856$	−24.3471	−0.832167
$857$	−27.1178	−0.926326	−0.463163	−	0.886273i	$-0.653286\pi$
$857$	−27.1178	−0.926326	−0.463163	+	0.886273i	$0.653286\pi$
$858$	−37.6689	−1.28600
$859$	1.00000	0.0341196
$859$	1.00000	0.0341196
$860$	−12.3008	−0.419453
$861$	0.870071	0.0296519
$862$	3.30946	0.112721
$863$	−31.8138	−1.08295	−0.541476	−	0.840716i	$-0.682134\pi$
$863$	−31.8138	−1.08295	−0.541476	+	0.840716i	$0.682134\pi$
$864$	−27.8132	−0.946225
$865$	5.36536	0.182428
$866$	47.3486	1.60897
$867$	−27.8336	−0.945278
$868$	9.79630	0.332508
$869$	−27.0593	−0.917924
$870$	6.23220	0.211291
$871$	4.48725	0.152045
$872$	−1.50010	−0.0507999
$873$	−1.67105	−0.0565564
$874$	20.1205	0.680586
$875$	−4.53553	−0.153329
$876$	−1.96253	−0.0663077
$877$	−33.3615	−1.12654	−0.563269	−	0.826273i	$-0.690457\pi$
$877$	−33.3615	−1.12654	−0.563269	+	0.826273i	$0.690457\pi$
$878$	78.6438	2.65410
$879$	45.2312	1.52561
$880$	0.697276	0.0235052
$881$	42.8465	1.44354	0.721768	−	0.692135i	$-0.243330\pi$
$881$	42.8465	1.44354	0.721768	+	0.692135i	$0.243330\pi$
$882$	0.728449	0.0245282
$883$	9.68545	0.325941	0.162971	−	0.986631i	$-0.447892\pi$
$883$	9.68545	0.325941	0.162971	+	0.986631i	$0.447892\pi$
$884$	−1.12560	−0.0378579
$885$	2.67679	0.0899794
$886$	−16.9177	−0.568360
$887$	43.7699	1.46965	0.734825	−	0.678257i	$-0.237264\pi$
$887$	43.7699	1.46965	0.734825	+	0.678257i	$0.237264\pi$
$888$	37.0717	1.24404
$889$	9.87026	0.331038
$890$	10.8338	0.363150
$891$	26.3435	0.882542
$892$	25.9043	0.867338
$893$	15.6674	0.524289
$894$	−3.62441	−0.121218
$895$	−10.1801	−0.340282
$896$	−19.1761	−0.640629
$897$	30.4438	1.01649
$898$	−27.6495	−0.922674
$899$	−10.4343	−0.348004
$900$	5.03341	0.167780
$901$	−0.493692	−0.0164473
$902$	−4.06220	−0.135256
$903$	−13.0366	−0.433830
$904$	−48.5296	−1.61407
$905$	−0.0120868	−0.000401778 0
$906$	45.8369	1.52283
$907$	−27.8142	−0.923555	−0.461777	−	0.886996i	$-0.652788\pi$
$907$	−27.8142	−0.923555	−0.461777	+	0.886996i	$0.652788\pi$
$908$	−0.488831	−0.0162224
$909$	1.41130	0.0468097
$910$	3.21763	0.106664
$911$	−14.6180	−0.484315	−0.242158	−	0.970237i	$-0.577855\pi$
$911$	−14.6180	−0.484315	−0.242158	+	0.970237i	$0.577855\pi$
$912$	1.04861	0.0347229
$913$	−8.14036	−0.269407
$914$	−3.18041	−0.105199
$915$	−3.45165	−0.114108
$916$	59.3940	1.96243
$917$	11.1886	0.369482
$918$	1.40896	0.0465025
$919$	6.45187	0.212827	0.106414	−	0.994322i	$-0.466063\pi$
$919$	6.45187	0.212827	0.106414	+	0.994322i	$0.466063\pi$
$920$	−8.83955	−0.291431
$921$	27.8269	0.916928
$922$	−1.05467	−0.0347337
$923$	23.8555	0.785213
$924$	18.0992	0.595419
$925$	35.0986	1.15403
$926$	81.4351	2.67612
$927$	1.80817	0.0593881
$928$	18.1899	0.597114
$929$	−1.29950	−0.0426353	−0.0213177	−	0.999773i	$-0.506786\pi$
$929$	−1.29950	−0.0426353	−0.0213177	+	0.999773i	$0.506786\pi$
$930$	−5.15226	−0.168949
$931$	1.40893	0.0461759
$932$	48.6573	1.59382
$933$	−12.6994	−0.415761
$934$	12.3692	0.404734
$935$	0.172371	0.00563712
$936$	−2.92356	−0.0955596
$937$	1.91733	0.0626365	0.0313183	−	0.999509i	$-0.490029\pi$
$937$	1.91733	0.0626365	0.0313183	+	0.999509i	$0.490029\pi$
$938$	−3.44884	−0.112609
$939$	−21.3990	−0.698329
$940$	−17.1917	−0.560731
$941$	−1.80444	−0.0588230	−0.0294115	−	0.999567i	$-0.509363\pi$
$941$	−1.80444	−0.0588230	−0.0294115	+	0.999567i	$0.509363\pi$
$942$	−70.7154	−2.30403
$943$	3.28304	0.106910
$944$	−1.60100	−0.0521083
$945$	−2.51787	−0.0819065
$946$	60.8653	1.97890
$947$	16.3540	0.531434	0.265717	−	0.964051i	$-0.414391\pi$
$947$	16.3540	0.531434	0.265717	+	0.964051i	$0.414391\pi$
$948$	44.6526	1.45025
$949$	1.07923	0.0350333
$950$	15.5729	0.505253
$951$	−47.3353	−1.53495
$952$	0.346374	0.0112260
$953$	30.8309	0.998711	0.499355	−	0.866397i	$-0.333570\pi$
$953$	30.8309	0.998711	0.499355	+	0.866397i	$0.333570\pi$
$954$	−3.20270	−0.103691
$955$	0.568892	0.0184089
$956$	0.490789	0.0158733
$957$	−19.2779	−0.623168
$958$	24.6954	0.797871
$959$	−18.9964	−0.613426
$960$	9.67176	0.312155
$961$	−22.3738	−0.721735
$962$	−50.9178	−1.64166
$963$	−2.48918	−0.0802126
$964$	3.74494	0.120616
$965$	5.62819	0.181178
$966$	−23.3987	−0.752840
$967$	1.59032	0.0511412	0.0255706	−	0.999673i	$-0.491860\pi$
$967$	1.59032	0.0511412	0.0255706	+	0.999673i	$0.491860\pi$
$968$	0.0986416	0.00317046
$969$	0.259222	0.00832740
$970$	5.67308	0.182152
$971$	−29.7004	−0.953130	−0.476565	−	0.879139i	$-0.658118\pi$
$971$	−29.7004	−0.953130	−0.476565	+	0.879139i	$0.658118\pi$
$972$	10.8845	0.349120
$973$	−18.2226	−0.584189
$974$	−58.3140	−1.86850
$975$	23.5630	0.754620
$976$	2.06445	0.0660814
$977$	60.2229	1.92670	0.963351	−	0.268245i	$-0.0864437\pi$
$977$	60.2229	1.92670	0.963351	+	0.268245i	$0.0864437\pi$
$978$	80.7048	2.58066
$979$	−33.5120	−1.07105
$980$	−1.54601	−0.0493854
$981$	−0.153366	−0.00489660
$982$	60.3426	1.92561
$983$	32.9902	1.05222	0.526112	−	0.850415i	$-0.323649\pi$
$983$	32.9902	1.05222	0.526112	+	0.850415i	$0.323649\pi$
$984$	2.68386	0.0855585
$985$	−8.60548	−0.274193
$986$	−0.921463	−0.0293454
$987$	−18.2200	−0.579950
$988$	−14.1232	−0.449319
$989$	−49.1909	−1.56418
$990$	1.11821	0.0355390
$991$	51.8481	1.64701	0.823505	−	0.567309i	$-0.192015\pi$
$991$	51.8481	1.64701	0.823505	+	0.567309i	$0.192015\pi$
$992$	−15.0379	−0.477454
$993$	2.65026	0.0841036
$994$	−18.3350	−0.581551
$995$	−5.50910	−0.174650
$996$	13.4330	0.425642
$997$	−36.4501	−1.15439	−0.577193	−	0.816608i	$-0.695852\pi$
$997$	−36.4501	−1.15439	−0.577193	+	0.816608i	$0.695852\pi$
$998$	23.0091	0.728341
$999$	39.8444	1.26062

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6013.2.a.f.1.11	✓	110

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6013.2.a.f.1.11	✓	110	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:	\( N \)	\(=\)	\( 6013 = 7 \cdot 859 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6013.a (trivial)

\(f(q)\)	\(=\)	\(q-2.30986 q^{2} +1.63849 q^{3} +3.33543 q^{4} -0.463511 q^{5} -3.78466 q^{6} -1.00000 q^{7} -3.08465 q^{8} -0.315366 q^{9} +O(q^{10})\)	\(q-2.30986 q^{2} +1.63849 q^{3} +3.33543 q^{4} -0.463511 q^{5} -3.78466 q^{6} -1.00000 q^{7} -3.08465 q^{8} -0.315366 q^{9} +1.07064 q^{10} -3.31180 q^{11} +5.46505 q^{12} -3.00533 q^{13} +2.30986 q^{14} -0.759456 q^{15} +0.454235 q^{16} +0.112289 q^{17} +0.728449 q^{18} +1.40893 q^{19} -1.54601 q^{20} -1.63849 q^{21} +7.64978 q^{22} -6.18250 q^{23} -5.05415 q^{24} -4.78516 q^{25} +6.94187 q^{26} -5.43218 q^{27} -3.33543 q^{28} +3.55266 q^{29} +1.75423 q^{30} -2.93704 q^{31} +5.12008 q^{32} -5.42634 q^{33} -0.259372 q^{34} +0.463511 q^{35} -1.05188 q^{36} -7.33489 q^{37} -3.25443 q^{38} -4.92419 q^{39} +1.42977 q^{40} -0.531021 q^{41} +3.78466 q^{42} +7.95648 q^{43} -11.0463 q^{44} +0.146175 q^{45} +14.2807 q^{46} +11.1201 q^{47} +0.744257 q^{48} +1.00000 q^{49} +11.0530 q^{50} +0.183985 q^{51} -10.0241 q^{52} -4.39660 q^{53} +12.5475 q^{54} +1.53506 q^{55} +3.08465 q^{56} +2.30851 q^{57} -8.20614 q^{58} -3.52462 q^{59} -2.53311 q^{60} +4.54489 q^{61} +6.78414 q^{62} +0.315366 q^{63} -12.7351 q^{64} +1.39300 q^{65} +12.5341 q^{66} -1.49310 q^{67} +0.374534 q^{68} -10.1299 q^{69} -1.07064 q^{70} -7.93773 q^{71} +0.972793 q^{72} -0.359105 q^{73} +16.9425 q^{74} -7.84041 q^{75} +4.69939 q^{76} +3.31180 q^{77} +11.3742 q^{78} +8.17057 q^{79} -0.210543 q^{80} -7.95445 q^{81} +1.22658 q^{82} +2.45799 q^{83} -5.46505 q^{84} -0.0520474 q^{85} -18.3783 q^{86} +5.82099 q^{87} +10.2157 q^{88} +10.1190 q^{89} -0.337644 q^{90} +3.00533 q^{91} -20.6213 q^{92} -4.81230 q^{93} -25.6857 q^{94} -0.653055 q^{95} +8.38918 q^{96} +5.29876 q^{97} -2.30986 q^{98} +1.04443 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 110 q + 16 q^{2} + 29 q^{3} + 118 q^{4} + 12 q^{6} - 110 q^{7} + 57 q^{8} + 127 q^{9}+O(q^{10}) \) 110 * q + 16 * q^2 + 29 * q^3 + 118 * q^4 + 12 * q^6 - 110 * q^7 + 57 * q^8 + 127 * q^9	\( 110 q + 16 q^{2} + 29 q^{3} + 118 q^{4} + 12 q^{6} - 110 q^{7} + 57 q^{8} + 127 q^{9} + 3 q^{10} + 52 q^{11} + 62 q^{12} - 9 q^{13} - 16 q^{14} + 39 q^{15} + 146 q^{16} + 11 q^{17} + 60 q^{18} + 14 q^{19} + 18 q^{20} - 29 q^{21} + 32 q^{22} + 73 q^{23} + 24 q^{24} + 132 q^{25} - 7 q^{26} + 116 q^{27} - 118 q^{28} + 35 q^{29} + 18 q^{30} + 36 q^{31} + 140 q^{32} + 42 q^{33} - 7 q^{34} + 180 q^{36} + 49 q^{37} + 45 q^{39} + 6 q^{40} - 14 q^{41} - 12 q^{42} + 58 q^{43} + 92 q^{44} + 17 q^{45} + 27 q^{46} + 87 q^{47} + 98 q^{48} + 110 q^{49} + 91 q^{50} + 42 q^{51} + 16 q^{52} + 95 q^{53} + 41 q^{54} + 8 q^{55} - 57 q^{56} + 61 q^{57} + 46 q^{58} + 114 q^{59} + 81 q^{60} - 47 q^{61} + 31 q^{62} - 127 q^{63} + 199 q^{64} + 62 q^{65} + 21 q^{66} + 95 q^{67} + 60 q^{68} - 39 q^{69} - 3 q^{70} + 131 q^{71} + 186 q^{72} + 31 q^{73} + 23 q^{74} + 121 q^{75} + 14 q^{76} - 52 q^{77} + 110 q^{78} + 9 q^{79} + 61 q^{80} + 194 q^{81} + 45 q^{82} + 73 q^{83} - 62 q^{84} + 59 q^{85} + 72 q^{86} + 64 q^{87} + 100 q^{88} - 17 q^{89} + 11 q^{90} + 9 q^{91} + 192 q^{92} + 85 q^{93} - 11 q^{94} + 108 q^{95} + 68 q^{96} + 32 q^{97} + 16 q^{98} + 160 q^{99}+O(q^{100}) \) 110 * q + 16 * q^2 + 29 * q^3 + 118 * q^4 + 12 * q^6 - 110 * q^7 + 57 * q^8 + 127 * q^9 + 3 * q^10 + 52 * q^11 + 62 * q^12 - 9 * q^13 - 16 * q^14 + 39 * q^15 + 146 * q^16 + 11 * q^17 + 60 * q^18 + 14 * q^19 + 18 * q^20 - 29 * q^21 + 32 * q^22 + 73 * q^23 + 24 * q^24 + 132 * q^25 - 7 * q^26 + 116 * q^27 - 118 * q^28 + 35 * q^29 + 18 * q^30 + 36 * q^31 + 140 * q^32 + 42 * q^33 - 7 * q^34 + 180 * q^36 + 49 * q^37 + 45 * q^39 + 6 * q^40 - 14 * q^41 - 12 * q^42 + 58 * q^43 + 92 * q^44 + 17 * q^45 + 27 * q^46 + 87 * q^47 + 98 * q^48 + 110 * q^49 + 91 * q^50 + 42 * q^51 + 16 * q^52 + 95 * q^53 + 41 * q^54 + 8 * q^55 - 57 * q^56 + 61 * q^57 + 46 * q^58 + 114 * q^59 + 81 * q^60 - 47 * q^61 + 31 * q^62 - 127 * q^63 + 199 * q^64 + 62 * q^65 + 21 * q^66 + 95 * q^67 + 60 * q^68 - 39 * q^69 - 3 * q^70 + 131 * q^71 + 186 * q^72 + 31 * q^73 + 23 * q^74 + 121 * q^75 + 14 * q^76 - 52 * q^77 + 110 * q^78 + 9 * q^79 + 61 * q^80 + 194 * q^81 + 45 * q^82 + 73 * q^83 - 62 * q^84 + 59 * q^85 + 72 * q^86 + 64 * q^87 + 100 * q^88 - 17 * q^89 + 11 * q^90 + 9 * q^91 + 192 * q^92 + 85 * q^93 - 11 * q^94 + 108 * q^95 + 68 * q^96 + 32 * q^97 + 16 * q^98 + 160 * q^99

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