LMFDB - Embedded newform 6015.2.a.i.1.18

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6015,2,Mod(1,6015)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6015, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 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("6015.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6015 = 3 \cdot 5 \cdot 401 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6015.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:	$48.0300168158$
Analytic rank:	$0$
Dimension:	$43$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.18
Character	$\chi$	$=$	6015.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.497996 q^{2} +1.00000 q^{3} -1.75200 q^{4} +1.00000 q^{5} -0.497996 q^{6} +2.05942 q^{7} +1.86848 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-0.497996 q^{2} +1.00000 q^{3} -1.75200 q^{4} +1.00000 q^{5} -0.497996 q^{6} +2.05942 q^{7} +1.86848 q^{8} +1.00000 q^{9} -0.497996 q^{10} -6.46309 q^{11} -1.75200 q^{12} -3.17711 q^{13} -1.02558 q^{14} +1.00000 q^{15} +2.57351 q^{16} +7.02381 q^{17} -0.497996 q^{18} +5.83187 q^{19} -1.75200 q^{20} +2.05942 q^{21} +3.21859 q^{22} +8.58188 q^{23} +1.86848 q^{24} +1.00000 q^{25} +1.58219 q^{26} +1.00000 q^{27} -3.60811 q^{28} +9.02789 q^{29} -0.497996 q^{30} -4.74837 q^{31} -5.01855 q^{32} -6.46309 q^{33} -3.49783 q^{34} +2.05942 q^{35} -1.75200 q^{36} -11.2607 q^{37} -2.90425 q^{38} -3.17711 q^{39} +1.86848 q^{40} -9.13253 q^{41} -1.02558 q^{42} +8.04532 q^{43} +11.3233 q^{44} +1.00000 q^{45} -4.27374 q^{46} -6.35712 q^{47} +2.57351 q^{48} -2.75878 q^{49} -0.497996 q^{50} +7.02381 q^{51} +5.56629 q^{52} +2.51273 q^{53} -0.497996 q^{54} -6.46309 q^{55} +3.84799 q^{56} +5.83187 q^{57} -4.49585 q^{58} -9.93022 q^{59} -1.75200 q^{60} +6.89166 q^{61} +2.36467 q^{62} +2.05942 q^{63} -2.64780 q^{64} -3.17711 q^{65} +3.21859 q^{66} +12.4205 q^{67} -12.3057 q^{68} +8.58188 q^{69} -1.02558 q^{70} +4.23449 q^{71} +1.86848 q^{72} +2.54760 q^{73} +5.60780 q^{74} +1.00000 q^{75} -10.2174 q^{76} -13.3102 q^{77} +1.58219 q^{78} -11.4537 q^{79} +2.57351 q^{80} +1.00000 q^{81} +4.54796 q^{82} -10.7488 q^{83} -3.60811 q^{84} +7.02381 q^{85} -4.00653 q^{86} +9.02789 q^{87} -12.0762 q^{88} +9.77556 q^{89} -0.497996 q^{90} -6.54300 q^{91} -15.0355 q^{92} -4.74837 q^{93} +3.16582 q^{94} +5.83187 q^{95} -5.01855 q^{96} +8.63662 q^{97} +1.37386 q^{98} -6.46309 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 43 q + 3 q^{2} + 43 q^{3} + 61 q^{4} + 43 q^{5} + 3 q^{6} + 14 q^{7} + 18 q^{8} + 43 q^{9}+O(q^{10}) $ 43 * q + 3 * q^2 + 43 * q^3 + 61 * q^4 + 43 * q^5 + 3 * q^6 + 14 * q^7 + 18 * q^8 + 43 * q^9	\( 43 q + 3 q^{2} + 43 q^{3} + 61 q^{4} + 43 q^{5} + 3 q^{6} + 14 q^{7} + 18 q^{8} + 43 q^{9} + 3 q^{10} + 19 q^{11} + 61 q^{12} + 8 q^{13} + 6 q^{14} + 43 q^{15} + 85 q^{16} + 40 q^{17} + 3 q^{18} + 43 q^{19} + 61 q^{20} + 14 q^{21} + 19 q^{22} + 12 q^{23} + 18 q^{24} + 43 q^{25} + 43 q^{27} + 36 q^{28} + 41 q^{29} + 3 q^{30} + 33 q^{31} + 4 q^{32} + 19 q^{33} + 20 q^{34} + 14 q^{35} + 61 q^{36} + 12 q^{37} + 10 q^{38} + 8 q^{39} + 18 q^{40} + 47 q^{41} + 6 q^{42} + 73 q^{43} + 5 q^{44} + 43 q^{45} + 21 q^{46} + 32 q^{47} + 85 q^{48} + 87 q^{49} + 3 q^{50} + 40 q^{51} + 18 q^{52} + 17 q^{53} + 3 q^{54} + 19 q^{55} + 15 q^{56} + 43 q^{57} - 16 q^{58} + 21 q^{59} + 61 q^{60} + 77 q^{61} + 15 q^{62} + 14 q^{63} + 112 q^{64} + 8 q^{65} + 19 q^{66} + 26 q^{67} + 50 q^{68} + 12 q^{69} + 6 q^{70} + 2 q^{71} + 18 q^{72} + 49 q^{73} - 34 q^{74} + 43 q^{75} + 50 q^{76} - 2 q^{77} + 59 q^{79} + 85 q^{80} + 43 q^{81} - 45 q^{82} - 3 q^{83} + 36 q^{84} + 40 q^{85} - 35 q^{86} + 41 q^{87} - 13 q^{88} + 57 q^{89} + 3 q^{90} + 11 q^{91} - 9 q^{92} + 33 q^{93} + 52 q^{94} + 43 q^{95} + 4 q^{96} + 7 q^{97} - 32 q^{98} + 19 q^{99}+O(q^{100}) \) 43 * q + 3 * q^2 + 43 * q^3 + 61 * q^4 + 43 * q^5 + 3 * q^6 + 14 * q^7 + 18 * q^8 + 43 * q^9 + 3 * q^10 + 19 * q^11 + 61 * q^12 + 8 * q^13 + 6 * q^14 + 43 * q^15 + 85 * q^16 + 40 * q^17 + 3 * q^18 + 43 * q^19 + 61 * q^20 + 14 * q^21 + 19 * q^22 + 12 * q^23 + 18 * q^24 + 43 * q^25 + 43 * q^27 + 36 * q^28 + 41 * q^29 + 3 * q^30 + 33 * q^31 + 4 * q^32 + 19 * q^33 + 20 * q^34 + 14 * q^35 + 61 * q^36 + 12 * q^37 + 10 * q^38 + 8 * q^39 + 18 * q^40 + 47 * q^41 + 6 * q^42 + 73 * q^43 + 5 * q^44 + 43 * q^45 + 21 * q^46 + 32 * q^47 + 85 * q^48 + 87 * q^49 + 3 * q^50 + 40 * q^51 + 18 * q^52 + 17 * q^53 + 3 * q^54 + 19 * q^55 + 15 * q^56 + 43 * q^57 - 16 * q^58 + 21 * q^59 + 61 * q^60 + 77 * q^61 + 15 * q^62 + 14 * q^63 + 112 * q^64 + 8 * q^65 + 19 * q^66 + 26 * q^67 + 50 * q^68 + 12 * q^69 + 6 * q^70 + 2 * q^71 + 18 * q^72 + 49 * q^73 - 34 * q^74 + 43 * q^75 + 50 * q^76 - 2 * q^77 + 59 * q^79 + 85 * q^80 + 43 * q^81 - 45 * q^82 - 3 * q^83 + 36 * q^84 + 40 * q^85 - 35 * q^86 + 41 * q^87 - 13 * q^88 + 57 * q^89 + 3 * q^90 + 11 * q^91 - 9 * q^92 + 33 * q^93 + 52 * q^94 + 43 * q^95 + 4 * q^96 + 7 * q^97 - 32 * q^98 + 19 * 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 $

$2$	−0.497996	−0.352136	−0.176068	−	0.984378i	$-0.556338\pi$
$2$	−0.497996	−0.352136	−0.176068	+	0.984378i	$0.556338\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	−1.75200	−0.876000
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	−0.497996	−0.203306
$7$	2.05942	0.778388	0.389194	−	0.921156i	$-0.372753\pi$
$7$	2.05942	0.778388	0.389194	+	0.921156i	$0.372753\pi$
$8$	1.86848	0.660607
$9$	1.00000	0.333333
$10$	−0.497996	−0.157480
$11$	−6.46309	−1.94870	−0.974348	−	0.225047i	$-0.927746\pi$
$11$	−6.46309	−1.94870	−0.974348	+	0.225047i	$0.927746\pi$
$12$	−1.75200	−0.505759
$13$	−3.17711	−0.881171	−0.440585	−	0.897711i	$-0.645229\pi$
$13$	−3.17711	−0.881171	−0.440585	+	0.897711i	$0.645229\pi$
$14$	−1.02558	−0.274099
$15$	1.00000	0.258199
$16$	2.57351	0.643377
$17$	7.02381	1.70352	0.851762	−	0.523929i	$-0.175534\pi$
$17$	7.02381	1.70352	0.851762	+	0.523929i	$0.175534\pi$
$18$	−0.497996	−0.117379
$19$	5.83187	1.33792	0.668962	−	0.743297i	$-0.266739\pi$
$19$	5.83187	1.33792	0.668962	+	0.743297i	$0.266739\pi$
$20$	−1.75200	−0.391759
$21$	2.05942	0.449403
$22$	3.21859	0.686206
$23$	8.58188	1.78945	0.894723	−	0.446622i	$-0.147373\pi$
$23$	8.58188	1.78945	0.894723	+	0.446622i	$0.147373\pi$
$24$	1.86848	0.381402
$25$	1.00000	0.200000
$26$	1.58219	0.310292
$27$	1.00000	0.192450
$28$	−3.60811	−0.681868
$29$	9.02789	1.67644	0.838219	−	0.545334i	$-0.183597\pi$
$29$	9.02789	1.67644	0.838219	+	0.545334i	$0.183597\pi$
$30$	−0.497996	−0.0909211
$31$	−4.74837	−0.852832	−0.426416	−	0.904527i	$-0.640224\pi$
$31$	−4.74837	−0.852832	−0.426416	+	0.904527i	$0.640224\pi$
$32$	−5.01855	−0.887163
$33$	−6.46309	−1.12508
$34$	−3.49783	−0.599872
$35$	2.05942	0.348106
$36$	−1.75200	−0.292000
$37$	−11.2607	−1.85125	−0.925627	−	0.378437i	$-0.876462\pi$
$37$	−11.2607	−1.85125	−0.925627	+	0.378437i	$0.876462\pi$
$38$	−2.90425	−0.471131
$39$	−3.17711	−0.508744
$40$	1.86848	0.295433
$41$	−9.13253	−1.42626	−0.713131	−	0.701031i	$-0.752723\pi$
$41$	−9.13253	−1.42626	−0.713131	+	0.701031i	$0.752723\pi$
$42$	−1.02558	−0.158251
$43$	8.04532	1.22690	0.613450	−	0.789734i	$-0.289781\pi$
$43$	8.04532	1.22690	0.613450	+	0.789734i	$0.289781\pi$
$44$	11.3233	1.70706
$45$	1.00000	0.149071
$46$	−4.27374	−0.630128
$47$	−6.35712	−0.927281	−0.463641	−	0.886023i	$-0.653457\pi$
$47$	−6.35712	−0.927281	−0.463641	+	0.886023i	$0.653457\pi$
$48$	2.57351	0.371454
$49$	−2.75878	−0.394111
$50$	−0.497996	−0.0704272
$51$	7.02381	0.983530
$52$	5.56629	0.771906
$53$	2.51273	0.345150	0.172575	−	0.984996i	$-0.444791\pi$
$53$	2.51273	0.345150	0.172575	+	0.984996i	$0.444791\pi$
$54$	−0.497996	−0.0677686
$55$	−6.46309	−0.871483
$56$	3.84799	0.514209
$57$	5.83187	0.772450
$58$	−4.49585	−0.590334
$59$	−9.93022	−1.29280	−0.646402	−	0.762997i	$-0.723727\pi$
$59$	−9.93022	−1.29280	−0.646402	+	0.762997i	$0.723727\pi$
$60$	−1.75200	−0.226182
$61$	6.89166	0.882387	0.441193	−	0.897412i	$-0.354555\pi$
$61$	6.89166	0.882387	0.441193	+	0.897412i	$0.354555\pi$
$62$	2.36467	0.300313
$63$	2.05942	0.259463
$64$	−2.64780	−0.330974
$65$	−3.17711	−0.394072
$66$	3.21859	0.396181
$67$	12.4205	1.51740	0.758702	−	0.651437i	$-0.225834\pi$
$67$	12.4205	1.51740	0.758702	+	0.651437i	$0.225834\pi$
$68$	−12.3057	−1.49229
$69$	8.58188	1.03314
$70$	−1.02558	−0.122581
$71$	4.23449	0.502541	0.251270	−	0.967917i	$-0.419152\pi$
$71$	4.23449	0.502541	0.251270	+	0.967917i	$0.419152\pi$
$72$	1.86848	0.220202
$73$	2.54760	0.298175	0.149087	−	0.988824i	$-0.452366\pi$
$73$	2.54760	0.298175	0.149087	+	0.988824i	$0.452366\pi$
$74$	5.60780	0.651893
$75$	1.00000	0.115470
$76$	−10.2174	−1.17202
$77$	−13.3102	−1.51684
$78$	1.58219	0.179147
$79$	−11.4537	−1.28864	−0.644321	−	0.764755i	$-0.722860\pi$
$79$	−11.4537	−1.28864	−0.644321	+	0.764755i	$0.722860\pi$
$80$	2.57351	0.287727
$81$	1.00000	0.111111
$82$	4.54796	0.502238
$83$	−10.7488	−1.17983	−0.589914	−	0.807466i	$-0.700839\pi$
$83$	−10.7488	−1.17983	−0.589914	+	0.807466i	$0.700839\pi$
$84$	−3.60811	−0.393677
$85$	7.02381	0.761839
$86$	−4.00653	−0.432035
$87$	9.02789	0.967892
$88$	−12.0762	−1.28732
$89$	9.77556	1.03621	0.518104	−	0.855318i	$-0.326638\pi$
$89$	9.77556	1.03621	0.518104	+	0.855318i	$0.326638\pi$
$90$	−0.497996	−0.0524933
$91$	−6.54300	−0.685893
$92$	−15.0355	−1.56755
$93$	−4.74837	−0.492383
$94$	3.16582	0.326529
$95$	5.83187	0.598337
$96$	−5.01855	−0.512204
$97$	8.63662	0.876916	0.438458	−	0.898752i	$-0.355525\pi$
$97$	8.63662	0.876916	0.438458	+	0.898752i	$0.355525\pi$
$98$	1.37386	0.138781
$99$	−6.46309	−0.649565
$100$	−1.75200	−0.175200
$101$	−9.21375	−0.916802	−0.458401	−	0.888745i	$-0.651578\pi$
$101$	−9.21375	−0.916802	−0.458401	+	0.888745i	$0.651578\pi$
$102$	−3.49783	−0.346336
$103$	9.37257	0.923507	0.461753	−	0.887008i	$-0.347221\pi$
$103$	9.37257	0.923507	0.461753	+	0.887008i	$0.347221\pi$
$104$	−5.93636	−0.582108
$105$	2.05942	0.200979
$106$	−1.25133	−0.121540
$107$	16.2520	1.57114	0.785569	−	0.618774i	$-0.212370\pi$
$107$	16.2520	1.57114	0.785569	+	0.618774i	$0.212370\pi$
$108$	−1.75200	−0.168586
$109$	−17.4124	−1.66780	−0.833900	−	0.551915i	$-0.813897\pi$
$109$	−17.4124	−1.66780	−0.833900	+	0.551915i	$0.813897\pi$
$110$	3.21859	0.306881
$111$	−11.2607	−1.06882
$112$	5.29994	0.500797
$113$	10.4780	0.985690	0.492845	−	0.870117i	$-0.335957\pi$
$113$	10.4780	0.985690	0.492845	+	0.870117i	$0.335957\pi$
$114$	−2.90425	−0.272008
$115$	8.58188	0.800264
$116$	−15.8169	−1.46856
$117$	−3.17711	−0.293724
$118$	4.94521	0.455243
$119$	14.4650	1.32600
$120$	1.86848	0.170568
$121$	30.7716	2.79742
$122$	−3.43202	−0.310720
$123$	−9.13253	−0.823452
$124$	8.31914	0.747081
$125$	1.00000	0.0894427
$126$	−1.02558	−0.0913662
$127$	21.1367	1.87558	0.937790	−	0.347204i	$-0.112869\pi$
$127$	21.1367	1.87558	0.937790	+	0.347204i	$0.112869\pi$
$128$	11.3557	1.00371
$129$	8.04532	0.708351
$130$	1.58219	0.138767
$131$	3.12057	0.272645	0.136323	−	0.990664i	$-0.456472\pi$
$131$	3.12057	0.272645	0.136323	+	0.990664i	$0.456472\pi$
$132$	11.3233	0.985570
$133$	12.0103	1.04142
$134$	−6.18535	−0.534333
$135$	1.00000	0.0860663
$136$	13.1238	1.12536
$137$	7.11948	0.608258	0.304129	−	0.952631i	$-0.401635\pi$
$137$	7.11948	0.608258	0.304129	+	0.952631i	$0.401635\pi$
$138$	−4.27374	−0.363805
$139$	−0.883520	−0.0749392	−0.0374696	−	0.999298i	$-0.511930\pi$
$139$	−0.883520	−0.0749392	−0.0374696	+	0.999298i	$0.511930\pi$
$140$	−3.60811	−0.304941
$141$	−6.35712	−0.535366
$142$	−2.10876	−0.176963
$143$	20.5339	1.71713
$144$	2.57351	0.214459
$145$	9.02789	0.749726
$146$	−1.26870	−0.104998
$147$	−2.75878	−0.227540
$148$	19.7288	1.62170
$149$	1.44429	0.118321	0.0591606	−	0.998248i	$-0.481158\pi$
$149$	1.44429	0.118321	0.0591606	+	0.998248i	$0.481158\pi$
$150$	−0.497996	−0.0406612
$151$	−6.47849	−0.527212	−0.263606	−	0.964630i	$-0.584912\pi$
$151$	−6.47849	−0.527212	−0.263606	+	0.964630i	$0.584912\pi$
$152$	10.8967	0.883842
$153$	7.02381	0.567841
$154$	6.62844	0.534135
$155$	−4.74837	−0.381398
$156$	5.56629	0.445660
$157$	−8.97055	−0.715928	−0.357964	−	0.933735i	$-0.616529\pi$
$157$	−8.97055	−0.715928	−0.357964	+	0.933735i	$0.616529\pi$
$158$	5.70390	0.453778
$159$	2.51273	0.199272
$160$	−5.01855	−0.396752
$161$	17.6737	1.39288
$162$	−0.497996	−0.0391262
$163$	12.4303	0.973613	0.486806	−	0.873510i	$-0.338162\pi$
$163$	12.4303	0.973613	0.486806	+	0.873510i	$0.338162\pi$
$164$	16.0002	1.24941
$165$	−6.46309	−0.503151
$166$	5.35283	0.415460
$167$	11.1992	0.866620	0.433310	−	0.901245i	$-0.357346\pi$
$167$	11.1992	0.866620	0.433310	+	0.901245i	$0.357346\pi$
$168$	3.84799	0.296879
$169$	−2.90599	−0.223538
$170$	−3.49783	−0.268271
$171$	5.83187	0.445974
$172$	−14.0954	−1.07476
$173$	−3.74336	−0.284603	−0.142301	−	0.989823i	$-0.545450\pi$
$173$	−3.74336	−0.284603	−0.142301	+	0.989823i	$0.545450\pi$
$174$	−4.49585	−0.340829
$175$	2.05942	0.155678
$176$	−16.6328	−1.25375
$177$	−9.93022	−0.746401
$178$	−4.86819	−0.364886
$179$	−10.7983	−0.807100	−0.403550	−	0.914958i	$-0.632224\pi$
$179$	−10.7983	−0.807100	−0.403550	+	0.914958i	$0.632224\pi$
$180$	−1.75200	−0.130586
$181$	7.63533	0.567530	0.283765	−	0.958894i	$-0.408416\pi$
$181$	7.63533	0.567530	0.283765	+	0.958894i	$0.408416\pi$
$182$	3.25839	0.241528
$183$	6.89166	0.509446
$184$	16.0351	1.18212
$185$	−11.2607	−0.827906
$186$	2.36467	0.173386
$187$	−45.3955	−3.31965
$188$	11.1377	0.812299
$189$	2.05942	0.149801
$190$	−2.90425	−0.210696
$191$	−22.0450	−1.59512	−0.797560	−	0.603239i	$-0.793876\pi$
$191$	−22.0450	−1.59512	−0.797560	+	0.603239i	$0.793876\pi$
$192$	−2.64780	−0.191088
$193$	16.6492	1.19844	0.599220	−	0.800585i	$-0.295478\pi$
$193$	16.6492	1.19844	0.599220	+	0.800585i	$0.295478\pi$
$194$	−4.30100	−0.308794
$195$	−3.17711	−0.227517
$196$	4.83338	0.345242
$197$	13.5319	0.964111	0.482056	−	0.876141i	$-0.339890\pi$
$197$	13.5319	0.964111	0.482056	+	0.876141i	$0.339890\pi$
$198$	3.21859	0.228735
$199$	17.4047	1.23378	0.616892	−	0.787048i	$-0.288392\pi$
$199$	17.4047	1.23378	0.616892	+	0.787048i	$0.288392\pi$
$200$	1.86848	0.132121
$201$	12.4205	0.876074
$202$	4.58841	0.322839
$203$	18.5922	1.30492
$204$	−12.3057	−0.861573
$205$	−9.13253	−0.637844
$206$	−4.66750	−0.325200
$207$	8.58188	0.596482
$208$	−8.17630	−0.566925
$209$	−37.6919	−2.60721
$210$	−1.02558	−0.0707720
$211$	7.56372	0.520708	0.260354	−	0.965513i	$-0.416161\pi$
$211$	7.56372	0.520708	0.260354	+	0.965513i	$0.416161\pi$
$212$	−4.40230	−0.302351
$213$	4.23449	0.290142
$214$	−8.09342	−0.553255
$215$	8.04532	0.548686
$216$	1.86848	0.127134
$217$	−9.77890	−0.663835
$218$	8.67127	0.587293
$219$	2.54760	0.172151
$220$	11.3233	0.763419
$221$	−22.3154	−1.50110
$222$	5.60780	0.376371
$223$	−1.37065	−0.0917857	−0.0458928	−	0.998946i	$-0.514613\pi$
$223$	−1.37065	−0.0917857	−0.0458928	+	0.998946i	$0.514613\pi$
$224$	−10.3353	−0.690558
$225$	1.00000	0.0666667
$226$	−5.21801	−0.347097
$227$	16.5176	1.09631	0.548154	−	0.836377i	$-0.315331\pi$
$227$	16.5176	1.09631	0.548154	+	0.836377i	$0.315331\pi$
$228$	−10.2174	−0.676667
$229$	9.87952	0.652857	0.326428	−	0.945222i	$-0.394155\pi$
$229$	9.87952	0.652857	0.326428	+	0.945222i	$0.394155\pi$
$230$	−4.27374	−0.281802
$231$	−13.3102	−0.875749
$232$	16.8684	1.10747
$233$	−5.16405	−0.338308	−0.169154	−	0.985590i	$-0.554104\pi$
$233$	−5.16405	−0.338308	−0.169154	+	0.985590i	$0.554104\pi$
$234$	1.58219	0.103431
$235$	−6.35712	−0.414693
$236$	17.3978	1.13250
$237$	−11.4537	−0.743998
$238$	−7.20350	−0.466934
$239$	−14.7027	−0.951039	−0.475520	−	0.879705i	$-0.657740\pi$
$239$	−14.7027	−0.951039	−0.475520	+	0.879705i	$0.657740\pi$
$240$	2.57351	0.166119
$241$	−8.32849	−0.536485	−0.268242	−	0.963351i	$-0.586443\pi$
$241$	−8.32849	−0.536485	−0.268242	+	0.963351i	$0.586443\pi$
$242$	−15.3241	−0.985071
$243$	1.00000	0.0641500
$244$	−12.0742	−0.772971
$245$	−2.75878	−0.176252
$246$	4.54796	0.289967
$247$	−18.5285	−1.17894
$248$	−8.87223	−0.563387
$249$	−10.7488	−0.681174
$250$	−0.497996	−0.0314960
$251$	13.9925	0.883202	0.441601	−	0.897212i	$-0.354411\pi$
$251$	13.9925	0.883202	0.441601	+	0.897212i	$0.354411\pi$
$252$	−3.60811	−0.227289
$253$	−55.4655	−3.48709
$254$	−10.5260	−0.660459
$255$	7.02381	0.439848
$256$	−0.359497	−0.0224686
$257$	6.86632	0.428309	0.214155	−	0.976800i	$-0.431300\pi$
$257$	6.86632	0.428309	0.214155	+	0.976800i	$0.431300\pi$
$258$	−4.00653	−0.249436
$259$	−23.1906	−1.44100
$260$	5.56629	0.345207
$261$	9.02789	0.558812
$262$	−1.55403	−0.0960082
$263$	5.33516	0.328980	0.164490	−	0.986379i	$-0.447402\pi$
$263$	5.33516	0.328980	0.164490	+	0.986379i	$0.447402\pi$
$264$	−12.0762	−0.743236
$265$	2.51273	0.154356
$266$	−5.98107	−0.366723
$267$	9.77556	0.598255
$268$	−21.7607	−1.32925
$269$	−5.01704	−0.305894	−0.152947	−	0.988234i	$-0.548876\pi$
$269$	−5.01704	−0.305894	−0.152947	+	0.988234i	$0.548876\pi$
$270$	−0.497996	−0.0303070
$271$	26.6419	1.61838	0.809189	−	0.587549i	$-0.199907\pi$
$271$	26.6419	1.61838	0.809189	+	0.587549i	$0.199907\pi$
$272$	18.0758	1.09601
$273$	−6.54300	−0.396001
$274$	−3.54547	−0.214190
$275$	−6.46309	−0.389739
$276$	−15.0355	−0.905028
$277$	5.89411	0.354143	0.177071	−	0.984198i	$-0.443338\pi$
$277$	5.89411	0.354143	0.177071	+	0.984198i	$0.443338\pi$
$278$	0.439989	0.0263888
$279$	−4.74837	−0.284277
$280$	3.84799	0.229961
$281$	16.6266	0.991860	0.495930	−	0.868363i	$-0.334827\pi$
$281$	16.6266	0.991860	0.495930	+	0.868363i	$0.334827\pi$
$282$	3.16582	0.188522
$283$	−17.1366	−1.01867	−0.509334	−	0.860569i	$-0.670108\pi$
$283$	−17.1366	−1.01867	−0.509334	+	0.860569i	$0.670108\pi$
$284$	−7.41882	−0.440226
$285$	5.83187	0.345450
$286$	−10.2258	−0.604665
$287$	−18.8077	−1.11019
$288$	−5.01855	−0.295721
$289$	32.3339	1.90199
$290$	−4.49585	−0.264005
$291$	8.63662	0.506288
$292$	−4.46340	−0.261201
$293$	7.46723	0.436240	0.218120	−	0.975922i	$-0.430008\pi$
$293$	7.46723	0.436240	0.218120	+	0.975922i	$0.430008\pi$
$294$	1.37386	0.0801251
$295$	−9.93022	−0.578160
$296$	−21.0405	−1.22295
$297$	−6.46309	−0.375027
$298$	−0.719252	−0.0416652
$299$	−27.2655	−1.57681
$300$	−1.75200	−0.101152
$301$	16.5687	0.955004
$302$	3.22626	0.185650
$303$	−9.21375	−0.529316
$304$	15.0084	0.860788
$305$	6.89166	0.394615
$306$	−3.49783	−0.199957
$307$	21.7612	1.24197	0.620987	−	0.783820i	$-0.286732\pi$
$307$	21.7612	1.24197	0.620987	+	0.783820i	$0.286732\pi$
$308$	23.3195	1.32875
$309$	9.37257	0.533187
$310$	2.36467	0.134304
$311$	3.57877	0.202934	0.101467	−	0.994839i	$-0.467646\pi$
$311$	3.57877	0.202934	0.101467	+	0.994839i	$0.467646\pi$
$312$	−5.93636	−0.336080
$313$	15.3082	0.865271	0.432635	−	0.901569i	$-0.357584\pi$
$313$	15.3082	0.865271	0.432635	+	0.901569i	$0.357584\pi$
$314$	4.46729	0.252104
$315$	2.05942	0.116035
$316$	20.0669	1.12885
$317$	−8.50419	−0.477643	−0.238821	−	0.971063i	$-0.576761\pi$
$317$	−8.50419	−0.477643	−0.238821	+	0.971063i	$0.576761\pi$
$318$	−1.25133	−0.0701710
$319$	−58.3481	−3.26687
$320$	−2.64780	−0.148016
$321$	16.2520	0.907097
$322$	−8.80143	−0.490485
$323$	40.9620	2.27918
$324$	−1.75200	−0.0973334
$325$	−3.17711	−0.176234
$326$	−6.19021	−0.342844
$327$	−17.4124	−0.962905
$328$	−17.0639	−0.942199
$329$	−13.0920	−0.721785
$330$	3.21859	0.177178
$331$	−14.8858	−0.818197	−0.409098	−	0.912490i	$-0.634157\pi$
$331$	−14.8858	−0.818197	−0.409098	+	0.912490i	$0.634157\pi$
$332$	18.8318	1.03353
$333$	−11.2607	−0.617085
$334$	−5.57715	−0.305168
$335$	12.4205	0.678604
$336$	5.29994	0.289135
$337$	−13.9815	−0.761619	−0.380809	−	0.924654i	$-0.624355\pi$
$337$	−13.9815	−0.761619	−0.380809	+	0.924654i	$0.624355\pi$
$338$	1.44717	0.0787157
$339$	10.4780	0.569089
$340$	−12.3057	−0.667371
$341$	30.6891	1.66191
$342$	−2.90425	−0.157044
$343$	−20.0974	−1.08516
$344$	15.0325	0.810499
$345$	8.58188	0.462033
$346$	1.86418	0.100219
$347$	3.81290	0.204687	0.102344	−	0.994749i	$-0.467366\pi$
$347$	3.81290	0.204687	0.102344	+	0.994749i	$0.467366\pi$
$348$	−15.8169	−0.847873
$349$	−1.72328	−0.0922449	−0.0461225	−	0.998936i	$-0.514686\pi$
$349$	−1.72328	−0.0922449	−0.0461225	+	0.998936i	$0.514686\pi$
$350$	−1.02558	−0.0548197
$351$	−3.17711	−0.169581
$352$	32.4354	1.72881
$353$	3.93931	0.209668	0.104834	−	0.994490i	$-0.466569\pi$
$353$	3.93931	0.209668	0.104834	+	0.994490i	$0.466569\pi$
$354$	4.94521	0.262835
$355$	4.23449	0.224743
$356$	−17.1268	−0.907718
$357$	14.4650	0.765569
$358$	5.37748	0.284209
$359$	15.7637	0.831979	0.415989	−	0.909369i	$-0.363435\pi$
$359$	15.7637	0.831979	0.415989	+	0.909369i	$0.363435\pi$
$360$	1.86848	0.0984775
$361$	15.0107	0.790038
$362$	−3.80236	−0.199848
$363$	30.7716	1.61509
$364$	11.4633	0.600843
$365$	2.54760	0.133348
$366$	−3.43202	−0.179394
$367$	20.9397	1.09304	0.546522	−	0.837445i	$-0.315951\pi$
$367$	20.9397	1.09304	0.546522	+	0.837445i	$0.315951\pi$
$368$	22.0855	1.15129
$369$	−9.13253	−0.475420
$370$	5.60780	0.291536
$371$	5.17477	0.268661
$372$	8.31914	0.431327
$373$	27.6545	1.43189	0.715947	−	0.698155i	$-0.245995\pi$
$373$	27.6545	1.43189	0.715947	+	0.698155i	$0.245995\pi$
$374$	22.6068	1.16897
$375$	1.00000	0.0516398
$376$	−11.8781	−0.612569
$377$	−28.6826	−1.47723
$378$	−1.02558	−0.0527503
$379$	−5.91080	−0.303617	−0.151809	−	0.988410i	$-0.548510\pi$
$379$	−5.91080	−0.303617	−0.151809	+	0.988410i	$0.548510\pi$
$380$	−10.2174	−0.524144
$381$	21.1367	1.08287
$382$	10.9783	0.561700
$383$	16.0734	0.821313	0.410657	−	0.911790i	$-0.365299\pi$
$383$	16.0734	0.821313	0.410657	+	0.911790i	$0.365299\pi$
$384$	11.3557	0.579493
$385$	−13.3102	−0.678353
$386$	−8.29125	−0.422014
$387$	8.04532	0.408966
$388$	−15.1314	−0.768178
$389$	−13.0788	−0.663124	−0.331562	−	0.943433i	$-0.607576\pi$
$389$	−13.0788	−0.663124	−0.331562	+	0.943433i	$0.607576\pi$
$390$	1.58219	0.0801171
$391$	60.2775	3.04836
$392$	−5.15472	−0.260353
$393$	3.12057	0.157412
$394$	−6.73885	−0.339498
$395$	−11.4537	−0.576299
$396$	11.3233	0.569019
$397$	25.5509	1.28236	0.641180	−	0.767390i	$-0.278445\pi$
$397$	25.5509	1.28236	0.641180	+	0.767390i	$0.278445\pi$
$398$	−8.66744	−0.434460
$399$	12.0103	0.601266
$400$	2.57351	0.128675
$401$	1.00000	0.0499376
$401$	1.00000	0.0499376
$402$	−6.18535	−0.308497
$403$	15.0861	0.751491
$404$	16.1425	0.803119
$405$	1.00000	0.0496904
$406$	−9.25885	−0.459509
$407$	72.7792	3.60753
$408$	13.1238	0.649727
$409$	−19.8493	−0.981486	−0.490743	−	0.871304i	$-0.663275\pi$
$409$	−19.8493	−0.981486	−0.490743	+	0.871304i	$0.663275\pi$
$410$	4.54796	0.224608
$411$	7.11948	0.351178
$412$	−16.4207	−0.808992
$413$	−20.4505	−1.00630
$414$	−4.27374	−0.210043
$415$	−10.7488	−0.527635
$416$	15.9445	0.781743
$417$	−0.883520	−0.0432662
$418$	18.7704	0.918091
$419$	−33.1077	−1.61742	−0.808708	−	0.588211i	$-0.799833\pi$
$419$	−33.1077	−1.61742	−0.808708	+	0.588211i	$0.799833\pi$
$420$	−3.60811	−0.176058
$421$	3.72681	0.181633	0.0908167	−	0.995868i	$-0.471052\pi$
$421$	3.72681	0.181633	0.0908167	+	0.995868i	$0.471052\pi$
$422$	−3.76670	−0.183360
$423$	−6.35712	−0.309094
$424$	4.69498	0.228009
$425$	7.02381	0.340705
$426$	−2.10876	−0.102170
$427$	14.1928	0.686840
$428$	−28.4735	−1.37632
$429$	20.5339	0.991388
$430$	−4.00653	−0.193212
$431$	−38.6826	−1.86328	−0.931638	−	0.363387i	$-0.881620\pi$
$431$	−38.6826	−1.86328	−0.931638	+	0.363387i	$0.881620\pi$
$432$	2.57351	0.123818
$433$	13.5043	0.648977	0.324489	−	0.945890i	$-0.394808\pi$
$433$	13.5043	0.648977	0.324489	+	0.945890i	$0.394808\pi$
$434$	4.86985	0.233760
$435$	9.02789	0.432854
$436$	30.5064	1.46099
$437$	50.0484	2.39414
$438$	−1.26870	−0.0606206
$439$	0.498938	0.0238130	0.0119065	−	0.999929i	$-0.496210\pi$
$439$	0.498938	0.0238130	0.0119065	+	0.999929i	$0.496210\pi$
$440$	−12.0762	−0.575708
$441$	−2.75878	−0.131370
$442$	11.1130	0.528590
$443$	−22.2212	−1.05576	−0.527880	−	0.849319i	$-0.677013\pi$
$443$	−22.2212	−1.05576	−0.527880	+	0.849319i	$0.677013\pi$
$444$	19.7288	0.936289
$445$	9.77556	0.463406
$446$	0.682579	0.0323210
$447$	1.44429	0.0683128
$448$	−5.45293	−0.257627
$449$	5.55989	0.262387	0.131194	−	0.991357i	$-0.458119\pi$
$449$	5.55989	0.262387	0.131194	+	0.991357i	$0.458119\pi$
$450$	−0.497996	−0.0234757
$451$	59.0244	2.77935
$452$	−18.3575	−0.863465
$453$	−6.47849	−0.304386
$454$	−8.22567	−0.386050
$455$	−6.54300	−0.306741
$456$	10.8967	0.510286
$457$	34.0360	1.59214	0.796068	−	0.605207i	$-0.206910\pi$
$457$	34.0360	1.59214	0.796068	+	0.605207i	$0.206910\pi$
$458$	−4.91996	−0.229894
$459$	7.02381	0.327843
$460$	−15.0355	−0.701032
$461$	−22.8984	−1.06648	−0.533241	−	0.845963i	$-0.679026\pi$
$461$	−22.8984	−1.06648	−0.533241	+	0.845963i	$0.679026\pi$
$462$	6.62844	0.308383
$463$	−36.0225	−1.67411	−0.837054	−	0.547120i	$-0.815724\pi$
$463$	−36.0225	−1.67411	−0.837054	+	0.547120i	$0.815724\pi$
$464$	23.2333	1.07858
$465$	−4.74837	−0.220200
$466$	2.57167	0.119130
$467$	16.6306	0.769572	0.384786	−	0.923006i	$-0.374275\pi$
$467$	16.6306	0.769572	0.384786	+	0.923006i	$0.374275\pi$
$468$	5.56629	0.257302
$469$	25.5790	1.18113
$470$	3.16582	0.146028
$471$	−8.97055	−0.413341
$472$	−18.5544	−0.854036
$473$	−51.9976	−2.39085
$474$	5.70390	0.261989
$475$	5.83187	0.267585
$476$	−25.3427	−1.16158
$477$	2.51273	0.115050
$478$	7.32188	0.334895
$479$	−0.281415	−0.0128582	−0.00642908	−	0.999979i	$-0.502046\pi$
$479$	−0.281415	−0.0128582	−0.00642908	+	0.999979i	$0.502046\pi$
$480$	−5.01855	−0.229065
$481$	35.7766	1.63127
$482$	4.14755	0.188916
$483$	17.6737	0.804182
$484$	−53.9118	−2.45054
$485$	8.63662	0.392169
$486$	−0.497996	−0.0225895
$487$	−15.1883	−0.688247	−0.344124	−	0.938924i	$-0.611824\pi$
$487$	−15.1883	−0.688247	−0.344124	+	0.938924i	$0.611824\pi$
$488$	12.8769	0.582911
$489$	12.4303	0.562116
$490$	1.37386	0.0620647
$491$	−15.1506	−0.683737	−0.341868	−	0.939748i	$-0.611060\pi$
$491$	−15.1506	−0.683737	−0.341868	+	0.939748i	$0.611060\pi$
$492$	16.0002	0.721344
$493$	63.4102	2.85585
$494$	9.22710	0.415147
$495$	−6.46309	−0.290494
$496$	−12.2200	−0.548692
$497$	8.72059	0.391172
$498$	5.35283	0.239866
$499$	−7.74634	−0.346774	−0.173387	−	0.984854i	$-0.555471\pi$
$499$	−7.74634	−0.346774	−0.173387	+	0.984854i	$0.555471\pi$
$500$	−1.75200	−0.0783518
$501$	11.1992	0.500343
$502$	−6.96823	−0.311007
$503$	−25.8275	−1.15159	−0.575797	−	0.817593i	$-0.695308\pi$
$503$	−25.8275	−1.15159	−0.575797	+	0.817593i	$0.695308\pi$
$504$	3.84799	0.171403
$505$	−9.21375	−0.410006
$506$	27.6216	1.22793
$507$	−2.90599	−0.129060
$508$	−37.0315	−1.64301
$509$	19.2036	0.851184	0.425592	−	0.904915i	$-0.360066\pi$
$509$	19.2036	0.851184	0.425592	+	0.904915i	$0.360066\pi$
$510$	−3.49783	−0.154886
$511$	5.24659	0.232096
$512$	−22.5324	−0.995799
$513$	5.83187	0.257483
$514$	−3.41940	−0.150823
$515$	9.37257	0.413005
$516$	−14.0954	−0.620515
$517$	41.0867	1.80699
$518$	11.5488	0.507426
$519$	−3.74336	−0.164315
$520$	−5.93636	−0.260327
$521$	17.4852	0.766042	0.383021	−	0.923740i	$-0.374884\pi$
$521$	17.4852	0.766042	0.383021	+	0.923740i	$0.374884\pi$
$522$	−4.49585	−0.196778
$523$	−24.9123	−1.08934	−0.544669	−	0.838651i	$-0.683345\pi$
$523$	−24.9123	−1.08934	−0.544669	+	0.838651i	$0.683345\pi$
$524$	−5.46724	−0.238837
$525$	2.05942	0.0898806
$526$	−2.65689	−0.115846
$527$	−33.3516	−1.45282
$528$	−16.6328	−0.723850
$529$	50.6487	2.20212
$530$	−1.25133	−0.0543542
$531$	−9.93022	−0.430935
$532$	−21.0420	−0.912288
$533$	29.0150	1.25678
$534$	−4.86819	−0.210667
$535$	16.2520	0.702635
$536$	23.2074	1.00241
$537$	−10.7983	−0.465979
$538$	2.49846	0.107716
$539$	17.8302	0.768003
$540$	−1.75200	−0.0753941
$541$	42.0133	1.80629	0.903147	−	0.429332i	$-0.141251\pi$
$541$	42.0133	1.80629	0.903147	+	0.429332i	$0.141251\pi$
$542$	−13.2675	−0.569889
$543$	7.63533	0.327664
$544$	−35.2494	−1.51130
$545$	−17.4124	−0.745863
$546$	3.25839	0.139446
$547$	−10.6723	−0.456315	−0.228158	−	0.973624i	$-0.573270\pi$
$547$	−10.6723	−0.456315	−0.228158	+	0.973624i	$0.573270\pi$
$548$	−12.4733	−0.532834
$549$	6.89166	0.294129
$550$	3.21859	0.137241
$551$	52.6495	2.24294
$552$	16.0351	0.682498
$553$	−23.5880	−1.00306
$554$	−2.93524	−0.124706
$555$	−11.2607	−0.477992
$556$	1.54793	0.0656468
$557$	−21.9659	−0.930725	−0.465362	−	0.885120i	$-0.654076\pi$
$557$	−21.9659	−0.930725	−0.465362	+	0.885120i	$0.654076\pi$
$558$	2.36467	0.100104
$559$	−25.5608	−1.08111
$560$	5.29994	0.223963
$561$	−45.3955	−1.91660
$562$	−8.27997	−0.349270
$563$	−8.61160	−0.362936	−0.181468	−	0.983397i	$-0.558085\pi$
$563$	−8.61160	−0.362936	−0.181468	+	0.983397i	$0.558085\pi$
$564$	11.1377	0.468981
$565$	10.4780	0.440814
$566$	8.53397	0.358710
$567$	2.05942	0.0864876
$568$	7.91205	0.331982
$569$	−5.40908	−0.226760	−0.113380	−	0.993552i	$-0.536168\pi$
$569$	−5.40908	−0.226760	−0.113380	+	0.993552i	$0.536168\pi$
$570$	−2.90425	−0.121645
$571$	−8.89745	−0.372346	−0.186173	−	0.982517i	$-0.559609\pi$
$571$	−8.89745	−0.372346	−0.186173	+	0.982517i	$0.559609\pi$
$572$	−35.9755	−1.50421
$573$	−22.0450	−0.920943
$574$	9.36617	0.390936
$575$	8.58188	0.357889
$576$	−2.64780	−0.110325
$577$	−9.41424	−0.391920	−0.195960	−	0.980612i	$-0.562782\pi$
$577$	−9.41424	−0.391920	−0.195960	+	0.980612i	$0.562782\pi$
$578$	−16.1021	−0.669761
$579$	16.6492	0.691919
$580$	−15.8169	−0.656760
$581$	−22.1362	−0.918365
$582$	−4.30100	−0.178282
$583$	−16.2400	−0.672592
$584$	4.76015	0.196976
$585$	−3.17711	−0.131357
$586$	−3.71865	−0.153616
$587$	1.08983	0.0449820	0.0224910	−	0.999747i	$-0.492840\pi$
$587$	1.08983	0.0449820	0.0224910	+	0.999747i	$0.492840\pi$
$588$	4.83338	0.199325
$589$	−27.6919	−1.14102
$590$	4.94521	0.203591
$591$	13.5319	0.556630
$592$	−28.9796	−1.19105
$593$	−26.3039	−1.08017	−0.540086	−	0.841610i	$-0.681608\pi$
$593$	−26.3039	−1.08017	−0.540086	+	0.841610i	$0.681608\pi$
$594$	3.21859	0.132060
$595$	14.4650	0.593007
$596$	−2.53041	−0.103649
$597$	17.4047	0.712325
$598$	13.5781	0.555251
$599$	13.8998	0.567931	0.283965	−	0.958835i	$-0.408350\pi$
$599$	13.8998	0.567931	0.283965	+	0.958835i	$0.408350\pi$
$600$	1.86848	0.0762804
$601$	46.6401	1.90249	0.951245	−	0.308436i	$-0.0998057\pi$
$601$	46.6401	1.90249	0.951245	+	0.308436i	$0.0998057\pi$
$602$	−8.25114	−0.336291
$603$	12.4205	0.505802
$604$	11.3503	0.461838
$605$	30.7716	1.25104
$606$	4.58841	0.186391
$607$	10.5856	0.429658	0.214829	−	0.976652i	$-0.431081\pi$
$607$	10.5856	0.429658	0.214829	+	0.976652i	$0.431081\pi$
$608$	−29.2676	−1.18696
$609$	18.5922	0.753396
$610$	−3.43202	−0.138958
$611$	20.1972	0.817093
$612$	−12.3057	−0.497429
$613$	7.23191	0.292094	0.146047	−	0.989278i	$-0.453345\pi$
$613$	7.23191	0.292094	0.146047	+	0.989278i	$0.453345\pi$
$614$	−10.8370	−0.437344
$615$	−9.13253	−0.368259
$616$	−24.8699	−1.00204
$617$	−11.5268	−0.464052	−0.232026	−	0.972710i	$-0.574535\pi$
$617$	−11.5268	−0.464052	−0.232026	+	0.972710i	$0.574535\pi$
$618$	−4.66750	−0.187754
$619$	3.02426	0.121555	0.0607776	−	0.998151i	$-0.480642\pi$
$619$	3.02426	0.121555	0.0607776	+	0.998151i	$0.480642\pi$
$620$	8.31914	0.334105
$621$	8.58188	0.344379
$622$	−1.78221	−0.0714603
$623$	20.1320	0.806572
$624$	−8.17630	−0.327314
$625$	1.00000	0.0400000
$626$	−7.62342	−0.304693
$627$	−37.6919	−1.50527
$628$	15.7164	0.627153
$629$	−79.0933	−3.15366
$630$	−1.02558	−0.0408602
$631$	40.8480	1.62613	0.813066	−	0.582171i	$-0.197797\pi$
$631$	40.8480	1.62613	0.813066	+	0.582171i	$0.197797\pi$
$632$	−21.4010	−0.851287
$633$	7.56372	0.300631
$634$	4.23505	0.168195
$635$	21.1367	0.838785
$636$	−4.40230	−0.174563
$637$	8.76494	0.347279
$638$	29.0571	1.15038
$639$	4.23449	0.167514
$640$	11.3557	0.448873
$641$	4.86390	0.192112	0.0960562	−	0.995376i	$-0.469377\pi$
$641$	4.86390	0.192112	0.0960562	+	0.995376i	$0.469377\pi$
$642$	−8.09342	−0.319422
$643$	34.9008	1.37635	0.688176	−	0.725544i	$-0.258412\pi$
$643$	34.9008	1.37635	0.688176	+	0.725544i	$0.258412\pi$
$644$	−30.9644	−1.22017
$645$	8.04532	0.316784
$646$	−20.3989	−0.802583
$647$	−27.7883	−1.09247	−0.546236	−	0.837631i	$-0.683940\pi$
$647$	−27.7883	−1.09247	−0.546236	+	0.837631i	$0.683940\pi$
$648$	1.86848	0.0734008
$649$	64.1800	2.51928
$650$	1.58219	0.0620584
$651$	−9.77890	−0.383265
$652$	−21.7778	−0.852885
$653$	17.3026	0.677102	0.338551	−	0.940948i	$-0.390063\pi$
$653$	17.3026	0.677102	0.338551	+	0.940948i	$0.390063\pi$
$654$	8.67127	0.339074
$655$	3.12057	0.121931
$656$	−23.5026	−0.917623
$657$	2.54760	0.0993915
$658$	6.51976	0.254167
$659$	−48.8533	−1.90305	−0.951527	−	0.307565i	$-0.900486\pi$
$659$	−48.8533	−1.90305	−0.951527	+	0.307565i	$0.900486\pi$
$660$	11.3233	0.440760
$661$	17.2017	0.669069	0.334534	−	0.942384i	$-0.391421\pi$
$661$	17.2017	0.669069	0.334534	+	0.942384i	$0.391421\pi$
$662$	7.41305	0.288117
$663$	−22.3154	−0.866658
$664$	−20.0838	−0.779403
$665$	12.0103	0.465739
$666$	5.60780	0.217298
$667$	77.4763	2.99989
$668$	−19.6210	−0.759159
$669$	−1.37065	−0.0529925
$670$	−6.18535	−0.238961
$671$	−44.5415	−1.71950
$672$	−10.3353	−0.398694
$673$	43.2567	1.66742	0.833711	−	0.552201i	$-0.186212\pi$
$673$	43.2567	1.66742	0.833711	+	0.552201i	$0.186212\pi$
$674$	6.96271	0.268193
$675$	1.00000	0.0384900
$676$	5.09130	0.195819
$677$	7.79880	0.299732	0.149866	−	0.988706i	$-0.452116\pi$
$677$	7.79880	0.299732	0.149866	+	0.988706i	$0.452116\pi$
$678$	−5.21801	−0.200397
$679$	17.7864	0.682581
$680$	13.1238	0.503276
$681$	16.5176	0.632954
$682$	−15.2831	−0.585218
$683$	34.5910	1.32359	0.661794	−	0.749686i	$-0.269795\pi$
$683$	34.5910	1.32359	0.661794	+	0.749686i	$0.269795\pi$
$684$	−10.2174	−0.390674
$685$	7.11948	0.272021
$686$	10.0084	0.382124
$687$	9.87952	0.376927
$688$	20.7047	0.789358
$689$	−7.98321	−0.304136
$690$	−4.27374	−0.162698
$691$	13.6437	0.519032	0.259516	−	0.965739i	$-0.416437\pi$
$691$	13.6437	0.519032	0.259516	+	0.965739i	$0.416437\pi$
$692$	6.55838	0.249312
$693$	−13.3102	−0.505614
$694$	−1.89881	−0.0720778
$695$	−0.883520	−0.0335138
$696$	16.8684	0.639396
$697$	−64.1451	−2.42967
$698$	0.858184	0.0324828
$699$	−5.16405	−0.195322
$700$	−3.60811	−0.136374
$701$	5.39946	0.203935	0.101967	−	0.994788i	$-0.467486\pi$
$701$	5.39946	0.203935	0.101967	+	0.994788i	$0.467486\pi$
$702$	1.58219	0.0597157
$703$	−65.6712	−2.47684
$704$	17.1129	0.644968
$705$	−6.35712	−0.239423
$706$	−1.96176	−0.0738317
$707$	−18.9750	−0.713628
$708$	17.3978	0.653848
$709$	−40.6291	−1.52586	−0.762929	−	0.646483i	$-0.776239\pi$
$709$	−40.6291	−1.52586	−0.762929	+	0.646483i	$0.776239\pi$
$710$	−2.10876	−0.0791402
$711$	−11.4537	−0.429548
$712$	18.2654	0.684526
$713$	−40.7499	−1.52610
$714$	−7.20350	−0.269584
$715$	20.5339	0.767926
$716$	18.9186	0.707019
$717$	−14.7027	−0.549083
$718$	−7.85028	−0.292970
$719$	−51.3098	−1.91353	−0.956767	−	0.290857i	$-0.906060\pi$
$719$	−51.3098	−1.91353	−0.956767	+	0.290857i	$0.906060\pi$
$720$	2.57351	0.0959089
$721$	19.3021	0.718847
$722$	−7.47528	−0.278201
$723$	−8.32849	−0.309740
$724$	−13.3771	−0.497156
$725$	9.02789	0.335287
$726$	−15.3241	−0.568731
$727$	27.2983	1.01244	0.506220	−	0.862405i	$-0.331042\pi$
$727$	27.2983	1.01244	0.506220	+	0.862405i	$0.331042\pi$
$728$	−12.2255	−0.453106
$729$	1.00000	0.0370370
$730$	−1.26870	−0.0469565
$731$	56.5088	2.09005
$732$	−12.0742	−0.446275
$733$	−5.09981	−0.188366	−0.0941829	−	0.995555i	$-0.530024\pi$
$733$	−5.09981	−0.188366	−0.0941829	+	0.995555i	$0.530024\pi$
$734$	−10.4279	−0.384900
$735$	−2.75878	−0.101759
$736$	−43.0686	−1.58753
$737$	−80.2748	−2.95696
$738$	4.54796	0.167413
$739$	−27.0368	−0.994565	−0.497283	−	0.867589i	$-0.665669\pi$
$739$	−27.0368	−0.994565	−0.497283	+	0.867589i	$0.665669\pi$
$740$	19.7288	0.725246
$741$	−18.5285	−0.680661
$742$	−2.57701	−0.0946051
$743$	−18.2983	−0.671298	−0.335649	−	0.941987i	$-0.608956\pi$
$743$	−18.2983	−0.671298	−0.335649	+	0.941987i	$0.608956\pi$
$744$	−8.87223	−0.325272
$745$	1.44429	0.0529149
$746$	−13.7718	−0.504221
$747$	−10.7488	−0.393276
$748$	79.5330	2.90801
$749$	33.4697	1.22296
$750$	−0.497996	−0.0181842
$751$	9.86994	0.360159	0.180080	−	0.983652i	$-0.442364\pi$
$751$	9.86994	0.360159	0.180080	+	0.983652i	$0.442364\pi$
$752$	−16.3601	−0.596591
$753$	13.9925	0.509917
$754$	14.2838	0.520185
$755$	−6.47849	−0.235776
$756$	−3.60811	−0.131226
$757$	−22.3059	−0.810723	−0.405361	−	0.914157i	$-0.632854\pi$
$757$	−22.3059	−0.810723	−0.405361	+	0.914157i	$0.632854\pi$
$758$	2.94355	0.106915
$759$	−55.4655	−2.01327
$760$	10.8967	0.395266
$761$	−39.3425	−1.42616	−0.713082	−	0.701081i	$-0.752701\pi$
$761$	−39.3425	−1.42616	−0.713082	+	0.701081i	$0.752701\pi$
$762$	−10.5260	−0.381316
$763$	−35.8594	−1.29820
$764$	38.6229	1.39733
$765$	7.02381	0.253946
$766$	−8.00449	−0.289214
$767$	31.5494	1.13918
$768$	−0.359497	−0.0129722
$769$	2.73633	0.0986745	0.0493372	−	0.998782i	$-0.484289\pi$
$769$	2.73633	0.0986745	0.0493372	+	0.998782i	$0.484289\pi$
$770$	6.62844	0.238872
$771$	6.86632	0.247285
$772$	−29.1695	−1.04983
$773$	−10.6968	−0.384736	−0.192368	−	0.981323i	$-0.561617\pi$
$773$	−10.6968	−0.384736	−0.192368	+	0.981323i	$0.561617\pi$
$774$	−4.00653	−0.144012
$775$	−4.74837	−0.170566
$776$	16.1373	0.579297
$777$	−23.1906	−0.831959
$778$	6.51321	0.233510
$779$	−53.2597	−1.90823
$780$	5.56629	0.199305
$781$	−27.3679	−0.979299
$782$	−30.0179	−1.07344
$783$	9.02789	0.322631
$784$	−7.09974	−0.253562
$785$	−8.97055	−0.320173
$786$	−1.55403	−0.0554304
$787$	−41.0435	−1.46304	−0.731521	−	0.681819i	$-0.761189\pi$
$787$	−41.0435	−1.46304	−0.731521	+	0.681819i	$0.761189\pi$
$788$	−23.7080	−0.844562
$789$	5.33516	0.189937
$790$	5.70390	0.202936
$791$	21.5787	0.767250
$792$	−12.0762	−0.429108
$793$	−21.8955	−0.777534
$794$	−12.7242	−0.451565
$795$	2.51273	0.0891173
$796$	−30.4930	−1.08079
$797$	11.8706	0.420480	0.210240	−	0.977650i	$-0.432575\pi$
$797$	11.8706	0.420480	0.210240	+	0.977650i	$0.432575\pi$
$798$	−5.98107	−0.211728
$799$	−44.6512	−1.57965
$800$	−5.01855	−0.177433
$801$	9.77556	0.345402
$802$	−0.497996	−0.0175848
$803$	−16.4654	−0.581051
$804$	−21.7607	−0.767441
$805$	17.6737	0.622917
$806$	−7.51280	−0.264627
$807$	−5.01704	−0.176608
$808$	−17.2157	−0.605646
$809$	−39.7601	−1.39789	−0.698946	−	0.715175i	$-0.746347\pi$
$809$	−39.7601	−1.39789	−0.698946	+	0.715175i	$0.746347\pi$
$810$	−0.497996	−0.0174978
$811$	−4.09523	−0.143803	−0.0719015	−	0.997412i	$-0.522907\pi$
$811$	−4.09523	−0.143803	−0.0719015	+	0.997412i	$0.522907\pi$
$812$	−32.5736	−1.14311
$813$	26.6419	0.934371
$814$	−36.2437	−1.27034
$815$	12.4303	0.435413
$816$	18.0758	0.632780
$817$	46.9193	1.64150
$818$	9.88488	0.345617
$819$	−6.54300	−0.228631
$820$	16.0002	0.558751
$821$	−27.0183	−0.942946	−0.471473	−	0.881880i	$-0.656278\pi$
$821$	−27.0183	−0.942946	−0.471473	+	0.881880i	$0.656278\pi$
$822$	−3.54547	−0.123662
$823$	−12.3362	−0.430014	−0.215007	−	0.976612i	$-0.568978\pi$
$823$	−12.3362	−0.430014	−0.215007	+	0.976612i	$0.568978\pi$
$824$	17.5125	0.610075
$825$	−6.46309	−0.225016
$826$	10.1843	0.354356
$827$	22.6384	0.787215	0.393607	−	0.919279i	$-0.371227\pi$
$827$	22.6384	0.787215	0.393607	+	0.919279i	$0.371227\pi$
$828$	−15.0355	−0.522518
$829$	−4.59025	−0.159426	−0.0797130	−	0.996818i	$-0.525400\pi$
$829$	−4.59025	−0.159426	−0.0797130	+	0.996818i	$0.525400\pi$
$830$	5.35283	0.185799
$831$	5.89411	0.204464
$832$	8.41233	0.291645
$833$	−19.3771	−0.671378
$834$	0.439989	0.0152356
$835$	11.1992	0.387564
$836$	66.0363	2.28391
$837$	−4.74837	−0.164128
$838$	16.4875	0.569550
$839$	−4.11095	−0.141926	−0.0709628	−	0.997479i	$-0.522607\pi$
$839$	−4.11095	−0.141926	−0.0709628	+	0.997479i	$0.522607\pi$
$840$	3.84799	0.132768
$841$	52.5028	1.81044
$842$	−1.85593	−0.0639597
$843$	16.6266	0.572651
$844$	−13.2516	−0.456140
$845$	−2.90599	−0.0999692
$846$	3.16582	0.108843
$847$	63.3717	2.17748
$848$	6.46653	0.222061
$849$	−17.1366	−0.588128
$850$	−3.49783	−0.119974
$851$	−96.6383	−3.31272
$852$	−7.41882	−0.254165
$853$	−35.0588	−1.20039	−0.600195	−	0.799854i	$-0.704910\pi$
$853$	−35.0588	−1.20039	−0.600195	+	0.799854i	$0.704910\pi$
$854$	−7.06797	−0.241861
$855$	5.83187	0.199446
$856$	30.3665	1.03791
$857$	−29.1051	−0.994211	−0.497105	−	0.867690i	$-0.665604\pi$
$857$	−29.1051	−0.994211	−0.497105	+	0.867690i	$0.665604\pi$
$858$	−10.2258	−0.349103
$859$	16.9159	0.577162	0.288581	−	0.957455i	$-0.406817\pi$
$859$	16.9159	0.577162	0.288581	+	0.957455i	$0.406817\pi$
$860$	−14.0954	−0.480649
$861$	−18.8077	−0.640966
$862$	19.2638	0.656127
$863$	30.5031	1.03834	0.519169	−	0.854672i	$-0.326242\pi$
$863$	30.5031	1.03834	0.519169	+	0.854672i	$0.326242\pi$
$864$	−5.01855	−0.170735
$865$	−3.74336	−0.127278
$866$	−6.72510	−0.228528
$867$	32.3339	1.09812
$868$	17.1326	0.581519
$869$	74.0264	2.51117
$870$	−4.49585	−0.152424
$871$	−39.4612	−1.33709
$872$	−32.5346	−1.10176
$873$	8.63662	0.292305
$874$	−24.9239	−0.843063
$875$	2.05942	0.0696212
$876$	−4.46340	−0.150804
$877$	−45.0979	−1.52285	−0.761423	−	0.648255i	$-0.775499\pi$
$877$	−45.0979	−1.52285	−0.761423	+	0.648255i	$0.775499\pi$
$878$	−0.248469	−0.00838543
$879$	7.46723	0.251863
$880$	−16.6328	−0.560692
$881$	51.1266	1.72250	0.861249	−	0.508182i	$-0.169682\pi$
$881$	51.1266	1.72250	0.861249	+	0.508182i	$0.169682\pi$
$882$	1.37386	0.0462603
$883$	5.62016	0.189134	0.0945668	−	0.995519i	$-0.469853\pi$
$883$	5.62016	0.189134	0.0945668	+	0.995519i	$0.469853\pi$
$884$	39.0966	1.31496
$885$	−9.93022	−0.333801
$886$	11.0660	0.371771
$887$	−17.9704	−0.603388	−0.301694	−	0.953405i	$-0.597552\pi$
$887$	−17.9704	−0.603388	−0.301694	+	0.953405i	$0.597552\pi$
$888$	−21.0405	−0.706072
$889$	43.5294	1.45993
$890$	−4.86819	−0.163182
$891$	−6.46309	−0.216522
$892$	2.40138	0.0804043
$893$	−37.0739	−1.24063
$894$	−0.719252	−0.0240554
$895$	−10.7983	−0.360946
$896$	23.3862	0.781277
$897$	−27.2655	−0.910370
$898$	−2.76880	−0.0923961
$899$	−42.8677	−1.42972
$900$	−1.75200	−0.0584000
$901$	17.6489	0.587971
$902$	−29.3939	−0.978709
$903$	16.5687	0.551372
$904$	19.5780	0.651154
$905$	7.63533	0.253807
$906$	3.22626	0.107185
$907$	−19.5541	−0.649282	−0.324641	−	0.945837i	$-0.605243\pi$
$907$	−19.5541	−0.649282	−0.324641	+	0.945837i	$0.605243\pi$
$908$	−28.9388	−0.960366
$909$	−9.21375	−0.305601
$910$	3.25839	0.108014
$911$	−16.1713	−0.535778	−0.267889	−	0.963450i	$-0.586326\pi$
$911$	−16.1713	−0.535778	−0.267889	+	0.963450i	$0.586326\pi$
$912$	15.0084	0.496976
$913$	69.4702	2.29913
$914$	−16.9498	−0.560649
$915$	6.89166	0.227831
$916$	−17.3089	−0.571903
$917$	6.42657	0.212224
$918$	−3.49783	−0.115445
$919$	4.08837	0.134863	0.0674315	−	0.997724i	$-0.478520\pi$
$919$	4.08837	0.134863	0.0674315	+	0.997724i	$0.478520\pi$
$920$	16.0351	0.528660
$921$	21.7612	0.717055
$922$	11.4033	0.375547
$923$	−13.4534	−0.442824
$924$	23.3195	0.767157
$925$	−11.2607	−0.370251
$926$	17.9391	0.589514
$927$	9.37257	0.307836
$928$	−45.3070	−1.48727
$929$	−9.58318	−0.314414	−0.157207	−	0.987566i	$-0.550249\pi$
$929$	−9.58318	−0.314414	−0.157207	+	0.987566i	$0.550249\pi$
$930$	2.36467	0.0775405
$931$	−16.0888	−0.527291
$932$	9.04742	0.296358
$933$	3.57877	0.117164
$934$	−8.28196	−0.270994
$935$	−45.3955	−1.48459
$936$	−5.93636	−0.194036
$937$	−21.3632	−0.697904	−0.348952	−	0.937141i	$-0.613462\pi$
$937$	−21.3632	−0.697904	−0.348952	+	0.937141i	$0.613462\pi$
$938$	−12.7383	−0.415919
$939$	15.3082	0.499564
$940$	11.1377	0.363271
$941$	−1.22549	−0.0399499	−0.0199750	−	0.999800i	$-0.506359\pi$
$941$	−1.22549	−0.0399499	−0.0199750	+	0.999800i	$0.506359\pi$
$942$	4.46729	0.145552
$943$	−78.3743	−2.55222
$944$	−25.5555	−0.831760
$945$	2.05942	0.0669930
$946$	25.8946	0.841906
$947$	1.46001	0.0474440	0.0237220	−	0.999719i	$-0.492448\pi$
$947$	1.46001	0.0474440	0.0237220	+	0.999719i	$0.492448\pi$
$948$	20.0669	0.651743
$949$	−8.09401	−0.262743
$950$	−2.90425	−0.0942262
$951$	−8.50419	−0.275767
$952$	27.0275	0.875968
$953$	12.5572	0.406767	0.203384	−	0.979099i	$-0.434806\pi$
$953$	12.5572	0.406767	0.203384	+	0.979099i	$0.434806\pi$
$954$	−1.25133	−0.0405132
$955$	−22.0450	−0.713360
$956$	25.7592	0.833111
$957$	−58.3481	−1.88613
$958$	0.140143	0.00452783
$959$	14.6620	0.473461
$960$	−2.64780	−0.0854572
$961$	−8.45300	−0.272677
$962$	−17.8166	−0.574429
$963$	16.2520	0.523713
$964$	14.5915	0.469961
$965$	16.6492	0.535958
$966$	−8.80143	−0.283181
$967$	−33.0869	−1.06400	−0.532001	−	0.846744i	$-0.678560\pi$
$967$	−33.0869	−1.06400	−0.532001	+	0.846744i	$0.678560\pi$
$968$	57.4960	1.84799
$969$	40.9620	1.31589
$970$	−4.30100	−0.138097
$971$	−6.93809	−0.222654	−0.111327	−	0.993784i	$-0.535510\pi$
$971$	−6.93809	−0.222654	−0.111327	+	0.993784i	$0.535510\pi$
$972$	−1.75200	−0.0561954
$973$	−1.81954	−0.0583318
$974$	7.56370	0.242357
$975$	−3.17711	−0.101749
$976$	17.7357	0.567707
$977$	2.14130	0.0685063	0.0342532	−	0.999413i	$-0.489095\pi$
$977$	2.14130	0.0685063	0.0342532	+	0.999413i	$0.489095\pi$
$978$	−6.19021	−0.197941
$979$	−63.1804	−2.01925
$980$	4.83338	0.154397
$981$	−17.4124	−0.555934
$982$	7.54493	0.240768
$983$	32.1688	1.02603	0.513013	−	0.858381i	$-0.328529\pi$
$983$	32.1688	1.02603	0.513013	+	0.858381i	$0.328529\pi$
$984$	−17.0639	−0.543979
$985$	13.5319	0.431164
$986$	−31.5780	−1.00565
$987$	−13.0920	−0.416723
$988$	32.4619	1.03275
$989$	69.0439	2.19547
$990$	3.21859	0.102294
$991$	−32.1639	−1.02172	−0.510860	−	0.859664i	$-0.670673\pi$
$991$	−32.1639	−1.02172	−0.510860	+	0.859664i	$0.670673\pi$
$992$	23.8299	0.756601
$993$	−14.8858	−0.472386
$994$	−4.34282	−0.137746
$995$	17.4047	0.551765
$996$	18.8318	0.596709
$997$	52.9912	1.67825	0.839125	−	0.543939i	$-0.183068\pi$
$997$	52.9912	1.67825	0.839125	+	0.543939i	$0.183068\pi$
$998$	3.85764	0.122111
$999$	−11.2607	−0.356274

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6015.2.a.i.1.18	✓	43

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6015.2.a.i.1.18	✓	43	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:	\( N \)	\(=\)	\( 6015 = 3 \cdot 5 \cdot 401 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6015.a (trivial)

\(f(q)\)	\(=\)	\(q-0.497996 q^{2} +1.00000 q^{3} -1.75200 q^{4} +1.00000 q^{5} -0.497996 q^{6} +2.05942 q^{7} +1.86848 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-0.497996 q^{2} +1.00000 q^{3} -1.75200 q^{4} +1.00000 q^{5} -0.497996 q^{6} +2.05942 q^{7} +1.86848 q^{8} +1.00000 q^{9} -0.497996 q^{10} -6.46309 q^{11} -1.75200 q^{12} -3.17711 q^{13} -1.02558 q^{14} +1.00000 q^{15} +2.57351 q^{16} +7.02381 q^{17} -0.497996 q^{18} +5.83187 q^{19} -1.75200 q^{20} +2.05942 q^{21} +3.21859 q^{22} +8.58188 q^{23} +1.86848 q^{24} +1.00000 q^{25} +1.58219 q^{26} +1.00000 q^{27} -3.60811 q^{28} +9.02789 q^{29} -0.497996 q^{30} -4.74837 q^{31} -5.01855 q^{32} -6.46309 q^{33} -3.49783 q^{34} +2.05942 q^{35} -1.75200 q^{36} -11.2607 q^{37} -2.90425 q^{38} -3.17711 q^{39} +1.86848 q^{40} -9.13253 q^{41} -1.02558 q^{42} +8.04532 q^{43} +11.3233 q^{44} +1.00000 q^{45} -4.27374 q^{46} -6.35712 q^{47} +2.57351 q^{48} -2.75878 q^{49} -0.497996 q^{50} +7.02381 q^{51} +5.56629 q^{52} +2.51273 q^{53} -0.497996 q^{54} -6.46309 q^{55} +3.84799 q^{56} +5.83187 q^{57} -4.49585 q^{58} -9.93022 q^{59} -1.75200 q^{60} +6.89166 q^{61} +2.36467 q^{62} +2.05942 q^{63} -2.64780 q^{64} -3.17711 q^{65} +3.21859 q^{66} +12.4205 q^{67} -12.3057 q^{68} +8.58188 q^{69} -1.02558 q^{70} +4.23449 q^{71} +1.86848 q^{72} +2.54760 q^{73} +5.60780 q^{74} +1.00000 q^{75} -10.2174 q^{76} -13.3102 q^{77} +1.58219 q^{78} -11.4537 q^{79} +2.57351 q^{80} +1.00000 q^{81} +4.54796 q^{82} -10.7488 q^{83} -3.60811 q^{84} +7.02381 q^{85} -4.00653 q^{86} +9.02789 q^{87} -12.0762 q^{88} +9.77556 q^{89} -0.497996 q^{90} -6.54300 q^{91} -15.0355 q^{92} -4.74837 q^{93} +3.16582 q^{94} +5.83187 q^{95} -5.01855 q^{96} +8.63662 q^{97} +1.37386 q^{98} -6.46309 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 43 q + 3 q^{2} + 43 q^{3} + 61 q^{4} + 43 q^{5} + 3 q^{6} + 14 q^{7} + 18 q^{8} + 43 q^{9}+O(q^{10}) \) 43 * q + 3 * q^2 + 43 * q^3 + 61 * q^4 + 43 * q^5 + 3 * q^6 + 14 * q^7 + 18 * q^8 + 43 * q^9	\( 43 q + 3 q^{2} + 43 q^{3} + 61 q^{4} + 43 q^{5} + 3 q^{6} + 14 q^{7} + 18 q^{8} + 43 q^{9} + 3 q^{10} + 19 q^{11} + 61 q^{12} + 8 q^{13} + 6 q^{14} + 43 q^{15} + 85 q^{16} + 40 q^{17} + 3 q^{18} + 43 q^{19} + 61 q^{20} + 14 q^{21} + 19 q^{22} + 12 q^{23} + 18 q^{24} + 43 q^{25} + 43 q^{27} + 36 q^{28} + 41 q^{29} + 3 q^{30} + 33 q^{31} + 4 q^{32} + 19 q^{33} + 20 q^{34} + 14 q^{35} + 61 q^{36} + 12 q^{37} + 10 q^{38} + 8 q^{39} + 18 q^{40} + 47 q^{41} + 6 q^{42} + 73 q^{43} + 5 q^{44} + 43 q^{45} + 21 q^{46} + 32 q^{47} + 85 q^{48} + 87 q^{49} + 3 q^{50} + 40 q^{51} + 18 q^{52} + 17 q^{53} + 3 q^{54} + 19 q^{55} + 15 q^{56} + 43 q^{57} - 16 q^{58} + 21 q^{59} + 61 q^{60} + 77 q^{61} + 15 q^{62} + 14 q^{63} + 112 q^{64} + 8 q^{65} + 19 q^{66} + 26 q^{67} + 50 q^{68} + 12 q^{69} + 6 q^{70} + 2 q^{71} + 18 q^{72} + 49 q^{73} - 34 q^{74} + 43 q^{75} + 50 q^{76} - 2 q^{77} + 59 q^{79} + 85 q^{80} + 43 q^{81} - 45 q^{82} - 3 q^{83} + 36 q^{84} + 40 q^{85} - 35 q^{86} + 41 q^{87} - 13 q^{88} + 57 q^{89} + 3 q^{90} + 11 q^{91} - 9 q^{92} + 33 q^{93} + 52 q^{94} + 43 q^{95} + 4 q^{96} + 7 q^{97} - 32 q^{98} + 19 q^{99}+O(q^{100}) \) 43 * q + 3 * q^2 + 43 * q^3 + 61 * q^4 + 43 * q^5 + 3 * q^6 + 14 * q^7 + 18 * q^8 + 43 * q^9 + 3 * q^10 + 19 * q^11 + 61 * q^12 + 8 * q^13 + 6 * q^14 + 43 * q^15 + 85 * q^16 + 40 * q^17 + 3 * q^18 + 43 * q^19 + 61 * q^20 + 14 * q^21 + 19 * q^22 + 12 * q^23 + 18 * q^24 + 43 * q^25 + 43 * q^27 + 36 * q^28 + 41 * q^29 + 3 * q^30 + 33 * q^31 + 4 * q^32 + 19 * q^33 + 20 * q^34 + 14 * q^35 + 61 * q^36 + 12 * q^37 + 10 * q^38 + 8 * q^39 + 18 * q^40 + 47 * q^41 + 6 * q^42 + 73 * q^43 + 5 * q^44 + 43 * q^45 + 21 * q^46 + 32 * q^47 + 85 * q^48 + 87 * q^49 + 3 * q^50 + 40 * q^51 + 18 * q^52 + 17 * q^53 + 3 * q^54 + 19 * q^55 + 15 * q^56 + 43 * q^57 - 16 * q^58 + 21 * q^59 + 61 * q^60 + 77 * q^61 + 15 * q^62 + 14 * q^63 + 112 * q^64 + 8 * q^65 + 19 * q^66 + 26 * q^67 + 50 * q^68 + 12 * q^69 + 6 * q^70 + 2 * q^71 + 18 * q^72 + 49 * q^73 - 34 * q^74 + 43 * q^75 + 50 * q^76 - 2 * q^77 + 59 * q^79 + 85 * q^80 + 43 * q^81 - 45 * q^82 - 3 * q^83 + 36 * q^84 + 40 * q^85 - 35 * q^86 + 41 * q^87 - 13 * q^88 + 57 * q^89 + 3 * q^90 + 11 * q^91 - 9 * q^92 + 33 * q^93 + 52 * q^94 + 43 * q^95 + 4 * q^96 + 7 * q^97 - 32 * q^98 + 19 * q^99

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