LMFDB - Embedded newform 4015.2.a.h.1.25

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4015,2,Mod(1,4015)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4015, 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("4015.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4015 = 5 \cdot 11 \cdot 73 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4015.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:	$32.0599364115$
Analytic rank:	$0$
Dimension:	$37$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.25
Character	$\chi$	$=$	4015.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.15422 q^{2} -2.27984 q^{3} -0.667766 q^{4} +1.00000 q^{5} -2.63145 q^{6} -3.20405 q^{7} -3.07920 q^{8} +2.19767 q^{9} +O(q^{10})$	\(q+1.15422 q^{2} -2.27984 q^{3} -0.667766 q^{4} +1.00000 q^{5} -2.63145 q^{6} -3.20405 q^{7} -3.07920 q^{8} +2.19767 q^{9} +1.15422 q^{10} +1.00000 q^{11} +1.52240 q^{12} -5.66015 q^{13} -3.69819 q^{14} -2.27984 q^{15} -2.21856 q^{16} -4.52607 q^{17} +2.53661 q^{18} +4.04933 q^{19} -0.667766 q^{20} +7.30472 q^{21} +1.15422 q^{22} -6.42618 q^{23} +7.02009 q^{24} +1.00000 q^{25} -6.53309 q^{26} +1.82918 q^{27} +2.13955 q^{28} +0.112396 q^{29} -2.63145 q^{30} -7.88760 q^{31} +3.59769 q^{32} -2.27984 q^{33} -5.22410 q^{34} -3.20405 q^{35} -1.46753 q^{36} -9.62475 q^{37} +4.67383 q^{38} +12.9043 q^{39} -3.07920 q^{40} -3.07626 q^{41} +8.43129 q^{42} -0.751656 q^{43} -0.667766 q^{44} +2.19767 q^{45} -7.41726 q^{46} -9.75931 q^{47} +5.05796 q^{48} +3.26593 q^{49} +1.15422 q^{50} +10.3187 q^{51} +3.77966 q^{52} +7.14813 q^{53} +2.11128 q^{54} +1.00000 q^{55} +9.86591 q^{56} -9.23182 q^{57} +0.129731 q^{58} +2.92563 q^{59} +1.52240 q^{60} +9.27987 q^{61} -9.10407 q^{62} -7.04145 q^{63} +8.58965 q^{64} -5.66015 q^{65} -2.63145 q^{66} -5.53467 q^{67} +3.02235 q^{68} +14.6507 q^{69} -3.69819 q^{70} +1.61411 q^{71} -6.76708 q^{72} +1.00000 q^{73} -11.1091 q^{74} -2.27984 q^{75} -2.70400 q^{76} -3.20405 q^{77} +14.8944 q^{78} +0.505167 q^{79} -2.21856 q^{80} -10.7633 q^{81} -3.55069 q^{82} +2.46997 q^{83} -4.87784 q^{84} -4.52607 q^{85} -0.867580 q^{86} -0.256246 q^{87} -3.07920 q^{88} +10.2082 q^{89} +2.53661 q^{90} +18.1354 q^{91} +4.29118 q^{92} +17.9825 q^{93} -11.2644 q^{94} +4.04933 q^{95} -8.20215 q^{96} +3.17998 q^{97} +3.76961 q^{98} +2.19767 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 37 q + 5 q^{2} + 3 q^{3} + 43 q^{4} + 37 q^{5} + 9 q^{6} + 6 q^{7} + 12 q^{8} + 50 q^{9}+O(q^{10}) $ 37 * q + 5 * q^2 + 3 * q^3 + 43 * q^4 + 37 * q^5 + 9 * q^6 + 6 * q^7 + 12 * q^8 + 50 * q^9	\( 37 q + 5 q^{2} + 3 q^{3} + 43 q^{4} + 37 q^{5} + 9 q^{6} + 6 q^{7} + 12 q^{8} + 50 q^{9} + 5 q^{10} + 37 q^{11} + 6 q^{12} + 11 q^{13} + 11 q^{14} + 3 q^{15} + 43 q^{16} + 38 q^{17} + 11 q^{18} + 34 q^{19} + 43 q^{20} + 39 q^{21} + 5 q^{22} + 4 q^{23} + 25 q^{24} + 37 q^{25} - 9 q^{26} + 3 q^{27} + 14 q^{28} + 58 q^{29} + 9 q^{30} + 8 q^{31} + 14 q^{32} + 3 q^{33} + 8 q^{34} + 6 q^{35} + 20 q^{36} + 2 q^{37} + 15 q^{38} + 14 q^{39} + 12 q^{40} + 62 q^{41} - 13 q^{42} + 30 q^{43} + 43 q^{44} + 50 q^{45} + 31 q^{46} + 5 q^{47} - 25 q^{48} + 59 q^{49} + 5 q^{50} + 23 q^{51} - q^{52} + 18 q^{53} + 13 q^{54} + 37 q^{55} + 22 q^{56} + 5 q^{57} - 40 q^{58} + 15 q^{59} + 6 q^{60} + 57 q^{61} + 20 q^{62} - 29 q^{63} + 10 q^{64} + 11 q^{65} + 9 q^{66} - 14 q^{67} + 53 q^{68} + 24 q^{69} + 11 q^{70} + 8 q^{71} + 15 q^{72} + 37 q^{73} + 7 q^{74} + 3 q^{75} + 59 q^{76} + 6 q^{77} + q^{78} + 42 q^{79} + 43 q^{80} + 61 q^{81} - 22 q^{82} + 44 q^{83} + 66 q^{84} + 38 q^{85} - q^{86} - 26 q^{87} + 12 q^{88} + 69 q^{89} + 11 q^{90} - 10 q^{91} - 21 q^{92} - 26 q^{93} + 29 q^{94} + 34 q^{95} - 9 q^{96} + 37 q^{97} - 15 q^{98} + 50 q^{99}+O(q^{100}) \) 37 * q + 5 * q^2 + 3 * q^3 + 43 * q^4 + 37 * q^5 + 9 * q^6 + 6 * q^7 + 12 * q^8 + 50 * q^9 + 5 * q^10 + 37 * q^11 + 6 * q^12 + 11 * q^13 + 11 * q^14 + 3 * q^15 + 43 * q^16 + 38 * q^17 + 11 * q^18 + 34 * q^19 + 43 * q^20 + 39 * q^21 + 5 * q^22 + 4 * q^23 + 25 * q^24 + 37 * q^25 - 9 * q^26 + 3 * q^27 + 14 * q^28 + 58 * q^29 + 9 * q^30 + 8 * q^31 + 14 * q^32 + 3 * q^33 + 8 * q^34 + 6 * q^35 + 20 * q^36 + 2 * q^37 + 15 * q^38 + 14 * q^39 + 12 * q^40 + 62 * q^41 - 13 * q^42 + 30 * q^43 + 43 * q^44 + 50 * q^45 + 31 * q^46 + 5 * q^47 - 25 * q^48 + 59 * q^49 + 5 * q^50 + 23 * q^51 - q^52 + 18 * q^53 + 13 * q^54 + 37 * q^55 + 22 * q^56 + 5 * q^57 - 40 * q^58 + 15 * q^59 + 6 * q^60 + 57 * q^61 + 20 * q^62 - 29 * q^63 + 10 * q^64 + 11 * q^65 + 9 * q^66 - 14 * q^67 + 53 * q^68 + 24 * q^69 + 11 * q^70 + 8 * q^71 + 15 * q^72 + 37 * q^73 + 7 * q^74 + 3 * q^75 + 59 * q^76 + 6 * q^77 + q^78 + 42 * q^79 + 43 * q^80 + 61 * q^81 - 22 * q^82 + 44 * q^83 + 66 * q^84 + 38 * q^85 - q^86 - 26 * q^87 + 12 * q^88 + 69 * q^89 + 11 * q^90 - 10 * q^91 - 21 * q^92 - 26 * q^93 + 29 * q^94 + 34 * q^95 - 9 * q^96 + 37 * q^97 - 15 * q^98 + 50 * 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 $

$2$	1.15422	0.816160	0.408080	−	0.912946i	$-0.366198\pi$
$2$	1.15422	0.816160	0.408080	+	0.912946i	$0.366198\pi$
$3$	−2.27984	−1.31627	−0.658133	−	0.752901i	$-0.728654\pi$
$3$	−2.27984	−1.31627	−0.658133	+	0.752901i	$0.728654\pi$
$4$	−0.667766	−0.333883
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	−2.63145	−1.07428
$7$	−3.20405	−1.21102	−0.605508	−	0.795839i	$-0.707030\pi$
$7$	−3.20405	−1.21102	−0.605508	+	0.795839i	$0.707030\pi$
$8$	−3.07920	−1.08866
$9$	2.19767	0.732558
$10$	1.15422	0.364998
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	1.52240	0.439479
$13$	−5.66015	−1.56984	−0.784922	−	0.619594i	$-0.787297\pi$
$13$	−5.66015	−1.56984	−0.784922	+	0.619594i	$0.787297\pi$
$14$	−3.69819	−0.988383
$15$	−2.27984	−0.588652
$16$	−2.21856	−0.554639
$17$	−4.52607	−1.09773	−0.548867	−	0.835910i	$-0.684940\pi$
$17$	−4.52607	−1.09773	−0.548867	+	0.835910i	$0.684940\pi$
$18$	2.53661	0.597884
$19$	4.04933	0.928980	0.464490	−	0.885578i	$-0.346238\pi$
$19$	4.04933	0.928980	0.464490	+	0.885578i	$0.346238\pi$
$20$	−0.667766	−0.149317
$21$	7.30472	1.59402
$22$	1.15422	0.246082
$23$	−6.42618	−1.33995	−0.669976	−	0.742383i	$-0.733696\pi$
$23$	−6.42618	−1.33995	−0.669976	+	0.742383i	$0.733696\pi$
$24$	7.02009	1.43297
$25$	1.00000	0.200000
$26$	−6.53309	−1.28124
$27$	1.82918	0.352025
$28$	2.13955	0.404338
$29$	0.112396	0.0208715	0.0104357	−	0.999946i	$-0.496678\pi$
$29$	0.112396	0.0208715	0.0104357	+	0.999946i	$0.496678\pi$
$30$	−2.63145	−0.480435
$31$	−7.88760	−1.41666	−0.708328	−	0.705884i	$-0.750550\pi$
$31$	−7.88760	−1.41666	−0.708328	+	0.705884i	$0.750550\pi$
$32$	3.59769	0.635987
$33$	−2.27984	−0.396869
$34$	−5.22410	−0.895926
$35$	−3.20405	−0.541583
$36$	−1.46753	−0.244588
$37$	−9.62475	−1.58230	−0.791150	−	0.611622i	$-0.790517\pi$
$37$	−9.62475	−1.58230	−0.791150	+	0.611622i	$0.790517\pi$
$38$	4.67383	0.758196
$39$	12.9043	2.06633
$40$	−3.07920	−0.486864
$41$	−3.07626	−0.480431	−0.240215	−	0.970720i	$-0.577218\pi$
$41$	−3.07626	−0.480431	−0.240215	+	0.970720i	$0.577218\pi$
$42$	8.43129	1.30098
$43$	−0.751656	−0.114627	−0.0573133	−	0.998356i	$-0.518253\pi$
$43$	−0.751656	−0.114627	−0.0573133	+	0.998356i	$0.518253\pi$
$44$	−0.667766	−0.100669
$45$	2.19767	0.327610
$46$	−7.41726	−1.09362
$47$	−9.75931	−1.42354	−0.711771	−	0.702412i	$-0.752107\pi$
$47$	−9.75931	−1.42354	−0.711771	+	0.702412i	$0.752107\pi$
$48$	5.05796	0.730053
$49$	3.26593	0.466561
$50$	1.15422	0.163232
$51$	10.3187	1.44491
$52$	3.77966	0.524144
$53$	7.14813	0.981872	0.490936	−	0.871196i	$-0.336655\pi$
$53$	7.14813	0.981872	0.490936	+	0.871196i	$0.336655\pi$
$54$	2.11128	0.287309
$55$	1.00000	0.134840
$56$	9.86591	1.31839
$57$	−9.23182	−1.22279
$58$	0.129731	0.0170345
$59$	2.92563	0.380884	0.190442	−	0.981698i	$-0.439008\pi$
$59$	2.92563	0.380884	0.190442	+	0.981698i	$0.439008\pi$
$60$	1.52240	0.196541
$61$	9.27987	1.18817	0.594083	−	0.804404i	$-0.297515\pi$
$61$	9.27987	1.18817	0.594083	+	0.804404i	$0.297515\pi$
$62$	−9.10407	−1.15622
$63$	−7.04145	−0.887140
$64$	8.58965	1.07371
$65$	−5.66015	−0.702056
$66$	−2.63145	−0.323909
$67$	−5.53467	−0.676168	−0.338084	−	0.941116i	$-0.609779\pi$
$67$	−5.53467	−0.676168	−0.338084	+	0.941116i	$0.609779\pi$
$68$	3.02235	0.366514
$69$	14.6507	1.76373
$70$	−3.69819	−0.442018
$71$	1.61411	0.191559	0.0957796	−	0.995403i	$-0.469466\pi$
$71$	1.61411	0.191559	0.0957796	+	0.995403i	$0.469466\pi$
$72$	−6.76708	−0.797508
$73$	1.00000	0.117041
$73$	1.00000	0.117041
$74$	−11.1091	−1.29141
$75$	−2.27984	−0.263253
$76$	−2.70400	−0.310170
$77$	−3.20405	−0.365135
$78$	14.8944	1.68646
$79$	0.505167	0.0568357	0.0284179	−	0.999596i	$-0.490953\pi$
$79$	0.505167	0.0568357	0.0284179	+	0.999596i	$0.490953\pi$
$80$	−2.21856	−0.248042
$81$	−10.7633	−1.19592
$82$	−3.55069	−0.392108
$83$	2.46997	0.271115	0.135557	−	0.990769i	$-0.456717\pi$
$83$	2.46997	0.271115	0.135557	+	0.990769i	$0.456717\pi$
$84$	−4.87784	−0.532216
$85$	−4.52607	−0.490921
$86$	−0.867580	−0.0935536
$87$	−0.256246	−0.0274724
$88$	−3.07920	−0.328244
$89$	10.2082	1.08207	0.541034	−	0.841001i	$-0.318033\pi$
$89$	10.2082	1.08207	0.541034	+	0.841001i	$0.318033\pi$
$90$	2.53661	0.267382
$91$	18.1354	1.90111
$92$	4.29118	0.447387
$93$	17.9825	1.86470
$94$	−11.2644	−1.16184
$95$	4.04933	0.415452
$96$	−8.20215	−0.837129
$97$	3.17998	0.322878	0.161439	−	0.986883i	$-0.448386\pi$
$97$	3.17998	0.322878	0.161439	+	0.986883i	$0.448386\pi$
$98$	3.76961	0.380788
$99$	2.19767	0.220875
$100$	−0.667766	−0.0667766
$101$	−7.94121	−0.790179	−0.395090	−	0.918643i	$-0.629287\pi$
$101$	−7.94121	−0.790179	−0.395090	+	0.918643i	$0.629287\pi$
$102$	11.9101	1.17928
$103$	2.33626	0.230198	0.115099	−	0.993354i	$-0.463281\pi$
$103$	2.33626	0.230198	0.115099	+	0.993354i	$0.463281\pi$
$104$	17.4288	1.70903
$105$	7.30472	0.712868
$106$	8.25055	0.801364
$107$	12.2130	1.18067	0.590337	−	0.807157i	$-0.298995\pi$
$107$	12.2130	1.18067	0.590337	+	0.807157i	$0.298995\pi$
$108$	−1.22146	−0.117535
$109$	−0.538617	−0.0515901	−0.0257951	−	0.999667i	$-0.508212\pi$
$109$	−0.538617	−0.0515901	−0.0257951	+	0.999667i	$0.508212\pi$
$110$	1.15422	0.110051
$111$	21.9429	2.08273
$112$	7.10837	0.671677
$113$	8.02434	0.754866	0.377433	−	0.926037i	$-0.376807\pi$
$113$	8.02434	0.754866	0.377433	+	0.926037i	$0.376807\pi$
$114$	−10.6556	−0.997988
$115$	−6.42618	−0.599245
$116$	−0.0750544	−0.00696863
$117$	−12.4392	−1.15000
$118$	3.37683	0.310863
$119$	14.5017	1.32937
$120$	7.02009	0.640843
$121$	1.00000	0.0909091
$122$	10.7111	0.969734
$123$	7.01338	0.632375
$124$	5.26707	0.472997
$125$	1.00000	0.0894427
$126$	−8.12742	−0.724048
$127$	−8.45848	−0.750568	−0.375284	−	0.926910i	$-0.622455\pi$
$127$	−8.45848	−0.750568	−0.375284	+	0.926910i	$0.622455\pi$
$128$	2.71902	0.240329
$129$	1.71366	0.150879
$130$	−6.53309	−0.572990
$131$	−4.85067	−0.423805	−0.211903	−	0.977291i	$-0.567966\pi$
$131$	−4.85067	−0.423805	−0.211903	+	0.977291i	$0.567966\pi$
$132$	1.52240	0.132508
$133$	−12.9742	−1.12501
$134$	−6.38825	−0.551861
$135$	1.82918	0.157430
$136$	13.9367	1.19506
$137$	−10.4567	−0.893376	−0.446688	−	0.894690i	$-0.647397\pi$
$137$	−10.4567	−0.893376	−0.446688	+	0.894690i	$0.647397\pi$
$138$	16.9102	1.43949
$139$	2.26075	0.191754	0.0958770	−	0.995393i	$-0.469434\pi$
$139$	2.26075	0.191754	0.0958770	+	0.995393i	$0.469434\pi$
$140$	2.13955	0.180825
$141$	22.2497	1.87376
$142$	1.86304	0.156343
$143$	−5.66015	−0.473326
$144$	−4.87567	−0.406305
$145$	0.112396	0.00933401
$146$	1.15422	0.0955243
$147$	−7.44579	−0.614118
$148$	6.42708	0.528303
$149$	6.13807	0.502850	0.251425	−	0.967877i	$-0.419101\pi$
$149$	6.13807	0.502850	0.251425	+	0.967877i	$0.419101\pi$
$150$	−2.63145	−0.214857
$151$	−13.4012	−1.09057	−0.545287	−	0.838249i	$-0.683579\pi$
$151$	−13.4012	−1.09057	−0.545287	+	0.838249i	$0.683579\pi$
$152$	−12.4687	−1.01134
$153$	−9.94682	−0.804153
$154$	−3.69819	−0.298009
$155$	−7.88760	−0.633548
$156$	−8.61702	−0.689913
$157$	19.7871	1.57918	0.789592	−	0.613632i	$-0.210292\pi$
$157$	19.7871	1.57918	0.789592	+	0.613632i	$0.210292\pi$
$158$	0.583076	0.0463870
$159$	−16.2966	−1.29240
$160$	3.59769	0.284422
$161$	20.5898	1.62270
$162$	−12.4232	−0.976059
$163$	−9.80532	−0.768012	−0.384006	−	0.923331i	$-0.625456\pi$
$163$	−9.80532	−0.768012	−0.384006	+	0.923331i	$0.625456\pi$
$164$	2.05422	0.160408
$165$	−2.27984	−0.177485
$166$	2.85091	0.221273
$167$	−20.5097	−1.58709	−0.793545	−	0.608511i	$-0.791767\pi$
$167$	−20.5097	−1.58709	−0.793545	+	0.608511i	$0.791767\pi$
$168$	−22.4927	−1.73535
$169$	19.0373	1.46441
$170$	−5.22410	−0.400670
$171$	8.89910	0.680531
$172$	0.501930	0.0382718
$173$	4.29185	0.326303	0.163152	−	0.986601i	$-0.447834\pi$
$173$	4.29185	0.326303	0.163152	+	0.986601i	$0.447834\pi$
$174$	−0.295765	−0.0224219
$175$	−3.20405	−0.242203
$176$	−2.21856	−0.167230
$177$	−6.66997	−0.501346
$178$	11.7826	0.883141
$179$	4.66488	0.348670	0.174335	−	0.984686i	$-0.444223\pi$
$179$	4.66488	0.348670	0.174335	+	0.984686i	$0.444223\pi$
$180$	−1.46753	−0.109383
$181$	22.4370	1.66773	0.833863	−	0.551971i	$-0.186124\pi$
$181$	22.4370	1.66773	0.833863	+	0.551971i	$0.186124\pi$
$182$	20.9323	1.55161
$183$	−21.1566	−1.56394
$184$	19.7875	1.45875
$185$	−9.62475	−0.707626
$186$	20.7558	1.52189
$187$	−4.52607	−0.330979
$188$	6.51693	0.475296
$189$	−5.86077	−0.426308
$190$	4.67383	0.339076
$191$	−20.6211	−1.49209	−0.746045	−	0.665896i	$-0.768050\pi$
$191$	−20.6211	−1.49209	−0.746045	+	0.665896i	$0.768050\pi$
$192$	−19.5830	−1.41328
$193$	−1.24626	−0.0897075	−0.0448537	−	0.998994i	$-0.514282\pi$
$193$	−1.24626	−0.0897075	−0.0448537	+	0.998994i	$0.514282\pi$
$194$	3.67041	0.263520
$195$	12.9043	0.924093
$196$	−2.18087	−0.155777
$197$	17.2698	1.23042	0.615210	−	0.788363i	$-0.289071\pi$
$197$	17.2698	1.23042	0.615210	+	0.788363i	$0.289071\pi$
$198$	2.53661	0.180269
$199$	7.27341	0.515599	0.257799	−	0.966198i	$-0.417003\pi$
$199$	7.27341	0.515599	0.257799	+	0.966198i	$0.417003\pi$
$200$	−3.07920	−0.217732
$201$	12.6182	0.890017
$202$	−9.16593	−0.644913
$203$	−0.360123	−0.0252757
$204$	−6.89049	−0.482430
$205$	−3.07626	−0.214855
$206$	2.69656	0.187879
$207$	−14.1227	−0.981592
$208$	12.5574	0.870698
$209$	4.04933	0.280098
$210$	8.43129	0.581814
$211$	−18.4011	−1.26679	−0.633393	−	0.773831i	$-0.718338\pi$
$211$	−18.4011	−1.26679	−0.633393	+	0.773831i	$0.718338\pi$
$212$	−4.77328	−0.327830
$213$	−3.67990	−0.252143
$214$	14.0965	0.963618
$215$	−0.751656	−0.0512625
$216$	−5.63240	−0.383236
$217$	25.2723	1.71559
$218$	−0.621685	−0.0421058
$219$	−2.27984	−0.154057
$220$	−0.667766	−0.0450208
$221$	25.6183	1.72327
$222$	25.3270	1.69984
$223$	18.2622	1.22293	0.611465	−	0.791271i	$-0.290580\pi$
$223$	18.2622	1.22293	0.611465	+	0.791271i	$0.290580\pi$
$224$	−11.5272	−0.770191
$225$	2.19767	0.146512
$226$	9.26188	0.616091
$227$	1.96225	0.130239	0.0651196	−	0.997877i	$-0.479257\pi$
$227$	1.96225	0.130239	0.0651196	+	0.997877i	$0.479257\pi$
$228$	6.16470	0.408267
$229$	4.05503	0.267964	0.133982	−	0.990984i	$-0.457224\pi$
$229$	4.05503	0.267964	0.133982	+	0.990984i	$0.457224\pi$
$230$	−7.41726	−0.489080
$231$	7.30472	0.480615
$232$	−0.346091	−0.0227220
$233$	−10.6973	−0.700805	−0.350403	−	0.936599i	$-0.613955\pi$
$233$	−10.6973	−0.700805	−0.350403	+	0.936599i	$0.613955\pi$
$234$	−14.3576	−0.938586
$235$	−9.75931	−0.636627
$236$	−1.95363	−0.127171
$237$	−1.15170	−0.0748110
$238$	16.7383	1.08498
$239$	20.6767	1.33746	0.668731	−	0.743505i	$-0.266838\pi$
$239$	20.6767	1.33746	0.668731	+	0.743505i	$0.266838\pi$
$240$	5.05796	0.326490
$241$	−18.0638	−1.16359	−0.581797	−	0.813334i	$-0.697650\pi$
$241$	−18.0638	−1.16359	−0.581797	+	0.813334i	$0.697650\pi$
$242$	1.15422	0.0741964
$243$	19.0510	1.22212
$244$	−6.19678	−0.396708
$245$	3.26593	0.208652
$246$	8.09501	0.516119
$247$	−22.9198	−1.45835
$248$	24.2875	1.54226
$249$	−5.63115	−0.356860
$250$	1.15422	0.0729996
$251$	−1.98746	−0.125448	−0.0627238	−	0.998031i	$-0.519979\pi$
$251$	−1.98746	−0.125448	−0.0627238	+	0.998031i	$0.519979\pi$
$252$	4.70204	0.296201
$253$	−6.42618	−0.404011
$254$	−9.76298	−0.612584
$255$	10.3187	0.646183
$256$	−14.0410	−0.877560
$257$	22.9528	1.43175	0.715877	−	0.698226i	$-0.246027\pi$
$257$	22.9528	1.43175	0.715877	+	0.698226i	$0.246027\pi$
$258$	1.97794	0.123141
$259$	30.8382	1.91619
$260$	3.77966	0.234404
$261$	0.247010	0.0152896
$262$	−5.59876	−0.345893
$263$	16.9416	1.04466	0.522332	−	0.852742i	$-0.325062\pi$
$263$	16.9416	1.04466	0.522332	+	0.852742i	$0.325062\pi$
$264$	7.02009	0.432056
$265$	7.14813	0.439106
$266$	−14.9752	−0.918188
$267$	−23.2731	−1.42429
$268$	3.69586	0.225761
$269$	−12.4753	−0.760635	−0.380318	−	0.924856i	$-0.624185\pi$
$269$	−12.4753	−0.760635	−0.380318	+	0.924856i	$0.624185\pi$
$270$	2.11128	0.128488
$271$	3.94056	0.239372	0.119686	−	0.992812i	$-0.461811\pi$
$271$	3.94056	0.239372	0.119686	+	0.992812i	$0.461811\pi$
$272$	10.0413	0.608846
$273$	−41.3458	−2.50236
$274$	−12.0694	−0.729138
$275$	1.00000	0.0603023
$276$	−9.78322	−0.588881
$277$	21.1218	1.26909	0.634543	−	0.772888i	$-0.281188\pi$
$277$	21.1218	1.26909	0.634543	+	0.772888i	$0.281188\pi$
$278$	2.60941	0.156502
$279$	−17.3344	−1.03778
$280$	9.86591	0.589601
$281$	−6.59520	−0.393437	−0.196718	−	0.980460i	$-0.563028\pi$
$281$	−6.59520	−0.393437	−0.196718	+	0.980460i	$0.563028\pi$
$282$	25.6811	1.52929
$283$	29.1875	1.73502	0.867508	−	0.497423i	$-0.165720\pi$
$283$	29.1875	1.73502	0.867508	+	0.497423i	$0.165720\pi$
$284$	−1.07784	−0.0639583
$285$	−9.23182	−0.546846
$286$	−6.53309	−0.386310
$287$	9.85648	0.581809
$288$	7.90654	0.465898
$289$	3.48531	0.205018
$290$	0.129731	0.00761804
$291$	−7.24985	−0.424994
$292$	−0.667766	−0.0390780
$293$	13.5006	0.788711	0.394355	−	0.918958i	$-0.370968\pi$
$293$	13.5006	0.788711	0.394355	+	0.918958i	$0.370968\pi$
$294$	−8.59411	−0.501219
$295$	2.92563	0.170337
$296$	29.6365	1.72259
$297$	1.82918	0.106140
$298$	7.08471	0.410406
$299$	36.3732	2.10352
$300$	1.52240	0.0878958
$301$	2.40834	0.138815
$302$	−15.4680	−0.890084
$303$	18.1047	1.04009
$304$	−8.98367	−0.515249
$305$	9.27987	0.531364
$306$	−11.4809	−0.656318
$307$	−19.9301	−1.13747	−0.568735	−	0.822521i	$-0.692567\pi$
$307$	−19.9301	−1.13747	−0.568735	+	0.822521i	$0.692567\pi$
$308$	2.13955	0.121912
$309$	−5.32629	−0.303002
$310$	−9.10407	−0.517076
$311$	−20.3307	−1.15285	−0.576424	−	0.817151i	$-0.695552\pi$
$311$	−20.3307	−1.15285	−0.576424	+	0.817151i	$0.695552\pi$
$312$	−39.7348	−2.24954
$313$	23.8034	1.34544	0.672722	−	0.739895i	$-0.265125\pi$
$313$	23.8034	1.34544	0.672722	+	0.739895i	$0.265125\pi$
$314$	22.8388	1.28887
$315$	−7.04145	−0.396741
$316$	−0.337333	−0.0189765
$317$	9.47657	0.532257	0.266128	−	0.963938i	$-0.414255\pi$
$317$	9.47657	0.532257	0.266128	+	0.963938i	$0.414255\pi$
$318$	−18.8099	−1.05481
$319$	0.112396	0.00629299
$320$	8.58965	0.480176
$321$	−27.8436	−1.55408
$322$	23.7653	1.32439
$323$	−18.3275	−1.01977
$324$	7.18733	0.399296
$325$	−5.66015	−0.313969
$326$	−11.3175	−0.626821
$327$	1.22796	0.0679064
$328$	9.47241	0.523027
$329$	31.2693	1.72393
$330$	−2.63145	−0.144856
$331$	10.4906	0.576618	0.288309	−	0.957537i	$-0.406907\pi$
$331$	10.4906	0.576618	0.288309	+	0.957537i	$0.406907\pi$
$332$	−1.64936	−0.0905206
$333$	−21.1521	−1.15913
$334$	−23.6728	−1.29532
$335$	−5.53467	−0.302391
$336$	−16.2059	−0.884107
$337$	−8.90822	−0.485262	−0.242631	−	0.970119i	$-0.578010\pi$
$337$	−8.90822	−0.485262	−0.242631	+	0.970119i	$0.578010\pi$
$338$	21.9734	1.19519
$339$	−18.2942	−0.993605
$340$	3.02235	0.163910
$341$	−7.88760	−0.427138
$342$	10.2716	0.555423
$343$	11.9642	0.646004
$344$	2.31450	0.124790
$345$	14.6507	0.788766
$346$	4.95375	0.266315
$347$	2.10445	0.112973	0.0564865	−	0.998403i	$-0.482010\pi$
$347$	2.10445	0.112973	0.0564865	+	0.998403i	$0.482010\pi$
$348$	0.171112	0.00917257
$349$	−3.71439	−0.198827	−0.0994134	−	0.995046i	$-0.531697\pi$
$349$	−3.71439	−0.198827	−0.0994134	+	0.995046i	$0.531697\pi$
$350$	−3.69819	−0.197677
$351$	−10.3534	−0.552625
$352$	3.59769	0.191757
$353$	−26.9097	−1.43226	−0.716130	−	0.697967i	$-0.754088\pi$
$353$	−26.9097	−1.43226	−0.716130	+	0.697967i	$0.754088\pi$
$354$	−7.69864	−0.409178
$355$	1.61411	0.0856678
$356$	−6.81669	−0.361284
$357$	−33.0617	−1.74981
$358$	5.38432	0.284570
$359$	−35.4592	−1.87147	−0.935733	−	0.352710i	$-0.885260\pi$
$359$	−35.4592	−1.87147	−0.935733	+	0.352710i	$0.885260\pi$
$360$	−6.76708	−0.356656
$361$	−2.60294	−0.136997
$362$	25.8973	1.36113
$363$	−2.27984	−0.119661
$364$	−12.1102	−0.634747
$365$	1.00000	0.0523424
$366$	−24.4195	−1.27643
$367$	−20.6518	−1.07802	−0.539008	−	0.842301i	$-0.681201\pi$
$367$	−20.6518	−1.07802	−0.539008	+	0.842301i	$0.681201\pi$
$368$	14.2569	0.743190
$369$	−6.76061	−0.351943
$370$	−11.1091	−0.577536
$371$	−22.9030	−1.18906
$372$	−12.0081	−0.622590
$373$	−0.187311	−0.00969858	−0.00484929	−	0.999988i	$-0.501544\pi$
$373$	−0.187311	−0.00969858	−0.00484929	+	0.999988i	$0.501544\pi$
$374$	−5.22410	−0.270132
$375$	−2.27984	−0.117730
$376$	30.0509	1.54976
$377$	−0.636181	−0.0327650
$378$	−6.76464	−0.347936
$379$	29.7056	1.52587	0.762937	−	0.646472i	$-0.223756\pi$
$379$	29.7056	1.52587	0.762937	+	0.646472i	$0.223756\pi$
$380$	−2.70400	−0.138712
$381$	19.2840	0.987948
$382$	−23.8014	−1.21778
$383$	−32.9288	−1.68258	−0.841290	−	0.540583i	$-0.818204\pi$
$383$	−32.9288	−1.68258	−0.841290	+	0.540583i	$0.818204\pi$
$384$	−6.19892	−0.316337
$385$	−3.20405	−0.163293
$386$	−1.43846	−0.0732157
$387$	−1.65190	−0.0839706
$388$	−2.12348	−0.107803
$389$	−27.2925	−1.38378	−0.691891	−	0.722002i	$-0.743222\pi$
$389$	−27.2925	−1.38378	−0.691891	+	0.722002i	$0.743222\pi$
$390$	14.8944	0.754207
$391$	29.0854	1.47091
$392$	−10.0564	−0.507927
$393$	11.0588	0.557841
$394$	19.9332	1.00422
$395$	0.505167	0.0254177
$396$	−1.46753	−0.0737462
$397$	18.6857	0.937806	0.468903	−	0.883250i	$-0.344649\pi$
$397$	18.6857	0.937806	0.468903	+	0.883250i	$0.344649\pi$
$398$	8.39515	0.420811
$399$	29.5792	1.48081
$400$	−2.21856	−0.110928
$401$	−9.50134	−0.474474	−0.237237	−	0.971452i	$-0.576242\pi$
$401$	−9.50134	−0.474474	−0.237237	+	0.971452i	$0.576242\pi$
$402$	14.5642	0.726396
$403$	44.6451	2.22393
$404$	5.30286	0.263827
$405$	−10.7633	−0.534830
$406$	−0.415663	−0.0206290
$407$	−9.62475	−0.477081
$408$	−31.7734	−1.57302
$409$	−23.8360	−1.17861	−0.589307	−	0.807909i	$-0.700599\pi$
$409$	−23.8360	−1.17861	−0.589307	+	0.807909i	$0.700599\pi$
$410$	−3.55069	−0.175356
$411$	23.8396	1.17592
$412$	−1.56007	−0.0768592
$413$	−9.37386	−0.461257
$414$	−16.3007	−0.801136
$415$	2.46997	0.121246
$416$	−20.3635	−0.998401
$417$	−5.15414	−0.252399
$418$	4.67383	0.228605
$419$	−27.5247	−1.34467	−0.672335	−	0.740247i	$-0.734708\pi$
$419$	−27.5247	−1.34467	−0.672335	+	0.740247i	$0.734708\pi$
$420$	−4.87784	−0.238014
$421$	−22.6777	−1.10524	−0.552621	−	0.833433i	$-0.686372\pi$
$421$	−22.6777	−1.10524	−0.552621	+	0.833433i	$0.686372\pi$
$422$	−21.2390	−1.03390
$423$	−21.4478	−1.04283
$424$	−22.0105	−1.06893
$425$	−4.52607	−0.219547
$426$	−4.24744	−0.205789
$427$	−29.7332	−1.43889
$428$	−8.15541	−0.394207
$429$	12.9043	0.623023
$430$	−0.867580	−0.0418384
$431$	−3.67464	−0.177001	−0.0885007	−	0.996076i	$-0.528208\pi$
$431$	−3.67464	−0.177001	−0.0885007	+	0.996076i	$0.528208\pi$
$432$	−4.05813	−0.195247
$433$	5.20449	0.250112	0.125056	−	0.992150i	$-0.460089\pi$
$433$	5.20449	0.250112	0.125056	+	0.992150i	$0.460089\pi$
$434$	29.1699	1.40020
$435$	−0.256246	−0.0122860
$436$	0.359670	0.0172251
$437$	−26.0217	−1.24479
$438$	−2.63145	−0.125735
$439$	−34.1386	−1.62935	−0.814673	−	0.579920i	$-0.803084\pi$
$439$	−34.1386	−1.62935	−0.814673	+	0.579920i	$0.803084\pi$
$440$	−3.07920	−0.146795
$441$	7.17744	0.341783
$442$	29.5692	1.40646
$443$	−17.7599	−0.843800	−0.421900	−	0.906642i	$-0.638637\pi$
$443$	−17.7599	−0.843800	−0.421900	+	0.906642i	$0.638637\pi$
$444$	−14.6527	−0.695387
$445$	10.2082	0.483916
$446$	21.0787	0.998107
$447$	−13.9938	−0.661885
$448$	−27.5217	−1.30028
$449$	25.5737	1.20690	0.603449	−	0.797401i	$-0.293793\pi$
$449$	25.5737	1.20690	0.603449	+	0.797401i	$0.293793\pi$
$450$	2.53661	0.119577
$451$	−3.07626	−0.144855
$452$	−5.35838	−0.252037
$453$	30.5526	1.43549
$454$	2.26488	0.106296
$455$	18.1354	0.850201
$456$	28.4266	1.33120
$457$	−5.61746	−0.262774	−0.131387	−	0.991331i	$-0.541943\pi$
$457$	−5.61746	−0.262774	−0.131387	+	0.991331i	$0.541943\pi$
$458$	4.68041	0.218701
$459$	−8.27898	−0.386430
$460$	4.29118	0.200078
$461$	−26.9737	−1.25629	−0.628144	−	0.778097i	$-0.716185\pi$
$461$	−26.9737	−1.25629	−0.628144	+	0.778097i	$0.716185\pi$
$462$	8.43129	0.392259
$463$	−6.44965	−0.299740	−0.149870	−	0.988706i	$-0.547886\pi$
$463$	−6.44965	−0.299740	−0.149870	+	0.988706i	$0.547886\pi$
$464$	−0.249358	−0.0115761
$465$	17.9825	0.833918
$466$	−12.3471	−0.571969
$467$	17.9830	0.832155	0.416077	−	0.909329i	$-0.363405\pi$
$467$	17.9830	0.832155	0.416077	+	0.909329i	$0.363405\pi$
$468$	8.30645	0.383966
$469$	17.7334	0.818850
$470$	−11.2644	−0.519590
$471$	−45.1115	−2.07863
$472$	−9.00860	−0.414654
$473$	−0.751656	−0.0345612
$474$	−1.32932	−0.0610577
$475$	4.04933	0.185796
$476$	−9.68377	−0.443855
$477$	15.7093	0.719278
$478$	23.8655	1.09158
$479$	−28.3279	−1.29433	−0.647167	−	0.762348i	$-0.724046\pi$
$479$	−28.3279	−1.29433	−0.647167	+	0.762348i	$0.724046\pi$
$480$	−8.20215	−0.374375
$481$	54.4776	2.48396
$482$	−20.8497	−0.949679
$483$	−46.9415	−2.13591
$484$	−0.667766	−0.0303530
$485$	3.17998	0.144395
$486$	21.9891	0.997446
$487$	−14.3592	−0.650678	−0.325339	−	0.945597i	$-0.605478\pi$
$487$	−14.3592	−0.650678	−0.325339	+	0.945597i	$0.605478\pi$
$488$	−28.5746	−1.29351
$489$	22.3546	1.01091
$490$	3.76961	0.170294
$491$	18.2794	0.824936	0.412468	−	0.910972i	$-0.364667\pi$
$491$	18.2794	0.824936	0.412468	+	0.910972i	$0.364667\pi$
$492$	−4.68329	−0.211139
$493$	−0.508714	−0.0229113
$494$	−26.4546	−1.19025
$495$	2.19767	0.0987781
$496$	17.4991	0.785733
$497$	−5.17167	−0.231981
$498$	−6.49961	−0.291254
$499$	11.6383	0.521000	0.260500	−	0.965474i	$-0.416113\pi$
$499$	11.6383	0.521000	0.260500	+	0.965474i	$0.416113\pi$
$500$	−0.667766	−0.0298634
$501$	46.7589	2.08903
$502$	−2.29398	−0.102385
$503$	9.98072	0.445018	0.222509	−	0.974931i	$-0.428575\pi$
$503$	9.98072	0.445018	0.222509	+	0.974931i	$0.428575\pi$
$504$	21.6820	0.965795
$505$	−7.94121	−0.353379
$506$	−7.41726	−0.329737
$507$	−43.4021	−1.92756
$508$	5.64828	0.250602
$509$	1.22996	0.0545170	0.0272585	−	0.999628i	$-0.491322\pi$
$509$	1.22996	0.0545170	0.0272585	+	0.999628i	$0.491322\pi$
$510$	11.9101	0.527389
$511$	−3.20405	−0.141739
$512$	−21.6444	−0.956558
$513$	7.40694	0.327024
$514$	26.4926	1.16854
$515$	2.33626	0.102948
$516$	−1.14432	−0.0503759
$517$	−9.75931	−0.429214
$518$	35.5942	1.56392
$519$	−9.78473	−0.429502
$520$	17.4288	0.764301
$521$	−1.96598	−0.0861311	−0.0430656	−	0.999072i	$-0.513712\pi$
$521$	−1.96598	−0.0861311	−0.0430656	+	0.999072i	$0.513712\pi$
$522$	0.285106	0.0124787
$523$	45.0345	1.96922	0.984612	−	0.174757i	$-0.0559141\pi$
$523$	45.0345	1.96922	0.984612	+	0.174757i	$0.0559141\pi$
$524$	3.23911	0.141501
$525$	7.30472	0.318804
$526$	19.5544	0.852614
$527$	35.6998	1.55511
$528$	5.05796	0.220119
$529$	18.2958	0.795471
$530$	8.25055	0.358381
$531$	6.42958	0.279020
$532$	8.66375	0.375621
$533$	17.4121	0.754201
$534$	−26.8624	−1.16245
$535$	12.2130	0.528013
$536$	17.0424	0.736118
$537$	−10.6352	−0.458942
$538$	−14.3994	−0.620800
$539$	3.26593	0.140673
$540$	−1.22146	−0.0525633
$541$	45.9707	1.97643	0.988216	−	0.153063i	$-0.0489137\pi$
$541$	45.9707	1.97643	0.988216	+	0.153063i	$0.0489137\pi$
$542$	4.54829	0.195366
$543$	−51.1527	−2.19517
$544$	−16.2834	−0.698144
$545$	−0.538617	−0.0230718
$546$	−47.7224	−2.04233
$547$	−24.3657	−1.04180	−0.520901	−	0.853617i	$-0.674404\pi$
$547$	−24.3657	−1.04180	−0.520901	+	0.853617i	$0.674404\pi$
$548$	6.98262	0.298283
$549$	20.3941	0.870401
$550$	1.15422	0.0492163
$551$	0.455130	0.0193892
$552$	−45.1124	−1.92011
$553$	−1.61858	−0.0688290
$554$	24.3793	1.03578
$555$	21.9429	0.931425
$556$	−1.50965	−0.0640234
$557$	−21.3349	−0.903989	−0.451995	−	0.892021i	$-0.649287\pi$
$557$	−21.3349	−0.903989	−0.451995	+	0.892021i	$0.649287\pi$
$558$	−20.0078	−0.846996
$559$	4.25449	0.179946
$560$	7.10837	0.300383
$561$	10.3187	0.435657
$562$	−7.61235	−0.321107
$563$	−38.0253	−1.60257	−0.801287	−	0.598281i	$-0.795851\pi$
$563$	−38.0253	−1.60257	−0.801287	+	0.598281i	$0.795851\pi$
$564$	−14.8576	−0.625616
$565$	8.02434	0.337586
$566$	33.6889	1.41605
$567$	34.4860	1.44827
$568$	−4.97016	−0.208543
$569$	−27.4676	−1.15150	−0.575750	−	0.817625i	$-0.695290\pi$
$569$	−27.4676	−1.15150	−0.575750	+	0.817625i	$0.695290\pi$
$570$	−10.6556	−0.446314
$571$	−20.4366	−0.855244	−0.427622	−	0.903958i	$-0.640649\pi$
$571$	−20.4366	−0.855244	−0.427622	+	0.903958i	$0.640649\pi$
$572$	3.77966	0.158035
$573$	47.0128	1.96399
$574$	11.3766	0.474850
$575$	−6.42618	−0.267990
$576$	18.8773	0.786552
$577$	−38.4056	−1.59885	−0.799423	−	0.600769i	$-0.794861\pi$
$577$	−38.4056	−1.59885	−0.799423	+	0.600769i	$0.794861\pi$
$578$	4.02283	0.167328
$579$	2.84127	0.118079
$580$	−0.0750544	−0.00311646
$581$	−7.91392	−0.328325
$582$	−8.36795	−0.346863
$583$	7.14813	0.296045
$584$	−3.07920	−0.127418
$585$	−12.4392	−0.514296
$586$	15.5827	0.643714
$587$	−25.8542	−1.06712	−0.533558	−	0.845764i	$-0.679145\pi$
$587$	−25.8542	−1.06712	−0.533558	+	0.845764i	$0.679145\pi$
$588$	4.97204	0.205044
$589$	−31.9395	−1.31604
$590$	3.37683	0.139022
$591$	−39.3723	−1.61956
$592$	21.3531	0.877606
$593$	34.2685	1.40724	0.703619	−	0.710577i	$-0.251566\pi$
$593$	34.2685	1.40724	0.703619	+	0.710577i	$0.251566\pi$
$594$	2.11128	0.0866269
$595$	14.5017	0.594514
$596$	−4.09879	−0.167893
$597$	−16.5822	−0.678665
$598$	41.9828	1.71681
$599$	−7.35461	−0.300501	−0.150251	−	0.988648i	$-0.548008\pi$
$599$	−7.35461	−0.300501	−0.150251	+	0.988648i	$0.548008\pi$
$600$	7.02009	0.286594
$601$	27.6582	1.12820	0.564101	−	0.825706i	$-0.309223\pi$
$601$	27.6582	1.12820	0.564101	+	0.825706i	$0.309223\pi$
$602$	2.77977	0.113295
$603$	−12.1634	−0.495332
$604$	8.94887	0.364124
$605$	1.00000	0.0406558
$606$	20.8969	0.848877
$607$	27.4514	1.11422	0.557109	−	0.830439i	$-0.311911\pi$
$607$	27.4514	1.11422	0.557109	+	0.830439i	$0.311911\pi$
$608$	14.5682	0.590819
$609$	0.821024	0.0332696
$610$	10.7111	0.433678
$611$	55.2392	2.23474
$612$	6.64215	0.268493
$613$	44.1459	1.78304	0.891519	−	0.452984i	$-0.149640\pi$
$613$	44.1459	1.78304	0.891519	+	0.452984i	$0.149640\pi$
$614$	−23.0038	−0.928357
$615$	7.01338	0.282807
$616$	9.86591	0.397509
$617$	35.6448	1.43501	0.717504	−	0.696555i	$-0.245285\pi$
$617$	35.6448	1.43501	0.717504	+	0.696555i	$0.245285\pi$
$618$	−6.14774	−0.247298
$619$	−32.7044	−1.31450	−0.657249	−	0.753673i	$-0.728280\pi$
$619$	−32.7044	−1.31450	−0.657249	+	0.753673i	$0.728280\pi$
$620$	5.26707	0.211531
$621$	−11.7546	−0.471697
$622$	−23.4662	−0.940908
$623$	−32.7076	−1.31040
$624$	−28.6288	−1.14607
$625$	1.00000	0.0400000
$626$	27.4744	1.09810
$627$	−9.23182	−0.368684
$628$	−13.2132	−0.527262
$629$	43.5623	1.73694
$630$	−8.12742	−0.323804
$631$	−38.9557	−1.55080	−0.775401	−	0.631470i	$-0.782452\pi$
$631$	−38.9557	−1.55080	−0.775401	+	0.631470i	$0.782452\pi$
$632$	−1.55551	−0.0618749
$633$	41.9516	1.66743
$634$	10.9381	0.434407
$635$	−8.45848	−0.335664
$636$	10.8823	0.431512
$637$	−18.4856	−0.732428
$638$	0.129731	0.00513608
$639$	3.54728	0.140328
$640$	2.71902	0.107479
$641$	−19.9011	−0.786045	−0.393023	−	0.919529i	$-0.628571\pi$
$641$	−19.9011	−0.786045	−0.393023	+	0.919529i	$0.628571\pi$
$642$	−32.1378	−1.26838
$643$	−48.9902	−1.93199	−0.965993	−	0.258569i	$-0.916749\pi$
$643$	−48.9902	−1.93199	−0.965993	+	0.258569i	$0.916749\pi$
$644$	−13.7492	−0.541793
$645$	1.71366	0.0674752
$646$	−21.1541	−0.832297
$647$	−8.04197	−0.316163	−0.158081	−	0.987426i	$-0.550531\pi$
$647$	−8.04197	−0.316163	−0.158081	+	0.987426i	$0.550531\pi$
$648$	33.1422	1.30195
$649$	2.92563	0.114841
$650$	−6.53309	−0.256249
$651$	−57.6167	−2.25818
$652$	6.54766	0.256426
$653$	−19.2255	−0.752354	−0.376177	−	0.926548i	$-0.622762\pi$
$653$	−19.2255	−0.752354	−0.376177	+	0.926548i	$0.622762\pi$
$654$	1.41734	0.0554225
$655$	−4.85067	−0.189531
$656$	6.82485	0.266466
$657$	2.19767	0.0857394
$658$	36.0918	1.40700
$659$	−21.2278	−0.826917	−0.413459	−	0.910523i	$-0.635679\pi$
$659$	−21.2278	−0.826917	−0.413459	+	0.910523i	$0.635679\pi$
$660$	1.52240	0.0592593
$661$	39.1429	1.52248	0.761242	−	0.648468i	$-0.224590\pi$
$661$	39.1429	1.52248	0.761242	+	0.648468i	$0.224590\pi$
$662$	12.1086	0.470613
$663$	−58.4055	−2.26828
$664$	−7.60555	−0.295152
$665$	−12.9742	−0.503120
$666$	−24.4142	−0.946032
$667$	−0.722279	−0.0279668
$668$	13.6957	0.529902
$669$	−41.6350	−1.60970
$670$	−6.38825	−0.246800
$671$	9.27987	0.358246
$672$	26.2801	1.01378
$673$	−38.9225	−1.50035	−0.750176	−	0.661238i	$-0.770031\pi$
$673$	−38.9225	−1.50035	−0.750176	+	0.661238i	$0.770031\pi$
$674$	−10.2821	−0.396051
$675$	1.82918	0.0704050
$676$	−12.7125	−0.488942
$677$	−11.6945	−0.449457	−0.224729	−	0.974421i	$-0.572150\pi$
$677$	−11.6945	−0.449457	−0.224729	+	0.974421i	$0.572150\pi$
$678$	−21.1156	−0.810941
$679$	−10.1888	−0.391011
$680$	13.9367	0.534447
$681$	−4.47362	−0.171430
$682$	−9.10407	−0.348613
$683$	45.5694	1.74367	0.871833	−	0.489803i	$-0.162931\pi$
$683$	45.5694	1.74367	0.871833	+	0.489803i	$0.162931\pi$
$684$	−5.94252	−0.227218
$685$	−10.4567	−0.399530
$686$	13.8093	0.527242
$687$	−9.24482	−0.352712
$688$	1.66759	0.0635764
$689$	−40.4595	−1.54139
$690$	16.9102	0.643759
$691$	33.2386	1.26445	0.632227	−	0.774783i	$-0.282141\pi$
$691$	33.2386	1.26445	0.632227	+	0.774783i	$0.282141\pi$
$692$	−2.86595	−0.108947
$693$	−7.04145	−0.267483
$694$	2.42901	0.0922040
$695$	2.26075	0.0857550
$696$	0.789032	0.0299082
$697$	13.9234	0.527385
$698$	−4.28724	−0.162274
$699$	24.3882	0.922446
$700$	2.13955	0.0808675
$701$	−4.11565	−0.155446	−0.0777230	−	0.996975i	$-0.524765\pi$
$701$	−4.11565	−0.155446	−0.0777230	+	0.996975i	$0.524765\pi$
$702$	−11.9502	−0.451030
$703$	−38.9738	−1.46992
$704$	8.58965	0.323735
$705$	22.2497	0.837971
$706$	−31.0599	−1.16895
$707$	25.4440	0.956920
$708$	4.45398	0.167391
$709$	−0.642630	−0.0241345	−0.0120672	−	0.999927i	$-0.503841\pi$
$709$	−0.642630	−0.0241345	−0.0120672	+	0.999927i	$0.503841\pi$
$710$	1.86304	0.0699187
$711$	1.11019	0.0416355
$712$	−31.4331	−1.17801
$713$	50.6872	1.89825
$714$	−38.1606	−1.42812
$715$	−5.66015	−0.211678
$716$	−3.11505	−0.116415
$717$	−47.1395	−1.76046
$718$	−40.9279	−1.52741
$719$	17.5093	0.652985	0.326493	−	0.945200i	$-0.394133\pi$
$719$	17.5093	0.652985	0.326493	+	0.945200i	$0.394133\pi$
$720$	−4.87567	−0.181705
$721$	−7.48548	−0.278774
$722$	−3.00437	−0.111811
$723$	41.1827	1.53160
$724$	−14.9826	−0.556825
$725$	0.112396	0.00417429
$726$	−2.63145	−0.0976622
$727$	40.2867	1.49415	0.747075	−	0.664740i	$-0.231458\pi$
$727$	40.2867	1.49415	0.747075	+	0.664740i	$0.231458\pi$
$728$	−55.8426	−2.06966
$729$	−11.1434	−0.412719
$730$	1.15422	0.0427198
$731$	3.40205	0.125829
$732$	14.1277	0.522174
$733$	−0.0844658	−0.00311981	−0.00155991	−	0.999999i	$-0.500497\pi$
$733$	−0.0844658	−0.00311981	−0.00155991	+	0.999999i	$0.500497\pi$
$734$	−23.8368	−0.879834
$735$	−7.44579	−0.274642
$736$	−23.1194	−0.852192
$737$	−5.53467	−0.203872
$738$	−7.80326	−0.287242
$739$	4.20935	0.154843	0.0774217	−	0.996998i	$-0.475331\pi$
$739$	4.20935	0.154843	0.0774217	+	0.996998i	$0.475331\pi$
$740$	6.42708	0.236264
$741$	52.2536	1.91958
$742$	−26.4352	−0.970465
$743$	30.9115	1.13403	0.567016	−	0.823707i	$-0.308098\pi$
$743$	30.9115	1.13403	0.567016	+	0.823707i	$0.308098\pi$
$744$	−55.3717	−2.03002
$745$	6.13807	0.224881
$746$	−0.216199	−0.00791560
$747$	5.42820	0.198607
$748$	3.02235	0.110508
$749$	−39.1310	−1.42981
$750$	−2.63145	−0.0960869
$751$	−39.5932	−1.44478	−0.722389	−	0.691487i	$-0.756956\pi$
$751$	−39.5932	−1.44478	−0.722389	+	0.691487i	$0.756956\pi$
$752$	21.6516	0.789552
$753$	4.53110	0.165122
$754$	−0.734295	−0.0267415
$755$	−13.4012	−0.487720
$756$	3.91362	0.142337
$757$	15.0107	0.545574	0.272787	−	0.962074i	$-0.412055\pi$
$757$	15.0107	0.545574	0.272787	+	0.962074i	$0.412055\pi$
$758$	34.2869	1.24536
$759$	14.6507	0.531786
$760$	−12.4687	−0.452287
$761$	48.0875	1.74317	0.871585	−	0.490244i	$-0.163092\pi$
$761$	48.0875	1.74317	0.871585	+	0.490244i	$0.163092\pi$
$762$	22.2580	0.806324
$763$	1.72575	0.0624765
$764$	13.7701	0.498183
$765$	−9.94682	−0.359628
$766$	−38.0072	−1.37326
$767$	−16.5595	−0.597929
$768$	32.0111	1.15510
$769$	−3.09827	−0.111726	−0.0558632	−	0.998438i	$-0.517791\pi$
$769$	−3.09827	−0.111726	−0.0558632	+	0.998438i	$0.517791\pi$
$770$	−3.69819	−0.133274
$771$	−52.3286	−1.88457
$772$	0.832207	0.0299518
$773$	−16.9812	−0.610771	−0.305386	−	0.952229i	$-0.598785\pi$
$773$	−16.9812	−0.610771	−0.305386	+	0.952229i	$0.598785\pi$
$774$	−1.90666	−0.0685334
$775$	−7.88760	−0.283331
$776$	−9.79180	−0.351505
$777$	−70.3061	−2.52222
$778$	−31.5016	−1.12939
$779$	−12.4568	−0.446310
$780$	−8.61702	−0.308539
$781$	1.61411	0.0577573
$782$	33.5710	1.20050
$783$	0.205593	0.00734728
$784$	−7.24564	−0.258773
$785$	19.7871	0.706232
$786$	12.7643	0.455287
$787$	19.8276	0.706777	0.353388	−	0.935477i	$-0.385029\pi$
$787$	19.8276	0.706777	0.353388	+	0.935477i	$0.385029\pi$
$788$	−11.5322	−0.410816
$789$	−38.6242	−1.37506
$790$	0.583076	0.0207449
$791$	−25.7104	−0.914155
$792$	−6.76708	−0.240458
$793$	−52.5255	−1.86524
$794$	21.5674	0.765400
$795$	−16.2966	−0.577981
$796$	−4.85694	−0.172150
$797$	−48.0787	−1.70303	−0.851517	−	0.524327i	$-0.824317\pi$
$797$	−48.0787	−1.70303	−0.851517	+	0.524327i	$0.824317\pi$
$798$	34.1411	1.20858
$799$	44.1713	1.56267
$800$	3.59769	0.127197
$801$	22.4343	0.792678
$802$	−10.9667	−0.387247
$803$	1.00000	0.0352892
$804$	−8.42598	−0.297161
$805$	20.5898	0.725695
$806$	51.5304	1.81508
$807$	28.4418	1.00120
$808$	24.4526	0.860238
$809$	37.5456	1.32003	0.660017	−	0.751251i	$-0.270549\pi$
$809$	37.5456	1.32003	0.660017	+	0.751251i	$0.270549\pi$
$810$	−12.4232	−0.436507
$811$	10.6926	0.375468	0.187734	−	0.982220i	$-0.439886\pi$
$811$	10.6926	0.375468	0.187734	+	0.982220i	$0.439886\pi$
$812$	0.240478	0.00843912
$813$	−8.98385	−0.315078
$814$	−11.1091	−0.389375
$815$	−9.80532	−0.343465
$816$	−22.8927	−0.801404
$817$	−3.04370	−0.106486
$818$	−27.5121	−0.961937
$819$	39.8557	1.39267
$820$	2.05422	0.0717364
$821$	−29.9649	−1.04578	−0.522890	−	0.852400i	$-0.675146\pi$
$821$	−29.9649	−1.04578	−0.522890	+	0.852400i	$0.675146\pi$
$822$	27.5163	0.959740
$823$	−13.2979	−0.463536	−0.231768	−	0.972771i	$-0.574451\pi$
$823$	−13.2979	−0.463536	−0.231768	+	0.972771i	$0.574451\pi$
$824$	−7.19380	−0.250608
$825$	−2.27984	−0.0793739
$826$	−10.8195	−0.376460
$827$	−1.61296	−0.0560881	−0.0280440	−	0.999607i	$-0.508928\pi$
$827$	−1.61296	−0.0560881	−0.0280440	+	0.999607i	$0.508928\pi$
$828$	9.43062	0.327737
$829$	31.2249	1.08449	0.542243	−	0.840222i	$-0.317575\pi$
$829$	31.2249	1.08449	0.542243	+	0.840222i	$0.317575\pi$
$830$	2.85091	0.0989564
$831$	−48.1543	−1.67046
$832$	−48.6188	−1.68555
$833$	−14.7818	−0.512159
$834$	−5.94904	−0.205998
$835$	−20.5097	−0.709768
$836$	−2.70400	−0.0935199
$837$	−14.4278	−0.498698
$838$	−31.7697	−1.09747
$839$	−11.7095	−0.404256	−0.202128	−	0.979359i	$-0.564786\pi$
$839$	−11.7095	−0.404256	−0.202128	+	0.979359i	$0.564786\pi$
$840$	−22.4927	−0.776072
$841$	−28.9874	−0.999564
$842$	−26.1751	−0.902055
$843$	15.0360	0.517868
$844$	12.2876	0.422958
$845$	19.0373	0.654905
$846$	−24.7555	−0.851113
$847$	−3.20405	−0.110092
$848$	−15.8585	−0.544585
$849$	−66.5428	−2.28374
$850$	−5.22410	−0.179185
$851$	61.8504	2.12021
$852$	2.45731	0.0841862
$853$	−0.101494	−0.00347508	−0.00173754	−	0.999998i	$-0.500553\pi$
$853$	−0.101494	−0.00347508	−0.00173754	+	0.999998i	$0.500553\pi$
$854$	−34.3188	−1.17436
$855$	8.89910	0.304343
$856$	−37.6062	−1.28535
$857$	−4.04771	−0.138267	−0.0691336	−	0.997607i	$-0.522023\pi$
$857$	−4.04771	−0.138267	−0.0691336	+	0.997607i	$0.522023\pi$
$858$	14.8944	0.508487
$859$	21.2906	0.726424	0.363212	−	0.931706i	$-0.381680\pi$
$859$	21.2906	0.726424	0.363212	+	0.931706i	$0.381680\pi$
$860$	0.501930	0.0171157
$861$	−22.4712	−0.765816
$862$	−4.24137	−0.144461
$863$	22.5041	0.766047	0.383023	−	0.923739i	$-0.374883\pi$
$863$	22.5041	0.766047	0.383023	+	0.923739i	$0.374883\pi$
$864$	6.58080	0.223884
$865$	4.29185	0.145927
$866$	6.00715	0.204131
$867$	−7.94594	−0.269858
$868$	−16.8760	−0.572807
$869$	0.505167	0.0171366
$870$	−0.295765	−0.0100274
$871$	31.3271	1.06148
$872$	1.65851	0.0561642
$873$	6.98856	0.236527
$874$	−30.0349	−1.01595
$875$	−3.20405	−0.108317
$876$	1.52240	0.0514371
$877$	−0.0515298	−0.00174004	−0.000870019	−	1.00000i	$-0.500277\pi$
$877$	−0.0515298	−0.00174004	−0.000870019		1.00000i	$0.500277\pi$
$878$	−39.4036	−1.32981
$879$	−30.7791	−1.03815
$880$	−2.21856	−0.0747876
$881$	18.9239	0.637562	0.318781	−	0.947828i	$-0.396727\pi$
$881$	18.9239	0.637562	0.318781	+	0.947828i	$0.396727\pi$
$882$	8.28438	0.278949
$883$	−24.5255	−0.825349	−0.412675	−	0.910879i	$-0.635405\pi$
$883$	−24.5255	−0.825349	−0.412675	+	0.910879i	$0.635405\pi$
$884$	−17.1070	−0.575370
$885$	−6.66997	−0.224209
$886$	−20.4990	−0.688676
$887$	−33.2967	−1.11799	−0.558996	−	0.829170i	$-0.688813\pi$
$887$	−33.2967	−1.11799	−0.558996	+	0.829170i	$0.688813\pi$
$888$	−67.5666	−2.26739
$889$	27.1014	0.908951
$890$	11.7826	0.394953
$891$	−10.7633	−0.360582
$892$	−12.1949	−0.408316
$893$	−39.5186	−1.32244
$894$	−16.1520	−0.540204
$895$	4.66488	0.155930
$896$	−8.71186	−0.291043
$897$	−82.9251	−2.76879
$898$	29.5178	0.985023
$899$	−0.886538	−0.0295677
$900$	−1.46753	−0.0489177
$901$	−32.3529	−1.07783
$902$	−3.55069	−0.118225
$903$	−5.49064	−0.182717
$904$	−24.7085	−0.821794
$905$	22.4370	0.745830
$906$	35.2646	1.17159
$907$	−18.9028	−0.627658	−0.313829	−	0.949480i	$-0.601612\pi$
$907$	−18.9028	−0.627658	−0.313829	+	0.949480i	$0.601612\pi$
$908$	−1.31032	−0.0434846
$909$	−17.4522	−0.578852
$910$	20.9323	0.693900
$911$	−45.8282	−1.51836	−0.759178	−	0.650883i	$-0.774399\pi$
$911$	−45.8282	−1.51836	−0.759178	+	0.650883i	$0.774399\pi$
$912$	20.4813	0.678205
$913$	2.46997	0.0817442
$914$	−6.48381	−0.214465
$915$	−21.1566	−0.699417
$916$	−2.70781	−0.0894685
$917$	15.5418	0.513235
$918$	−9.55580	−0.315388
$919$	23.7117	0.782175	0.391088	−	0.920353i	$-0.372099\pi$
$919$	23.7117	0.782175	0.391088	+	0.920353i	$0.372099\pi$
$920$	19.7875	0.652375
$921$	45.4374	1.49721
$922$	−31.1337	−1.02533
$923$	−9.13609	−0.300718
$924$	−4.87784	−0.160469
$925$	−9.62475	−0.316460
$926$	−7.44434	−0.244636
$927$	5.13433	0.168633
$928$	0.404367	0.0132740
$929$	24.0108	0.787770	0.393885	−	0.919160i	$-0.371131\pi$
$929$	24.0108	0.787770	0.393885	+	0.919160i	$0.371131\pi$
$930$	20.7558	0.680610
$931$	13.2248	0.433425
$932$	7.14331	0.233987
$933$	46.3507	1.51745
$934$	20.7564	0.679172
$935$	−4.52607	−0.148018
$936$	38.3027	1.25196
$937$	−10.2899	−0.336156	−0.168078	−	0.985774i	$-0.553756\pi$
$937$	−10.2899	−0.336156	−0.168078	+	0.985774i	$0.553756\pi$
$938$	20.4683	0.668313
$939$	−54.2678	−1.77096
$940$	6.51693	0.212559
$941$	40.7408	1.32811	0.664056	−	0.747683i	$-0.268834\pi$
$941$	40.7408	1.32811	0.664056	+	0.747683i	$0.268834\pi$
$942$	−52.0688	−1.69649
$943$	19.7686	0.643754
$944$	−6.49068	−0.211254
$945$	−5.86077	−0.190651
$946$	−0.867580	−0.0282075
$947$	49.9011	1.62157	0.810784	−	0.585346i	$-0.199041\pi$
$947$	49.9011	1.62157	0.810784	+	0.585346i	$0.199041\pi$
$948$	0.769066	0.0249781
$949$	−5.66015	−0.183736
$950$	4.67383	0.151639
$951$	−21.6051	−0.700592
$952$	−44.6538	−1.44724
$953$	20.6157	0.667809	0.333905	−	0.942607i	$-0.391634\pi$
$953$	20.6157	0.667809	0.333905	+	0.942607i	$0.391634\pi$
$954$	18.1320	0.587046
$955$	−20.6211	−0.667283
$956$	−13.8072	−0.446555
$957$	−0.256246	−0.00828325
$958$	−32.6967	−1.05638
$959$	33.5038	1.08189
$960$	−19.5830	−0.632040
$961$	31.2143	1.00691
$962$	62.8794	2.02731
$963$	26.8401	0.864912
$964$	12.0624	0.388504
$965$	−1.24626	−0.0401184
$966$	−54.1810	−1.74325
$967$	−57.1845	−1.83893	−0.919465	−	0.393173i	$-0.871377\pi$
$967$	−57.1845	−1.83893	−0.919465	+	0.393173i	$0.871377\pi$
$968$	−3.07920	−0.0989693
$969$	41.7839	1.34229
$970$	3.67041	0.117850
$971$	34.2366	1.09870	0.549352	−	0.835591i	$-0.314875\pi$
$971$	34.2366	1.09870	0.549352	+	0.835591i	$0.314875\pi$
$972$	−12.7216	−0.408045
$973$	−7.24354	−0.232217
$974$	−16.5738	−0.531057
$975$	12.9043	0.413267
$976$	−20.5879	−0.659004
$977$	29.3779	0.939882	0.469941	−	0.882698i	$-0.344275\pi$
$977$	29.3779	0.939882	0.469941	+	0.882698i	$0.344275\pi$
$978$	25.8022	0.825063
$979$	10.2082	0.326256
$980$	−2.18087	−0.0696654
$981$	−1.18370	−0.0377928
$982$	21.0985	0.673280
$983$	54.0997	1.72551	0.862756	−	0.505620i	$-0.168736\pi$
$983$	54.0997	1.72551	0.862756	+	0.505620i	$0.168736\pi$
$984$	−21.5956	−0.688442
$985$	17.2698	0.550260
$986$	−0.587170	−0.0186993
$987$	−71.2890	−2.26915
$988$	15.3051	0.486919
$989$	4.83028	0.153594
$990$	2.53661	0.0806187
$991$	−40.6350	−1.29081	−0.645407	−	0.763839i	$-0.723312\pi$
$991$	−40.6350	−1.29081	−0.645407	+	0.763839i	$0.723312\pi$
$992$	−28.3771	−0.900975
$993$	−23.9170	−0.758983
$994$	−5.96927	−0.189334
$995$	7.27341	0.230583
$996$	3.76029	0.119149
$997$	6.67828	0.211503	0.105752	−	0.994393i	$-0.466275\pi$
$997$	6.67828	0.211503	0.105752	+	0.994393i	$0.466275\pi$
$998$	13.4332	0.425219
$999$	−17.6054	−0.557009

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4015.2.a.h.1.25	✓	37

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4015.2.a.h.1.25	✓	37	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 4015 = 5 \cdot 11 \cdot 73 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4015.a (trivial)

\(f(q)\)	\(=\)	\(q+1.15422 q^{2} -2.27984 q^{3} -0.667766 q^{4} +1.00000 q^{5} -2.63145 q^{6} -3.20405 q^{7} -3.07920 q^{8} +2.19767 q^{9} +O(q^{10})\)	\(q+1.15422 q^{2} -2.27984 q^{3} -0.667766 q^{4} +1.00000 q^{5} -2.63145 q^{6} -3.20405 q^{7} -3.07920 q^{8} +2.19767 q^{9} +1.15422 q^{10} +1.00000 q^{11} +1.52240 q^{12} -5.66015 q^{13} -3.69819 q^{14} -2.27984 q^{15} -2.21856 q^{16} -4.52607 q^{17} +2.53661 q^{18} +4.04933 q^{19} -0.667766 q^{20} +7.30472 q^{21} +1.15422 q^{22} -6.42618 q^{23} +7.02009 q^{24} +1.00000 q^{25} -6.53309 q^{26} +1.82918 q^{27} +2.13955 q^{28} +0.112396 q^{29} -2.63145 q^{30} -7.88760 q^{31} +3.59769 q^{32} -2.27984 q^{33} -5.22410 q^{34} -3.20405 q^{35} -1.46753 q^{36} -9.62475 q^{37} +4.67383 q^{38} +12.9043 q^{39} -3.07920 q^{40} -3.07626 q^{41} +8.43129 q^{42} -0.751656 q^{43} -0.667766 q^{44} +2.19767 q^{45} -7.41726 q^{46} -9.75931 q^{47} +5.05796 q^{48} +3.26593 q^{49} +1.15422 q^{50} +10.3187 q^{51} +3.77966 q^{52} +7.14813 q^{53} +2.11128 q^{54} +1.00000 q^{55} +9.86591 q^{56} -9.23182 q^{57} +0.129731 q^{58} +2.92563 q^{59} +1.52240 q^{60} +9.27987 q^{61} -9.10407 q^{62} -7.04145 q^{63} +8.58965 q^{64} -5.66015 q^{65} -2.63145 q^{66} -5.53467 q^{67} +3.02235 q^{68} +14.6507 q^{69} -3.69819 q^{70} +1.61411 q^{71} -6.76708 q^{72} +1.00000 q^{73} -11.1091 q^{74} -2.27984 q^{75} -2.70400 q^{76} -3.20405 q^{77} +14.8944 q^{78} +0.505167 q^{79} -2.21856 q^{80} -10.7633 q^{81} -3.55069 q^{82} +2.46997 q^{83} -4.87784 q^{84} -4.52607 q^{85} -0.867580 q^{86} -0.256246 q^{87} -3.07920 q^{88} +10.2082 q^{89} +2.53661 q^{90} +18.1354 q^{91} +4.29118 q^{92} +17.9825 q^{93} -11.2644 q^{94} +4.04933 q^{95} -8.20215 q^{96} +3.17998 q^{97} +3.76961 q^{98} +2.19767 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 37 q + 5 q^{2} + 3 q^{3} + 43 q^{4} + 37 q^{5} + 9 q^{6} + 6 q^{7} + 12 q^{8} + 50 q^{9}+O(q^{10}) \) 37 * q + 5 * q^2 + 3 * q^3 + 43 * q^4 + 37 * q^5 + 9 * q^6 + 6 * q^7 + 12 * q^8 + 50 * q^9	\( 37 q + 5 q^{2} + 3 q^{3} + 43 q^{4} + 37 q^{5} + 9 q^{6} + 6 q^{7} + 12 q^{8} + 50 q^{9} + 5 q^{10} + 37 q^{11} + 6 q^{12} + 11 q^{13} + 11 q^{14} + 3 q^{15} + 43 q^{16} + 38 q^{17} + 11 q^{18} + 34 q^{19} + 43 q^{20} + 39 q^{21} + 5 q^{22} + 4 q^{23} + 25 q^{24} + 37 q^{25} - 9 q^{26} + 3 q^{27} + 14 q^{28} + 58 q^{29} + 9 q^{30} + 8 q^{31} + 14 q^{32} + 3 q^{33} + 8 q^{34} + 6 q^{35} + 20 q^{36} + 2 q^{37} + 15 q^{38} + 14 q^{39} + 12 q^{40} + 62 q^{41} - 13 q^{42} + 30 q^{43} + 43 q^{44} + 50 q^{45} + 31 q^{46} + 5 q^{47} - 25 q^{48} + 59 q^{49} + 5 q^{50} + 23 q^{51} - q^{52} + 18 q^{53} + 13 q^{54} + 37 q^{55} + 22 q^{56} + 5 q^{57} - 40 q^{58} + 15 q^{59} + 6 q^{60} + 57 q^{61} + 20 q^{62} - 29 q^{63} + 10 q^{64} + 11 q^{65} + 9 q^{66} - 14 q^{67} + 53 q^{68} + 24 q^{69} + 11 q^{70} + 8 q^{71} + 15 q^{72} + 37 q^{73} + 7 q^{74} + 3 q^{75} + 59 q^{76} + 6 q^{77} + q^{78} + 42 q^{79} + 43 q^{80} + 61 q^{81} - 22 q^{82} + 44 q^{83} + 66 q^{84} + 38 q^{85} - q^{86} - 26 q^{87} + 12 q^{88} + 69 q^{89} + 11 q^{90} - 10 q^{91} - 21 q^{92} - 26 q^{93} + 29 q^{94} + 34 q^{95} - 9 q^{96} + 37 q^{97} - 15 q^{98} + 50 q^{99}+O(q^{100}) \) 37 * q + 5 * q^2 + 3 * q^3 + 43 * q^4 + 37 * q^5 + 9 * q^6 + 6 * q^7 + 12 * q^8 + 50 * q^9 + 5 * q^10 + 37 * q^11 + 6 * q^12 + 11 * q^13 + 11 * q^14 + 3 * q^15 + 43 * q^16 + 38 * q^17 + 11 * q^18 + 34 * q^19 + 43 * q^20 + 39 * q^21 + 5 * q^22 + 4 * q^23 + 25 * q^24 + 37 * q^25 - 9 * q^26 + 3 * q^27 + 14 * q^28 + 58 * q^29 + 9 * q^30 + 8 * q^31 + 14 * q^32 + 3 * q^33 + 8 * q^34 + 6 * q^35 + 20 * q^36 + 2 * q^37 + 15 * q^38 + 14 * q^39 + 12 * q^40 + 62 * q^41 - 13 * q^42 + 30 * q^43 + 43 * q^44 + 50 * q^45 + 31 * q^46 + 5 * q^47 - 25 * q^48 + 59 * q^49 + 5 * q^50 + 23 * q^51 - q^52 + 18 * q^53 + 13 * q^54 + 37 * q^55 + 22 * q^56 + 5 * q^57 - 40 * q^58 + 15 * q^59 + 6 * q^60 + 57 * q^61 + 20 * q^62 - 29 * q^63 + 10 * q^64 + 11 * q^65 + 9 * q^66 - 14 * q^67 + 53 * q^68 + 24 * q^69 + 11 * q^70 + 8 * q^71 + 15 * q^72 + 37 * q^73 + 7 * q^74 + 3 * q^75 + 59 * q^76 + 6 * q^77 + q^78 + 42 * q^79 + 43 * q^80 + 61 * q^81 - 22 * q^82 + 44 * q^83 + 66 * q^84 + 38 * q^85 - q^86 - 26 * q^87 + 12 * q^88 + 69 * q^89 + 11 * q^90 - 10 * q^91 - 21 * q^92 - 26 * q^93 + 29 * q^94 + 34 * q^95 - 9 * q^96 + 37 * q^97 - 15 * q^98 + 50 * q^99

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