LMFDB - Embedded newform 2005.2.a.g.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2005,2,Mod(1,2005)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2005, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("2005.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2005 = 5 \cdot 401 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2005.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:	$16.0100056053$
Analytic rank:	$0$
Dimension:	$37$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Character	$\chi$	$=$	2005.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.65893 q^{2} +1.77446 q^{3} +5.06989 q^{4} +1.00000 q^{5} -4.71815 q^{6} -1.53323 q^{7} -8.16262 q^{8} +0.148702 q^{9} +O(q^{10})$	\(q-2.65893 q^{2} +1.77446 q^{3} +5.06989 q^{4} +1.00000 q^{5} -4.71815 q^{6} -1.53323 q^{7} -8.16262 q^{8} +0.148702 q^{9} -2.65893 q^{10} +0.141236 q^{11} +8.99631 q^{12} +3.71643 q^{13} +4.07675 q^{14} +1.77446 q^{15} +11.5640 q^{16} +5.10165 q^{17} -0.395387 q^{18} -2.87968 q^{19} +5.06989 q^{20} -2.72065 q^{21} -0.375536 q^{22} +4.96397 q^{23} -14.4842 q^{24} +1.00000 q^{25} -9.88171 q^{26} -5.05951 q^{27} -7.77332 q^{28} -0.313727 q^{29} -4.71815 q^{30} +1.27724 q^{31} -14.4227 q^{32} +0.250618 q^{33} -13.5649 q^{34} -1.53323 q^{35} +0.753903 q^{36} -11.6078 q^{37} +7.65686 q^{38} +6.59465 q^{39} -8.16262 q^{40} +6.57119 q^{41} +7.23402 q^{42} +5.17837 q^{43} +0.716052 q^{44} +0.148702 q^{45} -13.1988 q^{46} +11.0191 q^{47} +20.5199 q^{48} -4.64920 q^{49} -2.65893 q^{50} +9.05266 q^{51} +18.8419 q^{52} +10.8499 q^{53} +13.4529 q^{54} +0.141236 q^{55} +12.5152 q^{56} -5.10987 q^{57} +0.834176 q^{58} -11.5237 q^{59} +8.99631 q^{60} +0.359611 q^{61} -3.39608 q^{62} -0.227994 q^{63} +15.2207 q^{64} +3.71643 q^{65} -0.666374 q^{66} -3.49996 q^{67} +25.8648 q^{68} +8.80835 q^{69} +4.07675 q^{70} +3.17218 q^{71} -1.21380 q^{72} +14.5569 q^{73} +30.8643 q^{74} +1.77446 q^{75} -14.5997 q^{76} -0.216548 q^{77} -17.5347 q^{78} +6.00178 q^{79} +11.5640 q^{80} -9.42399 q^{81} -17.4723 q^{82} +12.6357 q^{83} -13.7934 q^{84} +5.10165 q^{85} -13.7689 q^{86} -0.556695 q^{87} -1.15286 q^{88} -2.65083 q^{89} -0.395387 q^{90} -5.69814 q^{91} +25.1668 q^{92} +2.26640 q^{93} -29.2990 q^{94} -2.87968 q^{95} -25.5924 q^{96} -2.28186 q^{97} +12.3619 q^{98} +0.0210021 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 37 q + 11 q^{2} + 13 q^{3} + 43 q^{4} + 37 q^{5} - 2 q^{6} + 34 q^{7} + 27 q^{8} + 50 q^{9}+O(q^{10}) $ 37 * q + 11 * q^2 + 13 * q^3 + 43 * q^4 + 37 * q^5 - 2 * q^6 + 34 * q^7 + 27 * q^8 + 50 * q^9	\( 37 q + 11 q^{2} + 13 q^{3} + 43 q^{4} + 37 q^{5} - 2 q^{6} + 34 q^{7} + 27 q^{8} + 50 q^{9} + 11 q^{10} + 38 q^{11} + 24 q^{12} + 17 q^{13} + 14 q^{14} + 13 q^{15} + 47 q^{16} + 22 q^{17} + 18 q^{18} + 6 q^{19} + 43 q^{20} + 4 q^{21} + 18 q^{22} + 45 q^{23} - 19 q^{24} + 37 q^{25} - q^{26} + 43 q^{27} + 46 q^{28} + 17 q^{29} - 2 q^{30} - 13 q^{31} + 50 q^{32} + 12 q^{33} - 30 q^{34} + 34 q^{35} + 43 q^{36} + 9 q^{37} + q^{38} - 7 q^{39} + 27 q^{40} + 12 q^{41} - 38 q^{42} + 53 q^{43} + 36 q^{44} + 50 q^{45} - 15 q^{46} + 39 q^{47} - 6 q^{48} + 37 q^{49} + 11 q^{50} + 38 q^{51} + 17 q^{52} + 19 q^{53} - 62 q^{54} + 38 q^{55} + 18 q^{56} + 6 q^{57} - 13 q^{58} + 33 q^{59} + 24 q^{60} - 11 q^{61} + q^{62} + 98 q^{63} + 15 q^{64} + 17 q^{65} - 70 q^{66} + 49 q^{67} + 32 q^{68} - 36 q^{69} + 14 q^{70} + 19 q^{71} + 5 q^{72} + 39 q^{73} + 21 q^{74} + 13 q^{75} - 33 q^{76} + 34 q^{77} - 22 q^{78} - 9 q^{79} + 47 q^{80} + 49 q^{81} + 14 q^{82} + 114 q^{83} - 50 q^{84} + 22 q^{85} + 9 q^{86} + 56 q^{87} + 14 q^{88} + 2 q^{89} + 18 q^{90} - 29 q^{91} + 47 q^{92} - 7 q^{93} - 52 q^{94} + 6 q^{95} - 89 q^{96} + 4 q^{97} + 14 q^{98} + 57 q^{99}+O(q^{100}) \) 37 * q + 11 * q^2 + 13 * q^3 + 43 * q^4 + 37 * q^5 - 2 * q^6 + 34 * q^7 + 27 * q^8 + 50 * q^9 + 11 * q^10 + 38 * q^11 + 24 * q^12 + 17 * q^13 + 14 * q^14 + 13 * q^15 + 47 * q^16 + 22 * q^17 + 18 * q^18 + 6 * q^19 + 43 * q^20 + 4 * q^21 + 18 * q^22 + 45 * q^23 - 19 * q^24 + 37 * q^25 - q^26 + 43 * q^27 + 46 * q^28 + 17 * q^29 - 2 * q^30 - 13 * q^31 + 50 * q^32 + 12 * q^33 - 30 * q^34 + 34 * q^35 + 43 * q^36 + 9 * q^37 + q^38 - 7 * q^39 + 27 * q^40 + 12 * q^41 - 38 * q^42 + 53 * q^43 + 36 * q^44 + 50 * q^45 - 15 * q^46 + 39 * q^47 - 6 * q^48 + 37 * q^49 + 11 * q^50 + 38 * q^51 + 17 * q^52 + 19 * q^53 - 62 * q^54 + 38 * q^55 + 18 * q^56 + 6 * q^57 - 13 * q^58 + 33 * q^59 + 24 * q^60 - 11 * q^61 + q^62 + 98 * q^63 + 15 * q^64 + 17 * q^65 - 70 * q^66 + 49 * q^67 + 32 * q^68 - 36 * q^69 + 14 * q^70 + 19 * q^71 + 5 * q^72 + 39 * q^73 + 21 * q^74 + 13 * q^75 - 33 * q^76 + 34 * q^77 - 22 * q^78 - 9 * q^79 + 47 * q^80 + 49 * q^81 + 14 * q^82 + 114 * q^83 - 50 * q^84 + 22 * q^85 + 9 * q^86 + 56 * q^87 + 14 * q^88 + 2 * q^89 + 18 * q^90 - 29 * q^91 + 47 * q^92 - 7 * q^93 - 52 * q^94 + 6 * q^95 - 89 * q^96 + 4 * q^97 + 14 * q^98 + 57 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	−2.65893	−1.88015	−0.940073	−	0.340974i	$-0.889243\pi$
$2$	−2.65893	−1.88015	−0.940073	+	0.340974i	$0.889243\pi$
$3$	1.77446	1.02448	0.512242	−	0.858841i	$-0.328815\pi$
$3$	1.77446	1.02448	0.512242	+	0.858841i	$0.328815\pi$
$4$	5.06989	2.53495
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	−4.71815	−1.92618
$7$	−1.53323	−0.579507	−0.289753	−	0.957101i	$-0.593573\pi$
$7$	−1.53323	−0.579507	−0.289753	+	0.957101i	$0.593573\pi$
$8$	−8.16262	−2.88592
$9$	0.148702	0.0495673
$10$	−2.65893	−0.840827
$11$	0.141236	0.0425843	0.0212921	−	0.999773i	$-0.493222\pi$
$11$	0.141236	0.0425843	0.0212921	+	0.999773i	$0.493222\pi$
$12$	8.99631	2.59701
$13$	3.71643	1.03075	0.515376	−	0.856964i	$-0.327652\pi$
$13$	3.71643	1.03075	0.515376	+	0.856964i	$0.327652\pi$
$14$	4.07675	1.08956
$15$	1.77446	0.458163
$16$	11.5640	2.89101
$17$	5.10165	1.23733	0.618666	−	0.785654i	$-0.287674\pi$
$17$	5.10165	1.23733	0.618666	+	0.785654i	$0.287674\pi$
$18$	−0.395387	−0.0931937
$19$	−2.87968	−0.660644	−0.330322	−	0.943868i	$-0.607157\pi$
$19$	−2.87968	−0.660644	−0.330322	+	0.943868i	$0.607157\pi$
$20$	5.06989	1.13366
$21$	−2.72065	−0.593696
$22$	−0.375536	−0.0800646
$23$	4.96397	1.03506	0.517529	−	0.855666i	$-0.326852\pi$
$23$	4.96397	1.03506	0.517529	+	0.855666i	$0.326852\pi$
$24$	−14.4842	−2.95658
$25$	1.00000	0.200000
$26$	−9.88171	−1.93796
$27$	−5.05951	−0.973703
$28$	−7.77332	−1.46902
$29$	−0.313727	−0.0582576	−0.0291288	−	0.999576i	$-0.509273\pi$
$29$	−0.313727	−0.0582576	−0.0291288	+	0.999576i	$0.509273\pi$
$30$	−4.71815	−0.861413
$31$	1.27724	0.229398	0.114699	−	0.993400i	$-0.463410\pi$
$31$	1.27724	0.229398	0.114699	+	0.993400i	$0.463410\pi$
$32$	−14.4227	−2.54959
$33$	0.250618	0.0436269
$34$	−13.5649	−2.32636
$35$	−1.53323	−0.259163
$36$	0.753903	0.125650
$37$	−11.6078	−1.90831	−0.954155	−	0.299313i	$-0.903242\pi$
$37$	−11.6078	−1.90831	−0.954155	+	0.299313i	$0.903242\pi$
$38$	7.65686	1.24211
$39$	6.59465	1.05599
$40$	−8.16262	−1.29062
$41$	6.57119	1.02625	0.513123	−	0.858315i	$-0.328488\pi$
$41$	6.57119	1.02625	0.513123	+	0.858315i	$0.328488\pi$
$42$	7.23402	1.11623
$43$	5.17837	0.789694	0.394847	−	0.918747i	$-0.370798\pi$
$43$	5.17837	0.789694	0.394847	+	0.918747i	$0.370798\pi$
$44$	0.716052	0.107949
$45$	0.148702	0.0221672
$46$	−13.1988	−1.94606
$47$	11.0191	1.60730	0.803651	−	0.595101i	$-0.202888\pi$
$47$	11.0191	1.60730	0.803651	+	0.595101i	$0.202888\pi$
$48$	20.5199	2.96179
$49$	−4.64920	−0.664172
$50$	−2.65893	−0.376029
$51$	9.05266	1.26763
$52$	18.8419	2.61290
$53$	10.8499	1.49035	0.745173	−	0.666871i	$-0.232367\pi$
$53$	10.8499	1.49035	0.745173	+	0.666871i	$0.232367\pi$
$54$	13.4529	1.83070
$55$	0.141236	0.0190443
$56$	12.5152	1.67241
$57$	−5.10987	−0.676819
$58$	0.834176	0.109533
$59$	−11.5237	−1.50026	−0.750130	−	0.661291i	$-0.770009\pi$
$59$	−11.5237	−1.50026	−0.750130	+	0.661291i	$0.770009\pi$
$60$	8.99631	1.16142
$61$	0.359611	0.0460435	0.0230218	−	0.999735i	$-0.492671\pi$
$61$	0.359611	0.0460435	0.0230218	+	0.999735i	$0.492671\pi$
$62$	−3.39608	−0.431302
$63$	−0.227994	−0.0287246
$64$	15.2207	1.90259
$65$	3.71643	0.460966
$66$	−0.666374	−0.0820249
$67$	−3.49996	−0.427588	−0.213794	−	0.976879i	$-0.568582\pi$
$67$	−3.49996	−0.427588	−0.213794	+	0.976879i	$0.568582\pi$
$68$	25.8648	3.13657
$69$	8.80835	1.06040
$70$	4.07675	0.487265
$71$	3.17218	0.376469	0.188235	−	0.982124i	$-0.439724\pi$
$71$	3.17218	0.376469	0.188235	+	0.982124i	$0.439724\pi$
$72$	−1.21380	−0.143047
$73$	14.5569	1.70376	0.851878	−	0.523741i	$-0.175464\pi$
$73$	14.5569	1.70376	0.851878	+	0.523741i	$0.175464\pi$
$74$	30.8643	3.58790
$75$	1.77446	0.204897
$76$	−14.5997	−1.67470
$77$	−0.216548	−0.0246779
$78$	−17.5347	−1.98541
$79$	6.00178	0.675253	0.337627	−	0.941280i	$-0.390376\pi$
$79$	6.00178	0.675253	0.337627	+	0.941280i	$0.390376\pi$
$80$	11.5640	1.29290
$81$	−9.42399	−1.04711
$82$	−17.4723	−1.92949
$83$	12.6357	1.38695	0.693474	−	0.720482i	$-0.256079\pi$
$83$	12.6357	1.38695	0.693474	+	0.720482i	$0.256079\pi$
$84$	−13.7934	−1.50499
$85$	5.10165	0.553351
$86$	−13.7689	−1.48474
$87$	−0.556695	−0.0596839
$88$	−1.15286	−0.122895
$89$	−2.65083	−0.280987	−0.140494	−	0.990082i	$-0.544869\pi$
$89$	−2.65083	−0.280987	−0.140494	+	0.990082i	$0.544869\pi$
$90$	−0.395387	−0.0416775
$91$	−5.69814	−0.597328
$92$	25.1668	2.62382
$93$	2.26640	0.235015
$94$	−29.2990	−3.02196
$95$	−2.87968	−0.295449
$96$	−25.5924	−2.61201
$97$	−2.28186	−0.231688	−0.115844	−	0.993267i	$-0.536957\pi$
$97$	−2.28186	−0.231688	−0.115844	+	0.993267i	$0.536957\pi$
$98$	12.3619	1.24874
$99$	0.0210021	0.00211079
$100$	5.06989	0.506989
$101$	9.61910	0.957136	0.478568	−	0.878051i	$-0.341156\pi$
$101$	9.61910	0.957136	0.478568	+	0.878051i	$0.341156\pi$
$102$	−24.0704	−2.38332
$103$	5.94941	0.586213	0.293107	−	0.956080i	$-0.405311\pi$
$103$	5.94941	0.586213	0.293107	+	0.956080i	$0.405311\pi$
$104$	−30.3358	−2.97467
$105$	−2.72065	−0.265509
$106$	−28.8490	−2.80207
$107$	7.26874	0.702695	0.351348	−	0.936245i	$-0.385724\pi$
$107$	7.26874	0.702695	0.351348	+	0.936245i	$0.385724\pi$
$108$	−25.6512	−2.46828
$109$	−8.40298	−0.804860	−0.402430	−	0.915451i	$-0.631834\pi$
$109$	−8.40298	−0.804860	−0.402430	+	0.915451i	$0.631834\pi$
$110$	−0.375536	−0.0358060
$111$	−20.5975	−1.95503
$112$	−17.7303	−1.67536
$113$	−17.7544	−1.67020	−0.835098	−	0.550101i	$-0.814589\pi$
$113$	−17.7544	−1.67020	−0.835098	+	0.550101i	$0.814589\pi$
$114$	13.5868	1.27252
$115$	4.96397	0.462892
$116$	−1.59056	−0.147680
$117$	0.552640	0.0510916
$118$	30.6407	2.82071
$119$	−7.82201	−0.717042
$120$	−14.4842	−1.32222
$121$	−10.9801	−0.998187
$122$	−0.956181	−0.0865685
$123$	11.6603	1.05137
$124$	6.47545	0.581513
$125$	1.00000	0.0894427
$126$	0.606220	0.0540064
$127$	2.77157	0.245937	0.122969	−	0.992411i	$-0.460759\pi$
$127$	2.77157	0.245937	0.122969	+	0.992411i	$0.460759\pi$
$128$	−11.6255	−1.02756
$129$	9.18880	0.809029
$130$	−9.88171	−0.866683
$131$	7.95776	0.695273	0.347636	−	0.937629i	$-0.386984\pi$
$131$	7.95776	0.695273	0.347636	+	0.937629i	$0.386984\pi$
$132$	1.27060	0.110592
$133$	4.41521	0.382848
$134$	9.30613	0.803927
$135$	−5.05951	−0.435453
$136$	−41.6428	−3.57084
$137$	−1.20468	−0.102923	−0.0514616	−	0.998675i	$-0.516388\pi$
$137$	−1.20468	−0.102923	−0.0514616	+	0.998675i	$0.516388\pi$
$138$	−23.4208	−1.99371
$139$	22.5935	1.91635	0.958176	−	0.286178i	$-0.0923850\pi$
$139$	22.5935	1.91635	0.958176	+	0.286178i	$0.0923850\pi$
$140$	−7.77332	−0.656965
$141$	19.5529	1.64665
$142$	−8.43461	−0.707816
$143$	0.524894	0.0438938
$144$	1.71959	0.143299
$145$	−0.313727	−0.0260536
$146$	−38.7057	−3.20331
$147$	−8.24981	−0.680433
$148$	−58.8503	−4.83746
$149$	0.212573	0.0174146	0.00870731	−	0.999962i	$-0.497228\pi$
$149$	0.212573	0.0174146	0.00870731	+	0.999962i	$0.497228\pi$
$150$	−4.71815	−0.385236
$151$	1.62685	0.132391	0.0661957	−	0.997807i	$-0.478914\pi$
$151$	1.62685	0.132391	0.0661957	+	0.997807i	$0.478914\pi$
$152$	23.5057	1.90657
$153$	0.758625	0.0613312
$154$	0.575784	0.0463980
$155$	1.27724	0.102590
$156$	33.4341	2.67687
$157$	17.6782	1.41088	0.705438	−	0.708772i	$-0.250751\pi$
$157$	17.6782	1.41088	0.705438	+	0.708772i	$0.250751\pi$
$158$	−15.9583	−1.26957
$159$	19.2527	1.52684
$160$	−14.4227	−1.14021
$161$	−7.61091	−0.599824
$162$	25.0577	1.96872
$163$	9.25759	0.725111	0.362555	−	0.931962i	$-0.381904\pi$
$163$	9.25759	0.725111	0.362555	+	0.931962i	$0.381904\pi$
$164$	33.3152	2.60148
$165$	0.250618	0.0195105
$166$	−33.5974	−2.60766
$167$	−0.118924	−0.00920263	−0.00460131	−	0.999989i	$-0.501465\pi$
$167$	−0.118924	−0.00920263	−0.00460131	+	0.999989i	$0.501465\pi$
$168$	22.2077	1.71336
$169$	0.811833	0.0624487
$170$	−13.5649	−1.04038
$171$	−0.428214	−0.0327463
$172$	26.2538	2.00183
$173$	−10.6009	−0.805968	−0.402984	−	0.915207i	$-0.632027\pi$
$173$	−10.6009	−0.805968	−0.402984	+	0.915207i	$0.632027\pi$
$174$	1.48021	0.112214
$175$	−1.53323	−0.115901
$176$	1.63326	0.123111
$177$	−20.4483	−1.53699
$178$	7.04836	0.528297
$179$	9.20526	0.688033	0.344017	−	0.938964i	$-0.388212\pi$
$179$	9.20526	0.688033	0.344017	+	0.938964i	$0.388212\pi$
$180$	0.753903	0.0561926
$181$	−12.2001	−0.906823	−0.453411	−	0.891301i	$-0.649793\pi$
$181$	−12.2001	−0.906823	−0.453411	+	0.891301i	$0.649793\pi$
$182$	15.1509	1.12306
$183$	0.638115	0.0471709
$184$	−40.5190	−2.98710
$185$	−11.6078	−0.853422
$186$	−6.02620	−0.441862
$187$	0.720537	0.0526909
$188$	55.8657	4.07442
$189$	7.75740	0.564268
$190$	7.65686	0.555487
$191$	17.4723	1.26425	0.632126	−	0.774866i	$-0.282183\pi$
$191$	17.4723	1.26425	0.632126	+	0.774866i	$0.282183\pi$
$192$	27.0086	1.94918
$193$	7.44155	0.535655	0.267827	−	0.963467i	$-0.413694\pi$
$193$	7.44155	0.535655	0.267827	+	0.963467i	$0.413694\pi$
$194$	6.06730	0.435607
$195$	6.59465	0.472252
$196$	−23.5710	−1.68364
$197$	−9.78238	−0.696966	−0.348483	−	0.937315i	$-0.613303\pi$
$197$	−9.78238	−0.696966	−0.348483	+	0.937315i	$0.613303\pi$
$198$	−0.0558430	−0.00396859
$199$	4.62008	0.327509	0.163755	−	0.986501i	$-0.447639\pi$
$199$	4.62008	0.327509	0.163755	+	0.986501i	$0.447639\pi$
$200$	−8.16262	−0.577184
$201$	−6.21053	−0.438057
$202$	−25.5765	−1.79955
$203$	0.481015	0.0337607
$204$	45.8960	3.21336
$205$	6.57119	0.458952
$206$	−15.8191	−1.10217
$207$	0.738151	0.0513050
$208$	42.9769	2.97991
$209$	−0.406715	−0.0281330
$210$	7.23402	0.499195
$211$	−19.6781	−1.35469	−0.677347	−	0.735663i	$-0.736871\pi$
$211$	−19.6781	−1.35469	−0.677347	+	0.735663i	$0.736871\pi$
$212$	55.0077	3.77795
$213$	5.62891	0.385686
$214$	−19.3270	−1.32117
$215$	5.17837	0.353162
$216$	41.2989	2.81003
$217$	−1.95830	−0.132938
$218$	22.3429	1.51325
$219$	25.8306	1.74547
$220$	0.716052	0.0482762
$221$	18.9599	1.27538
$222$	54.7674	3.67575
$223$	−16.7675	−1.12283	−0.561417	−	0.827533i	$-0.689744\pi$
$223$	−16.7675	−1.12283	−0.561417	+	0.827533i	$0.689744\pi$
$224$	22.1133	1.47751
$225$	0.148702	0.00991346
$226$	47.2077	3.14021
$227$	15.7373	1.04452	0.522260	−	0.852786i	$-0.325089\pi$
$227$	15.7373	1.04452	0.522260	+	0.852786i	$0.325089\pi$
$228$	−25.9065	−1.71570
$229$	3.98042	0.263033	0.131517	−	0.991314i	$-0.458015\pi$
$229$	3.98042	0.263033	0.131517	+	0.991314i	$0.458015\pi$
$230$	−13.1988	−0.870304
$231$	−0.384255	−0.0252821
$232$	2.56083	0.168127
$233$	−12.6721	−0.830177	−0.415088	−	0.909781i	$-0.636249\pi$
$233$	−12.6721	−0.830177	−0.415088	+	0.909781i	$0.636249\pi$
$234$	−1.46943	−0.0960596
$235$	11.0191	0.718807
$236$	−58.4240	−3.80308
$237$	10.6499	0.691786
$238$	20.7981	1.34814
$239$	−17.3999	−1.12551	−0.562753	−	0.826625i	$-0.690258\pi$
$239$	−17.3999	−1.12551	−0.562753	+	0.826625i	$0.690258\pi$
$240$	20.5199	1.32455
$241$	−24.1309	−1.55441	−0.777203	−	0.629250i	$-0.783362\pi$
$241$	−24.1309	−1.55441	−0.777203	+	0.629250i	$0.783362\pi$
$242$	29.1952	1.87674
$243$	−1.54395	−0.0990447
$244$	1.82319	0.116718
$245$	−4.64920	−0.297027
$246$	−31.0039	−1.97673
$247$	−10.7021	−0.680959
$248$	−10.4256	−0.662026
$249$	22.4215	1.42091
$250$	−2.65893	−0.168165
$251$	19.7012	1.24353	0.621765	−	0.783204i	$-0.286416\pi$
$251$	19.7012	1.24353	0.621765	+	0.783204i	$0.286416\pi$
$252$	−1.15591	−0.0728153
$253$	0.701091	0.0440772
$254$	−7.36941	−0.462398
$255$	9.05266	0.566900
$256$	0.469956	0.0293722
$257$	30.3747	1.89472	0.947362	−	0.320165i	$-0.103738\pi$
$257$	30.3747	1.89472	0.947362	+	0.320165i	$0.103738\pi$
$258$	−24.4324	−1.52109
$259$	17.7974	1.10588
$260$	18.8419	1.16852
$261$	−0.0466517	−0.00288767
$262$	−21.1591	−1.30721
$263$	−8.31802	−0.512911	−0.256456	−	0.966556i	$-0.582555\pi$
$263$	−8.31802	−0.512911	−0.256456	+	0.966556i	$0.582555\pi$
$264$	−2.04570	−0.125904
$265$	10.8499	0.666503
$266$	−11.7397	−0.719809
$267$	−4.70379	−0.287867
$268$	−17.7444	−1.08391
$269$	4.12021	0.251214	0.125607	−	0.992080i	$-0.459912\pi$
$269$	4.12021	0.251214	0.125607	+	0.992080i	$0.459912\pi$
$270$	13.4529	0.818715
$271$	10.7626	0.653779	0.326889	−	0.945063i	$-0.394000\pi$
$271$	10.7626	0.653779	0.326889	+	0.945063i	$0.394000\pi$
$272$	58.9956	3.57713
$273$	−10.1111	−0.611953
$274$	3.20317	0.193510
$275$	0.141236	0.00851686
$276$	44.6574	2.68806
$277$	6.23910	0.374871	0.187435	−	0.982277i	$-0.439982\pi$
$277$	6.23910	0.374871	0.187435	+	0.982277i	$0.439982\pi$
$278$	−60.0744	−3.60302
$279$	0.189927	0.0113707
$280$	12.5152	0.747925
$281$	23.5136	1.40270	0.701351	−	0.712816i	$-0.252581\pi$
$281$	23.5136	1.40270	0.701351	+	0.712816i	$0.252581\pi$
$282$	−51.9898	−3.09595
$283$	18.2653	1.08576	0.542880	−	0.839810i	$-0.317334\pi$
$283$	18.2653	1.08576	0.542880	+	0.839810i	$0.317334\pi$
$284$	16.0826	0.954329
$285$	−5.10987	−0.302683
$286$	−1.39565	−0.0825268
$287$	−10.0751	−0.594717
$288$	−2.14468	−0.126376
$289$	9.02681	0.530989
$290$	0.834176	0.0489845
$291$	−4.04907	−0.237360
$292$	73.8019	4.31893
$293$	6.95777	0.406477	0.203239	−	0.979129i	$-0.434853\pi$
$293$	6.95777	0.406477	0.203239	+	0.979129i	$0.434853\pi$
$294$	21.9357	1.27931
$295$	−11.5237	−0.670936
$296$	94.7500	5.50723
$297$	−0.714585	−0.0414644
$298$	−0.565215	−0.0327420
$299$	18.4482	1.06689
$300$	8.99631	0.519402
$301$	−7.93964	−0.457633
$302$	−4.32568	−0.248915
$303$	17.0687	0.980570
$304$	−33.3007	−1.90992
$305$	0.359611	0.0205913
$306$	−2.01713	−0.115311
$307$	9.03228	0.515499	0.257750	−	0.966212i	$-0.417019\pi$
$307$	9.03228	0.515499	0.257750	+	0.966212i	$0.417019\pi$
$308$	−1.09787	−0.0625571
$309$	10.5570	0.600566
$310$	−3.39608	−0.192884
$311$	−12.2746	−0.696029	−0.348014	−	0.937489i	$-0.613144\pi$
$311$	−12.2746	−0.696029	−0.348014	+	0.937489i	$0.613144\pi$
$312$	−53.8296	−3.04750
$313$	−8.72353	−0.493083	−0.246542	−	0.969132i	$-0.579294\pi$
$313$	−8.72353	−0.493083	−0.246542	+	0.969132i	$0.579294\pi$
$314$	−47.0051	−2.65265
$315$	−0.227994	−0.0128460
$316$	30.4284	1.71173
$317$	−26.2241	−1.47289	−0.736446	−	0.676497i	$-0.763497\pi$
$317$	−26.2241	−1.47289	−0.736446	+	0.676497i	$0.763497\pi$
$318$	−51.1914	−2.87067
$319$	−0.0443095	−0.00248086
$320$	15.2207	0.850866
$321$	12.8981	0.719900
$322$	20.2368	1.12776
$323$	−14.6911	−0.817435
$324$	−47.7786	−2.65437
$325$	3.71643	0.206150
$326$	−24.6153	−1.36331
$327$	−14.9107	−0.824566
$328$	−53.6381	−2.96167
$329$	−16.8948	−0.931443
$330$	−0.666374	−0.0366827
$331$	18.5960	1.02213	0.511063	−	0.859543i	$-0.329252\pi$
$331$	18.5960	1.02213	0.511063	+	0.859543i	$0.329252\pi$
$332$	64.0616	3.51584
$333$	−1.72610	−0.0945897
$334$	0.316211	0.0173023
$335$	−3.49996	−0.191223
$336$	−31.4617	−1.71638
$337$	−14.7795	−0.805089	−0.402545	−	0.915400i	$-0.631874\pi$
$337$	−14.7795	−0.805089	−0.402545	+	0.915400i	$0.631874\pi$
$338$	−2.15860	−0.117413
$339$	−31.5045	−1.71109
$340$	25.8648	1.40272
$341$	0.180392	0.00976877
$342$	1.13859	0.0615678
$343$	17.8609	0.964399
$344$	−42.2691	−2.27900
$345$	8.80835	0.474226
$346$	28.1869	1.51534
$347$	−21.2169	−1.13898	−0.569492	−	0.821997i	$-0.692860\pi$
$347$	−21.2169	−1.13898	−0.569492	+	0.821997i	$0.692860\pi$
$348$	−2.82238	−0.151296
$349$	−24.3071	−1.30113	−0.650565	−	0.759450i	$-0.725468\pi$
$349$	−24.3071	−1.30113	−0.650565	+	0.759450i	$0.725468\pi$
$350$	4.07675	0.217911
$351$	−18.8033	−1.00365
$352$	−2.03700	−0.108572
$353$	0.179103	0.00953270	0.00476635	−	0.999989i	$-0.498483\pi$
$353$	0.179103	0.00953270	0.00476635	+	0.999989i	$0.498483\pi$
$354$	54.3707	2.88977
$355$	3.17218	0.168362
$356$	−13.4394	−0.712288
$357$	−13.8798	−0.734598
$358$	−24.4761	−1.29360
$359$	21.4473	1.13195	0.565974	−	0.824423i	$-0.308500\pi$
$359$	21.4473	1.13195	0.565974	+	0.824423i	$0.308500\pi$
$360$	−1.21380	−0.0639727
$361$	−10.7075	−0.563550
$362$	32.4390	1.70496
$363$	−19.4836	−1.02263
$364$	−28.8890	−1.51419
$365$	14.5569	0.761943
$366$	−1.69670	−0.0886881
$367$	−16.5366	−0.863202	−0.431601	−	0.902065i	$-0.642051\pi$
$367$	−16.5366	−0.863202	−0.431601	+	0.902065i	$0.642051\pi$
$368$	57.4034	2.99236
$369$	0.977148	0.0508683
$370$	30.8643	1.60456
$371$	−16.6354	−0.863666
$372$	11.4904	0.595750
$373$	26.0721	1.34996	0.674981	−	0.737835i	$-0.264152\pi$
$373$	26.0721	1.34996	0.674981	+	0.737835i	$0.264152\pi$
$374$	−1.91585	−0.0990665
$375$	1.77446	0.0916326
$376$	−89.9448	−4.63855
$377$	−1.16594	−0.0600491
$378$	−20.6264	−1.06091
$379$	−32.6987	−1.67962	−0.839811	−	0.542879i	$-0.817334\pi$
$379$	−32.6987	−1.67962	−0.839811	+	0.542879i	$0.817334\pi$
$380$	−14.5997	−0.748947
$381$	4.91804	0.251959
$382$	−46.4576	−2.37698
$383$	−16.5778	−0.847085	−0.423542	−	0.905876i	$-0.639214\pi$
$383$	−16.5778	−0.847085	−0.423542	+	0.905876i	$0.639214\pi$
$384$	−20.6290	−1.05272
$385$	−0.216548	−0.0110363
$386$	−19.7865	−1.00711
$387$	0.770034	0.0391430
$388$	−11.5688	−0.587316
$389$	20.9140	1.06038	0.530190	−	0.847879i	$-0.322121\pi$
$389$	20.9140	1.06038	0.530190	+	0.847879i	$0.322121\pi$
$390$	−17.5347	−0.887903
$391$	25.3244	1.28071
$392$	37.9497	1.91675
$393$	14.1207	0.712296
$394$	26.0106	1.31040
$395$	6.00178	0.301982
$396$	0.106478	0.00535073
$397$	9.07241	0.455331	0.227666	−	0.973739i	$-0.426891\pi$
$397$	9.07241	0.455331	0.227666	+	0.973739i	$0.426891\pi$
$398$	−12.2845	−0.615765
$399$	7.83461	0.392221
$400$	11.5640	0.578201
$401$	−1.00000	−0.0499376
$401$	−1.00000	−0.0499376
$402$	16.5133	0.823611
$403$	4.74676	0.236453
$404$	48.7678	2.42629
$405$	−9.42399	−0.468282
$406$	−1.27898	−0.0634749
$407$	−1.63944	−0.0812640
$408$	−73.8934	−3.65827
$409$	−18.1387	−0.896903	−0.448451	−	0.893807i	$-0.648024\pi$
$409$	−18.1387	−0.896903	−0.448451	+	0.893807i	$0.648024\pi$
$410$	−17.4723	−0.862896
$411$	−2.13766	−0.105443
$412$	30.1629	1.48602
$413$	17.6685	0.869411
$414$	−1.96269	−0.0964609
$415$	12.6357	0.620262
$416$	−53.6008	−2.62799
$417$	40.0912	1.96327
$418$	1.08142	0.0528942
$419$	−0.747825	−0.0365336	−0.0182668	−	0.999833i	$-0.505815\pi$
$419$	−0.747825	−0.0365336	−0.0182668	+	0.999833i	$0.505815\pi$
$420$	−13.7934	−0.673050
$421$	−23.0555	−1.12365	−0.561827	−	0.827254i	$-0.689901\pi$
$421$	−23.0555	−1.12365	−0.561827	+	0.827254i	$0.689901\pi$
$422$	52.3226	2.54702
$423$	1.63856	0.0796696
$424$	−88.5635	−4.30102
$425$	5.10165	0.247466
$426$	−14.9669	−0.725147
$427$	−0.551368	−0.0266825
$428$	36.8517	1.78129
$429$	0.931402	0.0449685
$430$	−13.7689	−0.663996
$431$	−17.5951	−0.847525	−0.423762	−	0.905773i	$-0.639291\pi$
$431$	−17.5951	−0.847525	−0.423762	+	0.905773i	$0.639291\pi$
$432$	−58.5083	−2.81498
$433$	−19.3802	−0.931354	−0.465677	−	0.884955i	$-0.654189\pi$
$433$	−19.3802	−0.931354	−0.465677	+	0.884955i	$0.654189\pi$
$434$	5.20697	0.249943
$435$	−0.556695	−0.0266915
$436$	−42.6022	−2.04028
$437$	−14.2946	−0.683805
$438$	−68.6817	−3.28174
$439$	14.3001	0.682506	0.341253	−	0.939971i	$-0.389149\pi$
$439$	14.3001	0.682506	0.341253	+	0.939971i	$0.389149\pi$
$440$	−1.15286	−0.0549603
$441$	−0.691345	−0.0329212
$442$	−50.4130	−2.39790
$443$	32.3802	1.53843	0.769214	−	0.638992i	$-0.220648\pi$
$443$	32.3802	1.53843	0.769214	+	0.638992i	$0.220648\pi$
$444$	−104.427	−4.95590
$445$	−2.65083	−0.125661
$446$	44.5835	2.11109
$447$	0.377201	0.0178410
$448$	−23.3369	−1.10257
$449$	34.2163	1.61476	0.807382	−	0.590028i	$-0.200883\pi$
$449$	34.2163	1.61476	0.807382	+	0.590028i	$0.200883\pi$
$450$	−0.395387	−0.0186387
$451$	0.928089	0.0437020
$452$	−90.0130	−4.23386
$453$	2.88678	0.135633
$454$	−41.8443	−1.96385
$455$	−5.69814	−0.267133
$456$	41.7099	1.95325
$457$	29.3369	1.37232	0.686161	−	0.727449i	$-0.259294\pi$
$457$	29.3369	1.37232	0.686161	+	0.727449i	$0.259294\pi$
$458$	−10.5836	−0.494541
$459$	−25.8118	−1.20479
$460$	25.1668	1.17341
$461$	−35.7135	−1.66334	−0.831672	−	0.555267i	$-0.812616\pi$
$461$	−35.7135	−1.66334	−0.831672	+	0.555267i	$0.812616\pi$
$462$	1.02171	0.0475340
$463$	−18.7081	−0.869437	−0.434718	−	0.900566i	$-0.643152\pi$
$463$	−18.7081	−0.869437	−0.434718	+	0.900566i	$0.643152\pi$
$464$	−3.62794	−0.168423
$465$	2.26640	0.105102
$466$	33.6942	1.56085
$467$	−9.10841	−0.421487	−0.210743	−	0.977541i	$-0.567588\pi$
$467$	−9.10841	−0.421487	−0.210743	+	0.977541i	$0.567588\pi$
$468$	2.80182	0.129514
$469$	5.36625	0.247790
$470$	−29.2990	−1.35146
$471$	31.3693	1.44542
$472$	94.0637	4.32963
$473$	0.731373	0.0336286
$474$	−28.3173	−1.30066
$475$	−2.87968	−0.132129
$476$	−39.6567	−1.81766
$477$	1.61340	0.0738724
$478$	46.2650	2.11611
$479$	−24.9979	−1.14218	−0.571092	−	0.820886i	$-0.693480\pi$
$479$	−24.9979	−1.14218	−0.571092	+	0.820886i	$0.693480\pi$
$480$	−25.5924	−1.16813
$481$	−43.1395	−1.96699
$482$	64.1622	2.92251
$483$	−13.5052	−0.614510
$484$	−55.6677	−2.53035
$485$	−2.28186	−0.103614
$486$	4.10526	0.186218
$487$	−9.93572	−0.450230	−0.225115	−	0.974332i	$-0.572276\pi$
$487$	−9.93572	−0.450230	−0.225115	+	0.974332i	$0.572276\pi$
$488$	−2.93537	−0.132878
$489$	16.4272	0.742864
$490$	12.3619	0.558453
$491$	−9.82914	−0.443583	−0.221791	−	0.975094i	$-0.571190\pi$
$491$	−9.82914	−0.443583	−0.221791	+	0.975094i	$0.571190\pi$
$492$	59.1164	2.66518
$493$	−1.60052	−0.0720839
$494$	28.4561	1.28030
$495$	0.0210021	0.000943973 0
$496$	14.7700	0.663192
$497$	−4.86369	−0.218166
$498$	−59.6172	−2.67151
$499$	−18.9207	−0.847007	−0.423503	−	0.905895i	$-0.639200\pi$
$499$	−18.9207	−0.847007	−0.423503	+	0.905895i	$0.639200\pi$
$500$	5.06989	0.226732
$501$	−0.211026	−0.00942795
$502$	−52.3841	−2.33802
$503$	−8.93684	−0.398474	−0.199237	−	0.979951i	$-0.563846\pi$
$503$	−8.93684	−0.398474	−0.199237	+	0.979951i	$0.563846\pi$
$504$	1.86103	0.0828969
$505$	9.61910	0.428044
$506$	−1.86415	−0.0828716
$507$	1.44056	0.0639777
$508$	14.0516	0.623438
$509$	19.5045	0.864520	0.432260	−	0.901749i	$-0.357716\pi$
$509$	19.5045	0.864520	0.432260	+	0.901749i	$0.357716\pi$
$510$	−24.0704	−1.06585
$511$	−22.3191	−0.987338
$512$	22.0015	0.972338
$513$	14.5698	0.643271
$514$	−80.7642	−3.56236
$515$	5.94941	0.262163
$516$	46.5862	2.05085
$517$	1.55630	0.0684458
$518$	−47.3221	−2.07921
$519$	−18.8108	−0.825701
$520$	−30.3358	−1.33031
$521$	21.1615	0.927102	0.463551	−	0.886070i	$-0.346575\pi$
$521$	21.1615	0.927102	0.463551	+	0.886070i	$0.346575\pi$
$522$	0.124044	0.00542924
$523$	18.9971	0.830685	0.415342	−	0.909665i	$-0.363662\pi$
$523$	18.9971	0.830685	0.415342	+	0.909665i	$0.363662\pi$
$524$	40.3450	1.76248
$525$	−2.72065	−0.118739
$526$	22.1170	0.964347
$527$	6.51601	0.283842
$528$	2.89815	0.126126
$529$	1.64095	0.0713457
$530$	−28.8490	−1.25312
$531$	−1.71360	−0.0743638
$532$	22.3847	0.970498
$533$	24.4213	1.05781
$534$	12.5070	0.541232
$535$	7.26874	0.314255
$536$	28.5688	1.23399
$537$	16.3343	0.704879
$538$	−10.9553	−0.472318
$539$	−0.656635	−0.0282833
$540$	−25.6512	−1.10385
$541$	29.2783	1.25877	0.629387	−	0.777092i	$-0.283306\pi$
$541$	29.2783	1.25877	0.629387	+	0.777092i	$0.283306\pi$
$542$	−28.6168	−1.22920
$543$	−21.6485	−0.929025
$544$	−73.5793	−3.15469
$545$	−8.40298	−0.359944
$546$	26.8847	1.15056
$547$	−12.5989	−0.538691	−0.269345	−	0.963044i	$-0.586807\pi$
$547$	−12.5989	−0.538691	−0.269345	+	0.963044i	$0.586807\pi$
$548$	−6.10762	−0.260905
$549$	0.0534749	0.00228225
$550$	−0.375536	−0.0160129
$551$	0.903432	0.0384875
$552$	−71.8992	−3.06023
$553$	−9.20212	−0.391314
$554$	−16.5893	−0.704812
$555$	−20.5975	−0.874317
$556$	114.546	4.85785
$557$	−2.59732	−0.110052	−0.0550261	−	0.998485i	$-0.517524\pi$
$557$	−2.59732	−0.110052	−0.0550261	+	0.998485i	$0.517524\pi$
$558$	−0.505003	−0.0213785
$559$	19.2450	0.813979
$560$	−17.7303	−0.749243
$561$	1.27856	0.0539809
$562$	−62.5208	−2.63728
$563$	9.46818	0.399036	0.199518	−	0.979894i	$-0.436062\pi$
$563$	9.46818	0.399036	0.199518	+	0.979894i	$0.436062\pi$
$564$	99.1313	4.17418
$565$	−17.7544	−0.746934
$566$	−48.5662	−2.04139
$567$	14.4492	0.606808
$568$	−25.8933	−1.08646
$569$	−3.20426	−0.134330	−0.0671648	−	0.997742i	$-0.521395\pi$
$569$	−3.20426	−0.134330	−0.0671648	+	0.997742i	$0.521395\pi$
$570$	13.5868	0.569087
$571$	16.1416	0.675503	0.337752	−	0.941235i	$-0.390334\pi$
$571$	16.1416	0.675503	0.337752	+	0.941235i	$0.390334\pi$
$572$	2.66115	0.111268
$573$	31.0039	1.29521
$574$	26.7891	1.11815
$575$	4.96397	0.207012
$576$	2.26335	0.0943064
$577$	44.6048	1.85692	0.928462	−	0.371428i	$-0.121132\pi$
$577$	44.6048	1.85692	0.928462	+	0.371428i	$0.121132\pi$
$578$	−24.0016	−0.998336
$579$	13.2047	0.548770
$580$	−1.59056	−0.0660444
$581$	−19.3734	−0.803746
$582$	10.7662	0.446272
$583$	1.53240	0.0634653
$584$	−118.822	−4.91691
$585$	0.552640	0.0228488
$586$	−18.5002	−0.764237
$587$	5.71629	0.235936	0.117968	−	0.993017i	$-0.462362\pi$
$587$	5.71629	0.235936	0.117968	+	0.993017i	$0.462362\pi$
$588$	−41.8257	−1.72486
$589$	−3.67803	−0.151551
$590$	30.6407	1.26146
$591$	−17.3584	−0.714030
$592$	−134.233	−5.51694
$593$	−33.5540	−1.37790	−0.688949	−	0.724810i	$-0.741928\pi$
$593$	−33.5540	−1.37790	−0.688949	+	0.724810i	$0.741928\pi$
$594$	1.90003	0.0779592
$595$	−7.82201	−0.320671
$596$	1.07772	0.0441451
$597$	8.19815	0.335528
$598$	−49.0525	−2.00590
$599$	−9.56458	−0.390798	−0.195399	−	0.980724i	$-0.562600\pi$
$599$	−9.56458	−0.390798	−0.195399	+	0.980724i	$0.562600\pi$
$600$	−14.4842	−0.591316
$601$	8.15619	0.332698	0.166349	−	0.986067i	$-0.446802\pi$
$601$	8.15619	0.332698	0.166349	+	0.986067i	$0.446802\pi$
$602$	21.1109	0.860417
$603$	−0.520450	−0.0211944
$604$	8.24796	0.335605
$605$	−10.9801	−0.446403
$606$	−45.3844	−1.84361
$607$	3.08956	0.125401	0.0627007	−	0.998032i	$-0.480029\pi$
$607$	3.08956	0.125401	0.0627007	+	0.998032i	$0.480029\pi$
$608$	41.5326	1.68437
$609$	0.853542	0.0345873
$610$	−0.956181	−0.0387146
$611$	40.9517	1.65673
$612$	3.84614	0.155471
$613$	−21.3411	−0.861959	−0.430979	−	0.902362i	$-0.641832\pi$
$613$	−21.3411	−0.861959	−0.430979	+	0.902362i	$0.641832\pi$
$614$	−24.0162	−0.969214
$615$	11.6603	0.470188
$616$	1.76760	0.0712185
$617$	−31.1645	−1.25463	−0.627317	−	0.778764i	$-0.715847\pi$
$617$	−31.1645	−1.25463	−0.627317	+	0.778764i	$0.715847\pi$
$618$	−28.0703	−1.12915
$619$	−22.9437	−0.922187	−0.461094	−	0.887352i	$-0.652543\pi$
$619$	−22.9437	−0.922187	−0.461094	+	0.887352i	$0.652543\pi$
$620$	6.47545	0.260060
$621$	−25.1152	−1.00784
$622$	32.6373	1.30863
$623$	4.06434	0.162834
$624$	76.2606	3.05287
$625$	1.00000	0.0400000
$626$	23.1952	0.927068
$627$	−0.721698	−0.0288218
$628$	89.6266	3.57649
$629$	−59.2189	−2.36121
$630$	0.606220	0.0241524
$631$	−13.2570	−0.527753	−0.263876	−	0.964556i	$-0.585001\pi$
$631$	−13.2570	−0.527753	−0.263876	+	0.964556i	$0.585001\pi$
$632$	−48.9903	−1.94873
$633$	−34.9179	−1.38786
$634$	69.7279	2.76925
$635$	2.77157	0.109987
$636$	97.6089	3.87045
$637$	−17.2784	−0.684596
$638$	0.117816	0.00466437
$639$	0.471710	0.0186605
$640$	−11.6255	−0.459540
$641$	−18.7999	−0.742552	−0.371276	−	0.928522i	$-0.621080\pi$
$641$	−18.7999	−0.742552	−0.371276	+	0.928522i	$0.621080\pi$
$642$	−34.2950	−1.35352
$643$	−12.6655	−0.499479	−0.249739	−	0.968313i	$-0.580345\pi$
$643$	−12.6655	−0.499479	−0.249739	+	0.968313i	$0.580345\pi$
$644$	−38.5865	−1.52052
$645$	9.18880	0.361809
$646$	39.0626	1.53690
$647$	23.8255	0.936676	0.468338	−	0.883549i	$-0.344853\pi$
$647$	23.8255	0.936676	0.468338	+	0.883549i	$0.344853\pi$
$648$	76.9245	3.02188
$649$	−1.62756	−0.0638875
$650$	−9.88171	−0.387593
$651$	−3.47492	−0.136193
$652$	46.9350	1.83812
$653$	−20.6263	−0.807169	−0.403584	−	0.914942i	$-0.632236\pi$
$653$	−20.6263	−0.807169	−0.403584	+	0.914942i	$0.632236\pi$
$654$	39.6466	1.55030
$655$	7.95776	0.310935
$656$	75.9894	2.96689
$657$	2.16464	0.0844505
$658$	44.9221	1.75125
$659$	−4.84091	−0.188575	−0.0942874	−	0.995545i	$-0.530057\pi$
$659$	−4.84091	−0.188575	−0.0942874	+	0.995545i	$0.530057\pi$
$660$	1.27060	0.0494582
$661$	−29.4365	−1.14495	−0.572474	−	0.819923i	$-0.694016\pi$
$661$	−29.4365	−1.14495	−0.572474	+	0.819923i	$0.694016\pi$
$662$	−49.4453	−1.92175
$663$	33.6436	1.30661
$664$	−103.140	−4.00262
$665$	4.41521	0.171215
$666$	4.58958	0.177842
$667$	−1.55733	−0.0603000
$668$	−0.602933	−0.0233282
$669$	−29.7532	−1.15033
$670$	9.30613	0.359527
$671$	0.0507901	0.00196073
$672$	39.2391	1.51368
$673$	−6.13787	−0.236597	−0.118299	−	0.992978i	$-0.537744\pi$
$673$	−6.13787	−0.236597	−0.118299	+	0.992978i	$0.537744\pi$
$674$	39.2975	1.51368
$675$	−5.05951	−0.194741
$676$	4.11591	0.158304
$677$	−40.5679	−1.55915	−0.779575	−	0.626309i	$-0.784565\pi$
$677$	−40.5679	−1.55915	−0.779575	+	0.626309i	$0.784565\pi$
$678$	83.7681	3.21710
$679$	3.49862	0.134265
$680$	−41.6428	−1.59693
$681$	27.9252	1.07009
$682$	−0.479649	−0.0183667
$683$	−32.0676	−1.22703	−0.613516	−	0.789682i	$-0.710246\pi$
$683$	−32.0676	−1.22703	−0.613516	+	0.789682i	$0.710246\pi$
$684$	−2.17100	−0.0830101
$685$	−1.20468	−0.0460286
$686$	−47.4909	−1.81321
$687$	7.06308	0.269473
$688$	59.8828	2.28301
$689$	40.3228	1.53618
$690$	−23.4208	−0.891613
$691$	46.0394	1.75142	0.875711	−	0.482836i	$-0.160393\pi$
$691$	46.0394	1.75142	0.875711	+	0.482836i	$0.160393\pi$
$692$	−53.7452	−2.04309
$693$	−0.0322010	−0.00122322
$694$	56.4143	2.14146
$695$	22.5935	0.857019
$696$	4.54409	0.172243
$697$	33.5239	1.26981
$698$	64.6309	2.44631
$699$	−22.4861	−0.850502
$700$	−7.77332	−0.293804
$701$	−19.1865	−0.724665	−0.362332	−	0.932049i	$-0.618019\pi$
$701$	−19.1865	−0.724665	−0.362332	+	0.932049i	$0.618019\pi$
$702$	49.9966	1.88700
$703$	33.4267	1.26071
$704$	2.14972	0.0810206
$705$	19.5529	0.736406
$706$	−0.476222	−0.0179229
$707$	−14.7483	−0.554667
$708$	−103.671	−3.89619
$709$	47.9062	1.79915	0.899577	−	0.436761i	$-0.143875\pi$
$709$	47.9062	1.79915	0.899577	+	0.436761i	$0.143875\pi$
$710$	−8.43461	−0.316545
$711$	0.892476	0.0334705
$712$	21.6377	0.810908
$713$	6.34016	0.237441
$714$	36.9054	1.38115
$715$	0.524894	0.0196299
$716$	46.6697	1.74413
$717$	−30.8754	−1.15306
$718$	−57.0269	−2.12823
$719$	−11.7818	−0.439387	−0.219693	−	0.975569i	$-0.570506\pi$
$719$	−11.7818	−0.439387	−0.219693	+	0.975569i	$0.570506\pi$
$720$	1.71959	0.0640854
$721$	−9.12183	−0.339715
$722$	28.4703	1.05956
$723$	−42.8192	−1.59246
$724$	−61.8529	−2.29875
$725$	−0.313727	−0.0116515
$726$	51.8056	1.92269
$727$	2.28911	0.0848984	0.0424492	−	0.999099i	$-0.486484\pi$
$727$	2.28911	0.0848984	0.0424492	+	0.999099i	$0.486484\pi$
$728$	46.5118	1.72384
$729$	25.5323	0.945641
$730$	−38.7057	−1.43256
$731$	26.4182	0.977113
$732$	3.23518	0.119576
$733$	−44.6414	−1.64887	−0.824434	−	0.565957i	$-0.808507\pi$
$733$	−44.6414	−1.64887	−0.824434	+	0.565957i	$0.808507\pi$
$734$	43.9696	1.62295
$735$	−8.24981	−0.304299
$736$	−71.5936	−2.63897
$737$	−0.494320	−0.0182085
$738$	−2.59816	−0.0956398
$739$	−43.5701	−1.60275	−0.801376	−	0.598161i	$-0.795898\pi$
$739$	−43.5701	−1.60275	−0.801376	+	0.598161i	$0.795898\pi$
$740$	−58.8503	−2.16338
$741$	−18.9905	−0.697632
$742$	44.2323	1.62382
$743$	16.5076	0.605604	0.302802	−	0.953054i	$-0.402078\pi$
$743$	16.5076	0.605604	0.302802	+	0.953054i	$0.402078\pi$
$744$	−18.4998	−0.678235
$745$	0.212573	0.00778805
$746$	−69.3238	−2.53812
$747$	1.87895	0.0687472
$748$	3.65304	0.133569
$749$	−11.1447	−0.407217
$750$	−4.71815	−0.172283
$751$	−35.0335	−1.27839	−0.639195	−	0.769044i	$-0.720732\pi$
$751$	−35.0335	−1.27839	−0.639195	+	0.769044i	$0.720732\pi$
$752$	127.425	4.64672
$753$	34.9590	1.27398
$754$	3.10015	0.112901
$755$	1.62685	0.0592072
$756$	39.3292	1.43039
$757$	−43.4003	−1.57741	−0.788705	−	0.614771i	$-0.789248\pi$
$757$	−43.4003	−1.57741	−0.788705	+	0.614771i	$0.789248\pi$
$758$	86.9436	3.15793
$759$	1.24406	0.0451564
$760$	23.5057	0.852642
$761$	−21.7912	−0.789931	−0.394966	−	0.918696i	$-0.629244\pi$
$761$	−21.7912	−0.789931	−0.394966	+	0.918696i	$0.629244\pi$
$762$	−13.0767	−0.473719
$763$	12.8837	0.466422
$764$	88.5827	3.20481
$765$	0.758625	0.0274281
$766$	44.0791	1.59264
$767$	−42.8270	−1.54639
$768$	0.833917	0.0300914
$769$	40.9554	1.47689	0.738444	−	0.674315i	$-0.235561\pi$
$769$	40.9554	1.47689	0.738444	+	0.674315i	$0.235561\pi$
$770$	0.575784	0.0207498
$771$	53.8987	1.94111
$772$	37.7279	1.35786
$773$	6.61682	0.237991	0.118995	−	0.992895i	$-0.462033\pi$
$773$	6.61682	0.237991	0.118995	+	0.992895i	$0.462033\pi$
$774$	−2.04746	−0.0735945
$775$	1.27724	0.0458797
$776$	18.6260	0.668633
$777$	31.5808	1.13296
$778$	−55.6087	−1.99367
$779$	−18.9229	−0.677983
$780$	33.4341	1.19713
$781$	0.448027	0.0160317
$782$	−67.3357	−2.40792
$783$	1.58730	0.0567256
$784$	−53.7635	−1.92012
$785$	17.6782	0.630962
$786$	−37.5459	−1.33922
$787$	13.4320	0.478798	0.239399	−	0.970921i	$-0.423050\pi$
$787$	13.4320	0.478798	0.239399	+	0.970921i	$0.423050\pi$
$788$	−49.5956	−1.76677
$789$	−14.7600	−0.525469
$790$	−15.9583	−0.567771
$791$	27.2216	0.967890
$792$	−0.171432	−0.00609157
$793$	1.33647	0.0474594
$794$	−24.1229	−0.856089
$795$	19.2527	0.682822
$796$	23.4233	0.830218
$797$	−26.6853	−0.945242	−0.472621	−	0.881266i	$-0.656692\pi$
$797$	−26.6853	−0.945242	−0.472621	+	0.881266i	$0.656692\pi$
$798$	−20.8317	−0.737433
$799$	56.2156	1.98876
$800$	−14.4227	−0.509918
$801$	−0.394183	−0.0139278
$802$	2.65893	0.0938900
$803$	2.05596	0.0725532
$804$	−31.4867	−1.11045
$805$	−7.61091	−0.268249
$806$	−12.6213	−0.444565
$807$	7.31114	0.257364
$808$	−78.5170	−2.76222
$809$	−39.5717	−1.39127	−0.695633	−	0.718397i	$-0.744876\pi$
$809$	−39.5717	−1.39127	−0.695633	+	0.718397i	$0.744876\pi$
$810$	25.0577	0.880438
$811$	39.9332	1.40225	0.701123	−	0.713040i	$-0.252682\pi$
$811$	39.9332	1.40225	0.701123	+	0.713040i	$0.252682\pi$
$812$	2.43870	0.0855815
$813$	19.0977	0.669786
$814$	4.35915	0.152788
$815$	9.25759	0.324279
$816$	104.685	3.66471
$817$	−14.9120	−0.521706
$818$	48.2296	1.68631
$819$	−0.847325	−0.0296079
$820$	33.3152	1.16342
$821$	33.4467	1.16730	0.583649	−	0.812006i	$-0.301625\pi$
$821$	33.4467	1.16730	0.583649	+	0.812006i	$0.301625\pi$
$822$	5.68389	0.198248
$823$	−39.7091	−1.38417	−0.692086	−	0.721815i	$-0.743308\pi$
$823$	−39.7091	−1.38417	−0.692086	+	0.721815i	$0.743308\pi$
$824$	−48.5628	−1.69177
$825$	0.250618	0.00872538
$826$	−46.9793	−1.63462
$827$	43.3596	1.50776	0.753881	−	0.657011i	$-0.228180\pi$
$827$	43.3596	1.50776	0.753881	+	0.657011i	$0.228180\pi$
$828$	3.74235	0.130056
$829$	48.6748	1.69055	0.845273	−	0.534335i	$-0.179438\pi$
$829$	48.6748	1.69055	0.845273	+	0.534335i	$0.179438\pi$
$830$	−33.5974	−1.16618
$831$	11.0710	0.384049
$832$	56.5668	1.96110
$833$	−23.7186	−0.821800
$834$	−106.599	−3.69124
$835$	−0.118924	−0.00411554
$836$	−2.06200	−0.0713157
$837$	−6.46219	−0.223366
$838$	1.98841	0.0686885
$839$	−22.0888	−0.762590	−0.381295	−	0.924453i	$-0.624522\pi$
$839$	−22.0888	−0.762590	−0.381295	+	0.924453i	$0.624522\pi$
$840$	22.2077	0.766238
$841$	−28.9016	−0.996606
$842$	61.3028	2.11263
$843$	41.7238	1.43705
$844$	−99.7657	−3.43408
$845$	0.811833	0.0279279
$846$	−4.35682	−0.149790
$847$	16.8350	0.578456
$848$	125.468	4.30860
$849$	32.4111	1.11234
$850$	−13.5649	−0.465273
$851$	−57.6207	−1.97521
$852$	28.5380	0.977694
$853$	17.3015	0.592394	0.296197	−	0.955127i	$-0.404282\pi$
$853$	17.3015	0.592394	0.296197	+	0.955127i	$0.404282\pi$
$854$	1.46605	0.0501671
$855$	−0.428214	−0.0146446
$856$	−59.3319	−2.02792
$857$	−13.5404	−0.462533	−0.231266	−	0.972890i	$-0.574287\pi$
$857$	−13.5404	−0.462533	−0.231266	+	0.972890i	$0.574287\pi$
$858$	−2.47653	−0.0845473
$859$	−35.8722	−1.22394	−0.611972	−	0.790879i	$-0.709624\pi$
$859$	−35.8722	−1.22394	−0.611972	+	0.790879i	$0.709624\pi$
$860$	26.2538	0.895247
$861$	−17.8779	−0.609278
$862$	46.7840	1.59347
$863$	34.5898	1.17745	0.588725	−	0.808333i	$-0.299630\pi$
$863$	34.5898	1.17745	0.588725	+	0.808333i	$0.299630\pi$
$864$	72.9716	2.48254
$865$	−10.6009	−0.360440
$866$	51.5306	1.75108
$867$	16.0177	0.543989
$868$	−9.92836	−0.336991
$869$	0.847668	0.0287552
$870$	1.48021	0.0501838
$871$	−13.0073	−0.440737
$872$	68.5904	2.32276
$873$	−0.339317	−0.0114841
$874$	38.0084	1.28565
$875$	−1.53323	−0.0518327
$876$	130.958	4.42467
$877$	23.5202	0.794222	0.397111	−	0.917771i	$-0.370013\pi$
$877$	23.5202	0.794222	0.397111	+	0.917771i	$0.370013\pi$
$878$	−38.0229	−1.28321
$879$	12.3463	0.416430
$880$	1.63326	0.0550571
$881$	−2.90590	−0.0979023	−0.0489512	−	0.998801i	$-0.515588\pi$
$881$	−2.90590	−0.0979023	−0.0489512	+	0.998801i	$0.515588\pi$
$882$	1.83824	0.0618966
$883$	−45.6044	−1.53471	−0.767356	−	0.641221i	$-0.778428\pi$
$883$	−45.6044	−1.53471	−0.767356	+	0.641221i	$0.778428\pi$
$884$	96.1247	3.23302
$885$	−20.4483	−0.687364
$886$	−86.0965	−2.89247
$887$	−1.29032	−0.0433248	−0.0216624	−	0.999765i	$-0.506896\pi$
$887$	−1.29032	−0.0433248	−0.0216624	+	0.999765i	$0.506896\pi$
$888$	168.130	5.64207
$889$	−4.24946	−0.142522
$890$	7.04836	0.236262
$891$	−1.33101	−0.0445904
$892$	−85.0094	−2.84632
$893$	−31.7315	−1.06185
$894$	−1.00295	−0.0335437
$895$	9.20526	0.307698
$896$	17.8246	0.595479
$897$	32.7356	1.09301
$898$	−90.9785	−3.03599
$899$	−0.400703	−0.0133642
$900$	0.753903	0.0251301
$901$	55.3523	1.84405
$902$	−2.46772	−0.0821661
$903$	−14.0886	−0.468838
$904$	144.923	4.82006
$905$	−12.2001	−0.405543
$906$	−7.67574	−0.255009
$907$	−49.7231	−1.65103	−0.825513	−	0.564382i	$-0.809114\pi$
$907$	−49.7231	−1.65103	−0.825513	+	0.564382i	$0.809114\pi$
$908$	79.7864	2.64780
$909$	1.43038	0.0474426
$910$	15.1509	0.502249
$911$	−16.4017	−0.543412	−0.271706	−	0.962380i	$-0.587588\pi$
$911$	−16.4017	−0.543412	−0.271706	+	0.962380i	$0.587588\pi$
$912$	−59.0907	−1.95669
$913$	1.78462	0.0590622
$914$	−78.0047	−2.58017
$915$	0.638115	0.0210954
$916$	20.1803	0.666776
$917$	−12.2011	−0.402915
$918$	68.6318	2.26519
$919$	7.16042	0.236200	0.118100	−	0.993002i	$-0.462320\pi$
$919$	7.16042	0.236200	0.118100	+	0.993002i	$0.462320\pi$
$920$	−40.5190	−1.33587
$921$	16.0274	0.528121
$922$	94.9597	3.12733
$923$	11.7892	0.388046
$924$	−1.94813	−0.0640888
$925$	−11.6078	−0.381662
$926$	49.7433	1.63467
$927$	0.884689	0.0290570
$928$	4.52477	0.148533
$929$	−10.8669	−0.356530	−0.178265	−	0.983983i	$-0.557048\pi$
$929$	−10.8669	−0.356530	−0.178265	+	0.983983i	$0.557048\pi$
$930$	−6.02620	−0.197607
$931$	13.3882	0.438781
$932$	−64.2462	−2.10445
$933$	−21.7808	−0.713070
$934$	24.2186	0.792456
$935$	0.720537	0.0235641
$936$	−4.51099	−0.147446
$937$	51.1625	1.67141	0.835704	−	0.549181i	$-0.185060\pi$
$937$	51.1625	1.67141	0.835704	+	0.549181i	$0.185060\pi$
$938$	−14.2685	−0.465882
$939$	−15.4795	−0.505156
$940$	55.8657	1.82214
$941$	−15.2427	−0.496898	−0.248449	−	0.968645i	$-0.579921\pi$
$941$	−15.2427	−0.496898	−0.248449	+	0.968645i	$0.579921\pi$
$942$	−83.4085	−2.71760
$943$	32.6191	1.06223
$944$	−133.261	−4.33726
$945$	7.75740	0.252348
$946$	−1.94467	−0.0632266
$947$	6.28761	0.204320	0.102160	−	0.994768i	$-0.467425\pi$
$947$	6.28761	0.204320	0.102160	+	0.994768i	$0.467425\pi$
$948$	53.9939	1.75364
$949$	54.0996	1.75615
$950$	7.65686	0.248421
$951$	−46.5335	−1.50895
$952$	63.8481	2.06933
$953$	−18.0932	−0.586097	−0.293048	−	0.956098i	$-0.594670\pi$
$953$	−18.0932	−0.586097	−0.293048	+	0.956098i	$0.594670\pi$
$954$	−4.28991	−0.138891
$955$	17.4723	0.565391
$956$	−88.2156	−2.85310
$957$	−0.0786254	−0.00254160
$958$	66.4676	2.14747
$959$	1.84706	0.0596447
$960$	27.0086	0.871698
$961$	−29.3687	−0.947376
$962$	114.705	3.69823
$963$	1.08087	0.0348307
$964$	−122.341	−3.94034
$965$	7.44155	0.239552
$966$	35.9094	1.15537
$967$	−61.8439	−1.98876	−0.994382	−	0.105848i	$-0.966244\pi$
$967$	−61.8439	−1.98876	−0.994382	+	0.105848i	$0.966244\pi$
$968$	89.6260	2.88069
$969$	−26.0688	−0.837449
$970$	6.06730	0.194809
$971$	37.2914	1.19674	0.598369	−	0.801220i	$-0.295816\pi$
$971$	37.2914	1.19674	0.598369	+	0.801220i	$0.295816\pi$
$972$	−7.82768	−0.251073
$973$	−34.6410	−1.11054
$974$	26.4183	0.846499
$975$	6.59465	0.211198
$976$	4.15856	0.133112
$977$	−51.0216	−1.63232	−0.816162	−	0.577823i	$-0.803902\pi$
$977$	−51.0216	−1.63232	−0.816162	+	0.577823i	$0.803902\pi$
$978$	−43.6788	−1.39669
$979$	−0.374393	−0.0119656
$980$	−23.5710	−0.752946
$981$	−1.24954	−0.0398947
$982$	26.1350	0.834000
$983$	8.46074	0.269856	0.134928	−	0.990855i	$-0.456920\pi$
$983$	8.46074	0.269856	0.134928	+	0.990855i	$0.456920\pi$
$984$	−95.1786	−3.03418
$985$	−9.78238	−0.311692
$986$	4.25567	0.135528
$987$	−29.9792	−0.954248
$988$	−54.2586	−1.72620
$989$	25.7053	0.817380
$990$	−0.0558430	−0.00177481
$991$	35.1326	1.11602	0.558011	−	0.829833i	$-0.311565\pi$
$991$	35.1326	1.11602	0.558011	+	0.829833i	$0.311565\pi$
$992$	−18.4211	−0.584872
$993$	32.9977	1.04715
$994$	12.9322	0.410185
$995$	4.62008	0.146467
$996$	113.675	3.60192
$997$	−19.6256	−0.621548	−0.310774	−	0.950484i	$-0.600588\pi$
$997$	−19.6256	−0.621548	−0.310774	+	0.950484i	$0.600588\pi$
$998$	50.3087	1.59250
$999$	58.7297	1.85813

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2005.2.a.g.1.1	✓	37

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2005.2.a.g.1.1	✓	37	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 2005 = 5 \cdot 401 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2005.a (trivial)

\(f(q)\)	\(=\)	\(q-2.65893 q^{2} +1.77446 q^{3} +5.06989 q^{4} +1.00000 q^{5} -4.71815 q^{6} -1.53323 q^{7} -8.16262 q^{8} +0.148702 q^{9} +O(q^{10})\)	\(q-2.65893 q^{2} +1.77446 q^{3} +5.06989 q^{4} +1.00000 q^{5} -4.71815 q^{6} -1.53323 q^{7} -8.16262 q^{8} +0.148702 q^{9} -2.65893 q^{10} +0.141236 q^{11} +8.99631 q^{12} +3.71643 q^{13} +4.07675 q^{14} +1.77446 q^{15} +11.5640 q^{16} +5.10165 q^{17} -0.395387 q^{18} -2.87968 q^{19} +5.06989 q^{20} -2.72065 q^{21} -0.375536 q^{22} +4.96397 q^{23} -14.4842 q^{24} +1.00000 q^{25} -9.88171 q^{26} -5.05951 q^{27} -7.77332 q^{28} -0.313727 q^{29} -4.71815 q^{30} +1.27724 q^{31} -14.4227 q^{32} +0.250618 q^{33} -13.5649 q^{34} -1.53323 q^{35} +0.753903 q^{36} -11.6078 q^{37} +7.65686 q^{38} +6.59465 q^{39} -8.16262 q^{40} +6.57119 q^{41} +7.23402 q^{42} +5.17837 q^{43} +0.716052 q^{44} +0.148702 q^{45} -13.1988 q^{46} +11.0191 q^{47} +20.5199 q^{48} -4.64920 q^{49} -2.65893 q^{50} +9.05266 q^{51} +18.8419 q^{52} +10.8499 q^{53} +13.4529 q^{54} +0.141236 q^{55} +12.5152 q^{56} -5.10987 q^{57} +0.834176 q^{58} -11.5237 q^{59} +8.99631 q^{60} +0.359611 q^{61} -3.39608 q^{62} -0.227994 q^{63} +15.2207 q^{64} +3.71643 q^{65} -0.666374 q^{66} -3.49996 q^{67} +25.8648 q^{68} +8.80835 q^{69} +4.07675 q^{70} +3.17218 q^{71} -1.21380 q^{72} +14.5569 q^{73} +30.8643 q^{74} +1.77446 q^{75} -14.5997 q^{76} -0.216548 q^{77} -17.5347 q^{78} +6.00178 q^{79} +11.5640 q^{80} -9.42399 q^{81} -17.4723 q^{82} +12.6357 q^{83} -13.7934 q^{84} +5.10165 q^{85} -13.7689 q^{86} -0.556695 q^{87} -1.15286 q^{88} -2.65083 q^{89} -0.395387 q^{90} -5.69814 q^{91} +25.1668 q^{92} +2.26640 q^{93} -29.2990 q^{94} -2.87968 q^{95} -25.5924 q^{96} -2.28186 q^{97} +12.3619 q^{98} +0.0210021 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 37 q + 11 q^{2} + 13 q^{3} + 43 q^{4} + 37 q^{5} - 2 q^{6} + 34 q^{7} + 27 q^{8} + 50 q^{9}+O(q^{10}) \) 37 * q + 11 * q^2 + 13 * q^3 + 43 * q^4 + 37 * q^5 - 2 * q^6 + 34 * q^7 + 27 * q^8 + 50 * q^9	\( 37 q + 11 q^{2} + 13 q^{3} + 43 q^{4} + 37 q^{5} - 2 q^{6} + 34 q^{7} + 27 q^{8} + 50 q^{9} + 11 q^{10} + 38 q^{11} + 24 q^{12} + 17 q^{13} + 14 q^{14} + 13 q^{15} + 47 q^{16} + 22 q^{17} + 18 q^{18} + 6 q^{19} + 43 q^{20} + 4 q^{21} + 18 q^{22} + 45 q^{23} - 19 q^{24} + 37 q^{25} - q^{26} + 43 q^{27} + 46 q^{28} + 17 q^{29} - 2 q^{30} - 13 q^{31} + 50 q^{32} + 12 q^{33} - 30 q^{34} + 34 q^{35} + 43 q^{36} + 9 q^{37} + q^{38} - 7 q^{39} + 27 q^{40} + 12 q^{41} - 38 q^{42} + 53 q^{43} + 36 q^{44} + 50 q^{45} - 15 q^{46} + 39 q^{47} - 6 q^{48} + 37 q^{49} + 11 q^{50} + 38 q^{51} + 17 q^{52} + 19 q^{53} - 62 q^{54} + 38 q^{55} + 18 q^{56} + 6 q^{57} - 13 q^{58} + 33 q^{59} + 24 q^{60} - 11 q^{61} + q^{62} + 98 q^{63} + 15 q^{64} + 17 q^{65} - 70 q^{66} + 49 q^{67} + 32 q^{68} - 36 q^{69} + 14 q^{70} + 19 q^{71} + 5 q^{72} + 39 q^{73} + 21 q^{74} + 13 q^{75} - 33 q^{76} + 34 q^{77} - 22 q^{78} - 9 q^{79} + 47 q^{80} + 49 q^{81} + 14 q^{82} + 114 q^{83} - 50 q^{84} + 22 q^{85} + 9 q^{86} + 56 q^{87} + 14 q^{88} + 2 q^{89} + 18 q^{90} - 29 q^{91} + 47 q^{92} - 7 q^{93} - 52 q^{94} + 6 q^{95} - 89 q^{96} + 4 q^{97} + 14 q^{98} + 57 q^{99}+O(q^{100}) \) 37 * q + 11 * q^2 + 13 * q^3 + 43 * q^4 + 37 * q^5 - 2 * q^6 + 34 * q^7 + 27 * q^8 + 50 * q^9 + 11 * q^10 + 38 * q^11 + 24 * q^12 + 17 * q^13 + 14 * q^14 + 13 * q^15 + 47 * q^16 + 22 * q^17 + 18 * q^18 + 6 * q^19 + 43 * q^20 + 4 * q^21 + 18 * q^22 + 45 * q^23 - 19 * q^24 + 37 * q^25 - q^26 + 43 * q^27 + 46 * q^28 + 17 * q^29 - 2 * q^30 - 13 * q^31 + 50 * q^32 + 12 * q^33 - 30 * q^34 + 34 * q^35 + 43 * q^36 + 9 * q^37 + q^38 - 7 * q^39 + 27 * q^40 + 12 * q^41 - 38 * q^42 + 53 * q^43 + 36 * q^44 + 50 * q^45 - 15 * q^46 + 39 * q^47 - 6 * q^48 + 37 * q^49 + 11 * q^50 + 38 * q^51 + 17 * q^52 + 19 * q^53 - 62 * q^54 + 38 * q^55 + 18 * q^56 + 6 * q^57 - 13 * q^58 + 33 * q^59 + 24 * q^60 - 11 * q^61 + q^62 + 98 * q^63 + 15 * q^64 + 17 * q^65 - 70 * q^66 + 49 * q^67 + 32 * q^68 - 36 * q^69 + 14 * q^70 + 19 * q^71 + 5 * q^72 + 39 * q^73 + 21 * q^74 + 13 * q^75 - 33 * q^76 + 34 * q^77 - 22 * q^78 - 9 * q^79 + 47 * q^80 + 49 * q^81 + 14 * q^82 + 114 * q^83 - 50 * q^84 + 22 * q^85 + 9 * q^86 + 56 * q^87 + 14 * q^88 + 2 * q^89 + 18 * q^90 - 29 * q^91 + 47 * q^92 - 7 * q^93 - 52 * q^94 + 6 * q^95 - 89 * q^96 + 4 * q^97 + 14 * q^98 + 57 * q^99

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