LMFDB - Embedded newform 6015.2.a.c.1.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("6015.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6015 = 3 \cdot 5 \cdot 401 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6015.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$48.0300168158$
Analytic rank:	$1$
Dimension:	$28$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.7
Character	$\chi$	$=$	6015.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.62087 q^{2} +1.00000 q^{3} +0.627218 q^{4} -1.00000 q^{5} -1.62087 q^{6} +2.78454 q^{7} +2.22510 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.62087 q^{2} +1.00000 q^{3} +0.627218 q^{4} -1.00000 q^{5} -1.62087 q^{6} +2.78454 q^{7} +2.22510 q^{8} +1.00000 q^{9} +1.62087 q^{10} +1.67535 q^{11} +0.627218 q^{12} -5.48224 q^{13} -4.51338 q^{14} -1.00000 q^{15} -4.86103 q^{16} -5.96866 q^{17} -1.62087 q^{18} +7.74371 q^{19} -0.627218 q^{20} +2.78454 q^{21} -2.71552 q^{22} +4.09024 q^{23} +2.22510 q^{24} +1.00000 q^{25} +8.88600 q^{26} +1.00000 q^{27} +1.74652 q^{28} +0.557056 q^{29} +1.62087 q^{30} -5.85394 q^{31} +3.42890 q^{32} +1.67535 q^{33} +9.67442 q^{34} -2.78454 q^{35} +0.627218 q^{36} -11.2872 q^{37} -12.5515 q^{38} -5.48224 q^{39} -2.22510 q^{40} -1.44843 q^{41} -4.51338 q^{42} -0.430890 q^{43} +1.05081 q^{44} -1.00000 q^{45} -6.62975 q^{46} +6.97031 q^{47} -4.86103 q^{48} +0.753684 q^{49} -1.62087 q^{50} -5.96866 q^{51} -3.43856 q^{52} -10.1731 q^{53} -1.62087 q^{54} -1.67535 q^{55} +6.19589 q^{56} +7.74371 q^{57} -0.902915 q^{58} +6.89659 q^{59} -0.627218 q^{60} +9.62299 q^{61} +9.48848 q^{62} +2.78454 q^{63} +4.16427 q^{64} +5.48224 q^{65} -2.71552 q^{66} -11.1264 q^{67} -3.74365 q^{68} +4.09024 q^{69} +4.51338 q^{70} +0.840297 q^{71} +2.22510 q^{72} -10.4235 q^{73} +18.2950 q^{74} +1.00000 q^{75} +4.85699 q^{76} +4.66507 q^{77} +8.88600 q^{78} -13.4846 q^{79} +4.86103 q^{80} +1.00000 q^{81} +2.34771 q^{82} +1.06041 q^{83} +1.74652 q^{84} +5.96866 q^{85} +0.698416 q^{86} +0.557056 q^{87} +3.72781 q^{88} -14.5572 q^{89} +1.62087 q^{90} -15.2655 q^{91} +2.56547 q^{92} -5.85394 q^{93} -11.2980 q^{94} -7.74371 q^{95} +3.42890 q^{96} -0.863013 q^{97} -1.22162 q^{98} +1.67535 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q - q^{2} + 28 q^{3} + 21 q^{4} - 28 q^{5} - q^{6} - 20 q^{7} + 28 q^{9}+O(q^{10}) $ 28 * q - q^2 + 28 * q^3 + 21 * q^4 - 28 * q^5 - q^6 - 20 * q^7 + 28 * q^9	\( 28 q - q^{2} + 28 q^{3} + 21 q^{4} - 28 q^{5} - q^{6} - 20 q^{7} + 28 q^{9} + q^{10} - q^{11} + 21 q^{12} - 18 q^{13} - 4 q^{14} - 28 q^{15} - q^{16} - 28 q^{17} - q^{18} - 19 q^{19} - 21 q^{20} - 20 q^{21} - 35 q^{22} + 2 q^{23} + 28 q^{25} - 20 q^{26} + 28 q^{27} - 54 q^{28} + 9 q^{29} + q^{30} - 19 q^{31} - 6 q^{32} - q^{33} - 16 q^{34} + 20 q^{35} + 21 q^{36} - 32 q^{37} - 2 q^{38} - 18 q^{39} - 27 q^{41} - 4 q^{42} - 77 q^{43} + q^{44} - 28 q^{45} - 19 q^{46} + 10 q^{47} - q^{48} - 4 q^{49} - q^{50} - 28 q^{51} - 34 q^{52} - 21 q^{53} - q^{54} + q^{55} - 9 q^{56} - 19 q^{57} - 46 q^{58} - 7 q^{59} - 21 q^{60} - 31 q^{61} - 7 q^{62} - 20 q^{63} - 46 q^{64} + 18 q^{65} - 35 q^{66} - 50 q^{67} - 68 q^{68} + 2 q^{69} + 4 q^{70} - 4 q^{71} - 87 q^{73} + 4 q^{74} + 28 q^{75} - 40 q^{76} - 8 q^{77} - 20 q^{78} - 65 q^{79} + q^{80} + 28 q^{81} - 41 q^{82} + 13 q^{83} - 54 q^{84} + 28 q^{85} - 17 q^{86} + 9 q^{87} - 117 q^{88} - 33 q^{89} + q^{90} - 33 q^{91} + 3 q^{92} - 19 q^{93} - 60 q^{94} + 19 q^{95} - 6 q^{96} - 75 q^{97} - 18 q^{98} - q^{99}+O(q^{100}) \) 28 * q - q^2 + 28 * q^3 + 21 * q^4 - 28 * q^5 - q^6 - 20 * q^7 + 28 * q^9 + q^10 - q^11 + 21 * q^12 - 18 * q^13 - 4 * q^14 - 28 * q^15 - q^16 - 28 * q^17 - q^18 - 19 * q^19 - 21 * q^20 - 20 * q^21 - 35 * q^22 + 2 * q^23 + 28 * q^25 - 20 * q^26 + 28 * q^27 - 54 * q^28 + 9 * q^29 + q^30 - 19 * q^31 - 6 * q^32 - q^33 - 16 * q^34 + 20 * q^35 + 21 * q^36 - 32 * q^37 - 2 * q^38 - 18 * q^39 - 27 * q^41 - 4 * q^42 - 77 * q^43 + q^44 - 28 * q^45 - 19 * q^46 + 10 * q^47 - q^48 - 4 * q^49 - q^50 - 28 * q^51 - 34 * q^52 - 21 * q^53 - q^54 + q^55 - 9 * q^56 - 19 * q^57 - 46 * q^58 - 7 * q^59 - 21 * q^60 - 31 * q^61 - 7 * q^62 - 20 * q^63 - 46 * q^64 + 18 * q^65 - 35 * q^66 - 50 * q^67 - 68 * q^68 + 2 * q^69 + 4 * q^70 - 4 * q^71 - 87 * q^73 + 4 * q^74 + 28 * q^75 - 40 * q^76 - 8 * q^77 - 20 * q^78 - 65 * q^79 + q^80 + 28 * q^81 - 41 * q^82 + 13 * q^83 - 54 * q^84 + 28 * q^85 - 17 * q^86 + 9 * q^87 - 117 * q^88 - 33 * q^89 + q^90 - 33 * q^91 + 3 * q^92 - 19 * q^93 - 60 * q^94 + 19 * q^95 - 6 * q^96 - 75 * q^97 - 18 * q^98 - 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 $

$2$	−1.62087	−1.14613	−0.573064	−	0.819511i	$-0.694245\pi$
$2$	−1.62087	−1.14613	−0.573064	+	0.819511i	$0.694245\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	0.627218	0.313609
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	−1.62087	−0.661717
$7$	2.78454	1.05246	0.526229	−	0.850343i	$-0.323605\pi$
$7$	2.78454	1.05246	0.526229	+	0.850343i	$0.323605\pi$
$8$	2.22510	0.786692
$9$	1.00000	0.333333
$10$	1.62087	0.512564
$11$	1.67535	0.505136	0.252568	−	0.967579i	$-0.418725\pi$
$11$	1.67535	0.505136	0.252568	+	0.967579i	$0.418725\pi$
$12$	0.627218	0.181062
$13$	−5.48224	−1.52050	−0.760250	−	0.649631i	$-0.774924\pi$
$13$	−5.48224	−1.52050	−0.760250	+	0.649631i	$0.774924\pi$
$14$	−4.51338	−1.20625
$15$	−1.00000	−0.258199
$16$	−4.86103	−1.21526
$17$	−5.96866	−1.44761	−0.723806	−	0.690003i	$-0.757609\pi$
$17$	−5.96866	−1.44761	−0.723806	+	0.690003i	$0.757609\pi$
$18$	−1.62087	−0.382043
$19$	7.74371	1.77653	0.888264	−	0.459333i	$-0.151912\pi$
$19$	7.74371	1.77653	0.888264	+	0.459333i	$0.151912\pi$
$20$	−0.627218	−0.140250
$21$	2.78454	0.607637
$22$	−2.71552	−0.578950
$23$	4.09024	0.852875	0.426437	−	0.904517i	$-0.359768\pi$
$23$	4.09024	0.852875	0.426437	+	0.904517i	$0.359768\pi$
$24$	2.22510	0.454197
$25$	1.00000	0.200000
$26$	8.88600	1.74269
$27$	1.00000	0.192450
$28$	1.74652	0.330060
$29$	0.557056	0.103443	0.0517214	−	0.998662i	$-0.483529\pi$
$29$	0.557056	0.103443	0.0517214	+	0.998662i	$0.483529\pi$
$30$	1.62087	0.295929
$31$	−5.85394	−1.05140	−0.525700	−	0.850670i	$-0.676196\pi$
$31$	−5.85394	−1.05140	−0.525700	+	0.850670i	$0.676196\pi$
$32$	3.42890	0.606149
$33$	1.67535	0.291640
$34$	9.67442	1.65915
$35$	−2.78454	−0.470674
$36$	0.627218	0.104536
$37$	−11.2872	−1.85560	−0.927798	−	0.373082i	$-0.878301\pi$
$37$	−11.2872	−1.85560	−0.927798	+	0.373082i	$0.878301\pi$
$38$	−12.5515	−2.03613
$39$	−5.48224	−0.877861
$40$	−2.22510	−0.351819
$41$	−1.44843	−0.226206	−0.113103	−	0.993583i	$-0.536079\pi$
$41$	−1.44843	−0.226206	−0.113103	+	0.993583i	$0.536079\pi$
$42$	−4.51338	−0.696430
$43$	−0.430890	−0.0657101	−0.0328550	−	0.999460i	$-0.510460\pi$
$43$	−0.430890	−0.0657101	−0.0328550	+	0.999460i	$0.510460\pi$
$44$	1.05081	0.158415
$45$	−1.00000	−0.149071
$46$	−6.62975	−0.977503
$47$	6.97031	1.01672	0.508362	−	0.861143i	$-0.330251\pi$
$47$	6.97031	1.01672	0.508362	+	0.861143i	$0.330251\pi$
$48$	−4.86103	−0.701630
$49$	0.753684	0.107669
$50$	−1.62087	−0.229226
$51$	−5.96866	−0.835780
$52$	−3.43856	−0.476842
$53$	−10.1731	−1.39738	−0.698691	−	0.715424i	$-0.746234\pi$
$53$	−10.1731	−1.39738	−0.698691	+	0.715424i	$0.746234\pi$
$54$	−1.62087	−0.220572
$55$	−1.67535	−0.225904
$56$	6.19589	0.827961
$57$	7.74371	1.02568
$58$	−0.902915	−0.118559
$59$	6.89659	0.897860	0.448930	−	0.893567i	$-0.351805\pi$
$59$	6.89659	0.897860	0.448930	+	0.893567i	$0.351805\pi$
$60$	−0.627218	−0.0809735
$61$	9.62299	1.23210	0.616049	−	0.787708i	$-0.288732\pi$
$61$	9.62299	1.23210	0.616049	+	0.787708i	$0.288732\pi$
$62$	9.48848	1.20504
$63$	2.78454	0.350820
$64$	4.16427	0.520534
$65$	5.48224	0.679988
$66$	−2.71552	−0.334257
$67$	−11.1264	−1.35930	−0.679650	−	0.733536i	$-0.737869\pi$
$67$	−11.1264	−1.35930	−0.679650	+	0.733536i	$0.737869\pi$
$68$	−3.74365	−0.453984
$69$	4.09024	0.492407
$70$	4.51338	0.539452
$71$	0.840297	0.0997249	0.0498625	−	0.998756i	$-0.484122\pi$
$71$	0.840297	0.0997249	0.0498625	+	0.998756i	$0.484122\pi$
$72$	2.22510	0.262231
$73$	−10.4235	−1.21998	−0.609989	−	0.792410i	$-0.708826\pi$
$73$	−10.4235	−1.21998	−0.609989	+	0.792410i	$0.708826\pi$
$74$	18.2950	2.12675
$75$	1.00000	0.115470
$76$	4.85699	0.557135
$77$	4.66507	0.531635
$78$	8.88600	1.00614
$79$	−13.4846	−1.51713	−0.758567	−	0.651595i	$-0.774100\pi$
$79$	−13.4846	−1.51713	−0.758567	+	0.651595i	$0.774100\pi$
$80$	4.86103	0.543480
$81$	1.00000	0.111111
$82$	2.34771	0.259261
$83$	1.06041	0.116395	0.0581977	−	0.998305i	$-0.481465\pi$
$83$	1.06041	0.116395	0.0581977	+	0.998305i	$0.481465\pi$
$84$	1.74652	0.190560
$85$	5.96866	0.647392
$86$	0.698416	0.0753122
$87$	0.557056	0.0597227
$88$	3.72781	0.397386
$89$	−14.5572	−1.54306	−0.771530	−	0.636193i	$-0.780508\pi$
$89$	−14.5572	−1.54306	−0.771530	+	0.636193i	$0.780508\pi$
$90$	1.62087	0.170855
$91$	−15.2655	−1.60026
$92$	2.56547	0.267469
$93$	−5.85394	−0.607026
$94$	−11.2980	−1.16530
$95$	−7.74371	−0.794487
$96$	3.42890	0.349961
$97$	−0.863013	−0.0876256	−0.0438128	−	0.999040i	$-0.513951\pi$
$97$	−0.863013	−0.0876256	−0.0438128	+	0.999040i	$0.513951\pi$
$98$	−1.22162	−0.123403
$99$	1.67535	0.168379
$100$	0.627218	0.0627218
$101$	−2.82945	−0.281541	−0.140770	−	0.990042i	$-0.544958\pi$
$101$	−2.82945	−0.281541	−0.140770	+	0.990042i	$0.544958\pi$
$102$	9.67442	0.957910
$103$	−4.68881	−0.462002	−0.231001	−	0.972954i	$-0.574200\pi$
$103$	−4.68881	−0.462002	−0.231001	+	0.972954i	$0.574200\pi$
$104$	−12.1985	−1.19617
$105$	−2.78454	−0.271744
$106$	16.4892	1.60158
$107$	1.48458	0.143520	0.0717600	−	0.997422i	$-0.477138\pi$
$107$	1.48458	0.143520	0.0717600	+	0.997422i	$0.477138\pi$
$108$	0.627218	0.0603541
$109$	9.76818	0.935622	0.467811	−	0.883829i	$-0.345043\pi$
$109$	9.76818	0.935622	0.467811	+	0.883829i	$0.345043\pi$
$110$	2.71552	0.258914
$111$	−11.2872	−1.07133
$112$	−13.5358	−1.27901
$113$	11.8263	1.11253	0.556265	−	0.831005i	$-0.312234\pi$
$113$	11.8263	1.11253	0.556265	+	0.831005i	$0.312234\pi$
$114$	−12.5515	−1.17556
$115$	−4.09024	−0.381417
$116$	0.349395	0.0324406
$117$	−5.48224	−0.506833
$118$	−11.1785	−1.02906
$119$	−16.6200	−1.52355
$120$	−2.22510	−0.203123
$121$	−8.19322	−0.744838
$122$	−15.5976	−1.41214
$123$	−1.44843	−0.130600
$124$	−3.67170	−0.329728
$125$	−1.00000	−0.0894427
$126$	−4.51338	−0.402084
$127$	−1.10813	−0.0983310	−0.0491655	−	0.998791i	$-0.515656\pi$
$127$	−1.10813	−0.0983310	−0.0491655	+	0.998791i	$0.515656\pi$
$128$	−13.6075	−1.20275
$129$	−0.430890	−0.0379377
$130$	−8.88600	−0.779354
$131$	−2.08280	−0.181975	−0.0909874	−	0.995852i	$-0.529002\pi$
$131$	−2.08280	−0.181975	−0.0909874	+	0.995852i	$0.529002\pi$
$132$	1.05081	0.0914610
$133$	21.5627	1.86972
$134$	18.0344	1.55793
$135$	−1.00000	−0.0860663
$136$	−13.2809	−1.13883
$137$	2.03669	0.174006	0.0870030	−	0.996208i	$-0.472271\pi$
$137$	2.03669	0.174006	0.0870030	+	0.996208i	$0.472271\pi$
$138$	−6.62975	−0.564362
$139$	−15.0909	−1.27999	−0.639997	−	0.768377i	$-0.721064\pi$
$139$	−15.0909	−1.27999	−0.639997	+	0.768377i	$0.721064\pi$
$140$	−1.74652	−0.147607
$141$	6.97031	0.587006
$142$	−1.36201	−0.114297
$143$	−9.18465	−0.768059
$144$	−4.86103	−0.405086
$145$	−0.557056	−0.0462610
$146$	16.8951	1.39825
$147$	0.753684	0.0621628
$148$	−7.07950	−0.581932
$149$	9.88112	0.809493	0.404747	−	0.914429i	$-0.367360\pi$
$149$	9.88112	0.809493	0.404747	+	0.914429i	$0.367360\pi$
$150$	−1.62087	−0.132343
$151$	13.3838	1.08916	0.544579	−	0.838709i	$-0.316689\pi$
$151$	13.3838	1.08916	0.544579	+	0.838709i	$0.316689\pi$
$152$	17.2305	1.39758
$153$	−5.96866	−0.482538
$154$	−7.56148	−0.609321
$155$	5.85394	0.470200
$156$	−3.43856	−0.275305
$157$	4.12231	0.328996	0.164498	−	0.986377i	$-0.447400\pi$
$157$	4.12231	0.328996	0.164498	+	0.986377i	$0.447400\pi$
$158$	21.8567	1.73883
$159$	−10.1731	−0.806778
$160$	−3.42890	−0.271078
$161$	11.3895	0.897615
$162$	−1.62087	−0.127348
$163$	−9.95407	−0.779663	−0.389832	−	0.920886i	$-0.627467\pi$
$163$	−9.95407	−0.779663	−0.389832	+	0.920886i	$0.627467\pi$
$164$	−0.908478	−0.0709402
$165$	−1.67535	−0.130426
$166$	−1.71879	−0.133404
$167$	10.4129	0.805775	0.402888	−	0.915249i	$-0.368007\pi$
$167$	10.4129	0.805775	0.402888	+	0.915249i	$0.368007\pi$
$168$	6.19589	0.478023
$169$	17.0550	1.31192
$170$	−9.67442	−0.741994
$171$	7.74371	0.592176
$172$	−0.270262	−0.0206073
$173$	−18.3704	−1.39668	−0.698339	−	0.715768i	$-0.746077\pi$
$173$	−18.3704	−1.39668	−0.698339	+	0.715768i	$0.746077\pi$
$174$	−0.902915	−0.0684498
$175$	2.78454	0.210492
$176$	−8.14391	−0.613871
$177$	6.89659	0.518380
$178$	23.5953	1.76854
$179$	−20.7358	−1.54987	−0.774933	−	0.632043i	$-0.782217\pi$
$179$	−20.7358	−1.54987	−0.774933	+	0.632043i	$0.782217\pi$
$180$	−0.627218	−0.0467500
$181$	−6.88218	−0.511549	−0.255774	−	0.966737i	$-0.582330\pi$
$181$	−6.88218	−0.511549	−0.255774	+	0.966737i	$0.582330\pi$
$182$	24.7434	1.83411
$183$	9.62299	0.711352
$184$	9.10120	0.670950
$185$	11.2872	0.829848
$186$	9.48848	0.695729
$187$	−9.99957	−0.731241
$188$	4.37190	0.318854
$189$	2.78454	0.202546
$190$	12.5515	0.910584
$191$	−9.02594	−0.653094	−0.326547	−	0.945181i	$-0.605885\pi$
$191$	−9.02594	−0.653094	−0.326547	+	0.945181i	$0.605885\pi$
$192$	4.16427	0.300530
$193$	10.9791	0.790294	0.395147	−	0.918618i	$-0.370694\pi$
$193$	10.9791	0.790294	0.395147	+	0.918618i	$0.370694\pi$
$194$	1.39883	0.100430
$195$	5.48224	0.392591
$196$	0.472724	0.0337660
$197$	13.4443	0.957865	0.478933	−	0.877852i	$-0.341024\pi$
$197$	13.4443	0.957865	0.478933	+	0.877852i	$0.341024\pi$
$198$	−2.71552	−0.192983
$199$	11.4969	0.814994	0.407497	−	0.913207i	$-0.366402\pi$
$199$	11.4969	0.814994	0.407497	+	0.913207i	$0.366402\pi$
$200$	2.22510	0.157338
$201$	−11.1264	−0.784793
$202$	4.58616	0.322681
$203$	1.55115	0.108869
$204$	−3.74365	−0.262108
$205$	1.44843	0.101162
$206$	7.59994	0.529513
$207$	4.09024	0.284292
$208$	26.6494	1.84780
$209$	12.9734	0.897388
$210$	4.51338	0.311453
$211$	11.3493	0.781316	0.390658	−	0.920536i	$-0.372248\pi$
$211$	11.3493	0.781316	0.390658	+	0.920536i	$0.372248\pi$
$212$	−6.38074	−0.438231
$213$	0.840297	0.0575762
$214$	−2.40631	−0.164492
$215$	0.430890	0.0293864
$216$	2.22510	0.151399
$217$	−16.3006	−1.10655
$218$	−15.8329	−1.07234
$219$	−10.4235	−0.704354
$220$	−1.05081	−0.0708454
$221$	32.7216	2.20110
$222$	18.2950	1.22788
$223$	−12.7519	−0.853933	−0.426967	−	0.904267i	$-0.640418\pi$
$223$	−12.7519	−0.853933	−0.426967	+	0.904267i	$0.640418\pi$
$224$	9.54792	0.637947
$225$	1.00000	0.0666667
$226$	−19.1690	−1.27510
$227$	19.8737	1.31906	0.659532	−	0.751677i	$-0.270755\pi$
$227$	19.8737	1.31906	0.659532	+	0.751677i	$0.270755\pi$
$228$	4.85699	0.321662
$229$	−0.865236	−0.0571764	−0.0285882	−	0.999591i	$-0.509101\pi$
$229$	−0.865236	−0.0571764	−0.0285882	+	0.999591i	$0.509101\pi$
$230$	6.62975	0.437153
$231$	4.66507	0.306939
$232$	1.23951	0.0813776
$233$	15.0638	0.986863	0.493431	−	0.869785i	$-0.335742\pi$
$233$	15.0638	0.986863	0.493431	+	0.869785i	$0.335742\pi$
$234$	8.88600	0.580896
$235$	−6.97031	−0.454693
$236$	4.32566	0.281577
$237$	−13.4846	−0.875917
$238$	26.9388	1.74619
$239$	20.6683	1.33692	0.668461	−	0.743747i	$-0.266953\pi$
$239$	20.6683	1.33692	0.668461	+	0.743747i	$0.266953\pi$
$240$	4.86103	0.313778
$241$	−14.7887	−0.952623	−0.476312	−	0.879277i	$-0.658027\pi$
$241$	−14.7887	−0.952623	−0.476312	+	0.879277i	$0.658027\pi$
$242$	13.2801	0.853679
$243$	1.00000	0.0641500
$244$	6.03571	0.386397
$245$	−0.753684	−0.0481511
$246$	2.34771	0.149684
$247$	−42.4529	−2.70121
$248$	−13.0256	−0.827127
$249$	1.06041	0.0672009
$250$	1.62087	0.102513
$251$	−5.20633	−0.328621	−0.164310	−	0.986409i	$-0.552540\pi$
$251$	−5.20633	−0.328621	−0.164310	+	0.986409i	$0.552540\pi$
$252$	1.74652	0.110020
$253$	6.85257	0.430817
$254$	1.79614	0.112700
$255$	5.96866	0.373772
$256$	13.7275	0.857969
$257$	−6.11152	−0.381226	−0.190613	−	0.981665i	$-0.561048\pi$
$257$	−6.11152	−0.381226	−0.190613	+	0.981665i	$0.561048\pi$
$258$	0.698416	0.0434815
$259$	−31.4296	−1.95294
$260$	3.43856	0.213250
$261$	0.557056	0.0344809
$262$	3.37594	0.208566
$263$	0.693864	0.0427855	0.0213928	−	0.999771i	$-0.493190\pi$
$263$	0.693864	0.0427855	0.0213928	+	0.999771i	$0.493190\pi$
$264$	3.72781	0.229431
$265$	10.1731	0.624928
$266$	−34.9503	−2.14294
$267$	−14.5572	−0.890886
$268$	−6.97865	−0.426289
$269$	9.86774	0.601647	0.300823	−	0.953680i	$-0.402739\pi$
$269$	9.86774	0.601647	0.300823	+	0.953680i	$0.402739\pi$
$270$	1.62087	0.0986430
$271$	−20.9614	−1.27332	−0.636658	−	0.771146i	$-0.719684\pi$
$271$	−20.9614	−1.27332	−0.636658	+	0.771146i	$0.719684\pi$
$272$	29.0139	1.75922
$273$	−15.2655	−0.923913
$274$	−3.30120	−0.199433
$275$	1.67535	0.101027
$276$	2.56547	0.154423
$277$	−25.4079	−1.52661	−0.763305	−	0.646038i	$-0.776425\pi$
$277$	−25.4079	−1.52661	−0.763305	+	0.646038i	$0.776425\pi$
$278$	24.4604	1.46704
$279$	−5.85394	−0.350466
$280$	−6.19589	−0.370275
$281$	−5.34529	−0.318873	−0.159437	−	0.987208i	$-0.550968\pi$
$281$	−5.34529	−0.318873	−0.159437	+	0.987208i	$0.550968\pi$
$282$	−11.2980	−0.672784
$283$	2.93784	0.174637	0.0873183	−	0.996180i	$-0.472170\pi$
$283$	2.93784	0.174637	0.0873183	+	0.996180i	$0.472170\pi$
$284$	0.527049	0.0312746
$285$	−7.74371	−0.458698
$286$	14.8871	0.880294
$287$	−4.03321	−0.238073
$288$	3.42890	0.202050
$289$	18.6249	1.09558
$290$	0.902915	0.0530210
$291$	−0.863013	−0.0505907
$292$	−6.53780	−0.382596
$293$	−6.31240	−0.368774	−0.184387	−	0.982854i	$-0.559030\pi$
$293$	−6.31240	−0.368774	−0.184387	+	0.982854i	$0.559030\pi$
$294$	−1.22162	−0.0712466
$295$	−6.89659	−0.401535
$296$	−25.1151	−1.45978
$297$	1.67535	0.0972134
$298$	−16.0160	−0.927783
$299$	−22.4237	−1.29680
$300$	0.627218	0.0362124
$301$	−1.19983	−0.0691571
$302$	−21.6934	−1.24831
$303$	−2.82945	−0.162548
$304$	−37.6424	−2.15894
$305$	−9.62299	−0.551011
$306$	9.67442	0.553050
$307$	−31.2988	−1.78632	−0.893159	−	0.449741i	$-0.851516\pi$
$307$	−31.2988	−1.78632	−0.893159	+	0.449741i	$0.851516\pi$
$308$	2.92602	0.166725
$309$	−4.68881	−0.266737
$310$	−9.48848	−0.538909
$311$	6.18244	0.350574	0.175287	−	0.984517i	$-0.443915\pi$
$311$	6.18244	0.350574	0.175287	+	0.984517i	$0.443915\pi$
$312$	−12.1985	−0.690606
$313$	−8.43077	−0.476535	−0.238268	−	0.971200i	$-0.576580\pi$
$313$	−8.43077	−0.476535	−0.238268	+	0.971200i	$0.576580\pi$
$314$	−6.68173	−0.377072
$315$	−2.78454	−0.156891
$316$	−8.45777	−0.475786
$317$	26.5812	1.49295	0.746475	−	0.665413i	$-0.231745\pi$
$317$	26.5812	1.49295	0.746475	+	0.665413i	$0.231745\pi$
$318$	16.4892	0.924671
$319$	0.933262	0.0522526
$320$	−4.16427	−0.232790
$321$	1.48458	0.0828613
$322$	−18.4608	−1.02878
$323$	−46.2196	−2.57172
$324$	0.627218	0.0348454
$325$	−5.48224	−0.304100
$326$	16.1343	0.893594
$327$	9.76818	0.540182
$328$	−3.22289	−0.177955
$329$	19.4091	1.07006
$330$	2.71552	0.149484
$331$	−16.4771	−0.905664	−0.452832	−	0.891596i	$-0.649586\pi$
$331$	−16.4771	−0.905664	−0.452832	+	0.891596i	$0.649586\pi$
$332$	0.665110	0.0365026
$333$	−11.2872	−0.618532
$334$	−16.8780	−0.923521
$335$	11.1264	0.607898
$336$	−13.5358	−0.738436
$337$	26.1763	1.42591	0.712957	−	0.701207i	$-0.247355\pi$
$337$	26.1763	1.42591	0.712957	+	0.701207i	$0.247355\pi$
$338$	−27.6439	−1.50363
$339$	11.8263	0.642319
$340$	3.74365	0.203028
$341$	−9.80738	−0.531099
$342$	−12.5515	−0.678709
$343$	−17.3931	−0.939141
$344$	−0.958773	−0.0516936
$345$	−4.09024	−0.220211
$346$	29.7761	1.60077
$347$	−2.20488	−0.118364	−0.0591819	−	0.998247i	$-0.518849\pi$
$347$	−2.20488	−0.118364	−0.0591819	+	0.998247i	$0.518849\pi$
$348$	0.349395	0.0187296
$349$	−6.40998	−0.343118	−0.171559	−	0.985174i	$-0.554880\pi$
$349$	−6.40998	−0.343118	−0.171559	+	0.985174i	$0.554880\pi$
$350$	−4.51338	−0.241250
$351$	−5.48224	−0.292620
$352$	5.74459	0.306188
$353$	−34.1392	−1.81705	−0.908523	−	0.417835i	$-0.862789\pi$
$353$	−34.1392	−1.81705	−0.908523	+	0.417835i	$0.862789\pi$
$354$	−11.1785	−0.594129
$355$	−0.840297	−0.0445983
$356$	−9.13054	−0.483917
$357$	−16.6200	−0.879624
$358$	33.6100	1.77635
$359$	14.7552	0.778750	0.389375	−	0.921079i	$-0.372691\pi$
$359$	14.7552	0.778750	0.389375	+	0.921079i	$0.372691\pi$
$360$	−2.22510	−0.117273
$361$	40.9650	2.15605
$362$	11.1551	0.586300
$363$	−8.19322	−0.430032
$364$	−9.57482	−0.501857
$365$	10.4235	0.545590
$366$	−15.5976	−0.815300
$367$	14.5447	0.759227	0.379613	−	0.925145i	$-0.376057\pi$
$367$	14.5447	0.759227	0.379613	+	0.925145i	$0.376057\pi$
$368$	−19.8828	−1.03646
$369$	−1.44843	−0.0754020
$370$	−18.2950	−0.951112
$371$	−28.3274	−1.47069
$372$	−3.67170	−0.190369
$373$	−6.90783	−0.357674	−0.178837	−	0.983879i	$-0.557233\pi$
$373$	−6.90783	−0.357674	−0.178837	+	0.983879i	$0.557233\pi$
$374$	16.2080	0.838096
$375$	−1.00000	−0.0516398
$376$	15.5096	0.799849
$377$	−3.05392	−0.157285
$378$	−4.51338	−0.232143
$379$	−34.8101	−1.78808	−0.894038	−	0.447992i	$-0.852139\pi$
$379$	−34.8101	−1.78808	−0.894038	+	0.447992i	$0.852139\pi$
$380$	−4.85699	−0.249158
$381$	−1.10813	−0.0567714
$382$	14.6299	0.748530
$383$	5.41439	0.276662	0.138331	−	0.990386i	$-0.455826\pi$
$383$	5.41439	0.276662	0.138331	+	0.990386i	$0.455826\pi$
$384$	−13.6075	−0.694407
$385$	−4.66507	−0.237754
$386$	−17.7957	−0.905778
$387$	−0.430890	−0.0219034
$388$	−0.541297	−0.0274802
$389$	−7.93436	−0.402288	−0.201144	−	0.979562i	$-0.564466\pi$
$389$	−7.93436	−0.402288	−0.201144	+	0.979562i	$0.564466\pi$
$390$	−8.88600	−0.449960
$391$	−24.4133	−1.23463
$392$	1.67702	0.0847025
$393$	−2.08280	−0.105063
$394$	−21.7914	−1.09784
$395$	13.4846	0.678483
$396$	1.05081	0.0528050
$397$	−9.06214	−0.454816	−0.227408	−	0.973800i	$-0.573025\pi$
$397$	−9.06214	−0.454816	−0.227408	+	0.973800i	$0.573025\pi$
$398$	−18.6350	−0.934087
$399$	21.5627	1.07948
$400$	−4.86103	−0.243052
$401$	1.00000	0.0499376
$401$	1.00000	0.0499376
$402$	18.0344	0.899473
$403$	32.0927	1.59865
$404$	−1.77468	−0.0882936
$405$	−1.00000	−0.0496904
$406$	−2.51421	−0.124778
$407$	−18.9099	−0.937328
$408$	−13.2809	−0.657501
$409$	−15.5671	−0.769743	−0.384872	−	0.922970i	$-0.625754\pi$
$409$	−15.5671	−0.769743	−0.384872	+	0.922970i	$0.625754\pi$
$410$	−2.34771	−0.115945
$411$	2.03669	0.100462
$412$	−2.94090	−0.144888
$413$	19.2039	0.944960
$414$	−6.62975	−0.325834
$415$	−1.06041	−0.0520536
$416$	−18.7981	−0.921650
$417$	−15.0909	−0.739005
$418$	−21.0282	−1.02852
$419$	19.2746	0.941624	0.470812	−	0.882234i	$-0.343961\pi$
$419$	19.2746	0.941624	0.470812	+	0.882234i	$0.343961\pi$
$420$	−1.74652	−0.0852212
$421$	31.6708	1.54354	0.771770	−	0.635902i	$-0.219372\pi$
$421$	31.6708	1.54354	0.771770	+	0.635902i	$0.219372\pi$
$422$	−18.3957	−0.895488
$423$	6.97031	0.338908
$424$	−22.6361	−1.09931
$425$	−5.96866	−0.289523
$426$	−1.36201	−0.0659897
$427$	26.7956	1.29673
$428$	0.931156	0.0450091
$429$	−9.18465	−0.443439
$430$	−0.698416	−0.0336806
$431$	−26.5438	−1.27857	−0.639285	−	0.768970i	$-0.720770\pi$
$431$	−26.5438	−1.27857	−0.639285	+	0.768970i	$0.720770\pi$
$432$	−4.86103	−0.233877
$433$	−36.4617	−1.75224	−0.876118	−	0.482096i	$-0.839876\pi$
$433$	−36.4617	−1.75224	−0.876118	+	0.482096i	$0.839876\pi$
$434$	26.4211	1.26825
$435$	−0.557056	−0.0267088
$436$	6.12678	0.293419
$437$	31.6736	1.51516
$438$	16.8951	0.807280
$439$	29.7243	1.41866	0.709331	−	0.704875i	$-0.248997\pi$
$439$	29.7243	1.41866	0.709331	+	0.704875i	$0.248997\pi$
$440$	−3.72781	−0.177717
$441$	0.753684	0.0358897
$442$	−53.0375	−2.52274
$443$	−27.7081	−1.31645	−0.658227	−	0.752820i	$-0.728693\pi$
$443$	−27.7081	−1.31645	−0.658227	+	0.752820i	$0.728693\pi$
$444$	−7.07950	−0.335978
$445$	14.5572	0.690078
$446$	20.6692	0.978717
$447$	9.88112	0.467361
$448$	11.5956	0.547840
$449$	−18.6485	−0.880077	−0.440039	−	0.897979i	$-0.645035\pi$
$449$	−18.6485	−0.880077	−0.440039	+	0.897979i	$0.645035\pi$
$450$	−1.62087	−0.0764085
$451$	−2.42661	−0.114265
$452$	7.41770	0.348899
$453$	13.3838	0.628826
$454$	−32.2127	−1.51182
$455$	15.2655	0.715660
$456$	17.2305	0.806893
$457$	−35.5771	−1.66423	−0.832113	−	0.554606i	$-0.812869\pi$
$457$	−35.5771	−1.66423	−0.832113	+	0.554606i	$0.812869\pi$
$458$	1.40243	0.0655315
$459$	−5.96866	−0.278593
$460$	−2.56547	−0.119616
$461$	8.54986	0.398206	0.199103	−	0.979979i	$-0.436197\pi$
$461$	8.54986	0.398206	0.199103	+	0.979979i	$0.436197\pi$
$462$	−7.56148	−0.351792
$463$	−8.52927	−0.396389	−0.198194	−	0.980163i	$-0.563508\pi$
$463$	−8.52927	−0.396389	−0.198194	+	0.980163i	$0.563508\pi$
$464$	−2.70787	−0.125710
$465$	5.85394	0.271470
$466$	−24.4165	−1.13107
$467$	41.1000	1.90188	0.950941	−	0.309373i	$-0.100119\pi$
$467$	41.1000	1.90188	0.950941	+	0.309373i	$0.100119\pi$
$468$	−3.43856	−0.158947
$469$	−30.9818	−1.43061
$470$	11.2980	0.521136
$471$	4.12231	0.189946
$472$	15.3456	0.706339
$473$	−0.721890	−0.0331925
$474$	21.8567	1.00391
$475$	7.74371	0.355306
$476$	−10.4244	−0.477800
$477$	−10.1731	−0.465794
$478$	−33.5007	−1.53228
$479$	−21.6760	−0.990400	−0.495200	−	0.868779i	$-0.664905\pi$
$479$	−21.6760	−0.990400	−0.495200	+	0.868779i	$0.664905\pi$
$480$	−3.42890	−0.156507
$481$	61.8789	2.82144
$482$	23.9705	1.09183
$483$	11.3895	0.518238
$484$	−5.13893	−0.233588
$485$	0.863013	0.0391874
$486$	−1.62087	−0.0735241
$487$	1.56155	0.0707604	0.0353802	−	0.999374i	$-0.488736\pi$
$487$	1.56155	0.0707604	0.0353802	+	0.999374i	$0.488736\pi$
$488$	21.4121	0.969281
$489$	−9.95407	−0.450139
$490$	1.22162	0.0551874
$491$	5.89634	0.266098	0.133049	−	0.991109i	$-0.457523\pi$
$491$	5.89634	0.266098	0.133049	+	0.991109i	$0.457523\pi$
$492$	−0.908478	−0.0409574
$493$	−3.32488	−0.149745
$494$	68.8105	3.09593
$495$	−1.67535	−0.0753012
$496$	28.4562	1.27772
$497$	2.33984	0.104956
$498$	−1.71879	−0.0770209
$499$	−25.0633	−1.12199	−0.560993	−	0.827821i	$-0.689581\pi$
$499$	−25.0633	−1.12199	−0.560993	+	0.827821i	$0.689581\pi$
$500$	−0.627218	−0.0280500
$501$	10.4129	0.465215
$502$	8.43879	0.376642
$503$	−7.18083	−0.320177	−0.160089	−	0.987103i	$-0.551178\pi$
$503$	−7.18083	−0.320177	−0.160089	+	0.987103i	$0.551178\pi$
$504$	6.19589	0.275987
$505$	2.82945	0.125909
$506$	−11.1071	−0.493772
$507$	17.0550	0.757438
$508$	−0.695041	−0.0308375
$509$	−30.0375	−1.33139	−0.665695	−	0.746224i	$-0.731865\pi$
$509$	−30.0375	−1.33139	−0.665695	+	0.746224i	$0.731865\pi$
$510$	−9.67442	−0.428391
$511$	−29.0247	−1.28398
$512$	4.96459	0.219406
$513$	7.74371	0.341893
$514$	9.90598	0.436934
$515$	4.68881	0.206614
$516$	−0.270262	−0.0118976
$517$	11.6777	0.513584
$518$	50.9432	2.23832
$519$	−18.3704	−0.806372
$520$	12.1985	0.534941
$521$	37.0495	1.62317	0.811584	−	0.584236i	$-0.198606\pi$
$521$	37.0495	1.62317	0.811584	+	0.584236i	$0.198606\pi$
$522$	−0.902915	−0.0395195
$523$	−23.1109	−1.01057	−0.505284	−	0.862953i	$-0.668612\pi$
$523$	−23.1109	−1.01057	−0.505284	+	0.862953i	$0.668612\pi$
$524$	−1.30637	−0.0570689
$525$	2.78454	0.121527
$526$	−1.12466	−0.0490377
$527$	34.9402	1.52202
$528$	−8.14391	−0.354418
$529$	−6.26992	−0.272605
$530$	−16.4892	−0.716247
$531$	6.89659	0.299287
$532$	13.5245	0.586361
$533$	7.94062	0.343946
$534$	23.5953	1.02107
$535$	−1.48458	−0.0641841
$536$	−24.7573	−1.06935
$537$	−20.7358	−0.894816
$538$	−15.9943	−0.689564
$539$	1.26268	0.0543876
$540$	−0.627218	−0.0269912
$541$	36.5355	1.57078	0.785392	−	0.618998i	$-0.212461\pi$
$541$	36.5355	1.57078	0.785392	+	0.618998i	$0.212461\pi$
$542$	33.9757	1.45938
$543$	−6.88218	−0.295343
$544$	−20.4659	−0.877470
$545$	−9.76818	−0.418423
$546$	24.7434	1.05892
$547$	0.840409	0.0359333	0.0179667	−	0.999839i	$-0.494281\pi$
$547$	0.840409	0.0359333	0.0179667	+	0.999839i	$0.494281\pi$
$548$	1.27745	0.0545698
$549$	9.62299	0.410699
$550$	−2.71552	−0.115790
$551$	4.31368	0.183769
$552$	9.10120	0.387373
$553$	−37.5484	−1.59672
$554$	41.1828	1.74969
$555$	11.2872	0.479113
$556$	−9.46528	−0.401417
$557$	−25.7085	−1.08930	−0.544652	−	0.838662i	$-0.683338\pi$
$557$	−25.7085	−1.08930	−0.544652	+	0.838662i	$0.683338\pi$
$558$	9.48848	0.401679
$559$	2.36224	0.0999122
$560$	13.5358	0.571990
$561$	−9.99957	−0.422182
$562$	8.66401	0.365469
$563$	−30.8737	−1.30117	−0.650586	−	0.759433i	$-0.725477\pi$
$563$	−30.8737	−1.30117	−0.650586	+	0.759433i	$0.725477\pi$
$564$	4.37190	0.184090
$565$	−11.8263	−0.497538
$566$	−4.76186	−0.200156
$567$	2.78454	0.116940
$568$	1.86975	0.0784528
$569$	−17.4669	−0.732252	−0.366126	−	0.930565i	$-0.619316\pi$
$569$	−17.4669	−0.732252	−0.366126	+	0.930565i	$0.619316\pi$
$570$	12.5515	0.525726
$571$	−16.4614	−0.688889	−0.344444	−	0.938807i	$-0.611933\pi$
$571$	−16.4614	−0.688889	−0.344444	+	0.938807i	$0.611933\pi$
$572$	−5.76078	−0.240870
$573$	−9.02594	−0.377064
$574$	6.53730	0.272862
$575$	4.09024	0.170575
$576$	4.16427	0.173511
$577$	−32.4316	−1.35014	−0.675072	−	0.737752i	$-0.735887\pi$
$577$	−32.4316	−1.35014	−0.675072	+	0.737752i	$0.735887\pi$
$578$	−30.1886	−1.25568
$579$	10.9791	0.456276
$580$	−0.349395	−0.0145079
$581$	2.95277	0.122501
$582$	1.39883	0.0579834
$583$	−17.0434	−0.705867
$584$	−23.1933	−0.959746
$585$	5.48224	0.226663
$586$	10.2316	0.422662
$587$	−25.1699	−1.03887	−0.519436	−	0.854509i	$-0.673858\pi$
$587$	−25.1699	−1.03887	−0.519436	+	0.854509i	$0.673858\pi$
$588$	0.472724	0.0194948
$589$	−45.3312	−1.86784
$590$	11.1785	0.460211
$591$	13.4443	0.553024
$592$	54.8672	2.25503
$593$	−24.6222	−1.01111	−0.505556	−	0.862794i	$-0.668713\pi$
$593$	−24.6222	−1.01111	−0.505556	+	0.862794i	$0.668713\pi$
$594$	−2.71552	−0.111419
$595$	16.6200	0.681353
$596$	6.19762	0.253864
$597$	11.4969	0.470537
$598$	36.3459	1.48629
$599$	−42.3265	−1.72941	−0.864707	−	0.502277i	$-0.832496\pi$
$599$	−42.3265	−1.72941	−0.864707	+	0.502277i	$0.832496\pi$
$600$	2.22510	0.0908394
$601$	29.6300	1.20863	0.604317	−	0.796744i	$-0.293446\pi$
$601$	29.6300	1.20863	0.604317	+	0.796744i	$0.293446\pi$
$602$	1.94477	0.0792629
$603$	−11.1264	−0.453100
$604$	8.39456	0.341570
$605$	8.19322	0.333102
$606$	4.58616	0.186300
$607$	−35.2809	−1.43201	−0.716004	−	0.698096i	$-0.754031\pi$
$607$	−35.2809	−1.43201	−0.716004	+	0.698096i	$0.754031\pi$
$608$	26.5524	1.07684
$609$	1.55115	0.0628557
$610$	15.5976	0.631529
$611$	−38.2129	−1.54593
$612$	−3.74365	−0.151328
$613$	2.81122	0.113544	0.0567720	−	0.998387i	$-0.481919\pi$
$613$	2.81122	0.113544	0.0567720	+	0.998387i	$0.481919\pi$
$614$	50.7313	2.04735
$615$	1.44843	0.0584062
$616$	10.3803	0.418233
$617$	−25.4415	−1.02423	−0.512117	−	0.858916i	$-0.671139\pi$
$617$	−25.4415	−1.02423	−0.512117	+	0.858916i	$0.671139\pi$
$618$	7.59994	0.305715
$619$	33.8389	1.36010	0.680051	−	0.733165i	$-0.261958\pi$
$619$	33.8389	1.36010	0.680051	+	0.733165i	$0.261958\pi$
$620$	3.67170	0.147459
$621$	4.09024	0.164136
$622$	−10.0209	−0.401803
$623$	−40.5352	−1.62401
$624$	26.6494	1.06683
$625$	1.00000	0.0400000
$626$	13.6652	0.546170
$627$	12.9734	0.518107
$628$	2.58559	0.103176
$629$	67.3692	2.68619
$630$	4.51338	0.179817
$631$	14.7480	0.587109	0.293554	−	0.955942i	$-0.405162\pi$
$631$	14.7480	0.587109	0.293554	+	0.955942i	$0.405162\pi$
$632$	−30.0045	−1.19352
$633$	11.3493	0.451093
$634$	−43.0847	−1.71111
$635$	1.10813	0.0439749
$636$	−6.38074	−0.253013
$637$	−4.13188	−0.163711
$638$	−1.51270	−0.0598882
$639$	0.840297	0.0332416
$640$	13.6075	0.537885
$641$	29.0580	1.14772	0.573861	−	0.818952i	$-0.305445\pi$
$641$	29.0580	1.14772	0.573861	+	0.818952i	$0.305445\pi$
$642$	−2.40631	−0.0949696
$643$	−22.0642	−0.870126	−0.435063	−	0.900400i	$-0.643274\pi$
$643$	−22.0642	−0.870126	−0.435063	+	0.900400i	$0.643274\pi$
$644$	7.14367	0.281500
$645$	0.430890	0.0169663
$646$	74.9159	2.94752
$647$	13.3958	0.526642	0.263321	−	0.964708i	$-0.415182\pi$
$647$	13.3958	0.526642	0.263321	+	0.964708i	$0.415182\pi$
$648$	2.22510	0.0874102
$649$	11.5542	0.453541
$650$	8.88600	0.348537
$651$	−16.3006	−0.638869
$652$	−6.24337	−0.244509
$653$	18.0673	0.707029	0.353514	−	0.935429i	$-0.384987\pi$
$653$	18.0673	0.707029	0.353514	+	0.935429i	$0.384987\pi$
$654$	−15.8329	−0.619117
$655$	2.08280	0.0813816
$656$	7.04085	0.274899
$657$	−10.4235	−0.406659
$658$	−31.4597	−1.22643
$659$	−1.95189	−0.0760350	−0.0380175	−	0.999277i	$-0.512104\pi$
$659$	−1.95189	−0.0760350	−0.0380175	+	0.999277i	$0.512104\pi$
$660$	−1.05081	−0.0409026
$661$	−26.9923	−1.04988	−0.524939	−	0.851140i	$-0.675912\pi$
$661$	−26.9923	−1.04988	−0.524939	+	0.851140i	$0.675912\pi$
$662$	26.7073	1.03801
$663$	32.7216	1.27080
$664$	2.35953	0.0915673
$665$	−21.5627	−0.836165
$666$	18.2950	0.708917
$667$	2.27849	0.0882237
$668$	6.53116	0.252698
$669$	−12.7519	−0.493019
$670$	−18.0344	−0.696729
$671$	16.1218	0.622376
$672$	9.54792	0.368319
$673$	−39.5047	−1.52279	−0.761397	−	0.648286i	$-0.775486\pi$
$673$	−39.5047	−1.52279	−0.761397	+	0.648286i	$0.775486\pi$
$674$	−42.4284	−1.63428
$675$	1.00000	0.0384900
$676$	10.6972	0.411430
$677$	1.35447	0.0520566	0.0260283	−	0.999661i	$-0.491714\pi$
$677$	1.35447	0.0520566	0.0260283	+	0.999661i	$0.491714\pi$
$678$	−19.1690	−0.736180
$679$	−2.40310	−0.0922224
$680$	13.2809	0.509298
$681$	19.8737	0.761562
$682$	15.8965	0.608708
$683$	−4.11294	−0.157377	−0.0786886	−	0.996899i	$-0.525073\pi$
$683$	−4.11294	−0.157377	−0.0786886	+	0.996899i	$0.525073\pi$
$684$	4.85699	0.185712
$685$	−2.03669	−0.0778178
$686$	28.1920	1.07638
$687$	−0.865236	−0.0330108
$688$	2.09457	0.0798547
$689$	55.7713	2.12472
$690$	6.62975	0.252390
$691$	−33.8128	−1.28630	−0.643151	−	0.765740i	$-0.722373\pi$
$691$	−33.8128	−1.28630	−0.643151	+	0.765740i	$0.722373\pi$
$692$	−11.5223	−0.438010
$693$	4.66507	0.177212
$694$	3.57381	0.135660
$695$	15.0909	0.572431
$696$	1.23951	0.0469834
$697$	8.64516	0.327459
$698$	10.3897	0.393257
$699$	15.0638	0.569766
$700$	1.74652	0.0660121
$701$	46.8794	1.77061	0.885305	−	0.465012i	$-0.153950\pi$
$701$	46.8794	1.77061	0.885305	+	0.465012i	$0.153950\pi$
$702$	8.88600	0.335380
$703$	−87.4044	−3.29652
$704$	6.97659	0.262940
$705$	−6.97031	−0.262517
$706$	55.3352	2.08257
$707$	−7.87872	−0.296310
$708$	4.32566	0.162568
$709$	−6.44131	−0.241909	−0.120954	−	0.992658i	$-0.538595\pi$
$709$	−6.44131	−0.241909	−0.120954	+	0.992658i	$0.538595\pi$
$710$	1.36201	0.0511154
$711$	−13.4846	−0.505711
$712$	−32.3912	−1.21391
$713$	−23.9440	−0.896711
$714$	26.9388	1.00816
$715$	9.18465	0.343486
$716$	−13.0059	−0.486052
$717$	20.6683	0.771873
$718$	−23.9163	−0.892547
$719$	11.6126	0.433078	0.216539	−	0.976274i	$-0.430523\pi$
$719$	11.6126	0.433078	0.216539	+	0.976274i	$0.430523\pi$
$720$	4.86103	0.181160
$721$	−13.0562	−0.486238
$722$	−66.3989	−2.47111
$723$	−14.7887	−0.549997
$724$	−4.31663	−0.160426
$725$	0.557056	0.0206885
$726$	13.2801	0.492872
$727$	25.8677	0.959378	0.479689	−	0.877439i	$-0.340749\pi$
$727$	25.8677	0.959378	0.479689	+	0.877439i	$0.340749\pi$
$728$	−33.9674	−1.25891
$729$	1.00000	0.0370370
$730$	−16.8951	−0.625316
$731$	2.57184	0.0951228
$732$	6.03571	0.223086
$733$	7.16179	0.264527	0.132263	−	0.991215i	$-0.457776\pi$
$733$	7.16179	0.264527	0.132263	+	0.991215i	$0.457776\pi$
$734$	−23.5750	−0.870171
$735$	−0.753684	−0.0278001
$736$	14.0250	0.516969
$737$	−18.6405	−0.686632
$738$	2.34771	0.0864204
$739$	−11.1023	−0.408404	−0.204202	−	0.978929i	$-0.565460\pi$
$739$	−11.1023	−0.408404	−0.204202	+	0.978929i	$0.565460\pi$
$740$	7.07950	0.260248
$741$	−42.4529	−1.55954
$742$	45.9150	1.68559
$743$	−16.4442	−0.603280	−0.301640	−	0.953422i	$-0.597534\pi$
$743$	−16.4442	−0.603280	−0.301640	+	0.953422i	$0.597534\pi$
$744$	−13.0256	−0.477542
$745$	−9.88112	−0.362016
$746$	11.1967	0.409940
$747$	1.06041	0.0387985
$748$	−6.27191	−0.229324
$749$	4.13388	0.151049
$750$	1.62087	0.0591858
$751$	−5.34295	−0.194967	−0.0974834	−	0.995237i	$-0.531079\pi$
$751$	−5.34295	−0.194967	−0.0974834	+	0.995237i	$0.531079\pi$
$752$	−33.8829	−1.23558
$753$	−5.20633	−0.189729
$754$	4.95000	0.180268
$755$	−13.3838	−0.487086
$756$	1.74652	0.0635201
$757$	12.1859	0.442906	0.221453	−	0.975171i	$-0.428920\pi$
$757$	12.1859	0.442906	0.221453	+	0.975171i	$0.428920\pi$
$758$	56.4226	2.04936
$759$	6.85257	0.248733
$760$	−17.2305	−0.625017
$761$	32.2138	1.16775	0.583874	−	0.811844i	$-0.301536\pi$
$761$	32.2138	1.16775	0.583874	+	0.811844i	$0.301536\pi$
$762$	1.79614	0.0650673
$763$	27.1999	0.984703
$764$	−5.66123	−0.204816
$765$	5.96866	0.215797
$766$	−8.77602	−0.317091
$767$	−37.8088	−1.36520
$768$	13.7275	0.495348
$769$	−13.8521	−0.499521	−0.249760	−	0.968308i	$-0.580352\pi$
$769$	−13.8521	−0.499521	−0.249760	+	0.968308i	$0.580352\pi$
$770$	7.56148	0.272497
$771$	−6.11152	−0.220101
$772$	6.88630	0.247843
$773$	−43.1022	−1.55028	−0.775139	−	0.631790i	$-0.782320\pi$
$773$	−43.1022	−1.55028	−0.775139	+	0.631790i	$0.782320\pi$
$774$	0.698416	0.0251041
$775$	−5.85394	−0.210280
$776$	−1.92029	−0.0689344
$777$	−31.4296	−1.12753
$778$	12.8606	0.461073
$779$	−11.2162	−0.401861
$780$	3.43856	0.123120
$781$	1.40779	0.0503746
$782$	39.5707	1.41505
$783$	0.557056	0.0199076
$784$	−3.66369	−0.130846
$785$	−4.12231	−0.147132
$786$	3.37594	0.120416
$787$	32.1058	1.14445	0.572224	−	0.820097i	$-0.306081\pi$
$787$	32.1058	1.14445	0.572224	+	0.820097i	$0.306081\pi$
$788$	8.43249	0.300395
$789$	0.693864	0.0247022
$790$	−21.8567	−0.777628
$791$	32.9310	1.17089
$792$	3.72781	0.132462
$793$	−52.7555	−1.87340
$794$	14.6885	0.521277
$795$	10.1731	0.360802
$796$	7.21106	0.255589
$797$	7.90262	0.279925	0.139963	−	0.990157i	$-0.455302\pi$
$797$	7.90262	0.279925	0.139963	+	0.990157i	$0.455302\pi$
$798$	−34.9503	−1.23723
$799$	−41.6034	−1.47182
$800$	3.42890	0.121230
$801$	−14.5572	−0.514354
$802$	−1.62087	−0.0572349
$803$	−17.4630	−0.616254
$804$	−6.97865	−0.246118
$805$	−11.3895	−0.401426
$806$	−52.0181	−1.83226
$807$	9.86774	0.347361
$808$	−6.29581	−0.221486
$809$	−29.0405	−1.02101	−0.510505	−	0.859875i	$-0.670542\pi$
$809$	−29.0405	−1.02101	−0.510505	+	0.859875i	$0.670542\pi$
$810$	1.62087	0.0569515
$811$	36.6821	1.28808	0.644041	−	0.764991i	$-0.277257\pi$
$811$	36.6821	1.28808	0.644041	+	0.764991i	$0.277257\pi$
$812$	0.972907	0.0341423
$813$	−20.9614	−0.735149
$814$	30.6505	1.07430
$815$	9.95407	0.348676
$816$	29.0139	1.01569
$817$	−3.33668	−0.116736
$818$	25.2322	0.882224
$819$	−15.2655	−0.533421
$820$	0.908478	0.0317254
$821$	−15.3634	−0.536187	−0.268093	−	0.963393i	$-0.586394\pi$
$821$	−15.3634	−0.536187	−0.268093	+	0.963393i	$0.586394\pi$
$822$	−3.30120	−0.115143
$823$	20.7713	0.724041	0.362020	−	0.932170i	$-0.382087\pi$
$823$	20.7713	0.724041	0.362020	+	0.932170i	$0.382087\pi$
$824$	−10.4331	−0.363453
$825$	1.67535	0.0583281
$826$	−31.1270	−1.08305
$827$	−6.35545	−0.221001	−0.110500	−	0.993876i	$-0.535245\pi$
$827$	−6.35545	−0.221001	−0.110500	+	0.993876i	$0.535245\pi$
$828$	2.56547	0.0891563
$829$	−9.39618	−0.326343	−0.163171	−	0.986598i	$-0.552172\pi$
$829$	−9.39618	−0.326343	−0.163171	+	0.986598i	$0.552172\pi$
$830$	1.71879	0.0596601
$831$	−25.4079	−0.881389
$832$	−22.8295	−0.791472
$833$	−4.49849	−0.155863
$834$	24.4604	0.846994
$835$	−10.4129	−0.360354
$836$	8.13714	0.281429
$837$	−5.85394	−0.202342
$838$	−31.2415	−1.07922
$839$	−13.2107	−0.456083	−0.228042	−	0.973651i	$-0.573232\pi$
$839$	−13.2107	−0.456083	−0.228042	+	0.973651i	$0.573232\pi$
$840$	−6.19589	−0.213779
$841$	−28.6897	−0.989300
$842$	−51.3342	−1.76909
$843$	−5.34529	−0.184101
$844$	7.11846	0.245028
$845$	−17.0550	−0.586709
$846$	−11.2980	−0.388432
$847$	−22.8144	−0.783911
$848$	49.4517	1.69818
$849$	2.93784	0.100826
$850$	9.67442	0.331830
$851$	−46.1672	−1.58259
$852$	0.527049	0.0180564
$853$	27.6275	0.945946	0.472973	−	0.881077i	$-0.343181\pi$
$853$	27.6275	0.945946	0.472973	+	0.881077i	$0.343181\pi$
$854$	−43.4322	−1.48622
$855$	−7.74371	−0.264829
$856$	3.30335	0.112906
$857$	11.0208	0.376465	0.188232	−	0.982125i	$-0.439724\pi$
$857$	11.0208	0.376465	0.188232	+	0.982125i	$0.439724\pi$
$858$	14.8871	0.508238
$859$	43.8214	1.49517	0.747583	−	0.664169i	$-0.231214\pi$
$859$	43.8214	1.49517	0.747583	+	0.664169i	$0.231214\pi$
$860$	0.270262	0.00921585
$861$	−4.03321	−0.137451
$862$	43.0240	1.46540
$863$	−23.4640	−0.798725	−0.399362	−	0.916793i	$-0.630768\pi$
$863$	−23.4640	−0.798725	−0.399362	+	0.916793i	$0.630768\pi$
$864$	3.42890	0.116654
$865$	18.3704	0.624613
$866$	59.0996	2.00829
$867$	18.6249	0.632535
$868$	−10.2240	−0.347025
$869$	−22.5913	−0.766358
$870$	0.902915	0.0306117
$871$	60.9974	2.06682
$872$	21.7352	0.736046
$873$	−0.863013	−0.0292085
$874$	−51.3388	−1.73656
$875$	−2.78454	−0.0941348
$876$	−6.53780	−0.220892
$877$	41.4857	1.40087	0.700436	−	0.713715i	$-0.252989\pi$
$877$	41.4857	1.40087	0.700436	+	0.713715i	$0.252989\pi$
$878$	−48.1792	−1.62597
$879$	−6.31240	−0.212912
$880$	8.14391	0.274531
$881$	14.1048	0.475202	0.237601	−	0.971363i	$-0.423639\pi$
$881$	14.1048	0.475202	0.237601	+	0.971363i	$0.423639\pi$
$882$	−1.22162	−0.0411342
$883$	−3.17993	−0.107013	−0.0535066	−	0.998567i	$-0.517040\pi$
$883$	−3.17993	−0.107013	−0.0535066	+	0.998567i	$0.517040\pi$
$884$	20.5236	0.690283
$885$	−6.89659	−0.231826
$886$	44.9113	1.50882
$887$	−16.5624	−0.556111	−0.278055	−	0.960565i	$-0.589690\pi$
$887$	−16.5624	−0.556111	−0.278055	+	0.960565i	$0.589690\pi$
$888$	−25.1151	−0.842806
$889$	−3.08565	−0.103489
$890$	−23.5953	−0.790917
$891$	1.67535	0.0561262
$892$	−7.99825	−0.267801
$893$	53.9760	1.80624
$894$	−16.0160	−0.535655
$895$	20.7358	0.693122
$896$	−37.8908	−1.26584
$897$	−22.4237	−0.748705
$898$	30.2268	1.00868
$899$	−3.26097	−0.108760
$900$	0.627218	0.0209073
$901$	60.7197	2.02287
$902$	3.93323	0.130962
$903$	−1.19983	−0.0399279
$904$	26.3148	0.875218
$905$	6.88218	0.228772
$906$	−21.6934	−0.720715
$907$	−38.5428	−1.27979	−0.639897	−	0.768461i	$-0.721023\pi$
$907$	−38.5428	−1.27979	−0.639897	+	0.768461i	$0.721023\pi$
$908$	12.4651	0.413670
$909$	−2.82945	−0.0938468
$910$	−24.7434	−0.820237
$911$	53.4359	1.77041	0.885205	−	0.465201i	$-0.154018\pi$
$911$	53.4359	1.77041	0.885205	+	0.465201i	$0.154018\pi$
$912$	−37.6424	−1.24646
$913$	1.77656	0.0587955
$914$	57.6658	1.90742
$915$	−9.62299	−0.318126
$916$	−0.542691	−0.0179310
$917$	−5.79964	−0.191521
$918$	9.67442	0.319303
$919$	15.7163	0.518432	0.259216	−	0.965819i	$-0.416536\pi$
$919$	15.7163	0.518432	0.259216	+	0.965819i	$0.416536\pi$
$920$	−9.10120	−0.300058
$921$	−31.2988	−1.03133
$922$	−13.8582	−0.456395
$923$	−4.60671	−0.151632
$924$	2.92602	0.0962589
$925$	−11.2872	−0.371119
$926$	13.8248	0.454312
$927$	−4.68881	−0.154001
$928$	1.91009	0.0627017
$929$	56.0097	1.83762	0.918809	−	0.394702i	$-0.129152\pi$
$929$	56.0097	1.83762	0.918809	+	0.394702i	$0.129152\pi$
$930$	−9.48848	−0.311139
$931$	5.83631	0.191277
$932$	9.44829	0.309489
$933$	6.18244	0.202404
$934$	−66.6177	−2.17980
$935$	9.99957	0.327021
$936$	−12.1985	−0.398722
$937$	−41.3126	−1.34962	−0.674811	−	0.737990i	$-0.735775\pi$
$937$	−41.3126	−1.34962	−0.674811	+	0.737990i	$0.735775\pi$
$938$	50.2175	1.63966
$939$	−8.43077	−0.275128
$940$	−4.37190	−0.142596
$941$	10.3374	0.336989	0.168495	−	0.985703i	$-0.446109\pi$
$941$	10.3374	0.336989	0.168495	+	0.985703i	$0.446109\pi$
$942$	−6.68173	−0.217702
$943$	−5.92441	−0.192925
$944$	−33.5246	−1.09113
$945$	−2.78454	−0.0905812
$946$	1.17009	0.0380429
$947$	17.1382	0.556916	0.278458	−	0.960448i	$-0.410177\pi$
$947$	17.1382	0.556916	0.278458	+	0.960448i	$0.410177\pi$
$948$	−8.45777	−0.274695
$949$	57.1441	1.85498
$950$	−12.5515	−0.407226
$951$	26.5812	0.861956
$952$	−36.9812	−1.19857
$953$	−42.5868	−1.37952	−0.689761	−	0.724037i	$-0.742284\pi$
$953$	−42.5868	−1.37952	−0.689761	+	0.724037i	$0.742284\pi$
$954$	16.4892	0.533859
$955$	9.02594	0.292073
$956$	12.9635	0.419271
$957$	0.933262	0.0301681
$958$	35.1339	1.13512
$959$	5.67124	0.183134
$960$	−4.16427	−0.134401
$961$	3.26864	0.105440
$962$	−100.298	−3.23373
$963$	1.48458	0.0478400
$964$	−9.27573	−0.298751
$965$	−10.9791	−0.353430
$966$	−18.4608	−0.593967
$967$	27.0345	0.869370	0.434685	−	0.900583i	$-0.356860\pi$
$967$	27.0345	0.869370	0.434685	+	0.900583i	$0.356860\pi$
$968$	−18.2307	−0.585958
$969$	−46.2196	−1.48479
$970$	−1.39883	−0.0449137
$971$	−0.940917	−0.0301954	−0.0150977	−	0.999886i	$-0.504806\pi$
$971$	−0.940917	−0.0301954	−0.0150977	+	0.999886i	$0.504806\pi$
$972$	0.627218	0.0201180
$973$	−42.0213	−1.34714
$974$	−2.53106	−0.0811004
$975$	−5.48224	−0.175572
$976$	−46.7777	−1.49732
$977$	20.8175	0.666012	0.333006	−	0.942925i	$-0.391937\pi$
$977$	20.8175	0.666012	0.333006	+	0.942925i	$0.391937\pi$
$978$	16.1343	0.515917
$979$	−24.3884	−0.779455
$980$	−0.472724	−0.0151006
$981$	9.76818	0.311874
$982$	−9.55720	−0.304983
$983$	−13.4958	−0.430448	−0.215224	−	0.976565i	$-0.569048\pi$
$983$	−13.4958	−0.430448	−0.215224	+	0.976565i	$0.569048\pi$
$984$	−3.22289	−0.102742
$985$	−13.4443	−0.428370
$986$	5.38919	0.171627
$987$	19.4091	0.617800
$988$	−26.6272	−0.847124
$989$	−1.76244	−0.0560425
$990$	2.71552	0.0863048
$991$	22.0135	0.699281	0.349640	−	0.936884i	$-0.386304\pi$
$991$	22.0135	0.699281	0.349640	+	0.936884i	$0.386304\pi$
$992$	−20.0726	−0.637305
$993$	−16.4771	−0.522886
$994$	−3.79258	−0.120293
$995$	−11.4969	−0.364476
$996$	0.665110	0.0210748
$997$	−36.4112	−1.15315	−0.576577	−	0.817043i	$-0.695612\pi$
$997$	−36.4112	−1.15315	−0.576577	+	0.817043i	$0.695612\pi$
$998$	40.6243	1.28594
$999$	−11.2872	−0.357110

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6015.2.a.c.1.7	✓	28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6015.2.a.c.1.7	✓	28	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 6015 = 3 \cdot 5 \cdot 401 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6015.a (trivial)

\(f(q)\)	\(=\)	\(q-1.62087 q^{2} +1.00000 q^{3} +0.627218 q^{4} -1.00000 q^{5} -1.62087 q^{6} +2.78454 q^{7} +2.22510 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.62087 q^{2} +1.00000 q^{3} +0.627218 q^{4} -1.00000 q^{5} -1.62087 q^{6} +2.78454 q^{7} +2.22510 q^{8} +1.00000 q^{9} +1.62087 q^{10} +1.67535 q^{11} +0.627218 q^{12} -5.48224 q^{13} -4.51338 q^{14} -1.00000 q^{15} -4.86103 q^{16} -5.96866 q^{17} -1.62087 q^{18} +7.74371 q^{19} -0.627218 q^{20} +2.78454 q^{21} -2.71552 q^{22} +4.09024 q^{23} +2.22510 q^{24} +1.00000 q^{25} +8.88600 q^{26} +1.00000 q^{27} +1.74652 q^{28} +0.557056 q^{29} +1.62087 q^{30} -5.85394 q^{31} +3.42890 q^{32} +1.67535 q^{33} +9.67442 q^{34} -2.78454 q^{35} +0.627218 q^{36} -11.2872 q^{37} -12.5515 q^{38} -5.48224 q^{39} -2.22510 q^{40} -1.44843 q^{41} -4.51338 q^{42} -0.430890 q^{43} +1.05081 q^{44} -1.00000 q^{45} -6.62975 q^{46} +6.97031 q^{47} -4.86103 q^{48} +0.753684 q^{49} -1.62087 q^{50} -5.96866 q^{51} -3.43856 q^{52} -10.1731 q^{53} -1.62087 q^{54} -1.67535 q^{55} +6.19589 q^{56} +7.74371 q^{57} -0.902915 q^{58} +6.89659 q^{59} -0.627218 q^{60} +9.62299 q^{61} +9.48848 q^{62} +2.78454 q^{63} +4.16427 q^{64} +5.48224 q^{65} -2.71552 q^{66} -11.1264 q^{67} -3.74365 q^{68} +4.09024 q^{69} +4.51338 q^{70} +0.840297 q^{71} +2.22510 q^{72} -10.4235 q^{73} +18.2950 q^{74} +1.00000 q^{75} +4.85699 q^{76} +4.66507 q^{77} +8.88600 q^{78} -13.4846 q^{79} +4.86103 q^{80} +1.00000 q^{81} +2.34771 q^{82} +1.06041 q^{83} +1.74652 q^{84} +5.96866 q^{85} +0.698416 q^{86} +0.557056 q^{87} +3.72781 q^{88} -14.5572 q^{89} +1.62087 q^{90} -15.2655 q^{91} +2.56547 q^{92} -5.85394 q^{93} -11.2980 q^{94} -7.74371 q^{95} +3.42890 q^{96} -0.863013 q^{97} -1.22162 q^{98} +1.67535 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q - q^{2} + 28 q^{3} + 21 q^{4} - 28 q^{5} - q^{6} - 20 q^{7} + 28 q^{9}+O(q^{10}) \) 28 * q - q^2 + 28 * q^3 + 21 * q^4 - 28 * q^5 - q^6 - 20 * q^7 + 28 * q^9	\( 28 q - q^{2} + 28 q^{3} + 21 q^{4} - 28 q^{5} - q^{6} - 20 q^{7} + 28 q^{9} + q^{10} - q^{11} + 21 q^{12} - 18 q^{13} - 4 q^{14} - 28 q^{15} - q^{16} - 28 q^{17} - q^{18} - 19 q^{19} - 21 q^{20} - 20 q^{21} - 35 q^{22} + 2 q^{23} + 28 q^{25} - 20 q^{26} + 28 q^{27} - 54 q^{28} + 9 q^{29} + q^{30} - 19 q^{31} - 6 q^{32} - q^{33} - 16 q^{34} + 20 q^{35} + 21 q^{36} - 32 q^{37} - 2 q^{38} - 18 q^{39} - 27 q^{41} - 4 q^{42} - 77 q^{43} + q^{44} - 28 q^{45} - 19 q^{46} + 10 q^{47} - q^{48} - 4 q^{49} - q^{50} - 28 q^{51} - 34 q^{52} - 21 q^{53} - q^{54} + q^{55} - 9 q^{56} - 19 q^{57} - 46 q^{58} - 7 q^{59} - 21 q^{60} - 31 q^{61} - 7 q^{62} - 20 q^{63} - 46 q^{64} + 18 q^{65} - 35 q^{66} - 50 q^{67} - 68 q^{68} + 2 q^{69} + 4 q^{70} - 4 q^{71} - 87 q^{73} + 4 q^{74} + 28 q^{75} - 40 q^{76} - 8 q^{77} - 20 q^{78} - 65 q^{79} + q^{80} + 28 q^{81} - 41 q^{82} + 13 q^{83} - 54 q^{84} + 28 q^{85} - 17 q^{86} + 9 q^{87} - 117 q^{88} - 33 q^{89} + q^{90} - 33 q^{91} + 3 q^{92} - 19 q^{93} - 60 q^{94} + 19 q^{95} - 6 q^{96} - 75 q^{97} - 18 q^{98} - q^{99}+O(q^{100}) \) 28 * q - q^2 + 28 * q^3 + 21 * q^4 - 28 * q^5 - q^6 - 20 * q^7 + 28 * q^9 + q^10 - q^11 + 21 * q^12 - 18 * q^13 - 4 * q^14 - 28 * q^15 - q^16 - 28 * q^17 - q^18 - 19 * q^19 - 21 * q^20 - 20 * q^21 - 35 * q^22 + 2 * q^23 + 28 * q^25 - 20 * q^26 + 28 * q^27 - 54 * q^28 + 9 * q^29 + q^30 - 19 * q^31 - 6 * q^32 - q^33 - 16 * q^34 + 20 * q^35 + 21 * q^36 - 32 * q^37 - 2 * q^38 - 18 * q^39 - 27 * q^41 - 4 * q^42 - 77 * q^43 + q^44 - 28 * q^45 - 19 * q^46 + 10 * q^47 - q^48 - 4 * q^49 - q^50 - 28 * q^51 - 34 * q^52 - 21 * q^53 - q^54 + q^55 - 9 * q^56 - 19 * q^57 - 46 * q^58 - 7 * q^59 - 21 * q^60 - 31 * q^61 - 7 * q^62 - 20 * q^63 - 46 * q^64 + 18 * q^65 - 35 * q^66 - 50 * q^67 - 68 * q^68 + 2 * q^69 + 4 * q^70 - 4 * q^71 - 87 * q^73 + 4 * q^74 + 28 * q^75 - 40 * q^76 - 8 * q^77 - 20 * q^78 - 65 * q^79 + q^80 + 28 * q^81 - 41 * q^82 + 13 * q^83 - 54 * q^84 + 28 * q^85 - 17 * q^86 + 9 * q^87 - 117 * q^88 - 33 * q^89 + q^90 - 33 * q^91 + 3 * q^92 - 19 * q^93 - 60 * q^94 + 19 * q^95 - 6 * q^96 - 75 * q^97 - 18 * q^98 - q^99

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