LMFDB - Embedded newform 2001.2.a.m.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2001,2,Mod(1,2001)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2001, 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("2001.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2001 = 3 \cdot 23 \cdot 29 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2001.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:	$15.9780654445$
Analytic rank:	$1$
Dimension:	$14$
Coefficient field:	$\mathbb{Q}[x]/(x^{14} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{14} - 2 x^{13} - 18 x^{12} + 34 x^{11} + 124 x^{10} - 216 x^{9} - 420 x^{8} + 647 x^{7} + 750 x^{6} + \cdots - 64 $ x^14 - 2x^13 - 18x^12 + 34x^11 + 124x^10 - 216x^9 - 420x^8 + 647x^7 + 750x^6 - 939x^5 - 717x^4 + 604x^3 + 352x^2 - 128*x - 64
Coefficient ring:	$\Z[a_1, \ldots, a_{17}]$
Coefficient ring index:	$ 2^{3} $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$2.31598$ of defining polynomial
Character	$\chi$	$=$	2001.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.31598 q^{2} -1.00000 q^{3} +3.36376 q^{4} -2.86683 q^{5} +2.31598 q^{6} +3.60131 q^{7} -3.15843 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-2.31598 q^{2} -1.00000 q^{3} +3.36376 q^{4} -2.86683 q^{5} +2.31598 q^{6} +3.60131 q^{7} -3.15843 q^{8} +1.00000 q^{9} +6.63952 q^{10} +0.489865 q^{11} -3.36376 q^{12} +2.88891 q^{13} -8.34055 q^{14} +2.86683 q^{15} +0.587346 q^{16} -6.07526 q^{17} -2.31598 q^{18} -0.208958 q^{19} -9.64332 q^{20} -3.60131 q^{21} -1.13452 q^{22} -1.00000 q^{23} +3.15843 q^{24} +3.21872 q^{25} -6.69064 q^{26} -1.00000 q^{27} +12.1139 q^{28} -1.00000 q^{29} -6.63952 q^{30} -6.93798 q^{31} +4.95658 q^{32} -0.489865 q^{33} +14.0702 q^{34} -10.3243 q^{35} +3.36376 q^{36} -5.06467 q^{37} +0.483943 q^{38} -2.88891 q^{39} +9.05469 q^{40} +9.28334 q^{41} +8.34055 q^{42} +7.52223 q^{43} +1.64779 q^{44} -2.86683 q^{45} +2.31598 q^{46} -1.61063 q^{47} -0.587346 q^{48} +5.96943 q^{49} -7.45448 q^{50} +6.07526 q^{51} +9.71758 q^{52} +10.1414 q^{53} +2.31598 q^{54} -1.40436 q^{55} -11.3745 q^{56} +0.208958 q^{57} +2.31598 q^{58} +10.2020 q^{59} +9.64332 q^{60} -9.55359 q^{61} +16.0682 q^{62} +3.60131 q^{63} -12.6540 q^{64} -8.28200 q^{65} +1.13452 q^{66} -12.1104 q^{67} -20.4357 q^{68} +1.00000 q^{69} +23.9110 q^{70} +2.69908 q^{71} -3.15843 q^{72} -4.65365 q^{73} +11.7297 q^{74} -3.21872 q^{75} -0.702885 q^{76} +1.76416 q^{77} +6.69064 q^{78} +7.85970 q^{79} -1.68382 q^{80} +1.00000 q^{81} -21.5000 q^{82} -1.79638 q^{83} -12.1139 q^{84} +17.4167 q^{85} -17.4213 q^{86} +1.00000 q^{87} -1.54721 q^{88} -7.62479 q^{89} +6.63952 q^{90} +10.4038 q^{91} -3.36376 q^{92} +6.93798 q^{93} +3.73019 q^{94} +0.599048 q^{95} -4.95658 q^{96} +5.18136 q^{97} -13.8251 q^{98} +0.489865 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 14 q - 2 q^{2} - 14 q^{3} + 12 q^{4} - 3 q^{5} + 2 q^{6} - 3 q^{7} - 6 q^{8} + 14 q^{9}+O(q^{10}) $ 14 * q - 2 * q^2 - 14 * q^3 + 12 * q^4 - 3 * q^5 + 2 * q^6 - 3 * q^7 - 6 * q^8 + 14 * q^9	\( 14 q - 2 q^{2} - 14 q^{3} + 12 q^{4} - 3 q^{5} + 2 q^{6} - 3 q^{7} - 6 q^{8} + 14 q^{9} - 5 q^{10} - 12 q^{11} - 12 q^{12} + 13 q^{13} - 9 q^{14} + 3 q^{15} - 14 q^{17} - 2 q^{18} - 9 q^{19} - 2 q^{20} + 3 q^{21} - 9 q^{22} - 14 q^{23} + 6 q^{24} + 13 q^{25} - 16 q^{26} - 14 q^{27} + 3 q^{28} - 14 q^{29} + 5 q^{30} - 28 q^{31} - 4 q^{32} + 12 q^{33} + 14 q^{34} - 9 q^{35} + 12 q^{36} - 12 q^{37} + 2 q^{38} - 13 q^{39} - 20 q^{40} - 25 q^{41} + 9 q^{42} + 5 q^{43} - 37 q^{44} - 3 q^{45} + 2 q^{46} - 17 q^{47} + 17 q^{49} - 44 q^{50} + 14 q^{51} + 25 q^{52} - 17 q^{53} + 2 q^{54} + q^{55} - 54 q^{56} + 9 q^{57} + 2 q^{58} - 18 q^{59} + 2 q^{60} - 13 q^{61} - 8 q^{62} - 3 q^{63} + 20 q^{64} - 16 q^{65} + 9 q^{66} + 2 q^{67} - 19 q^{68} + 14 q^{69} + 14 q^{70} - 55 q^{71} - 6 q^{72} + 19 q^{73} + 4 q^{74} - 13 q^{75} - 32 q^{76} - 19 q^{77} + 16 q^{78} - 68 q^{79} - 2 q^{80} + 14 q^{81} - 12 q^{82} - 21 q^{83} - 3 q^{84} + 16 q^{85} - 22 q^{86} + 14 q^{87} - 25 q^{88} - 17 q^{89} - 5 q^{90} - 30 q^{91} - 12 q^{92} + 28 q^{93} + 16 q^{94} - 55 q^{95} + 4 q^{96} + 25 q^{97} - 31 q^{98} - 12 q^{99}+O(q^{100}) \) 14 * q - 2 * q^2 - 14 * q^3 + 12 * q^4 - 3 * q^5 + 2 * q^6 - 3 * q^7 - 6 * q^8 + 14 * q^9 - 5 * q^10 - 12 * q^11 - 12 * q^12 + 13 * q^13 - 9 * q^14 + 3 * q^15 - 14 * q^17 - 2 * q^18 - 9 * q^19 - 2 * q^20 + 3 * q^21 - 9 * q^22 - 14 * q^23 + 6 * q^24 + 13 * q^25 - 16 * q^26 - 14 * q^27 + 3 * q^28 - 14 * q^29 + 5 * q^30 - 28 * q^31 - 4 * q^32 + 12 * q^33 + 14 * q^34 - 9 * q^35 + 12 * q^36 - 12 * q^37 + 2 * q^38 - 13 * q^39 - 20 * q^40 - 25 * q^41 + 9 * q^42 + 5 * q^43 - 37 * q^44 - 3 * q^45 + 2 * q^46 - 17 * q^47 + 17 * q^49 - 44 * q^50 + 14 * q^51 + 25 * q^52 - 17 * q^53 + 2 * q^54 + q^55 - 54 * q^56 + 9 * q^57 + 2 * q^58 - 18 * q^59 + 2 * q^60 - 13 * q^61 - 8 * q^62 - 3 * q^63 + 20 * q^64 - 16 * q^65 + 9 * q^66 + 2 * q^67 - 19 * q^68 + 14 * q^69 + 14 * q^70 - 55 * q^71 - 6 * q^72 + 19 * q^73 + 4 * q^74 - 13 * q^75 - 32 * q^76 - 19 * q^77 + 16 * q^78 - 68 * q^79 - 2 * q^80 + 14 * q^81 - 12 * q^82 - 21 * q^83 - 3 * q^84 + 16 * q^85 - 22 * q^86 + 14 * q^87 - 25 * q^88 - 17 * q^89 - 5 * q^90 - 30 * q^91 - 12 * q^92 + 28 * q^93 + 16 * q^94 - 55 * q^95 + 4 * q^96 + 25 * q^97 - 31 * q^98 - 12 * 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 $

$2$	−2.31598	−1.63764	−0.818822	−	0.574047i	$-0.805373\pi$
$2$	−2.31598	−1.63764	−0.818822	+	0.574047i	$0.805373\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	3.36376	1.68188
$5$	−2.86683	−1.28209	−0.641043	−	0.767505i	$-0.721498\pi$
$5$	−2.86683	−1.28209	−0.641043	+	0.767505i	$0.721498\pi$
$6$	2.31598	0.945494
$7$	3.60131	1.36117	0.680583	−	0.732671i	$-0.261726\pi$
$7$	3.60131	1.36117	0.680583	+	0.732671i	$0.261726\pi$
$8$	−3.15843	−1.11667
$9$	1.00000	0.333333
$10$	6.63952	2.09960
$11$	0.489865	0.147700	0.0738500	−	0.997269i	$-0.476471\pi$
$11$	0.489865	0.147700	0.0738500	+	0.997269i	$0.476471\pi$
$12$	−3.36376	−0.971033
$13$	2.88891	0.801238	0.400619	−	0.916245i	$-0.368795\pi$
$13$	2.88891	0.801238	0.400619	+	0.916245i	$0.368795\pi$
$14$	−8.34055	−2.22911
$15$	2.86683	0.740212
$16$	0.587346	0.146837
$17$	−6.07526	−1.47347	−0.736733	−	0.676184i	$-0.763632\pi$
$17$	−6.07526	−1.47347	−0.736733	+	0.676184i	$0.763632\pi$
$18$	−2.31598	−0.545881
$19$	−0.208958	−0.0479383	−0.0239692	−	0.999713i	$-0.507630\pi$
$19$	−0.208958	−0.0479383	−0.0239692	+	0.999713i	$0.507630\pi$
$20$	−9.64332	−2.15631
$21$	−3.60131	−0.785870
$22$	−1.13452	−0.241880
$23$	−1.00000	−0.208514
$23$	−1.00000	−0.208514
$24$	3.15843	0.644712
$25$	3.21872	0.643743
$26$	−6.69064	−1.31214
$27$	−1.00000	−0.192450
$28$	12.1139	2.28932
$29$	−1.00000	−0.185695
$29$	−1.00000	−0.185695
$30$	−6.63952	−1.21220
$31$	−6.93798	−1.24610	−0.623049	−	0.782183i	$-0.714106\pi$
$31$	−6.93798	−1.24610	−0.623049	+	0.782183i	$0.714106\pi$
$32$	4.95658	0.876208
$33$	−0.489865	−0.0852746
$34$	14.0702	2.41301
$35$	−10.3243	−1.74513
$36$	3.36376	0.560626
$37$	−5.06467	−0.832627	−0.416313	−	0.909221i	$-0.636678\pi$
$37$	−5.06467	−0.832627	−0.416313	+	0.909221i	$0.636678\pi$
$38$	0.483943	0.0785060
$39$	−2.88891	−0.462595
$40$	9.05469	1.43167
$41$	9.28334	1.44981	0.724907	−	0.688847i	$-0.241883\pi$
$41$	9.28334	1.44981	0.724907	+	0.688847i	$0.241883\pi$
$42$	8.34055	1.28698
$43$	7.52223	1.14713	0.573565	−	0.819160i	$-0.305560\pi$
$43$	7.52223	1.14713	0.573565	+	0.819160i	$0.305560\pi$
$44$	1.64779	0.248413
$45$	−2.86683	−0.427362
$46$	2.31598	0.341472
$47$	−1.61063	−0.234935	−0.117468	−	0.993077i	$-0.537478\pi$
$47$	−1.61063	−0.234935	−0.117468	+	0.993077i	$0.537478\pi$
$48$	−0.587346	−0.0847761
$49$	5.96943	0.852775
$50$	−7.45448	−1.05422
$51$	6.07526	0.850706
$52$	9.71758	1.34759
$53$	10.1414	1.39303	0.696516	−	0.717541i	$-0.254733\pi$
$53$	10.1414	1.39303	0.696516	+	0.717541i	$0.254733\pi$
$54$	2.31598	0.315165
$55$	−1.40436	−0.189364
$56$	−11.3745	−1.51998
$57$	0.208958	0.0276772
$58$	2.31598	0.304103
$59$	10.2020	1.32818	0.664091	−	0.747652i	$-0.268819\pi$
$59$	10.2020	1.32818	0.664091	+	0.747652i	$0.268819\pi$
$60$	9.64332	1.24495
$61$	−9.55359	−1.22321	−0.611606	−	0.791163i	$-0.709476\pi$
$61$	−9.55359	−1.22321	−0.611606	+	0.791163i	$0.709476\pi$
$62$	16.0682	2.04067
$63$	3.60131	0.453722
$64$	−12.6540	−1.58175
$65$	−8.28200	−1.02726
$66$	1.13452	0.139649
$67$	−12.1104	−1.47953	−0.739763	−	0.672867i	$-0.765062\pi$
$67$	−12.1104	−1.47953	−0.739763	+	0.672867i	$0.765062\pi$
$68$	−20.4357	−2.47819
$69$	1.00000	0.120386
$70$	23.9110	2.85791
$71$	2.69908	0.320321	0.160161	−	0.987091i	$-0.448799\pi$
$71$	2.69908	0.320321	0.160161	+	0.987091i	$0.448799\pi$
$72$	−3.15843	−0.372225
$73$	−4.65365	−0.544668	−0.272334	−	0.962203i	$-0.587796\pi$
$73$	−4.65365	−0.544668	−0.272334	+	0.962203i	$0.587796\pi$
$74$	11.7297	1.36355
$75$	−3.21872	−0.371665
$76$	−0.702885	−0.0806265
$77$	1.76416	0.201044
$78$	6.69064	0.757566
$79$	7.85970	0.884285	0.442142	−	0.896945i	$-0.354219\pi$
$79$	7.85970	0.884285	0.442142	+	0.896945i	$0.354219\pi$
$80$	−1.68382	−0.188257
$81$	1.00000	0.111111
$82$	−21.5000	−2.37428
$83$	−1.79638	−0.197178	−0.0985889	−	0.995128i	$-0.531433\pi$
$83$	−1.79638	−0.197178	−0.0985889	+	0.995128i	$0.531433\pi$
$84$	−12.1139	−1.32174
$85$	17.4167	1.88911
$86$	−17.4213	−1.87859
$87$	1.00000	0.107211
$88$	−1.54721	−0.164933
$89$	−7.62479	−0.808227	−0.404113	−	0.914709i	$-0.632420\pi$
$89$	−7.62479	−0.808227	−0.404113	+	0.914709i	$0.632420\pi$
$90$	6.63952	0.699867
$91$	10.4038	1.09062
$92$	−3.36376	−0.350696
$93$	6.93798	0.719435
$94$	3.73019	0.384740
$95$	0.599048	0.0614611
$96$	−4.95658	−0.505879
$97$	5.18136	0.526087	0.263044	−	0.964784i	$-0.415274\pi$
$97$	5.18136	0.526087	0.263044	+	0.964784i	$0.415274\pi$
$98$	−13.8251	−1.39654
$99$	0.489865	0.0492333
$100$	10.8270	1.08270
$101$	−13.7012	−1.36332	−0.681662	−	0.731667i	$-0.738742\pi$
$101$	−13.7012	−1.36332	−0.681662	+	0.731667i	$0.738742\pi$
$102$	−14.0702	−1.39315
$103$	13.5310	1.33325	0.666626	−	0.745393i	$-0.267738\pi$
$103$	13.5310	1.33325	0.666626	+	0.745393i	$0.267738\pi$
$104$	−9.12441	−0.894722
$105$	10.3243	1.00755
$106$	−23.4873	−2.28129
$107$	0.886283	0.0856802	0.0428401	−	0.999082i	$-0.486359\pi$
$107$	0.886283	0.0856802	0.0428401	+	0.999082i	$0.486359\pi$
$108$	−3.36376	−0.323678
$109$	−2.81821	−0.269936	−0.134968	−	0.990850i	$-0.543093\pi$
$109$	−2.81821	−0.269936	−0.134968	+	0.990850i	$0.543093\pi$
$110$	3.25247	0.310111
$111$	5.06467	0.480717
$112$	2.11521	0.199869
$113$	−16.3262	−1.53584	−0.767920	−	0.640546i	$-0.778708\pi$
$113$	−16.3262	−1.53584	−0.767920	+	0.640546i	$0.778708\pi$
$114$	−0.483943	−0.0453254
$115$	2.86683	0.267333
$116$	−3.36376	−0.312317
$117$	2.88891	0.267079
$118$	−23.6275	−2.17509
$119$	−21.8789	−2.00563
$120$	−9.05469	−0.826576
$121$	−10.7600	−0.978185
$122$	22.1259	2.00318
$123$	−9.28334	−0.837050
$124$	−23.3377	−2.09579
$125$	5.10664	0.456751
$126$	−8.34055	−0.743036
$127$	−5.94903	−0.527891	−0.263945	−	0.964538i	$-0.585024\pi$
$127$	−5.94903	−0.527891	−0.263945	+	0.964538i	$0.585024\pi$
$128$	19.3933	1.71414
$129$	−7.52223	−0.662296
$130$	19.1809	1.68228
$131$	8.74603	0.764144	0.382072	−	0.924133i	$-0.375211\pi$
$131$	8.74603	0.764144	0.382072	+	0.924133i	$0.375211\pi$
$132$	−1.64779	−0.143422
$133$	−0.752524	−0.0652521
$134$	28.0475	2.42294
$135$	2.86683	0.246737
$136$	19.1883	1.64538
$137$	−4.87871	−0.416816	−0.208408	−	0.978042i	$-0.566828\pi$
$137$	−4.87871	−0.416816	−0.208408	+	0.978042i	$0.566828\pi$
$138$	−2.31598	−0.197149
$139$	8.31445	0.705223	0.352611	−	0.935770i	$-0.385294\pi$
$139$	8.31445	0.705223	0.352611	+	0.935770i	$0.385294\pi$
$140$	−34.7286	−2.93510
$141$	1.61063	0.135640
$142$	−6.25100	−0.524573
$143$	1.41518	0.118343
$144$	0.587346	0.0489455
$145$	2.86683	0.238077
$146$	10.7777	0.891973
$147$	−5.96943	−0.492350
$148$	−17.0363	−1.40038
$149$	−22.8015	−1.86797	−0.933987	−	0.357307i	$-0.883695\pi$
$149$	−22.8015	−1.86797	−0.933987	+	0.357307i	$0.883695\pi$
$150$	7.45448	0.608656
$151$	−17.4224	−1.41782	−0.708908	−	0.705301i	$-0.750812\pi$
$151$	−17.4224	−1.41782	−0.708908	+	0.705301i	$0.750812\pi$
$152$	0.659981	0.0535315
$153$	−6.07526	−0.491155
$154$	−4.08575	−0.329239
$155$	19.8900	1.59760
$156$	−9.71758	−0.778029
$157$	9.18382	0.732949	0.366474	−	0.930428i	$-0.380565\pi$
$157$	9.18382	0.732949	0.366474	+	0.930428i	$0.380565\pi$
$158$	−18.2029	−1.44814
$159$	−10.1414	−0.804267
$160$	−14.2097	−1.12337
$161$	−3.60131	−0.283823
$162$	−2.31598	−0.181960
$163$	15.9352	1.24814	0.624072	−	0.781367i	$-0.285477\pi$
$163$	15.9352	1.24814	0.624072	+	0.781367i	$0.285477\pi$
$164$	31.2269	2.43841
$165$	1.40436	0.109329
$166$	4.16037	0.322907
$167$	21.1433	1.63612	0.818058	−	0.575136i	$-0.195051\pi$
$167$	21.1433	1.63612	0.818058	+	0.575136i	$0.195051\pi$
$168$	11.3745	0.877561
$169$	−4.65422	−0.358017
$170$	−40.3368	−3.09369
$171$	−0.208958	−0.0159794
$172$	25.3030	1.92933
$173$	13.5153	1.02755	0.513776	−	0.857924i	$-0.328246\pi$
$173$	13.5153	1.02755	0.513776	+	0.857924i	$0.328246\pi$
$174$	−2.31598	−0.175574
$175$	11.5916	0.876242
$176$	0.287721	0.0216877
$177$	−10.2020	−0.766826
$178$	17.6589	1.32359
$179$	−7.42060	−0.554641	−0.277321	−	0.960777i	$-0.589446\pi$
$179$	−7.42060	−0.554641	−0.277321	+	0.960777i	$0.589446\pi$
$180$	−9.64332	−0.718771
$181$	4.32130	0.321200	0.160600	−	0.987020i	$-0.448657\pi$
$181$	4.32130	0.321200	0.160600	+	0.987020i	$0.448657\pi$
$182$	−24.0951	−1.78605
$183$	9.55359	0.706221
$184$	3.15843	0.232843
$185$	14.5196	1.06750
$186$	−16.0682	−1.17818
$187$	−2.97606	−0.217631
$188$	−5.41778	−0.395132
$189$	−3.60131	−0.261957
$190$	−1.38738	−0.100651
$191$	−1.47681	−0.106858	−0.0534291	−	0.998572i	$-0.517015\pi$
$191$	−1.47681	−0.106858	−0.0534291	+	0.998572i	$0.517015\pi$
$192$	12.6540	0.913226
$193$	−15.2102	−1.09485	−0.547427	−	0.836853i	$-0.684393\pi$
$193$	−15.2102	−1.09485	−0.547427	+	0.836853i	$0.684393\pi$
$194$	−11.9999	−0.861543
$195$	8.28200	0.593087
$196$	20.0797	1.43426
$197$	−2.57123	−0.183192	−0.0915961	−	0.995796i	$-0.529197\pi$
$197$	−2.57123	−0.183192	−0.0915961	+	0.995796i	$0.529197\pi$
$198$	−1.13452	−0.0806267
$199$	−15.7035	−1.11319	−0.556596	−	0.830783i	$-0.687893\pi$
$199$	−15.7035	−1.11319	−0.556596	+	0.830783i	$0.687893\pi$
$200$	−10.1661	−0.718852
$201$	12.1104	0.854205
$202$	31.7318	2.23264
$203$	−3.60131	−0.252762
$204$	20.4357	1.43078
$205$	−26.6138	−1.85879
$206$	−31.3376	−2.18339
$207$	−1.00000	−0.0695048
$208$	1.69679	0.117651
$209$	−0.102361	−0.00708049
$210$	−23.9110	−1.65001
$211$	−23.4076	−1.61145	−0.805723	−	0.592292i	$-0.798223\pi$
$211$	−23.4076	−1.61145	−0.805723	+	0.592292i	$0.798223\pi$
$212$	34.1133	2.34291
$213$	−2.69908	−0.184938
$214$	−2.05261	−0.140314
$215$	−21.5650	−1.47072
$216$	3.15843	0.214904
$217$	−24.9858	−1.69615
$218$	6.52692	0.442059
$219$	4.65365	0.314464
$220$	−4.72393	−0.318487
$221$	−17.5508	−1.18060
$222$	−11.7297	−0.787244
$223$	−15.7410	−1.05410	−0.527048	−	0.849836i	$-0.676701\pi$
$223$	−15.7410	−1.05410	−0.527048	+	0.849836i	$0.676701\pi$
$224$	17.8502	1.19267
$225$	3.21872	0.214581
$226$	37.8111	2.51516
$227$	−22.0224	−1.46168	−0.730840	−	0.682549i	$-0.760871\pi$
$227$	−22.0224	−1.46168	−0.730840	+	0.682549i	$0.760871\pi$
$228$	0.702885	0.0465497
$229$	−16.1546	−1.06752	−0.533762	−	0.845635i	$-0.679222\pi$
$229$	−16.1546	−1.06752	−0.533762	+	0.845635i	$0.679222\pi$
$230$	−6.63952	−0.437797
$231$	−1.76416	−0.116073
$232$	3.15843	0.207361
$233$	−18.8801	−1.23688	−0.618440	−	0.785832i	$-0.712235\pi$
$233$	−18.8801	−1.23688	−0.618440	+	0.785832i	$0.712235\pi$
$234$	−6.69064	−0.437381
$235$	4.61741	0.301207
$236$	34.3169	2.23384
$237$	−7.85970	−0.510542
$238$	50.6710	3.28451
$239$	−13.8197	−0.893921	−0.446960	−	0.894554i	$-0.647493\pi$
$239$	−13.8197	−0.893921	−0.446960	+	0.894554i	$0.647493\pi$
$240$	1.68382	0.108690
$241$	−4.07448	−0.262460	−0.131230	−	0.991352i	$-0.541893\pi$
$241$	−4.07448	−0.262460	−0.131230	+	0.991352i	$0.541893\pi$
$242$	24.9200	1.60192
$243$	−1.00000	−0.0641500
$244$	−32.1359	−2.05729
$245$	−17.1133	−1.09333
$246$	21.5000	1.37079
$247$	−0.603661	−0.0384100
$248$	21.9131	1.39149
$249$	1.79638	0.113841
$250$	−11.8269	−0.747996
$251$	6.49386	0.409889	0.204945	−	0.978774i	$-0.434299\pi$
$251$	6.49386	0.409889	0.204945	+	0.978774i	$0.434299\pi$
$252$	12.1139	0.763106
$253$	−0.489865	−0.0307976
$254$	13.7778	0.864498
$255$	−17.4167	−1.09068
$256$	−19.6064	−1.22540
$257$	15.0388	0.938097	0.469049	−	0.883172i	$-0.344597\pi$
$257$	15.0388	0.938097	0.469049	+	0.883172i	$0.344597\pi$
$258$	17.4213	1.08460
$259$	−18.2394	−1.13334
$260$	−27.8586	−1.72772
$261$	−1.00000	−0.0618984
$262$	−20.2556	−1.25140
$263$	−18.5844	−1.14597	−0.572983	−	0.819567i	$-0.694214\pi$
$263$	−18.5844	−1.14597	−0.572983	+	0.819567i	$0.694214\pi$
$264$	1.54721	0.0952240
$265$	−29.0737	−1.78599
$266$	1.74283	0.106860
$267$	7.62479	0.466630
$268$	−40.7366	−2.48838
$269$	−10.7377	−0.654686	−0.327343	−	0.944905i	$-0.606153\pi$
$269$	−10.7377	−0.654686	−0.327343	+	0.944905i	$0.606153\pi$
$270$	−6.63952	−0.404068
$271$	2.66418	0.161837	0.0809187	−	0.996721i	$-0.474215\pi$
$271$	2.66418	0.161837	0.0809187	+	0.996721i	$0.474215\pi$
$272$	−3.56828	−0.216359
$273$	−10.4038	−0.629669
$274$	11.2990	0.682597
$275$	1.57674	0.0950809
$276$	3.36376	0.202474
$277$	17.2762	1.03803	0.519013	−	0.854767i	$-0.326300\pi$
$277$	17.2762	1.03803	0.519013	+	0.854767i	$0.326300\pi$
$278$	−19.2561	−1.15490
$279$	−6.93798	−0.415366
$280$	32.6087	1.94874
$281$	−26.7094	−1.59335	−0.796674	−	0.604409i	$-0.793409\pi$
$281$	−26.7094	−1.59335	−0.796674	+	0.604409i	$0.793409\pi$
$282$	−3.73019	−0.222130
$283$	25.3486	1.50682	0.753410	−	0.657551i	$-0.228408\pi$
$283$	25.3486	1.50682	0.753410	+	0.657551i	$0.228408\pi$
$284$	9.07904	0.538742
$285$	−0.599048	−0.0354846
$286$	−3.27752	−0.193804
$287$	33.4322	1.97344
$288$	4.95658	0.292069
$289$	19.9087	1.17110
$290$	−6.63952	−0.389886
$291$	−5.18136	−0.303737
$292$	−15.6537	−0.916066
$293$	−5.13931	−0.300242	−0.150121	−	0.988668i	$-0.547966\pi$
$293$	−5.13931	−0.300242	−0.150121	+	0.988668i	$0.547966\pi$
$294$	13.8251	0.806294
$295$	−29.2473	−1.70284
$296$	15.9964	0.929773
$297$	−0.489865	−0.0284249
$298$	52.8079	3.05908
$299$	−2.88891	−0.167070
$300$	−10.8270	−0.625096
$301$	27.0899	1.56144
$302$	40.3500	2.32188
$303$	13.7012	0.787115
$304$	−0.122731	−0.00703910
$305$	27.3885	1.56826
$306$	14.0702	0.804338
$307$	19.5783	1.11739	0.558695	−	0.829373i	$-0.311302\pi$
$307$	19.5783	1.11739	0.558695	+	0.829373i	$0.311302\pi$
$308$	5.93419	0.338132
$309$	−13.5310	−0.769753
$310$	−46.0648	−2.61631
$311$	−34.2429	−1.94174	−0.970868	−	0.239617i	$-0.922978\pi$
$311$	−34.2429	−1.94174	−0.970868	+	0.239617i	$0.922978\pi$
$312$	9.12441	0.516568
$313$	−6.49992	−0.367397	−0.183699	−	0.982983i	$-0.558807\pi$
$313$	−6.49992	−0.367397	−0.183699	+	0.982983i	$0.558807\pi$
$314$	−21.2695	−1.20031
$315$	−10.3243	−0.581711
$316$	26.4381	1.48726
$317$	−15.0420	−0.844842	−0.422421	−	0.906400i	$-0.638820\pi$
$317$	−15.0420	−0.844842	−0.422421	+	0.906400i	$0.638820\pi$
$318$	23.4873	1.31710
$319$	−0.489865	−0.0274272
$320$	36.2770	2.02794
$321$	−0.886283	−0.0494675
$322$	8.34055	0.464801
$323$	1.26948	0.0706355
$324$	3.36376	0.186875
$325$	9.29857	0.515792
$326$	−36.9057	−2.04402
$327$	2.81821	0.155847
$328$	−29.3208	−1.61897
$329$	−5.80039	−0.319786
$330$	−3.25247	−0.179043
$331$	−2.36598	−0.130046	−0.0650229	−	0.997884i	$-0.520712\pi$
$331$	−2.36598	−0.130046	−0.0650229	+	0.997884i	$0.520712\pi$
$332$	−6.04257	−0.331629
$333$	−5.06467	−0.277542
$334$	−48.9674	−2.67938
$335$	34.7186	1.89688
$336$	−2.11521	−0.115394
$337$	9.98588	0.543965	0.271983	−	0.962302i	$-0.412321\pi$
$337$	9.98588	0.543965	0.271983	+	0.962302i	$0.412321\pi$
$338$	10.7791	0.586304
$339$	16.3262	0.886718
$340$	58.5856	3.17725
$341$	−3.39868	−0.184049
$342$	0.483943	0.0261687
$343$	−3.71141	−0.200397
$344$	−23.7585	−1.28097
$345$	−2.86683	−0.154345
$346$	−31.3012	−1.68277
$347$	6.98651	0.375055	0.187528	−	0.982259i	$-0.439953\pi$
$347$	6.98651	0.375055	0.187528	+	0.982259i	$0.439953\pi$
$348$	3.36376	0.180316
$349$	26.5857	1.42310	0.711550	−	0.702636i	$-0.247994\pi$
$349$	26.5857	1.42310	0.711550	+	0.702636i	$0.247994\pi$
$350$	−26.8459	−1.43497
$351$	−2.88891	−0.154198
$352$	2.42806	0.129416
$353$	7.02757	0.374040	0.187020	−	0.982356i	$-0.440117\pi$
$353$	7.02757	0.374040	0.187020	+	0.982356i	$0.440117\pi$
$354$	23.6275	1.25579
$355$	−7.73780	−0.410680
$356$	−25.6480	−1.35934
$357$	21.8789	1.15795
$358$	17.1859	0.908305
$359$	−26.5303	−1.40022	−0.700108	−	0.714037i	$-0.746865\pi$
$359$	−26.5303	−1.40022	−0.700108	+	0.714037i	$0.746865\pi$
$360$	9.05469	0.477224
$361$	−18.9563	−0.997702
$362$	−10.0080	−0.526011
$363$	10.7600	0.564755
$364$	34.9960	1.83429
$365$	13.3412	0.698311
$366$	−22.1259	−1.15654
$367$	−34.2926	−1.79006	−0.895029	−	0.446007i	$-0.852845\pi$
$367$	−34.2926	−1.79006	−0.895029	+	0.446007i	$0.852845\pi$
$368$	−0.587346	−0.0306175
$369$	9.28334	0.483271
$370$	−33.6270	−1.74818
$371$	36.5224	1.89615
$372$	23.3377	1.21000
$373$	−14.1764	−0.734028	−0.367014	−	0.930215i	$-0.619620\pi$
$373$	−14.1764	−0.734028	−0.367014	+	0.930215i	$0.619620\pi$
$374$	6.89249	0.356402
$375$	−5.10664	−0.263706
$376$	5.08707	0.262346
$377$	−2.88891	−0.148786
$378$	8.34055	0.428992
$379$	−25.6733	−1.31875	−0.659374	−	0.751815i	$-0.729178\pi$
$379$	−25.6733	−1.31875	−0.659374	+	0.751815i	$0.729178\pi$
$380$	2.01505	0.103370
$381$	5.94903	0.304778
$382$	3.42026	0.174996
$383$	17.9881	0.919147	0.459573	−	0.888140i	$-0.348002\pi$
$383$	17.9881	0.919147	0.459573	+	0.888140i	$0.348002\pi$
$384$	−19.3933	−0.989660
$385$	−5.05754	−0.257756
$386$	35.2265	1.79298
$387$	7.52223	0.382377
$388$	17.4288	0.884814
$389$	−23.3777	−1.18530	−0.592648	−	0.805462i	$-0.701917\pi$
$389$	−23.3777	−1.18530	−0.592648	+	0.805462i	$0.701917\pi$
$390$	−19.1809	−0.971265
$391$	6.07526	0.307239
$392$	−18.8540	−0.952272
$393$	−8.74603	−0.441179
$394$	5.95491	0.300004
$395$	−22.5324	−1.13373
$396$	1.64779	0.0828045
$397$	34.1121	1.71204	0.856018	−	0.516945i	$-0.172931\pi$
$397$	34.1121	1.71204	0.856018	+	0.516945i	$0.172931\pi$
$398$	36.3690	1.82301
$399$	0.752524	0.0376733
$400$	1.89050	0.0945250
$401$	−4.90447	−0.244918	−0.122459	−	0.992474i	$-0.539078\pi$
$401$	−4.90447	−0.244918	−0.122459	+	0.992474i	$0.539078\pi$
$402$	−28.0475	−1.39888
$403$	−20.0432	−0.998422
$404$	−46.0876	−2.29294
$405$	−2.86683	−0.142454
$406$	8.34055	0.413935
$407$	−2.48101	−0.122979
$408$	−19.1883	−0.949961
$409$	−6.13942	−0.303575	−0.151787	−	0.988413i	$-0.548503\pi$
$409$	−6.13942	−0.303575	−0.151787	+	0.988413i	$0.548503\pi$
$410$	61.6369	3.04403
$411$	4.87871	0.240649
$412$	45.5151	2.24237
$413$	36.7404	1.80788
$414$	2.31598	0.113824
$415$	5.14990	0.252799
$416$	14.3191	0.702052
$417$	−8.31445	−0.407160
$418$	0.237067	0.0115953
$419$	1.46153	0.0714006	0.0357003	−	0.999363i	$-0.488634\pi$
$419$	1.46153	0.0714006	0.0357003	+	0.999363i	$0.488634\pi$
$420$	34.7286	1.69458
$421$	32.7873	1.59796	0.798978	−	0.601360i	$-0.205374\pi$
$421$	32.7873	1.59796	0.798978	+	0.601360i	$0.205374\pi$
$422$	54.2115	2.63898
$423$	−1.61063	−0.0783117
$424$	−32.0310	−1.55556
$425$	−19.5545	−0.948534
$426$	6.25100	0.302862
$427$	−34.4054	−1.66499
$428$	2.98124	0.144104
$429$	−1.41518	−0.0683253
$430$	49.9440	2.40851
$431$	−27.1771	−1.30908	−0.654539	−	0.756029i	$-0.727137\pi$
$431$	−27.1771	−1.30908	−0.654539	+	0.756029i	$0.727137\pi$
$432$	−0.587346	−0.0282587
$433$	30.6675	1.47379	0.736893	−	0.676009i	$-0.236292\pi$
$433$	30.6675	1.47379	0.736893	+	0.676009i	$0.236292\pi$
$434$	57.8666	2.77769
$435$	−2.86683	−0.137454
$436$	−9.47978	−0.453999
$437$	0.208958	0.00999584
$438$	−10.7777	−0.514981
$439$	3.50454	0.167263	0.0836313	−	0.996497i	$-0.473348\pi$
$439$	3.50454	0.167263	0.0836313	+	0.996497i	$0.473348\pi$
$440$	4.43558	0.211458
$441$	5.96943	0.284258
$442$	40.6474	1.93340
$443$	−5.91295	−0.280933	−0.140466	−	0.990085i	$-0.544860\pi$
$443$	−5.91295	−0.280933	−0.140466	+	0.990085i	$0.544860\pi$
$444$	17.0363	0.808508
$445$	21.8590	1.03622
$446$	36.4558	1.72623
$447$	22.8015	1.07848
$448$	−45.5711	−2.15303
$449$	22.8726	1.07942	0.539711	−	0.841850i	$-0.318533\pi$
$449$	22.8726	1.07942	0.539711	+	0.841850i	$0.318533\pi$
$450$	−7.45448	−0.351408
$451$	4.54759	0.214137
$452$	−54.9174	−2.58310
$453$	17.4224	0.818577
$454$	51.0035	2.39371
$455$	−29.8261	−1.39827
$456$	−0.659981	−0.0309064
$457$	16.5249	0.773001	0.386500	−	0.922289i	$-0.373684\pi$
$457$	16.5249	0.773001	0.386500	+	0.922289i	$0.373684\pi$
$458$	37.4136	1.74822
$459$	6.07526	0.283569
$460$	9.64332	0.449622
$461$	−6.64056	−0.309282	−0.154641	−	0.987971i	$-0.549422\pi$
$461$	−6.64056	−0.309282	−0.154641	+	0.987971i	$0.549422\pi$
$462$	4.08575	0.190086
$463$	−18.7173	−0.869868	−0.434934	−	0.900462i	$-0.643228\pi$
$463$	−18.7173	−0.869868	−0.434934	+	0.900462i	$0.643228\pi$
$464$	−0.587346	−0.0272669
$465$	−19.8900	−0.922377
$466$	43.7260	2.02557
$467$	7.74364	0.358333	0.179167	−	0.983819i	$-0.442660\pi$
$467$	7.74364	0.358333	0.179167	+	0.983819i	$0.442660\pi$
$468$	9.71758	0.449195
$469$	−43.6135	−2.01388
$470$	−10.6938	−0.493270
$471$	−9.18382	−0.423168
$472$	−32.2222	−1.48315
$473$	3.68488	0.169431
$474$	18.2029	0.836086
$475$	−0.672578	−0.0308600
$476$	−73.5952	−3.37323
$477$	10.1414	0.464344
$478$	32.0061	1.46392
$479$	19.4249	0.887547	0.443773	−	0.896139i	$-0.353640\pi$
$479$	19.4249	0.887547	0.443773	+	0.896139i	$0.353640\pi$
$480$	14.2097	0.648580
$481$	−14.6314	−0.667133
$482$	9.43640	0.429816
$483$	3.60131	0.163865
$484$	−36.1941	−1.64519
$485$	−14.8541	−0.674489
$486$	2.31598	0.105055
$487$	10.6818	0.484040	0.242020	−	0.970271i	$-0.422190\pi$
$487$	10.6818	0.484040	0.242020	+	0.970271i	$0.422190\pi$
$488$	30.1743	1.36593
$489$	−15.9352	−0.720616
$490$	39.6341	1.79049
$491$	1.90753	0.0860855	0.0430427	−	0.999073i	$-0.486295\pi$
$491$	1.90753	0.0860855	0.0430427	+	0.999073i	$0.486295\pi$
$492$	−31.2269	−1.40782
$493$	6.07526	0.273616
$494$	1.39807	0.0629020
$495$	−1.40436	−0.0631213
$496$	−4.07499	−0.182973
$497$	9.72021	0.436011
$498$	−4.16037	−0.186430
$499$	−13.2192	−0.591774	−0.295887	−	0.955223i	$-0.595615\pi$
$499$	−13.2192	−0.591774	−0.295887	+	0.955223i	$0.595615\pi$
$500$	17.1775	0.768200
$501$	−21.1433	−0.944612
$502$	−15.0397	−0.671253
$503$	27.6893	1.23460	0.617302	−	0.786726i	$-0.288226\pi$
$503$	27.6893	1.23460	0.617302	+	0.786726i	$0.288226\pi$
$504$	−11.3745	−0.506660
$505$	39.2791	1.74790
$506$	1.13452	0.0504355
$507$	4.65422	0.206701
$508$	−20.0111	−0.887848
$509$	9.69520	0.429732	0.214866	−	0.976644i	$-0.431069\pi$
$509$	9.69520	0.429732	0.214866	+	0.976644i	$0.431069\pi$
$510$	40.3368	1.78614
$511$	−16.7592	−0.741384
$512$	6.62141	0.292628
$513$	0.208958	0.00922574
$514$	−34.8296	−1.53627
$515$	−38.7911	−1.70934
$516$	−25.3030	−1.11390
$517$	−0.788994	−0.0346999
$518$	42.2422	1.85601
$519$	−13.5153	−0.593258
$520$	26.1581	1.14711
$521$	24.2177	1.06100	0.530498	−	0.847686i	$-0.322005\pi$
$521$	24.2177	1.06100	0.530498	+	0.847686i	$0.322005\pi$
$522$	2.31598	0.101368
$523$	−32.5030	−1.42126	−0.710629	−	0.703567i	$-0.751590\pi$
$523$	−32.5030	−1.42126	−0.710629	+	0.703567i	$0.751590\pi$
$524$	29.4195	1.28520
$525$	−11.5916	−0.505899
$526$	43.0412	1.87668
$527$	42.1500	1.83608
$528$	−0.287721	−0.0125214
$529$	1.00000	0.0434783
$530$	67.3342	2.92481
$531$	10.2020	0.442727
$532$	−2.53131	−0.109746
$533$	26.8187	1.16165
$534$	−17.6589	−0.764174
$535$	−2.54082	−0.109849
$536$	38.2500	1.65215
$537$	7.42060	0.320222
$538$	24.8682	1.07214
$539$	2.92422	0.125955
$540$	9.64332	0.414982
$541$	−2.49329	−0.107195	−0.0535974	−	0.998563i	$-0.517069\pi$
$541$	−2.49329	−0.107195	−0.0535974	+	0.998563i	$0.517069\pi$
$542$	−6.17019	−0.265032
$543$	−4.32130	−0.185445
$544$	−30.1125	−1.29106
$545$	8.07934	0.346081
$546$	24.0951	1.03117
$547$	−44.0449	−1.88322	−0.941612	−	0.336699i	$-0.890690\pi$
$547$	−44.0449	−1.88322	−0.941612	+	0.336699i	$0.890690\pi$
$548$	−16.4108	−0.701035
$549$	−9.55359	−0.407737
$550$	−3.65169	−0.155709
$551$	0.208958	0.00890193
$552$	−3.15843	−0.134432
$553$	28.3052	1.20366
$554$	−40.0113	−1.69992
$555$	−14.5196	−0.616321
$556$	27.9678	1.18610
$557$	1.56699	0.0663954	0.0331977	−	0.999449i	$-0.489431\pi$
$557$	1.56699	0.0663954	0.0331977	+	0.999449i	$0.489431\pi$
$558$	16.0682	0.680222
$559$	21.7310	0.919124
$560$	−6.06396	−0.256249
$561$	2.97606	0.125649
$562$	61.8584	2.60934
$563$	−24.2279	−1.02109	−0.510543	−	0.859852i	$-0.670556\pi$
$563$	−24.2279	−1.02109	−0.510543	+	0.859852i	$0.670556\pi$
$564$	5.41778	0.228130
$565$	46.8045	1.96908
$566$	−58.7069	−2.46763
$567$	3.60131	0.151241
$568$	−8.52485	−0.357695
$569$	−14.7118	−0.616753	−0.308376	−	0.951264i	$-0.599786\pi$
$569$	−14.7118	−0.616753	−0.308376	+	0.951264i	$0.599786\pi$
$570$	1.38738	0.0581111
$571$	17.6613	0.739103	0.369551	−	0.929210i	$-0.379511\pi$
$571$	17.6613	0.739103	0.369551	+	0.929210i	$0.379511\pi$
$572$	4.76031	0.199038
$573$	1.47681	0.0616946
$574$	−77.4282	−3.23179
$575$	−3.21872	−0.134230
$576$	−12.6540	−0.527251
$577$	12.7470	0.530665	0.265333	−	0.964157i	$-0.414518\pi$
$577$	12.7470	0.530665	0.265333	+	0.964157i	$0.414518\pi$
$578$	−46.1082	−1.91785
$579$	15.2102	0.632115
$580$	9.64332	0.400417
$581$	−6.46930	−0.268392
$582$	11.9999	0.497412
$583$	4.96793	0.205751
$584$	14.6982	0.608217
$585$	−8.28200	−0.342419
$586$	11.9025	0.491689
$587$	−0.658885	−0.0271951	−0.0135976	−	0.999908i	$-0.504328\pi$
$587$	−0.658885	−0.0271951	−0.0135976	+	0.999908i	$0.504328\pi$
$588$	−20.0797	−0.828073
$589$	1.44975	0.0597359
$590$	67.7361	2.78865
$591$	2.57123	0.105766
$592$	−2.97471	−0.122260
$593$	−34.1532	−1.40250	−0.701251	−	0.712914i	$-0.747375\pi$
$593$	−34.1532	−1.40250	−0.701251	+	0.712914i	$0.747375\pi$
$594$	1.13452	0.0465498
$595$	62.7230	2.57139
$596$	−76.6988	−3.14171
$597$	15.7035	0.642702
$598$	6.69064	0.273601
$599$	−11.7324	−0.479373	−0.239687	−	0.970850i	$-0.577045\pi$
$599$	−11.7324	−0.479373	−0.239687	+	0.970850i	$0.577045\pi$
$600$	10.1661	0.415029
$601$	−22.1962	−0.905400	−0.452700	−	0.891663i	$-0.649539\pi$
$601$	−22.1962	−0.905400	−0.452700	+	0.891663i	$0.649539\pi$
$602$	−62.7396	−2.55707
$603$	−12.1104	−0.493175
$604$	−58.6048	−2.38460
$605$	30.8472	1.25412
$606$	−31.7318	−1.28901
$607$	−48.0676	−1.95100	−0.975501	−	0.219995i	$-0.929396\pi$
$607$	−48.0676	−1.95100	−0.975501	+	0.219995i	$0.929396\pi$
$608$	−1.03572	−0.0420040
$609$	3.60131	0.145932
$610$	−63.4312	−2.56825
$611$	−4.65297	−0.188239
$612$	−20.4357	−0.826063
$613$	7.40933	0.299260	0.149630	−	0.988742i	$-0.452192\pi$
$613$	7.40933	0.299260	0.149630	+	0.988742i	$0.452192\pi$
$614$	−45.3428	−1.82989
$615$	26.6138	1.07317
$616$	−5.57197	−0.224501
$617$	−13.8020	−0.555649	−0.277824	−	0.960632i	$-0.589613\pi$
$617$	−13.8020	−0.555649	−0.277824	+	0.960632i	$0.589613\pi$
$618$	31.3376	1.26058
$619$	−15.4327	−0.620294	−0.310147	−	0.950689i	$-0.600378\pi$
$619$	−15.4327	−0.620294	−0.310147	+	0.950689i	$0.600378\pi$
$620$	66.9052	2.68698
$621$	1.00000	0.0401286
$622$	79.3058	3.17987
$623$	−27.4592	−1.10013
$624$	−1.69679	−0.0679259
$625$	−30.7334	−1.22934
$626$	15.0537	0.601666
$627$	0.102361	0.00408792
$628$	30.8921	1.23273
$629$	30.7692	1.22685
$630$	23.9110	0.952635
$631$	29.3091	1.16678	0.583388	−	0.812193i	$-0.301727\pi$
$631$	29.3091	1.16678	0.583388	+	0.812193i	$0.301727\pi$
$632$	−24.8243	−0.987458
$633$	23.4076	0.930369
$634$	34.8369	1.38355
$635$	17.0549	0.676801
$636$	−34.1133	−1.35268
$637$	17.2451	0.683276
$638$	1.13452	0.0449160
$639$	2.69908	0.106774
$640$	−55.5973	−2.19768
$641$	1.75725	0.0694071	0.0347035	−	0.999398i	$-0.488951\pi$
$641$	1.75725	0.0694071	0.0347035	+	0.999398i	$0.488951\pi$
$642$	2.05261	0.0810102
$643$	−33.6057	−1.32528	−0.662639	−	0.748939i	$-0.730564\pi$
$643$	−33.6057	−1.32528	−0.662639	+	0.748939i	$0.730564\pi$
$644$	−12.1139	−0.477356
$645$	21.5650	0.849120
$646$	−2.94008	−0.115676
$647$	20.4559	0.804204	0.402102	−	0.915595i	$-0.368280\pi$
$647$	20.4559	0.804204	0.402102	+	0.915595i	$0.368280\pi$
$648$	−3.15843	−0.124075
$649$	4.99759	0.196172
$650$	−21.5353	−0.844684
$651$	24.9858	0.979271
$652$	53.6022	2.09923
$653$	11.8457	0.463559	0.231780	−	0.972768i	$-0.425545\pi$
$653$	11.8457	0.463559	0.231780	+	0.972768i	$0.425545\pi$
$654$	−6.52692	−0.255223
$655$	−25.0734	−0.979698
$656$	5.45253	0.212886
$657$	−4.65365	−0.181556
$658$	13.4336	0.523695
$659$	1.45749	0.0567757	0.0283878	−	0.999597i	$-0.490963\pi$
$659$	1.45749	0.0567757	0.0283878	+	0.999597i	$0.490963\pi$
$660$	4.72393	0.183879
$661$	−3.17925	−0.123659	−0.0618293	−	0.998087i	$-0.519693\pi$
$661$	−3.17925	−0.123659	−0.0618293	+	0.998087i	$0.519693\pi$
$662$	5.47955	0.212969
$663$	17.5508	0.681618
$664$	5.67373	0.220183
$665$	2.15736	0.0836588
$666$	11.7297	0.454515
$667$	1.00000	0.0387202
$668$	71.1208	2.75175
$669$	15.7410	0.608582
$670$	−80.4075	−3.10641
$671$	−4.67997	−0.180668
$672$	−17.8502	−0.688586
$673$	−35.6189	−1.37301	−0.686503	−	0.727127i	$-0.740855\pi$
$673$	−35.6189	−1.37301	−0.686503	+	0.727127i	$0.740855\pi$
$674$	−23.1271	−0.890822
$675$	−3.21872	−0.123888
$676$	−15.6557	−0.602141
$677$	−34.7094	−1.33399	−0.666994	−	0.745063i	$-0.732420\pi$
$677$	−34.7094	−1.33399	−0.666994	+	0.745063i	$0.732420\pi$
$678$	−37.8111	−1.45213
$679$	18.6597	0.716092
$680$	−55.0095	−2.10952
$681$	22.0224	0.843901
$682$	7.87126	0.301406
$683$	38.2453	1.46342	0.731708	−	0.681618i	$-0.238723\pi$
$683$	38.2453	1.46342	0.731708	+	0.681618i	$0.238723\pi$
$684$	−0.702885	−0.0268755
$685$	13.9864	0.534394
$686$	8.59555	0.328179
$687$	16.1546	0.616335
$688$	4.41815	0.168441
$689$	29.2976	1.11615
$690$	6.63952	0.252762
$691$	−18.9352	−0.720331	−0.360165	−	0.932888i	$-0.617280\pi$
$691$	−18.9352	−0.720331	−0.360165	+	0.932888i	$0.617280\pi$
$692$	45.4623	1.72822
$693$	1.76416	0.0670148
$694$	−16.1806	−0.614207
$695$	−23.8361	−0.904156
$696$	−3.15843	−0.119720
$697$	−56.3987	−2.13625
$698$	−61.5719	−2.33053
$699$	18.8801	0.714113
$700$	38.9913	1.47373
$701$	23.3256	0.880995	0.440498	−	0.897754i	$-0.354802\pi$
$701$	23.3256	0.880995	0.440498	+	0.897754i	$0.354802\pi$
$702$	6.69064	0.252522
$703$	1.05831	0.0399148
$704$	−6.19877	−0.233625
$705$	−4.61741	−0.173902
$706$	−16.2757	−0.612544
$707$	−49.3424	−1.85571
$708$	−34.3169	−1.28971
$709$	−24.5991	−0.923839	−0.461919	−	0.886922i	$-0.652839\pi$
$709$	−24.5991	−0.923839	−0.461919	+	0.886922i	$0.652839\pi$
$710$	17.9206	0.672547
$711$	7.85970	0.294762
$712$	24.0824	0.902526
$713$	6.93798	0.259829
$714$	−50.6710	−1.89631
$715$	−4.05707	−0.151726
$716$	−24.9611	−0.932839
$717$	13.8197	0.516105
$718$	61.4437	2.29306
$719$	23.4718	0.875352	0.437676	−	0.899133i	$-0.355802\pi$
$719$	23.4718	0.875352	0.437676	+	0.899133i	$0.355802\pi$
$720$	−1.68382	−0.0627523
$721$	48.7294	1.81478
$722$	43.9025	1.63388
$723$	4.07448	0.151531
$724$	14.5358	0.540219
$725$	−3.21872	−0.119540
$726$	−24.9200	−0.924868
$727$	−22.5482	−0.836266	−0.418133	−	0.908386i	$-0.637315\pi$
$727$	−22.5482	−0.836266	−0.418133	+	0.908386i	$0.637315\pi$
$728$	−32.8598	−1.21787
$729$	1.00000	0.0370370
$730$	−30.8980	−1.14359
$731$	−45.6995	−1.69026
$732$	32.1359	1.18778
$733$	−18.3331	−0.677149	−0.338574	−	0.940940i	$-0.609945\pi$
$733$	−18.3331	−0.677149	−0.338574	+	0.940940i	$0.609945\pi$
$734$	79.4209	2.93148
$735$	17.1133	0.631235
$736$	−4.95658	−0.182702
$737$	−5.93249	−0.218526
$738$	−21.5000	−0.791426
$739$	33.6701	1.23858	0.619288	−	0.785164i	$-0.287421\pi$
$739$	33.6701	1.23858	0.619288	+	0.785164i	$0.287421\pi$
$740$	48.8402	1.79540
$741$	0.603661	0.0221760
$742$	−84.5851	−3.10522
$743$	−18.9673	−0.695843	−0.347921	−	0.937524i	$-0.613112\pi$
$743$	−18.9673	−0.695843	−0.347921	+	0.937524i	$0.613112\pi$
$744$	−21.9131	−0.803374
$745$	65.3681	2.39490
$746$	32.8323	1.20208
$747$	−1.79638	−0.0657259
$748$	−10.0107	−0.366029
$749$	3.19178	0.116625
$750$	11.8269	0.431856
$751$	−1.06184	−0.0387470	−0.0193735	−	0.999812i	$-0.506167\pi$
$751$	−1.06184	−0.0387470	−0.0193735	+	0.999812i	$0.506167\pi$
$752$	−0.945999	−0.0344970
$753$	−6.49386	−0.236650
$754$	6.69064	0.243659
$755$	49.9471	1.81776
$756$	−12.1139	−0.440579
$757$	−14.5206	−0.527761	−0.263880	−	0.964555i	$-0.585002\pi$
$757$	−14.5206	−0.527761	−0.263880	+	0.964555i	$0.585002\pi$
$758$	59.4587	2.15964
$759$	0.489865	0.0177810
$760$	−1.89205	−0.0686320
$761$	−40.3345	−1.46213	−0.731063	−	0.682310i	$-0.760975\pi$
$761$	−40.3345	−1.46213	−0.731063	+	0.682310i	$0.760975\pi$
$762$	−13.7778	−0.499118
$763$	−10.1493	−0.367428
$764$	−4.96763	−0.179723
$765$	17.4167	0.629703
$766$	−41.6600	−1.50524
$767$	29.4725	1.06419
$768$	19.6064	0.707485
$769$	−10.0707	−0.363158	−0.181579	−	0.983376i	$-0.558121\pi$
$769$	−10.0707	−0.363158	−0.181579	+	0.983376i	$0.558121\pi$
$770$	11.7132	0.422113
$771$	−15.0388	−0.541611
$772$	−51.1634	−1.84141
$773$	40.1438	1.44387	0.721937	−	0.691959i	$-0.243252\pi$
$773$	40.1438	1.44387	0.721937	+	0.691959i	$0.243252\pi$
$774$	−17.4213	−0.626197
$775$	−22.3314	−0.802167
$776$	−16.3650	−0.587468
$777$	18.2394	0.654337
$778$	54.1422	1.94109
$779$	−1.93983	−0.0695017
$780$	27.8586	0.997500
$781$	1.32218	0.0473115
$782$	−14.0702	−0.503148
$783$	1.00000	0.0357371
$784$	3.50612	0.125219
$785$	−26.3285	−0.939703
$786$	20.2556	0.722494
$787$	−1.18087	−0.0420933	−0.0210467	−	0.999778i	$-0.506700\pi$
$787$	−1.18087	−0.0420933	−0.0210467	+	0.999778i	$0.506700\pi$
$788$	−8.64898	−0.308107
$789$	18.5844	0.661624
$790$	52.1846	1.85664
$791$	−58.7957	−2.09053
$792$	−1.54721	−0.0549776
$793$	−27.5994	−0.980084
$794$	−79.0029	−2.80371
$795$	29.0737	1.03114
$796$	−52.8228	−1.87225
$797$	−27.8099	−0.985077	−0.492538	−	0.870291i	$-0.663931\pi$
$797$	−27.8099	−0.985077	−0.492538	+	0.870291i	$0.663931\pi$
$798$	−1.74283	−0.0616955
$799$	9.78501	0.346169
$800$	15.9538	0.564053
$801$	−7.62479	−0.269409
$802$	11.3586	0.401088
$803$	−2.27966	−0.0804475
$804$	40.7366	1.43667
$805$	10.3243	0.363885
$806$	46.4196	1.63506
$807$	10.7377	0.377983
$808$	43.2744	1.52239
$809$	1.32667	0.0466432	0.0233216	−	0.999728i	$-0.492576\pi$
$809$	1.32667	0.0466432	0.0233216	+	0.999728i	$0.492576\pi$
$810$	6.63952	0.233289
$811$	−17.3003	−0.607497	−0.303748	−	0.952752i	$-0.598238\pi$
$811$	−17.3003	−0.607497	−0.303748	+	0.952752i	$0.598238\pi$
$812$	−12.1139	−0.425116
$813$	−2.66418	−0.0934369
$814$	5.74596	0.201396
$815$	−45.6836	−1.60023
$816$	3.56828	0.124915
$817$	−1.57183	−0.0549915
$818$	14.2188	0.497147
$819$	10.4038	0.363540
$820$	−89.5222	−3.12625
$821$	6.86557	0.239610	0.119805	−	0.992797i	$-0.461773\pi$
$821$	6.86557	0.239610	0.119805	+	0.992797i	$0.461773\pi$
$822$	−11.2990	−0.394098
$823$	12.8510	0.447959	0.223980	−	0.974594i	$-0.428095\pi$
$823$	12.8510	0.447959	0.223980	+	0.974594i	$0.428095\pi$
$824$	−42.7368	−1.48881
$825$	−1.57674	−0.0548950
$826$	−85.0900	−2.96066
$827$	26.4853	0.920983	0.460491	−	0.887664i	$-0.347673\pi$
$827$	26.4853	0.920983	0.460491	+	0.887664i	$0.347673\pi$
$828$	−3.36376	−0.116899
$829$	29.5767	1.02724	0.513621	−	0.858017i	$-0.328304\pi$
$829$	29.5767	1.02724	0.513621	+	0.858017i	$0.328304\pi$
$830$	−11.9271	−0.413994
$831$	−17.2762	−0.599304
$832$	−36.5563	−1.26736
$833$	−36.2658	−1.25654
$834$	19.2561	0.666784
$835$	−60.6142	−2.09764
$836$	−0.344319	−0.0119085
$837$	6.93798	0.239812
$838$	−3.38488	−0.116929
$839$	18.3216	0.632531	0.316265	−	0.948671i	$-0.397571\pi$
$839$	18.3216	0.632531	0.316265	+	0.948671i	$0.397571\pi$
$840$	−32.6087	−1.12511
$841$	1.00000	0.0344828
$842$	−75.9348	−2.61688
$843$	26.7094	0.919920
$844$	−78.7375	−2.71026
$845$	13.3429	0.459008
$846$	3.73019	0.128247
$847$	−38.7502	−1.33147
$848$	5.95653	0.204548
$849$	−25.3486	−0.869963
$850$	45.2879	1.55336
$851$	5.06467	0.173615
$852$	−9.07904	−0.311043
$853$	36.3737	1.24541	0.622706	−	0.782456i	$-0.286033\pi$
$853$	36.3737	1.24541	0.622706	+	0.782456i	$0.286033\pi$
$854$	79.6822	2.72667
$855$	0.599048	0.0204870
$856$	−2.79927	−0.0956769
$857$	12.8909	0.440344	0.220172	−	0.975461i	$-0.429338\pi$
$857$	12.8909	0.440344	0.220172	+	0.975461i	$0.429338\pi$
$858$	3.27752	0.111893
$859$	13.1919	0.450102	0.225051	−	0.974347i	$-0.427745\pi$
$859$	13.1919	0.450102	0.225051	+	0.974347i	$0.427745\pi$
$860$	−72.5393	−2.47357
$861$	−33.4322	−1.13937
$862$	62.9417	2.14380
$863$	−22.4029	−0.762603	−0.381302	−	0.924451i	$-0.624524\pi$
$863$	−22.4029	−0.762603	−0.381302	+	0.924451i	$0.624524\pi$
$864$	−4.95658	−0.168626
$865$	−38.7462	−1.31741
$866$	−71.0253	−2.41354
$867$	−19.9087	−0.676136
$868$	−84.0462	−2.85271
$869$	3.85019	0.130609
$870$	6.63952	0.225101
$871$	−34.9859	−1.18545
$872$	8.90113	0.301430
$873$	5.18136	0.175362
$874$	−0.483943	−0.0163696
$875$	18.3906	0.621715
$876$	15.6537	0.528891
$877$	24.5509	0.829024	0.414512	−	0.910044i	$-0.363952\pi$
$877$	24.5509	0.829024	0.414512	+	0.910044i	$0.363952\pi$
$878$	−8.11644	−0.273917
$879$	5.13931	0.173345
$880$	−0.824846	−0.0278056
$881$	−31.0084	−1.04470	−0.522350	−	0.852731i	$-0.674944\pi$
$881$	−31.0084	−1.04470	−0.522350	+	0.852731i	$0.674944\pi$
$882$	−13.8251	−0.465514
$883$	38.3023	1.28898	0.644488	−	0.764615i	$-0.277071\pi$
$883$	38.3023	1.28898	0.644488	+	0.764615i	$0.277071\pi$
$884$	−59.0368	−1.98562
$885$	29.2473	0.983136
$886$	13.6943	0.460068
$887$	−1.22792	−0.0412294	−0.0206147	−	0.999787i	$-0.506562\pi$
$887$	−1.22792	−0.0412294	−0.0206147	+	0.999787i	$0.506562\pi$
$888$	−15.9964	−0.536805
$889$	−21.4243	−0.718548
$890$	−50.6250	−1.69695
$891$	0.489865	0.0164111
$892$	−52.9489	−1.77286
$893$	0.336555	0.0112624
$894$	−52.8079	−1.76616
$895$	21.2736	0.711098
$896$	69.8413	2.33323
$897$	2.88891	0.0964578
$898$	−52.9723	−1.76771
$899$	6.93798	0.231395
$900$	10.8270	0.360899
$901$	−61.6117	−2.05258
$902$	−10.5321	−0.350681
$903$	−27.0899	−0.901495
$904$	51.5652	1.71503
$905$	−12.3884	−0.411806
$906$	−40.3500	−1.34054
$907$	−46.6379	−1.54859	−0.774293	−	0.632828i	$-0.781894\pi$
$907$	−46.6379	−1.54859	−0.774293	+	0.632828i	$0.781894\pi$
$908$	−74.0781	−2.45837
$909$	−13.7012	−0.454441
$910$	69.0765	2.28986
$911$	14.2047	0.470623	0.235311	−	0.971920i	$-0.424389\pi$
$911$	14.2047	0.470623	0.235311	+	0.971920i	$0.424389\pi$
$912$	0.122731	0.00406403
$913$	−0.879982	−0.0291232
$914$	−38.2712	−1.26590
$915$	−27.3885	−0.905436
$916$	−54.3400	−1.79544
$917$	31.4971	1.04013
$918$	−14.0702	−0.464385
$919$	27.6942	0.913546	0.456773	−	0.889583i	$-0.349005\pi$
$919$	27.6942	0.913546	0.456773	+	0.889583i	$0.349005\pi$
$920$	−9.05469	−0.298524
$921$	−19.5783	−0.645125
$922$	15.3794	0.506493
$923$	7.79738	0.256654
$924$	−5.93419	−0.195221
$925$	−16.3017	−0.535998
$926$	43.3489	1.42453
$927$	13.5310	0.444417
$928$	−4.95658	−0.162708
$929$	−31.4646	−1.03232	−0.516160	−	0.856492i	$-0.672639\pi$
$929$	−31.4646	−1.03232	−0.516160	+	0.856492i	$0.672639\pi$
$930$	46.0648	1.51053
$931$	−1.24736	−0.0408806
$932$	−63.5082	−2.08028
$933$	34.2429	1.12106
$934$	−17.9341	−0.586822
$935$	8.53185	0.279021
$936$	−9.12441	−0.298241
$937$	−42.5528	−1.39014	−0.695070	−	0.718942i	$-0.744627\pi$
$937$	−42.5528	−1.39014	−0.695070	+	0.718942i	$0.744627\pi$
$938$	101.008	3.29802
$939$	6.49992	0.212117
$940$	15.5319	0.506593
$941$	−53.6015	−1.74736	−0.873680	−	0.486501i	$-0.838273\pi$
$941$	−53.6015	−1.74736	−0.873680	+	0.486501i	$0.838273\pi$
$942$	21.2695	0.692999
$943$	−9.28334	−0.302307
$944$	5.99208	0.195026
$945$	10.3243	0.335851
$946$	−8.53411	−0.277468
$947$	6.75896	0.219637	0.109818	−	0.993952i	$-0.464973\pi$
$947$	6.75896	0.219637	0.109818	+	0.993952i	$0.464973\pi$
$948$	−26.4381	−0.858670
$949$	−13.4440	−0.436409
$950$	1.55768	0.0505377
$951$	15.0420	0.487770
$952$	69.1029	2.23964
$953$	−2.12857	−0.0689513	−0.0344756	−	0.999406i	$-0.510976\pi$
$953$	−2.12857	−0.0689513	−0.0344756	+	0.999406i	$0.510976\pi$
$954$	−23.4873	−0.760430
$955$	4.23377	0.137001
$956$	−46.4860	−1.50347
$957$	0.489865	0.0158351
$958$	−44.9877	−1.45349
$959$	−17.5697	−0.567357
$960$	−36.2770	−1.17083
$961$	17.1356	0.552760
$962$	33.8859	1.09253
$963$	0.886283	0.0285601
$964$	−13.7056	−0.441426
$965$	43.6051	1.40370
$966$	−8.34055	−0.268353
$967$	49.9771	1.60715	0.803577	−	0.595201i	$-0.202928\pi$
$967$	49.9771	1.60715	0.803577	+	0.595201i	$0.202928\pi$
$968$	33.9848	1.09231
$969$	−1.26948	−0.0407814
$970$	34.4017	1.10457
$971$	3.70618	0.118937	0.0594684	−	0.998230i	$-0.481059\pi$
$971$	3.70618	0.118937	0.0594684	+	0.998230i	$0.481059\pi$
$972$	−3.36376	−0.107893
$973$	29.9429	0.959926
$974$	−24.7389	−0.792685
$975$	−9.29857	−0.297793
$976$	−5.61126	−0.179612
$977$	36.6110	1.17129	0.585645	−	0.810568i	$-0.300841\pi$
$977$	36.6110	1.17129	0.585645	+	0.810568i	$0.300841\pi$
$978$	36.9057	1.18011
$979$	−3.73512	−0.119375
$980$	−57.5651	−1.83885
$981$	−2.81821	−0.0899786
$982$	−4.41779	−0.140977
$983$	−2.20529	−0.0703378	−0.0351689	−	0.999381i	$-0.511197\pi$
$983$	−2.20529	−0.0703378	−0.0351689	+	0.999381i	$0.511197\pi$
$984$	29.3208	0.934713
$985$	7.37127	0.234868
$986$	−14.0702	−0.448085
$987$	5.80039	0.184628
$988$	−2.03057	−0.0646010
$989$	−7.52223	−0.239193
$990$	3.25247	0.103370
$991$	−29.6667	−0.942394	−0.471197	−	0.882028i	$-0.656178\pi$
$991$	−29.6667	−0.942394	−0.471197	+	0.882028i	$0.656178\pi$
$992$	−34.3887	−1.09184
$993$	2.36598	0.0750820
$994$	−22.5118	−0.714031
$995$	45.0193	1.42721
$996$	6.04257	0.191466
$997$	26.9367	0.853094	0.426547	−	0.904465i	$-0.359730\pi$
$997$	26.9367	0.853094	0.426547	+	0.904465i	$0.359730\pi$
$998$	30.6155	0.969116
$999$	5.06467	0.160239

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2001.2.a.m.1.2	✓	14
3.2	odd	2		6003.2.a.p.1.13		14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2001.2.a.m.1.2	✓	14	1.1	even	1	trivial
6003.2.a.p.1.13		14	3.2	odd	2

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:	\( N \)	\(=\)	\( 2001 = 3 \cdot 23 \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2001.a (trivial)

\(f(q)\)	\(=\)	\(q-2.31598 q^{2} -1.00000 q^{3} +3.36376 q^{4} -2.86683 q^{5} +2.31598 q^{6} +3.60131 q^{7} -3.15843 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-2.31598 q^{2} -1.00000 q^{3} +3.36376 q^{4} -2.86683 q^{5} +2.31598 q^{6} +3.60131 q^{7} -3.15843 q^{8} +1.00000 q^{9} +6.63952 q^{10} +0.489865 q^{11} -3.36376 q^{12} +2.88891 q^{13} -8.34055 q^{14} +2.86683 q^{15} +0.587346 q^{16} -6.07526 q^{17} -2.31598 q^{18} -0.208958 q^{19} -9.64332 q^{20} -3.60131 q^{21} -1.13452 q^{22} -1.00000 q^{23} +3.15843 q^{24} +3.21872 q^{25} -6.69064 q^{26} -1.00000 q^{27} +12.1139 q^{28} -1.00000 q^{29} -6.63952 q^{30} -6.93798 q^{31} +4.95658 q^{32} -0.489865 q^{33} +14.0702 q^{34} -10.3243 q^{35} +3.36376 q^{36} -5.06467 q^{37} +0.483943 q^{38} -2.88891 q^{39} +9.05469 q^{40} +9.28334 q^{41} +8.34055 q^{42} +7.52223 q^{43} +1.64779 q^{44} -2.86683 q^{45} +2.31598 q^{46} -1.61063 q^{47} -0.587346 q^{48} +5.96943 q^{49} -7.45448 q^{50} +6.07526 q^{51} +9.71758 q^{52} +10.1414 q^{53} +2.31598 q^{54} -1.40436 q^{55} -11.3745 q^{56} +0.208958 q^{57} +2.31598 q^{58} +10.2020 q^{59} +9.64332 q^{60} -9.55359 q^{61} +16.0682 q^{62} +3.60131 q^{63} -12.6540 q^{64} -8.28200 q^{65} +1.13452 q^{66} -12.1104 q^{67} -20.4357 q^{68} +1.00000 q^{69} +23.9110 q^{70} +2.69908 q^{71} -3.15843 q^{72} -4.65365 q^{73} +11.7297 q^{74} -3.21872 q^{75} -0.702885 q^{76} +1.76416 q^{77} +6.69064 q^{78} +7.85970 q^{79} -1.68382 q^{80} +1.00000 q^{81} -21.5000 q^{82} -1.79638 q^{83} -12.1139 q^{84} +17.4167 q^{85} -17.4213 q^{86} +1.00000 q^{87} -1.54721 q^{88} -7.62479 q^{89} +6.63952 q^{90} +10.4038 q^{91} -3.36376 q^{92} +6.93798 q^{93} +3.73019 q^{94} +0.599048 q^{95} -4.95658 q^{96} +5.18136 q^{97} -13.8251 q^{98} +0.489865 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q - 2 q^{2} - 14 q^{3} + 12 q^{4} - 3 q^{5} + 2 q^{6} - 3 q^{7} - 6 q^{8} + 14 q^{9}+O(q^{10}) \) 14 * q - 2 * q^2 - 14 * q^3 + 12 * q^4 - 3 * q^5 + 2 * q^6 - 3 * q^7 - 6 * q^8 + 14 * q^9	\( 14 q - 2 q^{2} - 14 q^{3} + 12 q^{4} - 3 q^{5} + 2 q^{6} - 3 q^{7} - 6 q^{8} + 14 q^{9} - 5 q^{10} - 12 q^{11} - 12 q^{12} + 13 q^{13} - 9 q^{14} + 3 q^{15} - 14 q^{17} - 2 q^{18} - 9 q^{19} - 2 q^{20} + 3 q^{21} - 9 q^{22} - 14 q^{23} + 6 q^{24} + 13 q^{25} - 16 q^{26} - 14 q^{27} + 3 q^{28} - 14 q^{29} + 5 q^{30} - 28 q^{31} - 4 q^{32} + 12 q^{33} + 14 q^{34} - 9 q^{35} + 12 q^{36} - 12 q^{37} + 2 q^{38} - 13 q^{39} - 20 q^{40} - 25 q^{41} + 9 q^{42} + 5 q^{43} - 37 q^{44} - 3 q^{45} + 2 q^{46} - 17 q^{47} + 17 q^{49} - 44 q^{50} + 14 q^{51} + 25 q^{52} - 17 q^{53} + 2 q^{54} + q^{55} - 54 q^{56} + 9 q^{57} + 2 q^{58} - 18 q^{59} + 2 q^{60} - 13 q^{61} - 8 q^{62} - 3 q^{63} + 20 q^{64} - 16 q^{65} + 9 q^{66} + 2 q^{67} - 19 q^{68} + 14 q^{69} + 14 q^{70} - 55 q^{71} - 6 q^{72} + 19 q^{73} + 4 q^{74} - 13 q^{75} - 32 q^{76} - 19 q^{77} + 16 q^{78} - 68 q^{79} - 2 q^{80} + 14 q^{81} - 12 q^{82} - 21 q^{83} - 3 q^{84} + 16 q^{85} - 22 q^{86} + 14 q^{87} - 25 q^{88} - 17 q^{89} - 5 q^{90} - 30 q^{91} - 12 q^{92} + 28 q^{93} + 16 q^{94} - 55 q^{95} + 4 q^{96} + 25 q^{97} - 31 q^{98} - 12 q^{99}+O(q^{100}) \) 14 * q - 2 * q^2 - 14 * q^3 + 12 * q^4 - 3 * q^5 + 2 * q^6 - 3 * q^7 - 6 * q^8 + 14 * q^9 - 5 * q^10 - 12 * q^11 - 12 * q^12 + 13 * q^13 - 9 * q^14 + 3 * q^15 - 14 * q^17 - 2 * q^18 - 9 * q^19 - 2 * q^20 + 3 * q^21 - 9 * q^22 - 14 * q^23 + 6 * q^24 + 13 * q^25 - 16 * q^26 - 14 * q^27 + 3 * q^28 - 14 * q^29 + 5 * q^30 - 28 * q^31 - 4 * q^32 + 12 * q^33 + 14 * q^34 - 9 * q^35 + 12 * q^36 - 12 * q^37 + 2 * q^38 - 13 * q^39 - 20 * q^40 - 25 * q^41 + 9 * q^42 + 5 * q^43 - 37 * q^44 - 3 * q^45 + 2 * q^46 - 17 * q^47 + 17 * q^49 - 44 * q^50 + 14 * q^51 + 25 * q^52 - 17 * q^53 + 2 * q^54 + q^55 - 54 * q^56 + 9 * q^57 + 2 * q^58 - 18 * q^59 + 2 * q^60 - 13 * q^61 - 8 * q^62 - 3 * q^63 + 20 * q^64 - 16 * q^65 + 9 * q^66 + 2 * q^67 - 19 * q^68 + 14 * q^69 + 14 * q^70 - 55 * q^71 - 6 * q^72 + 19 * q^73 + 4 * q^74 - 13 * q^75 - 32 * q^76 - 19 * q^77 + 16 * q^78 - 68 * q^79 - 2 * q^80 + 14 * q^81 - 12 * q^82 - 21 * q^83 - 3 * q^84 + 16 * q^85 - 22 * q^86 + 14 * q^87 - 25 * q^88 - 17 * q^89 - 5 * q^90 - 30 * q^91 - 12 * q^92 + 28 * q^93 + 16 * q^94 - 55 * q^95 + 4 * q^96 + 25 * q^97 - 31 * q^98 - 12 * q^99

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