LMFDB - Embedded newform 2001.2.a.n.1.15

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:	$0$
Dimension:	$16$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - x^{15} - 28 x^{14} + 27 x^{13} + 316 x^{12} - 295 x^{11} - 1835 x^{10} + 1665 x^{9} + \cdots - 192 $ x^16 - x^15 - 28x^14 + 27x^13 + 316x^12 - 295x^11 - 1835x^10 + 1665x^9 + 5778x^8 - 5124x^7 - 9405x^6 + 8288x^5 + 6405x^4 - 6032x^3 - 400x^2 + 1088x - 192
Coefficient ring:	$\Z[a_1, \ldots, a_{17}]$
Coefficient ring index:	$ 2^{5} $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.15
Root			$-2.50224$ 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)

$f(q)$	$=$	$q+2.50224 q^{2} +1.00000 q^{3} +4.26120 q^{4} +0.499377 q^{5} +2.50224 q^{6} +0.377265 q^{7} +5.65806 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+2.50224 q^{2} +1.00000 q^{3} +4.26120 q^{4} +0.499377 q^{5} +2.50224 q^{6} +0.377265 q^{7} +5.65806 q^{8} +1.00000 q^{9} +1.24956 q^{10} +0.280990 q^{11} +4.26120 q^{12} +2.81091 q^{13} +0.944007 q^{14} +0.499377 q^{15} +5.63543 q^{16} +3.47193 q^{17} +2.50224 q^{18} -3.13228 q^{19} +2.12795 q^{20} +0.377265 q^{21} +0.703104 q^{22} -1.00000 q^{23} +5.65806 q^{24} -4.75062 q^{25} +7.03357 q^{26} +1.00000 q^{27} +1.60760 q^{28} -1.00000 q^{29} +1.24956 q^{30} -8.49306 q^{31} +2.78506 q^{32} +0.280990 q^{33} +8.68760 q^{34} +0.188397 q^{35} +4.26120 q^{36} -3.30358 q^{37} -7.83770 q^{38} +2.81091 q^{39} +2.82551 q^{40} -3.07528 q^{41} +0.944007 q^{42} +6.93400 q^{43} +1.19735 q^{44} +0.499377 q^{45} -2.50224 q^{46} +1.62857 q^{47} +5.63543 q^{48} -6.85767 q^{49} -11.8872 q^{50} +3.47193 q^{51} +11.9779 q^{52} +5.80717 q^{53} +2.50224 q^{54} +0.140320 q^{55} +2.13459 q^{56} -3.13228 q^{57} -2.50224 q^{58} +4.19192 q^{59} +2.12795 q^{60} +14.5885 q^{61} -21.2517 q^{62} +0.377265 q^{63} -4.30197 q^{64} +1.40370 q^{65} +0.703104 q^{66} +6.61416 q^{67} +14.7946 q^{68} -1.00000 q^{69} +0.471415 q^{70} -8.99710 q^{71} +5.65806 q^{72} -3.65881 q^{73} -8.26635 q^{74} -4.75062 q^{75} -13.3473 q^{76} +0.106008 q^{77} +7.03357 q^{78} +10.1301 q^{79} +2.81420 q^{80} +1.00000 q^{81} -7.69509 q^{82} +14.4012 q^{83} +1.60760 q^{84} +1.73380 q^{85} +17.3505 q^{86} -1.00000 q^{87} +1.58986 q^{88} -15.5648 q^{89} +1.24956 q^{90} +1.06046 q^{91} -4.26120 q^{92} -8.49306 q^{93} +4.07507 q^{94} -1.56419 q^{95} +2.78506 q^{96} +0.680933 q^{97} -17.1595 q^{98} +0.280990 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - q^{2} + 16 q^{3} + 25 q^{4} + 3 q^{5} - q^{6} + 13 q^{7} + 16 q^{9}+O(q^{10}) $ 16 * q - q^2 + 16 * q^3 + 25 * q^4 + 3 * q^5 - q^6 + 13 * q^7 + 16 * q^9	\( 16 q - q^{2} + 16 q^{3} + 25 q^{4} + 3 q^{5} - q^{6} + 13 q^{7} + 16 q^{9} + 11 q^{10} + 8 q^{11} + 25 q^{12} + 19 q^{13} + 16 q^{14} + 3 q^{15} + 31 q^{16} - 4 q^{17} - q^{18} + 19 q^{19} + 16 q^{20} + 13 q^{21} + 6 q^{22} - 16 q^{23} + 23 q^{25} - 15 q^{26} + 16 q^{27} + 18 q^{28} - 16 q^{29} + 11 q^{30} + 24 q^{31} - 21 q^{32} + 8 q^{33} - 9 q^{34} - 13 q^{35} + 25 q^{36} + 26 q^{37} + 19 q^{39} - 22 q^{40} - 15 q^{41} + 16 q^{42} + 33 q^{43} + 6 q^{44} + 3 q^{45} + q^{46} + 13 q^{47} + 31 q^{48} + 41 q^{49} + 13 q^{50} - 4 q^{51} - 26 q^{52} + 5 q^{53} - q^{54} + 9 q^{55} + 40 q^{56} + 19 q^{57} + q^{58} + 2 q^{59} + 16 q^{60} + 29 q^{61} - 32 q^{62} + 13 q^{63} + 28 q^{64} + 18 q^{65} + 6 q^{66} + 32 q^{67} - 26 q^{68} - 16 q^{69} + 18 q^{70} + 29 q^{71} + 19 q^{73} - 16 q^{74} + 23 q^{75} + 64 q^{76} - 21 q^{77} - 15 q^{78} + 56 q^{79} + 16 q^{81} + 14 q^{82} + 5 q^{83} + 18 q^{84} + 16 q^{85} - 20 q^{86} - 16 q^{87} + q^{88} + 7 q^{89} + 11 q^{90} - 6 q^{91} - 25 q^{92} + 24 q^{93} - 11 q^{94} + 39 q^{95} - 21 q^{96} + 35 q^{97} - 109 q^{98} + 8 q^{99}+O(q^{100}) \) 16 * q - q^2 + 16 * q^3 + 25 * q^4 + 3 * q^5 - q^6 + 13 * q^7 + 16 * q^9 + 11 * q^10 + 8 * q^11 + 25 * q^12 + 19 * q^13 + 16 * q^14 + 3 * q^15 + 31 * q^16 - 4 * q^17 - q^18 + 19 * q^19 + 16 * q^20 + 13 * q^21 + 6 * q^22 - 16 * q^23 + 23 * q^25 - 15 * q^26 + 16 * q^27 + 18 * q^28 - 16 * q^29 + 11 * q^30 + 24 * q^31 - 21 * q^32 + 8 * q^33 - 9 * q^34 - 13 * q^35 + 25 * q^36 + 26 * q^37 + 19 * q^39 - 22 * q^40 - 15 * q^41 + 16 * q^42 + 33 * q^43 + 6 * q^44 + 3 * q^45 + q^46 + 13 * q^47 + 31 * q^48 + 41 * q^49 + 13 * q^50 - 4 * q^51 - 26 * q^52 + 5 * q^53 - q^54 + 9 * q^55 + 40 * q^56 + 19 * q^57 + q^58 + 2 * q^59 + 16 * q^60 + 29 * q^61 - 32 * q^62 + 13 * q^63 + 28 * q^64 + 18 * q^65 + 6 * q^66 + 32 * q^67 - 26 * q^68 - 16 * q^69 + 18 * q^70 + 29 * q^71 + 19 * q^73 - 16 * q^74 + 23 * q^75 + 64 * q^76 - 21 * q^77 - 15 * q^78 + 56 * q^79 + 16 * q^81 + 14 * q^82 + 5 * q^83 + 18 * q^84 + 16 * q^85 - 20 * q^86 - 16 * q^87 + q^88 + 7 * q^89 + 11 * q^90 - 6 * q^91 - 25 * q^92 + 24 * q^93 - 11 * q^94 + 39 * q^95 - 21 * q^96 + 35 * q^97 - 109 * q^98 + 8 * 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 $

$2$	2.50224	1.76935	0.884675	−	0.466208i	$-0.154380\pi$
$2$	2.50224	1.76935	0.884675	+	0.466208i	$0.154380\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	4.26120	2.13060
$5$	0.499377	0.223328	0.111664	−	0.993746i	$-0.464382\pi$
$5$	0.499377	0.223328	0.111664	+	0.993746i	$0.464382\pi$
$6$	2.50224	1.02153
$7$	0.377265	0.142593	0.0712963	−	0.997455i	$-0.477286\pi$
$7$	0.377265	0.142593	0.0712963	+	0.997455i	$0.477286\pi$
$8$	5.65806	2.00043
$9$	1.00000	0.333333
$10$	1.24956	0.395146
$11$	0.280990	0.0847216	0.0423608	−	0.999102i	$-0.486512\pi$
$11$	0.280990	0.0847216	0.0423608	+	0.999102i	$0.486512\pi$
$12$	4.26120	1.23010
$13$	2.81091	0.779606	0.389803	−	0.920898i	$-0.372543\pi$
$13$	2.81091	0.779606	0.389803	+	0.920898i	$0.372543\pi$
$14$	0.944007	0.252296
$15$	0.499377	0.128939
$16$	5.63543	1.40886
$17$	3.47193	0.842067	0.421033	−	0.907045i	$-0.361667\pi$
$17$	3.47193	0.842067	0.421033	+	0.907045i	$0.361667\pi$
$18$	2.50224	0.589783
$19$	−3.13228	−0.718593	−0.359297	−	0.933223i	$-0.616983\pi$
$19$	−3.13228	−0.718593	−0.359297	+	0.933223i	$0.616983\pi$
$20$	2.12795	0.475823
$21$	0.377265	0.0823259
$22$	0.703104	0.149902
$23$	−1.00000	−0.208514
$23$	−1.00000	−0.208514
$24$	5.65806	1.15495
$25$	−4.75062	−0.950124
$26$	7.03357	1.37940
$27$	1.00000	0.192450
$28$	1.60760	0.303808
$29$	−1.00000	−0.185695
$29$	−1.00000	−0.185695
$30$	1.24956	0.228138
$31$	−8.49306	−1.52540	−0.762700	−	0.646753i	$-0.776127\pi$
$31$	−8.49306	−1.52540	−0.762700	+	0.646753i	$0.776127\pi$
$32$	2.78506	0.492334
$33$	0.280990	0.0489141
$34$	8.68760	1.48991
$35$	0.188397	0.0318450
$36$	4.26120	0.710200
$37$	−3.30358	−0.543106	−0.271553	−	0.962424i	$-0.587537\pi$
$37$	−3.30358	−0.543106	−0.271553	+	0.962424i	$0.587537\pi$
$38$	−7.83770	−1.27144
$39$	2.81091	0.450106
$40$	2.82551	0.446752
$41$	−3.07528	−0.480278	−0.240139	−	0.970739i	$-0.577193\pi$
$41$	−3.07528	−0.480278	−0.240139	+	0.970739i	$0.577193\pi$
$42$	0.944007	0.145663
$43$	6.93400	1.05743	0.528713	−	0.848801i	$-0.322675\pi$
$43$	6.93400	1.05743	0.528713	+	0.848801i	$0.322675\pi$
$44$	1.19735	0.180508
$45$	0.499377	0.0744427
$46$	−2.50224	−0.368935
$47$	1.62857	0.237551	0.118776	−	0.992921i	$-0.462103\pi$
$47$	1.62857	0.237551	0.118776	+	0.992921i	$0.462103\pi$
$48$	5.63543	0.813404
$49$	−6.85767	−0.979667
$50$	−11.8872	−1.68110
$51$	3.47193	0.486168
$52$	11.9779	1.66103
$53$	5.80717	0.797676	0.398838	−	0.917021i	$-0.369414\pi$
$53$	5.80717	0.797676	0.398838	+	0.917021i	$0.369414\pi$
$54$	2.50224	0.340512
$55$	0.140320	0.0189207
$56$	2.13459	0.285246
$57$	−3.13228	−0.414880
$58$	−2.50224	−0.328560
$59$	4.19192	0.545742	0.272871	−	0.962051i	$-0.412027\pi$
$59$	4.19192	0.545742	0.272871	+	0.962051i	$0.412027\pi$
$60$	2.12795	0.274717
$61$	14.5885	1.86786	0.933932	−	0.357451i	$-0.116354\pi$
$61$	14.5885	1.86786	0.933932	+	0.357451i	$0.116354\pi$
$62$	−21.2517	−2.69897
$63$	0.377265	0.0475309
$64$	−4.30197	−0.537746
$65$	1.40370	0.174108
$66$	0.703104	0.0865461
$67$	6.61416	0.808048	0.404024	−	0.914748i	$-0.367611\pi$
$67$	6.61416	0.808048	0.404024	+	0.914748i	$0.367611\pi$
$68$	14.7946	1.79411
$69$	−1.00000	−0.120386
$70$	0.471415	0.0563449
$71$	−8.99710	−1.06776	−0.533880	−	0.845561i	$-0.679266\pi$
$71$	−8.99710	−1.06776	−0.533880	+	0.845561i	$0.679266\pi$
$72$	5.65806	0.666809
$73$	−3.65881	−0.428231	−0.214115	−	0.976808i	$-0.568687\pi$
$73$	−3.65881	−0.428231	−0.214115	+	0.976808i	$0.568687\pi$
$74$	−8.26635	−0.960944
$75$	−4.75062	−0.548555
$76$	−13.3473	−1.53104
$77$	0.106008	0.0120807
$78$	7.03357	0.796395
$79$	10.1301	1.13973	0.569865	−	0.821738i	$-0.306995\pi$
$79$	10.1301	1.13973	0.569865	+	0.821738i	$0.306995\pi$
$80$	2.81420	0.314638
$81$	1.00000	0.111111
$82$	−7.69509	−0.849780
$83$	14.4012	1.58073	0.790367	−	0.612633i	$-0.209890\pi$
$83$	14.4012	1.58073	0.790367	+	0.612633i	$0.209890\pi$
$84$	1.60760	0.175404
$85$	1.73380	0.188057
$86$	17.3505	1.87096
$87$	−1.00000	−0.107211
$88$	1.58986	0.169480
$89$	−15.5648	−1.64987	−0.824933	−	0.565230i	$-0.808787\pi$
$89$	−15.5648	−1.64987	−0.824933	+	0.565230i	$0.808787\pi$
$90$	1.24956	0.131715
$91$	1.06046	0.111166
$92$	−4.26120	−0.444261
$93$	−8.49306	−0.880690
$94$	4.07507	0.420311
$95$	−1.56419	−0.160482
$96$	2.78506	0.284249
$97$	0.680933	0.0691383	0.0345691	−	0.999402i	$-0.488994\pi$
$97$	0.680933	0.0691383	0.0345691	+	0.999402i	$0.488994\pi$
$98$	−17.1595	−1.73337
$99$	0.280990	0.0282405
$100$	−20.2434	−2.02434
$101$	−3.18551	−0.316970	−0.158485	−	0.987361i	$-0.550661\pi$
$101$	−3.18551	−0.316970	−0.158485	+	0.987361i	$0.550661\pi$
$102$	8.68760	0.860201
$103$	−10.4798	−1.03261	−0.516305	−	0.856405i	$-0.672693\pi$
$103$	−10.4798	−1.03261	−0.516305	+	0.856405i	$0.672693\pi$
$104$	15.9043	1.55955
$105$	0.188397	0.0183857
$106$	14.5309	1.41137
$107$	6.58541	0.636636	0.318318	−	0.947984i	$-0.396882\pi$
$107$	6.58541	0.636636	0.318318	+	0.947984i	$0.396882\pi$
$108$	4.26120	0.410034
$109$	0.159462	0.0152737	0.00763685	−	0.999971i	$-0.497569\pi$
$109$	0.159462	0.0152737	0.00763685	+	0.999971i	$0.497569\pi$
$110$	0.351114	0.0334774
$111$	−3.30358	−0.313562
$112$	2.12605	0.200893
$113$	−15.4677	−1.45508	−0.727538	−	0.686067i	$-0.759336\pi$
$113$	−15.4677	−1.45508	−0.727538	+	0.686067i	$0.759336\pi$
$114$	−7.83770	−0.734068
$115$	−0.499377	−0.0465672
$116$	−4.26120	−0.395643
$117$	2.81091	0.259869
$118$	10.4892	0.965609
$119$	1.30984	0.120073
$120$	2.82551	0.257932
$121$	−10.9210	−0.992822
$122$	36.5039	3.30491
$123$	−3.07528	−0.277289
$124$	−36.1906	−3.25002
$125$	−4.86924	−0.435518
$126$	0.944007	0.0840988
$127$	10.3000	0.913977	0.456989	−	0.889473i	$-0.348928\pi$
$127$	10.3000	0.913977	0.456989	+	0.889473i	$0.348928\pi$
$128$	−16.3347	−1.44379
$129$	6.93400	0.610505
$130$	3.51240	0.308058
$131$	−5.86940	−0.512812	−0.256406	−	0.966569i	$-0.582538\pi$
$131$	−5.86940	−0.512812	−0.256406	+	0.966569i	$0.582538\pi$
$132$	1.19735	0.104216
$133$	−1.18170	−0.102466
$134$	16.5502	1.42972
$135$	0.499377	0.0429795
$136$	19.6444	1.68449
$137$	−8.10245	−0.692239	−0.346119	−	0.938190i	$-0.612501\pi$
$137$	−8.10245	−0.692239	−0.346119	+	0.938190i	$0.612501\pi$
$138$	−2.50224	−0.213005
$139$	−0.897029	−0.0760850	−0.0380425	−	0.999276i	$-0.512112\pi$
$139$	−0.897029	−0.0760850	−0.0380425	+	0.999276i	$0.512112\pi$
$140$	0.802799	0.0678489
$141$	1.62857	0.137150
$142$	−22.5129	−1.88924
$143$	0.789837	0.0660495
$144$	5.63543	0.469619
$145$	−0.499377	−0.0414710
$146$	−9.15521	−0.757690
$147$	−6.85767	−0.565611
$148$	−14.0772	−1.15714
$149$	−8.58730	−0.703499	−0.351749	−	0.936094i	$-0.614413\pi$
$149$	−8.58730	−0.703499	−0.351749	+	0.936094i	$0.614413\pi$
$150$	−11.8872	−0.970585
$151$	−19.7857	−1.61013	−0.805067	−	0.593183i	$-0.797871\pi$
$151$	−19.7857	−1.61013	−0.805067	+	0.593183i	$0.797871\pi$
$152$	−17.7226	−1.43749
$153$	3.47193	0.280689
$154$	0.265256	0.0213750
$155$	−4.24124	−0.340665
$156$	11.9779	0.958996
$157$	−1.76040	−0.140495	−0.0702476	−	0.997530i	$-0.522379\pi$
$157$	−1.76040	−0.140495	−0.0702476	+	0.997530i	$0.522379\pi$
$158$	25.3480	2.01658
$159$	5.80717	0.460538
$160$	1.39080	0.109952
$161$	−0.377265	−0.0297326
$162$	2.50224	0.196594
$163$	16.4964	1.29210	0.646048	−	0.763296i	$-0.276420\pi$
$163$	16.4964	1.29210	0.646048	+	0.763296i	$0.276420\pi$
$164$	−13.1044	−1.02328
$165$	0.140320	0.0109239
$166$	36.0352	2.79687
$167$	−21.1152	−1.63394	−0.816970	−	0.576680i	$-0.804348\pi$
$167$	−21.1152	−1.63394	−0.816970	+	0.576680i	$0.804348\pi$
$168$	2.13459	0.164687
$169$	−5.09878	−0.392214
$170$	4.33839	0.332739
$171$	−3.13228	−0.239531
$172$	29.5472	2.25295
$173$	−1.30202	−0.0989910	−0.0494955	−	0.998774i	$-0.515761\pi$
$173$	−1.30202	−0.0989910	−0.0494955	+	0.998774i	$0.515761\pi$
$174$	−2.50224	−0.189694
$175$	−1.79224	−0.135481
$176$	1.58350	0.119361
$177$	4.19192	0.315084
$178$	−38.9469	−2.91919
$179$	5.51022	0.411853	0.205927	−	0.978567i	$-0.433979\pi$
$179$	5.51022	0.411853	0.205927	+	0.978567i	$0.433979\pi$
$180$	2.12795	0.158608
$181$	3.29654	0.245030	0.122515	−	0.992467i	$-0.460904\pi$
$181$	3.29654	0.245030	0.122515	+	0.992467i	$0.460904\pi$
$182$	2.65352	0.196692
$183$	14.5885	1.07841
$184$	−5.65806	−0.417118
$185$	−1.64973	−0.121291
$186$	−21.2517	−1.55825
$187$	0.975578	0.0713413
$188$	6.93966	0.506127
$189$	0.377265	0.0274420
$190$	−3.91397	−0.283949
$191$	−22.1285	−1.60116	−0.800581	−	0.599225i	$-0.795476\pi$
$191$	−22.1285	−1.60116	−0.800581	+	0.599225i	$0.795476\pi$
$192$	−4.30197	−0.310468
$193$	18.7430	1.34915	0.674574	−	0.738207i	$-0.264327\pi$
$193$	18.7430	1.34915	0.674574	+	0.738207i	$0.264327\pi$
$194$	1.70386	0.122330
$195$	1.40370	0.100521
$196$	−29.2219	−2.08728
$197$	16.3147	1.16237	0.581186	−	0.813771i	$-0.302589\pi$
$197$	16.3147	1.16237	0.581186	+	0.813771i	$0.302589\pi$
$198$	0.703104	0.0499674
$199$	12.9140	0.915453	0.457726	−	0.889093i	$-0.348664\pi$
$199$	12.9140	0.915453	0.457726	+	0.889093i	$0.348664\pi$
$200$	−26.8793	−1.90066
$201$	6.61416	0.466527
$202$	−7.97091	−0.560831
$203$	−0.377265	−0.0264788
$204$	14.7946	1.03583
$205$	−1.53572	−0.107260
$206$	−26.2231	−1.82705
$207$	−1.00000	−0.0695048
$208$	15.8407	1.09835
$209$	−0.880138	−0.0608804
$210$	0.471415	0.0325307
$211$	14.4592	0.995414	0.497707	−	0.867345i	$-0.334176\pi$
$211$	14.4592	0.995414	0.497707	+	0.867345i	$0.334176\pi$
$212$	24.7455	1.69953
$213$	−8.99710	−0.616471
$214$	16.4783	1.12643
$215$	3.46268	0.236153
$216$	5.65806	0.384983
$217$	−3.20413	−0.217511
$218$	0.399012	0.0270245
$219$	−3.65881	−0.247239
$220$	0.597931	0.0403125
$221$	9.75929	0.656481
$222$	−8.26635	−0.554801
$223$	7.78586	0.521380	0.260690	−	0.965423i	$-0.416050\pi$
$223$	7.78586	0.521380	0.260690	+	0.965423i	$0.416050\pi$
$224$	1.05071	0.0702032
$225$	−4.75062	−0.316708
$226$	−38.7038	−2.57454
$227$	−19.0309	−1.26313	−0.631563	−	0.775325i	$-0.717586\pi$
$227$	−19.0309	−1.26313	−0.631563	+	0.775325i	$0.717586\pi$
$228$	−13.3473	−0.883944
$229$	−29.2950	−1.93587	−0.967935	−	0.251201i	$-0.919175\pi$
$229$	−29.2950	−1.93587	−0.967935	+	0.251201i	$0.919175\pi$
$230$	−1.24956	−0.0823936
$231$	0.106008	0.00697479
$232$	−5.65806	−0.371470
$233$	−13.0823	−0.857053	−0.428526	−	0.903529i	$-0.640967\pi$
$233$	−13.0823	−0.857053	−0.428526	+	0.903529i	$0.640967\pi$
$234$	7.03357	0.459799
$235$	0.813270	0.0530519
$236$	17.8626	1.16276
$237$	10.1301	0.658023
$238$	3.27753	0.212450
$239$	25.0289	1.61899	0.809494	−	0.587128i	$-0.199742\pi$
$239$	25.0289	1.61899	0.809494	+	0.587128i	$0.199742\pi$
$240$	2.81420	0.181656
$241$	−0.924120	−0.0595278	−0.0297639	−	0.999557i	$-0.509476\pi$
$241$	−0.924120	−0.0595278	−0.0297639	+	0.999557i	$0.509476\pi$
$242$	−27.3271	−1.75665
$243$	1.00000	0.0641500
$244$	62.1645	3.97967
$245$	−3.42456	−0.218787
$246$	−7.69509	−0.490621
$247$	−8.80455	−0.560220
$248$	−48.0543	−3.05145
$249$	14.4012	0.912638
$250$	−12.1840	−0.770584
$251$	−0.948617	−0.0598762	−0.0299381	−	0.999552i	$-0.509531\pi$
$251$	−0.948617	−0.0598762	−0.0299381	+	0.999552i	$0.509531\pi$
$252$	1.60760	0.101269
$253$	−0.280990	−0.0176657
$254$	25.7731	1.61715
$255$	1.73380	0.108575
$256$	−32.2693	−2.01683
$257$	11.2748	0.703302	0.351651	−	0.936131i	$-0.385620\pi$
$257$	11.2748	0.703302	0.351651	+	0.936131i	$0.385620\pi$
$258$	17.3505	1.08020
$259$	−1.24633	−0.0774429
$260$	5.98147	0.370955
$261$	−1.00000	−0.0618984
$262$	−14.6866	−0.907343
$263$	18.0974	1.11593	0.557965	−	0.829864i	$-0.311582\pi$
$263$	18.0974	1.11593	0.557965	+	0.829864i	$0.311582\pi$
$264$	1.58986	0.0978491
$265$	2.89997	0.178144
$266$	−2.95689	−0.181298
$267$	−15.5648	−0.952551
$268$	28.1842	1.72163
$269$	−16.1467	−0.984479	−0.492240	−	0.870460i	$-0.663822\pi$
$269$	−16.1467	−0.984479	−0.492240	+	0.870460i	$0.663822\pi$
$270$	1.24956	0.0760459
$271$	12.1429	0.737631	0.368815	−	0.929503i	$-0.379763\pi$
$271$	12.1429	0.737631	0.368815	+	0.929503i	$0.379763\pi$
$272$	19.5658	1.18635
$273$	1.06046	0.0641818
$274$	−20.2743	−1.22481
$275$	−1.33488	−0.0804961
$276$	−4.26120	−0.256494
$277$	3.34216	0.200811	0.100405	−	0.994947i	$-0.467986\pi$
$277$	3.34216	0.200811	0.100405	+	0.994947i	$0.467986\pi$
$278$	−2.24458	−0.134621
$279$	−8.49306	−0.508466
$280$	1.06596	0.0637036
$281$	−0.0599960	−0.00357906	−0.00178953	−	0.999998i	$-0.500570\pi$
$281$	−0.0599960	−0.00357906	−0.00178953	+	0.999998i	$0.500570\pi$
$282$	4.07507	0.242667
$283$	14.3954	0.855718	0.427859	−	0.903845i	$-0.359268\pi$
$283$	14.3954	0.855718	0.427859	+	0.903845i	$0.359268\pi$
$284$	−38.3384	−2.27497
$285$	−1.56419	−0.0926544
$286$	1.97636	0.116865
$287$	−1.16019	−0.0684841
$288$	2.78506	0.164111
$289$	−4.94570	−0.290923
$290$	−1.24956	−0.0733767
$291$	0.680933	0.0399170
$292$	−15.5909	−0.912389
$293$	11.9152	0.696091	0.348046	−	0.937478i	$-0.386845\pi$
$293$	11.9152	0.696091	0.348046	+	0.937478i	$0.386845\pi$
$294$	−17.1595	−1.00076
$295$	2.09335	0.121880
$296$	−18.6919	−1.08644
$297$	0.280990	0.0163047
$298$	−21.4875	−1.24474
$299$	−2.81091	−0.162559
$300$	−20.2434	−1.16875
$301$	2.61595	0.150781
$302$	−49.5085	−2.84889
$303$	−3.18551	−0.183003
$304$	−17.6517	−1.01240
$305$	7.28515	0.417147
$306$	8.68760	0.496637
$307$	3.76417	0.214832	0.107416	−	0.994214i	$-0.465742\pi$
$307$	3.76417	0.214832	0.107416	+	0.994214i	$0.465742\pi$
$308$	0.451720	0.0257391
$309$	−10.4798	−0.596178
$310$	−10.6126	−0.602755
$311$	21.5328	1.22101	0.610506	−	0.792011i	$-0.290966\pi$
$311$	21.5328	1.22101	0.610506	+	0.792011i	$0.290966\pi$
$312$	15.9043	0.900404
$313$	8.37433	0.473345	0.236673	−	0.971589i	$-0.423943\pi$
$313$	8.37433	0.473345	0.236673	+	0.971589i	$0.423943\pi$
$314$	−4.40494	−0.248585
$315$	0.188397	0.0106150
$316$	43.1666	2.42831
$317$	29.4201	1.65240	0.826200	−	0.563377i	$-0.190498\pi$
$317$	29.4201	1.65240	0.826200	+	0.563377i	$0.190498\pi$
$318$	14.5309	0.814854
$319$	−0.280990	−0.0157324
$320$	−2.14830	−0.120094
$321$	6.58541	0.367562
$322$	−0.944007	−0.0526074
$323$	−10.8750	−0.605104
$324$	4.26120	0.236733
$325$	−13.3536	−0.740723
$326$	41.2779	2.28617
$327$	0.159462	0.00881828
$328$	−17.4001	−0.960762
$329$	0.614402	0.0338731
$330$	0.351114	0.0193282
$331$	−8.34926	−0.458917	−0.229458	−	0.973318i	$-0.573695\pi$
$331$	−8.34926	−0.458917	−0.229458	+	0.973318i	$0.573695\pi$
$332$	61.3663	3.36791
$333$	−3.30358	−0.181035
$334$	−52.8352	−2.89101
$335$	3.30296	0.180460
$336$	2.12605	0.115985
$337$	22.0675	1.20209	0.601047	−	0.799214i	$-0.294751\pi$
$337$	22.0675	1.20209	0.601047	+	0.799214i	$0.294751\pi$
$338$	−12.7584	−0.693964
$339$	−15.4677	−0.840089
$340$	7.38808	0.400675
$341$	−2.38647	−0.129234
$342$	−7.83770	−0.423814
$343$	−5.22801	−0.282286
$344$	39.2330	2.11530
$345$	−0.499377	−0.0268856
$346$	−3.25797	−0.175150
$347$	32.3908	1.73883	0.869414	−	0.494084i	$-0.164496\pi$
$347$	32.3908	1.73883	0.869414	+	0.494084i	$0.164496\pi$
$348$	−4.26120	−0.228424
$349$	−16.8925	−0.904233	−0.452117	−	0.891959i	$-0.649331\pi$
$349$	−16.8925	−0.904233	−0.452117	+	0.891959i	$0.649331\pi$
$350$	−4.48462	−0.239713
$351$	2.81091	0.150035
$352$	0.782574	0.0417113
$353$	−31.9878	−1.70254	−0.851269	−	0.524730i	$-0.824166\pi$
$353$	−31.9878	−1.70254	−0.851269	+	0.524730i	$0.824166\pi$
$354$	10.4892	0.557494
$355$	−4.49295	−0.238461
$356$	−66.3248	−3.51521
$357$	1.30984	0.0693239
$358$	13.7879	0.728713
$359$	5.58652	0.294845	0.147423	−	0.989074i	$-0.452902\pi$
$359$	5.58652	0.294845	0.147423	+	0.989074i	$0.452902\pi$
$360$	2.82551	0.148917
$361$	−9.18885	−0.483624
$362$	8.24872	0.433543
$363$	−10.9210	−0.573206
$364$	4.51882	0.236851
$365$	−1.82712	−0.0956360
$366$	36.5039	1.90809
$367$	2.70892	0.141404	0.0707022	−	0.997497i	$-0.477476\pi$
$367$	2.70892	0.141404	0.0707022	+	0.997497i	$0.477476\pi$
$368$	−5.63543	−0.293767
$369$	−3.07528	−0.160093
$370$	−4.12803	−0.214606
$371$	2.19084	0.113743
$372$	−36.1906	−1.87640
$373$	25.1027	1.29977	0.649883	−	0.760034i	$-0.274818\pi$
$373$	25.1027	1.29977	0.649883	+	0.760034i	$0.274818\pi$
$374$	2.44113	0.126228
$375$	−4.86924	−0.251446
$376$	9.21455	0.475204
$377$	−2.81091	−0.144769
$378$	0.944007	0.0485545
$379$	−25.8338	−1.32700	−0.663498	−	0.748178i	$-0.730929\pi$
$379$	−25.8338	−1.32700	−0.663498	+	0.748178i	$0.730929\pi$
$380$	−6.66531	−0.341923
$381$	10.3000	0.527685
$382$	−55.3708	−2.83302
$383$	18.0940	0.924561	0.462281	−	0.886734i	$-0.347031\pi$
$383$	18.0940	0.924561	0.462281	+	0.886734i	$0.347031\pi$
$384$	−16.3347	−0.833575
$385$	0.0529378	0.00269796
$386$	46.8994	2.38711
$387$	6.93400	0.352475
$388$	2.90159	0.147306
$389$	−0.751401	−0.0380976	−0.0190488	−	0.999819i	$-0.506064\pi$
$389$	−0.751401	−0.0380976	−0.0190488	+	0.999819i	$0.506064\pi$
$390$	3.51240	0.177857
$391$	−3.47193	−0.175583
$392$	−38.8011	−1.95975
$393$	−5.86940	−0.296072
$394$	40.8232	2.05664
$395$	5.05876	0.254534
$396$	1.19735	0.0601693
$397$	36.7706	1.84546	0.922731	−	0.385445i	$-0.125952\pi$
$397$	36.7706	1.84546	0.922731	+	0.385445i	$0.125952\pi$
$398$	32.3140	1.61976
$399$	−1.18170	−0.0591589
$400$	−26.7718	−1.33859
$401$	27.6609	1.38132	0.690659	−	0.723181i	$-0.257321\pi$
$401$	27.6609	1.38132	0.690659	+	0.723181i	$0.257321\pi$
$402$	16.5502	0.825449
$403$	−23.8732	−1.18921
$404$	−13.5741	−0.675337
$405$	0.499377	0.0248142
$406$	−0.944007	−0.0468503
$407$	−0.928273	−0.0460128
$408$	19.6444	0.972543
$409$	16.6783	0.824691	0.412345	−	0.911028i	$-0.364710\pi$
$409$	16.6783	0.824691	0.412345	+	0.911028i	$0.364710\pi$
$410$	−3.84275	−0.189780
$411$	−8.10245	−0.399664
$412$	−44.6567	−2.20008
$413$	1.58147	0.0778188
$414$	−2.50224	−0.122978
$415$	7.19162	0.353023
$416$	7.82856	0.383827
$417$	−0.897029	−0.0439277
$418$	−2.20232	−0.107719
$419$	4.12698	0.201616	0.100808	−	0.994906i	$-0.467857\pi$
$419$	4.12698	0.201616	0.100808	+	0.994906i	$0.467857\pi$
$420$	0.802799	0.0391726
$421$	10.9526	0.533795	0.266897	−	0.963725i	$-0.414002\pi$
$421$	10.9526	0.533795	0.266897	+	0.963725i	$0.414002\pi$
$422$	36.1804	1.76124
$423$	1.62857	0.0791837
$424$	32.8573	1.59569
$425$	−16.4938	−0.800068
$426$	−22.5129	−1.09075
$427$	5.50372	0.266344
$428$	28.0618	1.35642
$429$	0.789837	0.0381337
$430$	8.66446	0.417837
$431$	−20.7355	−0.998793	−0.499396	−	0.866374i	$-0.666445\pi$
$431$	−20.7355	−0.998793	−0.499396	+	0.866374i	$0.666445\pi$
$432$	5.63543	0.271135
$433$	23.2333	1.11652	0.558261	−	0.829665i	$-0.311469\pi$
$433$	23.2333	1.11652	0.558261	+	0.829665i	$0.311469\pi$
$434$	−8.01751	−0.384853
$435$	−0.499377	−0.0239433
$436$	0.679500	0.0325422
$437$	3.13228	0.149837
$438$	−9.15521	−0.437453
$439$	8.90645	0.425082	0.212541	−	0.977152i	$-0.431826\pi$
$439$	8.90645	0.425082	0.212541	+	0.977152i	$0.431826\pi$
$440$	0.793939	0.0378496
$441$	−6.85767	−0.326556
$442$	24.4201	1.16154
$443$	−6.58936	−0.313070	−0.156535	−	0.987672i	$-0.550032\pi$
$443$	−6.58936	−0.313070	−0.156535	+	0.987672i	$0.550032\pi$
$444$	−14.0772	−0.668076
$445$	−7.77271	−0.368462
$446$	19.4821	0.922504
$447$	−8.58730	−0.406165
$448$	−1.62298	−0.0766786
$449$	−2.64648	−0.124895	−0.0624477	−	0.998048i	$-0.519891\pi$
$449$	−2.64648	−0.124895	−0.0624477	+	0.998048i	$0.519891\pi$
$450$	−11.8872	−0.560368
$451$	−0.864123	−0.0406899
$452$	−65.9109	−3.10019
$453$	−19.7857	−0.929612
$454$	−47.6199	−2.23491
$455$	0.529568	0.0248265
$456$	−17.7226	−0.829938
$457$	28.1702	1.31775	0.658873	−	0.752255i	$-0.271034\pi$
$457$	28.1702	1.31775	0.658873	+	0.752255i	$0.271034\pi$
$458$	−73.3032	−3.42523
$459$	3.47193	0.162056
$460$	−2.12795	−0.0992160
$461$	−9.37170	−0.436484	−0.218242	−	0.975895i	$-0.570032\pi$
$461$	−9.37170	−0.436484	−0.218242	+	0.975895i	$0.570032\pi$
$462$	0.265256	0.0123408
$463$	−9.05249	−0.420705	−0.210353	−	0.977626i	$-0.567461\pi$
$463$	−9.05249	−0.420705	−0.210353	+	0.977626i	$0.567461\pi$
$464$	−5.63543	−0.261618
$465$	−4.24124	−0.196683
$466$	−32.7351	−1.51643
$467$	−24.7217	−1.14398	−0.571992	−	0.820259i	$-0.693829\pi$
$467$	−24.7217	−1.14398	−0.571992	+	0.820259i	$0.693829\pi$
$468$	11.9779	0.553676
$469$	2.49529	0.115222
$470$	2.03500	0.0938674
$471$	−1.76040	−0.0811149
$472$	23.7182	1.09172
$473$	1.94838	0.0895868
$474$	25.3480	1.16427
$475$	14.8803	0.682753
$476$	5.58148	0.255827
$477$	5.80717	0.265892
$478$	62.6284	2.86456
$479$	6.57206	0.300285	0.150143	−	0.988664i	$-0.452027\pi$
$479$	6.57206	0.300285	0.150143	+	0.988664i	$0.452027\pi$
$480$	1.39080	0.0634809
$481$	−9.28608	−0.423409
$482$	−2.31237	−0.105326
$483$	−0.377265	−0.0171661
$484$	−46.5368	−2.11531
$485$	0.340042	0.0154405
$486$	2.50224	0.113504
$487$	−1.76562	−0.0800077	−0.0400038	−	0.999200i	$-0.512737\pi$
$487$	−1.76562	−0.0800077	−0.0400038	+	0.999200i	$0.512737\pi$
$488$	82.5426	3.73653
$489$	16.4964	0.745992
$490$	−8.56908	−0.387111
$491$	0.943575	0.0425829	0.0212915	−	0.999773i	$-0.493222\pi$
$491$	0.943575	0.0425829	0.0212915	+	0.999773i	$0.493222\pi$
$492$	−13.1044	−0.590791
$493$	−3.47193	−0.156368
$494$	−22.0311	−0.991225
$495$	0.140320	0.00630691
$496$	−47.8621	−2.14907
$497$	−3.39429	−0.152255
$498$	36.0352	1.61478
$499$	−17.7953	−0.796626	−0.398313	−	0.917250i	$-0.630404\pi$
$499$	−17.7953	−0.796626	−0.398313	+	0.917250i	$0.630404\pi$
$500$	−20.7488	−0.927914
$501$	−21.1152	−0.943355
$502$	−2.37367	−0.105942
$503$	−0.846449	−0.0377413	−0.0188706	−	0.999822i	$-0.506007\pi$
$503$	−0.846449	−0.0377413	−0.0188706	+	0.999822i	$0.506007\pi$
$504$	2.13459	0.0950821
$505$	−1.59077	−0.0707884
$506$	−0.703104	−0.0312568
$507$	−5.09878	−0.226445
$508$	43.8904	1.94732
$509$	−15.7969	−0.700184	−0.350092	−	0.936715i	$-0.613850\pi$
$509$	−15.7969	−0.700184	−0.350092	+	0.936715i	$0.613850\pi$
$510$	4.33839	0.192107
$511$	−1.38034	−0.0610626
$512$	−48.0762	−2.12469
$513$	−3.13228	−0.138293
$514$	28.2122	1.24439
$515$	−5.23340	−0.230611
$516$	29.5472	1.30074
$517$	0.457611	0.0201257
$518$	−3.11860	−0.137024
$519$	−1.30202	−0.0571525
$520$	7.94225	0.348291
$521$	−31.9344	−1.39907	−0.699536	−	0.714597i	$-0.746610\pi$
$521$	−31.9344	−1.39907	−0.699536	+	0.714597i	$0.746610\pi$
$522$	−2.50224	−0.109520
$523$	6.79011	0.296911	0.148455	−	0.988919i	$-0.452570\pi$
$523$	6.79011	0.296911	0.148455	+	0.988919i	$0.452570\pi$
$524$	−25.0107	−1.09260
$525$	−1.79224	−0.0782199
$526$	45.2839	1.97447
$527$	−29.4873	−1.28449
$528$	1.58350	0.0689129
$529$	1.00000	0.0434783
$530$	7.25641	0.315198
$531$	4.19192	0.181914
$532$	−5.03545	−0.218314
$533$	−8.64434	−0.374428
$534$	−38.9469	−1.68540
$535$	3.28860	0.142179
$536$	37.4233	1.61644
$537$	5.51022	0.237784
$538$	−40.4028	−1.74189
$539$	−1.92694	−0.0829990
$540$	2.12795	0.0915722
$541$	14.3565	0.617236	0.308618	−	0.951186i	$-0.400134\pi$
$541$	14.3565	0.617236	0.308618	+	0.951186i	$0.400134\pi$
$542$	30.3845	1.30513
$543$	3.29654	0.141468
$544$	9.66954	0.414578
$545$	0.0796317	0.00341105
$546$	2.65352	0.113560
$547$	28.5383	1.22021	0.610104	−	0.792321i	$-0.291128\pi$
$547$	28.5383	1.22021	0.610104	+	0.792321i	$0.291128\pi$
$548$	−34.5261	−1.47488
$549$	14.5885	0.622621
$550$	−3.34018	−0.142426
$551$	3.13228	0.133439
$552$	−5.65806	−0.240823
$553$	3.82175	0.162517
$554$	8.36288	0.355305
$555$	−1.64973	−0.0700273
$556$	−3.82242	−0.162107
$557$	21.9328	0.929324	0.464662	−	0.885488i	$-0.346176\pi$
$557$	21.9328	0.929324	0.464662	+	0.885488i	$0.346176\pi$
$558$	−21.2517	−0.899655
$559$	19.4909	0.824375
$560$	1.06170	0.0448650
$561$	0.975578	0.0411889
$562$	−0.150124	−0.00633261
$563$	−15.4453	−0.650941	−0.325471	−	0.945552i	$-0.605523\pi$
$563$	−15.4453	−0.650941	−0.325471	+	0.945552i	$0.605523\pi$
$564$	6.93966	0.292212
$565$	−7.72421	−0.324960
$566$	36.0208	1.51407
$567$	0.377265	0.0158436
$568$	−50.9062	−2.13598
$569$	21.7539	0.911970	0.455985	−	0.889987i	$-0.349287\pi$
$569$	21.7539	0.911970	0.455985	+	0.889987i	$0.349287\pi$
$570$	−3.91397	−0.163938
$571$	−15.6666	−0.655626	−0.327813	−	0.944743i	$-0.606312\pi$
$571$	−15.6666	−0.655626	−0.327813	+	0.944743i	$0.606312\pi$
$572$	3.36566	0.140725
$573$	−22.1285	−0.924431
$574$	−2.90308	−0.121172
$575$	4.75062	0.198115
$576$	−4.30197	−0.179249
$577$	22.7042	0.945186	0.472593	−	0.881281i	$-0.343318\pi$
$577$	22.7042	0.945186	0.472593	+	0.881281i	$0.343318\pi$
$578$	−12.3753	−0.514745
$579$	18.7430	0.778931
$580$	−2.12795	−0.0883581
$581$	5.43306	0.225401
$582$	1.70386	0.0706272
$583$	1.63176	0.0675804
$584$	−20.7018	−0.856645
$585$	1.40370	0.0580360
$586$	29.8146	1.23163
$587$	0.863910	0.0356574	0.0178287	−	0.999841i	$-0.494325\pi$
$587$	0.863910	0.0356574	0.0178287	+	0.999841i	$0.494325\pi$
$588$	−29.2219	−1.20509
$589$	26.6026	1.09614
$590$	5.23806	0.215648
$591$	16.3147	0.671096
$592$	−18.6171	−0.765158
$593$	−31.8728	−1.30886	−0.654429	−	0.756123i	$-0.727091\pi$
$593$	−31.8728	−1.30886	−0.654429	+	0.756123i	$0.727091\pi$
$594$	0.703104	0.0288487
$595$	0.654103	0.0268156
$596$	−36.5922	−1.49887
$597$	12.9140	0.528537
$598$	−7.03357	−0.287624
$599$	20.4372	0.835042	0.417521	−	0.908667i	$-0.362899\pi$
$599$	20.4372	0.835042	0.417521	+	0.908667i	$0.362899\pi$
$600$	−26.8793	−1.09734
$601$	−5.55415	−0.226559	−0.113279	−	0.993563i	$-0.536135\pi$
$601$	−5.55415	−0.226559	−0.113279	+	0.993563i	$0.536135\pi$
$602$	6.54574	0.266785
$603$	6.61416	0.269349
$604$	−84.3107	−3.43055
$605$	−5.45372	−0.221725
$606$	−7.97091	−0.323796
$607$	8.04486	0.326531	0.163265	−	0.986582i	$-0.447797\pi$
$607$	8.04486	0.326531	0.163265	+	0.986582i	$0.447797\pi$
$608$	−8.72358	−0.353788
$609$	−0.377265	−0.0152875
$610$	18.2292	0.738079
$611$	4.57776	0.185196
$612$	14.7946	0.598036
$613$	2.92270	0.118047	0.0590234	−	0.998257i	$-0.481201\pi$
$613$	2.92270	0.118047	0.0590234	+	0.998257i	$0.481201\pi$
$614$	9.41884	0.380114
$615$	−1.53572	−0.0619264
$616$	0.599798	0.0241665
$617$	−32.7544	−1.31864	−0.659322	−	0.751861i	$-0.729157\pi$
$617$	−32.7544	−1.31864	−0.659322	+	0.751861i	$0.729157\pi$
$618$	−26.2231	−1.05485
$619$	7.77841	0.312641	0.156320	−	0.987706i	$-0.450037\pi$
$619$	7.77841	0.312641	0.156320	+	0.987706i	$0.450037\pi$
$620$	−18.0728	−0.725820
$621$	−1.00000	−0.0401286
$622$	53.8802	2.16040
$623$	−5.87205	−0.235259
$624$	15.8407	0.634135
$625$	21.3215	0.852861
$626$	20.9546	0.837513
$627$	−0.880138	−0.0351493
$628$	−7.50142	−0.299339
$629$	−11.4698	−0.457331
$630$	0.471415	0.0187816
$631$	45.0815	1.79467	0.897333	−	0.441354i	$-0.145502\pi$
$631$	45.0815	1.79467	0.897333	+	0.441354i	$0.145502\pi$
$632$	57.3170	2.27995
$633$	14.4592	0.574702
$634$	73.6162	2.92367
$635$	5.14359	0.204117
$636$	24.7455	0.981223
$637$	−19.2763	−0.763755
$638$	−0.703104	−0.0278362
$639$	−8.99710	−0.355920
$640$	−8.15716	−0.322440
$641$	25.1043	0.991561	0.495780	−	0.868448i	$-0.334882\pi$
$641$	25.1043	0.991561	0.495780	+	0.868448i	$0.334882\pi$
$642$	16.4783	0.650346
$643$	37.8245	1.49165	0.745826	−	0.666140i	$-0.232055\pi$
$643$	37.8245	1.49165	0.745826	+	0.666140i	$0.232055\pi$
$644$	−1.60760	−0.0633483
$645$	3.46268	0.136343
$646$	−27.2120	−1.07064
$647$	6.99373	0.274952	0.137476	−	0.990505i	$-0.456101\pi$
$647$	6.99373	0.274952	0.137476	+	0.990505i	$0.456101\pi$
$648$	5.65806	0.222270
$649$	1.17789	0.0462362
$650$	−33.4138	−1.31060
$651$	−3.20413	−0.125580
$652$	70.2944	2.75294
$653$	−34.0332	−1.33182	−0.665911	−	0.746031i	$-0.731957\pi$
$653$	−34.0332	−1.33182	−0.665911	+	0.746031i	$0.731957\pi$
$654$	0.399012	0.0156026
$655$	−2.93104	−0.114525
$656$	−17.3305	−0.676643
$657$	−3.65881	−0.142744
$658$	1.53738	0.0599333
$659$	27.9925	1.09043	0.545217	−	0.838295i	$-0.316447\pi$
$659$	27.9925	1.09043	0.545217	+	0.838295i	$0.316447\pi$
$660$	0.597931	0.0232744
$661$	−27.9800	−1.08829	−0.544147	−	0.838990i	$-0.683147\pi$
$661$	−27.9800	−1.08829	−0.544147	+	0.838990i	$0.683147\pi$
$662$	−20.8918	−0.811984
$663$	9.75929	0.379019
$664$	81.4828	3.16215
$665$	−0.590113	−0.0228836
$666$	−8.26635	−0.320315
$667$	1.00000	0.0387202
$668$	−89.9759	−3.48127
$669$	7.78586	0.301019
$670$	8.26479	0.319297
$671$	4.09922	0.158249
$672$	1.05071	0.0405318
$673$	49.9531	1.92555	0.962776	−	0.270300i	$-0.0871228\pi$
$673$	49.9531	1.92555	0.962776	+	0.270300i	$0.0871228\pi$
$674$	55.2182	2.12692
$675$	−4.75062	−0.182852
$676$	−21.7269	−0.835651
$677$	13.7220	0.527380	0.263690	−	0.964607i	$-0.415060\pi$
$677$	13.7220	0.527380	0.263690	+	0.964607i	$0.415060\pi$
$678$	−38.7038	−1.48641
$679$	0.256892	0.00985861
$680$	9.80997	0.376195
$681$	−19.0309	−0.729266
$682$	−5.97151	−0.228661
$683$	−51.7531	−1.98028	−0.990138	−	0.140095i	$-0.955259\pi$
$683$	−51.7531	−1.98028	−0.990138	+	0.140095i	$0.955259\pi$
$684$	−13.3473	−0.510345
$685$	−4.04618	−0.154596
$686$	−13.0817	−0.499463
$687$	−29.2950	−1.11768
$688$	39.0761	1.48976
$689$	16.3234	0.621873
$690$	−1.24956	−0.0475700
$691$	−24.2514	−0.922566	−0.461283	−	0.887253i	$-0.652611\pi$
$691$	−24.2514	−0.922566	−0.461283	+	0.887253i	$0.652611\pi$
$692$	−5.54818	−0.210910
$693$	0.106008	0.00402690
$694$	81.0495	3.07660
$695$	−0.447956	−0.0169919
$696$	−5.65806	−0.214468
$697$	−10.6772	−0.404426
$698$	−42.2690	−1.59991
$699$	−13.0823	−0.494820
$700$	−7.63710	−0.288655
$701$	−3.36677	−0.127161	−0.0635807	−	0.997977i	$-0.520252\pi$
$701$	−3.36677	−0.127161	−0.0635807	+	0.997977i	$0.520252\pi$
$702$	7.03357	0.265465
$703$	10.3477	0.390272
$704$	−1.20881	−0.0455587
$705$	0.813270	0.0306295
$706$	−80.0410	−3.01238
$707$	−1.20178	−0.0451976
$708$	17.8626	0.671319
$709$	15.4206	0.579133	0.289566	−	0.957158i	$-0.406489\pi$
$709$	15.4206	0.579133	0.289566	+	0.957158i	$0.406489\pi$
$710$	−11.2424	−0.421921
$711$	10.1301	0.379910
$712$	−88.0667	−3.30044
$713$	8.49306	0.318068
$714$	3.27753	0.122658
$715$	0.394427	0.0147507
$716$	23.4802	0.877495
$717$	25.0289	0.934723
$718$	13.9788	0.521685
$719$	−29.3650	−1.09513	−0.547565	−	0.836763i	$-0.684445\pi$
$719$	−29.3650	−1.09513	−0.547565	+	0.836763i	$0.684445\pi$
$720$	2.81420	0.104879
$721$	−3.95368	−0.147243
$722$	−22.9927	−0.855700
$723$	−0.924120	−0.0343684
$724$	14.0472	0.522060
$725$	4.75062	0.176434
$726$	−27.3271	−1.01420
$727$	19.1116	0.708811	0.354405	−	0.935092i	$-0.384683\pi$
$727$	19.1116	0.708811	0.354405	+	0.935092i	$0.384683\pi$
$728$	6.00014	0.222380
$729$	1.00000	0.0370370
$730$	−4.57190	−0.169214
$731$	24.0744	0.890423
$732$	62.1645	2.29766
$733$	−35.6961	−1.31846	−0.659232	−	0.751939i	$-0.729119\pi$
$733$	−35.6961	−1.31846	−0.659232	+	0.751939i	$0.729119\pi$
$734$	6.77836	0.250194
$735$	−3.42456	−0.126317
$736$	−2.78506	−0.102659
$737$	1.85851	0.0684591
$738$	−7.69509	−0.283260
$739$	17.4540	0.642057	0.321028	−	0.947070i	$-0.395972\pi$
$739$	17.4540	0.642057	0.321028	+	0.947070i	$0.395972\pi$
$740$	−7.02985	−0.258422
$741$	−8.80455	−0.323443
$742$	5.48200	0.201251
$743$	22.3796	0.821028	0.410514	−	0.911854i	$-0.365349\pi$
$743$	22.3796	0.821028	0.410514	+	0.911854i	$0.365349\pi$
$744$	−48.0543	−1.76176
$745$	−4.28830	−0.157111
$746$	62.8129	2.29974
$747$	14.4012	0.526912
$748$	4.15713	0.152000
$749$	2.48444	0.0907796
$750$	−12.1840	−0.444897
$751$	20.1094	0.733804	0.366902	−	0.930260i	$-0.380418\pi$
$751$	20.1094	0.733804	0.366902	+	0.930260i	$0.380418\pi$
$752$	9.17768	0.334676
$753$	−0.948617	−0.0345695
$754$	−7.03357	−0.256148
$755$	−9.88051	−0.359589
$756$	1.60760	0.0584679
$757$	37.1745	1.35113	0.675565	−	0.737300i	$-0.263900\pi$
$757$	37.1745	1.35113	0.675565	+	0.737300i	$0.263900\pi$
$758$	−64.6424	−2.34792
$759$	−0.280990	−0.0101993
$760$	−8.85027	−0.321033
$761$	−51.3836	−1.86265	−0.931327	−	0.364184i	$-0.881348\pi$
$761$	−51.3836	−1.86265	−0.931327	+	0.364184i	$0.881348\pi$
$762$	25.7731	0.933660
$763$	0.0601594	0.00217792
$764$	−94.2940	−3.41144
$765$	1.73380	0.0626858
$766$	45.2756	1.63587
$767$	11.7831	0.425464
$768$	−32.2693	−1.16442
$769$	−32.3771	−1.16755	−0.583775	−	0.811916i	$-0.698425\pi$
$769$	−32.3771	−1.16755	−0.583775	+	0.811916i	$0.698425\pi$
$770$	0.132463	0.00477363
$771$	11.2748	0.406052
$772$	79.8675	2.87449
$773$	−13.8667	−0.498751	−0.249375	−	0.968407i	$-0.580225\pi$
$773$	−13.8667	−0.498751	−0.249375	+	0.968407i	$0.580225\pi$
$774$	17.3505	0.623652
$775$	40.3473	1.44932
$776$	3.85276	0.138306
$777$	−1.24633	−0.0447117
$778$	−1.88019	−0.0674079
$779$	9.63262	0.345125
$780$	5.98147	0.214171
$781$	−2.52809	−0.0904623
$782$	−8.68760	−0.310668
$783$	−1.00000	−0.0357371
$784$	−38.6459	−1.38021
$785$	−0.879103	−0.0313765
$786$	−14.6866	−0.523855
$787$	30.4534	1.08555	0.542773	−	0.839879i	$-0.317374\pi$
$787$	30.4534	1.08555	0.542773	+	0.839879i	$0.317374\pi$
$788$	69.5201	2.47655
$789$	18.0974	0.644283
$790$	12.6582	0.450360
$791$	−5.83541	−0.207483
$792$	1.58986	0.0564932
$793$	41.0069	1.45620
$794$	92.0087	3.26527
$795$	2.89997	0.102851
$796$	55.0293	1.95046
$797$	−24.1771	−0.856395	−0.428198	−	0.903685i	$-0.640851\pi$
$797$	−24.1771	−0.856395	−0.428198	+	0.903685i	$0.640851\pi$
$798$	−2.95689	−0.104673
$799$	5.65428	0.200034
$800$	−13.2308	−0.467779
$801$	−15.5648	−0.549955
$802$	69.2141	2.44404
$803$	−1.02809	−0.0362804
$804$	28.1842	0.993982
$805$	−0.188397	−0.00664014
$806$	−59.7366	−2.10413
$807$	−16.1467	−0.568389
$808$	−18.0238	−0.634076
$809$	28.4412	0.999941	0.499970	−	0.866042i	$-0.333344\pi$
$809$	28.4412	0.999941	0.499970	+	0.866042i	$0.333344\pi$
$810$	1.24956	0.0439051
$811$	−6.10171	−0.214260	−0.107130	−	0.994245i	$-0.534166\pi$
$811$	−6.10171	−0.214260	−0.107130	+	0.994245i	$0.534166\pi$
$812$	−1.60760	−0.0564157
$813$	12.1429	0.425871
$814$	−2.32276	−0.0814128
$815$	8.23792	0.288562
$816$	19.5658	0.684941
$817$	−21.7192	−0.759859
$818$	41.7332	1.45917
$819$	1.06046	0.0370554
$820$	−6.54403	−0.228527
$821$	−34.8159	−1.21508	−0.607542	−	0.794288i	$-0.707844\pi$
$821$	−34.8159	−1.21508	−0.607542	+	0.794288i	$0.707844\pi$
$822$	−20.2743	−0.707146
$823$	28.6531	0.998783	0.499392	−	0.866376i	$-0.333557\pi$
$823$	28.6531	0.998783	0.499392	+	0.866376i	$0.333557\pi$
$824$	−59.2957	−2.06566
$825$	−1.33488	−0.0464745
$826$	3.95720	0.137689
$827$	35.5993	1.23791	0.618954	−	0.785427i	$-0.287557\pi$
$827$	35.5993	1.23791	0.618954	+	0.785427i	$0.287557\pi$
$828$	−4.26120	−0.148087
$829$	−32.0733	−1.11395	−0.556976	−	0.830529i	$-0.688038\pi$
$829$	−32.0733	−1.11395	−0.556976	+	0.830529i	$0.688038\pi$
$830$	17.9951	0.624621
$831$	3.34216	0.115938
$832$	−12.0924	−0.419230
$833$	−23.8094	−0.824945
$834$	−2.24458	−0.0777235
$835$	−10.5444	−0.364905
$836$	−3.75044	−0.129712
$837$	−8.49306	−0.293563
$838$	10.3267	0.356729
$839$	−1.42992	−0.0493662	−0.0246831	−	0.999695i	$-0.507858\pi$
$839$	−1.42992	−0.0493662	−0.0246831	+	0.999695i	$0.507858\pi$
$840$	1.06596	0.0367793
$841$	1.00000	0.0344828
$842$	27.4059	0.944470
$843$	−0.0599960	−0.00206637
$844$	61.6136	2.12083
$845$	−2.54622	−0.0875925
$846$	4.07507	0.140104
$847$	−4.12013	−0.141569
$848$	32.7259	1.12381
$849$	14.3954	0.494049
$850$	−41.2715	−1.41560
$851$	3.30358	0.113245
$852$	−38.3384	−1.31345
$853$	−1.61657	−0.0553503	−0.0276752	−	0.999617i	$-0.508810\pi$
$853$	−1.61657	−0.0553503	−0.0276752	+	0.999617i	$0.508810\pi$
$854$	13.7716	0.471255
$855$	−1.56419	−0.0534941
$856$	37.2607	1.27354
$857$	−29.6871	−1.01409	−0.507046	−	0.861919i	$-0.669263\pi$
$857$	−29.6871	−1.01409	−0.507046	+	0.861919i	$0.669263\pi$
$858$	1.97636	0.0674719
$859$	32.4766	1.10809	0.554044	−	0.832487i	$-0.313084\pi$
$859$	32.4766	1.10809	0.554044	+	0.832487i	$0.313084\pi$
$860$	14.7552	0.503147
$861$	−1.16019	−0.0395393
$862$	−51.8851	−1.76721
$863$	−1.28776	−0.0438357	−0.0219179	−	0.999760i	$-0.506977\pi$
$863$	−1.28776	−0.0438357	−0.0219179	+	0.999760i	$0.506977\pi$
$864$	2.78506	0.0947497
$865$	−0.650201	−0.0221075
$866$	58.1353	1.97552
$867$	−4.94570	−0.167965
$868$	−13.6535	−0.463428
$869$	2.84647	0.0965598
$870$	−1.24956	−0.0423641
$871$	18.5918	0.629959
$872$	0.902247	0.0305539
$873$	0.680933	0.0230461
$874$	7.83770	0.265114
$875$	−1.83699	−0.0621017
$876$	−15.5909	−0.526768
$877$	20.5699	0.694595	0.347297	−	0.937755i	$-0.387099\pi$
$877$	20.5699	0.694595	0.347297	+	0.937755i	$0.387099\pi$
$878$	22.2861	0.752119
$879$	11.9152	0.401888
$880$	0.790763	0.0266566
$881$	15.6728	0.528030	0.264015	−	0.964519i	$-0.414953\pi$
$881$	15.6728	0.528030	0.264015	+	0.964519i	$0.414953\pi$
$882$	−17.1595	−0.577792
$883$	−24.2059	−0.814594	−0.407297	−	0.913296i	$-0.633529\pi$
$883$	−24.2059	−0.814594	−0.407297	+	0.913296i	$0.633529\pi$
$884$	41.5863	1.39870
$885$	2.09335	0.0703672
$886$	−16.4881	−0.553930
$887$	−12.4786	−0.418990	−0.209495	−	0.977810i	$-0.567182\pi$
$887$	−12.4786	−0.418990	−0.209495	+	0.977810i	$0.567182\pi$
$888$	−18.6919	−0.627259
$889$	3.88583	0.130326
$890$	−19.4492	−0.651938
$891$	0.280990	0.00941352
$892$	33.1771	1.11085
$893$	−5.10113	−0.170703
$894$	−21.4875	−0.718648
$895$	2.75168	0.0919785
$896$	−6.16250	−0.205875
$897$	−2.81091	−0.0938536
$898$	−6.62214	−0.220984
$899$	8.49306	0.283260
$900$	−20.2434	−0.674778
$901$	20.1621	0.671696
$902$	−2.16224	−0.0719948
$903$	2.61595	0.0870535
$904$	−87.5171	−2.91078
$905$	1.64621	0.0547220
$906$	−49.5085	−1.64481
$907$	−20.8227	−0.691407	−0.345704	−	0.938344i	$-0.612360\pi$
$907$	−20.8227	−0.691407	−0.345704	+	0.938344i	$0.612360\pi$
$908$	−81.0945	−2.69122
$909$	−3.18551	−0.105657
$910$	1.32511	0.0439268
$911$	−46.6670	−1.54615	−0.773074	−	0.634316i	$-0.781282\pi$
$911$	−46.6670	−1.54615	−0.773074	+	0.634316i	$0.781282\pi$
$912$	−17.6517	−0.584507
$913$	4.04659	0.133922
$914$	70.4885	2.33155
$915$	7.28515	0.240840
$916$	−124.832	−4.12457
$917$	−2.21432	−0.0731232
$918$	8.68760	0.286734
$919$	−8.68386	−0.286454	−0.143227	−	0.989690i	$-0.545748\pi$
$919$	−8.68386	−0.286454	−0.143227	+	0.989690i	$0.545748\pi$
$920$	−2.82551	−0.0931542
$921$	3.76417	0.124033
$922$	−23.4502	−0.772293
$923$	−25.2900	−0.832432
$924$	0.451720	0.0148605
$925$	15.6941	0.516018
$926$	−22.6515	−0.744375
$927$	−10.4798	−0.344203
$928$	−2.78506	−0.0914241
$929$	−16.0979	−0.528156	−0.264078	−	0.964501i	$-0.585068\pi$
$929$	−16.0979	−0.528156	−0.264078	+	0.964501i	$0.585068\pi$
$930$	−10.6126	−0.348001
$931$	21.4801	0.703982
$932$	−55.7465	−1.82604
$933$	21.5328	0.704952
$934$	−61.8596	−2.02411
$935$	0.487181	0.0159325
$936$	15.9043	0.519849
$937$	−40.3985	−1.31976	−0.659881	−	0.751370i	$-0.729393\pi$
$937$	−40.3985	−1.31976	−0.659881	+	0.751370i	$0.729393\pi$
$938$	6.24381	0.203868
$939$	8.37433	0.273286
$940$	3.46551	0.113032
$941$	−1.57266	−0.0512674	−0.0256337	−	0.999671i	$-0.508160\pi$
$941$	−1.57266	−0.0512674	−0.0256337	+	0.999671i	$0.508160\pi$
$942$	−4.40494	−0.143521
$943$	3.07528	0.100145
$944$	23.6233	0.768873
$945$	0.188397	0.00612857
$946$	4.87532	0.158510
$947$	−42.5119	−1.38145	−0.690725	−	0.723118i	$-0.742708\pi$
$947$	−42.5119	−1.38145	−0.690725	+	0.723118i	$0.742708\pi$
$948$	43.1666	1.40198
$949$	−10.2846	−0.333851
$950$	37.2340	1.20803
$951$	29.4201	0.954013
$952$	7.41114	0.240197
$953$	21.9061	0.709608	0.354804	−	0.934941i	$-0.384548\pi$
$953$	21.9061	0.709608	0.354804	+	0.934941i	$0.384548\pi$
$954$	14.5309	0.470456
$955$	−11.0505	−0.357585
$956$	106.653	3.44942
$957$	−0.280990	−0.00908311
$958$	16.4449	0.531310
$959$	−3.05677	−0.0987082
$960$	−2.14830	−0.0693362
$961$	41.1321	1.32684
$962$	−23.2360	−0.749158
$963$	6.58541	0.212212
$964$	−3.93786	−0.126830
$965$	9.35980	0.301303
$966$	−0.944007	−0.0303729
$967$	32.3109	1.03905	0.519524	−	0.854456i	$-0.326109\pi$
$967$	32.3109	1.03905	0.519524	+	0.854456i	$0.326109\pi$
$968$	−61.7920	−1.98607
$969$	−10.8750	−0.349357
$970$	0.850867	0.0273197
$971$	−11.7064	−0.375677	−0.187839	−	0.982200i	$-0.560148\pi$
$971$	−11.7064	−0.375677	−0.187839	+	0.982200i	$0.560148\pi$
$972$	4.26120	0.136678
$973$	−0.338418	−0.0108492
$974$	−4.41799	−0.141562
$975$	−13.3536	−0.427657
$976$	82.2124	2.63155
$977$	−5.86810	−0.187737	−0.0938685	−	0.995585i	$-0.529923\pi$
$977$	−5.86810	−0.187737	−0.0938685	+	0.995585i	$0.529923\pi$
$978$	41.2779	1.31992
$979$	−4.37355	−0.139779
$980$	−14.5928	−0.466148
$981$	0.159462	0.00509123
$982$	2.36105	0.0753441
$983$	−18.1817	−0.579907	−0.289953	−	0.957041i	$-0.593640\pi$
$983$	−18.1817	−0.579907	−0.289953	+	0.957041i	$0.593640\pi$
$984$	−17.4001	−0.554696
$985$	8.14717	0.259591
$986$	−8.68760	−0.276670
$987$	0.614402	0.0195566
$988$	−37.5179	−1.19360
$989$	−6.93400	−0.220488
$990$	0.351114	0.0111591
$991$	45.5666	1.44747	0.723736	−	0.690077i	$-0.242423\pi$
$991$	45.5666	1.44747	0.723736	+	0.690077i	$0.242423\pi$
$992$	−23.6537	−0.751006
$993$	−8.34926	−0.264956
$994$	−8.49332	−0.269392
$995$	6.44898	0.204446
$996$	61.3663	1.94447
$997$	23.5989	0.747384	0.373692	−	0.927553i	$-0.378092\pi$
$997$	23.5989	0.747384	0.373692	+	0.927553i	$0.378092\pi$
$998$	−44.5280	−1.40951
$999$	−3.30358	−0.104521

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2001.2.a.n.1.15	✓	16
3.2	odd	2		6003.2.a.r.1.2		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2001.2.a.n.1.15	✓	16	1.1	even	1	trivial
6003.2.a.r.1.2		16	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)

\(f(q)\)	\(=\)	\(q+2.50224 q^{2} +1.00000 q^{3} +4.26120 q^{4} +0.499377 q^{5} +2.50224 q^{6} +0.377265 q^{7} +5.65806 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+2.50224 q^{2} +1.00000 q^{3} +4.26120 q^{4} +0.499377 q^{5} +2.50224 q^{6} +0.377265 q^{7} +5.65806 q^{8} +1.00000 q^{9} +1.24956 q^{10} +0.280990 q^{11} +4.26120 q^{12} +2.81091 q^{13} +0.944007 q^{14} +0.499377 q^{15} +5.63543 q^{16} +3.47193 q^{17} +2.50224 q^{18} -3.13228 q^{19} +2.12795 q^{20} +0.377265 q^{21} +0.703104 q^{22} -1.00000 q^{23} +5.65806 q^{24} -4.75062 q^{25} +7.03357 q^{26} +1.00000 q^{27} +1.60760 q^{28} -1.00000 q^{29} +1.24956 q^{30} -8.49306 q^{31} +2.78506 q^{32} +0.280990 q^{33} +8.68760 q^{34} +0.188397 q^{35} +4.26120 q^{36} -3.30358 q^{37} -7.83770 q^{38} +2.81091 q^{39} +2.82551 q^{40} -3.07528 q^{41} +0.944007 q^{42} +6.93400 q^{43} +1.19735 q^{44} +0.499377 q^{45} -2.50224 q^{46} +1.62857 q^{47} +5.63543 q^{48} -6.85767 q^{49} -11.8872 q^{50} +3.47193 q^{51} +11.9779 q^{52} +5.80717 q^{53} +2.50224 q^{54} +0.140320 q^{55} +2.13459 q^{56} -3.13228 q^{57} -2.50224 q^{58} +4.19192 q^{59} +2.12795 q^{60} +14.5885 q^{61} -21.2517 q^{62} +0.377265 q^{63} -4.30197 q^{64} +1.40370 q^{65} +0.703104 q^{66} +6.61416 q^{67} +14.7946 q^{68} -1.00000 q^{69} +0.471415 q^{70} -8.99710 q^{71} +5.65806 q^{72} -3.65881 q^{73} -8.26635 q^{74} -4.75062 q^{75} -13.3473 q^{76} +0.106008 q^{77} +7.03357 q^{78} +10.1301 q^{79} +2.81420 q^{80} +1.00000 q^{81} -7.69509 q^{82} +14.4012 q^{83} +1.60760 q^{84} +1.73380 q^{85} +17.3505 q^{86} -1.00000 q^{87} +1.58986 q^{88} -15.5648 q^{89} +1.24956 q^{90} +1.06046 q^{91} -4.26120 q^{92} -8.49306 q^{93} +4.07507 q^{94} -1.56419 q^{95} +2.78506 q^{96} +0.680933 q^{97} -17.1595 q^{98} +0.280990 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - q^{2} + 16 q^{3} + 25 q^{4} + 3 q^{5} - q^{6} + 13 q^{7} + 16 q^{9}+O(q^{10}) \) 16 * q - q^2 + 16 * q^3 + 25 * q^4 + 3 * q^5 - q^6 + 13 * q^7 + 16 * q^9	\( 16 q - q^{2} + 16 q^{3} + 25 q^{4} + 3 q^{5} - q^{6} + 13 q^{7} + 16 q^{9} + 11 q^{10} + 8 q^{11} + 25 q^{12} + 19 q^{13} + 16 q^{14} + 3 q^{15} + 31 q^{16} - 4 q^{17} - q^{18} + 19 q^{19} + 16 q^{20} + 13 q^{21} + 6 q^{22} - 16 q^{23} + 23 q^{25} - 15 q^{26} + 16 q^{27} + 18 q^{28} - 16 q^{29} + 11 q^{30} + 24 q^{31} - 21 q^{32} + 8 q^{33} - 9 q^{34} - 13 q^{35} + 25 q^{36} + 26 q^{37} + 19 q^{39} - 22 q^{40} - 15 q^{41} + 16 q^{42} + 33 q^{43} + 6 q^{44} + 3 q^{45} + q^{46} + 13 q^{47} + 31 q^{48} + 41 q^{49} + 13 q^{50} - 4 q^{51} - 26 q^{52} + 5 q^{53} - q^{54} + 9 q^{55} + 40 q^{56} + 19 q^{57} + q^{58} + 2 q^{59} + 16 q^{60} + 29 q^{61} - 32 q^{62} + 13 q^{63} + 28 q^{64} + 18 q^{65} + 6 q^{66} + 32 q^{67} - 26 q^{68} - 16 q^{69} + 18 q^{70} + 29 q^{71} + 19 q^{73} - 16 q^{74} + 23 q^{75} + 64 q^{76} - 21 q^{77} - 15 q^{78} + 56 q^{79} + 16 q^{81} + 14 q^{82} + 5 q^{83} + 18 q^{84} + 16 q^{85} - 20 q^{86} - 16 q^{87} + q^{88} + 7 q^{89} + 11 q^{90} - 6 q^{91} - 25 q^{92} + 24 q^{93} - 11 q^{94} + 39 q^{95} - 21 q^{96} + 35 q^{97} - 109 q^{98} + 8 q^{99}+O(q^{100}) \) 16 * q - q^2 + 16 * q^3 + 25 * q^4 + 3 * q^5 - q^6 + 13 * q^7 + 16 * q^9 + 11 * q^10 + 8 * q^11 + 25 * q^12 + 19 * q^13 + 16 * q^14 + 3 * q^15 + 31 * q^16 - 4 * q^17 - q^18 + 19 * q^19 + 16 * q^20 + 13 * q^21 + 6 * q^22 - 16 * q^23 + 23 * q^25 - 15 * q^26 + 16 * q^27 + 18 * q^28 - 16 * q^29 + 11 * q^30 + 24 * q^31 - 21 * q^32 + 8 * q^33 - 9 * q^34 - 13 * q^35 + 25 * q^36 + 26 * q^37 + 19 * q^39 - 22 * q^40 - 15 * q^41 + 16 * q^42 + 33 * q^43 + 6 * q^44 + 3 * q^45 + q^46 + 13 * q^47 + 31 * q^48 + 41 * q^49 + 13 * q^50 - 4 * q^51 - 26 * q^52 + 5 * q^53 - q^54 + 9 * q^55 + 40 * q^56 + 19 * q^57 + q^58 + 2 * q^59 + 16 * q^60 + 29 * q^61 - 32 * q^62 + 13 * q^63 + 28 * q^64 + 18 * q^65 + 6 * q^66 + 32 * q^67 - 26 * q^68 - 16 * q^69 + 18 * q^70 + 29 * q^71 + 19 * q^73 - 16 * q^74 + 23 * q^75 + 64 * q^76 - 21 * q^77 - 15 * q^78 + 56 * q^79 + 16 * q^81 + 14 * q^82 + 5 * q^83 + 18 * q^84 + 16 * q^85 - 20 * q^86 - 16 * q^87 + q^88 + 7 * q^89 + 11 * q^90 - 6 * q^91 - 25 * q^92 + 24 * q^93 - 11 * q^94 + 39 * q^95 - 21 * q^96 + 35 * q^97 - 109 * q^98 + 8 * q^99

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