LMFDB - Embedded newform 2001.2.a.m.1.8

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			1.8
Root			$-0.429717$ 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)

$f(q)$	$=$	$q+0.429717 q^{2} -1.00000 q^{3} -1.81534 q^{4} -3.93237 q^{5} -0.429717 q^{6} +0.264416 q^{7} -1.63952 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+0.429717 q^{2} -1.00000 q^{3} -1.81534 q^{4} -3.93237 q^{5} -0.429717 q^{6} +0.264416 q^{7} -1.63952 q^{8} +1.00000 q^{9} -1.68981 q^{10} +3.34312 q^{11} +1.81534 q^{12} +0.652888 q^{13} +0.113624 q^{14} +3.93237 q^{15} +2.92616 q^{16} +2.18859 q^{17} +0.429717 q^{18} +4.72209 q^{19} +7.13861 q^{20} -0.264416 q^{21} +1.43660 q^{22} -1.00000 q^{23} +1.63952 q^{24} +10.4636 q^{25} +0.280557 q^{26} -1.00000 q^{27} -0.480006 q^{28} -1.00000 q^{29} +1.68981 q^{30} -2.95247 q^{31} +4.53645 q^{32} -3.34312 q^{33} +0.940475 q^{34} -1.03978 q^{35} -1.81534 q^{36} -10.8205 q^{37} +2.02916 q^{38} -0.652888 q^{39} +6.44719 q^{40} -6.32816 q^{41} -0.113624 q^{42} +4.30095 q^{43} -6.06892 q^{44} -3.93237 q^{45} -0.429717 q^{46} -0.521743 q^{47} -2.92616 q^{48} -6.93008 q^{49} +4.49637 q^{50} -2.18859 q^{51} -1.18522 q^{52} -12.1941 q^{53} -0.429717 q^{54} -13.1464 q^{55} -0.433515 q^{56} -4.72209 q^{57} -0.429717 q^{58} -3.05882 q^{59} -7.13861 q^{60} +10.5567 q^{61} -1.26872 q^{62} +0.264416 q^{63} -3.90293 q^{64} -2.56740 q^{65} -1.43660 q^{66} +2.07050 q^{67} -3.97305 q^{68} +1.00000 q^{69} -0.446813 q^{70} +2.54342 q^{71} -1.63952 q^{72} +11.0474 q^{73} -4.64974 q^{74} -10.4636 q^{75} -8.57221 q^{76} +0.883977 q^{77} -0.280557 q^{78} -3.22467 q^{79} -11.5067 q^{80} +1.00000 q^{81} -2.71932 q^{82} +7.56795 q^{83} +0.480006 q^{84} -8.60636 q^{85} +1.84819 q^{86} +1.00000 q^{87} -5.48111 q^{88} -16.5243 q^{89} -1.68981 q^{90} +0.172634 q^{91} +1.81534 q^{92} +2.95247 q^{93} -0.224202 q^{94} -18.5690 q^{95} -4.53645 q^{96} +5.97928 q^{97} -2.97797 q^{98} +3.34312 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	0.429717	0.303856	0.151928	−	0.988392i	$-0.451452\pi$
$2$	0.429717	0.303856	0.151928	+	0.988392i	$0.451452\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	−1.81534	−0.907672
$5$	−3.93237	−1.75861	−0.879305	−	0.476258i	$-0.841993\pi$
$5$	−3.93237	−1.75861	−0.879305	+	0.476258i	$0.841993\pi$
$6$	−0.429717	−0.175431
$7$	0.264416	0.0999400	0.0499700	−	0.998751i	$-0.484087\pi$
$7$	0.264416	0.0999400	0.0499700	+	0.998751i	$0.484087\pi$
$8$	−1.63952	−0.579657
$9$	1.00000	0.333333
$10$	−1.68981	−0.534364
$11$	3.34312	1.00799	0.503995	−	0.863707i	$-0.331863\pi$
$11$	3.34312	1.00799	0.503995	+	0.863707i	$0.331863\pi$
$12$	1.81534	0.524045
$13$	0.652888	0.181078	0.0905392	−	0.995893i	$-0.471141\pi$
$13$	0.652888	0.181078	0.0905392	+	0.995893i	$0.471141\pi$
$14$	0.113624	0.0303673
$15$	3.93237	1.01533
$16$	2.92616	0.731540
$17$	2.18859	0.530812	0.265406	−	0.964137i	$-0.414494\pi$
$17$	2.18859	0.530812	0.265406	+	0.964137i	$0.414494\pi$
$18$	0.429717	0.101285
$19$	4.72209	1.08332	0.541661	−	0.840597i	$-0.317796\pi$
$19$	4.72209	1.08332	0.541661	+	0.840597i	$0.317796\pi$
$20$	7.13861	1.59624
$21$	−0.264416	−0.0577004
$22$	1.43660	0.306284
$23$	−1.00000	−0.208514
$23$	−1.00000	−0.208514
$24$	1.63952	0.334665
$25$	10.4636	2.09271
$26$	0.280557	0.0550217
$27$	−1.00000	−0.192450
$28$	−0.480006	−0.0907127
$29$	−1.00000	−0.185695
$29$	−1.00000	−0.185695
$30$	1.68981	0.308515
$31$	−2.95247	−0.530279	−0.265139	−	0.964210i	$-0.585418\pi$
$31$	−2.95247	−0.530279	−0.265139	+	0.964210i	$0.585418\pi$
$32$	4.53645	0.801939
$33$	−3.34312	−0.581963
$34$	0.940475	0.161290
$35$	−1.03978	−0.175756
$36$	−1.81534	−0.302557
$37$	−10.8205	−1.77888	−0.889438	−	0.457056i	$-0.848904\pi$
$37$	−10.8205	−1.77888	−0.889438	+	0.457056i	$0.848904\pi$
$38$	2.02916	0.329173
$39$	−0.652888	−0.104546
$40$	6.44719	1.01939
$41$	−6.32816	−0.988293	−0.494146	−	0.869379i	$-0.664519\pi$
$41$	−6.32816	−0.988293	−0.494146	+	0.869379i	$0.664519\pi$
$42$	−0.113624	−0.0175326
$43$	4.30095	0.655889	0.327944	−	0.944697i	$-0.393644\pi$
$43$	4.30095	0.655889	0.327944	+	0.944697i	$0.393644\pi$
$44$	−6.06892	−0.914924
$45$	−3.93237	−0.586204
$46$	−0.429717	−0.0633583
$47$	−0.521743	−0.0761040	−0.0380520	−	0.999276i	$-0.512115\pi$
$47$	−0.521743	−0.0761040	−0.0380520	+	0.999276i	$0.512115\pi$
$48$	−2.92616	−0.422355
$49$	−6.93008	−0.990012
$50$	4.49637	0.635882
$51$	−2.18859	−0.306464
$52$	−1.18522	−0.164360
$53$	−12.1941	−1.67499	−0.837497	−	0.546443i	$-0.815982\pi$
$53$	−12.1941	−1.67499	−0.837497	+	0.546443i	$0.815982\pi$
$54$	−0.429717	−0.0584771
$55$	−13.1464	−1.77266
$56$	−0.433515	−0.0579309
$57$	−4.72209	−0.625456
$58$	−0.429717	−0.0564246
$59$	−3.05882	−0.398225	−0.199112	−	0.979977i	$-0.563806\pi$
$59$	−3.05882	−0.398225	−0.199112	+	0.979977i	$0.563806\pi$
$60$	−7.13861	−0.921590
$61$	10.5567	1.35165	0.675823	−	0.737064i	$-0.263789\pi$
$61$	10.5567	1.35165	0.675823	+	0.737064i	$0.263789\pi$
$62$	−1.26872	−0.161128
$63$	0.264416	0.0333133
$64$	−3.90293	−0.487866
$65$	−2.56740	−0.318447
$66$	−1.43660	−0.176833
$67$	2.07050	0.252951	0.126476	−	0.991970i	$-0.459633\pi$
$67$	2.07050	0.252951	0.126476	+	0.991970i	$0.459633\pi$
$68$	−3.97305	−0.481803
$69$	1.00000	0.120386
$70$	−0.446813	−0.0534043
$71$	2.54342	0.301849	0.150924	−	0.988545i	$-0.451775\pi$
$71$	2.54342	0.301849	0.150924	+	0.988545i	$0.451775\pi$
$72$	−1.63952	−0.193219
$73$	11.0474	1.29300	0.646501	−	0.762913i	$-0.276232\pi$
$73$	11.0474	1.29300	0.646501	+	0.762913i	$0.276232\pi$
$74$	−4.64974	−0.540522
$75$	−10.4636	−1.20823
$76$	−8.57221	−0.983300
$77$	0.883977	0.100739
$78$	−0.280557	−0.0317668
$79$	−3.22467	−0.362804	−0.181402	−	0.983409i	$-0.558063\pi$
$79$	−3.22467	−0.362804	−0.181402	+	0.983409i	$0.558063\pi$
$80$	−11.5067	−1.28649
$81$	1.00000	0.111111
$82$	−2.71932	−0.300298
$83$	7.56795	0.830690	0.415345	−	0.909664i	$-0.363661\pi$
$83$	7.56795	0.830690	0.415345	+	0.909664i	$0.363661\pi$
$84$	0.480006	0.0523730
$85$	−8.60636	−0.933491
$86$	1.84819	0.199296
$87$	1.00000	0.107211
$88$	−5.48111	−0.584288
$89$	−16.5243	−1.75157	−0.875785	−	0.482701i	$-0.839656\pi$
$89$	−16.5243	−1.75157	−0.875785	+	0.482701i	$0.839656\pi$
$90$	−1.68981	−0.178121
$91$	0.172634	0.0180970
$92$	1.81534	0.189263
$93$	2.95247	0.306156
$94$	−0.224202	−0.0231246
$95$	−18.5690	−1.90514
$96$	−4.53645	−0.463000
$97$	5.97928	0.607104	0.303552	−	0.952815i	$-0.401827\pi$
$97$	5.97928	0.607104	0.303552	+	0.952815i	$0.401827\pi$
$98$	−2.97797	−0.300821
$99$	3.34312	0.335997
$100$	−18.9950	−1.89950
$101$	12.7365	1.26733	0.633666	−	0.773607i	$-0.281550\pi$
$101$	12.7365	1.26733	0.633666	+	0.773607i	$0.281550\pi$
$102$	−0.940475	−0.0931209
$103$	6.71017	0.661173	0.330586	−	0.943776i	$-0.392754\pi$
$103$	6.71017	0.661173	0.330586	+	0.943776i	$0.392754\pi$
$104$	−1.07042	−0.104963
$105$	1.03978	0.101472
$106$	−5.24002	−0.508956
$107$	10.3265	0.998299	0.499150	−	0.866516i	$-0.333646\pi$
$107$	10.3265	0.998299	0.499150	+	0.866516i	$0.333646\pi$
$108$	1.81534	0.174682
$109$	3.53727	0.338809	0.169405	−	0.985547i	$-0.445815\pi$
$109$	3.53727	0.338809	0.169405	+	0.985547i	$0.445815\pi$
$110$	−5.64924	−0.538633
$111$	10.8205	1.02703
$112$	0.773724	0.0731101
$113$	2.98406	0.280717	0.140359	−	0.990101i	$-0.455174\pi$
$113$	2.98406	0.280717	0.140359	+	0.990101i	$0.455174\pi$
$114$	−2.02916	−0.190048
$115$	3.93237	0.366696
$116$	1.81534	0.168550
$117$	0.652888	0.0603595
$118$	−1.31443	−0.121003
$119$	0.578700	0.0530493
$120$	−6.44719	−0.588546
$121$	0.176483	0.0160439
$122$	4.53639	0.410705
$123$	6.32816	0.570591
$124$	5.35974	0.481319
$125$	−21.4847	−1.92165
$126$	0.113624	0.0101224
$127$	−3.31490	−0.294149	−0.147075	−	0.989125i	$-0.546986\pi$
$127$	−3.31490	−0.294149	−0.147075	+	0.989125i	$0.546986\pi$
$128$	−10.7501	−0.950180
$129$	−4.30095	−0.378678
$130$	−1.10325	−0.0967618
$131$	−19.4144	−1.69624	−0.848122	−	0.529801i	$-0.822266\pi$
$131$	−19.4144	−1.69624	−0.848122	+	0.529801i	$0.822266\pi$
$132$	6.06892	0.528232
$133$	1.24860	0.108267
$134$	0.889727	0.0768607
$135$	3.93237	0.338445
$136$	−3.58824	−0.307689
$137$	−22.2832	−1.90379	−0.951893	−	0.306431i	$-0.900865\pi$
$137$	−22.2832	−1.90379	−0.951893	+	0.306431i	$0.900865\pi$
$138$	0.429717	0.0365799
$139$	−13.2316	−1.12229	−0.561144	−	0.827718i	$-0.689639\pi$
$139$	−13.2316	−1.12229	−0.561144	+	0.827718i	$0.689639\pi$
$140$	1.88756	0.159528
$141$	0.521743	0.0439387
$142$	1.09295	0.0917184
$143$	2.18269	0.182525
$144$	2.92616	0.243847
$145$	3.93237	0.326566
$146$	4.74726	0.392886
$147$	6.93008	0.571584
$148$	19.6429	1.61464
$149$	−13.7856	−1.12936	−0.564679	−	0.825311i	$-0.691000\pi$
$149$	−13.7856	−1.12936	−0.564679	+	0.825311i	$0.691000\pi$
$150$	−4.49637	−0.367127
$151$	−2.45650	−0.199907	−0.0999534	−	0.994992i	$-0.531869\pi$
$151$	−2.45650	−0.199907	−0.0999534	+	0.994992i	$0.531869\pi$
$152$	−7.74194	−0.627955
$153$	2.18859	0.176937
$154$	0.379860	0.0306100
$155$	11.6102	0.932553
$156$	1.18522	0.0948932
$157$	−11.7259	−0.935828	−0.467914	−	0.883774i	$-0.654994\pi$
$157$	−11.7259	−0.935828	−0.467914	+	0.883774i	$0.654994\pi$
$158$	−1.38569	−0.110240
$159$	12.1941	0.967058
$160$	−17.8390	−1.41030
$161$	−0.264416	−0.0208389
$162$	0.429717	0.0337617
$163$	18.6881	1.46377	0.731883	−	0.681431i	$-0.238642\pi$
$163$	18.6881	1.46377	0.731883	+	0.681431i	$0.238642\pi$
$164$	11.4878	0.897046
$165$	13.1464	1.02345
$166$	3.25208	0.252410
$167$	3.47606	0.268986	0.134493	−	0.990915i	$-0.457059\pi$
$167$	3.47606	0.268986	0.134493	+	0.990915i	$0.457059\pi$
$168$	0.433515	0.0334464
$169$	−12.5737	−0.967211
$170$	−3.69830	−0.283647
$171$	4.72209	0.361107
$172$	−7.80770	−0.595332
$173$	−5.26597	−0.400365	−0.200182	−	0.979759i	$-0.564153\pi$
$173$	−5.26597	−0.400365	−0.200182	+	0.979759i	$0.564153\pi$
$174$	0.429717	0.0325767
$175$	2.76674	0.209146
$176$	9.78251	0.737385
$177$	3.05882	0.229915
$178$	−7.10076	−0.532225
$179$	4.47515	0.334488	0.167244	−	0.985916i	$-0.446513\pi$
$179$	4.47515	0.334488	0.167244	+	0.985916i	$0.446513\pi$
$180$	7.13861	0.532080
$181$	7.51226	0.558382	0.279191	−	0.960236i	$-0.409934\pi$
$181$	7.51226	0.558382	0.279191	+	0.960236i	$0.409934\pi$
$182$	0.0741838	0.00549887
$183$	−10.5567	−0.780373
$184$	1.63952	0.120867
$185$	42.5502	3.12835
$186$	1.26872	0.0930274
$187$	7.31674	0.535053
$188$	0.947142	0.0690774
$189$	−0.264416	−0.0192335
$190$	−7.97942	−0.578888
$191$	−19.4407	−1.40668	−0.703339	−	0.710855i	$-0.748308\pi$
$191$	−19.4407	−1.40668	−0.703339	+	0.710855i	$0.748308\pi$
$192$	3.90293	0.281669
$193$	2.58415	0.186011	0.0930055	−	0.995666i	$-0.470353\pi$
$193$	2.58415	0.186011	0.0930055	+	0.995666i	$0.470353\pi$
$194$	2.56940	0.184472
$195$	2.56740	0.183855
$196$	12.5805	0.898606
$197$	−15.5639	−1.10888	−0.554440	−	0.832224i	$-0.687068\pi$
$197$	−15.5639	−1.10888	−0.554440	+	0.832224i	$0.687068\pi$
$198$	1.43660	0.102095
$199$	−18.4304	−1.30649	−0.653247	−	0.757145i	$-0.726594\pi$
$199$	−18.4304	−1.30649	−0.653247	+	0.757145i	$0.726594\pi$
$200$	−17.1552	−1.21305
$201$	−2.07050	−0.146042
$202$	5.47310	0.385086
$203$	−0.264416	−0.0185584
$204$	3.97305	0.278169
$205$	24.8847	1.73802
$206$	2.88347	0.200901
$207$	−1.00000	−0.0695048
$208$	1.91045	0.132466
$209$	15.7865	1.09198
$210$	0.446813	0.0308330
$211$	−10.8852	−0.749371	−0.374685	−	0.927152i	$-0.622249\pi$
$211$	−10.8852	−0.749371	−0.374685	+	0.927152i	$0.622249\pi$
$212$	22.1365	1.52034
$213$	−2.54342	−0.174272
$214$	4.43747	0.303339
$215$	−16.9129	−1.15345
$216$	1.63952	0.111555
$217$	−0.780680	−0.0529960
$218$	1.52003	0.102949
$219$	−11.0474	−0.746515
$220$	23.8653	1.60900
$221$	1.42891	0.0961186
$222$	4.64974	0.312070
$223$	−16.6396	−1.11427	−0.557136	−	0.830421i	$-0.688100\pi$
$223$	−16.6396	−1.11427	−0.557136	+	0.830421i	$0.688100\pi$
$224$	1.19951	0.0801458
$225$	10.4636	0.697571
$226$	1.28230	0.0852975
$227$	8.99168	0.596799	0.298399	−	0.954441i	$-0.403547\pi$
$227$	8.99168	0.596799	0.298399	+	0.954441i	$0.403547\pi$
$228$	8.57221	0.567709
$229$	10.7841	0.712635	0.356318	−	0.934365i	$-0.384032\pi$
$229$	10.7841	0.712635	0.356318	+	0.934365i	$0.384032\pi$
$230$	1.68981	0.111423
$231$	−0.883977	−0.0581614
$232$	1.63952	0.107640
$233$	−14.1636	−0.927886	−0.463943	−	0.885865i	$-0.653566\pi$
$233$	−14.1636	−0.927886	−0.463943	+	0.885865i	$0.653566\pi$
$234$	0.280557	0.0183406
$235$	2.05169	0.133837
$236$	5.55282	0.361457
$237$	3.22467	0.209465
$238$	0.248677	0.0161193
$239$	−30.6122	−1.98014	−0.990070	−	0.140573i	$-0.955106\pi$
$239$	−30.6122	−1.98014	−0.990070	+	0.140573i	$0.955106\pi$
$240$	11.5067	0.742757
$241$	−22.0173	−1.41826	−0.709130	−	0.705078i	$-0.750912\pi$
$241$	−22.0173	−1.41826	−0.709130	+	0.705078i	$0.750912\pi$
$242$	0.0758379	0.00487504
$243$	−1.00000	−0.0641500
$244$	−19.1640	−1.22685
$245$	27.2517	1.74105
$246$	2.71932	0.173377
$247$	3.08299	0.196166
$248$	4.84062	0.307380
$249$	−7.56795	−0.479599
$250$	−9.23236	−0.583906
$251$	−2.60369	−0.164343	−0.0821716	−	0.996618i	$-0.526186\pi$
$251$	−2.60369	−0.164343	−0.0821716	+	0.996618i	$0.526186\pi$
$252$	−0.480006	−0.0302376
$253$	−3.34312	−0.210180
$254$	−1.42447	−0.0893790
$255$	8.60636	0.538951
$256$	3.18637	0.199148
$257$	7.30649	0.455767	0.227883	−	0.973688i	$-0.426820\pi$
$257$	7.30649	0.455767	0.227883	+	0.973688i	$0.426820\pi$
$258$	−1.84819	−0.115063
$259$	−2.86111	−0.177781
$260$	4.66071	0.289045
$261$	−1.00000	−0.0618984
$262$	−8.34269	−0.515413
$263$	6.69175	0.412631	0.206316	−	0.978485i	$-0.433853\pi$
$263$	6.69175	0.412631	0.206316	+	0.978485i	$0.433853\pi$
$264$	5.48111	0.337339
$265$	47.9519	2.94566
$266$	0.536543	0.0328976
$267$	16.5243	1.01127
$268$	−3.75866	−0.229597
$269$	−11.0247	−0.672190	−0.336095	−	0.941828i	$-0.609106\pi$
$269$	−11.0247	−0.672190	−0.336095	+	0.941828i	$0.609106\pi$
$270$	1.68981	0.102838
$271$	18.1408	1.10198	0.550988	−	0.834513i	$-0.314251\pi$
$271$	18.1408	1.10198	0.550988	+	0.834513i	$0.314251\pi$
$272$	6.40417	0.388310
$273$	−0.172634	−0.0104483
$274$	−9.57548	−0.578476
$275$	34.9810	2.10943
$276$	−1.81534	−0.109271
$277$	−23.0017	−1.38204	−0.691019	−	0.722837i	$-0.742838\pi$
$277$	−23.0017	−1.38204	−0.691019	+	0.722837i	$0.742838\pi$
$278$	−5.68584	−0.341014
$279$	−2.95247	−0.176760
$280$	1.70474	0.101878
$281$	27.6029	1.64665	0.823325	−	0.567571i	$-0.192117\pi$
$281$	27.6029	1.64665	0.823325	+	0.567571i	$0.192117\pi$
$282$	0.224202	0.0133510
$283$	12.4133	0.737896	0.368948	−	0.929450i	$-0.379718\pi$
$283$	12.4133	0.737896	0.368948	+	0.929450i	$0.379718\pi$
$284$	−4.61718	−0.273979
$285$	18.5690	1.09993
$286$	0.937937	0.0554614
$287$	−1.67327	−0.0987700
$288$	4.53645	0.267313
$289$	−12.2101	−0.718239
$290$	1.68981	0.0992289
$291$	−5.97928	−0.350512
$292$	−20.0548	−1.17362
$293$	−22.6436	−1.32286	−0.661428	−	0.750009i	$-0.730049\pi$
$293$	−22.6436	−1.32286	−0.661428	+	0.750009i	$0.730049\pi$
$294$	2.97797	0.173679
$295$	12.0284	0.700323
$296$	17.7404	1.03114
$297$	−3.34312	−0.193988
$298$	−5.92389	−0.343162
$299$	−0.652888	−0.0377575
$300$	18.9950	1.09667
$301$	1.13724	0.0655495
$302$	−1.05560	−0.0607428
$303$	−12.7365	−0.731694
$304$	13.8176	0.792492
$305$	−41.5128	−2.37702
$306$	0.940475	0.0537634
$307$	25.5728	1.45952	0.729760	−	0.683704i	$-0.239632\pi$
$307$	25.5728	1.45952	0.729760	+	0.683704i	$0.239632\pi$
$308$	−1.60472	−0.0914375
$309$	−6.71017	−0.381728
$310$	4.98910	0.283362
$311$	17.4722	0.990759	0.495380	−	0.868677i	$-0.335029\pi$
$311$	17.4722	0.990759	0.495380	+	0.868677i	$0.335029\pi$
$312$	1.07042	0.0606006
$313$	−25.1991	−1.42434	−0.712169	−	0.702008i	$-0.752287\pi$
$313$	−25.1991	−1.42434	−0.712169	+	0.702008i	$0.752287\pi$
$314$	−5.03881	−0.284357
$315$	−1.03978	−0.0585852
$316$	5.85388	0.329307
$317$	−14.5528	−0.817369	−0.408685	−	0.912676i	$-0.634012\pi$
$317$	−14.5528	−0.817369	−0.408685	+	0.912676i	$0.634012\pi$
$318$	5.24002	0.293846
$319$	−3.34312	−0.187179
$320$	15.3478	0.857966
$321$	−10.3265	−0.576368
$322$	−0.113624	−0.00633203
$323$	10.3347	0.575040
$324$	−1.81534	−0.100852
$325$	6.83153	0.378945
$326$	8.03059	0.444773
$327$	−3.53727	−0.195612
$328$	10.3751	0.572871
$329$	−0.137957	−0.00760583
$330$	5.64924	0.310980
$331$	3.13170	0.172134	0.0860670	−	0.996289i	$-0.472570\pi$
$331$	3.13170	0.172134	0.0860670	+	0.996289i	$0.472570\pi$
$332$	−13.7384	−0.753994
$333$	−10.8205	−0.592959
$334$	1.49372	0.0817329
$335$	−8.14196	−0.444843
$336$	−0.773724	−0.0422101
$337$	−9.70563	−0.528699	−0.264350	−	0.964427i	$-0.585157\pi$
$337$	−9.70563	−0.528699	−0.264350	+	0.964427i	$0.585157\pi$
$338$	−5.40315	−0.293892
$339$	−2.98406	−0.162072
$340$	15.6235	0.847304
$341$	−9.87046	−0.534515
$342$	2.02916	0.109724
$343$	−3.68334	−0.198882
$344$	−7.05148	−0.380190
$345$	−3.93237	−0.211712
$346$	−2.26288	−0.121653
$347$	12.1133	0.650274	0.325137	−	0.945667i	$-0.394590\pi$
$347$	12.1133	0.650274	0.325137	+	0.945667i	$0.394590\pi$
$348$	−1.81534	−0.0973126
$349$	4.07892	0.218339	0.109170	−	0.994023i	$-0.465181\pi$
$349$	4.07892	0.218339	0.109170	+	0.994023i	$0.465181\pi$
$350$	1.18891	0.0635501
$351$	−0.652888	−0.0348486
$352$	15.1659	0.808347
$353$	3.02538	0.161025	0.0805124	−	0.996754i	$-0.474344\pi$
$353$	3.02538	0.161025	0.0805124	+	0.996754i	$0.474344\pi$
$354$	1.31443	0.0698611
$355$	−10.0017	−0.530834
$356$	29.9972	1.58985
$357$	−0.578700	−0.0306280
$358$	1.92305	0.101636
$359$	−7.77931	−0.410576	−0.205288	−	0.978702i	$-0.565813\pi$
$359$	−7.77931	−0.410576	−0.205288	+	0.978702i	$0.565813\pi$
$360$	6.44719	0.339797
$361$	3.29811	0.173585
$362$	3.22814	0.169667
$363$	−0.176483	−0.00926298
$364$	−0.313390	−0.0164261
$365$	−43.4426	−2.27389
$366$	−4.53639	−0.237121
$367$	25.2589	1.31850	0.659251	−	0.751923i	$-0.270873\pi$
$367$	25.2589	1.31850	0.659251	+	0.751923i	$0.270873\pi$
$368$	−2.92616	−0.152537
$369$	−6.32816	−0.329431
$370$	18.2845	0.950567
$371$	−3.22433	−0.167399
$372$	−5.35974	−0.277890
$373$	−4.21349	−0.218166	−0.109083	−	0.994033i	$-0.534791\pi$
$373$	−4.21349	−0.218166	−0.109083	+	0.994033i	$0.534791\pi$
$374$	3.14413	0.162579
$375$	21.4847	1.10947
$376$	0.855406	0.0441142
$377$	−0.652888	−0.0336254
$378$	−0.113624	−0.00584420
$379$	−26.2411	−1.34791	−0.673957	−	0.738770i	$-0.735407\pi$
$379$	−26.2411	−1.34791	−0.673957	+	0.738770i	$0.735407\pi$
$380$	33.7091	1.72924
$381$	3.31490	0.169827
$382$	−8.35398	−0.427427
$383$	−27.2849	−1.39419	−0.697097	−	0.716977i	$-0.745525\pi$
$383$	−27.2849	−1.39419	−0.697097	+	0.716977i	$0.745525\pi$
$384$	10.7501	0.548587
$385$	−3.47613	−0.177160
$386$	1.11045	0.0565205
$387$	4.30095	0.218630
$388$	−10.8544	−0.551051
$389$	3.44307	0.174571	0.0872854	−	0.996183i	$-0.472181\pi$
$389$	3.44307	0.174571	0.0872854	+	0.996183i	$0.472181\pi$
$390$	1.10325	0.0558654
$391$	−2.18859	−0.110682
$392$	11.3620	0.573867
$393$	19.4144	0.979327
$394$	−6.68806	−0.336939
$395$	12.6806	0.638030
$396$	−6.06892	−0.304975
$397$	18.3446	0.920691	0.460346	−	0.887740i	$-0.347725\pi$
$397$	18.3446	0.920691	0.460346	+	0.887740i	$0.347725\pi$
$398$	−7.91984	−0.396986
$399$	−1.24860	−0.0625080
$400$	30.6180	1.53090
$401$	−31.8212	−1.58907	−0.794536	−	0.607217i	$-0.792286\pi$
$401$	−31.8212	−1.58907	−0.794536	+	0.607217i	$0.792286\pi$
$402$	−0.889727	−0.0443755
$403$	−1.92763	−0.0960220
$404$	−23.1212	−1.15032
$405$	−3.93237	−0.195401
$406$	−0.113624	−0.00563907
$407$	−36.1742	−1.79309
$408$	3.58824	0.177644
$409$	36.1282	1.78642	0.893211	−	0.449637i	$-0.148447\pi$
$409$	36.1282	1.78642	0.893211	+	0.449637i	$0.148447\pi$
$410$	10.6934	0.528108
$411$	22.2832	1.09915
$412$	−12.1813	−0.600128
$413$	−0.808803	−0.0397986
$414$	−0.429717	−0.0211194
$415$	−29.7600	−1.46086
$416$	2.96180	0.145214
$417$	13.2316	0.647954
$418$	6.78374	0.331803
$419$	−21.0179	−1.02679	−0.513397	−	0.858151i	$-0.671613\pi$
$419$	−21.0179	−1.02679	−0.513397	+	0.858151i	$0.671613\pi$
$420$	−1.88756	−0.0921037
$421$	−1.86480	−0.0908846	−0.0454423	−	0.998967i	$-0.514470\pi$
$421$	−1.86480	−0.0908846	−0.0454423	+	0.998967i	$0.514470\pi$
$422$	−4.67757	−0.227701
$423$	−0.521743	−0.0253680
$424$	19.9925	0.970921
$425$	22.9005	1.11084
$426$	−1.09295	−0.0529536
$427$	2.79136	0.135083
$428$	−18.7461	−0.906128
$429$	−2.18269	−0.105381
$430$	−7.26778	−0.350483
$431$	−12.8006	−0.616586	−0.308293	−	0.951292i	$-0.599758\pi$
$431$	−12.8006	−0.616586	−0.308293	+	0.951292i	$0.599758\pi$
$432$	−2.92616	−0.140785
$433$	18.5123	0.889645	0.444823	−	0.895619i	$-0.353267\pi$
$433$	18.5123	0.889645	0.444823	+	0.895619i	$0.353267\pi$
$434$	−0.335471	−0.0161031
$435$	−3.93237	−0.188543
$436$	−6.42137	−0.307528
$437$	−4.72209	−0.225888
$438$	−4.74726	−0.226833
$439$	−27.6587	−1.32008	−0.660038	−	0.751232i	$-0.729460\pi$
$439$	−27.6587	−1.32008	−0.660038	+	0.751232i	$0.729460\pi$
$440$	21.5538	1.02754
$441$	−6.93008	−0.330004
$442$	0.614025	0.0292062
$443$	−1.84575	−0.0876942	−0.0438471	−	0.999038i	$-0.513961\pi$
$443$	−1.84575	−0.0876942	−0.0438471	+	0.999038i	$0.513961\pi$
$444$	−19.6429	−0.932210
$445$	64.9796	3.08033
$446$	−7.15033	−0.338578
$447$	13.7856	0.652035
$448$	−1.03200	−0.0487573
$449$	−25.4935	−1.20311	−0.601557	−	0.798830i	$-0.705453\pi$
$449$	−25.4935	−1.20311	−0.601557	+	0.798830i	$0.705453\pi$
$450$	4.49637	0.211961
$451$	−21.1558	−0.996190
$452$	−5.41710	−0.254799
$453$	2.45650	0.115416
$454$	3.86387	0.181341
$455$	−0.678862	−0.0318255
$456$	7.74194	0.362550
$457$	17.0135	0.795858	0.397929	−	0.917416i	$-0.369729\pi$
$457$	17.0135	0.795858	0.397929	+	0.917416i	$0.369729\pi$
$458$	4.63412	0.216538
$459$	−2.18859	−0.102155
$460$	−7.13861	−0.332839
$461$	−11.1651	−0.520011	−0.260006	−	0.965607i	$-0.583724\pi$
$461$	−11.1651	−0.520011	−0.260006	+	0.965607i	$0.583724\pi$
$462$	−0.379860	−0.0176727
$463$	−17.2002	−0.799363	−0.399681	−	0.916654i	$-0.630879\pi$
$463$	−17.2002	−0.799363	−0.399681	+	0.916654i	$0.630879\pi$
$464$	−2.92616	−0.135844
$465$	−11.6102	−0.538410
$466$	−6.08632	−0.281943
$467$	30.6388	1.41779	0.708897	−	0.705312i	$-0.249193\pi$
$467$	30.6388	1.41779	0.708897	+	0.705312i	$0.249193\pi$
$468$	−1.18522	−0.0547866
$469$	0.547473	0.0252799
$470$	0.881644	0.0406672
$471$	11.7259	0.540301
$472$	5.01499	0.230834
$473$	14.3786	0.661129
$474$	1.38569	0.0636470
$475$	49.4098	2.26708
$476$	−1.05054	−0.0481514
$477$	−12.1941	−0.558331
$478$	−13.1546	−0.601677
$479$	−31.0993	−1.42096	−0.710482	−	0.703715i	$-0.751523\pi$
$479$	−31.0993	−1.42096	−0.710482	+	0.703715i	$0.751523\pi$
$480$	17.8390	0.814237
$481$	−7.06456	−0.322116
$482$	−9.46121	−0.430946
$483$	0.264416	0.0120314
$484$	−0.320378	−0.0145626
$485$	−23.5128	−1.06766
$486$	−0.429717	−0.0194924
$487$	29.9073	1.35523	0.677614	−	0.735418i	$-0.263014\pi$
$487$	29.9073	1.35523	0.677614	+	0.735418i	$0.263014\pi$
$488$	−17.3079	−0.783490
$489$	−18.6881	−0.845105
$490$	11.7105	0.529027
$491$	10.0846	0.455114	0.227557	−	0.973765i	$-0.426926\pi$
$491$	10.0846	0.455114	0.227557	+	0.973765i	$0.426926\pi$
$492$	−11.4878	−0.517910
$493$	−2.18859	−0.0985693
$494$	1.32481	0.0596062
$495$	−13.1464	−0.590887
$496$	−8.63938	−0.387920
$497$	0.672522	0.0301667
$498$	−3.25208	−0.145729
$499$	26.3156	1.17805	0.589025	−	0.808115i	$-0.299512\pi$
$499$	26.3156	1.17805	0.589025	+	0.808115i	$0.299512\pi$
$500$	39.0022	1.74423
$501$	−3.47606	−0.155299
$502$	−1.11885	−0.0499366
$503$	−15.3285	−0.683466	−0.341733	−	0.939797i	$-0.611014\pi$
$503$	−15.3285	−0.683466	−0.341733	+	0.939797i	$0.611014\pi$
$504$	−0.433515	−0.0193103
$505$	−50.0848	−2.22874
$506$	−1.43660	−0.0638645
$507$	12.5737	0.558419
$508$	6.01767	0.266991
$509$	21.0479	0.932934	0.466467	−	0.884539i	$-0.345527\pi$
$509$	21.0479	0.932934	0.466467	+	0.884539i	$0.345527\pi$
$510$	3.69830	0.163763
$511$	2.92112	0.129223
$512$	22.8694	1.01069
$513$	−4.72209	−0.208485
$514$	3.13972	0.138487
$515$	−26.3869	−1.16275
$516$	7.80770	0.343715
$517$	−1.74425	−0.0767121
$518$	−1.22947	−0.0540197
$519$	5.26597	0.231151
$520$	4.20929	0.184590
$521$	−20.9676	−0.918607	−0.459303	−	0.888280i	$-0.651901\pi$
$521$	−20.9676	−0.918607	−0.459303	+	0.888280i	$0.651901\pi$
$522$	−0.429717	−0.0188082
$523$	−0.712618	−0.0311606	−0.0155803	−	0.999879i	$-0.504960\pi$
$523$	−0.712618	−0.0311606	−0.0155803	+	0.999879i	$0.504960\pi$
$524$	35.2438	1.53963
$525$	−2.76674	−0.120750
$526$	2.87556	0.125380
$527$	−6.46175	−0.281478
$528$	−9.78251	−0.425729
$529$	1.00000	0.0434783
$530$	20.6057	0.895056
$531$	−3.05882	−0.132742
$532$	−2.26663	−0.0982710
$533$	−4.13158	−0.178959
$534$	7.10076	0.307280
$535$	−40.6076	−1.75562
$536$	−3.39461	−0.146625
$537$	−4.47515	−0.193117
$538$	−4.73751	−0.204249
$539$	−23.1681	−0.997922
$540$	−7.13861	−0.307197
$541$	33.0085	1.41914	0.709572	−	0.704633i	$-0.248888\pi$
$541$	33.0085	1.41914	0.709572	+	0.704633i	$0.248888\pi$
$542$	7.79542	0.334842
$543$	−7.51226	−0.322382
$544$	9.92845	0.425679
$545$	−13.9099	−0.595834
$546$	−0.0741838	−0.00317477
$547$	−29.4618	−1.25969	−0.629847	−	0.776719i	$-0.716883\pi$
$547$	−29.4618	−1.25969	−0.629847	+	0.776719i	$0.716883\pi$
$548$	40.4517	1.72801
$549$	10.5567	0.450548
$550$	15.0319	0.640963
$551$	−4.72209	−0.201168
$552$	−1.63952	−0.0697825
$553$	−0.852655	−0.0362586
$554$	−9.88421	−0.419940
$555$	−42.5502	−1.80615
$556$	24.0199	1.01867
$557$	38.4373	1.62864	0.814320	−	0.580417i	$-0.197110\pi$
$557$	38.4373	1.62864	0.814320	+	0.580417i	$0.197110\pi$
$558$	−1.26872	−0.0537094
$559$	2.80804	0.118767
$560$	−3.04257	−0.128572
$561$	−7.31674	−0.308913
$562$	11.8614	0.500344
$563$	−14.8453	−0.625656	−0.312828	−	0.949810i	$-0.601276\pi$
$563$	−14.8453	−0.625656	−0.312828	+	0.949810i	$0.601276\pi$
$564$	−0.947142	−0.0398819
$565$	−11.7345	−0.493672
$566$	5.33422	0.224214
$567$	0.264416	0.0111044
$568$	−4.16998	−0.174969
$569$	13.2521	0.555558	0.277779	−	0.960645i	$-0.410402\pi$
$569$	13.2521	0.555558	0.277779	+	0.960645i	$0.410402\pi$
$570$	7.97942	0.334221
$571$	14.8030	0.619487	0.309744	−	0.950820i	$-0.399757\pi$
$571$	14.8030	0.619487	0.309744	+	0.950820i	$0.399757\pi$
$572$	−3.96232	−0.165673
$573$	19.4407	0.812146
$574$	−0.719032	−0.0300118
$575$	−10.4636	−0.436361
$576$	−3.90293	−0.162622
$577$	34.3080	1.42826	0.714130	−	0.700013i	$-0.246822\pi$
$577$	34.3080	1.42826	0.714130	+	0.700013i	$0.246822\pi$
$578$	−5.24687	−0.218241
$579$	−2.58415	−0.107394
$580$	−7.13861	−0.296415
$581$	2.00109	0.0830192
$582$	−2.56940	−0.106505
$583$	−40.7665	−1.68838
$584$	−18.1124	−0.749498
$585$	−2.56740	−0.106149
$586$	−9.73035	−0.401957
$587$	3.03981	0.125466	0.0627332	−	0.998030i	$-0.480018\pi$
$587$	3.03981	0.125466	0.0627332	+	0.998030i	$0.480018\pi$
$588$	−12.5805	−0.518810
$589$	−13.9418	−0.574462
$590$	5.16882	0.212797
$591$	15.5639	0.640212
$592$	−31.6624	−1.30132
$593$	9.15034	0.375759	0.187880	−	0.982192i	$-0.439838\pi$
$593$	9.15034	0.375759	0.187880	+	0.982192i	$0.439838\pi$
$594$	−1.43660	−0.0589443
$595$	−2.27566	−0.0932931
$596$	25.0255	1.02509
$597$	18.4304	0.754305
$598$	−0.280557	−0.0114728
$599$	41.0842	1.67865	0.839327	−	0.543626i	$-0.182949\pi$
$599$	41.0842	1.67865	0.839327	+	0.543626i	$0.182949\pi$
$600$	17.1552	0.700357
$601$	36.3427	1.48245	0.741224	−	0.671257i	$-0.234245\pi$
$601$	36.3427	1.48245	0.741224	+	0.671257i	$0.234245\pi$
$602$	0.488692	0.0199176
$603$	2.07050	0.0843171
$604$	4.45938	0.181450
$605$	−0.693999	−0.0282151
$606$	−5.47310	−0.222329
$607$	20.3547	0.826171	0.413086	−	0.910692i	$-0.364451\pi$
$607$	20.3547	0.826171	0.413086	+	0.910692i	$0.364451\pi$
$608$	21.4215	0.868758
$609$	0.264416	0.0107147
$610$	−17.8388	−0.722270
$611$	−0.340639	−0.0137808
$612$	−3.97305	−0.160601
$613$	10.7638	0.434747	0.217373	−	0.976089i	$-0.430251\pi$
$613$	10.7638	0.434747	0.217373	+	0.976089i	$0.430251\pi$
$614$	10.9891	0.443483
$615$	−24.8847	−1.00345
$616$	−1.44930	−0.0583938
$617$	−28.9340	−1.16484	−0.582419	−	0.812889i	$-0.697893\pi$
$617$	−28.9340	−1.16484	−0.582419	+	0.812889i	$0.697893\pi$
$618$	−2.88347	−0.115990
$619$	20.9923	0.843751	0.421875	−	0.906654i	$-0.361372\pi$
$619$	20.9923	0.843751	0.421875	+	0.906654i	$0.361372\pi$
$620$	−21.0765	−0.846452
$621$	1.00000	0.0401286
$622$	7.50811	0.301048
$623$	−4.36929	−0.175052
$624$	−1.91045	−0.0764793
$625$	32.1683	1.28673
$626$	−10.8285	−0.432793
$627$	−15.7865	−0.630453
$628$	21.2865	0.849425
$629$	−23.6816	−0.944248
$630$	−0.446813	−0.0178014
$631$	−19.2392	−0.765899	−0.382949	−	0.923769i	$-0.625092\pi$
$631$	−19.2392	−0.765899	−0.382949	+	0.923769i	$0.625092\pi$
$632$	5.28690	0.210302
$633$	10.8852	0.432649
$634$	−6.25360	−0.248362
$635$	13.0354	0.517294
$636$	−22.1365	−0.877771
$637$	−4.52457	−0.179270
$638$	−1.43660	−0.0568754
$639$	2.54342	0.100616
$640$	42.2733	1.67100
$641$	−4.79064	−0.189219	−0.0946094	−	0.995514i	$-0.530160\pi$
$641$	−4.79064	−0.189219	−0.0946094	+	0.995514i	$0.530160\pi$
$642$	−4.43747	−0.175133
$643$	−13.8827	−0.547482	−0.273741	−	0.961803i	$-0.588261\pi$
$643$	−13.8827	−0.547482	−0.273741	+	0.961803i	$0.588261\pi$
$644$	0.480006	0.0189149
$645$	16.9129	0.665946
$646$	4.44101	0.174729
$647$	−46.0508	−1.81044	−0.905222	−	0.424938i	$-0.860296\pi$
$647$	−46.0508	−1.81044	−0.905222	+	0.424938i	$0.860296\pi$
$648$	−1.63952	−0.0644063
$649$	−10.2260	−0.401407
$650$	2.93562	0.115145
$651$	0.780680	0.0305973
$652$	−33.9253	−1.32862
$653$	6.27782	0.245670	0.122835	−	0.992427i	$-0.460801\pi$
$653$	6.27782	0.245670	0.122835	+	0.992427i	$0.460801\pi$
$654$	−1.52003	−0.0594377
$655$	76.3446	2.98303
$656$	−18.5172	−0.722976
$657$	11.0474	0.431001
$658$	−0.0592826	−0.00231108
$659$	−3.00066	−0.116889	−0.0584445	−	0.998291i	$-0.518614\pi$
$659$	−3.00066	−0.116889	−0.0584445	+	0.998291i	$0.518614\pi$
$660$	−23.8653	−0.928954
$661$	16.0618	0.624733	0.312366	−	0.949962i	$-0.398878\pi$
$661$	16.0618	0.624733	0.312366	+	0.949962i	$0.398878\pi$
$662$	1.34575	0.0523039
$663$	−1.42891	−0.0554941
$664$	−12.4078	−0.481515
$665$	−4.90995	−0.190400
$666$	−4.64974	−0.180174
$667$	1.00000	0.0387202
$668$	−6.31025	−0.244151
$669$	16.6396	0.643325
$670$	−3.49874	−0.135168
$671$	35.2923	1.36244
$672$	−1.19951	−0.0462722
$673$	24.0623	0.927533	0.463767	−	0.885957i	$-0.346498\pi$
$673$	24.0623	0.927533	0.463767	+	0.885957i	$0.346498\pi$
$674$	−4.17067	−0.160648
$675$	−10.4636	−0.402743
$676$	22.8257	0.877910
$677$	−11.7826	−0.452841	−0.226420	−	0.974030i	$-0.572702\pi$
$677$	−11.7826	−0.452841	−0.226420	+	0.974030i	$0.572702\pi$
$678$	−1.28230	−0.0492465
$679$	1.58102	0.0606739
$680$	14.1103	0.541105
$681$	−8.99168	−0.344562
$682$	−4.24150	−0.162416
$683$	−21.9964	−0.841668	−0.420834	−	0.907138i	$-0.638263\pi$
$683$	−21.9964	−0.841668	−0.420834	+	0.907138i	$0.638263\pi$
$684$	−8.57221	−0.327767
$685$	87.6260	3.34802
$686$	−1.58279	−0.0604314
$687$	−10.7841	−0.411440
$688$	12.5853	0.479809
$689$	−7.96140	−0.303305
$690$	−1.68981	−0.0643299
$691$	31.1468	1.18488	0.592440	−	0.805615i	$-0.298165\pi$
$691$	31.1468	1.18488	0.592440	+	0.805615i	$0.298165\pi$
$692$	9.55955	0.363400
$693$	0.883977	0.0335795
$694$	5.20527	0.197589
$695$	52.0315	1.97367
$696$	−1.63952	−0.0621457
$697$	−13.8498	−0.524598
$698$	1.75278	0.0663437
$699$	14.1636	0.535715
$700$	−5.02258	−0.189836
$701$	9.59412	0.362365	0.181183	−	0.983449i	$-0.442008\pi$
$701$	9.59412	0.362365	0.181183	+	0.983449i	$0.442008\pi$
$702$	−0.280557	−0.0105889
$703$	−51.0953	−1.92709
$704$	−13.0480	−0.491764
$705$	−2.05169	−0.0772710
$706$	1.30006	0.0489283
$707$	3.36774	0.126657
$708$	−5.55282	−0.208688
$709$	−17.3939	−0.653240	−0.326620	−	0.945156i	$-0.605910\pi$
$709$	−17.3939	−0.653240	−0.326620	+	0.945156i	$0.605910\pi$
$710$	−4.29789	−0.161297
$711$	−3.22467	−0.120935
$712$	27.0918	1.01531
$713$	2.95247	0.110571
$714$	−0.248677	−0.00930650
$715$	−8.58313	−0.320991
$716$	−8.12393	−0.303605
$717$	30.6122	1.14323
$718$	−3.34290	−0.124756
$719$	−21.6712	−0.808198	−0.404099	−	0.914715i	$-0.632415\pi$
$719$	−21.6712	−0.808198	−0.404099	+	0.914715i	$0.632415\pi$
$720$	−11.5067	−0.428831
$721$	1.77428	0.0660776
$722$	1.41725	0.0527447
$723$	22.0173	0.818833
$724$	−13.6373	−0.506827
$725$	−10.4636	−0.388607
$726$	−0.0758379	−0.00281461
$727$	−42.6546	−1.58197	−0.790986	−	0.611834i	$-0.790432\pi$
$727$	−42.6546	−1.58197	−0.790986	+	0.611834i	$0.790432\pi$
$728$	−0.283037	−0.0104900
$729$	1.00000	0.0370370
$730$	−18.6680	−0.690934
$731$	9.41303	0.348153
$732$	19.1640	0.708322
$733$	31.1920	1.15210	0.576052	−	0.817413i	$-0.304593\pi$
$733$	31.1920	1.15210	0.576052	+	0.817413i	$0.304593\pi$
$734$	10.8542	0.400634
$735$	−27.2517	−1.00519
$736$	−4.53645	−0.167216
$737$	6.92193	0.254972
$738$	−2.71932	−0.100099
$739$	−17.1112	−0.629447	−0.314724	−	0.949183i	$-0.601912\pi$
$739$	−17.1112	−0.629447	−0.314724	+	0.949183i	$0.601912\pi$
$740$	−77.2432	−2.83952
$741$	−3.08299	−0.113257
$742$	−1.38555	−0.0508651
$743$	−3.45706	−0.126827	−0.0634136	−	0.997987i	$-0.520199\pi$
$743$	−3.45706	−0.126827	−0.0634136	+	0.997987i	$0.520199\pi$
$744$	−4.84062	−0.177466
$745$	54.2100	1.98610
$746$	−1.81061	−0.0662910
$747$	7.56795	0.276897
$748$	−13.2824	−0.485652
$749$	2.73049	0.0997700
$750$	9.23236	0.337118
$751$	−22.1896	−0.809709	−0.404855	−	0.914381i	$-0.632678\pi$
$751$	−22.1896	−0.809709	−0.404855	+	0.914381i	$0.632678\pi$
$752$	−1.52670	−0.0556731
$753$	2.60369	0.0948836
$754$	−0.280557	−0.0102173
$755$	9.65986	0.351558
$756$	0.480006	0.0174577
$757$	−14.5708	−0.529586	−0.264793	−	0.964305i	$-0.585304\pi$
$757$	−14.5708	−0.529586	−0.264793	+	0.964305i	$0.585304\pi$
$758$	−11.2762	−0.409571
$759$	3.34312	0.121348
$760$	30.4442	1.10433
$761$	31.6298	1.14658	0.573290	−	0.819353i	$-0.305667\pi$
$761$	31.6298	1.14658	0.573290	+	0.819353i	$0.305667\pi$
$762$	1.42447	0.0516030
$763$	0.935313	0.0338606
$764$	35.2915	1.27680
$765$	−8.60636	−0.311164
$766$	−11.7248	−0.423634
$767$	−1.99707	−0.0721100
$768$	−3.18637	−0.114978
$769$	−1.76911	−0.0637957	−0.0318979	−	0.999491i	$-0.510155\pi$
$769$	−1.76911	−0.0637957	−0.0318979	+	0.999491i	$0.510155\pi$
$770$	−1.49375	−0.0538310
$771$	−7.30649	−0.263137
$772$	−4.69112	−0.168837
$773$	21.3755	0.768822	0.384411	−	0.923162i	$-0.374405\pi$
$773$	21.3755	0.768822	0.384411	+	0.923162i	$0.374405\pi$
$774$	1.84819	0.0664318
$775$	−30.8933	−1.10972
$776$	−9.80313	−0.351912
$777$	2.86111	0.102642
$778$	1.47955	0.0530443
$779$	−29.8821	−1.07064
$780$	−4.66071	−0.166880
$781$	8.50297	0.304260
$782$	−0.940475	−0.0336313
$783$	1.00000	0.0357371
$784$	−20.2785	−0.724233
$785$	46.1106	1.64576
$786$	8.34269	0.297574
$787$	−51.7747	−1.84557	−0.922784	−	0.385317i	$-0.874092\pi$
$787$	−51.7747	−1.84557	−0.922784	+	0.385317i	$0.874092\pi$
$788$	28.2538	1.00650
$789$	−6.69175	−0.238233
$790$	5.44907	0.193869
$791$	0.789035	0.0280549
$792$	−5.48111	−0.194763
$793$	6.89233	0.244754
$794$	7.88300	0.279757
$795$	−47.9519	−1.70068
$796$	33.4575	1.18587
$797$	22.6353	0.801782	0.400891	−	0.916126i	$-0.368701\pi$
$797$	22.6353	0.801782	0.400891	+	0.916126i	$0.368701\pi$
$798$	−0.536543	−0.0189934
$799$	−1.14188	−0.0403969
$800$	47.4675	1.67823
$801$	−16.5243	−0.583857
$802$	−13.6741	−0.482849
$803$	36.9329	1.30333
$804$	3.75866	0.132558
$805$	1.03978	0.0366476
$806$	−0.828334	−0.0291768
$807$	11.0247	0.388089
$808$	−20.8817	−0.734617
$809$	28.7763	1.01172	0.505861	−	0.862615i	$-0.331175\pi$
$809$	28.7763	1.01172	0.505861	+	0.862615i	$0.331175\pi$
$810$	−1.68981	−0.0593738
$811$	−38.5887	−1.35503	−0.677516	−	0.735508i	$-0.736944\pi$
$811$	−38.5887	−1.35503	−0.677516	+	0.735508i	$0.736944\pi$
$812$	0.480006	0.0168449
$813$	−18.1408	−0.636226
$814$	−15.5447	−0.544840
$815$	−73.4886	−2.57419
$816$	−6.40417	−0.224191
$817$	20.3095	0.710538
$818$	15.5249	0.542815
$819$	0.172634	0.00603233
$820$	−45.1743	−1.57755
$821$	−16.0346	−0.559610	−0.279805	−	0.960057i	$-0.590270\pi$
$821$	−16.0346	−0.559610	−0.279805	+	0.960057i	$0.590270\pi$
$822$	9.57548	0.333983
$823$	6.06181	0.211301	0.105651	−	0.994403i	$-0.466307\pi$
$823$	6.06181	0.211301	0.105651	+	0.994403i	$0.466307\pi$
$824$	−11.0014	−0.383253
$825$	−34.9810	−1.21788
$826$	−0.347556	−0.0120930
$827$	−6.48326	−0.225445	−0.112723	−	0.993627i	$-0.535957\pi$
$827$	−6.48326	−0.225445	−0.112723	+	0.993627i	$0.535957\pi$
$828$	1.81534	0.0630875
$829$	−22.8406	−0.793287	−0.396644	−	0.917973i	$-0.629825\pi$
$829$	−22.8406	−0.793287	−0.396644	+	0.917973i	$0.629825\pi$
$830$	−12.7884	−0.443891
$831$	23.0017	0.797920
$832$	−2.54817	−0.0883420
$833$	−15.1671	−0.525510
$834$	5.68584	0.196884
$835$	−13.6692	−0.473041
$836$	−28.6580	−0.991157
$837$	2.95247	0.102052
$838$	−9.03176	−0.311997
$839$	45.4261	1.56828	0.784142	−	0.620581i	$-0.213103\pi$
$839$	45.4261	1.56828	0.784142	+	0.620581i	$0.213103\pi$
$840$	−1.70474	−0.0588192
$841$	1.00000	0.0344828
$842$	−0.801335	−0.0276158
$843$	−27.6029	−0.950693
$844$	19.7604	0.680183
$845$	49.4446	1.70095
$846$	−0.224202	−0.00770821
$847$	0.0466651	0.00160343
$848$	−35.6820	−1.22532
$849$	−12.4133	−0.426025
$850$	9.84072	0.337534
$851$	10.8205	0.370921
$852$	4.61718	0.158182
$853$	−43.9423	−1.50455	−0.752277	−	0.658846i	$-0.771045\pi$
$853$	−43.9423	−1.50455	−0.752277	+	0.658846i	$0.771045\pi$
$854$	1.19949	0.0410459
$855$	−18.5690	−0.635047
$856$	−16.9305	−0.578671
$857$	−1.78836	−0.0610891	−0.0305445	−	0.999533i	$-0.509724\pi$
$857$	−1.78836	−0.0610891	−0.0305445	+	0.999533i	$0.509724\pi$
$858$	−0.937937	−0.0320206
$859$	−34.3712	−1.17273	−0.586366	−	0.810046i	$-0.699442\pi$
$859$	−34.3712	−1.17273	−0.586366	+	0.810046i	$0.699442\pi$
$860$	30.7028	1.04696
$861$	1.67327	0.0570249
$862$	−5.50065	−0.187353
$863$	25.6500	0.873137	0.436569	−	0.899671i	$-0.356194\pi$
$863$	25.6500	0.873137	0.436569	+	0.899671i	$0.356194\pi$
$864$	−4.53645	−0.154333
$865$	20.7078	0.704086
$866$	7.95505	0.270324
$867$	12.2101	0.414675
$868$	1.41720	0.0481030
$869$	−10.7805	−0.365702
$870$	−1.68981	−0.0572898
$871$	1.35180	0.0458040
$872$	−5.79942	−0.196393
$873$	5.97928	0.202368
$874$	−2.02916	−0.0686374
$875$	−5.68092	−0.192050
$876$	20.0548	0.677591
$877$	19.0441	0.643074	0.321537	−	0.946897i	$-0.395800\pi$
$877$	19.0441	0.643074	0.321537	+	0.946897i	$0.395800\pi$
$878$	−11.8854	−0.401113
$879$	22.6436	0.763751
$880$	−38.4685	−1.29677
$881$	−18.9432	−0.638212	−0.319106	−	0.947719i	$-0.603383\pi$
$881$	−18.9432	−0.638212	−0.319106	+	0.947719i	$0.603383\pi$
$882$	−2.97797	−0.100274
$883$	−32.8619	−1.10589	−0.552946	−	0.833217i	$-0.686496\pi$
$883$	−32.8619	−1.10589	−0.552946	+	0.833217i	$0.686496\pi$
$884$	−2.59395	−0.0872441
$885$	−12.0284	−0.404331
$886$	−0.793149	−0.0266464
$887$	24.9869	0.838978	0.419489	−	0.907760i	$-0.362209\pi$
$887$	24.9869	0.838978	0.419489	+	0.907760i	$0.362209\pi$
$888$	−17.7404	−0.595328
$889$	−0.876512	−0.0293973
$890$	27.9228	0.935976
$891$	3.34312	0.111999
$892$	30.2066	1.01139
$893$	−2.46371	−0.0824451
$894$	5.92389	0.198125
$895$	−17.5979	−0.588234
$896$	−2.84249	−0.0949610
$897$	0.652888	0.0217993
$898$	−10.9550	−0.365573
$899$	2.95247	0.0984702
$900$	−18.9950	−0.633165
$901$	−26.6880	−0.889106
$902$	−9.09102	−0.302698
$903$	−1.13724	−0.0378450
$904$	−4.89243	−0.162720
$905$	−29.5410	−0.981976
$906$	1.05560	0.0350699
$907$	−11.2172	−0.372460	−0.186230	−	0.982506i	$-0.559627\pi$
$907$	−11.2172	−0.372460	−0.186230	+	0.982506i	$0.559627\pi$
$908$	−16.3230	−0.541697
$909$	12.7365	0.422444
$910$	−0.291718	−0.00967037
$911$	−30.3791	−1.00650	−0.503252	−	0.864140i	$-0.667863\pi$
$911$	−30.3791	−1.00650	−0.503252	+	0.864140i	$0.667863\pi$
$912$	−13.8176	−0.457546
$913$	25.3006	0.837328
$914$	7.31099	0.241826
$915$	41.5128	1.37237
$916$	−19.5769	−0.646839
$917$	−5.13348	−0.169523
$918$	−0.940475	−0.0310403
$919$	−41.7168	−1.37611	−0.688054	−	0.725659i	$-0.741535\pi$
$919$	−41.7168	−1.37611	−0.688054	+	0.725659i	$0.741535\pi$
$920$	−6.44719	−0.212558
$921$	−25.5728	−0.842654
$922$	−4.79784	−0.158008
$923$	1.66057	0.0546583
$924$	1.60472	0.0527915
$925$	−113.221	−3.72268
$926$	−7.39123	−0.242891
$927$	6.71017	0.220391
$928$	−4.53645	−0.148916
$929$	32.8798	1.07875	0.539375	−	0.842066i	$-0.318661\pi$
$929$	32.8798	1.07875	0.539375	+	0.842066i	$0.318661\pi$
$930$	−4.98910	−0.163599
$931$	−32.7245	−1.07250
$932$	25.7117	0.842216
$933$	−17.4722	−0.572015
$934$	13.1660	0.430805
$935$	−28.7721	−0.940950
$936$	−1.07042	−0.0349878
$937$	−34.1174	−1.11457	−0.557284	−	0.830322i	$-0.688157\pi$
$937$	−34.1174	−1.11457	−0.557284	+	0.830322i	$0.688157\pi$
$938$	0.235258	0.00768146
$939$	25.1991	0.822342
$940$	−3.72452	−0.121480
$941$	19.1523	0.624348	0.312174	−	0.950025i	$-0.398943\pi$
$941$	19.1523	0.624348	0.312174	+	0.950025i	$0.398943\pi$
$942$	5.03881	0.164173
$943$	6.32816	0.206073
$944$	−8.95060	−0.291317
$945$	1.03978	0.0338242
$946$	6.17873	0.200888
$947$	27.3369	0.888331	0.444165	−	0.895945i	$-0.353500\pi$
$947$	27.3369	0.888331	0.444165	+	0.895945i	$0.353500\pi$
$948$	−5.85388	−0.190125
$949$	7.21272	0.234135
$950$	21.2322	0.688865
$951$	14.5528	0.471908
$952$	−0.948788	−0.0307504
$953$	15.2018	0.492436	0.246218	−	0.969214i	$-0.420812\pi$
$953$	15.2018	0.492436	0.246218	+	0.969214i	$0.420812\pi$
$954$	−5.24002	−0.169652
$955$	76.4480	2.47380
$956$	55.5717	1.79732
$957$	3.34312	0.108068
$958$	−13.3639	−0.431768
$959$	−5.89205	−0.190264
$960$	−15.3478	−0.495347
$961$	−22.2829	−0.718805
$962$	−3.03576	−0.0978768
$963$	10.3265	0.332766
$964$	39.9690	1.28731
$965$	−10.1618	−0.327121
$966$	0.113624	0.00365580
$967$	−27.3795	−0.880466	−0.440233	−	0.897884i	$-0.645104\pi$
$967$	−27.3795	−0.880466	−0.440233	+	0.897884i	$0.645104\pi$
$968$	−0.289348	−0.00929998
$969$	−10.3347	−0.331999
$970$	−10.1038	−0.324414
$971$	52.2224	1.67590	0.837948	−	0.545750i	$-0.183755\pi$
$971$	52.2224	1.67590	0.837948	+	0.545750i	$0.183755\pi$
$972$	1.81534	0.0582272
$973$	−3.49865	−0.112161
$974$	12.8517	0.411794
$975$	−6.83153	−0.218784
$976$	30.8905	0.988782
$977$	31.1787	0.997496	0.498748	−	0.866747i	$-0.333793\pi$
$977$	31.1787	0.997496	0.498748	+	0.866747i	$0.333793\pi$
$978$	−8.03059	−0.256790
$979$	−55.2427	−1.76557
$980$	−49.4712	−1.58030
$981$	3.53727	0.112936
$982$	4.33354	0.138289
$983$	42.1186	1.34337	0.671687	−	0.740835i	$-0.265570\pi$
$983$	42.1186	1.34337	0.671687	+	0.740835i	$0.265570\pi$
$984$	−10.3751	−0.330747
$985$	61.2030	1.95009
$986$	−0.940475	−0.0299508
$987$	0.137957	0.00439123
$988$	−5.59669	−0.178054
$989$	−4.30095	−0.136762
$990$	−5.64924	−0.179544
$991$	−37.9228	−1.20466	−0.602329	−	0.798248i	$-0.705760\pi$
$991$	−37.9228	−1.20466	−0.602329	+	0.798248i	$0.705760\pi$
$992$	−13.3937	−0.425251
$993$	−3.13170	−0.0993816
$994$	0.288994	0.00916633
$995$	72.4751	2.29761
$996$	13.7384	0.435319
$997$	11.3857	0.360588	0.180294	−	0.983613i	$-0.442295\pi$
$997$	11.3857	0.360588	0.180294	+	0.983613i	$0.442295\pi$
$998$	11.3083	0.357957
$999$	10.8205	0.342345

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2001.2.a.m.1.8	✓	14
3.2	odd	2		6003.2.a.p.1.7		14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2001.2.a.m.1.8	✓	14	1.1	even	1	trivial
6003.2.a.p.1.7		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)

\(f(q)\)	\(=\)	\(q+0.429717 q^{2} -1.00000 q^{3} -1.81534 q^{4} -3.93237 q^{5} -0.429717 q^{6} +0.264416 q^{7} -1.63952 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+0.429717 q^{2} -1.00000 q^{3} -1.81534 q^{4} -3.93237 q^{5} -0.429717 q^{6} +0.264416 q^{7} -1.63952 q^{8} +1.00000 q^{9} -1.68981 q^{10} +3.34312 q^{11} +1.81534 q^{12} +0.652888 q^{13} +0.113624 q^{14} +3.93237 q^{15} +2.92616 q^{16} +2.18859 q^{17} +0.429717 q^{18} +4.72209 q^{19} +7.13861 q^{20} -0.264416 q^{21} +1.43660 q^{22} -1.00000 q^{23} +1.63952 q^{24} +10.4636 q^{25} +0.280557 q^{26} -1.00000 q^{27} -0.480006 q^{28} -1.00000 q^{29} +1.68981 q^{30} -2.95247 q^{31} +4.53645 q^{32} -3.34312 q^{33} +0.940475 q^{34} -1.03978 q^{35} -1.81534 q^{36} -10.8205 q^{37} +2.02916 q^{38} -0.652888 q^{39} +6.44719 q^{40} -6.32816 q^{41} -0.113624 q^{42} +4.30095 q^{43} -6.06892 q^{44} -3.93237 q^{45} -0.429717 q^{46} -0.521743 q^{47} -2.92616 q^{48} -6.93008 q^{49} +4.49637 q^{50} -2.18859 q^{51} -1.18522 q^{52} -12.1941 q^{53} -0.429717 q^{54} -13.1464 q^{55} -0.433515 q^{56} -4.72209 q^{57} -0.429717 q^{58} -3.05882 q^{59} -7.13861 q^{60} +10.5567 q^{61} -1.26872 q^{62} +0.264416 q^{63} -3.90293 q^{64} -2.56740 q^{65} -1.43660 q^{66} +2.07050 q^{67} -3.97305 q^{68} +1.00000 q^{69} -0.446813 q^{70} +2.54342 q^{71} -1.63952 q^{72} +11.0474 q^{73} -4.64974 q^{74} -10.4636 q^{75} -8.57221 q^{76} +0.883977 q^{77} -0.280557 q^{78} -3.22467 q^{79} -11.5067 q^{80} +1.00000 q^{81} -2.71932 q^{82} +7.56795 q^{83} +0.480006 q^{84} -8.60636 q^{85} +1.84819 q^{86} +1.00000 q^{87} -5.48111 q^{88} -16.5243 q^{89} -1.68981 q^{90} +0.172634 q^{91} +1.81534 q^{92} +2.95247 q^{93} -0.224202 q^{94} -18.5690 q^{95} -4.53645 q^{96} +5.97928 q^{97} -2.97797 q^{98} +3.34312 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q - 2 q^{2} - 14 q^{3} + 12 q^{4} - 3 q^{5} + 2 q^{6} - 3 q^{7} - 6 q^{8} + 14 q^{9}+O(q^{10}) \) 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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