LMFDB - Embedded newform 2001.2.a.o.1.17

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:	$20$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - 2 x^{19} - 33 x^{18} + 64 x^{17} + 453 x^{16} - 846 x^{15} - 3353 x^{14} + 5985 x^{13} + \cdots - 256 $ x^20 - 2x^19 - 33x^18 + 64x^17 + 453x^16 - 846x^15 - 3353x^14 + 5985x^13 + 14484x^12 - 24566x^11 - 36791x^10 + 59410x^9 + 52109x^8 - 82362x^7 - 34967x^6 + 60661x^5 + 5201x^4 - 19624x^3 + 2768x^2 + 1408*x - 256
Coefficient ring:	$\Z[a_1, \ldots, a_{17}]$
Coefficient ring index:	$ 2^{7} $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.17
Root			$2.44527$ 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)

$f(q)$	$=$	$q+2.44527 q^{2} +1.00000 q^{3} +3.97935 q^{4} -1.74520 q^{5} +2.44527 q^{6} +5.10283 q^{7} +4.84005 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+2.44527 q^{2} +1.00000 q^{3} +3.97935 q^{4} -1.74520 q^{5} +2.44527 q^{6} +5.10283 q^{7} +4.84005 q^{8} +1.00000 q^{9} -4.26748 q^{10} -5.64276 q^{11} +3.97935 q^{12} +6.72828 q^{13} +12.4778 q^{14} -1.74520 q^{15} +3.87652 q^{16} -0.427470 q^{17} +2.44527 q^{18} -1.22783 q^{19} -6.94475 q^{20} +5.10283 q^{21} -13.7981 q^{22} +1.00000 q^{23} +4.84005 q^{24} -1.95428 q^{25} +16.4525 q^{26} +1.00000 q^{27} +20.3059 q^{28} +1.00000 q^{29} -4.26748 q^{30} +5.44908 q^{31} -0.200940 q^{32} -5.64276 q^{33} -1.04528 q^{34} -8.90544 q^{35} +3.97935 q^{36} -10.5826 q^{37} -3.00237 q^{38} +6.72828 q^{39} -8.44684 q^{40} +6.52884 q^{41} +12.4778 q^{42} -4.88914 q^{43} -22.4545 q^{44} -1.74520 q^{45} +2.44527 q^{46} -8.92503 q^{47} +3.87652 q^{48} +19.0388 q^{49} -4.77875 q^{50} -0.427470 q^{51} +26.7742 q^{52} +5.99381 q^{53} +2.44527 q^{54} +9.84773 q^{55} +24.6979 q^{56} -1.22783 q^{57} +2.44527 q^{58} +0.440433 q^{59} -6.94475 q^{60} -6.08220 q^{61} +13.3245 q^{62} +5.10283 q^{63} -8.24440 q^{64} -11.7422 q^{65} -13.7981 q^{66} +6.28479 q^{67} -1.70105 q^{68} +1.00000 q^{69} -21.7762 q^{70} +3.56305 q^{71} +4.84005 q^{72} -7.59201 q^{73} -25.8774 q^{74} -1.95428 q^{75} -4.88596 q^{76} -28.7940 q^{77} +16.4525 q^{78} +14.5546 q^{79} -6.76530 q^{80} +1.00000 q^{81} +15.9648 q^{82} -8.12019 q^{83} +20.3059 q^{84} +0.746019 q^{85} -11.9553 q^{86} +1.00000 q^{87} -27.3112 q^{88} +4.45271 q^{89} -4.26748 q^{90} +34.3333 q^{91} +3.97935 q^{92} +5.44908 q^{93} -21.8241 q^{94} +2.14280 q^{95} -0.200940 q^{96} -8.18389 q^{97} +46.5551 q^{98} -5.64276 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + 2 q^{2} + 20 q^{3} + 30 q^{4} - q^{5} + 2 q^{6} + 9 q^{7} + 6 q^{8} + 20 q^{9}+O(q^{10}) $ 20 * q + 2 * q^2 + 20 * q^3 + 30 * q^4 - q^5 + 2 * q^6 + 9 * q^7 + 6 * q^8 + 20 * q^9	\( 20 q + 2 q^{2} + 20 q^{3} + 30 q^{4} - q^{5} + 2 q^{6} + 9 q^{7} + 6 q^{8} + 20 q^{9} + 7 q^{10} + 30 q^{12} + 21 q^{13} - q^{14} - q^{15} + 58 q^{16} - 4 q^{17} + 2 q^{18} + 7 q^{19} - 20 q^{20} + 9 q^{21} + 7 q^{22} + 20 q^{23} + 6 q^{24} + 47 q^{25} + 8 q^{26} + 20 q^{27} + 11 q^{28} + 20 q^{29} + 7 q^{30} + 28 q^{31} + 14 q^{32} + 16 q^{34} + 9 q^{35} + 30 q^{36} + 14 q^{37} - 20 q^{38} + 21 q^{39} + 34 q^{40} + 7 q^{41} - q^{42} + 3 q^{43} - q^{44} - q^{45} + 2 q^{46} + 3 q^{47} + 58 q^{48} + 35 q^{49} - 24 q^{50} - 4 q^{51} + 73 q^{52} - 19 q^{53} + 2 q^{54} + 29 q^{55} - 30 q^{56} + 7 q^{57} + 2 q^{58} + 20 q^{59} - 20 q^{60} + 15 q^{61} + 12 q^{62} + 9 q^{63} + 82 q^{64} - 28 q^{65} + 7 q^{66} + 20 q^{67} - 23 q^{68} + 20 q^{69} - 24 q^{70} + 63 q^{71} + 6 q^{72} + 19 q^{73} + 16 q^{74} + 47 q^{75} - 44 q^{76} - 7 q^{77} + 8 q^{78} + 32 q^{79} - 56 q^{80} + 20 q^{81} - 20 q^{82} - 21 q^{83} + 11 q^{84} + 4 q^{85} - 6 q^{86} + 20 q^{87} + 55 q^{88} - 13 q^{89} + 7 q^{90} + 70 q^{91} + 30 q^{92} + 28 q^{93} - 12 q^{94} + 9 q^{95} + 14 q^{96} - 9 q^{97} + 31 q^{98}+O(q^{100}) \) 20 * q + 2 * q^2 + 20 * q^3 + 30 * q^4 - q^5 + 2 * q^6 + 9 * q^7 + 6 * q^8 + 20 * q^9 + 7 * q^10 + 30 * q^12 + 21 * q^13 - q^14 - q^15 + 58 * q^16 - 4 * q^17 + 2 * q^18 + 7 * q^19 - 20 * q^20 + 9 * q^21 + 7 * q^22 + 20 * q^23 + 6 * q^24 + 47 * q^25 + 8 * q^26 + 20 * q^27 + 11 * q^28 + 20 * q^29 + 7 * q^30 + 28 * q^31 + 14 * q^32 + 16 * q^34 + 9 * q^35 + 30 * q^36 + 14 * q^37 - 20 * q^38 + 21 * q^39 + 34 * q^40 + 7 * q^41 - q^42 + 3 * q^43 - q^44 - q^45 + 2 * q^46 + 3 * q^47 + 58 * q^48 + 35 * q^49 - 24 * q^50 - 4 * q^51 + 73 * q^52 - 19 * q^53 + 2 * q^54 + 29 * q^55 - 30 * q^56 + 7 * q^57 + 2 * q^58 + 20 * q^59 - 20 * q^60 + 15 * q^61 + 12 * q^62 + 9 * q^63 + 82 * q^64 - 28 * q^65 + 7 * q^66 + 20 * q^67 - 23 * q^68 + 20 * q^69 - 24 * q^70 + 63 * q^71 + 6 * q^72 + 19 * q^73 + 16 * q^74 + 47 * q^75 - 44 * q^76 - 7 * q^77 + 8 * q^78 + 32 * q^79 - 56 * q^80 + 20 * q^81 - 20 * q^82 - 21 * q^83 + 11 * q^84 + 4 * q^85 - 6 * q^86 + 20 * q^87 + 55 * q^88 - 13 * q^89 + 7 * q^90 + 70 * q^91 + 30 * q^92 + 28 * q^93 - 12 * q^94 + 9 * q^95 + 14 * q^96 - 9 * q^97 + 31 * q^98

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 $

$2$	2.44527	1.72907	0.864534	−	0.502575i	$-0.167614\pi$
$2$	2.44527	1.72907	0.864534	+	0.502575i	$0.167614\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	3.97935	1.98967
$5$	−1.74520	−0.780476	−0.390238	−	0.920714i	$-0.627607\pi$
$5$	−1.74520	−0.780476	−0.390238	+	0.920714i	$0.627607\pi$
$6$	2.44527	0.998278
$7$	5.10283	1.92869	0.964344	−	0.264654i	$-0.0852576\pi$
$7$	5.10283	1.92869	0.964344	+	0.264654i	$0.0852576\pi$
$8$	4.84005	1.71121
$9$	1.00000	0.333333
$10$	−4.26748	−1.34950
$11$	−5.64276	−1.70136	−0.850678	−	0.525688i	$-0.823808\pi$
$11$	−5.64276	−1.70136	−0.850678	+	0.525688i	$0.823808\pi$
$12$	3.97935	1.14874
$13$	6.72828	1.86609	0.933045	−	0.359759i	$-0.117141\pi$
$13$	6.72828	1.86609	0.933045	+	0.359759i	$0.117141\pi$
$14$	12.4778	3.33483
$15$	−1.74520	−0.450608
$16$	3.87652	0.969131
$17$	−0.427470	−0.103677	−0.0518383	−	0.998655i	$-0.516508\pi$
$17$	−0.427470	−0.103677	−0.0518383	+	0.998655i	$0.516508\pi$
$18$	2.44527	0.576356
$19$	−1.22783	−0.281683	−0.140842	−	0.990032i	$-0.544981\pi$
$19$	−1.22783	−0.281683	−0.140842	+	0.990032i	$0.544981\pi$
$20$	−6.94475	−1.55289
$21$	5.10283	1.11353
$22$	−13.7981	−2.94176
$23$	1.00000	0.208514
$23$	1.00000	0.208514
$24$	4.84005	0.987970
$25$	−1.95428	−0.390857
$26$	16.4525	3.22660
$27$	1.00000	0.192450
$28$	20.3059	3.83746
$29$	1.00000	0.185695
$29$	1.00000	0.185695
$30$	−4.26748	−0.779132
$31$	5.44908	0.978684	0.489342	−	0.872092i	$-0.337237\pi$
$31$	5.44908	0.978684	0.489342	+	0.872092i	$0.337237\pi$
$32$	−0.200940	−0.0355216
$33$	−5.64276	−0.982278
$34$	−1.04528	−0.179264
$35$	−8.90544	−1.50529
$36$	3.97935	0.663225
$37$	−10.5826	−1.73977	−0.869887	−	0.493250i	$-0.835809\pi$
$37$	−10.5826	−1.73977	−0.869887	+	0.493250i	$0.835809\pi$
$38$	−3.00237	−0.487049
$39$	6.72828	1.07739
$40$	−8.44684	−1.33556
$41$	6.52884	1.01963	0.509817	−	0.860283i	$-0.329713\pi$
$41$	6.52884	1.01963	0.509817	+	0.860283i	$0.329713\pi$
$42$	12.4778	1.92537
$43$	−4.88914	−0.745586	−0.372793	−	0.927914i	$-0.621600\pi$
$43$	−4.88914	−0.745586	−0.372793	+	0.927914i	$0.621600\pi$
$44$	−22.4545	−3.38514
$45$	−1.74520	−0.260159
$46$	2.44527	0.360536
$47$	−8.92503	−1.30185	−0.650925	−	0.759142i	$-0.725619\pi$
$47$	−8.92503	−1.30185	−0.650925	+	0.759142i	$0.725619\pi$
$48$	3.87652	0.559528
$49$	19.0388	2.71983
$50$	−4.77875	−0.675818
$51$	−0.427470	−0.0598577
$52$	26.7742	3.71291
$53$	5.99381	0.823313	0.411657	−	0.911339i	$-0.364950\pi$
$53$	5.99381	0.823313	0.411657	+	0.911339i	$0.364950\pi$
$54$	2.44527	0.332759
$55$	9.84773	1.32787
$56$	24.6979	3.30040
$57$	−1.22783	−0.162630
$58$	2.44527	0.321080
$59$	0.440433	0.0573395	0.0286697	−	0.999589i	$-0.490873\pi$
$59$	0.440433	0.0573395	0.0286697	+	0.999589i	$0.490873\pi$
$60$	−6.94475	−0.896564
$61$	−6.08220	−0.778746	−0.389373	−	0.921080i	$-0.627308\pi$
$61$	−6.08220	−0.778746	−0.389373	+	0.921080i	$0.627308\pi$
$62$	13.3245	1.69221
$63$	5.10283	0.642896
$64$	−8.24440	−1.03055
$65$	−11.7422	−1.45644
$66$	−13.7981	−1.69842
$67$	6.28479	0.767810	0.383905	−	0.923373i	$-0.374579\pi$
$67$	6.28479	0.767810	0.383905	+	0.923373i	$0.374579\pi$
$68$	−1.70105	−0.206283
$69$	1.00000	0.120386
$70$	−21.7762	−2.60276
$71$	3.56305	0.422856	0.211428	−	0.977394i	$-0.432189\pi$
$71$	3.56305	0.422856	0.211428	+	0.977394i	$0.432189\pi$
$72$	4.84005	0.570405
$73$	−7.59201	−0.888577	−0.444289	−	0.895884i	$-0.646544\pi$
$73$	−7.59201	−0.888577	−0.444289	+	0.895884i	$0.646544\pi$
$74$	−25.8774	−3.00819
$75$	−1.95428	−0.225661
$76$	−4.88596	−0.560458
$77$	−28.7940	−3.28138
$78$	16.4525	1.86288
$79$	14.5546	1.63752	0.818758	−	0.574139i	$-0.194663\pi$
$79$	14.5546	1.63752	0.818758	+	0.574139i	$0.194663\pi$
$80$	−6.76530	−0.756384
$81$	1.00000	0.111111
$82$	15.9648	1.76302
$83$	−8.12019	−0.891306	−0.445653	−	0.895206i	$-0.647029\pi$
$83$	−8.12019	−0.891306	−0.445653	+	0.895206i	$0.647029\pi$
$84$	20.3059	2.21556
$85$	0.746019	0.0809172
$86$	−11.9553	−1.28917
$87$	1.00000	0.107211
$88$	−27.3112	−2.91138
$89$	4.45271	0.471986	0.235993	−	0.971755i	$-0.424166\pi$
$89$	4.45271	0.471986	0.235993	+	0.971755i	$0.424166\pi$
$90$	−4.26748	−0.449832
$91$	34.3333	3.59910
$92$	3.97935	0.414876
$93$	5.44908	0.565043
$94$	−21.8241	−2.25099
$95$	2.14280	0.219847
$96$	−0.200940	−0.0205084
$97$	−8.18389	−0.830948	−0.415474	−	0.909605i	$-0.636384\pi$
$97$	−8.18389	−0.830948	−0.415474	+	0.909605i	$0.636384\pi$
$98$	46.5551	4.70278
$99$	−5.64276	−0.567118
$100$	−7.77678	−0.777678
$101$	−17.5954	−1.75081	−0.875406	−	0.483388i	$-0.839406\pi$
$101$	−17.5954	−1.75081	−0.875406	+	0.483388i	$0.839406\pi$
$102$	−1.04528	−0.103498
$103$	11.7113	1.15395	0.576973	−	0.816763i	$-0.304234\pi$
$103$	11.7113	1.15395	0.576973	+	0.816763i	$0.304234\pi$
$104$	32.5652	3.19328
$105$	−8.90544	−0.869082
$106$	14.6565	1.42356
$107$	−11.2667	−1.08919	−0.544597	−	0.838698i	$-0.683317\pi$
$107$	−11.2667	−1.08919	−0.544597	+	0.838698i	$0.683317\pi$
$108$	3.97935	0.382913
$109$	−15.2337	−1.45913	−0.729563	−	0.683913i	$-0.760277\pi$
$109$	−15.2337	−1.45913	−0.729563	+	0.683913i	$0.760277\pi$
$110$	24.0804	2.29597
$111$	−10.5826	−1.00446
$112$	19.7812	1.86915
$113$	8.40919	0.791070	0.395535	−	0.918451i	$-0.370559\pi$
$113$	8.40919	0.791070	0.395535	+	0.918451i	$0.370559\pi$
$114$	−3.00237	−0.281198
$115$	−1.74520	−0.162741
$116$	3.97935	0.369473
$117$	6.72828	0.622030
$118$	1.07698	0.0991439
$119$	−2.18130	−0.199960
$120$	−8.44684	−0.771087
$121$	20.8407	1.89461
$122$	−14.8726	−1.34651
$123$	6.52884	0.588686
$124$	21.6838	1.94726
$125$	12.1366	1.08553
$126$	12.4778	1.11161
$127$	−22.3171	−1.98032	−0.990159	−	0.139947i	$-0.955307\pi$
$127$	−22.3171	−1.98032	−0.990159	+	0.139947i	$0.955307\pi$
$128$	−19.7579	−1.74637
$129$	−4.88914	−0.430464
$130$	−28.7128	−2.51828
$131$	1.92039	0.167785	0.0838925	−	0.996475i	$-0.473265\pi$
$131$	1.92039	0.167785	0.0838925	+	0.996475i	$0.473265\pi$
$132$	−22.4545	−1.95441
$133$	−6.26539	−0.543278
$134$	15.3680	1.32759
$135$	−1.74520	−0.150203
$136$	−2.06897	−0.177413
$137$	−3.76984	−0.322079	−0.161040	−	0.986948i	$-0.551485\pi$
$137$	−3.76984	−0.322079	−0.161040	+	0.986948i	$0.551485\pi$
$138$	2.44527	0.208155
$139$	1.93727	0.164317	0.0821585	−	0.996619i	$-0.473819\pi$
$139$	1.93727	0.164317	0.0821585	+	0.996619i	$0.473819\pi$
$140$	−35.4379	−2.99505
$141$	−8.92503	−0.751623
$142$	8.71262	0.731146
$143$	−37.9661	−3.17488
$144$	3.87652	0.323044
$145$	−1.74520	−0.144931
$146$	−18.5645	−1.53641
$147$	19.0388	1.57030
$148$	−42.1120	−3.46159
$149$	−13.6999	−1.12234	−0.561171	−	0.827700i	$-0.689649\pi$
$149$	−13.6999	−1.12234	−0.561171	+	0.827700i	$0.689649\pi$
$150$	−4.77875	−0.390184
$151$	−5.39735	−0.439230	−0.219615	−	0.975587i	$-0.570480\pi$
$151$	−5.39735	−0.439230	−0.219615	+	0.975587i	$0.570480\pi$
$152$	−5.94274	−0.482020
$153$	−0.427470	−0.0345589
$154$	−70.4091	−5.67373
$155$	−9.50972	−0.763839
$156$	26.7742	2.14365
$157$	0.0239922	0.00191479	0.000957394	−	1.00000i	$-0.499695\pi$
$157$	0.0239922	0.00191479	0.000957394		1.00000i	$0.499695\pi$
$158$	35.5898	2.83138
$159$	5.99381	0.475340
$160$	0.350681	0.0277238
$161$	5.10283	0.402159
$162$	2.44527	0.192119
$163$	0.0252041	0.00197414	0.000987068	−	1.00000i	$-0.499686\pi$
$163$	0.0252041	0.00197414	0.000987068		1.00000i	$0.499686\pi$
$164$	25.9806	2.02874
$165$	9.84773	0.766645
$166$	−19.8561	−1.54113
$167$	7.32969	0.567188	0.283594	−	0.958944i	$-0.408473\pi$
$167$	7.32969	0.567188	0.283594	+	0.958944i	$0.408473\pi$
$168$	24.6979	1.90549
$169$	32.2698	2.48229
$170$	1.82422	0.139911
$171$	−1.22783	−0.0938943
$172$	−19.4556	−1.48347
$173$	−19.5370	−1.48537	−0.742685	−	0.669641i	$-0.766448\pi$
$173$	−19.5370	−1.48537	−0.742685	+	0.669641i	$0.766448\pi$
$174$	2.44527	0.185376
$175$	−9.97237	−0.753840
$176$	−21.8743	−1.64884
$177$	0.440433	0.0331050
$178$	10.8881	0.816096
$179$	6.09592	0.455631	0.227815	−	0.973704i	$-0.426842\pi$
$179$	6.09592	0.455631	0.227815	+	0.973704i	$0.426842\pi$
$180$	−6.94475	−0.517631
$181$	6.02909	0.448139	0.224069	−	0.974573i	$-0.428066\pi$
$181$	6.02909	0.448139	0.224069	+	0.974573i	$0.428066\pi$
$182$	83.9541	6.22309
$183$	−6.08220	−0.449609
$184$	4.84005	0.356813
$185$	18.4688	1.35785
$186$	13.3245	0.976998
$187$	2.41211	0.176391
$188$	−35.5158	−2.59026
$189$	5.10283	0.371176
$190$	5.23973	0.380130
$191$	12.5256	0.906318	0.453159	−	0.891430i	$-0.350297\pi$
$191$	12.5256	0.906318	0.453159	+	0.891430i	$0.350297\pi$
$192$	−8.24440	−0.594988
$193$	9.90192	0.712756	0.356378	−	0.934342i	$-0.384012\pi$
$193$	9.90192	0.712756	0.356378	+	0.934342i	$0.384012\pi$
$194$	−20.0118	−1.43676
$195$	−11.7422	−0.840876
$196$	75.7622	5.41158
$197$	−6.13949	−0.437421	−0.218710	−	0.975790i	$-0.570185\pi$
$197$	−6.13949	−0.437421	−0.218710	+	0.975790i	$0.570185\pi$
$198$	−13.7981	−0.980586
$199$	14.2857	1.01268	0.506342	−	0.862333i	$-0.330997\pi$
$199$	14.2857	1.01268	0.506342	+	0.862333i	$0.330997\pi$
$200$	−9.45882	−0.668840
$201$	6.28479	0.443295
$202$	−43.0256	−3.02727
$203$	5.10283	0.358148
$204$	−1.70105	−0.119097
$205$	−11.3941	−0.795800
$206$	28.6372	1.99525
$207$	1.00000	0.0695048
$208$	26.0824	1.80849
$209$	6.92833	0.479243
$210$	−21.7762	−1.50270
$211$	8.67262	0.597048	0.298524	−	0.954402i	$-0.403506\pi$
$211$	8.67262	0.597048	0.298524	+	0.954402i	$0.403506\pi$
$212$	23.8515	1.63813
$213$	3.56305	0.244136
$214$	−27.5502	−1.88329
$215$	8.53251	0.581912
$216$	4.84005	0.329323
$217$	27.8057	1.88757
$218$	−37.2506	−2.52293
$219$	−7.59201	−0.513020
$220$	39.1875	2.64202
$221$	−2.87614	−0.193470
$222$	−25.8774	−1.73678
$223$	−6.91512	−0.463071	−0.231535	−	0.972827i	$-0.574375\pi$
$223$	−6.91512	−0.463071	−0.231535	+	0.972827i	$0.574375\pi$
$224$	−1.02536	−0.0685100
$225$	−1.95428	−0.130286
$226$	20.5627	1.36781
$227$	−10.0823	−0.669187	−0.334593	−	0.942363i	$-0.608599\pi$
$227$	−10.0823	−0.669187	−0.334593	+	0.942363i	$0.608599\pi$
$228$	−4.88596	−0.323580
$229$	−10.2947	−0.680292	−0.340146	−	0.940373i	$-0.610476\pi$
$229$	−10.2947	−0.680292	−0.340146	+	0.940373i	$0.610476\pi$
$230$	−4.26748	−0.281389
$231$	−28.7940	−1.89451
$232$	4.84005	0.317765
$233$	3.95614	0.259175	0.129588	−	0.991568i	$-0.458635\pi$
$233$	3.95614	0.259175	0.129588	+	0.991568i	$0.458635\pi$
$234$	16.4525	1.07553
$235$	15.5759	1.01606
$236$	1.75264	0.114087
$237$	14.5546	0.945420
$238$	−5.33388	−0.345744
$239$	−29.3893	−1.90104	−0.950518	−	0.310670i	$-0.899447\pi$
$239$	−29.3893	−1.90104	−0.950518	+	0.310670i	$0.899447\pi$
$240$	−6.76530	−0.436698
$241$	−13.4864	−0.868737	−0.434369	−	0.900735i	$-0.643028\pi$
$241$	−13.4864	−0.868737	−0.434369	+	0.900735i	$0.643028\pi$
$242$	50.9612	3.27591
$243$	1.00000	0.0641500
$244$	−24.2032	−1.54945
$245$	−33.2265	−2.12277
$246$	15.9648	1.01788
$247$	−8.26117	−0.525646
$248$	26.3738	1.67474
$249$	−8.12019	−0.514596
$250$	29.6773	1.87696
$251$	8.57329	0.541141	0.270571	−	0.962700i	$-0.412788\pi$
$251$	8.57329	0.541141	0.270571	+	0.962700i	$0.412788\pi$
$252$	20.3059	1.27915
$253$	−5.64276	−0.354757
$254$	−54.5712	−3.42410
$255$	0.746019	0.0467176
$256$	−31.8247	−1.98904
$257$	28.3655	1.76939	0.884695	−	0.466169i	$-0.154366\pi$
$257$	28.3655	1.76939	0.884695	+	0.466169i	$0.154366\pi$
$258$	−11.9553	−0.744302
$259$	−54.0014	−3.35548
$260$	−46.7263	−2.89784
$261$	1.00000	0.0618984
$262$	4.69587	0.290112
$263$	−12.4022	−0.764750	−0.382375	−	0.924007i	$-0.624894\pi$
$263$	−12.4022	−0.764750	−0.382375	+	0.924007i	$0.624894\pi$
$264$	−27.3112	−1.68089
$265$	−10.4604	−0.642576
$266$	−15.3206	−0.939365
$267$	4.45271	0.272501
$268$	25.0094	1.52769
$269$	26.8677	1.63815	0.819075	−	0.573686i	$-0.194487\pi$
$269$	26.8677	1.63815	0.819075	+	0.573686i	$0.194487\pi$
$270$	−4.26748	−0.259711
$271$	2.24407	0.136317	0.0681587	−	0.997674i	$-0.478288\pi$
$271$	2.24407	0.136317	0.0681587	+	0.997674i	$0.478288\pi$
$272$	−1.65710	−0.100476
$273$	34.3333	2.07794
$274$	−9.21828	−0.556896
$275$	11.0275	0.664986
$276$	3.97935	0.239529
$277$	−1.42115	−0.0853887	−0.0426944	−	0.999088i	$-0.513594\pi$
$277$	−1.42115	−0.0853887	−0.0426944	+	0.999088i	$0.513594\pi$
$278$	4.73715	0.284115
$279$	5.44908	0.326228
$280$	−43.1027	−2.57588
$281$	24.2843	1.44868	0.724339	−	0.689444i	$-0.242145\pi$
$281$	24.2843	1.44868	0.724339	+	0.689444i	$0.242145\pi$
$282$	−21.8241	−1.29961
$283$	−19.9648	−1.18678	−0.593392	−	0.804914i	$-0.702212\pi$
$283$	−19.9648	−1.18678	−0.593392	+	0.804914i	$0.702212\pi$
$284$	14.1786	0.841346
$285$	2.14280	0.126929
$286$	−92.8373	−5.48959
$287$	33.3156	1.96656
$288$	−0.200940	−0.0118405
$289$	−16.8173	−0.989251
$290$	−4.26748	−0.250595
$291$	−8.18389	−0.479748
$292$	−30.2113	−1.76798
$293$	−11.9515	−0.698216	−0.349108	−	0.937083i	$-0.613515\pi$
$293$	−11.9515	−0.698216	−0.349108	+	0.937083i	$0.613515\pi$
$294$	46.5551	2.71515
$295$	−0.768643	−0.0447521
$296$	−51.2204	−2.97713
$297$	−5.64276	−0.327426
$298$	−33.5000	−1.94060
$299$	6.72828	0.389107
$300$	−7.77678	−0.448993
$301$	−24.9484	−1.43800
$302$	−13.1980	−0.759458
$303$	−17.5954	−1.01083
$304$	−4.75970	−0.272988
$305$	10.6146	0.607793
$306$	−1.04528	−0.0597547
$307$	−12.3877	−0.707006	−0.353503	−	0.935433i	$-0.615010\pi$
$307$	−12.3877	−0.707006	−0.353503	+	0.935433i	$0.615010\pi$
$308$	−114.581	−6.52888
$309$	11.7113	0.666231
$310$	−23.2539	−1.32073
$311$	11.8535	0.672150	0.336075	−	0.941835i	$-0.390900\pi$
$311$	11.8535	0.672150	0.336075	+	0.941835i	$0.390900\pi$
$312$	32.5652	1.84364
$313$	−19.8879	−1.12413	−0.562065	−	0.827093i	$-0.689993\pi$
$313$	−19.8879	−1.12413	−0.562065	+	0.827093i	$0.689993\pi$
$314$	0.0586675	0.00331080
$315$	−8.90544	−0.501765
$316$	57.9177	3.25812
$317$	9.90945	0.556570	0.278285	−	0.960499i	$-0.410234\pi$
$317$	9.90945	0.556570	0.278285	+	0.960499i	$0.410234\pi$
$318$	14.6565	0.821895
$319$	−5.64276	−0.315934
$320$	14.3881	0.804320
$321$	−11.2667	−0.628846
$322$	12.4778	0.695360
$323$	0.524859	0.0292040
$324$	3.97935	0.221075
$325$	−13.1490	−0.729374
$326$	0.0616308	0.00341341
$327$	−15.2337	−0.842427
$328$	31.5999	1.74481
$329$	−45.5429	−2.51086
$330$	24.0804	1.32558
$331$	−10.0660	−0.553276	−0.276638	−	0.960974i	$-0.589220\pi$
$331$	−10.0660	−0.553276	−0.276638	+	0.960974i	$0.589220\pi$
$332$	−32.3131	−1.77341
$333$	−10.5826	−0.579925
$334$	17.9231	0.980707
$335$	−10.9682	−0.599257
$336$	19.7812	1.07915
$337$	8.52111	0.464175	0.232087	−	0.972695i	$-0.425444\pi$
$337$	8.52111	0.464175	0.232087	+	0.972695i	$0.425444\pi$
$338$	78.9084	4.29205
$339$	8.40919	0.456724
$340$	2.96867	0.160999
$341$	−30.7478	−1.66509
$342$	−3.00237	−0.162350
$343$	61.4321	3.31702
$344$	−23.6636	−1.27586
$345$	−1.74520	−0.0939583
$346$	−47.7732	−2.56830
$347$	36.6769	1.96892	0.984461	−	0.175605i	$-0.0561883\pi$
$347$	36.6769	1.96892	0.984461	+	0.175605i	$0.0561883\pi$
$348$	3.97935	0.213316
$349$	16.0444	0.858835	0.429417	−	0.903106i	$-0.358719\pi$
$349$	16.0444	0.858835	0.429417	+	0.903106i	$0.358719\pi$
$350$	−24.3851	−1.30344
$351$	6.72828	0.359129
$352$	1.13386	0.0604348
$353$	−16.0098	−0.852117	−0.426059	−	0.904696i	$-0.640098\pi$
$353$	−16.0098	−0.852117	−0.426059	+	0.904696i	$0.640098\pi$
$354$	1.07698	0.0572407
$355$	−6.21822	−0.330029
$356$	17.7189	0.939099
$357$	−2.18130	−0.115447
$358$	14.9062	0.787816
$359$	−22.6647	−1.19620	−0.598098	−	0.801423i	$-0.704077\pi$
$359$	−22.6647	−1.19620	−0.598098	+	0.801423i	$0.704077\pi$
$360$	−8.44684	−0.445187
$361$	−17.4924	−0.920655
$362$	14.7428	0.774862
$363$	20.8407	1.09385
$364$	136.624	7.16105
$365$	13.2496	0.693514
$366$	−14.8726	−0.777405
$367$	−21.6748	−1.13142	−0.565708	−	0.824605i	$-0.691397\pi$
$367$	−21.6748	−1.13142	−0.565708	+	0.824605i	$0.691397\pi$
$368$	3.87652	0.202078
$369$	6.52884	0.339878
$370$	45.1612	2.34782
$371$	30.5854	1.58791
$372$	21.6838	1.12425
$373$	−0.141606	−0.00733210	−0.00366605	−	0.999993i	$-0.501167\pi$
$373$	−0.141606	−0.00733210	−0.00366605	+	0.999993i	$0.501167\pi$
$374$	5.89826	0.304992
$375$	12.1366	0.626731
$376$	−43.1976	−2.22774
$377$	6.72828	0.346524
$378$	12.4778	0.641788
$379$	20.6660	1.06154	0.530771	−	0.847515i	$-0.321902\pi$
$379$	20.6660	1.06154	0.530771	+	0.847515i	$0.321902\pi$
$380$	8.52696	0.437424
$381$	−22.3171	−1.14334
$382$	30.6284	1.56709
$383$	−12.1786	−0.622298	−0.311149	−	0.950361i	$-0.600714\pi$
$383$	−12.1786	−0.622298	−0.311149	+	0.950361i	$0.600714\pi$
$384$	−19.7579	−1.00827
$385$	50.2512	2.56104
$386$	24.2129	1.23240
$387$	−4.88914	−0.248529
$388$	−32.5665	−1.65332
$389$	36.0697	1.82880	0.914402	−	0.404807i	$-0.132661\pi$
$389$	36.0697	1.82880	0.914402	+	0.404807i	$0.132661\pi$
$390$	−28.7128	−1.45393
$391$	−0.427470	−0.0216181
$392$	92.1488	4.65422
$393$	1.92039	0.0968707
$394$	−15.0127	−0.756330
$395$	−25.4006	−1.27804
$396$	−22.4545	−1.12838
$397$	29.7914	1.49519	0.747595	−	0.664155i	$-0.231209\pi$
$397$	29.7914	1.49519	0.747595	+	0.664155i	$0.231209\pi$
$398$	34.9323	1.75100
$399$	−6.26539	−0.313662
$400$	−7.57583	−0.378791
$401$	−17.1118	−0.854521	−0.427261	−	0.904129i	$-0.640521\pi$
$401$	−17.1118	−0.854521	−0.427261	+	0.904129i	$0.640521\pi$
$402$	15.3680	0.766487
$403$	36.6630	1.82631
$404$	−70.0184	−3.48355
$405$	−1.74520	−0.0867196
$406$	12.4778	0.619262
$407$	59.7152	2.95997
$408$	−2.06897	−0.102429
$409$	−2.30574	−0.114011	−0.0570057	−	0.998374i	$-0.518155\pi$
$409$	−2.30574	−0.114011	−0.0570057	+	0.998374i	$0.518155\pi$
$410$	−27.8617	−1.37599
$411$	−3.76984	−0.185952
$412$	46.6033	2.29598
$413$	2.24745	0.110590
$414$	2.44527	0.120179
$415$	14.1713	0.695643
$416$	−1.35198	−0.0662865
$417$	1.93727	0.0948685
$418$	16.9417	0.828643
$419$	13.5344	0.661199	0.330600	−	0.943771i	$-0.392749\pi$
$419$	13.5344	0.661199	0.330600	+	0.943771i	$0.392749\pi$
$420$	−35.4379	−1.72919
$421$	29.2502	1.42557	0.712783	−	0.701385i	$-0.247435\pi$
$421$	29.2502	1.42557	0.712783	+	0.701385i	$0.247435\pi$
$422$	21.2069	1.03234
$423$	−8.92503	−0.433950
$424$	29.0103	1.40887
$425$	0.835397	0.0405227
$426$	8.71262	0.422128
$427$	−31.0364	−1.50196
$428$	−44.8342	−2.16714
$429$	−37.9661	−1.83302
$430$	20.8643	1.00617
$431$	21.8598	1.05295	0.526476	−	0.850190i	$-0.323513\pi$
$431$	21.8598	1.05295	0.526476	+	0.850190i	$0.323513\pi$
$432$	3.87652	0.186509
$433$	−7.10245	−0.341322	−0.170661	−	0.985330i	$-0.554590\pi$
$433$	−7.10245	−0.341322	−0.170661	+	0.985330i	$0.554590\pi$
$434$	67.9925	3.26374
$435$	−1.74520	−0.0836758
$436$	−60.6203	−2.90319
$437$	−1.22783	−0.0587350
$438$	−18.5645	−0.887047
$439$	−28.6168	−1.36581	−0.682903	−	0.730509i	$-0.739283\pi$
$439$	−28.6168	−1.36581	−0.682903	+	0.730509i	$0.739283\pi$
$440$	47.6635	2.27227
$441$	19.0388	0.906611
$442$	−7.03294	−0.334523
$443$	17.1209	0.813440	0.406720	−	0.913553i	$-0.366672\pi$
$443$	17.1209	0.813440	0.406720	+	0.913553i	$0.366672\pi$
$444$	−42.1120	−1.99855
$445$	−7.77085	−0.368374
$446$	−16.9093	−0.800680
$447$	−13.6999	−0.647984
$448$	−42.0698	−1.98761
$449$	14.4814	0.683419	0.341710	−	0.939806i	$-0.388994\pi$
$449$	14.4814	0.683419	0.341710	+	0.939806i	$0.388994\pi$
$450$	−4.77875	−0.225273
$451$	−36.8407	−1.73476
$452$	33.4631	1.57397
$453$	−5.39735	−0.253589
$454$	−24.6540	−1.15707
$455$	−59.9183	−2.80902
$456$	−5.94274	−0.278294
$457$	27.8152	1.30114	0.650569	−	0.759447i	$-0.274530\pi$
$457$	27.8152	1.30114	0.650569	+	0.759447i	$0.274530\pi$
$458$	−25.1733	−1.17627
$459$	−0.427470	−0.0199526
$460$	−6.94475	−0.323801
$461$	15.2303	0.709346	0.354673	−	0.934990i	$-0.384592\pi$
$461$	15.2303	0.709346	0.354673	+	0.934990i	$0.384592\pi$
$462$	−70.4091	−3.27573
$463$	26.1514	1.21536	0.607680	−	0.794182i	$-0.292100\pi$
$463$	26.1514	1.21536	0.607680	+	0.794182i	$0.292100\pi$
$464$	3.87652	0.179963
$465$	−9.50972	−0.441003
$466$	9.67384	0.448132
$467$	−17.6426	−0.816402	−0.408201	−	0.912892i	$-0.633844\pi$
$467$	−17.6426	−0.816402	−0.408201	+	0.912892i	$0.633844\pi$
$468$	26.7742	1.23764
$469$	32.0702	1.48086
$470$	38.0874	1.75684
$471$	0.0239922	0.00110550
$472$	2.13172	0.0981202
$473$	27.5882	1.26851
$474$	35.5898	1.63470
$475$	2.39952	0.110098
$476$	−8.68017	−0.397855
$477$	5.99381	0.274438
$478$	−71.8648	−3.28702
$479$	−5.12689	−0.234253	−0.117127	−	0.993117i	$-0.537368\pi$
$479$	−5.12689	−0.234253	−0.117127	+	0.993117i	$0.537368\pi$
$480$	0.350681	0.0160063
$481$	−71.2030	−3.24658
$482$	−32.9780	−1.50211
$483$	5.10283	0.232187
$484$	82.9324	3.76966
$485$	14.2825	0.648535
$486$	2.44527	0.110920
$487$	6.10506	0.276647	0.138323	−	0.990387i	$-0.455829\pi$
$487$	6.10506	0.276647	0.138323	+	0.990387i	$0.455829\pi$
$488$	−29.4381	−1.33260
$489$	0.0252041	0.00113977
$490$	−81.2479	−3.67041
$491$	5.01074	0.226131	0.113066	−	0.993588i	$-0.463933\pi$
$491$	5.01074	0.226131	0.113066	+	0.993588i	$0.463933\pi$
$492$	25.9806	1.17129
$493$	−0.427470	−0.0192523
$494$	−20.2008	−0.908877
$495$	9.84773	0.442622
$496$	21.1235	0.948473
$497$	18.1816	0.815557
$498$	−19.8561	−0.889771
$499$	26.9336	1.20571	0.602856	−	0.797850i	$-0.294029\pi$
$499$	26.9336	1.20571	0.602856	+	0.797850i	$0.294029\pi$
$500$	48.2958	2.15985
$501$	7.32969	0.327466
$502$	20.9640	0.935670
$503$	2.34501	0.104559	0.0522794	−	0.998632i	$-0.483351\pi$
$503$	2.34501	0.104559	0.0522794	+	0.998632i	$0.483351\pi$
$504$	24.6979	1.10013
$505$	30.7075	1.36647
$506$	−13.7981	−0.613399
$507$	32.2698	1.43315
$508$	−88.8073	−3.94019
$509$	25.6358	1.13629	0.568143	−	0.822930i	$-0.307662\pi$
$509$	25.6358	1.13629	0.568143	+	0.822930i	$0.307662\pi$
$510$	1.82422	0.0807778
$511$	−38.7407	−1.71379
$512$	−38.3041	−1.69282
$513$	−1.22783	−0.0542099
$514$	69.3613	3.05940
$515$	−20.4385	−0.900628
$516$	−19.4556	−0.856484
$517$	50.3618	2.21491
$518$	−132.048	−5.80185
$519$	−19.5370	−0.857579
$520$	−56.8327	−2.49228
$521$	0.166481	0.00729366	0.00364683	−	0.999993i	$-0.498839\pi$
$521$	0.166481	0.00729366	0.00364683	+	0.999993i	$0.498839\pi$
$522$	2.44527	0.107027
$523$	44.8249	1.96005	0.980027	−	0.198864i	$-0.0637253\pi$
$523$	44.8249	1.96005	0.980027	+	0.198864i	$0.0637253\pi$
$524$	7.64189	0.333838
$525$	−9.97237	−0.435230
$526$	−30.3266	−1.32230
$527$	−2.32932	−0.101467
$528$	−21.8743	−0.951956
$529$	1.00000	0.0434783
$530$	−25.5785	−1.11106
$531$	0.440433	0.0191132
$532$	−24.9322	−1.08095
$533$	43.9279	1.90273
$534$	10.8881	0.471173
$535$	19.6626	0.850090
$536$	30.4187	1.31389
$537$	6.09592	0.263059
$538$	65.6987	2.83247
$539$	−107.432	−4.62740
$540$	−6.94475	−0.298855
$541$	−8.32708	−0.358009	−0.179005	−	0.983848i	$-0.557288\pi$
$541$	−8.32708	−0.358009	−0.179005	+	0.983848i	$0.557288\pi$
$542$	5.48735	0.235702
$543$	6.02909	0.258733
$544$	0.0858960	0.00368276
$545$	26.5859	1.13881
$546$	83.9541	3.59291
$547$	32.0556	1.37060	0.685299	−	0.728262i	$-0.259671\pi$
$547$	32.0556	1.37060	0.685299	+	0.728262i	$0.259671\pi$
$548$	−15.0015	−0.640833
$549$	−6.08220	−0.259582
$550$	26.9653	1.14981
$551$	−1.22783	−0.0523072
$552$	4.84005	0.206006
$553$	74.2694	3.15826
$554$	−3.47510	−0.147643
$555$	18.4688	0.783957
$556$	7.70907	0.326937
$557$	15.4539	0.654803	0.327402	−	0.944885i	$-0.393827\pi$
$557$	15.4539	0.654803	0.327402	+	0.944885i	$0.393827\pi$
$558$	13.3245	0.564070
$559$	−32.8955	−1.39133
$560$	−34.5222	−1.45883
$561$	2.41211	0.101839
$562$	59.3816	2.50486
$563$	−10.5091	−0.442905	−0.221453	−	0.975171i	$-0.571080\pi$
$563$	−10.5091	−0.442905	−0.221453	+	0.975171i	$0.571080\pi$
$564$	−35.5158	−1.49549
$565$	−14.6757	−0.617411
$566$	−48.8193	−2.05203
$567$	5.10283	0.214299
$568$	17.2453	0.723597
$569$	2.83273	0.118754	0.0593770	−	0.998236i	$-0.481089\pi$
$569$	2.83273	0.118754	0.0593770	+	0.998236i	$0.481089\pi$
$570$	5.23973	0.219468
$571$	−18.5624	−0.776812	−0.388406	−	0.921488i	$-0.626974\pi$
$571$	−18.5624	−0.776812	−0.388406	+	0.921488i	$0.626974\pi$
$572$	−151.080	−6.31698
$573$	12.5256	0.523263
$574$	81.4656	3.40031
$575$	−1.95428	−0.0814993
$576$	−8.24440	−0.343517
$577$	−17.3886	−0.723897	−0.361949	−	0.932198i	$-0.617888\pi$
$577$	−17.3886	−0.723897	−0.361949	+	0.932198i	$0.617888\pi$
$578$	−41.1228	−1.71048
$579$	9.90192	0.411510
$580$	−6.94475	−0.288365
$581$	−41.4359	−1.71905
$582$	−20.0118	−0.829517
$583$	−33.8216	−1.40075
$584$	−36.7457	−1.52055
$585$	−11.7422	−0.485480
$586$	−29.2247	−1.20726
$587$	−5.05110	−0.208481	−0.104241	−	0.994552i	$-0.533241\pi$
$587$	−5.05110	−0.208481	−0.104241	+	0.994552i	$0.533241\pi$
$588$	75.7622	3.12438
$589$	−6.69053	−0.275679
$590$	−1.87954	−0.0773794
$591$	−6.13949	−0.252545
$592$	−41.0238	−1.68607
$593$	−13.2024	−0.542158	−0.271079	−	0.962557i	$-0.587381\pi$
$593$	−13.2024	−0.542158	−0.271079	+	0.962557i	$0.587381\pi$
$594$	−13.7981	−0.566142
$595$	3.80681	0.156064
$596$	−54.5168	−2.23310
$597$	14.2857	0.584673
$598$	16.4525	0.672792
$599$	19.1932	0.784212	0.392106	−	0.919920i	$-0.371747\pi$
$599$	19.1932	0.784212	0.392106	+	0.919920i	$0.371747\pi$
$600$	−9.45882	−0.386155
$601$	7.62036	0.310841	0.155421	−	0.987848i	$-0.450327\pi$
$601$	7.62036	0.310841	0.155421	+	0.987848i	$0.450327\pi$
$602$	−61.0056	−2.48640
$603$	6.28479	0.255937
$604$	−21.4779	−0.873924
$605$	−36.3711	−1.47870
$606$	−43.0256	−1.74780
$607$	−19.0718	−0.774101	−0.387051	−	0.922059i	$-0.626506\pi$
$607$	−19.0718	−0.774101	−0.387051	+	0.922059i	$0.626506\pi$
$608$	0.246720	0.0100058
$609$	5.10283	0.206777
$610$	25.9557	1.05092
$611$	−60.0501	−2.42937
$612$	−1.70105	−0.0687609
$613$	−20.5471	−0.829891	−0.414945	−	0.909846i	$-0.636199\pi$
$613$	−20.5471	−0.829891	−0.414945	+	0.909846i	$0.636199\pi$
$614$	−30.2914	−1.22246
$615$	−11.3941	−0.459456
$616$	−139.364	−5.61515
$617$	−13.7223	−0.552438	−0.276219	−	0.961095i	$-0.589082\pi$
$617$	−13.7223	−0.552438	−0.276219	+	0.961095i	$0.589082\pi$
$618$	28.6372	1.15196
$619$	27.1177	1.08995	0.544976	−	0.838452i	$-0.316539\pi$
$619$	27.1177	1.08995	0.544976	+	0.838452i	$0.316539\pi$
$620$	−37.8425	−1.51979
$621$	1.00000	0.0401286
$622$	28.9850	1.16219
$623$	22.7214	0.910313
$624$	26.0824	1.04413
$625$	−11.4094	−0.456374
$626$	−48.6313	−1.94370
$627$	6.92833	0.276691
$628$	0.0954734	0.00380980
$629$	4.52376	0.180374
$630$	−21.7762	−0.867585
$631$	−8.00036	−0.318489	−0.159245	−	0.987239i	$-0.550906\pi$
$631$	−8.00036	−0.318489	−0.159245	+	0.987239i	$0.550906\pi$
$632$	70.4447	2.80214
$633$	8.67262	0.344706
$634$	24.2313	0.962348
$635$	38.9477	1.54559
$636$	23.8515	0.945772
$637$	128.099	5.07546
$638$	−13.7981	−0.546271
$639$	3.56305	0.140952
$640$	34.4815	1.36300
$641$	−21.8605	−0.863436	−0.431718	−	0.902009i	$-0.642092\pi$
$641$	−21.8605	−0.863436	−0.431718	+	0.902009i	$0.642092\pi$
$642$	−27.5502	−1.08732
$643$	29.0946	1.14738	0.573689	−	0.819073i	$-0.305512\pi$
$643$	29.0946	1.14738	0.573689	+	0.819073i	$0.305512\pi$
$644$	20.3059	0.800166
$645$	8.53251	0.335967
$646$	1.28342	0.0504956
$647$	−4.13054	−0.162388	−0.0811941	−	0.996698i	$-0.525873\pi$
$647$	−4.13054	−0.162388	−0.0811941	+	0.996698i	$0.525873\pi$
$648$	4.84005	0.190135
$649$	−2.48526	−0.0975548
$650$	−32.1528	−1.26114
$651$	27.8057	1.08979
$652$	0.100296	0.00392789
$653$	14.6791	0.574436	0.287218	−	0.957865i	$-0.407270\pi$
$653$	14.6791	0.574436	0.287218	+	0.957865i	$0.407270\pi$
$654$	−37.2506	−1.45661
$655$	−3.35146	−0.130952
$656$	25.3092	0.988159
$657$	−7.59201	−0.296192
$658$	−111.365	−4.34145
$659$	−8.51122	−0.331550	−0.165775	−	0.986164i	$-0.553013\pi$
$659$	−8.51122	−0.331550	−0.165775	+	0.986164i	$0.553013\pi$
$660$	39.1875	1.52537
$661$	3.66553	0.142573	0.0712864	−	0.997456i	$-0.477290\pi$
$661$	3.66553	0.142573	0.0712864	+	0.997456i	$0.477290\pi$
$662$	−24.6140	−0.956651
$663$	−2.87614	−0.111700
$664$	−39.3021	−1.52522
$665$	10.9343	0.424016
$666$	−25.8774	−1.00273
$667$	1.00000	0.0387202
$668$	29.1674	1.12852
$669$	−6.91512	−0.267354
$670$	−26.8202	−1.03616
$671$	34.3204	1.32492
$672$	−1.02536	−0.0395543
$673$	41.8994	1.61510	0.807551	−	0.589798i	$-0.200793\pi$
$673$	41.8994	1.61510	0.807551	+	0.589798i	$0.200793\pi$
$674$	20.8364	0.802589
$675$	−1.95428	−0.0752204
$676$	128.413	4.93896
$677$	25.4243	0.977133	0.488567	−	0.872527i	$-0.337520\pi$
$677$	25.4243	0.977133	0.488567	+	0.872527i	$0.337520\pi$
$678$	20.5627	0.789707
$679$	−41.7609	−1.60264
$680$	3.61077	0.138467
$681$	−10.0823	−0.386355
$682$	−75.1868	−2.87905
$683$	0.993670	0.0380217	0.0190109	−	0.999819i	$-0.493948\pi$
$683$	0.993670	0.0380217	0.0190109	+	0.999819i	$0.493948\pi$
$684$	−4.88596	−0.186819
$685$	6.57911	0.251375
$686$	150.218	5.73535
$687$	−10.2947	−0.392766
$688$	−18.9529	−0.722571
$689$	40.3281	1.53638
$690$	−4.26748	−0.162460
$691$	−2.93531	−0.111664	−0.0558322	−	0.998440i	$-0.517781\pi$
$691$	−2.93531	−0.111664	−0.0558322	+	0.998440i	$0.517781\pi$
$692$	−77.7445	−2.95540
$693$	−28.7940	−1.09379
$694$	89.6851	3.40440
$695$	−3.38092	−0.128246
$696$	4.84005	0.183461
$697$	−2.79088	−0.105712
$698$	39.2328	1.48498
$699$	3.95614	0.149635
$700$	−39.6836	−1.49990
$701$	26.7695	1.01107	0.505536	−	0.862806i	$-0.331295\pi$
$701$	26.7695	1.01107	0.505536	+	0.862806i	$0.331295\pi$
$702$	16.4525	0.620959
$703$	12.9937	0.490065
$704$	46.5212	1.75333
$705$	15.5759	0.586624
$706$	−39.1484	−1.47337
$707$	−89.7865	−3.37677
$708$	1.75264	0.0658681
$709$	−38.4277	−1.44318	−0.721591	−	0.692319i	$-0.756589\pi$
$709$	−38.4277	−1.44318	−0.721591	+	0.692319i	$0.756589\pi$
$710$	−15.2052	−0.570642
$711$	14.5546	0.545839
$712$	21.5513	0.807669
$713$	5.44908	0.204070
$714$	−5.33388	−0.199615
$715$	66.2583	2.47792
$716$	24.2578	0.906557
$717$	−29.3893	−1.09756
$718$	−55.4213	−2.06830
$719$	9.36859	0.349390	0.174695	−	0.984623i	$-0.444106\pi$
$719$	9.36859	0.349390	0.174695	+	0.984623i	$0.444106\pi$
$720$	−6.76530	−0.252128
$721$	59.7606	2.22560
$722$	−42.7738	−1.59187
$723$	−13.4864	−0.501566
$724$	23.9919	0.891650
$725$	−1.95428	−0.0725803
$726$	50.9612	1.89135
$727$	−3.00591	−0.111483	−0.0557415	−	0.998445i	$-0.517752\pi$
$727$	−3.00591	−0.111483	−0.0557415	+	0.998445i	$0.517752\pi$
$728$	166.175	6.15884
$729$	1.00000	0.0370370
$730$	32.3988	1.19913
$731$	2.08996	0.0772999
$732$	−24.2032	−0.894577
$733$	3.57332	0.131984	0.0659919	−	0.997820i	$-0.478979\pi$
$733$	3.57332	0.131984	0.0659919	+	0.997820i	$0.478979\pi$
$734$	−53.0008	−1.95630
$735$	−33.2265	−1.22558
$736$	−0.200940	−0.00740676
$737$	−35.4636	−1.30632
$738$	15.9648	0.587672
$739$	29.3307	1.07895	0.539474	−	0.842003i	$-0.318623\pi$
$739$	29.3307	1.07895	0.539474	+	0.842003i	$0.318623\pi$
$740$	73.4938	2.70169
$741$	−8.26117	−0.303482
$742$	74.7895	2.74561
$743$	11.5099	0.422259	0.211129	−	0.977458i	$-0.432286\pi$
$743$	11.5099	0.422259	0.211129	+	0.977458i	$0.432286\pi$
$744$	26.3738	0.966910
$745$	23.9091	0.875961
$746$	−0.346266	−0.0126777
$747$	−8.12019	−0.297102
$748$	9.59862	0.350960
$749$	−57.4921	−2.10071
$750$	29.6773	1.08366
$751$	14.4430	0.527033	0.263517	−	0.964655i	$-0.415118\pi$
$751$	14.4430	0.527033	0.263517	+	0.964655i	$0.415118\pi$
$752$	−34.5981	−1.26166
$753$	8.57329	0.312428
$754$	16.4525	0.599164
$755$	9.41944	0.342808
$756$	20.3059	0.738520
$757$	23.0783	0.838796	0.419398	−	0.907803i	$-0.362241\pi$
$757$	23.0783	0.838796	0.419398	+	0.907803i	$0.362241\pi$
$758$	50.5340	1.83548
$759$	−5.64276	−0.204819
$760$	10.3713	0.376205
$761$	−42.2443	−1.53135	−0.765677	−	0.643226i	$-0.777596\pi$
$761$	−42.2443	−1.53135	−0.765677	+	0.643226i	$0.777596\pi$
$762$	−54.5712	−1.97691
$763$	−77.7351	−2.81420
$764$	49.8436	1.80328
$765$	0.746019	0.0269724
$766$	−29.7800	−1.07600
$767$	2.96336	0.107001
$768$	−31.8247	−1.14837
$769$	44.6402	1.60977	0.804884	−	0.593433i	$-0.202228\pi$
$769$	44.6402	1.60977	0.804884	+	0.593433i	$0.202228\pi$
$770$	122.878	4.42821
$771$	28.3655	1.02156
$772$	39.4032	1.41815
$773$	−29.2734	−1.05289	−0.526445	−	0.850209i	$-0.676475\pi$
$773$	−29.2734	−1.05289	−0.526445	+	0.850209i	$0.676475\pi$
$774$	−11.9553	−0.429723
$775$	−10.6490	−0.382525
$776$	−39.6104	−1.42193
$777$	−54.0014	−1.93729
$778$	88.2001	3.16213
$779$	−8.01630	−0.287214
$780$	−46.7263	−1.67307
$781$	−20.1054	−0.719428
$782$	−1.04528	−0.0373791
$783$	1.00000	0.0357371
$784$	73.8045	2.63588
$785$	−0.0418712	−0.00149445
$786$	4.69587	0.167496
$787$	−2.63680	−0.0939917	−0.0469959	−	0.998895i	$-0.514965\pi$
$787$	−2.63680	−0.0939917	−0.0469959	+	0.998895i	$0.514965\pi$
$788$	−24.4312	−0.870325
$789$	−12.4022	−0.441528
$790$	−62.1113	−2.20982
$791$	42.9106	1.52573
$792$	−27.3112	−0.970461
$793$	−40.9228	−1.45321
$794$	72.8481	2.58528
$795$	−10.4604	−0.370992
$796$	56.8476	2.01491
$797$	−2.62808	−0.0930912	−0.0465456	−	0.998916i	$-0.514821\pi$
$797$	−2.62808	−0.0930912	−0.0465456	+	0.998916i	$0.514821\pi$
$798$	−15.3206	−0.542343
$799$	3.81518	0.134971
$800$	0.392695	0.0138839
$801$	4.45271	0.157329
$802$	−41.8429	−1.47752
$803$	42.8399	1.51179
$804$	25.0094	0.882013
$805$	−8.90544	−0.313876
$806$	89.6509	3.15782
$807$	26.8677	0.945787
$808$	−85.1628	−2.99602
$809$	−43.6439	−1.53444	−0.767219	−	0.641385i	$-0.778360\pi$
$809$	−43.6439	−1.53444	−0.767219	+	0.641385i	$0.778360\pi$
$810$	−4.26748	−0.149944
$811$	−39.6254	−1.39143	−0.695717	−	0.718316i	$-0.744913\pi$
$811$	−39.6254	−1.39143	−0.695717	+	0.718316i	$0.744913\pi$
$812$	20.3059	0.712598
$813$	2.24407	0.0787029
$814$	146.020	5.11800
$815$	−0.0439861	−0.00154077
$816$	−1.65710	−0.0580100
$817$	6.00302	0.210019
$818$	−5.63815	−0.197133
$819$	34.3333	1.19970
$820$	−45.3412	−1.58338
$821$	−7.02625	−0.245218	−0.122609	−	0.992455i	$-0.539126\pi$
$821$	−7.02625	−0.245218	−0.122609	+	0.992455i	$0.539126\pi$
$822$	−9.21828	−0.321524
$823$	10.0297	0.349614	0.174807	−	0.984603i	$-0.444070\pi$
$823$	10.0297	0.349614	0.174807	+	0.984603i	$0.444070\pi$
$824$	56.6831	1.97465
$825$	11.0275	0.383930
$826$	5.49563	0.191217
$827$	9.94286	0.345747	0.172874	−	0.984944i	$-0.444695\pi$
$827$	9.94286	0.345747	0.172874	+	0.984944i	$0.444695\pi$
$828$	3.97935	0.138292
$829$	−34.6153	−1.20224	−0.601119	−	0.799159i	$-0.705278\pi$
$829$	−34.6153	−1.20224	−0.601119	+	0.799159i	$0.705278\pi$
$830$	34.6527	1.20281
$831$	−1.42115	−0.0492992
$832$	−55.4707	−1.92310
$833$	−8.13853	−0.281983
$834$	4.73715	0.164034
$835$	−12.7918	−0.442677
$836$	27.5703	0.953537
$837$	5.44908	0.188348
$838$	33.0953	1.14326
$839$	36.0858	1.24582	0.622909	−	0.782294i	$-0.285951\pi$
$839$	36.0858	1.24582	0.622909	+	0.782294i	$0.285951\pi$
$840$	−43.1027	−1.48719
$841$	1.00000	0.0344828
$842$	71.5246	2.46490
$843$	24.2843	0.836395
$844$	34.5114	1.18793
$845$	−56.3172	−1.93737
$846$	−21.8241	−0.750329
$847$	106.346	3.65411
$848$	23.2352	0.797898
$849$	−19.9648	−0.685190
$850$	2.04277	0.0700665
$851$	−10.5826	−0.362768
$852$	14.1786	0.485751
$853$	−20.5219	−0.702656	−0.351328	−	0.936253i	$-0.614270\pi$
$853$	−20.5219	−0.702656	−0.351328	+	0.936253i	$0.614270\pi$
$854$	−75.8925	−2.59699
$855$	2.14280	0.0732823
$856$	−54.5314	−1.86384
$857$	40.8417	1.39513	0.697563	−	0.716523i	$-0.254268\pi$
$857$	40.8417	1.39513	0.697563	+	0.716523i	$0.254268\pi$
$858$	−92.8373	−3.16941
$859$	−26.1071	−0.890762	−0.445381	−	0.895341i	$-0.646932\pi$
$859$	−26.1071	−0.890762	−0.445381	+	0.895341i	$0.646932\pi$
$860$	33.9538	1.15782
$861$	33.3156	1.13539
$862$	53.4532	1.82062
$863$	−24.0875	−0.819949	−0.409974	−	0.912097i	$-0.634462\pi$
$863$	−24.0875	−0.819949	−0.409974	+	0.912097i	$0.634462\pi$
$864$	−0.200940	−0.00683613
$865$	34.0959	1.15930
$866$	−17.3674	−0.590169
$867$	−16.8173	−0.571144
$868$	110.649	3.75566
$869$	−82.1278	−2.78600
$870$	−4.26748	−0.144681
$871$	42.2859	1.43280
$872$	−73.7319	−2.49688
$873$	−8.18389	−0.276983
$874$	−3.00237	−0.101557
$875$	61.9310	2.09365
$876$	−30.2113	−1.02074
$877$	−22.3908	−0.756085	−0.378043	−	0.925788i	$-0.623403\pi$
$877$	−22.3908	−0.756085	−0.378043	+	0.925788i	$0.623403\pi$
$878$	−69.9759	−2.36157
$879$	−11.9515	−0.403115
$880$	38.1750	1.28688
$881$	5.28714	0.178128	0.0890642	−	0.996026i	$-0.471612\pi$
$881$	5.28714	0.178128	0.0890642	+	0.996026i	$0.471612\pi$
$882$	46.5551	1.56759
$883$	−15.6717	−0.527395	−0.263697	−	0.964605i	$-0.584942\pi$
$883$	−15.6717	−0.527395	−0.263697	+	0.964605i	$0.584942\pi$
$884$	−11.4452	−0.384942
$885$	−0.768643	−0.0258376
$886$	41.8653	1.40649
$887$	−9.06847	−0.304489	−0.152245	−	0.988343i	$-0.548650\pi$
$887$	−9.06847	−0.304489	−0.152245	+	0.988343i	$0.548650\pi$
$888$	−51.2204	−1.71885
$889$	−113.880	−3.81941
$890$	−19.0018	−0.636943
$891$	−5.64276	−0.189039
$892$	−27.5177	−0.921360
$893$	10.9584	0.366709
$894$	−33.5000	−1.12041
$895$	−10.6386	−0.355609
$896$	−100.821	−3.36820
$897$	6.72828	0.224651
$898$	35.4109	1.18168
$899$	5.44908	0.181737
$900$	−7.77678	−0.259226
$901$	−2.56217	−0.0853584
$902$	−90.0854	−2.99952
$903$	−24.9484	−0.830231
$904$	40.7009	1.35369
$905$	−10.5220	−0.349762
$906$	−13.1980	−0.438473
$907$	31.3343	1.04044	0.520219	−	0.854033i	$-0.325850\pi$
$907$	31.3343	1.04044	0.520219	+	0.854033i	$0.325850\pi$
$908$	−40.1211	−1.33146
$909$	−17.5954	−0.583604
$910$	−146.517	−4.85698
$911$	20.8240	0.689929	0.344965	−	0.938616i	$-0.387891\pi$
$911$	20.8240	0.689929	0.344965	+	0.938616i	$0.387891\pi$
$912$	−4.75970	−0.157610
$913$	45.8202	1.51643
$914$	68.0156	2.24976
$915$	10.6146	0.350909
$916$	−40.9661	−1.35356
$917$	9.79940	0.323605
$918$	−1.04528	−0.0344994
$919$	48.3596	1.59524	0.797618	−	0.603163i	$-0.206093\pi$
$919$	48.3596	1.59524	0.797618	+	0.603163i	$0.206093\pi$
$920$	−8.44684	−0.278484
$921$	−12.3877	−0.408190
$922$	37.2422	1.22651
$923$	23.9732	0.789087
$924$	−114.581	−3.76945
$925$	20.6815	0.680003
$926$	63.9473	2.10144
$927$	11.7113	0.384649
$928$	−0.200940	−0.00659619
$929$	37.0018	1.21399	0.606995	−	0.794706i	$-0.292375\pi$
$929$	37.0018	1.21399	0.606995	+	0.794706i	$0.292375\pi$
$930$	−23.2539	−0.762524
$931$	−23.3764	−0.766131
$932$	15.7429	0.515675
$933$	11.8535	0.388066
$934$	−43.1409	−1.41161
$935$	−4.20961	−0.137669
$936$	32.5652	1.06443
$937$	−45.0999	−1.47335	−0.736675	−	0.676247i	$-0.763605\pi$
$937$	−45.0999	−1.47335	−0.736675	+	0.676247i	$0.763605\pi$
$938$	78.4203	2.56051
$939$	−19.8879	−0.649017
$940$	61.9821	2.02163
$941$	2.74512	0.0894883	0.0447442	−	0.998998i	$-0.485753\pi$
$941$	2.74512	0.0894883	0.0447442	+	0.998998i	$0.485753\pi$
$942$	0.0586675	0.00191149
$943$	6.52884	0.212608
$944$	1.70735	0.0555695
$945$	−8.90544	−0.289694
$946$	67.4606	2.19333
$947$	−22.5531	−0.732876	−0.366438	−	0.930442i	$-0.619423\pi$
$947$	−22.5531	−0.732876	−0.366438	+	0.930442i	$0.619423\pi$
$948$	57.9177	1.88108
$949$	−51.0812	−1.65817
$950$	5.86749	0.190366
$951$	9.90945	0.321336
$952$	−10.5576	−0.342174
$953$	−46.4313	−1.50406	−0.752029	−	0.659130i	$-0.770925\pi$
$953$	−46.4313	−1.50406	−0.752029	+	0.659130i	$0.770925\pi$
$954$	14.6565	0.474521
$955$	−21.8596	−0.707360
$956$	−116.950	−3.78244
$957$	−5.64276	−0.182404
$958$	−12.5366	−0.405040
$959$	−19.2368	−0.621190
$960$	14.3881	0.464374
$961$	−1.30753	−0.0421783
$962$	−174.111	−5.61355
$963$	−11.2667	−0.363065
$964$	−53.6672	−1.72850
$965$	−17.2808	−0.556289
$966$	12.4778	0.401466
$967$	40.8729	1.31439	0.657193	−	0.753723i	$-0.271744\pi$
$967$	40.8729	1.31439	0.657193	+	0.753723i	$0.271744\pi$
$968$	100.870	3.24208
$969$	0.524859	0.0168609
$970$	34.9246	1.12136
$971$	41.7944	1.34124	0.670622	−	0.741799i	$-0.266027\pi$
$971$	41.7944	1.34124	0.670622	+	0.741799i	$0.266027\pi$
$972$	3.97935	0.127638
$973$	9.88555	0.316916
$974$	14.9285	0.478341
$975$	−13.1490	−0.421104
$976$	−23.5778	−0.754707
$977$	17.6158	0.563581	0.281790	−	0.959476i	$-0.409072\pi$
$977$	17.6158	0.563581	0.281790	+	0.959476i	$0.409072\pi$
$978$	0.0616308	0.00197074
$979$	−25.1255	−0.803016
$980$	−132.220	−4.22361
$981$	−15.2337	−0.486375
$982$	12.2526	0.390996
$983$	−3.62572	−0.115642	−0.0578212	−	0.998327i	$-0.518415\pi$
$983$	−3.62572	−0.115642	−0.0578212	+	0.998327i	$0.518415\pi$
$984$	31.5999	1.00737
$985$	10.7146	0.341397
$986$	−1.04528	−0.0332885
$987$	−45.5429	−1.44965
$988$	−32.8741	−1.04586
$989$	−4.88914	−0.155465
$990$	24.0804	0.765324
$991$	27.8298	0.884044	0.442022	−	0.897004i	$-0.354261\pi$
$991$	27.8298	0.884044	0.442022	+	0.897004i	$0.354261\pi$
$992$	−1.09494	−0.0347644
$993$	−10.0660	−0.319434
$994$	44.4590	1.41015
$995$	−24.9313	−0.790375
$996$	−32.3131	−1.02388
$997$	−54.2859	−1.71925	−0.859626	−	0.510923i	$-0.829304\pi$
$997$	−54.2859	−1.71925	−0.859626	+	0.510923i	$0.829304\pi$
$998$	65.8599	2.08476
$999$	−10.5826	−0.334820

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2001.2.a.o.1.17	✓	20
3.2	odd	2		6003.2.a.s.1.4		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2001.2.a.o.1.17	✓	20	1.1	even	1	trivial
6003.2.a.s.1.4		20	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)

\(f(q)\)	\(=\)	\(q+2.44527 q^{2} +1.00000 q^{3} +3.97935 q^{4} -1.74520 q^{5} +2.44527 q^{6} +5.10283 q^{7} +4.84005 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+2.44527 q^{2} +1.00000 q^{3} +3.97935 q^{4} -1.74520 q^{5} +2.44527 q^{6} +5.10283 q^{7} +4.84005 q^{8} +1.00000 q^{9} -4.26748 q^{10} -5.64276 q^{11} +3.97935 q^{12} +6.72828 q^{13} +12.4778 q^{14} -1.74520 q^{15} +3.87652 q^{16} -0.427470 q^{17} +2.44527 q^{18} -1.22783 q^{19} -6.94475 q^{20} +5.10283 q^{21} -13.7981 q^{22} +1.00000 q^{23} +4.84005 q^{24} -1.95428 q^{25} +16.4525 q^{26} +1.00000 q^{27} +20.3059 q^{28} +1.00000 q^{29} -4.26748 q^{30} +5.44908 q^{31} -0.200940 q^{32} -5.64276 q^{33} -1.04528 q^{34} -8.90544 q^{35} +3.97935 q^{36} -10.5826 q^{37} -3.00237 q^{38} +6.72828 q^{39} -8.44684 q^{40} +6.52884 q^{41} +12.4778 q^{42} -4.88914 q^{43} -22.4545 q^{44} -1.74520 q^{45} +2.44527 q^{46} -8.92503 q^{47} +3.87652 q^{48} +19.0388 q^{49} -4.77875 q^{50} -0.427470 q^{51} +26.7742 q^{52} +5.99381 q^{53} +2.44527 q^{54} +9.84773 q^{55} +24.6979 q^{56} -1.22783 q^{57} +2.44527 q^{58} +0.440433 q^{59} -6.94475 q^{60} -6.08220 q^{61} +13.3245 q^{62} +5.10283 q^{63} -8.24440 q^{64} -11.7422 q^{65} -13.7981 q^{66} +6.28479 q^{67} -1.70105 q^{68} +1.00000 q^{69} -21.7762 q^{70} +3.56305 q^{71} +4.84005 q^{72} -7.59201 q^{73} -25.8774 q^{74} -1.95428 q^{75} -4.88596 q^{76} -28.7940 q^{77} +16.4525 q^{78} +14.5546 q^{79} -6.76530 q^{80} +1.00000 q^{81} +15.9648 q^{82} -8.12019 q^{83} +20.3059 q^{84} +0.746019 q^{85} -11.9553 q^{86} +1.00000 q^{87} -27.3112 q^{88} +4.45271 q^{89} -4.26748 q^{90} +34.3333 q^{91} +3.97935 q^{92} +5.44908 q^{93} -21.8241 q^{94} +2.14280 q^{95} -0.200940 q^{96} -8.18389 q^{97} +46.5551 q^{98} -5.64276 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 2 q^{2} + 20 q^{3} + 30 q^{4} - q^{5} + 2 q^{6} + 9 q^{7} + 6 q^{8} + 20 q^{9}+O(q^{10}) \) 20 * q + 2 * q^2 + 20 * q^3 + 30 * q^4 - q^5 + 2 * q^6 + 9 * q^7 + 6 * q^8 + 20 * q^9	\( 20 q + 2 q^{2} + 20 q^{3} + 30 q^{4} - q^{5} + 2 q^{6} + 9 q^{7} + 6 q^{8} + 20 q^{9} + 7 q^{10} + 30 q^{12} + 21 q^{13} - q^{14} - q^{15} + 58 q^{16} - 4 q^{17} + 2 q^{18} + 7 q^{19} - 20 q^{20} + 9 q^{21} + 7 q^{22} + 20 q^{23} + 6 q^{24} + 47 q^{25} + 8 q^{26} + 20 q^{27} + 11 q^{28} + 20 q^{29} + 7 q^{30} + 28 q^{31} + 14 q^{32} + 16 q^{34} + 9 q^{35} + 30 q^{36} + 14 q^{37} - 20 q^{38} + 21 q^{39} + 34 q^{40} + 7 q^{41} - q^{42} + 3 q^{43} - q^{44} - q^{45} + 2 q^{46} + 3 q^{47} + 58 q^{48} + 35 q^{49} - 24 q^{50} - 4 q^{51} + 73 q^{52} - 19 q^{53} + 2 q^{54} + 29 q^{55} - 30 q^{56} + 7 q^{57} + 2 q^{58} + 20 q^{59} - 20 q^{60} + 15 q^{61} + 12 q^{62} + 9 q^{63} + 82 q^{64} - 28 q^{65} + 7 q^{66} + 20 q^{67} - 23 q^{68} + 20 q^{69} - 24 q^{70} + 63 q^{71} + 6 q^{72} + 19 q^{73} + 16 q^{74} + 47 q^{75} - 44 q^{76} - 7 q^{77} + 8 q^{78} + 32 q^{79} - 56 q^{80} + 20 q^{81} - 20 q^{82} - 21 q^{83} + 11 q^{84} + 4 q^{85} - 6 q^{86} + 20 q^{87} + 55 q^{88} - 13 q^{89} + 7 q^{90} + 70 q^{91} + 30 q^{92} + 28 q^{93} - 12 q^{94} + 9 q^{95} + 14 q^{96} - 9 q^{97} + 31 q^{98}+O(q^{100}) \) 20 * q + 2 * q^2 + 20 * q^3 + 30 * q^4 - q^5 + 2 * q^6 + 9 * q^7 + 6 * q^8 + 20 * q^9 + 7 * q^10 + 30 * q^12 + 21 * q^13 - q^14 - q^15 + 58 * q^16 - 4 * q^17 + 2 * q^18 + 7 * q^19 - 20 * q^20 + 9 * q^21 + 7 * q^22 + 20 * q^23 + 6 * q^24 + 47 * q^25 + 8 * q^26 + 20 * q^27 + 11 * q^28 + 20 * q^29 + 7 * q^30 + 28 * q^31 + 14 * q^32 + 16 * q^34 + 9 * q^35 + 30 * q^36 + 14 * q^37 - 20 * q^38 + 21 * q^39 + 34 * q^40 + 7 * q^41 - q^42 + 3 * q^43 - q^44 - q^45 + 2 * q^46 + 3 * q^47 + 58 * q^48 + 35 * q^49 - 24 * q^50 - 4 * q^51 + 73 * q^52 - 19 * q^53 + 2 * q^54 + 29 * q^55 - 30 * q^56 + 7 * q^57 + 2 * q^58 + 20 * q^59 - 20 * q^60 + 15 * q^61 + 12 * q^62 + 9 * q^63 + 82 * q^64 - 28 * q^65 + 7 * q^66 + 20 * q^67 - 23 * q^68 + 20 * q^69 - 24 * q^70 + 63 * q^71 + 6 * q^72 + 19 * q^73 + 16 * q^74 + 47 * q^75 - 44 * q^76 - 7 * q^77 + 8 * q^78 + 32 * q^79 - 56 * q^80 + 20 * q^81 - 20 * q^82 - 21 * q^83 + 11 * q^84 + 4 * q^85 - 6 * q^86 + 20 * q^87 + 55 * q^88 - 13 * q^89 + 7 * q^90 + 70 * q^91 + 30 * q^92 + 28 * q^93 - 12 * q^94 + 9 * q^95 + 14 * q^96 - 9 * q^97 + 31 * q^98

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