LMFDB - Embedded newform 2001.2.a.o.1.16

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			1.16
Root			$2.23669$ 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)

$f(q)$	$=$	$q+2.23669 q^{2} +1.00000 q^{3} +3.00280 q^{4} +1.57347 q^{5} +2.23669 q^{6} -1.14044 q^{7} +2.24296 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+2.23669 q^{2} +1.00000 q^{3} +3.00280 q^{4} +1.57347 q^{5} +2.23669 q^{6} -1.14044 q^{7} +2.24296 q^{8} +1.00000 q^{9} +3.51938 q^{10} -1.30124 q^{11} +3.00280 q^{12} +3.08159 q^{13} -2.55082 q^{14} +1.57347 q^{15} -0.988785 q^{16} +0.952730 q^{17} +2.23669 q^{18} +8.67005 q^{19} +4.72483 q^{20} -1.14044 q^{21} -2.91048 q^{22} +1.00000 q^{23} +2.24296 q^{24} -2.52418 q^{25} +6.89257 q^{26} +1.00000 q^{27} -3.42453 q^{28} +1.00000 q^{29} +3.51938 q^{30} +3.26607 q^{31} -6.69753 q^{32} -1.30124 q^{33} +2.13097 q^{34} -1.79446 q^{35} +3.00280 q^{36} -0.355229 q^{37} +19.3923 q^{38} +3.08159 q^{39} +3.52924 q^{40} -0.628348 q^{41} -2.55082 q^{42} +6.66758 q^{43} -3.90736 q^{44} +1.57347 q^{45} +2.23669 q^{46} -2.60698 q^{47} -0.988785 q^{48} -5.69939 q^{49} -5.64581 q^{50} +0.952730 q^{51} +9.25340 q^{52} -12.1642 q^{53} +2.23669 q^{54} -2.04747 q^{55} -2.55797 q^{56} +8.67005 q^{57} +2.23669 q^{58} +2.41797 q^{59} +4.72483 q^{60} +10.3061 q^{61} +7.30521 q^{62} -1.14044 q^{63} -13.0028 q^{64} +4.84880 q^{65} -2.91048 q^{66} -15.3115 q^{67} +2.86086 q^{68} +1.00000 q^{69} -4.01366 q^{70} -6.42392 q^{71} +2.24296 q^{72} +13.2169 q^{73} -0.794539 q^{74} -2.52418 q^{75} +26.0344 q^{76} +1.48399 q^{77} +6.89257 q^{78} -11.1972 q^{79} -1.55583 q^{80} +1.00000 q^{81} -1.40542 q^{82} -7.28190 q^{83} -3.42453 q^{84} +1.49910 q^{85} +14.9133 q^{86} +1.00000 q^{87} -2.91863 q^{88} -2.34116 q^{89} +3.51938 q^{90} -3.51438 q^{91} +3.00280 q^{92} +3.26607 q^{93} -5.83103 q^{94} +13.6421 q^{95} -6.69753 q^{96} -11.8007 q^{97} -12.7478 q^{98} -1.30124 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	2.23669	1.58158	0.790791	−	0.612086i	$-0.209670\pi$
$2$	2.23669	1.58158	0.790791	+	0.612086i	$0.209670\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	3.00280	1.50140
$5$	1.57347	0.703679	0.351840	−	0.936060i	$-0.385556\pi$
$5$	1.57347	0.703679	0.351840	+	0.936060i	$0.385556\pi$
$6$	2.23669	0.913127
$7$	−1.14044	−0.431047	−0.215524	−	0.976499i	$-0.569146\pi$
$7$	−1.14044	−0.431047	−0.215524	+	0.976499i	$0.569146\pi$
$8$	2.24296	0.793007
$9$	1.00000	0.333333
$10$	3.51938	1.11293
$11$	−1.30124	−0.392339	−0.196169	−	0.980570i	$-0.562850\pi$
$11$	−1.30124	−0.392339	−0.196169	+	0.980570i	$0.562850\pi$
$12$	3.00280	0.866834
$13$	3.08159	0.854679	0.427339	−	0.904091i	$-0.359451\pi$
$13$	3.08159	0.854679	0.427339	+	0.904091i	$0.359451\pi$
$14$	−2.55082	−0.681736
$15$	1.57347	0.406269
$16$	−0.988785	−0.247196
$17$	0.952730	0.231071	0.115535	−	0.993303i	$-0.463142\pi$
$17$	0.952730	0.231071	0.115535	+	0.993303i	$0.463142\pi$
$18$	2.23669	0.527194
$19$	8.67005	1.98905	0.994523	−	0.104516i	$-0.0333294\pi$
$19$	8.67005	1.98905	0.994523	+	0.104516i	$0.0333294\pi$
$20$	4.72483	1.05650
$21$	−1.14044	−0.248865
$22$	−2.91048	−0.620515
$23$	1.00000	0.208514
$23$	1.00000	0.208514
$24$	2.24296	0.457843
$25$	−2.52418	−0.504835
$26$	6.89257	1.35174
$27$	1.00000	0.192450
$28$	−3.42453	−0.647174
$29$	1.00000	0.185695
$29$	1.00000	0.185695
$30$	3.51938	0.642548
$31$	3.26607	0.586604	0.293302	−	0.956020i	$-0.405246\pi$
$31$	3.26607	0.586604	0.293302	+	0.956020i	$0.405246\pi$
$32$	−6.69753	−1.18397
$33$	−1.30124	−0.226517
$34$	2.13097	0.365458
$35$	−1.79446	−0.303319
$36$	3.00280	0.500467
$37$	−0.355229	−0.0583993	−0.0291997	−	0.999574i	$-0.509296\pi$
$37$	−0.355229	−0.0583993	−0.0291997	+	0.999574i	$0.509296\pi$
$38$	19.3923	3.14584
$39$	3.08159	0.493449
$40$	3.52924	0.558022
$41$	−0.628348	−0.0981314	−0.0490657	−	0.998796i	$-0.515624\pi$
$41$	−0.628348	−0.0981314	−0.0490657	+	0.998796i	$0.515624\pi$
$42$	−2.55082	−0.393601
$43$	6.66758	1.01680	0.508398	−	0.861122i	$-0.330238\pi$
$43$	6.66758	1.01680	0.508398	+	0.861122i	$0.330238\pi$
$44$	−3.90736	−0.589057
$45$	1.57347	0.234560
$46$	2.23669	0.329783
$47$	−2.60698	−0.380268	−0.190134	−	0.981758i	$-0.560892\pi$
$47$	−2.60698	−0.380268	−0.190134	+	0.981758i	$0.560892\pi$
$48$	−0.988785	−0.142719
$49$	−5.69939	−0.814198
$50$	−5.64581	−0.798438
$51$	0.952730	0.133409
$52$	9.25340	1.28322
$53$	−12.1642	−1.67088	−0.835440	−	0.549582i	$-0.814787\pi$
$53$	−12.1642	−1.67088	−0.835440	+	0.549582i	$0.814787\pi$
$54$	2.23669	0.304376
$55$	−2.04747	−0.276081
$56$	−2.55797	−0.341823
$57$	8.67005	1.14838
$58$	2.23669	0.293692
$59$	2.41797	0.314793	0.157396	−	0.987535i	$-0.449690\pi$
$59$	2.41797	0.314793	0.157396	+	0.987535i	$0.449690\pi$
$60$	4.72483	0.609973
$61$	10.3061	1.31956	0.659778	−	0.751460i	$-0.270650\pi$
$61$	10.3061	1.31956	0.659778	+	0.751460i	$0.270650\pi$
$62$	7.30521	0.927762
$63$	−1.14044	−0.143682
$64$	−13.0028	−1.62535
$65$	4.84880	0.601420
$66$	−2.91048	−0.358255
$67$	−15.3115	−1.87060	−0.935299	−	0.353859i	$-0.884869\pi$
$67$	−15.3115	−1.87060	−0.935299	+	0.353859i	$0.884869\pi$
$68$	2.86086	0.346930
$69$	1.00000	0.120386
$70$	−4.01366	−0.479724
$71$	−6.42392	−0.762379	−0.381189	−	0.924497i	$-0.624485\pi$
$71$	−6.42392	−0.762379	−0.381189	+	0.924497i	$0.624485\pi$
$72$	2.24296	0.264336
$73$	13.2169	1.54692	0.773459	−	0.633847i	$-0.218525\pi$
$73$	13.2169	1.54692	0.773459	+	0.633847i	$0.218525\pi$
$74$	−0.794539	−0.0923633
$75$	−2.52418	−0.291467
$76$	26.0344	2.98636
$77$	1.48399	0.169116
$78$	6.89257	0.780430
$79$	−11.1972	−1.25979	−0.629894	−	0.776681i	$-0.716902\pi$
$79$	−11.1972	−1.25979	−0.629894	+	0.776681i	$0.716902\pi$
$80$	−1.55583	−0.173947
$81$	1.00000	0.111111
$82$	−1.40542	−0.155203
$83$	−7.28190	−0.799292	−0.399646	−	0.916669i	$-0.630867\pi$
$83$	−7.28190	−0.799292	−0.399646	+	0.916669i	$0.630867\pi$
$84$	−3.42453	−0.373646
$85$	1.49910	0.162600
$86$	14.9133	1.60815
$87$	1.00000	0.107211
$88$	−2.91863	−0.311127
$89$	−2.34116	−0.248162	−0.124081	−	0.992272i	$-0.539598\pi$
$89$	−2.34116	−0.248162	−0.124081	+	0.992272i	$0.539598\pi$
$90$	3.51938	0.370975
$91$	−3.51438	−0.368407
$92$	3.00280	0.313064
$93$	3.26607	0.338676
$94$	−5.83103	−0.601424
$95$	13.6421	1.39965
$96$	−6.69753	−0.683564
$97$	−11.8007	−1.19818	−0.599091	−	0.800681i	$-0.704471\pi$
$97$	−11.8007	−1.19818	−0.599091	+	0.800681i	$0.704471\pi$
$98$	−12.7478	−1.28772
$99$	−1.30124	−0.130780
$100$	−7.57960	−0.757960
$101$	10.5799	1.05273	0.526367	−	0.850257i	$-0.323554\pi$
$101$	10.5799	1.05273	0.526367	+	0.850257i	$0.323554\pi$
$102$	2.13097	0.210997
$103$	−11.0516	−1.08894	−0.544472	−	0.838779i	$-0.683270\pi$
$103$	−11.0516	−1.08894	−0.544472	+	0.838779i	$0.683270\pi$
$104$	6.91188	0.677766
$105$	−1.79446	−0.175121
$106$	−27.2076	−2.64263
$107$	−15.2123	−1.47063	−0.735314	−	0.677727i	$-0.762965\pi$
$107$	−15.2123	−1.47063	−0.735314	+	0.677727i	$0.762965\pi$
$108$	3.00280	0.288945
$109$	−14.5941	−1.39787	−0.698933	−	0.715188i	$-0.746341\pi$
$109$	−14.5941	−1.39787	−0.698933	+	0.715188i	$0.746341\pi$
$110$	−4.57956	−0.436644
$111$	−0.355229	−0.0337169
$112$	1.12765	0.106553
$113$	6.55583	0.616720	0.308360	−	0.951270i	$-0.400220\pi$
$113$	6.55583	0.616720	0.308360	+	0.951270i	$0.400220\pi$
$114$	19.3923	1.81625
$115$	1.57347	0.146727
$116$	3.00280	0.278803
$117$	3.08159	0.284893
$118$	5.40826	0.497871
$119$	−1.08653	−0.0996025
$120$	3.52924	0.322174
$121$	−9.30678	−0.846070
$122$	23.0515	2.08699
$123$	−0.628348	−0.0566562
$124$	9.80737	0.880728
$125$	−11.8391	−1.05892
$126$	−2.55082	−0.227245
$127$	16.0271	1.42217	0.711086	−	0.703105i	$-0.248204\pi$
$127$	16.0271	1.42217	0.711086	+	0.703105i	$0.248204\pi$
$128$	−15.6881	−1.38665
$129$	6.66758	0.587048
$130$	10.8453	0.951195
$131$	2.65214	0.231718	0.115859	−	0.993266i	$-0.463038\pi$
$131$	2.65214	0.231718	0.115859	+	0.993266i	$0.463038\pi$
$132$	−3.90736	−0.340092
$133$	−9.88770	−0.857373
$134$	−34.2471	−2.95850
$135$	1.57347	0.135423
$136$	2.13694	0.183241
$137$	−18.0071	−1.53845	−0.769226	−	0.638976i	$-0.779358\pi$
$137$	−18.0071	−1.53845	−0.769226	+	0.638976i	$0.779358\pi$
$138$	2.23669	0.190400
$139$	8.15473	0.691675	0.345838	−	0.938294i	$-0.387595\pi$
$139$	8.15473	0.691675	0.345838	+	0.938294i	$0.387595\pi$
$140$	−5.38840	−0.455403
$141$	−2.60698	−0.219548
$142$	−14.3683	−1.20576
$143$	−4.00989	−0.335323
$144$	−0.988785	−0.0823987
$145$	1.57347	0.130670
$146$	29.5621	2.44658
$147$	−5.69939	−0.470078
$148$	−1.06668	−0.0876808
$149$	16.2814	1.33382	0.666911	−	0.745137i	$-0.267616\pi$
$149$	16.2814	1.33382	0.666911	+	0.745137i	$0.267616\pi$
$150$	−5.64581	−0.460979
$151$	14.1810	1.15403	0.577015	−	0.816733i	$-0.304217\pi$
$151$	14.1810	1.15403	0.577015	+	0.816733i	$0.304217\pi$
$152$	19.4466	1.57733
$153$	0.952730	0.0770237
$154$	3.31923	0.267471
$155$	5.13908	0.412781
$156$	9.25340	0.740865
$157$	3.86239	0.308253	0.154126	−	0.988051i	$-0.450744\pi$
$157$	3.86239	0.308253	0.154126	+	0.988051i	$0.450744\pi$
$158$	−25.0448	−1.99246
$159$	−12.1642	−0.964683
$160$	−10.5384	−0.833133
$161$	−1.14044	−0.0898795
$162$	2.23669	0.175731
$163$	−1.55619	−0.121890	−0.0609451	−	0.998141i	$-0.519411\pi$
$163$	−1.55619	−0.121890	−0.0609451	+	0.998141i	$0.519411\pi$
$164$	−1.88680	−0.147335
$165$	−2.04747	−0.159395
$166$	−16.2874	−1.26415
$167$	11.7141	0.906462	0.453231	−	0.891393i	$-0.350271\pi$
$167$	11.7141	0.906462	0.453231	+	0.891393i	$0.350271\pi$
$168$	−2.55797	−0.197352
$169$	−3.50381	−0.269524
$170$	3.35302	0.257165
$171$	8.67005	0.663015
$172$	20.0214	1.52662
$173$	−2.44162	−0.185633	−0.0928163	−	0.995683i	$-0.529587\pi$
$173$	−2.44162	−0.185633	−0.0928163	+	0.995683i	$0.529587\pi$
$174$	2.23669	0.169563
$175$	2.87868	0.217608
$176$	1.28665	0.0969846
$177$	2.41797	0.181746
$178$	−5.23645	−0.392489
$179$	22.4278	1.67633	0.838165	−	0.545417i	$-0.183629\pi$
$179$	22.4278	1.67633	0.838165	+	0.545417i	$0.183629\pi$
$180$	4.72483	0.352168
$181$	−22.1929	−1.64958	−0.824791	−	0.565438i	$-0.808707\pi$
$181$	−22.1929	−1.64958	−0.824791	+	0.565438i	$0.808707\pi$
$182$	−7.86059	−0.582666
$183$	10.3061	0.761846
$184$	2.24296	0.165353
$185$	−0.558944	−0.0410944
$186$	7.30521	0.535644
$187$	−1.23973	−0.0906581
$188$	−7.82826	−0.570934
$189$	−1.14044	−0.0829550
$190$	30.5132	2.21366
$191$	−14.7128	−1.06458	−0.532291	−	0.846561i	$-0.678669\pi$
$191$	−14.7128	−1.06458	−0.532291	+	0.846561i	$0.678669\pi$
$192$	−13.0028	−0.938394
$193$	−7.60757	−0.547605	−0.273802	−	0.961786i	$-0.588281\pi$
$193$	−7.60757	−0.547605	−0.273802	+	0.961786i	$0.588281\pi$
$194$	−26.3946	−1.89502
$195$	4.84880	0.347230
$196$	−17.1141	−1.22244
$197$	1.23151	0.0877413	0.0438707	−	0.999037i	$-0.486031\pi$
$197$	1.23151	0.0877413	0.0438707	+	0.999037i	$0.486031\pi$
$198$	−2.91048	−0.206838
$199$	−15.5740	−1.10401	−0.552006	−	0.833840i	$-0.686137\pi$
$199$	−15.5740	−1.10401	−0.552006	+	0.833840i	$0.686137\pi$
$200$	−5.66163	−0.400338
$201$	−15.3115	−1.07999
$202$	23.6639	1.66499
$203$	−1.14044	−0.0800434
$204$	2.86086	0.200300
$205$	−0.988689	−0.0690531
$206$	−24.7190	−1.72225
$207$	1.00000	0.0695048
$208$	−3.04703	−0.211273
$209$	−11.2818	−0.780380
$210$	−4.01366	−0.276969
$211$	15.5974	1.07377	0.536884	−	0.843656i	$-0.319601\pi$
$211$	15.5974	1.07377	0.536884	+	0.843656i	$0.319601\pi$
$212$	−36.5266	−2.50866
$213$	−6.42392	−0.440160
$214$	−34.0252	−2.32592
$215$	10.4913	0.715498
$216$	2.24296	0.152614
$217$	−3.72477	−0.252854
$218$	−32.6426	−2.21084
$219$	13.2169	0.893113
$220$	−6.14814	−0.414508
$221$	2.93592	0.197491
$222$	−0.794539	−0.0533260
$223$	17.8181	1.19319	0.596595	−	0.802542i	$-0.296520\pi$
$223$	17.8181	1.19319	0.596595	+	0.802542i	$0.296520\pi$
$224$	7.63816	0.510346
$225$	−2.52418	−0.168278
$226$	14.6634	0.975394
$227$	10.4634	0.694482	0.347241	−	0.937776i	$-0.387119\pi$
$227$	10.4634	0.694482	0.347241	+	0.937776i	$0.387119\pi$
$228$	26.0344	1.72417
$229$	21.8271	1.44237	0.721187	−	0.692741i	$-0.243597\pi$
$229$	21.8271	1.44237	0.721187	+	0.692741i	$0.243597\pi$
$230$	3.51938	0.232061
$231$	1.48399	0.0976394
$232$	2.24296	0.147258
$233$	−12.9430	−0.847927	−0.423964	−	0.905679i	$-0.639362\pi$
$233$	−12.9430	−0.847927	−0.423964	+	0.905679i	$0.639362\pi$
$234$	6.89257	0.450582
$235$	−4.10202	−0.267587
$236$	7.26069	0.472630
$237$	−11.1972	−0.727339
$238$	−2.43025	−0.157529
$239$	−14.6272	−0.946155	−0.473078	−	0.881021i	$-0.656857\pi$
$239$	−14.6272	−0.946155	−0.473078	+	0.881021i	$0.656857\pi$
$240$	−1.55583	−0.100428
$241$	22.7468	1.46525	0.732624	−	0.680633i	$-0.238295\pi$
$241$	22.7468	1.46525	0.732624	+	0.680633i	$0.238295\pi$
$242$	−20.8164	−1.33813
$243$	1.00000	0.0641500
$244$	30.9471	1.98118
$245$	−8.96784	−0.572935
$246$	−1.40542	−0.0896064
$247$	26.7175	1.70000
$248$	7.32567	0.465181
$249$	−7.28190	−0.461472
$250$	−26.4805	−1.67477
$251$	25.2420	1.59326	0.796632	−	0.604465i	$-0.206613\pi$
$251$	25.2420	1.59326	0.796632	+	0.604465i	$0.206613\pi$
$252$	−3.42453	−0.215725
$253$	−1.30124	−0.0818082
$254$	35.8476	2.24928
$255$	1.49910	0.0938771
$256$	−9.08405	−0.567753
$257$	−13.0322	−0.812929	−0.406464	−	0.913667i	$-0.633238\pi$
$257$	−13.0322	−0.812929	−0.406464	+	0.913667i	$0.633238\pi$
$258$	14.9133	0.928464
$259$	0.405119	0.0251729
$260$	14.5600	0.902972
$261$	1.00000	0.0618984
$262$	5.93202	0.366482
$263$	−1.27846	−0.0788334	−0.0394167	−	0.999223i	$-0.512550\pi$
$263$	−1.27846	−0.0788334	−0.0394167	+	0.999223i	$0.512550\pi$
$264$	−2.91863	−0.179629
$265$	−19.1400	−1.17576
$266$	−22.1158	−1.35600
$267$	−2.34116	−0.143277
$268$	−45.9774	−2.80852
$269$	24.0766	1.46798	0.733988	−	0.679163i	$-0.237657\pi$
$269$	24.0766	1.46798	0.733988	+	0.679163i	$0.237657\pi$
$270$	3.51938	0.214183
$271$	28.3552	1.72246	0.861229	−	0.508217i	$-0.169695\pi$
$271$	28.3552	1.72246	0.861229	+	0.508217i	$0.169695\pi$
$272$	−0.942045	−0.0571199
$273$	−3.51438	−0.212700
$274$	−40.2764	−2.43319
$275$	3.28456	0.198066
$276$	3.00280	0.180747
$277$	4.97856	0.299132	0.149566	−	0.988752i	$-0.452212\pi$
$277$	4.97856	0.299132	0.149566	+	0.988752i	$0.452212\pi$
$278$	18.2396	1.09394
$279$	3.26607	0.195535
$280$	−4.02490	−0.240534
$281$	−12.8688	−0.767688	−0.383844	−	0.923398i	$-0.625400\pi$
$281$	−12.8688	−0.767688	−0.383844	+	0.923398i	$0.625400\pi$
$282$	−5.83103	−0.347233
$283$	4.67882	0.278127	0.139063	−	0.990283i	$-0.455591\pi$
$283$	4.67882	0.278127	0.139063	+	0.990283i	$0.455591\pi$
$284$	−19.2898	−1.14464
$285$	13.6421	0.808089
$286$	−8.96889	−0.530341
$287$	0.716595	0.0422993
$288$	−6.69753	−0.394656
$289$	−16.0923	−0.946606
$290$	3.51938	0.206665
$291$	−11.8007	−0.691771
$292$	39.6876	2.32254
$293$	20.7309	1.21111	0.605557	−	0.795802i	$-0.292950\pi$
$293$	20.7309	1.21111	0.605557	+	0.795802i	$0.292950\pi$
$294$	−12.7478	−0.743466
$295$	3.80462	0.221513
$296$	−0.796766	−0.0463111
$297$	−1.30124	−0.0755056
$298$	36.4165	2.10955
$299$	3.08159	0.178213
$300$	−7.57960	−0.437609
$301$	−7.60400	−0.438287
$302$	31.7185	1.82519
$303$	10.5799	0.607797
$304$	−8.57282	−0.491685
$305$	16.2163	0.928545
$306$	2.13097	0.121819
$307$	7.18488	0.410063	0.205032	−	0.978755i	$-0.434270\pi$
$307$	7.18488	0.410063	0.205032	+	0.978755i	$0.434270\pi$
$308$	4.45613	0.253911
$309$	−11.0516	−0.628702
$310$	11.4946	0.652847
$311$	−17.0694	−0.967918	−0.483959	−	0.875091i	$-0.660802\pi$
$311$	−17.0694	−0.967918	−0.483959	+	0.875091i	$0.660802\pi$
$312$	6.91188	0.391308
$313$	−17.2928	−0.977450	−0.488725	−	0.872438i	$-0.662538\pi$
$313$	−17.2928	−0.977450	−0.488725	+	0.872438i	$0.662538\pi$
$314$	8.63900	0.487527
$315$	−1.79446	−0.101106
$316$	−33.6231	−1.89145
$317$	−20.9272	−1.17539	−0.587694	−	0.809083i	$-0.699964\pi$
$317$	−20.9272	−1.17539	−0.587694	+	0.809083i	$0.699964\pi$
$318$	−27.2076	−1.52572
$319$	−1.30124	−0.0728554
$320$	−20.4595	−1.14372
$321$	−15.2123	−0.849067
$322$	−2.55082	−0.142152
$323$	8.26022	0.459611
$324$	3.00280	0.166822
$325$	−7.77848	−0.431472
$326$	−3.48072	−0.192779
$327$	−14.5941	−0.807058
$328$	−1.40936	−0.0778189
$329$	2.97312	0.163913
$330$	−4.57956	−0.252096
$331$	−21.5231	−1.18301	−0.591507	−	0.806300i	$-0.701467\pi$
$331$	−21.5231	−1.18301	−0.591507	+	0.806300i	$0.701467\pi$
$332$	−21.8661	−1.20006
$333$	−0.355229	−0.0194664
$334$	26.2008	1.43364
$335$	−24.0923	−1.31630
$336$	1.12765	0.0615185
$337$	3.74142	0.203808	0.101904	−	0.994794i	$-0.467506\pi$
$337$	3.74142	0.203808	0.101904	+	0.994794i	$0.467506\pi$
$338$	−7.83696	−0.426274
$339$	6.55583	0.356064
$340$	4.50149	0.244128
$341$	−4.24994	−0.230147
$342$	19.3923	1.04861
$343$	14.4829	0.782005
$344$	14.9551	0.806326
$345$	1.57347	0.0847130
$346$	−5.46115	−0.293593
$347$	13.0539	0.700768	0.350384	−	0.936606i	$-0.386051\pi$
$347$	13.0539	0.700768	0.350384	+	0.936606i	$0.386051\pi$
$348$	3.00280	0.160967
$349$	−13.4154	−0.718111	−0.359055	−	0.933316i	$-0.616901\pi$
$349$	−13.4154	−0.718111	−0.359055	+	0.933316i	$0.616901\pi$
$350$	6.43873	0.344165
$351$	3.08159	0.164483
$352$	8.71509	0.464516
$353$	6.86450	0.365361	0.182680	−	0.983172i	$-0.441523\pi$
$353$	6.86450	0.365361	0.182680	+	0.983172i	$0.441523\pi$
$354$	5.40826	0.287446
$355$	−10.1079	−0.536470
$356$	−7.03003	−0.372591
$357$	−1.08653	−0.0575055
$358$	50.1641	2.65125
$359$	−22.9641	−1.21200	−0.605999	−	0.795466i	$-0.707226\pi$
$359$	−22.9641	−1.21200	−0.605999	+	0.795466i	$0.707226\pi$
$360$	3.52924	0.186007
$361$	56.1698	2.95631
$362$	−49.6386	−2.60895
$363$	−9.30678	−0.488479
$364$	−10.5530	−0.553126
$365$	20.7964	1.08853
$366$	23.0515	1.20492
$367$	−1.17977	−0.0615834	−0.0307917	−	0.999526i	$-0.509803\pi$
$367$	−1.17977	−0.0615834	−0.0307917	+	0.999526i	$0.509803\pi$
$368$	−0.988785	−0.0515440
$369$	−0.628348	−0.0327105
$370$	−1.25019	−0.0649942
$371$	13.8726	0.720228
$372$	9.80737	0.508488
$373$	20.2830	1.05021	0.525107	−	0.851036i	$-0.324025\pi$
$373$	20.2830	1.05021	0.525107	+	0.851036i	$0.324025\pi$
$374$	−2.77290	−0.143383
$375$	−11.8391	−0.611369
$376$	−5.84736	−0.301555
$377$	3.08159	0.158710
$378$	−2.55082	−0.131200
$379$	18.0683	0.928107	0.464053	−	0.885807i	$-0.346395\pi$
$379$	18.0683	0.928107	0.464053	+	0.885807i	$0.346395\pi$
$380$	40.9645	2.10144
$381$	16.0271	0.821091
$382$	−32.9081	−1.68372
$383$	−5.89138	−0.301035	−0.150518	−	0.988607i	$-0.548094\pi$
$383$	−5.89138	−0.301035	−0.150518	+	0.988607i	$0.548094\pi$
$384$	−15.6881	−0.800582
$385$	2.33502	0.119004
$386$	−17.0158	−0.866082
$387$	6.66758	0.338932
$388$	−35.4353	−1.79895
$389$	33.1378	1.68016	0.840078	−	0.542466i	$-0.182509\pi$
$389$	33.1378	1.68016	0.840078	+	0.542466i	$0.182509\pi$
$390$	10.8453	0.549173
$391$	0.952730	0.0481816
$392$	−12.7835	−0.645665
$393$	2.65214	0.133783
$394$	2.75451	0.138770
$395$	−17.6186	−0.886487
$396$	−3.90736	−0.196352
$397$	−33.8045	−1.69660	−0.848300	−	0.529516i	$-0.822374\pi$
$397$	−33.8045	−1.69660	−0.848300	+	0.529516i	$0.822374\pi$
$398$	−34.8343	−1.74608
$399$	−9.88770	−0.495004
$400$	2.49587	0.124793
$401$	−4.06176	−0.202835	−0.101417	−	0.994844i	$-0.532338\pi$
$401$	−4.06176	−0.202835	−0.101417	+	0.994844i	$0.532338\pi$
$402$	−34.2471	−1.70809
$403$	10.0647	0.501358
$404$	31.7692	1.58058
$405$	1.57347	0.0781866
$406$	−2.55082	−0.126595
$407$	0.462238	0.0229123
$408$	2.13694	0.105794
$409$	−27.9929	−1.38416	−0.692080	−	0.721821i	$-0.743306\pi$
$409$	−27.9929	−1.38416	−0.692080	+	0.721821i	$0.743306\pi$
$410$	−2.21140	−0.109213
$411$	−18.0071	−0.888226
$412$	−33.1857	−1.63494
$413$	−2.75756	−0.135691
$414$	2.23669	0.109928
$415$	−11.4579	−0.562445
$416$	−20.6390	−1.01191
$417$	8.15473	0.399339
$418$	−25.2340	−1.23423
$419$	25.8764	1.26414	0.632072	−	0.774909i	$-0.282205\pi$
$419$	25.8764	1.26414	0.632072	+	0.774909i	$0.282205\pi$
$420$	−5.38840	−0.262927
$421$	−10.9231	−0.532359	−0.266180	−	0.963923i	$-0.585761\pi$
$421$	−10.9231	−0.532359	−0.266180	+	0.963923i	$0.585761\pi$
$422$	34.8866	1.69825
$423$	−2.60698	−0.126756
$424$	−27.2838	−1.32502
$425$	−2.40486	−0.116653
$426$	−14.3683	−0.696148
$427$	−11.7535	−0.568791
$428$	−45.6795	−2.20800
$429$	−4.00989	−0.193599
$430$	23.4658	1.13162
$431$	−27.4514	−1.32229	−0.661144	−	0.750259i	$-0.729929\pi$
$431$	−27.4514	−1.32229	−0.661144	+	0.750259i	$0.729929\pi$
$432$	−0.988785	−0.0475729
$433$	−17.8782	−0.859169	−0.429585	−	0.903027i	$-0.641340\pi$
$433$	−17.8782	−0.859169	−0.429585	+	0.903027i	$0.641340\pi$
$434$	−8.33117	−0.399909
$435$	1.57347	0.0754423
$436$	−43.8233	−2.09876
$437$	8.67005	0.414745
$438$	29.5621	1.41253
$439$	−9.49416	−0.453132	−0.226566	−	0.973996i	$-0.572750\pi$
$439$	−9.49416	−0.453132	−0.226566	+	0.973996i	$0.572750\pi$
$440$	−4.59239	−0.218934
$441$	−5.69939	−0.271399
$442$	6.56676	0.312349
$443$	−3.12331	−0.148393	−0.0741965	−	0.997244i	$-0.523639\pi$
$443$	−3.12331	−0.148393	−0.0741965	+	0.997244i	$0.523639\pi$
$444$	−1.06668	−0.0506225
$445$	−3.68375	−0.174627
$446$	39.8537	1.88713
$447$	16.2814	0.770083
$448$	14.8289	0.700600
$449$	−26.9547	−1.27207	−0.636035	−	0.771660i	$-0.719427\pi$
$449$	−26.9547	−1.27207	−0.636035	+	0.771660i	$0.719427\pi$
$450$	−5.64581	−0.266146
$451$	0.817631	0.0385007
$452$	19.6858	0.925944
$453$	14.1810	0.666280
$454$	23.4035	1.09838
$455$	−5.52978	−0.259240
$456$	19.4466	0.910670
$457$	22.7136	1.06250	0.531249	−	0.847215i	$-0.321723\pi$
$457$	22.7136	1.06250	0.531249	+	0.847215i	$0.321723\pi$
$458$	48.8205	2.28123
$459$	0.952730	0.0444696
$460$	4.72483	0.220296
$461$	−27.9294	−1.30080	−0.650402	−	0.759591i	$-0.725399\pi$
$461$	−27.9294	−1.30080	−0.650402	+	0.759591i	$0.725399\pi$
$462$	3.31923	0.154425
$463$	33.6028	1.56165	0.780827	−	0.624747i	$-0.214798\pi$
$463$	33.6028	1.56165	0.780827	+	0.624747i	$0.214798\pi$
$464$	−0.988785	−0.0459032
$465$	5.13908	0.238319
$466$	−28.9496	−1.34107
$467$	−35.7447	−1.65407	−0.827034	−	0.562152i	$-0.809974\pi$
$467$	−35.7447	−1.65407	−0.827034	+	0.562152i	$0.809974\pi$
$468$	9.25340	0.427739
$469$	17.4619	0.806316
$470$	−9.17497	−0.423210
$471$	3.86239	0.177970
$472$	5.42341	0.249633
$473$	−8.67612	−0.398928
$474$	−25.0448	−1.15035
$475$	−21.8847	−1.00414
$476$	−3.26265	−0.149543
$477$	−12.1642	−0.556960
$478$	−32.7166	−1.49642
$479$	26.3368	1.20336	0.601679	−	0.798738i	$-0.294499\pi$
$479$	26.3368	1.20336	0.601679	+	0.798738i	$0.294499\pi$
$480$	−10.5384	−0.481010
$481$	−1.09467	−0.0499127
$482$	50.8776	2.31741
$483$	−1.14044	−0.0518920
$484$	−27.9464	−1.27029
$485$	−18.5682	−0.843136
$486$	2.23669	0.101459
$487$	5.96952	0.270505	0.135252	−	0.990811i	$-0.456815\pi$
$487$	5.96952	0.270505	0.135252	+	0.990811i	$0.456815\pi$
$488$	23.1161	1.04642
$489$	−1.55619	−0.0703733
$490$	−20.0583	−0.906143
$491$	−41.3497	−1.86608	−0.933042	−	0.359768i	$-0.882856\pi$
$491$	−41.3497	−1.86608	−0.933042	+	0.359768i	$0.882856\pi$
$492$	−1.88680	−0.0850637
$493$	0.952730	0.0429088
$494$	59.7590	2.68868
$495$	−2.04747	−0.0920268
$496$	−3.22944	−0.145006
$497$	7.32611	0.328621
$498$	−16.2874	−0.729855
$499$	7.27760	0.325790	0.162895	−	0.986643i	$-0.447917\pi$
$499$	7.27760	0.325790	0.162895	+	0.986643i	$0.447917\pi$
$500$	−35.5505	−1.58987
$501$	11.7141	0.523346
$502$	56.4588	2.51988
$503$	7.97620	0.355641	0.177821	−	0.984063i	$-0.443095\pi$
$503$	7.97620	0.355641	0.177821	+	0.984063i	$0.443095\pi$
$504$	−2.55797	−0.113941
$505$	16.6471	0.740788
$506$	−2.91048	−0.129386
$507$	−3.50381	−0.155610
$508$	48.1261	2.13525
$509$	25.5873	1.13414	0.567069	−	0.823670i	$-0.308077\pi$
$509$	25.5873	1.13414	0.567069	+	0.823670i	$0.308077\pi$
$510$	3.35302	0.148474
$511$	−15.0731	−0.666794
$512$	11.0580	0.488701
$513$	8.67005	0.382792
$514$	−29.1491	−1.28571
$515$	−17.3894	−0.766267
$516$	20.0214	0.881394
$517$	3.39231	0.149194
$518$	0.906127	0.0398129
$519$	−2.44162	−0.107175
$520$	10.8757	0.476930
$521$	−17.4085	−0.762679	−0.381340	−	0.924435i	$-0.624537\pi$
$521$	−17.4085	−0.762679	−0.381340	+	0.924435i	$0.624537\pi$
$522$	2.23669	0.0978975
$523$	43.2639	1.89180	0.945899	−	0.324460i	$-0.105183\pi$
$523$	43.2639	1.89180	0.945899	+	0.324460i	$0.105183\pi$
$524$	7.96384	0.347902
$525$	2.87868	0.125636
$526$	−2.85953	−0.124682
$527$	3.11169	0.135547
$528$	1.28665	0.0559941
$529$	1.00000	0.0434783
$530$	−42.8104	−1.85957
$531$	2.41797	0.104931
$532$	−29.6908	−1.28726
$533$	−1.93631	−0.0838709
$534$	−5.23645	−0.226604
$535$	−23.9362	−1.03485
$536$	−34.3431	−1.48340
$537$	22.4278	0.967830
$538$	53.8520	2.32172
$539$	7.41627	0.319441
$540$	4.72483	0.203324
$541$	29.9155	1.28617	0.643085	−	0.765795i	$-0.277654\pi$
$541$	29.9155	1.28617	0.643085	+	0.765795i	$0.277654\pi$
$542$	63.4220	2.72421
$543$	−22.1929	−0.952386
$544$	−6.38094	−0.273581
$545$	−22.9635	−0.983649
$546$	−7.86059	−0.336402
$547$	−3.30645	−0.141374	−0.0706868	−	0.997499i	$-0.522519\pi$
$547$	−3.30645	−0.141374	−0.0706868	+	0.997499i	$0.522519\pi$
$548$	−54.0718	−2.30983
$549$	10.3061	0.439852
$550$	7.34656	0.313258
$551$	8.67005	0.369357
$552$	2.24296	0.0954668
$553$	12.7698	0.543028
$554$	11.1355	0.473102
$555$	−0.558944	−0.0237259
$556$	24.4870	1.03848
$557$	−28.1444	−1.19252	−0.596258	−	0.802793i	$-0.703347\pi$
$557$	−28.1444	−1.19252	−0.596258	+	0.802793i	$0.703347\pi$
$558$	7.30521	0.309254
$559$	20.5467	0.869034
$560$	1.77433	0.0749793
$561$	−1.23973	−0.0523414
$562$	−28.7836	−1.21416
$563$	14.6078	0.615646	0.307823	−	0.951444i	$-0.400400\pi$
$563$	14.6078	0.615646	0.307823	+	0.951444i	$0.400400\pi$
$564$	−7.82826	−0.329629
$565$	10.3154	0.433973
$566$	10.4651	0.439880
$567$	−1.14044	−0.0478941
$568$	−14.4086	−0.604571
$569$	−34.4616	−1.44470	−0.722352	−	0.691525i	$-0.756939\pi$
$569$	−34.4616	−1.44470	−0.722352	+	0.691525i	$0.756939\pi$
$570$	30.5132	1.27806
$571$	28.1489	1.17800	0.588998	−	0.808134i	$-0.299523\pi$
$571$	28.1489	1.17800	0.588998	+	0.808134i	$0.299523\pi$
$572$	−12.0409	−0.503455
$573$	−14.7128	−0.614637
$574$	1.60280	0.0668997
$575$	−2.52418	−0.105265
$576$	−13.0028	−0.541782
$577$	6.82193	0.284001	0.142000	−	0.989867i	$-0.454647\pi$
$577$	6.82193	0.284001	0.142000	+	0.989867i	$0.454647\pi$
$578$	−35.9936	−1.49714
$579$	−7.60757	−0.316160
$580$	4.72483	0.196188
$581$	8.30459	0.344533
$582$	−26.3946	−1.09409
$583$	15.8285	0.655550
$584$	29.6449	1.22672
$585$	4.84880	0.200473
$586$	46.3687	1.91548
$587$	25.6256	1.05768	0.528842	−	0.848721i	$-0.322627\pi$
$587$	25.6256	1.05768	0.528842	+	0.848721i	$0.322627\pi$
$588$	−17.1141	−0.705775
$589$	28.3170	1.16678
$590$	8.50976	0.350341
$591$	1.23151	0.0506575
$592$	0.351245	0.0144361
$593$	−24.3247	−0.998895	−0.499447	−	0.866344i	$-0.666464\pi$
$593$	−24.3247	−0.998895	−0.499447	+	0.866344i	$0.666464\pi$
$594$	−2.91048	−0.119418
$595$	−1.70963	−0.0700882
$596$	48.8898	2.00260
$597$	−15.5740	−0.637401
$598$	6.89257	0.281858
$599$	38.0266	1.55372	0.776861	−	0.629672i	$-0.216811\pi$
$599$	38.0266	1.55372	0.776861	+	0.629672i	$0.216811\pi$
$600$	−5.66163	−0.231135
$601$	12.5901	0.513560	0.256780	−	0.966470i	$-0.417338\pi$
$601$	12.5901	0.513560	0.256780	+	0.966470i	$0.417338\pi$
$602$	−17.0078	−0.693187
$603$	−15.3115	−0.623533
$604$	42.5826	1.73266
$605$	−14.6440	−0.595362
$606$	23.6639	0.961280
$607$	37.7974	1.53415	0.767074	−	0.641559i	$-0.221712\pi$
$607$	37.7974	1.53415	0.767074	+	0.641559i	$0.221712\pi$
$608$	−58.0680	−2.35497
$609$	−1.14044	−0.0462131
$610$	36.2710	1.46857
$611$	−8.03365	−0.325007
$612$	2.86086	0.115643
$613$	−2.26295	−0.0913997	−0.0456999	−	0.998955i	$-0.514552\pi$
$613$	−2.26295	−0.0913997	−0.0456999	+	0.998955i	$0.514552\pi$
$614$	16.0704	0.648548
$615$	−0.988689	−0.0398678
$616$	3.32853	0.134110
$617$	39.4885	1.58975	0.794873	−	0.606776i	$-0.207537\pi$
$617$	39.4885	1.58975	0.794873	+	0.606776i	$0.207537\pi$
$618$	−24.7190	−0.994344
$619$	−7.03540	−0.282777	−0.141388	−	0.989954i	$-0.545157\pi$
$619$	−7.03540	−0.282777	−0.141388	+	0.989954i	$0.545157\pi$
$620$	15.4316	0.619750
$621$	1.00000	0.0401286
$622$	−38.1791	−1.53084
$623$	2.66996	0.106970
$624$	−3.04703	−0.121979
$625$	−6.00764	−0.240306
$626$	−38.6788	−1.54592
$627$	−11.2818	−0.450552
$628$	11.5980	0.462811
$629$	−0.338438	−0.0134944
$630$	−4.01366	−0.159908
$631$	−20.8932	−0.831744	−0.415872	−	0.909423i	$-0.636524\pi$
$631$	−20.8932	−0.831744	−0.415872	+	0.909423i	$0.636524\pi$
$632$	−25.1150	−0.999021
$633$	15.5974	0.619940
$634$	−46.8077	−1.85897
$635$	25.2182	1.00075
$636$	−36.5266	−1.44838
$637$	−17.5632	−0.695878
$638$	−2.91048	−0.115227
$639$	−6.42392	−0.254126
$640$	−24.6849	−0.975756
$641$	0.865058	0.0341677	0.0170839	−	0.999854i	$-0.494562\pi$
$641$	0.865058	0.0341677	0.0170839	+	0.999854i	$0.494562\pi$
$642$	−34.0252	−1.34287
$643$	10.6972	0.421858	0.210929	−	0.977501i	$-0.432351\pi$
$643$	10.6972	0.421858	0.210929	+	0.977501i	$0.432351\pi$
$644$	−3.42453	−0.134945
$645$	10.4913	0.413093
$646$	18.4756	0.726912
$647$	−32.6235	−1.28256	−0.641282	−	0.767305i	$-0.721597\pi$
$647$	−32.6235	−1.28256	−0.641282	+	0.767305i	$0.721597\pi$
$648$	2.24296	0.0881118
$649$	−3.14636	−0.123505
$650$	−17.3981	−0.682409
$651$	−3.72477	−0.145985
$652$	−4.67293	−0.183006
$653$	−43.1255	−1.68763	−0.843815	−	0.536634i	$-0.819696\pi$
$653$	−43.1255	−1.68763	−0.843815	+	0.536634i	$0.819696\pi$
$654$	−32.6426	−1.27643
$655$	4.17307	0.163055
$656$	0.621301	0.0242577
$657$	13.2169	0.515639
$658$	6.64996	0.259242
$659$	28.4086	1.10664	0.553321	−	0.832968i	$-0.313360\pi$
$659$	28.4086	1.10664	0.553321	+	0.832968i	$0.313360\pi$
$660$	−6.14814	−0.239316
$661$	43.9655	1.71006	0.855030	−	0.518579i	$-0.173539\pi$
$661$	43.9655	1.71006	0.855030	+	0.518579i	$0.173539\pi$
$662$	−48.1405	−1.87103
$663$	2.93592	0.114022
$664$	−16.3330	−0.633844
$665$	−15.5581	−0.603315
$666$	−0.794539	−0.0307878
$667$	1.00000	0.0387202
$668$	35.1750	1.36096
$669$	17.8181	0.688889
$670$	−53.8870	−2.08184
$671$	−13.4107	−0.517713
$672$	7.63816	0.294648
$673$	30.7401	1.18494	0.592472	−	0.805591i	$-0.298152\pi$
$673$	30.7401	1.18494	0.592472	+	0.805591i	$0.298152\pi$
$674$	8.36842	0.322340
$675$	−2.52418	−0.0971556
$676$	−10.5213	−0.404664
$677$	−38.2858	−1.47144	−0.735722	−	0.677284i	$-0.763157\pi$
$677$	−38.2858	−1.47144	−0.735722	+	0.677284i	$0.763157\pi$
$678$	14.6634	0.563144
$679$	13.4581	0.516473
$680$	3.36242	0.128943
$681$	10.4634	0.400959
$682$	−9.50582	−0.363997
$683$	45.1031	1.72582	0.862912	−	0.505354i	$-0.168638\pi$
$683$	45.1031	1.72582	0.862912	+	0.505354i	$0.168638\pi$
$684$	26.0344	0.995452
$685$	−28.3338	−1.08258
$686$	32.3939	1.23680
$687$	21.8271	0.832755
$688$	−6.59280	−0.251348
$689$	−37.4850	−1.42807
$690$	3.51938	0.133981
$691$	17.1384	0.651976	0.325988	−	0.945374i	$-0.394303\pi$
$691$	17.1384	0.651976	0.325988	+	0.945374i	$0.394303\pi$
$692$	−7.33169	−0.278709
$693$	1.48399	0.0563721
$694$	29.1975	1.10832
$695$	12.8313	0.486718
$696$	2.24296	0.0850192
$697$	−0.598646	−0.0226753
$698$	−30.0062	−1.13575
$699$	−12.9430	−0.489551
$700$	8.64411	0.326717
$701$	−24.2631	−0.916404	−0.458202	−	0.888848i	$-0.651506\pi$
$701$	−24.2631	−0.916404	−0.458202	+	0.888848i	$0.651506\pi$
$702$	6.89257	0.260143
$703$	−3.07986	−0.116159
$704$	16.9197	0.637686
$705$	−4.10202	−0.154491
$706$	15.3538	0.577848
$707$	−12.0657	−0.453778
$708$	7.26069	0.272873
$709$	8.99755	0.337910	0.168955	−	0.985624i	$-0.445961\pi$
$709$	8.99755	0.337910	0.168955	+	0.985624i	$0.445961\pi$
$710$	−22.6082	−0.848471
$711$	−11.1972	−0.419929
$712$	−5.25113	−0.196794
$713$	3.26607	0.122315
$714$	−2.43025	−0.0909497
$715$	−6.30945	−0.235960
$716$	67.3461	2.51684
$717$	−14.6272	−0.546263
$718$	−51.3636	−1.91687
$719$	19.9934	0.745627	0.372813	−	0.927906i	$-0.378393\pi$
$719$	19.9934	0.745627	0.372813	+	0.927906i	$0.378393\pi$
$720$	−1.55583	−0.0579823
$721$	12.6037	0.469386
$722$	125.635	4.67564
$723$	22.7468	0.845962
$724$	−66.6407	−2.47668
$725$	−2.52418	−0.0937456
$726$	−20.8164	−0.772570
$727$	−3.76420	−0.139606	−0.0698032	−	0.997561i	$-0.522237\pi$
$727$	−3.76420	−0.139606	−0.0698032	+	0.997561i	$0.522237\pi$
$728$	−7.88261	−0.292149
$729$	1.00000	0.0370370
$730$	46.5152	1.72161
$731$	6.35240	0.234952
$732$	30.9471	1.14384
$733$	−25.7160	−0.949842	−0.474921	−	0.880028i	$-0.657523\pi$
$733$	−25.7160	−0.949842	−0.474921	+	0.880028i	$0.657523\pi$
$734$	−2.63878	−0.0973993
$735$	−8.96784	−0.330784
$736$	−6.69753	−0.246874
$737$	19.9239	0.733908
$738$	−1.40542	−0.0517343
$739$	−13.9417	−0.512854	−0.256427	−	0.966564i	$-0.582545\pi$
$739$	−13.9417	−0.512854	−0.256427	+	0.966564i	$0.582545\pi$
$740$	−1.67840	−0.0616992
$741$	26.7175	0.981493
$742$	31.0287	1.13910
$743$	−34.4984	−1.26562	−0.632811	−	0.774306i	$-0.718099\pi$
$743$	−34.4984	−1.26562	−0.632811	+	0.774306i	$0.718099\pi$
$744$	7.32567	0.268572
$745$	25.6183	0.938584
$746$	45.3669	1.66100
$747$	−7.28190	−0.266431
$748$	−3.72266	−0.136114
$749$	17.3488	0.633910
$750$	−26.4805	−0.966930
$751$	−22.4970	−0.820929	−0.410464	−	0.911877i	$-0.634633\pi$
$751$	−22.4970	−0.820929	−0.410464	+	0.911877i	$0.634633\pi$
$752$	2.57775	0.0940007
$753$	25.2420	0.919871
$754$	6.89257	0.251013
$755$	22.3134	0.812068
$756$	−3.42453	−0.124549
$757$	37.5685	1.36545	0.682724	−	0.730676i	$-0.260795\pi$
$757$	37.5685	1.36545	0.682724	+	0.730676i	$0.260795\pi$
$758$	40.4133	1.46788
$759$	−1.30124	−0.0472320
$760$	30.5987	1.10993
$761$	−25.9101	−0.939241	−0.469621	−	0.882868i	$-0.655609\pi$
$761$	−25.9101	−0.939241	−0.469621	+	0.882868i	$0.655609\pi$
$762$	35.8476	1.29862
$763$	16.6438	0.602546
$764$	−44.1797	−1.59837
$765$	1.49910	0.0542000
$766$	−13.1772	−0.476112
$767$	7.45119	0.269047
$768$	−9.08405	−0.327793
$769$	19.9645	0.719939	0.359970	−	0.932964i	$-0.382787\pi$
$769$	19.9645	0.719939	0.359970	+	0.932964i	$0.382787\pi$
$770$	5.22273	0.188214
$771$	−13.0322	−0.469345
$772$	−22.8440	−0.822174
$773$	−20.3926	−0.733469	−0.366735	−	0.930326i	$-0.619524\pi$
$773$	−20.3926	−0.733469	−0.366735	+	0.930326i	$0.619524\pi$
$774$	14.9133	0.536049
$775$	−8.24415	−0.296138
$776$	−26.4686	−0.950167
$777$	0.405119	0.0145336
$778$	74.1192	2.65730
$779$	−5.44781	−0.195188
$780$	14.5600	0.521331
$781$	8.35906	0.299111
$782$	2.13097	0.0762032
$783$	1.00000	0.0357371
$784$	5.63547	0.201267
$785$	6.07738	0.216911
$786$	5.93202	0.211588
$787$	16.1358	0.575180	0.287590	−	0.957754i	$-0.407146\pi$
$787$	16.1358	0.575180	0.287590	+	0.957754i	$0.407146\pi$
$788$	3.69797	0.131735
$789$	−1.27846	−0.0455145
$790$	−39.4074	−1.40205
$791$	−7.47655	−0.265835
$792$	−2.91863	−0.103709
$793$	31.7591	1.12780
$794$	−75.6104	−2.68331
$795$	−19.1400	−0.678827
$796$	−46.7656	−1.65756
$797$	−14.0400	−0.497323	−0.248661	−	0.968590i	$-0.579991\pi$
$797$	−14.0400	−0.497323	−0.248661	+	0.968590i	$0.579991\pi$
$798$	−22.1158	−0.782890
$799$	−2.48375	−0.0878688
$800$	16.9058	0.597709
$801$	−2.34116	−0.0827207
$802$	−9.08492	−0.320800
$803$	−17.1983	−0.606915
$804$	−45.9774	−1.62150
$805$	−1.79446	−0.0632464
$806$	22.5116	0.792939
$807$	24.0766	0.847536
$808$	23.7302	0.834826
$809$	−15.8028	−0.555596	−0.277798	−	0.960640i	$-0.589605\pi$
$809$	−15.8028	−0.555596	−0.277798	+	0.960640i	$0.589605\pi$
$810$	3.51938	0.123658
$811$	40.9044	1.43635	0.718175	−	0.695863i	$-0.244978\pi$
$811$	40.9044	1.43635	0.718175	+	0.695863i	$0.244978\pi$
$812$	−3.42453	−0.120177
$813$	28.3552	0.994462
$814$	1.03389	0.0362377
$815$	−2.44863	−0.0857716
$816$	−0.942045	−0.0329782
$817$	57.8083	2.02245
$818$	−62.6116	−2.18916
$819$	−3.51438	−0.122802
$820$	−2.96884	−0.103676
$821$	8.42661	0.294091	0.147045	−	0.989130i	$-0.453024\pi$
$821$	8.42661	0.294091	0.147045	+	0.989130i	$0.453024\pi$
$822$	−40.2764	−1.40480
$823$	−23.8716	−0.832112	−0.416056	−	0.909339i	$-0.636588\pi$
$823$	−23.8716	−0.832112	−0.416056	+	0.909339i	$0.636588\pi$
$824$	−24.7883	−0.863540
$825$	3.28456	0.114354
$826$	−6.16782	−0.214606
$827$	−32.4400	−1.12805	−0.564024	−	0.825758i	$-0.690747\pi$
$827$	−32.4400	−1.12805	−0.564024	+	0.825758i	$0.690747\pi$
$828$	3.00280	0.104355
$829$	53.2876	1.85075	0.925377	−	0.379047i	$-0.123748\pi$
$829$	53.2876	1.85075	0.925377	+	0.379047i	$0.123748\pi$
$830$	−25.6278	−0.889553
$831$	4.97856	0.172704
$832$	−40.0692	−1.38915
$833$	−5.42998	−0.188138
$834$	18.2396	0.631587
$835$	18.4318	0.637859
$836$	−33.8771	−1.17166
$837$	3.26607	0.112892
$838$	57.8776	1.99935
$839$	22.2893	0.769511	0.384756	−	0.923018i	$-0.374286\pi$
$839$	22.2893	0.769511	0.384756	+	0.923018i	$0.374286\pi$
$840$	−4.02490	−0.138872
$841$	1.00000	0.0344828
$842$	−24.4316	−0.841970
$843$	−12.8688	−0.443225
$844$	46.8358	1.61216
$845$	−5.51316	−0.189658
$846$	−5.83103	−0.200475
$847$	10.6138	0.364696
$848$	12.0278	0.413035
$849$	4.67882	0.160577
$850$	−5.37894	−0.184496
$851$	−0.355229	−0.0121771
$852$	−19.2898	−0.660856
$853$	−27.8308	−0.952908	−0.476454	−	0.879199i	$-0.658078\pi$
$853$	−27.8308	−0.952908	−0.476454	+	0.879199i	$0.658078\pi$
$854$	−26.2890	−0.899590
$855$	13.6421	0.466550
$856$	−34.1206	−1.16622
$857$	−19.6332	−0.670656	−0.335328	−	0.942101i	$-0.608847\pi$
$857$	−19.6332	−0.670656	−0.335328	+	0.942101i	$0.608847\pi$
$858$	−8.96889	−0.306193
$859$	1.46200	0.0498826	0.0249413	−	0.999689i	$-0.492060\pi$
$859$	1.46200	0.0498826	0.0249413	+	0.999689i	$0.492060\pi$
$860$	31.5032	1.07425
$861$	0.716595	0.0244215
$862$	−61.4004	−2.09131
$863$	26.6467	0.907063	0.453531	−	0.891240i	$-0.350164\pi$
$863$	26.6467	0.907063	0.453531	+	0.891240i	$0.350164\pi$
$864$	−6.69753	−0.227855
$865$	−3.84182	−0.130626
$866$	−39.9880	−1.35885
$867$	−16.0923	−0.546523
$868$	−11.1847	−0.379635
$869$	14.5703	0.494264
$870$	3.51938	0.119318
$871$	−47.1837	−1.59876
$872$	−32.7341	−1.10852
$873$	−11.8007	−0.399394
$874$	19.3923	0.655953
$875$	13.5018	0.456445
$876$	39.6876	1.34092
$877$	31.4952	1.06352	0.531759	−	0.846896i	$-0.321531\pi$
$877$	31.4952	1.06352	0.531759	+	0.846896i	$0.321531\pi$
$878$	−21.2355	−0.716665
$879$	20.7309	0.699237
$880$	2.02451	0.0682461
$881$	7.13909	0.240522	0.120261	−	0.992742i	$-0.461627\pi$
$881$	7.13909	0.240522	0.120261	+	0.992742i	$0.461627\pi$
$882$	−12.7478	−0.429240
$883$	−1.35272	−0.0455225	−0.0227613	−	0.999741i	$-0.507246\pi$
$883$	−1.35272	−0.0455225	−0.0227613	+	0.999741i	$0.507246\pi$
$884$	8.81599	0.296514
$885$	3.80462	0.127891
$886$	−6.98589	−0.234696
$887$	−1.45689	−0.0489175	−0.0244588	−	0.999701i	$-0.507786\pi$
$887$	−1.45689	−0.0489175	−0.0244588	+	0.999701i	$0.507786\pi$
$888$	−0.796766	−0.0267377
$889$	−18.2780	−0.613023
$890$	−8.23943	−0.276186
$891$	−1.30124	−0.0435932
$892$	53.5043	1.79146
$893$	−22.6027	−0.756370
$894$	36.4165	1.21795
$895$	35.2895	1.17960
$896$	17.8914	0.597711
$897$	3.08159	0.102891
$898$	−60.2894	−2.01188
$899$	3.26607	0.108930
$900$	−7.57960	−0.252653
$901$	−11.5892	−0.386092
$902$	1.82879	0.0608921
$903$	−7.60400	−0.253045
$904$	14.7045	0.489063
$905$	−34.9199	−1.16078
$906$	31.7185	1.05378
$907$	35.3343	1.17326	0.586628	−	0.809857i	$-0.300455\pi$
$907$	35.3343	1.17326	0.586628	+	0.809857i	$0.300455\pi$
$908$	31.4196	1.04270
$909$	10.5799	0.350912
$910$	−12.3684	−0.410010
$911$	−5.39393	−0.178709	−0.0893545	−	0.996000i	$-0.528480\pi$
$911$	−5.39393	−0.178709	−0.0893545	+	0.996000i	$0.528480\pi$
$912$	−8.57282	−0.283874
$913$	9.47550	0.313593
$914$	50.8035	1.68043
$915$	16.2163	0.536096
$916$	65.5424	2.16558
$917$	−3.02461	−0.0998815
$918$	2.13097	0.0703324
$919$	45.9900	1.51707	0.758535	−	0.651633i	$-0.225916\pi$
$919$	45.9900	1.51707	0.758535	+	0.651633i	$0.225916\pi$
$920$	3.52924	0.116356
$921$	7.18488	0.236750
$922$	−62.4696	−2.05733
$923$	−19.7959	−0.651589
$924$	4.45613	0.146596
$925$	0.896662	0.0294821
$926$	75.1592	2.46988
$927$	−11.0516	−0.362981
$928$	−6.69753	−0.219857
$929$	−0.661920	−0.0217169	−0.0108584	−	0.999941i	$-0.503456\pi$
$929$	−0.661920	−0.0217169	−0.0108584	+	0.999941i	$0.503456\pi$
$930$	11.4946	0.376921
$931$	−49.4140	−1.61948
$932$	−38.8654	−1.27308
$933$	−17.0694	−0.558828
$934$	−79.9500	−2.61604
$935$	−1.95068	−0.0637942
$936$	6.91188	0.225922
$937$	−23.8325	−0.778572	−0.389286	−	0.921117i	$-0.627278\pi$
$937$	−23.8325	−0.778572	−0.389286	+	0.921117i	$0.627278\pi$
$938$	39.0569	1.27525
$939$	−17.2928	−0.564331
$940$	−12.3176	−0.401755
$941$	34.9866	1.14053	0.570265	−	0.821461i	$-0.306841\pi$
$941$	34.9866	1.14053	0.570265	+	0.821461i	$0.306841\pi$
$942$	8.63900	0.281474
$943$	−0.628348	−0.0204618
$944$	−2.39085	−0.0778156
$945$	−1.79446	−0.0583738
$946$	−19.4058	−0.630938
$947$	−7.97469	−0.259143	−0.129571	−	0.991570i	$-0.541360\pi$
$947$	−7.97469	−0.259143	−0.129571	+	0.991570i	$0.541360\pi$
$948$	−33.6231	−1.09203
$949$	40.7290	1.32212
$950$	−48.9495	−1.58813
$951$	−20.9272	−0.678611
$952$	−2.43706	−0.0789854
$953$	−43.5349	−1.41023	−0.705116	−	0.709092i	$-0.749105\pi$
$953$	−43.5349	−1.41023	−0.705116	+	0.709092i	$0.749105\pi$
$954$	−27.2076	−0.880878
$955$	−23.1503	−0.749125
$956$	−43.9226	−1.42056
$957$	−1.30124	−0.0420631
$958$	58.9073	1.90321
$959$	20.5361	0.663146
$960$	−20.4595	−0.660328
$961$	−20.3328	−0.655896
$962$	−2.44844	−0.0789410
$963$	−15.2123	−0.490209
$964$	68.3041	2.19993
$965$	−11.9703	−0.385338
$966$	−2.55082	−0.0820714
$967$	−40.8214	−1.31273	−0.656364	−	0.754444i	$-0.727906\pi$
$967$	−40.8214	−1.31273	−0.656364	+	0.754444i	$0.727906\pi$
$968$	−20.8747	−0.670939
$969$	8.26022	0.265356
$970$	−41.5313	−1.33349
$971$	−52.6494	−1.68960	−0.844799	−	0.535083i	$-0.820280\pi$
$971$	−52.6494	−1.68960	−0.844799	+	0.535083i	$0.820280\pi$
$972$	3.00280	0.0963149
$973$	−9.30001	−0.298145
$974$	13.3520	0.427826
$975$	−7.77848	−0.249111
$976$	−10.1905	−0.326189
$977$	32.1539	1.02869	0.514347	−	0.857582i	$-0.328034\pi$
$977$	32.1539	1.02869	0.514347	+	0.857582i	$0.328034\pi$
$978$	−3.48072	−0.111301
$979$	3.04641	0.0973636
$980$	−26.9287	−0.860205
$981$	−14.5941	−0.465955
$982$	−92.4865	−2.95136
$983$	29.2726	0.933651	0.466826	−	0.884349i	$-0.345398\pi$
$983$	29.2726	0.933651	0.466826	+	0.884349i	$0.345398\pi$
$984$	−1.40936	−0.0449287
$985$	1.93775	0.0617417
$986$	2.13097	0.0678638
$987$	2.97312	0.0946354
$988$	80.2275	2.55238
$989$	6.66758	0.212017
$990$	−4.57956	−0.145548
$991$	23.4314	0.744323	0.372162	−	0.928168i	$-0.378617\pi$
$991$	23.4314	0.744323	0.372162	+	0.928168i	$0.378617\pi$
$992$	−21.8746	−0.694520
$993$	−21.5231	−0.683013
$994$	16.3863	0.519741
$995$	−24.5053	−0.776870
$996$	−21.8661	−0.692854
$997$	28.5685	0.904773	0.452386	−	0.891822i	$-0.350573\pi$
$997$	28.5685	0.904773	0.452386	+	0.891822i	$0.350573\pi$
$998$	16.2778	0.515264
$999$	−0.355229	−0.0112390

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2001.2.a.o.1.16	✓	20
3.2	odd	2		6003.2.a.s.1.5		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2001.2.a.o.1.16	✓	20	1.1	even	1	trivial
6003.2.a.s.1.5		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)

\(f(q)\)	\(=\)	\(q+2.23669 q^{2} +1.00000 q^{3} +3.00280 q^{4} +1.57347 q^{5} +2.23669 q^{6} -1.14044 q^{7} +2.24296 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+2.23669 q^{2} +1.00000 q^{3} +3.00280 q^{4} +1.57347 q^{5} +2.23669 q^{6} -1.14044 q^{7} +2.24296 q^{8} +1.00000 q^{9} +3.51938 q^{10} -1.30124 q^{11} +3.00280 q^{12} +3.08159 q^{13} -2.55082 q^{14} +1.57347 q^{15} -0.988785 q^{16} +0.952730 q^{17} +2.23669 q^{18} +8.67005 q^{19} +4.72483 q^{20} -1.14044 q^{21} -2.91048 q^{22} +1.00000 q^{23} +2.24296 q^{24} -2.52418 q^{25} +6.89257 q^{26} +1.00000 q^{27} -3.42453 q^{28} +1.00000 q^{29} +3.51938 q^{30} +3.26607 q^{31} -6.69753 q^{32} -1.30124 q^{33} +2.13097 q^{34} -1.79446 q^{35} +3.00280 q^{36} -0.355229 q^{37} +19.3923 q^{38} +3.08159 q^{39} +3.52924 q^{40} -0.628348 q^{41} -2.55082 q^{42} +6.66758 q^{43} -3.90736 q^{44} +1.57347 q^{45} +2.23669 q^{46} -2.60698 q^{47} -0.988785 q^{48} -5.69939 q^{49} -5.64581 q^{50} +0.952730 q^{51} +9.25340 q^{52} -12.1642 q^{53} +2.23669 q^{54} -2.04747 q^{55} -2.55797 q^{56} +8.67005 q^{57} +2.23669 q^{58} +2.41797 q^{59} +4.72483 q^{60} +10.3061 q^{61} +7.30521 q^{62} -1.14044 q^{63} -13.0028 q^{64} +4.84880 q^{65} -2.91048 q^{66} -15.3115 q^{67} +2.86086 q^{68} +1.00000 q^{69} -4.01366 q^{70} -6.42392 q^{71} +2.24296 q^{72} +13.2169 q^{73} -0.794539 q^{74} -2.52418 q^{75} +26.0344 q^{76} +1.48399 q^{77} +6.89257 q^{78} -11.1972 q^{79} -1.55583 q^{80} +1.00000 q^{81} -1.40542 q^{82} -7.28190 q^{83} -3.42453 q^{84} +1.49910 q^{85} +14.9133 q^{86} +1.00000 q^{87} -2.91863 q^{88} -2.34116 q^{89} +3.51938 q^{90} -3.51438 q^{91} +3.00280 q^{92} +3.26607 q^{93} -5.83103 q^{94} +13.6421 q^{95} -6.69753 q^{96} -11.8007 q^{97} -12.7478 q^{98} -1.30124 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 2 q^{2} + 20 q^{3} + 30 q^{4} - q^{5} + 2 q^{6} + 9 q^{7} + 6 q^{8} + 20 q^{9}+O(q^{10}) \) 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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