LMFDB - Embedded newform 2001.2.a.o.1.9

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			1.9
Root			$-0.302778$ of defining polynomial
Character	$\chi$	$=$	2001.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.302778 q^{2} +1.00000 q^{3} -1.90833 q^{4} +3.34986 q^{5} -0.302778 q^{6} +0.428154 q^{7} +1.18336 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-0.302778 q^{2} +1.00000 q^{3} -1.90833 q^{4} +3.34986 q^{5} -0.302778 q^{6} +0.428154 q^{7} +1.18336 q^{8} +1.00000 q^{9} -1.01426 q^{10} +4.01497 q^{11} -1.90833 q^{12} +5.31187 q^{13} -0.129636 q^{14} +3.34986 q^{15} +3.45836 q^{16} +1.05018 q^{17} -0.302778 q^{18} -3.12533 q^{19} -6.39262 q^{20} +0.428154 q^{21} -1.21565 q^{22} +1.00000 q^{23} +1.18336 q^{24} +6.22156 q^{25} -1.60832 q^{26} +1.00000 q^{27} -0.817056 q^{28} +1.00000 q^{29} -1.01426 q^{30} -10.3617 q^{31} -3.41383 q^{32} +4.01497 q^{33} -0.317973 q^{34} +1.43425 q^{35} -1.90833 q^{36} -10.3543 q^{37} +0.946281 q^{38} +5.31187 q^{39} +3.96408 q^{40} +7.14375 q^{41} -0.129636 q^{42} +3.22443 q^{43} -7.66187 q^{44} +3.34986 q^{45} -0.302778 q^{46} +10.8487 q^{47} +3.45836 q^{48} -6.81668 q^{49} -1.88375 q^{50} +1.05018 q^{51} -10.1368 q^{52} -9.70877 q^{53} -0.302778 q^{54} +13.4496 q^{55} +0.506658 q^{56} -3.12533 q^{57} -0.302778 q^{58} -4.68976 q^{59} -6.39262 q^{60} -4.20131 q^{61} +3.13730 q^{62} +0.428154 q^{63} -5.88308 q^{64} +17.7940 q^{65} -1.21565 q^{66} -3.89854 q^{67} -2.00409 q^{68} +1.00000 q^{69} -0.434261 q^{70} +13.7035 q^{71} +1.18336 q^{72} +8.38069 q^{73} +3.13506 q^{74} +6.22156 q^{75} +5.96414 q^{76} +1.71902 q^{77} -1.60832 q^{78} +8.80707 q^{79} +11.5850 q^{80} +1.00000 q^{81} -2.16297 q^{82} +7.18985 q^{83} -0.817056 q^{84} +3.51797 q^{85} -0.976287 q^{86} +1.00000 q^{87} +4.75114 q^{88} -10.2900 q^{89} -1.01426 q^{90} +2.27430 q^{91} -1.90833 q^{92} -10.3617 q^{93} -3.28475 q^{94} -10.4694 q^{95} -3.41383 q^{96} -3.31072 q^{97} +2.06394 q^{98} +4.01497 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−0.302778	−0.214097	−0.107048	−	0.994254i	$-0.534140\pi$
$2$	−0.302778	−0.214097	−0.107048	+	0.994254i	$0.534140\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	−1.90833	−0.954163
$5$	3.34986	1.49810	0.749051	−	0.662512i	$-0.230510\pi$
$5$	3.34986	1.49810	0.749051	+	0.662512i	$0.230510\pi$
$6$	−0.302778	−0.123609
$7$	0.428154	0.161827	0.0809134	−	0.996721i	$-0.474216\pi$
$7$	0.428154	0.161827	0.0809134	+	0.996721i	$0.474216\pi$
$8$	1.18336	0.418379
$9$	1.00000	0.333333
$10$	−1.01426	−0.320739
$11$	4.01497	1.21056	0.605279	−	0.796013i	$-0.293061\pi$
$11$	4.01497	1.21056	0.605279	+	0.796013i	$0.293061\pi$
$12$	−1.90833	−0.550886
$13$	5.31187	1.47325	0.736624	−	0.676302i	$-0.236419\pi$
$13$	5.31187	1.47325	0.736624	+	0.676302i	$0.236419\pi$
$14$	−0.129636	−0.0346466
$15$	3.34986	0.864930
$16$	3.45836	0.864589
$17$	1.05018	0.254707	0.127354	−	0.991857i	$-0.459352\pi$
$17$	1.05018	0.254707	0.127354	+	0.991857i	$0.459352\pi$
$18$	−0.302778	−0.0713655
$19$	−3.12533	−0.717000	−0.358500	−	0.933530i	$-0.616712\pi$
$19$	−3.12533	−0.717000	−0.358500	+	0.933530i	$0.616712\pi$
$20$	−6.39262	−1.42943
$21$	0.428154	0.0934308
$22$	−1.21565	−0.259176
$23$	1.00000	0.208514
$23$	1.00000	0.208514
$24$	1.18336	0.241552
$25$	6.22156	1.24431
$26$	−1.60832	−0.315418
$27$	1.00000	0.192450
$28$	−0.817056	−0.154409
$29$	1.00000	0.185695
$29$	1.00000	0.185695
$30$	−1.01426	−0.185179
$31$	−10.3617	−1.86102	−0.930508	−	0.366271i	$-0.880634\pi$
$31$	−10.3617	−1.86102	−0.930508	+	0.366271i	$0.880634\pi$
$32$	−3.41383	−0.603485
$33$	4.01497	0.698916
$34$	−0.317973	−0.0545319
$35$	1.43425	0.242433
$36$	−1.90833	−0.318054
$37$	−10.3543	−1.70224	−0.851119	−	0.524972i	$-0.824076\pi$
$37$	−10.3543	−1.70224	−0.851119	+	0.524972i	$0.824076\pi$
$38$	0.946281	0.153507
$39$	5.31187	0.850581
$40$	3.96408	0.626775
$41$	7.14375	1.11567	0.557833	−	0.829953i	$-0.311633\pi$
$41$	7.14375	1.11567	0.557833	+	0.829953i	$0.311633\pi$
$42$	−0.129636	−0.0200032
$43$	3.22443	0.491721	0.245861	−	0.969305i	$-0.420929\pi$
$43$	3.22443	0.491721	0.245861	+	0.969305i	$0.420929\pi$
$44$	−7.66187	−1.15507
$45$	3.34986	0.499368
$46$	−0.302778	−0.0446422
$47$	10.8487	1.58244	0.791222	−	0.611529i	$-0.209445\pi$
$47$	10.8487	1.58244	0.791222	+	0.611529i	$0.209445\pi$
$48$	3.45836	0.499171
$49$	−6.81668	−0.973812
$50$	−1.88375	−0.266403
$51$	1.05018	0.147055
$52$	−10.1368	−1.40572
$53$	−9.70877	−1.33360	−0.666801	−	0.745236i	$-0.732337\pi$
$53$	−9.70877	−1.33360	−0.666801	+	0.745236i	$0.732337\pi$
$54$	−0.302778	−0.0412029
$55$	13.4496	1.81354
$56$	0.506658	0.0677050
$57$	−3.12533	−0.413960
$58$	−0.302778	−0.0397567
$59$	−4.68976	−0.610555	−0.305277	−	0.952263i	$-0.598749\pi$
$59$	−4.68976	−0.610555	−0.305277	+	0.952263i	$0.598749\pi$
$60$	−6.39262	−0.825284
$61$	−4.20131	−0.537923	−0.268962	−	0.963151i	$-0.586680\pi$
$61$	−4.20131	−0.537923	−0.268962	+	0.963151i	$0.586680\pi$
$62$	3.13730	0.398437
$63$	0.428154	0.0539423
$64$	−5.88308	−0.735385
$65$	17.7940	2.20708
$66$	−1.21565	−0.149636
$67$	−3.89854	−0.476283	−0.238141	−	0.971231i	$-0.576538\pi$
$67$	−3.89854	−0.476283	−0.238141	+	0.971231i	$0.576538\pi$
$68$	−2.00409	−0.243032
$69$	1.00000	0.120386
$70$	−0.434261	−0.0519041
$71$	13.7035	1.62630	0.813152	−	0.582052i	$-0.197750\pi$
$71$	13.7035	1.62630	0.813152	+	0.582052i	$0.197750\pi$
$72$	1.18336	0.139460
$73$	8.38069	0.980886	0.490443	−	0.871473i	$-0.336835\pi$
$73$	8.38069	0.980886	0.490443	+	0.871473i	$0.336835\pi$
$74$	3.13506	0.364443
$75$	6.22156	0.718403
$76$	5.96414	0.684134
$77$	1.71902	0.195901
$78$	−1.60832	−0.182106
$79$	8.80707	0.990873	0.495437	−	0.868644i	$-0.335008\pi$
$79$	8.80707	0.990873	0.495437	+	0.868644i	$0.335008\pi$
$80$	11.5850	1.29524
$81$	1.00000	0.111111
$82$	−2.16297	−0.238860
$83$	7.18985	0.789189	0.394594	−	0.918855i	$-0.370885\pi$
$83$	7.18985	0.789189	0.394594	+	0.918855i	$0.370885\pi$
$84$	−0.817056	−0.0891482
$85$	3.51797	0.381577
$86$	−0.976287	−0.105276
$87$	1.00000	0.107211
$88$	4.75114	0.506473
$89$	−10.2900	−1.09074	−0.545368	−	0.838197i	$-0.683610\pi$
$89$	−10.2900	−1.09074	−0.545368	+	0.838197i	$0.683610\pi$
$90$	−1.01426	−0.106913
$91$	2.27430	0.238411
$92$	−1.90833	−0.198957
$93$	−10.3617	−1.07446
$94$	−3.28475	−0.338796
$95$	−10.4694	−1.07414
$96$	−3.41383	−0.348422
$97$	−3.31072	−0.336153	−0.168076	−	0.985774i	$-0.553756\pi$
$97$	−3.31072	−0.336153	−0.168076	+	0.985774i	$0.553756\pi$
$98$	2.06394	0.208490
$99$	4.01497	0.403520
$100$	−11.8728	−1.18728
$101$	−4.08415	−0.406388	−0.203194	−	0.979138i	$-0.565132\pi$
$101$	−4.08415	−0.406388	−0.203194	+	0.979138i	$0.565132\pi$
$102$	−0.317973	−0.0314840
$103$	14.4370	1.42252	0.711260	−	0.702929i	$-0.248125\pi$
$103$	14.4370	1.42252	0.711260	+	0.702929i	$0.248125\pi$
$104$	6.28584	0.616377
$105$	1.43425	0.139969
$106$	2.93960	0.285520
$107$	6.88495	0.665593	0.332796	−	0.942999i	$-0.392008\pi$
$107$	6.88495	0.665593	0.332796	+	0.942999i	$0.392008\pi$
$108$	−1.90833	−0.183629
$109$	−15.2270	−1.45848	−0.729240	−	0.684257i	$-0.760126\pi$
$109$	−15.2270	−1.45848	−0.729240	+	0.684257i	$0.760126\pi$
$110$	−4.07224	−0.388273
$111$	−10.3543	−0.982788
$112$	1.48071	0.139914
$113$	−5.66251	−0.532684	−0.266342	−	0.963879i	$-0.585815\pi$
$113$	−5.66251	−0.532684	−0.266342	+	0.963879i	$0.585815\pi$
$114$	0.946281	0.0886274
$115$	3.34986	0.312376
$116$	−1.90833	−0.177184
$117$	5.31187	0.491083
$118$	1.41996	0.130718
$119$	0.449640	0.0412184
$120$	3.96408	0.361869
$121$	5.11998	0.465453
$122$	1.27207	0.115168
$123$	7.14375	0.644130
$124$	19.7735	1.77571
$125$	4.09204	0.366003
$126$	−0.129636	−0.0115489
$127$	6.52259	0.578786	0.289393	−	0.957210i	$-0.406546\pi$
$127$	6.52259	0.578786	0.289393	+	0.957210i	$0.406546\pi$
$128$	8.60892	0.760928
$129$	3.22443	0.283895
$130$	−5.38765	−0.472528
$131$	−5.30306	−0.463331	−0.231665	−	0.972796i	$-0.574417\pi$
$131$	−5.30306	−0.463331	−0.231665	+	0.972796i	$0.574417\pi$
$132$	−7.66187	−0.666880
$133$	−1.33812	−0.116030
$134$	1.18039	0.101970
$135$	3.34986	0.288310
$136$	1.24274	0.106564
$137$	−13.1674	−1.12496	−0.562482	−	0.826810i	$-0.690153\pi$
$137$	−13.1674	−1.12496	−0.562482	+	0.826810i	$0.690153\pi$
$138$	−0.302778	−0.0257742
$139$	−2.28705	−0.193985	−0.0969925	−	0.995285i	$-0.530922\pi$
$139$	−2.28705	−0.193985	−0.0969925	+	0.995285i	$0.530922\pi$
$140$	−2.73702	−0.231321
$141$	10.8487	0.913624
$142$	−4.14911	−0.348186
$143$	21.3270	1.78345
$144$	3.45836	0.288196
$145$	3.34986	0.278191
$146$	−2.53749	−0.210004
$147$	−6.81668	−0.562231
$148$	19.7594	1.62421
$149$	−11.9584	−0.979672	−0.489836	−	0.871815i	$-0.662943\pi$
$149$	−11.9584	−0.979672	−0.489836	+	0.871815i	$0.662943\pi$
$150$	−1.88375	−0.153808
$151$	24.0005	1.95313	0.976567	−	0.215213i	$-0.0690446\pi$
$151$	24.0005	1.95313	0.976567	+	0.215213i	$0.0690446\pi$
$152$	−3.69838	−0.299978
$153$	1.05018	0.0849024
$154$	−0.520483	−0.0419417
$155$	−34.7102	−2.78799
$156$	−10.1368	−0.811592
$157$	2.54328	0.202976	0.101488	−	0.994837i	$-0.467640\pi$
$157$	2.54328	0.202976	0.101488	+	0.994837i	$0.467640\pi$
$158$	−2.66659	−0.212143
$159$	−9.70877	−0.769955
$160$	−11.4358	−0.904082
$161$	0.428154	0.0337432
$162$	−0.302778	−0.0237885
$163$	−20.4369	−1.60074	−0.800372	−	0.599504i	$-0.795365\pi$
$163$	−20.4369	−1.60074	−0.800372	+	0.599504i	$0.795365\pi$
$164$	−13.6326	−1.06453
$165$	13.4496	1.04705
$166$	−2.17693	−0.168963
$167$	12.3398	0.954885	0.477443	−	0.878663i	$-0.341564\pi$
$167$	12.3398	0.954885	0.477443	+	0.878663i	$0.341564\pi$
$168$	0.506658	0.0390895
$169$	15.2160	1.17046
$170$	−1.06516	−0.0816944
$171$	−3.12533	−0.239000
$172$	−6.15326	−0.469182
$173$	−11.3271	−0.861186	−0.430593	−	0.902546i	$-0.641696\pi$
$173$	−11.3271	−0.861186	−0.430593	+	0.902546i	$0.641696\pi$
$174$	−0.302778	−0.0229536
$175$	2.66378	0.201363
$176$	13.8852	1.04664
$177$	−4.68976	−0.352504
$178$	3.11558	0.233523
$179$	12.6720	0.947153	0.473577	−	0.880753i	$-0.342963\pi$
$179$	12.6720	0.947153	0.473577	+	0.880753i	$0.342963\pi$
$180$	−6.39262	−0.476478
$181$	21.2565	1.57998	0.789992	−	0.613117i	$-0.210084\pi$
$181$	21.2565	1.57998	0.789992	+	0.613117i	$0.210084\pi$
$182$	−0.688608	−0.0510430
$183$	−4.20131	−0.310570
$184$	1.18336	0.0872382
$185$	−34.6855	−2.55013
$186$	3.13730	0.230038
$187$	4.21646	0.308338
$188$	−20.7028	−1.50991
$189$	0.428154	0.0311436
$190$	3.16991	0.229969
$191$	−11.9418	−0.864078	−0.432039	−	0.901855i	$-0.642206\pi$
$191$	−11.9418	−0.864078	−0.432039	+	0.901855i	$0.642206\pi$
$192$	−5.88308	−0.424575
$193$	9.05494	0.651789	0.325894	−	0.945406i	$-0.394335\pi$
$193$	9.05494	0.651789	0.325894	+	0.945406i	$0.394335\pi$
$194$	1.00241	0.0719692
$195$	17.7940	1.27426
$196$	13.0085	0.929175
$197$	6.84424	0.487632	0.243816	−	0.969822i	$-0.421601\pi$
$197$	6.84424	0.487632	0.243816	+	0.969822i	$0.421601\pi$
$198$	−1.21565	−0.0863922
$199$	12.4741	0.884269	0.442134	−	0.896949i	$-0.354221\pi$
$199$	12.4741	0.884269	0.442134	+	0.896949i	$0.354221\pi$
$200$	7.36232	0.520594
$201$	−3.89854	−0.274982
$202$	1.23659	0.0870063
$203$	0.428154	0.0300505
$204$	−2.00409	−0.140315
$205$	23.9305	1.67138
$206$	−4.37121	−0.304556
$207$	1.00000	0.0695048
$208$	18.3704	1.27375
$209$	−12.5481	−0.867970
$210$	−0.434261	−0.0299669
$211$	−16.1997	−1.11524	−0.557618	−	0.830098i	$-0.688285\pi$
$211$	−16.1997	−1.11524	−0.557618	+	0.830098i	$0.688285\pi$
$212$	18.5275	1.27247
$213$	13.7035	0.938947
$214$	−2.08461	−0.142501
$215$	10.8014	0.736649
$216$	1.18336	0.0805172
$217$	−4.43640	−0.301162
$218$	4.61040	0.312256
$219$	8.38069	0.566315
$220$	−25.6662	−1.73041
$221$	5.57845	0.375247
$222$	3.13506	0.210412
$223$	−4.70284	−0.314926	−0.157463	−	0.987525i	$-0.550331\pi$
$223$	−4.70284	−0.314926	−0.157463	+	0.987525i	$0.550331\pi$
$224$	−1.46164	−0.0976601
$225$	6.22156	0.414770
$226$	1.71448	0.114046
$227$	−27.4304	−1.82062	−0.910309	−	0.413928i	$-0.864156\pi$
$227$	−27.4304	−1.82062	−0.910309	+	0.413928i	$0.864156\pi$
$228$	5.96414	0.394985
$229$	0.510879	0.0337598	0.0168799	−	0.999858i	$-0.494627\pi$
$229$	0.510879	0.0337598	0.0168799	+	0.999858i	$0.494627\pi$
$230$	−1.01426	−0.0668786
$231$	1.71902	0.113103
$232$	1.18336	0.0776911
$233$	11.3044	0.740577	0.370289	−	0.928917i	$-0.379259\pi$
$233$	11.3044	0.740577	0.370289	+	0.928917i	$0.379259\pi$
$234$	−1.60832	−0.105139
$235$	36.3416	2.37066
$236$	8.94959	0.582569
$237$	8.80707	0.572081
$238$	−0.136141	−0.00882473
$239$	−10.3539	−0.669737	−0.334868	−	0.942265i	$-0.608692\pi$
$239$	−10.3539	−0.669737	−0.334868	+	0.942265i	$0.608692\pi$
$240$	11.5850	0.747809
$241$	−3.01550	−0.194246	−0.0971228	−	0.995272i	$-0.530964\pi$
$241$	−3.01550	−0.194246	−0.0971228	+	0.995272i	$0.530964\pi$
$242$	−1.55022	−0.0996518
$243$	1.00000	0.0641500
$244$	8.01748	0.513266
$245$	−22.8349	−1.45887
$246$	−2.16297	−0.137906
$247$	−16.6014	−1.05632
$248$	−12.2616	−0.778611
$249$	7.18985	0.455638
$250$	−1.23898	−0.0783601
$251$	16.0714	1.01442	0.507208	−	0.861823i	$-0.330677\pi$
$251$	16.0714	1.01442	0.507208	+	0.861823i	$0.330677\pi$
$252$	−0.817056	−0.0514697
$253$	4.01497	0.252419
$254$	−1.97490	−0.123916
$255$	3.51797	0.220304
$256$	9.15957	0.572473
$257$	19.4598	1.21387	0.606935	−	0.794752i	$-0.292399\pi$
$257$	19.4598	1.21387	0.606935	+	0.794752i	$0.292399\pi$
$258$	−0.976287	−0.0607810
$259$	−4.43324	−0.275468
$260$	−33.9568	−2.10591
$261$	1.00000	0.0618984
$262$	1.60565	0.0991975
$263$	28.1751	1.73735	0.868675	−	0.495382i	$-0.164972\pi$
$263$	28.1751	1.73735	0.868675	+	0.495382i	$0.164972\pi$
$264$	4.75114	0.292412
$265$	−32.5230	−1.99787
$266$	0.405154	0.0248416
$267$	−10.2900	−0.629737
$268$	7.43969	0.454451
$269$	−12.0815	−0.736623	−0.368312	−	0.929702i	$-0.620064\pi$
$269$	−12.0815	−0.736623	−0.368312	+	0.929702i	$0.620064\pi$
$270$	−1.01426	−0.0617262
$271$	−29.4534	−1.78917	−0.894583	−	0.446903i	$-0.852527\pi$
$271$	−29.4534	−1.78917	−0.894583	+	0.446903i	$0.852527\pi$
$272$	3.63191	0.220217
$273$	2.27430	0.137647
$274$	3.98679	0.240851
$275$	24.9794	1.50631
$276$	−1.90833	−0.114868
$277$	10.2385	0.615172	0.307586	−	0.951520i	$-0.400479\pi$
$277$	10.2385	0.615172	0.307586	+	0.951520i	$0.400479\pi$
$278$	0.692469	0.0415315
$279$	−10.3617	−0.620339
$280$	1.69723	0.101429
$281$	−16.2447	−0.969077	−0.484538	−	0.874770i	$-0.661012\pi$
$281$	−16.2447	−0.969077	−0.484538	+	0.874770i	$0.661012\pi$
$282$	−3.28475	−0.195604
$283$	18.9453	1.12618	0.563091	−	0.826395i	$-0.309612\pi$
$283$	18.9453	1.12618	0.563091	+	0.826395i	$0.309612\pi$
$284$	−26.1507	−1.55176
$285$	−10.4694	−0.620154
$286$	−6.45736	−0.381831
$287$	3.05862	0.180545
$288$	−3.41383	−0.201162
$289$	−15.8971	−0.935124
$290$	−1.01426	−0.0595597
$291$	−3.31072	−0.194078
$292$	−15.9931	−0.935924
$293$	−12.8758	−0.752213	−0.376106	−	0.926577i	$-0.622737\pi$
$293$	−12.8758	−0.752213	−0.376106	+	0.926577i	$0.622737\pi$
$294$	2.06394	0.120372
$295$	−15.7100	−0.914674
$296$	−12.2528	−0.712182
$297$	4.01497	0.232972
$298$	3.62075	0.209744
$299$	5.31187	0.307194
$300$	−11.8728	−0.685474
$301$	1.38055	0.0795737
$302$	−7.26683	−0.418159
$303$	−4.08415	−0.234628
$304$	−10.8085	−0.619910
$305$	−14.0738	−0.805864
$306$	−0.317973	−0.0181773
$307$	−19.1819	−1.09477	−0.547385	−	0.836881i	$-0.684377\pi$
$307$	−19.1819	−1.09477	−0.547385	+	0.836881i	$0.684377\pi$
$308$	−3.28046	−0.186921
$309$	14.4370	0.821292
$310$	10.5095	0.596900
$311$	−25.1290	−1.42493	−0.712466	−	0.701707i	$-0.752422\pi$
$311$	−25.1290	−1.42493	−0.712466	+	0.701707i	$0.752422\pi$
$312$	6.28584	0.355866
$313$	−1.00877	−0.0570190	−0.0285095	−	0.999594i	$-0.509076\pi$
$313$	−1.00877	−0.0570190	−0.0285095	+	0.999594i	$0.509076\pi$
$314$	−0.770051	−0.0434565
$315$	1.43425	0.0808111
$316$	−16.8068	−0.945454
$317$	−3.08943	−0.173520	−0.0867599	−	0.996229i	$-0.527651\pi$
$317$	−3.08943	−0.173520	−0.0867599	+	0.996229i	$0.527651\pi$
$318$	2.93960	0.164845
$319$	4.01497	0.224795
$320$	−19.7075	−1.10168
$321$	6.88495	0.384280
$322$	−0.129636	−0.00722431
$323$	−3.28217	−0.182625
$324$	−1.90833	−0.106018
$325$	33.0481	1.83318
$326$	6.18786	0.342714
$327$	−15.2270	−0.842054
$328$	8.45359	0.466772
$329$	4.64490	0.256082
$330$	−4.07224	−0.224169
$331$	14.8847	0.818139	0.409069	−	0.912503i	$-0.365853\pi$
$331$	14.8847	0.818139	0.409069	+	0.912503i	$0.365853\pi$
$332$	−13.7206	−0.753015
$333$	−10.3543	−0.567413
$334$	−3.73623	−0.204438
$335$	−13.0596	−0.713520
$336$	1.48071	0.0807792
$337$	23.9721	1.30584	0.652921	−	0.757426i	$-0.273543\pi$
$337$	23.9721	1.30584	0.652921	+	0.757426i	$0.273543\pi$
$338$	−4.60708	−0.250592
$339$	−5.66251	−0.307545
$340$	−6.71343	−0.364087
$341$	−41.6019	−2.25287
$342$	0.946281	0.0511690
$343$	−5.91566	−0.319416
$344$	3.81565	0.205726
$345$	3.34986	0.180350
$346$	3.42961	0.184377
$347$	−29.4423	−1.58055	−0.790273	−	0.612755i	$-0.790061\pi$
$347$	−29.4423	−1.58055	−0.790273	+	0.612755i	$0.790061\pi$
$348$	−1.90833	−0.102297
$349$	−4.84185	−0.259178	−0.129589	−	0.991568i	$-0.541366\pi$
$349$	−4.84185	−0.259178	−0.129589	+	0.991568i	$0.541366\pi$
$350$	−0.806535	−0.0431111
$351$	5.31187	0.283527
$352$	−13.7064	−0.730554
$353$	11.1009	0.590839	0.295420	−	0.955368i	$-0.404541\pi$
$353$	11.1009	0.590839	0.295420	+	0.955368i	$0.404541\pi$
$354$	1.41996	0.0754699
$355$	45.9047	2.43637
$356$	19.6366	1.04074
$357$	0.449640	0.0237975
$358$	−3.83682	−0.202782
$359$	21.0718	1.11213	0.556063	−	0.831140i	$-0.312311\pi$
$359$	21.0718	1.11213	0.556063	+	0.831140i	$0.312311\pi$
$360$	3.96408	0.208925
$361$	−9.23232	−0.485912
$362$	−6.43601	−0.338269
$363$	5.11998	0.268729
$364$	−4.34010	−0.227483
$365$	28.0741	1.46947
$366$	1.27207	0.0664920
$367$	−31.5820	−1.64857	−0.824283	−	0.566178i	$-0.808421\pi$
$367$	−31.5820	−1.64857	−0.824283	+	0.566178i	$0.808421\pi$
$368$	3.45836	0.180279
$369$	7.14375	0.371889
$370$	10.5020	0.545974
$371$	−4.15684	−0.215813
$372$	19.7735	1.02521
$373$	−6.16681	−0.319305	−0.159653	−	0.987173i	$-0.551037\pi$
$373$	−6.16681	−0.319305	−0.159653	+	0.987173i	$0.551037\pi$
$374$	−1.27665	−0.0660141
$375$	4.09204	0.211312
$376$	12.8379	0.662062
$377$	5.31187	0.273575
$378$	−0.129636	−0.00666774
$379$	12.6195	0.648219	0.324109	−	0.946020i	$-0.394935\pi$
$379$	12.6195	0.648219	0.324109	+	0.946020i	$0.394935\pi$
$380$	19.9790	1.02490
$381$	6.52259	0.334163
$382$	3.61572	0.184996
$383$	−5.45898	−0.278941	−0.139470	−	0.990226i	$-0.544540\pi$
$383$	−5.45898	−0.278941	−0.139470	+	0.990226i	$0.544540\pi$
$384$	8.60892	0.439322
$385$	5.75849	0.293480
$386$	−2.74164	−0.139546
$387$	3.22443	0.163907
$388$	6.31794	0.320745
$389$	−17.4154	−0.882996	−0.441498	−	0.897262i	$-0.645553\pi$
$389$	−17.4154	−0.882996	−0.441498	+	0.897262i	$0.645553\pi$
$390$	−5.38765	−0.272814
$391$	1.05018	0.0531101
$392$	−8.06656	−0.407423
$393$	−5.30306	−0.267504
$394$	−2.07229	−0.104400
$395$	29.5025	1.48443
$396$	−7.66187	−0.385023
$397$	−29.5353	−1.48234	−0.741168	−	0.671320i	$-0.765728\pi$
$397$	−29.5353	−1.48234	−0.741168	+	0.671320i	$0.765728\pi$
$398$	−3.77690	−0.189319
$399$	−1.33812	−0.0669898
$400$	21.5164	1.07582
$401$	−19.0745	−0.952537	−0.476268	−	0.879300i	$-0.658011\pi$
$401$	−19.0745	−0.952537	−0.476268	+	0.879300i	$0.658011\pi$
$402$	1.18039	0.0588727
$403$	−55.0401	−2.74174
$404$	7.79389	0.387760
$405$	3.34986	0.166456
$406$	−0.129636	−0.00643371
$407$	−41.5723	−2.06066
$408$	1.24274	0.0615249
$409$	33.1090	1.63714	0.818568	−	0.574410i	$-0.194768\pi$
$409$	33.1090	1.63714	0.818568	+	0.574410i	$0.194768\pi$
$410$	−7.24565	−0.357837
$411$	−13.1674	−0.649498
$412$	−27.5505	−1.35731
$413$	−2.00794	−0.0988042
$414$	−0.302778	−0.0148807
$415$	24.0850	1.18229
$416$	−18.1338	−0.889084
$417$	−2.28705	−0.111997
$418$	3.79929	0.185829
$419$	17.5578	0.857754	0.428877	−	0.903363i	$-0.358909\pi$
$419$	17.5578	0.857754	0.428877	+	0.903363i	$0.358909\pi$
$420$	−2.73702	−0.133553
$421$	−4.35212	−0.212109	−0.106055	−	0.994360i	$-0.533822\pi$
$421$	−4.35212	−0.212109	−0.106055	+	0.994360i	$0.533822\pi$
$422$	4.90493	0.238768
$423$	10.8487	0.527481
$424$	−11.4889	−0.557952
$425$	6.53378	0.316935
$426$	−4.14911	−0.201025
$427$	−1.79881	−0.0870504
$428$	−13.1387	−0.635084
$429$	21.3270	1.02968
$430$	−3.27043	−0.157714
$431$	0.733390	0.0353261	0.0176631	−	0.999844i	$-0.494377\pi$
$431$	0.733390	0.0353261	0.0176631	+	0.999844i	$0.494377\pi$
$432$	3.45836	0.166390
$433$	21.2117	1.01937	0.509686	−	0.860361i	$-0.329762\pi$
$433$	21.2117	1.01937	0.509686	+	0.860361i	$0.329762\pi$
$434$	1.34325	0.0644778
$435$	3.34986	0.160613
$436$	29.0580	1.39163
$437$	−3.12533	−0.149505
$438$	−2.53749	−0.121246
$439$	−25.0957	−1.19775	−0.598877	−	0.800841i	$-0.704386\pi$
$439$	−25.0957	−1.19775	−0.598877	+	0.800841i	$0.704386\pi$
$440$	15.9156	0.758748
$441$	−6.81668	−0.324604
$442$	−1.68903	−0.0803391
$443$	35.2387	1.67424	0.837121	−	0.547017i	$-0.184237\pi$
$443$	35.2387	1.67424	0.837121	+	0.547017i	$0.184237\pi$
$444$	19.7594	0.937740
$445$	−34.4700	−1.63403
$446$	1.42392	0.0674245
$447$	−11.9584	−0.565614
$448$	−2.51886	−0.119005
$449$	−11.4866	−0.542086	−0.271043	−	0.962567i	$-0.587369\pi$
$449$	−11.4866	−0.542086	−0.271043	+	0.962567i	$0.587369\pi$
$450$	−1.88375	−0.0888009
$451$	28.6819	1.35058
$452$	10.8059	0.508267
$453$	24.0005	1.12764
$454$	8.30532	0.389788
$455$	7.61858	0.357164
$456$	−3.69838	−0.173192
$457$	10.2250	0.478307	0.239154	−	0.970982i	$-0.423130\pi$
$457$	10.2250	0.478307	0.239154	+	0.970982i	$0.423130\pi$
$458$	−0.154683	−0.00722786
$459$	1.05018	0.0490184
$460$	−6.39262	−0.298057
$461$	8.68719	0.404603	0.202301	−	0.979323i	$-0.435158\pi$
$461$	8.68719	0.404603	0.202301	+	0.979323i	$0.435158\pi$
$462$	−0.520483	−0.0242151
$463$	−11.5538	−0.536950	−0.268475	−	0.963287i	$-0.586520\pi$
$463$	−11.5538	−0.536950	−0.268475	+	0.963287i	$0.586520\pi$
$464$	3.45836	0.160550
$465$	−34.7102	−1.60965
$466$	−3.42273	−0.158555
$467$	−33.0201	−1.52799	−0.763994	−	0.645223i	$-0.776764\pi$
$467$	−33.0201	−1.52799	−0.763994	+	0.645223i	$0.776764\pi$
$468$	−10.1368	−0.468573
$469$	−1.66917	−0.0770753
$470$	−11.0034	−0.507551
$471$	2.54328	0.117188
$472$	−5.54966	−0.255444
$473$	12.9460	0.595257
$474$	−2.66659	−0.122481
$475$	−19.4444	−0.892171
$476$	−0.858060	−0.0393291
$477$	−9.70877	−0.444534
$478$	3.13493	0.143388
$479$	−18.5401	−0.847118	−0.423559	−	0.905869i	$-0.639219\pi$
$479$	−18.5401	−0.847118	−0.423559	+	0.905869i	$0.639219\pi$
$480$	−11.4358	−0.521972
$481$	−55.0008	−2.50782
$482$	0.913029	0.0415873
$483$	0.428154	0.0194817
$484$	−9.77059	−0.444118
$485$	−11.0905	−0.503592
$486$	−0.302778	−0.0137343
$487$	7.53967	0.341655	0.170828	−	0.985301i	$-0.445356\pi$
$487$	7.53967	0.341655	0.170828	+	0.985301i	$0.445356\pi$
$488$	−4.97165	−0.225056
$489$	−20.4369	−0.924190
$490$	6.91392	0.312339
$491$	1.90597	0.0860154	0.0430077	−	0.999075i	$-0.486306\pi$
$491$	1.90597	0.0860154	0.0430077	+	0.999075i	$0.486306\pi$
$492$	−13.6326	−0.614605
$493$	1.05018	0.0472979
$494$	5.02653	0.226154
$495$	13.4496	0.604514
$496$	−35.8345	−1.60901
$497$	5.86719	0.263180
$498$	−2.17693	−0.0975506
$499$	9.26667	0.414833	0.207417	−	0.978253i	$-0.433494\pi$
$499$	9.26667	0.414833	0.207417	+	0.978253i	$0.433494\pi$
$500$	−7.80895	−0.349227
$501$	12.3398	0.551303
$502$	−4.86606	−0.217183
$503$	−16.4993	−0.735667	−0.367833	−	0.929892i	$-0.619900\pi$
$503$	−16.4993	−0.735667	−0.367833	+	0.929892i	$0.619900\pi$
$504$	0.506658	0.0225683
$505$	−13.6813	−0.608811
$506$	−1.21565	−0.0540420
$507$	15.2160	0.675767
$508$	−12.4472	−0.552256
$509$	−19.3897	−0.859434	−0.429717	−	0.902964i	$-0.641387\pi$
$509$	−19.3897	−0.859434	−0.429717	+	0.902964i	$0.641387\pi$
$510$	−1.06516	−0.0471663
$511$	3.58822	0.158734
$512$	−19.9912	−0.883493
$513$	−3.12533	−0.137987
$514$	−5.89201	−0.259885
$515$	48.3619	2.13108
$516$	−6.15326	−0.270882
$517$	43.5571	1.91564
$518$	1.34229	0.0589767
$519$	−11.3271	−0.497206
$520$	21.0567	0.923396
$521$	19.8726	0.870633	0.435316	−	0.900277i	$-0.356636\pi$
$521$	19.8726	0.870633	0.435316	+	0.900277i	$0.356636\pi$
$522$	−0.302778	−0.0132522
$523$	5.32708	0.232937	0.116468	−	0.993194i	$-0.462843\pi$
$523$	5.32708	0.232937	0.116468	+	0.993194i	$0.462843\pi$
$524$	10.1200	0.442093
$525$	2.66378	0.116257
$526$	−8.53080	−0.371961
$527$	−10.8817	−0.474014
$528$	13.8852	0.604276
$529$	1.00000	0.0434783
$530$	9.84726	0.427738
$531$	−4.68976	−0.203518
$532$	2.55357	0.110711
$533$	37.9467	1.64365
$534$	3.11558	0.134824
$535$	23.0636	0.997127
$536$	−4.61336	−0.199267
$537$	12.6720	0.546839
$538$	3.65802	0.157709
$539$	−27.3688	−1.17886
$540$	−6.39262	−0.275095
$541$	−39.5108	−1.69870	−0.849351	−	0.527828i	$-0.823007\pi$
$541$	−39.5108	−1.69870	−0.849351	+	0.527828i	$0.823007\pi$
$542$	8.91784	0.383054
$543$	21.2565	0.912205
$544$	−3.58515	−0.153712
$545$	−51.0083	−2.18495
$546$	−0.688608	−0.0294697
$547$	25.8008	1.10316	0.551581	−	0.834121i	$-0.314025\pi$
$547$	25.8008	1.10316	0.551581	+	0.834121i	$0.314025\pi$
$548$	25.1276	1.07340
$549$	−4.20131	−0.179308
$550$	−7.56321	−0.322496
$551$	−3.12533	−0.133143
$552$	1.18336	0.0503670
$553$	3.77078	0.160350
$554$	−3.09999	−0.131706
$555$	−34.6855	−1.47232
$556$	4.36443	0.185093
$557$	−22.5345	−0.954818	−0.477409	−	0.878681i	$-0.658424\pi$
$557$	−22.5345	−0.954818	−0.477409	+	0.878681i	$0.658424\pi$
$558$	3.13730	0.132812
$559$	17.1278	0.724428
$560$	4.96016	0.209605
$561$	4.21646	0.178019
$562$	4.91854	0.207476
$563$	−4.25638	−0.179385	−0.0896926	−	0.995969i	$-0.528588\pi$
$563$	−4.25638	−0.179385	−0.0896926	+	0.995969i	$0.528588\pi$
$564$	−20.7028	−0.871746
$565$	−18.9686	−0.798015
$566$	−5.73623	−0.241112
$567$	0.428154	0.0179808
$568$	16.2161	0.680412
$569$	−41.4992	−1.73974	−0.869868	−	0.493284i	$-0.835796\pi$
$569$	−41.4992	−1.73974	−0.869868	+	0.493284i	$0.835796\pi$
$570$	3.16991	0.132773
$571$	20.8965	0.874490	0.437245	−	0.899343i	$-0.355954\pi$
$571$	20.8965	0.874490	0.437245	+	0.899343i	$0.355954\pi$
$572$	−40.6989	−1.70171
$573$	−11.9418	−0.498876
$574$	−0.926084	−0.0386540
$575$	6.22156	0.259457
$576$	−5.88308	−0.245128
$577$	10.2811	0.428007	0.214004	−	0.976833i	$-0.431350\pi$
$577$	10.2811	0.428007	0.214004	+	0.976833i	$0.431350\pi$
$578$	4.81330	0.200207
$579$	9.05494	0.376310
$580$	−6.39262	−0.265439
$581$	3.07836	0.127712
$582$	1.00241	0.0415514
$583$	−38.9804	−1.61440
$584$	9.91734	0.410382
$585$	17.7940	0.735693
$586$	3.89851	0.161046
$587$	−11.8524	−0.489201	−0.244601	−	0.969624i	$-0.578657\pi$
$587$	−11.8524	−0.489201	−0.244601	+	0.969624i	$0.578657\pi$
$588$	13.0085	0.536460
$589$	32.3837	1.33435
$590$	4.75666	0.195829
$591$	6.84424	0.281534
$592$	−35.8089	−1.47174
$593$	6.17813	0.253705	0.126853	−	0.991922i	$-0.459512\pi$
$593$	6.17813	0.253705	0.126853	+	0.991922i	$0.459512\pi$
$594$	−1.21565	−0.0498785
$595$	1.50623	0.0617495
$596$	22.8205	0.934766
$597$	12.4741	0.510533
$598$	−1.60832	−0.0657691
$599$	18.0981	0.739467	0.369734	−	0.929138i	$-0.379449\pi$
$599$	18.0981	0.739467	0.369734	+	0.929138i	$0.379449\pi$
$600$	7.36232	0.300565
$601$	−6.20128	−0.252956	−0.126478	−	0.991969i	$-0.540367\pi$
$601$	−6.20128	−0.252956	−0.126478	+	0.991969i	$0.540367\pi$
$602$	−0.418001	−0.0170364
$603$	−3.89854	−0.158761
$604$	−45.8008	−1.86361
$605$	17.1512	0.697296
$606$	1.23659	0.0502331
$607$	13.0037	0.527804	0.263902	−	0.964550i	$-0.414990\pi$
$607$	13.0037	0.527804	0.263902	+	0.964550i	$0.414990\pi$
$608$	10.6693	0.432698
$609$	0.428154	0.0173497
$610$	4.26124	0.172533
$611$	57.6269	2.33133
$612$	−2.00409	−0.0810107
$613$	−26.0974	−1.05406	−0.527031	−	0.849846i	$-0.676695\pi$
$613$	−26.0974	−1.05406	−0.527031	+	0.849846i	$0.676695\pi$
$614$	5.80787	0.234386
$615$	23.9305	0.964973
$616$	2.03422	0.0819609
$617$	−4.77204	−0.192115	−0.0960576	−	0.995376i	$-0.530623\pi$
$617$	−4.77204	−0.192115	−0.0960576	+	0.995376i	$0.530623\pi$
$618$	−4.37121	−0.175836
$619$	7.79517	0.313314	0.156657	−	0.987653i	$-0.449928\pi$
$619$	7.79517	0.313314	0.156657	+	0.987653i	$0.449928\pi$
$620$	66.2384	2.66020
$621$	1.00000	0.0401286
$622$	7.60850	0.305073
$623$	−4.40569	−0.176510
$624$	18.3704	0.735403
$625$	−17.4000	−0.696001
$626$	0.305434	0.0122076
$627$	−12.5481	−0.501123
$628$	−4.85341	−0.193672
$629$	−10.8739	−0.433572
$630$	−0.434261	−0.0173014
$631$	13.9161	0.553990	0.276995	−	0.960871i	$-0.410661\pi$
$631$	13.9161	0.553990	0.276995	+	0.960871i	$0.410661\pi$
$632$	10.4219	0.414561
$633$	−16.1997	−0.643882
$634$	0.935413	0.0371500
$635$	21.8498	0.867082
$636$	18.5275	0.734663
$637$	−36.2094	−1.43467
$638$	−1.21565	−0.0481279
$639$	13.7035	0.542101
$640$	28.8387	1.13995
$641$	−7.91467	−0.312611	−0.156305	−	0.987709i	$-0.549958\pi$
$641$	−7.91467	−0.312611	−0.156305	+	0.987709i	$0.549958\pi$
$642$	−2.08461	−0.0822731
$643$	−13.3238	−0.525439	−0.262720	−	0.964872i	$-0.584619\pi$
$643$	−13.3238	−0.525439	−0.262720	+	0.964872i	$0.584619\pi$
$644$	−0.817056	−0.0321965
$645$	10.8014	0.425304
$646$	0.993770	0.0390994
$647$	1.47922	0.0581543	0.0290771	−	0.999577i	$-0.490743\pi$
$647$	1.47922	0.0581543	0.0290771	+	0.999577i	$0.490743\pi$
$648$	1.18336	0.0464866
$649$	−18.8292	−0.739113
$650$	−10.0063	−0.392478
$651$	−4.43640	−0.173876
$652$	39.0003	1.52737
$653$	28.7736	1.12600	0.562998	−	0.826458i	$-0.309648\pi$
$653$	28.7736	1.12600	0.562998	+	0.826458i	$0.309648\pi$
$654$	4.61040	0.180281
$655$	−17.7645	−0.694117
$656$	24.7056	0.964592
$657$	8.38069	0.326962
$658$	−1.40638	−0.0548262
$659$	−18.2082	−0.709293	−0.354646	−	0.935001i	$-0.615399\pi$
$659$	−18.2082	−0.709293	−0.354646	+	0.935001i	$0.615399\pi$
$660$	−25.6662	−0.999055
$661$	13.9217	0.541493	0.270746	−	0.962651i	$-0.412729\pi$
$661$	13.9217	0.541493	0.270746	+	0.962651i	$0.412729\pi$
$662$	−4.50677	−0.175161
$663$	5.57845	0.216649
$664$	8.50816	0.330180
$665$	−4.48252	−0.173824
$666$	3.13506	0.121481
$667$	1.00000	0.0387202
$668$	−23.5484	−0.911116
$669$	−4.70284	−0.181822
$670$	3.95415	0.152762
$671$	−16.8682	−0.651188
$672$	−1.46164	−0.0563841
$673$	−29.7330	−1.14612	−0.573062	−	0.819512i	$-0.694245\pi$
$673$	−29.7330	−1.14612	−0.573062	+	0.819512i	$0.694245\pi$
$674$	−7.25822	−0.279576
$675$	6.22156	0.239468
$676$	−29.0371	−1.11681
$677$	0.854675	0.0328478	0.0164239	−	0.999865i	$-0.494772\pi$
$677$	0.854675	0.0328478	0.0164239	+	0.999865i	$0.494772\pi$
$678$	1.71448	0.0658443
$679$	−1.41750	−0.0543986
$680$	4.16301	0.159644
$681$	−27.4304	−1.05113
$682$	12.5962	0.482332
$683$	−17.6454	−0.675183	−0.337591	−	0.941293i	$-0.609612\pi$
$683$	−17.6454	−0.675183	−0.337591	+	0.941293i	$0.609612\pi$
$684$	5.96414	0.228045
$685$	−44.1088	−1.68531
$686$	1.79113	0.0683858
$687$	0.510879	0.0194912
$688$	11.1512	0.425137
$689$	−51.5718	−1.96473
$690$	−1.01426	−0.0386124
$691$	−27.0772	−1.03007	−0.515033	−	0.857170i	$-0.672220\pi$
$691$	−27.0772	−1.03007	−0.515033	+	0.857170i	$0.672220\pi$
$692$	21.6159	0.821712
$693$	1.71902	0.0653003
$694$	8.91449	0.338389
$695$	−7.66129	−0.290609
$696$	1.18336	0.0448550
$697$	7.50225	0.284168
$698$	1.46601	0.0554891
$699$	11.3044	0.427573
$700$	−5.08336	−0.192133
$701$	−41.8074	−1.57904	−0.789522	−	0.613722i	$-0.789672\pi$
$701$	−41.8074	−1.57904	−0.789522	+	0.613722i	$0.789672\pi$
$702$	−1.60832	−0.0607021
$703$	32.3606	1.22050
$704$	−23.6204	−0.890227
$705$	36.3416	1.36870
$706$	−3.36110	−0.126497
$707$	−1.74864	−0.0657645
$708$	8.94959	0.336346
$709$	28.6271	1.07511	0.537557	−	0.843228i	$-0.319347\pi$
$709$	28.6271	1.07511	0.537557	+	0.843228i	$0.319347\pi$
$710$	−13.8989	−0.521618
$711$	8.80707	0.330291
$712$	−12.1767	−0.456342
$713$	−10.3617	−0.388049
$714$	−0.136141	−0.00509496
$715$	71.4425	2.67180
$716$	−24.1824	−0.903738
$717$	−10.3539	−0.386673
$718$	−6.38008	−0.238102
$719$	−32.5891	−1.21537	−0.607685	−	0.794178i	$-0.707902\pi$
$719$	−32.5891	−1.21537	−0.607685	+	0.794178i	$0.707902\pi$
$720$	11.5850	0.431748
$721$	6.18125	0.230202
$722$	2.79535	0.104032
$723$	−3.01550	−0.112148
$724$	−40.5644	−1.50756
$725$	6.22156	0.231063
$726$	−1.55022	−0.0575340
$727$	46.4493	1.72271	0.861354	−	0.508005i	$-0.169617\pi$
$727$	46.4493	1.72271	0.861354	+	0.508005i	$0.169617\pi$
$728$	2.69130	0.0997464
$729$	1.00000	0.0370370
$730$	−8.50024	−0.314608
$731$	3.38625	0.125245
$732$	8.01748	0.296334
$733$	−49.8584	−1.84156	−0.920781	−	0.390079i	$-0.872448\pi$
$733$	−49.8584	−1.84156	−0.920781	+	0.390079i	$0.872448\pi$
$734$	9.56233	0.352952
$735$	−22.8349	−0.842279
$736$	−3.41383	−0.125835
$737$	−15.6525	−0.576568
$738$	−2.16297	−0.0796201
$739$	−42.1893	−1.55196	−0.775979	−	0.630759i	$-0.782744\pi$
$739$	−42.1893	−1.55196	−0.775979	+	0.630759i	$0.782744\pi$
$740$	66.1912	2.43324
$741$	−16.6014	−0.609866
$742$	1.25860	0.0462047
$743$	9.91569	0.363771	0.181886	−	0.983320i	$-0.441780\pi$
$743$	9.91569	0.363771	0.181886	+	0.983320i	$0.441780\pi$
$744$	−12.2616	−0.449531
$745$	−40.0590	−1.46765
$746$	1.86718	0.0683622
$747$	7.18985	0.263063
$748$	−8.04637	−0.294205
$749$	2.94781	0.107711
$750$	−1.23898	−0.0452412
$751$	−18.1042	−0.660632	−0.330316	−	0.943870i	$-0.607155\pi$
$751$	−18.1042	−0.660632	−0.330316	+	0.943870i	$0.607155\pi$
$752$	37.5186	1.36816
$753$	16.0714	0.585674
$754$	−1.60832	−0.0585716
$755$	80.3983	2.92600
$756$	−0.817056	−0.0297161
$757$	−9.06824	−0.329591	−0.164795	−	0.986328i	$-0.552696\pi$
$757$	−9.06824	−0.329591	−0.164795	+	0.986328i	$0.552696\pi$
$758$	−3.82090	−0.138781
$759$	4.01497	0.145734
$760$	−12.3890	−0.449398
$761$	−53.3930	−1.93549	−0.967747	−	0.251924i	$-0.918937\pi$
$761$	−53.3930	−1.93549	−0.967747	+	0.251924i	$0.918937\pi$
$762$	−1.97490	−0.0715430
$763$	−6.51949	−0.236021
$764$	22.7888	0.824471
$765$	3.51797	0.127192
$766$	1.65286	0.0597203
$767$	−24.9114	−0.899499
$768$	9.15957	0.330517
$769$	21.6662	0.781305	0.390652	−	0.920538i	$-0.372249\pi$
$769$	21.6662	0.781305	0.390652	+	0.920538i	$0.372249\pi$
$770$	−1.74354	−0.0628330
$771$	19.4598	0.700828
$772$	−17.2798	−0.621912
$773$	26.9885	0.970710	0.485355	−	0.874317i	$-0.338690\pi$
$773$	26.9885	0.970710	0.485355	+	0.874317i	$0.338690\pi$
$774$	−0.976287	−0.0350919
$775$	−64.4659	−2.31568
$776$	−3.91776	−0.140639
$777$	−4.43324	−0.159041
$778$	5.27301	0.189046
$779$	−22.3266	−0.799932
$780$	−33.9568	−1.21585
$781$	55.0190	1.96874
$782$	−0.317973	−0.0113707
$783$	1.00000	0.0357371
$784$	−23.5745	−0.841947
$785$	8.51964	0.304079
$786$	1.60565	0.0572717
$787$	40.2357	1.43425	0.717125	−	0.696945i	$-0.245458\pi$
$787$	40.2357	1.43425	0.717125	+	0.696945i	$0.245458\pi$
$788$	−13.0610	−0.465280
$789$	28.1751	1.00306
$790$	−8.93270	−0.317811
$791$	−2.42442	−0.0862025
$792$	4.75114	0.168824
$793$	−22.3169	−0.792495
$794$	8.94265	0.317363
$795$	−32.5230	−1.15347
$796$	−23.8047	−0.843736
$797$	25.7410	0.911792	0.455896	−	0.890033i	$-0.349319\pi$
$797$	25.7410	0.911792	0.455896	+	0.890033i	$0.349319\pi$
$798$	0.405154	0.0143423
$799$	11.3931	0.403060
$800$	−21.2393	−0.750923
$801$	−10.2900	−0.363579
$802$	5.77535	0.203935
$803$	33.6482	1.18742
$804$	7.43969	0.262377
$805$	1.43425	0.0505508
$806$	16.6649	0.586997
$807$	−12.0815	−0.425290
$808$	−4.83300	−0.170024
$809$	−37.9813	−1.33535	−0.667675	−	0.744453i	$-0.732711\pi$
$809$	−37.9813	−1.33535	−0.667675	+	0.744453i	$0.732711\pi$
$810$	−1.01426	−0.0356376
$811$	41.0679	1.44209	0.721045	−	0.692888i	$-0.243662\pi$
$811$	41.0679	1.44209	0.721045	+	0.692888i	$0.243662\pi$
$812$	−0.817056	−0.0286731
$813$	−29.4534	−1.03297
$814$	12.5872	0.441180
$815$	−68.4608	−2.39808
$816$	3.63191	0.127142
$817$	−10.0774	−0.352564
$818$	−10.0247	−0.350505
$819$	2.27430	0.0794704
$820$	−45.6673	−1.59477
$821$	43.9349	1.53334	0.766670	−	0.642042i	$-0.221912\pi$
$821$	43.9349	1.53334	0.766670	+	0.642042i	$0.221912\pi$
$822$	3.98679	0.139055
$823$	−7.58709	−0.264469	−0.132235	−	0.991218i	$-0.542215\pi$
$823$	−7.58709	−0.264469	−0.132235	+	0.991218i	$0.542215\pi$
$824$	17.0841	0.595153
$825$	24.9794	0.869670
$826$	0.607960	0.0211536
$827$	32.5844	1.13307	0.566536	−	0.824037i	$-0.308283\pi$
$827$	32.5844	1.13307	0.566536	+	0.824037i	$0.308283\pi$
$828$	−1.90833	−0.0663189
$829$	52.0958	1.80936	0.904681	−	0.426089i	$-0.140109\pi$
$829$	52.0958	1.80936	0.904681	+	0.426089i	$0.140109\pi$
$830$	−7.29241	−0.253123
$831$	10.2385	0.355169
$832$	−31.2502	−1.08341
$833$	−7.15877	−0.248037
$834$	0.692469	0.0239782
$835$	41.3367	1.43052
$836$	23.9459	0.828185
$837$	−10.3617	−0.358153
$838$	−5.31611	−0.183642
$839$	37.5788	1.29736	0.648682	−	0.761059i	$-0.275320\pi$
$839$	37.5788	1.29736	0.648682	+	0.761059i	$0.275320\pi$
$840$	1.69723	0.0585601
$841$	1.00000	0.0344828
$842$	1.31773	0.0454119
$843$	−16.2447	−0.559497
$844$	30.9144	1.06412
$845$	50.9715	1.75347
$846$	−3.28475	−0.112932
$847$	2.19214	0.0753227
$848$	−33.5764	−1.15302
$849$	18.9453	0.650201
$850$	−1.97829	−0.0678547
$851$	−10.3543	−0.354941
$852$	−26.1507	−0.895908
$853$	−1.37770	−0.0471717	−0.0235858	−	0.999722i	$-0.507508\pi$
$853$	−1.37770	−0.0471717	−0.0235858	+	0.999722i	$0.507508\pi$
$854$	0.544640	0.0186372
$855$	−10.4694	−0.358046
$856$	8.14734	0.278470
$857$	10.7773	0.368145	0.184072	−	0.982913i	$-0.441072\pi$
$857$	10.7773	0.368145	0.184072	+	0.982913i	$0.441072\pi$
$858$	−6.45736	−0.220451
$859$	−43.8307	−1.49549	−0.747743	−	0.663988i	$-0.768862\pi$
$859$	−43.8307	−1.49549	−0.747743	+	0.663988i	$0.768862\pi$
$860$	−20.6126	−0.702883
$861$	3.05862	0.104238
$862$	−0.222054	−0.00756320
$863$	31.7238	1.07989	0.539946	−	0.841700i	$-0.318445\pi$
$863$	31.7238	1.07989	0.539946	+	0.841700i	$0.318445\pi$
$864$	−3.41383	−0.116141
$865$	−37.9443	−1.29015
$866$	−6.42245	−0.218244
$867$	−15.8971	−0.539894
$868$	8.46609	0.287358
$869$	35.3601	1.19951
$870$	−1.01426	−0.0343868
$871$	−20.7086	−0.701683
$872$	−18.0189	−0.610199
$873$	−3.31072	−0.112051
$874$	0.946281	0.0320084
$875$	1.75202	0.0592292
$876$	−15.9931	−0.540356
$877$	58.0758	1.96108	0.980540	−	0.196319i	$-0.0628988\pi$
$877$	58.0758	1.96108	0.980540	+	0.196319i	$0.0628988\pi$
$878$	7.59844	0.256435
$879$	−12.8758	−0.434290
$880$	46.5134	1.56797
$881$	50.1319	1.68899	0.844493	−	0.535567i	$-0.179902\pi$
$881$	50.1319	1.68899	0.844493	+	0.535567i	$0.179902\pi$
$882$	2.06394	0.0694966
$883$	10.4412	0.351375	0.175687	−	0.984446i	$-0.443785\pi$
$883$	10.4412	0.351375	0.175687	+	0.984446i	$0.443785\pi$
$884$	−10.6455	−0.358047
$885$	−15.7100	−0.528087
$886$	−10.6695	−0.358450
$887$	33.4645	1.12363	0.561815	−	0.827263i	$-0.310103\pi$
$887$	33.4645	1.12363	0.561815	+	0.827263i	$0.310103\pi$
$888$	−12.2528	−0.411178
$889$	2.79267	0.0936632
$890$	10.4368	0.349841
$891$	4.01497	0.134507
$892$	8.97456	0.300490
$893$	−33.9057	−1.13461
$894$	3.62075	0.121096
$895$	42.4496	1.41893
$896$	3.68594	0.123139
$897$	5.31187	0.177358
$898$	3.47789	0.116059
$899$	−10.3617	−0.345582
$900$	−11.8728	−0.395758
$901$	−10.1960	−0.339678
$902$	−8.68426	−0.289154
$903$	1.38055	0.0459419
$904$	−6.70076	−0.222864
$905$	71.2064	2.36698
$906$	−7.26683	−0.241424
$907$	−38.3696	−1.27404	−0.637021	−	0.770846i	$-0.719834\pi$
$907$	−38.3696	−1.27404	−0.637021	+	0.770846i	$0.719834\pi$
$908$	52.3461	1.73717
$909$	−4.08415	−0.135463
$910$	−2.30674	−0.0764677
$911$	−30.9361	−1.02496	−0.512480	−	0.858699i	$-0.671273\pi$
$911$	−30.9361	−1.02496	−0.512480	+	0.858699i	$0.671273\pi$
$912$	−10.8085	−0.357905
$913$	28.8670	0.955360
$914$	−3.09592	−0.102404
$915$	−14.0738	−0.465266
$916$	−0.974923	−0.0322124
$917$	−2.27052	−0.0749793
$918$	−0.317973	−0.0104947
$919$	−15.7028	−0.517986	−0.258993	−	0.965879i	$-0.583391\pi$
$919$	−15.7028	−0.517986	−0.258993	+	0.965879i	$0.583391\pi$
$920$	3.96408	0.130692
$921$	−19.1819	−0.632066
$922$	−2.63029	−0.0866241
$923$	72.7911	2.39595
$924$	−3.28046	−0.107919
$925$	−64.4200	−2.11811
$926$	3.49824	0.114959
$927$	14.4370	0.474173
$928$	−3.41383	−0.112064
$929$	40.9864	1.34472	0.672360	−	0.740224i	$-0.265281\pi$
$929$	40.9864	1.34472	0.672360	+	0.740224i	$0.265281\pi$
$930$	10.5095	0.344620
$931$	21.3044	0.698223
$932$	−21.5725	−0.706631
$933$	−25.1290	−0.822685
$934$	9.99777	0.327137
$935$	14.1245	0.461922
$936$	6.28584	0.205459
$937$	−28.1083	−0.918260	−0.459130	−	0.888369i	$-0.651839\pi$
$937$	−28.1083	−0.918260	−0.459130	+	0.888369i	$0.651839\pi$
$938$	0.505390	0.0165016
$939$	−1.00877	−0.0329200
$940$	−69.3515	−2.26200
$941$	−3.64388	−0.118787	−0.0593935	−	0.998235i	$-0.518917\pi$
$941$	−3.64388	−0.118787	−0.0593935	+	0.998235i	$0.518917\pi$
$942$	−0.770051	−0.0250896
$943$	7.14375	0.232632
$944$	−16.2189	−0.527879
$945$	1.43425	0.0466563
$946$	−3.91976	−0.127443
$947$	−19.1649	−0.622775	−0.311388	−	0.950283i	$-0.600794\pi$
$947$	−19.1649	−0.622775	−0.311388	+	0.950283i	$0.600794\pi$
$948$	−16.8068	−0.545858
$949$	44.5172	1.44509
$950$	5.88734	0.191011
$951$	−3.08943	−0.100182
$952$	0.532084	0.0172450
$953$	31.6253	1.02445	0.512223	−	0.858853i	$-0.328822\pi$
$953$	31.6253	1.02445	0.512223	+	0.858853i	$0.328822\pi$
$954$	2.93960	0.0951732
$955$	−40.0033	−1.29448
$956$	19.7586	0.639038
$957$	4.01497	0.129786
$958$	5.61353	0.181365
$959$	−5.63765	−0.182049
$960$	−19.7075	−0.636056
$961$	76.3649	2.46338
$962$	16.6531	0.536916
$963$	6.88495	0.221864
$964$	5.75456	0.185342
$965$	30.3328	0.976446
$966$	−0.129636	−0.00417096
$967$	−27.6891	−0.890421	−0.445211	−	0.895426i	$-0.646871\pi$
$967$	−27.6891	−0.890421	−0.445211	+	0.895426i	$0.646871\pi$
$968$	6.05876	0.194736
$969$	−3.28217	−0.105439
$970$	3.35795	0.107817
$971$	−35.9385	−1.15332	−0.576661	−	0.816984i	$-0.695644\pi$
$971$	−35.9385	−1.15332	−0.576661	+	0.816984i	$0.695644\pi$
$972$	−1.90833	−0.0612096
$973$	−0.979208	−0.0313920
$974$	−2.28285	−0.0731472
$975$	33.0481	1.05839
$976$	−14.5296	−0.465083
$977$	38.4441	1.22993	0.614967	−	0.788553i	$-0.289169\pi$
$977$	38.4441	1.22993	0.614967	+	0.788553i	$0.289169\pi$
$978$	6.18786	0.197866
$979$	−41.3140	−1.32040
$980$	43.5765	1.39200
$981$	−15.2270	−0.486160
$982$	−0.577088	−0.0184156
$983$	−17.4592	−0.556863	−0.278431	−	0.960456i	$-0.589814\pi$
$983$	−17.4592	−0.556863	−0.278431	+	0.960456i	$0.589814\pi$
$984$	8.45359	0.269491
$985$	22.9272	0.730522
$986$	−0.317973	−0.0101263
$987$	4.64490	0.147849
$988$	31.6808	1.00790
$989$	3.22443	0.102531
$990$	−4.07224	−0.129424
$991$	42.9628	1.36476	0.682380	−	0.730998i	$-0.260945\pi$
$991$	42.9628	1.36476	0.682380	+	0.730998i	$0.260945\pi$
$992$	35.3731	1.12310
$993$	14.8847	0.472353
$994$	−1.77646	−0.0563458
$995$	41.7866	1.32473
$996$	−13.7206	−0.434753
$997$	−16.7387	−0.530121	−0.265061	−	0.964232i	$-0.585392\pi$
$997$	−16.7387	−0.530121	−0.265061	+	0.964232i	$0.585392\pi$
$998$	−2.80575	−0.0888144
$999$	−10.3543	−0.327596

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2001.2.a.o.1.9	✓	20
3.2	odd	2		6003.2.a.s.1.12		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2001.2.a.o.1.9	✓	20	1.1	even	1	trivial
6003.2.a.s.1.12		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)

\(f(q)\)	\(=\)	\(q-0.302778 q^{2} +1.00000 q^{3} -1.90833 q^{4} +3.34986 q^{5} -0.302778 q^{6} +0.428154 q^{7} +1.18336 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-0.302778 q^{2} +1.00000 q^{3} -1.90833 q^{4} +3.34986 q^{5} -0.302778 q^{6} +0.428154 q^{7} +1.18336 q^{8} +1.00000 q^{9} -1.01426 q^{10} +4.01497 q^{11} -1.90833 q^{12} +5.31187 q^{13} -0.129636 q^{14} +3.34986 q^{15} +3.45836 q^{16} +1.05018 q^{17} -0.302778 q^{18} -3.12533 q^{19} -6.39262 q^{20} +0.428154 q^{21} -1.21565 q^{22} +1.00000 q^{23} +1.18336 q^{24} +6.22156 q^{25} -1.60832 q^{26} +1.00000 q^{27} -0.817056 q^{28} +1.00000 q^{29} -1.01426 q^{30} -10.3617 q^{31} -3.41383 q^{32} +4.01497 q^{33} -0.317973 q^{34} +1.43425 q^{35} -1.90833 q^{36} -10.3543 q^{37} +0.946281 q^{38} +5.31187 q^{39} +3.96408 q^{40} +7.14375 q^{41} -0.129636 q^{42} +3.22443 q^{43} -7.66187 q^{44} +3.34986 q^{45} -0.302778 q^{46} +10.8487 q^{47} +3.45836 q^{48} -6.81668 q^{49} -1.88375 q^{50} +1.05018 q^{51} -10.1368 q^{52} -9.70877 q^{53} -0.302778 q^{54} +13.4496 q^{55} +0.506658 q^{56} -3.12533 q^{57} -0.302778 q^{58} -4.68976 q^{59} -6.39262 q^{60} -4.20131 q^{61} +3.13730 q^{62} +0.428154 q^{63} -5.88308 q^{64} +17.7940 q^{65} -1.21565 q^{66} -3.89854 q^{67} -2.00409 q^{68} +1.00000 q^{69} -0.434261 q^{70} +13.7035 q^{71} +1.18336 q^{72} +8.38069 q^{73} +3.13506 q^{74} +6.22156 q^{75} +5.96414 q^{76} +1.71902 q^{77} -1.60832 q^{78} +8.80707 q^{79} +11.5850 q^{80} +1.00000 q^{81} -2.16297 q^{82} +7.18985 q^{83} -0.817056 q^{84} +3.51797 q^{85} -0.976287 q^{86} +1.00000 q^{87} +4.75114 q^{88} -10.2900 q^{89} -1.01426 q^{90} +2.27430 q^{91} -1.90833 q^{92} -10.3617 q^{93} -3.28475 q^{94} -10.4694 q^{95} -3.41383 q^{96} -3.31072 q^{97} +2.06394 q^{98} +4.01497 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 2 q^{2} + 20 q^{3} + 30 q^{4} - q^{5} + 2 q^{6} + 9 q^{7} + 6 q^{8} + 20 q^{9}+O(q^{10}) \) 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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