LMFDB - Embedded newform 2001.2.a.l.1.10

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:	$11$
Coefficient field:	$\mathbb{Q}[x]/(x^{11} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{11} - 2 x^{10} - 18 x^{9} + 30 x^{8} + 124 x^{7} - 152 x^{6} - 408 x^{5} + 285 x^{4} + 634 x^{3} + \cdots - 108 $ x^11 - 2x^10 - 18x^9 + 30x^8 + 124x^7 - 152x^6 - 408x^5 + 285x^4 + 634x^3 - 93x^2 - 369x - 108
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 3 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.10
Root			$2.70316$ 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)

$f(q)$	$=$	$q+2.70316 q^{2} -1.00000 q^{3} +5.30708 q^{4} +2.79988 q^{5} -2.70316 q^{6} +0.880738 q^{7} +8.93955 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+2.70316 q^{2} -1.00000 q^{3} +5.30708 q^{4} +2.79988 q^{5} -2.70316 q^{6} +0.880738 q^{7} +8.93955 q^{8} +1.00000 q^{9} +7.56852 q^{10} -5.67616 q^{11} -5.30708 q^{12} -3.71641 q^{13} +2.38078 q^{14} -2.79988 q^{15} +13.5509 q^{16} +4.80704 q^{17} +2.70316 q^{18} +6.68378 q^{19} +14.8592 q^{20} -0.880738 q^{21} -15.3436 q^{22} +1.00000 q^{23} -8.93955 q^{24} +2.83932 q^{25} -10.0460 q^{26} -1.00000 q^{27} +4.67414 q^{28} -1.00000 q^{29} -7.56852 q^{30} +0.779005 q^{31} +18.7511 q^{32} +5.67616 q^{33} +12.9942 q^{34} +2.46596 q^{35} +5.30708 q^{36} -8.14977 q^{37} +18.0673 q^{38} +3.71641 q^{39} +25.0297 q^{40} +6.06174 q^{41} -2.38078 q^{42} +9.54562 q^{43} -30.1238 q^{44} +2.79988 q^{45} +2.70316 q^{46} -7.68018 q^{47} -13.5509 q^{48} -6.22430 q^{49} +7.67515 q^{50} -4.80704 q^{51} -19.7233 q^{52} -9.73506 q^{53} -2.70316 q^{54} -15.8926 q^{55} +7.87341 q^{56} -6.68378 q^{57} -2.70316 q^{58} +5.14558 q^{59} -14.8592 q^{60} -7.99562 q^{61} +2.10578 q^{62} +0.880738 q^{63} +23.5855 q^{64} -10.4055 q^{65} +15.3436 q^{66} -8.36073 q^{67} +25.5113 q^{68} -1.00000 q^{69} +6.66589 q^{70} +8.52656 q^{71} +8.93955 q^{72} -12.6677 q^{73} -22.0301 q^{74} -2.83932 q^{75} +35.4713 q^{76} -4.99921 q^{77} +10.0460 q^{78} +15.1051 q^{79} +37.9409 q^{80} +1.00000 q^{81} +16.3859 q^{82} -0.302272 q^{83} -4.67414 q^{84} +13.4591 q^{85} +25.8033 q^{86} +1.00000 q^{87} -50.7423 q^{88} -10.7142 q^{89} +7.56852 q^{90} -3.27318 q^{91} +5.30708 q^{92} -0.779005 q^{93} -20.7608 q^{94} +18.7138 q^{95} -18.7511 q^{96} -0.884027 q^{97} -16.8253 q^{98} -5.67616 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 11 q + 2 q^{2} - 11 q^{3} + 18 q^{4} + 2 q^{5} - 2 q^{6} + 3 q^{7} + 18 q^{8} + 11 q^{9}+O(q^{10}) $ 11 * q + 2 * q^2 - 11 * q^3 + 18 * q^4 + 2 * q^5 - 2 * q^6 + 3 * q^7 + 18 * q^8 + 11 * q^9	\( 11 q + 2 q^{2} - 11 q^{3} + 18 q^{4} + 2 q^{5} - 2 q^{6} + 3 q^{7} + 18 q^{8} + 11 q^{9} + 14 q^{10} + 11 q^{11} - 18 q^{12} - 5 q^{13} + 17 q^{14} - 2 q^{15} + 20 q^{16} + 15 q^{17} + 2 q^{18} - 6 q^{19} + 21 q^{20} - 3 q^{21} - 10 q^{22} + 11 q^{23} - 18 q^{24} + 3 q^{25} - 5 q^{26} - 11 q^{27} + 7 q^{28} - 11 q^{29} - 14 q^{30} + 35 q^{31} + 28 q^{32} - 11 q^{33} + 28 q^{34} + 15 q^{35} + 18 q^{36} - 28 q^{37} - 2 q^{38} + 5 q^{39} - q^{40} + 10 q^{41} - 17 q^{42} - 6 q^{43} + 18 q^{44} + 2 q^{45} + 2 q^{46} + 15 q^{47} - 20 q^{48} + 22 q^{49} + 15 q^{50} - 15 q^{51} - 36 q^{52} - 7 q^{53} - 2 q^{54} - 12 q^{55} + 56 q^{56} + 6 q^{57} - 2 q^{58} - 20 q^{59} - 21 q^{60} - 20 q^{61} - 11 q^{62} + 3 q^{63} + 36 q^{64} + 11 q^{65} + 10 q^{66} - 39 q^{67} + 35 q^{68} - 11 q^{69} + 38 q^{70} + 49 q^{71} + 18 q^{72} - 3 q^{73} + 37 q^{74} - 3 q^{75} - 18 q^{76} + 25 q^{77} + 5 q^{78} + 41 q^{79} + 51 q^{80} + 11 q^{81} - 19 q^{82} + 13 q^{83} - 7 q^{84} + 62 q^{86} + 11 q^{87} - 40 q^{88} + 34 q^{89} + 14 q^{90} + 2 q^{91} + 18 q^{92} - 35 q^{93} - 14 q^{94} + 25 q^{95} - 28 q^{96} - 11 q^{97} + 53 q^{98} + 11 q^{99}+O(q^{100}) \) 11 * q + 2 * q^2 - 11 * q^3 + 18 * q^4 + 2 * q^5 - 2 * q^6 + 3 * q^7 + 18 * q^8 + 11 * q^9 + 14 * q^10 + 11 * q^11 - 18 * q^12 - 5 * q^13 + 17 * q^14 - 2 * q^15 + 20 * q^16 + 15 * q^17 + 2 * q^18 - 6 * q^19 + 21 * q^20 - 3 * q^21 - 10 * q^22 + 11 * q^23 - 18 * q^24 + 3 * q^25 - 5 * q^26 - 11 * q^27 + 7 * q^28 - 11 * q^29 - 14 * q^30 + 35 * q^31 + 28 * q^32 - 11 * q^33 + 28 * q^34 + 15 * q^35 + 18 * q^36 - 28 * q^37 - 2 * q^38 + 5 * q^39 - q^40 + 10 * q^41 - 17 * q^42 - 6 * q^43 + 18 * q^44 + 2 * q^45 + 2 * q^46 + 15 * q^47 - 20 * q^48 + 22 * q^49 + 15 * q^50 - 15 * q^51 - 36 * q^52 - 7 * q^53 - 2 * q^54 - 12 * q^55 + 56 * q^56 + 6 * q^57 - 2 * q^58 - 20 * q^59 - 21 * q^60 - 20 * q^61 - 11 * q^62 + 3 * q^63 + 36 * q^64 + 11 * q^65 + 10 * q^66 - 39 * q^67 + 35 * q^68 - 11 * q^69 + 38 * q^70 + 49 * q^71 + 18 * q^72 - 3 * q^73 + 37 * q^74 - 3 * q^75 - 18 * q^76 + 25 * q^77 + 5 * q^78 + 41 * q^79 + 51 * q^80 + 11 * q^81 - 19 * q^82 + 13 * q^83 - 7 * q^84 + 62 * q^86 + 11 * q^87 - 40 * q^88 + 34 * q^89 + 14 * q^90 + 2 * q^91 + 18 * q^92 - 35 * q^93 - 14 * q^94 + 25 * q^95 - 28 * q^96 - 11 * q^97 + 53 * q^98 + 11 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	2.70316	1.91142	0.955711	−	0.294305i	$-0.0950882\pi$
$2$	2.70316	1.91142	0.955711	+	0.294305i	$0.0950882\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	5.30708	2.65354
$5$	2.79988	1.25214	0.626072	−	0.779765i	$-0.284662\pi$
$5$	2.79988	1.25214	0.626072	+	0.779765i	$0.284662\pi$
$6$	−2.70316	−1.10356
$7$	0.880738	0.332888	0.166444	−	0.986051i	$-0.446772\pi$
$7$	0.880738	0.332888	0.166444	+	0.986051i	$0.446772\pi$
$8$	8.93955	3.16061
$9$	1.00000	0.333333
$10$	7.56852	2.39338
$11$	−5.67616	−1.71143	−0.855713	−	0.517451i	$-0.826881\pi$
$11$	−5.67616	−1.71143	−0.855713	+	0.517451i	$0.826881\pi$
$12$	−5.30708	−1.53202
$13$	−3.71641	−1.03075	−0.515373	−	0.856966i	$-0.672347\pi$
$13$	−3.71641	−1.03075	−0.515373	+	0.856966i	$0.672347\pi$
$14$	2.38078	0.636289
$15$	−2.79988	−0.722926
$16$	13.5509	3.38772
$17$	4.80704	1.16588	0.582939	−	0.812516i	$-0.301903\pi$
$17$	4.80704	1.16588	0.582939	+	0.812516i	$0.301903\pi$
$18$	2.70316	0.637141
$19$	6.68378	1.53336	0.766682	−	0.642027i	$-0.221907\pi$
$19$	6.68378	1.53336	0.766682	+	0.642027i	$0.221907\pi$
$20$	14.8592	3.32261
$21$	−0.880738	−0.192193
$22$	−15.3436	−3.27126
$23$	1.00000	0.208514
$23$	1.00000	0.208514
$24$	−8.93955	−1.82478
$25$	2.83932	0.567865
$26$	−10.0460	−1.97019
$27$	−1.00000	−0.192450
$28$	4.67414	0.883330
$29$	−1.00000	−0.185695
$29$	−1.00000	−0.185695
$30$	−7.56852	−1.38182
$31$	0.779005	0.139913	0.0699567	−	0.997550i	$-0.477714\pi$
$31$	0.779005	0.139913	0.0699567	+	0.997550i	$0.477714\pi$
$32$	18.7511	3.31476
$33$	5.67616	0.988092
$34$	12.9942	2.22849
$35$	2.46596	0.416823
$36$	5.30708	0.884513
$37$	−8.14977	−1.33981	−0.669907	−	0.742445i	$-0.733666\pi$
$37$	−8.14977	−1.33981	−0.669907	+	0.742445i	$0.733666\pi$
$38$	18.0673	2.93091
$39$	3.71641	0.595101
$40$	25.0297	3.95754
$41$	6.06174	0.946686	0.473343	−	0.880878i	$-0.343047\pi$
$41$	6.06174	0.946686	0.473343	+	0.880878i	$0.343047\pi$
$42$	−2.38078	−0.367362
$43$	9.54562	1.45569	0.727847	−	0.685740i	$-0.240521\pi$
$43$	9.54562	1.45569	0.727847	+	0.685740i	$0.240521\pi$
$44$	−30.1238	−4.54133
$45$	2.79988	0.417381
$46$	2.70316	0.398559
$47$	−7.68018	−1.12027	−0.560135	−	0.828402i	$-0.689251\pi$
$47$	−7.68018	−1.12027	−0.560135	+	0.828402i	$0.689251\pi$
$48$	−13.5509	−1.95590
$49$	−6.22430	−0.889186
$50$	7.67515	1.08543
$51$	−4.80704	−0.673120
$52$	−19.7233	−2.73512
$53$	−9.73506	−1.33721	−0.668607	−	0.743616i	$-0.733109\pi$
$53$	−9.73506	−1.33721	−0.668607	+	0.743616i	$0.733109\pi$
$54$	−2.70316	−0.367854
$55$	−15.8926	−2.14295
$56$	7.87341	1.05213
$57$	−6.68378	−0.885288
$58$	−2.70316	−0.354942
$59$	5.14558	0.669898	0.334949	−	0.942236i	$-0.391281\pi$
$59$	5.14558	0.669898	0.334949	+	0.942236i	$0.391281\pi$
$60$	−14.8592	−1.91831
$61$	−7.99562	−1.02373	−0.511867	−	0.859065i	$-0.671046\pi$
$61$	−7.99562	−1.02373	−0.511867	+	0.859065i	$0.671046\pi$
$62$	2.10578	0.267434
$63$	0.880738	0.110963
$64$	23.5855	2.94819
$65$	−10.4055	−1.29064
$66$	15.3436	1.88866
$67$	−8.36073	−1.02143	−0.510713	−	0.859751i	$-0.670619\pi$
$67$	−8.36073	−1.02143	−0.510713	+	0.859751i	$0.670619\pi$
$68$	25.5113	3.09370
$69$	−1.00000	−0.120386
$70$	6.66589	0.796726
$71$	8.52656	1.01192	0.505958	−	0.862558i	$-0.331139\pi$
$71$	8.52656	1.01192	0.505958	+	0.862558i	$0.331139\pi$
$72$	8.93955	1.05354
$73$	−12.6677	−1.48264	−0.741321	−	0.671150i	$-0.765801\pi$
$73$	−12.6677	−1.48264	−0.741321	+	0.671150i	$0.765801\pi$
$74$	−22.0301	−2.56095
$75$	−2.83932	−0.327857
$76$	35.4713	4.06884
$77$	−4.99921	−0.569713
$78$	10.0460	1.13749
$79$	15.1051	1.69945	0.849726	−	0.527224i	$-0.176767\pi$
$79$	15.1051	1.69945	0.849726	+	0.527224i	$0.176767\pi$
$80$	37.9409	4.24192
$81$	1.00000	0.111111
$82$	16.3859	1.80952
$83$	−0.302272	−0.0331786	−0.0165893	−	0.999862i	$-0.505281\pi$
$83$	−0.302272	−0.0331786	−0.0165893	+	0.999862i	$0.505281\pi$
$84$	−4.67414	−0.509991
$85$	13.4591	1.45985
$86$	25.8033	2.78245
$87$	1.00000	0.107211
$88$	−50.7423	−5.40915
$89$	−10.7142	−1.13570	−0.567852	−	0.823131i	$-0.692225\pi$
$89$	−10.7142	−1.13570	−0.567852	+	0.823131i	$0.692225\pi$
$90$	7.56852	0.797792
$91$	−3.27318	−0.343123
$92$	5.30708	0.553301
$93$	−0.779005	−0.0807791
$94$	−20.7608	−2.14131
$95$	18.7138	1.91999
$96$	−18.7511	−1.91378
$97$	−0.884027	−0.0897593	−0.0448797	−	0.998992i	$-0.514290\pi$
$97$	−0.884027	−0.0897593	−0.0448797	+	0.998992i	$0.514290\pi$
$98$	−16.8253	−1.69961
$99$	−5.67616	−0.570475
$100$	15.0685	1.50685
$101$	−1.36093	−0.135418	−0.0677089	−	0.997705i	$-0.521569\pi$
$101$	−1.36093	−0.135418	−0.0677089	+	0.997705i	$0.521569\pi$
$102$	−12.9942	−1.28662
$103$	−5.31264	−0.523470	−0.261735	−	0.965140i	$-0.584295\pi$
$103$	−5.31264	−0.523470	−0.261735	+	0.965140i	$0.584295\pi$
$104$	−33.2230	−3.25779
$105$	−2.46596	−0.240653
$106$	−26.3154	−2.55598
$107$	7.83080	0.757032	0.378516	−	0.925595i	$-0.376434\pi$
$107$	7.83080	0.757032	0.378516	+	0.925595i	$0.376434\pi$
$108$	−5.30708	−0.510674
$109$	11.2420	1.07679	0.538393	−	0.842694i	$-0.319032\pi$
$109$	11.2420	1.07679	0.538393	+	0.842694i	$0.319032\pi$
$110$	−42.9601	−4.09609
$111$	8.14977	0.773542
$112$	11.9348	1.12773
$113$	−17.4918	−1.64549	−0.822745	−	0.568411i	$-0.807558\pi$
$113$	−17.4918	−1.64549	−0.822745	+	0.568411i	$0.807558\pi$
$114$	−18.0673	−1.69216
$115$	2.79988	0.261090
$116$	−5.30708	−0.492750
$117$	−3.71641	−0.343582
$118$	13.9093	1.28046
$119$	4.23374	0.388106
$120$	−25.0297	−2.28489
$121$	21.2188	1.92898
$122$	−21.6134	−1.95679
$123$	−6.06174	−0.546569
$124$	4.13424	0.371266
$125$	−6.04963	−0.541095
$126$	2.38078	0.212096
$127$	0.206399	0.0183149	0.00915747	−	0.999958i	$-0.497085\pi$
$127$	0.206399	0.0183149	0.00915747	+	0.999958i	$0.497085\pi$
$128$	26.2532	2.32048
$129$	−9.54562	−0.840445
$130$	−28.1277	−2.46696
$131$	9.50384	0.830354	0.415177	−	0.909741i	$-0.363720\pi$
$131$	9.50384	0.830354	0.415177	+	0.909741i	$0.363720\pi$
$132$	30.1238	2.62194
$133$	5.88666	0.510438
$134$	−22.6004	−1.95238
$135$	−2.79988	−0.240975
$136$	42.9728	3.68488
$137$	4.27725	0.365430	0.182715	−	0.983166i	$-0.441511\pi$
$137$	4.27725	0.365430	0.182715	+	0.983166i	$0.441511\pi$
$138$	−2.70316	−0.230108
$139$	−9.47109	−0.803327	−0.401663	−	0.915787i	$-0.631568\pi$
$139$	−9.47109	−0.803327	−0.401663	+	0.915787i	$0.631568\pi$
$140$	13.0870	1.10606
$141$	7.68018	0.646788
$142$	23.0487	1.93420
$143$	21.0949	1.76405
$144$	13.5509	1.12924
$145$	−2.79988	−0.232517
$146$	−34.2428	−2.83396
$147$	6.22430	0.513372
$148$	−43.2514	−3.55525
$149$	−20.3448	−1.66671	−0.833354	−	0.552740i	$-0.813582\pi$
$149$	−20.3448	−1.66671	−0.833354	+	0.552740i	$0.813582\pi$
$150$	−7.67515	−0.626673
$151$	−14.3715	−1.16953	−0.584766	−	0.811202i	$-0.698814\pi$
$151$	−14.3715	−1.16953	−0.584766	+	0.811202i	$0.698814\pi$
$152$	59.7500	4.84636
$153$	4.80704	0.388626
$154$	−13.5137	−1.08896
$155$	2.18112	0.175192
$156$	19.7233	1.57912
$157$	−18.9351	−1.51118	−0.755592	−	0.655043i	$-0.772651\pi$
$157$	−18.9351	−1.51118	−0.755592	+	0.655043i	$0.772651\pi$
$158$	40.8314	3.24837
$159$	9.73506	0.772041
$160$	52.5009	4.15056
$161$	0.880738	0.0694119
$162$	2.70316	0.212380
$163$	12.4920	0.978447	0.489224	−	0.872158i	$-0.337280\pi$
$163$	12.4920	0.978447	0.489224	+	0.872158i	$0.337280\pi$
$164$	32.1701	2.51207
$165$	15.8926	1.23723
$166$	−0.817089	−0.0634184
$167$	8.77674	0.679165	0.339582	−	0.940576i	$-0.389714\pi$
$167$	8.77674	0.679165	0.339582	+	0.940576i	$0.389714\pi$
$168$	−7.87341	−0.607447
$169$	0.811682	0.0624371
$170$	36.3822	2.79038
$171$	6.68378	0.511121
$172$	50.6593	3.86274
$173$	14.7668	1.12270	0.561351	−	0.827578i	$-0.310282\pi$
$173$	14.7668	1.12270	0.561351	+	0.827578i	$0.310282\pi$
$174$	2.70316	0.204926
$175$	2.50070	0.189035
$176$	−76.9170	−5.79784
$177$	−5.14558	−0.386766
$178$	−28.9622	−2.17081
$179$	−7.96536	−0.595359	−0.297679	−	0.954666i	$-0.596213\pi$
$179$	−7.96536	−0.595359	−0.297679	+	0.954666i	$0.596213\pi$
$180$	14.8592	1.10754
$181$	10.2864	0.764579	0.382289	−	0.924043i	$-0.375136\pi$
$181$	10.2864	0.764579	0.382289	+	0.924043i	$0.375136\pi$
$182$	−8.84794	−0.655853
$183$	7.99562	0.591053
$184$	8.93955	0.659033
$185$	−22.8184	−1.67764
$186$	−2.10578	−0.154403
$187$	−27.2855	−1.99531
$188$	−40.7593	−2.97268
$189$	−0.880738	−0.0640643
$190$	50.5863	3.66992
$191$	23.0537	1.66811	0.834054	−	0.551683i	$-0.186014\pi$
$191$	23.0537	1.66811	0.834054	+	0.551683i	$0.186014\pi$
$192$	−23.5855	−1.70214
$193$	5.67387	0.408414	0.204207	−	0.978928i	$-0.434538\pi$
$193$	5.67387	0.408414	0.204207	+	0.978928i	$0.434538\pi$
$194$	−2.38967	−0.171568
$195$	10.4055	0.745153
$196$	−33.0328	−2.35949
$197$	7.96762	0.567669	0.283835	−	0.958873i	$-0.408393\pi$
$197$	7.96762	0.567669	0.283835	+	0.958873i	$0.408393\pi$
$198$	−15.3436	−1.09042
$199$	−6.95306	−0.492889	−0.246445	−	0.969157i	$-0.579262\pi$
$199$	−6.95306	−0.492889	−0.246445	+	0.969157i	$0.579262\pi$
$200$	25.3823	1.79480
$201$	8.36073	0.589721
$202$	−3.67882	−0.258841
$203$	−0.880738	−0.0618157
$204$	−25.5113	−1.78615
$205$	16.9722	1.18539
$206$	−14.3609	−1.00057
$207$	1.00000	0.0695048
$208$	−50.3607	−3.49188
$209$	−37.9382	−2.62424
$210$	−6.66589	−0.459990
$211$	5.75864	0.396441	0.198221	−	0.980157i	$-0.436484\pi$
$211$	5.75864	0.396441	0.198221	+	0.980157i	$0.436484\pi$
$212$	−51.6647	−3.54835
$213$	−8.52656	−0.584230
$214$	21.1679	1.44701
$215$	26.7266	1.82274
$216$	−8.93955	−0.608260
$217$	0.686100	0.0465755
$218$	30.3889	2.05819
$219$	12.6677	0.856004
$220$	−84.3430	−5.68640
$221$	−17.8649	−1.20172
$222$	22.0301	1.47857
$223$	12.0916	0.809713	0.404856	−	0.914380i	$-0.367322\pi$
$223$	12.0916	0.809713	0.404856	+	0.914380i	$0.367322\pi$
$224$	16.5148	1.10344
$225$	2.83932	0.189288
$226$	−47.2831	−3.14523
$227$	−27.0451	−1.79505	−0.897523	−	0.440968i	$-0.854635\pi$
$227$	−27.0451	−1.79505	−0.897523	+	0.440968i	$0.854635\pi$
$228$	−35.4713	−2.34914
$229$	−5.32014	−0.351565	−0.175782	−	0.984429i	$-0.556245\pi$
$229$	−5.32014	−0.351565	−0.175782	+	0.984429i	$0.556245\pi$
$230$	7.56852	0.499054
$231$	4.99921	0.328924
$232$	−8.93955	−0.586911
$233$	23.8743	1.56406	0.782028	−	0.623244i	$-0.214186\pi$
$233$	23.8743	1.56406	0.782028	+	0.623244i	$0.214186\pi$
$234$	−10.0460	−0.656730
$235$	−21.5036	−1.40274
$236$	27.3080	1.77760
$237$	−15.1051	−0.981179
$238$	11.4445	0.741836
$239$	−8.24781	−0.533506	−0.266753	−	0.963765i	$-0.585951\pi$
$239$	−8.24781	−0.533506	−0.266753	+	0.963765i	$0.585951\pi$
$240$	−37.9409	−2.44907
$241$	10.5594	0.680192	0.340096	−	0.940391i	$-0.389540\pi$
$241$	10.5594	0.680192	0.340096	+	0.940391i	$0.389540\pi$
$242$	57.3577	3.68709
$243$	−1.00000	−0.0641500
$244$	−42.4334	−2.71652
$245$	−17.4273	−1.11339
$246$	−16.3859	−1.04472
$247$	−24.8396	−1.58051
$248$	6.96396	0.442212
$249$	0.302272	0.0191557
$250$	−16.3531	−1.03426
$251$	−15.9674	−1.00785	−0.503927	−	0.863746i	$-0.668112\pi$
$251$	−15.9674	−1.00785	−0.503927	+	0.863746i	$0.668112\pi$
$252$	4.67414	0.294443
$253$	−5.67616	−0.356857
$254$	0.557929	0.0350076
$255$	−13.4591	−0.842843
$256$	23.7956	1.48722
$257$	−5.13834	−0.320521	−0.160260	−	0.987075i	$-0.551233\pi$
$257$	−5.13834	−0.320521	−0.160260	+	0.987075i	$0.551233\pi$
$258$	−25.8033	−1.60645
$259$	−7.17782	−0.446008
$260$	−55.2227	−3.42477
$261$	−1.00000	−0.0618984
$262$	25.6904	1.58716
$263$	22.1102	1.36337	0.681687	−	0.731644i	$-0.261246\pi$
$263$	22.1102	1.36337	0.681687	+	0.731644i	$0.261246\pi$
$264$	50.7423	3.12297
$265$	−27.2570	−1.67438
$266$	15.9126	0.975663
$267$	10.7142	0.655699
$268$	−44.3710	−2.71039
$269$	20.1023	1.22566	0.612828	−	0.790216i	$-0.290032\pi$
$269$	20.1023	1.22566	0.612828	+	0.790216i	$0.290032\pi$
$270$	−7.56852	−0.460606
$271$	6.90145	0.419233	0.209617	−	0.977784i	$-0.432778\pi$
$271$	6.90145	0.419233	0.209617	+	0.977784i	$0.432778\pi$
$272$	65.1397	3.94967
$273$	3.27318	0.198102
$274$	11.5621	0.698491
$275$	−16.1165	−0.971859
$276$	−5.30708	−0.319448
$277$	24.5794	1.47683	0.738416	−	0.674345i	$-0.235574\pi$
$277$	24.5794	1.47683	0.738416	+	0.674345i	$0.235574\pi$
$278$	−25.6019	−1.53550
$279$	0.779005	0.0466378
$280$	22.0446	1.31742
$281$	−17.2690	−1.03018	−0.515090	−	0.857136i	$-0.672241\pi$
$281$	−17.2690	−1.03018	−0.515090	+	0.857136i	$0.672241\pi$
$282$	20.7608	1.23629
$283$	−7.22081	−0.429232	−0.214616	−	0.976698i	$-0.568850\pi$
$283$	−7.22081	−0.429232	−0.214616	+	0.976698i	$0.568850\pi$
$284$	45.2511	2.68516
$285$	−18.7138	−1.10851
$286$	57.0229	3.37184
$287$	5.33881	0.315140
$288$	18.7511	1.10492
$289$	6.10760	0.359271
$290$	−7.56852	−0.444439
$291$	0.884027	0.0518226
$292$	−67.2285	−3.93425
$293$	−18.2359	−1.06535	−0.532677	−	0.846319i	$-0.678814\pi$
$293$	−18.2359	−1.06535	−0.532677	+	0.846319i	$0.678814\pi$
$294$	16.8253	0.981270
$295$	14.4070	0.838809
$296$	−72.8553	−4.23463
$297$	5.67616	0.329364
$298$	−54.9951	−3.18578
$299$	−3.71641	−0.214925
$300$	−15.0685	−0.869981
$301$	8.40720	0.484583
$302$	−38.8484	−2.23547
$303$	1.36093	0.0781835
$304$	90.5712	5.19461
$305$	−22.3868	−1.28186
$306$	12.9942	0.742828
$307$	−14.8966	−0.850193	−0.425097	−	0.905148i	$-0.639760\pi$
$307$	−14.8966	−0.850193	−0.425097	+	0.905148i	$0.639760\pi$
$308$	−26.5312	−1.51175
$309$	5.31264	0.302226
$310$	5.89592	0.334866
$311$	−1.07620	−0.0610259	−0.0305129	−	0.999534i	$-0.509714\pi$
$311$	−1.07620	−0.0610259	−0.0305129	+	0.999534i	$0.509714\pi$
$312$	33.2230	1.88088
$313$	−24.6270	−1.39200	−0.696000	−	0.718042i	$-0.745039\pi$
$313$	−24.6270	−1.39200	−0.696000	+	0.718042i	$0.745039\pi$
$314$	−51.1846	−2.88851
$315$	2.46596	0.138941
$316$	80.1637	4.50956
$317$	10.3442	0.580988	0.290494	−	0.956877i	$-0.406180\pi$
$317$	10.3442	0.580988	0.290494	+	0.956877i	$0.406180\pi$
$318$	26.3154	1.47570
$319$	5.67616	0.317804
$320$	66.0367	3.69156
$321$	−7.83080	−0.437073
$322$	2.38078	0.132676
$323$	32.1292	1.78771
$324$	5.30708	0.294838
$325$	−10.5521	−0.585324
$326$	33.7678	1.87023
$327$	−11.2420	−0.621683
$328$	54.1893	2.99210
$329$	−6.76423	−0.372924
$330$	42.9601	2.36488
$331$	−14.0821	−0.774025	−0.387012	−	0.922075i	$-0.626493\pi$
$331$	−14.0821	−0.774025	−0.387012	+	0.922075i	$0.626493\pi$
$332$	−1.60418	−0.0880408
$333$	−8.14977	−0.446605
$334$	23.7249	1.29817
$335$	−23.4090	−1.27897
$336$	−11.9348	−0.651096
$337$	−0.569964	−0.0310479	−0.0155240	−	0.999879i	$-0.504942\pi$
$337$	−0.569964	−0.0310479	−0.0155240	+	0.999879i	$0.504942\pi$
$338$	2.19411	0.119344
$339$	17.4918	0.950024
$340$	71.4286	3.87376
$341$	−4.42176	−0.239452
$342$	18.0673	0.976969
$343$	−11.6471	−0.628887
$344$	85.3336	4.60088
$345$	−2.79988	−0.150740
$346$	39.9171	2.14596
$347$	−12.4225	−0.666877	−0.333438	−	0.942772i	$-0.608209\pi$
$347$	−12.4225	−0.666877	−0.333438	+	0.942772i	$0.608209\pi$
$348$	5.30708	0.284489
$349$	−28.4638	−1.52363	−0.761816	−	0.647793i	$-0.775692\pi$
$349$	−28.4638	−1.52363	−0.761816	+	0.647793i	$0.775692\pi$
$350$	6.75980	0.361326
$351$	3.71641	0.198367
$352$	−106.434	−5.67297
$353$	27.0042	1.43729	0.718644	−	0.695378i	$-0.244763\pi$
$353$	27.0042	1.43729	0.718644	+	0.695378i	$0.244763\pi$
$354$	−13.9093	−0.739273
$355$	23.8733	1.26706
$356$	−56.8611	−3.01363
$357$	−4.23374	−0.224073
$358$	−21.5316	−1.13798
$359$	14.0693	0.742551	0.371276	−	0.928523i	$-0.378921\pi$
$359$	14.0693	0.742551	0.371276	+	0.928523i	$0.378921\pi$
$360$	25.0297	1.31918
$361$	25.6729	1.35120
$362$	27.8057	1.46143
$363$	−21.2188	−1.11370
$364$	−17.3710	−0.910489
$365$	−35.4680	−1.85648
$366$	21.6134	1.12975
$367$	34.8397	1.81862	0.909310	−	0.416120i	$-0.136610\pi$
$367$	34.8397	1.81862	0.909310	+	0.416120i	$0.136610\pi$
$368$	13.5509	0.706389
$369$	6.06174	0.315562
$370$	−61.6817	−3.20668
$371$	−8.57404	−0.445142
$372$	−4.13424	−0.214350
$373$	22.0794	1.14323	0.571613	−	0.820523i	$-0.306318\pi$
$373$	22.0794	1.14323	0.571613	+	0.820523i	$0.306318\pi$
$374$	−73.7571	−3.81389
$375$	6.04963	0.312402
$376$	−68.6574	−3.54073
$377$	3.71641	0.191405
$378$	−2.38078	−0.122454
$379$	−7.46769	−0.383590	−0.191795	−	0.981435i	$-0.561431\pi$
$379$	−7.46769	−0.383590	−0.191795	+	0.981435i	$0.561431\pi$
$380$	99.3154	5.09477
$381$	−0.206399	−0.0105741
$382$	62.3178	3.18846
$383$	−30.9640	−1.58218	−0.791092	−	0.611697i	$-0.790487\pi$
$383$	−30.9640	−1.58218	−0.791092	+	0.611697i	$0.790487\pi$
$384$	−26.2532	−1.33973
$385$	−13.9972	−0.713363
$386$	15.3374	0.780652
$387$	9.54562	0.485231
$388$	−4.69160	−0.238180
$389$	−20.5067	−1.03973	−0.519864	−	0.854249i	$-0.674018\pi$
$389$	−20.5067	−1.03973	−0.519864	+	0.854249i	$0.674018\pi$
$390$	28.1277	1.42430
$391$	4.80704	0.243102
$392$	−55.6425	−2.81037
$393$	−9.50384	−0.479405
$394$	21.5378	1.08506
$395$	42.2924	2.12796
$396$	−30.1238	−1.51378
$397$	−18.4473	−0.925843	−0.462922	−	0.886399i	$-0.653199\pi$
$397$	−18.4473	−0.925843	−0.462922	+	0.886399i	$0.653199\pi$
$398$	−18.7952	−0.942120
$399$	−5.88666	−0.294701
$400$	38.4754	1.92377
$401$	−15.7291	−0.785475	−0.392738	−	0.919651i	$-0.628472\pi$
$401$	−15.7291	−0.785475	−0.392738	+	0.919651i	$0.628472\pi$
$402$	22.6004	1.12721
$403$	−2.89510	−0.144215
$404$	−7.22257	−0.359336
$405$	2.79988	0.139127
$406$	−2.38078	−0.118156
$407$	46.2594	2.29299
$408$	−42.9728	−2.12747
$409$	−7.14903	−0.353497	−0.176748	−	0.984256i	$-0.556558\pi$
$409$	−7.14903	−0.353497	−0.176748	+	0.984256i	$0.556558\pi$
$410$	45.8785	2.26578
$411$	−4.27725	−0.210981
$412$	−28.1946	−1.38905
$413$	4.53191	0.223001
$414$	2.70316	0.132853
$415$	−0.846325	−0.0415444
$416$	−69.6869	−3.41668
$417$	9.47109	0.463801
$418$	−102.553	−5.01603
$419$	−14.7980	−0.722928	−0.361464	−	0.932386i	$-0.617723\pi$
$419$	−14.7980	−0.722928	−0.361464	+	0.932386i	$0.617723\pi$
$420$	−13.0870	−0.638582
$421$	6.98352	0.340356	0.170178	−	0.985413i	$-0.445566\pi$
$421$	6.98352	0.340356	0.170178	+	0.985413i	$0.445566\pi$
$422$	15.5665	0.757767
$423$	−7.68018	−0.373423
$424$	−87.0271	−4.22641
$425$	13.6487	0.662061
$426$	−23.0487	−1.11671
$427$	−7.04205	−0.340789
$428$	41.5586	2.00881
$429$	−21.0949	−1.01847
$430$	72.2463	3.48402
$431$	18.2431	0.878737	0.439368	−	0.898307i	$-0.355202\pi$
$431$	18.2431	0.878737	0.439368	+	0.898307i	$0.355202\pi$
$432$	−13.5509	−0.651968
$433$	−6.54148	−0.314364	−0.157182	−	0.987570i	$-0.550241\pi$
$433$	−6.54148	−0.314364	−0.157182	+	0.987570i	$0.550241\pi$
$434$	1.85464	0.0890255
$435$	2.79988	0.134244
$436$	59.6620	2.85729
$437$	6.68378	0.319728
$438$	34.2428	1.63619
$439$	−24.9232	−1.18952	−0.594760	−	0.803904i	$-0.702753\pi$
$439$	−24.9232	−1.18952	−0.594760	+	0.803904i	$0.702753\pi$
$440$	−142.072	−6.77303
$441$	−6.22430	−0.296395
$442$	−48.2917	−2.29700
$443$	−31.7227	−1.50719	−0.753594	−	0.657340i	$-0.771682\pi$
$443$	−31.7227	−1.50719	−0.753594	+	0.657340i	$0.771682\pi$
$444$	43.2514	2.05262
$445$	−29.9985	−1.42207
$446$	32.6855	1.54770
$447$	20.3448	0.962274
$448$	20.7727	0.981417
$449$	27.6235	1.30363	0.651816	−	0.758377i	$-0.274008\pi$
$449$	27.6235	1.30363	0.651816	+	0.758377i	$0.274008\pi$
$450$	7.67515	0.361810
$451$	−34.4074	−1.62018
$452$	−92.8303	−4.36637
$453$	14.3715	0.675230
$454$	−73.1072	−3.43109
$455$	−9.16452	−0.429639
$456$	−59.7500	−2.79805
$457$	3.37558	0.157903	0.0789516	−	0.996878i	$-0.474843\pi$
$457$	3.37558	0.157903	0.0789516	+	0.996878i	$0.474843\pi$
$458$	−14.3812	−0.671989
$459$	−4.80704	−0.224373
$460$	14.8592	0.692812
$461$	39.9849	1.86228	0.931140	−	0.364661i	$-0.118815\pi$
$461$	39.9849	1.86228	0.931140	+	0.364661i	$0.118815\pi$
$462$	13.5137	0.628713
$463$	9.18722	0.426966	0.213483	−	0.976947i	$-0.431519\pi$
$463$	9.18722	0.426966	0.213483	+	0.976947i	$0.431519\pi$
$464$	−13.5509	−0.629085
$465$	−2.18112	−0.101147
$466$	64.5360	2.98957
$467$	13.0823	0.605378	0.302689	−	0.953089i	$-0.402116\pi$
$467$	13.0823	0.605378	0.302689	+	0.953089i	$0.402116\pi$
$468$	−19.7233	−0.911708
$469$	−7.36362	−0.340020
$470$	−58.1276	−2.68123
$471$	18.9351	0.872482
$472$	45.9992	2.11729
$473$	−54.1825	−2.49131
$474$	−40.8314	−1.87545
$475$	18.9774	0.870743
$476$	22.4688	1.02986
$477$	−9.73506	−0.445738
$478$	−22.2951	−1.01976
$479$	41.5385	1.89794	0.948972	−	0.315361i	$-0.102125\pi$
$479$	41.5385	1.89794	0.948972	+	0.315361i	$0.102125\pi$
$480$	−52.5009	−2.39633
$481$	30.2879	1.38101
$482$	28.5438	1.30013
$483$	−0.880738	−0.0400750
$484$	112.610	5.11862
$485$	−2.47517	−0.112392
$486$	−2.70316	−0.122618
$487$	22.4277	1.01630	0.508148	−	0.861270i	$-0.330330\pi$
$487$	22.4277	1.01630	0.508148	+	0.861270i	$0.330330\pi$
$488$	−71.4773	−3.23563
$489$	−12.4920	−0.564907
$490$	−47.1088	−2.12816
$491$	13.8826	0.626513	0.313256	−	0.949669i	$-0.398580\pi$
$491$	13.8826	0.626513	0.313256	+	0.949669i	$0.398580\pi$
$492$	−32.1701	−1.45034
$493$	−4.80704	−0.216498
$494$	−67.1455	−3.02102
$495$	−15.8926	−0.714317
$496$	10.5562	0.473988
$497$	7.50967	0.336855
$498$	0.817089	0.0366146
$499$	−10.9367	−0.489592	−0.244796	−	0.969575i	$-0.578721\pi$
$499$	−10.9367	−0.489592	−0.244796	+	0.969575i	$0.578721\pi$
$500$	−32.1059	−1.43582
$501$	−8.77674	−0.392116
$502$	−43.1625	−1.92644
$503$	−3.54058	−0.157867	−0.0789334	−	0.996880i	$-0.525151\pi$
$503$	−3.54058	−0.157867	−0.0789334	+	0.996880i	$0.525151\pi$
$504$	7.87341	0.350709
$505$	−3.81044	−0.169563
$506$	−15.3436	−0.682105
$507$	−0.811682	−0.0360481
$508$	1.09537	0.0485994
$509$	12.3607	0.547878	0.273939	−	0.961747i	$-0.411673\pi$
$509$	12.3607	0.547878	0.273939	+	0.961747i	$0.411673\pi$
$510$	−36.3822	−1.61103
$511$	−11.1569	−0.493554
$512$	11.8168	0.522233
$513$	−6.68378	−0.295096
$514$	−13.8898	−0.612651
$515$	−14.8748	−0.655460
$516$	−50.6593	−2.23015
$517$	43.5939	1.91726
$518$	−19.4028	−0.852509
$519$	−14.7668	−0.648192
$520$	−93.0205	−4.07922
$521$	34.5365	1.51307	0.756535	−	0.653953i	$-0.226891\pi$
$521$	34.5365	1.51307	0.756535	+	0.653953i	$0.226891\pi$
$522$	−2.70316	−0.118314
$523$	31.4234	1.37405	0.687024	−	0.726634i	$-0.258917\pi$
$523$	31.4234	1.37405	0.687024	+	0.726634i	$0.258917\pi$
$524$	50.4376	2.20338
$525$	−2.50070	−0.109140
$526$	59.7675	2.60599
$527$	3.74471	0.163122
$528$	76.9170	3.34738
$529$	1.00000	0.0434783
$530$	−73.6801	−3.20046
$531$	5.14558	0.223299
$532$	31.2409	1.35447
$533$	−22.5279	−0.975792
$534$	28.9622	1.25332
$535$	21.9253	0.947913
$536$	−74.7412	−3.22833
$537$	7.96536	0.343730
$538$	54.3396	2.34275
$539$	35.3301	1.52178
$540$	−14.8592	−0.639437
$541$	28.3717	1.21980	0.609898	−	0.792480i	$-0.291210\pi$
$541$	28.3717	1.21980	0.609898	+	0.792480i	$0.291210\pi$
$542$	18.6557	0.801332
$543$	−10.2864	−0.441430
$544$	90.1374	3.86461
$545$	31.4762	1.34829
$546$	8.84794	0.378657
$547$	20.4656	0.875046	0.437523	−	0.899207i	$-0.355856\pi$
$547$	20.4656	0.875046	0.437523	+	0.899207i	$0.355856\pi$
$548$	22.6997	0.969682
$549$	−7.99562	−0.341245
$550$	−43.5653	−1.85763
$551$	−6.68378	−0.284738
$552$	−8.93955	−0.380493
$553$	13.3036	0.565727
$554$	66.4420	2.82285
$555$	22.8184	0.968586
$556$	−50.2638	−2.13166
$557$	33.3630	1.41363	0.706817	−	0.707396i	$-0.250130\pi$
$557$	33.3630	1.41363	0.706817	+	0.707396i	$0.250130\pi$
$558$	2.10578	0.0891446
$559$	−35.4754	−1.50045
$560$	33.4160	1.41208
$561$	27.2855	1.15199
$562$	−46.6808	−1.96911
$563$	21.5508	0.908257	0.454129	−	0.890936i	$-0.349951\pi$
$563$	21.5508	0.908257	0.454129	+	0.890936i	$0.349951\pi$
$564$	40.7593	1.71628
$565$	−48.9749	−2.06039
$566$	−19.5190	−0.820445
$567$	0.880738	0.0369875
$568$	76.2236	3.19827
$569$	12.9510	0.542934	0.271467	−	0.962448i	$-0.412491\pi$
$569$	12.9510	0.542934	0.271467	+	0.962448i	$0.412491\pi$
$570$	−50.5863	−2.11883
$571$	3.76335	0.157491	0.0787456	−	0.996895i	$-0.474909\pi$
$571$	3.76335	0.157491	0.0787456	+	0.996895i	$0.474909\pi$
$572$	111.952	4.68096
$573$	−23.0537	−0.963082
$574$	14.4317	0.602366
$575$	2.83932	0.118408
$576$	23.5855	0.982731
$577$	9.05091	0.376794	0.188397	−	0.982093i	$-0.439671\pi$
$577$	9.05091	0.376794	0.188397	+	0.982093i	$0.439671\pi$
$578$	16.5098	0.686718
$579$	−5.67387	−0.235798
$580$	−14.8592	−0.616993
$581$	−0.266222	−0.0110448
$582$	2.38967	0.0990549
$583$	55.2578	2.28854
$584$	−113.244	−4.68605
$585$	−10.4055	−0.430214
$586$	−49.2946	−2.03634
$587$	−7.59812	−0.313608	−0.156804	−	0.987630i	$-0.550119\pi$
$587$	−7.59812	−0.313608	−0.156804	+	0.987630i	$0.550119\pi$
$588$	33.0328	1.36225
$589$	5.20670	0.214538
$590$	38.9445	1.60332
$591$	−7.96762	−0.327744
$592$	−110.437	−4.53892
$593$	7.95422	0.326641	0.163320	−	0.986573i	$-0.447780\pi$
$593$	7.95422	0.326641	0.163320	+	0.986573i	$0.447780\pi$
$594$	15.3436	0.629554
$595$	11.8540	0.485965
$596$	−107.971	−4.42267
$597$	6.95306	0.284570
$598$	−10.0460	−0.410813
$599$	31.2856	1.27830	0.639148	−	0.769084i	$-0.279287\pi$
$599$	31.2856	1.27830	0.639148	+	0.769084i	$0.279287\pi$
$600$	−25.3823	−1.03623
$601$	14.4217	0.588274	0.294137	−	0.955763i	$-0.404968\pi$
$601$	14.4217	0.588274	0.294137	+	0.955763i	$0.404968\pi$
$602$	22.7260	0.926242
$603$	−8.36073	−0.340475
$604$	−76.2704	−3.10340
$605$	59.4100	2.41536
$606$	3.67882	0.149442
$607$	−27.1287	−1.10112	−0.550560	−	0.834796i	$-0.685586\pi$
$607$	−27.1287	−1.10112	−0.550560	+	0.834796i	$0.685586\pi$
$608$	125.328	5.08274
$609$	0.880738	0.0356893
$610$	−60.5150	−2.45018
$611$	28.5427	1.15471
$612$	25.5113	1.03123
$613$	−7.58210	−0.306238	−0.153119	−	0.988208i	$-0.548932\pi$
$613$	−7.58210	−0.306238	−0.153119	+	0.988208i	$0.548932\pi$
$614$	−40.2679	−1.62508
$615$	−16.9722	−0.684383
$616$	−44.6907	−1.80064
$617$	40.3076	1.62272	0.811361	−	0.584546i	$-0.198727\pi$
$617$	40.3076	1.62272	0.811361	+	0.584546i	$0.198727\pi$
$618$	14.3609	0.577681
$619$	7.17677	0.288459	0.144229	−	0.989544i	$-0.453930\pi$
$619$	7.17677	0.288459	0.144229	+	0.989544i	$0.453930\pi$
$620$	11.5754	0.464878
$621$	−1.00000	−0.0401286
$622$	−2.90915	−0.116646
$623$	−9.43642	−0.378062
$624$	50.3607	2.01604
$625$	−31.1349	−1.24539
$626$	−66.5707	−2.66070
$627$	37.9382	1.51510
$628$	−100.490	−4.00998
$629$	−39.1762	−1.56206
$630$	6.66589	0.265575
$631$	−13.8537	−0.551506	−0.275753	−	0.961229i	$-0.588927\pi$
$631$	−13.8537	−0.551506	−0.275753	+	0.961229i	$0.588927\pi$
$632$	135.033	5.37131
$633$	−5.75864	−0.228885
$634$	27.9620	1.11051
$635$	0.577892	0.0229329
$636$	51.6647	2.04864
$637$	23.1320	0.916525
$638$	15.3436	0.607457
$639$	8.52656	0.337305
$640$	73.5058	2.90557
$641$	−2.14458	−0.0847056	−0.0423528	−	0.999103i	$-0.513485\pi$
$641$	−2.14458	−0.0847056	−0.0423528	+	0.999103i	$0.513485\pi$
$642$	−21.1679	−0.835431
$643$	−48.1250	−1.89786	−0.948932	−	0.315481i	$-0.897834\pi$
$643$	−48.1250	−1.89786	−0.948932	+	0.315481i	$0.897834\pi$
$644$	4.67414	0.184187
$645$	−26.7266	−1.05236
$646$	86.8503	3.41708
$647$	14.6607	0.576370	0.288185	−	0.957575i	$-0.406948\pi$
$647$	14.6607	0.576370	0.288185	+	0.957575i	$0.406948\pi$
$648$	8.93955	0.351179
$649$	−29.2071	−1.14648
$650$	−28.5240	−1.11880
$651$	−0.686100	−0.0268904
$652$	66.2959	2.59635
$653$	30.0473	1.17584	0.587921	−	0.808918i	$-0.299947\pi$
$653$	30.0473	1.17584	0.587921	+	0.808918i	$0.299947\pi$
$654$	−30.3889	−1.18830
$655$	26.6096	1.03972
$656$	82.1421	3.20711
$657$	−12.6677	−0.494214
$658$	−18.2848	−0.712816
$659$	17.5722	0.684516	0.342258	−	0.939606i	$-0.388808\pi$
$659$	17.5722	0.684516	0.342258	+	0.939606i	$0.388808\pi$
$660$	84.3430	3.28305
$661$	−22.2147	−0.864052	−0.432026	−	0.901861i	$-0.642201\pi$
$661$	−22.2147	−0.864052	−0.432026	+	0.901861i	$0.642201\pi$
$662$	−38.0663	−1.47949
$663$	17.8649	0.693815
$664$	−2.70218	−0.104865
$665$	16.4819	0.639142
$666$	−22.0301	−0.853650
$667$	−1.00000	−0.0387202
$668$	46.5788	1.80219
$669$	−12.0916	−0.467488
$670$	−63.2784	−2.44466
$671$	45.3844	1.75205
$672$	−16.5148	−0.637074
$673$	28.1597	1.08547	0.542737	−	0.839902i	$-0.317388\pi$
$673$	28.1597	1.08547	0.542737	+	0.839902i	$0.317388\pi$
$674$	−1.54070	−0.0593457
$675$	−2.83932	−0.109286
$676$	4.30766	0.165679
$677$	0.245245	0.00942553	0.00471277	−	0.999989i	$-0.498500\pi$
$677$	0.245245	0.00942553	0.00471277	+	0.999989i	$0.498500\pi$
$678$	47.2831	1.81590
$679$	−0.778596	−0.0298798
$680$	120.319	4.61401
$681$	27.0451	1.03637
$682$	−11.9527	−0.457693
$683$	28.9636	1.10826	0.554131	−	0.832430i	$-0.313051\pi$
$683$	28.9636	1.10826	0.554131	+	0.832430i	$0.313051\pi$
$684$	35.4713	1.35628
$685$	11.9758	0.457571
$686$	−31.4841	−1.20207
$687$	5.32014	0.202976
$688$	129.352	4.93149
$689$	36.1795	1.37833
$690$	−7.56852	−0.288129
$691$	−35.3723	−1.34563	−0.672813	−	0.739813i	$-0.734914\pi$
$691$	−35.3723	−1.34563	−0.672813	+	0.739813i	$0.734914\pi$
$692$	78.3687	2.97913
$693$	−4.99921	−0.189904
$694$	−33.5801	−1.27468
$695$	−26.5179	−1.00588
$696$	8.93955	0.338853
$697$	29.1390	1.10372
$698$	−76.9422	−2.91231
$699$	−23.8743	−0.903008
$700$	13.2714	0.501612
$701$	19.9823	0.754722	0.377361	−	0.926066i	$-0.376832\pi$
$701$	19.9823	0.754722	0.377361	+	0.926066i	$0.376832\pi$
$702$	10.0460	0.379164
$703$	−54.4712	−2.05442
$704$	−133.875	−5.04561
$705$	21.5036	0.809872
$706$	72.9966	2.74726
$707$	−1.19862	−0.0450789
$708$	−27.3080	−1.02630
$709$	−13.0449	−0.489911	−0.244956	−	0.969534i	$-0.578773\pi$
$709$	−13.0449	−0.489911	−0.244956	+	0.969534i	$0.578773\pi$
$710$	64.5334	2.42190
$711$	15.1051	0.566484
$712$	−95.7803	−3.58952
$713$	0.779005	0.0291740
$714$	−11.4445	−0.428299
$715$	59.0632	2.20884
$716$	−42.2727	−1.57981
$717$	8.24781	0.308020
$718$	38.0317	1.41933
$719$	8.19259	0.305532	0.152766	−	0.988262i	$-0.451182\pi$
$719$	8.19259	0.305532	0.152766	+	0.988262i	$0.451182\pi$
$720$	37.9409	1.41397
$721$	−4.67905	−0.174257
$722$	69.3978	2.58272
$723$	−10.5594	−0.392709
$724$	54.5905	2.02884
$725$	−2.83932	−0.105450
$726$	−57.3577	−2.12874
$727$	−28.0803	−1.04144	−0.520721	−	0.853727i	$-0.674337\pi$
$727$	−28.0803	−1.04144	−0.520721	+	0.853727i	$0.674337\pi$
$728$	−29.2608	−1.08448
$729$	1.00000	0.0370370
$730$	−95.8758	−3.54852
$731$	45.8862	1.69716
$732$	42.4334	1.56838
$733$	−32.2797	−1.19228	−0.596140	−	0.802881i	$-0.703300\pi$
$733$	−32.2797	−1.19228	−0.596140	+	0.802881i	$0.703300\pi$
$734$	94.1774	3.47615
$735$	17.4273	0.642815
$736$	18.7511	0.691176
$737$	47.4568	1.74809
$738$	16.3859	0.603172
$739$	2.56275	0.0942721	0.0471361	−	0.998888i	$-0.484991\pi$
$739$	2.56275	0.0942721	0.0471361	+	0.998888i	$0.484991\pi$
$740$	−121.099	−4.45168
$741$	24.8396	0.912507
$742$	−23.1770	−0.850855
$743$	35.8227	1.31421	0.657104	−	0.753800i	$-0.271781\pi$
$743$	35.8227	1.31421	0.657104	+	0.753800i	$0.271781\pi$
$744$	−6.96396	−0.255311
$745$	−56.9629	−2.08696
$746$	59.6841	2.18519
$747$	−0.302272	−0.0110595
$748$	−144.806	−5.29464
$749$	6.89689	0.252007
$750$	16.3531	0.597132
$751$	−42.9765	−1.56824	−0.784118	−	0.620612i	$-0.786884\pi$
$751$	−42.9765	−1.56824	−0.784118	+	0.620612i	$0.786884\pi$
$752$	−104.073	−3.79516
$753$	15.9674	0.581885
$754$	10.0460	0.365855
$755$	−40.2383	−1.46442
$756$	−4.67414	−0.169997
$757$	−32.0132	−1.16354	−0.581769	−	0.813354i	$-0.697639\pi$
$757$	−32.0132	−1.16354	−0.581769	+	0.813354i	$0.697639\pi$
$758$	−20.1864	−0.733202
$759$	5.67616	0.206031
$760$	167.293	6.06834
$761$	11.4559	0.415278	0.207639	−	0.978206i	$-0.433422\pi$
$761$	11.4559	0.415278	0.207639	+	0.978206i	$0.433422\pi$
$762$	−0.557929	−0.0202116
$763$	9.90124	0.358449
$764$	122.348	4.42639
$765$	13.4591	0.486616
$766$	−83.7005	−3.02422
$767$	−19.1231	−0.690495
$768$	−23.7956	−0.858648
$769$	−0.0983888	−0.00354799	−0.00177400	−	0.999998i	$-0.500565\pi$
$769$	−0.0983888	−0.00354799	−0.00177400	+	0.999998i	$0.500565\pi$
$770$	−37.8366	−1.36354
$771$	5.13834	0.185053
$772$	30.1117	1.08374
$773$	12.4020	0.446070	0.223035	−	0.974810i	$-0.428404\pi$
$773$	12.4020	0.446070	0.223035	+	0.974810i	$0.428404\pi$
$774$	25.8033	0.927482
$775$	2.21185	0.0794519
$776$	−7.90281	−0.283694
$777$	7.17782	0.257503
$778$	−55.4328	−1.98736
$779$	40.5153	1.45161
$780$	55.2227	1.97729
$781$	−48.3981	−1.73182
$782$	12.9942	0.464671
$783$	1.00000	0.0357371
$784$	−84.3449	−3.01232
$785$	−53.0159	−1.89222
$786$	−25.6904	−0.916346
$787$	26.7197	0.952455	0.476227	−	0.879322i	$-0.342004\pi$
$787$	26.7197	0.952455	0.476227	+	0.879322i	$0.342004\pi$
$788$	42.2848	1.50633
$789$	−22.1102	−0.787145
$790$	114.323	4.06743
$791$	−15.4057	−0.547763
$792$	−50.7423	−1.80305
$793$	29.7150	1.05521
$794$	−49.8660	−1.76968
$795$	27.2570	0.966706
$796$	−36.9004	−1.30790
$797$	20.2834	0.718474	0.359237	−	0.933246i	$-0.383037\pi$
$797$	20.2834	0.718474	0.359237	+	0.933246i	$0.383037\pi$
$798$	−15.9126	−0.563299
$799$	−36.9189	−1.30610
$800$	53.2406	1.88234
$801$	−10.7142	−0.378568
$802$	−42.5184	−1.50138
$803$	71.9039	2.53743
$804$	44.3710	1.56485
$805$	2.46596	0.0869137
$806$	−7.82592	−0.275656
$807$	−20.1023	−0.707633
$808$	−12.1661	−0.428003
$809$	35.7621	1.25733	0.628665	−	0.777676i	$-0.283602\pi$
$809$	35.7621	1.25733	0.628665	+	0.777676i	$0.283602\pi$
$810$	7.56852	0.265931
$811$	26.4097	0.927370	0.463685	−	0.886000i	$-0.346527\pi$
$811$	26.4097	0.927370	0.463685	+	0.886000i	$0.346527\pi$
$812$	−4.67414	−0.164030
$813$	−6.90145	−0.242045
$814$	125.047	4.38288
$815$	34.9760	1.22516
$816$	−65.1397	−2.28034
$817$	63.8008	2.23211
$818$	−19.3250	−0.675682
$819$	−3.27318	−0.114374
$820$	90.0725	3.14547
$821$	21.8673	0.763172	0.381586	−	0.924333i	$-0.375378\pi$
$821$	21.8673	0.763172	0.381586	+	0.924333i	$0.375378\pi$
$822$	−11.5621	−0.403274
$823$	−33.6657	−1.17351	−0.586756	−	0.809764i	$-0.699595\pi$
$823$	−33.6657	−1.17351	−0.586756	+	0.809764i	$0.699595\pi$
$824$	−47.4927	−1.65449
$825$	16.1165	0.561103
$826$	12.2505	0.426249
$827$	−49.4034	−1.71793	−0.858963	−	0.512038i	$-0.828891\pi$
$827$	−49.4034	−1.71793	−0.858963	+	0.512038i	$0.828891\pi$
$828$	5.30708	0.184434
$829$	3.54310	0.123057	0.0615285	−	0.998105i	$-0.480402\pi$
$829$	3.54310	0.123057	0.0615285	+	0.998105i	$0.480402\pi$
$830$	−2.28775	−0.0794090
$831$	−24.5794	−0.852650
$832$	−87.6535	−3.03884
$833$	−29.9204	−1.03668
$834$	25.6019	0.886520
$835$	24.5738	0.850412
$836$	−201.341	−6.96351
$837$	−0.779005	−0.0269264
$838$	−40.0013	−1.38182
$839$	−27.3924	−0.945691	−0.472846	−	0.881145i	$-0.656773\pi$
$839$	−27.3924	−0.945691	−0.472846	+	0.881145i	$0.656773\pi$
$840$	−22.0446	−0.760611
$841$	1.00000	0.0344828
$842$	18.8776	0.650564
$843$	17.2690	0.594775
$844$	30.5615	1.05197
$845$	2.27261	0.0781802
$846$	−20.7608	−0.713770
$847$	18.6882	0.642133
$848$	−131.919	−4.53011
$849$	7.22081	0.247817
$850$	36.8947	1.26548
$851$	−8.14977	−0.279371
$852$	−45.2511	−1.55028
$853$	18.4109	0.630376	0.315188	−	0.949029i	$-0.397932\pi$
$853$	18.4109	0.630376	0.315188	+	0.949029i	$0.397932\pi$
$854$	−19.0358	−0.651391
$855$	18.7138	0.639997
$856$	70.0039	2.39268
$857$	40.3861	1.37956	0.689782	−	0.724018i	$-0.257707\pi$
$857$	40.3861	1.37956	0.689782	+	0.724018i	$0.257707\pi$
$858$	−57.0229	−1.94673
$859$	38.5166	1.31417	0.657085	−	0.753816i	$-0.271789\pi$
$859$	38.5166	1.31417	0.657085	+	0.753816i	$0.271789\pi$
$860$	141.840	4.83670
$861$	−5.33881	−0.181946
$862$	49.3139	1.67964
$863$	22.4884	0.765513	0.382756	−	0.923849i	$-0.374975\pi$
$863$	22.4884	0.765513	0.382756	+	0.923849i	$0.374975\pi$
$864$	−18.7511	−0.637927
$865$	41.3454	1.40578
$866$	−17.6827	−0.600882
$867$	−6.10760	−0.207425
$868$	3.64118	0.123590
$869$	−85.7387	−2.90849
$870$	7.56852	0.256597
$871$	31.0719	1.05283
$872$	100.498	3.40330
$873$	−0.884027	−0.0299198
$874$	18.0673	0.611136
$875$	−5.32814	−0.180124
$876$	67.2285	2.27144
$877$	−2.78341	−0.0939892	−0.0469946	−	0.998895i	$-0.514964\pi$
$877$	−2.78341	−0.0939892	−0.0469946	+	0.998895i	$0.514964\pi$
$878$	−67.3714	−2.27367
$879$	18.2359	0.615082
$880$	−215.358	−7.25973
$881$	−0.347005	−0.0116909	−0.00584544	−	0.999983i	$-0.501861\pi$
$881$	−0.347005	−0.0116909	−0.00584544	+	0.999983i	$0.501861\pi$
$882$	−16.8253	−0.566537
$883$	−31.9999	−1.07688	−0.538442	−	0.842663i	$-0.680987\pi$
$883$	−31.9999	−1.07688	−0.538442	+	0.842663i	$0.680987\pi$
$884$	−94.8104	−3.18882
$885$	−14.4070	−0.484287
$886$	−85.7514	−2.88087
$887$	54.2012	1.81990	0.909949	−	0.414721i	$-0.136121\pi$
$887$	54.2012	1.81990	0.909949	+	0.414721i	$0.136121\pi$
$888$	72.8553	2.44486
$889$	0.181783	0.00609682
$890$	−81.0907	−2.71817
$891$	−5.67616	−0.190158
$892$	64.1710	2.14860
$893$	−51.3326	−1.71778
$894$	54.9951	1.83931
$895$	−22.3020	−0.745475
$896$	23.1222	0.772459
$897$	3.71641	0.124087
$898$	74.6706	2.49179
$899$	−0.779005	−0.0259813
$900$	15.0685	0.502284
$901$	−46.7968	−1.55903
$902$	−93.0088	−3.09685
$903$	−8.40720	−0.279774
$904$	−156.369	−5.20075
$905$	28.8005	0.957363
$906$	38.8484	1.29065
$907$	−8.16651	−0.271164	−0.135582	−	0.990766i	$-0.543290\pi$
$907$	−8.16651	−0.271164	−0.135582	+	0.990766i	$0.543290\pi$
$908$	−143.530	−4.76322
$909$	−1.36093	−0.0451392
$910$	−24.7732	−0.821222
$911$	21.0259	0.696618	0.348309	−	0.937380i	$-0.386756\pi$
$911$	21.0259	0.696618	0.348309	+	0.937380i	$0.386756\pi$
$912$	−90.5712	−2.99911
$913$	1.71574	0.0567828
$914$	9.12474	0.301820
$915$	22.3868	0.740084
$916$	−28.2344	−0.932890
$917$	8.37039	0.276415
$918$	−12.9942	−0.428872
$919$	−12.9335	−0.426638	−0.213319	−	0.976983i	$-0.568427\pi$
$919$	−12.9335	−0.426638	−0.213319	+	0.976983i	$0.568427\pi$
$920$	25.0297	0.825204
$921$	14.8966	0.490859
$922$	108.085	3.55961
$923$	−31.6882	−1.04303
$924$	26.5312	0.872812
$925$	−23.1398	−0.760833
$926$	24.8345	0.816113
$927$	−5.31264	−0.174490
$928$	−18.7511	−0.615536
$929$	−13.5273	−0.443817	−0.221909	−	0.975067i	$-0.571229\pi$
$929$	−13.5273	−0.443817	−0.221909	+	0.975067i	$0.571229\pi$
$930$	−5.89592	−0.193335
$931$	−41.6018	−1.36344
$932$	126.703	4.15028
$933$	1.07620	0.0352333
$934$	35.3636	1.15713
$935$	−76.3961	−2.49842
$936$	−33.2230	−1.08593
$937$	−4.15878	−0.135862	−0.0679308	−	0.997690i	$-0.521640\pi$
$937$	−4.15878	−0.135862	−0.0679308	+	0.997690i	$0.521640\pi$
$938$	−19.9050	−0.649923
$939$	24.6270	0.803671
$940$	−114.121	−3.72222
$941$	−46.9661	−1.53105	−0.765525	−	0.643406i	$-0.777521\pi$
$941$	−46.9661	−1.53105	−0.765525	+	0.643406i	$0.777521\pi$
$942$	51.1846	1.66768
$943$	6.06174	0.197398
$944$	69.7273	2.26943
$945$	−2.46596	−0.0802177
$946$	−146.464	−4.76195
$947$	−6.09656	−0.198112	−0.0990558	−	0.995082i	$-0.531582\pi$
$947$	−6.09656	−0.198112	−0.0990558	+	0.995082i	$0.531582\pi$
$948$	−80.1637	−2.60360
$949$	47.0783	1.52823
$950$	51.2990	1.66436
$951$	−10.3442	−0.335433
$952$	37.8478	1.22665
$953$	−9.32474	−0.302058	−0.151029	−	0.988529i	$-0.548259\pi$
$953$	−9.32474	−0.302058	−0.151029	+	0.988529i	$0.548259\pi$
$954$	−26.3154	−0.851994
$955$	64.5476	2.08871
$956$	−43.7717	−1.41568
$957$	−5.67616	−0.183484
$958$	112.285	3.62777
$959$	3.76713	0.121647
$960$	−66.0367	−2.13132
$961$	−30.3932	−0.980424
$962$	81.8730	2.63969
$963$	7.83080	0.252344
$964$	56.0396	1.80492
$965$	15.8862	0.511393
$966$	−2.38078	−0.0766002
$967$	−43.6266	−1.40294	−0.701468	−	0.712701i	$-0.747472\pi$
$967$	−43.6266	−1.40294	−0.701468	+	0.712701i	$0.747472\pi$
$968$	189.686	6.09675
$969$	−32.1292	−1.03214
$970$	−6.69078	−0.214828
$971$	19.3929	0.622347	0.311173	−	0.950353i	$-0.399278\pi$
$971$	19.3929	0.622347	0.311173	+	0.950353i	$0.399278\pi$
$972$	−5.30708	−0.170225
$973$	−8.34155	−0.267418
$974$	60.6256	1.94257
$975$	10.5521	0.337937
$976$	−108.348	−3.46813
$977$	−58.1111	−1.85914	−0.929569	−	0.368649i	$-0.879820\pi$
$977$	−58.1111	−1.85914	−0.929569	+	0.368649i	$0.879820\pi$
$978$	−33.7678	−1.07978
$979$	60.8155	1.94367
$980$	−92.4879	−2.95442
$981$	11.2420	0.358929
$982$	37.5269	1.19753
$983$	30.4731	0.971942	0.485971	−	0.873975i	$-0.338466\pi$
$983$	30.4731	0.971942	0.485971	+	0.873975i	$0.338466\pi$
$984$	−54.1893	−1.72749
$985$	22.3084	0.710804
$986$	−12.9942	−0.413819
$987$	6.76423	0.215308
$988$	−131.826	−4.19394
$989$	9.54562	0.303533
$990$	−42.9601	−1.36536
$991$	11.8870	0.377603	0.188802	−	0.982015i	$-0.439540\pi$
$991$	11.8870	0.377603	0.188802	+	0.982015i	$0.439540\pi$
$992$	14.6072	0.463780
$993$	14.0821	0.446883
$994$	20.2998	0.643872
$995$	−19.4677	−0.617168
$996$	1.60418	0.0508304
$997$	−33.6336	−1.06519	−0.532593	−	0.846371i	$-0.678782\pi$
$997$	−33.6336	−1.06519	−0.532593	+	0.846371i	$0.678782\pi$
$998$	−29.5635	−0.935818
$999$	8.14977	0.257847

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2001.2.a.l.1.10	✓	11
3.2	odd	2		6003.2.a.m.1.2		11

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2001.2.a.l.1.10	✓	11	1.1	even	1	trivial
6003.2.a.m.1.2		11	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)

\(f(q)\)	\(=\)	\(q+2.70316 q^{2} -1.00000 q^{3} +5.30708 q^{4} +2.79988 q^{5} -2.70316 q^{6} +0.880738 q^{7} +8.93955 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+2.70316 q^{2} -1.00000 q^{3} +5.30708 q^{4} +2.79988 q^{5} -2.70316 q^{6} +0.880738 q^{7} +8.93955 q^{8} +1.00000 q^{9} +7.56852 q^{10} -5.67616 q^{11} -5.30708 q^{12} -3.71641 q^{13} +2.38078 q^{14} -2.79988 q^{15} +13.5509 q^{16} +4.80704 q^{17} +2.70316 q^{18} +6.68378 q^{19} +14.8592 q^{20} -0.880738 q^{21} -15.3436 q^{22} +1.00000 q^{23} -8.93955 q^{24} +2.83932 q^{25} -10.0460 q^{26} -1.00000 q^{27} +4.67414 q^{28} -1.00000 q^{29} -7.56852 q^{30} +0.779005 q^{31} +18.7511 q^{32} +5.67616 q^{33} +12.9942 q^{34} +2.46596 q^{35} +5.30708 q^{36} -8.14977 q^{37} +18.0673 q^{38} +3.71641 q^{39} +25.0297 q^{40} +6.06174 q^{41} -2.38078 q^{42} +9.54562 q^{43} -30.1238 q^{44} +2.79988 q^{45} +2.70316 q^{46} -7.68018 q^{47} -13.5509 q^{48} -6.22430 q^{49} +7.67515 q^{50} -4.80704 q^{51} -19.7233 q^{52} -9.73506 q^{53} -2.70316 q^{54} -15.8926 q^{55} +7.87341 q^{56} -6.68378 q^{57} -2.70316 q^{58} +5.14558 q^{59} -14.8592 q^{60} -7.99562 q^{61} +2.10578 q^{62} +0.880738 q^{63} +23.5855 q^{64} -10.4055 q^{65} +15.3436 q^{66} -8.36073 q^{67} +25.5113 q^{68} -1.00000 q^{69} +6.66589 q^{70} +8.52656 q^{71} +8.93955 q^{72} -12.6677 q^{73} -22.0301 q^{74} -2.83932 q^{75} +35.4713 q^{76} -4.99921 q^{77} +10.0460 q^{78} +15.1051 q^{79} +37.9409 q^{80} +1.00000 q^{81} +16.3859 q^{82} -0.302272 q^{83} -4.67414 q^{84} +13.4591 q^{85} +25.8033 q^{86} +1.00000 q^{87} -50.7423 q^{88} -10.7142 q^{89} +7.56852 q^{90} -3.27318 q^{91} +5.30708 q^{92} -0.779005 q^{93} -20.7608 q^{94} +18.7138 q^{95} -18.7511 q^{96} -0.884027 q^{97} -16.8253 q^{98} -5.67616 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 11 q + 2 q^{2} - 11 q^{3} + 18 q^{4} + 2 q^{5} - 2 q^{6} + 3 q^{7} + 18 q^{8} + 11 q^{9}+O(q^{10}) \) 11 * q + 2 * q^2 - 11 * q^3 + 18 * q^4 + 2 * q^5 - 2 * q^6 + 3 * q^7 + 18 * q^8 + 11 * q^9	\( 11 q + 2 q^{2} - 11 q^{3} + 18 q^{4} + 2 q^{5} - 2 q^{6} + 3 q^{7} + 18 q^{8} + 11 q^{9} + 14 q^{10} + 11 q^{11} - 18 q^{12} - 5 q^{13} + 17 q^{14} - 2 q^{15} + 20 q^{16} + 15 q^{17} + 2 q^{18} - 6 q^{19} + 21 q^{20} - 3 q^{21} - 10 q^{22} + 11 q^{23} - 18 q^{24} + 3 q^{25} - 5 q^{26} - 11 q^{27} + 7 q^{28} - 11 q^{29} - 14 q^{30} + 35 q^{31} + 28 q^{32} - 11 q^{33} + 28 q^{34} + 15 q^{35} + 18 q^{36} - 28 q^{37} - 2 q^{38} + 5 q^{39} - q^{40} + 10 q^{41} - 17 q^{42} - 6 q^{43} + 18 q^{44} + 2 q^{45} + 2 q^{46} + 15 q^{47} - 20 q^{48} + 22 q^{49} + 15 q^{50} - 15 q^{51} - 36 q^{52} - 7 q^{53} - 2 q^{54} - 12 q^{55} + 56 q^{56} + 6 q^{57} - 2 q^{58} - 20 q^{59} - 21 q^{60} - 20 q^{61} - 11 q^{62} + 3 q^{63} + 36 q^{64} + 11 q^{65} + 10 q^{66} - 39 q^{67} + 35 q^{68} - 11 q^{69} + 38 q^{70} + 49 q^{71} + 18 q^{72} - 3 q^{73} + 37 q^{74} - 3 q^{75} - 18 q^{76} + 25 q^{77} + 5 q^{78} + 41 q^{79} + 51 q^{80} + 11 q^{81} - 19 q^{82} + 13 q^{83} - 7 q^{84} + 62 q^{86} + 11 q^{87} - 40 q^{88} + 34 q^{89} + 14 q^{90} + 2 q^{91} + 18 q^{92} - 35 q^{93} - 14 q^{94} + 25 q^{95} - 28 q^{96} - 11 q^{97} + 53 q^{98} + 11 q^{99}+O(q^{100}) \) 11 * q + 2 * q^2 - 11 * q^3 + 18 * q^4 + 2 * q^5 - 2 * q^6 + 3 * q^7 + 18 * q^8 + 11 * q^9 + 14 * q^10 + 11 * q^11 - 18 * q^12 - 5 * q^13 + 17 * q^14 - 2 * q^15 + 20 * q^16 + 15 * q^17 + 2 * q^18 - 6 * q^19 + 21 * q^20 - 3 * q^21 - 10 * q^22 + 11 * q^23 - 18 * q^24 + 3 * q^25 - 5 * q^26 - 11 * q^27 + 7 * q^28 - 11 * q^29 - 14 * q^30 + 35 * q^31 + 28 * q^32 - 11 * q^33 + 28 * q^34 + 15 * q^35 + 18 * q^36 - 28 * q^37 - 2 * q^38 + 5 * q^39 - q^40 + 10 * q^41 - 17 * q^42 - 6 * q^43 + 18 * q^44 + 2 * q^45 + 2 * q^46 + 15 * q^47 - 20 * q^48 + 22 * q^49 + 15 * q^50 - 15 * q^51 - 36 * q^52 - 7 * q^53 - 2 * q^54 - 12 * q^55 + 56 * q^56 + 6 * q^57 - 2 * q^58 - 20 * q^59 - 21 * q^60 - 20 * q^61 - 11 * q^62 + 3 * q^63 + 36 * q^64 + 11 * q^65 + 10 * q^66 - 39 * q^67 + 35 * q^68 - 11 * q^69 + 38 * q^70 + 49 * q^71 + 18 * q^72 - 3 * q^73 + 37 * q^74 - 3 * q^75 - 18 * q^76 + 25 * q^77 + 5 * q^78 + 41 * q^79 + 51 * q^80 + 11 * q^81 - 19 * q^82 + 13 * q^83 - 7 * q^84 + 62 * q^86 + 11 * q^87 - 40 * q^88 + 34 * q^89 + 14 * q^90 + 2 * q^91 + 18 * q^92 - 35 * q^93 - 14 * q^94 + 25 * q^95 - 28 * q^96 - 11 * q^97 + 53 * q^98 + 11 * q^99

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