LMFDB - Embedded newform 2001.2.a.k.1.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2001,2,Mod(1,2001)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2001, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0, 0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("2001.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2001 = 3 \cdot 23 \cdot 29 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2001.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$15.9780654445$
Analytic rank:	$0$
Dimension:	$10$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - x^{9} - 17x^{8} + 23x^{7} + 69x^{6} - 88x^{5} - 106x^{4} + 101x^{3} + 60x^{2} - 23x - 11 $ x^10 - x^9 - 17x^8 + 23x^7 + 69x^6 - 88x^5 - 106x^4 + 101x^3 + 60x^2 - 23x - 11
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.8
Root			$-1.34161$ 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)

$f(q)$	$=$	$q+2.08881 q^{2} -1.00000 q^{3} +2.36311 q^{4} +0.182168 q^{5} -2.08881 q^{6} +1.65593 q^{7} +0.758471 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+2.08881 q^{2} -1.00000 q^{3} +2.36311 q^{4} +0.182168 q^{5} -2.08881 q^{6} +1.65593 q^{7} +0.758471 q^{8} +1.00000 q^{9} +0.380514 q^{10} -1.24834 q^{11} -2.36311 q^{12} +4.57911 q^{13} +3.45892 q^{14} -0.182168 q^{15} -3.14192 q^{16} +5.83690 q^{17} +2.08881 q^{18} +0.930336 q^{19} +0.430484 q^{20} -1.65593 q^{21} -2.60755 q^{22} -1.00000 q^{23} -0.758471 q^{24} -4.96681 q^{25} +9.56487 q^{26} -1.00000 q^{27} +3.91315 q^{28} +1.00000 q^{29} -0.380514 q^{30} +6.08976 q^{31} -8.07982 q^{32} +1.24834 q^{33} +12.1922 q^{34} +0.301658 q^{35} +2.36311 q^{36} +2.01691 q^{37} +1.94329 q^{38} -4.57911 q^{39} +0.138169 q^{40} +5.93284 q^{41} -3.45892 q^{42} +6.30244 q^{43} -2.94997 q^{44} +0.182168 q^{45} -2.08881 q^{46} +11.9221 q^{47} +3.14192 q^{48} -4.25790 q^{49} -10.3747 q^{50} -5.83690 q^{51} +10.8209 q^{52} -0.787969 q^{53} -2.08881 q^{54} -0.227408 q^{55} +1.25598 q^{56} -0.930336 q^{57} +2.08881 q^{58} +0.995830 q^{59} -0.430484 q^{60} -8.77657 q^{61} +12.7203 q^{62} +1.65593 q^{63} -10.5933 q^{64} +0.834168 q^{65} +2.60755 q^{66} +0.890575 q^{67} +13.7933 q^{68} +1.00000 q^{69} +0.630105 q^{70} +13.8495 q^{71} +0.758471 q^{72} -0.935317 q^{73} +4.21293 q^{74} +4.96681 q^{75} +2.19849 q^{76} -2.06717 q^{77} -9.56487 q^{78} -11.4223 q^{79} -0.572359 q^{80} +1.00000 q^{81} +12.3926 q^{82} +14.8776 q^{83} -3.91315 q^{84} +1.06330 q^{85} +13.1646 q^{86} -1.00000 q^{87} -0.946832 q^{88} -7.42248 q^{89} +0.380514 q^{90} +7.58268 q^{91} -2.36311 q^{92} -6.08976 q^{93} +24.9030 q^{94} +0.169478 q^{95} +8.07982 q^{96} +0.195926 q^{97} -8.89392 q^{98} -1.24834 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q + 3 q^{2} - 10 q^{3} + 17 q^{4} + 6 q^{5} - 3 q^{6} + 3 q^{7} - 6 q^{8} + 10 q^{9}+O(q^{10}) $ 10 * q + 3 * q^2 - 10 * q^3 + 17 * q^4 + 6 * q^5 - 3 * q^6 + 3 * q^7 - 6 * q^8 + 10 * q^9	\( 10 q + 3 q^{2} - 10 q^{3} + 17 q^{4} + 6 q^{5} - 3 q^{6} + 3 q^{7} - 6 q^{8} + 10 q^{9} - 4 q^{10} + 9 q^{11} - 17 q^{12} - 16 q^{13} + 16 q^{14} - 6 q^{15} + 27 q^{16} + 3 q^{18} + q^{19} + 21 q^{20} - 3 q^{21} + 17 q^{22} - 10 q^{23} + 6 q^{24} - 4 q^{25} + 28 q^{26} - 10 q^{27} - 14 q^{28} + 10 q^{29} + 4 q^{30} + 17 q^{31} + 21 q^{32} - 9 q^{33} - 3 q^{34} + 29 q^{35} + 17 q^{36} + q^{37} + 32 q^{38} + 16 q^{39} + 13 q^{40} - 16 q^{42} - 5 q^{43} + 33 q^{44} + 6 q^{45} - 3 q^{46} + 15 q^{47} - 27 q^{48} + 31 q^{49} - 22 q^{50} - 21 q^{52} + 35 q^{53} - 3 q^{54} - 20 q^{55} + 18 q^{56} - q^{57} + 3 q^{58} + 49 q^{59} - 21 q^{60} + 8 q^{61} + 15 q^{62} + 3 q^{63} + 12 q^{64} - 3 q^{65} - 17 q^{66} + 35 q^{67} - 18 q^{68} + 10 q^{69} - 16 q^{70} + 30 q^{71} - 6 q^{72} - 15 q^{73} + 23 q^{74} + 4 q^{75} + 10 q^{76} + 23 q^{77} - 28 q^{78} + 24 q^{79} + 23 q^{80} + 10 q^{81} - 5 q^{82} + q^{83} + 14 q^{84} - 10 q^{86} - 10 q^{87} + 18 q^{88} + 15 q^{89} - 4 q^{90} + 26 q^{91} - 17 q^{92} - 17 q^{93} + 3 q^{94} + 7 q^{95} - 21 q^{96} - 35 q^{97} + 3 q^{98} + 9 q^{99}+O(q^{100}) \) 10 * q + 3 * q^2 - 10 * q^3 + 17 * q^4 + 6 * q^5 - 3 * q^6 + 3 * q^7 - 6 * q^8 + 10 * q^9 - 4 * q^10 + 9 * q^11 - 17 * q^12 - 16 * q^13 + 16 * q^14 - 6 * q^15 + 27 * q^16 + 3 * q^18 + q^19 + 21 * q^20 - 3 * q^21 + 17 * q^22 - 10 * q^23 + 6 * q^24 - 4 * q^25 + 28 * q^26 - 10 * q^27 - 14 * q^28 + 10 * q^29 + 4 * q^30 + 17 * q^31 + 21 * q^32 - 9 * q^33 - 3 * q^34 + 29 * q^35 + 17 * q^36 + q^37 + 32 * q^38 + 16 * q^39 + 13 * q^40 - 16 * q^42 - 5 * q^43 + 33 * q^44 + 6 * q^45 - 3 * q^46 + 15 * q^47 - 27 * q^48 + 31 * q^49 - 22 * q^50 - 21 * q^52 + 35 * q^53 - 3 * q^54 - 20 * q^55 + 18 * q^56 - q^57 + 3 * q^58 + 49 * q^59 - 21 * q^60 + 8 * q^61 + 15 * q^62 + 3 * q^63 + 12 * q^64 - 3 * q^65 - 17 * q^66 + 35 * q^67 - 18 * q^68 + 10 * q^69 - 16 * q^70 + 30 * q^71 - 6 * q^72 - 15 * q^73 + 23 * q^74 + 4 * q^75 + 10 * q^76 + 23 * q^77 - 28 * q^78 + 24 * q^79 + 23 * q^80 + 10 * q^81 - 5 * q^82 + q^83 + 14 * q^84 - 10 * q^86 - 10 * q^87 + 18 * q^88 + 15 * q^89 - 4 * q^90 + 26 * q^91 - 17 * q^92 - 17 * q^93 + 3 * q^94 + 7 * q^95 - 21 * q^96 - 35 * q^97 + 3 * q^98 + 9 * 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 $

$2$	2.08881	1.47701	0.738505	−	0.674248i	$-0.235532\pi$
$2$	2.08881	1.47701	0.738505	+	0.674248i	$0.235532\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	2.36311	1.18156
$5$	0.182168	0.0814681	0.0407341	−	0.999170i	$-0.487030\pi$
$5$	0.182168	0.0814681	0.0407341	+	0.999170i	$0.487030\pi$
$6$	−2.08881	−0.852752
$7$	1.65593	0.625883	0.312941	−	0.949772i	$-0.398686\pi$
$7$	1.65593	0.625883	0.312941	+	0.949772i	$0.398686\pi$
$8$	0.758471	0.268160
$9$	1.00000	0.333333
$10$	0.380514	0.120329
$11$	−1.24834	−0.376389	−0.188195	−	0.982132i	$-0.560264\pi$
$11$	−1.24834	−0.376389	−0.188195	+	0.982132i	$0.560264\pi$
$12$	−2.36311	−0.682172
$13$	4.57911	1.27002	0.635008	−	0.772506i	$-0.280997\pi$
$13$	4.57911	1.27002	0.635008	+	0.772506i	$0.280997\pi$
$14$	3.45892	0.924434
$15$	−0.182168	−0.0470357
$16$	−3.14192	−0.785481
$17$	5.83690	1.41566	0.707828	−	0.706385i	$-0.249675\pi$
$17$	5.83690	1.41566	0.707828	+	0.706385i	$0.249675\pi$
$18$	2.08881	0.492336
$19$	0.930336	0.213434	0.106717	−	0.994289i	$-0.465966\pi$
$19$	0.930336	0.213434	0.106717	+	0.994289i	$0.465966\pi$
$20$	0.430484	0.0962592
$21$	−1.65593	−0.361353
$22$	−2.60755	−0.555931
$23$	−1.00000	−0.208514
$23$	−1.00000	−0.208514
$24$	−0.758471	−0.154822
$25$	−4.96681	−0.993363
$26$	9.56487	1.87583
$27$	−1.00000	−0.192450
$28$	3.91315	0.739515
$29$	1.00000	0.185695
$29$	1.00000	0.185695
$30$	−0.380514	−0.0694721
$31$	6.08976	1.09375	0.546876	−	0.837213i	$-0.315817\pi$
$31$	6.08976	1.09375	0.546876	+	0.837213i	$0.315817\pi$
$32$	−8.07982	−1.42832
$33$	1.24834	0.217309
$34$	12.1922	2.09094
$35$	0.301658	0.0509895
$36$	2.36311	0.393852
$37$	2.01691	0.331577	0.165789	−	0.986161i	$-0.446983\pi$
$37$	2.01691	0.331577	0.165789	+	0.986161i	$0.446983\pi$
$38$	1.94329	0.315244
$39$	−4.57911	−0.733244
$40$	0.138169	0.0218465
$41$	5.93284	0.926554	0.463277	−	0.886214i	$-0.346674\pi$
$41$	5.93284	0.926554	0.463277	+	0.886214i	$0.346674\pi$
$42$	−3.45892	−0.533722
$43$	6.30244	0.961114	0.480557	−	0.876964i	$-0.340435\pi$
$43$	6.30244	0.961114	0.480557	+	0.876964i	$0.340435\pi$
$44$	−2.94997	−0.444725
$45$	0.182168	0.0271560
$46$	−2.08881	−0.307978
$47$	11.9221	1.73902	0.869510	−	0.493916i	$-0.164435\pi$
$47$	11.9221	1.73902	0.869510	+	0.493916i	$0.164435\pi$
$48$	3.14192	0.453498
$49$	−4.25790	−0.608271
$50$	−10.3747	−1.46721
$51$	−5.83690	−0.817330
$52$	10.8209	1.50060
$53$	−0.787969	−0.108236	−0.0541180	−	0.998535i	$-0.517235\pi$
$53$	−0.787969	−0.108236	−0.0541180	+	0.998535i	$0.517235\pi$
$54$	−2.08881	−0.284251
$55$	−0.227408	−0.0306637
$56$	1.25598	0.167837
$57$	−0.930336	−0.123226
$58$	2.08881	0.274274
$59$	0.995830	0.129646	0.0648230	−	0.997897i	$-0.479352\pi$
$59$	0.995830	0.129646	0.0648230	+	0.997897i	$0.479352\pi$
$60$	−0.430484	−0.0555753
$61$	−8.77657	−1.12372	−0.561862	−	0.827231i	$-0.689915\pi$
$61$	−8.77657	−1.12372	−0.561862	+	0.827231i	$0.689915\pi$
$62$	12.7203	1.61548
$63$	1.65593	0.208628
$64$	−10.5933	−1.32417
$65$	0.834168	0.103466
$66$	2.60755	0.320967
$67$	0.890575	0.108801	0.0544005	−	0.998519i	$-0.482675\pi$
$67$	0.890575	0.108801	0.0544005	+	0.998519i	$0.482675\pi$
$68$	13.7933	1.67268
$69$	1.00000	0.120386
$70$	0.630105	0.0753119
$71$	13.8495	1.64364	0.821818	−	0.569751i	$-0.192960\pi$
$71$	13.8495	1.64364	0.821818	+	0.569751i	$0.192960\pi$
$72$	0.758471	0.0893867
$73$	−0.935317	−0.109471	−0.0547353	−	0.998501i	$-0.517432\pi$
$73$	−0.935317	−0.109471	−0.0547353	+	0.998501i	$0.517432\pi$
$74$	4.21293	0.489743
$75$	4.96681	0.573518
$76$	2.19849	0.252184
$77$	−2.06717	−0.235576
$78$	−9.56487	−1.08301
$79$	−11.4223	−1.28511	−0.642554	−	0.766240i	$-0.722125\pi$
$79$	−11.4223	−1.28511	−0.642554	+	0.766240i	$0.722125\pi$
$80$	−0.572359	−0.0639917
$81$	1.00000	0.111111
$82$	12.3926	1.36853
$83$	14.8776	1.63303	0.816513	−	0.577327i	$-0.195904\pi$
$83$	14.8776	1.63303	0.816513	+	0.577327i	$0.195904\pi$
$84$	−3.91315	−0.426959
$85$	1.06330	0.115331
$86$	13.1646	1.41957
$87$	−1.00000	−0.107211
$88$	−0.946832	−0.100933
$89$	−7.42248	−0.786782	−0.393391	−	0.919371i	$-0.628698\pi$
$89$	−7.42248	−0.786782	−0.393391	+	0.919371i	$0.628698\pi$
$90$	0.380514	0.0401097
$91$	7.58268	0.794881
$92$	−2.36311	−0.246371
$93$	−6.08976	−0.631478
$94$	24.9030	2.56855
$95$	0.169478	0.0173880
$96$	8.07982	0.824643
$97$	0.195926	0.0198933	0.00994666	−	0.999951i	$-0.496834\pi$
$97$	0.195926	0.0198933	0.00994666	+	0.999951i	$0.496834\pi$
$98$	−8.89392	−0.898422
$99$	−1.24834	−0.125463
$100$	−11.7371	−1.17371
$101$	−4.99772	−0.497292	−0.248646	−	0.968594i	$-0.579986\pi$
$101$	−4.99772	−0.497292	−0.248646	+	0.968594i	$0.579986\pi$
$102$	−12.1922	−1.20720
$103$	−7.40281	−0.729420	−0.364710	−	0.931121i	$-0.618832\pi$
$103$	−7.40281	−0.729420	−0.364710	+	0.931121i	$0.618832\pi$
$104$	3.47312	0.340568
$105$	−0.301658	−0.0294388
$106$	−1.64592	−0.159865
$107$	9.67451	0.935271	0.467635	−	0.883921i	$-0.345106\pi$
$107$	9.67451	0.935271	0.467635	+	0.883921i	$0.345106\pi$
$108$	−2.36311	−0.227391
$109$	−2.95633	−0.283165	−0.141583	−	0.989926i	$-0.545219\pi$
$109$	−2.95633	−0.283165	−0.141583	+	0.989926i	$0.545219\pi$
$110$	−0.475012	−0.0452906
$111$	−2.01691	−0.191436
$112$	−5.20281	−0.491619
$113$	8.23551	0.774731	0.387366	−	0.921926i	$-0.373385\pi$
$113$	8.23551	0.774731	0.387366	+	0.921926i	$0.373385\pi$
$114$	−1.94329	−0.182006
$115$	−0.182168	−0.0169873
$116$	2.36311	0.219409
$117$	4.57911	0.423339
$118$	2.08010	0.191488
$119$	9.66550	0.886035
$120$	−0.138169	−0.0126131
$121$	−9.44164	−0.858331
$122$	−18.3326	−1.65975
$123$	−5.93284	−0.534946
$124$	14.3908	1.29233
$125$	−1.81564	−0.162396
$126$	3.45892	0.308145
$127$	1.39730	0.123991	0.0619953	−	0.998076i	$-0.480254\pi$
$127$	1.39730	0.123991	0.0619953	+	0.998076i	$0.480254\pi$
$128$	−5.96777	−0.527481
$129$	−6.30244	−0.554899
$130$	1.74242	0.152820
$131$	−8.14479	−0.711614	−0.355807	−	0.934560i	$-0.615794\pi$
$131$	−8.14479	−0.711614	−0.355807	+	0.934560i	$0.615794\pi$
$132$	2.94997	0.256762
$133$	1.54057	0.133584
$134$	1.86024	0.160700
$135$	−0.182168	−0.0156786
$136$	4.42712	0.379623
$137$	−16.8808	−1.44223	−0.721114	−	0.692816i	$-0.756370\pi$
$137$	−16.8808	−1.44223	−0.721114	+	0.692816i	$0.756370\pi$
$138$	2.08881	0.177811
$139$	−13.7845	−1.16919	−0.584593	−	0.811327i	$-0.698746\pi$
$139$	−13.7845	−1.16919	−0.584593	+	0.811327i	$0.698746\pi$
$140$	0.712851	0.0602469
$141$	−11.9221	−1.00402
$142$	28.9290	2.42766
$143$	−5.71629	−0.478021
$144$	−3.14192	−0.261827
$145$	0.182168	0.0151283
$146$	−1.95370	−0.161689
$147$	4.25790	0.351185
$148$	4.76618	0.391777
$149$	−19.7181	−1.61537	−0.807684	−	0.589616i	$-0.799279\pi$
$149$	−19.7181	−1.61537	−0.807684	+	0.589616i	$0.799279\pi$
$150$	10.3747	0.847092
$151$	15.2119	1.23793	0.618963	−	0.785420i	$-0.287553\pi$
$151$	15.2119	1.23793	0.618963	+	0.785420i	$0.287553\pi$
$152$	0.705633	0.0572344
$153$	5.83690	0.471885
$154$	−4.31791	−0.347947
$155$	1.10936	0.0891060
$156$	−10.8209	−0.866369
$157$	12.3102	0.982459	0.491230	−	0.871030i	$-0.336548\pi$
$157$	12.3102	0.982459	0.491230	+	0.871030i	$0.336548\pi$
$158$	−23.8590	−1.89812
$159$	0.787969	0.0624900
$160$	−1.47189	−0.116363
$161$	−1.65593	−0.130506
$162$	2.08881	0.164112
$163$	−15.7649	−1.23480	−0.617400	−	0.786649i	$-0.711814\pi$
$163$	−15.7649	−1.23480	−0.617400	+	0.786649i	$0.711814\pi$
$164$	14.0200	1.09478
$165$	0.227408	0.0177037
$166$	31.0764	2.41199
$167$	−8.30041	−0.642305	−0.321152	−	0.947027i	$-0.604070\pi$
$167$	−8.30041	−0.642305	−0.321152	+	0.947027i	$0.604070\pi$
$168$	−1.25598	−0.0969006
$169$	7.96823	0.612941
$170$	2.22102	0.170345
$171$	0.930336	0.0711446
$172$	14.8934	1.13561
$173$	−22.0702	−1.67797	−0.838984	−	0.544156i	$-0.816850\pi$
$173$	−22.0702	−1.67797	−0.838984	+	0.544156i	$0.816850\pi$
$174$	−2.08881	−0.158352
$175$	−8.22470	−0.621729
$176$	3.92220	0.295647
$177$	−0.995830	−0.0748511
$178$	−15.5041	−1.16208
$179$	−2.00797	−0.150083	−0.0750415	−	0.997180i	$-0.523909\pi$
$179$	−2.00797	−0.150083	−0.0750415	+	0.997180i	$0.523909\pi$
$180$	0.430484	0.0320864
$181$	−11.3883	−0.846489	−0.423244	−	0.906016i	$-0.639109\pi$
$181$	−11.3883	−0.846489	−0.423244	+	0.906016i	$0.639109\pi$
$182$	15.8388	1.17405
$183$	8.77657	0.648783
$184$	−0.758471	−0.0559153
$185$	0.367416	0.0270130
$186$	−12.7203	−0.932699
$187$	−7.28645	−0.532838
$188$	28.1733	2.05475
$189$	−1.65593	−0.120451
$190$	0.354006	0.0256823
$191$	16.0431	1.16084	0.580419	−	0.814318i	$-0.302889\pi$
$191$	16.0431	1.16084	0.580419	+	0.814318i	$0.302889\pi$
$192$	10.5933	0.764507
$193$	−9.55632	−0.687879	−0.343940	−	0.938992i	$-0.611762\pi$
$193$	−9.55632	−0.687879	−0.343940	+	0.938992i	$0.611762\pi$
$194$	0.409252	0.0293826
$195$	−0.834168	−0.0597360
$196$	−10.0619	−0.718706
$197$	10.2608	0.731049	0.365525	−	0.930802i	$-0.380890\pi$
$197$	10.2608	0.731049	0.365525	+	0.930802i	$0.380890\pi$
$198$	−2.60755	−0.185310
$199$	9.59152	0.679925	0.339963	−	0.940439i	$-0.389586\pi$
$199$	9.59152	0.679925	0.339963	+	0.940439i	$0.389586\pi$
$200$	−3.76719	−0.266380
$201$	−0.890575	−0.0628163
$202$	−10.4393	−0.734505
$203$	1.65593	0.116223
$204$	−13.7933	−0.965721
$205$	1.08078	0.0754846
$206$	−15.4630	−1.07736
$207$	−1.00000	−0.0695048
$208$	−14.3872	−0.997574
$209$	−1.16138	−0.0803342
$210$	−0.630105	−0.0434814
$211$	0.546238	0.0376045	0.0188023	−	0.999823i	$-0.494015\pi$
$211$	0.546238	0.0376045	0.0188023	+	0.999823i	$0.494015\pi$
$212$	−1.86206	−0.127887
$213$	−13.8495	−0.948953
$214$	20.2082	1.38140
$215$	1.14811	0.0783001
$216$	−0.758471	−0.0516074
$217$	10.0842	0.684561
$218$	−6.17521	−0.418238
$219$	0.935317	0.0632029
$220$	−0.537392	−0.0362309
$221$	26.7278	1.79791
$222$	−4.21293	−0.282753
$223$	−23.2486	−1.55684	−0.778422	−	0.627742i	$-0.783979\pi$
$223$	−23.2486	−1.55684	−0.778422	+	0.627742i	$0.783979\pi$
$224$	−13.3796	−0.893963
$225$	−4.96681	−0.331121
$226$	17.2024	1.14429
$227$	13.2865	0.881857	0.440928	−	0.897542i	$-0.354649\pi$
$227$	13.2865	0.881857	0.440928	+	0.897542i	$0.354649\pi$
$228$	−2.19849	−0.145598
$229$	−5.29286	−0.349762	−0.174881	−	0.984590i	$-0.555954\pi$
$229$	−5.29286	−0.349762	−0.174881	+	0.984590i	$0.555954\pi$
$230$	−0.380514	−0.0250904
$231$	2.06717	0.136010
$232$	0.758471	0.0497961
$233$	2.24837	0.147296	0.0736479	−	0.997284i	$-0.476536\pi$
$233$	2.24837	0.147296	0.0736479	+	0.997284i	$0.476536\pi$
$234$	9.56487	0.625275
$235$	2.17183	0.141675
$236$	2.35326	0.153184
$237$	11.4223	0.741958
$238$	20.1894	1.30868
$239$	−10.2161	−0.660822	−0.330411	−	0.943837i	$-0.607187\pi$
$239$	−10.2161	−0.660822	−0.330411	+	0.943837i	$0.607187\pi$
$240$	0.572359	0.0369456
$241$	−5.43718	−0.350239	−0.175120	−	0.984547i	$-0.556031\pi$
$241$	−5.43718	−0.350239	−0.175120	+	0.984547i	$0.556031\pi$
$242$	−19.7218	−1.26776
$243$	−1.00000	−0.0641500
$244$	−20.7400	−1.32774
$245$	−0.775654	−0.0495547
$246$	−12.3926	−0.790120
$247$	4.26011	0.271064
$248$	4.61891	0.293301
$249$	−14.8776	−0.942828
$250$	−3.79252	−0.239860
$251$	−18.6749	−1.17875	−0.589376	−	0.807859i	$-0.700626\pi$
$251$	−18.6749	−1.17875	−0.589376	+	0.807859i	$0.700626\pi$
$252$	3.91315	0.246505
$253$	1.24834	0.0784826
$254$	2.91870	0.183135
$255$	−1.06330	−0.0665863
$256$	8.72113	0.545071
$257$	−20.4178	−1.27363	−0.636813	−	0.771019i	$-0.719747\pi$
$257$	−20.4178	−1.27363	−0.636813	+	0.771019i	$0.719747\pi$
$258$	−13.1646	−0.819591
$259$	3.33985	0.207528
$260$	1.97123	0.122251
$261$	1.00000	0.0618984
$262$	−17.0129	−1.05106
$263$	9.57459	0.590395	0.295197	−	0.955436i	$-0.404615\pi$
$263$	9.57459	0.590395	0.295197	+	0.955436i	$0.404615\pi$
$264$	0.946832	0.0582735
$265$	−0.143543	−0.00881778
$266$	3.21795	0.197305
$267$	7.42248	0.454249
$268$	2.10453	0.128555
$269$	−18.1486	−1.10654	−0.553270	−	0.833002i	$-0.686620\pi$
$269$	−18.1486	−1.10654	−0.553270	+	0.833002i	$0.686620\pi$
$270$	−0.380514	−0.0231574
$271$	−20.9277	−1.27127	−0.635635	−	0.771990i	$-0.719262\pi$
$271$	−20.9277	−1.27127	−0.635635	+	0.771990i	$0.719262\pi$
$272$	−18.3391	−1.11197
$273$	−7.58268	−0.458925
$274$	−35.2608	−2.13018
$275$	6.20029	0.373891
$276$	2.36311	0.142243
$277$	9.52367	0.572222	0.286111	−	0.958197i	$-0.407637\pi$
$277$	9.52367	0.572222	0.286111	+	0.958197i	$0.407637\pi$
$278$	−28.7931	−1.72690
$279$	6.08976	0.364584
$280$	0.228799	0.0136733
$281$	29.8149	1.77860	0.889302	−	0.457320i	$-0.151190\pi$
$281$	29.8149	1.77860	0.889302	+	0.457320i	$0.151190\pi$
$282$	−24.9030	−1.48295
$283$	−5.03871	−0.299520	−0.149760	−	0.988722i	$-0.547850\pi$
$283$	−5.03871	−0.299520	−0.149760	+	0.988722i	$0.547850\pi$
$284$	32.7280	1.94205
$285$	−0.169478	−0.0100390
$286$	−11.9402	−0.706041
$287$	9.82437	0.579914
$288$	−8.07982	−0.476108
$289$	17.0694	1.00408
$290$	0.380514	0.0223446
$291$	−0.195926	−0.0114854
$292$	−2.21026	−0.129346
$293$	−3.55901	−0.207920	−0.103960	−	0.994581i	$-0.533151\pi$
$293$	−3.55901	−0.207920	−0.103960	+	0.994581i	$0.533151\pi$
$294$	8.89392	0.518704
$295$	0.181409	0.0105620
$296$	1.52977	0.0889158
$297$	1.24834	0.0724362
$298$	−41.1872	−2.38591
$299$	−4.57911	−0.264817
$300$	11.7371	0.677644
$301$	10.4364	0.601544
$302$	31.7747	1.82843
$303$	4.99772	0.287112
$304$	−2.92305	−0.167648
$305$	−1.59881	−0.0915477
$306$	12.1922	0.696979
$307$	13.0739	0.746166	0.373083	−	0.927798i	$-0.378301\pi$
$307$	13.0739	0.746166	0.373083	+	0.927798i	$0.378301\pi$
$308$	−4.88495	−0.278346
$309$	7.40281	0.421131
$310$	2.31724	0.131610
$311$	−6.36818	−0.361106	−0.180553	−	0.983565i	$-0.557789\pi$
$311$	−6.36818	−0.361106	−0.180553	+	0.983565i	$0.557789\pi$
$312$	−3.47312	−0.196627
$313$	15.6031	0.881938	0.440969	−	0.897522i	$-0.354635\pi$
$313$	15.6031	0.881938	0.440969	+	0.897522i	$0.354635\pi$
$314$	25.7136	1.45110
$315$	0.301658	0.0169965
$316$	−26.9922	−1.51843
$317$	−29.9720	−1.68339	−0.841697	−	0.539950i	$-0.818443\pi$
$317$	−29.9720	−1.68339	−0.841697	+	0.539950i	$0.818443\pi$
$318$	1.64592	0.0922984
$319$	−1.24834	−0.0698938
$320$	−1.92977	−0.107877
$321$	−9.67451	−0.539979
$322$	−3.45892	−0.192758
$323$	5.43028	0.302149
$324$	2.36311	0.131284
$325$	−22.7436	−1.26159
$326$	−32.9298	−1.82381
$327$	2.95633	0.163486
$328$	4.49989	0.248465
$329$	19.7422	1.08842
$330$	0.475012	0.0261486
$331$	22.5681	1.24045	0.620227	−	0.784422i	$-0.287040\pi$
$331$	22.5681	1.24045	0.620227	+	0.784422i	$0.287040\pi$
$332$	35.1574	1.92951
$333$	2.01691	0.110526
$334$	−17.3379	−0.948690
$335$	0.162235	0.00886382
$336$	5.20281	0.283836
$337$	7.00379	0.381521	0.190760	−	0.981637i	$-0.438905\pi$
$337$	7.00379	0.381521	0.190760	+	0.981637i	$0.438905\pi$
$338$	16.6441	0.905319
$339$	−8.23551	−0.447291
$340$	2.51269	0.136270
$341$	−7.60210	−0.411677
$342$	1.94329	0.105081
$343$	−18.6423	−1.00659
$344$	4.78022	0.257732
$345$	0.182168	0.00980761
$346$	−46.1004	−2.47837
$347$	18.7749	1.00789	0.503944	−	0.863736i	$-0.331882\pi$
$347$	18.7749	1.00789	0.503944	+	0.863736i	$0.331882\pi$
$348$	−2.36311	−0.126676
$349$	13.6876	0.732681	0.366340	−	0.930481i	$-0.380611\pi$
$349$	13.6876	0.732681	0.366340	+	0.930481i	$0.380611\pi$
$350$	−17.1798	−0.918299
$351$	−4.57911	−0.244415
$352$	10.0864	0.537606
$353$	28.2224	1.50213	0.751063	−	0.660230i	$-0.229541\pi$
$353$	28.2224	1.50213	0.751063	+	0.660230i	$0.229541\pi$
$354$	−2.08010	−0.110556
$355$	2.52294	0.133904
$356$	−17.5402	−0.929627
$357$	−9.66550	−0.511552
$358$	−4.19427	−0.221674
$359$	−13.9966	−0.738713	−0.369356	−	0.929288i	$-0.620422\pi$
$359$	−13.9966	−0.738713	−0.369356	+	0.929288i	$0.620422\pi$
$360$	0.138169	0.00728217
$361$	−18.1345	−0.954446
$362$	−23.7880	−1.25027
$363$	9.44164	0.495558
$364$	17.9187	0.939196
$365$	−0.170385	−0.00891837
$366$	18.3326	0.958258
$367$	26.4872	1.38262	0.691312	−	0.722557i	$-0.257033\pi$
$367$	26.4872	1.38262	0.691312	+	0.722557i	$0.257033\pi$
$368$	3.14192	0.163784
$369$	5.93284	0.308851
$370$	0.767462	0.0398984
$371$	−1.30482	−0.0677430
$372$	−14.3908	−0.746127
$373$	−25.9239	−1.34229	−0.671143	−	0.741328i	$-0.734196\pi$
$373$	−25.9239	−1.34229	−0.671143	+	0.741328i	$0.734196\pi$
$374$	−15.2200	−0.787007
$375$	1.81564	0.0937591
$376$	9.04259	0.466336
$377$	4.57911	0.235836
$378$	−3.45892	−0.177907
$379$	−26.1149	−1.34143	−0.670715	−	0.741715i	$-0.734013\pi$
$379$	−26.1149	−1.34143	−0.670715	+	0.741715i	$0.734013\pi$
$380$	0.400495	0.0205450
$381$	−1.39730	−0.0715861
$382$	33.5109	1.71457
$383$	19.0768	0.974781	0.487391	−	0.873184i	$-0.337949\pi$
$383$	19.0768	0.974781	0.487391	+	0.873184i	$0.337949\pi$
$384$	5.96777	0.304541
$385$	−0.376572	−0.0191919
$386$	−19.9613	−1.01600
$387$	6.30244	0.320371
$388$	0.462996	0.0235051
$389$	−20.7218	−1.05063	−0.525317	−	0.850906i	$-0.676053\pi$
$389$	−20.7218	−1.05063	−0.525317	+	0.850906i	$0.676053\pi$
$390$	−1.74242	−0.0882307
$391$	−5.83690	−0.295185
$392$	−3.22949	−0.163114
$393$	8.14479	0.410850
$394$	21.4328	1.07977
$395$	−2.08078	−0.104695
$396$	−2.94997	−0.148242
$397$	16.7674	0.841531	0.420766	−	0.907169i	$-0.361761\pi$
$397$	16.7674	0.841531	0.420766	+	0.907169i	$0.361761\pi$
$398$	20.0348	1.00426
$399$	−1.54057	−0.0771250
$400$	15.6054	0.780268
$401$	29.3917	1.46775	0.733877	−	0.679283i	$-0.237709\pi$
$401$	29.3917	1.46775	0.733877	+	0.679283i	$0.237709\pi$
$402$	−1.86024	−0.0927803
$403$	27.8857	1.38908
$404$	−11.8102	−0.587579
$405$	0.182168	0.00905202
$406$	3.45892	0.171663
$407$	−2.51779	−0.124802
$408$	−4.42712	−0.219175
$409$	−5.71653	−0.282664	−0.141332	−	0.989962i	$-0.545139\pi$
$409$	−5.71653	−0.282664	−0.141332	+	0.989962i	$0.545139\pi$
$410$	2.25753	0.111491
$411$	16.8808	0.832671
$412$	−17.4937	−0.861851
$413$	1.64902	0.0811432
$414$	−2.08881	−0.102659
$415$	2.71022	0.133040
$416$	−36.9983	−1.81399
$417$	13.7845	0.675030
$418$	−2.42589	−0.118654
$419$	−25.1308	−1.22772	−0.613859	−	0.789416i	$-0.710384\pi$
$419$	−25.1308	−1.22772	−0.613859	+	0.789416i	$0.710384\pi$
$420$	−0.712851	−0.0347836
$421$	−19.6823	−0.959256	−0.479628	−	0.877472i	$-0.659228\pi$
$421$	−19.6823	−0.959256	−0.479628	+	0.877472i	$0.659228\pi$
$422$	1.14098	0.0555423
$423$	11.9221	0.579673
$424$	−0.597652	−0.0290246
$425$	−28.9908	−1.40626
$426$	−28.9290	−1.40161
$427$	−14.5334	−0.703319
$428$	22.8620	1.10507
$429$	5.71629	0.275985
$430$	2.39817	0.115650
$431$	−25.4201	−1.22444	−0.612221	−	0.790687i	$-0.709724\pi$
$431$	−25.4201	−1.22444	−0.612221	+	0.790687i	$0.709724\pi$
$432$	3.14192	0.151166
$433$	−17.4859	−0.840320	−0.420160	−	0.907450i	$-0.638026\pi$
$433$	−17.4859	−0.840320	−0.420160	+	0.907450i	$0.638026\pi$
$434$	21.0640	1.01110
$435$	−0.182168	−0.00873430
$436$	−6.98615	−0.334576
$437$	−0.930336	−0.0445040
$438$	1.95370	0.0933513
$439$	−24.5739	−1.17285	−0.586424	−	0.810004i	$-0.699465\pi$
$439$	−24.5739	−1.17285	−0.586424	+	0.810004i	$0.699465\pi$
$440$	−0.172483	−0.00822279
$441$	−4.25790	−0.202757
$442$	55.8292	2.65552
$443$	−25.4187	−1.20768	−0.603839	−	0.797106i	$-0.706363\pi$
$443$	−25.4187	−1.20768	−0.603839	+	0.797106i	$0.706363\pi$
$444$	−4.76618	−0.226193
$445$	−1.35214	−0.0640976
$446$	−48.5619	−2.29947
$447$	19.7181	0.932633
$448$	−17.5418	−0.828772
$449$	20.5591	0.970244	0.485122	−	0.874447i	$-0.338775\pi$
$449$	20.5591	0.970244	0.485122	+	0.874447i	$0.338775\pi$
$450$	−10.3747	−0.489069
$451$	−7.40622	−0.348745
$452$	19.4614	0.915389
$453$	−15.2119	−0.714717
$454$	27.7530	1.30251
$455$	1.38132	0.0647575
$456$	−0.705633	−0.0330443
$457$	−25.6456	−1.19965	−0.599826	−	0.800130i	$-0.704764\pi$
$457$	−25.6456	−1.19965	−0.599826	+	0.800130i	$0.704764\pi$
$458$	−11.0558	−0.516602
$459$	−5.83690	−0.272443
$460$	−0.430484	−0.0200714
$461$	−28.7290	−1.33804	−0.669020	−	0.743244i	$-0.733286\pi$
$461$	−28.7290	−1.33804	−0.669020	+	0.743244i	$0.733286\pi$
$462$	4.31791	0.200887
$463$	−6.25682	−0.290779	−0.145390	−	0.989374i	$-0.546444\pi$
$463$	−6.25682	−0.290779	−0.145390	+	0.989374i	$0.546444\pi$
$464$	−3.14192	−0.145860
$465$	−1.10936	−0.0514454
$466$	4.69641	0.217557
$467$	22.5900	1.04534	0.522671	−	0.852534i	$-0.324936\pi$
$467$	22.5900	1.04534	0.522671	+	0.852534i	$0.324936\pi$
$468$	10.8209	0.500198
$469$	1.47473	0.0680967
$470$	4.53654	0.209255
$471$	−12.3102	−0.567223
$472$	0.755308	0.0347659
$473$	−7.86761	−0.361753
$474$	23.8590	1.09588
$475$	−4.62081	−0.212017
$476$	22.8407	1.04690
$477$	−0.787969	−0.0360786
$478$	−21.3394	−0.976040
$479$	39.6504	1.81167	0.905835	−	0.423630i	$-0.139244\pi$
$479$	39.6504	1.81167	0.905835	+	0.423630i	$0.139244\pi$
$480$	1.47189	0.0671821
$481$	9.23563	0.421108
$482$	−11.3572	−0.517307
$483$	1.65593	0.0753474
$484$	−22.3117	−1.01417
$485$	0.0356916	0.00162067
$486$	−2.08881	−0.0947502
$487$	5.68697	0.257701	0.128851	−	0.991664i	$-0.458871\pi$
$487$	5.68697	0.257701	0.128851	+	0.991664i	$0.458871\pi$
$488$	−6.65678	−0.301338
$489$	15.7649	0.712912
$490$	−1.62019	−0.0731928
$491$	−19.2734	−0.869798	−0.434899	−	0.900479i	$-0.643216\pi$
$491$	−19.2734	−0.869798	−0.434899	+	0.900479i	$0.643216\pi$
$492$	−14.0200	−0.632069
$493$	5.83690	0.262881
$494$	8.89854	0.400364
$495$	−0.227408	−0.0102212
$496$	−19.1336	−0.859122
$497$	22.9338	1.02872
$498$	−31.0764	−1.39257
$499$	6.22010	0.278450	0.139225	−	0.990261i	$-0.455539\pi$
$499$	6.22010	0.278450	0.139225	+	0.990261i	$0.455539\pi$
$500$	−4.29056	−0.191879
$501$	8.30041	0.370835
$502$	−39.0083	−1.74103
$503$	4.93702	0.220131	0.110065	−	0.993924i	$-0.464894\pi$
$503$	4.93702	0.220131	0.110065	+	0.993924i	$0.464894\pi$
$504$	1.25598	0.0559456
$505$	−0.910427	−0.0405135
$506$	2.60755	0.115920
$507$	−7.96823	−0.353881
$508$	3.30199	0.146502
$509$	21.9083	0.971067	0.485533	−	0.874218i	$-0.338625\pi$
$509$	21.9083	0.971067	0.485533	+	0.874218i	$0.338625\pi$
$510$	−2.22102	−0.0983486
$511$	−1.54882	−0.0685158
$512$	30.1523	1.33256
$513$	−0.930336	−0.0410753
$514$	−42.6488	−1.88116
$515$	−1.34856	−0.0594245
$516$	−14.8934	−0.655645
$517$	−14.8829	−0.654548
$518$	6.97631	0.306521
$519$	22.0702	0.968775
$520$	0.632693	0.0277454
$521$	32.0102	1.40239	0.701197	−	0.712968i	$-0.252649\pi$
$521$	32.0102	1.40239	0.701197	+	0.712968i	$0.252649\pi$
$522$	2.08881	0.0914246
$523$	6.04239	0.264215	0.132108	−	0.991235i	$-0.457826\pi$
$523$	6.04239	0.264215	0.132108	+	0.991235i	$0.457826\pi$
$524$	−19.2471	−0.840811
$525$	8.22470	0.358955
$526$	19.9995	0.872018
$527$	35.5453	1.54838
$528$	−3.92220	−0.170692
$529$	1.00000	0.0434783
$530$	−0.299834	−0.0130239
$531$	0.995830	0.0432153
$532$	3.64054	0.157838
$533$	27.1671	1.17674
$534$	15.5041	0.670929
$535$	1.76239	0.0761948
$536$	0.675476	0.0291761
$537$	2.00797	0.0866505
$538$	−37.9089	−1.63437
$539$	5.31531	0.228947
$540$	−0.430484	−0.0185251
$541$	13.6380	0.586343	0.293172	−	0.956060i	$-0.405289\pi$
$541$	13.6380	0.586343	0.293172	+	0.956060i	$0.405289\pi$
$542$	−43.7140	−1.87768
$543$	11.3883	0.488720
$544$	−47.1611	−2.02201
$545$	−0.538550	−0.0230689
$546$	−15.8388	−0.677836
$547$	−21.4434	−0.916854	−0.458427	−	0.888732i	$-0.651587\pi$
$547$	−21.4434	−0.916854	−0.458427	+	0.888732i	$0.651587\pi$
$548$	−39.8913	−1.70407
$549$	−8.77657	−0.374575
$550$	12.9512	0.552241
$551$	0.930336	0.0396336
$552$	0.758471	0.0322827
$553$	−18.9145	−0.804327
$554$	19.8931	0.845177
$555$	−0.367416	−0.0155960
$556$	−32.5743	−1.38146
$557$	43.9272	1.86126	0.930628	−	0.365965i	$-0.119261\pi$
$557$	43.9272	1.86126	0.930628	+	0.365965i	$0.119261\pi$
$558$	12.7203	0.538494
$559$	28.8596	1.22063
$560$	−0.947786	−0.0400513
$561$	7.28645	0.307634
$562$	62.2775	2.62702
$563$	3.21011	0.135290	0.0676450	−	0.997709i	$-0.478451\pi$
$563$	3.21011	0.135290	0.0676450	+	0.997709i	$0.478451\pi$
$564$	−28.1733	−1.18631
$565$	1.50025	0.0631159
$566$	−10.5249	−0.442394
$567$	1.65593	0.0695425
$568$	10.5045	0.440757
$569$	−31.1328	−1.30515	−0.652577	−	0.757722i	$-0.726312\pi$
$569$	−31.1328	−1.30515	−0.652577	+	0.757722i	$0.726312\pi$
$570$	−0.354006	−0.0148277
$571$	19.5646	0.818755	0.409377	−	0.912365i	$-0.365746\pi$
$571$	19.5646	0.818755	0.409377	+	0.912365i	$0.365746\pi$
$572$	−13.5082	−0.564808
$573$	−16.0431	−0.670210
$574$	20.5212	0.856538
$575$	4.96681	0.207130
$576$	−10.5933	−0.441388
$577$	−24.7987	−1.03238	−0.516191	−	0.856473i	$-0.672651\pi$
$577$	−24.7987	−1.03238	−0.516191	+	0.856473i	$0.672651\pi$
$578$	35.6547	1.48304
$579$	9.55632	0.397147
$580$	0.430484	0.0178749
$581$	24.6362	1.02208
$582$	−0.409252	−0.0169641
$583$	0.983656	0.0407388
$584$	−0.709412	−0.0293557
$585$	0.834168	0.0344886
$586$	−7.43409	−0.307099
$587$	−23.9697	−0.989335	−0.494668	−	0.869082i	$-0.664710\pi$
$587$	−23.9697	−0.989335	−0.494668	+	0.869082i	$0.664710\pi$
$588$	10.0619	0.414945
$589$	5.66552	0.233444
$590$	0.378927	0.0156002
$591$	−10.2608	−0.422071
$592$	−6.33697	−0.260448
$593$	26.6311	1.09361	0.546803	−	0.837261i	$-0.315844\pi$
$593$	26.6311	1.09361	0.546803	+	0.837261i	$0.315844\pi$
$594$	2.60755	0.106989
$595$	1.76075	0.0721836
$596$	−46.5960	−1.90865
$597$	−9.59152	−0.392555
$598$	−9.56487	−0.391137
$599$	−27.4004	−1.11955	−0.559776	−	0.828644i	$-0.689113\pi$
$599$	−27.4004	−1.11955	−0.559776	+	0.828644i	$0.689113\pi$
$600$	3.76719	0.153795
$601$	−45.8798	−1.87147	−0.935737	−	0.352698i	$-0.885264\pi$
$601$	−45.8798	−1.87147	−0.935737	+	0.352698i	$0.885264\pi$
$602$	21.7996	0.888487
$603$	0.890575	0.0362670
$604$	35.9474	1.46268
$605$	−1.71997	−0.0699266
$606$	10.4393	0.424067
$607$	−17.3867	−0.705706	−0.352853	−	0.935679i	$-0.614788\pi$
$607$	−17.3867	−0.705706	−0.352853	+	0.935679i	$0.614788\pi$
$608$	−7.51694	−0.304852
$609$	−1.65593	−0.0671017
$610$	−3.33961	−0.135217
$611$	54.5927	2.20858
$612$	13.7933	0.557559
$613$	42.6895	1.72421	0.862106	−	0.506729i	$-0.169145\pi$
$613$	42.6895	1.72421	0.862106	+	0.506729i	$0.169145\pi$
$614$	27.3088	1.10209
$615$	−1.08078	−0.0435811
$616$	−1.56789	−0.0631720
$617$	20.0611	0.807629	0.403815	−	0.914841i	$-0.367684\pi$
$617$	20.0611	0.807629	0.403815	+	0.914841i	$0.367684\pi$
$618$	15.4630	0.622014
$619$	−15.7267	−0.632108	−0.316054	−	0.948741i	$-0.602358\pi$
$619$	−15.7267	−0.632108	−0.316054	+	0.948741i	$0.602358\pi$
$620$	2.62154	0.105284
$621$	1.00000	0.0401286
$622$	−13.3019	−0.533358
$623$	−12.2911	−0.492433
$624$	14.3872	0.575949
$625$	24.5033	0.980133
$626$	32.5918	1.30263
$627$	1.16138	0.0463810
$628$	29.0903	1.16083
$629$	11.7725	0.469399
$630$	0.630105	0.0251040
$631$	13.7221	0.546266	0.273133	−	0.961976i	$-0.411940\pi$
$631$	13.7221	0.546266	0.273133	+	0.961976i	$0.411940\pi$
$632$	−8.66348	−0.344615
$633$	−0.546238	−0.0217110
$634$	−62.6057	−2.48639
$635$	0.254544	0.0101013
$636$	1.86206	0.0738355
$637$	−19.4974	−0.772514
$638$	−2.60755	−0.103234
$639$	13.8495	0.547878
$640$	−1.08714	−0.0429729
$641$	33.2217	1.31218	0.656089	−	0.754683i	$-0.272210\pi$
$641$	33.2217	1.31218	0.656089	+	0.754683i	$0.272210\pi$
$642$	−20.2082	−0.797554
$643$	−6.76304	−0.266708	−0.133354	−	0.991068i	$-0.542575\pi$
$643$	−6.76304	−0.266708	−0.133354	+	0.991068i	$0.542575\pi$
$644$	−3.91315	−0.154200
$645$	−1.14811	−0.0452066
$646$	11.3428	0.446276
$647$	43.4884	1.70970	0.854852	−	0.518872i	$-0.173648\pi$
$647$	43.4884	1.70970	0.854852	+	0.518872i	$0.173648\pi$
$648$	0.758471	0.0297956
$649$	−1.24314	−0.0487974
$650$	−47.5069	−1.86338
$651$	−10.0842	−0.395231
$652$	−37.2542	−1.45899
$653$	−19.4313	−0.760405	−0.380203	−	0.924903i	$-0.624146\pi$
$653$	−19.4313	−0.760405	−0.380203	+	0.924903i	$0.624146\pi$
$654$	6.17521	0.241470
$655$	−1.48372	−0.0579738
$656$	−18.6405	−0.727791
$657$	−0.935317	−0.0364902
$658$	41.2376	1.60761
$659$	−4.31361	−0.168034	−0.0840172	−	0.996464i	$-0.526775\pi$
$659$	−4.31361	−0.168034	−0.0840172	+	0.996464i	$0.526775\pi$
$660$	0.537392	0.0209179
$661$	−19.8534	−0.772209	−0.386105	−	0.922455i	$-0.626180\pi$
$661$	−19.8534	−0.772209	−0.386105	+	0.922455i	$0.626180\pi$
$662$	47.1404	1.83216
$663$	−26.7278	−1.03802
$664$	11.2842	0.437912
$665$	0.280643	0.0108829
$666$	4.21293	0.163248
$667$	−1.00000	−0.0387202
$668$	−19.6148	−0.758919
$669$	23.2486	0.898844
$670$	0.338877	0.0130919
$671$	10.9562	0.422958
$672$	13.3796	0.516130
$673$	−20.4133	−0.786874	−0.393437	−	0.919352i	$-0.628714\pi$
$673$	−20.4133	−0.786874	−0.393437	+	0.919352i	$0.628714\pi$
$674$	14.6296	0.563509
$675$	4.96681	0.191173
$676$	18.8298	0.724224
$677$	−8.09399	−0.311077	−0.155539	−	0.987830i	$-0.549711\pi$
$677$	−8.09399	−0.311077	−0.155539	+	0.987830i	$0.549711\pi$
$678$	−17.2024	−0.660654
$679$	0.324440	0.0124509
$680$	0.806481	0.0309271
$681$	−13.2865	−0.509140
$682$	−15.8793	−0.608051
$683$	12.7532	0.487986	0.243993	−	0.969777i	$-0.421543\pi$
$683$	12.7532	0.487986	0.243993	+	0.969777i	$0.421543\pi$
$684$	2.19849	0.0840613
$685$	−3.07515	−0.117496
$686$	−38.9401	−1.48674
$687$	5.29286	0.201935
$688$	−19.8018	−0.754937
$689$	−3.60820	−0.137461
$690$	0.380514	0.0144859
$691$	45.8305	1.74347	0.871736	−	0.489975i	$-0.162994\pi$
$691$	45.8305	1.74347	0.871736	+	0.489975i	$0.162994\pi$
$692$	−52.1544	−1.98261
$693$	−2.06717	−0.0785252
$694$	39.2171	1.48866
$695$	−2.51110	−0.0952514
$696$	−0.758471	−0.0287498
$697$	34.6294	1.31168
$698$	28.5908	1.08218
$699$	−2.24837	−0.0850412
$700$	−19.4359	−0.734607
$701$	14.6683	0.554015	0.277008	−	0.960868i	$-0.410657\pi$
$701$	14.6683	0.554015	0.277008	+	0.960868i	$0.410657\pi$
$702$	−9.56487	−0.361003
$703$	1.87640	0.0707698
$704$	13.2241	0.498402
$705$	−2.17183	−0.0817959
$706$	58.9511	2.21865
$707$	−8.27588	−0.311247
$708$	−2.35326	−0.0884408
$709$	44.4625	1.66982	0.834912	−	0.550384i	$-0.185519\pi$
$709$	44.4625	1.66982	0.834912	+	0.550384i	$0.185519\pi$
$710$	5.26994	0.197777
$711$	−11.4223	−0.428370
$712$	−5.62974	−0.210983
$713$	−6.08976	−0.228063
$714$	−20.1894	−0.755567
$715$	−1.04133	−0.0389434
$716$	−4.74507	−0.177331
$717$	10.2161	0.381526
$718$	−29.2362	−1.09109
$719$	−2.58422	−0.0963750	−0.0481875	−	0.998838i	$-0.515345\pi$
$719$	−2.58422	−0.0963750	−0.0481875	+	0.998838i	$0.515345\pi$
$720$	−0.572359	−0.0213306
$721$	−12.2585	−0.456531
$722$	−37.8794	−1.40973
$723$	5.43718	0.202211
$724$	−26.9119	−1.00017
$725$	−4.96681	−0.184463
$726$	19.7218	0.731943
$727$	2.83517	0.105151	0.0525753	−	0.998617i	$-0.483257\pi$
$727$	2.83517	0.105151	0.0525753	+	0.998617i	$0.483257\pi$
$728$	5.75125	0.213155
$729$	1.00000	0.0370370
$730$	−0.355902	−0.0131725
$731$	36.7867	1.36061
$732$	20.7400	0.766573
$733$	16.2391	0.599803	0.299902	−	0.953970i	$-0.403046\pi$
$733$	16.2391	0.599803	0.299902	+	0.953970i	$0.403046\pi$
$734$	55.3267	2.04215
$735$	0.775654	0.0286104
$736$	8.07982	0.297826
$737$	−1.11174	−0.0409516
$738$	12.3926	0.456176
$739$	38.7897	1.42690	0.713451	−	0.700706i	$-0.247131\pi$
$739$	38.7897	1.42690	0.713451	+	0.700706i	$0.247131\pi$
$740$	0.868246	0.0319174
$741$	−4.26011	−0.156499
$742$	−2.72552	−0.100057
$743$	5.63923	0.206883	0.103442	−	0.994636i	$-0.467015\pi$
$743$	5.63923	0.206883	0.103442	+	0.994636i	$0.467015\pi$
$744$	−4.61891	−0.169337
$745$	−3.59201	−0.131601
$746$	−54.1499	−1.98257
$747$	14.8776	0.544342
$748$	−17.2187	−0.629578
$749$	16.0203	0.585370
$750$	3.79252	0.138483
$751$	15.5645	0.567955	0.283978	−	0.958831i	$-0.408346\pi$
$751$	15.5645	0.567955	0.283978	+	0.958831i	$0.408346\pi$
$752$	−37.4584	−1.36597
$753$	18.6749	0.680553
$754$	9.56487	0.348332
$755$	2.77113	0.100852
$756$	−3.91315	−0.142320
$757$	−1.33729	−0.0486045	−0.0243023	−	0.999705i	$-0.507736\pi$
$757$	−1.33729	−0.0486045	−0.0243023	+	0.999705i	$0.507736\pi$
$758$	−54.5489	−1.98130
$759$	−1.24834	−0.0453120
$760$	0.128544	0.00466278
$761$	43.5261	1.57782	0.788910	−	0.614508i	$-0.210646\pi$
$761$	43.5261	1.57782	0.788910	+	0.614508i	$0.210646\pi$
$762$	−2.91870	−0.105733
$763$	−4.89548	−0.177228
$764$	37.9116	1.37160
$765$	1.06330	0.0384436
$766$	39.8478	1.43976
$767$	4.56001	0.164652
$768$	−8.72113	−0.314697
$769$	10.6912	0.385536	0.192768	−	0.981244i	$-0.438254\pi$
$769$	10.6912	0.385536	0.192768	+	0.981244i	$0.438254\pi$
$770$	−0.786587	−0.0283466
$771$	20.4178	0.735328
$772$	−22.5827	−0.812768
$773$	50.8158	1.82772	0.913859	−	0.406032i	$-0.133088\pi$
$773$	50.8158	1.82772	0.913859	+	0.406032i	$0.133088\pi$
$774$	13.1646	0.473191
$775$	−30.2467	−1.08649
$776$	0.148605	0.00533459
$777$	−3.33985	−0.119817
$778$	−43.2837	−1.55180
$779$	5.51953	0.197758
$780$	−1.97123	−0.0705815
$781$	−17.2889	−0.618647
$782$	−12.1922	−0.435991
$783$	−1.00000	−0.0357371
$784$	13.3780	0.477785
$785$	2.24252	0.0800391
$786$	17.0129	0.606830
$787$	46.6255	1.66202	0.831010	−	0.556257i	$-0.187763\pi$
$787$	46.6255	1.66202	0.831010	+	0.556257i	$0.187763\pi$
$788$	24.2473	0.863776
$789$	−9.57459	−0.340864
$790$	−4.34635	−0.154636
$791$	13.6374	0.484891
$792$	−0.946832	−0.0336442
$793$	−40.1888	−1.42715
$794$	35.0238	1.24295
$795$	0.143543	0.00509095
$796$	22.6659	0.803370
$797$	−10.3688	−0.367283	−0.183642	−	0.982993i	$-0.558789\pi$
$797$	−10.3688	−0.367283	−0.183642	+	0.982993i	$0.558789\pi$
$798$	−3.21795	−0.113914
$799$	69.5882	2.46185
$800$	40.1309	1.41884
$801$	−7.42248	−0.262261
$802$	61.3937	2.16789
$803$	1.16760	0.0412036
$804$	−2.10453	−0.0742210
$805$	−0.301658	−0.0106320
$806$	58.2477	2.05169
$807$	18.1486	0.638861
$808$	−3.79063	−0.133354
$809$	41.7875	1.46917	0.734586	−	0.678516i	$-0.237376\pi$
$809$	41.7875	1.46917	0.734586	+	0.678516i	$0.237376\pi$
$810$	0.380514	0.0133699
$811$	−52.7642	−1.85280	−0.926400	−	0.376540i	$-0.877114\pi$
$811$	−52.7642	−1.85280	−0.926400	+	0.376540i	$0.877114\pi$
$812$	3.91315	0.137325
$813$	20.9277	0.733968
$814$	−5.25917	−0.184334
$815$	−2.87186	−0.100597
$816$	18.3391	0.641997
$817$	5.86339	0.205134
$818$	−11.9407	−0.417497
$819$	7.58268	0.264960
$820$	2.55399	0.0891893
$821$	−11.8624	−0.414000	−0.207000	−	0.978341i	$-0.566370\pi$
$821$	−11.8624	−0.414000	−0.207000	+	0.978341i	$0.566370\pi$
$822$	35.2608	1.22986
$823$	−19.5122	−0.680153	−0.340076	−	0.940398i	$-0.610453\pi$
$823$	−19.5122	−0.680153	−0.340076	+	0.940398i	$0.610453\pi$
$824$	−5.61482	−0.195601
$825$	−6.20029	−0.215866
$826$	3.44449	0.119849
$827$	12.9946	0.451866	0.225933	−	0.974143i	$-0.427457\pi$
$827$	12.9946	0.451866	0.225933	+	0.974143i	$0.427457\pi$
$828$	−2.36311	−0.0821238
$829$	−32.4072	−1.12555	−0.562774	−	0.826611i	$-0.690266\pi$
$829$	−32.4072	−1.12555	−0.562774	+	0.826611i	$0.690266\pi$
$830$	5.66113	0.196501
$831$	−9.52367	−0.330372
$832$	−48.5080	−1.68171
$833$	−24.8529	−0.861103
$834$	28.7931	0.997025
$835$	−1.51207	−0.0523274
$836$	−2.74447	−0.0949193
$837$	−6.08976	−0.210493
$838$	−52.4933	−1.81335
$839$	32.8658	1.13465	0.567327	−	0.823493i	$-0.307978\pi$
$839$	32.8658	1.13465	0.567327	+	0.823493i	$0.307978\pi$
$840$	−0.228799	−0.00789431
$841$	1.00000	0.0344828
$842$	−41.1125	−1.41683
$843$	−29.8149	−1.02688
$844$	1.29082	0.0444319
$845$	1.45156	0.0499351
$846$	24.9030	0.856183
$847$	−15.6347	−0.537214
$848$	2.47574	0.0850173
$849$	5.03871	0.172928
$850$	−60.5562	−2.07706
$851$	−2.01691	−0.0691386
$852$	−32.7280	−1.12124
$853$	−19.0654	−0.652788	−0.326394	−	0.945234i	$-0.605834\pi$
$853$	−19.0654	−0.652788	−0.326394	+	0.945234i	$0.605834\pi$
$854$	−30.3574	−1.03881
$855$	0.169478	0.00579601
$856$	7.33784	0.250802
$857$	−33.8199	−1.15527	−0.577633	−	0.816296i	$-0.696024\pi$
$857$	−33.8199	−1.15527	−0.577633	+	0.816296i	$0.696024\pi$
$858$	11.9402	0.407633
$859$	−42.1877	−1.43943	−0.719713	−	0.694271i	$-0.755727\pi$
$859$	−42.1877	−1.43943	−0.719713	+	0.694271i	$0.755727\pi$
$860$	2.71310	0.0925160
$861$	−9.82437	−0.334814
$862$	−53.0976	−1.80851
$863$	2.70791	0.0921784	0.0460892	−	0.998937i	$-0.485324\pi$
$863$	2.70791	0.0921784	0.0460892	+	0.998937i	$0.485324\pi$
$864$	8.07982	0.274881
$865$	−4.02049	−0.136701
$866$	−36.5247	−1.24116
$867$	−17.0694	−0.579707
$868$	23.8301	0.808847
$869$	14.2589	0.483701
$870$	−0.380514	−0.0129006
$871$	4.07804	0.138179
$872$	−2.24229	−0.0759336
$873$	0.195926	0.00663110
$874$	−1.94329	−0.0657328
$875$	−3.00657	−0.101641
$876$	2.21026	0.0746778
$877$	−25.2907	−0.854005	−0.427003	−	0.904250i	$-0.640430\pi$
$877$	−25.2907	−0.854005	−0.427003	+	0.904250i	$0.640430\pi$
$878$	−51.3301	−1.73231
$879$	3.55901	0.120043
$880$	0.714500	0.0240858
$881$	16.6376	0.560535	0.280267	−	0.959922i	$-0.409577\pi$
$881$	16.6376	0.560535	0.280267	+	0.959922i	$0.409577\pi$
$882$	−8.89392	−0.299474
$883$	3.55963	0.119791	0.0598955	−	0.998205i	$-0.480923\pi$
$883$	3.55963	0.119791	0.0598955	+	0.998205i	$0.480923\pi$
$884$	63.1608	2.12433
$885$	−0.181409	−0.00609798
$886$	−53.0947	−1.78375
$887$	33.9465	1.13981	0.569906	−	0.821710i	$-0.306980\pi$
$887$	33.9465	1.13981	0.569906	+	0.821710i	$0.306980\pi$
$888$	−1.52977	−0.0513356
$889$	2.31384	0.0776036
$890$	−2.82436	−0.0946728
$891$	−1.24834	−0.0418210
$892$	−54.9391	−1.83950
$893$	11.0916	0.371165
$894$	41.1872	1.37751
$895$	−0.365789	−0.0122270
$896$	−9.88220	−0.330141
$897$	4.57911	0.152892
$898$	42.9440	1.43306
$899$	6.08976	0.203105
$900$	−11.7371	−0.391238
$901$	−4.59930	−0.153225
$902$	−15.4702	−0.515100
$903$	−10.4364	−0.347302
$904$	6.24640	0.207752
$905$	−2.07459	−0.0689619
$906$	−31.7747	−1.05564
$907$	12.4010	0.411768	0.205884	−	0.978576i	$-0.433993\pi$
$907$	12.4010	0.411768	0.205884	+	0.978576i	$0.433993\pi$
$908$	31.3975	1.04196
$909$	−4.99772	−0.165764
$910$	2.88532	0.0956474
$911$	−40.1853	−1.33140	−0.665699	−	0.746220i	$-0.731867\pi$
$911$	−40.1853	−1.33140	−0.665699	+	0.746220i	$0.731867\pi$
$912$	2.92305	0.0967917
$913$	−18.5723	−0.614653
$914$	−53.5688	−1.77190
$915$	1.59881	0.0528551
$916$	−12.5076	−0.413264
$917$	−13.4872	−0.445387
$918$	−12.1922	−0.402401
$919$	21.9928	0.725476	0.362738	−	0.931891i	$-0.381842\pi$
$919$	21.9928	0.725476	0.362738	+	0.931891i	$0.381842\pi$
$920$	−0.138169	−0.00455531
$921$	−13.0739	−0.430799
$922$	−60.0092	−1.97630
$923$	63.4184	2.08744
$924$	4.88495	0.160703
$925$	−10.0176	−0.329377
$926$	−13.0693	−0.429484
$927$	−7.40281	−0.243140
$928$	−8.07982	−0.265233
$929$	1.97287	0.0647278	0.0323639	−	0.999476i	$-0.489696\pi$
$929$	1.97287	0.0647278	0.0323639	+	0.999476i	$0.489696\pi$
$930$	−2.31724	−0.0759853
$931$	−3.96127	−0.129826
$932$	5.31315	0.174038
$933$	6.36818	0.208485
$934$	47.1862	1.54398
$935$	−1.32736	−0.0434093
$936$	3.47312	0.113523
$937$	−56.4084	−1.84278	−0.921391	−	0.388637i	$-0.872946\pi$
$937$	−56.4084	−1.84278	−0.921391	+	0.388637i	$0.872946\pi$
$938$	3.08043	0.100579
$939$	−15.6031	−0.509187
$940$	5.13228	0.167397
$941$	−30.7782	−1.00334	−0.501670	−	0.865059i	$-0.667281\pi$
$941$	−30.7782	−1.00334	−0.501670	+	0.865059i	$0.667281\pi$
$942$	−25.7136	−0.837794
$943$	−5.93284	−0.193200
$944$	−3.12882	−0.101834
$945$	−0.301658	−0.00981293
$946$	−16.4339	−0.534313
$947$	−32.7331	−1.06368	−0.531841	−	0.846844i	$-0.678499\pi$
$947$	−32.7331	−1.06368	−0.531841	+	0.846844i	$0.678499\pi$
$948$	26.9922	0.876665
$949$	−4.28292	−0.139029
$950$	−9.65197	−0.313151
$951$	29.9720	0.971908
$952$	7.33100	0.237599
$953$	−8.70678	−0.282040	−0.141020	−	0.990007i	$-0.545038\pi$
$953$	−8.70678	−0.282040	−0.141020	+	0.990007i	$0.545038\pi$
$954$	−1.64592	−0.0532885
$955$	2.92254	0.0945713
$956$	−24.1417	−0.780798
$957$	1.24834	0.0403532
$958$	82.8219	2.67585
$959$	−27.9535	−0.902665
$960$	1.92977	0.0622830
$961$	6.08514	0.196295
$962$	19.2914	0.621981
$963$	9.67451	0.311757
$964$	−12.8487	−0.413828
$965$	−1.74086	−0.0560402
$966$	3.45892	0.111289
$967$	−26.1726	−0.841654	−0.420827	−	0.907141i	$-0.638260\pi$
$967$	−26.1726	−0.841654	−0.420827	+	0.907141i	$0.638260\pi$
$968$	−7.16122	−0.230170
$969$	−5.43028	−0.174446
$970$	0.0745528	0.00239375
$971$	7.67492	0.246300	0.123150	−	0.992388i	$-0.460700\pi$
$971$	7.67492	0.246300	0.123150	+	0.992388i	$0.460700\pi$
$972$	−2.36311	−0.0757969
$973$	−22.8262	−0.731773
$974$	11.8790	0.380627
$975$	22.7436	0.728377
$976$	27.5753	0.882664
$977$	2.19159	0.0701153	0.0350576	−	0.999385i	$-0.488839\pi$
$977$	2.19159	0.0701153	0.0350576	+	0.999385i	$0.488839\pi$
$978$	32.9298	1.05298
$979$	9.26580	0.296136
$980$	−1.83296	−0.0585517
$981$	−2.95633	−0.0943884
$982$	−40.2585	−1.28470
$983$	−56.7386	−1.80968	−0.904840	−	0.425752i	$-0.860010\pi$
$983$	−56.7386	−1.80968	−0.904840	+	0.425752i	$0.860010\pi$
$984$	−4.49989	−0.143451
$985$	1.86919	0.0595572
$986$	12.1922	0.388277
$987$	−19.7422	−0.628401
$988$	10.0671	0.320278
$989$	−6.30244	−0.200406
$990$	−0.475012	−0.0150969
$991$	19.0554	0.605314	0.302657	−	0.953100i	$-0.402126\pi$
$991$	19.0554	0.605314	0.302657	+	0.953100i	$0.402126\pi$
$992$	−49.2041	−1.56223
$993$	−22.5681	−0.716177
$994$	47.9043	1.51943
$995$	1.74727	0.0553922
$996$	−35.1574	−1.11400
$997$	20.3421	0.644241	0.322120	−	0.946699i	$-0.395604\pi$
$997$	20.3421	0.644241	0.322120	+	0.946699i	$0.395604\pi$
$998$	12.9926	0.411273
$999$	−2.01691	−0.0638121

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2001.2.a.k.1.8	✓	10
3.2	odd	2		6003.2.a.k.1.3		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2001.2.a.k.1.8	✓	10	1.1	even	1	trivial
6003.2.a.k.1.3		10	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)

\(f(q)\)	\(=\)	\(q+2.08881 q^{2} -1.00000 q^{3} +2.36311 q^{4} +0.182168 q^{5} -2.08881 q^{6} +1.65593 q^{7} +0.758471 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+2.08881 q^{2} -1.00000 q^{3} +2.36311 q^{4} +0.182168 q^{5} -2.08881 q^{6} +1.65593 q^{7} +0.758471 q^{8} +1.00000 q^{9} +0.380514 q^{10} -1.24834 q^{11} -2.36311 q^{12} +4.57911 q^{13} +3.45892 q^{14} -0.182168 q^{15} -3.14192 q^{16} +5.83690 q^{17} +2.08881 q^{18} +0.930336 q^{19} +0.430484 q^{20} -1.65593 q^{21} -2.60755 q^{22} -1.00000 q^{23} -0.758471 q^{24} -4.96681 q^{25} +9.56487 q^{26} -1.00000 q^{27} +3.91315 q^{28} +1.00000 q^{29} -0.380514 q^{30} +6.08976 q^{31} -8.07982 q^{32} +1.24834 q^{33} +12.1922 q^{34} +0.301658 q^{35} +2.36311 q^{36} +2.01691 q^{37} +1.94329 q^{38} -4.57911 q^{39} +0.138169 q^{40} +5.93284 q^{41} -3.45892 q^{42} +6.30244 q^{43} -2.94997 q^{44} +0.182168 q^{45} -2.08881 q^{46} +11.9221 q^{47} +3.14192 q^{48} -4.25790 q^{49} -10.3747 q^{50} -5.83690 q^{51} +10.8209 q^{52} -0.787969 q^{53} -2.08881 q^{54} -0.227408 q^{55} +1.25598 q^{56} -0.930336 q^{57} +2.08881 q^{58} +0.995830 q^{59} -0.430484 q^{60} -8.77657 q^{61} +12.7203 q^{62} +1.65593 q^{63} -10.5933 q^{64} +0.834168 q^{65} +2.60755 q^{66} +0.890575 q^{67} +13.7933 q^{68} +1.00000 q^{69} +0.630105 q^{70} +13.8495 q^{71} +0.758471 q^{72} -0.935317 q^{73} +4.21293 q^{74} +4.96681 q^{75} +2.19849 q^{76} -2.06717 q^{77} -9.56487 q^{78} -11.4223 q^{79} -0.572359 q^{80} +1.00000 q^{81} +12.3926 q^{82} +14.8776 q^{83} -3.91315 q^{84} +1.06330 q^{85} +13.1646 q^{86} -1.00000 q^{87} -0.946832 q^{88} -7.42248 q^{89} +0.380514 q^{90} +7.58268 q^{91} -2.36311 q^{92} -6.08976 q^{93} +24.9030 q^{94} +0.169478 q^{95} +8.07982 q^{96} +0.195926 q^{97} -8.89392 q^{98} -1.24834 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + 3 q^{2} - 10 q^{3} + 17 q^{4} + 6 q^{5} - 3 q^{6} + 3 q^{7} - 6 q^{8} + 10 q^{9}+O(q^{10}) \) 10 * q + 3 * q^2 - 10 * q^3 + 17 * q^4 + 6 * q^5 - 3 * q^6 + 3 * q^7 - 6 * q^8 + 10 * q^9	\( 10 q + 3 q^{2} - 10 q^{3} + 17 q^{4} + 6 q^{5} - 3 q^{6} + 3 q^{7} - 6 q^{8} + 10 q^{9} - 4 q^{10} + 9 q^{11} - 17 q^{12} - 16 q^{13} + 16 q^{14} - 6 q^{15} + 27 q^{16} + 3 q^{18} + q^{19} + 21 q^{20} - 3 q^{21} + 17 q^{22} - 10 q^{23} + 6 q^{24} - 4 q^{25} + 28 q^{26} - 10 q^{27} - 14 q^{28} + 10 q^{29} + 4 q^{30} + 17 q^{31} + 21 q^{32} - 9 q^{33} - 3 q^{34} + 29 q^{35} + 17 q^{36} + q^{37} + 32 q^{38} + 16 q^{39} + 13 q^{40} - 16 q^{42} - 5 q^{43} + 33 q^{44} + 6 q^{45} - 3 q^{46} + 15 q^{47} - 27 q^{48} + 31 q^{49} - 22 q^{50} - 21 q^{52} + 35 q^{53} - 3 q^{54} - 20 q^{55} + 18 q^{56} - q^{57} + 3 q^{58} + 49 q^{59} - 21 q^{60} + 8 q^{61} + 15 q^{62} + 3 q^{63} + 12 q^{64} - 3 q^{65} - 17 q^{66} + 35 q^{67} - 18 q^{68} + 10 q^{69} - 16 q^{70} + 30 q^{71} - 6 q^{72} - 15 q^{73} + 23 q^{74} + 4 q^{75} + 10 q^{76} + 23 q^{77} - 28 q^{78} + 24 q^{79} + 23 q^{80} + 10 q^{81} - 5 q^{82} + q^{83} + 14 q^{84} - 10 q^{86} - 10 q^{87} + 18 q^{88} + 15 q^{89} - 4 q^{90} + 26 q^{91} - 17 q^{92} - 17 q^{93} + 3 q^{94} + 7 q^{95} - 21 q^{96} - 35 q^{97} + 3 q^{98} + 9 q^{99}+O(q^{100}) \) 10 * q + 3 * q^2 - 10 * q^3 + 17 * q^4 + 6 * q^5 - 3 * q^6 + 3 * q^7 - 6 * q^8 + 10 * q^9 - 4 * q^10 + 9 * q^11 - 17 * q^12 - 16 * q^13 + 16 * q^14 - 6 * q^15 + 27 * q^16 + 3 * q^18 + q^19 + 21 * q^20 - 3 * q^21 + 17 * q^22 - 10 * q^23 + 6 * q^24 - 4 * q^25 + 28 * q^26 - 10 * q^27 - 14 * q^28 + 10 * q^29 + 4 * q^30 + 17 * q^31 + 21 * q^32 - 9 * q^33 - 3 * q^34 + 29 * q^35 + 17 * q^36 + q^37 + 32 * q^38 + 16 * q^39 + 13 * q^40 - 16 * q^42 - 5 * q^43 + 33 * q^44 + 6 * q^45 - 3 * q^46 + 15 * q^47 - 27 * q^48 + 31 * q^49 - 22 * q^50 - 21 * q^52 + 35 * q^53 - 3 * q^54 - 20 * q^55 + 18 * q^56 - q^57 + 3 * q^58 + 49 * q^59 - 21 * q^60 + 8 * q^61 + 15 * q^62 + 3 * q^63 + 12 * q^64 - 3 * q^65 - 17 * q^66 + 35 * q^67 - 18 * q^68 + 10 * q^69 - 16 * q^70 + 30 * q^71 - 6 * q^72 - 15 * q^73 + 23 * q^74 + 4 * q^75 + 10 * q^76 + 23 * q^77 - 28 * q^78 + 24 * q^79 + 23 * q^80 + 10 * q^81 - 5 * q^82 + q^83 + 14 * q^84 - 10 * q^86 - 10 * q^87 + 18 * q^88 + 15 * q^89 - 4 * q^90 + 26 * q^91 - 17 * q^92 - 17 * q^93 + 3 * q^94 + 7 * q^95 - 21 * q^96 - 35 * q^97 + 3 * q^98 + 9 * q^99

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