LMFDB - Embedded newform 2001.2.a.k.1.6

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			1.6
Root			$-1.52497$ of defining polynomial
Character	$\chi$	$=$	2001.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.676519 q^{2} -1.00000 q^{3} -1.54232 q^{4} -1.80585 q^{5} -0.676519 q^{6} -4.44627 q^{7} -2.39645 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+0.676519 q^{2} -1.00000 q^{3} -1.54232 q^{4} -1.80585 q^{5} -0.676519 q^{6} -4.44627 q^{7} -2.39645 q^{8} +1.00000 q^{9} -1.22169 q^{10} -1.20345 q^{11} +1.54232 q^{12} -3.05496 q^{13} -3.00799 q^{14} +1.80585 q^{15} +1.46340 q^{16} -6.57035 q^{17} +0.676519 q^{18} -2.24073 q^{19} +2.78521 q^{20} +4.44627 q^{21} -0.814156 q^{22} -1.00000 q^{23} +2.39645 q^{24} -1.73890 q^{25} -2.06674 q^{26} -1.00000 q^{27} +6.85758 q^{28} +1.00000 q^{29} +1.22169 q^{30} +2.34985 q^{31} +5.78292 q^{32} +1.20345 q^{33} -4.44497 q^{34} +8.02931 q^{35} -1.54232 q^{36} -8.63631 q^{37} -1.51589 q^{38} +3.05496 q^{39} +4.32763 q^{40} -1.57477 q^{41} +3.00799 q^{42} +6.47389 q^{43} +1.85610 q^{44} -1.80585 q^{45} -0.676519 q^{46} -8.54965 q^{47} -1.46340 q^{48} +12.7693 q^{49} -1.17640 q^{50} +6.57035 q^{51} +4.71172 q^{52} +11.5800 q^{53} -0.676519 q^{54} +2.17325 q^{55} +10.6553 q^{56} +2.24073 q^{57} +0.676519 q^{58} -6.15579 q^{59} -2.78521 q^{60} -0.352405 q^{61} +1.58972 q^{62} -4.44627 q^{63} +0.985449 q^{64} +5.51680 q^{65} +0.814156 q^{66} +1.02872 q^{67} +10.1336 q^{68} +1.00000 q^{69} +5.43198 q^{70} -3.08000 q^{71} -2.39645 q^{72} -8.06192 q^{73} -5.84263 q^{74} +1.73890 q^{75} +3.45592 q^{76} +5.35086 q^{77} +2.06674 q^{78} +4.13197 q^{79} -2.64269 q^{80} +1.00000 q^{81} -1.06536 q^{82} -1.05082 q^{83} -6.85758 q^{84} +11.8651 q^{85} +4.37971 q^{86} -1.00000 q^{87} +2.88400 q^{88} +2.79007 q^{89} -1.22169 q^{90} +13.5832 q^{91} +1.54232 q^{92} -2.34985 q^{93} -5.78400 q^{94} +4.04642 q^{95} -5.78292 q^{96} +8.49231 q^{97} +8.63870 q^{98} -1.20345 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	0.676519	0.478371	0.239186	−	0.970974i	$-0.423120\pi$
$2$	0.676519	0.478371	0.239186	+	0.970974i	$0.423120\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	−1.54232	−0.771161
$5$	−1.80585	−0.807601	−0.403801	−	0.914847i	$-0.632311\pi$
$5$	−1.80585	−0.807601	−0.403801	+	0.914847i	$0.632311\pi$
$6$	−0.676519	−0.276188
$7$	−4.44627	−1.68053	−0.840267	−	0.542173i	$-0.817602\pi$
$7$	−4.44627	−1.68053	−0.840267	+	0.542173i	$0.817602\pi$
$8$	−2.39645	−0.847272
$9$	1.00000	0.333333
$10$	−1.22169	−0.386333
$11$	−1.20345	−0.362853	−0.181427	−	0.983404i	$-0.558072\pi$
$11$	−1.20345	−0.362853	−0.181427	+	0.983404i	$0.558072\pi$
$12$	1.54232	0.445230
$13$	−3.05496	−0.847292	−0.423646	−	0.905828i	$-0.639250\pi$
$13$	−3.05496	−0.847292	−0.423646	+	0.905828i	$0.639250\pi$
$14$	−3.00799	−0.803919
$15$	1.80585	0.466269
$16$	1.46340	0.365850
$17$	−6.57035	−1.59354	−0.796772	−	0.604280i	$-0.793461\pi$
$17$	−6.57035	−1.59354	−0.796772	+	0.604280i	$0.793461\pi$
$18$	0.676519	0.159457
$19$	−2.24073	−0.514058	−0.257029	−	0.966404i	$-0.582744\pi$
$19$	−2.24073	−0.514058	−0.257029	+	0.966404i	$0.582744\pi$
$20$	2.78521	0.622791
$21$	4.44627	0.970256
$22$	−0.814156	−0.173579
$23$	−1.00000	−0.208514
$23$	−1.00000	−0.208514
$24$	2.39645	0.489173
$25$	−1.73890	−0.347780
$26$	−2.06674	−0.405320
$27$	−1.00000	−0.192450
$28$	6.85758	1.29596
$29$	1.00000	0.185695
$29$	1.00000	0.185695
$30$	1.22169	0.223050
$31$	2.34985	0.422045	0.211022	−	0.977481i	$-0.432321\pi$
$31$	2.34985	0.422045	0.211022	+	0.977481i	$0.432321\pi$
$32$	5.78292	1.02228
$33$	1.20345	0.209493
$34$	−4.44497	−0.762306
$35$	8.02931	1.35720
$36$	−1.54232	−0.257054
$37$	−8.63631	−1.41980	−0.709900	−	0.704302i	$-0.751260\pi$
$37$	−8.63631	−1.41980	−0.709900	+	0.704302i	$0.751260\pi$
$38$	−1.51589	−0.245910
$39$	3.05496	0.489184
$40$	4.32763	0.684258
$41$	−1.57477	−0.245937	−0.122969	−	0.992411i	$-0.539241\pi$
$41$	−1.57477	−0.245937	−0.122969	+	0.992411i	$0.539241\pi$
$42$	3.00799	0.464143
$43$	6.47389	0.987259	0.493629	−	0.869672i	$-0.335670\pi$
$43$	6.47389	0.987259	0.493629	+	0.869672i	$0.335670\pi$
$44$	1.85610	0.279818
$45$	−1.80585	−0.269200
$46$	−0.676519	−0.0997473
$47$	−8.54965	−1.24709	−0.623547	−	0.781786i	$-0.714309\pi$
$47$	−8.54965	−1.24709	−0.623547	+	0.781786i	$0.714309\pi$
$48$	−1.46340	−0.211224
$49$	12.7693	1.82419
$50$	−1.17640	−0.166368
$51$	6.57035	0.920033
$52$	4.71172	0.653399
$53$	11.5800	1.59063	0.795315	−	0.606197i	$-0.207306\pi$
$53$	11.5800	1.59063	0.795315	+	0.606197i	$0.207306\pi$
$54$	−0.676519	−0.0920626
$55$	2.17325	0.293041
$56$	10.6553	1.42387
$57$	2.24073	0.296791
$58$	0.676519	0.0888313
$59$	−6.15579	−0.801416	−0.400708	−	0.916206i	$-0.631236\pi$
$59$	−6.15579	−0.801416	−0.400708	+	0.916206i	$0.631236\pi$
$60$	−2.78521	−0.359568
$61$	−0.352405	−0.0451209	−0.0225604	−	0.999745i	$-0.507182\pi$
$61$	−0.352405	−0.0451209	−0.0225604	+	0.999745i	$0.507182\pi$
$62$	1.58972	0.201894
$63$	−4.44627	−0.560178
$64$	0.985449	0.123181
$65$	5.51680	0.684274
$66$	0.814156	0.100216
$67$	1.02872	0.125678	0.0628389	−	0.998024i	$-0.479985\pi$
$67$	1.02872	0.125678	0.0628389	+	0.998024i	$0.479985\pi$
$68$	10.1336	1.22888
$69$	1.00000	0.120386
$70$	5.43198	0.649246
$71$	−3.08000	−0.365529	−0.182764	−	0.983157i	$-0.558505\pi$
$71$	−3.08000	−0.365529	−0.182764	+	0.983157i	$0.558505\pi$
$72$	−2.39645	−0.282424
$73$	−8.06192	−0.943577	−0.471788	−	0.881712i	$-0.656391\pi$
$73$	−8.06192	−0.943577	−0.471788	+	0.881712i	$0.656391\pi$
$74$	−5.84263	−0.679192
$75$	1.73890	0.200791
$76$	3.45592	0.396421
$77$	5.35086	0.609787
$78$	2.06674	0.234012
$79$	4.13197	0.464883	0.232441	−	0.972610i	$-0.425329\pi$
$79$	4.13197	0.464883	0.232441	+	0.972610i	$0.425329\pi$
$80$	−2.64269	−0.295461
$81$	1.00000	0.111111
$82$	−1.06536	−0.117649
$83$	−1.05082	−0.115343	−0.0576715	−	0.998336i	$-0.518368\pi$
$83$	−1.05082	−0.115343	−0.0576715	+	0.998336i	$0.518368\pi$
$84$	−6.85758	−0.748224
$85$	11.8651	1.28695
$86$	4.37971	0.472276
$87$	−1.00000	−0.107211
$88$	2.88400	0.307436
$89$	2.79007	0.295747	0.147874	−	0.989006i	$-0.452757\pi$
$89$	2.79007	0.295747	0.147874	+	0.989006i	$0.452757\pi$
$90$	−1.22169	−0.128778
$91$	13.5832	1.42390
$92$	1.54232	0.160798
$93$	−2.34985	−0.243668
$94$	−5.78400	−0.596574
$95$	4.04642	0.415154
$96$	−5.78292	−0.590216
$97$	8.49231	0.862264	0.431132	−	0.902289i	$-0.358114\pi$
$97$	8.49231	0.862264	0.431132	+	0.902289i	$0.358114\pi$
$98$	8.63870	0.872641
$99$	−1.20345	−0.120951
$100$	2.68194	0.268194
$101$	−17.0960	−1.70112	−0.850558	−	0.525881i	$-0.823736\pi$
$101$	−17.0960	−1.70112	−0.850558	+	0.525881i	$0.823736\pi$
$102$	4.44497	0.440117
$103$	−3.01098	−0.296681	−0.148340	−	0.988936i	$-0.547393\pi$
$103$	−3.01098	−0.296681	−0.148340	+	0.988936i	$0.547393\pi$
$104$	7.32104	0.717887
$105$	−8.02931	−0.783580
$106$	7.83406	0.760911
$107$	5.04070	0.487302	0.243651	−	0.969863i	$-0.421655\pi$
$107$	5.04070	0.487302	0.243651	+	0.969863i	$0.421655\pi$
$108$	1.54232	0.148410
$109$	15.6993	1.50372	0.751859	−	0.659323i	$-0.229157\pi$
$109$	15.6993	1.50372	0.751859	+	0.659323i	$0.229157\pi$
$110$	1.47024	0.140182
$111$	8.63631	0.819722
$112$	−6.50668	−0.614824
$113$	7.47730	0.703405	0.351702	−	0.936112i	$-0.385603\pi$
$113$	7.47730	0.703405	0.351702	+	0.936112i	$0.385603\pi$
$114$	1.51589	0.141976
$115$	1.80585	0.168397
$116$	−1.54232	−0.143201
$117$	−3.05496	−0.282431
$118$	−4.16451	−0.383374
$119$	29.2136	2.67800
$120$	−4.32763	−0.395057
$121$	−9.55171	−0.868337
$122$	−0.238409	−0.0215845
$123$	1.57477	0.141992
$124$	−3.62422	−0.325465
$125$	12.1695	1.08847
$126$	−3.00799	−0.267973
$127$	−13.3040	−1.18054	−0.590271	−	0.807205i	$-0.700979\pi$
$127$	−13.3040	−1.18054	−0.590271	+	0.807205i	$0.700979\pi$
$128$	−10.8992	−0.963358
$129$	−6.47389	−0.569994
$130$	3.73222	0.327337
$131$	2.38913	0.208739	0.104369	−	0.994539i	$-0.466718\pi$
$131$	2.38913	0.208739	0.104369	+	0.994539i	$0.466718\pi$
$132$	−1.85610	−0.161553
$133$	9.96288	0.863891
$134$	0.695947	0.0601207
$135$	1.80585	0.155423
$136$	15.7455	1.35017
$137$	−20.7731	−1.77476	−0.887381	−	0.461036i	$-0.847478\pi$
$137$	−20.7731	−1.77476	−0.887381	+	0.461036i	$0.847478\pi$
$138$	0.676519	0.0575891
$139$	−14.9484	−1.26790	−0.633952	−	0.773372i	$-0.718568\pi$
$139$	−14.9484	−1.26790	−0.633952	+	0.773372i	$0.718568\pi$
$140$	−12.3838	−1.04662
$141$	8.54965	0.720010
$142$	−2.08368	−0.174859
$143$	3.67648	0.307443
$144$	1.46340	0.121950
$145$	−1.80585	−0.149968
$146$	−5.45404	−0.451380
$147$	−12.7693	−1.05320
$148$	13.3200	1.09490
$149$	4.47172	0.366337	0.183169	−	0.983082i	$-0.441365\pi$
$149$	4.47172	0.366337	0.183169	+	0.983082i	$0.441365\pi$
$150$	1.17640	0.0960525
$151$	9.66669	0.786664	0.393332	−	0.919396i	$-0.371322\pi$
$151$	9.66669	0.786664	0.393332	+	0.919396i	$0.371322\pi$
$152$	5.36978	0.435547
$153$	−6.57035	−0.531181
$154$	3.61996	0.291705
$155$	−4.24347	−0.340844
$156$	−4.71172	−0.377240
$157$	−5.80134	−0.462997	−0.231499	−	0.972835i	$-0.574363\pi$
$157$	−5.80134	−0.462997	−0.231499	+	0.972835i	$0.574363\pi$
$158$	2.79536	0.222387
$159$	−11.5800	−0.918350
$160$	−10.4431	−0.825599
$161$	4.44627	0.350415
$162$	0.676519	0.0531524
$163$	−20.1694	−1.57979	−0.789895	−	0.613242i	$-0.789865\pi$
$163$	−20.1694	−1.57979	−0.789895	+	0.613242i	$0.789865\pi$
$164$	2.42880	0.189657
$165$	−2.17325	−0.169187
$166$	−0.710903	−0.0551768
$167$	7.19069	0.556432	0.278216	−	0.960518i	$-0.410257\pi$
$167$	7.19069	0.556432	0.278216	+	0.960518i	$0.410257\pi$
$168$	−10.6553	−0.822071
$169$	−3.66725	−0.282096
$170$	8.02695	0.615639
$171$	−2.24073	−0.171353
$172$	−9.98482	−0.761336
$173$	−15.0384	−1.14335	−0.571675	−	0.820480i	$-0.693706\pi$
$173$	−15.0384	−1.14335	−0.571675	+	0.820480i	$0.693706\pi$
$174$	−0.676519	−0.0512868
$175$	7.73162	0.584456
$176$	−1.76113	−0.132750
$177$	6.15579	0.462698
$178$	1.88754	0.141477
$179$	10.0005	0.747471	0.373736	−	0.927535i	$-0.378077\pi$
$179$	10.0005	0.747471	0.373736	+	0.927535i	$0.378077\pi$
$180$	2.78521	0.207597
$181$	−11.6624	−0.866858	−0.433429	−	0.901188i	$-0.642696\pi$
$181$	−11.6624	−0.866858	−0.433429	+	0.901188i	$0.642696\pi$
$182$	9.18927	0.681154
$183$	0.352405	0.0260506
$184$	2.39645	0.176669
$185$	15.5959	1.14663
$186$	−1.58972	−0.116564
$187$	7.90708	0.578223
$188$	13.1863	0.961710
$189$	4.44627	0.323419
$190$	2.73748	0.198598
$191$	4.81810	0.348626	0.174313	−	0.984690i	$-0.444230\pi$
$191$	4.81810	0.348626	0.174313	+	0.984690i	$0.444230\pi$
$192$	−0.985449	−0.0711187
$193$	−26.0157	−1.87265	−0.936325	−	0.351133i	$-0.885796\pi$
$193$	−26.0157	−1.87265	−0.936325	+	0.351133i	$0.885796\pi$
$194$	5.74521	0.412482
$195$	−5.51680	−0.395066
$196$	−19.6944	−1.40675
$197$	9.97511	0.710697	0.355349	−	0.934734i	$-0.384362\pi$
$197$	9.97511	0.710697	0.355349	+	0.934734i	$0.384362\pi$
$198$	−0.814156	−0.0578595
$199$	18.3470	1.30058	0.650292	−	0.759684i	$-0.274647\pi$
$199$	18.3470	1.30058	0.650292	+	0.759684i	$0.274647\pi$
$200$	4.16718	0.294664
$201$	−1.02872	−0.0725602
$202$	−11.5658	−0.813765
$203$	−4.44627	−0.312067
$204$	−10.1336	−0.709494
$205$	2.84380	0.198619
$206$	−2.03699	−0.141923
$207$	−1.00000	−0.0695048
$208$	−4.47063	−0.309982
$209$	2.69660	0.186528
$210$	−5.43198	−0.374842
$211$	−16.5709	−1.14079	−0.570394	−	0.821371i	$-0.693210\pi$
$211$	−16.5709	−1.14079	−0.570394	+	0.821371i	$0.693210\pi$
$212$	−17.8600	−1.22663
$213$	3.08000	0.211038
$214$	3.41013	0.233111
$215$	−11.6909	−0.797312
$216$	2.39645	0.163058
$217$	−10.4481	−0.709260
$218$	10.6209	0.719336
$219$	8.06192	0.544774
$220$	−3.35185	−0.225982
$221$	20.0721	1.35020
$222$	5.84263	0.392132
$223$	−9.89206	−0.662422	−0.331211	−	0.943557i	$-0.607457\pi$
$223$	−9.89206	−0.662422	−0.331211	+	0.943557i	$0.607457\pi$
$224$	−25.7124	−1.71798
$225$	−1.73890	−0.115927
$226$	5.05853	0.336489
$227$	11.8612	0.787258	0.393629	−	0.919269i	$-0.371219\pi$
$227$	11.8612	0.787258	0.393629	+	0.919269i	$0.371219\pi$
$228$	−3.45592	−0.228874
$229$	−26.6481	−1.76095	−0.880477	−	0.474089i	$-0.842777\pi$
$229$	−26.6481	−1.76095	−0.880477	+	0.474089i	$0.842777\pi$
$230$	1.22169	0.0805561
$231$	−5.35086	−0.352061
$232$	−2.39645	−0.157335
$233$	−5.10509	−0.334445	−0.167223	−	0.985919i	$-0.553480\pi$
$233$	−5.10509	−0.334445	−0.167223	+	0.985919i	$0.553480\pi$
$234$	−2.06674	−0.135107
$235$	15.4394	1.00716
$236$	9.49422	0.618021
$237$	−4.13197	−0.268400
$238$	19.7635	1.28108
$239$	10.0944	0.652950	0.326475	−	0.945206i	$-0.394139\pi$
$239$	10.0944	0.652950	0.326475	+	0.945206i	$0.394139\pi$
$240$	2.64269	0.170585
$241$	3.36654	0.216858	0.108429	−	0.994104i	$-0.465418\pi$
$241$	3.36654	0.216858	0.108429	+	0.994104i	$0.465418\pi$
$242$	−6.46191	−0.415388
$243$	−1.00000	−0.0641500
$244$	0.543523	0.0347955
$245$	−23.0595	−1.47322
$246$	1.06536	0.0679249
$247$	6.84532	0.435557
$248$	−5.63128	−0.357587
$249$	1.05082	0.0665933
$250$	8.23287	0.520692
$251$	4.68444	0.295679	0.147839	−	0.989011i	$-0.452768\pi$
$251$	4.68444	0.295679	0.147839	+	0.989011i	$0.452768\pi$
$252$	6.85758	0.431987
$253$	1.20345	0.0756602
$254$	−9.00044	−0.564738
$255$	−11.8651	−0.743020
$256$	−9.34438	−0.584024
$257$	−28.4842	−1.77680	−0.888398	−	0.459074i	$-0.848181\pi$
$257$	−28.4842	−1.77680	−0.888398	+	0.459074i	$0.848181\pi$
$258$	−4.37971	−0.272669
$259$	38.3994	2.38602
$260$	−8.50868	−0.527686
$261$	1.00000	0.0618984
$262$	1.61629	0.0998547
$263$	15.3003	0.943459	0.471730	−	0.881743i	$-0.343630\pi$
$263$	15.3003	0.943459	0.471730	+	0.881743i	$0.343630\pi$
$264$	−2.88400	−0.177498
$265$	−20.9117	−1.28459
$266$	6.74008	0.413261
$267$	−2.79007	−0.170750
$268$	−1.58661	−0.0969179
$269$	11.6444	0.709971	0.354986	−	0.934872i	$-0.384486\pi$
$269$	11.6444	0.709971	0.354986	+	0.934872i	$0.384486\pi$
$270$	1.22169	0.0743499
$271$	24.5547	1.49159	0.745796	−	0.666174i	$-0.232069\pi$
$271$	24.5547	1.49159	0.745796	+	0.666174i	$0.232069\pi$
$272$	−9.61506	−0.582999
$273$	−13.5832	−0.822091
$274$	−14.0534	−0.848995
$275$	2.09268	0.126193
$276$	−1.54232	−0.0928369
$277$	−12.1114	−0.727705	−0.363853	−	0.931457i	$-0.618539\pi$
$277$	−12.1114	−0.727705	−0.363853	+	0.931457i	$0.618539\pi$
$278$	−10.1129	−0.606529
$279$	2.34985	0.140682
$280$	−19.2418	−1.14992
$281$	−18.1178	−1.08082	−0.540408	−	0.841403i	$-0.681730\pi$
$281$	−18.1178	−1.08082	−0.540408	+	0.841403i	$0.681730\pi$
$282$	5.78400	0.344432
$283$	−0.417794	−0.0248352	−0.0124176	−	0.999923i	$-0.503953\pi$
$283$	−0.417794	−0.0248352	−0.0124176	+	0.999923i	$0.503953\pi$
$284$	4.75035	0.281882
$285$	−4.04642	−0.239689
$286$	2.48721	0.147072
$287$	7.00185	0.413306
$288$	5.78292	0.340762
$289$	26.1695	1.53938
$290$	−1.22169	−0.0717403
$291$	−8.49231	−0.497828
$292$	12.4341	0.727649
$293$	25.6351	1.49762	0.748810	−	0.662785i	$-0.230626\pi$
$293$	25.6351	1.49762	0.748810	+	0.662785i	$0.230626\pi$
$294$	−8.63870	−0.503819
$295$	11.1165	0.647225
$296$	20.6965	1.20296
$297$	1.20345	0.0698312
$298$	3.02520	0.175245
$299$	3.05496	0.176673
$300$	−2.68194	−0.154842
$301$	−28.7847	−1.65912
$302$	6.53970	0.376318
$303$	17.0960	0.982140
$304$	−3.27908	−0.188068
$305$	0.636392	0.0364397
$306$	−4.44497	−0.254102
$307$	12.6821	0.723803	0.361901	−	0.932216i	$-0.382128\pi$
$307$	12.6821	0.723803	0.361901	+	0.932216i	$0.382128\pi$
$308$	−8.25275	−0.470244
$309$	3.01098	0.171289
$310$	−2.87079	−0.163050
$311$	−4.59395	−0.260499	−0.130250	−	0.991481i	$-0.541578\pi$
$311$	−4.59395	−0.260499	−0.130250	+	0.991481i	$0.541578\pi$
$312$	−7.32104	−0.414472
$313$	1.81844	0.102784	0.0513922	−	0.998679i	$-0.483634\pi$
$313$	1.81844	0.102784	0.0513922	+	0.998679i	$0.483634\pi$
$314$	−3.92472	−0.221485
$315$	8.02931	0.452400
$316$	−6.37283	−0.358500
$317$	−1.90790	−0.107158	−0.0535790	−	0.998564i	$-0.517063\pi$
$317$	−1.90790	−0.107158	−0.0535790	+	0.998564i	$0.517063\pi$
$318$	−7.83406	−0.439312
$319$	−1.20345	−0.0673802
$320$	−1.77958	−0.0994813
$321$	−5.04070	−0.281344
$322$	3.00799	0.167629
$323$	14.7224	0.819174
$324$	−1.54232	−0.0856846
$325$	5.31226	0.294671
$326$	−13.6450	−0.755726
$327$	−15.6993	−0.868172
$328$	3.77385	0.208376
$329$	38.0141	2.09578
$330$	−1.47024	−0.0809343
$331$	−25.1550	−1.38264	−0.691321	−	0.722548i	$-0.742971\pi$
$331$	−25.1550	−1.38264	−0.691321	+	0.722548i	$0.742971\pi$
$332$	1.62071	0.0889480
$333$	−8.63631	−0.473267
$334$	4.86464	0.266181
$335$	−1.85771	−0.101498
$336$	6.50668	0.354969
$337$	0.556403	0.0303092	0.0151546	−	0.999885i	$-0.495176\pi$
$337$	0.556403	0.0303092	0.0151546	+	0.999885i	$0.495176\pi$
$338$	−2.48096	−0.134947
$339$	−7.47730	−0.406111
$340$	−18.2998	−0.992445
$341$	−2.82792	−0.153140
$342$	−1.51589	−0.0819701
$343$	−25.6521	−1.38508
$344$	−15.5143	−0.836477
$345$	−1.80585	−0.0972238
$346$	−10.1738	−0.546946
$347$	10.0168	0.537732	0.268866	−	0.963178i	$-0.413351\pi$
$347$	10.0168	0.537732	0.268866	+	0.963178i	$0.413351\pi$
$348$	1.54232	0.0826771
$349$	−8.01232	−0.428889	−0.214445	−	0.976736i	$-0.568794\pi$
$349$	−8.01232	−0.428889	−0.214445	+	0.976736i	$0.568794\pi$
$350$	5.23059	0.279587
$351$	3.05496	0.163061
$352$	−6.95944	−0.370939
$353$	8.43622	0.449014	0.224507	−	0.974472i	$-0.427923\pi$
$353$	8.43622	0.449014	0.224507	+	0.974472i	$0.427923\pi$
$354$	4.16451	0.221341
$355$	5.56203	0.295202
$356$	−4.30319	−0.228069
$357$	−29.2136	−1.54615
$358$	6.76552	0.357569
$359$	17.8109	0.940023	0.470011	−	0.882660i	$-0.344250\pi$
$359$	17.8109	0.940023	0.470011	+	0.882660i	$0.344250\pi$
$360$	4.32763	0.228086
$361$	−13.9791	−0.735745
$362$	−7.88982	−0.414680
$363$	9.55171	0.501335
$364$	−20.9496	−1.09806
$365$	14.5586	0.762034
$366$	0.238409	0.0124618
$367$	29.2520	1.52694	0.763471	−	0.645842i	$-0.223494\pi$
$367$	29.2520	1.52694	0.763471	+	0.645842i	$0.223494\pi$
$368$	−1.46340	−0.0762851
$369$	−1.57477	−0.0819791
$370$	10.5509	0.548516
$371$	−51.4876	−2.67311
$372$	3.62422	0.187907
$373$	−29.6981	−1.53771	−0.768855	−	0.639423i	$-0.779173\pi$
$373$	−29.6981	−1.53771	−0.768855	+	0.639423i	$0.779173\pi$
$374$	5.34929	0.276605
$375$	−12.1695	−0.628428
$376$	20.4888	1.05663
$377$	−3.05496	−0.157338
$378$	3.00799	0.154714
$379$	8.27683	0.425152	0.212576	−	0.977144i	$-0.431815\pi$
$379$	8.27683	0.425152	0.212576	+	0.977144i	$0.431815\pi$
$380$	−6.24088	−0.320150
$381$	13.3040	0.681587
$382$	3.25954	0.166772
$383$	−24.9707	−1.27594	−0.637972	−	0.770059i	$-0.720227\pi$
$383$	−24.9707	−1.27594	−0.637972	+	0.770059i	$0.720227\pi$
$384$	10.8992	0.556195
$385$	−9.66286	−0.492465
$386$	−17.6001	−0.895822
$387$	6.47389	0.329086
$388$	−13.0979	−0.664944
$389$	21.7567	1.10311	0.551554	−	0.834139i	$-0.314035\pi$
$389$	21.7567	1.10311	0.551554	+	0.834139i	$0.314035\pi$
$390$	−3.73222	−0.188988
$391$	6.57035	0.332277
$392$	−30.6011	−1.54559
$393$	−2.38913	−0.120515
$394$	6.74835	0.339977
$395$	−7.46172	−0.375440
$396$	1.85610	0.0932728
$397$	−25.4546	−1.27753	−0.638766	−	0.769401i	$-0.720555\pi$
$397$	−25.4546	−1.27753	−0.638766	+	0.769401i	$0.720555\pi$
$398$	12.4121	0.622162
$399$	−9.96288	−0.498768
$400$	−2.54471	−0.127235
$401$	11.4283	0.570702	0.285351	−	0.958423i	$-0.407890\pi$
$401$	11.4283	0.570702	0.285351	+	0.958423i	$0.407890\pi$
$402$	−0.695947	−0.0347107
$403$	−7.17867	−0.357595
$404$	26.3676	1.31184
$405$	−1.80585	−0.0897335
$406$	−3.00799	−0.149284
$407$	10.3934	0.515179
$408$	−15.7455	−0.779519
$409$	−1.27697	−0.0631420	−0.0315710	−	0.999502i	$-0.510051\pi$
$409$	−1.27697	−0.0631420	−0.0315710	+	0.999502i	$0.510051\pi$
$410$	1.92388	0.0950138
$411$	20.7731	1.02466
$412$	4.64390	0.228789
$413$	27.3703	1.34681
$414$	−0.676519	−0.0332491
$415$	1.89763	0.0931512
$416$	−17.6665	−0.866174
$417$	14.9484	0.732025
$418$	1.82430	0.0892294
$419$	−10.5176	−0.513820	−0.256910	−	0.966435i	$-0.582704\pi$
$419$	−10.5176	−0.513820	−0.256910	+	0.966435i	$0.582704\pi$
$420$	12.3838	0.604267
$421$	−18.7938	−0.915952	−0.457976	−	0.888964i	$-0.651426\pi$
$421$	−18.7938	−0.915952	−0.457976	+	0.888964i	$0.651426\pi$
$422$	−11.2105	−0.545720
$423$	−8.54965	−0.415698
$424$	−27.7508	−1.34770
$425$	11.4252	0.554203
$426$	2.08368	0.100955
$427$	1.56689	0.0758272
$428$	−7.77438	−0.375789
$429$	−3.67648	−0.177502
$430$	−7.90911	−0.381411
$431$	5.42412	0.261270	0.130635	−	0.991430i	$-0.458298\pi$
$431$	5.42412	0.261270	0.130635	+	0.991430i	$0.458298\pi$
$432$	−1.46340	−0.0704079
$433$	−8.03271	−0.386028	−0.193014	−	0.981196i	$-0.561826\pi$
$433$	−8.03271	−0.386028	−0.193014	+	0.981196i	$0.561826\pi$
$434$	−7.06831	−0.339290
$435$	1.80585	0.0865840
$436$	−24.2134	−1.15961
$437$	2.24073	0.107188
$438$	5.45404	0.260604
$439$	−12.2945	−0.586786	−0.293393	−	0.955992i	$-0.594784\pi$
$439$	−12.2945	−0.586786	−0.293393	+	0.955992i	$0.594784\pi$
$440$	−5.20808	−0.248285
$441$	12.7693	0.608064
$442$	13.5792	0.645896
$443$	5.21201	0.247630	0.123815	−	0.992305i	$-0.460487\pi$
$443$	5.21201	0.247630	0.123815	+	0.992305i	$0.460487\pi$
$444$	−13.3200	−0.632138
$445$	−5.03846	−0.238846
$446$	−6.69217	−0.316883
$447$	−4.47172	−0.211505
$448$	−4.38158	−0.207010
$449$	25.2315	1.19075	0.595373	−	0.803449i	$-0.297004\pi$
$449$	25.2315	1.19075	0.595373	+	0.803449i	$0.297004\pi$
$450$	−1.17640	−0.0554560
$451$	1.89515	0.0892392
$452$	−11.5324	−0.542438
$453$	−9.66669	−0.454181
$454$	8.02435	0.376601
$455$	−24.5292	−1.14995
$456$	−5.36978	−0.251463
$457$	−20.5153	−0.959664	−0.479832	−	0.877361i	$-0.659302\pi$
$457$	−20.5153	−0.959664	−0.479832	+	0.877361i	$0.659302\pi$
$458$	−18.0279	−0.842389
$459$	6.57035	0.306678
$460$	−2.78521	−0.129861
$461$	17.7416	0.826310	0.413155	−	0.910661i	$-0.364427\pi$
$461$	17.7416	0.826310	0.413155	+	0.910661i	$0.364427\pi$
$462$	−3.61996	−0.168416
$463$	25.4877	1.18451	0.592257	−	0.805749i	$-0.298237\pi$
$463$	25.4877	1.18451	0.592257	+	0.805749i	$0.298237\pi$
$464$	1.46340	0.0679367
$465$	4.24347	0.196786
$466$	−3.45369	−0.159989
$467$	−3.94325	−0.182472	−0.0912358	−	0.995829i	$-0.529082\pi$
$467$	−3.94325	−0.182472	−0.0912358	+	0.995829i	$0.529082\pi$
$468$	4.71172	0.217800
$469$	−4.57396	−0.211206
$470$	10.4450	0.481794
$471$	5.80134	0.267312
$472$	14.7520	0.679018
$473$	−7.79099	−0.358230
$474$	−2.79536	−0.128395
$475$	3.89640	0.178779
$476$	−45.0567	−2.06517
$477$	11.5800	0.530210
$478$	6.82903	0.312352
$479$	−0.584497	−0.0267064	−0.0133532	−	0.999911i	$-0.504251\pi$
$479$	−0.584497	−0.0267064	−0.0133532	+	0.999911i	$0.504251\pi$
$480$	10.4431	0.476660
$481$	26.3835	1.20299
$482$	2.27753	0.103738
$483$	−4.44627	−0.202312
$484$	14.7318	0.669628
$485$	−15.3359	−0.696365
$486$	−0.676519	−0.0306875
$487$	−10.8422	−0.491309	−0.245655	−	0.969357i	$-0.579003\pi$
$487$	−10.8422	−0.491309	−0.245655	+	0.969357i	$0.579003\pi$
$488$	0.844521	0.0382297
$489$	20.1694	0.912092
$490$	−15.6002	−0.704746
$491$	4.73316	0.213604	0.106802	−	0.994280i	$-0.465939\pi$
$491$	4.73316	0.213604	0.106802	+	0.994280i	$0.465939\pi$
$492$	−2.42880	−0.109499
$493$	−6.57035	−0.295914
$494$	4.63099	0.208358
$495$	2.17325	0.0976803
$496$	3.43877	0.154405
$497$	13.6945	0.614284
$498$	0.710903	0.0318563
$499$	25.0439	1.12112	0.560560	−	0.828114i	$-0.310586\pi$
$499$	25.0439	1.12112	0.560560	+	0.828114i	$0.310586\pi$
$500$	−18.7692	−0.839385
$501$	−7.19069	−0.321256
$502$	3.16911	0.141444
$503$	8.07677	0.360125	0.180063	−	0.983655i	$-0.442370\pi$
$503$	8.07677	0.360125	0.180063	+	0.983655i	$0.442370\pi$
$504$	10.6553	0.474623
$505$	30.8729	1.37382
$506$	0.814156	0.0361936
$507$	3.66725	0.162868
$508$	20.5191	0.910388
$509$	−13.6489	−0.604975	−0.302488	−	0.953153i	$-0.597817\pi$
$509$	−13.6489	−0.604975	−0.302488	+	0.953153i	$0.597817\pi$
$510$	−8.02695	−0.355439
$511$	35.8455	1.58571
$512$	15.4767	0.683978
$513$	2.24073	0.0989305
$514$	−19.2701	−0.849968
$515$	5.43738	0.239600
$516$	9.98482	0.439557
$517$	10.2891	0.452512
$518$	25.9779	1.14140
$519$	15.0384	0.660114
$520$	−13.2207	−0.579767
$521$	22.6165	0.990847	0.495423	−	0.868652i	$-0.335013\pi$
$521$	22.6165	0.990847	0.495423	+	0.868652i	$0.335013\pi$
$522$	0.676519	0.0296104
$523$	2.40915	0.105345	0.0526724	−	0.998612i	$-0.483226\pi$
$523$	2.40915	0.105345	0.0526724	+	0.998612i	$0.483226\pi$
$524$	−3.68480	−0.160971
$525$	−7.73162	−0.337436
$526$	10.3510	0.451324
$527$	−15.4393	−0.672547
$528$	1.76113	0.0766433
$529$	1.00000	0.0434783
$530$	−14.1472	−0.614513
$531$	−6.15579	−0.267139
$532$	−15.3660	−0.666199
$533$	4.81084	0.208381
$534$	−1.88754	−0.0816818
$535$	−9.10275	−0.393546
$536$	−2.46527	−0.106483
$537$	−10.0005	−0.431553
$538$	7.87765	0.339630
$539$	−15.3672	−0.661914
$540$	−2.78521	−0.119856
$541$	−0.501966	−0.0215812	−0.0107906	−	0.999942i	$-0.503435\pi$
$541$	−0.501966	−0.0215812	−0.0107906	+	0.999942i	$0.503435\pi$
$542$	16.6117	0.713535
$543$	11.6624	0.500481
$544$	−37.9958	−1.62906
$545$	−28.3506	−1.21441
$546$	−9.18927	−0.393264
$547$	34.6720	1.48247	0.741235	−	0.671246i	$-0.234241\pi$
$547$	34.6720	1.48247	0.741235	+	0.671246i	$0.234241\pi$
$548$	32.0388	1.36863
$549$	−0.352405	−0.0150403
$550$	1.41573	0.0603671
$551$	−2.24073	−0.0954581
$552$	−2.39645	−0.102000
$553$	−18.3719	−0.781251
$554$	−8.19361	−0.348113
$555$	−15.5959	−0.662009
$556$	23.0552	0.977758
$557$	10.7212	0.454272	0.227136	−	0.973863i	$-0.427064\pi$
$557$	10.7212	0.454272	0.227136	+	0.973863i	$0.427064\pi$
$558$	1.58972	0.0672980
$559$	−19.7774	−0.836497
$560$	11.7501	0.496532
$561$	−7.90708	−0.333837
$562$	−12.2570	−0.517031
$563$	−36.3492	−1.53193	−0.765967	−	0.642880i	$-0.777740\pi$
$563$	−36.3492	−1.53193	−0.765967	+	0.642880i	$0.777740\pi$
$564$	−13.1863	−0.555244
$565$	−13.5029	−0.568071
$566$	−0.282645	−0.0118805
$567$	−4.44627	−0.186726
$568$	7.38106	0.309703
$569$	18.6121	0.780262	0.390131	−	0.920759i	$-0.372430\pi$
$569$	18.6121	0.780262	0.390131	+	0.920759i	$0.372430\pi$
$570$	−2.73748	−0.114660
$571$	12.1827	0.509832	0.254916	−	0.966963i	$-0.417952\pi$
$571$	12.1827	0.509832	0.254916	+	0.966963i	$0.417952\pi$
$572$	−5.67032	−0.237088
$573$	−4.81810	−0.201279
$574$	4.73688	0.197714
$575$	1.73890	0.0725171
$576$	0.985449	0.0410604
$577$	−18.5881	−0.773835	−0.386917	−	0.922114i	$-0.626460\pi$
$577$	−18.5881	−0.773835	−0.386917	+	0.922114i	$0.626460\pi$
$578$	17.7042	0.736397
$579$	26.0157	1.08118
$580$	2.78521	0.115649
$581$	4.67225	0.193838
$582$	−5.74521	−0.238147
$583$	−13.9359	−0.577165
$584$	19.3200	0.799466
$585$	5.51680	0.228091
$586$	17.3426	0.716418
$587$	−18.5251	−0.764612	−0.382306	−	0.924036i	$-0.624870\pi$
$587$	−18.5251	−0.764612	−0.382306	+	0.924036i	$0.624870\pi$
$588$	19.6944	0.812185
$589$	−5.26536	−0.216955
$590$	7.52049	0.309614
$591$	−9.97511	−0.410321
$592$	−12.6384	−0.519435
$593$	−22.0097	−0.903829	−0.451915	−	0.892061i	$-0.649259\pi$
$593$	−22.0097	−0.903829	−0.451915	+	0.892061i	$0.649259\pi$
$594$	0.814156	0.0334052
$595$	−52.7554	−2.16276
$596$	−6.89683	−0.282505
$597$	−18.3470	−0.750893
$598$	2.06674	0.0845151
$599$	25.7854	1.05356	0.526782	−	0.850001i	$-0.323398\pi$
$599$	25.7854	1.05356	0.526782	+	0.850001i	$0.323398\pi$
$600$	−4.16718	−0.170124
$601$	13.4458	0.548465	0.274232	−	0.961663i	$-0.411576\pi$
$601$	13.4458	0.548465	0.274232	+	0.961663i	$0.411576\pi$
$602$	−19.4734	−0.793676
$603$	1.02872	0.0418926
$604$	−14.9092	−0.606645
$605$	17.2490	0.701271
$606$	11.5658	0.469828
$607$	−27.4175	−1.11284	−0.556420	−	0.830901i	$-0.687825\pi$
$607$	−27.4175	−1.11284	−0.556420	+	0.830901i	$0.687825\pi$
$608$	−12.9579	−0.525513
$609$	4.44627	0.180172
$610$	0.430531	0.0174317
$611$	26.1188	1.05665
$612$	10.1336	0.409626
$613$	−40.0774	−1.61871	−0.809356	−	0.587319i	$-0.800183\pi$
$613$	−40.0774	−1.61871	−0.809356	+	0.587319i	$0.800183\pi$
$614$	8.57965	0.346246
$615$	−2.84380	−0.114673
$616$	−12.8231	−0.516656
$617$	4.99212	0.200975	0.100487	−	0.994938i	$-0.467960\pi$
$617$	4.99212	0.200975	0.100487	+	0.994938i	$0.467960\pi$
$618$	2.03699	0.0819396
$619$	−31.1905	−1.25365	−0.626826	−	0.779159i	$-0.715646\pi$
$619$	−31.1905	−1.25365	−0.626826	+	0.779159i	$0.715646\pi$
$620$	6.54480	0.262846
$621$	1.00000	0.0401286
$622$	−3.10790	−0.124615
$623$	−12.4054	−0.497013
$624$	4.47063	0.178968
$625$	−13.2817	−0.531269
$626$	1.23021	0.0491691
$627$	−2.69660	−0.107692
$628$	8.94753	0.357045
$629$	56.7436	2.26252
$630$	5.43198	0.216415
$631$	29.4354	1.17180	0.585902	−	0.810382i	$-0.300741\pi$
$631$	29.4354	1.17180	0.585902	+	0.810382i	$0.300741\pi$
$632$	−9.90205	−0.393882
$633$	16.5709	0.658635
$634$	−1.29073	−0.0512613
$635$	24.0251	0.953408
$636$	17.8600	0.708196
$637$	−39.0098	−1.54562
$638$	−0.814156	−0.0322327
$639$	−3.08000	−0.121843
$640$	19.6823	0.778010
$641$	6.16488	0.243498	0.121749	−	0.992561i	$-0.461150\pi$
$641$	6.16488	0.243498	0.121749	+	0.992561i	$0.461150\pi$
$642$	−3.41013	−0.134587
$643$	−17.8201	−0.702757	−0.351378	−	0.936234i	$-0.614287\pi$
$643$	−17.8201	−0.702757	−0.351378	+	0.936234i	$0.614287\pi$
$644$	−6.85758	−0.270227
$645$	11.6909	0.460328
$646$	9.95995	0.391869
$647$	33.2373	1.30669	0.653347	−	0.757059i	$-0.273364\pi$
$647$	33.2373	1.30669	0.653347	+	0.757059i	$0.273364\pi$
$648$	−2.39645	−0.0941414
$649$	7.40818	0.290796
$650$	3.59384	0.140962
$651$	10.4481	0.409492
$652$	31.1077	1.21827
$653$	2.86743	0.112211	0.0561056	−	0.998425i	$-0.482132\pi$
$653$	2.86743	0.112211	0.0561056	+	0.998425i	$0.482132\pi$
$654$	−10.6209	−0.415309
$655$	−4.31441	−0.168578
$656$	−2.30452	−0.0899763
$657$	−8.06192	−0.314526
$658$	25.7172	1.00256
$659$	48.5269	1.89034	0.945170	−	0.326580i	$-0.105896\pi$
$659$	48.5269	1.89034	0.945170	+	0.326580i	$0.105896\pi$
$660$	3.35185	0.130471
$661$	−7.84015	−0.304946	−0.152473	−	0.988308i	$-0.548724\pi$
$661$	−7.84015	−0.304946	−0.152473	+	0.988308i	$0.548724\pi$
$662$	−17.0178	−0.661416
$663$	−20.0721	−0.779537
$664$	2.51825	0.0977269
$665$	−17.9915	−0.697680
$666$	−5.84263	−0.226397
$667$	−1.00000	−0.0387202
$668$	−11.0904	−0.429099
$669$	9.89206	0.382449
$670$	−1.25678	−0.0485535
$671$	0.424102	0.0163723
$672$	25.7124	0.991878
$673$	43.6667	1.68323	0.841614	−	0.540079i	$-0.181606\pi$
$673$	43.6667	1.68323	0.841614	+	0.540079i	$0.181606\pi$
$674$	0.376417	0.0144991
$675$	1.73890	0.0669303
$676$	5.65608	0.217542
$677$	35.0350	1.34650	0.673252	−	0.739413i	$-0.264897\pi$
$677$	35.0350	1.34650	0.673252	+	0.739413i	$0.264897\pi$
$678$	−5.05853	−0.194272
$679$	−37.7591	−1.44906
$680$	−28.4341	−1.09040
$681$	−11.8612	−0.454524
$682$	−1.91314	−0.0732579
$683$	34.9144	1.33596	0.667982	−	0.744178i	$-0.267158\pi$
$683$	34.9144	1.33596	0.667982	+	0.744178i	$0.267158\pi$
$684$	3.45592	0.132140
$685$	37.5131	1.43330
$686$	−17.3541	−0.662583
$687$	26.6481	1.01669
$688$	9.47390	0.361189
$689$	−35.3762	−1.34773
$690$	−1.22169	−0.0465091
$691$	42.8296	1.62931	0.814657	−	0.579943i	$-0.196925\pi$
$691$	42.8296	1.62931	0.814657	+	0.579943i	$0.196925\pi$
$692$	23.1941	0.881708
$693$	5.35086	0.203262
$694$	6.77658	0.257235
$695$	26.9945	1.02396
$696$	2.39645	0.0908371
$697$	10.3468	0.391912
$698$	−5.42048	−0.205168
$699$	5.10509	0.193092
$700$	−11.9246	−0.450709
$701$	−31.6050	−1.19370	−0.596852	−	0.802351i	$-0.703582\pi$
$701$	−31.6050	−1.19370	−0.596852	+	0.802351i	$0.703582\pi$
$702$	2.06674	0.0780039
$703$	19.3516	0.729860
$704$	−1.18594	−0.0446967
$705$	−15.4394	−0.581481
$706$	5.70726	0.214796
$707$	76.0135	2.85878
$708$	−9.49422	−0.356814
$709$	−50.5318	−1.89776	−0.948881	−	0.315635i	$-0.897782\pi$
$709$	−50.5318	−1.89776	−0.948881	+	0.315635i	$0.897782\pi$
$710$	3.76282	0.141216
$711$	4.13197	0.154961
$712$	−6.68627	−0.250579
$713$	−2.34985	−0.0880024
$714$	−19.7635	−0.739632
$715$	−6.63918	−0.248291
$716$	−15.4240	−0.576421
$717$	−10.0944	−0.376981
$718$	12.0494	0.449680
$719$	15.3215	0.571394	0.285697	−	0.958320i	$-0.407775\pi$
$719$	15.3215	0.571394	0.285697	+	0.958320i	$0.407775\pi$
$720$	−2.64269	−0.0984871
$721$	13.3876	0.498582
$722$	−9.45716	−0.351959
$723$	−3.36654	−0.125203
$724$	17.9871	0.668487
$725$	−1.73890	−0.0645811
$726$	6.46191	0.239824
$727$	42.4863	1.57573	0.787865	−	0.615848i	$-0.211186\pi$
$727$	42.4863	1.57573	0.787865	+	0.615848i	$0.211186\pi$
$728$	−32.5513	−1.20643
$729$	1.00000	0.0370370
$730$	9.84919	0.364535
$731$	−42.5357	−1.57324
$732$	−0.543523	−0.0200892
$733$	−20.4112	−0.753904	−0.376952	−	0.926233i	$-0.623028\pi$
$733$	−20.4112	−0.753904	−0.376952	+	0.926233i	$0.623028\pi$
$734$	19.7895	0.730445
$735$	23.0595	0.850564
$736$	−5.78292	−0.213161
$737$	−1.23801	−0.0456026
$738$	−1.06536	−0.0392164
$739$	−39.5199	−1.45376	−0.726881	−	0.686763i	$-0.759031\pi$
$739$	−39.5199	−1.45376	−0.726881	+	0.686763i	$0.759031\pi$
$740$	−24.0539	−0.884239
$741$	−6.84532	−0.251469
$742$	−34.8324	−1.27874
$743$	−1.06179	−0.0389533	−0.0194767	−	0.999810i	$-0.506200\pi$
$743$	−1.06179	−0.0389533	−0.0194767	+	0.999810i	$0.506200\pi$
$744$	5.63128	0.206453
$745$	−8.07526	−0.295855
$746$	−20.0914	−0.735597
$747$	−1.05082	−0.0384477
$748$	−12.1953	−0.445903
$749$	−22.4123	−0.818928
$750$	−8.23287	−0.300622
$751$	−12.3874	−0.452021	−0.226010	−	0.974125i	$-0.572568\pi$
$751$	−12.3874	−0.452021	−0.226010	+	0.974125i	$0.572568\pi$
$752$	−12.5116	−0.456250
$753$	−4.68444	−0.170710
$754$	−2.06674	−0.0752661
$755$	−17.4566	−0.635311
$756$	−6.85758	−0.249408
$757$	−5.54913	−0.201687	−0.100843	−	0.994902i	$-0.532154\pi$
$757$	−5.54913	−0.201687	−0.100843	+	0.994902i	$0.532154\pi$
$758$	5.59943	0.203381
$759$	−1.20345	−0.0436824
$760$	−9.69703	−0.351748
$761$	−42.7973	−1.55140	−0.775700	−	0.631102i	$-0.782603\pi$
$761$	−42.7973	−1.55140	−0.775700	+	0.631102i	$0.782603\pi$
$762$	9.00044	0.326051
$763$	−69.8033	−2.52705
$764$	−7.43106	−0.268846
$765$	11.8651	0.428983
$766$	−16.8932	−0.610375
$767$	18.8057	0.679033
$768$	9.34438	0.337186
$769$	−19.0214	−0.685931	−0.342965	−	0.939348i	$-0.611431\pi$
$769$	−19.0214	−0.685931	−0.342965	+	0.939348i	$0.611431\pi$
$770$	−6.53711	−0.235581
$771$	28.4842	1.02583
$772$	40.1246	1.44412
$773$	48.4032	1.74094	0.870472	−	0.492219i	$-0.163814\pi$
$773$	48.4032	1.74094	0.870472	+	0.492219i	$0.163814\pi$
$774$	4.37971	0.157425
$775$	−4.08615	−0.146779
$776$	−20.3514	−0.730572
$777$	−38.3994	−1.37757
$778$	14.7188	0.527695
$779$	3.52862	0.126426
$780$	8.50868	0.304659
$781$	3.70662	0.132633
$782$	4.44497	0.158952
$783$	−1.00000	−0.0357371
$784$	18.6867	0.667381
$785$	10.4764	0.373917
$786$	−1.61629	−0.0576511
$787$	10.9688	0.390995	0.195497	−	0.980704i	$-0.437368\pi$
$787$	10.9688	0.390995	0.195497	+	0.980704i	$0.437368\pi$
$788$	−15.3848	−0.548062
$789$	−15.3003	−0.544706
$790$	−5.04800	−0.179600
$791$	−33.2461	−1.18210
$792$	2.88400	0.102479
$793$	1.07658	0.0382306
$794$	−17.2206	−0.611135
$795$	20.9117	0.741661
$796$	−28.2970	−1.00296
$797$	18.8889	0.669080	0.334540	−	0.942382i	$-0.391419\pi$
$797$	18.8889	0.669080	0.334540	+	0.942382i	$0.391419\pi$
$798$	−6.74008	−0.238596
$799$	56.1742	1.98730
$800$	−10.0559	−0.355530
$801$	2.79007	0.0985824
$802$	7.73146	0.273007
$803$	9.70211	0.342380
$804$	1.58661	0.0559556
$805$	−8.02931	−0.282996
$806$	−4.85651	−0.171063
$807$	−11.6444	−0.409902
$808$	40.9697	1.44131
$809$	−46.2240	−1.62515	−0.812574	−	0.582858i	$-0.801934\pi$
$809$	−46.2240	−1.62515	−0.812574	+	0.582858i	$0.801934\pi$
$810$	−1.22169	−0.0429259
$811$	−26.7571	−0.939567	−0.469784	−	0.882782i	$-0.655668\pi$
$811$	−26.7571	−0.939567	−0.469784	+	0.882782i	$0.655668\pi$
$812$	6.85758	0.240654
$813$	−24.5547	−0.861171
$814$	7.03130	0.246447
$815$	36.4230	1.27584
$816$	9.61506	0.336594
$817$	−14.5062	−0.507508
$818$	−0.863894	−0.0302053
$819$	13.5832	0.474634
$820$	−4.38605	−0.153168
$821$	15.1449	0.528560	0.264280	−	0.964446i	$-0.414866\pi$
$821$	15.1449	0.528560	0.264280	+	0.964446i	$0.414866\pi$
$822$	14.0534	0.490168
$823$	−39.7433	−1.38537	−0.692683	−	0.721242i	$-0.743571\pi$
$823$	−39.7433	−1.38537	−0.692683	+	0.721242i	$0.743571\pi$
$824$	7.21566	0.251369
$825$	−2.09268	−0.0728576
$826$	18.5166	0.644273
$827$	−52.1210	−1.81242	−0.906212	−	0.422824i	$-0.861039\pi$
$827$	−52.1210	−1.81242	−0.906212	+	0.422824i	$0.861039\pi$
$828$	1.54232	0.0535994
$829$	33.0195	1.14681	0.573407	−	0.819271i	$-0.305622\pi$
$829$	33.0195	1.14681	0.573407	+	0.819271i	$0.305622\pi$
$830$	1.28379	0.0445608
$831$	12.1114	0.420141
$832$	−3.01050	−0.104370
$833$	−83.8991	−2.90693
$834$	10.1129	0.350180
$835$	−12.9853	−0.449376
$836$	−4.15902	−0.143843
$837$	−2.34985	−0.0812226
$838$	−7.11538	−0.245797
$839$	−28.7654	−0.993092	−0.496546	−	0.868011i	$-0.665399\pi$
$839$	−28.7654	−0.993092	−0.496546	+	0.868011i	$0.665399\pi$
$840$	19.2418	0.663906
$841$	1.00000	0.0344828
$842$	−12.7143	−0.438165
$843$	18.1178	0.624010
$844$	25.5577	0.879732
$845$	6.62251	0.227821
$846$	−5.78400	−0.198858
$847$	42.4695	1.45927
$848$	16.9461	0.581932
$849$	0.417794	0.0143386
$850$	7.72935	0.265115
$851$	8.63631	0.296049
$852$	−4.75035	−0.162744
$853$	36.1981	1.23940	0.619700	−	0.784839i	$-0.287254\pi$
$853$	36.1981	1.23940	0.619700	+	0.784839i	$0.287254\pi$
$854$	1.06003	0.0362735
$855$	4.04642	0.138385
$856$	−12.0798	−0.412878
$857$	46.2205	1.57886	0.789432	−	0.613839i	$-0.210375\pi$
$857$	46.2205	1.57886	0.789432	+	0.613839i	$0.210375\pi$
$858$	−2.48721	−0.0849119
$859$	44.6583	1.52372	0.761860	−	0.647742i	$-0.224286\pi$
$859$	44.6583	1.52372	0.761860	+	0.647742i	$0.224286\pi$
$860$	18.0311	0.614856
$861$	−7.00185	−0.238622
$862$	3.66952	0.124984
$863$	−5.47987	−0.186537	−0.0932685	−	0.995641i	$-0.529732\pi$
$863$	−5.47987	−0.186537	−0.0932685	+	0.995641i	$0.529732\pi$
$864$	−5.78292	−0.196739
$865$	27.1572	0.923372
$866$	−5.43428	−0.184664
$867$	−26.1695	−0.888764
$868$	16.1143	0.546954
$869$	−4.97261	−0.168684
$870$	1.22169	0.0414193
$871$	−3.14269	−0.106486
$872$	−37.6225	−1.27406
$873$	8.49231	0.287421
$874$	1.51589	0.0512759
$875$	−54.1087	−1.82921
$876$	−12.4341	−0.420109
$877$	20.0817	0.678111	0.339056	−	0.940766i	$-0.389893\pi$
$877$	20.0817	0.678111	0.339056	+	0.940766i	$0.389893\pi$
$878$	−8.31748	−0.280701
$879$	−25.6351	−0.864651
$880$	3.18034	0.107209
$881$	3.95781	0.133342	0.0666709	−	0.997775i	$-0.478762\pi$
$881$	3.95781	0.133342	0.0666709	+	0.997775i	$0.478762\pi$
$882$	8.63870	0.290880
$883$	−11.7593	−0.395731	−0.197866	−	0.980229i	$-0.563401\pi$
$883$	−11.7593	−0.395731	−0.197866	+	0.980229i	$0.563401\pi$
$884$	−30.9577	−1.04122
$885$	−11.1165	−0.373675
$886$	3.52603	0.118459
$887$	−47.1597	−1.58347	−0.791734	−	0.610867i	$-0.790821\pi$
$887$	−47.1597	−1.58347	−0.791734	+	0.610867i	$0.790821\pi$
$888$	−20.6965	−0.694528
$889$	59.1534	1.98394
$890$	−3.40861	−0.114257
$891$	−1.20345	−0.0403170
$892$	15.2567	0.510834
$893$	19.1574	0.641078
$894$	−3.02520	−0.101178
$895$	−18.0594	−0.603659
$896$	48.4606	1.61896
$897$	−3.05496	−0.102002
$898$	17.0696	0.569619
$899$	2.34985	0.0783718
$900$	2.68194	0.0893981
$901$	−76.0844	−2.53474
$902$	1.28211	0.0426895
$903$	28.7847	0.957894
$904$	−17.9190	−0.595976
$905$	21.0605	0.700076
$906$	−6.53970	−0.217267
$907$	10.5576	0.350559	0.175279	−	0.984519i	$-0.443917\pi$
$907$	10.5576	0.350559	0.175279	+	0.984519i	$0.443917\pi$
$908$	−18.2938	−0.607103
$909$	−17.0960	−0.567039
$910$	−16.5945	−0.550101
$911$	4.94764	0.163923	0.0819614	−	0.996636i	$-0.473882\pi$
$911$	4.94764	0.163923	0.0819614	+	0.996636i	$0.473882\pi$
$912$	3.27908	0.108581
$913$	1.26461	0.0418526
$914$	−13.8790	−0.459075
$915$	−0.636392	−0.0210385
$916$	41.0999	1.35798
$917$	−10.6227	−0.350793
$918$	4.44497	0.146706
$919$	24.8410	0.819428	0.409714	−	0.912214i	$-0.365629\pi$
$919$	24.8410	0.819428	0.409714	+	0.912214i	$0.365629\pi$
$920$	−4.32763	−0.142678
$921$	−12.6821	−0.417888
$922$	12.0026	0.395283
$923$	9.40927	0.309710
$924$	8.25275	0.271496
$925$	15.0177	0.493778
$926$	17.2429	0.566638
$927$	−3.01098	−0.0988936
$928$	5.78292	0.189833
$929$	−11.1501	−0.365822	−0.182911	−	0.983130i	$-0.558552\pi$
$929$	−11.1501	−0.365822	−0.182911	+	0.983130i	$0.558552\pi$
$930$	2.87079	0.0941369
$931$	−28.6126	−0.937740
$932$	7.87369	0.257911
$933$	4.59395	0.150399
$934$	−2.66768	−0.0872892
$935$	−14.2790	−0.466974
$936$	7.32104	0.239296
$937$	−26.2983	−0.859129	−0.429564	−	0.903036i	$-0.641333\pi$
$937$	−26.2983	−0.859129	−0.429564	+	0.903036i	$0.641333\pi$
$938$	−3.09437	−0.101035
$939$	−1.81844	−0.0593426
$940$	−23.8125	−0.776679
$941$	−44.4861	−1.45020	−0.725102	−	0.688641i	$-0.758207\pi$
$941$	−44.4861	−1.45020	−0.725102	+	0.688641i	$0.758207\pi$
$942$	3.92472	0.127874
$943$	1.57477	0.0512815
$944$	−9.00840	−0.293198
$945$	−8.02931	−0.261193
$946$	−5.27075	−0.171367
$947$	52.8987	1.71898	0.859488	−	0.511157i	$-0.170783\pi$
$947$	52.8987	1.71898	0.859488	+	0.511157i	$0.170783\pi$
$948$	6.37283	0.206980
$949$	24.6288	0.799485
$950$	2.63599	0.0855227
$951$	1.90790	0.0618677
$952$	−70.0088	−2.26900
$953$	51.7818	1.67738	0.838688	−	0.544612i	$-0.183323\pi$
$953$	51.7818	1.67738	0.838688	+	0.544612i	$0.183323\pi$
$954$	7.83406	0.253637
$955$	−8.70077	−0.281550
$956$	−15.5688	−0.503530
$957$	1.20345	0.0389020
$958$	−0.395424	−0.0127756
$959$	92.3627	2.98255
$960$	1.77958	0.0574355
$961$	−25.4782	−0.821878
$962$	17.8490	0.575474
$963$	5.04070	0.162434
$964$	−5.19229	−0.167232
$965$	46.9805	1.51236
$966$	−3.00799	−0.0967804
$967$	−16.0172	−0.515078	−0.257539	−	0.966268i	$-0.582912\pi$
$967$	−16.0172	−0.515078	−0.257539	+	0.966268i	$0.582912\pi$
$968$	22.8902	0.735718
$969$	−14.7224	−0.472950
$970$	−10.3750	−0.333121
$971$	−21.5095	−0.690272	−0.345136	−	0.938553i	$-0.612167\pi$
$971$	−21.5095	−0.690272	−0.345136	+	0.938553i	$0.612167\pi$
$972$	1.54232	0.0494700
$973$	66.4645	2.13075
$974$	−7.33499	−0.235028
$975$	−5.31226	−0.170128
$976$	−0.515711	−0.0165075
$977$	−48.4917	−1.55139	−0.775694	−	0.631109i	$-0.782600\pi$
$977$	−48.4917	−1.55139	−0.775694	+	0.631109i	$0.782600\pi$
$978$	13.6450	0.436319
$979$	−3.35771	−0.107313
$980$	35.5652	1.13609
$981$	15.6993	0.501240
$982$	3.20207	0.102182
$983$	23.9560	0.764077	0.382038	−	0.924146i	$-0.375222\pi$
$983$	23.9560	0.764077	0.382038	+	0.924146i	$0.375222\pi$
$984$	−3.77385	−0.120306
$985$	−18.0136	−0.573960
$986$	−4.44497	−0.141557
$987$	−38.0141	−1.21000
$988$	−10.5577	−0.335885
$989$	−6.47389	−0.205858
$990$	1.47024	0.0467274
$991$	54.4244	1.72885	0.864425	−	0.502762i	$-0.167683\pi$
$991$	54.4244	1.72885	0.864425	+	0.502762i	$0.167683\pi$
$992$	13.5890	0.431450
$993$	25.1550	0.798269
$994$	9.26461	0.293856
$995$	−33.1320	−1.05035
$996$	−1.62071	−0.0513542
$997$	−13.9042	−0.440350	−0.220175	−	0.975460i	$-0.570663\pi$
$997$	−13.9042	−0.440350	−0.220175	+	0.975460i	$0.570663\pi$
$998$	16.9427	0.536312
$999$	8.63631	0.273241

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2001.2.a.k.1.6	✓	10
3.2	odd	2		6003.2.a.k.1.5		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2001.2.a.k.1.6	✓	10	1.1	even	1	trivial
6003.2.a.k.1.5		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)

\(f(q)\)	\(=\)	\(q+0.676519 q^{2} -1.00000 q^{3} -1.54232 q^{4} -1.80585 q^{5} -0.676519 q^{6} -4.44627 q^{7} -2.39645 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+0.676519 q^{2} -1.00000 q^{3} -1.54232 q^{4} -1.80585 q^{5} -0.676519 q^{6} -4.44627 q^{7} -2.39645 q^{8} +1.00000 q^{9} -1.22169 q^{10} -1.20345 q^{11} +1.54232 q^{12} -3.05496 q^{13} -3.00799 q^{14} +1.80585 q^{15} +1.46340 q^{16} -6.57035 q^{17} +0.676519 q^{18} -2.24073 q^{19} +2.78521 q^{20} +4.44627 q^{21} -0.814156 q^{22} -1.00000 q^{23} +2.39645 q^{24} -1.73890 q^{25} -2.06674 q^{26} -1.00000 q^{27} +6.85758 q^{28} +1.00000 q^{29} +1.22169 q^{30} +2.34985 q^{31} +5.78292 q^{32} +1.20345 q^{33} -4.44497 q^{34} +8.02931 q^{35} -1.54232 q^{36} -8.63631 q^{37} -1.51589 q^{38} +3.05496 q^{39} +4.32763 q^{40} -1.57477 q^{41} +3.00799 q^{42} +6.47389 q^{43} +1.85610 q^{44} -1.80585 q^{45} -0.676519 q^{46} -8.54965 q^{47} -1.46340 q^{48} +12.7693 q^{49} -1.17640 q^{50} +6.57035 q^{51} +4.71172 q^{52} +11.5800 q^{53} -0.676519 q^{54} +2.17325 q^{55} +10.6553 q^{56} +2.24073 q^{57} +0.676519 q^{58} -6.15579 q^{59} -2.78521 q^{60} -0.352405 q^{61} +1.58972 q^{62} -4.44627 q^{63} +0.985449 q^{64} +5.51680 q^{65} +0.814156 q^{66} +1.02872 q^{67} +10.1336 q^{68} +1.00000 q^{69} +5.43198 q^{70} -3.08000 q^{71} -2.39645 q^{72} -8.06192 q^{73} -5.84263 q^{74} +1.73890 q^{75} +3.45592 q^{76} +5.35086 q^{77} +2.06674 q^{78} +4.13197 q^{79} -2.64269 q^{80} +1.00000 q^{81} -1.06536 q^{82} -1.05082 q^{83} -6.85758 q^{84} +11.8651 q^{85} +4.37971 q^{86} -1.00000 q^{87} +2.88400 q^{88} +2.79007 q^{89} -1.22169 q^{90} +13.5832 q^{91} +1.54232 q^{92} -2.34985 q^{93} -5.78400 q^{94} +4.04642 q^{95} -5.78292 q^{96} +8.49231 q^{97} +8.63870 q^{98} -1.20345 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + 3 q^{2} - 10 q^{3} + 17 q^{4} + 6 q^{5} - 3 q^{6} + 3 q^{7} - 6 q^{8} + 10 q^{9}+O(q^{10}) \) 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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