LMFDB - Embedded newform 2013.2.a.e.1.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2013,2,Mod(1,2013)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2013, 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("2013.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2013 = 3 \cdot 11 \cdot 61 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2013.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:	$16.0738859269$
Analytic rank:	$0$
Dimension:	$13$
Coefficient field:	$\mathbb{Q}[x]/(x^{13} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{13} - 2 x^{12} - 19 x^{11} + 35 x^{10} + 136 x^{9} - 220 x^{8} - 469 x^{7} + 610 x^{6} + 841 x^{5} + \cdots - 47 $ x^13 - 2x^12 - 19x^11 + 35x^10 + 136x^9 - 220x^8 - 469x^7 + 610x^6 + 841x^5 - 760x^4 - 742x^3 + 366x^2 + 236x - 47
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.8
Root			$0.822526$ of defining polynomial
Character	$\chi$	$=$	2013.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.822526 q^{2} -1.00000 q^{3} -1.32345 q^{4} +2.11599 q^{5} -0.822526 q^{6} +0.404149 q^{7} -2.73363 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+0.822526 q^{2} -1.00000 q^{3} -1.32345 q^{4} +2.11599 q^{5} -0.822526 q^{6} +0.404149 q^{7} -2.73363 q^{8} +1.00000 q^{9} +1.74046 q^{10} +1.00000 q^{11} +1.32345 q^{12} +4.06066 q^{13} +0.332423 q^{14} -2.11599 q^{15} +0.398423 q^{16} +0.0205369 q^{17} +0.822526 q^{18} +3.97586 q^{19} -2.80041 q^{20} -0.404149 q^{21} +0.822526 q^{22} -8.67841 q^{23} +2.73363 q^{24} -0.522583 q^{25} +3.34000 q^{26} -1.00000 q^{27} -0.534871 q^{28} -5.89217 q^{29} -1.74046 q^{30} +5.40170 q^{31} +5.79496 q^{32} -1.00000 q^{33} +0.0168922 q^{34} +0.855175 q^{35} -1.32345 q^{36} +1.99527 q^{37} +3.27025 q^{38} -4.06066 q^{39} -5.78433 q^{40} +6.26962 q^{41} -0.332423 q^{42} +7.16134 q^{43} -1.32345 q^{44} +2.11599 q^{45} -7.13822 q^{46} +8.53737 q^{47} -0.398423 q^{48} -6.83666 q^{49} -0.429838 q^{50} -0.0205369 q^{51} -5.37409 q^{52} +5.18361 q^{53} -0.822526 q^{54} +2.11599 q^{55} -1.10479 q^{56} -3.97586 q^{57} -4.84647 q^{58} -0.638698 q^{59} +2.80041 q^{60} -1.00000 q^{61} +4.44304 q^{62} +0.404149 q^{63} +3.96966 q^{64} +8.59233 q^{65} -0.822526 q^{66} +15.2035 q^{67} -0.0271796 q^{68} +8.67841 q^{69} +0.703404 q^{70} +11.4793 q^{71} -2.73363 q^{72} -15.0344 q^{73} +1.64116 q^{74} +0.522583 q^{75} -5.26185 q^{76} +0.404149 q^{77} -3.34000 q^{78} +10.9481 q^{79} +0.843060 q^{80} +1.00000 q^{81} +5.15693 q^{82} +4.60944 q^{83} +0.534871 q^{84} +0.0434559 q^{85} +5.89039 q^{86} +5.89217 q^{87} -2.73363 q^{88} +12.7830 q^{89} +1.74046 q^{90} +1.64111 q^{91} +11.4855 q^{92} -5.40170 q^{93} +7.02221 q^{94} +8.41288 q^{95} -5.79496 q^{96} -0.603085 q^{97} -5.62333 q^{98} +1.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 13 q + 2 q^{2} - 13 q^{3} + 16 q^{4} + 3 q^{5} - 2 q^{6} + 11 q^{7} + 9 q^{8} + 13 q^{9}+O(q^{10}) $ 13 * q + 2 * q^2 - 13 * q^3 + 16 * q^4 + 3 * q^5 - 2 * q^6 + 11 * q^7 + 9 * q^8 + 13 * q^9	\( 13 q + 2 q^{2} - 13 q^{3} + 16 q^{4} + 3 q^{5} - 2 q^{6} + 11 q^{7} + 9 q^{8} + 13 q^{9} + 6 q^{10} + 13 q^{11} - 16 q^{12} + 13 q^{13} + q^{14} - 3 q^{15} + 18 q^{16} + 17 q^{17} + 2 q^{18} + 14 q^{19} - 7 q^{20} - 11 q^{21} + 2 q^{22} + 7 q^{23} - 9 q^{24} + 18 q^{25} - 10 q^{26} - 13 q^{27} + 19 q^{28} - 6 q^{29} - 6 q^{30} + 27 q^{31} + 5 q^{32} - 13 q^{33} + 6 q^{34} + 14 q^{35} + 16 q^{36} + 10 q^{37} + 2 q^{38} - 13 q^{39} + 8 q^{40} + 3 q^{41} - q^{42} + 29 q^{43} + 16 q^{44} + 3 q^{45} - 24 q^{46} + 8 q^{47} - 18 q^{48} + 8 q^{49} - 27 q^{50} - 17 q^{51} + 37 q^{52} - 24 q^{53} - 2 q^{54} + 3 q^{55} + 24 q^{56} - 14 q^{57} - 5 q^{58} + 13 q^{59} + 7 q^{60} - 13 q^{61} + 39 q^{62} + 11 q^{63} + 47 q^{64} - 11 q^{65} - 2 q^{66} + 44 q^{67} - 8 q^{68} - 7 q^{69} - 12 q^{70} + 3 q^{71} + 9 q^{72} + 48 q^{73} - 22 q^{74} - 18 q^{75} + 47 q^{76} + 11 q^{77} + 10 q^{78} - 17 q^{79} - 26 q^{80} + 13 q^{81} + 56 q^{82} + 50 q^{83} - 19 q^{84} + 8 q^{85} + 18 q^{86} + 6 q^{87} + 9 q^{88} - 15 q^{89} + 6 q^{90} + 47 q^{91} + 14 q^{92} - 27 q^{93} + 45 q^{94} - q^{95} - 5 q^{96} + 27 q^{97} + 47 q^{98} + 13 q^{99}+O(q^{100}) \) 13 * q + 2 * q^2 - 13 * q^3 + 16 * q^4 + 3 * q^5 - 2 * q^6 + 11 * q^7 + 9 * q^8 + 13 * q^9 + 6 * q^10 + 13 * q^11 - 16 * q^12 + 13 * q^13 + q^14 - 3 * q^15 + 18 * q^16 + 17 * q^17 + 2 * q^18 + 14 * q^19 - 7 * q^20 - 11 * q^21 + 2 * q^22 + 7 * q^23 - 9 * q^24 + 18 * q^25 - 10 * q^26 - 13 * q^27 + 19 * q^28 - 6 * q^29 - 6 * q^30 + 27 * q^31 + 5 * q^32 - 13 * q^33 + 6 * q^34 + 14 * q^35 + 16 * q^36 + 10 * q^37 + 2 * q^38 - 13 * q^39 + 8 * q^40 + 3 * q^41 - q^42 + 29 * q^43 + 16 * q^44 + 3 * q^45 - 24 * q^46 + 8 * q^47 - 18 * q^48 + 8 * q^49 - 27 * q^50 - 17 * q^51 + 37 * q^52 - 24 * q^53 - 2 * q^54 + 3 * q^55 + 24 * q^56 - 14 * q^57 - 5 * q^58 + 13 * q^59 + 7 * q^60 - 13 * q^61 + 39 * q^62 + 11 * q^63 + 47 * q^64 - 11 * q^65 - 2 * q^66 + 44 * q^67 - 8 * q^68 - 7 * q^69 - 12 * q^70 + 3 * q^71 + 9 * q^72 + 48 * q^73 - 22 * q^74 - 18 * q^75 + 47 * q^76 + 11 * q^77 + 10 * q^78 - 17 * q^79 - 26 * q^80 + 13 * q^81 + 56 * q^82 + 50 * q^83 - 19 * q^84 + 8 * q^85 + 18 * q^86 + 6 * q^87 + 9 * q^88 - 15 * q^89 + 6 * q^90 + 47 * q^91 + 14 * q^92 - 27 * q^93 + 45 * q^94 - q^95 - 5 * q^96 + 27 * q^97 + 47 * q^98 + 13 * 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 $

$2$	0.822526	0.581614	0.290807	−	0.956782i	$-0.406076\pi$
$2$	0.822526	0.581614	0.290807	+	0.956782i	$0.406076\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	−1.32345	−0.661725
$5$	2.11599	0.946300	0.473150	−	0.880982i	$-0.343117\pi$
$5$	2.11599	0.946300	0.473150	+	0.880982i	$0.343117\pi$
$6$	−0.822526	−0.335795
$7$	0.404149	0.152754	0.0763769	−	0.997079i	$-0.475665\pi$
$7$	0.404149	0.152754	0.0763769	+	0.997079i	$0.475665\pi$
$8$	−2.73363	−0.966482
$9$	1.00000	0.333333
$10$	1.74046	0.550381
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	1.32345	0.382047
$13$	4.06066	1.12623	0.563113	−	0.826380i	$-0.309604\pi$
$13$	4.06066	1.12623	0.563113	+	0.826380i	$0.309604\pi$
$14$	0.332423	0.0888438
$15$	−2.11599	−0.546346
$16$	0.398423	0.0996058
$17$	0.0205369	0.00498093	0.00249047	−	0.999997i	$-0.499207\pi$
$17$	0.0205369	0.00498093	0.00249047	+	0.999997i	$0.499207\pi$
$18$	0.822526	0.193871
$19$	3.97586	0.912124	0.456062	−	0.889948i	$-0.349259\pi$
$19$	3.97586	0.912124	0.456062	+	0.889948i	$0.349259\pi$
$20$	−2.80041	−0.626191
$21$	−0.404149	−0.0881925
$22$	0.822526	0.175363
$23$	−8.67841	−1.80957	−0.904787	−	0.425864i	$-0.859970\pi$
$23$	−8.67841	−1.80957	−0.904787	+	0.425864i	$0.859970\pi$
$24$	2.73363	0.557999
$25$	−0.522583	−0.104517
$26$	3.34000	0.655028
$27$	−1.00000	−0.192450
$28$	−0.534871	−0.101081
$29$	−5.89217	−1.09415	−0.547075	−	0.837084i	$-0.684259\pi$
$29$	−5.89217	−1.09415	−0.547075	+	0.837084i	$0.684259\pi$
$30$	−1.74046	−0.317763
$31$	5.40170	0.970174	0.485087	−	0.874466i	$-0.338788\pi$
$31$	5.40170	0.970174	0.485087	+	0.874466i	$0.338788\pi$
$32$	5.79496	1.02441
$33$	−1.00000	−0.174078
$34$	0.0168922	0.00289698
$35$	0.855175	0.144551
$36$	−1.32345	−0.220575
$37$	1.99527	0.328020	0.164010	−	0.986459i	$-0.447557\pi$
$37$	1.99527	0.328020	0.164010	+	0.986459i	$0.447557\pi$
$38$	3.27025	0.530504
$39$	−4.06066	−0.650227
$40$	−5.78433	−0.914582
$41$	6.26962	0.979150	0.489575	−	0.871961i	$-0.337152\pi$
$41$	6.26962	0.979150	0.489575	+	0.871961i	$0.337152\pi$
$42$	−0.332423	−0.0512940
$43$	7.16134	1.09209	0.546047	−	0.837754i	$-0.316132\pi$
$43$	7.16134	1.09209	0.546047	+	0.837754i	$0.316132\pi$
$44$	−1.32345	−0.199518
$45$	2.11599	0.315433
$46$	−7.13822	−1.05247
$47$	8.53737	1.24530	0.622652	−	0.782499i	$-0.286055\pi$
$47$	8.53737	1.24530	0.622652	+	0.782499i	$0.286055\pi$
$48$	−0.398423	−0.0575075
$49$	−6.83666	−0.976666
$50$	−0.429838	−0.0607883
$51$	−0.0205369	−0.00287574
$52$	−5.37409	−0.745252
$53$	5.18361	0.712024	0.356012	−	0.934481i	$-0.384136\pi$
$53$	5.18361	0.712024	0.356012	+	0.934481i	$0.384136\pi$
$54$	−0.822526	−0.111932
$55$	2.11599	0.285320
$56$	−1.10479	−0.147634
$57$	−3.97586	−0.526615
$58$	−4.84647	−0.636372
$59$	−0.638698	−0.0831514	−0.0415757	−	0.999135i	$-0.513238\pi$
$59$	−0.638698	−0.0831514	−0.0415757	+	0.999135i	$0.513238\pi$
$60$	2.80041	0.361531
$61$	−1.00000	−0.128037
$61$	−1.00000	−0.128037
$62$	4.44304	0.564267
$63$	0.404149	0.0509180
$64$	3.96966	0.496208
$65$	8.59233	1.06575
$66$	−0.822526	−0.101246
$67$	15.2035	1.85740	0.928700	−	0.370831i	$-0.120927\pi$
$67$	15.2035	1.85740	0.928700	+	0.370831i	$0.120927\pi$
$68$	−0.0271796	−0.00329601
$69$	8.67841	1.04476
$70$	0.703404	0.0840729
$71$	11.4793	1.36234	0.681168	−	0.732127i	$-0.261472\pi$
$71$	11.4793	1.36234	0.681168	+	0.732127i	$0.261472\pi$
$72$	−2.73363	−0.322161
$73$	−15.0344	−1.75965	−0.879823	−	0.475301i	$-0.842339\pi$
$73$	−15.0344	−1.75965	−0.879823	+	0.475301i	$0.842339\pi$
$74$	1.64116	0.190781
$75$	0.522583	0.0603427
$76$	−5.26185	−0.603576
$77$	0.404149	0.0460570
$78$	−3.34000	−0.378181
$79$	10.9481	1.23175	0.615877	−	0.787842i	$-0.288802\pi$
$79$	10.9481	1.23175	0.615877	+	0.787842i	$0.288802\pi$
$80$	0.843060	0.0942570
$81$	1.00000	0.111111
$82$	5.15693	0.569487
$83$	4.60944	0.505952	0.252976	−	0.967473i	$-0.418591\pi$
$83$	4.60944	0.505952	0.252976	+	0.967473i	$0.418591\pi$
$84$	0.534871	0.0583592
$85$	0.0434559	0.00471346
$86$	5.89039	0.635177
$87$	5.89217	0.631707
$88$	−2.73363	−0.291405
$89$	12.7830	1.35500	0.677500	−	0.735523i	$-0.263063\pi$
$89$	12.7830	1.35500	0.677500	+	0.735523i	$0.263063\pi$
$90$	1.74046	0.183460
$91$	1.64111	0.172035
$92$	11.4855	1.19744
$93$	−5.40170	−0.560130
$94$	7.02221	0.724286
$95$	8.41288	0.863143
$96$	−5.79496	−0.591446
$97$	−0.603085	−0.0612340	−0.0306170	−	0.999531i	$-0.509747\pi$
$97$	−0.603085	−0.0612340	−0.0306170	+	0.999531i	$0.509747\pi$
$98$	−5.62333	−0.568043
$99$	1.00000	0.100504
$100$	0.691613	0.0691613
$101$	−14.6545	−1.45818	−0.729088	−	0.684420i	$-0.760056\pi$
$101$	−14.6545	−1.45818	−0.729088	+	0.684420i	$0.760056\pi$
$102$	−0.0168922	−0.00167257
$103$	11.1666	1.10028	0.550138	−	0.835074i	$-0.314575\pi$
$103$	11.1666	1.10028	0.550138	+	0.835074i	$0.314575\pi$
$104$	−11.1003	−1.08848
$105$	−0.855175	−0.0834566
$106$	4.26366	0.414123
$107$	−8.54990	−0.826550	−0.413275	−	0.910606i	$-0.635615\pi$
$107$	−8.54990	−0.826550	−0.413275	+	0.910606i	$0.635615\pi$
$108$	1.32345	0.127349
$109$	14.0443	1.34520	0.672598	−	0.740008i	$-0.265178\pi$
$109$	14.0443	1.34520	0.672598	+	0.740008i	$0.265178\pi$
$110$	1.74046	0.165946
$111$	−1.99527	−0.189383
$112$	0.161022	0.0152152
$113$	9.57510	0.900749	0.450375	−	0.892840i	$-0.351290\pi$
$113$	9.57510	0.900749	0.450375	+	0.892840i	$0.351290\pi$
$114$	−3.27025	−0.306287
$115$	−18.3634	−1.71240
$116$	7.79800	0.724026
$117$	4.06066	0.375409
$118$	−0.525346	−0.0483620
$119$	0.00829997	0.000760857 0
$120$	5.78433	0.528034
$121$	1.00000	0.0909091
$122$	−0.822526	−0.0744680
$123$	−6.26962	−0.565313
$124$	−7.14889	−0.641989
$125$	−11.6857	−1.04520
$126$	0.332423	0.0296146
$127$	6.13941	0.544785	0.272392	−	0.962186i	$-0.412185\pi$
$127$	6.13941	0.544785	0.272392	+	0.962186i	$0.412185\pi$
$128$	−8.32478	−0.735813
$129$	−7.16134	−0.630521
$130$	7.06741	0.619853
$131$	5.50042	0.480574	0.240287	−	0.970702i	$-0.422758\pi$
$131$	5.50042	0.480574	0.240287	+	0.970702i	$0.422758\pi$
$132$	1.32345	0.115192
$133$	1.60684	0.139331
$134$	12.5053	1.08029
$135$	−2.11599	−0.182115
$136$	−0.0561402	−0.00481399
$137$	−2.78969	−0.238339	−0.119170	−	0.992874i	$-0.538023\pi$
$137$	−2.78969	−0.238339	−0.119170	+	0.992874i	$0.538023\pi$
$138$	7.13822	0.607646
$139$	−11.0724	−0.939148	−0.469574	−	0.882893i	$-0.655592\pi$
$139$	−11.0724	−0.939148	−0.469574	+	0.882893i	$0.655592\pi$
$140$	−1.13178	−0.0956531
$141$	−8.53737	−0.718976
$142$	9.44198	0.792354
$143$	4.06066	0.339570
$144$	0.398423	0.0332019
$145$	−12.4678	−1.03539
$146$	−12.3662	−1.02343
$147$	6.83666	0.563879
$148$	−2.64064	−0.217059
$149$	0.473710	0.0388079	0.0194039	−	0.999812i	$-0.493823\pi$
$149$	0.473710	0.0388079	0.0194039	+	0.999812i	$0.493823\pi$
$150$	0.429838	0.0350961
$151$	13.2622	1.07927	0.539633	−	0.841900i	$-0.318563\pi$
$151$	13.2622	1.07927	0.539633	+	0.841900i	$0.318563\pi$
$152$	−10.8685	−0.881552
$153$	0.0205369	0.00166031
$154$	0.332423	0.0267874
$155$	11.4300	0.918076
$156$	5.37409	0.430271
$157$	−12.7759	−1.01963	−0.509814	−	0.860285i	$-0.670286\pi$
$157$	−12.7759	−1.01963	−0.509814	+	0.860285i	$0.670286\pi$
$158$	9.00508	0.716405
$159$	−5.18361	−0.411087
$160$	12.2621	0.969403
$161$	−3.50737	−0.276419
$162$	0.822526	0.0646238
$163$	24.5359	1.92180	0.960900	−	0.276897i	$-0.0893060\pi$
$163$	24.5359	1.92180	0.960900	+	0.276897i	$0.0893060\pi$
$164$	−8.29753	−0.647928
$165$	−2.11599	−0.164730
$166$	3.79139	0.294269
$167$	3.95593	0.306119	0.153060	−	0.988217i	$-0.451087\pi$
$167$	3.95593	0.306119	0.153060	+	0.988217i	$0.451087\pi$
$168$	1.10479	0.0852365
$169$	3.48899	0.268384
$170$	0.0357436	0.00274141
$171$	3.97586	0.304041
$172$	−9.47768	−0.722666
$173$	−21.5757	−1.64037	−0.820186	−	0.572097i	$-0.806130\pi$
$173$	−21.5757	−1.64037	−0.820186	+	0.572097i	$0.806130\pi$
$174$	4.84647	0.367410
$175$	−0.211201	−0.0159653
$176$	0.398423	0.0300323
$177$	0.638698	0.0480075
$178$	10.5144	0.788086
$179$	−13.5654	−1.01392	−0.506962	−	0.861968i	$-0.669232\pi$
$179$	−13.5654	−1.01392	−0.506962	+	0.861968i	$0.669232\pi$
$180$	−2.80041	−0.208730
$181$	−20.9000	−1.55349	−0.776744	−	0.629817i	$-0.783130\pi$
$181$	−20.9000	−1.55349	−0.776744	+	0.629817i	$0.783130\pi$
$182$	1.34986	0.100058
$183$	1.00000	0.0739221
$184$	23.7235	1.74892
$185$	4.22197	0.310405
$186$	−4.44304	−0.325780
$187$	0.0205369	0.00150181
$188$	−11.2988	−0.824049
$189$	−0.404149	−0.0293975
$190$	6.91981	0.502016
$191$	2.45440	0.177594	0.0887971	−	0.996050i	$-0.471698\pi$
$191$	2.45440	0.177594	0.0887971	+	0.996050i	$0.471698\pi$
$192$	−3.96966	−0.286486
$193$	−8.31456	−0.598495	−0.299248	−	0.954176i	$-0.596736\pi$
$193$	−8.31456	−0.598495	−0.299248	+	0.954176i	$0.596736\pi$
$194$	−0.496053	−0.0356146
$195$	−8.59233	−0.615309
$196$	9.04799	0.646285
$197$	18.8004	1.33947	0.669736	−	0.742599i	$-0.266407\pi$
$197$	18.8004	1.33947	0.669736	+	0.742599i	$0.266407\pi$
$198$	0.822526	0.0584544
$199$	−7.84162	−0.555877	−0.277939	−	0.960599i	$-0.589651\pi$
$199$	−7.84162	−0.555877	−0.277939	+	0.960599i	$0.589651\pi$
$200$	1.42855	0.101013
$201$	−15.2035	−1.07237
$202$	−12.0537	−0.848096
$203$	−2.38131	−0.167136
$204$	0.0271796	0.00190295
$205$	13.2665	0.926569
$206$	9.18480	0.639935
$207$	−8.67841	−0.603191
$208$	1.61786	0.112179
$209$	3.97586	0.275016
$210$	−0.703404	−0.0485395
$211$	−25.6632	−1.76673	−0.883364	−	0.468688i	$-0.844727\pi$
$211$	−25.6632	−1.76673	−0.883364	+	0.468688i	$0.844727\pi$
$212$	−6.86025	−0.471164
$213$	−11.4793	−0.786545
$214$	−7.03252	−0.480733
$215$	15.1533	1.03345
$216$	2.73363	0.186000
$217$	2.18309	0.148198
$218$	11.5518	0.782385
$219$	15.0344	1.01593
$220$	−2.80041	−0.188804
$221$	0.0833935	0.00560966
$222$	−1.64116	−0.110147
$223$	1.31581	0.0881130	0.0440565	−	0.999029i	$-0.485972\pi$
$223$	1.31581	0.0881130	0.0440565	+	0.999029i	$0.485972\pi$
$224$	2.34203	0.156483
$225$	−0.522583	−0.0348389
$226$	7.87577	0.523888
$227$	7.33476	0.486825	0.243413	−	0.969923i	$-0.421733\pi$
$227$	7.33476	0.486825	0.243413	+	0.969923i	$0.421733\pi$
$228$	5.26185	0.348475
$229$	−4.61757	−0.305137	−0.152569	−	0.988293i	$-0.548755\pi$
$229$	−4.61757	−0.305137	−0.152569	+	0.988293i	$0.548755\pi$
$230$	−15.1044	−0.995955
$231$	−0.404149	−0.0265910
$232$	16.1070	1.05748
$233$	29.1255	1.90807	0.954036	−	0.299692i	$-0.0968839\pi$
$233$	29.1255	1.90807	0.954036	+	0.299692i	$0.0968839\pi$
$234$	3.34000	0.218343
$235$	18.0650	1.17843
$236$	0.845285	0.0550234
$237$	−10.9481	−0.711154
$238$	0.00682694	0.000442525 0
$239$	−30.6121	−1.98013	−0.990064	−	0.140614i	$-0.955092\pi$
$239$	−30.6121	−1.98013	−0.990064	+	0.140614i	$0.955092\pi$
$240$	−0.843060	−0.0544193
$241$	22.3844	1.44191	0.720954	−	0.692983i	$-0.243704\pi$
$241$	22.3844	1.44191	0.720954	+	0.692983i	$0.243704\pi$
$242$	0.822526	0.0528740
$243$	−1.00000	−0.0641500
$244$	1.32345	0.0847253
$245$	−14.4663	−0.924219
$246$	−5.15693	−0.328794
$247$	16.1446	1.02726
$248$	−14.7662	−0.937656
$249$	−4.60944	−0.292112
$250$	−9.61182	−0.607905
$251$	21.4637	1.35478	0.677390	−	0.735624i	$-0.263111\pi$
$251$	21.4637	1.35478	0.677390	+	0.735624i	$0.263111\pi$
$252$	−0.534871	−0.0336937
$253$	−8.67841	−0.545607
$254$	5.04983	0.316854
$255$	−0.0434559	−0.00272132
$256$	−14.7867	−0.924167
$257$	4.42849	0.276242	0.138121	−	0.990415i	$-0.455894\pi$
$257$	4.42849	0.276242	0.138121	+	0.990415i	$0.455894\pi$
$258$	−5.89039	−0.366720
$259$	0.806385	0.0501064
$260$	−11.3715	−0.705232
$261$	−5.89217	−0.364716
$262$	4.52424	0.279509
$263$	−26.2060	−1.61593	−0.807966	−	0.589230i	$-0.799431\pi$
$263$	−26.2060	−1.61593	−0.807966	+	0.589230i	$0.799431\pi$
$264$	2.73363	0.168243
$265$	10.9685	0.673788
$266$	1.32167	0.0810366
$267$	−12.7830	−0.782309
$268$	−20.1211	−1.22909
$269$	−11.4188	−0.696217	−0.348109	−	0.937454i	$-0.613176\pi$
$269$	−11.4188	−0.696217	−0.348109	+	0.937454i	$0.613176\pi$
$270$	−1.74046	−0.105921
$271$	2.05980	0.125124	0.0625620	−	0.998041i	$-0.480073\pi$
$271$	2.05980	0.125124	0.0625620	+	0.998041i	$0.480073\pi$
$272$	0.00818239	0.000496130 0
$273$	−1.64111	−0.0993246
$274$	−2.29459	−0.138621
$275$	−0.522583	−0.0315129
$276$	−11.4855	−0.691343
$277$	27.0262	1.62385	0.811923	−	0.583765i	$-0.198421\pi$
$277$	27.0262	1.62385	0.811923	+	0.583765i	$0.198421\pi$
$278$	−9.10733	−0.546221
$279$	5.40170	0.323391
$280$	−2.33773	−0.139706
$281$	4.85590	0.289679	0.144839	−	0.989455i	$-0.453733\pi$
$281$	4.85590	0.289679	0.144839	+	0.989455i	$0.453733\pi$
$282$	−7.02221	−0.418167
$283$	15.0805	0.896442	0.448221	−	0.893923i	$-0.352058\pi$
$283$	15.0805	0.896442	0.448221	+	0.893923i	$0.352058\pi$
$284$	−15.1922	−0.901493
$285$	−8.41288	−0.498336
$286$	3.34000	0.197498
$287$	2.53386	0.149569
$288$	5.79496	0.341472
$289$	−16.9996	−0.999975
$290$	−10.2551	−0.602199
$291$	0.603085	0.0353535
$292$	19.8973	1.16440
$293$	−19.5057	−1.13954	−0.569769	−	0.821805i	$-0.692967\pi$
$293$	−19.5057	−1.13954	−0.569769	+	0.821805i	$0.692967\pi$
$294$	5.62333	0.327960
$295$	−1.35148	−0.0786861
$296$	−5.45432	−0.317026
$297$	−1.00000	−0.0580259
$298$	0.389639	0.0225712
$299$	−35.2401	−2.03799
$300$	−0.691613	−0.0399303
$301$	2.89425	0.166822
$302$	10.9085	0.627716
$303$	14.6545	0.841879
$304$	1.58407	0.0908529
$305$	−2.11599	−0.121161
$306$	0.0168922	0.000965660 0
$307$	7.49773	0.427918	0.213959	−	0.976843i	$-0.431364\pi$
$307$	7.49773	0.427918	0.213959	+	0.976843i	$0.431364\pi$
$308$	−0.534871	−0.0304771
$309$	−11.1666	−0.635244
$310$	9.40143	0.533966
$311$	17.7437	1.00616	0.503078	−	0.864241i	$-0.332201\pi$
$311$	17.7437	1.00616	0.503078	+	0.864241i	$0.332201\pi$
$312$	11.1003	0.628433
$313$	13.3708	0.755763	0.377882	−	0.925854i	$-0.376653\pi$
$313$	13.3708	0.755763	0.377882	+	0.925854i	$0.376653\pi$
$314$	−10.5085	−0.593030
$315$	0.855175	0.0481837
$316$	−14.4892	−0.815083
$317$	−10.5527	−0.592699	−0.296350	−	0.955079i	$-0.595769\pi$
$317$	−10.5527	−0.592699	−0.296350	+	0.955079i	$0.595769\pi$
$318$	−4.26366	−0.239094
$319$	−5.89217	−0.329898
$320$	8.39977	0.469561
$321$	8.54990	0.477209
$322$	−2.88490	−0.160769
$323$	0.0816519	0.00454323
$324$	−1.32345	−0.0735250
$325$	−2.12203	−0.117709
$326$	20.1814	1.11775
$327$	−14.0443	−0.776650
$328$	−17.1388	−0.946331
$329$	3.45037	0.190225
$330$	−1.74046	−0.0958090
$331$	−5.63583	−0.309773	−0.154887	−	0.987932i	$-0.549501\pi$
$331$	−5.63583	−0.309773	−0.154887	+	0.987932i	$0.549501\pi$
$332$	−6.10037	−0.334801
$333$	1.99527	0.109340
$334$	3.25386	0.178043
$335$	32.1704	1.75766
$336$	−0.161022	−0.00878449
$337$	21.1177	1.15036	0.575178	−	0.818028i	$-0.304933\pi$
$337$	21.1177	1.15036	0.575178	+	0.818028i	$0.304933\pi$
$338$	2.86979	0.156096
$339$	−9.57510	−0.520048
$340$	−0.0575118	−0.00311901
$341$	5.40170	0.292519
$342$	3.27025	0.176835
$343$	−5.59207	−0.301943
$344$	−19.5764	−1.05549
$345$	18.3634	0.988654
$346$	−17.7466	−0.954063
$347$	−24.5687	−1.31892	−0.659458	−	0.751742i	$-0.729214\pi$
$347$	−24.5687	−1.31892	−0.659458	+	0.751742i	$0.729214\pi$
$348$	−7.79800	−0.418017
$349$	3.91197	0.209403	0.104701	−	0.994504i	$-0.466611\pi$
$349$	3.91197	0.209403	0.104701	+	0.994504i	$0.466611\pi$
$350$	−0.173719	−0.00928565
$351$	−4.06066	−0.216742
$352$	5.79496	0.308873
$353$	−28.5152	−1.51771	−0.758856	−	0.651259i	$-0.774241\pi$
$353$	−28.5152	−1.51771	−0.758856	+	0.651259i	$0.774241\pi$
$354$	0.525346	0.0279218
$355$	24.2900	1.28918
$356$	−16.9177	−0.896638
$357$	−0.00829997	−0.000439281 0
$358$	−11.1579	−0.589712
$359$	−27.2384	−1.43759	−0.718793	−	0.695224i	$-0.755305\pi$
$359$	−27.2384	−1.43759	−0.718793	+	0.695224i	$0.755305\pi$
$360$	−5.78433	−0.304861
$361$	−3.19255	−0.168029
$362$	−17.1908	−0.903530
$363$	−1.00000	−0.0524864
$364$	−2.17193	−0.113840
$365$	−31.8127	−1.66515
$366$	0.822526	0.0429941
$367$	−37.7100	−1.96845	−0.984224	−	0.176927i	$-0.943384\pi$
$367$	−37.7100	−1.96845	−0.984224	+	0.176927i	$0.943384\pi$
$368$	−3.45768	−0.180244
$369$	6.26962	0.326383
$370$	3.47268	0.180536
$371$	2.09495	0.108764
$372$	7.14889	0.370653
$373$	4.83715	0.250458	0.125229	−	0.992128i	$-0.460033\pi$
$373$	4.83715	0.250458	0.125229	+	0.992128i	$0.460033\pi$
$374$	0.0168922	0.000873472 0
$375$	11.6857	0.603449
$376$	−23.3380	−1.20356
$377$	−23.9261	−1.23226
$378$	−0.332423	−0.0170980
$379$	−35.2816	−1.81229	−0.906146	−	0.422965i	$-0.860989\pi$
$379$	−35.2816	−1.81229	−0.906146	+	0.422965i	$0.860989\pi$
$380$	−11.1340	−0.571164
$381$	−6.13941	−0.314532
$382$	2.01881	0.103291
$383$	18.3228	0.936253	0.468127	−	0.883661i	$-0.344929\pi$
$383$	18.3228	0.936253	0.468127	+	0.883661i	$0.344929\pi$
$384$	8.32478	0.424822
$385$	0.855175	0.0435838
$386$	−6.83894	−0.348093
$387$	7.16134	0.364031
$388$	0.798153	0.0405201
$389$	−34.4388	−1.74612	−0.873059	−	0.487614i	$-0.837867\pi$
$389$	−34.4388	−1.74612	−0.873059	+	0.487614i	$0.837867\pi$
$390$	−7.06741	−0.357872
$391$	−0.178228	−0.00901337
$392$	18.6889	0.943931
$393$	−5.50042	−0.277460
$394$	15.4638	0.779056
$395$	23.1660	1.16561
$396$	−1.32345	−0.0665059
$397$	−6.67209	−0.334862	−0.167431	−	0.985884i	$-0.553547\pi$
$397$	−6.67209	−0.334862	−0.167431	+	0.985884i	$0.553547\pi$
$398$	−6.44993	−0.323306
$399$	−1.60684	−0.0804425
$400$	−0.208209	−0.0104105
$401$	−19.4145	−0.969515	−0.484757	−	0.874649i	$-0.661092\pi$
$401$	−19.4145	−0.969515	−0.484757	+	0.874649i	$0.661092\pi$
$402$	−12.5053	−0.623706
$403$	21.9345	1.09264
$404$	19.3945	0.964912
$405$	2.11599	0.105144
$406$	−1.95869	−0.0972083
$407$	1.99527	0.0989018
$408$	0.0561402	0.00277936
$409$	0.767851	0.0379678	0.0189839	−	0.999820i	$-0.493957\pi$
$409$	0.767851	0.0379678	0.0189839	+	0.999820i	$0.493957\pi$
$410$	10.9120	0.538906
$411$	2.78969	0.137605
$412$	−14.7784	−0.728080
$413$	−0.258129	−0.0127017
$414$	−7.13822	−0.350824
$415$	9.75354	0.478782
$416$	23.5314	1.15372
$417$	11.0724	0.542217
$418$	3.27025	0.159953
$419$	17.3337	0.846806	0.423403	−	0.905941i	$-0.360835\pi$
$419$	17.3337	0.846806	0.423403	+	0.905941i	$0.360835\pi$
$420$	1.13178	0.0552253
$421$	12.0651	0.588016	0.294008	−	0.955803i	$-0.405011\pi$
$421$	12.0651	0.588016	0.294008	+	0.955803i	$0.405011\pi$
$422$	−21.1087	−1.02755
$423$	8.53737	0.415101
$424$	−14.1700	−0.688158
$425$	−0.0107322	−0.000520590 0
$426$	−9.44198	−0.457466
$427$	−0.404149	−0.0195581
$428$	11.3154	0.546949
$429$	−4.06066	−0.196051
$430$	12.4640	0.601068
$431$	−29.2010	−1.40656	−0.703282	−	0.710911i	$-0.748283\pi$
$431$	−29.2010	−1.40656	−0.703282	+	0.710911i	$0.748283\pi$
$432$	−0.398423	−0.0191692
$433$	−35.8038	−1.72062	−0.860311	−	0.509769i	$-0.829731\pi$
$433$	−35.8038	−1.72062	−0.860311	+	0.509769i	$0.829731\pi$
$434$	1.79565	0.0861939
$435$	12.4678	0.597785
$436$	−18.5869	−0.890151
$437$	−34.5041	−1.65056
$438$	12.3662	0.590880
$439$	40.8584	1.95006	0.975032	−	0.222063i	$-0.0712791\pi$
$439$	40.8584	1.95006	0.975032	+	0.222063i	$0.0712791\pi$
$440$	−5.78433	−0.275757
$441$	−6.83666	−0.325555
$442$	0.0685934	0.00326265
$443$	−27.9834	−1.32953	−0.664767	−	0.747051i	$-0.731469\pi$
$443$	−27.9834	−1.32953	−0.664767	+	0.747051i	$0.731469\pi$
$444$	2.64064	0.125319
$445$	27.0488	1.28224
$446$	1.08229	0.0512477
$447$	−0.473710	−0.0224057
$448$	1.60433	0.0757977
$449$	−25.0254	−1.18102	−0.590512	−	0.807029i	$-0.701074\pi$
$449$	−25.0254	−1.18102	−0.590512	+	0.807029i	$0.701074\pi$
$450$	−0.429838	−0.0202628
$451$	6.26962	0.295225
$452$	−12.6722	−0.596049
$453$	−13.2622	−0.623115
$454$	6.03303	0.283144
$455$	3.47258	0.162797
$456$	10.8685	0.508964
$457$	3.70365	0.173249	0.0866247	−	0.996241i	$-0.472392\pi$
$457$	3.70365	0.173249	0.0866247	+	0.996241i	$0.472392\pi$
$458$	−3.79807	−0.177472
$459$	−0.0205369	−0.000958581 0
$460$	24.3031	1.13314
$461$	−15.8022	−0.735982	−0.367991	−	0.929829i	$-0.619954\pi$
$461$	−15.8022	−0.735982	−0.367991	+	0.929829i	$0.619954\pi$
$462$	−0.332423	−0.0154657
$463$	−25.2470	−1.17333	−0.586665	−	0.809830i	$-0.699559\pi$
$463$	−25.2470	−1.17333	−0.586665	+	0.809830i	$0.699559\pi$
$464$	−2.34758	−0.108984
$465$	−11.4300	−0.530051
$466$	23.9564	1.10976
$467$	−17.2785	−0.799552	−0.399776	−	0.916613i	$-0.630912\pi$
$467$	−17.2785	−0.799552	−0.399776	+	0.916613i	$0.630912\pi$
$468$	−5.37409	−0.248417
$469$	6.14447	0.283725
$470$	14.8589	0.685391
$471$	12.7759	0.588683
$472$	1.74596	0.0803643
$473$	7.16134	0.329279
$474$	−9.00508	−0.413617
$475$	−2.07771	−0.0953321
$476$	−0.0109846	−0.000503478 0
$477$	5.18361	0.237341
$478$	−25.1792	−1.15167
$479$	10.8839	0.497297	0.248648	−	0.968594i	$-0.420014\pi$
$479$	10.8839	0.497297	0.248648	+	0.968594i	$0.420014\pi$
$480$	−12.2621	−0.559685
$481$	8.10212	0.369425
$482$	18.4118	0.838634
$483$	3.50737	0.159591
$484$	−1.32345	−0.0601569
$485$	−1.27612	−0.0579457
$486$	−0.822526	−0.0373105
$487$	39.0162	1.76799	0.883997	−	0.467492i	$-0.154842\pi$
$487$	39.0162	1.76799	0.883997	+	0.467492i	$0.154842\pi$
$488$	2.73363	0.123745
$489$	−24.5359	−1.10955
$490$	−11.8989	−0.537539
$491$	30.0322	1.35533	0.677667	−	0.735369i	$-0.262991\pi$
$491$	30.0322	1.35533	0.677667	+	0.735369i	$0.262991\pi$
$492$	8.29753	0.374082
$493$	−0.121007	−0.00544989
$494$	13.2794	0.597467
$495$	2.11599	0.0951067
$496$	2.15216	0.0966350
$497$	4.63933	0.208102
$498$	−3.79139	−0.169896
$499$	25.6100	1.14646	0.573232	−	0.819393i	$-0.305690\pi$
$499$	25.6100	1.14646	0.573232	+	0.819393i	$0.305690\pi$
$500$	15.4655	0.691638
$501$	−3.95593	−0.176738
$502$	17.6545	0.787958
$503$	−9.23707	−0.411861	−0.205930	−	0.978567i	$-0.566022\pi$
$503$	−9.23707	−0.411861	−0.205930	+	0.978567i	$0.566022\pi$
$504$	−1.10479	−0.0492113
$505$	−31.0088	−1.37987
$506$	−7.13822	−0.317333
$507$	−3.48899	−0.154952
$508$	−8.12521	−0.360498
$509$	32.4717	1.43928	0.719642	−	0.694345i	$-0.244306\pi$
$509$	32.4717	1.43928	0.719642	+	0.694345i	$0.244306\pi$
$510$	−0.0357436	−0.00158276
$511$	−6.07615	−0.268793
$512$	4.48713	0.198305
$513$	−3.97586	−0.175538
$514$	3.64255	0.160666
$515$	23.6284	1.04119
$516$	9.47768	0.417232
$517$	8.53737	0.375473
$518$	0.663273	0.0291425
$519$	21.5757	0.947069
$520$	−23.4882	−1.03003
$521$	12.2202	0.535375	0.267687	−	0.963506i	$-0.413741\pi$
$521$	12.2202	0.535375	0.267687	+	0.963506i	$0.413741\pi$
$522$	−4.84647	−0.212124
$523$	−24.8557	−1.08686	−0.543432	−	0.839453i	$-0.682876\pi$
$523$	−24.8557	−1.08686	−0.543432	+	0.839453i	$0.682876\pi$
$524$	−7.27954	−0.318008
$525$	0.211201	0.00921758
$526$	−21.5551	−0.939848
$527$	0.110934	0.00483238
$528$	−0.398423	−0.0173392
$529$	52.3148	2.27456
$530$	9.02186	0.391884
$531$	−0.638698	−0.0277171
$532$	−2.12657	−0.0921986
$533$	25.4588	1.10274
$534$	−10.5144	−0.455002
$535$	−18.0915	−0.782164
$536$	−41.5606	−1.79515
$537$	13.5654	0.585389
$538$	−9.39227	−0.404930
$539$	−6.83666	−0.294476
$540$	2.80041	0.120510
$541$	6.76305	0.290766	0.145383	−	0.989375i	$-0.453559\pi$
$541$	6.76305	0.290766	0.145383	+	0.989375i	$0.453559\pi$
$542$	1.69424	0.0727739
$543$	20.9000	0.896906
$544$	0.119011	0.00510254
$545$	29.7175	1.27296
$546$	−1.34986	−0.0577686
$547$	22.0518	0.942865	0.471432	−	0.881902i	$-0.343737\pi$
$547$	22.0518	0.942865	0.471432	+	0.881902i	$0.343737\pi$
$548$	3.69202	0.157715
$549$	−1.00000	−0.0426790
$550$	−0.429838	−0.0183284
$551$	−23.4264	−0.998000
$552$	−23.7235	−1.00974
$553$	4.42465	0.188155
$554$	22.2297	0.944451
$555$	−4.22197	−0.179213
$556$	14.6538	0.621458
$557$	14.7373	0.624438	0.312219	−	0.950010i	$-0.398928\pi$
$557$	14.7373	0.624438	0.312219	+	0.950010i	$0.398928\pi$
$558$	4.44304	0.188089
$559$	29.0798	1.22994
$560$	0.340722	0.0143981
$561$	−0.0205369	−0.000867069 0
$562$	3.99411	0.168481
$563$	−6.78450	−0.285933	−0.142966	−	0.989728i	$-0.545664\pi$
$563$	−6.78450	−0.285933	−0.142966	+	0.989728i	$0.545664\pi$
$564$	11.2988	0.475765
$565$	20.2608	0.852379
$566$	12.4041	0.521383
$567$	0.404149	0.0169727
$568$	−31.3800	−1.31667
$569$	10.9922	0.460817	0.230409	−	0.973094i	$-0.425994\pi$
$569$	10.9922	0.460817	0.230409	+	0.973094i	$0.425994\pi$
$570$	−6.91981	−0.289839
$571$	−41.9268	−1.75458	−0.877290	−	0.479961i	$-0.840651\pi$
$571$	−41.9268	−1.75458	−0.877290	+	0.479961i	$0.840651\pi$
$572$	−5.37409	−0.224702
$573$	−2.45440	−0.102534
$574$	2.08417	0.0869914
$575$	4.53519	0.189130
$576$	3.96966	0.165403
$577$	22.2721	0.927200	0.463600	−	0.886045i	$-0.346558\pi$
$577$	22.2721	0.927200	0.463600	+	0.886045i	$0.346558\pi$
$578$	−13.9826	−0.581599
$579$	8.31456	0.345541
$580$	16.5005	0.685146
$581$	1.86290	0.0772861
$582$	0.496053	0.0205621
$583$	5.18361	0.214683
$584$	41.0985	1.70067
$585$	8.59233	0.355249
$586$	−16.0440	−0.662771
$587$	−37.4028	−1.54378	−0.771888	−	0.635758i	$-0.780688\pi$
$587$	−37.4028	−1.54378	−0.771888	+	0.635758i	$0.780688\pi$
$588$	−9.04799	−0.373133
$589$	21.4764	0.884920
$590$	−1.11163	−0.0457649
$591$	−18.8004	−0.773345
$592$	0.794962	0.0326727
$593$	−39.4377	−1.61951	−0.809756	−	0.586767i	$-0.800400\pi$
$593$	−39.4377	−1.61951	−0.809756	+	0.586767i	$0.800400\pi$
$594$	−0.822526	−0.0337487
$595$	0.0175627	0.000719999 0
$596$	−0.626932	−0.0256801
$597$	7.84162	0.320936
$598$	−28.9859	−1.18532
$599$	20.8174	0.850578	0.425289	−	0.905058i	$-0.360172\pi$
$599$	20.8174	0.850578	0.425289	+	0.905058i	$0.360172\pi$
$600$	−1.42855	−0.0583201
$601$	5.46084	0.222752	0.111376	−	0.993778i	$-0.464474\pi$
$601$	5.46084	0.222752	0.111376	+	0.993778i	$0.464474\pi$
$602$	2.38059	0.0970258
$603$	15.2035	0.619134
$604$	−17.5519	−0.714178
$605$	2.11599	0.0860273
$606$	12.0537	0.489648
$607$	0.731366	0.0296852	0.0148426	−	0.999890i	$-0.495275\pi$
$607$	0.731366	0.0296852	0.0148426	+	0.999890i	$0.495275\pi$
$608$	23.0400	0.934394
$609$	2.38131	0.0964957
$610$	−1.74046	−0.0704691
$611$	34.6674	1.40249
$612$	−0.0271796	−0.00109867
$613$	5.30018	0.214072	0.107036	−	0.994255i	$-0.465864\pi$
$613$	5.30018	0.214072	0.107036	+	0.994255i	$0.465864\pi$
$614$	6.16708	0.248883
$615$	−13.2665	−0.534955
$616$	−1.10479	−0.0445133
$617$	−16.1004	−0.648176	−0.324088	−	0.946027i	$-0.605057\pi$
$617$	−16.1004	−0.648176	−0.324088	+	0.946027i	$0.605057\pi$
$618$	−9.18480	−0.369467
$619$	16.9174	0.679968	0.339984	−	0.940431i	$-0.389578\pi$
$619$	16.9174	0.679968	0.339984	+	0.940431i	$0.389578\pi$
$620$	−15.1270	−0.607514
$621$	8.67841	0.348253
$622$	14.5947	0.585194
$623$	5.16625	0.206981
$624$	−1.61786	−0.0647664
$625$	−22.1140	−0.884560
$626$	10.9978	0.439562
$627$	−3.97586	−0.158780
$628$	16.9083	0.674714
$629$	0.0409767	0.00163385
$630$	0.703404	0.0280243
$631$	−43.2520	−1.72184	−0.860918	−	0.508743i	$-0.830110\pi$
$631$	−43.2520	−1.72184	−0.860918	+	0.508743i	$0.830110\pi$
$632$	−29.9279	−1.19047
$633$	25.6632	1.02002
$634$	−8.67988	−0.344722
$635$	12.9909	0.515530
$636$	6.86025	0.272027
$637$	−27.7614	−1.09995
$638$	−4.84647	−0.191873
$639$	11.4793	0.454112
$640$	−17.6152	−0.696300
$641$	22.4987	0.888644	0.444322	−	0.895867i	$-0.353445\pi$
$641$	22.4987	0.888644	0.444322	+	0.895867i	$0.353445\pi$
$642$	7.03252	0.277551
$643$	16.3425	0.644487	0.322243	−	0.946657i	$-0.395563\pi$
$643$	16.3425	0.644487	0.322243	+	0.946657i	$0.395563\pi$
$644$	4.64183	0.182914
$645$	−15.1533	−0.596662
$646$	0.0671608	0.00264241
$647$	−18.5358	−0.728719	−0.364360	−	0.931258i	$-0.618712\pi$
$647$	−18.5358	−0.728719	−0.364360	+	0.931258i	$0.618712\pi$
$648$	−2.73363	−0.107387
$649$	−0.638698	−0.0250711
$650$	−1.74543	−0.0684613
$651$	−2.18309	−0.0855621
$652$	−32.4720	−1.27170
$653$	38.4291	1.50385	0.751924	−	0.659249i	$-0.229126\pi$
$653$	38.4291	1.50385	0.751924	+	0.659249i	$0.229126\pi$
$654$	−11.5518	−0.451710
$655$	11.6388	0.454767
$656$	2.49796	0.0975291
$657$	−15.0344	−0.586549
$658$	2.83802	0.110637
$659$	−13.0048	−0.506594	−0.253297	−	0.967389i	$-0.581515\pi$
$659$	−13.0048	−0.506594	−0.253297	+	0.967389i	$0.581515\pi$
$660$	2.80041	0.109006
$661$	17.4699	0.679500	0.339750	−	0.940516i	$-0.389658\pi$
$661$	17.4699	0.679500	0.339750	+	0.940516i	$0.389658\pi$
$662$	−4.63562	−0.180168
$663$	−0.0833935	−0.00323874
$664$	−12.6005	−0.488994
$665$	3.40006	0.131848
$666$	1.64116	0.0635937
$667$	51.1347	1.97994
$668$	−5.23548	−0.202567
$669$	−1.31581	−0.0508721
$670$	26.4610	1.02228
$671$	−1.00000	−0.0386046
$672$	−2.34203	−0.0903457
$673$	−21.0297	−0.810637	−0.405319	−	0.914175i	$-0.632839\pi$
$673$	−21.0297	−0.810637	−0.405319	+	0.914175i	$0.632839\pi$
$674$	17.3699	0.669063
$675$	0.522583	0.0201142
$676$	−4.61751	−0.177596
$677$	38.9808	1.49816	0.749078	−	0.662482i	$-0.230497\pi$
$677$	38.9808	1.49816	0.749078	+	0.662482i	$0.230497\pi$
$678$	−7.87577	−0.302467
$679$	−0.243736	−0.00935373
$680$	−0.118792	−0.00455547
$681$	−7.33476	−0.281069
$682$	4.44304	0.170133
$683$	−12.0413	−0.460746	−0.230373	−	0.973102i	$-0.573995\pi$
$683$	−12.0413	−0.460746	−0.230373	+	0.973102i	$0.573995\pi$
$684$	−5.26185	−0.201192
$685$	−5.90296	−0.225540
$686$	−4.59962	−0.175614
$687$	4.61757	0.176171
$688$	2.85325	0.108779
$689$	21.0489	0.801899
$690$	15.1044	0.575015
$691$	20.6612	0.785988	0.392994	−	0.919541i	$-0.371439\pi$
$691$	20.6612	0.785988	0.392994	+	0.919541i	$0.371439\pi$
$692$	28.5544	1.08548
$693$	0.404149	0.0153523
$694$	−20.2084	−0.767099
$695$	−23.4291	−0.888715
$696$	−16.1070	−0.610534
$697$	0.128759	0.00487708
$698$	3.21770	0.121792
$699$	−29.1255	−1.10163
$700$	0.279514	0.0105647
$701$	−11.9387	−0.450920	−0.225460	−	0.974252i	$-0.572388\pi$
$701$	−11.9387	−0.450920	−0.225460	+	0.974252i	$0.572388\pi$
$702$	−3.34000	−0.126060
$703$	7.93291	0.299195
$704$	3.96966	0.149612
$705$	−18.0650	−0.680367
$706$	−23.4545	−0.882722
$707$	−5.92260	−0.222742
$708$	−0.845285	−0.0317678
$709$	−15.3955	−0.578189	−0.289095	−	0.957300i	$-0.593354\pi$
$709$	−15.3955	−0.578189	−0.289095	+	0.957300i	$0.593354\pi$
$710$	19.9792	0.749804
$711$	10.9481	0.410585
$712$	−34.9440	−1.30958
$713$	−46.8782	−1.75560
$714$	−0.00682694	−0.000255492 0
$715$	8.59233	0.321335
$716$	17.9531	0.670939
$717$	30.6121	1.14323
$718$	−22.4043	−0.836120
$719$	18.8466	0.702859	0.351430	−	0.936214i	$-0.385696\pi$
$719$	18.8466	0.702859	0.351430	+	0.936214i	$0.385696\pi$
$720$	0.843060	0.0314190
$721$	4.51296	0.168071
$722$	−2.62596	−0.0977280
$723$	−22.3844	−0.832486
$724$	27.6602	1.02798
$725$	3.07915	0.114357
$726$	−0.822526	−0.0305268
$727$	−34.5785	−1.28245	−0.641223	−	0.767354i	$-0.721573\pi$
$727$	−34.5785	−1.28245	−0.641223	+	0.767354i	$0.721573\pi$
$728$	−4.48619	−0.166269
$729$	1.00000	0.0370370
$730$	−26.1668	−0.968476
$731$	0.147072	0.00543965
$732$	−1.32345	−0.0489161
$733$	−18.9209	−0.698859	−0.349430	−	0.936963i	$-0.613625\pi$
$733$	−18.9209	−0.698859	−0.349430	+	0.936963i	$0.613625\pi$
$734$	−31.0175	−1.14488
$735$	14.4663	0.533598
$736$	−50.2911	−1.85375
$737$	15.2035	0.560027
$738$	5.15693	0.189829
$739$	15.6521	0.575773	0.287886	−	0.957665i	$-0.407047\pi$
$739$	15.6521	0.575773	0.287886	+	0.957665i	$0.407047\pi$
$740$	−5.58757	−0.205403
$741$	−16.1446	−0.593088
$742$	1.72315	0.0632589
$743$	12.8846	0.472691	0.236346	−	0.971669i	$-0.424050\pi$
$743$	12.8846	0.472691	0.236346	+	0.971669i	$0.424050\pi$
$744$	14.7662	0.541356
$745$	1.00237	0.0367239
$746$	3.97868	0.145670
$747$	4.60944	0.168651
$748$	−0.0271796	−0.000993785 0
$749$	−3.45543	−0.126259
$750$	9.61182	0.350974
$751$	4.34890	0.158693	0.0793467	−	0.996847i	$-0.474717\pi$
$751$	4.34890	0.158693	0.0793467	+	0.996847i	$0.474717\pi$
$752$	3.40149	0.124039
$753$	−21.4637	−0.782182
$754$	−19.6799	−0.716699
$755$	28.0628	1.02131
$756$	0.534871	0.0194531
$757$	39.4539	1.43398	0.716989	−	0.697085i	$-0.245520\pi$
$757$	39.4539	1.43398	0.716989	+	0.697085i	$0.245520\pi$
$758$	−29.0200	−1.05405
$759$	8.67841	0.315006
$760$	−22.9977	−0.834213
$761$	−38.6312	−1.40038	−0.700190	−	0.713957i	$-0.746901\pi$
$761$	−38.6312	−1.40038	−0.700190	+	0.713957i	$0.746901\pi$
$762$	−5.04983	−0.182936
$763$	5.67597	0.205484
$764$	−3.24828	−0.117519
$765$	0.0434559	0.00157115
$766$	15.0710	0.544538
$767$	−2.59354	−0.0936472
$768$	14.7867	0.533568
$769$	−29.2863	−1.05609	−0.528046	−	0.849216i	$-0.677075\pi$
$769$	−29.2863	−1.05609	−0.528046	+	0.849216i	$0.677075\pi$
$770$	0.703404	0.0253489
$771$	−4.42849	−0.159488
$772$	11.0039	0.396039
$773$	1.46255	0.0526041	0.0263020	−	0.999654i	$-0.491627\pi$
$773$	1.46255	0.0526041	0.0263020	+	0.999654i	$0.491627\pi$
$774$	5.89039	0.211726
$775$	−2.82284	−0.101399
$776$	1.64861	0.0591816
$777$	−0.806385	−0.0289289
$778$	−28.3268	−1.01557
$779$	24.9271	0.893107
$780$	11.3715	0.407166
$781$	11.4793	0.410760
$782$	−0.146597	−0.00524230
$783$	5.89217	0.210569
$784$	−2.72389	−0.0972817
$785$	−27.0337	−0.964874
$786$	−4.52424	−0.161374
$787$	25.9663	0.925600	0.462800	−	0.886463i	$-0.346845\pi$
$787$	25.9663	0.925600	0.462800	+	0.886463i	$0.346845\pi$
$788$	−24.8814	−0.886363
$789$	26.2060	0.932958
$790$	19.0547	0.677934
$791$	3.86976	0.137593
$792$	−2.73363	−0.0971351
$793$	−4.06066	−0.144198
$794$	−5.48797	−0.194761
$795$	−10.9685	−0.389012
$796$	10.3780	0.367838
$797$	−31.4932	−1.11555	−0.557773	−	0.829993i	$-0.688344\pi$
$797$	−31.4932	−1.11555	−0.557773	+	0.829993i	$0.688344\pi$
$798$	−1.32167	−0.0467865
$799$	0.175331	0.00620278
$800$	−3.02835	−0.107068
$801$	12.7830	0.451666
$802$	−15.9689	−0.563883
$803$	−15.0344	−0.530553
$804$	20.1211	0.709615
$805$	−7.42156	−0.261576
$806$	18.0417	0.635492
$807$	11.4188	0.401961
$808$	40.0599	1.40930
$809$	8.19184	0.288010	0.144005	−	0.989577i	$-0.454002\pi$
$809$	8.19184	0.288010	0.144005	+	0.989577i	$0.454002\pi$
$810$	1.74046	0.0611535
$811$	8.90734	0.312779	0.156389	−	0.987695i	$-0.450015\pi$
$811$	8.90734	0.312779	0.156389	+	0.987695i	$0.450015\pi$
$812$	3.15155	0.110598
$813$	−2.05980	−0.0722404
$814$	1.64116	0.0575227
$815$	51.9177	1.81860
$816$	−0.00818239	−0.000286441 0
$817$	28.4725	0.996126
$818$	0.631577	0.0220826
$819$	1.64111	0.0573451
$820$	−17.5575	−0.613135
$821$	−25.1573	−0.877995	−0.438997	−	0.898488i	$-0.644666\pi$
$821$	−25.1573	−0.877995	−0.438997	+	0.898488i	$0.644666\pi$
$822$	2.29459	0.0800331
$823$	50.8751	1.77340	0.886698	−	0.462350i	$-0.152994\pi$
$823$	50.8751	1.77340	0.886698	+	0.462350i	$0.152994\pi$
$824$	−30.5252	−1.06340
$825$	0.522583	0.0181940
$826$	−0.212318	−0.00738748
$827$	43.4799	1.51195	0.755973	−	0.654603i	$-0.227164\pi$
$827$	43.4799	1.51195	0.755973	+	0.654603i	$0.227164\pi$
$828$	11.4855	0.399147
$829$	−34.9915	−1.21530	−0.607652	−	0.794203i	$-0.707889\pi$
$829$	−34.9915	−1.21530	−0.607652	+	0.794203i	$0.707889\pi$
$830$	8.02254	0.278466
$831$	−27.0262	−0.937528
$832$	16.1195	0.558842
$833$	−0.140404	−0.00486471
$834$	9.10733	0.315361
$835$	8.37072	0.289681
$836$	−5.26185	−0.181985
$837$	−5.40170	−0.186710
$838$	14.2574	0.492514
$839$	31.5500	1.08923	0.544614	−	0.838687i	$-0.316676\pi$
$839$	31.5500	1.08923	0.544614	+	0.838687i	$0.316676\pi$
$840$	2.33773	0.0806593
$841$	5.71771	0.197162
$842$	9.92384	0.341998
$843$	−4.85590	−0.167246
$844$	33.9640	1.16909
$845$	7.38267	0.253972
$846$	7.02221	0.241429
$847$	0.404149	0.0138867
$848$	2.06527	0.0709217
$849$	−15.0805	−0.517561
$850$	−0.00882755	−0.000302782 0
$851$	−17.3158	−0.593577
$852$	15.1922	0.520477
$853$	−4.60871	−0.157799	−0.0788997	−	0.996883i	$-0.525141\pi$
$853$	−4.60871	−0.157799	−0.0788997	+	0.996883i	$0.525141\pi$
$854$	−0.332423	−0.0113753
$855$	8.41288	0.287714
$856$	23.3722	0.798846
$857$	49.6081	1.69458	0.847290	−	0.531131i	$-0.178233\pi$
$857$	49.6081	1.69458	0.847290	+	0.531131i	$0.178233\pi$
$858$	−3.34000	−0.114026
$859$	−57.5877	−1.96487	−0.982433	−	0.186617i	$-0.940248\pi$
$859$	−57.5877	−1.96487	−0.982433	+	0.186617i	$0.940248\pi$
$860$	−20.0547	−0.683859
$861$	−2.53386	−0.0863537
$862$	−24.0186	−0.818077
$863$	−40.8905	−1.39193	−0.695964	−	0.718076i	$-0.745023\pi$
$863$	−40.8905	−1.39193	−0.695964	+	0.718076i	$0.745023\pi$
$864$	−5.79496	−0.197149
$865$	−45.6540	−1.55228
$866$	−29.4496	−1.00074
$867$	16.9996	0.577336
$868$	−2.88921	−0.0980663
$869$	10.9481	0.371388
$870$	10.2551	0.347680
$871$	61.7362	2.09185
$872$	−38.3918	−1.30011
$873$	−0.603085	−0.0204113
$874$	−28.3806	−0.959987
$875$	−4.72278	−0.159659
$876$	−19.8973	−0.672268
$877$	−7.81665	−0.263949	−0.131975	−	0.991253i	$-0.542132\pi$
$877$	−7.81665	−0.263949	−0.131975	+	0.991253i	$0.542132\pi$
$878$	33.6071	1.13418
$879$	19.5057	0.657912
$880$	0.843060	0.0284196
$881$	−16.7321	−0.563719	−0.281860	−	0.959456i	$-0.590951\pi$
$881$	−16.7321	−0.563719	−0.281860	+	0.959456i	$0.590951\pi$
$882$	−5.62333	−0.189348
$883$	−18.3230	−0.616617	−0.308308	−	0.951286i	$-0.599763\pi$
$883$	−18.3230	−0.616617	−0.308308	+	0.951286i	$0.599763\pi$
$884$	−0.110367	−0.00371205
$885$	1.35148	0.0454295
$886$	−23.0171	−0.773275
$887$	36.8957	1.23884	0.619419	−	0.785061i	$-0.287368\pi$
$887$	36.8957	1.23884	0.619419	+	0.785061i	$0.287368\pi$
$888$	5.45432	0.183035
$889$	2.48124	0.0832180
$890$	22.2483	0.745766
$891$	1.00000	0.0335013
$892$	−1.74141	−0.0583066
$893$	33.9434	1.13587
$894$	−0.389639	−0.0130315
$895$	−28.7042	−0.959476
$896$	−3.36445	−0.112398
$897$	35.2401	1.17663
$898$	−20.5841	−0.686900
$899$	−31.8278	−1.06152
$900$	0.691613	0.0230538
$901$	0.106455	0.00354654
$902$	5.15693	0.171707
$903$	−2.89425	−0.0963145
$904$	−26.1747	−0.870558
$905$	−44.2243	−1.47006
$906$	−10.9085	−0.362412
$907$	−1.15826	−0.0384593	−0.0192297	−	0.999815i	$-0.506121\pi$
$907$	−1.15826	−0.0384593	−0.0192297	+	0.999815i	$0.506121\pi$
$908$	−9.70720	−0.322145
$909$	−14.6545	−0.486059
$910$	2.85629	0.0946850
$911$	−39.7016	−1.31537	−0.657686	−	0.753292i	$-0.728465\pi$
$911$	−39.7016	−1.31537	−0.657686	+	0.753292i	$0.728465\pi$
$912$	−1.58407	−0.0524540
$913$	4.60944	0.152550
$914$	3.04635	0.100764
$915$	2.11599	0.0699525
$916$	6.11112	0.201917
$917$	2.22299	0.0734096
$918$	−0.0168922	−0.000557524 0
$919$	34.7872	1.14752	0.573762	−	0.819022i	$-0.305483\pi$
$919$	34.7872	1.14752	0.573762	+	0.819022i	$0.305483\pi$
$920$	50.1988	1.65500
$921$	−7.49773	−0.247059
$922$	−12.9977	−0.428057
$923$	46.6134	1.53430
$924$	0.534871	0.0175960
$925$	−1.04269	−0.0342835
$926$	−20.7663	−0.682424
$927$	11.1666	0.366758
$928$	−34.1449	−1.12086
$929$	−16.5877	−0.544226	−0.272113	−	0.962265i	$-0.587722\pi$
$929$	−16.5877	−0.544226	−0.272113	+	0.962265i	$0.587722\pi$
$930$	−9.40143	−0.308285
$931$	−27.1816	−0.890841
$932$	−38.5461	−1.26262
$933$	−17.7437	−0.580904
$934$	−14.2120	−0.465030
$935$	0.0434559	0.00142116
$936$	−11.1003	−0.362826
$937$	29.0025	0.947470	0.473735	−	0.880667i	$-0.342905\pi$
$937$	29.0025	0.947470	0.473735	+	0.880667i	$0.342905\pi$
$938$	5.05399	0.165018
$939$	−13.3708	−0.436340
$940$	−23.9081	−0.779797
$941$	41.2410	1.34442	0.672210	−	0.740361i	$-0.265345\pi$
$941$	41.2410	1.34442	0.672210	+	0.740361i	$0.265345\pi$
$942$	10.5085	0.342386
$943$	−54.4103	−1.77184
$944$	−0.254472	−0.00828236
$945$	−0.855175	−0.0278189
$946$	5.89039	0.191513
$947$	−14.9009	−0.484214	−0.242107	−	0.970250i	$-0.577839\pi$
$947$	−14.9009	−0.484214	−0.242107	+	0.970250i	$0.577839\pi$
$948$	14.4892	0.470588
$949$	−61.0497	−1.98176
$950$	−1.70897	−0.0554465
$951$	10.5527	0.342195
$952$	−0.0226890	−0.000735355 0
$953$	−29.4563	−0.954185	−0.477092	−	0.878853i	$-0.658309\pi$
$953$	−29.4563	−0.954185	−0.477092	+	0.878853i	$0.658309\pi$
$954$	4.26366	0.138041
$955$	5.19349	0.168057
$956$	40.5135	1.31030
$957$	5.89217	0.190467
$958$	8.95227	0.289235
$959$	−1.12745	−0.0364073
$960$	−8.39977	−0.271101
$961$	−1.82161	−0.0587617
$962$	6.66420	0.214862
$963$	−8.54990	−0.275517
$964$	−29.6247	−0.954147
$965$	−17.5935	−0.566356
$966$	2.88490	0.0928202
$967$	39.2447	1.26202	0.631012	−	0.775773i	$-0.282640\pi$
$967$	39.2447	1.26202	0.631012	+	0.775773i	$0.282640\pi$
$968$	−2.73363	−0.0878620
$969$	−0.0816519	−0.00262304
$970$	−1.04964	−0.0337020
$971$	19.0146	0.610207	0.305104	−	0.952319i	$-0.401309\pi$
$971$	19.0146	0.610207	0.305104	+	0.952319i	$0.401309\pi$
$972$	1.32345	0.0424497
$973$	−4.47489	−0.143458
$974$	32.0919	1.02829
$975$	2.12203	0.0679594
$976$	−0.398423	−0.0127532
$977$	15.7282	0.503188	0.251594	−	0.967833i	$-0.419045\pi$
$977$	15.7282	0.503188	0.251594	+	0.967833i	$0.419045\pi$
$978$	−20.1814	−0.645330
$979$	12.7830	0.408548
$980$	19.1455	0.611579
$981$	14.0443	0.448399
$982$	24.7023	0.788281
$983$	−41.9230	−1.33714	−0.668568	−	0.743651i	$-0.733092\pi$
$983$	−41.9230	−1.33714	−0.668568	+	0.743651i	$0.733092\pi$
$984$	17.1388	0.546365
$985$	39.7815	1.26754
$986$	−0.0995315	−0.00316973
$987$	−3.45037	−0.109826
$988$	−21.3666	−0.679763
$989$	−62.1491	−1.97623
$990$	1.74046	0.0553154
$991$	17.5601	0.557816	0.278908	−	0.960318i	$-0.410027\pi$
$991$	17.5601	0.557816	0.278908	+	0.960318i	$0.410027\pi$
$992$	31.3027	0.993861
$993$	5.63583	0.178848
$994$	3.81597	0.121035
$995$	−16.5928	−0.526027
$996$	6.10037	0.193298
$997$	−11.7778	−0.373008	−0.186504	−	0.982454i	$-0.559716\pi$
$997$	−11.7778	−0.373008	−0.186504	+	0.982454i	$0.559716\pi$
$998$	21.0649	0.666799
$999$	−1.99527	−0.0631275

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2013.2.a.e.1.8	✓	13
3.2	odd	2		6039.2.a.i.1.6		13

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2013.2.a.e.1.8	✓	13	1.1	even	1	trivial
6039.2.a.i.1.6		13	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:	\( N \)	\(=\)	\( 2013 = 3 \cdot 11 \cdot 61 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2013.a (trivial)

\(f(q)\)	\(=\)	\(q+0.822526 q^{2} -1.00000 q^{3} -1.32345 q^{4} +2.11599 q^{5} -0.822526 q^{6} +0.404149 q^{7} -2.73363 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+0.822526 q^{2} -1.00000 q^{3} -1.32345 q^{4} +2.11599 q^{5} -0.822526 q^{6} +0.404149 q^{7} -2.73363 q^{8} +1.00000 q^{9} +1.74046 q^{10} +1.00000 q^{11} +1.32345 q^{12} +4.06066 q^{13} +0.332423 q^{14} -2.11599 q^{15} +0.398423 q^{16} +0.0205369 q^{17} +0.822526 q^{18} +3.97586 q^{19} -2.80041 q^{20} -0.404149 q^{21} +0.822526 q^{22} -8.67841 q^{23} +2.73363 q^{24} -0.522583 q^{25} +3.34000 q^{26} -1.00000 q^{27} -0.534871 q^{28} -5.89217 q^{29} -1.74046 q^{30} +5.40170 q^{31} +5.79496 q^{32} -1.00000 q^{33} +0.0168922 q^{34} +0.855175 q^{35} -1.32345 q^{36} +1.99527 q^{37} +3.27025 q^{38} -4.06066 q^{39} -5.78433 q^{40} +6.26962 q^{41} -0.332423 q^{42} +7.16134 q^{43} -1.32345 q^{44} +2.11599 q^{45} -7.13822 q^{46} +8.53737 q^{47} -0.398423 q^{48} -6.83666 q^{49} -0.429838 q^{50} -0.0205369 q^{51} -5.37409 q^{52} +5.18361 q^{53} -0.822526 q^{54} +2.11599 q^{55} -1.10479 q^{56} -3.97586 q^{57} -4.84647 q^{58} -0.638698 q^{59} +2.80041 q^{60} -1.00000 q^{61} +4.44304 q^{62} +0.404149 q^{63} +3.96966 q^{64} +8.59233 q^{65} -0.822526 q^{66} +15.2035 q^{67} -0.0271796 q^{68} +8.67841 q^{69} +0.703404 q^{70} +11.4793 q^{71} -2.73363 q^{72} -15.0344 q^{73} +1.64116 q^{74} +0.522583 q^{75} -5.26185 q^{76} +0.404149 q^{77} -3.34000 q^{78} +10.9481 q^{79} +0.843060 q^{80} +1.00000 q^{81} +5.15693 q^{82} +4.60944 q^{83} +0.534871 q^{84} +0.0434559 q^{85} +5.89039 q^{86} +5.89217 q^{87} -2.73363 q^{88} +12.7830 q^{89} +1.74046 q^{90} +1.64111 q^{91} +11.4855 q^{92} -5.40170 q^{93} +7.02221 q^{94} +8.41288 q^{95} -5.79496 q^{96} -0.603085 q^{97} -5.62333 q^{98} +1.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 13 q + 2 q^{2} - 13 q^{3} + 16 q^{4} + 3 q^{5} - 2 q^{6} + 11 q^{7} + 9 q^{8} + 13 q^{9}+O(q^{10}) \) 13 * q + 2 * q^2 - 13 * q^3 + 16 * q^4 + 3 * q^5 - 2 * q^6 + 11 * q^7 + 9 * q^8 + 13 * q^9	\( 13 q + 2 q^{2} - 13 q^{3} + 16 q^{4} + 3 q^{5} - 2 q^{6} + 11 q^{7} + 9 q^{8} + 13 q^{9} + 6 q^{10} + 13 q^{11} - 16 q^{12} + 13 q^{13} + q^{14} - 3 q^{15} + 18 q^{16} + 17 q^{17} + 2 q^{18} + 14 q^{19} - 7 q^{20} - 11 q^{21} + 2 q^{22} + 7 q^{23} - 9 q^{24} + 18 q^{25} - 10 q^{26} - 13 q^{27} + 19 q^{28} - 6 q^{29} - 6 q^{30} + 27 q^{31} + 5 q^{32} - 13 q^{33} + 6 q^{34} + 14 q^{35} + 16 q^{36} + 10 q^{37} + 2 q^{38} - 13 q^{39} + 8 q^{40} + 3 q^{41} - q^{42} + 29 q^{43} + 16 q^{44} + 3 q^{45} - 24 q^{46} + 8 q^{47} - 18 q^{48} + 8 q^{49} - 27 q^{50} - 17 q^{51} + 37 q^{52} - 24 q^{53} - 2 q^{54} + 3 q^{55} + 24 q^{56} - 14 q^{57} - 5 q^{58} + 13 q^{59} + 7 q^{60} - 13 q^{61} + 39 q^{62} + 11 q^{63} + 47 q^{64} - 11 q^{65} - 2 q^{66} + 44 q^{67} - 8 q^{68} - 7 q^{69} - 12 q^{70} + 3 q^{71} + 9 q^{72} + 48 q^{73} - 22 q^{74} - 18 q^{75} + 47 q^{76} + 11 q^{77} + 10 q^{78} - 17 q^{79} - 26 q^{80} + 13 q^{81} + 56 q^{82} + 50 q^{83} - 19 q^{84} + 8 q^{85} + 18 q^{86} + 6 q^{87} + 9 q^{88} - 15 q^{89} + 6 q^{90} + 47 q^{91} + 14 q^{92} - 27 q^{93} + 45 q^{94} - q^{95} - 5 q^{96} + 27 q^{97} + 47 q^{98} + 13 q^{99}+O(q^{100}) \) 13 * q + 2 * q^2 - 13 * q^3 + 16 * q^4 + 3 * q^5 - 2 * q^6 + 11 * q^7 + 9 * q^8 + 13 * q^9 + 6 * q^10 + 13 * q^11 - 16 * q^12 + 13 * q^13 + q^14 - 3 * q^15 + 18 * q^16 + 17 * q^17 + 2 * q^18 + 14 * q^19 - 7 * q^20 - 11 * q^21 + 2 * q^22 + 7 * q^23 - 9 * q^24 + 18 * q^25 - 10 * q^26 - 13 * q^27 + 19 * q^28 - 6 * q^29 - 6 * q^30 + 27 * q^31 + 5 * q^32 - 13 * q^33 + 6 * q^34 + 14 * q^35 + 16 * q^36 + 10 * q^37 + 2 * q^38 - 13 * q^39 + 8 * q^40 + 3 * q^41 - q^42 + 29 * q^43 + 16 * q^44 + 3 * q^45 - 24 * q^46 + 8 * q^47 - 18 * q^48 + 8 * q^49 - 27 * q^50 - 17 * q^51 + 37 * q^52 - 24 * q^53 - 2 * q^54 + 3 * q^55 + 24 * q^56 - 14 * q^57 - 5 * q^58 + 13 * q^59 + 7 * q^60 - 13 * q^61 + 39 * q^62 + 11 * q^63 + 47 * q^64 - 11 * q^65 - 2 * q^66 + 44 * q^67 - 8 * q^68 - 7 * q^69 - 12 * q^70 + 3 * q^71 + 9 * q^72 + 48 * q^73 - 22 * q^74 - 18 * q^75 + 47 * q^76 + 11 * q^77 + 10 * q^78 - 17 * q^79 - 26 * q^80 + 13 * q^81 + 56 * q^82 + 50 * q^83 - 19 * q^84 + 8 * q^85 + 18 * q^86 + 6 * q^87 + 9 * q^88 - 15 * q^89 + 6 * q^90 + 47 * q^91 + 14 * q^92 - 27 * q^93 + 45 * q^94 - q^95 - 5 * q^96 + 27 * q^97 + 47 * q^98 + 13 * q^99

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