LMFDB - Embedded newform 2013.2.a.e.1.5

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			1.5
Root			$-0.948254$ 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)

$f(q)$	$=$	$q-0.948254 q^{2} -1.00000 q^{3} -1.10081 q^{4} -2.25122 q^{5} +0.948254 q^{6} +5.24025 q^{7} +2.94036 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-0.948254 q^{2} -1.00000 q^{3} -1.10081 q^{4} -2.25122 q^{5} +0.948254 q^{6} +5.24025 q^{7} +2.94036 q^{8} +1.00000 q^{9} +2.13473 q^{10} +1.00000 q^{11} +1.10081 q^{12} +5.44016 q^{13} -4.96909 q^{14} +2.25122 q^{15} -0.586583 q^{16} +4.46012 q^{17} -0.948254 q^{18} +2.98902 q^{19} +2.47818 q^{20} -5.24025 q^{21} -0.948254 q^{22} +0.200434 q^{23} -2.94036 q^{24} +0.0679998 q^{25} -5.15865 q^{26} -1.00000 q^{27} -5.76854 q^{28} -1.81818 q^{29} -2.13473 q^{30} +0.728977 q^{31} -5.32449 q^{32} -1.00000 q^{33} -4.22933 q^{34} -11.7970 q^{35} -1.10081 q^{36} -3.44866 q^{37} -2.83436 q^{38} -5.44016 q^{39} -6.61940 q^{40} +2.51230 q^{41} +4.96909 q^{42} +7.72081 q^{43} -1.10081 q^{44} -2.25122 q^{45} -0.190062 q^{46} -9.29908 q^{47} +0.586583 q^{48} +20.4602 q^{49} -0.0644811 q^{50} -4.46012 q^{51} -5.98860 q^{52} -1.48505 q^{53} +0.948254 q^{54} -2.25122 q^{55} +15.4082 q^{56} -2.98902 q^{57} +1.72409 q^{58} +1.65543 q^{59} -2.47818 q^{60} -1.00000 q^{61} -0.691255 q^{62} +5.24025 q^{63} +6.22214 q^{64} -12.2470 q^{65} +0.948254 q^{66} +16.1730 q^{67} -4.90976 q^{68} -0.200434 q^{69} +11.1865 q^{70} +1.39117 q^{71} +2.94036 q^{72} -8.30506 q^{73} +3.27021 q^{74} -0.0679998 q^{75} -3.29036 q^{76} +5.24025 q^{77} +5.15865 q^{78} -11.7081 q^{79} +1.32053 q^{80} +1.00000 q^{81} -2.38230 q^{82} -1.10951 q^{83} +5.76854 q^{84} -10.0407 q^{85} -7.32129 q^{86} +1.81818 q^{87} +2.94036 q^{88} +6.80479 q^{89} +2.13473 q^{90} +28.5078 q^{91} -0.220640 q^{92} -0.728977 q^{93} +8.81789 q^{94} -6.72896 q^{95} +5.32449 q^{96} -9.30845 q^{97} -19.4015 q^{98} +1.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−0.948254	−0.670517	−0.335259	−	0.942126i	$-0.608824\pi$
$2$	−0.948254	−0.670517	−0.335259	+	0.942126i	$0.608824\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	−1.10081	−0.550407
$5$	−2.25122	−1.00678	−0.503389	−	0.864060i	$-0.667914\pi$
$5$	−2.25122	−1.00678	−0.503389	+	0.864060i	$0.667914\pi$
$6$	0.948254	0.387123
$7$	5.24025	1.98063	0.990315	−	0.138842i	$-0.0443379\pi$
$7$	5.24025	1.98063	0.990315	+	0.138842i	$0.0443379\pi$
$8$	2.94036	1.03957
$9$	1.00000	0.333333
$10$	2.13473	0.675061
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	1.10081	0.317777
$13$	5.44016	1.50883	0.754414	−	0.656399i	$-0.227921\pi$
$13$	5.44016	1.50883	0.754414	+	0.656399i	$0.227921\pi$
$14$	−4.96909	−1.32805
$15$	2.25122	0.581263
$16$	−0.586583	−0.146646
$17$	4.46012	1.08174	0.540869	−	0.841107i	$-0.318095\pi$
$17$	4.46012	1.08174	0.540869	+	0.841107i	$0.318095\pi$
$18$	−0.948254	−0.223506
$19$	2.98902	0.685729	0.342865	−	0.939385i	$-0.388603\pi$
$19$	2.98902	0.685729	0.342865	+	0.939385i	$0.388603\pi$
$20$	2.47818	0.554137
$21$	−5.24025	−1.14352
$22$	−0.948254	−0.202169
$23$	0.200434	0.0417934	0.0208967	−	0.999782i	$-0.493348\pi$
$23$	0.200434	0.0417934	0.0208967	+	0.999782i	$0.493348\pi$
$24$	−2.94036	−0.600199
$25$	0.0679998	0.0136000
$26$	−5.15865	−1.01169
$27$	−1.00000	−0.192450
$28$	−5.76854	−1.09015
$29$	−1.81818	−0.337627	−0.168813	−	0.985648i	$-0.553994\pi$
$29$	−1.81818	−0.337627	−0.168813	+	0.985648i	$0.553994\pi$
$30$	−2.13473	−0.389747
$31$	0.728977	0.130928	0.0654640	−	0.997855i	$-0.479147\pi$
$31$	0.728977	0.130928	0.0654640	+	0.997855i	$0.479147\pi$
$32$	−5.32449	−0.941246
$33$	−1.00000	−0.174078
$34$	−4.22933	−0.725324
$35$	−11.7970	−1.99405
$36$	−1.10081	−0.183469
$37$	−3.44866	−0.566956	−0.283478	−	0.958979i	$-0.591488\pi$
$37$	−3.44866	−0.566956	−0.283478	+	0.958979i	$0.591488\pi$
$38$	−2.83436	−0.459793
$39$	−5.44016	−0.871122
$40$	−6.61940	−1.04662
$41$	2.51230	0.392355	0.196178	−	0.980568i	$-0.437147\pi$
$41$	2.51230	0.392355	0.196178	+	0.980568i	$0.437147\pi$
$42$	4.96909	0.766748
$43$	7.72081	1.17741	0.588706	−	0.808347i	$-0.299638\pi$
$43$	7.72081	1.17741	0.588706	+	0.808347i	$0.299638\pi$
$44$	−1.10081	−0.165954
$45$	−2.25122	−0.335592
$46$	−0.190062	−0.0280232
$47$	−9.29908	−1.35641	−0.678205	−	0.734873i	$-0.737242\pi$
$47$	−9.29908	−1.35641	−0.678205	+	0.734873i	$0.737242\pi$
$48$	0.586583	0.0846659
$49$	20.4602	2.92289
$50$	−0.0644811	−0.00911900
$51$	−4.46012	−0.624542
$52$	−5.98860	−0.830469
$53$	−1.48505	−0.203987	−0.101994	−	0.994785i	$-0.532522\pi$
$53$	−1.48505	−0.203987	−0.101994	+	0.994785i	$0.532522\pi$
$54$	0.948254	0.129041
$55$	−2.25122	−0.303555
$56$	15.4082	2.05901
$57$	−2.98902	−0.395906
$58$	1.72409	0.226385
$59$	1.65543	0.215518	0.107759	−	0.994177i	$-0.465632\pi$
$59$	1.65543	0.215518	0.107759	+	0.994177i	$0.465632\pi$
$60$	−2.47818	−0.319931
$61$	−1.00000	−0.128037
$61$	−1.00000	−0.128037
$62$	−0.691255	−0.0877895
$63$	5.24025	0.660210
$64$	6.22214	0.777767
$65$	−12.2470	−1.51905
$66$	0.948254	0.116722
$67$	16.1730	1.97585	0.987923	−	0.154948i	$-0.0495211\pi$
$67$	16.1730	1.97585	0.987923	+	0.154948i	$0.0495211\pi$
$68$	−4.90976	−0.595396
$69$	−0.200434	−0.0241294
$70$	11.1865	1.33705
$71$	1.39117	0.165101	0.0825506	−	0.996587i	$-0.473693\pi$
$71$	1.39117	0.165101	0.0825506	+	0.996587i	$0.473693\pi$
$72$	2.94036	0.346525
$73$	−8.30506	−0.972034	−0.486017	−	0.873949i	$-0.661551\pi$
$73$	−8.30506	−0.972034	−0.486017	+	0.873949i	$0.661551\pi$
$74$	3.27021	0.380154
$75$	−0.0679998	−0.00785194
$76$	−3.29036	−0.377430
$77$	5.24025	0.597182
$78$	5.15865	0.584102
$79$	−11.7081	−1.31726	−0.658630	−	0.752467i	$-0.728864\pi$
$79$	−11.7081	−1.31726	−0.658630	+	0.752467i	$0.728864\pi$
$80$	1.32053	0.147640
$81$	1.00000	0.111111
$82$	−2.38230	−0.263081
$83$	−1.10951	−0.121785	−0.0608924	−	0.998144i	$-0.519395\pi$
$83$	−1.10951	−0.121785	−0.0608924	+	0.998144i	$0.519395\pi$
$84$	5.76854	0.629399
$85$	−10.0407	−1.08907
$86$	−7.32129	−0.789475
$87$	1.81818	0.194929
$88$	2.94036	0.313443
$89$	6.80479	0.721306	0.360653	−	0.932700i	$-0.382554\pi$
$89$	6.80479	0.721306	0.360653	+	0.932700i	$0.382554\pi$
$90$	2.13473	0.225020
$91$	28.5078	2.98843
$92$	−0.220640	−0.0230034
$93$	−0.728977	−0.0755914
$94$	8.81789	0.909496
$95$	−6.72896	−0.690377
$96$	5.32449	0.543429
$97$	−9.30845	−0.945130	−0.472565	−	0.881296i	$-0.656672\pi$
$97$	−9.30845	−0.945130	−0.472565	+	0.881296i	$0.656672\pi$
$98$	−19.4015	−1.95985
$99$	1.00000	0.100504
$100$	−0.0748551	−0.00748551
$101$	9.37877	0.933223	0.466611	−	0.884462i	$-0.345475\pi$
$101$	9.37877	0.933223	0.466611	+	0.884462i	$0.345475\pi$
$102$	4.22933	0.418766
$103$	−9.63463	−0.949328	−0.474664	−	0.880167i	$-0.657430\pi$
$103$	−9.63463	−0.949328	−0.474664	+	0.880167i	$0.657430\pi$
$104$	15.9960	1.56854
$105$	11.7970	1.15127
$106$	1.40820	0.136777
$107$	3.02397	0.292338	0.146169	−	0.989260i	$-0.453306\pi$
$107$	3.02397	0.292338	0.146169	+	0.989260i	$0.453306\pi$
$108$	1.10081	0.105926
$109$	3.74875	0.359065	0.179533	−	0.983752i	$-0.442541\pi$
$109$	3.74875	0.359065	0.179533	+	0.983752i	$0.442541\pi$
$110$	2.13473	0.203539
$111$	3.44866	0.327332
$112$	−3.07384	−0.290451
$113$	−3.50360	−0.329591	−0.164795	−	0.986328i	$-0.552696\pi$
$113$	−3.50360	−0.329591	−0.164795	+	0.986328i	$0.552696\pi$
$114$	2.83436	0.265462
$115$	−0.451221	−0.0420766
$116$	2.00147	0.185832
$117$	5.44016	0.502943
$118$	−1.56977	−0.144509
$119$	23.3722	2.14252
$120$	6.61940	0.604266
$121$	1.00000	0.0909091
$122$	0.948254	0.0858509
$123$	−2.51230	−0.226526
$124$	−0.802467	−0.0720637
$125$	11.1030	0.993085
$126$	−4.96909	−0.442682
$127$	5.45206	0.483792	0.241896	−	0.970302i	$-0.422231\pi$
$127$	5.45206	0.483792	0.241896	+	0.970302i	$0.422231\pi$
$128$	4.74881	0.419740
$129$	−7.72081	−0.679779
$130$	11.6133	1.01855
$131$	−16.4647	−1.43853	−0.719265	−	0.694736i	$-0.755521\pi$
$131$	−16.4647	−1.43853	−0.719265	+	0.694736i	$0.755521\pi$
$132$	1.10081	0.0958135
$133$	15.6632	1.35818
$134$	−15.3361	−1.32484
$135$	2.25122	0.193754
$136$	13.1144	1.12455
$137$	1.13223	0.0967330	0.0483665	−	0.998830i	$-0.484598\pi$
$137$	1.13223	0.0967330	0.0483665	+	0.998830i	$0.484598\pi$
$138$	0.190062	0.0161792
$139$	17.6358	1.49585	0.747923	−	0.663785i	$-0.231051\pi$
$139$	17.6358	1.49585	0.747923	+	0.663785i	$0.231051\pi$
$140$	12.9863	1.09754
$141$	9.29908	0.783124
$142$	−1.31918	−0.110703
$143$	5.44016	0.454929
$144$	−0.586583	−0.0488819
$145$	4.09312	0.339915
$146$	7.87531	0.651766
$147$	−20.4602	−1.68753
$148$	3.79633	0.312057
$149$	18.5492	1.51961	0.759804	−	0.650152i	$-0.225295\pi$
$149$	18.5492	1.51961	0.759804	+	0.650152i	$0.225295\pi$
$150$	0.0644811	0.00526486
$151$	−22.4227	−1.82474	−0.912368	−	0.409371i	$-0.865748\pi$
$151$	−22.4227	−1.82474	−0.912368	+	0.409371i	$0.865748\pi$
$152$	8.78881	0.712867
$153$	4.46012	0.360580
$154$	−4.96909	−0.400421
$155$	−1.64109	−0.131815
$156$	5.98860	0.479471
$157$	−7.31110	−0.583489	−0.291745	−	0.956496i	$-0.594236\pi$
$157$	−7.31110	−0.583489	−0.291745	+	0.956496i	$0.594236\pi$
$158$	11.1022	0.883246
$159$	1.48505	0.117772
$160$	11.9866	0.947625
$161$	1.05032	0.0827772
$162$	−0.948254	−0.0745019
$163$	−1.04410	−0.0817803	−0.0408902	−	0.999164i	$-0.513019\pi$
$163$	−1.04410	−0.0817803	−0.0408902	+	0.999164i	$0.513019\pi$
$164$	−2.76557	−0.215955
$165$	2.25122	0.175257
$166$	1.05210	0.0816588
$167$	−0.242267	−0.0187472	−0.00937360	−	0.999956i	$-0.502984\pi$
$167$	−0.242267	−0.0187472	−0.00937360	+	0.999956i	$0.502984\pi$
$168$	−15.4082	−1.18877
$169$	16.5953	1.27656
$170$	9.52116	0.730240
$171$	2.98902	0.228576
$172$	−8.49917	−0.648056
$173$	−23.7589	−1.80636	−0.903179	−	0.429264i	$-0.858773\pi$
$173$	−23.7589	−1.80636	−0.903179	+	0.429264i	$0.858773\pi$
$174$	−1.72409	−0.130703
$175$	0.356336	0.0269365
$176$	−0.586583	−0.0442153
$177$	−1.65543	−0.124429
$178$	−6.45267	−0.483648
$179$	−2.79602	−0.208984	−0.104492	−	0.994526i	$-0.533322\pi$
$179$	−2.79602	−0.208984	−0.104492	+	0.994526i	$0.533322\pi$
$180$	2.47818	0.184712
$181$	12.5589	0.933499	0.466750	−	0.884390i	$-0.345425\pi$
$181$	12.5589	0.933499	0.466750	+	0.884390i	$0.345425\pi$
$182$	−27.0326	−2.00379
$183$	1.00000	0.0739221
$184$	0.589348	0.0434473
$185$	7.76370	0.570799
$186$	0.691255	0.0506853
$187$	4.46012	0.326156
$188$	10.2366	0.746577
$189$	−5.24025	−0.381172
$190$	6.38076	0.462909
$191$	−2.74577	−0.198677	−0.0993386	−	0.995054i	$-0.531673\pi$
$191$	−2.74577	−0.198677	−0.0993386	+	0.995054i	$0.531673\pi$
$192$	−6.22214	−0.449044
$193$	26.5728	1.91275	0.956377	−	0.292135i	$-0.0943658\pi$
$193$	26.5728	1.91275	0.956377	+	0.292135i	$0.0943658\pi$
$194$	8.82678	0.633726
$195$	12.2470	0.877026
$196$	−22.5229	−1.60878
$197$	−8.49601	−0.605316	−0.302658	−	0.953099i	$-0.597874\pi$
$197$	−8.49601	−0.605316	−0.302658	+	0.953099i	$0.597874\pi$
$198$	−0.948254	−0.0673895
$199$	−7.89518	−0.559674	−0.279837	−	0.960047i	$-0.590280\pi$
$199$	−7.89518	−0.559674	−0.279837	+	0.960047i	$0.590280\pi$
$200$	0.199944	0.0141382
$201$	−16.1730	−1.14075
$202$	−8.89346	−0.625742
$203$	−9.52770	−0.668714
$204$	4.90976	0.343752
$205$	−5.65574	−0.395014
$206$	9.13608	0.636541
$207$	0.200434	0.0139311
$208$	−3.19110	−0.221263
$209$	2.98902	0.206755
$210$	−11.1865	−0.771944
$211$	16.1525	1.11199	0.555993	−	0.831187i	$-0.312338\pi$
$211$	16.1525	1.11199	0.555993	+	0.831187i	$0.312338\pi$
$212$	1.63476	0.112276
$213$	−1.39117	−0.0953212
$214$	−2.86750	−0.196018
$215$	−17.3813	−1.18539
$216$	−2.94036	−0.200066
$217$	3.82002	0.259320
$218$	−3.55477	−0.240759
$219$	8.30506	0.561204
$220$	2.47818	0.167079
$221$	24.2638	1.63216
$222$	−3.27021	−0.219482
$223$	−22.7987	−1.52672	−0.763358	−	0.645976i	$-0.776451\pi$
$223$	−22.7987	−1.52672	−0.763358	+	0.645976i	$0.776451\pi$
$224$	−27.9017	−1.86426
$225$	0.0679998	0.00453332
$226$	3.32230	0.220996
$227$	15.8784	1.05389	0.526943	−	0.849901i	$-0.323338\pi$
$227$	15.8784	1.05389	0.526943	+	0.849901i	$0.323338\pi$
$228$	3.29036	0.217909
$229$	25.2540	1.66883	0.834414	−	0.551138i	$-0.185806\pi$
$229$	25.2540	1.66883	0.834414	+	0.551138i	$0.185806\pi$
$230$	0.427873	0.0282131
$231$	−5.24025	−0.344783
$232$	−5.34609	−0.350988
$233$	−11.6859	−0.765568	−0.382784	−	0.923838i	$-0.625035\pi$
$233$	−11.6859	−0.765568	−0.382784	+	0.923838i	$0.625035\pi$
$234$	−5.15865	−0.337232
$235$	20.9343	1.36560
$236$	−1.82232	−0.118623
$237$	11.7081	0.760520
$238$	−22.1628	−1.43660
$239$	−23.1115	−1.49496	−0.747478	−	0.664287i	$-0.768735\pi$
$239$	−23.1115	−1.49496	−0.747478	+	0.664287i	$0.768735\pi$
$240$	−1.32053	−0.0852397
$241$	3.54114	0.228105	0.114052	−	0.993475i	$-0.463617\pi$
$241$	3.54114	0.228105	0.114052	+	0.993475i	$0.463617\pi$
$242$	−0.948254	−0.0609561
$243$	−1.00000	−0.0641500
$244$	1.10081	0.0704724
$245$	−46.0605	−2.94270
$246$	2.38230	0.151890
$247$	16.2608	1.03465
$248$	2.14345	0.136109
$249$	1.10951	0.0703125
$250$	−10.5285	−0.665880
$251$	−19.2885	−1.21748	−0.608740	−	0.793370i	$-0.708325\pi$
$251$	−19.2885	−1.21748	−0.608740	+	0.793370i	$0.708325\pi$
$252$	−5.76854	−0.363384
$253$	0.200434	0.0126012
$254$	−5.16994	−0.324391
$255$	10.0407	0.628775
$256$	−16.9474	−1.05921
$257$	28.5441	1.78053	0.890267	−	0.455440i	$-0.150518\pi$
$257$	28.5441	1.78053	0.890267	+	0.455440i	$0.150518\pi$
$258$	7.32129	0.455804
$259$	−18.0719	−1.12293
$260$	13.4817	0.836097
$261$	−1.81818	−0.112542
$262$	15.6127	0.964559
$263$	−18.1170	−1.11714	−0.558570	−	0.829457i	$-0.688650\pi$
$263$	−18.1170	−1.11714	−0.558570	+	0.829457i	$0.688650\pi$
$264$	−2.94036	−0.180967
$265$	3.34317	0.205370
$266$	−14.8527	−0.910680
$267$	−6.80479	−0.416446
$268$	−17.8034	−1.08752
$269$	8.76351	0.534321	0.267160	−	0.963652i	$-0.413915\pi$
$269$	8.76351	0.534321	0.267160	+	0.963652i	$0.413915\pi$
$270$	−2.13473	−0.129916
$271$	−21.6248	−1.31361	−0.656806	−	0.754059i	$-0.728093\pi$
$271$	−21.6248	−1.31361	−0.656806	+	0.754059i	$0.728093\pi$
$272$	−2.61623	−0.158632
$273$	−28.5078	−1.72537
$274$	−1.07364	−0.0648612
$275$	0.0679998	0.00410054
$276$	0.220640	0.0132810
$277$	17.1283	1.02914	0.514571	−	0.857448i	$-0.327951\pi$
$277$	17.1283	1.02914	0.514571	+	0.857448i	$0.327951\pi$
$278$	−16.7232	−1.00299
$279$	0.728977	0.0436427
$280$	−34.6873	−2.07297
$281$	−14.8880	−0.888144	−0.444072	−	0.895991i	$-0.646467\pi$
$281$	−14.8880	−0.888144	−0.444072	+	0.895991i	$0.646467\pi$
$282$	−8.81789	−0.525098
$283$	19.7803	1.17582	0.587908	−	0.808928i	$-0.299952\pi$
$283$	19.7803	1.17582	0.587908	+	0.808928i	$0.299952\pi$
$284$	−1.53142	−0.0908728
$285$	6.72896	0.398589
$286$	−5.15865	−0.305037
$287$	13.1651	0.777110
$288$	−5.32449	−0.313749
$289$	2.89269	0.170158
$290$	−3.88132	−0.227919
$291$	9.30845	0.545671
$292$	9.14233	0.535014
$293$	−16.9333	−0.989256	−0.494628	−	0.869105i	$-0.664696\pi$
$293$	−16.9333	−0.989256	−0.494628	+	0.869105i	$0.664696\pi$
$294$	19.4015	1.13152
$295$	−3.72673	−0.216979
$296$	−10.1403	−0.589393
$297$	−1.00000	−0.0580259
$298$	−17.5893	−1.01892
$299$	1.09039	0.0630590
$300$	0.0748551	0.00432176
$301$	40.4590	2.33202
$302$	21.2625	1.22352
$303$	−9.37877	−0.538796
$304$	−1.75331	−0.100559
$305$	2.25122	0.128905
$306$	−4.22933	−0.241775
$307$	1.52740	0.0871733	0.0435866	−	0.999050i	$-0.486122\pi$
$307$	1.52740	0.0871733	0.0435866	+	0.999050i	$0.486122\pi$
$308$	−5.76854	−0.328693
$309$	9.63463	0.548095
$310$	1.55617	0.0883845
$311$	31.7654	1.80125	0.900626	−	0.434596i	$-0.143109\pi$
$311$	31.7654	1.80125	0.900626	+	0.434596i	$0.143109\pi$
$312$	−15.9960	−0.905596
$313$	−16.9039	−0.955467	−0.477733	−	0.878505i	$-0.658542\pi$
$313$	−16.9039	−0.955467	−0.477733	+	0.878505i	$0.658542\pi$
$314$	6.93278	0.391239
$315$	−11.7970	−0.664684
$316$	12.8884	0.725029
$317$	20.3557	1.14329	0.571646	−	0.820501i	$-0.306305\pi$
$317$	20.3557	1.14329	0.571646	+	0.820501i	$0.306305\pi$
$318$	−1.40820	−0.0789682
$319$	−1.81818	−0.101798
$320$	−14.0074	−0.783038
$321$	−3.02397	−0.168782
$322$	−0.995975	−0.0555035
$323$	13.3314	0.741780
$324$	−1.10081	−0.0611563
$325$	0.369929	0.0205200
$326$	0.990074	0.0548351
$327$	−3.74875	−0.207306
$328$	7.38706	0.407882
$329$	−48.7295	−2.68655
$330$	−2.13473	−0.117513
$331$	16.6765	0.916621	0.458311	−	0.888792i	$-0.348455\pi$
$331$	16.6765	0.916621	0.458311	+	0.888792i	$0.348455\pi$
$332$	1.22137	0.0670312
$333$	−3.44866	−0.188985
$334$	0.229731	0.0125703
$335$	−36.4090	−1.98924
$336$	3.07384	0.167692
$337$	−6.60838	−0.359981	−0.179991	−	0.983668i	$-0.557607\pi$
$337$	−6.60838	−0.359981	−0.179991	+	0.983668i	$0.557607\pi$
$338$	−15.7366	−0.855956
$339$	3.50360	0.190289
$340$	11.0530	0.599431
$341$	0.728977	0.0394763
$342$	−2.83436	−0.153264
$343$	70.5351	3.80854
$344$	22.7020	1.22401
$345$	0.451221	0.0242929
$346$	22.5295	1.21119
$347$	16.0359	0.860851	0.430425	−	0.902626i	$-0.358364\pi$
$347$	16.0359	0.860851	0.430425	+	0.902626i	$0.358364\pi$
$348$	−2.00147	−0.107290
$349$	6.89281	0.368964	0.184482	−	0.982836i	$-0.440939\pi$
$349$	6.89281	0.368964	0.184482	+	0.982836i	$0.440939\pi$
$350$	−0.337897	−0.0180614
$351$	−5.44016	−0.290374
$352$	−5.32449	−0.283796
$353$	−13.3187	−0.708884	−0.354442	−	0.935078i	$-0.615329\pi$
$353$	−13.3187	−0.708884	−0.354442	+	0.935078i	$0.615329\pi$
$354$	1.56977	0.0834321
$355$	−3.13183	−0.166220
$356$	−7.49080	−0.397012
$357$	−23.3722	−1.23699
$358$	2.65134	0.140127
$359$	35.5183	1.87458	0.937291	−	0.348547i	$-0.113325\pi$
$359$	35.5183	1.87458	0.937291	+	0.348547i	$0.113325\pi$
$360$	−6.61940	−0.348873
$361$	−10.0657	−0.529775
$362$	−11.9091	−0.625927
$363$	−1.00000	−0.0524864
$364$	−31.3818	−1.64485
$365$	18.6965	0.978622
$366$	−0.948254	−0.0495661
$367$	−11.8248	−0.617250	−0.308625	−	0.951184i	$-0.599869\pi$
$367$	−11.8248	−0.617250	−0.308625	+	0.951184i	$0.599869\pi$
$368$	−0.117571	−0.00612882
$369$	2.51230	0.130785
$370$	−7.36196	−0.382730
$371$	−7.78203	−0.404023
$372$	0.802467	0.0416060
$373$	−21.2527	−1.10042	−0.550211	−	0.835026i	$-0.685453\pi$
$373$	−21.2527	−1.10042	−0.550211	+	0.835026i	$0.685453\pi$
$374$	−4.22933	−0.218694
$375$	−11.1030	−0.573358
$376$	−27.3426	−1.41009
$377$	−9.89116	−0.509421
$378$	4.96909	0.255583
$379$	25.3787	1.30362	0.651808	−	0.758384i	$-0.274011\pi$
$379$	25.3787	1.30362	0.651808	+	0.758384i	$0.274011\pi$
$380$	7.40733	0.379988
$381$	−5.45206	−0.279318
$382$	2.60369	0.133216
$383$	8.43965	0.431246	0.215623	−	0.976477i	$-0.430822\pi$
$383$	8.43965	0.431246	0.215623	+	0.976477i	$0.430822\pi$
$384$	−4.74881	−0.242337
$385$	−11.7970	−0.601229
$386$	−25.1978	−1.28253
$387$	7.72081	0.392471
$388$	10.2469	0.520206
$389$	24.0747	1.22063	0.610317	−	0.792158i	$-0.291042\pi$
$389$	24.0747	1.22063	0.610317	+	0.792158i	$0.291042\pi$
$390$	−11.6133	−0.588061
$391$	0.893960	0.0452095
$392$	60.1605	3.03856
$393$	16.4647	0.830535
$394$	8.05638	0.405875
$395$	26.3574	1.32619
$396$	−1.10081	−0.0553180
$397$	−11.1126	−0.557724	−0.278862	−	0.960331i	$-0.589957\pi$
$397$	−11.1126	−0.557724	−0.278862	+	0.960331i	$0.589957\pi$
$398$	7.48664	0.375271
$399$	−15.6632	−0.784143
$400$	−0.0398875	−0.00199437
$401$	−25.1568	−1.25627	−0.628136	−	0.778104i	$-0.716182\pi$
$401$	−25.1568	−1.25627	−0.628136	+	0.778104i	$0.716182\pi$
$402$	15.3361	0.764896
$403$	3.96575	0.197548
$404$	−10.3243	−0.513652
$405$	−2.25122	−0.111864
$406$	9.03469	0.448384
$407$	−3.44866	−0.170944
$408$	−13.1144	−0.649258
$409$	4.15275	0.205340	0.102670	−	0.994715i	$-0.467261\pi$
$409$	4.15275	0.205340	0.102670	+	0.994715i	$0.467261\pi$
$410$	5.36308	0.264864
$411$	−1.13223	−0.0558488
$412$	10.6059	0.522516
$413$	8.67485	0.426862
$414$	−0.190062	−0.00934106
$415$	2.49776	0.122610
$416$	−28.9661	−1.42018
$417$	−17.6358	−0.863627
$418$	−2.83436	−0.138633
$419$	34.2797	1.67467	0.837337	−	0.546688i	$-0.184111\pi$
$419$	34.2797	1.67467	0.837337	+	0.546688i	$0.184111\pi$
$420$	−12.9863	−0.633665
$421$	−36.7527	−1.79122	−0.895609	−	0.444842i	$-0.853260\pi$
$421$	−36.7527	−1.79122	−0.895609	+	0.444842i	$0.853260\pi$
$422$	−15.3167	−0.745606
$423$	−9.29908	−0.452137
$424$	−4.36658	−0.212060
$425$	0.303287	0.0147116
$426$	1.31918	0.0639145
$427$	−5.24025	−0.253594
$428$	−3.32883	−0.160905
$429$	−5.44016	−0.262653
$430$	16.4818	0.794825
$431$	5.91425	0.284879	0.142440	−	0.989803i	$-0.454505\pi$
$431$	5.91425	0.284879	0.142440	+	0.989803i	$0.454505\pi$
$432$	0.586583	0.0282220
$433$	12.9638	0.623001	0.311500	−	0.950246i	$-0.399168\pi$
$433$	12.9638	0.623001	0.311500	+	0.950246i	$0.399168\pi$
$434$	−3.62235	−0.173878
$435$	−4.09312	−0.196250
$436$	−4.12668	−0.197632
$437$	0.599102	0.0286589
$438$	−7.87531	−0.376297
$439$	−29.2711	−1.39704	−0.698518	−	0.715593i	$-0.746157\pi$
$439$	−29.2711	−1.39704	−0.698518	+	0.715593i	$0.746157\pi$
$440$	−6.61940	−0.315568
$441$	20.4602	0.974297
$442$	−23.0082	−1.09439
$443$	3.21165	0.152590	0.0762951	−	0.997085i	$-0.475691\pi$
$443$	3.21165	0.152590	0.0762951	+	0.997085i	$0.475691\pi$
$444$	−3.79633	−0.180166
$445$	−15.3191	−0.726194
$446$	21.6190	1.02369
$447$	−18.5492	−0.877346
$448$	32.6056	1.54047
$449$	−11.0578	−0.521849	−0.260924	−	0.965359i	$-0.584027\pi$
$449$	−11.0578	−0.521849	−0.260924	+	0.965359i	$0.584027\pi$
$450$	−0.0644811	−0.00303967
$451$	2.51230	0.118300
$452$	3.85681	0.181409
$453$	22.4227	1.05351
$454$	−15.0568	−0.706649
$455$	−64.1774	−3.00868
$456$	−8.78881	−0.411574
$457$	8.45879	0.395685	0.197843	−	0.980234i	$-0.436606\pi$
$457$	8.45879	0.395685	0.197843	+	0.980234i	$0.436606\pi$
$458$	−23.9472	−1.11898
$459$	−4.46012	−0.208181
$460$	0.496711	0.0231593
$461$	8.02284	0.373661	0.186830	−	0.982392i	$-0.440178\pi$
$461$	8.02284	0.373661	0.186830	+	0.982392i	$0.440178\pi$
$462$	4.96909	0.231183
$463$	20.0463	0.931630	0.465815	−	0.884882i	$-0.345761\pi$
$463$	20.0463	0.931630	0.465815	+	0.884882i	$0.345761\pi$
$464$	1.06651	0.0495115
$465$	1.64109	0.0761036
$466$	11.0812	0.513326
$467$	−9.41646	−0.435742	−0.217871	−	0.975978i	$-0.569911\pi$
$467$	−9.41646	−0.435742	−0.217871	+	0.975978i	$0.569911\pi$
$468$	−5.98860	−0.276823
$469$	84.7505	3.91342
$470$	−19.8510	−0.915660
$471$	7.31110	0.336878
$472$	4.86755	0.224047
$473$	7.72081	0.355003
$474$	−11.1022	−0.509942
$475$	0.203253	0.00932589
$476$	−25.7284	−1.17926
$477$	−1.48505	−0.0679957
$478$	21.9155	1.00239
$479$	15.6024	0.712890	0.356445	−	0.934316i	$-0.383989\pi$
$479$	15.6024	0.712890	0.356445	+	0.934316i	$0.383989\pi$
$480$	−11.9866	−0.547111
$481$	−18.7613	−0.855439
$482$	−3.35790	−0.152948
$483$	−1.05032	−0.0477914
$484$	−1.10081	−0.0500370
$485$	20.9554	0.951535
$486$	0.948254	0.0430137
$487$	28.6801	1.29962	0.649811	−	0.760096i	$-0.274848\pi$
$487$	28.6801	1.29962	0.649811	+	0.760096i	$0.274848\pi$
$488$	−2.94036	−0.133104
$489$	1.04410	0.0472159
$490$	43.6771	1.97313
$491$	0.942339	0.0425271	0.0212636	−	0.999774i	$-0.493231\pi$
$491$	0.942339	0.0425271	0.0212636	+	0.999774i	$0.493231\pi$
$492$	2.76557	0.124682
$493$	−8.10929	−0.365224
$494$	−15.4193	−0.693749
$495$	−2.25122	−0.101185
$496$	−0.427605	−0.0192000
$497$	7.29007	0.327004
$498$	−1.05210	−0.0471458
$499$	−3.01444	−0.134945	−0.0674725	−	0.997721i	$-0.521493\pi$
$499$	−3.01444	−0.134945	−0.0674725	+	0.997721i	$0.521493\pi$
$500$	−12.2224	−0.546601
$501$	0.242267	0.0108237
$502$	18.2904	0.816341
$503$	43.9550	1.95986	0.979929	−	0.199346i	$-0.0638817\pi$
$503$	43.9550	1.95986	0.979929	+	0.199346i	$0.0638817\pi$
$504$	15.4082	0.686337
$505$	−21.1137	−0.939547
$506$	−0.190062	−0.00844931
$507$	−16.5953	−0.737023
$508$	−6.00170	−0.266282
$509$	−23.9124	−1.05990	−0.529950	−	0.848029i	$-0.677789\pi$
$509$	−23.9124	−1.05990	−0.529950	+	0.848029i	$0.677789\pi$
$510$	−9.52116	−0.421604
$511$	−43.5206	−1.92524
$512$	6.57278	0.290479
$513$	−2.98902	−0.131969
$514$	−27.0671	−1.19388
$515$	21.6897	0.955762
$516$	8.49917	0.374155
$517$	−9.29908	−0.408973
$518$	17.1367	0.752944
$519$	23.7589	1.04290
$520$	−36.0106	−1.57917
$521$	−37.7693	−1.65470	−0.827351	−	0.561685i	$-0.810153\pi$
$521$	−37.7693	−1.65470	−0.827351	+	0.561685i	$0.810153\pi$
$522$	1.72409	0.0754616
$523$	−3.21011	−0.140368	−0.0701842	−	0.997534i	$-0.522359\pi$
$523$	−3.21011	−0.140368	−0.0701842	+	0.997534i	$0.522359\pi$
$524$	18.1246	0.791776
$525$	−0.356336	−0.0155518
$526$	17.1795	0.749062
$527$	3.25133	0.141630
$528$	0.586583	0.0255277
$529$	−22.9598	−0.998253
$530$	−3.17018	−0.137704
$531$	1.65543	0.0718394
$532$	−17.2423	−0.747549
$533$	13.6673	0.591996
$534$	6.45267	0.279234
$535$	−6.80763	−0.294320
$536$	47.5544	2.05404
$537$	2.79602	0.120657
$538$	−8.31004	−0.358271
$539$	20.4602	0.881285
$540$	−2.47818	−0.106644
$541$	−15.9679	−0.686512	−0.343256	−	0.939242i	$-0.611530\pi$
$541$	−15.9679	−0.686512	−0.343256	+	0.939242i	$0.611530\pi$
$542$	20.5058	0.880800
$543$	−12.5589	−0.538956
$544$	−23.7479	−1.01818
$545$	−8.43927	−0.361499
$546$	27.0326	1.15689
$547$	−13.1472	−0.562132	−0.281066	−	0.959688i	$-0.590688\pi$
$547$	−13.1472	−0.562132	−0.281066	+	0.959688i	$0.590688\pi$
$548$	−1.24638	−0.0532425
$549$	−1.00000	−0.0426790
$550$	−0.0644811	−0.00274948
$551$	−5.43458	−0.231521
$552$	−0.589348	−0.0250843
$553$	−61.3532	−2.60900
$554$	−16.2420	−0.690057
$555$	−7.76370	−0.329551
$556$	−19.4137	−0.823324
$557$	0.120019	0.00508539	0.00254269	−	0.999997i	$-0.499191\pi$
$557$	0.120019	0.00508539	0.00254269	+	0.999997i	$0.499191\pi$
$558$	−0.691255	−0.0292632
$559$	42.0024	1.77651
$560$	6.91990	0.292419
$561$	−4.46012	−0.188307
$562$	14.1176	0.595516
$563$	−22.3237	−0.940831	−0.470415	−	0.882445i	$-0.655896\pi$
$563$	−22.3237	−0.940831	−0.470415	+	0.882445i	$0.655896\pi$
$564$	−10.2366	−0.431037
$565$	7.88738	0.331825
$566$	−18.7568	−0.788405
$567$	5.24025	0.220070
$568$	4.09053	0.171635
$569$	−6.42634	−0.269406	−0.134703	−	0.990886i	$-0.543008\pi$
$569$	−6.42634	−0.269406	−0.134703	+	0.990886i	$0.543008\pi$
$570$	−6.38076	−0.267261
$571$	−21.3502	−0.893479	−0.446740	−	0.894664i	$-0.647415\pi$
$571$	−21.3502	−0.893479	−0.446740	+	0.894664i	$0.647415\pi$
$572$	−5.98860	−0.250396
$573$	2.74577	0.114706
$574$	−12.4838	−0.521066
$575$	0.0136295	0.000568388 0
$576$	6.22214	0.259256
$577$	−4.88600	−0.203407	−0.101703	−	0.994815i	$-0.532429\pi$
$577$	−4.88600	−0.203407	−0.101703	+	0.994815i	$0.532429\pi$
$578$	−2.74301	−0.114094
$579$	−26.5728	−1.10433
$580$	−4.50576	−0.187092
$581$	−5.81413	−0.241211
$582$	−8.82678	−0.365882
$583$	−1.48505	−0.0615044
$584$	−24.4199	−1.01050
$585$	−12.2470	−0.506351
$586$	16.0571	0.663313
$587$	−32.3274	−1.33429	−0.667147	−	0.744926i	$-0.732485\pi$
$587$	−32.3274	−1.33429	−0.667147	+	0.744926i	$0.732485\pi$
$588$	22.5229	0.928829
$589$	2.17893	0.0897812
$590$	3.53389	0.145488
$591$	8.49601	0.349479
$592$	2.02293	0.0831417
$593$	18.0269	0.740275	0.370137	−	0.928977i	$-0.379311\pi$
$593$	18.0269	0.740275	0.370137	+	0.928977i	$0.379311\pi$
$594$	0.948254	0.0389074
$595$	−52.6159	−2.15704
$596$	−20.4192	−0.836402
$597$	7.89518	0.323128
$598$	−1.03397	−0.0422821
$599$	−6.99770	−0.285918	−0.142959	−	0.989729i	$-0.545662\pi$
$599$	−6.99770	−0.285918	−0.142959	+	0.989729i	$0.545662\pi$
$600$	−0.199944	−0.00816267
$601$	27.9227	1.13899	0.569496	−	0.821994i	$-0.307138\pi$
$601$	27.9227	1.13899	0.569496	+	0.821994i	$0.307138\pi$
$602$	−38.3654	−1.56366
$603$	16.1730	0.658615
$604$	24.6832	1.00435
$605$	−2.25122	−0.0915252
$606$	8.89346	0.361272
$607$	47.3972	1.92379	0.961897	−	0.273412i	$-0.0881522\pi$
$607$	47.3972	1.92379	0.961897	+	0.273412i	$0.0881522\pi$
$608$	−15.9150	−0.645440
$609$	9.52770	0.386082
$610$	−2.13473	−0.0864327
$611$	−50.5884	−2.04659
$612$	−4.90976	−0.198465
$613$	−36.7435	−1.48406	−0.742028	−	0.670369i	$-0.766136\pi$
$613$	−36.7435	−1.48406	−0.742028	+	0.670369i	$0.766136\pi$
$614$	−1.44836	−0.0584512
$615$	5.65574	0.228062
$616$	15.4082	0.620815
$617$	23.6451	0.951917	0.475958	−	0.879468i	$-0.342101\pi$
$617$	23.6451	0.951917	0.475958	+	0.879468i	$0.342101\pi$
$618$	−9.13608	−0.367507
$619$	−8.49054	−0.341264	−0.170632	−	0.985335i	$-0.554581\pi$
$619$	−8.49054	−0.341264	−0.170632	+	0.985335i	$0.554581\pi$
$620$	1.80653	0.0725521
$621$	−0.200434	−0.00804314
$622$	−30.1217	−1.20777
$623$	35.6588	1.42864
$624$	3.19110	0.127746
$625$	−25.3354	−1.01341
$626$	16.0292	0.640657
$627$	−2.98902	−0.119370
$628$	8.04815	0.321156
$629$	−15.3815	−0.613299
$630$	11.1865	0.445682
$631$	13.5216	0.538288	0.269144	−	0.963100i	$-0.413259\pi$
$631$	13.5216	0.538288	0.269144	+	0.963100i	$0.413259\pi$
$632$	−34.4259	−1.36939
$633$	−16.1525	−0.642005
$634$	−19.3024	−0.766597
$635$	−12.2738	−0.487071
$636$	−1.63476	−0.0648225
$637$	111.307	4.41014
$638$	1.72409	0.0682575
$639$	1.39117	0.0550337
$640$	−10.6906	−0.422584
$641$	−11.5595	−0.456574	−0.228287	−	0.973594i	$-0.573312\pi$
$641$	−11.5595	−0.456574	−0.228287	+	0.973594i	$0.573312\pi$
$642$	2.86750	0.113171
$643$	−19.4275	−0.766147	−0.383073	−	0.923718i	$-0.625134\pi$
$643$	−19.4275	−0.766147	−0.383073	+	0.923718i	$0.625134\pi$
$644$	−1.15621	−0.0455611
$645$	17.3813	0.684386
$646$	−12.6416	−0.497376
$647$	−27.7606	−1.09138	−0.545690	−	0.837987i	$-0.683732\pi$
$647$	−27.7606	−1.09138	−0.545690	+	0.837987i	$0.683732\pi$
$648$	2.94036	0.115508
$649$	1.65543	0.0649812
$650$	−0.350787	−0.0137590
$651$	−3.82002	−0.149718
$652$	1.14936	0.0450124
$653$	23.0651	0.902608	0.451304	−	0.892370i	$-0.350959\pi$
$653$	23.0651	0.902608	0.451304	+	0.892370i	$0.350959\pi$
$654$	3.55477	0.139003
$655$	37.0657	1.44828
$656$	−1.47367	−0.0575372
$657$	−8.30506	−0.324011
$658$	46.2080	1.80137
$659$	7.13729	0.278029	0.139015	−	0.990290i	$-0.455606\pi$
$659$	7.13729	0.278029	0.139015	+	0.990290i	$0.455606\pi$
$660$	−2.47818	−0.0964628
$661$	−16.0929	−0.625941	−0.312971	−	0.949763i	$-0.601324\pi$
$661$	−16.0929	−0.625941	−0.312971	+	0.949763i	$0.601324\pi$
$662$	−15.8135	−0.614610
$663$	−24.2638	−0.942326
$664$	−3.26237	−0.126604
$665$	−35.2614	−1.36738
$666$	3.27021	0.126718
$667$	−0.364424	−0.0141106
$668$	0.266691	0.0103186
$669$	22.7987	0.881450
$670$	34.5250	1.33382
$671$	−1.00000	−0.0386046
$672$	27.9017	1.07633
$673$	34.6989	1.33755	0.668773	−	0.743467i	$-0.266820\pi$
$673$	34.6989	1.33755	0.668773	+	0.743467i	$0.266820\pi$
$674$	6.26643	0.241374
$675$	−0.0679998	−0.00261731
$676$	−18.2683	−0.702628
$677$	−46.9863	−1.80583	−0.902916	−	0.429818i	$-0.858578\pi$
$677$	−46.9863	−1.80583	−0.902916	+	0.429818i	$0.858578\pi$
$678$	−3.32230	−0.127592
$679$	−48.7786	−1.87195
$680$	−29.5234	−1.13217
$681$	−15.8784	−0.608461
$682$	−0.691255	−0.0264695
$683$	1.54777	0.0592238	0.0296119	−	0.999561i	$-0.490573\pi$
$683$	1.54777	0.0592238	0.0296119	+	0.999561i	$0.490573\pi$
$684$	−3.29036	−0.125810
$685$	−2.54890	−0.0973886
$686$	−66.8852	−2.55369
$687$	−25.2540	−0.963498
$688$	−4.52889	−0.172662
$689$	−8.07889	−0.307781
$690$	−0.427873	−0.0162888
$691$	18.0655	0.687245	0.343623	−	0.939108i	$-0.388346\pi$
$691$	18.0655	0.687245	0.343623	+	0.939108i	$0.388346\pi$
$692$	26.1542	0.994232
$693$	5.24025	0.199061
$694$	−15.2061	−0.577215
$695$	−39.7020	−1.50598
$696$	5.34609	0.202643
$697$	11.2052	0.424426
$698$	−6.53614	−0.247396
$699$	11.6859	0.442001
$700$	−0.392259	−0.0148260
$701$	−21.0050	−0.793346	−0.396673	−	0.917960i	$-0.629835\pi$
$701$	−21.0050	−0.793346	−0.396673	+	0.917960i	$0.629835\pi$
$702$	5.15865	0.194701
$703$	−10.3081	−0.388779
$704$	6.22214	0.234506
$705$	−20.9343	−0.788431
$706$	12.6295	0.475319
$707$	49.1471	1.84837
$708$	1.82232	0.0684868
$709$	−12.9485	−0.486291	−0.243146	−	0.969990i	$-0.578179\pi$
$709$	−12.9485	−0.486291	−0.243146	+	0.969990i	$0.578179\pi$
$710$	2.96977	0.111453
$711$	−11.7081	−0.439087
$712$	20.0085	0.749851
$713$	0.146112	0.00547193
$714$	22.1628	0.829421
$715$	−12.2470	−0.458012
$716$	3.07789	0.115026
$717$	23.1115	0.863113
$718$	−33.6804	−1.25694
$719$	11.2061	0.417917	0.208958	−	0.977925i	$-0.432993\pi$
$719$	11.2061	0.417917	0.208958	+	0.977925i	$0.432993\pi$
$720$	1.32053	0.0492132
$721$	−50.4879	−1.88027
$722$	9.54487	0.355223
$723$	−3.54114	−0.131696
$724$	−13.8251	−0.513804
$725$	−0.123636	−0.00459171
$726$	0.948254	0.0351930
$727$	35.9986	1.33511	0.667557	−	0.744559i	$-0.267340\pi$
$727$	35.9986	1.33511	0.667557	+	0.744559i	$0.267340\pi$
$728$	83.8232	3.10669
$729$	1.00000	0.0370370
$730$	−17.7291	−0.656183
$731$	34.4358	1.27365
$732$	−1.10081	−0.0406872
$733$	23.6506	0.873554	0.436777	−	0.899570i	$-0.356120\pi$
$733$	23.6506	0.873554	0.436777	+	0.899570i	$0.356120\pi$
$734$	11.2129	0.413877
$735$	46.0605	1.69897
$736$	−1.06721	−0.0393378
$737$	16.1730	0.595740
$738$	−2.38230	−0.0876936
$739$	−14.8095	−0.544778	−0.272389	−	0.962187i	$-0.587814\pi$
$739$	−14.8095	−0.544778	−0.272389	+	0.962187i	$0.587814\pi$
$740$	−8.54639	−0.314171
$741$	−16.2608	−0.597354
$742$	7.37934	0.270904
$743$	13.3290	0.488994	0.244497	−	0.969650i	$-0.421377\pi$
$743$	13.3290	0.488994	0.244497	+	0.969650i	$0.421377\pi$
$744$	−2.14345	−0.0785828
$745$	−41.7583	−1.52991
$746$	20.1529	0.737852
$747$	−1.10951	−0.0405950
$748$	−4.90976	−0.179519
$749$	15.8464	0.579014
$750$	10.5285	0.384446
$751$	1.50326	0.0548546	0.0274273	−	0.999624i	$-0.491269\pi$
$751$	1.50326	0.0548546	0.0274273	+	0.999624i	$0.491269\pi$
$752$	5.45468	0.198912
$753$	19.2885	0.702912
$754$	9.37934	0.341575
$755$	50.4785	1.83710
$756$	5.76854	0.209800
$757$	−12.6961	−0.461449	−0.230724	−	0.973019i	$-0.574110\pi$
$757$	−12.6961	−0.461449	−0.230724	+	0.973019i	$0.574110\pi$
$758$	−24.0655	−0.874097
$759$	−0.200434	−0.00727529
$760$	−19.7856	−0.717698
$761$	−1.08972	−0.0395022	−0.0197511	−	0.999805i	$-0.506287\pi$
$761$	−1.08972	−0.0395022	−0.0197511	+	0.999805i	$0.506287\pi$
$762$	5.16994	0.187287
$763$	19.6444	0.711175
$764$	3.02258	0.109353
$765$	−10.0407	−0.363023
$766$	−8.00294	−0.289158
$767$	9.00578	0.325180
$768$	16.9474	0.611535
$769$	17.6529	0.636579	0.318289	−	0.947994i	$-0.396892\pi$
$769$	17.6529	0.636579	0.318289	+	0.947994i	$0.396892\pi$
$770$	11.1865	0.403135
$771$	−28.5441	−1.02799
$772$	−29.2517	−1.05279
$773$	−12.7055	−0.456986	−0.228493	−	0.973546i	$-0.573380\pi$
$773$	−12.7055	−0.456986	−0.228493	+	0.973546i	$0.573380\pi$
$774$	−7.32129	−0.263158
$775$	0.0495702	0.00178062
$776$	−27.3702	−0.982533
$777$	18.0719	0.648324
$778$	−22.8289	−0.818456
$779$	7.50932	0.269049
$780$	−13.4817	−0.482721
$781$	1.39117	0.0497799
$782$	−0.847702	−0.0303138
$783$	1.81818	0.0649763
$784$	−12.0016	−0.428630
$785$	16.4589	0.587443
$786$	−15.6127	−0.556888
$787$	−14.3201	−0.510456	−0.255228	−	0.966881i	$-0.582151\pi$
$787$	−14.3201	−0.510456	−0.255228	+	0.966881i	$0.582151\pi$
$788$	9.35252	0.333170
$789$	18.1170	0.644981
$790$	−24.9936	−0.889231
$791$	−18.3597	−0.652797
$792$	2.94036	0.104481
$793$	−5.44016	−0.193186
$794$	10.5375	0.373963
$795$	−3.34317	−0.118570
$796$	8.69112	0.308049
$797$	55.4418	1.96385	0.981924	−	0.189275i	$-0.0606138\pi$
$797$	55.4418	1.96385	0.981924	+	0.189275i	$0.0606138\pi$
$798$	14.8527	0.525781
$799$	−41.4750	−1.46728
$800$	−0.362064	−0.0128009
$801$	6.80479	0.240435
$802$	23.8551	0.842352
$803$	−8.30506	−0.293079
$804$	17.8034	0.627879
$805$	−2.36451	−0.0833382
$806$	−3.76054	−0.132459
$807$	−8.76351	−0.308490
$808$	27.5770	0.970154
$809$	37.9294	1.33353	0.666763	−	0.745270i	$-0.267679\pi$
$809$	37.9294	1.33353	0.666763	+	0.745270i	$0.267679\pi$
$810$	2.13473	0.0750068
$811$	−3.23359	−0.113547	−0.0567733	−	0.998387i	$-0.518081\pi$
$811$	−3.23359	−0.113547	−0.0567733	+	0.998387i	$0.518081\pi$
$812$	10.4882	0.368065
$813$	21.6248	0.758415
$814$	3.27021	0.114621
$815$	2.35050	0.0823345
$816$	2.61623	0.0915864
$817$	23.0777	0.807386
$818$	−3.93786	−0.137684
$819$	28.5078	0.996143
$820$	6.22592	0.217418
$821$	−44.4292	−1.55059	−0.775295	−	0.631599i	$-0.782399\pi$
$821$	−44.4292	−1.55059	−0.775295	+	0.631599i	$0.782399\pi$
$822$	1.07364	0.0374476
$823$	11.0243	0.384284	0.192142	−	0.981367i	$-0.438457\pi$
$823$	11.0243	0.384284	0.192142	+	0.981367i	$0.438457\pi$
$824$	−28.3293	−0.986897
$825$	−0.0679998	−0.00236745
$826$	−8.22597	−0.286218
$827$	38.2151	1.32887	0.664435	−	0.747346i	$-0.268672\pi$
$827$	38.2151	1.32887	0.664435	+	0.747346i	$0.268672\pi$
$828$	−0.220640	−0.00766779
$829$	5.10113	0.177170	0.0885848	−	0.996069i	$-0.471766\pi$
$829$	5.10113	0.177170	0.0885848	+	0.996069i	$0.471766\pi$
$830$	−2.36851	−0.0822122
$831$	−17.1283	−0.594175
$832$	33.8494	1.17352
$833$	91.2552	3.16181
$834$	16.7232	0.579077
$835$	0.545397	0.0188742
$836$	−3.29036	−0.113799
$837$	−0.728977	−0.0251971
$838$	−32.5059	−1.12290
$839$	22.4559	0.775262	0.387631	−	0.921815i	$-0.373293\pi$
$839$	22.4559	0.775262	0.387631	+	0.921815i	$0.373293\pi$
$840$	34.6873	1.19683
$841$	−25.6942	−0.886008
$842$	34.8509	1.20104
$843$	14.8880	0.512770
$844$	−17.7809	−0.612045
$845$	−37.3597	−1.28521
$846$	8.81789	0.303165
$847$	5.24025	0.180057
$848$	0.871104	0.0299138
$849$	−19.7803	−0.678858
$850$	−0.287594	−0.00986438
$851$	−0.691229	−0.0236950
$852$	1.53142	0.0524654
$853$	4.17359	0.142901	0.0714505	−	0.997444i	$-0.477237\pi$
$853$	4.17359	0.142901	0.0714505	+	0.997444i	$0.477237\pi$
$854$	4.96909	0.170039
$855$	−6.72896	−0.230126
$856$	8.89157	0.303908
$857$	54.4319	1.85936	0.929679	−	0.368371i	$-0.120084\pi$
$857$	54.4319	1.85936	0.929679	+	0.368371i	$0.120084\pi$
$858$	5.15865	0.176113
$859$	−18.6033	−0.634737	−0.317368	−	0.948302i	$-0.602799\pi$
$859$	−18.6033	−0.634737	−0.317368	+	0.948302i	$0.602799\pi$
$860$	19.1335	0.652447
$861$	−13.1651	−0.448665
$862$	−5.60821	−0.191016
$863$	51.6257	1.75736	0.878679	−	0.477412i	$-0.158425\pi$
$863$	51.6257	1.75736	0.878679	+	0.477412i	$0.158425\pi$
$864$	5.32449	0.181143
$865$	53.4866	1.81860
$866$	−12.2930	−0.417733
$867$	−2.89269	−0.0982411
$868$	−4.20513	−0.142731
$869$	−11.7081	−0.397169
$870$	3.88132	0.131589
$871$	87.9836	2.98121
$872$	11.0227	0.373275
$873$	−9.30845	−0.315043
$874$	−0.568101	−0.0192163
$875$	58.1827	1.96693
$876$	−9.14233	−0.308891
$877$	−49.5572	−1.67343	−0.836715	−	0.547639i	$-0.815527\pi$
$877$	−49.5572	−1.67343	−0.836715	+	0.547639i	$0.815527\pi$
$878$	27.7565	0.936736
$879$	16.9333	0.571147
$880$	1.32053	0.0445150
$881$	48.5126	1.63443	0.817216	−	0.576332i	$-0.195516\pi$
$881$	48.5126	1.63443	0.817216	+	0.576332i	$0.195516\pi$
$882$	−19.4015	−0.653283
$883$	−26.0469	−0.876549	−0.438275	−	0.898841i	$-0.644410\pi$
$883$	−26.0469	−0.876549	−0.438275	+	0.898841i	$0.644410\pi$
$884$	−26.7099	−0.898350
$885$	3.72673	0.125273
$886$	−3.04546	−0.102314
$887$	46.1043	1.54803	0.774015	−	0.633168i	$-0.218246\pi$
$887$	46.1043	1.54803	0.774015	+	0.633168i	$0.218246\pi$
$888$	10.1403	0.340286
$889$	28.5702	0.958213
$890$	14.5264	0.486926
$891$	1.00000	0.0335013
$892$	25.0971	0.840315
$893$	−27.7952	−0.930130
$894$	17.5893	0.588276
$895$	6.29445	0.210400
$896$	24.8850	0.831348
$897$	−1.09039	−0.0364071
$898$	10.4856	0.349909
$899$	−1.32541	−0.0442048
$900$	−0.0748551	−0.00249517
$901$	−6.62350	−0.220661
$902$	−2.38230	−0.0793219
$903$	−40.4590	−1.34639
$904$	−10.3018	−0.342634
$905$	−28.2730	−0.939826
$906$	−21.2625	−0.706398
$907$	4.84142	0.160757	0.0803783	−	0.996764i	$-0.474387\pi$
$907$	4.84142	0.160757	0.0803783	+	0.996764i	$0.474387\pi$
$908$	−17.4791	−0.580066
$909$	9.37877	0.311074
$910$	60.8565	2.01737
$911$	37.1866	1.23205	0.616024	−	0.787727i	$-0.288742\pi$
$911$	37.1866	1.23205	0.616024	+	0.787727i	$0.288742\pi$
$912$	1.75331	0.0580579
$913$	−1.10951	−0.0367195
$914$	−8.02108	−0.265314
$915$	−2.25122	−0.0744231
$916$	−27.7999	−0.918534
$917$	−86.2793	−2.84919
$918$	4.22933	0.139589
$919$	−42.7495	−1.41018	−0.705088	−	0.709120i	$-0.749092\pi$
$919$	−42.7495	−1.41018	−0.705088	+	0.709120i	$0.749092\pi$
$920$	−1.32675	−0.0437418
$921$	−1.52740	−0.0503295
$922$	−7.60769	−0.250546
$923$	7.56817	0.249109
$924$	5.76854	0.189771
$925$	−0.234508	−0.00771058
$926$	−19.0090	−0.624674
$927$	−9.63463	−0.316443
$928$	9.68087	0.317790
$929$	22.1672	0.727284	0.363642	−	0.931539i	$-0.381533\pi$
$929$	22.1672	0.727284	0.363642	+	0.931539i	$0.381533\pi$
$930$	−1.55617	−0.0510288
$931$	61.1562	2.00431
$932$	12.8640	0.421374
$933$	−31.7654	−1.03995
$934$	8.92920	0.292172
$935$	−10.0407	−0.328367
$936$	15.9960	0.522846
$937$	25.4112	0.830148	0.415074	−	0.909788i	$-0.363756\pi$
$937$	25.4112	0.830148	0.415074	+	0.909788i	$0.363756\pi$
$938$	−80.3651	−2.62401
$939$	16.9039	0.551639
$940$	−23.0447	−0.751637
$941$	35.3840	1.15348	0.576742	−	0.816926i	$-0.304324\pi$
$941$	35.3840	1.15348	0.576742	+	0.816926i	$0.304324\pi$
$942$	−6.93278	−0.225882
$943$	0.503550	0.0163978
$944$	−0.971045	−0.0316048
$945$	11.7970	0.383755
$946$	−7.32129	−0.238036
$947$	15.1601	0.492638	0.246319	−	0.969189i	$-0.420779\pi$
$947$	15.1601	0.492638	0.246319	+	0.969189i	$0.420779\pi$
$948$	−12.8884	−0.418596
$949$	−45.1808	−1.46663
$950$	−0.192736	−0.00625317
$951$	−20.3557	−0.660080
$952$	68.7226	2.22731
$953$	−50.7429	−1.64372	−0.821862	−	0.569687i	$-0.807065\pi$
$953$	−50.7429	−1.64372	−0.821862	+	0.569687i	$0.807065\pi$
$954$	1.40820	0.0455923
$955$	6.18134	0.200024
$956$	25.4414	0.822834
$957$	1.81818	0.0587733
$958$	−14.7950	−0.478005
$959$	5.93318	0.191592
$960$	14.0074	0.452087
$961$	−30.4686	−0.982858
$962$	17.7904	0.573587
$963$	3.02397	0.0974461
$964$	−3.89814	−0.125550
$965$	−59.8213	−1.92572
$966$	0.995975	0.0320450
$967$	1.89879	0.0610611	0.0305305	−	0.999534i	$-0.490280\pi$
$967$	1.89879	0.0610611	0.0305305	+	0.999534i	$0.490280\pi$
$968$	2.94036	0.0945068
$969$	−13.3314	−0.428267
$970$	−19.8710	−0.638021
$971$	28.5211	0.915284	0.457642	−	0.889136i	$-0.348694\pi$
$971$	28.5211	0.915284	0.457642	+	0.889136i	$0.348694\pi$
$972$	1.10081	0.0353086
$973$	92.4159	2.96272
$974$	−27.1961	−0.871418
$975$	−0.369929	−0.0118472
$976$	0.586583	0.0187761
$977$	−44.8572	−1.43511	−0.717554	−	0.696502i	$-0.754739\pi$
$977$	−44.8572	−1.43511	−0.717554	+	0.696502i	$0.754739\pi$
$978$	−0.990074	−0.0316591
$979$	6.80479	0.217482
$980$	50.7041	1.61968
$981$	3.74875	0.119688
$982$	−0.893577	−0.0285152
$983$	15.8302	0.504904	0.252452	−	0.967609i	$-0.418763\pi$
$983$	15.8302	0.504904	0.252452	+	0.967609i	$0.418763\pi$
$984$	−7.38706	−0.235491
$985$	19.1264	0.609418
$986$	7.68967	0.244889
$987$	48.7295	1.55108
$988$	−17.9001	−0.569477
$989$	1.54751	0.0492080
$990$	2.13473	0.0678462
$991$	−12.4145	−0.394359	−0.197180	−	0.980367i	$-0.563178\pi$
$991$	−12.4145	−0.394359	−0.197180	+	0.980367i	$0.563178\pi$
$992$	−3.88143	−0.123236
$993$	−16.6765	−0.529211
$994$	−6.91284	−0.219262
$995$	17.7738	0.563467
$996$	−1.22137	−0.0387005
$997$	−16.4628	−0.521383	−0.260691	−	0.965422i	$-0.583950\pi$
$997$	−16.4628	−0.521383	−0.260691	+	0.965422i	$0.583950\pi$
$998$	2.85846	0.0904829
$999$	3.44866	0.109111

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2013.2.a.e.1.5	✓	13
3.2	odd	2		6039.2.a.i.1.9		13

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2013.2.a.e.1.5	✓	13	1.1	even	1	trivial
6039.2.a.i.1.9		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)

\(f(q)\)	\(=\)	\(q-0.948254 q^{2} -1.00000 q^{3} -1.10081 q^{4} -2.25122 q^{5} +0.948254 q^{6} +5.24025 q^{7} +2.94036 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-0.948254 q^{2} -1.00000 q^{3} -1.10081 q^{4} -2.25122 q^{5} +0.948254 q^{6} +5.24025 q^{7} +2.94036 q^{8} +1.00000 q^{9} +2.13473 q^{10} +1.00000 q^{11} +1.10081 q^{12} +5.44016 q^{13} -4.96909 q^{14} +2.25122 q^{15} -0.586583 q^{16} +4.46012 q^{17} -0.948254 q^{18} +2.98902 q^{19} +2.47818 q^{20} -5.24025 q^{21} -0.948254 q^{22} +0.200434 q^{23} -2.94036 q^{24} +0.0679998 q^{25} -5.15865 q^{26} -1.00000 q^{27} -5.76854 q^{28} -1.81818 q^{29} -2.13473 q^{30} +0.728977 q^{31} -5.32449 q^{32} -1.00000 q^{33} -4.22933 q^{34} -11.7970 q^{35} -1.10081 q^{36} -3.44866 q^{37} -2.83436 q^{38} -5.44016 q^{39} -6.61940 q^{40} +2.51230 q^{41} +4.96909 q^{42} +7.72081 q^{43} -1.10081 q^{44} -2.25122 q^{45} -0.190062 q^{46} -9.29908 q^{47} +0.586583 q^{48} +20.4602 q^{49} -0.0644811 q^{50} -4.46012 q^{51} -5.98860 q^{52} -1.48505 q^{53} +0.948254 q^{54} -2.25122 q^{55} +15.4082 q^{56} -2.98902 q^{57} +1.72409 q^{58} +1.65543 q^{59} -2.47818 q^{60} -1.00000 q^{61} -0.691255 q^{62} +5.24025 q^{63} +6.22214 q^{64} -12.2470 q^{65} +0.948254 q^{66} +16.1730 q^{67} -4.90976 q^{68} -0.200434 q^{69} +11.1865 q^{70} +1.39117 q^{71} +2.94036 q^{72} -8.30506 q^{73} +3.27021 q^{74} -0.0679998 q^{75} -3.29036 q^{76} +5.24025 q^{77} +5.15865 q^{78} -11.7081 q^{79} +1.32053 q^{80} +1.00000 q^{81} -2.38230 q^{82} -1.10951 q^{83} +5.76854 q^{84} -10.0407 q^{85} -7.32129 q^{86} +1.81818 q^{87} +2.94036 q^{88} +6.80479 q^{89} +2.13473 q^{90} +28.5078 q^{91} -0.220640 q^{92} -0.728977 q^{93} +8.81789 q^{94} -6.72896 q^{95} +5.32449 q^{96} -9.30845 q^{97} -19.4015 q^{98} +1.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 13 q + 2 q^{2} - 13 q^{3} + 16 q^{4} + 3 q^{5} - 2 q^{6} + 11 q^{7} + 9 q^{8} + 13 q^{9}+O(q^{10}) \) 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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