LMFDB - Embedded newform 2013.2.a.f.1.7

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} - 4 x^{12} - 11 x^{11} + 55 x^{10} + 32 x^{9} - 266 x^{8} + 13 x^{7} + 534 x^{6} - 141 x^{5} + \cdots - 11 $ x^13 - 4x^12 - 11x^11 + 55x^10 + 32x^9 - 266x^8 + 13x^7 + 534x^6 - 141x^5 - 404x^4 + 98x^3 + 118x^2 - 16x - 11
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			1.7
Root			$0.468970$ 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)

$f(q)$	$=$	$q+0.468970 q^{2} +1.00000 q^{3} -1.78007 q^{4} -3.25579 q^{5} +0.468970 q^{6} -3.43403 q^{7} -1.77274 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+0.468970 q^{2} +1.00000 q^{3} -1.78007 q^{4} -3.25579 q^{5} +0.468970 q^{6} -3.43403 q^{7} -1.77274 q^{8} +1.00000 q^{9} -1.52687 q^{10} -1.00000 q^{11} -1.78007 q^{12} -6.24548 q^{13} -1.61046 q^{14} -3.25579 q^{15} +2.72877 q^{16} +4.43634 q^{17} +0.468970 q^{18} +2.00167 q^{19} +5.79552 q^{20} -3.43403 q^{21} -0.468970 q^{22} -5.24027 q^{23} -1.77274 q^{24} +5.60015 q^{25} -2.92895 q^{26} +1.00000 q^{27} +6.11281 q^{28} +2.01247 q^{29} -1.52687 q^{30} +2.78091 q^{31} +4.82519 q^{32} -1.00000 q^{33} +2.08051 q^{34} +11.1805 q^{35} -1.78007 q^{36} +9.46308 q^{37} +0.938726 q^{38} -6.24548 q^{39} +5.77166 q^{40} -6.90514 q^{41} -1.61046 q^{42} +7.06425 q^{43} +1.78007 q^{44} -3.25579 q^{45} -2.45753 q^{46} -3.28507 q^{47} +2.72877 q^{48} +4.79257 q^{49} +2.62630 q^{50} +4.43634 q^{51} +11.1174 q^{52} -3.39708 q^{53} +0.468970 q^{54} +3.25579 q^{55} +6.08764 q^{56} +2.00167 q^{57} +0.943788 q^{58} +6.95400 q^{59} +5.79552 q^{60} -1.00000 q^{61} +1.30417 q^{62} -3.43403 q^{63} -3.19467 q^{64} +20.3340 q^{65} -0.468970 q^{66} -13.7103 q^{67} -7.89698 q^{68} -5.24027 q^{69} +5.24331 q^{70} +11.0077 q^{71} -1.77274 q^{72} -1.02864 q^{73} +4.43790 q^{74} +5.60015 q^{75} -3.56312 q^{76} +3.43403 q^{77} -2.92895 q^{78} -10.9648 q^{79} -8.88430 q^{80} +1.00000 q^{81} -3.23831 q^{82} +10.7032 q^{83} +6.11281 q^{84} -14.4438 q^{85} +3.31292 q^{86} +2.01247 q^{87} +1.77274 q^{88} +5.93188 q^{89} -1.52687 q^{90} +21.4472 q^{91} +9.32803 q^{92} +2.78091 q^{93} -1.54060 q^{94} -6.51703 q^{95} +4.82519 q^{96} +1.30698 q^{97} +2.24757 q^{98} -1.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 13 q + 4 q^{2} + 13 q^{3} + 12 q^{4} + 7 q^{5} + 4 q^{6} + 5 q^{7} + 15 q^{8} + 13 q^{9}+O(q^{10}) $ 13 * q + 4 * q^2 + 13 * q^3 + 12 * q^4 + 7 * q^5 + 4 * q^6 + 5 * q^7 + 15 * q^8 + 13 * q^9	\( 13 q + 4 q^{2} + 13 q^{3} + 12 q^{4} + 7 q^{5} + 4 q^{6} + 5 q^{7} + 15 q^{8} + 13 q^{9} + 8 q^{10} - 13 q^{11} + 12 q^{12} - 9 q^{13} + 19 q^{14} + 7 q^{15} + 18 q^{16} + 7 q^{17} + 4 q^{18} + 2 q^{19} + 15 q^{20} + 5 q^{21} - 4 q^{22} + 23 q^{23} + 15 q^{24} + 10 q^{25} + 8 q^{26} + 13 q^{27} + 9 q^{28} + 16 q^{29} + 8 q^{30} + 9 q^{31} + 29 q^{32} - 13 q^{33} + 2 q^{34} + 16 q^{35} + 12 q^{36} + 14 q^{37} + 8 q^{38} - 9 q^{39} + 16 q^{40} + 19 q^{41} + 19 q^{42} + 7 q^{43} - 12 q^{44} + 7 q^{45} + 4 q^{46} + 26 q^{47} + 18 q^{48} + 8 q^{49} - 15 q^{50} + 7 q^{51} - 17 q^{52} + 18 q^{53} + 4 q^{54} - 7 q^{55} + 44 q^{56} + 2 q^{57} - q^{58} + 31 q^{59} + 15 q^{60} - 13 q^{61} - 5 q^{62} + 5 q^{63} - 17 q^{64} + 31 q^{65} - 4 q^{66} + 14 q^{67} - 32 q^{68} + 23 q^{69} - 20 q^{70} + 37 q^{71} + 15 q^{72} - 16 q^{73} - 6 q^{74} + 10 q^{75} - 7 q^{76} - 5 q^{77} + 8 q^{78} - 17 q^{79} - 2 q^{80} + 13 q^{81} - 2 q^{82} + 30 q^{83} + 9 q^{84} - 16 q^{85} - 22 q^{86} + 16 q^{87} - 15 q^{88} + 35 q^{89} + 8 q^{90} - q^{91} + 24 q^{92} + 9 q^{93} - 11 q^{94} + 13 q^{95} + 29 q^{96} - q^{97} - q^{98} - 13 q^{99}+O(q^{100}) \) 13 * q + 4 * q^2 + 13 * q^3 + 12 * q^4 + 7 * q^5 + 4 * q^6 + 5 * q^7 + 15 * q^8 + 13 * q^9 + 8 * q^10 - 13 * q^11 + 12 * q^12 - 9 * q^13 + 19 * q^14 + 7 * q^15 + 18 * q^16 + 7 * q^17 + 4 * q^18 + 2 * q^19 + 15 * q^20 + 5 * q^21 - 4 * q^22 + 23 * q^23 + 15 * q^24 + 10 * q^25 + 8 * q^26 + 13 * q^27 + 9 * q^28 + 16 * q^29 + 8 * q^30 + 9 * q^31 + 29 * q^32 - 13 * q^33 + 2 * q^34 + 16 * q^35 + 12 * q^36 + 14 * q^37 + 8 * q^38 - 9 * q^39 + 16 * q^40 + 19 * q^41 + 19 * q^42 + 7 * q^43 - 12 * q^44 + 7 * q^45 + 4 * q^46 + 26 * q^47 + 18 * q^48 + 8 * q^49 - 15 * q^50 + 7 * q^51 - 17 * q^52 + 18 * q^53 + 4 * q^54 - 7 * q^55 + 44 * q^56 + 2 * q^57 - q^58 + 31 * q^59 + 15 * q^60 - 13 * q^61 - 5 * q^62 + 5 * q^63 - 17 * q^64 + 31 * q^65 - 4 * q^66 + 14 * q^67 - 32 * q^68 + 23 * q^69 - 20 * q^70 + 37 * q^71 + 15 * q^72 - 16 * q^73 - 6 * q^74 + 10 * q^75 - 7 * q^76 - 5 * q^77 + 8 * q^78 - 17 * q^79 - 2 * q^80 + 13 * q^81 - 2 * q^82 + 30 * q^83 + 9 * q^84 - 16 * q^85 - 22 * q^86 + 16 * q^87 - 15 * q^88 + 35 * q^89 + 8 * q^90 - q^91 + 24 * q^92 + 9 * q^93 - 11 * q^94 + 13 * q^95 + 29 * q^96 - q^97 - 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 $

$2$	0.468970	0.331612	0.165806	−	0.986158i	$-0.446977\pi$
$2$	0.468970	0.331612	0.165806	+	0.986158i	$0.446977\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	−1.78007	−0.890033
$5$	−3.25579	−1.45603	−0.728016	−	0.685560i	$-0.759557\pi$
$5$	−3.25579	−1.45603	−0.728016	+	0.685560i	$0.759557\pi$
$6$	0.468970	0.191456
$7$	−3.43403	−1.29794	−0.648971	−	0.760813i	$-0.724800\pi$
$7$	−3.43403	−1.29794	−0.648971	+	0.760813i	$0.724800\pi$
$8$	−1.77274	−0.626758
$9$	1.00000	0.333333
$10$	−1.52687	−0.482838
$11$	−1.00000	−0.301511
$11$	−1.00000	−0.301511
$12$	−1.78007	−0.513861
$13$	−6.24548	−1.73219	−0.866093	−	0.499883i	$-0.833376\pi$
$13$	−6.24548	−1.73219	−0.866093	+	0.499883i	$0.833376\pi$
$14$	−1.61046	−0.430413
$15$	−3.25579	−0.840641
$16$	2.72877	0.682193
$17$	4.43634	1.07597	0.537985	−	0.842954i	$-0.319186\pi$
$17$	4.43634	1.07597	0.537985	+	0.842954i	$0.319186\pi$
$18$	0.468970	0.110537
$19$	2.00167	0.459216	0.229608	−	0.973283i	$-0.426256\pi$
$19$	2.00167	0.459216	0.229608	+	0.973283i	$0.426256\pi$
$20$	5.79552	1.29592
$21$	−3.43403	−0.749367
$22$	−0.468970	−0.0999848
$23$	−5.24027	−1.09267	−0.546336	−	0.837566i	$-0.683978\pi$
$23$	−5.24027	−1.09267	−0.546336	+	0.837566i	$0.683978\pi$
$24$	−1.77274	−0.361859
$25$	5.60015	1.12003
$26$	−2.92895	−0.574413
$27$	1.00000	0.192450
$28$	6.11281	1.15521
$29$	2.01247	0.373706	0.186853	−	0.982388i	$-0.440171\pi$
$29$	2.01247	0.373706	0.186853	+	0.982388i	$0.440171\pi$
$30$	−1.52687	−0.278767
$31$	2.78091	0.499467	0.249733	−	0.968315i	$-0.419657\pi$
$31$	2.78091	0.499467	0.249733	+	0.968315i	$0.419657\pi$
$32$	4.82519	0.852981
$33$	−1.00000	−0.174078
$34$	2.08051	0.356805
$35$	11.1805	1.88985
$36$	−1.78007	−0.296678
$37$	9.46308	1.55572	0.777860	−	0.628438i	$-0.216305\pi$
$37$	9.46308	1.55572	0.777860	+	0.628438i	$0.216305\pi$
$38$	0.938726	0.152281
$39$	−6.24548	−1.00008
$40$	5.77166	0.912580
$41$	−6.90514	−1.07840	−0.539201	−	0.842177i	$-0.681274\pi$
$41$	−6.90514	−1.07840	−0.539201	+	0.842177i	$0.681274\pi$
$42$	−1.61046	−0.248499
$43$	7.06425	1.07729	0.538644	−	0.842533i	$-0.318937\pi$
$43$	7.06425	1.07729	0.538644	+	0.842533i	$0.318937\pi$
$44$	1.78007	0.268355
$45$	−3.25579	−0.485344
$46$	−2.45753	−0.362343
$47$	−3.28507	−0.479177	−0.239588	−	0.970875i	$-0.577013\pi$
$47$	−3.28507	−0.479177	−0.239588	+	0.970875i	$0.577013\pi$
$48$	2.72877	0.393864
$49$	4.79257	0.684653
$50$	2.62630	0.371416
$51$	4.43634	0.621212
$52$	11.1174	1.54170
$53$	−3.39708	−0.466625	−0.233312	−	0.972402i	$-0.574957\pi$
$53$	−3.39708	−0.466625	−0.233312	+	0.972402i	$0.574957\pi$
$54$	0.468970	0.0638188
$55$	3.25579	0.439010
$56$	6.08764	0.813495
$57$	2.00167	0.265128
$58$	0.943788	0.123925
$59$	6.95400	0.905333	0.452667	−	0.891680i	$-0.350473\pi$
$59$	6.95400	0.905333	0.452667	+	0.891680i	$0.350473\pi$
$60$	5.79552	0.748198
$61$	−1.00000	−0.128037
$61$	−1.00000	−0.128037
$62$	1.30417	0.165629
$63$	−3.43403	−0.432647
$64$	−3.19467	−0.399334
$65$	20.3340	2.52212
$66$	−0.468970	−0.0577262
$67$	−13.7103	−1.67498	−0.837491	−	0.546452i	$-0.815978\pi$
$67$	−13.7103	−1.67498	−0.837491	+	0.546452i	$0.815978\pi$
$68$	−7.89698	−0.957650
$69$	−5.24027	−0.630854
$70$	5.24331	0.626695
$71$	11.0077	1.30637	0.653186	−	0.757197i	$-0.273432\pi$
$71$	11.0077	1.30637	0.653186	+	0.757197i	$0.273432\pi$
$72$	−1.77274	−0.208919
$73$	−1.02864	−0.120393	−0.0601965	−	0.998187i	$-0.519173\pi$
$73$	−1.02864	−0.120393	−0.0601965	+	0.998187i	$0.519173\pi$
$74$	4.43790	0.515895
$75$	5.60015	0.646650
$76$	−3.56312	−0.408717
$77$	3.43403	0.391344
$78$	−2.92895	−0.331638
$79$	−10.9648	−1.23364	−0.616818	−	0.787105i	$-0.711579\pi$
$79$	−10.9648	−1.23364	−0.616818	+	0.787105i	$0.711579\pi$
$80$	−8.88430	−0.993295
$81$	1.00000	0.111111
$82$	−3.23831	−0.357611
$83$	10.7032	1.17483	0.587415	−	0.809286i	$-0.300146\pi$
$83$	10.7032	1.17483	0.587415	+	0.809286i	$0.300146\pi$
$84$	6.11281	0.666962
$85$	−14.4438	−1.56665
$86$	3.31292	0.357242
$87$	2.01247	0.215759
$88$	1.77274	0.188975
$89$	5.93188	0.628778	0.314389	−	0.949294i	$-0.398200\pi$
$89$	5.93188	0.628778	0.314389	+	0.949294i	$0.398200\pi$
$90$	−1.52687	−0.160946
$91$	21.4472	2.24828
$92$	9.32803	0.972515
$93$	2.78091	0.288367
$94$	−1.54060	−0.158901
$95$	−6.51703	−0.668633
$96$	4.82519	0.492469
$97$	1.30698	0.132704	0.0663519	−	0.997796i	$-0.478864\pi$
$97$	1.30698	0.132704	0.0663519	+	0.997796i	$0.478864\pi$
$98$	2.24757	0.227039
$99$	−1.00000	−0.100504
$100$	−9.96865	−0.996865
$101$	−9.38234	−0.933578	−0.466789	−	0.884369i	$-0.654589\pi$
$101$	−9.38234	−0.933578	−0.466789	+	0.884369i	$0.654589\pi$
$102$	2.08051	0.206001
$103$	3.32165	0.327292	0.163646	−	0.986519i	$-0.447675\pi$
$103$	3.32165	0.327292	0.163646	+	0.986519i	$0.447675\pi$
$104$	11.0716	1.08566
$105$	11.1805	1.09110
$106$	−1.59313	−0.154738
$107$	−4.48068	−0.433163	−0.216582	−	0.976265i	$-0.569491\pi$
$107$	−4.48068	−0.433163	−0.216582	+	0.976265i	$0.569491\pi$
$108$	−1.78007	−0.171287
$109$	−4.81609	−0.461297	−0.230649	−	0.973037i	$-0.574085\pi$
$109$	−4.81609	−0.461297	−0.230649	+	0.973037i	$0.574085\pi$
$110$	1.52687	0.145581
$111$	9.46308	0.898195
$112$	−9.37069	−0.885447
$113$	0.395739	0.0372280	0.0186140	−	0.999827i	$-0.494075\pi$
$113$	0.395739	0.0372280	0.0186140	+	0.999827i	$0.494075\pi$
$114$	0.938726	0.0879197
$115$	17.0612	1.59097
$116$	−3.58233	−0.332611
$117$	−6.24548	−0.577395
$118$	3.26122	0.300219
$119$	−15.2345	−1.39655
$120$	5.77166	0.526878
$121$	1.00000	0.0909091
$122$	−0.468970	−0.0424586
$123$	−6.90514	−0.622616
$124$	−4.95021	−0.444542
$125$	−1.95397	−0.174769
$126$	−1.61046	−0.143471
$127$	1.20543	0.106965	0.0534823	−	0.998569i	$-0.482968\pi$
$127$	1.20543	0.106965	0.0534823	+	0.998569i	$0.482968\pi$
$128$	−11.1486	−0.985405
$129$	7.06425	0.621973
$130$	9.53602	0.836365
$131$	13.5694	1.18556	0.592781	−	0.805364i	$-0.298030\pi$
$131$	13.5694	1.18556	0.592781	+	0.805364i	$0.298030\pi$
$132$	1.78007	0.154935
$133$	−6.87381	−0.596035
$134$	−6.42973	−0.555444
$135$	−3.25579	−0.280214
$136$	−7.86447	−0.674373
$137$	14.7030	1.25617	0.628083	−	0.778147i	$-0.283840\pi$
$137$	14.7030	1.25617	0.628083	+	0.778147i	$0.283840\pi$
$138$	−2.45753	−0.209199
$139$	−9.78375	−0.829847	−0.414923	−	0.909856i	$-0.636192\pi$
$139$	−9.78375	−0.829847	−0.414923	+	0.909856i	$0.636192\pi$
$140$	−19.9020	−1.68203
$141$	−3.28507	−0.276653
$142$	5.16228	0.433209
$143$	6.24548	0.522274
$144$	2.72877	0.227398
$145$	−6.55218	−0.544129
$146$	−0.482401	−0.0399238
$147$	4.79257	0.395285
$148$	−16.8449	−1.38464
$149$	−4.72991	−0.387490	−0.193745	−	0.981052i	$-0.562063\pi$
$149$	−4.72991	−0.387490	−0.193745	+	0.981052i	$0.562063\pi$
$150$	2.62630	0.214437
$151$	−2.54722	−0.207290	−0.103645	−	0.994614i	$-0.533051\pi$
$151$	−2.54722	−0.207290	−0.103645	+	0.994614i	$0.533051\pi$
$152$	−3.54845	−0.287817
$153$	4.43634	0.358657
$154$	1.61046	0.129774
$155$	−9.05406	−0.727240
$156$	11.1174	0.890103
$157$	10.2105	0.814886	0.407443	−	0.913231i	$-0.366421\pi$
$157$	10.2105	0.814886	0.407443	+	0.913231i	$0.366421\pi$
$158$	−5.14217	−0.409089
$159$	−3.39708	−0.269406
$160$	−15.7098	−1.24197
$161$	17.9953	1.41822
$162$	0.468970	0.0368458
$163$	15.2623	1.19544	0.597718	−	0.801706i	$-0.296074\pi$
$163$	15.2623	1.19544	0.597718	+	0.801706i	$0.296074\pi$
$164$	12.2916	0.959814
$165$	3.25579	0.253463
$166$	5.01948	0.389588
$167$	15.3766	1.18988	0.594939	−	0.803771i	$-0.297176\pi$
$167$	15.3766	1.18988	0.594939	+	0.803771i	$0.297176\pi$
$168$	6.08764	0.469672
$169$	26.0061	2.00047
$170$	−6.77370	−0.519519
$171$	2.00167	0.153072
$172$	−12.5748	−0.958823
$173$	23.3965	1.77880	0.889402	−	0.457126i	$-0.151121\pi$
$173$	23.3965	1.77880	0.889402	+	0.457126i	$0.151121\pi$
$174$	0.943788	0.0715484
$175$	−19.2311	−1.45373
$176$	−2.72877	−0.205689
$177$	6.95400	0.522694
$178$	2.78188	0.208510
$179$	−6.26673	−0.468397	−0.234199	−	0.972189i	$-0.575247\pi$
$179$	−6.26673	−0.468397	−0.234199	+	0.972189i	$0.575247\pi$
$180$	5.79552	0.431973
$181$	−23.6286	−1.75630	−0.878151	−	0.478383i	$-0.841223\pi$
$181$	−23.6286	−1.75630	−0.878151	+	0.478383i	$0.841223\pi$
$182$	10.0581	0.745555
$183$	−1.00000	−0.0739221
$184$	9.28963	0.684841
$185$	−30.8098	−2.26518
$186$	1.30417	0.0956260
$187$	−4.43634	−0.324417
$188$	5.84765	0.426483
$189$	−3.43403	−0.249789
$190$	−3.05629	−0.221727
$191$	−4.95906	−0.358825	−0.179413	−	0.983774i	$-0.557420\pi$
$191$	−4.95906	−0.358825	−0.179413	+	0.983774i	$0.557420\pi$
$192$	−3.19467	−0.230556
$193$	−6.72933	−0.484388	−0.242194	−	0.970228i	$-0.577867\pi$
$193$	−6.72933	−0.484388	−0.242194	+	0.970228i	$0.577867\pi$
$194$	0.612935	0.0440061
$195$	20.3340	1.45615
$196$	−8.53110	−0.609364
$197$	8.95161	0.637776	0.318888	−	0.947792i	$-0.396691\pi$
$197$	8.95161	0.637776	0.318888	+	0.947792i	$0.396691\pi$
$198$	−0.468970	−0.0333283
$199$	6.33890	0.449353	0.224676	−	0.974433i	$-0.427868\pi$
$199$	6.33890	0.449353	0.224676	+	0.974433i	$0.427868\pi$
$200$	−9.92761	−0.701988
$201$	−13.7103	−0.967051
$202$	−4.40004	−0.309586
$203$	−6.91089	−0.485049
$204$	−7.89698	−0.552899
$205$	22.4817	1.57019
$206$	1.55775	0.108534
$207$	−5.24027	−0.364224
$208$	−17.0425	−1.18168
$209$	−2.00167	−0.138459
$210$	5.24331	0.361823
$211$	−12.2782	−0.845268	−0.422634	−	0.906301i	$-0.638894\pi$
$211$	−12.2782	−0.845268	−0.422634	+	0.906301i	$0.638894\pi$
$212$	6.04703	0.415312
$213$	11.0077	0.754234
$214$	−2.10130	−0.143642
$215$	−22.9997	−1.56857
$216$	−1.77274	−0.120620
$217$	−9.54974	−0.648279
$218$	−2.25860	−0.152972
$219$	−1.02864	−0.0695089
$220$	−5.79552	−0.390734
$221$	−27.7071	−1.86378
$222$	4.43790	0.297852
$223$	−0.874257	−0.0585446	−0.0292723	−	0.999571i	$-0.509319\pi$
$223$	−0.874257	−0.0585446	−0.0292723	+	0.999571i	$0.509319\pi$
$224$	−16.5699	−1.10712
$225$	5.60015	0.373344
$226$	0.185590	0.0123453
$227$	10.4092	0.690885	0.345443	−	0.938440i	$-0.387729\pi$
$227$	10.4092	0.690885	0.345443	+	0.938440i	$0.387729\pi$
$228$	−3.56312	−0.235973
$229$	−13.6935	−0.904892	−0.452446	−	0.891792i	$-0.649449\pi$
$229$	−13.6935	−0.904892	−0.452446	+	0.891792i	$0.649449\pi$
$230$	8.00120	0.527583
$231$	3.43403	0.225943
$232$	−3.56758	−0.234223
$233$	−6.74441	−0.441841	−0.220921	−	0.975292i	$-0.570906\pi$
$233$	−6.74441	−0.441841	−0.220921	+	0.975292i	$0.570906\pi$
$234$	−2.92895	−0.191471
$235$	10.6955	0.697697
$236$	−12.3786	−0.805777
$237$	−10.9648	−0.712241
$238$	−7.14454	−0.463112
$239$	19.8593	1.28459	0.642295	−	0.766458i	$-0.277982\pi$
$239$	19.8593	1.28459	0.642295	+	0.766458i	$0.277982\pi$
$240$	−8.88430	−0.573479
$241$	−23.6717	−1.52483	−0.762415	−	0.647089i	$-0.775986\pi$
$241$	−23.6717	−1.52483	−0.762415	+	0.647089i	$0.775986\pi$
$242$	0.468970	0.0301465
$243$	1.00000	0.0641500
$244$	1.78007	0.113957
$245$	−15.6036	−0.996877
$246$	−3.23831	−0.206467
$247$	−12.5014	−0.795447
$248$	−4.92983	−0.313045
$249$	10.7032	0.678288
$250$	−0.916355	−0.0579554
$251$	−22.7517	−1.43608	−0.718038	−	0.696004i	$-0.754960\pi$
$251$	−22.7517	−1.43608	−0.718038	+	0.696004i	$0.754960\pi$
$252$	6.11281	0.385071
$253$	5.24027	0.329453
$254$	0.565310	0.0354707
$255$	−14.4438	−0.904505
$256$	1.16099	0.0725622
$257$	5.16686	0.322300	0.161150	−	0.986930i	$-0.448480\pi$
$257$	5.16686	0.322300	0.161150	+	0.986930i	$0.448480\pi$
$258$	3.31292	0.206254
$259$	−32.4965	−2.01923
$260$	−36.1958	−2.24477
$261$	2.01247	0.124569
$262$	6.36363	0.393147
$263$	−27.5651	−1.69974	−0.849869	−	0.526994i	$-0.823319\pi$
$263$	−27.5651	−1.69974	−0.849869	+	0.526994i	$0.823319\pi$
$264$	1.77274	0.109105
$265$	11.0602	0.679421
$266$	−3.22361	−0.197652
$267$	5.93188	0.363025
$268$	24.4053	1.49079
$269$	21.8629	1.33300	0.666501	−	0.745504i	$-0.267791\pi$
$269$	21.8629	1.33300	0.666501	+	0.745504i	$0.267791\pi$
$270$	−1.52687	−0.0929222
$271$	17.0898	1.03813	0.519067	−	0.854734i	$-0.326280\pi$
$271$	17.0898	1.03813	0.519067	+	0.854734i	$0.326280\pi$
$272$	12.1058	0.734020
$273$	21.4472	1.29804
$274$	6.89529	0.416560
$275$	−5.60015	−0.337702
$276$	9.32803	0.561482
$277$	−11.7573	−0.706425	−0.353213	−	0.935543i	$-0.614911\pi$
$277$	−11.7573	−0.706425	−0.353213	+	0.935543i	$0.614911\pi$
$278$	−4.58829	−0.275187
$279$	2.78091	0.166489
$280$	−19.8201	−1.18448
$281$	17.9185	1.06893	0.534465	−	0.845190i	$-0.320513\pi$
$281$	17.9185	1.06893	0.534465	+	0.845190i	$0.320513\pi$
$282$	−1.54060	−0.0917414
$283$	27.2207	1.61810	0.809050	−	0.587740i	$-0.199982\pi$
$283$	27.2207	1.61810	0.809050	+	0.587740i	$0.199982\pi$
$284$	−19.5944	−1.16271
$285$	−6.51703	−0.386035
$286$	2.92895	0.173192
$287$	23.7125	1.39970
$288$	4.82519	0.284327
$289$	2.68111	0.157712
$290$	−3.07277	−0.180440
$291$	1.30698	0.0766165
$292$	1.83104	0.107154
$293$	2.74534	0.160385	0.0801923	−	0.996779i	$-0.474447\pi$
$293$	2.74534	0.160385	0.0801923	+	0.996779i	$0.474447\pi$
$294$	2.24757	0.131081
$295$	−22.6407	−1.31819
$296$	−16.7756	−0.975060
$297$	−1.00000	−0.0580259
$298$	−2.21819	−0.128496
$299$	32.7280	1.89271
$300$	−9.96865	−0.575540
$301$	−24.2589	−1.39826
$302$	−1.19457	−0.0687397
$303$	−9.38234	−0.539001
$304$	5.46211	0.313274
$305$	3.25579	0.186426
$306$	2.08051	0.118935
$307$	24.6262	1.40549	0.702745	−	0.711442i	$-0.251958\pi$
$307$	24.6262	1.40549	0.702745	+	0.711442i	$0.251958\pi$
$308$	−6.11281	−0.348309
$309$	3.32165	0.188962
$310$	−4.24608	−0.241161
$311$	−5.12305	−0.290502	−0.145251	−	0.989395i	$-0.546399\pi$
$311$	−5.12305	−0.290502	−0.145251	+	0.989395i	$0.546399\pi$
$312$	11.0716	0.626806
$313$	6.63621	0.375101	0.187550	−	0.982255i	$-0.439945\pi$
$313$	6.63621	0.375101	0.187550	+	0.982255i	$0.439945\pi$
$314$	4.78841	0.270226
$315$	11.1805	0.629948
$316$	19.5181	1.09798
$317$	21.5260	1.20902	0.604511	−	0.796597i	$-0.293369\pi$
$317$	21.5260	1.20902	0.604511	+	0.796597i	$0.293369\pi$
$318$	−1.59313	−0.0893383
$319$	−2.01247	−0.112677
$320$	10.4012	0.581444
$321$	−4.48068	−0.250087
$322$	8.43924	0.470300
$323$	8.88011	0.494102
$324$	−1.78007	−0.0988926
$325$	−34.9757	−1.94010
$326$	7.15757	0.396421
$327$	−4.81609	−0.266330
$328$	12.2410	0.675897
$329$	11.2810	0.621944
$330$	1.52687	0.0840513
$331$	−31.8784	−1.75219	−0.876097	−	0.482134i	$-0.839862\pi$
$331$	−31.8784	−1.75219	−0.876097	+	0.482134i	$0.839862\pi$
$332$	−19.0524	−1.04564
$333$	9.46308	0.518573
$334$	7.21118	0.394578
$335$	44.6379	2.43883
$336$	−9.37069	−0.511213
$337$	14.3893	0.783836	0.391918	−	0.920000i	$-0.371812\pi$
$337$	14.3893	0.783836	0.391918	+	0.920000i	$0.371812\pi$
$338$	12.1961	0.663379
$339$	0.395739	0.0214936
$340$	25.7109	1.39437
$341$	−2.78091	−0.150595
$342$	0.938726	0.0507605
$343$	7.58038	0.409302
$344$	−12.5231	−0.675199
$345$	17.0612	0.918545
$346$	10.9723	0.589873
$347$	−8.27031	−0.443973	−0.221987	−	0.975050i	$-0.571254\pi$
$347$	−8.27031	−0.443973	−0.221987	+	0.975050i	$0.571254\pi$
$348$	−3.58233	−0.192033
$349$	−7.70568	−0.412476	−0.206238	−	0.978502i	$-0.566122\pi$
$349$	−7.70568	−0.412476	−0.206238	+	0.978502i	$0.566122\pi$
$350$	−9.01881	−0.482076
$351$	−6.24548	−0.333359
$352$	−4.82519	−0.257183
$353$	19.5302	1.03949	0.519743	−	0.854323i	$-0.326028\pi$
$353$	19.5302	1.03949	0.519743	+	0.854323i	$0.326028\pi$
$354$	3.26122	0.173332
$355$	−35.8387	−1.90212
$356$	−10.5591	−0.559634
$357$	−15.2345	−0.806297
$358$	−2.93891	−0.155326
$359$	31.5005	1.66254	0.831268	−	0.555873i	$-0.187616\pi$
$359$	31.5005	1.66254	0.831268	+	0.555873i	$0.187616\pi$
$360$	5.77166	0.304193
$361$	−14.9933	−0.789121
$362$	−11.0811	−0.582411
$363$	1.00000	0.0524864
$364$	−38.1774	−2.00104
$365$	3.34903	0.175296
$366$	−0.468970	−0.0245135
$367$	18.6783	0.975002	0.487501	−	0.873122i	$-0.337909\pi$
$367$	18.6783	0.975002	0.487501	+	0.873122i	$0.337909\pi$
$368$	−14.2995	−0.745413
$369$	−6.90514	−0.359467
$370$	−14.4489	−0.751161
$371$	11.6657	0.605652
$372$	−4.95021	−0.256656
$373$	18.7522	0.970954	0.485477	−	0.874250i	$-0.338646\pi$
$373$	18.7522	0.970954	0.485477	+	0.874250i	$0.338646\pi$
$374$	−2.08051	−0.107581
$375$	−1.95397	−0.100903
$376$	5.82357	0.300328
$377$	−12.5688	−0.647329
$378$	−1.61046	−0.0828330
$379$	11.9393	0.613280	0.306640	−	0.951826i	$-0.400795\pi$
$379$	11.9393	0.613280	0.306640	+	0.951826i	$0.400795\pi$
$380$	11.6007	0.595106
$381$	1.20543	0.0617560
$382$	−2.32565	−0.118991
$383$	29.2370	1.49394	0.746971	−	0.664856i	$-0.231507\pi$
$383$	29.2370	1.49394	0.746971	+	0.664856i	$0.231507\pi$
$384$	−11.1486	−0.568924
$385$	−11.1805	−0.569810
$386$	−3.15585	−0.160629
$387$	7.06425	0.359096
$388$	−2.32651	−0.118111
$389$	37.0444	1.87823	0.939114	−	0.343606i	$-0.111648\pi$
$389$	37.0444	1.87823	0.939114	+	0.343606i	$0.111648\pi$
$390$	9.53602	0.482875
$391$	−23.2476	−1.17568
$392$	−8.49597	−0.429112
$393$	13.5694	0.684485
$394$	4.19804	0.211494
$395$	35.6991	1.79622
$396$	1.78007	0.0894517
$397$	34.3833	1.72565	0.862825	−	0.505503i	$-0.168693\pi$
$397$	34.3833	1.72565	0.862825	+	0.505503i	$0.168693\pi$
$398$	2.97275	0.149011
$399$	−6.87381	−0.344121
$400$	15.2815	0.764077
$401$	6.10544	0.304891	0.152446	−	0.988312i	$-0.451285\pi$
$401$	6.10544	0.304891	0.152446	+	0.988312i	$0.451285\pi$
$402$	−6.42973	−0.320686
$403$	−17.3681	−0.865169
$404$	16.7012	0.830915
$405$	−3.25579	−0.161781
$406$	−3.24100	−0.160848
$407$	−9.46308	−0.469067
$408$	−7.86447	−0.389349
$409$	−28.6700	−1.41764	−0.708819	−	0.705390i	$-0.750772\pi$
$409$	−28.6700	−1.41764	−0.708819	+	0.705390i	$0.750772\pi$
$410$	10.5432	0.520693
$411$	14.7030	0.725247
$412$	−5.91276	−0.291301
$413$	−23.8802	−1.17507
$414$	−2.45753	−0.120781
$415$	−34.8474	−1.71059
$416$	−30.1356	−1.47752
$417$	−9.78375	−0.479112
$418$	−0.938726	−0.0459146
$419$	−20.7874	−1.01553	−0.507766	−	0.861495i	$-0.669529\pi$
$419$	−20.7874	−1.01553	−0.507766	+	0.861495i	$0.669529\pi$
$420$	−19.9020	−0.971118
$421$	−8.10045	−0.394792	−0.197396	−	0.980324i	$-0.563248\pi$
$421$	−8.10045	−0.394792	−0.197396	+	0.980324i	$0.563248\pi$
$422$	−5.75812	−0.280301
$423$	−3.28507	−0.159726
$424$	6.02214	0.292461
$425$	24.8442	1.20512
$426$	5.16228	0.250113
$427$	3.43403	0.166184
$428$	7.97590	0.385530
$429$	6.24548	0.301535
$430$	−10.7862	−0.520156
$431$	−5.58219	−0.268885	−0.134442	−	0.990921i	$-0.542924\pi$
$431$	−5.58219	−0.268885	−0.134442	+	0.990921i	$0.542924\pi$
$432$	2.72877	0.131288
$433$	29.3293	1.40948	0.704739	−	0.709467i	$-0.251064\pi$
$433$	29.3293	1.40948	0.704739	+	0.709467i	$0.251064\pi$
$434$	−4.47854	−0.214977
$435$	−6.55218	−0.314153
$436$	8.57296	0.410570
$437$	−10.4893	−0.501772
$438$	−0.482401	−0.0230500
$439$	−25.9500	−1.23852	−0.619262	−	0.785184i	$-0.712568\pi$
$439$	−25.9500	−1.23852	−0.619262	+	0.785184i	$0.712568\pi$
$440$	−5.77166	−0.275153
$441$	4.79257	0.228218
$442$	−12.9938	−0.618052
$443$	−34.4019	−1.63448	−0.817241	−	0.576296i	$-0.804497\pi$
$443$	−34.4019	−1.63448	−0.817241	+	0.576296i	$0.804497\pi$
$444$	−16.8449	−0.799424
$445$	−19.3129	−0.915521
$446$	−0.410001	−0.0194141
$447$	−4.72991	−0.223717
$448$	10.9706	0.518313
$449$	36.2156	1.70912	0.854561	−	0.519351i	$-0.173826\pi$
$449$	36.2156	1.70912	0.854561	+	0.519351i	$0.173826\pi$
$450$	2.62630	0.123805
$451$	6.90514	0.325150
$452$	−0.704442	−0.0331342
$453$	−2.54722	−0.119679
$454$	4.88162	0.229106
$455$	−69.8275	−3.27356
$456$	−3.54845	−0.166171
$457$	23.2923	1.08957	0.544783	−	0.838577i	$-0.316612\pi$
$457$	23.2923	1.08957	0.544783	+	0.838577i	$0.316612\pi$
$458$	−6.42184	−0.300073
$459$	4.43634	0.207071
$460$	−30.3701	−1.41601
$461$	−28.2651	−1.31644	−0.658219	−	0.752827i	$-0.728690\pi$
$461$	−28.2651	−1.31644	−0.658219	+	0.752827i	$0.728690\pi$
$462$	1.61046	0.0749253
$463$	−32.3472	−1.50330	−0.751651	−	0.659561i	$-0.770742\pi$
$463$	−32.3472	−1.50330	−0.751651	+	0.659561i	$0.770742\pi$
$464$	5.49157	0.254940
$465$	−9.05406	−0.419872
$466$	−3.16293	−0.146520
$467$	−3.30570	−0.152969	−0.0764847	−	0.997071i	$-0.524370\pi$
$467$	−3.30570	−0.152969	−0.0764847	+	0.997071i	$0.524370\pi$
$468$	11.1174	0.513901
$469$	47.0816	2.17403
$470$	5.01587	0.231365
$471$	10.2105	0.470474
$472$	−12.3276	−0.567425
$473$	−7.06425	−0.324815
$474$	−5.14217	−0.236188
$475$	11.2097	0.514336
$476$	27.1185	1.24297
$477$	−3.39708	−0.155542
$478$	9.31341	0.425985
$479$	−10.4588	−0.477875	−0.238937	−	0.971035i	$-0.576799\pi$
$479$	−10.4588	−0.477875	−0.238937	+	0.971035i	$0.576799\pi$
$480$	−15.7098	−0.717051
$481$	−59.1015	−2.69480
$482$	−11.1013	−0.505652
$483$	17.9953	0.818812
$484$	−1.78007	−0.0809121
$485$	−4.25525	−0.193221
$486$	0.468970	0.0212729
$487$	19.8688	0.900340	0.450170	−	0.892943i	$-0.351363\pi$
$487$	19.8688	0.900340	0.450170	+	0.892943i	$0.351363\pi$
$488$	1.77274	0.0802481
$489$	15.2623	0.690185
$490$	−7.31762	−0.330576
$491$	33.9034	1.53004	0.765020	−	0.644007i	$-0.222729\pi$
$491$	33.9034	1.53004	0.765020	+	0.644007i	$0.222729\pi$
$492$	12.2916	0.554149
$493$	8.92800	0.402097
$494$	−5.86280	−0.263780
$495$	3.25579	0.146337
$496$	7.58848	0.340733
$497$	−37.8007	−1.69560
$498$	5.01948	0.224928
$499$	−9.07523	−0.406263	−0.203131	−	0.979151i	$-0.565112\pi$
$499$	−9.07523	−0.406263	−0.203131	+	0.979151i	$0.565112\pi$
$500$	3.47820	0.155550
$501$	15.3766	0.686977
$502$	−10.6699	−0.476220
$503$	−13.7668	−0.613830	−0.306915	−	0.951737i	$-0.599297\pi$
$503$	−13.7668	−0.613830	−0.306915	+	0.951737i	$0.599297\pi$
$504$	6.08764	0.271165
$505$	30.5469	1.35932
$506$	2.45753	0.109251
$507$	26.0061	1.15497
$508$	−2.14574	−0.0952020
$509$	27.0557	1.19922	0.599611	−	0.800292i	$-0.295322\pi$
$509$	27.0557	1.19922	0.599611	+	0.800292i	$0.295322\pi$
$510$	−6.77370	−0.299945
$511$	3.53238	0.156263
$512$	22.8416	1.00947
$513$	2.00167	0.0883761
$514$	2.42310	0.106878
$515$	−10.8146	−0.476548
$516$	−12.5748	−0.553577
$517$	3.28507	0.144477
$518$	−15.2399	−0.669602
$519$	23.3965	1.02699
$520$	−36.0468	−1.58076
$521$	−39.6985	−1.73922	−0.869611	−	0.493737i	$-0.835631\pi$
$521$	−39.6985	−1.73922	−0.869611	+	0.493737i	$0.835631\pi$
$522$	0.943788	0.0413085
$523$	−25.4026	−1.11078	−0.555390	−	0.831590i	$-0.687431\pi$
$523$	−25.4026	−1.11078	−0.555390	+	0.831590i	$0.687431\pi$
$524$	−24.1544	−1.05519
$525$	−19.2311	−0.839314
$526$	−12.9272	−0.563653
$527$	12.3371	0.537411
$528$	−2.72877	−0.118755
$529$	4.46043	0.193932
$530$	5.18689	0.225304
$531$	6.95400	0.301778
$532$	12.2358	0.530491
$533$	43.1260	1.86799
$534$	2.78188	0.120384
$535$	14.5881	0.630700
$536$	24.3048	1.04981
$537$	−6.26673	−0.270429
$538$	10.2530	0.442039
$539$	−4.79257	−0.206431
$540$	5.79552	0.249399
$541$	−29.6053	−1.27283	−0.636415	−	0.771347i	$-0.719583\pi$
$541$	−29.6053	−1.27283	−0.636415	+	0.771347i	$0.719583\pi$
$542$	8.01462	0.344258
$543$	−23.6286	−1.01400
$544$	21.4062	0.917782
$545$	15.6802	0.671664
$546$	10.0581	0.430446
$547$	6.80847	0.291109	0.145555	−	0.989350i	$-0.453503\pi$
$547$	6.80847	0.291109	0.145555	+	0.989350i	$0.453503\pi$
$548$	−26.1724	−1.11803
$549$	−1.00000	−0.0426790
$550$	−2.62630	−0.111986
$551$	4.02831	0.171612
$552$	9.28963	0.395393
$553$	37.6535	1.60119
$554$	−5.51381	−0.234259
$555$	−30.8098	−1.30780
$556$	17.4157	0.738592
$557$	−31.2260	−1.32309	−0.661544	−	0.749906i	$-0.730099\pi$
$557$	−31.2260	−1.32309	−0.661544	+	0.749906i	$0.730099\pi$
$558$	1.30417	0.0552097
$559$	−44.1197	−1.86606
$560$	30.5090	1.28924
$561$	−4.43634	−0.187302
$562$	8.40326	0.354470
$563$	39.1364	1.64940	0.824701	−	0.565570i	$-0.191344\pi$
$563$	39.1364	1.64940	0.824701	+	0.565570i	$0.191344\pi$
$564$	5.84765	0.246230
$565$	−1.28844	−0.0542052
$566$	12.7657	0.536581
$567$	−3.43403	−0.144216
$568$	−19.5138	−0.818779
$569$	−6.79224	−0.284746	−0.142373	−	0.989813i	$-0.545473\pi$
$569$	−6.79224	−0.284746	−0.142373	+	0.989813i	$0.545473\pi$
$570$	−3.05629	−0.128014
$571$	30.3770	1.27124	0.635618	−	0.772004i	$-0.280745\pi$
$571$	30.3770	1.27124	0.635618	+	0.772004i	$0.280745\pi$
$572$	−11.1174	−0.464841
$573$	−4.95906	−0.207168
$574$	11.1204	0.464158
$575$	−29.3463	−1.22383
$576$	−3.19467	−0.133111
$577$	−8.71413	−0.362774	−0.181387	−	0.983412i	$-0.558059\pi$
$577$	−8.71413	−0.362774	−0.181387	+	0.983412i	$0.558059\pi$
$578$	1.25736	0.0522992
$579$	−6.72933	−0.279661
$580$	11.6633	0.484293
$581$	−36.7551	−1.52486
$582$	0.612935	0.0254070
$583$	3.39708	0.140693
$584$	1.82351	0.0754572
$585$	20.3340	0.840706
$586$	1.28748	0.0531855
$587$	33.8989	1.39916	0.699580	−	0.714555i	$-0.253371\pi$
$587$	33.8989	1.39916	0.699580	+	0.714555i	$0.253371\pi$
$588$	−8.53110	−0.351816
$589$	5.56648	0.229363
$590$	−10.6178	−0.437129
$591$	8.95161	0.368220
$592$	25.8226	1.06130
$593$	−11.0493	−0.453740	−0.226870	−	0.973925i	$-0.572849\pi$
$593$	−11.0493	−0.453740	−0.226870	+	0.973925i	$0.572849\pi$
$594$	−0.468970	−0.0192421
$595$	49.6004	2.03342
$596$	8.41957	0.344879
$597$	6.33890	0.259434
$598$	15.3485	0.627645
$599$	40.5277	1.65592	0.827958	−	0.560791i	$-0.189503\pi$
$599$	40.5277	1.65592	0.827958	+	0.560791i	$0.189503\pi$
$600$	−9.92761	−0.405293
$601$	−3.05022	−0.124421	−0.0622106	−	0.998063i	$-0.519815\pi$
$601$	−3.05022	−0.124421	−0.0622106	+	0.998063i	$0.519815\pi$
$602$	−11.3767	−0.463679
$603$	−13.7103	−0.558327
$604$	4.53422	0.184495
$605$	−3.25579	−0.132367
$606$	−4.40004	−0.178739
$607$	−38.5560	−1.56494	−0.782469	−	0.622690i	$-0.786040\pi$
$607$	−38.5560	−1.56494	−0.782469	+	0.622690i	$0.786040\pi$
$608$	9.65846	0.391702
$609$	−6.91089	−0.280043
$610$	1.52687	0.0618210
$611$	20.5169	0.830023
$612$	−7.89698	−0.319217
$613$	−36.0475	−1.45594	−0.727972	−	0.685607i	$-0.759537\pi$
$613$	−36.0475	−1.45594	−0.727972	+	0.685607i	$0.759537\pi$
$614$	11.5489	0.466077
$615$	22.4817	0.906549
$616$	−6.08764	−0.245278
$617$	20.1078	0.809510	0.404755	−	0.914425i	$-0.367357\pi$
$617$	20.1078	0.809510	0.404755	+	0.914425i	$0.367357\pi$
$618$	1.55775	0.0626621
$619$	46.0006	1.84892	0.924460	−	0.381280i	$-0.124516\pi$
$619$	46.0006	1.84892	0.924460	+	0.381280i	$0.124516\pi$
$620$	16.1168	0.647268
$621$	−5.24027	−0.210285
$622$	−2.40256	−0.0963338
$623$	−20.3703	−0.816117
$624$	−17.0425	−0.682246
$625$	−21.6390	−0.865562
$626$	3.11219	0.124388
$627$	−2.00167	−0.0799392
$628$	−18.1754	−0.725276
$629$	41.9814	1.67391
$630$	5.24331	0.208898
$631$	−41.3031	−1.64425	−0.822124	−	0.569308i	$-0.807211\pi$
$631$	−41.3031	−1.64425	−0.822124	+	0.569308i	$0.807211\pi$
$632$	19.4377	0.773191
$633$	−12.2782	−0.488016
$634$	10.0951	0.400926
$635$	−3.92462	−0.155744
$636$	6.04703	0.239780
$637$	−29.9319	−1.18595
$638$	−0.943788	−0.0373649
$639$	11.0077	0.435457
$640$	36.2974	1.43478
$641$	−9.05117	−0.357500	−0.178750	−	0.983895i	$-0.557205\pi$
$641$	−9.05117	−0.357500	−0.178750	+	0.983895i	$0.557205\pi$
$642$	−2.10130	−0.0829318
$643$	40.7525	1.60712	0.803562	−	0.595221i	$-0.202936\pi$
$643$	40.7525	1.60712	0.803562	+	0.595221i	$0.202936\pi$
$644$	−32.0328	−1.26227
$645$	−22.9997	−0.905613
$646$	4.16451	0.163850
$647$	−28.8295	−1.13340	−0.566702	−	0.823923i	$-0.691781\pi$
$647$	−28.8295	−1.13340	−0.566702	+	0.823923i	$0.691781\pi$
$648$	−1.77274	−0.0696398
$649$	−6.95400	−0.272968
$650$	−16.4025	−0.643361
$651$	−9.54974	−0.374284
$652$	−27.1679	−1.06398
$653$	17.2920	0.676690	0.338345	−	0.941022i	$-0.390133\pi$
$653$	17.2920	0.676690	0.338345	+	0.941022i	$0.390133\pi$
$654$	−2.25860	−0.0883183
$655$	−44.1790	−1.72622
$656$	−18.8426	−0.735678
$657$	−1.02864	−0.0401310
$658$	5.29047	0.206244
$659$	−7.68996	−0.299558	−0.149779	−	0.988719i	$-0.547856\pi$
$659$	−7.68996	−0.299558	−0.149779	+	0.988719i	$0.547856\pi$
$660$	−5.79552	−0.225590
$661$	5.25986	0.204585	0.102292	−	0.994754i	$-0.467382\pi$
$661$	5.25986	0.204585	0.102292	+	0.994754i	$0.467382\pi$
$662$	−14.9500	−0.581049
$663$	−27.7071	−1.07605
$664$	−18.9740	−0.736334
$665$	22.3797	0.867847
$666$	4.43790	0.171965
$667$	−10.5459	−0.408338
$668$	−27.3714	−1.05903
$669$	−0.874257	−0.0338007
$670$	20.9338	0.808744
$671$	1.00000	0.0386046
$672$	−16.5699	−0.639196
$673$	−42.5265	−1.63928	−0.819638	−	0.572881i	$-0.805826\pi$
$673$	−42.5265	−1.63928	−0.819638	+	0.572881i	$0.805826\pi$
$674$	6.74816	0.259930
$675$	5.60015	0.215550
$676$	−46.2925	−1.78048
$677$	−21.8036	−0.837982	−0.418991	−	0.907990i	$-0.637616\pi$
$677$	−21.8036	−0.837982	−0.418991	+	0.907990i	$0.637616\pi$
$678$	0.185590	0.00712753
$679$	−4.48821	−0.172242
$680$	25.6050	0.981909
$681$	10.4092	0.398883
$682$	−1.30417	−0.0499391
$683$	−3.87219	−0.148165	−0.0740826	−	0.997252i	$-0.523603\pi$
$683$	−3.87219	−0.148165	−0.0740826	+	0.997252i	$0.523603\pi$
$684$	−3.56312	−0.136239
$685$	−47.8700	−1.82902
$686$	3.55497	0.135730
$687$	−13.6935	−0.522440
$688$	19.2767	0.734919
$689$	21.2164	0.808281
$690$	8.00120	0.304600
$691$	26.2173	0.997353	0.498677	−	0.866788i	$-0.333820\pi$
$691$	26.2173	0.997353	0.498677	+	0.866788i	$0.333820\pi$
$692$	−41.6474	−1.58320
$693$	3.43403	0.130448
$694$	−3.87853	−0.147227
$695$	31.8538	1.20828
$696$	−3.56758	−0.135229
$697$	−30.6336	−1.16033
$698$	−3.61374	−0.136782
$699$	−6.74441	−0.255097
$700$	34.2327	1.29387
$701$	14.6365	0.552812	0.276406	−	0.961041i	$-0.410857\pi$
$701$	14.6365	0.552812	0.276406	+	0.961041i	$0.410857\pi$
$702$	−2.92895	−0.110546
$703$	18.9420	0.714411
$704$	3.19467	0.120404
$705$	10.6955	0.402816
$706$	9.15907	0.344706
$707$	32.2193	1.21173
$708$	−12.3786	−0.465216
$709$	−18.9404	−0.711321	−0.355661	−	0.934615i	$-0.615744\pi$
$709$	−18.9404	−0.711321	−0.355661	+	0.934615i	$0.615744\pi$
$710$	−16.8073	−0.630766
$711$	−10.9648	−0.411212
$712$	−10.5157	−0.394092
$713$	−14.5727	−0.545753
$714$	−7.14454	−0.267378
$715$	−20.3340	−0.760447
$716$	11.1552	0.416889
$717$	19.8593	0.741658
$718$	14.7728	0.551317
$719$	−10.5219	−0.392399	−0.196199	−	0.980564i	$-0.562860\pi$
$719$	−10.5219	−0.392399	−0.196199	+	0.980564i	$0.562860\pi$
$720$	−8.88430	−0.331098
$721$	−11.4067	−0.424806
$722$	−7.03141	−0.261682
$723$	−23.6717	−0.880360
$724$	42.0606	1.56317
$725$	11.2701	0.418563
$726$	0.468970	0.0174051
$727$	−49.5012	−1.83590	−0.917949	−	0.396699i	$-0.870156\pi$
$727$	−49.5012	−1.83590	−0.917949	+	0.396699i	$0.870156\pi$
$728$	−38.0203	−1.40912
$729$	1.00000	0.0370370
$730$	1.57059	0.0581303
$731$	31.3394	1.15913
$732$	1.78007	0.0657932
$733$	28.5502	1.05453	0.527263	−	0.849702i	$-0.323218\pi$
$733$	28.5502	1.05453	0.527263	+	0.849702i	$0.323218\pi$
$734$	8.75959	0.323322
$735$	−15.6036	−0.575547
$736$	−25.2853	−0.932029
$737$	13.7103	0.505026
$738$	−3.23831	−0.119204
$739$	21.0440	0.774115	0.387057	−	0.922056i	$-0.373492\pi$
$739$	21.0440	0.774115	0.387057	+	0.922056i	$0.373492\pi$
$740$	54.8434	2.01609
$741$	−12.5014	−0.459251
$742$	5.47086	0.200841
$743$	−17.4017	−0.638405	−0.319202	−	0.947687i	$-0.603415\pi$
$743$	−17.4017	−0.638405	−0.319202	+	0.947687i	$0.603415\pi$
$744$	−4.92983	−0.180736
$745$	15.3996	0.564198
$746$	8.79424	0.321980
$747$	10.7032	0.391610
$748$	7.89698	0.288742
$749$	15.3868	0.562221
$750$	−0.916355	−0.0334606
$751$	23.4793	0.856773	0.428387	−	0.903596i	$-0.359082\pi$
$751$	23.4793	0.856773	0.428387	+	0.903596i	$0.359082\pi$
$752$	−8.96421	−0.326891
$753$	−22.7517	−0.829119
$754$	−5.89441	−0.214662
$755$	8.29320	0.301820
$756$	6.11281	0.222321
$757$	−18.9342	−0.688174	−0.344087	−	0.938938i	$-0.611812\pi$
$757$	−18.9342	−0.688174	−0.344087	+	0.938938i	$0.611812\pi$
$758$	5.59917	0.203371
$759$	5.24027	0.190210
$760$	11.5530	0.419071
$761$	−6.95761	−0.252213	−0.126106	−	0.992017i	$-0.540248\pi$
$761$	−6.95761	−0.252213	−0.126106	+	0.992017i	$0.540248\pi$
$762$	0.565310	0.0204790
$763$	16.5386	0.598737
$764$	8.82747	0.319367
$765$	−14.4438	−0.522216
$766$	13.7113	0.495409
$767$	−43.4311	−1.56821
$768$	1.16099	0.0418938
$769$	−22.1075	−0.797217	−0.398609	−	0.917121i	$-0.630507\pi$
$769$	−22.1075	−0.797217	−0.398609	+	0.917121i	$0.630507\pi$
$770$	−5.24331	−0.188956
$771$	5.16686	0.186080
$772$	11.9787	0.431121
$773$	22.7271	0.817437	0.408718	−	0.912661i	$-0.365976\pi$
$773$	22.7271	0.817437	0.408718	+	0.912661i	$0.365976\pi$
$774$	3.31292	0.119081
$775$	15.5735	0.559418
$776$	−2.31693	−0.0831731
$777$	−32.4965	−1.16581
$778$	17.3727	0.622843
$779$	−13.8218	−0.495219
$780$	−36.1958	−1.29602
$781$	−11.0077	−0.393886
$782$	−10.9024	−0.389870
$783$	2.01247	0.0719198
$784$	13.0778	0.467065
$785$	−33.2432	−1.18650
$786$	6.36363	0.226983
$787$	0.0752940	0.00268394	0.00134197	−	0.999999i	$-0.499573\pi$
$787$	0.0752940	0.00268394	0.00134197	+	0.999999i	$0.499573\pi$
$788$	−15.9345	−0.567642
$789$	−27.5651	−0.981344
$790$	16.7418	0.595647
$791$	−1.35898	−0.0483198
$792$	1.77274	0.0629915
$793$	6.24548	0.221784
$794$	16.1248	0.572246
$795$	11.0602	0.392264
$796$	−11.2837	−0.399939
$797$	22.0267	0.780225	0.390112	−	0.920767i	$-0.372436\pi$
$797$	22.0267	0.780225	0.390112	+	0.920767i	$0.372436\pi$
$798$	−3.22361	−0.114115
$799$	−14.5737	−0.515580
$800$	27.0218	0.955365
$801$	5.93188	0.209593
$802$	2.86327	0.101106
$803$	1.02864	0.0362998
$804$	24.4053	0.860708
$805$	−58.5887	−2.06498
$806$	−8.14514	−0.286900
$807$	21.8629	0.769609
$808$	16.6324	0.585127
$809$	18.2011	0.639918	0.319959	−	0.947431i	$-0.396331\pi$
$809$	18.2011	0.639918	0.319959	+	0.947431i	$0.396331\pi$
$810$	−1.52687	−0.0536486
$811$	51.6355	1.81317	0.906584	−	0.422025i	$-0.138680\pi$
$811$	51.6355	1.81317	0.906584	+	0.422025i	$0.138680\pi$
$812$	12.3018	0.431710
$813$	17.0898	0.599367
$814$	−4.43790	−0.155548
$815$	−49.6908	−1.74059
$816$	12.1058	0.423786
$817$	14.1403	0.494708
$818$	−13.4454	−0.470106
$819$	21.4472	0.749425
$820$	−40.0189	−1.39752
$821$	−1.06685	−0.0372334	−0.0186167	−	0.999827i	$-0.505926\pi$
$821$	−1.06685	−0.0372334	−0.0186167	+	0.999827i	$0.505926\pi$
$822$	6.89529	0.240501
$823$	41.1805	1.43546	0.717731	−	0.696321i	$-0.245181\pi$
$823$	41.1805	1.43546	0.717731	+	0.696321i	$0.245181\pi$
$824$	−5.88842	−0.205133
$825$	−5.60015	−0.194972
$826$	−11.1991	−0.389667
$827$	6.70863	0.233282	0.116641	−	0.993174i	$-0.462787\pi$
$827$	6.70863	0.233282	0.116641	+	0.993174i	$0.462787\pi$
$828$	9.32803	0.324172
$829$	50.0952	1.73988	0.869939	−	0.493159i	$-0.164158\pi$
$829$	50.0952	1.73988	0.869939	+	0.493159i	$0.164158\pi$
$830$	−16.3424	−0.567252
$831$	−11.7573	−0.407855
$832$	19.9523	0.691721
$833$	21.2615	0.736666
$834$	−4.58829	−0.158879
$835$	−50.0630	−1.73250
$836$	3.56312	0.123233
$837$	2.78091	0.0961224
$838$	−9.74868	−0.336763
$839$	16.6741	0.575655	0.287827	−	0.957682i	$-0.407067\pi$
$839$	16.6741	0.575655	0.287827	+	0.957682i	$0.407067\pi$
$840$	−19.8201	−0.683857
$841$	−24.9500	−0.860344
$842$	−3.79887	−0.130918
$843$	17.9185	0.617148
$844$	21.8561	0.752317
$845$	−84.6702	−2.91274
$846$	−1.54060	−0.0529669
$847$	−3.43403	−0.117995
$848$	−9.26986	−0.318328
$849$	27.2207	0.934210
$850$	11.6512	0.399632
$851$	−49.5891	−1.69989
$852$	−19.5944	−0.671294
$853$	37.6327	1.28852	0.644259	−	0.764807i	$-0.277166\pi$
$853$	37.6327	1.28852	0.644259	+	0.764807i	$0.277166\pi$
$854$	1.61046	0.0551087
$855$	−6.51703	−0.222878
$856$	7.94307	0.271488
$857$	37.9851	1.29755	0.648773	−	0.760982i	$-0.275282\pi$
$857$	37.9851	1.29755	0.648773	+	0.760982i	$0.275282\pi$
$858$	2.92895	0.0999925
$859$	−4.26900	−0.145656	−0.0728282	−	0.997345i	$-0.523202\pi$
$859$	−4.26900	−0.145656	−0.0728282	+	0.997345i	$0.523202\pi$
$860$	40.9410	1.39608
$861$	23.7125	0.808119
$862$	−2.61788	−0.0891654
$863$	−5.50516	−0.187398	−0.0936990	−	0.995601i	$-0.529869\pi$
$863$	−5.50516	−0.187398	−0.0936990	+	0.995601i	$0.529869\pi$
$864$	4.82519	0.164156
$865$	−76.1741	−2.59000
$866$	13.7546	0.467399
$867$	2.68111	0.0910551
$868$	16.9992	0.576990
$869$	10.9648	0.371956
$870$	−3.07277	−0.104177
$871$	85.6275	2.90138
$872$	8.53766	0.289122
$873$	1.30698	0.0442346
$874$	−4.91918	−0.166394
$875$	6.71000	0.226840
$876$	1.83104	0.0618653
$877$	−37.6292	−1.27065	−0.635324	−	0.772246i	$-0.719133\pi$
$877$	−37.6292	−1.27065	−0.635324	+	0.772246i	$0.719133\pi$
$878$	−12.1698	−0.410709
$879$	2.74534	0.0925981
$880$	8.88430	0.299490
$881$	25.6031	0.862589	0.431295	−	0.902211i	$-0.358057\pi$
$881$	25.6031	0.862589	0.431295	+	0.902211i	$0.358057\pi$
$882$	2.24757	0.0756797
$883$	16.3426	0.549972	0.274986	−	0.961448i	$-0.411327\pi$
$883$	16.3426	0.549972	0.274986	+	0.961448i	$0.411327\pi$
$884$	49.3205	1.65883
$885$	−22.6407	−0.761060
$886$	−16.1334	−0.542014
$887$	−4.22569	−0.141885	−0.0709425	−	0.997480i	$-0.522601\pi$
$887$	−4.22569	−0.141885	−0.0709425	+	0.997480i	$0.522601\pi$
$888$	−16.7756	−0.562951
$889$	−4.13948	−0.138834
$890$	−9.05720	−0.303598
$891$	−1.00000	−0.0335013
$892$	1.55624	0.0521067
$893$	−6.57564	−0.220046
$894$	−2.21819	−0.0741873
$895$	20.4031	0.682002
$896$	38.2846	1.27900
$897$	32.7280	1.09276
$898$	16.9841	0.566765
$899$	5.59650	0.186654
$900$	−9.96865	−0.332288
$901$	−15.0706	−0.502075
$902$	3.23831	0.107824
$903$	−24.2589	−0.807284
$904$	−0.701542	−0.0233329
$905$	76.9298	2.55723
$906$	−1.19457	−0.0396869
$907$	4.49047	0.149104	0.0745519	−	0.997217i	$-0.476247\pi$
$907$	4.49047	0.149104	0.0745519	+	0.997217i	$0.476247\pi$
$908$	−18.5291	−0.614911
$909$	−9.38234	−0.311193
$910$	−32.7470	−1.08555
$911$	−6.20158	−0.205468	−0.102734	−	0.994709i	$-0.532759\pi$
$911$	−6.20158	−0.205468	−0.102734	+	0.994709i	$0.532759\pi$
$912$	5.46211	0.180869
$913$	−10.7032	−0.354224
$914$	10.9234	0.361313
$915$	3.25579	0.107633
$916$	24.3754	0.805384
$917$	−46.5977	−1.53879
$918$	2.08051	0.0686671
$919$	57.4546	1.89525	0.947627	−	0.319380i	$-0.103475\pi$
$919$	57.4546	1.89525	0.947627	+	0.319380i	$0.103475\pi$
$920$	−30.2451	−0.997150
$921$	24.6262	0.811460
$922$	−13.2555	−0.436546
$923$	−68.7483	−2.26288
$924$	−6.11281	−0.201097
$925$	52.9947	1.74245
$926$	−15.1699	−0.498513
$927$	3.32165	0.109097
$928$	9.71055	0.318764
$929$	−14.0361	−0.460511	−0.230255	−	0.973130i	$-0.573956\pi$
$929$	−14.0361	−0.460511	−0.230255	+	0.973130i	$0.573956\pi$
$930$	−4.24608	−0.139235
$931$	9.59317	0.314403
$932$	12.0055	0.393253
$933$	−5.12305	−0.167721
$934$	−1.55027	−0.0507265
$935$	14.4438	0.472362
$936$	11.0716	0.361887
$937$	28.3710	0.926840	0.463420	−	0.886139i	$-0.346622\pi$
$937$	28.3710	0.926840	0.463420	+	0.886139i	$0.346622\pi$
$938$	22.0799	0.720934
$939$	6.63621	0.216565
$940$	−19.0387	−0.620974
$941$	−41.8840	−1.36538	−0.682690	−	0.730708i	$-0.739190\pi$
$941$	−41.8840	−1.36538	−0.682690	+	0.730708i	$0.739190\pi$
$942$	4.78841	0.156015
$943$	36.1848	1.17834
$944$	18.9759	0.617612
$945$	11.1805	0.363701
$946$	−3.31292	−0.107712
$947$	41.3592	1.34399	0.671996	−	0.740555i	$-0.265437\pi$
$947$	41.3592	1.34399	0.671996	+	0.740555i	$0.265437\pi$
$948$	19.5181	0.633918
$949$	6.42434	0.208543
$950$	5.25701	0.170560
$951$	21.5260	0.698029
$952$	27.0068	0.875297
$953$	−41.6088	−1.34784	−0.673920	−	0.738804i	$-0.735391\pi$
$953$	−41.6088	−1.34784	−0.673920	+	0.738804i	$0.735391\pi$
$954$	−1.59313	−0.0515795
$955$	16.1457	0.522461
$956$	−35.3508	−1.14333
$957$	−2.01247	−0.0650539
$958$	−4.90486	−0.158469
$959$	−50.4907	−1.63043
$960$	10.4012	0.335697
$961$	−23.2665	−0.750533
$962$	−27.7168	−0.893627
$963$	−4.48068	−0.144388
$964$	42.1372	1.35715
$965$	21.9093	0.705284
$966$	8.43924	0.271528
$967$	−21.0341	−0.676410	−0.338205	−	0.941072i	$-0.609820\pi$
$967$	−21.0341	−0.676410	−0.338205	+	0.941072i	$0.609820\pi$
$968$	−1.77274	−0.0569780
$969$	8.88011	0.285270
$970$	−1.99559	−0.0640744
$971$	−47.5838	−1.52704	−0.763518	−	0.645786i	$-0.776530\pi$
$971$	−47.5838	−1.52704	−0.763518	+	0.645786i	$0.776530\pi$
$972$	−1.78007	−0.0570957
$973$	33.5977	1.07709
$974$	9.31786	0.298564
$975$	−34.9757	−1.12012
$976$	−2.72877	−0.0873459
$977$	4.54384	0.145370	0.0726852	−	0.997355i	$-0.476843\pi$
$977$	4.54384	0.145370	0.0726852	+	0.997355i	$0.476843\pi$
$978$	7.15757	0.228874
$979$	−5.93188	−0.189584
$980$	27.7754	0.887254
$981$	−4.81609	−0.153766
$982$	15.8997	0.507379
$983$	−7.20373	−0.229763	−0.114882	−	0.993379i	$-0.536649\pi$
$983$	−7.20373	−0.229763	−0.114882	+	0.993379i	$0.536649\pi$
$984$	12.2410	0.390229
$985$	−29.1445	−0.928622
$986$	4.18697	0.133340
$987$	11.2810	0.359079
$988$	22.2534	0.707974
$989$	−37.0186	−1.17712
$990$	1.52687	0.0485270
$991$	−9.75410	−0.309849	−0.154925	−	0.987926i	$-0.549513\pi$
$991$	−9.75410	−0.309849	−0.154925	+	0.987926i	$0.549513\pi$
$992$	13.4184	0.426036
$993$	−31.8784	−1.01163
$994$	−17.7274	−0.562280
$995$	−20.6381	−0.654272
$996$	−19.0524	−0.603699
$997$	43.2494	1.36972	0.684862	−	0.728673i	$-0.259863\pi$
$997$	43.2494	1.36972	0.684862	+	0.728673i	$0.259863\pi$
$998$	−4.25601	−0.134722
$999$	9.46308	0.299398

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2013.2.a.f.1.7	✓	13
3.2	odd	2		6039.2.a.g.1.7		13

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2013.2.a.f.1.7	✓	13	1.1	even	1	trivial
6039.2.a.g.1.7		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)

\(f(q)\)	\(=\)	\(q+0.468970 q^{2} +1.00000 q^{3} -1.78007 q^{4} -3.25579 q^{5} +0.468970 q^{6} -3.43403 q^{7} -1.77274 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+0.468970 q^{2} +1.00000 q^{3} -1.78007 q^{4} -3.25579 q^{5} +0.468970 q^{6} -3.43403 q^{7} -1.77274 q^{8} +1.00000 q^{9} -1.52687 q^{10} -1.00000 q^{11} -1.78007 q^{12} -6.24548 q^{13} -1.61046 q^{14} -3.25579 q^{15} +2.72877 q^{16} +4.43634 q^{17} +0.468970 q^{18} +2.00167 q^{19} +5.79552 q^{20} -3.43403 q^{21} -0.468970 q^{22} -5.24027 q^{23} -1.77274 q^{24} +5.60015 q^{25} -2.92895 q^{26} +1.00000 q^{27} +6.11281 q^{28} +2.01247 q^{29} -1.52687 q^{30} +2.78091 q^{31} +4.82519 q^{32} -1.00000 q^{33} +2.08051 q^{34} +11.1805 q^{35} -1.78007 q^{36} +9.46308 q^{37} +0.938726 q^{38} -6.24548 q^{39} +5.77166 q^{40} -6.90514 q^{41} -1.61046 q^{42} +7.06425 q^{43} +1.78007 q^{44} -3.25579 q^{45} -2.45753 q^{46} -3.28507 q^{47} +2.72877 q^{48} +4.79257 q^{49} +2.62630 q^{50} +4.43634 q^{51} +11.1174 q^{52} -3.39708 q^{53} +0.468970 q^{54} +3.25579 q^{55} +6.08764 q^{56} +2.00167 q^{57} +0.943788 q^{58} +6.95400 q^{59} +5.79552 q^{60} -1.00000 q^{61} +1.30417 q^{62} -3.43403 q^{63} -3.19467 q^{64} +20.3340 q^{65} -0.468970 q^{66} -13.7103 q^{67} -7.89698 q^{68} -5.24027 q^{69} +5.24331 q^{70} +11.0077 q^{71} -1.77274 q^{72} -1.02864 q^{73} +4.43790 q^{74} +5.60015 q^{75} -3.56312 q^{76} +3.43403 q^{77} -2.92895 q^{78} -10.9648 q^{79} -8.88430 q^{80} +1.00000 q^{81} -3.23831 q^{82} +10.7032 q^{83} +6.11281 q^{84} -14.4438 q^{85} +3.31292 q^{86} +2.01247 q^{87} +1.77274 q^{88} +5.93188 q^{89} -1.52687 q^{90} +21.4472 q^{91} +9.32803 q^{92} +2.78091 q^{93} -1.54060 q^{94} -6.51703 q^{95} +4.82519 q^{96} +1.30698 q^{97} +2.24757 q^{98} -1.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 13 q + 4 q^{2} + 13 q^{3} + 12 q^{4} + 7 q^{5} + 4 q^{6} + 5 q^{7} + 15 q^{8} + 13 q^{9}+O(q^{10}) \) 13 * q + 4 * q^2 + 13 * q^3 + 12 * q^4 + 7 * q^5 + 4 * q^6 + 5 * q^7 + 15 * q^8 + 13 * q^9	\( 13 q + 4 q^{2} + 13 q^{3} + 12 q^{4} + 7 q^{5} + 4 q^{6} + 5 q^{7} + 15 q^{8} + 13 q^{9} + 8 q^{10} - 13 q^{11} + 12 q^{12} - 9 q^{13} + 19 q^{14} + 7 q^{15} + 18 q^{16} + 7 q^{17} + 4 q^{18} + 2 q^{19} + 15 q^{20} + 5 q^{21} - 4 q^{22} + 23 q^{23} + 15 q^{24} + 10 q^{25} + 8 q^{26} + 13 q^{27} + 9 q^{28} + 16 q^{29} + 8 q^{30} + 9 q^{31} + 29 q^{32} - 13 q^{33} + 2 q^{34} + 16 q^{35} + 12 q^{36} + 14 q^{37} + 8 q^{38} - 9 q^{39} + 16 q^{40} + 19 q^{41} + 19 q^{42} + 7 q^{43} - 12 q^{44} + 7 q^{45} + 4 q^{46} + 26 q^{47} + 18 q^{48} + 8 q^{49} - 15 q^{50} + 7 q^{51} - 17 q^{52} + 18 q^{53} + 4 q^{54} - 7 q^{55} + 44 q^{56} + 2 q^{57} - q^{58} + 31 q^{59} + 15 q^{60} - 13 q^{61} - 5 q^{62} + 5 q^{63} - 17 q^{64} + 31 q^{65} - 4 q^{66} + 14 q^{67} - 32 q^{68} + 23 q^{69} - 20 q^{70} + 37 q^{71} + 15 q^{72} - 16 q^{73} - 6 q^{74} + 10 q^{75} - 7 q^{76} - 5 q^{77} + 8 q^{78} - 17 q^{79} - 2 q^{80} + 13 q^{81} - 2 q^{82} + 30 q^{83} + 9 q^{84} - 16 q^{85} - 22 q^{86} + 16 q^{87} - 15 q^{88} + 35 q^{89} + 8 q^{90} - q^{91} + 24 q^{92} + 9 q^{93} - 11 q^{94} + 13 q^{95} + 29 q^{96} - q^{97} - q^{98} - 13 q^{99}+O(q^{100}) \) 13 * q + 4 * q^2 + 13 * q^3 + 12 * q^4 + 7 * q^5 + 4 * q^6 + 5 * q^7 + 15 * q^8 + 13 * q^9 + 8 * q^10 - 13 * q^11 + 12 * q^12 - 9 * q^13 + 19 * q^14 + 7 * q^15 + 18 * q^16 + 7 * q^17 + 4 * q^18 + 2 * q^19 + 15 * q^20 + 5 * q^21 - 4 * q^22 + 23 * q^23 + 15 * q^24 + 10 * q^25 + 8 * q^26 + 13 * q^27 + 9 * q^28 + 16 * q^29 + 8 * q^30 + 9 * q^31 + 29 * q^32 - 13 * q^33 + 2 * q^34 + 16 * q^35 + 12 * q^36 + 14 * q^37 + 8 * q^38 - 9 * q^39 + 16 * q^40 + 19 * q^41 + 19 * q^42 + 7 * q^43 - 12 * q^44 + 7 * q^45 + 4 * q^46 + 26 * q^47 + 18 * q^48 + 8 * q^49 - 15 * q^50 + 7 * q^51 - 17 * q^52 + 18 * q^53 + 4 * q^54 - 7 * q^55 + 44 * q^56 + 2 * q^57 - q^58 + 31 * q^59 + 15 * q^60 - 13 * q^61 - 5 * q^62 + 5 * q^63 - 17 * q^64 + 31 * q^65 - 4 * q^66 + 14 * q^67 - 32 * q^68 + 23 * q^69 - 20 * q^70 + 37 * q^71 + 15 * q^72 - 16 * q^73 - 6 * q^74 + 10 * q^75 - 7 * q^76 - 5 * q^77 + 8 * q^78 - 17 * q^79 - 2 * q^80 + 13 * q^81 - 2 * q^82 + 30 * q^83 + 9 * q^84 - 16 * q^85 - 22 * q^86 + 16 * q^87 - 15 * q^88 + 35 * q^89 + 8 * q^90 - q^91 + 24 * q^92 + 9 * q^93 - 11 * q^94 + 13 * q^95 + 29 * q^96 - q^97 - q^98 - 13 * q^99

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