LMFDB - Embedded newform 2013.2.a.c.1.3

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:	$1$
Dimension:	$12$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 5x^{11} - 5x^{10} + 48x^{9} - 173x^{7} + 29x^{6} + 281x^{5} - 41x^{4} - 201x^{3} + 8x^{2} + 49x + 8 $ x^12 - 5x^11 - 5x^10 + 48x^9 - 173x^7 + 29x^6 + 281x^5 - 41x^4 - 201x^3 + 8x^2 + 49x + 8
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			1.3
Root			$-1.31792$ 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)

$f(q)$	$=$	$q-2.31792 q^{2} +1.00000 q^{3} +3.37276 q^{4} -2.47951 q^{5} -2.31792 q^{6} +3.26859 q^{7} -3.18195 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-2.31792 q^{2} +1.00000 q^{3} +3.37276 q^{4} -2.47951 q^{5} -2.31792 q^{6} +3.26859 q^{7} -3.18195 q^{8} +1.00000 q^{9} +5.74732 q^{10} +1.00000 q^{11} +3.37276 q^{12} +6.05111 q^{13} -7.57633 q^{14} -2.47951 q^{15} +0.629993 q^{16} -6.63735 q^{17} -2.31792 q^{18} -4.68664 q^{19} -8.36281 q^{20} +3.26859 q^{21} -2.31792 q^{22} -6.72397 q^{23} -3.18195 q^{24} +1.14799 q^{25} -14.0260 q^{26} +1.00000 q^{27} +11.0242 q^{28} -6.44005 q^{29} +5.74732 q^{30} -6.17187 q^{31} +4.90363 q^{32} +1.00000 q^{33} +15.3849 q^{34} -8.10451 q^{35} +3.37276 q^{36} -6.59063 q^{37} +10.8633 q^{38} +6.05111 q^{39} +7.88969 q^{40} +8.91287 q^{41} -7.57633 q^{42} -8.98140 q^{43} +3.37276 q^{44} -2.47951 q^{45} +15.5856 q^{46} +10.7447 q^{47} +0.629993 q^{48} +3.68368 q^{49} -2.66095 q^{50} -6.63735 q^{51} +20.4089 q^{52} +11.7082 q^{53} -2.31792 q^{54} -2.47951 q^{55} -10.4005 q^{56} -4.68664 q^{57} +14.9275 q^{58} +3.81524 q^{59} -8.36281 q^{60} -1.00000 q^{61} +14.3059 q^{62} +3.26859 q^{63} -12.6262 q^{64} -15.0038 q^{65} -2.31792 q^{66} +3.27788 q^{67} -22.3862 q^{68} -6.72397 q^{69} +18.7856 q^{70} -13.3606 q^{71} -3.18195 q^{72} -6.29610 q^{73} +15.2766 q^{74} +1.14799 q^{75} -15.8069 q^{76} +3.26859 q^{77} -14.0260 q^{78} -5.89560 q^{79} -1.56208 q^{80} +1.00000 q^{81} -20.6593 q^{82} -6.77257 q^{83} +11.0242 q^{84} +16.4574 q^{85} +20.8182 q^{86} -6.44005 q^{87} -3.18195 q^{88} -2.86664 q^{89} +5.74732 q^{90} +19.7786 q^{91} -22.6783 q^{92} -6.17187 q^{93} -24.9054 q^{94} +11.6206 q^{95} +4.90363 q^{96} +8.49974 q^{97} -8.53848 q^{98} +1.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 7 q^{2} + 12 q^{3} + 13 q^{4} - 7 q^{5} - 7 q^{6} - 15 q^{7} - 18 q^{8} + 12 q^{9}+O(q^{10}) $ 12 * q - 7 * q^2 + 12 * q^3 + 13 * q^4 - 7 * q^5 - 7 * q^6 - 15 * q^7 - 18 * q^8 + 12 * q^9	\( 12 q - 7 q^{2} + 12 q^{3} + 13 q^{4} - 7 q^{5} - 7 q^{6} - 15 q^{7} - 18 q^{8} + 12 q^{9} - 6 q^{10} + 12 q^{11} + 13 q^{12} - 11 q^{13} + 3 q^{14} - 7 q^{15} + 19 q^{16} - 33 q^{17} - 7 q^{18} - 24 q^{19} - 11 q^{20} - 15 q^{21} - 7 q^{22} - 9 q^{23} - 18 q^{24} + 11 q^{25} - 16 q^{26} + 12 q^{27} - 41 q^{28} - 16 q^{29} - 6 q^{30} + q^{31} - 28 q^{32} + 12 q^{33} + 32 q^{34} - 22 q^{35} + 13 q^{36} - 6 q^{37} + 12 q^{38} - 11 q^{39} + 26 q^{40} - 21 q^{41} + 3 q^{42} - 39 q^{43} + 13 q^{44} - 7 q^{45} - 18 q^{47} + 19 q^{48} + 31 q^{49} - 44 q^{50} - 33 q^{51} + 3 q^{52} - 14 q^{53} - 7 q^{54} - 7 q^{55} + 16 q^{56} - 24 q^{57} + 33 q^{58} - 23 q^{59} - 11 q^{60} - 12 q^{61} - 25 q^{62} - 15 q^{63} + 12 q^{64} - 29 q^{65} - 7 q^{66} - 96 q^{68} - 9 q^{69} + 44 q^{70} - 19 q^{71} - 18 q^{72} - 42 q^{73} + 38 q^{74} + 11 q^{75} + 11 q^{76} - 15 q^{77} - 16 q^{78} - 11 q^{79} - 44 q^{80} + 12 q^{81} - 14 q^{82} - 56 q^{83} - 41 q^{84} + 16 q^{85} - 18 q^{86} - 16 q^{87} - 18 q^{88} - 55 q^{89} - 6 q^{90} + 11 q^{91} - 4 q^{92} + q^{93} - 5 q^{94} + 15 q^{95} - 28 q^{96} - 7 q^{97} + 6 q^{98} + 12 q^{99}+O(q^{100}) \) 12 * q - 7 * q^2 + 12 * q^3 + 13 * q^4 - 7 * q^5 - 7 * q^6 - 15 * q^7 - 18 * q^8 + 12 * q^9 - 6 * q^10 + 12 * q^11 + 13 * q^12 - 11 * q^13 + 3 * q^14 - 7 * q^15 + 19 * q^16 - 33 * q^17 - 7 * q^18 - 24 * q^19 - 11 * q^20 - 15 * q^21 - 7 * q^22 - 9 * q^23 - 18 * q^24 + 11 * q^25 - 16 * q^26 + 12 * q^27 - 41 * q^28 - 16 * q^29 - 6 * q^30 + q^31 - 28 * q^32 + 12 * q^33 + 32 * q^34 - 22 * q^35 + 13 * q^36 - 6 * q^37 + 12 * q^38 - 11 * q^39 + 26 * q^40 - 21 * q^41 + 3 * q^42 - 39 * q^43 + 13 * q^44 - 7 * q^45 - 18 * q^47 + 19 * q^48 + 31 * q^49 - 44 * q^50 - 33 * q^51 + 3 * q^52 - 14 * q^53 - 7 * q^54 - 7 * q^55 + 16 * q^56 - 24 * q^57 + 33 * q^58 - 23 * q^59 - 11 * q^60 - 12 * q^61 - 25 * q^62 - 15 * q^63 + 12 * q^64 - 29 * q^65 - 7 * q^66 - 96 * q^68 - 9 * q^69 + 44 * q^70 - 19 * q^71 - 18 * q^72 - 42 * q^73 + 38 * q^74 + 11 * q^75 + 11 * q^76 - 15 * q^77 - 16 * q^78 - 11 * q^79 - 44 * q^80 + 12 * q^81 - 14 * q^82 - 56 * q^83 - 41 * q^84 + 16 * q^85 - 18 * q^86 - 16 * q^87 - 18 * q^88 - 55 * q^89 - 6 * q^90 + 11 * q^91 - 4 * q^92 + q^93 - 5 * q^94 + 15 * q^95 - 28 * q^96 - 7 * q^97 + 6 * q^98 + 12 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	−2.31792	−1.63902	−0.819509	−	0.573066i	$-0.805754\pi$
$2$	−2.31792	−1.63902	−0.819509	+	0.573066i	$0.805754\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	3.37276	1.68638
$5$	−2.47951	−1.10887	−0.554436	−	0.832226i	$-0.687066\pi$
$5$	−2.47951	−1.10887	−0.554436	+	0.832226i	$0.687066\pi$
$6$	−2.31792	−0.946288
$7$	3.26859	1.23541	0.617705	−	0.786410i	$-0.288062\pi$
$7$	3.26859	1.23541	0.617705	+	0.786410i	$0.288062\pi$
$8$	−3.18195	−1.12499
$9$	1.00000	0.333333
$10$	5.74732	1.81746
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	3.37276	0.973632
$13$	6.05111	1.67827	0.839137	−	0.543920i	$-0.183060\pi$
$13$	6.05111	1.67827	0.839137	+	0.543920i	$0.183060\pi$
$14$	−7.57633	−2.02486
$15$	−2.47951	−0.640208
$16$	0.629993	0.157498
$17$	−6.63735	−1.60979	−0.804897	−	0.593414i	$-0.797780\pi$
$17$	−6.63735	−1.60979	−0.804897	+	0.593414i	$0.797780\pi$
$18$	−2.31792	−0.546339
$19$	−4.68664	−1.07519	−0.537595	−	0.843203i	$-0.680667\pi$
$19$	−4.68664	−1.07519	−0.537595	+	0.843203i	$0.680667\pi$
$20$	−8.36281	−1.86998
$21$	3.26859	0.713265
$22$	−2.31792	−0.494183
$23$	−6.72397	−1.40204	−0.701022	−	0.713139i	$-0.747273\pi$
$23$	−6.72397	−1.40204	−0.701022	+	0.713139i	$0.747273\pi$
$24$	−3.18195	−0.649513
$25$	1.14799	0.229598
$26$	−14.0260	−2.75072
$27$	1.00000	0.192450
$28$	11.0242	2.08337
$29$	−6.44005	−1.19589	−0.597944	−	0.801538i	$-0.704015\pi$
$29$	−6.44005	−1.19589	−0.597944	+	0.801538i	$0.704015\pi$
$30$	5.74732	1.04931
$31$	−6.17187	−1.10850	−0.554250	−	0.832350i	$-0.686995\pi$
$31$	−6.17187	−1.10850	−0.554250	+	0.832350i	$0.686995\pi$
$32$	4.90363	0.866847
$33$	1.00000	0.174078
$34$	15.3849	2.63848
$35$	−8.10451	−1.36991
$36$	3.37276	0.562127
$37$	−6.59063	−1.08349	−0.541747	−	0.840542i	$-0.682237\pi$
$37$	−6.59063	−1.08349	−0.541747	+	0.840542i	$0.682237\pi$
$38$	10.8633	1.76225
$39$	6.05111	0.968952
$40$	7.88969	1.24747
$41$	8.91287	1.39196	0.695978	−	0.718063i	$-0.254971\pi$
$41$	8.91287	1.39196	0.695978	+	0.718063i	$0.254971\pi$
$42$	−7.57633	−1.16905
$43$	−8.98140	−1.36965	−0.684825	−	0.728707i	$-0.740122\pi$
$43$	−8.98140	−1.36965	−0.684825	+	0.728707i	$0.740122\pi$
$44$	3.37276	0.508463
$45$	−2.47951	−0.369624
$46$	15.5856	2.29798
$47$	10.7447	1.56728	0.783639	−	0.621217i	$-0.213361\pi$
$47$	10.7447	1.56728	0.783639	+	0.621217i	$0.213361\pi$
$48$	0.629993	0.0909316
$49$	3.68368	0.526240
$50$	−2.66095	−0.376315
$51$	−6.63735	−0.929415
$52$	20.4089	2.83021
$53$	11.7082	1.60825	0.804125	−	0.594460i	$-0.202634\pi$
$53$	11.7082	1.60825	0.804125	+	0.594460i	$0.202634\pi$
$54$	−2.31792	−0.315429
$55$	−2.47951	−0.334338
$56$	−10.4005	−1.38982
$57$	−4.68664	−0.620761
$58$	14.9275	1.96008
$59$	3.81524	0.496702	0.248351	−	0.968670i	$-0.420111\pi$
$59$	3.81524	0.496702	0.248351	+	0.968670i	$0.420111\pi$
$60$	−8.36281	−1.07963
$61$	−1.00000	−0.128037
$61$	−1.00000	−0.128037
$62$	14.3059	1.81685
$63$	3.26859	0.411804
$64$	−12.6262	−1.57828
$65$	−15.0038	−1.86099
$66$	−2.31792	−0.285316
$67$	3.27788	0.400456	0.200228	−	0.979749i	$-0.435832\pi$
$67$	3.27788	0.400456	0.200228	+	0.979749i	$0.435832\pi$
$68$	−22.3862	−2.71473
$69$	−6.72397	−0.809471
$70$	18.7856	2.24531
$71$	−13.3606	−1.58561	−0.792804	−	0.609476i	$-0.791380\pi$
$71$	−13.3606	−1.58561	−0.792804	+	0.609476i	$0.791380\pi$
$72$	−3.18195	−0.374997
$73$	−6.29610	−0.736903	−0.368451	−	0.929647i	$-0.620112\pi$
$73$	−6.29610	−0.736903	−0.368451	+	0.929647i	$0.620112\pi$
$74$	15.2766	1.77587
$75$	1.14799	0.132558
$76$	−15.8069	−1.81318
$77$	3.26859	0.372490
$78$	−14.0260	−1.58813
$79$	−5.89560	−0.663307	−0.331653	−	0.943401i	$-0.607606\pi$
$79$	−5.89560	−0.663307	−0.331653	+	0.943401i	$0.607606\pi$
$80$	−1.56208	−0.174645
$81$	1.00000	0.111111
$82$	−20.6593	−2.28144
$83$	−6.77257	−0.743386	−0.371693	−	0.928356i	$-0.621223\pi$
$83$	−6.77257	−0.743386	−0.371693	+	0.928356i	$0.621223\pi$
$84$	11.0242	1.20284
$85$	16.4574	1.78506
$86$	20.8182	2.24488
$87$	−6.44005	−0.690446
$88$	−3.18195	−0.339197
$89$	−2.86664	−0.303863	−0.151932	−	0.988391i	$-0.548549\pi$
$89$	−2.86664	−0.303863	−0.151932	+	0.988391i	$0.548549\pi$
$90$	5.74732	0.605821
$91$	19.7786	2.07336
$92$	−22.6783	−2.36438
$93$	−6.17187	−0.639993
$94$	−24.9054	−2.56880
$95$	11.6206	1.19225
$96$	4.90363	0.500475
$97$	8.49974	0.863018	0.431509	−	0.902109i	$-0.357981\pi$
$97$	8.49974	0.863018	0.431509	+	0.902109i	$0.357981\pi$
$98$	−8.53848	−0.862517
$99$	1.00000	0.100504
$100$	3.87189	0.387189
$101$	−4.21053	−0.418964	−0.209482	−	0.977813i	$-0.567178\pi$
$101$	−4.21053	−0.418964	−0.209482	+	0.977813i	$0.567178\pi$
$102$	15.3849	1.52333
$103$	−18.1476	−1.78813	−0.894067	−	0.447934i	$-0.852160\pi$
$103$	−18.1476	−1.78813	−0.894067	+	0.447934i	$0.852160\pi$
$104$	−19.2543	−1.88804
$105$	−8.10451	−0.790920
$106$	−27.1388	−2.63595
$107$	−6.78421	−0.655854	−0.327927	−	0.944703i	$-0.606350\pi$
$107$	−6.78421	−0.655854	−0.327927	+	0.944703i	$0.606350\pi$
$108$	3.37276	0.324544
$109$	−1.58488	−0.151804	−0.0759021	−	0.997115i	$-0.524184\pi$
$109$	−1.58488	−0.151804	−0.0759021	+	0.997115i	$0.524184\pi$
$110$	5.74732	0.547985
$111$	−6.59063	−0.625555
$112$	2.05919	0.194575
$113$	0.642108	0.0604045	0.0302022	−	0.999544i	$-0.490385\pi$
$113$	0.642108	0.0604045	0.0302022	+	0.999544i	$0.490385\pi$
$114$	10.8633	1.01744
$115$	16.6722	1.55469
$116$	−21.7207	−2.01672
$117$	6.05111	0.559425
$118$	−8.84342	−0.814103
$119$	−21.6948	−1.98876
$120$	7.88969	0.720227
$121$	1.00000	0.0909091
$122$	2.31792	0.209855
$123$	8.91287	0.803646
$124$	−20.8162	−1.86935
$125$	9.55111	0.854278
$126$	−7.57633	−0.674954
$127$	11.6746	1.03595	0.517975	−	0.855396i	$-0.326686\pi$
$127$	11.6746	1.03595	0.517975	+	0.855396i	$0.326686\pi$
$128$	19.4593	1.71998
$129$	−8.98140	−0.790768
$130$	34.7776	3.05020
$131$	−6.62541	−0.578865	−0.289432	−	0.957198i	$-0.593467\pi$
$131$	−6.62541	−0.578865	−0.289432	+	0.957198i	$0.593467\pi$
$132$	3.37276	0.293561
$133$	−15.3187	−1.32830
$134$	−7.59786	−0.656355
$135$	−2.47951	−0.213403
$136$	21.1197	1.81100
$137$	−6.72646	−0.574681	−0.287340	−	0.957829i	$-0.592771\pi$
$137$	−6.72646	−0.574681	−0.287340	+	0.957829i	$0.592771\pi$
$138$	15.5856	1.32674
$139$	17.5108	1.48525	0.742625	−	0.669707i	$-0.233580\pi$
$139$	17.5108	1.48525	0.742625	+	0.669707i	$0.233580\pi$
$140$	−27.3346	−2.31019
$141$	10.7447	0.904868
$142$	30.9688	2.59884
$143$	6.05111	0.506019
$144$	0.629993	0.0524994
$145$	15.9682	1.32609
$146$	14.5939	1.20780
$147$	3.68368	0.303825
$148$	−22.2286	−1.82718
$149$	−21.6874	−1.77670	−0.888352	−	0.459163i	$-0.848149\pi$
$149$	−21.6874	−1.77670	−0.888352	+	0.459163i	$0.848149\pi$
$150$	−2.66095	−0.217266
$151$	−12.3753	−1.00709	−0.503544	−	0.863970i	$-0.667971\pi$
$151$	−12.3753	−1.00709	−0.503544	+	0.863970i	$0.667971\pi$
$152$	14.9127	1.20958
$153$	−6.63735	−0.536598
$154$	−7.57633	−0.610518
$155$	15.3032	1.22919
$156$	20.4089	1.63402
$157$	6.60694	0.527292	0.263646	−	0.964620i	$-0.415075\pi$
$157$	6.60694	0.527292	0.263646	+	0.964620i	$0.415075\pi$
$158$	13.6655	1.08717
$159$	11.7082	0.928524
$160$	−12.1586	−0.961223
$161$	−21.9779	−1.73210
$162$	−2.31792	−0.182113
$163$	−8.97660	−0.703102	−0.351551	−	0.936169i	$-0.614346\pi$
$163$	−8.97660	−0.703102	−0.351551	+	0.936169i	$0.614346\pi$
$164$	30.0610	2.34737
$165$	−2.47951	−0.193030
$166$	15.6983	1.21842
$167$	−6.34806	−0.491228	−0.245614	−	0.969368i	$-0.578990\pi$
$167$	−6.34806	−0.491228	−0.245614	+	0.969368i	$0.578990\pi$
$168$	−10.4005	−0.802415
$169$	23.6159	1.81661
$170$	−38.1470	−2.92574
$171$	−4.68664	−0.358396
$172$	−30.2921	−2.30975
$173$	−10.8803	−0.827215	−0.413607	−	0.910455i	$-0.635731\pi$
$173$	−10.8803	−0.827215	−0.413607	+	0.910455i	$0.635731\pi$
$174$	14.9275	1.13165
$175$	3.75230	0.283648
$176$	0.629993	0.0474875
$177$	3.81524	0.286771
$178$	6.64465	0.498038
$179$	21.7370	1.62470	0.812351	−	0.583168i	$-0.198187\pi$
$179$	21.7370	1.62470	0.812351	+	0.583168i	$0.198187\pi$
$180$	−8.36281	−0.623327
$181$	−2.85061	−0.211884	−0.105942	−	0.994372i	$-0.533786\pi$
$181$	−2.85061	−0.211884	−0.105942	+	0.994372i	$0.533786\pi$
$182$	−45.8452	−3.39827
$183$	−1.00000	−0.0739221
$184$	21.3953	1.57729
$185$	16.3416	1.20146
$186$	14.3059	1.04896
$187$	−6.63735	−0.485371
$188$	36.2393	2.64303
$189$	3.26859	0.237755
$190$	−26.9356	−1.95412
$191$	16.8513	1.21932	0.609659	−	0.792664i	$-0.291307\pi$
$191$	16.8513	1.21932	0.609659	+	0.792664i	$0.291307\pi$
$192$	−12.6262	−0.911218
$193$	−0.0491126	−0.00353520	−0.00176760	−	0.999998i	$-0.500563\pi$
$193$	−0.0491126	−0.00353520	−0.00176760	+	0.999998i	$0.500563\pi$
$194$	−19.7017	−1.41450
$195$	−15.0038	−1.07444
$196$	12.4242	0.887440
$197$	6.18214	0.440459	0.220230	−	0.975448i	$-0.429319\pi$
$197$	6.18214	0.440459	0.220230	+	0.975448i	$0.429319\pi$
$198$	−2.31792	−0.164728
$199$	−7.69298	−0.545341	−0.272670	−	0.962108i	$-0.587907\pi$
$199$	−7.69298	−0.545341	−0.272670	+	0.962108i	$0.587907\pi$
$200$	−3.65284	−0.258295
$201$	3.27788	0.231204
$202$	9.75968	0.686689
$203$	−21.0499	−1.47741
$204$	−22.3862	−1.56735
$205$	−22.0996	−1.54350
$206$	42.0647	2.93078
$207$	−6.72397	−0.467348
$208$	3.81215	0.264325
$209$	−4.68664	−0.324182
$210$	18.7856	1.29633
$211$	−25.7265	−1.77108	−0.885541	−	0.464561i	$-0.846212\pi$
$211$	−25.7265	−1.77108	−0.885541	+	0.464561i	$0.846212\pi$
$212$	39.4891	2.71212
$213$	−13.3606	−0.915452
$214$	15.7253	1.07496
$215$	22.2695	1.51877
$216$	−3.18195	−0.216504
$217$	−20.1733	−1.36945
$218$	3.67363	0.248810
$219$	−6.29610	−0.425451
$220$	−8.36281	−0.563820
$221$	−40.1633	−2.70168
$222$	15.2766	1.02530
$223$	13.4211	0.898741	0.449371	−	0.893345i	$-0.351648\pi$
$223$	13.4211	0.898741	0.449371	+	0.893345i	$0.351648\pi$
$224$	16.0280	1.07091
$225$	1.14799	0.0765326
$226$	−1.48836	−0.0990040
$227$	−22.1736	−1.47171	−0.735856	−	0.677138i	$-0.763220\pi$
$227$	−22.1736	−1.47171	−0.735856	+	0.677138i	$0.763220\pi$
$228$	−15.8069	−1.04684
$229$	8.20706	0.542338	0.271169	−	0.962532i	$-0.412590\pi$
$229$	8.20706	0.542338	0.271169	+	0.962532i	$0.412590\pi$
$230$	−38.6448	−2.54816
$231$	3.26859	0.215057
$232$	20.4919	1.34536
$233$	−15.5362	−1.01781	−0.508906	−	0.860822i	$-0.669950\pi$
$233$	−15.5362	−1.01781	−0.508906	+	0.860822i	$0.669950\pi$
$234$	−14.0260	−0.916907
$235$	−26.6417	−1.73791
$236$	12.8679	0.837628
$237$	−5.89560	−0.382960
$238$	50.2868	3.25961
$239$	7.51917	0.486375	0.243187	−	0.969979i	$-0.421807\pi$
$239$	7.51917	0.486375	0.243187	+	0.969979i	$0.421807\pi$
$240$	−1.56208	−0.100832
$241$	−15.5840	−1.00385	−0.501927	−	0.864910i	$-0.667376\pi$
$241$	−15.5840	−1.00385	−0.501927	+	0.864910i	$0.667376\pi$
$242$	−2.31792	−0.149002
$243$	1.00000	0.0641500
$244$	−3.37276	−0.215919
$245$	−9.13373	−0.583533
$246$	−20.6593	−1.31719
$247$	−28.3594	−1.80446
$248$	19.6386	1.24705
$249$	−6.77257	−0.429194
$250$	−22.1387	−1.40018
$251$	29.0362	1.83275	0.916373	−	0.400326i	$-0.131103\pi$
$251$	29.0362	1.83275	0.916373	+	0.400326i	$0.131103\pi$
$252$	11.0242	0.694457
$253$	−6.72397	−0.422732
$254$	−27.0607	−1.69794
$255$	16.4574	1.03060
$256$	−19.8527	−1.24080
$257$	7.42017	0.462858	0.231429	−	0.972852i	$-0.425660\pi$
$257$	7.42017	0.462858	0.231429	+	0.972852i	$0.425660\pi$
$258$	20.8182	1.29608
$259$	−21.5421	−1.33856
$260$	−50.6042	−3.13834
$261$	−6.44005	−0.398629
$262$	15.3572	0.948770
$263$	5.43921	0.335396	0.167698	−	0.985838i	$-0.446367\pi$
$263$	5.43921	0.335396	0.167698	+	0.985838i	$0.446367\pi$
$264$	−3.18195	−0.195836
$265$	−29.0307	−1.78334
$266$	35.5076	2.17711
$267$	−2.86664	−0.175436
$268$	11.0555	0.675322
$269$	−10.2198	−0.623113	−0.311557	−	0.950228i	$-0.600850\pi$
$269$	−10.2198	−0.623113	−0.311557	+	0.950228i	$0.600850\pi$
$270$	5.74732	0.349771
$271$	7.36832	0.447593	0.223797	−	0.974636i	$-0.428155\pi$
$271$	7.36832	0.447593	0.223797	+	0.974636i	$0.428155\pi$
$272$	−4.18148	−0.253540
$273$	19.7786	1.19705
$274$	15.5914	0.941912
$275$	1.14799	0.0692263
$276$	−22.6783	−1.36508
$277$	−19.2638	−1.15745	−0.578725	−	0.815523i	$-0.696450\pi$
$277$	−19.2638	−1.15745	−0.578725	+	0.815523i	$0.696450\pi$
$278$	−40.5888	−2.43435
$279$	−6.17187	−0.369500
$280$	25.7882	1.54114
$281$	1.00514	0.0599619	0.0299809	−	0.999550i	$-0.490455\pi$
$281$	1.00514	0.0599619	0.0299809	+	0.999550i	$0.490455\pi$
$282$	−24.9054	−1.48309
$283$	14.9883	0.890965	0.445482	−	0.895291i	$-0.353032\pi$
$283$	14.9883	0.890965	0.445482	+	0.895291i	$0.353032\pi$
$284$	−45.0620	−2.67394
$285$	11.6206	0.688344
$286$	−14.0260	−0.829374
$287$	29.1325	1.71964
$288$	4.90363	0.288949
$289$	27.0544	1.59144
$290$	−37.0130	−2.17348
$291$	8.49974	0.498263
$292$	−21.2352	−1.24270
$293$	−32.8105	−1.91681	−0.958404	−	0.285416i	$-0.907868\pi$
$293$	−32.8105	−1.91681	−0.958404	+	0.285416i	$0.907868\pi$
$294$	−8.53848	−0.497974
$295$	−9.45993	−0.550779
$296$	20.9711	1.21892
$297$	1.00000	0.0580259
$298$	50.2698	2.91205
$299$	−40.6875	−2.35302
$300$	3.87189	0.223544
$301$	−29.3565	−1.69208
$302$	28.6850	1.65063
$303$	−4.21053	−0.241889
$304$	−2.95255	−0.169340
$305$	2.47951	0.141977
$306$	15.3849	0.879494
$307$	7.14961	0.408050	0.204025	−	0.978966i	$-0.434598\pi$
$307$	7.14961	0.408050	0.204025	+	0.978966i	$0.434598\pi$
$308$	11.0242	0.628160
$309$	−18.1476	−1.03238
$310$	−35.4717	−2.01466
$311$	−18.8314	−1.06783	−0.533916	−	0.845538i	$-0.679280\pi$
$311$	−18.8314	−1.06783	−0.533916	+	0.845538i	$0.679280\pi$
$312$	−19.2543	−1.09006
$313$	23.7753	1.34386	0.671928	−	0.740616i	$-0.265466\pi$
$313$	23.7753	1.34386	0.671928	+	0.740616i	$0.265466\pi$
$314$	−15.3144	−0.864240
$315$	−8.10451	−0.456638
$316$	−19.8845	−1.11859
$317$	−15.5940	−0.875848	−0.437924	−	0.899012i	$-0.644286\pi$
$317$	−15.5940	−0.875848	−0.437924	+	0.899012i	$0.644286\pi$
$318$	−27.1388	−1.52187
$319$	−6.44005	−0.360573
$320$	31.3069	1.75011
$321$	−6.78421	−0.378658
$322$	50.9431	2.83895
$323$	31.1069	1.73083
$324$	3.37276	0.187376
$325$	6.94660	0.385328
$326$	20.8071	1.15240
$327$	−1.58488	−0.0876442
$328$	−28.3603	−1.56594
$329$	35.1200	1.93623
$330$	5.74732	0.316379
$331$	−18.3454	−1.00835	−0.504177	−	0.863600i	$-0.668204\pi$
$331$	−18.3454	−1.00835	−0.504177	+	0.863600i	$0.668204\pi$
$332$	−22.8422	−1.25363
$333$	−6.59063	−0.361165
$334$	14.7143	0.805131
$335$	−8.12754	−0.444055
$336$	2.05919	0.112338
$337$	−0.343178	−0.0186941	−0.00934704	−	0.999956i	$-0.502975\pi$
$337$	−0.343178	−0.0186941	−0.00934704	+	0.999956i	$0.502975\pi$
$338$	−54.7397	−2.97745
$339$	0.642108	0.0348745
$340$	55.5069	3.01028
$341$	−6.17187	−0.334226
$342$	10.8633	0.587418
$343$	−10.8397	−0.585288
$344$	28.5784	1.54084
$345$	16.6722	0.897600
$346$	25.2197	1.35582
$347$	−2.46579	−0.132370	−0.0661852	−	0.997807i	$-0.521083\pi$
$347$	−2.46579	−0.132370	−0.0661852	+	0.997807i	$0.521083\pi$
$348$	−21.7207	−1.16435
$349$	26.2419	1.40470	0.702348	−	0.711834i	$-0.252135\pi$
$349$	26.2419	1.40470	0.702348	+	0.711834i	$0.252135\pi$
$350$	−8.69755	−0.464904
$351$	6.05111	0.322984
$352$	4.90363	0.261364
$353$	−8.93973	−0.475814	−0.237907	−	0.971288i	$-0.576461\pi$
$353$	−8.93973	−0.475814	−0.237907	+	0.971288i	$0.576461\pi$
$354$	−8.84342	−0.470022
$355$	33.1277	1.75824
$356$	−9.66849	−0.512429
$357$	−21.6948	−1.14821
$358$	−50.3848	−2.66292
$359$	24.1204	1.27303	0.636513	−	0.771266i	$-0.280376\pi$
$359$	24.1204	1.27303	0.636513	+	0.771266i	$0.280376\pi$
$360$	7.88969	0.415823
$361$	2.96461	0.156032
$362$	6.60750	0.347282
$363$	1.00000	0.0524864
$364$	66.7084	3.49647
$365$	15.6113	0.817131
$366$	2.31792	0.121160
$367$	4.09954	0.213994	0.106997	−	0.994259i	$-0.465876\pi$
$367$	4.09954	0.213994	0.106997	+	0.994259i	$0.465876\pi$
$368$	−4.23605	−0.220819
$369$	8.91287	0.463985
$370$	−37.8785	−1.96921
$371$	38.2694	1.98685
$372$	−20.8162	−1.07927
$373$	4.36673	0.226101	0.113050	−	0.993589i	$-0.463938\pi$
$373$	4.36673	0.226101	0.113050	+	0.993589i	$0.463938\pi$
$374$	15.3849	0.795532
$375$	9.55111	0.493217
$376$	−34.1891	−1.76317
$377$	−38.9694	−2.00703
$378$	−7.57633	−0.389685
$379$	38.3572	1.97028	0.985139	−	0.171761i	$-0.0549457\pi$
$379$	38.3572	1.97028	0.985139	+	0.171761i	$0.0549457\pi$
$380$	39.1935	2.01058
$381$	11.6746	0.598106
$382$	−39.0600	−1.99848
$383$	3.77120	0.192699	0.0963497	−	0.995348i	$-0.469283\pi$
$383$	3.77120	0.192699	0.0963497	+	0.995348i	$0.469283\pi$
$384$	19.4593	0.993029
$385$	−8.10451	−0.413044
$386$	0.113839	0.00579426
$387$	−8.98140	−0.456550
$388$	28.6676	1.45538
$389$	33.2927	1.68800	0.844002	−	0.536339i	$-0.180193\pi$
$389$	33.2927	1.68800	0.844002	+	0.536339i	$0.180193\pi$
$390$	34.7776	1.76103
$391$	44.6294	2.25700
$392$	−11.7213	−0.592014
$393$	−6.62541	−0.334208
$394$	−14.3297	−0.721921
$395$	14.6182	0.735523
$396$	3.37276	0.169488
$397$	−19.5260	−0.979980	−0.489990	−	0.871728i	$-0.663000\pi$
$397$	−19.5260	−0.979980	−0.489990	+	0.871728i	$0.663000\pi$
$398$	17.8317	0.893823
$399$	−15.3187	−0.766895
$400$	0.723225	0.0361612
$401$	−38.0053	−1.89789	−0.948946	−	0.315438i	$-0.897848\pi$
$401$	−38.0053	−1.89789	−0.948946	+	0.315438i	$0.897848\pi$
$402$	−7.59786	−0.378947
$403$	−37.3466	−1.86037
$404$	−14.2011	−0.706532
$405$	−2.47951	−0.123208
$406$	48.7920	2.42150
$407$	−6.59063	−0.326686
$408$	21.1197	1.04558
$409$	−2.79051	−0.137982	−0.0689909	−	0.997617i	$-0.521978\pi$
$409$	−2.79051	−0.137982	−0.0689909	+	0.997617i	$0.521978\pi$
$410$	51.2251	2.52983
$411$	−6.72646	−0.331792
$412$	−61.2074	−3.01547
$413$	12.4704	0.613630
$414$	15.5856	0.765992
$415$	16.7927	0.824320
$416$	29.6724	1.45481
$417$	17.5108	0.857510
$418$	10.8633	0.531340
$419$	−1.30588	−0.0637964	−0.0318982	−	0.999491i	$-0.510155\pi$
$419$	−1.30588	−0.0637964	−0.0318982	+	0.999491i	$0.510155\pi$
$420$	−27.3346	−1.33379
$421$	−18.6901	−0.910897	−0.455449	−	0.890262i	$-0.650521\pi$
$421$	−18.6901	−0.910897	−0.455449	+	0.890262i	$0.650521\pi$
$422$	59.6319	2.90284
$423$	10.7447	0.522426
$424$	−37.2550	−1.80927
$425$	−7.61961	−0.369605
$426$	30.9688	1.50044
$427$	−3.26859	−0.158178
$428$	−22.8815	−1.10602
$429$	6.05111	0.292150
$430$	−51.6190	−2.48929
$431$	−4.71349	−0.227041	−0.113520	−	0.993536i	$-0.536213\pi$
$431$	−4.71349	−0.227041	−0.113520	+	0.993536i	$0.536213\pi$
$432$	0.629993	0.0303105
$433$	−27.0077	−1.29791	−0.648953	−	0.760829i	$-0.724793\pi$
$433$	−27.0077	−1.29791	−0.648953	+	0.760829i	$0.724793\pi$
$434$	46.7602	2.24456
$435$	15.9682	0.765616
$436$	−5.34543	−0.255999
$437$	31.5128	1.50746
$438$	14.5939	0.697322
$439$	28.0507	1.33879	0.669394	−	0.742907i	$-0.266554\pi$
$439$	28.0507	1.33879	0.669394	+	0.742907i	$0.266554\pi$
$440$	7.88969	0.376126
$441$	3.68368	0.175413
$442$	93.0954	4.42810
$443$	12.6047	0.598866	0.299433	−	0.954117i	$-0.403202\pi$
$443$	12.6047	0.598866	0.299433	+	0.954117i	$0.403202\pi$
$444$	−22.2286	−1.05492
$445$	7.10788	0.336946
$446$	−31.1090	−1.47305
$447$	−21.6874	−1.02578
$448$	−41.2699	−1.94982
$449$	9.95289	0.469706	0.234853	−	0.972031i	$-0.424539\pi$
$449$	9.95289	0.469706	0.234853	+	0.972031i	$0.424539\pi$
$450$	−2.66095	−0.125438
$451$	8.91287	0.419691
$452$	2.16568	0.101865
$453$	−12.3753	−0.581442
$454$	51.3966	2.41216
$455$	−49.0413	−2.29909
$456$	14.9127	0.698350
$457$	31.4066	1.46914	0.734569	−	0.678534i	$-0.237384\pi$
$457$	31.4066	1.46914	0.734569	+	0.678534i	$0.237384\pi$
$458$	−19.0233	−0.888902
$459$	−6.63735	−0.309805
$460$	56.2313	2.62180
$461$	29.2165	1.36075	0.680373	−	0.732866i	$-0.261818\pi$
$461$	29.2165	1.36075	0.680373	+	0.732866i	$0.261818\pi$
$462$	−7.57633	−0.352483
$463$	−26.3649	−1.22528	−0.612640	−	0.790362i	$-0.709892\pi$
$463$	−26.3649	−1.22528	−0.612640	+	0.790362i	$0.709892\pi$
$464$	−4.05718	−0.188350
$465$	15.3032	0.709671
$466$	36.0117	1.66821
$467$	−14.1452	−0.654563	−0.327281	−	0.944927i	$-0.606132\pi$
$467$	−14.1452	−0.654563	−0.327281	+	0.944927i	$0.606132\pi$
$468$	20.4089	0.943403
$469$	10.7140	0.494728
$470$	61.7533	2.84847
$471$	6.60694	0.304432
$472$	−12.1399	−0.558784
$473$	−8.98140	−0.412965
$474$	13.6655	0.627679
$475$	−5.38021	−0.246861
$476$	−73.1713	−3.35380
$477$	11.7082	0.536083
$478$	−17.4289	−0.797177
$479$	3.16963	0.144824	0.0724121	−	0.997375i	$-0.476930\pi$
$479$	3.16963	0.144824	0.0724121	+	0.997375i	$0.476930\pi$
$480$	−12.1586	−0.554962
$481$	−39.8806	−1.81840
$482$	36.1225	1.64534
$483$	−21.9779	−1.00003
$484$	3.37276	0.153307
$485$	−21.0752	−0.956976
$486$	−2.31792	−0.105143
$487$	−1.73207	−0.0784876	−0.0392438	−	0.999230i	$-0.512495\pi$
$487$	−1.73207	−0.0784876	−0.0392438	+	0.999230i	$0.512495\pi$
$488$	3.18195	0.144040
$489$	−8.97660	−0.405936
$490$	21.1713	0.956421
$491$	−33.0415	−1.49114	−0.745572	−	0.666425i	$-0.767824\pi$
$491$	−33.0415	−1.49114	−0.745572	+	0.666425i	$0.767824\pi$
$492$	30.0610	1.35525
$493$	42.7449	1.92513
$494$	65.7348	2.95755
$495$	−2.47951	−0.111446
$496$	−3.88823	−0.174587
$497$	−43.6702	−1.95888
$498$	15.6983	0.703457
$499$	−14.4982	−0.649027	−0.324514	−	0.945881i	$-0.605201\pi$
$499$	−14.4982	−0.649027	−0.324514	+	0.945881i	$0.605201\pi$
$500$	32.2136	1.44064
$501$	−6.34806	−0.283610
$502$	−67.3035	−3.00390
$503$	−38.2279	−1.70450	−0.852250	−	0.523136i	$-0.824762\pi$
$503$	−38.2279	−1.70450	−0.852250	+	0.523136i	$0.824762\pi$
$504$	−10.4005	−0.463275
$505$	10.4401	0.464577
$506$	15.5856	0.692866
$507$	23.6159	1.04882
$508$	39.3755	1.74701
$509$	−0.825848	−0.0366051	−0.0183025	−	0.999832i	$-0.505826\pi$
$509$	−0.825848	−0.0366051	−0.0183025	+	0.999832i	$0.505826\pi$
$510$	−38.1470	−1.68918
$511$	−20.5794	−0.910378
$512$	7.09846	0.313711
$513$	−4.68664	−0.206920
$514$	−17.1994	−0.758632
$515$	44.9972	1.98281
$516$	−30.2921	−1.33354
$517$	10.7447	0.472552
$518$	49.9329	2.19392
$519$	−10.8803	−0.477593
$520$	47.7414	2.09360
$521$	12.2959	0.538695	0.269348	−	0.963043i	$-0.413192\pi$
$521$	12.2959	0.538695	0.269348	+	0.963043i	$0.413192\pi$
$522$	14.9275	0.653360
$523$	−23.6237	−1.03299	−0.516496	−	0.856290i	$-0.672764\pi$
$523$	−23.6237	−1.03299	−0.516496	+	0.856290i	$0.672764\pi$
$524$	−22.3459	−0.976186
$525$	3.75230	0.163764
$526$	−12.6077	−0.549721
$527$	40.9649	1.78446
$528$	0.629993	0.0274169
$529$	22.2118	0.965730
$530$	67.2910	2.92293
$531$	3.81524	0.165567
$532$	−51.6663	−2.24002
$533$	53.9327	2.33608
$534$	6.64465	0.287542
$535$	16.8215	0.727259
$536$	−10.4300	−0.450509
$537$	21.7370	0.938023
$538$	23.6887	1.02129
$539$	3.68368	0.158667
$540$	−8.36281	−0.359878
$541$	10.5431	0.453283	0.226642	−	0.973978i	$-0.427225\pi$
$541$	10.5431	0.453283	0.226642	+	0.973978i	$0.427225\pi$
$542$	−17.0792	−0.733614
$543$	−2.85061	−0.122332
$544$	−32.5471	−1.39545
$545$	3.92974	0.168331
$546$	−45.8452	−1.96199
$547$	−9.08152	−0.388298	−0.194149	−	0.980972i	$-0.562194\pi$
$547$	−9.08152	−0.388298	−0.194149	+	0.980972i	$0.562194\pi$
$548$	−22.6868	−0.969130
$549$	−1.00000	−0.0426790
$550$	−2.66095	−0.113463
$551$	30.1822	1.28580
$552$	21.3953	0.910646
$553$	−19.2703	−0.819457
$554$	44.6520	1.89708
$555$	16.3416	0.693661
$556$	59.0599	2.50470
$557$	5.77966	0.244892	0.122446	−	0.992475i	$-0.460926\pi$
$557$	5.77966	0.244892	0.122446	+	0.992475i	$0.460926\pi$
$558$	14.3059	0.605618
$559$	−54.3474	−2.29865
$560$	−5.10578	−0.215759
$561$	−6.63735	−0.280229
$562$	−2.32985	−0.0982786
$563$	−15.7767	−0.664909	−0.332455	−	0.943119i	$-0.607877\pi$
$563$	−15.7767	−0.664909	−0.332455	+	0.943119i	$0.607877\pi$
$564$	36.2393	1.52595
$565$	−1.59212	−0.0669808
$566$	−34.7418	−1.46031
$567$	3.26859	0.137268
$568$	42.5127	1.78379
$569$	−21.8817	−0.917329	−0.458665	−	0.888609i	$-0.651672\pi$
$569$	−21.8817	−0.917329	−0.458665	+	0.888609i	$0.651672\pi$
$570$	−26.9356	−1.12821
$571$	0.534112	0.0223519	0.0111759	−	0.999938i	$-0.496443\pi$
$571$	0.534112	0.0223519	0.0111759	+	0.999938i	$0.496443\pi$
$572$	20.4089	0.853340
$573$	16.8513	0.703973
$574$	−67.5269	−2.81852
$575$	−7.71904	−0.321906
$576$	−12.6262	−0.526092
$577$	−8.32355	−0.346514	−0.173257	−	0.984877i	$-0.555429\pi$
$577$	−8.32355	−0.346514	−0.173257	+	0.984877i	$0.555429\pi$
$578$	−62.7101	−2.60839
$579$	−0.0491126	−0.00204105
$580$	53.8569	2.23629
$581$	−22.1367	−0.918387
$582$	−19.7017	−0.816663
$583$	11.7082	0.484906
$584$	20.0339	0.829008
$585$	−15.0038	−0.620331
$586$	76.0521	3.14168
$587$	−19.5104	−0.805281	−0.402641	−	0.915358i	$-0.631908\pi$
$587$	−19.5104	−0.805281	−0.402641	+	0.915358i	$0.631908\pi$
$588$	12.4242	0.512364
$589$	28.9253	1.19185
$590$	21.9274	0.902736
$591$	6.18214	0.254299
$592$	−4.15205	−0.170648
$593$	−20.9055	−0.858486	−0.429243	−	0.903189i	$-0.641220\pi$
$593$	−20.9055	−0.858486	−0.429243	+	0.903189i	$0.641220\pi$
$594$	−2.31792	−0.0951055
$595$	53.7925	2.20528
$596$	−73.1465	−2.99620
$597$	−7.69298	−0.314853
$598$	94.3103	3.85664
$599$	17.3363	0.708341	0.354170	−	0.935181i	$-0.384763\pi$
$599$	17.3363	0.708341	0.354170	+	0.935181i	$0.384763\pi$
$600$	−3.65284	−0.149127
$601$	10.8920	0.444293	0.222147	−	0.975013i	$-0.428694\pi$
$601$	10.8920	0.444293	0.222147	+	0.975013i	$0.428694\pi$
$602$	68.0461	2.77335
$603$	3.27788	0.133485
$604$	−41.7389	−1.69833
$605$	−2.47951	−0.100807
$606$	9.75968	0.396460
$607$	34.3377	1.39372	0.696862	−	0.717205i	$-0.254579\pi$
$607$	34.3377	1.39372	0.696862	+	0.717205i	$0.254579\pi$
$608$	−22.9816	−0.932025
$609$	−21.0499	−0.852984
$610$	−5.74732	−0.232702
$611$	65.0174	2.63032
$612$	−22.3862	−0.904908
$613$	−7.44572	−0.300730	−0.150365	−	0.988631i	$-0.548045\pi$
$613$	−7.44572	−0.300730	−0.150365	+	0.988631i	$0.548045\pi$
$614$	−16.5722	−0.668801
$615$	−22.0996	−0.891141
$616$	−10.4005	−0.419048
$617$	−23.0634	−0.928497	−0.464249	−	0.885705i	$-0.653676\pi$
$617$	−23.0634	−0.928497	−0.464249	+	0.885705i	$0.653676\pi$
$618$	42.0647	1.69209
$619$	−16.8519	−0.677334	−0.338667	−	0.940906i	$-0.609976\pi$
$619$	−16.8519	−0.677334	−0.338667	+	0.940906i	$0.609976\pi$
$620$	51.6142	2.07287
$621$	−6.72397	−0.269824
$622$	43.6497	1.75020
$623$	−9.36987	−0.375396
$624$	3.81215	0.152608
$625$	−29.4221	−1.17688
$626$	−55.1092	−2.20261
$627$	−4.68664	−0.187166
$628$	22.2836	0.889214
$629$	43.7444	1.74420
$630$	18.7856	0.748437
$631$	30.8979	1.23002	0.615012	−	0.788518i	$-0.289151\pi$
$631$	30.8979	1.23002	0.615012	+	0.788518i	$0.289151\pi$
$632$	18.7595	0.746213
$633$	−25.7265	−1.02253
$634$	36.1458	1.43553
$635$	−28.9473	−1.14874
$636$	39.4891	1.56584
$637$	22.2903	0.883175
$638$	14.9275	0.590986
$639$	−13.3606	−0.528536
$640$	−48.2496	−1.90723
$641$	7.28363	0.287686	0.143843	−	0.989601i	$-0.454054\pi$
$641$	7.28363	0.287686	0.143843	+	0.989601i	$0.454054\pi$
$642$	15.7253	0.620627
$643$	−37.6899	−1.48634	−0.743172	−	0.669101i	$-0.766679\pi$
$643$	−37.6899	−1.48634	−0.743172	+	0.669101i	$0.766679\pi$
$644$	−74.1262	−2.92098
$645$	22.2695	0.876861
$646$	−72.1033	−2.83687
$647$	49.6098	1.95036	0.975181	−	0.221409i	$-0.0710656\pi$
$647$	49.6098	1.95036	0.975181	+	0.221409i	$0.0710656\pi$
$648$	−3.18195	−0.124999
$649$	3.81524	0.149761
$650$	−16.1017	−0.631560
$651$	−20.1733	−0.790654
$652$	−30.2759	−1.18570
$653$	−23.6399	−0.925101	−0.462551	−	0.886593i	$-0.653066\pi$
$653$	−23.6399	−0.925101	−0.462551	+	0.886593i	$0.653066\pi$
$654$	3.67363	0.143650
$655$	16.4278	0.641887
$656$	5.61504	0.219231
$657$	−6.29610	−0.245634
$658$	−81.4055	−3.17352
$659$	28.7430	1.11967	0.559834	−	0.828605i	$-0.310865\pi$
$659$	28.7430	1.11967	0.559834	+	0.828605i	$0.310865\pi$
$660$	−8.36281	−0.325522
$661$	5.89740	0.229382	0.114691	−	0.993401i	$-0.463412\pi$
$661$	5.89740	0.229382	0.114691	+	0.993401i	$0.463412\pi$
$662$	42.5232	1.65271
$663$	−40.1633	−1.55981
$664$	21.5500	0.836301
$665$	37.9829	1.47292
$666$	15.2766	0.591955
$667$	43.3027	1.67669
$668$	−21.4105	−0.828397
$669$	13.4211	0.518889
$670$	18.8390	0.727814
$671$	−1.00000	−0.0386046
$672$	16.0280	0.618292
$673$	23.9587	0.923539	0.461769	−	0.887000i	$-0.347215\pi$
$673$	23.9587	0.923539	0.461769	+	0.887000i	$0.347215\pi$
$674$	0.795459	0.0306400
$675$	1.14799	0.0441861
$676$	79.6507	3.06349
$677$	10.7860	0.414539	0.207270	−	0.978284i	$-0.433542\pi$
$677$	10.7860	0.414539	0.207270	+	0.978284i	$0.433542\pi$
$678$	−1.48836	−0.0571600
$679$	27.7822	1.06618
$680$	−52.3667	−2.00817
$681$	−22.1736	−0.849693
$682$	14.3059	0.547802
$683$	28.2231	1.07993	0.539964	−	0.841688i	$-0.318438\pi$
$683$	28.2231	1.07993	0.539964	+	0.841688i	$0.318438\pi$
$684$	−15.8069	−0.604393
$685$	16.6784	0.637247
$686$	25.1256	0.959298
$687$	8.20706	0.313119
$688$	−5.65822	−0.215718
$689$	70.8478	2.69909
$690$	−38.6448	−1.47118
$691$	−9.63955	−0.366706	−0.183353	−	0.983047i	$-0.558695\pi$
$691$	−9.63955	−0.366706	−0.183353	+	0.983047i	$0.558695\pi$
$692$	−36.6967	−1.39500
$693$	3.26859	0.124163
$694$	5.71550	0.216958
$695$	−43.4184	−1.64695
$696$	20.4919	0.776744
$697$	−59.1578	−2.24076
$698$	−60.8266	−2.30232
$699$	−15.5362	−0.587634
$700$	12.6556	0.478338
$701$	−5.33675	−0.201566	−0.100783	−	0.994908i	$-0.532135\pi$
$701$	−5.33675	−0.201566	−0.100783	+	0.994908i	$0.532135\pi$
$702$	−14.0260	−0.529377
$703$	30.8879	1.16496
$704$	−12.6262	−0.475868
$705$	−26.6417	−1.00338
$706$	20.7216	0.779867
$707$	−13.7625	−0.517592
$708$	12.8679	0.483605
$709$	41.2039	1.54744	0.773722	−	0.633525i	$-0.218393\pi$
$709$	41.2039	1.54744	0.773722	+	0.633525i	$0.218393\pi$
$710$	−76.7875	−2.88178
$711$	−5.89560	−0.221102
$712$	9.12151	0.341843
$713$	41.4995	1.55417
$714$	50.2868	1.88194
$715$	−15.0038	−0.561110
$716$	73.3138	2.73987
$717$	7.51917	0.280809
$718$	−55.9092	−2.08651
$719$	13.1824	0.491620	0.245810	−	0.969318i	$-0.420946\pi$
$719$	13.1824	0.491620	0.245810	+	0.969318i	$0.420946\pi$
$720$	−1.56208	−0.0582151
$721$	−59.3170	−2.20908
$722$	−6.87173	−0.255739
$723$	−15.5840	−0.579576
$724$	−9.61444	−0.357318
$725$	−7.39310	−0.274573
$726$	−2.31792	−0.0860261
$727$	−9.00135	−0.333842	−0.166921	−	0.985970i	$-0.553382\pi$
$727$	−9.00135	−0.333842	−0.166921	+	0.985970i	$0.553382\pi$
$728$	−62.9345	−2.33251
$729$	1.00000	0.0370370
$730$	−36.1857	−1.33929
$731$	59.6127	2.20486
$732$	−3.37276	−0.124661
$733$	−29.6369	−1.09467	−0.547333	−	0.836915i	$-0.684357\pi$
$733$	−29.6369	−1.09467	−0.547333	+	0.836915i	$0.684357\pi$
$734$	−9.50240	−0.350740
$735$	−9.13373	−0.336903
$736$	−32.9719	−1.21536
$737$	3.27788	0.120742
$738$	−20.6593	−0.760480
$739$	−23.8776	−0.878350	−0.439175	−	0.898401i	$-0.644729\pi$
$739$	−23.8776	−0.878350	−0.439175	+	0.898401i	$0.644729\pi$
$740$	55.1162	2.02611
$741$	−28.3594	−1.04181
$742$	−88.7055	−3.25648
$743$	−46.5931	−1.70933	−0.854667	−	0.519177i	$-0.826238\pi$
$743$	−46.5931	−1.70933	−0.854667	+	0.519177i	$0.826238\pi$
$744$	19.6386	0.719986
$745$	53.7743	1.97014
$746$	−10.1217	−0.370583
$747$	−6.77257	−0.247795
$748$	−22.3862	−0.818520
$749$	−22.1748	−0.810250
$750$	−22.1387	−0.808392
$751$	−11.2932	−0.412095	−0.206047	−	0.978542i	$-0.566060\pi$
$751$	−11.2932	−0.412095	−0.206047	+	0.978542i	$0.566060\pi$
$752$	6.76909	0.246843
$753$	29.0362	1.05814
$754$	90.3280	3.28955
$755$	30.6847	1.11673
$756$	11.0242	0.400945
$757$	24.6228	0.894931	0.447466	−	0.894301i	$-0.352327\pi$
$757$	24.6228	0.894931	0.447466	+	0.894301i	$0.352327\pi$
$758$	−88.9090	−3.22932
$759$	−6.72397	−0.244065
$760$	−36.9762	−1.34127
$761$	37.1943	1.34829	0.674146	−	0.738598i	$-0.264512\pi$
$761$	37.1943	1.34829	0.674146	+	0.738598i	$0.264512\pi$
$762$	−27.0607	−0.980307
$763$	−5.18033	−0.187540
$764$	56.8354	2.05623
$765$	16.4574	0.595019
$766$	−8.74135	−0.315838
$767$	23.0864	0.833602
$768$	−19.8527	−0.716374
$769$	−29.5613	−1.06601	−0.533004	−	0.846113i	$-0.678937\pi$
$769$	−29.5613	−1.06601	−0.533004	+	0.846113i	$0.678937\pi$
$770$	18.7856	0.676987
$771$	7.42017	0.267231
$772$	−0.165645	−0.00596170
$773$	9.44618	0.339755	0.169878	−	0.985465i	$-0.445663\pi$
$773$	9.44618	0.339755	0.169878	+	0.985465i	$0.445663\pi$
$774$	20.8182	0.748294
$775$	−7.08524	−0.254509
$776$	−27.0458	−0.970886
$777$	−21.5421	−0.772818
$778$	−77.1698	−2.76667
$779$	−41.7714	−1.49662
$780$	−50.6042	−1.81192
$781$	−13.3606	−0.478079
$782$	−103.447	−3.69927
$783$	−6.44005	−0.230149
$784$	2.32069	0.0828818
$785$	−16.3820	−0.584699
$786$	15.3572	0.547772
$787$	19.3687	0.690421	0.345211	−	0.938525i	$-0.387807\pi$
$787$	19.3687	0.690421	0.345211	+	0.938525i	$0.387807\pi$
$788$	20.8509	0.742782
$789$	5.43921	0.193641
$790$	−33.8839	−1.20554
$791$	2.09879	0.0746243
$792$	−3.18195	−0.113066
$793$	−6.05111	−0.214881
$794$	45.2596	1.60620
$795$	−29.0307	−1.02961
$796$	−25.9466	−0.919652
$797$	6.30009	0.223161	0.111580	−	0.993755i	$-0.464409\pi$
$797$	6.30009	0.223161	0.111580	+	0.993755i	$0.464409\pi$
$798$	35.5076	1.25695
$799$	−71.3164	−2.52299
$800$	5.62931	0.199026
$801$	−2.86664	−0.101288
$802$	88.0932	3.11068
$803$	−6.29610	−0.222185
$804$	11.0555	0.389897
$805$	54.4945	1.92068
$806$	86.5666	3.04918
$807$	−10.2198	−0.359755
$808$	13.3977	0.471330
$809$	5.41537	0.190394	0.0951971	−	0.995458i	$-0.469652\pi$
$809$	5.41537	0.190394	0.0951971	+	0.995458i	$0.469652\pi$
$810$	5.74732	0.201940
$811$	−29.7092	−1.04323	−0.521616	−	0.853180i	$-0.674671\pi$
$811$	−29.7092	−1.04323	−0.521616	+	0.853180i	$0.674671\pi$
$812$	−70.9962	−2.49148
$813$	7.36832	0.258418
$814$	15.2766	0.535444
$815$	22.2576	0.779650
$816$	−4.18148	−0.146381
$817$	42.0926	1.47263
$818$	6.46818	0.226155
$819$	19.7786	0.691120
$820$	−74.5366	−2.60293
$821$	−22.5460	−0.786862	−0.393431	−	0.919354i	$-0.628712\pi$
$821$	−22.5460	−0.786862	−0.393431	+	0.919354i	$0.628712\pi$
$822$	15.5914	0.543813
$823$	26.8510	0.935967	0.467984	−	0.883737i	$-0.344981\pi$
$823$	26.8510	0.935967	0.467984	+	0.883737i	$0.344981\pi$
$824$	57.7447	2.01163
$825$	1.14799	0.0399678
$826$	−28.9055	−1.00575
$827$	−24.0270	−0.835502	−0.417751	−	0.908562i	$-0.637182\pi$
$827$	−24.0270	−0.835502	−0.417751	+	0.908562i	$0.637182\pi$
$828$	−22.6783	−0.788127
$829$	38.6281	1.34161	0.670805	−	0.741634i	$-0.265949\pi$
$829$	38.6281	1.34161	0.670805	+	0.741634i	$0.265949\pi$
$830$	−38.9241	−1.35108
$831$	−19.2638	−0.668254
$832$	−76.4025	−2.64878
$833$	−24.4499	−0.847138
$834$	−40.5888	−1.40547
$835$	15.7401	0.544709
$836$	−15.8069	−0.546694
$837$	−6.17187	−0.213331
$838$	3.02693	0.104563
$839$	49.6307	1.71344	0.856720	−	0.515781i	$-0.172498\pi$
$839$	49.6307	1.71344	0.856720	+	0.515781i	$0.172498\pi$
$840$	25.7882	0.889776
$841$	12.4742	0.430146
$842$	43.3221	1.49298
$843$	1.00514	0.0346190
$844$	−86.7692	−2.98672
$845$	−58.5559	−2.01438
$846$	−24.9054	−0.856265
$847$	3.26859	0.112310
$848$	7.37610	0.253296
$849$	14.9883	0.514399
$850$	17.6616	0.605790
$851$	44.3152	1.51911
$852$	−45.0620	−1.54380
$853$	1.49047	0.0510326	0.0255163	−	0.999674i	$-0.491877\pi$
$853$	1.49047	0.0510326	0.0255163	+	0.999674i	$0.491877\pi$
$854$	7.57633	0.259257
$855$	11.6206	0.397416
$856$	21.5870	0.737830
$857$	5.29697	0.180941	0.0904705	−	0.995899i	$-0.471163\pi$
$857$	5.29697	0.180941	0.0904705	+	0.995899i	$0.471163\pi$
$858$	−14.0260	−0.478839
$859$	−46.5876	−1.58955	−0.794774	−	0.606905i	$-0.792411\pi$
$859$	−46.5876	−1.58955	−0.794774	+	0.606905i	$0.792411\pi$
$860$	75.1097	2.56122
$861$	29.1325	0.992833
$862$	10.9255	0.372124
$863$	−56.2138	−1.91354	−0.956770	−	0.290847i	$-0.906063\pi$
$863$	−56.2138	−1.91354	−0.956770	+	0.290847i	$0.906063\pi$
$864$	4.90363	0.166825
$865$	26.9779	0.917276
$866$	62.6017	2.12729
$867$	27.0544	0.918817
$868$	−68.0397	−2.30942
$869$	−5.89560	−0.199995
$870$	−37.0130	−1.25486
$871$	19.8348	0.672076
$872$	5.04302	0.170778
$873$	8.49974	0.287673
$874$	−73.0443	−2.47076
$875$	31.2187	1.05538
$876$	−21.2352	−0.717472
$877$	14.3453	0.484408	0.242204	−	0.970225i	$-0.422130\pi$
$877$	14.3453	0.484408	0.242204	+	0.970225i	$0.422130\pi$
$878$	−65.0194	−2.19430
$879$	−32.8105	−1.10667
$880$	−1.56208	−0.0526576
$881$	23.0396	0.776225	0.388112	−	0.921612i	$-0.373127\pi$
$881$	23.0396	0.776225	0.388112	+	0.921612i	$0.373127\pi$
$882$	−8.53848	−0.287506
$883$	−19.9199	−0.670358	−0.335179	−	0.942155i	$-0.608797\pi$
$883$	−19.9199	−0.670358	−0.335179	+	0.942155i	$0.608797\pi$
$884$	−135.461	−4.55605
$885$	−9.45993	−0.317992
$886$	−29.2167	−0.981553
$887$	−7.91120	−0.265632	−0.132816	−	0.991141i	$-0.542402\pi$
$887$	−7.91120	−0.265632	−0.132816	+	0.991141i	$0.542402\pi$
$888$	20.9711	0.703743
$889$	38.1594	1.27982
$890$	−16.4755	−0.552260
$891$	1.00000	0.0335013
$892$	45.2661	1.51562
$893$	−50.3566	−1.68512
$894$	50.2698	1.68127
$895$	−53.8973	−1.80159
$896$	63.6045	2.12488
$897$	−40.6875	−1.35851
$898$	−23.0700	−0.769857
$899$	39.7471	1.32564
$900$	3.87189	0.129063
$901$	−77.7117	−2.58895
$902$	−20.6593	−0.687880
$903$	−29.3565	−0.976924
$904$	−2.04316	−0.0679544
$905$	7.06814	0.234953
$906$	28.6850	0.952994
$907$	−14.9038	−0.494872	−0.247436	−	0.968904i	$-0.579588\pi$
$907$	−14.9038	−0.494872	−0.247436	+	0.968904i	$0.579588\pi$
$908$	−74.7862	−2.48187
$909$	−4.21053	−0.139655
$910$	113.674	3.76825
$911$	−52.3222	−1.73351	−0.866756	−	0.498732i	$-0.833799\pi$
$911$	−52.3222	−1.73351	−0.866756	+	0.498732i	$0.833799\pi$
$912$	−2.95255	−0.0977687
$913$	−6.77257	−0.224139
$914$	−72.7980	−2.40794
$915$	2.47951	0.0819702
$916$	27.6805	0.914588
$917$	−21.6557	−0.715136
$918$	15.3849	0.507776
$919$	21.3325	0.703693	0.351846	−	0.936058i	$-0.385554\pi$
$919$	21.3325	0.703693	0.351846	+	0.936058i	$0.385554\pi$
$920$	−53.0501	−1.74901
$921$	7.14961	0.235588
$922$	−67.7215	−2.23029
$923$	−80.8462	−2.66109
$924$	11.0242	0.362669
$925$	−7.56598	−0.248768
$926$	61.1117	2.00826
$927$	−18.1476	−0.596045
$928$	−31.5796	−1.03665
$929$	22.5813	0.740867	0.370433	−	0.928859i	$-0.379209\pi$
$929$	22.5813	0.740867	0.370433	+	0.928859i	$0.379209\pi$
$930$	−35.4717	−1.16316
$931$	−17.2641	−0.565807
$932$	−52.3999	−1.71642
$933$	−18.8314	−0.616513
$934$	32.7875	1.07284
$935$	16.4574	0.538215
$936$	−19.2543	−0.629347
$937$	−34.3641	−1.12263	−0.561314	−	0.827603i	$-0.689704\pi$
$937$	−34.3641	−1.12263	−0.561314	+	0.827603i	$0.689704\pi$
$938$	−24.8343	−0.810868
$939$	23.7753	0.775876
$940$	−89.8559	−2.93078
$941$	−6.54597	−0.213393	−0.106696	−	0.994292i	$-0.534027\pi$
$941$	−6.54597	−0.213393	−0.106696	+	0.994292i	$0.534027\pi$
$942$	−15.3144	−0.498969
$943$	−59.9299	−1.95158
$944$	2.40357	0.0782296
$945$	−8.10451	−0.263640
$946$	20.8182	0.676858
$947$	−54.5844	−1.77375	−0.886877	−	0.462005i	$-0.847130\pi$
$947$	−54.5844	−1.77375	−0.886877	+	0.462005i	$0.847130\pi$
$948$	−19.8845	−0.645817
$949$	−38.0984	−1.23673
$950$	12.4709	0.404610
$951$	−15.5940	−0.505671
$952$	69.0317	2.23733
$953$	22.4941	0.728654	0.364327	−	0.931271i	$-0.381299\pi$
$953$	22.4941	0.728654	0.364327	+	0.931271i	$0.381299\pi$
$954$	−27.1388	−0.878650
$955$	−41.7830	−1.35207
$956$	25.3604	0.820213
$957$	−6.44005	−0.208177
$958$	−7.34696	−0.237369
$959$	−21.9860	−0.709967
$960$	31.3069	1.01042
$961$	7.09198	0.228774
$962$	92.4402	2.98039
$963$	−6.78421	−0.218618
$964$	−52.5612	−1.69288
$965$	0.121775	0.00392009
$966$	50.9431	1.63907
$967$	12.2301	0.393294	0.196647	−	0.980474i	$-0.436995\pi$
$967$	12.2301	0.393294	0.196647	+	0.980474i	$0.436995\pi$
$968$	−3.18195	−0.102272
$969$	31.1069	0.999297
$970$	48.8507	1.56850
$971$	43.7846	1.40511	0.702557	−	0.711627i	$-0.252041\pi$
$971$	43.7846	1.40511	0.702557	+	0.711627i	$0.252041\pi$
$972$	3.37276	0.108181
$973$	57.2358	1.83489
$974$	4.01480	0.128643
$975$	6.94660	0.222469
$976$	−0.629993	−0.0201656
$977$	31.3439	1.00278	0.501390	−	0.865221i	$-0.332822\pi$
$977$	31.3439	1.00278	0.501390	+	0.865221i	$0.332822\pi$
$978$	20.8071	0.665337
$979$	−2.86664	−0.0916183
$980$	−30.8059	−0.984058
$981$	−1.58488	−0.0506014
$982$	76.5877	2.44401
$983$	−44.4268	−1.41699	−0.708497	−	0.705713i	$-0.750627\pi$
$983$	−44.4268	−1.41699	−0.708497	+	0.705713i	$0.750627\pi$
$984$	−28.3603	−0.904094
$985$	−15.3287	−0.488413
$986$	−99.0792	−3.15533
$987$	35.1200	1.11788
$988$	−95.6493	−3.04301
$989$	60.3907	1.92031
$990$	5.74732	0.182662
$991$	8.16593	0.259399	0.129700	−	0.991553i	$-0.458599\pi$
$991$	8.16593	0.259399	0.129700	+	0.991553i	$0.458599\pi$
$992$	−30.2646	−0.960901
$993$	−18.3454	−0.582174
$994$	101.224	3.21064
$995$	19.0748	0.604713
$996$	−22.8422	−0.723784
$997$	−11.9667	−0.378989	−0.189494	−	0.981882i	$-0.560685\pi$
$997$	−11.9667	−0.378989	−0.189494	+	0.981882i	$0.560685\pi$
$998$	33.6056	1.06377
$999$	−6.59063	−0.208518

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2013.2.a.c.1.3	✓	12
3.2	odd	2		6039.2.a.f.1.10		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2013.2.a.c.1.3	✓	12	1.1	even	1	trivial
6039.2.a.f.1.10		12	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)

\(f(q)\)	\(=\)	\(q-2.31792 q^{2} +1.00000 q^{3} +3.37276 q^{4} -2.47951 q^{5} -2.31792 q^{6} +3.26859 q^{7} -3.18195 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-2.31792 q^{2} +1.00000 q^{3} +3.37276 q^{4} -2.47951 q^{5} -2.31792 q^{6} +3.26859 q^{7} -3.18195 q^{8} +1.00000 q^{9} +5.74732 q^{10} +1.00000 q^{11} +3.37276 q^{12} +6.05111 q^{13} -7.57633 q^{14} -2.47951 q^{15} +0.629993 q^{16} -6.63735 q^{17} -2.31792 q^{18} -4.68664 q^{19} -8.36281 q^{20} +3.26859 q^{21} -2.31792 q^{22} -6.72397 q^{23} -3.18195 q^{24} +1.14799 q^{25} -14.0260 q^{26} +1.00000 q^{27} +11.0242 q^{28} -6.44005 q^{29} +5.74732 q^{30} -6.17187 q^{31} +4.90363 q^{32} +1.00000 q^{33} +15.3849 q^{34} -8.10451 q^{35} +3.37276 q^{36} -6.59063 q^{37} +10.8633 q^{38} +6.05111 q^{39} +7.88969 q^{40} +8.91287 q^{41} -7.57633 q^{42} -8.98140 q^{43} +3.37276 q^{44} -2.47951 q^{45} +15.5856 q^{46} +10.7447 q^{47} +0.629993 q^{48} +3.68368 q^{49} -2.66095 q^{50} -6.63735 q^{51} +20.4089 q^{52} +11.7082 q^{53} -2.31792 q^{54} -2.47951 q^{55} -10.4005 q^{56} -4.68664 q^{57} +14.9275 q^{58} +3.81524 q^{59} -8.36281 q^{60} -1.00000 q^{61} +14.3059 q^{62} +3.26859 q^{63} -12.6262 q^{64} -15.0038 q^{65} -2.31792 q^{66} +3.27788 q^{67} -22.3862 q^{68} -6.72397 q^{69} +18.7856 q^{70} -13.3606 q^{71} -3.18195 q^{72} -6.29610 q^{73} +15.2766 q^{74} +1.14799 q^{75} -15.8069 q^{76} +3.26859 q^{77} -14.0260 q^{78} -5.89560 q^{79} -1.56208 q^{80} +1.00000 q^{81} -20.6593 q^{82} -6.77257 q^{83} +11.0242 q^{84} +16.4574 q^{85} +20.8182 q^{86} -6.44005 q^{87} -3.18195 q^{88} -2.86664 q^{89} +5.74732 q^{90} +19.7786 q^{91} -22.6783 q^{92} -6.17187 q^{93} -24.9054 q^{94} +11.6206 q^{95} +4.90363 q^{96} +8.49974 q^{97} -8.53848 q^{98} +1.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 7 q^{2} + 12 q^{3} + 13 q^{4} - 7 q^{5} - 7 q^{6} - 15 q^{7} - 18 q^{8} + 12 q^{9}+O(q^{10}) \) 12 * q - 7 * q^2 + 12 * q^3 + 13 * q^4 - 7 * q^5 - 7 * q^6 - 15 * q^7 - 18 * q^8 + 12 * q^9	\( 12 q - 7 q^{2} + 12 q^{3} + 13 q^{4} - 7 q^{5} - 7 q^{6} - 15 q^{7} - 18 q^{8} + 12 q^{9} - 6 q^{10} + 12 q^{11} + 13 q^{12} - 11 q^{13} + 3 q^{14} - 7 q^{15} + 19 q^{16} - 33 q^{17} - 7 q^{18} - 24 q^{19} - 11 q^{20} - 15 q^{21} - 7 q^{22} - 9 q^{23} - 18 q^{24} + 11 q^{25} - 16 q^{26} + 12 q^{27} - 41 q^{28} - 16 q^{29} - 6 q^{30} + q^{31} - 28 q^{32} + 12 q^{33} + 32 q^{34} - 22 q^{35} + 13 q^{36} - 6 q^{37} + 12 q^{38} - 11 q^{39} + 26 q^{40} - 21 q^{41} + 3 q^{42} - 39 q^{43} + 13 q^{44} - 7 q^{45} - 18 q^{47} + 19 q^{48} + 31 q^{49} - 44 q^{50} - 33 q^{51} + 3 q^{52} - 14 q^{53} - 7 q^{54} - 7 q^{55} + 16 q^{56} - 24 q^{57} + 33 q^{58} - 23 q^{59} - 11 q^{60} - 12 q^{61} - 25 q^{62} - 15 q^{63} + 12 q^{64} - 29 q^{65} - 7 q^{66} - 96 q^{68} - 9 q^{69} + 44 q^{70} - 19 q^{71} - 18 q^{72} - 42 q^{73} + 38 q^{74} + 11 q^{75} + 11 q^{76} - 15 q^{77} - 16 q^{78} - 11 q^{79} - 44 q^{80} + 12 q^{81} - 14 q^{82} - 56 q^{83} - 41 q^{84} + 16 q^{85} - 18 q^{86} - 16 q^{87} - 18 q^{88} - 55 q^{89} - 6 q^{90} + 11 q^{91} - 4 q^{92} + q^{93} - 5 q^{94} + 15 q^{95} - 28 q^{96} - 7 q^{97} + 6 q^{98} + 12 q^{99}+O(q^{100}) \) 12 * q - 7 * q^2 + 12 * q^3 + 13 * q^4 - 7 * q^5 - 7 * q^6 - 15 * q^7 - 18 * q^8 + 12 * q^9 - 6 * q^10 + 12 * q^11 + 13 * q^12 - 11 * q^13 + 3 * q^14 - 7 * q^15 + 19 * q^16 - 33 * q^17 - 7 * q^18 - 24 * q^19 - 11 * q^20 - 15 * q^21 - 7 * q^22 - 9 * q^23 - 18 * q^24 + 11 * q^25 - 16 * q^26 + 12 * q^27 - 41 * q^28 - 16 * q^29 - 6 * q^30 + q^31 - 28 * q^32 + 12 * q^33 + 32 * q^34 - 22 * q^35 + 13 * q^36 - 6 * q^37 + 12 * q^38 - 11 * q^39 + 26 * q^40 - 21 * q^41 + 3 * q^42 - 39 * q^43 + 13 * q^44 - 7 * q^45 - 18 * q^47 + 19 * q^48 + 31 * q^49 - 44 * q^50 - 33 * q^51 + 3 * q^52 - 14 * q^53 - 7 * q^54 - 7 * q^55 + 16 * q^56 - 24 * q^57 + 33 * q^58 - 23 * q^59 - 11 * q^60 - 12 * q^61 - 25 * q^62 - 15 * q^63 + 12 * q^64 - 29 * q^65 - 7 * q^66 - 96 * q^68 - 9 * q^69 + 44 * q^70 - 19 * q^71 - 18 * q^72 - 42 * q^73 + 38 * q^74 + 11 * q^75 + 11 * q^76 - 15 * q^77 - 16 * q^78 - 11 * q^79 - 44 * q^80 + 12 * q^81 - 14 * q^82 - 56 * q^83 - 41 * q^84 + 16 * q^85 - 18 * q^86 - 16 * q^87 - 18 * q^88 - 55 * q^89 - 6 * q^90 + 11 * q^91 - 4 * q^92 + q^93 - 5 * q^94 + 15 * q^95 - 28 * q^96 - 7 * q^97 + 6 * q^98 + 12 * q^99

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