LMFDB - Embedded newform 2013.2.a.d.1.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2013, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0, 0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("2013.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2013 = 3 \cdot 11 \cdot 61 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2013.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$16.0738859269$
Analytic rank:	$1$
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} - x^{11} - 16 x^{10} + 13 x^{9} + 93 x^{8} - 59 x^{7} - 238 x^{6} + 108 x^{5} + 257 x^{4} + \cdots + 1 $ x^12 - x^11 - 16x^10 + 13x^9 + 93x^8 - 59x^7 - 238x^6 + 108x^5 + 257x^4 - 71x^3 - 93x^2 + 13x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.5
Root			$-0.811354$ 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)

$f(q)$	$=$	$q-0.811354 q^{2} -1.00000 q^{3} -1.34170 q^{4} +0.350684 q^{5} +0.811354 q^{6} +3.06527 q^{7} +2.71131 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-0.811354 q^{2} -1.00000 q^{3} -1.34170 q^{4} +0.350684 q^{5} +0.811354 q^{6} +3.06527 q^{7} +2.71131 q^{8} +1.00000 q^{9} -0.284529 q^{10} -1.00000 q^{11} +1.34170 q^{12} -5.45552 q^{13} -2.48702 q^{14} -0.350684 q^{15} +0.483577 q^{16} -2.06199 q^{17} -0.811354 q^{18} +1.40317 q^{19} -0.470515 q^{20} -3.06527 q^{21} +0.811354 q^{22} +0.147981 q^{23} -2.71131 q^{24} -4.87702 q^{25} +4.42636 q^{26} -1.00000 q^{27} -4.11269 q^{28} +2.86506 q^{29} +0.284529 q^{30} +4.16462 q^{31} -5.81497 q^{32} +1.00000 q^{33} +1.67301 q^{34} +1.07494 q^{35} -1.34170 q^{36} -0.144684 q^{37} -1.13847 q^{38} +5.45552 q^{39} +0.950813 q^{40} +3.77643 q^{41} +2.48702 q^{42} +2.48169 q^{43} +1.34170 q^{44} +0.350684 q^{45} -0.120065 q^{46} -5.49942 q^{47} -0.483577 q^{48} +2.39589 q^{49} +3.95699 q^{50} +2.06199 q^{51} +7.31969 q^{52} -4.06954 q^{53} +0.811354 q^{54} -0.350684 q^{55} +8.31089 q^{56} -1.40317 q^{57} -2.32458 q^{58} +3.27787 q^{59} +0.470515 q^{60} -1.00000 q^{61} -3.37898 q^{62} +3.06527 q^{63} +3.75084 q^{64} -1.91317 q^{65} -0.811354 q^{66} -12.0165 q^{67} +2.76658 q^{68} -0.147981 q^{69} -0.872160 q^{70} +10.3117 q^{71} +2.71131 q^{72} -5.13147 q^{73} +0.117390 q^{74} +4.87702 q^{75} -1.88264 q^{76} -3.06527 q^{77} -4.42636 q^{78} -7.67884 q^{79} +0.169583 q^{80} +1.00000 q^{81} -3.06402 q^{82} +15.8628 q^{83} +4.11269 q^{84} -0.723108 q^{85} -2.01353 q^{86} -2.86506 q^{87} -2.71131 q^{88} +3.35464 q^{89} -0.284529 q^{90} -16.7227 q^{91} -0.198547 q^{92} -4.16462 q^{93} +4.46198 q^{94} +0.492070 q^{95} +5.81497 q^{96} -5.17684 q^{97} -1.94392 q^{98} -1.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + q^{2} - 12 q^{3} + 9 q^{4} - 3 q^{5} - q^{6} - 9 q^{7} + 6 q^{8} + 12 q^{9}+O(q^{10}) $ 12 * q + q^2 - 12 * q^3 + 9 * q^4 - 3 * q^5 - q^6 - 9 * q^7 + 6 * q^8 + 12 * q^9	\( 12 q + q^{2} - 12 q^{3} + 9 q^{4} - 3 q^{5} - q^{6} - 9 q^{7} + 6 q^{8} + 12 q^{9} - 8 q^{10} - 12 q^{11} - 9 q^{12} - q^{13} - 3 q^{14} + 3 q^{15} + 3 q^{16} + 9 q^{17} + q^{18} - 20 q^{19} - 9 q^{20} + 9 q^{21} - q^{22} - 9 q^{23} - 6 q^{24} + 3 q^{25} - 18 q^{26} - 12 q^{27} - 31 q^{28} + 18 q^{29} + 8 q^{30} - 21 q^{31} + 18 q^{32} + 12 q^{33} - 12 q^{34} - 4 q^{35} + 9 q^{36} - 18 q^{37} - 2 q^{38} + q^{39} - 26 q^{40} + 15 q^{41} + 3 q^{42} - 33 q^{43} - 9 q^{44} - 3 q^{45} - 28 q^{46} - 20 q^{47} - 3 q^{48} + 15 q^{49} - 2 q^{50} - 9 q^{51} - 27 q^{52} - q^{54} + 3 q^{55} - 8 q^{56} + 20 q^{57} - 11 q^{58} - 21 q^{59} + 9 q^{60} - 12 q^{61} - 9 q^{62} - 9 q^{63} - 12 q^{64} + 17 q^{65} + q^{66} - 34 q^{67} - 16 q^{68} + 9 q^{69} - 36 q^{70} - 5 q^{71} + 6 q^{72} - 2 q^{73} + 6 q^{74} - 3 q^{75} - 27 q^{76} + 9 q^{77} + 18 q^{78} - 31 q^{79} - 60 q^{80} + 12 q^{81} - 12 q^{82} - 32 q^{83} + 31 q^{84} - 40 q^{85} + 18 q^{86} - 18 q^{87} - 6 q^{88} + 27 q^{89} - 8 q^{90} - 45 q^{91} - 78 q^{92} + 21 q^{93} - 13 q^{94} + 37 q^{95} - 18 q^{96} - 19 q^{97} + 4 q^{98} - 12 q^{99}+O(q^{100}) \) 12 * q + q^2 - 12 * q^3 + 9 * q^4 - 3 * q^5 - q^6 - 9 * q^7 + 6 * q^8 + 12 * q^9 - 8 * q^10 - 12 * q^11 - 9 * q^12 - q^13 - 3 * q^14 + 3 * q^15 + 3 * q^16 + 9 * q^17 + q^18 - 20 * q^19 - 9 * q^20 + 9 * q^21 - q^22 - 9 * q^23 - 6 * q^24 + 3 * q^25 - 18 * q^26 - 12 * q^27 - 31 * q^28 + 18 * q^29 + 8 * q^30 - 21 * q^31 + 18 * q^32 + 12 * q^33 - 12 * q^34 - 4 * q^35 + 9 * q^36 - 18 * q^37 - 2 * q^38 + q^39 - 26 * q^40 + 15 * q^41 + 3 * q^42 - 33 * q^43 - 9 * q^44 - 3 * q^45 - 28 * q^46 - 20 * q^47 - 3 * q^48 + 15 * q^49 - 2 * q^50 - 9 * q^51 - 27 * q^52 - q^54 + 3 * q^55 - 8 * q^56 + 20 * q^57 - 11 * q^58 - 21 * q^59 + 9 * q^60 - 12 * q^61 - 9 * q^62 - 9 * q^63 - 12 * q^64 + 17 * q^65 + q^66 - 34 * q^67 - 16 * q^68 + 9 * q^69 - 36 * q^70 - 5 * q^71 + 6 * q^72 - 2 * q^73 + 6 * q^74 - 3 * q^75 - 27 * q^76 + 9 * q^77 + 18 * q^78 - 31 * q^79 - 60 * q^80 + 12 * q^81 - 12 * q^82 - 32 * q^83 + 31 * q^84 - 40 * q^85 + 18 * q^86 - 18 * q^87 - 6 * q^88 + 27 * q^89 - 8 * q^90 - 45 * q^91 - 78 * q^92 + 21 * q^93 - 13 * q^94 + 37 * q^95 - 18 * q^96 - 19 * q^97 + 4 * 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 $

$2$	−0.811354	−0.573714	−0.286857	−	0.957973i	$-0.592610\pi$
$2$	−0.811354	−0.573714	−0.286857	+	0.957973i	$0.592610\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	−1.34170	−0.670852
$5$	0.350684	0.156831	0.0784154	−	0.996921i	$-0.475014\pi$
$5$	0.350684	0.156831	0.0784154	+	0.996921i	$0.475014\pi$
$6$	0.811354	0.331234
$7$	3.06527	1.15856	0.579282	−	0.815127i	$-0.303333\pi$
$7$	3.06527	1.15856	0.579282	+	0.815127i	$0.303333\pi$
$8$	2.71131	0.958592
$9$	1.00000	0.333333
$10$	−0.284529	−0.0899761
$11$	−1.00000	−0.301511
$11$	−1.00000	−0.301511
$12$	1.34170	0.387317
$13$	−5.45552	−1.51309	−0.756544	−	0.653942i	$-0.773114\pi$
$13$	−5.45552	−1.51309	−0.756544	+	0.653942i	$0.773114\pi$
$14$	−2.48702	−0.664685
$15$	−0.350684	−0.0905463
$16$	0.483577	0.120894
$17$	−2.06199	−0.500106	−0.250053	−	0.968232i	$-0.580448\pi$
$17$	−2.06199	−0.500106	−0.250053	+	0.968232i	$0.580448\pi$
$18$	−0.811354	−0.191238
$19$	1.40317	0.321910	0.160955	−	0.986962i	$-0.448543\pi$
$19$	1.40317	0.321910	0.160955	+	0.986962i	$0.448543\pi$
$20$	−0.470515	−0.105210
$21$	−3.06527	−0.668897
$22$	0.811354	0.172981
$23$	0.147981	0.0308562	0.0154281	−	0.999881i	$-0.495089\pi$
$23$	0.147981	0.0308562	0.0154281	+	0.999881i	$0.495089\pi$
$24$	−2.71131	−0.553443
$25$	−4.87702	−0.975404
$26$	4.42636	0.868080
$27$	−1.00000	−0.192450
$28$	−4.11269	−0.777225
$29$	2.86506	0.532028	0.266014	−	0.963969i	$-0.414293\pi$
$29$	2.86506	0.532028	0.266014	+	0.963969i	$0.414293\pi$
$30$	0.284529	0.0519477
$31$	4.16462	0.747988	0.373994	−	0.927431i	$-0.377988\pi$
$31$	4.16462	0.747988	0.373994	+	0.927431i	$0.377988\pi$
$32$	−5.81497	−1.02795
$33$	1.00000	0.174078
$34$	1.67301	0.286918
$35$	1.07494	0.181699
$36$	−1.34170	−0.223617
$37$	−0.144684	−0.0237860	−0.0118930	−	0.999929i	$-0.503786\pi$
$37$	−0.144684	−0.0237860	−0.0118930	+	0.999929i	$0.503786\pi$
$38$	−1.13847	−0.184684
$39$	5.45552	0.873582
$40$	0.950813	0.150337
$41$	3.77643	0.589779	0.294890	−	0.955531i	$-0.404717\pi$
$41$	3.77643	0.589779	0.294890	+	0.955531i	$0.404717\pi$
$42$	2.48702	0.383756
$43$	2.48169	0.378454	0.189227	−	0.981933i	$-0.439402\pi$
$43$	2.48169	0.378454	0.189227	+	0.981933i	$0.439402\pi$
$44$	1.34170	0.202269
$45$	0.350684	0.0522769
$46$	−0.120065	−0.0177027
$47$	−5.49942	−0.802173	−0.401087	−	0.916040i	$-0.631367\pi$
$47$	−5.49942	−0.802173	−0.401087	+	0.916040i	$0.631367\pi$
$48$	−0.483577	−0.0697984
$49$	2.39589	0.342271
$50$	3.95699	0.559603
$51$	2.06199	0.288736
$52$	7.31969	1.01506
$53$	−4.06954	−0.558995	−0.279497	−	0.960146i	$-0.590168\pi$
$53$	−4.06954	−0.558995	−0.279497	+	0.960146i	$0.590168\pi$
$54$	0.811354	0.110411
$55$	−0.350684	−0.0472863
$56$	8.31089	1.11059
$57$	−1.40317	−0.185855
$58$	−2.32458	−0.305232
$59$	3.27787	0.426742	0.213371	−	0.976971i	$-0.431556\pi$
$59$	3.27787	0.426742	0.213371	+	0.976971i	$0.431556\pi$
$60$	0.470515	0.0607432
$61$	−1.00000	−0.128037
$61$	−1.00000	−0.128037
$62$	−3.37898	−0.429131
$63$	3.06527	0.386188
$64$	3.75084	0.468855
$65$	−1.91317	−0.237299
$66$	−0.811354	−0.0998708
$67$	−12.0165	−1.46804	−0.734022	−	0.679126i	$-0.762359\pi$
$67$	−12.0165	−1.46804	−0.734022	+	0.679126i	$0.762359\pi$
$68$	2.76658	0.335497
$69$	−0.147981	−0.0178148
$70$	−0.872160	−0.104243
$71$	10.3117	1.22378	0.611888	−	0.790944i	$-0.290410\pi$
$71$	10.3117	1.22378	0.611888	+	0.790944i	$0.290410\pi$
$72$	2.71131	0.319531
$73$	−5.13147	−0.600593	−0.300296	−	0.953846i	$-0.597086\pi$
$73$	−5.13147	−0.600593	−0.300296	+	0.953846i	$0.597086\pi$
$74$	0.117390	0.0136463
$75$	4.87702	0.563150
$76$	−1.88264	−0.215954
$77$	−3.06527	−0.349320
$78$	−4.42636	−0.501186
$79$	−7.67884	−0.863937	−0.431968	−	0.901889i	$-0.642181\pi$
$79$	−7.67884	−0.863937	−0.431968	+	0.901889i	$0.642181\pi$
$80$	0.169583	0.0189600
$81$	1.00000	0.111111
$82$	−3.06402	−0.338365
$83$	15.8628	1.74117	0.870585	−	0.492017i	$-0.163740\pi$
$83$	15.8628	1.74117	0.870585	+	0.492017i	$0.163740\pi$
$84$	4.11269	0.448731
$85$	−0.723108	−0.0784321
$86$	−2.01353	−0.217124
$87$	−2.86506	−0.307167
$88$	−2.71131	−0.289026
$89$	3.35464	0.355591	0.177796	−	0.984067i	$-0.443103\pi$
$89$	3.35464	0.355591	0.177796	+	0.984067i	$0.443103\pi$
$90$	−0.284529	−0.0299920
$91$	−16.7227	−1.75301
$92$	−0.198547	−0.0207000
$93$	−4.16462	−0.431851
$94$	4.46198	0.460218
$95$	0.492070	0.0504854
$96$	5.81497	0.593487
$97$	−5.17684	−0.525628	−0.262814	−	0.964847i	$-0.584651\pi$
$97$	−5.17684	−0.525628	−0.262814	+	0.964847i	$0.584651\pi$
$98$	−1.94392	−0.196366
$99$	−1.00000	−0.100504
$100$	6.54352	0.654352
$101$	−8.46305	−0.842105	−0.421053	−	0.907036i	$-0.638339\pi$
$101$	−8.46305	−0.842105	−0.421053	+	0.907036i	$0.638339\pi$
$102$	−1.67301	−0.165652
$103$	7.06816	0.696447	0.348223	−	0.937412i	$-0.386785\pi$
$103$	7.06816	0.696447	0.348223	+	0.937412i	$0.386785\pi$
$104$	−14.7916	−1.45043
$105$	−1.07494	−0.104904
$106$	3.30184	0.320703
$107$	−11.9968	−1.15978	−0.579889	−	0.814696i	$-0.696904\pi$
$107$	−11.9968	−1.15978	−0.579889	+	0.814696i	$0.696904\pi$
$108$	1.34170	0.129106
$109$	−5.28742	−0.506443	−0.253222	−	0.967408i	$-0.581490\pi$
$109$	−5.28742	−0.506443	−0.253222	+	0.967408i	$0.581490\pi$
$110$	0.284529	0.0271288
$111$	0.144684	0.0137328
$112$	1.48230	0.140064
$113$	−7.22992	−0.680133	−0.340067	−	0.940401i	$-0.610450\pi$
$113$	−7.22992	−0.680133	−0.340067	+	0.940401i	$0.610450\pi$
$114$	1.13847	0.106627
$115$	0.0518947	0.00483921
$116$	−3.84406	−0.356912
$117$	−5.45552	−0.504363
$118$	−2.65952	−0.244828
$119$	−6.32056	−0.579405
$120$	−0.950813	−0.0867969
$121$	1.00000	0.0909091
$122$	0.811354	0.0734566
$123$	−3.77643	−0.340509
$124$	−5.58769	−0.501789
$125$	−3.46372	−0.309804
$126$	−2.48702	−0.221562
$127$	−19.2693	−1.70988	−0.854939	−	0.518729i	$-0.826405\pi$
$127$	−19.2693	−1.70988	−0.854939	+	0.518729i	$0.826405\pi$
$128$	8.58667	0.758961
$129$	−2.48169	−0.218500
$130$	1.55226	0.136142
$131$	−19.0697	−1.66613	−0.833063	−	0.553178i	$-0.813415\pi$
$131$	−19.0697	−1.66613	−0.833063	+	0.553178i	$0.813415\pi$
$132$	−1.34170	−0.116780
$133$	4.30110	0.372953
$134$	9.74960	0.842238
$135$	−0.350684	−0.0301821
$136$	−5.59069	−0.479398
$137$	−5.26924	−0.450182	−0.225091	−	0.974338i	$-0.572268\pi$
$137$	−5.26924	−0.450182	−0.225091	+	0.974338i	$0.572268\pi$
$138$	0.120065	0.0102206
$139$	−14.8768	−1.26184	−0.630918	−	0.775849i	$-0.717322\pi$
$139$	−14.8768	−1.26184	−0.630918	+	0.775849i	$0.717322\pi$
$140$	−1.44226	−0.121893
$141$	5.49942	0.463135
$142$	−8.36646	−0.702098
$143$	5.45552	0.456213
$144$	0.483577	0.0402981
$145$	1.00473	0.0834385
$146$	4.16344	0.344569
$147$	−2.39589	−0.197610
$148$	0.194124	0.0159569
$149$	−23.4135	−1.91811	−0.959054	−	0.283222i	$-0.908597\pi$
$149$	−23.4135	−1.91811	−0.959054	+	0.283222i	$0.908597\pi$
$150$	−3.95699	−0.323087
$151$	−11.9086	−0.969111	−0.484556	−	0.874761i	$-0.661019\pi$
$151$	−11.9086	−0.969111	−0.484556	+	0.874761i	$0.661019\pi$
$152$	3.80443	0.308580
$153$	−2.06199	−0.166702
$154$	2.48702	0.200410
$155$	1.46047	0.117308
$156$	−7.31969	−0.586044
$157$	−12.0808	−0.964150	−0.482075	−	0.876130i	$-0.660117\pi$
$157$	−12.0808	−0.964150	−0.482075	+	0.876130i	$0.660117\pi$
$158$	6.23026	0.495653
$159$	4.06954	0.322736
$160$	−2.03922	−0.161214
$161$	0.453603	0.0357489
$162$	−0.811354	−0.0637460
$163$	−1.04500	−0.0818510	−0.0409255	−	0.999162i	$-0.513031\pi$
$163$	−1.04500	−0.0818510	−0.0409255	+	0.999162i	$0.513031\pi$
$164$	−5.06685	−0.395654
$165$	0.350684	0.0273007
$166$	−12.8704	−0.998935
$167$	3.91541	0.302983	0.151492	−	0.988459i	$-0.451592\pi$
$167$	3.91541	0.302983	0.151492	+	0.988459i	$0.451592\pi$
$168$	−8.31089	−0.641199
$169$	16.7627	1.28944
$170$	0.586697	0.0449976
$171$	1.40317	0.107303
$172$	−3.32969	−0.253886
$173$	6.91306	0.525590	0.262795	−	0.964852i	$-0.415356\pi$
$173$	6.91306	0.525590	0.262795	+	0.964852i	$0.415356\pi$
$174$	2.32458	0.176226
$175$	−14.9494	−1.13007
$176$	−0.483577	−0.0364510
$177$	−3.27787	−0.246380
$178$	−2.72180	−0.204008
$179$	−8.22908	−0.615070	−0.307535	−	0.951537i	$-0.599504\pi$
$179$	−8.22908	−0.615070	−0.307535	+	0.951537i	$0.599504\pi$
$180$	−0.470515	−0.0350701
$181$	−20.2042	−1.50177	−0.750883	−	0.660435i	$-0.770372\pi$
$181$	−20.2042	−1.50177	−0.750883	+	0.660435i	$0.770372\pi$
$182$	13.5680	1.00573
$183$	1.00000	0.0739221
$184$	0.401223	0.0295785
$185$	−0.0507386	−0.00373037
$186$	3.37898	0.247759
$187$	2.06199	0.150788
$188$	7.37860	0.538140
$189$	−3.06527	−0.222966
$190$	−0.399243	−0.0289642
$191$	18.4767	1.33693	0.668463	−	0.743745i	$-0.266952\pi$
$191$	18.4767	1.33693	0.668463	+	0.743745i	$0.266952\pi$
$192$	−3.75084	−0.270694
$193$	−15.8196	−1.13872	−0.569359	−	0.822089i	$-0.692808\pi$
$193$	−15.8196	−1.13872	−0.569359	+	0.822089i	$0.692808\pi$
$194$	4.20025	0.301560
$195$	1.91317	0.137005
$196$	−3.21458	−0.229613
$197$	14.3733	1.02405	0.512026	−	0.858970i	$-0.328895\pi$
$197$	14.3733	1.02405	0.512026	+	0.858970i	$0.328895\pi$
$198$	0.811354	0.0576605
$199$	−8.22066	−0.582747	−0.291374	−	0.956609i	$-0.594112\pi$
$199$	−8.22066	−0.582747	−0.291374	+	0.956609i	$0.594112\pi$
$200$	−13.2231	−0.935014
$201$	12.0165	0.847575
$202$	6.86653	0.483128
$203$	8.78219	0.616389
$204$	−2.76658	−0.193699
$205$	1.32433	0.0924955
$206$	−5.73479	−0.399562
$207$	0.147981	0.0102854
$208$	−2.63817	−0.182924
$209$	−1.40317	−0.0970594
$210$	0.872160	0.0601848
$211$	12.6667	0.872013	0.436007	−	0.899943i	$-0.356392\pi$
$211$	12.6667	0.872013	0.436007	+	0.899943i	$0.356392\pi$
$212$	5.46012	0.375003
$213$	−10.3117	−0.706548
$214$	9.73368	0.665381
$215$	0.870289	0.0593532
$216$	−2.71131	−0.184481
$217$	12.7657	0.866592
$218$	4.28997	0.290554
$219$	5.13147	0.346752
$220$	0.470515	0.0317221
$221$	11.2492	0.756705
$222$	−0.117390	−0.00787872
$223$	0.384419	0.0257426	0.0128713	−	0.999917i	$-0.495903\pi$
$223$	0.384419	0.0257426	0.0128713	+	0.999917i	$0.495903\pi$
$224$	−17.8245	−1.19095
$225$	−4.87702	−0.325135
$226$	5.86603	0.390202
$227$	10.5003	0.696930	0.348465	−	0.937322i	$-0.386703\pi$
$227$	10.5003	0.696930	0.348465	+	0.937322i	$0.386703\pi$
$228$	1.88264	0.124681
$229$	15.4219	1.01911	0.509555	−	0.860438i	$-0.329810\pi$
$229$	15.4219	1.01911	0.509555	+	0.860438i	$0.329810\pi$
$230$	−0.0421050	−0.00277632
$231$	3.06527	0.201680
$232$	7.76806	0.509998
$233$	12.1580	0.796496	0.398248	−	0.917278i	$-0.369618\pi$
$233$	12.1580	0.796496	0.398248	+	0.917278i	$0.369618\pi$
$234$	4.42636	0.289360
$235$	−1.92856	−0.125806
$236$	−4.39793	−0.286281
$237$	7.67884	0.498794
$238$	5.12822	0.332413
$239$	−5.12659	−0.331612	−0.165806	−	0.986158i	$-0.553023\pi$
$239$	−5.12659	−0.331612	−0.165806	+	0.986158i	$0.553023\pi$
$240$	−0.169583	−0.0109465
$241$	4.26966	0.275033	0.137516	−	0.990499i	$-0.456088\pi$
$241$	4.26966	0.275033	0.137516	+	0.990499i	$0.456088\pi$
$242$	−0.811354	−0.0521558
$243$	−1.00000	−0.0641500
$244$	1.34170	0.0858938
$245$	0.840203	0.0536786
$246$	3.06402	0.195355
$247$	−7.65503	−0.487078
$248$	11.2916	0.717015
$249$	−15.8628	−1.00527
$250$	2.81030	0.177739
$251$	24.4387	1.54256	0.771278	−	0.636498i	$-0.219618\pi$
$251$	24.4387	1.54256	0.771278	+	0.636498i	$0.219618\pi$
$252$	−4.11269	−0.259075
$253$	−0.147981	−0.00930350
$254$	15.6343	0.980981
$255$	0.723108	0.0452828
$256$	−14.4685	−0.904282
$257$	−11.0393	−0.688616	−0.344308	−	0.938857i	$-0.611886\pi$
$257$	−11.0393	−0.688616	−0.344308	+	0.938857i	$0.611886\pi$
$258$	2.01353	0.125357
$259$	−0.443497	−0.0275576
$260$	2.56690	0.159192
$261$	2.86506	0.177343
$262$	15.4723	0.955880
$263$	13.5468	0.835331	0.417665	−	0.908601i	$-0.362848\pi$
$263$	13.5468	0.835331	0.417665	+	0.908601i	$0.362848\pi$
$264$	2.71131	0.166869
$265$	−1.42713	−0.0876676
$266$	−3.48972	−0.213968
$267$	−3.35464	−0.205301
$268$	16.1225	0.984840
$269$	−8.89405	−0.542280	−0.271140	−	0.962540i	$-0.587401\pi$
$269$	−8.89405	−0.542280	−0.271140	+	0.962540i	$0.587401\pi$
$270$	0.284529	0.0173159
$271$	−28.9586	−1.75911	−0.879555	−	0.475798i	$-0.842159\pi$
$271$	−28.9586	−1.75911	−0.879555	+	0.475798i	$0.842159\pi$
$272$	−0.997132	−0.0604600
$273$	16.7227	1.01210
$274$	4.27522	0.258276
$275$	4.87702	0.294095
$276$	0.198547	0.0119511
$277$	16.3364	0.981558	0.490779	−	0.871284i	$-0.336712\pi$
$277$	16.3364	0.981558	0.490779	+	0.871284i	$0.336712\pi$
$278$	12.0704	0.723934
$279$	4.16462	0.249329
$280$	2.91450	0.174175
$281$	21.1539	1.26194	0.630968	−	0.775809i	$-0.282658\pi$
$281$	21.1539	1.26194	0.630968	+	0.775809i	$0.282658\pi$
$282$	−4.46198	−0.265707
$283$	−29.7641	−1.76929	−0.884646	−	0.466263i	$-0.845600\pi$
$283$	−29.7641	−1.76929	−0.884646	+	0.466263i	$0.845600\pi$
$284$	−13.8353	−0.820973
$285$	−0.492070	−0.0291477
$286$	−4.42636	−0.261736
$287$	11.5758	0.683297
$288$	−5.81497	−0.342650
$289$	−12.7482	−0.749894
$290$	−0.815194	−0.0478698
$291$	5.17684	0.303471
$292$	6.88491	0.402909
$293$	14.1561	0.827006	0.413503	−	0.910503i	$-0.364305\pi$
$293$	14.1561	0.827006	0.413503	+	0.910503i	$0.364305\pi$
$294$	1.94392	0.113372
$295$	1.14950	0.0669264
$296$	−0.392284	−0.0228010
$297$	1.00000	0.0580259
$298$	18.9966	1.10045
$299$	−0.807314	−0.0466882
$300$	−6.54352	−0.377790
$301$	7.60704	0.438463
$302$	9.66213	0.555993
$303$	8.46305	0.486190
$304$	0.678542	0.0389170
$305$	−0.350684	−0.0200801
$306$	1.67301	0.0956394
$307$	−27.2699	−1.55638	−0.778188	−	0.628032i	$-0.783861\pi$
$307$	−27.2699	−1.55638	−0.778188	+	0.628032i	$0.783861\pi$
$308$	4.11269	0.234342
$309$	−7.06816	−0.402094
$310$	−1.18496	−0.0673010
$311$	4.17556	0.236774	0.118387	−	0.992968i	$-0.462228\pi$
$311$	4.17556	0.236774	0.118387	+	0.992968i	$0.462228\pi$
$312$	14.7916	0.837408
$313$	−3.37580	−0.190812	−0.0954059	−	0.995438i	$-0.530415\pi$
$313$	−3.37580	−0.190812	−0.0954059	+	0.995438i	$0.530415\pi$
$314$	9.80179	0.553147
$315$	1.07494	0.0605662
$316$	10.3027	0.579574
$317$	−16.3928	−0.920711	−0.460355	−	0.887735i	$-0.652278\pi$
$317$	−16.3928	−0.920711	−0.460355	+	0.887735i	$0.652278\pi$
$318$	−3.30184	−0.185158
$319$	−2.86506	−0.160413
$320$	1.31536	0.0735310
$321$	11.9968	0.669598
$322$	−0.368033	−0.0205097
$323$	−2.89333	−0.160989
$324$	−1.34170	−0.0745391
$325$	26.6067	1.47587
$326$	0.847868	0.0469591
$327$	5.28742	0.292395
$328$	10.2391	0.565357
$329$	−16.8572	−0.929369
$330$	−0.284529	−0.0156628
$331$	−5.86712	−0.322486	−0.161243	−	0.986915i	$-0.551550\pi$
$331$	−5.86712	−0.322486	−0.161243	+	0.986915i	$0.551550\pi$
$332$	−21.2832	−1.16807
$333$	−0.144684	−0.00792866
$334$	−3.17678	−0.173826
$335$	−4.21398	−0.230235
$336$	−1.48230	−0.0808659
$337$	21.3314	1.16199	0.580997	−	0.813906i	$-0.302663\pi$
$337$	21.3314	1.16199	0.580997	+	0.813906i	$0.302663\pi$
$338$	−13.6005	−0.739768
$339$	7.22992	0.392675
$340$	0.970197	0.0526163
$341$	−4.16462	−0.225527
$342$	−1.13847	−0.0615614
$343$	−14.1128	−0.762022
$344$	6.72861	0.362782
$345$	−0.0518947	−0.00279392
$346$	−5.60894	−0.301539
$347$	−35.8160	−1.92270	−0.961351	−	0.275327i	$-0.911214\pi$
$347$	−35.8160	−1.92270	−0.961351	+	0.275327i	$0.911214\pi$
$348$	3.84406	0.206063
$349$	−12.5671	−0.672701	−0.336351	−	0.941737i	$-0.609193\pi$
$349$	−12.5671	−0.672701	−0.336351	+	0.941737i	$0.609193\pi$
$350$	12.1293	0.648336
$351$	5.45552	0.291194
$352$	5.81497	0.309939
$353$	15.3693	0.818023	0.409012	−	0.912529i	$-0.365874\pi$
$353$	15.3693	0.818023	0.409012	+	0.912529i	$0.365874\pi$
$354$	2.65952	0.141352
$355$	3.61616	0.191926
$356$	−4.50094	−0.238549
$357$	6.32056	0.334520
$358$	6.67670	0.352874
$359$	15.4909	0.817580	0.408790	−	0.912629i	$-0.365951\pi$
$359$	15.4909	0.817580	0.408790	+	0.912629i	$0.365951\pi$
$360$	0.950813	0.0501122
$361$	−17.0311	−0.896374
$362$	16.3928	0.861585
$363$	−1.00000	−0.0524864
$364$	22.4368	1.17601
$365$	−1.79953	−0.0941915
$366$	−0.811354	−0.0424102
$367$	−23.8478	−1.24485	−0.622423	−	0.782681i	$-0.713852\pi$
$367$	−23.8478	−1.24485	−0.622423	+	0.782681i	$0.713852\pi$
$368$	0.0715604	0.00373034
$369$	3.77643	0.196593
$370$	0.0411670	0.00214017
$371$	−12.4743	−0.647631
$372$	5.58769	0.289708
$373$	10.7371	0.555945	0.277973	−	0.960589i	$-0.410338\pi$
$373$	10.7371	0.555945	0.277973	+	0.960589i	$0.410338\pi$
$374$	−1.67301	−0.0865091
$375$	3.46372	0.178866
$376$	−14.9106	−0.768957
$377$	−15.6304	−0.805006
$378$	2.48702	0.127919
$379$	10.4369	0.536108	0.268054	−	0.963404i	$-0.413619\pi$
$379$	10.4369	0.536108	0.268054	+	0.963404i	$0.413619\pi$
$380$	−0.660213	−0.0338682
$381$	19.2693	0.987198
$382$	−14.9911	−0.767014
$383$	−32.7915	−1.67557	−0.837784	−	0.546002i	$-0.816149\pi$
$383$	−32.7915	−1.67557	−0.837784	+	0.546002i	$0.816149\pi$
$384$	−8.58667	−0.438187
$385$	−1.07494	−0.0547842
$386$	12.8353	0.653298
$387$	2.48169	0.126151
$388$	6.94578	0.352619
$389$	3.79669	0.192500	0.0962499	−	0.995357i	$-0.469315\pi$
$389$	3.79669	0.192500	0.0962499	+	0.995357i	$0.469315\pi$
$390$	−1.55226	−0.0786015
$391$	−0.305136	−0.0154314
$392$	6.49600	0.328098
$393$	19.0697	0.961939
$394$	−11.6618	−0.587513
$395$	−2.69285	−0.135492
$396$	1.34170	0.0674232
$397$	−5.74208	−0.288187	−0.144093	−	0.989564i	$-0.546027\pi$
$397$	−5.74208	−0.288187	−0.144093	+	0.989564i	$0.546027\pi$
$398$	6.66987	0.334330
$399$	−4.30110	−0.215324
$400$	−2.35842	−0.117921
$401$	12.8703	0.642710	0.321355	−	0.946959i	$-0.395862\pi$
$401$	12.8703	0.642710	0.321355	+	0.946959i	$0.395862\pi$
$402$	−9.74960	−0.486266
$403$	−22.7202	−1.13177
$404$	11.3549	0.564928
$405$	0.350684	0.0174256
$406$	−7.12547	−0.353631
$407$	0.144684	0.00717174
$408$	5.59069	0.276780
$409$	17.6215	0.871328	0.435664	−	0.900109i	$-0.356514\pi$
$409$	17.6215	0.871328	0.435664	+	0.900109i	$0.356514\pi$
$410$	−1.07450	−0.0530660
$411$	5.26924	0.259912
$412$	−9.48338	−0.467213
$413$	10.0476	0.494409
$414$	−0.120065	−0.00590089
$415$	5.56284	0.273069
$416$	31.7237	1.55538
$417$	14.8768	0.728522
$418$	1.13847	0.0556844
$419$	−10.1071	−0.493762	−0.246881	−	0.969046i	$-0.579406\pi$
$419$	−10.1071	−0.493762	−0.246881	+	0.969046i	$0.579406\pi$
$420$	1.44226	0.0703749
$421$	−6.08544	−0.296586	−0.148293	−	0.988943i	$-0.547378\pi$
$421$	−6.08544	−0.296586	−0.148293	+	0.988943i	$0.547378\pi$
$422$	−10.2772	−0.500286
$423$	−5.49942	−0.267391
$424$	−11.0338	−0.535848
$425$	10.0564	0.487806
$426$	8.36646	0.405356
$427$	−3.06527	−0.148339
$428$	16.0962	0.778039
$429$	−5.45552	−0.263395
$430$	−0.706113	−0.0340518
$431$	10.2081	0.491707	0.245853	−	0.969307i	$-0.420932\pi$
$431$	10.2081	0.491707	0.245853	+	0.969307i	$0.420932\pi$
$432$	−0.483577	−0.0232661
$433$	−2.53260	−0.121709	−0.0608545	−	0.998147i	$-0.519383\pi$
$433$	−2.53260	−0.121709	−0.0608545	+	0.998147i	$0.519383\pi$
$434$	−10.3575	−0.497176
$435$	−1.00473	−0.0481732
$436$	7.09416	0.339748
$437$	0.207643	0.00993291
$438$	−4.16344	−0.198937
$439$	37.0940	1.77040	0.885201	−	0.465209i	$-0.154021\pi$
$439$	37.0940	1.77040	0.885201	+	0.465209i	$0.154021\pi$
$440$	−0.950813	−0.0453282
$441$	2.39589	0.114090
$442$	−9.12711	−0.434132
$443$	6.46823	0.307315	0.153657	−	0.988124i	$-0.450895\pi$
$443$	6.46823	0.307315	0.153657	+	0.988124i	$0.450895\pi$
$444$	−0.194124	−0.00921270
$445$	1.17642	0.0557677
$446$	−0.311900	−0.0147689
$447$	23.4135	1.10742
$448$	11.4974	0.543199
$449$	17.8163	0.840801	0.420400	−	0.907339i	$-0.361890\pi$
$449$	17.8163	0.840801	0.420400	+	0.907339i	$0.361890\pi$
$450$	3.95699	0.186534
$451$	−3.77643	−0.177825
$452$	9.70041	0.456269
$453$	11.9086	0.559517
$454$	−8.51948	−0.399839
$455$	−5.86437	−0.274926
$456$	−3.80443	−0.178159
$457$	35.0188	1.63811	0.819055	−	0.573715i	$-0.194498\pi$
$457$	35.0188	1.63811	0.819055	+	0.573715i	$0.194498\pi$
$458$	−12.5127	−0.584678
$459$	2.06199	0.0962455
$460$	−0.0696274	−0.00324639
$461$	0.991967	0.0462005	0.0231002	−	0.999733i	$-0.492646\pi$
$461$	0.991967	0.0462005	0.0231002	+	0.999733i	$0.492646\pi$
$462$	−2.48702	−0.115707
$463$	−15.6278	−0.726286	−0.363143	−	0.931733i	$-0.618296\pi$
$463$	−15.6278	−0.726286	−0.363143	+	0.931733i	$0.618296\pi$
$464$	1.38548	0.0643192
$465$	−1.46047	−0.0677275
$466$	−9.86443	−0.456961
$467$	−25.6358	−1.18628	−0.593142	−	0.805098i	$-0.702113\pi$
$467$	−25.6358	−1.18628	−0.593142	+	0.805098i	$0.702113\pi$
$468$	7.31969	0.338353
$469$	−36.8337	−1.70082
$470$	1.56475	0.0721764
$471$	12.0808	0.556652
$472$	8.88731	0.409072
$473$	−2.48169	−0.114108
$474$	−6.23026	−0.286165
$475$	−6.84330	−0.313992
$476$	8.48032	0.388695
$477$	−4.06954	−0.186332
$478$	4.15948	0.190250
$479$	23.4825	1.07294	0.536472	−	0.843918i	$-0.319757\pi$
$479$	23.4825	1.07294	0.536472	+	0.843918i	$0.319757\pi$
$480$	2.03922	0.0930771
$481$	0.789328	0.0359903
$482$	−3.46420	−0.157790
$483$	−0.453603	−0.0206396
$484$	−1.34170	−0.0609865
$485$	−1.81544	−0.0824347
$486$	0.811354	0.0368038
$487$	−5.68347	−0.257543	−0.128771	−	0.991674i	$-0.541103\pi$
$487$	−5.68347	−0.257543	−0.128771	+	0.991674i	$0.541103\pi$
$488$	−2.71131	−0.122735
$489$	1.04500	0.0472567
$490$	−0.681702	−0.0307962
$491$	1.93005	0.0871018	0.0435509	−	0.999051i	$-0.486133\pi$
$491$	1.93005	0.0871018	0.0435509	+	0.999051i	$0.486133\pi$
$492$	5.06685	0.228431
$493$	−5.90773	−0.266071
$494$	6.21094	0.279443
$495$	−0.350684	−0.0157621
$496$	2.01392	0.0904275
$497$	31.6082	1.41782
$498$	12.8704	0.576735
$499$	4.02644	0.180248	0.0901242	−	0.995931i	$-0.471274\pi$
$499$	4.02644	0.180248	0.0901242	+	0.995931i	$0.471274\pi$
$500$	4.64728	0.207833
$501$	−3.91541	−0.174928
$502$	−19.8284	−0.884987
$503$	−2.06560	−0.0921004	−0.0460502	−	0.998939i	$-0.514663\pi$
$503$	−2.06560	−0.0921004	−0.0460502	+	0.998939i	$0.514663\pi$
$504$	8.31089	0.370197
$505$	−2.96786	−0.132068
$506$	0.120065	0.00533755
$507$	−16.7627	−0.744457
$508$	25.8537	1.14707
$509$	−31.3994	−1.39175	−0.695876	−	0.718162i	$-0.744984\pi$
$509$	−31.3994	−1.39175	−0.695876	+	0.718162i	$0.744984\pi$
$510$	−0.586697	−0.0259794
$511$	−15.7293	−0.695825
$512$	−5.43424	−0.240162
$513$	−1.40317	−0.0619515
$514$	8.95683	0.395069
$515$	2.47870	0.109224
$516$	3.32969	0.146581
$517$	5.49942	0.241864
$518$	0.359833	0.0158102
$519$	−6.91306	−0.303450
$520$	−5.18718	−0.227473
$521$	17.7173	0.776210	0.388105	−	0.921615i	$-0.373130\pi$
$521$	17.7173	0.776210	0.388105	+	0.921615i	$0.373130\pi$
$522$	−2.32458	−0.101744
$523$	−7.36710	−0.322141	−0.161070	−	0.986943i	$-0.551495\pi$
$523$	−7.36710	−0.322141	−0.161070	+	0.986943i	$0.551495\pi$
$524$	25.5859	1.11772
$525$	14.9494	0.652445
$526$	−10.9912	−0.479241
$527$	−8.58741	−0.374073
$528$	0.483577	0.0210450
$529$	−22.9781	−0.999048
$530$	1.15790	0.0502962
$531$	3.27787	0.142247
$532$	−5.77081	−0.250196
$533$	−20.6024	−0.892388
$534$	2.72180	0.117784
$535$	−4.20710	−0.181889
$536$	−32.5803	−1.40725
$537$	8.22908	0.355111
$538$	7.21623	0.311114
$539$	−2.39589	−0.103198
$540$	0.470515	0.0202477
$541$	4.67387	0.200945	0.100473	−	0.994940i	$-0.467965\pi$
$541$	4.67387	0.200945	0.100473	+	0.994940i	$0.467965\pi$
$542$	23.4957	1.00923
$543$	20.2042	0.867045
$544$	11.9904	0.514084
$545$	−1.85422	−0.0794259
$546$	−13.5680	−0.580657
$547$	15.6137	0.667596	0.333798	−	0.942645i	$-0.391670\pi$
$547$	15.6137	0.667596	0.333798	+	0.942645i	$0.391670\pi$
$548$	7.06976	0.302005
$549$	−1.00000	−0.0426790
$550$	−3.95699	−0.168727
$551$	4.02017	0.171265
$552$	−0.401223	−0.0170772
$553$	−23.5377	−1.00093
$554$	−13.2546	−0.563134
$555$	0.0507386	0.00215373
$556$	19.9603	0.846506
$557$	32.6435	1.38315	0.691575	−	0.722304i	$-0.256917\pi$
$557$	32.6435	1.38315	0.691575	+	0.722304i	$0.256917\pi$
$558$	−3.37898	−0.143044
$559$	−13.5389	−0.572634
$560$	0.519818	0.0219663
$561$	−2.06199	−0.0870573
$562$	−17.1633	−0.723991
$563$	−44.4977	−1.87535	−0.937676	−	0.347509i	$-0.887027\pi$
$563$	−44.4977	−1.87535	−0.937676	+	0.347509i	$0.887027\pi$
$564$	−7.37860	−0.310695
$565$	−2.53542	−0.106666
$566$	24.1492	1.01507
$567$	3.06527	0.128729
$568$	27.9582	1.17310
$569$	−14.4354	−0.605162	−0.302581	−	0.953124i	$-0.597848\pi$
$569$	−14.4354	−0.605162	−0.302581	+	0.953124i	$0.597848\pi$
$570$	0.399243	0.0167225
$571$	27.2352	1.13976	0.569879	−	0.821729i	$-0.306990\pi$
$571$	27.2352	1.13976	0.569879	+	0.821729i	$0.306990\pi$
$572$	−7.31969	−0.306052
$573$	−18.4767	−0.771875
$574$	−9.39206	−0.392017
$575$	−0.721708	−0.0300973
$576$	3.75084	0.156285
$577$	18.4252	0.767050	0.383525	−	0.923531i	$-0.374710\pi$
$577$	18.4252	0.767050	0.383525	+	0.923531i	$0.374710\pi$
$578$	10.3433	0.430225
$579$	15.8196	0.657439
$580$	−1.34805	−0.0559749
$581$	48.6239	2.01726
$582$	−4.20025	−0.174106
$583$	4.06954	0.168543
$584$	−13.9130	−0.575723
$585$	−1.91317	−0.0790997
$586$	−11.4856	−0.474465
$587$	−17.0540	−0.703893	−0.351946	−	0.936020i	$-0.614480\pi$
$587$	−17.0540	−0.703893	−0.351946	+	0.936020i	$0.614480\pi$
$588$	3.21458	0.132567
$589$	5.84367	0.240784
$590$	−0.932651	−0.0383966
$591$	−14.3733	−0.591237
$592$	−0.0699661	−0.00287559
$593$	8.28898	0.340388	0.170194	−	0.985411i	$-0.445561\pi$
$593$	8.28898	0.340388	0.170194	+	0.985411i	$0.445561\pi$
$594$	−0.811354	−0.0332903
$595$	−2.21652	−0.0908686
$596$	31.4140	1.28677
$597$	8.22066	0.336449
$598$	0.655018	0.0267857
$599$	16.6039	0.678418	0.339209	−	0.940711i	$-0.389841\pi$
$599$	16.6039	0.678418	0.339209	+	0.940711i	$0.389841\pi$
$600$	13.2231	0.539831
$601$	28.2882	1.15390	0.576950	−	0.816780i	$-0.304243\pi$
$601$	28.2882	1.15390	0.576950	+	0.816780i	$0.304243\pi$
$602$	−6.17201	−0.251552
$603$	−12.0165	−0.489348
$604$	15.9779	0.650130
$605$	0.350684	0.0142573
$606$	−6.86653	−0.278934
$607$	15.1496	0.614901	0.307451	−	0.951564i	$-0.400524\pi$
$607$	15.1496	0.614901	0.307451	+	0.951564i	$0.400524\pi$
$608$	−8.15939	−0.330907
$609$	−8.78219	−0.355872
$610$	0.284529	0.0115203
$611$	30.0022	1.21376
$612$	2.76658	0.111832
$613$	−38.2662	−1.54556	−0.772779	−	0.634675i	$-0.781134\pi$
$613$	−38.2662	−1.54556	−0.772779	+	0.634675i	$0.781134\pi$
$614$	22.1256	0.892915
$615$	−1.32433	−0.0534023
$616$	−8.31089	−0.334855
$617$	16.9404	0.681994	0.340997	−	0.940064i	$-0.389235\pi$
$617$	16.9404	0.681994	0.340997	+	0.940064i	$0.389235\pi$
$618$	5.73479	0.230687
$619$	−42.4150	−1.70480	−0.852401	−	0.522889i	$-0.824854\pi$
$619$	−42.4150	−1.70480	−0.852401	+	0.522889i	$0.824854\pi$
$620$	−1.95951	−0.0786960
$621$	−0.147981	−0.00593828
$622$	−3.38786	−0.135841
$623$	10.2829	0.411975
$624$	2.63817	0.105611
$625$	23.1704	0.926817
$626$	2.73897	0.109471
$627$	1.40317	0.0560373
$628$	16.2088	0.646802
$629$	0.298338	0.0118955
$630$	−0.872160	−0.0347477
$631$	−10.5987	−0.421927	−0.210963	−	0.977494i	$-0.567660\pi$
$631$	−10.5987	−0.421927	−0.210963	+	0.977494i	$0.567660\pi$
$632$	−20.8197	−0.828162
$633$	−12.6667	−0.503457
$634$	13.3004	0.528225
$635$	−6.75746	−0.268161
$636$	−5.46012	−0.216508
$637$	−13.0708	−0.517886
$638$	2.32458	0.0920310
$639$	10.3117	0.407925
$640$	3.01121	0.119029
$641$	−13.4569	−0.531515	−0.265758	−	0.964040i	$-0.585622\pi$
$641$	−13.4569	−0.531515	−0.265758	+	0.964040i	$0.585622\pi$
$642$	−9.73368	−0.384158
$643$	41.9992	1.65629	0.828143	−	0.560517i	$-0.189398\pi$
$643$	41.9992	1.65629	0.828143	+	0.560517i	$0.189398\pi$
$644$	−0.608601	−0.0239822
$645$	−0.870289	−0.0342676
$646$	2.34751	0.0923617
$647$	−22.4826	−0.883883	−0.441941	−	0.897044i	$-0.645710\pi$
$647$	−22.4826	−0.883883	−0.441941	+	0.897044i	$0.645710\pi$
$648$	2.71131	0.106510
$649$	−3.27787	−0.128668
$650$	−21.5874	−0.846729
$651$	−12.7657	−0.500327
$652$	1.40208	0.0549099
$653$	−32.6465	−1.27756	−0.638779	−	0.769390i	$-0.720560\pi$
$653$	−32.6465	−1.27756	−0.638779	+	0.769390i	$0.720560\pi$
$654$	−4.28997	−0.167751
$655$	−6.68744	−0.261300
$656$	1.82620	0.0713009
$657$	−5.13147	−0.200198
$658$	13.6772	0.533192
$659$	−44.5231	−1.73437	−0.867186	−	0.497984i	$-0.834074\pi$
$659$	−44.5231	−1.73437	−0.867186	+	0.497984i	$0.834074\pi$
$660$	−0.470515	−0.0183148
$661$	22.1696	0.862297	0.431149	−	0.902281i	$-0.358108\pi$
$661$	22.1696	0.862297	0.431149	+	0.902281i	$0.358108\pi$
$662$	4.76031	0.185015
$663$	−11.2492	−0.436884
$664$	43.0090	1.66907
$665$	1.50833	0.0584905
$666$	0.117390	0.00454878
$667$	0.423975	0.0164164
$668$	−5.25332	−0.203257
$669$	−0.384419	−0.0148625
$670$	3.41903	0.132089
$671$	1.00000	0.0386046
$672$	17.8245	0.687593
$673$	37.7568	1.45542	0.727708	−	0.685887i	$-0.240585\pi$
$673$	37.7568	1.45542	0.727708	+	0.685887i	$0.240585\pi$
$674$	−17.3073	−0.666652
$675$	4.87702	0.187717
$676$	−22.4906	−0.865021
$677$	−20.5477	−0.789711	−0.394855	−	0.918743i	$-0.629205\pi$
$677$	−20.5477	−0.789711	−0.394855	+	0.918743i	$0.629205\pi$
$678$	−5.86603	−0.225283
$679$	−15.8684	−0.608974
$680$	−1.96057	−0.0751843
$681$	−10.5003	−0.402373
$682$	3.37898	0.129388
$683$	−5.07792	−0.194301	−0.0971506	−	0.995270i	$-0.530973\pi$
$683$	−5.07792	−0.194301	−0.0971506	+	0.995270i	$0.530973\pi$
$684$	−1.88264	−0.0719846
$685$	−1.84784	−0.0706024
$686$	11.4505	0.437183
$687$	−15.4219	−0.588384
$688$	1.20009	0.0457529
$689$	22.2015	0.845808
$690$	0.0421050	0.00160291
$691$	34.7498	1.32194	0.660972	−	0.750410i	$-0.270144\pi$
$691$	34.7498	1.32194	0.660972	+	0.750410i	$0.270144\pi$
$692$	−9.27528	−0.352593
$693$	−3.06527	−0.116440
$694$	29.0594	1.10308
$695$	−5.21707	−0.197895
$696$	−7.76806	−0.294447
$697$	−7.78696	−0.294952
$698$	10.1964	0.385938
$699$	−12.1580	−0.459857
$700$	20.0577	0.758108
$701$	−6.15899	−0.232622	−0.116311	−	0.993213i	$-0.537107\pi$
$701$	−6.15899	−0.232622	−0.116311	+	0.993213i	$0.537107\pi$
$702$	−4.42636	−0.167062
$703$	−0.203017	−0.00765693
$704$	−3.75084	−0.141365
$705$	1.92856	0.0726339
$706$	−12.4699	−0.469312
$707$	−25.9416	−0.975633
$708$	4.39793	0.165284
$709$	5.81568	0.218412	0.109206	−	0.994019i	$-0.465169\pi$
$709$	5.81568	0.218412	0.109206	+	0.994019i	$0.465169\pi$
$710$	−2.93399	−0.110111
$711$	−7.67884	−0.287979
$712$	9.09546	0.340867
$713$	0.616286	0.0230801
$714$	−5.12822	−0.191919
$715$	1.91317	0.0715483
$716$	11.0410	0.412621
$717$	5.12659	0.191456
$718$	−12.5686	−0.469057
$719$	−22.1738	−0.826944	−0.413472	−	0.910517i	$-0.635684\pi$
$719$	−22.1738	−0.826944	−0.413472	+	0.910517i	$0.635684\pi$
$720$	0.169583	0.00631999
$721$	21.6659	0.806878
$722$	13.8183	0.514263
$723$	−4.26966	−0.158790
$724$	27.1081	1.00746
$725$	−13.9730	−0.518943
$726$	0.811354	0.0301122
$727$	−25.0474	−0.928955	−0.464478	−	0.885585i	$-0.653758\pi$
$727$	−25.0474	−0.928955	−0.464478	+	0.885585i	$0.653758\pi$
$728$	−45.3402	−1.68042
$729$	1.00000	0.0370370
$730$	1.46005	0.0540390
$731$	−5.11721	−0.189267
$732$	−1.34170	−0.0495908
$733$	1.09363	0.0403940	0.0201970	−	0.999796i	$-0.493571\pi$
$733$	1.09363	0.0403940	0.0201970	+	0.999796i	$0.493571\pi$
$734$	19.3490	0.714186
$735$	−0.840203	−0.0309914
$736$	−0.860506	−0.0317187
$737$	12.0165	0.442632
$738$	−3.06402	−0.112788
$739$	35.5704	1.30848	0.654239	−	0.756288i	$-0.272989\pi$
$739$	35.5704	1.30848	0.654239	+	0.756288i	$0.272989\pi$
$740$	0.0680761	0.00250253
$741$	7.65503	0.281214
$742$	10.1210	0.371555
$743$	42.9021	1.57392	0.786962	−	0.617001i	$-0.211653\pi$
$743$	42.9021	1.57392	0.786962	+	0.617001i	$0.211653\pi$
$744$	−11.2916	−0.413969
$745$	−8.21075	−0.300819
$746$	−8.71158	−0.318954
$747$	15.8628	0.580390
$748$	−2.76658	−0.101156
$749$	−36.7736	−1.34368
$750$	−2.81030	−0.102618
$751$	24.4082	0.890667	0.445333	−	0.895365i	$-0.353085\pi$
$751$	24.4082	0.890667	0.445333	+	0.895365i	$0.353085\pi$
$752$	−2.65940	−0.0969782
$753$	−24.4387	−0.890595
$754$	12.6818	0.461843
$755$	−4.17617	−0.151987
$756$	4.11269	0.149577
$757$	−0.348726	−0.0126747	−0.00633733	−	0.999980i	$-0.502017\pi$
$757$	−0.348726	−0.0126747	−0.00633733	+	0.999980i	$0.502017\pi$
$758$	−8.46803	−0.307573
$759$	0.147981	0.00537138
$760$	1.33415	0.0483948
$761$	18.6006	0.674271	0.337135	−	0.941456i	$-0.390542\pi$
$761$	18.6006	0.674271	0.337135	+	0.941456i	$0.390542\pi$
$762$	−15.6343	−0.566370
$763$	−16.2074	−0.586747
$764$	−24.7903	−0.896880
$765$	−0.723108	−0.0261440
$766$	26.6055	0.961297
$767$	−17.8825	−0.645699
$768$	14.4685	0.522088
$769$	11.4172	0.411714	0.205857	−	0.978582i	$-0.434002\pi$
$769$	11.4172	0.411714	0.205857	+	0.978582i	$0.434002\pi$
$770$	0.872160	0.0314305
$771$	11.0393	0.397572
$772$	21.2252	0.763911
$773$	−19.2564	−0.692604	−0.346302	−	0.938123i	$-0.612563\pi$
$773$	−19.2564	−0.692604	−0.346302	+	0.938123i	$0.612563\pi$
$774$	−2.01353	−0.0723747
$775$	−20.3109	−0.729590
$776$	−14.0360	−0.503863
$777$	0.443497	0.0159104
$778$	−3.08046	−0.110440
$779$	5.29898	0.189856
$780$	−2.56690	−0.0919098
$781$	−10.3117	−0.368982
$782$	0.247573	0.00885321
$783$	−2.86506	−0.102389
$784$	1.15860	0.0413786
$785$	−4.23654	−0.151209
$786$	−15.4723	−0.551878
$787$	−28.7433	−1.02459	−0.512294	−	0.858810i	$-0.671204\pi$
$787$	−28.7433	−1.02459	−0.512294	+	0.858810i	$0.671204\pi$
$788$	−19.2846	−0.686987
$789$	−13.5468	−0.482278
$790$	2.18485	0.0777336
$791$	−22.1617	−0.787978
$792$	−2.71131	−0.0963421
$793$	5.45552	0.193731
$794$	4.65886	0.165337
$795$	1.42713	0.0506149
$796$	11.0297	0.390937
$797$	15.3196	0.542647	0.271323	−	0.962488i	$-0.412539\pi$
$797$	15.3196	0.542647	0.271323	+	0.962488i	$0.412539\pi$
$798$	3.48972	0.123535
$799$	11.3398	0.401172
$800$	28.3597	1.00267
$801$	3.35464	0.118530
$802$	−10.4423	−0.368732
$803$	5.13147	0.181086
$804$	−16.1225	−0.568598
$805$	0.159071	0.00560653
$806$	18.4341	0.649314
$807$	8.89405	0.313086
$808$	−22.9459	−0.807235
$809$	−14.8613	−0.522494	−0.261247	−	0.965272i	$-0.584134\pi$
$809$	−14.8613	−0.522494	−0.261247	+	0.965272i	$0.584134\pi$
$810$	−0.284529	−0.00999734
$811$	−43.3181	−1.52110	−0.760552	−	0.649277i	$-0.775071\pi$
$811$	−43.3181	−1.52110	−0.760552	+	0.649277i	$0.775071\pi$
$812$	−11.7831	−0.413506
$813$	28.9586	1.01562
$814$	−0.117390	−0.00411453
$815$	−0.366466	−0.0128368
$816$	0.997132	0.0349066
$817$	3.48223	0.121828
$818$	−14.2973	−0.499893
$819$	−16.7227	−0.584337
$820$	−1.77686	−0.0620508
$821$	42.6323	1.48788	0.743939	−	0.668248i	$-0.232956\pi$
$821$	42.6323	1.48788	0.743939	+	0.668248i	$0.232956\pi$
$822$	−4.27522	−0.149115
$823$	44.1113	1.53762	0.768811	−	0.639476i	$-0.220849\pi$
$823$	44.1113	1.53762	0.768811	+	0.639476i	$0.220849\pi$
$824$	19.1640	0.667608
$825$	−4.87702	−0.169796
$826$	−8.15214	−0.283649
$827$	−0.210906	−0.00733390	−0.00366695	−	0.999993i	$-0.501167\pi$
$827$	−0.210906	−0.00733390	−0.00366695	+	0.999993i	$0.501167\pi$
$828$	−0.198547	−0.00689999
$829$	19.5308	0.678332	0.339166	−	0.940727i	$-0.389855\pi$
$829$	19.5308	0.678332	0.339166	+	0.940727i	$0.389855\pi$
$830$	−4.51344	−0.156664
$831$	−16.3364	−0.566703
$832$	−20.4628	−0.709420
$833$	−4.94031	−0.171172
$834$	−12.0704	−0.417963
$835$	1.37307	0.0475171
$836$	1.88264	0.0651125
$837$	−4.16462	−0.143950
$838$	8.20041	0.283278
$839$	−51.4138	−1.77500	−0.887501	−	0.460806i	$-0.847560\pi$
$839$	−51.4138	−1.77500	−0.887501	+	0.460806i	$0.847560\pi$
$840$	−2.91450	−0.100560
$841$	−20.7914	−0.716946
$842$	4.93745	0.170156
$843$	−21.1539	−0.728579
$844$	−16.9950	−0.584992
$845$	5.87841	0.202223
$846$	4.46198	0.153406
$847$	3.06527	0.105324
$848$	−1.96794	−0.0675793
$849$	29.7641	1.02150
$850$	−8.15928	−0.279861
$851$	−0.0214106	−0.000733945 0
$852$	13.8353	0.473989
$853$	28.7095	0.982994	0.491497	−	0.870879i	$-0.336450\pi$
$853$	28.7095	0.982994	0.491497	+	0.870879i	$0.336450\pi$
$854$	2.48702	0.0851042
$855$	0.492070	0.0168285
$856$	−32.5271	−1.11175
$857$	−29.3799	−1.00360	−0.501799	−	0.864985i	$-0.667328\pi$
$857$	−29.3799	−1.00360	−0.501799	+	0.864985i	$0.667328\pi$
$858$	4.42636	0.151113
$859$	11.3543	0.387405	0.193702	−	0.981060i	$-0.437950\pi$
$859$	11.3543	0.387405	0.193702	+	0.981060i	$0.437950\pi$
$860$	−1.16767	−0.0398172
$861$	−11.5758	−0.394502
$862$	−8.28239	−0.282099
$863$	13.4097	0.456471	0.228235	−	0.973606i	$-0.426704\pi$
$863$	13.4097	0.456471	0.228235	+	0.973606i	$0.426704\pi$
$864$	5.81497	0.197829
$865$	2.42430	0.0824288
$866$	2.05484	0.0698262
$867$	12.7482	0.432951
$868$	−17.1278	−0.581355
$869$	7.67884	0.260487
$870$	0.815194	0.0276377
$871$	65.5560	2.22128
$872$	−14.3358	−0.485472
$873$	−5.17684	−0.175209
$874$	−0.168472	−0.00569865
$875$	−10.6172	−0.358928
$876$	−6.88491	−0.232620
$877$	30.9542	1.04525	0.522624	−	0.852563i	$-0.324953\pi$
$877$	30.9542	1.04525	0.522624	+	0.852563i	$0.324953\pi$
$878$	−30.0964	−1.01570
$879$	−14.1561	−0.477472
$880$	−0.169583	−0.00571664
$881$	21.7719	0.733515	0.366757	−	0.930317i	$-0.380468\pi$
$881$	21.7719	0.733515	0.366757	+	0.930317i	$0.380468\pi$
$882$	−1.94392	−0.0654552
$883$	−12.9715	−0.436527	−0.218264	−	0.975890i	$-0.570039\pi$
$883$	−12.9715	−0.436527	−0.218264	+	0.975890i	$0.570039\pi$
$884$	−15.0931	−0.507637
$885$	−1.14950	−0.0386400
$886$	−5.24803	−0.176311
$887$	19.9273	0.669092	0.334546	−	0.942379i	$-0.391417\pi$
$887$	19.9273	0.669092	0.334546	+	0.942379i	$0.391417\pi$
$888$	0.392284	0.0131642
$889$	−59.0658	−1.98100
$890$	−0.954494	−0.0319947
$891$	−1.00000	−0.0335013
$892$	−0.515777	−0.0172695
$893$	−7.71664	−0.258227
$894$	−18.9966	−0.635343
$895$	−2.88581	−0.0964620
$896$	26.3205	0.879305
$897$	0.807314	0.0269554
$898$	−14.4553	−0.482379
$899$	11.9319	0.397951
$900$	6.54352	0.218117
$901$	8.39136	0.279557
$902$	3.06402	0.102021
$903$	−7.60704	−0.253147
$904$	−19.6025	−0.651970
$905$	−7.08530	−0.235523
$906$	−9.66213	−0.321003
$907$	−31.0013	−1.02938	−0.514691	−	0.857376i	$-0.672093\pi$
$907$	−31.0013	−1.02938	−0.514691	+	0.857376i	$0.672093\pi$
$908$	−14.0883	−0.467537
$909$	−8.46305	−0.280702
$910$	4.75809	0.157729
$911$	−31.3158	−1.03754	−0.518770	−	0.854914i	$-0.673610\pi$
$911$	−31.3158	−1.03754	−0.518770	+	0.854914i	$0.673610\pi$
$912$	−0.678542	−0.0224688
$913$	−15.8628	−0.524983
$914$	−28.4126	−0.939807
$915$	0.350684	0.0115933
$916$	−20.6917	−0.683673
$917$	−58.4538	−1.93031
$918$	−1.67301	−0.0552174
$919$	22.9889	0.758333	0.379166	−	0.925329i	$-0.376211\pi$
$919$	22.9889	0.758333	0.379166	+	0.925329i	$0.376211\pi$
$920$	0.140702	0.00463882
$921$	27.2699	0.898574
$922$	−0.804837	−0.0265059
$923$	−56.2558	−1.85168
$924$	−4.11269	−0.135298
$925$	0.705629	0.0232009
$926$	12.6797	0.416681
$927$	7.06816	0.232149
$928$	−16.6602	−0.546899
$929$	26.5210	0.870125	0.435063	−	0.900400i	$-0.356726\pi$
$929$	26.5210	0.870125	0.435063	+	0.900400i	$0.356726\pi$
$930$	1.18496	0.0388563
$931$	3.36185	0.110180
$932$	−16.3124	−0.534331
$933$	−4.17556	−0.136702
$934$	20.7997	0.680588
$935$	0.723108	0.0236482
$936$	−14.7916	−0.483478
$937$	−25.2739	−0.825663	−0.412831	−	0.910807i	$-0.635460\pi$
$937$	−25.2739	−0.825663	−0.412831	+	0.910807i	$0.635460\pi$
$938$	29.8852	0.975786
$939$	3.37580	0.110165
$940$	2.58756	0.0843969
$941$	10.3509	0.337429	0.168715	−	0.985665i	$-0.446038\pi$
$941$	10.3509	0.337429	0.168715	+	0.985665i	$0.446038\pi$
$942$	−9.80179	−0.319359
$943$	0.558841	0.0181984
$944$	1.58510	0.0515907
$945$	−1.07494	−0.0349679
$946$	2.01353	0.0654654
$947$	7.06389	0.229545	0.114773	−	0.993392i	$-0.463386\pi$
$947$	7.06389	0.229545	0.114773	+	0.993392i	$0.463386\pi$
$948$	−10.3027	−0.334617
$949$	27.9948	0.908750
$950$	5.55234	0.180142
$951$	16.3928	0.531572
$952$	−17.1370	−0.555413
$953$	14.0331	0.454578	0.227289	−	0.973827i	$-0.427014\pi$
$953$	14.0331	0.454578	0.227289	+	0.973827i	$0.427014\pi$
$954$	3.30184	0.106901
$955$	6.47949	0.209671
$956$	6.87837	0.222462
$957$	2.86506	0.0926143
$958$	−19.0526	−0.615563
$959$	−16.1517	−0.521564
$960$	−1.31536	−0.0424531
$961$	−13.6559	−0.440514
$962$	−0.640425	−0.0206481
$963$	−11.9968	−0.386593
$964$	−5.72861	−0.184506
$965$	−5.54768	−0.178586
$966$	0.368033	0.0118413
$967$	28.8586	0.928029	0.464015	−	0.885827i	$-0.346408\pi$
$967$	28.8586	0.928029	0.464015	+	0.885827i	$0.346408\pi$
$968$	2.71131	0.0871447
$969$	2.89333	0.0929470
$970$	1.47296	0.0472940
$971$	11.5064	0.369259	0.184630	−	0.982808i	$-0.440891\pi$
$971$	11.5064	0.369259	0.184630	+	0.982808i	$0.440891\pi$
$972$	1.34170	0.0430352
$973$	−45.6016	−1.46192
$974$	4.61131	0.147756
$975$	−26.6067	−0.852096
$976$	−0.483577	−0.0154789
$977$	48.8381	1.56247	0.781234	−	0.624238i	$-0.214590\pi$
$977$	48.8381	1.56247	0.781234	+	0.624238i	$0.214590\pi$
$978$	−0.847868	−0.0271118
$979$	−3.35464	−0.107215
$980$	−1.12730	−0.0360104
$981$	−5.28742	−0.168814
$982$	−1.56595	−0.0499716
$983$	19.1197	0.609823	0.304911	−	0.952381i	$-0.401373\pi$
$983$	19.1197	0.609823	0.304911	+	0.952381i	$0.401373\pi$
$984$	−10.2391	−0.326409
$985$	5.04048	0.160603
$986$	4.79326	0.152649
$987$	16.8572	0.536572
$988$	10.2708	0.326757
$989$	0.367243	0.0116776
$990$	0.284529	0.00904294
$991$	30.2963	0.962393	0.481197	−	0.876613i	$-0.340202\pi$
$991$	30.2963	0.962393	0.481197	+	0.876613i	$0.340202\pi$
$992$	−24.2171	−0.768894
$993$	5.86712	0.186187
$994$	−25.6455	−0.813425
$995$	−2.88286	−0.0913928
$996$	21.2832	0.674384
$997$	44.3179	1.40356	0.701782	−	0.712392i	$-0.252388\pi$
$997$	44.3179	1.40356	0.701782	+	0.712392i	$0.252388\pi$
$998$	−3.26687	−0.103411
$999$	0.144684	0.00457761

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2013.2.a.d.1.5	✓	12
3.2	odd	2		6039.2.a.e.1.8		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2013.2.a.d.1.5	✓	12	1.1	even	1	trivial
6039.2.a.e.1.8		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)

\(f(q)\)	\(=\)	\(q-0.811354 q^{2} -1.00000 q^{3} -1.34170 q^{4} +0.350684 q^{5} +0.811354 q^{6} +3.06527 q^{7} +2.71131 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-0.811354 q^{2} -1.00000 q^{3} -1.34170 q^{4} +0.350684 q^{5} +0.811354 q^{6} +3.06527 q^{7} +2.71131 q^{8} +1.00000 q^{9} -0.284529 q^{10} -1.00000 q^{11} +1.34170 q^{12} -5.45552 q^{13} -2.48702 q^{14} -0.350684 q^{15} +0.483577 q^{16} -2.06199 q^{17} -0.811354 q^{18} +1.40317 q^{19} -0.470515 q^{20} -3.06527 q^{21} +0.811354 q^{22} +0.147981 q^{23} -2.71131 q^{24} -4.87702 q^{25} +4.42636 q^{26} -1.00000 q^{27} -4.11269 q^{28} +2.86506 q^{29} +0.284529 q^{30} +4.16462 q^{31} -5.81497 q^{32} +1.00000 q^{33} +1.67301 q^{34} +1.07494 q^{35} -1.34170 q^{36} -0.144684 q^{37} -1.13847 q^{38} +5.45552 q^{39} +0.950813 q^{40} +3.77643 q^{41} +2.48702 q^{42} +2.48169 q^{43} +1.34170 q^{44} +0.350684 q^{45} -0.120065 q^{46} -5.49942 q^{47} -0.483577 q^{48} +2.39589 q^{49} +3.95699 q^{50} +2.06199 q^{51} +7.31969 q^{52} -4.06954 q^{53} +0.811354 q^{54} -0.350684 q^{55} +8.31089 q^{56} -1.40317 q^{57} -2.32458 q^{58} +3.27787 q^{59} +0.470515 q^{60} -1.00000 q^{61} -3.37898 q^{62} +3.06527 q^{63} +3.75084 q^{64} -1.91317 q^{65} -0.811354 q^{66} -12.0165 q^{67} +2.76658 q^{68} -0.147981 q^{69} -0.872160 q^{70} +10.3117 q^{71} +2.71131 q^{72} -5.13147 q^{73} +0.117390 q^{74} +4.87702 q^{75} -1.88264 q^{76} -3.06527 q^{77} -4.42636 q^{78} -7.67884 q^{79} +0.169583 q^{80} +1.00000 q^{81} -3.06402 q^{82} +15.8628 q^{83} +4.11269 q^{84} -0.723108 q^{85} -2.01353 q^{86} -2.86506 q^{87} -2.71131 q^{88} +3.35464 q^{89} -0.284529 q^{90} -16.7227 q^{91} -0.198547 q^{92} -4.16462 q^{93} +4.46198 q^{94} +0.492070 q^{95} +5.81497 q^{96} -5.17684 q^{97} -1.94392 q^{98} -1.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + q^{2} - 12 q^{3} + 9 q^{4} - 3 q^{5} - q^{6} - 9 q^{7} + 6 q^{8} + 12 q^{9}+O(q^{10}) \) 12 * q + q^2 - 12 * q^3 + 9 * q^4 - 3 * q^5 - q^6 - 9 * q^7 + 6 * q^8 + 12 * q^9	\( 12 q + q^{2} - 12 q^{3} + 9 q^{4} - 3 q^{5} - q^{6} - 9 q^{7} + 6 q^{8} + 12 q^{9} - 8 q^{10} - 12 q^{11} - 9 q^{12} - q^{13} - 3 q^{14} + 3 q^{15} + 3 q^{16} + 9 q^{17} + q^{18} - 20 q^{19} - 9 q^{20} + 9 q^{21} - q^{22} - 9 q^{23} - 6 q^{24} + 3 q^{25} - 18 q^{26} - 12 q^{27} - 31 q^{28} + 18 q^{29} + 8 q^{30} - 21 q^{31} + 18 q^{32} + 12 q^{33} - 12 q^{34} - 4 q^{35} + 9 q^{36} - 18 q^{37} - 2 q^{38} + q^{39} - 26 q^{40} + 15 q^{41} + 3 q^{42} - 33 q^{43} - 9 q^{44} - 3 q^{45} - 28 q^{46} - 20 q^{47} - 3 q^{48} + 15 q^{49} - 2 q^{50} - 9 q^{51} - 27 q^{52} - q^{54} + 3 q^{55} - 8 q^{56} + 20 q^{57} - 11 q^{58} - 21 q^{59} + 9 q^{60} - 12 q^{61} - 9 q^{62} - 9 q^{63} - 12 q^{64} + 17 q^{65} + q^{66} - 34 q^{67} - 16 q^{68} + 9 q^{69} - 36 q^{70} - 5 q^{71} + 6 q^{72} - 2 q^{73} + 6 q^{74} - 3 q^{75} - 27 q^{76} + 9 q^{77} + 18 q^{78} - 31 q^{79} - 60 q^{80} + 12 q^{81} - 12 q^{82} - 32 q^{83} + 31 q^{84} - 40 q^{85} + 18 q^{86} - 18 q^{87} - 6 q^{88} + 27 q^{89} - 8 q^{90} - 45 q^{91} - 78 q^{92} + 21 q^{93} - 13 q^{94} + 37 q^{95} - 18 q^{96} - 19 q^{97} + 4 q^{98} - 12 q^{99}+O(q^{100}) \) 12 * q + q^2 - 12 * q^3 + 9 * q^4 - 3 * q^5 - q^6 - 9 * q^7 + 6 * q^8 + 12 * q^9 - 8 * q^10 - 12 * q^11 - 9 * q^12 - q^13 - 3 * q^14 + 3 * q^15 + 3 * q^16 + 9 * q^17 + q^18 - 20 * q^19 - 9 * q^20 + 9 * q^21 - q^22 - 9 * q^23 - 6 * q^24 + 3 * q^25 - 18 * q^26 - 12 * q^27 - 31 * q^28 + 18 * q^29 + 8 * q^30 - 21 * q^31 + 18 * q^32 + 12 * q^33 - 12 * q^34 - 4 * q^35 + 9 * q^36 - 18 * q^37 - 2 * q^38 + q^39 - 26 * q^40 + 15 * q^41 + 3 * q^42 - 33 * q^43 - 9 * q^44 - 3 * q^45 - 28 * q^46 - 20 * q^47 - 3 * q^48 + 15 * q^49 - 2 * q^50 - 9 * q^51 - 27 * q^52 - q^54 + 3 * q^55 - 8 * q^56 + 20 * q^57 - 11 * q^58 - 21 * q^59 + 9 * q^60 - 12 * q^61 - 9 * q^62 - 9 * q^63 - 12 * q^64 + 17 * q^65 + q^66 - 34 * q^67 - 16 * q^68 + 9 * q^69 - 36 * q^70 - 5 * q^71 + 6 * q^72 - 2 * q^73 + 6 * q^74 - 3 * q^75 - 27 * q^76 + 9 * q^77 + 18 * q^78 - 31 * q^79 - 60 * q^80 + 12 * q^81 - 12 * q^82 - 32 * q^83 + 31 * q^84 - 40 * q^85 + 18 * q^86 - 18 * q^87 - 6 * q^88 + 27 * q^89 - 8 * q^90 - 45 * q^91 - 78 * q^92 + 21 * q^93 - 13 * q^94 + 37 * q^95 - 18 * q^96 - 19 * q^97 + 4 * q^98 - 12 * q^99

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