LMFDB - Embedded newform 6018.2.a.z.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6018,2,Mod(1,6018)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6018, 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("6018.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6018 = 2 \cdot 3 \cdot 17 \cdot 59 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6018.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:	$48.0539719364$
Analytic rank:	$0$
Dimension:	$11$
Coefficient field:	$\mathbb{Q}[x]/(x^{11} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{11} - 4 x^{10} - 27 x^{9} + 117 x^{8} + 200 x^{7} - 1023 x^{6} - 484 x^{5} + 3403 x^{4} + 562 x^{3} + \cdots + 1200 $ x^11 - 4x^10 - 27x^9 + 117x^8 + 200x^7 - 1023x^6 - 484x^5 + 3403x^4 + 562x^3 - 4372x^2 - 692x + 1200
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$-1.55818$ of defining polynomial
Character	$\chi$	$=$	6018.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -1.55818 q^{5} -1.00000 q^{6} -1.66703 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -1.55818 q^{5} -1.00000 q^{6} -1.66703 q^{7} +1.00000 q^{8} +1.00000 q^{9} -1.55818 q^{10} +1.97996 q^{11} -1.00000 q^{12} -6.77634 q^{13} -1.66703 q^{14} +1.55818 q^{15} +1.00000 q^{16} -1.00000 q^{17} +1.00000 q^{18} -2.39081 q^{19} -1.55818 q^{20} +1.66703 q^{21} +1.97996 q^{22} +2.83641 q^{23} -1.00000 q^{24} -2.57206 q^{25} -6.77634 q^{26} -1.00000 q^{27} -1.66703 q^{28} -4.91208 q^{29} +1.55818 q^{30} +6.04328 q^{31} +1.00000 q^{32} -1.97996 q^{33} -1.00000 q^{34} +2.59753 q^{35} +1.00000 q^{36} -8.15591 q^{37} -2.39081 q^{38} +6.77634 q^{39} -1.55818 q^{40} +4.26004 q^{41} +1.66703 q^{42} +9.40525 q^{43} +1.97996 q^{44} -1.55818 q^{45} +2.83641 q^{46} +7.17870 q^{47} -1.00000 q^{48} -4.22103 q^{49} -2.57206 q^{50} +1.00000 q^{51} -6.77634 q^{52} +6.54262 q^{53} -1.00000 q^{54} -3.08515 q^{55} -1.66703 q^{56} +2.39081 q^{57} -4.91208 q^{58} -1.00000 q^{59} +1.55818 q^{60} +2.18090 q^{61} +6.04328 q^{62} -1.66703 q^{63} +1.00000 q^{64} +10.5588 q^{65} -1.97996 q^{66} +15.7230 q^{67} -1.00000 q^{68} -2.83641 q^{69} +2.59753 q^{70} -2.46506 q^{71} +1.00000 q^{72} -8.40971 q^{73} -8.15591 q^{74} +2.57206 q^{75} -2.39081 q^{76} -3.30065 q^{77} +6.77634 q^{78} -0.283473 q^{79} -1.55818 q^{80} +1.00000 q^{81} +4.26004 q^{82} +3.96255 q^{83} +1.66703 q^{84} +1.55818 q^{85} +9.40525 q^{86} +4.91208 q^{87} +1.97996 q^{88} -5.98985 q^{89} -1.55818 q^{90} +11.2963 q^{91} +2.83641 q^{92} -6.04328 q^{93} +7.17870 q^{94} +3.72533 q^{95} -1.00000 q^{96} -3.10822 q^{97} -4.22103 q^{98} +1.97996 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 11 q + 11 q^{2} - 11 q^{3} + 11 q^{4} + 4 q^{5} - 11 q^{6} + 3 q^{7} + 11 q^{8} + 11 q^{9}+O(q^{10}) $ 11 * q + 11 * q^2 - 11 * q^3 + 11 * q^4 + 4 * q^5 - 11 * q^6 + 3 * q^7 + 11 * q^8 + 11 * q^9	\( 11 q + 11 q^{2} - 11 q^{3} + 11 q^{4} + 4 q^{5} - 11 q^{6} + 3 q^{7} + 11 q^{8} + 11 q^{9} + 4 q^{10} + 9 q^{11} - 11 q^{12} + 6 q^{13} + 3 q^{14} - 4 q^{15} + 11 q^{16} - 11 q^{17} + 11 q^{18} - q^{19} + 4 q^{20} - 3 q^{21} + 9 q^{22} + 10 q^{23} - 11 q^{24} + 15 q^{25} + 6 q^{26} - 11 q^{27} + 3 q^{28} + 14 q^{29} - 4 q^{30} + 17 q^{31} + 11 q^{32} - 9 q^{33} - 11 q^{34} + 8 q^{35} + 11 q^{36} + 30 q^{37} - q^{38} - 6 q^{39} + 4 q^{40} + 10 q^{41} - 3 q^{42} + 11 q^{43} + 9 q^{44} + 4 q^{45} + 10 q^{46} - 6 q^{47} - 11 q^{48} + 18 q^{49} + 15 q^{50} + 11 q^{51} + 6 q^{52} + 10 q^{53} - 11 q^{54} - 11 q^{55} + 3 q^{56} + q^{57} + 14 q^{58} - 11 q^{59} - 4 q^{60} + 13 q^{61} + 17 q^{62} + 3 q^{63} + 11 q^{64} + 32 q^{65} - 9 q^{66} + 26 q^{67} - 11 q^{68} - 10 q^{69} + 8 q^{70} + 14 q^{71} + 11 q^{72} + 20 q^{73} + 30 q^{74} - 15 q^{75} - q^{76} + 26 q^{77} - 6 q^{78} + 15 q^{79} + 4 q^{80} + 11 q^{81} + 10 q^{82} + 2 q^{83} - 3 q^{84} - 4 q^{85} + 11 q^{86} - 14 q^{87} + 9 q^{88} + q^{89} + 4 q^{90} + 17 q^{91} + 10 q^{92} - 17 q^{93} - 6 q^{94} + 3 q^{95} - 11 q^{96} + 33 q^{97} + 18 q^{98} + 9 q^{99}+O(q^{100}) \) 11 * q + 11 * q^2 - 11 * q^3 + 11 * q^4 + 4 * q^5 - 11 * q^6 + 3 * q^7 + 11 * q^8 + 11 * q^9 + 4 * q^10 + 9 * q^11 - 11 * q^12 + 6 * q^13 + 3 * q^14 - 4 * q^15 + 11 * q^16 - 11 * q^17 + 11 * q^18 - q^19 + 4 * q^20 - 3 * q^21 + 9 * q^22 + 10 * q^23 - 11 * q^24 + 15 * q^25 + 6 * q^26 - 11 * q^27 + 3 * q^28 + 14 * q^29 - 4 * q^30 + 17 * q^31 + 11 * q^32 - 9 * q^33 - 11 * q^34 + 8 * q^35 + 11 * q^36 + 30 * q^37 - q^38 - 6 * q^39 + 4 * q^40 + 10 * q^41 - 3 * q^42 + 11 * q^43 + 9 * q^44 + 4 * q^45 + 10 * q^46 - 6 * q^47 - 11 * q^48 + 18 * q^49 + 15 * q^50 + 11 * q^51 + 6 * q^52 + 10 * q^53 - 11 * q^54 - 11 * q^55 + 3 * q^56 + q^57 + 14 * q^58 - 11 * q^59 - 4 * q^60 + 13 * q^61 + 17 * q^62 + 3 * q^63 + 11 * q^64 + 32 * q^65 - 9 * q^66 + 26 * q^67 - 11 * q^68 - 10 * q^69 + 8 * q^70 + 14 * q^71 + 11 * q^72 + 20 * q^73 + 30 * q^74 - 15 * q^75 - q^76 + 26 * q^77 - 6 * q^78 + 15 * q^79 + 4 * q^80 + 11 * q^81 + 10 * q^82 + 2 * q^83 - 3 * q^84 - 4 * q^85 + 11 * q^86 - 14 * q^87 + 9 * q^88 + q^89 + 4 * q^90 + 17 * q^91 + 10 * q^92 - 17 * q^93 - 6 * q^94 + 3 * q^95 - 11 * q^96 + 33 * q^97 + 18 * q^98 + 9 * 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 $

$2$	1.00000	0.707107
$2$	1.00000	0.707107
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	1.00000	0.500000
$5$	−1.55818	−0.696841	−0.348420	−	0.937338i	$-0.613282\pi$
$5$	−1.55818	−0.696841	−0.348420	+	0.937338i	$0.613282\pi$
$6$	−1.00000	−0.408248
$7$	−1.66703	−0.630076	−0.315038	−	0.949079i	$-0.602017\pi$
$7$	−1.66703	−0.630076	−0.315038	+	0.949079i	$0.602017\pi$
$8$	1.00000	0.353553
$9$	1.00000	0.333333
$10$	−1.55818	−0.492741
$11$	1.97996	0.596981	0.298491	−	0.954413i	$-0.403517\pi$
$11$	1.97996	0.596981	0.298491	+	0.954413i	$0.403517\pi$
$12$	−1.00000	−0.288675
$13$	−6.77634	−1.87942	−0.939710	−	0.341973i	$-0.888905\pi$
$13$	−6.77634	−1.87942	−0.939710	+	0.341973i	$0.888905\pi$
$14$	−1.66703	−0.445531
$15$	1.55818	0.402321
$16$	1.00000	0.250000
$17$	−1.00000	−0.242536
$17$	−1.00000	−0.242536
$18$	1.00000	0.235702
$19$	−2.39081	−0.548491	−0.274245	−	0.961660i	$-0.588428\pi$
$19$	−2.39081	−0.548491	−0.274245	+	0.961660i	$0.588428\pi$
$20$	−1.55818	−0.348420
$21$	1.66703	0.363775
$22$	1.97996	0.422130
$23$	2.83641	0.591431	0.295716	−	0.955276i	$-0.404442\pi$
$23$	2.83641	0.591431	0.295716	+	0.955276i	$0.404442\pi$
$24$	−1.00000	−0.204124
$25$	−2.57206	−0.514413
$26$	−6.77634	−1.32895
$27$	−1.00000	−0.192450
$28$	−1.66703	−0.315038
$29$	−4.91208	−0.912150	−0.456075	−	0.889941i	$-0.650745\pi$
$29$	−4.91208	−0.912150	−0.456075	+	0.889941i	$0.650745\pi$
$30$	1.55818	0.284484
$31$	6.04328	1.08540	0.542702	−	0.839925i	$-0.317401\pi$
$31$	6.04328	1.08540	0.542702	+	0.839925i	$0.317401\pi$
$32$	1.00000	0.176777
$33$	−1.97996	−0.344667
$34$	−1.00000	−0.171499
$35$	2.59753	0.439063
$36$	1.00000	0.166667
$37$	−8.15591	−1.34082	−0.670412	−	0.741989i	$-0.733883\pi$
$37$	−8.15591	−1.34082	−0.670412	+	0.741989i	$0.733883\pi$
$38$	−2.39081	−0.387841
$39$	6.77634	1.08508
$40$	−1.55818	−0.246370
$41$	4.26004	0.665307	0.332653	−	0.943049i	$-0.392056\pi$
$41$	4.26004	0.665307	0.332653	+	0.943049i	$0.392056\pi$
$42$	1.66703	0.257228
$43$	9.40525	1.43429	0.717144	−	0.696926i	$-0.245449\pi$
$43$	9.40525	1.43429	0.717144	+	0.696926i	$0.245449\pi$
$44$	1.97996	0.298491
$45$	−1.55818	−0.232280
$46$	2.83641	0.418205
$47$	7.17870	1.04712	0.523560	−	0.851989i	$-0.324603\pi$
$47$	7.17870	1.04712	0.523560	+	0.851989i	$0.324603\pi$
$48$	−1.00000	−0.144338
$49$	−4.22103	−0.603004
$50$	−2.57206	−0.363745
$51$	1.00000	0.140028
$52$	−6.77634	−0.939710
$53$	6.54262	0.898698	0.449349	−	0.893356i	$-0.351656\pi$
$53$	6.54262	0.898698	0.449349	+	0.893356i	$0.351656\pi$
$54$	−1.00000	−0.136083
$55$	−3.08515	−0.416001
$56$	−1.66703	−0.222766
$57$	2.39081	0.316671
$58$	−4.91208	−0.644988
$59$	−1.00000	−0.130189
$59$	−1.00000	−0.130189
$60$	1.55818	0.201161
$61$	2.18090	0.279236	0.139618	−	0.990205i	$-0.455413\pi$
$61$	2.18090	0.279236	0.139618	+	0.990205i	$0.455413\pi$
$62$	6.04328	0.767497
$63$	−1.66703	−0.210025
$64$	1.00000	0.125000
$65$	10.5588	1.30966
$66$	−1.97996	−0.243717
$67$	15.7230	1.92087	0.960435	−	0.278506i	$-0.0898391\pi$
$67$	15.7230	1.92087	0.960435	+	0.278506i	$0.0898391\pi$
$68$	−1.00000	−0.121268
$69$	−2.83641	−0.341463
$70$	2.59753	0.310464
$71$	−2.46506	−0.292548	−0.146274	−	0.989244i	$-0.546728\pi$
$71$	−2.46506	−0.292548	−0.146274	+	0.989244i	$0.546728\pi$
$72$	1.00000	0.117851
$73$	−8.40971	−0.984282	−0.492141	−	0.870515i	$-0.663786\pi$
$73$	−8.40971	−0.984282	−0.492141	+	0.870515i	$0.663786\pi$
$74$	−8.15591	−0.948105
$75$	2.57206	0.296996
$76$	−2.39081	−0.274245
$77$	−3.30065	−0.376144
$78$	6.77634	0.767270
$79$	−0.283473	−0.0318932	−0.0159466	−	0.999873i	$-0.505076\pi$
$79$	−0.283473	−0.0318932	−0.0159466	+	0.999873i	$0.505076\pi$
$80$	−1.55818	−0.174210
$81$	1.00000	0.111111
$82$	4.26004	0.470443
$83$	3.96255	0.434946	0.217473	−	0.976066i	$-0.430219\pi$
$83$	3.96255	0.434946	0.217473	+	0.976066i	$0.430219\pi$
$84$	1.66703	0.181887
$85$	1.55818	0.169009
$86$	9.40525	1.01419
$87$	4.91208	0.526630
$88$	1.97996	0.211065
$89$	−5.98985	−0.634923	−0.317462	−	0.948271i	$-0.602830\pi$
$89$	−5.98985	−0.634923	−0.317462	+	0.948271i	$0.602830\pi$
$90$	−1.55818	−0.164247
$91$	11.2963	1.18418
$92$	2.83641	0.295716
$93$	−6.04328	−0.626659
$94$	7.17870	0.740426
$95$	3.72533	0.382211
$96$	−1.00000	−0.102062
$97$	−3.10822	−0.315592	−0.157796	−	0.987472i	$-0.550439\pi$
$97$	−3.10822	−0.315592	−0.157796	+	0.987472i	$0.550439\pi$
$98$	−4.22103	−0.426388
$99$	1.97996	0.198994
$100$	−2.57206	−0.257206
$101$	−11.6688	−1.16109	−0.580543	−	0.814230i	$-0.697160\pi$
$101$	−11.6688	−1.16109	−0.580543	+	0.814230i	$0.697160\pi$
$102$	1.00000	0.0990148
$103$	−1.41322	−0.139249	−0.0696243	−	0.997573i	$-0.522180\pi$
$103$	−1.41322	−0.139249	−0.0696243	+	0.997573i	$0.522180\pi$
$104$	−6.77634	−0.664475
$105$	−2.59753	−0.253493
$106$	6.54262	0.635476
$107$	11.3684	1.09902	0.549510	−	0.835487i	$-0.314814\pi$
$107$	11.3684	1.09902	0.549510	+	0.835487i	$0.314814\pi$
$108$	−1.00000	−0.0962250
$109$	14.5385	1.39254	0.696269	−	0.717781i	$-0.254842\pi$
$109$	14.5385	1.39254	0.696269	+	0.717781i	$0.254842\pi$
$110$	−3.08515	−0.294157
$111$	8.15591	0.774125
$112$	−1.66703	−0.157519
$113$	13.5405	1.27378	0.636891	−	0.770954i	$-0.280220\pi$
$113$	13.5405	1.27378	0.636891	+	0.770954i	$0.280220\pi$
$114$	2.39081	0.223920
$115$	−4.41964	−0.412134
$116$	−4.91208	−0.456075
$117$	−6.77634	−0.626473
$118$	−1.00000	−0.0920575
$119$	1.66703	0.152816
$120$	1.55818	0.142242
$121$	−7.07974	−0.643613
$122$	2.18090	0.197450
$123$	−4.26004	−0.384115
$124$	6.04328	0.542702
$125$	11.7987	1.05530
$126$	−1.66703	−0.148510
$127$	−7.26083	−0.644294	−0.322147	−	0.946690i	$-0.604405\pi$
$127$	−7.26083	−0.644294	−0.322147	+	0.946690i	$0.604405\pi$
$128$	1.00000	0.0883883
$129$	−9.40525	−0.828086
$130$	10.5588	0.926067
$131$	−3.48904	−0.304839	−0.152420	−	0.988316i	$-0.548707\pi$
$131$	−3.48904	−0.304839	−0.152420	+	0.988316i	$0.548707\pi$
$132$	−1.97996	−0.172334
$133$	3.98555	0.345591
$134$	15.7230	1.35826
$135$	1.55818	0.134107
$136$	−1.00000	−0.0857493
$137$	7.76997	0.663834	0.331917	−	0.943309i	$-0.392305\pi$
$137$	7.76997	0.663834	0.331917	+	0.943309i	$0.392305\pi$
$138$	−2.83641	−0.241451
$139$	−8.41649	−0.713877	−0.356939	−	0.934128i	$-0.616179\pi$
$139$	−8.41649	−0.713877	−0.356939	+	0.934128i	$0.616179\pi$
$140$	2.59753	0.219531
$141$	−7.17870	−0.604555
$142$	−2.46506	−0.206863
$143$	−13.4169	−1.12198
$144$	1.00000	0.0833333
$145$	7.65392	0.635624
$146$	−8.40971	−0.695993
$147$	4.22103	0.348144
$148$	−8.15591	−0.670412
$149$	20.0144	1.63964	0.819822	−	0.572618i	$-0.194072\pi$
$149$	20.0144	1.63964	0.819822	+	0.572618i	$0.194072\pi$
$150$	2.57206	0.210008
$151$	−15.1815	−1.23545	−0.617726	−	0.786393i	$-0.711946\pi$
$151$	−15.1815	−1.23545	−0.617726	+	0.786393i	$0.711946\pi$
$152$	−2.39081	−0.193921
$153$	−1.00000	−0.0808452
$154$	−3.30065	−0.265974
$155$	−9.41653	−0.756354
$156$	6.77634	0.542542
$157$	6.60417	0.527070	0.263535	−	0.964650i	$-0.415112\pi$
$157$	6.60417	0.527070	0.263535	+	0.964650i	$0.415112\pi$
$158$	−0.283473	−0.0225519
$159$	−6.54262	−0.518864
$160$	−1.55818	−0.123185
$161$	−4.72836	−0.372647
$162$	1.00000	0.0785674
$163$	6.85769	0.537136	0.268568	−	0.963261i	$-0.413450\pi$
$163$	6.85769	0.537136	0.268568	+	0.963261i	$0.413450\pi$
$164$	4.26004	0.332653
$165$	3.08515	0.240178
$166$	3.96255	0.307553
$167$	5.16446	0.399638	0.199819	−	0.979833i	$-0.435965\pi$
$167$	5.16446	0.399638	0.199819	+	0.979833i	$0.435965\pi$
$168$	1.66703	0.128614
$169$	32.9188	2.53222
$170$	1.55818	0.119507
$171$	−2.39081	−0.182830
$172$	9.40525	0.717144
$173$	14.8427	1.12847	0.564233	−	0.825615i	$-0.309172\pi$
$173$	14.8427	1.12847	0.564233	+	0.825615i	$0.309172\pi$
$174$	4.91208	0.372384
$175$	4.28770	0.324120
$176$	1.97996	0.149245
$177$	1.00000	0.0751646
$178$	−5.98985	−0.448959
$179$	9.32987	0.697347	0.348674	−	0.937244i	$-0.386632\pi$
$179$	9.32987	0.697347	0.348674	+	0.937244i	$0.386632\pi$
$180$	−1.55818	−0.116140
$181$	−7.91363	−0.588216	−0.294108	−	0.955772i	$-0.595022\pi$
$181$	−7.91363	−0.588216	−0.294108	+	0.955772i	$0.595022\pi$
$182$	11.2963	0.837340
$183$	−2.18090	−0.161217
$184$	2.83641	0.209103
$185$	12.7084	0.934340
$186$	−6.04328	−0.443114
$187$	−1.97996	−0.144789
$188$	7.17870	0.523560
$189$	1.66703	0.121258
$190$	3.72533	0.270264
$191$	−12.9468	−0.936796	−0.468398	−	0.883518i	$-0.655169\pi$
$191$	−12.9468	−0.936796	−0.468398	+	0.883518i	$0.655169\pi$
$192$	−1.00000	−0.0721688
$193$	−0.354766	−0.0255366	−0.0127683	−	0.999918i	$-0.504064\pi$
$193$	−0.354766	−0.0255366	−0.0127683	+	0.999918i	$0.504064\pi$
$194$	−3.10822	−0.223157
$195$	−10.5588	−0.756130
$196$	−4.22103	−0.301502
$197$	5.41594	0.385870	0.192935	−	0.981212i	$-0.438199\pi$
$197$	5.41594	0.385870	0.192935	+	0.981212i	$0.438199\pi$
$198$	1.97996	0.140710
$199$	22.1123	1.56750	0.783750	−	0.621076i	$-0.213304\pi$
$199$	22.1123	1.56750	0.783750	+	0.621076i	$0.213304\pi$
$200$	−2.57206	−0.181872
$201$	−15.7230	−1.10901
$202$	−11.6688	−0.821011
$203$	8.18856	0.574725
$204$	1.00000	0.0700140
$205$	−6.63792	−0.463613
$206$	−1.41322	−0.0984636
$207$	2.83641	0.197144
$208$	−6.77634	−0.469855
$209$	−4.73373	−0.327439
$210$	−2.59753	−0.179247
$211$	17.5114	1.20554	0.602768	−	0.797917i	$-0.294065\pi$
$211$	17.5114	1.20554	0.602768	+	0.797917i	$0.294065\pi$
$212$	6.54262	0.449349
$213$	2.46506	0.168903
$214$	11.3684	0.777125
$215$	−14.6551	−0.999470
$216$	−1.00000	−0.0680414
$217$	−10.0743	−0.683888
$218$	14.5385	0.984674
$219$	8.40971	0.568276
$220$	−3.08515	−0.208000
$221$	6.77634	0.455826
$222$	8.15591	0.547389
$223$	−25.1785	−1.68608	−0.843040	−	0.537851i	$-0.819236\pi$
$223$	−25.1785	−1.68608	−0.843040	+	0.537851i	$0.819236\pi$
$224$	−1.66703	−0.111383
$225$	−2.57206	−0.171471
$226$	13.5405	0.900700
$227$	22.8075	1.51379	0.756893	−	0.653538i	$-0.226716\pi$
$227$	22.8075	1.51379	0.756893	+	0.653538i	$0.226716\pi$
$228$	2.39081	0.158336
$229$	12.8728	0.850658	0.425329	−	0.905039i	$-0.360158\pi$
$229$	12.8728	0.850658	0.425329	+	0.905039i	$0.360158\pi$
$230$	−4.41964	−0.291422
$231$	3.30065	0.217167
$232$	−4.91208	−0.322494
$233$	−3.46997	−0.227325	−0.113663	−	0.993519i	$-0.536258\pi$
$233$	−3.46997	−0.227325	−0.113663	+	0.993519i	$0.536258\pi$
$234$	−6.77634	−0.442983
$235$	−11.1857	−0.729676
$236$	−1.00000	−0.0650945
$237$	0.283473	0.0184136
$238$	1.66703	0.108057
$239$	−7.47119	−0.483271	−0.241635	−	0.970367i	$-0.577684\pi$
$239$	−7.47119	−0.483271	−0.241635	+	0.970367i	$0.577684\pi$
$240$	1.55818	0.100580
$241$	29.2894	1.88670	0.943349	−	0.331801i	$-0.107656\pi$
$241$	29.2894	1.88670	0.943349	+	0.331801i	$0.107656\pi$
$242$	−7.07974	−0.455103
$243$	−1.00000	−0.0641500
$244$	2.18090	0.139618
$245$	6.57713	0.420197
$246$	−4.26004	−0.271610
$247$	16.2010	1.03084
$248$	6.04328	0.383748
$249$	−3.96255	−0.251116
$250$	11.7987	0.746213
$251$	9.96953	0.629271	0.314636	−	0.949213i	$-0.398118\pi$
$251$	9.96953	0.629271	0.314636	+	0.949213i	$0.398118\pi$
$252$	−1.66703	−0.105013
$253$	5.61598	0.353074
$254$	−7.26083	−0.455585
$255$	−1.55818	−0.0975772
$256$	1.00000	0.0625000
$257$	1.56463	0.0975988	0.0487994	−	0.998809i	$-0.484460\pi$
$257$	1.56463	0.0975988	0.0487994	+	0.998809i	$0.484460\pi$
$258$	−9.40525	−0.585545
$259$	13.5961	0.844821
$260$	10.5588	0.654828
$261$	−4.91208	−0.304050
$262$	−3.48904	−0.215554
$263$	−0.228095	−0.0140649	−0.00703246	−	0.999975i	$-0.502239\pi$
$263$	−0.228095	−0.0140649	−0.00703246	+	0.999975i	$0.502239\pi$
$264$	−1.97996	−0.121858
$265$	−10.1946	−0.626250
$266$	3.98555	0.244370
$267$	5.98985	0.366573
$268$	15.7230	0.960435
$269$	−3.85471	−0.235026	−0.117513	−	0.993071i	$-0.537492\pi$
$269$	−3.85471	−0.235026	−0.117513	+	0.993071i	$0.537492\pi$
$270$	1.55818	0.0948280
$271$	13.9785	0.849135	0.424568	−	0.905396i	$-0.360426\pi$
$271$	13.9785	0.849135	0.424568	+	0.905396i	$0.360426\pi$
$272$	−1.00000	−0.0606339
$273$	−11.2963	−0.683686
$274$	7.76997	0.469401
$275$	−5.09259	−0.307095
$276$	−2.83641	−0.170732
$277$	21.2804	1.27862	0.639309	−	0.768950i	$-0.279220\pi$
$277$	21.2804	1.27862	0.639309	+	0.768950i	$0.279220\pi$
$278$	−8.41649	−0.504787
$279$	6.04328	0.361801
$280$	2.59753	0.155232
$281$	−10.3784	−0.619126	−0.309563	−	0.950879i	$-0.600183\pi$
$281$	−10.3784	−0.619126	−0.309563	+	0.950879i	$0.600183\pi$
$282$	−7.17870	−0.427485
$283$	−3.26560	−0.194120	−0.0970599	−	0.995279i	$-0.530944\pi$
$283$	−3.26560	−0.194120	−0.0970599	+	0.995279i	$0.530944\pi$
$284$	−2.46506	−0.146274
$285$	−3.72533	−0.220669
$286$	−13.4169	−0.793359
$287$	−7.10160	−0.419194
$288$	1.00000	0.0589256
$289$	1.00000	0.0588235
$290$	7.65392	0.449454
$291$	3.10822	0.182207
$292$	−8.40971	−0.492141
$293$	−12.5140	−0.731073	−0.365536	−	0.930797i	$-0.619114\pi$
$293$	−12.5140	−0.731073	−0.365536	+	0.930797i	$0.619114\pi$
$294$	4.22103	0.246175
$295$	1.55818	0.0907209
$296$	−8.15591	−0.474053
$297$	−1.97996	−0.114889
$298$	20.0144	1.15940
$299$	−19.2205	−1.11155
$300$	2.57206	0.148498
$301$	−15.6788	−0.903711
$302$	−15.1815	−0.873597
$303$	11.6688	0.670353
$304$	−2.39081	−0.137123
$305$	−3.39825	−0.194583
$306$	−1.00000	−0.0571662
$307$	18.2155	1.03961	0.519807	−	0.854283i	$-0.326004\pi$
$307$	18.2155	1.03961	0.519807	+	0.854283i	$0.326004\pi$
$308$	−3.30065	−0.188072
$309$	1.41322	0.0803952
$310$	−9.41653	−0.534823
$311$	−14.8072	−0.839637	−0.419818	−	0.907608i	$-0.637906\pi$
$311$	−14.8072	−0.839637	−0.419818	+	0.907608i	$0.637906\pi$
$312$	6.77634	0.383635
$313$	19.1373	1.08171	0.540853	−	0.841117i	$-0.318101\pi$
$313$	19.1373	1.08171	0.540853	+	0.841117i	$0.318101\pi$
$314$	6.60417	0.372695
$315$	2.59753	0.146354
$316$	−0.283473	−0.0159466
$317$	−12.3067	−0.691212	−0.345606	−	0.938380i	$-0.612327\pi$
$317$	−12.3067	−0.691212	−0.345606	+	0.938380i	$0.612327\pi$
$318$	−6.54262	−0.366892
$319$	−9.72574	−0.544537
$320$	−1.55818	−0.0871051
$321$	−11.3684	−0.634520
$322$	−4.72836	−0.263501
$323$	2.39081	0.133028
$324$	1.00000	0.0555556
$325$	17.4292	0.966798
$326$	6.85769	0.379812
$327$	−14.5385	−0.803983
$328$	4.26004	0.235221
$329$	−11.9671	−0.659766
$330$	3.08515	0.169832
$331$	−9.60702	−0.528050	−0.264025	−	0.964516i	$-0.585050\pi$
$331$	−9.60702	−0.528050	−0.264025	+	0.964516i	$0.585050\pi$
$332$	3.96255	0.217473
$333$	−8.15591	−0.446941
$334$	5.16446	0.282587
$335$	−24.4993	−1.33854
$336$	1.66703	0.0909437
$337$	28.8677	1.57252	0.786261	−	0.617895i	$-0.212014\pi$
$337$	28.8677	1.57252	0.786261	+	0.617895i	$0.212014\pi$
$338$	32.9188	1.79055
$339$	−13.5405	−0.735418
$340$	1.55818	0.0845044
$341$	11.9655	0.647966
$342$	−2.39081	−0.129280
$343$	18.7057	1.01001
$344$	9.40525	0.507097
$345$	4.41964	0.237945
$346$	14.8427	0.797947
$347$	5.77139	0.309824	0.154912	−	0.987928i	$-0.450491\pi$
$347$	5.77139	0.309824	0.154912	+	0.987928i	$0.450491\pi$
$348$	4.91208	0.263315
$349$	−25.2841	−1.35343	−0.676715	−	0.736245i	$-0.736597\pi$
$349$	−25.2841	−1.35343	−0.676715	+	0.736245i	$0.736597\pi$
$350$	4.28770	0.229187
$351$	6.77634	0.361694
$352$	1.97996	0.105532
$353$	−33.2856	−1.77161	−0.885807	−	0.464054i	$-0.846394\pi$
$353$	−33.2856	−1.77161	−0.885807	+	0.464054i	$0.846394\pi$
$354$	1.00000	0.0531494
$355$	3.84101	0.203860
$356$	−5.98985	−0.317462
$357$	−1.66703	−0.0882284
$358$	9.32987	0.493099
$359$	−30.0685	−1.58695	−0.793477	−	0.608600i	$-0.791731\pi$
$359$	−30.0685	−1.58695	−0.793477	+	0.608600i	$0.791731\pi$
$360$	−1.55818	−0.0821235
$361$	−13.2840	−0.699158
$362$	−7.91363	−0.415931
$363$	7.07974	0.371590
$364$	11.2963	0.592089
$365$	13.1039	0.685888
$366$	−2.18090	−0.113998
$367$	19.7030	1.02849	0.514244	−	0.857644i	$-0.328073\pi$
$367$	19.7030	1.02849	0.514244	+	0.857644i	$0.328073\pi$
$368$	2.83641	0.147858
$369$	4.26004	0.221769
$370$	12.7084	0.660678
$371$	−10.9067	−0.566249
$372$	−6.04328	−0.313329
$373$	33.2926	1.72382	0.861912	−	0.507058i	$-0.169267\pi$
$373$	33.2926	1.72382	0.861912	+	0.507058i	$0.169267\pi$
$374$	−1.97996	−0.102381
$375$	−11.7987	−0.609280
$376$	7.17870	0.370213
$377$	33.2859	1.71431
$378$	1.66703	0.0857426
$379$	1.52149	0.0781534	0.0390767	−	0.999236i	$-0.487558\pi$
$379$	1.52149	0.0781534	0.0390767	+	0.999236i	$0.487558\pi$
$380$	3.72533	0.191105
$381$	7.26083	0.371983
$382$	−12.9468	−0.662415
$383$	2.26627	0.115801	0.0579004	−	0.998322i	$-0.481559\pi$
$383$	2.26627	0.115801	0.0579004	+	0.998322i	$0.481559\pi$
$384$	−1.00000	−0.0510310
$385$	5.14302	0.262112
$386$	−0.354766	−0.0180571
$387$	9.40525	0.478096
$388$	−3.10822	−0.157796
$389$	14.9176	0.756353	0.378177	−	0.925733i	$-0.376551\pi$
$389$	14.9176	0.756353	0.378177	+	0.925733i	$0.376551\pi$
$390$	−10.5588	−0.534665
$391$	−2.83641	−0.143443
$392$	−4.22103	−0.213194
$393$	3.48904	0.175999
$394$	5.41594	0.272851
$395$	0.441703	0.0222245
$396$	1.97996	0.0994969
$397$	18.6580	0.936420	0.468210	−	0.883617i	$-0.344899\pi$
$397$	18.6580	0.936420	0.468210	+	0.883617i	$0.344899\pi$
$398$	22.1123	1.10839
$399$	−3.98555	−0.199527
$400$	−2.57206	−0.128603
$401$	−36.7588	−1.83564	−0.917822	−	0.396991i	$-0.870054\pi$
$401$	−36.7588	−1.83564	−0.917822	+	0.396991i	$0.870054\pi$
$402$	−15.7230	−0.784192
$403$	−40.9513	−2.03993
$404$	−11.6688	−0.580543
$405$	−1.55818	−0.0774267
$406$	8.18856	0.406392
$407$	−16.1484	−0.800447
$408$	1.00000	0.0495074
$409$	28.6561	1.41695	0.708476	−	0.705735i	$-0.249383\pi$
$409$	28.6561	1.41695	0.708476	+	0.705735i	$0.249383\pi$
$410$	−6.63792	−0.327824
$411$	−7.76997	−0.383264
$412$	−1.41322	−0.0696243
$413$	1.66703	0.0820290
$414$	2.83641	0.139402
$415$	−6.17438	−0.303088
$416$	−6.77634	−0.332238
$417$	8.41649	0.412157
$418$	−4.73373	−0.231534
$419$	33.8962	1.65594	0.827970	−	0.560773i	$-0.189496\pi$
$419$	33.8962	1.65594	0.827970	+	0.560773i	$0.189496\pi$
$420$	−2.59753	−0.126747
$421$	10.0798	0.491261	0.245631	−	0.969364i	$-0.421005\pi$
$421$	10.0798	0.491261	0.245631	+	0.969364i	$0.421005\pi$
$422$	17.5114	0.852442
$423$	7.17870	0.349040
$424$	6.54262	0.317738
$425$	2.57206	0.124763
$426$	2.46506	0.119432
$427$	−3.63562	−0.175940
$428$	11.3684	0.549510
$429$	13.4169	0.647775
$430$	−14.6551	−0.706732
$431$	31.8771	1.53547	0.767734	−	0.640769i	$-0.221384\pi$
$431$	31.8771	1.53547	0.767734	+	0.640769i	$0.221384\pi$
$432$	−1.00000	−0.0481125
$433$	−30.4948	−1.46549	−0.732744	−	0.680504i	$-0.761761\pi$
$433$	−30.4948	−1.46549	−0.732744	+	0.680504i	$0.761761\pi$
$434$	−10.0743	−0.483582
$435$	−7.65392	−0.366977
$436$	14.5385	0.696269
$437$	−6.78132	−0.324395
$438$	8.40971	0.401832
$439$	−39.4425	−1.88249	−0.941243	−	0.337730i	$-0.890341\pi$
$439$	−39.4425	−1.88249	−0.941243	+	0.337730i	$0.890341\pi$
$440$	−3.08515	−0.147079
$441$	−4.22103	−0.201001
$442$	6.77634	0.322318
$443$	21.9370	1.04226	0.521130	−	0.853477i	$-0.325511\pi$
$443$	21.9370	1.04226	0.521130	+	0.853477i	$0.325511\pi$
$444$	8.15591	0.387062
$445$	9.33329	0.442440
$446$	−25.1785	−1.19224
$447$	−20.0144	−0.946649
$448$	−1.66703	−0.0787596
$449$	−2.49114	−0.117564	−0.0587821	−	0.998271i	$-0.518722\pi$
$449$	−2.49114	−0.117564	−0.0587821	+	0.998271i	$0.518722\pi$
$450$	−2.57206	−0.121248
$451$	8.43473	0.397176
$452$	13.5405	0.636891
$453$	15.1815	0.713289
$454$	22.8075	1.07041
$455$	−17.6018	−0.825184
$456$	2.39081	0.111960
$457$	20.0805	0.939324	0.469662	−	0.882846i	$-0.344376\pi$
$457$	20.0805	0.939324	0.469662	+	0.882846i	$0.344376\pi$
$458$	12.8728	0.601506
$459$	1.00000	0.0466760
$460$	−4.41964	−0.206067
$461$	21.9373	1.02172	0.510860	−	0.859664i	$-0.329327\pi$
$461$	21.9373	1.02172	0.510860	+	0.859664i	$0.329327\pi$
$462$	3.30065	0.153560
$463$	−10.1675	−0.472526	−0.236263	−	0.971689i	$-0.575923\pi$
$463$	−10.1675	−0.472526	−0.236263	+	0.971689i	$0.575923\pi$
$464$	−4.91208	−0.228038
$465$	9.41653	0.436681
$466$	−3.46997	−0.160743
$467$	−18.6819	−0.864496	−0.432248	−	0.901755i	$-0.642280\pi$
$467$	−18.6819	−0.864496	−0.432248	+	0.901755i	$0.642280\pi$
$468$	−6.77634	−0.313237
$469$	−26.2106	−1.21029
$470$	−11.1857	−0.515959
$471$	−6.60417	−0.304304
$472$	−1.00000	−0.0460287
$473$	18.6220	0.856243
$474$	0.283473	0.0130204
$475$	6.14933	0.282151
$476$	1.66703	0.0764080
$477$	6.54262	0.299566
$478$	−7.47119	−0.341724
$479$	−14.1653	−0.647230	−0.323615	−	0.946189i	$-0.604898\pi$
$479$	−14.1653	−0.647230	−0.323615	+	0.946189i	$0.604898\pi$
$480$	1.55818	0.0711210
$481$	55.2673	2.51997
$482$	29.2894	1.33410
$483$	4.72836	0.215148
$484$	−7.07974	−0.321807
$485$	4.84317	0.219917
$486$	−1.00000	−0.0453609
$487$	34.8923	1.58112	0.790561	−	0.612383i	$-0.209789\pi$
$487$	34.8923	1.58112	0.790561	+	0.612383i	$0.209789\pi$
$488$	2.18090	0.0987249
$489$	−6.85769	−0.310115
$490$	6.57713	0.297124
$491$	5.74414	0.259229	0.129615	−	0.991564i	$-0.458626\pi$
$491$	5.74414	0.259229	0.129615	+	0.991564i	$0.458626\pi$
$492$	−4.26004	−0.192057
$493$	4.91208	0.221229
$494$	16.2010	0.728917
$495$	−3.08515	−0.138667
$496$	6.04328	0.271351
$497$	4.10931	0.184328
$498$	−3.96255	−0.177566
$499$	−24.7178	−1.10652	−0.553261	−	0.833008i	$-0.686617\pi$
$499$	−24.7178	−1.10652	−0.553261	+	0.833008i	$0.686617\pi$
$500$	11.7987	0.527652
$501$	−5.16446	−0.230731
$502$	9.96953	0.444962
$503$	−19.6459	−0.875970	−0.437985	−	0.898982i	$-0.644308\pi$
$503$	−19.6459	−0.875970	−0.437985	+	0.898982i	$0.644308\pi$
$504$	−1.66703	−0.0742552
$505$	18.1821	0.809092
$506$	5.61598	0.249661
$507$	−32.9188	−1.46198
$508$	−7.26083	−0.322147
$509$	−14.4289	−0.639551	−0.319775	−	0.947493i	$-0.603607\pi$
$509$	−14.4289	−0.639551	−0.319775	+	0.947493i	$0.603607\pi$
$510$	−1.55818	−0.0689975
$511$	14.0192	0.620173
$512$	1.00000	0.0441942
$513$	2.39081	0.105557
$514$	1.56463	0.0690128
$515$	2.20205	0.0970341
$516$	−9.40525	−0.414043
$517$	14.2136	0.625112
$518$	13.5961	0.597379
$519$	−14.8427	−0.651521
$520$	10.5588	0.463033
$521$	−34.9307	−1.53034	−0.765171	−	0.643828i	$-0.777345\pi$
$521$	−34.9307	−1.53034	−0.765171	+	0.643828i	$0.777345\pi$
$522$	−4.91208	−0.214996
$523$	25.0046	1.09337	0.546687	−	0.837337i	$-0.315889\pi$
$523$	25.0046	1.09337	0.546687	+	0.837337i	$0.315889\pi$
$524$	−3.48904	−0.152420
$525$	−4.28770	−0.187131
$526$	−0.228095	−0.00994540
$527$	−6.04328	−0.263249
$528$	−1.97996	−0.0861669
$529$	−14.9548	−0.650209
$530$	−10.1946	−0.442825
$531$	−1.00000	−0.0433963
$532$	3.98555	0.172796
$533$	−28.8675	−1.25039
$534$	5.98985	0.259206
$535$	−17.7140	−0.765842
$536$	15.7230	0.679130
$537$	−9.32987	−0.402614
$538$	−3.85471	−0.166188
$539$	−8.35748	−0.359982
$540$	1.55818	0.0670535
$541$	7.83615	0.336903	0.168451	−	0.985710i	$-0.446123\pi$
$541$	7.83615	0.336903	0.168451	+	0.985710i	$0.446123\pi$
$542$	13.9785	0.600429
$543$	7.91363	0.339606
$544$	−1.00000	−0.0428746
$545$	−22.6537	−0.970378
$546$	−11.2963	−0.483439
$547$	−9.77497	−0.417948	−0.208974	−	0.977921i	$-0.567012\pi$
$547$	−9.77497	−0.417948	−0.208974	+	0.977921i	$0.567012\pi$
$548$	7.76997	0.331917
$549$	2.18090	0.0930787
$550$	−5.09259	−0.217149
$551$	11.7439	0.500306
$552$	−2.83641	−0.120725
$553$	0.472557	0.0200952
$554$	21.2804	0.904120
$555$	−12.7084	−0.539442
$556$	−8.41649	−0.356939
$557$	5.83878	0.247397	0.123698	−	0.992320i	$-0.460524\pi$
$557$	5.83878	0.247397	0.123698	+	0.992320i	$0.460524\pi$
$558$	6.04328	0.255832
$559$	−63.7332	−2.69563
$560$	2.59753	0.109766
$561$	1.97996	0.0835941
$562$	−10.3784	−0.437788
$563$	−11.9811	−0.504942	−0.252471	−	0.967605i	$-0.581243\pi$
$563$	−11.9811	−0.504942	−0.252471	+	0.967605i	$0.581243\pi$
$564$	−7.17870	−0.302278
$565$	−21.0986	−0.887623
$566$	−3.26560	−0.137263
$567$	−1.66703	−0.0700085
$568$	−2.46506	−0.103431
$569$	−16.2412	−0.680865	−0.340433	−	0.940269i	$-0.610574\pi$
$569$	−16.2412	−0.680865	−0.340433	+	0.940269i	$0.610574\pi$
$570$	−3.72533	−0.156037
$571$	−9.40431	−0.393558	−0.196779	−	0.980448i	$-0.563048\pi$
$571$	−9.40431	−0.393558	−0.196779	+	0.980448i	$0.563048\pi$
$572$	−13.4169	−0.560989
$573$	12.9468	0.540859
$574$	−7.10160	−0.296415
$575$	−7.29542	−0.304240
$576$	1.00000	0.0416667
$577$	−20.2315	−0.842250	−0.421125	−	0.907003i	$-0.638365\pi$
$577$	−20.2315	−0.842250	−0.421125	+	0.907003i	$0.638365\pi$
$578$	1.00000	0.0415945
$579$	0.354766	0.0147436
$580$	7.65392	0.317812
$581$	−6.60567	−0.274049
$582$	3.10822	0.128840
$583$	12.9542	0.536506
$584$	−8.40971	−0.347996
$585$	10.5588	0.436552
$586$	−12.5140	−0.516947
$587$	20.8243	0.859513	0.429756	−	0.902945i	$-0.358599\pi$
$587$	20.8243	0.859513	0.429756	+	0.902945i	$0.358599\pi$
$588$	4.22103	0.174072
$589$	−14.4484	−0.595334
$590$	1.55818	0.0641494
$591$	−5.41594	−0.222782
$592$	−8.15591	−0.335206
$593$	−12.7810	−0.524854	−0.262427	−	0.964952i	$-0.584523\pi$
$593$	−12.7810	−0.524854	−0.262427	+	0.964952i	$0.584523\pi$
$594$	−1.97996	−0.0812389
$595$	−2.59753	−0.106488
$596$	20.0144	0.819822
$597$	−22.1123	−0.904997
$598$	−19.2205	−0.785983
$599$	−30.2956	−1.23785	−0.618923	−	0.785452i	$-0.712431\pi$
$599$	−30.2956	−1.23785	−0.618923	+	0.785452i	$0.712431\pi$
$600$	2.57206	0.105004
$601$	21.6463	0.882971	0.441485	−	0.897268i	$-0.354452\pi$
$601$	21.6463	0.882971	0.441485	+	0.897268i	$0.354452\pi$
$602$	−15.6788	−0.639020
$603$	15.7230	0.640290
$604$	−15.1815	−0.617726
$605$	11.0315	0.448496
$606$	11.6688	0.474011
$607$	−26.4784	−1.07472	−0.537362	−	0.843352i	$-0.680579\pi$
$607$	−26.4784	−1.07472	−0.537362	+	0.843352i	$0.680579\pi$
$608$	−2.39081	−0.0969603
$609$	−8.18856	−0.331817
$610$	−3.39825	−0.137591
$611$	−48.6453	−1.96798
$612$	−1.00000	−0.0404226
$613$	33.5622	1.35557	0.677783	−	0.735262i	$-0.262941\pi$
$613$	33.5622	1.35557	0.677783	+	0.735262i	$0.262941\pi$
$614$	18.2155	0.735119
$615$	6.63792	0.267667
$616$	−3.30065	−0.132987
$617$	−4.18241	−0.168378	−0.0841888	−	0.996450i	$-0.526830\pi$
$617$	−4.18241	−0.168378	−0.0841888	+	0.996450i	$0.526830\pi$
$618$	1.41322	0.0568480
$619$	28.1519	1.13152	0.565761	−	0.824569i	$-0.308583\pi$
$619$	28.1519	1.13152	0.565761	+	0.824569i	$0.308583\pi$
$620$	−9.41653	−0.378177
$621$	−2.83641	−0.113821
$622$	−14.8072	−0.593713
$623$	9.98524	0.400050
$624$	6.77634	0.271271
$625$	−5.52416	−0.220966
$626$	19.1373	0.764882
$627$	4.73373	0.189047
$628$	6.60417	0.263535
$629$	8.15591	0.325197
$630$	2.59753	0.103488
$631$	−15.4858	−0.616482	−0.308241	−	0.951308i	$-0.599740\pi$
$631$	−15.4858	−0.616482	−0.308241	+	0.951308i	$0.599740\pi$
$632$	−0.283473	−0.0112760
$633$	−17.5114	−0.696016
$634$	−12.3067	−0.488760
$635$	11.3137	0.448970
$636$	−6.54262	−0.259432
$637$	28.6031	1.13330
$638$	−9.72574	−0.385046
$639$	−2.46506	−0.0975161
$640$	−1.55818	−0.0615926
$641$	9.48250	0.374536	0.187268	−	0.982309i	$-0.440037\pi$
$641$	9.48250	0.374536	0.187268	+	0.982309i	$0.440037\pi$
$642$	−11.3684	−0.448673
$643$	−7.57735	−0.298821	−0.149411	−	0.988775i	$-0.547738\pi$
$643$	−7.57735	−0.298821	−0.149411	+	0.988775i	$0.547738\pi$
$644$	−4.72836	−0.186324
$645$	14.6551	0.577044
$646$	2.39081	0.0940654
$647$	7.83632	0.308078	0.154039	−	0.988065i	$-0.450772\pi$
$647$	7.83632	0.308078	0.154039	+	0.988065i	$0.450772\pi$
$648$	1.00000	0.0392837
$649$	−1.97996	−0.0777204
$650$	17.4292	0.683629
$651$	10.0743	0.394843
$652$	6.85769	0.268568
$653$	−40.3747	−1.57998	−0.789992	−	0.613118i	$-0.789915\pi$
$653$	−40.3747	−1.57998	−0.789992	+	0.613118i	$0.789915\pi$
$654$	−14.5385	−0.568502
$655$	5.43657	0.212424
$656$	4.26004	0.166327
$657$	−8.40971	−0.328094
$658$	−11.9671	−0.466525
$659$	0.870048	0.0338922	0.0169461	−	0.999856i	$-0.494606\pi$
$659$	0.870048	0.0338922	0.0169461	+	0.999856i	$0.494606\pi$
$660$	3.08515	0.120089
$661$	−29.1720	−1.13466	−0.567329	−	0.823491i	$-0.692023\pi$
$661$	−29.1720	−1.13466	−0.567329	+	0.823491i	$0.692023\pi$
$662$	−9.60702	−0.373388
$663$	−6.77634	−0.263171
$664$	3.96255	0.153777
$665$	−6.21022	−0.240822
$666$	−8.15591	−0.316035
$667$	−13.9327	−0.539474
$668$	5.16446	0.199819
$669$	25.1785	0.973458
$670$	−24.4993	−0.946491
$671$	4.31811	0.166699
$672$	1.66703	0.0643069
$673$	−11.5070	−0.443562	−0.221781	−	0.975096i	$-0.571187\pi$
$673$	−11.5070	−0.443562	−0.221781	+	0.975096i	$0.571187\pi$
$674$	28.8677	1.11194
$675$	2.57206	0.0989988
$676$	32.9188	1.26611
$677$	−44.3087	−1.70292	−0.851461	−	0.524418i	$-0.824283\pi$
$677$	−44.3087	−1.70292	−0.851461	+	0.524418i	$0.824283\pi$
$678$	−13.5405	−0.520019
$679$	5.18148	0.198847
$680$	1.55818	0.0597536
$681$	−22.8075	−0.873985
$682$	11.9655	0.458181
$683$	37.1832	1.42278	0.711389	−	0.702799i	$-0.248067\pi$
$683$	37.1832	1.42278	0.711389	+	0.702799i	$0.248067\pi$
$684$	−2.39081	−0.0914151
$685$	−12.1070	−0.462586
$686$	18.7057	0.714188
$687$	−12.8728	−0.491127
$688$	9.40525	0.358572
$689$	−44.3351	−1.68903
$690$	4.41964	0.168253
$691$	−37.6436	−1.43203	−0.716015	−	0.698085i	$-0.754036\pi$
$691$	−37.6436	−1.43203	−0.716015	+	0.698085i	$0.754036\pi$
$692$	14.8427	0.564233
$693$	−3.30065	−0.125381
$694$	5.77139	0.219079
$695$	13.1144	0.497459
$696$	4.91208	0.186192
$697$	−4.26004	−0.161361
$698$	−25.2841	−0.957019
$699$	3.46997	0.131246
$700$	4.28770	0.162060
$701$	−18.8932	−0.713586	−0.356793	−	0.934183i	$-0.616130\pi$
$701$	−18.8932	−0.713586	−0.356793	+	0.934183i	$0.616130\pi$
$702$	6.77634	0.255757
$703$	19.4993	0.735429
$704$	1.97996	0.0746227
$705$	11.1857	0.421279
$706$	−33.2856	−1.25272
$707$	19.4521	0.731573
$708$	1.00000	0.0375823
$709$	−12.1621	−0.456757	−0.228378	−	0.973572i	$-0.573342\pi$
$709$	−12.1621	−0.456757	−0.228378	+	0.973572i	$0.573342\pi$
$710$	3.84101	0.144151
$711$	−0.283473	−0.0106311
$712$	−5.98985	−0.224479
$713$	17.1412	0.641942
$714$	−1.66703	−0.0623869
$715$	20.9060	0.781840
$716$	9.32987	0.348674
$717$	7.47119	0.279017
$718$	−30.0685	−1.12215
$719$	−6.71075	−0.250269	−0.125134	−	0.992140i	$-0.539936\pi$
$719$	−6.71075	−0.250269	−0.125134	+	0.992140i	$0.539936\pi$
$720$	−1.55818	−0.0580701
$721$	2.35587	0.0877372
$722$	−13.2840	−0.494379
$723$	−29.2894	−1.08929
$724$	−7.91363	−0.294108
$725$	12.6342	0.469222
$726$	7.07974	0.262754
$727$	35.2038	1.30564	0.652819	−	0.757514i	$-0.273586\pi$
$727$	35.2038	1.30564	0.652819	+	0.757514i	$0.273586\pi$
$728$	11.2963	0.418670
$729$	1.00000	0.0370370
$730$	13.1039	0.484996
$731$	−9.40525	−0.347866
$732$	−2.18090	−0.0806086
$733$	6.06092	0.223865	0.111933	−	0.993716i	$-0.464296\pi$
$733$	6.06092	0.223865	0.111933	+	0.993716i	$0.464296\pi$
$734$	19.7030	0.727250
$735$	−6.57713	−0.242601
$736$	2.83641	0.104551
$737$	31.1310	1.14672
$738$	4.26004	0.156814
$739$	−2.43773	−0.0896733	−0.0448366	−	0.998994i	$-0.514277\pi$
$739$	−2.43773	−0.0896733	−0.0448366	+	0.998994i	$0.514277\pi$
$740$	12.7084	0.467170
$741$	−16.2010	−0.595158
$742$	−10.9067	−0.400398
$743$	−14.3791	−0.527517	−0.263758	−	0.964589i	$-0.584962\pi$
$743$	−14.3791	−0.527517	−0.263758	+	0.964589i	$0.584962\pi$
$744$	−6.04328	−0.221557
$745$	−31.1861	−1.14257
$746$	33.2926	1.21893
$747$	3.96255	0.144982
$748$	−1.97996	−0.0723946
$749$	−18.9513	−0.692467
$750$	−11.7987	−0.430826
$751$	12.5259	0.457075	0.228537	−	0.973535i	$-0.426606\pi$
$751$	12.5259	0.457075	0.228537	+	0.973535i	$0.426606\pi$
$752$	7.17870	0.261780
$753$	−9.96953	−0.363310
$754$	33.2859	1.21220
$755$	23.6556	0.860914
$756$	1.66703	0.0606291
$757$	20.1359	0.731853	0.365926	−	0.930644i	$-0.380752\pi$
$757$	20.1359	0.731853	0.365926	+	0.930644i	$0.380752\pi$
$758$	1.52149	0.0552628
$759$	−5.61598	−0.203847
$760$	3.72533	0.135132
$761$	−31.6103	−1.14587	−0.572937	−	0.819600i	$-0.694196\pi$
$761$	−31.6103	−1.14587	−0.572937	+	0.819600i	$0.694196\pi$
$762$	7.26083	0.263032
$763$	−24.2361	−0.877406
$764$	−12.9468	−0.468398
$765$	1.55818	0.0563362
$766$	2.26627	0.0818835
$767$	6.77634	0.244680
$768$	−1.00000	−0.0360844
$769$	26.2521	0.946675	0.473338	−	0.880881i	$-0.343049\pi$
$769$	26.2521	0.946675	0.473338	+	0.880881i	$0.343049\pi$
$770$	5.14302	0.185341
$771$	−1.56463	−0.0563487
$772$	−0.354766	−0.0127683
$773$	17.6023	0.633111	0.316556	−	0.948574i	$-0.397474\pi$
$773$	17.6023	0.633111	0.316556	+	0.948574i	$0.397474\pi$
$774$	9.40525	0.338065
$775$	−15.5437	−0.558346
$776$	−3.10822	−0.111578
$777$	−13.5961	−0.487758
$778$	14.9176	0.534823
$779$	−10.1850	−0.364914
$780$	−10.5588	−0.378065
$781$	−4.88072	−0.174646
$782$	−2.83641	−0.101430
$783$	4.91208	0.175543
$784$	−4.22103	−0.150751
$785$	−10.2905	−0.367284
$786$	3.48904	0.124450
$787$	−15.7716	−0.562196	−0.281098	−	0.959679i	$-0.590699\pi$
$787$	−15.7716	−0.562196	−0.281098	+	0.959679i	$0.590699\pi$
$788$	5.41594	0.192935
$789$	0.228095	0.00812038
$790$	0.441703	0.0157151
$791$	−22.5723	−0.802580
$792$	1.97996	0.0703549
$793$	−14.7786	−0.524802
$794$	18.6580	0.662149
$795$	10.1946	0.361565
$796$	22.1123	0.783750
$797$	−27.5996	−0.977630	−0.488815	−	0.872388i	$-0.662571\pi$
$797$	−27.5996	−0.977630	−0.488815	+	0.872388i	$0.662571\pi$
$798$	−3.98555	−0.141087
$799$	−7.17870	−0.253964
$800$	−2.57206	−0.0909362
$801$	−5.98985	−0.211641
$802$	−36.7588	−1.29800
$803$	−16.6509	−0.587598
$804$	−15.7230	−0.554507
$805$	7.36765	0.259676
$806$	−40.9513	−1.44245
$807$	3.85471	0.135692
$808$	−11.6688	−0.410506
$809$	−4.51031	−0.158574	−0.0792870	−	0.996852i	$-0.525264\pi$
$809$	−4.51031	−0.158574	−0.0792870	+	0.996852i	$0.525264\pi$
$810$	−1.55818	−0.0547490
$811$	35.0552	1.23095	0.615477	−	0.788155i	$-0.288964\pi$
$811$	35.0552	1.23095	0.615477	+	0.788155i	$0.288964\pi$
$812$	8.18856	0.287362
$813$	−13.9785	−0.490249
$814$	−16.1484	−0.566001
$815$	−10.6855	−0.374298
$816$	1.00000	0.0350070
$817$	−22.4862	−0.786693
$818$	28.6561	1.00194
$819$	11.2963	0.394726
$820$	−6.63792	−0.231806
$821$	−0.961678	−0.0335628	−0.0167814	−	0.999859i	$-0.505342\pi$
$821$	−0.961678	−0.0335628	−0.0167814	+	0.999859i	$0.505342\pi$
$822$	−7.76997	−0.271009
$823$	−27.2421	−0.949600	−0.474800	−	0.880094i	$-0.657480\pi$
$823$	−27.2421	−0.949600	−0.474800	+	0.880094i	$0.657480\pi$
$824$	−1.41322	−0.0492318
$825$	5.09259	0.177301
$826$	1.66703	0.0580032
$827$	50.2481	1.74730	0.873649	−	0.486557i	$-0.161748\pi$
$827$	50.2481	1.74730	0.873649	+	0.486557i	$0.161748\pi$
$828$	2.83641	0.0985719
$829$	46.5481	1.61668	0.808342	−	0.588713i	$-0.200365\pi$
$829$	46.5481	1.61668	0.808342	+	0.588713i	$0.200365\pi$
$830$	−6.17438	−0.214316
$831$	−21.2804	−0.738211
$832$	−6.77634	−0.234927
$833$	4.22103	0.146250
$834$	8.41649	0.291439
$835$	−8.04718	−0.278484
$836$	−4.73373	−0.163719
$837$	−6.04328	−0.208886
$838$	33.8962	1.17093
$839$	−28.5838	−0.986823	−0.493411	−	0.869796i	$-0.664250\pi$
$839$	−28.5838	−0.986823	−0.493411	+	0.869796i	$0.664250\pi$
$840$	−2.59753	−0.0896234
$841$	−4.87147	−0.167982
$842$	10.0798	0.347374
$843$	10.3784	0.357452
$844$	17.5114	0.602768
$845$	−51.2936	−1.76455
$846$	7.17870	0.246809
$847$	11.8021	0.405526
$848$	6.54262	0.224675
$849$	3.26560	0.112075
$850$	2.57206	0.0882211
$851$	−23.1335	−0.793005
$852$	2.46506	0.0844514
$853$	−38.7646	−1.32727	−0.663637	−	0.748055i	$-0.730988\pi$
$853$	−38.7646	−1.32727	−0.663637	+	0.748055i	$0.730988\pi$
$854$	−3.63562	−0.124408
$855$	3.72533	0.127404
$856$	11.3684	0.388563
$857$	−13.8090	−0.471707	−0.235853	−	0.971789i	$-0.575789\pi$
$857$	−13.8090	−0.471707	−0.235853	+	0.971789i	$0.575789\pi$
$858$	13.4169	0.458046
$859$	−23.9138	−0.815929	−0.407964	−	0.912998i	$-0.633761\pi$
$859$	−23.9138	−0.815929	−0.407964	+	0.912998i	$0.633761\pi$
$860$	−14.6551	−0.499735
$861$	7.10160	0.242022
$862$	31.8771	1.08574
$863$	−23.2199	−0.790416	−0.395208	−	0.918592i	$-0.629327\pi$
$863$	−23.2199	−0.790416	−0.395208	+	0.918592i	$0.629327\pi$
$864$	−1.00000	−0.0340207
$865$	−23.1276	−0.786362
$866$	−30.4948	−1.03626
$867$	−1.00000	−0.0339618
$868$	−10.0743	−0.341944
$869$	−0.561267	−0.0190397
$870$	−7.65392	−0.259492
$871$	−106.544	−3.61012
$872$	14.5385	0.492337
$873$	−3.10822	−0.105197
$874$	−6.78132	−0.229382
$875$	−19.6687	−0.664923
$876$	8.40971	0.284138
$877$	21.8111	0.736507	0.368254	−	0.929725i	$-0.379956\pi$
$877$	21.8111	0.736507	0.368254	+	0.929725i	$0.379956\pi$
$878$	−39.4425	−1.33112
$879$	12.5140	0.422085
$880$	−3.08515	−0.104000
$881$	30.1681	1.01639	0.508195	−	0.861242i	$-0.330313\pi$
$881$	30.1681	1.01639	0.508195	+	0.861242i	$0.330313\pi$
$882$	−4.22103	−0.142129
$883$	−23.3678	−0.786388	−0.393194	−	0.919455i	$-0.628630\pi$
$883$	−23.3678	−0.786388	−0.393194	+	0.919455i	$0.628630\pi$
$884$	6.77634	0.227913
$885$	−1.55818	−0.0523778
$886$	21.9370	0.736989
$887$	30.3770	1.01996	0.509980	−	0.860187i	$-0.329653\pi$
$887$	30.3770	1.01996	0.509980	+	0.860187i	$0.329653\pi$
$888$	8.15591	0.273694
$889$	12.1040	0.405955
$890$	9.33329	0.312853
$891$	1.97996	0.0663313
$892$	−25.1785	−0.843040
$893$	−17.1629	−0.574336
$894$	−20.0144	−0.669382
$895$	−14.5377	−0.485940
$896$	−1.66703	−0.0556914
$897$	19.2205	0.641753
$898$	−2.49114	−0.0831304
$899$	−29.6851	−0.990052
$900$	−2.57206	−0.0857355
$901$	−6.54262	−0.217966
$902$	8.43473	0.280846
$903$	15.6788	0.521758
$904$	13.5405	0.450350
$905$	12.3309	0.409893
$906$	15.1815	0.504371
$907$	19.3673	0.643081	0.321541	−	0.946896i	$-0.395799\pi$
$907$	19.3673	0.643081	0.321541	+	0.946896i	$0.395799\pi$
$908$	22.8075	0.756893
$909$	−11.6688	−0.387028
$910$	−17.6018	−0.583493
$911$	37.4710	1.24147	0.620735	−	0.784020i	$-0.286834\pi$
$911$	37.4710	1.24147	0.620735	+	0.784020i	$0.286834\pi$
$912$	2.39081	0.0791678
$913$	7.84570	0.259655
$914$	20.0805	0.664202
$915$	3.39825	0.112343
$916$	12.8728	0.425329
$917$	5.81633	0.192072
$918$	1.00000	0.0330049
$919$	10.8298	0.357241	0.178621	−	0.983918i	$-0.442837\pi$
$919$	10.8298	0.357241	0.178621	+	0.983918i	$0.442837\pi$
$920$	−4.41964	−0.145711
$921$	−18.2155	−0.600222
$922$	21.9373	0.722465
$923$	16.7041	0.549821
$924$	3.30065	0.108583
$925$	20.9775	0.689737
$926$	−10.1675	−0.334126
$927$	−1.41322	−0.0464162
$928$	−4.91208	−0.161247
$929$	32.7174	1.07342	0.536712	−	0.843765i	$-0.319666\pi$
$929$	32.7174	1.07342	0.536712	+	0.843765i	$0.319666\pi$
$930$	9.41653	0.308780
$931$	10.0917	0.330742
$932$	−3.46997	−0.113663
$933$	14.8072	0.484765
$934$	−18.6819	−0.611291
$935$	3.08515	0.100895
$936$	−6.77634	−0.221492
$937$	33.4798	1.09374	0.546869	−	0.837218i	$-0.315820\pi$
$937$	33.4798	1.09374	0.546869	+	0.837218i	$0.315820\pi$
$938$	−26.2106	−0.855807
$939$	−19.1373	−0.624523
$940$	−11.1857	−0.364838
$941$	9.37821	0.305721	0.152860	−	0.988248i	$-0.451151\pi$
$941$	9.37821	0.305721	0.152860	+	0.988248i	$0.451151\pi$
$942$	−6.60417	−0.215175
$943$	12.0832	0.393483
$944$	−1.00000	−0.0325472
$945$	−2.59753	−0.0844977
$946$	18.6220	0.605455
$947$	58.3954	1.89760	0.948798	−	0.315883i	$-0.102301\pi$
$947$	58.3954	1.89760	0.948798	+	0.315883i	$0.102301\pi$
$948$	0.283473	0.00920678
$949$	56.9871	1.84988
$950$	6.14933	0.199511
$951$	12.3067	0.399071
$952$	1.66703	0.0540286
$953$	−5.67876	−0.183953	−0.0919766	−	0.995761i	$-0.529318\pi$
$953$	−5.67876	−0.183953	−0.0919766	+	0.995761i	$0.529318\pi$
$954$	6.54262	0.211825
$955$	20.1735	0.652798
$956$	−7.47119	−0.241635
$957$	9.72574	0.314389
$958$	−14.1653	−0.457661
$959$	−12.9527	−0.418266
$960$	1.55818	0.0502901
$961$	5.52118	0.178103
$962$	55.2673	1.78189
$963$	11.3684	0.366340
$964$	29.2894	0.943349
$965$	0.552791	0.0177950
$966$	4.72836	0.152133
$967$	−37.4267	−1.20356	−0.601781	−	0.798661i	$-0.705542\pi$
$967$	−37.4267	−1.20356	−0.601781	+	0.798661i	$0.705542\pi$
$968$	−7.07974	−0.227552
$969$	−2.39081	−0.0768040
$970$	4.84317	0.155505
$971$	−44.1686	−1.41744	−0.708719	−	0.705491i	$-0.750727\pi$
$971$	−44.1686	−1.41744	−0.708719	+	0.705491i	$0.750727\pi$
$972$	−1.00000	−0.0320750
$973$	14.0305	0.449797
$974$	34.8923	1.11802
$975$	−17.4292	−0.558181
$976$	2.18090	0.0698091
$977$	28.9267	0.925448	0.462724	−	0.886502i	$-0.346872\pi$
$977$	28.9267	0.925448	0.462724	+	0.886502i	$0.346872\pi$
$978$	−6.85769	−0.219285
$979$	−11.8597	−0.379037
$980$	6.57713	0.210099
$981$	14.5385	0.464180
$982$	5.74414	0.183303
$983$	50.4235	1.60826	0.804130	−	0.594453i	$-0.202631\pi$
$983$	50.4235	1.60826	0.804130	+	0.594453i	$0.202631\pi$
$984$	−4.26004	−0.135805
$985$	−8.43903	−0.268890
$986$	4.91208	0.156433
$987$	11.9671	0.380916
$988$	16.2010	0.515422
$989$	26.6771	0.848282
$990$	−3.08515	−0.0980524
$991$	27.6045	0.876887	0.438443	−	0.898759i	$-0.355530\pi$
$991$	27.6045	0.876887	0.438443	+	0.898759i	$0.355530\pi$
$992$	6.04328	0.191874
$993$	9.60702	0.304870
$994$	4.10931	0.130339
$995$	−34.4550	−1.09230
$996$	−3.96255	−0.125558
$997$	25.9381	0.821467	0.410733	−	0.911755i	$-0.365273\pi$
$997$	25.9381	0.821467	0.410733	+	0.911755i	$0.365273\pi$
$998$	−24.7178	−0.782430
$999$	8.15591	0.258042

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6018.2.a.z.1.3	✓	11

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6018.2.a.z.1.3	✓	11	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 6018 = 2 \cdot 3 \cdot 17 \cdot 59 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6018.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -1.55818 q^{5} -1.00000 q^{6} -1.66703 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -1.55818 q^{5} -1.00000 q^{6} -1.66703 q^{7} +1.00000 q^{8} +1.00000 q^{9} -1.55818 q^{10} +1.97996 q^{11} -1.00000 q^{12} -6.77634 q^{13} -1.66703 q^{14} +1.55818 q^{15} +1.00000 q^{16} -1.00000 q^{17} +1.00000 q^{18} -2.39081 q^{19} -1.55818 q^{20} +1.66703 q^{21} +1.97996 q^{22} +2.83641 q^{23} -1.00000 q^{24} -2.57206 q^{25} -6.77634 q^{26} -1.00000 q^{27} -1.66703 q^{28} -4.91208 q^{29} +1.55818 q^{30} +6.04328 q^{31} +1.00000 q^{32} -1.97996 q^{33} -1.00000 q^{34} +2.59753 q^{35} +1.00000 q^{36} -8.15591 q^{37} -2.39081 q^{38} +6.77634 q^{39} -1.55818 q^{40} +4.26004 q^{41} +1.66703 q^{42} +9.40525 q^{43} +1.97996 q^{44} -1.55818 q^{45} +2.83641 q^{46} +7.17870 q^{47} -1.00000 q^{48} -4.22103 q^{49} -2.57206 q^{50} +1.00000 q^{51} -6.77634 q^{52} +6.54262 q^{53} -1.00000 q^{54} -3.08515 q^{55} -1.66703 q^{56} +2.39081 q^{57} -4.91208 q^{58} -1.00000 q^{59} +1.55818 q^{60} +2.18090 q^{61} +6.04328 q^{62} -1.66703 q^{63} +1.00000 q^{64} +10.5588 q^{65} -1.97996 q^{66} +15.7230 q^{67} -1.00000 q^{68} -2.83641 q^{69} +2.59753 q^{70} -2.46506 q^{71} +1.00000 q^{72} -8.40971 q^{73} -8.15591 q^{74} +2.57206 q^{75} -2.39081 q^{76} -3.30065 q^{77} +6.77634 q^{78} -0.283473 q^{79} -1.55818 q^{80} +1.00000 q^{81} +4.26004 q^{82} +3.96255 q^{83} +1.66703 q^{84} +1.55818 q^{85} +9.40525 q^{86} +4.91208 q^{87} +1.97996 q^{88} -5.98985 q^{89} -1.55818 q^{90} +11.2963 q^{91} +2.83641 q^{92} -6.04328 q^{93} +7.17870 q^{94} +3.72533 q^{95} -1.00000 q^{96} -3.10822 q^{97} -4.22103 q^{98} +1.97996 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 11 q + 11 q^{2} - 11 q^{3} + 11 q^{4} + 4 q^{5} - 11 q^{6} + 3 q^{7} + 11 q^{8} + 11 q^{9}+O(q^{10}) \) 11 * q + 11 * q^2 - 11 * q^3 + 11 * q^4 + 4 * q^5 - 11 * q^6 + 3 * q^7 + 11 * q^8 + 11 * q^9	\( 11 q + 11 q^{2} - 11 q^{3} + 11 q^{4} + 4 q^{5} - 11 q^{6} + 3 q^{7} + 11 q^{8} + 11 q^{9} + 4 q^{10} + 9 q^{11} - 11 q^{12} + 6 q^{13} + 3 q^{14} - 4 q^{15} + 11 q^{16} - 11 q^{17} + 11 q^{18} - q^{19} + 4 q^{20} - 3 q^{21} + 9 q^{22} + 10 q^{23} - 11 q^{24} + 15 q^{25} + 6 q^{26} - 11 q^{27} + 3 q^{28} + 14 q^{29} - 4 q^{30} + 17 q^{31} + 11 q^{32} - 9 q^{33} - 11 q^{34} + 8 q^{35} + 11 q^{36} + 30 q^{37} - q^{38} - 6 q^{39} + 4 q^{40} + 10 q^{41} - 3 q^{42} + 11 q^{43} + 9 q^{44} + 4 q^{45} + 10 q^{46} - 6 q^{47} - 11 q^{48} + 18 q^{49} + 15 q^{50} + 11 q^{51} + 6 q^{52} + 10 q^{53} - 11 q^{54} - 11 q^{55} + 3 q^{56} + q^{57} + 14 q^{58} - 11 q^{59} - 4 q^{60} + 13 q^{61} + 17 q^{62} + 3 q^{63} + 11 q^{64} + 32 q^{65} - 9 q^{66} + 26 q^{67} - 11 q^{68} - 10 q^{69} + 8 q^{70} + 14 q^{71} + 11 q^{72} + 20 q^{73} + 30 q^{74} - 15 q^{75} - q^{76} + 26 q^{77} - 6 q^{78} + 15 q^{79} + 4 q^{80} + 11 q^{81} + 10 q^{82} + 2 q^{83} - 3 q^{84} - 4 q^{85} + 11 q^{86} - 14 q^{87} + 9 q^{88} + q^{89} + 4 q^{90} + 17 q^{91} + 10 q^{92} - 17 q^{93} - 6 q^{94} + 3 q^{95} - 11 q^{96} + 33 q^{97} + 18 q^{98} + 9 q^{99}+O(q^{100}) \) 11 * q + 11 * q^2 - 11 * q^3 + 11 * q^4 + 4 * q^5 - 11 * q^6 + 3 * q^7 + 11 * q^8 + 11 * q^9 + 4 * q^10 + 9 * q^11 - 11 * q^12 + 6 * q^13 + 3 * q^14 - 4 * q^15 + 11 * q^16 - 11 * q^17 + 11 * q^18 - q^19 + 4 * q^20 - 3 * q^21 + 9 * q^22 + 10 * q^23 - 11 * q^24 + 15 * q^25 + 6 * q^26 - 11 * q^27 + 3 * q^28 + 14 * q^29 - 4 * q^30 + 17 * q^31 + 11 * q^32 - 9 * q^33 - 11 * q^34 + 8 * q^35 + 11 * q^36 + 30 * q^37 - q^38 - 6 * q^39 + 4 * q^40 + 10 * q^41 - 3 * q^42 + 11 * q^43 + 9 * q^44 + 4 * q^45 + 10 * q^46 - 6 * q^47 - 11 * q^48 + 18 * q^49 + 15 * q^50 + 11 * q^51 + 6 * q^52 + 10 * q^53 - 11 * q^54 - 11 * q^55 + 3 * q^56 + q^57 + 14 * q^58 - 11 * q^59 - 4 * q^60 + 13 * q^61 + 17 * q^62 + 3 * q^63 + 11 * q^64 + 32 * q^65 - 9 * q^66 + 26 * q^67 - 11 * q^68 - 10 * q^69 + 8 * q^70 + 14 * q^71 + 11 * q^72 + 20 * q^73 + 30 * q^74 - 15 * q^75 - q^76 + 26 * q^77 - 6 * q^78 + 15 * q^79 + 4 * q^80 + 11 * q^81 + 10 * q^82 + 2 * q^83 - 3 * q^84 - 4 * q^85 + 11 * q^86 - 14 * q^87 + 9 * q^88 + q^89 + 4 * q^90 + 17 * q^91 + 10 * q^92 - 17 * q^93 - 6 * q^94 + 3 * q^95 - 11 * q^96 + 33 * q^97 + 18 * q^98 + 9 * q^99

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