LMFDB - Embedded newform 8034.2.a.q.1.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8034,2,Mod(1,8034)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8034, 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("8034.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8034 = 2 \cdot 3 \cdot 13 \cdot 103 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8034.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:	$64.1518129839$
Analytic rank:	$1$
Dimension:	$8$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 2x^{7} - 11x^{6} + 21x^{5} + 23x^{4} - 29x^{3} - 27x^{2} + x + 3 $ x^8 - 2x^7 - 11x^6 + 21x^5 + 23x^4 - 29x^3 - 27x^2 + x + 3
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			$0.315468$ of defining polynomial
Character	$\chi$	$=$	8034.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -0.684532 q^{5} +1.00000 q^{6} -1.46314 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -0.684532 q^{5} +1.00000 q^{6} -1.46314 q^{7} +1.00000 q^{8} +1.00000 q^{9} -0.684532 q^{10} -0.852331 q^{11} +1.00000 q^{12} -1.00000 q^{13} -1.46314 q^{14} -0.684532 q^{15} +1.00000 q^{16} +4.18602 q^{17} +1.00000 q^{18} -7.25777 q^{19} -0.684532 q^{20} -1.46314 q^{21} -0.852331 q^{22} +8.93399 q^{23} +1.00000 q^{24} -4.53142 q^{25} -1.00000 q^{26} +1.00000 q^{27} -1.46314 q^{28} -9.35782 q^{29} -0.684532 q^{30} -7.80209 q^{31} +1.00000 q^{32} -0.852331 q^{33} +4.18602 q^{34} +1.00156 q^{35} +1.00000 q^{36} -5.54810 q^{37} -7.25777 q^{38} -1.00000 q^{39} -0.684532 q^{40} +7.52426 q^{41} -1.46314 q^{42} +10.1742 q^{43} -0.852331 q^{44} -0.684532 q^{45} +8.93399 q^{46} -6.03336 q^{47} +1.00000 q^{48} -4.85923 q^{49} -4.53142 q^{50} +4.18602 q^{51} -1.00000 q^{52} +4.03835 q^{53} +1.00000 q^{54} +0.583447 q^{55} -1.46314 q^{56} -7.25777 q^{57} -9.35782 q^{58} -11.8277 q^{59} -0.684532 q^{60} -5.34907 q^{61} -7.80209 q^{62} -1.46314 q^{63} +1.00000 q^{64} +0.684532 q^{65} -0.852331 q^{66} -8.90152 q^{67} +4.18602 q^{68} +8.93399 q^{69} +1.00156 q^{70} +7.58775 q^{71} +1.00000 q^{72} -3.57276 q^{73} -5.54810 q^{74} -4.53142 q^{75} -7.25777 q^{76} +1.24708 q^{77} -1.00000 q^{78} +7.23728 q^{79} -0.684532 q^{80} +1.00000 q^{81} +7.52426 q^{82} -9.34849 q^{83} -1.46314 q^{84} -2.86546 q^{85} +10.1742 q^{86} -9.35782 q^{87} -0.852331 q^{88} +1.49352 q^{89} -0.684532 q^{90} +1.46314 q^{91} +8.93399 q^{92} -7.80209 q^{93} -6.03336 q^{94} +4.96817 q^{95} +1.00000 q^{96} -13.1229 q^{97} -4.85923 q^{98} -0.852331 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 8 q^{2} + 8 q^{3} + 8 q^{4} - 6 q^{5} + 8 q^{6} - 3 q^{7} + 8 q^{8} + 8 q^{9}+O(q^{10}) $ 8 * q + 8 * q^2 + 8 * q^3 + 8 * q^4 - 6 * q^5 + 8 * q^6 - 3 * q^7 + 8 * q^8 + 8 * q^9	\( 8 q + 8 q^{2} + 8 q^{3} + 8 q^{4} - 6 q^{5} + 8 q^{6} - 3 q^{7} + 8 q^{8} + 8 q^{9} - 6 q^{10} - 15 q^{11} + 8 q^{12} - 8 q^{13} - 3 q^{14} - 6 q^{15} + 8 q^{16} - 11 q^{17} + 8 q^{18} - 15 q^{19} - 6 q^{20} - 3 q^{21} - 15 q^{22} + q^{23} + 8 q^{24} - 10 q^{25} - 8 q^{26} + 8 q^{27} - 3 q^{28} - 10 q^{29} - 6 q^{30} - 3 q^{31} + 8 q^{32} - 15 q^{33} - 11 q^{34} - 12 q^{35} + 8 q^{36} - 26 q^{37} - 15 q^{38} - 8 q^{39} - 6 q^{40} - 12 q^{41} - 3 q^{42} - 4 q^{43} - 15 q^{44} - 6 q^{45} + q^{46} - 6 q^{47} + 8 q^{48} - 5 q^{49} - 10 q^{50} - 11 q^{51} - 8 q^{52} - 4 q^{53} + 8 q^{54} - 3 q^{56} - 15 q^{57} - 10 q^{58} - 19 q^{59} - 6 q^{60} - 14 q^{61} - 3 q^{62} - 3 q^{63} + 8 q^{64} + 6 q^{65} - 15 q^{66} - 13 q^{67} - 11 q^{68} + q^{69} - 12 q^{70} - 31 q^{71} + 8 q^{72} - 27 q^{73} - 26 q^{74} - 10 q^{75} - 15 q^{76} - 30 q^{77} - 8 q^{78} - 13 q^{79} - 6 q^{80} + 8 q^{81} - 12 q^{82} - 28 q^{83} - 3 q^{84} + 15 q^{85} - 4 q^{86} - 10 q^{87} - 15 q^{88} - 2 q^{89} - 6 q^{90} + 3 q^{91} + q^{92} - 3 q^{93} - 6 q^{94} - 18 q^{95} + 8 q^{96} - 30 q^{97} - 5 q^{98} - 15 q^{99}+O(q^{100}) \) 8 * q + 8 * q^2 + 8 * q^3 + 8 * q^4 - 6 * q^5 + 8 * q^6 - 3 * q^7 + 8 * q^8 + 8 * q^9 - 6 * q^10 - 15 * q^11 + 8 * q^12 - 8 * q^13 - 3 * q^14 - 6 * q^15 + 8 * q^16 - 11 * q^17 + 8 * q^18 - 15 * q^19 - 6 * q^20 - 3 * q^21 - 15 * q^22 + q^23 + 8 * q^24 - 10 * q^25 - 8 * q^26 + 8 * q^27 - 3 * q^28 - 10 * q^29 - 6 * q^30 - 3 * q^31 + 8 * q^32 - 15 * q^33 - 11 * q^34 - 12 * q^35 + 8 * q^36 - 26 * q^37 - 15 * q^38 - 8 * q^39 - 6 * q^40 - 12 * q^41 - 3 * q^42 - 4 * q^43 - 15 * q^44 - 6 * q^45 + q^46 - 6 * q^47 + 8 * q^48 - 5 * q^49 - 10 * q^50 - 11 * q^51 - 8 * q^52 - 4 * q^53 + 8 * q^54 - 3 * q^56 - 15 * q^57 - 10 * q^58 - 19 * q^59 - 6 * q^60 - 14 * q^61 - 3 * q^62 - 3 * q^63 + 8 * q^64 + 6 * q^65 - 15 * q^66 - 13 * q^67 - 11 * q^68 + q^69 - 12 * q^70 - 31 * q^71 + 8 * q^72 - 27 * q^73 - 26 * q^74 - 10 * q^75 - 15 * q^76 - 30 * q^77 - 8 * q^78 - 13 * q^79 - 6 * q^80 + 8 * q^81 - 12 * q^82 - 28 * q^83 - 3 * q^84 + 15 * q^85 - 4 * q^86 - 10 * q^87 - 15 * q^88 - 2 * q^89 - 6 * q^90 + 3 * q^91 + q^92 - 3 * q^93 - 6 * q^94 - 18 * q^95 + 8 * q^96 - 30 * q^97 - 5 * q^98 - 15 * 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
$5$	−0.684532	−0.306132	−0.153066	−	0.988216i	$-0.548915\pi$
$5$	−0.684532	−0.306132	−0.153066	+	0.988216i	$0.548915\pi$
$6$	1.00000	0.408248
$7$	−1.46314	−0.553014	−0.276507	−	0.961012i	$-0.589177\pi$
$7$	−1.46314	−0.553014	−0.276507	+	0.961012i	$0.589177\pi$
$8$	1.00000	0.353553
$9$	1.00000	0.333333
$10$	−0.684532	−0.216468
$11$	−0.852331	−0.256987	−0.128494	−	0.991710i	$-0.541014\pi$
$11$	−0.852331	−0.256987	−0.128494	+	0.991710i	$0.541014\pi$
$12$	1.00000	0.288675
$13$	−1.00000	−0.277350
$13$	−1.00000	−0.277350
$14$	−1.46314	−0.391040
$15$	−0.684532	−0.176745
$16$	1.00000	0.250000
$17$	4.18602	1.01526	0.507630	−	0.861575i	$-0.330522\pi$
$17$	4.18602	1.01526	0.507630	+	0.861575i	$0.330522\pi$
$18$	1.00000	0.235702
$19$	−7.25777	−1.66505	−0.832523	−	0.553991i	$-0.813104\pi$
$19$	−7.25777	−1.66505	−0.832523	+	0.553991i	$0.813104\pi$
$20$	−0.684532	−0.153066
$21$	−1.46314	−0.319283
$22$	−0.852331	−0.181718
$23$	8.93399	1.86287	0.931433	−	0.363913i	$-0.118560\pi$
$23$	8.93399	1.86287	0.931433	+	0.363913i	$0.118560\pi$
$24$	1.00000	0.204124
$25$	−4.53142	−0.906283
$26$	−1.00000	−0.196116
$27$	1.00000	0.192450
$28$	−1.46314	−0.276507
$29$	−9.35782	−1.73770	−0.868852	−	0.495072i	$-0.835142\pi$
$29$	−9.35782	−1.73770	−0.868852	+	0.495072i	$0.835142\pi$
$30$	−0.684532	−0.124978
$31$	−7.80209	−1.40130	−0.700649	−	0.713506i	$-0.747106\pi$
$31$	−7.80209	−1.40130	−0.700649	+	0.713506i	$0.747106\pi$
$32$	1.00000	0.176777
$33$	−0.852331	−0.148372
$34$	4.18602	0.717897
$35$	1.00156	0.169295
$36$	1.00000	0.166667
$37$	−5.54810	−0.912102	−0.456051	−	0.889954i	$-0.650736\pi$
$37$	−5.54810	−0.912102	−0.456051	+	0.889954i	$0.650736\pi$
$38$	−7.25777	−1.17737
$39$	−1.00000	−0.160128
$40$	−0.684532	−0.108234
$41$	7.52426	1.17509	0.587546	−	0.809191i	$-0.300094\pi$
$41$	7.52426	1.17509	0.587546	+	0.809191i	$0.300094\pi$
$42$	−1.46314	−0.225767
$43$	10.1742	1.55155	0.775776	−	0.631008i	$-0.217358\pi$
$43$	10.1742	1.55155	0.775776	+	0.631008i	$0.217358\pi$
$44$	−0.852331	−0.128494
$45$	−0.684532	−0.102044
$46$	8.93399	1.31724
$47$	−6.03336	−0.880056	−0.440028	−	0.897984i	$-0.645031\pi$
$47$	−6.03336	−0.880056	−0.440028	+	0.897984i	$0.645031\pi$
$48$	1.00000	0.144338
$49$	−4.85923	−0.694175
$50$	−4.53142	−0.640839
$51$	4.18602	0.586160
$52$	−1.00000	−0.138675
$53$	4.03835	0.554710	0.277355	−	0.960767i	$-0.410542\pi$
$53$	4.03835	0.554710	0.277355	+	0.960767i	$0.410542\pi$
$54$	1.00000	0.136083
$55$	0.583447	0.0786720
$56$	−1.46314	−0.195520
$57$	−7.25777	−0.961315
$58$	−9.35782	−1.22874
$59$	−11.8277	−1.53984	−0.769918	−	0.638143i	$-0.779703\pi$
$59$	−11.8277	−1.53984	−0.769918	+	0.638143i	$0.779703\pi$
$60$	−0.684532	−0.0883727
$61$	−5.34907	−0.684878	−0.342439	−	0.939540i	$-0.611253\pi$
$61$	−5.34907	−0.684878	−0.342439	+	0.939540i	$0.611253\pi$
$62$	−7.80209	−0.990867
$63$	−1.46314	−0.184338
$64$	1.00000	0.125000
$65$	0.684532	0.0849057
$66$	−0.852331	−0.104915
$67$	−8.90152	−1.08749	−0.543747	−	0.839249i	$-0.682995\pi$
$67$	−8.90152	−1.08749	−0.543747	+	0.839249i	$0.682995\pi$
$68$	4.18602	0.507630
$69$	8.93399	1.07553
$70$	1.00156	0.119710
$71$	7.58775	0.900500	0.450250	−	0.892902i	$-0.351335\pi$
$71$	7.58775	0.900500	0.450250	+	0.892902i	$0.351335\pi$
$72$	1.00000	0.117851
$73$	−3.57276	−0.418160	−0.209080	−	0.977899i	$-0.567047\pi$
$73$	−3.57276	−0.418160	−0.209080	+	0.977899i	$0.567047\pi$
$74$	−5.54810	−0.644953
$75$	−4.53142	−0.523243
$76$	−7.25777	−0.832523
$77$	1.24708	0.142118
$78$	−1.00000	−0.113228
$79$	7.23728	0.814258	0.407129	−	0.913371i	$-0.366530\pi$
$79$	7.23728	0.814258	0.407129	+	0.913371i	$0.366530\pi$
$80$	−0.684532	−0.0765330
$81$	1.00000	0.111111
$82$	7.52426	0.830915
$83$	−9.34849	−1.02613	−0.513065	−	0.858350i	$-0.671490\pi$
$83$	−9.34849	−1.02613	−0.513065	+	0.858350i	$0.671490\pi$
$84$	−1.46314	−0.159641
$85$	−2.86546	−0.310803
$86$	10.1742	1.09711
$87$	−9.35782	−1.00326
$88$	−0.852331	−0.0908588
$89$	1.49352	0.158313	0.0791564	−	0.996862i	$-0.474777\pi$
$89$	1.49352	0.158313	0.0791564	+	0.996862i	$0.474777\pi$
$90$	−0.684532	−0.0721560
$91$	1.46314	0.153378
$92$	8.93399	0.931433
$93$	−7.80209	−0.809039
$94$	−6.03336	−0.622293
$95$	4.96817	0.509724
$96$	1.00000	0.102062
$97$	−13.1229	−1.33242	−0.666212	−	0.745762i	$-0.732085\pi$
$97$	−13.1229	−1.33242	−0.666212	+	0.745762i	$0.732085\pi$
$98$	−4.85923	−0.490856
$99$	−0.852331	−0.0856625
$100$	−4.53142	−0.453142
$101$	14.3892	1.43178	0.715892	−	0.698212i	$-0.246021\pi$
$101$	14.3892	1.43178	0.715892	+	0.698212i	$0.246021\pi$
$102$	4.18602	0.414478
$103$	−1.00000	−0.0985329
$103$	−1.00000	−0.0985329
$104$	−1.00000	−0.0980581
$105$	1.00156	0.0977426
$106$	4.03835	0.392239
$107$	−8.77589	−0.848397	−0.424199	−	0.905569i	$-0.639444\pi$
$107$	−8.77589	−0.848397	−0.424199	+	0.905569i	$0.639444\pi$
$108$	1.00000	0.0962250
$109$	2.87277	0.275161	0.137581	−	0.990491i	$-0.456067\pi$
$109$	2.87277	0.275161	0.137581	+	0.990491i	$0.456067\pi$
$110$	0.583447	0.0556295
$111$	−5.54810	−0.526602
$112$	−1.46314	−0.138254
$113$	4.54248	0.427321	0.213660	−	0.976908i	$-0.431461\pi$
$113$	4.54248	0.427321	0.213660	+	0.976908i	$0.431461\pi$
$114$	−7.25777	−0.679752
$115$	−6.11560	−0.570283
$116$	−9.35782	−0.868852
$117$	−1.00000	−0.0924500
$118$	−11.8277	−1.08883
$119$	−6.12472	−0.561453
$120$	−0.684532	−0.0624889
$121$	−10.2735	−0.933957
$122$	−5.34907	−0.484282
$123$	7.52426	0.678440
$124$	−7.80209	−0.700649
$125$	6.52456	0.583574
$126$	−1.46314	−0.130347
$127$	−18.0691	−1.60337	−0.801687	−	0.597743i	$-0.796064\pi$
$127$	−18.0691	−1.60337	−0.801687	+	0.597743i	$0.796064\pi$
$128$	1.00000	0.0883883
$129$	10.1742	0.895789
$130$	0.684532	0.0600374
$131$	18.7682	1.63978	0.819891	−	0.572520i	$-0.194034\pi$
$131$	18.7682	1.63978	0.819891	+	0.572520i	$0.194034\pi$
$132$	−0.852331	−0.0741859
$133$	10.6191	0.920794
$134$	−8.90152	−0.768974
$135$	−0.684532	−0.0589151
$136$	4.18602	0.358948
$137$	−12.6165	−1.07790	−0.538950	−	0.842337i	$-0.681179\pi$
$137$	−12.6165	−1.07790	−0.538950	+	0.842337i	$0.681179\pi$
$138$	8.93399	0.760512
$139$	−1.54440	−0.130994	−0.0654972	−	0.997853i	$-0.520863\pi$
$139$	−1.54440	−0.130994	−0.0654972	+	0.997853i	$0.520863\pi$
$140$	1.00156	0.0846476
$141$	−6.03336	−0.508100
$142$	7.58775	0.636750
$143$	0.852331	0.0712755
$144$	1.00000	0.0833333
$145$	6.40572	0.531966
$146$	−3.57276	−0.295684
$147$	−4.85923	−0.400782
$148$	−5.54810	−0.456051
$149$	−14.4252	−1.18176	−0.590880	−	0.806759i	$-0.701219\pi$
$149$	−14.4252	−1.18176	−0.590880	+	0.806759i	$0.701219\pi$
$150$	−4.53142	−0.369989
$151$	−13.4386	−1.09362	−0.546808	−	0.837258i	$-0.684157\pi$
$151$	−13.4386	−1.09362	−0.546808	+	0.837258i	$0.684157\pi$
$152$	−7.25777	−0.588683
$153$	4.18602	0.338420
$154$	1.24708	0.100492
$155$	5.34078	0.428982
$156$	−1.00000	−0.0800641
$157$	−1.79833	−0.143523	−0.0717614	−	0.997422i	$-0.522862\pi$
$157$	−1.79833	−0.143523	−0.0717614	+	0.997422i	$0.522862\pi$
$158$	7.23728	0.575767
$159$	4.03835	0.320262
$160$	−0.684532	−0.0541170
$161$	−13.0717	−1.03019
$162$	1.00000	0.0785674
$163$	13.8168	1.08222	0.541108	−	0.840953i	$-0.318005\pi$
$163$	13.8168	1.08222	0.541108	+	0.840953i	$0.318005\pi$
$164$	7.52426	0.587546
$165$	0.583447	0.0454213
$166$	−9.34849	−0.725584
$167$	−1.72810	−0.133724	−0.0668622	−	0.997762i	$-0.521299\pi$
$167$	−1.72810	−0.133724	−0.0668622	+	0.997762i	$0.521299\pi$
$168$	−1.46314	−0.112884
$169$	1.00000	0.0769231
$170$	−2.86546	−0.219771
$171$	−7.25777	−0.555015
$172$	10.1742	0.775776
$173$	15.9660	1.21387	0.606935	−	0.794751i	$-0.292399\pi$
$173$	15.9660	1.21387	0.606935	+	0.794751i	$0.292399\pi$
$174$	−9.35782	−0.709414
$175$	6.63009	0.501187
$176$	−0.852331	−0.0642468
$177$	−11.8277	−0.889025
$178$	1.49352	0.111944
$179$	2.82006	0.210781	0.105391	−	0.994431i	$-0.466391\pi$
$179$	2.82006	0.210781	0.105391	+	0.994431i	$0.466391\pi$
$180$	−0.684532	−0.0510220
$181$	1.24487	0.0925302	0.0462651	−	0.998929i	$-0.485268\pi$
$181$	1.24487	0.0925302	0.0462651	+	0.998929i	$0.485268\pi$
$182$	1.46314	0.108455
$183$	−5.34907	−0.395414
$184$	8.93399	0.658622
$185$	3.79785	0.279223
$186$	−7.80209	−0.572077
$187$	−3.56787	−0.260909
$188$	−6.03336	−0.440028
$189$	−1.46314	−0.106428
$190$	4.96817	0.360429
$191$	−20.9678	−1.51718	−0.758590	−	0.651569i	$-0.774111\pi$
$191$	−20.9678	−1.51718	−0.758590	+	0.651569i	$0.774111\pi$
$192$	1.00000	0.0721688
$193$	16.7859	1.20828	0.604140	−	0.796879i	$-0.293517\pi$
$193$	16.7859	1.20828	0.604140	+	0.796879i	$0.293517\pi$
$194$	−13.1229	−0.942166
$195$	0.684532	0.0490203
$196$	−4.85923	−0.347088
$197$	−17.9766	−1.28078	−0.640390	−	0.768050i	$-0.721227\pi$
$197$	−17.9766	−1.28078	−0.640390	+	0.768050i	$0.721227\pi$
$198$	−0.852331	−0.0605725
$199$	25.9055	1.83639	0.918197	−	0.396124i	$-0.129645\pi$
$199$	25.9055	1.83639	0.918197	+	0.396124i	$0.129645\pi$
$200$	−4.53142	−0.320420
$201$	−8.90152	−0.627865
$202$	14.3892	1.01242
$203$	13.6918	0.960974
$204$	4.18602	0.293080
$205$	−5.15059	−0.359733
$206$	−1.00000	−0.0696733
$207$	8.93399	0.620955
$208$	−1.00000	−0.0693375
$209$	6.18602	0.427896
$210$	1.00156	0.0691145
$211$	−24.6481	−1.69684	−0.848421	−	0.529322i	$-0.822446\pi$
$211$	−24.6481	−1.69684	−0.848421	+	0.529322i	$0.822446\pi$
$212$	4.03835	0.277355
$213$	7.58775	0.519904
$214$	−8.77589	−0.599908
$215$	−6.96457	−0.474980
$216$	1.00000	0.0680414
$217$	11.4155	0.774937
$218$	2.87277	0.194568
$219$	−3.57276	−0.241425
$220$	0.583447	0.0393360
$221$	−4.18602	−0.281582
$222$	−5.54810	−0.372364
$223$	6.56161	0.439398	0.219699	−	0.975568i	$-0.429493\pi$
$223$	6.56161	0.439398	0.219699	+	0.975568i	$0.429493\pi$
$224$	−1.46314	−0.0977600
$225$	−4.53142	−0.302094
$226$	4.54248	0.302161
$227$	−5.97922	−0.396855	−0.198427	−	0.980116i	$-0.563583\pi$
$227$	−5.97922	−0.396855	−0.198427	+	0.980116i	$0.563583\pi$
$228$	−7.25777	−0.480657
$229$	0.430082	0.0284206	0.0142103	−	0.999899i	$-0.495477\pi$
$229$	0.430082	0.0284206	0.0142103	+	0.999899i	$0.495477\pi$
$230$	−6.11560	−0.403251
$231$	1.24708	0.0820516
$232$	−9.35782	−0.614371
$233$	6.90703	0.452495	0.226247	−	0.974070i	$-0.427354\pi$
$233$	6.90703	0.452495	0.226247	+	0.974070i	$0.427354\pi$
$234$	−1.00000	−0.0653720
$235$	4.13003	0.269413
$236$	−11.8277	−0.769918
$237$	7.23728	0.470112
$238$	−6.12472	−0.397007
$239$	9.90323	0.640587	0.320293	−	0.947318i	$-0.396218\pi$
$239$	9.90323	0.640587	0.320293	+	0.947318i	$0.396218\pi$
$240$	−0.684532	−0.0441863
$241$	−5.75164	−0.370496	−0.185248	−	0.982692i	$-0.559309\pi$
$241$	−5.75164	−0.370496	−0.185248	+	0.982692i	$0.559309\pi$
$242$	−10.2735	−0.660408
$243$	1.00000	0.0641500
$244$	−5.34907	−0.342439
$245$	3.32630	0.212509
$246$	7.52426	0.479729
$247$	7.25777	0.461801
$248$	−7.80209	−0.495433
$249$	−9.34849	−0.592437
$250$	6.52456	0.412649
$251$	−11.5382	−0.728282	−0.364141	−	0.931344i	$-0.618637\pi$
$251$	−11.5382	−0.728282	−0.364141	+	0.931344i	$0.618637\pi$
$252$	−1.46314	−0.0921690
$253$	−7.61471	−0.478733
$254$	−18.0691	−1.13376
$255$	−2.86546	−0.179442
$256$	1.00000	0.0625000
$257$	−22.3502	−1.39416	−0.697082	−	0.716991i	$-0.745519\pi$
$257$	−22.3502	−1.39416	−0.697082	+	0.716991i	$0.745519\pi$
$258$	10.1742	0.633419
$259$	8.11763	0.504405
$260$	0.684532	0.0424529
$261$	−9.35782	−0.579234
$262$	18.7682	1.15950
$263$	−31.2570	−1.92739	−0.963696	−	0.267003i	$-0.913967\pi$
$263$	−31.2570	−1.92739	−0.963696	+	0.267003i	$0.913967\pi$
$264$	−0.852331	−0.0524573
$265$	−2.76438	−0.169815
$266$	10.6191	0.651099
$267$	1.49352	0.0914019
$268$	−8.90152	−0.543747
$269$	−25.3631	−1.54642	−0.773209	−	0.634151i	$-0.781350\pi$
$269$	−25.3631	−1.54642	−0.773209	+	0.634151i	$0.781350\pi$
$270$	−0.684532	−0.0416593
$271$	12.2195	0.742280	0.371140	−	0.928577i	$-0.378967\pi$
$271$	12.2195	0.742280	0.371140	+	0.928577i	$0.378967\pi$
$272$	4.18602	0.253815
$273$	1.46314	0.0885531
$274$	−12.6165	−0.762191
$275$	3.86227	0.232903
$276$	8.93399	0.537763
$277$	−25.3017	−1.52023	−0.760115	−	0.649789i	$-0.774857\pi$
$277$	−25.3017	−1.52023	−0.760115	+	0.649789i	$0.774857\pi$
$278$	−1.54440	−0.0926271
$279$	−7.80209	−0.467099
$280$	1.00156	0.0598549
$281$	−19.7540	−1.17842	−0.589212	−	0.807978i	$-0.700562\pi$
$281$	−19.7540	−1.17842	−0.589212	+	0.807978i	$0.700562\pi$
$282$	−6.03336	−0.359281
$283$	3.83554	0.227999	0.114000	−	0.993481i	$-0.463634\pi$
$283$	3.83554	0.227999	0.114000	+	0.993481i	$0.463634\pi$
$284$	7.58775	0.450250
$285$	4.96817	0.294289
$286$	0.852331	0.0503994
$287$	−11.0090	−0.649842
$288$	1.00000	0.0589256
$289$	0.522771	0.0307512
$290$	6.40572	0.376157
$291$	−13.1229	−0.769276
$292$	−3.57276	−0.209080
$293$	−14.5198	−0.848257	−0.424128	−	0.905602i	$-0.639419\pi$
$293$	−14.5198	−0.848257	−0.424128	+	0.905602i	$0.639419\pi$
$294$	−4.85923	−0.283396
$295$	8.09644	0.471393
$296$	−5.54810	−0.322477
$297$	−0.852331	−0.0494572
$298$	−14.4252	−0.835631
$299$	−8.93399	−0.516666
$300$	−4.53142	−0.261621
$301$	−14.8863	−0.858030
$302$	−13.4386	−0.773304
$303$	14.3892	0.826640
$304$	−7.25777	−0.416261
$305$	3.66161	0.209663
$306$	4.18602	0.239299
$307$	7.02841	0.401132	0.200566	−	0.979680i	$-0.435722\pi$
$307$	7.02841	0.401132	0.200566	+	0.979680i	$0.435722\pi$
$308$	1.24708	0.0710588
$309$	−1.00000	−0.0568880
$310$	5.34078	0.303336
$311$	32.0849	1.81937	0.909683	−	0.415304i	$-0.136325\pi$
$311$	32.0849	1.81937	0.909683	+	0.415304i	$0.136325\pi$
$312$	−1.00000	−0.0566139
$313$	28.9318	1.63532	0.817661	−	0.575699i	$-0.195270\pi$
$313$	28.9318	1.63532	0.817661	+	0.575699i	$0.195270\pi$
$314$	−1.79833	−0.101486
$315$	1.00156	0.0564317
$316$	7.23728	0.407129
$317$	9.30284	0.522500	0.261250	−	0.965271i	$-0.415865\pi$
$317$	9.30284	0.522500	0.261250	+	0.965271i	$0.415865\pi$
$318$	4.03835	0.226460
$319$	7.97596	0.446568
$320$	−0.684532	−0.0382665
$321$	−8.77589	−0.489822
$322$	−13.0717	−0.728455
$323$	−30.3812	−1.69045
$324$	1.00000	0.0555556
$325$	4.53142	0.251358
$326$	13.8168	0.765242
$327$	2.87277	0.158864
$328$	7.52426	0.415458
$329$	8.82763	0.486683
$330$	0.583447	0.0321177
$331$	−31.1194	−1.71048	−0.855240	−	0.518233i	$-0.826590\pi$
$331$	−31.1194	−1.71048	−0.855240	+	0.518233i	$0.826590\pi$
$332$	−9.34849	−0.513065
$333$	−5.54810	−0.304034
$334$	−1.72810	−0.0945574
$335$	6.09337	0.332917
$336$	−1.46314	−0.0798207
$337$	−20.6049	−1.12242	−0.561211	−	0.827673i	$-0.689665\pi$
$337$	−20.6049	−1.12242	−0.561211	+	0.827673i	$0.689665\pi$
$338$	1.00000	0.0543928
$339$	4.54248	0.246714
$340$	−2.86546	−0.155402
$341$	6.64996	0.360116
$342$	−7.25777	−0.392455
$343$	17.3517	0.936903
$344$	10.1742	0.548557
$345$	−6.11560	−0.329253
$346$	15.9660	0.858336
$347$	10.1696	0.545934	0.272967	−	0.962023i	$-0.411995\pi$
$347$	10.1696	0.545934	0.272967	+	0.962023i	$0.411995\pi$
$348$	−9.35782	−0.501632
$349$	28.8819	1.54601	0.773007	−	0.634397i	$-0.218752\pi$
$349$	28.8819	1.54601	0.773007	+	0.634397i	$0.218752\pi$
$350$	6.63009	0.354393
$351$	−1.00000	−0.0533761
$352$	−0.852331	−0.0454294
$353$	−6.13386	−0.326473	−0.163236	−	0.986587i	$-0.552193\pi$
$353$	−6.13386	−0.326473	−0.163236	+	0.986587i	$0.552193\pi$
$354$	−11.8277	−0.628635
$355$	−5.19406	−0.275672
$356$	1.49352	0.0791564
$357$	−6.12472	−0.324155
$358$	2.82006	0.149045
$359$	0.812147	0.0428635	0.0214317	−	0.999770i	$-0.493178\pi$
$359$	0.812147	0.0428635	0.0214317	+	0.999770i	$0.493178\pi$
$360$	−0.684532	−0.0360780
$361$	33.6752	1.77238
$362$	1.24487	0.0654288
$363$	−10.2735	−0.539221
$364$	1.46314	0.0766892
$365$	2.44567	0.128012
$366$	−5.34907	−0.279600
$367$	12.5112	0.653080	0.326540	−	0.945183i	$-0.394117\pi$
$367$	12.5112	0.653080	0.326540	+	0.945183i	$0.394117\pi$
$368$	8.93399	0.465716
$369$	7.52426	0.391697
$370$	3.79785	0.197441
$371$	−5.90866	−0.306763
$372$	−7.80209	−0.404520
$373$	−30.5555	−1.58210	−0.791051	−	0.611751i	$-0.790466\pi$
$373$	−30.5555	−1.58210	−0.791051	+	0.611751i	$0.790466\pi$
$374$	−3.56787	−0.184490
$375$	6.52456	0.336927
$376$	−6.03336	−0.311147
$377$	9.35782	0.481952
$378$	−1.46314	−0.0752557
$379$	15.5193	0.797175	0.398587	−	0.917130i	$-0.369501\pi$
$379$	15.5193	0.797175	0.398587	+	0.917130i	$0.369501\pi$
$380$	4.96817	0.254862
$381$	−18.0691	−0.925709
$382$	−20.9678	−1.07281
$383$	10.4672	0.534850	0.267425	−	0.963579i	$-0.413827\pi$
$383$	10.4672	0.534850	0.267425	+	0.963579i	$0.413827\pi$
$384$	1.00000	0.0510310
$385$	−0.853664	−0.0435067
$386$	16.7859	0.854382
$387$	10.1742	0.517184
$388$	−13.1229	−0.666212
$389$	−2.93656	−0.148890	−0.0744448	−	0.997225i	$-0.523718\pi$
$389$	−2.93656	−0.148890	−0.0744448	+	0.997225i	$0.523718\pi$
$390$	0.684532	0.0346626
$391$	37.3979	1.89129
$392$	−4.85923	−0.245428
$393$	18.7682	0.946728
$394$	−17.9766	−0.905648
$395$	−4.95415	−0.249270
$396$	−0.852331	−0.0428312
$397$	22.2722	1.11781	0.558906	−	0.829231i	$-0.311221\pi$
$397$	22.2722	1.11781	0.558906	+	0.829231i	$0.311221\pi$
$398$	25.9055	1.29853
$399$	10.6191	0.531620
$400$	−4.53142	−0.226571
$401$	−18.6195	−0.929812	−0.464906	−	0.885360i	$-0.653912\pi$
$401$	−18.6195	−0.929812	−0.464906	+	0.885360i	$0.653912\pi$
$402$	−8.90152	−0.443967
$403$	7.80209	0.388650
$404$	14.3892	0.715892
$405$	−0.684532	−0.0340147
$406$	13.6918	0.679511
$407$	4.72881	0.234399
$408$	4.18602	0.207239
$409$	10.9971	0.543770	0.271885	−	0.962330i	$-0.412353\pi$
$409$	10.9971	0.543770	0.271885	+	0.962330i	$0.412353\pi$
$410$	−5.15059	−0.254370
$411$	−12.6165	−0.622326
$412$	−1.00000	−0.0492665
$413$	17.3056	0.851551
$414$	8.93399	0.439082
$415$	6.39934	0.314131
$416$	−1.00000	−0.0490290
$417$	−1.54440	−0.0756297
$418$	6.18602	0.302568
$419$	39.0531	1.90787	0.953934	−	0.300016i	$-0.0969921\pi$
$419$	39.0531	1.90787	0.953934	+	0.300016i	$0.0969921\pi$
$420$	1.00156	0.0488713
$421$	11.4572	0.558388	0.279194	−	0.960235i	$-0.409933\pi$
$421$	11.4572	0.558388	0.279194	+	0.960235i	$0.409933\pi$
$422$	−24.6481	−1.19985
$423$	−6.03336	−0.293352
$424$	4.03835	0.196120
$425$	−18.9686	−0.920112
$426$	7.58775	0.367628
$427$	7.82642	0.378747
$428$	−8.77589	−0.424199
$429$	0.852331	0.0411509
$430$	−6.96457	−0.335861
$431$	39.7986	1.91703	0.958516	−	0.285040i	$-0.0920068\pi$
$431$	39.7986	1.91703	0.958516	+	0.285040i	$0.0920068\pi$
$432$	1.00000	0.0481125
$433$	−11.5754	−0.556280	−0.278140	−	0.960541i	$-0.589718\pi$
$433$	−11.5754	−0.556280	−0.278140	+	0.960541i	$0.589718\pi$
$434$	11.4155	0.547963
$435$	6.40572	0.307131
$436$	2.87277	0.137581
$437$	−64.8408	−3.10176
$438$	−3.57276	−0.170713
$439$	−20.5325	−0.979963	−0.489982	−	0.871733i	$-0.662997\pi$
$439$	−20.5325	−0.979963	−0.489982	+	0.871733i	$0.662997\pi$
$440$	0.583447	0.0278148
$441$	−4.85923	−0.231392
$442$	−4.18602	−0.199109
$443$	−36.0312	−1.71189	−0.855947	−	0.517064i	$-0.827025\pi$
$443$	−36.0312	−1.71189	−0.855947	+	0.517064i	$0.827025\pi$
$444$	−5.54810	−0.263301
$445$	−1.02236	−0.0484646
$446$	6.56161	0.310701
$447$	−14.4252	−0.682290
$448$	−1.46314	−0.0691268
$449$	9.61670	0.453840	0.226920	−	0.973913i	$-0.427134\pi$
$449$	9.61670	0.453840	0.226920	+	0.973913i	$0.427134\pi$
$450$	−4.53142	−0.213613
$451$	−6.41316	−0.301984
$452$	4.54248	0.213660
$453$	−13.4386	−0.631400
$454$	−5.97922	−0.280619
$455$	−1.00156	−0.0469540
$456$	−7.25777	−0.339876
$457$	29.8318	1.39547	0.697736	−	0.716355i	$-0.254191\pi$
$457$	29.8318	1.39547	0.697736	+	0.716355i	$0.254191\pi$
$458$	0.430082	0.0200964
$459$	4.18602	0.195387
$460$	−6.11560	−0.285141
$461$	36.5689	1.70318	0.851592	−	0.524205i	$-0.175638\pi$
$461$	36.5689	1.70318	0.851592	+	0.524205i	$0.175638\pi$
$462$	1.24708	0.0580193
$463$	−18.0887	−0.840654	−0.420327	−	0.907373i	$-0.638085\pi$
$463$	−18.0887	−0.840654	−0.420327	+	0.907373i	$0.638085\pi$
$464$	−9.35782	−0.434426
$465$	5.34078	0.247673
$466$	6.90703	0.319962
$467$	−5.84376	−0.270417	−0.135209	−	0.990817i	$-0.543170\pi$
$467$	−5.84376	−0.270417	−0.135209	+	0.990817i	$0.543170\pi$
$468$	−1.00000	−0.0462250
$469$	13.0241	0.601399
$470$	4.13003	0.190504
$471$	−1.79833	−0.0828629
$472$	−11.8277	−0.544414
$473$	−8.67179	−0.398729
$474$	7.23728	0.332419
$475$	32.8880	1.50900
$476$	−6.12472	−0.280726
$477$	4.03835	0.184903
$478$	9.90323	0.452963
$479$	17.0996	0.781299	0.390650	−	0.920539i	$-0.372250\pi$
$479$	17.0996	0.781299	0.390650	+	0.920539i	$0.372250\pi$
$480$	−0.684532	−0.0312445
$481$	5.54810	0.252971
$482$	−5.75164	−0.261980
$483$	−13.0717	−0.594781
$484$	−10.2735	−0.466979
$485$	8.98301	0.407898
$486$	1.00000	0.0453609
$487$	3.52339	0.159660	0.0798300	−	0.996808i	$-0.474562\pi$
$487$	3.52339	0.159660	0.0798300	+	0.996808i	$0.474562\pi$
$488$	−5.34907	−0.242141
$489$	13.8168	0.624817
$490$	3.32630	0.150267
$491$	29.6720	1.33908	0.669540	−	0.742776i	$-0.266491\pi$
$491$	29.6720	1.33908	0.669540	+	0.742776i	$0.266491\pi$
$492$	7.52426	0.339220
$493$	−39.1720	−1.76422
$494$	7.25777	0.326542
$495$	0.583447	0.0262240
$496$	−7.80209	−0.350324
$497$	−11.1019	−0.497989
$498$	−9.34849	−0.418916
$499$	−40.7675	−1.82500	−0.912501	−	0.409073i	$-0.865852\pi$
$499$	−40.7675	−1.82500	−0.912501	+	0.409073i	$0.865852\pi$
$500$	6.52456	0.291787
$501$	−1.72810	−0.0772058
$502$	−11.5382	−0.514973
$503$	17.0140	0.758616	0.379308	−	0.925270i	$-0.376162\pi$
$503$	17.0140	0.758616	0.379308	+	0.925270i	$0.376162\pi$
$504$	−1.46314	−0.0651733
$505$	−9.84989	−0.438314
$506$	−7.61471	−0.338515
$507$	1.00000	0.0444116
$508$	−18.0691	−0.801687
$509$	−40.3013	−1.78632	−0.893161	−	0.449736i	$-0.851518\pi$
$509$	−40.3013	−1.78632	−0.893161	+	0.449736i	$0.851518\pi$
$510$	−2.86546	−0.126885
$511$	5.22744	0.231248
$512$	1.00000	0.0441942
$513$	−7.25777	−0.320438
$514$	−22.3502	−0.985823
$515$	0.684532	0.0301641
$516$	10.1742	0.447895
$517$	5.14242	0.226163
$518$	8.11763	0.356668
$519$	15.9660	0.700829
$520$	0.684532	0.0300187
$521$	11.5494	0.505988	0.252994	−	0.967468i	$-0.418585\pi$
$521$	11.5494	0.505988	0.252994	+	0.967468i	$0.418585\pi$
$522$	−9.35782	−0.409581
$523$	−8.70958	−0.380843	−0.190422	−	0.981702i	$-0.560986\pi$
$523$	−8.70958	−0.380843	−0.190422	+	0.981702i	$0.560986\pi$
$524$	18.7682	0.819891
$525$	6.63009	0.289361
$526$	−31.2570	−1.36287
$527$	−32.6597	−1.42268
$528$	−0.852331	−0.0370929
$529$	56.8162	2.47027
$530$	−2.76438	−0.120077
$531$	−11.8277	−0.513279
$532$	10.6191	0.460397
$533$	−7.52426	−0.325912
$534$	1.49352	0.0646309
$535$	6.00738	0.259722
$536$	−8.90152	−0.384487
$537$	2.82006	0.121695
$538$	−25.3631	−1.09348
$539$	4.14167	0.178394
$540$	−0.684532	−0.0294576
$541$	4.66688	0.200645	0.100322	−	0.994955i	$-0.468013\pi$
$541$	4.66688	0.200645	0.100322	+	0.994955i	$0.468013\pi$
$542$	12.2195	0.524871
$543$	1.24487	0.0534224
$544$	4.18602	0.179474
$545$	−1.96650	−0.0842356
$546$	1.46314	0.0626165
$547$	4.57821	0.195750	0.0978750	−	0.995199i	$-0.468795\pi$
$547$	4.57821	0.195750	0.0978750	+	0.995199i	$0.468795\pi$
$548$	−12.6165	−0.538950
$549$	−5.34907	−0.228293
$550$	3.86227	0.164688
$551$	67.9169	2.89336
$552$	8.93399	0.380256
$553$	−10.5891	−0.450296
$554$	−25.3017	−1.07496
$555$	3.79785	0.161210
$556$	−1.54440	−0.0654972
$557$	−3.88709	−0.164701	−0.0823506	−	0.996603i	$-0.526243\pi$
$557$	−3.88709	−0.164701	−0.0823506	+	0.996603i	$0.526243\pi$
$558$	−7.80209	−0.330289
$559$	−10.1742	−0.430323
$560$	1.00156	0.0423238
$561$	−3.56787	−0.150636
$562$	−19.7540	−0.833272
$563$	−5.37558	−0.226554	−0.113277	−	0.993563i	$-0.536135\pi$
$563$	−5.37558	−0.226554	−0.113277	+	0.993563i	$0.536135\pi$
$564$	−6.03336	−0.254050
$565$	−3.10947	−0.130816
$566$	3.83554	0.161220
$567$	−1.46314	−0.0614460
$568$	7.58775	0.318375
$569$	−39.2744	−1.64647	−0.823235	−	0.567701i	$-0.807833\pi$
$569$	−39.2744	−1.64647	−0.823235	+	0.567701i	$0.807833\pi$
$570$	4.96817	0.208094
$571$	−41.4880	−1.73622	−0.868109	−	0.496374i	$-0.834664\pi$
$571$	−41.4880	−1.73622	−0.868109	+	0.496374i	$0.834664\pi$
$572$	0.852331	0.0356377
$573$	−20.9678	−0.875944
$574$	−11.0090	−0.459508
$575$	−40.4836	−1.68828
$576$	1.00000	0.0416667
$577$	−8.07627	−0.336220	−0.168110	−	0.985768i	$-0.553766\pi$
$577$	−8.07627	−0.336220	−0.168110	+	0.985768i	$0.553766\pi$
$578$	0.522771	0.0217444
$579$	16.7859	0.697600
$580$	6.40572	0.265983
$581$	13.6781	0.567464
$582$	−13.1229	−0.543960
$583$	−3.44201	−0.142554
$584$	−3.57276	−0.147842
$585$	0.684532	0.0283019
$586$	−14.5198	−0.599808
$587$	19.5273	0.805978	0.402989	−	0.915205i	$-0.367971\pi$
$587$	19.5273	0.805978	0.402989	+	0.915205i	$0.367971\pi$
$588$	−4.85923	−0.200391
$589$	56.6258	2.33322
$590$	8.09644	0.333325
$591$	−17.9766	−0.739459
$592$	−5.54810	−0.228025
$593$	−0.575372	−0.0236277	−0.0118138	−	0.999930i	$-0.503761\pi$
$593$	−0.575372	−0.0236277	−0.0118138	+	0.999930i	$0.503761\pi$
$594$	−0.852331	−0.0349716
$595$	4.19257	0.171879
$596$	−14.4252	−0.590880
$597$	25.9055	1.06024
$598$	−8.93399	−0.365338
$599$	25.9104	1.05867	0.529335	−	0.848413i	$-0.322441\pi$
$599$	25.9104	1.05867	0.529335	+	0.848413i	$0.322441\pi$
$600$	−4.53142	−0.184994
$601$	−22.9714	−0.937021	−0.468511	−	0.883458i	$-0.655209\pi$
$601$	−22.9714	−0.937021	−0.468511	+	0.883458i	$0.655209\pi$
$602$	−14.8863	−0.606719
$603$	−8.90152	−0.362498
$604$	−13.4386	−0.546808
$605$	7.03256	0.285914
$606$	14.3892	0.584523
$607$	36.9422	1.49944	0.749718	−	0.661758i	$-0.230189\pi$
$607$	36.9422	1.49944	0.749718	+	0.661758i	$0.230189\pi$
$608$	−7.25777	−0.294341
$609$	13.6918	0.554819
$610$	3.66161	0.148254
$611$	6.03336	0.244084
$612$	4.18602	0.169210
$613$	−33.7561	−1.36340	−0.681698	−	0.731634i	$-0.738758\pi$
$613$	−33.7561	−1.36340	−0.681698	+	0.731634i	$0.738758\pi$
$614$	7.02841	0.283643
$615$	−5.15059	−0.207692
$616$	1.24708	0.0502462
$617$	1.86602	0.0751230	0.0375615	−	0.999294i	$-0.488041\pi$
$617$	1.86602	0.0751230	0.0375615	+	0.999294i	$0.488041\pi$
$618$	−1.00000	−0.0402259
$619$	−10.9504	−0.440135	−0.220067	−	0.975485i	$-0.570628\pi$
$619$	−10.9504	−0.440135	−0.220067	+	0.975485i	$0.570628\pi$
$620$	5.34078	0.214491
$621$	8.93399	0.358509
$622$	32.0849	1.28649
$623$	−2.18522	−0.0875492
$624$	−1.00000	−0.0400320
$625$	18.1908	0.727633
$626$	28.9318	1.15635
$627$	6.18602	0.247046
$628$	−1.79833	−0.0717614
$629$	−23.2245	−0.926020
$630$	1.00156	0.0399033
$631$	25.2078	1.00350	0.501752	−	0.865011i	$-0.332689\pi$
$631$	25.2078	1.00350	0.501752	+	0.865011i	$0.332689\pi$
$632$	7.23728	0.287884
$633$	−24.6481	−0.979672
$634$	9.30284	0.369463
$635$	12.3689	0.490844
$636$	4.03835	0.160131
$637$	4.85923	0.192530
$638$	7.97596	0.315771
$639$	7.58775	0.300167
$640$	−0.684532	−0.0270585
$641$	−2.86519	−0.113168	−0.0565841	−	0.998398i	$-0.518021\pi$
$641$	−2.86519	−0.113168	−0.0565841	+	0.998398i	$0.518021\pi$
$642$	−8.77589	−0.346357
$643$	−19.7103	−0.777300	−0.388650	−	0.921385i	$-0.627059\pi$
$643$	−19.7103	−0.777300	−0.388650	+	0.921385i	$0.627059\pi$
$644$	−13.0717	−0.515095
$645$	−6.96457	−0.274230
$646$	−30.3812	−1.19533
$647$	1.42474	0.0560124	0.0280062	−	0.999608i	$-0.491084\pi$
$647$	1.42474	0.0560124	0.0280062	+	0.999608i	$0.491084\pi$
$648$	1.00000	0.0392837
$649$	10.0811	0.395718
$650$	4.53142	0.177737
$651$	11.4155	0.447410
$652$	13.8168	0.541108
$653$	0.388474	0.0152022	0.00760109	−	0.999971i	$-0.497580\pi$
$653$	0.388474	0.0152022	0.00760109	+	0.999971i	$0.497580\pi$
$654$	2.87277	0.112334
$655$	−12.8474	−0.501989
$656$	7.52426	0.293773
$657$	−3.57276	−0.139387
$658$	8.82763	0.344137
$659$	10.4609	0.407501	0.203750	−	0.979023i	$-0.434687\pi$
$659$	10.4609	0.407501	0.203750	+	0.979023i	$0.434687\pi$
$660$	0.583447	0.0227107
$661$	23.1355	0.899866	0.449933	−	0.893062i	$-0.351448\pi$
$661$	23.1355	0.899866	0.449933	+	0.893062i	$0.351448\pi$
$662$	−31.1194	−1.20949
$663$	−4.18602	−0.162572
$664$	−9.34849	−0.362792
$665$	−7.26912	−0.281884
$666$	−5.54810	−0.214984
$667$	−83.6027	−3.23711
$668$	−1.72810	−0.0668622
$669$	6.56161	0.253686
$670$	6.09337	0.235408
$671$	4.55917	0.176005
$672$	−1.46314	−0.0564418
$673$	38.6514	1.48990	0.744952	−	0.667118i	$-0.232472\pi$
$673$	38.6514	1.48990	0.744952	+	0.667118i	$0.232472\pi$
$674$	−20.6049	−0.793673
$675$	−4.53142	−0.174414
$676$	1.00000	0.0384615
$677$	−0.167047	−0.00642015	−0.00321007	−	0.999995i	$-0.501022\pi$
$677$	−0.167047	−0.00642015	−0.00321007	+	0.999995i	$0.501022\pi$
$678$	4.54248	0.174453
$679$	19.2005	0.736849
$680$	−2.86546	−0.109886
$681$	−5.97922	−0.229124
$682$	6.64996	0.254640
$683$	39.5523	1.51343	0.756714	−	0.653746i	$-0.226804\pi$
$683$	39.5523	1.51343	0.756714	+	0.653746i	$0.226804\pi$
$684$	−7.25777	−0.277508
$685$	8.63640	0.329980
$686$	17.3517	0.662490
$687$	0.430082	0.0164087
$688$	10.1742	0.387888
$689$	−4.03835	−0.153849
$690$	−6.11560	−0.232817
$691$	24.2086	0.920938	0.460469	−	0.887676i	$-0.347681\pi$
$691$	24.2086	0.920938	0.460469	+	0.887676i	$0.347681\pi$
$692$	15.9660	0.606935
$693$	1.24708	0.0473725
$694$	10.1696	0.386034
$695$	1.05719	0.0401016
$696$	−9.35782	−0.354707
$697$	31.4967	1.19302
$698$	28.8819	1.09320
$699$	6.90703	0.261248
$700$	6.63009	0.250594
$701$	51.5781	1.94808	0.974038	−	0.226382i	$-0.0726899\pi$
$701$	51.5781	1.94808	0.974038	+	0.226382i	$0.0726899\pi$
$702$	−1.00000	−0.0377426
$703$	40.2668	1.51869
$704$	−0.852331	−0.0321234
$705$	4.13003	0.155546
$706$	−6.13386	−0.230851
$707$	−21.0534	−0.791796
$708$	−11.8277	−0.444512
$709$	24.1093	0.905443	0.452722	−	0.891652i	$-0.350453\pi$
$709$	24.1093	0.905443	0.452722	+	0.891652i	$0.350453\pi$
$710$	−5.19406	−0.194929
$711$	7.23728	0.271419
$712$	1.49352	0.0559720
$713$	−69.7038	−2.61043
$714$	−6.12472	−0.229212
$715$	−0.583447	−0.0218197
$716$	2.82006	0.105391
$717$	9.90323	0.369843
$718$	0.812147	0.0303090
$719$	4.60391	0.171697	0.0858484	−	0.996308i	$-0.472640\pi$
$719$	4.60391	0.171697	0.0858484	+	0.996308i	$0.472640\pi$
$720$	−0.684532	−0.0255110
$721$	1.46314	0.0544901
$722$	33.6752	1.25326
$723$	−5.75164	−0.213906
$724$	1.24487	0.0462651
$725$	42.4042	1.57485
$726$	−10.2735	−0.381287
$727$	−16.3844	−0.607665	−0.303832	−	0.952726i	$-0.598266\pi$
$727$	−16.3844	−0.607665	−0.303832	+	0.952726i	$0.598266\pi$
$728$	1.46314	0.0542275
$729$	1.00000	0.0370370
$730$	2.44567	0.0905182
$731$	42.5895	1.57523
$732$	−5.34907	−0.197707
$733$	42.0161	1.55190	0.775950	−	0.630794i	$-0.217271\pi$
$733$	42.0161	1.55190	0.775950	+	0.630794i	$0.217271\pi$
$734$	12.5112	0.461797
$735$	3.32630	0.122692
$736$	8.93399	0.329311
$737$	7.58704	0.279472
$738$	7.52426	0.276972
$739$	−8.32382	−0.306197	−0.153098	−	0.988211i	$-0.548925\pi$
$739$	−8.32382	−0.306197	−0.153098	+	0.988211i	$0.548925\pi$
$740$	3.79785	0.139612
$741$	7.25777	0.266621
$742$	−5.90866	−0.216914
$743$	18.0533	0.662313	0.331156	−	0.943576i	$-0.392561\pi$
$743$	18.0533	0.662313	0.331156	+	0.943576i	$0.392561\pi$
$744$	−7.80209	−0.286039
$745$	9.87452	0.361775
$746$	−30.5555	−1.11871
$747$	−9.34849	−0.342043
$748$	−3.56787	−0.130454
$749$	12.8403	0.469176
$750$	6.52456	0.238243
$751$	1.59769	0.0583006	0.0291503	−	0.999575i	$-0.490720\pi$
$751$	1.59769	0.0583006	0.0291503	+	0.999575i	$0.490720\pi$
$752$	−6.03336	−0.220014
$753$	−11.5382	−0.420474
$754$	9.35782	0.340792
$755$	9.19914	0.334791
$756$	−1.46314	−0.0532138
$757$	3.29104	0.119615	0.0598075	−	0.998210i	$-0.480951\pi$
$757$	3.29104	0.119615	0.0598075	+	0.998210i	$0.480951\pi$
$758$	15.5193	0.563688
$759$	−7.61471	−0.276397
$760$	4.96817	0.180215
$761$	−8.64206	−0.313274	−0.156637	−	0.987656i	$-0.550065\pi$
$761$	−8.64206	−0.313274	−0.156637	+	0.987656i	$0.550065\pi$
$762$	−18.0691	−0.654575
$763$	−4.20325	−0.152168
$764$	−20.9678	−0.758590
$765$	−2.86546	−0.103601
$766$	10.4672	0.378196
$767$	11.8277	0.427074
$768$	1.00000	0.0360844
$769$	0.571955	0.0206252	0.0103126	−	0.999947i	$-0.496717\pi$
$769$	0.571955	0.0206252	0.0103126	+	0.999947i	$0.496717\pi$
$770$	−0.853664	−0.0307639
$771$	−22.3502	−0.804921
$772$	16.7859	0.604140
$773$	−19.1356	−0.688260	−0.344130	−	0.938922i	$-0.611826\pi$
$773$	−19.1356	−0.688260	−0.344130	+	0.938922i	$0.611826\pi$
$774$	10.1742	0.365705
$775$	35.3545	1.26997
$776$	−13.1229	−0.471083
$777$	8.11763	0.291218
$778$	−2.93656	−0.105281
$779$	−54.6093	−1.95658
$780$	0.684532	0.0245102
$781$	−6.46727	−0.231417
$782$	37.3979	1.33735
$783$	−9.35782	−0.334421
$784$	−4.85923	−0.173544
$785$	1.23102	0.0439369
$786$	18.7682	0.669438
$787$	−42.5567	−1.51698	−0.758491	−	0.651684i	$-0.774063\pi$
$787$	−42.5567	−1.51698	−0.758491	+	0.651684i	$0.774063\pi$
$788$	−17.9766	−0.640390
$789$	−31.2570	−1.11278
$790$	−4.95415	−0.176261
$791$	−6.64627	−0.236314
$792$	−0.852331	−0.0302863
$793$	5.34907	0.189951
$794$	22.2722	0.790412
$795$	−2.76438	−0.0980425
$796$	25.9055	0.918197
$797$	0.0328812	0.00116471	0.000582356	−	1.00000i	$-0.499815\pi$
$797$	0.0328812	0.00116471	0.000582356		1.00000i	$0.499815\pi$
$798$	10.6191	0.375912
$799$	−25.2558	−0.893485
$800$	−4.53142	−0.160210
$801$	1.49352	0.0527709
$802$	−18.6195	−0.657476
$803$	3.04517	0.107462
$804$	−8.90152	−0.313932
$805$	8.94796	0.315374
$806$	7.80209	0.274817
$807$	−25.3631	−0.892825
$808$	14.3892	0.506212
$809$	19.4008	0.682097	0.341049	−	0.940046i	$-0.389218\pi$
$809$	19.4008	0.682097	0.341049	+	0.940046i	$0.389218\pi$
$810$	−0.684532	−0.0240520
$811$	38.7459	1.36055	0.680275	−	0.732957i	$-0.261860\pi$
$811$	38.7459	1.36055	0.680275	+	0.732957i	$0.261860\pi$
$812$	13.6918	0.480487
$813$	12.2195	0.428555
$814$	4.72881	0.165745
$815$	−9.45804	−0.331301
$816$	4.18602	0.146540
$817$	−73.8420	−2.58341
$818$	10.9971	0.384504
$819$	1.46314	0.0511262
$820$	−5.15059	−0.179867
$821$	−24.2407	−0.846007	−0.423004	−	0.906128i	$-0.639024\pi$
$821$	−24.2407	−0.846007	−0.423004	+	0.906128i	$0.639024\pi$
$822$	−12.6165	−0.440051
$823$	38.9787	1.35871	0.679356	−	0.733809i	$-0.262259\pi$
$823$	38.9787	1.35871	0.679356	+	0.733809i	$0.262259\pi$
$824$	−1.00000	−0.0348367
$825$	3.86227	0.134467
$826$	17.3056	0.602137
$827$	8.70842	0.302821	0.151411	−	0.988471i	$-0.451618\pi$
$827$	8.70842	0.302821	0.151411	+	0.988471i	$0.451618\pi$
$828$	8.93399	0.310478
$829$	−6.34971	−0.220535	−0.110267	−	0.993902i	$-0.535171\pi$
$829$	−6.34971	−0.220535	−0.110267	+	0.993902i	$0.535171\pi$
$830$	6.39934	0.222124
$831$	−25.3017	−0.877705
$832$	−1.00000	−0.0346688
$833$	−20.3408	−0.704768
$834$	−1.54440	−0.0534783
$835$	1.18294	0.0409373
$836$	6.18602	0.213948
$837$	−7.80209	−0.269680
$838$	39.0531	1.34907
$839$	−15.7795	−0.544769	−0.272384	−	0.962189i	$-0.587812\pi$
$839$	−15.7795	−0.544769	−0.272384	+	0.962189i	$0.587812\pi$
$840$	1.00156	0.0345572
$841$	58.5688	2.01961
$842$	11.4572	0.394840
$843$	−19.7540	−0.680364
$844$	−24.6481	−0.848421
$845$	−0.684532	−0.0235486
$846$	−6.03336	−0.207431
$847$	15.0316	0.516492
$848$	4.03835	0.138678
$849$	3.83554	0.131635
$850$	−18.9686	−0.650618
$851$	−49.5666	−1.69912
$852$	7.58775	0.259952
$853$	−20.0221	−0.685544	−0.342772	−	0.939419i	$-0.611366\pi$
$853$	−20.0221	−0.685544	−0.342772	+	0.939419i	$0.611366\pi$
$854$	7.82642	0.267815
$855$	4.96817	0.169908
$856$	−8.77589	−0.299954
$857$	−9.39879	−0.321057	−0.160528	−	0.987031i	$-0.551320\pi$
$857$	−9.39879	−0.321057	−0.160528	+	0.987031i	$0.551320\pi$
$858$	0.852331	0.0290981
$859$	5.29957	0.180819	0.0904095	−	0.995905i	$-0.471182\pi$
$859$	5.29957	0.180819	0.0904095	+	0.995905i	$0.471182\pi$
$860$	−6.96457	−0.237490
$861$	−11.0090	−0.375187
$862$	39.7986	1.35555
$863$	−2.97386	−0.101231	−0.0506157	−	0.998718i	$-0.516118\pi$
$863$	−2.97386	−0.101231	−0.0506157	+	0.998718i	$0.516118\pi$
$864$	1.00000	0.0340207
$865$	−10.9292	−0.371605
$866$	−11.5754	−0.393349
$867$	0.522771	0.0177542
$868$	11.4155	0.387469
$869$	−6.16856	−0.209254
$870$	6.40572	0.217174
$871$	8.90152	0.301616
$872$	2.87277	0.0972842
$873$	−13.1229	−0.444141
$874$	−64.8408	−2.19327
$875$	−9.54632	−0.322725
$876$	−3.57276	−0.120712
$877$	−26.9787	−0.911005	−0.455503	−	0.890234i	$-0.650540\pi$
$877$	−26.9787	−0.911005	−0.455503	+	0.890234i	$0.650540\pi$
$878$	−20.5325	−0.692939
$879$	−14.5198	−0.489741
$880$	0.583447	0.0196680
$881$	−34.1276	−1.14979	−0.574895	−	0.818228i	$-0.694957\pi$
$881$	−34.1276	−1.14979	−0.574895	+	0.818228i	$0.694957\pi$
$882$	−4.85923	−0.163619
$883$	−46.6544	−1.57004	−0.785022	−	0.619468i	$-0.787349\pi$
$883$	−46.6544	−1.57004	−0.785022	+	0.619468i	$0.787349\pi$
$884$	−4.18602	−0.140791
$885$	8.09644	0.272159
$886$	−36.0312	−1.21049
$887$	−24.5155	−0.823150	−0.411575	−	0.911376i	$-0.635021\pi$
$887$	−24.5155	−0.823150	−0.411575	+	0.911376i	$0.635021\pi$
$888$	−5.54810	−0.186182
$889$	26.4376	0.886689
$890$	−1.02236	−0.0342696
$891$	−0.852331	−0.0285542
$892$	6.56161	0.219699
$893$	43.7887	1.46533
$894$	−14.4252	−0.482452
$895$	−1.93042	−0.0645269
$896$	−1.46314	−0.0488800
$897$	−8.93399	−0.298297
$898$	9.61670	0.320913
$899$	73.0106	2.43504
$900$	−4.53142	−0.151047
$901$	16.9046	0.563175
$902$	−6.41316	−0.213535
$903$	−14.8863	−0.495384
$904$	4.54248	0.151081
$905$	−0.852151	−0.0283265
$906$	−13.4386	−0.446467
$907$	2.23575	0.0742369	0.0371184	−	0.999311i	$-0.488182\pi$
$907$	2.23575	0.0742369	0.0371184	+	0.999311i	$0.488182\pi$
$908$	−5.97922	−0.198427
$909$	14.3892	0.477261
$910$	−1.00156	−0.0332015
$911$	18.3515	0.608013	0.304006	−	0.952670i	$-0.401676\pi$
$911$	18.3515	0.608013	0.304006	+	0.952670i	$0.401676\pi$
$912$	−7.25777	−0.240329
$913$	7.96801	0.263702
$914$	29.8318	0.986747
$915$	3.66161	0.121049
$916$	0.430082	0.0142103
$917$	−27.4604	−0.906822
$918$	4.18602	0.138159
$919$	21.8184	0.719722	0.359861	−	0.933006i	$-0.382824\pi$
$919$	21.8184	0.719722	0.359861	+	0.933006i	$0.382824\pi$
$920$	−6.11560	−0.201625
$921$	7.02841	0.231594
$922$	36.5689	1.20433
$923$	−7.58775	−0.249754
$924$	1.24708	0.0410258
$925$	25.1407	0.826622
$926$	−18.0887	−0.594432
$927$	−1.00000	−0.0328443
$928$	−9.35782	−0.307185
$929$	−7.80628	−0.256116	−0.128058	−	0.991767i	$-0.540874\pi$
$929$	−7.80628	−0.256116	−0.128058	+	0.991767i	$0.540874\pi$
$930$	5.34078	0.175131
$931$	35.2671	1.15583
$932$	6.90703	0.226247
$933$	32.0849	1.05041
$934$	−5.84376	−0.191214
$935$	2.44232	0.0798725
$936$	−1.00000	−0.0326860
$937$	38.5723	1.26010	0.630052	−	0.776553i	$-0.283034\pi$
$937$	38.5723	1.26010	0.630052	+	0.776553i	$0.283034\pi$
$938$	13.0241	0.425253
$939$	28.9318	0.944154
$940$	4.13003	0.134707
$941$	−51.8436	−1.69005	−0.845026	−	0.534725i	$-0.820415\pi$
$941$	−51.8436	−1.69005	−0.845026	+	0.534725i	$0.820415\pi$
$942$	−1.79833	−0.0585929
$943$	67.2216	2.18904
$944$	−11.8277	−0.384959
$945$	1.00156	0.0325809
$946$	−8.67179	−0.281944
$947$	2.87685	0.0934851	0.0467425	−	0.998907i	$-0.485116\pi$
$947$	2.87685	0.0934851	0.0467425	+	0.998907i	$0.485116\pi$
$948$	7.23728	0.235056
$949$	3.57276	0.115977
$950$	32.8880	1.06703
$951$	9.30284	0.301665
$952$	−6.12472	−0.198503
$953$	−21.8274	−0.707057	−0.353529	−	0.935424i	$-0.615018\pi$
$953$	−21.8274	−0.707057	−0.353529	+	0.935424i	$0.615018\pi$
$954$	4.03835	0.130746
$955$	14.3531	0.464457
$956$	9.90323	0.320293
$957$	7.97596	0.257826
$958$	17.0996	0.552462
$959$	18.4597	0.596094
$960$	−0.684532	−0.0220932
$961$	29.8727	0.963634
$962$	5.54810	0.178878
$963$	−8.77589	−0.282799
$964$	−5.75164	−0.185248
$965$	−11.4905	−0.369893
$966$	−13.0717	−0.420574
$967$	21.5613	0.693363	0.346682	−	0.937983i	$-0.387308\pi$
$967$	21.5613	0.693363	0.346682	+	0.937983i	$0.387308\pi$
$968$	−10.2735	−0.330204
$969$	−30.3812	−0.975983
$970$	8.98301	0.288427
$971$	−8.58069	−0.275367	−0.137684	−	0.990476i	$-0.543966\pi$
$971$	−8.58069	−0.275367	−0.137684	+	0.990476i	$0.543966\pi$
$972$	1.00000	0.0320750
$973$	2.25967	0.0724418
$974$	3.52339	0.112897
$975$	4.53142	0.145121
$976$	−5.34907	−0.171219
$977$	27.0817	0.866419	0.433210	−	0.901293i	$-0.357381\pi$
$977$	27.0817	0.866419	0.433210	+	0.901293i	$0.357381\pi$
$978$	13.8168	0.441813
$979$	−1.27297	−0.0406844
$980$	3.32630	0.106255
$981$	2.87277	0.0917204
$982$	29.6720	0.946872
$983$	16.2844	0.519391	0.259695	−	0.965691i	$-0.416378\pi$
$983$	16.2844	0.519391	0.259695	+	0.965691i	$0.416378\pi$
$984$	7.52426	0.239865
$985$	12.3056	0.392088
$986$	−39.1720	−1.24749
$987$	8.82763	0.280987
$988$	7.25777	0.230900
$989$	90.8963	2.89033
$990$	0.583447	0.0185432
$991$	6.54497	0.207908	0.103954	−	0.994582i	$-0.466851\pi$
$991$	6.54497	0.207908	0.103954	+	0.994582i	$0.466851\pi$
$992$	−7.80209	−0.247717
$993$	−31.1194	−0.987546
$994$	−11.1019	−0.352132
$995$	−17.7332	−0.562179
$996$	−9.34849	−0.296218
$997$	29.6005	0.937457	0.468728	−	0.883342i	$-0.344712\pi$
$997$	29.6005	0.937457	0.468728	+	0.883342i	$0.344712\pi$
$998$	−40.7675	−1.29047
$999$	−5.54810	−0.175534

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8034.2.a.q.1.5	✓	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8034.2.a.q.1.5	✓	8	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:	\( N \)	\(=\)	\( 8034 = 2 \cdot 3 \cdot 13 \cdot 103 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8034.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -0.684532 q^{5} +1.00000 q^{6} -1.46314 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -0.684532 q^{5} +1.00000 q^{6} -1.46314 q^{7} +1.00000 q^{8} +1.00000 q^{9} -0.684532 q^{10} -0.852331 q^{11} +1.00000 q^{12} -1.00000 q^{13} -1.46314 q^{14} -0.684532 q^{15} +1.00000 q^{16} +4.18602 q^{17} +1.00000 q^{18} -7.25777 q^{19} -0.684532 q^{20} -1.46314 q^{21} -0.852331 q^{22} +8.93399 q^{23} +1.00000 q^{24} -4.53142 q^{25} -1.00000 q^{26} +1.00000 q^{27} -1.46314 q^{28} -9.35782 q^{29} -0.684532 q^{30} -7.80209 q^{31} +1.00000 q^{32} -0.852331 q^{33} +4.18602 q^{34} +1.00156 q^{35} +1.00000 q^{36} -5.54810 q^{37} -7.25777 q^{38} -1.00000 q^{39} -0.684532 q^{40} +7.52426 q^{41} -1.46314 q^{42} +10.1742 q^{43} -0.852331 q^{44} -0.684532 q^{45} +8.93399 q^{46} -6.03336 q^{47} +1.00000 q^{48} -4.85923 q^{49} -4.53142 q^{50} +4.18602 q^{51} -1.00000 q^{52} +4.03835 q^{53} +1.00000 q^{54} +0.583447 q^{55} -1.46314 q^{56} -7.25777 q^{57} -9.35782 q^{58} -11.8277 q^{59} -0.684532 q^{60} -5.34907 q^{61} -7.80209 q^{62} -1.46314 q^{63} +1.00000 q^{64} +0.684532 q^{65} -0.852331 q^{66} -8.90152 q^{67} +4.18602 q^{68} +8.93399 q^{69} +1.00156 q^{70} +7.58775 q^{71} +1.00000 q^{72} -3.57276 q^{73} -5.54810 q^{74} -4.53142 q^{75} -7.25777 q^{76} +1.24708 q^{77} -1.00000 q^{78} +7.23728 q^{79} -0.684532 q^{80} +1.00000 q^{81} +7.52426 q^{82} -9.34849 q^{83} -1.46314 q^{84} -2.86546 q^{85} +10.1742 q^{86} -9.35782 q^{87} -0.852331 q^{88} +1.49352 q^{89} -0.684532 q^{90} +1.46314 q^{91} +8.93399 q^{92} -7.80209 q^{93} -6.03336 q^{94} +4.96817 q^{95} +1.00000 q^{96} -13.1229 q^{97} -4.85923 q^{98} -0.852331 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 8 q^{2} + 8 q^{3} + 8 q^{4} - 6 q^{5} + 8 q^{6} - 3 q^{7} + 8 q^{8} + 8 q^{9}+O(q^{10}) \) 8 * q + 8 * q^2 + 8 * q^3 + 8 * q^4 - 6 * q^5 + 8 * q^6 - 3 * q^7 + 8 * q^8 + 8 * q^9	\( 8 q + 8 q^{2} + 8 q^{3} + 8 q^{4} - 6 q^{5} + 8 q^{6} - 3 q^{7} + 8 q^{8} + 8 q^{9} - 6 q^{10} - 15 q^{11} + 8 q^{12} - 8 q^{13} - 3 q^{14} - 6 q^{15} + 8 q^{16} - 11 q^{17} + 8 q^{18} - 15 q^{19} - 6 q^{20} - 3 q^{21} - 15 q^{22} + q^{23} + 8 q^{24} - 10 q^{25} - 8 q^{26} + 8 q^{27} - 3 q^{28} - 10 q^{29} - 6 q^{30} - 3 q^{31} + 8 q^{32} - 15 q^{33} - 11 q^{34} - 12 q^{35} + 8 q^{36} - 26 q^{37} - 15 q^{38} - 8 q^{39} - 6 q^{40} - 12 q^{41} - 3 q^{42} - 4 q^{43} - 15 q^{44} - 6 q^{45} + q^{46} - 6 q^{47} + 8 q^{48} - 5 q^{49} - 10 q^{50} - 11 q^{51} - 8 q^{52} - 4 q^{53} + 8 q^{54} - 3 q^{56} - 15 q^{57} - 10 q^{58} - 19 q^{59} - 6 q^{60} - 14 q^{61} - 3 q^{62} - 3 q^{63} + 8 q^{64} + 6 q^{65} - 15 q^{66} - 13 q^{67} - 11 q^{68} + q^{69} - 12 q^{70} - 31 q^{71} + 8 q^{72} - 27 q^{73} - 26 q^{74} - 10 q^{75} - 15 q^{76} - 30 q^{77} - 8 q^{78} - 13 q^{79} - 6 q^{80} + 8 q^{81} - 12 q^{82} - 28 q^{83} - 3 q^{84} + 15 q^{85} - 4 q^{86} - 10 q^{87} - 15 q^{88} - 2 q^{89} - 6 q^{90} + 3 q^{91} + q^{92} - 3 q^{93} - 6 q^{94} - 18 q^{95} + 8 q^{96} - 30 q^{97} - 5 q^{98} - 15 q^{99}+O(q^{100}) \) 8 * q + 8 * q^2 + 8 * q^3 + 8 * q^4 - 6 * q^5 + 8 * q^6 - 3 * q^7 + 8 * q^8 + 8 * q^9 - 6 * q^10 - 15 * q^11 + 8 * q^12 - 8 * q^13 - 3 * q^14 - 6 * q^15 + 8 * q^16 - 11 * q^17 + 8 * q^18 - 15 * q^19 - 6 * q^20 - 3 * q^21 - 15 * q^22 + q^23 + 8 * q^24 - 10 * q^25 - 8 * q^26 + 8 * q^27 - 3 * q^28 - 10 * q^29 - 6 * q^30 - 3 * q^31 + 8 * q^32 - 15 * q^33 - 11 * q^34 - 12 * q^35 + 8 * q^36 - 26 * q^37 - 15 * q^38 - 8 * q^39 - 6 * q^40 - 12 * q^41 - 3 * q^42 - 4 * q^43 - 15 * q^44 - 6 * q^45 + q^46 - 6 * q^47 + 8 * q^48 - 5 * q^49 - 10 * q^50 - 11 * q^51 - 8 * q^52 - 4 * q^53 + 8 * q^54 - 3 * q^56 - 15 * q^57 - 10 * q^58 - 19 * q^59 - 6 * q^60 - 14 * q^61 - 3 * q^62 - 3 * q^63 + 8 * q^64 + 6 * q^65 - 15 * q^66 - 13 * q^67 - 11 * q^68 + q^69 - 12 * q^70 - 31 * q^71 + 8 * q^72 - 27 * q^73 - 26 * q^74 - 10 * q^75 - 15 * q^76 - 30 * q^77 - 8 * q^78 - 13 * q^79 - 6 * q^80 + 8 * q^81 - 12 * q^82 - 28 * q^83 - 3 * q^84 + 15 * q^85 - 4 * q^86 - 10 * q^87 - 15 * q^88 - 2 * q^89 - 6 * q^90 + 3 * q^91 + q^92 - 3 * q^93 - 6 * q^94 - 18 * q^95 + 8 * q^96 - 30 * q^97 - 5 * q^98 - 15 * q^99

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