LMFDB - Embedded newform 8022.2.a.p.1.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8022,2,Mod(1,8022)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8022, 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("8022.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8022 = 2 \cdot 3 \cdot 7 \cdot 191 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8022.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:	$64.0559925015$
Analytic rank:	$1$
Dimension:	$9$
Coefficient field:	$\mathbb{Q}[x]/(x^{9} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{9} - 17x^{7} - 12x^{6} + 72x^{5} + 81x^{4} - 67x^{3} - 105x^{2} - 17x + 6 $ x^9 - 17x^7 - 12x^6 + 72x^5 + 81x^4 - 67x^3 - 105x^2 - 17*x + 6
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.9
Root			$1.28832$ of defining polynomial
Character	$\chi$	$=$	8022.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +3.94651 q^{5} -1.00000 q^{6} +1.00000 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +3.94651 q^{5} -1.00000 q^{6} +1.00000 q^{7} +1.00000 q^{8} +1.00000 q^{9} +3.94651 q^{10} -2.25610 q^{11} -1.00000 q^{12} -6.54514 q^{13} +1.00000 q^{14} -3.94651 q^{15} +1.00000 q^{16} +0.785920 q^{17} +1.00000 q^{18} -7.36045 q^{19} +3.94651 q^{20} -1.00000 q^{21} -2.25610 q^{22} -0.429872 q^{23} -1.00000 q^{24} +10.5749 q^{25} -6.54514 q^{26} -1.00000 q^{27} +1.00000 q^{28} -10.0968 q^{29} -3.94651 q^{30} -8.58370 q^{31} +1.00000 q^{32} +2.25610 q^{33} +0.785920 q^{34} +3.94651 q^{35} +1.00000 q^{36} +12.1347 q^{37} -7.36045 q^{38} +6.54514 q^{39} +3.94651 q^{40} -6.02711 q^{41} -1.00000 q^{42} +2.79767 q^{43} -2.25610 q^{44} +3.94651 q^{45} -0.429872 q^{46} -10.0648 q^{47} -1.00000 q^{48} +1.00000 q^{49} +10.5749 q^{50} -0.785920 q^{51} -6.54514 q^{52} +6.97501 q^{53} -1.00000 q^{54} -8.90371 q^{55} +1.00000 q^{56} +7.36045 q^{57} -10.0968 q^{58} -6.13545 q^{59} -3.94651 q^{60} -10.8656 q^{61} -8.58370 q^{62} +1.00000 q^{63} +1.00000 q^{64} -25.8304 q^{65} +2.25610 q^{66} -7.46296 q^{67} +0.785920 q^{68} +0.429872 q^{69} +3.94651 q^{70} +6.37363 q^{71} +1.00000 q^{72} -1.83429 q^{73} +12.1347 q^{74} -10.5749 q^{75} -7.36045 q^{76} -2.25610 q^{77} +6.54514 q^{78} -5.22919 q^{79} +3.94651 q^{80} +1.00000 q^{81} -6.02711 q^{82} +10.8771 q^{83} -1.00000 q^{84} +3.10164 q^{85} +2.79767 q^{86} +10.0968 q^{87} -2.25610 q^{88} -1.03959 q^{89} +3.94651 q^{90} -6.54514 q^{91} -0.429872 q^{92} +8.58370 q^{93} -10.0648 q^{94} -29.0481 q^{95} -1.00000 q^{96} -13.0792 q^{97} +1.00000 q^{98} -2.25610 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 9 q + 9 q^{2} - 9 q^{3} + 9 q^{4} - 4 q^{5} - 9 q^{6} + 9 q^{7} + 9 q^{8} + 9 q^{9}+O(q^{10}) $ 9 * q + 9 * q^2 - 9 * q^3 + 9 * q^4 - 4 * q^5 - 9 * q^6 + 9 * q^7 + 9 * q^8 + 9 * q^9	\( 9 q + 9 q^{2} - 9 q^{3} + 9 q^{4} - 4 q^{5} - 9 q^{6} + 9 q^{7} + 9 q^{8} + 9 q^{9} - 4 q^{10} - 3 q^{11} - 9 q^{12} - 9 q^{13} + 9 q^{14} + 4 q^{15} + 9 q^{16} - 12 q^{17} + 9 q^{18} - 18 q^{19} - 4 q^{20} - 9 q^{21} - 3 q^{22} + q^{23} - 9 q^{24} + 9 q^{25} - 9 q^{26} - 9 q^{27} + 9 q^{28} - 11 q^{29} + 4 q^{30} - 22 q^{31} + 9 q^{32} + 3 q^{33} - 12 q^{34} - 4 q^{35} + 9 q^{36} + 8 q^{37} - 18 q^{38} + 9 q^{39} - 4 q^{40} - 22 q^{41} - 9 q^{42} - 3 q^{43} - 3 q^{44} - 4 q^{45} + q^{46} - 49 q^{47} - 9 q^{48} + 9 q^{49} + 9 q^{50} + 12 q^{51} - 9 q^{52} + 8 q^{53} - 9 q^{54} - 19 q^{55} + 9 q^{56} + 18 q^{57} - 11 q^{58} - 18 q^{59} + 4 q^{60} + 3 q^{61} - 22 q^{62} + 9 q^{63} + 9 q^{64} - 32 q^{65} + 3 q^{66} - 11 q^{67} - 12 q^{68} - q^{69} - 4 q^{70} - 7 q^{71} + 9 q^{72} - 23 q^{73} + 8 q^{74} - 9 q^{75} - 18 q^{76} - 3 q^{77} + 9 q^{78} - 17 q^{79} - 4 q^{80} + 9 q^{81} - 22 q^{82} - 30 q^{83} - 9 q^{84} + 18 q^{85} - 3 q^{86} + 11 q^{87} - 3 q^{88} + 23 q^{89} - 4 q^{90} - 9 q^{91} + q^{92} + 22 q^{93} - 49 q^{94} - 30 q^{95} - 9 q^{96} - 46 q^{97} + 9 q^{98} - 3 q^{99}+O(q^{100}) \) 9 * q + 9 * q^2 - 9 * q^3 + 9 * q^4 - 4 * q^5 - 9 * q^6 + 9 * q^7 + 9 * q^8 + 9 * q^9 - 4 * q^10 - 3 * q^11 - 9 * q^12 - 9 * q^13 + 9 * q^14 + 4 * q^15 + 9 * q^16 - 12 * q^17 + 9 * q^18 - 18 * q^19 - 4 * q^20 - 9 * q^21 - 3 * q^22 + q^23 - 9 * q^24 + 9 * q^25 - 9 * q^26 - 9 * q^27 + 9 * q^28 - 11 * q^29 + 4 * q^30 - 22 * q^31 + 9 * q^32 + 3 * q^33 - 12 * q^34 - 4 * q^35 + 9 * q^36 + 8 * q^37 - 18 * q^38 + 9 * q^39 - 4 * q^40 - 22 * q^41 - 9 * q^42 - 3 * q^43 - 3 * q^44 - 4 * q^45 + q^46 - 49 * q^47 - 9 * q^48 + 9 * q^49 + 9 * q^50 + 12 * q^51 - 9 * q^52 + 8 * q^53 - 9 * q^54 - 19 * q^55 + 9 * q^56 + 18 * q^57 - 11 * q^58 - 18 * q^59 + 4 * q^60 + 3 * q^61 - 22 * q^62 + 9 * q^63 + 9 * q^64 - 32 * q^65 + 3 * q^66 - 11 * q^67 - 12 * q^68 - q^69 - 4 * q^70 - 7 * q^71 + 9 * q^72 - 23 * q^73 + 8 * q^74 - 9 * q^75 - 18 * q^76 - 3 * q^77 + 9 * q^78 - 17 * q^79 - 4 * q^80 + 9 * q^81 - 22 * q^82 - 30 * q^83 - 9 * q^84 + 18 * q^85 - 3 * q^86 + 11 * q^87 - 3 * q^88 + 23 * q^89 - 4 * q^90 - 9 * q^91 + q^92 + 22 * q^93 - 49 * q^94 - 30 * q^95 - 9 * q^96 - 46 * q^97 + 9 * q^98 - 3 * 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
$5$	3.94651	1.76493	0.882465	−	0.470377i	$-0.155882\pi$
$5$	3.94651	1.76493	0.882465	+	0.470377i	$0.155882\pi$
$6$	−1.00000	−0.408248
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	1.00000	0.353553
$9$	1.00000	0.333333
$10$	3.94651	1.24799
$11$	−2.25610	−0.680240	−0.340120	−	0.940382i	$-0.610468\pi$
$11$	−2.25610	−0.680240	−0.340120	+	0.940382i	$0.610468\pi$
$12$	−1.00000	−0.288675
$13$	−6.54514	−1.81529	−0.907647	−	0.419734i	$-0.862123\pi$
$13$	−6.54514	−1.81529	−0.907647	+	0.419734i	$0.862123\pi$
$14$	1.00000	0.267261
$15$	−3.94651	−1.01898
$16$	1.00000	0.250000
$17$	0.785920	0.190614	0.0953068	−	0.995448i	$-0.469617\pi$
$17$	0.785920	0.190614	0.0953068	+	0.995448i	$0.469617\pi$
$18$	1.00000	0.235702
$19$	−7.36045	−1.68860	−0.844302	−	0.535868i	$-0.819985\pi$
$19$	−7.36045	−1.68860	−0.844302	+	0.535868i	$0.819985\pi$
$20$	3.94651	0.882465
$21$	−1.00000	−0.218218
$22$	−2.25610	−0.481002
$23$	−0.429872	−0.0896345	−0.0448172	−	0.998995i	$-0.514271\pi$
$23$	−0.429872	−0.0896345	−0.0448172	+	0.998995i	$0.514271\pi$
$24$	−1.00000	−0.204124
$25$	10.5749	2.11498
$26$	−6.54514	−1.28361
$27$	−1.00000	−0.192450
$28$	1.00000	0.188982
$29$	−10.0968	−1.87492	−0.937460	−	0.348092i	$-0.886830\pi$
$29$	−10.0968	−1.87492	−0.937460	+	0.348092i	$0.886830\pi$
$30$	−3.94651	−0.720530
$31$	−8.58370	−1.54168	−0.770839	−	0.637030i	$-0.780163\pi$
$31$	−8.58370	−1.54168	−0.770839	+	0.637030i	$0.780163\pi$
$32$	1.00000	0.176777
$33$	2.25610	0.392737
$34$	0.785920	0.134784
$35$	3.94651	0.667081
$36$	1.00000	0.166667
$37$	12.1347	1.99493	0.997466	−	0.0711432i	$-0.0226647\pi$
$37$	12.1347	1.99493	0.997466	+	0.0711432i	$0.0226647\pi$
$38$	−7.36045	−1.19402
$39$	6.54514	1.04806
$40$	3.94651	0.623997
$41$	−6.02711	−0.941276	−0.470638	−	0.882326i	$-0.655976\pi$
$41$	−6.02711	−0.941276	−0.470638	+	0.882326i	$0.655976\pi$
$42$	−1.00000	−0.154303
$43$	2.79767	0.426641	0.213320	−	0.976982i	$-0.431572\pi$
$43$	2.79767	0.426641	0.213320	+	0.976982i	$0.431572\pi$
$44$	−2.25610	−0.340120
$45$	3.94651	0.588310
$46$	−0.429872	−0.0633812
$47$	−10.0648	−1.46810	−0.734050	−	0.679096i	$-0.762372\pi$
$47$	−10.0648	−1.46810	−0.734050	+	0.679096i	$0.762372\pi$
$48$	−1.00000	−0.144338
$49$	1.00000	0.142857
$50$	10.5749	1.49552
$51$	−0.785920	−0.110051
$52$	−6.54514	−0.907647
$53$	6.97501	0.958091	0.479046	−	0.877790i	$-0.340983\pi$
$53$	6.97501	0.958091	0.479046	+	0.877790i	$0.340983\pi$
$54$	−1.00000	−0.136083
$55$	−8.90371	−1.20058
$56$	1.00000	0.133631
$57$	7.36045	0.974916
$58$	−10.0968	−1.32577
$59$	−6.13545	−0.798768	−0.399384	−	0.916784i	$-0.630776\pi$
$59$	−6.13545	−0.798768	−0.399384	+	0.916784i	$0.630776\pi$
$60$	−3.94651	−0.509492
$61$	−10.8656	−1.39120	−0.695599	−	0.718430i	$-0.744861\pi$
$61$	−10.8656	−1.39120	−0.695599	+	0.718430i	$0.744861\pi$
$62$	−8.58370	−1.09013
$63$	1.00000	0.125988
$64$	1.00000	0.125000
$65$	−25.8304	−3.20387
$66$	2.25610	0.277707
$67$	−7.46296	−0.911745	−0.455873	−	0.890045i	$-0.650673\pi$
$67$	−7.46296	−0.911745	−0.455873	+	0.890045i	$0.650673\pi$
$68$	0.785920	0.0953068
$69$	0.429872	0.0517505
$70$	3.94651	0.471698
$71$	6.37363	0.756411	0.378206	−	0.925722i	$-0.376541\pi$
$71$	6.37363	0.756411	0.378206	+	0.925722i	$0.376541\pi$
$72$	1.00000	0.117851
$73$	−1.83429	−0.214688	−0.107344	−	0.994222i	$-0.534235\pi$
$73$	−1.83429	−0.214688	−0.107344	+	0.994222i	$0.534235\pi$
$74$	12.1347	1.41063
$75$	−10.5749	−1.22108
$76$	−7.36045	−0.844302
$77$	−2.25610	−0.257106
$78$	6.54514	0.741091
$79$	−5.22919	−0.588330	−0.294165	−	0.955755i	$-0.595042\pi$
$79$	−5.22919	−0.588330	−0.294165	+	0.955755i	$0.595042\pi$
$80$	3.94651	0.441233
$81$	1.00000	0.111111
$82$	−6.02711	−0.665582
$83$	10.8771	1.19391	0.596956	−	0.802274i	$-0.296377\pi$
$83$	10.8771	1.19391	0.596956	+	0.802274i	$0.296377\pi$
$84$	−1.00000	−0.109109
$85$	3.10164	0.336420
$86$	2.79767	0.301681
$87$	10.0968	1.08249
$88$	−2.25610	−0.240501
$89$	−1.03959	−0.110197	−0.0550983	−	0.998481i	$-0.517547\pi$
$89$	−1.03959	−0.110197	−0.0550983	+	0.998481i	$0.517547\pi$
$90$	3.94651	0.415998
$91$	−6.54514	−0.686117
$92$	−0.429872	−0.0448172
$93$	8.58370	0.890088
$94$	−10.0648	−1.03810
$95$	−29.0481	−2.98027
$96$	−1.00000	−0.102062
$97$	−13.0792	−1.32800	−0.663998	−	0.747734i	$-0.731142\pi$
$97$	−13.0792	−1.32800	−0.663998	+	0.747734i	$0.731142\pi$
$98$	1.00000	0.101015
$99$	−2.25610	−0.226747
$100$	10.5749	1.05749
$101$	1.16636	0.116057	0.0580286	−	0.998315i	$-0.481519\pi$
$101$	1.16636	0.116057	0.0580286	+	0.998315i	$0.481519\pi$
$102$	−0.785920	−0.0778177
$103$	8.68862	0.856115	0.428057	−	0.903752i	$-0.359198\pi$
$103$	8.68862	0.856115	0.428057	+	0.903752i	$0.359198\pi$
$104$	−6.54514	−0.641804
$105$	−3.94651	−0.385139
$106$	6.97501	0.677473
$107$	−17.6259	−1.70396	−0.851981	−	0.523573i	$-0.824599\pi$
$107$	−17.6259	−1.70396	−0.851981	+	0.523573i	$0.824599\pi$
$108$	−1.00000	−0.0962250
$109$	−12.9738	−1.24266	−0.621332	−	0.783547i	$-0.713408\pi$
$109$	−12.9738	−1.24266	−0.621332	+	0.783547i	$0.713408\pi$
$110$	−8.90371	−0.848936
$111$	−12.1347	−1.15177
$112$	1.00000	0.0944911
$113$	12.6578	1.19075	0.595375	−	0.803448i	$-0.297004\pi$
$113$	12.6578	1.19075	0.595375	+	0.803448i	$0.297004\pi$
$114$	7.36045	0.689370
$115$	−1.69649	−0.158199
$116$	−10.0968	−0.937460
$117$	−6.54514	−0.605098
$118$	−6.13545	−0.564814
$119$	0.785920	0.0720452
$120$	−3.94651	−0.360265
$121$	−5.91001	−0.537274
$122$	−10.8656	−0.983725
$123$	6.02711	0.543446
$124$	−8.58370	−0.770839
$125$	22.0014	1.96786
$126$	1.00000	0.0890871
$127$	−3.28280	−0.291302	−0.145651	−	0.989336i	$-0.546528\pi$
$127$	−3.28280	−0.291302	−0.145651	+	0.989336i	$0.546528\pi$
$128$	1.00000	0.0883883
$129$	−2.79767	−0.246321
$130$	−25.8304	−2.26548
$131$	12.1998	1.06590	0.532952	−	0.846146i	$-0.321083\pi$
$131$	12.1998	1.06590	0.532952	+	0.846146i	$0.321083\pi$
$132$	2.25610	0.196368
$133$	−7.36045	−0.638232
$134$	−7.46296	−0.644701
$135$	−3.94651	−0.339661
$136$	0.785920	0.0673921
$137$	13.7984	1.17887	0.589437	−	0.807814i	$-0.299349\pi$
$137$	13.7984	1.17887	0.589437	+	0.807814i	$0.299349\pi$
$138$	0.429872	0.0365931
$139$	13.9650	1.18449	0.592247	−	0.805756i	$-0.298241\pi$
$139$	13.9650	1.18449	0.592247	+	0.805756i	$0.298241\pi$
$140$	3.94651	0.333541
$141$	10.0648	0.847607
$142$	6.37363	0.534864
$143$	14.7665	1.23484
$144$	1.00000	0.0833333
$145$	−39.8469	−3.30911
$146$	−1.83429	−0.151807
$147$	−1.00000	−0.0824786
$148$	12.1347	0.997466
$149$	−0.930392	−0.0762207	−0.0381103	−	0.999274i	$-0.512134\pi$
$149$	−0.930392	−0.0762207	−0.0381103	+	0.999274i	$0.512134\pi$
$150$	−10.5749	−0.863437
$151$	−20.1106	−1.63657	−0.818287	−	0.574809i	$-0.805076\pi$
$151$	−20.1106	−1.63657	−0.818287	+	0.574809i	$0.805076\pi$
$152$	−7.36045	−0.597012
$153$	0.785920	0.0635379
$154$	−2.25610	−0.181802
$155$	−33.8756	−2.72095
$156$	6.54514	0.524030
$157$	−2.36720	−0.188923	−0.0944614	−	0.995529i	$-0.530113\pi$
$157$	−2.36720	−0.188923	−0.0944614	+	0.995529i	$0.530113\pi$
$158$	−5.22919	−0.416012
$159$	−6.97501	−0.553154
$160$	3.94651	0.311999
$161$	−0.429872	−0.0338787
$162$	1.00000	0.0785674
$163$	−10.5267	−0.824517	−0.412259	−	0.911067i	$-0.635260\pi$
$163$	−10.5267	−0.824517	−0.412259	+	0.911067i	$0.635260\pi$
$164$	−6.02711	−0.470638
$165$	8.90371	0.693153
$166$	10.8771	0.844224
$167$	−0.429686	−0.0332501	−0.0166251	−	0.999862i	$-0.505292\pi$
$167$	−0.429686	−0.0332501	−0.0166251	+	0.999862i	$0.505292\pi$
$168$	−1.00000	−0.0771517
$169$	29.8388	2.29529
$170$	3.10164	0.237885
$171$	−7.36045	−0.562868
$172$	2.79767	0.213320
$173$	10.9274	0.830793	0.415397	−	0.909640i	$-0.363643\pi$
$173$	10.9274	0.830793	0.415397	+	0.909640i	$0.363643\pi$
$174$	10.0968	0.765433
$175$	10.5749	0.799388
$176$	−2.25610	−0.170060
$177$	6.13545	0.461169
$178$	−1.03959	−0.0779207
$179$	3.40478	0.254485	0.127243	−	0.991872i	$-0.459387\pi$
$179$	3.40478	0.254485	0.127243	+	0.991872i	$0.459387\pi$
$180$	3.94651	0.294155
$181$	0.690419	0.0513185	0.0256592	−	0.999671i	$-0.491832\pi$
$181$	0.690419	0.0513185	0.0256592	+	0.999671i	$0.491832\pi$
$182$	−6.54514	−0.485158
$183$	10.8656	0.803208
$184$	−0.429872	−0.0316906
$185$	47.8897	3.52092
$186$	8.58370	0.629387
$187$	−1.77311	−0.129663
$188$	−10.0648	−0.734050
$189$	−1.00000	−0.0727393
$190$	−29.0481	−2.10737
$191$	−1.00000	−0.0723575
$191$	−1.00000	−0.0723575
$192$	−1.00000	−0.0721688
$193$	21.0045	1.51194	0.755968	−	0.654609i	$-0.227167\pi$
$193$	21.0045	1.51194	0.755968	+	0.654609i	$0.227167\pi$
$194$	−13.0792	−0.939035
$195$	25.8304	1.84975
$196$	1.00000	0.0714286
$197$	22.4327	1.59827	0.799133	−	0.601155i	$-0.205292\pi$
$197$	22.4327	1.59827	0.799133	+	0.601155i	$0.205292\pi$
$198$	−2.25610	−0.160334
$199$	−13.4521	−0.953596	−0.476798	−	0.879013i	$-0.658203\pi$
$199$	−13.4521	−0.953596	−0.476798	+	0.879013i	$0.658203\pi$
$200$	10.5749	0.747759
$201$	7.46296	0.526396
$202$	1.16636	0.0820649
$203$	−10.0968	−0.708653
$204$	−0.785920	−0.0550254
$205$	−23.7860	−1.66129
$206$	8.68862	0.605365
$207$	−0.429872	−0.0298782
$208$	−6.54514	−0.453824
$209$	16.6059	1.14866
$210$	−3.94651	−0.272335
$211$	6.36420	0.438129	0.219065	−	0.975710i	$-0.429699\pi$
$211$	6.36420	0.438129	0.219065	+	0.975710i	$0.429699\pi$
$212$	6.97501	0.479046
$213$	−6.37363	−0.436714
$214$	−17.6259	−1.20488
$215$	11.0410	0.752992
$216$	−1.00000	−0.0680414
$217$	−8.58370	−0.582699
$218$	−12.9738	−0.878696
$219$	1.83429	0.123950
$220$	−8.90371	−0.600288
$221$	−5.14395	−0.346020
$222$	−12.1347	−0.814428
$223$	9.93430	0.665250	0.332625	−	0.943059i	$-0.392066\pi$
$223$	9.93430	0.665250	0.332625	+	0.943059i	$0.392066\pi$
$224$	1.00000	0.0668153
$225$	10.5749	0.704994
$226$	12.6578	0.841987
$227$	8.35228	0.554360	0.277180	−	0.960818i	$-0.410600\pi$
$227$	8.35228	0.554360	0.277180	+	0.960818i	$0.410600\pi$
$228$	7.36045	0.487458
$229$	14.1731	0.936587	0.468293	−	0.883573i	$-0.344869\pi$
$229$	14.1731	0.936587	0.468293	+	0.883573i	$0.344869\pi$
$230$	−1.69649	−0.111863
$231$	2.25610	0.148441
$232$	−10.0968	−0.662885
$233$	16.6531	1.09098	0.545492	−	0.838116i	$-0.316343\pi$
$233$	16.6531	1.09098	0.545492	+	0.838116i	$0.316343\pi$
$234$	−6.54514	−0.427869
$235$	−39.7207	−2.59109
$236$	−6.13545	−0.399384
$237$	5.22919	0.339672
$238$	0.785920	0.0509436
$239$	−9.20559	−0.595460	−0.297730	−	0.954650i	$-0.596230\pi$
$239$	−9.20559	−0.595460	−0.297730	+	0.954650i	$0.596230\pi$
$240$	−3.94651	−0.254746
$241$	−6.84743	−0.441082	−0.220541	−	0.975378i	$-0.570782\pi$
$241$	−6.84743	−0.441082	−0.220541	+	0.975378i	$0.570782\pi$
$242$	−5.91001	−0.379910
$243$	−1.00000	−0.0641500
$244$	−10.8656	−0.695599
$245$	3.94651	0.252133
$246$	6.02711	0.384274
$247$	48.1752	3.06531
$248$	−8.58370	−0.545065
$249$	−10.8771	−0.689306
$250$	22.0014	1.39149
$251$	15.4690	0.976397	0.488199	−	0.872733i	$-0.337654\pi$
$251$	15.4690	0.976397	0.488199	+	0.872733i	$0.337654\pi$
$252$	1.00000	0.0629941
$253$	0.969834	0.0609729
$254$	−3.28280	−0.205981
$255$	−3.10164	−0.194232
$256$	1.00000	0.0625000
$257$	−4.43690	−0.276766	−0.138383	−	0.990379i	$-0.544191\pi$
$257$	−4.43690	−0.276766	−0.138383	+	0.990379i	$0.544191\pi$
$258$	−2.79767	−0.174175
$259$	12.1347	0.754014
$260$	−25.8304	−1.60193
$261$	−10.0968	−0.624974
$262$	12.1998	0.753708
$263$	−11.3612	−0.700560	−0.350280	−	0.936645i	$-0.613914\pi$
$263$	−11.3612	−0.700560	−0.350280	+	0.936645i	$0.613914\pi$
$264$	2.25610	0.138853
$265$	27.5269	1.69096
$266$	−7.36045	−0.451298
$267$	1.03959	0.0636220
$268$	−7.46296	−0.455873
$269$	−19.7590	−1.20473	−0.602364	−	0.798221i	$-0.705775\pi$
$269$	−19.7590	−1.20473	−0.602364	+	0.798221i	$0.705775\pi$
$270$	−3.94651	−0.240177
$271$	−3.39544	−0.206258	−0.103129	−	0.994668i	$-0.532885\pi$
$271$	−3.39544	−0.206258	−0.103129	+	0.994668i	$0.532885\pi$
$272$	0.785920	0.0476534
$273$	6.54514	0.396130
$274$	13.7984	0.833590
$275$	−23.8580	−1.43869
$276$	0.429872	0.0258752
$277$	17.0460	1.02419	0.512096	−	0.858928i	$-0.328869\pi$
$277$	17.0460	1.02419	0.512096	+	0.858928i	$0.328869\pi$
$278$	13.9650	0.837564
$279$	−8.58370	−0.513893
$280$	3.94651	0.235849
$281$	−2.18186	−0.130159	−0.0650793	−	0.997880i	$-0.520730\pi$
$281$	−2.18186	−0.130159	−0.0650793	+	0.997880i	$0.520730\pi$
$282$	10.0648	0.599349
$283$	3.81067	0.226521	0.113260	−	0.993565i	$-0.463871\pi$
$283$	3.81067	0.226521	0.113260	+	0.993565i	$0.463871\pi$
$284$	6.37363	0.378206
$285$	29.0481	1.72066
$286$	14.7665	0.873161
$287$	−6.02711	−0.355769
$288$	1.00000	0.0589256
$289$	−16.3823	−0.963666
$290$	−39.8469	−2.33989
$291$	13.0792	0.766719
$292$	−1.83429	−0.107344
$293$	−14.0302	−0.819650	−0.409825	−	0.912164i	$-0.634410\pi$
$293$	−14.0302	−0.819650	−0.409825	+	0.912164i	$0.634410\pi$
$294$	−1.00000	−0.0583212
$295$	−24.2136	−1.40977
$296$	12.1347	0.705315
$297$	2.25610	0.130912
$298$	−0.930392	−0.0538961
$299$	2.81357	0.162713
$300$	−10.5749	−0.610542
$301$	2.79767	0.161255
$302$	−20.1106	−1.15723
$303$	−1.16636	−0.0670057
$304$	−7.36045	−0.422151
$305$	−42.8811	−2.45537
$306$	0.785920	0.0449280
$307$	6.51774	0.371987	0.185994	−	0.982551i	$-0.440450\pi$
$307$	6.51774	0.371987	0.185994	+	0.982551i	$0.440450\pi$
$308$	−2.25610	−0.128553
$309$	−8.68862	−0.494278
$310$	−33.8756	−1.92401
$311$	5.11990	0.290323	0.145161	−	0.989408i	$-0.453630\pi$
$311$	5.11990	0.290323	0.145161	+	0.989408i	$0.453630\pi$
$312$	6.54514	0.370545
$313$	−24.5998	−1.39047	−0.695233	−	0.718785i	$-0.744699\pi$
$313$	−24.5998	−1.39047	−0.695233	+	0.718785i	$0.744699\pi$
$314$	−2.36720	−0.133589
$315$	3.94651	0.222360
$316$	−5.22919	−0.294165
$317$	0.945995	0.0531324	0.0265662	−	0.999647i	$-0.491543\pi$
$317$	0.945995	0.0531324	0.0265662	+	0.999647i	$0.491543\pi$
$318$	−6.97501	−0.391139
$319$	22.7793	1.27540
$320$	3.94651	0.220616
$321$	17.6259	0.983783
$322$	−0.429872	−0.0239558
$323$	−5.78473	−0.321871
$324$	1.00000	0.0555556
$325$	−69.2142	−3.83931
$326$	−10.5267	−0.583022
$327$	12.9738	0.717452
$328$	−6.02711	−0.332791
$329$	−10.0648	−0.554889
$330$	8.90371	0.490133
$331$	−21.2386	−1.16738	−0.583690	−	0.811976i	$-0.698392\pi$
$331$	−21.2386	−1.16738	−0.583690	+	0.811976i	$0.698392\pi$
$332$	10.8771	0.596956
$333$	12.1347	0.664977
$334$	−0.429686	−0.0235114
$335$	−29.4526	−1.60917
$336$	−1.00000	−0.0545545
$337$	12.3269	0.671491	0.335745	−	0.941953i	$-0.391012\pi$
$337$	12.3269	0.671491	0.335745	+	0.941953i	$0.391012\pi$
$338$	29.8388	1.62302
$339$	−12.6578	−0.687480
$340$	3.10164	0.168210
$341$	19.3657	1.04871
$342$	−7.36045	−0.398008
$343$	1.00000	0.0539949
$344$	2.79767	0.150840
$345$	1.69649	0.0913360
$346$	10.9274	0.587460
$347$	27.3519	1.46833	0.734164	−	0.678972i	$-0.237574\pi$
$347$	27.3519	1.46833	0.734164	+	0.678972i	$0.237574\pi$
$348$	10.0968	0.541243
$349$	34.2687	1.83436	0.917180	−	0.398473i	$-0.130460\pi$
$349$	34.2687	1.83436	0.917180	+	0.398473i	$0.130460\pi$
$350$	10.5749	0.565252
$351$	6.54514	0.349354
$352$	−2.25610	−0.120251
$353$	−12.7304	−0.677571	−0.338785	−	0.940864i	$-0.610016\pi$
$353$	−12.7304	−0.677571	−0.338785	+	0.940864i	$0.610016\pi$
$354$	6.13545	0.326096
$355$	25.1536	1.33501
$356$	−1.03959	−0.0550983
$357$	−0.785920	−0.0415953
$358$	3.40478	0.179948
$359$	−4.35713	−0.229961	−0.114980	−	0.993368i	$-0.536681\pi$
$359$	−4.35713	−0.229961	−0.114980	+	0.993368i	$0.536681\pi$
$360$	3.94651	0.207999
$361$	35.1763	1.85138
$362$	0.690419	0.0362876
$363$	5.91001	0.310195
$364$	−6.54514	−0.343058
$365$	−7.23905	−0.378909
$366$	10.8656	0.567954
$367$	24.6065	1.28445	0.642224	−	0.766517i	$-0.278012\pi$
$367$	24.6065	1.28445	0.642224	+	0.766517i	$0.278012\pi$
$368$	−0.429872	−0.0224086
$369$	−6.02711	−0.313759
$370$	47.8897	2.48966
$371$	6.97501	0.362124
$372$	8.58370	0.445044
$373$	−19.3363	−1.00120	−0.500598	−	0.865680i	$-0.666886\pi$
$373$	−19.3363	−1.00120	−0.500598	+	0.865680i	$0.666886\pi$
$374$	−1.77311	−0.0916855
$375$	−22.0014	−1.13615
$376$	−10.0648	−0.519051
$377$	66.0847	3.40353
$378$	−1.00000	−0.0514344
$379$	−23.5293	−1.20862	−0.604309	−	0.796750i	$-0.706551\pi$
$379$	−23.5293	−1.20862	−0.604309	+	0.796750i	$0.706551\pi$
$380$	−29.0481	−1.49013
$381$	3.28280	0.168183
$382$	−1.00000	−0.0511645
$383$	0.483530	0.0247072	0.0123536	−	0.999924i	$-0.496068\pi$
$383$	0.483530	0.0247072	0.0123536	+	0.999924i	$0.496068\pi$
$384$	−1.00000	−0.0510310
$385$	−8.90371	−0.453775
$386$	21.0045	1.06910
$387$	2.79767	0.142214
$388$	−13.0792	−0.663998
$389$	30.1836	1.53037	0.765185	−	0.643810i	$-0.222647\pi$
$389$	30.1836	1.53037	0.765185	+	0.643810i	$0.222647\pi$
$390$	25.8304	1.30797
$391$	−0.337845	−0.0170855
$392$	1.00000	0.0505076
$393$	−12.1998	−0.615400
$394$	22.4327	1.13014
$395$	−20.6370	−1.03836
$396$	−2.25610	−0.113373
$397$	18.1865	0.912757	0.456378	−	0.889786i	$-0.349146\pi$
$397$	18.1865	0.912757	0.456378	+	0.889786i	$0.349146\pi$
$398$	−13.4521	−0.674294
$399$	7.36045	0.368484
$400$	10.5749	0.528745
$401$	−15.3075	−0.764422	−0.382211	−	0.924075i	$-0.624837\pi$
$401$	−15.3075	−0.764422	−0.382211	+	0.924075i	$0.624837\pi$
$402$	7.46296	0.372218
$403$	56.1815	2.79860
$404$	1.16636	0.0580286
$405$	3.94651	0.196103
$406$	−10.0968	−0.501094
$407$	−27.3771	−1.35703
$408$	−0.785920	−0.0389088
$409$	−4.48333	−0.221687	−0.110843	−	0.993838i	$-0.535355\pi$
$409$	−4.48333	−0.221687	−0.110843	+	0.993838i	$0.535355\pi$
$410$	−23.7860	−1.17471
$411$	−13.7984	−0.680624
$412$	8.68862	0.428057
$413$	−6.13545	−0.301906
$414$	−0.429872	−0.0211271
$415$	42.9264	2.10717
$416$	−6.54514	−0.320902
$417$	−13.9650	−0.683868
$418$	16.6059	0.812222
$419$	−33.1504	−1.61950	−0.809752	−	0.586772i	$-0.800398\pi$
$419$	−33.1504	−1.61950	−0.809752	+	0.586772i	$0.800398\pi$
$420$	−3.94651	−0.192570
$421$	20.0276	0.976083	0.488042	−	0.872820i	$-0.337711\pi$
$421$	20.0276	0.976083	0.488042	+	0.872820i	$0.337711\pi$
$422$	6.36420	0.309804
$423$	−10.0648	−0.489366
$424$	6.97501	0.338736
$425$	8.31103	0.403144
$426$	−6.37363	−0.308804
$427$	−10.8656	−0.525823
$428$	−17.6259	−0.851981
$429$	−14.7665	−0.712933
$430$	11.0410	0.532446
$431$	−11.7743	−0.567149	−0.283574	−	0.958950i	$-0.591520\pi$
$431$	−11.7743	−0.567149	−0.283574	+	0.958950i	$0.591520\pi$
$432$	−1.00000	−0.0481125
$433$	−35.2246	−1.69279	−0.846393	−	0.532558i	$-0.821231\pi$
$433$	−35.2246	−1.69279	−0.846393	+	0.532558i	$0.821231\pi$
$434$	−8.58370	−0.412031
$435$	39.8469	1.91051
$436$	−12.9738	−0.621332
$437$	3.16405	0.151357
$438$	1.83429	0.0876459
$439$	18.7136	0.893150	0.446575	−	0.894746i	$-0.352644\pi$
$439$	18.7136	0.893150	0.446575	+	0.894746i	$0.352644\pi$
$440$	−8.90371	−0.424468
$441$	1.00000	0.0476190
$442$	−5.14395	−0.244673
$443$	−17.5232	−0.832552	−0.416276	−	0.909238i	$-0.636665\pi$
$443$	−17.5232	−0.832552	−0.416276	+	0.909238i	$0.636665\pi$
$444$	−12.1347	−0.575887
$445$	−4.10276	−0.194489
$446$	9.93430	0.470403
$447$	0.930392	0.0440060
$448$	1.00000	0.0472456
$449$	−22.8635	−1.07900	−0.539498	−	0.841987i	$-0.681386\pi$
$449$	−22.8635	−1.07900	−0.539498	+	0.841987i	$0.681386\pi$
$450$	10.5749	0.498506
$451$	13.5978	0.640293
$452$	12.6578	0.595375
$453$	20.1106	0.944877
$454$	8.35228	0.391992
$455$	−25.8304	−1.21095
$456$	7.36045	0.344685
$457$	−17.7411	−0.829894	−0.414947	−	0.909846i	$-0.636200\pi$
$457$	−17.7411	−0.829894	−0.414947	+	0.909846i	$0.636200\pi$
$458$	14.1731	0.662267
$459$	−0.785920	−0.0366836
$460$	−1.69649	−0.0790993
$461$	2.63154	0.122563	0.0612816	−	0.998121i	$-0.480481\pi$
$461$	2.63154	0.122563	0.0612816	+	0.998121i	$0.480481\pi$
$462$	2.25610	0.104963
$463$	−0.657828	−0.0305719	−0.0152859	−	0.999883i	$-0.504866\pi$
$463$	−0.657828	−0.0305719	−0.0152859	+	0.999883i	$0.504866\pi$
$464$	−10.0968	−0.468730
$465$	33.8756	1.57094
$466$	16.6531	0.771442
$467$	−6.15972	−0.285038	−0.142519	−	0.989792i	$-0.545520\pi$
$467$	−6.15972	−0.285038	−0.142519	+	0.989792i	$0.545520\pi$
$468$	−6.54514	−0.302549
$469$	−7.46296	−0.344607
$470$	−39.7207	−1.83218
$471$	2.36720	0.109075
$472$	−6.13545	−0.282407
$473$	−6.31183	−0.290218
$474$	5.22919	0.240185
$475$	−77.8361	−3.57136
$476$	0.785920	0.0360226
$477$	6.97501	0.319364
$478$	−9.20559	−0.421054
$479$	−32.0243	−1.46323	−0.731613	−	0.681720i	$-0.761232\pi$
$479$	−32.0243	−1.46323	−0.731613	+	0.681720i	$0.761232\pi$
$480$	−3.94651	−0.180132
$481$	−79.4233	−3.62139
$482$	−6.84743	−0.311892
$483$	0.429872	0.0195598
$484$	−5.91001	−0.268637
$485$	−51.6173	−2.34382
$486$	−1.00000	−0.0453609
$487$	21.6693	0.981930	0.490965	−	0.871179i	$-0.336644\pi$
$487$	21.6693	0.981930	0.490965	+	0.871179i	$0.336644\pi$
$488$	−10.8656	−0.491863
$489$	10.5267	0.476035
$490$	3.94651	0.178285
$491$	24.1863	1.09151	0.545756	−	0.837944i	$-0.316243\pi$
$491$	24.1863	1.09151	0.545756	+	0.837944i	$0.316243\pi$
$492$	6.02711	0.271723
$493$	−7.93524	−0.357385
$494$	48.1752	2.16750
$495$	−8.90371	−0.400192
$496$	−8.58370	−0.385419
$497$	6.37363	0.285897
$498$	−10.8771	−0.487413
$499$	−19.3792	−0.867530	−0.433765	−	0.901026i	$-0.642815\pi$
$499$	−19.3792	−0.867530	−0.433765	+	0.901026i	$0.642815\pi$
$500$	22.0014	0.983932
$501$	0.429686	0.0191970
$502$	15.4690	0.690417
$503$	−26.9030	−1.19954	−0.599772	−	0.800171i	$-0.704742\pi$
$503$	−26.9030	−1.19954	−0.599772	+	0.800171i	$0.704742\pi$
$504$	1.00000	0.0445435
$505$	4.60305	0.204833
$506$	0.969834	0.0431144
$507$	−29.8388	−1.32519
$508$	−3.28280	−0.145651
$509$	42.4967	1.88363	0.941816	−	0.336128i	$-0.109118\pi$
$509$	42.4967	1.88363	0.941816	+	0.336128i	$0.109118\pi$
$510$	−3.10164	−0.137343
$511$	−1.83429	−0.0811444
$512$	1.00000	0.0441942
$513$	7.36045	0.324972
$514$	−4.43690	−0.195703
$515$	34.2897	1.51098
$516$	−2.79767	−0.123161
$517$	22.7072	0.998659
$518$	12.1347	0.533168
$519$	−10.9274	−0.479659
$520$	−25.8304	−1.13274
$521$	−37.7233	−1.65269	−0.826345	−	0.563164i	$-0.809584\pi$
$521$	−37.7233	−1.65269	−0.826345	+	0.563164i	$0.809584\pi$
$522$	−10.0968	−0.441923
$523$	−34.1022	−1.49119	−0.745593	−	0.666402i	$-0.767834\pi$
$523$	−34.1022	−1.49119	−0.745593	+	0.666402i	$0.767834\pi$
$524$	12.1998	0.532952
$525$	−10.5749	−0.461527
$526$	−11.3612	−0.495371
$527$	−6.74610	−0.293865
$528$	2.25610	0.0981842
$529$	−22.8152	−0.991966
$530$	27.5269	1.19569
$531$	−6.13545	−0.266256
$532$	−7.36045	−0.319116
$533$	39.4482	1.70869
$534$	1.03959	0.0449875
$535$	−69.5608	−3.00737
$536$	−7.46296	−0.322351
$537$	−3.40478	−0.146927
$538$	−19.7590	−0.851872
$539$	−2.25610	−0.0971771
$540$	−3.94651	−0.169831
$541$	46.0198	1.97854	0.989272	−	0.146084i	$-0.0466670\pi$
$541$	46.0198	1.97854	0.989272	+	0.146084i	$0.0466670\pi$
$542$	−3.39544	−0.145847
$543$	−0.690419	−0.0296287
$544$	0.785920	0.0336960
$545$	−51.2011	−2.19322
$546$	6.54514	0.280106
$547$	9.38473	0.401262	0.200631	−	0.979667i	$-0.435701\pi$
$547$	9.38473	0.401262	0.200631	+	0.979667i	$0.435701\pi$
$548$	13.7984	0.589437
$549$	−10.8656	−0.463733
$550$	−23.8580	−1.01731
$551$	74.3167	3.16600
$552$	0.429872	0.0182966
$553$	−5.22919	−0.222368
$554$	17.0460	0.724213
$555$	−47.8897	−2.03280
$556$	13.9650	0.592247
$557$	21.6222	0.916160	0.458080	−	0.888911i	$-0.348537\pi$
$557$	21.6222	0.916160	0.458080	+	0.888911i	$0.348537\pi$
$558$	−8.58370	−0.363377
$559$	−18.3111	−0.774479
$560$	3.94651	0.166770
$561$	1.77311	0.0748609
$562$	−2.18186	−0.0920361
$563$	20.4642	0.862463	0.431231	−	0.902241i	$-0.358079\pi$
$563$	20.4642	0.862463	0.431231	+	0.902241i	$0.358079\pi$
$564$	10.0648	0.423804
$565$	49.9542	2.10159
$566$	3.81067	0.160174
$567$	1.00000	0.0419961
$568$	6.37363	0.267432
$569$	−16.9841	−0.712013	−0.356006	−	0.934484i	$-0.615862\pi$
$569$	−16.9841	−0.712013	−0.356006	+	0.934484i	$0.615862\pi$
$570$	29.0481	1.21669
$571$	15.8957	0.665213	0.332607	−	0.943066i	$-0.392072\pi$
$571$	15.8957	0.665213	0.332607	+	0.943066i	$0.392072\pi$
$572$	14.7665	0.617418
$573$	1.00000	0.0417756
$574$	−6.02711	−0.251567
$575$	−4.54585	−0.189575
$576$	1.00000	0.0416667
$577$	−32.1695	−1.33923	−0.669617	−	0.742707i	$-0.733542\pi$
$577$	−32.1695	−1.33923	−0.669617	+	0.742707i	$0.733542\pi$
$578$	−16.3823	−0.681415
$579$	−21.0045	−0.872916
$580$	−39.8469	−1.65455
$581$	10.8771	0.451257
$582$	13.0792	0.542152
$583$	−15.7363	−0.651732
$584$	−1.83429	−0.0759036
$585$	−25.8304	−1.06796
$586$	−14.0302	−0.579580
$587$	33.9256	1.40026	0.700129	−	0.714017i	$-0.253126\pi$
$587$	33.9256	1.40026	0.700129	+	0.714017i	$0.253126\pi$
$588$	−1.00000	−0.0412393
$589$	63.1799	2.60328
$590$	−24.2136	−0.996858
$591$	−22.4327	−0.922759
$592$	12.1347	0.498733
$593$	12.1393	0.498500	0.249250	−	0.968439i	$-0.419816\pi$
$593$	12.1393	0.498500	0.249250	+	0.968439i	$0.419816\pi$
$594$	2.25610	0.0925689
$595$	3.10164	0.127155
$596$	−0.930392	−0.0381103
$597$	13.4521	0.550559
$598$	2.81357	0.115055
$599$	−37.1655	−1.51854	−0.759270	−	0.650776i	$-0.774444\pi$
$599$	−37.1655	−1.51854	−0.759270	+	0.650776i	$0.774444\pi$
$600$	−10.5749	−0.431719
$601$	−36.1064	−1.47281	−0.736406	−	0.676539i	$-0.763479\pi$
$601$	−36.1064	−1.47281	−0.736406	+	0.676539i	$0.763479\pi$
$602$	2.79767	0.114025
$603$	−7.46296	−0.303915
$604$	−20.1106	−0.818287
$605$	−23.3239	−0.948251
$606$	−1.16636	−0.0473802
$607$	−34.0549	−1.38224	−0.691122	−	0.722738i	$-0.742883\pi$
$607$	−34.0549	−1.38224	−0.691122	+	0.722738i	$0.742883\pi$
$608$	−7.36045	−0.298506
$609$	10.0968	0.409141
$610$	−42.8811	−1.73621
$611$	65.8754	2.66503
$612$	0.785920	0.0317689
$613$	−29.1576	−1.17766	−0.588832	−	0.808255i	$-0.700412\pi$
$613$	−29.1576	−1.17766	−0.588832	+	0.808255i	$0.700412\pi$
$614$	6.51774	0.263035
$615$	23.7860	0.959144
$616$	−2.25610	−0.0909009
$617$	−35.9765	−1.44836	−0.724180	−	0.689611i	$-0.757781\pi$
$617$	−35.9765	−1.44836	−0.724180	+	0.689611i	$0.757781\pi$
$618$	−8.68862	−0.349507
$619$	−20.0966	−0.807751	−0.403875	−	0.914814i	$-0.632337\pi$
$619$	−20.0966	−0.807751	−0.403875	+	0.914814i	$0.632337\pi$
$620$	−33.8756	−1.36048
$621$	0.429872	0.0172502
$622$	5.11990	0.205289
$623$	−1.03959	−0.0416504
$624$	6.54514	0.262015
$625$	33.9541	1.35816
$626$	−24.5998	−0.983208
$627$	−16.6059	−0.663177
$628$	−2.36720	−0.0944614
$629$	9.53690	0.380261
$630$	3.94651	0.157233
$631$	−24.9212	−0.992098	−0.496049	−	0.868294i	$-0.665216\pi$
$631$	−24.9212	−0.992098	−0.496049	+	0.868294i	$0.665216\pi$
$632$	−5.22919	−0.208006
$633$	−6.36420	−0.252954
$634$	0.945995	0.0375703
$635$	−12.9556	−0.514127
$636$	−6.97501	−0.276577
$637$	−6.54514	−0.259328
$638$	22.7793	0.901841
$639$	6.37363	0.252137
$640$	3.94651	0.155999
$641$	19.4663	0.768873	0.384436	−	0.923151i	$-0.374396\pi$
$641$	19.4663	0.768873	0.384436	+	0.923151i	$0.374396\pi$
$642$	17.6259	0.695639
$643$	23.8018	0.938650	0.469325	−	0.883025i	$-0.344497\pi$
$643$	23.8018	0.938650	0.469325	+	0.883025i	$0.344497\pi$
$644$	−0.429872	−0.0169393
$645$	−11.0410	−0.434740
$646$	−5.78473	−0.227597
$647$	−22.3917	−0.880310	−0.440155	−	0.897922i	$-0.645077\pi$
$647$	−22.3917	−0.880310	−0.440155	+	0.897922i	$0.645077\pi$
$648$	1.00000	0.0392837
$649$	13.8422	0.543354
$650$	−69.2142	−2.71480
$651$	8.58370	0.336422
$652$	−10.5267	−0.412259
$653$	29.2684	1.14536	0.572680	−	0.819779i	$-0.305904\pi$
$653$	29.2684	1.14536	0.572680	+	0.819779i	$0.305904\pi$
$654$	12.9738	0.507315
$655$	48.1467	1.88125
$656$	−6.02711	−0.235319
$657$	−1.83429	−0.0715626
$658$	−10.0648	−0.392366
$659$	−40.6954	−1.58527	−0.792634	−	0.609698i	$-0.791291\pi$
$659$	−40.6954	−1.58527	−0.792634	+	0.609698i	$0.791291\pi$
$660$	8.90371	0.346577
$661$	14.6612	0.570256	0.285128	−	0.958489i	$-0.407964\pi$
$661$	14.6612	0.570256	0.285128	+	0.958489i	$0.407964\pi$
$662$	−21.2386	−0.825463
$663$	5.14395	0.199775
$664$	10.8771	0.422112
$665$	−29.0481	−1.12644
$666$	12.1347	0.470210
$667$	4.34031	0.168058
$668$	−0.429686	−0.0166251
$669$	−9.93430	−0.384082
$670$	−29.4526	−1.13785
$671$	24.5139	0.946348
$672$	−1.00000	−0.0385758
$673$	38.1106	1.46905	0.734527	−	0.678579i	$-0.237404\pi$
$673$	38.1106	1.46905	0.734527	+	0.678579i	$0.237404\pi$
$674$	12.3269	0.474816
$675$	−10.5749	−0.407028
$676$	29.8388	1.14765
$677$	−30.4448	−1.17009	−0.585044	−	0.811001i	$-0.698923\pi$
$677$	−30.4448	−1.17009	−0.585044	+	0.811001i	$0.698923\pi$
$678$	−12.6578	−0.486122
$679$	−13.0792	−0.501936
$680$	3.10164	0.118942
$681$	−8.35228	−0.320060
$682$	19.3657	0.741550
$683$	26.3660	1.00887	0.504434	−	0.863450i	$-0.331701\pi$
$683$	26.3660	1.00887	0.504434	+	0.863450i	$0.331701\pi$
$684$	−7.36045	−0.281434
$685$	54.4554	2.08063
$686$	1.00000	0.0381802
$687$	−14.1731	−0.540738
$688$	2.79767	0.106660
$689$	−45.6524	−1.73922
$690$	1.69649	0.0645843
$691$	2.88084	0.109592	0.0547961	−	0.998498i	$-0.482549\pi$
$691$	2.88084	0.109592	0.0547961	+	0.998498i	$0.482549\pi$
$692$	10.9274	0.415397
$693$	−2.25610	−0.0857022
$694$	27.3519	1.03826
$695$	55.1129	2.09055
$696$	10.0968	0.382717
$697$	−4.73682	−0.179420
$698$	34.2687	1.29709
$699$	−16.6531	−0.629880
$700$	10.5749	0.399694
$701$	−31.6330	−1.19476	−0.597381	−	0.801958i	$-0.703792\pi$
$701$	−31.6330	−1.19476	−0.597381	+	0.801958i	$0.703792\pi$
$702$	6.54514	0.247030
$703$	−89.3169	−3.36865
$704$	−2.25610	−0.0850300
$705$	39.7207	1.49597
$706$	−12.7304	−0.479115
$707$	1.16636	0.0438655
$708$	6.13545	0.230584
$709$	−32.3979	−1.21673	−0.608363	−	0.793659i	$-0.708174\pi$
$709$	−32.3979	−1.21673	−0.608363	+	0.793659i	$0.708174\pi$
$710$	25.1536	0.943997
$711$	−5.22919	−0.196110
$712$	−1.03959	−0.0389604
$713$	3.68989	0.138187
$714$	−0.785920	−0.0294123
$715$	58.2760	2.17940
$716$	3.40478	0.127243
$717$	9.20559	0.343789
$718$	−4.35713	−0.162607
$719$	42.9219	1.60072	0.800358	−	0.599522i	$-0.204643\pi$
$719$	42.9219	1.60072	0.800358	+	0.599522i	$0.204643\pi$
$720$	3.94651	0.147078
$721$	8.68862	0.323581
$722$	35.1763	1.30913
$723$	6.84743	0.254659
$724$	0.690419	0.0256592
$725$	−106.772	−3.96542
$726$	5.91001	0.219341
$727$	35.7653	1.32646	0.663231	−	0.748415i	$-0.269185\pi$
$727$	35.7653	1.32646	0.663231	+	0.748415i	$0.269185\pi$
$728$	−6.54514	−0.242579
$729$	1.00000	0.0370370
$730$	−7.23905	−0.267929
$731$	2.19875	0.0813236
$732$	10.8656	0.401604
$733$	20.2416	0.747642	0.373821	−	0.927501i	$-0.378047\pi$
$733$	20.2416	0.747642	0.373821	+	0.927501i	$0.378047\pi$
$734$	24.6065	0.908242
$735$	−3.94651	−0.145569
$736$	−0.429872	−0.0158453
$737$	16.8372	0.620205
$738$	−6.02711	−0.221861
$739$	−43.3148	−1.59336	−0.796680	−	0.604402i	$-0.793412\pi$
$739$	−43.3148	−1.59336	−0.796680	+	0.604402i	$0.793412\pi$
$740$	47.8897	1.76046
$741$	−48.1752	−1.76976
$742$	6.97501	0.256061
$743$	−48.8791	−1.79320	−0.896601	−	0.442840i	$-0.853971\pi$
$743$	−48.8791	−1.79320	−0.896601	+	0.442840i	$0.853971\pi$
$744$	8.58370	0.314694
$745$	−3.67180	−0.134524
$746$	−19.3363	−0.707952
$747$	10.8771	0.397971
$748$	−1.77311	−0.0648315
$749$	−17.6259	−0.644037
$750$	−22.0014	−0.803377
$751$	31.1005	1.13487	0.567437	−	0.823417i	$-0.307935\pi$
$751$	31.1005	1.13487	0.567437	+	0.823417i	$0.307935\pi$
$752$	−10.0648	−0.367025
$753$	−15.4690	−0.563723
$754$	66.0847	2.40666
$755$	−79.3665	−2.88844
$756$	−1.00000	−0.0363696
$757$	31.1366	1.13168	0.565839	−	0.824516i	$-0.308552\pi$
$757$	31.1366	1.13168	0.565839	+	0.824516i	$0.308552\pi$
$758$	−23.5293	−0.854622
$759$	−0.969834	−0.0352027
$760$	−29.0481	−1.05368
$761$	36.9936	1.34102	0.670509	−	0.741902i	$-0.266076\pi$
$761$	36.9936	1.34102	0.670509	+	0.741902i	$0.266076\pi$
$762$	3.28280	0.118923
$763$	−12.9738	−0.469683
$764$	−1.00000	−0.0361787
$765$	3.10164	0.112140
$766$	0.483530	0.0174707
$767$	40.1574	1.45000
$768$	−1.00000	−0.0360844
$769$	5.54368	0.199910	0.0999550	−	0.994992i	$-0.468130\pi$
$769$	5.54368	0.199910	0.0999550	+	0.994992i	$0.468130\pi$
$770$	−8.90371	−0.320868
$771$	4.43690	0.159791
$772$	21.0045	0.755968
$773$	−35.5312	−1.27797	−0.638984	−	0.769220i	$-0.720645\pi$
$773$	−35.5312	−1.27797	−0.638984	+	0.769220i	$0.720645\pi$
$774$	2.79767	0.100560
$775$	−90.7718	−3.26062
$776$	−13.0792	−0.469518
$777$	−12.1347	−0.435330
$778$	30.1836	1.08214
$779$	44.3622	1.58944
$780$	25.8304	0.924877
$781$	−14.3796	−0.514541
$782$	−0.337845	−0.0120813
$783$	10.0968	0.360829
$784$	1.00000	0.0357143
$785$	−9.34215	−0.333436
$786$	−12.1998	−0.435153
$787$	−28.1545	−1.00360	−0.501800	−	0.864984i	$-0.667329\pi$
$787$	−28.1545	−1.00360	−0.501800	+	0.864984i	$0.667329\pi$
$788$	22.4327	0.799133
$789$	11.3612	0.404468
$790$	−20.6370	−0.734233
$791$	12.6578	0.450061
$792$	−2.25610	−0.0801670
$793$	71.1168	2.52543
$794$	18.1865	0.645416
$795$	−27.5269	−0.976279
$796$	−13.4521	−0.476798
$797$	23.2319	0.822917	0.411458	−	0.911429i	$-0.365020\pi$
$797$	23.2319	0.822917	0.411458	+	0.911429i	$0.365020\pi$
$798$	7.36045	0.260557
$799$	−7.91011	−0.279840
$800$	10.5749	0.373879
$801$	−1.03959	−0.0367322
$802$	−15.3075	−0.540528
$803$	4.13835	0.146039
$804$	7.46296	0.263198
$805$	−1.69649	−0.0597935
$806$	56.1815	1.97891
$807$	19.7590	0.695551
$808$	1.16636	0.0410324
$809$	−16.7178	−0.587766	−0.293883	−	0.955841i	$-0.594948\pi$
$809$	−16.7178	−0.587766	−0.293883	+	0.955841i	$0.594948\pi$
$810$	3.94651	0.138666
$811$	−23.9953	−0.842591	−0.421295	−	0.906924i	$-0.638424\pi$
$811$	−23.9953	−0.842591	−0.421295	+	0.906924i	$0.638424\pi$
$812$	−10.0968	−0.354327
$813$	3.39544	0.119083
$814$	−27.3771	−0.959567
$815$	−41.5438	−1.45522
$816$	−0.785920	−0.0275127
$817$	−20.5921	−0.720428
$818$	−4.48333	−0.156756
$819$	−6.54514	−0.228706
$820$	−23.7860	−0.830643
$821$	−45.7929	−1.59818	−0.799092	−	0.601208i	$-0.794686\pi$
$821$	−45.7929	−1.59818	−0.799092	+	0.601208i	$0.794686\pi$
$822$	−13.7984	−0.481274
$823$	4.73553	0.165070	0.0825351	−	0.996588i	$-0.473698\pi$
$823$	4.73553	0.165070	0.0825351	+	0.996588i	$0.473698\pi$
$824$	8.68862	0.302682
$825$	23.8580	0.830630
$826$	−6.13545	−0.213480
$827$	48.6311	1.69107	0.845535	−	0.533921i	$-0.179282\pi$
$827$	48.6311	1.69107	0.845535	+	0.533921i	$0.179282\pi$
$828$	−0.429872	−0.0149391
$829$	−20.8727	−0.724939	−0.362470	−	0.931996i	$-0.618066\pi$
$829$	−20.8727	−0.724939	−0.362470	+	0.931996i	$0.618066\pi$
$830$	42.9264	1.49000
$831$	−17.0460	−0.591318
$832$	−6.54514	−0.226912
$833$	0.785920	0.0272305
$834$	−13.9650	−0.483568
$835$	−1.69576	−0.0586842
$836$	16.6059	0.574328
$837$	8.58370	0.296696
$838$	−33.1504	−1.14516
$839$	−49.0920	−1.69484	−0.847421	−	0.530921i	$-0.821846\pi$
$839$	−49.0920	−1.69484	−0.847421	+	0.530921i	$0.821846\pi$
$840$	−3.94651	−0.136167
$841$	72.9445	2.51533
$842$	20.0276	0.690195
$843$	2.18186	0.0751471
$844$	6.36420	0.219065
$845$	117.759	4.05104
$846$	−10.0648	−0.346034
$847$	−5.91001	−0.203070
$848$	6.97501	0.239523
$849$	−3.81067	−0.130782
$850$	8.31103	0.285066
$851$	−5.21637	−0.178815
$852$	−6.37363	−0.218357
$853$	28.4402	0.973774	0.486887	−	0.873465i	$-0.338132\pi$
$853$	28.4402	0.973774	0.486887	+	0.873465i	$0.338132\pi$
$854$	−10.8656	−0.371813
$855$	−29.0481	−0.993423
$856$	−17.6259	−0.602441
$857$	−11.6306	−0.397294	−0.198647	−	0.980071i	$-0.563655\pi$
$857$	−11.6306	−0.397294	−0.198647	+	0.980071i	$0.563655\pi$
$858$	−14.7665	−0.504120
$859$	18.4985	0.631160	0.315580	−	0.948899i	$-0.397801\pi$
$859$	18.4985	0.631160	0.315580	+	0.948899i	$0.397801\pi$
$860$	11.0410	0.376496
$861$	6.02711	0.205403
$862$	−11.7743	−0.401035
$863$	21.6023	0.735350	0.367675	−	0.929954i	$-0.380154\pi$
$863$	21.6023	0.735350	0.367675	+	0.929954i	$0.380154\pi$
$864$	−1.00000	−0.0340207
$865$	43.1250	1.46629
$866$	−35.2246	−1.19698
$867$	16.3823	0.556373
$868$	−8.58370	−0.291350
$869$	11.7976	0.400206
$870$	39.8469	1.35094
$871$	48.8461	1.65509
$872$	−12.9738	−0.439348
$873$	−13.0792	−0.442666
$874$	3.16405	0.107026
$875$	22.0014	0.743783
$876$	1.83429	0.0619750
$877$	−31.2867	−1.05648	−0.528238	−	0.849096i	$-0.677147\pi$
$877$	−31.2867	−1.05648	−0.528238	+	0.849096i	$0.677147\pi$
$878$	18.7136	0.631552
$879$	14.0302	0.473225
$880$	−8.90371	−0.300144
$881$	−23.3639	−0.787150	−0.393575	−	0.919292i	$-0.628762\pi$
$881$	−23.3639	−0.787150	−0.393575	+	0.919292i	$0.628762\pi$
$882$	1.00000	0.0336718
$883$	17.9919	0.605477	0.302739	−	0.953074i	$-0.402099\pi$
$883$	17.9919	0.605477	0.302739	+	0.953074i	$0.402099\pi$
$884$	−5.14395	−0.173010
$885$	24.2136	0.813931
$886$	−17.5232	−0.588703
$887$	−27.4832	−0.922796	−0.461398	−	0.887193i	$-0.652652\pi$
$887$	−27.4832	−0.922796	−0.461398	+	0.887193i	$0.652652\pi$
$888$	−12.1347	−0.407214
$889$	−3.28280	−0.110102
$890$	−4.10276	−0.137525
$891$	−2.25610	−0.0755822
$892$	9.93430	0.332625
$893$	74.0813	2.47904
$894$	0.930392	0.0311170
$895$	13.4370	0.449149
$896$	1.00000	0.0334077
$897$	−2.81357	−0.0939424
$898$	−22.8635	−0.762966
$899$	86.6675	2.89052
$900$	10.5749	0.352497
$901$	5.48180	0.182625
$902$	13.5978	0.452756
$903$	−2.79767	−0.0931007
$904$	12.6578	0.420994
$905$	2.72474	0.0905736
$906$	20.1106	0.668129
$907$	−11.7462	−0.390025	−0.195013	−	0.980801i	$-0.562475\pi$
$907$	−11.7462	−0.390025	−0.195013	+	0.980801i	$0.562475\pi$
$908$	8.35228	0.277180
$909$	1.16636	0.0386857
$910$	−25.8304	−0.856270
$911$	26.4192	0.875306	0.437653	−	0.899144i	$-0.355810\pi$
$911$	26.4192	0.875306	0.437653	+	0.899144i	$0.355810\pi$
$912$	7.36045	0.243729
$913$	−24.5397	−0.812147
$914$	−17.7411	−0.586824
$915$	42.8811	1.41761
$916$	14.1731	0.468293
$917$	12.1998	0.402874
$918$	−0.785920	−0.0259392
$919$	0.314508	0.0103747	0.00518733	−	0.999987i	$-0.498349\pi$
$919$	0.314508	0.0103747	0.00518733	+	0.999987i	$0.498349\pi$
$920$	−1.69649	−0.0559317
$921$	−6.51774	−0.214767
$922$	2.63154	0.0866653
$923$	−41.7163	−1.37311
$924$	2.25610	0.0742203
$925$	128.323	4.21924
$926$	−0.657828	−0.0216176
$927$	8.68862	0.285372
$928$	−10.0968	−0.331442
$929$	−36.0086	−1.18140	−0.590702	−	0.806889i	$-0.701149\pi$
$929$	−36.0086	−1.18140	−0.590702	+	0.806889i	$0.701149\pi$
$930$	33.8756	1.11083
$931$	−7.36045	−0.241229
$932$	16.6531	0.545492
$933$	−5.11990	−0.167618
$934$	−6.15972	−0.201552
$935$	−6.99760	−0.228846
$936$	−6.54514	−0.213935
$937$	−10.8397	−0.354117	−0.177059	−	0.984200i	$-0.556658\pi$
$937$	−10.8397	−0.354117	−0.177059	+	0.984200i	$0.556658\pi$
$938$	−7.46296	−0.243674
$939$	24.5998	0.802786
$940$	−39.7207	−1.29555
$941$	29.8689	0.973698	0.486849	−	0.873486i	$-0.338146\pi$
$941$	29.8689	0.973698	0.486849	+	0.873486i	$0.338146\pi$
$942$	2.36720	0.0771274
$943$	2.59088	0.0843708
$944$	−6.13545	−0.199692
$945$	−3.94651	−0.128380
$946$	−6.31183	−0.205215
$947$	6.30109	0.204758	0.102379	−	0.994745i	$-0.467355\pi$
$947$	6.30109	0.204758	0.102379	+	0.994745i	$0.467355\pi$
$948$	5.22919	0.169836
$949$	12.0057	0.389722
$950$	−77.8361	−2.52534
$951$	−0.945995	−0.0306760
$952$	0.785920	0.0254718
$953$	−41.6305	−1.34854	−0.674272	−	0.738483i	$-0.735543\pi$
$953$	−41.6305	−1.34854	−0.674272	+	0.738483i	$0.735543\pi$
$954$	6.97501	0.225824
$955$	−3.94651	−0.127706
$956$	−9.20559	−0.297730
$957$	−22.7793	−0.736350
$958$	−32.0243	−1.03466
$959$	13.7984	0.445573
$960$	−3.94651	−0.127373
$961$	42.6799	1.37677
$962$	−79.4233	−2.56071
$963$	−17.6259	−0.567987
$964$	−6.84743	−0.220541
$965$	82.8943	2.66846
$966$	0.429872	0.0138309
$967$	8.96096	0.288165	0.144083	−	0.989566i	$-0.453977\pi$
$967$	8.96096	0.288165	0.144083	+	0.989566i	$0.453977\pi$
$968$	−5.91001	−0.189955
$969$	5.78473	0.185832
$970$	−51.6173	−1.65733
$971$	18.4758	0.592917	0.296458	−	0.955046i	$-0.404194\pi$
$971$	18.4758	0.592917	0.296458	+	0.955046i	$0.404194\pi$
$972$	−1.00000	−0.0320750
$973$	13.9650	0.447697
$974$	21.6693	0.694329
$975$	69.2142	2.21663
$976$	−10.8656	−0.347799
$977$	−9.82994	−0.314488	−0.157244	−	0.987560i	$-0.550261\pi$
$977$	−9.82994	−0.314488	−0.157244	+	0.987560i	$0.550261\pi$
$978$	10.5267	0.336608
$979$	2.34542	0.0749601
$980$	3.94651	0.126066
$981$	−12.9738	−0.414221
$982$	24.1863	0.771815
$983$	19.9676	0.636867	0.318434	−	0.947945i	$-0.396843\pi$
$983$	19.9676	0.636867	0.318434	+	0.947945i	$0.396843\pi$
$984$	6.02711	0.192137
$985$	88.5309	2.82083
$986$	−7.93524	−0.252710
$987$	10.0648	0.320365
$988$	48.1752	1.53266
$989$	−1.20264	−0.0382417
$990$	−8.90371	−0.282979
$991$	−13.1439	−0.417531	−0.208765	−	0.977966i	$-0.566944\pi$
$991$	−13.1439	−0.417531	−0.208765	+	0.977966i	$0.566944\pi$
$992$	−8.58370	−0.272533
$993$	21.2386	0.673987
$994$	6.37363	0.202159
$995$	−53.0889	−1.68303
$996$	−10.8771	−0.344653
$997$	−22.5542	−0.714298	−0.357149	−	0.934047i	$-0.616251\pi$
$997$	−22.5542	−0.714298	−0.357149	+	0.934047i	$0.616251\pi$
$998$	−19.3792	−0.613436
$999$	−12.1347	−0.383925

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8022.2.a.p.1.9	✓	9

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8022.2.a.p.1.9	✓	9	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:	\( N \)	\(=\)	\( 8022 = 2 \cdot 3 \cdot 7 \cdot 191 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8022.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +3.94651 q^{5} -1.00000 q^{6} +1.00000 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +3.94651 q^{5} -1.00000 q^{6} +1.00000 q^{7} +1.00000 q^{8} +1.00000 q^{9} +3.94651 q^{10} -2.25610 q^{11} -1.00000 q^{12} -6.54514 q^{13} +1.00000 q^{14} -3.94651 q^{15} +1.00000 q^{16} +0.785920 q^{17} +1.00000 q^{18} -7.36045 q^{19} +3.94651 q^{20} -1.00000 q^{21} -2.25610 q^{22} -0.429872 q^{23} -1.00000 q^{24} +10.5749 q^{25} -6.54514 q^{26} -1.00000 q^{27} +1.00000 q^{28} -10.0968 q^{29} -3.94651 q^{30} -8.58370 q^{31} +1.00000 q^{32} +2.25610 q^{33} +0.785920 q^{34} +3.94651 q^{35} +1.00000 q^{36} +12.1347 q^{37} -7.36045 q^{38} +6.54514 q^{39} +3.94651 q^{40} -6.02711 q^{41} -1.00000 q^{42} +2.79767 q^{43} -2.25610 q^{44} +3.94651 q^{45} -0.429872 q^{46} -10.0648 q^{47} -1.00000 q^{48} +1.00000 q^{49} +10.5749 q^{50} -0.785920 q^{51} -6.54514 q^{52} +6.97501 q^{53} -1.00000 q^{54} -8.90371 q^{55} +1.00000 q^{56} +7.36045 q^{57} -10.0968 q^{58} -6.13545 q^{59} -3.94651 q^{60} -10.8656 q^{61} -8.58370 q^{62} +1.00000 q^{63} +1.00000 q^{64} -25.8304 q^{65} +2.25610 q^{66} -7.46296 q^{67} +0.785920 q^{68} +0.429872 q^{69} +3.94651 q^{70} +6.37363 q^{71} +1.00000 q^{72} -1.83429 q^{73} +12.1347 q^{74} -10.5749 q^{75} -7.36045 q^{76} -2.25610 q^{77} +6.54514 q^{78} -5.22919 q^{79} +3.94651 q^{80} +1.00000 q^{81} -6.02711 q^{82} +10.8771 q^{83} -1.00000 q^{84} +3.10164 q^{85} +2.79767 q^{86} +10.0968 q^{87} -2.25610 q^{88} -1.03959 q^{89} +3.94651 q^{90} -6.54514 q^{91} -0.429872 q^{92} +8.58370 q^{93} -10.0648 q^{94} -29.0481 q^{95} -1.00000 q^{96} -13.0792 q^{97} +1.00000 q^{98} -2.25610 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 9 q + 9 q^{2} - 9 q^{3} + 9 q^{4} - 4 q^{5} - 9 q^{6} + 9 q^{7} + 9 q^{8} + 9 q^{9}+O(q^{10}) \) 9 * q + 9 * q^2 - 9 * q^3 + 9 * q^4 - 4 * q^5 - 9 * q^6 + 9 * q^7 + 9 * q^8 + 9 * q^9	\( 9 q + 9 q^{2} - 9 q^{3} + 9 q^{4} - 4 q^{5} - 9 q^{6} + 9 q^{7} + 9 q^{8} + 9 q^{9} - 4 q^{10} - 3 q^{11} - 9 q^{12} - 9 q^{13} + 9 q^{14} + 4 q^{15} + 9 q^{16} - 12 q^{17} + 9 q^{18} - 18 q^{19} - 4 q^{20} - 9 q^{21} - 3 q^{22} + q^{23} - 9 q^{24} + 9 q^{25} - 9 q^{26} - 9 q^{27} + 9 q^{28} - 11 q^{29} + 4 q^{30} - 22 q^{31} + 9 q^{32} + 3 q^{33} - 12 q^{34} - 4 q^{35} + 9 q^{36} + 8 q^{37} - 18 q^{38} + 9 q^{39} - 4 q^{40} - 22 q^{41} - 9 q^{42} - 3 q^{43} - 3 q^{44} - 4 q^{45} + q^{46} - 49 q^{47} - 9 q^{48} + 9 q^{49} + 9 q^{50} + 12 q^{51} - 9 q^{52} + 8 q^{53} - 9 q^{54} - 19 q^{55} + 9 q^{56} + 18 q^{57} - 11 q^{58} - 18 q^{59} + 4 q^{60} + 3 q^{61} - 22 q^{62} + 9 q^{63} + 9 q^{64} - 32 q^{65} + 3 q^{66} - 11 q^{67} - 12 q^{68} - q^{69} - 4 q^{70} - 7 q^{71} + 9 q^{72} - 23 q^{73} + 8 q^{74} - 9 q^{75} - 18 q^{76} - 3 q^{77} + 9 q^{78} - 17 q^{79} - 4 q^{80} + 9 q^{81} - 22 q^{82} - 30 q^{83} - 9 q^{84} + 18 q^{85} - 3 q^{86} + 11 q^{87} - 3 q^{88} + 23 q^{89} - 4 q^{90} - 9 q^{91} + q^{92} + 22 q^{93} - 49 q^{94} - 30 q^{95} - 9 q^{96} - 46 q^{97} + 9 q^{98} - 3 q^{99}+O(q^{100}) \) 9 * q + 9 * q^2 - 9 * q^3 + 9 * q^4 - 4 * q^5 - 9 * q^6 + 9 * q^7 + 9 * q^8 + 9 * q^9 - 4 * q^10 - 3 * q^11 - 9 * q^12 - 9 * q^13 + 9 * q^14 + 4 * q^15 + 9 * q^16 - 12 * q^17 + 9 * q^18 - 18 * q^19 - 4 * q^20 - 9 * q^21 - 3 * q^22 + q^23 - 9 * q^24 + 9 * q^25 - 9 * q^26 - 9 * q^27 + 9 * q^28 - 11 * q^29 + 4 * q^30 - 22 * q^31 + 9 * q^32 + 3 * q^33 - 12 * q^34 - 4 * q^35 + 9 * q^36 + 8 * q^37 - 18 * q^38 + 9 * q^39 - 4 * q^40 - 22 * q^41 - 9 * q^42 - 3 * q^43 - 3 * q^44 - 4 * q^45 + q^46 - 49 * q^47 - 9 * q^48 + 9 * q^49 + 9 * q^50 + 12 * q^51 - 9 * q^52 + 8 * q^53 - 9 * q^54 - 19 * q^55 + 9 * q^56 + 18 * q^57 - 11 * q^58 - 18 * q^59 + 4 * q^60 + 3 * q^61 - 22 * q^62 + 9 * q^63 + 9 * q^64 - 32 * q^65 + 3 * q^66 - 11 * q^67 - 12 * q^68 - q^69 - 4 * q^70 - 7 * q^71 + 9 * q^72 - 23 * q^73 + 8 * q^74 - 9 * q^75 - 18 * q^76 - 3 * q^77 + 9 * q^78 - 17 * q^79 - 4 * q^80 + 9 * q^81 - 22 * q^82 - 30 * q^83 - 9 * q^84 + 18 * q^85 - 3 * q^86 + 11 * q^87 - 3 * q^88 + 23 * q^89 - 4 * q^90 - 9 * q^91 + q^92 + 22 * q^93 - 49 * q^94 - 30 * q^95 - 9 * q^96 - 46 * q^97 + 9 * q^98 - 3 * q^99

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