LMFDB - Embedded newform 8034.2.a.z.1.2

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:	$0$
Dimension:	$14$
Coefficient field:	$\mathbb{Q}[x]/(x^{14} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{14} - 3 x^{13} - 36 x^{12} + 108 x^{11} + 434 x^{10} - 1239 x^{9} - 2404 x^{8} + 6204 x^{7} + \cdots + 1552 $ x^14 - 3x^13 - 36x^12 + 108x^11 + 434x^10 - 1239x^9 - 2404x^8 + 6204x^7 + 6361x^6 - 14618x^5 - 7015x^4 + 15763x^3 + 1118x^2 - 6316*x + 1552
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$3.65422$ 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)

$f(q)$	$=$	$q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -3.65422 q^{5} +1.00000 q^{6} -2.98447 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -3.65422 q^{5} +1.00000 q^{6} -2.98447 q^{7} -1.00000 q^{8} +1.00000 q^{9} +3.65422 q^{10} +3.60891 q^{11} -1.00000 q^{12} +1.00000 q^{13} +2.98447 q^{14} +3.65422 q^{15} +1.00000 q^{16} -3.22106 q^{17} -1.00000 q^{18} +3.44921 q^{19} -3.65422 q^{20} +2.98447 q^{21} -3.60891 q^{22} +3.62176 q^{23} +1.00000 q^{24} +8.35335 q^{25} -1.00000 q^{26} -1.00000 q^{27} -2.98447 q^{28} +10.0281 q^{29} -3.65422 q^{30} +10.2641 q^{31} -1.00000 q^{32} -3.60891 q^{33} +3.22106 q^{34} +10.9059 q^{35} +1.00000 q^{36} +1.67832 q^{37} -3.44921 q^{38} -1.00000 q^{39} +3.65422 q^{40} -8.55999 q^{41} -2.98447 q^{42} +5.42205 q^{43} +3.60891 q^{44} -3.65422 q^{45} -3.62176 q^{46} -11.8155 q^{47} -1.00000 q^{48} +1.90705 q^{49} -8.35335 q^{50} +3.22106 q^{51} +1.00000 q^{52} -1.05673 q^{53} +1.00000 q^{54} -13.1878 q^{55} +2.98447 q^{56} -3.44921 q^{57} -10.0281 q^{58} -5.39663 q^{59} +3.65422 q^{60} -6.09399 q^{61} -10.2641 q^{62} -2.98447 q^{63} +1.00000 q^{64} -3.65422 q^{65} +3.60891 q^{66} +0.180935 q^{67} -3.22106 q^{68} -3.62176 q^{69} -10.9059 q^{70} -2.75179 q^{71} -1.00000 q^{72} -6.96603 q^{73} -1.67832 q^{74} -8.35335 q^{75} +3.44921 q^{76} -10.7707 q^{77} +1.00000 q^{78} -10.7353 q^{79} -3.65422 q^{80} +1.00000 q^{81} +8.55999 q^{82} -10.8822 q^{83} +2.98447 q^{84} +11.7705 q^{85} -5.42205 q^{86} -10.0281 q^{87} -3.60891 q^{88} +14.5772 q^{89} +3.65422 q^{90} -2.98447 q^{91} +3.62176 q^{92} -10.2641 q^{93} +11.8155 q^{94} -12.6042 q^{95} +1.00000 q^{96} +4.83370 q^{97} -1.90705 q^{98} +3.60891 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 14 q - 14 q^{2} - 14 q^{3} + 14 q^{4} - 3 q^{5} + 14 q^{6} + 4 q^{7} - 14 q^{8} + 14 q^{9}+O(q^{10}) $ 14 * q - 14 * q^2 - 14 * q^3 + 14 * q^4 - 3 * q^5 + 14 * q^6 + 4 * q^7 - 14 * q^8 + 14 * q^9	\( 14 q - 14 q^{2} - 14 q^{3} + 14 q^{4} - 3 q^{5} + 14 q^{6} + 4 q^{7} - 14 q^{8} + 14 q^{9} + 3 q^{10} + 5 q^{11} - 14 q^{12} + 14 q^{13} - 4 q^{14} + 3 q^{15} + 14 q^{16} - 7 q^{17} - 14 q^{18} + 31 q^{19} - 3 q^{20} - 4 q^{21} - 5 q^{22} + 14 q^{23} + 14 q^{24} + 11 q^{25} - 14 q^{26} - 14 q^{27} + 4 q^{28} + 9 q^{29} - 3 q^{30} + 23 q^{31} - 14 q^{32} - 5 q^{33} + 7 q^{34} - 2 q^{35} + 14 q^{36} + 12 q^{37} - 31 q^{38} - 14 q^{39} + 3 q^{40} - 5 q^{41} + 4 q^{42} - 2 q^{43} + 5 q^{44} - 3 q^{45} - 14 q^{46} - 11 q^{47} - 14 q^{48} + 52 q^{49} - 11 q^{50} + 7 q^{51} + 14 q^{52} + 6 q^{53} + 14 q^{54} + 30 q^{55} - 4 q^{56} - 31 q^{57} - 9 q^{58} - 4 q^{59} + 3 q^{60} + 12 q^{61} - 23 q^{62} + 4 q^{63} + 14 q^{64} - 3 q^{65} + 5 q^{66} + 24 q^{67} - 7 q^{68} - 14 q^{69} + 2 q^{70} + 20 q^{71} - 14 q^{72} + 2 q^{73} - 12 q^{74} - 11 q^{75} + 31 q^{76} - 28 q^{77} + 14 q^{78} + 59 q^{79} - 3 q^{80} + 14 q^{81} + 5 q^{82} + q^{83} - 4 q^{84} - 29 q^{85} + 2 q^{86} - 9 q^{87} - 5 q^{88} + 6 q^{89} + 3 q^{90} + 4 q^{91} + 14 q^{92} - 23 q^{93} + 11 q^{94} - 58 q^{95} + 14 q^{96} - 6 q^{97} - 52 q^{98} + 5 q^{99}+O(q^{100}) \) 14 * q - 14 * q^2 - 14 * q^3 + 14 * q^4 - 3 * q^5 + 14 * q^6 + 4 * q^7 - 14 * q^8 + 14 * q^9 + 3 * q^10 + 5 * q^11 - 14 * q^12 + 14 * q^13 - 4 * q^14 + 3 * q^15 + 14 * q^16 - 7 * q^17 - 14 * q^18 + 31 * q^19 - 3 * q^20 - 4 * q^21 - 5 * q^22 + 14 * q^23 + 14 * q^24 + 11 * q^25 - 14 * q^26 - 14 * q^27 + 4 * q^28 + 9 * q^29 - 3 * q^30 + 23 * q^31 - 14 * q^32 - 5 * q^33 + 7 * q^34 - 2 * q^35 + 14 * q^36 + 12 * q^37 - 31 * q^38 - 14 * q^39 + 3 * q^40 - 5 * q^41 + 4 * q^42 - 2 * q^43 + 5 * q^44 - 3 * q^45 - 14 * q^46 - 11 * q^47 - 14 * q^48 + 52 * q^49 - 11 * q^50 + 7 * q^51 + 14 * q^52 + 6 * q^53 + 14 * q^54 + 30 * q^55 - 4 * q^56 - 31 * q^57 - 9 * q^58 - 4 * q^59 + 3 * q^60 + 12 * q^61 - 23 * q^62 + 4 * q^63 + 14 * q^64 - 3 * q^65 + 5 * q^66 + 24 * q^67 - 7 * q^68 - 14 * q^69 + 2 * q^70 + 20 * q^71 - 14 * q^72 + 2 * q^73 - 12 * q^74 - 11 * q^75 + 31 * q^76 - 28 * q^77 + 14 * q^78 + 59 * q^79 - 3 * q^80 + 14 * q^81 + 5 * q^82 + q^83 - 4 * q^84 - 29 * q^85 + 2 * q^86 - 9 * q^87 - 5 * q^88 + 6 * q^89 + 3 * q^90 + 4 * q^91 + 14 * q^92 - 23 * q^93 + 11 * q^94 - 58 * q^95 + 14 * q^96 - 6 * q^97 - 52 * q^98 + 5 * 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
$5$	−3.65422	−1.63422	−0.817109	−	0.576483i	$-0.804425\pi$
$5$	−3.65422	−1.63422	−0.817109	+	0.576483i	$0.804425\pi$
$6$	1.00000	0.408248
$7$	−2.98447	−1.12802	−0.564012	−	0.825767i	$-0.690743\pi$
$7$	−2.98447	−1.12802	−0.564012	+	0.825767i	$0.690743\pi$
$8$	−1.00000	−0.353553
$9$	1.00000	0.333333
$10$	3.65422	1.15557
$11$	3.60891	1.08813	0.544064	−	0.839044i	$-0.316885\pi$
$11$	3.60891	1.08813	0.544064	+	0.839044i	$0.316885\pi$
$12$	−1.00000	−0.288675
$13$	1.00000	0.277350
$13$	1.00000	0.277350
$14$	2.98447	0.797633
$15$	3.65422	0.943517
$16$	1.00000	0.250000
$17$	−3.22106	−0.781221	−0.390611	−	0.920556i	$-0.627736\pi$
$17$	−3.22106	−0.781221	−0.390611	+	0.920556i	$0.627736\pi$
$18$	−1.00000	−0.235702
$19$	3.44921	0.791304	0.395652	−	0.918401i	$-0.370519\pi$
$19$	3.44921	0.791304	0.395652	+	0.918401i	$0.370519\pi$
$20$	−3.65422	−0.817109
$21$	2.98447	0.651265
$22$	−3.60891	−0.769423
$23$	3.62176	0.755188	0.377594	−	0.925971i	$-0.376751\pi$
$23$	3.62176	0.755188	0.377594	+	0.925971i	$0.376751\pi$
$24$	1.00000	0.204124
$25$	8.35335	1.67067
$26$	−1.00000	−0.196116
$27$	−1.00000	−0.192450
$28$	−2.98447	−0.564012
$29$	10.0281	1.86216	0.931082	−	0.364809i	$-0.118866\pi$
$29$	10.0281	1.86216	0.931082	+	0.364809i	$0.118866\pi$
$30$	−3.65422	−0.667167
$31$	10.2641	1.84349	0.921745	−	0.387798i	$-0.126764\pi$
$31$	10.2641	1.84349	0.921745	+	0.387798i	$0.126764\pi$
$32$	−1.00000	−0.176777
$33$	−3.60891	−0.628231
$34$	3.22106	0.552407
$35$	10.9059	1.84344
$36$	1.00000	0.166667
$37$	1.67832	0.275913	0.137957	−	0.990438i	$-0.455947\pi$
$37$	1.67832	0.275913	0.137957	+	0.990438i	$0.455947\pi$
$38$	−3.44921	−0.559536
$39$	−1.00000	−0.160128
$40$	3.65422	0.577784
$41$	−8.55999	−1.33685	−0.668423	−	0.743781i	$-0.733030\pi$
$41$	−8.55999	−1.33685	−0.668423	+	0.743781i	$0.733030\pi$
$42$	−2.98447	−0.460514
$43$	5.42205	0.826855	0.413428	−	0.910537i	$-0.364331\pi$
$43$	5.42205	0.826855	0.413428	+	0.910537i	$0.364331\pi$
$44$	3.60891	0.544064
$45$	−3.65422	−0.544740
$46$	−3.62176	−0.533999
$47$	−11.8155	−1.72347	−0.861737	−	0.507355i	$-0.830623\pi$
$47$	−11.8155	−1.72347	−0.861737	+	0.507355i	$0.830623\pi$
$48$	−1.00000	−0.144338
$49$	1.90705	0.272436
$50$	−8.35335	−1.18134
$51$	3.22106	0.451038
$52$	1.00000	0.138675
$53$	−1.05673	−0.145153	−0.0725767	−	0.997363i	$-0.523122\pi$
$53$	−1.05673	−0.145153	−0.0725767	+	0.997363i	$0.523122\pi$
$54$	1.00000	0.136083
$55$	−13.1878	−1.77824
$56$	2.98447	0.398816
$57$	−3.44921	−0.456859
$58$	−10.0281	−1.31675
$59$	−5.39663	−0.702582	−0.351291	−	0.936266i	$-0.614257\pi$
$59$	−5.39663	−0.702582	−0.351291	+	0.936266i	$0.614257\pi$
$60$	3.65422	0.471758
$61$	−6.09399	−0.780255	−0.390128	−	0.920761i	$-0.627569\pi$
$61$	−6.09399	−0.780255	−0.390128	+	0.920761i	$0.627569\pi$
$62$	−10.2641	−1.30354
$63$	−2.98447	−0.376008
$64$	1.00000	0.125000
$65$	−3.65422	−0.453251
$66$	3.60891	0.444227
$67$	0.180935	0.0221047	0.0110524	−	0.999939i	$-0.496482\pi$
$67$	0.180935	0.0221047	0.0110524	+	0.999939i	$0.496482\pi$
$68$	−3.22106	−0.390611
$69$	−3.62176	−0.436008
$70$	−10.9059	−1.30351
$71$	−2.75179	−0.326577	−0.163288	−	0.986578i	$-0.552210\pi$
$71$	−2.75179	−0.326577	−0.163288	+	0.986578i	$0.552210\pi$
$72$	−1.00000	−0.117851
$73$	−6.96603	−0.815313	−0.407656	−	0.913135i	$-0.633654\pi$
$73$	−6.96603	−0.815313	−0.407656	+	0.913135i	$0.633654\pi$
$74$	−1.67832	−0.195100
$75$	−8.35335	−0.964562
$76$	3.44921	0.395652
$77$	−10.7707	−1.22743
$78$	1.00000	0.113228
$79$	−10.7353	−1.20782	−0.603908	−	0.797054i	$-0.706391\pi$
$79$	−10.7353	−1.20782	−0.603908	+	0.797054i	$0.706391\pi$
$80$	−3.65422	−0.408555
$81$	1.00000	0.111111
$82$	8.55999	0.945293
$83$	−10.8822	−1.19447	−0.597236	−	0.802065i	$-0.703734\pi$
$83$	−10.8822	−1.19447	−0.597236	+	0.802065i	$0.703734\pi$
$84$	2.98447	0.325632
$85$	11.7705	1.27669
$86$	−5.42205	−0.584675
$87$	−10.0281	−1.07512
$88$	−3.60891	−0.384711
$89$	14.5772	1.54518	0.772591	−	0.634904i	$-0.218960\pi$
$89$	14.5772	1.54518	0.772591	+	0.634904i	$0.218960\pi$
$90$	3.65422	0.385189
$91$	−2.98447	−0.312857
$92$	3.62176	0.377594
$93$	−10.2641	−1.06434
$94$	11.8155	1.21868
$95$	−12.6042	−1.29316
$96$	1.00000	0.102062
$97$	4.83370	0.490788	0.245394	−	0.969423i	$-0.421083\pi$
$97$	4.83370	0.490788	0.245394	+	0.969423i	$0.421083\pi$
$98$	−1.90705	−0.192642
$99$	3.60891	0.362709
$100$	8.35335	0.835335
$101$	19.3390	1.92431	0.962153	−	0.272510i	$-0.0878538\pi$
$101$	19.3390	1.92431	0.962153	+	0.272510i	$0.0878538\pi$
$102$	−3.22106	−0.318932
$103$	−1.00000	−0.0985329
$103$	−1.00000	−0.0985329
$104$	−1.00000	−0.0980581
$105$	−10.9059	−1.06431
$106$	1.05673	0.102639
$107$	−3.71319	−0.358968	−0.179484	−	0.983761i	$-0.557443\pi$
$107$	−3.71319	−0.358968	−0.179484	+	0.983761i	$0.557443\pi$
$108$	−1.00000	−0.0962250
$109$	3.22996	0.309374	0.154687	−	0.987964i	$-0.450563\pi$
$109$	3.22996	0.309374	0.154687	+	0.987964i	$0.450563\pi$
$110$	13.1878	1.25741
$111$	−1.67832	−0.159299
$112$	−2.98447	−0.282006
$113$	10.2893	0.967933	0.483966	−	0.875087i	$-0.339196\pi$
$113$	10.2893	0.967933	0.483966	+	0.875087i	$0.339196\pi$
$114$	3.44921	0.323048
$115$	−13.2347	−1.23414
$116$	10.0281	0.931082
$117$	1.00000	0.0924500
$118$	5.39663	0.496800
$119$	9.61314	0.881236
$120$	−3.65422	−0.333583
$121$	2.02426	0.184023
$122$	6.09399	0.551724
$123$	8.55999	0.771828
$124$	10.2641	0.921745
$125$	−12.2539	−1.09602
$126$	2.98447	0.265878
$127$	−2.88893	−0.256351	−0.128175	−	0.991752i	$-0.540912\pi$
$127$	−2.88893	−0.256351	−0.128175	+	0.991752i	$0.540912\pi$
$128$	−1.00000	−0.0883883
$129$	−5.42205	−0.477385
$130$	3.65422	0.320497
$131$	−12.7736	−1.11604	−0.558018	−	0.829829i	$-0.688438\pi$
$131$	−12.7736	−1.11604	−0.558018	+	0.829829i	$0.688438\pi$
$132$	−3.60891	−0.314116
$133$	−10.2941	−0.892609
$134$	−0.180935	−0.0156304
$135$	3.65422	0.314506
$136$	3.22106	0.276203
$137$	6.17778	0.527804	0.263902	−	0.964550i	$-0.414990\pi$
$137$	6.17778	0.527804	0.263902	+	0.964550i	$0.414990\pi$
$138$	3.62176	0.308304
$139$	21.1507	1.79398	0.896988	−	0.442056i	$-0.145751\pi$
$139$	21.1507	1.79398	0.896988	+	0.442056i	$0.145751\pi$
$140$	10.9059	0.921718
$141$	11.8155	0.995048
$142$	2.75179	0.230925
$143$	3.60891	0.301793
$144$	1.00000	0.0833333
$145$	−36.6448	−3.04318
$146$	6.96603	0.576513
$147$	−1.90705	−0.157291
$148$	1.67832	0.137957
$149$	−18.7861	−1.53901	−0.769507	−	0.638639i	$-0.779498\pi$
$149$	−18.7861	−1.53901	−0.769507	+	0.638639i	$0.779498\pi$
$150$	8.35335	0.682048
$151$	−3.44672	−0.280490	−0.140245	−	0.990117i	$-0.544789\pi$
$151$	−3.44672	−0.280490	−0.140245	+	0.990117i	$0.544789\pi$
$152$	−3.44921	−0.279768
$153$	−3.22106	−0.260407
$154$	10.7707	0.867927
$155$	−37.5074	−3.01266
$156$	−1.00000	−0.0800641
$157$	10.8821	0.868485	0.434243	−	0.900796i	$-0.357016\pi$
$157$	10.8821	0.868485	0.434243	+	0.900796i	$0.357016\pi$
$158$	10.7353	0.854055
$159$	1.05673	0.0838044
$160$	3.65422	0.288892
$161$	−10.8090	−0.851870
$162$	−1.00000	−0.0785674
$163$	−12.0749	−0.945783	−0.472891	−	0.881121i	$-0.656790\pi$
$163$	−12.0749	−0.945783	−0.472891	+	0.881121i	$0.656790\pi$
$164$	−8.55999	−0.668423
$165$	13.1878	1.02667
$166$	10.8822	0.844619
$167$	−8.34086	−0.645435	−0.322718	−	0.946495i	$-0.604596\pi$
$167$	−8.34086	−0.645435	−0.322718	+	0.946495i	$0.604596\pi$
$168$	−2.98447	−0.230257
$169$	1.00000	0.0769231
$170$	−11.7705	−0.902753
$171$	3.44921	0.263768
$172$	5.42205	0.413428
$173$	0.521491	0.0396482	0.0198241	−	0.999803i	$-0.493689\pi$
$173$	0.521491	0.0396482	0.0198241	+	0.999803i	$0.493689\pi$
$174$	10.0281	0.760226
$175$	−24.9303	−1.88455
$176$	3.60891	0.272032
$177$	5.39663	0.405636
$178$	−14.5772	−1.09261
$179$	0.618878	0.0462571	0.0231286	−	0.999732i	$-0.492637\pi$
$179$	0.618878	0.0462571	0.0231286	+	0.999732i	$0.492637\pi$
$180$	−3.65422	−0.272370
$181$	−2.04131	−0.151730	−0.0758648	−	0.997118i	$-0.524172\pi$
$181$	−2.04131	−0.151730	−0.0758648	+	0.997118i	$0.524172\pi$
$182$	2.98447	0.221224
$183$	6.09399	0.450481
$184$	−3.62176	−0.266999
$185$	−6.13294	−0.450903
$186$	10.2641	0.752601
$187$	−11.6245	−0.850069
$188$	−11.8155	−0.861737
$189$	2.98447	0.217088
$190$	12.6042	0.914404
$191$	6.52988	0.472486	0.236243	−	0.971694i	$-0.424084\pi$
$191$	6.52988	0.472486	0.236243	+	0.971694i	$0.424084\pi$
$192$	−1.00000	−0.0721688
$193$	24.4949	1.76318	0.881590	−	0.472017i	$-0.156474\pi$
$193$	24.4949	1.76318	0.881590	+	0.472017i	$0.156474\pi$
$194$	−4.83370	−0.347040
$195$	3.65422	0.261684
$196$	1.90705	0.136218
$197$	9.11126	0.649151	0.324575	−	0.945860i	$-0.394779\pi$
$197$	9.11126	0.649151	0.324575	+	0.945860i	$0.394779\pi$
$198$	−3.60891	−0.256474
$199$	12.5933	0.892713	0.446356	−	0.894855i	$-0.352721\pi$
$199$	12.5933	0.892713	0.446356	+	0.894855i	$0.352721\pi$
$200$	−8.35335	−0.590671
$201$	−0.180935	−0.0127622
$202$	−19.3390	−1.36069
$203$	−29.9284	−2.10056
$204$	3.22106	0.225519
$205$	31.2801	2.18470
$206$	1.00000	0.0696733
$207$	3.62176	0.251729
$208$	1.00000	0.0693375
$209$	12.4479	0.861040
$210$	10.9059	0.752580
$211$	17.7445	1.22158	0.610791	−	0.791792i	$-0.290851\pi$
$211$	17.7445	1.22158	0.610791	+	0.791792i	$0.290851\pi$
$212$	−1.05673	−0.0725767
$213$	2.75179	0.188549
$214$	3.71319	0.253828
$215$	−19.8134	−1.35126
$216$	1.00000	0.0680414
$217$	−30.6329	−2.07950
$218$	−3.22996	−0.218760
$219$	6.96603	0.470721
$220$	−13.1878	−0.889120
$221$	−3.22106	−0.216672
$222$	1.67832	0.112641
$223$	−3.57710	−0.239540	−0.119770	−	0.992802i	$-0.538216\pi$
$223$	−3.57710	−0.239540	−0.119770	+	0.992802i	$0.538216\pi$
$224$	2.98447	0.199408
$225$	8.35335	0.556890
$226$	−10.2893	−0.684432
$227$	−9.58324	−0.636062	−0.318031	−	0.948080i	$-0.603022\pi$
$227$	−9.58324	−0.636062	−0.318031	+	0.948080i	$0.603022\pi$
$228$	−3.44921	−0.228430
$229$	1.79903	0.118883	0.0594415	−	0.998232i	$-0.481068\pi$
$229$	1.79903	0.118883	0.0594415	+	0.998232i	$0.481068\pi$
$230$	13.2347	0.872671
$231$	10.7707	0.708659
$232$	−10.0281	−0.658375
$233$	−11.6052	−0.760281	−0.380140	−	0.924929i	$-0.624124\pi$
$233$	−11.6052	−0.760281	−0.380140	+	0.924929i	$0.624124\pi$
$234$	−1.00000	−0.0653720
$235$	43.1766	2.81653
$236$	−5.39663	−0.351291
$237$	10.7353	0.697333
$238$	−9.61314	−0.623128
$239$	13.3711	0.864904	0.432452	−	0.901657i	$-0.357648\pi$
$239$	13.3711	0.864904	0.432452	+	0.901657i	$0.357648\pi$
$240$	3.65422	0.235879
$241$	−24.8787	−1.60258	−0.801290	−	0.598276i	$-0.795853\pi$
$241$	−24.8787	−1.60258	−0.801290	+	0.598276i	$0.795853\pi$
$242$	−2.02426	−0.130124
$243$	−1.00000	−0.0641500
$244$	−6.09399	−0.390128
$245$	−6.96880	−0.445221
$246$	−8.55999	−0.545765
$247$	3.44921	0.219468
$248$	−10.2641	−0.651772
$249$	10.8822	0.689629
$250$	12.2539	0.775004
$251$	−11.1588	−0.704338	−0.352169	−	0.935936i	$-0.614556\pi$
$251$	−11.1588	−0.704338	−0.352169	+	0.935936i	$0.614556\pi$
$252$	−2.98447	−0.188004
$253$	13.0706	0.821742
$254$	2.88893	0.181267
$255$	−11.7705	−0.737095
$256$	1.00000	0.0625000
$257$	3.46229	0.215972	0.107986	−	0.994152i	$-0.465560\pi$
$257$	3.46229	0.215972	0.107986	+	0.994152i	$0.465560\pi$
$258$	5.42205	0.337562
$259$	−5.00888	−0.311237
$260$	−3.65422	−0.226625
$261$	10.0281	0.620722
$262$	12.7736	0.789156
$263$	13.6573	0.842145	0.421073	−	0.907027i	$-0.361654\pi$
$263$	13.6573	0.842145	0.421073	+	0.907027i	$0.361654\pi$
$264$	3.60891	0.222113
$265$	3.86154	0.237212
$266$	10.2941	0.631170
$267$	−14.5772	−0.892112
$268$	0.180935	0.0110524
$269$	−5.74928	−0.350540	−0.175270	−	0.984520i	$-0.556080\pi$
$269$	−5.74928	−0.350540	−0.175270	+	0.984520i	$0.556080\pi$
$270$	−3.65422	−0.222389
$271$	27.8621	1.69250	0.846251	−	0.532784i	$-0.178854\pi$
$271$	27.8621	1.69250	0.846251	+	0.532784i	$0.178854\pi$
$272$	−3.22106	−0.195305
$273$	2.98447	0.180628
$274$	−6.17778	−0.373214
$275$	30.1465	1.81790
$276$	−3.62176	−0.218004
$277$	−15.1301	−0.909080	−0.454540	−	0.890726i	$-0.650196\pi$
$277$	−15.1301	−0.909080	−0.454540	+	0.890726i	$0.650196\pi$
$278$	−21.1507	−1.26853
$279$	10.2641	0.614496
$280$	−10.9059	−0.651753
$281$	−12.8516	−0.766660	−0.383330	−	0.923611i	$-0.625223\pi$
$281$	−12.8516	−0.766660	−0.383330	+	0.923611i	$0.625223\pi$
$282$	−11.8155	−0.703605
$283$	15.6158	0.928265	0.464133	−	0.885766i	$-0.346366\pi$
$283$	15.6158	0.928265	0.464133	+	0.885766i	$0.346366\pi$
$284$	−2.75179	−0.163288
$285$	12.6042	0.746608
$286$	−3.60891	−0.213400
$287$	25.5470	1.50799
$288$	−1.00000	−0.0589256
$289$	−6.62479	−0.389694
$290$	36.6448	2.15186
$291$	−4.83370	−0.283357
$292$	−6.96603	−0.407656
$293$	−0.430891	−0.0251729	−0.0125865	−	0.999921i	$-0.504006\pi$
$293$	−0.430891	−0.0251729	−0.0125865	+	0.999921i	$0.504006\pi$
$294$	1.90705	0.111222
$295$	19.7205	1.14817
$296$	−1.67832	−0.0975501
$297$	−3.60891	−0.209410
$298$	18.7861	1.08825
$299$	3.62176	0.209452
$300$	−8.35335	−0.482281
$301$	−16.1819	−0.932712
$302$	3.44672	0.198336
$303$	−19.3390	−1.11100
$304$	3.44921	0.197826
$305$	22.2688	1.27511
$306$	3.22106	0.184136
$307$	14.2854	0.815310	0.407655	−	0.913136i	$-0.366347\pi$
$307$	14.2854	0.815310	0.407655	+	0.913136i	$0.366347\pi$
$308$	−10.7707	−0.613717
$309$	1.00000	0.0568880
$310$	37.5074	2.13028
$311$	−24.1330	−1.36846	−0.684229	−	0.729267i	$-0.739861\pi$
$311$	−24.1330	−1.36846	−0.684229	+	0.729267i	$0.739861\pi$
$312$	1.00000	0.0566139
$313$	−9.19697	−0.519844	−0.259922	−	0.965630i	$-0.583697\pi$
$313$	−9.19697	−0.519844	−0.259922	+	0.965630i	$0.583697\pi$
$314$	−10.8821	−0.614112
$315$	10.9059	0.614479
$316$	−10.7353	−0.603908
$317$	−2.36054	−0.132581	−0.0662906	−	0.997800i	$-0.521116\pi$
$317$	−2.36054	−0.132581	−0.0662906	+	0.997800i	$0.521116\pi$
$318$	−1.05673	−0.0592586
$319$	36.1904	2.02627
$320$	−3.65422	−0.204277
$321$	3.71319	0.207250
$322$	10.8090	0.602363
$323$	−11.1101	−0.618183
$324$	1.00000	0.0555556
$325$	8.35335	0.463361
$326$	12.0749	0.668770
$327$	−3.22996	−0.178617
$328$	8.55999	0.472646
$329$	35.2631	1.94412
$330$	−13.1878	−0.725963
$331$	6.21190	0.341437	0.170718	−	0.985320i	$-0.445391\pi$
$331$	6.21190	0.341437	0.170718	+	0.985320i	$0.445391\pi$
$332$	−10.8822	−0.597236
$333$	1.67832	0.0919711
$334$	8.34086	0.456392
$335$	−0.661178	−0.0361240
$336$	2.98447	0.162816
$337$	−4.22189	−0.229981	−0.114991	−	0.993367i	$-0.536684\pi$
$337$	−4.22189	−0.229981	−0.114991	+	0.993367i	$0.536684\pi$
$338$	−1.00000	−0.0543928
$339$	−10.2893	−0.558836
$340$	11.7705	0.638343
$341$	37.0423	2.00595
$342$	−3.44921	−0.186512
$343$	15.1997	0.820709
$344$	−5.42205	−0.292338
$345$	13.2347	0.712533
$346$	−0.521491	−0.0280355
$347$	8.70941	0.467546	0.233773	−	0.972291i	$-0.424893\pi$
$347$	8.70941	0.467546	0.233773	+	0.972291i	$0.424893\pi$
$348$	−10.0281	−0.537561
$349$	28.7741	1.54024	0.770122	−	0.637897i	$-0.220195\pi$
$349$	28.7741	1.54024	0.770122	+	0.637897i	$0.220195\pi$
$350$	24.9303	1.33258
$351$	−1.00000	−0.0533761
$352$	−3.60891	−0.192356
$353$	−36.8607	−1.96190	−0.980949	−	0.194266i	$-0.937767\pi$
$353$	−36.8607	−1.96190	−0.980949	+	0.194266i	$0.937767\pi$
$354$	−5.39663	−0.286828
$355$	10.0556	0.533698
$356$	14.5772	0.772591
$357$	−9.61314	−0.508782
$358$	−0.618878	−0.0327087
$359$	−14.3225	−0.755914	−0.377957	−	0.925823i	$-0.623373\pi$
$359$	−14.3225	−0.755914	−0.377957	+	0.925823i	$0.623373\pi$
$360$	3.65422	0.192595
$361$	−7.10293	−0.373839
$362$	2.04131	0.107289
$363$	−2.02426	−0.106246
$364$	−2.98447	−0.156429
$365$	25.4554	1.33240
$366$	−6.09399	−0.318538
$367$	−34.5226	−1.80207	−0.901033	−	0.433751i	$-0.857190\pi$
$367$	−34.5226	−1.80207	−0.901033	+	0.433751i	$0.857190\pi$
$368$	3.62176	0.188797
$369$	−8.55999	−0.445615
$370$	6.13294	0.318836
$371$	3.15379	0.163736
$372$	−10.2641	−0.532169
$373$	8.12912	0.420910	0.210455	−	0.977604i	$-0.432505\pi$
$373$	8.12912	0.420910	0.210455	+	0.977604i	$0.432505\pi$
$374$	11.6245	0.601089
$375$	12.2539	0.632788
$376$	11.8155	0.609340
$377$	10.0281	0.516472
$378$	−2.98447	−0.153505
$379$	2.40752	0.123666	0.0618330	−	0.998087i	$-0.480305\pi$
$379$	2.40752	0.123666	0.0618330	+	0.998087i	$0.480305\pi$
$380$	−12.6042	−0.646581
$381$	2.88893	0.148004
$382$	−6.52988	−0.334098
$383$	1.19419	0.0610202	0.0305101	−	0.999534i	$-0.490287\pi$
$383$	1.19419	0.0610202	0.0305101	+	0.999534i	$0.490287\pi$
$384$	1.00000	0.0510310
$385$	39.3585	2.00590
$386$	−24.4949	−1.24676
$387$	5.42205	0.275618
$388$	4.83370	0.245394
$389$	8.39661	0.425725	0.212863	−	0.977082i	$-0.431721\pi$
$389$	8.39661	0.425725	0.212863	+	0.977082i	$0.431721\pi$
$390$	−3.65422	−0.185039
$391$	−11.6659	−0.589969
$392$	−1.90705	−0.0963208
$393$	12.7736	0.644343
$394$	−9.11126	−0.459019
$395$	39.2292	1.97383
$396$	3.60891	0.181355
$397$	27.5942	1.38491	0.692457	−	0.721459i	$-0.256528\pi$
$397$	27.5942	1.38491	0.692457	+	0.721459i	$0.256528\pi$
$398$	−12.5933	−0.631243
$399$	10.2941	0.515348
$400$	8.35335	0.417668
$401$	−23.5959	−1.17832	−0.589160	−	0.808016i	$-0.700541\pi$
$401$	−23.5959	−1.17832	−0.589160	+	0.808016i	$0.700541\pi$
$402$	0.180935	0.00902423
$403$	10.2641	0.511292
$404$	19.3390	0.962153
$405$	−3.65422	−0.181580
$406$	29.9284	1.48532
$407$	6.05690	0.300229
$408$	−3.22106	−0.159466
$409$	29.0562	1.43674	0.718369	−	0.695662i	$-0.244889\pi$
$409$	29.0562	1.43674	0.718369	+	0.695662i	$0.244889\pi$
$410$	−31.2801	−1.54482
$411$	−6.17778	−0.304728
$412$	−1.00000	−0.0492665
$413$	16.1061	0.792529
$414$	−3.62176	−0.178000
$415$	39.7658	1.95203
$416$	−1.00000	−0.0490290
$417$	−21.1507	−1.03575
$418$	−12.4479	−0.608847
$419$	−1.78495	−0.0872007	−0.0436003	−	0.999049i	$-0.513883\pi$
$419$	−1.78495	−0.0872007	−0.0436003	+	0.999049i	$0.513883\pi$
$420$	−10.9059	−0.532154
$421$	27.8302	1.35636	0.678180	−	0.734896i	$-0.262769\pi$
$421$	27.8302	1.35636	0.678180	+	0.734896i	$0.262769\pi$
$422$	−17.7445	−0.863790
$423$	−11.8155	−0.574491
$424$	1.05673	0.0513195
$425$	−26.9066	−1.30516
$426$	−2.75179	−0.133324
$427$	18.1873	0.880146
$428$	−3.71319	−0.179484
$429$	−3.60891	−0.174240
$430$	19.8134	0.955487
$431$	19.4588	0.937296	0.468648	−	0.883385i	$-0.344741\pi$
$431$	19.4588	0.937296	0.468648	+	0.883385i	$0.344741\pi$
$432$	−1.00000	−0.0481125
$433$	13.0229	0.625839	0.312919	−	0.949780i	$-0.398693\pi$
$433$	13.0229	0.625839	0.312919	+	0.949780i	$0.398693\pi$
$434$	30.6329	1.47043
$435$	36.6448	1.75698
$436$	3.22996	0.154687
$437$	12.4922	0.597583
$438$	−6.96603	−0.332850
$439$	34.1765	1.63115	0.815577	−	0.578649i	$-0.196420\pi$
$439$	34.1765	1.63115	0.815577	+	0.578649i	$0.196420\pi$
$440$	13.1878	0.628703
$441$	1.90705	0.0908121
$442$	3.22106	0.153210
$443$	−8.66649	−0.411758	−0.205879	−	0.978578i	$-0.566005\pi$
$443$	−8.66649	−0.411758	−0.205879	+	0.978578i	$0.566005\pi$
$444$	−1.67832	−0.0796493
$445$	−53.2684	−2.52517
$446$	3.57710	0.169381
$447$	18.7861	0.888550
$448$	−2.98447	−0.141003
$449$	−36.3559	−1.71574	−0.857869	−	0.513868i	$-0.828212\pi$
$449$	−36.3559	−1.71574	−0.857869	+	0.513868i	$0.828212\pi$
$450$	−8.35335	−0.393781
$451$	−30.8923	−1.45466
$452$	10.2893	0.483966
$453$	3.44672	0.161941
$454$	9.58324	0.449764
$455$	10.9059	0.511277
$456$	3.44921	0.161524
$457$	−18.0303	−0.843423	−0.421711	−	0.906730i	$-0.638570\pi$
$457$	−18.0303	−0.843423	−0.421711	+	0.906730i	$0.638570\pi$
$458$	−1.79903	−0.0840630
$459$	3.22106	0.150346
$460$	−13.2347	−0.617071
$461$	−14.6852	−0.683960	−0.341980	−	0.939707i	$-0.611097\pi$
$461$	−14.6852	−0.683960	−0.341980	+	0.939707i	$0.611097\pi$
$462$	−10.7707	−0.501098
$463$	3.25879	0.151449	0.0757243	−	0.997129i	$-0.475873\pi$
$463$	3.25879	0.151449	0.0757243	+	0.997129i	$0.475873\pi$
$464$	10.0281	0.465541
$465$	37.5074	1.73936
$466$	11.6052	0.537600
$467$	6.15730	0.284926	0.142463	−	0.989800i	$-0.454498\pi$
$467$	6.15730	0.284926	0.142463	+	0.989800i	$0.454498\pi$
$468$	1.00000	0.0462250
$469$	−0.539995	−0.0249347
$470$	−43.1766	−1.99159
$471$	−10.8821	−0.501420
$472$	5.39663	0.248400
$473$	19.5677	0.899725
$474$	−10.7353	−0.493089
$475$	28.8125	1.32201
$476$	9.61314	0.440618
$477$	−1.05673	−0.0483845
$478$	−13.3711	−0.611580
$479$	−2.77400	−0.126748	−0.0633738	−	0.997990i	$-0.520186\pi$
$479$	−2.77400	−0.126748	−0.0633738	+	0.997990i	$0.520186\pi$
$480$	−3.65422	−0.166792
$481$	1.67832	0.0765246
$482$	24.8787	1.13320
$483$	10.8090	0.491827
$484$	2.02426	0.0920117
$485$	−17.6634	−0.802055
$486$	1.00000	0.0453609
$487$	−8.81991	−0.399668	−0.199834	−	0.979830i	$-0.564040\pi$
$487$	−8.81991	−0.399668	−0.199834	+	0.979830i	$0.564040\pi$
$488$	6.09399	0.275862
$489$	12.0749	0.546048
$490$	6.96880	0.314818
$491$	−6.48893	−0.292841	−0.146421	−	0.989222i	$-0.546775\pi$
$491$	−6.48893	−0.292841	−0.146421	+	0.989222i	$0.546775\pi$
$492$	8.55999	0.385914
$493$	−32.3010	−1.45476
$494$	−3.44921	−0.155187
$495$	−13.1878	−0.592747
$496$	10.2641	0.460872
$497$	8.21262	0.368386
$498$	−10.8822	−0.487641
$499$	22.9419	1.02702	0.513511	−	0.858083i	$-0.328345\pi$
$499$	22.9419	1.02702	0.513511	+	0.858083i	$0.328345\pi$
$500$	−12.2539	−0.548011
$501$	8.34086	0.372642
$502$	11.1588	0.498042
$503$	−3.11600	−0.138936	−0.0694678	−	0.997584i	$-0.522130\pi$
$503$	−3.11600	−0.138936	−0.0694678	+	0.997584i	$0.522130\pi$
$504$	2.98447	0.132939
$505$	−70.6692	−3.14474
$506$	−13.0706	−0.581059
$507$	−1.00000	−0.0444116
$508$	−2.88893	−0.128175
$509$	−30.7411	−1.36258	−0.681289	−	0.732015i	$-0.738580\pi$
$509$	−30.7411	−1.36258	−0.681289	+	0.732015i	$0.738580\pi$
$510$	11.7705	0.521205
$511$	20.7899	0.919692
$512$	−1.00000	−0.0441942
$513$	−3.44921	−0.152286
$514$	−3.46229	−0.152715
$515$	3.65422	0.161024
$516$	−5.42205	−0.238693
$517$	−42.6413	−1.87536
$518$	5.00888	0.220078
$519$	−0.521491	−0.0228909
$520$	3.65422	0.160248
$521$	−14.4527	−0.633184	−0.316592	−	0.948562i	$-0.602539\pi$
$521$	−14.4527	−0.633184	−0.316592	+	0.948562i	$0.602539\pi$
$522$	−10.0281	−0.438916
$523$	8.53779	0.373331	0.186666	−	0.982423i	$-0.440232\pi$
$523$	8.53779	0.373331	0.186666	+	0.982423i	$0.440232\pi$
$524$	−12.7736	−0.558018
$525$	24.9303	1.08805
$526$	−13.6573	−0.595487
$527$	−33.0613	−1.44017
$528$	−3.60891	−0.157058
$529$	−9.88288	−0.429691
$530$	−3.86154	−0.167734
$531$	−5.39663	−0.234194
$532$	−10.2941	−0.446304
$533$	−8.55999	−0.370774
$534$	14.5772	0.630818
$535$	13.5688	0.586632
$536$	−0.180935	−0.00781521
$537$	−0.618878	−0.0267066
$538$	5.74928	0.247869
$539$	6.88239	0.296446
$540$	3.65422	0.157253
$541$	32.3463	1.39068	0.695339	−	0.718682i	$-0.255254\pi$
$541$	32.3463	1.39068	0.695339	+	0.718682i	$0.255254\pi$
$542$	−27.8621	−1.19678
$543$	2.04131	0.0876012
$544$	3.22106	0.138102
$545$	−11.8030	−0.505585
$546$	−2.98447	−0.127723
$547$	31.2297	1.33528	0.667642	−	0.744482i	$-0.267304\pi$
$547$	31.2297	1.33528	0.667642	+	0.744482i	$0.267304\pi$
$548$	6.17778	0.263902
$549$	−6.09399	−0.260085
$550$	−30.1465	−1.28545
$551$	34.5889	1.47354
$552$	3.62176	0.154152
$553$	32.0392	1.36244
$554$	15.1301	0.642817
$555$	6.13294	0.260329
$556$	21.1507	0.896988
$557$	−4.47599	−0.189654	−0.0948269	−	0.995494i	$-0.530230\pi$
$557$	−4.47599	−0.189654	−0.0948269	+	0.995494i	$0.530230\pi$
$558$	−10.2641	−0.434515
$559$	5.42205	0.229328
$560$	10.9059	0.460859
$561$	11.6245	0.490787
$562$	12.8516	0.542111
$563$	−17.1857	−0.724291	−0.362146	−	0.932122i	$-0.617956\pi$
$563$	−17.1857	−0.724291	−0.362146	+	0.932122i	$0.617956\pi$
$564$	11.8155	0.497524
$565$	−37.5993	−1.58181
$566$	−15.6158	−0.656382
$567$	−2.98447	−0.125336
$568$	2.75179	0.115462
$569$	22.7396	0.953295	0.476647	−	0.879095i	$-0.341852\pi$
$569$	22.7396	0.953295	0.476647	+	0.879095i	$0.341852\pi$
$570$	−12.6042	−0.527932
$571$	−27.4741	−1.14976	−0.574878	−	0.818239i	$-0.694950\pi$
$571$	−27.4741	−1.14976	−0.574878	+	0.818239i	$0.694950\pi$
$572$	3.60891	0.150896
$573$	−6.52988	−0.272790
$574$	−25.5470	−1.06631
$575$	30.2538	1.26167
$576$	1.00000	0.0416667
$577$	3.03374	0.126296	0.0631480	−	0.998004i	$-0.479886\pi$
$577$	3.03374	0.126296	0.0631480	+	0.998004i	$0.479886\pi$
$578$	6.62479	0.275555
$579$	−24.4949	−1.01797
$580$	−36.6448	−1.52159
$581$	32.4775	1.34739
$582$	4.83370	0.200363
$583$	−3.81366	−0.157946
$584$	6.96603	0.288257
$585$	−3.65422	−0.151084
$586$	0.430891	0.0177999
$587$	11.2031	0.462403	0.231202	−	0.972906i	$-0.425734\pi$
$587$	11.2031	0.462403	0.231202	+	0.972906i	$0.425734\pi$
$588$	−1.90705	−0.0786456
$589$	35.4031	1.45876
$590$	−19.7205	−0.811880
$591$	−9.11126	−0.374787
$592$	1.67832	0.0689783
$593$	−32.3805	−1.32971	−0.664854	−	0.746973i	$-0.731506\pi$
$593$	−32.3805	−1.32971	−0.664854	+	0.746973i	$0.731506\pi$
$594$	3.60891	0.148076
$595$	−35.1286	−1.44013
$596$	−18.7861	−0.769507
$597$	−12.5933	−0.515408
$598$	−3.62176	−0.148105
$599$	−6.75671	−0.276072	−0.138036	−	0.990427i	$-0.544079\pi$
$599$	−6.75671	−0.276072	−0.138036	+	0.990427i	$0.544079\pi$
$600$	8.35335	0.341024
$601$	−12.4093	−0.506186	−0.253093	−	0.967442i	$-0.581448\pi$
$601$	−12.4093	−0.506186	−0.253093	+	0.967442i	$0.581448\pi$
$602$	16.1819	0.659527
$603$	0.180935	0.00736825
$604$	−3.44672	−0.140245
$605$	−7.39709	−0.300735
$606$	19.3390	0.785595
$607$	−25.9148	−1.05185	−0.525925	−	0.850531i	$-0.676281\pi$
$607$	−25.9148	−1.05185	−0.525925	+	0.850531i	$0.676281\pi$
$608$	−3.44921	−0.139884
$609$	29.9284	1.21276
$610$	−22.2688	−0.901637
$611$	−11.8155	−0.478006
$612$	−3.22106	−0.130204
$613$	−23.1794	−0.936209	−0.468104	−	0.883673i	$-0.655063\pi$
$613$	−23.1794	−0.936209	−0.468104	+	0.883673i	$0.655063\pi$
$614$	−14.2854	−0.576511
$615$	−31.2801	−1.26134
$616$	10.7707	0.433963
$617$	40.3280	1.62354	0.811771	−	0.583975i	$-0.198503\pi$
$617$	40.3280	1.62354	0.811771	+	0.583975i	$0.198503\pi$
$618$	−1.00000	−0.0402259
$619$	43.6810	1.75569	0.877844	−	0.478947i	$-0.158981\pi$
$619$	43.6810	1.75569	0.877844	+	0.478947i	$0.158981\pi$
$620$	−37.5074	−1.50633
$621$	−3.62176	−0.145336
$622$	24.1330	0.967646
$623$	−43.5053	−1.74300
$624$	−1.00000	−0.0400320
$625$	3.01172	0.120469
$626$	9.19697	0.367585
$627$	−12.4479	−0.497122
$628$	10.8821	0.434243
$629$	−5.40595	−0.215549
$630$	−10.9059	−0.434502
$631$	14.6223	0.582106	0.291053	−	0.956707i	$-0.405994\pi$
$631$	14.6223	0.582106	0.291053	+	0.956707i	$0.405994\pi$
$632$	10.7353	0.427027
$633$	−17.7445	−0.705281
$634$	2.36054	0.0937491
$635$	10.5568	0.418933
$636$	1.05673	0.0419022
$637$	1.90705	0.0755602
$638$	−36.1904	−1.43279
$639$	−2.75179	−0.108859
$640$	3.65422	0.144446
$641$	28.3955	1.12156	0.560778	−	0.827966i	$-0.310502\pi$
$641$	28.3955	1.12156	0.560778	+	0.827966i	$0.310502\pi$
$642$	−3.71319	−0.146548
$643$	0.636461	0.0250996	0.0125498	−	0.999921i	$-0.496005\pi$
$643$	0.636461	0.0250996	0.0125498	+	0.999921i	$0.496005\pi$
$644$	−10.8090	−0.425935
$645$	19.8134	0.780152
$646$	11.1101	0.437121
$647$	17.1375	0.673745	0.336873	−	0.941550i	$-0.390631\pi$
$647$	17.1375	0.673745	0.336873	+	0.941550i	$0.390631\pi$
$648$	−1.00000	−0.0392837
$649$	−19.4760	−0.764499
$650$	−8.35335	−0.327645
$651$	30.6329	1.20060
$652$	−12.0749	−0.472891
$653$	33.3214	1.30397	0.651983	−	0.758234i	$-0.273937\pi$
$653$	33.3214	1.30397	0.651983	+	0.758234i	$0.273937\pi$
$654$	3.22996	0.126301
$655$	46.6776	1.82385
$656$	−8.55999	−0.334211
$657$	−6.96603	−0.271771
$658$	−35.2631	−1.37470
$659$	27.5855	1.07458	0.537290	−	0.843398i	$-0.319448\pi$
$659$	27.5855	1.07458	0.537290	+	0.843398i	$0.319448\pi$
$660$	13.1878	0.513334
$661$	−29.5537	−1.14951	−0.574754	−	0.818327i	$-0.694902\pi$
$661$	−29.5537	−1.14951	−0.574754	+	0.818327i	$0.694902\pi$
$662$	−6.21190	−0.241432
$663$	3.22106	0.125095
$664$	10.8822	0.422310
$665$	37.6168	1.45872
$666$	−1.67832	−0.0650334
$667$	36.3192	1.40629
$668$	−8.34086	−0.322718
$669$	3.57710	0.138299
$670$	0.661178	0.0255435
$671$	−21.9927	−0.849018
$672$	−2.98447	−0.115128
$673$	45.7948	1.76526	0.882629	−	0.470070i	$-0.155771\pi$
$673$	45.7948	1.76526	0.882629	+	0.470070i	$0.155771\pi$
$674$	4.22189	0.162621
$675$	−8.35335	−0.321521
$676$	1.00000	0.0384615
$677$	47.4498	1.82364	0.911822	−	0.410586i	$-0.134676\pi$
$677$	47.4498	1.82364	0.911822	+	0.410586i	$0.134676\pi$
$678$	10.2893	0.395157
$679$	−14.4260	−0.553620
$680$	−11.7705	−0.451377
$681$	9.58324	0.367230
$682$	−37.0423	−1.41842
$683$	−43.5510	−1.66643	−0.833217	−	0.552946i	$-0.813504\pi$
$683$	−43.5510	−1.66643	−0.833217	+	0.552946i	$0.813504\pi$
$684$	3.44921	0.131884
$685$	−22.5750	−0.862547
$686$	−15.1997	−0.580329
$687$	−1.79903	−0.0686371
$688$	5.42205	0.206714
$689$	−1.05673	−0.0402583
$690$	−13.2347	−0.503837
$691$	−28.3542	−1.07865	−0.539323	−	0.842099i	$-0.681320\pi$
$691$	−28.3542	−1.07865	−0.539323	+	0.842099i	$0.681320\pi$
$692$	0.521491	0.0198241
$693$	−10.7707	−0.409145
$694$	−8.70941	−0.330605
$695$	−77.2892	−2.93175
$696$	10.0281	0.380113
$697$	27.5722	1.04437
$698$	−28.7741	−1.08912
$699$	11.6052	0.438948
$700$	−24.9303	−0.942277
$701$	18.4813	0.698029	0.349015	−	0.937117i	$-0.386516\pi$
$701$	18.4813	0.698029	0.349015	+	0.937117i	$0.386516\pi$
$702$	1.00000	0.0377426
$703$	5.78887	0.218331
$704$	3.60891	0.136016
$705$	−43.1766	−1.62613
$706$	36.8607	1.38727
$707$	−57.7167	−2.17066
$708$	5.39663	0.202818
$709$	−14.2180	−0.533967	−0.266983	−	0.963701i	$-0.586027\pi$
$709$	−14.2180	−0.533967	−0.266983	+	0.963701i	$0.586027\pi$
$710$	−10.0556	−0.377382
$711$	−10.7353	−0.402605
$712$	−14.5772	−0.546305
$713$	37.1741	1.39218
$714$	9.61314	0.359763
$715$	−13.1878	−0.493195
$716$	0.618878	0.0231286
$717$	−13.3711	−0.499353
$718$	14.3225	0.534512
$719$	15.1883	0.566430	0.283215	−	0.959056i	$-0.408599\pi$
$719$	15.1883	0.566430	0.283215	+	0.959056i	$0.408599\pi$
$720$	−3.65422	−0.136185
$721$	2.98447	0.111147
$722$	7.10293	0.264344
$723$	24.8787	0.925250
$724$	−2.04131	−0.0758648
$725$	83.7679	3.11106
$726$	2.02426	0.0751273
$727$	−52.9433	−1.96356	−0.981780	−	0.190023i	$-0.939144\pi$
$727$	−52.9433	−1.96356	−0.981780	+	0.190023i	$0.939144\pi$
$728$	2.98447	0.110612
$729$	1.00000	0.0370370
$730$	−25.4554	−0.942148
$731$	−17.4647	−0.645957
$732$	6.09399	0.225240
$733$	6.09050	0.224958	0.112479	−	0.993654i	$-0.464121\pi$
$733$	6.09050	0.224958	0.112479	+	0.993654i	$0.464121\pi$
$734$	34.5226	1.27425
$735$	6.96880	0.257048
$736$	−3.62176	−0.133500
$737$	0.652979	0.0240528
$738$	8.55999	0.315098
$739$	30.0628	1.10588	0.552939	−	0.833221i	$-0.313506\pi$
$739$	30.0628	1.10588	0.552939	+	0.833221i	$0.313506\pi$
$740$	−6.13294	−0.225451
$741$	−3.44921	−0.126710
$742$	−3.15379	−0.115779
$743$	33.9672	1.24614	0.623068	−	0.782167i	$-0.285886\pi$
$743$	33.9672	1.24614	0.623068	+	0.782167i	$0.285886\pi$
$744$	10.2641	0.376301
$745$	68.6484	2.51508
$746$	−8.12912	−0.297628
$747$	−10.8822	−0.398157
$748$	−11.6245	−0.425034
$749$	11.0819	0.404924
$750$	−12.2539	−0.447449
$751$	19.3629	0.706564	0.353282	−	0.935517i	$-0.385066\pi$
$751$	19.3629	0.706564	0.353282	+	0.935517i	$0.385066\pi$
$752$	−11.8155	−0.430868
$753$	11.1588	0.406650
$754$	−10.0281	−0.365201
$755$	12.5951	0.458382
$756$	2.98447	0.108544
$757$	26.6070	0.967047	0.483523	−	0.875331i	$-0.339357\pi$
$757$	26.6070	0.967047	0.483523	+	0.875331i	$0.339357\pi$
$758$	−2.40752	−0.0874451
$759$	−13.0706	−0.474433
$760$	12.6042	0.457202
$761$	−43.0014	−1.55880	−0.779399	−	0.626527i	$-0.784476\pi$
$761$	−43.0014	−1.55880	−0.779399	+	0.626527i	$0.784476\pi$
$762$	−2.88893	−0.104655
$763$	−9.63972	−0.348981
$764$	6.52988	0.236243
$765$	11.7705	0.425562
$766$	−1.19419	−0.0431478
$767$	−5.39663	−0.194861
$768$	−1.00000	−0.0360844
$769$	−22.3786	−0.806992	−0.403496	−	0.914981i	$-0.632205\pi$
$769$	−22.3786	−0.806992	−0.403496	+	0.914981i	$0.632205\pi$
$770$	−39.3585	−1.41838
$771$	−3.46229	−0.124692
$772$	24.4949	0.881590
$773$	−19.9798	−0.718623	−0.359311	−	0.933218i	$-0.616988\pi$
$773$	−19.9798	−0.718623	−0.359311	+	0.933218i	$0.616988\pi$
$774$	−5.42205	−0.194892
$775$	85.7397	3.07986
$776$	−4.83370	−0.173520
$777$	5.00888	0.179693
$778$	−8.39661	−0.301033
$779$	−29.5252	−1.05785
$780$	3.65422	0.130842
$781$	−9.93096	−0.355358
$782$	11.6659	0.417171
$783$	−10.0281	−0.358374
$784$	1.90705	0.0681091
$785$	−39.7656	−1.41929
$786$	−12.7736	−0.455620
$787$	−8.82544	−0.314593	−0.157297	−	0.987551i	$-0.550278\pi$
$787$	−8.82544	−0.314593	−0.157297	+	0.987551i	$0.550278\pi$
$788$	9.11126	0.324575
$789$	−13.6573	−0.486213
$790$	−39.2292	−1.39571
$791$	−30.7080	−1.09185
$792$	−3.60891	−0.128237
$793$	−6.09399	−0.216404
$794$	−27.5942	−0.979282
$795$	−3.86154	−0.136955
$796$	12.5933	0.446356
$797$	35.3181	1.25103	0.625516	−	0.780211i	$-0.284888\pi$
$797$	35.3181	1.25103	0.625516	+	0.780211i	$0.284888\pi$
$798$	−10.2941	−0.364406
$799$	38.0585	1.34641
$800$	−8.35335	−0.295336
$801$	14.5772	0.515061
$802$	23.5959	0.833199
$803$	−25.1398	−0.887165
$804$	−0.180935	−0.00638109
$805$	39.4986	1.39214
$806$	−10.2641	−0.361538
$807$	5.74928	0.202384
$808$	−19.3390	−0.680345
$809$	−15.2083	−0.534695	−0.267348	−	0.963600i	$-0.586147\pi$
$809$	−15.2083	−0.534695	−0.267348	+	0.963600i	$0.586147\pi$
$810$	3.65422	0.128396
$811$	−28.6151	−1.00481	−0.502406	−	0.864632i	$-0.667552\pi$
$811$	−28.6151	−1.00481	−0.502406	+	0.864632i	$0.667552\pi$
$812$	−29.9284	−1.05028
$813$	−27.8621	−0.977167
$814$	−6.05690	−0.212294
$815$	44.1246	1.54562
$816$	3.22106	0.112760
$817$	18.7018	0.654294
$818$	−29.0562	−1.01593
$819$	−2.98447	−0.104286
$820$	31.2801	1.09235
$821$	10.5559	0.368402	0.184201	−	0.982889i	$-0.441030\pi$
$821$	10.5559	0.368402	0.184201	+	0.982889i	$0.441030\pi$
$822$	6.17778	0.215475
$823$	45.8400	1.59788	0.798942	−	0.601409i	$-0.205394\pi$
$823$	45.8400	1.59788	0.798942	+	0.601409i	$0.205394\pi$
$824$	1.00000	0.0348367
$825$	−30.1465	−1.04957
$826$	−16.1061	−0.560402
$827$	18.7075	0.650524	0.325262	−	0.945624i	$-0.394548\pi$
$827$	18.7075	0.650524	0.325262	+	0.945624i	$0.394548\pi$
$828$	3.62176	0.125865
$829$	25.2491	0.876939	0.438469	−	0.898746i	$-0.355521\pi$
$829$	25.2491	0.876939	0.438469	+	0.898746i	$0.355521\pi$
$830$	−39.7658	−1.38029
$831$	15.1301	0.524858
$832$	1.00000	0.0346688
$833$	−6.14273	−0.212833
$834$	21.1507	0.732387
$835$	30.4794	1.05478
$836$	12.4479	0.430520
$837$	−10.2641	−0.354780
$838$	1.78495	0.0616602
$839$	−2.86052	−0.0987561	−0.0493780	−	0.998780i	$-0.515724\pi$
$839$	−2.86052	−0.0987561	−0.0493780	+	0.998780i	$0.515724\pi$
$840$	10.9059	0.376290
$841$	71.5621	2.46766
$842$	−27.8302	−0.959092
$843$	12.8516	0.442631
$844$	17.7445	0.610791
$845$	−3.65422	−0.125709
$846$	11.8155	0.406227
$847$	−6.04133	−0.207583
$848$	−1.05673	−0.0362884
$849$	−15.6158	−0.535934
$850$	26.9066	0.922889
$851$	6.07845	0.208367
$852$	2.75179	0.0942746
$853$	0.732442	0.0250783	0.0125392	−	0.999921i	$-0.496009\pi$
$853$	0.732442	0.0250783	0.0125392	+	0.999921i	$0.496009\pi$
$854$	−18.1873	−0.622357
$855$	−12.6042	−0.431054
$856$	3.71319	0.126914
$857$	7.42670	0.253691	0.126846	−	0.991922i	$-0.459515\pi$
$857$	7.42670	0.253691	0.126846	+	0.991922i	$0.459515\pi$
$858$	3.60891	0.123206
$859$	−39.9238	−1.36218	−0.681092	−	0.732198i	$-0.738494\pi$
$859$	−39.9238	−1.36218	−0.681092	+	0.732198i	$0.738494\pi$
$860$	−19.8134	−0.675631
$861$	−25.5470	−0.870640
$862$	−19.4588	−0.662768
$863$	38.5926	1.31371	0.656854	−	0.754017i	$-0.271887\pi$
$863$	38.5926	1.31371	0.656854	+	0.754017i	$0.271887\pi$
$864$	1.00000	0.0340207
$865$	−1.90564	−0.0647939
$866$	−13.0229	−0.442535
$867$	6.62479	0.224990
$868$	−30.6329	−1.03975
$869$	−38.7428	−1.31426
$870$	−36.6448	−1.24237
$871$	0.180935	0.00613075
$872$	−3.22996	−0.109380
$873$	4.83370	0.163596
$874$	−12.4922	−0.422555
$875$	36.5714	1.23634
$876$	6.96603	0.235360
$877$	−39.9231	−1.34811	−0.674053	−	0.738683i	$-0.735448\pi$
$877$	−39.9231	−1.34811	−0.674053	+	0.738683i	$0.735448\pi$
$878$	−34.1765	−1.15340
$879$	0.430891	0.0145336
$880$	−13.1878	−0.444560
$881$	38.7918	1.30693	0.653464	−	0.756958i	$-0.273315\pi$
$881$	38.7918	1.30693	0.653464	+	0.756958i	$0.273315\pi$
$882$	−1.90705	−0.0642139
$883$	32.9394	1.10850	0.554250	−	0.832350i	$-0.313005\pi$
$883$	32.9394	1.10850	0.554250	+	0.832350i	$0.313005\pi$
$884$	−3.22106	−0.108336
$885$	−19.7205	−0.662898
$886$	8.66649	0.291157
$887$	−26.5041	−0.889921	−0.444960	−	0.895550i	$-0.646782\pi$
$887$	−26.5041	−0.889921	−0.444960	+	0.895550i	$0.646782\pi$
$888$	1.67832	0.0563206
$889$	8.62191	0.289170
$890$	53.2684	1.78556
$891$	3.60891	0.120903
$892$	−3.57710	−0.119770
$893$	−40.7543	−1.36379
$894$	−18.7861	−0.628300
$895$	−2.26152	−0.0755942
$896$	2.98447	0.0997041
$897$	−3.62176	−0.120927
$898$	36.3559	1.21321
$899$	102.929	3.43288
$900$	8.35335	0.278445
$901$	3.40380	0.113397
$902$	30.8923	1.02860
$903$	16.1819	0.538502
$904$	−10.2893	−0.342216
$905$	7.45942	0.247959
$906$	−3.44672	−0.114510
$907$	10.6403	0.353305	0.176652	−	0.984273i	$-0.443473\pi$
$907$	10.6403	0.353305	0.176652	+	0.984273i	$0.443473\pi$
$908$	−9.58324	−0.318031
$909$	19.3390	0.641435
$910$	−10.9059	−0.361528
$911$	−6.76727	−0.224210	−0.112105	−	0.993696i	$-0.535759\pi$
$911$	−6.76727	−0.224210	−0.112105	+	0.993696i	$0.535759\pi$
$912$	−3.44921	−0.114215
$913$	−39.2728	−1.29974
$914$	18.0303	0.596390
$915$	−22.2688	−0.736184
$916$	1.79903	0.0594415
$917$	38.1224	1.25891
$918$	−3.22106	−0.106311
$919$	−5.40519	−0.178301	−0.0891504	−	0.996018i	$-0.528415\pi$
$919$	−5.40519	−0.178301	−0.0891504	+	0.996018i	$0.528415\pi$
$920$	13.2347	0.436335
$921$	−14.2854	−0.470719
$922$	14.6852	0.483632
$923$	−2.75179	−0.0905761
$924$	10.7707	0.354330
$925$	14.0196	0.460960
$926$	−3.25879	−0.107090
$927$	−1.00000	−0.0328443
$928$	−10.0281	−0.329187
$929$	21.0061	0.689189	0.344595	−	0.938752i	$-0.388016\pi$
$929$	21.0061	0.689189	0.344595	+	0.938752i	$0.388016\pi$
$930$	−37.5074	−1.22991
$931$	6.57784	0.215580
$932$	−11.6052	−0.380140
$933$	24.1330	0.790079
$934$	−6.15730	−0.201473
$935$	42.4786	1.38920
$936$	−1.00000	−0.0326860
$937$	18.7281	0.611821	0.305910	−	0.952060i	$-0.401039\pi$
$937$	18.7281	0.611821	0.305910	+	0.952060i	$0.401039\pi$
$938$	0.539995	0.0176315
$939$	9.19697	0.300132
$940$	43.1766	1.40827
$941$	−2.89919	−0.0945108	−0.0472554	−	0.998883i	$-0.515047\pi$
$941$	−2.89919	−0.0945108	−0.0472554	+	0.998883i	$0.515047\pi$
$942$	10.8821	0.354558
$943$	−31.0022	−1.00957
$944$	−5.39663	−0.175645
$945$	−10.9059	−0.354770
$946$	−19.5677	−0.636202
$947$	24.6654	0.801519	0.400760	−	0.916183i	$-0.368746\pi$
$947$	24.6654	0.801519	0.400760	+	0.916183i	$0.368746\pi$
$948$	10.7353	0.348666
$949$	−6.96603	−0.226127
$950$	−28.8125	−0.934800
$951$	2.36054	0.0765458
$952$	−9.61314	−0.311564
$953$	30.6857	0.994007	0.497003	−	0.867749i	$-0.334434\pi$
$953$	30.6857	0.994007	0.497003	+	0.867749i	$0.334434\pi$
$954$	1.05673	0.0342130
$955$	−23.8616	−0.772145
$956$	13.3711	0.432452
$957$	−36.1904	−1.16987
$958$	2.77400	0.0896240
$959$	−18.4374	−0.595375
$960$	3.65422	0.117940
$961$	74.3520	2.39845
$962$	−1.67832	−0.0541111
$963$	−3.71319	−0.119656
$964$	−24.8787	−0.801290
$965$	−89.5097	−2.88142
$966$	−10.8090	−0.347774
$967$	11.1796	0.359512	0.179756	−	0.983711i	$-0.442469\pi$
$967$	11.1796	0.359512	0.179756	+	0.983711i	$0.442469\pi$
$968$	−2.02426	−0.0650621
$969$	11.1101	0.356908
$970$	17.6634	0.567139
$971$	28.0430	0.899944	0.449972	−	0.893043i	$-0.351434\pi$
$971$	28.0430	0.899944	0.449972	+	0.893043i	$0.351434\pi$
$972$	−1.00000	−0.0320750
$973$	−63.1235	−2.02365
$974$	8.81991	0.282608
$975$	−8.35335	−0.267521
$976$	−6.09399	−0.195064
$977$	−6.07447	−0.194339	−0.0971697	−	0.995268i	$-0.530979\pi$
$977$	−6.07447	−0.194339	−0.0971697	+	0.995268i	$0.530979\pi$
$978$	−12.0749	−0.386114
$979$	52.6079	1.68136
$980$	−6.96880	−0.222610
$981$	3.22996	0.103125
$982$	6.48893	0.207070
$983$	45.8073	1.46103	0.730513	−	0.682899i	$-0.239281\pi$
$983$	45.8073	1.46103	0.730513	+	0.682899i	$0.239281\pi$
$984$	−8.55999	−0.272883
$985$	−33.2946	−1.06085
$986$	32.3010	1.02867
$987$	−35.2631	−1.12244
$988$	3.44921	0.109734
$989$	19.6374	0.624432
$990$	13.1878	0.419135
$991$	46.5207	1.47778	0.738889	−	0.673827i	$-0.235351\pi$
$991$	46.5207	1.47778	0.738889	+	0.673827i	$0.235351\pi$
$992$	−10.2641	−0.325886
$993$	−6.21190	−0.197129
$994$	−8.21262	−0.260488
$995$	−46.0186	−1.45889
$996$	10.8822	0.344814
$997$	−18.0516	−0.571700	−0.285850	−	0.958274i	$-0.592276\pi$
$997$	−18.0516	−0.571700	−0.285850	+	0.958274i	$0.592276\pi$
$998$	−22.9419	−0.726214
$999$	−1.67832	−0.0530996

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8034.2.a.z.1.2	✓	14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8034.2.a.z.1.2	✓	14	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)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -3.65422 q^{5} +1.00000 q^{6} -2.98447 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -3.65422 q^{5} +1.00000 q^{6} -2.98447 q^{7} -1.00000 q^{8} +1.00000 q^{9} +3.65422 q^{10} +3.60891 q^{11} -1.00000 q^{12} +1.00000 q^{13} +2.98447 q^{14} +3.65422 q^{15} +1.00000 q^{16} -3.22106 q^{17} -1.00000 q^{18} +3.44921 q^{19} -3.65422 q^{20} +2.98447 q^{21} -3.60891 q^{22} +3.62176 q^{23} +1.00000 q^{24} +8.35335 q^{25} -1.00000 q^{26} -1.00000 q^{27} -2.98447 q^{28} +10.0281 q^{29} -3.65422 q^{30} +10.2641 q^{31} -1.00000 q^{32} -3.60891 q^{33} +3.22106 q^{34} +10.9059 q^{35} +1.00000 q^{36} +1.67832 q^{37} -3.44921 q^{38} -1.00000 q^{39} +3.65422 q^{40} -8.55999 q^{41} -2.98447 q^{42} +5.42205 q^{43} +3.60891 q^{44} -3.65422 q^{45} -3.62176 q^{46} -11.8155 q^{47} -1.00000 q^{48} +1.90705 q^{49} -8.35335 q^{50} +3.22106 q^{51} +1.00000 q^{52} -1.05673 q^{53} +1.00000 q^{54} -13.1878 q^{55} +2.98447 q^{56} -3.44921 q^{57} -10.0281 q^{58} -5.39663 q^{59} +3.65422 q^{60} -6.09399 q^{61} -10.2641 q^{62} -2.98447 q^{63} +1.00000 q^{64} -3.65422 q^{65} +3.60891 q^{66} +0.180935 q^{67} -3.22106 q^{68} -3.62176 q^{69} -10.9059 q^{70} -2.75179 q^{71} -1.00000 q^{72} -6.96603 q^{73} -1.67832 q^{74} -8.35335 q^{75} +3.44921 q^{76} -10.7707 q^{77} +1.00000 q^{78} -10.7353 q^{79} -3.65422 q^{80} +1.00000 q^{81} +8.55999 q^{82} -10.8822 q^{83} +2.98447 q^{84} +11.7705 q^{85} -5.42205 q^{86} -10.0281 q^{87} -3.60891 q^{88} +14.5772 q^{89} +3.65422 q^{90} -2.98447 q^{91} +3.62176 q^{92} -10.2641 q^{93} +11.8155 q^{94} -12.6042 q^{95} +1.00000 q^{96} +4.83370 q^{97} -1.90705 q^{98} +3.60891 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q - 14 q^{2} - 14 q^{3} + 14 q^{4} - 3 q^{5} + 14 q^{6} + 4 q^{7} - 14 q^{8} + 14 q^{9}+O(q^{10}) \) 14 * q - 14 * q^2 - 14 * q^3 + 14 * q^4 - 3 * q^5 + 14 * q^6 + 4 * q^7 - 14 * q^8 + 14 * q^9	\( 14 q - 14 q^{2} - 14 q^{3} + 14 q^{4} - 3 q^{5} + 14 q^{6} + 4 q^{7} - 14 q^{8} + 14 q^{9} + 3 q^{10} + 5 q^{11} - 14 q^{12} + 14 q^{13} - 4 q^{14} + 3 q^{15} + 14 q^{16} - 7 q^{17} - 14 q^{18} + 31 q^{19} - 3 q^{20} - 4 q^{21} - 5 q^{22} + 14 q^{23} + 14 q^{24} + 11 q^{25} - 14 q^{26} - 14 q^{27} + 4 q^{28} + 9 q^{29} - 3 q^{30} + 23 q^{31} - 14 q^{32} - 5 q^{33} + 7 q^{34} - 2 q^{35} + 14 q^{36} + 12 q^{37} - 31 q^{38} - 14 q^{39} + 3 q^{40} - 5 q^{41} + 4 q^{42} - 2 q^{43} + 5 q^{44} - 3 q^{45} - 14 q^{46} - 11 q^{47} - 14 q^{48} + 52 q^{49} - 11 q^{50} + 7 q^{51} + 14 q^{52} + 6 q^{53} + 14 q^{54} + 30 q^{55} - 4 q^{56} - 31 q^{57} - 9 q^{58} - 4 q^{59} + 3 q^{60} + 12 q^{61} - 23 q^{62} + 4 q^{63} + 14 q^{64} - 3 q^{65} + 5 q^{66} + 24 q^{67} - 7 q^{68} - 14 q^{69} + 2 q^{70} + 20 q^{71} - 14 q^{72} + 2 q^{73} - 12 q^{74} - 11 q^{75} + 31 q^{76} - 28 q^{77} + 14 q^{78} + 59 q^{79} - 3 q^{80} + 14 q^{81} + 5 q^{82} + q^{83} - 4 q^{84} - 29 q^{85} + 2 q^{86} - 9 q^{87} - 5 q^{88} + 6 q^{89} + 3 q^{90} + 4 q^{91} + 14 q^{92} - 23 q^{93} + 11 q^{94} - 58 q^{95} + 14 q^{96} - 6 q^{97} - 52 q^{98} + 5 q^{99}+O(q^{100}) \) 14 * q - 14 * q^2 - 14 * q^3 + 14 * q^4 - 3 * q^5 + 14 * q^6 + 4 * q^7 - 14 * q^8 + 14 * q^9 + 3 * q^10 + 5 * q^11 - 14 * q^12 + 14 * q^13 - 4 * q^14 + 3 * q^15 + 14 * q^16 - 7 * q^17 - 14 * q^18 + 31 * q^19 - 3 * q^20 - 4 * q^21 - 5 * q^22 + 14 * q^23 + 14 * q^24 + 11 * q^25 - 14 * q^26 - 14 * q^27 + 4 * q^28 + 9 * q^29 - 3 * q^30 + 23 * q^31 - 14 * q^32 - 5 * q^33 + 7 * q^34 - 2 * q^35 + 14 * q^36 + 12 * q^37 - 31 * q^38 - 14 * q^39 + 3 * q^40 - 5 * q^41 + 4 * q^42 - 2 * q^43 + 5 * q^44 - 3 * q^45 - 14 * q^46 - 11 * q^47 - 14 * q^48 + 52 * q^49 - 11 * q^50 + 7 * q^51 + 14 * q^52 + 6 * q^53 + 14 * q^54 + 30 * q^55 - 4 * q^56 - 31 * q^57 - 9 * q^58 - 4 * q^59 + 3 * q^60 + 12 * q^61 - 23 * q^62 + 4 * q^63 + 14 * q^64 - 3 * q^65 + 5 * q^66 + 24 * q^67 - 7 * q^68 - 14 * q^69 + 2 * q^70 + 20 * q^71 - 14 * q^72 + 2 * q^73 - 12 * q^74 - 11 * q^75 + 31 * q^76 - 28 * q^77 + 14 * q^78 + 59 * q^79 - 3 * q^80 + 14 * q^81 + 5 * q^82 + q^83 - 4 * q^84 - 29 * q^85 + 2 * q^86 - 9 * q^87 - 5 * q^88 + 6 * q^89 + 3 * q^90 + 4 * q^91 + 14 * q^92 - 23 * q^93 + 11 * q^94 - 58 * q^95 + 14 * q^96 - 6 * q^97 - 52 * q^98 + 5 * q^99

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