LMFDB - Embedded newform 8034.2.a.p.1.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8034, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("8034.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8034 = 2 \cdot 3 \cdot 13 \cdot 103 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8034.a (trivial)

Newform invariants

comment: select newform

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

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

Self dual:	yes
Analytic conductor:	$64.1518129839$
Analytic rank:	$1$
Dimension:	$8$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{7} - 12x^{6} + 12x^{5} + 43x^{4} - 38x^{3} - 49x^{2} + 23x + 20 $ x^8 - x^7 - 12x^6 + 12x^5 + 43x^4 - 38x^3 - 49x^2 + 23x + 20
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.7
Root			$-2.57192$ of defining polynomial
Character	$\chi$	$=$	8034.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -0.176895 q^{5} +1.00000 q^{6} -2.27129 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -0.176895 q^{5} +1.00000 q^{6} -2.27129 q^{7} +1.00000 q^{8} +1.00000 q^{9} -0.176895 q^{10} -2.71409 q^{11} +1.00000 q^{12} +1.00000 q^{13} -2.27129 q^{14} -0.176895 q^{15} +1.00000 q^{16} -1.27485 q^{17} +1.00000 q^{18} +3.21336 q^{19} -0.176895 q^{20} -2.27129 q^{21} -2.71409 q^{22} -5.17288 q^{23} +1.00000 q^{24} -4.96871 q^{25} +1.00000 q^{26} +1.00000 q^{27} -2.27129 q^{28} -0.285145 q^{29} -0.176895 q^{30} +9.70181 q^{31} +1.00000 q^{32} -2.71409 q^{33} -1.27485 q^{34} +0.401781 q^{35} +1.00000 q^{36} -9.47971 q^{37} +3.21336 q^{38} +1.00000 q^{39} -0.176895 q^{40} +1.27770 q^{41} -2.27129 q^{42} +8.05978 q^{43} -2.71409 q^{44} -0.176895 q^{45} -5.17288 q^{46} -10.5112 q^{47} +1.00000 q^{48} -1.84124 q^{49} -4.96871 q^{50} -1.27485 q^{51} +1.00000 q^{52} -1.60081 q^{53} +1.00000 q^{54} +0.480111 q^{55} -2.27129 q^{56} +3.21336 q^{57} -0.285145 q^{58} -12.8286 q^{59} -0.176895 q^{60} -5.88767 q^{61} +9.70181 q^{62} -2.27129 q^{63} +1.00000 q^{64} -0.176895 q^{65} -2.71409 q^{66} -5.59876 q^{67} -1.27485 q^{68} -5.17288 q^{69} +0.401781 q^{70} +2.87751 q^{71} +1.00000 q^{72} +14.5396 q^{73} -9.47971 q^{74} -4.96871 q^{75} +3.21336 q^{76} +6.16450 q^{77} +1.00000 q^{78} -6.63863 q^{79} -0.176895 q^{80} +1.00000 q^{81} +1.27770 q^{82} +0.0726498 q^{83} -2.27129 q^{84} +0.225515 q^{85} +8.05978 q^{86} -0.285145 q^{87} -2.71409 q^{88} -0.653992 q^{89} -0.176895 q^{90} -2.27129 q^{91} -5.17288 q^{92} +9.70181 q^{93} -10.5112 q^{94} -0.568428 q^{95} +1.00000 q^{96} -12.7299 q^{97} -1.84124 q^{98} -2.71409 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 8 q^{2} + 8 q^{3} + 8 q^{4} - 8 q^{5} + 8 q^{6} - 6 q^{7} + 8 q^{8} + 8 q^{9}+O(q^{10}) $ 8 * q + 8 * q^2 + 8 * q^3 + 8 * q^4 - 8 * q^5 + 8 * q^6 - 6 * q^7 + 8 * q^8 + 8 * q^9	\( 8 q + 8 q^{2} + 8 q^{3} + 8 q^{4} - 8 q^{5} + 8 q^{6} - 6 q^{7} + 8 q^{8} + 8 q^{9} - 8 q^{10} - 7 q^{11} + 8 q^{12} + 8 q^{13} - 6 q^{14} - 8 q^{15} + 8 q^{16} - 20 q^{17} + 8 q^{18} - 12 q^{19} - 8 q^{20} - 6 q^{21} - 7 q^{22} - 14 q^{23} + 8 q^{24} - 2 q^{25} + 8 q^{26} + 8 q^{27} - 6 q^{28} - 25 q^{29} - 8 q^{30} - 12 q^{31} + 8 q^{32} - 7 q^{33} - 20 q^{34} - 18 q^{35} + 8 q^{36} - 15 q^{37} - 12 q^{38} + 8 q^{39} - 8 q^{40} - 18 q^{41} - 6 q^{42} - 8 q^{43} - 7 q^{44} - 8 q^{45} - 14 q^{46} - 12 q^{47} + 8 q^{48} - 8 q^{49} - 2 q^{50} - 20 q^{51} + 8 q^{52} - 25 q^{53} + 8 q^{54} - 8 q^{55} - 6 q^{56} - 12 q^{57} - 25 q^{58} - 9 q^{59} - 8 q^{60} - 2 q^{61} - 12 q^{62} - 6 q^{63} + 8 q^{64} - 8 q^{65} - 7 q^{66} - 8 q^{67} - 20 q^{68} - 14 q^{69} - 18 q^{70} - 13 q^{71} + 8 q^{72} - 2 q^{73} - 15 q^{74} - 2 q^{75} - 12 q^{76} - 5 q^{77} + 8 q^{78} + q^{79} - 8 q^{80} + 8 q^{81} - 18 q^{82} - 6 q^{83} - 6 q^{84} + 5 q^{85} - 8 q^{86} - 25 q^{87} - 7 q^{88} - 17 q^{89} - 8 q^{90} - 6 q^{91} - 14 q^{92} - 12 q^{93} - 12 q^{94} + 10 q^{95} + 8 q^{96} + 19 q^{97} - 8 q^{98} - 7 q^{99}+O(q^{100}) \) 8 * q + 8 * q^2 + 8 * q^3 + 8 * q^4 - 8 * q^5 + 8 * q^6 - 6 * q^7 + 8 * q^8 + 8 * q^9 - 8 * q^10 - 7 * q^11 + 8 * q^12 + 8 * q^13 - 6 * q^14 - 8 * q^15 + 8 * q^16 - 20 * q^17 + 8 * q^18 - 12 * q^19 - 8 * q^20 - 6 * q^21 - 7 * q^22 - 14 * q^23 + 8 * q^24 - 2 * q^25 + 8 * q^26 + 8 * q^27 - 6 * q^28 - 25 * q^29 - 8 * q^30 - 12 * q^31 + 8 * q^32 - 7 * q^33 - 20 * q^34 - 18 * q^35 + 8 * q^36 - 15 * q^37 - 12 * q^38 + 8 * q^39 - 8 * q^40 - 18 * q^41 - 6 * q^42 - 8 * q^43 - 7 * q^44 - 8 * q^45 - 14 * q^46 - 12 * q^47 + 8 * q^48 - 8 * q^49 - 2 * q^50 - 20 * q^51 + 8 * q^52 - 25 * q^53 + 8 * q^54 - 8 * q^55 - 6 * q^56 - 12 * q^57 - 25 * q^58 - 9 * q^59 - 8 * q^60 - 2 * q^61 - 12 * q^62 - 6 * q^63 + 8 * q^64 - 8 * q^65 - 7 * q^66 - 8 * q^67 - 20 * q^68 - 14 * q^69 - 18 * q^70 - 13 * q^71 + 8 * q^72 - 2 * q^73 - 15 * q^74 - 2 * q^75 - 12 * q^76 - 5 * q^77 + 8 * q^78 + q^79 - 8 * q^80 + 8 * q^81 - 18 * q^82 - 6 * q^83 - 6 * q^84 + 5 * q^85 - 8 * q^86 - 25 * q^87 - 7 * q^88 - 17 * q^89 - 8 * q^90 - 6 * q^91 - 14 * q^92 - 12 * q^93 - 12 * q^94 + 10 * q^95 + 8 * q^96 + 19 * q^97 - 8 * q^98 - 7 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	1.00000	0.707107
$2$	1.00000	0.707107
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	1.00000	0.500000
$5$	−0.176895	−0.0791100	−0.0395550	−	0.999217i	$-0.512594\pi$
$5$	−0.176895	−0.0791100	−0.0395550	+	0.999217i	$0.512594\pi$
$6$	1.00000	0.408248
$7$	−2.27129	−0.858467	−0.429234	−	0.903193i	$-0.641216\pi$
$7$	−2.27129	−0.858467	−0.429234	+	0.903193i	$0.641216\pi$
$8$	1.00000	0.353553
$9$	1.00000	0.333333
$10$	−0.176895	−0.0559392
$11$	−2.71409	−0.818330	−0.409165	−	0.912460i	$-0.634180\pi$
$11$	−2.71409	−0.818330	−0.409165	+	0.912460i	$0.634180\pi$
$12$	1.00000	0.288675
$13$	1.00000	0.277350
$13$	1.00000	0.277350
$14$	−2.27129	−0.607028
$15$	−0.176895	−0.0456742
$16$	1.00000	0.250000
$17$	−1.27485	−0.309196	−0.154598	−	0.987977i	$-0.549408\pi$
$17$	−1.27485	−0.309196	−0.154598	+	0.987977i	$0.549408\pi$
$18$	1.00000	0.235702
$19$	3.21336	0.737194	0.368597	−	0.929589i	$-0.379838\pi$
$19$	3.21336	0.737194	0.368597	+	0.929589i	$0.379838\pi$
$20$	−0.176895	−0.0395550
$21$	−2.27129	−0.495636
$22$	−2.71409	−0.578647
$23$	−5.17288	−1.07862	−0.539310	−	0.842107i	$-0.681315\pi$
$23$	−5.17288	−1.07862	−0.539310	+	0.842107i	$0.681315\pi$
$24$	1.00000	0.204124
$25$	−4.96871	−0.993742
$26$	1.00000	0.196116
$27$	1.00000	0.192450
$28$	−2.27129	−0.429234
$29$	−0.285145	−0.0529501	−0.0264751	−	0.999649i	$-0.508428\pi$
$29$	−0.285145	−0.0529501	−0.0264751	+	0.999649i	$0.508428\pi$
$30$	−0.176895	−0.0322965
$31$	9.70181	1.74250	0.871249	−	0.490842i	$-0.163311\pi$
$31$	9.70181	1.74250	0.871249	+	0.490842i	$0.163311\pi$
$32$	1.00000	0.176777
$33$	−2.71409	−0.472463
$34$	−1.27485	−0.218635
$35$	0.401781	0.0679134
$36$	1.00000	0.166667
$37$	−9.47971	−1.55846	−0.779228	−	0.626741i	$-0.784388\pi$
$37$	−9.47971	−1.55846	−0.779228	+	0.626741i	$0.784388\pi$
$38$	3.21336	0.521275
$39$	1.00000	0.160128
$40$	−0.176895	−0.0279696
$41$	1.27770	0.199544	0.0997720	−	0.995010i	$-0.468189\pi$
$41$	1.27770	0.199544	0.0997720	+	0.995010i	$0.468189\pi$
$42$	−2.27129	−0.350468
$43$	8.05978	1.22910	0.614552	−	0.788876i	$-0.289337\pi$
$43$	8.05978	1.22910	0.614552	+	0.788876i	$0.289337\pi$
$44$	−2.71409	−0.409165
$45$	−0.176895	−0.0263700
$46$	−5.17288	−0.762700
$47$	−10.5112	−1.53321	−0.766606	−	0.642118i	$-0.778056\pi$
$47$	−10.5112	−1.53321	−0.766606	+	0.642118i	$0.778056\pi$
$48$	1.00000	0.144338
$49$	−1.84124	−0.263034
$50$	−4.96871	−0.702681
$51$	−1.27485	−0.178515
$52$	1.00000	0.138675
$53$	−1.60081	−0.219888	−0.109944	−	0.993938i	$-0.535067\pi$
$53$	−1.60081	−0.219888	−0.109944	+	0.993938i	$0.535067\pi$
$54$	1.00000	0.136083
$55$	0.480111	0.0647381
$56$	−2.27129	−0.303514
$57$	3.21336	0.425619
$58$	−0.285145	−0.0374414
$59$	−12.8286	−1.67014	−0.835072	−	0.550141i	$-0.814574\pi$
$59$	−12.8286	−1.67014	−0.835072	+	0.550141i	$0.814574\pi$
$60$	−0.176895	−0.0228371
$61$	−5.88767	−0.753839	−0.376919	−	0.926246i	$-0.623017\pi$
$61$	−5.88767	−0.753839	−0.376919	+	0.926246i	$0.623017\pi$
$62$	9.70181	1.23213
$63$	−2.27129	−0.286156
$64$	1.00000	0.125000
$65$	−0.176895	−0.0219412
$66$	−2.71409	−0.334082
$67$	−5.59876	−0.683997	−0.341999	−	0.939700i	$-0.611104\pi$
$67$	−5.59876	−0.683997	−0.341999	+	0.939700i	$0.611104\pi$
$68$	−1.27485	−0.154598
$69$	−5.17288	−0.622742
$70$	0.401781	0.0480220
$71$	2.87751	0.341497	0.170749	−	0.985315i	$-0.445381\pi$
$71$	2.87751	0.341497	0.170749	+	0.985315i	$0.445381\pi$
$72$	1.00000	0.117851
$73$	14.5396	1.70173	0.850864	−	0.525386i	$-0.176079\pi$
$73$	14.5396	1.70173	0.850864	+	0.525386i	$0.176079\pi$
$74$	−9.47971	−1.10199
$75$	−4.96871	−0.573737
$76$	3.21336	0.368597
$77$	6.16450	0.702510
$78$	1.00000	0.113228
$79$	−6.63863	−0.746904	−0.373452	−	0.927649i	$-0.621826\pi$
$79$	−6.63863	−0.746904	−0.373452	+	0.927649i	$0.621826\pi$
$80$	−0.176895	−0.0197775
$81$	1.00000	0.111111
$82$	1.27770	0.141099
$83$	0.0726498	0.00797435	0.00398718	−	0.999992i	$-0.498731\pi$
$83$	0.0726498	0.00797435	0.00398718	+	0.999992i	$0.498731\pi$
$84$	−2.27129	−0.247818
$85$	0.225515	0.0244605
$86$	8.05978	0.869108
$87$	−0.285145	−0.0305708
$88$	−2.71409	−0.289323
$89$	−0.653992	−0.0693230	−0.0346615	−	0.999399i	$-0.511035\pi$
$89$	−0.653992	−0.0693230	−0.0346615	+	0.999399i	$0.511035\pi$
$90$	−0.176895	−0.0186464
$91$	−2.27129	−0.238096
$92$	−5.17288	−0.539310
$93$	9.70181	1.00603
$94$	−10.5112	−1.08414
$95$	−0.568428	−0.0583195
$96$	1.00000	0.102062
$97$	−12.7299	−1.29253	−0.646263	−	0.763115i	$-0.723669\pi$
$97$	−12.7299	−1.29253	−0.646263	+	0.763115i	$0.723669\pi$
$98$	−1.84124	−0.185993
$99$	−2.71409	−0.272777
$100$	−4.96871	−0.496871
$101$	−6.23848	−0.620752	−0.310376	−	0.950614i	$-0.600455\pi$
$101$	−6.23848	−0.620752	−0.310376	+	0.950614i	$0.600455\pi$
$102$	−1.27485	−0.126229
$103$	1.00000	0.0985329
$103$	1.00000	0.0985329
$104$	1.00000	0.0980581
$105$	0.401781	0.0392098
$106$	−1.60081	−0.155484
$107$	−11.5703	−1.11854	−0.559272	−	0.828984i	$-0.688919\pi$
$107$	−11.5703	−1.11854	−0.559272	+	0.828984i	$0.688919\pi$
$108$	1.00000	0.0962250
$109$	6.93363	0.664121	0.332061	−	0.943258i	$-0.392256\pi$
$109$	6.93363	0.664121	0.332061	+	0.943258i	$0.392256\pi$
$110$	0.480111	0.0457768
$111$	−9.47971	−0.899775
$112$	−2.27129	−0.214617
$113$	−1.66928	−0.157033	−0.0785166	−	0.996913i	$-0.525018\pi$
$113$	−1.66928	−0.157033	−0.0785166	+	0.996913i	$0.525018\pi$
$114$	3.21336	0.300958
$115$	0.915059	0.0853297
$116$	−0.285145	−0.0264751
$117$	1.00000	0.0924500
$118$	−12.8286	−1.18097
$119$	2.89555	0.265435
$120$	−0.176895	−0.0161483
$121$	−3.63369	−0.330336
$122$	−5.88767	−0.533044
$123$	1.27770	0.115207
$124$	9.70181	0.871249
$125$	1.76342	0.157725
$126$	−2.27129	−0.202343
$127$	22.5037	1.99688	0.998441	−	0.0558160i	$-0.0177760\pi$
$127$	22.5037	1.99688	0.998441	+	0.0558160i	$0.0177760\pi$
$128$	1.00000	0.0883883
$129$	8.05978	0.709624
$130$	−0.176895	−0.0155147
$131$	−7.67061	−0.670184	−0.335092	−	0.942185i	$-0.608767\pi$
$131$	−7.67061	−0.670184	−0.335092	+	0.942185i	$0.608767\pi$
$132$	−2.71409	−0.236232
$133$	−7.29847	−0.632857
$134$	−5.59876	−0.483659
$135$	−0.176895	−0.0152247
$136$	−1.27485	−0.109317
$137$	−10.5486	−0.901231	−0.450615	−	0.892718i	$-0.648795\pi$
$137$	−10.5486	−0.901231	−0.450615	+	0.892718i	$0.648795\pi$
$138$	−5.17288	−0.440345
$139$	−16.2854	−1.38131	−0.690655	−	0.723184i	$-0.742678\pi$
$139$	−16.2854	−1.38131	−0.690655	+	0.723184i	$0.742678\pi$
$140$	0.401781	0.0339567
$141$	−10.5112	−0.885200
$142$	2.87751	0.241475
$143$	−2.71409	−0.226964
$144$	1.00000	0.0833333
$145$	0.0504409	0.00418889
$146$	14.5396	1.20330
$147$	−1.84124	−0.151863
$148$	−9.47971	−0.779228
$149$	−0.0615531	−0.00504263	−0.00252131	−	0.999997i	$-0.500803\pi$
$149$	−0.0615531	−0.00504263	−0.00252131	+	0.999997i	$0.500803\pi$
$150$	−4.96871	−0.405693
$151$	−22.1661	−1.80385	−0.901925	−	0.431893i	$-0.857846\pi$
$151$	−22.1661	−1.80385	−0.901925	+	0.431893i	$0.857846\pi$
$152$	3.21336	0.260638
$153$	−1.27485	−0.103065
$154$	6.16450	0.496749
$155$	−1.71621	−0.137849
$156$	1.00000	0.0800641
$157$	−7.48677	−0.597509	−0.298755	−	0.954330i	$-0.596571\pi$
$157$	−7.48677	−0.597509	−0.298755	+	0.954330i	$0.596571\pi$
$158$	−6.63863	−0.528141
$159$	−1.60081	−0.126952
$160$	−0.176895	−0.0139848
$161$	11.7491	0.925960
$162$	1.00000	0.0785674
$163$	−10.2653	−0.804044	−0.402022	−	0.915630i	$-0.631692\pi$
$163$	−10.2653	−0.804044	−0.402022	+	0.915630i	$0.631692\pi$
$164$	1.27770	0.0997720
$165$	0.480111	0.0373766
$166$	0.0726498	0.00563872
$167$	−10.4308	−0.807156	−0.403578	−	0.914945i	$-0.632234\pi$
$167$	−10.4308	−0.807156	−0.403578	+	0.914945i	$0.632234\pi$
$168$	−2.27129	−0.175234
$169$	1.00000	0.0769231
$170$	0.225515	0.0172962
$171$	3.21336	0.245731
$172$	8.05978	0.614552
$173$	0.217123	0.0165075	0.00825377	−	0.999966i	$-0.497373\pi$
$173$	0.217123	0.0165075	0.00825377	+	0.999966i	$0.497373\pi$
$174$	−0.285145	−0.0216168
$175$	11.2854	0.853095
$176$	−2.71409	−0.204583
$177$	−12.8286	−0.964258
$178$	−0.653992	−0.0490188
$179$	−14.1914	−1.06072	−0.530358	−	0.847774i	$-0.677942\pi$
$179$	−14.1914	−1.06072	−0.530358	+	0.847774i	$0.677942\pi$
$180$	−0.176895	−0.0131850
$181$	1.16144	0.0863291	0.0431646	−	0.999068i	$-0.486256\pi$
$181$	1.16144	0.0863291	0.0431646	+	0.999068i	$0.486256\pi$
$182$	−2.27129	−0.168359
$183$	−5.88767	−0.435229
$184$	−5.17288	−0.381350
$185$	1.67692	0.123289
$186$	9.70181	0.711371
$187$	3.46006	0.253025
$188$	−10.5112	−0.766606
$189$	−2.27129	−0.165212
$190$	−0.568428	−0.0412381
$191$	11.6703	0.844435	0.422218	−	0.906494i	$-0.361252\pi$
$191$	11.6703	0.844435	0.422218	+	0.906494i	$0.361252\pi$
$192$	1.00000	0.0721688
$193$	22.6608	1.63116	0.815581	−	0.578642i	$-0.196417\pi$
$193$	22.6608	1.63116	0.815581	+	0.578642i	$0.196417\pi$
$194$	−12.7299	−0.913953
$195$	−0.176895	−0.0126677
$196$	−1.84124	−0.131517
$197$	18.2090	1.29734	0.648669	−	0.761071i	$-0.275326\pi$
$197$	18.2090	1.29734	0.648669	+	0.761071i	$0.275326\pi$
$198$	−2.71409	−0.192882
$199$	12.2916	0.871325	0.435663	−	0.900110i	$-0.356514\pi$
$199$	12.2916	0.871325	0.435663	+	0.900110i	$0.356514\pi$
$200$	−4.96871	−0.351341
$201$	−5.59876	−0.394906
$202$	−6.23848	−0.438938
$203$	0.647648	0.0454560
$204$	−1.27485	−0.0892573
$205$	−0.226020	−0.0157859
$206$	1.00000	0.0696733
$207$	−5.17288	−0.359540
$208$	1.00000	0.0693375
$209$	−8.72135	−0.603268
$210$	0.401781	0.0277255
$211$	13.5139	0.930336	0.465168	−	0.885222i	$-0.345994\pi$
$211$	13.5139	0.930336	0.465168	+	0.885222i	$0.345994\pi$
$212$	−1.60081	−0.109944
$213$	2.87751	0.197163
$214$	−11.5703	−0.790930
$215$	−1.42574	−0.0972345
$216$	1.00000	0.0680414
$217$	−22.0356	−1.49588
$218$	6.93363	0.469605
$219$	14.5396	0.982493
$220$	0.480111	0.0323691
$221$	−1.27485	−0.0857557
$222$	−9.47971	−0.636237
$223$	−16.3292	−1.09349	−0.546743	−	0.837301i	$-0.684132\pi$
$223$	−16.3292	−1.09349	−0.546743	+	0.837301i	$0.684132\pi$
$224$	−2.27129	−0.151757
$225$	−4.96871	−0.331247
$226$	−1.66928	−0.111039
$227$	−18.7344	−1.24345	−0.621723	−	0.783237i	$-0.713567\pi$
$227$	−18.7344	−1.24345	−0.621723	+	0.783237i	$0.713567\pi$
$228$	3.21336	0.212810
$229$	10.1789	0.672641	0.336320	−	0.941748i	$-0.390818\pi$
$229$	10.1789	0.672641	0.336320	+	0.941748i	$0.390818\pi$
$230$	0.915059	0.0603372
$231$	6.16450	0.405594
$232$	−0.285145	−0.0187207
$233$	7.07885	0.463751	0.231875	−	0.972745i	$-0.425514\pi$
$233$	7.07885	0.463751	0.231875	+	0.972745i	$0.425514\pi$
$234$	1.00000	0.0653720
$235$	1.85938	0.121292
$236$	−12.8286	−0.835072
$237$	−6.63863	−0.431225
$238$	2.89555	0.187691
$239$	−1.44245	−0.0933044	−0.0466522	−	0.998911i	$-0.514855\pi$
$239$	−1.44245	−0.0933044	−0.0466522	+	0.998911i	$0.514855\pi$
$240$	−0.176895	−0.0114185
$241$	−5.60544	−0.361078	−0.180539	−	0.983568i	$-0.557784\pi$
$241$	−5.60544	−0.361078	−0.180539	+	0.983568i	$0.557784\pi$
$242$	−3.63369	−0.233583
$243$	1.00000	0.0641500
$244$	−5.88767	−0.376919
$245$	0.325706	0.0208086
$246$	1.27770	0.0814635
$247$	3.21336	0.204461
$248$	9.70181	0.616066
$249$	0.0726498	0.00460400
$250$	1.76342	0.111528
$251$	24.3219	1.53518	0.767591	−	0.640940i	$-0.221455\pi$
$251$	24.3219	1.53518	0.767591	+	0.640940i	$0.221455\pi$
$252$	−2.27129	−0.143078
$253$	14.0397	0.882667
$254$	22.5037	1.41201
$255$	0.225515	0.0141223
$256$	1.00000	0.0625000
$257$	−4.59049	−0.286347	−0.143173	−	0.989698i	$-0.545731\pi$
$257$	−4.59049	−0.286347	−0.143173	+	0.989698i	$0.545731\pi$
$258$	8.05978	0.501780
$259$	21.5312	1.33788
$260$	−0.176895	−0.0109706
$261$	−0.285145	−0.0176500
$262$	−7.67061	−0.473892
$263$	9.20402	0.567544	0.283772	−	0.958892i	$-0.408414\pi$
$263$	9.20402	0.567544	0.283772	+	0.958892i	$0.408414\pi$
$264$	−2.71409	−0.167041
$265$	0.283175	0.0173953
$266$	−7.29847	−0.447498
$267$	−0.653992	−0.0400237
$268$	−5.59876	−0.341999
$269$	−23.4505	−1.42980	−0.714902	−	0.699225i	$-0.753529\pi$
$269$	−23.4505	−1.42980	−0.714902	+	0.699225i	$0.753529\pi$
$270$	−0.176895	−0.0107655
$271$	8.79415	0.534207	0.267103	−	0.963668i	$-0.413933\pi$
$271$	8.79415	0.534207	0.267103	+	0.963668i	$0.413933\pi$
$272$	−1.27485	−0.0772991
$273$	−2.27129	−0.137465
$274$	−10.5486	−0.637266
$275$	13.4855	0.813209
$276$	−5.17288	−0.311371
$277$	−18.3506	−1.10258	−0.551289	−	0.834314i	$-0.685864\pi$
$277$	−18.3506	−1.10258	−0.551289	+	0.834314i	$0.685864\pi$
$278$	−16.2854	−0.976734
$279$	9.70181	0.580832
$280$	0.401781	0.0240110
$281$	18.9440	1.13010	0.565051	−	0.825056i	$-0.308856\pi$
$281$	18.9440	1.13010	0.565051	+	0.825056i	$0.308856\pi$
$282$	−10.5112	−0.625931
$283$	−12.9387	−0.769124	−0.384562	−	0.923099i	$-0.625648\pi$
$283$	−12.9387	−0.769124	−0.384562	+	0.923099i	$0.625648\pi$
$284$	2.87751	0.170749
$285$	−0.568428	−0.0336708
$286$	−2.71409	−0.160488
$287$	−2.90204	−0.171302
$288$	1.00000	0.0589256
$289$	−15.3748	−0.904398
$290$	0.0504409	0.00296199
$291$	−12.7299	−0.746240
$292$	14.5396	0.850864
$293$	29.3750	1.71611	0.858054	−	0.513559i	$-0.171673\pi$
$293$	29.3750	1.71611	0.858054	+	0.513559i	$0.171673\pi$
$294$	−1.84124	−0.107383
$295$	2.26932	0.132125
$296$	−9.47971	−0.550997
$297$	−2.71409	−0.157488
$298$	−0.0615531	−0.00356568
$299$	−5.17288	−0.299155
$300$	−4.96871	−0.286868
$301$	−18.3061	−1.05515
$302$	−22.1661	−1.27551
$303$	−6.23848	−0.358392
$304$	3.21336	0.184299
$305$	1.04150	0.0596362
$306$	−1.27485	−0.0728783
$307$	6.16534	0.351874	0.175937	−	0.984401i	$-0.443704\pi$
$307$	6.16534	0.351874	0.175937	+	0.984401i	$0.443704\pi$
$308$	6.16450	0.351255
$309$	1.00000	0.0568880
$310$	−1.71621	−0.0974739
$311$	−23.7221	−1.34515	−0.672577	−	0.740027i	$-0.734813\pi$
$311$	−23.7221	−1.34515	−0.672577	+	0.740027i	$0.734813\pi$
$312$	1.00000	0.0566139
$313$	−27.9972	−1.58250	−0.791249	−	0.611494i	$-0.790569\pi$
$313$	−27.9972	−1.58250	−0.791249	+	0.611494i	$0.790569\pi$
$314$	−7.48677	−0.422503
$315$	0.401781	0.0226378
$316$	−6.63863	−0.373452
$317$	−18.7148	−1.05113	−0.525564	−	0.850754i	$-0.676146\pi$
$317$	−18.7148	−1.05113	−0.525564	+	0.850754i	$0.676146\pi$
$318$	−1.60081	−0.0897688
$319$	0.773911	0.0433307
$320$	−0.176895	−0.00988875
$321$	−11.5703	−0.645791
$322$	11.7491	0.654753
$323$	−4.09654	−0.227938
$324$	1.00000	0.0555556
$325$	−4.96871	−0.275614
$326$	−10.2653	−0.568545
$327$	6.93363	0.383431
$328$	1.27770	0.0705494
$329$	23.8739	1.31621
$330$	0.480111	0.0264292
$331$	13.3720	0.734993	0.367497	−	0.930025i	$-0.380215\pi$
$331$	13.3720	0.734993	0.367497	+	0.930025i	$0.380215\pi$
$332$	0.0726498	0.00398718
$333$	−9.47971	−0.519485
$334$	−10.4308	−0.570746
$335$	0.990395	0.0541110
$336$	−2.27129	−0.123909
$337$	3.80770	0.207419	0.103709	−	0.994608i	$-0.466929\pi$
$337$	3.80770	0.207419	0.103709	+	0.994608i	$0.466929\pi$
$338$	1.00000	0.0543928
$339$	−1.66928	−0.0906631
$340$	0.225515	0.0122303
$341$	−26.3316	−1.42594
$342$	3.21336	0.173758
$343$	20.0810	1.08427
$344$	8.05978	0.434554
$345$	0.915059	0.0492651
$346$	0.217123	0.0116726
$347$	−23.1127	−1.24076	−0.620378	−	0.784303i	$-0.713021\pi$
$347$	−23.1127	−1.24076	−0.620378	+	0.784303i	$0.713021\pi$
$348$	−0.285145	−0.0152854
$349$	−37.1158	−1.98676	−0.993382	−	0.114854i	$-0.963360\pi$
$349$	−37.1158	−1.98676	−0.993382	+	0.114854i	$0.963360\pi$
$350$	11.2854	0.603229
$351$	1.00000	0.0533761
$352$	−2.71409	−0.144662
$353$	17.5574	0.934484	0.467242	−	0.884130i	$-0.345248\pi$
$353$	17.5574	0.934484	0.467242	+	0.884130i	$0.345248\pi$
$354$	−12.8286	−0.681833
$355$	−0.509018	−0.0270158
$356$	−0.653992	−0.0346615
$357$	2.89555	0.153249
$358$	−14.1914	−0.750039
$359$	−17.8402	−0.941571	−0.470786	−	0.882248i	$-0.656030\pi$
$359$	−17.8402	−0.941571	−0.470786	+	0.882248i	$0.656030\pi$
$360$	−0.176895	−0.00932320
$361$	−8.67434	−0.456544
$362$	1.16144	0.0610439
$363$	−3.63369	−0.190719
$364$	−2.27129	−0.119048
$365$	−2.57198	−0.134624
$366$	−5.88767	−0.307753
$367$	35.2583	1.84047	0.920235	−	0.391365i	$-0.127997\pi$
$367$	35.2583	1.84047	0.920235	+	0.391365i	$0.127997\pi$
$368$	−5.17288	−0.269655
$369$	1.27770	0.0665146
$370$	1.67692	0.0871788
$371$	3.63590	0.188766
$372$	9.70181	0.503016
$373$	10.1618	0.526157	0.263079	−	0.964774i	$-0.415262\pi$
$373$	10.1618	0.526157	0.263079	+	0.964774i	$0.415262\pi$
$374$	3.46006	0.178916
$375$	1.76342	0.0910625
$376$	−10.5112	−0.542072
$377$	−0.285145	−0.0146857
$378$	−2.27129	−0.116823
$379$	−5.06559	−0.260202	−0.130101	−	0.991501i	$-0.541530\pi$
$379$	−5.06559	−0.260202	−0.130101	+	0.991501i	$0.541530\pi$
$380$	−0.568428	−0.0291597
$381$	22.5037	1.15290
$382$	11.6703	0.597106
$383$	−7.62919	−0.389833	−0.194917	−	0.980820i	$-0.562444\pi$
$383$	−7.62919	−0.389833	−0.194917	+	0.980820i	$0.562444\pi$
$384$	1.00000	0.0510310
$385$	−1.09047	−0.0555756
$386$	22.6608	1.15341
$387$	8.05978	0.409702
$388$	−12.7299	−0.646263
$389$	21.7999	1.10530	0.552648	−	0.833415i	$-0.313617\pi$
$389$	21.7999	1.10530	0.552648	+	0.833415i	$0.313617\pi$
$390$	−0.176895	−0.00895744
$391$	6.59464	0.333505
$392$	−1.84124	−0.0929964
$393$	−7.67061	−0.386931
$394$	18.2090	0.917357
$395$	1.17434	0.0590876
$396$	−2.71409	−0.136388
$397$	8.50492	0.426850	0.213425	−	0.976959i	$-0.431538\pi$
$397$	8.50492	0.426850	0.213425	+	0.976959i	$0.431538\pi$
$398$	12.2916	0.616120
$399$	−7.29847	−0.365380
$400$	−4.96871	−0.248435
$401$	15.7272	0.785379	0.392690	−	0.919671i	$-0.371545\pi$
$401$	15.7272	0.785379	0.392690	+	0.919671i	$0.371545\pi$
$402$	−5.59876	−0.279241
$403$	9.70181	0.483282
$404$	−6.23848	−0.310376
$405$	−0.176895	−0.00879000
$406$	0.647648	0.0321422
$407$	25.7288	1.27533
$408$	−1.27485	−0.0631145
$409$	−34.0608	−1.68420	−0.842099	−	0.539322i	$-0.818680\pi$
$409$	−34.0608	−1.68420	−0.842099	+	0.539322i	$0.818680\pi$
$410$	−0.226020	−0.0111623
$411$	−10.5486	−0.520326
$412$	1.00000	0.0492665
$413$	29.1375	1.43376
$414$	−5.17288	−0.254233
$415$	−0.0128514	−0.000630851 0
$416$	1.00000	0.0490290
$417$	−16.2854	−0.797500
$418$	−8.72135	−0.426575
$419$	−2.24624	−0.109736	−0.0548681	−	0.998494i	$-0.517474\pi$
$419$	−2.24624	−0.109736	−0.0548681	+	0.998494i	$0.517474\pi$
$420$	0.401781	0.0196049
$421$	38.1757	1.86057	0.930285	−	0.366837i	$-0.119559\pi$
$421$	38.1757	1.86057	0.930285	+	0.366837i	$0.119559\pi$
$422$	13.5139	0.657847
$423$	−10.5112	−0.511071
$424$	−1.60081	−0.0777421
$425$	6.33435	0.307261
$426$	2.87751	0.139416
$427$	13.3726	0.647146
$428$	−11.5703	−0.559272
$429$	−2.71409	−0.131038
$430$	−1.42574	−0.0687552
$431$	25.0726	1.20770	0.603852	−	0.797096i	$-0.293632\pi$
$431$	25.0726	1.20770	0.603852	+	0.797096i	$0.293632\pi$
$432$	1.00000	0.0481125
$433$	−26.0304	−1.25094	−0.625472	−	0.780247i	$-0.715093\pi$
$433$	−26.0304	−1.25094	−0.625472	+	0.780247i	$0.715093\pi$
$434$	−22.0356	−1.05774
$435$	0.0504409	0.00241845
$436$	6.93363	0.332061
$437$	−16.6223	−0.795153
$438$	14.5396	0.694727
$439$	−11.6922	−0.558040	−0.279020	−	0.960285i	$-0.590010\pi$
$439$	−11.6922	−0.558040	−0.279020	+	0.960285i	$0.590010\pi$
$440$	0.480111	0.0228884
$441$	−1.84124	−0.0876779
$442$	−1.27485	−0.0606384
$443$	30.0093	1.42578	0.712892	−	0.701273i	$-0.247385\pi$
$443$	30.0093	1.42578	0.712892	+	0.701273i	$0.247385\pi$
$444$	−9.47971	−0.449887
$445$	0.115688	0.00548415
$446$	−16.3292	−0.773211
$447$	−0.0615531	−0.00291136
$448$	−2.27129	−0.107308
$449$	−37.0292	−1.74752	−0.873759	−	0.486360i	$-0.838324\pi$
$449$	−37.0292	−1.74752	−0.873759	+	0.486360i	$0.838324\pi$
$450$	−4.96871	−0.234227
$451$	−3.46781	−0.163293
$452$	−1.66928	−0.0785166
$453$	−22.1661	−1.04145
$454$	−18.7344	−0.879249
$455$	0.401781	0.0188358
$456$	3.21336	0.150479
$457$	−5.35914	−0.250690	−0.125345	−	0.992113i	$-0.540004\pi$
$457$	−5.35914	−0.250690	−0.125345	+	0.992113i	$0.540004\pi$
$458$	10.1789	0.475629
$459$	−1.27485	−0.0595049
$460$	0.915059	0.0426648
$461$	3.26454	0.152045	0.0760223	−	0.997106i	$-0.475778\pi$
$461$	3.26454	0.152045	0.0760223	+	0.997106i	$0.475778\pi$
$462$	6.16450	0.286798
$463$	26.1498	1.21529	0.607643	−	0.794210i	$-0.292115\pi$
$463$	26.1498	1.21529	0.607643	+	0.794210i	$0.292115\pi$
$464$	−0.285145	−0.0132375
$465$	−1.71621	−0.0795871
$466$	7.07885	0.327921
$467$	38.6655	1.78922	0.894612	−	0.446843i	$-0.147452\pi$
$467$	38.6655	1.78922	0.894612	+	0.446843i	$0.147452\pi$
$468$	1.00000	0.0462250
$469$	12.7164	0.587190
$470$	1.85938	0.0857667
$471$	−7.48677	−0.344972
$472$	−12.8286	−0.590485
$473$	−21.8750	−1.00581
$474$	−6.63863	−0.304922
$475$	−15.9662	−0.732581
$476$	2.89555	0.132718
$477$	−1.60081	−0.0732959
$478$	−1.44245	−0.0659761
$479$	35.5368	1.62372	0.811858	−	0.583855i	$-0.198456\pi$
$479$	35.5368	1.62372	0.811858	+	0.583855i	$0.198456\pi$
$480$	−0.176895	−0.00807413
$481$	−9.47971	−0.432238
$482$	−5.60544	−0.255321
$483$	11.7491	0.534603
$484$	−3.63369	−0.165168
$485$	2.25186	0.102252
$486$	1.00000	0.0453609
$487$	37.1580	1.68379	0.841895	−	0.539641i	$-0.181440\pi$
$487$	37.1580	1.68379	0.841895	+	0.539641i	$0.181440\pi$
$488$	−5.88767	−0.266522
$489$	−10.2653	−0.464215
$490$	0.325706	0.0147139
$491$	16.7762	0.757100	0.378550	−	0.925581i	$-0.376423\pi$
$491$	16.7762	0.757100	0.378550	+	0.925581i	$0.376423\pi$
$492$	1.27770	0.0576034
$493$	0.363517	0.0163720
$494$	3.21336	0.144576
$495$	0.480111	0.0215794
$496$	9.70181	0.435624
$497$	−6.53566	−0.293164
$498$	0.0726498	0.00325552
$499$	−33.7571	−1.51118	−0.755588	−	0.655048i	$-0.772649\pi$
$499$	−33.7571	−1.51118	−0.755588	+	0.655048i	$0.772649\pi$
$500$	1.76342	0.0788625
$501$	−10.4308	−0.466012
$502$	24.3219	1.08554
$503$	37.2596	1.66132	0.830662	−	0.556777i	$-0.187962\pi$
$503$	37.2596	1.66132	0.830662	+	0.556777i	$0.187962\pi$
$504$	−2.27129	−0.101171
$505$	1.10356	0.0491077
$506$	14.0397	0.624140
$507$	1.00000	0.0444116
$508$	22.5037	0.998441
$509$	−5.35975	−0.237567	−0.118783	−	0.992920i	$-0.537899\pi$
$509$	−5.35975	−0.237567	−0.118783	+	0.992920i	$0.537899\pi$
$510$	0.225515	0.00998597
$511$	−33.0236	−1.46088
$512$	1.00000	0.0441942
$513$	3.21336	0.141873
$514$	−4.59049	−0.202478
$515$	−0.176895	−0.00779494
$516$	8.05978	0.354812
$517$	28.5283	1.25467
$518$	21.5312	0.946026
$519$	0.217123	0.00953064
$520$	−0.176895	−0.00775737
$521$	−39.1861	−1.71677	−0.858386	−	0.513004i	$-0.828533\pi$
$521$	−39.1861	−1.71677	−0.858386	+	0.513004i	$0.828533\pi$
$522$	−0.285145	−0.0124805
$523$	17.7336	0.775437	0.387718	−	0.921778i	$-0.373263\pi$
$523$	17.7336	0.775437	0.387718	+	0.921778i	$0.373263\pi$
$524$	−7.67061	−0.335092
$525$	11.2854	0.492535
$526$	9.20402	0.401315
$527$	−12.3684	−0.538774
$528$	−2.71409	−0.118116
$529$	3.75869	0.163421
$530$	0.283175	0.0123004
$531$	−12.8286	−0.556715
$532$	−7.29847	−0.316429
$533$	1.27770	0.0553435
$534$	−0.653992	−0.0283010
$535$	2.04673	0.0884880
$536$	−5.59876	−0.241830
$537$	−14.1914	−0.612405
$538$	−23.4505	−1.01102
$539$	4.99729	0.215248
$540$	−0.176895	−0.00761236
$541$	−8.59755	−0.369638	−0.184819	−	0.982773i	$-0.559170\pi$
$541$	−8.59755	−0.369638	−0.184819	+	0.982773i	$0.559170\pi$
$542$	8.79415	0.377741
$543$	1.16144	0.0498421
$544$	−1.27485	−0.0546587
$545$	−1.22653	−0.0525386
$546$	−2.27129	−0.0972023
$547$	43.7055	1.86871	0.934356	−	0.356341i	$-0.115976\pi$
$547$	43.7055	1.86871	0.934356	+	0.356341i	$0.115976\pi$
$548$	−10.5486	−0.450615
$549$	−5.88767	−0.251280
$550$	13.4855	0.575025
$551$	−0.916273	−0.0390345
$552$	−5.17288	−0.220172
$553$	15.0783	0.641193
$554$	−18.3506	−0.779640
$555$	1.67692	0.0711812
$556$	−16.2854	−0.690655
$557$	−14.4394	−0.611818	−0.305909	−	0.952061i	$-0.598960\pi$
$557$	−14.4394	−0.611818	−0.305909	+	0.952061i	$0.598960\pi$
$558$	9.70181	0.410711
$559$	8.05978	0.340892
$560$	0.401781	0.0169783
$561$	3.46006	0.146084
$562$	18.9440	0.799103
$563$	−18.9142	−0.797138	−0.398569	−	0.917138i	$-0.630493\pi$
$563$	−18.9142	−0.797138	−0.398569	+	0.917138i	$0.630493\pi$
$564$	−10.5112	−0.442600
$565$	0.295289	0.0124229
$566$	−12.9387	−0.543853
$567$	−2.27129	−0.0953853
$568$	2.87751	0.120737
$569$	−24.8554	−1.04199	−0.520996	−	0.853559i	$-0.674440\pi$
$569$	−24.8554	−1.04199	−0.520996	+	0.853559i	$0.674440\pi$
$570$	−0.568428	−0.0238088
$571$	6.98909	0.292484	0.146242	−	0.989249i	$-0.453282\pi$
$571$	6.98909	0.292484	0.146242	+	0.989249i	$0.453282\pi$
$572$	−2.71409	−0.113482
$573$	11.6703	0.487535
$574$	−2.90204	−0.121129
$575$	25.7025	1.07187
$576$	1.00000	0.0416667
$577$	−9.87183	−0.410970	−0.205485	−	0.978660i	$-0.565877\pi$
$577$	−9.87183	−0.410970	−0.205485	+	0.978660i	$0.565877\pi$
$578$	−15.3748	−0.639506
$579$	22.6608	0.941752
$580$	0.0504409	0.00209444
$581$	−0.165009	−0.00684572
$582$	−12.7299	−0.527671
$583$	4.34474	0.179941
$584$	14.5396	0.601652
$585$	−0.176895	−0.00731372
$586$	29.3750	1.21347
$587$	4.97985	0.205540	0.102770	−	0.994705i	$-0.467229\pi$
$587$	4.97985	0.205540	0.102770	+	0.994705i	$0.467229\pi$
$588$	−1.84124	−0.0759313
$589$	31.1754	1.28456
$590$	2.26932	0.0934266
$591$	18.2090	0.749019
$592$	−9.47971	−0.389614
$593$	46.7631	1.92033	0.960165	−	0.279434i	$-0.0901467\pi$
$593$	46.7631	1.92033	0.960165	+	0.279434i	$0.0901467\pi$
$594$	−2.71409	−0.111361
$595$	−0.512210	−0.0209986
$596$	−0.0615531	−0.00252131
$597$	12.2916	0.503060
$598$	−5.17288	−0.211535
$599$	−4.44409	−0.181581	−0.0907903	−	0.995870i	$-0.528939\pi$
$599$	−4.44409	−0.181581	−0.0907903	+	0.995870i	$0.528939\pi$
$600$	−4.96871	−0.202847
$601$	21.4328	0.874262	0.437131	−	0.899398i	$-0.355995\pi$
$601$	21.4328	0.874262	0.437131	+	0.899398i	$0.355995\pi$
$602$	−18.3061	−0.746101
$603$	−5.59876	−0.227999
$604$	−22.1661	−0.901925
$605$	0.642783	0.0261329
$606$	−6.23848	−0.253421
$607$	33.3991	1.35563	0.677815	−	0.735233i	$-0.262927\pi$
$607$	33.3991	1.35563	0.677815	+	0.735233i	$0.262927\pi$
$608$	3.21336	0.130319
$609$	0.647648	0.0262440
$610$	1.04150	0.0421691
$611$	−10.5112	−0.425236
$612$	−1.27485	−0.0515327
$613$	−6.85009	−0.276673	−0.138336	−	0.990385i	$-0.544175\pi$
$613$	−6.85009	−0.276673	−0.138336	+	0.990385i	$0.544175\pi$
$614$	6.16534	0.248813
$615$	−0.226020	−0.00911401
$616$	6.16450	0.248375
$617$	5.02106	0.202140	0.101070	−	0.994879i	$-0.467773\pi$
$617$	5.02106	0.202140	0.101070	+	0.994879i	$0.467773\pi$
$618$	1.00000	0.0402259
$619$	28.5512	1.14757	0.573784	−	0.819007i	$-0.305475\pi$
$619$	28.5512	1.14757	0.573784	+	0.819007i	$0.305475\pi$
$620$	−1.71621	−0.0689245
$621$	−5.17288	−0.207581
$622$	−23.7221	−0.951168
$623$	1.48541	0.0595116
$624$	1.00000	0.0400320
$625$	24.5316	0.981264
$626$	−27.9972	−1.11899
$627$	−8.72135	−0.348297
$628$	−7.48677	−0.298755
$629$	12.0852	0.481869
$630$	0.401781	0.0160073
$631$	6.62844	0.263874	0.131937	−	0.991258i	$-0.457880\pi$
$631$	6.62844	0.263874	0.131937	+	0.991258i	$0.457880\pi$
$632$	−6.63863	−0.264071
$633$	13.5139	0.537130
$634$	−18.7148	−0.743260
$635$	−3.98080	−0.157973
$636$	−1.60081	−0.0634761
$637$	−1.84124	−0.0729524
$638$	0.773911	0.0306394
$639$	2.87751	0.113832
$640$	−0.176895	−0.00699240
$641$	−42.6143	−1.68317	−0.841583	−	0.540128i	$-0.818376\pi$
$641$	−42.6143	−1.68317	−0.841583	+	0.540128i	$0.818376\pi$
$642$	−11.5703	−0.456643
$643$	21.0931	0.831830	0.415915	−	0.909403i	$-0.363461\pi$
$643$	21.0931	0.831830	0.415915	+	0.909403i	$0.363461\pi$
$644$	11.7491	0.462980
$645$	−1.42574	−0.0561384
$646$	−4.09654	−0.161176
$647$	−22.8446	−0.898116	−0.449058	−	0.893503i	$-0.648240\pi$
$647$	−22.8446	−0.898116	−0.449058	+	0.893503i	$0.648240\pi$
$648$	1.00000	0.0392837
$649$	34.8181	1.36673
$650$	−4.96871	−0.194889
$651$	−22.0356	−0.863645
$652$	−10.2653	−0.402022
$653$	−31.8354	−1.24581	−0.622907	−	0.782296i	$-0.714049\pi$
$653$	−31.8354	−1.24581	−0.622907	+	0.782296i	$0.714049\pi$
$654$	6.93363	0.271126
$655$	1.35689	0.0530183
$656$	1.27770	0.0498860
$657$	14.5396	0.567243
$658$	23.8739	0.930703
$659$	25.7481	1.00300	0.501501	−	0.865157i	$-0.332781\pi$
$659$	25.7481	1.00300	0.501501	+	0.865157i	$0.332781\pi$
$660$	0.480111	0.0186883
$661$	−1.32062	−0.0513662	−0.0256831	−	0.999670i	$-0.508176\pi$
$661$	−1.32062	−0.0513662	−0.0256831	+	0.999670i	$0.508176\pi$
$662$	13.3720	0.519719
$663$	−1.27485	−0.0495110
$664$	0.0726498	0.00281936
$665$	1.29107	0.0500654
$666$	−9.47971	−0.367331
$667$	1.47502	0.0571131
$668$	−10.4308	−0.403578
$669$	−16.3292	−0.631324
$670$	0.990395	0.0382623
$671$	15.9797	0.616889
$672$	−2.27129	−0.0876170
$673$	−0.296006	−0.0114102	−0.00570510	−	0.999984i	$-0.501816\pi$
$673$	−0.296006	−0.0114102	−0.00570510	+	0.999984i	$0.501816\pi$
$674$	3.80770	0.146667
$675$	−4.96871	−0.191246
$676$	1.00000	0.0384615
$677$	3.77625	0.145133	0.0725665	−	0.997364i	$-0.476881\pi$
$677$	3.77625	0.145133	0.0725665	+	0.997364i	$0.476881\pi$
$678$	−1.66928	−0.0641085
$679$	28.9133	1.10959
$680$	0.225515	0.00864810
$681$	−18.7344	−0.717904
$682$	−26.3316	−1.00829
$683$	−23.1624	−0.886284	−0.443142	−	0.896451i	$-0.646136\pi$
$683$	−23.1624	−0.886284	−0.443142	+	0.896451i	$0.646136\pi$
$684$	3.21336	0.122866
$685$	1.86600	0.0712964
$686$	20.0810	0.766697
$687$	10.1789	0.388349
$688$	8.05978	0.307276
$689$	−1.60081	−0.0609859
$690$	0.915059	0.0348357
$691$	−19.9671	−0.759585	−0.379792	−	0.925072i	$-0.624005\pi$
$691$	−19.9671	−0.759585	−0.379792	+	0.925072i	$0.624005\pi$
$692$	0.217123	0.00825377
$693$	6.16450	0.234170
$694$	−23.1127	−0.877347
$695$	2.88081	0.109275
$696$	−0.285145	−0.0108084
$697$	−1.62888	−0.0616983
$698$	−37.1158	−1.40485
$699$	7.07885	0.267747
$700$	11.2854	0.426547
$701$	−26.3663	−0.995841	−0.497920	−	0.867223i	$-0.665903\pi$
$701$	−26.3663	−0.995841	−0.497920	+	0.867223i	$0.665903\pi$
$702$	1.00000	0.0377426
$703$	−30.4617	−1.14888
$704$	−2.71409	−0.102291
$705$	1.85938	0.0700282
$706$	17.5574	0.660780
$707$	14.1694	0.532896
$708$	−12.8286	−0.482129
$709$	6.64584	0.249590	0.124795	−	0.992183i	$-0.460173\pi$
$709$	6.64584	0.249590	0.124795	+	0.992183i	$0.460173\pi$
$710$	−0.509018	−0.0191031
$711$	−6.63863	−0.248968
$712$	−0.653992	−0.0245094
$713$	−50.1863	−1.87949
$714$	2.89555	0.108363
$715$	0.480111	0.0179551
$716$	−14.1914	−0.530358
$717$	−1.44245	−0.0538693
$718$	−17.8402	−0.665792
$719$	−43.4955	−1.62211	−0.811054	−	0.584971i	$-0.801106\pi$
$719$	−43.4955	−1.62211	−0.811054	+	0.584971i	$0.801106\pi$
$720$	−0.176895	−0.00659250
$721$	−2.27129	−0.0845873
$722$	−8.67434	−0.322826
$723$	−5.60544	−0.208469
$724$	1.16144	0.0431646
$725$	1.41680	0.0526188
$726$	−3.63369	−0.134859
$727$	−26.5065	−0.983070	−0.491535	−	0.870858i	$-0.663564\pi$
$727$	−26.5065	−0.983070	−0.491535	+	0.870858i	$0.663564\pi$
$728$	−2.27129	−0.0841797
$729$	1.00000	0.0370370
$730$	−2.57198	−0.0951933
$731$	−10.2750	−0.380035
$732$	−5.88767	−0.217614
$733$	34.9059	1.28928	0.644639	−	0.764487i	$-0.277008\pi$
$733$	34.9059	1.28928	0.644639	+	0.764487i	$0.277008\pi$
$734$	35.2583	1.30141
$735$	0.325706	0.0120138
$736$	−5.17288	−0.190675
$737$	15.1956	0.559736
$738$	1.27770	0.0470330
$739$	0.525193	0.0193196	0.00965978	−	0.999953i	$-0.496925\pi$
$739$	0.525193	0.0193196	0.00965978	+	0.999953i	$0.496925\pi$
$740$	1.67692	0.0616447
$741$	3.21336	0.118046
$742$	3.63590	0.133478
$743$	−25.3373	−0.929534	−0.464767	−	0.885433i	$-0.653862\pi$
$743$	−25.3373	−0.929534	−0.464767	+	0.885433i	$0.653862\pi$
$744$	9.70181	0.355686
$745$	0.0108885	0.000398922 0
$746$	10.1618	0.372049
$747$	0.0726498	0.00265812
$748$	3.46006	0.126512
$749$	26.2795	0.960233
$750$	1.76342	0.0643909
$751$	−32.8909	−1.20021	−0.600104	−	0.799922i	$-0.704874\pi$
$751$	−32.8909	−1.20021	−0.600104	+	0.799922i	$0.704874\pi$
$752$	−10.5112	−0.383303
$753$	24.3219	0.886338
$754$	−0.285145	−0.0103844
$755$	3.92108	0.142703
$756$	−2.27129	−0.0826061
$757$	48.3175	1.75613	0.878064	−	0.478543i	$-0.158835\pi$
$757$	48.3175	1.75613	0.878064	+	0.478543i	$0.158835\pi$
$758$	−5.06559	−0.183990
$759$	14.0397	0.509608
$760$	−0.568428	−0.0206190
$761$	15.1021	0.547449	0.273725	−	0.961808i	$-0.411744\pi$
$761$	15.1021	0.547449	0.273725	+	0.961808i	$0.411744\pi$
$762$	22.5037	0.815224
$763$	−15.7483	−0.570126
$764$	11.6703	0.422218
$765$	0.225515	0.00815351
$766$	−7.62919	−0.275654
$767$	−12.8286	−0.463215
$768$	1.00000	0.0360844
$769$	−33.1059	−1.19383	−0.596914	−	0.802305i	$-0.703607\pi$
$769$	−33.1059	−1.19383	−0.596914	+	0.802305i	$0.703607\pi$
$770$	−1.09047	−0.0392979
$771$	−4.59049	−0.165322
$772$	22.6608	0.815581
$773$	36.0016	1.29489	0.647443	−	0.762114i	$-0.275838\pi$
$773$	36.0016	1.29489	0.647443	+	0.762114i	$0.275838\pi$
$774$	8.05978	0.289703
$775$	−48.2055	−1.73159
$776$	−12.7299	−0.456977
$777$	21.5312	0.772427
$778$	21.7999	0.781563
$779$	4.10572	0.147103
$780$	−0.176895	−0.00633387
$781$	−7.80982	−0.279457
$782$	6.59464	0.235824
$783$	−0.285145	−0.0101903
$784$	−1.84124	−0.0657584
$785$	1.32437	0.0472689
$786$	−7.67061	−0.273601
$787$	4.73682	0.168849	0.0844247	−	0.996430i	$-0.473095\pi$
$787$	4.73682	0.168849	0.0844247	+	0.996430i	$0.473095\pi$
$788$	18.2090	0.648669
$789$	9.20402	0.327672
$790$	1.17434	0.0417813
$791$	3.79143	0.134808
$792$	−2.71409	−0.0964411
$793$	−5.88767	−0.209077
$794$	8.50492	0.301828
$795$	0.283175	0.0100432
$796$	12.2916	0.435663
$797$	−21.6794	−0.767923	−0.383962	−	0.923349i	$-0.625441\pi$
$797$	−21.6794	−0.767923	−0.383962	+	0.923349i	$0.625441\pi$
$798$	−7.29847	−0.258363
$799$	13.4002	0.474064
$800$	−4.96871	−0.175670
$801$	−0.653992	−0.0231077
$802$	15.7272	0.555347
$803$	−39.4618	−1.39258
$804$	−5.59876	−0.197453
$805$	−2.07836	−0.0732527
$806$	9.70181	0.341732
$807$	−23.4505	−0.825498
$808$	−6.23848	−0.219469
$809$	−30.9493	−1.08812	−0.544060	−	0.839046i	$-0.683114\pi$
$809$	−30.9493	−1.08812	−0.544060	+	0.839046i	$0.683114\pi$
$810$	−0.176895	−0.00621547
$811$	37.7469	1.32547	0.662737	−	0.748852i	$-0.269395\pi$
$811$	37.7469	1.32547	0.662737	+	0.748852i	$0.269395\pi$
$812$	0.647648	0.0227280
$813$	8.79415	0.308424
$814$	25.7288	0.901795
$815$	1.81589	0.0636079
$816$	−1.27485	−0.0446287
$817$	25.8989	0.906089
$818$	−34.0608	−1.19091
$819$	−2.27129	−0.0793653
$820$	−0.226020	−0.00789296
$821$	3.95792	0.138132	0.0690661	−	0.997612i	$-0.477998\pi$
$821$	3.95792	0.138132	0.0690661	+	0.997612i	$0.477998\pi$
$822$	−10.5486	−0.367926
$823$	31.8005	1.10850	0.554249	−	0.832351i	$-0.313006\pi$
$823$	31.8005	1.10850	0.554249	+	0.832351i	$0.313006\pi$
$824$	1.00000	0.0348367
$825$	13.4855	0.469506
$826$	29.1375	1.01382
$827$	33.1679	1.15336	0.576680	−	0.816970i	$-0.304348\pi$
$827$	33.1679	1.15336	0.576680	+	0.816970i	$0.304348\pi$
$828$	−5.17288	−0.179770
$829$	−31.9306	−1.10900	−0.554498	−	0.832185i	$-0.687090\pi$
$829$	−31.9306	−1.10900	−0.554498	+	0.832185i	$0.687090\pi$
$830$	−0.0128514	−0.000446079 0
$831$	−18.3506	−0.636574
$832$	1.00000	0.0346688
$833$	2.34730	0.0813291
$834$	−16.2854	−0.563918
$835$	1.84515	0.0638541
$836$	−8.72135	−0.301634
$837$	9.70181	0.335344
$838$	−2.24624	−0.0775952
$839$	−23.6933	−0.817983	−0.408991	−	0.912538i	$-0.634119\pi$
$839$	−23.6933	−0.817983	−0.408991	+	0.912538i	$0.634119\pi$
$840$	0.401781	0.0138628
$841$	−28.9187	−0.997196
$842$	38.1757	1.31562
$843$	18.9440	0.652465
$844$	13.5139	0.465168
$845$	−0.176895	−0.00608539
$846$	−10.5112	−0.361381
$847$	8.25317	0.283582
$848$	−1.60081	−0.0549719
$849$	−12.9387	−0.444054
$850$	6.33435	0.217267
$851$	49.0374	1.68098
$852$	2.87751	0.0985817
$853$	4.20275	0.143899	0.0719497	−	0.997408i	$-0.477078\pi$
$853$	4.20275	0.143899	0.0719497	+	0.997408i	$0.477078\pi$
$854$	13.3726	0.457601
$855$	−0.568428	−0.0194398
$856$	−11.5703	−0.395465
$857$	20.2970	0.693334	0.346667	−	0.937988i	$-0.387313\pi$
$857$	20.2970	0.693334	0.346667	+	0.937988i	$0.387313\pi$
$858$	−2.71409	−0.0926577
$859$	−47.4721	−1.61973	−0.809863	−	0.586619i	$-0.800459\pi$
$859$	−47.4721	−1.61973	−0.809863	+	0.586619i	$0.800459\pi$
$860$	−1.42574	−0.0486173
$861$	−2.90204	−0.0989012
$862$	25.0726	0.853976
$863$	46.6099	1.58662	0.793310	−	0.608817i	$-0.208356\pi$
$863$	46.6099	1.58662	0.793310	+	0.608817i	$0.208356\pi$
$864$	1.00000	0.0340207
$865$	−0.0384080	−0.00130591
$866$	−26.0304	−0.884551
$867$	−15.3748	−0.522154
$868$	−22.0356	−0.747939
$869$	18.0179	0.611215
$870$	0.0504409	0.00171011
$871$	−5.59876	−0.189707
$872$	6.93363	0.234802
$873$	−12.7299	−0.430842
$874$	−16.6223	−0.562258
$875$	−4.00524	−0.135402
$876$	14.5396	0.491247
$877$	15.5316	0.524464	0.262232	−	0.965005i	$-0.415542\pi$
$877$	15.5316	0.524464	0.262232	+	0.965005i	$0.415542\pi$
$878$	−11.6922	−0.394594
$879$	29.3750	0.990796
$880$	0.480111	0.0161845
$881$	40.1055	1.35119	0.675594	−	0.737273i	$-0.263887\pi$
$881$	40.1055	1.35119	0.675594	+	0.737273i	$0.263887\pi$
$882$	−1.84124	−0.0619976
$883$	26.6775	0.897770	0.448885	−	0.893590i	$-0.351821\pi$
$883$	26.6775	0.897770	0.448885	+	0.893590i	$0.351821\pi$
$884$	−1.27485	−0.0428778
$885$	2.26932	0.0762825
$886$	30.0093	1.00818
$887$	−24.7471	−0.830927	−0.415463	−	0.909610i	$-0.636381\pi$
$887$	−24.7471	−0.830927	−0.415463	+	0.909610i	$0.636381\pi$
$888$	−9.47971	−0.318118
$889$	−51.1125	−1.71426
$890$	0.115688	0.00387788
$891$	−2.71409	−0.0909256
$892$	−16.3292	−0.546743
$893$	−33.7761	−1.13028
$894$	−0.0615531	−0.00205864
$895$	2.51039	0.0839132
$896$	−2.27129	−0.0758785
$897$	−5.17288	−0.172717
$898$	−37.0292	−1.23568
$899$	−2.76643	−0.0922655
$900$	−4.96871	−0.165624
$901$	2.04079	0.0679885
$902$	−3.46781	−0.115465
$903$	−18.3061	−0.609189
$904$	−1.66928	−0.0555196
$905$	−0.205453	−0.00682950
$906$	−22.1661	−0.736419
$907$	40.1069	1.33173	0.665864	−	0.746073i	$-0.268063\pi$
$907$	40.1069	1.33173	0.665864	+	0.746073i	$0.268063\pi$
$908$	−18.7344	−0.621723
$909$	−6.23848	−0.206917
$910$	0.401781	0.0133189
$911$	−40.7050	−1.34862	−0.674308	−	0.738450i	$-0.735558\pi$
$911$	−40.7050	−1.34862	−0.674308	+	0.738450i	$0.735558\pi$
$912$	3.21336	0.106405
$913$	−0.197178	−0.00652566
$914$	−5.35914	−0.177265
$915$	1.04150	0.0344310
$916$	10.1789	0.336320
$917$	17.4222	0.575331
$918$	−1.27485	−0.0420763
$919$	9.78953	0.322927	0.161463	−	0.986879i	$-0.448379\pi$
$919$	9.78953	0.322927	0.161463	+	0.986879i	$0.448379\pi$
$920$	0.915059	0.0301686
$921$	6.16534	0.203155
$922$	3.26454	0.107512
$923$	2.87751	0.0947143
$924$	6.16450	0.202797
$925$	47.1019	1.54870
$926$	26.1498	0.859337
$927$	1.00000	0.0328443
$928$	−0.285145	−0.00936035
$929$	17.7964	0.583882	0.291941	−	0.956436i	$-0.405699\pi$
$929$	17.7964	0.583882	0.291941	+	0.956436i	$0.405699\pi$
$930$	−1.71621	−0.0562766
$931$	−5.91655	−0.193907
$932$	7.07885	0.231875
$933$	−23.7221	−0.776625
$934$	38.6655	1.26517
$935$	−0.612069	−0.0200168
$936$	1.00000	0.0326860
$937$	51.6569	1.68756	0.843778	−	0.536692i	$-0.180326\pi$
$937$	51.6569	1.68756	0.843778	+	0.536692i	$0.180326\pi$
$938$	12.7164	0.415206
$939$	−27.9972	−0.913656
$940$	1.85938	0.0606462
$941$	−51.2893	−1.67198	−0.835991	−	0.548743i	$-0.815107\pi$
$941$	−51.2893	−1.67198	−0.835991	+	0.548743i	$0.815107\pi$
$942$	−7.48677	−0.243932
$943$	−6.60941	−0.215232
$944$	−12.8286	−0.417536
$945$	0.401781	0.0130699
$946$	−21.8750	−0.711218
$947$	−48.1169	−1.56359	−0.781794	−	0.623537i	$-0.785695\pi$
$947$	−48.1169	−1.56359	−0.781794	+	0.623537i	$0.785695\pi$
$948$	−6.63863	−0.215613
$949$	14.5396	0.471974
$950$	−15.9662	−0.518013
$951$	−18.7148	−0.606869
$952$	2.89555	0.0938455
$953$	23.0991	0.748253	0.374126	−	0.927378i	$-0.377943\pi$
$953$	23.0991	0.748253	0.374126	+	0.927378i	$0.377943\pi$
$954$	−1.60081	−0.0518280
$955$	−2.06443	−0.0668033
$956$	−1.44245	−0.0466522
$957$	0.773911	0.0250170
$958$	35.5368	1.14814
$959$	23.9590	0.773677
$960$	−0.176895	−0.00570927
$961$	63.1252	2.03630
$962$	−9.47971	−0.305638
$963$	−11.5703	−0.372848
$964$	−5.60544	−0.180539
$965$	−4.00860	−0.129041
$966$	11.7491	0.378022
$967$	8.44094	0.271442	0.135721	−	0.990747i	$-0.456665\pi$
$967$	8.44094	0.271442	0.135721	+	0.990747i	$0.456665\pi$
$968$	−3.63369	−0.116791
$969$	−4.09654	−0.131600
$970$	2.25186	0.0723029
$971$	29.1344	0.934969	0.467484	−	0.884001i	$-0.345160\pi$
$971$	29.1344	0.934969	0.467484	+	0.884001i	$0.345160\pi$
$972$	1.00000	0.0320750
$973$	36.9889	1.18581
$974$	37.1580	1.19062
$975$	−4.96871	−0.159126
$976$	−5.88767	−0.188460
$977$	34.8260	1.11418	0.557091	−	0.830451i	$-0.311917\pi$
$977$	34.8260	1.11418	0.557091	+	0.830451i	$0.311917\pi$
$978$	−10.2653	−0.328250
$979$	1.77500	0.0567291
$980$	0.325706	0.0104043
$981$	6.93363	0.221374
$982$	16.7762	0.535350
$983$	18.1396	0.578563	0.289282	−	0.957244i	$-0.406584\pi$
$983$	18.1396	0.578563	0.289282	+	0.957244i	$0.406584\pi$
$984$	1.27770	0.0407317
$985$	−3.22109	−0.102632
$986$	0.363517	0.0115767
$987$	23.8739	0.759916
$988$	3.21336	0.102230
$989$	−41.6923	−1.32574
$990$	0.480111	0.0152589
$991$	−27.8138	−0.883533	−0.441767	−	0.897130i	$-0.645648\pi$
$991$	−27.8138	−0.883533	−0.441767	+	0.897130i	$0.645648\pi$
$992$	9.70181	0.308033
$993$	13.3720	0.424349
$994$	−6.53566	−0.207298
$995$	−2.17432	−0.0689306
$996$	0.0726498	0.00230200
$997$	40.4673	1.28161	0.640806	−	0.767703i	$-0.278600\pi$
$997$	40.4673	1.28161	0.640806	+	0.767703i	$0.278600\pi$
$998$	−33.7571	−1.06856
$999$	−9.47971	−0.299925

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8034.2.a.p.1.7	✓	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8034.2.a.p.1.7	✓	8	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 8034 = 2 \cdot 3 \cdot 13 \cdot 103 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8034.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -0.176895 q^{5} +1.00000 q^{6} -2.27129 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -0.176895 q^{5} +1.00000 q^{6} -2.27129 q^{7} +1.00000 q^{8} +1.00000 q^{9} -0.176895 q^{10} -2.71409 q^{11} +1.00000 q^{12} +1.00000 q^{13} -2.27129 q^{14} -0.176895 q^{15} +1.00000 q^{16} -1.27485 q^{17} +1.00000 q^{18} +3.21336 q^{19} -0.176895 q^{20} -2.27129 q^{21} -2.71409 q^{22} -5.17288 q^{23} +1.00000 q^{24} -4.96871 q^{25} +1.00000 q^{26} +1.00000 q^{27} -2.27129 q^{28} -0.285145 q^{29} -0.176895 q^{30} +9.70181 q^{31} +1.00000 q^{32} -2.71409 q^{33} -1.27485 q^{34} +0.401781 q^{35} +1.00000 q^{36} -9.47971 q^{37} +3.21336 q^{38} +1.00000 q^{39} -0.176895 q^{40} +1.27770 q^{41} -2.27129 q^{42} +8.05978 q^{43} -2.71409 q^{44} -0.176895 q^{45} -5.17288 q^{46} -10.5112 q^{47} +1.00000 q^{48} -1.84124 q^{49} -4.96871 q^{50} -1.27485 q^{51} +1.00000 q^{52} -1.60081 q^{53} +1.00000 q^{54} +0.480111 q^{55} -2.27129 q^{56} +3.21336 q^{57} -0.285145 q^{58} -12.8286 q^{59} -0.176895 q^{60} -5.88767 q^{61} +9.70181 q^{62} -2.27129 q^{63} +1.00000 q^{64} -0.176895 q^{65} -2.71409 q^{66} -5.59876 q^{67} -1.27485 q^{68} -5.17288 q^{69} +0.401781 q^{70} +2.87751 q^{71} +1.00000 q^{72} +14.5396 q^{73} -9.47971 q^{74} -4.96871 q^{75} +3.21336 q^{76} +6.16450 q^{77} +1.00000 q^{78} -6.63863 q^{79} -0.176895 q^{80} +1.00000 q^{81} +1.27770 q^{82} +0.0726498 q^{83} -2.27129 q^{84} +0.225515 q^{85} +8.05978 q^{86} -0.285145 q^{87} -2.71409 q^{88} -0.653992 q^{89} -0.176895 q^{90} -2.27129 q^{91} -5.17288 q^{92} +9.70181 q^{93} -10.5112 q^{94} -0.568428 q^{95} +1.00000 q^{96} -12.7299 q^{97} -1.84124 q^{98} -2.71409 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 8 q^{2} + 8 q^{3} + 8 q^{4} - 8 q^{5} + 8 q^{6} - 6 q^{7} + 8 q^{8} + 8 q^{9}+O(q^{10}) \) 8 * q + 8 * q^2 + 8 * q^3 + 8 * q^4 - 8 * q^5 + 8 * q^6 - 6 * q^7 + 8 * q^8 + 8 * q^9	\( 8 q + 8 q^{2} + 8 q^{3} + 8 q^{4} - 8 q^{5} + 8 q^{6} - 6 q^{7} + 8 q^{8} + 8 q^{9} - 8 q^{10} - 7 q^{11} + 8 q^{12} + 8 q^{13} - 6 q^{14} - 8 q^{15} + 8 q^{16} - 20 q^{17} + 8 q^{18} - 12 q^{19} - 8 q^{20} - 6 q^{21} - 7 q^{22} - 14 q^{23} + 8 q^{24} - 2 q^{25} + 8 q^{26} + 8 q^{27} - 6 q^{28} - 25 q^{29} - 8 q^{30} - 12 q^{31} + 8 q^{32} - 7 q^{33} - 20 q^{34} - 18 q^{35} + 8 q^{36} - 15 q^{37} - 12 q^{38} + 8 q^{39} - 8 q^{40} - 18 q^{41} - 6 q^{42} - 8 q^{43} - 7 q^{44} - 8 q^{45} - 14 q^{46} - 12 q^{47} + 8 q^{48} - 8 q^{49} - 2 q^{50} - 20 q^{51} + 8 q^{52} - 25 q^{53} + 8 q^{54} - 8 q^{55} - 6 q^{56} - 12 q^{57} - 25 q^{58} - 9 q^{59} - 8 q^{60} - 2 q^{61} - 12 q^{62} - 6 q^{63} + 8 q^{64} - 8 q^{65} - 7 q^{66} - 8 q^{67} - 20 q^{68} - 14 q^{69} - 18 q^{70} - 13 q^{71} + 8 q^{72} - 2 q^{73} - 15 q^{74} - 2 q^{75} - 12 q^{76} - 5 q^{77} + 8 q^{78} + q^{79} - 8 q^{80} + 8 q^{81} - 18 q^{82} - 6 q^{83} - 6 q^{84} + 5 q^{85} - 8 q^{86} - 25 q^{87} - 7 q^{88} - 17 q^{89} - 8 q^{90} - 6 q^{91} - 14 q^{92} - 12 q^{93} - 12 q^{94} + 10 q^{95} + 8 q^{96} + 19 q^{97} - 8 q^{98} - 7 q^{99}+O(q^{100}) \) 8 * q + 8 * q^2 + 8 * q^3 + 8 * q^4 - 8 * q^5 + 8 * q^6 - 6 * q^7 + 8 * q^8 + 8 * q^9 - 8 * q^10 - 7 * q^11 + 8 * q^12 + 8 * q^13 - 6 * q^14 - 8 * q^15 + 8 * q^16 - 20 * q^17 + 8 * q^18 - 12 * q^19 - 8 * q^20 - 6 * q^21 - 7 * q^22 - 14 * q^23 + 8 * q^24 - 2 * q^25 + 8 * q^26 + 8 * q^27 - 6 * q^28 - 25 * q^29 - 8 * q^30 - 12 * q^31 + 8 * q^32 - 7 * q^33 - 20 * q^34 - 18 * q^35 + 8 * q^36 - 15 * q^37 - 12 * q^38 + 8 * q^39 - 8 * q^40 - 18 * q^41 - 6 * q^42 - 8 * q^43 - 7 * q^44 - 8 * q^45 - 14 * q^46 - 12 * q^47 + 8 * q^48 - 8 * q^49 - 2 * q^50 - 20 * q^51 + 8 * q^52 - 25 * q^53 + 8 * q^54 - 8 * q^55 - 6 * q^56 - 12 * q^57 - 25 * q^58 - 9 * q^59 - 8 * q^60 - 2 * q^61 - 12 * q^62 - 6 * q^63 + 8 * q^64 - 8 * q^65 - 7 * q^66 - 8 * q^67 - 20 * q^68 - 14 * q^69 - 18 * q^70 - 13 * q^71 + 8 * q^72 - 2 * q^73 - 15 * q^74 - 2 * q^75 - 12 * q^76 - 5 * q^77 + 8 * q^78 + q^79 - 8 * q^80 + 8 * q^81 - 18 * q^82 - 6 * q^83 - 6 * q^84 + 5 * q^85 - 8 * q^86 - 25 * q^87 - 7 * q^88 - 17 * q^89 - 8 * q^90 - 6 * q^91 - 14 * q^92 - 12 * q^93 - 12 * q^94 + 10 * q^95 + 8 * q^96 + 19 * q^97 - 8 * q^98 - 7 * q^99

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