LMFDB - Embedded newform 8034.2.a.s.1.1

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:	$10$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - 4x^{9} - 15x^{8} + 72x^{7} - 27x^{6} - 115x^{5} + 54x^{4} + 68x^{3} - 15x^{2} - 15x - 2 $ x^10 - 4x^9 - 15x^8 + 72x^7 - 27x^6 - 115x^5 + 54x^4 + 68x^3 - 15x^2 - 15*x - 2
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			1.1
Root			$-0.297898$ 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)

$f(q)$	$=$	$q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -4.09900 q^{5} +1.00000 q^{6} -3.00074 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -4.09900 q^{5} +1.00000 q^{6} -3.00074 q^{7} -1.00000 q^{8} +1.00000 q^{9} +4.09900 q^{10} +5.49150 q^{11} -1.00000 q^{12} -1.00000 q^{13} +3.00074 q^{14} +4.09900 q^{15} +1.00000 q^{16} +3.29864 q^{17} -1.00000 q^{18} -3.28293 q^{19} -4.09900 q^{20} +3.00074 q^{21} -5.49150 q^{22} -7.30311 q^{23} +1.00000 q^{24} +11.8018 q^{25} +1.00000 q^{26} -1.00000 q^{27} -3.00074 q^{28} -8.18560 q^{29} -4.09900 q^{30} -1.14159 q^{31} -1.00000 q^{32} -5.49150 q^{33} -3.29864 q^{34} +12.3000 q^{35} +1.00000 q^{36} -7.54165 q^{37} +3.28293 q^{38} +1.00000 q^{39} +4.09900 q^{40} -11.1898 q^{41} -3.00074 q^{42} +11.1479 q^{43} +5.49150 q^{44} -4.09900 q^{45} +7.30311 q^{46} +12.6586 q^{47} -1.00000 q^{48} +2.00445 q^{49} -11.8018 q^{50} -3.29864 q^{51} -1.00000 q^{52} +12.3552 q^{53} +1.00000 q^{54} -22.5096 q^{55} +3.00074 q^{56} +3.28293 q^{57} +8.18560 q^{58} +0.0926322 q^{59} +4.09900 q^{60} +1.02154 q^{61} +1.14159 q^{62} -3.00074 q^{63} +1.00000 q^{64} +4.09900 q^{65} +5.49150 q^{66} -12.0763 q^{67} +3.29864 q^{68} +7.30311 q^{69} -12.3000 q^{70} -1.06287 q^{71} -1.00000 q^{72} +4.32004 q^{73} +7.54165 q^{74} -11.8018 q^{75} -3.28293 q^{76} -16.4786 q^{77} -1.00000 q^{78} +3.54232 q^{79} -4.09900 q^{80} +1.00000 q^{81} +11.1898 q^{82} +14.0459 q^{83} +3.00074 q^{84} -13.5211 q^{85} -11.1479 q^{86} +8.18560 q^{87} -5.49150 q^{88} +5.66860 q^{89} +4.09900 q^{90} +3.00074 q^{91} -7.30311 q^{92} +1.14159 q^{93} -12.6586 q^{94} +13.4567 q^{95} +1.00000 q^{96} +9.68043 q^{97} -2.00445 q^{98} +5.49150 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q - 10 q^{2} - 10 q^{3} + 10 q^{4} + 6 q^{5} + 10 q^{6} - 9 q^{7} - 10 q^{8} + 10 q^{9}+O(q^{10}) $ 10 * q - 10 * q^2 - 10 * q^3 + 10 * q^4 + 6 * q^5 + 10 * q^6 - 9 * q^7 - 10 * q^8 + 10 * q^9	\( 10 q - 10 q^{2} - 10 q^{3} + 10 q^{4} + 6 q^{5} + 10 q^{6} - 9 q^{7} - 10 q^{8} + 10 q^{9} - 6 q^{10} - q^{11} - 10 q^{12} - 10 q^{13} + 9 q^{14} - 6 q^{15} + 10 q^{16} + 5 q^{17} - 10 q^{18} - 9 q^{19} + 6 q^{20} + 9 q^{21} + q^{22} + q^{23} + 10 q^{24} + 20 q^{25} + 10 q^{26} - 10 q^{27} - 9 q^{28} - 22 q^{29} + 6 q^{30} - 13 q^{31} - 10 q^{32} + q^{33} - 5 q^{34} + 14 q^{35} + 10 q^{36} + 10 q^{37} + 9 q^{38} + 10 q^{39} - 6 q^{40} - 18 q^{41} - 9 q^{42} + 10 q^{43} - q^{44} + 6 q^{45} - q^{46} + 28 q^{47} - 10 q^{48} + 11 q^{49} - 20 q^{50} - 5 q^{51} - 10 q^{52} + 6 q^{53} + 10 q^{54} - 26 q^{55} + 9 q^{56} + 9 q^{57} + 22 q^{58} + 7 q^{59} - 6 q^{60} - 20 q^{61} + 13 q^{62} - 9 q^{63} + 10 q^{64} - 6 q^{65} - q^{66} - 21 q^{67} + 5 q^{68} - q^{69} - 14 q^{70} - 19 q^{71} - 10 q^{72} + 3 q^{73} - 10 q^{74} - 20 q^{75} - 9 q^{76} + 28 q^{77} - 10 q^{78} - 11 q^{79} + 6 q^{80} + 10 q^{81} + 18 q^{82} + 20 q^{83} + 9 q^{84} - q^{85} - 10 q^{86} + 22 q^{87} + q^{88} + 22 q^{89} - 6 q^{90} + 9 q^{91} + q^{92} + 13 q^{93} - 28 q^{94} + 10 q^{96} - 10 q^{97} - 11 q^{98} - q^{99}+O(q^{100}) \) 10 * q - 10 * q^2 - 10 * q^3 + 10 * q^4 + 6 * q^5 + 10 * q^6 - 9 * q^7 - 10 * q^8 + 10 * q^9 - 6 * q^10 - q^11 - 10 * q^12 - 10 * q^13 + 9 * q^14 - 6 * q^15 + 10 * q^16 + 5 * q^17 - 10 * q^18 - 9 * q^19 + 6 * q^20 + 9 * q^21 + q^22 + q^23 + 10 * q^24 + 20 * q^25 + 10 * q^26 - 10 * q^27 - 9 * q^28 - 22 * q^29 + 6 * q^30 - 13 * q^31 - 10 * q^32 + q^33 - 5 * q^34 + 14 * q^35 + 10 * q^36 + 10 * q^37 + 9 * q^38 + 10 * q^39 - 6 * q^40 - 18 * q^41 - 9 * q^42 + 10 * q^43 - q^44 + 6 * q^45 - q^46 + 28 * q^47 - 10 * q^48 + 11 * q^49 - 20 * q^50 - 5 * q^51 - 10 * q^52 + 6 * q^53 + 10 * q^54 - 26 * q^55 + 9 * q^56 + 9 * q^57 + 22 * q^58 + 7 * q^59 - 6 * q^60 - 20 * q^61 + 13 * q^62 - 9 * q^63 + 10 * q^64 - 6 * q^65 - q^66 - 21 * q^67 + 5 * q^68 - q^69 - 14 * q^70 - 19 * q^71 - 10 * q^72 + 3 * q^73 - 10 * q^74 - 20 * q^75 - 9 * q^76 + 28 * q^77 - 10 * q^78 - 11 * q^79 + 6 * q^80 + 10 * q^81 + 18 * q^82 + 20 * q^83 + 9 * q^84 - q^85 - 10 * q^86 + 22 * q^87 + q^88 + 22 * q^89 - 6 * q^90 + 9 * q^91 + q^92 + 13 * q^93 - 28 * q^94 + 10 * q^96 - 10 * q^97 - 11 * q^98 - 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
$5$	−4.09900	−1.83313	−0.916564	−	0.399889i	$-0.869049\pi$
$5$	−4.09900	−1.83313	−0.916564	+	0.399889i	$0.869049\pi$
$6$	1.00000	0.408248
$7$	−3.00074	−1.13417	−0.567087	−	0.823658i	$-0.691930\pi$
$7$	−3.00074	−1.13417	−0.567087	+	0.823658i	$0.691930\pi$
$8$	−1.00000	−0.353553
$9$	1.00000	0.333333
$10$	4.09900	1.29622
$11$	5.49150	1.65575	0.827874	−	0.560914i	$-0.189550\pi$
$11$	5.49150	1.65575	0.827874	+	0.560914i	$0.189550\pi$
$12$	−1.00000	−0.288675
$13$	−1.00000	−0.277350
$13$	−1.00000	−0.277350
$14$	3.00074	0.801982
$15$	4.09900	1.05836
$16$	1.00000	0.250000
$17$	3.29864	0.800038	0.400019	−	0.916507i	$-0.369004\pi$
$17$	3.29864	0.800038	0.400019	+	0.916507i	$0.369004\pi$
$18$	−1.00000	−0.235702
$19$	−3.28293	−0.753155	−0.376577	−	0.926385i	$-0.622899\pi$
$19$	−3.28293	−0.753155	−0.376577	+	0.926385i	$0.622899\pi$
$20$	−4.09900	−0.916564
$21$	3.00074	0.654815
$22$	−5.49150	−1.17079
$23$	−7.30311	−1.52280	−0.761402	−	0.648280i	$-0.775488\pi$
$23$	−7.30311	−1.52280	−0.761402	+	0.648280i	$0.775488\pi$
$24$	1.00000	0.204124
$25$	11.8018	2.36036
$26$	1.00000	0.196116
$27$	−1.00000	−0.192450
$28$	−3.00074	−0.567087
$29$	−8.18560	−1.52003	−0.760014	−	0.649907i	$-0.774808\pi$
$29$	−8.18560	−1.52003	−0.760014	+	0.649907i	$0.774808\pi$
$30$	−4.09900	−0.748371
$31$	−1.14159	−0.205036	−0.102518	−	0.994731i	$-0.532690\pi$
$31$	−1.14159	−0.205036	−0.102518	+	0.994731i	$0.532690\pi$
$32$	−1.00000	−0.176777
$33$	−5.49150	−0.955947
$34$	−3.29864	−0.565712
$35$	12.3000	2.07908
$36$	1.00000	0.166667
$37$	−7.54165	−1.23984	−0.619920	−	0.784665i	$-0.712835\pi$
$37$	−7.54165	−1.23984	−0.619920	+	0.784665i	$0.712835\pi$
$38$	3.28293	0.532561
$39$	1.00000	0.160128
$40$	4.09900	0.648108
$41$	−11.1898	−1.74756	−0.873780	−	0.486321i	$-0.838339\pi$
$41$	−11.1898	−1.74756	−0.873780	+	0.486321i	$0.838339\pi$
$42$	−3.00074	−0.463024
$43$	11.1479	1.70004	0.850022	−	0.526748i	$-0.176589\pi$
$43$	11.1479	1.70004	0.850022	+	0.526748i	$0.176589\pi$
$44$	5.49150	0.827874
$45$	−4.09900	−0.611042
$46$	7.30311	1.07678
$47$	12.6586	1.84644	0.923222	−	0.384266i	$-0.125545\pi$
$47$	12.6586	1.84644	0.923222	+	0.384266i	$0.125545\pi$
$48$	−1.00000	−0.144338
$49$	2.00445	0.286350
$50$	−11.8018	−1.66902
$51$	−3.29864	−0.461902
$52$	−1.00000	−0.138675
$53$	12.3552	1.69712	0.848562	−	0.529096i	$-0.177469\pi$
$53$	12.3552	1.69712	0.848562	+	0.529096i	$0.177469\pi$
$54$	1.00000	0.136083
$55$	−22.5096	−3.03520
$56$	3.00074	0.400991
$57$	3.28293	0.434834
$58$	8.18560	1.07482
$59$	0.0926322	0.0120597	0.00602984	−	0.999982i	$-0.498081\pi$
$59$	0.0926322	0.0120597	0.00602984	+	0.999982i	$0.498081\pi$
$60$	4.09900	0.529178
$61$	1.02154	0.130795	0.0653974	−	0.997859i	$-0.479168\pi$
$61$	1.02154	0.130795	0.0653974	+	0.997859i	$0.479168\pi$
$62$	1.14159	0.144982
$63$	−3.00074	−0.378058
$64$	1.00000	0.125000
$65$	4.09900	0.508418
$66$	5.49150	0.675956
$67$	−12.0763	−1.47536	−0.737679	−	0.675152i	$-0.764078\pi$
$67$	−12.0763	−1.47536	−0.737679	+	0.675152i	$0.764078\pi$
$68$	3.29864	0.400019
$69$	7.30311	0.879191
$70$	−12.3000	−1.47013
$71$	−1.06287	−0.126139	−0.0630697	−	0.998009i	$-0.520089\pi$
$71$	−1.06287	−0.126139	−0.0630697	+	0.998009i	$0.520089\pi$
$72$	−1.00000	−0.117851
$73$	4.32004	0.505623	0.252811	−	0.967516i	$-0.418645\pi$
$73$	4.32004	0.505623	0.252811	+	0.967516i	$0.418645\pi$
$74$	7.54165	0.876699
$75$	−11.8018	−1.36275
$76$	−3.28293	−0.376577
$77$	−16.4786	−1.87791
$78$	−1.00000	−0.113228
$79$	3.54232	0.398542	0.199271	−	0.979944i	$-0.436143\pi$
$79$	3.54232	0.398542	0.199271	+	0.979944i	$0.436143\pi$
$80$	−4.09900	−0.458282
$81$	1.00000	0.111111
$82$	11.1898	1.23571
$83$	14.0459	1.54173	0.770866	−	0.636997i	$-0.219824\pi$
$83$	14.0459	1.54173	0.770866	+	0.636997i	$0.219824\pi$
$84$	3.00074	0.327408
$85$	−13.5211	−1.46657
$86$	−11.1479	−1.20211
$87$	8.18560	0.877588
$88$	−5.49150	−0.585395
$89$	5.66860	0.600870	0.300435	−	0.953802i	$-0.402868\pi$
$89$	5.66860	0.600870	0.300435	+	0.953802i	$0.402868\pi$
$90$	4.09900	0.432072
$91$	3.00074	0.314563
$92$	−7.30311	−0.761402
$93$	1.14159	0.118377
$94$	−12.6586	−1.30563
$95$	13.4567	1.38063
$96$	1.00000	0.102062
$97$	9.68043	0.982898	0.491449	−	0.870906i	$-0.336467\pi$
$97$	9.68043	0.982898	0.491449	+	0.870906i	$0.336467\pi$
$98$	−2.00445	−0.202480
$99$	5.49150	0.551916
$100$	11.8018	1.18018
$101$	9.83117	0.978238	0.489119	−	0.872217i	$-0.337318\pi$
$101$	9.83117	0.978238	0.489119	+	0.872217i	$0.337318\pi$
$102$	3.29864	0.326614
$103$	−1.00000	−0.0985329
$103$	−1.00000	−0.0985329
$104$	1.00000	0.0980581
$105$	−12.3000	−1.20036
$106$	−12.3552	−1.20005
$107$	13.3163	1.28734	0.643670	−	0.765303i	$-0.277411\pi$
$107$	13.3163	1.28734	0.643670	+	0.765303i	$0.277411\pi$
$108$	−1.00000	−0.0962250
$109$	−12.2924	−1.17740	−0.588701	−	0.808351i	$-0.700360\pi$
$109$	−12.2924	−1.17740	−0.588701	+	0.808351i	$0.700360\pi$
$110$	22.5096	2.14621
$111$	7.54165	0.715822
$112$	−3.00074	−0.283543
$113$	8.74494	0.822655	0.411327	−	0.911488i	$-0.365065\pi$
$113$	8.74494	0.822655	0.411327	+	0.911488i	$0.365065\pi$
$114$	−3.28293	−0.307474
$115$	29.9354	2.79149
$116$	−8.18560	−0.760014
$117$	−1.00000	−0.0924500
$118$	−0.0926322	−0.00852748
$119$	−9.89836	−0.907382
$120$	−4.09900	−0.374186
$121$	19.1565	1.74150
$122$	−1.02154	−0.0924859
$123$	11.1898	1.00895
$124$	−1.14159	−0.102518
$125$	−27.8805	−2.49371
$126$	3.00074	0.267327
$127$	−11.3506	−1.00721	−0.503603	−	0.863935i	$-0.667993\pi$
$127$	−11.3506	−1.00721	−0.503603	+	0.863935i	$0.667993\pi$
$128$	−1.00000	−0.0883883
$129$	−11.1479	−0.981521
$130$	−4.09900	−0.359506
$131$	10.6293	0.928682	0.464341	−	0.885656i	$-0.346291\pi$
$131$	10.6293	0.928682	0.464341	+	0.885656i	$0.346291\pi$
$132$	−5.49150	−0.477973
$133$	9.85121	0.854208
$134$	12.0763	1.04324
$135$	4.09900	0.352786
$136$	−3.29864	−0.282856
$137$	12.0265	1.02749	0.513747	−	0.857942i	$-0.328257\pi$
$137$	12.0265	1.02749	0.513747	+	0.857942i	$0.328257\pi$
$138$	−7.30311	−0.621682
$139$	−5.59254	−0.474353	−0.237177	−	0.971467i	$-0.576222\pi$
$139$	−5.59254	−0.474353	−0.237177	+	0.971467i	$0.576222\pi$
$140$	12.3000	1.03954
$141$	−12.6586	−1.06605
$142$	1.06287	0.0891940
$143$	−5.49150	−0.459222
$144$	1.00000	0.0833333
$145$	33.5528	2.78640
$146$	−4.32004	−0.357529
$147$	−2.00445	−0.165324
$148$	−7.54165	−0.619920
$149$	−15.1475	−1.24093	−0.620465	−	0.784234i	$-0.713056\pi$
$149$	−15.1475	−1.24093	−0.620465	+	0.784234i	$0.713056\pi$
$150$	11.8018	0.963611
$151$	0.505643	0.0411487	0.0205743	−	0.999788i	$-0.493451\pi$
$151$	0.505643	0.0411487	0.0205743	+	0.999788i	$0.493451\pi$
$152$	3.28293	0.266280
$153$	3.29864	0.266679
$154$	16.4786	1.32788
$155$	4.67938	0.375856
$156$	1.00000	0.0800641
$157$	2.96021	0.236250	0.118125	−	0.992999i	$-0.462312\pi$
$157$	2.96021	0.236250	0.118125	+	0.992999i	$0.462312\pi$
$158$	−3.54232	−0.281812
$159$	−12.3552	−0.979835
$160$	4.09900	0.324054
$161$	21.9147	1.72712
$162$	−1.00000	−0.0785674
$163$	17.0796	1.33777	0.668887	−	0.743364i	$-0.266771\pi$
$163$	17.0796	1.33777	0.668887	+	0.743364i	$0.266771\pi$
$164$	−11.1898	−0.873780
$165$	22.5096	1.75237
$166$	−14.0459	−1.09017
$167$	16.4047	1.26943	0.634716	−	0.772746i	$-0.281117\pi$
$167$	16.4047	1.26943	0.634716	+	0.772746i	$0.281117\pi$
$168$	−3.00074	−0.231512
$169$	1.00000	0.0769231
$170$	13.5211	1.03702
$171$	−3.28293	−0.251052
$172$	11.1479	0.850022
$173$	18.1033	1.37637	0.688185	−	0.725535i	$-0.258408\pi$
$173$	18.1033	1.37637	0.688185	+	0.725535i	$0.258408\pi$
$174$	−8.18560	−0.620549
$175$	−35.4141	−2.67705
$176$	5.49150	0.413937
$177$	−0.0926322	−0.00696266
$178$	−5.66860	−0.424880
$179$	11.8026	0.882167	0.441084	−	0.897466i	$-0.354594\pi$
$179$	11.8026	0.882167	0.441084	+	0.897466i	$0.354594\pi$
$180$	−4.09900	−0.305521
$181$	13.3538	0.992580	0.496290	−	0.868157i	$-0.334695\pi$
$181$	13.3538	0.992580	0.496290	+	0.868157i	$0.334695\pi$
$182$	−3.00074	−0.222430
$183$	−1.02154	−0.0755145
$184$	7.30311	0.538392
$185$	30.9132	2.27278
$186$	−1.14159	−0.0837055
$187$	18.1145	1.32466
$188$	12.6586	0.923222
$189$	3.00074	0.218272
$190$	−13.4567	−0.976252
$191$	−25.4836	−1.84393	−0.921963	−	0.387279i	$-0.873415\pi$
$191$	−25.4836	−1.84393	−0.921963	+	0.387279i	$0.873415\pi$
$192$	−1.00000	−0.0721688
$193$	−15.5011	−1.11579	−0.557896	−	0.829911i	$-0.688391\pi$
$193$	−15.5011	−1.11579	−0.557896	+	0.829911i	$0.688391\pi$
$194$	−9.68043	−0.695014
$195$	−4.09900	−0.293535
$196$	2.00445	0.143175
$197$	−6.11322	−0.435549	−0.217774	−	0.975999i	$-0.569880\pi$
$197$	−6.11322	−0.435549	−0.217774	+	0.975999i	$0.569880\pi$
$198$	−5.49150	−0.390264
$199$	5.71794	0.405334	0.202667	−	0.979248i	$-0.435039\pi$
$199$	5.71794	0.405334	0.202667	+	0.979248i	$0.435039\pi$
$200$	−11.8018	−0.834512
$201$	12.0763	0.851798
$202$	−9.83117	−0.691719
$203$	24.5629	1.72398
$204$	−3.29864	−0.230951
$205$	45.8672	3.20350
$206$	1.00000	0.0696733
$207$	−7.30311	−0.507601
$208$	−1.00000	−0.0693375
$209$	−18.0282	−1.24703
$210$	12.3000	0.848783
$211$	−23.5539	−1.62152	−0.810759	−	0.585380i	$-0.800945\pi$
$211$	−23.5539	−1.62152	−0.810759	+	0.585380i	$0.800945\pi$
$212$	12.3552	0.848562
$213$	1.06287	0.0728266
$214$	−13.3163	−0.910286
$215$	−45.6953	−3.11640
$216$	1.00000	0.0680414
$217$	3.42562	0.232546
$218$	12.2924	0.832548
$219$	−4.32004	−0.291921
$220$	−22.5096	−1.51760
$221$	−3.29864	−0.221890
$222$	−7.54165	−0.506162
$223$	−18.7087	−1.25283	−0.626415	−	0.779490i	$-0.715478\pi$
$223$	−18.7087	−1.25283	−0.626415	+	0.779490i	$0.715478\pi$
$224$	3.00074	0.200495
$225$	11.8018	0.786785
$226$	−8.74494	−0.581705
$227$	−29.0106	−1.92550	−0.962751	−	0.270390i	$-0.912847\pi$
$227$	−29.0106	−1.92550	−0.962751	+	0.270390i	$0.912847\pi$
$228$	3.28293	0.217417
$229$	4.97298	0.328624	0.164312	−	0.986408i	$-0.447460\pi$
$229$	4.97298	0.328624	0.164312	+	0.986408i	$0.447460\pi$
$230$	−29.9354	−1.97388
$231$	16.4786	1.08421
$232$	8.18560	0.537411
$233$	−5.62501	−0.368507	−0.184253	−	0.982879i	$-0.558987\pi$
$233$	−5.62501	−0.368507	−0.184253	+	0.982879i	$0.558987\pi$
$234$	1.00000	0.0653720
$235$	−51.8875	−3.38477
$236$	0.0926322	0.00602984
$237$	−3.54232	−0.230099
$238$	9.89836	0.641616
$239$	−10.9696	−0.709567	−0.354784	−	0.934948i	$-0.615445\pi$
$239$	−10.9696	−0.709567	−0.354784	+	0.934948i	$0.615445\pi$
$240$	4.09900	0.264589
$241$	8.12615	0.523451	0.261726	−	0.965142i	$-0.415708\pi$
$241$	8.12615	0.523451	0.261726	+	0.965142i	$0.415708\pi$
$242$	−19.1565	−1.23143
$243$	−1.00000	−0.0641500
$244$	1.02154	0.0653974
$245$	−8.21623	−0.524916
$246$	−11.1898	−0.713439
$247$	3.28293	0.208888
$248$	1.14159	0.0724911
$249$	−14.0459	−0.890120
$250$	27.8805	1.76332
$251$	15.4133	0.972877	0.486439	−	0.873715i	$-0.338296\pi$
$251$	15.4133	0.972877	0.486439	+	0.873715i	$0.338296\pi$
$252$	−3.00074	−0.189029
$253$	−40.1050	−2.52138
$254$	11.3506	0.712202
$255$	13.5211	0.846725
$256$	1.00000	0.0625000
$257$	−11.6822	−0.728714	−0.364357	−	0.931259i	$-0.618711\pi$
$257$	−11.6822	−0.728714	−0.364357	+	0.931259i	$0.618711\pi$
$258$	11.1479	0.694040
$259$	22.6305	1.40619
$260$	4.09900	0.254209
$261$	−8.18560	−0.506676
$262$	−10.6293	−0.656678
$263$	−0.114081	−0.00703454	−0.00351727	−	0.999994i	$-0.501120\pi$
$263$	−0.114081	−0.00703454	−0.00351727	+	0.999994i	$0.501120\pi$
$264$	5.49150	0.337978
$265$	−50.6441	−3.11104
$266$	−9.85121	−0.604016
$267$	−5.66860	−0.346913
$268$	−12.0763	−0.737679
$269$	−13.0625	−0.796432	−0.398216	−	0.917292i	$-0.630371\pi$
$269$	−13.0625	−0.796432	−0.398216	+	0.917292i	$0.630371\pi$
$270$	−4.09900	−0.249457
$271$	1.02651	0.0623562	0.0311781	−	0.999514i	$-0.490074\pi$
$271$	1.02651	0.0623562	0.0311781	+	0.999514i	$0.490074\pi$
$272$	3.29864	0.200009
$273$	−3.00074	−0.181613
$274$	−12.0265	−0.726548
$275$	64.8094	3.90815
$276$	7.30311	0.439595
$277$	−11.7430	−0.705566	−0.352783	−	0.935705i	$-0.614765\pi$
$277$	−11.7430	−0.705566	−0.352783	+	0.935705i	$0.614765\pi$
$278$	5.59254	0.335418
$279$	−1.14159	−0.0683452
$280$	−12.3000	−0.735067
$281$	−18.9654	−1.13138	−0.565691	−	0.824617i	$-0.691390\pi$
$281$	−18.9654	−1.13138	−0.565691	+	0.824617i	$0.691390\pi$
$282$	12.6586	0.753808
$283$	−12.3622	−0.734859	−0.367430	−	0.930051i	$-0.619762\pi$
$283$	−12.3622	−0.734859	−0.367430	+	0.930051i	$0.619762\pi$
$284$	−1.06287	−0.0630697
$285$	−13.4567	−0.797106
$286$	5.49150	0.324719
$287$	33.5778	1.98204
$288$	−1.00000	−0.0589256
$289$	−6.11898	−0.359940
$290$	−33.5528	−1.97029
$291$	−9.68043	−0.567477
$292$	4.32004	0.252811
$293$	10.9274	0.638383	0.319191	−	0.947690i	$-0.396589\pi$
$293$	10.9274	0.638383	0.319191	+	0.947690i	$0.396589\pi$
$294$	2.00445	0.116902
$295$	−0.379699	−0.0221069
$296$	7.54165	0.438350
$297$	−5.49150	−0.318649
$298$	15.1475	0.877470
$299$	7.30311	0.422350
$300$	−11.8018	−0.681376
$301$	−33.4521	−1.92814
$302$	−0.505643	−0.0290965
$303$	−9.83117	−0.564786
$304$	−3.28293	−0.188289
$305$	−4.18729	−0.239764
$306$	−3.29864	−0.188571
$307$	8.74651	0.499190	0.249595	−	0.968350i	$-0.419703\pi$
$307$	8.74651	0.499190	0.249595	+	0.968350i	$0.419703\pi$
$308$	−16.4786	−0.938953
$309$	1.00000	0.0568880
$310$	−4.67938	−0.265771
$311$	12.6819	0.719123	0.359562	−	0.933121i	$-0.382926\pi$
$311$	12.6819	0.719123	0.359562	+	0.933121i	$0.382926\pi$
$312$	−1.00000	−0.0566139
$313$	6.64211	0.375434	0.187717	−	0.982223i	$-0.439891\pi$
$313$	6.64211	0.375434	0.187717	+	0.982223i	$0.439891\pi$
$314$	−2.96021	−0.167054
$315$	12.3000	0.693028
$316$	3.54232	0.199271
$317$	27.2292	1.52934	0.764672	−	0.644420i	$-0.222901\pi$
$317$	27.2292	1.52934	0.764672	+	0.644420i	$0.222901\pi$
$318$	12.3552	0.692848
$319$	−44.9512	−2.51678
$320$	−4.09900	−0.229141
$321$	−13.3163	−0.743246
$322$	−21.9147	−1.22126
$323$	−10.8292	−0.602552
$324$	1.00000	0.0555556
$325$	−11.8018	−0.654645
$326$	−17.0796	−0.945949
$327$	12.2924	0.679773
$328$	11.1898	0.617856
$329$	−37.9852	−2.09419
$330$	−22.5096	−1.23911
$331$	−9.40347	−0.516862	−0.258431	−	0.966030i	$-0.583205\pi$
$331$	−9.40347	−0.516862	−0.258431	+	0.966030i	$0.583205\pi$
$332$	14.0459	0.770866
$333$	−7.54165	−0.413280
$334$	−16.4047	−0.897623
$335$	49.5008	2.70452
$336$	3.00074	0.163704
$337$	−19.4972	−1.06208	−0.531041	−	0.847346i	$-0.678199\pi$
$337$	−19.4972	−1.06208	−0.531041	+	0.847346i	$0.678199\pi$
$338$	−1.00000	−0.0543928
$339$	−8.74494	−0.474960
$340$	−13.5211	−0.733285
$341$	−6.26904	−0.339487
$342$	3.28293	0.177520
$343$	14.9904	0.809403
$344$	−11.1479	−0.601056
$345$	−29.9354	−1.61167
$346$	−18.1033	−0.973241
$347$	17.1464	0.920469	0.460235	−	0.887797i	$-0.347765\pi$
$347$	17.1464	0.920469	0.460235	+	0.887797i	$0.347765\pi$
$348$	8.18560	0.438794
$349$	24.2217	1.29656	0.648278	−	0.761403i	$-0.275489\pi$
$349$	24.2217	1.29656	0.648278	+	0.761403i	$0.275489\pi$
$350$	35.4141	1.89296
$351$	1.00000	0.0533761
$352$	−5.49150	−0.292698
$353$	6.52930	0.347520	0.173760	−	0.984788i	$-0.444408\pi$
$353$	6.52930	0.347520	0.173760	+	0.984788i	$0.444408\pi$
$354$	0.0926322	0.00492334
$355$	4.35670	0.231229
$356$	5.66860	0.300435
$357$	9.89836	0.523877
$358$	−11.8026	−0.623786
$359$	27.3163	1.44170	0.720850	−	0.693091i	$-0.243752\pi$
$359$	27.3163	1.44170	0.720850	+	0.693091i	$0.243752\pi$
$360$	4.09900	0.216036
$361$	−8.22240	−0.432758
$362$	−13.3538	−0.701860
$363$	−19.1565	−1.00546
$364$	3.00074	0.157282
$365$	−17.7078	−0.926871
$366$	1.02154	0.0533968
$367$	−29.8312	−1.55718	−0.778588	−	0.627536i	$-0.784064\pi$
$367$	−29.8312	−1.55718	−0.778588	+	0.627536i	$0.784064\pi$
$368$	−7.30311	−0.380701
$369$	−11.1898	−0.582520
$370$	−30.9132	−1.60710
$371$	−37.0749	−1.92483
$372$	1.14159	0.0591887
$373$	18.1957	0.942136	0.471068	−	0.882097i	$-0.343869\pi$
$373$	18.1957	0.942136	0.471068	+	0.882097i	$0.343869\pi$
$374$	−18.1145	−0.936677
$375$	27.8805	1.43974
$376$	−12.6586	−0.652817
$377$	8.18560	0.421580
$378$	−3.00074	−0.154341
$379$	−8.76132	−0.450039	−0.225019	−	0.974354i	$-0.572245\pi$
$379$	−8.76132	−0.450039	−0.225019	+	0.974354i	$0.572245\pi$
$380$	13.4567	0.690314
$381$	11.3506	0.581511
$382$	25.4836	1.30385
$383$	−7.54390	−0.385475	−0.192738	−	0.981250i	$-0.561737\pi$
$383$	−7.54390	−0.385475	−0.192738	+	0.981250i	$0.561737\pi$
$384$	1.00000	0.0510310
$385$	67.5456	3.44244
$386$	15.5011	0.788983
$387$	11.1479	0.566681
$388$	9.68043	0.491449
$389$	−35.1494	−1.78214	−0.891072	−	0.453863i	$-0.850046\pi$
$389$	−35.1494	−1.78214	−0.891072	+	0.453863i	$0.850046\pi$
$390$	4.09900	0.207561
$391$	−24.0903	−1.21830
$392$	−2.00445	−0.101240
$393$	−10.6293	−0.536175
$394$	6.11322	0.307980
$395$	−14.5200	−0.730579
$396$	5.49150	0.275958
$397$	−19.4035	−0.973835	−0.486917	−	0.873448i	$-0.661879\pi$
$397$	−19.4035	−0.973835	−0.486917	+	0.873448i	$0.661879\pi$
$398$	−5.71794	−0.286615
$399$	−9.85121	−0.493177
$400$	11.8018	0.590089
$401$	−23.1733	−1.15722	−0.578611	−	0.815604i	$-0.696405\pi$
$401$	−23.1733	−1.15722	−0.578611	+	0.815604i	$0.696405\pi$
$402$	−12.0763	−0.602312
$403$	1.14159	0.0568667
$404$	9.83117	0.489119
$405$	−4.09900	−0.203681
$406$	−24.5629	−1.21903
$407$	−41.4149	−2.05286
$408$	3.29864	0.163307
$409$	−36.6244	−1.81096	−0.905481	−	0.424387i	$-0.860490\pi$
$409$	−36.6244	−1.81096	−0.905481	+	0.424387i	$0.860490\pi$
$410$	−45.8672	−2.26522
$411$	−12.0265	−0.593224
$412$	−1.00000	−0.0492665
$413$	−0.277965	−0.0136778
$414$	7.30311	0.358928
$415$	−57.5739	−2.82619
$416$	1.00000	0.0490290
$417$	5.59254	0.273868
$418$	18.0282	0.881787
$419$	2.59984	0.127011	0.0635053	−	0.997982i	$-0.479772\pi$
$419$	2.59984	0.127011	0.0635053	+	0.997982i	$0.479772\pi$
$420$	−12.3000	−0.600180
$421$	−1.98180	−0.0965871	−0.0482935	−	0.998833i	$-0.515378\pi$
$421$	−1.98180	−0.0965871	−0.0482935	+	0.998833i	$0.515378\pi$
$422$	23.5539	1.14659
$423$	12.6586	0.615482
$424$	−12.3552	−0.600024
$425$	38.9298	1.88837
$426$	−1.06287	−0.0514962
$427$	−3.06538	−0.148344
$428$	13.3163	0.643670
$429$	5.49150	0.265132
$430$	45.6953	2.20362
$431$	10.8821	0.524171	0.262086	−	0.965045i	$-0.415590\pi$
$431$	10.8821	0.524171	0.262086	+	0.965045i	$0.415590\pi$
$432$	−1.00000	−0.0481125
$433$	9.72178	0.467199	0.233600	−	0.972333i	$-0.424950\pi$
$433$	9.72178	0.467199	0.233600	+	0.972333i	$0.424950\pi$
$434$	−3.42562	−0.164435
$435$	−33.5528	−1.60873
$436$	−12.2924	−0.588701
$437$	23.9756	1.14691
$438$	4.32004	0.206420
$439$	0.721018	0.0344123	0.0172062	−	0.999852i	$-0.494523\pi$
$439$	0.721018	0.0344123	0.0172062	+	0.999852i	$0.494523\pi$
$440$	22.5096	1.07310
$441$	2.00445	0.0954500
$442$	3.29864	0.156900
$443$	27.9667	1.32874	0.664368	−	0.747406i	$-0.268701\pi$
$443$	27.9667	1.32874	0.664368	+	0.747406i	$0.268701\pi$
$444$	7.54165	0.357911
$445$	−23.2356	−1.10147
$446$	18.7087	0.885884
$447$	15.1475	0.716452
$448$	−3.00074	−0.141772
$449$	20.8541	0.984167	0.492083	−	0.870548i	$-0.336236\pi$
$449$	20.8541	0.984167	0.492083	+	0.870548i	$0.336236\pi$
$450$	−11.8018	−0.556341
$451$	−61.4490	−2.89352
$452$	8.74494	0.411327
$453$	−0.505643	−0.0237572
$454$	29.0106	1.36154
$455$	−12.3000	−0.576634
$456$	−3.28293	−0.153737
$457$	−32.0159	−1.49764	−0.748821	−	0.662773i	$-0.769380\pi$
$457$	−32.0159	−1.49764	−0.748821	+	0.662773i	$0.769380\pi$
$458$	−4.97298	−0.232372
$459$	−3.29864	−0.153967
$460$	29.9354	1.39575
$461$	19.5855	0.912188	0.456094	−	0.889932i	$-0.349248\pi$
$461$	19.5855	0.912188	0.456094	+	0.889932i	$0.349248\pi$
$462$	−16.4786	−0.766652
$463$	6.66000	0.309517	0.154758	−	0.987952i	$-0.450540\pi$
$463$	6.66000	0.309517	0.154758	+	0.987952i	$0.450540\pi$
$464$	−8.18560	−0.380007
$465$	−4.67938	−0.217001
$466$	5.62501	0.260574
$467$	−31.7157	−1.46763	−0.733813	−	0.679351i	$-0.762261\pi$
$467$	−31.7157	−1.46763	−0.733813	+	0.679351i	$0.762261\pi$
$468$	−1.00000	−0.0462250
$469$	36.2379	1.67331
$470$	51.8875	2.39339
$471$	−2.96021	−0.136399
$472$	−0.0926322	−0.00426374
$473$	61.2188	2.81484
$474$	3.54232	0.162704
$475$	−38.7444	−1.77771
$476$	−9.89836	−0.453691
$477$	12.3552	0.565708
$478$	10.9696	0.501740
$479$	2.86936	0.131105	0.0655523	−	0.997849i	$-0.479119\pi$
$479$	2.86936	0.131105	0.0655523	+	0.997849i	$0.479119\pi$
$480$	−4.09900	−0.187093
$481$	7.54165	0.343870
$482$	−8.12615	−0.370136
$483$	−21.9147	−0.997155
$484$	19.1565	0.870751
$485$	−39.6800	−1.80178
$486$	1.00000	0.0453609
$487$	−28.9279	−1.31085	−0.655423	−	0.755262i	$-0.727510\pi$
$487$	−28.9279	−1.31085	−0.655423	+	0.755262i	$0.727510\pi$
$488$	−1.02154	−0.0462430
$489$	−17.0796	−0.772364
$490$	8.21623	0.371172
$491$	−19.2666	−0.869488	−0.434744	−	0.900554i	$-0.643161\pi$
$491$	−19.2666	−0.869488	−0.434744	+	0.900554i	$0.643161\pi$
$492$	11.1898	0.504477
$493$	−27.0013	−1.21608
$494$	−3.28293	−0.147706
$495$	−22.5096	−1.01173
$496$	−1.14159	−0.0512589
$497$	3.18939	0.143064
$498$	14.0459	0.629410
$499$	19.7101	0.882344	0.441172	−	0.897423i	$-0.354563\pi$
$499$	19.7101	0.882344	0.441172	+	0.897423i	$0.354563\pi$
$500$	−27.8805	−1.24685
$501$	−16.4047	−0.732906
$502$	−15.4133	−0.687928
$503$	−7.31709	−0.326253	−0.163126	−	0.986605i	$-0.552158\pi$
$503$	−7.31709	−0.326253	−0.163126	+	0.986605i	$0.552158\pi$
$504$	3.00074	0.133664
$505$	−40.2979	−1.79323
$506$	40.1050	1.78288
$507$	−1.00000	−0.0444116
$508$	−11.3506	−0.503603
$509$	2.36507	0.104830	0.0524149	−	0.998625i	$-0.483308\pi$
$509$	2.36507	0.104830	0.0524149	+	0.998625i	$0.483308\pi$
$510$	−13.5211	−0.598725
$511$	−12.9633	−0.573464
$512$	−1.00000	−0.0441942
$513$	3.28293	0.144945
$514$	11.6822	0.515279
$515$	4.09900	0.180623
$516$	−11.1479	−0.490760
$517$	69.5146	3.05725
$518$	−22.6305	−0.994329
$519$	−18.1033	−0.794648
$520$	−4.09900	−0.179753
$521$	23.0440	1.00957	0.504787	−	0.863244i	$-0.331571\pi$
$521$	23.0440	1.00957	0.504787	+	0.863244i	$0.331571\pi$
$522$	8.18560	0.358274
$523$	26.6252	1.16424	0.582119	−	0.813104i	$-0.302224\pi$
$523$	26.6252	1.16424	0.582119	+	0.813104i	$0.302224\pi$
$524$	10.6293	0.464341
$525$	35.4141	1.54560
$526$	0.114081	0.00497417
$527$	−3.76569	−0.164036
$528$	−5.49150	−0.238987
$529$	30.3354	1.31893
$530$	50.6441	2.19984
$531$	0.0926322	0.00401989
$532$	9.85121	0.427104
$533$	11.1898	0.484686
$534$	5.66860	0.245304
$535$	−54.5837	−2.35986
$536$	12.0763	0.521618
$537$	−11.8026	−0.509320
$538$	13.0625	0.563163
$539$	11.0074	0.474123
$540$	4.09900	0.176393
$541$	−28.8762	−1.24148	−0.620742	−	0.784015i	$-0.713169\pi$
$541$	−28.8762	−1.24148	−0.620742	+	0.784015i	$0.713169\pi$
$542$	−1.02651	−0.0440925
$543$	−13.3538	−0.573066
$544$	−3.29864	−0.141428
$545$	50.3866	2.15833
$546$	3.00074	0.128420
$547$	−41.1434	−1.75916	−0.879582	−	0.475748i	$-0.842178\pi$
$547$	−41.1434	−1.75916	−0.879582	+	0.475748i	$0.842178\pi$
$548$	12.0265	0.513747
$549$	1.02154	0.0435983
$550$	−64.8094	−2.76348
$551$	26.8727	1.14482
$552$	−7.30311	−0.310841
$553$	−10.6296	−0.452016
$554$	11.7430	0.498911
$555$	−30.9132	−1.31219
$556$	−5.59254	−0.237177
$557$	17.0771	0.723579	0.361790	−	0.932260i	$-0.382166\pi$
$557$	17.0771	0.723579	0.361790	+	0.932260i	$0.382166\pi$
$558$	1.14159	0.0483274
$559$	−11.1479	−0.471507
$560$	12.3000	0.519771
$561$	−18.1145	−0.764793
$562$	18.9654	0.800008
$563$	15.3378	0.646413	0.323206	−	0.946329i	$-0.395239\pi$
$563$	15.3378	0.646413	0.323206	+	0.946329i	$0.395239\pi$
$564$	−12.6586	−0.533023
$565$	−35.8455	−1.50803
$566$	12.3622	0.519624
$567$	−3.00074	−0.126019
$568$	1.06287	0.0445970
$569$	−5.83732	−0.244713	−0.122357	−	0.992486i	$-0.539045\pi$
$569$	−5.83732	−0.244713	−0.122357	+	0.992486i	$0.539045\pi$
$570$	13.4567	0.563639
$571$	−6.96900	−0.291644	−0.145822	−	0.989311i	$-0.546583\pi$
$571$	−6.96900	−0.291644	−0.145822	+	0.989311i	$0.546583\pi$
$572$	−5.49150	−0.229611
$573$	25.4836	1.06459
$574$	−33.5778	−1.40151
$575$	−86.1897	−3.59436
$576$	1.00000	0.0416667
$577$	−18.3481	−0.763840	−0.381920	−	0.924195i	$-0.624737\pi$
$577$	−18.3481	−0.763840	−0.381920	+	0.924195i	$0.624737\pi$
$578$	6.11898	0.254516
$579$	15.5011	0.644202
$580$	33.5528	1.39320
$581$	−42.1480	−1.74859
$582$	9.68043	0.401267
$583$	67.8488	2.81001
$584$	−4.32004	−0.178765
$585$	4.09900	0.169473
$586$	−10.9274	−0.451405
$587$	23.0096	0.949708	0.474854	−	0.880064i	$-0.342501\pi$
$587$	23.0096	0.949708	0.474854	+	0.880064i	$0.342501\pi$
$588$	−2.00445	−0.0826621
$589$	3.74776	0.154424
$590$	0.379699	0.0156320
$591$	6.11322	0.251464
$592$	−7.54165	−0.309960
$593$	−10.4914	−0.430828	−0.215414	−	0.976523i	$-0.569110\pi$
$593$	−10.4914	−0.430828	−0.215414	+	0.976523i	$0.569110\pi$
$594$	5.49150	0.225319
$595$	40.5734	1.66335
$596$	−15.1475	−0.620465
$597$	−5.71794	−0.234020
$598$	−7.30311	−0.298646
$599$	7.58134	0.309765	0.154883	−	0.987933i	$-0.450500\pi$
$599$	7.58134	0.309765	0.154883	+	0.987933i	$0.450500\pi$
$600$	11.8018	0.481806
$601$	−30.1311	−1.22907	−0.614537	−	0.788888i	$-0.710657\pi$
$601$	−30.1311	−1.22907	−0.614537	+	0.788888i	$0.710657\pi$
$602$	33.4521	1.36340
$603$	−12.0763	−0.491786
$604$	0.505643	0.0205743
$605$	−78.5225	−3.19239
$606$	9.83117	0.399364
$607$	46.2317	1.87649	0.938243	−	0.345977i	$-0.112453\pi$
$607$	46.2317	1.87649	0.938243	+	0.345977i	$0.112453\pi$
$608$	3.28293	0.133140
$609$	−24.5629	−0.995338
$610$	4.18729	0.169539
$611$	−12.6586	−0.512112
$612$	3.29864	0.133340
$613$	7.16508	0.289395	0.144697	−	0.989476i	$-0.453779\pi$
$613$	7.16508	0.289395	0.144697	+	0.989476i	$0.453779\pi$
$614$	−8.74651	−0.352980
$615$	−45.8672	−1.84954
$616$	16.4786	0.663940
$617$	−13.9001	−0.559596	−0.279798	−	0.960059i	$-0.590268\pi$
$617$	−13.9001	−0.559596	−0.279798	+	0.960059i	$0.590268\pi$
$618$	−1.00000	−0.0402259
$619$	30.5667	1.22858	0.614290	−	0.789080i	$-0.289442\pi$
$619$	30.5667	1.22858	0.614290	+	0.789080i	$0.289442\pi$
$620$	4.67938	0.187928
$621$	7.30311	0.293064
$622$	−12.6819	−0.508497
$623$	−17.0100	−0.681491
$624$	1.00000	0.0400320
$625$	55.2731	2.21092
$626$	−6.64211	−0.265472
$627$	18.0282	0.719976
$628$	2.96021	0.118125
$629$	−24.8772	−0.991918
$630$	−12.3000	−0.490045
$631$	19.5989	0.780220	0.390110	−	0.920768i	$-0.372437\pi$
$631$	19.5989	0.780220	0.390110	+	0.920768i	$0.372437\pi$
$632$	−3.54232	−0.140906
$633$	23.5539	0.936184
$634$	−27.2292	−1.08141
$635$	46.5262	1.84634
$636$	−12.3552	−0.489917
$637$	−2.00445	−0.0794192
$638$	44.9512	1.77963
$639$	−1.06287	−0.0420464
$640$	4.09900	0.162027
$641$	−5.43907	−0.214830	−0.107415	−	0.994214i	$-0.534257\pi$
$641$	−5.43907	−0.214830	−0.107415	+	0.994214i	$0.534257\pi$
$642$	13.3163	0.525554
$643$	−6.07912	−0.239737	−0.119869	−	0.992790i	$-0.538247\pi$
$643$	−6.07912	−0.239737	−0.119869	+	0.992790i	$0.538247\pi$
$644$	21.9147	0.863562
$645$	45.6953	1.79925
$646$	10.8292	0.426069
$647$	29.0813	1.14330	0.571652	−	0.820496i	$-0.306303\pi$
$647$	29.0813	1.14330	0.571652	+	0.820496i	$0.306303\pi$
$648$	−1.00000	−0.0392837
$649$	0.508689	0.0199678
$650$	11.8018	0.462904
$651$	−3.42562	−0.134261
$652$	17.0796	0.668887
$653$	−6.28732	−0.246042	−0.123021	−	0.992404i	$-0.539258\pi$
$653$	−6.28732	−0.246042	−0.123021	+	0.992404i	$0.539258\pi$
$654$	−12.2924	−0.480672
$655$	−43.5693	−1.70239
$656$	−11.1898	−0.436890
$657$	4.32004	0.168541
$658$	37.9852	1.48082
$659$	−37.5484	−1.46268	−0.731339	−	0.682014i	$-0.761104\pi$
$659$	−37.5484	−1.46268	−0.731339	+	0.682014i	$0.761104\pi$
$660$	22.5096	0.876186
$661$	−18.0959	−0.703848	−0.351924	−	0.936028i	$-0.614473\pi$
$661$	−18.0959	−0.703848	−0.351924	+	0.936028i	$0.614473\pi$
$662$	9.40347	0.365476
$663$	3.29864	0.128109
$664$	−14.0459	−0.545085
$665$	−40.3801	−1.56587
$666$	7.54165	0.292233
$667$	59.7803	2.31470
$668$	16.4047	0.634716
$669$	18.7087	0.723321
$670$	−49.5008	−1.91238
$671$	5.60979	0.216563
$672$	−3.00074	−0.115756
$673$	47.9300	1.84756	0.923782	−	0.382919i	$-0.125081\pi$
$673$	47.9300	1.84756	0.923782	+	0.382919i	$0.125081\pi$
$674$	19.4972	0.751005
$675$	−11.8018	−0.454251
$676$	1.00000	0.0384615
$677$	36.3762	1.39805	0.699026	−	0.715096i	$-0.253617\pi$
$677$	36.3762	1.39805	0.699026	+	0.715096i	$0.253617\pi$
$678$	8.74494	0.335847
$679$	−29.0485	−1.11478
$680$	13.5211	0.518511
$681$	29.0106	1.11169
$682$	6.26904	0.240054
$683$	−23.7452	−0.908584	−0.454292	−	0.890853i	$-0.650108\pi$
$683$	−23.7452	−0.908584	−0.454292	+	0.890853i	$0.650108\pi$
$684$	−3.28293	−0.125526
$685$	−49.2966	−1.88353
$686$	−14.9904	−0.572334
$687$	−4.97298	−0.189731
$688$	11.1479	0.425011
$689$	−12.3552	−0.470697
$690$	29.9354	1.13962
$691$	−29.3331	−1.11588	−0.557942	−	0.829880i	$-0.688409\pi$
$691$	−29.3331	−1.11588	−0.557942	+	0.829880i	$0.688409\pi$
$692$	18.1033	0.688185
$693$	−16.4786	−0.625969
$694$	−17.1464	−0.650870
$695$	22.9238	0.869550
$696$	−8.18560	−0.310274
$697$	−36.9113	−1.39811
$698$	−24.2217	−0.916804
$699$	5.62501	0.212758
$700$	−35.4141	−1.33853
$701$	−24.7623	−0.935258	−0.467629	−	0.883925i	$-0.654892\pi$
$701$	−24.7623	−0.935258	−0.467629	+	0.883925i	$0.654892\pi$
$702$	−1.00000	−0.0377426
$703$	24.7587	0.933791
$704$	5.49150	0.206969
$705$	51.8875	1.95420
$706$	−6.52930	−0.245734
$707$	−29.5008	−1.10949
$708$	−0.0926322	−0.00348133
$709$	9.71518	0.364861	0.182431	−	0.983219i	$-0.441604\pi$
$709$	9.71518	0.364861	0.182431	+	0.983219i	$0.441604\pi$
$710$	−4.35670	−0.163504
$711$	3.54232	0.132847
$712$	−5.66860	−0.212440
$713$	8.33716	0.312229
$714$	−9.89836	−0.370437
$715$	22.5096	0.841812
$716$	11.8026	0.441084
$717$	10.9696	0.409669
$718$	−27.3163	−1.01944
$719$	24.6644	0.919825	0.459913	−	0.887964i	$-0.347881\pi$
$719$	24.6644	0.919825	0.459913	+	0.887964i	$0.347881\pi$
$720$	−4.09900	−0.152761
$721$	3.00074	0.111753
$722$	8.22240	0.306006
$723$	−8.12615	−0.302215
$724$	13.3538	0.496290
$725$	−96.6046	−3.58781
$726$	19.1565	0.710965
$727$	−3.82663	−0.141922	−0.0709609	−	0.997479i	$-0.522607\pi$
$727$	−3.82663	−0.141922	−0.0709609	+	0.997479i	$0.522607\pi$
$728$	−3.00074	−0.111215
$729$	1.00000	0.0370370
$730$	17.7078	0.655397
$731$	36.7730	1.36010
$732$	−1.02154	−0.0377572
$733$	1.04614	0.0386400	0.0193200	−	0.999813i	$-0.493850\pi$
$733$	1.04614	0.0386400	0.0193200	+	0.999813i	$0.493850\pi$
$734$	29.8312	1.10109
$735$	8.21623	0.303060
$736$	7.30311	0.269196
$737$	−66.3171	−2.44282
$738$	11.1898	0.411904
$739$	2.23168	0.0820937	0.0410468	−	0.999157i	$-0.486931\pi$
$739$	2.23168	0.0820937	0.0410468	+	0.999157i	$0.486931\pi$
$740$	30.9132	1.13639
$741$	−3.28293	−0.120601
$742$	37.0749	1.36106
$743$	44.8196	1.64427	0.822136	−	0.569291i	$-0.192782\pi$
$743$	44.8196	1.64427	0.822136	+	0.569291i	$0.192782\pi$
$744$	−1.14159	−0.0418527
$745$	62.0895	2.27478
$746$	−18.1957	−0.666190
$747$	14.0459	0.513911
$748$	18.1145	0.662330
$749$	−39.9589	−1.46007
$750$	−27.8805	−1.01805
$751$	9.39288	0.342751	0.171376	−	0.985206i	$-0.445179\pi$
$751$	9.39288	0.342751	0.171376	+	0.985206i	$0.445179\pi$
$752$	12.6586	0.461611
$753$	−15.4133	−0.561691
$754$	−8.18560	−0.298102
$755$	−2.07263	−0.0754307
$756$	3.00074	0.109136
$757$	−13.4849	−0.490118	−0.245059	−	0.969508i	$-0.578807\pi$
$757$	−13.4849	−0.490118	−0.245059	+	0.969508i	$0.578807\pi$
$758$	8.76132	0.318226
$759$	40.1050	1.45572
$760$	−13.4567	−0.488126
$761$	24.5977	0.891664	0.445832	−	0.895117i	$-0.352908\pi$
$761$	24.5977	0.891664	0.445832	+	0.895117i	$0.352908\pi$
$762$	−11.3506	−0.411190
$763$	36.8864	1.33538
$764$	−25.4836	−0.921963
$765$	−13.5211	−0.488857
$766$	7.54390	0.272572
$767$	−0.0926322	−0.00334475
$768$	−1.00000	−0.0360844
$769$	20.3859	0.735133	0.367567	−	0.929997i	$-0.380191\pi$
$769$	20.3859	0.735133	0.367567	+	0.929997i	$0.380191\pi$
$770$	−67.5456	−2.43417
$771$	11.6822	0.420723
$772$	−15.5011	−0.557896
$773$	−8.25983	−0.297085	−0.148543	−	0.988906i	$-0.547458\pi$
$773$	−8.25983	−0.297085	−0.148543	+	0.988906i	$0.547458\pi$
$774$	−11.1479	−0.400704
$775$	−13.4728	−0.483957
$776$	−9.68043	−0.347507
$777$	−22.6305	−0.811866
$778$	35.1494	1.26017
$779$	36.7354	1.31618
$780$	−4.09900	−0.146768
$781$	−5.83674	−0.208855
$782$	24.0903	0.861468
$783$	8.18560	0.292529
$784$	2.00445	0.0715875
$785$	−12.1339	−0.433077
$786$	10.6293	0.379133
$787$	−40.3011	−1.43658	−0.718290	−	0.695744i	$-0.755075\pi$
$787$	−40.3011	−1.43658	−0.718290	+	0.695744i	$0.755075\pi$
$788$	−6.11322	−0.217774
$789$	0.114081	0.00406139
$790$	14.5200	0.516597
$791$	−26.2413	−0.933033
$792$	−5.49150	−0.195132
$793$	−1.02154	−0.0362760
$794$	19.4035	0.688605
$795$	50.6441	1.79616
$796$	5.71794	0.202667
$797$	22.9299	0.812220	0.406110	−	0.913824i	$-0.366885\pi$
$797$	22.9299	0.812220	0.406110	+	0.913824i	$0.366885\pi$
$798$	9.85121	0.348729
$799$	41.7561	1.47723
$800$	−11.8018	−0.417256
$801$	5.66860	0.200290
$802$	23.1733	0.818279
$803$	23.7235	0.837184
$804$	12.0763	0.425899
$805$	−89.8285	−3.16604
$806$	−1.14159	−0.0402108
$807$	13.0625	0.459820
$808$	−9.83117	−0.345859
$809$	15.2701	0.536867	0.268433	−	0.963298i	$-0.413494\pi$
$809$	15.2701	0.536867	0.268433	+	0.963298i	$0.413494\pi$
$810$	4.09900	0.144024
$811$	−41.6426	−1.46227	−0.731134	−	0.682234i	$-0.761009\pi$
$811$	−41.6426	−1.46227	−0.731134	+	0.682234i	$0.761009\pi$
$812$	24.5629	0.861988
$813$	−1.02651	−0.0360014
$814$	41.4149	1.45159
$815$	−70.0090	−2.45231
$816$	−3.29864	−0.115475
$817$	−36.5978	−1.28040
$818$	36.6244	1.28054
$819$	3.00074	0.104854
$820$	45.8672	1.60175
$821$	−45.6196	−1.59214	−0.796068	−	0.605208i	$-0.793090\pi$
$821$	−45.6196	−1.59214	−0.796068	+	0.605208i	$0.793090\pi$
$822$	12.0265	0.419472
$823$	−3.47425	−0.121105	−0.0605524	−	0.998165i	$-0.519286\pi$
$823$	−3.47425	−0.121105	−0.0605524	+	0.998165i	$0.519286\pi$
$824$	1.00000	0.0348367
$825$	−64.8094	−2.25637
$826$	0.277965	0.00967165
$827$	−5.43521	−0.189001	−0.0945004	−	0.995525i	$-0.530125\pi$
$827$	−5.43521	−0.189001	−0.0945004	+	0.995525i	$0.530125\pi$
$828$	−7.30311	−0.253801
$829$	35.3330	1.22717	0.613583	−	0.789631i	$-0.289728\pi$
$829$	35.3330	1.22717	0.613583	+	0.789631i	$0.289728\pi$
$830$	57.5739	1.99842
$831$	11.7430	0.407359
$832$	−1.00000	−0.0346688
$833$	6.61196	0.229091
$834$	−5.59254	−0.193654
$835$	−67.2427	−2.32703
$836$	−18.0282	−0.623517
$837$	1.14159	0.0394591
$838$	−2.59984	−0.0898100
$839$	−0.127299	−0.00439486	−0.00219743	−	0.999998i	$-0.500699\pi$
$839$	−0.127299	−0.00439486	−0.00219743	+	0.999998i	$0.500699\pi$
$840$	12.3000	0.424391
$841$	38.0040	1.31048
$842$	1.98180	0.0682974
$843$	18.9654	0.653203
$844$	−23.5539	−0.810759
$845$	−4.09900	−0.141010
$846$	−12.6586	−0.435211
$847$	−57.4838	−1.97517
$848$	12.3552	0.424281
$849$	12.3622	0.424271
$850$	−38.9298	−1.33528
$851$	55.0775	1.88803
$852$	1.06287	0.0364133
$853$	−14.2842	−0.489082	−0.244541	−	0.969639i	$-0.578637\pi$
$853$	−14.2842	−0.489082	−0.244541	+	0.969639i	$0.578637\pi$
$854$	3.06538	0.104895
$855$	13.4567	0.460209
$856$	−13.3163	−0.455143
$857$	20.5394	0.701612	0.350806	−	0.936448i	$-0.385908\pi$
$857$	20.5394	0.701612	0.350806	+	0.936448i	$0.385908\pi$
$858$	−5.49150	−0.187477
$859$	24.5915	0.839052	0.419526	−	0.907743i	$-0.362196\pi$
$859$	24.5915	0.839052	0.419526	+	0.907743i	$0.362196\pi$
$860$	−45.6953	−1.55820
$861$	−33.5778	−1.14433
$862$	−10.8821	−0.370645
$863$	−40.9221	−1.39300	−0.696502	−	0.717555i	$-0.745261\pi$
$863$	−40.9221	−1.39300	−0.696502	+	0.717555i	$0.745261\pi$
$864$	1.00000	0.0340207
$865$	−74.2055	−2.52306
$866$	−9.72178	−0.330360
$867$	6.11898	0.207811
$868$	3.42562	0.116273
$869$	19.4526	0.659886
$870$	33.5528	1.13754
$871$	12.0763	0.409191
$872$	12.2924	0.416274
$873$	9.68043	0.327633
$874$	−23.9756	−0.810985
$875$	83.6621	2.82829
$876$	−4.32004	−0.145961
$877$	21.2615	0.717949	0.358974	−	0.933347i	$-0.383127\pi$
$877$	21.2615	0.717949	0.358974	+	0.933347i	$0.383127\pi$
$878$	−0.721018	−0.0243332
$879$	−10.9274	−0.368570
$880$	−22.5096	−0.758799
$881$	28.2082	0.950359	0.475180	−	0.879889i	$-0.342383\pi$
$881$	28.2082	0.950359	0.475180	+	0.879889i	$0.342383\pi$
$882$	−2.00445	−0.0674933
$883$	−22.3357	−0.751656	−0.375828	−	0.926689i	$-0.622642\pi$
$883$	−22.3357	−0.751656	−0.375828	+	0.926689i	$0.622642\pi$
$884$	−3.29864	−0.110945
$885$	0.379699	0.0127634
$886$	−27.9667	−0.939558
$887$	−13.8566	−0.465261	−0.232630	−	0.972565i	$-0.574733\pi$
$887$	−13.8566	−0.465261	−0.232630	+	0.972565i	$0.574733\pi$
$888$	−7.54165	−0.253081
$889$	34.0603	1.14235
$890$	23.2356	0.778858
$891$	5.49150	0.183972
$892$	−18.7087	−0.626415
$893$	−41.5572	−1.39066
$894$	−15.1475	−0.506608
$895$	−48.3788	−1.61712
$896$	3.00074	0.100248
$897$	−7.30311	−0.243844
$898$	−20.8541	−0.695911
$899$	9.34460	0.311660
$900$	11.8018	0.393393
$901$	40.7555	1.35776
$902$	61.4490	2.04603
$903$	33.4521	1.11321
$904$	−8.74494	−0.290852
$905$	−54.7372	−1.81952
$906$	0.505643	0.0167989
$907$	2.58154	0.0857185	0.0428593	−	0.999081i	$-0.486353\pi$
$907$	2.58154	0.0857185	0.0428593	+	0.999081i	$0.486353\pi$
$908$	−29.0106	−0.962751
$909$	9.83117	0.326079
$910$	12.3000	0.407742
$911$	−55.6813	−1.84480	−0.922402	−	0.386232i	$-0.873776\pi$
$911$	−55.6813	−1.84480	−0.922402	+	0.386232i	$0.873776\pi$
$912$	3.28293	0.108709
$913$	77.1327	2.55272
$914$	32.0159	1.05899
$915$	4.18729	0.138428
$916$	4.97298	0.164312
$917$	−31.8956	−1.05329
$918$	3.29864	0.108871
$919$	−8.31197	−0.274186	−0.137093	−	0.990558i	$-0.543776\pi$
$919$	−8.31197	−0.274186	−0.137093	+	0.990558i	$0.543776\pi$
$920$	−29.9354	−0.986942
$921$	−8.74651	−0.288207
$922$	−19.5855	−0.645014
$923$	1.06287	0.0349848
$924$	16.4786	0.542105
$925$	−89.0049	−2.92646
$926$	−6.66000	−0.218861
$927$	−1.00000	−0.0328443
$928$	8.18560	0.268705
$929$	−5.72926	−0.187971	−0.0939855	−	0.995574i	$-0.529961\pi$
$929$	−5.72926	−0.187971	−0.0939855	+	0.995574i	$0.529961\pi$
$930$	4.67938	0.153443
$931$	−6.58046	−0.215666
$932$	−5.62501	−0.184253
$933$	−12.6819	−0.415186
$934$	31.7157	1.03777
$935$	−74.2511	−2.42827
$936$	1.00000	0.0326860
$937$	−50.5074	−1.65001	−0.825003	−	0.565128i	$-0.808827\pi$
$937$	−50.5074	−1.65001	−0.825003	+	0.565128i	$0.808827\pi$
$938$	−36.2379	−1.18321
$939$	−6.64211	−0.216757
$940$	−51.8875	−1.69238
$941$	−59.2685	−1.93210	−0.966048	−	0.258361i	$-0.916818\pi$
$941$	−59.2685	−1.93210	−0.966048	+	0.258361i	$0.916818\pi$
$942$	2.96021	0.0964487
$943$	81.7207	2.66119
$944$	0.0926322	0.00301492
$945$	−12.3000	−0.400120
$946$	−61.2188	−1.99040
$947$	−38.1271	−1.23896	−0.619482	−	0.785011i	$-0.712657\pi$
$947$	−38.1271	−1.23896	−0.619482	+	0.785011i	$0.712657\pi$
$948$	−3.54232	−0.115049
$949$	−4.32004	−0.140234
$950$	38.7444	1.25703
$951$	−27.2292	−0.882967
$952$	9.89836	0.320808
$953$	−16.4396	−0.532531	−0.266265	−	0.963900i	$-0.585790\pi$
$953$	−16.4396	−0.532531	−0.266265	+	0.963900i	$0.585790\pi$
$954$	−12.3552	−0.400016
$955$	104.457	3.38015
$956$	−10.9696	−0.354784
$957$	44.9512	1.45307
$958$	−2.86936	−0.0927049
$959$	−36.0884	−1.16536
$960$	4.09900	0.132295
$961$	−29.6968	−0.957960
$962$	−7.54165	−0.243153
$963$	13.3163	0.429113
$964$	8.12615	0.261726
$965$	63.5388	2.04539
$966$	21.9147	0.705095
$967$	−20.4771	−0.658501	−0.329250	−	0.944243i	$-0.606796\pi$
$967$	−20.4771	−0.658501	−0.329250	+	0.944243i	$0.606796\pi$
$968$	−19.1565	−0.615714
$969$	10.8292	0.347884
$970$	39.6800	1.27405
$971$	−23.4032	−0.751043	−0.375522	−	0.926814i	$-0.622536\pi$
$971$	−23.4032	−0.751043	−0.375522	+	0.926814i	$0.622536\pi$
$972$	−1.00000	−0.0320750
$973$	16.7818	0.537999
$974$	28.9279	0.926909
$975$	11.8018	0.377959
$976$	1.02154	0.0326987
$977$	2.67460	0.0855680	0.0427840	−	0.999084i	$-0.486377\pi$
$977$	2.67460	0.0855680	0.0427840	+	0.999084i	$0.486377\pi$
$978$	17.0796	0.546144
$979$	31.1291	0.994890
$980$	−8.21623	−0.262458
$981$	−12.2924	−0.392467
$982$	19.2666	0.614821
$983$	−49.5956	−1.58185	−0.790927	−	0.611910i	$-0.790401\pi$
$983$	−49.5956	−1.58185	−0.790927	+	0.611910i	$0.790401\pi$
$984$	−11.1898	−0.356719
$985$	25.0581	0.798416
$986$	27.0013	0.859898
$987$	37.9852	1.20908
$988$	3.28293	0.104444
$989$	−81.4146	−2.58883
$990$	22.5096	0.715403
$991$	11.9608	0.379947	0.189974	−	0.981789i	$-0.439160\pi$
$991$	11.9608	0.379947	0.189974	+	0.981789i	$0.439160\pi$
$992$	1.14159	0.0362455
$993$	9.40347	0.298410
$994$	−3.18939	−0.101161
$995$	−23.4378	−0.743029
$996$	−14.0459	−0.445060
$997$	28.8504	0.913700	0.456850	−	0.889544i	$-0.348978\pi$
$997$	28.8504	0.913700	0.456850	+	0.889544i	$0.348978\pi$
$998$	−19.7101	−0.623911
$999$	7.54165	0.238607

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8034.2.a.s.1.1	✓	10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8034.2.a.s.1.1	✓	10	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)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -4.09900 q^{5} +1.00000 q^{6} -3.00074 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -4.09900 q^{5} +1.00000 q^{6} -3.00074 q^{7} -1.00000 q^{8} +1.00000 q^{9} +4.09900 q^{10} +5.49150 q^{11} -1.00000 q^{12} -1.00000 q^{13} +3.00074 q^{14} +4.09900 q^{15} +1.00000 q^{16} +3.29864 q^{17} -1.00000 q^{18} -3.28293 q^{19} -4.09900 q^{20} +3.00074 q^{21} -5.49150 q^{22} -7.30311 q^{23} +1.00000 q^{24} +11.8018 q^{25} +1.00000 q^{26} -1.00000 q^{27} -3.00074 q^{28} -8.18560 q^{29} -4.09900 q^{30} -1.14159 q^{31} -1.00000 q^{32} -5.49150 q^{33} -3.29864 q^{34} +12.3000 q^{35} +1.00000 q^{36} -7.54165 q^{37} +3.28293 q^{38} +1.00000 q^{39} +4.09900 q^{40} -11.1898 q^{41} -3.00074 q^{42} +11.1479 q^{43} +5.49150 q^{44} -4.09900 q^{45} +7.30311 q^{46} +12.6586 q^{47} -1.00000 q^{48} +2.00445 q^{49} -11.8018 q^{50} -3.29864 q^{51} -1.00000 q^{52} +12.3552 q^{53} +1.00000 q^{54} -22.5096 q^{55} +3.00074 q^{56} +3.28293 q^{57} +8.18560 q^{58} +0.0926322 q^{59} +4.09900 q^{60} +1.02154 q^{61} +1.14159 q^{62} -3.00074 q^{63} +1.00000 q^{64} +4.09900 q^{65} +5.49150 q^{66} -12.0763 q^{67} +3.29864 q^{68} +7.30311 q^{69} -12.3000 q^{70} -1.06287 q^{71} -1.00000 q^{72} +4.32004 q^{73} +7.54165 q^{74} -11.8018 q^{75} -3.28293 q^{76} -16.4786 q^{77} -1.00000 q^{78} +3.54232 q^{79} -4.09900 q^{80} +1.00000 q^{81} +11.1898 q^{82} +14.0459 q^{83} +3.00074 q^{84} -13.5211 q^{85} -11.1479 q^{86} +8.18560 q^{87} -5.49150 q^{88} +5.66860 q^{89} +4.09900 q^{90} +3.00074 q^{91} -7.30311 q^{92} +1.14159 q^{93} -12.6586 q^{94} +13.4567 q^{95} +1.00000 q^{96} +9.68043 q^{97} -2.00445 q^{98} +5.49150 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - 10 q^{2} - 10 q^{3} + 10 q^{4} + 6 q^{5} + 10 q^{6} - 9 q^{7} - 10 q^{8} + 10 q^{9}+O(q^{10}) \) 10 * q - 10 * q^2 - 10 * q^3 + 10 * q^4 + 6 * q^5 + 10 * q^6 - 9 * q^7 - 10 * q^8 + 10 * q^9	\( 10 q - 10 q^{2} - 10 q^{3} + 10 q^{4} + 6 q^{5} + 10 q^{6} - 9 q^{7} - 10 q^{8} + 10 q^{9} - 6 q^{10} - q^{11} - 10 q^{12} - 10 q^{13} + 9 q^{14} - 6 q^{15} + 10 q^{16} + 5 q^{17} - 10 q^{18} - 9 q^{19} + 6 q^{20} + 9 q^{21} + q^{22} + q^{23} + 10 q^{24} + 20 q^{25} + 10 q^{26} - 10 q^{27} - 9 q^{28} - 22 q^{29} + 6 q^{30} - 13 q^{31} - 10 q^{32} + q^{33} - 5 q^{34} + 14 q^{35} + 10 q^{36} + 10 q^{37} + 9 q^{38} + 10 q^{39} - 6 q^{40} - 18 q^{41} - 9 q^{42} + 10 q^{43} - q^{44} + 6 q^{45} - q^{46} + 28 q^{47} - 10 q^{48} + 11 q^{49} - 20 q^{50} - 5 q^{51} - 10 q^{52} + 6 q^{53} + 10 q^{54} - 26 q^{55} + 9 q^{56} + 9 q^{57} + 22 q^{58} + 7 q^{59} - 6 q^{60} - 20 q^{61} + 13 q^{62} - 9 q^{63} + 10 q^{64} - 6 q^{65} - q^{66} - 21 q^{67} + 5 q^{68} - q^{69} - 14 q^{70} - 19 q^{71} - 10 q^{72} + 3 q^{73} - 10 q^{74} - 20 q^{75} - 9 q^{76} + 28 q^{77} - 10 q^{78} - 11 q^{79} + 6 q^{80} + 10 q^{81} + 18 q^{82} + 20 q^{83} + 9 q^{84} - q^{85} - 10 q^{86} + 22 q^{87} + q^{88} + 22 q^{89} - 6 q^{90} + 9 q^{91} + q^{92} + 13 q^{93} - 28 q^{94} + 10 q^{96} - 10 q^{97} - 11 q^{98} - q^{99}+O(q^{100}) \) 10 * q - 10 * q^2 - 10 * q^3 + 10 * q^4 + 6 * q^5 + 10 * q^6 - 9 * q^7 - 10 * q^8 + 10 * q^9 - 6 * q^10 - q^11 - 10 * q^12 - 10 * q^13 + 9 * q^14 - 6 * q^15 + 10 * q^16 + 5 * q^17 - 10 * q^18 - 9 * q^19 + 6 * q^20 + 9 * q^21 + q^22 + q^23 + 10 * q^24 + 20 * q^25 + 10 * q^26 - 10 * q^27 - 9 * q^28 - 22 * q^29 + 6 * q^30 - 13 * q^31 - 10 * q^32 + q^33 - 5 * q^34 + 14 * q^35 + 10 * q^36 + 10 * q^37 + 9 * q^38 + 10 * q^39 - 6 * q^40 - 18 * q^41 - 9 * q^42 + 10 * q^43 - q^44 + 6 * q^45 - q^46 + 28 * q^47 - 10 * q^48 + 11 * q^49 - 20 * q^50 - 5 * q^51 - 10 * q^52 + 6 * q^53 + 10 * q^54 - 26 * q^55 + 9 * q^56 + 9 * q^57 + 22 * q^58 + 7 * q^59 - 6 * q^60 - 20 * q^61 + 13 * q^62 - 9 * q^63 + 10 * q^64 - 6 * q^65 - q^66 - 21 * q^67 + 5 * q^68 - q^69 - 14 * q^70 - 19 * q^71 - 10 * q^72 + 3 * q^73 - 10 * q^74 - 20 * q^75 - 9 * q^76 + 28 * q^77 - 10 * q^78 - 11 * q^79 + 6 * q^80 + 10 * q^81 + 18 * q^82 + 20 * q^83 + 9 * q^84 - q^85 - 10 * q^86 + 22 * q^87 + q^88 + 22 * q^89 - 6 * q^90 + 9 * q^91 + q^92 + 13 * q^93 - 28 * q^94 + 10 * q^96 - 10 * q^97 - 11 * q^98 - q^99

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