LMFDB - Embedded newform 4134.2.a.x.1.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4134,2,Mod(1,4134)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4134, 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("4134.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4134 = 2 \cdot 3 \cdot 13 \cdot 53 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4134.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:	$33.0101561956$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 2x^{7} - 21x^{6} + 43x^{5} + 96x^{4} - 235x^{3} + 136x^{2} - 8x - 8 $ x^8 - 2x^7 - 21x^6 + 43x^5 + 96x^4 - 235x^3 + 136x^2 - 8*x - 8
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			1.4
Root			$0.552454$ of defining polynomial
Character	$\chi$	$=$	4134.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +0.552454 q^{5} +1.00000 q^{6} -0.872745 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +0.552454 q^{5} +1.00000 q^{6} -0.872745 q^{7} +1.00000 q^{8} +1.00000 q^{9} +0.552454 q^{10} +5.54614 q^{11} +1.00000 q^{12} -1.00000 q^{13} -0.872745 q^{14} +0.552454 q^{15} +1.00000 q^{16} +0.913665 q^{17} +1.00000 q^{18} +3.27878 q^{19} +0.552454 q^{20} -0.872745 q^{21} +5.54614 q^{22} +5.85417 q^{23} +1.00000 q^{24} -4.69479 q^{25} -1.00000 q^{26} +1.00000 q^{27} -0.872745 q^{28} +4.98035 q^{29} +0.552454 q^{30} -6.23785 q^{31} +1.00000 q^{32} +5.54614 q^{33} +0.913665 q^{34} -0.482152 q^{35} +1.00000 q^{36} -4.72678 q^{37} +3.27878 q^{38} -1.00000 q^{39} +0.552454 q^{40} +5.34156 q^{41} -0.872745 q^{42} -5.92983 q^{43} +5.54614 q^{44} +0.552454 q^{45} +5.85417 q^{46} -1.59894 q^{47} +1.00000 q^{48} -6.23832 q^{49} -4.69479 q^{50} +0.913665 q^{51} -1.00000 q^{52} +1.00000 q^{53} +1.00000 q^{54} +3.06399 q^{55} -0.872745 q^{56} +3.27878 q^{57} +4.98035 q^{58} +0.199350 q^{59} +0.552454 q^{60} +12.0418 q^{61} -6.23785 q^{62} -0.872745 q^{63} +1.00000 q^{64} -0.552454 q^{65} +5.54614 q^{66} +5.88462 q^{67} +0.913665 q^{68} +5.85417 q^{69} -0.482152 q^{70} -1.42481 q^{71} +1.00000 q^{72} -5.84619 q^{73} -4.72678 q^{74} -4.69479 q^{75} +3.27878 q^{76} -4.84037 q^{77} -1.00000 q^{78} -5.74595 q^{79} +0.552454 q^{80} +1.00000 q^{81} +5.34156 q^{82} -6.36819 q^{83} -0.872745 q^{84} +0.504758 q^{85} -5.92983 q^{86} +4.98035 q^{87} +5.54614 q^{88} +9.03991 q^{89} +0.552454 q^{90} +0.872745 q^{91} +5.85417 q^{92} -6.23785 q^{93} -1.59894 q^{94} +1.81137 q^{95} +1.00000 q^{96} +7.55037 q^{97} -6.23832 q^{98} +5.54614 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 8 q^{2} + 8 q^{3} + 8 q^{4} + 2 q^{5} + 8 q^{6} + 7 q^{7} + 8 q^{8} + 8 q^{9}+O(q^{10}) $ 8 * q + 8 * q^2 + 8 * q^3 + 8 * q^4 + 2 * q^5 + 8 * q^6 + 7 * q^7 + 8 * q^8 + 8 * q^9	\( 8 q + 8 q^{2} + 8 q^{3} + 8 q^{4} + 2 q^{5} + 8 q^{6} + 7 q^{7} + 8 q^{8} + 8 q^{9} + 2 q^{10} + 7 q^{11} + 8 q^{12} - 8 q^{13} + 7 q^{14} + 2 q^{15} + 8 q^{16} + 8 q^{17} + 8 q^{18} + 11 q^{19} + 2 q^{20} + 7 q^{21} + 7 q^{22} + 5 q^{23} + 8 q^{24} + 6 q^{25} - 8 q^{26} + 8 q^{27} + 7 q^{28} + 13 q^{29} + 2 q^{30} + 12 q^{31} + 8 q^{32} + 7 q^{33} + 8 q^{34} + 14 q^{35} + 8 q^{36} + 10 q^{37} + 11 q^{38} - 8 q^{39} + 2 q^{40} + 19 q^{41} + 7 q^{42} + 10 q^{43} + 7 q^{44} + 2 q^{45} + 5 q^{46} + 6 q^{47} + 8 q^{48} + 15 q^{49} + 6 q^{50} + 8 q^{51} - 8 q^{52} + 8 q^{53} + 8 q^{54} + 5 q^{55} + 7 q^{56} + 11 q^{57} + 13 q^{58} + 11 q^{59} + 2 q^{60} + 6 q^{61} + 12 q^{62} + 7 q^{63} + 8 q^{64} - 2 q^{65} + 7 q^{66} + 5 q^{67} + 8 q^{68} + 5 q^{69} + 14 q^{70} - 6 q^{71} + 8 q^{72} + 18 q^{73} + 10 q^{74} + 6 q^{75} + 11 q^{76} - 8 q^{77} - 8 q^{78} + 17 q^{79} + 2 q^{80} + 8 q^{81} + 19 q^{82} + 16 q^{83} + 7 q^{84} + 25 q^{85} + 10 q^{86} + 13 q^{87} + 7 q^{88} - 8 q^{89} + 2 q^{90} - 7 q^{91} + 5 q^{92} + 12 q^{93} + 6 q^{94} - 30 q^{95} + 8 q^{96} + 11 q^{97} + 15 q^{98} + 7 q^{99}+O(q^{100}) \) 8 * q + 8 * q^2 + 8 * q^3 + 8 * q^4 + 2 * q^5 + 8 * q^6 + 7 * q^7 + 8 * q^8 + 8 * q^9 + 2 * q^10 + 7 * q^11 + 8 * q^12 - 8 * q^13 + 7 * q^14 + 2 * q^15 + 8 * q^16 + 8 * q^17 + 8 * q^18 + 11 * q^19 + 2 * q^20 + 7 * q^21 + 7 * q^22 + 5 * q^23 + 8 * q^24 + 6 * q^25 - 8 * q^26 + 8 * q^27 + 7 * q^28 + 13 * q^29 + 2 * q^30 + 12 * q^31 + 8 * q^32 + 7 * q^33 + 8 * q^34 + 14 * q^35 + 8 * q^36 + 10 * q^37 + 11 * q^38 - 8 * q^39 + 2 * q^40 + 19 * q^41 + 7 * q^42 + 10 * q^43 + 7 * q^44 + 2 * q^45 + 5 * q^46 + 6 * q^47 + 8 * q^48 + 15 * q^49 + 6 * q^50 + 8 * q^51 - 8 * q^52 + 8 * q^53 + 8 * q^54 + 5 * q^55 + 7 * q^56 + 11 * q^57 + 13 * q^58 + 11 * q^59 + 2 * q^60 + 6 * q^61 + 12 * q^62 + 7 * q^63 + 8 * q^64 - 2 * q^65 + 7 * q^66 + 5 * q^67 + 8 * q^68 + 5 * q^69 + 14 * q^70 - 6 * q^71 + 8 * q^72 + 18 * q^73 + 10 * q^74 + 6 * q^75 + 11 * q^76 - 8 * q^77 - 8 * q^78 + 17 * q^79 + 2 * q^80 + 8 * q^81 + 19 * q^82 + 16 * q^83 + 7 * q^84 + 25 * q^85 + 10 * q^86 + 13 * q^87 + 7 * q^88 - 8 * q^89 + 2 * q^90 - 7 * q^91 + 5 * q^92 + 12 * q^93 + 6 * q^94 - 30 * q^95 + 8 * q^96 + 11 * q^97 + 15 * 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
$5$	0.552454	0.247065	0.123533	−	0.992341i	$-0.460578\pi$
$5$	0.552454	0.247065	0.123533	+	0.992341i	$0.460578\pi$
$6$	1.00000	0.408248
$7$	−0.872745	−0.329867	−0.164933	−	0.986305i	$-0.552741\pi$
$7$	−0.872745	−0.329867	−0.164933	+	0.986305i	$0.552741\pi$
$8$	1.00000	0.353553
$9$	1.00000	0.333333
$10$	0.552454	0.174701
$11$	5.54614	1.67222	0.836112	−	0.548559i	$-0.184823\pi$
$11$	5.54614	1.67222	0.836112	+	0.548559i	$0.184823\pi$
$12$	1.00000	0.288675
$13$	−1.00000	−0.277350
$13$	−1.00000	−0.277350
$14$	−0.872745	−0.233251
$15$	0.552454	0.142643
$16$	1.00000	0.250000
$17$	0.913665	0.221596	0.110798	−	0.993843i	$-0.464659\pi$
$17$	0.913665	0.221596	0.110798	+	0.993843i	$0.464659\pi$
$18$	1.00000	0.235702
$19$	3.27878	0.752203	0.376102	−	0.926578i	$-0.377264\pi$
$19$	3.27878	0.752203	0.376102	+	0.926578i	$0.377264\pi$
$20$	0.552454	0.123533
$21$	−0.872745	−0.190449
$22$	5.54614	1.18244
$23$	5.85417	1.22068	0.610339	−	0.792140i	$-0.291033\pi$
$23$	5.85417	1.22068	0.610339	+	0.792140i	$0.291033\pi$
$24$	1.00000	0.204124
$25$	−4.69479	−0.938959
$26$	−1.00000	−0.196116
$27$	1.00000	0.192450
$28$	−0.872745	−0.164933
$29$	4.98035	0.924828	0.462414	−	0.886664i	$-0.346983\pi$
$29$	4.98035	0.924828	0.462414	+	0.886664i	$0.346983\pi$
$30$	0.552454	0.100864
$31$	−6.23785	−1.12035	−0.560176	−	0.828374i	$-0.689266\pi$
$31$	−6.23785	−1.12035	−0.560176	+	0.828374i	$0.689266\pi$
$32$	1.00000	0.176777
$33$	5.54614	0.965459
$34$	0.913665	0.156692
$35$	−0.482152	−0.0814985
$36$	1.00000	0.166667
$37$	−4.72678	−0.777078	−0.388539	−	0.921432i	$-0.627020\pi$
$37$	−4.72678	−0.777078	−0.388539	+	0.921432i	$0.627020\pi$
$38$	3.27878	0.531888
$39$	−1.00000	−0.160128
$40$	0.552454	0.0873507
$41$	5.34156	0.834212	0.417106	−	0.908858i	$-0.363044\pi$
$41$	5.34156	0.834212	0.417106	+	0.908858i	$0.363044\pi$
$42$	−0.872745	−0.134668
$43$	−5.92983	−0.904290	−0.452145	−	0.891944i	$-0.649341\pi$
$43$	−5.92983	−0.904290	−0.452145	+	0.891944i	$0.649341\pi$
$44$	5.54614	0.836112
$45$	0.552454	0.0823550
$46$	5.85417	0.863150
$47$	−1.59894	−0.233229	−0.116615	−	0.993177i	$-0.537204\pi$
$47$	−1.59894	−0.233229	−0.116615	+	0.993177i	$0.537204\pi$
$48$	1.00000	0.144338
$49$	−6.23832	−0.891188
$50$	−4.69479	−0.663944
$51$	0.913665	0.127939
$52$	−1.00000	−0.138675
$53$	1.00000	0.137361
$53$	1.00000	0.137361
$54$	1.00000	0.136083
$55$	3.06399	0.413148
$56$	−0.872745	−0.116625
$57$	3.27878	0.434285
$58$	4.98035	0.653952
$59$	0.199350	0.0259532	0.0129766	−	0.999916i	$-0.495869\pi$
$59$	0.199350	0.0259532	0.0129766	+	0.999916i	$0.495869\pi$
$60$	0.552454	0.0713215
$61$	12.0418	1.54179	0.770897	−	0.636960i	$-0.219808\pi$
$61$	12.0418	1.54179	0.770897	+	0.636960i	$0.219808\pi$
$62$	−6.23785	−0.792208
$63$	−0.872745	−0.109956
$64$	1.00000	0.125000
$65$	−0.552454	−0.0685235
$66$	5.54614	0.682683
$67$	5.88462	0.718921	0.359460	−	0.933160i	$-0.382961\pi$
$67$	5.88462	0.718921	0.359460	+	0.933160i	$0.382961\pi$
$68$	0.913665	0.110798
$69$	5.85417	0.704759
$70$	−0.482152	−0.0576282
$71$	−1.42481	−0.169094	−0.0845471	−	0.996419i	$-0.526944\pi$
$71$	−1.42481	−0.169094	−0.0845471	+	0.996419i	$0.526944\pi$
$72$	1.00000	0.117851
$73$	−5.84619	−0.684245	−0.342122	−	0.939655i	$-0.611146\pi$
$73$	−5.84619	−0.684245	−0.342122	+	0.939655i	$0.611146\pi$
$74$	−4.72678	−0.549477
$75$	−4.69479	−0.542108
$76$	3.27878	0.376102
$77$	−4.84037	−0.551611
$78$	−1.00000	−0.113228
$79$	−5.74595	−0.646470	−0.323235	−	0.946319i	$-0.604770\pi$
$79$	−5.74595	−0.646470	−0.323235	+	0.946319i	$0.604770\pi$
$80$	0.552454	0.0617663
$81$	1.00000	0.111111
$82$	5.34156	0.589877
$83$	−6.36819	−0.699000	−0.349500	−	0.936936i	$-0.613648\pi$
$83$	−6.36819	−0.699000	−0.349500	+	0.936936i	$0.613648\pi$
$84$	−0.872745	−0.0952243
$85$	0.504758	0.0547487
$86$	−5.92983	−0.639430
$87$	4.98035	0.533950
$88$	5.54614	0.591220
$89$	9.03991	0.958228	0.479114	−	0.877753i	$-0.340958\pi$
$89$	9.03991	0.958228	0.479114	+	0.877753i	$0.340958\pi$
$90$	0.552454	0.0582338
$91$	0.872745	0.0914886
$92$	5.85417	0.610339
$93$	−6.23785	−0.646835
$94$	−1.59894	−0.164918
$95$	1.81137	0.185843
$96$	1.00000	0.102062
$97$	7.55037	0.766624	0.383312	−	0.923619i	$-0.374783\pi$
$97$	7.55037	0.766624	0.383312	+	0.923619i	$0.374783\pi$
$98$	−6.23832	−0.630165
$99$	5.54614	0.557408
$100$	−4.69479	−0.469479
$101$	11.5516	1.14943	0.574715	−	0.818354i	$-0.305113\pi$
$101$	11.5516	1.14943	0.574715	+	0.818354i	$0.305113\pi$
$102$	0.913665	0.0904664
$103$	4.37678	0.431257	0.215628	−	0.976475i	$-0.430820\pi$
$103$	4.37678	0.431257	0.215628	+	0.976475i	$0.430820\pi$
$104$	−1.00000	−0.0980581
$105$	−0.482152	−0.0470532
$106$	1.00000	0.0971286
$107$	1.66056	0.160532	0.0802662	−	0.996773i	$-0.474423\pi$
$107$	1.66056	0.160532	0.0802662	+	0.996773i	$0.474423\pi$
$108$	1.00000	0.0962250
$109$	16.8427	1.61324	0.806619	−	0.591072i	$-0.201295\pi$
$109$	16.8427	1.61324	0.806619	+	0.591072i	$0.201295\pi$
$110$	3.06399	0.292140
$111$	−4.72678	−0.448646
$112$	−0.872745	−0.0824667
$113$	−1.31059	−0.123290	−0.0616451	−	0.998098i	$-0.519635\pi$
$113$	−1.31059	−0.123290	−0.0616451	+	0.998098i	$0.519635\pi$
$114$	3.27878	0.307086
$115$	3.23416	0.301587
$116$	4.98035	0.462414
$117$	−1.00000	−0.0924500
$118$	0.199350	0.0183517
$119$	−0.797397	−0.0730973
$120$	0.552454	0.0504319
$121$	19.7597	1.79633
$122$	12.0418	1.09021
$123$	5.34156	0.481632
$124$	−6.23785	−0.560176
$125$	−5.35593	−0.479049
$126$	−0.872745	−0.0777503
$127$	−10.9773	−0.974082	−0.487041	−	0.873379i	$-0.661924\pi$
$127$	−10.9773	−0.974082	−0.487041	+	0.873379i	$0.661924\pi$
$128$	1.00000	0.0883883
$129$	−5.92983	−0.522092
$130$	−0.552454	−0.0484534
$131$	−8.17595	−0.714336	−0.357168	−	0.934040i	$-0.616258\pi$
$131$	−8.17595	−0.714336	−0.357168	+	0.934040i	$0.616258\pi$
$132$	5.54614	0.482730
$133$	−2.86154	−0.248127
$134$	5.88462	0.508354
$135$	0.552454	0.0475477
$136$	0.913665	0.0783462
$137$	5.66459	0.483959	0.241979	−	0.970281i	$-0.422203\pi$
$137$	5.66459	0.483959	0.241979	+	0.970281i	$0.422203\pi$
$138$	5.85417	0.498340
$139$	−1.77792	−0.150801	−0.0754005	−	0.997153i	$-0.524024\pi$
$139$	−1.77792	−0.150801	−0.0754005	+	0.997153i	$0.524024\pi$
$140$	−0.482152	−0.0407493
$141$	−1.59894	−0.134655
$142$	−1.42481	−0.119568
$143$	−5.54614	−0.463792
$144$	1.00000	0.0833333
$145$	2.75142	0.228493
$146$	−5.84619	−0.483834
$147$	−6.23832	−0.514528
$148$	−4.72678	−0.388539
$149$	1.11730	0.0915330	0.0457665	−	0.998952i	$-0.485427\pi$
$149$	1.11730	0.0915330	0.0457665	+	0.998952i	$0.485427\pi$
$150$	−4.69479	−0.383328
$151$	−14.2577	−1.16028	−0.580138	−	0.814518i	$-0.697001\pi$
$151$	−14.2577	−1.16028	−0.580138	+	0.814518i	$0.697001\pi$
$152$	3.27878	0.265944
$153$	0.913665	0.0738655
$154$	−4.84037	−0.390048
$155$	−3.44613	−0.276800
$156$	−1.00000	−0.0800641
$157$	−0.934037	−0.0745442	−0.0372721	−	0.999305i	$-0.511867\pi$
$157$	−0.934037	−0.0745442	−0.0372721	+	0.999305i	$0.511867\pi$
$158$	−5.74595	−0.457123
$159$	1.00000	0.0793052
$160$	0.552454	0.0436753
$161$	−5.10920	−0.402661
$162$	1.00000	0.0785674
$163$	15.5716	1.21966	0.609830	−	0.792533i	$-0.291238\pi$
$163$	15.5716	1.21966	0.609830	+	0.792533i	$0.291238\pi$
$164$	5.34156	0.417106
$165$	3.06399	0.238531
$166$	−6.36819	−0.494267
$167$	18.6491	1.44311	0.721555	−	0.692357i	$-0.243428\pi$
$167$	18.6491	1.44311	0.721555	+	0.692357i	$0.243428\pi$
$168$	−0.872745	−0.0673338
$169$	1.00000	0.0769231
$170$	0.504758	0.0387132
$171$	3.27878	0.250734
$172$	−5.92983	−0.452145
$173$	0.0879976	0.00669033	0.00334517	−	0.999994i	$-0.498935\pi$
$173$	0.0879976	0.00669033	0.00334517	+	0.999994i	$0.498935\pi$
$174$	4.98035	0.377559
$175$	4.09736	0.309731
$176$	5.54614	0.418056
$177$	0.199350	0.0149841
$178$	9.03991	0.677570
$179$	12.1153	0.905544	0.452772	−	0.891626i	$-0.350435\pi$
$179$	12.1153	0.905544	0.452772	+	0.891626i	$0.350435\pi$
$180$	0.552454	0.0411775
$181$	−8.49159	−0.631175	−0.315587	−	0.948897i	$-0.602202\pi$
$181$	−8.49159	−0.631175	−0.315587	+	0.948897i	$0.602202\pi$
$182$	0.872745	0.0646922
$183$	12.0418	0.890155
$184$	5.85417	0.431575
$185$	−2.61133	−0.191989
$186$	−6.23785	−0.457382
$187$	5.06732	0.370559
$188$	−1.59894	−0.116615
$189$	−0.872745	−0.0634829
$190$	1.81137	0.131411
$191$	4.69352	0.339611	0.169805	−	0.985478i	$-0.445686\pi$
$191$	4.69352	0.339611	0.169805	+	0.985478i	$0.445686\pi$
$192$	1.00000	0.0721688
$193$	−27.3973	−1.97210	−0.986052	−	0.166437i	$-0.946774\pi$
$193$	−27.3973	−1.97210	−0.986052	+	0.166437i	$0.946774\pi$
$194$	7.55037	0.542085
$195$	−0.552454	−0.0395621
$196$	−6.23832	−0.445594
$197$	−18.5497	−1.32161	−0.660806	−	0.750556i	$-0.729786\pi$
$197$	−18.5497	−1.32161	−0.660806	+	0.750556i	$0.729786\pi$
$198$	5.54614	0.394147
$199$	−1.42414	−0.100955	−0.0504774	−	0.998725i	$-0.516074\pi$
$199$	−1.42414	−0.100955	−0.0504774	+	0.998725i	$0.516074\pi$
$200$	−4.69479	−0.331972
$201$	5.88462	0.415069
$202$	11.5516	0.812770
$203$	−4.34658	−0.305070
$204$	0.913665	0.0639694
$205$	2.95097	0.206105
$206$	4.37678	0.304945
$207$	5.85417	0.406893
$208$	−1.00000	−0.0693375
$209$	18.1846	1.25785
$210$	−0.482152	−0.0332716
$211$	1.14724	0.0789793	0.0394897	−	0.999220i	$-0.487427\pi$
$211$	1.14724	0.0789793	0.0394897	+	0.999220i	$0.487427\pi$
$212$	1.00000	0.0686803
$213$	−1.42481	−0.0976266
$214$	1.66056	0.113514
$215$	−3.27596	−0.223418
$216$	1.00000	0.0680414
$217$	5.44406	0.369567
$218$	16.8427	1.14073
$219$	−5.84619	−0.395049
$220$	3.06399	0.206574
$221$	−0.913665	−0.0614598
$222$	−4.72678	−0.317241
$223$	−24.4238	−1.63554	−0.817769	−	0.575547i	$-0.804789\pi$
$223$	−24.4238	−1.63554	−0.817769	+	0.575547i	$0.804789\pi$
$224$	−0.872745	−0.0583127
$225$	−4.69479	−0.312986
$226$	−1.31059	−0.0871794
$227$	0.788722	0.0523493	0.0261746	−	0.999657i	$-0.491667\pi$
$227$	0.788722	0.0523493	0.0261746	+	0.999657i	$0.491667\pi$
$228$	3.27878	0.217142
$229$	21.2711	1.40563	0.702816	−	0.711372i	$-0.251926\pi$
$229$	21.2711	1.40563	0.702816	+	0.711372i	$0.251926\pi$
$230$	3.23416	0.213254
$231$	−4.84037	−0.318473
$232$	4.98035	0.326976
$233$	−17.8915	−1.17211	−0.586056	−	0.810270i	$-0.699320\pi$
$233$	−17.8915	−1.17211	−0.586056	+	0.810270i	$0.699320\pi$
$234$	−1.00000	−0.0653720
$235$	−0.883341	−0.0576228
$236$	0.199350	0.0129766
$237$	−5.74595	−0.373239
$238$	−0.797397	−0.0516876
$239$	−27.0812	−1.75174	−0.875870	−	0.482547i	$-0.839712\pi$
$239$	−27.0812	−1.75174	−0.875870	+	0.482547i	$0.839712\pi$
$240$	0.552454	0.0356608
$241$	−5.71829	−0.368347	−0.184174	−	0.982894i	$-0.558961\pi$
$241$	−5.71829	−0.368347	−0.184174	+	0.982894i	$0.558961\pi$
$242$	19.7597	1.27020
$243$	1.00000	0.0641500
$244$	12.0418	0.770897
$245$	−3.44638	−0.220181
$246$	5.34156	0.340566
$247$	−3.27878	−0.208624
$248$	−6.23785	−0.396104
$249$	−6.36819	−0.403568
$250$	−5.35593	−0.338739
$251$	−5.80253	−0.366252	−0.183126	−	0.983089i	$-0.558622\pi$
$251$	−5.80253	−0.366252	−0.183126	+	0.983089i	$0.558622\pi$
$252$	−0.872745	−0.0549778
$253$	32.4680	2.04125
$254$	−10.9773	−0.688780
$255$	0.504758	0.0316092
$256$	1.00000	0.0625000
$257$	7.59288	0.473631	0.236815	−	0.971555i	$-0.423896\pi$
$257$	7.59288	0.473631	0.236815	+	0.971555i	$0.423896\pi$
$258$	−5.92983	−0.369175
$259$	4.12528	0.256332
$260$	−0.552454	−0.0342618
$261$	4.98035	0.308276
$262$	−8.17595	−0.505112
$263$	−6.83092	−0.421213	−0.210606	−	0.977571i	$-0.567544\pi$
$263$	−6.83092	−0.421213	−0.210606	+	0.977571i	$0.567544\pi$
$264$	5.54614	0.341341
$265$	0.552454	0.0339370
$266$	−2.86154	−0.175452
$267$	9.03991	0.553233
$268$	5.88462	0.359460
$269$	−13.3751	−0.815497	−0.407748	−	0.913094i	$-0.633686\pi$
$269$	−13.3751	−0.815497	−0.407748	+	0.913094i	$0.633686\pi$
$270$	0.552454	0.0336213
$271$	13.4947	0.819744	0.409872	−	0.912143i	$-0.365573\pi$
$271$	13.4947	0.819744	0.409872	+	0.912143i	$0.365573\pi$
$272$	0.913665	0.0553991
$273$	0.872745	0.0528209
$274$	5.66459	0.342210
$275$	−26.0380	−1.57015
$276$	5.85417	0.352379
$277$	−19.3434	−1.16223	−0.581115	−	0.813821i	$-0.697383\pi$
$277$	−19.3434	−1.16223	−0.581115	+	0.813821i	$0.697383\pi$
$278$	−1.77792	−0.106632
$279$	−6.23785	−0.373450
$280$	−0.482152	−0.0288141
$281$	19.9983	1.19300	0.596498	−	0.802614i	$-0.296558\pi$
$281$	19.9983	1.19300	0.596498	+	0.802614i	$0.296558\pi$
$282$	−1.59894	−0.0952155
$283$	28.6734	1.70446	0.852229	−	0.523170i	$-0.175251\pi$
$283$	28.6734	1.70446	0.852229	+	0.523170i	$0.175251\pi$
$284$	−1.42481	−0.0845471
$285$	1.81137	0.107297
$286$	−5.54614	−0.327950
$287$	−4.66182	−0.275179
$288$	1.00000	0.0589256
$289$	−16.1652	−0.950895
$290$	2.75142	0.161569
$291$	7.55037	0.442611
$292$	−5.84619	−0.342122
$293$	−4.37035	−0.255319	−0.127659	−	0.991818i	$-0.540746\pi$
$293$	−4.37035	−0.255319	−0.127659	+	0.991818i	$0.540746\pi$
$294$	−6.23832	−0.363826
$295$	0.110132	0.00641213
$296$	−4.72678	−0.274739
$297$	5.54614	0.321820
$298$	1.11730	0.0647236
$299$	−5.85417	−0.338555
$300$	−4.69479	−0.271054
$301$	5.17523	0.298295
$302$	−14.2577	−0.820439
$303$	11.5516	0.663624
$304$	3.27878	0.188051
$305$	6.65254	0.380923
$306$	0.913665	0.0522308
$307$	−9.89793	−0.564905	−0.282452	−	0.959281i	$-0.591148\pi$
$307$	−9.89793	−0.564905	−0.282452	+	0.959281i	$0.591148\pi$
$308$	−4.84037	−0.275805
$309$	4.37678	0.248986
$310$	−3.44613	−0.195727
$311$	−27.7590	−1.57407	−0.787033	−	0.616911i	$-0.788384\pi$
$311$	−27.7590	−1.57407	−0.787033	+	0.616911i	$0.788384\pi$
$312$	−1.00000	−0.0566139
$313$	15.6658	0.885483	0.442741	−	0.896649i	$-0.354006\pi$
$313$	15.6658	0.885483	0.442741	+	0.896649i	$0.354006\pi$
$314$	−0.934037	−0.0527107
$315$	−0.482152	−0.0271662
$316$	−5.74595	−0.323235
$317$	7.40408	0.415854	0.207927	−	0.978144i	$-0.433328\pi$
$317$	7.40408	0.415854	0.207927	+	0.978144i	$0.433328\pi$
$318$	1.00000	0.0560772
$319$	27.6217	1.54652
$320$	0.552454	0.0308831
$321$	1.66056	0.0926835
$322$	−5.10920	−0.284724
$323$	2.99571	0.166686
$324$	1.00000	0.0555556
$325$	4.69479	0.260420
$326$	15.5716	0.862429
$327$	16.8427	0.931403
$328$	5.34156	0.294938
$329$	1.39547	0.0769346
$330$	3.06399	0.168667
$331$	14.1558	0.778074	0.389037	−	0.921222i	$-0.372808\pi$
$331$	14.1558	0.778074	0.389037	+	0.921222i	$0.372808\pi$
$332$	−6.36819	−0.349500
$333$	−4.72678	−0.259026
$334$	18.6491	1.02043
$335$	3.25098	0.177620
$336$	−0.872745	−0.0476122
$337$	−19.7999	−1.07857	−0.539286	−	0.842123i	$-0.681306\pi$
$337$	−19.7999	−1.07857	−0.539286	+	0.842123i	$0.681306\pi$
$338$	1.00000	0.0543928
$339$	−1.31059	−0.0711817
$340$	0.504758	0.0273744
$341$	−34.5960	−1.87348
$342$	3.27878	0.177296
$343$	11.5537	0.623840
$344$	−5.92983	−0.319715
$345$	3.23416	0.174121
$346$	0.0879976	0.00473078
$347$	10.8646	0.583240	0.291620	−	0.956534i	$-0.405806\pi$
$347$	10.8646	0.583240	0.291620	+	0.956534i	$0.405806\pi$
$348$	4.98035	0.266975
$349$	−8.27767	−0.443093	−0.221547	−	0.975150i	$-0.571111\pi$
$349$	−8.27767	−0.443093	−0.221547	+	0.975150i	$0.571111\pi$
$350$	4.09736	0.219013
$351$	−1.00000	−0.0533761
$352$	5.54614	0.295610
$353$	−25.2326	−1.34299	−0.671497	−	0.741007i	$-0.734348\pi$
$353$	−25.2326	−1.34299	−0.671497	+	0.741007i	$0.734348\pi$
$354$	0.199350	0.0105954
$355$	−0.787144	−0.0417773
$356$	9.03991	0.479114
$357$	−0.797397	−0.0422027
$358$	12.1153	0.640316
$359$	−23.0838	−1.21832	−0.609159	−	0.793048i	$-0.708493\pi$
$359$	−23.0838	−1.21832	−0.609159	+	0.793048i	$0.708493\pi$
$360$	0.552454	0.0291169
$361$	−8.24962	−0.434190
$362$	−8.49159	−0.446308
$363$	19.7597	1.03711
$364$	0.872745	0.0457443
$365$	−3.22975	−0.169053
$366$	12.0418	0.629435
$367$	7.26730	0.379350	0.189675	−	0.981847i	$-0.439257\pi$
$367$	7.26730	0.379350	0.189675	+	0.981847i	$0.439257\pi$
$368$	5.85417	0.305170
$369$	5.34156	0.278071
$370$	−2.61133	−0.135757
$371$	−0.872745	−0.0453107
$372$	−6.23785	−0.323418
$373$	−35.2304	−1.82416	−0.912082	−	0.410008i	$-0.865526\pi$
$373$	−35.2304	−1.82416	−0.912082	+	0.410008i	$0.865526\pi$
$374$	5.06732	0.262025
$375$	−5.35593	−0.276579
$376$	−1.59894	−0.0824590
$377$	−4.98035	−0.256501
$378$	−0.872745	−0.0448892
$379$	−10.6429	−0.546688	−0.273344	−	0.961916i	$-0.588130\pi$
$379$	−10.6429	−0.546688	−0.273344	+	0.961916i	$0.588130\pi$
$380$	1.81137	0.0929215
$381$	−10.9773	−0.562386
$382$	4.69352	0.240141
$383$	−18.8018	−0.960729	−0.480364	−	0.877069i	$-0.659496\pi$
$383$	−18.8018	−0.960729	−0.480364	+	0.877069i	$0.659496\pi$
$384$	1.00000	0.0510310
$385$	−2.67408	−0.136284
$386$	−27.3973	−1.39449
$387$	−5.92983	−0.301430
$388$	7.55037	0.383312
$389$	−7.86615	−0.398830	−0.199415	−	0.979915i	$-0.563904\pi$
$389$	−7.86615	−0.398830	−0.199415	+	0.979915i	$0.563904\pi$
$390$	−0.552454	−0.0279746
$391$	5.34875	0.270498
$392$	−6.23832	−0.315083
$393$	−8.17595	−0.412422
$394$	−18.5497	−0.934521
$395$	−3.17437	−0.159720
$396$	5.54614	0.278704
$397$	−27.0817	−1.35919	−0.679595	−	0.733588i	$-0.737844\pi$
$397$	−27.0817	−1.35919	−0.679595	+	0.733588i	$0.737844\pi$
$398$	−1.42414	−0.0713858
$399$	−2.86154	−0.143256
$400$	−4.69479	−0.234740
$401$	−27.4065	−1.36861	−0.684307	−	0.729194i	$-0.739895\pi$
$401$	−27.4065	−1.36861	−0.684307	+	0.729194i	$0.739895\pi$
$402$	5.88462	0.293498
$403$	6.23785	0.310730
$404$	11.5516	0.574715
$405$	0.552454	0.0274517
$406$	−4.34658	−0.215717
$407$	−26.2154	−1.29945
$408$	0.913665	0.0452332
$409$	−1.44261	−0.0713323	−0.0356662	−	0.999364i	$-0.511355\pi$
$409$	−1.44261	−0.0713323	−0.0356662	+	0.999364i	$0.511355\pi$
$410$	2.95097	0.145738
$411$	5.66459	0.279414
$412$	4.37678	0.215628
$413$	−0.173982	−0.00856110
$414$	5.85417	0.287717
$415$	−3.51813	−0.172698
$416$	−1.00000	−0.0490290
$417$	−1.77792	−0.0870650
$418$	18.1846	0.889436
$419$	29.2588	1.42938	0.714692	−	0.699439i	$-0.246567\pi$
$419$	29.2588	1.42938	0.714692	+	0.699439i	$0.246567\pi$
$420$	−0.482152	−0.0235266
$421$	−36.5577	−1.78171	−0.890856	−	0.454286i	$-0.849894\pi$
$421$	−36.5577	−1.78171	−0.890856	+	0.454286i	$0.849894\pi$
$422$	1.14724	0.0558468
$423$	−1.59894	−0.0777431
$424$	1.00000	0.0485643
$425$	−4.28947	−0.208070
$426$	−1.42481	−0.0690325
$427$	−10.5094	−0.508586
$428$	1.66056	0.0802662
$429$	−5.54614	−0.267770
$430$	−3.27596	−0.157981
$431$	32.7056	1.57537	0.787686	−	0.616076i	$-0.211279\pi$
$431$	32.7056	1.57537	0.787686	+	0.616076i	$0.211279\pi$
$432$	1.00000	0.0481125
$433$	−5.42474	−0.260696	−0.130348	−	0.991468i	$-0.541610\pi$
$433$	−5.42474	−0.260696	−0.130348	+	0.991468i	$0.541610\pi$
$434$	5.44406	0.261323
$435$	2.75142	0.131920
$436$	16.8427	0.806619
$437$	19.1945	0.918198
$438$	−5.84619	−0.279342
$439$	−25.6955	−1.22638	−0.613190	−	0.789935i	$-0.710114\pi$
$439$	−25.6955	−1.22638	−0.613190	+	0.789935i	$0.710114\pi$
$440$	3.06399	0.146070
$441$	−6.23832	−0.297063
$442$	−0.913665	−0.0434586
$443$	8.96308	0.425849	0.212924	−	0.977069i	$-0.431701\pi$
$443$	8.96308	0.425849	0.212924	+	0.977069i	$0.431701\pi$
$444$	−4.72678	−0.224323
$445$	4.99414	0.236745
$446$	−24.4238	−1.15650
$447$	1.11730	0.0528466
$448$	−0.872745	−0.0412333
$449$	−19.9529	−0.941633	−0.470817	−	0.882231i	$-0.656041\pi$
$449$	−19.9529	−0.941633	−0.470817	+	0.882231i	$0.656041\pi$
$450$	−4.69479	−0.221315
$451$	29.6250	1.39499
$452$	−1.31059	−0.0616451
$453$	−14.2577	−0.669886
$454$	0.788722	0.0370165
$455$	0.482152	0.0226036
$456$	3.27878	0.153543
$457$	18.5542	0.867928	0.433964	−	0.900930i	$-0.357114\pi$
$457$	18.5542	0.867928	0.433964	+	0.900930i	$0.357114\pi$
$458$	21.2711	0.993932
$459$	0.913665	0.0426462
$460$	3.23416	0.150793
$461$	0.326061	0.0151862	0.00759309	−	0.999971i	$-0.497583\pi$
$461$	0.326061	0.0151862	0.00759309	+	0.999971i	$0.497583\pi$
$462$	−4.84037	−0.225194
$463$	−12.4075	−0.576626	−0.288313	−	0.957536i	$-0.593094\pi$
$463$	−12.4075	−0.576626	−0.288313	+	0.957536i	$0.593094\pi$
$464$	4.98035	0.231207
$465$	−3.44613	−0.159810
$466$	−17.8915	−0.828809
$467$	9.02962	0.417841	0.208921	−	0.977933i	$-0.433005\pi$
$467$	9.02962	0.417841	0.208921	+	0.977933i	$0.433005\pi$
$468$	−1.00000	−0.0462250
$469$	−5.13577	−0.237148
$470$	−0.883341	−0.0407455
$471$	−0.934037	−0.0430381
$472$	0.199350	0.00917585
$473$	−32.8876	−1.51218
$474$	−5.74595	−0.263920
$475$	−15.3932	−0.706288
$476$	−0.797397	−0.0365486
$477$	1.00000	0.0457869
$478$	−27.0812	−1.23867
$479$	−5.98213	−0.273331	−0.136665	−	0.990617i	$-0.543639\pi$
$479$	−5.98213	−0.273331	−0.136665	+	0.990617i	$0.543639\pi$
$480$	0.552454	0.0252160
$481$	4.72678	0.215523
$482$	−5.71829	−0.260461
$483$	−5.10920	−0.232476
$484$	19.7597	0.898167
$485$	4.17123	0.189406
$486$	1.00000	0.0453609
$487$	42.1354	1.90934	0.954668	−	0.297673i	$-0.0962104\pi$
$487$	42.1354	1.90934	0.954668	+	0.297673i	$0.0962104\pi$
$488$	12.0418	0.545106
$489$	15.5716	0.704170
$490$	−3.44638	−0.155692
$491$	17.2789	0.779786	0.389893	−	0.920860i	$-0.372512\pi$
$491$	17.2789	0.779786	0.389893	+	0.920860i	$0.372512\pi$
$492$	5.34156	0.240816
$493$	4.55037	0.204939
$494$	−3.27878	−0.147519
$495$	3.06399	0.137716
$496$	−6.23785	−0.280088
$497$	1.24350	0.0557786
$498$	−6.36819	−0.285365
$499$	−18.6857	−0.836486	−0.418243	−	0.908335i	$-0.637354\pi$
$499$	−18.6857	−0.836486	−0.418243	+	0.908335i	$0.637354\pi$
$500$	−5.35593	−0.239524
$501$	18.6491	0.833180
$502$	−5.80253	−0.258980
$503$	−22.4941	−1.00296	−0.501482	−	0.865168i	$-0.667212\pi$
$503$	−22.4941	−1.00296	−0.501482	+	0.865168i	$0.667212\pi$
$504$	−0.872745	−0.0388752
$505$	6.38174	0.283984
$506$	32.4680	1.44338
$507$	1.00000	0.0444116
$508$	−10.9773	−0.487041
$509$	9.49616	0.420910	0.210455	−	0.977604i	$-0.432505\pi$
$509$	9.49616	0.420910	0.210455	+	0.977604i	$0.432505\pi$
$510$	0.504758	0.0223511
$511$	5.10223	0.225709
$512$	1.00000	0.0441942
$513$	3.27878	0.144762
$514$	7.59288	0.334908
$515$	2.41797	0.106548
$516$	−5.92983	−0.261046
$517$	−8.86794	−0.390012
$518$	4.12528	0.181254
$519$	0.0879976	0.00386266
$520$	−0.552454	−0.0242267
$521$	21.1385	0.926093	0.463046	−	0.886334i	$-0.346756\pi$
$521$	21.1385	0.926093	0.463046	+	0.886334i	$0.346756\pi$
$522$	4.98035	0.217984
$523$	35.5896	1.55622	0.778111	−	0.628126i	$-0.216178\pi$
$523$	35.5896	1.55622	0.778111	+	0.628126i	$0.216178\pi$
$524$	−8.17595	−0.357168
$525$	4.09736	0.178823
$526$	−6.83092	−0.297842
$527$	−5.69931	−0.248266
$528$	5.54614	0.241365
$529$	11.2713	0.490055
$530$	0.552454	0.0239971
$531$	0.199350	0.00865107
$532$	−2.86154	−0.124063
$533$	−5.34156	−0.231369
$534$	9.03991	0.391195
$535$	0.917384	0.0396620
$536$	5.88462	0.254177
$537$	12.1153	0.522816
$538$	−13.3751	−0.576643
$539$	−34.5986	−1.49027
$540$	0.552454	0.0237738
$541$	−13.1008	−0.563248	−0.281624	−	0.959525i	$-0.590873\pi$
$541$	−13.1008	−0.563248	−0.281624	+	0.959525i	$0.590873\pi$
$542$	13.4947	0.579647
$543$	−8.49159	−0.364409
$544$	0.913665	0.0391731
$545$	9.30482	0.398575
$546$	0.872745	0.0373500
$547$	22.8681	0.977768	0.488884	−	0.872349i	$-0.337404\pi$
$547$	22.8681	0.977768	0.488884	+	0.872349i	$0.337404\pi$
$548$	5.66459	0.241979
$549$	12.0418	0.513931
$550$	−26.0380	−1.11026
$551$	16.3295	0.695658
$552$	5.85417	0.249170
$553$	5.01475	0.213249
$554$	−19.3434	−0.821821
$555$	−2.61133	−0.110845
$556$	−1.77792	−0.0754005
$557$	−46.6156	−1.97517	−0.987584	−	0.157091i	$-0.949789\pi$
$557$	−46.6156	−1.97517	−0.987584	+	0.157091i	$0.949789\pi$
$558$	−6.23785	−0.264069
$559$	5.92983	0.250805
$560$	−0.482152	−0.0203746
$561$	5.06732	0.213942
$562$	19.9983	0.843576
$563$	0.416526	0.0175545	0.00877724	−	0.999961i	$-0.497206\pi$
$563$	0.416526	0.0175545	0.00877724	+	0.999961i	$0.497206\pi$
$564$	−1.59894	−0.0673275
$565$	−0.724043	−0.0304607
$566$	28.6734	1.20523
$567$	−0.872745	−0.0366519
$568$	−1.42481	−0.0597839
$569$	32.8148	1.37567	0.687833	−	0.725869i	$-0.258562\pi$
$569$	32.8148	1.37567	0.687833	+	0.725869i	$0.258562\pi$
$570$	1.81137	0.0758701
$571$	−13.6927	−0.573021	−0.286510	−	0.958077i	$-0.592495\pi$
$571$	−13.6927	−0.573021	−0.286510	+	0.958077i	$0.592495\pi$
$572$	−5.54614	−0.231896
$573$	4.69352	0.196074
$574$	−4.66182	−0.194581
$575$	−27.4841	−1.14617
$576$	1.00000	0.0416667
$577$	18.4395	0.767646	0.383823	−	0.923407i	$-0.374607\pi$
$577$	18.4395	0.767646	0.383823	+	0.923407i	$0.374607\pi$
$578$	−16.1652	−0.672384
$579$	−27.3973	−1.13859
$580$	2.75142	0.114246
$581$	5.55781	0.230577
$582$	7.55037	0.312973
$583$	5.54614	0.229698
$584$	−5.84619	−0.241917
$585$	−0.552454	−0.0228412
$586$	−4.37035	−0.180538
$587$	32.1824	1.32831	0.664154	−	0.747595i	$-0.268792\pi$
$587$	32.1824	1.32831	0.664154	+	0.747595i	$0.268792\pi$
$588$	−6.23832	−0.257264
$589$	−20.4525	−0.842732
$590$	0.110132	0.00453406
$591$	−18.5497	−0.763034
$592$	−4.72678	−0.194270
$593$	−23.0786	−0.947724	−0.473862	−	0.880599i	$-0.657141\pi$
$593$	−23.0786	−0.947724	−0.473862	+	0.880599i	$0.657141\pi$
$594$	5.54614	0.227561
$595$	−0.440525	−0.0180598
$596$	1.11730	0.0457665
$597$	−1.42414	−0.0582863
$598$	−5.85417	−0.239395
$599$	28.3859	1.15982	0.579909	−	0.814682i	$-0.303088\pi$
$599$	28.3859	1.15982	0.579909	+	0.814682i	$0.303088\pi$
$600$	−4.69479	−0.191664
$601$	−8.58379	−0.350140	−0.175070	−	0.984556i	$-0.556015\pi$
$601$	−8.58379	−0.350140	−0.175070	+	0.984556i	$0.556015\pi$
$602$	5.17523	0.210926
$603$	5.88462	0.239640
$604$	−14.2577	−0.580138
$605$	10.9163	0.443811
$606$	11.5516	0.469253
$607$	−20.4177	−0.828729	−0.414365	−	0.910111i	$-0.635996\pi$
$607$	−20.4177	−0.828729	−0.414365	+	0.910111i	$0.635996\pi$
$608$	3.27878	0.132972
$609$	−4.34658	−0.176132
$610$	6.65254	0.269353
$611$	1.59894	0.0646862
$612$	0.913665	0.0369327
$613$	−21.4524	−0.866454	−0.433227	−	0.901285i	$-0.642625\pi$
$613$	−21.4524	−0.866454	−0.433227	+	0.901285i	$0.642625\pi$
$614$	−9.89793	−0.399448
$615$	2.95097	0.118995
$616$	−4.84037	−0.195024
$617$	−11.9556	−0.481316	−0.240658	−	0.970610i	$-0.577363\pi$
$617$	−11.9556	−0.481316	−0.240658	+	0.970610i	$0.577363\pi$
$618$	4.37678	0.176060
$619$	42.2139	1.69672	0.848360	−	0.529420i	$-0.177590\pi$
$619$	42.2139	1.69672	0.848360	+	0.529420i	$0.177590\pi$
$620$	−3.44613	−0.138400
$621$	5.85417	0.234920
$622$	−27.7590	−1.11303
$623$	−7.88954	−0.316088
$624$	−1.00000	−0.0400320
$625$	20.5151	0.820603
$626$	15.6658	0.626131
$627$	18.1846	0.726221
$628$	−0.934037	−0.0372721
$629$	−4.31870	−0.172198
$630$	−0.482152	−0.0192094
$631$	18.6496	0.742429	0.371214	−	0.928547i	$-0.378941\pi$
$631$	18.6496	0.742429	0.371214	+	0.928547i	$0.378941\pi$
$632$	−5.74595	−0.228562
$633$	1.14724	0.0455987
$634$	7.40408	0.294053
$635$	−6.06448	−0.240662
$636$	1.00000	0.0396526
$637$	6.23832	0.247171
$638$	27.6217	1.09355
$639$	−1.42481	−0.0563648
$640$	0.552454	0.0218377
$641$	16.6256	0.656671	0.328336	−	0.944561i	$-0.393512\pi$
$641$	16.6256	0.656671	0.328336	+	0.944561i	$0.393512\pi$
$642$	1.66056	0.0655371
$643$	7.52171	0.296627	0.148314	−	0.988940i	$-0.452615\pi$
$643$	7.52171	0.296627	0.148314	+	0.988940i	$0.452615\pi$
$644$	−5.10920	−0.201330
$645$	−3.27596	−0.128991
$646$	2.99571	0.117864
$647$	−49.4247	−1.94308	−0.971542	−	0.236868i	$-0.923879\pi$
$647$	−49.4247	−1.94308	−0.971542	+	0.236868i	$0.923879\pi$
$648$	1.00000	0.0392837
$649$	1.10563	0.0433996
$650$	4.69479	0.184145
$651$	5.44406	0.213369
$652$	15.5716	0.609830
$653$	15.2335	0.596134	0.298067	−	0.954545i	$-0.403658\pi$
$653$	15.2335	0.596134	0.298067	+	0.954545i	$0.403658\pi$
$654$	16.8427	0.658601
$655$	−4.51684	−0.176487
$656$	5.34156	0.208553
$657$	−5.84619	−0.228082
$658$	1.39547	0.0544010
$659$	−23.6037	−0.919469	−0.459734	−	0.888056i	$-0.652055\pi$
$659$	−23.6037	−0.919469	−0.459734	+	0.888056i	$0.652055\pi$
$660$	3.06399	0.119266
$661$	34.7714	1.35245	0.676226	−	0.736694i	$-0.263614\pi$
$661$	34.7714	1.35245	0.676226	+	0.736694i	$0.263614\pi$
$662$	14.1558	0.550181
$663$	−0.913665	−0.0354838
$664$	−6.36819	−0.247134
$665$	−1.58087	−0.0613034
$666$	−4.72678	−0.183159
$667$	29.1558	1.12892
$668$	18.6491	0.721555
$669$	−24.4238	−0.944278
$670$	3.25098	0.125596
$671$	66.7855	2.57822
$672$	−0.872745	−0.0336669
$673$	−45.8088	−1.76580	−0.882899	−	0.469563i	$-0.844412\pi$
$673$	−45.8088	−1.76580	−0.882899	+	0.469563i	$0.844412\pi$
$674$	−19.7999	−0.762665
$675$	−4.69479	−0.180703
$676$	1.00000	0.0384615
$677$	3.40088	0.130706	0.0653532	−	0.997862i	$-0.479183\pi$
$677$	3.40088	0.130706	0.0653532	+	0.997862i	$0.479183\pi$
$678$	−1.31059	−0.0503330
$679$	−6.58955	−0.252884
$680$	0.504758	0.0193566
$681$	0.788722	0.0302239
$682$	−34.5960	−1.32475
$683$	−6.99266	−0.267567	−0.133783	−	0.991011i	$-0.542713\pi$
$683$	−6.99266	−0.267567	−0.133783	+	0.991011i	$0.542713\pi$
$684$	3.27878	0.125367
$685$	3.12943	0.119569
$686$	11.5537	0.441121
$687$	21.2711	0.811542
$688$	−5.92983	−0.226072
$689$	−1.00000	−0.0380970
$690$	3.23416	0.123122
$691$	25.0154	0.951631	0.475816	−	0.879545i	$-0.342153\pi$
$691$	25.0154	0.951631	0.475816	+	0.879545i	$0.342153\pi$
$692$	0.0879976	0.00334517
$693$	−4.84037	−0.183870
$694$	10.8646	0.412413
$695$	−0.982218	−0.0372577
$696$	4.98035	0.188780
$697$	4.88040	0.184858
$698$	−8.27767	−0.313314
$699$	−17.8915	−0.676720
$700$	4.09736	0.154866
$701$	−7.46092	−0.281795	−0.140897	−	0.990024i	$-0.544999\pi$
$701$	−7.46092	−0.281795	−0.140897	+	0.990024i	$0.544999\pi$
$702$	−1.00000	−0.0377426
$703$	−15.4981	−0.584521
$704$	5.54614	0.209028
$705$	−0.883341	−0.0332685
$706$	−25.2326	−0.949640
$707$	−10.0816	−0.379159
$708$	0.199350	0.00749205
$709$	−33.9118	−1.27358	−0.636791	−	0.771036i	$-0.719739\pi$
$709$	−33.9118	−1.27358	−0.636791	+	0.771036i	$0.719739\pi$
$710$	−0.787144	−0.0295410
$711$	−5.74595	−0.215490
$712$	9.03991	0.338785
$713$	−36.5174	−1.36759
$714$	−0.797397	−0.0298418
$715$	−3.06399	−0.114587
$716$	12.1153	0.452772
$717$	−27.0812	−1.01137
$718$	−23.0838	−0.861481
$719$	−25.8431	−0.963783	−0.481892	−	0.876231i	$-0.660050\pi$
$719$	−25.8431	−0.963783	−0.481892	+	0.876231i	$0.660050\pi$
$720$	0.552454	0.0205888
$721$	−3.81981	−0.142257
$722$	−8.24962	−0.307019
$723$	−5.71829	−0.212665
$724$	−8.49159	−0.315587
$725$	−23.3817	−0.868375
$726$	19.7597	0.733350
$727$	−0.930766	−0.0345202	−0.0172601	−	0.999851i	$-0.505494\pi$
$727$	−0.930766	−0.0345202	−0.0172601	+	0.999851i	$0.505494\pi$
$728$	0.872745	0.0323461
$729$	1.00000	0.0370370
$730$	−3.22975	−0.119538
$731$	−5.41788	−0.200387
$732$	12.0418	0.445077
$733$	10.0414	0.370887	0.185443	−	0.982655i	$-0.440628\pi$
$733$	10.0414	0.370887	0.185443	+	0.982655i	$0.440628\pi$
$734$	7.26730	0.268241
$735$	−3.44638	−0.127122
$736$	5.85417	0.215787
$737$	32.6369	1.20220
$738$	5.34156	0.196626
$739$	32.2320	1.18567	0.592837	−	0.805322i	$-0.298008\pi$
$739$	32.2320	1.18567	0.592837	+	0.805322i	$0.298008\pi$
$740$	−2.61133	−0.0959944
$741$	−3.27878	−0.120449
$742$	−0.872745	−0.0320395
$743$	−11.0555	−0.405587	−0.202793	−	0.979222i	$-0.565002\pi$
$743$	−11.0555	−0.405587	−0.202793	+	0.979222i	$0.565002\pi$
$744$	−6.23785	−0.228691
$745$	0.617258	0.0226146
$746$	−35.2304	−1.28988
$747$	−6.36819	−0.233000
$748$	5.06732	0.185279
$749$	−1.44925	−0.0529543
$750$	−5.35593	−0.195571
$751$	−26.9776	−0.984427	−0.492213	−	0.870475i	$-0.663812\pi$
$751$	−26.9776	−0.984427	−0.492213	+	0.870475i	$0.663812\pi$
$752$	−1.59894	−0.0583073
$753$	−5.80253	−0.211456
$754$	−4.98035	−0.181374
$755$	−7.87673	−0.286664
$756$	−0.872745	−0.0317414
$757$	−2.99525	−0.108864	−0.0544320	−	0.998517i	$-0.517335\pi$
$757$	−2.99525	−0.108864	−0.0544320	+	0.998517i	$0.517335\pi$
$758$	−10.6429	−0.386567
$759$	32.4680	1.17851
$760$	1.81137	0.0657055
$761$	1.63320	0.0592034	0.0296017	−	0.999562i	$-0.490576\pi$
$761$	1.63320	0.0592034	0.0296017	+	0.999562i	$0.490576\pi$
$762$	−10.9773	−0.397667
$763$	−14.6994	−0.532153
$764$	4.69352	0.169805
$765$	0.504758	0.0182496
$766$	−18.8018	−0.679338
$767$	−0.199350	−0.00719813
$768$	1.00000	0.0360844
$769$	28.4270	1.02511	0.512553	−	0.858656i	$-0.328700\pi$
$769$	28.4270	1.02511	0.512553	+	0.858656i	$0.328700\pi$
$770$	−2.67408	−0.0963672
$771$	7.59288	0.273451
$772$	−27.3973	−0.986052
$773$	23.0601	0.829413	0.414707	−	0.909955i	$-0.363884\pi$
$773$	23.0601	0.829413	0.414707	+	0.909955i	$0.363884\pi$
$774$	−5.92983	−0.213143
$775$	29.2854	1.05196
$776$	7.55037	0.271043
$777$	4.12528	0.147993
$778$	−7.86615	−0.282015
$779$	17.5138	0.627497
$780$	−0.552454	−0.0197810
$781$	−7.90222	−0.282764
$782$	5.34875	0.191271
$783$	4.98035	0.177983
$784$	−6.23832	−0.222797
$785$	−0.516012	−0.0184173
$786$	−8.17595	−0.291626
$787$	4.79053	0.170764	0.0853820	−	0.996348i	$-0.472789\pi$
$787$	4.79053	0.170764	0.0853820	+	0.996348i	$0.472789\pi$
$788$	−18.5497	−0.660806
$789$	−6.83092	−0.243187
$790$	−3.17437	−0.112939
$791$	1.14381	0.0406693
$792$	5.54614	0.197073
$793$	−12.0418	−0.427617
$794$	−27.0817	−0.961092
$795$	0.552454	0.0195935
$796$	−1.42414	−0.0504774
$797$	−5.70650	−0.202135	−0.101067	−	0.994880i	$-0.532226\pi$
$797$	−5.70650	−0.202135	−0.101067	+	0.994880i	$0.532226\pi$
$798$	−2.86154	−0.101297
$799$	−1.46090	−0.0516828
$800$	−4.69479	−0.165986
$801$	9.03991	0.319409
$802$	−27.4065	−0.967756
$803$	−32.4238	−1.14421
$804$	5.88462	0.207535
$805$	−2.82260	−0.0994834
$806$	6.23785	0.219719
$807$	−13.3751	−0.470827
$808$	11.5516	0.406385
$809$	−30.4823	−1.07170	−0.535851	−	0.844313i	$-0.680009\pi$
$809$	−30.4823	−1.07170	−0.535851	+	0.844313i	$0.680009\pi$
$810$	0.552454	0.0194113
$811$	−26.5745	−0.933156	−0.466578	−	0.884480i	$-0.654513\pi$
$811$	−26.5745	−0.933156	−0.466578	+	0.884480i	$0.654513\pi$
$812$	−4.34658	−0.152535
$813$	13.4947	0.473280
$814$	−26.2154	−0.918849
$815$	8.60258	0.301335
$816$	0.913665	0.0319847
$817$	−19.4426	−0.680210
$818$	−1.44261	−0.0504396
$819$	0.872745	0.0304962
$820$	2.95097	0.103052
$821$	47.7700	1.66719	0.833593	−	0.552379i	$-0.186280\pi$
$821$	47.7700	1.66719	0.833593	+	0.552379i	$0.186280\pi$
$822$	5.66459	0.197575
$823$	−41.1554	−1.43459	−0.717293	−	0.696772i	$-0.754619\pi$
$823$	−41.1554	−1.43459	−0.717293	+	0.696772i	$0.754619\pi$
$824$	4.37678	0.152472
$825$	−26.0380	−0.906526
$826$	−0.173982	−0.00605361
$827$	31.7790	1.10506	0.552532	−	0.833492i	$-0.313662\pi$
$827$	31.7790	1.10506	0.552532	+	0.833492i	$0.313662\pi$
$828$	5.85417	0.203446
$829$	−6.09615	−0.211728	−0.105864	−	0.994381i	$-0.533761\pi$
$829$	−6.09615	−0.211728	−0.105864	+	0.994381i	$0.533761\pi$
$830$	−3.51813	−0.122116
$831$	−19.3434	−0.671014
$832$	−1.00000	−0.0346688
$833$	−5.69973	−0.197484
$834$	−1.77792	−0.0615643
$835$	10.3028	0.356542
$836$	18.1846	0.628926
$837$	−6.23785	−0.215612
$838$	29.2588	1.01073
$839$	−31.0336	−1.07140	−0.535700	−	0.844408i	$-0.679952\pi$
$839$	−31.0336	−1.07140	−0.535700	+	0.844408i	$0.679952\pi$
$840$	−0.482152	−0.0166358
$841$	−4.19611	−0.144694
$842$	−36.5577	−1.25986
$843$	19.9983	0.688777
$844$	1.14724	0.0394897
$845$	0.552454	0.0190050
$846$	−1.59894	−0.0549727
$847$	−17.2452	−0.592551
$848$	1.00000	0.0343401
$849$	28.6734	0.984069
$850$	−4.28947	−0.147128
$851$	−27.6714	−0.948562
$852$	−1.42481	−0.0488133
$853$	36.2372	1.24074	0.620370	−	0.784310i	$-0.286983\pi$
$853$	36.2372	1.24074	0.620370	+	0.784310i	$0.286983\pi$
$854$	−10.5094	−0.359625
$855$	1.81137	0.0619477
$856$	1.66056	0.0567568
$857$	−35.1922	−1.20214	−0.601072	−	0.799195i	$-0.705259\pi$
$857$	−35.1922	−1.20214	−0.601072	+	0.799195i	$0.705259\pi$
$858$	−5.54614	−0.189342
$859$	53.3770	1.82120	0.910599	−	0.413291i	$-0.135621\pi$
$859$	53.3770	1.82120	0.910599	+	0.413291i	$0.135621\pi$
$860$	−3.27596	−0.111709
$861$	−4.66182	−0.158874
$862$	32.7056	1.11396
$863$	−28.0721	−0.955584	−0.477792	−	0.878473i	$-0.658563\pi$
$863$	−28.0721	−0.955584	−0.477792	+	0.878473i	$0.658563\pi$
$864$	1.00000	0.0340207
$865$	0.0486146	0.00165295
$866$	−5.42474	−0.184340
$867$	−16.1652	−0.549000
$868$	5.44406	0.184783
$869$	−31.8678	−1.08104
$870$	2.75142	0.0932817
$871$	−5.88462	−0.199393
$872$	16.8427	0.570366
$873$	7.55037	0.255541
$874$	19.1945	0.649264
$875$	4.67436	0.158022
$876$	−5.84619	−0.197524
$877$	32.8144	1.10806	0.554032	−	0.832496i	$-0.313089\pi$
$877$	32.8144	1.10806	0.554032	+	0.832496i	$0.313089\pi$
$878$	−25.6955	−0.867182
$879$	−4.37035	−0.147408
$880$	3.06399	0.103287
$881$	2.85440	0.0961671	0.0480836	−	0.998843i	$-0.484689\pi$
$881$	2.85440	0.0961671	0.0480836	+	0.998843i	$0.484689\pi$
$882$	−6.23832	−0.210055
$883$	−45.9603	−1.54669	−0.773344	−	0.633987i	$-0.781417\pi$
$883$	−45.9603	−1.54669	−0.773344	+	0.633987i	$0.781417\pi$
$884$	−0.913665	−0.0307299
$885$	0.110132	0.00370205
$886$	8.96308	0.301121
$887$	5.76985	0.193733	0.0968663	−	0.995297i	$-0.469118\pi$
$887$	5.76985	0.193733	0.0968663	+	0.995297i	$0.469118\pi$
$888$	−4.72678	−0.158620
$889$	9.58042	0.321317
$890$	4.99414	0.167404
$891$	5.54614	0.185803
$892$	−24.4238	−0.817769
$893$	−5.24257	−0.175436
$894$	1.11730	0.0373682
$895$	6.69317	0.223728
$896$	−0.872745	−0.0291564
$897$	−5.85417	−0.195465
$898$	−19.9529	−0.665835
$899$	−31.0667	−1.03613
$900$	−4.69479	−0.156493
$901$	0.913665	0.0304386
$902$	29.6250	0.986406
$903$	5.17523	0.172221
$904$	−1.31059	−0.0435897
$905$	−4.69121	−0.155941
$906$	−14.2577	−0.473681
$907$	−34.0227	−1.12971	−0.564853	−	0.825192i	$-0.691067\pi$
$907$	−34.0227	−1.12971	−0.564853	+	0.825192i	$0.691067\pi$
$908$	0.788722	0.0261746
$909$	11.5516	0.383143
$910$	0.482152	0.0159832
$911$	−6.85815	−0.227221	−0.113610	−	0.993525i	$-0.536242\pi$
$911$	−6.85815	−0.227221	−0.113610	+	0.993525i	$0.536242\pi$
$912$	3.27878	0.108571
$913$	−35.3189	−1.16888
$914$	18.5542	0.613718
$915$	6.65254	0.219926
$916$	21.2711	0.702816
$917$	7.13552	0.235636
$918$	0.913665	0.0301555
$919$	−21.7828	−0.718547	−0.359274	−	0.933232i	$-0.616976\pi$
$919$	−21.7828	−0.718547	−0.359274	+	0.933232i	$0.616976\pi$
$920$	3.23416	0.106627
$921$	−9.89793	−0.326148
$922$	0.326061	0.0107383
$923$	1.42481	0.0468983
$924$	−4.84037	−0.159236
$925$	22.1913	0.729644
$926$	−12.4075	−0.407736
$927$	4.37678	0.143752
$928$	4.98035	0.163488
$929$	42.8633	1.40630	0.703149	−	0.711042i	$-0.251777\pi$
$929$	42.8633	1.40630	0.703149	+	0.711042i	$0.251777\pi$
$930$	−3.44613	−0.113003
$931$	−20.4541	−0.670354
$932$	−17.8915	−0.586056
$933$	−27.7590	−0.908788
$934$	9.02962	0.295458
$935$	2.79946	0.0915521
$936$	−1.00000	−0.0326860
$937$	15.6768	0.512139	0.256070	−	0.966658i	$-0.417572\pi$
$937$	15.6768	0.512139	0.256070	+	0.966658i	$0.417572\pi$
$938$	−5.13577	−0.167689
$939$	15.6658	0.511234
$940$	−0.883341	−0.0288114
$941$	−12.1604	−0.396417	−0.198208	−	0.980160i	$-0.563512\pi$
$941$	−12.1604	−0.396417	−0.198208	+	0.980160i	$0.563512\pi$
$942$	−0.934037	−0.0304326
$943$	31.2704	1.01830
$944$	0.199350	0.00648830
$945$	−0.482152	−0.0156844
$946$	−32.8876	−1.06927
$947$	−22.9230	−0.744899	−0.372449	−	0.928053i	$-0.621482\pi$
$947$	−22.9230	−0.744899	−0.372449	+	0.928053i	$0.621482\pi$
$948$	−5.74595	−0.186620
$949$	5.84619	0.189775
$950$	−15.3932	−0.499421
$951$	7.40408	0.240094
$952$	−0.797397	−0.0258438
$953$	18.3264	0.593649	0.296825	−	0.954932i	$-0.404072\pi$
$953$	18.3264	0.593649	0.296825	+	0.954932i	$0.404072\pi$
$954$	1.00000	0.0323762
$955$	2.59295	0.0839060
$956$	−27.0812	−0.875870
$957$	27.6217	0.892883
$958$	−5.98213	−0.193274
$959$	−4.94374	−0.159642
$960$	0.552454	0.0178304
$961$	7.91080	0.255187
$962$	4.72678	0.152398
$963$	1.66056	0.0535108
$964$	−5.71829	−0.184174
$965$	−15.1358	−0.487238
$966$	−5.10920	−0.164386
$967$	−20.3518	−0.654468	−0.327234	−	0.944943i	$-0.606117\pi$
$967$	−20.3518	−0.654468	−0.327234	+	0.944943i	$0.606117\pi$
$968$	19.7597	0.635100
$969$	2.99571	0.0962359
$970$	4.17123	0.133930
$971$	21.7460	0.697864	0.348932	−	0.937148i	$-0.386544\pi$
$971$	21.7460	0.697864	0.348932	+	0.937148i	$0.386544\pi$
$972$	1.00000	0.0320750
$973$	1.55167	0.0497442
$974$	42.1354	1.35010
$975$	4.69479	0.150354
$976$	12.0418	0.385448
$977$	20.5145	0.656317	0.328158	−	0.944623i	$-0.393572\pi$
$977$	20.5145	0.656317	0.328158	+	0.944623i	$0.393572\pi$
$978$	15.5716	0.497924
$979$	50.1366	1.60237
$980$	−3.44638	−0.110091
$981$	16.8427	0.537746
$982$	17.2789	0.551392
$983$	−30.0597	−0.958754	−0.479377	−	0.877609i	$-0.659137\pi$
$983$	−30.0597	−0.958754	−0.479377	+	0.877609i	$0.659137\pi$
$984$	5.34156	0.170283
$985$	−10.2479	−0.326524
$986$	4.55037	0.144913
$987$	1.39547	0.0444182
$988$	−3.27878	−0.104312
$989$	−34.7142	−1.10385
$990$	3.06399	0.0973799
$991$	−12.8333	−0.407662	−0.203831	−	0.979006i	$-0.565339\pi$
$991$	−12.8333	−0.407662	−0.203831	+	0.979006i	$0.565339\pi$
$992$	−6.23785	−0.198052
$993$	14.1558	0.449221
$994$	1.24350	0.0394414
$995$	−0.786773	−0.0249424
$996$	−6.36819	−0.201784
$997$	29.9961	0.949987	0.474993	−	0.879989i	$-0.342450\pi$
$997$	29.9961	0.949987	0.474993	+	0.879989i	$0.342450\pi$
$998$	−18.6857	−0.591485
$999$	−4.72678	−0.149549

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4134.2.a.x.1.4	✓	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4134.2.a.x.1.4	✓	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:	\( N \)	\(=\)	\( 4134 = 2 \cdot 3 \cdot 13 \cdot 53 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4134.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +0.552454 q^{5} +1.00000 q^{6} -0.872745 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +0.552454 q^{5} +1.00000 q^{6} -0.872745 q^{7} +1.00000 q^{8} +1.00000 q^{9} +0.552454 q^{10} +5.54614 q^{11} +1.00000 q^{12} -1.00000 q^{13} -0.872745 q^{14} +0.552454 q^{15} +1.00000 q^{16} +0.913665 q^{17} +1.00000 q^{18} +3.27878 q^{19} +0.552454 q^{20} -0.872745 q^{21} +5.54614 q^{22} +5.85417 q^{23} +1.00000 q^{24} -4.69479 q^{25} -1.00000 q^{26} +1.00000 q^{27} -0.872745 q^{28} +4.98035 q^{29} +0.552454 q^{30} -6.23785 q^{31} +1.00000 q^{32} +5.54614 q^{33} +0.913665 q^{34} -0.482152 q^{35} +1.00000 q^{36} -4.72678 q^{37} +3.27878 q^{38} -1.00000 q^{39} +0.552454 q^{40} +5.34156 q^{41} -0.872745 q^{42} -5.92983 q^{43} +5.54614 q^{44} +0.552454 q^{45} +5.85417 q^{46} -1.59894 q^{47} +1.00000 q^{48} -6.23832 q^{49} -4.69479 q^{50} +0.913665 q^{51} -1.00000 q^{52} +1.00000 q^{53} +1.00000 q^{54} +3.06399 q^{55} -0.872745 q^{56} +3.27878 q^{57} +4.98035 q^{58} +0.199350 q^{59} +0.552454 q^{60} +12.0418 q^{61} -6.23785 q^{62} -0.872745 q^{63} +1.00000 q^{64} -0.552454 q^{65} +5.54614 q^{66} +5.88462 q^{67} +0.913665 q^{68} +5.85417 q^{69} -0.482152 q^{70} -1.42481 q^{71} +1.00000 q^{72} -5.84619 q^{73} -4.72678 q^{74} -4.69479 q^{75} +3.27878 q^{76} -4.84037 q^{77} -1.00000 q^{78} -5.74595 q^{79} +0.552454 q^{80} +1.00000 q^{81} +5.34156 q^{82} -6.36819 q^{83} -0.872745 q^{84} +0.504758 q^{85} -5.92983 q^{86} +4.98035 q^{87} +5.54614 q^{88} +9.03991 q^{89} +0.552454 q^{90} +0.872745 q^{91} +5.85417 q^{92} -6.23785 q^{93} -1.59894 q^{94} +1.81137 q^{95} +1.00000 q^{96} +7.55037 q^{97} -6.23832 q^{98} +5.54614 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 8 q^{2} + 8 q^{3} + 8 q^{4} + 2 q^{5} + 8 q^{6} + 7 q^{7} + 8 q^{8} + 8 q^{9}+O(q^{10}) \) 8 * q + 8 * q^2 + 8 * q^3 + 8 * q^4 + 2 * q^5 + 8 * q^6 + 7 * q^7 + 8 * q^8 + 8 * q^9	\( 8 q + 8 q^{2} + 8 q^{3} + 8 q^{4} + 2 q^{5} + 8 q^{6} + 7 q^{7} + 8 q^{8} + 8 q^{9} + 2 q^{10} + 7 q^{11} + 8 q^{12} - 8 q^{13} + 7 q^{14} + 2 q^{15} + 8 q^{16} + 8 q^{17} + 8 q^{18} + 11 q^{19} + 2 q^{20} + 7 q^{21} + 7 q^{22} + 5 q^{23} + 8 q^{24} + 6 q^{25} - 8 q^{26} + 8 q^{27} + 7 q^{28} + 13 q^{29} + 2 q^{30} + 12 q^{31} + 8 q^{32} + 7 q^{33} + 8 q^{34} + 14 q^{35} + 8 q^{36} + 10 q^{37} + 11 q^{38} - 8 q^{39} + 2 q^{40} + 19 q^{41} + 7 q^{42} + 10 q^{43} + 7 q^{44} + 2 q^{45} + 5 q^{46} + 6 q^{47} + 8 q^{48} + 15 q^{49} + 6 q^{50} + 8 q^{51} - 8 q^{52} + 8 q^{53} + 8 q^{54} + 5 q^{55} + 7 q^{56} + 11 q^{57} + 13 q^{58} + 11 q^{59} + 2 q^{60} + 6 q^{61} + 12 q^{62} + 7 q^{63} + 8 q^{64} - 2 q^{65} + 7 q^{66} + 5 q^{67} + 8 q^{68} + 5 q^{69} + 14 q^{70} - 6 q^{71} + 8 q^{72} + 18 q^{73} + 10 q^{74} + 6 q^{75} + 11 q^{76} - 8 q^{77} - 8 q^{78} + 17 q^{79} + 2 q^{80} + 8 q^{81} + 19 q^{82} + 16 q^{83} + 7 q^{84} + 25 q^{85} + 10 q^{86} + 13 q^{87} + 7 q^{88} - 8 q^{89} + 2 q^{90} - 7 q^{91} + 5 q^{92} + 12 q^{93} + 6 q^{94} - 30 q^{95} + 8 q^{96} + 11 q^{97} + 15 q^{98} + 7 q^{99}+O(q^{100}) \) 8 * q + 8 * q^2 + 8 * q^3 + 8 * q^4 + 2 * q^5 + 8 * q^6 + 7 * q^7 + 8 * q^8 + 8 * q^9 + 2 * q^10 + 7 * q^11 + 8 * q^12 - 8 * q^13 + 7 * q^14 + 2 * q^15 + 8 * q^16 + 8 * q^17 + 8 * q^18 + 11 * q^19 + 2 * q^20 + 7 * q^21 + 7 * q^22 + 5 * q^23 + 8 * q^24 + 6 * q^25 - 8 * q^26 + 8 * q^27 + 7 * q^28 + 13 * q^29 + 2 * q^30 + 12 * q^31 + 8 * q^32 + 7 * q^33 + 8 * q^34 + 14 * q^35 + 8 * q^36 + 10 * q^37 + 11 * q^38 - 8 * q^39 + 2 * q^40 + 19 * q^41 + 7 * q^42 + 10 * q^43 + 7 * q^44 + 2 * q^45 + 5 * q^46 + 6 * q^47 + 8 * q^48 + 15 * q^49 + 6 * q^50 + 8 * q^51 - 8 * q^52 + 8 * q^53 + 8 * q^54 + 5 * q^55 + 7 * q^56 + 11 * q^57 + 13 * q^58 + 11 * q^59 + 2 * q^60 + 6 * q^61 + 12 * q^62 + 7 * q^63 + 8 * q^64 - 2 * q^65 + 7 * q^66 + 5 * q^67 + 8 * q^68 + 5 * q^69 + 14 * q^70 - 6 * q^71 + 8 * q^72 + 18 * q^73 + 10 * q^74 + 6 * q^75 + 11 * q^76 - 8 * q^77 - 8 * q^78 + 17 * q^79 + 2 * q^80 + 8 * q^81 + 19 * q^82 + 16 * q^83 + 7 * q^84 + 25 * q^85 + 10 * q^86 + 13 * q^87 + 7 * q^88 - 8 * q^89 + 2 * q^90 - 7 * q^91 + 5 * q^92 + 12 * q^93 + 6 * q^94 - 30 * q^95 + 8 * q^96 + 11 * q^97 + 15 * q^98 + 7 * q^99

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