LMFDB - Embedded newform 4730.2.a.bf.1.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4730,2,Mod(1,4730)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4730, 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("4730.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4730 = 2 \cdot 5 \cdot 11 \cdot 43 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4730.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:	$37.7692401561$
Analytic rank:	$0$
Dimension:	$13$
Coefficient field:	$\mathbb{Q}[x]/(x^{13} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{13} - 32 x^{11} - 5 x^{10} + 376 x^{9} + 100 x^{8} - 1985 x^{7} - 576 x^{6} + 4708 x^{5} + 889 x^{4} + \cdots - 128 $ x^13 - 32x^11 - 5x^10 + 376x^9 + 100x^8 - 1985x^7 - 576x^6 + 4708x^5 + 889x^4 - 4774x^3 - 296x^2 + 1648*x - 128
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.5
Root			$1.16663$ of defining polynomial
Character	$\chi$	$=$	4730.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -1.16663 q^{3} +1.00000 q^{4} -1.00000 q^{5} -1.16663 q^{6} -3.85859 q^{7} +1.00000 q^{8} -1.63898 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -1.16663 q^{3} +1.00000 q^{4} -1.00000 q^{5} -1.16663 q^{6} -3.85859 q^{7} +1.00000 q^{8} -1.63898 q^{9} -1.00000 q^{10} +1.00000 q^{11} -1.16663 q^{12} -3.76512 q^{13} -3.85859 q^{14} +1.16663 q^{15} +1.00000 q^{16} -5.05803 q^{17} -1.63898 q^{18} -2.28887 q^{19} -1.00000 q^{20} +4.50153 q^{21} +1.00000 q^{22} -3.15631 q^{23} -1.16663 q^{24} +1.00000 q^{25} -3.76512 q^{26} +5.41196 q^{27} -3.85859 q^{28} +8.35160 q^{29} +1.16663 q^{30} -3.01484 q^{31} +1.00000 q^{32} -1.16663 q^{33} -5.05803 q^{34} +3.85859 q^{35} -1.63898 q^{36} -4.67122 q^{37} -2.28887 q^{38} +4.39249 q^{39} -1.00000 q^{40} -9.20945 q^{41} +4.50153 q^{42} +1.00000 q^{43} +1.00000 q^{44} +1.63898 q^{45} -3.15631 q^{46} +6.69155 q^{47} -1.16663 q^{48} +7.88868 q^{49} +1.00000 q^{50} +5.90083 q^{51} -3.76512 q^{52} +4.13953 q^{53} +5.41196 q^{54} -1.00000 q^{55} -3.85859 q^{56} +2.67026 q^{57} +8.35160 q^{58} +10.9802 q^{59} +1.16663 q^{60} +7.94861 q^{61} -3.01484 q^{62} +6.32415 q^{63} +1.00000 q^{64} +3.76512 q^{65} -1.16663 q^{66} +7.87269 q^{67} -5.05803 q^{68} +3.68223 q^{69} +3.85859 q^{70} -0.268322 q^{71} -1.63898 q^{72} -3.06434 q^{73} -4.67122 q^{74} -1.16663 q^{75} -2.28887 q^{76} -3.85859 q^{77} +4.39249 q^{78} -12.8076 q^{79} -1.00000 q^{80} -1.39679 q^{81} -9.20945 q^{82} -9.21995 q^{83} +4.50153 q^{84} +5.05803 q^{85} +1.00000 q^{86} -9.74320 q^{87} +1.00000 q^{88} -4.61307 q^{89} +1.63898 q^{90} +14.5280 q^{91} -3.15631 q^{92} +3.51719 q^{93} +6.69155 q^{94} +2.28887 q^{95} -1.16663 q^{96} -11.3046 q^{97} +7.88868 q^{98} -1.63898 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 13 q + 13 q^{2} + 13 q^{4} - 13 q^{5} + 7 q^{7} + 13 q^{8} + 25 q^{9}+O(q^{10}) $ 13 * q + 13 * q^2 + 13 * q^4 - 13 * q^5 + 7 * q^7 + 13 * q^8 + 25 * q^9	$ 13 q + 13 q^{2} + 13 q^{4} - 13 q^{5} + 7 q^{7} + 13 q^{8} + 25 q^{9} - 13 q^{10} + 13 q^{11} + 11 q^{13} + 7 q^{14} + 13 q^{16} - 2 q^{17} + 25 q^{18} + 7 q^{19} - 13 q^{20} + 12 q^{21} + 13 q^{22} + 12 q^{23} + 13 q^{25} + 11 q^{26} - 15 q^{27} + 7 q^{28} + 14 q^{29} + 20 q^{31} + 13 q^{32} - 2 q^{34} - 7 q^{35} + 25 q^{36} + 17 q^{37} + 7 q^{38} - 4 q^{39} - 13 q^{40} + 9 q^{41} + 12 q^{42} + 13 q^{43} + 13 q^{44} - 25 q^{45} + 12 q^{46} - 9 q^{47} + 30 q^{49} + 13 q^{50} - 3 q^{51} + 11 q^{52} + 22 q^{53} - 15 q^{54} - 13 q^{55} + 7 q^{56} + 17 q^{57} + 14 q^{58} + 19 q^{59} + 2 q^{61} + 20 q^{62} + 12 q^{63} + 13 q^{64} - 11 q^{65} + 9 q^{67} - 2 q^{68} - 6 q^{69} - 7 q^{70} + 6 q^{71} + 25 q^{72} + 7 q^{73} + 17 q^{74} + 7 q^{76} + 7 q^{77} - 4 q^{78} + 50 q^{79} - 13 q^{80} + 85 q^{81} + 9 q^{82} + q^{83} + 12 q^{84} + 2 q^{85} + 13 q^{86} - 21 q^{87} + 13 q^{88} + 5 q^{89} - 25 q^{90} + 5 q^{91} + 12 q^{92} + 3 q^{93} - 9 q^{94} - 7 q^{95} + 20 q^{97} + 30 q^{98} + 25 q^{99}+O(q^{100}) $ 13 * q + 13 * q^2 + 13 * q^4 - 13 * q^5 + 7 * q^7 + 13 * q^8 + 25 * q^9 - 13 * q^10 + 13 * q^11 + 11 * q^13 + 7 * q^14 + 13 * q^16 - 2 * q^17 + 25 * q^18 + 7 * q^19 - 13 * q^20 + 12 * q^21 + 13 * q^22 + 12 * q^23 + 13 * q^25 + 11 * q^26 - 15 * q^27 + 7 * q^28 + 14 * q^29 + 20 * q^31 + 13 * q^32 - 2 * q^34 - 7 * q^35 + 25 * q^36 + 17 * q^37 + 7 * q^38 - 4 * q^39 - 13 * q^40 + 9 * q^41 + 12 * q^42 + 13 * q^43 + 13 * q^44 - 25 * q^45 + 12 * q^46 - 9 * q^47 + 30 * q^49 + 13 * q^50 - 3 * q^51 + 11 * q^52 + 22 * q^53 - 15 * q^54 - 13 * q^55 + 7 * q^56 + 17 * q^57 + 14 * q^58 + 19 * q^59 + 2 * q^61 + 20 * q^62 + 12 * q^63 + 13 * q^64 - 11 * q^65 + 9 * q^67 - 2 * q^68 - 6 * q^69 - 7 * q^70 + 6 * q^71 + 25 * q^72 + 7 * q^73 + 17 * q^74 + 7 * q^76 + 7 * q^77 - 4 * q^78 + 50 * q^79 - 13 * q^80 + 85 * q^81 + 9 * q^82 + q^83 + 12 * q^84 + 2 * q^85 + 13 * q^86 - 21 * q^87 + 13 * q^88 + 5 * q^89 - 25 * q^90 + 5 * q^91 + 12 * q^92 + 3 * q^93 - 9 * q^94 - 7 * q^95 + 20 * q^97 + 30 * q^98 + 25 * 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
$3$	−1.16663	−0.673552	−0.336776	−	0.941585i	$-0.609337\pi$
$3$	−1.16663	−0.673552	−0.336776	+	0.941585i	$0.609337\pi$
$4$	1.00000	0.500000
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	−1.16663	−0.476273
$7$	−3.85859	−1.45841	−0.729204	−	0.684296i	$-0.760110\pi$
$7$	−3.85859	−1.45841	−0.729204	+	0.684296i	$0.760110\pi$
$8$	1.00000	0.353553
$9$	−1.63898	−0.546327
$10$	−1.00000	−0.316228
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	−1.16663	−0.336776
$13$	−3.76512	−1.04426	−0.522129	−	0.852867i	$-0.674862\pi$
$13$	−3.76512	−1.04426	−0.522129	+	0.852867i	$0.674862\pi$
$14$	−3.85859	−1.03125
$15$	1.16663	0.301222
$16$	1.00000	0.250000
$17$	−5.05803	−1.22675	−0.613376	−	0.789791i	$-0.710189\pi$
$17$	−5.05803	−1.22675	−0.613376	+	0.789791i	$0.710189\pi$
$18$	−1.63898	−0.386312
$19$	−2.28887	−0.525103	−0.262551	−	0.964918i	$-0.584564\pi$
$19$	−2.28887	−0.525103	−0.262551	+	0.964918i	$0.584564\pi$
$20$	−1.00000	−0.223607
$21$	4.50153	0.982314
$22$	1.00000	0.213201
$23$	−3.15631	−0.658136	−0.329068	−	0.944306i	$-0.606734\pi$
$23$	−3.15631	−0.658136	−0.329068	+	0.944306i	$0.606734\pi$
$24$	−1.16663	−0.238137
$25$	1.00000	0.200000
$26$	−3.76512	−0.738401
$27$	5.41196	1.04153
$28$	−3.85859	−0.729204
$29$	8.35160	1.55085	0.775427	−	0.631437i	$-0.217535\pi$
$29$	8.35160	1.55085	0.775427	+	0.631437i	$0.217535\pi$
$30$	1.16663	0.212996
$31$	−3.01484	−0.541482	−0.270741	−	0.962652i	$-0.587269\pi$
$31$	−3.01484	−0.541482	−0.270741	+	0.962652i	$0.587269\pi$
$32$	1.00000	0.176777
$33$	−1.16663	−0.203084
$34$	−5.05803	−0.867444
$35$	3.85859	0.652220
$36$	−1.63898	−0.273164
$37$	−4.67122	−0.767943	−0.383972	−	0.923345i	$-0.625444\pi$
$37$	−4.67122	−0.767943	−0.383972	+	0.923345i	$0.625444\pi$
$38$	−2.28887	−0.371304
$39$	4.39249	0.703362
$40$	−1.00000	−0.158114
$41$	−9.20945	−1.43827	−0.719137	−	0.694868i	$-0.755463\pi$
$41$	−9.20945	−1.43827	−0.719137	+	0.694868i	$0.755463\pi$
$42$	4.50153	0.694601
$43$	1.00000	0.152499
$43$	1.00000	0.152499
$44$	1.00000	0.150756
$45$	1.63898	0.244325
$46$	−3.15631	−0.465372
$47$	6.69155	0.976064	0.488032	−	0.872826i	$-0.337715\pi$
$47$	6.69155	0.976064	0.488032	+	0.872826i	$0.337715\pi$
$48$	−1.16663	−0.168388
$49$	7.88868	1.12695
$50$	1.00000	0.141421
$51$	5.90083	0.826281
$52$	−3.76512	−0.522129
$53$	4.13953	0.568608	0.284304	−	0.958734i	$-0.408238\pi$
$53$	4.13953	0.568608	0.284304	+	0.958734i	$0.408238\pi$
$54$	5.41196	0.736475
$55$	−1.00000	−0.134840
$56$	−3.85859	−0.515625
$57$	2.67026	0.353684
$58$	8.35160	1.09662
$59$	10.9802	1.42950	0.714752	−	0.699378i	$-0.246540\pi$
$59$	10.9802	1.42950	0.714752	+	0.699378i	$0.246540\pi$
$60$	1.16663	0.150611
$61$	7.94861	1.01772	0.508858	−	0.860851i	$-0.330068\pi$
$61$	7.94861	1.01772	0.508858	+	0.860851i	$0.330068\pi$
$62$	−3.01484	−0.382885
$63$	6.32415	0.796768
$64$	1.00000	0.125000
$65$	3.76512	0.467006
$66$	−1.16663	−0.143602
$67$	7.87269	0.961802	0.480901	−	0.876775i	$-0.340310\pi$
$67$	7.87269	0.961802	0.480901	+	0.876775i	$0.340310\pi$
$68$	−5.05803	−0.613376
$69$	3.68223	0.443289
$70$	3.85859	0.461189
$71$	−0.268322	−0.0318439	−0.0159220	−	0.999873i	$-0.505068\pi$
$71$	−0.268322	−0.0318439	−0.0159220	+	0.999873i	$0.505068\pi$
$72$	−1.63898	−0.193156
$73$	−3.06434	−0.358654	−0.179327	−	0.983790i	$-0.557392\pi$
$73$	−3.06434	−0.358654	−0.179327	+	0.983790i	$0.557392\pi$
$74$	−4.67122	−0.543018
$75$	−1.16663	−0.134710
$76$	−2.28887	−0.262551
$77$	−3.85859	−0.439727
$78$	4.39249	0.497352
$79$	−12.8076	−1.44096	−0.720482	−	0.693474i	$-0.756079\pi$
$79$	−12.8076	−1.44096	−0.720482	+	0.693474i	$0.756079\pi$
$80$	−1.00000	−0.111803
$81$	−1.39679	−0.155199
$82$	−9.20945	−1.01701
$83$	−9.21995	−1.01202	−0.506010	−	0.862527i	$-0.668880\pi$
$83$	−9.21995	−1.01202	−0.506010	+	0.862527i	$0.668880\pi$
$84$	4.50153	0.491157
$85$	5.05803	0.548620
$86$	1.00000	0.107833
$87$	−9.74320	−1.04458
$88$	1.00000	0.106600
$89$	−4.61307	−0.488985	−0.244492	−	0.969651i	$-0.578621\pi$
$89$	−4.61307	−0.488985	−0.244492	+	0.969651i	$0.578621\pi$
$90$	1.63898	0.172764
$91$	14.5280	1.52295
$92$	−3.15631	−0.329068
$93$	3.51719	0.364716
$94$	6.69155	0.690181
$95$	2.28887	0.234833
$96$	−1.16663	−0.119068
$97$	−11.3046	−1.14781	−0.573904	−	0.818923i	$-0.694572\pi$
$97$	−11.3046	−1.14781	−0.573904	+	0.818923i	$0.694572\pi$
$98$	7.88868	0.796877
$99$	−1.63898	−0.164724
$100$	1.00000	0.100000
$101$	15.7257	1.56476	0.782382	−	0.622799i	$-0.214004\pi$
$101$	15.7257	1.56476	0.782382	+	0.622799i	$0.214004\pi$
$102$	5.90083	0.584269
$103$	0.0209618	0.00206543	0.00103271	−	0.999999i	$-0.499671\pi$
$103$	0.0209618	0.00206543	0.00103271	+	0.999999i	$0.499671\pi$
$104$	−3.76512	−0.369201
$105$	−4.50153	−0.439304
$106$	4.13953	0.402067
$107$	−2.59376	−0.250748	−0.125374	−	0.992110i	$-0.540013\pi$
$107$	−2.59376	−0.250748	−0.125374	+	0.992110i	$0.540013\pi$
$108$	5.41196	0.520766
$109$	10.4693	1.00278	0.501391	−	0.865221i	$-0.332822\pi$
$109$	10.4693	1.00278	0.501391	+	0.865221i	$0.332822\pi$
$110$	−1.00000	−0.0953463
$111$	5.44957	0.517250
$112$	−3.85859	−0.364602
$113$	11.2356	1.05696	0.528478	−	0.848947i	$-0.322763\pi$
$113$	11.2356	1.05696	0.528478	+	0.848947i	$0.322763\pi$
$114$	2.67026	0.250093
$115$	3.15631	0.294327
$116$	8.35160	0.775427
$117$	6.17097	0.570506
$118$	10.9802	1.01081
$119$	19.5168	1.78910
$120$	1.16663	0.106498
$121$	1.00000	0.0909091
$122$	7.94861	0.719634
$123$	10.7440	0.968753
$124$	−3.01484	−0.270741
$125$	−1.00000	−0.0894427
$126$	6.32415	0.563400
$127$	−6.04085	−0.536038	−0.268019	−	0.963414i	$-0.586369\pi$
$127$	−6.04085	−0.536038	−0.268019	+	0.963414i	$0.586369\pi$
$128$	1.00000	0.0883883
$129$	−1.16663	−0.102716
$130$	3.76512	0.330223
$131$	1.66995	0.145904	0.0729519	−	0.997335i	$-0.476758\pi$
$131$	1.66995	0.145904	0.0729519	+	0.997335i	$0.476758\pi$
$132$	−1.16663	−0.101542
$133$	8.83180	0.765814
$134$	7.87269	0.680097
$135$	−5.41196	−0.465787
$136$	−5.05803	−0.433722
$137$	5.55653	0.474727	0.237363	−	0.971421i	$-0.423717\pi$
$137$	5.55653	0.474727	0.237363	+	0.971421i	$0.423717\pi$
$138$	3.68223	0.313452
$139$	16.6438	1.41171	0.705853	−	0.708358i	$-0.250564\pi$
$139$	16.6438	1.41171	0.705853	+	0.708358i	$0.250564\pi$
$140$	3.85859	0.326110
$141$	−7.80655	−0.657430
$142$	−0.268322	−0.0225171
$143$	−3.76512	−0.314855
$144$	−1.63898	−0.136582
$145$	−8.35160	−0.693563
$146$	−3.06434	−0.253606
$147$	−9.20315	−0.759063
$148$	−4.67122	−0.383972
$149$	13.2473	1.08526	0.542629	−	0.839972i	$-0.317429\pi$
$149$	13.2473	1.08526	0.542629	+	0.839972i	$0.317429\pi$
$150$	−1.16663	−0.0952547
$151$	−9.37827	−0.763193	−0.381597	−	0.924329i	$-0.624626\pi$
$151$	−9.37827	−0.763193	−0.381597	+	0.924329i	$0.624626\pi$
$152$	−2.28887	−0.185652
$153$	8.29001	0.670208
$154$	−3.85859	−0.310934
$155$	3.01484	0.242158
$156$	4.39249	0.351681
$157$	−12.4335	−0.992301	−0.496150	−	0.868237i	$-0.665254\pi$
$157$	−12.4335	−0.992301	−0.496150	+	0.868237i	$0.665254\pi$
$158$	−12.8076	−1.01892
$159$	−4.82928	−0.382987
$160$	−1.00000	−0.0790569
$161$	12.1789	0.959830
$162$	−1.39679	−0.109742
$163$	−3.64178	−0.285246	−0.142623	−	0.989777i	$-0.545554\pi$
$163$	−3.64178	−0.285246	−0.142623	+	0.989777i	$0.545554\pi$
$164$	−9.20945	−0.719137
$165$	1.16663	0.0908218
$166$	−9.21995	−0.715607
$167$	−18.5093	−1.43229	−0.716147	−	0.697949i	$-0.754096\pi$
$167$	−18.5093	−1.43229	−0.716147	+	0.697949i	$0.754096\pi$
$168$	4.50153	0.347300
$169$	1.17615	0.0904728
$170$	5.05803	0.387933
$171$	3.75142	0.286878
$172$	1.00000	0.0762493
$173$	10.1268	0.769927	0.384963	−	0.922932i	$-0.374214\pi$
$173$	10.1268	0.769927	0.384963	+	0.922932i	$0.374214\pi$
$174$	−9.74320	−0.738630
$175$	−3.85859	−0.291682
$176$	1.00000	0.0753778
$177$	−12.8098	−0.962845
$178$	−4.61307	−0.345765
$179$	21.3948	1.59912	0.799561	−	0.600585i	$-0.205065\pi$
$179$	21.3948	1.59912	0.799561	+	0.600585i	$0.205065\pi$
$180$	1.63898	0.122163
$181$	−3.69809	−0.274877	−0.137438	−	0.990510i	$-0.543887\pi$
$181$	−3.69809	−0.274877	−0.137438	+	0.990510i	$0.543887\pi$
$182$	14.5280	1.07689
$183$	−9.27306	−0.685485
$184$	−3.15631	−0.232686
$185$	4.67122	0.343435
$186$	3.51719	0.257893
$187$	−5.05803	−0.369879
$188$	6.69155	0.488032
$189$	−20.8825	−1.51898
$190$	2.28887	0.166052
$191$	4.35977	0.315462	0.157731	−	0.987482i	$-0.449582\pi$
$191$	4.35977	0.315462	0.157731	+	0.987482i	$0.449582\pi$
$192$	−1.16663	−0.0841940
$193$	19.7345	1.42052	0.710259	−	0.703940i	$-0.248578\pi$
$193$	19.7345	1.42052	0.710259	+	0.703940i	$0.248578\pi$
$194$	−11.3046	−0.811623
$195$	−4.39249	−0.314553
$196$	7.88868	0.563477
$197$	−1.78207	−0.126967	−0.0634837	−	0.997983i	$-0.520221\pi$
$197$	−1.78207	−0.126967	−0.0634837	+	0.997983i	$0.520221\pi$
$198$	−1.63898	−0.116477
$199$	−2.27826	−0.161502	−0.0807509	−	0.996734i	$-0.525732\pi$
$199$	−2.27826	−0.161502	−0.0807509	+	0.996734i	$0.525732\pi$
$200$	1.00000	0.0707107
$201$	−9.18449	−0.647824
$202$	15.7257	1.10646
$203$	−32.2254	−2.26178
$204$	5.90083	0.413141
$205$	9.20945	0.643216
$206$	0.0209618	0.00146048
$207$	5.17313	0.359558
$208$	−3.76512	−0.261064
$209$	−2.28887	−0.158325
$210$	−4.50153	−0.310635
$211$	9.06403	0.623994	0.311997	−	0.950083i	$-0.399002\pi$
$211$	9.06403	0.623994	0.311997	+	0.950083i	$0.399002\pi$
$212$	4.13953	0.284304
$213$	0.313031	0.0214485
$214$	−2.59376	−0.177306
$215$	−1.00000	−0.0681994
$216$	5.41196	0.368237
$217$	11.6330	0.789701
$218$	10.4693	0.709074
$219$	3.57494	0.241572
$220$	−1.00000	−0.0674200
$221$	19.0441	1.28104
$222$	5.44957	0.365751
$223$	16.9366	1.13416	0.567078	−	0.823664i	$-0.308074\pi$
$223$	16.9366	1.13416	0.567078	+	0.823664i	$0.308074\pi$
$224$	−3.85859	−0.257813
$225$	−1.63898	−0.109265
$226$	11.2356	0.747381
$227$	−1.38386	−0.0918498	−0.0459249	−	0.998945i	$-0.514623\pi$
$227$	−1.38386	−0.0918498	−0.0459249	+	0.998945i	$0.514623\pi$
$228$	2.67026	0.176842
$229$	2.27661	0.150443	0.0752213	−	0.997167i	$-0.476034\pi$
$229$	2.27661	0.150443	0.0752213	+	0.997167i	$0.476034\pi$
$230$	3.15631	0.208121
$231$	4.50153	0.296179
$232$	8.35160	0.548310
$233$	−13.2311	−0.866800	−0.433400	−	0.901202i	$-0.642686\pi$
$233$	−13.2311	−0.866800	−0.433400	+	0.901202i	$0.642686\pi$
$234$	6.17097	0.403409
$235$	−6.69155	−0.436509
$236$	10.9802	0.714752
$237$	14.9416	0.970564
$238$	19.5168	1.26509
$239$	−4.10701	−0.265661	−0.132830	−	0.991139i	$-0.542407\pi$
$239$	−4.10701	−0.265661	−0.132830	+	0.991139i	$0.542407\pi$
$240$	1.16663	0.0753054
$241$	−29.9152	−1.92700	−0.963502	−	0.267700i	$-0.913736\pi$
$241$	−29.9152	−1.92700	−0.963502	+	0.267700i	$0.913736\pi$
$242$	1.00000	0.0642824
$243$	−14.6063	−0.936998
$244$	7.94861	0.508858
$245$	−7.88868	−0.503989
$246$	10.7440	0.685012
$247$	8.61788	0.548342
$248$	−3.01484	−0.191443
$249$	10.7562	0.681649
$250$	−1.00000	−0.0632456
$251$	−13.7265	−0.866406	−0.433203	−	0.901296i	$-0.642617\pi$
$251$	−13.7265	−0.866406	−0.433203	+	0.901296i	$0.642617\pi$
$252$	6.32415	0.398384
$253$	−3.15631	−0.198435
$254$	−6.04085	−0.379036
$255$	−5.90083	−0.369524
$256$	1.00000	0.0625000
$257$	27.0551	1.68765	0.843824	−	0.536620i	$-0.180299\pi$
$257$	27.0551	1.68765	0.843824	+	0.536620i	$0.180299\pi$
$258$	−1.16663	−0.0726310
$259$	18.0243	1.11997
$260$	3.76512	0.233503
$261$	−13.6881	−0.847274
$262$	1.66995	0.103170
$263$	−25.1289	−1.54951	−0.774756	−	0.632260i	$-0.782127\pi$
$263$	−25.1289	−1.54951	−0.774756	+	0.632260i	$0.782127\pi$
$264$	−1.16663	−0.0718009
$265$	−4.13953	−0.254289
$266$	8.83180	0.541513
$267$	5.38174	0.329357
$268$	7.87269	0.480901
$269$	−6.21186	−0.378744	−0.189372	−	0.981905i	$-0.560645\pi$
$269$	−6.21186	−0.378744	−0.189372	+	0.981905i	$0.560645\pi$
$270$	−5.41196	−0.329361
$271$	17.5757	1.06765	0.533824	−	0.845595i	$-0.320754\pi$
$271$	17.5757	1.06765	0.533824	+	0.845595i	$0.320754\pi$
$272$	−5.05803	−0.306688
$273$	−16.9488	−1.02579
$274$	5.55653	0.335682
$275$	1.00000	0.0603023
$276$	3.68223	0.221644
$277$	16.0544	0.964615	0.482308	−	0.876002i	$-0.339799\pi$
$277$	16.0544	0.964615	0.482308	+	0.876002i	$0.339799\pi$
$278$	16.6438	0.998227
$279$	4.94127	0.295826
$280$	3.85859	0.230595
$281$	24.8877	1.48468	0.742339	−	0.670024i	$-0.233716\pi$
$281$	24.8877	1.48468	0.742339	+	0.670024i	$0.233716\pi$
$282$	−7.80655	−0.464873
$283$	−16.8565	−1.00201	−0.501006	−	0.865444i	$-0.667037\pi$
$283$	−16.8565	−1.00201	−0.501006	+	0.865444i	$0.667037\pi$
$284$	−0.268322	−0.0159220
$285$	−2.67026	−0.158172
$286$	−3.76512	−0.222636
$287$	35.5355	2.09759
$288$	−1.63898	−0.0965780
$289$	8.58362	0.504919
$290$	−8.35160	−0.490423
$291$	13.1882	0.773109
$292$	−3.06434	−0.179327
$293$	−21.4833	−1.25507	−0.627535	−	0.778589i	$-0.715936\pi$
$293$	−21.4833	−1.25507	−0.627535	+	0.778589i	$0.715936\pi$
$294$	−9.20315	−0.536738
$295$	−10.9802	−0.639293
$296$	−4.67122	−0.271509
$297$	5.41196	0.314034
$298$	13.2473	0.767393
$299$	11.8839	0.687263
$300$	−1.16663	−0.0673552
$301$	−3.85859	−0.222405
$302$	−9.37827	−0.539659
$303$	−18.3460	−1.05395
$304$	−2.28887	−0.131276
$305$	−7.94861	−0.455136
$306$	8.29001	0.473909
$307$	−10.0990	−0.576380	−0.288190	−	0.957573i	$-0.593054\pi$
$307$	−10.0990	−0.576380	−0.288190	+	0.957573i	$0.593054\pi$
$308$	−3.85859	−0.219863
$309$	−0.0244546	−0.00139117
$310$	3.01484	0.171231
$311$	−22.4101	−1.27076	−0.635381	−	0.772199i	$-0.719157\pi$
$311$	−22.4101	−1.27076	−0.635381	+	0.772199i	$0.719157\pi$
$312$	4.39249	0.248676
$313$	18.7363	1.05904	0.529518	−	0.848299i	$-0.322373\pi$
$313$	18.7363	1.05904	0.529518	+	0.848299i	$0.322373\pi$
$314$	−12.4335	−0.701663
$315$	−6.32415	−0.356326
$316$	−12.8076	−0.720482
$317$	30.9181	1.73653	0.868266	−	0.496100i	$-0.165235\pi$
$317$	30.9181	1.73653	0.868266	+	0.496100i	$0.165235\pi$
$318$	−4.82928	−0.270813
$319$	8.35160	0.467600
$320$	−1.00000	−0.0559017
$321$	3.02595	0.168892
$322$	12.1789	0.678703
$323$	11.5772	0.644171
$324$	−1.39679	−0.0775994
$325$	−3.76512	−0.208851
$326$	−3.64178	−0.201700
$327$	−12.2138	−0.675426
$328$	−9.20945	−0.508507
$329$	−25.8199	−1.42350
$330$	1.16663	0.0642207
$331$	−4.28823	−0.235702	−0.117851	−	0.993031i	$-0.537601\pi$
$331$	−4.28823	−0.235702	−0.117851	+	0.993031i	$0.537601\pi$
$332$	−9.21995	−0.506010
$333$	7.65604	0.419549
$334$	−18.5093	−1.01279
$335$	−7.87269	−0.430131
$336$	4.50153	0.245579
$337$	2.20531	0.120131	0.0600655	−	0.998194i	$-0.480869\pi$
$337$	2.20531	0.120131	0.0600655	+	0.998194i	$0.480869\pi$
$338$	1.17615	0.0639739
$339$	−13.1077	−0.711915
$340$	5.05803	0.274310
$341$	−3.01484	−0.163263
$342$	3.75142	0.202853
$343$	−3.42905	−0.185152
$344$	1.00000	0.0539164
$345$	−3.68223	−0.198245
$346$	10.1268	0.544421
$347$	−13.2410	−0.710816	−0.355408	−	0.934711i	$-0.615658\pi$
$347$	−13.2410	−0.710816	−0.355408	+	0.934711i	$0.615658\pi$
$348$	−9.74320	−0.522291
$349$	28.1887	1.50891	0.754454	−	0.656353i	$-0.227902\pi$
$349$	28.1887	1.50891	0.754454	+	0.656353i	$0.227902\pi$
$350$	−3.85859	−0.206250
$351$	−20.3767	−1.08763
$352$	1.00000	0.0533002
$353$	34.0257	1.81100	0.905502	−	0.424342i	$-0.139494\pi$
$353$	34.0257	1.81100	0.905502	+	0.424342i	$0.139494\pi$
$354$	−12.8098	−0.680834
$355$	0.268322	0.0142410
$356$	−4.61307	−0.244492
$357$	−22.7688	−1.20506
$358$	21.3948	1.13075
$359$	31.7592	1.67619	0.838094	−	0.545527i	$-0.183670\pi$
$359$	31.7592	1.67619	0.838094	+	0.545527i	$0.183670\pi$
$360$	1.63898	0.0863820
$361$	−13.7611	−0.724267
$362$	−3.69809	−0.194367
$363$	−1.16663	−0.0612320
$364$	14.5280	0.761477
$365$	3.06434	0.160395
$366$	−9.27306	−0.484711
$367$	7.76648	0.405407	0.202703	−	0.979240i	$-0.435027\pi$
$367$	7.76648	0.405407	0.202703	+	0.979240i	$0.435027\pi$
$368$	−3.15631	−0.164534
$369$	15.0941	0.785769
$370$	4.67122	0.242845
$371$	−15.9727	−0.829262
$372$	3.51719	0.182358
$373$	−26.4763	−1.37089	−0.685445	−	0.728124i	$-0.740392\pi$
$373$	−26.4763	−1.37089	−0.685445	+	0.728124i	$0.740392\pi$
$374$	−5.05803	−0.261544
$375$	1.16663	0.0602443
$376$	6.69155	0.345091
$377$	−31.4448	−1.61949
$378$	−20.8825	−1.07408
$379$	−3.14282	−0.161436	−0.0807180	−	0.996737i	$-0.525721\pi$
$379$	−3.14282	−0.161436	−0.0807180	+	0.996737i	$0.525721\pi$
$380$	2.28887	0.117417
$381$	7.04741	0.361050
$382$	4.35977	0.223065
$383$	23.6271	1.20729	0.603645	−	0.797253i	$-0.293714\pi$
$383$	23.6271	1.20729	0.603645	+	0.797253i	$0.293714\pi$
$384$	−1.16663	−0.0595342
$385$	3.85859	0.196652
$386$	19.7345	1.00446
$387$	−1.63898	−0.0833142
$388$	−11.3046	−0.573904
$389$	28.0363	1.42150	0.710748	−	0.703447i	$-0.248357\pi$
$389$	28.0363	1.42150	0.710748	+	0.703447i	$0.248357\pi$
$390$	−4.39249	−0.222422
$391$	15.9647	0.807369
$392$	7.88868	0.398439
$393$	−1.94820	−0.0982738
$394$	−1.78207	−0.0897795
$395$	12.8076	0.644419
$396$	−1.63898	−0.0823620
$397$	11.7912	0.591786	0.295893	−	0.955221i	$-0.404383\pi$
$397$	11.7912	0.591786	0.295893	+	0.955221i	$0.404383\pi$
$398$	−2.27826	−0.114199
$399$	−10.3034	−0.515816
$400$	1.00000	0.0500000
$401$	−4.46116	−0.222780	−0.111390	−	0.993777i	$-0.535530\pi$
$401$	−4.46116	−0.222780	−0.111390	+	0.993777i	$0.535530\pi$
$402$	−9.18449	−0.458081
$403$	11.3512	0.565446
$404$	15.7257	0.782382
$405$	1.39679	0.0694071
$406$	−32.2254	−1.59932
$407$	−4.67122	−0.231544
$408$	5.90083	0.292134
$409$	−8.24320	−0.407600	−0.203800	−	0.979013i	$-0.565329\pi$
$409$	−8.24320	−0.407600	−0.203800	+	0.979013i	$0.565329\pi$
$410$	9.20945	0.454822
$411$	−6.48240	−0.319753
$412$	0.0209618	0.00103271
$413$	−42.3681	−2.08480
$414$	5.17313	0.254246
$415$	9.21995	0.452589
$416$	−3.76512	−0.184600
$417$	−19.4171	−0.950858
$418$	−2.28887	−0.111952
$419$	2.25172	0.110003	0.0550017	−	0.998486i	$-0.482484\pi$
$419$	2.25172	0.110003	0.0550017	+	0.998486i	$0.482484\pi$
$420$	−4.50153	−0.219652
$421$	−36.6258	−1.78503	−0.892517	−	0.451013i	$-0.851063\pi$
$421$	−36.6258	−1.78503	−0.892517	+	0.451013i	$0.851063\pi$
$422$	9.06403	0.441230
$423$	−10.9673	−0.533250
$424$	4.13953	0.201033
$425$	−5.05803	−0.245350
$426$	0.313031	0.0151664
$427$	−30.6704	−1.48424
$428$	−2.59376	−0.125374
$429$	4.39249	0.212072
$430$	−1.00000	−0.0482243
$431$	−20.8183	−1.00278	−0.501391	−	0.865221i	$-0.667178\pi$
$431$	−20.8183	−1.00278	−0.501391	+	0.865221i	$0.667178\pi$
$432$	5.41196	0.260383
$433$	−14.0428	−0.674852	−0.337426	−	0.941352i	$-0.609556\pi$
$433$	−14.0428	−0.674852	−0.337426	+	0.941352i	$0.609556\pi$
$434$	11.6330	0.558403
$435$	9.74320	0.467151
$436$	10.4693	0.501391
$437$	7.22438	0.345589
$438$	3.57494	0.170817
$439$	−18.1912	−0.868219	−0.434110	−	0.900860i	$-0.642937\pi$
$439$	−18.1912	−0.868219	−0.434110	+	0.900860i	$0.642937\pi$
$440$	−1.00000	−0.0476731
$441$	−12.9294	−0.615686
$442$	19.0441	0.905835
$443$	−15.2466	−0.724387	−0.362194	−	0.932103i	$-0.617972\pi$
$443$	−15.2466	−0.724387	−0.362194	+	0.932103i	$0.617972\pi$
$444$	5.44957	0.258625
$445$	4.61307	0.218681
$446$	16.9366	0.801969
$447$	−15.4546	−0.730978
$448$	−3.85859	−0.182301
$449$	33.2136	1.56745	0.783724	−	0.621109i	$-0.213318\pi$
$449$	33.2136	1.56745	0.783724	+	0.621109i	$0.213318\pi$
$450$	−1.63898	−0.0772624
$451$	−9.20945	−0.433656
$452$	11.2356	0.528478
$453$	10.9409	0.514050
$454$	−1.38386	−0.0649476
$455$	−14.5280	−0.681085
$456$	2.67026	0.125046
$457$	−9.26528	−0.433412	−0.216706	−	0.976237i	$-0.569531\pi$
$457$	−9.26528	−0.433412	−0.216706	+	0.976237i	$0.569531\pi$
$458$	2.27661	0.106379
$459$	−27.3738	−1.27770
$460$	3.15631	0.147164
$461$	−2.70163	−0.125828	−0.0629138	−	0.998019i	$-0.520039\pi$
$461$	−2.70163	−0.125828	−0.0629138	+	0.998019i	$0.520039\pi$
$462$	4.50153	0.209430
$463$	4.80337	0.223231	0.111616	−	0.993751i	$-0.464397\pi$
$463$	4.80337	0.223231	0.111616	+	0.993751i	$0.464397\pi$
$464$	8.35160	0.387713
$465$	−3.51719	−0.163106
$466$	−13.2311	−0.612920
$467$	18.0499	0.835250	0.417625	−	0.908619i	$-0.362863\pi$
$467$	18.0499	0.835250	0.417625	+	0.908619i	$0.362863\pi$
$468$	6.17097	0.285253
$469$	−30.3774	−1.40270
$470$	−6.69155	−0.308658
$471$	14.5052	0.668366
$472$	10.9802	0.505406
$473$	1.00000	0.0459800
$474$	14.9416	0.686293
$475$	−2.28887	−0.105021
$476$	19.5168	0.894552
$477$	−6.78461	−0.310646
$478$	−4.10701	−0.187850
$479$	−6.10912	−0.279133	−0.139566	−	0.990213i	$-0.544571\pi$
$479$	−6.10912	−0.279133	−0.139566	+	0.990213i	$0.544571\pi$
$480$	1.16663	0.0532490
$481$	17.5877	0.801930
$482$	−29.9152	−1.36260
$483$	−14.2082	−0.646496
$484$	1.00000	0.0454545
$485$	11.3046	0.513315
$486$	−14.6063	−0.662557
$487$	23.7496	1.07620	0.538099	−	0.842881i	$-0.319143\pi$
$487$	23.7496	1.07620	0.538099	+	0.842881i	$0.319143\pi$
$488$	7.94861	0.359817
$489$	4.24860	0.192128
$490$	−7.88868	−0.356374
$491$	−14.1754	−0.639727	−0.319864	−	0.947464i	$-0.603637\pi$
$491$	−14.1754	−0.639727	−0.319864	+	0.947464i	$0.603637\pi$
$492$	10.7440	0.484377
$493$	−42.2426	−1.90251
$494$	8.61788	0.387737
$495$	1.63898	0.0736668
$496$	−3.01484	−0.135370
$497$	1.03534	0.0464414
$498$	10.7562	0.481998
$499$	27.1431	1.21509	0.607547	−	0.794284i	$-0.292154\pi$
$499$	27.1431	1.21509	0.607547	+	0.794284i	$0.292154\pi$
$500$	−1.00000	−0.0447214
$501$	21.5935	0.964725
$502$	−13.7265	−0.612642
$503$	−30.7431	−1.37077	−0.685383	−	0.728183i	$-0.740365\pi$
$503$	−30.7431	−1.37077	−0.685383	+	0.728183i	$0.740365\pi$
$504$	6.32415	0.281700
$505$	−15.7257	−0.699784
$506$	−3.15631	−0.140315
$507$	−1.37212	−0.0609382
$508$	−6.04085	−0.268019
$509$	25.8806	1.14714	0.573568	−	0.819158i	$-0.305559\pi$
$509$	25.8806	1.14714	0.573568	+	0.819158i	$0.305559\pi$
$510$	−5.90083	−0.261293
$511$	11.8240	0.523064
$512$	1.00000	0.0441942
$513$	−12.3873	−0.546912
$514$	27.0551	1.19335
$515$	−0.0209618	−0.000923688 0
$516$	−1.16663	−0.0513579
$517$	6.69155	0.294294
$518$	18.0243	0.791942
$519$	−11.8142	−0.518586
$520$	3.76512	0.165112
$521$	−33.3838	−1.46257	−0.731286	−	0.682071i	$-0.761079\pi$
$521$	−33.3838	−1.46257	−0.731286	+	0.682071i	$0.761079\pi$
$522$	−13.6881	−0.599113
$523$	4.19598	0.183478	0.0917388	−	0.995783i	$-0.470758\pi$
$523$	4.19598	0.183478	0.0917388	+	0.995783i	$0.470758\pi$
$524$	1.66995	0.0729519
$525$	4.50153	0.196463
$526$	−25.1289	−1.09567
$527$	15.2491	0.664263
$528$	−1.16663	−0.0507709
$529$	−13.0377	−0.566857
$530$	−4.13953	−0.179810
$531$	−17.9964	−0.780977
$532$	8.83180	0.382907
$533$	34.6747	1.50193
$534$	5.38174	0.232890
$535$	2.59376	0.112138
$536$	7.87269	0.340048
$537$	−24.9597	−1.07709
$538$	−6.21186	−0.267812
$539$	7.88868	0.339790
$540$	−5.41196	−0.232894
$541$	−5.64222	−0.242578	−0.121289	−	0.992617i	$-0.538703\pi$
$541$	−5.64222	−0.242578	−0.121289	+	0.992617i	$0.538703\pi$
$542$	17.5757	0.754942
$543$	4.31429	0.185144
$544$	−5.05803	−0.216861
$545$	−10.4693	−0.448458
$546$	−16.9488	−0.725342
$547$	−6.02043	−0.257415	−0.128707	−	0.991683i	$-0.541083\pi$
$547$	−6.02043	−0.257415	−0.128707	+	0.991683i	$0.541083\pi$
$548$	5.55653	0.237363
$549$	−13.0276	−0.556006
$550$	1.00000	0.0426401
$551$	−19.1157	−0.814358
$552$	3.68223	0.156726
$553$	49.4191	2.10151
$554$	16.0544	0.682086
$555$	−5.44957	−0.231321
$556$	16.6438	0.705853
$557$	11.2765	0.477801	0.238900	−	0.971044i	$-0.423213\pi$
$557$	11.2765	0.477801	0.238900	+	0.971044i	$0.423213\pi$
$558$	4.94127	0.209181
$559$	−3.76512	−0.159248
$560$	3.85859	0.163055
$561$	5.90083	0.249133
$562$	24.8877	1.04983
$563$	11.7883	0.496818	0.248409	−	0.968655i	$-0.420092\pi$
$563$	11.7883	0.496818	0.248409	+	0.968655i	$0.420092\pi$
$564$	−7.80655	−0.328715
$565$	−11.2356	−0.472685
$566$	−16.8565	−0.708530
$567$	5.38963	0.226343
$568$	−0.268322	−0.0112585
$569$	22.6922	0.951305	0.475653	−	0.879633i	$-0.342212\pi$
$569$	22.6922	0.951305	0.475653	+	0.879633i	$0.342212\pi$
$570$	−2.67026	−0.111845
$571$	12.6479	0.529300	0.264650	−	0.964345i	$-0.414744\pi$
$571$	12.6479	0.529300	0.264650	+	0.964345i	$0.414744\pi$
$572$	−3.76512	−0.157428
$573$	−5.08623	−0.212480
$574$	35.5355	1.48322
$575$	−3.15631	−0.131627
$576$	−1.63898	−0.0682909
$577$	17.2584	0.718478	0.359239	−	0.933246i	$-0.383036\pi$
$577$	17.2584	0.718478	0.359239	+	0.933246i	$0.383036\pi$
$578$	8.58362	0.357031
$579$	−23.0228	−0.956793
$580$	−8.35160	−0.346781
$581$	35.5760	1.47594
$582$	13.1882	0.546670
$583$	4.13953	0.171442
$584$	−3.06434	−0.126803
$585$	−6.17097	−0.255138
$586$	−21.4833	−0.887468
$587$	−29.1683	−1.20391	−0.601953	−	0.798532i	$-0.705610\pi$
$587$	−29.1683	−1.20391	−0.601953	+	0.798532i	$0.705610\pi$
$588$	−9.20315	−0.379531
$589$	6.90058	0.284334
$590$	−10.9802	−0.452049
$591$	2.07901	0.0855192
$592$	−4.67122	−0.191986
$593$	−32.4227	−1.33144	−0.665720	−	0.746202i	$-0.731875\pi$
$593$	−32.4227	−1.33144	−0.665720	+	0.746202i	$0.731875\pi$
$594$	5.41196	0.222055
$595$	−19.5168	−0.800112
$596$	13.2473	0.542629
$597$	2.65788	0.108780
$598$	11.8839	0.485968
$599$	−38.8717	−1.58826	−0.794128	−	0.607751i	$-0.792072\pi$
$599$	−38.8717	−1.58826	−0.794128	+	0.607751i	$0.792072\pi$
$600$	−1.16663	−0.0476273
$601$	−6.81472	−0.277978	−0.138989	−	0.990294i	$-0.544385\pi$
$601$	−6.81472	−0.277978	−0.138989	+	0.990294i	$0.544385\pi$
$602$	−3.85859	−0.157264
$603$	−12.9032	−0.525459
$604$	−9.37827	−0.381597
$605$	−1.00000	−0.0406558
$606$	−18.3460	−0.745255
$607$	−38.9902	−1.58256	−0.791282	−	0.611451i	$-0.790586\pi$
$607$	−38.9902	−1.58256	−0.791282	+	0.611451i	$0.790586\pi$
$608$	−2.28887	−0.0928260
$609$	37.5950	1.52343
$610$	−7.94861	−0.321830
$611$	−25.1945	−1.01926
$612$	8.29001	0.335104
$613$	36.6149	1.47886	0.739430	−	0.673233i	$-0.235095\pi$
$613$	36.6149	1.47886	0.739430	+	0.673233i	$0.235095\pi$
$614$	−10.0990	−0.407563
$615$	−10.7440	−0.433240
$616$	−3.85859	−0.155467
$617$	−25.6334	−1.03196	−0.515980	−	0.856600i	$-0.672572\pi$
$617$	−25.6334	−1.03196	−0.515980	+	0.856600i	$0.672572\pi$
$618$	−0.0244546	−0.000983708 0
$619$	39.4243	1.58460	0.792298	−	0.610134i	$-0.208885\pi$
$619$	39.4243	1.58460	0.792298	+	0.610134i	$0.208885\pi$
$620$	3.01484	0.121079
$621$	−17.0818	−0.685469
$622$	−22.4101	−0.898565
$623$	17.7999	0.713140
$624$	4.39249	0.175840
$625$	1.00000	0.0400000
$626$	18.7363	0.748852
$627$	2.67026	0.106640
$628$	−12.4335	−0.496150
$629$	23.6271	0.942076
$630$	−6.32415	−0.251960
$631$	−8.96733	−0.356984	−0.178492	−	0.983941i	$-0.557122\pi$
$631$	−8.96733	−0.356984	−0.178492	+	0.983941i	$0.557122\pi$
$632$	−12.8076	−0.509458
$633$	−10.5743	−0.420292
$634$	30.9181	1.22791
$635$	6.04085	0.239724
$636$	−4.82928	−0.191494
$637$	−29.7019	−1.17683
$638$	8.35160	0.330643
$639$	0.439775	0.0173972
$640$	−1.00000	−0.0395285
$641$	20.2791	0.800975	0.400487	−	0.916302i	$-0.368841\pi$
$641$	20.2791	0.800975	0.400487	+	0.916302i	$0.368841\pi$
$642$	3.02595	0.119425
$643$	−32.8809	−1.29670	−0.648349	−	0.761343i	$-0.724540\pi$
$643$	−32.8809	−1.29670	−0.648349	+	0.761343i	$0.724540\pi$
$644$	12.1789	0.479915
$645$	1.16663	0.0459359
$646$	11.5772	0.455498
$647$	−7.90777	−0.310886	−0.155443	−	0.987845i	$-0.549681\pi$
$647$	−7.90777	−0.310886	−0.155443	+	0.987845i	$0.549681\pi$
$648$	−1.39679	−0.0548711
$649$	10.9802	0.431011
$650$	−3.76512	−0.147680
$651$	−13.5714	−0.531905
$652$	−3.64178	−0.142623
$653$	17.0189	0.666001	0.333001	−	0.942927i	$-0.391939\pi$
$653$	17.0189	0.666001	0.333001	+	0.942927i	$0.391939\pi$
$654$	−12.2138	−0.477598
$655$	−1.66995	−0.0652502
$656$	−9.20945	−0.359569
$657$	5.02240	0.195942
$658$	−25.8199	−1.00657
$659$	−5.57919	−0.217334	−0.108667	−	0.994078i	$-0.534658\pi$
$659$	−5.57919	−0.217334	−0.108667	+	0.994078i	$0.534658\pi$
$660$	1.16663	0.0454109
$661$	−30.8866	−1.20135	−0.600674	−	0.799494i	$-0.705101\pi$
$661$	−30.8866	−1.20135	−0.600674	+	0.799494i	$0.705101\pi$
$662$	−4.28823	−0.166667
$663$	−22.2173	−0.862850
$664$	−9.21995	−0.357803
$665$	−8.83180	−0.342483
$666$	7.65604	0.296666
$667$	−26.3602	−1.02067
$668$	−18.5093	−0.716147
$669$	−19.7586	−0.763913
$670$	−7.87269	−0.304148
$671$	7.94861	0.306853
$672$	4.50153	0.173650
$673$	18.5532	0.715172	0.357586	−	0.933880i	$-0.383600\pi$
$673$	18.5532	0.715172	0.357586	+	0.933880i	$0.383600\pi$
$674$	2.20531	0.0849455
$675$	5.41196	0.208306
$676$	1.17615	0.0452364
$677$	34.7398	1.33516	0.667580	−	0.744538i	$-0.267330\pi$
$677$	34.7398	1.33516	0.667580	+	0.744538i	$0.267330\pi$
$678$	−13.1077	−0.503400
$679$	43.6198	1.67397
$680$	5.05803	0.193966
$681$	1.61444	0.0618656
$682$	−3.01484	−0.115444
$683$	2.46507	0.0943232	0.0471616	−	0.998887i	$-0.484982\pi$
$683$	2.46507	0.0943232	0.0471616	+	0.998887i	$0.484982\pi$
$684$	3.75142	0.143439
$685$	−5.55653	−0.212304
$686$	−3.42905	−0.130922
$687$	−2.65595	−0.101331
$688$	1.00000	0.0381246
$689$	−15.5858	−0.593773
$690$	−3.68223	−0.140180
$691$	37.1239	1.41226	0.706130	−	0.708082i	$-0.250439\pi$
$691$	37.1239	1.41226	0.706130	+	0.708082i	$0.250439\pi$
$692$	10.1268	0.384963
$693$	6.32415	0.240235
$694$	−13.2410	−0.502623
$695$	−16.6438	−0.631334
$696$	−9.74320	−0.369315
$697$	46.5816	1.76441
$698$	28.1887	1.06696
$699$	15.4358	0.583835
$700$	−3.85859	−0.145841
$701$	11.6976	0.441811	0.220905	−	0.975295i	$-0.429099\pi$
$701$	11.6976	0.441811	0.220905	+	0.975295i	$0.429099\pi$
$702$	−20.3767	−0.769069
$703$	10.6918	0.403249
$704$	1.00000	0.0376889
$705$	7.80655	0.294012
$706$	34.0257	1.28057
$707$	−60.6789	−2.28206
$708$	−12.8098	−0.481423
$709$	28.8600	1.08386	0.541930	−	0.840424i	$-0.317694\pi$
$709$	28.8600	1.08386	0.541930	+	0.840424i	$0.317694\pi$
$710$	0.268322	0.0100699
$711$	20.9914	0.787238
$712$	−4.61307	−0.172882
$713$	9.51577	0.356368
$714$	−22.7688	−0.852103
$715$	3.76512	0.140808
$716$	21.3948	0.799561
$717$	4.79135	0.178936
$718$	31.7592	1.18524
$719$	7.37005	0.274857	0.137428	−	0.990512i	$-0.456116\pi$
$719$	7.37005	0.274857	0.137428	+	0.990512i	$0.456116\pi$
$720$	1.63898	0.0610813
$721$	−0.0808829	−0.00301224
$722$	−13.7611	−0.512134
$723$	34.8998	1.29794
$724$	−3.69809	−0.137438
$725$	8.35160	0.310171
$726$	−1.16663	−0.0432976
$727$	−51.1623	−1.89750	−0.948752	−	0.316021i	$-0.897653\pi$
$727$	−51.1623	−1.89750	−0.948752	+	0.316021i	$0.897653\pi$
$728$	14.5280	0.538445
$729$	21.2305	0.786316
$730$	3.06434	0.113416
$731$	−5.05803	−0.187078
$732$	−9.27306	−0.342742
$733$	−7.81541	−0.288669	−0.144334	−	0.989529i	$-0.546104\pi$
$733$	−7.81541	−0.288669	−0.144334	+	0.989529i	$0.546104\pi$
$734$	7.76648	0.286666
$735$	9.20315	0.339463
$736$	−3.15631	−0.116343
$737$	7.87269	0.289994
$738$	15.0941	0.555623
$739$	−24.5364	−0.902587	−0.451293	−	0.892376i	$-0.649037\pi$
$739$	−24.5364	−0.902587	−0.451293	+	0.892376i	$0.649037\pi$
$740$	4.67122	0.171717
$741$	−10.0538	−0.369337
$742$	−15.9727	−0.586377
$743$	39.5998	1.45278	0.726388	−	0.687285i	$-0.241198\pi$
$743$	39.5998	1.45278	0.726388	+	0.687285i	$0.241198\pi$
$744$	3.51719	0.128947
$745$	−13.2473	−0.485342
$746$	−26.4763	−0.969366
$747$	15.1113	0.552895
$748$	−5.05803	−0.184940
$749$	10.0083	0.365694
$750$	1.16663	0.0425992
$751$	−2.91107	−0.106227	−0.0531133	−	0.998588i	$-0.516914\pi$
$751$	−2.91107	−0.106227	−0.0531133	+	0.998588i	$0.516914\pi$
$752$	6.69155	0.244016
$753$	16.0137	0.583570
$754$	−31.4448	−1.14515
$755$	9.37827	0.341310
$756$	−20.8825	−0.759490
$757$	−9.30032	−0.338026	−0.169013	−	0.985614i	$-0.554058\pi$
$757$	−9.30032	−0.338026	−0.169013	+	0.985614i	$0.554058\pi$
$758$	−3.14282	−0.114152
$759$	3.68223	0.133657
$760$	2.28887	0.0830261
$761$	−6.37837	−0.231216	−0.115608	−	0.993295i	$-0.536882\pi$
$761$	−6.37837	−0.231216	−0.115608	+	0.993295i	$0.536882\pi$
$762$	7.04741	0.255301
$763$	−40.3969	−1.46246
$764$	4.35977	0.157731
$765$	−8.29001	−0.299726
$766$	23.6271	0.853683
$767$	−41.3419	−1.49277
$768$	−1.16663	−0.0420970
$769$	2.53071	0.0912598	0.0456299	−	0.998958i	$-0.485471\pi$
$769$	2.53071	0.0912598	0.0456299	+	0.998958i	$0.485471\pi$
$770$	3.85859	0.139054
$771$	−31.5631	−1.13672
$772$	19.7345	0.710259
$773$	−26.4419	−0.951048	−0.475524	−	0.879703i	$-0.657741\pi$
$773$	−26.4419	−0.951048	−0.475524	+	0.879703i	$0.657741\pi$
$774$	−1.63898	−0.0589120
$775$	−3.01484	−0.108296
$776$	−11.3046	−0.405811
$777$	−21.0276	−0.754362
$778$	28.0363	1.00515
$779$	21.0792	0.755242
$780$	−4.39249	−0.157276
$781$	−0.268322	−0.00960131
$782$	15.9647	0.570896
$783$	45.1985	1.61526
$784$	7.88868	0.281739
$785$	12.4335	0.443770
$786$	−1.94820	−0.0694901
$787$	42.1429	1.50223	0.751116	−	0.660170i	$-0.229516\pi$
$787$	42.1429	1.50223	0.751116	+	0.660170i	$0.229516\pi$
$788$	−1.78207	−0.0634837
$789$	29.3160	1.04368
$790$	12.8076	0.455673
$791$	−43.3535	−1.54147
$792$	−1.63898	−0.0582387
$793$	−29.9275	−1.06276
$794$	11.7912	0.418456
$795$	4.82928	0.171277
$796$	−2.27826	−0.0807509
$797$	25.2137	0.893117	0.446558	−	0.894754i	$-0.352650\pi$
$797$	25.2137	0.893117	0.446558	+	0.894754i	$0.352650\pi$
$798$	−10.3034	−0.364737
$799$	−33.8461	−1.19739
$800$	1.00000	0.0353553
$801$	7.56075	0.267146
$802$	−4.46116	−0.157529
$803$	−3.06434	−0.108138
$804$	−9.18449	−0.323912
$805$	−12.1789	−0.429249
$806$	11.3512	0.399831
$807$	7.24692	0.255104
$808$	15.7257	0.553228
$809$	26.8631	0.944456	0.472228	−	0.881476i	$-0.343450\pi$
$809$	26.8631	0.944456	0.472228	+	0.881476i	$0.343450\pi$
$810$	1.39679	0.0490782
$811$	−25.5513	−0.897229	−0.448614	−	0.893725i	$-0.648082\pi$
$811$	−25.5513	−0.897229	−0.448614	+	0.893725i	$0.648082\pi$
$812$	−32.2254	−1.13089
$813$	−20.5043	−0.719117
$814$	−4.67122	−0.163726
$815$	3.64178	0.127566
$816$	5.90083	0.206570
$817$	−2.28887	−0.0800775
$818$	−8.24320	−0.288217
$819$	−23.8112	−0.832031
$820$	9.20945	0.321608
$821$	52.8976	1.84614	0.923069	−	0.384633i	$-0.125672\pi$
$821$	52.8976	1.84614	0.923069	+	0.384633i	$0.125672\pi$
$822$	−6.48240	−0.226100
$823$	−28.6027	−0.997027	−0.498513	−	0.866882i	$-0.666121\pi$
$823$	−28.6027	−0.997027	−0.498513	+	0.866882i	$0.666121\pi$
$824$	0.0209618	0.000730239 0
$825$	−1.16663	−0.0406167
$826$	−42.3681	−1.47418
$827$	−21.9377	−0.762848	−0.381424	−	0.924400i	$-0.624566\pi$
$827$	−21.9377	−0.762848	−0.381424	+	0.924400i	$0.624566\pi$
$828$	5.17313	0.179779
$829$	52.8622	1.83598	0.917990	−	0.396603i	$-0.129811\pi$
$829$	52.8622	1.83598	0.917990	+	0.396603i	$0.129811\pi$
$830$	9.21995	0.320029
$831$	−18.7295	−0.649719
$832$	−3.76512	−0.130532
$833$	−39.9012	−1.38249
$834$	−19.4171	−0.672358
$835$	18.5093	0.640542
$836$	−2.28887	−0.0791623
$837$	−16.3162	−0.563970
$838$	2.25172	0.0777842
$839$	−4.98574	−0.172127	−0.0860634	−	0.996290i	$-0.527429\pi$
$839$	−4.98574	−0.172127	−0.0860634	+	0.996290i	$0.527429\pi$
$840$	−4.50153	−0.155317
$841$	40.7493	1.40515
$842$	−36.6258	−1.26221
$843$	−29.0347	−1.00001
$844$	9.06403	0.311997
$845$	−1.17615	−0.0404607
$846$	−10.9673	−0.377065
$847$	−3.85859	−0.132583
$848$	4.13953	0.142152
$849$	19.6652	0.674908
$850$	−5.05803	−0.173489
$851$	14.7438	0.505411
$852$	0.313031	0.0107243
$853$	39.6940	1.35910	0.679548	−	0.733631i	$-0.262176\pi$
$853$	39.6940	1.35910	0.679548	+	0.733631i	$0.262176\pi$
$854$	−30.6704	−1.04952
$855$	−3.75142	−0.128296
$856$	−2.59376	−0.0886530
$857$	−24.1322	−0.824340	−0.412170	−	0.911107i	$-0.635229\pi$
$857$	−24.1322	−0.824340	−0.412170	+	0.911107i	$0.635229\pi$
$858$	4.39249	0.149957
$859$	17.2624	0.588987	0.294493	−	0.955653i	$-0.404849\pi$
$859$	17.2624	0.588987	0.294493	+	0.955653i	$0.404849\pi$
$860$	−1.00000	−0.0340997
$861$	−41.4566	−1.41284
$862$	−20.8183	−0.709074
$863$	−32.7803	−1.11586	−0.557928	−	0.829889i	$-0.688403\pi$
$863$	−32.7803	−1.11586	−0.557928	+	0.829889i	$0.688403\pi$
$864$	5.41196	0.184119
$865$	−10.1268	−0.344322
$866$	−14.0428	−0.477193
$867$	−10.0139	−0.340089
$868$	11.6330	0.394851
$869$	−12.8076	−0.434467
$870$	9.74320	0.330326
$871$	−29.6416	−1.00437
$872$	10.4693	0.354537
$873$	18.5280	0.627079
$874$	7.22438	0.244368
$875$	3.85859	0.130444
$876$	3.57494	0.120786
$877$	37.3756	1.26208	0.631042	−	0.775749i	$-0.282628\pi$
$877$	37.3756	1.26208	0.631042	+	0.775749i	$0.282628\pi$
$878$	−18.1912	−0.613924
$879$	25.0630	0.845354
$880$	−1.00000	−0.0337100
$881$	4.33370	0.146006	0.0730029	−	0.997332i	$-0.476742\pi$
$881$	4.33370	0.146006	0.0730029	+	0.997332i	$0.476742\pi$
$882$	−12.9294	−0.435356
$883$	44.1723	1.48651	0.743257	−	0.669006i	$-0.233280\pi$
$883$	44.1723	1.48651	0.743257	+	0.669006i	$0.233280\pi$
$884$	19.0441	0.640522
$885$	12.8098	0.430597
$886$	−15.2466	−0.512219
$887$	6.30202	0.211601	0.105801	−	0.994387i	$-0.466259\pi$
$887$	6.30202	0.211601	0.105801	+	0.994387i	$0.466259\pi$
$888$	5.44957	0.182875
$889$	23.3091	0.781763
$890$	4.61307	0.154631
$891$	−1.39679	−0.0467942
$892$	16.9366	0.567078
$893$	−15.3161	−0.512534
$894$	−15.4546	−0.516879
$895$	−21.3948	−0.715149
$896$	−3.85859	−0.128906
$897$	−13.8641	−0.462907
$898$	33.2136	1.10835
$899$	−25.1788	−0.839759
$900$	−1.63898	−0.0546327
$901$	−20.9378	−0.697540
$902$	−9.20945	−0.306641
$903$	4.50153	0.149801
$904$	11.2356	0.373690
$905$	3.69809	0.122929
$906$	10.9409	0.363488
$907$	−49.5306	−1.64464	−0.822318	−	0.569028i	$-0.807320\pi$
$907$	−49.5306	−1.64464	−0.822318	+	0.569028i	$0.807320\pi$
$908$	−1.38386	−0.0459249
$909$	−25.7741	−0.854874
$910$	−14.5280	−0.481600
$911$	−10.3520	−0.342978	−0.171489	−	0.985186i	$-0.554858\pi$
$911$	−10.3520	−0.342978	−0.171489	+	0.985186i	$0.554858\pi$
$912$	2.67026	0.0884211
$913$	−9.21995	−0.305136
$914$	−9.26528	−0.306468
$915$	9.27306	0.306558
$916$	2.27661	0.0752213
$917$	−6.44363	−0.212787
$918$	−27.3738	−0.903471
$919$	−7.21290	−0.237932	−0.118966	−	0.992898i	$-0.537958\pi$
$919$	−7.21290	−0.237932	−0.118966	+	0.992898i	$0.537958\pi$
$920$	3.15631	0.104060
$921$	11.7818	0.388222
$922$	−2.70163	−0.0889735
$923$	1.01026	0.0332532
$924$	4.50153	0.148089
$925$	−4.67122	−0.153589
$926$	4.80337	0.157848
$927$	−0.0343560	−0.00112840
$928$	8.35160	0.274155
$929$	−11.4708	−0.376344	−0.188172	−	0.982136i	$-0.560256\pi$
$929$	−11.4708	−0.376344	−0.188172	+	0.982136i	$0.560256\pi$
$930$	−3.51719	−0.115333
$931$	−18.0562	−0.591767
$932$	−13.2311	−0.433400
$933$	26.1443	0.855925
$934$	18.0499	0.590611
$935$	5.05803	0.165415
$936$	6.17097	0.201704
$937$	45.2862	1.47944	0.739718	−	0.672917i	$-0.234959\pi$
$937$	45.2862	1.47944	0.739718	+	0.672917i	$0.234959\pi$
$938$	−30.3774	−0.991859
$939$	−21.8582	−0.713316
$940$	−6.69155	−0.218254
$941$	−38.4723	−1.25416	−0.627081	−	0.778954i	$-0.715750\pi$
$941$	−38.4723	−1.25416	−0.627081	+	0.778954i	$0.715750\pi$
$942$	14.5052	0.472606
$943$	29.0679	0.946580
$944$	10.9802	0.357376
$945$	20.8825	0.679308
$946$	1.00000	0.0325128
$947$	−57.4837	−1.86797	−0.933985	−	0.357312i	$-0.883693\pi$
$947$	−57.4837	−1.86797	−0.933985	+	0.357312i	$0.883693\pi$
$948$	14.9416	0.485282
$949$	11.5376	0.374527
$950$	−2.28887	−0.0742608
$951$	−36.0698	−1.16964
$952$	19.5168	0.632544
$953$	−3.41714	−0.110692	−0.0553460	−	0.998467i	$-0.517626\pi$
$953$	−3.41714	−0.110692	−0.0553460	+	0.998467i	$0.517626\pi$
$954$	−6.78461	−0.219660
$955$	−4.35977	−0.141079
$956$	−4.10701	−0.132830
$957$	−9.74320	−0.314953
$958$	−6.10912	−0.197377
$959$	−21.4404	−0.692345
$960$	1.16663	0.0376527
$961$	−21.9107	−0.706798
$962$	17.5877	0.567050
$963$	4.25113	0.136991
$964$	−29.9152	−0.963502
$965$	−19.7345	−0.635275
$966$	−14.2082	−0.457142
$967$	37.5678	1.20810	0.604050	−	0.796947i	$-0.293553\pi$
$967$	37.5678	1.20810	0.604050	+	0.796947i	$0.293553\pi$
$968$	1.00000	0.0321412
$969$	−13.5062	−0.433883
$970$	11.3046	0.362969
$971$	4.51313	0.144833	0.0724166	−	0.997374i	$-0.476929\pi$
$971$	4.51313	0.144833	0.0724166	+	0.997374i	$0.476929\pi$
$972$	−14.6063	−0.468499
$973$	−64.2214	−2.05884
$974$	23.7496	0.760987
$975$	4.39249	0.140672
$976$	7.94861	0.254429
$977$	−53.3121	−1.70561	−0.852803	−	0.522232i	$-0.825099\pi$
$977$	−53.3121	−1.70561	−0.852803	+	0.522232i	$0.825099\pi$
$978$	4.24860	0.135855
$979$	−4.61307	−0.147435
$980$	−7.88868	−0.251995
$981$	−17.1591	−0.547847
$982$	−14.1754	−0.452356
$983$	57.7544	1.84208	0.921039	−	0.389470i	$-0.127342\pi$
$983$	57.7544	1.84208	0.921039	+	0.389470i	$0.127342\pi$
$984$	10.7440	0.342506
$985$	1.78207	0.0567816
$986$	−42.2426	−1.34528
$987$	30.1222	0.958801
$988$	8.61788	0.274171
$989$	−3.15631	−0.100365
$990$	1.63898	0.0520903
$991$	−11.9262	−0.378848	−0.189424	−	0.981895i	$-0.560662\pi$
$991$	−11.9262	−0.378848	−0.189424	+	0.981895i	$0.560662\pi$
$992$	−3.01484	−0.0957213
$993$	5.00276	0.158758
$994$	1.03534	0.0328391
$995$	2.27826	0.0722258
$996$	10.7562	0.340824
$997$	46.9692	1.48753	0.743765	−	0.668442i	$-0.233038\pi$
$997$	46.9692	1.48753	0.743765	+	0.668442i	$0.233038\pi$
$998$	27.1431	0.859201
$999$	−25.2804	−0.799838

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4730.2.a.bf.1.5	✓	13

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4730.2.a.bf.1.5	✓	13	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:	\( N \)	\(=\)	\( 4730 = 2 \cdot 5 \cdot 11 \cdot 43 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4730.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -1.16663 q^{3} +1.00000 q^{4} -1.00000 q^{5} -1.16663 q^{6} -3.85859 q^{7} +1.00000 q^{8} -1.63898 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -1.16663 q^{3} +1.00000 q^{4} -1.00000 q^{5} -1.16663 q^{6} -3.85859 q^{7} +1.00000 q^{8} -1.63898 q^{9} -1.00000 q^{10} +1.00000 q^{11} -1.16663 q^{12} -3.76512 q^{13} -3.85859 q^{14} +1.16663 q^{15} +1.00000 q^{16} -5.05803 q^{17} -1.63898 q^{18} -2.28887 q^{19} -1.00000 q^{20} +4.50153 q^{21} +1.00000 q^{22} -3.15631 q^{23} -1.16663 q^{24} +1.00000 q^{25} -3.76512 q^{26} +5.41196 q^{27} -3.85859 q^{28} +8.35160 q^{29} +1.16663 q^{30} -3.01484 q^{31} +1.00000 q^{32} -1.16663 q^{33} -5.05803 q^{34} +3.85859 q^{35} -1.63898 q^{36} -4.67122 q^{37} -2.28887 q^{38} +4.39249 q^{39} -1.00000 q^{40} -9.20945 q^{41} +4.50153 q^{42} +1.00000 q^{43} +1.00000 q^{44} +1.63898 q^{45} -3.15631 q^{46} +6.69155 q^{47} -1.16663 q^{48} +7.88868 q^{49} +1.00000 q^{50} +5.90083 q^{51} -3.76512 q^{52} +4.13953 q^{53} +5.41196 q^{54} -1.00000 q^{55} -3.85859 q^{56} +2.67026 q^{57} +8.35160 q^{58} +10.9802 q^{59} +1.16663 q^{60} +7.94861 q^{61} -3.01484 q^{62} +6.32415 q^{63} +1.00000 q^{64} +3.76512 q^{65} -1.16663 q^{66} +7.87269 q^{67} -5.05803 q^{68} +3.68223 q^{69} +3.85859 q^{70} -0.268322 q^{71} -1.63898 q^{72} -3.06434 q^{73} -4.67122 q^{74} -1.16663 q^{75} -2.28887 q^{76} -3.85859 q^{77} +4.39249 q^{78} -12.8076 q^{79} -1.00000 q^{80} -1.39679 q^{81} -9.20945 q^{82} -9.21995 q^{83} +4.50153 q^{84} +5.05803 q^{85} +1.00000 q^{86} -9.74320 q^{87} +1.00000 q^{88} -4.61307 q^{89} +1.63898 q^{90} +14.5280 q^{91} -3.15631 q^{92} +3.51719 q^{93} +6.69155 q^{94} +2.28887 q^{95} -1.16663 q^{96} -11.3046 q^{97} +7.88868 q^{98} -1.63898 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 13 q + 13 q^{2} + 13 q^{4} - 13 q^{5} + 7 q^{7} + 13 q^{8} + 25 q^{9}+O(q^{10}) \) 13 * q + 13 * q^2 + 13 * q^4 - 13 * q^5 + 7 * q^7 + 13 * q^8 + 25 * q^9	\( 13 q + 13 q^{2} + 13 q^{4} - 13 q^{5} + 7 q^{7} + 13 q^{8} + 25 q^{9} - 13 q^{10} + 13 q^{11} + 11 q^{13} + 7 q^{14} + 13 q^{16} - 2 q^{17} + 25 q^{18} + 7 q^{19} - 13 q^{20} + 12 q^{21} + 13 q^{22} + 12 q^{23} + 13 q^{25} + 11 q^{26} - 15 q^{27} + 7 q^{28} + 14 q^{29} + 20 q^{31} + 13 q^{32} - 2 q^{34} - 7 q^{35} + 25 q^{36} + 17 q^{37} + 7 q^{38} - 4 q^{39} - 13 q^{40} + 9 q^{41} + 12 q^{42} + 13 q^{43} + 13 q^{44} - 25 q^{45} + 12 q^{46} - 9 q^{47} + 30 q^{49} + 13 q^{50} - 3 q^{51} + 11 q^{52} + 22 q^{53} - 15 q^{54} - 13 q^{55} + 7 q^{56} + 17 q^{57} + 14 q^{58} + 19 q^{59} + 2 q^{61} + 20 q^{62} + 12 q^{63} + 13 q^{64} - 11 q^{65} + 9 q^{67} - 2 q^{68} - 6 q^{69} - 7 q^{70} + 6 q^{71} + 25 q^{72} + 7 q^{73} + 17 q^{74} + 7 q^{76} + 7 q^{77} - 4 q^{78} + 50 q^{79} - 13 q^{80} + 85 q^{81} + 9 q^{82} + q^{83} + 12 q^{84} + 2 q^{85} + 13 q^{86} - 21 q^{87} + 13 q^{88} + 5 q^{89} - 25 q^{90} + 5 q^{91} + 12 q^{92} + 3 q^{93} - 9 q^{94} - 7 q^{95} + 20 q^{97} + 30 q^{98} + 25 q^{99}+O(q^{100}) \) 13 * q + 13 * q^2 + 13 * q^4 - 13 * q^5 + 7 * q^7 + 13 * q^8 + 25 * q^9 - 13 * q^10 + 13 * q^11 + 11 * q^13 + 7 * q^14 + 13 * q^16 - 2 * q^17 + 25 * q^18 + 7 * q^19 - 13 * q^20 + 12 * q^21 + 13 * q^22 + 12 * q^23 + 13 * q^25 + 11 * q^26 - 15 * q^27 + 7 * q^28 + 14 * q^29 + 20 * q^31 + 13 * q^32 - 2 * q^34 - 7 * q^35 + 25 * q^36 + 17 * q^37 + 7 * q^38 - 4 * q^39 - 13 * q^40 + 9 * q^41 + 12 * q^42 + 13 * q^43 + 13 * q^44 - 25 * q^45 + 12 * q^46 - 9 * q^47 + 30 * q^49 + 13 * q^50 - 3 * q^51 + 11 * q^52 + 22 * q^53 - 15 * q^54 - 13 * q^55 + 7 * q^56 + 17 * q^57 + 14 * q^58 + 19 * q^59 + 2 * q^61 + 20 * q^62 + 12 * q^63 + 13 * q^64 - 11 * q^65 + 9 * q^67 - 2 * q^68 - 6 * q^69 - 7 * q^70 + 6 * q^71 + 25 * q^72 + 7 * q^73 + 17 * q^74 + 7 * q^76 + 7 * q^77 - 4 * q^78 + 50 * q^79 - 13 * q^80 + 85 * q^81 + 9 * q^82 + q^83 + 12 * q^84 + 2 * q^85 + 13 * q^86 - 21 * q^87 + 13 * q^88 + 5 * q^89 - 25 * q^90 + 5 * q^91 + 12 * q^92 + 3 * q^93 - 9 * q^94 - 7 * q^95 + 20 * q^97 + 30 * q^98 + 25 * q^99

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