LMFDB - Embedded newform 4730.2.a.bf.1.3

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			1.3
Root			$2.61361$ 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)

$f(q)$	$=$	$q+1.00000 q^{2} -2.61361 q^{3} +1.00000 q^{4} -1.00000 q^{5} -2.61361 q^{6} +0.881450 q^{7} +1.00000 q^{8} +3.83093 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -2.61361 q^{3} +1.00000 q^{4} -1.00000 q^{5} -2.61361 q^{6} +0.881450 q^{7} +1.00000 q^{8} +3.83093 q^{9} -1.00000 q^{10} +1.00000 q^{11} -2.61361 q^{12} -6.07569 q^{13} +0.881450 q^{14} +2.61361 q^{15} +1.00000 q^{16} -6.61083 q^{17} +3.83093 q^{18} -1.59458 q^{19} -1.00000 q^{20} -2.30376 q^{21} +1.00000 q^{22} +1.90303 q^{23} -2.61361 q^{24} +1.00000 q^{25} -6.07569 q^{26} -2.17173 q^{27} +0.881450 q^{28} -3.16799 q^{29} +2.61361 q^{30} +7.78274 q^{31} +1.00000 q^{32} -2.61361 q^{33} -6.61083 q^{34} -0.881450 q^{35} +3.83093 q^{36} +3.74873 q^{37} -1.59458 q^{38} +15.8795 q^{39} -1.00000 q^{40} +7.16918 q^{41} -2.30376 q^{42} +1.00000 q^{43} +1.00000 q^{44} -3.83093 q^{45} +1.90303 q^{46} -12.3298 q^{47} -2.61361 q^{48} -6.22305 q^{49} +1.00000 q^{50} +17.2781 q^{51} -6.07569 q^{52} +8.84537 q^{53} -2.17173 q^{54} -1.00000 q^{55} +0.881450 q^{56} +4.16762 q^{57} -3.16799 q^{58} +4.82604 q^{59} +2.61361 q^{60} -6.29159 q^{61} +7.78274 q^{62} +3.37677 q^{63} +1.00000 q^{64} +6.07569 q^{65} -2.61361 q^{66} -7.78393 q^{67} -6.61083 q^{68} -4.97378 q^{69} -0.881450 q^{70} +4.25244 q^{71} +3.83093 q^{72} -6.44173 q^{73} +3.74873 q^{74} -2.61361 q^{75} -1.59458 q^{76} +0.881450 q^{77} +15.8795 q^{78} +5.91937 q^{79} -1.00000 q^{80} -5.81675 q^{81} +7.16918 q^{82} -8.39798 q^{83} -2.30376 q^{84} +6.61083 q^{85} +1.00000 q^{86} +8.27988 q^{87} +1.00000 q^{88} +14.5173 q^{89} -3.83093 q^{90} -5.35542 q^{91} +1.90303 q^{92} -20.3410 q^{93} -12.3298 q^{94} +1.59458 q^{95} -2.61361 q^{96} +3.95643 q^{97} -6.22305 q^{98} +3.83093 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	−2.61361	−1.50897	−0.754483	−	0.656320i	$-0.772112\pi$
$3$	−2.61361	−1.50897	−0.754483	+	0.656320i	$0.772112\pi$
$4$	1.00000	0.500000
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	−2.61361	−1.06700
$7$	0.881450	0.333157	0.166578	−	0.986028i	$-0.446728\pi$
$7$	0.881450	0.333157	0.166578	+	0.986028i	$0.446728\pi$
$8$	1.00000	0.353553
$9$	3.83093	1.27698
$10$	−1.00000	−0.316228
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	−2.61361	−0.754483
$13$	−6.07569	−1.68509	−0.842547	−	0.538623i	$-0.818945\pi$
$13$	−6.07569	−1.68509	−0.842547	+	0.538623i	$0.818945\pi$
$14$	0.881450	0.235577
$15$	2.61361	0.674830
$16$	1.00000	0.250000
$17$	−6.61083	−1.60336	−0.801681	−	0.597752i	$-0.796061\pi$
$17$	−6.61083	−1.60336	−0.801681	+	0.597752i	$0.796061\pi$
$18$	3.83093	0.902959
$19$	−1.59458	−0.365823	−0.182911	−	0.983129i	$-0.558552\pi$
$19$	−1.59458	−0.365823	−0.182911	+	0.983129i	$0.558552\pi$
$20$	−1.00000	−0.223607
$21$	−2.30376	−0.502722
$22$	1.00000	0.213201
$23$	1.90303	0.396810	0.198405	−	0.980120i	$-0.436424\pi$
$23$	1.90303	0.396810	0.198405	+	0.980120i	$0.436424\pi$
$24$	−2.61361	−0.533500
$25$	1.00000	0.200000
$26$	−6.07569	−1.19154
$27$	−2.17173	−0.417949
$28$	0.881450	0.166578
$29$	−3.16799	−0.588281	−0.294141	−	0.955762i	$-0.595033\pi$
$29$	−3.16799	−0.588281	−0.294141	+	0.955762i	$0.595033\pi$
$30$	2.61361	0.477177
$31$	7.78274	1.39782	0.698911	−	0.715209i	$-0.253669\pi$
$31$	7.78274	1.39782	0.698911	+	0.715209i	$0.253669\pi$
$32$	1.00000	0.176777
$33$	−2.61361	−0.454970
$34$	−6.61083	−1.13375
$35$	−0.881450	−0.148992
$36$	3.83093	0.638489
$37$	3.74873	0.616288	0.308144	−	0.951340i	$-0.400292\pi$
$37$	3.74873	0.616288	0.308144	+	0.951340i	$0.400292\pi$
$38$	−1.59458	−0.258676
$39$	15.8795	2.54275
$40$	−1.00000	−0.158114
$41$	7.16918	1.11964	0.559819	−	0.828615i	$-0.310871\pi$
$41$	7.16918	1.11964	0.559819	+	0.828615i	$0.310871\pi$
$42$	−2.30376	−0.355478
$43$	1.00000	0.152499
$43$	1.00000	0.152499
$44$	1.00000	0.150756
$45$	−3.83093	−0.571082
$46$	1.90303	0.280587
$47$	−12.3298	−1.79849	−0.899244	−	0.437447i	$-0.855883\pi$
$47$	−12.3298	−1.79849	−0.899244	+	0.437447i	$0.855883\pi$
$48$	−2.61361	−0.377241
$49$	−6.22305	−0.889007
$50$	1.00000	0.141421
$51$	17.2781	2.41942
$52$	−6.07569	−0.842547
$53$	8.84537	1.21501	0.607503	−	0.794318i	$-0.292171\pi$
$53$	8.84537	1.21501	0.607503	+	0.794318i	$0.292171\pi$
$54$	−2.17173	−0.295535
$55$	−1.00000	−0.134840
$56$	0.881450	0.117789
$57$	4.16762	0.552014
$58$	−3.16799	−0.415978
$59$	4.82604	0.628296	0.314148	−	0.949374i	$-0.398281\pi$
$59$	4.82604	0.628296	0.314148	+	0.949374i	$0.398281\pi$
$60$	2.61361	0.337415
$61$	−6.29159	−0.805556	−0.402778	−	0.915298i	$-0.631955\pi$
$61$	−6.29159	−0.805556	−0.402778	+	0.915298i	$0.631955\pi$
$62$	7.78274	0.988409
$63$	3.37677	0.425434
$64$	1.00000	0.125000
$65$	6.07569	0.753597
$66$	−2.61361	−0.321713
$67$	−7.78393	−0.950958	−0.475479	−	0.879727i	$-0.657725\pi$
$67$	−7.78393	−0.950958	−0.475479	+	0.879727i	$0.657725\pi$
$68$	−6.61083	−0.801681
$69$	−4.97378	−0.598773
$70$	−0.881450	−0.105353
$71$	4.25244	0.504672	0.252336	−	0.967640i	$-0.418801\pi$
$71$	4.25244	0.504672	0.252336	+	0.967640i	$0.418801\pi$
$72$	3.83093	0.451480
$73$	−6.44173	−0.753948	−0.376974	−	0.926224i	$-0.623035\pi$
$73$	−6.44173	−0.753948	−0.376974	+	0.926224i	$0.623035\pi$
$74$	3.74873	0.435781
$75$	−2.61361	−0.301793
$76$	−1.59458	−0.182911
$77$	0.881450	0.100451
$78$	15.8795	1.79799
$79$	5.91937	0.665982	0.332991	−	0.942930i	$-0.391942\pi$
$79$	5.91937	0.665982	0.332991	+	0.942930i	$0.391942\pi$
$80$	−1.00000	−0.111803
$81$	−5.81675	−0.646306
$82$	7.16918	0.791704
$83$	−8.39798	−0.921798	−0.460899	−	0.887453i	$-0.652473\pi$
$83$	−8.39798	−0.921798	−0.460899	+	0.887453i	$0.652473\pi$
$84$	−2.30376	−0.251361
$85$	6.61083	0.717046
$86$	1.00000	0.107833
$87$	8.27988	0.887696
$88$	1.00000	0.106600
$89$	14.5173	1.53883	0.769414	−	0.638751i	$-0.220549\pi$
$89$	14.5173	1.53883	0.769414	+	0.638751i	$0.220549\pi$
$90$	−3.83093	−0.403816
$91$	−5.35542	−0.561400
$92$	1.90303	0.198405
$93$	−20.3410	−2.10926
$94$	−12.3298	−1.27172
$95$	1.59458	0.163601
$96$	−2.61361	−0.266750
$97$	3.95643	0.401715	0.200857	−	0.979620i	$-0.435627\pi$
$97$	3.95643	0.401715	0.200857	+	0.979620i	$0.435627\pi$
$98$	−6.22305	−0.628623
$99$	3.83093	0.385023
$100$	1.00000	0.100000
$101$	−9.97999	−0.993047	−0.496523	−	0.868023i	$-0.665390\pi$
$101$	−9.97999	−0.993047	−0.496523	+	0.868023i	$0.665390\pi$
$102$	17.2781	1.71079
$103$	0.780011	0.0768568	0.0384284	−	0.999261i	$-0.487765\pi$
$103$	0.780011	0.0768568	0.0384284	+	0.999261i	$0.487765\pi$
$104$	−6.07569	−0.595771
$105$	2.30376	0.224824
$106$	8.84537	0.859139
$107$	13.7654	1.33075	0.665375	−	0.746509i	$-0.268272\pi$
$107$	13.7654	1.33075	0.665375	+	0.746509i	$0.268272\pi$
$108$	−2.17173	−0.208975
$109$	15.6196	1.49608	0.748042	−	0.663651i	$-0.230994\pi$
$109$	15.6196	1.49608	0.748042	+	0.663651i	$0.230994\pi$
$110$	−1.00000	−0.0953463
$111$	−9.79771	−0.929957
$112$	0.881450	0.0832892
$113$	−6.48394	−0.609958	−0.304979	−	0.952359i	$-0.598649\pi$
$113$	−6.48394	−0.609958	−0.304979	+	0.952359i	$0.598649\pi$
$114$	4.16762	0.390333
$115$	−1.90303	−0.177459
$116$	−3.16799	−0.294141
$117$	−23.2756	−2.15183
$118$	4.82604	0.444273
$119$	−5.82712	−0.534171
$120$	2.61361	0.238588
$121$	1.00000	0.0909091
$122$	−6.29159	−0.569614
$123$	−18.7374	−1.68950
$124$	7.78274	0.698911
$125$	−1.00000	−0.0894427
$126$	3.37677	0.300827
$127$	2.02587	0.179767	0.0898837	−	0.995952i	$-0.471350\pi$
$127$	2.02587	0.179767	0.0898837	+	0.995952i	$0.471350\pi$
$128$	1.00000	0.0883883
$129$	−2.61361	−0.230115
$130$	6.07569	0.532873
$131$	−12.5615	−1.09750	−0.548751	−	0.835986i	$-0.684896\pi$
$131$	−12.5615	−1.09750	−0.548751	+	0.835986i	$0.684896\pi$
$132$	−2.61361	−0.227485
$133$	−1.40555	−0.121876
$134$	−7.78393	−0.672429
$135$	2.17173	0.186913
$136$	−6.61083	−0.566874
$137$	19.0211	1.62508	0.812542	−	0.582902i	$-0.198083\pi$
$137$	19.0211	1.62508	0.812542	+	0.582902i	$0.198083\pi$
$138$	−4.97378	−0.423396
$139$	11.1258	0.943677	0.471839	−	0.881685i	$-0.343590\pi$
$139$	11.1258	0.943677	0.471839	+	0.881685i	$0.343590\pi$
$140$	−0.881450	−0.0744961
$141$	32.2253	2.71386
$142$	4.25244	0.356857
$143$	−6.07569	−0.508075
$144$	3.83093	0.319244
$145$	3.16799	0.263087
$146$	−6.44173	−0.533122
$147$	16.2646	1.34148
$148$	3.74873	0.308144
$149$	−9.99029	−0.818436	−0.409218	−	0.912437i	$-0.634198\pi$
$149$	−9.99029	−0.818436	−0.409218	+	0.912437i	$0.634198\pi$
$150$	−2.61361	−0.213400
$151$	−1.15872	−0.0942957	−0.0471478	−	0.998888i	$-0.515013\pi$
$151$	−1.15872	−0.0942957	−0.0471478	+	0.998888i	$0.515013\pi$
$152$	−1.59458	−0.129338
$153$	−25.3257	−2.04746
$154$	0.881450	0.0710293
$155$	−7.78274	−0.625125
$156$	15.8795	1.27137
$157$	24.8105	1.98009	0.990046	−	0.140744i	$-0.0449494\pi$
$157$	24.8105	1.98009	0.990046	+	0.140744i	$0.0449494\pi$
$158$	5.91937	0.470920
$159$	−23.1183	−1.83340
$160$	−1.00000	−0.0790569
$161$	1.67743	0.132200
$162$	−5.81675	−0.457007
$163$	12.5250	0.981031	0.490515	−	0.871433i	$-0.336809\pi$
$163$	12.5250	0.981031	0.490515	+	0.871433i	$0.336809\pi$
$164$	7.16918	0.559819
$165$	2.61361	0.203469
$166$	−8.39798	−0.651809
$167$	24.0151	1.85835	0.929173	−	0.369645i	$-0.120521\pi$
$167$	24.0151	1.85835	0.929173	+	0.369645i	$0.120521\pi$
$168$	−2.30376	−0.177739
$169$	23.9140	1.83954
$170$	6.61083	0.507028
$171$	−6.10875	−0.467148
$172$	1.00000	0.0762493
$173$	−17.8221	−1.35499	−0.677496	−	0.735526i	$-0.736935\pi$
$173$	−17.8221	−1.35499	−0.677496	+	0.735526i	$0.736935\pi$
$174$	8.27988	0.627696
$175$	0.881450	0.0666313
$176$	1.00000	0.0753778
$177$	−12.6134	−0.948078
$178$	14.5173	1.08812
$179$	4.37125	0.326723	0.163361	−	0.986566i	$-0.447766\pi$
$179$	4.37125	0.326723	0.163361	+	0.986566i	$0.447766\pi$
$180$	−3.83093	−0.285541
$181$	10.6388	0.790773	0.395386	−	0.918515i	$-0.370611\pi$
$181$	10.6388	0.790773	0.395386	+	0.918515i	$0.370611\pi$
$182$	−5.35542	−0.396970
$183$	16.4437	1.21556
$184$	1.90303	0.140294
$185$	−3.74873	−0.275612
$186$	−20.3410	−1.49148
$187$	−6.61083	−0.483432
$188$	−12.3298	−0.899244
$189$	−1.91427	−0.139243
$190$	1.59458	0.115683
$191$	19.9082	1.44050	0.720252	−	0.693712i	$-0.244026\pi$
$191$	19.9082	1.44050	0.720252	+	0.693712i	$0.244026\pi$
$192$	−2.61361	−0.188621
$193$	10.7455	0.773480	0.386740	−	0.922189i	$-0.373601\pi$
$193$	10.7455	0.773480	0.386740	+	0.922189i	$0.373601\pi$
$194$	3.95643	0.284055
$195$	−15.8795	−1.13715
$196$	−6.22305	−0.444503
$197$	−6.53034	−0.465267	−0.232634	−	0.972564i	$-0.574734\pi$
$197$	−6.53034	−0.465267	−0.232634	+	0.972564i	$0.574734\pi$
$198$	3.83093	0.272253
$199$	18.5722	1.31655	0.658273	−	0.752779i	$-0.271287\pi$
$199$	18.5722	1.31655	0.658273	+	0.752779i	$0.271287\pi$
$200$	1.00000	0.0707107
$201$	20.3441	1.43496
$202$	−9.97999	−0.702190
$203$	−2.79243	−0.195990
$204$	17.2781	1.20971
$205$	−7.16918	−0.500717
$206$	0.780011	0.0543460
$207$	7.29040	0.506718
$208$	−6.07569	−0.421273
$209$	−1.59458	−0.110300
$210$	2.30376	0.158975
$211$	−23.6147	−1.62571	−0.812853	−	0.582469i	$-0.802087\pi$
$211$	−23.6147	−1.62571	−0.812853	+	0.582469i	$0.802087\pi$
$212$	8.84537	0.607503
$213$	−11.1142	−0.761532
$214$	13.7654	0.940982
$215$	−1.00000	−0.0681994
$216$	−2.17173	−0.147767
$217$	6.86009	0.465694
$218$	15.6196	1.05789
$219$	16.8362	1.13768
$220$	−1.00000	−0.0674200
$221$	40.1654	2.70182
$222$	−9.79771	−0.657579
$223$	−11.8260	−0.791929	−0.395965	−	0.918266i	$-0.629590\pi$
$223$	−11.8260	−0.791929	−0.395965	+	0.918266i	$0.629590\pi$
$224$	0.881450	0.0588943
$225$	3.83093	0.255395
$226$	−6.48394	−0.431306
$227$	20.5501	1.36396	0.681981	−	0.731370i	$-0.261119\pi$
$227$	20.5501	1.36396	0.681981	+	0.731370i	$0.261119\pi$
$228$	4.16762	0.276007
$229$	21.7488	1.43720	0.718600	−	0.695424i	$-0.244783\pi$
$229$	21.7488	1.43720	0.718600	+	0.695424i	$0.244783\pi$
$230$	−1.90303	−0.125482
$231$	−2.30376	−0.151576
$232$	−3.16799	−0.207989
$233$	7.30511	0.478574	0.239287	−	0.970949i	$-0.423086\pi$
$233$	7.30511	0.478574	0.239287	+	0.970949i	$0.423086\pi$
$234$	−23.2756	−1.52157
$235$	12.3298	0.804308
$236$	4.82604	0.314148
$237$	−15.4709	−1.00494
$238$	−5.82712	−0.377716
$239$	−15.1275	−0.978518	−0.489259	−	0.872139i	$-0.662733\pi$
$239$	−15.1275	−0.978518	−0.489259	+	0.872139i	$0.662733\pi$
$240$	2.61361	0.168707
$241$	23.2924	1.50040	0.750198	−	0.661213i	$-0.229958\pi$
$241$	23.2924	1.50040	0.750198	+	0.661213i	$0.229958\pi$
$242$	1.00000	0.0642824
$243$	21.7179	1.39320
$244$	−6.29159	−0.402778
$245$	6.22305	0.397576
$246$	−18.7374	−1.19465
$247$	9.68820	0.616446
$248$	7.78274	0.494204
$249$	21.9490	1.39096
$250$	−1.00000	−0.0632456
$251$	−6.47298	−0.408571	−0.204286	−	0.978911i	$-0.565487\pi$
$251$	−6.47298	−0.408571	−0.204286	+	0.978911i	$0.565487\pi$
$252$	3.37677	0.212717
$253$	1.90303	0.119643
$254$	2.02587	0.127115
$255$	−17.2781	−1.08200
$256$	1.00000	0.0625000
$257$	19.8928	1.24088	0.620440	−	0.784254i	$-0.286954\pi$
$257$	19.8928	1.24088	0.620440	+	0.784254i	$0.286954\pi$
$258$	−2.61361	−0.162716
$259$	3.30432	0.205320
$260$	6.07569	0.376798
$261$	−12.1364	−0.751222
$262$	−12.5615	−0.776050
$263$	−23.5082	−1.44958	−0.724790	−	0.688970i	$-0.758063\pi$
$263$	−23.5082	−1.44958	−0.724790	+	0.688970i	$0.758063\pi$
$264$	−2.61361	−0.160856
$265$	−8.84537	−0.543367
$266$	−1.40555	−0.0861796
$267$	−37.9424	−2.32204
$268$	−7.78393	−0.475479
$269$	−0.123729	−0.00754387	−0.00377194	−	0.999993i	$-0.501201\pi$
$269$	−0.123729	−0.00754387	−0.00377194	+	0.999993i	$0.501201\pi$
$270$	2.17173	0.132167
$271$	−0.206038	−0.0125159	−0.00625797	−	0.999980i	$-0.501992\pi$
$271$	−0.206038	−0.0125159	−0.00625797	+	0.999980i	$0.501992\pi$
$272$	−6.61083	−0.400841
$273$	13.9969	0.847134
$274$	19.0211	1.14911
$275$	1.00000	0.0603023
$276$	−4.97378	−0.299386
$277$	−15.6731	−0.941704	−0.470852	−	0.882212i	$-0.656053\pi$
$277$	−15.6731	−0.941704	−0.470852	+	0.882212i	$0.656053\pi$
$278$	11.1258	0.667281
$279$	29.8151	1.78499
$280$	−0.881450	−0.0526767
$281$	29.8787	1.78241	0.891207	−	0.453596i	$-0.149859\pi$
$281$	29.8787	1.78241	0.891207	+	0.453596i	$0.149859\pi$
$282$	32.2253	1.91899
$283$	−9.07865	−0.539670	−0.269835	−	0.962907i	$-0.586969\pi$
$283$	−9.07865	−0.539670	−0.269835	+	0.962907i	$0.586969\pi$
$284$	4.25244	0.252336
$285$	−4.16762	−0.246868
$286$	−6.07569	−0.359263
$287$	6.31927	0.373015
$288$	3.83093	0.225740
$289$	26.7031	1.57077
$290$	3.16799	0.186031
$291$	−10.3406	−0.606174
$292$	−6.44173	−0.376974
$293$	−12.6194	−0.737232	−0.368616	−	0.929582i	$-0.620168\pi$
$293$	−12.6194	−0.737232	−0.368616	+	0.929582i	$0.620168\pi$
$294$	16.2646	0.948570
$295$	−4.82604	−0.280983
$296$	3.74873	0.217891
$297$	−2.17173	−0.126017
$298$	−9.99029	−0.578722
$299$	−11.5623	−0.668662
$300$	−2.61361	−0.150897
$301$	0.881450	0.0508059
$302$	−1.15872	−0.0666771
$303$	26.0838	1.49847
$304$	−1.59458	−0.0914557
$305$	6.29159	0.360256
$306$	−25.3257	−1.44777
$307$	5.09549	0.290815	0.145408	−	0.989372i	$-0.453551\pi$
$307$	5.09549	0.290815	0.145408	+	0.989372i	$0.453551\pi$
$308$	0.881450	0.0502253
$309$	−2.03864	−0.115974
$310$	−7.78274	−0.442030
$311$	26.9660	1.52910	0.764550	−	0.644565i	$-0.222961\pi$
$311$	26.9660	1.52910	0.764550	+	0.644565i	$0.222961\pi$
$312$	15.8795	0.898997
$313$	−3.49719	−0.197673	−0.0988366	−	0.995104i	$-0.531512\pi$
$313$	−3.49719	−0.197673	−0.0988366	+	0.995104i	$0.531512\pi$
$314$	24.8105	1.40014
$315$	−3.37677	−0.190260
$316$	5.91937	0.332991
$317$	2.46634	0.138523	0.0692617	−	0.997599i	$-0.477936\pi$
$317$	2.46634	0.138523	0.0692617	+	0.997599i	$0.477936\pi$
$318$	−23.1183	−1.29641
$319$	−3.16799	−0.177373
$320$	−1.00000	−0.0559017
$321$	−35.9773	−2.00806
$322$	1.67743	0.0934795
$323$	10.5415	0.586547
$324$	−5.81675	−0.323153
$325$	−6.07569	−0.337019
$326$	12.5250	0.693693
$327$	−40.8234	−2.25754
$328$	7.16918	0.395852
$329$	−10.8681	−0.599178
$330$	2.61361	0.143874
$331$	−9.52802	−0.523708	−0.261854	−	0.965108i	$-0.584334\pi$
$331$	−9.52802	−0.523708	−0.261854	+	0.965108i	$0.584334\pi$
$332$	−8.39798	−0.460899
$333$	14.3611	0.786986
$334$	24.0151	1.31405
$335$	7.78393	0.425281
$336$	−2.30376	−0.125681
$337$	12.4590	0.678685	0.339342	−	0.940663i	$-0.389795\pi$
$337$	12.4590	0.678685	0.339342	+	0.940663i	$0.389795\pi$
$338$	23.9140	1.30075
$339$	16.9465	0.920406
$340$	6.61083	0.358523
$341$	7.78274	0.421459
$342$	−6.10875	−0.330323
$343$	−11.6555	−0.629335
$344$	1.00000	0.0539164
$345$	4.97378	0.267779
$346$	−17.8221	−0.958124
$347$	14.7880	0.793863	0.396931	−	0.917848i	$-0.370075\pi$
$347$	14.7880	0.793863	0.396931	+	0.917848i	$0.370075\pi$
$348$	8.27988	0.443848
$349$	11.1748	0.598171	0.299086	−	0.954226i	$-0.403318\pi$
$349$	11.1748	0.598171	0.299086	+	0.954226i	$0.403318\pi$
$350$	0.881450	0.0471155
$351$	13.1948	0.704284
$352$	1.00000	0.0533002
$353$	−32.8622	−1.74908	−0.874539	−	0.484955i	$-0.838836\pi$
$353$	−32.8622	−1.74908	−0.874539	+	0.484955i	$0.838836\pi$
$354$	−12.6134	−0.670392
$355$	−4.25244	−0.225696
$356$	14.5173	0.769414
$357$	15.2298	0.806046
$358$	4.37125	0.231028
$359$	18.5947	0.981391	0.490696	−	0.871331i	$-0.336743\pi$
$359$	18.5947	0.981391	0.490696	+	0.871331i	$0.336743\pi$
$360$	−3.83093	−0.201908
$361$	−16.4573	−0.866174
$362$	10.6388	0.559161
$363$	−2.61361	−0.137179
$364$	−5.35542	−0.280700
$365$	6.44173	0.337176
$366$	16.4437	0.859528
$367$	27.1813	1.41885	0.709425	−	0.704781i	$-0.248955\pi$
$367$	27.1813	1.41885	0.709425	+	0.704781i	$0.248955\pi$
$368$	1.90303	0.0992025
$369$	27.4646	1.42975
$370$	−3.74873	−0.194887
$371$	7.79675	0.404787
$372$	−20.3410	−1.05463
$373$	−10.9314	−0.566005	−0.283003	−	0.959119i	$-0.591331\pi$
$373$	−10.9314	−0.566005	−0.283003	+	0.959119i	$0.591331\pi$
$374$	−6.61083	−0.341838
$375$	2.61361	0.134966
$376$	−12.3298	−0.635862
$377$	19.2477	0.991309
$378$	−1.91427	−0.0984594
$379$	−35.8223	−1.84007	−0.920034	−	0.391838i	$-0.871839\pi$
$379$	−35.8223	−1.84007	−0.920034	+	0.391838i	$0.871839\pi$
$380$	1.59458	0.0818005
$381$	−5.29484	−0.271263
$382$	19.9082	1.01859
$383$	−11.8569	−0.605859	−0.302929	−	0.953013i	$-0.597965\pi$
$383$	−11.8569	−0.605859	−0.302929	+	0.953013i	$0.597965\pi$
$384$	−2.61361	−0.133375
$385$	−0.881450	−0.0449228
$386$	10.7455	0.546933
$387$	3.83093	0.194737
$388$	3.95643	0.200857
$389$	2.65249	0.134486	0.0672432	−	0.997737i	$-0.478580\pi$
$389$	2.65249	0.134486	0.0672432	+	0.997737i	$0.478580\pi$
$390$	−15.8795	−0.804088
$391$	−12.5806	−0.636231
$392$	−6.22305	−0.314311
$393$	32.8307	1.65609
$394$	−6.53034	−0.328994
$395$	−5.91937	−0.297836
$396$	3.83093	0.192512
$397$	23.4796	1.17841	0.589205	−	0.807984i	$-0.299441\pi$
$397$	23.4796	1.17841	0.589205	+	0.807984i	$0.299441\pi$
$398$	18.5722	0.930939
$399$	3.67354	0.183907
$400$	1.00000	0.0500000
$401$	14.8649	0.742319	0.371159	−	0.928569i	$-0.378960\pi$
$401$	14.8649	0.742319	0.371159	+	0.928569i	$0.378960\pi$
$402$	20.3441	1.01467
$403$	−47.2855	−2.35546
$404$	−9.97999	−0.496523
$405$	5.81675	0.289037
$406$	−2.79243	−0.138586
$407$	3.74873	0.185818
$408$	17.2781	0.855394
$409$	13.3349	0.659370	0.329685	−	0.944091i	$-0.393057\pi$
$409$	13.3349	0.659370	0.329685	+	0.944091i	$0.393057\pi$
$410$	−7.16918	−0.354061
$411$	−49.7137	−2.45220
$412$	0.780011	0.0384284
$413$	4.25391	0.209321
$414$	7.29040	0.358303
$415$	8.39798	0.412240
$416$	−6.07569	−0.297885
$417$	−29.0784	−1.42398
$418$	−1.59458	−0.0779937
$419$	13.4409	0.656633	0.328316	−	0.944568i	$-0.393519\pi$
$419$	13.4409	0.656633	0.328316	+	0.944568i	$0.393519\pi$
$420$	2.30376	0.112412
$421$	9.78705	0.476992	0.238496	−	0.971144i	$-0.423346\pi$
$421$	9.78705	0.476992	0.238496	+	0.971144i	$0.423346\pi$
$422$	−23.6147	−1.14955
$423$	−47.2347	−2.29663
$424$	8.84537	0.429569
$425$	−6.61083	−0.320673
$426$	−11.1142	−0.538484
$427$	−5.54572	−0.268376
$428$	13.7654	0.665375
$429$	15.8795	0.766667
$430$	−1.00000	−0.0482243
$431$	−39.2910	−1.89258	−0.946291	−	0.323316i	$-0.895202\pi$
$431$	−39.2910	−1.89258	−0.946291	+	0.323316i	$0.895202\pi$
$432$	−2.17173	−0.104487
$433$	34.9697	1.68054	0.840268	−	0.542172i	$-0.182398\pi$
$433$	34.9697	1.68054	0.840268	+	0.542172i	$0.182398\pi$
$434$	6.86009	0.329295
$435$	−8.27988	−0.396990
$436$	15.6196	0.748042
$437$	−3.03455	−0.145162
$438$	16.8362	0.804462
$439$	−1.14756	−0.0547702	−0.0273851	−	0.999625i	$-0.508718\pi$
$439$	−1.14756	−0.0547702	−0.0273851	+	0.999625i	$0.508718\pi$
$440$	−1.00000	−0.0476731
$441$	−23.8401	−1.13524
$442$	40.1654	1.91047
$443$	2.40564	0.114296	0.0571478	−	0.998366i	$-0.481799\pi$
$443$	2.40564	0.114296	0.0571478	+	0.998366i	$0.481799\pi$
$444$	−9.79771	−0.464979
$445$	−14.5173	−0.688184
$446$	−11.8260	−0.559979
$447$	26.1107	1.23499
$448$	0.881450	0.0416446
$449$	15.0760	0.711479	0.355740	−	0.934585i	$-0.384229\pi$
$449$	15.0760	0.711479	0.355740	+	0.934585i	$0.384229\pi$
$450$	3.83093	0.180592
$451$	7.16918	0.337584
$452$	−6.48394	−0.304979
$453$	3.02845	0.142289
$454$	20.5501	0.964466
$455$	5.35542	0.251066
$456$	4.16762	0.195166
$457$	8.86295	0.414591	0.207296	−	0.978278i	$-0.433534\pi$
$457$	8.86295	0.414591	0.207296	+	0.978278i	$0.433534\pi$
$458$	21.7488	1.01625
$459$	14.3569	0.670125
$460$	−1.90303	−0.0887295
$461$	−30.0315	−1.39870	−0.699352	−	0.714777i	$-0.746528\pi$
$461$	−30.0315	−1.39870	−0.699352	+	0.714777i	$0.746528\pi$
$462$	−2.30376	−0.107181
$463$	5.52756	0.256887	0.128444	−	0.991717i	$-0.459002\pi$
$463$	5.52756	0.256887	0.128444	+	0.991717i	$0.459002\pi$
$464$	−3.16799	−0.147070
$465$	20.3410	0.943292
$466$	7.30511	0.338403
$467$	−36.2153	−1.67585	−0.837923	−	0.545789i	$-0.816230\pi$
$467$	−36.2153	−1.67585	−0.837923	+	0.545789i	$0.816230\pi$
$468$	−23.2756	−1.07591
$469$	−6.86114	−0.316818
$470$	12.3298	0.568732
$471$	−64.8448	−2.98789
$472$	4.82604	0.222136
$473$	1.00000	0.0459800
$474$	−15.4709	−0.710602
$475$	−1.59458	−0.0731646
$476$	−5.82712	−0.267086
$477$	33.8860	1.55153
$478$	−15.1275	−0.691917
$479$	−37.7653	−1.72554	−0.862770	−	0.505597i	$-0.831272\pi$
$479$	−37.7653	−1.72554	−0.862770	+	0.505597i	$0.831272\pi$
$480$	2.61361	0.119294
$481$	−22.7761	−1.03850
$482$	23.2924	1.06094
$483$	−4.38414	−0.199485
$484$	1.00000	0.0454545
$485$	−3.95643	−0.179652
$486$	21.7179	0.985143
$487$	−25.7226	−1.16560	−0.582800	−	0.812615i	$-0.698043\pi$
$487$	−25.7226	−1.16560	−0.582800	+	0.812615i	$0.698043\pi$
$488$	−6.29159	−0.284807
$489$	−32.7353	−1.48034
$490$	6.22305	0.281129
$491$	−1.78560	−0.0805828	−0.0402914	−	0.999188i	$-0.512829\pi$
$491$	−1.78560	−0.0805828	−0.0402914	+	0.999188i	$0.512829\pi$
$492$	−18.7374	−0.844748
$493$	20.9431	0.943228
$494$	9.68820	0.435893
$495$	−3.83093	−0.172188
$496$	7.78274	0.349455
$497$	3.74831	0.168135
$498$	21.9490	0.983558
$499$	−35.4149	−1.58539	−0.792695	−	0.609618i	$-0.791323\pi$
$499$	−35.4149	−1.58539	−0.792695	+	0.609618i	$0.791323\pi$
$500$	−1.00000	−0.0447214
$501$	−62.7660	−2.80418
$502$	−6.47298	−0.288903
$503$	22.0363	0.982550	0.491275	−	0.871005i	$-0.336531\pi$
$503$	22.0363	0.982550	0.491275	+	0.871005i	$0.336531\pi$
$504$	3.37677	0.150413
$505$	9.97999	0.444104
$506$	1.90303	0.0846002
$507$	−62.5018	−2.77580
$508$	2.02587	0.0898837
$509$	−4.04984	−0.179506	−0.0897529	−	0.995964i	$-0.528608\pi$
$509$	−4.04984	−0.179506	−0.0897529	+	0.995964i	$0.528608\pi$
$510$	−17.2781	−0.765088
$511$	−5.67807	−0.251183
$512$	1.00000	0.0441942
$513$	3.46301	0.152895
$514$	19.8928	0.877435
$515$	−0.780011	−0.0343714
$516$	−2.61361	−0.115058
$517$	−12.3298	−0.542265
$518$	3.30432	0.145183
$519$	46.5801	2.04464
$520$	6.07569	0.266437
$521$	−10.0001	−0.438111	−0.219056	−	0.975712i	$-0.570298\pi$
$521$	−10.0001	−0.438111	−0.219056	+	0.975712i	$0.570298\pi$
$522$	−12.1364	−0.531194
$523$	6.76617	0.295864	0.147932	−	0.988998i	$-0.452738\pi$
$523$	6.76617	0.295864	0.147932	+	0.988998i	$0.452738\pi$
$524$	−12.5615	−0.548751
$525$	−2.30376	−0.100544
$526$	−23.5082	−1.02501
$527$	−51.4504	−2.24121
$528$	−2.61361	−0.113743
$529$	−19.3785	−0.842542
$530$	−8.84537	−0.384218
$531$	18.4882	0.802320
$532$	−1.40555	−0.0609382
$533$	−43.5577	−1.88669
$534$	−37.9424	−1.64193
$535$	−13.7654	−0.595130
$536$	−7.78393	−0.336214
$537$	−11.4247	−0.493014
$538$	−0.123729	−0.00533432
$539$	−6.22305	−0.268046
$540$	2.17173	0.0934563
$541$	−17.8195	−0.766122	−0.383061	−	0.923723i	$-0.625130\pi$
$541$	−17.8195	−0.766122	−0.383061	+	0.923723i	$0.625130\pi$
$542$	−0.206038	−0.00885011
$543$	−27.8055	−1.19325
$544$	−6.61083	−0.283437
$545$	−15.6196	−0.669069
$546$	13.9969	0.599014
$547$	19.5478	0.835802	0.417901	−	0.908493i	$-0.362766\pi$
$547$	19.5478	0.835802	0.417901	+	0.908493i	$0.362766\pi$
$548$	19.0211	0.812542
$549$	−24.1027	−1.02868
$550$	1.00000	0.0426401
$551$	5.05163	0.215207
$552$	−4.97378	−0.211698
$553$	5.21763	0.221876
$554$	−15.6731	−0.665885
$555$	9.79771	0.415889
$556$	11.1258	0.471839
$557$	42.8182	1.81426	0.907132	−	0.420846i	$-0.138267\pi$
$557$	42.8182	1.81426	0.907132	+	0.420846i	$0.138267\pi$
$558$	29.8151	1.26218
$559$	−6.07569	−0.256974
$560$	−0.881450	−0.0372481
$561$	17.2781	0.729482
$562$	29.8787	1.26036
$563$	−42.3419	−1.78450	−0.892250	−	0.451543i	$-0.850874\pi$
$563$	−42.3419	−1.78450	−0.892250	+	0.451543i	$0.850874\pi$
$564$	32.2253	1.35693
$565$	6.48394	0.272782
$566$	−9.07865	−0.381604
$567$	−5.12718	−0.215321
$568$	4.25244	0.178428
$569$	15.7452	0.660072	0.330036	−	0.943968i	$-0.392939\pi$
$569$	15.7452	0.660072	0.330036	+	0.943968i	$0.392939\pi$
$570$	−4.16762	−0.174562
$571$	7.66332	0.320700	0.160350	−	0.987060i	$-0.448738\pi$
$571$	7.66332	0.320700	0.160350	+	0.987060i	$0.448738\pi$
$572$	−6.07569	−0.254037
$573$	−52.0321	−2.17367
$574$	6.31927	0.263761
$575$	1.90303	0.0793620
$576$	3.83093	0.159622
$577$	−42.0284	−1.74967	−0.874833	−	0.484424i	$-0.839029\pi$
$577$	−42.0284	−1.74967	−0.874833	+	0.484424i	$0.839029\pi$
$578$	26.7031	1.11070
$579$	−28.0846	−1.16715
$580$	3.16799	0.131544
$581$	−7.40239	−0.307103
$582$	−10.3406	−0.428630
$583$	8.84537	0.366338
$584$	−6.44173	−0.266561
$585$	23.2756	0.962326
$586$	−12.6194	−0.521302
$587$	1.15858	0.0478196	0.0239098	−	0.999714i	$-0.492389\pi$
$587$	1.15858	0.0478196	0.0239098	+	0.999714i	$0.492389\pi$
$588$	16.2646	0.670740
$589$	−12.4102	−0.511355
$590$	−4.82604	−0.198685
$591$	17.0677	0.702072
$592$	3.74873	0.154072
$593$	−4.13863	−0.169953	−0.0849766	−	0.996383i	$-0.527082\pi$
$593$	−4.13863	−0.169953	−0.0849766	+	0.996383i	$0.527082\pi$
$594$	−2.17173	−0.0891071
$595$	5.82712	0.238889
$596$	−9.99029	−0.409218
$597$	−48.5403	−1.98662
$598$	−11.5623	−0.472816
$599$	20.5290	0.838794	0.419397	−	0.907803i	$-0.362242\pi$
$599$	20.5290	0.838794	0.419397	+	0.907803i	$0.362242\pi$
$600$	−2.61361	−0.106700
$601$	19.7931	0.807375	0.403688	−	0.914897i	$-0.367728\pi$
$601$	19.7931	0.807375	0.403688	+	0.914897i	$0.367728\pi$
$602$	0.881450	0.0359252
$603$	−29.8197	−1.21435
$604$	−1.15872	−0.0471478
$605$	−1.00000	−0.0406558
$606$	26.0838	1.05958
$607$	−20.7049	−0.840384	−0.420192	−	0.907435i	$-0.638037\pi$
$607$	−20.7049	−0.840384	−0.420192	+	0.907435i	$0.638037\pi$
$608$	−1.59458	−0.0646690
$609$	7.29830	0.295742
$610$	6.29159	0.254739
$611$	74.9121	3.03062
$612$	−25.3257	−1.02373
$613$	35.5051	1.43404	0.717019	−	0.697054i	$-0.245506\pi$
$613$	35.5051	1.43404	0.717019	+	0.697054i	$0.245506\pi$
$614$	5.09549	0.205637
$615$	18.7374	0.755565
$616$	0.881450	0.0355146
$617$	34.8611	1.40345	0.701727	−	0.712446i	$-0.252413\pi$
$617$	34.8611	1.40345	0.701727	+	0.712446i	$0.252413\pi$
$618$	−2.03864	−0.0820062
$619$	26.5928	1.06886	0.534428	−	0.845214i	$-0.320527\pi$
$619$	26.5928	1.06886	0.534428	+	0.845214i	$0.320527\pi$
$620$	−7.78274	−0.312562
$621$	−4.13288	−0.165847
$622$	26.9660	1.08124
$623$	12.7962	0.512671
$624$	15.8795	0.635687
$625$	1.00000	0.0400000
$626$	−3.49719	−0.139776
$627$	4.16762	0.166439
$628$	24.8105	0.990046
$629$	−24.7822	−0.988133
$630$	−3.37677	−0.134534
$631$	8.75865	0.348676	0.174338	−	0.984686i	$-0.444221\pi$
$631$	8.75865	0.348676	0.174338	+	0.984686i	$0.444221\pi$
$632$	5.91937	0.235460
$633$	61.7196	2.45313
$634$	2.46634	0.0979509
$635$	−2.02587	−0.0803944
$636$	−23.1183	−0.916701
$637$	37.8093	1.49806
$638$	−3.16799	−0.125422
$639$	16.2908	0.644454
$640$	−1.00000	−0.0395285
$641$	18.4370	0.728217	0.364108	−	0.931357i	$-0.381374\pi$
$641$	18.4370	0.728217	0.364108	+	0.931357i	$0.381374\pi$
$642$	−35.9773	−1.41991
$643$	20.2150	0.797204	0.398602	−	0.917124i	$-0.369496\pi$
$643$	20.2150	0.797204	0.398602	+	0.917124i	$0.369496\pi$
$644$	1.67743	0.0661000
$645$	2.61361	0.102911
$646$	10.5415	0.414751
$647$	−39.5194	−1.55367	−0.776834	−	0.629706i	$-0.783176\pi$
$647$	−39.5194	−1.55367	−0.776834	+	0.629706i	$0.783176\pi$
$648$	−5.81675	−0.228504
$649$	4.82604	0.189439
$650$	−6.07569	−0.238308
$651$	−17.9296	−0.702716
$652$	12.5250	0.490515
$653$	−5.61823	−0.219858	−0.109929	−	0.993939i	$-0.535062\pi$
$653$	−5.61823	−0.219858	−0.109929	+	0.993939i	$0.535062\pi$
$654$	−40.8234	−1.59632
$655$	12.5615	0.490817
$656$	7.16918	0.279909
$657$	−24.6778	−0.962775
$658$	−10.8681	−0.423683
$659$	−20.6197	−0.803228	−0.401614	−	0.915809i	$-0.631551\pi$
$659$	−20.6197	−0.803228	−0.401614	+	0.915809i	$0.631551\pi$
$660$	2.61361	0.101734
$661$	−9.71150	−0.377734	−0.188867	−	0.982003i	$-0.560481\pi$
$661$	−9.71150	−0.377734	−0.188867	+	0.982003i	$0.560481\pi$
$662$	−9.52802	−0.370317
$663$	−104.976	−4.07695
$664$	−8.39798	−0.325905
$665$	1.40555	0.0545048
$666$	14.3611	0.556483
$667$	−6.02880	−0.233436
$668$	24.0151	0.929173
$669$	30.9086	1.19499
$670$	7.78393	0.300719
$671$	−6.29159	−0.242884
$672$	−2.30376	−0.0888695
$673$	34.2384	1.31979	0.659897	−	0.751356i	$-0.270600\pi$
$673$	34.2384	1.31979	0.659897	+	0.751356i	$0.270600\pi$
$674$	12.4590	0.479903
$675$	−2.17173	−0.0835899
$676$	23.9140	0.919770
$677$	−25.2026	−0.968615	−0.484308	−	0.874898i	$-0.660928\pi$
$677$	−25.2026	−0.968615	−0.484308	+	0.874898i	$0.660928\pi$
$678$	16.9465	0.650825
$679$	3.48740	0.133834
$680$	6.61083	0.253514
$681$	−53.7100	−2.05817
$682$	7.78274	0.298016
$683$	−30.4342	−1.16453	−0.582267	−	0.812998i	$-0.697834\pi$
$683$	−30.4342	−1.16453	−0.582267	+	0.812998i	$0.697834\pi$
$684$	−6.10875	−0.233574
$685$	−19.0211	−0.726760
$686$	−11.6555	−0.445007
$687$	−56.8427	−2.16868
$688$	1.00000	0.0381246
$689$	−53.7418	−2.04740
$690$	4.97378	0.189349
$691$	−38.7300	−1.47336	−0.736679	−	0.676242i	$-0.763607\pi$
$691$	−38.7300	−1.47336	−0.736679	+	0.676242i	$0.763607\pi$
$692$	−17.8221	−0.677496
$693$	3.37677	0.128273
$694$	14.7880	0.561346
$695$	−11.1258	−0.422025
$696$	8.27988	0.313848
$697$	−47.3943	−1.79519
$698$	11.1748	0.422971
$699$	−19.0927	−0.722152
$700$	0.881450	0.0333157
$701$	−7.01983	−0.265135	−0.132568	−	0.991174i	$-0.542322\pi$
$701$	−7.01983	−0.265135	−0.132568	+	0.991174i	$0.542322\pi$
$702$	13.1948	0.498004
$703$	−5.97767	−0.225452
$704$	1.00000	0.0376889
$705$	−32.2253	−1.21367
$706$	−32.8622	−1.23679
$707$	−8.79686	−0.330840
$708$	−12.6134	−0.474039
$709$	24.1643	0.907508	0.453754	−	0.891127i	$-0.350084\pi$
$709$	24.1643	0.907508	0.453754	+	0.891127i	$0.350084\pi$
$710$	−4.25244	−0.159591
$711$	22.6767	0.850443
$712$	14.5173	0.544058
$713$	14.8108	0.554670
$714$	15.2298	0.569960
$715$	6.07569	0.227218
$716$	4.37125	0.163361
$717$	39.5374	1.47655
$718$	18.5947	0.693948
$719$	47.7856	1.78210	0.891051	−	0.453903i	$-0.149969\pi$
$719$	47.7856	1.78210	0.891051	+	0.453903i	$0.149969\pi$
$720$	−3.83093	−0.142770
$721$	0.687541	0.0256054
$722$	−16.4573	−0.612477
$723$	−60.8772	−2.26405
$724$	10.6388	0.395386
$725$	−3.16799	−0.117656
$726$	−2.61361	−0.0970000
$727$	19.1015	0.708437	0.354218	−	0.935163i	$-0.384747\pi$
$727$	19.1015	0.708437	0.354218	+	0.935163i	$0.384747\pi$
$728$	−5.35542	−0.198485
$729$	−39.3117	−1.45599
$730$	6.44173	0.238419
$731$	−6.61083	−0.244511
$732$	16.4437	0.607778
$733$	34.1410	1.26103	0.630514	−	0.776178i	$-0.282844\pi$
$733$	34.1410	1.26103	0.630514	+	0.776178i	$0.282844\pi$
$734$	27.1813	1.00328
$735$	−16.2646	−0.599928
$736$	1.90303	0.0701468
$737$	−7.78393	−0.286725
$738$	27.4646	1.01099
$739$	−31.2299	−1.14881	−0.574406	−	0.818571i	$-0.694767\pi$
$739$	−31.2299	−1.14881	−0.574406	+	0.818571i	$0.694767\pi$
$740$	−3.74873	−0.137806
$741$	−25.3211	−0.930195
$742$	7.79675	0.286228
$743$	17.6911	0.649022	0.324511	−	0.945882i	$-0.394800\pi$
$743$	17.6911	0.649022	0.324511	+	0.945882i	$0.394800\pi$
$744$	−20.3410	−0.745738
$745$	9.99029	0.366016
$746$	−10.9314	−0.400226
$747$	−32.1721	−1.17711
$748$	−6.61083	−0.241716
$749$	12.1335	0.443348
$750$	2.61361	0.0954354
$751$	20.7215	0.756137	0.378068	−	0.925778i	$-0.376588\pi$
$751$	20.7215	0.756137	0.378068	+	0.925778i	$0.376588\pi$
$752$	−12.3298	−0.449622
$753$	16.9178	0.616520
$754$	19.2477	0.700961
$755$	1.15872	0.0421703
$756$	−1.91427	−0.0696213
$757$	−39.3806	−1.43131	−0.715657	−	0.698452i	$-0.753873\pi$
$757$	−39.3806	−1.43131	−0.715657	+	0.698452i	$0.753873\pi$
$758$	−35.8223	−1.30113
$759$	−4.97378	−0.180537
$760$	1.59458	0.0578417
$761$	25.5078	0.924659	0.462329	−	0.886708i	$-0.347014\pi$
$761$	25.5078	0.924659	0.462329	+	0.886708i	$0.347014\pi$
$762$	−5.29484	−0.191812
$763$	13.7679	0.498431
$764$	19.9082	0.720252
$765$	25.3257	0.915651
$766$	−11.8569	−0.428407
$767$	−29.3215	−1.05874
$768$	−2.61361	−0.0943104
$769$	45.6956	1.64782	0.823912	−	0.566718i	$-0.191787\pi$
$769$	45.6956	1.64782	0.823912	+	0.566718i	$0.191787\pi$
$770$	−0.881450	−0.0317652
$771$	−51.9920	−1.87245
$772$	10.7455	0.386740
$773$	−9.19292	−0.330646	−0.165323	−	0.986239i	$-0.552867\pi$
$773$	−9.19292	−0.330646	−0.165323	+	0.986239i	$0.552867\pi$
$774$	3.83093	0.137700
$775$	7.78274	0.279564
$776$	3.95643	0.142028
$777$	−8.63619	−0.309821
$778$	2.65249	0.0950962
$779$	−11.4319	−0.409589
$780$	−15.8795	−0.568576
$781$	4.25244	0.152164
$782$	−12.5806	−0.449883
$783$	6.88002	0.245872
$784$	−6.22305	−0.222252
$785$	−24.8105	−0.885524
$786$	32.8307	1.17103
$787$	24.4487	0.871503	0.435752	−	0.900067i	$-0.356483\pi$
$787$	24.4487	0.871503	0.435752	+	0.900067i	$0.356483\pi$
$788$	−6.53034	−0.232634
$789$	61.4413	2.18737
$790$	−5.91937	−0.210602
$791$	−5.71527	−0.203212
$792$	3.83093	0.136126
$793$	38.2258	1.35744
$794$	23.4796	0.833261
$795$	23.1183	0.819922
$796$	18.5722	0.658273
$797$	−9.11415	−0.322840	−0.161420	−	0.986886i	$-0.551607\pi$
$797$	−9.11415	−0.322840	−0.161420	+	0.986886i	$0.551607\pi$
$798$	3.67354	0.130042
$799$	81.5104	2.88363
$800$	1.00000	0.0353553
$801$	55.6147	1.96505
$802$	14.8649	0.524899
$803$	−6.44173	−0.227324
$804$	20.3441	0.717482
$805$	−1.67743	−0.0591216
$806$	−47.2855	−1.66556
$807$	0.323378	0.0113834
$808$	−9.97999	−0.351095
$809$	−37.2246	−1.30875	−0.654374	−	0.756171i	$-0.727068\pi$
$809$	−37.2246	−1.30875	−0.654374	+	0.756171i	$0.727068\pi$
$810$	5.81675	0.204380
$811$	−15.8260	−0.555725	−0.277862	−	0.960621i	$-0.589626\pi$
$811$	−15.8260	−0.555725	−0.277862	+	0.960621i	$0.589626\pi$
$812$	−2.79243	−0.0979949
$813$	0.538503	0.0188861
$814$	3.74873	0.131393
$815$	−12.5250	−0.438730
$816$	17.2781	0.604855
$817$	−1.59458	−0.0557875
$818$	13.3349	0.466245
$819$	−20.5162	−0.716895
$820$	−7.16918	−0.250359
$821$	11.5666	0.403678	0.201839	−	0.979419i	$-0.435308\pi$
$821$	11.5666	0.403678	0.201839	+	0.979419i	$0.435308\pi$
$822$	−49.7137	−1.73397
$823$	−39.0398	−1.36084	−0.680422	−	0.732821i	$-0.738203\pi$
$823$	−39.0398	−1.36084	−0.680422	+	0.732821i	$0.738203\pi$
$824$	0.780011	0.0271730
$825$	−2.61361	−0.0909941
$826$	4.25391	0.148012
$827$	23.9556	0.833017	0.416508	−	0.909132i	$-0.363254\pi$
$827$	23.9556	0.833017	0.416508	+	0.909132i	$0.363254\pi$
$828$	7.29040	0.253359
$829$	19.1803	0.666158	0.333079	−	0.942899i	$-0.391912\pi$
$829$	19.1803	0.666158	0.333079	+	0.942899i	$0.391912\pi$
$830$	8.39798	0.291498
$831$	40.9632	1.42100
$832$	−6.07569	−0.210637
$833$	41.1395	1.42540
$834$	−29.0784	−1.00690
$835$	−24.0151	−0.831078
$836$	−1.59458	−0.0551499
$837$	−16.9020	−0.584219
$838$	13.4409	0.464310
$839$	42.9410	1.48249	0.741244	−	0.671236i	$-0.234236\pi$
$839$	42.9410	1.48249	0.741244	+	0.671236i	$0.234236\pi$
$840$	2.30376	0.0794873
$841$	−18.9638	−0.653925
$842$	9.78705	0.337284
$843$	−78.0912	−2.68960
$844$	−23.6147	−0.812853
$845$	−23.9140	−0.822667
$846$	−47.2347	−1.62396
$847$	0.881450	0.0302870
$848$	8.84537	0.303751
$849$	23.7280	0.814343
$850$	−6.61083	−0.226750
$851$	7.13397	0.244549
$852$	−11.1142	−0.380766
$853$	−30.1347	−1.03179	−0.515896	−	0.856651i	$-0.672541\pi$
$853$	−30.1347	−1.03179	−0.515896	+	0.856651i	$0.672541\pi$
$854$	−5.54572	−0.189771
$855$	6.10875	0.208915
$856$	13.7654	0.470491
$857$	−9.14189	−0.312281	−0.156140	−	0.987735i	$-0.549905\pi$
$857$	−9.14189	−0.312281	−0.156140	+	0.987735i	$0.549905\pi$
$858$	15.8795	0.542116
$859$	35.2103	1.20136	0.600680	−	0.799490i	$-0.294897\pi$
$859$	35.2103	1.20136	0.600680	+	0.799490i	$0.294897\pi$
$860$	−1.00000	−0.0340997
$861$	−16.5161	−0.562867
$862$	−39.2910	−1.33826
$863$	−18.9005	−0.643380	−0.321690	−	0.946845i	$-0.604251\pi$
$863$	−18.9005	−0.643380	−0.321690	+	0.946845i	$0.604251\pi$
$864$	−2.17173	−0.0738837
$865$	17.8221	0.605971
$866$	34.9697	1.18832
$867$	−69.7914	−2.37024
$868$	6.86009	0.232847
$869$	5.91937	0.200801
$870$	−8.27988	−0.280714
$871$	47.2927	1.60245
$872$	15.6196	0.528946
$873$	15.1568	0.512981
$874$	−3.03455	−0.102645
$875$	−0.881450	−0.0297984
$876$	16.8362	0.568841
$877$	23.3674	0.789062	0.394531	−	0.918883i	$-0.370907\pi$
$877$	23.3674	0.789062	0.394531	+	0.918883i	$0.370907\pi$
$878$	−1.14756	−0.0387284
$879$	32.9821	1.11246
$880$	−1.00000	−0.0337100
$881$	55.5887	1.87283	0.936415	−	0.350895i	$-0.114122\pi$
$881$	55.5887	1.87283	0.936415	+	0.350895i	$0.114122\pi$
$882$	−23.8401	−0.802737
$883$	−19.3782	−0.652130	−0.326065	−	0.945347i	$-0.605723\pi$
$883$	−19.3782	−0.652130	−0.326065	+	0.945347i	$0.605723\pi$
$884$	40.1654	1.35091
$885$	12.6134	0.423993
$886$	2.40564	0.0808192
$887$	−20.8706	−0.700765	−0.350382	−	0.936607i	$-0.613948\pi$
$887$	−20.8706	−0.700765	−0.350382	+	0.936607i	$0.613948\pi$
$888$	−9.79771	−0.328789
$889$	1.78571	0.0598907
$890$	−14.5173	−0.486620
$891$	−5.81675	−0.194869
$892$	−11.8260	−0.395965
$893$	19.6609	0.657928
$894$	26.1107	0.873271
$895$	−4.37125	−0.146115
$896$	0.881450	0.0294472
$897$	30.2192	1.00899
$898$	15.0760	0.503092
$899$	−24.6556	−0.822312
$900$	3.83093	0.127698
$901$	−58.4753	−1.94809
$902$	7.16918	0.238708
$903$	−2.30376	−0.0766644
$904$	−6.48394	−0.215653
$905$	−10.6388	−0.353644
$906$	3.02845	0.100613
$907$	34.0028	1.12904	0.564522	−	0.825418i	$-0.309060\pi$
$907$	34.0028	1.12904	0.564522	+	0.825418i	$0.309060\pi$
$908$	20.5501	0.681981
$909$	−38.2327	−1.26810
$910$	5.35542	0.177530
$911$	10.8221	0.358552	0.179276	−	0.983799i	$-0.442624\pi$
$911$	10.8221	0.358552	0.179276	+	0.983799i	$0.442624\pi$
$912$	4.16762	0.138004
$913$	−8.39798	−0.277932
$914$	8.86295	0.293160
$915$	−16.4437	−0.543613
$916$	21.7488	0.718600
$917$	−11.0723	−0.365640
$918$	14.3569	0.473850
$919$	35.9048	1.18439	0.592194	−	0.805795i	$-0.298262\pi$
$919$	35.9048	1.18439	0.592194	+	0.805795i	$0.298262\pi$
$920$	−1.90303	−0.0627412
$921$	−13.3176	−0.438830
$922$	−30.0315	−0.989033
$923$	−25.8365	−0.850419
$924$	−2.30376	−0.0757882
$925$	3.74873	0.123258
$926$	5.52756	0.181647
$927$	2.98817	0.0981444
$928$	−3.16799	−0.103994
$929$	−23.9691	−0.786401	−0.393200	−	0.919453i	$-0.628632\pi$
$929$	−23.9691	−0.786401	−0.393200	+	0.919453i	$0.628632\pi$
$930$	20.3410	0.667008
$931$	9.92317	0.325219
$932$	7.30511	0.239287
$933$	−70.4784	−2.30736
$934$	−36.2153	−1.18500
$935$	6.61083	0.216197
$936$	−23.2756	−0.760786
$937$	−38.1709	−1.24699	−0.623494	−	0.781828i	$-0.714287\pi$
$937$	−38.1709	−1.24699	−0.623494	+	0.781828i	$0.714287\pi$
$938$	−6.86114	−0.224024
$939$	9.14029	0.298282
$940$	12.3298	0.402154
$941$	33.3013	1.08559	0.542795	−	0.839865i	$-0.317366\pi$
$941$	33.3013	1.08559	0.542795	+	0.839865i	$0.317366\pi$
$942$	−64.8448	−2.11276
$943$	13.6432	0.444284
$944$	4.82604	0.157074
$945$	1.91427	0.0622712
$946$	1.00000	0.0325128
$947$	−27.6796	−0.899467	−0.449733	−	0.893163i	$-0.648481\pi$
$947$	−27.6796	−0.899467	−0.449733	+	0.893163i	$0.648481\pi$
$948$	−15.4709	−0.502472
$949$	39.1380	1.27047
$950$	−1.59458	−0.0517352
$951$	−6.44604	−0.209027
$952$	−5.82712	−0.188858
$953$	−26.6247	−0.862459	−0.431230	−	0.902242i	$-0.641920\pi$
$953$	−26.6247	−0.862459	−0.431230	+	0.902242i	$0.641920\pi$
$954$	33.8860	1.09710
$955$	−19.9082	−0.644213
$956$	−15.1275	−0.489259
$957$	8.27988	0.267650
$958$	−37.7653	−1.22014
$959$	16.7662	0.541408
$960$	2.61361	0.0843537
$961$	29.5710	0.953904
$962$	−22.7761	−0.734332
$963$	52.7343	1.69934
$964$	23.2924	0.750198
$965$	−10.7455	−0.345911
$966$	−4.38414	−0.141057
$967$	38.3834	1.23433	0.617164	−	0.786835i	$-0.288282\pi$
$967$	38.3834	1.23433	0.617164	+	0.786835i	$0.288282\pi$
$968$	1.00000	0.0321412
$969$	−27.5514	−0.885079
$970$	−3.95643	−0.127033
$971$	−4.13789	−0.132791	−0.0663955	−	0.997793i	$-0.521150\pi$
$971$	−4.13789	−0.132791	−0.0663955	+	0.997793i	$0.521150\pi$
$972$	21.7179	0.696602
$973$	9.80683	0.314392
$974$	−25.7226	−0.824204
$975$	15.8795	0.508550
$976$	−6.29159	−0.201389
$977$	21.1621	0.677034	0.338517	−	0.940960i	$-0.390075\pi$
$977$	21.1621	0.677034	0.338517	+	0.940960i	$0.390075\pi$
$978$	−32.7353	−1.04676
$979$	14.5173	0.463974
$980$	6.22305	0.198788
$981$	59.8376	1.91047
$982$	−1.78560	−0.0569807
$983$	−26.0831	−0.831923	−0.415961	−	0.909382i	$-0.636555\pi$
$983$	−26.0831	−0.831923	−0.415961	+	0.909382i	$0.636555\pi$
$984$	−18.7374	−0.597327
$985$	6.53034	0.208074
$986$	20.9431	0.666963
$987$	28.4050	0.904140
$988$	9.68820	0.308223
$989$	1.90303	0.0605130
$990$	−3.83093	−0.121755
$991$	25.7153	0.816874	0.408437	−	0.912786i	$-0.366074\pi$
$991$	25.7153	0.816874	0.408437	+	0.912786i	$0.366074\pi$
$992$	7.78274	0.247102
$993$	24.9025	0.790257
$994$	3.74831	0.118889
$995$	−18.5722	−0.588777
$996$	21.9490	0.695480
$997$	−8.66972	−0.274573	−0.137286	−	0.990531i	$-0.543838\pi$
$997$	−8.66972	−0.274573	−0.137286	+	0.990531i	$0.543838\pi$
$998$	−35.4149	−1.12104
$999$	−8.14123	−0.257577

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4730.2.a.bf.1.3	✓	13

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4730.2.a.bf.1.3	✓	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)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -2.61361 q^{3} +1.00000 q^{4} -1.00000 q^{5} -2.61361 q^{6} +0.881450 q^{7} +1.00000 q^{8} +3.83093 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -2.61361 q^{3} +1.00000 q^{4} -1.00000 q^{5} -2.61361 q^{6} +0.881450 q^{7} +1.00000 q^{8} +3.83093 q^{9} -1.00000 q^{10} +1.00000 q^{11} -2.61361 q^{12} -6.07569 q^{13} +0.881450 q^{14} +2.61361 q^{15} +1.00000 q^{16} -6.61083 q^{17} +3.83093 q^{18} -1.59458 q^{19} -1.00000 q^{20} -2.30376 q^{21} +1.00000 q^{22} +1.90303 q^{23} -2.61361 q^{24} +1.00000 q^{25} -6.07569 q^{26} -2.17173 q^{27} +0.881450 q^{28} -3.16799 q^{29} +2.61361 q^{30} +7.78274 q^{31} +1.00000 q^{32} -2.61361 q^{33} -6.61083 q^{34} -0.881450 q^{35} +3.83093 q^{36} +3.74873 q^{37} -1.59458 q^{38} +15.8795 q^{39} -1.00000 q^{40} +7.16918 q^{41} -2.30376 q^{42} +1.00000 q^{43} +1.00000 q^{44} -3.83093 q^{45} +1.90303 q^{46} -12.3298 q^{47} -2.61361 q^{48} -6.22305 q^{49} +1.00000 q^{50} +17.2781 q^{51} -6.07569 q^{52} +8.84537 q^{53} -2.17173 q^{54} -1.00000 q^{55} +0.881450 q^{56} +4.16762 q^{57} -3.16799 q^{58} +4.82604 q^{59} +2.61361 q^{60} -6.29159 q^{61} +7.78274 q^{62} +3.37677 q^{63} +1.00000 q^{64} +6.07569 q^{65} -2.61361 q^{66} -7.78393 q^{67} -6.61083 q^{68} -4.97378 q^{69} -0.881450 q^{70} +4.25244 q^{71} +3.83093 q^{72} -6.44173 q^{73} +3.74873 q^{74} -2.61361 q^{75} -1.59458 q^{76} +0.881450 q^{77} +15.8795 q^{78} +5.91937 q^{79} -1.00000 q^{80} -5.81675 q^{81} +7.16918 q^{82} -8.39798 q^{83} -2.30376 q^{84} +6.61083 q^{85} +1.00000 q^{86} +8.27988 q^{87} +1.00000 q^{88} +14.5173 q^{89} -3.83093 q^{90} -5.35542 q^{91} +1.90303 q^{92} -20.3410 q^{93} -12.3298 q^{94} +1.59458 q^{95} -2.61361 q^{96} +3.95643 q^{97} -6.22305 q^{98} +3.83093 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 13 q + 13 q^{2} + 13 q^{4} - 13 q^{5} + 7 q^{7} + 13 q^{8} + 25 q^{9}+O(q^{10}) \) 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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