LMFDB - Embedded newform 4730.2.a.bf.1.13

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			1.13
Root			$-3.30461$ 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)

$f(q)$	$=$	$q+1.00000 q^{2} +3.30461 q^{3} +1.00000 q^{4} -1.00000 q^{5} +3.30461 q^{6} -0.676945 q^{7} +1.00000 q^{8} +7.92047 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +3.30461 q^{3} +1.00000 q^{4} -1.00000 q^{5} +3.30461 q^{6} -0.676945 q^{7} +1.00000 q^{8} +7.92047 q^{9} -1.00000 q^{10} +1.00000 q^{11} +3.30461 q^{12} -3.96088 q^{13} -0.676945 q^{14} -3.30461 q^{15} +1.00000 q^{16} -2.43964 q^{17} +7.92047 q^{18} +1.47849 q^{19} -1.00000 q^{20} -2.23704 q^{21} +1.00000 q^{22} +3.38657 q^{23} +3.30461 q^{24} +1.00000 q^{25} -3.96088 q^{26} +16.2602 q^{27} -0.676945 q^{28} +2.44967 q^{29} -3.30461 q^{30} +8.31634 q^{31} +1.00000 q^{32} +3.30461 q^{33} -2.43964 q^{34} +0.676945 q^{35} +7.92047 q^{36} +11.2005 q^{37} +1.47849 q^{38} -13.0892 q^{39} -1.00000 q^{40} -4.31368 q^{41} -2.23704 q^{42} +1.00000 q^{43} +1.00000 q^{44} -7.92047 q^{45} +3.38657 q^{46} +7.27516 q^{47} +3.30461 q^{48} -6.54175 q^{49} +1.00000 q^{50} -8.06207 q^{51} -3.96088 q^{52} +9.23964 q^{53} +16.2602 q^{54} -1.00000 q^{55} -0.676945 q^{56} +4.88583 q^{57} +2.44967 q^{58} +1.87853 q^{59} -3.30461 q^{60} -14.6864 q^{61} +8.31634 q^{62} -5.36172 q^{63} +1.00000 q^{64} +3.96088 q^{65} +3.30461 q^{66} -2.45232 q^{67} -2.43964 q^{68} +11.1913 q^{69} +0.676945 q^{70} +8.83857 q^{71} +7.92047 q^{72} +5.06238 q^{73} +11.2005 q^{74} +3.30461 q^{75} +1.47849 q^{76} -0.676945 q^{77} -13.0892 q^{78} +6.51534 q^{79} -1.00000 q^{80} +29.9724 q^{81} -4.31368 q^{82} -5.30438 q^{83} -2.23704 q^{84} +2.43964 q^{85} +1.00000 q^{86} +8.09520 q^{87} +1.00000 q^{88} -16.4475 q^{89} -7.92047 q^{90} +2.68130 q^{91} +3.38657 q^{92} +27.4823 q^{93} +7.27516 q^{94} -1.47849 q^{95} +3.30461 q^{96} -16.6841 q^{97} -6.54175 q^{98} +7.92047 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	3.30461	1.90792	0.953960	−	0.299935i	$-0.0969649\pi$
$3$	3.30461	1.90792	0.953960	+	0.299935i	$0.0969649\pi$
$4$	1.00000	0.500000
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	3.30461	1.34910
$7$	−0.676945	−0.255861	−0.127931	−	0.991783i	$-0.540833\pi$
$7$	−0.676945	−0.255861	−0.127931	+	0.991783i	$0.540833\pi$
$8$	1.00000	0.353553
$9$	7.92047	2.64016
$10$	−1.00000	−0.316228
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	3.30461	0.953960
$13$	−3.96088	−1.09855	−0.549276	−	0.835641i	$-0.685096\pi$
$13$	−3.96088	−1.09855	−0.549276	+	0.835641i	$0.685096\pi$
$14$	−0.676945	−0.180921
$15$	−3.30461	−0.853248
$16$	1.00000	0.250000
$17$	−2.43964	−0.591700	−0.295850	−	0.955234i	$-0.595603\pi$
$17$	−2.43964	−0.591700	−0.295850	+	0.955234i	$0.595603\pi$
$18$	7.92047	1.86687
$19$	1.47849	0.339189	0.169594	−	0.985514i	$-0.445754\pi$
$19$	1.47849	0.339189	0.169594	+	0.985514i	$0.445754\pi$
$20$	−1.00000	−0.223607
$21$	−2.23704	−0.488162
$22$	1.00000	0.213201
$23$	3.38657	0.706150	0.353075	−	0.935595i	$-0.385136\pi$
$23$	3.38657	0.706150	0.353075	+	0.935595i	$0.385136\pi$
$24$	3.30461	0.674551
$25$	1.00000	0.200000
$26$	−3.96088	−0.776793
$27$	16.2602	3.12929
$28$	−0.676945	−0.127931
$29$	2.44967	0.454892	0.227446	−	0.973791i	$-0.426963\pi$
$29$	2.44967	0.454892	0.227446	+	0.973791i	$0.426963\pi$
$30$	−3.30461	−0.603337
$31$	8.31634	1.49366	0.746829	−	0.665016i	$-0.231575\pi$
$31$	8.31634	1.49366	0.746829	+	0.665016i	$0.231575\pi$
$32$	1.00000	0.176777
$33$	3.30461	0.575259
$34$	−2.43964	−0.418395
$35$	0.676945	0.114425
$36$	7.92047	1.32008
$37$	11.2005	1.84135	0.920673	−	0.390334i	$-0.127640\pi$
$37$	11.2005	1.84135	0.920673	+	0.390334i	$0.127640\pi$
$38$	1.47849	0.239843
$39$	−13.0892	−2.09595
$40$	−1.00000	−0.158114
$41$	−4.31368	−0.673684	−0.336842	−	0.941561i	$-0.609359\pi$
$41$	−4.31368	−0.673684	−0.336842	+	0.941561i	$0.609359\pi$
$42$	−2.23704	−0.345183
$43$	1.00000	0.152499
$43$	1.00000	0.152499
$44$	1.00000	0.150756
$45$	−7.92047	−1.18071
$46$	3.38657	0.499323
$47$	7.27516	1.06119	0.530596	−	0.847625i	$-0.321968\pi$
$47$	7.27516	1.06119	0.530596	+	0.847625i	$0.321968\pi$
$48$	3.30461	0.476980
$49$	−6.54175	−0.934535
$50$	1.00000	0.141421
$51$	−8.06207	−1.12892
$52$	−3.96088	−0.549276
$53$	9.23964	1.26916	0.634581	−	0.772857i	$-0.281173\pi$
$53$	9.23964	1.26916	0.634581	+	0.772857i	$0.281173\pi$
$54$	16.2602	2.21274
$55$	−1.00000	−0.134840
$56$	−0.676945	−0.0904606
$57$	4.88583	0.647145
$58$	2.44967	0.321657
$59$	1.87853	0.244563	0.122282	−	0.992495i	$-0.460979\pi$
$59$	1.87853	0.244563	0.122282	+	0.992495i	$0.460979\pi$
$60$	−3.30461	−0.426624
$61$	−14.6864	−1.88040	−0.940198	−	0.340630i	$-0.889360\pi$
$61$	−14.6864	−1.88040	−0.940198	+	0.340630i	$0.889360\pi$
$62$	8.31634	1.05618
$63$	−5.36172	−0.675513
$64$	1.00000	0.125000
$65$	3.96088	0.491287
$66$	3.30461	0.406770
$67$	−2.45232	−0.299599	−0.149799	−	0.988716i	$-0.547863\pi$
$67$	−2.45232	−0.299599	−0.149799	+	0.988716i	$0.547863\pi$
$68$	−2.43964	−0.295850
$69$	11.1913	1.34728
$70$	0.676945	0.0809104
$71$	8.83857	1.04895	0.524473	−	0.851427i	$-0.324262\pi$
$71$	8.83857	1.04895	0.524473	+	0.851427i	$0.324262\pi$
$72$	7.92047	0.933436
$73$	5.06238	0.592507	0.296253	−	0.955109i	$-0.404263\pi$
$73$	5.06238	0.592507	0.296253	+	0.955109i	$0.404263\pi$
$74$	11.2005	1.30203
$75$	3.30461	0.381584
$76$	1.47849	0.169594
$77$	−0.676945	−0.0771450
$78$	−13.0892	−1.48206
$79$	6.51534	0.733033	0.366517	−	0.930411i	$-0.380550\pi$
$79$	6.51534	0.733033	0.366517	+	0.930411i	$0.380550\pi$
$80$	−1.00000	−0.111803
$81$	29.9724	3.33027
$82$	−4.31368	−0.476366
$83$	−5.30438	−0.582231	−0.291116	−	0.956688i	$-0.594026\pi$
$83$	−5.30438	−0.582231	−0.291116	+	0.956688i	$0.594026\pi$
$84$	−2.23704	−0.244081
$85$	2.43964	0.264616
$86$	1.00000	0.107833
$87$	8.09520	0.867897
$88$	1.00000	0.106600
$89$	−16.4475	−1.74343	−0.871716	−	0.490011i	$-0.836993\pi$
$89$	−16.4475	−1.74343	−0.871716	+	0.490011i	$0.836993\pi$
$90$	−7.92047	−0.834891
$91$	2.68130	0.281077
$92$	3.38657	0.353075
$93$	27.4823	2.84978
$94$	7.27516	0.750376
$95$	−1.47849	−0.151690
$96$	3.30461	0.337276
$97$	−16.6841	−1.69401	−0.847004	−	0.531586i	$-0.821596\pi$
$97$	−16.6841	−1.69401	−0.847004	+	0.531586i	$0.821596\pi$
$98$	−6.54175	−0.660816
$99$	7.92047	0.796037
$100$	1.00000	0.100000
$101$	9.00199	0.895732	0.447866	−	0.894101i	$-0.352184\pi$
$101$	9.00199	0.895732	0.447866	+	0.894101i	$0.352184\pi$
$102$	−8.06207	−0.798264
$103$	4.73558	0.466610	0.233305	−	0.972404i	$-0.425046\pi$
$103$	4.73558	0.466610	0.233305	+	0.972404i	$0.425046\pi$
$104$	−3.96088	−0.388397
$105$	2.23704	0.218313
$106$	9.23964	0.897433
$107$	7.25685	0.701546	0.350773	−	0.936460i	$-0.385919\pi$
$107$	7.25685	0.701546	0.350773	+	0.936460i	$0.385919\pi$
$108$	16.2602	1.56464
$109$	−9.44895	−0.905045	−0.452523	−	0.891753i	$-0.649476\pi$
$109$	−9.44895	−0.905045	−0.452523	+	0.891753i	$0.649476\pi$
$110$	−1.00000	−0.0953463
$111$	37.0132	3.51314
$112$	−0.676945	−0.0639653
$113$	−16.2365	−1.52741	−0.763703	−	0.645568i	$-0.776621\pi$
$113$	−16.2365	−1.52741	−0.763703	+	0.645568i	$0.776621\pi$
$114$	4.88583	0.457600
$115$	−3.38657	−0.315800
$116$	2.44967	0.227446
$117$	−31.3721	−2.90035
$118$	1.87853	0.172932
$119$	1.65150	0.151393
$120$	−3.30461	−0.301669
$121$	1.00000	0.0909091
$122$	−14.6864	−1.32964
$123$	−14.2550	−1.28533
$124$	8.31634	0.746829
$125$	−1.00000	−0.0894427
$126$	−5.36172	−0.477660
$127$	9.05438	0.803446	0.401723	−	0.915761i	$-0.368411\pi$
$127$	9.05438	0.803446	0.401723	+	0.915761i	$0.368411\pi$
$128$	1.00000	0.0883883
$129$	3.30461	0.290955
$130$	3.96088	0.347393
$131$	−10.2913	−0.899154	−0.449577	−	0.893242i	$-0.648425\pi$
$131$	−10.2913	−0.899154	−0.449577	+	0.893242i	$0.648425\pi$
$132$	3.30461	0.287630
$133$	−1.00086	−0.0867852
$134$	−2.45232	−0.211848
$135$	−16.2602	−1.39946
$136$	−2.43964	−0.209197
$137$	−16.2179	−1.38559	−0.692794	−	0.721135i	$-0.743621\pi$
$137$	−16.2179	−1.38559	−0.692794	+	0.721135i	$0.743621\pi$
$138$	11.1913	0.952668
$139$	−17.3571	−1.47221	−0.736104	−	0.676868i	$-0.763337\pi$
$139$	−17.3571	−1.47221	−0.736104	+	0.676868i	$0.763337\pi$
$140$	0.676945	0.0572123
$141$	24.0416	2.02467
$142$	8.83857	0.741716
$143$	−3.96088	−0.331226
$144$	7.92047	0.660039
$145$	−2.44967	−0.203434
$146$	5.06238	0.418965
$147$	−21.6179	−1.78302
$148$	11.2005	0.920673
$149$	−9.35161	−0.766114	−0.383057	−	0.923725i	$-0.625129\pi$
$149$	−9.35161	−0.766114	−0.383057	+	0.923725i	$0.625129\pi$
$150$	3.30461	0.269821
$151$	−2.95411	−0.240402	−0.120201	−	0.992750i	$-0.538354\pi$
$151$	−2.95411	−0.240402	−0.120201	+	0.992750i	$0.538354\pi$
$152$	1.47849	0.119921
$153$	−19.3231	−1.56218
$154$	−0.676945	−0.0545498
$155$	−8.31634	−0.667984
$156$	−13.0892	−1.04797
$157$	−5.28247	−0.421587	−0.210794	−	0.977531i	$-0.567605\pi$
$157$	−5.28247	−0.421587	−0.210794	+	0.977531i	$0.567605\pi$
$158$	6.51534	0.518333
$159$	30.5334	2.42146
$160$	−1.00000	−0.0790569
$161$	−2.29252	−0.180676
$162$	29.9724	2.35486
$163$	−0.152295	−0.0119287	−0.00596433	−	0.999982i	$-0.501899\pi$
$163$	−0.152295	−0.0119287	−0.00596433	+	0.999982i	$0.501899\pi$
$164$	−4.31368	−0.336842
$165$	−3.30461	−0.257264
$166$	−5.30438	−0.411700
$167$	−15.9649	−1.23540	−0.617699	−	0.786415i	$-0.711935\pi$
$167$	−15.9649	−1.23540	−0.617699	+	0.786415i	$0.711935\pi$
$168$	−2.23704	−0.172591
$169$	2.68861	0.206816
$170$	2.43964	0.187112
$171$	11.7103	0.895511
$172$	1.00000	0.0762493
$173$	−12.2545	−0.931692	−0.465846	−	0.884866i	$-0.654250\pi$
$173$	−12.2545	−0.931692	−0.465846	+	0.884866i	$0.654250\pi$
$174$	8.09520	0.613696
$175$	−0.676945	−0.0511722
$176$	1.00000	0.0753778
$177$	6.20780	0.466607
$178$	−16.4475	−1.23279
$179$	8.15698	0.609681	0.304841	−	0.952403i	$-0.401397\pi$
$179$	8.15698	0.609681	0.304841	+	0.952403i	$0.401397\pi$
$180$	−7.92047	−0.590357
$181$	−13.5358	−1.00611	−0.503055	−	0.864254i	$-0.667791\pi$
$181$	−13.5358	−1.00611	−0.503055	+	0.864254i	$0.667791\pi$
$182$	2.68130	0.198751
$183$	−48.5327	−3.58764
$184$	3.38657	0.249662
$185$	−11.2005	−0.823475
$186$	27.4823	2.01510
$187$	−2.43964	−0.178404
$188$	7.27516	0.530596
$189$	−11.0073	−0.800663
$190$	−1.47849	−0.107261
$191$	−19.3235	−1.39820	−0.699098	−	0.715026i	$-0.746415\pi$
$191$	−19.3235	−1.39820	−0.699098	+	0.715026i	$0.746415\pi$
$192$	3.30461	0.238490
$193$	18.0569	1.29977	0.649883	−	0.760035i	$-0.274818\pi$
$193$	18.0569	1.29977	0.649883	+	0.760035i	$0.274818\pi$
$194$	−16.6841	−1.19785
$195$	13.0892	0.937337
$196$	−6.54175	−0.467268
$197$	−8.44971	−0.602017	−0.301008	−	0.953621i	$-0.597323\pi$
$197$	−8.44971	−0.602017	−0.301008	+	0.953621i	$0.597323\pi$
$198$	7.92047	0.562883
$199$	−11.9972	−0.850456	−0.425228	−	0.905086i	$-0.639806\pi$
$199$	−11.9972	−0.850456	−0.425228	+	0.905086i	$0.639806\pi$
$200$	1.00000	0.0707107
$201$	−8.10398	−0.571611
$202$	9.00199	0.633378
$203$	−1.65829	−0.116389
$204$	−8.06207	−0.564458
$205$	4.31368	0.301280
$206$	4.73558	0.329943
$207$	26.8233	1.86435
$208$	−3.96088	−0.274638
$209$	1.47849	0.102269
$210$	2.23704	0.154371
$211$	22.8792	1.57507	0.787535	−	0.616270i	$-0.211357\pi$
$211$	22.8792	1.57507	0.787535	+	0.616270i	$0.211357\pi$
$212$	9.23964	0.634581
$213$	29.2081	2.00130
$214$	7.25685	0.496068
$215$	−1.00000	−0.0681994
$216$	16.2602	1.10637
$217$	−5.62970	−0.382169
$218$	−9.44895	−0.639964
$219$	16.7292	1.13045
$220$	−1.00000	−0.0674200
$221$	9.66314	0.650013
$222$	37.0132	2.48417
$223$	−19.3913	−1.29854	−0.649269	−	0.760559i	$-0.724925\pi$
$223$	−19.3913	−1.29854	−0.649269	+	0.760559i	$0.724925\pi$
$224$	−0.676945	−0.0452303
$225$	7.92047	0.528031
$226$	−16.2365	−1.08004
$227$	−26.9170	−1.78654	−0.893271	−	0.449519i	$-0.851595\pi$
$227$	−26.9170	−1.78654	−0.893271	+	0.449519i	$0.851595\pi$
$228$	4.88583	0.323572
$229$	9.32600	0.616280	0.308140	−	0.951341i	$-0.400294\pi$
$229$	9.32600	0.616280	0.308140	+	0.951341i	$0.400294\pi$
$230$	−3.38657	−0.223304
$231$	−2.23704	−0.147187
$232$	2.44967	0.160828
$233$	−4.22910	−0.277057	−0.138529	−	0.990358i	$-0.544237\pi$
$233$	−4.22910	−0.277057	−0.138529	+	0.990358i	$0.544237\pi$
$234$	−31.3721	−2.05086
$235$	−7.27516	−0.474579
$236$	1.87853	0.122282
$237$	21.5307	1.39857
$238$	1.65150	0.107051
$239$	27.1055	1.75331	0.876656	−	0.481118i	$-0.159769\pi$
$239$	27.1055	1.75331	0.876656	+	0.481118i	$0.159769\pi$
$240$	−3.30461	−0.213312
$241$	−3.64322	−0.234681	−0.117340	−	0.993092i	$-0.537437\pi$
$241$	−3.64322	−0.234681	−0.117340	+	0.993092i	$0.537437\pi$
$242$	1.00000	0.0642824
$243$	50.2665	3.22460
$244$	−14.6864	−0.940198
$245$	6.54175	0.417937
$246$	−14.2550	−0.908868
$247$	−5.85612	−0.372616
$248$	8.31634	0.528088
$249$	−17.5289	−1.11085
$250$	−1.00000	−0.0632456
$251$	28.9498	1.82730	0.913648	−	0.406506i	$-0.133253\pi$
$251$	28.9498	1.82730	0.913648	+	0.406506i	$0.133253\pi$
$252$	−5.36172	−0.337757
$253$	3.38657	0.212912
$254$	9.05438	0.568122
$255$	8.06207	0.504866
$256$	1.00000	0.0625000
$257$	9.62097	0.600140	0.300070	−	0.953917i	$-0.402990\pi$
$257$	9.62097	0.600140	0.300070	+	0.953917i	$0.402990\pi$
$258$	3.30461	0.205736
$259$	−7.58211	−0.471129
$260$	3.96088	0.245644
$261$	19.4025	1.20099
$262$	−10.2913	−0.635798
$263$	−29.6602	−1.82892	−0.914462	−	0.404671i	$-0.867386\pi$
$263$	−29.6602	−1.82892	−0.914462	+	0.404671i	$0.867386\pi$
$264$	3.30461	0.203385
$265$	−9.23964	−0.567586
$266$	−1.00086	−0.0613664
$267$	−54.3527	−3.32633
$268$	−2.45232	−0.149799
$269$	−15.7263	−0.958852	−0.479426	−	0.877582i	$-0.659155\pi$
$269$	−15.7263	−0.958852	−0.479426	+	0.877582i	$0.659155\pi$
$270$	−16.2602	−0.989567
$271$	2.41395	0.146637	0.0733185	−	0.997309i	$-0.476641\pi$
$271$	2.41395	0.146637	0.0733185	+	0.997309i	$0.476641\pi$
$272$	−2.43964	−0.147925
$273$	8.86066	0.536272
$274$	−16.2179	−0.979759
$275$	1.00000	0.0603023
$276$	11.1913	0.673638
$277$	−3.14074	−0.188709	−0.0943544	−	0.995539i	$-0.530079\pi$
$277$	−3.14074	−0.188709	−0.0943544	+	0.995539i	$0.530079\pi$
$278$	−17.3571	−1.04101
$279$	65.8693	3.94349
$280$	0.676945	0.0404552
$281$	8.06027	0.480835	0.240418	−	0.970670i	$-0.422716\pi$
$281$	8.06027	0.480835	0.240418	+	0.970670i	$0.422716\pi$
$282$	24.0416	1.43166
$283$	32.6449	1.94054	0.970268	−	0.242032i	$-0.0778140\pi$
$283$	32.6449	1.94054	0.970268	+	0.242032i	$0.0778140\pi$
$284$	8.83857	0.524473
$285$	−4.88583	−0.289412
$286$	−3.96088	−0.234212
$287$	2.92012	0.172369
$288$	7.92047	0.466718
$289$	−11.0482	−0.649891
$290$	−2.44967	−0.143849
$291$	−55.1343	−3.23203
$292$	5.06238	0.296253
$293$	23.9367	1.39839	0.699197	−	0.714929i	$-0.253541\pi$
$293$	23.9367	1.39839	0.699197	+	0.714929i	$0.253541\pi$
$294$	−21.6179	−1.26078
$295$	−1.87853	−0.109372
$296$	11.2005	0.651014
$297$	16.2602	0.943515
$298$	−9.35161	−0.541724
$299$	−13.4138	−0.775742
$300$	3.30461	0.190792
$301$	−0.676945	−0.0390185
$302$	−2.95411	−0.169990
$303$	29.7481	1.70898
$304$	1.47849	0.0847972
$305$	14.6864	0.840938
$306$	−19.3231	−1.10463
$307$	−24.8926	−1.42069	−0.710347	−	0.703851i	$-0.751462\pi$
$307$	−24.8926	−1.42069	−0.710347	+	0.703851i	$0.751462\pi$
$308$	−0.676945	−0.0385725
$309$	15.6492	0.890255
$310$	−8.31634	−0.472336
$311$	15.6134	0.885357	0.442678	−	0.896680i	$-0.354028\pi$
$311$	15.6134	0.885357	0.442678	+	0.896680i	$0.354028\pi$
$312$	−13.0892	−0.741030
$313$	−12.0771	−0.682640	−0.341320	−	0.939947i	$-0.610874\pi$
$313$	−12.0771	−0.682640	−0.341320	+	0.939947i	$0.610874\pi$
$314$	−5.28247	−0.298107
$315$	5.36172	0.302099
$316$	6.51534	0.366517
$317$	−3.32552	−0.186780	−0.0933899	−	0.995630i	$-0.529770\pi$
$317$	−3.32552	−0.186780	−0.0933899	+	0.995630i	$0.529770\pi$
$318$	30.5334	1.71223
$319$	2.44967	0.137155
$320$	−1.00000	−0.0559017
$321$	23.9811	1.33849
$322$	−2.29252	−0.127757
$323$	−3.60698	−0.200698
$324$	29.9724	1.66513
$325$	−3.96088	−0.219710
$326$	−0.152295	−0.00843484
$327$	−31.2251	−1.72675
$328$	−4.31368	−0.238183
$329$	−4.92489	−0.271518
$330$	−3.30461	−0.181913
$331$	−5.98882	−0.329175	−0.164588	−	0.986362i	$-0.552629\pi$
$331$	−5.98882	−0.329175	−0.164588	+	0.986362i	$0.552629\pi$
$332$	−5.30438	−0.291116
$333$	88.7130	4.86144
$334$	−15.9649	−0.873558
$335$	2.45232	0.133985
$336$	−2.23704	−0.122041
$337$	−1.92465	−0.104842	−0.0524212	−	0.998625i	$-0.516694\pi$
$337$	−1.92465	−0.104842	−0.0524212	+	0.998625i	$0.516694\pi$
$338$	2.68861	0.146241
$339$	−53.6555	−2.91417
$340$	2.43964	0.132308
$341$	8.31634	0.450355
$342$	11.7103	0.633222
$343$	9.16702	0.494972
$344$	1.00000	0.0539164
$345$	−11.1913	−0.602520
$346$	−12.2545	−0.658806
$347$	−14.2654	−0.765809	−0.382905	−	0.923788i	$-0.625076\pi$
$347$	−14.2654	−0.765809	−0.382905	+	0.923788i	$0.625076\pi$
$348$	8.09520	0.433948
$349$	12.5777	0.673267	0.336634	−	0.941636i	$-0.390712\pi$
$349$	12.5777	0.673267	0.336634	+	0.941636i	$0.390712\pi$
$350$	−0.676945	−0.0361842
$351$	−64.4050	−3.43768
$352$	1.00000	0.0533002
$353$	−12.9817	−0.690949	−0.345474	−	0.938428i	$-0.612282\pi$
$353$	−12.9817	−0.690949	−0.345474	+	0.938428i	$0.612282\pi$
$354$	6.20780	0.329941
$355$	−8.83857	−0.469103
$356$	−16.4475	−0.871716
$357$	5.45758	0.288846
$358$	8.15698	0.431110
$359$	14.4988	0.765219	0.382609	−	0.923910i	$-0.375026\pi$
$359$	14.4988	0.765219	0.382609	+	0.923910i	$0.375026\pi$
$360$	−7.92047	−0.417445
$361$	−16.8141	−0.884951
$362$	−13.5358	−0.711428
$363$	3.30461	0.173447
$364$	2.68130	0.140538
$365$	−5.06238	−0.264977
$366$	−48.5327	−2.53685
$367$	−4.16242	−0.217276	−0.108638	−	0.994081i	$-0.534649\pi$
$367$	−4.16242	−0.217276	−0.108638	+	0.994081i	$0.534649\pi$
$368$	3.38657	0.176537
$369$	−34.1664	−1.77863
$370$	−11.2005	−0.582285
$371$	−6.25472	−0.324729
$372$	27.4823	1.42489
$373$	31.7738	1.64519	0.822593	−	0.568631i	$-0.192527\pi$
$373$	31.7738	1.64519	0.822593	+	0.568631i	$0.192527\pi$
$374$	−2.43964	−0.126151
$375$	−3.30461	−0.170650
$376$	7.27516	0.375188
$377$	−9.70285	−0.499722
$378$	−11.0073	−0.566154
$379$	26.8216	1.37773	0.688867	−	0.724888i	$-0.258108\pi$
$379$	26.8216	1.37773	0.688867	+	0.724888i	$0.258108\pi$
$380$	−1.47849	−0.0758449
$381$	29.9212	1.53291
$382$	−19.3235	−0.988674
$383$	34.1094	1.74291	0.871454	−	0.490477i	$-0.163178\pi$
$383$	34.1094	1.74291	0.871454	+	0.490477i	$0.163178\pi$
$384$	3.30461	0.168638
$385$	0.676945	0.0345003
$386$	18.0569	0.919073
$387$	7.92047	0.402620
$388$	−16.6841	−0.847004
$389$	−0.877885	−0.0445105	−0.0222553	−	0.999752i	$-0.507085\pi$
$389$	−0.877885	−0.0445105	−0.0222553	+	0.999752i	$0.507085\pi$
$390$	13.0892	0.662797
$391$	−8.26202	−0.417829
$392$	−6.54175	−0.330408
$393$	−34.0087	−1.71551
$394$	−8.44971	−0.425690
$395$	−6.51534	−0.327822
$396$	7.92047	0.398019
$397$	−25.4297	−1.27628	−0.638140	−	0.769920i	$-0.720296\pi$
$397$	−25.4297	−1.27628	−0.638140	+	0.769920i	$0.720296\pi$
$398$	−11.9972	−0.601363
$399$	−3.30744	−0.165579
$400$	1.00000	0.0500000
$401$	15.5181	0.774937	0.387468	−	0.921883i	$-0.373350\pi$
$401$	15.5181	0.774937	0.387468	+	0.921883i	$0.373350\pi$
$402$	−8.10398	−0.404190
$403$	−32.9401	−1.64086
$404$	9.00199	0.447866
$405$	−29.9724	−1.48934
$406$	−1.65829	−0.0822995
$407$	11.2005	0.555187
$408$	−8.06207	−0.399132
$409$	23.6642	1.17012	0.585059	−	0.810991i	$-0.301071\pi$
$409$	23.6642	1.17012	0.585059	+	0.810991i	$0.301071\pi$
$410$	4.31368	0.213037
$411$	−53.5939	−2.64359
$412$	4.73558	0.233305
$413$	−1.27166	−0.0625742
$414$	26.8233	1.31829
$415$	5.30438	0.260382
$416$	−3.96088	−0.194198
$417$	−57.3584	−2.80886
$418$	1.47849	0.0723153
$419$	−16.0191	−0.782582	−0.391291	−	0.920267i	$-0.627971\pi$
$419$	−16.0191	−0.782582	−0.391291	+	0.920267i	$0.627971\pi$
$420$	2.23704	0.109156
$421$	2.89947	0.141312	0.0706558	−	0.997501i	$-0.477491\pi$
$421$	2.89947	0.141312	0.0706558	+	0.997501i	$0.477491\pi$
$422$	22.8792	1.11374
$423$	57.6227	2.80171
$424$	9.23964	0.448716
$425$	−2.43964	−0.118340
$426$	29.2081	1.41514
$427$	9.94185	0.481120
$428$	7.25685	0.350773
$429$	−13.0892	−0.631952
$430$	−1.00000	−0.0482243
$431$	36.0935	1.73856	0.869280	−	0.494319i	$-0.164583\pi$
$431$	36.0935	1.73856	0.869280	+	0.494319i	$0.164583\pi$
$432$	16.2602	0.782322
$433$	−28.4339	−1.36645	−0.683223	−	0.730210i	$-0.739422\pi$
$433$	−28.4339	−1.36645	−0.683223	+	0.730210i	$0.739422\pi$
$434$	−5.62970	−0.270234
$435$	−8.09520	−0.388135
$436$	−9.44895	−0.452523
$437$	5.00701	0.239518
$438$	16.7292	0.799352
$439$	17.4292	0.831850	0.415925	−	0.909399i	$-0.363458\pi$
$439$	17.4292	0.831850	0.415925	+	0.909399i	$0.363458\pi$
$440$	−1.00000	−0.0476731
$441$	−51.8137	−2.46732
$442$	9.66314	0.459629
$443$	−19.2963	−0.916796	−0.458398	−	0.888747i	$-0.651577\pi$
$443$	−19.2963	−0.916796	−0.458398	+	0.888747i	$0.651577\pi$
$444$	37.0132	1.75657
$445$	16.4475	0.779687
$446$	−19.3913	−0.918205
$447$	−30.9035	−1.46168
$448$	−0.676945	−0.0319826
$449$	−23.6300	−1.11517	−0.557585	−	0.830120i	$-0.688272\pi$
$449$	−23.6300	−1.11517	−0.557585	+	0.830120i	$0.688272\pi$
$450$	7.92047	0.373375
$451$	−4.31368	−0.203123
$452$	−16.2365	−0.763703
$453$	−9.76218	−0.458667
$454$	−26.9170	−1.26328
$455$	−2.68130	−0.125701
$456$	4.88583	0.228800
$457$	−9.26335	−0.433321	−0.216661	−	0.976247i	$-0.569516\pi$
$457$	−9.26335	−0.433321	−0.216661	+	0.976247i	$0.569516\pi$
$458$	9.32600	0.435775
$459$	−39.6692	−1.85160
$460$	−3.38657	−0.157900
$461$	22.8018	1.06199	0.530993	−	0.847376i	$-0.321819\pi$
$461$	22.8018	1.06199	0.530993	+	0.847376i	$0.321819\pi$
$462$	−2.23704	−0.104077
$463$	28.3243	1.31634	0.658172	−	0.752868i	$-0.271330\pi$
$463$	28.3243	1.31634	0.658172	+	0.752868i	$0.271330\pi$
$464$	2.44967	0.113723
$465$	−27.4823	−1.27446
$466$	−4.22910	−0.195909
$467$	22.8550	1.05760	0.528801	−	0.848746i	$-0.322642\pi$
$467$	22.8550	1.05760	0.528801	+	0.848746i	$0.322642\pi$
$468$	−31.3721	−1.45017
$469$	1.66009	0.0766557
$470$	−7.27516	−0.335578
$471$	−17.4565	−0.804354
$472$	1.87853	0.0864661
$473$	1.00000	0.0459800
$474$	21.5307	0.988937
$475$	1.47849	0.0678377
$476$	1.65150	0.0756965
$477$	73.1822	3.35078
$478$	27.1055	1.23978
$479$	33.3747	1.52493	0.762465	−	0.647029i	$-0.223989\pi$
$479$	33.3747	1.52493	0.762465	+	0.647029i	$0.223989\pi$
$480$	−3.30461	−0.150834
$481$	−44.3638	−2.02281
$482$	−3.64322	−0.165944
$483$	−7.57591	−0.344716
$484$	1.00000	0.0454545
$485$	16.6841	0.757584
$486$	50.2665	2.28014
$487$	−35.4355	−1.60574	−0.802868	−	0.596157i	$-0.796694\pi$
$487$	−35.4355	−1.60574	−0.802868	+	0.596157i	$0.796694\pi$
$488$	−14.6864	−0.664820
$489$	−0.503276	−0.0227589
$490$	6.54175	0.295526
$491$	10.2100	0.460769	0.230384	−	0.973100i	$-0.426002\pi$
$491$	10.2100	0.460769	0.230384	+	0.973100i	$0.426002\pi$
$492$	−14.2550	−0.642667
$493$	−5.97631	−0.269159
$494$	−5.85612	−0.263479
$495$	−7.92047	−0.355999
$496$	8.31634	0.373415
$497$	−5.98323	−0.268384
$498$	−17.5289	−0.785490
$499$	18.9638	0.848937	0.424469	−	0.905443i	$-0.360461\pi$
$499$	18.9638	0.848937	0.424469	+	0.905443i	$0.360461\pi$
$500$	−1.00000	−0.0447214
$501$	−52.7577	−2.35704
$502$	28.9498	1.29209
$503$	3.80534	0.169672	0.0848359	−	0.996395i	$-0.472963\pi$
$503$	3.80534	0.169672	0.0848359	+	0.996395i	$0.472963\pi$
$504$	−5.36172	−0.238830
$505$	−9.00199	−0.400583
$506$	3.38657	0.150552
$507$	8.88481	0.394588
$508$	9.05438	0.401723
$509$	−41.5482	−1.84159	−0.920796	−	0.390045i	$-0.872460\pi$
$509$	−41.5482	−1.84159	−0.920796	+	0.390045i	$0.872460\pi$
$510$	8.06207	0.356994
$511$	−3.42695	−0.151599
$512$	1.00000	0.0441942
$513$	24.0406	1.06142
$514$	9.62097	0.424363
$515$	−4.73558	−0.208674
$516$	3.30461	0.145477
$517$	7.27516	0.319961
$518$	−7.58211	−0.333139
$519$	−40.4964	−1.77759
$520$	3.96088	0.173696
$521$	−27.0241	−1.18395	−0.591974	−	0.805957i	$-0.701651\pi$
$521$	−27.0241	−1.18395	−0.591974	+	0.805957i	$0.701651\pi$
$522$	19.4025	0.849225
$523$	17.1384	0.749410	0.374705	−	0.927144i	$-0.377744\pi$
$523$	17.1384	0.749410	0.374705	+	0.927144i	$0.377744\pi$
$524$	−10.2913	−0.449577
$525$	−2.23704	−0.0976325
$526$	−29.6602	−1.29324
$527$	−20.2889	−0.883797
$528$	3.30461	0.143815
$529$	−11.5311	−0.501353
$530$	−9.23964	−0.401344
$531$	14.8788	0.645685
$532$	−1.00086	−0.0433926
$533$	17.0860	0.740076
$534$	−54.3527	−2.35207
$535$	−7.25685	−0.313741
$536$	−2.45232	−0.105924
$537$	26.9557	1.16322
$538$	−15.7263	−0.678010
$539$	−6.54175	−0.281773
$540$	−16.2602	−0.699730
$541$	17.2997	0.743772	0.371886	−	0.928278i	$-0.378711\pi$
$541$	17.2997	0.743772	0.371886	+	0.928278i	$0.378711\pi$
$542$	2.41395	0.103688
$543$	−44.7307	−1.91958
$544$	−2.43964	−0.104599
$545$	9.44895	0.404749
$546$	8.86066	0.379201
$547$	19.7981	0.846504	0.423252	−	0.906012i	$-0.360888\pi$
$547$	19.7981	0.846504	0.423252	+	0.906012i	$0.360888\pi$
$548$	−16.2179	−0.692794
$549$	−116.323	−4.96454
$550$	1.00000	0.0426401
$551$	3.62180	0.154294
$552$	11.1913	0.476334
$553$	−4.41053	−0.187555
$554$	−3.14074	−0.133437
$555$	−37.0132	−1.57112
$556$	−17.3571	−0.736104
$557$	−43.5172	−1.84388	−0.921942	−	0.387328i	$-0.873398\pi$
$557$	−43.5172	−1.84388	−0.921942	+	0.387328i	$0.873398\pi$
$558$	65.8693	2.78847
$559$	−3.96088	−0.167528
$560$	0.676945	0.0286061
$561$	−8.06207	−0.340381
$562$	8.06027	0.340002
$563$	−21.4447	−0.903787	−0.451893	−	0.892072i	$-0.649251\pi$
$563$	−21.4447	−0.903787	−0.451893	+	0.892072i	$0.649251\pi$
$564$	24.0416	1.01233
$565$	16.2365	0.683076
$566$	32.6449	1.37217
$567$	−20.2897	−0.852087
$568$	8.83857	0.370858
$569$	9.22680	0.386808	0.193404	−	0.981119i	$-0.438047\pi$
$569$	9.22680	0.386808	0.193404	+	0.981119i	$0.438047\pi$
$570$	−4.88583	−0.204645
$571$	−19.9634	−0.835443	−0.417722	−	0.908575i	$-0.637171\pi$
$571$	−19.9634	−0.835443	−0.417722	+	0.908575i	$0.637171\pi$
$572$	−3.96088	−0.165613
$573$	−63.8565	−2.66765
$574$	2.92012	0.121884
$575$	3.38657	0.141230
$576$	7.92047	0.330020
$577$	1.20303	0.0500828	0.0250414	−	0.999686i	$-0.492028\pi$
$577$	1.20303	0.0500828	0.0250414	+	0.999686i	$0.492028\pi$
$578$	−11.0482	−0.459543
$579$	59.6711	2.47985
$580$	−2.44967	−0.101717
$581$	3.59077	0.148970
$582$	−55.1343	−2.28539
$583$	9.23964	0.382667
$584$	5.06238	0.209483
$585$	31.3721	1.29708
$586$	23.9367	0.988814
$587$	17.4649	0.720852	0.360426	−	0.932788i	$-0.382631\pi$
$587$	17.4649	0.720852	0.360426	+	0.932788i	$0.382631\pi$
$588$	−21.6179	−0.891509
$589$	12.2956	0.506632
$590$	−1.87853	−0.0773377
$591$	−27.9230	−1.14860
$592$	11.2005	0.460337
$593$	−9.04775	−0.371547	−0.185773	−	0.982593i	$-0.559479\pi$
$593$	−9.04775	−0.371547	−0.185773	+	0.982593i	$0.559479\pi$
$594$	16.2602	0.667166
$595$	−1.65150	−0.0677050
$596$	−9.35161	−0.383057
$597$	−39.6460	−1.62260
$598$	−13.4138	−0.548532
$599$	−17.1612	−0.701187	−0.350594	−	0.936528i	$-0.614020\pi$
$599$	−17.1612	−0.701187	−0.350594	+	0.936528i	$0.614020\pi$
$600$	3.30461	0.134910
$601$	−19.3655	−0.789937	−0.394968	−	0.918695i	$-0.629244\pi$
$601$	−19.3655	−0.789937	−0.394968	+	0.918695i	$0.629244\pi$
$602$	−0.676945	−0.0275902
$603$	−19.4235	−0.790988
$604$	−2.95411	−0.120201
$605$	−1.00000	−0.0406558
$606$	29.7481	1.20843
$607$	9.69049	0.393325	0.196662	−	0.980471i	$-0.436990\pi$
$607$	9.69049	0.393325	0.196662	+	0.980471i	$0.436990\pi$
$608$	1.47849	0.0599606
$609$	−5.48001	−0.222061
$610$	14.6864	0.594633
$611$	−28.8161	−1.16577
$612$	−19.3231	−0.781090
$613$	−10.2335	−0.413325	−0.206663	−	0.978412i	$-0.566260\pi$
$613$	−10.2335	−0.413325	−0.206663	+	0.978412i	$0.566260\pi$
$614$	−24.8926	−1.00458
$615$	14.2550	0.574819
$616$	−0.676945	−0.0272749
$617$	27.5357	1.10855	0.554273	−	0.832335i	$-0.312996\pi$
$617$	27.5357	1.10855	0.554273	+	0.832335i	$0.312996\pi$
$618$	15.6492	0.629505
$619$	32.7425	1.31603	0.658016	−	0.753004i	$-0.271396\pi$
$619$	32.7425	1.31603	0.658016	+	0.753004i	$0.271396\pi$
$620$	−8.31634	−0.333992
$621$	55.0665	2.20974
$622$	15.6134	0.626042
$623$	11.1341	0.446077
$624$	−13.0892	−0.523987
$625$	1.00000	0.0400000
$626$	−12.0771	−0.482699
$627$	4.88583	0.195121
$628$	−5.28247	−0.210794
$629$	−27.3251	−1.08952
$630$	5.36172	0.213616
$631$	1.26167	0.0502261	0.0251131	−	0.999685i	$-0.492005\pi$
$631$	1.26167	0.0502261	0.0251131	+	0.999685i	$0.492005\pi$
$632$	6.51534	0.259166
$633$	75.6070	3.00511
$634$	−3.32552	−0.132073
$635$	−9.05438	−0.359312
$636$	30.5334	1.21073
$637$	25.9111	1.02664
$638$	2.44967	0.0969832
$639$	70.0056	2.76938
$640$	−1.00000	−0.0395285
$641$	−10.6406	−0.420279	−0.210139	−	0.977671i	$-0.567392\pi$
$641$	−10.6406	−0.420279	−0.210139	+	0.977671i	$0.567392\pi$
$642$	23.9811	0.946458
$643$	15.9591	0.629365	0.314683	−	0.949197i	$-0.398102\pi$
$643$	15.9591	0.629365	0.314683	+	0.949197i	$0.398102\pi$
$644$	−2.29252	−0.0903381
$645$	−3.30461	−0.130119
$646$	−3.60698	−0.141915
$647$	25.7481	1.01226	0.506132	−	0.862456i	$-0.331075\pi$
$647$	25.7481	1.01226	0.506132	+	0.862456i	$0.331075\pi$
$648$	29.9724	1.17743
$649$	1.87853	0.0737386
$650$	−3.96088	−0.155359
$651$	−18.6040	−0.729148
$652$	−0.152295	−0.00596433
$653$	20.5634	0.804710	0.402355	−	0.915484i	$-0.368192\pi$
$653$	20.5634	0.804710	0.402355	+	0.915484i	$0.368192\pi$
$654$	−31.2251	−1.22100
$655$	10.2913	0.402114
$656$	−4.31368	−0.168421
$657$	40.0964	1.56431
$658$	−4.92489	−0.191992
$659$	−25.7968	−1.00490	−0.502451	−	0.864606i	$-0.667568\pi$
$659$	−25.7968	−1.00490	−0.502451	+	0.864606i	$0.667568\pi$
$660$	−3.30461	−0.128632
$661$	4.79294	0.186424	0.0932120	−	0.995646i	$-0.470287\pi$
$661$	4.79294	0.186424	0.0932120	+	0.995646i	$0.470287\pi$
$662$	−5.98882	−0.232762
$663$	31.9329	1.24017
$664$	−5.30438	−0.205850
$665$	1.00086	0.0388115
$666$	88.7130	3.43756
$667$	8.29598	0.321222
$668$	−15.9649	−0.617699
$669$	−64.0808	−2.47751
$670$	2.45232	0.0947415
$671$	−14.6864	−0.566960
$672$	−2.23704	−0.0862957
$673$	39.4943	1.52239	0.761196	−	0.648522i	$-0.224613\pi$
$673$	39.4943	1.52239	0.761196	+	0.648522i	$0.224613\pi$
$674$	−1.92465	−0.0741348
$675$	16.2602	0.625857
$676$	2.68861	0.103408
$677$	−38.2045	−1.46832	−0.734159	−	0.678977i	$-0.762423\pi$
$677$	−38.2045	−1.46832	−0.734159	+	0.678977i	$0.762423\pi$
$678$	−53.6555	−2.06063
$679$	11.2942	0.433431
$680$	2.43964	0.0935559
$681$	−88.9502	−3.40858
$682$	8.31634	0.318449
$683$	−29.5186	−1.12950	−0.564749	−	0.825263i	$-0.691027\pi$
$683$	−29.5186	−1.12950	−0.564749	+	0.825263i	$0.691027\pi$
$684$	11.7103	0.447756
$685$	16.2179	0.619654
$686$	9.16702	0.349998
$687$	30.8188	1.17581
$688$	1.00000	0.0381246
$689$	−36.5971	−1.39424
$690$	−11.1913	−0.426046
$691$	29.2300	1.11196	0.555981	−	0.831195i	$-0.312343\pi$
$691$	29.2300	1.11196	0.555981	+	0.831195i	$0.312343\pi$
$692$	−12.2545	−0.465846
$693$	−5.36172	−0.203675
$694$	−14.2654	−0.541509
$695$	17.3571	0.658392
$696$	8.09520	0.306848
$697$	10.5238	0.398618
$698$	12.5777	0.476072
$699$	−13.9755	−0.528603
$700$	−0.676945	−0.0255861
$701$	7.25187	0.273899	0.136950	−	0.990578i	$-0.456270\pi$
$701$	7.25187	0.273899	0.136950	+	0.990578i	$0.456270\pi$
$702$	−64.4050	−2.43081
$703$	16.5598	0.624564
$704$	1.00000	0.0376889
$705$	−24.0416	−0.905459
$706$	−12.9817	−0.488575
$707$	−6.09385	−0.229183
$708$	6.20780	0.233303
$709$	−34.1209	−1.28144	−0.640719	−	0.767775i	$-0.721364\pi$
$709$	−34.1209	−1.28144	−0.640719	+	0.767775i	$0.721364\pi$
$710$	−8.83857	−0.331706
$711$	51.6046	1.93532
$712$	−16.4475	−0.616396
$713$	28.1639	1.05475
$714$	5.45758	0.204245
$715$	3.96088	0.148129
$716$	8.15698	0.304841
$717$	89.5734	3.34518
$718$	14.4988	0.541091
$719$	34.0289	1.26906	0.634531	−	0.772897i	$-0.281193\pi$
$719$	34.0289	1.26906	0.634531	+	0.772897i	$0.281193\pi$
$720$	−7.92047	−0.295178
$721$	−3.20572	−0.119387
$722$	−16.8141	−0.625755
$723$	−12.0394	−0.447752
$724$	−13.5358	−0.503055
$725$	2.44967	0.0909783
$726$	3.30461	0.122646
$727$	21.9246	0.813138	0.406569	−	0.913620i	$-0.366725\pi$
$727$	21.9246	0.813138	0.406569	+	0.913620i	$0.366725\pi$
$728$	2.68130	0.0993756
$729$	76.1942	2.82201
$730$	−5.06238	−0.187367
$731$	−2.43964	−0.0902334
$732$	−48.5327	−1.79382
$733$	−26.8182	−0.990552	−0.495276	−	0.868736i	$-0.664933\pi$
$733$	−26.8182	−0.990552	−0.495276	+	0.868736i	$0.664933\pi$
$734$	−4.16242	−0.153638
$735$	21.6179	0.797390
$736$	3.38657	0.124831
$737$	−2.45232	−0.0903325
$738$	−34.1664	−1.25768
$739$	15.8968	0.584772	0.292386	−	0.956300i	$-0.405551\pi$
$739$	15.8968	0.584772	0.292386	+	0.956300i	$0.405551\pi$
$740$	−11.2005	−0.411738
$741$	−19.3522	−0.710922
$742$	−6.25472	−0.229618
$743$	26.6094	0.976204	0.488102	−	0.872787i	$-0.337689\pi$
$743$	26.6094	0.976204	0.488102	+	0.872787i	$0.337689\pi$
$744$	27.4823	1.00755
$745$	9.35161	0.342617
$746$	31.7738	1.16332
$747$	−42.0132	−1.53718
$748$	−2.43964	−0.0892021
$749$	−4.91249	−0.179498
$750$	−3.30461	−0.120667
$751$	9.86322	0.359914	0.179957	−	0.983674i	$-0.442404\pi$
$751$	9.86322	0.359914	0.179957	+	0.983674i	$0.442404\pi$
$752$	7.27516	0.265298
$753$	95.6680	3.48633
$754$	−9.70285	−0.353357
$755$	2.95411	0.107511
$756$	−11.0073	−0.400331
$757$	20.6951	0.752176	0.376088	−	0.926584i	$-0.377269\pi$
$757$	20.6951	0.752176	0.376088	+	0.926584i	$0.377269\pi$
$758$	26.8216	0.974205
$759$	11.1913	0.406219
$760$	−1.47849	−0.0536304
$761$	27.8460	1.00942	0.504708	−	0.863290i	$-0.331600\pi$
$761$	27.8460	1.00942	0.504708	+	0.863290i	$0.331600\pi$
$762$	29.9212	1.08393
$763$	6.39642	0.231566
$764$	−19.3235	−0.699098
$765$	19.3231	0.698628
$766$	34.1094	1.23242
$767$	−7.44062	−0.268665
$768$	3.30461	0.119245
$769$	11.7386	0.423304	0.211652	−	0.977345i	$-0.432116\pi$
$769$	11.7386	0.423304	0.211652	+	0.977345i	$0.432116\pi$
$770$	0.676945	0.0243954
$771$	31.7936	1.14502
$772$	18.0569	0.649883
$773$	11.9546	0.429976	0.214988	−	0.976617i	$-0.431029\pi$
$773$	11.9546	0.429976	0.214988	+	0.976617i	$0.431029\pi$
$774$	7.92047	0.284695
$775$	8.31634	0.298732
$776$	−16.6841	−0.598923
$777$	−25.0559	−0.898876
$778$	−0.877885	−0.0314737
$779$	−6.37773	−0.228506
$780$	13.0892	0.468668
$781$	8.83857	0.316269
$782$	−8.26202	−0.295449
$783$	39.8322	1.42349
$784$	−6.54175	−0.233634
$785$	5.28247	0.188539
$786$	−34.0087	−1.21305
$787$	−19.1096	−0.681183	−0.340592	−	0.940211i	$-0.610627\pi$
$787$	−19.1096	−0.681183	−0.340592	+	0.940211i	$0.610627\pi$
$788$	−8.44971	−0.301008
$789$	−98.0154	−3.48944
$790$	−6.51534	−0.231806
$791$	10.9912	0.390804
$792$	7.92047	0.281442
$793$	58.1710	2.06571
$794$	−25.4297	−0.902466
$795$	−30.5334	−1.08291
$796$	−11.9972	−0.425228
$797$	−0.297496	−0.0105378	−0.00526892	−	0.999986i	$-0.501677\pi$
$797$	−0.297496	−0.0105378	−0.00526892	+	0.999986i	$0.501677\pi$
$798$	−3.30744	−0.117082
$799$	−17.7488	−0.627907
$800$	1.00000	0.0353553
$801$	−130.272	−4.60293
$802$	15.5181	0.547963
$803$	5.06238	0.178647
$804$	−8.10398	−0.285805
$805$	2.29252	0.0808009
$806$	−32.9401	−1.16026
$807$	−51.9695	−1.82941
$808$	9.00199	0.316689
$809$	11.2834	0.396705	0.198352	−	0.980131i	$-0.436441\pi$
$809$	11.2834	0.396705	0.198352	+	0.980131i	$0.436441\pi$
$810$	−29.9724	−1.05312
$811$	−35.8029	−1.25721	−0.628605	−	0.777725i	$-0.716374\pi$
$811$	−35.8029	−1.25721	−0.628605	+	0.777725i	$0.716374\pi$
$812$	−1.65829	−0.0581946
$813$	7.97717	0.279771
$814$	11.2005	0.392576
$815$	0.152295	0.00533466
$816$	−8.06207	−0.282229
$817$	1.47849	0.0517258
$818$	23.6642	0.827399
$819$	21.2372	0.742087
$820$	4.31368	0.150640
$821$	−8.80261	−0.307213	−0.153607	−	0.988132i	$-0.549089\pi$
$821$	−8.80261	−0.307213	−0.153607	+	0.988132i	$0.549089\pi$
$822$	−53.5939	−1.86930
$823$	−4.94921	−0.172519	−0.0862593	−	0.996273i	$-0.527491\pi$
$823$	−4.94921	−0.172519	−0.0862593	+	0.996273i	$0.527491\pi$
$824$	4.73558	0.164972
$825$	3.30461	0.115052
$826$	−1.27166	−0.0442467
$827$	−19.5859	−0.681070	−0.340535	−	0.940232i	$-0.610608\pi$
$827$	−19.5859	−0.681070	−0.340535	+	0.940232i	$0.610608\pi$
$828$	26.8233	0.932173
$829$	23.8513	0.828389	0.414194	−	0.910188i	$-0.364063\pi$
$829$	23.8513	0.828389	0.414194	+	0.910188i	$0.364063\pi$
$830$	5.30438	0.184118
$831$	−10.3789	−0.360041
$832$	−3.96088	−0.137319
$833$	15.9595	0.552964
$834$	−57.3584	−1.98616
$835$	15.9649	0.552487
$836$	1.47849	0.0511346
$837$	135.226	4.67408
$838$	−16.0191	−0.553369
$839$	16.0606	0.554474	0.277237	−	0.960802i	$-0.410581\pi$
$839$	16.0606	0.554474	0.277237	+	0.960802i	$0.410581\pi$
$840$	2.23704	0.0771853
$841$	−22.9991	−0.793074
$842$	2.89947	0.0999224
$843$	26.6361	0.917395
$844$	22.8792	0.787535
$845$	−2.68861	−0.0924910
$846$	57.6227	1.98111
$847$	−0.676945	−0.0232601
$848$	9.23964	0.317290
$849$	107.879	3.70239
$850$	−2.43964	−0.0836790
$851$	37.9312	1.30027
$852$	29.2081	1.00065
$853$	14.9965	0.513469	0.256735	−	0.966482i	$-0.417353\pi$
$853$	14.9965	0.513469	0.256735	+	0.966482i	$0.417353\pi$
$854$	9.94185	0.340203
$855$	−11.7103	−0.400485
$856$	7.25685	0.248034
$857$	−21.9522	−0.749873	−0.374936	−	0.927051i	$-0.622335\pi$
$857$	−21.9522	−0.749873	−0.374936	+	0.927051i	$0.622335\pi$
$858$	−13.0892	−0.446858
$859$	6.73823	0.229906	0.114953	−	0.993371i	$-0.463328\pi$
$859$	6.73823	0.229906	0.114953	+	0.993371i	$0.463328\pi$
$860$	−1.00000	−0.0340997
$861$	9.64988	0.328867
$862$	36.0935	1.22935
$863$	−40.6180	−1.38265	−0.691326	−	0.722543i	$-0.742973\pi$
$863$	−40.6180	−1.38265	−0.691326	+	0.722543i	$0.742973\pi$
$864$	16.2602	0.553185
$865$	12.2545	0.416666
$866$	−28.4339	−0.966223
$867$	−36.5099	−1.23994
$868$	−5.62970	−0.191085
$869$	6.51534	0.221018
$870$	−8.09520	−0.274453
$871$	9.71337	0.329125
$872$	−9.44895	−0.319982
$873$	−132.146	−4.47245
$874$	5.00701	0.169365
$875$	0.676945	0.0228849
$876$	16.7292	0.565227
$877$	−23.7664	−0.802533	−0.401266	−	0.915961i	$-0.631430\pi$
$877$	−23.7664	−0.802533	−0.401266	+	0.915961i	$0.631430\pi$
$878$	17.4292	0.588207
$879$	79.1014	2.66802
$880$	−1.00000	−0.0337100
$881$	−11.1950	−0.377168	−0.188584	−	0.982057i	$-0.560390\pi$
$881$	−11.1950	−0.377168	−0.188584	+	0.982057i	$0.560390\pi$
$882$	−51.8137	−1.74466
$883$	42.1459	1.41832	0.709161	−	0.705046i	$-0.249074\pi$
$883$	42.1459	1.41832	0.709161	+	0.705046i	$0.249074\pi$
$884$	9.66314	0.325006
$885$	−6.20780	−0.208673
$886$	−19.2963	−0.648273
$887$	−55.0513	−1.84844	−0.924221	−	0.381857i	$-0.875285\pi$
$887$	−55.0513	−1.84844	−0.924221	+	0.381857i	$0.875285\pi$
$888$	37.0132	1.24208
$889$	−6.12932	−0.205571
$890$	16.4475	0.551322
$891$	29.9724	1.00411
$892$	−19.3913	−0.649269
$893$	10.7562	0.359944
$894$	−30.9035	−1.03357
$895$	−8.15698	−0.272658
$896$	−0.676945	−0.0226151
$897$	−44.3275	−1.48005
$898$	−23.6300	−0.788545
$899$	20.3723	0.679453
$900$	7.92047	0.264016
$901$	−22.5414	−0.750963
$902$	−4.31368	−0.143630
$903$	−2.23704	−0.0744441
$904$	−16.2365	−0.540019
$905$	13.5358	0.449946
$906$	−9.76218	−0.324327
$907$	6.60026	0.219158	0.109579	−	0.993978i	$-0.465050\pi$
$907$	6.60026	0.219158	0.109579	+	0.993978i	$0.465050\pi$
$908$	−26.9170	−0.893271
$909$	71.3000	2.36487
$910$	−2.68130	−0.0888843
$911$	32.7077	1.08365	0.541827	−	0.840490i	$-0.317733\pi$
$911$	32.7077	1.08365	0.541827	+	0.840490i	$0.317733\pi$
$912$	4.88583	0.161786
$913$	−5.30438	−0.175549
$914$	−9.26335	−0.306404
$915$	48.5327	1.60444
$916$	9.32600	0.308140
$917$	6.96663	0.230059
$918$	−39.6692	−1.30928
$919$	11.2922	0.372496	0.186248	−	0.982503i	$-0.440367\pi$
$919$	11.2922	0.372496	0.186248	+	0.982503i	$0.440367\pi$
$920$	−3.38657	−0.111652
$921$	−82.2604	−2.71057
$922$	22.8018	0.750937
$923$	−35.0086	−1.15232
$924$	−2.23704	−0.0735933
$925$	11.2005	0.368269
$926$	28.3243	0.930795
$927$	37.5080	1.23192
$928$	2.44967	0.0804142
$929$	32.9114	1.07979	0.539893	−	0.841734i	$-0.318465\pi$
$929$	32.9114	1.07979	0.539893	+	0.841734i	$0.318465\pi$
$930$	−27.4823	−0.901179
$931$	−9.67190	−0.316984
$932$	−4.22910	−0.138529
$933$	51.5964	1.68919
$934$	22.8550	0.747837
$935$	2.43964	0.0797848
$936$	−31.3721	−1.02543
$937$	−15.6220	−0.510350	−0.255175	−	0.966895i	$-0.582133\pi$
$937$	−15.6220	−0.510350	−0.255175	+	0.966895i	$0.582133\pi$
$938$	1.66009	0.0542038
$939$	−39.9103	−1.30242
$940$	−7.27516	−0.237290
$941$	−3.79032	−0.123561	−0.0617804	−	0.998090i	$-0.519678\pi$
$941$	−3.79032	−0.123561	−0.0617804	+	0.998090i	$0.519678\pi$
$942$	−17.4565	−0.568764
$943$	−14.6086	−0.475721
$944$	1.87853	0.0611408
$945$	11.0073	0.358067
$946$	1.00000	0.0325128
$947$	14.2981	0.464625	0.232312	−	0.972641i	$-0.425371\pi$
$947$	14.2981	0.464625	0.232312	+	0.972641i	$0.425371\pi$
$948$	21.5307	0.699284
$949$	−20.0515	−0.650899
$950$	1.47849	0.0479685
$951$	−10.9896	−0.356361
$952$	1.65150	0.0535255
$953$	−34.1947	−1.10768	−0.553838	−	0.832625i	$-0.686837\pi$
$953$	−34.1947	−1.10768	−0.553838	+	0.832625i	$0.686837\pi$
$954$	73.1822	2.36936
$955$	19.3235	0.625292
$956$	27.1055	0.876656
$957$	8.09520	0.261681
$958$	33.3747	1.07829
$959$	10.9786	0.354518
$960$	−3.30461	−0.106656
$961$	38.1614	1.23101
$962$	−44.3638	−1.43035
$963$	57.4777	1.85219
$964$	−3.64322	−0.117340
$965$	−18.0569	−0.581273
$966$	−7.57591	−0.243751
$967$	17.3858	0.559090	0.279545	−	0.960133i	$-0.409816\pi$
$967$	17.3858	0.559090	0.279545	+	0.960133i	$0.409816\pi$
$968$	1.00000	0.0321412
$969$	−11.9197	−0.382915
$970$	16.6841	0.535693
$971$	−40.3039	−1.29341	−0.646706	−	0.762739i	$-0.723854\pi$
$971$	−40.3039	−1.29341	−0.646706	+	0.762739i	$0.723854\pi$
$972$	50.2665	1.61230
$973$	11.7498	0.376681
$974$	−35.4355	−1.13543
$975$	−13.0892	−0.419190
$976$	−14.6864	−0.470099
$977$	−18.3480	−0.587004	−0.293502	−	0.955958i	$-0.594821\pi$
$977$	−18.3480	−0.587004	−0.293502	+	0.955958i	$0.594821\pi$
$978$	−0.503276	−0.0160930
$979$	−16.4475	−0.525665
$980$	6.54175	0.208968
$981$	−74.8401	−2.38946
$982$	10.2100	0.325813
$983$	16.4070	0.523301	0.261650	−	0.965163i	$-0.415733\pi$
$983$	16.4070	0.523301	0.261650	+	0.965163i	$0.415733\pi$
$984$	−14.2550	−0.454434
$985$	8.44971	0.269230
$986$	−5.97631	−0.190324
$987$	−16.2748	−0.518034
$988$	−5.85612	−0.186308
$989$	3.38657	0.107687
$990$	−7.92047	−0.251729
$991$	9.64013	0.306229	0.153114	−	0.988208i	$-0.451070\pi$
$991$	9.64013	0.306229	0.153114	+	0.988208i	$0.451070\pi$
$992$	8.31634	0.264044
$993$	−19.7907	−0.628040
$994$	−5.98323	−0.189776
$995$	11.9972	0.380335
$996$	−17.5289	−0.555425
$997$	−54.1525	−1.71503	−0.857514	−	0.514461i	$-0.827992\pi$
$997$	−54.1525	−1.71503	−0.857514	+	0.514461i	$0.827992\pi$
$998$	18.9638	0.600289
$999$	182.123	5.76210

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4730.2.a.bf.1.13	✓	13

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4730.2.a.bf.1.13	✓	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)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +3.30461 q^{3} +1.00000 q^{4} -1.00000 q^{5} +3.30461 q^{6} -0.676945 q^{7} +1.00000 q^{8} +7.92047 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +3.30461 q^{3} +1.00000 q^{4} -1.00000 q^{5} +3.30461 q^{6} -0.676945 q^{7} +1.00000 q^{8} +7.92047 q^{9} -1.00000 q^{10} +1.00000 q^{11} +3.30461 q^{12} -3.96088 q^{13} -0.676945 q^{14} -3.30461 q^{15} +1.00000 q^{16} -2.43964 q^{17} +7.92047 q^{18} +1.47849 q^{19} -1.00000 q^{20} -2.23704 q^{21} +1.00000 q^{22} +3.38657 q^{23} +3.30461 q^{24} +1.00000 q^{25} -3.96088 q^{26} +16.2602 q^{27} -0.676945 q^{28} +2.44967 q^{29} -3.30461 q^{30} +8.31634 q^{31} +1.00000 q^{32} +3.30461 q^{33} -2.43964 q^{34} +0.676945 q^{35} +7.92047 q^{36} +11.2005 q^{37} +1.47849 q^{38} -13.0892 q^{39} -1.00000 q^{40} -4.31368 q^{41} -2.23704 q^{42} +1.00000 q^{43} +1.00000 q^{44} -7.92047 q^{45} +3.38657 q^{46} +7.27516 q^{47} +3.30461 q^{48} -6.54175 q^{49} +1.00000 q^{50} -8.06207 q^{51} -3.96088 q^{52} +9.23964 q^{53} +16.2602 q^{54} -1.00000 q^{55} -0.676945 q^{56} +4.88583 q^{57} +2.44967 q^{58} +1.87853 q^{59} -3.30461 q^{60} -14.6864 q^{61} +8.31634 q^{62} -5.36172 q^{63} +1.00000 q^{64} +3.96088 q^{65} +3.30461 q^{66} -2.45232 q^{67} -2.43964 q^{68} +11.1913 q^{69} +0.676945 q^{70} +8.83857 q^{71} +7.92047 q^{72} +5.06238 q^{73} +11.2005 q^{74} +3.30461 q^{75} +1.47849 q^{76} -0.676945 q^{77} -13.0892 q^{78} +6.51534 q^{79} -1.00000 q^{80} +29.9724 q^{81} -4.31368 q^{82} -5.30438 q^{83} -2.23704 q^{84} +2.43964 q^{85} +1.00000 q^{86} +8.09520 q^{87} +1.00000 q^{88} -16.4475 q^{89} -7.92047 q^{90} +2.68130 q^{91} +3.38657 q^{92} +27.4823 q^{93} +7.27516 q^{94} -1.47849 q^{95} +3.30461 q^{96} -16.6841 q^{97} -6.54175 q^{98} +7.92047 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 13 q + 13 q^{2} + 13 q^{4} - 13 q^{5} + 7 q^{7} + 13 q^{8} + 25 q^{9}+O(q^{10}) \) 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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