LMFDB - Embedded newform 4730.2.a.bf.1.11

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			1.11
Root			$-2.24942$ 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)

$f(q)$	$=$	$q+1.00000 q^{2} +2.24942 q^{3} +1.00000 q^{4} -1.00000 q^{5} +2.24942 q^{6} -1.43432 q^{7} +1.00000 q^{8} +2.05989 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +2.24942 q^{3} +1.00000 q^{4} -1.00000 q^{5} +2.24942 q^{6} -1.43432 q^{7} +1.00000 q^{8} +2.05989 q^{9} -1.00000 q^{10} +1.00000 q^{11} +2.24942 q^{12} +4.69328 q^{13} -1.43432 q^{14} -2.24942 q^{15} +1.00000 q^{16} +2.69172 q^{17} +2.05989 q^{18} +5.09763 q^{19} -1.00000 q^{20} -3.22639 q^{21} +1.00000 q^{22} +2.31042 q^{23} +2.24942 q^{24} +1.00000 q^{25} +4.69328 q^{26} -2.11469 q^{27} -1.43432 q^{28} -5.94499 q^{29} -2.24942 q^{30} -6.78435 q^{31} +1.00000 q^{32} +2.24942 q^{33} +2.69172 q^{34} +1.43432 q^{35} +2.05989 q^{36} +3.88177 q^{37} +5.09763 q^{38} +10.5572 q^{39} -1.00000 q^{40} +7.01704 q^{41} -3.22639 q^{42} +1.00000 q^{43} +1.00000 q^{44} -2.05989 q^{45} +2.31042 q^{46} +0.722561 q^{47} +2.24942 q^{48} -4.94272 q^{49} +1.00000 q^{50} +6.05480 q^{51} +4.69328 q^{52} +9.28737 q^{53} -2.11469 q^{54} -1.00000 q^{55} -1.43432 q^{56} +11.4667 q^{57} -5.94499 q^{58} -14.7355 q^{59} -2.24942 q^{60} +11.9068 q^{61} -6.78435 q^{62} -2.95455 q^{63} +1.00000 q^{64} -4.69328 q^{65} +2.24942 q^{66} +9.71230 q^{67} +2.69172 q^{68} +5.19710 q^{69} +1.43432 q^{70} +12.2764 q^{71} +2.05989 q^{72} -6.20325 q^{73} +3.88177 q^{74} +2.24942 q^{75} +5.09763 q^{76} -1.43432 q^{77} +10.5572 q^{78} -10.4505 q^{79} -1.00000 q^{80} -10.9365 q^{81} +7.01704 q^{82} +4.45987 q^{83} -3.22639 q^{84} -2.69172 q^{85} +1.00000 q^{86} -13.3728 q^{87} +1.00000 q^{88} -6.38594 q^{89} -2.05989 q^{90} -6.73167 q^{91} +2.31042 q^{92} -15.2609 q^{93} +0.722561 q^{94} -5.09763 q^{95} +2.24942 q^{96} +0.328464 q^{97} -4.94272 q^{98} +2.05989 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	2.24942	1.29870	0.649352	−	0.760488i	$-0.275040\pi$
$3$	2.24942	1.29870	0.649352	+	0.760488i	$0.275040\pi$
$4$	1.00000	0.500000
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	2.24942	0.918322
$7$	−1.43432	−0.542123	−0.271061	−	0.962562i	$-0.587375\pi$
$7$	−1.43432	−0.542123	−0.271061	+	0.962562i	$0.587375\pi$
$8$	1.00000	0.353553
$9$	2.05989	0.686631
$10$	−1.00000	−0.316228
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	2.24942	0.649352
$13$	4.69328	1.30168	0.650840	−	0.759215i	$-0.274417\pi$
$13$	4.69328	1.30168	0.650840	+	0.759215i	$0.274417\pi$
$14$	−1.43432	−0.383339
$15$	−2.24942	−0.580798
$16$	1.00000	0.250000
$17$	2.69172	0.652837	0.326418	−	0.945225i	$-0.394158\pi$
$17$	2.69172	0.652837	0.326418	+	0.945225i	$0.394158\pi$
$18$	2.05989	0.485522
$19$	5.09763	1.16948	0.584738	−	0.811222i	$-0.301197\pi$
$19$	5.09763	1.16948	0.584738	+	0.811222i	$0.301197\pi$
$20$	−1.00000	−0.223607
$21$	−3.22639	−0.704057
$22$	1.00000	0.213201
$23$	2.31042	0.481755	0.240877	−	0.970556i	$-0.422565\pi$
$23$	2.31042	0.481755	0.240877	+	0.970556i	$0.422565\pi$
$24$	2.24942	0.459161
$25$	1.00000	0.200000
$26$	4.69328	0.920427
$27$	−2.11469	−0.406973
$28$	−1.43432	−0.271061
$29$	−5.94499	−1.10396	−0.551979	−	0.833858i	$-0.686127\pi$
$29$	−5.94499	−1.10396	−0.551979	+	0.833858i	$0.686127\pi$
$30$	−2.24942	−0.410686
$31$	−6.78435	−1.21851	−0.609253	−	0.792976i	$-0.708531\pi$
$31$	−6.78435	−1.21851	−0.609253	+	0.792976i	$0.708531\pi$
$32$	1.00000	0.176777
$33$	2.24942	0.391574
$34$	2.69172	0.461625
$35$	1.43432	0.242445
$36$	2.05989	0.343316
$37$	3.88177	0.638159	0.319080	−	0.947728i	$-0.396626\pi$
$37$	3.88177	0.638159	0.319080	+	0.947728i	$0.396626\pi$
$38$	5.09763	0.826944
$39$	10.5572	1.69050
$40$	−1.00000	−0.158114
$41$	7.01704	1.09588	0.547939	−	0.836518i	$-0.315413\pi$
$41$	7.01704	1.09588	0.547939	+	0.836518i	$0.315413\pi$
$42$	−3.22639	−0.497843
$43$	1.00000	0.152499
$43$	1.00000	0.152499
$44$	1.00000	0.150756
$45$	−2.05989	−0.307071
$46$	2.31042	0.340652
$47$	0.722561	0.105396	0.0526982	−	0.998610i	$-0.483218\pi$
$47$	0.722561	0.105396	0.0526982	+	0.998610i	$0.483218\pi$
$48$	2.24942	0.324676
$49$	−4.94272	−0.706103
$50$	1.00000	0.141421
$51$	6.05480	0.847842
$52$	4.69328	0.650840
$53$	9.28737	1.27572	0.637859	−	0.770153i	$-0.279820\pi$
$53$	9.28737	1.27572	0.637859	+	0.770153i	$0.279820\pi$
$54$	−2.11469	−0.287773
$55$	−1.00000	−0.134840
$56$	−1.43432	−0.191669
$57$	11.4667	1.51880
$58$	−5.94499	−0.780616
$59$	−14.7355	−1.91840	−0.959200	−	0.282728i	$-0.908760\pi$
$59$	−14.7355	−1.91840	−0.959200	+	0.282728i	$0.908760\pi$
$60$	−2.24942	−0.290399
$61$	11.9068	1.52451	0.762255	−	0.647277i	$-0.224092\pi$
$61$	11.9068	1.52451	0.762255	+	0.647277i	$0.224092\pi$
$62$	−6.78435	−0.861614
$63$	−2.95455	−0.372238
$64$	1.00000	0.125000
$65$	−4.69328	−0.582129
$66$	2.24942	0.276885
$67$	9.71230	1.18655	0.593273	−	0.805001i	$-0.297835\pi$
$67$	9.71230	1.18655	0.593273	+	0.805001i	$0.297835\pi$
$68$	2.69172	0.326418
$69$	5.19710	0.625657
$70$	1.43432	0.171434
$71$	12.2764	1.45695	0.728473	−	0.685075i	$-0.240231\pi$
$71$	12.2764	1.45695	0.728473	+	0.685075i	$0.240231\pi$
$72$	2.05989	0.242761
$73$	−6.20325	−0.726035	−0.363018	−	0.931782i	$-0.618254\pi$
$73$	−6.20325	−0.726035	−0.363018	+	0.931782i	$0.618254\pi$
$74$	3.88177	0.451247
$75$	2.24942	0.259741
$76$	5.09763	0.584738
$77$	−1.43432	−0.163456
$78$	10.5572	1.19536
$79$	−10.4505	−1.17577	−0.587885	−	0.808944i	$-0.700039\pi$
$79$	−10.4505	−1.17577	−0.587885	+	0.808944i	$0.700039\pi$
$80$	−1.00000	−0.111803
$81$	−10.9365	−1.21517
$82$	7.01704	0.774903
$83$	4.45987	0.489534	0.244767	−	0.969582i	$-0.421288\pi$
$83$	4.45987	0.489534	0.244767	+	0.969582i	$0.421288\pi$
$84$	−3.22639	−0.352028
$85$	−2.69172	−0.291958
$86$	1.00000	0.107833
$87$	−13.3728	−1.43371
$88$	1.00000	0.106600
$89$	−6.38594	−0.676908	−0.338454	−	0.940983i	$-0.609904\pi$
$89$	−6.38594	−0.676908	−0.338454	+	0.940983i	$0.609904\pi$
$90$	−2.05989	−0.217132
$91$	−6.73167	−0.705671
$92$	2.31042	0.240877
$93$	−15.2609	−1.58248
$94$	0.722561	0.0745265
$95$	−5.09763	−0.523006
$96$	2.24942	0.229581
$97$	0.328464	0.0333505	0.0166753	−	0.999861i	$-0.494692\pi$
$97$	0.328464	0.0333505	0.0166753	+	0.999861i	$0.494692\pi$
$98$	−4.94272	−0.499290
$99$	2.05989	0.207027
$100$	1.00000	0.100000
$101$	13.3472	1.32809	0.664047	−	0.747691i	$-0.268837\pi$
$101$	13.3472	1.32809	0.664047	+	0.747691i	$0.268837\pi$
$102$	6.05480	0.599515
$103$	15.0788	1.48576	0.742879	−	0.669426i	$-0.233460\pi$
$103$	15.0788	1.48576	0.742879	+	0.669426i	$0.233460\pi$
$104$	4.69328	0.460214
$105$	3.22639	0.314864
$106$	9.28737	0.902069
$107$	−1.72911	−0.167160	−0.0835798	−	0.996501i	$-0.526635\pi$
$107$	−1.72911	−0.167160	−0.0835798	+	0.996501i	$0.526635\pi$
$108$	−2.11469	−0.203487
$109$	9.13341	0.874822	0.437411	−	0.899262i	$-0.355895\pi$
$109$	9.13341	0.874822	0.437411	+	0.899262i	$0.355895\pi$
$110$	−1.00000	−0.0953463
$111$	8.73174	0.828780
$112$	−1.43432	−0.135531
$113$	4.62839	0.435403	0.217701	−	0.976015i	$-0.430144\pi$
$113$	4.62839	0.435403	0.217701	+	0.976015i	$0.430144\pi$
$114$	11.4667	1.07396
$115$	−2.31042	−0.215447
$116$	−5.94499	−0.551979
$117$	9.66765	0.893775
$118$	−14.7355	−1.35651
$119$	−3.86079	−0.353918
$120$	−2.24942	−0.205343
$121$	1.00000	0.0909091
$122$	11.9068	1.07799
$123$	15.7843	1.42322
$124$	−6.78435	−0.609253
$125$	−1.00000	−0.0894427
$126$	−2.95455	−0.263212
$127$	−7.81461	−0.693435	−0.346717	−	0.937970i	$-0.612704\pi$
$127$	−7.81461	−0.693435	−0.346717	+	0.937970i	$0.612704\pi$
$128$	1.00000	0.0883883
$129$	2.24942	0.198050
$130$	−4.69328	−0.411628
$131$	−6.71338	−0.586551	−0.293275	−	0.956028i	$-0.594745\pi$
$131$	−6.71338	−0.586551	−0.293275	+	0.956028i	$0.594745\pi$
$132$	2.24942	0.195787
$133$	−7.31164	−0.633999
$134$	9.71230	0.839015
$135$	2.11469	0.182004
$136$	2.69172	0.230813
$137$	−14.4584	−1.23526	−0.617632	−	0.786467i	$-0.711908\pi$
$137$	−14.4584	−1.23526	−0.617632	+	0.786467i	$0.711908\pi$
$138$	5.19710	0.442406
$139$	1.30594	0.110768	0.0553840	−	0.998465i	$-0.482362\pi$
$139$	1.30594	0.110768	0.0553840	+	0.998465i	$0.482362\pi$
$140$	1.43432	0.121222
$141$	1.62534	0.136879
$142$	12.2764	1.03022
$143$	4.69328	0.392472
$144$	2.05989	0.171658
$145$	5.94499	0.493705
$146$	−6.20325	−0.513385
$147$	−11.1183	−0.917019
$148$	3.88177	0.319080
$149$	9.28161	0.760379	0.380190	−	0.924909i	$-0.375859\pi$
$149$	9.28161	0.760379	0.380190	+	0.924909i	$0.375859\pi$
$150$	2.24942	0.183664
$151$	−5.35962	−0.436160	−0.218080	−	0.975931i	$-0.569979\pi$
$151$	−5.35962	−0.436160	−0.218080	+	0.975931i	$0.569979\pi$
$152$	5.09763	0.413472
$153$	5.54465	0.448258
$154$	−1.43432	−0.115581
$155$	6.78435	0.544932
$156$	10.5572	0.845249
$157$	18.6665	1.48975	0.744876	−	0.667203i	$-0.232509\pi$
$157$	18.6665	1.48975	0.744876	+	0.667203i	$0.232509\pi$
$158$	−10.4505	−0.831395
$159$	20.8912	1.65678
$160$	−1.00000	−0.0790569
$161$	−3.31388	−0.261170
$162$	−10.9365	−0.859254
$163$	23.7568	1.86078	0.930388	−	0.366577i	$-0.119470\pi$
$163$	23.7568	1.86078	0.930388	+	0.366577i	$0.119470\pi$
$164$	7.01704	0.547939
$165$	−2.24942	−0.175117
$166$	4.45987	0.346153
$167$	−4.94648	−0.382770	−0.191385	−	0.981515i	$-0.561298\pi$
$167$	−4.94648	−0.382770	−0.191385	+	0.981515i	$0.561298\pi$
$168$	−3.22639	−0.248922
$169$	9.02685	0.694373
$170$	−2.69172	−0.206445
$171$	10.5006	0.802999
$172$	1.00000	0.0762493
$173$	24.4374	1.85794	0.928971	−	0.370154i	$-0.120695\pi$
$173$	24.4374	1.85794	0.928971	+	0.370154i	$0.120695\pi$
$174$	−13.3728	−1.01379
$175$	−1.43432	−0.108425
$176$	1.00000	0.0753778
$177$	−33.1464	−2.49143
$178$	−6.38594	−0.478646
$179$	−16.6363	−1.24346	−0.621729	−	0.783233i	$-0.713569\pi$
$179$	−16.6363	−1.24346	−0.621729	+	0.783233i	$0.713569\pi$
$180$	−2.05989	−0.153535
$181$	−14.4304	−1.07260	−0.536302	−	0.844026i	$-0.680179\pi$
$181$	−14.4304	−1.07260	−0.536302	+	0.844026i	$0.680179\pi$
$182$	−6.73167	−0.498985
$183$	26.7834	1.97989
$184$	2.31042	0.170326
$185$	−3.88177	−0.285394
$186$	−15.2609	−1.11898
$187$	2.69172	0.196838
$188$	0.722561	0.0526982
$189$	3.03315	0.220629
$190$	−5.09763	−0.369821
$191$	6.94965	0.502859	0.251430	−	0.967876i	$-0.419099\pi$
$191$	6.94965	0.502859	0.251430	+	0.967876i	$0.419099\pi$
$192$	2.24942	0.162338
$193$	3.04767	0.219376	0.109688	−	0.993966i	$-0.465015\pi$
$193$	3.04767	0.219376	0.109688	+	0.993966i	$0.465015\pi$
$194$	0.328464	0.0235824
$195$	−10.5572	−0.756014
$196$	−4.94272	−0.353051
$197$	−12.9605	−0.923398	−0.461699	−	0.887037i	$-0.652760\pi$
$197$	−12.9605	−0.923398	−0.461699	+	0.887037i	$0.652760\pi$
$198$	2.05989	0.146390
$199$	5.53937	0.392675	0.196338	−	0.980536i	$-0.437095\pi$
$199$	5.53937	0.392675	0.196338	+	0.980536i	$0.437095\pi$
$200$	1.00000	0.0707107
$201$	21.8471	1.54097
$202$	13.3472	0.939104
$203$	8.52703	0.598480
$204$	6.05480	0.423921
$205$	−7.01704	−0.490092
$206$	15.0788	1.05059
$207$	4.75921	0.330788
$208$	4.69328	0.325420
$209$	5.09763	0.352610
$210$	3.22639	0.222642
$211$	1.49551	0.102955	0.0514775	−	0.998674i	$-0.483607\pi$
$211$	1.49551	0.102955	0.0514775	+	0.998674i	$0.483607\pi$
$212$	9.28737	0.637859
$213$	27.6149	1.89214
$214$	−1.72911	−0.118200
$215$	−1.00000	−0.0681994
$216$	−2.11469	−0.143887
$217$	9.73095	0.660580
$218$	9.13341	0.618593
$219$	−13.9537	−0.942905
$220$	−1.00000	−0.0674200
$221$	12.6330	0.849785
$222$	8.73174	0.586036
$223$	−20.6795	−1.38480	−0.692400	−	0.721514i	$-0.743447\pi$
$223$	−20.6795	−1.38480	−0.692400	+	0.721514i	$0.743447\pi$
$224$	−1.43432	−0.0958347
$225$	2.05989	0.137326
$226$	4.62839	0.307876
$227$	−21.9344	−1.45583	−0.727917	−	0.685665i	$-0.759512\pi$
$227$	−21.9344	−1.45583	−0.727917	+	0.685665i	$0.759512\pi$
$228$	11.4667	0.759401
$229$	−21.3370	−1.40999	−0.704995	−	0.709212i	$-0.749051\pi$
$229$	−21.3370	−1.40999	−0.704995	+	0.709212i	$0.749051\pi$
$230$	−2.31042	−0.152344
$231$	−3.22639	−0.212281
$232$	−5.94499	−0.390308
$233$	−18.4304	−1.20741	−0.603706	−	0.797207i	$-0.706310\pi$
$233$	−18.4304	−1.20741	−0.603706	+	0.797207i	$0.706310\pi$
$234$	9.66765	0.631994
$235$	−0.722561	−0.0471347
$236$	−14.7355	−0.959200
$237$	−23.5075	−1.52698
$238$	−3.86079	−0.250258
$239$	4.81697	0.311584	0.155792	−	0.987790i	$-0.450207\pi$
$239$	4.81697	0.311584	0.155792	+	0.987790i	$0.450207\pi$
$240$	−2.24942	−0.145199
$241$	5.77599	0.372064	0.186032	−	0.982544i	$-0.440437\pi$
$241$	5.77599	0.372064	0.186032	+	0.982544i	$0.440437\pi$
$242$	1.00000	0.0642824
$243$	−18.2568	−1.17117
$244$	11.9068	0.762255
$245$	4.94272	0.315779
$246$	15.7843	1.00637
$247$	23.9246	1.52228
$248$	−6.78435	−0.430807
$249$	10.0321	0.635760
$250$	−1.00000	−0.0632456
$251$	−27.9375	−1.76340	−0.881701	−	0.471809i	$-0.843601\pi$
$251$	−27.9375	−1.76340	−0.881701	+	0.471809i	$0.843601\pi$
$252$	−2.95455	−0.186119
$253$	2.31042	0.145255
$254$	−7.81461	−0.490332
$255$	−6.05480	−0.379166
$256$	1.00000	0.0625000
$257$	−9.69635	−0.604841	−0.302421	−	0.953175i	$-0.597795\pi$
$257$	−9.69635	−0.604841	−0.302421	+	0.953175i	$0.597795\pi$
$258$	2.24942	0.140043
$259$	−5.56771	−0.345961
$260$	−4.69328	−0.291065
$261$	−12.2461	−0.758012
$262$	−6.71338	−0.414754
$263$	−20.4163	−1.25892	−0.629461	−	0.777032i	$-0.716724\pi$
$263$	−20.4163	−1.25892	−0.629461	+	0.777032i	$0.716724\pi$
$264$	2.24942	0.138442
$265$	−9.28737	−0.570518
$266$	−7.31164	−0.448305
$267$	−14.3647	−0.879103
$268$	9.71230	0.593273
$269$	13.9619	0.851273	0.425637	−	0.904894i	$-0.360050\pi$
$269$	13.9619	0.851273	0.425637	+	0.904894i	$0.360050\pi$
$270$	2.11469	0.128696
$271$	−18.0976	−1.09935	−0.549675	−	0.835379i	$-0.685248\pi$
$271$	−18.0976	−1.09935	−0.549675	+	0.835379i	$0.685248\pi$
$272$	2.69172	0.163209
$273$	−15.1424	−0.916457
$274$	−14.4584	−0.873463
$275$	1.00000	0.0603023
$276$	5.19710	0.312828
$277$	−8.13107	−0.488549	−0.244274	−	0.969706i	$-0.578550\pi$
$277$	−8.13107	−0.488549	−0.244274	+	0.969706i	$0.578550\pi$
$278$	1.30594	0.0783248
$279$	−13.9751	−0.836664
$280$	1.43432	0.0857171
$281$	−5.99636	−0.357713	−0.178856	−	0.983875i	$-0.557240\pi$
$281$	−5.99636	−0.357713	−0.178856	+	0.983875i	$0.557240\pi$
$282$	1.62534	0.0967878
$283$	−21.0031	−1.24850	−0.624252	−	0.781223i	$-0.714596\pi$
$283$	−21.0031	−1.24850	−0.624252	+	0.781223i	$0.714596\pi$
$284$	12.2764	0.728473
$285$	−11.4667	−0.679229
$286$	4.69328	0.277519
$287$	−10.0647	−0.594100
$288$	2.05989	0.121380
$289$	−9.75467	−0.573804
$290$	5.94499	0.349102
$291$	0.738855	0.0433124
$292$	−6.20325	−0.363018
$293$	−29.8493	−1.74382	−0.871908	−	0.489671i	$-0.837117\pi$
$293$	−29.8493	−1.74382	−0.871908	+	0.489671i	$0.837117\pi$
$294$	−11.1183	−0.648430
$295$	14.7355	0.857935
$296$	3.88177	0.225623
$297$	−2.11469	−0.122707
$298$	9.28161	0.537669
$299$	10.8434	0.627091
$300$	2.24942	0.129870
$301$	−1.43432	−0.0826729
$302$	−5.35962	−0.308412
$303$	30.0234	1.72480
$304$	5.09763	0.292369
$305$	−11.9068	−0.681782
$306$	5.54465	0.316966
$307$	3.81085	0.217497	0.108748	−	0.994069i	$-0.465316\pi$
$307$	3.81085	0.217497	0.108748	+	0.994069i	$0.465316\pi$
$308$	−1.43432	−0.0817281
$309$	33.9185	1.92956
$310$	6.78435	0.385325
$311$	17.9922	1.02025	0.510123	−	0.860101i	$-0.329600\pi$
$311$	17.9922	1.02025	0.510123	+	0.860101i	$0.329600\pi$
$312$	10.5572	0.597681
$313$	4.23321	0.239275	0.119638	−	0.992818i	$-0.461827\pi$
$313$	4.23321	0.239275	0.119638	+	0.992818i	$0.461827\pi$
$314$	18.6665	1.05341
$315$	2.95455	0.166470
$316$	−10.4505	−0.587885
$317$	22.6847	1.27410	0.637050	−	0.770822i	$-0.280154\pi$
$317$	22.6847	1.27410	0.637050	+	0.770822i	$0.280154\pi$
$318$	20.8912	1.17152
$319$	−5.94499	−0.332856
$320$	−1.00000	−0.0559017
$321$	−3.88950	−0.217091
$322$	−3.31388	−0.184675
$323$	13.7214	0.763477
$324$	−10.9365	−0.607584
$325$	4.69328	0.260336
$326$	23.7568	1.31577
$327$	20.5449	1.13613
$328$	7.01704	0.387451
$329$	−1.03639	−0.0571378
$330$	−2.24942	−0.123827
$331$	20.9408	1.15101	0.575505	−	0.817798i	$-0.304805\pi$
$331$	20.9408	1.15101	0.575505	+	0.817798i	$0.304805\pi$
$332$	4.45987	0.244767
$333$	7.99604	0.438180
$334$	−4.94648	−0.270660
$335$	−9.71230	−0.530640
$336$	−3.22639	−0.176014
$337$	12.2906	0.669512	0.334756	−	0.942305i	$-0.391346\pi$
$337$	12.2906	0.669512	0.334756	+	0.942305i	$0.391346\pi$
$338$	9.02685	0.490996
$339$	10.4112	0.565459
$340$	−2.69172	−0.145979
$341$	−6.78435	−0.367393
$342$	10.5006	0.567806
$343$	17.1297	0.924917
$344$	1.00000	0.0539164
$345$	−5.19710	−0.279802
$346$	24.4374	1.31376
$347$	−31.6551	−1.69933	−0.849667	−	0.527319i	$-0.823197\pi$
$347$	−31.6551	−1.69933	−0.849667	+	0.527319i	$0.823197\pi$
$348$	−13.3728	−0.716857
$349$	21.3475	1.14270	0.571352	−	0.820705i	$-0.306419\pi$
$349$	21.3475	1.14270	0.571352	+	0.820705i	$0.306419\pi$
$350$	−1.43432	−0.0766677
$351$	−9.92484	−0.529749
$352$	1.00000	0.0533002
$353$	−16.1131	−0.857611	−0.428806	−	0.903397i	$-0.641065\pi$
$353$	−16.1131	−0.857611	−0.428806	+	0.903397i	$0.641065\pi$
$354$	−33.1464	−1.76171
$355$	−12.2764	−0.651566
$356$	−6.38594	−0.338454
$357$	−8.68453	−0.459634
$358$	−16.6363	−0.879257
$359$	−21.6717	−1.14379	−0.571894	−	0.820328i	$-0.693791\pi$
$359$	−21.6717	−1.14379	−0.571894	+	0.820328i	$0.693791\pi$
$360$	−2.05989	−0.108566
$361$	6.98581	0.367674
$362$	−14.4304	−0.758446
$363$	2.24942	0.118064
$364$	−6.73167	−0.352835
$365$	6.20325	0.324693
$366$	26.7834	1.39999
$367$	−15.0819	−0.787269	−0.393635	−	0.919267i	$-0.628782\pi$
$367$	−15.0819	−0.787269	−0.393635	+	0.919267i	$0.628782\pi$
$368$	2.31042	0.120439
$369$	14.4544	0.752464
$370$	−3.88177	−0.201804
$371$	−13.3211	−0.691596
$372$	−15.2609	−0.791239
$373$	−23.7371	−1.22906	−0.614529	−	0.788894i	$-0.710654\pi$
$373$	−23.7371	−1.22906	−0.614529	+	0.788894i	$0.710654\pi$
$374$	2.69172	0.139185
$375$	−2.24942	−0.116160
$376$	0.722561	0.0372632
$377$	−27.9015	−1.43700
$378$	3.03315	0.156008
$379$	11.5566	0.593622	0.296811	−	0.954936i	$-0.404077\pi$
$379$	11.5566	0.593622	0.296811	+	0.954936i	$0.404077\pi$
$380$	−5.09763	−0.261503
$381$	−17.5784	−0.900566
$382$	6.94965	0.355575
$383$	24.9628	1.27554	0.637769	−	0.770228i	$-0.279857\pi$
$383$	24.9628	1.27554	0.637769	+	0.770228i	$0.279857\pi$
$384$	2.24942	0.114790
$385$	1.43432	0.0730998
$386$	3.04767	0.155122
$387$	2.05989	0.104710
$388$	0.328464	0.0166753
$389$	−26.8036	−1.35899	−0.679497	−	0.733678i	$-0.737802\pi$
$389$	−26.8036	−1.35899	−0.679497	+	0.733678i	$0.737802\pi$
$390$	−10.5572	−0.534582
$391$	6.21898	0.314507
$392$	−4.94272	−0.249645
$393$	−15.1012	−0.761756
$394$	−12.9605	−0.652941
$395$	10.4505	0.525820
$396$	2.05989	0.103514
$397$	−6.69149	−0.335836	−0.167918	−	0.985801i	$-0.553704\pi$
$397$	−6.69149	−0.335836	−0.167918	+	0.985801i	$0.553704\pi$
$398$	5.53937	0.277663
$399$	−16.4470	−0.823377
$400$	1.00000	0.0500000
$401$	−7.04199	−0.351660	−0.175830	−	0.984421i	$-0.556261\pi$
$401$	−7.04199	−0.351660	−0.175830	+	0.984421i	$0.556261\pi$
$402$	21.8471	1.08963
$403$	−31.8409	−1.58611
$404$	13.3472	0.664047
$405$	10.9365	0.543440
$406$	8.52703	0.423190
$407$	3.88177	0.192412
$408$	6.05480	0.299757
$409$	0.530901	0.0262514	0.0131257	−	0.999914i	$-0.495822\pi$
$409$	0.530901	0.0262514	0.0131257	+	0.999914i	$0.495822\pi$
$410$	−7.01704	−0.346547
$411$	−32.5230	−1.60424
$412$	15.0788	0.742879
$413$	21.1355	1.04001
$414$	4.75921	0.233902
$415$	−4.45987	−0.218926
$416$	4.69328	0.230107
$417$	2.93760	0.143855
$418$	5.09763	0.249333
$419$	−21.8429	−1.06710	−0.533548	−	0.845770i	$-0.679142\pi$
$419$	−21.8429	−1.06710	−0.533548	+	0.845770i	$0.679142\pi$
$420$	3.22639	0.157432
$421$	−29.9008	−1.45727	−0.728637	−	0.684900i	$-0.759846\pi$
$421$	−29.9008	−1.45727	−0.728637	+	0.684900i	$0.759846\pi$
$422$	1.49551	0.0728002
$423$	1.48840	0.0723684
$424$	9.28737	0.451034
$425$	2.69172	0.130567
$426$	27.6149	1.33795
$427$	−17.0782	−0.826472
$428$	−1.72911	−0.0835798
$429$	10.5572	0.509704
$430$	−1.00000	−0.0482243
$431$	−3.74480	−0.180381	−0.0901903	−	0.995925i	$-0.528748\pi$
$431$	−3.74480	−0.180381	−0.0901903	+	0.995925i	$0.528748\pi$
$432$	−2.11469	−0.101743
$433$	15.2090	0.730898	0.365449	−	0.930831i	$-0.380915\pi$
$433$	15.2090	0.730898	0.365449	+	0.930831i	$0.380915\pi$
$434$	9.73095	0.467100
$435$	13.3728	0.641176
$436$	9.13341	0.437411
$437$	11.7776	0.563401
$438$	−13.9537	−0.666734
$439$	−35.0097	−1.67092	−0.835462	−	0.549548i	$-0.814800\pi$
$439$	−35.0097	−1.67092	−0.835462	+	0.549548i	$0.814800\pi$
$440$	−1.00000	−0.0476731
$441$	−10.1815	−0.484832
$442$	12.6330	0.600889
$443$	−31.3131	−1.48773	−0.743864	−	0.668330i	$-0.767009\pi$
$443$	−31.3131	−1.48773	−0.743864	+	0.668330i	$0.767009\pi$
$444$	8.73174	0.414390
$445$	6.38594	0.302723
$446$	−20.6795	−0.979201
$447$	20.8782	0.987507
$448$	−1.43432	−0.0677653
$449$	1.28870	0.0608177	0.0304088	−	0.999538i	$-0.490319\pi$
$449$	1.28870	0.0608177	0.0304088	+	0.999538i	$0.490319\pi$
$450$	2.05989	0.0971043
$451$	7.01704	0.330420
$452$	4.62839	0.217701
$453$	−12.0560	−0.566443
$454$	−21.9344	−1.02943
$455$	6.73167	0.315586
$456$	11.4667	0.536978
$457$	−35.6533	−1.66779	−0.833895	−	0.551922i	$-0.813894\pi$
$457$	−35.6533	−1.66779	−0.833895	+	0.551922i	$0.813894\pi$
$458$	−21.3370	−0.997014
$459$	−5.69215	−0.265687
$460$	−2.31042	−0.107724
$461$	−10.0290	−0.467096	−0.233548	−	0.972345i	$-0.575034\pi$
$461$	−10.0290	−0.467096	−0.233548	+	0.972345i	$0.575034\pi$
$462$	−3.22639	−0.150105
$463$	−26.9399	−1.25200	−0.626001	−	0.779822i	$-0.715309\pi$
$463$	−26.9399	−1.25200	−0.626001	+	0.779822i	$0.715309\pi$
$464$	−5.94499	−0.275989
$465$	15.2609	0.707706
$466$	−18.4304	−0.853770
$467$	−17.3201	−0.801479	−0.400740	−	0.916192i	$-0.631247\pi$
$467$	−17.3201	−0.801479	−0.400740	+	0.916192i	$0.631247\pi$
$468$	9.66765	0.446887
$469$	−13.9306	−0.643254
$470$	−0.722561	−0.0333293
$471$	41.9889	1.93475
$472$	−14.7355	−0.678257
$473$	1.00000	0.0459800
$474$	−23.5075	−1.07974
$475$	5.09763	0.233895
$476$	−3.86079	−0.176959
$477$	19.1310	0.875948
$478$	4.81697	0.220323
$479$	−29.6771	−1.35598	−0.677990	−	0.735071i	$-0.737149\pi$
$479$	−29.6771	−1.35598	−0.677990	+	0.735071i	$0.737149\pi$
$480$	−2.24942	−0.102672
$481$	18.2182	0.830680
$482$	5.77599	0.263089
$483$	−7.45431	−0.339183
$484$	1.00000	0.0454545
$485$	−0.328464	−0.0149148
$486$	−18.2568	−0.828143
$487$	20.7138	0.938631	0.469316	−	0.883030i	$-0.344501\pi$
$487$	20.7138	0.938631	0.469316	+	0.883030i	$0.344501\pi$
$488$	11.9068	0.538996
$489$	53.4390	2.41660
$490$	4.94272	0.223289
$491$	0.702895	0.0317212	0.0158606	−	0.999874i	$-0.494951\pi$
$491$	0.702895	0.0317212	0.0158606	+	0.999874i	$0.494951\pi$
$492$	15.7843	0.711611
$493$	−16.0022	−0.720704
$494$	23.9246	1.07642
$495$	−2.05989	−0.0925854
$496$	−6.78435	−0.304627
$497$	−17.6084	−0.789843
$498$	10.0321	0.449550
$499$	7.52040	0.336659	0.168330	−	0.985731i	$-0.446163\pi$
$499$	7.52040	0.336659	0.168330	+	0.985731i	$0.446163\pi$
$500$	−1.00000	−0.0447214
$501$	−11.1267	−0.497105
$502$	−27.9375	−1.24691
$503$	20.6329	0.919975	0.459988	−	0.887925i	$-0.347854\pi$
$503$	20.6329	0.919975	0.459988	+	0.887925i	$0.347854\pi$
$504$	−2.95455	−0.131606
$505$	−13.3472	−0.593942
$506$	2.31042	0.102710
$507$	20.3052	0.901785
$508$	−7.81461	−0.346717
$509$	41.8117	1.85327	0.926636	−	0.375959i	$-0.122687\pi$
$509$	41.8117	1.85327	0.926636	+	0.375959i	$0.122687\pi$
$510$	−6.05480	−0.268111
$511$	8.89746	0.393600
$512$	1.00000	0.0441942
$513$	−10.7799	−0.475945
$514$	−9.69635	−0.427687
$515$	−15.0788	−0.664451
$516$	2.24942	0.0990252
$517$	0.722561	0.0317782
$518$	−5.56771	−0.244631
$519$	54.9700	2.41292
$520$	−4.69328	−0.205814
$521$	−23.7301	−1.03964	−0.519818	−	0.854277i	$-0.674000\pi$
$521$	−23.7301	−1.03964	−0.519818	+	0.854277i	$0.674000\pi$
$522$	−12.2461	−0.535995
$523$	24.1764	1.05716	0.528581	−	0.848883i	$-0.322724\pi$
$523$	24.1764	1.05716	0.528581	+	0.848883i	$0.322724\pi$
$524$	−6.71338	−0.293275
$525$	−3.22639	−0.140811
$526$	−20.4163	−0.890193
$527$	−18.2616	−0.795486
$528$	2.24942	0.0978935
$529$	−17.6620	−0.767912
$530$	−9.28737	−0.403417
$531$	−30.3536	−1.31723
$532$	−7.31164	−0.317000
$533$	32.9329	1.42648
$534$	−14.3647	−0.621620
$535$	1.72911	0.0747561
$536$	9.71230	0.419508
$537$	−37.4221	−1.61488
$538$	13.9619	0.601941
$539$	−4.94272	−0.212898
$540$	2.11469	0.0910019
$541$	−10.3446	−0.444750	−0.222375	−	0.974961i	$-0.571381\pi$
$541$	−10.3446	−0.444750	−0.222375	+	0.974961i	$0.571381\pi$
$542$	−18.0976	−0.777357
$543$	−32.4601	−1.39300
$544$	2.69172	0.115406
$545$	−9.13341	−0.391232
$546$	−15.1424	−0.648033
$547$	11.4357	0.488955	0.244477	−	0.969655i	$-0.421384\pi$
$547$	11.4357	0.488955	0.244477	+	0.969655i	$0.421384\pi$
$548$	−14.4584	−0.617632
$549$	24.5268	1.04678
$550$	1.00000	0.0426401
$551$	−30.3054	−1.29105
$552$	5.19710	0.221203
$553$	14.9893	0.637412
$554$	−8.13107	−0.345456
$555$	−8.73174	−0.370642
$556$	1.30594	0.0553840
$557$	42.4216	1.79746	0.898731	−	0.438500i	$-0.144490\pi$
$557$	42.4216	1.79746	0.898731	+	0.438500i	$0.144490\pi$
$558$	−13.9751	−0.591611
$559$	4.69328	0.198504
$560$	1.43432	0.0606112
$561$	6.05480	0.255634
$562$	−5.99636	−0.252941
$563$	27.0026	1.13802	0.569012	−	0.822330i	$-0.307326\pi$
$563$	27.0026	1.13802	0.569012	+	0.822330i	$0.307326\pi$
$564$	1.62534	0.0684393
$565$	−4.62839	−0.194718
$566$	−21.0031	−0.882826
$567$	15.6865	0.658771
$568$	12.2764	0.515108
$569$	−35.6919	−1.49628	−0.748141	−	0.663540i	$-0.769053\pi$
$569$	−35.6919	−1.49628	−0.748141	+	0.663540i	$0.769053\pi$
$570$	−11.4667	−0.480288
$571$	−4.76591	−0.199447	−0.0997235	−	0.995015i	$-0.531796\pi$
$571$	−4.76591	−0.199447	−0.0997235	+	0.995015i	$0.531796\pi$
$572$	4.69328	0.196236
$573$	15.6327	0.653065
$574$	−10.0647	−0.420092
$575$	2.31042	0.0963510
$576$	2.05989	0.0858289
$577$	−17.3230	−0.721167	−0.360583	−	0.932727i	$-0.617422\pi$
$577$	−17.3230	−0.721167	−0.360583	+	0.932727i	$0.617422\pi$
$578$	−9.75467	−0.405741
$579$	6.85550	0.284905
$580$	5.94499	0.246852
$581$	−6.39689	−0.265388
$582$	0.738855	0.0306265
$583$	9.28737	0.384643
$584$	−6.20325	−0.256692
$585$	−9.66765	−0.399708
$586$	−29.8493	−1.23306
$587$	34.5220	1.42488	0.712438	−	0.701735i	$-0.247591\pi$
$587$	34.5220	1.42488	0.712438	+	0.701735i	$0.247591\pi$
$588$	−11.1183	−0.458509
$589$	−34.5841	−1.42501
$590$	14.7355	0.606651
$591$	−29.1536	−1.19922
$592$	3.88177	0.159540
$593$	6.36844	0.261521	0.130760	−	0.991414i	$-0.458258\pi$
$593$	6.36844	0.261521	0.130760	+	0.991414i	$0.458258\pi$
$594$	−2.11469	−0.0867669
$595$	3.86079	0.158277
$596$	9.28161	0.380190
$597$	12.4604	0.509969
$598$	10.8434	0.443420
$599$	41.4623	1.69410	0.847051	−	0.531511i	$-0.178376\pi$
$599$	41.4623	1.69410	0.847051	+	0.531511i	$0.178376\pi$
$600$	2.24942	0.0918322
$601$	−20.1939	−0.823725	−0.411863	−	0.911246i	$-0.635122\pi$
$601$	−20.1939	−0.823725	−0.411863	+	0.911246i	$0.635122\pi$
$602$	−1.43432	−0.0584586
$603$	20.0063	0.814720
$604$	−5.35962	−0.218080
$605$	−1.00000	−0.0406558
$606$	30.0234	1.21962
$607$	20.7568	0.842491	0.421246	−	0.906947i	$-0.361593\pi$
$607$	20.7568	0.842491	0.421246	+	0.906947i	$0.361593\pi$
$608$	5.09763	0.206736
$609$	19.1809	0.777249
$610$	−11.9068	−0.482093
$611$	3.39118	0.137192
$612$	5.54465	0.224129
$613$	−18.5042	−0.747376	−0.373688	−	0.927554i	$-0.621907\pi$
$613$	−18.5042	−0.747376	−0.373688	+	0.927554i	$0.621907\pi$
$614$	3.81085	0.153793
$615$	−15.7843	−0.636484
$616$	−1.43432	−0.0577905
$617$	−9.52812	−0.383587	−0.191794	−	0.981435i	$-0.561430\pi$
$617$	−9.52812	−0.383587	−0.191794	+	0.981435i	$0.561430\pi$
$618$	33.9185	1.36440
$619$	−8.29009	−0.333207	−0.166604	−	0.986024i	$-0.553280\pi$
$619$	−8.29009	−0.333207	−0.166604	+	0.986024i	$0.553280\pi$
$620$	6.78435	0.272466
$621$	−4.88582	−0.196061
$622$	17.9922	0.721423
$623$	9.15949	0.366967
$624$	10.5572	0.422624
$625$	1.00000	0.0400000
$626$	4.23321	0.169193
$627$	11.4667	0.457936
$628$	18.6665	0.744876
$629$	10.4486	0.416614
$630$	2.95455	0.117712
$631$	39.4944	1.57225	0.786123	−	0.618070i	$-0.212085\pi$
$631$	39.4944	1.57225	0.786123	+	0.618070i	$0.212085\pi$
$632$	−10.4505	−0.415698
$633$	3.36403	0.133708
$634$	22.6847	0.900925
$635$	7.81461	0.310113
$636$	20.8912	0.828390
$637$	−23.1976	−0.919121
$638$	−5.94499	−0.235365
$639$	25.2882	1.00038
$640$	−1.00000	−0.0395285
$641$	15.3879	0.607787	0.303893	−	0.952706i	$-0.401713\pi$
$641$	15.3879	0.607787	0.303893	+	0.952706i	$0.401713\pi$
$642$	−3.88950	−0.153506
$643$	6.81634	0.268810	0.134405	−	0.990926i	$-0.457088\pi$
$643$	6.81634	0.268810	0.134405	+	0.990926i	$0.457088\pi$
$644$	−3.31388	−0.130585
$645$	−2.24942	−0.0885709
$646$	13.7214	0.539860
$647$	−28.1040	−1.10488	−0.552442	−	0.833551i	$-0.686304\pi$
$647$	−28.1040	−1.10488	−0.552442	+	0.833551i	$0.686304\pi$
$648$	−10.9365	−0.429627
$649$	−14.7355	−0.578419
$650$	4.69328	0.184085
$651$	21.8890	0.857897
$652$	23.7568	0.930388
$653$	−13.1673	−0.515277	−0.257639	−	0.966241i	$-0.582944\pi$
$653$	−13.1673	−0.515277	−0.257639	+	0.966241i	$0.582944\pi$
$654$	20.5449	0.803369
$655$	6.71338	0.262313
$656$	7.01704	0.273970
$657$	−12.7780	−0.498519
$658$	−1.03639	−0.0404025
$659$	34.7212	1.35254	0.676272	−	0.736652i	$-0.263594\pi$
$659$	34.7212	1.35254	0.676272	+	0.736652i	$0.263594\pi$
$660$	−2.24942	−0.0875586
$661$	30.9514	1.20387	0.601935	−	0.798545i	$-0.294396\pi$
$661$	30.9514	1.20387	0.601935	+	0.798545i	$0.294396\pi$
$662$	20.9408	0.813887
$663$	28.4169	1.10362
$664$	4.45987	0.173077
$665$	7.31164	0.283533
$666$	7.99604	0.309840
$667$	−13.7354	−0.531837
$668$	−4.94648	−0.191385
$669$	−46.5168	−1.79844
$670$	−9.71230	−0.375219
$671$	11.9068	0.459657
$672$	−3.22639	−0.124461
$673$	−26.2301	−1.01110	−0.505549	−	0.862798i	$-0.668710\pi$
$673$	−26.2301	−1.01110	−0.505549	+	0.862798i	$0.668710\pi$
$674$	12.2906	0.473416
$675$	−2.11469	−0.0813946
$676$	9.02685	0.347187
$677$	−9.28209	−0.356740	−0.178370	−	0.983963i	$-0.557082\pi$
$677$	−9.28209	−0.356740	−0.178370	+	0.983963i	$0.557082\pi$
$678$	10.4112	0.399840
$679$	−0.471124	−0.0180801
$680$	−2.69172	−0.103223
$681$	−49.3396	−1.89070
$682$	−6.78435	−0.259786
$683$	19.0813	0.730124	0.365062	−	0.930983i	$-0.381048\pi$
$683$	19.0813	0.730124	0.365062	+	0.930983i	$0.381048\pi$
$684$	10.5006	0.401499
$685$	14.4584	0.552427
$686$	17.1297	0.654015
$687$	−47.9960	−1.83116
$688$	1.00000	0.0381246
$689$	43.5882	1.66058
$690$	−5.19710	−0.197850
$691$	−22.5886	−0.859311	−0.429656	−	0.902993i	$-0.641365\pi$
$691$	−22.5886	−0.859311	−0.429656	+	0.902993i	$0.641365\pi$
$692$	24.4374	0.928971
$693$	−2.95455	−0.112234
$694$	−31.6551	−1.20161
$695$	−1.30594	−0.0495370
$696$	−13.3728	−0.506894
$697$	18.8879	0.715430
$698$	21.3475	0.808014
$699$	−41.4576	−1.56807
$700$	−1.43432	−0.0542123
$701$	−40.5973	−1.53334	−0.766669	−	0.642042i	$-0.778087\pi$
$701$	−40.5973	−1.53334	−0.766669	+	0.642042i	$0.778087\pi$
$702$	−9.92484	−0.374589
$703$	19.7878	0.746312
$704$	1.00000	0.0376889
$705$	−1.62534	−0.0612140
$706$	−16.1131	−0.606423
$707$	−19.1442	−0.719990
$708$	−33.1464	−1.24572
$709$	39.4834	1.48283	0.741414	−	0.671048i	$-0.234155\pi$
$709$	39.4834	1.48283	0.741414	+	0.671048i	$0.234155\pi$
$710$	−12.2764	−0.460727
$711$	−21.5269	−0.807321
$712$	−6.38594	−0.239323
$713$	−15.6747	−0.587021
$714$	−8.68453	−0.325010
$715$	−4.69328	−0.175519
$716$	−16.6363	−0.621729
$717$	10.8354	0.404655
$718$	−21.6717	−0.808780
$719$	17.8020	0.663902	0.331951	−	0.943297i	$-0.392293\pi$
$719$	17.8020	0.663902	0.331951	+	0.943297i	$0.392293\pi$
$720$	−2.05989	−0.0767677
$721$	−21.6278	−0.805463
$722$	6.98581	0.259985
$723$	12.9926	0.483201
$724$	−14.4304	−0.536302
$725$	−5.94499	−0.220791
$726$	2.24942	0.0834838
$727$	39.2561	1.45593	0.727964	−	0.685615i	$-0.240467\pi$
$727$	39.2561	1.45593	0.727964	+	0.685615i	$0.240467\pi$
$728$	−6.73167	−0.249492
$729$	−8.25756	−0.305836
$730$	6.20325	0.229593
$731$	2.69172	0.0995567
$732$	26.7834	0.989944
$733$	38.5716	1.42467	0.712337	−	0.701838i	$-0.247637\pi$
$733$	38.5716	1.42467	0.712337	+	0.701838i	$0.247637\pi$
$734$	−15.0819	−0.556683
$735$	11.1183	0.410103
$736$	2.31042	0.0851630
$737$	9.71230	0.357757
$738$	14.4544	0.532073
$739$	23.2463	0.855128	0.427564	−	0.903985i	$-0.359372\pi$
$739$	23.2463	0.855128	0.427564	+	0.903985i	$0.359372\pi$
$740$	−3.88177	−0.142697
$741$	53.8164	1.97700
$742$	−13.3211	−0.489032
$743$	18.0655	0.662760	0.331380	−	0.943497i	$-0.392486\pi$
$743$	18.0655	0.662760	0.331380	+	0.943497i	$0.392486\pi$
$744$	−15.2609	−0.559491
$745$	−9.28161	−0.340052
$746$	−23.7371	−0.869076
$747$	9.18686	0.336130
$748$	2.69172	0.0984189
$749$	2.48011	0.0906211
$750$	−2.24942	−0.0821372
$751$	−37.8733	−1.38202	−0.691008	−	0.722847i	$-0.742833\pi$
$751$	−37.8733	−1.38202	−0.691008	+	0.722847i	$0.742833\pi$
$752$	0.722561	0.0263491
$753$	−62.8433	−2.29014
$754$	−27.9015	−1.01611
$755$	5.35962	0.195057
$756$	3.03315	0.110315
$757$	−0.0136388	−0.000495711 0	−0.000247856	−	1.00000i	$-0.500079\pi$
$757$	−0.0136388	−0.000495711 0	−0.000247856		1.00000i	$0.500079\pi$
$758$	11.5566	0.419754
$759$	5.19710	0.188643
$760$	−5.09763	−0.184910
$761$	11.8236	0.428606	0.214303	−	0.976767i	$-0.431252\pi$
$761$	11.8236	0.428606	0.214303	+	0.976767i	$0.431252\pi$
$762$	−17.5784	−0.636796
$763$	−13.1003	−0.474261
$764$	6.94965	0.251430
$765$	−5.54465	−0.200467
$766$	24.9628	0.901942
$767$	−69.1578	−2.49714
$768$	2.24942	0.0811690
$769$	−35.4685	−1.27903	−0.639514	−	0.768779i	$-0.720864\pi$
$769$	−35.4685	−1.27903	−0.639514	+	0.768779i	$0.720864\pi$
$770$	1.43432	0.0516894
$771$	−21.8112	−0.785510
$772$	3.04767	0.109688
$773$	2.29853	0.0826723	0.0413361	−	0.999145i	$-0.486839\pi$
$773$	2.29853	0.0826723	0.0413361	+	0.999145i	$0.486839\pi$
$774$	2.05989	0.0740414
$775$	−6.78435	−0.243701
$776$	0.328464	0.0117912
$777$	−12.5241	−0.449300
$778$	−26.8036	−0.960954
$779$	35.7703	1.28160
$780$	−10.5572	−0.378007
$781$	12.2764	0.439286
$782$	6.21898	0.222390
$783$	12.5718	0.449281
$784$	−4.94272	−0.176526
$785$	−18.6665	−0.666237
$786$	−15.1012	−0.538643
$787$	−6.00131	−0.213924	−0.106962	−	0.994263i	$-0.534112\pi$
$787$	−6.00131	−0.213924	−0.106962	+	0.994263i	$0.534112\pi$
$788$	−12.9605	−0.461699
$789$	−45.9248	−1.63497
$790$	10.4505	0.371811
$791$	−6.63861	−0.236042
$792$	2.05989	0.0731951
$793$	55.8819	1.98443
$794$	−6.69149	−0.237472
$795$	−20.8912	−0.740934
$796$	5.53937	0.196338
$797$	48.1581	1.70585	0.852924	−	0.522036i	$-0.174827\pi$
$797$	48.1581	1.70585	0.852924	+	0.522036i	$0.174827\pi$
$798$	−16.4470	−0.582216
$799$	1.94493	0.0688066
$800$	1.00000	0.0353553
$801$	−13.1544	−0.464786
$802$	−7.04199	−0.248661
$803$	−6.20325	−0.218908
$804$	21.8471	0.770486
$805$	3.31388	0.116799
$806$	−31.8409	−1.12155
$807$	31.4062	1.10555
$808$	13.3472	0.469552
$809$	−30.9838	−1.08933	−0.544666	−	0.838653i	$-0.683343\pi$
$809$	−30.9838	−1.08933	−0.544666	+	0.838653i	$0.683343\pi$
$810$	10.9365	0.384270
$811$	−4.33544	−0.152238	−0.0761190	−	0.997099i	$-0.524253\pi$
$811$	−4.33544	−0.152238	−0.0761190	+	0.997099i	$0.524253\pi$
$812$	8.52703	0.299240
$813$	−40.7091	−1.42773
$814$	3.88177	0.136056
$815$	−23.7568	−0.832164
$816$	6.05480	0.211960
$817$	5.09763	0.178343
$818$	0.530901	0.0185625
$819$	−13.8665	−0.484536
$820$	−7.01704	−0.245046
$821$	12.9425	0.451695	0.225847	−	0.974163i	$-0.427485\pi$
$821$	12.9425	0.451695	0.225847	+	0.974163i	$0.427485\pi$
$822$	−32.5230	−1.13437
$823$	26.9475	0.939331	0.469665	−	0.882844i	$-0.344375\pi$
$823$	26.9475	0.939331	0.469665	+	0.882844i	$0.344375\pi$
$824$	15.0788	0.525295
$825$	2.24942	0.0783148
$826$	21.1355	0.735397
$827$	−12.4487	−0.432884	−0.216442	−	0.976295i	$-0.569445\pi$
$827$	−12.4487	−0.432884	−0.216442	+	0.976295i	$0.569445\pi$
$828$	4.75921	0.165394
$829$	−1.36229	−0.0473144	−0.0236572	−	0.999720i	$-0.507531\pi$
$829$	−1.36229	−0.0473144	−0.0236572	+	0.999720i	$0.507531\pi$
$830$	−4.45987	−0.154804
$831$	−18.2902	−0.634480
$832$	4.69328	0.162710
$833$	−13.3044	−0.460970
$834$	2.93760	0.101721
$835$	4.94648	0.171180
$836$	5.09763	0.176305
$837$	14.3468	0.495899
$838$	−21.8429	−0.754551
$839$	26.2011	0.904564	0.452282	−	0.891875i	$-0.350610\pi$
$839$	26.2011	0.904564	0.452282	+	0.891875i	$0.350610\pi$
$840$	3.22639	0.111321
$841$	6.34294	0.218722
$842$	−29.9008	−1.03045
$843$	−13.4883	−0.464563
$844$	1.49551	0.0514775
$845$	−9.02685	−0.310533
$846$	1.48840	0.0511722
$847$	−1.43432	−0.0492839
$848$	9.28737	0.318929
$849$	−47.2448	−1.62144
$850$	2.69172	0.0923251
$851$	8.96851	0.307436
$852$	27.6149	0.946070
$853$	25.9974	0.890135	0.445068	−	0.895497i	$-0.353180\pi$
$853$	25.9974	0.890135	0.445068	+	0.895497i	$0.353180\pi$
$854$	−17.0782	−0.584404
$855$	−10.5006	−0.359112
$856$	−1.72911	−0.0590999
$857$	4.12590	0.140938	0.0704690	−	0.997514i	$-0.477550\pi$
$857$	4.12590	0.140938	0.0704690	+	0.997514i	$0.477550\pi$
$858$	10.5572	0.360415
$859$	49.0374	1.67313	0.836567	−	0.547864i	$-0.184559\pi$
$859$	49.0374	1.67313	0.836567	+	0.547864i	$0.184559\pi$
$860$	−1.00000	−0.0340997
$861$	−22.6397	−0.771560
$862$	−3.74480	−0.127548
$863$	−12.7928	−0.435472	−0.217736	−	0.976008i	$-0.569867\pi$
$863$	−12.7928	−0.435472	−0.217736	+	0.976008i	$0.569867\pi$
$864$	−2.11469	−0.0719433
$865$	−24.4374	−0.830897
$866$	15.2090	0.516823
$867$	−21.9424	−0.745201
$868$	9.73095	0.330290
$869$	−10.4505	−0.354508
$870$	13.3728	0.453380
$871$	45.5825	1.54451
$872$	9.13341	0.309296
$873$	0.676602	0.0228995
$874$	11.7776	0.398385
$875$	1.43432	0.0484889
$876$	−13.9537	−0.471452
$877$	36.9386	1.24733	0.623664	−	0.781693i	$-0.285643\pi$
$877$	36.9386	1.24733	0.623664	+	0.781693i	$0.285643\pi$
$878$	−35.0097	−1.18152
$879$	−67.1437	−2.26470
$880$	−1.00000	−0.0337100
$881$	50.0472	1.68613	0.843066	−	0.537811i	$-0.180748\pi$
$881$	50.0472	1.68613	0.843066	+	0.537811i	$0.180748\pi$
$882$	−10.1815	−0.342828
$883$	44.2846	1.49030	0.745148	−	0.666899i	$-0.232379\pi$
$883$	44.2846	1.49030	0.745148	+	0.666899i	$0.232379\pi$
$884$	12.6330	0.424893
$885$	33.1464	1.11420
$886$	−31.3131	−1.05198
$887$	−37.3745	−1.25491	−0.627456	−	0.778652i	$-0.715904\pi$
$887$	−37.3745	−1.25491	−0.627456	+	0.778652i	$0.715904\pi$
$888$	8.73174	0.293018
$889$	11.2087	0.375927
$890$	6.38594	0.214057
$891$	−10.9365	−0.366387
$892$	−20.6795	−0.692400
$893$	3.68335	0.123259
$894$	20.8782	0.698273
$895$	16.6363	0.556091
$896$	−1.43432	−0.0479173
$897$	24.3914	0.814406
$898$	1.28870	0.0430046
$899$	40.3329	1.34518
$900$	2.05989	0.0686631
$901$	24.9989	0.832836
$902$	7.01704	0.233642
$903$	−3.22639	−0.107368
$904$	4.62839	0.153938
$905$	14.4304	0.479683
$906$	−12.0560	−0.400535
$907$	−13.2860	−0.441154	−0.220577	−	0.975370i	$-0.570794\pi$
$907$	−13.2860	−0.441154	−0.220577	+	0.975370i	$0.570794\pi$
$908$	−21.9344	−0.727917
$909$	27.4938	0.911911
$910$	6.73167	0.223153
$911$	−37.1564	−1.23105	−0.615523	−	0.788119i	$-0.711055\pi$
$911$	−37.1564	−1.23105	−0.615523	+	0.788119i	$0.711055\pi$
$912$	11.4667	0.379701
$913$	4.45987	0.147600
$914$	−35.6533	−1.17931
$915$	−26.7834	−0.885433
$916$	−21.3370	−0.704995
$917$	9.62915	0.317982
$918$	−5.69215	−0.187869
$919$	12.2813	0.405122	0.202561	−	0.979270i	$-0.435074\pi$
$919$	12.2813	0.405122	0.202561	+	0.979270i	$0.435074\pi$
$920$	−2.31042	−0.0761721
$921$	8.57221	0.282464
$922$	−10.0290	−0.330286
$923$	57.6167	1.89648
$924$	−3.22639	−0.106141
$925$	3.88177	0.127632
$926$	−26.9399	−0.885299
$927$	31.0607	1.02017
$928$	−5.94499	−0.195154
$929$	−16.4206	−0.538741	−0.269371	−	0.963037i	$-0.586816\pi$
$929$	−16.4206	−0.538741	−0.269371	+	0.963037i	$0.586816\pi$
$930$	15.2609	0.500424
$931$	−25.1962	−0.825770
$932$	−18.4304	−0.603706
$933$	40.4721	1.32500
$934$	−17.3201	−0.566731
$935$	−2.69172	−0.0880285
$936$	9.66765	0.315997
$937$	37.7828	1.23431	0.617156	−	0.786841i	$-0.288285\pi$
$937$	37.7828	1.23431	0.617156	+	0.786841i	$0.288285\pi$
$938$	−13.9306	−0.454849
$939$	9.52228	0.310748
$940$	−0.722561	−0.0235673
$941$	−17.0274	−0.555077	−0.277539	−	0.960715i	$-0.589519\pi$
$941$	−17.0274	−0.555077	−0.277539	+	0.960715i	$0.589519\pi$
$942$	41.9889	1.36807
$943$	16.2123	0.527945
$944$	−14.7355	−0.479600
$945$	−3.03315	−0.0986684
$946$	1.00000	0.0325128
$947$	−2.03265	−0.0660521	−0.0330260	−	0.999454i	$-0.510514\pi$
$947$	−2.03265	−0.0660521	−0.0330260	+	0.999454i	$0.510514\pi$
$948$	−23.5075	−0.763489
$949$	−29.1136	−0.945066
$950$	5.09763	0.165389
$951$	51.0274	1.65468
$952$	−3.86079	−0.125129
$953$	1.53425	0.0496994	0.0248497	−	0.999691i	$-0.492089\pi$
$953$	1.53425	0.0496994	0.0248497	+	0.999691i	$0.492089\pi$
$954$	19.1310	0.619389
$955$	−6.94965	−0.224885
$956$	4.81697	0.155792
$957$	−13.3728	−0.432281
$958$	−29.6771	−0.958823
$959$	20.7380	0.669664
$960$	−2.24942	−0.0725997
$961$	15.0275	0.484757
$962$	18.2182	0.587379
$963$	−3.56179	−0.114777
$964$	5.77599	0.186032
$965$	−3.04767	−0.0981081
$966$	−7.45431	−0.239838
$967$	−12.6438	−0.406597	−0.203298	−	0.979117i	$-0.565166\pi$
$967$	−12.6438	−0.406597	−0.203298	+	0.979117i	$0.565166\pi$
$968$	1.00000	0.0321412
$969$	30.8651	0.991531
$970$	−0.328464	−0.0105464
$971$	22.1070	0.709446	0.354723	−	0.934971i	$-0.384575\pi$
$971$	22.1070	0.709446	0.354723	+	0.934971i	$0.384575\pi$
$972$	−18.2568	−0.585586
$973$	−1.87313	−0.0600499
$974$	20.7138	0.663713
$975$	10.5572	0.338100
$976$	11.9068	0.381128
$977$	6.61636	0.211676	0.105838	−	0.994383i	$-0.466248\pi$
$977$	6.61636	0.211676	0.105838	+	0.994383i	$0.466248\pi$
$978$	53.4390	1.70879
$979$	−6.38594	−0.204096
$980$	4.94272	0.157889
$981$	18.8139	0.600680
$982$	0.702895	0.0224303
$983$	−45.9786	−1.46649	−0.733245	−	0.679964i	$-0.761995\pi$
$983$	−45.9786	−1.46649	−0.733245	+	0.679964i	$0.761995\pi$
$984$	15.7843	0.503185
$985$	12.9605	0.412956
$986$	−16.0022	−0.509615
$987$	−2.33127	−0.0742050
$988$	23.9246	0.761142
$989$	2.31042	0.0734669
$990$	−2.05989	−0.0654677
$991$	17.3138	0.549991	0.274995	−	0.961446i	$-0.411324\pi$
$991$	17.3138	0.549991	0.274995	+	0.961446i	$0.411324\pi$
$992$	−6.78435	−0.215403
$993$	47.1047	1.49482
$994$	−17.6084	−0.558503
$995$	−5.53937	−0.175610
$996$	10.0321	0.317880
$997$	−42.1164	−1.33384	−0.666921	−	0.745129i	$-0.732388\pi$
$997$	−42.1164	−1.33384	−0.666921	+	0.745129i	$0.732388\pi$
$998$	7.52040	0.238054
$999$	−8.20876	−0.259714

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4730.2.a.bf.1.11	✓	13

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4730.2.a.bf.1.11	✓	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)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +2.24942 q^{3} +1.00000 q^{4} -1.00000 q^{5} +2.24942 q^{6} -1.43432 q^{7} +1.00000 q^{8} +2.05989 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +2.24942 q^{3} +1.00000 q^{4} -1.00000 q^{5} +2.24942 q^{6} -1.43432 q^{7} +1.00000 q^{8} +2.05989 q^{9} -1.00000 q^{10} +1.00000 q^{11} +2.24942 q^{12} +4.69328 q^{13} -1.43432 q^{14} -2.24942 q^{15} +1.00000 q^{16} +2.69172 q^{17} +2.05989 q^{18} +5.09763 q^{19} -1.00000 q^{20} -3.22639 q^{21} +1.00000 q^{22} +2.31042 q^{23} +2.24942 q^{24} +1.00000 q^{25} +4.69328 q^{26} -2.11469 q^{27} -1.43432 q^{28} -5.94499 q^{29} -2.24942 q^{30} -6.78435 q^{31} +1.00000 q^{32} +2.24942 q^{33} +2.69172 q^{34} +1.43432 q^{35} +2.05989 q^{36} +3.88177 q^{37} +5.09763 q^{38} +10.5572 q^{39} -1.00000 q^{40} +7.01704 q^{41} -3.22639 q^{42} +1.00000 q^{43} +1.00000 q^{44} -2.05989 q^{45} +2.31042 q^{46} +0.722561 q^{47} +2.24942 q^{48} -4.94272 q^{49} +1.00000 q^{50} +6.05480 q^{51} +4.69328 q^{52} +9.28737 q^{53} -2.11469 q^{54} -1.00000 q^{55} -1.43432 q^{56} +11.4667 q^{57} -5.94499 q^{58} -14.7355 q^{59} -2.24942 q^{60} +11.9068 q^{61} -6.78435 q^{62} -2.95455 q^{63} +1.00000 q^{64} -4.69328 q^{65} +2.24942 q^{66} +9.71230 q^{67} +2.69172 q^{68} +5.19710 q^{69} +1.43432 q^{70} +12.2764 q^{71} +2.05989 q^{72} -6.20325 q^{73} +3.88177 q^{74} +2.24942 q^{75} +5.09763 q^{76} -1.43432 q^{77} +10.5572 q^{78} -10.4505 q^{79} -1.00000 q^{80} -10.9365 q^{81} +7.01704 q^{82} +4.45987 q^{83} -3.22639 q^{84} -2.69172 q^{85} +1.00000 q^{86} -13.3728 q^{87} +1.00000 q^{88} -6.38594 q^{89} -2.05989 q^{90} -6.73167 q^{91} +2.31042 q^{92} -15.2609 q^{93} +0.722561 q^{94} -5.09763 q^{95} +2.24942 q^{96} +0.328464 q^{97} -4.94272 q^{98} +2.05989 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 13 q + 13 q^{2} + 13 q^{4} - 13 q^{5} + 7 q^{7} + 13 q^{8} + 25 q^{9}+O(q^{10}) \) 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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