LMFDB - Embedded newform 4730.2.a.bf.1.8

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			1.8
Root			$-0.921464$ 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)

$f(q)$	$=$	$q+1.00000 q^{2} +0.921464 q^{3} +1.00000 q^{4} -1.00000 q^{5} +0.921464 q^{6} -3.84192 q^{7} +1.00000 q^{8} -2.15090 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +0.921464 q^{3} +1.00000 q^{4} -1.00000 q^{5} +0.921464 q^{6} -3.84192 q^{7} +1.00000 q^{8} -2.15090 q^{9} -1.00000 q^{10} +1.00000 q^{11} +0.921464 q^{12} +3.36077 q^{13} -3.84192 q^{14} -0.921464 q^{15} +1.00000 q^{16} +4.48968 q^{17} -2.15090 q^{18} -6.54987 q^{19} -1.00000 q^{20} -3.54019 q^{21} +1.00000 q^{22} +2.73904 q^{23} +0.921464 q^{24} +1.00000 q^{25} +3.36077 q^{26} -4.74637 q^{27} -3.84192 q^{28} +2.61423 q^{29} -0.921464 q^{30} -0.588567 q^{31} +1.00000 q^{32} +0.921464 q^{33} +4.48968 q^{34} +3.84192 q^{35} -2.15090 q^{36} -0.240321 q^{37} -6.54987 q^{38} +3.09682 q^{39} -1.00000 q^{40} +10.0856 q^{41} -3.54019 q^{42} +1.00000 q^{43} +1.00000 q^{44} +2.15090 q^{45} +2.73904 q^{46} +9.27274 q^{47} +0.921464 q^{48} +7.76033 q^{49} +1.00000 q^{50} +4.13708 q^{51} +3.36077 q^{52} +12.6401 q^{53} -4.74637 q^{54} -1.00000 q^{55} -3.84192 q^{56} -6.03547 q^{57} +2.61423 q^{58} +12.5429 q^{59} -0.921464 q^{60} -9.61487 q^{61} -0.588567 q^{62} +8.26360 q^{63} +1.00000 q^{64} -3.36077 q^{65} +0.921464 q^{66} -8.11130 q^{67} +4.48968 q^{68} +2.52392 q^{69} +3.84192 q^{70} -10.4421 q^{71} -2.15090 q^{72} +11.8631 q^{73} -0.240321 q^{74} +0.921464 q^{75} -6.54987 q^{76} -3.84192 q^{77} +3.09682 q^{78} +5.98496 q^{79} -1.00000 q^{80} +2.07910 q^{81} +10.0856 q^{82} +8.56754 q^{83} -3.54019 q^{84} -4.48968 q^{85} +1.00000 q^{86} +2.40892 q^{87} +1.00000 q^{88} +13.9559 q^{89} +2.15090 q^{90} -12.9118 q^{91} +2.73904 q^{92} -0.542343 q^{93} +9.27274 q^{94} +6.54987 q^{95} +0.921464 q^{96} -8.94728 q^{97} +7.76033 q^{98} -2.15090 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	0.921464	0.532007	0.266004	−	0.963972i	$-0.414297\pi$
$3$	0.921464	0.532007	0.266004	+	0.963972i	$0.414297\pi$
$4$	1.00000	0.500000
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	0.921464	0.376186
$7$	−3.84192	−1.45211	−0.726054	−	0.687638i	$-0.758648\pi$
$7$	−3.84192	−1.45211	−0.726054	+	0.687638i	$0.758648\pi$
$8$	1.00000	0.353553
$9$	−2.15090	−0.716968
$10$	−1.00000	−0.316228
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	0.921464	0.266004
$13$	3.36077	0.932109	0.466054	−	0.884756i	$-0.345675\pi$
$13$	3.36077	0.932109	0.466054	+	0.884756i	$0.345675\pi$
$14$	−3.84192	−1.02680
$15$	−0.921464	−0.237921
$16$	1.00000	0.250000
$17$	4.48968	1.08891	0.544453	−	0.838791i	$-0.316737\pi$
$17$	4.48968	1.08891	0.544453	+	0.838791i	$0.316737\pi$
$18$	−2.15090	−0.506973
$19$	−6.54987	−1.50264	−0.751322	−	0.659936i	$-0.770583\pi$
$19$	−6.54987	−1.50264	−0.751322	+	0.659936i	$0.770583\pi$
$20$	−1.00000	−0.223607
$21$	−3.54019	−0.772532
$22$	1.00000	0.213201
$23$	2.73904	0.571128	0.285564	−	0.958360i	$-0.407819\pi$
$23$	2.73904	0.571128	0.285564	+	0.958360i	$0.407819\pi$
$24$	0.921464	0.188093
$25$	1.00000	0.200000
$26$	3.36077	0.659100
$27$	−4.74637	−0.913440
$28$	−3.84192	−0.726054
$29$	2.61423	0.485451	0.242726	−	0.970095i	$-0.421959\pi$
$29$	2.61423	0.485451	0.242726	+	0.970095i	$0.421959\pi$
$30$	−0.921464	−0.168235
$31$	−0.588567	−0.105710	−0.0528549	−	0.998602i	$-0.516832\pi$
$31$	−0.588567	−0.105710	−0.0528549	+	0.998602i	$0.516832\pi$
$32$	1.00000	0.176777
$33$	0.921464	0.160406
$34$	4.48968	0.769973
$35$	3.84192	0.649402
$36$	−2.15090	−0.358484
$37$	−0.240321	−0.0395085	−0.0197543	−	0.999805i	$-0.506288\pi$
$37$	−0.240321	−0.0395085	−0.0197543	+	0.999805i	$0.506288\pi$
$38$	−6.54987	−1.06253
$39$	3.09682	0.495889
$40$	−1.00000	−0.158114
$41$	10.0856	1.57511	0.787556	−	0.616244i	$-0.211346\pi$
$41$	10.0856	1.57511	0.787556	+	0.616244i	$0.211346\pi$
$42$	−3.54019	−0.546263
$43$	1.00000	0.152499
$43$	1.00000	0.152499
$44$	1.00000	0.150756
$45$	2.15090	0.320638
$46$	2.73904	0.403849
$47$	9.27274	1.35257	0.676284	−	0.736641i	$-0.263589\pi$
$47$	9.27274	1.35257	0.676284	+	0.736641i	$0.263589\pi$
$48$	0.921464	0.133002
$49$	7.76033	1.10862
$50$	1.00000	0.141421
$51$	4.13708	0.579306
$52$	3.36077	0.466054
$53$	12.6401	1.73625	0.868127	−	0.496343i	$-0.165324\pi$
$53$	12.6401	1.73625	0.868127	+	0.496343i	$0.165324\pi$
$54$	−4.74637	−0.645899
$55$	−1.00000	−0.134840
$56$	−3.84192	−0.513398
$57$	−6.03547	−0.799417
$58$	2.61423	0.343266
$59$	12.5429	1.63294	0.816470	−	0.577388i	$-0.195928\pi$
$59$	12.5429	1.63294	0.816470	+	0.577388i	$0.195928\pi$
$60$	−0.921464	−0.118960
$61$	−9.61487	−1.23106	−0.615529	−	0.788114i	$-0.711057\pi$
$61$	−9.61487	−1.23106	−0.615529	+	0.788114i	$0.711057\pi$
$62$	−0.588567	−0.0747481
$63$	8.26360	1.04112
$64$	1.00000	0.125000
$65$	−3.36077	−0.416852
$66$	0.921464	0.113424
$67$	−8.11130	−0.990953	−0.495477	−	0.868621i	$-0.665007\pi$
$67$	−8.11130	−0.990953	−0.495477	+	0.868621i	$0.665007\pi$
$68$	4.48968	0.544453
$69$	2.52392	0.303845
$70$	3.84192	0.459197
$71$	−10.4421	−1.23925	−0.619624	−	0.784898i	$-0.712715\pi$
$71$	−10.4421	−1.23925	−0.619624	+	0.784898i	$0.712715\pi$
$72$	−2.15090	−0.253487
$73$	11.8631	1.38848	0.694238	−	0.719746i	$-0.255742\pi$
$73$	11.8631	1.38848	0.694238	+	0.719746i	$0.255742\pi$
$74$	−0.240321	−0.0279367
$75$	0.921464	0.106401
$76$	−6.54987	−0.751322
$77$	−3.84192	−0.437827
$78$	3.09682	0.350646
$79$	5.98496	0.673360	0.336680	−	0.941619i	$-0.390696\pi$
$79$	5.98496	0.673360	0.336680	+	0.941619i	$0.390696\pi$
$80$	−1.00000	−0.111803
$81$	2.07910	0.231012
$82$	10.0856	1.11377
$83$	8.56754	0.940410	0.470205	−	0.882557i	$-0.344180\pi$
$83$	8.56754	0.940410	0.470205	+	0.882557i	$0.344180\pi$
$84$	−3.54019	−0.386266
$85$	−4.48968	−0.486974
$86$	1.00000	0.107833
$87$	2.40892	0.258264
$88$	1.00000	0.106600
$89$	13.9559	1.47933	0.739664	−	0.672977i	$-0.234985\pi$
$89$	13.9559	1.47933	0.739664	+	0.672977i	$0.234985\pi$
$90$	2.15090	0.226725
$91$	−12.9118	−1.35352
$92$	2.73904	0.285564
$93$	−0.542343	−0.0562384
$94$	9.27274	0.956410
$95$	6.54987	0.672003
$96$	0.921464	0.0940465
$97$	−8.94728	−0.908458	−0.454229	−	0.890885i	$-0.650085\pi$
$97$	−8.94728	−0.908458	−0.454229	+	0.890885i	$0.650085\pi$
$98$	7.76033	0.783911
$99$	−2.15090	−0.216174
$100$	1.00000	0.100000
$101$	6.76897	0.673538	0.336769	−	0.941587i	$-0.390666\pi$
$101$	6.76897	0.673538	0.336769	+	0.941587i	$0.390666\pi$
$102$	4.13708	0.409632
$103$	−11.8563	−1.16824	−0.584119	−	0.811668i	$-0.698560\pi$
$103$	−11.8563	−1.16824	−0.584119	+	0.811668i	$0.698560\pi$
$104$	3.36077	0.329550
$105$	3.54019	0.345487
$106$	12.6401	1.22772
$107$	−15.8462	−1.53191	−0.765956	−	0.642893i	$-0.777734\pi$
$107$	−15.8462	−1.53191	−0.765956	+	0.642893i	$0.777734\pi$
$108$	−4.74637	−0.456720
$109$	−9.86228	−0.944635	−0.472318	−	0.881428i	$-0.656582\pi$
$109$	−9.86228	−0.944635	−0.472318	+	0.881428i	$0.656582\pi$
$110$	−1.00000	−0.0953463
$111$	−0.221447	−0.0210188
$112$	−3.84192	−0.363027
$113$	11.1604	1.04988	0.524942	−	0.851138i	$-0.324087\pi$
$113$	11.1604	1.04988	0.524942	+	0.851138i	$0.324087\pi$
$114$	−6.03547	−0.565273
$115$	−2.73904	−0.255416
$116$	2.61423	0.242726
$117$	−7.22869	−0.668292
$118$	12.5429	1.15466
$119$	−17.2490	−1.58121
$120$	−0.921464	−0.0841177
$121$	1.00000	0.0909091
$122$	−9.61487	−0.870489
$123$	9.29355	0.837971
$124$	−0.588567	−0.0528549
$125$	−1.00000	−0.0894427
$126$	8.26360	0.736180
$127$	20.5175	1.82064	0.910318	−	0.413909i	$-0.135837\pi$
$127$	20.5175	1.82064	0.910318	+	0.413909i	$0.135837\pi$
$128$	1.00000	0.0883883
$129$	0.921464	0.0811304
$130$	−3.36077	−0.294759
$131$	−9.26132	−0.809166	−0.404583	−	0.914501i	$-0.632583\pi$
$131$	−9.26132	−0.809166	−0.404583	+	0.914501i	$0.632583\pi$
$132$	0.921464	0.0802031
$133$	25.1641	2.18200
$134$	−8.11130	−0.700710
$135$	4.74637	0.408503
$136$	4.48968	0.384987
$137$	20.5662	1.75709	0.878545	−	0.477659i	$-0.158515\pi$
$137$	20.5662	1.75709	0.878545	+	0.477659i	$0.158515\pi$
$138$	2.52392	0.214851
$139$	−9.86057	−0.836362	−0.418181	−	0.908364i	$-0.637332\pi$
$139$	−9.86057	−0.836362	−0.418181	+	0.908364i	$0.637332\pi$
$140$	3.84192	0.324701
$141$	8.54449	0.719576
$142$	−10.4421	−0.876281
$143$	3.36077	0.281041
$144$	−2.15090	−0.179242
$145$	−2.61423	−0.217100
$146$	11.8631	0.981800
$147$	7.15086	0.589793
$148$	−0.240321	−0.0197543
$149$	4.43344	0.363201	0.181601	−	0.983372i	$-0.441872\pi$
$149$	4.43344	0.363201	0.181601	+	0.983372i	$0.441872\pi$
$150$	0.921464	0.0752372
$151$	18.0595	1.46966	0.734832	−	0.678250i	$-0.237261\pi$
$151$	18.0595	1.46966	0.734832	+	0.678250i	$0.237261\pi$
$152$	−6.54987	−0.531265
$153$	−9.65687	−0.780712
$154$	−3.84192	−0.309590
$155$	0.588567	0.0472749
$156$	3.09682	0.247944
$157$	19.0697	1.52193	0.760965	−	0.648793i	$-0.224726\pi$
$157$	19.0697	1.52193	0.760965	+	0.648793i	$0.224726\pi$
$158$	5.98496	0.476138
$159$	11.6474	0.923699
$160$	−1.00000	−0.0790569
$161$	−10.5231	−0.829340
$162$	2.07910	0.163350
$163$	−11.5905	−0.907835	−0.453917	−	0.891044i	$-0.649974\pi$
$163$	−11.5905	−0.907835	−0.453917	+	0.891044i	$0.649974\pi$
$164$	10.0856	0.787556
$165$	−0.921464	−0.0717359
$166$	8.56754	0.664970
$167$	6.33426	0.490160	0.245080	−	0.969503i	$-0.421186\pi$
$167$	6.33426	0.490160	0.245080	+	0.969503i	$0.421186\pi$
$168$	−3.54019	−0.273131
$169$	−1.70526	−0.131174
$170$	−4.48968	−0.344343
$171$	14.0881	1.07735
$172$	1.00000	0.0762493
$173$	−2.54982	−0.193860	−0.0969298	−	0.995291i	$-0.530902\pi$
$173$	−2.54982	−0.193860	−0.0969298	+	0.995291i	$0.530902\pi$
$174$	2.40892	0.182620
$175$	−3.84192	−0.290422
$176$	1.00000	0.0753778
$177$	11.5578	0.868736
$178$	13.9559	1.04604
$179$	−6.35898	−0.475293	−0.237646	−	0.971352i	$-0.576376\pi$
$179$	−6.35898	−0.475293	−0.237646	+	0.971352i	$0.576376\pi$
$180$	2.15090	0.160319
$181$	4.96116	0.368760	0.184380	−	0.982855i	$-0.440972\pi$
$181$	4.96116	0.368760	0.184380	+	0.982855i	$0.440972\pi$
$182$	−12.9118	−0.957085
$183$	−8.85975	−0.654932
$184$	2.73904	0.201924
$185$	0.240321	0.0176687
$186$	−0.542343	−0.0397665
$187$	4.48968	0.328318
$188$	9.27274	0.676284
$189$	18.2352	1.32641
$190$	6.54987	0.475178
$191$	2.82460	0.204381	0.102190	−	0.994765i	$-0.467415\pi$
$191$	2.82460	0.204381	0.102190	+	0.994765i	$0.467415\pi$
$192$	0.921464	0.0665009
$193$	−0.714821	−0.0514540	−0.0257270	−	0.999669i	$-0.508190\pi$
$193$	−0.714821	−0.0514540	−0.0257270	+	0.999669i	$0.508190\pi$
$194$	−8.94728	−0.642377
$195$	−3.09682	−0.221768
$196$	7.76033	0.554309
$197$	−8.23931	−0.587026	−0.293513	−	0.955955i	$-0.594824\pi$
$197$	−8.23931	−0.587026	−0.293513	+	0.955955i	$0.594824\pi$
$198$	−2.15090	−0.152858
$199$	−9.90281	−0.701991	−0.350996	−	0.936377i	$-0.614157\pi$
$199$	−9.90281	−0.701991	−0.350996	+	0.936377i	$0.614157\pi$
$200$	1.00000	0.0707107
$201$	−7.47427	−0.527194
$202$	6.76897	0.476263
$203$	−10.0437	−0.704928
$204$	4.13708	0.289653
$205$	−10.0856	−0.704411
$206$	−11.8563	−0.826069
$207$	−5.89140	−0.409481
$208$	3.36077	0.233027
$209$	−6.54987	−0.453064
$210$	3.54019	0.244296
$211$	−14.6306	−1.00722	−0.503608	−	0.863933i	$-0.667994\pi$
$211$	−14.6306	−1.00722	−0.503608	+	0.863933i	$0.667994\pi$
$212$	12.6401	0.868127
$213$	−9.62201	−0.659289
$214$	−15.8462	−1.08322
$215$	−1.00000	−0.0681994
$216$	−4.74637	−0.322950
$217$	2.26123	0.153502
$218$	−9.86228	−0.667958
$219$	10.9315	0.738679
$220$	−1.00000	−0.0674200
$221$	15.0888	1.01498
$222$	−0.221447	−0.0148626
$223$	16.2067	1.08528	0.542639	−	0.839966i	$-0.317425\pi$
$223$	16.2067	1.08528	0.542639	+	0.839966i	$0.317425\pi$
$224$	−3.84192	−0.256699
$225$	−2.15090	−0.143394
$226$	11.1604	0.742381
$227$	−7.28678	−0.483640	−0.241820	−	0.970321i	$-0.577744\pi$
$227$	−7.28678	−0.483640	−0.241820	+	0.970321i	$0.577744\pi$
$228$	−6.03547	−0.399709
$229$	−7.26471	−0.480065	−0.240033	−	0.970765i	$-0.577158\pi$
$229$	−7.26471	−0.480065	−0.240033	+	0.970765i	$0.577158\pi$
$230$	−2.73904	−0.180607
$231$	−3.54019	−0.232927
$232$	2.61423	0.171633
$233$	19.0465	1.24778	0.623890	−	0.781512i	$-0.285551\pi$
$233$	19.0465	1.24778	0.623890	+	0.781512i	$0.285551\pi$
$234$	−7.22869	−0.472554
$235$	−9.27274	−0.604887
$236$	12.5429	0.816470
$237$	5.51492	0.358233
$238$	−17.2490	−1.11808
$239$	8.88667	0.574831	0.287416	−	0.957806i	$-0.407204\pi$
$239$	8.88667	0.574831	0.287416	+	0.957806i	$0.407204\pi$
$240$	−0.921464	−0.0594802
$241$	2.76143	0.177880	0.0889398	−	0.996037i	$-0.471652\pi$
$241$	2.76143	0.177880	0.0889398	+	0.996037i	$0.471652\pi$
$242$	1.00000	0.0642824
$243$	16.1549	1.03634
$244$	−9.61487	−0.615529
$245$	−7.76033	−0.495789
$246$	9.29355	0.592535
$247$	−22.0126	−1.40063
$248$	−0.588567	−0.0373741
$249$	7.89468	0.500305
$250$	−1.00000	−0.0632456
$251$	2.07731	0.131118	0.0655592	−	0.997849i	$-0.479117\pi$
$251$	2.07731	0.131118	0.0655592	+	0.997849i	$0.479117\pi$
$252$	8.26360	0.520558
$253$	2.73904	0.172202
$254$	20.5175	1.28738
$255$	−4.13708	−0.259074
$256$	1.00000	0.0625000
$257$	−18.3451	−1.14434	−0.572168	−	0.820137i	$-0.693897\pi$
$257$	−18.3451	−1.14434	−0.572168	+	0.820137i	$0.693897\pi$
$258$	0.921464	0.0573678
$259$	0.923293	0.0573706
$260$	−3.36077	−0.208426
$261$	−5.62297	−0.348053
$262$	−9.26132	−0.572167
$263$	12.4911	0.770237	0.385119	−	0.922867i	$-0.374161\pi$
$263$	12.4911	0.770237	0.385119	+	0.922867i	$0.374161\pi$
$264$	0.921464	0.0567122
$265$	−12.6401	−0.776476
$266$	25.1641	1.54291
$267$	12.8599	0.787013
$268$	−8.11130	−0.495477
$269$	27.5872	1.68202	0.841010	−	0.541020i	$-0.181962\pi$
$269$	27.5872	1.68202	0.841010	+	0.541020i	$0.181962\pi$
$270$	4.74637	0.288855
$271$	16.8218	1.02185	0.510927	−	0.859624i	$-0.329302\pi$
$271$	16.8218	1.02185	0.510927	+	0.859624i	$0.329302\pi$
$272$	4.48968	0.272227
$273$	−11.8977	−0.720084
$274$	20.5662	1.24245
$275$	1.00000	0.0603023
$276$	2.52392	0.151922
$277$	−25.2847	−1.51921	−0.759607	−	0.650383i	$-0.774608\pi$
$277$	−25.2847	−1.51921	−0.759607	+	0.650383i	$0.774608\pi$
$278$	−9.86057	−0.591397
$279$	1.26595	0.0757906
$280$	3.84192	0.229598
$281$	−6.07659	−0.362499	−0.181250	−	0.983437i	$-0.558014\pi$
$281$	−6.07659	−0.362499	−0.181250	+	0.983437i	$0.558014\pi$
$282$	8.54449	0.508817
$283$	25.4783	1.51453	0.757265	−	0.653108i	$-0.226535\pi$
$283$	25.4783	1.51453	0.757265	+	0.653108i	$0.226535\pi$
$284$	−10.4421	−0.619624
$285$	6.03547	0.357510
$286$	3.36077	0.198726
$287$	−38.7482	−2.28723
$288$	−2.15090	−0.126743
$289$	3.15721	0.185718
$290$	−2.61423	−0.153513
$291$	−8.24459	−0.483306
$292$	11.8631	0.694238
$293$	−5.56061	−0.324854	−0.162427	−	0.986721i	$-0.551932\pi$
$293$	−5.56061	−0.324854	−0.162427	+	0.986721i	$0.551932\pi$
$294$	7.15086	0.417047
$295$	−12.5429	−0.730273
$296$	−0.240321	−0.0139684
$297$	−4.74637	−0.275412
$298$	4.43344	0.256822
$299$	9.20526	0.532354
$300$	0.921464	0.0532007
$301$	−3.84192	−0.221444
$302$	18.0595	1.03921
$303$	6.23736	0.358327
$304$	−6.54987	−0.375661
$305$	9.61487	0.550546
$306$	−9.65687	−0.552046
$307$	−21.8905	−1.24936	−0.624680	−	0.780881i	$-0.714770\pi$
$307$	−21.8905	−1.24936	−0.624680	+	0.780881i	$0.714770\pi$
$308$	−3.84192	−0.218914
$309$	−10.9252	−0.621511
$310$	0.588567	0.0334284
$311$	−3.49295	−0.198067	−0.0990337	−	0.995084i	$-0.531575\pi$
$311$	−3.49295	−0.198067	−0.0990337	+	0.995084i	$0.531575\pi$
$312$	3.09682	0.175323
$313$	−33.6717	−1.90324	−0.951618	−	0.307282i	$-0.900580\pi$
$313$	−33.6717	−1.90324	−0.951618	+	0.307282i	$0.900580\pi$
$314$	19.0697	1.07617
$315$	−8.26360	−0.465601
$316$	5.98496	0.336680
$317$	−18.5042	−1.03930	−0.519650	−	0.854379i	$-0.673938\pi$
$317$	−18.5042	−1.03930	−0.519650	+	0.854379i	$0.673938\pi$
$318$	11.6474	0.653154
$319$	2.61423	0.146369
$320$	−1.00000	−0.0559017
$321$	−14.6017	−0.814988
$322$	−10.5231	−0.586432
$323$	−29.4068	−1.63624
$324$	2.07910	0.115506
$325$	3.36077	0.186422
$326$	−11.5905	−0.641936
$327$	−9.08773	−0.502553
$328$	10.0856	0.556886
$329$	−35.6251	−1.96408
$330$	−0.921464	−0.0507249
$331$	13.8933	0.763646	0.381823	−	0.924235i	$-0.375296\pi$
$331$	13.8933	0.763646	0.381823	+	0.924235i	$0.375296\pi$
$332$	8.56754	0.470205
$333$	0.516907	0.0283264
$334$	6.33426	0.346595
$335$	8.11130	0.443168
$336$	−3.54019	−0.193133
$337$	5.09506	0.277546	0.138773	−	0.990324i	$-0.455684\pi$
$337$	5.09506	0.277546	0.138773	+	0.990324i	$0.455684\pi$
$338$	−1.70526	−0.0927537
$339$	10.2839	0.558546
$340$	−4.48968	−0.243487
$341$	−0.588567	−0.0318727
$342$	14.0881	0.761800
$343$	−2.92111	−0.157725
$344$	1.00000	0.0539164
$345$	−2.52392	−0.135883
$346$	−2.54982	−0.137079
$347$	−27.6747	−1.48565	−0.742827	−	0.669483i	$-0.766516\pi$
$347$	−27.6747	−1.48565	−0.742827	+	0.669483i	$0.766516\pi$
$348$	2.40892	0.129132
$349$	5.36885	0.287388	0.143694	−	0.989622i	$-0.454102\pi$
$349$	5.36885	0.287388	0.143694	+	0.989622i	$0.454102\pi$
$350$	−3.84192	−0.205359
$351$	−15.9514	−0.851425
$352$	1.00000	0.0533002
$353$	−24.2743	−1.29199	−0.645996	−	0.763341i	$-0.723558\pi$
$353$	−24.2743	−1.29199	−0.645996	+	0.763341i	$0.723558\pi$
$354$	11.5578	0.614289
$355$	10.4421	0.554209
$356$	13.9559	0.739664
$357$	−15.8943	−0.841216
$358$	−6.35898	−0.336083
$359$	11.0758	0.584559	0.292280	−	0.956333i	$-0.405586\pi$
$359$	11.0758	0.584559	0.292280	+	0.956333i	$0.405586\pi$
$360$	2.15090	0.113363
$361$	23.9008	1.25794
$362$	4.96116	0.260753
$363$	0.921464	0.0483643
$364$	−12.9118	−0.676761
$365$	−11.8631	−0.620945
$366$	−8.85975	−0.463107
$367$	−0.627963	−0.0327794	−0.0163897	−	0.999866i	$-0.505217\pi$
$367$	−0.627963	−0.0327794	−0.0163897	+	0.999866i	$0.505217\pi$
$368$	2.73904	0.142782
$369$	−21.6932	−1.12930
$370$	0.240321	0.0124937
$371$	−48.5623	−2.52123
$372$	−0.542343	−0.0281192
$373$	−34.8731	−1.80566	−0.902830	−	0.429999i	$-0.858514\pi$
$373$	−34.8731	−1.80566	−0.902830	+	0.429999i	$0.858514\pi$
$374$	4.48968	0.232156
$375$	−0.921464	−0.0475842
$376$	9.27274	0.478205
$377$	8.78583	0.452493
$378$	18.2352	0.937916
$379$	19.7139	1.01264	0.506318	−	0.862347i	$-0.331006\pi$
$379$	19.7139	1.01264	0.506318	+	0.862347i	$0.331006\pi$
$380$	6.54987	0.336001
$381$	18.9062	0.968592
$382$	2.82460	0.144519
$383$	−32.6656	−1.66914	−0.834568	−	0.550906i	$-0.814282\pi$
$383$	−32.6656	−1.66914	−0.834568	+	0.550906i	$0.814282\pi$
$384$	0.921464	0.0470232
$385$	3.84192	0.195802
$386$	−0.714821	−0.0363834
$387$	−2.15090	−0.109337
$388$	−8.94728	−0.454229
$389$	13.0008	0.659164	0.329582	−	0.944127i	$-0.393092\pi$
$389$	13.0008	0.659164	0.329582	+	0.944127i	$0.393092\pi$
$390$	−3.09682	−0.156814
$391$	12.2974	0.621906
$392$	7.76033	0.391956
$393$	−8.53397	−0.430482
$394$	−8.23931	−0.415090
$395$	−5.98496	−0.301136
$396$	−2.15090	−0.108087
$397$	7.23835	0.363282	0.181641	−	0.983365i	$-0.441859\pi$
$397$	7.23835	0.363282	0.181641	+	0.983365i	$0.441859\pi$
$398$	−9.90281	−0.496383
$399$	23.1878	1.16084
$400$	1.00000	0.0500000
$401$	25.5243	1.27462	0.637312	−	0.770606i	$-0.280046\pi$
$401$	25.5243	1.27462	0.637312	+	0.770606i	$0.280046\pi$
$402$	−7.47427	−0.372783
$403$	−1.97804	−0.0985330
$404$	6.76897	0.336769
$405$	−2.07910	−0.103312
$406$	−10.0437	−0.498459
$407$	−0.240321	−0.0119123
$408$	4.13708	0.204816
$409$	−8.29621	−0.410221	−0.205111	−	0.978739i	$-0.565755\pi$
$409$	−8.29621	−0.410221	−0.205111	+	0.978739i	$0.565755\pi$
$410$	−10.0856	−0.498094
$411$	18.9510	0.934785
$412$	−11.8563	−0.584119
$413$	−48.1886	−2.37121
$414$	−5.89140	−0.289547
$415$	−8.56754	−0.420564
$416$	3.36077	0.164775
$417$	−9.08615	−0.444951
$418$	−6.54987	−0.320365
$419$	3.75774	0.183578	0.0917888	−	0.995778i	$-0.470742\pi$
$419$	3.75774	0.183578	0.0917888	+	0.995778i	$0.470742\pi$
$420$	3.54019	0.172743
$421$	0.464546	0.0226406	0.0113203	−	0.999936i	$-0.496397\pi$
$421$	0.464546	0.0226406	0.0113203	+	0.999936i	$0.496397\pi$
$422$	−14.6306	−0.712209
$423$	−19.9448	−0.969748
$424$	12.6401	0.613858
$425$	4.48968	0.217781
$426$	−9.62201	−0.466188
$427$	36.9395	1.78763
$428$	−15.8462	−0.765956
$429$	3.09682	0.149516
$430$	−1.00000	−0.0482243
$431$	−23.9618	−1.15420	−0.577099	−	0.816674i	$-0.695815\pi$
$431$	−23.9618	−1.15420	−0.577099	+	0.816674i	$0.695815\pi$
$432$	−4.74637	−0.228360
$433$	−29.5327	−1.41925	−0.709626	−	0.704578i	$-0.751136\pi$
$433$	−29.5327	−1.41925	−0.709626	+	0.704578i	$0.751136\pi$
$434$	2.26123	0.108542
$435$	−2.40892	−0.115499
$436$	−9.86228	−0.472318
$437$	−17.9403	−0.858202
$438$	10.9315	0.522325
$439$	−22.1469	−1.05701	−0.528507	−	0.848929i	$-0.677248\pi$
$439$	−22.1469	−1.05701	−0.528507	+	0.848929i	$0.677248\pi$
$440$	−1.00000	−0.0476731
$441$	−16.6917	−0.794844
$442$	15.0888	0.717699
$443$	37.4638	1.77996	0.889979	−	0.456002i	$-0.150719\pi$
$443$	37.4638	1.77996	0.889979	+	0.456002i	$0.150719\pi$
$444$	−0.221447	−0.0105094
$445$	−13.9559	−0.661575
$446$	16.2067	0.767408
$447$	4.08525	0.193226
$448$	−3.84192	−0.181514
$449$	39.1108	1.84575	0.922875	−	0.385099i	$-0.125833\pi$
$449$	39.1108	1.84575	0.922875	+	0.385099i	$0.125833\pi$
$450$	−2.15090	−0.101395
$451$	10.0856	0.474914
$452$	11.1604	0.524942
$453$	16.6412	0.781872
$454$	−7.28678	−0.341985
$455$	12.9118	0.605314
$456$	−6.03547	−0.282637
$457$	7.77236	0.363576	0.181788	−	0.983338i	$-0.441812\pi$
$457$	7.77236	0.363576	0.181788	+	0.983338i	$0.441812\pi$
$458$	−7.26471	−0.339458
$459$	−21.3097	−0.994651
$460$	−2.73904	−0.127708
$461$	8.64592	0.402680	0.201340	−	0.979521i	$-0.435470\pi$
$461$	8.64592	0.402680	0.201340	+	0.979521i	$0.435470\pi$
$462$	−3.54019	−0.164704
$463$	22.3778	1.03999	0.519993	−	0.854171i	$-0.325935\pi$
$463$	22.3778	1.03999	0.519993	+	0.854171i	$0.325935\pi$
$464$	2.61423	0.121363
$465$	0.542343	0.0251506
$466$	19.0465	0.882314
$467$	25.2601	1.16890	0.584450	−	0.811430i	$-0.301310\pi$
$467$	25.2601	1.16890	0.584450	+	0.811430i	$0.301310\pi$
$468$	−7.22869	−0.334146
$469$	31.1629	1.43897
$470$	−9.27274	−0.427720
$471$	17.5721	0.809678
$472$	12.5429	0.577331
$473$	1.00000	0.0459800
$474$	5.51492	0.253309
$475$	−6.54987	−0.300529
$476$	−17.2490	−0.790605
$477$	−27.1877	−1.24484
$478$	8.88667	0.406467
$479$	24.8707	1.13637	0.568186	−	0.822900i	$-0.307646\pi$
$479$	24.8707	1.13637	0.568186	+	0.822900i	$0.307646\pi$
$480$	−0.921464	−0.0420589
$481$	−0.807662	−0.0368262
$482$	2.76143	0.125780
$483$	−9.69670	−0.441215
$484$	1.00000	0.0454545
$485$	8.94728	0.406275
$486$	16.1549	0.732803
$487$	−15.1078	−0.684598	−0.342299	−	0.939591i	$-0.611206\pi$
$487$	−15.1078	−0.684598	−0.342299	+	0.939591i	$0.611206\pi$
$488$	−9.61487	−0.435245
$489$	−10.6802	−0.482975
$490$	−7.76033	−0.350576
$491$	−20.9423	−0.945114	−0.472557	−	0.881300i	$-0.656669\pi$
$491$	−20.9423	−0.945114	−0.472557	+	0.881300i	$0.656669\pi$
$492$	9.29355	0.418985
$493$	11.7371	0.528611
$494$	−22.0126	−0.990393
$495$	2.15090	0.0966760
$496$	−0.588567	−0.0264274
$497$	40.1177	1.79952
$498$	7.89468	0.353769
$499$	−25.5069	−1.14184	−0.570922	−	0.821004i	$-0.693414\pi$
$499$	−25.5069	−1.14184	−0.570922	+	0.821004i	$0.693414\pi$
$500$	−1.00000	−0.0447214
$501$	5.83679	0.260769
$502$	2.07731	0.0927147
$503$	−10.1492	−0.452532	−0.226266	−	0.974066i	$-0.572652\pi$
$503$	−10.1492	−0.452532	−0.226266	+	0.974066i	$0.572652\pi$
$504$	8.26360	0.368090
$505$	−6.76897	−0.301215
$506$	2.73904	0.121765
$507$	−1.57133	−0.0697853
$508$	20.5175	0.910318
$509$	−31.3909	−1.39138	−0.695689	−	0.718343i	$-0.744901\pi$
$509$	−31.3909	−1.39138	−0.695689	+	0.718343i	$0.744901\pi$
$510$	−4.13708	−0.183193
$511$	−45.5772	−2.01622
$512$	1.00000	0.0441942
$513$	31.0881	1.37257
$514$	−18.3451	−0.809167
$515$	11.8563	0.522452
$516$	0.921464	0.0405652
$517$	9.27274	0.407815
$518$	0.923293	0.0405672
$519$	−2.34957	−0.103135
$520$	−3.36077	−0.147379
$521$	6.33199	0.277409	0.138705	−	0.990334i	$-0.455706\pi$
$521$	6.33199	0.277409	0.138705	+	0.990334i	$0.455706\pi$
$522$	−5.62297	−0.246111
$523$	21.1781	0.926055	0.463027	−	0.886344i	$-0.346763\pi$
$523$	21.1781	0.926055	0.463027	+	0.886344i	$0.346763\pi$
$524$	−9.26132	−0.404583
$525$	−3.54019	−0.154506
$526$	12.4911	0.544640
$527$	−2.64248	−0.115108
$528$	0.921464	0.0401016
$529$	−15.4977	−0.673812
$530$	−12.6401	−0.549051
$531$	−26.9785	−1.17077
$532$	25.1641	1.09100
$533$	33.8954	1.46817
$534$	12.8599	0.556502
$535$	15.8462	0.685092
$536$	−8.11130	−0.350355
$537$	−5.85957	−0.252859
$538$	27.5872	1.18937
$539$	7.76033	0.334261
$540$	4.74637	0.204251
$541$	22.5374	0.968958	0.484479	−	0.874803i	$-0.339009\pi$
$541$	22.5374	0.968958	0.484479	+	0.874803i	$0.339009\pi$
$542$	16.8218	0.722560
$543$	4.57153	0.196183
$544$	4.48968	0.192493
$545$	9.86228	0.422454
$546$	−11.8977	−0.509176
$547$	−3.63414	−0.155384	−0.0776922	−	0.996977i	$-0.524755\pi$
$547$	−3.63414	−0.155384	−0.0776922	+	0.996977i	$0.524755\pi$
$548$	20.5662	0.878545
$549$	20.6807	0.882629
$550$	1.00000	0.0426401
$551$	−17.1229	−0.729460
$552$	2.52392	0.107425
$553$	−22.9937	−0.977792
$554$	−25.2847	−1.07425
$555$	0.221447	0.00939990
$556$	−9.86057	−0.418181
$557$	18.0972	0.766804	0.383402	−	0.923582i	$-0.374752\pi$
$557$	18.0972	0.766804	0.383402	+	0.923582i	$0.374752\pi$
$558$	1.26595	0.0535920
$559$	3.36077	0.142145
$560$	3.84192	0.162351
$561$	4.13708	0.174667
$562$	−6.07659	−0.256326
$563$	−19.0052	−0.800975	−0.400488	−	0.916302i	$-0.631159\pi$
$563$	−19.0052	−0.800975	−0.400488	+	0.916302i	$0.631159\pi$
$564$	8.54449	0.359788
$565$	−11.1604	−0.469523
$566$	25.4783	1.07093
$567$	−7.98775	−0.335454
$568$	−10.4421	−0.438141
$569$	−21.5947	−0.905297	−0.452649	−	0.891689i	$-0.649521\pi$
$569$	−21.5947	−0.905297	−0.452649	+	0.891689i	$0.649521\pi$
$570$	6.03547	0.252798
$571$	−45.5796	−1.90745	−0.953723	−	0.300686i	$-0.902784\pi$
$571$	−45.5796	−1.90745	−0.953723	+	0.300686i	$0.902784\pi$
$572$	3.36077	0.140521
$573$	2.60277	0.108732
$574$	−38.7482	−1.61732
$575$	2.73904	0.114226
$576$	−2.15090	−0.0896210
$577$	−4.24414	−0.176686	−0.0883430	−	0.996090i	$-0.528157\pi$
$577$	−4.24414	−0.176686	−0.0883430	+	0.996090i	$0.528157\pi$
$578$	3.15721	0.131323
$579$	−0.658682	−0.0273739
$580$	−2.61423	−0.108550
$581$	−32.9158	−1.36558
$582$	−8.24459	−0.341749
$583$	12.6401	0.523500
$584$	11.8631	0.490900
$585$	7.22869	0.298869
$586$	−5.56061	−0.229707
$587$	0.406717	0.0167870	0.00839351	−	0.999965i	$-0.497328\pi$
$587$	0.406717	0.0167870	0.00839351	+	0.999965i	$0.497328\pi$
$588$	7.15086	0.294896
$589$	3.85504	0.158844
$590$	−12.5429	−0.516381
$591$	−7.59222	−0.312302
$592$	−0.240321	−0.00987713
$593$	24.2297	0.994993	0.497497	−	0.867466i	$-0.334253\pi$
$593$	24.2297	0.994993	0.497497	+	0.867466i	$0.334253\pi$
$594$	−4.74637	−0.194746
$595$	17.2490	0.707139
$596$	4.43344	0.181601
$597$	−9.12508	−0.373465
$598$	9.20526	0.376431
$599$	31.8343	1.30072	0.650358	−	0.759628i	$-0.274619\pi$
$599$	31.8343	1.30072	0.650358	+	0.759628i	$0.274619\pi$
$600$	0.921464	0.0376186
$601$	23.6792	0.965894	0.482947	−	0.875650i	$-0.339566\pi$
$601$	23.6792	0.965894	0.482947	+	0.875650i	$0.339566\pi$
$602$	−3.84192	−0.156585
$603$	17.4466	0.710482
$604$	18.0595	0.734832
$605$	−1.00000	−0.0406558
$606$	6.23736	0.253375
$607$	17.8004	0.722497	0.361249	−	0.932470i	$-0.382351\pi$
$607$	17.8004	0.722497	0.361249	+	0.932470i	$0.382351\pi$
$608$	−6.54987	−0.265632
$609$	−9.25488	−0.375027
$610$	9.61487	0.389295
$611$	31.1635	1.26074
$612$	−9.65687	−0.390356
$613$	1.56785	0.0633247	0.0316624	−	0.999499i	$-0.489920\pi$
$613$	1.56785	0.0633247	0.0316624	+	0.999499i	$0.489920\pi$
$614$	−21.8905	−0.883431
$615$	−9.29355	−0.374752
$616$	−3.84192	−0.154795
$617$	−11.8883	−0.478605	−0.239302	−	0.970945i	$-0.576919\pi$
$617$	−11.8883	−0.478605	−0.239302	+	0.970945i	$0.576919\pi$
$618$	−10.9252	−0.439475
$619$	−22.1870	−0.891772	−0.445886	−	0.895090i	$-0.647111\pi$
$619$	−22.1870	−0.891772	−0.445886	+	0.895090i	$0.647111\pi$
$620$	0.588567	0.0236374
$621$	−13.0005	−0.521691
$622$	−3.49295	−0.140055
$623$	−53.6176	−2.14814
$624$	3.09682	0.123972
$625$	1.00000	0.0400000
$626$	−33.6717	−1.34579
$627$	−6.03547	−0.241033
$628$	19.0697	0.760965
$629$	−1.07896	−0.0430211
$630$	−8.26360	−0.329230
$631$	29.8463	1.18816	0.594081	−	0.804405i	$-0.297516\pi$
$631$	29.8463	1.18816	0.594081	+	0.804405i	$0.297516\pi$
$632$	5.98496	0.238069
$633$	−13.4816	−0.535846
$634$	−18.5042	−0.734896
$635$	−20.5175	−0.814213
$636$	11.6474	0.461850
$637$	26.0806	1.03335
$638$	2.61423	0.103499
$639$	22.4600	0.888502
$640$	−1.00000	−0.0395285
$641$	0.667023	0.0263458	0.0131729	−	0.999913i	$-0.495807\pi$
$641$	0.667023	0.0263458	0.0131729	+	0.999913i	$0.495807\pi$
$642$	−14.6017	−0.576284
$643$	46.1975	1.82185	0.910926	−	0.412570i	$-0.135369\pi$
$643$	46.1975	1.82185	0.910926	+	0.412570i	$0.135369\pi$
$644$	−10.5231	−0.414670
$645$	−0.921464	−0.0362826
$646$	−29.4068	−1.15700
$647$	11.9147	0.468415	0.234207	−	0.972187i	$-0.424751\pi$
$647$	11.9147	0.468415	0.234207	+	0.972187i	$0.424751\pi$
$648$	2.07910	0.0816749
$649$	12.5429	0.492350
$650$	3.36077	0.131820
$651$	2.08364	0.0816642
$652$	−11.5905	−0.453917
$653$	29.0362	1.13627	0.568137	−	0.822934i	$-0.307664\pi$
$653$	29.0362	1.13627	0.568137	+	0.822934i	$0.307664\pi$
$654$	−9.08773	−0.355358
$655$	9.26132	0.361870
$656$	10.0856	0.393778
$657$	−25.5165	−0.995493
$658$	−35.6251	−1.38881
$659$	19.8186	0.772023	0.386011	−	0.922494i	$-0.373853\pi$
$659$	19.8186	0.772023	0.386011	+	0.922494i	$0.373853\pi$
$660$	−0.921464	−0.0358679
$661$	−13.0120	−0.506108	−0.253054	−	0.967452i	$-0.581435\pi$
$661$	−13.0120	−0.506108	−0.253054	+	0.967452i	$0.581435\pi$
$662$	13.8933	0.539979
$663$	13.9037	0.539977
$664$	8.56754	0.332485
$665$	−25.1641	−0.975820
$666$	0.516907	0.0200298
$667$	7.16048	0.277255
$668$	6.33426	0.245080
$669$	14.9339	0.577376
$670$	8.11130	0.313367
$671$	−9.61487	−0.371178
$672$	−3.54019	−0.136566
$673$	−26.7712	−1.03195	−0.515977	−	0.856602i	$-0.672571\pi$
$673$	−26.7712	−1.03195	−0.515977	+	0.856602i	$0.672571\pi$
$674$	5.09506	0.196254
$675$	−4.74637	−0.182688
$676$	−1.70526	−0.0655868
$677$	−9.86767	−0.379245	−0.189623	−	0.981857i	$-0.560726\pi$
$677$	−9.86767	−0.379245	−0.189623	+	0.981857i	$0.560726\pi$
$678$	10.2839	0.394952
$679$	34.3747	1.31918
$680$	−4.48968	−0.172171
$681$	−6.71450	−0.257300
$682$	−0.588567	−0.0225374
$683$	18.8993	0.723163	0.361581	−	0.932341i	$-0.382237\pi$
$683$	18.8993	0.723163	0.361581	+	0.932341i	$0.382237\pi$
$684$	14.0881	0.538674
$685$	−20.5662	−0.785795
$686$	−2.92111	−0.111528
$687$	−6.69417	−0.255398
$688$	1.00000	0.0381246
$689$	42.4805	1.61838
$690$	−2.52392	−0.0960841
$691$	−18.8426	−0.716805	−0.358402	−	0.933567i	$-0.616678\pi$
$691$	−18.8426	−0.716805	−0.358402	+	0.933567i	$0.616678\pi$
$692$	−2.54982	−0.0969298
$693$	8.26360	0.313908
$694$	−27.6747	−1.05052
$695$	9.86057	0.374033
$696$	2.40892	0.0913100
$697$	45.2812	1.71515
$698$	5.36885	0.203214
$699$	17.5507	0.663829
$700$	−3.84192	−0.145211
$701$	−28.3200	−1.06963	−0.534816	−	0.844969i	$-0.679619\pi$
$701$	−28.3200	−1.06963	−0.534816	+	0.844969i	$0.679619\pi$
$702$	−15.9514	−0.602048
$703$	1.57407	0.0593672
$704$	1.00000	0.0376889
$705$	−8.54449	−0.321804
$706$	−24.2743	−0.913576
$707$	−26.0058	−0.978050
$708$	11.5578	0.434368
$709$	30.6657	1.15167	0.575837	−	0.817564i	$-0.304676\pi$
$709$	30.6657	1.15167	0.575837	+	0.817564i	$0.304676\pi$
$710$	10.4421	0.391885
$711$	−12.8731	−0.482778
$712$	13.9559	0.523021
$713$	−1.61211	−0.0603739
$714$	−15.8943	−0.594829
$715$	−3.36077	−0.125685
$716$	−6.35898	−0.237646
$717$	8.18875	0.305814
$718$	11.0758	0.413346
$719$	8.13201	0.303273	0.151636	−	0.988436i	$-0.451546\pi$
$719$	8.13201	0.303273	0.151636	+	0.988436i	$0.451546\pi$
$720$	2.15090	0.0801595
$721$	45.5510	1.69641
$722$	23.9008	0.889496
$723$	2.54456	0.0946332
$724$	4.96116	0.184380
$725$	2.61423	0.0970902
$726$	0.921464	0.0341987
$727$	−51.9357	−1.92619	−0.963094	−	0.269166i	$-0.913252\pi$
$727$	−51.9357	−1.92619	−0.963094	+	0.269166i	$0.913252\pi$
$728$	−12.9118	−0.478542
$729$	8.64887	0.320329
$730$	−11.8631	−0.439074
$731$	4.48968	0.166057
$732$	−8.85975	−0.327466
$733$	−25.6325	−0.946758	−0.473379	−	0.880859i	$-0.656966\pi$
$733$	−25.6325	−0.946758	−0.473379	+	0.880859i	$0.656966\pi$
$734$	−0.627963	−0.0231785
$735$	−7.15086	−0.263763
$736$	2.73904	0.100962
$737$	−8.11130	−0.298784
$738$	−21.6932	−0.798539
$739$	25.0386	0.921060	0.460530	−	0.887644i	$-0.347659\pi$
$739$	25.0386	0.921060	0.460530	+	0.887644i	$0.347659\pi$
$740$	0.240321	0.00883437
$741$	−20.2838	−0.745144
$742$	−48.5623	−1.78278
$743$	−44.8111	−1.64396	−0.821980	−	0.569517i	$-0.807130\pi$
$743$	−44.8111	−1.64396	−0.821980	+	0.569517i	$0.807130\pi$
$744$	−0.542343	−0.0198833
$745$	−4.43344	−0.162429
$746$	−34.8731	−1.27679
$747$	−18.4280	−0.674244
$748$	4.48968	0.164159
$749$	60.8798	2.22450
$750$	−0.921464	−0.0336471
$751$	−11.6909	−0.426605	−0.213303	−	0.976986i	$-0.568422\pi$
$751$	−11.6909	−0.426605	−0.213303	+	0.976986i	$0.568422\pi$
$752$	9.27274	0.338142
$753$	1.91416	0.0697559
$754$	8.78583	0.319961
$755$	−18.0595	−0.657253
$756$	18.2352	0.663207
$757$	−16.0482	−0.583281	−0.291640	−	0.956528i	$-0.594201\pi$
$757$	−16.0482	−0.583281	−0.291640	+	0.956528i	$0.594201\pi$
$758$	19.7139	0.716042
$759$	2.52392	0.0916126
$760$	6.54987	0.237589
$761$	11.6821	0.423474	0.211737	−	0.977327i	$-0.432088\pi$
$761$	11.6821	0.423474	0.211737	+	0.977327i	$0.432088\pi$
$762$	18.9062	0.684898
$763$	37.8901	1.37171
$764$	2.82460	0.102190
$765$	9.65687	0.349145
$766$	−32.6656	−1.18026
$767$	42.1536	1.52208
$768$	0.921464	0.0332505
$769$	−52.4264	−1.89055	−0.945273	−	0.326281i	$-0.894204\pi$
$769$	−52.4264	−1.89055	−0.945273	+	0.326281i	$0.894204\pi$
$770$	3.84192	0.138453
$771$	−16.9043	−0.608795
$772$	−0.714821	−0.0257270
$773$	−23.2049	−0.834622	−0.417311	−	0.908764i	$-0.637027\pi$
$773$	−23.2049	−0.834622	−0.417311	+	0.908764i	$0.637027\pi$
$774$	−2.15090	−0.0773127
$775$	−0.588567	−0.0211420
$776$	−8.94728	−0.321189
$777$	0.850781	0.0305216
$778$	13.0008	0.466100
$779$	−66.0596	−2.36683
$780$	−3.09682	−0.110884
$781$	−10.4421	−0.373648
$782$	12.2974	0.439754
$783$	−12.4081	−0.443430
$784$	7.76033	0.277154
$785$	−19.0697	−0.680628
$786$	−8.53397	−0.304397
$787$	22.4183	0.799126	0.399563	−	0.916706i	$-0.369162\pi$
$787$	22.4183	0.799126	0.399563	+	0.916706i	$0.369162\pi$
$788$	−8.23931	−0.293513
$789$	11.5101	0.409772
$790$	−5.98496	−0.212935
$791$	−42.8774	−1.52455
$792$	−2.15090	−0.0764291
$793$	−32.3133	−1.14748
$794$	7.23835	0.256879
$795$	−11.6474	−0.413091
$796$	−9.90281	−0.350996
$797$	30.7866	1.09052	0.545259	−	0.838267i	$-0.316431\pi$
$797$	30.7866	1.09052	0.545259	+	0.838267i	$0.316431\pi$
$798$	23.1878	0.820838
$799$	41.6316	1.47282
$800$	1.00000	0.0353553
$801$	−30.0179	−1.06063
$802$	25.5243	0.901295
$803$	11.8631	0.418641
$804$	−7.47427	−0.263597
$805$	10.5231	0.370892
$806$	−1.97804	−0.0696733
$807$	25.4206	0.894847
$808$	6.76897	0.238132
$809$	3.76887	0.132506	0.0662532	−	0.997803i	$-0.478895\pi$
$809$	3.76887	0.132506	0.0662532	+	0.997803i	$0.478895\pi$
$810$	−2.07910	−0.0730523
$811$	2.67036	0.0937691	0.0468846	−	0.998900i	$-0.485071\pi$
$811$	2.67036	0.0937691	0.0468846	+	0.998900i	$0.485071\pi$
$812$	−10.0437	−0.352464
$813$	15.5007	0.543634
$814$	−0.240321	−0.00842324
$815$	11.5905	0.405996
$816$	4.13708	0.144827
$817$	−6.54987	−0.229151
$818$	−8.29621	−0.290070
$819$	27.7720	0.970433
$820$	−10.0856	−0.352206
$821$	2.90152	0.101264	0.0506320	−	0.998717i	$-0.483876\pi$
$821$	2.90152	0.101264	0.0506320	+	0.998717i	$0.483876\pi$
$822$	18.9510	0.660993
$823$	39.2886	1.36952	0.684758	−	0.728771i	$-0.259908\pi$
$823$	39.2886	1.36952	0.684758	+	0.728771i	$0.259908\pi$
$824$	−11.8563	−0.413034
$825$	0.921464	0.0320812
$826$	−48.1886	−1.67670
$827$	−24.0062	−0.834776	−0.417388	−	0.908728i	$-0.637054\pi$
$827$	−24.0062	−0.834776	−0.417388	+	0.908728i	$0.637054\pi$
$828$	−5.89140	−0.204740
$829$	37.6561	1.30785	0.653925	−	0.756559i	$-0.273121\pi$
$829$	37.6561	1.30785	0.653925	+	0.756559i	$0.273121\pi$
$830$	−8.56754	−0.297384
$831$	−23.2990	−0.808232
$832$	3.36077	0.116514
$833$	34.8414	1.20718
$834$	−9.08615	−0.314628
$835$	−6.33426	−0.219206
$836$	−6.54987	−0.226532
$837$	2.79356	0.0965595
$838$	3.75774	0.129809
$839$	27.5505	0.951150	0.475575	−	0.879675i	$-0.342240\pi$
$839$	27.5505	0.951150	0.475575	+	0.879675i	$0.342240\pi$
$840$	3.54019	0.122148
$841$	−22.1658	−0.764337
$842$	0.464546	0.0160093
$843$	−5.59936	−0.192852
$844$	−14.6306	−0.503608
$845$	1.70526	0.0586626
$846$	−19.9448	−0.685716
$847$	−3.84192	−0.132010
$848$	12.6401	0.434063
$849$	23.4774	0.805741
$850$	4.48968	0.153995
$851$	−0.658248	−0.0225644
$852$	−9.62201	−0.329645
$853$	−15.3388	−0.525189	−0.262595	−	0.964906i	$-0.584578\pi$
$853$	−15.3388	−0.525189	−0.262595	+	0.964906i	$0.584578\pi$
$854$	36.9395	1.26404
$855$	−14.0881	−0.481804
$856$	−15.8462	−0.541612
$857$	−25.9966	−0.888026	−0.444013	−	0.896020i	$-0.646446\pi$
$857$	−25.9966	−0.888026	−0.444013	+	0.896020i	$0.646446\pi$
$858$	3.09682	0.105724
$859$	−31.7364	−1.08283	−0.541416	−	0.840755i	$-0.682112\pi$
$859$	−31.7364	−1.08283	−0.541416	+	0.840755i	$0.682112\pi$
$860$	−1.00000	−0.0340997
$861$	−35.7050	−1.21682
$862$	−23.9618	−0.816142
$863$	9.44518	0.321518	0.160759	−	0.986994i	$-0.448606\pi$
$863$	9.44518	0.321518	0.160759	+	0.986994i	$0.448606\pi$
$864$	−4.74637	−0.161475
$865$	2.54982	0.0866966
$866$	−29.5327	−1.00356
$867$	2.90925	0.0988035
$868$	2.26123	0.0767510
$869$	5.98496	0.203026
$870$	−2.40892	−0.0816701
$871$	−27.2602	−0.923676
$872$	−9.86228	−0.333979
$873$	19.2447	0.651336
$874$	−17.9403	−0.606841
$875$	3.84192	0.129880
$876$	10.9315	0.369340
$877$	−24.3574	−0.822492	−0.411246	−	0.911524i	$-0.634906\pi$
$877$	−24.3574	−0.822492	−0.411246	+	0.911524i	$0.634906\pi$
$878$	−22.1469	−0.747422
$879$	−5.12390	−0.172825
$880$	−1.00000	−0.0337100
$881$	9.70156	0.326854	0.163427	−	0.986555i	$-0.447745\pi$
$881$	9.70156	0.326854	0.163427	+	0.986555i	$0.447745\pi$
$882$	−16.6917	−0.562039
$883$	2.39138	0.0804763	0.0402382	−	0.999190i	$-0.487188\pi$
$883$	2.39138	0.0804763	0.0402382	+	0.999190i	$0.487188\pi$
$884$	15.0888	0.507490
$885$	−11.5578	−0.388511
$886$	37.4638	1.25862
$887$	−55.8144	−1.87407	−0.937033	−	0.349241i	$-0.886439\pi$
$887$	−55.8144	−1.87407	−0.937033	+	0.349241i	$0.886439\pi$
$888$	−0.221447	−0.00743128
$889$	−78.8267	−2.64376
$890$	−13.9559	−0.467804
$891$	2.07910	0.0696526
$892$	16.2067	0.542639
$893$	−60.7352	−2.03243
$894$	4.08525	0.136631
$895$	6.35898	0.212557
$896$	−3.84192	−0.128349
$897$	8.48231	0.283216
$898$	39.1108	1.30514
$899$	−1.53865	−0.0513169
$900$	−2.15090	−0.0716968
$901$	56.7500	1.89062
$902$	10.0856	0.335815
$903$	−3.54019	−0.117810
$904$	11.1604	0.371190
$905$	−4.96116	−0.164914
$906$	16.6412	0.552867
$907$	−6.13589	−0.203739	−0.101869	−	0.994798i	$-0.532482\pi$
$907$	−6.13589	−0.203739	−0.101869	+	0.994798i	$0.532482\pi$
$908$	−7.28678	−0.241820
$909$	−14.5594	−0.482905
$910$	12.9118	0.428021
$911$	41.6942	1.38139	0.690696	−	0.723146i	$-0.257305\pi$
$911$	41.6942	1.38139	0.690696	+	0.723146i	$0.257305\pi$
$912$	−6.03547	−0.199854
$913$	8.56754	0.283544
$914$	7.77236	0.257087
$915$	8.85975	0.292894
$916$	−7.26471	−0.240033
$917$	35.5812	1.17500
$918$	−21.3097	−0.703324
$919$	−11.6575	−0.384546	−0.192273	−	0.981341i	$-0.561586\pi$
$919$	−11.6575	−0.384546	−0.192273	+	0.981341i	$0.561586\pi$
$920$	−2.73904	−0.0903033
$921$	−20.1713	−0.664668
$922$	8.64592	0.284738
$923$	−35.0934	−1.15511
$924$	−3.54019	−0.116464
$925$	−0.240321	−0.00790170
$926$	22.3778	0.735381
$927$	25.5018	0.837589
$928$	2.61423	0.0858164
$929$	20.8673	0.684634	0.342317	−	0.939585i	$-0.388788\pi$
$929$	20.8673	0.684634	0.342317	+	0.939585i	$0.388788\pi$
$930$	0.542343	0.0177841
$931$	−50.8291	−1.66586
$932$	19.0465	0.623890
$933$	−3.21863	−0.105373
$934$	25.2601	0.826537
$935$	−4.48968	−0.146828
$936$	−7.22869	−0.236277
$937$	−3.29248	−0.107560	−0.0537802	−	0.998553i	$-0.517127\pi$
$937$	−3.29248	−0.107560	−0.0537802	+	0.998553i	$0.517127\pi$
$938$	31.1629	1.01751
$939$	−31.0272	−1.01254
$940$	−9.27274	−0.302443
$941$	34.4049	1.12157	0.560784	−	0.827962i	$-0.310500\pi$
$941$	34.4049	1.12157	0.560784	+	0.827962i	$0.310500\pi$
$942$	17.5721	0.572529
$943$	27.6249	0.899591
$944$	12.5429	0.408235
$945$	−18.2352	−0.593190
$946$	1.00000	0.0325128
$947$	−30.8053	−1.00104	−0.500519	−	0.865725i	$-0.666858\pi$
$947$	−30.8053	−1.00104	−0.500519	+	0.865725i	$0.666858\pi$
$948$	5.51492	0.179116
$949$	39.8692	1.29421
$950$	−6.54987	−0.212506
$951$	−17.0510	−0.552915
$952$	−17.2490	−0.559042
$953$	−7.40881	−0.239995	−0.119997	−	0.992774i	$-0.538289\pi$
$953$	−7.40881	−0.239995	−0.119997	+	0.992774i	$0.538289\pi$
$954$	−27.1877	−0.880234
$955$	−2.82460	−0.0914019
$956$	8.88667	0.287416
$957$	2.40892	0.0778694
$958$	24.8707	0.803536
$959$	−79.0137	−2.55149
$960$	−0.921464	−0.0297401
$961$	−30.6536	−0.988825
$962$	−0.807662	−0.0260401
$963$	34.0837	1.09833
$964$	2.76143	0.0889398
$965$	0.714821	0.0230109
$966$	−9.69670	−0.311986
$967$	48.0204	1.54423	0.772116	−	0.635482i	$-0.219198\pi$
$967$	48.0204	1.54423	0.772116	+	0.635482i	$0.219198\pi$
$968$	1.00000	0.0321412
$969$	−27.0973	−0.870491
$970$	8.94728	0.287280
$971$	−33.0553	−1.06079	−0.530397	−	0.847749i	$-0.677957\pi$
$971$	−33.0553	−1.06079	−0.530397	+	0.847749i	$0.677957\pi$
$972$	16.1549	0.518170
$973$	37.8835	1.21449
$974$	−15.1078	−0.484084
$975$	3.09682	0.0991777
$976$	−9.61487	−0.307764
$977$	−4.57570	−0.146389	−0.0731947	−	0.997318i	$-0.523319\pi$
$977$	−4.57570	−0.146389	−0.0731947	+	0.997318i	$0.523319\pi$
$978$	−10.6802	−0.341515
$979$	13.9559	0.446034
$980$	−7.76033	−0.247895
$981$	21.2128	0.677273
$982$	−20.9423	−0.668296
$983$	23.2444	0.741382	0.370691	−	0.928756i	$-0.379121\pi$
$983$	23.2444	0.741382	0.370691	+	0.928756i	$0.379121\pi$
$984$	9.29355	0.296267
$985$	8.23931	0.262526
$986$	11.7371	0.373784
$987$	−32.8272	−1.04490
$988$	−22.0126	−0.700313
$989$	2.73904	0.0870963
$990$	2.15090	0.0683602
$991$	31.6459	1.00526	0.502632	−	0.864500i	$-0.332365\pi$
$991$	31.6459	1.00526	0.502632	+	0.864500i	$0.332365\pi$
$992$	−0.588567	−0.0186870
$993$	12.8022	0.406265
$994$	40.1177	1.27246
$995$	9.90281	0.313940
$996$	7.89468	0.250152
$997$	49.3229	1.56207	0.781036	−	0.624486i	$-0.214691\pi$
$997$	49.3229	1.56207	0.781036	+	0.624486i	$0.214691\pi$
$998$	−25.5069	−0.807405
$999$	1.14065	0.0360886

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4730.2.a.bf.1.8	✓	13

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4730.2.a.bf.1.8	✓	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)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +0.921464 q^{3} +1.00000 q^{4} -1.00000 q^{5} +0.921464 q^{6} -3.84192 q^{7} +1.00000 q^{8} -2.15090 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +0.921464 q^{3} +1.00000 q^{4} -1.00000 q^{5} +0.921464 q^{6} -3.84192 q^{7} +1.00000 q^{8} -2.15090 q^{9} -1.00000 q^{10} +1.00000 q^{11} +0.921464 q^{12} +3.36077 q^{13} -3.84192 q^{14} -0.921464 q^{15} +1.00000 q^{16} +4.48968 q^{17} -2.15090 q^{18} -6.54987 q^{19} -1.00000 q^{20} -3.54019 q^{21} +1.00000 q^{22} +2.73904 q^{23} +0.921464 q^{24} +1.00000 q^{25} +3.36077 q^{26} -4.74637 q^{27} -3.84192 q^{28} +2.61423 q^{29} -0.921464 q^{30} -0.588567 q^{31} +1.00000 q^{32} +0.921464 q^{33} +4.48968 q^{34} +3.84192 q^{35} -2.15090 q^{36} -0.240321 q^{37} -6.54987 q^{38} +3.09682 q^{39} -1.00000 q^{40} +10.0856 q^{41} -3.54019 q^{42} +1.00000 q^{43} +1.00000 q^{44} +2.15090 q^{45} +2.73904 q^{46} +9.27274 q^{47} +0.921464 q^{48} +7.76033 q^{49} +1.00000 q^{50} +4.13708 q^{51} +3.36077 q^{52} +12.6401 q^{53} -4.74637 q^{54} -1.00000 q^{55} -3.84192 q^{56} -6.03547 q^{57} +2.61423 q^{58} +12.5429 q^{59} -0.921464 q^{60} -9.61487 q^{61} -0.588567 q^{62} +8.26360 q^{63} +1.00000 q^{64} -3.36077 q^{65} +0.921464 q^{66} -8.11130 q^{67} +4.48968 q^{68} +2.52392 q^{69} +3.84192 q^{70} -10.4421 q^{71} -2.15090 q^{72} +11.8631 q^{73} -0.240321 q^{74} +0.921464 q^{75} -6.54987 q^{76} -3.84192 q^{77} +3.09682 q^{78} +5.98496 q^{79} -1.00000 q^{80} +2.07910 q^{81} +10.0856 q^{82} +8.56754 q^{83} -3.54019 q^{84} -4.48968 q^{85} +1.00000 q^{86} +2.40892 q^{87} +1.00000 q^{88} +13.9559 q^{89} +2.15090 q^{90} -12.9118 q^{91} +2.73904 q^{92} -0.542343 q^{93} +9.27274 q^{94} +6.54987 q^{95} +0.921464 q^{96} -8.94728 q^{97} +7.76033 q^{98} -2.15090 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 13 q + 13 q^{2} + 13 q^{4} - 13 q^{5} + 7 q^{7} + 13 q^{8} + 25 q^{9}+O(q^{10}) \) 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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