LMFDB - Embedded newform 4730.2.a.bc.1.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4730, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0, 0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("4730.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4730 = 2 \cdot 5 \cdot 11 \cdot 43 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4730.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$37.7692401561$
Analytic rank:	$0$
Dimension:	$11$
Coefficient field:	$\mathbb{Q}[x]/(x^{11} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{11} - 24x^{9} - x^{8} + 200x^{7} + 14x^{6} - 653x^{5} - 26x^{4} + 620x^{3} - 177x^{2} - 90x + 32 $ x^11 - 24x^9 - x^8 + 200x^7 + 14x^6 - 653x^5 - 26x^4 + 620x^3 - 177x^2 - 90x + 32
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.5
Root			$-0.419974$ 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)

$f(q)$	$=$	$q-1.00000 q^{2} -0.419974 q^{3} +1.00000 q^{4} -1.00000 q^{5} +0.419974 q^{6} +3.08102 q^{7} -1.00000 q^{8} -2.82362 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -0.419974 q^{3} +1.00000 q^{4} -1.00000 q^{5} +0.419974 q^{6} +3.08102 q^{7} -1.00000 q^{8} -2.82362 q^{9} +1.00000 q^{10} +1.00000 q^{11} -0.419974 q^{12} +4.96282 q^{13} -3.08102 q^{14} +0.419974 q^{15} +1.00000 q^{16} -3.87595 q^{17} +2.82362 q^{18} +2.03492 q^{19} -1.00000 q^{20} -1.29395 q^{21} -1.00000 q^{22} +9.26536 q^{23} +0.419974 q^{24} +1.00000 q^{25} -4.96282 q^{26} +2.44577 q^{27} +3.08102 q^{28} -10.5516 q^{29} -0.419974 q^{30} -0.272486 q^{31} -1.00000 q^{32} -0.419974 q^{33} +3.87595 q^{34} -3.08102 q^{35} -2.82362 q^{36} +8.16766 q^{37} -2.03492 q^{38} -2.08425 q^{39} +1.00000 q^{40} +6.48873 q^{41} +1.29395 q^{42} -1.00000 q^{43} +1.00000 q^{44} +2.82362 q^{45} -9.26536 q^{46} -4.31345 q^{47} -0.419974 q^{48} +2.49271 q^{49} -1.00000 q^{50} +1.62780 q^{51} +4.96282 q^{52} +3.72526 q^{53} -2.44577 q^{54} -1.00000 q^{55} -3.08102 q^{56} -0.854612 q^{57} +10.5516 q^{58} -2.66755 q^{59} +0.419974 q^{60} +9.70121 q^{61} +0.272486 q^{62} -8.69965 q^{63} +1.00000 q^{64} -4.96282 q^{65} +0.419974 q^{66} -13.8771 q^{67} -3.87595 q^{68} -3.89121 q^{69} +3.08102 q^{70} -9.19575 q^{71} +2.82362 q^{72} +5.36492 q^{73} -8.16766 q^{74} -0.419974 q^{75} +2.03492 q^{76} +3.08102 q^{77} +2.08425 q^{78} -4.13756 q^{79} -1.00000 q^{80} +7.44371 q^{81} -6.48873 q^{82} +10.3975 q^{83} -1.29395 q^{84} +3.87595 q^{85} +1.00000 q^{86} +4.43141 q^{87} -1.00000 q^{88} +14.4819 q^{89} -2.82362 q^{90} +15.2906 q^{91} +9.26536 q^{92} +0.114437 q^{93} +4.31345 q^{94} -2.03492 q^{95} +0.419974 q^{96} -6.03266 q^{97} -2.49271 q^{98} -2.82362 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 11 q - 11 q^{2} + 11 q^{4} - 11 q^{5} - 11 q^{8} + 15 q^{9}+O(q^{10}) $ 11 * q - 11 * q^2 + 11 * q^4 - 11 * q^5 - 11 * q^8 + 15 * q^9	$ 11 q - 11 q^{2} + 11 q^{4} - 11 q^{5} - 11 q^{8} + 15 q^{9} + 11 q^{10} + 11 q^{11} - q^{13} + 11 q^{16} - 15 q^{17} - 15 q^{18} + 14 q^{19} - 11 q^{20} + 7 q^{21} - 11 q^{22} - 2 q^{23} + 11 q^{25} + q^{26} + 3 q^{27} + 6 q^{29} + 13 q^{31} - 11 q^{32} + 15 q^{34} + 15 q^{36} + 16 q^{37} - 14 q^{38} + 4 q^{39} + 11 q^{40} - 7 q^{41} - 7 q^{42} - 11 q^{43} + 11 q^{44} - 15 q^{45} + 2 q^{46} - 19 q^{47} + 23 q^{49} - 11 q^{50} + 32 q^{51} - q^{52} - 16 q^{53} - 3 q^{54} - 11 q^{55} - 2 q^{57} - 6 q^{58} + 7 q^{59} + 20 q^{61} - 13 q^{62} + 11 q^{64} + q^{65} + 9 q^{67} - 15 q^{68} + 10 q^{69} + 13 q^{71} - 15 q^{72} + 20 q^{73} - 16 q^{74} + 14 q^{76} - 4 q^{78} + 13 q^{79} - 11 q^{80} + 19 q^{81} + 7 q^{82} - 6 q^{83} + 7 q^{84} + 15 q^{85} + 11 q^{86} - 23 q^{87} - 11 q^{88} + 10 q^{89} + 15 q^{90} + 43 q^{91} - 2 q^{92} + 22 q^{93} + 19 q^{94} - 14 q^{95} + 3 q^{97} - 23 q^{98} + 15 q^{99}+O(q^{100}) $ 11 * q - 11 * q^2 + 11 * q^4 - 11 * q^5 - 11 * q^8 + 15 * q^9 + 11 * q^10 + 11 * q^11 - q^13 + 11 * q^16 - 15 * q^17 - 15 * q^18 + 14 * q^19 - 11 * q^20 + 7 * q^21 - 11 * q^22 - 2 * q^23 + 11 * q^25 + q^26 + 3 * q^27 + 6 * q^29 + 13 * q^31 - 11 * q^32 + 15 * q^34 + 15 * q^36 + 16 * q^37 - 14 * q^38 + 4 * q^39 + 11 * q^40 - 7 * q^41 - 7 * q^42 - 11 * q^43 + 11 * q^44 - 15 * q^45 + 2 * q^46 - 19 * q^47 + 23 * q^49 - 11 * q^50 + 32 * q^51 - q^52 - 16 * q^53 - 3 * q^54 - 11 * q^55 - 2 * q^57 - 6 * q^58 + 7 * q^59 + 20 * q^61 - 13 * q^62 + 11 * q^64 + q^65 + 9 * q^67 - 15 * q^68 + 10 * q^69 + 13 * q^71 - 15 * q^72 + 20 * q^73 - 16 * q^74 + 14 * q^76 - 4 * q^78 + 13 * q^79 - 11 * q^80 + 19 * q^81 + 7 * q^82 - 6 * q^83 + 7 * q^84 + 15 * q^85 + 11 * q^86 - 23 * q^87 - 11 * q^88 + 10 * q^89 + 15 * q^90 + 43 * q^91 - 2 * q^92 + 22 * q^93 + 19 * q^94 - 14 * q^95 + 3 * q^97 - 23 * q^98 + 15 * 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
$3$	−0.419974	−0.242472	−0.121236	−	0.992624i	$-0.538686\pi$
$3$	−0.419974	−0.242472	−0.121236	+	0.992624i	$0.538686\pi$
$4$	1.00000	0.500000
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	0.419974	0.171454
$7$	3.08102	1.16452	0.582259	−	0.813003i	$-0.302169\pi$
$7$	3.08102	1.16452	0.582259	+	0.813003i	$0.302169\pi$
$8$	−1.00000	−0.353553
$9$	−2.82362	−0.941207
$10$	1.00000	0.316228
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	−0.419974	−0.121236
$13$	4.96282	1.37644	0.688219	−	0.725503i	$-0.258393\pi$
$13$	4.96282	1.37644	0.688219	+	0.725503i	$0.258393\pi$
$14$	−3.08102	−0.823438
$15$	0.419974	0.108437
$16$	1.00000	0.250000
$17$	−3.87595	−0.940055	−0.470028	−	0.882652i	$-0.655756\pi$
$17$	−3.87595	−0.940055	−0.470028	+	0.882652i	$0.655756\pi$
$18$	2.82362	0.665534
$19$	2.03492	0.466842	0.233421	−	0.972376i	$-0.425008\pi$
$19$	2.03492	0.466842	0.233421	+	0.972376i	$0.425008\pi$
$20$	−1.00000	−0.223607
$21$	−1.29395	−0.282363
$22$	−1.00000	−0.213201
$23$	9.26536	1.93196	0.965981	−	0.258614i	$-0.0832657\pi$
$23$	9.26536	1.93196	0.965981	+	0.258614i	$0.0832657\pi$
$24$	0.419974	0.0857268
$25$	1.00000	0.200000
$26$	−4.96282	−0.973289
$27$	2.44577	0.470689
$28$	3.08102	0.582259
$29$	−10.5516	−1.95939	−0.979695	−	0.200494i	$-0.935745\pi$
$29$	−10.5516	−1.95939	−0.979695	+	0.200494i	$0.935745\pi$
$30$	−0.419974	−0.0766764
$31$	−0.272486	−0.0489399	−0.0244699	−	0.999701i	$-0.507790\pi$
$31$	−0.272486	−0.0489399	−0.0244699	+	0.999701i	$0.507790\pi$
$32$	−1.00000	−0.176777
$33$	−0.419974	−0.0731081
$34$	3.87595	0.664719
$35$	−3.08102	−0.520788
$36$	−2.82362	−0.470604
$37$	8.16766	1.34275	0.671377	−	0.741116i	$-0.265703\pi$
$37$	8.16766	1.34275	0.671377	+	0.741116i	$0.265703\pi$
$38$	−2.03492	−0.330107
$39$	−2.08425	−0.333748
$40$	1.00000	0.158114
$41$	6.48873	1.01337	0.506685	−	0.862131i	$-0.330871\pi$
$41$	6.48873	1.01337	0.506685	+	0.862131i	$0.330871\pi$
$42$	1.29395	0.199661
$43$	−1.00000	−0.152499
$43$	−1.00000	−0.152499
$44$	1.00000	0.150756
$45$	2.82362	0.420921
$46$	−9.26536	−1.36610
$47$	−4.31345	−0.629182	−0.314591	−	0.949227i	$-0.601867\pi$
$47$	−4.31345	−0.629182	−0.314591	+	0.949227i	$0.601867\pi$
$48$	−0.419974	−0.0606180
$49$	2.49271	0.356102
$50$	−1.00000	−0.141421
$51$	1.62780	0.227937
$52$	4.96282	0.688219
$53$	3.72526	0.511704	0.255852	−	0.966716i	$-0.417644\pi$
$53$	3.72526	0.511704	0.255852	+	0.966716i	$0.417644\pi$
$54$	−2.44577	−0.332827
$55$	−1.00000	−0.134840
$56$	−3.08102	−0.411719
$57$	−0.854612	−0.113196
$58$	10.5516	1.38550
$59$	−2.66755	−0.347285	−0.173642	−	0.984809i	$-0.555554\pi$
$59$	−2.66755	−0.347285	−0.173642	+	0.984809i	$0.555554\pi$
$60$	0.419974	0.0542184
$61$	9.70121	1.24211	0.621057	−	0.783766i	$-0.286704\pi$
$61$	9.70121	1.24211	0.621057	+	0.783766i	$0.286704\pi$
$62$	0.272486	0.0346057
$63$	−8.69965	−1.09605
$64$	1.00000	0.125000
$65$	−4.96282	−0.615562
$66$	0.419974	0.0516952
$67$	−13.8771	−1.69536	−0.847678	−	0.530511i	$-0.822000\pi$
$67$	−13.8771	−1.69536	−0.847678	+	0.530511i	$0.822000\pi$
$68$	−3.87595	−0.470028
$69$	−3.89121	−0.468447
$70$	3.08102	0.368253
$71$	−9.19575	−1.09133	−0.545667	−	0.838002i	$-0.683724\pi$
$71$	−9.19575	−1.09133	−0.545667	+	0.838002i	$0.683724\pi$
$72$	2.82362	0.332767
$73$	5.36492	0.627917	0.313958	−	0.949437i	$-0.398345\pi$
$73$	5.36492	0.627917	0.313958	+	0.949437i	$0.398345\pi$
$74$	−8.16766	−0.949471
$75$	−0.419974	−0.0484944
$76$	2.03492	0.233421
$77$	3.08102	0.351115
$78$	2.08425	0.235995
$79$	−4.13756	−0.465512	−0.232756	−	0.972535i	$-0.574774\pi$
$79$	−4.13756	−0.465512	−0.232756	+	0.972535i	$0.574774\pi$
$80$	−1.00000	−0.111803
$81$	7.44371	0.827078
$82$	−6.48873	−0.716561
$83$	10.3975	1.14127	0.570635	−	0.821204i	$-0.306697\pi$
$83$	10.3975	1.14127	0.570635	+	0.821204i	$0.306697\pi$
$84$	−1.29395	−0.141182
$85$	3.87595	0.420405
$86$	1.00000	0.107833
$87$	4.43141	0.475097
$88$	−1.00000	−0.106600
$89$	14.4819	1.53508	0.767541	−	0.641000i	$-0.221480\pi$
$89$	14.4819	1.53508	0.767541	+	0.641000i	$0.221480\pi$
$90$	−2.82362	−0.297636
$91$	15.2906	1.60289
$92$	9.26536	0.965981
$93$	0.114437	0.0118666
$94$	4.31345	0.444899
$95$	−2.03492	−0.208778
$96$	0.419974	0.0428634
$97$	−6.03266	−0.612524	−0.306262	−	0.951947i	$-0.599078\pi$
$97$	−6.03266	−0.612524	−0.306262	+	0.951947i	$0.599078\pi$
$98$	−2.49271	−0.251802
$99$	−2.82362	−0.283785
$100$	1.00000	0.100000
$101$	−2.41810	−0.240610	−0.120305	−	0.992737i	$-0.538387\pi$
$101$	−2.41810	−0.240610	−0.120305	+	0.992737i	$0.538387\pi$
$102$	−1.62780	−0.161176
$103$	−3.20342	−0.315642	−0.157821	−	0.987468i	$-0.550447\pi$
$103$	−3.20342	−0.315642	−0.157821	+	0.987468i	$0.550447\pi$
$104$	−4.96282	−0.486644
$105$	1.29395	0.126277
$106$	−3.72526	−0.361829
$107$	−6.54483	−0.632712	−0.316356	−	0.948641i	$-0.602459\pi$
$107$	−6.54483	−0.632712	−0.316356	+	0.948641i	$0.602459\pi$
$108$	2.44577	0.235344
$109$	10.5429	1.00983	0.504915	−	0.863169i	$-0.331524\pi$
$109$	10.5429	1.00983	0.504915	+	0.863169i	$0.331524\pi$
$110$	1.00000	0.0953463
$111$	−3.43020	−0.325580
$112$	3.08102	0.291129
$113$	−10.0279	−0.943350	−0.471675	−	0.881773i	$-0.656350\pi$
$113$	−10.0279	−0.943350	−0.471675	+	0.881773i	$0.656350\pi$
$114$	0.854612	0.0800417
$115$	−9.26536	−0.864000
$116$	−10.5516	−0.979695
$117$	−14.0131	−1.29551
$118$	2.66755	0.245567
$119$	−11.9419	−1.09471
$120$	−0.419974	−0.0383382
$121$	1.00000	0.0909091
$122$	−9.70121	−0.878307
$123$	−2.72510	−0.245714
$124$	−0.272486	−0.0244699
$125$	−1.00000	−0.0894427
$126$	8.69965	0.775026
$127$	12.0998	1.07368	0.536842	−	0.843683i	$-0.319617\pi$
$127$	12.0998	1.07368	0.536842	+	0.843683i	$0.319617\pi$
$128$	−1.00000	−0.0883883
$129$	0.419974	0.0369767
$130$	4.96282	0.435268
$131$	−12.5975	−1.10065	−0.550326	−	0.834950i	$-0.685497\pi$
$131$	−12.5975	−1.10065	−0.550326	+	0.834950i	$0.685497\pi$
$132$	−0.419974	−0.0365540
$133$	6.26963	0.543646
$134$	13.8771	1.19880
$135$	−2.44577	−0.210498
$136$	3.87595	0.332360
$137$	−8.84383	−0.755579	−0.377790	−	0.925891i	$-0.623316\pi$
$137$	−8.84383	−0.755579	−0.377790	+	0.925891i	$0.623316\pi$
$138$	3.89121	0.331242
$139$	5.50569	0.466986	0.233493	−	0.972358i	$-0.424984\pi$
$139$	5.50569	0.466986	0.233493	+	0.972358i	$0.424984\pi$
$140$	−3.08102	−0.260394
$141$	1.81154	0.152559
$142$	9.19575	0.771690
$143$	4.96282	0.415012
$144$	−2.82362	−0.235302
$145$	10.5516	0.876266
$146$	−5.36492	−0.444004
$147$	−1.04687	−0.0863447
$148$	8.16766	0.671377
$149$	20.0757	1.64467	0.822334	−	0.569005i	$-0.192671\pi$
$149$	20.0757	1.64467	0.822334	+	0.569005i	$0.192671\pi$
$150$	0.419974	0.0342907
$151$	8.94545	0.727970	0.363985	−	0.931405i	$-0.381416\pi$
$151$	8.94545	0.727970	0.363985	+	0.931405i	$0.381416\pi$
$152$	−2.03492	−0.165053
$153$	10.9442	0.884787
$154$	−3.08102	−0.248276
$155$	0.272486	0.0218866
$156$	−2.08425	−0.166874
$157$	15.1511	1.20919	0.604596	−	0.796533i	$-0.293335\pi$
$157$	15.1511	1.20919	0.604596	+	0.796533i	$0.293335\pi$
$158$	4.13756	0.329166
$159$	−1.56451	−0.124074
$160$	1.00000	0.0790569
$161$	28.5468	2.24980
$162$	−7.44371	−0.584833
$163$	2.29757	0.179959	0.0899797	−	0.995944i	$-0.471320\pi$
$163$	2.29757	0.179959	0.0899797	+	0.995944i	$0.471320\pi$
$164$	6.48873	0.506685
$165$	0.419974	0.0326949
$166$	−10.3975	−0.807000
$167$	−6.86355	−0.531117	−0.265559	−	0.964095i	$-0.585556\pi$
$167$	−6.86355	−0.531117	−0.265559	+	0.964095i	$0.585556\pi$
$168$	1.29395	0.0998304
$169$	11.6296	0.894582
$170$	−3.87595	−0.297272
$171$	−5.74583	−0.439395
$172$	−1.00000	−0.0762493
$173$	−7.63502	−0.580480	−0.290240	−	0.956954i	$-0.593735\pi$
$173$	−7.63502	−0.580480	−0.290240	+	0.956954i	$0.593735\pi$
$174$	−4.43141	−0.335945
$175$	3.08102	0.232904
$176$	1.00000	0.0753778
$177$	1.12030	0.0842069
$178$	−14.4819	−1.08547
$179$	8.27843	0.618759	0.309380	−	0.950939i	$-0.399879\pi$
$179$	8.27843	0.618759	0.309380	+	0.950939i	$0.399879\pi$
$180$	2.82362	0.210460
$181$	0.536292	0.0398622	0.0199311	−	0.999801i	$-0.493655\pi$
$181$	0.536292	0.0398622	0.0199311	+	0.999801i	$0.493655\pi$
$182$	−15.2906	−1.13341
$183$	−4.07426	−0.301178
$184$	−9.26536	−0.683052
$185$	−8.16766	−0.600498
$186$	−0.114437	−0.00839092
$187$	−3.87595	−0.283437
$188$	−4.31345	−0.314591
$189$	7.53548	0.548125
$190$	2.03492	0.147628
$191$	13.0237	0.942362	0.471181	−	0.882036i	$-0.343828\pi$
$191$	13.0237	0.942362	0.471181	+	0.882036i	$0.343828\pi$
$192$	−0.419974	−0.0303090
$193$	−1.09998	−0.0791785	−0.0395892	−	0.999216i	$-0.512605\pi$
$193$	−1.09998	−0.0791785	−0.0395892	+	0.999216i	$0.512605\pi$
$194$	6.03266	0.433120
$195$	2.08425	0.149257
$196$	2.49271	0.178051
$197$	−16.6085	−1.18330	−0.591652	−	0.806194i	$-0.701524\pi$
$197$	−16.6085	−1.18330	−0.591652	+	0.806194i	$0.701524\pi$
$198$	2.82362	0.200666
$199$	16.2081	1.14896	0.574480	−	0.818519i	$-0.305204\pi$
$199$	16.2081	1.14896	0.574480	+	0.818519i	$0.305204\pi$
$200$	−1.00000	−0.0707107
$201$	5.82802	0.411077
$202$	2.41810	0.170137
$203$	−32.5099	−2.28174
$204$	1.62780	0.113969
$205$	−6.48873	−0.453193
$206$	3.20342	0.223193
$207$	−26.1619	−1.81838
$208$	4.96282	0.344110
$209$	2.03492	0.140758
$210$	−1.29395	−0.0892910
$211$	−27.3716	−1.88434	−0.942169	−	0.335139i	$-0.891217\pi$
$211$	−27.3716	−1.88434	−0.942169	+	0.335139i	$0.891217\pi$
$212$	3.72526	0.255852
$213$	3.86197	0.264618
$214$	6.54483	0.447395
$215$	1.00000	0.0681994
$216$	−2.44577	−0.166414
$217$	−0.839535	−0.0569914
$218$	−10.5429	−0.714058
$219$	−2.25313	−0.152252
$220$	−1.00000	−0.0674200
$221$	−19.2356	−1.29393
$222$	3.43020	0.230220
$223$	6.89059	0.461428	0.230714	−	0.973022i	$-0.425894\pi$
$223$	6.89059	0.461428	0.230714	+	0.973022i	$0.425894\pi$
$224$	−3.08102	−0.205860
$225$	−2.82362	−0.188241
$226$	10.0279	0.667049
$227$	2.58662	0.171680	0.0858400	−	0.996309i	$-0.472643\pi$
$227$	2.58662	0.171680	0.0858400	+	0.996309i	$0.472643\pi$
$228$	−0.854612	−0.0565981
$229$	−20.0548	−1.32526	−0.662628	−	0.748949i	$-0.730559\pi$
$229$	−20.0548	−1.32526	−0.662628	+	0.748949i	$0.730559\pi$
$230$	9.26536	0.610940
$231$	−1.29395	−0.0851357
$232$	10.5516	0.692749
$233$	4.02190	0.263483	0.131742	−	0.991284i	$-0.457943\pi$
$233$	4.02190	0.263483	0.131742	+	0.991284i	$0.457943\pi$
$234$	14.0131	0.916067
$235$	4.31345	0.281379
$236$	−2.66755	−0.173642
$237$	1.73767	0.112874
$238$	11.9419	0.774077
$239$	29.9090	1.93465	0.967327	−	0.253531i	$-0.0815920\pi$
$239$	29.9090	1.93465	0.967327	+	0.253531i	$0.0815920\pi$
$240$	0.419974	0.0271092
$241$	1.00496	0.0647352	0.0323676	−	0.999476i	$-0.489695\pi$
$241$	1.00496	0.0647352	0.0323676	+	0.999476i	$0.489695\pi$
$242$	−1.00000	−0.0642824
$243$	−10.4635	−0.671232
$244$	9.70121	0.621057
$245$	−2.49271	−0.159254
$246$	2.72510	0.173746
$247$	10.0989	0.642579
$248$	0.272486	0.0173029
$249$	−4.36666	−0.276726
$250$	1.00000	0.0632456
$251$	7.67101	0.484190	0.242095	−	0.970253i	$-0.422165\pi$
$251$	7.67101	0.484190	0.242095	+	0.970253i	$0.422165\pi$
$252$	−8.69965	−0.548026
$253$	9.26536	0.582508
$254$	−12.0998	−0.759209
$255$	−1.62780	−0.101937
$256$	1.00000	0.0625000
$257$	15.2855	0.953481	0.476740	−	0.879044i	$-0.341818\pi$
$257$	15.2855	0.953481	0.476740	+	0.879044i	$0.341818\pi$
$258$	−0.419974	−0.0261464
$259$	25.1647	1.56366
$260$	−4.96282	−0.307781
$261$	29.7938	1.84419
$262$	12.5975	0.778279
$263$	14.5292	0.895911	0.447955	−	0.894056i	$-0.352152\pi$
$263$	14.5292	0.895911	0.447955	+	0.894056i	$0.352152\pi$
$264$	0.419974	0.0258476
$265$	−3.72526	−0.228841
$266$	−6.26963	−0.384415
$267$	−6.08204	−0.372215
$268$	−13.8771	−0.847678
$269$	−4.06685	−0.247960	−0.123980	−	0.992285i	$-0.539566\pi$
$269$	−4.06685	−0.247960	−0.123980	+	0.992285i	$0.539566\pi$
$270$	2.44577	0.148845
$271$	−11.3207	−0.687685	−0.343843	−	0.939027i	$-0.611729\pi$
$271$	−11.3207	−0.687685	−0.343843	+	0.939027i	$0.611729\pi$
$272$	−3.87595	−0.235014
$273$	−6.42164	−0.388655
$274$	8.84383	0.534275
$275$	1.00000	0.0603023
$276$	−3.89121	−0.234223
$277$	22.1605	1.33149	0.665747	−	0.746178i	$-0.268113\pi$
$277$	22.1605	1.33149	0.665747	+	0.746178i	$0.268113\pi$
$278$	−5.50569	−0.330209
$279$	0.769397	0.0460626
$280$	3.08102	0.184126
$281$	−16.3027	−0.972540	−0.486270	−	0.873809i	$-0.661643\pi$
$281$	−16.3027	−0.972540	−0.486270	+	0.873809i	$0.661643\pi$
$282$	−1.81154	−0.107876
$283$	−3.08180	−0.183194	−0.0915971	−	0.995796i	$-0.529197\pi$
$283$	−3.08180	−0.183194	−0.0915971	+	0.995796i	$0.529197\pi$
$284$	−9.19575	−0.545667
$285$	0.854612	0.0506228
$286$	−4.96282	−0.293458
$287$	19.9919	1.18009
$288$	2.82362	0.166384
$289$	−1.97704	−0.116296
$290$	−10.5516	−0.619614
$291$	2.53356	0.148520
$292$	5.36492	0.313958
$293$	20.9616	1.22459	0.612296	−	0.790629i	$-0.290246\pi$
$293$	20.9616	1.22459	0.612296	+	0.790629i	$0.290246\pi$
$294$	1.04687	0.0610549
$295$	2.66755	0.155310
$296$	−8.16766	−0.474735
$297$	2.44577	0.141918
$298$	−20.0757	−1.16296
$299$	45.9823	2.65923
$300$	−0.419974	−0.0242472
$301$	−3.08102	−0.177587
$302$	−8.94545	−0.514753
$303$	1.01554	0.0583412
$304$	2.03492	0.116710
$305$	−9.70121	−0.555490
$306$	−10.9442	−0.625639
$307$	14.6079	0.833716	0.416858	−	0.908972i	$-0.363131\pi$
$307$	14.6079	0.833716	0.416858	+	0.908972i	$0.363131\pi$
$308$	3.08102	0.175558
$309$	1.34535	0.0765345
$310$	−0.272486	−0.0154761
$311$	21.0949	1.19618	0.598091	−	0.801429i	$-0.295926\pi$
$311$	21.0949	1.19618	0.598091	+	0.801429i	$0.295926\pi$
$312$	2.08425	0.117998
$313$	−26.1722	−1.47934	−0.739669	−	0.672971i	$-0.765018\pi$
$313$	−26.1722	−1.47934	−0.739669	+	0.672971i	$0.765018\pi$
$314$	−15.1511	−0.855027
$315$	8.69965	0.490170
$316$	−4.13756	−0.232756
$317$	−2.82279	−0.158543	−0.0792717	−	0.996853i	$-0.525259\pi$
$317$	−2.82279	−0.158543	−0.0792717	+	0.996853i	$0.525259\pi$
$318$	1.56451	0.0877335
$319$	−10.5516	−0.590778
$320$	−1.00000	−0.0559017
$321$	2.74866	0.153415
$322$	−28.5468	−1.59085
$323$	−7.88723	−0.438857
$324$	7.44371	0.413539
$325$	4.96282	0.275288
$326$	−2.29757	−0.127250
$327$	−4.42776	−0.244856
$328$	−6.48873	−0.358280
$329$	−13.2899	−0.732693
$330$	−0.419974	−0.0231188
$331$	27.9232	1.53480	0.767399	−	0.641170i	$-0.221551\pi$
$331$	27.9232	1.53480	0.767399	+	0.641170i	$0.221551\pi$
$332$	10.3975	0.570635
$333$	−23.0624	−1.26381
$334$	6.86355	0.375557
$335$	13.8771	0.758187
$336$	−1.29395	−0.0705908
$337$	10.6973	0.582718	0.291359	−	0.956614i	$-0.405893\pi$
$337$	10.6973	0.582718	0.291359	+	0.956614i	$0.405893\pi$
$338$	−11.6296	−0.632565
$339$	4.21148	0.228736
$340$	3.87595	0.210203
$341$	−0.272486	−0.0147559
$342$	5.74583	0.310699
$343$	−13.8871	−0.749831
$344$	1.00000	0.0539164
$345$	3.89121	0.209496
$346$	7.63502	0.410461
$347$	−24.2060	−1.29945	−0.649724	−	0.760170i	$-0.725115\pi$
$347$	−24.2060	−1.29945	−0.649724	+	0.760170i	$0.725115\pi$
$348$	4.43141	0.237549
$349$	35.0672	1.87711	0.938553	−	0.345134i	$-0.112167\pi$
$349$	35.0672	1.87711	0.938553	+	0.345134i	$0.112167\pi$
$350$	−3.08102	−0.164688
$351$	12.1379	0.647874
$352$	−1.00000	−0.0533002
$353$	16.3562	0.870552	0.435276	−	0.900297i	$-0.356651\pi$
$353$	16.3562	0.870552	0.435276	+	0.900297i	$0.356651\pi$
$354$	−1.12030	−0.0595433
$355$	9.19575	0.488060
$356$	14.4819	0.767541
$357$	5.01528	0.265437
$358$	−8.27843	−0.437529
$359$	22.3116	1.17756	0.588779	−	0.808294i	$-0.299609\pi$
$359$	22.3116	1.17756	0.588779	+	0.808294i	$0.299609\pi$
$360$	−2.82362	−0.148818
$361$	−14.8591	−0.782059
$362$	−0.536292	−0.0281869
$363$	−0.419974	−0.0220429
$364$	15.2906	0.801443
$365$	−5.36492	−0.280813
$366$	4.07426	0.212965
$367$	23.1718	1.20956	0.604778	−	0.796394i	$-0.293262\pi$
$367$	23.1718	1.20956	0.604778	+	0.796394i	$0.293262\pi$
$368$	9.26536	0.482990
$369$	−18.3217	−0.953791
$370$	8.16766	0.424616
$371$	11.4776	0.595888
$372$	0.114437	0.00593328
$373$	17.0835	0.884548	0.442274	−	0.896880i	$-0.354172\pi$
$373$	17.0835	0.884548	0.442274	+	0.896880i	$0.354172\pi$
$374$	3.87595	0.200420
$375$	0.419974	0.0216874
$376$	4.31345	0.222449
$377$	−52.3659	−2.69698
$378$	−7.53548	−0.387583
$379$	16.9163	0.868930	0.434465	−	0.900689i	$-0.356937\pi$
$379$	16.9163	0.868930	0.434465	+	0.900689i	$0.356937\pi$
$380$	−2.03492	−0.104389
$381$	−5.08160	−0.260338
$382$	−13.0237	−0.666351
$383$	27.3917	1.39965	0.699825	−	0.714314i	$-0.253261\pi$
$383$	27.3917	1.39965	0.699825	+	0.714314i	$0.253261\pi$
$384$	0.419974	0.0214317
$385$	−3.08102	−0.157024
$386$	1.09998	0.0559876
$387$	2.82362	0.143533
$388$	−6.03266	−0.306262
$389$	14.2552	0.722769	0.361385	−	0.932417i	$-0.382304\pi$
$389$	14.2552	0.722769	0.361385	+	0.932417i	$0.382304\pi$
$390$	−2.08425	−0.105540
$391$	−35.9120	−1.81615
$392$	−2.49271	−0.125901
$393$	5.29064	0.266878
$394$	16.6085	0.836722
$395$	4.13756	0.208183
$396$	−2.82362	−0.141892
$397$	12.7090	0.637846	0.318923	−	0.947781i	$-0.396679\pi$
$397$	12.7090	0.637846	0.318923	+	0.947781i	$0.396679\pi$
$398$	−16.2081	−0.812437
$399$	−2.63308	−0.131819
$400$	1.00000	0.0500000
$401$	−8.42385	−0.420667	−0.210334	−	0.977630i	$-0.567455\pi$
$401$	−8.42385	−0.420667	−0.210334	+	0.977630i	$0.567455\pi$
$402$	−5.82802	−0.290675
$403$	−1.35230	−0.0673627
$404$	−2.41810	−0.120305
$405$	−7.44371	−0.369881
$406$	32.5099	1.61344
$407$	8.16766	0.404856
$408$	−1.62780	−0.0805880
$409$	−28.4803	−1.40826	−0.704129	−	0.710072i	$-0.748662\pi$
$409$	−28.4803	−1.40826	−0.704129	+	0.710072i	$0.748662\pi$
$410$	6.48873	0.320456
$411$	3.71418	0.183207
$412$	−3.20342	−0.157821
$413$	−8.21877	−0.404419
$414$	26.1619	1.28579
$415$	−10.3975	−0.510391
$416$	−4.96282	−0.243322
$417$	−2.31225	−0.113231
$418$	−2.03492	−0.0995310
$419$	16.8540	0.823372	0.411686	−	0.911326i	$-0.364940\pi$
$419$	16.8540	0.823372	0.411686	+	0.911326i	$0.364940\pi$
$420$	1.29395	0.0631383
$421$	16.3054	0.794675	0.397338	−	0.917672i	$-0.369934\pi$
$421$	16.3054	0.794675	0.397338	+	0.917672i	$0.369934\pi$
$422$	27.3716	1.33243
$423$	12.1796	0.592190
$424$	−3.72526	−0.180915
$425$	−3.87595	−0.188011
$426$	−3.86197	−0.187113
$427$	29.8897	1.44646
$428$	−6.54483	−0.316356
$429$	−2.08425	−0.100629
$430$	−1.00000	−0.0482243
$431$	−8.14801	−0.392476	−0.196238	−	0.980556i	$-0.562872\pi$
$431$	−8.14801	−0.392476	−0.196238	+	0.980556i	$0.562872\pi$
$432$	2.44577	0.117672
$433$	37.0222	1.77917	0.889585	−	0.456769i	$-0.150993\pi$
$433$	37.0222	1.77917	0.889585	+	0.456769i	$0.150993\pi$
$434$	0.839535	0.0402990
$435$	−4.43141	−0.212470
$436$	10.5429	0.504915
$437$	18.8542	0.901920
$438$	2.25313	0.107659
$439$	20.2147	0.964797	0.482398	−	0.875952i	$-0.339766\pi$
$439$	20.2147	0.964797	0.482398	+	0.875952i	$0.339766\pi$
$440$	1.00000	0.0476731
$441$	−7.03848	−0.335165
$442$	19.2356	0.914945
$443$	21.3778	1.01569	0.507845	−	0.861448i	$-0.330442\pi$
$443$	21.3778	1.01569	0.507845	+	0.861448i	$0.330442\pi$
$444$	−3.43020	−0.162790
$445$	−14.4819	−0.686510
$446$	−6.89059	−0.326279
$447$	−8.43129	−0.398786
$448$	3.08102	0.145565
$449$	−33.9420	−1.60182	−0.800912	−	0.598782i	$-0.795651\pi$
$449$	−33.9420	−1.60182	−0.800912	+	0.598782i	$0.795651\pi$
$450$	2.82362	0.133107
$451$	6.48873	0.305542
$452$	−10.0279	−0.471675
$453$	−3.75685	−0.176512
$454$	−2.58662	−0.121396
$455$	−15.2906	−0.716833
$456$	0.854612	0.0400209
$457$	−18.7159	−0.875492	−0.437746	−	0.899099i	$-0.644223\pi$
$457$	−18.7159	−0.875492	−0.437746	+	0.899099i	$0.644223\pi$
$458$	20.0548	0.937098
$459$	−9.47967	−0.442473
$460$	−9.26536	−0.432000
$461$	28.4256	1.32391	0.661956	−	0.749543i	$-0.269727\pi$
$461$	28.4256	1.32391	0.661956	+	0.749543i	$0.269727\pi$
$462$	1.29395	0.0602000
$463$	−25.7737	−1.19781	−0.598903	−	0.800821i	$-0.704397\pi$
$463$	−25.7737	−1.19781	−0.598903	+	0.800821i	$0.704397\pi$
$464$	−10.5516	−0.489848
$465$	−0.114437	−0.00530689
$466$	−4.02190	−0.186311
$467$	−35.0957	−1.62403	−0.812017	−	0.583633i	$-0.801630\pi$
$467$	−35.0957	−1.62403	−0.812017	+	0.583633i	$0.801630\pi$
$468$	−14.0131	−0.647757
$469$	−42.7557	−1.97427
$470$	−4.31345	−0.198965
$471$	−6.36308	−0.293195
$472$	2.66755	0.122784
$473$	−1.00000	−0.0459800
$474$	−1.73767	−0.0798137
$475$	2.03492	0.0933684
$476$	−11.9419	−0.547355
$477$	−10.5187	−0.481619
$478$	−29.9090	−1.36801
$479$	−5.42981	−0.248094	−0.124047	−	0.992276i	$-0.539587\pi$
$479$	−5.42981	−0.248094	−0.124047	+	0.992276i	$0.539587\pi$
$480$	−0.419974	−0.0191691
$481$	40.5346	1.84822
$482$	−1.00496	−0.0457747
$483$	−11.9889	−0.545515
$484$	1.00000	0.0454545
$485$	6.03266	0.273929
$486$	10.4635	0.474633
$487$	−16.0820	−0.728745	−0.364373	−	0.931253i	$-0.618717\pi$
$487$	−16.0820	−0.728745	−0.364373	+	0.931253i	$0.618717\pi$
$488$	−9.70121	−0.439153
$489$	−0.964919	−0.0436351
$490$	2.49271	0.112609
$491$	14.8732	0.671217	0.335608	−	0.942002i	$-0.391058\pi$
$491$	14.8732	0.671217	0.335608	+	0.942002i	$0.391058\pi$
$492$	−2.72510	−0.122857
$493$	40.8976	1.84193
$494$	−10.0989	−0.454372
$495$	2.82362	0.126912
$496$	−0.272486	−0.0122350
$497$	−28.3323	−1.27088
$498$	4.36666	0.195675
$499$	−0.707444	−0.0316695	−0.0158348	−	0.999875i	$-0.505041\pi$
$499$	−0.707444	−0.0316695	−0.0158348	+	0.999875i	$0.505041\pi$
$500$	−1.00000	−0.0447214
$501$	2.88251	0.128781
$502$	−7.67101	−0.342374
$503$	32.3728	1.44343	0.721717	−	0.692189i	$-0.243353\pi$
$503$	32.3728	1.44343	0.721717	+	0.692189i	$0.243353\pi$
$504$	8.69965	0.387513
$505$	2.41810	0.107604
$506$	−9.26536	−0.411896
$507$	−4.88412	−0.216911
$508$	12.0998	0.536842
$509$	−29.1048	−1.29005	−0.645023	−	0.764163i	$-0.723152\pi$
$509$	−29.1048	−1.29005	−0.645023	+	0.764163i	$0.723152\pi$
$510$	1.62780	0.0720801
$511$	16.5295	0.731220
$512$	−1.00000	−0.0441942
$513$	4.97694	0.219737
$514$	−15.2855	−0.674213
$515$	3.20342	0.141160
$516$	0.419974	0.0184883
$517$	−4.31345	−0.189705
$518$	−25.1647	−1.10568
$519$	3.20651	0.140750
$520$	4.96282	0.217634
$521$	−3.18958	−0.139738	−0.0698691	−	0.997556i	$-0.522258\pi$
$521$	−3.18958	−0.139738	−0.0698691	+	0.997556i	$0.522258\pi$
$522$	−29.7938	−1.30404
$523$	6.84483	0.299304	0.149652	−	0.988739i	$-0.452185\pi$
$523$	6.84483	0.299304	0.149652	+	0.988739i	$0.452185\pi$
$524$	−12.5975	−0.550326
$525$	−1.29395	−0.0564726
$526$	−14.5292	−0.633505
$527$	1.05614	0.0460062
$528$	−0.419974	−0.0182770
$529$	62.8469	2.73248
$530$	3.72526	0.161815
$531$	7.53214	0.326867
$532$	6.26963	0.271823
$533$	32.2024	1.39484
$534$	6.08204	0.263196
$535$	6.54483	0.282957
$536$	13.8771	0.599399
$537$	−3.47673	−0.150032
$538$	4.06685	0.175334
$539$	2.49271	0.107369
$540$	−2.44577	−0.105249
$541$	16.0735	0.691053	0.345526	−	0.938409i	$-0.387700\pi$
$541$	16.0735	0.691053	0.345526	+	0.938409i	$0.387700\pi$
$542$	11.3207	0.486267
$543$	−0.225229	−0.00966548
$544$	3.87595	0.166180
$545$	−10.5429	−0.451610
$546$	6.42164	0.274821
$547$	−11.2069	−0.479172	−0.239586	−	0.970875i	$-0.577012\pi$
$547$	−11.2069	−0.479172	−0.239586	+	0.970875i	$0.577012\pi$
$548$	−8.84383	−0.377790
$549$	−27.3926	−1.16909
$550$	−1.00000	−0.0426401
$551$	−21.4717	−0.914725
$552$	3.89121	0.165621
$553$	−12.7479	−0.542097
$554$	−22.1605	−0.941508
$555$	3.43020	0.145604
$556$	5.50569	0.233493
$557$	−5.26927	−0.223266	−0.111633	−	0.993749i	$-0.535608\pi$
$557$	−5.26927	−0.223266	−0.111633	+	0.993749i	$0.535608\pi$
$558$	−0.769397	−0.0325712
$559$	−4.96282	−0.209905
$560$	−3.08102	−0.130197
$561$	1.62780	0.0687256
$562$	16.3027	0.687690
$563$	14.0571	0.592434	0.296217	−	0.955121i	$-0.404275\pi$
$563$	14.0571	0.592434	0.296217	+	0.955121i	$0.404275\pi$
$564$	1.81154	0.0762795
$565$	10.0279	0.421879
$566$	3.08180	0.129538
$567$	22.9342	0.963148
$568$	9.19575	0.385845
$569$	28.7312	1.20447	0.602236	−	0.798318i	$-0.294276\pi$
$569$	28.7312	1.20447	0.602236	+	0.798318i	$0.294276\pi$
$570$	−0.854612	−0.0357958
$571$	36.8609	1.54258	0.771291	−	0.636483i	$-0.219611\pi$
$571$	36.8609	1.54258	0.771291	+	0.636483i	$0.219611\pi$
$572$	4.96282	0.207506
$573$	−5.46962	−0.228497
$574$	−19.9919	−0.834448
$575$	9.26536	0.386392
$576$	−2.82362	−0.117651
$577$	37.8735	1.57670	0.788348	−	0.615230i	$-0.210937\pi$
$577$	37.8735	1.57670	0.788348	+	0.615230i	$0.210937\pi$
$578$	1.97704	0.0822340
$579$	0.461964	0.0191986
$580$	10.5516	0.438133
$581$	32.0348	1.32903
$582$	−2.53356	−0.105019
$583$	3.72526	0.154284
$584$	−5.36492	−0.222002
$585$	14.0131	0.579371
$586$	−20.9616	−0.865917
$587$	−33.0448	−1.36391	−0.681953	−	0.731396i	$-0.738869\pi$
$587$	−33.0448	−1.36391	−0.681953	+	0.731396i	$0.738869\pi$
$588$	−1.04687	−0.0431724
$589$	−0.554486	−0.0228472
$590$	−2.66755	−0.109821
$591$	6.97512	0.286918
$592$	8.16766	0.335689
$593$	−37.3272	−1.53284	−0.766421	−	0.642338i	$-0.777965\pi$
$593$	−37.3272	−1.53284	−0.766421	+	0.642338i	$0.777965\pi$
$594$	−2.44577	−0.100351
$595$	11.9419	0.489570
$596$	20.0757	0.822334
$597$	−6.80697	−0.278591
$598$	−45.9823	−1.88036
$599$	−14.8205	−0.605549	−0.302775	−	0.953062i	$-0.597913\pi$
$599$	−14.8205	−0.605549	−0.302775	+	0.953062i	$0.597913\pi$
$600$	0.419974	0.0171454
$601$	27.0274	1.10247	0.551236	−	0.834349i	$-0.314156\pi$
$601$	27.0274	1.10247	0.551236	+	0.834349i	$0.314156\pi$
$602$	3.08102	0.125573
$603$	39.1837	1.59568
$604$	8.94545	0.363985
$605$	−1.00000	−0.0406558
$606$	−1.01554	−0.0412535
$607$	−29.0923	−1.18082	−0.590411	−	0.807103i	$-0.701034\pi$
$607$	−29.0923	−1.18082	−0.590411	+	0.807103i	$0.701034\pi$
$608$	−2.03492	−0.0825267
$609$	13.6533	0.553259
$610$	9.70121	0.392791
$611$	−21.4069	−0.866030
$612$	10.9442	0.442393
$613$	−20.8738	−0.843084	−0.421542	−	0.906809i	$-0.638511\pi$
$613$	−20.8738	−0.843084	−0.421542	+	0.906809i	$0.638511\pi$
$614$	−14.6079	−0.589526
$615$	2.72510	0.109887
$616$	−3.08102	−0.124138
$617$	−16.8448	−0.678145	−0.339073	−	0.940760i	$-0.610113\pi$
$617$	−16.8448	−0.678145	−0.339073	+	0.940760i	$0.610113\pi$
$618$	−1.34535	−0.0541181
$619$	12.1686	0.489097	0.244548	−	0.969637i	$-0.421360\pi$
$619$	12.1686	0.489097	0.244548	+	0.969637i	$0.421360\pi$
$620$	0.272486	0.0109433
$621$	22.6609	0.909352
$622$	−21.0949	−0.845828
$623$	44.6192	1.78763
$624$	−2.08425	−0.0834370
$625$	1.00000	0.0400000
$626$	26.1722	1.04605
$627$	−0.854612	−0.0341299
$628$	15.1511	0.604596
$629$	−31.6574	−1.26226
$630$	−8.69965	−0.346602
$631$	27.0636	1.07738	0.538692	−	0.842503i	$-0.318919\pi$
$631$	27.0636	1.07738	0.538692	+	0.842503i	$0.318919\pi$
$632$	4.13756	0.164583
$633$	11.4954	0.456899
$634$	2.82279	0.112107
$635$	−12.0998	−0.480166
$636$	−1.56451	−0.0620369
$637$	12.3709	0.490152
$638$	10.5516	0.417743
$639$	25.9653	1.02717
$640$	1.00000	0.0395285
$641$	2.06171	0.0814328	0.0407164	−	0.999171i	$-0.487036\pi$
$641$	2.06171	0.0814328	0.0407164	+	0.999171i	$0.487036\pi$
$642$	−2.74866	−0.108481
$643$	−48.9070	−1.92870	−0.964352	−	0.264623i	$-0.914752\pi$
$643$	−48.9070	−1.92870	−0.964352	+	0.264623i	$0.914752\pi$
$644$	28.5468	1.12490
$645$	−0.419974	−0.0165365
$646$	7.88723	0.310319
$647$	42.7605	1.68109	0.840544	−	0.541743i	$-0.182236\pi$
$647$	42.7605	1.68109	0.840544	+	0.541743i	$0.182236\pi$
$648$	−7.44371	−0.292416
$649$	−2.66755	−0.104710
$650$	−4.96282	−0.194658
$651$	0.352583	0.0138188
$652$	2.29757	0.0899797
$653$	19.7332	0.772221	0.386111	−	0.922452i	$-0.373818\pi$
$653$	19.7332	0.772221	0.386111	+	0.922452i	$0.373818\pi$
$654$	4.42776	0.173139
$655$	12.5975	0.492227
$656$	6.48873	0.253342
$657$	−15.1485	−0.591000
$658$	13.2899	0.518092
$659$	−32.6962	−1.27366	−0.636832	−	0.771003i	$-0.719755\pi$
$659$	−32.6962	−1.27366	−0.636832	+	0.771003i	$0.719755\pi$
$660$	0.419974	0.0163475
$661$	41.8236	1.62675	0.813375	−	0.581740i	$-0.197628\pi$
$661$	41.8236	1.62675	0.813375	+	0.581740i	$0.197628\pi$
$662$	−27.9232	−1.08527
$663$	8.07846	0.313741
$664$	−10.3975	−0.403500
$665$	−6.26963	−0.243126
$666$	23.0624	0.893649
$667$	−97.7648	−3.78547
$668$	−6.86355	−0.265559
$669$	−2.89387	−0.111884
$670$	−13.8771	−0.536119
$671$	9.70121	0.374511
$672$	1.29395	0.0499152
$673$	−47.5415	−1.83259	−0.916294	−	0.400505i	$-0.868835\pi$
$673$	−47.5415	−1.83259	−0.916294	+	0.400505i	$0.868835\pi$
$674$	−10.6973	−0.412044
$675$	2.44577	0.0941377
$676$	11.6296	0.447291
$677$	17.9465	0.689740	0.344870	−	0.938650i	$-0.387923\pi$
$677$	17.9465	0.689740	0.344870	+	0.938650i	$0.387923\pi$
$678$	−4.21148	−0.161741
$679$	−18.5868	−0.713295
$680$	−3.87595	−0.148636
$681$	−1.08631	−0.0416276
$682$	0.272486	0.0104340
$683$	50.8671	1.94638	0.973189	−	0.230009i	$-0.0738755\pi$
$683$	50.8671	1.94638	0.973189	+	0.230009i	$0.0738755\pi$
$684$	−5.74583	−0.219697
$685$	8.84383	0.337905
$686$	13.8871	0.530211
$687$	8.42248	0.321338
$688$	−1.00000	−0.0381246
$689$	18.4878	0.704329
$690$	−3.89121	−0.148136
$691$	−26.9878	−1.02667	−0.513333	−	0.858190i	$-0.671589\pi$
$691$	−26.9878	−1.02667	−0.513333	+	0.858190i	$0.671589\pi$
$692$	−7.63502	−0.290240
$693$	−8.69965	−0.330472
$694$	24.2060	0.918848
$695$	−5.50569	−0.208843
$696$	−4.43141	−0.167972
$697$	−25.1500	−0.952623
$698$	−35.0672	−1.32731
$699$	−1.68909	−0.0638873
$700$	3.08102	0.116452
$701$	−7.22798	−0.272997	−0.136498	−	0.990640i	$-0.543585\pi$
$701$	−7.22798	−0.272997	−0.136498	+	0.990640i	$0.543585\pi$
$702$	−12.1379	−0.458116
$703$	16.6205	0.626854
$704$	1.00000	0.0376889
$705$	−1.81154	−0.0682265
$706$	−16.3562	−0.615573
$707$	−7.45023	−0.280195
$708$	1.12030	0.0421034
$709$	33.0255	1.24030	0.620149	−	0.784484i	$-0.287072\pi$
$709$	33.0255	1.24030	0.620149	+	0.784484i	$0.287072\pi$
$710$	−9.19575	−0.345110
$711$	11.6829	0.438143
$712$	−14.4819	−0.542734
$713$	−2.52468	−0.0945500
$714$	−5.01528	−0.187692
$715$	−4.96282	−0.185599
$716$	8.27843	0.309380
$717$	−12.5610	−0.469100
$718$	−22.3116	−0.832660
$719$	−6.92480	−0.258251	−0.129126	−	0.991628i	$-0.541217\pi$
$719$	−6.92480	−0.258251	−0.129126	+	0.991628i	$0.541217\pi$
$720$	2.82362	0.105230
$721$	−9.86982	−0.367571
$722$	14.8591	0.552999
$723$	−0.422057	−0.0156965
$724$	0.536292	0.0199311
$725$	−10.5516	−0.391878
$726$	0.419974	0.0155867
$727$	−18.7467	−0.695277	−0.347639	−	0.937629i	$-0.613016\pi$
$727$	−18.7467	−0.695277	−0.347639	+	0.937629i	$0.613016\pi$
$728$	−15.2906	−0.566706
$729$	−17.9367	−0.664323
$730$	5.36492	0.198565
$731$	3.87595	0.143357
$732$	−4.07426	−0.150589
$733$	−23.2899	−0.860232	−0.430116	−	0.902774i	$-0.641527\pi$
$733$	−23.2899	−0.860232	−0.430116	+	0.902774i	$0.641527\pi$
$734$	−23.1718	−0.855285
$735$	1.04687	0.0386145
$736$	−9.26536	−0.341526
$737$	−13.8771	−0.511169
$738$	18.3217	0.674432
$739$	−20.6222	−0.758600	−0.379300	−	0.925274i	$-0.623835\pi$
$739$	−20.6222	−0.758600	−0.379300	+	0.925274i	$0.623835\pi$
$740$	−8.16766	−0.300249
$741$	−4.24128	−0.155807
$742$	−11.4776	−0.421356
$743$	16.7793	0.615572	0.307786	−	0.951456i	$-0.400412\pi$
$743$	16.7793	0.615572	0.307786	+	0.951456i	$0.400412\pi$
$744$	−0.114437	−0.00419546
$745$	−20.0757	−0.735518
$746$	−17.0835	−0.625470
$747$	−29.3585	−1.07417
$748$	−3.87595	−0.141719
$749$	−20.1648	−0.736805
$750$	−0.419974	−0.0153353
$751$	−21.2924	−0.776972	−0.388486	−	0.921455i	$-0.627002\pi$
$751$	−21.2924	−0.776972	−0.388486	+	0.921455i	$0.627002\pi$
$752$	−4.31345	−0.157295
$753$	−3.22163	−0.117403
$754$	52.3659	1.90705
$755$	−8.94545	−0.325558
$756$	7.53548	0.274063
$757$	−1.19074	−0.0432781	−0.0216391	−	0.999766i	$-0.506888\pi$
$757$	−1.19074	−0.0432781	−0.0216391	+	0.999766i	$0.506888\pi$
$758$	−16.9163	−0.614427
$759$	−3.89121	−0.141242
$760$	2.03492	0.0738142
$761$	32.7977	1.18892	0.594458	−	0.804126i	$-0.297367\pi$
$761$	32.7977	1.18892	0.594458	+	0.804126i	$0.297367\pi$
$762$	5.08160	0.184087
$763$	32.4831	1.17597
$764$	13.0237	0.471181
$765$	−10.9442	−0.395689
$766$	−27.3917	−0.989702
$767$	−13.2385	−0.478016
$768$	−0.419974	−0.0151545
$769$	−47.5887	−1.71609	−0.858047	−	0.513572i	$-0.828322\pi$
$769$	−47.5887	−1.71609	−0.858047	+	0.513572i	$0.828322\pi$
$770$	3.08102	0.111032
$771$	−6.41950	−0.231192
$772$	−1.09998	−0.0395892
$773$	−16.0575	−0.577548	−0.288774	−	0.957397i	$-0.593248\pi$
$773$	−16.0575	−0.577548	−0.288774	+	0.957397i	$0.593248\pi$
$774$	−2.82362	−0.101493
$775$	−0.272486	−0.00978798
$776$	6.03266	0.216560
$777$	−10.5685	−0.379144
$778$	−14.2552	−0.511075
$779$	13.2040	0.473083
$780$	2.08425	0.0746283
$781$	−9.19575	−0.329050
$782$	35.9120	1.28421
$783$	−25.8069	−0.922263
$784$	2.49271	0.0890254
$785$	−15.1511	−0.540767
$786$	−5.29064	−0.188711
$787$	−7.39034	−0.263437	−0.131719	−	0.991287i	$-0.542050\pi$
$787$	−7.39034	−0.263437	−0.131719	+	0.991287i	$0.542050\pi$
$788$	−16.6085	−0.591652
$789$	−6.10190	−0.217233
$790$	−4.13756	−0.147208
$791$	−30.8963	−1.09855
$792$	2.82362	0.100333
$793$	48.1454	1.70969
$794$	−12.7090	−0.451025
$795$	1.56451	0.0554875
$796$	16.2081	0.574480
$797$	19.9406	0.706332	0.353166	−	0.935561i	$-0.385105\pi$
$797$	19.9406	0.706332	0.353166	+	0.935561i	$0.385105\pi$
$798$	2.63308	0.0932100
$799$	16.7187	0.591465
$800$	−1.00000	−0.0353553
$801$	−40.8915	−1.44483
$802$	8.42385	0.297457
$803$	5.36492	0.189324
$804$	5.82802	0.205538
$805$	−28.5468	−1.00614
$806$	1.35230	0.0476326
$807$	1.70797	0.0601234
$808$	2.41810	0.0850685
$809$	25.8833	0.910009	0.455004	−	0.890489i	$-0.349638\pi$
$809$	25.8833	0.910009	0.455004	+	0.890489i	$0.349638\pi$
$810$	7.44371	0.261545
$811$	49.8887	1.75183	0.875914	−	0.482466i	$-0.160259\pi$
$811$	49.8887	1.75183	0.875914	+	0.482466i	$0.160259\pi$
$812$	−32.5099	−1.14087
$813$	4.75441	0.166745
$814$	−8.16766	−0.286276
$815$	−2.29757	−0.0804803
$816$	1.62780	0.0569843
$817$	−2.03492	−0.0711927
$818$	28.4803	0.995789
$819$	−43.1748	−1.50865
$820$	−6.48873	−0.226596
$821$	7.41542	0.258800	0.129400	−	0.991592i	$-0.458695\pi$
$821$	7.41542	0.258800	0.129400	+	0.991592i	$0.458695\pi$
$822$	−3.71418	−0.129547
$823$	−14.1699	−0.493933	−0.246967	−	0.969024i	$-0.579434\pi$
$823$	−14.1699	−0.493933	−0.246967	+	0.969024i	$0.579434\pi$
$824$	3.20342	0.111596
$825$	−0.419974	−0.0146216
$826$	8.21877	0.285968
$827$	−27.2628	−0.948021	−0.474011	−	0.880519i	$-0.657194\pi$
$827$	−27.2628	−0.948021	−0.474011	+	0.880519i	$0.657194\pi$
$828$	−26.1619	−0.909188
$829$	11.3256	0.393356	0.196678	−	0.980468i	$-0.436985\pi$
$829$	11.3256	0.393356	0.196678	+	0.980468i	$0.436985\pi$
$830$	10.3975	0.360901
$831$	−9.30682	−0.322850
$832$	4.96282	0.172055
$833$	−9.66162	−0.334755
$834$	2.31225	0.0800665
$835$	6.86355	0.237523
$836$	2.03492	0.0703790
$837$	−0.666437	−0.0230354
$838$	−16.8540	−0.582212
$839$	−16.5220	−0.570401	−0.285201	−	0.958468i	$-0.592060\pi$
$839$	−16.5220	−0.570401	−0.285201	+	0.958468i	$0.592060\pi$
$840$	−1.29395	−0.0446455
$841$	82.3371	2.83921
$842$	−16.3054	−0.561920
$843$	6.84673	0.235814
$844$	−27.3716	−0.942169
$845$	−11.6296	−0.400069
$846$	−12.1796	−0.418742
$847$	3.08102	0.105865
$848$	3.72526	0.127926
$849$	1.29428	0.0444195
$850$	3.87595	0.132944
$851$	75.6763	2.59415
$852$	3.86197	0.132309
$853$	−38.1889	−1.30756	−0.653781	−	0.756684i	$-0.726818\pi$
$853$	−38.1889	−1.30756	−0.653781	+	0.756684i	$0.726818\pi$
$854$	−29.8897	−1.02280
$855$	5.74583	0.196503
$856$	6.54483	0.223698
$857$	−32.4500	−1.10847	−0.554236	−	0.832360i	$-0.686990\pi$
$857$	−32.4500	−1.10847	−0.554236	+	0.832360i	$0.686990\pi$
$858$	2.08425	0.0711553
$859$	23.6325	0.806331	0.403165	−	0.915127i	$-0.367910\pi$
$859$	23.6325	0.806331	0.403165	+	0.915127i	$0.367910\pi$
$860$	1.00000	0.0340997
$861$	−8.39610	−0.286138
$862$	8.14801	0.277522
$863$	27.7154	0.943443	0.471722	−	0.881748i	$-0.343633\pi$
$863$	27.7154	0.943443	0.471722	+	0.881748i	$0.343633\pi$
$864$	−2.44577	−0.0832068
$865$	7.63502	0.259598
$866$	−37.0222	−1.25806
$867$	0.830305	0.0281986
$868$	−0.839535	−0.0284957
$869$	−4.13756	−0.140357
$870$	4.43141	0.150239
$871$	−68.8695	−2.33355
$872$	−10.5429	−0.357029
$873$	17.0340	0.576512
$874$	−18.8542	−0.637754
$875$	−3.08102	−0.104158
$876$	−2.25313	−0.0761262
$877$	−33.7075	−1.13822	−0.569110	−	0.822261i	$-0.692712\pi$
$877$	−33.7075	−1.13822	−0.569110	+	0.822261i	$0.692712\pi$
$878$	−20.2147	−0.682214
$879$	−8.80334	−0.296929
$880$	−1.00000	−0.0337100
$881$	−37.2119	−1.25370	−0.626850	−	0.779140i	$-0.715656\pi$
$881$	−37.2119	−1.25370	−0.626850	+	0.779140i	$0.715656\pi$
$882$	7.03848	0.236998
$883$	−26.0341	−0.876118	−0.438059	−	0.898946i	$-0.644334\pi$
$883$	−26.0341	−0.876118	−0.438059	+	0.898946i	$0.644334\pi$
$884$	−19.2356	−0.646964
$885$	−1.12030	−0.0376585
$886$	−21.3778	−0.718201
$887$	−21.2267	−0.712724	−0.356362	−	0.934348i	$-0.615983\pi$
$887$	−21.2267	−0.712724	−0.356362	+	0.934348i	$0.615983\pi$
$888$	3.43020	0.115110
$889$	37.2798	1.25032
$890$	14.4819	0.485436
$891$	7.44371	0.249374
$892$	6.89059	0.230714
$893$	−8.77751	−0.293728
$894$	8.43129	0.281984
$895$	−8.27843	−0.276718
$896$	−3.08102	−0.102930
$897$	−19.3114	−0.644788
$898$	33.9420	1.13266
$899$	2.87517	0.0958923
$900$	−2.82362	−0.0941207
$901$	−14.4389	−0.481030
$902$	−6.48873	−0.216051
$903$	1.29395	0.0430600
$904$	10.0279	0.333524
$905$	−0.536292	−0.0178269
$906$	3.75685	0.124813
$907$	20.7068	0.687559	0.343780	−	0.939050i	$-0.388293\pi$
$907$	20.7068	0.687559	0.343780	+	0.939050i	$0.388293\pi$
$908$	2.58662	0.0858400
$909$	6.82780	0.226464
$910$	15.2906	0.506877
$911$	4.04821	0.134123	0.0670616	−	0.997749i	$-0.478638\pi$
$911$	4.04821	0.134123	0.0670616	+	0.997749i	$0.478638\pi$
$912$	−0.854612	−0.0282990
$913$	10.3975	0.344106
$914$	18.7159	0.619066
$915$	4.07426	0.134691
$916$	−20.0548	−0.662628
$917$	−38.8133	−1.28173
$918$	9.47967	0.312876
$919$	−29.0280	−0.957545	−0.478772	−	0.877939i	$-0.658918\pi$
$919$	−29.0280	−0.957545	−0.478772	+	0.877939i	$0.658918\pi$
$920$	9.26536	0.305470
$921$	−6.13493	−0.202153
$922$	−28.4256	−0.936147
$923$	−45.6368	−1.50215
$924$	−1.29395	−0.0425678
$925$	8.16766	0.268551
$926$	25.7737	0.846977
$927$	9.04525	0.297085
$928$	10.5516	0.346374
$929$	51.0467	1.67479	0.837394	−	0.546600i	$-0.184078\pi$
$929$	51.0467	1.67479	0.837394	+	0.546600i	$0.184078\pi$
$930$	0.114437	0.00375253
$931$	5.07246	0.166243
$932$	4.02190	0.131742
$933$	−8.85930	−0.290041
$934$	35.0957	1.14837
$935$	3.87595	0.126757
$936$	14.0131	0.458033
$937$	−4.18143	−0.136601	−0.0683006	−	0.997665i	$-0.521758\pi$
$937$	−4.18143	−0.136601	−0.0683006	+	0.997665i	$0.521758\pi$
$938$	42.7557	1.39602
$939$	10.9916	0.358698
$940$	4.31345	0.140689
$941$	28.0453	0.914252	0.457126	−	0.889402i	$-0.348879\pi$
$941$	28.0453	0.914252	0.457126	+	0.889402i	$0.348879\pi$
$942$	6.36308	0.207320
$943$	60.1205	1.95779
$944$	−2.66755	−0.0868212
$945$	−7.53548	−0.245129
$946$	1.00000	0.0325128
$947$	−30.9043	−1.00426	−0.502128	−	0.864793i	$-0.667449\pi$
$947$	−30.9043	−1.00426	−0.502128	+	0.864793i	$0.667449\pi$
$948$	1.73767	0.0564368
$949$	26.6251	0.864289
$950$	−2.03492	−0.0660214
$951$	1.18550	0.0384424
$952$	11.9419	0.387039
$953$	−57.2421	−1.85425	−0.927127	−	0.374747i	$-0.877730\pi$
$953$	−57.2421	−1.85425	−0.927127	+	0.374747i	$0.877730\pi$
$954$	10.5187	0.340556
$955$	−13.0237	−0.421437
$956$	29.9090	0.967327
$957$	4.43141	0.143247
$958$	5.42981	0.175429
$959$	−27.2480	−0.879885
$960$	0.419974	0.0135546
$961$	−30.9258	−0.997605
$962$	−40.5346	−1.30689
$963$	18.4801	0.595513
$964$	1.00496	0.0323676
$965$	1.09998	0.0354097
$966$	11.9889	0.385737
$967$	−29.1555	−0.937578	−0.468789	−	0.883310i	$-0.655310\pi$
$967$	−29.1555	−0.937578	−0.468789	+	0.883310i	$0.655310\pi$
$968$	−1.00000	−0.0321412
$969$	3.31243	0.106411
$970$	−6.03266	−0.193697
$971$	−40.8494	−1.31092	−0.655460	−	0.755230i	$-0.727525\pi$
$971$	−40.8494	−1.31092	−0.655460	+	0.755230i	$0.727525\pi$
$972$	−10.4635	−0.335616
$973$	16.9632	0.543814
$974$	16.0820	0.515301
$975$	−2.08425	−0.0667496
$976$	9.70121	0.310528
$977$	18.4280	0.589564	0.294782	−	0.955564i	$-0.404753\pi$
$977$	18.4280	0.589564	0.294782	+	0.955564i	$0.404753\pi$
$978$	0.964919	0.0308547
$979$	14.4819	0.462845
$980$	−2.49271	−0.0796268
$981$	−29.7693	−0.950460
$982$	−14.8732	−0.474622
$983$	−8.74264	−0.278847	−0.139423	−	0.990233i	$-0.544525\pi$
$983$	−8.74264	−0.278847	−0.139423	+	0.990233i	$0.544525\pi$
$984$	2.72510	0.0868730
$985$	16.6085	0.529189
$986$	−40.8976	−1.30244
$987$	5.58139	0.177658
$988$	10.0989	0.321289
$989$	−9.26536	−0.294621
$990$	−2.82362	−0.0897406
$991$	26.8154	0.851820	0.425910	−	0.904766i	$-0.359954\pi$
$991$	26.8154	0.851820	0.425910	+	0.904766i	$0.359954\pi$
$992$	0.272486	0.00865143
$993$	−11.7270	−0.372146
$994$	28.3323	0.898647
$995$	−16.2081	−0.513830
$996$	−4.36666	−0.138363
$997$	−14.0677	−0.445530	−0.222765	−	0.974872i	$-0.571508\pi$
$997$	−14.0677	−0.445530	−0.222765	+	0.974872i	$0.571508\pi$
$998$	0.707444	0.0223938
$999$	19.9762	0.632019

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4730.2.a.bc.1.5	✓	11

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4730.2.a.bc.1.5	✓	11	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)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -0.419974 q^{3} +1.00000 q^{4} -1.00000 q^{5} +0.419974 q^{6} +3.08102 q^{7} -1.00000 q^{8} -2.82362 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -0.419974 q^{3} +1.00000 q^{4} -1.00000 q^{5} +0.419974 q^{6} +3.08102 q^{7} -1.00000 q^{8} -2.82362 q^{9} +1.00000 q^{10} +1.00000 q^{11} -0.419974 q^{12} +4.96282 q^{13} -3.08102 q^{14} +0.419974 q^{15} +1.00000 q^{16} -3.87595 q^{17} +2.82362 q^{18} +2.03492 q^{19} -1.00000 q^{20} -1.29395 q^{21} -1.00000 q^{22} +9.26536 q^{23} +0.419974 q^{24} +1.00000 q^{25} -4.96282 q^{26} +2.44577 q^{27} +3.08102 q^{28} -10.5516 q^{29} -0.419974 q^{30} -0.272486 q^{31} -1.00000 q^{32} -0.419974 q^{33} +3.87595 q^{34} -3.08102 q^{35} -2.82362 q^{36} +8.16766 q^{37} -2.03492 q^{38} -2.08425 q^{39} +1.00000 q^{40} +6.48873 q^{41} +1.29395 q^{42} -1.00000 q^{43} +1.00000 q^{44} +2.82362 q^{45} -9.26536 q^{46} -4.31345 q^{47} -0.419974 q^{48} +2.49271 q^{49} -1.00000 q^{50} +1.62780 q^{51} +4.96282 q^{52} +3.72526 q^{53} -2.44577 q^{54} -1.00000 q^{55} -3.08102 q^{56} -0.854612 q^{57} +10.5516 q^{58} -2.66755 q^{59} +0.419974 q^{60} +9.70121 q^{61} +0.272486 q^{62} -8.69965 q^{63} +1.00000 q^{64} -4.96282 q^{65} +0.419974 q^{66} -13.8771 q^{67} -3.87595 q^{68} -3.89121 q^{69} +3.08102 q^{70} -9.19575 q^{71} +2.82362 q^{72} +5.36492 q^{73} -8.16766 q^{74} -0.419974 q^{75} +2.03492 q^{76} +3.08102 q^{77} +2.08425 q^{78} -4.13756 q^{79} -1.00000 q^{80} +7.44371 q^{81} -6.48873 q^{82} +10.3975 q^{83} -1.29395 q^{84} +3.87595 q^{85} +1.00000 q^{86} +4.43141 q^{87} -1.00000 q^{88} +14.4819 q^{89} -2.82362 q^{90} +15.2906 q^{91} +9.26536 q^{92} +0.114437 q^{93} +4.31345 q^{94} -2.03492 q^{95} +0.419974 q^{96} -6.03266 q^{97} -2.49271 q^{98} -2.82362 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 11 q - 11 q^{2} + 11 q^{4} - 11 q^{5} - 11 q^{8} + 15 q^{9}+O(q^{10}) \) 11 * q - 11 * q^2 + 11 * q^4 - 11 * q^5 - 11 * q^8 + 15 * q^9	\( 11 q - 11 q^{2} + 11 q^{4} - 11 q^{5} - 11 q^{8} + 15 q^{9} + 11 q^{10} + 11 q^{11} - q^{13} + 11 q^{16} - 15 q^{17} - 15 q^{18} + 14 q^{19} - 11 q^{20} + 7 q^{21} - 11 q^{22} - 2 q^{23} + 11 q^{25} + q^{26} + 3 q^{27} + 6 q^{29} + 13 q^{31} - 11 q^{32} + 15 q^{34} + 15 q^{36} + 16 q^{37} - 14 q^{38} + 4 q^{39} + 11 q^{40} - 7 q^{41} - 7 q^{42} - 11 q^{43} + 11 q^{44} - 15 q^{45} + 2 q^{46} - 19 q^{47} + 23 q^{49} - 11 q^{50} + 32 q^{51} - q^{52} - 16 q^{53} - 3 q^{54} - 11 q^{55} - 2 q^{57} - 6 q^{58} + 7 q^{59} + 20 q^{61} - 13 q^{62} + 11 q^{64} + q^{65} + 9 q^{67} - 15 q^{68} + 10 q^{69} + 13 q^{71} - 15 q^{72} + 20 q^{73} - 16 q^{74} + 14 q^{76} - 4 q^{78} + 13 q^{79} - 11 q^{80} + 19 q^{81} + 7 q^{82} - 6 q^{83} + 7 q^{84} + 15 q^{85} + 11 q^{86} - 23 q^{87} - 11 q^{88} + 10 q^{89} + 15 q^{90} + 43 q^{91} - 2 q^{92} + 22 q^{93} + 19 q^{94} - 14 q^{95} + 3 q^{97} - 23 q^{98} + 15 q^{99}+O(q^{100}) \) 11 * q - 11 * q^2 + 11 * q^4 - 11 * q^5 - 11 * q^8 + 15 * q^9 + 11 * q^10 + 11 * q^11 - q^13 + 11 * q^16 - 15 * q^17 - 15 * q^18 + 14 * q^19 - 11 * q^20 + 7 * q^21 - 11 * q^22 - 2 * q^23 + 11 * q^25 + q^26 + 3 * q^27 + 6 * q^29 + 13 * q^31 - 11 * q^32 + 15 * q^34 + 15 * q^36 + 16 * q^37 - 14 * q^38 + 4 * q^39 + 11 * q^40 - 7 * q^41 - 7 * q^42 - 11 * q^43 + 11 * q^44 - 15 * q^45 + 2 * q^46 - 19 * q^47 + 23 * q^49 - 11 * q^50 + 32 * q^51 - q^52 - 16 * q^53 - 3 * q^54 - 11 * q^55 - 2 * q^57 - 6 * q^58 + 7 * q^59 + 20 * q^61 - 13 * q^62 + 11 * q^64 + q^65 + 9 * q^67 - 15 * q^68 + 10 * q^69 + 13 * q^71 - 15 * q^72 + 20 * q^73 - 16 * q^74 + 14 * q^76 - 4 * q^78 + 13 * q^79 - 11 * q^80 + 19 * q^81 + 7 * q^82 - 6 * q^83 + 7 * q^84 + 15 * q^85 + 11 * q^86 - 23 * q^87 - 11 * q^88 + 10 * q^89 + 15 * q^90 + 43 * q^91 - 2 * q^92 + 22 * q^93 + 19 * q^94 - 14 * q^95 + 3 * q^97 - 23 * q^98 + 15 * q^99

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