LMFDB - Embedded newform 4730.2.a.bb.1.4

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} - x^{10} - 22 x^{9} + 21 x^{8} + 165 x^{7} - 130 x^{6} - 535 x^{5} + 323 x^{4} + 710 x^{3} + \cdots + 128 $ x^11 - x^10 - 22x^9 + 21x^8 + 165x^7 - 130x^6 - 535x^5 + 323x^4 + 710x^3 - 343x^2 - 261*x + 128
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			1.4
Root			$1.48284$ 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)

$f(q)$	$=$	$q-1.00000 q^{2} -1.48284 q^{3} +1.00000 q^{4} -1.00000 q^{5} +1.48284 q^{6} +4.82678 q^{7} -1.00000 q^{8} -0.801199 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -1.48284 q^{3} +1.00000 q^{4} -1.00000 q^{5} +1.48284 q^{6} +4.82678 q^{7} -1.00000 q^{8} -0.801199 q^{9} +1.00000 q^{10} -1.00000 q^{11} -1.48284 q^{12} +3.11595 q^{13} -4.82678 q^{14} +1.48284 q^{15} +1.00000 q^{16} +7.03311 q^{17} +0.801199 q^{18} +6.23135 q^{19} -1.00000 q^{20} -7.15731 q^{21} +1.00000 q^{22} +1.11595 q^{23} +1.48284 q^{24} +1.00000 q^{25} -3.11595 q^{26} +5.63655 q^{27} +4.82678 q^{28} +3.16385 q^{29} -1.48284 q^{30} -4.13157 q^{31} -1.00000 q^{32} +1.48284 q^{33} -7.03311 q^{34} -4.82678 q^{35} -0.801199 q^{36} +3.75260 q^{37} -6.23135 q^{38} -4.62044 q^{39} +1.00000 q^{40} -5.76616 q^{41} +7.15731 q^{42} +1.00000 q^{43} -1.00000 q^{44} +0.801199 q^{45} -1.11595 q^{46} +10.3447 q^{47} -1.48284 q^{48} +16.2978 q^{49} -1.00000 q^{50} -10.4289 q^{51} +3.11595 q^{52} -10.1774 q^{53} -5.63655 q^{54} +1.00000 q^{55} -4.82678 q^{56} -9.24006 q^{57} -3.16385 q^{58} +9.27380 q^{59} +1.48284 q^{60} +11.2530 q^{61} +4.13157 q^{62} -3.86721 q^{63} +1.00000 q^{64} -3.11595 q^{65} -1.48284 q^{66} -11.3564 q^{67} +7.03311 q^{68} -1.65477 q^{69} +4.82678 q^{70} +1.75115 q^{71} +0.801199 q^{72} +6.29746 q^{73} -3.75260 q^{74} -1.48284 q^{75} +6.23135 q^{76} -4.82678 q^{77} +4.62044 q^{78} -9.80398 q^{79} -1.00000 q^{80} -5.95448 q^{81} +5.76616 q^{82} -7.75457 q^{83} -7.15731 q^{84} -7.03311 q^{85} -1.00000 q^{86} -4.69147 q^{87} +1.00000 q^{88} -11.1654 q^{89} -0.801199 q^{90} +15.0400 q^{91} +1.11595 q^{92} +6.12644 q^{93} -10.3447 q^{94} -6.23135 q^{95} +1.48284 q^{96} -0.459065 q^{97} -16.2978 q^{98} +0.801199 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 11 q - 11 q^{2} - q^{3} + 11 q^{4} - 11 q^{5} + q^{6} + 6 q^{7} - 11 q^{8} + 12 q^{9}+O(q^{10}) $ 11 * q - 11 * q^2 - q^3 + 11 * q^4 - 11 * q^5 + q^6 + 6 * q^7 - 11 * q^8 + 12 * q^9	\( 11 q - 11 q^{2} - q^{3} + 11 q^{4} - 11 q^{5} + q^{6} + 6 q^{7} - 11 q^{8} + 12 q^{9} + 11 q^{10} - 11 q^{11} - q^{12} + 4 q^{13} - 6 q^{14} + q^{15} + 11 q^{16} - 10 q^{17} - 12 q^{18} + 14 q^{19} - 11 q^{20} - 2 q^{21} + 11 q^{22} - 18 q^{23} + q^{24} + 11 q^{25} - 4 q^{26} + 2 q^{27} + 6 q^{28} - 6 q^{29} - q^{30} + 13 q^{31} - 11 q^{32} + q^{33} + 10 q^{34} - 6 q^{35} + 12 q^{36} + q^{37} - 14 q^{38} + 12 q^{39} + 11 q^{40} + 12 q^{41} + 2 q^{42} + 11 q^{43} - 11 q^{44} - 12 q^{45} + 18 q^{46} - 5 q^{47} - q^{48} + 31 q^{49} - 11 q^{50} + q^{51} + 4 q^{52} - 27 q^{53} - 2 q^{54} + 11 q^{55} - 6 q^{56} - 5 q^{57} + 6 q^{58} + 11 q^{59} + q^{60} + 36 q^{61} - 13 q^{62} + 17 q^{63} + 11 q^{64} - 4 q^{65} - q^{66} + 18 q^{67} - 10 q^{68} + 14 q^{69} + 6 q^{70} - 14 q^{71} - 12 q^{72} - 11 q^{73} - q^{74} - q^{75} + 14 q^{76} - 6 q^{77} - 12 q^{78} + 28 q^{79} - 11 q^{80} + 7 q^{81} - 12 q^{82} - 4 q^{83} - 2 q^{84} + 10 q^{85} - 11 q^{86} + 38 q^{87} + 11 q^{88} - 7 q^{89} + 12 q^{90} + 14 q^{91} - 18 q^{92} - 3 q^{93} + 5 q^{94} - 14 q^{95} + q^{96} - q^{97} - 31 q^{98} - 12 q^{99}+O(q^{100}) \) 11 * q - 11 * q^2 - q^3 + 11 * q^4 - 11 * q^5 + q^6 + 6 * q^7 - 11 * q^8 + 12 * q^9 + 11 * q^10 - 11 * q^11 - q^12 + 4 * q^13 - 6 * q^14 + q^15 + 11 * q^16 - 10 * q^17 - 12 * q^18 + 14 * q^19 - 11 * q^20 - 2 * q^21 + 11 * q^22 - 18 * q^23 + q^24 + 11 * q^25 - 4 * q^26 + 2 * q^27 + 6 * q^28 - 6 * q^29 - q^30 + 13 * q^31 - 11 * q^32 + q^33 + 10 * q^34 - 6 * q^35 + 12 * q^36 + q^37 - 14 * q^38 + 12 * q^39 + 11 * q^40 + 12 * q^41 + 2 * q^42 + 11 * q^43 - 11 * q^44 - 12 * q^45 + 18 * q^46 - 5 * q^47 - q^48 + 31 * q^49 - 11 * q^50 + q^51 + 4 * q^52 - 27 * q^53 - 2 * q^54 + 11 * q^55 - 6 * q^56 - 5 * q^57 + 6 * q^58 + 11 * q^59 + q^60 + 36 * q^61 - 13 * q^62 + 17 * q^63 + 11 * q^64 - 4 * q^65 - q^66 + 18 * q^67 - 10 * q^68 + 14 * q^69 + 6 * q^70 - 14 * q^71 - 12 * q^72 - 11 * q^73 - q^74 - q^75 + 14 * q^76 - 6 * q^77 - 12 * q^78 + 28 * q^79 - 11 * q^80 + 7 * q^81 - 12 * q^82 - 4 * q^83 - 2 * q^84 + 10 * q^85 - 11 * q^86 + 38 * q^87 + 11 * q^88 - 7 * q^89 + 12 * q^90 + 14 * q^91 - 18 * q^92 - 3 * q^93 + 5 * q^94 - 14 * q^95 + q^96 - q^97 - 31 * q^98 - 12 * 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
$3$	−1.48284	−0.856115	−0.428058	−	0.903751i	$-0.640802\pi$
$3$	−1.48284	−0.856115	−0.428058	+	0.903751i	$0.640802\pi$
$4$	1.00000	0.500000
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	1.48284	0.605365
$7$	4.82678	1.82435	0.912175	−	0.409801i	$-0.134402\pi$
$7$	4.82678	1.82435	0.912175	+	0.409801i	$0.134402\pi$
$8$	−1.00000	−0.353553
$9$	−0.801199	−0.267066
$10$	1.00000	0.316228
$11$	−1.00000	−0.301511
$11$	−1.00000	−0.301511
$12$	−1.48284	−0.428058
$13$	3.11595	0.864209	0.432105	−	0.901823i	$-0.357771\pi$
$13$	3.11595	0.864209	0.432105	+	0.901823i	$0.357771\pi$
$14$	−4.82678	−1.29001
$15$	1.48284	0.382866
$16$	1.00000	0.250000
$17$	7.03311	1.70578	0.852890	−	0.522091i	$-0.174848\pi$
$17$	7.03311	1.70578	0.852890	+	0.522091i	$0.174848\pi$
$18$	0.801199	0.188844
$19$	6.23135	1.42957	0.714785	−	0.699345i	$-0.246525\pi$
$19$	6.23135	1.42957	0.714785	+	0.699345i	$0.246525\pi$
$20$	−1.00000	−0.223607
$21$	−7.15731	−1.56185
$22$	1.00000	0.213201
$23$	1.11595	0.232692	0.116346	−	0.993209i	$-0.462882\pi$
$23$	1.11595	0.232692	0.116346	+	0.993209i	$0.462882\pi$
$24$	1.48284	0.302682
$25$	1.00000	0.200000
$26$	−3.11595	−0.611088
$27$	5.63655	1.08476
$28$	4.82678	0.912175
$29$	3.16385	0.587512	0.293756	−	0.955880i	$-0.405095\pi$
$29$	3.16385	0.587512	0.293756	+	0.955880i	$0.405095\pi$
$30$	−1.48284	−0.270727
$31$	−4.13157	−0.742052	−0.371026	−	0.928623i	$-0.620994\pi$
$31$	−4.13157	−0.742052	−0.371026	+	0.928623i	$0.620994\pi$
$32$	−1.00000	−0.176777
$33$	1.48284	0.258129
$34$	−7.03311	−1.20617
$35$	−4.82678	−0.815874
$36$	−0.801199	−0.133533
$37$	3.75260	0.616924	0.308462	−	0.951237i	$-0.400186\pi$
$37$	3.75260	0.616924	0.308462	+	0.951237i	$0.400186\pi$
$38$	−6.23135	−1.01086
$39$	−4.62044	−0.739863
$40$	1.00000	0.158114
$41$	−5.76616	−0.900524	−0.450262	−	0.892897i	$-0.648669\pi$
$41$	−5.76616	−0.900524	−0.450262	+	0.892897i	$0.648669\pi$
$42$	7.15731	1.10440
$43$	1.00000	0.152499
$43$	1.00000	0.152499
$44$	−1.00000	−0.150756
$45$	0.801199	0.119436
$46$	−1.11595	−0.164538
$47$	10.3447	1.50893	0.754464	−	0.656342i	$-0.227897\pi$
$47$	10.3447	1.50893	0.754464	+	0.656342i	$0.227897\pi$
$48$	−1.48284	−0.214029
$49$	16.2978	2.32825
$50$	−1.00000	−0.141421
$51$	−10.4289	−1.46034
$52$	3.11595	0.432105
$53$	−10.1774	−1.39797	−0.698987	−	0.715134i	$-0.746366\pi$
$53$	−10.1774	−1.39797	−0.698987	+	0.715134i	$0.746366\pi$
$54$	−5.63655	−0.767038
$55$	1.00000	0.134840
$56$	−4.82678	−0.645005
$57$	−9.24006	−1.22388
$58$	−3.16385	−0.415434
$59$	9.27380	1.20735	0.603673	−	0.797232i	$-0.293703\pi$
$59$	9.27380	1.20735	0.603673	+	0.797232i	$0.293703\pi$
$60$	1.48284	0.191433
$61$	11.2530	1.44080	0.720400	−	0.693559i	$-0.243958\pi$
$61$	11.2530	1.44080	0.720400	+	0.693559i	$0.243958\pi$
$62$	4.13157	0.524710
$63$	−3.86721	−0.487223
$64$	1.00000	0.125000
$65$	−3.11595	−0.386486
$66$	−1.48284	−0.182524
$67$	−11.3564	−1.38740	−0.693701	−	0.720263i	$-0.744021\pi$
$67$	−11.3564	−1.38740	−0.693701	+	0.720263i	$0.744021\pi$
$68$	7.03311	0.852890
$69$	−1.65477	−0.199211
$70$	4.82678	0.576910
$71$	1.75115	0.207823	0.103912	−	0.994587i	$-0.466864\pi$
$71$	1.75115	0.207823	0.103912	+	0.994587i	$0.466864\pi$
$72$	0.801199	0.0944222
$73$	6.29746	0.737062	0.368531	−	0.929615i	$-0.379861\pi$
$73$	6.29746	0.737062	0.368531	+	0.929615i	$0.379861\pi$
$74$	−3.75260	−0.436231
$75$	−1.48284	−0.171223
$76$	6.23135	0.714785
$77$	−4.82678	−0.550062
$78$	4.62044	0.523162
$79$	−9.80398	−1.10303	−0.551517	−	0.834164i	$-0.685951\pi$
$79$	−9.80398	−1.10303	−0.551517	+	0.834164i	$0.685951\pi$
$80$	−1.00000	−0.111803
$81$	−5.95448	−0.661609
$82$	5.76616	0.636766
$83$	−7.75457	−0.851174	−0.425587	−	0.904917i	$-0.639932\pi$
$83$	−7.75457	−0.851174	−0.425587	+	0.904917i	$0.639932\pi$
$84$	−7.15731	−0.780927
$85$	−7.03311	−0.762848
$86$	−1.00000	−0.107833
$87$	−4.69147	−0.502978
$88$	1.00000	0.106600
$89$	−11.1654	−1.18353	−0.591764	−	0.806111i	$-0.701568\pi$
$89$	−11.1654	−1.18353	−0.591764	+	0.806111i	$0.701568\pi$
$90$	−0.801199	−0.0844538
$91$	15.0400	1.57662
$92$	1.11595	0.116346
$93$	6.12644	0.635282
$94$	−10.3447	−1.06697
$95$	−6.23135	−0.639323
$96$	1.48284	0.151341
$97$	−0.459065	−0.0466110	−0.0233055	−	0.999728i	$-0.507419\pi$
$97$	−0.459065	−0.0466110	−0.0233055	+	0.999728i	$0.507419\pi$
$98$	−16.2978	−1.64632
$99$	0.801199	0.0805236
$100$	1.00000	0.100000
$101$	−5.99326	−0.596351	−0.298176	−	0.954511i	$-0.596378\pi$
$101$	−5.99326	−0.596351	−0.298176	+	0.954511i	$0.596378\pi$
$102$	10.4289	1.03262
$103$	12.0077	1.18315	0.591575	−	0.806250i	$-0.298506\pi$
$103$	12.0077	1.18315	0.591575	+	0.806250i	$0.298506\pi$
$104$	−3.11595	−0.305544
$105$	7.15731	0.698482
$106$	10.1774	0.988517
$107$	2.10185	0.203193	0.101597	−	0.994826i	$-0.467605\pi$
$107$	2.10185	0.203193	0.101597	+	0.994826i	$0.467605\pi$
$108$	5.63655	0.542378
$109$	7.83137	0.750109	0.375055	−	0.927003i	$-0.377624\pi$
$109$	7.83137	0.750109	0.375055	+	0.927003i	$0.377624\pi$
$110$	−1.00000	−0.0953463
$111$	−5.56449	−0.528158
$112$	4.82678	0.456088
$113$	−2.25538	−0.212169	−0.106084	−	0.994357i	$-0.533831\pi$
$113$	−2.25538	−0.212169	−0.106084	+	0.994357i	$0.533831\pi$
$114$	9.24006	0.865411
$115$	−1.11595	−0.104063
$116$	3.16385	0.293756
$117$	−2.49650	−0.230801
$118$	−9.27380	−0.853723
$119$	33.9472	3.11194
$120$	−1.48284	−0.135364
$121$	1.00000	0.0909091
$122$	−11.2530	−1.01880
$123$	8.55027	0.770952
$124$	−4.13157	−0.371026
$125$	−1.00000	−0.0894427
$126$	3.86721	0.344518
$127$	−20.9378	−1.85793	−0.928963	−	0.370173i	$-0.879298\pi$
$127$	−20.9378	−1.85793	−0.928963	+	0.370173i	$0.879298\pi$
$128$	−1.00000	−0.0883883
$129$	−1.48284	−0.130556
$130$	3.11595	0.273287
$131$	1.76078	0.153840	0.0769200	−	0.997037i	$-0.475491\pi$
$131$	1.76078	0.153840	0.0769200	+	0.997037i	$0.475491\pi$
$132$	1.48284	0.129064
$133$	30.0773	2.60803
$134$	11.3564	0.981041
$135$	−5.63655	−0.485117
$136$	−7.03311	−0.603084
$137$	9.43115	0.805758	0.402879	−	0.915253i	$-0.368010\pi$
$137$	9.43115	0.805758	0.402879	+	0.915253i	$0.368010\pi$
$138$	1.65477	0.140863
$139$	16.0028	1.35734	0.678670	−	0.734444i	$-0.262557\pi$
$139$	16.0028	1.35734	0.678670	+	0.734444i	$0.262557\pi$
$140$	−4.82678	−0.407937
$141$	−15.3395	−1.29182
$142$	−1.75115	−0.146953
$143$	−3.11595	−0.260569
$144$	−0.801199	−0.0667666
$145$	−3.16385	−0.262744
$146$	−6.29746	−0.521182
$147$	−24.1669	−1.99325
$148$	3.75260	0.308462
$149$	4.39902	0.360382	0.180191	−	0.983632i	$-0.442328\pi$
$149$	4.39902	0.360382	0.180191	+	0.983632i	$0.442328\pi$
$150$	1.48284	0.121073
$151$	−18.2702	−1.48680	−0.743402	−	0.668845i	$-0.766789\pi$
$151$	−18.2702	−1.48680	−0.743402	+	0.668845i	$0.766789\pi$
$152$	−6.23135	−0.505429
$153$	−5.63492	−0.455556
$154$	4.82678	0.388953
$155$	4.13157	0.331856
$156$	−4.62044	−0.369931
$157$	−8.48633	−0.677283	−0.338641	−	0.940916i	$-0.609967\pi$
$157$	−8.48633	−0.677283	−0.338641	+	0.940916i	$0.609967\pi$
$158$	9.80398	0.779963
$159$	15.0914	1.19683
$160$	1.00000	0.0790569
$161$	5.38644	0.424511
$162$	5.95448	0.467828
$163$	−5.34228	−0.418440	−0.209220	−	0.977869i	$-0.567092\pi$
$163$	−5.34228	−0.418440	−0.209220	+	0.977869i	$0.567092\pi$
$164$	−5.76616	−0.450262
$165$	−1.48284	−0.115439
$166$	7.75457	0.601871
$167$	−24.0863	−1.86385	−0.931925	−	0.362651i	$-0.881872\pi$
$167$	−24.0863	−1.86385	−0.931925	+	0.362651i	$0.881872\pi$
$168$	7.15731	0.552199
$169$	−3.29085	−0.253142
$170$	7.03311	0.539415
$171$	−4.99255	−0.381790
$172$	1.00000	0.0762493
$173$	−21.9002	−1.66504	−0.832522	−	0.553992i	$-0.813104\pi$
$173$	−21.9002	−1.66504	−0.832522	+	0.553992i	$0.813104\pi$
$174$	4.69147	0.355659
$175$	4.82678	0.364870
$176$	−1.00000	−0.0753778
$177$	−13.7515	−1.03363
$178$	11.1654	0.836880
$179$	6.07104	0.453770	0.226885	−	0.973921i	$-0.427146\pi$
$179$	6.07104	0.453770	0.226885	+	0.973921i	$0.427146\pi$
$180$	0.801199	0.0597179
$181$	10.3540	0.769606	0.384803	−	0.922999i	$-0.374269\pi$
$181$	10.3540	0.769606	0.384803	+	0.922999i	$0.374269\pi$
$182$	−15.0400	−1.11484
$183$	−16.6864	−1.23349
$184$	−1.11595	−0.0822690
$185$	−3.75260	−0.275897
$186$	−6.12644	−0.449212
$187$	−7.03311	−0.514312
$188$	10.3447	0.754464
$189$	27.2064	1.97897
$190$	6.23135	0.452069
$191$	−15.9490	−1.15403	−0.577015	−	0.816733i	$-0.695783\pi$
$191$	−15.9490	−1.15403	−0.577015	+	0.816733i	$0.695783\pi$
$192$	−1.48284	−0.107014
$193$	−2.80456	−0.201877	−0.100938	−	0.994893i	$-0.532185\pi$
$193$	−2.80456	−0.201877	−0.100938	+	0.994893i	$0.532185\pi$
$194$	0.459065	0.0329590
$195$	4.62044	0.330877
$196$	16.2978	1.16413
$197$	15.2867	1.08914	0.544568	−	0.838717i	$-0.316694\pi$
$197$	15.2867	1.08914	0.544568	+	0.838717i	$0.316694\pi$
$198$	−0.801199	−0.0569388
$199$	−10.4346	−0.739686	−0.369843	−	0.929094i	$-0.620589\pi$
$199$	−10.4346	−0.739686	−0.369843	+	0.929094i	$0.620589\pi$
$200$	−1.00000	−0.0707107
$201$	16.8396	1.18778
$202$	5.99326	0.421684
$203$	15.2712	1.07183
$204$	−10.4289	−0.730172
$205$	5.76616	0.402726
$206$	−12.0077	−0.836614
$207$	−0.894099	−0.0621442
$208$	3.11595	0.216052
$209$	−6.23135	−0.431031
$210$	−7.15731	−0.493902
$211$	18.4743	1.27183	0.635913	−	0.771761i	$-0.280624\pi$
$211$	18.4743	1.27183	0.635913	+	0.771761i	$0.280624\pi$
$212$	−10.1774	−0.698987
$213$	−2.59666	−0.177921
$214$	−2.10185	−0.143679
$215$	−1.00000	−0.0681994
$216$	−5.63655	−0.383519
$217$	−19.9422	−1.35376
$218$	−7.83137	−0.530407
$219$	−9.33810	−0.631010
$220$	1.00000	0.0674200
$221$	21.9148	1.47415
$222$	5.56449	0.373464
$223$	5.99924	0.401739	0.200870	−	0.979618i	$-0.435623\pi$
$223$	5.99924	0.401739	0.200870	+	0.979618i	$0.435623\pi$
$224$	−4.82678	−0.322503
$225$	−0.801199	−0.0534133
$226$	2.25538	0.150026
$227$	−9.51703	−0.631668	−0.315834	−	0.948815i	$-0.602284\pi$
$227$	−9.51703	−0.631668	−0.315834	+	0.948815i	$0.602284\pi$
$228$	−9.24006	−0.611938
$229$	21.3780	1.41270	0.706349	−	0.707863i	$-0.250341\pi$
$229$	21.3780	1.41270	0.706349	+	0.707863i	$0.250341\pi$
$230$	1.11595	0.0735836
$231$	7.15731	0.470917
$232$	−3.16385	−0.207717
$233$	−26.2946	−1.72262	−0.861308	−	0.508083i	$-0.830354\pi$
$233$	−26.2946	−1.72262	−0.861308	+	0.508083i	$0.830354\pi$
$234$	2.49650	0.163201
$235$	−10.3447	−0.674813
$236$	9.27380	0.603673
$237$	14.5377	0.944325
$238$	−33.9472	−2.20047
$239$	−10.0042	−0.647115	−0.323558	−	0.946209i	$-0.604879\pi$
$239$	−10.0042	−0.647115	−0.323558	+	0.946209i	$0.604879\pi$
$240$	1.48284	0.0957166
$241$	9.71227	0.625622	0.312811	−	0.949815i	$-0.398729\pi$
$241$	9.71227	0.625622	0.312811	+	0.949815i	$0.398729\pi$
$242$	−1.00000	−0.0642824
$243$	−8.08014	−0.518341
$244$	11.2530	0.720400
$245$	−16.2978	−1.04123
$246$	−8.55027	−0.545145
$247$	19.4166	1.23545
$248$	4.13157	0.262355
$249$	11.4987	0.728704
$250$	1.00000	0.0632456
$251$	25.5642	1.61360	0.806798	−	0.590828i	$-0.201199\pi$
$251$	25.5642	1.61360	0.806798	+	0.590828i	$0.201199\pi$
$252$	−3.86721	−0.243611
$253$	−1.11595	−0.0701592
$254$	20.9378	1.31375
$255$	10.4289	0.653086
$256$	1.00000	0.0625000
$257$	4.82868	0.301205	0.150603	−	0.988594i	$-0.451879\pi$
$257$	4.82868	0.301205	0.150603	+	0.988594i	$0.451879\pi$
$258$	1.48284	0.0923173
$259$	18.1130	1.12548
$260$	−3.11595	−0.193243
$261$	−2.53488	−0.156905
$262$	−1.76078	−0.108781
$263$	−10.2445	−0.631701	−0.315850	−	0.948809i	$-0.602290\pi$
$263$	−10.2445	−0.631701	−0.315850	+	0.948809i	$0.602290\pi$
$264$	−1.48284	−0.0912622
$265$	10.1774	0.625193
$266$	−30.0773	−1.84416
$267$	16.5564	1.01324
$268$	−11.3564	−0.693701
$269$	−13.6765	−0.833870	−0.416935	−	0.908936i	$-0.636896\pi$
$269$	−13.6765	−0.833870	−0.416935	+	0.908936i	$0.636896\pi$
$270$	5.63655	0.343030
$271$	−11.1336	−0.676318	−0.338159	−	0.941089i	$-0.609804\pi$
$271$	−11.1336	−0.676318	−0.338159	+	0.941089i	$0.609804\pi$
$272$	7.03311	0.426445
$273$	−22.3018	−1.34977
$274$	−9.43115	−0.569757
$275$	−1.00000	−0.0603023
$276$	−1.65477	−0.0996055
$277$	20.9792	1.26052	0.630258	−	0.776386i	$-0.282949\pi$
$277$	20.9792	1.26052	0.630258	+	0.776386i	$0.282949\pi$
$278$	−16.0028	−0.959784
$279$	3.31021	0.198177
$280$	4.82678	0.288455
$281$	−4.12104	−0.245841	−0.122920	−	0.992417i	$-0.539226\pi$
$281$	−4.12104	−0.245841	−0.122920	+	0.992417i	$0.539226\pi$
$282$	15.3395	0.913452
$283$	28.9926	1.72343	0.861716	−	0.507391i	$-0.169390\pi$
$283$	28.9926	1.72343	0.861716	+	0.507391i	$0.169390\pi$
$284$	1.75115	0.103912
$285$	9.24006	0.547334
$286$	3.11595	0.184250
$287$	−27.8320	−1.64287
$288$	0.801199	0.0472111
$289$	32.4646	1.90968
$290$	3.16385	0.185788
$291$	0.680718	0.0399044
$292$	6.29746	0.368531
$293$	−9.42775	−0.550775	−0.275388	−	0.961333i	$-0.588806\pi$
$293$	−9.42775	−0.550775	−0.275388	+	0.961333i	$0.588806\pi$
$294$	24.1669	1.40944
$295$	−9.27380	−0.539942
$296$	−3.75260	−0.218115
$297$	−5.63655	−0.327066
$298$	−4.39902	−0.254828
$299$	3.47725	0.201094
$300$	−1.48284	−0.0856115
$301$	4.82678	0.278211
$302$	18.2702	1.05133
$303$	8.88701	0.510545
$304$	6.23135	0.357392
$305$	−11.2530	−0.644345
$306$	5.63492	0.322127
$307$	20.6914	1.18092	0.590460	−	0.807067i	$-0.298946\pi$
$307$	20.6914	1.18092	0.590460	+	0.807067i	$0.298946\pi$
$308$	−4.82678	−0.275031
$309$	−17.8054	−1.01291
$310$	−4.13157	−0.234657
$311$	32.6114	1.84922	0.924612	−	0.380911i	$-0.124389\pi$
$311$	32.6114	1.84922	0.924612	+	0.380911i	$0.124389\pi$
$312$	4.62044	0.261581
$313$	30.0632	1.69927	0.849636	−	0.527370i	$-0.176822\pi$
$313$	30.0632	1.69927	0.849636	+	0.527370i	$0.176822\pi$
$314$	8.48633	0.478911
$315$	3.86721	0.217893
$316$	−9.80398	−0.551517
$317$	−5.56557	−0.312593	−0.156297	−	0.987710i	$-0.549956\pi$
$317$	−5.56557	−0.312593	−0.156297	+	0.987710i	$0.549956\pi$
$318$	−15.0914	−0.846285
$319$	−3.16385	−0.177142
$320$	−1.00000	−0.0559017
$321$	−3.11669	−0.173957
$322$	−5.38644	−0.300175
$323$	43.8257	2.43853
$324$	−5.95448	−0.330805
$325$	3.11595	0.172842
$326$	5.34228	0.295882
$327$	−11.6126	−0.642180
$328$	5.76616	0.318383
$329$	49.9315	2.75281
$330$	1.48284	0.0816274
$331$	−6.80814	−0.374209	−0.187105	−	0.982340i	$-0.559910\pi$
$331$	−6.80814	−0.374209	−0.187105	+	0.982340i	$0.559910\pi$
$332$	−7.75457	−0.425587
$333$	−3.00658	−0.164760
$334$	24.0863	1.31794
$335$	11.3564	0.620465
$336$	−7.15731	−0.390464
$337$	−17.6757	−0.962854	−0.481427	−	0.876486i	$-0.659881\pi$
$337$	−17.6757	−0.962854	−0.481427	+	0.876486i	$0.659881\pi$
$338$	3.29085	0.178999
$339$	3.34436	0.181641
$340$	−7.03311	−0.381424
$341$	4.13157	0.223737
$342$	4.99255	0.269966
$343$	44.8783	2.42320
$344$	−1.00000	−0.0539164
$345$	1.65477	0.0890899
$346$	21.9002	1.17736
$347$	−1.50630	−0.0808623	−0.0404311	−	0.999182i	$-0.512873\pi$
$347$	−1.50630	−0.0808623	−0.0404311	+	0.999182i	$0.512873\pi$
$348$	−4.69147	−0.251489
$349$	6.73446	0.360487	0.180244	−	0.983622i	$-0.442311\pi$
$349$	6.73446	0.360487	0.180244	+	0.983622i	$0.442311\pi$
$350$	−4.82678	−0.258002
$351$	17.5632	0.937455
$352$	1.00000	0.0533002
$353$	2.06180	0.109739	0.0548693	−	0.998494i	$-0.482526\pi$
$353$	2.06180	0.109739	0.0548693	+	0.998494i	$0.482526\pi$
$354$	13.7515	0.730885
$355$	−1.75115	−0.0929413
$356$	−11.1654	−0.591764
$357$	−50.3382	−2.66418
$358$	−6.07104	−0.320864
$359$	14.9385	0.788422	0.394211	−	0.919020i	$-0.371018\pi$
$359$	14.9385	0.788422	0.394211	+	0.919020i	$0.371018\pi$
$360$	−0.801199	−0.0422269
$361$	19.8297	1.04367
$362$	−10.3540	−0.544194
$363$	−1.48284	−0.0778287
$364$	15.0400	0.788310
$365$	−6.29746	−0.329624
$366$	16.6864	0.872210
$367$	14.7313	0.768966	0.384483	−	0.923132i	$-0.374380\pi$
$367$	14.7313	0.768966	0.384483	+	0.923132i	$0.374380\pi$
$368$	1.11595	0.0581729
$369$	4.61985	0.240500
$370$	3.75260	0.195088
$371$	−49.1241	−2.55039
$372$	6.12644	0.317641
$373$	−13.7561	−0.712263	−0.356131	−	0.934436i	$-0.615904\pi$
$373$	−13.7561	−0.712263	−0.356131	+	0.934436i	$0.615904\pi$
$374$	7.03311	0.363673
$375$	1.48284	0.0765733
$376$	−10.3447	−0.533486
$377$	9.85841	0.507734
$378$	−27.2064	−1.39935
$379$	−19.6061	−1.00710	−0.503550	−	0.863966i	$-0.667973\pi$
$379$	−19.6061	−1.00710	−0.503550	+	0.863966i	$0.667973\pi$
$380$	−6.23135	−0.319661
$381$	31.0472	1.59060
$382$	15.9490	0.816023
$383$	32.1235	1.64143	0.820716	−	0.571336i	$-0.193575\pi$
$383$	32.1235	1.64143	0.820716	+	0.571336i	$0.193575\pi$
$384$	1.48284	0.0756706
$385$	4.82678	0.245995
$386$	2.80456	0.142749
$387$	−0.801199	−0.0407273
$388$	−0.459065	−0.0233055
$389$	−23.0968	−1.17105	−0.585527	−	0.810653i	$-0.699112\pi$
$389$	−23.0968	−1.17105	−0.585527	+	0.810653i	$0.699112\pi$
$390$	−4.62044	−0.233965
$391$	7.84860	0.396921
$392$	−16.2978	−0.823162
$393$	−2.61095	−0.131705
$394$	−15.2867	−0.770135
$395$	9.80398	0.493292
$396$	0.801199	0.0402618
$397$	36.8054	1.84721	0.923604	−	0.383348i	$-0.125229\pi$
$397$	36.8054	1.84721	0.923604	+	0.383348i	$0.125229\pi$
$398$	10.4346	0.523037
$399$	−44.5997	−2.23278
$400$	1.00000	0.0500000
$401$	−6.49490	−0.324340	−0.162170	−	0.986763i	$-0.551849\pi$
$401$	−6.49490	−0.324340	−0.162170	+	0.986763i	$0.551849\pi$
$402$	−16.8396	−0.839884
$403$	−12.8738	−0.641288
$404$	−5.99326	−0.298176
$405$	5.95448	0.295881
$406$	−15.2712	−0.757897
$407$	−3.75260	−0.186010
$408$	10.4289	0.516310
$409$	18.1660	0.898249	0.449125	−	0.893469i	$-0.351736\pi$
$409$	18.1660	0.898249	0.449125	+	0.893469i	$0.351736\pi$
$410$	−5.76616	−0.284771
$411$	−13.9848	−0.689821
$412$	12.0077	0.591575
$413$	44.7626	2.20262
$414$	0.894099	0.0439426
$415$	7.75457	0.380657
$416$	−3.11595	−0.152772
$417$	−23.7295	−1.16204
$418$	6.23135	0.304785
$419$	−8.59949	−0.420113	−0.210056	−	0.977689i	$-0.567365\pi$
$419$	−8.59949	−0.420113	−0.210056	+	0.977689i	$0.567365\pi$
$420$	7.15731	0.349241
$421$	−30.7705	−1.49966	−0.749831	−	0.661630i	$-0.769865\pi$
$421$	−30.7705	−1.49966	−0.749831	+	0.661630i	$0.769865\pi$
$422$	−18.4743	−0.899317
$423$	−8.28816	−0.402984
$424$	10.1774	0.494259
$425$	7.03311	0.341156
$426$	2.59666	0.125809
$427$	54.3157	2.62852
$428$	2.10185	0.101597
$429$	4.62044	0.223077
$430$	1.00000	0.0482243
$431$	29.0510	1.39934	0.699669	−	0.714467i	$-0.253331\pi$
$431$	29.0510	1.39934	0.699669	+	0.714467i	$0.253331\pi$
$432$	5.63655	0.271189
$433$	−10.6572	−0.512152	−0.256076	−	0.966657i	$-0.582430\pi$
$433$	−10.6572	−0.512152	−0.256076	+	0.966657i	$0.582430\pi$
$434$	19.9422	0.957255
$435$	4.69147	0.224939
$436$	7.83137	0.375055
$437$	6.95388	0.332649
$438$	9.33810	0.446192
$439$	8.49937	0.405653	0.202826	−	0.979215i	$-0.434987\pi$
$439$	8.49937	0.405653	0.202826	+	0.979215i	$0.434987\pi$
$440$	−1.00000	−0.0476731
$441$	−13.0578	−0.621798
$442$	−21.9148	−1.04238
$443$	12.7886	0.607604	0.303802	−	0.952735i	$-0.401744\pi$
$443$	12.7886	0.607604	0.303802	+	0.952735i	$0.401744\pi$
$444$	−5.56449	−0.264079
$445$	11.1654	0.529290
$446$	−5.99924	−0.284072
$447$	−6.52302	−0.308528
$448$	4.82678	0.228044
$449$	−10.0081	−0.472312	−0.236156	−	0.971715i	$-0.575888\pi$
$449$	−10.0081	−0.472312	−0.236156	+	0.971715i	$0.575888\pi$
$450$	0.801199	0.0377689
$451$	5.76616	0.271518
$452$	−2.25538	−0.106084
$453$	27.0916	1.27288
$454$	9.51703	0.446656
$455$	−15.0400	−0.705086
$456$	9.24006	0.432706
$457$	−23.1307	−1.08201	−0.541004	−	0.841020i	$-0.681956\pi$
$457$	−23.1307	−1.08201	−0.541004	+	0.841020i	$0.681956\pi$
$458$	−21.3780	−0.998929
$459$	39.6425	1.85035
$460$	−1.11595	−0.0520315
$461$	−7.38407	−0.343910	−0.171955	−	0.985105i	$-0.555008\pi$
$461$	−7.38407	−0.343910	−0.171955	+	0.985105i	$0.555008\pi$
$462$	−7.15731	−0.332988
$463$	−26.1690	−1.21618	−0.608088	−	0.793870i	$-0.708063\pi$
$463$	−26.1690	−1.21618	−0.608088	+	0.793870i	$0.708063\pi$
$464$	3.16385	0.146878
$465$	−6.12644	−0.284107
$466$	26.2946	1.21807
$467$	−2.76399	−0.127902	−0.0639512	−	0.997953i	$-0.520370\pi$
$467$	−2.76399	−0.127902	−0.0639512	+	0.997953i	$0.520370\pi$
$468$	−2.49650	−0.115401
$469$	−54.8147	−2.53111
$470$	10.3447	0.477165
$471$	12.5838	0.579832
$472$	−9.27380	−0.426861
$473$	−1.00000	−0.0459800
$474$	−14.5377	−0.667738
$475$	6.23135	0.285914
$476$	33.9472	1.55597
$477$	8.15413	0.373352
$478$	10.0042	0.457579
$479$	36.2872	1.65800	0.829001	−	0.559247i	$-0.188910\pi$
$479$	36.2872	1.65800	0.829001	+	0.559247i	$0.188910\pi$
$480$	−1.48284	−0.0676819
$481$	11.6929	0.533151
$482$	−9.71227	−0.442382
$483$	−7.98721	−0.363431
$484$	1.00000	0.0454545
$485$	0.459065	0.0208451
$486$	8.08014	0.366523
$487$	12.2972	0.557240	0.278620	−	0.960401i	$-0.410123\pi$
$487$	12.2972	0.557240	0.278620	+	0.960401i	$0.410123\pi$
$488$	−11.2530	−0.509400
$489$	7.92173	0.358233
$490$	16.2978	0.736258
$491$	20.5937	0.929383	0.464691	−	0.885473i	$-0.346165\pi$
$491$	20.5937	0.929383	0.464691	+	0.885473i	$0.346165\pi$
$492$	8.55027	0.385476
$493$	22.2517	1.00217
$494$	−19.4166	−0.873593
$495$	−0.801199	−0.0360112
$496$	−4.13157	−0.185513
$497$	8.45240	0.379142
$498$	−11.4987	−0.515271
$499$	10.9689	0.491038	0.245519	−	0.969392i	$-0.421042\pi$
$499$	10.9689	0.491038	0.245519	+	0.969392i	$0.421042\pi$
$500$	−1.00000	−0.0447214
$501$	35.7159	1.59567
$502$	−25.5642	−1.14098
$503$	6.60727	0.294603	0.147302	−	0.989092i	$-0.452941\pi$
$503$	6.60727	0.294603	0.147302	+	0.989092i	$0.452941\pi$
$504$	3.86721	0.172259
$505$	5.99326	0.266696
$506$	1.11595	0.0496101
$507$	4.87979	0.216719
$508$	−20.9378	−0.928963
$509$	28.0503	1.24331	0.621654	−	0.783292i	$-0.286461\pi$
$509$	28.0503	1.24331	0.621654	+	0.783292i	$0.286461\pi$
$510$	−10.4289	−0.461801
$511$	30.3964	1.34466
$512$	−1.00000	−0.0441942
$513$	35.1233	1.55073
$514$	−4.82868	−0.212984
$515$	−12.0077	−0.529121
$516$	−1.48284	−0.0652782
$517$	−10.3447	−0.454959
$518$	−18.1130	−0.795838
$519$	32.4744	1.42547
$520$	3.11595	0.136643
$521$	37.5182	1.64370	0.821851	−	0.569702i	$-0.192941\pi$
$521$	37.5182	1.64370	0.821851	+	0.569702i	$0.192941\pi$
$522$	2.53488	0.110948
$523$	6.94141	0.303527	0.151763	−	0.988417i	$-0.451505\pi$
$523$	6.94141	0.303527	0.151763	+	0.988417i	$0.451505\pi$
$524$	1.76078	0.0769200
$525$	−7.15731	−0.312371
$526$	10.2445	0.446680
$527$	−29.0578	−1.26578
$528$	1.48284	0.0645321
$529$	−21.7547	−0.945855
$530$	−10.1774	−0.442078
$531$	−7.43017	−0.322442
$532$	30.0773	1.30402
$533$	−17.9671	−0.778241
$534$	−16.5564	−0.716466
$535$	−2.10185	−0.0908708
$536$	11.3564	0.490521
$537$	−9.00235	−0.388480
$538$	13.6765	0.589635
$539$	−16.2978	−0.701995
$540$	−5.63655	−0.242559
$541$	21.3494	0.917884	0.458942	−	0.888466i	$-0.348229\pi$
$541$	21.3494	0.917884	0.458942	+	0.888466i	$0.348229\pi$
$542$	11.1336	0.478229
$543$	−15.3533	−0.658872
$544$	−7.03311	−0.301542
$545$	−7.83137	−0.335459
$546$	22.3018	0.954431
$547$	−9.21096	−0.393832	−0.196916	−	0.980420i	$-0.563093\pi$
$547$	−9.21096	−0.393832	−0.196916	+	0.980420i	$0.563093\pi$
$548$	9.43115	0.402879
$549$	−9.01590	−0.384789
$550$	1.00000	0.0426401
$551$	19.7151	0.839890
$552$	1.65477	0.0704317
$553$	−47.3216	−2.01232
$554$	−20.9792	−0.891319
$555$	5.56449	0.236199
$556$	16.0028	0.678670
$557$	0.983118	0.0416560	0.0208280	−	0.999783i	$-0.493370\pi$
$557$	0.983118	0.0416560	0.0208280	+	0.999783i	$0.493370\pi$
$558$	−3.31021	−0.140132
$559$	3.11595	0.131791
$560$	−4.82678	−0.203969
$561$	10.4289	0.440310
$562$	4.12104	0.173836
$563$	−5.42395	−0.228592	−0.114296	−	0.993447i	$-0.536461\pi$
$563$	−5.42395	−0.228592	−0.114296	+	0.993447i	$0.536461\pi$
$564$	−15.3395	−0.645908
$565$	2.25538	0.0948847
$566$	−28.9926	−1.21865
$567$	−28.7410	−1.20701
$568$	−1.75115	−0.0734765
$569$	−34.1852	−1.43312	−0.716559	−	0.697527i	$-0.754284\pi$
$569$	−34.1852	−1.43312	−0.716559	+	0.697527i	$0.754284\pi$
$570$	−9.24006	−0.387024
$571$	21.9627	0.919111	0.459556	−	0.888149i	$-0.348009\pi$
$571$	21.9627	0.919111	0.459556	+	0.888149i	$0.348009\pi$
$572$	−3.11595	−0.130284
$573$	23.6498	0.987983
$574$	27.8320	1.16168
$575$	1.11595	0.0465384
$576$	−0.801199	−0.0333833
$577$	−13.5274	−0.563153	−0.281577	−	0.959539i	$-0.590857\pi$
$577$	−13.5274	−0.563153	−0.281577	+	0.959539i	$0.590857\pi$
$578$	−32.4646	−1.35035
$579$	4.15871	0.172830
$580$	−3.16385	−0.131372
$581$	−37.4296	−1.55284
$582$	−0.680718	−0.0282167
$583$	10.1774	0.421505
$584$	−6.29746	−0.260591
$585$	2.49650	0.103217
$586$	9.42775	0.389457
$587$	−41.1694	−1.69924	−0.849621	−	0.527394i	$-0.823169\pi$
$587$	−41.1694	−1.69924	−0.849621	+	0.527394i	$0.823169\pi$
$588$	−24.1669	−0.996627
$589$	−25.7452	−1.06081
$590$	9.27380	0.381796
$591$	−22.6677	−0.932426
$592$	3.75260	0.154231
$593$	7.26639	0.298395	0.149197	−	0.988807i	$-0.452331\pi$
$593$	7.26639	0.298395	0.149197	+	0.988807i	$0.452331\pi$
$594$	5.63655	0.231271
$595$	−33.9472	−1.39170
$596$	4.39902	0.180191
$597$	15.4727	0.633257
$598$	−3.47725	−0.142195
$599$	−1.35091	−0.0551967	−0.0275984	−	0.999619i	$-0.508786\pi$
$599$	−1.35091	−0.0551967	−0.0275984	+	0.999619i	$0.508786\pi$
$600$	1.48284	0.0605365
$601$	−9.92951	−0.405033	−0.202516	−	0.979279i	$-0.564912\pi$
$601$	−9.92951	−0.405033	−0.202516	+	0.979279i	$0.564912\pi$
$602$	−4.82678	−0.196725
$603$	9.09872	0.370528
$604$	−18.2702	−0.743402
$605$	−1.00000	−0.0406558
$606$	−8.88701	−0.361010
$607$	−23.4087	−0.950131	−0.475066	−	0.879950i	$-0.657576\pi$
$607$	−23.4087	−0.950131	−0.475066	+	0.879950i	$0.657576\pi$
$608$	−6.23135	−0.252714
$609$	−22.6447	−0.917609
$610$	11.2530	0.455621
$611$	32.2335	1.30403
$612$	−5.63492	−0.227778
$613$	−7.18631	−0.290252	−0.145126	−	0.989413i	$-0.546359\pi$
$613$	−7.18631	−0.290252	−0.145126	+	0.989413i	$0.546359\pi$
$614$	−20.6914	−0.835036
$615$	−8.55027	−0.344780
$616$	4.82678	0.194476
$617$	−7.29957	−0.293869	−0.146935	−	0.989146i	$-0.546941\pi$
$617$	−7.29957	−0.293869	−0.146935	+	0.989146i	$0.546941\pi$
$618$	17.8054	0.716238
$619$	35.5846	1.43027	0.715133	−	0.698989i	$-0.246366\pi$
$619$	35.5846	1.43027	0.715133	+	0.698989i	$0.246366\pi$
$620$	4.13157	0.165928
$621$	6.29011	0.252414
$622$	−32.6114	−1.30760
$623$	−53.8928	−2.15917
$624$	−4.62044	−0.184966
$625$	1.00000	0.0400000
$626$	−30.0632	−1.20157
$627$	9.24006	0.369013
$628$	−8.48633	−0.338641
$629$	26.3925	1.05234
$630$	−3.86721	−0.154073
$631$	−18.0131	−0.717090	−0.358545	−	0.933513i	$-0.616727\pi$
$631$	−18.0131	−0.717090	−0.358545	+	0.933513i	$0.616727\pi$
$632$	9.80398	0.389982
$633$	−27.3944	−1.08883
$634$	5.56557	0.221037
$635$	20.9378	0.830889
$636$	15.0914	0.598414
$637$	50.7831	2.01210
$638$	3.16385	0.125258
$639$	−1.40302	−0.0555026
$640$	1.00000	0.0395285
$641$	−9.51890	−0.375974	−0.187987	−	0.982172i	$-0.560196\pi$
$641$	−9.51890	−0.375974	−0.187987	+	0.982172i	$0.560196\pi$
$642$	3.11669	0.123006
$643$	−35.6561	−1.40614	−0.703069	−	0.711122i	$-0.748187\pi$
$643$	−35.6561	−1.40614	−0.703069	+	0.711122i	$0.748187\pi$
$644$	5.38644	0.212256
$645$	1.48284	0.0583866
$646$	−43.8257	−1.72430
$647$	20.4070	0.802281	0.401141	−	0.916017i	$-0.368614\pi$
$647$	20.4070	0.802281	0.401141	+	0.916017i	$0.368614\pi$
$648$	5.95448	0.233914
$649$	−9.27380	−0.364029
$650$	−3.11595	−0.122218
$651$	29.5709	1.15898
$652$	−5.34228	−0.209220
$653$	−35.5748	−1.39215	−0.696074	−	0.717970i	$-0.745072\pi$
$653$	−35.5748	−1.39215	−0.696074	+	0.717970i	$0.745072\pi$
$654$	11.6126	0.454090
$655$	−1.76078	−0.0687993
$656$	−5.76616	−0.225131
$657$	−5.04552	−0.196845
$658$	−49.9315	−1.94653
$659$	22.8345	0.889507	0.444754	−	0.895653i	$-0.353291\pi$
$659$	22.8345	0.889507	0.444754	+	0.895653i	$0.353291\pi$
$660$	−1.48284	−0.0577193
$661$	−0.0985728	−0.00383404	−0.00191702	−	0.999998i	$-0.500610\pi$
$661$	−0.0985728	−0.00383404	−0.00191702	+	0.999998i	$0.500610\pi$
$662$	6.80814	0.264606
$663$	−32.4961	−1.26204
$664$	7.75457	0.300936
$665$	−30.0773	−1.16635
$666$	3.00658	0.116503
$667$	3.53070	0.136709
$668$	−24.0863	−0.931925
$669$	−8.89589	−0.343935
$670$	−11.3564	−0.438735
$671$	−11.2530	−0.434417
$672$	7.15731	0.276099
$673$	−1.64560	−0.0634332	−0.0317166	−	0.999497i	$-0.510097\pi$
$673$	−1.64560	−0.0634332	−0.0317166	+	0.999497i	$0.510097\pi$
$674$	17.6757	0.680841
$675$	5.63655	0.216951
$676$	−3.29085	−0.126571
$677$	−12.0789	−0.464231	−0.232116	−	0.972688i	$-0.574565\pi$
$677$	−12.0789	−0.464231	−0.232116	+	0.972688i	$0.574565\pi$
$678$	−3.34436	−0.128439
$679$	−2.21581	−0.0850348
$680$	7.03311	0.269707
$681$	14.1122	0.540780
$682$	−4.13157	−0.158206
$683$	21.7046	0.830503	0.415251	−	0.909707i	$-0.363694\pi$
$683$	21.7046	0.830503	0.415251	+	0.909707i	$0.363694\pi$
$684$	−4.99255	−0.190895
$685$	−9.43115	−0.360346
$686$	−44.8783	−1.71346
$687$	−31.7001	−1.20943
$688$	1.00000	0.0381246
$689$	−31.7123	−1.20814
$690$	−1.65477	−0.0629961
$691$	−21.4673	−0.816656	−0.408328	−	0.912835i	$-0.633888\pi$
$691$	−21.4673	−0.816656	−0.408328	+	0.912835i	$0.633888\pi$
$692$	−21.9002	−0.832522
$693$	3.86721	0.146903
$694$	1.50630	0.0571783
$695$	−16.0028	−0.607021
$696$	4.69147	0.177830
$697$	−40.5541	−1.53609
$698$	−6.73446	−0.254903
$699$	38.9906	1.47476
$700$	4.82678	0.182435
$701$	−15.7822	−0.596085	−0.298042	−	0.954553i	$-0.596334\pi$
$701$	−15.7822	−0.596085	−0.298042	+	0.954553i	$0.596334\pi$
$702$	−17.5632	−0.662881
$703$	23.3838	0.881935
$704$	−1.00000	−0.0376889
$705$	15.3395	0.577718
$706$	−2.06180	−0.0775969
$707$	−28.9281	−1.08795
$708$	−13.7515	−0.516814
$709$	−49.3521	−1.85346	−0.926729	−	0.375731i	$-0.877392\pi$
$709$	−49.3521	−1.85346	−0.926729	+	0.375731i	$0.877392\pi$
$710$	1.75115	0.0657194
$711$	7.85495	0.294583
$712$	11.1654	0.418440
$713$	−4.61063	−0.172669
$714$	50.3382	1.88386
$715$	3.11595	0.116530
$716$	6.07104	0.226885
$717$	14.8345	0.554005
$718$	−14.9385	−0.557499
$719$	−39.6827	−1.47991	−0.739957	−	0.672654i	$-0.765154\pi$
$719$	−39.6827	−1.47991	−0.739957	+	0.672654i	$0.765154\pi$
$720$	0.801199	0.0298589
$721$	57.9583	2.15848
$722$	−19.8297	−0.737985
$723$	−14.4017	−0.535605
$724$	10.3540	0.384803
$725$	3.16385	0.117502
$726$	1.48284	0.0550332
$727$	−25.7743	−0.955917	−0.477959	−	0.878382i	$-0.658623\pi$
$727$	−25.7743	−0.955917	−0.477959	+	0.878382i	$0.658623\pi$
$728$	−15.0400	−0.557419
$729$	29.8450	1.10537
$730$	6.29746	0.233079
$731$	7.03311	0.260129
$732$	−16.6864	−0.616745
$733$	−8.72247	−0.322172	−0.161086	−	0.986940i	$-0.551500\pi$
$733$	−8.72247	−0.322172	−0.161086	+	0.986940i	$0.551500\pi$
$734$	−14.7313	−0.543741
$735$	24.1669	0.891410
$736$	−1.11595	−0.0411345
$737$	11.3564	0.418317
$738$	−4.61985	−0.170059
$739$	49.5319	1.82206	0.911030	−	0.412341i	$-0.135289\pi$
$739$	49.5319	1.82206	0.911030	+	0.412341i	$0.135289\pi$
$740$	−3.75260	−0.137948
$741$	−28.7916	−1.05769
$742$	49.1241	1.80340
$743$	33.6058	1.23288	0.616439	−	0.787403i	$-0.288575\pi$
$743$	33.6058	1.23288	0.616439	+	0.787403i	$0.288575\pi$
$744$	−6.12644	−0.224606
$745$	−4.39902	−0.161168
$746$	13.7561	0.503646
$747$	6.21295	0.227320
$748$	−7.03311	−0.257156
$749$	10.1452	0.370696
$750$	−1.48284	−0.0541455
$751$	−12.0723	−0.440525	−0.220263	−	0.975441i	$-0.570691\pi$
$751$	−12.0723	−0.440525	−0.220263	+	0.975441i	$0.570691\pi$
$752$	10.3447	0.377232
$753$	−37.9074	−1.38142
$754$	−9.85841	−0.359022
$755$	18.2702	0.664919
$756$	27.2064	0.989486
$757$	11.3058	0.410917	0.205459	−	0.978666i	$-0.434131\pi$
$757$	11.3058	0.410917	0.205459	+	0.978666i	$0.434131\pi$
$758$	19.6061	0.712127
$759$	1.65477	0.0600644
$760$	6.23135	0.226035
$761$	11.6839	0.423540	0.211770	−	0.977320i	$-0.432077\pi$
$761$	11.6839	0.423540	0.211770	+	0.977320i	$0.432077\pi$
$762$	−31.0472	−1.12472
$763$	37.8003	1.36846
$764$	−15.9490	−0.577015
$765$	5.63492	0.203731
$766$	−32.1235	−1.16067
$767$	28.8967	1.04340
$768$	−1.48284	−0.0535072
$769$	−39.7026	−1.43171	−0.715856	−	0.698248i	$-0.753963\pi$
$769$	−39.7026	−1.43171	−0.715856	+	0.698248i	$0.753963\pi$
$770$	−4.82678	−0.173945
$771$	−7.16014	−0.257866
$772$	−2.80456	−0.100938
$773$	31.8511	1.14560	0.572802	−	0.819694i	$-0.305856\pi$
$773$	31.8511	1.14560	0.572802	+	0.819694i	$0.305856\pi$
$774$	0.801199	0.0287985
$775$	−4.13157	−0.148410
$776$	0.459065	0.0164795
$777$	−26.8585	−0.963545
$778$	23.0968	0.828060
$779$	−35.9310	−1.28736
$780$	4.62044	0.165438
$781$	−1.75115	−0.0626610
$782$	−7.84860	−0.280665
$783$	17.8332	0.637307
$784$	16.2978	0.582063
$785$	8.48633	0.302890
$786$	2.61095	0.0931294
$787$	21.4486	0.764560	0.382280	−	0.924047i	$-0.375139\pi$
$787$	21.4486	0.764560	0.382280	+	0.924047i	$0.375139\pi$
$788$	15.2867	0.544568
$789$	15.1909	0.540809
$790$	−9.80398	−0.348810
$791$	−10.8862	−0.387070
$792$	−0.801199	−0.0284694
$793$	35.0638	1.24515
$794$	−36.8054	−1.30617
$795$	−15.0914	−0.535237
$796$	−10.4346	−0.369843
$797$	−24.7674	−0.877306	−0.438653	−	0.898657i	$-0.644544\pi$
$797$	−24.7674	−0.877306	−0.438653	+	0.898657i	$0.644544\pi$
$798$	44.5997	1.57881
$799$	72.7553	2.57390
$800$	−1.00000	−0.0353553
$801$	8.94569	0.316080
$802$	6.49490	0.229343
$803$	−6.29746	−0.222233
$804$	16.8396	0.593888
$805$	−5.38644	−0.189847
$806$	12.8738	0.453459
$807$	20.2800	0.713889
$808$	5.99326	0.210842
$809$	−19.4659	−0.684385	−0.342192	−	0.939630i	$-0.611169\pi$
$809$	−19.4659	−0.684385	−0.342192	+	0.939630i	$0.611169\pi$
$810$	−5.95448	−0.209219
$811$	15.6211	0.548532	0.274266	−	0.961654i	$-0.411565\pi$
$811$	15.6211	0.548532	0.274266	+	0.961654i	$0.411565\pi$
$812$	15.2712	0.535914
$813$	16.5093	0.579006
$814$	3.75260	0.131529
$815$	5.34228	0.187132
$816$	−10.4289	−0.365086
$817$	6.23135	0.218007
$818$	−18.1660	−0.635158
$819$	−12.0500	−0.421062
$820$	5.76616	0.201363
$821$	−37.8925	−1.32246	−0.661229	−	0.750185i	$-0.729965\pi$
$821$	−37.8925	−1.32246	−0.661229	+	0.750185i	$0.729965\pi$
$822$	13.9848	0.487777
$823$	−2.27751	−0.0793890	−0.0396945	−	0.999212i	$-0.512638\pi$
$823$	−2.27751	−0.0793890	−0.0396945	+	0.999212i	$0.512638\pi$
$824$	−12.0077	−0.418307
$825$	1.48284	0.0516257
$826$	−44.7626	−1.55749
$827$	−17.0461	−0.592749	−0.296375	−	0.955072i	$-0.595778\pi$
$827$	−17.0461	−0.592749	−0.296375	+	0.955072i	$0.595778\pi$
$828$	−0.894099	−0.0310721
$829$	49.9099	1.73344	0.866721	−	0.498793i	$-0.166223\pi$
$829$	49.9099	1.73344	0.866721	+	0.498793i	$0.166223\pi$
$830$	−7.75457	−0.269165
$831$	−31.1086	−1.07915
$832$	3.11595	0.108026
$833$	114.624	3.97149
$834$	23.7295	0.821686
$835$	24.0863	0.833539
$836$	−6.23135	−0.215516
$837$	−23.2878	−0.804945
$838$	8.59949	0.297064
$839$	18.6811	0.644944	0.322472	−	0.946579i	$-0.395486\pi$
$839$	18.6811	0.644944	0.322472	+	0.946579i	$0.395486\pi$
$840$	−7.15731	−0.246951
$841$	−18.9900	−0.654829
$842$	30.7705	1.06042
$843$	6.11082	0.210468
$844$	18.4743	0.635913
$845$	3.29085	0.113209
$846$	8.28816	0.284953
$847$	4.82678	0.165850
$848$	−10.1774	−0.349494
$849$	−42.9913	−1.47546
$850$	−7.03311	−0.241234
$851$	4.18772	0.143553
$852$	−2.59666	−0.0889603
$853$	−19.1968	−0.657287	−0.328644	−	0.944454i	$-0.606591\pi$
$853$	−19.1968	−0.657287	−0.328644	+	0.944454i	$0.606591\pi$
$854$	−54.3157	−1.85865
$855$	4.99255	0.170742
$856$	−2.10185	−0.0718397
$857$	−20.8282	−0.711478	−0.355739	−	0.934585i	$-0.615771\pi$
$857$	−20.8282	−0.711478	−0.355739	+	0.934585i	$0.615771\pi$
$858$	−4.62044	−0.157739
$859$	−44.8598	−1.53060	−0.765298	−	0.643676i	$-0.777408\pi$
$859$	−44.8598	−1.53060	−0.765298	+	0.643676i	$0.777408\pi$
$860$	−1.00000	−0.0340997
$861$	41.2703	1.40649
$862$	−29.0510	−0.989481
$863$	51.5633	1.75524	0.877618	−	0.479361i	$-0.159132\pi$
$863$	51.5633	1.75524	0.877618	+	0.479361i	$0.159132\pi$
$864$	−5.63655	−0.191759
$865$	21.9002	0.744630
$866$	10.6572	0.362146
$867$	−48.1397	−1.63491
$868$	−19.9422	−0.676881
$869$	9.80398	0.332577
$870$	−4.69147	−0.159056
$871$	−35.3859	−1.19901
$872$	−7.83137	−0.265204
$873$	0.367803	0.0124482
$874$	−6.95388	−0.235218
$875$	−4.82678	−0.163175
$876$	−9.33810	−0.315505
$877$	−21.6569	−0.731302	−0.365651	−	0.930752i	$-0.619154\pi$
$877$	−21.6569	−0.731302	−0.365651	+	0.930752i	$0.619154\pi$
$878$	−8.49937	−0.286840
$879$	13.9798	0.471527
$880$	1.00000	0.0337100
$881$	11.2800	0.380032	0.190016	−	0.981781i	$-0.439146\pi$
$881$	11.2800	0.380032	0.190016	+	0.981781i	$0.439146\pi$
$882$	13.0578	0.439678
$883$	−16.4809	−0.554627	−0.277314	−	0.960779i	$-0.589444\pi$
$883$	−16.4809	−0.554627	−0.277314	+	0.960779i	$0.589444\pi$
$884$	21.9148	0.737075
$885$	13.7515	0.462252
$886$	−12.7886	−0.429641
$887$	−18.6243	−0.625341	−0.312671	−	0.949862i	$-0.601224\pi$
$887$	−18.6243	−0.625341	−0.312671	+	0.949862i	$0.601224\pi$
$888$	5.56449	0.186732
$889$	−101.062	−3.38951
$890$	−11.1654	−0.374264
$891$	5.95448	0.199483
$892$	5.99924	0.200870
$893$	64.4613	2.15712
$894$	6.52302	0.218162
$895$	−6.07104	−0.202932
$896$	−4.82678	−0.161251
$897$	−5.15618	−0.172160
$898$	10.0081	0.333975
$899$	−13.0717	−0.435965
$900$	−0.801199	−0.0267066
$901$	−71.5788	−2.38464
$902$	−5.76616	−0.191992
$903$	−7.15731	−0.238181
$904$	2.25538	0.0750129
$905$	−10.3540	−0.344178
$906$	−27.0916	−0.900059
$907$	−40.8310	−1.35577	−0.677885	−	0.735168i	$-0.737103\pi$
$907$	−40.8310	−1.35577	−0.677885	+	0.735168i	$0.737103\pi$
$908$	−9.51703	−0.315834
$909$	4.80179	0.159265
$910$	15.0400	0.498571
$911$	26.0470	0.862977	0.431488	−	0.902118i	$-0.357989\pi$
$911$	26.0470	0.862977	0.431488	+	0.902118i	$0.357989\pi$
$912$	−9.24006	−0.305969
$913$	7.75457	0.256639
$914$	23.1307	0.765095
$915$	16.6864	0.551634
$916$	21.3780	0.706349
$917$	8.49889	0.280658
$918$	−39.6425	−1.30840
$919$	−45.7537	−1.50928	−0.754638	−	0.656141i	$-0.772188\pi$
$919$	−45.7537	−1.50928	−0.754638	+	0.656141i	$0.772188\pi$
$920$	1.11595	0.0367918
$921$	−30.6819	−1.01100
$922$	7.38407	0.243181
$923$	5.45649	0.179603
$924$	7.15731	0.235458
$925$	3.75260	0.123385
$926$	26.1690	0.859966
$927$	−9.62053	−0.315980
$928$	−3.16385	−0.103859
$929$	25.7773	0.845725	0.422862	−	0.906194i	$-0.361025\pi$
$929$	25.7773	0.845725	0.422862	+	0.906194i	$0.361025\pi$
$930$	6.12644	0.200894
$931$	101.557	3.32840
$932$	−26.2946	−0.861308
$933$	−48.3574	−1.58315
$934$	2.76399	0.0904406
$935$	7.03311	0.230007
$936$	2.49650	0.0816006
$937$	−44.7046	−1.46044	−0.730219	−	0.683214i	$-0.760582\pi$
$937$	−44.7046	−1.46044	−0.730219	+	0.683214i	$0.760582\pi$
$938$	54.8147	1.78976
$939$	−44.5788	−1.45477
$940$	−10.3447	−0.337406
$941$	33.2819	1.08496	0.542480	−	0.840069i	$-0.317485\pi$
$941$	33.2819	1.08496	0.542480	+	0.840069i	$0.317485\pi$
$942$	−12.5838	−0.410003
$943$	−6.43475	−0.209544
$944$	9.27380	0.301837
$945$	−27.2064	−0.885024
$946$	1.00000	0.0325128
$947$	45.2271	1.46968	0.734841	−	0.678239i	$-0.237257\pi$
$947$	45.2271	1.46968	0.734841	+	0.678239i	$0.237257\pi$
$948$	14.5377	0.472162
$949$	19.6226	0.636976
$950$	−6.23135	−0.202172
$951$	8.25282	0.267616
$952$	−33.9472	−1.10024
$953$	26.3035	0.852055	0.426027	−	0.904710i	$-0.359913\pi$
$953$	26.3035	0.852055	0.426027	+	0.904710i	$0.359913\pi$
$954$	−8.15413	−0.264000
$955$	15.9490	0.516098
$956$	−10.0042	−0.323558
$957$	4.69147	0.151654
$958$	−36.2872	−1.17238
$959$	45.5221	1.46998
$960$	1.48284	0.0478583
$961$	−13.9301	−0.449359
$962$	−11.6929	−0.376995
$963$	−1.68400	−0.0542661
$964$	9.71227	0.312811
$965$	2.80456	0.0902821
$966$	7.98721	0.256984
$967$	33.5040	1.07742	0.538708	−	0.842493i	$-0.318913\pi$
$967$	33.5040	1.07742	0.538708	+	0.842493i	$0.318913\pi$
$968$	−1.00000	−0.0321412
$969$	−64.9864	−2.08766
$970$	−0.459065	−0.0147397
$971$	−23.1013	−0.741356	−0.370678	−	0.928761i	$-0.620875\pi$
$971$	−23.1013	−0.741356	−0.370678	+	0.928761i	$0.620875\pi$
$972$	−8.08014	−0.259171
$973$	77.2419	2.47626
$974$	−12.2972	−0.394028
$975$	−4.62044	−0.147973
$976$	11.2530	0.360200
$977$	48.8724	1.56357	0.781783	−	0.623551i	$-0.214310\pi$
$977$	48.8724	1.56357	0.781783	+	0.623551i	$0.214310\pi$
$978$	−7.92173	−0.253309
$979$	11.1654	0.356847
$980$	−16.2978	−0.520613
$981$	−6.27449	−0.200329
$982$	−20.5937	−0.657173
$983$	−33.1114	−1.05609	−0.528045	−	0.849216i	$-0.677075\pi$
$983$	−33.1114	−1.05609	−0.528045	+	0.849216i	$0.677075\pi$
$984$	−8.55027	−0.272573
$985$	−15.2867	−0.487076
$986$	−22.2517	−0.708639
$987$	−74.0402	−2.35672
$988$	19.4166	0.617723
$989$	1.11595	0.0354852
$990$	0.801199	0.0254638
$991$	45.9388	1.45929	0.729647	−	0.683824i	$-0.239684\pi$
$991$	45.9388	1.45929	0.729647	+	0.683824i	$0.239684\pi$
$992$	4.13157	0.131177
$993$	10.0954	0.320366
$994$	−8.45240	−0.268094
$995$	10.4346	0.330798
$996$	11.4987	0.364352
$997$	2.25804	0.0715127	0.0357564	−	0.999361i	$-0.488616\pi$
$997$	2.25804	0.0715127	0.0357564	+	0.999361i	$0.488616\pi$
$998$	−10.9689	−0.347216
$999$	21.1517	0.669211

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4730.2.a.bb.1.4	✓	11

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4730.2.a.bb.1.4	✓	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)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -1.48284 q^{3} +1.00000 q^{4} -1.00000 q^{5} +1.48284 q^{6} +4.82678 q^{7} -1.00000 q^{8} -0.801199 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -1.48284 q^{3} +1.00000 q^{4} -1.00000 q^{5} +1.48284 q^{6} +4.82678 q^{7} -1.00000 q^{8} -0.801199 q^{9} +1.00000 q^{10} -1.00000 q^{11} -1.48284 q^{12} +3.11595 q^{13} -4.82678 q^{14} +1.48284 q^{15} +1.00000 q^{16} +7.03311 q^{17} +0.801199 q^{18} +6.23135 q^{19} -1.00000 q^{20} -7.15731 q^{21} +1.00000 q^{22} +1.11595 q^{23} +1.48284 q^{24} +1.00000 q^{25} -3.11595 q^{26} +5.63655 q^{27} +4.82678 q^{28} +3.16385 q^{29} -1.48284 q^{30} -4.13157 q^{31} -1.00000 q^{32} +1.48284 q^{33} -7.03311 q^{34} -4.82678 q^{35} -0.801199 q^{36} +3.75260 q^{37} -6.23135 q^{38} -4.62044 q^{39} +1.00000 q^{40} -5.76616 q^{41} +7.15731 q^{42} +1.00000 q^{43} -1.00000 q^{44} +0.801199 q^{45} -1.11595 q^{46} +10.3447 q^{47} -1.48284 q^{48} +16.2978 q^{49} -1.00000 q^{50} -10.4289 q^{51} +3.11595 q^{52} -10.1774 q^{53} -5.63655 q^{54} +1.00000 q^{55} -4.82678 q^{56} -9.24006 q^{57} -3.16385 q^{58} +9.27380 q^{59} +1.48284 q^{60} +11.2530 q^{61} +4.13157 q^{62} -3.86721 q^{63} +1.00000 q^{64} -3.11595 q^{65} -1.48284 q^{66} -11.3564 q^{67} +7.03311 q^{68} -1.65477 q^{69} +4.82678 q^{70} +1.75115 q^{71} +0.801199 q^{72} +6.29746 q^{73} -3.75260 q^{74} -1.48284 q^{75} +6.23135 q^{76} -4.82678 q^{77} +4.62044 q^{78} -9.80398 q^{79} -1.00000 q^{80} -5.95448 q^{81} +5.76616 q^{82} -7.75457 q^{83} -7.15731 q^{84} -7.03311 q^{85} -1.00000 q^{86} -4.69147 q^{87} +1.00000 q^{88} -11.1654 q^{89} -0.801199 q^{90} +15.0400 q^{91} +1.11595 q^{92} +6.12644 q^{93} -10.3447 q^{94} -6.23135 q^{95} +1.48284 q^{96} -0.459065 q^{97} -16.2978 q^{98} +0.801199 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 11 q - 11 q^{2} - q^{3} + 11 q^{4} - 11 q^{5} + q^{6} + 6 q^{7} - 11 q^{8} + 12 q^{9}+O(q^{10}) \) 11 * q - 11 * q^2 - q^3 + 11 * q^4 - 11 * q^5 + q^6 + 6 * q^7 - 11 * q^8 + 12 * q^9	\( 11 q - 11 q^{2} - q^{3} + 11 q^{4} - 11 q^{5} + q^{6} + 6 q^{7} - 11 q^{8} + 12 q^{9} + 11 q^{10} - 11 q^{11} - q^{12} + 4 q^{13} - 6 q^{14} + q^{15} + 11 q^{16} - 10 q^{17} - 12 q^{18} + 14 q^{19} - 11 q^{20} - 2 q^{21} + 11 q^{22} - 18 q^{23} + q^{24} + 11 q^{25} - 4 q^{26} + 2 q^{27} + 6 q^{28} - 6 q^{29} - q^{30} + 13 q^{31} - 11 q^{32} + q^{33} + 10 q^{34} - 6 q^{35} + 12 q^{36} + q^{37} - 14 q^{38} + 12 q^{39} + 11 q^{40} + 12 q^{41} + 2 q^{42} + 11 q^{43} - 11 q^{44} - 12 q^{45} + 18 q^{46} - 5 q^{47} - q^{48} + 31 q^{49} - 11 q^{50} + q^{51} + 4 q^{52} - 27 q^{53} - 2 q^{54} + 11 q^{55} - 6 q^{56} - 5 q^{57} + 6 q^{58} + 11 q^{59} + q^{60} + 36 q^{61} - 13 q^{62} + 17 q^{63} + 11 q^{64} - 4 q^{65} - q^{66} + 18 q^{67} - 10 q^{68} + 14 q^{69} + 6 q^{70} - 14 q^{71} - 12 q^{72} - 11 q^{73} - q^{74} - q^{75} + 14 q^{76} - 6 q^{77} - 12 q^{78} + 28 q^{79} - 11 q^{80} + 7 q^{81} - 12 q^{82} - 4 q^{83} - 2 q^{84} + 10 q^{85} - 11 q^{86} + 38 q^{87} + 11 q^{88} - 7 q^{89} + 12 q^{90} + 14 q^{91} - 18 q^{92} - 3 q^{93} + 5 q^{94} - 14 q^{95} + q^{96} - q^{97} - 31 q^{98} - 12 q^{99}+O(q^{100}) \) 11 * q - 11 * q^2 - q^3 + 11 * q^4 - 11 * q^5 + q^6 + 6 * q^7 - 11 * q^8 + 12 * q^9 + 11 * q^10 - 11 * q^11 - q^12 + 4 * q^13 - 6 * q^14 + q^15 + 11 * q^16 - 10 * q^17 - 12 * q^18 + 14 * q^19 - 11 * q^20 - 2 * q^21 + 11 * q^22 - 18 * q^23 + q^24 + 11 * q^25 - 4 * q^26 + 2 * q^27 + 6 * q^28 - 6 * q^29 - q^30 + 13 * q^31 - 11 * q^32 + q^33 + 10 * q^34 - 6 * q^35 + 12 * q^36 + q^37 - 14 * q^38 + 12 * q^39 + 11 * q^40 + 12 * q^41 + 2 * q^42 + 11 * q^43 - 11 * q^44 - 12 * q^45 + 18 * q^46 - 5 * q^47 - q^48 + 31 * q^49 - 11 * q^50 + q^51 + 4 * q^52 - 27 * q^53 - 2 * q^54 + 11 * q^55 - 6 * q^56 - 5 * q^57 + 6 * q^58 + 11 * q^59 + q^60 + 36 * q^61 - 13 * q^62 + 17 * q^63 + 11 * q^64 - 4 * q^65 - q^66 + 18 * q^67 - 10 * q^68 + 14 * q^69 + 6 * q^70 - 14 * q^71 - 12 * q^72 - 11 * q^73 - q^74 - q^75 + 14 * q^76 - 6 * q^77 - 12 * q^78 + 28 * q^79 - 11 * q^80 + 7 * q^81 - 12 * q^82 - 4 * q^83 - 2 * q^84 + 10 * q^85 - 11 * q^86 + 38 * q^87 + 11 * q^88 - 7 * q^89 + 12 * q^90 + 14 * q^91 - 18 * q^92 - 3 * q^93 + 5 * q^94 - 14 * q^95 + q^96 - q^97 - 31 * q^98 - 12 * q^99

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