LMFDB - Embedded newform 429.2.a.g.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [429,2,Mod(1,429)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(429, 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("429.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 429 = 3 \cdot 11 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	429.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:	$3.42558224671$
Analytic rank:	$0$
Dimension:	$3$
Coefficient field:	3.3.148.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - x^{2} - 3x + 1 $ x^3 - x^2 - 3*x + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$0.311108$ of defining polynomial
Character	$\chi$	$=$	429.1

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.21432 q^{2} +1.00000 q^{3} -0.525428 q^{4} +1.31111 q^{5} -1.21432 q^{6} +1.52543 q^{7} +3.06668 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.21432 q^{2} +1.00000 q^{3} -0.525428 q^{4} +1.31111 q^{5} -1.21432 q^{6} +1.52543 q^{7} +3.06668 q^{8} +1.00000 q^{9} -1.59210 q^{10} -1.00000 q^{11} -0.525428 q^{12} -1.00000 q^{13} -1.85236 q^{14} +1.31111 q^{15} -2.67307 q^{16} +2.21432 q^{17} -1.21432 q^{18} -1.52543 q^{19} -0.688892 q^{20} +1.52543 q^{21} +1.21432 q^{22} +7.95407 q^{23} +3.06668 q^{24} -3.28100 q^{25} +1.21432 q^{26} +1.00000 q^{27} -0.801502 q^{28} +7.39853 q^{29} -1.59210 q^{30} +4.68889 q^{31} -2.88739 q^{32} -1.00000 q^{33} -2.68889 q^{34} +2.00000 q^{35} -0.525428 q^{36} +8.85728 q^{37} +1.85236 q^{38} -1.00000 q^{39} +4.02074 q^{40} -3.52543 q^{41} -1.85236 q^{42} -8.77631 q^{43} +0.525428 q^{44} +1.31111 q^{45} -9.65878 q^{46} +9.18421 q^{47} -2.67307 q^{48} -4.67307 q^{49} +3.98418 q^{50} +2.21432 q^{51} +0.525428 q^{52} +3.67307 q^{53} -1.21432 q^{54} -1.31111 q^{55} +4.67799 q^{56} -1.52543 q^{57} -8.98418 q^{58} +9.37778 q^{59} -0.688892 q^{60} -11.4795 q^{61} -5.69381 q^{62} +1.52543 q^{63} +8.85236 q^{64} -1.31111 q^{65} +1.21432 q^{66} +5.25088 q^{67} -1.16346 q^{68} +7.95407 q^{69} -2.42864 q^{70} -14.4701 q^{71} +3.06668 q^{72} +3.13828 q^{73} -10.7556 q^{74} -3.28100 q^{75} +0.801502 q^{76} -1.52543 q^{77} +1.21432 q^{78} -5.03011 q^{79} -3.50468 q^{80} +1.00000 q^{81} +4.28100 q^{82} +5.37778 q^{83} -0.801502 q^{84} +2.90321 q^{85} +10.6572 q^{86} +7.39853 q^{87} -3.06668 q^{88} +0.688892 q^{89} -1.59210 q^{90} -1.52543 q^{91} -4.17929 q^{92} +4.68889 q^{93} -11.1526 q^{94} -2.00000 q^{95} -2.88739 q^{96} -12.8573 q^{97} +5.67460 q^{98} -1.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q + 3 q^{2} + 3 q^{3} + 5 q^{4} + 4 q^{5} + 3 q^{6} - 2 q^{7} + 9 q^{8} + 3 q^{9}+O(q^{10}) $ 3 * q + 3 * q^2 + 3 * q^3 + 5 * q^4 + 4 * q^5 + 3 * q^6 - 2 * q^7 + 9 * q^8 + 3 * q^9	\( 3 q + 3 q^{2} + 3 q^{3} + 5 q^{4} + 4 q^{5} + 3 q^{6} - 2 q^{7} + 9 q^{8} + 3 q^{9} + 2 q^{10} - 3 q^{11} + 5 q^{12} - 3 q^{13} - 12 q^{14} + 4 q^{15} + 5 q^{16} + 3 q^{18} + 2 q^{19} - 2 q^{20} - 2 q^{21} - 3 q^{22} + 4 q^{23} + 9 q^{24} - 3 q^{25} - 3 q^{26} + 3 q^{27} - 22 q^{28} + 2 q^{29} + 2 q^{30} + 14 q^{31} + 11 q^{32} - 3 q^{33} - 8 q^{34} + 6 q^{35} + 5 q^{36} + 12 q^{38} - 3 q^{39} - 8 q^{40} - 4 q^{41} - 12 q^{42} - 6 q^{43} - 5 q^{44} + 4 q^{45} - 22 q^{46} + 14 q^{47} + 5 q^{48} - q^{49} - q^{50} - 5 q^{52} - 2 q^{53} + 3 q^{54} - 4 q^{55} - 32 q^{56} + 2 q^{57} - 14 q^{58} + 28 q^{59} - 2 q^{60} - 8 q^{61} + 16 q^{62} - 2 q^{63} + 33 q^{64} - 4 q^{65} - 3 q^{66} + 2 q^{67} - 10 q^{68} + 4 q^{69} + 6 q^{70} + 10 q^{71} + 9 q^{72} - 24 q^{73} - 32 q^{74} - 3 q^{75} + 22 q^{76} + 2 q^{77} - 3 q^{78} - 22 q^{79} - 24 q^{80} + 3 q^{81} + 6 q^{82} + 16 q^{83} - 22 q^{84} + 2 q^{85} + 6 q^{86} + 2 q^{87} - 9 q^{88} + 2 q^{89} + 2 q^{90} + 2 q^{91} - 32 q^{92} + 14 q^{93} + 6 q^{94} - 6 q^{95} + 11 q^{96} - 12 q^{97} + 23 q^{98} - 3 q^{99}+O(q^{100}) \) 3 * q + 3 * q^2 + 3 * q^3 + 5 * q^4 + 4 * q^5 + 3 * q^6 - 2 * q^7 + 9 * q^8 + 3 * q^9 + 2 * q^10 - 3 * q^11 + 5 * q^12 - 3 * q^13 - 12 * q^14 + 4 * q^15 + 5 * q^16 + 3 * q^18 + 2 * q^19 - 2 * q^20 - 2 * q^21 - 3 * q^22 + 4 * q^23 + 9 * q^24 - 3 * q^25 - 3 * q^26 + 3 * q^27 - 22 * q^28 + 2 * q^29 + 2 * q^30 + 14 * q^31 + 11 * q^32 - 3 * q^33 - 8 * q^34 + 6 * q^35 + 5 * q^36 + 12 * q^38 - 3 * q^39 - 8 * q^40 - 4 * q^41 - 12 * q^42 - 6 * q^43 - 5 * q^44 + 4 * q^45 - 22 * q^46 + 14 * q^47 + 5 * q^48 - q^49 - q^50 - 5 * q^52 - 2 * q^53 + 3 * q^54 - 4 * q^55 - 32 * q^56 + 2 * q^57 - 14 * q^58 + 28 * q^59 - 2 * q^60 - 8 * q^61 + 16 * q^62 - 2 * q^63 + 33 * q^64 - 4 * q^65 - 3 * q^66 + 2 * q^67 - 10 * q^68 + 4 * q^69 + 6 * q^70 + 10 * q^71 + 9 * q^72 - 24 * q^73 - 32 * q^74 - 3 * q^75 + 22 * q^76 + 2 * q^77 - 3 * q^78 - 22 * q^79 - 24 * q^80 + 3 * q^81 + 6 * q^82 + 16 * q^83 - 22 * q^84 + 2 * q^85 + 6 * q^86 + 2 * q^87 - 9 * q^88 + 2 * q^89 + 2 * q^90 + 2 * q^91 - 32 * q^92 + 14 * q^93 + 6 * q^94 - 6 * q^95 + 11 * q^96 - 12 * q^97 + 23 * q^98 - 3 * 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 $

$2$	−1.21432	−0.858654	−0.429327	−	0.903149i	$-0.641249\pi$
$2$	−1.21432	−0.858654	−0.429327	+	0.903149i	$0.641249\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	−0.525428	−0.262714
$5$	1.31111	0.586345	0.293173	−	0.956060i	$-0.405289\pi$
$5$	1.31111	0.586345	0.293173	+	0.956060i	$0.405289\pi$
$6$	−1.21432	−0.495744
$7$	1.52543	0.576557	0.288279	−	0.957547i	$-0.406917\pi$
$7$	1.52543	0.576557	0.288279	+	0.957547i	$0.406917\pi$
$8$	3.06668	1.08423
$9$	1.00000	0.333333
$10$	−1.59210	−0.503468
$11$	−1.00000	−0.301511
$11$	−1.00000	−0.301511
$12$	−0.525428	−0.151678
$13$	−1.00000	−0.277350
$13$	−1.00000	−0.277350
$14$	−1.85236	−0.495063
$15$	1.31111	0.338527
$16$	−2.67307	−0.668268
$17$	2.21432	0.537051	0.268526	−	0.963273i	$-0.413464\pi$
$17$	2.21432	0.537051	0.268526	+	0.963273i	$0.413464\pi$
$18$	−1.21432	−0.286218
$19$	−1.52543	−0.349957	−0.174979	−	0.984572i	$-0.555986\pi$
$19$	−1.52543	−0.349957	−0.174979	+	0.984572i	$0.555986\pi$
$20$	−0.688892	−0.154041
$21$	1.52543	0.332876
$22$	1.21432	0.258894
$23$	7.95407	1.65854	0.829269	−	0.558850i	$-0.188757\pi$
$23$	7.95407	1.65854	0.829269	+	0.558850i	$0.188757\pi$
$24$	3.06668	0.625983
$25$	−3.28100	−0.656199
$26$	1.21432	0.238148
$27$	1.00000	0.192450
$28$	−0.801502	−0.151470
$29$	7.39853	1.37387	0.686936	−	0.726718i	$-0.258955\pi$
$29$	7.39853	1.37387	0.686936	+	0.726718i	$0.258955\pi$
$30$	−1.59210	−0.290677
$31$	4.68889	0.842150	0.421075	−	0.907026i	$-0.361653\pi$
$31$	4.68889	0.842150	0.421075	+	0.907026i	$0.361653\pi$
$32$	−2.88739	−0.510423
$33$	−1.00000	−0.174078
$34$	−2.68889	−0.461141
$35$	2.00000	0.338062
$36$	−0.525428	−0.0875713
$37$	8.85728	1.45613	0.728064	−	0.685509i	$-0.240420\pi$
$37$	8.85728	1.45613	0.728064	+	0.685509i	$0.240420\pi$
$38$	1.85236	0.300492
$39$	−1.00000	−0.160128
$40$	4.02074	0.635735
$41$	−3.52543	−0.550579	−0.275290	−	0.961361i	$-0.588774\pi$
$41$	−3.52543	−0.550579	−0.275290	+	0.961361i	$0.588774\pi$
$42$	−1.85236	−0.285825
$43$	−8.77631	−1.33838	−0.669188	−	0.743094i	$-0.733358\pi$
$43$	−8.77631	−1.33838	−0.669188	+	0.743094i	$0.733358\pi$
$44$	0.525428	0.0792112
$45$	1.31111	0.195448
$46$	−9.65878	−1.42411
$47$	9.18421	1.33965	0.669827	−	0.742517i	$-0.266368\pi$
$47$	9.18421	1.33965	0.669827	+	0.742517i	$0.266368\pi$
$48$	−2.67307	−0.385825
$49$	−4.67307	−0.667582
$50$	3.98418	0.563448
$51$	2.21432	0.310067
$52$	0.525428	0.0728637
$53$	3.67307	0.504535	0.252268	−	0.967658i	$-0.418824\pi$
$53$	3.67307	0.504535	0.252268	+	0.967658i	$0.418824\pi$
$54$	−1.21432	−0.165248
$55$	−1.31111	−0.176790
$56$	4.67799	0.625123
$57$	−1.52543	−0.202048
$58$	−8.98418	−1.17968
$59$	9.37778	1.22088	0.610442	−	0.792061i	$-0.290992\pi$
$59$	9.37778	1.22088	0.610442	+	0.792061i	$0.290992\pi$
$60$	−0.688892	−0.0889356
$61$	−11.4795	−1.46980	−0.734899	−	0.678176i	$-0.762771\pi$
$61$	−11.4795	−1.46980	−0.734899	+	0.678176i	$0.762771\pi$
$62$	−5.69381	−0.723115
$63$	1.52543	0.192186
$64$	8.85236	1.10654
$65$	−1.31111	−0.162623
$66$	1.21432	0.149472
$67$	5.25088	0.641498	0.320749	−	0.947164i	$-0.396065\pi$
$67$	5.25088	0.641498	0.320749	+	0.947164i	$0.396065\pi$
$68$	−1.16346	−0.141091
$69$	7.95407	0.957557
$70$	−2.42864	−0.290278
$71$	−14.4701	−1.71729	−0.858644	−	0.512572i	$-0.828693\pi$
$71$	−14.4701	−1.71729	−0.858644	+	0.512572i	$0.828693\pi$
$72$	3.06668	0.361411
$73$	3.13828	0.367307	0.183654	−	0.982991i	$-0.441208\pi$
$73$	3.13828	0.367307	0.183654	+	0.982991i	$0.441208\pi$
$74$	−10.7556	−1.25031
$75$	−3.28100	−0.378857
$76$	0.801502	0.0919385
$77$	−1.52543	−0.173839
$78$	1.21432	0.137495
$79$	−5.03011	−0.565932	−0.282966	−	0.959130i	$-0.591318\pi$
$79$	−5.03011	−0.565932	−0.282966	+	0.959130i	$0.591318\pi$
$80$	−3.50468	−0.391836
$81$	1.00000	0.111111
$82$	4.28100	0.472757
$83$	5.37778	0.590289	0.295144	−	0.955453i	$-0.404632\pi$
$83$	5.37778	0.590289	0.295144	+	0.955453i	$0.404632\pi$
$84$	−0.801502	−0.0874510
$85$	2.90321	0.314898
$86$	10.6572	1.14920
$87$	7.39853	0.793205
$88$	−3.06668	−0.326909
$89$	0.688892	0.0730224	0.0365112	−	0.999333i	$-0.488376\pi$
$89$	0.688892	0.0730224	0.0365112	+	0.999333i	$0.488376\pi$
$90$	−1.59210	−0.167823
$91$	−1.52543	−0.159908
$92$	−4.17929	−0.435721
$93$	4.68889	0.486215
$94$	−11.1526	−1.15030
$95$	−2.00000	−0.205196
$96$	−2.88739	−0.294693
$97$	−12.8573	−1.30546	−0.652729	−	0.757591i	$-0.726376\pi$
$97$	−12.8573	−1.30546	−0.652729	+	0.757591i	$0.726376\pi$
$98$	5.67460	0.573221
$99$	−1.00000	−0.100504
$100$	1.72393	0.172393
$101$	−16.0207	−1.59412	−0.797062	−	0.603898i	$-0.793614\pi$
$101$	−16.0207	−1.59412	−0.797062	+	0.603898i	$0.793614\pi$
$102$	−2.68889	−0.266240
$103$	−7.61285	−0.750116	−0.375058	−	0.927001i	$-0.622377\pi$
$103$	−7.61285	−0.750116	−0.375058	+	0.927001i	$0.622377\pi$
$104$	−3.06668	−0.300712
$105$	2.00000	0.195180
$106$	−4.46028	−0.433221
$107$	−12.9906	−1.25585	−0.627926	−	0.778273i	$-0.716096\pi$
$107$	−12.9906	−1.25585	−0.627926	+	0.778273i	$0.716096\pi$
$108$	−0.525428	−0.0505593
$109$	3.82071	0.365958	0.182979	−	0.983117i	$-0.441426\pi$
$109$	3.82071	0.365958	0.182979	+	0.983117i	$0.441426\pi$
$110$	1.59210	0.151801
$111$	8.85728	0.840696
$112$	−4.07758	−0.385295
$113$	−18.3368	−1.72498	−0.862489	−	0.506075i	$-0.831096\pi$
$113$	−18.3368	−1.72498	−0.862489	+	0.506075i	$0.831096\pi$
$114$	1.85236	0.173489
$115$	10.4286	0.972476
$116$	−3.88739	−0.360935
$117$	−1.00000	−0.0924500
$118$	−11.3876	−1.04832
$119$	3.37778	0.309641
$120$	4.02074	0.367042
$121$	1.00000	0.0909091
$122$	13.9398	1.26205
$123$	−3.52543	−0.317877
$124$	−2.46367	−0.221244
$125$	−10.8573	−0.971105
$126$	−1.85236	−0.165021
$127$	−20.5827	−1.82642	−0.913211	−	0.407486i	$-0.866405\pi$
$127$	−20.5827	−1.82642	−0.913211	+	0.407486i	$0.866405\pi$
$128$	−4.97481	−0.439715
$129$	−8.77631	−0.772711
$130$	1.59210	0.139637
$131$	−0.561993	−0.0491015	−0.0245508	−	0.999699i	$-0.507816\pi$
$131$	−0.561993	−0.0491015	−0.0245508	+	0.999699i	$0.507816\pi$
$132$	0.525428	0.0457326
$133$	−2.32693	−0.201770
$134$	−6.37625	−0.550824
$135$	1.31111	0.112842
$136$	6.79060	0.582289
$137$	5.07604	0.433676	0.216838	−	0.976208i	$-0.430426\pi$
$137$	5.07604	0.433676	0.216838	+	0.976208i	$0.430426\pi$
$138$	−9.65878	−0.822210
$139$	18.5511	1.57348	0.786742	−	0.617282i	$-0.211766\pi$
$139$	18.5511	1.57348	0.786742	+	0.617282i	$0.211766\pi$
$140$	−1.05086	−0.0888135
$141$	9.18421	0.773450
$142$	17.5714	1.47456
$143$	1.00000	0.0836242
$144$	−2.67307	−0.222756
$145$	9.70027	0.805563
$146$	−3.81087	−0.315390
$147$	−4.67307	−0.385428
$148$	−4.65386	−0.382545
$149$	−4.38271	−0.359045	−0.179523	−	0.983754i	$-0.557455\pi$
$149$	−4.38271	−0.359045	−0.179523	+	0.983754i	$0.557455\pi$
$150$	3.98418	0.325307
$151$	1.23014	0.100107	0.0500537	−	0.998747i	$-0.484061\pi$
$151$	1.23014	0.100107	0.0500537	+	0.998747i	$0.484061\pi$
$152$	−4.67799	−0.379435
$153$	2.21432	0.179017
$154$	1.85236	0.149267
$155$	6.14764	0.493791
$156$	0.525428	0.0420679
$157$	7.62714	0.608712	0.304356	−	0.952558i	$-0.401559\pi$
$157$	7.62714	0.608712	0.304356	+	0.952558i	$0.401559\pi$
$158$	6.10816	0.485939
$159$	3.67307	0.291293
$160$	−3.78568	−0.299284
$161$	12.1334	0.956242
$162$	−1.21432	−0.0954060
$163$	7.25088	0.567933	0.283967	−	0.958834i	$-0.408350\pi$
$163$	7.25088	0.567933	0.283967	+	0.958834i	$0.408350\pi$
$164$	1.85236	0.144645
$165$	−1.31111	−0.102070
$166$	−6.53035	−0.506853
$167$	0.295286	0.0228499	0.0114250	−	0.999935i	$-0.496363\pi$
$167$	0.295286	0.0228499	0.0114250	+	0.999935i	$0.496363\pi$
$168$	4.67799	0.360915
$169$	1.00000	0.0769231
$170$	−3.52543	−0.270388
$171$	−1.52543	−0.116652
$172$	4.61132	0.351610
$173$	−17.5605	−1.33510	−0.667549	−	0.744566i	$-0.732656\pi$
$173$	−17.5605	−1.33510	−0.667549	+	0.744566i	$0.732656\pi$
$174$	−8.98418	−0.681089
$175$	−5.00492	−0.378337
$176$	2.67307	0.201490
$177$	9.37778	0.704877
$178$	−0.836535	−0.0627010
$179$	12.0874	0.903456	0.451728	−	0.892156i	$-0.350808\pi$
$179$	12.0874	0.903456	0.451728	+	0.892156i	$0.350808\pi$
$180$	−0.688892	−0.0513470
$181$	7.71900	0.573749	0.286875	−	0.957968i	$-0.407384\pi$
$181$	7.71900	0.573749	0.286875	+	0.957968i	$0.407384\pi$
$182$	1.85236	0.137306
$183$	−11.4795	−0.848589
$184$	24.3926	1.79824
$185$	11.6128	0.853794
$186$	−5.69381	−0.417491
$187$	−2.21432	−0.161927
$188$	−4.82564	−0.351946
$189$	1.52543	0.110959
$190$	2.42864	0.176192
$191$	−16.6035	−1.20139	−0.600693	−	0.799480i	$-0.705109\pi$
$191$	−16.6035	−1.20139	−0.600693	+	0.799480i	$0.705109\pi$
$192$	8.85236	0.638864
$193$	−7.52543	−0.541692	−0.270846	−	0.962623i	$-0.587303\pi$
$193$	−7.52543	−0.541692	−0.270846	+	0.962623i	$0.587303\pi$
$194$	15.6128	1.12094
$195$	−1.31111	−0.0938904
$196$	2.45536	0.175383
$197$	12.2494	0.872730	0.436365	−	0.899770i	$-0.356266\pi$
$197$	12.2494	0.872730	0.436365	+	0.899770i	$0.356266\pi$
$198$	1.21432	0.0862979
$199$	11.6128	0.823213	0.411606	−	0.911362i	$-0.364968\pi$
$199$	11.6128	0.823213	0.411606	+	0.911362i	$0.364968\pi$
$200$	−10.0618	−0.711473
$201$	5.25088	0.370369
$202$	19.4543	1.36880
$203$	11.2859	0.792116
$204$	−1.16346	−0.0814588
$205$	−4.62222	−0.322830
$206$	9.24443	0.644090
$207$	7.95407	0.552846
$208$	2.67307	0.185344
$209$	1.52543	0.105516
$210$	−2.42864	−0.167592
$211$	5.16346	0.355468	0.177734	−	0.984079i	$-0.443123\pi$
$211$	5.16346	0.355468	0.177734	+	0.984079i	$0.443123\pi$
$212$	−1.92993	−0.132548
$213$	−14.4701	−0.991477
$214$	15.7748	1.07834
$215$	−11.5067	−0.784750
$216$	3.06668	0.208661
$217$	7.15257	0.485548
$218$	−4.63957	−0.314231
$219$	3.13828	0.212065
$220$	0.688892	0.0464451
$221$	−2.21432	−0.148951
$222$	−10.7556	−0.721867
$223$	−8.30174	−0.555926	−0.277963	−	0.960592i	$-0.589659\pi$
$223$	−8.30174	−0.555926	−0.277963	+	0.960592i	$0.589659\pi$
$224$	−4.40451	−0.294288
$225$	−3.28100	−0.218733
$226$	22.2667	1.48116
$227$	−5.27163	−0.349890	−0.174945	−	0.984578i	$-0.555975\pi$
$227$	−5.27163	−0.349890	−0.174945	+	0.984578i	$0.555975\pi$
$228$	0.801502	0.0530807
$229$	−25.5526	−1.68856	−0.844282	−	0.535898i	$-0.819973\pi$
$229$	−25.5526	−1.68856	−0.844282	+	0.535898i	$0.819973\pi$
$230$	−12.6637	−0.835020
$231$	−1.52543	−0.100366
$232$	22.6889	1.48960
$233$	2.40790	0.157747	0.0788733	−	0.996885i	$-0.474868\pi$
$233$	2.40790	0.157747	0.0788733	+	0.996885i	$0.474868\pi$
$234$	1.21432	0.0793826
$235$	12.0415	0.785500
$236$	−4.92735	−0.320743
$237$	−5.03011	−0.326741
$238$	−4.10171	−0.265874
$239$	17.8622	1.15541	0.577705	−	0.816246i	$-0.303948\pi$
$239$	17.8622	1.15541	0.577705	+	0.816246i	$0.303948\pi$
$240$	−3.50468	−0.226226
$241$	−3.93978	−0.253783	−0.126892	−	0.991917i	$-0.540500\pi$
$241$	−3.93978	−0.253783	−0.126892	+	0.991917i	$0.540500\pi$
$242$	−1.21432	−0.0780594
$243$	1.00000	0.0641500
$244$	6.03164	0.386136
$245$	−6.12690	−0.391433
$246$	4.28100	0.272946
$247$	1.52543	0.0970606
$248$	14.3793	0.913087
$249$	5.37778	0.340803
$250$	13.1842	0.833843
$251$	23.3590	1.47441	0.737205	−	0.675669i	$-0.236145\pi$
$251$	23.3590	1.47441	0.737205	+	0.675669i	$0.236145\pi$
$252$	−0.801502	−0.0504899
$253$	−7.95407	−0.500068
$254$	24.9940	1.56826
$255$	2.90321	0.181806
$256$	−11.6637	−0.728981
$257$	1.70471	0.106337	0.0531686	−	0.998586i	$-0.483068\pi$
$257$	1.70471	0.106337	0.0531686	+	0.998586i	$0.483068\pi$
$258$	10.6572	0.663491
$259$	13.5111	0.839541
$260$	0.688892	0.0427233
$261$	7.39853	0.457957
$262$	0.682439	0.0421612
$263$	−1.11108	−0.0685120	−0.0342560	−	0.999413i	$-0.510906\pi$
$263$	−1.11108	−0.0685120	−0.0342560	+	0.999413i	$0.510906\pi$
$264$	−3.06668	−0.188741
$265$	4.81579	0.295832
$266$	2.82564	0.173251
$267$	0.688892	0.0421595
$268$	−2.75896	−0.168530
$269$	8.79706	0.536366	0.268183	−	0.963368i	$-0.413577\pi$
$269$	8.79706	0.536366	0.268183	+	0.963368i	$0.413577\pi$
$270$	−1.59210	−0.0968924
$271$	27.3733	1.66281	0.831406	−	0.555665i	$-0.187536\pi$
$271$	27.3733	1.66281	0.831406	+	0.555665i	$0.187536\pi$
$272$	−5.91903	−0.358894
$273$	−1.52543	−0.0923231
$274$	−6.16394	−0.372377
$275$	3.28100	0.197852
$276$	−4.17929	−0.251563
$277$	−25.9081	−1.55667	−0.778334	−	0.627850i	$-0.783935\pi$
$277$	−25.9081	−1.55667	−0.778334	+	0.627850i	$0.783935\pi$
$278$	−22.5270	−1.35108
$279$	4.68889	0.280717
$280$	6.13335	0.366538
$281$	−5.76049	−0.343642	−0.171821	−	0.985128i	$-0.554965\pi$
$281$	−5.76049	−0.343642	−0.171821	+	0.985128i	$0.554965\pi$
$282$	−11.1526	−0.664126
$283$	−3.03011	−0.180121	−0.0900607	−	0.995936i	$-0.528706\pi$
$283$	−3.03011	−0.180121	−0.0900607	+	0.995936i	$0.528706\pi$
$284$	7.60300	0.451155
$285$	−2.00000	−0.118470
$286$	−1.21432	−0.0718042
$287$	−5.37778	−0.317441
$288$	−2.88739	−0.170141
$289$	−12.0968	−0.711576
$290$	−11.7792	−0.691700
$291$	−12.8573	−0.753707
$292$	−1.64894	−0.0964967
$293$	−9.07805	−0.530345	−0.265173	−	0.964201i	$-0.585429\pi$
$293$	−9.07805	−0.530345	−0.265173	+	0.964201i	$0.585429\pi$
$294$	5.67460	0.330950
$295$	12.2953	0.715859
$296$	27.1624	1.57878
$297$	−1.00000	−0.0580259
$298$	5.32201	0.308296
$299$	−7.95407	−0.459996
$300$	1.72393	0.0995309
$301$	−13.3876	−0.771650
$302$	−1.49378	−0.0859577
$303$	−16.0207	−0.920368
$304$	4.07758	0.233865
$305$	−15.0509	−0.861809
$306$	−2.68889	−0.153714
$307$	−5.43356	−0.310110	−0.155055	−	0.987906i	$-0.549555\pi$
$307$	−5.43356	−0.310110	−0.155055	+	0.987906i	$0.549555\pi$
$308$	0.801502	0.0456698
$309$	−7.61285	−0.433080
$310$	−7.46520	−0.423995
$311$	−9.46520	−0.536723	−0.268361	−	0.963318i	$-0.586482\pi$
$311$	−9.46520	−0.536723	−0.268361	+	0.963318i	$0.586482\pi$
$312$	−3.06668	−0.173616
$313$	−23.6400	−1.33621	−0.668107	−	0.744065i	$-0.732895\pi$
$313$	−23.6400	−1.33621	−0.668107	+	0.744065i	$0.732895\pi$
$314$	−9.26178	−0.522673
$315$	2.00000	0.112687
$316$	2.64296	0.148678
$317$	15.6479	0.878873	0.439436	−	0.898274i	$-0.355178\pi$
$317$	15.6479	0.878873	0.439436	+	0.898274i	$0.355178\pi$
$318$	−4.46028	−0.250120
$319$	−7.39853	−0.414238
$320$	11.6064	0.648817
$321$	−12.9906	−0.725066
$322$	−14.7338	−0.821081
$323$	−3.37778	−0.187945
$324$	−0.525428	−0.0291904
$325$	3.28100	0.181997
$326$	−8.80489	−0.487658
$327$	3.82071	0.211286
$328$	−10.8113	−0.596957
$329$	14.0098	0.772388
$330$	1.59210	0.0876424
$331$	−19.6795	−1.08168	−0.540842	−	0.841124i	$-0.681894\pi$
$331$	−19.6795	−1.08168	−0.540842	+	0.841124i	$0.681894\pi$
$332$	−2.82564	−0.155077
$333$	8.85728	0.485376
$334$	−0.358572	−0.0196202
$335$	6.88448	0.376139
$336$	−4.07758	−0.222450
$337$	10.9906	0.598698	0.299349	−	0.954144i	$-0.403231\pi$
$337$	10.9906	0.598698	0.299349	+	0.954144i	$0.403231\pi$
$338$	−1.21432	−0.0660503
$339$	−18.3368	−0.995917
$340$	−1.52543	−0.0827279
$341$	−4.68889	−0.253918
$342$	1.85236	0.100164
$343$	−17.8064	−0.961457
$344$	−26.9141	−1.45111
$345$	10.4286	0.561459
$346$	21.3240	1.14639
$347$	17.3176	0.929655	0.464828	−	0.885401i	$-0.346116\pi$
$347$	17.3176	0.929655	0.464828	+	0.885401i	$0.346116\pi$
$348$	−3.88739	−0.208386
$349$	−17.1842	−0.919850	−0.459925	−	0.887958i	$-0.652124\pi$
$349$	−17.1842	−0.919850	−0.459925	+	0.887958i	$0.652124\pi$
$350$	6.07758	0.324860
$351$	−1.00000	−0.0533761
$352$	2.88739	0.153898
$353$	−14.4351	−0.768302	−0.384151	−	0.923270i	$-0.625506\pi$
$353$	−14.4351	−0.768302	−0.384151	+	0.923270i	$0.625506\pi$
$354$	−11.3876	−0.605246
$355$	−18.9719	−1.00692
$356$	−0.361963	−0.0191840
$357$	3.37778	0.178771
$358$	−14.6780	−0.775756
$359$	−16.1476	−0.852240	−0.426120	−	0.904667i	$-0.640120\pi$
$359$	−16.1476	−0.852240	−0.426120	+	0.904667i	$0.640120\pi$
$360$	4.02074	0.211912
$361$	−16.6731	−0.877530
$362$	−9.37334	−0.492652
$363$	1.00000	0.0524864
$364$	0.801502	0.0420101
$365$	4.11462	0.215369
$366$	13.9398	0.728644
$367$	26.7971	1.39879	0.699397	−	0.714733i	$-0.253452\pi$
$367$	26.7971	1.39879	0.699397	+	0.714733i	$0.253452\pi$
$368$	−21.2618	−1.10835
$369$	−3.52543	−0.183526
$370$	−14.1017	−0.733113
$371$	5.60300	0.290893
$372$	−2.46367	−0.127736
$373$	13.3590	0.691705	0.345853	−	0.938289i	$-0.387590\pi$
$373$	13.3590	0.691705	0.345853	+	0.938289i	$0.387590\pi$
$374$	2.68889	0.139039
$375$	−10.8573	−0.560667
$376$	28.1650	1.45250
$377$	−7.39853	−0.381044
$378$	−1.85236	−0.0952750
$379$	6.85083	0.351903	0.175952	−	0.984399i	$-0.443700\pi$
$379$	6.85083	0.351903	0.175952	+	0.984399i	$0.443700\pi$
$380$	1.05086	0.0539077
$381$	−20.5827	−1.05449
$382$	20.1619	1.03157
$383$	3.57136	0.182488	0.0912440	−	0.995829i	$-0.470916\pi$
$383$	3.57136	0.182488	0.0912440	+	0.995829i	$0.470916\pi$
$384$	−4.97481	−0.253870
$385$	−2.00000	−0.101929
$386$	9.13828	0.465126
$387$	−8.77631	−0.446125
$388$	6.75557	0.342962
$389$	−8.35551	−0.423641	−0.211821	−	0.977309i	$-0.567939\pi$
$389$	−8.35551	−0.423641	−0.211821	+	0.977309i	$0.567939\pi$
$390$	1.59210	0.0806193
$391$	17.6128	0.890720
$392$	−14.3308	−0.723815
$393$	−0.561993	−0.0283488
$394$	−14.8746	−0.749373
$395$	−6.59502	−0.331831
$396$	0.525428	0.0264037
$397$	22.1847	1.11342	0.556709	−	0.830708i	$-0.312064\pi$
$397$	22.1847	1.11342	0.556709	+	0.830708i	$0.312064\pi$
$398$	−14.1017	−0.706855
$399$	−2.32693	−0.116492
$400$	8.77034	0.438517
$401$	20.6987	1.03365	0.516823	−	0.856092i	$-0.327115\pi$
$401$	20.6987	1.03365	0.516823	+	0.856092i	$0.327115\pi$
$402$	−6.37625	−0.318019
$403$	−4.68889	−0.233570
$404$	8.41774	0.418798
$405$	1.31111	0.0651495
$406$	−13.7047	−0.680154
$407$	−8.85728	−0.439039
$408$	6.79060	0.336185
$409$	20.8528	1.03111	0.515553	−	0.856858i	$-0.327586\pi$
$409$	20.8528	1.03111	0.515553	+	0.856858i	$0.327586\pi$
$410$	5.61285	0.277199
$411$	5.07604	0.250383
$412$	4.00000	0.197066
$413$	14.3051	0.703909
$414$	−9.65878	−0.474703
$415$	7.05086	0.346113
$416$	2.88739	0.141566
$417$	18.5511	0.908451
$418$	−1.85236	−0.0906017
$419$	−21.2400	−1.03764	−0.518821	−	0.854883i	$-0.673629\pi$
$419$	−21.2400	−1.03764	−0.518821	+	0.854883i	$0.673629\pi$
$420$	−1.05086	−0.0512765
$421$	−3.15257	−0.153647	−0.0768233	−	0.997045i	$-0.524478\pi$
$421$	−3.15257	−0.153647	−0.0768233	+	0.997045i	$0.524478\pi$
$422$	−6.27010	−0.305224
$423$	9.18421	0.446551
$424$	11.2641	0.547034
$425$	−7.26517	−0.352413
$426$	17.5714	0.851335
$427$	−17.5111	−0.847423
$428$	6.82564	0.329930
$429$	1.00000	0.0482805
$430$	13.9728	0.673828
$431$	40.1116	1.93211	0.966053	−	0.258345i	$-0.0831770\pi$
$431$	40.1116	1.93211	0.966053	+	0.258345i	$0.0831770\pi$
$432$	−2.67307	−0.128608
$433$	−36.1017	−1.73494	−0.867469	−	0.497492i	$-0.834254\pi$
$433$	−36.1017	−1.73494	−0.867469	+	0.497492i	$0.834254\pi$
$434$	−8.68550	−0.416917
$435$	9.70027	0.465092
$436$	−2.00751	−0.0961422
$437$	−12.1334	−0.580417
$438$	−3.81087	−0.182090
$439$	13.2050	0.630238	0.315119	−	0.949052i	$-0.397956\pi$
$439$	13.2050	0.630238	0.315119	+	0.949052i	$0.397956\pi$
$440$	−4.02074	−0.191681
$441$	−4.67307	−0.222527
$442$	2.68889	0.127898
$443$	13.9813	0.664270	0.332135	−	0.943232i	$-0.392231\pi$
$443$	13.9813	0.664270	0.332135	+	0.943232i	$0.392231\pi$
$444$	−4.65386	−0.220862
$445$	0.903212	0.0428164
$446$	10.0810	0.477348
$447$	−4.38271	−0.207295
$448$	13.5036	0.637987
$449$	19.3210	0.911812	0.455906	−	0.890028i	$-0.349315\pi$
$449$	19.3210	0.911812	0.455906	+	0.890028i	$0.349315\pi$
$450$	3.98418	0.187816
$451$	3.52543	0.166006
$452$	9.63465	0.453176
$453$	1.23014	0.0577971
$454$	6.40144	0.300435
$455$	−2.00000	−0.0937614
$456$	−4.67799	−0.219067
$457$	−36.3970	−1.70258	−0.851290	−	0.524696i	$-0.824179\pi$
$457$	−36.3970	−1.70258	−0.851290	+	0.524696i	$0.824179\pi$
$458$	31.0291	1.44989
$459$	2.21432	0.103356
$460$	−5.47949	−0.255483
$461$	−23.5254	−1.09569	−0.547844	−	0.836580i	$-0.684551\pi$
$461$	−23.5254	−1.09569	−0.547844	+	0.836580i	$0.684551\pi$
$462$	1.85236	0.0861794
$463$	−36.3531	−1.68947	−0.844735	−	0.535184i	$-0.820242\pi$
$463$	−36.3531	−1.68947	−0.844735	+	0.535184i	$0.820242\pi$
$464$	−19.7768	−0.918114
$465$	6.14764	0.285090
$466$	−2.92396	−0.135450
$467$	−32.5161	−1.50466	−0.752332	−	0.658784i	$-0.771071\pi$
$467$	−32.5161	−1.50466	−0.752332	+	0.658784i	$0.771071\pi$
$468$	0.525428	0.0242879
$469$	8.00984	0.369860
$470$	−14.6222	−0.674473
$471$	7.62714	0.351440
$472$	28.7586	1.32372
$473$	8.77631	0.403535
$474$	6.10816	0.280557
$475$	5.00492	0.229642
$476$	−1.77478	−0.0813470
$477$	3.67307	0.168178
$478$	−21.6904	−0.992097
$479$	33.6499	1.53750	0.768751	−	0.639548i	$-0.220878\pi$
$479$	33.6499	1.53750	0.768751	+	0.639548i	$0.220878\pi$
$480$	−3.78568	−0.172792
$481$	−8.85728	−0.403857
$482$	4.78415	0.217912
$483$	12.1334	0.552087
$484$	−0.525428	−0.0238831
$485$	−16.8573	−0.765450
$486$	−1.21432	−0.0550827
$487$	17.0988	0.774820	0.387410	−	0.921907i	$-0.373370\pi$
$487$	17.0988	0.774820	0.387410	+	0.921907i	$0.373370\pi$
$488$	−35.2039	−1.59361
$489$	7.25088	0.327896
$490$	7.44002	0.336106
$491$	30.2034	1.36306	0.681531	−	0.731790i	$-0.261315\pi$
$491$	30.2034	1.36306	0.681531	+	0.731790i	$0.261315\pi$
$492$	1.85236	0.0835107
$493$	16.3827	0.737840
$494$	−1.85236	−0.0833415
$495$	−1.31111	−0.0589299
$496$	−12.5337	−0.562782
$497$	−22.0731	−0.990115
$498$	−6.53035	−0.292632
$499$	38.1367	1.70724	0.853618	−	0.520900i	$-0.174404\pi$
$499$	38.1367	1.70724	0.853618	+	0.520900i	$0.174404\pi$
$500$	5.70471	0.255123
$501$	0.295286	0.0131924
$502$	−28.3654	−1.26601
$503$	−23.8666	−1.06416	−0.532081	−	0.846694i	$-0.678590\pi$
$503$	−23.8666	−1.06416	−0.532081	+	0.846694i	$0.678590\pi$
$504$	4.67799	0.208374
$505$	−21.0049	−0.934707
$506$	9.65878	0.429385
$507$	1.00000	0.0444116
$508$	10.8147	0.479826
$509$	12.8222	0.568336	0.284168	−	0.958774i	$-0.408283\pi$
$509$	12.8222	0.568336	0.284168	+	0.958774i	$0.408283\pi$
$510$	−3.52543	−0.156109
$511$	4.78721	0.211774
$512$	24.1131	1.06566
$513$	−1.52543	−0.0673493
$514$	−2.07007	−0.0913068
$515$	−9.98126	−0.439827
$516$	4.61132	0.203002
$517$	−9.18421	−0.403921
$518$	−16.4068	−0.720875
$519$	−17.5605	−0.770819
$520$	−4.02074	−0.176321
$521$	3.63158	0.159103	0.0795513	−	0.996831i	$-0.474651\pi$
$521$	3.63158	0.159103	0.0795513	+	0.996831i	$0.474651\pi$
$522$	−8.98418	−0.393227
$523$	−9.40837	−0.411399	−0.205700	−	0.978615i	$-0.565947\pi$
$523$	−9.40837	−0.411399	−0.205700	+	0.978615i	$0.565947\pi$
$524$	0.295286	0.0128996
$525$	−5.00492	−0.218433
$526$	1.34920	0.0588281
$527$	10.3827	0.452278
$528$	2.67307	0.116330
$529$	40.2672	1.75075
$530$	−5.84791	−0.254017
$531$	9.37778	0.406961
$532$	1.22263	0.0530079
$533$	3.52543	0.152703
$534$	−0.836535	−0.0362004
$535$	−17.0321	−0.736363
$536$	16.1028	0.695534
$537$	12.0874	0.521611
$538$	−10.6824	−0.460553
$539$	4.67307	0.201283
$540$	−0.688892	−0.0296452
$541$	−30.0000	−1.28980	−0.644900	−	0.764267i	$-0.723101\pi$
$541$	−30.0000	−1.28980	−0.644900	+	0.764267i	$0.723101\pi$
$542$	−33.2400	−1.42778
$543$	7.71900	0.331254
$544$	−6.39361	−0.274124
$545$	5.00937	0.214578
$546$	1.85236	0.0792736
$547$	1.73530	0.0741961	0.0370981	−	0.999312i	$-0.488189\pi$
$547$	1.73530	0.0741961	0.0370981	+	0.999312i	$0.488189\pi$
$548$	−2.66709	−0.113933
$549$	−11.4795	−0.489933
$550$	−3.98418	−0.169886
$551$	−11.2859	−0.480796
$552$	24.3926	1.03822
$553$	−7.67307	−0.326292
$554$	31.4608	1.33664
$555$	11.6128	0.492938
$556$	−9.74726	−0.413376
$557$	−21.2400	−0.899967	−0.449984	−	0.893037i	$-0.648570\pi$
$557$	−21.2400	−0.899967	−0.449984	+	0.893037i	$0.648570\pi$
$558$	−5.69381	−0.241038
$559$	8.77631	0.371198
$560$	−5.34614	−0.225916
$561$	−2.21432	−0.0934887
$562$	6.99508	0.295070
$563$	22.7841	0.960237	0.480119	−	0.877204i	$-0.340594\pi$
$563$	22.7841	0.960237	0.480119	+	0.877204i	$0.340594\pi$
$564$	−4.82564	−0.203196
$565$	−24.0415	−1.01143
$566$	3.67952	0.154662
$567$	1.52543	0.0640619
$568$	−44.3752	−1.86194
$569$	31.9704	1.34027	0.670134	−	0.742240i	$-0.266237\pi$
$569$	31.9704	1.34027	0.670134	+	0.742240i	$0.266237\pi$
$570$	2.42864	0.101725
$571$	14.7032	0.615309	0.307655	−	0.951498i	$-0.400456\pi$
$571$	14.7032	0.615309	0.307655	+	0.951498i	$0.400456\pi$
$572$	−0.525428	−0.0219692
$573$	−16.6035	−0.693620
$574$	6.53035	0.272572
$575$	−26.0973	−1.08833
$576$	8.85236	0.368848
$577$	18.9491	0.788863	0.394432	−	0.918925i	$-0.370942\pi$
$577$	18.9491	0.788863	0.394432	+	0.918925i	$0.370942\pi$
$578$	14.6894	0.610997
$579$	−7.52543	−0.312746
$580$	−5.09679	−0.211633
$581$	8.20342	0.340335
$582$	15.6128	0.647173
$583$	−3.67307	−0.152123
$584$	9.62408	0.398247
$585$	−1.31111	−0.0542076
$586$	11.0237	0.455383
$587$	−29.0736	−1.20000	−0.599998	−	0.800001i	$-0.704832\pi$
$587$	−29.0736	−1.20000	−0.599998	+	0.800001i	$0.704832\pi$
$588$	2.45536	0.101257
$589$	−7.15257	−0.294716
$590$	−14.9304	−0.614675
$591$	12.2494	0.503871
$592$	−23.6761	−0.973083
$593$	0.312639	0.0128386	0.00641928	−	0.999979i	$-0.497957\pi$
$593$	0.312639	0.0128386	0.00641928	+	0.999979i	$0.497957\pi$
$594$	1.21432	0.0498241
$595$	4.42864	0.181557
$596$	2.30279	0.0943262
$597$	11.6128	0.475282
$598$	9.65878	0.394977
$599$	−19.8666	−0.811729	−0.405865	−	0.913933i	$-0.633030\pi$
$599$	−19.8666	−0.811729	−0.405865	+	0.913933i	$0.633030\pi$
$600$	−10.0618	−0.410769
$601$	−23.9813	−0.978216	−0.489108	−	0.872223i	$-0.662678\pi$
$601$	−23.9813	−0.978216	−0.489108	+	0.872223i	$0.662678\pi$
$602$	16.2569	0.662580
$603$	5.25088	0.213833
$604$	−0.646350	−0.0262996
$605$	1.31111	0.0533041
$606$	19.4543	0.790277
$607$	12.5412	0.509034	0.254517	−	0.967068i	$-0.418084\pi$
$607$	12.5412	0.509034	0.254517	+	0.967068i	$0.418084\pi$
$608$	4.40451	0.178626
$609$	11.2859	0.457328
$610$	18.2766	0.739996
$611$	−9.18421	−0.371553
$612$	−1.16346	−0.0470303
$613$	3.79213	0.153163	0.0765814	−	0.997063i	$-0.475599\pi$
$613$	3.79213	0.153163	0.0765814	+	0.997063i	$0.475599\pi$
$614$	6.59808	0.266277
$615$	−4.62222	−0.186386
$616$	−4.67799	−0.188482
$617$	0.278989	0.0112317	0.00561583	−	0.999984i	$-0.498212\pi$
$617$	0.278989	0.0112317	0.00561583	+	0.999984i	$0.498212\pi$
$618$	9.24443	0.371866
$619$	9.69826	0.389806	0.194903	−	0.980823i	$-0.437561\pi$
$619$	9.69826	0.389806	0.194903	+	0.980823i	$0.437561\pi$
$620$	−3.23014	−0.129726
$621$	7.95407	0.319186
$622$	11.4938	0.460859
$623$	1.05086	0.0421016
$624$	2.67307	0.107008
$625$	2.16992	0.0867967
$626$	28.7066	1.14735
$627$	1.52543	0.0609197
$628$	−4.00751	−0.159917
$629$	19.6128	0.782015
$630$	−2.42864	−0.0967593
$631$	10.6889	0.425518	0.212759	−	0.977105i	$-0.431755\pi$
$631$	10.6889	0.425518	0.212759	+	0.977105i	$0.431755\pi$
$632$	−15.4257	−0.613602
$633$	5.16346	0.205229
$634$	−19.0015	−0.754647
$635$	−26.9862	−1.07091
$636$	−1.92993	−0.0765268
$637$	4.67307	0.185154
$638$	8.98418	0.355687
$639$	−14.4701	−0.572429
$640$	−6.52251	−0.257825
$641$	31.0321	1.22570	0.612848	−	0.790201i	$-0.290024\pi$
$641$	31.0321	1.22570	0.612848	+	0.790201i	$0.290024\pi$
$642$	15.7748	0.622581
$643$	24.6099	0.970521	0.485261	−	0.874370i	$-0.338725\pi$
$643$	24.6099	0.970521	0.485261	+	0.874370i	$0.338725\pi$
$644$	−6.37520	−0.251218
$645$	−11.5067	−0.453076
$646$	4.10171	0.161380
$647$	24.3368	0.956777	0.478389	−	0.878148i	$-0.341221\pi$
$647$	24.3368	0.956777	0.478389	+	0.878148i	$0.341221\pi$
$648$	3.06668	0.120470
$649$	−9.37778	−0.368110
$650$	−3.98418	−0.156272
$651$	7.15257	0.280331
$652$	−3.80981	−0.149204
$653$	−17.7877	−0.696086	−0.348043	−	0.937479i	$-0.613154\pi$
$653$	−17.7877	−0.696086	−0.348043	+	0.937479i	$0.613154\pi$
$654$	−4.63957	−0.181421
$655$	−0.736833	−0.0287904
$656$	9.42372	0.367934
$657$	3.13828	0.122436
$658$	−17.0124	−0.663214
$659$	28.8256	1.12289	0.561444	−	0.827515i	$-0.310246\pi$
$659$	28.8256	1.12289	0.561444	+	0.827515i	$0.310246\pi$
$660$	0.688892	0.0268151
$661$	−39.1655	−1.52336	−0.761680	−	0.647953i	$-0.775625\pi$
$661$	−39.1655	−1.52336	−0.761680	+	0.647953i	$0.775625\pi$
$662$	23.8972	0.928792
$663$	−2.21432	−0.0859971
$664$	16.4919	0.640011
$665$	−3.05086	−0.118307
$666$	−10.7556	−0.416770
$667$	58.8484	2.27862
$668$	−0.155152	−0.00600300
$669$	−8.30174	−0.320964
$670$	−8.35996	−0.322973
$671$	11.4795	0.443161
$672$	−4.40451	−0.169907
$673$	−46.8671	−1.80659	−0.903297	−	0.429015i	$-0.858861\pi$
$673$	−46.8671	−1.80659	−0.903297	+	0.429015i	$0.858861\pi$
$674$	−13.3461	−0.514074
$675$	−3.28100	−0.126286
$676$	−0.525428	−0.0202088
$677$	22.9699	0.882805	0.441402	−	0.897309i	$-0.354481\pi$
$677$	22.9699	0.882805	0.441402	+	0.897309i	$0.354481\pi$
$678$	22.2667	0.855148
$679$	−19.6128	−0.752672
$680$	8.90321	0.341423
$681$	−5.27163	−0.202009
$682$	5.69381	0.218027
$683$	−21.7333	−0.831601	−0.415801	−	0.909456i	$-0.636499\pi$
$683$	−21.7333	−0.831601	−0.415801	+	0.909456i	$0.636499\pi$
$684$	0.801502	0.0306462
$685$	6.65524	0.254284
$686$	21.6227	0.825558
$687$	−25.5526	−0.974893
$688$	23.4597	0.894393
$689$	−3.67307	−0.139933
$690$	−12.6637	−0.482099
$691$	33.4445	1.27229	0.636144	−	0.771571i	$-0.280529\pi$
$691$	33.4445	1.27229	0.636144	+	0.771571i	$0.280529\pi$
$692$	9.22675	0.350748
$693$	−1.52543	−0.0579462
$694$	−21.0291	−0.798252
$695$	24.3225	0.922604
$696$	22.6889	0.860020
$697$	−7.80642	−0.295689
$698$	20.8671	0.789832
$699$	2.40790	0.0910750
$700$	2.62972	0.0993942
$701$	−31.7540	−1.19933	−0.599667	−	0.800250i	$-0.704700\pi$
$701$	−31.7540	−1.19933	−0.599667	+	0.800250i	$0.704700\pi$
$702$	1.21432	0.0458315
$703$	−13.5111	−0.509582
$704$	−8.85236	−0.333636
$705$	12.0415	0.453509
$706$	17.5288	0.659706
$707$	−24.4385	−0.919104
$708$	−4.92735	−0.185181
$709$	25.3778	0.953083	0.476541	−	0.879152i	$-0.341890\pi$
$709$	25.3778	0.953083	0.476541	+	0.879152i	$0.341890\pi$
$710$	23.0379	0.864599
$711$	−5.03011	−0.188644
$712$	2.11261	0.0791734
$713$	37.2958	1.39674
$714$	−4.10171	−0.153503
$715$	1.31111	0.0490327
$716$	−6.35106	−0.237350
$717$	17.8622	0.667076
$718$	19.6084	0.731779
$719$	−11.6128	−0.433086	−0.216543	−	0.976273i	$-0.569478\pi$
$719$	−11.6128	−0.433086	−0.216543	+	0.976273i	$0.569478\pi$
$720$	−3.50468	−0.130612
$721$	−11.6128	−0.432485
$722$	20.2464	0.753494
$723$	−3.93978	−0.146522
$724$	−4.05578	−0.150732
$725$	−24.2745	−0.901534
$726$	−1.21432	−0.0450676
$727$	−42.5303	−1.57736	−0.788682	−	0.614802i	$-0.789236\pi$
$727$	−42.5303	−1.57736	−0.788682	+	0.614802i	$0.789236\pi$
$728$	−4.67799	−0.173378
$729$	1.00000	0.0370370
$730$	−4.99646	−0.184927
$731$	−19.4336	−0.718776
$732$	6.03164	0.222936
$733$	16.2997	0.602044	0.301022	−	0.953617i	$-0.402672\pi$
$733$	16.2997	0.602044	0.301022	+	0.953617i	$0.402672\pi$
$734$	−32.5402	−1.20108
$735$	−6.12690	−0.225994
$736$	−22.9665	−0.846556
$737$	−5.25088	−0.193419
$738$	4.28100	0.157586
$739$	27.5353	1.01290	0.506451	−	0.862269i	$-0.330957\pi$
$739$	27.5353	1.01290	0.506451	+	0.862269i	$0.330957\pi$
$740$	−6.10171	−0.224303
$741$	1.52543	0.0560380
$742$	−6.80384	−0.249777
$743$	34.1432	1.25259	0.626296	−	0.779585i	$-0.284570\pi$
$743$	34.1432	1.25259	0.626296	+	0.779585i	$0.284570\pi$
$744$	14.3793	0.527171
$745$	−5.74620	−0.210525
$746$	−16.2222	−0.593935
$747$	5.37778	0.196763
$748$	1.16346	0.0425405
$749$	−19.8163	−0.724071
$750$	13.1842	0.481419
$751$	5.08250	0.185463	0.0927315	−	0.995691i	$-0.470440\pi$
$751$	5.08250	0.185463	0.0927315	+	0.995691i	$0.470440\pi$
$752$	−24.5500	−0.895248
$753$	23.3590	0.851251
$754$	8.98418	0.327184
$755$	1.61285	0.0586975
$756$	−0.801502	−0.0291503
$757$	−20.1062	−0.730771	−0.365385	−	0.930856i	$-0.619063\pi$
$757$	−20.1062	−0.730771	−0.365385	+	0.930856i	$0.619063\pi$
$758$	−8.31909	−0.302163
$759$	−7.95407	−0.288714
$760$	−6.13335	−0.222480
$761$	−7.47505	−0.270970	−0.135485	−	0.990779i	$-0.543259\pi$
$761$	−7.47505	−0.270970	−0.135485	+	0.990779i	$0.543259\pi$
$762$	24.9940	0.905438
$763$	5.82822	0.210996
$764$	8.72393	0.315621
$765$	2.90321	0.104966
$766$	−4.33677	−0.156694
$767$	−9.37778	−0.338612
$768$	−11.6637	−0.420878
$769$	−50.9403	−1.83695	−0.918476	−	0.395476i	$-0.870580\pi$
$769$	−50.9403	−1.83695	−0.918476	+	0.395476i	$0.870580\pi$
$770$	2.42864	0.0875221
$771$	1.70471	0.0613938
$772$	3.95407	0.142310
$773$	47.7309	1.71676	0.858380	−	0.513015i	$-0.171471\pi$
$773$	47.7309	1.71676	0.858380	+	0.513015i	$0.171471\pi$
$774$	10.6572	0.383067
$775$	−15.3842	−0.552618
$776$	−39.4291	−1.41542
$777$	13.5111	0.484709
$778$	10.1463	0.363761
$779$	5.37778	0.192679
$780$	0.688892	0.0246663
$781$	14.4701	0.517782
$782$	−21.3876	−0.764820
$783$	7.39853	0.264402
$784$	12.4914	0.446123
$785$	10.0000	0.356915
$786$	0.682439	0.0243418
$787$	−17.6084	−0.627672	−0.313836	−	0.949477i	$-0.601614\pi$
$787$	−17.6084	−0.627672	−0.313836	+	0.949477i	$0.601614\pi$
$788$	−6.43615	−0.229278
$789$	−1.11108	−0.0395554
$790$	8.00846	0.284928
$791$	−27.9714	−0.994549
$792$	−3.06668	−0.108970
$793$	11.4795	0.407649
$794$	−26.9393	−0.956040
$795$	4.81579	0.170799
$796$	−6.10171	−0.216269
$797$	7.32741	0.259550	0.129775	−	0.991543i	$-0.458574\pi$
$797$	7.32741	0.259550	0.129775	+	0.991543i	$0.458574\pi$
$798$	2.82564	0.100026
$799$	20.3368	0.719463
$800$	9.47352	0.334939
$801$	0.688892	0.0243408
$802$	−25.1349	−0.887544
$803$	−3.13828	−0.110747
$804$	−2.75896	−0.0973010
$805$	15.9081	0.560688
$806$	5.69381	0.200556
$807$	8.79706	0.309671
$808$	−49.1304	−1.72840
$809$	19.2968	0.678440	0.339220	−	0.940707i	$-0.389837\pi$
$809$	19.2968	0.678440	0.339220	+	0.940707i	$0.389837\pi$
$810$	−1.59210	−0.0559408
$811$	31.6271	1.11058	0.555290	−	0.831657i	$-0.312607\pi$
$811$	31.6271	1.11058	0.555290	+	0.831657i	$0.312607\pi$
$812$	−5.92993	−0.208100
$813$	27.3733	0.960025
$814$	10.7556	0.376982
$815$	9.50669	0.333005
$816$	−5.91903	−0.207208
$817$	13.3876	0.468374
$818$	−25.3220	−0.885363
$819$	−1.52543	−0.0533028
$820$	2.42864	0.0848118
$821$	37.4652	1.30754	0.653772	−	0.756691i	$-0.273185\pi$
$821$	37.4652	1.30754	0.653772	+	0.756691i	$0.273185\pi$
$822$	−6.16394	−0.214992
$823$	28.8988	1.00735	0.503674	−	0.863894i	$-0.331981\pi$
$823$	28.8988	1.00735	0.503674	+	0.863894i	$0.331981\pi$
$824$	−23.3461	−0.813301
$825$	3.28100	0.114230
$826$	−17.3710	−0.604414
$827$	19.7319	0.686146	0.343073	−	0.939309i	$-0.388532\pi$
$827$	19.7319	0.686146	0.343073	+	0.939309i	$0.388532\pi$
$828$	−4.17929	−0.145240
$829$	−3.44785	−0.119749	−0.0598744	−	0.998206i	$-0.519070\pi$
$829$	−3.44785	−0.119749	−0.0598744	+	0.998206i	$0.519070\pi$
$830$	−8.56199	−0.297191
$831$	−25.9081	−0.898743
$832$	−8.85236	−0.306900
$833$	−10.3477	−0.358526
$834$	−22.5270	−0.780045
$835$	0.387152	0.0133980
$836$	−0.801502	−0.0277205
$837$	4.68889	0.162072
$838$	25.7921	0.890974
$839$	−52.2578	−1.80414	−0.902070	−	0.431590i	$-0.857953\pi$
$839$	−52.2578	−1.80414	−0.902070	+	0.431590i	$0.857953\pi$
$840$	6.13335	0.211621
$841$	25.7382	0.887525
$842$	3.82822	0.131929
$843$	−5.76049	−0.198402
$844$	−2.71303	−0.0933862
$845$	1.31111	0.0451035
$846$	−11.1526	−0.383433
$847$	1.52543	0.0524143
$848$	−9.81838	−0.337164
$849$	−3.03011	−0.103993
$850$	8.82225	0.302601
$851$	70.4514	2.41504
$852$	7.60300	0.260475
$853$	31.2988	1.07165	0.535826	−	0.844329i	$-0.320000\pi$
$853$	31.2988	1.07165	0.535826	+	0.844329i	$0.320000\pi$
$854$	21.2641	0.727643
$855$	−2.00000	−0.0683986
$856$	−39.8381	−1.36164
$857$	37.1131	1.26776	0.633879	−	0.773432i	$-0.281462\pi$
$857$	37.1131	1.26776	0.633879	+	0.773432i	$0.281462\pi$
$858$	−1.21432	−0.0414562
$859$	−16.6953	−0.569638	−0.284819	−	0.958581i	$-0.591933\pi$
$859$	−16.6953	−0.569638	−0.284819	+	0.958581i	$0.591933\pi$
$860$	6.04593	0.206165
$861$	−5.37778	−0.183274
$862$	−48.7083	−1.65901
$863$	−41.8765	−1.42549	−0.712746	−	0.701422i	$-0.752549\pi$
$863$	−41.8765	−1.42549	−0.712746	+	0.701422i	$0.752549\pi$
$864$	−2.88739	−0.0982310
$865$	−23.0237	−0.782828
$866$	43.8390	1.48971
$867$	−12.0968	−0.410828
$868$	−3.75815	−0.127560
$869$	5.03011	0.170635
$870$	−11.7792	−0.399353
$871$	−5.25088	−0.177919
$872$	11.7169	0.396784
$873$	−12.8573	−0.435153
$874$	14.7338	0.498377
$875$	−16.5620	−0.559898
$876$	−1.64894	−0.0557124
$877$	−6.54909	−0.221147	−0.110573	−	0.993868i	$-0.535269\pi$
$877$	−6.54909	−0.221147	−0.110573	+	0.993868i	$0.535269\pi$
$878$	−16.0350	−0.541156
$879$	−9.07805	−0.306195
$880$	3.50468	0.118143
$881$	−15.6316	−0.526641	−0.263321	−	0.964708i	$-0.584818\pi$
$881$	−15.6316	−0.526641	−0.263321	+	0.964708i	$0.584818\pi$
$882$	5.67460	0.191074
$883$	19.2257	0.646996	0.323498	−	0.946229i	$-0.395141\pi$
$883$	19.2257	0.646996	0.323498	+	0.946229i	$0.395141\pi$
$884$	1.16346	0.0391315
$885$	12.2953	0.413302
$886$	−16.9777	−0.570378
$887$	8.88892	0.298461	0.149230	−	0.988802i	$-0.452320\pi$
$887$	8.88892	0.298461	0.149230	+	0.988802i	$0.452320\pi$
$888$	27.1624	0.911511
$889$	−31.3975	−1.05304
$890$	−1.09679	−0.0367644
$891$	−1.00000	−0.0335013
$892$	4.36196	0.146049
$893$	−14.0098	−0.468822
$894$	5.32201	0.177995
$895$	15.8479	0.529737
$896$	−7.58871	−0.253521
$897$	−7.95407	−0.265579
$898$	−23.4618	−0.782931
$899$	34.6909	1.15701
$900$	1.72393	0.0574642
$901$	8.13335	0.270961
$902$	−4.28100	−0.142542
$903$	−13.3876	−0.445512
$904$	−56.2330	−1.87028
$905$	10.1204	0.336415
$906$	−1.49378	−0.0496277
$907$	−15.5714	−0.517039	−0.258519	−	0.966006i	$-0.583235\pi$
$907$	−15.5714	−0.517039	−0.258519	+	0.966006i	$0.583235\pi$
$908$	2.76986	0.0919210
$909$	−16.0207	−0.531375
$910$	2.42864	0.0805086
$911$	−42.5215	−1.40880	−0.704399	−	0.709804i	$-0.748784\pi$
$911$	−42.5215	−1.40880	−0.704399	+	0.709804i	$0.748784\pi$
$912$	4.07758	0.135022
$913$	−5.37778	−0.177979
$914$	44.1976	1.46193
$915$	−15.0509	−0.497566
$916$	13.4261	0.443609
$917$	−0.857279	−0.0283098
$918$	−2.68889	−0.0887467
$919$	−14.5640	−0.480422	−0.240211	−	0.970721i	$-0.577217\pi$
$919$	−14.5640	−0.480422	−0.240211	+	0.970721i	$0.577217\pi$
$920$	31.9813	1.05439
$921$	−5.43356	−0.179042
$922$	28.5674	0.940817
$923$	14.4701	0.476290
$924$	0.801502	0.0263675
$925$	−29.0607	−0.955510
$926$	44.1443	1.45067
$927$	−7.61285	−0.250039
$928$	−21.3624	−0.701256
$929$	−39.5689	−1.29821	−0.649107	−	0.760697i	$-0.724857\pi$
$929$	−39.5689	−1.29821	−0.649107	+	0.760697i	$0.724857\pi$
$930$	−7.46520	−0.244794
$931$	7.12843	0.233625
$932$	−1.26517	−0.0414422
$933$	−9.46520	−0.309877
$934$	39.4849	1.29199
$935$	−2.90321	−0.0949452
$936$	−3.06668	−0.100237
$937$	31.9625	1.04417	0.522085	−	0.852893i	$-0.325154\pi$
$937$	31.9625	1.04417	0.522085	+	0.852893i	$0.325154\pi$
$938$	−9.72651	−0.317582
$939$	−23.6400	−0.771464
$940$	−6.32693	−0.206362
$941$	50.1891	1.63612	0.818059	−	0.575134i	$-0.195050\pi$
$941$	50.1891	1.63612	0.818059	+	0.575134i	$0.195050\pi$
$942$	−9.26178	−0.301765
$943$	−28.0415	−0.913156
$944$	−25.0675	−0.815877
$945$	2.00000	0.0650600
$946$	−10.6572	−0.346497
$947$	−0.742662	−0.0241333	−0.0120666	−	0.999927i	$-0.503841\pi$
$947$	−0.742662	−0.0241333	−0.0120666	+	0.999927i	$0.503841\pi$
$948$	2.64296	0.0858393
$949$	−3.13828	−0.101873
$950$	−6.07758	−0.197183
$951$	15.6479	0.507417
$952$	10.3586	0.335723
$953$	42.3861	1.37302	0.686510	−	0.727120i	$-0.259142\pi$
$953$	42.3861	1.37302	0.686510	+	0.727120i	$0.259142\pi$
$954$	−4.46028	−0.144407
$955$	−21.7690	−0.704427
$956$	−9.38529	−0.303542
$957$	−7.39853	−0.239160
$958$	−40.8617	−1.32018
$959$	7.74314	0.250039
$960$	11.6064	0.374595
$961$	−9.01429	−0.290784
$962$	10.7556	0.346773
$963$	−12.9906	−0.418617
$964$	2.07007	0.0666724
$965$	−9.86665	−0.317619
$966$	−14.7338	−0.474051
$967$	−33.2083	−1.06791	−0.533954	−	0.845513i	$-0.679295\pi$
$967$	−33.2083	−1.06791	−0.533954	+	0.845513i	$0.679295\pi$
$968$	3.06668	0.0985667
$969$	−3.37778	−0.108510
$970$	20.4701	0.657256
$971$	29.2904	0.939973	0.469986	−	0.882674i	$-0.344259\pi$
$971$	29.2904	0.939973	0.469986	+	0.882674i	$0.344259\pi$
$972$	−0.525428	−0.0168531
$973$	28.2983	0.907203
$974$	−20.7634	−0.665302
$975$	3.28100	0.105076
$976$	30.6855	0.982219
$977$	−28.3847	−0.908107	−0.454054	−	0.890974i	$-0.650023\pi$
$977$	−28.3847	−0.908107	−0.454054	+	0.890974i	$0.650023\pi$
$978$	−8.80489	−0.281549
$979$	−0.688892	−0.0220171
$980$	3.21924	0.102835
$981$	3.82071	0.121986
$982$	−36.6766	−1.17040
$983$	44.2578	1.41161	0.705803	−	0.708409i	$-0.250587\pi$
$983$	44.2578	1.41161	0.705803	+	0.708409i	$0.250587\pi$
$984$	−10.8113	−0.344653
$985$	16.0602	0.511721
$986$	−19.8938	−0.633549
$987$	14.0098	0.445938
$988$	−0.801502	−0.0254992
$989$	−69.8074	−2.21975
$990$	1.59210	0.0506004
$991$	32.4197	1.02985	0.514924	−	0.857236i	$-0.327820\pi$
$991$	32.4197	1.02985	0.514924	+	0.857236i	$0.327820\pi$
$992$	−13.5387	−0.429853
$993$	−19.6795	−0.624511
$994$	26.8038	0.850166
$995$	15.2257	0.482687
$996$	−2.82564	−0.0895337
$997$	42.5205	1.34664	0.673319	−	0.739352i	$-0.264868\pi$
$997$	42.5205	1.34664	0.673319	+	0.739352i	$0.264868\pi$
$998$	−46.3102	−1.46592
$999$	8.85728	0.280232

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	429.2.a.g.1.1	✓	3
3.2	odd	2		1287.2.a.h.1.3		3
4.3	odd	2		6864.2.a.bs.1.2		3
11.10	odd	2		4719.2.a.q.1.3		3
13.12	even	2		5577.2.a.j.1.3		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
429.2.a.g.1.1	✓	3	1.1	even	1	trivial
1287.2.a.h.1.3		3	3.2	odd	2
4719.2.a.q.1.3		3	11.10	odd	2
5577.2.a.j.1.3		3	13.12	even	2
6864.2.a.bs.1.2		3	4.3	odd	2

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:	\( N \)	\(=\)	\( 429 = 3 \cdot 11 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	429.a (trivial)

\(f(q)\)	\(=\)	\(q-1.21432 q^{2} +1.00000 q^{3} -0.525428 q^{4} +1.31111 q^{5} -1.21432 q^{6} +1.52543 q^{7} +3.06668 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.21432 q^{2} +1.00000 q^{3} -0.525428 q^{4} +1.31111 q^{5} -1.21432 q^{6} +1.52543 q^{7} +3.06668 q^{8} +1.00000 q^{9} -1.59210 q^{10} -1.00000 q^{11} -0.525428 q^{12} -1.00000 q^{13} -1.85236 q^{14} +1.31111 q^{15} -2.67307 q^{16} +2.21432 q^{17} -1.21432 q^{18} -1.52543 q^{19} -0.688892 q^{20} +1.52543 q^{21} +1.21432 q^{22} +7.95407 q^{23} +3.06668 q^{24} -3.28100 q^{25} +1.21432 q^{26} +1.00000 q^{27} -0.801502 q^{28} +7.39853 q^{29} -1.59210 q^{30} +4.68889 q^{31} -2.88739 q^{32} -1.00000 q^{33} -2.68889 q^{34} +2.00000 q^{35} -0.525428 q^{36} +8.85728 q^{37} +1.85236 q^{38} -1.00000 q^{39} +4.02074 q^{40} -3.52543 q^{41} -1.85236 q^{42} -8.77631 q^{43} +0.525428 q^{44} +1.31111 q^{45} -9.65878 q^{46} +9.18421 q^{47} -2.67307 q^{48} -4.67307 q^{49} +3.98418 q^{50} +2.21432 q^{51} +0.525428 q^{52} +3.67307 q^{53} -1.21432 q^{54} -1.31111 q^{55} +4.67799 q^{56} -1.52543 q^{57} -8.98418 q^{58} +9.37778 q^{59} -0.688892 q^{60} -11.4795 q^{61} -5.69381 q^{62} +1.52543 q^{63} +8.85236 q^{64} -1.31111 q^{65} +1.21432 q^{66} +5.25088 q^{67} -1.16346 q^{68} +7.95407 q^{69} -2.42864 q^{70} -14.4701 q^{71} +3.06668 q^{72} +3.13828 q^{73} -10.7556 q^{74} -3.28100 q^{75} +0.801502 q^{76} -1.52543 q^{77} +1.21432 q^{78} -5.03011 q^{79} -3.50468 q^{80} +1.00000 q^{81} +4.28100 q^{82} +5.37778 q^{83} -0.801502 q^{84} +2.90321 q^{85} +10.6572 q^{86} +7.39853 q^{87} -3.06668 q^{88} +0.688892 q^{89} -1.59210 q^{90} -1.52543 q^{91} -4.17929 q^{92} +4.68889 q^{93} -11.1526 q^{94} -2.00000 q^{95} -2.88739 q^{96} -12.8573 q^{97} +5.67460 q^{98} -1.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q + 3 q^{2} + 3 q^{3} + 5 q^{4} + 4 q^{5} + 3 q^{6} - 2 q^{7} + 9 q^{8} + 3 q^{9}+O(q^{10}) \) 3 * q + 3 * q^2 + 3 * q^3 + 5 * q^4 + 4 * q^5 + 3 * q^6 - 2 * q^7 + 9 * q^8 + 3 * q^9	\( 3 q + 3 q^{2} + 3 q^{3} + 5 q^{4} + 4 q^{5} + 3 q^{6} - 2 q^{7} + 9 q^{8} + 3 q^{9} + 2 q^{10} - 3 q^{11} + 5 q^{12} - 3 q^{13} - 12 q^{14} + 4 q^{15} + 5 q^{16} + 3 q^{18} + 2 q^{19} - 2 q^{20} - 2 q^{21} - 3 q^{22} + 4 q^{23} + 9 q^{24} - 3 q^{25} - 3 q^{26} + 3 q^{27} - 22 q^{28} + 2 q^{29} + 2 q^{30} + 14 q^{31} + 11 q^{32} - 3 q^{33} - 8 q^{34} + 6 q^{35} + 5 q^{36} + 12 q^{38} - 3 q^{39} - 8 q^{40} - 4 q^{41} - 12 q^{42} - 6 q^{43} - 5 q^{44} + 4 q^{45} - 22 q^{46} + 14 q^{47} + 5 q^{48} - q^{49} - q^{50} - 5 q^{52} - 2 q^{53} + 3 q^{54} - 4 q^{55} - 32 q^{56} + 2 q^{57} - 14 q^{58} + 28 q^{59} - 2 q^{60} - 8 q^{61} + 16 q^{62} - 2 q^{63} + 33 q^{64} - 4 q^{65} - 3 q^{66} + 2 q^{67} - 10 q^{68} + 4 q^{69} + 6 q^{70} + 10 q^{71} + 9 q^{72} - 24 q^{73} - 32 q^{74} - 3 q^{75} + 22 q^{76} + 2 q^{77} - 3 q^{78} - 22 q^{79} - 24 q^{80} + 3 q^{81} + 6 q^{82} + 16 q^{83} - 22 q^{84} + 2 q^{85} + 6 q^{86} + 2 q^{87} - 9 q^{88} + 2 q^{89} + 2 q^{90} + 2 q^{91} - 32 q^{92} + 14 q^{93} + 6 q^{94} - 6 q^{95} + 11 q^{96} - 12 q^{97} + 23 q^{98} - 3 q^{99}+O(q^{100}) \) 3 * q + 3 * q^2 + 3 * q^3 + 5 * q^4 + 4 * q^5 + 3 * q^6 - 2 * q^7 + 9 * q^8 + 3 * q^9 + 2 * q^10 - 3 * q^11 + 5 * q^12 - 3 * q^13 - 12 * q^14 + 4 * q^15 + 5 * q^16 + 3 * q^18 + 2 * q^19 - 2 * q^20 - 2 * q^21 - 3 * q^22 + 4 * q^23 + 9 * q^24 - 3 * q^25 - 3 * q^26 + 3 * q^27 - 22 * q^28 + 2 * q^29 + 2 * q^30 + 14 * q^31 + 11 * q^32 - 3 * q^33 - 8 * q^34 + 6 * q^35 + 5 * q^36 + 12 * q^38 - 3 * q^39 - 8 * q^40 - 4 * q^41 - 12 * q^42 - 6 * q^43 - 5 * q^44 + 4 * q^45 - 22 * q^46 + 14 * q^47 + 5 * q^48 - q^49 - q^50 - 5 * q^52 - 2 * q^53 + 3 * q^54 - 4 * q^55 - 32 * q^56 + 2 * q^57 - 14 * q^58 + 28 * q^59 - 2 * q^60 - 8 * q^61 + 16 * q^62 - 2 * q^63 + 33 * q^64 - 4 * q^65 - 3 * q^66 + 2 * q^67 - 10 * q^68 + 4 * q^69 + 6 * q^70 + 10 * q^71 + 9 * q^72 - 24 * q^73 - 32 * q^74 - 3 * q^75 + 22 * q^76 + 2 * q^77 - 3 * q^78 - 22 * q^79 - 24 * q^80 + 3 * q^81 + 6 * q^82 + 16 * q^83 - 22 * q^84 + 2 * q^85 + 6 * q^86 + 2 * q^87 - 9 * q^88 + 2 * q^89 + 2 * q^90 + 2 * q^91 - 32 * q^92 + 14 * q^93 + 6 * q^94 - 6 * q^95 + 11 * q^96 - 12 * q^97 + 23 * q^98 - 3 * q^99

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