LMFDB - Embedded newform 4730.2.a.w.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:	$1$
Dimension:	$8$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{7} - 12x^{6} + 7x^{5} + 41x^{4} - 6x^{3} - 28x^{2} + 2x + 4 $ x^8 - x^7 - 12x^6 + 7x^5 + 41x^4 - 6x^3 - 28x^2 + 2x + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Root			$-0.402785$ 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)

$f(q)$	$=$	$q-1.00000 q^{2} -1.40279 q^{3} +1.00000 q^{4} +1.00000 q^{5} +1.40279 q^{6} +3.56264 q^{7} -1.00000 q^{8} -1.03219 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -1.40279 q^{3} +1.00000 q^{4} +1.00000 q^{5} +1.40279 q^{6} +3.56264 q^{7} -1.00000 q^{8} -1.03219 q^{9} -1.00000 q^{10} +1.00000 q^{11} -1.40279 q^{12} -2.43746 q^{13} -3.56264 q^{14} -1.40279 q^{15} +1.00000 q^{16} +0.571065 q^{17} +1.03219 q^{18} +3.41659 q^{19} +1.00000 q^{20} -4.99762 q^{21} -1.00000 q^{22} -4.43746 q^{23} +1.40279 q^{24} +1.00000 q^{25} +2.43746 q^{26} +5.65630 q^{27} +3.56264 q^{28} -1.21111 q^{29} +1.40279 q^{30} -9.06141 q^{31} -1.00000 q^{32} -1.40279 q^{33} -0.571065 q^{34} +3.56264 q^{35} -1.03219 q^{36} +1.75030 q^{37} -3.41659 q^{38} +3.41924 q^{39} -1.00000 q^{40} -2.15603 q^{41} +4.99762 q^{42} -1.00000 q^{43} +1.00000 q^{44} -1.03219 q^{45} +4.43746 q^{46} -8.49553 q^{47} -1.40279 q^{48} +5.69239 q^{49} -1.00000 q^{50} -0.801082 q^{51} -2.43746 q^{52} -1.12321 q^{53} -5.65630 q^{54} +1.00000 q^{55} -3.56264 q^{56} -4.79275 q^{57} +1.21111 q^{58} +10.8913 q^{59} -1.40279 q^{60} -14.6949 q^{61} +9.06141 q^{62} -3.67733 q^{63} +1.00000 q^{64} -2.43746 q^{65} +1.40279 q^{66} -13.3518 q^{67} +0.571065 q^{68} +6.22481 q^{69} -3.56264 q^{70} +10.1118 q^{71} +1.03219 q^{72} -10.4128 q^{73} -1.75030 q^{74} -1.40279 q^{75} +3.41659 q^{76} +3.56264 q^{77} -3.41924 q^{78} -7.31968 q^{79} +1.00000 q^{80} -4.83800 q^{81} +2.15603 q^{82} +10.0195 q^{83} -4.99762 q^{84} +0.571065 q^{85} +1.00000 q^{86} +1.69893 q^{87} -1.00000 q^{88} +8.64425 q^{89} +1.03219 q^{90} -8.68381 q^{91} -4.43746 q^{92} +12.7112 q^{93} +8.49553 q^{94} +3.41659 q^{95} +1.40279 q^{96} -14.9749 q^{97} -5.69239 q^{98} -1.03219 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 8 q^{2} - 7 q^{3} + 8 q^{4} + 8 q^{5} + 7 q^{6} - 6 q^{7} - 8 q^{8} + 7 q^{9}+O(q^{10}) $ 8 * q - 8 * q^2 - 7 * q^3 + 8 * q^4 + 8 * q^5 + 7 * q^6 - 6 * q^7 - 8 * q^8 + 7 * q^9	\( 8 q - 8 q^{2} - 7 q^{3} + 8 q^{4} + 8 q^{5} + 7 q^{6} - 6 q^{7} - 8 q^{8} + 7 q^{9} - 8 q^{10} + 8 q^{11} - 7 q^{12} - 2 q^{13} + 6 q^{14} - 7 q^{15} + 8 q^{16} - 8 q^{17} - 7 q^{18} + 8 q^{20} + 14 q^{21} - 8 q^{22} - 18 q^{23} + 7 q^{24} + 8 q^{25} + 2 q^{26} - 22 q^{27} - 6 q^{28} + 8 q^{29} + 7 q^{30} - 11 q^{31} - 8 q^{32} - 7 q^{33} + 8 q^{34} - 6 q^{35} + 7 q^{36} - 17 q^{37} - 6 q^{39} - 8 q^{40} + 12 q^{41} - 14 q^{42} - 8 q^{43} + 8 q^{44} + 7 q^{45} + 18 q^{46} - 19 q^{47} - 7 q^{48} - 2 q^{49} - 8 q^{50} - q^{51} - 2 q^{52} - 7 q^{53} + 22 q^{54} + 8 q^{55} + 6 q^{56} - 3 q^{57} - 8 q^{58} + q^{59} - 7 q^{60} + 6 q^{61} + 11 q^{62} - 15 q^{63} + 8 q^{64} - 2 q^{65} + 7 q^{66} - 22 q^{67} - 8 q^{68} + 8 q^{69} + 6 q^{70} - 14 q^{71} - 7 q^{72} - 13 q^{73} + 17 q^{74} - 7 q^{75} - 6 q^{77} + 6 q^{78} - 8 q^{79} + 8 q^{80} + 28 q^{81} - 12 q^{82} - 4 q^{83} + 14 q^{84} - 8 q^{85} + 8 q^{86} - 30 q^{87} - 8 q^{88} + 5 q^{89} - 7 q^{90} - 8 q^{91} - 18 q^{92} + q^{93} + 19 q^{94} + 7 q^{96} - 23 q^{97} + 2 q^{98} + 7 q^{99}+O(q^{100}) \) 8 * q - 8 * q^2 - 7 * q^3 + 8 * q^4 + 8 * q^5 + 7 * q^6 - 6 * q^7 - 8 * q^8 + 7 * q^9 - 8 * q^10 + 8 * q^11 - 7 * q^12 - 2 * q^13 + 6 * q^14 - 7 * q^15 + 8 * q^16 - 8 * q^17 - 7 * q^18 + 8 * q^20 + 14 * q^21 - 8 * q^22 - 18 * q^23 + 7 * q^24 + 8 * q^25 + 2 * q^26 - 22 * q^27 - 6 * q^28 + 8 * q^29 + 7 * q^30 - 11 * q^31 - 8 * q^32 - 7 * q^33 + 8 * q^34 - 6 * q^35 + 7 * q^36 - 17 * q^37 - 6 * q^39 - 8 * q^40 + 12 * q^41 - 14 * q^42 - 8 * q^43 + 8 * q^44 + 7 * q^45 + 18 * q^46 - 19 * q^47 - 7 * q^48 - 2 * q^49 - 8 * q^50 - q^51 - 2 * q^52 - 7 * q^53 + 22 * q^54 + 8 * q^55 + 6 * q^56 - 3 * q^57 - 8 * q^58 + q^59 - 7 * q^60 + 6 * q^61 + 11 * q^62 - 15 * q^63 + 8 * q^64 - 2 * q^65 + 7 * q^66 - 22 * q^67 - 8 * q^68 + 8 * q^69 + 6 * q^70 - 14 * q^71 - 7 * q^72 - 13 * q^73 + 17 * q^74 - 7 * q^75 - 6 * q^77 + 6 * q^78 - 8 * q^79 + 8 * q^80 + 28 * q^81 - 12 * q^82 - 4 * q^83 + 14 * q^84 - 8 * q^85 + 8 * q^86 - 30 * q^87 - 8 * q^88 + 5 * q^89 - 7 * q^90 - 8 * q^91 - 18 * q^92 + q^93 + 19 * q^94 + 7 * q^96 - 23 * q^97 + 2 * q^98 + 7 * 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
$3$	−1.40279	−0.809899	−0.404949	−	0.914339i	$-0.632711\pi$
$3$	−1.40279	−0.809899	−0.404949	+	0.914339i	$0.632711\pi$
$4$	1.00000	0.500000
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	1.40279	0.572685
$7$	3.56264	1.34655	0.673275	−	0.739392i	$-0.264887\pi$
$7$	3.56264	1.34655	0.673275	+	0.739392i	$0.264887\pi$
$8$	−1.00000	−0.353553
$9$	−1.03219	−0.344064
$10$	−1.00000	−0.316228
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	−1.40279	−0.404949
$13$	−2.43746	−0.676031	−0.338016	−	0.941141i	$-0.609756\pi$
$13$	−2.43746	−0.676031	−0.338016	+	0.941141i	$0.609756\pi$
$14$	−3.56264	−0.952155
$15$	−1.40279	−0.362198
$16$	1.00000	0.250000
$17$	0.571065	0.138504	0.0692518	−	0.997599i	$-0.477939\pi$
$17$	0.571065	0.138504	0.0692518	+	0.997599i	$0.477939\pi$
$18$	1.03219	0.243290
$19$	3.41659	0.783820	0.391910	−	0.920003i	$-0.371814\pi$
$19$	3.41659	0.783820	0.391910	+	0.920003i	$0.371814\pi$
$20$	1.00000	0.223607
$21$	−4.99762	−1.09057
$22$	−1.00000	−0.213201
$23$	−4.43746	−0.925275	−0.462638	−	0.886547i	$-0.653097\pi$
$23$	−4.43746	−0.925275	−0.462638	+	0.886547i	$0.653097\pi$
$24$	1.40279	0.286342
$25$	1.00000	0.200000
$26$	2.43746	0.478026
$27$	5.65630	1.08856
$28$	3.56264	0.673275
$29$	−1.21111	−0.224898	−0.112449	−	0.993657i	$-0.535869\pi$
$29$	−1.21111	−0.224898	−0.112449	+	0.993657i	$0.535869\pi$
$30$	1.40279	0.256112
$31$	−9.06141	−1.62748	−0.813739	−	0.581231i	$-0.802571\pi$
$31$	−9.06141	−1.62748	−0.813739	+	0.581231i	$0.802571\pi$
$32$	−1.00000	−0.176777
$33$	−1.40279	−0.244194
$34$	−0.571065	−0.0979369
$35$	3.56264	0.602196
$36$	−1.03219	−0.172032
$37$	1.75030	0.287748	0.143874	−	0.989596i	$-0.454044\pi$
$37$	1.75030	0.287748	0.143874	+	0.989596i	$0.454044\pi$
$38$	−3.41659	−0.554245
$39$	3.41924	0.547517
$40$	−1.00000	−0.158114
$41$	−2.15603	−0.336715	−0.168358	−	0.985726i	$-0.553846\pi$
$41$	−2.15603	−0.336715	−0.168358	+	0.985726i	$0.553846\pi$
$42$	4.99762	0.771149
$43$	−1.00000	−0.152499
$43$	−1.00000	−0.152499
$44$	1.00000	0.150756
$45$	−1.03219	−0.153870
$46$	4.43746	0.654268
$47$	−8.49553	−1.23920	−0.619600	−	0.784918i	$-0.712705\pi$
$47$	−8.49553	−1.23920	−0.619600	+	0.784918i	$0.712705\pi$
$48$	−1.40279	−0.202475
$49$	5.69239	0.813199
$50$	−1.00000	−0.141421
$51$	−0.801082	−0.112174
$52$	−2.43746	−0.338016
$53$	−1.12321	−0.154284	−0.0771422	−	0.997020i	$-0.524580\pi$
$53$	−1.12321	−0.154284	−0.0771422	+	0.997020i	$0.524580\pi$
$54$	−5.65630	−0.769725
$55$	1.00000	0.134840
$56$	−3.56264	−0.476078
$57$	−4.79275	−0.634815
$58$	1.21111	0.159027
$59$	10.8913	1.41792	0.708960	−	0.705249i	$-0.249165\pi$
$59$	10.8913	1.41792	0.708960	+	0.705249i	$0.249165\pi$
$60$	−1.40279	−0.181099
$61$	−14.6949	−1.88148	−0.940742	−	0.339122i	$-0.889870\pi$
$61$	−14.6949	−1.88148	−0.940742	+	0.339122i	$0.889870\pi$
$62$	9.06141	1.15080
$63$	−3.67733	−0.463300
$64$	1.00000	0.125000
$65$	−2.43746	−0.302330
$66$	1.40279	0.172671
$67$	−13.3518	−1.63119	−0.815593	−	0.578626i	$-0.803589\pi$
$67$	−13.3518	−1.63119	−0.815593	+	0.578626i	$0.803589\pi$
$68$	0.571065	0.0692518
$69$	6.22481	0.749379
$70$	−3.56264	−0.425817
$71$	10.1118	1.20005	0.600026	−	0.799981i	$-0.295157\pi$
$71$	10.1118	1.20005	0.600026	+	0.799981i	$0.295157\pi$
$72$	1.03219	0.121645
$73$	−10.4128	−1.21872	−0.609362	−	0.792892i	$-0.708574\pi$
$73$	−10.4128	−1.21872	−0.609362	+	0.792892i	$0.708574\pi$
$74$	−1.75030	−0.203469
$75$	−1.40279	−0.161980
$76$	3.41659	0.391910
$77$	3.56264	0.406000
$78$	−3.41924	−0.387153
$79$	−7.31968	−0.823528	−0.411764	−	0.911291i	$-0.635087\pi$
$79$	−7.31968	−0.823528	−0.411764	+	0.911291i	$0.635087\pi$
$80$	1.00000	0.111803
$81$	−4.83800	−0.537555
$82$	2.15603	0.238094
$83$	10.0195	1.09978	0.549891	−	0.835236i	$-0.314669\pi$
$83$	10.0195	1.09978	0.549891	+	0.835236i	$0.314669\pi$
$84$	−4.99762	−0.545285
$85$	0.571065	0.0619407
$86$	1.00000	0.107833
$87$	1.69893	0.182145
$88$	−1.00000	−0.106600
$89$	8.64425	0.916289	0.458144	−	0.888878i	$-0.348514\pi$
$89$	8.64425	0.916289	0.458144	+	0.888878i	$0.348514\pi$
$90$	1.03219	0.108803
$91$	−8.68381	−0.910310
$92$	−4.43746	−0.462638
$93$	12.7112	1.31809
$94$	8.49553	0.876247
$95$	3.41659	0.350535
$96$	1.40279	0.143171
$97$	−14.9749	−1.52047	−0.760237	−	0.649646i	$-0.774917\pi$
$97$	−14.9749	−1.52047	−0.760237	+	0.649646i	$0.774917\pi$
$98$	−5.69239	−0.575018
$99$	−1.03219	−0.103739
$100$	1.00000	0.100000
$101$	−16.6608	−1.65781	−0.828904	−	0.559390i	$-0.811035\pi$
$101$	−16.6608	−1.65781	−0.828904	+	0.559390i	$0.811035\pi$
$102$	0.801082	0.0793189
$103$	10.3346	1.01830	0.509151	−	0.860677i	$-0.329960\pi$
$103$	10.3346	1.01830	0.509151	+	0.860677i	$0.329960\pi$
$104$	2.43746	0.239013
$105$	−4.99762	−0.487717
$106$	1.12321	0.109096
$107$	−16.6657	−1.61114	−0.805568	−	0.592503i	$-0.798140\pi$
$107$	−16.6657	−1.61114	−0.805568	+	0.592503i	$0.798140\pi$
$108$	5.65630	0.544278
$109$	−4.53334	−0.434215	−0.217108	−	0.976148i	$-0.569662\pi$
$109$	−4.53334	−0.434215	−0.217108	+	0.976148i	$0.569662\pi$
$110$	−1.00000	−0.0953463
$111$	−2.45530	−0.233047
$112$	3.56264	0.336638
$113$	6.44206	0.606018	0.303009	−	0.952988i	$-0.402009\pi$
$113$	6.44206	0.606018	0.303009	+	0.952988i	$0.402009\pi$
$114$	4.79275	0.448882
$115$	−4.43746	−0.413796
$116$	−1.21111	−0.112449
$117$	2.51593	0.232598
$118$	−10.8913	−1.00262
$119$	2.03450	0.186502
$120$	1.40279	0.128056
$121$	1.00000	0.0909091
$122$	14.6949	1.33041
$123$	3.02445	0.272705
$124$	−9.06141	−0.813739
$125$	1.00000	0.0894427
$126$	3.67733	0.327603
$127$	−2.26560	−0.201040	−0.100520	−	0.994935i	$-0.532051\pi$
$127$	−2.26560	−0.201040	−0.100520	+	0.994935i	$0.532051\pi$
$128$	−1.00000	−0.0883883
$129$	1.40279	0.123508
$130$	2.43746	0.213780
$131$	7.02016	0.613354	0.306677	−	0.951814i	$-0.400783\pi$
$131$	7.02016	0.613354	0.306677	+	0.951814i	$0.400783\pi$
$132$	−1.40279	−0.122097
$133$	12.1721	1.05545
$134$	13.3518	1.15342
$135$	5.65630	0.486817
$136$	−0.571065	−0.0489684
$137$	10.5079	0.897749	0.448874	−	0.893595i	$-0.351825\pi$
$137$	10.5079	0.897749	0.448874	+	0.893595i	$0.351825\pi$
$138$	−6.22481	−0.529891
$139$	7.25241	0.615141	0.307571	−	0.951525i	$-0.400484\pi$
$139$	7.25241	0.615141	0.307571	+	0.951525i	$0.400484\pi$
$140$	3.56264	0.301098
$141$	11.9174	1.00363
$142$	−10.1118	−0.848564
$143$	−2.43746	−0.203831
$144$	−1.03219	−0.0860161
$145$	−1.21111	−0.100577
$146$	10.4128	0.861768
$147$	−7.98520	−0.658609
$148$	1.75030	0.143874
$149$	9.05630	0.741921	0.370961	−	0.928649i	$-0.379028\pi$
$149$	9.05630	0.741921	0.370961	+	0.928649i	$0.379028\pi$
$150$	1.40279	0.114537
$151$	12.9420	1.05320	0.526602	−	0.850112i	$-0.323466\pi$
$151$	12.9420	1.05320	0.526602	+	0.850112i	$0.323466\pi$
$152$	−3.41659	−0.277122
$153$	−0.589450	−0.0476542
$154$	−3.56264	−0.287086
$155$	−9.06141	−0.727830
$156$	3.41924	0.273758
$157$	−0.230233	−0.0183746	−0.00918729	−	0.999958i	$-0.502924\pi$
$157$	−0.230233	−0.0183746	−0.00918729	+	0.999958i	$0.502924\pi$
$158$	7.31968	0.582322
$159$	1.57562	0.124955
$160$	−1.00000	−0.0790569
$161$	−15.8091	−1.24593
$162$	4.83800	0.380109
$163$	−22.0127	−1.72417	−0.862086	−	0.506763i	$-0.830842\pi$
$163$	−22.0127	−1.72417	−0.862086	+	0.506763i	$0.830842\pi$
$164$	−2.15603	−0.168358
$165$	−1.40279	−0.109207
$166$	−10.0195	−0.777664
$167$	−7.53307	−0.582927	−0.291463	−	0.956582i	$-0.594142\pi$
$167$	−7.53307	−0.582927	−0.291463	+	0.956582i	$0.594142\pi$
$168$	4.99762	0.385575
$169$	−7.05877	−0.542982
$170$	−0.571065	−0.0437987
$171$	−3.52659	−0.269685
$172$	−1.00000	−0.0762493
$173$	11.0894	0.843115	0.421557	−	0.906802i	$-0.361484\pi$
$173$	11.0894	0.843115	0.421557	+	0.906802i	$0.361484\pi$
$174$	−1.69893	−0.128796
$175$	3.56264	0.269310
$176$	1.00000	0.0753778
$177$	−15.2781	−1.14837
$178$	−8.64425	−0.647914
$179$	9.08113	0.678755	0.339378	−	0.940650i	$-0.389784\pi$
$179$	9.08113	0.678755	0.339378	+	0.940650i	$0.389784\pi$
$180$	−1.03219	−0.0769351
$181$	14.1902	1.05475	0.527374	−	0.849633i	$-0.323177\pi$
$181$	14.1902	1.05475	0.527374	+	0.849633i	$0.323177\pi$
$182$	8.68381	0.643686
$183$	20.6137	1.52381
$184$	4.43746	0.327134
$185$	1.75030	0.128685
$186$	−12.7112	−0.932032
$187$	0.571065	0.0417604
$188$	−8.49553	−0.619600
$189$	20.1514	1.46580
$190$	−3.41659	−0.247866
$191$	3.26641	0.236349	0.118175	−	0.992993i	$-0.462296\pi$
$191$	3.26641	0.236349	0.118175	+	0.992993i	$0.462296\pi$
$192$	−1.40279	−0.101237
$193$	−17.0940	−1.23045	−0.615227	−	0.788350i	$-0.710935\pi$
$193$	−17.0940	−1.23045	−0.615227	+	0.788350i	$0.710935\pi$
$194$	14.9749	1.07514
$195$	3.41924	0.244857
$196$	5.69239	0.406599
$197$	−17.6943	−1.26066	−0.630332	−	0.776326i	$-0.717081\pi$
$197$	−17.6943	−1.26066	−0.630332	+	0.776326i	$0.717081\pi$
$198$	1.03219	0.0733548
$199$	−1.82392	−0.129294	−0.0646472	−	0.997908i	$-0.520592\pi$
$199$	−1.82392	−0.129294	−0.0646472	+	0.997908i	$0.520592\pi$
$200$	−1.00000	−0.0707107
$201$	18.7298	1.32110
$202$	16.6608	1.17225
$203$	−4.31476	−0.302837
$204$	−0.801082	−0.0560870
$205$	−2.15603	−0.150584
$206$	−10.3346	−0.720048
$207$	4.58032	0.318354
$208$	−2.43746	−0.169008
$209$	3.41659	0.236331
$210$	4.99762	0.344868
$211$	19.0331	1.31029	0.655146	−	0.755502i	$-0.272607\pi$
$211$	19.0331	1.31029	0.655146	+	0.755502i	$0.272607\pi$
$212$	−1.12321	−0.0771422
$213$	−14.1847	−0.971920
$214$	16.6657	1.13925
$215$	−1.00000	−0.0681994
$216$	−5.65630	−0.384863
$217$	−32.2825	−2.19148
$218$	4.53334	0.307036
$219$	14.6069	0.987042
$220$	1.00000	0.0674200
$221$	−1.39195	−0.0936328
$222$	2.45530	0.164789
$223$	6.57836	0.440519	0.220260	−	0.975441i	$-0.429310\pi$
$223$	6.57836	0.440519	0.220260	+	0.975441i	$0.429310\pi$
$224$	−3.56264	−0.238039
$225$	−1.03219	−0.0688129
$226$	−6.44206	−0.428519
$227$	5.81320	0.385836	0.192918	−	0.981215i	$-0.438205\pi$
$227$	5.81320	0.385836	0.192918	+	0.981215i	$0.438205\pi$
$228$	−4.79275	−0.317408
$229$	23.4664	1.55071	0.775353	−	0.631529i	$-0.217572\pi$
$229$	23.4664	1.55071	0.775353	+	0.631529i	$0.217572\pi$
$230$	4.43746	0.292598
$231$	−4.99762	−0.328819
$232$	1.21111	0.0795135
$233$	24.9211	1.63264	0.816318	−	0.577603i	$-0.196012\pi$
$233$	24.9211	1.63264	0.816318	+	0.577603i	$0.196012\pi$
$234$	−2.51593	−0.164472
$235$	−8.49553	−0.554187
$236$	10.8913	0.708960
$237$	10.2679	0.666974
$238$	−2.03450	−0.131877
$239$	−0.790243	−0.0511166	−0.0255583	−	0.999673i	$-0.508136\pi$
$239$	−0.790243	−0.0511166	−0.0255583	+	0.999673i	$0.508136\pi$
$240$	−1.40279	−0.0905494
$241$	8.67253	0.558647	0.279323	−	0.960197i	$-0.409890\pi$
$241$	8.67253	0.558647	0.279323	+	0.960197i	$0.409890\pi$
$242$	−1.00000	−0.0642824
$243$	−10.1822	−0.653191
$244$	−14.6949	−0.940742
$245$	5.69239	0.363674
$246$	−3.02445	−0.192832
$247$	−8.32783	−0.529887
$248$	9.06141	0.575400
$249$	−14.0552	−0.890712
$250$	−1.00000	−0.0632456
$251$	−27.6438	−1.74486	−0.872429	−	0.488740i	$-0.837457\pi$
$251$	−27.6438	−1.74486	−0.872429	+	0.488740i	$0.837457\pi$
$252$	−3.67733	−0.231650
$253$	−4.43746	−0.278981
$254$	2.26560	0.142156
$255$	−0.801082	−0.0501657
$256$	1.00000	0.0625000
$257$	−16.4773	−1.02783	−0.513914	−	0.857842i	$-0.671805\pi$
$257$	−16.4773	−1.02783	−0.513914	+	0.857842i	$0.671805\pi$
$258$	−1.40279	−0.0873336
$259$	6.23570	0.387468
$260$	−2.43746	−0.151165
$261$	1.25010	0.0773794
$262$	−7.02016	−0.433707
$263$	−8.10634	−0.499858	−0.249929	−	0.968264i	$-0.580407\pi$
$263$	−8.10634	−0.499858	−0.249929	+	0.968264i	$0.580407\pi$
$264$	1.40279	0.0863355
$265$	−1.12321	−0.0689981
$266$	−12.1721	−0.746319
$267$	−12.1260	−0.742101
$268$	−13.3518	−0.815593
$269$	−7.03321	−0.428822	−0.214411	−	0.976744i	$-0.568783\pi$
$269$	−7.03321	−0.428822	−0.214411	+	0.976744i	$0.568783\pi$
$270$	−5.65630	−0.344232
$271$	5.91758	0.359468	0.179734	−	0.983715i	$-0.442476\pi$
$271$	5.91758	0.359468	0.179734	+	0.983715i	$0.442476\pi$
$272$	0.571065	0.0346259
$273$	12.1815	0.737259
$274$	−10.5079	−0.634804
$275$	1.00000	0.0603023
$276$	6.22481	0.374690
$277$	21.9062	1.31622	0.658109	−	0.752922i	$-0.271356\pi$
$277$	21.9062	1.31622	0.658109	+	0.752922i	$0.271356\pi$
$278$	−7.25241	−0.434970
$279$	9.35313	0.559957
$280$	−3.56264	−0.212908
$281$	−8.36961	−0.499289	−0.249644	−	0.968338i	$-0.580314\pi$
$281$	−8.36961	−0.499289	−0.249644	+	0.968338i	$0.580314\pi$
$282$	−11.9174	−0.709671
$283$	−32.8250	−1.95124	−0.975622	−	0.219459i	$-0.929571\pi$
$283$	−32.8250	−1.95124	−0.975622	+	0.219459i	$0.929571\pi$
$284$	10.1118	0.600026
$285$	−4.79275	−0.283898
$286$	2.43746	0.144130
$287$	−7.68115	−0.453404
$288$	1.03219	0.0608226
$289$	−16.6739	−0.980817
$290$	1.21111	0.0711190
$291$	21.0066	1.23143
$292$	−10.4128	−0.609362
$293$	−2.05048	−0.119791	−0.0598953	−	0.998205i	$-0.519077\pi$
$293$	−2.05048	−0.119791	−0.0598953	+	0.998205i	$0.519077\pi$
$294$	7.98520	0.465707
$295$	10.8913	0.634113
$296$	−1.75030	−0.101734
$297$	5.65630	0.328212
$298$	−9.05630	−0.524618
$299$	10.8162	0.625515
$300$	−1.40279	−0.0809899
$301$	−3.56264	−0.205347
$302$	−12.9420	−0.744728
$303$	23.3715	1.34266
$304$	3.41659	0.195955
$305$	−14.6949	−0.841426
$306$	0.589450	0.0336966
$307$	−7.27539	−0.415229	−0.207614	−	0.978211i	$-0.566570\pi$
$307$	−7.27539	−0.415229	−0.207614	+	0.978211i	$0.566570\pi$
$308$	3.56264	0.203000
$309$	−14.4973	−0.824721
$310$	9.06141	0.514654
$311$	−8.62398	−0.489021	−0.244511	−	0.969647i	$-0.578627\pi$
$311$	−8.62398	−0.489021	−0.244511	+	0.969647i	$0.578627\pi$
$312$	−3.41924	−0.193576
$313$	−22.5430	−1.27421	−0.637103	−	0.770779i	$-0.719867\pi$
$313$	−22.5430	−1.27421	−0.637103	+	0.770779i	$0.719867\pi$
$314$	0.230233	0.0129928
$315$	−3.67733	−0.207194
$316$	−7.31968	−0.411764
$317$	−18.0512	−1.01386	−0.506929	−	0.861988i	$-0.669219\pi$
$317$	−18.0512	−1.01386	−0.506929	+	0.861988i	$0.669219\pi$
$318$	−1.57562	−0.0883563
$319$	−1.21111	−0.0678093
$320$	1.00000	0.0559017
$321$	23.3784	1.30486
$322$	15.8091	0.881006
$323$	1.95110	0.108562
$324$	−4.83800	−0.268778
$325$	−2.43746	−0.135206
$326$	22.0127	1.21917
$327$	6.35930	0.351670
$328$	2.15603	0.119047
$329$	−30.2665	−1.66865
$330$	1.40279	0.0772208
$331$	−33.7247	−1.85368	−0.926839	−	0.375458i	$-0.877485\pi$
$331$	−33.7247	−1.85368	−0.926839	+	0.375458i	$0.877485\pi$
$332$	10.0195	0.549891
$333$	−1.80665	−0.0990039
$334$	7.53307	0.412191
$335$	−13.3518	−0.729489
$336$	−4.99762	−0.272642
$337$	1.26061	0.0686701	0.0343350	−	0.999410i	$-0.489069\pi$
$337$	1.26061	0.0686701	0.0343350	+	0.999410i	$0.489069\pi$
$338$	7.05877	0.383946
$339$	−9.03682	−0.490813
$340$	0.571065	0.0309704
$341$	−9.06141	−0.490703
$342$	3.52659	0.190696
$343$	−4.65854	−0.251537
$344$	1.00000	0.0539164
$345$	6.22481	0.335133
$346$	−11.0894	−0.596172
$347$	0.986674	0.0529674	0.0264837	−	0.999649i	$-0.491569\pi$
$347$	0.986674	0.0529674	0.0264837	+	0.999649i	$0.491569\pi$
$348$	1.69893	0.0910723
$349$	−0.841591	−0.0450493	−0.0225247	−	0.999746i	$-0.507170\pi$
$349$	−0.841591	−0.0450493	−0.0225247	+	0.999746i	$0.507170\pi$
$350$	−3.56264	−0.190431
$351$	−13.7870	−0.735898
$352$	−1.00000	−0.0533002
$353$	−13.4485	−0.715793	−0.357897	−	0.933761i	$-0.616506\pi$
$353$	−13.4485	−0.715793	−0.357897	+	0.933761i	$0.616506\pi$
$354$	15.2781	0.812021
$355$	10.1118	0.536679
$356$	8.64425	0.458144
$357$	−2.85397	−0.151048
$358$	−9.08113	−0.479953
$359$	−31.4422	−1.65946	−0.829728	−	0.558168i	$-0.811505\pi$
$359$	−31.4422	−1.65946	−0.829728	+	0.558168i	$0.811505\pi$
$360$	1.03219	0.0544014
$361$	−7.32688	−0.385625
$362$	−14.1902	−0.745819
$363$	−1.40279	−0.0736271
$364$	−8.68381	−0.455155
$365$	−10.4128	−0.545030
$366$	−20.6137	−1.07750
$367$	−19.8204	−1.03462	−0.517308	−	0.855800i	$-0.673066\pi$
$367$	−19.8204	−1.03462	−0.517308	+	0.855800i	$0.673066\pi$
$368$	−4.43746	−0.231319
$369$	2.22544	0.115852
$370$	−1.75030	−0.0909940
$371$	−4.00158	−0.207752
$372$	12.7112	0.659046
$373$	−9.63530	−0.498897	−0.249448	−	0.968388i	$-0.580249\pi$
$373$	−9.63530	−0.498897	−0.249448	+	0.968388i	$0.580249\pi$
$374$	−0.571065	−0.0295291
$375$	−1.40279	−0.0724395
$376$	8.49553	0.438123
$377$	2.95204	0.152038
$378$	−20.1514	−1.03647
$379$	−29.8237	−1.53194	−0.765969	−	0.642877i	$-0.777741\pi$
$379$	−29.8237	−1.53194	−0.765969	+	0.642877i	$0.777741\pi$
$380$	3.41659	0.175268
$381$	3.17815	0.162822
$382$	−3.26641	−0.167124
$383$	−15.3592	−0.784819	−0.392410	−	0.919791i	$-0.628358\pi$
$383$	−15.3592	−0.784819	−0.392410	+	0.919791i	$0.628358\pi$
$384$	1.40279	0.0715856
$385$	3.56264	0.181569
$386$	17.0940	0.870062
$387$	1.03219	0.0524693
$388$	−14.9749	−0.760237
$389$	11.1995	0.567839	0.283919	−	0.958848i	$-0.408365\pi$
$389$	11.1995	0.567839	0.283919	+	0.958848i	$0.408365\pi$
$390$	−3.41924	−0.173140
$391$	−2.53408	−0.128154
$392$	−5.69239	−0.287509
$393$	−9.84778	−0.496755
$394$	17.6943	0.891424
$395$	−7.31968	−0.368293
$396$	−1.03219	−0.0518697
$397$	28.4868	1.42971	0.714857	−	0.699271i	$-0.246492\pi$
$397$	28.4868	1.42971	0.714857	+	0.699271i	$0.246492\pi$
$398$	1.82392	0.0914249
$399$	−17.0748	−0.854811
$400$	1.00000	0.0500000
$401$	23.6666	1.18185	0.590926	−	0.806726i	$-0.298762\pi$
$401$	23.6666	1.18185	0.590926	+	0.806726i	$0.298762\pi$
$402$	−18.7298	−0.934155
$403$	22.0869	1.10023
$404$	−16.6608	−0.828904
$405$	−4.83800	−0.240402
$406$	4.31476	0.214138
$407$	1.75030	0.0867594
$408$	0.801082	0.0396595
$409$	−8.60190	−0.425337	−0.212668	−	0.977124i	$-0.568215\pi$
$409$	−8.60190	−0.425337	−0.212668	+	0.977124i	$0.568215\pi$
$410$	2.15603	0.106479
$411$	−14.7403	−0.727085
$412$	10.3346	0.509151
$413$	38.8016	1.90930
$414$	−4.58032	−0.225110
$415$	10.0195	0.491838
$416$	2.43746	0.119507
$417$	−10.1736	−0.498202
$418$	−3.41659	−0.167111
$419$	2.33905	0.114270	0.0571350	−	0.998366i	$-0.481803\pi$
$419$	2.33905	0.114270	0.0571350	+	0.998366i	$0.481803\pi$
$420$	−4.99762	−0.243859
$421$	12.3054	0.599727	0.299864	−	0.953982i	$-0.403059\pi$
$421$	12.3054	0.599727	0.299864	+	0.953982i	$0.403059\pi$
$422$	−19.0331	−0.926516
$423$	8.76903	0.426365
$424$	1.12321	0.0545478
$425$	0.571065	0.0277007
$426$	14.1847	0.687251
$427$	−52.3525	−2.53351
$428$	−16.6657	−0.805568
$429$	3.41924	0.165082
$430$	1.00000	0.0482243
$431$	−17.8140	−0.858068	−0.429034	−	0.903288i	$-0.641146\pi$
$431$	−17.8140	−0.858068	−0.429034	+	0.903288i	$0.641146\pi$
$432$	5.65630	0.272139
$433$	−8.77481	−0.421691	−0.210845	−	0.977519i	$-0.567622\pi$
$433$	−8.77481	−0.421691	−0.210845	+	0.977519i	$0.567622\pi$
$434$	32.2825	1.54961
$435$	1.69893	0.0814575
$436$	−4.53334	−0.217108
$437$	−15.1610	−0.725250
$438$	−14.6069	−0.697944
$439$	12.5493	0.598947	0.299473	−	0.954105i	$-0.403189\pi$
$439$	12.5493	0.598947	0.299473	+	0.954105i	$0.403189\pi$
$440$	−1.00000	−0.0476731
$441$	−5.87565	−0.279793
$442$	1.39195	0.0662084
$443$	6.99077	0.332141	0.166071	−	0.986114i	$-0.446892\pi$
$443$	6.99077	0.332141	0.166071	+	0.986114i	$0.446892\pi$
$444$	−2.45530	−0.116523
$445$	8.64425	0.409777
$446$	−6.57836	−0.311494
$447$	−12.7041	−0.600881
$448$	3.56264	0.168319
$449$	10.4958	0.495329	0.247664	−	0.968846i	$-0.420337\pi$
$449$	10.4958	0.495329	0.247664	+	0.968846i	$0.420337\pi$
$450$	1.03219	0.0486581
$451$	−2.15603	−0.101523
$452$	6.44206	0.303009
$453$	−18.1548	−0.852988
$454$	−5.81320	−0.272827
$455$	−8.68381	−0.407103
$456$	4.79275	0.224441
$457$	5.49554	0.257070	0.128535	−	0.991705i	$-0.458972\pi$
$457$	5.49554	0.257070	0.128535	+	0.991705i	$0.458972\pi$
$458$	−23.4664	−1.09651
$459$	3.23012	0.150769
$460$	−4.43746	−0.206898
$461$	14.0949	0.656465	0.328233	−	0.944597i	$-0.393547\pi$
$461$	14.0949	0.656465	0.328233	+	0.944597i	$0.393547\pi$
$462$	4.99762	0.232510
$463$	−5.81097	−0.270059	−0.135029	−	0.990842i	$-0.543113\pi$
$463$	−5.81097	−0.270059	−0.135029	+	0.990842i	$0.543113\pi$
$464$	−1.21111	−0.0562245
$465$	12.7112	0.589469
$466$	−24.9211	−1.15445
$467$	−13.1482	−0.608425	−0.304212	−	0.952604i	$-0.598393\pi$
$467$	−13.1482	−0.608425	−0.304212	+	0.952604i	$0.598393\pi$
$468$	2.51593	0.116299
$469$	−47.5678	−2.19647
$470$	8.49553	0.391870
$471$	0.322967	0.0148815
$472$	−10.8913	−0.501311
$473$	−1.00000	−0.0459800
$474$	−10.2679	−0.471622
$475$	3.41659	0.156764
$476$	2.03450	0.0932511
$477$	1.15937	0.0530837
$478$	0.790243	0.0361449
$479$	15.9652	0.729468	0.364734	−	0.931112i	$-0.381160\pi$
$479$	15.9652	0.729468	0.364734	+	0.931112i	$0.381160\pi$
$480$	1.40279	0.0640281
$481$	−4.26630	−0.194527
$482$	−8.67253	−0.395023
$483$	22.1767	1.00908
$484$	1.00000	0.0454545
$485$	−14.9749	−0.679977
$486$	10.1822	0.461875
$487$	0.0999174	0.00452769	0.00226384	−	0.999997i	$-0.499279\pi$
$487$	0.0999174	0.00452769	0.00226384	+	0.999997i	$0.499279\pi$
$488$	14.6949	0.665205
$489$	30.8792	1.39640
$490$	−5.69239	−0.257156
$491$	−35.5843	−1.60590	−0.802948	−	0.596048i	$-0.796737\pi$
$491$	−35.5843	−1.60590	−0.802948	+	0.596048i	$0.796737\pi$
$492$	3.02445	0.136353
$493$	−0.691625	−0.0311492
$494$	8.32783	0.374687
$495$	−1.03219	−0.0463936
$496$	−9.06141	−0.406869
$497$	36.0247	1.61593
$498$	14.0552	0.629829
$499$	1.80603	0.0808490	0.0404245	−	0.999183i	$-0.487129\pi$
$499$	1.80603	0.0808490	0.0404245	+	0.999183i	$0.487129\pi$
$500$	1.00000	0.0447214
$501$	10.5673	0.472111
$502$	27.6438	1.23380
$503$	−8.10180	−0.361241	−0.180621	−	0.983553i	$-0.557811\pi$
$503$	−8.10180	−0.361241	−0.180621	+	0.983553i	$0.557811\pi$
$504$	3.67733	0.163801
$505$	−16.6608	−0.741395
$506$	4.43746	0.197269
$507$	9.90193	0.439760
$508$	−2.26560	−0.100520
$509$	−22.5360	−0.998890	−0.499445	−	0.866346i	$-0.666463\pi$
$509$	−22.5360	−0.998890	−0.499445	+	0.866346i	$0.666463\pi$
$510$	0.801082	0.0354725
$511$	−37.0970	−1.64107
$512$	−1.00000	−0.0441942
$513$	19.3253	0.853232
$514$	16.4773	0.726784
$515$	10.3346	0.455398
$516$	1.40279	0.0617542
$517$	−8.49553	−0.373633
$518$	−6.23570	−0.273981
$519$	−15.5561	−0.682837
$520$	2.43746	0.106890
$521$	32.2764	1.41405	0.707027	−	0.707186i	$-0.250036\pi$
$521$	32.2764	1.41405	0.707027	+	0.707186i	$0.250036\pi$
$522$	−1.25010	−0.0547155
$523$	−42.0453	−1.83851	−0.919256	−	0.393660i	$-0.871209\pi$
$523$	−42.0453	−1.83851	−0.919256	+	0.393660i	$0.871209\pi$
$524$	7.02016	0.306677
$525$	−4.99762	−0.218114
$526$	8.10634	0.353453
$527$	−5.17466	−0.225412
$528$	−1.40279	−0.0610484
$529$	−3.30891	−0.143866
$530$	1.12321	0.0487890
$531$	−11.2419	−0.487856
$532$	12.1721	0.527727
$533$	5.25524	0.227630
$534$	12.1260	0.524745
$535$	−16.6657	−0.720522
$536$	13.3518	0.576711
$537$	−12.7389	−0.549723
$538$	7.03321	0.303223
$539$	5.69239	0.245189
$540$	5.65630	0.243408
$541$	17.9394	0.771275	0.385637	−	0.922650i	$-0.373982\pi$
$541$	17.9394	0.771275	0.385637	+	0.922650i	$0.373982\pi$
$542$	−5.91758	−0.254182
$543$	−19.9058	−0.854239
$544$	−0.571065	−0.0244842
$545$	−4.53334	−0.194187
$546$	−12.1815	−0.521321
$547$	−39.1253	−1.67288	−0.836438	−	0.548062i	$-0.815366\pi$
$547$	−39.1253	−1.67288	−0.836438	+	0.548062i	$0.815366\pi$
$548$	10.5079	0.448874
$549$	15.1679	0.647352
$550$	−1.00000	−0.0426401
$551$	−4.13788	−0.176280
$552$	−6.22481	−0.264946
$553$	−26.0774	−1.10892
$554$	−21.9062	−0.930707
$555$	−2.45530	−0.104222
$556$	7.25241	0.307571
$557$	−2.82083	−0.119522	−0.0597612	−	0.998213i	$-0.519034\pi$
$557$	−2.82083	−0.119522	−0.0597612	+	0.998213i	$0.519034\pi$
$558$	−9.35313	−0.395950
$559$	2.43746	0.103094
$560$	3.56264	0.150549
$561$	−0.801082	−0.0338217
$562$	8.36961	0.353051
$563$	−6.66026	−0.280697	−0.140348	−	0.990102i	$-0.544822\pi$
$563$	−6.66026	−0.280697	−0.140348	+	0.990102i	$0.544822\pi$
$564$	11.9174	0.501813
$565$	6.44206	0.271019
$566$	32.8250	1.37974
$567$	−17.2360	−0.723845
$568$	−10.1118	−0.424282
$569$	−6.97653	−0.292471	−0.146236	−	0.989250i	$-0.546716\pi$
$569$	−6.97653	−0.292471	−0.146236	+	0.989250i	$0.546716\pi$
$570$	4.79275	0.200746
$571$	9.54538	0.399462	0.199731	−	0.979851i	$-0.435993\pi$
$571$	9.54538	0.399462	0.199731	+	0.979851i	$0.435993\pi$
$572$	−2.43746	−0.101916
$573$	−4.58208	−0.191419
$574$	7.68115	0.320605
$575$	−4.43746	−0.185055
$576$	−1.03219	−0.0430081
$577$	−40.2669	−1.67633	−0.838167	−	0.545413i	$-0.816373\pi$
$577$	−40.2669	−1.67633	−0.838167	+	0.545413i	$0.816373\pi$
$578$	16.6739	0.693542
$579$	23.9792	0.996542
$580$	−1.21111	−0.0502887
$581$	35.6958	1.48091
$582$	−21.0066	−0.870752
$583$	−1.12321	−0.0465185
$584$	10.4128	0.430884
$585$	2.51593	0.104021
$586$	2.05048	0.0847047
$587$	−20.1889	−0.833286	−0.416643	−	0.909070i	$-0.636794\pi$
$587$	−20.1889	−0.833286	−0.416643	+	0.909070i	$0.636794\pi$
$588$	−7.98520	−0.329304
$589$	−30.9592	−1.27565
$590$	−10.8913	−0.448386
$591$	24.8213	1.02101
$592$	1.75030	0.0719371
$593$	9.25475	0.380047	0.190024	−	0.981780i	$-0.439144\pi$
$593$	9.25475	0.380047	0.190024	+	0.981780i	$0.439144\pi$
$594$	−5.65630	−0.232081
$595$	2.03450	0.0834063
$596$	9.05630	0.370961
$597$	2.55857	0.104715
$598$	−10.8162	−0.442306
$599$	33.4136	1.36524	0.682621	−	0.730772i	$-0.260840\pi$
$599$	33.4136	1.36524	0.682621	+	0.730772i	$0.260840\pi$
$600$	1.40279	0.0572685
$601$	22.8329	0.931375	0.465687	−	0.884949i	$-0.345807\pi$
$601$	22.8329	0.931375	0.465687	+	0.884949i	$0.345807\pi$
$602$	3.56264	0.145202
$603$	13.7817	0.561233
$604$	12.9420	0.526602
$605$	1.00000	0.0406558
$606$	−23.3715	−0.949402
$607$	37.9956	1.54219	0.771096	−	0.636719i	$-0.219709\pi$
$607$	37.9956	1.54219	0.771096	+	0.636719i	$0.219709\pi$
$608$	−3.41659	−0.138561
$609$	6.05268	0.245267
$610$	14.6949	0.594978
$611$	20.7076	0.837738
$612$	−0.589450	−0.0238271
$613$	−24.0959	−0.973224	−0.486612	−	0.873618i	$-0.661767\pi$
$613$	−24.0959	−0.973224	−0.486612	+	0.873618i	$0.661767\pi$
$614$	7.27539	0.293611
$615$	3.02445	0.121957
$616$	−3.56264	−0.143543
$617$	10.6505	0.428774	0.214387	−	0.976749i	$-0.431225\pi$
$617$	10.6505	0.428774	0.214387	+	0.976749i	$0.431225\pi$
$618$	14.4973	0.583166
$619$	−10.2622	−0.412473	−0.206236	−	0.978502i	$-0.566122\pi$
$619$	−10.2622	−0.412473	−0.206236	+	0.978502i	$0.566122\pi$
$620$	−9.06141	−0.363915
$621$	−25.0996	−1.00721
$622$	8.62398	0.345790
$623$	30.7963	1.23383
$624$	3.41924	0.136879
$625$	1.00000	0.0400000
$626$	22.5430	0.900999
$627$	−4.79275	−0.191404
$628$	−0.230233	−0.00918729
$629$	0.999538	0.0398542
$630$	3.67733	0.146508
$631$	−14.9391	−0.594716	−0.297358	−	0.954766i	$-0.596105\pi$
$631$	−14.9391	−0.594716	−0.297358	+	0.954766i	$0.596105\pi$
$632$	7.31968	0.291161
$633$	−26.6993	−1.06120
$634$	18.0512	0.716905
$635$	−2.26560	−0.0899076
$636$	1.57562	0.0624773
$637$	−13.8750	−0.549748
$638$	1.21111	0.0479484
$639$	−10.4373	−0.412895
$640$	−1.00000	−0.0395285
$641$	32.5873	1.28712	0.643560	−	0.765396i	$-0.277457\pi$
$641$	32.5873	1.28712	0.643560	+	0.765396i	$0.277457\pi$
$642$	−23.3784	−0.922673
$643$	5.95261	0.234748	0.117374	−	0.993088i	$-0.462552\pi$
$643$	5.95261	0.234748	0.117374	+	0.993088i	$0.462552\pi$
$644$	−15.8091	−0.622965
$645$	1.40279	0.0552346
$646$	−1.95110	−0.0767649
$647$	43.7276	1.71911	0.859555	−	0.511043i	$-0.170741\pi$
$647$	43.7276	1.71911	0.859555	+	0.511043i	$0.170741\pi$
$648$	4.83800	0.190054
$649$	10.8913	0.427519
$650$	2.43746	0.0956052
$651$	45.2855	1.77488
$652$	−22.0127	−0.862086
$653$	−10.3512	−0.405075	−0.202538	−	0.979275i	$-0.564919\pi$
$653$	−10.3512	−0.405075	−0.202538	+	0.979275i	$0.564919\pi$
$654$	−6.35930	−0.248668
$655$	7.02016	0.274300
$656$	−2.15603	−0.0841788
$657$	10.7480	0.419319
$658$	30.2665	1.17991
$659$	18.6162	0.725185	0.362592	−	0.931948i	$-0.381892\pi$
$659$	18.6162	0.725185	0.362592	+	0.931948i	$0.381892\pi$
$660$	−1.40279	−0.0546033
$661$	16.8226	0.654325	0.327162	−	0.944968i	$-0.393908\pi$
$661$	16.8226	0.654325	0.327162	+	0.944968i	$0.393908\pi$
$662$	33.7247	1.31075
$663$	1.95261	0.0758331
$664$	−10.0195	−0.388832
$665$	12.1721	0.472013
$666$	1.80665	0.0700063
$667$	5.37427	0.208093
$668$	−7.53307	−0.291463
$669$	−9.22802	−0.356776
$670$	13.3518	0.515826
$671$	−14.6949	−0.567289
$672$	4.99762	0.192787
$673$	40.6581	1.56726	0.783628	−	0.621231i	$-0.213367\pi$
$673$	40.6581	1.56726	0.783628	+	0.621231i	$0.213367\pi$
$674$	−1.26061	−0.0485571
$675$	5.65630	0.217711
$676$	−7.05877	−0.271491
$677$	38.1731	1.46711	0.733556	−	0.679629i	$-0.237859\pi$
$677$	38.1731	1.46711	0.733556	+	0.679629i	$0.237859\pi$
$678$	9.03682	0.347057
$679$	−53.3503	−2.04740
$680$	−0.571065	−0.0218994
$681$	−8.15467	−0.312488
$682$	9.06141	0.346979
$683$	−15.9593	−0.610667	−0.305334	−	0.952245i	$-0.598768\pi$
$683$	−15.9593	−0.610667	−0.305334	+	0.952245i	$0.598768\pi$
$684$	−3.52659	−0.134842
$685$	10.5079	0.401485
$686$	4.65854	0.177864
$687$	−32.9184	−1.25591
$688$	−1.00000	−0.0381246
$689$	2.73778	0.104301
$690$	−6.22481	−0.236974
$691$	7.18988	0.273516	0.136758	−	0.990605i	$-0.456332\pi$
$691$	7.18988	0.273516	0.136758	+	0.990605i	$0.456332\pi$
$692$	11.0894	0.421557
$693$	−3.67733	−0.139690
$694$	−0.986674	−0.0374536
$695$	7.25241	0.275099
$696$	−1.69893	−0.0643978
$697$	−1.23123	−0.0466363
$698$	0.841591	0.0318547
$699$	−34.9589	−1.32227
$700$	3.56264	0.134655
$701$	20.3457	0.768446	0.384223	−	0.923240i	$-0.374469\pi$
$701$	20.3457	0.768446	0.384223	+	0.923240i	$0.374469\pi$
$702$	13.7870	0.520358
$703$	5.98008	0.225543
$704$	1.00000	0.0376889
$705$	11.9174	0.448835
$706$	13.4485	0.506142
$707$	−59.3563	−2.23232
$708$	−15.2781	−0.574186
$709$	35.3924	1.32919	0.664594	−	0.747204i	$-0.268604\pi$
$709$	35.3924	1.32919	0.664594	+	0.747204i	$0.268604\pi$
$710$	−10.1118	−0.379490
$711$	7.55532	0.283347
$712$	−8.64425	−0.323957
$713$	40.2097	1.50587
$714$	2.85397	0.106807
$715$	−2.43746	−0.0911560
$716$	9.08113	0.339378
$717$	1.10854	0.0413993
$718$	31.4422	1.17341
$719$	2.41134	0.0899279	0.0449639	−	0.998989i	$-0.485683\pi$
$719$	2.41134	0.0899279	0.0449639	+	0.998989i	$0.485683\pi$
$720$	−1.03219	−0.0384676
$721$	36.8186	1.37119
$722$	7.32688	0.272678
$723$	−12.1657	−0.452447
$724$	14.1902	0.527374
$725$	−1.21111	−0.0449796
$726$	1.40279	0.0520622
$727$	−45.0709	−1.67159	−0.835793	−	0.549045i	$-0.814992\pi$
$727$	−45.0709	−1.67159	−0.835793	+	0.549045i	$0.814992\pi$
$728$	8.68381	0.321843
$729$	28.7975	1.06657
$730$	10.4128	0.385394
$731$	−0.571065	−0.0211216
$732$	20.6137	0.761906
$733$	−46.6516	−1.72312	−0.861558	−	0.507658i	$-0.830511\pi$
$733$	−46.6516	−1.72312	−0.861558	+	0.507658i	$0.830511\pi$
$734$	19.8204	0.731583
$735$	−7.98520	−0.294539
$736$	4.43746	0.163567
$737$	−13.3518	−0.491821
$738$	−2.22544	−0.0819195
$739$	−47.1283	−1.73364	−0.866822	−	0.498618i	$-0.833841\pi$
$739$	−47.1283	−1.73364	−0.866822	+	0.498618i	$0.833841\pi$
$740$	1.75030	0.0643425
$741$	11.6822	0.429155
$742$	4.00158	0.146903
$743$	−0.300181	−0.0110126	−0.00550628	−	0.999985i	$-0.501753\pi$
$743$	−0.300181	−0.0110126	−0.00550628	+	0.999985i	$0.501753\pi$
$744$	−12.7112	−0.466016
$745$	9.05630	0.331797
$746$	9.63530	0.352773
$747$	−10.3421	−0.378396
$748$	0.571065	0.0208802
$749$	−59.3739	−2.16948
$750$	1.40279	0.0512225
$751$	−20.2972	−0.740654	−0.370327	−	0.928901i	$-0.620754\pi$
$751$	−20.2972	−0.740654	−0.370327	+	0.928901i	$0.620754\pi$
$752$	−8.49553	−0.309800
$753$	38.7783	1.41316
$754$	−2.95204	−0.107507
$755$	12.9420	0.471007
$756$	20.1514	0.732898
$757$	2.83059	0.102880	0.0514398	−	0.998676i	$-0.483619\pi$
$757$	2.83059	0.102880	0.0514398	+	0.998676i	$0.483619\pi$
$758$	29.8237	1.08324
$759$	6.22481	0.225946
$760$	−3.41659	−0.123933
$761$	13.7473	0.498339	0.249170	−	0.968460i	$-0.419842\pi$
$761$	13.7473	0.498339	0.249170	+	0.968460i	$0.419842\pi$
$762$	−3.17815	−0.115132
$763$	−16.1506	−0.584693
$764$	3.26641	0.118175
$765$	−0.589450	−0.0213116
$766$	15.3592	0.554951
$767$	−26.5470	−0.958558
$768$	−1.40279	−0.0506187
$769$	47.2099	1.70243	0.851217	−	0.524815i	$-0.175865\pi$
$769$	47.2099	1.70243	0.851217	+	0.524815i	$0.175865\pi$
$770$	−3.56264	−0.128389
$771$	23.1141	0.832436
$772$	−17.0940	−0.615227
$773$	−3.18521	−0.114564	−0.0572820	−	0.998358i	$-0.518243\pi$
$773$	−3.18521	−0.114564	−0.0572820	+	0.998358i	$0.518243\pi$
$774$	−1.03219	−0.0371014
$775$	−9.06141	−0.325496
$776$	14.9749	0.537569
$777$	−8.74735	−0.313809
$778$	−11.1995	−0.401523
$779$	−7.36627	−0.263924
$780$	3.41924	0.122428
$781$	10.1118	0.361829
$782$	2.53408	0.0906186
$783$	−6.85042	−0.244814
$784$	5.69239	0.203300
$785$	−0.230233	−0.00821736
$786$	9.84778	0.351259
$787$	15.2239	0.542675	0.271337	−	0.962484i	$-0.412534\pi$
$787$	15.2239	0.542675	0.271337	+	0.962484i	$0.412534\pi$
$788$	−17.6943	−0.630332
$789$	11.3715	0.404835
$790$	7.31968	0.260422
$791$	22.9507	0.816034
$792$	1.03219	0.0366774
$793$	35.8182	1.27194
$794$	−28.4868	−1.01096
$795$	1.57562	0.0558814
$796$	−1.82392	−0.0646472
$797$	−6.10160	−0.216130	−0.108065	−	0.994144i	$-0.534465\pi$
$797$	−6.10160	−0.216130	−0.108065	+	0.994144i	$0.534465\pi$
$798$	17.0748	0.604442
$799$	−4.85150	−0.171634
$800$	−1.00000	−0.0353553
$801$	−8.92254	−0.315262
$802$	−23.6666	−0.835696
$803$	−10.4128	−0.367459
$804$	18.7298	0.660548
$805$	−15.8091	−0.557197
$806$	−22.0869	−0.777977
$807$	9.86608	0.347302
$808$	16.6608	0.586124
$809$	−10.4143	−0.366146	−0.183073	−	0.983099i	$-0.558605\pi$
$809$	−10.4143	−0.366146	−0.183073	+	0.983099i	$0.558605\pi$
$810$	4.83800	0.169990
$811$	12.2084	0.428695	0.214348	−	0.976757i	$-0.431237\pi$
$811$	12.2084	0.428695	0.214348	+	0.976757i	$0.431237\pi$
$812$	−4.31476	−0.151418
$813$	−8.30110	−0.291132
$814$	−1.75030	−0.0613481
$815$	−22.0127	−0.771073
$816$	−0.801082	−0.0280435
$817$	−3.41659	−0.119531
$818$	8.60190	0.300759
$819$	8.96336	0.313205
$820$	−2.15603	−0.0752918
$821$	27.9267	0.974648	0.487324	−	0.873221i	$-0.337973\pi$
$821$	27.9267	0.974648	0.487324	+	0.873221i	$0.337973\pi$
$822$	14.7403	0.514127
$823$	34.5460	1.20420	0.602099	−	0.798422i	$-0.294331\pi$
$823$	34.5460	1.20420	0.602099	+	0.798422i	$0.294331\pi$
$824$	−10.3346	−0.360024
$825$	−1.40279	−0.0488387
$826$	−38.8016	−1.35008
$827$	−33.7306	−1.17293	−0.586464	−	0.809975i	$-0.699480\pi$
$827$	−33.7306	−1.17293	−0.586464	+	0.809975i	$0.699480\pi$
$828$	4.58032	0.159177
$829$	12.5358	0.435388	0.217694	−	0.976017i	$-0.430147\pi$
$829$	12.5358	0.435388	0.217694	+	0.976017i	$0.430147\pi$
$830$	−10.0195	−0.347782
$831$	−30.7298	−1.06600
$832$	−2.43746	−0.0845039
$833$	3.25073	0.112631
$834$	10.1736	0.352282
$835$	−7.53307	−0.260693
$836$	3.41659	0.118165
$837$	−51.2541	−1.77160
$838$	−2.33905	−0.0808011
$839$	45.8404	1.58259	0.791293	−	0.611437i	$-0.209408\pi$
$839$	45.8404	1.58259	0.791293	+	0.611437i	$0.209408\pi$
$840$	4.99762	0.172434
$841$	−27.5332	−0.949421
$842$	−12.3054	−0.424071
$843$	11.7408	0.404373
$844$	19.0331	0.655146
$845$	−7.05877	−0.242829
$846$	−8.76903	−0.301485
$847$	3.56264	0.122414
$848$	−1.12321	−0.0385711
$849$	46.0464	1.58031
$850$	−0.571065	−0.0195874
$851$	−7.76691	−0.266246
$852$	−14.1847	−0.485960
$853$	−6.41283	−0.219571	−0.109786	−	0.993955i	$-0.535016\pi$
$853$	−6.41283	−0.219571	−0.109786	+	0.993955i	$0.535016\pi$
$854$	52.3525	1.79147
$855$	−3.52659	−0.120607
$856$	16.6657	0.569623
$857$	−18.6748	−0.637919	−0.318959	−	0.947768i	$-0.603333\pi$
$857$	−18.6748	−0.637919	−0.318959	+	0.947768i	$0.603333\pi$
$858$	−3.41924	−0.116731
$859$	35.9718	1.22734	0.613671	−	0.789562i	$-0.289692\pi$
$859$	35.9718	1.22734	0.613671	+	0.789562i	$0.289692\pi$
$860$	−1.00000	−0.0340997
$861$	10.7750	0.367211
$862$	17.8140	0.606746
$863$	48.2998	1.64414	0.822071	−	0.569384i	$-0.192818\pi$
$863$	48.2998	1.64414	0.822071	+	0.569384i	$0.192818\pi$
$864$	−5.65630	−0.192431
$865$	11.0894	0.377052
$866$	8.77481	0.298180
$867$	23.3899	0.794362
$868$	−32.2825	−1.09574
$869$	−7.31968	−0.248303
$870$	−1.69893	−0.0575992
$871$	32.5446	1.10273
$872$	4.53334	0.153518
$873$	15.4570	0.523141
$874$	15.1610	0.512829
$875$	3.56264	0.120439
$876$	14.6069	0.493521
$877$	−25.3226	−0.855084	−0.427542	−	0.903995i	$-0.640620\pi$
$877$	−25.3226	−0.855084	−0.427542	+	0.903995i	$0.640620\pi$
$878$	−12.5493	−0.423519
$879$	2.87639	0.0970182
$880$	1.00000	0.0337100
$881$	−54.7626	−1.84500	−0.922499	−	0.385998i	$-0.873857\pi$
$881$	−54.7626	−1.84500	−0.922499	+	0.385998i	$0.873857\pi$
$882$	5.87565	0.197843
$883$	−24.5261	−0.825370	−0.412685	−	0.910874i	$-0.635409\pi$
$883$	−24.5261	−0.825370	−0.412685	+	0.910874i	$0.635409\pi$
$884$	−1.39195	−0.0468164
$885$	−15.2781	−0.513567
$886$	−6.99077	−0.234859
$887$	−46.0913	−1.54759	−0.773796	−	0.633434i	$-0.781645\pi$
$887$	−46.0913	−1.54759	−0.773796	+	0.633434i	$0.781645\pi$
$888$	2.45530	0.0823945
$889$	−8.07152	−0.270710
$890$	−8.64425	−0.289756
$891$	−4.83800	−0.162079
$892$	6.57836	0.220260
$893$	−29.0258	−0.971311
$894$	12.7041	0.424887
$895$	9.08113	0.303549
$896$	−3.56264	−0.119019
$897$	−15.1728	−0.506604
$898$	−10.4958	−0.350250
$899$	10.9744	0.366017
$900$	−1.03219	−0.0344064
$901$	−0.641425	−0.0213689
$902$	2.15603	0.0717879
$903$	4.99762	0.166310
$904$	−6.44206	−0.214260
$905$	14.1902	0.471698
$906$	18.1548	0.603154
$907$	−6.86825	−0.228057	−0.114028	−	0.993478i	$-0.536375\pi$
$907$	−6.86825	−0.228057	−0.114028	+	0.993478i	$0.536375\pi$
$908$	5.81320	0.192918
$909$	17.1971	0.570393
$910$	8.68381	0.287865
$911$	−42.3624	−1.40353	−0.701764	−	0.712410i	$-0.747604\pi$
$911$	−42.3624	−1.40353	−0.701764	+	0.712410i	$0.747604\pi$
$912$	−4.79275	−0.158704
$913$	10.0195	0.331597
$914$	−5.49554	−0.181776
$915$	20.6137	0.681469
$916$	23.4664	0.775353
$917$	25.0103	0.825913
$918$	−3.23012	−0.106610
$919$	−24.4710	−0.807225	−0.403612	−	0.914930i	$-0.632246\pi$
$919$	−24.4710	−0.807225	−0.403612	+	0.914930i	$0.632246\pi$
$920$	4.43746	0.146299
$921$	10.2058	0.336293
$922$	−14.0949	−0.464191
$923$	−24.6472	−0.811272
$924$	−4.99762	−0.164410
$925$	1.75030	0.0575496
$926$	5.81097	0.190960
$927$	−10.6673	−0.350361
$928$	1.21111	0.0397567
$929$	−39.1834	−1.28557	−0.642783	−	0.766049i	$-0.722220\pi$
$929$	−39.1834	−1.28557	−0.642783	+	0.766049i	$0.722220\pi$
$930$	−12.7112	−0.416817
$931$	19.4486	0.637402
$932$	24.9211	0.816318
$933$	12.0976	0.396058
$934$	13.1482	0.430221
$935$	0.571065	0.0186758
$936$	−2.51593	−0.0822359
$937$	12.5199	0.409007	0.204504	−	0.978866i	$-0.434442\pi$
$937$	12.5199	0.409007	0.204504	+	0.978866i	$0.434442\pi$
$938$	47.5678	1.55314
$939$	31.6230	1.03198
$940$	−8.49553	−0.277094
$941$	−52.5782	−1.71400	−0.856999	−	0.515317i	$-0.827674\pi$
$941$	−52.5782	−1.71400	−0.856999	+	0.515317i	$0.827674\pi$
$942$	−0.322967	−0.0105228
$943$	9.56730	0.311554
$944$	10.8913	0.354480
$945$	20.1514	0.655524
$946$	1.00000	0.0325128
$947$	−52.9906	−1.72196	−0.860981	−	0.508637i	$-0.830150\pi$
$947$	−52.9906	−1.72196	−0.860981	+	0.508637i	$0.830150\pi$
$948$	10.2679	0.333487
$949$	25.3808	0.823895
$950$	−3.41659	−0.110849
$951$	25.3220	0.821121
$952$	−2.03450	−0.0659385
$953$	37.1238	1.20256	0.601280	−	0.799039i	$-0.294658\pi$
$953$	37.1238	1.20256	0.601280	+	0.799039i	$0.294658\pi$
$954$	−1.15937	−0.0375359
$955$	3.26641	0.105699
$956$	−0.790243	−0.0255583
$957$	1.69893	0.0549187
$958$	−15.9652	−0.515812
$959$	37.4358	1.20886
$960$	−1.40279	−0.0452747
$961$	51.1092	1.64868
$962$	4.26630	0.137551
$963$	17.2022	0.554335
$964$	8.67253	0.279323
$965$	−17.0940	−0.550275
$966$	−22.1767	−0.713525
$967$	−3.43290	−0.110394	−0.0551972	−	0.998475i	$-0.517579\pi$
$967$	−3.43290	−0.110394	−0.0551972	+	0.998475i	$0.517579\pi$
$968$	−1.00000	−0.0321412
$969$	−2.73697	−0.0879242
$970$	14.9749	0.480816
$971$	−31.7997	−1.02050	−0.510251	−	0.860026i	$-0.670448\pi$
$971$	−31.7997	−1.02050	−0.510251	+	0.860026i	$0.670448\pi$
$972$	−10.1822	−0.326595
$973$	25.8377	0.828319
$974$	−0.0999174	−0.00320156
$975$	3.41924	0.109503
$976$	−14.6949	−0.470371
$977$	20.6566	0.660864	0.330432	−	0.943830i	$-0.392806\pi$
$977$	20.6566	0.660864	0.330432	+	0.943830i	$0.392806\pi$
$978$	−30.8792	−0.987407
$979$	8.64425	0.276272
$980$	5.69239	0.181837
$981$	4.67928	0.149398
$982$	35.5843	1.13554
$983$	34.0352	1.08555	0.542777	−	0.839877i	$-0.317373\pi$
$983$	34.0352	1.08555	0.542777	+	0.839877i	$0.317373\pi$
$984$	−3.02445	−0.0964158
$985$	−17.6943	−0.563786
$986$	0.691625	0.0220258
$987$	42.4574	1.35143
$988$	−8.32783	−0.264943
$989$	4.43746	0.141103
$990$	1.03219	0.0328053
$991$	−45.4511	−1.44380	−0.721902	−	0.691996i	$-0.756732\pi$
$991$	−45.4511	−1.44380	−0.721902	+	0.691996i	$0.756732\pi$
$992$	9.06141	0.287700
$993$	47.3086	1.50129
$994$	−36.0247	−1.14263
$995$	−1.82392	−0.0578222
$996$	−14.0552	−0.445356
$997$	−17.9923	−0.569821	−0.284911	−	0.958554i	$-0.591964\pi$
$997$	−17.9923	−0.569821	−0.284911	+	0.958554i	$0.591964\pi$
$998$	−1.80603	−0.0571689
$999$	9.90025	0.313230

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4730.2.a.w.1.4	✓	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4730.2.a.w.1.4	✓	8	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)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -1.40279 q^{3} +1.00000 q^{4} +1.00000 q^{5} +1.40279 q^{6} +3.56264 q^{7} -1.00000 q^{8} -1.03219 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -1.40279 q^{3} +1.00000 q^{4} +1.00000 q^{5} +1.40279 q^{6} +3.56264 q^{7} -1.00000 q^{8} -1.03219 q^{9} -1.00000 q^{10} +1.00000 q^{11} -1.40279 q^{12} -2.43746 q^{13} -3.56264 q^{14} -1.40279 q^{15} +1.00000 q^{16} +0.571065 q^{17} +1.03219 q^{18} +3.41659 q^{19} +1.00000 q^{20} -4.99762 q^{21} -1.00000 q^{22} -4.43746 q^{23} +1.40279 q^{24} +1.00000 q^{25} +2.43746 q^{26} +5.65630 q^{27} +3.56264 q^{28} -1.21111 q^{29} +1.40279 q^{30} -9.06141 q^{31} -1.00000 q^{32} -1.40279 q^{33} -0.571065 q^{34} +3.56264 q^{35} -1.03219 q^{36} +1.75030 q^{37} -3.41659 q^{38} +3.41924 q^{39} -1.00000 q^{40} -2.15603 q^{41} +4.99762 q^{42} -1.00000 q^{43} +1.00000 q^{44} -1.03219 q^{45} +4.43746 q^{46} -8.49553 q^{47} -1.40279 q^{48} +5.69239 q^{49} -1.00000 q^{50} -0.801082 q^{51} -2.43746 q^{52} -1.12321 q^{53} -5.65630 q^{54} +1.00000 q^{55} -3.56264 q^{56} -4.79275 q^{57} +1.21111 q^{58} +10.8913 q^{59} -1.40279 q^{60} -14.6949 q^{61} +9.06141 q^{62} -3.67733 q^{63} +1.00000 q^{64} -2.43746 q^{65} +1.40279 q^{66} -13.3518 q^{67} +0.571065 q^{68} +6.22481 q^{69} -3.56264 q^{70} +10.1118 q^{71} +1.03219 q^{72} -10.4128 q^{73} -1.75030 q^{74} -1.40279 q^{75} +3.41659 q^{76} +3.56264 q^{77} -3.41924 q^{78} -7.31968 q^{79} +1.00000 q^{80} -4.83800 q^{81} +2.15603 q^{82} +10.0195 q^{83} -4.99762 q^{84} +0.571065 q^{85} +1.00000 q^{86} +1.69893 q^{87} -1.00000 q^{88} +8.64425 q^{89} +1.03219 q^{90} -8.68381 q^{91} -4.43746 q^{92} +12.7112 q^{93} +8.49553 q^{94} +3.41659 q^{95} +1.40279 q^{96} -14.9749 q^{97} -5.69239 q^{98} -1.03219 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 8 q^{2} - 7 q^{3} + 8 q^{4} + 8 q^{5} + 7 q^{6} - 6 q^{7} - 8 q^{8} + 7 q^{9}+O(q^{10}) \) 8 * q - 8 * q^2 - 7 * q^3 + 8 * q^4 + 8 * q^5 + 7 * q^6 - 6 * q^7 - 8 * q^8 + 7 * q^9	\( 8 q - 8 q^{2} - 7 q^{3} + 8 q^{4} + 8 q^{5} + 7 q^{6} - 6 q^{7} - 8 q^{8} + 7 q^{9} - 8 q^{10} + 8 q^{11} - 7 q^{12} - 2 q^{13} + 6 q^{14} - 7 q^{15} + 8 q^{16} - 8 q^{17} - 7 q^{18} + 8 q^{20} + 14 q^{21} - 8 q^{22} - 18 q^{23} + 7 q^{24} + 8 q^{25} + 2 q^{26} - 22 q^{27} - 6 q^{28} + 8 q^{29} + 7 q^{30} - 11 q^{31} - 8 q^{32} - 7 q^{33} + 8 q^{34} - 6 q^{35} + 7 q^{36} - 17 q^{37} - 6 q^{39} - 8 q^{40} + 12 q^{41} - 14 q^{42} - 8 q^{43} + 8 q^{44} + 7 q^{45} + 18 q^{46} - 19 q^{47} - 7 q^{48} - 2 q^{49} - 8 q^{50} - q^{51} - 2 q^{52} - 7 q^{53} + 22 q^{54} + 8 q^{55} + 6 q^{56} - 3 q^{57} - 8 q^{58} + q^{59} - 7 q^{60} + 6 q^{61} + 11 q^{62} - 15 q^{63} + 8 q^{64} - 2 q^{65} + 7 q^{66} - 22 q^{67} - 8 q^{68} + 8 q^{69} + 6 q^{70} - 14 q^{71} - 7 q^{72} - 13 q^{73} + 17 q^{74} - 7 q^{75} - 6 q^{77} + 6 q^{78} - 8 q^{79} + 8 q^{80} + 28 q^{81} - 12 q^{82} - 4 q^{83} + 14 q^{84} - 8 q^{85} + 8 q^{86} - 30 q^{87} - 8 q^{88} + 5 q^{89} - 7 q^{90} - 8 q^{91} - 18 q^{92} + q^{93} + 19 q^{94} + 7 q^{96} - 23 q^{97} + 2 q^{98} + 7 q^{99}+O(q^{100}) \) 8 * q - 8 * q^2 - 7 * q^3 + 8 * q^4 + 8 * q^5 + 7 * q^6 - 6 * q^7 - 8 * q^8 + 7 * q^9 - 8 * q^10 + 8 * q^11 - 7 * q^12 - 2 * q^13 + 6 * q^14 - 7 * q^15 + 8 * q^16 - 8 * q^17 - 7 * q^18 + 8 * q^20 + 14 * q^21 - 8 * q^22 - 18 * q^23 + 7 * q^24 + 8 * q^25 + 2 * q^26 - 22 * q^27 - 6 * q^28 + 8 * q^29 + 7 * q^30 - 11 * q^31 - 8 * q^32 - 7 * q^33 + 8 * q^34 - 6 * q^35 + 7 * q^36 - 17 * q^37 - 6 * q^39 - 8 * q^40 + 12 * q^41 - 14 * q^42 - 8 * q^43 + 8 * q^44 + 7 * q^45 + 18 * q^46 - 19 * q^47 - 7 * q^48 - 2 * q^49 - 8 * q^50 - q^51 - 2 * q^52 - 7 * q^53 + 22 * q^54 + 8 * q^55 + 6 * q^56 - 3 * q^57 - 8 * q^58 + q^59 - 7 * q^60 + 6 * q^61 + 11 * q^62 - 15 * q^63 + 8 * q^64 - 2 * q^65 + 7 * q^66 - 22 * q^67 - 8 * q^68 + 8 * q^69 + 6 * q^70 - 14 * q^71 - 7 * q^72 - 13 * q^73 + 17 * q^74 - 7 * q^75 - 6 * q^77 + 6 * q^78 - 8 * q^79 + 8 * q^80 + 28 * q^81 - 12 * q^82 - 4 * q^83 + 14 * q^84 - 8 * q^85 + 8 * q^86 - 30 * q^87 - 8 * q^88 + 5 * q^89 - 7 * q^90 - 8 * q^91 - 18 * q^92 + q^93 + 19 * q^94 + 7 * q^96 - 23 * q^97 + 2 * q^98 + 7 * q^99

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