LMFDB - Embedded newform 4730.2.a.z.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("4730.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	yes
Analytic conductor:	$37.7692401561$
Analytic rank:	$0$
Dimension:	$10$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - 2x^{9} - 17x^{8} + 21x^{7} + 107x^{6} - 45x^{5} - 262x^{4} - 47x^{3} + 120x^{2} - 2x - 6 $ x^10 - 2x^9 - 17x^8 + 21x^7 + 107x^6 - 45x^5 - 262x^4 - 47x^3 + 120x^2 - 2*x - 6
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$2.27147$ 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)

$f(q)$	$=$	$q-1.00000 q^{2} -1.27147 q^{3} +1.00000 q^{4} +1.00000 q^{5} +1.27147 q^{6} -0.316678 q^{7} -1.00000 q^{8} -1.38335 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -1.27147 q^{3} +1.00000 q^{4} +1.00000 q^{5} +1.27147 q^{6} -0.316678 q^{7} -1.00000 q^{8} -1.38335 q^{9} -1.00000 q^{10} +1.00000 q^{11} -1.27147 q^{12} -0.503303 q^{13} +0.316678 q^{14} -1.27147 q^{15} +1.00000 q^{16} -3.04381 q^{17} +1.38335 q^{18} -5.80916 q^{19} +1.00000 q^{20} +0.402648 q^{21} -1.00000 q^{22} -9.28218 q^{23} +1.27147 q^{24} +1.00000 q^{25} +0.503303 q^{26} +5.57332 q^{27} -0.316678 q^{28} -7.93811 q^{29} +1.27147 q^{30} +1.74862 q^{31} -1.00000 q^{32} -1.27147 q^{33} +3.04381 q^{34} -0.316678 q^{35} -1.38335 q^{36} +8.96829 q^{37} +5.80916 q^{38} +0.639936 q^{39} -1.00000 q^{40} -0.430252 q^{41} -0.402648 q^{42} +1.00000 q^{43} +1.00000 q^{44} -1.38335 q^{45} +9.28218 q^{46} +10.5211 q^{47} -1.27147 q^{48} -6.89972 q^{49} -1.00000 q^{50} +3.87013 q^{51} -0.503303 q^{52} +4.68904 q^{53} -5.57332 q^{54} +1.00000 q^{55} +0.316678 q^{56} +7.38620 q^{57} +7.93811 q^{58} -2.98409 q^{59} -1.27147 q^{60} -7.67431 q^{61} -1.74862 q^{62} +0.438077 q^{63} +1.00000 q^{64} -0.503303 q^{65} +1.27147 q^{66} +9.75924 q^{67} -3.04381 q^{68} +11.8021 q^{69} +0.316678 q^{70} +3.96679 q^{71} +1.38335 q^{72} +3.46098 q^{73} -8.96829 q^{74} -1.27147 q^{75} -5.80916 q^{76} -0.316678 q^{77} -0.639936 q^{78} +5.32454 q^{79} +1.00000 q^{80} -2.93627 q^{81} +0.430252 q^{82} -10.1475 q^{83} +0.402648 q^{84} -3.04381 q^{85} -1.00000 q^{86} +10.0931 q^{87} -1.00000 q^{88} +5.40924 q^{89} +1.38335 q^{90} +0.159385 q^{91} -9.28218 q^{92} -2.22333 q^{93} -10.5211 q^{94} -5.80916 q^{95} +1.27147 q^{96} -1.27905 q^{97} +6.89972 q^{98} -1.38335 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q - 10 q^{2} + 8 q^{3} + 10 q^{4} + 10 q^{5} - 8 q^{6} + 3 q^{7} - 10 q^{8} + 14 q^{9}+O(q^{10}) $ 10 * q - 10 * q^2 + 8 * q^3 + 10 * q^4 + 10 * q^5 - 8 * q^6 + 3 * q^7 - 10 * q^8 + 14 * q^9	\( 10 q - 10 q^{2} + 8 q^{3} + 10 q^{4} + 10 q^{5} - 8 q^{6} + 3 q^{7} - 10 q^{8} + 14 q^{9} - 10 q^{10} + 10 q^{11} + 8 q^{12} + 7 q^{13} - 3 q^{14} + 8 q^{15} + 10 q^{16} + 2 q^{17} - 14 q^{18} - 7 q^{19} + 10 q^{20} - 2 q^{21} - 10 q^{22} + 12 q^{23} - 8 q^{24} + 10 q^{25} - 7 q^{26} + 23 q^{27} + 3 q^{28} - 12 q^{29} - 8 q^{30} + 16 q^{31} - 10 q^{32} + 8 q^{33} - 2 q^{34} + 3 q^{35} + 14 q^{36} + 19 q^{37} + 7 q^{38} + 6 q^{39} - 10 q^{40} + 9 q^{41} + 2 q^{42} + 10 q^{43} + 10 q^{44} + 14 q^{45} - 12 q^{46} + 29 q^{47} + 8 q^{48} + 23 q^{49} - 10 q^{50} - 7 q^{51} + 7 q^{52} + 6 q^{53} - 23 q^{54} + 10 q^{55} - 3 q^{56} + 23 q^{57} + 12 q^{58} + 29 q^{59} + 8 q^{60} - 4 q^{61} - 16 q^{62} + 10 q^{64} + 7 q^{65} - 8 q^{66} + 45 q^{67} + 2 q^{68} + 24 q^{69} - 3 q^{70} - 18 q^{71} - 14 q^{72} + 3 q^{73} - 19 q^{74} + 8 q^{75} - 7 q^{76} + 3 q^{77} - 6 q^{78} - 14 q^{79} + 10 q^{80} + 6 q^{81} - 9 q^{82} + 23 q^{83} - 2 q^{84} + 2 q^{85} - 10 q^{86} + 25 q^{87} - 10 q^{88} + q^{89} - 14 q^{90} + q^{91} + 12 q^{92} + 35 q^{93} - 29 q^{94} - 7 q^{95} - 8 q^{96} + 30 q^{97} - 23 q^{98} + 14 q^{99}+O(q^{100}) \) 10 * q - 10 * q^2 + 8 * q^3 + 10 * q^4 + 10 * q^5 - 8 * q^6 + 3 * q^7 - 10 * q^8 + 14 * q^9 - 10 * q^10 + 10 * q^11 + 8 * q^12 + 7 * q^13 - 3 * q^14 + 8 * q^15 + 10 * q^16 + 2 * q^17 - 14 * q^18 - 7 * q^19 + 10 * q^20 - 2 * q^21 - 10 * q^22 + 12 * q^23 - 8 * q^24 + 10 * q^25 - 7 * q^26 + 23 * q^27 + 3 * q^28 - 12 * q^29 - 8 * q^30 + 16 * q^31 - 10 * q^32 + 8 * q^33 - 2 * q^34 + 3 * q^35 + 14 * q^36 + 19 * q^37 + 7 * q^38 + 6 * q^39 - 10 * q^40 + 9 * q^41 + 2 * q^42 + 10 * q^43 + 10 * q^44 + 14 * q^45 - 12 * q^46 + 29 * q^47 + 8 * q^48 + 23 * q^49 - 10 * q^50 - 7 * q^51 + 7 * q^52 + 6 * q^53 - 23 * q^54 + 10 * q^55 - 3 * q^56 + 23 * q^57 + 12 * q^58 + 29 * q^59 + 8 * q^60 - 4 * q^61 - 16 * q^62 + 10 * q^64 + 7 * q^65 - 8 * q^66 + 45 * q^67 + 2 * q^68 + 24 * q^69 - 3 * q^70 - 18 * q^71 - 14 * q^72 + 3 * q^73 - 19 * q^74 + 8 * q^75 - 7 * q^76 + 3 * q^77 - 6 * q^78 - 14 * q^79 + 10 * q^80 + 6 * q^81 - 9 * q^82 + 23 * q^83 - 2 * q^84 + 2 * q^85 - 10 * q^86 + 25 * q^87 - 10 * q^88 + q^89 - 14 * q^90 + q^91 + 12 * q^92 + 35 * q^93 - 29 * q^94 - 7 * q^95 - 8 * q^96 + 30 * q^97 - 23 * q^98 + 14 * 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
$3$	−1.27147	−0.734086	−0.367043	−	0.930204i	$-0.619630\pi$
$3$	−1.27147	−0.734086	−0.367043	+	0.930204i	$0.619630\pi$
$4$	1.00000	0.500000
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	1.27147	0.519077
$7$	−0.316678	−0.119693	−0.0598465	−	0.998208i	$-0.519061\pi$
$7$	−0.316678	−0.119693	−0.0598465	+	0.998208i	$0.519061\pi$
$8$	−1.00000	−0.353553
$9$	−1.38335	−0.461118
$10$	−1.00000	−0.316228
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	−1.27147	−0.367043
$13$	−0.503303	−0.139591	−0.0697955	−	0.997561i	$-0.522235\pi$
$13$	−0.503303	−0.139591	−0.0697955	+	0.997561i	$0.522235\pi$
$14$	0.316678	0.0846357
$15$	−1.27147	−0.328293
$16$	1.00000	0.250000
$17$	−3.04381	−0.738233	−0.369117	−	0.929383i	$-0.620340\pi$
$17$	−3.04381	−0.738233	−0.369117	+	0.929383i	$0.620340\pi$
$18$	1.38335	0.326060
$19$	−5.80916	−1.33271	−0.666356	−	0.745633i	$-0.732147\pi$
$19$	−5.80916	−1.33271	−0.666356	+	0.745633i	$0.732147\pi$
$20$	1.00000	0.223607
$21$	0.402648	0.0878649
$22$	−1.00000	−0.213201
$23$	−9.28218	−1.93547	−0.967734	−	0.251973i	$-0.918921\pi$
$23$	−9.28218	−1.93547	−0.967734	+	0.251973i	$0.918921\pi$
$24$	1.27147	0.259539
$25$	1.00000	0.200000
$26$	0.503303	0.0987058
$27$	5.57332	1.07259
$28$	−0.316678	−0.0598465
$29$	−7.93811	−1.47407	−0.737035	−	0.675854i	$-0.763775\pi$
$29$	−7.93811	−1.47407	−0.737035	+	0.675854i	$0.763775\pi$
$30$	1.27147	0.232138
$31$	1.74862	0.314062	0.157031	−	0.987594i	$-0.449808\pi$
$31$	1.74862	0.314062	0.157031	+	0.987594i	$0.449808\pi$
$32$	−1.00000	−0.176777
$33$	−1.27147	−0.221335
$34$	3.04381	0.522010
$35$	−0.316678	−0.0535283
$36$	−1.38335	−0.230559
$37$	8.96829	1.47438	0.737189	−	0.675686i	$-0.236153\pi$
$37$	8.96829	1.47438	0.737189	+	0.675686i	$0.236153\pi$
$38$	5.80916	0.942370
$39$	0.639936	0.102472
$40$	−1.00000	−0.158114
$41$	−0.430252	−0.0671940	−0.0335970	−	0.999435i	$-0.510696\pi$
$41$	−0.430252	−0.0671940	−0.0335970	+	0.999435i	$0.510696\pi$
$42$	−0.402648	−0.0621299
$43$	1.00000	0.152499
$43$	1.00000	0.152499
$44$	1.00000	0.150756
$45$	−1.38335	−0.206218
$46$	9.28218	1.36858
$47$	10.5211	1.53466	0.767330	−	0.641252i	$-0.221585\pi$
$47$	10.5211	1.53466	0.767330	+	0.641252i	$0.221585\pi$
$48$	−1.27147	−0.183521
$49$	−6.89972	−0.985674
$50$	−1.00000	−0.141421
$51$	3.87013	0.541927
$52$	−0.503303	−0.0697955
$53$	4.68904	0.644089	0.322044	−	0.946725i	$-0.395630\pi$
$53$	4.68904	0.644089	0.322044	+	0.946725i	$0.395630\pi$
$54$	−5.57332	−0.758433
$55$	1.00000	0.134840
$56$	0.316678	0.0423178
$57$	7.38620	0.978326
$58$	7.93811	1.04233
$59$	−2.98409	−0.388496	−0.194248	−	0.980952i	$-0.562227\pi$
$59$	−2.98409	−0.388496	−0.194248	+	0.980952i	$0.562227\pi$
$60$	−1.27147	−0.164147
$61$	−7.67431	−0.982594	−0.491297	−	0.870992i	$-0.663477\pi$
$61$	−7.67431	−0.982594	−0.491297	+	0.870992i	$0.663477\pi$
$62$	−1.74862	−0.222075
$63$	0.438077	0.0551926
$64$	1.00000	0.125000
$65$	−0.503303	−0.0624270
$66$	1.27147	0.156508
$67$	9.75924	1.19228	0.596140	−	0.802880i	$-0.296700\pi$
$67$	9.75924	1.19228	0.596140	+	0.802880i	$0.296700\pi$
$68$	−3.04381	−0.369117
$69$	11.8021	1.42080
$70$	0.316678	0.0378502
$71$	3.96679	0.470771	0.235385	−	0.971902i	$-0.424365\pi$
$71$	3.96679	0.470771	0.235385	+	0.971902i	$0.424365\pi$
$72$	1.38335	0.163030
$73$	3.46098	0.405077	0.202539	−	0.979274i	$-0.435081\pi$
$73$	3.46098	0.405077	0.202539	+	0.979274i	$0.435081\pi$
$74$	−8.96829	−1.04254
$75$	−1.27147	−0.146817
$76$	−5.80916	−0.666356
$77$	−0.316678	−0.0360888
$78$	−0.639936	−0.0724585
$79$	5.32454	0.599058	0.299529	−	0.954087i	$-0.403171\pi$
$79$	5.32454	0.599058	0.299529	+	0.954087i	$0.403171\pi$
$80$	1.00000	0.111803
$81$	−2.93627	−0.326252
$82$	0.430252	0.0475134
$83$	−10.1475	−1.11383	−0.556914	−	0.830570i	$-0.688015\pi$
$83$	−10.1475	−1.11383	−0.556914	+	0.830570i	$0.688015\pi$
$84$	0.402648	0.0439324
$85$	−3.04381	−0.330148
$86$	−1.00000	−0.107833
$87$	10.0931	1.08209
$88$	−1.00000	−0.106600
$89$	5.40924	0.573378	0.286689	−	0.958024i	$-0.407445\pi$
$89$	5.40924	0.573378	0.286689	+	0.958024i	$0.407445\pi$
$90$	1.38335	0.145818
$91$	0.159385	0.0167081
$92$	−9.28218	−0.967734
$93$	−2.22333	−0.230548
$94$	−10.5211	−1.08517
$95$	−5.80916	−0.596007
$96$	1.27147	0.129769
$97$	−1.27905	−0.129868	−0.0649341	−	0.997890i	$-0.520684\pi$
$97$	−1.27905	−0.129868	−0.0649341	+	0.997890i	$0.520684\pi$
$98$	6.89972	0.696976
$99$	−1.38335	−0.139032
$100$	1.00000	0.100000
$101$	−7.34467	−0.730822	−0.365411	−	0.930846i	$-0.619072\pi$
$101$	−7.34467	−0.730822	−0.365411	+	0.930846i	$0.619072\pi$
$102$	−3.87013	−0.383200
$103$	−1.97820	−0.194918	−0.0974591	−	0.995240i	$-0.531072\pi$
$103$	−1.97820	−0.194918	−0.0974591	+	0.995240i	$0.531072\pi$
$104$	0.503303	0.0493529
$105$	0.402648	0.0392944
$106$	−4.68904	−0.455440
$107$	10.5975	1.02450	0.512248	−	0.858837i	$-0.328813\pi$
$107$	10.5975	1.02450	0.512248	+	0.858837i	$0.328813\pi$
$108$	5.57332	0.536293
$109$	5.64929	0.541104	0.270552	−	0.962705i	$-0.412794\pi$
$109$	5.64929	0.541104	0.270552	+	0.962705i	$0.412794\pi$
$110$	−1.00000	−0.0953463
$111$	−11.4030	−1.08232
$112$	−0.316678	−0.0299232
$113$	15.4883	1.45701	0.728506	−	0.685039i	$-0.240215\pi$
$113$	15.4883	1.45701	0.728506	+	0.685039i	$0.240215\pi$
$114$	−7.38620	−0.691781
$115$	−9.28218	−0.865568
$116$	−7.93811	−0.737035
$117$	0.696246	0.0643679
$118$	2.98409	0.274708
$119$	0.963908	0.0883613
$120$	1.27147	0.116069
$121$	1.00000	0.0909091
$122$	7.67431	0.694799
$123$	0.547054	0.0493262
$124$	1.74862	0.157031
$125$	1.00000	0.0894427
$126$	−0.438077	−0.0390270
$127$	20.8483	1.84999	0.924994	−	0.379982i	$-0.124070\pi$
$127$	20.8483	1.84999	0.924994	+	0.379982i	$0.124070\pi$
$128$	−1.00000	−0.0883883
$129$	−1.27147	−0.111947
$130$	0.503303	0.0441426
$131$	−0.202318	−0.0176766	−0.00883829	−	0.999961i	$-0.502813\pi$
$131$	−0.202318	−0.0176766	−0.00883829	+	0.999961i	$0.502813\pi$
$132$	−1.27147	−0.110668
$133$	1.83963	0.159516
$134$	−9.75924	−0.843070
$135$	5.57332	0.479675
$136$	3.04381	0.261005
$137$	−15.8441	−1.35366	−0.676828	−	0.736141i	$-0.736646\pi$
$137$	−15.8441	−1.35366	−0.676828	+	0.736141i	$0.736646\pi$
$138$	−11.8021	−1.00466
$139$	−2.71120	−0.229961	−0.114980	−	0.993368i	$-0.536681\pi$
$139$	−2.71120	−0.229961	−0.114980	+	0.993368i	$0.536681\pi$
$140$	−0.316678	−0.0267642
$141$	−13.3773	−1.12657
$142$	−3.96679	−0.332885
$143$	−0.503303	−0.0420883
$144$	−1.38335	−0.115279
$145$	−7.93811	−0.659224
$146$	−3.46098	−0.286433
$147$	8.77281	0.723569
$148$	8.96829	0.737189
$149$	10.9149	0.894187	0.447093	−	0.894487i	$-0.352459\pi$
$149$	10.9149	0.894187	0.447093	+	0.894487i	$0.352459\pi$
$150$	1.27147	0.103815
$151$	−0.0709238	−0.00577169	−0.00288585	−	0.999996i	$-0.500919\pi$
$151$	−0.0709238	−0.00577169	−0.00288585	+	0.999996i	$0.500919\pi$
$152$	5.80916	0.471185
$153$	4.21067	0.340413
$154$	0.316678	0.0255186
$155$	1.74862	0.140453
$156$	0.639936	0.0512359
$157$	−18.4300	−1.47087	−0.735437	−	0.677593i	$-0.763023\pi$
$157$	−18.4300	−1.47087	−0.735437	+	0.677593i	$0.763023\pi$
$158$	−5.32454	−0.423598
$159$	−5.96199	−0.472817
$160$	−1.00000	−0.0790569
$161$	2.93946	0.231662
$162$	2.93627	0.230695
$163$	8.53284	0.668344	0.334172	−	0.942512i	$-0.391543\pi$
$163$	8.53284	0.668344	0.334172	+	0.942512i	$0.391543\pi$
$164$	−0.430252	−0.0335970
$165$	−1.27147	−0.0989841
$166$	10.1475	0.787595
$167$	−5.40437	−0.418202	−0.209101	−	0.977894i	$-0.567054\pi$
$167$	−5.40437	−0.418202	−0.209101	+	0.977894i	$0.567054\pi$
$168$	−0.402648	−0.0310649
$169$	−12.7467	−0.980514
$170$	3.04381	0.233450
$171$	8.03612	0.614538
$172$	1.00000	0.0762493
$173$	6.57690	0.500033	0.250016	−	0.968242i	$-0.419564\pi$
$173$	6.57690	0.500033	0.250016	+	0.968242i	$0.419564\pi$
$174$	−10.0931	−0.765156
$175$	−0.316678	−0.0239386
$176$	1.00000	0.0753778
$177$	3.79419	0.285189
$178$	−5.40924	−0.405440
$179$	3.79891	0.283944	0.141972	−	0.989871i	$-0.454656\pi$
$179$	3.79891	0.283944	0.141972	+	0.989871i	$0.454656\pi$
$180$	−1.38335	−0.103109
$181$	7.79219	0.579189	0.289594	−	0.957149i	$-0.406480\pi$
$181$	7.79219	0.579189	0.289594	+	0.957149i	$0.406480\pi$
$182$	−0.159385	−0.0118144
$183$	9.75768	0.721308
$184$	9.28218	0.684291
$185$	8.96829	0.659362
$186$	2.22333	0.163022
$187$	−3.04381	−0.222586
$188$	10.5211	0.767330
$189$	−1.76495	−0.128381
$190$	5.80916	0.421441
$191$	−18.6062	−1.34630	−0.673149	−	0.739507i	$-0.735059\pi$
$191$	−18.6062	−1.34630	−0.673149	+	0.739507i	$0.735059\pi$
$192$	−1.27147	−0.0917607
$193$	−8.43218	−0.606961	−0.303481	−	0.952838i	$-0.598149\pi$
$193$	−8.43218	−0.606961	−0.303481	+	0.952838i	$0.598149\pi$
$194$	1.27905	0.0918306
$195$	0.639936	0.0458268
$196$	−6.89972	−0.492837
$197$	12.9260	0.920939	0.460470	−	0.887675i	$-0.347681\pi$
$197$	12.9260	0.920939	0.460470	+	0.887675i	$0.347681\pi$
$198$	1.38335	0.0983107
$199$	27.8773	1.97617	0.988084	−	0.153915i	$-0.0491883\pi$
$199$	27.8773	1.97617	0.988084	+	0.153915i	$0.0491883\pi$
$200$	−1.00000	−0.0707107
$201$	−12.4086	−0.875236
$202$	7.34467	0.516769
$203$	2.51382	0.176436
$204$	3.87013	0.270963
$205$	−0.430252	−0.0300501
$206$	1.97820	0.137828
$207$	12.8405	0.892479
$208$	−0.503303	−0.0348978
$209$	−5.80916	−0.401828
$210$	−0.402648	−0.0277853
$211$	−4.31767	−0.297241	−0.148620	−	0.988894i	$-0.547483\pi$
$211$	−4.31767	−0.297241	−0.148620	+	0.988894i	$0.547483\pi$
$212$	4.68904	0.322044
$213$	−5.04367	−0.345586
$214$	−10.5975	−0.724429
$215$	1.00000	0.0681994
$216$	−5.57332	−0.379216
$217$	−0.553750	−0.0375910
$218$	−5.64929	−0.382618
$219$	−4.40055	−0.297361
$220$	1.00000	0.0674200
$221$	1.53196	0.103051
$222$	11.4030	0.765316
$223$	11.4206	0.764777	0.382389	−	0.924002i	$-0.375102\pi$
$223$	11.4206	0.764777	0.382389	+	0.924002i	$0.375102\pi$
$224$	0.316678	0.0211589
$225$	−1.38335	−0.0922236
$226$	−15.4883	−1.03026
$227$	19.4623	1.29176	0.645878	−	0.763441i	$-0.276492\pi$
$227$	19.4623	1.29176	0.645878	+	0.763441i	$0.276492\pi$
$228$	7.38620	0.489163
$229$	−10.7545	−0.710678	−0.355339	−	0.934738i	$-0.615635\pi$
$229$	−10.7545	−0.710678	−0.355339	+	0.934738i	$0.615635\pi$
$230$	9.28218	0.612049
$231$	0.402648	0.0264923
$232$	7.93811	0.521163
$233$	−15.2663	−1.00013	−0.500065	−	0.865988i	$-0.666690\pi$
$233$	−15.2663	−1.00013	−0.500065	+	0.865988i	$0.666690\pi$
$234$	−0.696246	−0.0455150
$235$	10.5211	0.686321
$236$	−2.98409	−0.194248
$237$	−6.77002	−0.439760
$238$	−0.963908	−0.0624809
$239$	−4.58174	−0.296368	−0.148184	−	0.988960i	$-0.547343\pi$
$239$	−4.58174	−0.296368	−0.148184	+	0.988960i	$0.547343\pi$
$240$	−1.27147	−0.0820733
$241$	14.3755	0.926010	0.463005	−	0.886356i	$-0.346771\pi$
$241$	14.3755	0.926010	0.463005	+	0.886356i	$0.346771\pi$
$242$	−1.00000	−0.0642824
$243$	−12.9866	−0.833089
$244$	−7.67431	−0.491297
$245$	−6.89972	−0.440807
$246$	−0.547054	−0.0348789
$247$	2.92377	0.186035
$248$	−1.74862	−0.111038
$249$	12.9022	0.817645
$250$	−1.00000	−0.0632456
$251$	4.99686	0.315399	0.157700	−	0.987487i	$-0.449592\pi$
$251$	4.99686	0.315399	0.157700	+	0.987487i	$0.449592\pi$
$252$	0.438077	0.0275963
$253$	−9.28218	−0.583566
$254$	−20.8483	−1.30814
$255$	3.87013	0.242357
$256$	1.00000	0.0625000
$257$	−18.2445	−1.13806	−0.569032	−	0.822316i	$-0.692682\pi$
$257$	−18.2445	−1.13806	−0.569032	+	0.822316i	$0.692682\pi$
$258$	1.27147	0.0791585
$259$	−2.84006	−0.176473
$260$	−0.503303	−0.0312135
$261$	10.9812	0.679720
$262$	0.202318	0.0124992
$263$	−5.51612	−0.340139	−0.170069	−	0.985432i	$-0.554399\pi$
$263$	−5.51612	−0.340139	−0.170069	+	0.985432i	$0.554399\pi$
$264$	1.27147	0.0782538
$265$	4.68904	0.288045
$266$	−1.83963	−0.112795
$267$	−6.87771	−0.420909
$268$	9.75924	0.596140
$269$	8.01104	0.488441	0.244221	−	0.969720i	$-0.421468\pi$
$269$	8.01104	0.488441	0.244221	+	0.969720i	$0.421468\pi$
$270$	−5.57332	−0.339181
$271$	−29.9694	−1.82051	−0.910255	−	0.414048i	$-0.864115\pi$
$271$	−29.9694	−1.82051	−0.910255	+	0.414048i	$0.864115\pi$
$272$	−3.04381	−0.184558
$273$	−0.202654	−0.0122652
$274$	15.8441	0.957179
$275$	1.00000	0.0603023
$276$	11.8021	0.710400
$277$	−2.09014	−0.125584	−0.0627921	−	0.998027i	$-0.520001\pi$
$277$	−2.09014	−0.125584	−0.0627921	+	0.998027i	$0.520001\pi$
$278$	2.71120	0.162607
$279$	−2.41896	−0.144820
$280$	0.316678	0.0189251
$281$	31.3635	1.87099	0.935495	−	0.353340i	$-0.114954\pi$
$281$	31.3635	1.87099	0.935495	+	0.353340i	$0.114954\pi$
$282$	13.3773	0.796607
$283$	0.751951	0.0446988	0.0223494	−	0.999750i	$-0.492885\pi$
$283$	0.751951	0.0446988	0.0223494	+	0.999750i	$0.492885\pi$
$284$	3.96679	0.235385
$285$	7.38620	0.437520
$286$	0.503303	0.0297609
$287$	0.136251	0.00804265
$288$	1.38335	0.0815149
$289$	−7.73519	−0.455011
$290$	7.93811	0.466142
$291$	1.62628	0.0953343
$292$	3.46098	0.202539
$293$	−16.8372	−0.983640	−0.491820	−	0.870697i	$-0.663668\pi$
$293$	−16.8372	−0.983640	−0.491820	+	0.870697i	$0.663668\pi$
$294$	−8.77281	−0.511641
$295$	−2.98409	−0.173740
$296$	−8.96829	−0.521271
$297$	5.57332	0.323397
$298$	−10.9149	−0.632285
$299$	4.67175	0.270174
$300$	−1.27147	−0.0734086
$301$	−0.316678	−0.0182530
$302$	0.0709238	0.00408120
$303$	9.33856	0.536486
$304$	−5.80916	−0.333178
$305$	−7.67431	−0.439429
$306$	−4.21067	−0.240708
$307$	−2.41881	−0.138049	−0.0690243	−	0.997615i	$-0.521989\pi$
$307$	−2.41881	−0.138049	−0.0690243	+	0.997615i	$0.521989\pi$
$308$	−0.316678	−0.0180444
$309$	2.51523	0.143087
$310$	−1.74862	−0.0993151
$311$	29.5823	1.67746	0.838728	−	0.544551i	$-0.183300\pi$
$311$	29.5823	1.67746	0.838728	+	0.544551i	$0.183300\pi$
$312$	−0.639936	−0.0362293
$313$	26.2434	1.48336	0.741681	−	0.670753i	$-0.234029\pi$
$313$	26.2434	1.48336	0.741681	+	0.670753i	$0.234029\pi$
$314$	18.4300	1.04007
$315$	0.438077	0.0246829
$316$	5.32454	0.299529
$317$	−10.6549	−0.598439	−0.299219	−	0.954184i	$-0.596726\pi$
$317$	−10.6549	−0.598439	−0.299219	+	0.954184i	$0.596726\pi$
$318$	5.96199	0.334332
$319$	−7.93811	−0.444449
$320$	1.00000	0.0559017
$321$	−13.4744	−0.752069
$322$	−2.93946	−0.163810
$323$	17.6820	0.983853
$324$	−2.93627	−0.163126
$325$	−0.503303	−0.0279182
$326$	−8.53284	−0.472590
$327$	−7.18293	−0.397217
$328$	0.430252	0.0237567
$329$	−3.33180	−0.183688
$330$	1.27147	0.0699923
$331$	14.8383	0.815587	0.407794	−	0.913074i	$-0.366298\pi$
$331$	14.8383	0.815587	0.407794	+	0.913074i	$0.366298\pi$
$332$	−10.1475	−0.556914
$333$	−12.4063	−0.679862
$334$	5.40437	0.295714
$335$	9.75924	0.533204
$336$	0.402648	0.0219662
$337$	31.7045	1.72706	0.863528	−	0.504300i	$-0.168250\pi$
$337$	31.7045	1.72706	0.863528	+	0.504300i	$0.168250\pi$
$338$	12.7467	0.693328
$339$	−19.6929	−1.06957
$340$	−3.04381	−0.165074
$341$	1.74862	0.0946932
$342$	−8.03612	−0.434544
$343$	4.40173	0.237671
$344$	−1.00000	−0.0539164
$345$	11.8021	0.635401
$346$	−6.57690	−0.353577
$347$	−14.8944	−0.799573	−0.399786	−	0.916608i	$-0.630916\pi$
$347$	−14.8944	−0.799573	−0.399786	+	0.916608i	$0.630916\pi$
$348$	10.0931	0.541047
$349$	1.05540	0.0564945	0.0282472	−	0.999601i	$-0.491007\pi$
$349$	1.05540	0.0564945	0.0282472	+	0.999601i	$0.491007\pi$
$350$	0.316678	0.0169271
$351$	−2.80507	−0.149723
$352$	−1.00000	−0.0533002
$353$	−3.97273	−0.211447	−0.105724	−	0.994396i	$-0.533716\pi$
$353$	−3.97273	−0.211447	−0.105724	+	0.994396i	$0.533716\pi$
$354$	−3.79419	−0.201659
$355$	3.96679	0.210535
$356$	5.40924	0.286689
$357$	−1.22558	−0.0648648
$358$	−3.79891	−0.200779
$359$	13.7528	0.725847	0.362924	−	0.931819i	$-0.381779\pi$
$359$	13.7528	0.725847	0.362924	+	0.931819i	$0.381779\pi$
$360$	1.38335	0.0729091
$361$	14.7463	0.776123
$362$	−7.79219	−0.409548
$363$	−1.27147	−0.0667351
$364$	0.159385	0.00835403
$365$	3.46098	0.181156
$366$	−9.75768	−0.510042
$367$	17.0155	0.888204	0.444102	−	0.895976i	$-0.353523\pi$
$367$	17.0155	0.888204	0.444102	+	0.895976i	$0.353523\pi$
$368$	−9.28218	−0.483867
$369$	0.595191	0.0309844
$370$	−8.96829	−0.466239
$371$	−1.48491	−0.0770929
$372$	−2.22333	−0.115274
$373$	23.1769	1.20006	0.600028	−	0.799979i	$-0.295156\pi$
$373$	23.1769	1.20006	0.600028	+	0.799979i	$0.295156\pi$
$374$	3.04381	0.157392
$375$	−1.27147	−0.0656586
$376$	−10.5211	−0.542584
$377$	3.99527	0.205767
$378$	1.76495	0.0907791
$379$	−2.91256	−0.149608	−0.0748042	−	0.997198i	$-0.523833\pi$
$379$	−2.91256	−0.149608	−0.0748042	+	0.997198i	$0.523833\pi$
$380$	−5.80916	−0.298004
$381$	−26.5081	−1.35805
$382$	18.6062	0.951976
$383$	27.9708	1.42924	0.714621	−	0.699512i	$-0.246599\pi$
$383$	27.9708	1.42924	0.714621	+	0.699512i	$0.246599\pi$
$384$	1.27147	0.0648846
$385$	−0.316678	−0.0161394
$386$	8.43218	0.429186
$387$	−1.38335	−0.0703198
$388$	−1.27905	−0.0649341
$389$	26.3452	1.33575	0.667877	−	0.744272i	$-0.267203\pi$
$389$	26.3452	1.33575	0.667877	+	0.744272i	$0.267203\pi$
$390$	−0.639936	−0.0324044
$391$	28.2532	1.42883
$392$	6.89972	0.348488
$393$	0.257242	0.0129761
$394$	−12.9260	−0.651202
$395$	5.32454	0.267907
$396$	−1.38335	−0.0695161
$397$	9.86779	0.495250	0.247625	−	0.968856i	$-0.420350\pi$
$397$	9.86779	0.495250	0.247625	+	0.968856i	$0.420350\pi$
$398$	−27.8773	−1.39736
$399$	−2.33904	−0.117099
$400$	1.00000	0.0500000
$401$	−8.21715	−0.410345	−0.205172	−	0.978726i	$-0.565775\pi$
$401$	−8.21715	−0.410345	−0.205172	+	0.978726i	$0.565775\pi$
$402$	12.4086	0.618886
$403$	−0.880086	−0.0438402
$404$	−7.34467	−0.365411
$405$	−2.93627	−0.145904
$406$	−2.51382	−0.124759
$407$	8.96829	0.444542
$408$	−3.87013	−0.191600
$409$	24.7206	1.22236	0.611179	−	0.791493i	$-0.290696\pi$
$409$	24.7206	1.22236	0.611179	+	0.791493i	$0.290696\pi$
$410$	0.430252	0.0212486
$411$	20.1454	0.993700
$412$	−1.97820	−0.0974591
$413$	0.944995	0.0465002
$414$	−12.8405	−0.631078
$415$	−10.1475	−0.498119
$416$	0.503303	0.0246764
$417$	3.44722	0.168811
$418$	5.80916	0.284135
$419$	−10.3159	−0.503963	−0.251981	−	0.967732i	$-0.581082\pi$
$419$	−10.3159	−0.503963	−0.251981	+	0.967732i	$0.581082\pi$
$420$	0.402648	0.0196472
$421$	−29.5355	−1.43947	−0.719735	−	0.694249i	$-0.755737\pi$
$421$	−29.5355	−1.43947	−0.719735	+	0.694249i	$0.755737\pi$
$422$	4.31767	0.210181
$423$	−14.5544	−0.707660
$424$	−4.68904	−0.227720
$425$	−3.04381	−0.147647
$426$	5.04367	0.244366
$427$	2.43028	0.117610
$428$	10.5975	0.512248
$429$	0.639936	0.0308964
$430$	−1.00000	−0.0482243
$431$	−8.54566	−0.411630	−0.205815	−	0.978591i	$-0.565985\pi$
$431$	−8.54566	−0.411630	−0.205815	+	0.978591i	$0.565985\pi$
$432$	5.57332	0.268147
$433$	37.1283	1.78427	0.892137	−	0.451765i	$-0.149205\pi$
$433$	37.1283	1.78427	0.892137	+	0.451765i	$0.149205\pi$
$434$	0.553750	0.0265808
$435$	10.0931	0.483927
$436$	5.64929	0.270552
$437$	53.9217	2.57942
$438$	4.40055	0.210266
$439$	−10.0716	−0.480691	−0.240346	−	0.970687i	$-0.577261\pi$
$439$	−10.0716	−0.480691	−0.240346	+	0.970687i	$0.577261\pi$
$440$	−1.00000	−0.0476731
$441$	9.54475	0.454512
$442$	−1.53196	−0.0728679
$443$	35.7867	1.70028	0.850140	−	0.526557i	$-0.176517\pi$
$443$	35.7867	1.70028	0.850140	+	0.526557i	$0.176517\pi$
$444$	−11.4030	−0.541160
$445$	5.40924	0.256423
$446$	−11.4206	−0.540779
$447$	−13.8781	−0.656410
$448$	−0.316678	−0.0149616
$449$	−32.6197	−1.53942	−0.769709	−	0.638395i	$-0.779599\pi$
$449$	−32.6197	−1.53942	−0.769709	+	0.638395i	$0.779599\pi$
$450$	1.38335	0.0652119
$451$	−0.430252	−0.0202598
$452$	15.4883	0.728506
$453$	0.0901777	0.00423692
$454$	−19.4623	−0.913409
$455$	0.159385	0.00747207
$456$	−7.38620	−0.345890
$457$	3.22695	0.150950	0.0754751	−	0.997148i	$-0.475953\pi$
$457$	3.22695	0.150950	0.0754751	+	0.997148i	$0.475953\pi$
$458$	10.7545	0.502525
$459$	−16.9642	−0.791819
$460$	−9.28218	−0.432784
$461$	−11.1272	−0.518245	−0.259123	−	0.965844i	$-0.583433\pi$
$461$	−11.1272	−0.518245	−0.259123	+	0.965844i	$0.583433\pi$
$462$	−0.402648	−0.0187329
$463$	24.5307	1.14004	0.570020	−	0.821631i	$-0.306935\pi$
$463$	24.5307	1.14004	0.570020	+	0.821631i	$0.306935\pi$
$464$	−7.93811	−0.368518
$465$	−2.22333	−0.103104
$466$	15.2663	0.707198
$467$	13.5931	0.629012	0.314506	−	0.949256i	$-0.398161\pi$
$467$	13.5931	0.629012	0.314506	+	0.949256i	$0.398161\pi$
$468$	0.696246	0.0321840
$469$	−3.09053	−0.142708
$470$	−10.5211	−0.485302
$471$	23.4333	1.07975
$472$	2.98409	0.137354
$473$	1.00000	0.0459800
$474$	6.77002	0.310957
$475$	−5.80916	−0.266543
$476$	0.963908	0.0441807
$477$	−6.48660	−0.297001
$478$	4.58174	0.209564
$479$	37.2117	1.70025	0.850124	−	0.526583i	$-0.176527\pi$
$479$	37.2117	1.70025	0.850124	+	0.526583i	$0.176527\pi$
$480$	1.27147	0.0580346
$481$	−4.51377	−0.205810
$482$	−14.3755	−0.654788
$483$	−3.73745	−0.170060
$484$	1.00000	0.0454545
$485$	−1.27905	−0.0580788
$486$	12.9866	0.589083
$487$	12.2209	0.553782	0.276891	−	0.960901i	$-0.410696\pi$
$487$	12.2209	0.553782	0.276891	+	0.960901i	$0.410696\pi$
$488$	7.67431	0.347399
$489$	−10.8493	−0.490622
$490$	6.89972	0.311697
$491$	−12.1137	−0.546682	−0.273341	−	0.961917i	$-0.588129\pi$
$491$	−12.1137	−0.546682	−0.273341	+	0.961917i	$0.588129\pi$
$492$	0.547054	0.0246631
$493$	24.1621	1.08821
$494$	−2.92377	−0.131546
$495$	−1.38335	−0.0621771
$496$	1.74862	0.0785154
$497$	−1.25619	−0.0563480
$498$	−12.9022	−0.578162
$499$	2.61092	0.116881	0.0584404	−	0.998291i	$-0.481387\pi$
$499$	2.61092	0.116881	0.0584404	+	0.998291i	$0.481387\pi$
$500$	1.00000	0.0447214
$501$	6.87151	0.306996
$502$	−4.99686	−0.223021
$503$	17.7741	0.792506	0.396253	−	0.918141i	$-0.370310\pi$
$503$	17.7741	0.792506	0.396253	+	0.918141i	$0.370310\pi$
$504$	−0.438077	−0.0195135
$505$	−7.34467	−0.326834
$506$	9.28218	0.412643
$507$	16.2071	0.719782
$508$	20.8483	0.924994
$509$	−26.4370	−1.17180	−0.585900	−	0.810384i	$-0.699259\pi$
$509$	−26.4370	−1.17180	−0.585900	+	0.810384i	$0.699259\pi$
$510$	−3.87013	−0.171372
$511$	−1.09602	−0.0484849
$512$	−1.00000	−0.0441942
$513$	−32.3763	−1.42945
$514$	18.2445	0.804732
$515$	−1.97820	−0.0871701
$516$	−1.27147	−0.0559735
$517$	10.5211	0.462718
$518$	2.84006	0.124785
$519$	−8.36236	−0.367067
$520$	0.503303	0.0220713
$521$	2.97501	0.130337	0.0651687	−	0.997874i	$-0.479241\pi$
$521$	2.97501	0.130337	0.0651687	+	0.997874i	$0.479241\pi$
$522$	−10.9812	−0.480635
$523$	−24.3954	−1.06674	−0.533368	−	0.845883i	$-0.679074\pi$
$523$	−24.3954	−1.06674	−0.533368	+	0.845883i	$0.679074\pi$
$524$	−0.202318	−0.00883829
$525$	0.402648	0.0175730
$526$	5.51612	0.240514
$527$	−5.32248	−0.231851
$528$	−1.27147	−0.0553338
$529$	63.1589	2.74604
$530$	−4.68904	−0.203679
$531$	4.12805	0.179142
$532$	1.83963	0.0797582
$533$	0.216547	0.00937969
$534$	6.87771	0.297627
$535$	10.5975	0.458169
$536$	−9.75924	−0.421535
$537$	−4.83021	−0.208439
$538$	−8.01104	−0.345380
$539$	−6.89972	−0.297192
$540$	5.57332	0.239838
$541$	−1.92969	−0.0829639	−0.0414819	−	0.999139i	$-0.513208\pi$
$541$	−1.92969	−0.0829639	−0.0414819	+	0.999139i	$0.513208\pi$
$542$	29.9694	1.28730
$543$	−9.90757	−0.425174
$544$	3.04381	0.130502
$545$	5.64929	0.241989
$546$	0.202654	0.00867277
$547$	42.4996	1.81715	0.908577	−	0.417718i	$-0.137170\pi$
$547$	42.4996	1.81715	0.908577	+	0.417718i	$0.137170\pi$
$548$	−15.8441	−0.676828
$549$	10.6163	0.453092
$550$	−1.00000	−0.0426401
$551$	46.1138	1.96451
$552$	−11.8021	−0.502329
$553$	−1.68616	−0.0717030
$554$	2.09014	0.0888015
$555$	−11.4030	−0.484028
$556$	−2.71120	−0.114980
$557$	4.90565	0.207859	0.103929	−	0.994585i	$-0.466858\pi$
$557$	4.90565	0.207859	0.103929	+	0.994585i	$0.466858\pi$
$558$	2.41896	0.102403
$559$	−0.503303	−0.0212874
$560$	−0.316678	−0.0133821
$561$	3.87013	0.163397
$562$	−31.3635	−1.32299
$563$	26.8339	1.13091	0.565457	−	0.824778i	$-0.308700\pi$
$563$	26.8339	1.13091	0.565457	+	0.824778i	$0.308700\pi$
$564$	−13.3773	−0.563286
$565$	15.4883	0.651596
$566$	−0.751951	−0.0316068
$567$	0.929852	0.0390501
$568$	−3.96679	−0.166443
$569$	−2.23408	−0.0936574	−0.0468287	−	0.998903i	$-0.514911\pi$
$569$	−2.23408	−0.0936574	−0.0468287	+	0.998903i	$0.514911\pi$
$570$	−7.38620	−0.309374
$571$	8.07422	0.337896	0.168948	−	0.985625i	$-0.445963\pi$
$571$	8.07422	0.337896	0.168948	+	0.985625i	$0.445963\pi$
$572$	−0.503303	−0.0210441
$573$	23.6573	0.988298
$574$	−0.136251	−0.00568701
$575$	−9.28218	−0.387094
$576$	−1.38335	−0.0576397
$577$	12.0013	0.499622	0.249811	−	0.968295i	$-0.419632\pi$
$577$	12.0013	0.499622	0.249811	+	0.968295i	$0.419632\pi$
$578$	7.73519	0.321742
$579$	10.7213	0.445562
$580$	−7.93811	−0.329612
$581$	3.21347	0.133317
$582$	−1.62628	−0.0674116
$583$	4.68904	0.194200
$584$	−3.46098	−0.143216
$585$	0.696246	0.0287862
$586$	16.8372	0.695539
$587$	−40.9786	−1.69137	−0.845685	−	0.533683i	$-0.820808\pi$
$587$	−40.9786	−1.69137	−0.845685	+	0.533683i	$0.820808\pi$
$588$	8.77281	0.361785
$589$	−10.1580	−0.418554
$590$	2.98409	0.122853
$591$	−16.4351	−0.676049
$592$	8.96829	0.368595
$593$	−30.3713	−1.24720	−0.623599	−	0.781744i	$-0.714330\pi$
$593$	−30.3713	−1.24720	−0.623599	+	0.781744i	$0.714330\pi$
$594$	−5.57332	−0.228676
$595$	0.963908	0.0395164
$596$	10.9149	0.447093
$597$	−35.4452	−1.45068
$598$	−4.67175	−0.191042
$599$	−8.00755	−0.327180	−0.163590	−	0.986528i	$-0.552307\pi$
$599$	−8.00755	−0.327180	−0.163590	+	0.986528i	$0.552307\pi$
$600$	1.27147	0.0519077
$601$	6.53459	0.266552	0.133276	−	0.991079i	$-0.457450\pi$
$601$	6.53459	0.266552	0.133276	+	0.991079i	$0.457450\pi$
$602$	0.316678	0.0129068
$603$	−13.5005	−0.549782
$604$	−0.0709238	−0.00288585
$605$	1.00000	0.0406558
$606$	−9.33856	−0.379353
$607$	10.5037	0.426332	0.213166	−	0.977016i	$-0.431622\pi$
$607$	10.5037	0.426332	0.213166	+	0.977016i	$0.431622\pi$
$608$	5.80916	0.235593
$609$	−3.19626	−0.129519
$610$	7.67431	0.310724
$611$	−5.29530	−0.214225
$612$	4.21067	0.170206
$613$	0.0240921	0.000973071 0	0.000486536	−	1.00000i	$-0.499845\pi$
$613$	0.0240921	0.000973071 0	0.000486536		1.00000i	$0.499845\pi$
$614$	2.41881	0.0976150
$615$	0.547054	0.0220593
$616$	0.316678	0.0127593
$617$	11.7746	0.474028	0.237014	−	0.971506i	$-0.423831\pi$
$617$	11.7746	0.474028	0.237014	+	0.971506i	$0.423831\pi$
$618$	−2.51523	−0.101178
$619$	0.621622	0.0249851	0.0124925	−	0.999922i	$-0.496023\pi$
$619$	0.621622	0.0249851	0.0124925	+	0.999922i	$0.496023\pi$
$620$	1.74862	0.0702263
$621$	−51.7326	−2.07596
$622$	−29.5823	−1.18614
$623$	−1.71299	−0.0686293
$624$	0.639936	0.0256180
$625$	1.00000	0.0400000
$626$	−26.2434	−1.04890
$627$	7.38620	0.294976
$628$	−18.4300	−0.735437
$629$	−27.2978	−1.08844
$630$	−0.438077	−0.0174534
$631$	−1.38820	−0.0552633	−0.0276316	−	0.999618i	$-0.508797\pi$
$631$	−1.38820	−0.0552633	−0.0276316	+	0.999618i	$0.508797\pi$
$632$	−5.32454	−0.211799
$633$	5.48981	0.218200
$634$	10.6549	0.423160
$635$	20.8483	0.827340
$636$	−5.96199	−0.236408
$637$	3.47265	0.137591
$638$	7.93811	0.314273
$639$	−5.48747	−0.217081
$640$	−1.00000	−0.0395285
$641$	−3.82545	−0.151096	−0.0755481	−	0.997142i	$-0.524071\pi$
$641$	−3.82545	−0.151096	−0.0755481	+	0.997142i	$0.524071\pi$
$642$	13.4744	0.531793
$643$	14.7052	0.579918	0.289959	−	0.957039i	$-0.406358\pi$
$643$	14.7052	0.579918	0.289959	+	0.957039i	$0.406358\pi$
$644$	2.93946	0.115831
$645$	−1.27147	−0.0500642
$646$	−17.6820	−0.695689
$647$	24.8603	0.977359	0.488679	−	0.872464i	$-0.337479\pi$
$647$	24.8603	0.977359	0.488679	+	0.872464i	$0.337479\pi$
$648$	2.93627	0.115348
$649$	−2.98409	−0.117136
$650$	0.503303	0.0197412
$651$	0.704078	0.0275950
$652$	8.53284	0.334172
$653$	−41.6244	−1.62889	−0.814445	−	0.580241i	$-0.802958\pi$
$653$	−41.6244	−1.62889	−0.814445	+	0.580241i	$0.802958\pi$
$654$	7.18293	0.280875
$655$	−0.202318	−0.00790520
$656$	−0.430252	−0.0167985
$657$	−4.78776	−0.186788
$658$	3.33180	0.129887
$659$	13.6060	0.530016	0.265008	−	0.964246i	$-0.414625\pi$
$659$	13.6060	0.530016	0.265008	+	0.964246i	$0.414625\pi$
$660$	−1.27147	−0.0494921
$661$	38.6568	1.50358	0.751788	−	0.659404i	$-0.229191\pi$
$661$	38.6568	1.50358	0.751788	+	0.659404i	$0.229191\pi$
$662$	−14.8383	−0.576707
$663$	−1.94785	−0.0756481
$664$	10.1475	0.393798
$665$	1.83963	0.0713379
$666$	12.4063	0.480735
$667$	73.6830	2.85302
$668$	−5.40437	−0.209101
$669$	−14.5209	−0.561412
$670$	−9.75924	−0.377032
$671$	−7.67431	−0.296263
$672$	−0.402648	−0.0155325
$673$	−38.2515	−1.47449	−0.737243	−	0.675627i	$-0.763873\pi$
$673$	−38.2515	−1.47449	−0.737243	+	0.675627i	$0.763873\pi$
$674$	−31.7045	−1.22121
$675$	5.57332	0.214517
$676$	−12.7467	−0.490257
$677$	24.3649	0.936419	0.468209	−	0.883618i	$-0.344899\pi$
$677$	24.3649	0.936419	0.468209	+	0.883618i	$0.344899\pi$
$678$	19.6929	0.756302
$679$	0.405048	0.0155443
$680$	3.04381	0.116725
$681$	−24.7458	−0.948259
$682$	−1.74862	−0.0669582
$683$	−7.77868	−0.297643	−0.148821	−	0.988864i	$-0.547548\pi$
$683$	−7.77868	−0.297643	−0.148821	+	0.988864i	$0.547548\pi$
$684$	8.03612	0.307269
$685$	−15.8441	−0.605373
$686$	−4.40173	−0.168059
$687$	13.6741	0.521699
$688$	1.00000	0.0381246
$689$	−2.36001	−0.0899091
$690$	−11.8021	−0.449296
$691$	−6.48628	−0.246750	−0.123375	−	0.992360i	$-0.539372\pi$
$691$	−6.48628	−0.246750	−0.123375	+	0.992360i	$0.539372\pi$
$692$	6.57690	0.250016
$693$	0.438077	0.0166412
$694$	14.8944	0.565383
$695$	−2.71120	−0.102842
$696$	−10.0931	−0.382578
$697$	1.30961	0.0496049
$698$	−1.05540	−0.0399476
$699$	19.4107	0.734181
$700$	−0.316678	−0.0119693
$701$	−15.3333	−0.579130	−0.289565	−	0.957158i	$-0.593511\pi$
$701$	−15.3333	−0.579130	−0.289565	+	0.957158i	$0.593511\pi$
$702$	2.80507	0.105870
$703$	−52.0982	−1.96492
$704$	1.00000	0.0376889
$705$	−13.3773	−0.503819
$706$	3.97273	0.149516
$707$	2.32589	0.0874743
$708$	3.79419	0.142595
$709$	3.93645	0.147836	0.0739182	−	0.997264i	$-0.476450\pi$
$709$	3.93645	0.147836	0.0739182	+	0.997264i	$0.476450\pi$
$710$	−3.96679	−0.148871
$711$	−7.36573	−0.276236
$712$	−5.40924	−0.202720
$713$	−16.2310	−0.607857
$714$	1.22558	0.0458663
$715$	−0.503303	−0.0188225
$716$	3.79891	0.141972
$717$	5.82556	0.217560
$718$	−13.7528	−0.513251
$719$	−11.8565	−0.442171	−0.221086	−	0.975254i	$-0.570960\pi$
$719$	−11.8565	−0.442171	−0.221086	+	0.975254i	$0.570960\pi$
$720$	−1.38335	−0.0515546
$721$	0.626453	0.0233303
$722$	−14.7463	−0.548802
$723$	−18.2781	−0.679771
$724$	7.79219	0.289594
$725$	−7.93811	−0.294814
$726$	1.27147	0.0471888
$727$	13.4119	0.497421	0.248710	−	0.968578i	$-0.419993\pi$
$727$	13.4119	0.497421	0.248710	+	0.968578i	$0.419993\pi$
$728$	−0.159385	−0.00590719
$729$	25.3209	0.937811
$730$	−3.46098	−0.128097
$731$	−3.04381	−0.112580
$732$	9.75768	0.360654
$733$	−11.6652	−0.430862	−0.215431	−	0.976519i	$-0.569116\pi$
$733$	−11.6652	−0.430862	−0.215431	+	0.976519i	$0.569116\pi$
$734$	−17.0155	−0.628055
$735$	8.77281	0.323590
$736$	9.28218	0.342146
$737$	9.75924	0.359486
$738$	−0.595191	−0.0219093
$739$	−27.7796	−1.02189	−0.510944	−	0.859614i	$-0.670704\pi$
$739$	−27.7796	−1.02189	−0.510944	+	0.859614i	$0.670704\pi$
$740$	8.96829	0.329681
$741$	−3.71749	−0.136566
$742$	1.48491	0.0545129
$743$	−26.0764	−0.956651	−0.478325	−	0.878183i	$-0.658756\pi$
$743$	−26.0764	−0.956651	−0.478325	+	0.878183i	$0.658756\pi$
$744$	2.22333	0.0815111
$745$	10.9149	0.399892
$746$	−23.1769	−0.848567
$747$	14.0375	0.513606
$748$	−3.04381	−0.111293
$749$	−3.35599	−0.122625
$750$	1.27147	0.0464277
$751$	−15.2244	−0.555547	−0.277773	−	0.960647i	$-0.589596\pi$
$751$	−15.2244	−0.555547	−0.277773	+	0.960647i	$0.589596\pi$
$752$	10.5211	0.383665
$753$	−6.35338	−0.231530
$754$	−3.99527	−0.145499
$755$	−0.0709238	−0.00258118
$756$	−1.76495	−0.0641905
$757$	−6.43416	−0.233854	−0.116927	−	0.993141i	$-0.537304\pi$
$757$	−6.43416	−0.233854	−0.116927	+	0.993141i	$0.537304\pi$
$758$	2.91256	0.105789
$759$	11.8021	0.428387
$760$	5.80916	0.210720
$761$	−54.8295	−1.98757	−0.993785	−	0.111319i	$-0.964492\pi$
$761$	−54.8295	−1.98757	−0.993785	+	0.111319i	$0.964492\pi$
$762$	26.5081	0.960286
$763$	−1.78901	−0.0647664
$764$	−18.6062	−0.673149
$765$	4.21067	0.152237
$766$	−27.9708	−1.01063
$767$	1.50190	0.0542305
$768$	−1.27147	−0.0458804
$769$	−33.4535	−1.20637	−0.603183	−	0.797603i	$-0.706101\pi$
$769$	−33.4535	−1.20637	−0.603183	+	0.797603i	$0.706101\pi$
$770$	0.316678	0.0114123
$771$	23.1975	0.835436
$772$	−8.43218	−0.303481
$773$	0.553428	0.0199054	0.00995271	−	0.999950i	$-0.496832\pi$
$773$	0.553428	0.0199054	0.00995271	+	0.999950i	$0.496832\pi$
$774$	1.38335	0.0497236
$775$	1.74862	0.0628124
$776$	1.27905	0.0459153
$777$	3.61106	0.129546
$778$	−26.3452	−0.944520
$779$	2.49940	0.0895504
$780$	0.639936	0.0229134
$781$	3.96679	0.141943
$782$	−28.2532	−1.01033
$783$	−44.2416	−1.58107
$784$	−6.89972	−0.246418
$785$	−18.4300	−0.657795
$786$	−0.257242	−0.00917550
$787$	48.5017	1.72890	0.864450	−	0.502719i	$-0.167667\pi$
$787$	48.5017	1.72890	0.864450	+	0.502719i	$0.167667\pi$
$788$	12.9260	0.460470
$789$	7.01360	0.249691
$790$	−5.32454	−0.189439
$791$	−4.90479	−0.174394
$792$	1.38335	0.0491553
$793$	3.86250	0.137161
$794$	−9.86779	−0.350195
$795$	−5.96199	−0.211450
$796$	27.8773	0.988084
$797$	−39.0165	−1.38204	−0.691018	−	0.722837i	$-0.742838\pi$
$797$	−39.0165	−1.38204	−0.691018	+	0.722837i	$0.742838\pi$
$798$	2.33904	0.0828013
$799$	−32.0243	−1.13294
$800$	−1.00000	−0.0353553
$801$	−7.48289	−0.264395
$802$	8.21715	0.290157
$803$	3.46098	0.122135
$804$	−12.4086	−0.437618
$805$	2.93946	0.103602
$806$	0.880086	0.0309997
$807$	−10.1858	−0.358558
$808$	7.34467	0.258385
$809$	−32.7857	−1.15268	−0.576341	−	0.817209i	$-0.695520\pi$
$809$	−32.7857	−1.15268	−0.576341	+	0.817209i	$0.695520\pi$
$810$	2.93627	0.103170
$811$	22.0619	0.774698	0.387349	−	0.921933i	$-0.373391\pi$
$811$	22.0619	0.774698	0.387349	+	0.921933i	$0.373391\pi$
$812$	2.51382	0.0882179
$813$	38.1053	1.33641
$814$	−8.96829	−0.314339
$815$	8.53284	0.298892
$816$	3.87013	0.135482
$817$	−5.80916	−0.203237
$818$	−24.7206	−0.864337
$819$	−0.220486	−0.00770439
$820$	−0.430252	−0.0150250
$821$	−12.5094	−0.436580	−0.218290	−	0.975884i	$-0.570048\pi$
$821$	−12.5094	−0.436580	−0.218290	+	0.975884i	$0.570048\pi$
$822$	−20.1454	−0.702652
$823$	6.34676	0.221234	0.110617	−	0.993863i	$-0.464717\pi$
$823$	6.34676	0.221234	0.110617	+	0.993863i	$0.464717\pi$
$824$	1.97820	0.0689140
$825$	−1.27147	−0.0442670
$826$	−0.944995	−0.0328806
$827$	−48.8755	−1.69957	−0.849783	−	0.527133i	$-0.823267\pi$
$827$	−48.8755	−1.69957	−0.849783	+	0.527133i	$0.823267\pi$
$828$	12.8405	0.446240
$829$	−11.1419	−0.386974	−0.193487	−	0.981103i	$-0.561980\pi$
$829$	−11.1419	−0.386974	−0.193487	+	0.981103i	$0.561980\pi$
$830$	10.1475	0.352223
$831$	2.65756	0.0921897
$832$	−0.503303	−0.0174489
$833$	21.0015	0.727657
$834$	−3.44722	−0.119367
$835$	−5.40437	−0.187026
$836$	−5.80916	−0.200914
$837$	9.74563	0.336858
$838$	10.3159	0.356356
$839$	4.40504	0.152079	0.0760394	−	0.997105i	$-0.475773\pi$
$839$	4.40504	0.152079	0.0760394	+	0.997105i	$0.475773\pi$
$840$	−0.402648	−0.0138927
$841$	34.0136	1.17288
$842$	29.5355	1.01786
$843$	−39.8779	−1.37347
$844$	−4.31767	−0.148620
$845$	−12.7467	−0.438499
$846$	14.5544	0.500391
$847$	−0.316678	−0.0108812
$848$	4.68904	0.161022
$849$	−0.956086	−0.0328128
$850$	3.04381	0.104402
$851$	−83.2453	−2.85361
$852$	−5.04367	−0.172793
$853$	32.1697	1.10147	0.550735	−	0.834680i	$-0.314348\pi$
$853$	32.1697	1.10147	0.550735	+	0.834680i	$0.314348\pi$
$854$	−2.43028	−0.0831625
$855$	8.03612	0.274830
$856$	−10.5975	−0.362214
$857$	−55.9742	−1.91204	−0.956020	−	0.293300i	$-0.905246\pi$
$857$	−55.9742	−1.91204	−0.956020	+	0.293300i	$0.905246\pi$
$858$	−0.639936	−0.0218471
$859$	38.0150	1.29706	0.648528	−	0.761191i	$-0.275385\pi$
$859$	38.0150	1.29706	0.648528	+	0.761191i	$0.275385\pi$
$860$	1.00000	0.0340997
$861$	−0.173240	−0.00590400
$862$	8.54566	0.291066
$863$	−16.9960	−0.578551	−0.289276	−	0.957246i	$-0.593414\pi$
$863$	−16.9960	−0.578551	−0.289276	+	0.957246i	$0.593414\pi$
$864$	−5.57332	−0.189608
$865$	6.57690	0.223621
$866$	−37.1283	−1.26167
$867$	9.83510	0.334017
$868$	−0.553750	−0.0187955
$869$	5.32454	0.180623
$870$	−10.0931	−0.342188
$871$	−4.91185	−0.166432
$872$	−5.64929	−0.191309
$873$	1.76938	0.0598845
$874$	−53.9217	−1.82393
$875$	−0.316678	−0.0107057
$876$	−4.40055	−0.148681
$877$	22.1512	0.747993	0.373997	−	0.927430i	$-0.377987\pi$
$877$	22.1512	0.747993	0.373997	+	0.927430i	$0.377987\pi$
$878$	10.0716	0.339900
$879$	21.4081	0.722076
$880$	1.00000	0.0337100
$881$	11.7140	0.394656	0.197328	−	0.980338i	$-0.436774\pi$
$881$	11.7140	0.394656	0.197328	+	0.980338i	$0.436774\pi$
$882$	−9.54475	−0.321388
$883$	12.4442	0.418779	0.209390	−	0.977832i	$-0.432852\pi$
$883$	12.4442	0.418779	0.209390	+	0.977832i	$0.432852\pi$
$884$	1.53196	0.0515254
$885$	3.79419	0.127540
$886$	−35.7867	−1.20228
$887$	−23.9978	−0.805767	−0.402884	−	0.915251i	$-0.631992\pi$
$887$	−23.9978	−0.805767	−0.402884	+	0.915251i	$0.631992\pi$
$888$	11.4030	0.382658
$889$	−6.60219	−0.221431
$890$	−5.40924	−0.181318
$891$	−2.93627	−0.0983688
$892$	11.4206	0.382389
$893$	−61.1188	−2.04526
$894$	13.8781	0.464152
$895$	3.79891	0.126983
$896$	0.316678	0.0105795
$897$	−5.94000	−0.198331
$898$	32.6197	1.08853
$899$	−13.8808	−0.462949
$900$	−1.38335	−0.0461118
$901$	−14.2726	−0.475488
$902$	0.430252	0.0143258
$903$	0.402648	0.0133993
$904$	−15.4883	−0.515132
$905$	7.79219	0.259021
$906$	−0.0901777	−0.00299595
$907$	10.8665	0.360815	0.180407	−	0.983592i	$-0.442258\pi$
$907$	10.8665	0.360815	0.180407	+	0.983592i	$0.442258\pi$
$908$	19.4623	0.645878
$909$	10.1603	0.336995
$910$	−0.159385	−0.00528355
$911$	−6.94084	−0.229960	−0.114980	−	0.993368i	$-0.536680\pi$
$911$	−6.94084	−0.229960	−0.114980	+	0.993368i	$0.536680\pi$
$912$	7.38620	0.244581
$913$	−10.1475	−0.335832
$914$	−3.22695	−0.106738
$915$	9.75768	0.322579
$916$	−10.7545	−0.355339
$917$	0.0640695	0.00211576
$918$	16.9642	0.559900
$919$	51.7330	1.70651	0.853256	−	0.521492i	$-0.174624\pi$
$919$	51.7330	1.70651	0.853256	+	0.521492i	$0.174624\pi$
$920$	9.28218	0.306024
$921$	3.07545	0.101339
$922$	11.1272	0.366455
$923$	−1.99649	−0.0657154
$924$	0.402648	0.0132461
$925$	8.96829	0.294876
$926$	−24.5307	−0.806130
$927$	2.73656	0.0898803
$928$	7.93811	0.260581
$929$	−6.02374	−0.197632	−0.0988162	−	0.995106i	$-0.531506\pi$
$929$	−6.02374	−0.197632	−0.0988162	+	0.995106i	$0.531506\pi$
$930$	2.22333	0.0729058
$931$	40.0815	1.31362
$932$	−15.2663	−0.500065
$933$	−37.6131	−1.23140
$934$	−13.5931	−0.444778
$935$	−3.04381	−0.0995434
$936$	−0.696246	−0.0227575
$937$	−32.6799	−1.06761	−0.533804	−	0.845609i	$-0.679238\pi$
$937$	−32.6799	−1.06761	−0.533804	+	0.845609i	$0.679238\pi$
$938$	3.09053	0.100910
$939$	−33.3677	−1.08892
$940$	10.5211	0.343161
$941$	−32.4452	−1.05768	−0.528841	−	0.848721i	$-0.677373\pi$
$941$	−32.4452	−1.05768	−0.528841	+	0.848721i	$0.677373\pi$
$942$	−23.4333	−0.763497
$943$	3.99368	0.130052
$944$	−2.98409	−0.0971239
$945$	−1.76495	−0.0574137
$946$	−1.00000	−0.0325128
$947$	15.9886	0.519559	0.259780	−	0.965668i	$-0.416350\pi$
$947$	15.9886	0.519559	0.259780	+	0.965668i	$0.416350\pi$
$948$	−6.77002	−0.219880
$949$	−1.74192	−0.0565451
$950$	5.80916	0.188474
$951$	13.5474	0.439305
$952$	−0.963908	−0.0312404
$953$	−56.9964	−1.84629	−0.923147	−	0.384448i	$-0.874392\pi$
$953$	−56.9964	−1.84629	−0.923147	+	0.384448i	$0.874392\pi$
$954$	6.48660	0.210011
$955$	−18.6062	−0.602082
$956$	−4.58174	−0.148184
$957$	10.0931	0.326264
$958$	−37.2117	−1.20226
$959$	5.01749	0.162023
$960$	−1.27147	−0.0410366
$961$	−27.9423	−0.901365
$962$	4.51377	0.145530
$963$	−14.6601	−0.472414
$964$	14.3755	0.463005
$965$	−8.43218	−0.271441
$966$	3.73745	0.120250
$967$	24.9638	0.802783	0.401391	−	0.915907i	$-0.368527\pi$
$967$	24.9638	0.802783	0.401391	+	0.915907i	$0.368527\pi$
$968$	−1.00000	−0.0321412
$969$	−22.4822	−0.722233
$970$	1.27905	0.0410679
$971$	50.1432	1.60917	0.804586	−	0.593836i	$-0.202387\pi$
$971$	50.1432	1.60917	0.804586	+	0.593836i	$0.202387\pi$
$972$	−12.9866	−0.416544
$973$	0.858576	0.0275247
$974$	−12.2209	−0.391583
$975$	0.639936	0.0204944
$976$	−7.67431	−0.245649
$977$	5.59808	0.179098	0.0895492	−	0.995982i	$-0.471457\pi$
$977$	5.59808	0.179098	0.0895492	+	0.995982i	$0.471457\pi$
$978$	10.8493	0.346922
$979$	5.40924	0.172880
$980$	−6.89972	−0.220403
$981$	−7.81497	−0.249513
$982$	12.1137	0.386563
$983$	2.72248	0.0868337	0.0434168	−	0.999057i	$-0.486176\pi$
$983$	2.72248	0.0868337	0.0434168	+	0.999057i	$0.486176\pi$
$984$	−0.547054	−0.0174394
$985$	12.9260	0.411857
$986$	−24.1621	−0.769479
$987$	4.23630	0.134843
$988$	2.92377	0.0930174
$989$	−9.28218	−0.295156
$990$	1.38335	0.0439659
$991$	28.1134	0.893052	0.446526	−	0.894771i	$-0.352661\pi$
$991$	28.1134	0.893052	0.446526	+	0.894771i	$0.352661\pi$
$992$	−1.74862	−0.0555188
$993$	−18.8665	−0.598711
$994$	1.25619	0.0398440
$995$	27.8773	0.883769
$996$	12.9022	0.408823
$997$	26.4197	0.836721	0.418361	−	0.908281i	$-0.362605\pi$
$997$	26.4197	0.836721	0.418361	+	0.908281i	$0.362605\pi$
$998$	−2.61092	−0.0826473
$999$	49.9832	1.58140

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4730.2.a.z.1.3	✓	10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4730.2.a.z.1.3	✓	10	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)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -1.27147 q^{3} +1.00000 q^{4} +1.00000 q^{5} +1.27147 q^{6} -0.316678 q^{7} -1.00000 q^{8} -1.38335 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -1.27147 q^{3} +1.00000 q^{4} +1.00000 q^{5} +1.27147 q^{6} -0.316678 q^{7} -1.00000 q^{8} -1.38335 q^{9} -1.00000 q^{10} +1.00000 q^{11} -1.27147 q^{12} -0.503303 q^{13} +0.316678 q^{14} -1.27147 q^{15} +1.00000 q^{16} -3.04381 q^{17} +1.38335 q^{18} -5.80916 q^{19} +1.00000 q^{20} +0.402648 q^{21} -1.00000 q^{22} -9.28218 q^{23} +1.27147 q^{24} +1.00000 q^{25} +0.503303 q^{26} +5.57332 q^{27} -0.316678 q^{28} -7.93811 q^{29} +1.27147 q^{30} +1.74862 q^{31} -1.00000 q^{32} -1.27147 q^{33} +3.04381 q^{34} -0.316678 q^{35} -1.38335 q^{36} +8.96829 q^{37} +5.80916 q^{38} +0.639936 q^{39} -1.00000 q^{40} -0.430252 q^{41} -0.402648 q^{42} +1.00000 q^{43} +1.00000 q^{44} -1.38335 q^{45} +9.28218 q^{46} +10.5211 q^{47} -1.27147 q^{48} -6.89972 q^{49} -1.00000 q^{50} +3.87013 q^{51} -0.503303 q^{52} +4.68904 q^{53} -5.57332 q^{54} +1.00000 q^{55} +0.316678 q^{56} +7.38620 q^{57} +7.93811 q^{58} -2.98409 q^{59} -1.27147 q^{60} -7.67431 q^{61} -1.74862 q^{62} +0.438077 q^{63} +1.00000 q^{64} -0.503303 q^{65} +1.27147 q^{66} +9.75924 q^{67} -3.04381 q^{68} +11.8021 q^{69} +0.316678 q^{70} +3.96679 q^{71} +1.38335 q^{72} +3.46098 q^{73} -8.96829 q^{74} -1.27147 q^{75} -5.80916 q^{76} -0.316678 q^{77} -0.639936 q^{78} +5.32454 q^{79} +1.00000 q^{80} -2.93627 q^{81} +0.430252 q^{82} -10.1475 q^{83} +0.402648 q^{84} -3.04381 q^{85} -1.00000 q^{86} +10.0931 q^{87} -1.00000 q^{88} +5.40924 q^{89} +1.38335 q^{90} +0.159385 q^{91} -9.28218 q^{92} -2.22333 q^{93} -10.5211 q^{94} -5.80916 q^{95} +1.27147 q^{96} -1.27905 q^{97} +6.89972 q^{98} -1.38335 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - 10 q^{2} + 8 q^{3} + 10 q^{4} + 10 q^{5} - 8 q^{6} + 3 q^{7} - 10 q^{8} + 14 q^{9}+O(q^{10}) \) 10 * q - 10 * q^2 + 8 * q^3 + 10 * q^4 + 10 * q^5 - 8 * q^6 + 3 * q^7 - 10 * q^8 + 14 * q^9	\( 10 q - 10 q^{2} + 8 q^{3} + 10 q^{4} + 10 q^{5} - 8 q^{6} + 3 q^{7} - 10 q^{8} + 14 q^{9} - 10 q^{10} + 10 q^{11} + 8 q^{12} + 7 q^{13} - 3 q^{14} + 8 q^{15} + 10 q^{16} + 2 q^{17} - 14 q^{18} - 7 q^{19} + 10 q^{20} - 2 q^{21} - 10 q^{22} + 12 q^{23} - 8 q^{24} + 10 q^{25} - 7 q^{26} + 23 q^{27} + 3 q^{28} - 12 q^{29} - 8 q^{30} + 16 q^{31} - 10 q^{32} + 8 q^{33} - 2 q^{34} + 3 q^{35} + 14 q^{36} + 19 q^{37} + 7 q^{38} + 6 q^{39} - 10 q^{40} + 9 q^{41} + 2 q^{42} + 10 q^{43} + 10 q^{44} + 14 q^{45} - 12 q^{46} + 29 q^{47} + 8 q^{48} + 23 q^{49} - 10 q^{50} - 7 q^{51} + 7 q^{52} + 6 q^{53} - 23 q^{54} + 10 q^{55} - 3 q^{56} + 23 q^{57} + 12 q^{58} + 29 q^{59} + 8 q^{60} - 4 q^{61} - 16 q^{62} + 10 q^{64} + 7 q^{65} - 8 q^{66} + 45 q^{67} + 2 q^{68} + 24 q^{69} - 3 q^{70} - 18 q^{71} - 14 q^{72} + 3 q^{73} - 19 q^{74} + 8 q^{75} - 7 q^{76} + 3 q^{77} - 6 q^{78} - 14 q^{79} + 10 q^{80} + 6 q^{81} - 9 q^{82} + 23 q^{83} - 2 q^{84} + 2 q^{85} - 10 q^{86} + 25 q^{87} - 10 q^{88} + q^{89} - 14 q^{90} + q^{91} + 12 q^{92} + 35 q^{93} - 29 q^{94} - 7 q^{95} - 8 q^{96} + 30 q^{97} - 23 q^{98} + 14 q^{99}+O(q^{100}) \) 10 * q - 10 * q^2 + 8 * q^3 + 10 * q^4 + 10 * q^5 - 8 * q^6 + 3 * q^7 - 10 * q^8 + 14 * q^9 - 10 * q^10 + 10 * q^11 + 8 * q^12 + 7 * q^13 - 3 * q^14 + 8 * q^15 + 10 * q^16 + 2 * q^17 - 14 * q^18 - 7 * q^19 + 10 * q^20 - 2 * q^21 - 10 * q^22 + 12 * q^23 - 8 * q^24 + 10 * q^25 - 7 * q^26 + 23 * q^27 + 3 * q^28 - 12 * q^29 - 8 * q^30 + 16 * q^31 - 10 * q^32 + 8 * q^33 - 2 * q^34 + 3 * q^35 + 14 * q^36 + 19 * q^37 + 7 * q^38 + 6 * q^39 - 10 * q^40 + 9 * q^41 + 2 * q^42 + 10 * q^43 + 10 * q^44 + 14 * q^45 - 12 * q^46 + 29 * q^47 + 8 * q^48 + 23 * q^49 - 10 * q^50 - 7 * q^51 + 7 * q^52 + 6 * q^53 - 23 * q^54 + 10 * q^55 - 3 * q^56 + 23 * q^57 + 12 * q^58 + 29 * q^59 + 8 * q^60 - 4 * q^61 - 16 * q^62 + 10 * q^64 + 7 * q^65 - 8 * q^66 + 45 * q^67 + 2 * q^68 + 24 * q^69 - 3 * q^70 - 18 * q^71 - 14 * q^72 + 3 * q^73 - 19 * q^74 + 8 * q^75 - 7 * q^76 + 3 * q^77 - 6 * q^78 - 14 * q^79 + 10 * q^80 + 6 * q^81 - 9 * q^82 + 23 * q^83 - 2 * q^84 + 2 * q^85 - 10 * q^86 + 25 * q^87 - 10 * q^88 + q^89 - 14 * q^90 + q^91 + 12 * q^92 + 35 * q^93 - 29 * q^94 - 7 * q^95 - 8 * q^96 + 30 * q^97 - 23 * q^98 + 14 * q^99

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