LMFDB - Embedded newform 4730.2.a.z.1.8

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			1.8
Root			$-1.53249$ 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)

$f(q)$	$=$	$q-1.00000 q^{2} +2.53249 q^{3} +1.00000 q^{4} +1.00000 q^{5} -2.53249 q^{6} -0.583820 q^{7} -1.00000 q^{8} +3.41349 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +2.53249 q^{3} +1.00000 q^{4} +1.00000 q^{5} -2.53249 q^{6} -0.583820 q^{7} -1.00000 q^{8} +3.41349 q^{9} -1.00000 q^{10} +1.00000 q^{11} +2.53249 q^{12} -4.55520 q^{13} +0.583820 q^{14} +2.53249 q^{15} +1.00000 q^{16} +5.04549 q^{17} -3.41349 q^{18} -4.92944 q^{19} +1.00000 q^{20} -1.47852 q^{21} -1.00000 q^{22} -0.815754 q^{23} -2.53249 q^{24} +1.00000 q^{25} +4.55520 q^{26} +1.04716 q^{27} -0.583820 q^{28} +7.94882 q^{29} -2.53249 q^{30} -2.45826 q^{31} -1.00000 q^{32} +2.53249 q^{33} -5.04549 q^{34} -0.583820 q^{35} +3.41349 q^{36} +3.39751 q^{37} +4.92944 q^{38} -11.5360 q^{39} -1.00000 q^{40} +10.9373 q^{41} +1.47852 q^{42} +1.00000 q^{43} +1.00000 q^{44} +3.41349 q^{45} +0.815754 q^{46} +7.21973 q^{47} +2.53249 q^{48} -6.65915 q^{49} -1.00000 q^{50} +12.7776 q^{51} -4.55520 q^{52} +11.9243 q^{53} -1.04716 q^{54} +1.00000 q^{55} +0.583820 q^{56} -12.4837 q^{57} -7.94882 q^{58} +9.88656 q^{59} +2.53249 q^{60} -7.37908 q^{61} +2.45826 q^{62} -1.99286 q^{63} +1.00000 q^{64} -4.55520 q^{65} -2.53249 q^{66} +9.44673 q^{67} +5.04549 q^{68} -2.06589 q^{69} +0.583820 q^{70} +11.2834 q^{71} -3.41349 q^{72} -1.95228 q^{73} -3.39751 q^{74} +2.53249 q^{75} -4.92944 q^{76} -0.583820 q^{77} +11.5360 q^{78} +16.0023 q^{79} +1.00000 q^{80} -7.58855 q^{81} -10.9373 q^{82} +0.0176475 q^{83} -1.47852 q^{84} +5.04549 q^{85} -1.00000 q^{86} +20.1303 q^{87} -1.00000 q^{88} -4.04716 q^{89} -3.41349 q^{90} +2.65942 q^{91} -0.815754 q^{92} -6.22551 q^{93} -7.21973 q^{94} -4.92944 q^{95} -2.53249 q^{96} +3.09439 q^{97} +6.65915 q^{98} +3.41349 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	2.53249	1.46213	0.731066	−	0.682307i	$-0.239023\pi$
$3$	2.53249	1.46213	0.731066	+	0.682307i	$0.239023\pi$
$4$	1.00000	0.500000
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	−2.53249	−1.03388
$7$	−0.583820	−0.220663	−0.110332	−	0.993895i	$-0.535191\pi$
$7$	−0.583820	−0.220663	−0.110332	+	0.993895i	$0.535191\pi$
$8$	−1.00000	−0.353553
$9$	3.41349	1.13783
$10$	−1.00000	−0.316228
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	2.53249	0.731066
$13$	−4.55520	−1.26338	−0.631692	−	0.775219i	$-0.717639\pi$
$13$	−4.55520	−1.26338	−0.631692	+	0.775219i	$0.717639\pi$
$14$	0.583820	0.156032
$15$	2.53249	0.653885
$16$	1.00000	0.250000
$17$	5.04549	1.22371	0.611856	−	0.790969i	$-0.290423\pi$
$17$	5.04549	1.22371	0.611856	+	0.790969i	$0.290423\pi$
$18$	−3.41349	−0.804567
$19$	−4.92944	−1.13089	−0.565445	−	0.824786i	$-0.691296\pi$
$19$	−4.92944	−1.13089	−0.565445	+	0.824786i	$0.691296\pi$
$20$	1.00000	0.223607
$21$	−1.47852	−0.322639
$22$	−1.00000	−0.213201
$23$	−0.815754	−0.170096	−0.0850482	−	0.996377i	$-0.527104\pi$
$23$	−0.815754	−0.170096	−0.0850482	+	0.996377i	$0.527104\pi$
$24$	−2.53249	−0.516942
$25$	1.00000	0.200000
$26$	4.55520	0.893348
$27$	1.04716	0.201526
$28$	−0.583820	−0.110332
$29$	7.94882	1.47606	0.738029	−	0.674769i	$-0.235757\pi$
$29$	7.94882	1.47606	0.738029	+	0.674769i	$0.235757\pi$
$30$	−2.53249	−0.462367
$31$	−2.45826	−0.441516	−0.220758	−	0.975329i	$-0.570853\pi$
$31$	−2.45826	−0.441516	−0.220758	+	0.975329i	$0.570853\pi$
$32$	−1.00000	−0.176777
$33$	2.53249	0.440849
$34$	−5.04549	−0.865294
$35$	−0.583820	−0.0986836
$36$	3.41349	0.568915
$37$	3.39751	0.558547	0.279274	−	0.960212i	$-0.409906\pi$
$37$	3.39751	0.558547	0.279274	+	0.960212i	$0.409906\pi$
$38$	4.92944	0.799660
$39$	−11.5360	−1.84724
$40$	−1.00000	−0.158114
$41$	10.9373	1.70812	0.854059	−	0.520177i	$-0.174134\pi$
$41$	10.9373	1.70812	0.854059	+	0.520177i	$0.174134\pi$
$42$	1.47852	0.228140
$43$	1.00000	0.152499
$43$	1.00000	0.152499
$44$	1.00000	0.150756
$45$	3.41349	0.508853
$46$	0.815754	0.120276
$47$	7.21973	1.05311	0.526553	−	0.850143i	$-0.323484\pi$
$47$	7.21973	1.05311	0.526553	+	0.850143i	$0.323484\pi$
$48$	2.53249	0.365533
$49$	−6.65915	−0.951308
$50$	−1.00000	−0.141421
$51$	12.7776	1.78923
$52$	−4.55520	−0.631692
$53$	11.9243	1.63793	0.818964	−	0.573845i	$-0.194549\pi$
$53$	11.9243	1.63793	0.818964	+	0.573845i	$0.194549\pi$
$54$	−1.04716	−0.142500
$55$	1.00000	0.134840
$56$	0.583820	0.0780162
$57$	−12.4837	−1.65351
$58$	−7.94882	−1.04373
$59$	9.88656	1.28712	0.643560	−	0.765395i	$-0.277457\pi$
$59$	9.88656	1.28712	0.643560	+	0.765395i	$0.277457\pi$
$60$	2.53249	0.326943
$61$	−7.37908	−0.944794	−0.472397	−	0.881386i	$-0.656611\pi$
$61$	−7.37908	−0.944794	−0.472397	+	0.881386i	$0.656611\pi$
$62$	2.45826	0.312199
$63$	−1.99286	−0.251077
$64$	1.00000	0.125000
$65$	−4.55520	−0.565003
$66$	−2.53249	−0.311728
$67$	9.44673	1.15410	0.577051	−	0.816708i	$-0.304203\pi$
$67$	9.44673	1.15410	0.577051	+	0.816708i	$0.304203\pi$
$68$	5.04549	0.611856
$69$	−2.06589	−0.248703
$70$	0.583820	0.0697799
$71$	11.2834	1.33909	0.669547	−	0.742770i	$-0.266488\pi$
$71$	11.2834	1.33909	0.669547	+	0.742770i	$0.266488\pi$
$72$	−3.41349	−0.402284
$73$	−1.95228	−0.228497	−0.114249	−	0.993452i	$-0.536446\pi$
$73$	−1.95228	−0.228497	−0.114249	+	0.993452i	$0.536446\pi$
$74$	−3.39751	−0.394952
$75$	2.53249	0.292426
$76$	−4.92944	−0.565445
$77$	−0.583820	−0.0665325
$78$	11.5360	1.30619
$79$	16.0023	1.80040	0.900200	−	0.435476i	$-0.143420\pi$
$79$	16.0023	1.80040	0.900200	+	0.435476i	$0.143420\pi$
$80$	1.00000	0.111803
$81$	−7.58855	−0.843173
$82$	−10.9373	−1.20782
$83$	0.0176475	0.00193706	0.000968530	−	1.00000i	$-0.499692\pi$
$83$	0.0176475	0.00193706	0.000968530		1.00000i	$0.499692\pi$
$84$	−1.47852	−0.161319
$85$	5.04549	0.547260
$86$	−1.00000	−0.107833
$87$	20.1303	2.15819
$88$	−1.00000	−0.106600
$89$	−4.04716	−0.428998	−0.214499	−	0.976724i	$-0.568812\pi$
$89$	−4.04716	−0.428998	−0.214499	+	0.976724i	$0.568812\pi$
$90$	−3.41349	−0.359813
$91$	2.65942	0.278783
$92$	−0.815754	−0.0850482
$93$	−6.22551	−0.645555
$94$	−7.21973	−0.744658
$95$	−4.92944	−0.505750
$96$	−2.53249	−0.258471
$97$	3.09439	0.314188	0.157094	−	0.987584i	$-0.449787\pi$
$97$	3.09439	0.314188	0.157094	+	0.987584i	$0.449787\pi$
$98$	6.65915	0.672676
$99$	3.41349	0.343069
$100$	1.00000	0.100000
$101$	−16.2277	−1.61472	−0.807360	−	0.590060i	$-0.799104\pi$
$101$	−16.2277	−1.61472	−0.807360	+	0.590060i	$0.799104\pi$
$102$	−12.7776	−1.26517
$103$	15.8775	1.56445	0.782227	−	0.622994i	$-0.214084\pi$
$103$	15.8775	1.56445	0.782227	+	0.622994i	$0.214084\pi$
$104$	4.55520	0.446674
$105$	−1.47852	−0.144288
$106$	−11.9243	−1.15819
$107$	1.99047	0.192426	0.0962129	−	0.995361i	$-0.469327\pi$
$107$	1.99047	0.192426	0.0962129	+	0.995361i	$0.469327\pi$
$108$	1.04716	0.100763
$109$	5.94794	0.569710	0.284855	−	0.958571i	$-0.408055\pi$
$109$	5.94794	0.569710	0.284855	+	0.958571i	$0.408055\pi$
$110$	−1.00000	−0.0953463
$111$	8.60415	0.816670
$112$	−0.583820	−0.0551658
$113$	1.56740	0.147448	0.0737241	−	0.997279i	$-0.476512\pi$
$113$	1.56740	0.147448	0.0737241	+	0.997279i	$0.476512\pi$
$114$	12.4837	1.16921
$115$	−0.815754	−0.0760694
$116$	7.94882	0.738029
$117$	−15.5491	−1.43752
$118$	−9.88656	−0.910132
$119$	−2.94566	−0.270028
$120$	−2.53249	−0.231183
$121$	1.00000	0.0909091
$122$	7.37908	0.668070
$123$	27.6985	2.49749
$124$	−2.45826	−0.220758
$125$	1.00000	0.0894427
$126$	1.99286	0.177538
$127$	−14.2359	−1.26323	−0.631616	−	0.775281i	$-0.717608\pi$
$127$	−14.2359	−1.26323	−0.631616	+	0.775281i	$0.717608\pi$
$128$	−1.00000	−0.0883883
$129$	2.53249	0.222973
$130$	4.55520	0.399517
$131$	−9.61130	−0.839743	−0.419871	−	0.907584i	$-0.637925\pi$
$131$	−9.61130	−0.839743	−0.419871	+	0.907584i	$0.637925\pi$
$132$	2.53249	0.220425
$133$	2.87790	0.249546
$134$	−9.44673	−0.816073
$135$	1.04716	0.0901251
$136$	−5.04549	−0.432647
$137$	14.6263	1.24961	0.624803	−	0.780782i	$-0.285179\pi$
$137$	14.6263	1.24961	0.624803	+	0.780782i	$0.285179\pi$
$138$	2.06589	0.175860
$139$	11.7412	0.995879	0.497939	−	0.867212i	$-0.334090\pi$
$139$	11.7412	0.995879	0.497939	+	0.867212i	$0.334090\pi$
$140$	−0.583820	−0.0493418
$141$	18.2839	1.53978
$142$	−11.2834	−0.946882
$143$	−4.55520	−0.380925
$144$	3.41349	0.284458
$145$	7.94882	0.660113
$146$	1.95228	0.161572
$147$	−16.8642	−1.39094
$148$	3.39751	0.279274
$149$	−23.6217	−1.93516	−0.967581	−	0.252560i	$-0.918728\pi$
$149$	−23.6217	−1.93516	−0.967581	+	0.252560i	$0.918728\pi$
$150$	−2.53249	−0.206777
$151$	−5.02949	−0.409294	−0.204647	−	0.978836i	$-0.565605\pi$
$151$	−5.02949	−0.409294	−0.204647	+	0.978836i	$0.565605\pi$
$152$	4.92944	0.399830
$153$	17.2227	1.39238
$154$	0.583820	0.0470456
$155$	−2.45826	−0.197452
$156$	−11.5360	−0.923618
$157$	−14.0823	−1.12389	−0.561943	−	0.827176i	$-0.689946\pi$
$157$	−14.0823	−1.12389	−0.561943	+	0.827176i	$0.689946\pi$
$158$	−16.0023	−1.27308
$159$	30.1981	2.39487
$160$	−1.00000	−0.0790569
$161$	0.476254	0.0375340
$162$	7.58855	0.596213
$163$	18.3786	1.43952	0.719760	−	0.694223i	$-0.244252\pi$
$163$	18.3786	1.43952	0.719760	+	0.694223i	$0.244252\pi$
$164$	10.9373	0.854059
$165$	2.53249	0.197154
$166$	−0.0176475	−0.00136971
$167$	−4.93771	−0.382091	−0.191046	−	0.981581i	$-0.561188\pi$
$167$	−4.93771	−0.382091	−0.191046	+	0.981581i	$0.561188\pi$
$168$	1.47852	0.114070
$169$	7.74983	0.596141
$170$	−5.04549	−0.386971
$171$	−16.8266	−1.28676
$172$	1.00000	0.0762493
$173$	4.02612	0.306100	0.153050	−	0.988218i	$-0.451090\pi$
$173$	4.02612	0.306100	0.153050	+	0.988218i	$0.451090\pi$
$174$	−20.1303	−1.52607
$175$	−0.583820	−0.0441327
$176$	1.00000	0.0753778
$177$	25.0376	1.88194
$178$	4.04716	0.303347
$179$	22.7886	1.70330	0.851649	−	0.524112i	$-0.175603\pi$
$179$	22.7886	1.70330	0.851649	+	0.524112i	$0.175603\pi$
$180$	3.41349	0.254427
$181$	14.6773	1.09095	0.545477	−	0.838126i	$-0.316348\pi$
$181$	14.6773	1.09095	0.545477	+	0.838126i	$0.316348\pi$
$182$	−2.65942	−0.197129
$183$	−18.6874	−1.38141
$184$	0.815754	0.0601382
$185$	3.39751	0.249790
$186$	6.22551	0.456477
$187$	5.04549	0.368963
$188$	7.21973	0.526553
$189$	−0.611352	−0.0444693
$190$	4.92944	0.357619
$191$	−15.6918	−1.13542	−0.567708	−	0.823230i	$-0.692170\pi$
$191$	−15.6918	−1.13542	−0.567708	+	0.823230i	$0.692170\pi$
$192$	2.53249	0.182767
$193$	16.6265	1.19680	0.598400	−	0.801197i	$-0.295803\pi$
$193$	16.6265	1.19680	0.598400	+	0.801197i	$0.295803\pi$
$194$	−3.09439	−0.222164
$195$	−11.5360	−0.826109
$196$	−6.65915	−0.475654
$197$	−17.0689	−1.21611	−0.608056	−	0.793894i	$-0.708050\pi$
$197$	−17.0689	−1.21611	−0.608056	+	0.793894i	$0.708050\pi$
$198$	−3.41349	−0.242586
$199$	2.64964	0.187828	0.0939142	−	0.995580i	$-0.470062\pi$
$199$	2.64964	0.187828	0.0939142	+	0.995580i	$0.470062\pi$
$200$	−1.00000	−0.0707107
$201$	23.9237	1.68745
$202$	16.2277	1.14178
$203$	−4.64068	−0.325712
$204$	12.7776	0.894614
$205$	10.9373	0.763893
$206$	−15.8775	−1.10624
$207$	−2.78457	−0.193541
$208$	−4.55520	−0.315846
$209$	−4.92944	−0.340976
$210$	1.47852	0.102027
$211$	−12.3084	−0.847344	−0.423672	−	0.905816i	$-0.639259\pi$
$211$	−12.3084	−0.847344	−0.423672	+	0.905816i	$0.639259\pi$
$212$	11.9243	0.818964
$213$	28.5751	1.95793
$214$	−1.99047	−0.136066
$215$	1.00000	0.0681994
$216$	−1.04716	−0.0712501
$217$	1.43518	0.0974265
$218$	−5.94794	−0.402846
$219$	−4.94413	−0.334093
$220$	1.00000	0.0674200
$221$	−22.9832	−1.54602
$222$	−8.60415	−0.577473
$223$	−20.1134	−1.34690	−0.673448	−	0.739235i	$-0.735187\pi$
$223$	−20.1134	−1.34690	−0.673448	+	0.739235i	$0.735187\pi$
$224$	0.583820	0.0390081
$225$	3.41349	0.227566
$226$	−1.56740	−0.104262
$227$	−7.14194	−0.474027	−0.237014	−	0.971506i	$-0.576169\pi$
$227$	−7.14194	−0.474027	−0.237014	+	0.971506i	$0.576169\pi$
$228$	−12.4837	−0.826756
$229$	−8.41493	−0.556074	−0.278037	−	0.960570i	$-0.589684\pi$
$229$	−8.41493	−0.556074	−0.278037	+	0.960570i	$0.589684\pi$
$230$	0.815754	0.0537892
$231$	−1.47852	−0.0972793
$232$	−7.94882	−0.521865
$233$	−26.0543	−1.70687	−0.853437	−	0.521196i	$-0.825486\pi$
$233$	−26.0543	−1.70687	−0.853437	+	0.521196i	$0.825486\pi$
$234$	15.5491	1.01648
$235$	7.21973	0.470963
$236$	9.88656	0.643560
$237$	40.5256	2.63242
$238$	2.94566	0.190939
$239$	17.1905	1.11196	0.555980	−	0.831195i	$-0.312343\pi$
$239$	17.1905	1.11196	0.555980	+	0.831195i	$0.312343\pi$
$240$	2.53249	0.163471
$241$	−26.0696	−1.67929	−0.839644	−	0.543137i	$-0.817236\pi$
$241$	−26.0696	−1.67929	−0.839644	+	0.543137i	$0.817236\pi$
$242$	−1.00000	−0.0642824
$243$	−22.3594	−1.43436
$244$	−7.37908	−0.472397
$245$	−6.65915	−0.425438
$246$	−27.6985	−1.76599
$247$	22.4546	1.42875
$248$	2.45826	0.156100
$249$	0.0446920	0.00283224
$250$	−1.00000	−0.0632456
$251$	−19.8815	−1.25491	−0.627454	−	0.778654i	$-0.715903\pi$
$251$	−19.8815	−1.25491	−0.627454	+	0.778654i	$0.715903\pi$
$252$	−1.99286	−0.125539
$253$	−0.815754	−0.0512860
$254$	14.2359	0.893240
$255$	12.7776	0.800167
$256$	1.00000	0.0625000
$257$	9.58725	0.598036	0.299018	−	0.954247i	$-0.403341\pi$
$257$	9.58725	0.598036	0.299018	+	0.954247i	$0.403341\pi$
$258$	−2.53249	−0.157666
$259$	−1.98353	−0.123251
$260$	−4.55520	−0.282501
$261$	27.1332	1.67950
$262$	9.61130	0.593788
$263$	−1.68571	−0.103946	−0.0519728	−	0.998649i	$-0.516551\pi$
$263$	−1.68571	−0.103946	−0.0519728	+	0.998649i	$0.516551\pi$
$264$	−2.53249	−0.155864
$265$	11.9243	0.732504
$266$	−2.87790	−0.176456
$267$	−10.2494	−0.627252
$268$	9.44673	0.577051
$269$	1.64644	0.100385	0.0501927	−	0.998740i	$-0.484016\pi$
$269$	1.64644	0.100385	0.0501927	+	0.998740i	$0.484016\pi$
$270$	−1.04716	−0.0637281
$271$	−2.11722	−0.128612	−0.0643060	−	0.997930i	$-0.520483\pi$
$271$	−2.11722	−0.128612	−0.0643060	+	0.997930i	$0.520483\pi$
$272$	5.04549	0.305928
$273$	6.73494	0.407617
$274$	−14.6263	−0.883605
$275$	1.00000	0.0603023
$276$	−2.06589	−0.124352
$277$	11.7728	0.707357	0.353678	−	0.935367i	$-0.384931\pi$
$277$	11.7728	0.707357	0.353678	+	0.935367i	$0.384931\pi$
$278$	−11.7412	−0.704193
$279$	−8.39125	−0.502371
$280$	0.583820	0.0348899
$281$	6.18333	0.368867	0.184433	−	0.982845i	$-0.440955\pi$
$281$	6.18333	0.368867	0.184433	+	0.982845i	$0.440955\pi$
$282$	−18.2839	−1.08879
$283$	−29.0060	−1.72422	−0.862112	−	0.506717i	$-0.830859\pi$
$283$	−29.0060	−1.72422	−0.862112	+	0.506717i	$0.830859\pi$
$284$	11.2834	0.669547
$285$	−12.4837	−0.739473
$286$	4.55520	0.269355
$287$	−6.38541	−0.376919
$288$	−3.41349	−0.201142
$289$	8.45697	0.497469
$290$	−7.94882	−0.466771
$291$	7.83651	0.459384
$292$	−1.95228	−0.114249
$293$	31.7771	1.85644	0.928220	−	0.372033i	$-0.121339\pi$
$293$	31.7771	1.85644	0.928220	+	0.372033i	$0.121339\pi$
$294$	16.8642	0.983541
$295$	9.88656	0.575618
$296$	−3.39751	−0.197476
$297$	1.04716	0.0607623
$298$	23.6217	1.36837
$299$	3.71592	0.214897
$300$	2.53249	0.146213
$301$	−0.583820	−0.0336508
$302$	5.02949	0.289415
$303$	−41.0965	−2.36093
$304$	−4.92944	−0.282723
$305$	−7.37908	−0.422525
$306$	−17.2227	−0.984558
$307$	29.9260	1.70797	0.853984	−	0.520299i	$-0.174180\pi$
$307$	29.9260	1.70797	0.853984	+	0.520299i	$0.174180\pi$
$308$	−0.583820	−0.0332662
$309$	40.2095	2.28744
$310$	2.45826	0.139620
$311$	−33.8063	−1.91698	−0.958490	−	0.285127i	$-0.907964\pi$
$311$	−33.8063	−1.91698	−0.958490	+	0.285127i	$0.907964\pi$
$312$	11.5360	0.653096
$313$	−10.0501	−0.568065	−0.284032	−	0.958815i	$-0.591672\pi$
$313$	−10.0501	−0.568065	−0.284032	+	0.958815i	$0.591672\pi$
$314$	14.0823	0.794708
$315$	−1.99286	−0.112285
$316$	16.0023	0.900200
$317$	−5.78777	−0.325074	−0.162537	−	0.986702i	$-0.551968\pi$
$317$	−5.78777	−0.325074	−0.162537	+	0.986702i	$0.551968\pi$
$318$	−30.1981	−1.69343
$319$	7.94882	0.445048
$320$	1.00000	0.0559017
$321$	5.04083	0.281352
$322$	−0.476254	−0.0265406
$323$	−24.8714	−1.38388
$324$	−7.58855	−0.421586
$325$	−4.55520	−0.252677
$326$	−18.3786	−1.01789
$327$	15.0631	0.832991
$328$	−10.9373	−0.603911
$329$	−4.21502	−0.232382
$330$	−2.53249	−0.139409
$331$	−2.60786	−0.143341	−0.0716704	−	0.997428i	$-0.522833\pi$
$331$	−2.60786	−0.143341	−0.0716704	+	0.997428i	$0.522833\pi$
$332$	0.0176475	0.000968530 0
$333$	11.5974	0.635532
$334$	4.93771	0.270179
$335$	9.44673	0.516130
$336$	−1.47852	−0.0806597
$337$	−3.61378	−0.196855	−0.0984277	−	0.995144i	$-0.531381\pi$
$337$	−3.61378	−0.196855	−0.0984277	+	0.995144i	$0.531381\pi$
$338$	−7.74983	−0.421535
$339$	3.96941	0.215589
$340$	5.04549	0.273630
$341$	−2.45826	−0.133122
$342$	16.8266	0.909878
$343$	7.97449	0.430582
$344$	−1.00000	−0.0539164
$345$	−2.06589	−0.111224
$346$	−4.02612	−0.216445
$347$	−16.2439	−0.872016	−0.436008	−	0.899943i	$-0.643608\pi$
$347$	−16.2439	−0.872016	−0.436008	+	0.899943i	$0.643608\pi$
$348$	20.1303	1.07910
$349$	−36.5970	−1.95899	−0.979495	−	0.201468i	$-0.935429\pi$
$349$	−36.5970	−1.95899	−0.979495	+	0.201468i	$0.935429\pi$
$350$	0.583820	0.0312065
$351$	−4.77002	−0.254605
$352$	−1.00000	−0.0533002
$353$	−3.60517	−0.191884	−0.0959419	−	0.995387i	$-0.530586\pi$
$353$	−3.60517	−0.191884	−0.0959419	+	0.995387i	$0.530586\pi$
$354$	−25.0376	−1.33073
$355$	11.2834	0.598861
$356$	−4.04716	−0.214499
$357$	−7.45984	−0.394817
$358$	−22.7886	−1.20441
$359$	−0.996118	−0.0525731	−0.0262865	−	0.999654i	$-0.508368\pi$
$359$	−0.996118	−0.0525731	−0.0262865	+	0.999654i	$0.508368\pi$
$360$	−3.41349	−0.179907
$361$	5.29936	0.278913
$362$	−14.6773	−0.771421
$363$	2.53249	0.132921
$364$	2.65942	0.139391
$365$	−1.95228	−0.102187
$366$	18.6874	0.976807
$367$	−1.64638	−0.0859402	−0.0429701	−	0.999076i	$-0.513682\pi$
$367$	−1.64638	−0.0859402	−0.0429701	+	0.999076i	$0.513682\pi$
$368$	−0.815754	−0.0425241
$369$	37.3343	1.94355
$370$	−3.39751	−0.176628
$371$	−6.96164	−0.361431
$372$	−6.22551	−0.322778
$373$	−14.5695	−0.754381	−0.377190	−	0.926136i	$-0.623110\pi$
$373$	−14.5695	−0.754381	−0.377190	+	0.926136i	$0.623110\pi$
$374$	−5.04549	−0.260896
$375$	2.53249	0.130777
$376$	−7.21973	−0.372329
$377$	−36.2084	−1.86483
$378$	0.611352	0.0314446
$379$	17.4192	0.894765	0.447383	−	0.894343i	$-0.352356\pi$
$379$	17.4192	0.894765	0.447383	+	0.894343i	$0.352356\pi$
$380$	−4.92944	−0.252875
$381$	−36.0523	−1.84701
$382$	15.6918	0.802861
$383$	−30.5126	−1.55912	−0.779559	−	0.626328i	$-0.784557\pi$
$383$	−30.5126	−1.55912	−0.779559	+	0.626328i	$0.784557\pi$
$384$	−2.53249	−0.129235
$385$	−0.583820	−0.0297542
$386$	−16.6265	−0.846266
$387$	3.41349	0.173517
$388$	3.09439	0.157094
$389$	16.1307	0.817858	0.408929	−	0.912566i	$-0.365902\pi$
$389$	16.1307	0.817858	0.408929	+	0.912566i	$0.365902\pi$
$390$	11.5360	0.584147
$391$	−4.11588	−0.208149
$392$	6.65915	0.336338
$393$	−24.3405	−1.22782
$394$	17.0689	0.859920
$395$	16.0023	0.805163
$396$	3.41349	0.171534
$397$	−20.6024	−1.03401	−0.517003	−	0.855983i	$-0.672952\pi$
$397$	−20.6024	−1.03401	−0.517003	+	0.855983i	$0.672952\pi$
$398$	−2.64964	−0.132815
$399$	7.28826	0.364869
$400$	1.00000	0.0500000
$401$	7.69504	0.384272	0.192136	−	0.981368i	$-0.438459\pi$
$401$	7.69504	0.384272	0.192136	+	0.981368i	$0.438459\pi$
$402$	−23.9237	−1.19321
$403$	11.1979	0.557805
$404$	−16.2277	−0.807360
$405$	−7.58855	−0.377078
$406$	4.64068	0.230313
$407$	3.39751	0.168408
$408$	−12.7776	−0.632587
$409$	−35.5918	−1.75990	−0.879950	−	0.475066i	$-0.842424\pi$
$409$	−35.5918	−1.75990	−0.879950	+	0.475066i	$0.842424\pi$
$410$	−10.9373	−0.540154
$411$	37.0408	1.82709
$412$	15.8775	0.782227
$413$	−5.77197	−0.284020
$414$	2.78457	0.136854
$415$	0.0176475	0.000866280 0
$416$	4.55520	0.223337
$417$	29.7345	1.45611
$418$	4.92944	0.241107
$419$	23.2886	1.13772	0.568861	−	0.822434i	$-0.307384\pi$
$419$	23.2886	1.13772	0.568861	+	0.822434i	$0.307384\pi$
$420$	−1.47852	−0.0721442
$421$	−27.6647	−1.34830	−0.674148	−	0.738596i	$-0.735489\pi$
$421$	−27.6647	−1.34830	−0.674148	+	0.738596i	$0.735489\pi$
$422$	12.3084	0.599163
$423$	24.6445	1.19825
$424$	−11.9243	−0.579095
$425$	5.04549	0.244742
$426$	−28.5751	−1.38447
$427$	4.30805	0.208481
$428$	1.99047	0.0962129
$429$	−11.5360	−0.556962
$430$	−1.00000	−0.0482243
$431$	−31.7418	−1.52895	−0.764473	−	0.644656i	$-0.777001\pi$
$431$	−31.7418	−1.52895	−0.764473	+	0.644656i	$0.777001\pi$
$432$	1.04716	0.0503815
$433$	−3.14451	−0.151116	−0.0755579	−	0.997141i	$-0.524074\pi$
$433$	−3.14451	−0.151116	−0.0755579	+	0.997141i	$0.524074\pi$
$434$	−1.43518	−0.0688909
$435$	20.1303	0.965173
$436$	5.94794	0.284855
$437$	4.02121	0.192360
$438$	4.94413	0.236240
$439$	−1.21375	−0.0579292	−0.0289646	−	0.999580i	$-0.509221\pi$
$439$	−1.21375	−0.0579292	−0.0289646	+	0.999580i	$0.509221\pi$
$440$	−1.00000	−0.0476731
$441$	−22.7310	−1.08243
$442$	22.9832	1.09320
$443$	14.3917	0.683771	0.341886	−	0.939742i	$-0.388934\pi$
$443$	14.3917	0.683771	0.341886	+	0.939742i	$0.388934\pi$
$444$	8.60415	0.408335
$445$	−4.04716	−0.191854
$446$	20.1134	0.952399
$447$	−59.8216	−2.82946
$448$	−0.583820	−0.0275829
$449$	37.0597	1.74896	0.874478	−	0.485065i	$-0.161204\pi$
$449$	37.0597	1.74896	0.874478	+	0.485065i	$0.161204\pi$
$450$	−3.41349	−0.160913
$451$	10.9373	0.515017
$452$	1.56740	0.0737241
$453$	−12.7371	−0.598442
$454$	7.14194	0.335188
$455$	2.65942	0.124675
$456$	12.4837	0.584605
$457$	26.5804	1.24338	0.621690	−	0.783263i	$-0.286446\pi$
$457$	26.5804	1.24338	0.621690	+	0.783263i	$0.286446\pi$
$458$	8.41493	0.393204
$459$	5.28343	0.246609
$460$	−0.815754	−0.0380347
$461$	20.9312	0.974865	0.487433	−	0.873161i	$-0.337933\pi$
$461$	20.9312	0.974865	0.487433	+	0.873161i	$0.337933\pi$
$462$	1.47852	0.0687868
$463$	−15.7816	−0.733434	−0.366717	−	0.930333i	$-0.619518\pi$
$463$	−15.7816	−0.733434	−0.366717	+	0.930333i	$0.619518\pi$
$464$	7.94882	0.369015
$465$	−6.22551	−0.288701
$466$	26.0543	1.20694
$467$	−14.4659	−0.669400	−0.334700	−	0.942325i	$-0.608635\pi$
$467$	−14.4659	−0.669400	−0.334700	+	0.942325i	$0.608635\pi$
$468$	−15.5491	−0.718759
$469$	−5.51519	−0.254668
$470$	−7.21973	−0.333021
$471$	−35.6631	−1.64327
$472$	−9.88656	−0.455066
$473$	1.00000	0.0459800
$474$	−40.5256	−1.86140
$475$	−4.92944	−0.226178
$476$	−2.94566	−0.135014
$477$	40.7035	1.86368
$478$	−17.1905	−0.786275
$479$	0.630533	0.0288098	0.0144049	−	0.999896i	$-0.495415\pi$
$479$	0.630533	0.0288098	0.0144049	+	0.999896i	$0.495415\pi$
$480$	−2.53249	−0.115592
$481$	−15.4763	−0.705660
$482$	26.0696	1.18744
$483$	1.20611	0.0548797
$484$	1.00000	0.0454545
$485$	3.09439	0.140509
$486$	22.3594	1.01424
$487$	−26.5453	−1.20288	−0.601442	−	0.798916i	$-0.705407\pi$
$487$	−26.5453	−1.20288	−0.601442	+	0.798916i	$0.705407\pi$
$488$	7.37908	0.334035
$489$	46.5435	2.10477
$490$	6.65915	0.300830
$491$	11.5756	0.522401	0.261200	−	0.965285i	$-0.415882\pi$
$491$	11.5756	0.522401	0.261200	+	0.965285i	$0.415882\pi$
$492$	27.6985	1.24875
$493$	40.1057	1.80627
$494$	−22.4546	−1.01028
$495$	3.41349	0.153425
$496$	−2.45826	−0.110379
$497$	−6.58748	−0.295489
$498$	−0.0446920	−0.00200269
$499$	38.0328	1.70258	0.851291	−	0.524693i	$-0.175820\pi$
$499$	38.0328	1.70258	0.851291	+	0.524693i	$0.175820\pi$
$500$	1.00000	0.0447214
$501$	−12.5047	−0.558668
$502$	19.8815	0.887354
$503$	14.6478	0.653112	0.326556	−	0.945178i	$-0.394112\pi$
$503$	14.6478	0.653112	0.326556	+	0.945178i	$0.394112\pi$
$504$	1.99286	0.0887692
$505$	−16.2277	−0.722124
$506$	0.815754	0.0362647
$507$	19.6264	0.871637
$508$	−14.2359	−0.631616
$509$	22.6830	1.00541	0.502703	−	0.864459i	$-0.332339\pi$
$509$	22.6830	1.00541	0.502703	+	0.864459i	$0.332339\pi$
$510$	−12.7776	−0.565803
$511$	1.13978	0.0504210
$512$	−1.00000	−0.0441942
$513$	−5.16190	−0.227904
$514$	−9.58725	−0.422876
$515$	15.8775	0.699645
$516$	2.53249	0.111487
$517$	7.21973	0.317523
$518$	1.98353	0.0871515
$519$	10.1961	0.447559
$520$	4.55520	0.199759
$521$	6.33354	0.277478	0.138739	−	0.990329i	$-0.455695\pi$
$521$	6.33354	0.277478	0.138739	+	0.990329i	$0.455695\pi$
$522$	−27.1332	−1.18759
$523$	35.8448	1.56738	0.783691	−	0.621151i	$-0.213335\pi$
$523$	35.8448	1.56738	0.783691	+	0.621151i	$0.213335\pi$
$524$	−9.61130	−0.419871
$525$	−1.47852	−0.0645278
$526$	1.68571	0.0735007
$527$	−12.4031	−0.540289
$528$	2.53249	0.110212
$529$	−22.3345	−0.971067
$530$	−11.9243	−0.517958
$531$	33.7477	1.46452
$532$	2.87790	0.124773
$533$	−49.8215	−2.15801
$534$	10.2494	0.443534
$535$	1.99047	0.0860554
$536$	−9.44673	−0.408037
$537$	57.7118	2.49045
$538$	−1.64644	−0.0709832
$539$	−6.65915	−0.286830
$540$	1.04716	0.0450625
$541$	−33.6136	−1.44516	−0.722580	−	0.691287i	$-0.757044\pi$
$541$	−33.6136	−1.44516	−0.722580	+	0.691287i	$0.757044\pi$
$542$	2.11722	0.0909424
$543$	37.1700	1.59512
$544$	−5.04549	−0.216324
$545$	5.94794	0.254782
$546$	−6.73494	−0.288229
$547$	−8.36898	−0.357832	−0.178916	−	0.983864i	$-0.557259\pi$
$547$	−8.36898	−0.357832	−0.178916	+	0.983864i	$0.557259\pi$
$548$	14.6263	0.624803
$549$	−25.1884	−1.07502
$550$	−1.00000	−0.0426401
$551$	−39.1832	−1.66926
$552$	2.06589	0.0879299
$553$	−9.34247	−0.397282
$554$	−11.7728	−0.500177
$555$	8.60415	0.365226
$556$	11.7412	0.497939
$557$	4.53983	0.192359	0.0961793	−	0.995364i	$-0.469338\pi$
$557$	4.53983	0.192359	0.0961793	+	0.995364i	$0.469338\pi$
$558$	8.39125	0.355230
$559$	−4.55520	−0.192664
$560$	−0.583820	−0.0246709
$561$	12.7776	0.539472
$562$	−6.18333	−0.260828
$563$	17.1652	0.723427	0.361714	−	0.932289i	$-0.382192\pi$
$563$	17.1652	0.723427	0.361714	+	0.932289i	$0.382192\pi$
$564$	18.2839	0.769889
$565$	1.56740	0.0659408
$566$	29.0060	1.21921
$567$	4.43035	0.186057
$568$	−11.2834	−0.473441
$569$	−40.6384	−1.70365	−0.851824	−	0.523828i	$-0.824504\pi$
$569$	−40.6384	−1.70365	−0.851824	+	0.523828i	$0.824504\pi$
$570$	12.4837	0.522886
$571$	34.0159	1.42352	0.711761	−	0.702422i	$-0.247898\pi$
$571$	34.0159	1.42352	0.711761	+	0.702422i	$0.247898\pi$
$572$	−4.55520	−0.190462
$573$	−39.7392	−1.66013
$574$	6.38541	0.266522
$575$	−0.815754	−0.0340193
$576$	3.41349	0.142229
$577$	0.948124	0.0394709	0.0197355	−	0.999805i	$-0.493718\pi$
$577$	0.948124	0.0394709	0.0197355	+	0.999805i	$0.493718\pi$
$578$	−8.45697	−0.351764
$579$	42.1064	1.74988
$580$	7.94882	0.330057
$581$	−0.0103029	−0.000427438 0
$582$	−7.83651	−0.324834
$583$	11.9243	0.493854
$584$	1.95228	0.0807860
$585$	−15.5491	−0.642877
$586$	−31.7771	−1.31270
$587$	9.62369	0.397212	0.198606	−	0.980079i	$-0.436359\pi$
$587$	9.62369	0.397212	0.198606	+	0.980079i	$0.436359\pi$
$588$	−16.8642	−0.695469
$589$	12.1178	0.499307
$590$	−9.88656	−0.407023
$591$	−43.2269	−1.77812
$592$	3.39751	0.139637
$593$	17.5234	0.719599	0.359800	−	0.933030i	$-0.382845\pi$
$593$	17.5234	0.719599	0.359800	+	0.933030i	$0.382845\pi$
$594$	−1.04716	−0.0429654
$595$	−2.94566	−0.120760
$596$	−23.6217	−0.967581
$597$	6.71019	0.274630
$598$	−3.71592	−0.151955
$599$	1.17796	0.0481300	0.0240650	−	0.999710i	$-0.492339\pi$
$599$	1.17796	0.0481300	0.0240650	+	0.999710i	$0.492339\pi$
$600$	−2.53249	−0.103388
$601$	4.94523	0.201720	0.100860	−	0.994901i	$-0.467841\pi$
$601$	4.94523	0.201720	0.100860	+	0.994901i	$0.467841\pi$
$602$	0.583820	0.0237947
$603$	32.2463	1.31317
$604$	−5.02949	−0.204647
$605$	1.00000	0.0406558
$606$	41.0965	1.66943
$607$	47.2175	1.91650	0.958250	−	0.285932i	$-0.0923031\pi$
$607$	47.2175	1.91650	0.958250	+	0.285932i	$0.0923031\pi$
$608$	4.92944	0.199915
$609$	−11.7525	−0.476234
$610$	7.37908	0.298770
$611$	−32.8873	−1.33048
$612$	17.2227	0.696188
$613$	−11.0345	−0.445679	−0.222839	−	0.974855i	$-0.571533\pi$
$613$	−11.0345	−0.445679	−0.222839	+	0.974855i	$0.571533\pi$
$614$	−29.9260	−1.20772
$615$	27.6985	1.11691
$616$	0.583820	0.0235228
$617$	18.0283	0.725791	0.362895	−	0.931830i	$-0.381788\pi$
$617$	18.0283	0.725791	0.362895	+	0.931830i	$0.381788\pi$
$618$	−40.2095	−1.61746
$619$	15.4212	0.619830	0.309915	−	0.950764i	$-0.399699\pi$
$619$	15.4212	0.619830	0.309915	+	0.950764i	$0.399699\pi$
$620$	−2.45826	−0.0987261
$621$	−0.854224	−0.0342788
$622$	33.8063	1.35551
$623$	2.36281	0.0946641
$624$	−11.5360	−0.461809
$625$	1.00000	0.0400000
$626$	10.0501	0.401682
$627$	−12.4837	−0.498552
$628$	−14.0823	−0.561943
$629$	17.1421	0.683500
$630$	1.99286	0.0793976
$631$	−19.0201	−0.757180	−0.378590	−	0.925564i	$-0.623591\pi$
$631$	−19.0201	−0.757180	−0.378590	+	0.925564i	$0.623591\pi$
$632$	−16.0023	−0.636538
$633$	−31.1708	−1.23893
$634$	5.78777	0.229862
$635$	−14.2359	−0.564935
$636$	30.1981	1.19743
$637$	30.3338	1.20187
$638$	−7.94882	−0.314697
$639$	38.5158	1.52366
$640$	−1.00000	−0.0395285
$641$	−18.1488	−0.716836	−0.358418	−	0.933561i	$-0.616684\pi$
$641$	−18.1488	−0.716836	−0.358418	+	0.933561i	$0.616684\pi$
$642$	−5.04083	−0.198946
$643$	23.5214	0.927593	0.463796	−	0.885942i	$-0.346487\pi$
$643$	23.5214	0.927593	0.463796	+	0.885942i	$0.346487\pi$
$644$	0.476254	0.0187670
$645$	2.53249	0.0997166
$646$	24.8714	0.978553
$647$	−8.30021	−0.326315	−0.163157	−	0.986600i	$-0.552168\pi$
$647$	−8.30021	−0.326315	−0.163157	+	0.986600i	$0.552168\pi$
$648$	7.58855	0.298107
$649$	9.88656	0.388081
$650$	4.55520	0.178670
$651$	3.63458	0.142450
$652$	18.3786	0.719760
$653$	−35.7957	−1.40079	−0.700396	−	0.713754i	$-0.746993\pi$
$653$	−35.7957	−1.40079	−0.700396	+	0.713754i	$0.746993\pi$
$654$	−15.0631	−0.589013
$655$	−9.61130	−0.375544
$656$	10.9373	0.427029
$657$	−6.66410	−0.259991
$658$	4.21502	0.164319
$659$	8.74484	0.340651	0.170325	−	0.985388i	$-0.445518\pi$
$659$	8.74484	0.340651	0.170325	+	0.985388i	$0.445518\pi$
$660$	2.53249	0.0985769
$661$	−24.4400	−0.950607	−0.475304	−	0.879822i	$-0.657662\pi$
$661$	−24.4400	−0.950607	−0.475304	+	0.879822i	$0.657662\pi$
$662$	2.60786	0.101357
$663$	−58.2047	−2.26048
$664$	−0.0176475	−0.000684854 0
$665$	2.87790	0.111600
$666$	−11.5974	−0.449389
$667$	−6.48428	−0.251072
$668$	−4.93771	−0.191046
$669$	−50.9370	−1.96934
$670$	−9.44673	−0.364959
$671$	−7.37908	−0.284866
$672$	1.47852	0.0570350
$673$	33.8166	1.30354	0.651768	−	0.758419i	$-0.274028\pi$
$673$	33.8166	1.30354	0.651768	+	0.758419i	$0.274028\pi$
$674$	3.61378	0.139198
$675$	1.04716	0.0403052
$676$	7.74983	0.298070
$677$	−27.9108	−1.07270	−0.536349	−	0.843996i	$-0.680197\pi$
$677$	−27.9108	−1.07270	−0.536349	+	0.843996i	$0.680197\pi$
$678$	−3.96941	−0.152444
$679$	−1.80657	−0.0693297
$680$	−5.04549	−0.193486
$681$	−18.0869	−0.693090
$682$	2.45826	0.0941316
$683$	51.8370	1.98349	0.991745	−	0.128228i	$-0.0409289\pi$
$683$	51.8370	1.98349	0.991745	+	0.128228i	$0.0409289\pi$
$684$	−16.8266	−0.643381
$685$	14.6263	0.558841
$686$	−7.97449	−0.304467
$687$	−21.3107	−0.813054
$688$	1.00000	0.0381246
$689$	−54.3175	−2.06933
$690$	2.06589	0.0786469
$691$	15.0849	0.573856	0.286928	−	0.957952i	$-0.407366\pi$
$691$	15.0849	0.573856	0.286928	+	0.957952i	$0.407366\pi$
$692$	4.02612	0.153050
$693$	−1.99286	−0.0757027
$694$	16.2439	0.616608
$695$	11.7412	0.445371
$696$	−20.1303	−0.763036
$697$	55.1840	2.09024
$698$	36.5970	1.38522
$699$	−65.9822	−2.49568
$700$	−0.583820	−0.0220663
$701$	19.8774	0.750760	0.375380	−	0.926871i	$-0.377512\pi$
$701$	19.8774	0.750760	0.375380	+	0.926871i	$0.377512\pi$
$702$	4.77002	0.180033
$703$	−16.7478	−0.631656
$704$	1.00000	0.0376889
$705$	18.2839	0.688610
$706$	3.60517	0.135682
$707$	9.47407	0.356309
$708$	25.0376	0.940970
$709$	35.4530	1.33147	0.665734	−	0.746190i	$-0.268119\pi$
$709$	35.4530	1.33147	0.665734	+	0.746190i	$0.268119\pi$
$710$	−11.2834	−0.423458
$711$	54.6237	2.04855
$712$	4.04716	0.151674
$713$	2.00533	0.0751004
$714$	7.45984	0.279178
$715$	−4.55520	−0.170355
$716$	22.7886	0.851649
$717$	43.5347	1.62583
$718$	0.996118	0.0371748
$719$	−17.9118	−0.667998	−0.333999	−	0.942573i	$-0.608398\pi$
$719$	−17.9118	−0.667998	−0.333999	+	0.942573i	$0.608398\pi$
$720$	3.41349	0.127213
$721$	−9.26959	−0.345217
$722$	−5.29936	−0.197222
$723$	−66.0208	−2.45534
$724$	14.6773	0.545477
$725$	7.94882	0.295212
$726$	−2.53249	−0.0939894
$727$	−41.4357	−1.53677	−0.768383	−	0.639991i	$-0.778938\pi$
$727$	−41.4357	−1.53677	−0.768383	+	0.639991i	$0.778938\pi$
$728$	−2.65942	−0.0985645
$729$	−33.8592	−1.25404
$730$	1.95228	0.0722572
$731$	5.04549	0.186614
$732$	−18.6874	−0.690707
$733$	31.1540	1.15070	0.575349	−	0.817908i	$-0.304866\pi$
$733$	31.1540	1.15070	0.575349	+	0.817908i	$0.304866\pi$
$734$	1.64638	0.0607689
$735$	−16.8642	−0.622046
$736$	0.815754	0.0300691
$737$	9.44673	0.347975
$738$	−37.3343	−1.37430
$739$	50.0623	1.84157	0.920786	−	0.390068i	$-0.127549\pi$
$739$	50.0623	1.84157	0.920786	+	0.390068i	$0.127549\pi$
$740$	3.39751	0.124895
$741$	56.8659	2.08902
$742$	6.96164	0.255570
$743$	43.2272	1.58585	0.792926	−	0.609318i	$-0.208557\pi$
$743$	43.2272	1.58585	0.792926	+	0.609318i	$0.208557\pi$
$744$	6.22551	0.228238
$745$	−23.6217	−0.865431
$746$	14.5695	0.533428
$747$	0.0602394	0.00220405
$748$	5.04549	0.184481
$749$	−1.16207	−0.0424613
$750$	−2.53249	−0.0924733
$751$	−29.8808	−1.09037	−0.545183	−	0.838317i	$-0.683540\pi$
$751$	−29.8808	−1.09037	−0.545183	+	0.838317i	$0.683540\pi$
$752$	7.21973	0.263276
$753$	−50.3496	−1.83484
$754$	36.2084	1.31863
$755$	−5.02949	−0.183042
$756$	−0.611352	−0.0222347
$757$	28.0307	1.01879	0.509397	−	0.860532i	$-0.329869\pi$
$757$	28.0307	1.01879	0.509397	+	0.860532i	$0.329869\pi$
$758$	−17.4192	−0.632695
$759$	−2.06589	−0.0749869
$760$	4.92944	0.178809
$761$	10.4620	0.379247	0.189624	−	0.981857i	$-0.439273\pi$
$761$	10.4620	0.379247	0.189624	+	0.981857i	$0.439273\pi$
$762$	36.0523	1.30604
$763$	−3.47253	−0.125714
$764$	−15.6918	−0.567708
$765$	17.2227	0.622689
$766$	30.5126	1.10246
$767$	−45.0352	−1.62613
$768$	2.53249	0.0913833
$769$	16.1772	0.583366	0.291683	−	0.956515i	$-0.405785\pi$
$769$	16.1772	0.583366	0.291683	+	0.956515i	$0.405785\pi$
$770$	0.583820	0.0210394
$771$	24.2796	0.874408
$772$	16.6265	0.598400
$773$	−29.7787	−1.07106	−0.535532	−	0.844515i	$-0.679889\pi$
$773$	−29.7787	−1.07106	−0.535532	+	0.844515i	$0.679889\pi$
$774$	−3.41349	−0.122695
$775$	−2.45826	−0.0883033
$776$	−3.09439	−0.111082
$777$	−5.02327	−0.180209
$778$	−16.1307	−0.578313
$779$	−53.9147	−1.93169
$780$	−11.5360	−0.413054
$781$	11.2834	0.403752
$782$	4.11588	0.147184
$783$	8.32367	0.297464
$784$	−6.65915	−0.237827
$785$	−14.0823	−0.502617
$786$	24.3405	0.868196
$787$	9.30091	0.331542	0.165771	−	0.986164i	$-0.446989\pi$
$787$	9.30091	0.331542	0.165771	+	0.986164i	$0.446989\pi$
$788$	−17.0689	−0.608056
$789$	−4.26905	−0.151982
$790$	−16.0023	−0.569337
$791$	−0.915077	−0.0325364
$792$	−3.41349	−0.121293
$793$	33.6132	1.19364
$794$	20.6024	0.731153
$795$	30.1981	1.07102
$796$	2.64964	0.0939142
$797$	29.8483	1.05728	0.528641	−	0.848845i	$-0.322702\pi$
$797$	29.8483	1.05728	0.528641	+	0.848845i	$0.322702\pi$
$798$	−7.28826	−0.258001
$799$	36.4271	1.28870
$800$	−1.00000	−0.0353553
$801$	−13.8149	−0.488127
$802$	−7.69504	−0.271721
$803$	−1.95228	−0.0688946
$804$	23.9237	0.843725
$805$	0.476254	0.0167857
$806$	−11.1979	−0.394428
$807$	4.16960	0.146777
$808$	16.2277	0.570890
$809$	−25.3798	−0.892305	−0.446153	−	0.894957i	$-0.647206\pi$
$809$	−25.3798	−0.892305	−0.446153	+	0.894957i	$0.647206\pi$
$810$	7.58855	0.266635
$811$	25.9330	0.910632	0.455316	−	0.890330i	$-0.349526\pi$
$811$	25.9330	0.910632	0.455316	+	0.890330i	$0.349526\pi$
$812$	−4.64068	−0.162856
$813$	−5.36184	−0.188048
$814$	−3.39751	−0.119083
$815$	18.3786	0.643773
$816$	12.7776	0.447307
$817$	−4.92944	−0.172459
$818$	35.5918	1.24444
$819$	9.07789	0.317207
$820$	10.9373	0.381947
$821$	10.6854	0.372924	0.186462	−	0.982462i	$-0.440298\pi$
$821$	10.6854	0.372924	0.186462	+	0.982462i	$0.440298\pi$
$822$	−37.0408	−1.29195
$823$	−39.8524	−1.38917	−0.694583	−	0.719413i	$-0.744411\pi$
$823$	−39.8524	−1.38917	−0.694583	+	0.719413i	$0.744411\pi$
$824$	−15.8775	−0.553118
$825$	2.53249	0.0881699
$826$	5.77197	0.200833
$827$	34.0616	1.18444	0.592218	−	0.805778i	$-0.298252\pi$
$827$	34.0616	1.18444	0.592218	+	0.805778i	$0.298252\pi$
$828$	−2.78457	−0.0967704
$829$	−39.6901	−1.37849	−0.689247	−	0.724526i	$-0.742058\pi$
$829$	−39.6901	−1.37849	−0.689247	+	0.724526i	$0.742058\pi$
$830$	−0.0176475	−0.000612552 0
$831$	29.8144	1.03425
$832$	−4.55520	−0.157923
$833$	−33.5987	−1.16413
$834$	−29.7345	−1.02962
$835$	−4.93771	−0.170876
$836$	−4.92944	−0.170488
$837$	−2.57419	−0.0889770
$838$	−23.2886	−0.804490
$839$	−24.2538	−0.837333	−0.418667	−	0.908140i	$-0.637502\pi$
$839$	−24.2538	−0.837333	−0.418667	+	0.908140i	$0.637502\pi$
$840$	1.47852	0.0510137
$841$	34.1837	1.17875
$842$	27.6647	0.953390
$843$	15.6592	0.539332
$844$	−12.3084	−0.423672
$845$	7.74983	0.266602
$846$	−24.6445	−0.847294
$847$	−0.583820	−0.0200603
$848$	11.9243	0.409482
$849$	−73.4572	−2.52104
$850$	−5.04549	−0.173059
$851$	−2.77153	−0.0950069
$852$	28.5751	0.978966
$853$	42.6761	1.46120	0.730600	−	0.682805i	$-0.239240\pi$
$853$	42.6761	1.46120	0.730600	+	0.682805i	$0.239240\pi$
$854$	−4.30805	−0.147419
$855$	−16.8266	−0.575457
$856$	−1.99047	−0.0680328
$857$	40.1740	1.37232	0.686160	−	0.727451i	$-0.259295\pi$
$857$	40.1740	1.37232	0.686160	+	0.727451i	$0.259295\pi$
$858$	11.5360	0.393832
$859$	−54.1225	−1.84663	−0.923317	−	0.384038i	$-0.874533\pi$
$859$	−54.1225	−1.84663	−0.923317	+	0.384038i	$0.874533\pi$
$860$	1.00000	0.0340997
$861$	−16.1710	−0.551105
$862$	31.7418	1.08113
$863$	−12.4671	−0.424385	−0.212192	−	0.977228i	$-0.568060\pi$
$863$	−12.4671	−0.424385	−0.212192	+	0.977228i	$0.568060\pi$
$864$	−1.04716	−0.0356251
$865$	4.02612	0.136892
$866$	3.14451	0.106855
$867$	21.4172	0.727365
$868$	1.43518	0.0487132
$869$	16.0023	0.542841
$870$	−20.1303	−0.682480
$871$	−43.0317	−1.45807
$872$	−5.94794	−0.201423
$873$	10.5627	0.357492
$874$	−4.02121	−0.136019
$875$	−0.583820	−0.0197367
$876$	−4.94413	−0.167047
$877$	13.5911	0.458940	0.229470	−	0.973316i	$-0.426301\pi$
$877$	13.5911	0.458940	0.229470	+	0.973316i	$0.426301\pi$
$878$	1.21375	0.0409621
$879$	80.4751	2.71436
$880$	1.00000	0.0337100
$881$	−43.5037	−1.46568	−0.732839	−	0.680402i	$-0.761805\pi$
$881$	−43.5037	−1.46568	−0.732839	+	0.680402i	$0.761805\pi$
$882$	22.7310	0.765391
$883$	−33.3274	−1.12156	−0.560778	−	0.827966i	$-0.689498\pi$
$883$	−33.3274	−1.12156	−0.560778	+	0.827966i	$0.689498\pi$
$884$	−22.9832	−0.773009
$885$	25.0376	0.841629
$886$	−14.3917	−0.483499
$887$	6.15054	0.206515	0.103257	−	0.994655i	$-0.467073\pi$
$887$	6.15054	0.206515	0.103257	+	0.994655i	$0.467073\pi$
$888$	−8.60415	−0.288736
$889$	8.31121	0.278749
$890$	4.04716	0.135661
$891$	−7.58855	−0.254226
$892$	−20.1134	−0.673448
$893$	−35.5892	−1.19095
$894$	59.8216	2.00073
$895$	22.7886	0.761738
$896$	0.583820	0.0195041
$897$	9.41052	0.314208
$898$	−37.0597	−1.23670
$899$	−19.5403	−0.651704
$900$	3.41349	0.113783
$901$	60.1639	2.00435
$902$	−10.9373	−0.364172
$903$	−1.47852	−0.0492020
$904$	−1.56740	−0.0521308
$905$	14.6773	0.487890
$906$	12.7371	0.423163
$907$	0.695483	0.0230931	0.0115466	−	0.999933i	$-0.496325\pi$
$907$	0.695483	0.0230931	0.0115466	+	0.999933i	$0.496325\pi$
$908$	−7.14194	−0.237014
$909$	−55.3932	−1.83728
$910$	−2.65942	−0.0881588
$911$	3.77664	0.125126	0.0625629	−	0.998041i	$-0.480073\pi$
$911$	3.77664	0.125126	0.0625629	+	0.998041i	$0.480073\pi$
$912$	−12.4837	−0.413378
$913$	0.0176475	0.000584046 0
$914$	−26.5804	−0.879202
$915$	−18.6874	−0.617787
$916$	−8.41493	−0.278037
$917$	5.61127	0.185300
$918$	−5.28343	−0.174379
$919$	53.9165	1.77854	0.889271	−	0.457381i	$-0.151212\pi$
$919$	53.9165	1.77854	0.889271	+	0.457381i	$0.151212\pi$
$920$	0.815754	0.0268946
$921$	75.7873	2.49728
$922$	−20.9312	−0.689334
$923$	−51.3981	−1.69179
$924$	−1.47852	−0.0486396
$925$	3.39751	0.111709
$926$	15.7816	0.518616
$927$	54.1976	1.78008
$928$	−7.94882	−0.260933
$929$	3.14341	0.103132	0.0515659	−	0.998670i	$-0.483579\pi$
$929$	3.14341	0.103132	0.0515659	+	0.998670i	$0.483579\pi$
$930$	6.22551	0.204143
$931$	32.8259	1.07582
$932$	−26.0543	−0.853437
$933$	−85.6140	−2.80288
$934$	14.4659	0.473337
$935$	5.04549	0.165005
$936$	15.5491	0.508239
$937$	−6.42862	−0.210014	−0.105007	−	0.994471i	$-0.533486\pi$
$937$	−6.42862	−0.210014	−0.105007	+	0.994471i	$0.533486\pi$
$938$	5.51519	0.180077
$939$	−25.4517	−0.830586
$940$	7.21973	0.235481
$941$	−17.2433	−0.562115	−0.281058	−	0.959691i	$-0.590685\pi$
$941$	−17.2433	−0.562115	−0.281058	+	0.959691i	$0.590685\pi$
$942$	35.6631	1.16197
$943$	−8.92214	−0.290545
$944$	9.88656	0.321780
$945$	−0.611352	−0.0198873
$946$	−1.00000	−0.0325128
$947$	1.87122	0.0608066	0.0304033	−	0.999538i	$-0.490321\pi$
$947$	1.87122	0.0608066	0.0304033	+	0.999538i	$0.490321\pi$
$948$	40.5256	1.31621
$949$	8.89304	0.288680
$950$	4.92944	0.159932
$951$	−14.6575	−0.475301
$952$	2.94566	0.0954694
$953$	51.3865	1.66457	0.832285	−	0.554347i	$-0.187032\pi$
$953$	51.3865	1.66457	0.832285	+	0.554347i	$0.187032\pi$
$954$	−40.7035	−1.31782
$955$	−15.6918	−0.507774
$956$	17.1905	0.555980
$957$	20.1303	0.650719
$958$	−0.630533	−0.0203716
$959$	−8.53911	−0.275742
$960$	2.53249	0.0817357
$961$	−24.9570	−0.805063
$962$	15.4763	0.498977
$963$	6.79444	0.218948
$964$	−26.0696	−0.839644
$965$	16.6265	0.535226
$966$	−1.20611	−0.0388058
$967$	16.4900	0.530284	0.265142	−	0.964209i	$-0.414581\pi$
$967$	16.4900	0.530284	0.265142	+	0.964209i	$0.414581\pi$
$968$	−1.00000	−0.0321412
$969$	−62.9866	−2.02342
$970$	−3.09439	−0.0993549
$971$	−34.4893	−1.10681	−0.553407	−	0.832911i	$-0.686673\pi$
$971$	−34.4893	−1.10681	−0.553407	+	0.832911i	$0.686673\pi$
$972$	−22.3594	−0.717178
$973$	−6.85477	−0.219754
$974$	26.5453	0.850568
$975$	−11.5360	−0.369447
$976$	−7.37908	−0.236198
$977$	32.0527	1.02546	0.512729	−	0.858551i	$-0.328635\pi$
$977$	32.0527	1.02546	0.512729	+	0.858551i	$0.328635\pi$
$978$	−46.5435	−1.48830
$979$	−4.04716	−0.129348
$980$	−6.65915	−0.212719
$981$	20.3033	0.648233
$982$	−11.5756	−0.369393
$983$	33.0705	1.05478	0.527392	−	0.849622i	$-0.323170\pi$
$983$	33.0705	1.05478	0.527392	+	0.849622i	$0.323170\pi$
$984$	−27.6985	−0.882997
$985$	−17.0689	−0.543861
$986$	−40.1057	−1.27723
$987$	−10.6745	−0.339773
$988$	22.4546	0.714375
$989$	−0.815754	−0.0259395
$990$	−3.41349	−0.108488
$991$	17.7451	0.563693	0.281846	−	0.959460i	$-0.409053\pi$
$991$	17.7451	0.563693	0.281846	+	0.959460i	$0.409053\pi$
$992$	2.45826	0.0780498
$993$	−6.60436	−0.209583
$994$	6.58748	0.208942
$995$	2.64964	0.0839994
$996$	0.0446920	0.00141612
$997$	−17.4927	−0.553998	−0.276999	−	0.960870i	$-0.589340\pi$
$997$	−17.4927	−0.553998	−0.276999	+	0.960870i	$0.589340\pi$
$998$	−38.0328	−1.20391
$999$	3.55773	0.112562

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4730.2.a.z.1.8	✓	10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4730.2.a.z.1.8	✓	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)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +2.53249 q^{3} +1.00000 q^{4} +1.00000 q^{5} -2.53249 q^{6} -0.583820 q^{7} -1.00000 q^{8} +3.41349 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +2.53249 q^{3} +1.00000 q^{4} +1.00000 q^{5} -2.53249 q^{6} -0.583820 q^{7} -1.00000 q^{8} +3.41349 q^{9} -1.00000 q^{10} +1.00000 q^{11} +2.53249 q^{12} -4.55520 q^{13} +0.583820 q^{14} +2.53249 q^{15} +1.00000 q^{16} +5.04549 q^{17} -3.41349 q^{18} -4.92944 q^{19} +1.00000 q^{20} -1.47852 q^{21} -1.00000 q^{22} -0.815754 q^{23} -2.53249 q^{24} +1.00000 q^{25} +4.55520 q^{26} +1.04716 q^{27} -0.583820 q^{28} +7.94882 q^{29} -2.53249 q^{30} -2.45826 q^{31} -1.00000 q^{32} +2.53249 q^{33} -5.04549 q^{34} -0.583820 q^{35} +3.41349 q^{36} +3.39751 q^{37} +4.92944 q^{38} -11.5360 q^{39} -1.00000 q^{40} +10.9373 q^{41} +1.47852 q^{42} +1.00000 q^{43} +1.00000 q^{44} +3.41349 q^{45} +0.815754 q^{46} +7.21973 q^{47} +2.53249 q^{48} -6.65915 q^{49} -1.00000 q^{50} +12.7776 q^{51} -4.55520 q^{52} +11.9243 q^{53} -1.04716 q^{54} +1.00000 q^{55} +0.583820 q^{56} -12.4837 q^{57} -7.94882 q^{58} +9.88656 q^{59} +2.53249 q^{60} -7.37908 q^{61} +2.45826 q^{62} -1.99286 q^{63} +1.00000 q^{64} -4.55520 q^{65} -2.53249 q^{66} +9.44673 q^{67} +5.04549 q^{68} -2.06589 q^{69} +0.583820 q^{70} +11.2834 q^{71} -3.41349 q^{72} -1.95228 q^{73} -3.39751 q^{74} +2.53249 q^{75} -4.92944 q^{76} -0.583820 q^{77} +11.5360 q^{78} +16.0023 q^{79} +1.00000 q^{80} -7.58855 q^{81} -10.9373 q^{82} +0.0176475 q^{83} -1.47852 q^{84} +5.04549 q^{85} -1.00000 q^{86} +20.1303 q^{87} -1.00000 q^{88} -4.04716 q^{89} -3.41349 q^{90} +2.65942 q^{91} -0.815754 q^{92} -6.22551 q^{93} -7.21973 q^{94} -4.92944 q^{95} -2.53249 q^{96} +3.09439 q^{97} +6.65915 q^{98} +3.41349 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - 10 q^{2} + 8 q^{3} + 10 q^{4} + 10 q^{5} - 8 q^{6} + 3 q^{7} - 10 q^{8} + 14 q^{9}+O(q^{10}) \) 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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