LMFDB - Embedded newform 4830.2.a.cd.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4830,2,Mod(1,4830)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4830, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 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("4830.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4830 = 2 \cdot 3 \cdot 5 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4830.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:	$38.5677441763$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	4.4.10273.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - 2x^{3} - 5x^{2} + x + 2 $ x^4 - 2x^3 - 5x^2 + x + 2
Coefficient ring:	$\Z[a_1, \ldots, a_{29}]$
Coefficient ring index:	$ 2^{3} $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$3.35017$ of defining polynomial
Character	$\chi$	$=$	4830.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{5} +1.00000 q^{6} +1.00000 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{5} +1.00000 q^{6} +1.00000 q^{7} -1.00000 q^{8} +1.00000 q^{9} +1.00000 q^{10} +0.459752 q^{11} -1.00000 q^{12} +5.04663 q^{13} -1.00000 q^{14} +1.00000 q^{15} +1.00000 q^{16} -7.89431 q^{17} -1.00000 q^{18} +7.50638 q^{19} -1.00000 q^{20} -1.00000 q^{21} -0.459752 q^{22} -1.00000 q^{23} +1.00000 q^{24} +1.00000 q^{25} -5.04663 q^{26} -1.00000 q^{27} +1.00000 q^{28} -2.73422 q^{29} -1.00000 q^{30} -0.700346 q^{31} -1.00000 q^{32} -0.459752 q^{33} +7.89431 q^{34} -1.00000 q^{35} +1.00000 q^{36} +10.2067 q^{37} -7.50638 q^{38} -5.04663 q^{39} +1.00000 q^{40} +11.4007 q^{41} +1.00000 q^{42} -7.74697 q^{43} +0.459752 q^{44} -1.00000 q^{45} +1.00000 q^{46} +2.58687 q^{47} -1.00000 q^{48} +1.00000 q^{49} -1.00000 q^{50} +7.89431 q^{51} +5.04663 q^{52} +3.19397 q^{53} +1.00000 q^{54} -0.459752 q^{55} -1.00000 q^{56} -7.50638 q^{57} +2.73422 q^{58} -8.20672 q^{59} +1.00000 q^{60} +1.08050 q^{61} +0.700346 q^{62} +1.00000 q^{63} +1.00000 q^{64} -5.04663 q^{65} +0.459752 q^{66} +8.66648 q^{67} -7.89431 q^{68} +1.00000 q^{69} +1.00000 q^{70} -2.34628 q^{71} -1.00000 q^{72} -13.2872 q^{73} -10.2067 q^{74} -1.00000 q^{75} +7.50638 q^{76} +0.459752 q^{77} +5.04663 q^{78} +6.11347 q^{79} -1.00000 q^{80} +1.00000 q^{81} -11.4007 q^{82} +4.42588 q^{83} -1.00000 q^{84} +7.89431 q^{85} +7.74697 q^{86} +2.73422 q^{87} -0.459752 q^{88} -3.16010 q^{89} +1.00000 q^{90} +5.04663 q^{91} -1.00000 q^{92} +0.700346 q^{93} -2.58687 q^{94} -7.50638 q^{95} +1.00000 q^{96} -18.1729 q^{97} -1.00000 q^{98} +0.459752 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 4 q^{2} - 4 q^{3} + 4 q^{4} - 4 q^{5} + 4 q^{6} + 4 q^{7} - 4 q^{8} + 4 q^{9}+O(q^{10}) $ 4 * q - 4 * q^2 - 4 * q^3 + 4 * q^4 - 4 * q^5 + 4 * q^6 + 4 * q^7 - 4 * q^8 + 4 * q^9	\( 4 q - 4 q^{2} - 4 q^{3} + 4 q^{4} - 4 q^{5} + 4 q^{6} + 4 q^{7} - 4 q^{8} + 4 q^{9} + 4 q^{10} + 2 q^{11} - 4 q^{12} + 4 q^{13} - 4 q^{14} + 4 q^{15} + 4 q^{16} - 2 q^{17} - 4 q^{18} + 14 q^{19} - 4 q^{20} - 4 q^{21} - 2 q^{22} - 4 q^{23} + 4 q^{24} + 4 q^{25} - 4 q^{26} - 4 q^{27} + 4 q^{28} - 4 q^{29} - 4 q^{30} + 20 q^{31} - 4 q^{32} - 2 q^{33} + 2 q^{34} - 4 q^{35} + 4 q^{36} + 2 q^{37} - 14 q^{38} - 4 q^{39} + 4 q^{40} + 4 q^{42} + 8 q^{43} + 2 q^{44} - 4 q^{45} + 4 q^{46} - 6 q^{47} - 4 q^{48} + 4 q^{49} - 4 q^{50} + 2 q^{51} + 4 q^{52} + 6 q^{53} + 4 q^{54} - 2 q^{55} - 4 q^{56} - 14 q^{57} + 4 q^{58} + 6 q^{59} + 4 q^{60} + 4 q^{61} - 20 q^{62} + 4 q^{63} + 4 q^{64} - 4 q^{65} + 2 q^{66} - 4 q^{67} - 2 q^{68} + 4 q^{69} + 4 q^{70} - 16 q^{71} - 4 q^{72} - 14 q^{73} - 2 q^{74} - 4 q^{75} + 14 q^{76} + 2 q^{77} + 4 q^{78} + 18 q^{79} - 4 q^{80} + 4 q^{81} + 2 q^{83} - 4 q^{84} + 2 q^{85} - 8 q^{86} + 4 q^{87} - 2 q^{88} + 10 q^{89} + 4 q^{90} + 4 q^{91} - 4 q^{92} - 20 q^{93} + 6 q^{94} - 14 q^{95} + 4 q^{96} - 18 q^{97} - 4 q^{98} + 2 q^{99}+O(q^{100}) \) 4 * q - 4 * q^2 - 4 * q^3 + 4 * q^4 - 4 * q^5 + 4 * q^6 + 4 * q^7 - 4 * q^8 + 4 * q^9 + 4 * q^10 + 2 * q^11 - 4 * q^12 + 4 * q^13 - 4 * q^14 + 4 * q^15 + 4 * q^16 - 2 * q^17 - 4 * q^18 + 14 * q^19 - 4 * q^20 - 4 * q^21 - 2 * q^22 - 4 * q^23 + 4 * q^24 + 4 * q^25 - 4 * q^26 - 4 * q^27 + 4 * q^28 - 4 * q^29 - 4 * q^30 + 20 * q^31 - 4 * q^32 - 2 * q^33 + 2 * q^34 - 4 * q^35 + 4 * q^36 + 2 * q^37 - 14 * q^38 - 4 * q^39 + 4 * q^40 + 4 * q^42 + 8 * q^43 + 2 * q^44 - 4 * q^45 + 4 * q^46 - 6 * q^47 - 4 * q^48 + 4 * q^49 - 4 * q^50 + 2 * q^51 + 4 * q^52 + 6 * q^53 + 4 * q^54 - 2 * q^55 - 4 * q^56 - 14 * q^57 + 4 * q^58 + 6 * q^59 + 4 * q^60 + 4 * q^61 - 20 * q^62 + 4 * q^63 + 4 * q^64 - 4 * q^65 + 2 * q^66 - 4 * q^67 - 2 * q^68 + 4 * q^69 + 4 * q^70 - 16 * q^71 - 4 * q^72 - 14 * q^73 - 2 * q^74 - 4 * q^75 + 14 * q^76 + 2 * q^77 + 4 * q^78 + 18 * q^79 - 4 * q^80 + 4 * q^81 + 2 * q^83 - 4 * q^84 + 2 * q^85 - 8 * q^86 + 4 * q^87 - 2 * q^88 + 10 * q^89 + 4 * q^90 + 4 * q^91 - 4 * q^92 - 20 * q^93 + 6 * q^94 - 14 * q^95 + 4 * q^96 - 18 * q^97 - 4 * q^98 + 2 * 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
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	1.00000	0.500000
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	1.00000	0.408248
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	−1.00000	−0.353553
$9$	1.00000	0.333333
$10$	1.00000	0.316228
$11$	0.459752	0.138620	0.0693102	−	0.997595i	$-0.477920\pi$
$11$	0.459752	0.138620	0.0693102	+	0.997595i	$0.477920\pi$
$12$	−1.00000	−0.288675
$13$	5.04663	1.39968	0.699841	−	0.714299i	$-0.253254\pi$
$13$	5.04663	1.39968	0.699841	+	0.714299i	$0.253254\pi$
$14$	−1.00000	−0.267261
$15$	1.00000	0.258199
$16$	1.00000	0.250000
$17$	−7.89431	−1.91465	−0.957326	−	0.289010i	$-0.906674\pi$
$17$	−7.89431	−1.91465	−0.957326	+	0.289010i	$0.906674\pi$
$18$	−1.00000	−0.235702
$19$	7.50638	1.72208	0.861041	−	0.508536i	$-0.169813\pi$
$19$	7.50638	1.72208	0.861041	+	0.508536i	$0.169813\pi$
$20$	−1.00000	−0.223607
$21$	−1.00000	−0.218218
$22$	−0.459752	−0.0980194
$23$	−1.00000	−0.208514
$23$	−1.00000	−0.208514
$24$	1.00000	0.204124
$25$	1.00000	0.200000
$26$	−5.04663	−0.989725
$27$	−1.00000	−0.192450
$28$	1.00000	0.188982
$29$	−2.73422	−0.507731	−0.253866	−	0.967239i	$-0.581702\pi$
$29$	−2.73422	−0.507731	−0.253866	+	0.967239i	$0.581702\pi$
$30$	−1.00000	−0.182574
$31$	−0.700346	−0.125786	−0.0628929	−	0.998020i	$-0.520033\pi$
$31$	−0.700346	−0.125786	−0.0628929	+	0.998020i	$0.520033\pi$
$32$	−1.00000	−0.176777
$33$	−0.459752	−0.0800325
$34$	7.89431	1.35386
$35$	−1.00000	−0.169031
$36$	1.00000	0.166667
$37$	10.2067	1.67798	0.838988	−	0.544151i	$-0.183148\pi$
$37$	10.2067	1.67798	0.838988	+	0.544151i	$0.183148\pi$
$38$	−7.50638	−1.21770
$39$	−5.04663	−0.808107
$40$	1.00000	0.158114
$41$	11.4007	1.78049	0.890244	−	0.455483i	$-0.150533\pi$
$41$	11.4007	1.78049	0.890244	+	0.455483i	$0.150533\pi$
$42$	1.00000	0.154303
$43$	−7.74697	−1.18140	−0.590701	−	0.806890i	$-0.701149\pi$
$43$	−7.74697	−1.18140	−0.590701	+	0.806890i	$0.701149\pi$
$44$	0.459752	0.0693102
$45$	−1.00000	−0.149071
$46$	1.00000	0.147442
$47$	2.58687	0.377334	0.188667	−	0.982041i	$-0.439583\pi$
$47$	2.58687	0.377334	0.188667	+	0.982041i	$0.439583\pi$
$48$	−1.00000	−0.144338
$49$	1.00000	0.142857
$50$	−1.00000	−0.141421
$51$	7.89431	1.10543
$52$	5.04663	0.699841
$53$	3.19397	0.438725	0.219363	−	0.975643i	$-0.429602\pi$
$53$	3.19397	0.438725	0.219363	+	0.975643i	$0.429602\pi$
$54$	1.00000	0.136083
$55$	−0.459752	−0.0619929
$56$	−1.00000	−0.133631
$57$	−7.50638	−0.994244
$58$	2.73422	0.359020
$59$	−8.20672	−1.06842	−0.534212	−	0.845350i	$-0.679392\pi$
$59$	−8.20672	−1.06842	−0.534212	+	0.845350i	$0.679392\pi$
$60$	1.00000	0.129099
$61$	1.08050	0.138343	0.0691717	−	0.997605i	$-0.477964\pi$
$61$	1.08050	0.138343	0.0691717	+	0.997605i	$0.477964\pi$
$62$	0.700346	0.0889440
$63$	1.00000	0.125988
$64$	1.00000	0.125000
$65$	−5.04663	−0.625957
$66$	0.459752	0.0565915
$67$	8.66648	1.05878	0.529389	−	0.848379i	$-0.322421\pi$
$67$	8.66648	1.05878	0.529389	+	0.848379i	$0.322421\pi$
$68$	−7.89431	−0.957326
$69$	1.00000	0.120386
$70$	1.00000	0.119523
$71$	−2.34628	−0.278452	−0.139226	−	0.990261i	$-0.544461\pi$
$71$	−2.34628	−0.278452	−0.139226	+	0.990261i	$0.544461\pi$
$72$	−1.00000	−0.117851
$73$	−13.2872	−1.55515	−0.777576	−	0.628789i	$-0.783551\pi$
$73$	−13.2872	−1.55515	−0.777576	+	0.628789i	$0.783551\pi$
$74$	−10.2067	−1.18651
$75$	−1.00000	−0.115470
$76$	7.50638	0.861041
$77$	0.459752	0.0523936
$78$	5.04663	0.571418
$79$	6.11347	0.687819	0.343910	−	0.939003i	$-0.388249\pi$
$79$	6.11347	0.687819	0.343910	+	0.939003i	$0.388249\pi$
$80$	−1.00000	−0.111803
$81$	1.00000	0.111111
$82$	−11.4007	−1.25900
$83$	4.42588	0.485804	0.242902	−	0.970051i	$-0.421901\pi$
$83$	4.42588	0.485804	0.242902	+	0.970051i	$0.421901\pi$
$84$	−1.00000	−0.109109
$85$	7.89431	0.856259
$86$	7.74697	0.835377
$87$	2.73422	0.293139
$88$	−0.459752	−0.0490097
$89$	−3.16010	−0.334970	−0.167485	−	0.985875i	$-0.553565\pi$
$89$	−3.16010	−0.334970	−0.167485	+	0.985875i	$0.553565\pi$
$90$	1.00000	0.105409
$91$	5.04663	0.529030
$92$	−1.00000	−0.104257
$93$	0.700346	0.0726225
$94$	−2.58687	−0.266816
$95$	−7.50638	−0.770138
$96$	1.00000	0.102062
$97$	−18.1729	−1.84517	−0.922587	−	0.385789i	$-0.873929\pi$
$97$	−18.1729	−1.84517	−0.922587	+	0.385789i	$0.873929\pi$
$98$	−1.00000	−0.101015
$99$	0.459752	0.0462068
$100$	1.00000	0.100000
$101$	13.2533	1.31876	0.659379	−	0.751811i	$-0.270819\pi$
$101$	13.2533	1.31876	0.659379	+	0.751811i	$0.270819\pi$
$102$	−7.89431	−0.781654
$103$	5.40069	0.532146	0.266073	−	0.963953i	$-0.414274\pi$
$103$	5.40069	0.532146	0.266073	+	0.963953i	$0.414274\pi$
$104$	−5.04663	−0.494862
$105$	1.00000	0.0975900
$106$	−3.19397	−0.310226
$107$	−3.93226	−0.380146	−0.190073	−	0.981770i	$-0.560872\pi$
$107$	−3.93226	−0.380146	−0.190073	+	0.981770i	$0.560872\pi$
$108$	−1.00000	−0.0962250
$109$	−7.40069	−0.708858	−0.354429	−	0.935083i	$-0.615325\pi$
$109$	−7.40069	−0.708858	−0.354429	+	0.935083i	$0.615325\pi$
$110$	0.459752	0.0438356
$111$	−10.2067	−0.968779
$112$	1.00000	0.0944911
$113$	−4.11347	−0.386963	−0.193481	−	0.981104i	$-0.561978\pi$
$113$	−4.11347	−0.386963	−0.193481	+	0.981104i	$0.561978\pi$
$114$	7.50638	0.703037
$115$	1.00000	0.0932505
$116$	−2.73422	−0.253866
$117$	5.04663	0.466561
$118$	8.20672	0.755490
$119$	−7.89431	−0.723671
$120$	−1.00000	−0.0912871
$121$	−10.7886	−0.980784
$122$	−1.08050	−0.0978235
$123$	−11.4007	−1.02797
$124$	−0.700346	−0.0628929
$125$	−1.00000	−0.0894427
$126$	−1.00000	−0.0890871
$127$	−11.7470	−1.04238	−0.521188	−	0.853442i	$-0.674511\pi$
$127$	−11.7470	−1.04238	−0.521188	+	0.853442i	$0.674511\pi$
$128$	−1.00000	−0.0883883
$129$	7.74697	0.682083
$130$	5.04663	0.442618
$131$	13.6752	1.19480	0.597402	−	0.801942i	$-0.296200\pi$
$131$	13.6752	1.19480	0.597402	+	0.801942i	$0.296200\pi$
$132$	−0.459752	−0.0400163
$133$	7.50638	0.650885
$134$	−8.66648	−0.748669
$135$	1.00000	0.0860663
$136$	7.89431	0.676932
$137$	5.28722	0.451718	0.225859	−	0.974160i	$-0.427481\pi$
$137$	5.28722	0.451718	0.225859	+	0.974160i	$0.427481\pi$
$138$	−1.00000	−0.0851257
$139$	−8.20672	−0.696085	−0.348043	−	0.937479i	$-0.613154\pi$
$139$	−8.20672	−0.696085	−0.348043	+	0.937479i	$0.613154\pi$
$140$	−1.00000	−0.0845154
$141$	−2.58687	−0.217854
$142$	2.34628	0.196895
$143$	2.32020	0.194024
$144$	1.00000	0.0833333
$145$	2.73422	0.227064
$146$	13.2872	1.09966
$147$	−1.00000	−0.0824786
$148$	10.2067	0.838988
$149$	1.08050	0.0885177	0.0442589	−	0.999020i	$-0.485907\pi$
$149$	1.08050	0.0885177	0.0442589	+	0.999020i	$0.485907\pi$
$150$	1.00000	0.0816497
$151$	14.0933	1.14689	0.573446	−	0.819243i	$-0.305606\pi$
$151$	14.0933	1.14689	0.573446	+	0.819243i	$0.305606\pi$
$152$	−7.50638	−0.608848
$153$	−7.89431	−0.638217
$154$	−0.459752	−0.0370479
$155$	0.700346	0.0562531
$156$	−5.04663	−0.404053
$157$	9.01276	0.719296	0.359648	−	0.933088i	$-0.382897\pi$
$157$	9.01276	0.719296	0.359648	+	0.933088i	$0.382897\pi$
$158$	−6.11347	−0.486362
$159$	−3.19397	−0.253298
$160$	1.00000	0.0790569
$161$	−1.00000	−0.0788110
$162$	−1.00000	−0.0785674
$163$	1.90675	0.149348	0.0746740	−	0.997208i	$-0.476208\pi$
$163$	1.90675	0.149348	0.0746740	+	0.997208i	$0.476208\pi$
$164$	11.4007	0.890244
$165$	0.459752	0.0357916
$166$	−4.42588	−0.343515
$167$	−1.11844	−0.0865476	−0.0432738	−	0.999063i	$-0.513779\pi$
$167$	−1.11844	−0.0865476	−0.0432738	+	0.999063i	$0.513779\pi$
$168$	1.00000	0.0771517
$169$	12.4684	0.959110
$170$	−7.89431	−0.605466
$171$	7.50638	0.574027
$172$	−7.74697	−0.590701
$173$	7.39291	0.562072	0.281036	−	0.959697i	$-0.409322\pi$
$173$	7.39291	0.562072	0.281036	+	0.959697i	$0.409322\pi$
$174$	−2.73422	−0.207280
$175$	1.00000	0.0755929
$176$	0.459752	0.0346551
$177$	8.20672	0.616855
$178$	3.16010	0.236859
$179$	23.7209	1.77298	0.886491	−	0.462745i	$-0.153136\pi$
$179$	23.7209	1.77298	0.886491	+	0.462745i	$0.153136\pi$
$180$	−1.00000	−0.0745356
$181$	−7.46843	−0.555124	−0.277562	−	0.960708i	$-0.589526\pi$
$181$	−7.46843	−0.555124	−0.277562	+	0.960708i	$0.589526\pi$
$182$	−5.04663	−0.374081
$183$	−1.08050	−0.0798726
$184$	1.00000	0.0737210
$185$	−10.2067	−0.750413
$186$	−0.700346	−0.0513519
$187$	−3.62943	−0.265410
$188$	2.58687	0.188667
$189$	−1.00000	−0.0727393
$190$	7.50638	0.544570
$191$	26.3000	1.90300	0.951500	−	0.307650i	$-0.0995425\pi$
$191$	26.3000	1.90300	0.951500	+	0.307650i	$0.0995425\pi$
$192$	−1.00000	−0.0721688
$193$	16.3202	1.17475	0.587377	−	0.809314i	$-0.300161\pi$
$193$	16.3202	1.17475	0.587377	+	0.809314i	$0.300161\pi$
$194$	18.1729	1.30473
$195$	5.04663	0.361396
$196$	1.00000	0.0714286
$197$	3.40069	0.242289	0.121145	−	0.992635i	$-0.461344\pi$
$197$	3.40069	0.242289	0.121145	+	0.992635i	$0.461344\pi$
$198$	−0.459752	−0.0326731
$199$	−15.4939	−1.09834	−0.549168	−	0.835712i	$-0.685055\pi$
$199$	−15.4939	−1.09834	−0.549168	+	0.835712i	$0.685055\pi$
$200$	−1.00000	−0.0707107
$201$	−8.66648	−0.611286
$202$	−13.2533	−0.932502
$203$	−2.73422	−0.191904
$204$	7.89431	0.552713
$205$	−11.4007	−0.796259
$206$	−5.40069	−0.376284
$207$	−1.00000	−0.0695048
$208$	5.04663	0.349921
$209$	3.45107	0.238716
$210$	−1.00000	−0.0690066
$211$	−15.0128	−1.03352	−0.516760	−	0.856130i	$-0.672862\pi$
$211$	−15.0128	−1.03352	−0.516760	+	0.856130i	$0.672862\pi$
$212$	3.19397	0.219363
$213$	2.34628	0.160764
$214$	3.93226	0.268804
$215$	7.74697	0.528339
$216$	1.00000	0.0680414
$217$	−0.700346	−0.0475426
$218$	7.40069	0.501238
$219$	13.2872	0.897867
$220$	−0.459752	−0.0309965
$221$	−39.8396	−2.67990
$222$	10.2067	0.685030
$223$	−19.7345	−1.32152	−0.660761	−	0.750596i	$-0.729766\pi$
$223$	−19.7345	−1.32152	−0.660761	+	0.750596i	$0.729766\pi$
$224$	−1.00000	−0.0668153
$225$	1.00000	0.0666667
$226$	4.11347	0.273624
$227$	−21.8943	−1.45318	−0.726588	−	0.687073i	$-0.758895\pi$
$227$	−21.8943	−1.45318	−0.726588	+	0.687073i	$0.758895\pi$
$228$	−7.50638	−0.497122
$229$	20.8691	1.37907	0.689535	−	0.724252i	$-0.257815\pi$
$229$	20.8691	1.37907	0.689535	+	0.724252i	$0.257815\pi$
$230$	−1.00000	−0.0659380
$231$	−0.459752	−0.0302494
$232$	2.73422	0.179510
$233$	−3.17375	−0.207919	−0.103960	−	0.994582i	$-0.533151\pi$
$233$	−3.17375	−0.207919	−0.103960	+	0.994582i	$0.533151\pi$
$234$	−5.04663	−0.329908
$235$	−2.58687	−0.168749
$236$	−8.20672	−0.534212
$237$	−6.11347	−0.397113
$238$	7.89431	0.511712
$239$	16.0012	1.03503	0.517516	−	0.855673i	$-0.326857\pi$
$239$	16.0012	1.03503	0.517516	+	0.855673i	$0.326857\pi$
$240$	1.00000	0.0645497
$241$	10.4936	0.675954	0.337977	−	0.941154i	$-0.390257\pi$
$241$	10.4936	0.675954	0.337977	+	0.941154i	$0.390257\pi$
$242$	10.7886	0.693519
$243$	−1.00000	−0.0641500
$244$	1.08050	0.0691717
$245$	−1.00000	−0.0638877
$246$	11.4007	0.726882
$247$	37.8819	2.41037
$248$	0.700346	0.0444720
$249$	−4.42588	−0.280479
$250$	1.00000	0.0632456
$251$	17.5735	1.10923	0.554616	−	0.832106i	$-0.312865\pi$
$251$	17.5735	1.10923	0.554616	+	0.832106i	$0.312865\pi$
$252$	1.00000	0.0629941
$253$	−0.459752	−0.0289044
$254$	11.7470	0.737071
$255$	−7.89431	−0.494361
$256$	1.00000	0.0625000
$257$	−25.9954	−1.62155	−0.810773	−	0.585361i	$-0.800953\pi$
$257$	−25.9954	−1.62155	−0.810773	+	0.585361i	$0.800953\pi$
$258$	−7.74697	−0.482305
$259$	10.2067	0.634215
$260$	−5.04663	−0.312978
$261$	−2.73422	−0.169244
$262$	−13.6752	−0.844854
$263$	28.4812	1.75623	0.878113	−	0.478454i	$-0.158803\pi$
$263$	28.4812	1.75623	0.878113	+	0.478454i	$0.158803\pi$
$264$	0.459752	0.0282958
$265$	−3.19397	−0.196204
$266$	−7.50638	−0.460246
$267$	3.16010	0.193395
$268$	8.66648	0.529389
$269$	22.7218	1.38537	0.692686	−	0.721240i	$-0.256427\pi$
$269$	22.7218	1.38537	0.692686	+	0.721240i	$0.256427\pi$
$270$	−1.00000	−0.0608581
$271$	−22.7259	−1.38050	−0.690249	−	0.723572i	$-0.742499\pi$
$271$	−22.7259	−1.38050	−0.690249	+	0.723572i	$0.742499\pi$
$272$	−7.89431	−0.478663
$273$	−5.04663	−0.305436
$274$	−5.28722	−0.319413
$275$	0.459752	0.0277241
$276$	1.00000	0.0601929
$277$	15.4423	0.927841	0.463920	−	0.885877i	$-0.346442\pi$
$277$	15.4423	0.927841	0.463920	+	0.885877i	$0.346442\pi$
$278$	8.20672	0.492207
$279$	−0.700346	−0.0419286
$280$	1.00000	0.0597614
$281$	−23.0799	−1.37683	−0.688416	−	0.725316i	$-0.741694\pi$
$281$	−23.0799	−1.37683	−0.688416	+	0.725316i	$0.741694\pi$
$282$	2.58687	0.154046
$283$	20.7218	1.23178	0.615891	−	0.787831i	$-0.288796\pi$
$283$	20.7218	1.23178	0.615891	+	0.787831i	$0.288796\pi$
$284$	−2.34628	−0.139226
$285$	7.50638	0.444639
$286$	−2.32020	−0.137196
$287$	11.4007	0.672962
$288$	−1.00000	−0.0589256
$289$	45.3202	2.66589
$290$	−2.73422	−0.160559
$291$	18.1729	1.06531
$292$	−13.2872	−0.777576
$293$	7.17375	0.419095	0.209547	−	0.977798i	$-0.432801\pi$
$293$	7.17375	0.419095	0.209547	+	0.977798i	$0.432801\pi$
$294$	1.00000	0.0583212
$295$	8.20672	0.477814
$296$	−10.2067	−0.593254
$297$	−0.459752	−0.0266775
$298$	−1.08050	−0.0625915
$299$	−5.04663	−0.291854
$300$	−1.00000	−0.0577350
$301$	−7.74697	−0.446528
$302$	−14.0933	−0.810976
$303$	−13.2533	−0.761385
$304$	7.50638	0.430520
$305$	−1.08050	−0.0618690
$306$	7.89431	0.451288
$307$	21.5872	1.23205	0.616023	−	0.787728i	$-0.288743\pi$
$307$	21.5872	1.23205	0.616023	+	0.787728i	$0.288743\pi$
$308$	0.459752	0.0261968
$309$	−5.40069	−0.307235
$310$	−0.700346	−0.0397770
$311$	−0.0338705	−0.00192062	−0.000960309	−	1.00000i	$-0.500306\pi$
$311$	−0.0338705	−0.00192062	−0.000960309		1.00000i	$0.500306\pi$
$312$	5.04663	0.285709
$313$	8.69627	0.491542	0.245771	−	0.969328i	$-0.420959\pi$
$313$	8.69627	0.491542	0.245771	+	0.969328i	$0.420959\pi$
$314$	−9.01276	−0.508619
$315$	−1.00000	−0.0563436
$316$	6.11347	0.343910
$317$	−22.8946	−1.28589	−0.642945	−	0.765912i	$-0.722288\pi$
$317$	−22.8946	−1.28589	−0.642945	+	0.765912i	$0.722288\pi$
$318$	3.19397	0.179109
$319$	−1.25706	−0.0703819
$320$	−1.00000	−0.0559017
$321$	3.93226	0.219477
$322$	1.00000	0.0557278
$323$	−59.2577	−3.29719
$324$	1.00000	0.0555556
$325$	5.04663	0.279936
$326$	−1.90675	−0.105605
$327$	7.40069	0.409259
$328$	−11.4007	−0.629498
$329$	2.58687	0.142619
$330$	−0.459752	−0.0253085
$331$	−4.70813	−0.258782	−0.129391	−	0.991594i	$-0.541302\pi$
$331$	−4.70813	−0.258782	−0.129391	+	0.991594i	$0.541302\pi$
$332$	4.42588	0.242902
$333$	10.2067	0.559325
$334$	1.11844	0.0611984
$335$	−8.66648	−0.473500
$336$	−1.00000	−0.0545545
$337$	25.2611	1.37606	0.688031	−	0.725681i	$-0.258475\pi$
$337$	25.2611	1.37606	0.688031	+	0.725681i	$0.258475\pi$
$338$	−12.4684	−0.678193
$339$	4.11347	0.223413
$340$	7.89431	0.428129
$341$	−0.321985	−0.0174365
$342$	−7.50638	−0.405898
$343$	1.00000	0.0539949
$344$	7.74697	0.417689
$345$	−1.00000	−0.0538382
$346$	−7.39291	−0.397445
$347$	−0.692560	−0.0371786	−0.0185893	−	0.999827i	$-0.505917\pi$
$347$	−0.692560	−0.0371786	−0.0185893	+	0.999827i	$0.505917\pi$
$348$	2.73422	0.146569
$349$	9.06806	0.485402	0.242701	−	0.970101i	$-0.421967\pi$
$349$	9.06806	0.485402	0.242701	+	0.970101i	$0.421967\pi$
$350$	−1.00000	−0.0534522
$351$	−5.04663	−0.269369
$352$	−0.459752	−0.0245049
$353$	28.1563	1.49861	0.749306	−	0.662224i	$-0.230387\pi$
$353$	28.1563	1.49861	0.749306	+	0.662224i	$0.230387\pi$
$354$	−8.20672	−0.436182
$355$	2.34628	0.124528
$356$	−3.16010	−0.167485
$357$	7.89431	0.417811
$358$	−23.7209	−1.25369
$359$	19.7255	1.04107	0.520537	−	0.853839i	$-0.325732\pi$
$359$	19.7255	1.04107	0.520537	+	0.853839i	$0.325732\pi$
$360$	1.00000	0.0527046
$361$	37.3457	1.96556
$362$	7.46843	0.392532
$363$	10.7886	0.566256
$364$	5.04663	0.264515
$365$	13.2872	0.695485
$366$	1.08050	0.0564784
$367$	−21.4007	−1.11711	−0.558554	−	0.829468i	$-0.688643\pi$
$367$	−21.4007	−1.11711	−0.558554	+	0.829468i	$0.688643\pi$
$368$	−1.00000	−0.0521286
$369$	11.4007	0.593496
$370$	10.2067	0.530622
$371$	3.19397	0.165823
$372$	0.700346	0.0363112
$373$	22.9826	1.18999	0.594997	−	0.803728i	$-0.297153\pi$
$373$	22.9826	1.18999	0.594997	+	0.803728i	$0.297153\pi$
$374$	3.62943	0.187673
$375$	1.00000	0.0516398
$376$	−2.58687	−0.133408
$377$	−13.7986	−0.710662
$378$	1.00000	0.0514344
$379$	−0.967024	−0.0496727	−0.0248364	−	0.999692i	$-0.507906\pi$
$379$	−0.967024	−0.0496727	−0.0248364	+	0.999692i	$0.507906\pi$
$380$	−7.50638	−0.385069
$381$	11.7470	0.601816
$382$	−26.3000	−1.34562
$383$	5.31738	0.271705	0.135853	−	0.990729i	$-0.456623\pi$
$383$	5.31738	0.271705	0.135853	+	0.990729i	$0.456623\pi$
$384$	1.00000	0.0510310
$385$	−0.459752	−0.0234311
$386$	−16.3202	−0.830676
$387$	−7.74697	−0.393801
$388$	−18.1729	−0.922587
$389$	−4.32020	−0.219043	−0.109521	−	0.993984i	$-0.534932\pi$
$389$	−4.32020	−0.219043	−0.109521	+	0.993984i	$0.534932\pi$
$390$	−5.04663	−0.255546
$391$	7.89431	0.399233
$392$	−1.00000	−0.0505076
$393$	−13.6752	−0.689820
$394$	−3.40069	−0.171324
$395$	−6.11347	−0.307602
$396$	0.459752	0.0231034
$397$	−9.52781	−0.478187	−0.239094	−	0.970997i	$-0.576850\pi$
$397$	−9.52781	−0.478187	−0.239094	+	0.970997i	$0.576850\pi$
$398$	15.4939	0.776641
$399$	−7.50638	−0.375789
$400$	1.00000	0.0500000
$401$	7.86509	0.392764	0.196382	−	0.980527i	$-0.437081\pi$
$401$	7.86509	0.392764	0.196382	+	0.980527i	$0.437081\pi$
$402$	8.66648	0.432245
$403$	−3.53438	−0.176060
$404$	13.2533	0.659379
$405$	−1.00000	−0.0496904
$406$	2.73422	0.135697
$407$	4.69256	0.232602
$408$	−7.89431	−0.390827
$409$	33.0128	1.63238	0.816188	−	0.577787i	$-0.196083\pi$
$409$	33.0128	1.63238	0.816188	+	0.577787i	$0.196083\pi$
$410$	11.4007	0.563040
$411$	−5.28722	−0.260799
$412$	5.40069	0.266073
$413$	−8.20672	−0.403826
$414$	1.00000	0.0491473
$415$	−4.42588	−0.217258
$416$	−5.04663	−0.247431
$417$	8.20672	0.401885
$418$	−3.45107	−0.168797
$419$	−24.1729	−1.18092	−0.590461	−	0.807066i	$-0.701054\pi$
$419$	−24.1729	−1.18092	−0.590461	+	0.807066i	$0.701054\pi$
$420$	1.00000	0.0487950
$421$	15.7986	0.769975	0.384988	−	0.922922i	$-0.374206\pi$
$421$	15.7986	0.769975	0.384988	+	0.922922i	$0.374206\pi$
$422$	15.0128	0.730809
$423$	2.58687	0.125778
$424$	−3.19397	−0.155113
$425$	−7.89431	−0.382930
$426$	−2.34628	−0.113678
$427$	1.08050	0.0522889
$428$	−3.93226	−0.190073
$429$	−2.32020	−0.112020
$430$	−7.74697	−0.373592
$431$	17.7429	0.854645	0.427323	−	0.904099i	$-0.359457\pi$
$431$	17.7429	0.854645	0.427323	+	0.904099i	$0.359457\pi$
$432$	−1.00000	−0.0481125
$433$	19.8527	0.954058	0.477029	−	0.878888i	$-0.341714\pi$
$433$	19.8527	0.954058	0.477029	+	0.878888i	$0.341714\pi$
$434$	0.700346	0.0336177
$435$	−2.73422	−0.131096
$436$	−7.40069	−0.354429
$437$	−7.50638	−0.359079
$438$	−13.2872	−0.634888
$439$	−6.79360	−0.324241	−0.162120	−	0.986771i	$-0.551833\pi$
$439$	−6.79360	−0.324241	−0.162120	+	0.986771i	$0.551833\pi$
$440$	0.459752	0.0219178
$441$	1.00000	0.0476190
$442$	39.8396	1.89498
$443$	21.3330	1.01356	0.506780	−	0.862076i	$-0.330836\pi$
$443$	21.3330	1.01356	0.506780	+	0.862076i	$0.330836\pi$
$444$	−10.2067	−0.484390
$445$	3.16010	0.149803
$446$	19.7345	0.934457
$447$	−1.08050	−0.0511057
$448$	1.00000	0.0472456
$449$	41.1993	1.94431	0.972157	−	0.234332i	$-0.0752903\pi$
$449$	41.1993	1.94431	0.972157	+	0.234332i	$0.0752903\pi$
$450$	−1.00000	−0.0471405
$451$	5.24149	0.246812
$452$	−4.11347	−0.193481
$453$	−14.0933	−0.662159
$454$	21.8943	1.02755
$455$	−5.04663	−0.236589
$456$	7.50638	0.351518
$457$	−28.2739	−1.32260	−0.661298	−	0.750123i	$-0.729994\pi$
$457$	−28.2739	−1.32260	−0.661298	+	0.750123i	$0.729994\pi$
$458$	−20.8691	−0.975150
$459$	7.89431	0.368475
$460$	1.00000	0.0466252
$461$	−3.70903	−0.172747	−0.0863733	−	0.996263i	$-0.527528\pi$
$461$	−3.70903	−0.172747	−0.0863733	+	0.996263i	$0.527528\pi$
$462$	0.459752	0.0213896
$463$	16.9207	0.786373	0.393186	−	0.919459i	$-0.371373\pi$
$463$	16.9207	0.786373	0.393186	+	0.919459i	$0.371373\pi$
$464$	−2.73422	−0.126933
$465$	−0.700346	−0.0324778
$466$	3.17375	0.147021
$467$	16.2145	0.750318	0.375159	−	0.926960i	$-0.377588\pi$
$467$	16.2145	0.750318	0.375159	+	0.926960i	$0.377588\pi$
$468$	5.04663	0.233280
$469$	8.66648	0.400181
$470$	2.58687	0.119324
$471$	−9.01276	−0.415286
$472$	8.20672	0.377745
$473$	−3.56168	−0.163766
$474$	6.11347	0.280801
$475$	7.50638	0.344416
$476$	−7.89431	−0.361835
$477$	3.19397	0.146242
$478$	−16.0012	−0.731879
$479$	−18.8773	−0.862525	−0.431262	−	0.902227i	$-0.641932\pi$
$479$	−18.8773	−0.862525	−0.431262	+	0.902227i	$0.641932\pi$
$480$	−1.00000	−0.0456435
$481$	51.5095	2.34863
$482$	−10.4936	−0.477971
$483$	1.00000	0.0455016
$484$	−10.7886	−0.490392
$485$	18.1729	0.825187
$486$	1.00000	0.0453609
$487$	−36.6820	−1.66222	−0.831111	−	0.556106i	$-0.812295\pi$
$487$	−36.6820	−1.66222	−0.831111	+	0.556106i	$0.812295\pi$
$488$	−1.08050	−0.0489118
$489$	−1.90675	−0.0862261
$490$	1.00000	0.0451754
$491$	−28.2698	−1.27580	−0.637899	−	0.770120i	$-0.720196\pi$
$491$	−28.2698	−1.27580	−0.637899	+	0.770120i	$0.720196\pi$
$492$	−11.4007	−0.513983
$493$	21.5848	0.972129
$494$	−37.8819	−1.70439
$495$	−0.459752	−0.0206643
$496$	−0.700346	−0.0314465
$497$	−2.34628	−0.105245
$498$	4.42588	0.198328
$499$	−7.01276	−0.313934	−0.156967	−	0.987604i	$-0.550172\pi$
$499$	−7.01276	−0.313934	−0.156967	+	0.987604i	$0.550172\pi$
$500$	−1.00000	−0.0447214
$501$	1.11844	0.0499683
$502$	−17.5735	−0.784346
$503$	−31.6376	−1.41065	−0.705325	−	0.708884i	$-0.749199\pi$
$503$	−31.6376	−1.41065	−0.705325	+	0.708884i	$0.749199\pi$
$504$	−1.00000	−0.0445435
$505$	−13.2533	−0.589766
$506$	0.459752	0.0204385
$507$	−12.4684	−0.553743
$508$	−11.7470	−0.521188
$509$	13.8023	0.611775	0.305888	−	0.952068i	$-0.401047\pi$
$509$	13.8023	0.611775	0.305888	+	0.952068i	$0.401047\pi$
$510$	7.89431	0.349566
$511$	−13.2872	−0.587792
$512$	−1.00000	−0.0441942
$513$	−7.50638	−0.331415
$514$	25.9954	1.14661
$515$	−5.40069	−0.237983
$516$	7.74697	0.341041
$517$	1.18932	0.0523062
$518$	−10.2067	−0.448458
$519$	−7.39291	−0.324513
$520$	5.04663	0.221309
$521$	29.8023	1.30566	0.652831	−	0.757504i	$-0.273581\pi$
$521$	29.8023	1.30566	0.652831	+	0.757504i	$0.273581\pi$
$522$	2.73422	0.119673
$523$	−1.01647	−0.0444470	−0.0222235	−	0.999753i	$-0.507075\pi$
$523$	−1.01647	−0.0444470	−0.0222235	+	0.999753i	$0.507075\pi$
$524$	13.6752	0.597402
$525$	−1.00000	−0.0436436
$526$	−28.4812	−1.24184
$527$	5.52875	0.240836
$528$	−0.459752	−0.0200081
$529$	1.00000	0.0434783
$530$	3.19397	0.138737
$531$	−8.20672	−0.356141
$532$	7.50638	0.325443
$533$	57.5350	2.49212
$534$	−3.16010	−0.136751
$535$	3.93226	0.170006
$536$	−8.66648	−0.374335
$537$	−23.7209	−1.02363
$538$	−22.7218	−0.979606
$539$	0.459752	0.0198029
$540$	1.00000	0.0430331
$541$	22.9195	0.985386	0.492693	−	0.870203i	$-0.336012\pi$
$541$	22.9195	0.985386	0.492693	+	0.870203i	$0.336012\pi$
$542$	22.7259	0.976159
$543$	7.46843	0.320501
$544$	7.89431	0.338466
$545$	7.40069	0.317011
$546$	5.04663	0.215976
$547$	6.32020	0.270232	0.135116	−	0.990830i	$-0.456859\pi$
$547$	6.32020	0.270232	0.135116	+	0.990830i	$0.456859\pi$
$548$	5.28722	0.225859
$549$	1.08050	0.0461145
$550$	−0.459752	−0.0196039
$551$	−20.5241	−0.874354
$552$	−1.00000	−0.0425628
$553$	6.11347	0.259971
$554$	−15.4423	−0.656083
$555$	10.2067	0.433251
$556$	−8.20672	−0.348043
$557$	23.1014	0.978836	0.489418	−	0.872049i	$-0.337209\pi$
$557$	23.1014	0.978836	0.489418	+	0.872049i	$0.337209\pi$
$558$	0.700346	0.0296480
$559$	−39.0961	−1.65359
$560$	−1.00000	−0.0422577
$561$	3.62943	0.153234
$562$	23.0799	0.973568
$563$	−33.4641	−1.41035	−0.705173	−	0.709035i	$-0.749131\pi$
$563$	−33.4641	−1.41035	−0.705173	+	0.709035i	$0.749131\pi$
$564$	−2.58687	−0.108927
$565$	4.11347	0.173055
$566$	−20.7218	−0.871001
$567$	1.00000	0.0419961
$568$	2.34628	0.0984477
$569$	33.2814	1.39523	0.697614	−	0.716474i	$-0.254245\pi$
$569$	33.2814	1.39523	0.697614	+	0.716474i	$0.254245\pi$
$570$	−7.50638	−0.314408
$571$	37.1691	1.55548	0.777739	−	0.628587i	$-0.216366\pi$
$571$	37.1691	1.55548	0.777739	+	0.628587i	$0.216366\pi$
$572$	2.32020	0.0970122
$573$	−26.3000	−1.09870
$574$	−11.4007	−0.475856
$575$	−1.00000	−0.0417029
$576$	1.00000	0.0416667
$577$	−23.8617	−0.993374	−0.496687	−	0.867930i	$-0.665450\pi$
$577$	−23.8617	−0.993374	−0.496687	+	0.867930i	$0.665450\pi$
$578$	−45.3202	−1.88507
$579$	−16.3202	−0.678244
$580$	2.73422	0.113532
$581$	4.42588	0.183616
$582$	−18.1729	−0.753289
$583$	1.46843	0.0608163
$584$	13.2872	0.549829
$585$	−5.04663	−0.208652
$586$	−7.17375	−0.296345
$587$	−17.6549	−0.728697	−0.364349	−	0.931263i	$-0.618708\pi$
$587$	−17.6549	−0.728697	−0.364349	+	0.931263i	$0.618708\pi$
$588$	−1.00000	−0.0412393
$589$	−5.25706	−0.216613
$590$	−8.20672	−0.337865
$591$	−3.40069	−0.139886
$592$	10.2067	0.419494
$593$	36.1563	1.48476	0.742382	−	0.669977i	$-0.233696\pi$
$593$	36.1563	1.48476	0.742382	+	0.669977i	$0.233696\pi$
$594$	0.459752	0.0188638
$595$	7.89431	0.323635
$596$	1.08050	0.0442589
$597$	15.4939	0.634125
$598$	5.04663	0.206372
$599$	32.3874	1.32331	0.661656	−	0.749808i	$-0.269854\pi$
$599$	32.3874	1.32331	0.661656	+	0.749808i	$0.269854\pi$
$600$	1.00000	0.0408248
$601$	−0.387936	−0.0158243	−0.00791213	−	0.999969i	$-0.502519\pi$
$601$	−0.387936	−0.0158243	−0.00791213	+	0.999969i	$0.502519\pi$
$602$	7.74697	0.315743
$603$	8.66648	0.352926
$604$	14.0933	0.573446
$605$	10.7886	0.438620
$606$	13.2533	0.538381
$607$	22.4930	0.912965	0.456482	−	0.889732i	$-0.349109\pi$
$607$	22.4930	0.912965	0.456482	+	0.889732i	$0.349109\pi$
$608$	−7.50638	−0.304424
$609$	2.73422	0.110796
$610$	1.08050	0.0437480
$611$	13.0550	0.528148
$612$	−7.89431	−0.319109
$613$	18.1308	0.732297	0.366149	−	0.930556i	$-0.380676\pi$
$613$	18.1308	0.732297	0.366149	+	0.930556i	$0.380676\pi$
$614$	−21.5872	−0.871188
$615$	11.4007	0.459720
$616$	−0.459752	−0.0185239
$617$	12.2322	0.492451	0.246226	−	0.969213i	$-0.420810\pi$
$617$	12.2322	0.492451	0.246226	+	0.969213i	$0.420810\pi$
$618$	5.40069	0.217248
$619$	−31.3709	−1.26090	−0.630451	−	0.776229i	$-0.717130\pi$
$619$	−31.3709	−1.26090	−0.630451	+	0.776229i	$0.717130\pi$
$620$	0.700346	0.0281266
$621$	1.00000	0.0401286
$622$	0.0338705	0.00135808
$623$	−3.16010	−0.126607
$624$	−5.04663	−0.202027
$625$	1.00000	0.0400000
$626$	−8.69627	−0.347573
$627$	−3.45107	−0.137822
$628$	9.01276	0.359648
$629$	−80.5751	−3.21274
$630$	1.00000	0.0398410
$631$	37.6907	1.50044	0.750222	−	0.661186i	$-0.229947\pi$
$631$	37.6907	1.50044	0.750222	+	0.661186i	$0.229947\pi$
$632$	−6.11347	−0.243181
$633$	15.0128	0.596703
$634$	22.8946	0.909262
$635$	11.7470	0.466164
$636$	−3.19397	−0.126649
$637$	5.04663	0.199955
$638$	1.25706	0.0497675
$639$	−2.34628	−0.0928174
$640$	1.00000	0.0395285
$641$	31.7725	1.25494	0.627469	−	0.778642i	$-0.284091\pi$
$641$	31.7725	1.25494	0.627469	+	0.778642i	$0.284091\pi$
$642$	−3.93226	−0.155194
$643$	19.7345	0.778254	0.389127	−	0.921184i	$-0.372777\pi$
$643$	19.7345	0.778254	0.389127	+	0.921184i	$0.372777\pi$
$644$	−1.00000	−0.0394055
$645$	−7.74697	−0.305037
$646$	59.2577	2.33146
$647$	−42.8648	−1.68519	−0.842595	−	0.538547i	$-0.818973\pi$
$647$	−42.8648	−1.68519	−0.842595	+	0.538547i	$0.818973\pi$
$648$	−1.00000	−0.0392837
$649$	−3.77306	−0.148105
$650$	−5.04663	−0.197945
$651$	0.700346	0.0274487
$652$	1.90675	0.0746740
$653$	−31.7464	−1.24233	−0.621166	−	0.783679i	$-0.713341\pi$
$653$	−31.7464	−1.24233	−0.621166	+	0.783679i	$0.713341\pi$
$654$	−7.40069	−0.289390
$655$	−13.6752	−0.534333
$656$	11.4007	0.445122
$657$	−13.2872	−0.518384
$658$	−2.58687	−0.100847
$659$	−8.94094	−0.348290	−0.174145	−	0.984720i	$-0.555716\pi$
$659$	−8.94094	−0.348290	−0.174145	+	0.984720i	$0.555716\pi$
$660$	0.459752	0.0178958
$661$	26.4812	1.03000	0.514999	−	0.857191i	$-0.327792\pi$
$661$	26.4812	1.03000	0.514999	+	0.857191i	$0.327792\pi$
$662$	4.70813	0.182987
$663$	39.8396	1.54724
$664$	−4.42588	−0.171758
$665$	−7.50638	−0.291085
$666$	−10.2067	−0.395503
$667$	2.73422	0.105869
$668$	−1.11844	−0.0432738
$669$	19.7345	0.762981
$670$	8.66648	0.334815
$671$	0.496760	0.0191772
$672$	1.00000	0.0385758
$673$	−5.78863	−0.223135	−0.111568	−	0.993757i	$-0.535587\pi$
$673$	−5.78863	−0.223135	−0.111568	+	0.993757i	$0.535587\pi$
$674$	−25.2611	−0.973023
$675$	−1.00000	−0.0384900
$676$	12.4684	0.479555
$677$	−20.5744	−0.790740	−0.395370	−	0.918522i	$-0.629384\pi$
$677$	−20.5744	−0.790740	−0.395370	+	0.918522i	$0.629384\pi$
$678$	−4.11347	−0.157977
$679$	−18.1729	−0.697410
$680$	−7.89431	−0.302733
$681$	21.8943	0.838992
$682$	0.321985	0.0123295
$683$	−24.2698	−0.928659	−0.464329	−	0.885663i	$-0.653705\pi$
$683$	−24.2698	−0.928659	−0.464329	+	0.885663i	$0.653705\pi$
$684$	7.50638	0.287014
$685$	−5.28722	−0.202014
$686$	−1.00000	−0.0381802
$687$	−20.8691	−0.796207
$688$	−7.74697	−0.295351
$689$	16.1188	0.614076
$690$	1.00000	0.0380693
$691$	−7.72554	−0.293893	−0.146947	−	0.989144i	$-0.546945\pi$
$691$	−7.72554	−0.293893	−0.146947	+	0.989144i	$0.546945\pi$
$692$	7.39291	0.281036
$693$	0.459752	0.0174645
$694$	0.692560	0.0262892
$695$	8.20672	0.311299
$696$	−2.73422	−0.103640
$697$	−90.0006	−3.40902
$698$	−9.06806	−0.343231
$699$	3.17375	0.120042
$700$	1.00000	0.0377964
$701$	22.6404	0.855116	0.427558	−	0.903988i	$-0.359374\pi$
$701$	22.6404	0.855116	0.427558	+	0.903988i	$0.359374\pi$
$702$	5.04663	0.190473
$703$	76.6155	2.88961
$704$	0.459752	0.0173275
$705$	2.58687	0.0974273
$706$	−28.1563	−1.05968
$707$	13.2533	0.498444
$708$	8.20672	0.308428
$709$	37.6804	1.41512	0.707559	−	0.706654i	$-0.249796\pi$
$709$	37.6804	1.41512	0.707559	+	0.706654i	$0.249796\pi$
$710$	−2.34628	−0.0880543
$711$	6.11347	0.229273
$712$	3.16010	0.118430
$713$	0.700346	0.0262282
$714$	−7.89431	−0.295437
$715$	−2.32020	−0.0867704
$716$	23.7209	0.886491
$717$	−16.0012	−0.597576
$718$	−19.7255	−0.736150
$719$	−12.2881	−0.458269	−0.229135	−	0.973395i	$-0.573590\pi$
$719$	−12.2881	−0.458269	−0.229135	+	0.973395i	$0.573590\pi$
$720$	−1.00000	−0.0372678
$721$	5.40069	0.201132
$722$	−37.3457	−1.38986
$723$	−10.4936	−0.390262
$724$	−7.46843	−0.277562
$725$	−2.73422	−0.101546
$726$	−10.7886	−0.400404
$727$	20.6677	0.766522	0.383261	−	0.923640i	$-0.374801\pi$
$727$	20.6677	0.766522	0.383261	+	0.923640i	$0.374801\pi$
$728$	−5.04663	−0.187040
$729$	1.00000	0.0370370
$730$	−13.2872	−0.491782
$731$	61.1570	2.26197
$732$	−1.08050	−0.0399363
$733$	−18.8518	−0.696306	−0.348153	−	0.937438i	$-0.613191\pi$
$733$	−18.8518	−0.696306	−0.348153	+	0.937438i	$0.613191\pi$
$734$	21.4007	0.789914
$735$	1.00000	0.0368856
$736$	1.00000	0.0368605
$737$	3.98443	0.146768
$738$	−11.4007	−0.419665
$739$	−31.8564	−1.17186	−0.585928	−	0.810363i	$-0.699270\pi$
$739$	−31.8564	−1.17186	−0.585928	+	0.810363i	$0.699270\pi$
$740$	−10.2067	−0.375207
$741$	−37.8819	−1.39163
$742$	−3.19397	−0.117254
$743$	34.0411	1.24885	0.624423	−	0.781086i	$-0.285334\pi$
$743$	34.0411	1.24885	0.624423	+	0.781086i	$0.285334\pi$
$744$	−0.700346	−0.0256759
$745$	−1.08050	−0.0395863
$746$	−22.9826	−0.841453
$747$	4.42588	0.161935
$748$	−3.62943	−0.132705
$749$	−3.93226	−0.143682
$750$	−1.00000	−0.0365148
$751$	−20.0631	−0.732113	−0.366056	−	0.930593i	$-0.619292\pi$
$751$	−20.0631	−0.732113	−0.366056	+	0.930593i	$0.619292\pi$
$752$	2.58687	0.0943336
$753$	−17.5735	−0.640416
$754$	13.7986	0.502514
$755$	−14.0933	−0.512906
$756$	−1.00000	−0.0363696
$757$	9.54146	0.346790	0.173395	−	0.984852i	$-0.444526\pi$
$757$	9.54146	0.346790	0.173395	+	0.984852i	$0.444526\pi$
$758$	0.967024	0.0351239
$759$	0.459752	0.0166879
$760$	7.50638	0.272285
$761$	−10.3301	−0.374467	−0.187234	−	0.982315i	$-0.559952\pi$
$761$	−10.3301	−0.374467	−0.187234	+	0.982315i	$0.559952\pi$
$762$	−11.7470	−0.425548
$763$	−7.40069	−0.267923
$764$	26.3000	0.951500
$765$	7.89431	0.285420
$766$	−5.31738	−0.192125
$767$	−41.4163	−1.49545
$768$	−1.00000	−0.0360844
$769$	29.8011	1.07465	0.537327	−	0.843374i	$-0.319434\pi$
$769$	29.8011	1.07465	0.537327	+	0.843374i	$0.319434\pi$
$770$	0.459752	0.0165683
$771$	25.9954	0.936200
$772$	16.3202	0.587377
$773$	16.0660	0.577852	0.288926	−	0.957351i	$-0.406702\pi$
$773$	16.0660	0.577852	0.288926	+	0.957351i	$0.406702\pi$
$774$	7.74697	0.278459
$775$	−0.700346	−0.0251572
$776$	18.1729	0.652367
$777$	−10.2067	−0.366164
$778$	4.32020	0.154887
$779$	85.5779	3.06615
$780$	5.04663	0.180698
$781$	−1.07871	−0.0385992
$782$	−7.89431	−0.282300
$783$	2.73422	0.0977129
$784$	1.00000	0.0357143
$785$	−9.01276	−0.321679
$786$	13.6752	0.487777
$787$	−44.6696	−1.59230	−0.796150	−	0.605099i	$-0.793133\pi$
$787$	−44.6696	−1.59230	−0.796150	+	0.605099i	$0.793133\pi$
$788$	3.40069	0.121145
$789$	−28.4812	−1.01396
$790$	6.11347	0.217508
$791$	−4.11347	−0.146258
$792$	−0.459752	−0.0163366
$793$	5.45286	0.193637
$794$	9.52781	0.338129
$795$	3.19397	0.113278
$796$	−15.4939	−0.549168
$797$	2.85176	0.101015	0.0505073	−	0.998724i	$-0.483916\pi$
$797$	2.85176	0.101015	0.0505073	+	0.998724i	$0.483916\pi$
$798$	7.50638	0.265723
$799$	−20.4216	−0.722464
$800$	−1.00000	−0.0353553
$801$	−3.16010	−0.111657
$802$	−7.86509	−0.277726
$803$	−6.10882	−0.215576
$804$	−8.66648	−0.305643
$805$	1.00000	0.0352454
$806$	3.53438	0.124493
$807$	−22.7218	−0.799845
$808$	−13.2533	−0.466251
$809$	−37.8315	−1.33008	−0.665042	−	0.746806i	$-0.731587\pi$
$809$	−37.8315	−1.33008	−0.665042	+	0.746806i	$0.731587\pi$
$810$	1.00000	0.0351364
$811$	−47.7007	−1.67500	−0.837498	−	0.546440i	$-0.815983\pi$
$811$	−47.7007	−1.67500	−0.837498	+	0.546440i	$0.815983\pi$
$812$	−2.73422	−0.0959522
$813$	22.7259	0.797031
$814$	−4.69256	−0.164474
$815$	−1.90675	−0.0667905
$816$	7.89431	0.276356
$817$	−58.1517	−2.03447
$818$	−33.0128	−1.15426
$819$	5.04663	0.176343
$820$	−11.4007	−0.398129
$821$	14.7498	0.514771	0.257386	−	0.966309i	$-0.417139\pi$
$821$	14.7498	0.514771	0.257386	+	0.966309i	$0.417139\pi$
$822$	5.28722	0.184413
$823$	−49.3497	−1.72022	−0.860112	−	0.510105i	$-0.829606\pi$
$823$	−49.3497	−1.72022	−0.860112	+	0.510105i	$0.829606\pi$
$824$	−5.40069	−0.188142
$825$	−0.459752	−0.0160065
$826$	8.20672	0.285548
$827$	−25.9578	−0.902640	−0.451320	−	0.892362i	$-0.649047\pi$
$827$	−25.9578	−0.902640	−0.451320	+	0.892362i	$0.649047\pi$
$828$	−1.00000	−0.0347524
$829$	36.3078	1.26102	0.630510	−	0.776181i	$-0.282846\pi$
$829$	36.3078	1.26102	0.630510	+	0.776181i	$0.282846\pi$
$830$	4.42588	0.153625
$831$	−15.4423	−0.535689
$832$	5.04663	0.174960
$833$	−7.89431	−0.273522
$834$	−8.20672	−0.284176
$835$	1.11844	0.0387053
$836$	3.45107	0.119358
$837$	0.700346	0.0242075
$838$	24.1729	0.835037
$839$	−4.50606	−0.155566	−0.0777832	−	0.996970i	$-0.524784\pi$
$839$	−4.50606	−0.155566	−0.0777832	+	0.996970i	$0.524784\pi$
$840$	−1.00000	−0.0345033
$841$	−21.5241	−0.742209
$842$	−15.7986	−0.544455
$843$	23.0799	0.794915
$844$	−15.0128	−0.516760
$845$	−12.4684	−0.428927
$846$	−2.58687	−0.0889386
$847$	−10.7886	−0.370702
$848$	3.19397	0.109681
$849$	−20.7218	−0.711170
$850$	7.89431	0.270773
$851$	−10.2067	−0.349882
$852$	2.34628	0.0803822
$853$	37.4601	1.28261	0.641304	−	0.767287i	$-0.278394\pi$
$853$	37.4601	1.28261	0.641304	+	0.767287i	$0.278394\pi$
$854$	−1.08050	−0.0369738
$855$	−7.50638	−0.256713
$856$	3.93226	0.134402
$857$	−13.9039	−0.474948	−0.237474	−	0.971394i	$-0.576319\pi$
$857$	−13.9039	−0.474948	−0.237474	+	0.971394i	$0.576319\pi$
$858$	2.32020	0.0792102
$859$	−2.94966	−0.100641	−0.0503206	−	0.998733i	$-0.516024\pi$
$859$	−2.94966	−0.100641	−0.0503206	+	0.998733i	$0.516024\pi$
$860$	7.74697	0.264170
$861$	−11.4007	−0.388535
$862$	−17.7429	−0.604325
$863$	5.09044	0.173280	0.0866402	−	0.996240i	$-0.472387\pi$
$863$	5.09044	0.173280	0.0866402	+	0.996240i	$0.472387\pi$
$864$	1.00000	0.0340207
$865$	−7.39291	−0.251366
$866$	−19.8527	−0.674621
$867$	−45.3202	−1.53915
$868$	−0.700346	−0.0237713
$869$	2.81068	0.0953458
$870$	2.73422	0.0926986
$871$	43.7365	1.48195
$872$	7.40069	0.250619
$873$	−18.1729	−0.615058
$874$	7.50638	0.253907
$875$	−1.00000	−0.0338062
$876$	13.2872	0.448934
$877$	−53.7221	−1.81407	−0.907033	−	0.421059i	$-0.861659\pi$
$877$	−53.7221	−1.81407	−0.907033	+	0.421059i	$0.861659\pi$
$878$	6.79360	0.229273
$879$	−7.17375	−0.241965
$880$	−0.459752	−0.0154982
$881$	−30.3998	−1.02420	−0.512098	−	0.858927i	$-0.671131\pi$
$881$	−30.3998	−1.02420	−0.512098	+	0.858927i	$0.671131\pi$
$882$	−1.00000	−0.0336718
$883$	−4.84361	−0.163001	−0.0815003	−	0.996673i	$-0.525971\pi$
$883$	−4.84361	−0.163001	−0.0815003	+	0.996673i	$0.525971\pi$
$884$	−39.8396	−1.33995
$885$	−8.20672	−0.275866
$886$	−21.3330	−0.716695
$887$	10.1486	0.340755	0.170378	−	0.985379i	$-0.445501\pi$
$887$	10.1486	0.340755	0.170378	+	0.985379i	$0.445501\pi$
$888$	10.2067	0.342515
$889$	−11.7470	−0.393981
$890$	−3.16010	−0.105927
$891$	0.459752	0.0154023
$892$	−19.7345	−0.660761
$893$	19.4181	0.649800
$894$	1.08050	0.0361372
$895$	−23.7209	−0.792902
$896$	−1.00000	−0.0334077
$897$	5.04663	0.168502
$898$	−41.1993	−1.37484
$899$	1.91490	0.0638654
$900$	1.00000	0.0333333
$901$	−25.2142	−0.840006
$902$	−5.24149	−0.174522
$903$	7.74697	0.257803
$904$	4.11347	0.136812
$905$	7.46843	0.248259
$906$	14.0933	0.468217
$907$	−7.77184	−0.258060	−0.129030	−	0.991641i	$-0.541186\pi$
$907$	−7.77184	−0.258060	−0.129030	+	0.991641i	$0.541186\pi$
$908$	−21.8943	−0.726588
$909$	13.2533	0.439586
$910$	5.04663	0.167294
$911$	32.1308	1.06454	0.532271	−	0.846574i	$-0.321339\pi$
$911$	32.1308	1.06454	0.532271	+	0.846574i	$0.321339\pi$
$912$	−7.50638	−0.248561
$913$	2.03481	0.0673423
$914$	28.2739	0.935217
$915$	1.08050	0.0357201
$916$	20.8691	0.689535
$917$	13.6752	0.451593
$918$	−7.89431	−0.260551
$919$	1.34502	0.0443682	0.0221841	−	0.999754i	$-0.492938\pi$
$919$	1.34502	0.0443682	0.0221841	+	0.999754i	$0.492938\pi$
$920$	−1.00000	−0.0329690
$921$	−21.5872	−0.711322
$922$	3.70903	0.122150
$923$	−11.8408	−0.389745
$924$	−0.459752	−0.0151247
$925$	10.2067	0.335595
$926$	−16.9207	−0.556049
$927$	5.40069	0.177382
$928$	2.73422	0.0897550
$929$	−24.9723	−0.819315	−0.409658	−	0.912239i	$-0.634352\pi$
$929$	−24.9723	−0.819315	−0.409658	+	0.912239i	$0.634352\pi$
$930$	0.700346	0.0229652
$931$	7.50638	0.246012
$932$	−3.17375	−0.103960
$933$	0.0338705	0.00110887
$934$	−16.2145	−0.530555
$935$	3.62943	0.118695
$936$	−5.04663	−0.164954
$937$	−42.1480	−1.37691	−0.688457	−	0.725277i	$-0.741712\pi$
$937$	−42.1480	−1.37691	−0.688457	+	0.725277i	$0.741712\pi$
$938$	−8.66648	−0.282970
$939$	−8.69627	−0.283792
$940$	−2.58687	−0.0843745
$941$	2.54893	0.0830927	0.0415464	−	0.999137i	$-0.486772\pi$
$941$	2.54893	0.0830927	0.0415464	+	0.999137i	$0.486772\pi$
$942$	9.01276	0.293651
$943$	−11.4007	−0.371258
$944$	−8.20672	−0.267106
$945$	1.00000	0.0325300
$946$	3.56168	0.115800
$947$	56.8425	1.84713	0.923566	−	0.383440i	$-0.125261\pi$
$947$	56.8425	1.84713	0.923566	+	0.383440i	$0.125261\pi$
$948$	−6.11347	−0.198556
$949$	−67.0556	−2.17672
$950$	−7.50638	−0.243539
$951$	22.8946	0.742409
$952$	7.89431	0.255856
$953$	19.0503	0.617101	0.308550	−	0.951208i	$-0.400156\pi$
$953$	19.0503	0.617101	0.308550	+	0.951208i	$0.400156\pi$
$954$	−3.19397	−0.103409
$955$	−26.3000	−0.851047
$956$	16.0012	0.517516
$957$	1.25706	0.0406350
$958$	18.8773	0.609897
$959$	5.28722	0.170733
$960$	1.00000	0.0322749
$961$	−30.5095	−0.984178
$962$	−51.5095	−1.66073
$963$	−3.93226	−0.126715
$964$	10.4936	0.337977
$965$	−16.3202	−0.525366
$966$	−1.00000	−0.0321745
$967$	−20.6509	−0.664088	−0.332044	−	0.943264i	$-0.607738\pi$
$967$	−20.6509	−0.664088	−0.332044	+	0.943264i	$0.607738\pi$
$968$	10.7886	0.346760
$969$	59.2577	1.90363
$970$	−18.1729	−0.583495
$971$	−47.7072	−1.53100	−0.765499	−	0.643437i	$-0.777508\pi$
$971$	−47.7072	−1.53100	−0.765499	+	0.643437i	$0.777508\pi$
$972$	−1.00000	−0.0320750
$973$	−8.20672	−0.263095
$974$	36.6820	1.17537
$975$	−5.04663	−0.161621
$976$	1.08050	0.0345858
$977$	−28.5947	−0.914824	−0.457412	−	0.889255i	$-0.651224\pi$
$977$	−28.5947	−0.914824	−0.457412	+	0.889255i	$0.651224\pi$
$978$	1.90675	0.0609711
$979$	−1.45286	−0.0464336
$980$	−1.00000	−0.0319438
$981$	−7.40069	−0.236286
$982$	28.2698	0.902126
$983$	−33.6705	−1.07392	−0.536961	−	0.843607i	$-0.680428\pi$
$983$	−33.6705	−1.07392	−0.536961	+	0.843607i	$0.680428\pi$
$984$	11.4007	0.363441
$985$	−3.40069	−0.108355
$986$	−21.5848	−0.687399
$987$	−2.58687	−0.0823411
$988$	37.8819	1.20518
$989$	7.74697	0.246339
$990$	0.459752	0.0146119
$991$	−5.13088	−0.162988	−0.0814938	−	0.996674i	$-0.525969\pi$
$991$	−5.13088	−0.162988	−0.0814938	+	0.996674i	$0.525969\pi$
$992$	0.700346	0.0222360
$993$	4.70813	0.149408
$994$	2.34628	0.0744195
$995$	15.4939	0.491191
$996$	−4.42588	−0.140239
$997$	50.1955	1.58971	0.794854	−	0.606801i	$-0.207548\pi$
$997$	50.1955	1.58971	0.794854	+	0.606801i	$0.207548\pi$
$998$	7.01276	0.221985
$999$	−10.2067	−0.322926

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4830.2.a.cd.1.2	✓	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4830.2.a.cd.1.2	✓	4	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:	\( N \)	\(=\)	\( 4830 = 2 \cdot 3 \cdot 5 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4830.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{5} +1.00000 q^{6} +1.00000 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{5} +1.00000 q^{6} +1.00000 q^{7} -1.00000 q^{8} +1.00000 q^{9} +1.00000 q^{10} +0.459752 q^{11} -1.00000 q^{12} +5.04663 q^{13} -1.00000 q^{14} +1.00000 q^{15} +1.00000 q^{16} -7.89431 q^{17} -1.00000 q^{18} +7.50638 q^{19} -1.00000 q^{20} -1.00000 q^{21} -0.459752 q^{22} -1.00000 q^{23} +1.00000 q^{24} +1.00000 q^{25} -5.04663 q^{26} -1.00000 q^{27} +1.00000 q^{28} -2.73422 q^{29} -1.00000 q^{30} -0.700346 q^{31} -1.00000 q^{32} -0.459752 q^{33} +7.89431 q^{34} -1.00000 q^{35} +1.00000 q^{36} +10.2067 q^{37} -7.50638 q^{38} -5.04663 q^{39} +1.00000 q^{40} +11.4007 q^{41} +1.00000 q^{42} -7.74697 q^{43} +0.459752 q^{44} -1.00000 q^{45} +1.00000 q^{46} +2.58687 q^{47} -1.00000 q^{48} +1.00000 q^{49} -1.00000 q^{50} +7.89431 q^{51} +5.04663 q^{52} +3.19397 q^{53} +1.00000 q^{54} -0.459752 q^{55} -1.00000 q^{56} -7.50638 q^{57} +2.73422 q^{58} -8.20672 q^{59} +1.00000 q^{60} +1.08050 q^{61} +0.700346 q^{62} +1.00000 q^{63} +1.00000 q^{64} -5.04663 q^{65} +0.459752 q^{66} +8.66648 q^{67} -7.89431 q^{68} +1.00000 q^{69} +1.00000 q^{70} -2.34628 q^{71} -1.00000 q^{72} -13.2872 q^{73} -10.2067 q^{74} -1.00000 q^{75} +7.50638 q^{76} +0.459752 q^{77} +5.04663 q^{78} +6.11347 q^{79} -1.00000 q^{80} +1.00000 q^{81} -11.4007 q^{82} +4.42588 q^{83} -1.00000 q^{84} +7.89431 q^{85} +7.74697 q^{86} +2.73422 q^{87} -0.459752 q^{88} -3.16010 q^{89} +1.00000 q^{90} +5.04663 q^{91} -1.00000 q^{92} +0.700346 q^{93} -2.58687 q^{94} -7.50638 q^{95} +1.00000 q^{96} -18.1729 q^{97} -1.00000 q^{98} +0.459752 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 4 q^{2} - 4 q^{3} + 4 q^{4} - 4 q^{5} + 4 q^{6} + 4 q^{7} - 4 q^{8} + 4 q^{9}+O(q^{10}) \) 4 * q - 4 * q^2 - 4 * q^3 + 4 * q^4 - 4 * q^5 + 4 * q^6 + 4 * q^7 - 4 * q^8 + 4 * q^9	\( 4 q - 4 q^{2} - 4 q^{3} + 4 q^{4} - 4 q^{5} + 4 q^{6} + 4 q^{7} - 4 q^{8} + 4 q^{9} + 4 q^{10} + 2 q^{11} - 4 q^{12} + 4 q^{13} - 4 q^{14} + 4 q^{15} + 4 q^{16} - 2 q^{17} - 4 q^{18} + 14 q^{19} - 4 q^{20} - 4 q^{21} - 2 q^{22} - 4 q^{23} + 4 q^{24} + 4 q^{25} - 4 q^{26} - 4 q^{27} + 4 q^{28} - 4 q^{29} - 4 q^{30} + 20 q^{31} - 4 q^{32} - 2 q^{33} + 2 q^{34} - 4 q^{35} + 4 q^{36} + 2 q^{37} - 14 q^{38} - 4 q^{39} + 4 q^{40} + 4 q^{42} + 8 q^{43} + 2 q^{44} - 4 q^{45} + 4 q^{46} - 6 q^{47} - 4 q^{48} + 4 q^{49} - 4 q^{50} + 2 q^{51} + 4 q^{52} + 6 q^{53} + 4 q^{54} - 2 q^{55} - 4 q^{56} - 14 q^{57} + 4 q^{58} + 6 q^{59} + 4 q^{60} + 4 q^{61} - 20 q^{62} + 4 q^{63} + 4 q^{64} - 4 q^{65} + 2 q^{66} - 4 q^{67} - 2 q^{68} + 4 q^{69} + 4 q^{70} - 16 q^{71} - 4 q^{72} - 14 q^{73} - 2 q^{74} - 4 q^{75} + 14 q^{76} + 2 q^{77} + 4 q^{78} + 18 q^{79} - 4 q^{80} + 4 q^{81} + 2 q^{83} - 4 q^{84} + 2 q^{85} - 8 q^{86} + 4 q^{87} - 2 q^{88} + 10 q^{89} + 4 q^{90} + 4 q^{91} - 4 q^{92} - 20 q^{93} + 6 q^{94} - 14 q^{95} + 4 q^{96} - 18 q^{97} - 4 q^{98} + 2 q^{99}+O(q^{100}) \) 4 * q - 4 * q^2 - 4 * q^3 + 4 * q^4 - 4 * q^5 + 4 * q^6 + 4 * q^7 - 4 * q^8 + 4 * q^9 + 4 * q^10 + 2 * q^11 - 4 * q^12 + 4 * q^13 - 4 * q^14 + 4 * q^15 + 4 * q^16 - 2 * q^17 - 4 * q^18 + 14 * q^19 - 4 * q^20 - 4 * q^21 - 2 * q^22 - 4 * q^23 + 4 * q^24 + 4 * q^25 - 4 * q^26 - 4 * q^27 + 4 * q^28 - 4 * q^29 - 4 * q^30 + 20 * q^31 - 4 * q^32 - 2 * q^33 + 2 * q^34 - 4 * q^35 + 4 * q^36 + 2 * q^37 - 14 * q^38 - 4 * q^39 + 4 * q^40 + 4 * q^42 + 8 * q^43 + 2 * q^44 - 4 * q^45 + 4 * q^46 - 6 * q^47 - 4 * q^48 + 4 * q^49 - 4 * q^50 + 2 * q^51 + 4 * q^52 + 6 * q^53 + 4 * q^54 - 2 * q^55 - 4 * q^56 - 14 * q^57 + 4 * q^58 + 6 * q^59 + 4 * q^60 + 4 * q^61 - 20 * q^62 + 4 * q^63 + 4 * q^64 - 4 * q^65 + 2 * q^66 - 4 * q^67 - 2 * q^68 + 4 * q^69 + 4 * q^70 - 16 * q^71 - 4 * q^72 - 14 * q^73 - 2 * q^74 - 4 * q^75 + 14 * q^76 + 2 * q^77 + 4 * q^78 + 18 * q^79 - 4 * q^80 + 4 * q^81 + 2 * q^83 - 4 * q^84 + 2 * q^85 - 8 * q^86 + 4 * q^87 - 2 * q^88 + 10 * q^89 + 4 * q^90 + 4 * q^91 - 4 * q^92 - 20 * q^93 + 6 * q^94 - 14 * q^95 + 4 * q^96 - 18 * q^97 - 4 * q^98 + 2 * q^99

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