LMFDB - Embedded newform 4830.2.a.ce.1.3

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:	4.4.6809.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - 5x^{2} - x + 1 $ x^4 - 5*x^2 - x + 1
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			1.3
Root			$0.361989$ 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)

$f(q)$	$=$	$q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{5} +1.00000 q^{6} +1.00000 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{5} +1.00000 q^{6} +1.00000 q^{7} +1.00000 q^{8} +1.00000 q^{9} +1.00000 q^{10} +0.723979 q^{11} +1.00000 q^{12} +4.80105 q^{13} +1.00000 q^{14} +1.00000 q^{15} +1.00000 q^{16} -5.52503 q^{17} +1.00000 q^{18} -3.52503 q^{19} +1.00000 q^{20} +1.00000 q^{21} +0.723979 q^{22} +1.00000 q^{23} +1.00000 q^{24} +1.00000 q^{25} +4.80105 q^{26} +1.00000 q^{27} +1.00000 q^{28} +3.78710 q^{29} +1.00000 q^{30} -6.46191 q^{31} +1.00000 q^{32} +0.723979 q^{33} -5.52503 q^{34} +1.00000 q^{35} +1.00000 q^{36} +11.9869 q^{37} -3.52503 q^{38} +4.80105 q^{39} +1.00000 q^{40} +9.47586 q^{41} +1.00000 q^{42} +3.66086 q^{43} +0.723979 q^{44} +1.00000 q^{45} +1.00000 q^{46} +6.07707 q^{47} +1.00000 q^{48} +1.00000 q^{49} +1.00000 q^{50} -5.52503 q^{51} +4.80105 q^{52} -7.98693 q^{53} +1.00000 q^{54} +0.723979 q^{55} +1.00000 q^{56} -3.52503 q^{57} +3.78710 q^{58} +12.5390 q^{59} +1.00000 q^{60} -7.60209 q^{61} -6.46191 q^{62} +1.00000 q^{63} +1.00000 q^{64} +4.80105 q^{65} +0.723979 q^{66} -2.21290 q^{67} -5.52503 q^{68} +1.00000 q^{69} +1.00000 q^{70} +13.2630 q^{71} +1.00000 q^{72} -10.5390 q^{73} +11.9869 q^{74} +1.00000 q^{75} -3.52503 q^{76} +0.723979 q^{77} +4.80105 q^{78} +9.98693 q^{79} +1.00000 q^{80} +1.00000 q^{81} +9.47586 q^{82} -4.97298 q^{83} +1.00000 q^{84} -5.52503 q^{85} +3.66086 q^{86} +3.78710 q^{87} +0.723979 q^{88} +0.416209 q^{89} +1.00000 q^{90} +4.80105 q^{91} +1.00000 q^{92} -6.46191 q^{93} +6.07707 q^{94} -3.52503 q^{95} +1.00000 q^{96} +7.31212 q^{97} +1.00000 q^{98} +0.723979 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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} + 4 q^{12} + 2 q^{13} + 4 q^{14} + 4 q^{15} + 4 q^{16} - 2 q^{17} + 4 q^{18} + 6 q^{19} + 4 q^{20} + 4 q^{21} + 4 q^{23} + 4 q^{24} + 4 q^{25} + 2 q^{26} + 4 q^{27} + 4 q^{28} + 14 q^{29} + 4 q^{30} - 4 q^{31} + 4 q^{32} - 2 q^{34} + 4 q^{35} + 4 q^{36} + 6 q^{37} + 6 q^{38} + 2 q^{39} + 4 q^{40} + 4 q^{42} + 10 q^{43} + 4 q^{45} + 4 q^{46} + 10 q^{47} + 4 q^{48} + 4 q^{49} + 4 q^{50} - 2 q^{51} + 2 q^{52} + 10 q^{53} + 4 q^{54} + 4 q^{56} + 6 q^{57} + 14 q^{58} + 14 q^{59} + 4 q^{60} + 4 q^{61} - 4 q^{62} + 4 q^{63} + 4 q^{64} + 2 q^{65} - 10 q^{67} - 2 q^{68} + 4 q^{69} + 4 q^{70} + 14 q^{71} + 4 q^{72} - 6 q^{73} + 6 q^{74} + 4 q^{75} + 6 q^{76} + 2 q^{78} - 2 q^{79} + 4 q^{80} + 4 q^{81} + 6 q^{83} + 4 q^{84} - 2 q^{85} + 10 q^{86} + 14 q^{87} - 8 q^{89} + 4 q^{90} + 2 q^{91} + 4 q^{92} - 4 q^{93} + 10 q^{94} + 6 q^{95} + 4 q^{96} + 8 q^{97} + 4 q^{98}+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 + 4 * q^12 + 2 * q^13 + 4 * q^14 + 4 * q^15 + 4 * q^16 - 2 * q^17 + 4 * q^18 + 6 * q^19 + 4 * q^20 + 4 * q^21 + 4 * q^23 + 4 * q^24 + 4 * q^25 + 2 * q^26 + 4 * q^27 + 4 * q^28 + 14 * q^29 + 4 * q^30 - 4 * q^31 + 4 * q^32 - 2 * q^34 + 4 * q^35 + 4 * q^36 + 6 * q^37 + 6 * q^38 + 2 * q^39 + 4 * q^40 + 4 * q^42 + 10 * q^43 + 4 * q^45 + 4 * q^46 + 10 * q^47 + 4 * q^48 + 4 * q^49 + 4 * q^50 - 2 * q^51 + 2 * q^52 + 10 * q^53 + 4 * q^54 + 4 * q^56 + 6 * q^57 + 14 * q^58 + 14 * q^59 + 4 * q^60 + 4 * q^61 - 4 * q^62 + 4 * q^63 + 4 * q^64 + 2 * q^65 - 10 * q^67 - 2 * q^68 + 4 * q^69 + 4 * q^70 + 14 * q^71 + 4 * q^72 - 6 * q^73 + 6 * q^74 + 4 * q^75 + 6 * q^76 + 2 * q^78 - 2 * q^79 + 4 * q^80 + 4 * q^81 + 6 * q^83 + 4 * q^84 - 2 * q^85 + 10 * q^86 + 14 * q^87 - 8 * q^89 + 4 * q^90 + 2 * q^91 + 4 * q^92 - 4 * q^93 + 10 * q^94 + 6 * q^95 + 4 * q^96 + 8 * q^97 + 4 * q^98

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
$11$	0.723979	0.218288	0.109144	−	0.994026i	$-0.465189\pi$
$11$	0.723979	0.218288	0.109144	+	0.994026i	$0.465189\pi$
$12$	1.00000	0.288675
$13$	4.80105	1.33157	0.665785	−	0.746143i	$-0.268097\pi$
$13$	4.80105	1.33157	0.665785	+	0.746143i	$0.268097\pi$
$14$	1.00000	0.267261
$15$	1.00000	0.258199
$16$	1.00000	0.250000
$17$	−5.52503	−1.34002	−0.670008	−	0.742354i	$-0.733709\pi$
$17$	−5.52503	−1.34002	−0.670008	+	0.742354i	$0.733709\pi$
$18$	1.00000	0.235702
$19$	−3.52503	−0.808696	−0.404348	−	0.914605i	$-0.632502\pi$
$19$	−3.52503	−0.808696	−0.404348	+	0.914605i	$0.632502\pi$
$20$	1.00000	0.223607
$21$	1.00000	0.218218
$22$	0.723979	0.154353
$23$	1.00000	0.208514
$23$	1.00000	0.208514
$24$	1.00000	0.204124
$25$	1.00000	0.200000
$26$	4.80105	0.941563
$27$	1.00000	0.192450
$28$	1.00000	0.188982
$29$	3.78710	0.703246	0.351623	−	0.936142i	$-0.385630\pi$
$29$	3.78710	0.703246	0.351623	+	0.936142i	$0.385630\pi$
$30$	1.00000	0.182574
$31$	−6.46191	−1.16059	−0.580296	−	0.814405i	$-0.697063\pi$
$31$	−6.46191	−1.16059	−0.580296	+	0.814405i	$0.697063\pi$
$32$	1.00000	0.176777
$33$	0.723979	0.126028
$34$	−5.52503	−0.947534
$35$	1.00000	0.169031
$36$	1.00000	0.166667
$37$	11.9869	1.97064	0.985320	−	0.170719i	$-0.0546091\pi$
$37$	11.9869	1.97064	0.985320	+	0.170719i	$0.0546091\pi$
$38$	−3.52503	−0.571835
$39$	4.80105	0.768783
$40$	1.00000	0.158114
$41$	9.47586	1.47988	0.739940	−	0.672673i	$-0.234854\pi$
$41$	9.47586	1.47988	0.739940	+	0.672673i	$0.234854\pi$
$42$	1.00000	0.154303
$43$	3.66086	0.558276	0.279138	−	0.960251i	$-0.409951\pi$
$43$	3.66086	0.558276	0.279138	+	0.960251i	$0.409951\pi$
$44$	0.723979	0.109144
$45$	1.00000	0.149071
$46$	1.00000	0.147442
$47$	6.07707	0.886432	0.443216	−	0.896415i	$-0.353838\pi$
$47$	6.07707	0.886432	0.443216	+	0.896415i	$0.353838\pi$
$48$	1.00000	0.144338
$49$	1.00000	0.142857
$50$	1.00000	0.141421
$51$	−5.52503	−0.773658
$52$	4.80105	0.665785
$53$	−7.98693	−1.09709	−0.548545	−	0.836121i	$-0.684818\pi$
$53$	−7.98693	−1.09709	−0.548545	+	0.836121i	$0.684818\pi$
$54$	1.00000	0.136083
$55$	0.723979	0.0976213
$56$	1.00000	0.133631
$57$	−3.52503	−0.466901
$58$	3.78710	0.497270
$59$	12.5390	1.63244	0.816218	−	0.577744i	$-0.196067\pi$
$59$	12.5390	1.63244	0.816218	+	0.577744i	$0.196067\pi$
$60$	1.00000	0.129099
$61$	−7.60209	−0.973348	−0.486674	−	0.873584i	$-0.661790\pi$
$61$	−7.60209	−0.973348	−0.486674	+	0.873584i	$0.661790\pi$
$62$	−6.46191	−0.820663
$63$	1.00000	0.125988
$64$	1.00000	0.125000
$65$	4.80105	0.595497
$66$	0.723979	0.0891156
$67$	−2.21290	−0.270349	−0.135175	−	0.990822i	$-0.543160\pi$
$67$	−2.21290	−0.270349	−0.135175	+	0.990822i	$0.543160\pi$
$68$	−5.52503	−0.670008
$69$	1.00000	0.120386
$70$	1.00000	0.119523
$71$	13.2630	1.57402	0.787011	−	0.616938i	$-0.211627\pi$
$71$	13.2630	1.57402	0.787011	+	0.616938i	$0.211627\pi$
$72$	1.00000	0.117851
$73$	−10.5390	−1.23349	−0.616747	−	0.787162i	$-0.711550\pi$
$73$	−10.5390	−1.23349	−0.616747	+	0.787162i	$0.711550\pi$
$74$	11.9869	1.39345
$75$	1.00000	0.115470
$76$	−3.52503	−0.404348
$77$	0.723979	0.0825050
$78$	4.80105	0.543612
$79$	9.98693	1.12362	0.561809	−	0.827267i	$-0.310106\pi$
$79$	9.98693	1.12362	0.561809	+	0.827267i	$0.310106\pi$
$80$	1.00000	0.111803
$81$	1.00000	0.111111
$82$	9.47586	1.04643
$83$	−4.97298	−0.545856	−0.272928	−	0.962034i	$-0.587992\pi$
$83$	−4.97298	−0.545856	−0.272928	+	0.962034i	$0.587992\pi$
$84$	1.00000	0.109109
$85$	−5.52503	−0.599273
$86$	3.66086	0.394761
$87$	3.78710	0.406020
$88$	0.723979	0.0771764
$89$	0.416209	0.0441181	0.0220590	−	0.999757i	$-0.492978\pi$
$89$	0.416209	0.0441181	0.0220590	+	0.999757i	$0.492978\pi$
$90$	1.00000	0.105409
$91$	4.80105	0.503286
$92$	1.00000	0.104257
$93$	−6.46191	−0.670068
$94$	6.07707	0.626802
$95$	−3.52503	−0.361660
$96$	1.00000	0.102062
$97$	7.31212	0.742434	0.371217	−	0.928546i	$-0.378941\pi$
$97$	7.31212	0.742434	0.371217	+	0.928546i	$0.378941\pi$
$98$	1.00000	0.101015
$99$	0.723979	0.0727626
$100$	1.00000	0.100000
$101$	−17.3400	−1.72540	−0.862698	−	0.505719i	$-0.831227\pi$
$101$	−17.3400	−1.72540	−0.862698	+	0.505719i	$0.831227\pi$
$102$	−5.52503	−0.547059
$103$	−9.60209	−0.946122	−0.473061	−	0.881030i	$-0.656851\pi$
$103$	−9.60209	−0.946122	−0.473061	+	0.881030i	$0.656851\pi$
$104$	4.80105	0.470781
$105$	1.00000	0.0975900
$106$	−7.98693	−0.775759
$107$	14.6242	1.41378	0.706890	−	0.707324i	$-0.250098\pi$
$107$	14.6242	1.41378	0.706890	+	0.707324i	$0.250098\pi$
$108$	1.00000	0.0962250
$109$	−16.6242	−1.59231	−0.796157	−	0.605090i	$-0.793137\pi$
$109$	−16.6242	−1.59231	−0.796157	+	0.605090i	$0.793137\pi$
$110$	0.723979	0.0690286
$111$	11.9869	1.13775
$112$	1.00000	0.0944911
$113$	−17.5890	−1.65464	−0.827318	−	0.561734i	$-0.810135\pi$
$113$	−17.5890	−1.65464	−0.827318	+	0.561734i	$0.810135\pi$
$114$	−3.52503	−0.330149
$115$	1.00000	0.0932505
$116$	3.78710	0.351623
$117$	4.80105	0.443857
$118$	12.5390	1.15431
$119$	−5.52503	−0.506478
$120$	1.00000	0.0912871
$121$	−10.4759	−0.952350
$122$	−7.60209	−0.688261
$123$	9.47586	0.854409
$124$	−6.46191	−0.580296
$125$	1.00000	0.0894427
$126$	1.00000	0.0890871
$127$	−10.7109	−0.950440	−0.475220	−	0.879867i	$-0.657631\pi$
$127$	−10.7109	−0.950440	−0.475220	+	0.879867i	$0.657631\pi$
$128$	1.00000	0.0883883
$129$	3.66086	0.322321
$130$	4.80105	0.421080
$131$	10.6652	0.931824	0.465912	−	0.884831i	$-0.345726\pi$
$131$	10.6652	0.931824	0.465912	+	0.884831i	$0.345726\pi$
$132$	0.723979	0.0630142
$133$	−3.52503	−0.305658
$134$	−2.21290	−0.191166
$135$	1.00000	0.0860663
$136$	−5.52503	−0.473767
$137$	−4.66521	−0.398576	−0.199288	−	0.979941i	$-0.563863\pi$
$137$	−4.66521	−0.398576	−0.199288	+	0.979941i	$0.563863\pi$
$138$	1.00000	0.0851257
$139$	−5.83279	−0.494731	−0.247366	−	0.968922i	$-0.579565\pi$
$139$	−5.83279	−0.494731	−0.247366	+	0.968922i	$0.579565\pi$
$140$	1.00000	0.0845154
$141$	6.07707	0.511781
$142$	13.2630	1.11300
$143$	3.47586	0.290666
$144$	1.00000	0.0833333
$145$	3.78710	0.314501
$146$	−10.5390	−0.872212
$147$	1.00000	0.0824786
$148$	11.9869	0.985320
$149$	−3.44796	−0.282468	−0.141234	−	0.989976i	$-0.545107\pi$
$149$	−3.44796	−0.282468	−0.141234	+	0.989976i	$0.545107\pi$
$150$	1.00000	0.0816497
$151$	−5.60209	−0.455892	−0.227946	−	0.973674i	$-0.573201\pi$
$151$	−5.60209	−0.455892	−0.227946	+	0.973674i	$0.573201\pi$
$152$	−3.52503	−0.285917
$153$	−5.52503	−0.446672
$154$	0.723979	0.0583399
$155$	−6.46191	−0.519033
$156$	4.80105	0.384391
$157$	−13.7283	−1.09564	−0.547820	−	0.836596i	$-0.684542\pi$
$157$	−13.7283	−1.09564	−0.547820	+	0.836596i	$0.684542\pi$
$158$	9.98693	0.794518
$159$	−7.98693	−0.633405
$160$	1.00000	0.0790569
$161$	1.00000	0.0788110
$162$	1.00000	0.0785674
$163$	−0.524145	−0.0410542	−0.0205271	−	0.999789i	$-0.506534\pi$
$163$	−0.524145	−0.0410542	−0.0205271	+	0.999789i	$0.506534\pi$
$164$	9.47586	0.739940
$165$	0.723979	0.0563617
$166$	−4.97298	−0.385978
$167$	−1.65126	−0.127779	−0.0638893	−	0.997957i	$-0.520350\pi$
$167$	−1.65126	−0.127779	−0.0638893	+	0.997957i	$0.520350\pi$
$168$	1.00000	0.0771517
$169$	10.0501	0.773081
$170$	−5.52503	−0.423750
$171$	−3.52503	−0.269565
$172$	3.66086	0.279138
$173$	18.0640	1.37338	0.686690	−	0.726950i	$-0.259063\pi$
$173$	18.0640	1.37338	0.686690	+	0.726950i	$0.259063\pi$
$174$	3.78710	0.287099
$175$	1.00000	0.0755929
$176$	0.723979	0.0545719
$177$	12.5390	0.942487
$178$	0.416209	0.0311962
$179$	−3.32172	−0.248277	−0.124138	−	0.992265i	$-0.539617\pi$
$179$	−3.32172	−0.248277	−0.124138	+	0.992265i	$0.539617\pi$
$180$	1.00000	0.0745356
$181$	23.5760	1.75239	0.876194	−	0.481959i	$-0.160075\pi$
$181$	23.5760	1.75239	0.876194	+	0.481959i	$0.160075\pi$
$182$	4.80105	0.355877
$183$	−7.60209	−0.561963
$184$	1.00000	0.0737210
$185$	11.9869	0.881297
$186$	−6.46191	−0.473810
$187$	−4.00000	−0.292509
$188$	6.07707	0.443216
$189$	1.00000	0.0727393
$190$	−3.52503	−0.255732
$191$	−4.63732	−0.335544	−0.167772	−	0.985826i	$-0.553657\pi$
$191$	−4.63732	−0.335544	−0.167772	+	0.985826i	$0.553657\pi$
$192$	1.00000	0.0721688
$193$	22.9960	1.65529	0.827645	−	0.561252i	$-0.189680\pi$
$193$	22.9960	1.65529	0.827645	+	0.561252i	$0.189680\pi$
$194$	7.31212	0.524980
$195$	4.80105	0.343810
$196$	1.00000	0.0714286
$197$	10.9238	0.778289	0.389145	−	0.921177i	$-0.372771\pi$
$197$	10.9238	0.778289	0.389145	+	0.921177i	$0.372771\pi$
$198$	0.723979	0.0514509
$199$	1.44796	0.102643	0.0513215	−	0.998682i	$-0.483657\pi$
$199$	1.44796	0.102643	0.0513215	+	0.998682i	$0.483657\pi$
$200$	1.00000	0.0707107
$201$	−2.21290	−0.156086
$202$	−17.3400	−1.22004
$203$	3.78710	0.265802
$204$	−5.52503	−0.386829
$205$	9.47586	0.661822
$206$	−9.60209	−0.669010
$207$	1.00000	0.0695048
$208$	4.80105	0.332893
$209$	−2.55204	−0.176528
$210$	1.00000	0.0690066
$211$	1.52989	0.105322	0.0526610	−	0.998612i	$-0.483230\pi$
$211$	1.52989	0.105322	0.0526610	+	0.998612i	$0.483230\pi$
$212$	−7.98693	−0.548545
$213$	13.2630	0.908763
$214$	14.6242	0.999693
$215$	3.66086	0.249669
$216$	1.00000	0.0680414
$217$	−6.46191	−0.438663
$218$	−16.6242	−1.12594
$219$	−10.5390	−0.712158
$220$	0.723979	0.0488106
$221$	−26.5259	−1.78433
$222$	11.9869	0.804510
$223$	−24.6896	−1.65334	−0.826670	−	0.562687i	$-0.809768\pi$
$223$	−24.6896	−1.65334	−0.826670	+	0.562687i	$0.809768\pi$
$224$	1.00000	0.0668153
$225$	1.00000	0.0666667
$226$	−17.5890	−1.17000
$227$	0.547178	0.0363175	0.0181588	−	0.999835i	$-0.494220\pi$
$227$	0.547178	0.0363175	0.0181588	+	0.999835i	$0.494220\pi$
$228$	−3.52503	−0.233451
$229$	−11.4480	−0.756502	−0.378251	−	0.925703i	$-0.623474\pi$
$229$	−11.4480	−0.756502	−0.378251	+	0.925703i	$0.623474\pi$
$230$	1.00000	0.0659380
$231$	0.723979	0.0476343
$232$	3.78710	0.248635
$233$	8.62425	0.564993	0.282497	−	0.959268i	$-0.408837\pi$
$233$	8.62425	0.564993	0.282497	+	0.959268i	$0.408837\pi$
$234$	4.80105	0.313854
$235$	6.07707	0.396424
$236$	12.5390	0.816218
$237$	9.98693	0.648721
$238$	−5.52503	−0.358134
$239$	5.26295	0.340432	0.170216	−	0.985407i	$-0.445553\pi$
$239$	5.26295	0.340432	0.170216	+	0.985407i	$0.445553\pi$
$240$	1.00000	0.0645497
$241$	18.7013	1.20466	0.602329	−	0.798248i	$-0.294240\pi$
$241$	18.7013	1.20466	0.602329	+	0.798248i	$0.294240\pi$
$242$	−10.4759	−0.673413
$243$	1.00000	0.0641500
$244$	−7.60209	−0.486674
$245$	1.00000	0.0638877
$246$	9.47586	0.604158
$247$	−16.9238	−1.07684
$248$	−6.46191	−0.410331
$249$	−4.97298	−0.315150
$250$	1.00000	0.0632456
$251$	−3.61169	−0.227968	−0.113984	−	0.993483i	$-0.536361\pi$
$251$	−3.61169	−0.227968	−0.113984	+	0.993483i	$0.536361\pi$
$252$	1.00000	0.0629941
$253$	0.723979	0.0455161
$254$	−10.7109	−0.672062
$255$	−5.52503	−0.345991
$256$	1.00000	0.0625000
$257$	4.78274	0.298339	0.149170	−	0.988812i	$-0.452340\pi$
$257$	4.78274	0.298339	0.149170	+	0.988812i	$0.452340\pi$
$258$	3.66086	0.227915
$259$	11.9869	0.744832
$260$	4.80105	0.297748
$261$	3.78710	0.234415
$262$	10.6652	0.658899
$263$	3.05005	0.188074	0.0940371	−	0.995569i	$-0.470023\pi$
$263$	3.05005	0.188074	0.0940371	+	0.995569i	$0.470023\pi$
$264$	0.723979	0.0445578
$265$	−7.98693	−0.490633
$266$	−3.52503	−0.216133
$267$	0.416209	0.0254716
$268$	−2.21290	−0.135175
$269$	−18.0183	−1.09860	−0.549298	−	0.835627i	$-0.685105\pi$
$269$	−18.0183	−1.09860	−0.549298	+	0.835627i	$0.685105\pi$
$270$	1.00000	0.0608581
$271$	20.7423	1.26000	0.630002	−	0.776594i	$-0.283054\pi$
$271$	20.7423	1.26000	0.630002	+	0.776594i	$0.283054\pi$
$272$	−5.52503	−0.335004
$273$	4.80105	0.290573
$274$	−4.66521	−0.281836
$275$	0.723979	0.0436576
$276$	1.00000	0.0601929
$277$	24.8650	1.49400	0.746998	−	0.664826i	$-0.231494\pi$
$277$	24.8650	1.49400	0.746998	+	0.664826i	$0.231494\pi$
$278$	−5.83279	−0.349828
$279$	−6.46191	−0.386864
$280$	1.00000	0.0597614
$281$	5.91334	0.352760	0.176380	−	0.984322i	$-0.443561\pi$
$281$	5.91334	0.352760	0.176380	+	0.984322i	$0.443561\pi$
$282$	6.07707	0.361884
$283$	7.34002	0.436319	0.218159	−	0.975913i	$-0.429995\pi$
$283$	7.34002	0.436319	0.218159	+	0.975913i	$0.429995\pi$
$284$	13.2630	0.787011
$285$	−3.52503	−0.208804
$286$	3.47586	0.205532
$287$	9.47586	0.559342
$288$	1.00000	0.0589256
$289$	13.5259	0.795642
$290$	3.78710	0.222386
$291$	7.31212	0.428644
$292$	−10.5390	−0.616747
$293$	−17.0501	−0.996075	−0.498037	−	0.867156i	$-0.665946\pi$
$293$	−17.0501	−0.996075	−0.498037	+	0.867156i	$0.665946\pi$
$294$	1.00000	0.0583212
$295$	12.5390	0.730047
$296$	11.9869	0.696726
$297$	0.723979	0.0420095
$298$	−3.44796	−0.199735
$299$	4.80105	0.277652
$300$	1.00000	0.0577350
$301$	3.66086	0.211008
$302$	−5.60209	−0.322364
$303$	−17.3400	−0.996158
$304$	−3.52503	−0.202174
$305$	−7.60209	−0.435295
$306$	−5.52503	−0.315845
$307$	−24.4980	−1.39818	−0.699088	−	0.715036i	$-0.746410\pi$
$307$	−24.4980	−1.39818	−0.699088	+	0.715036i	$0.746410\pi$
$308$	0.723979	0.0412525
$309$	−9.60209	−0.546244
$310$	−6.46191	−0.367012
$311$	27.7249	1.57213	0.786066	−	0.618142i	$-0.212114\pi$
$311$	27.7249	1.57213	0.786066	+	0.618142i	$0.212114\pi$
$312$	4.80105	0.271806
$313$	0.661740	0.0374037	0.0187019	−	0.999825i	$-0.494047\pi$
$313$	0.661740	0.0374037	0.0187019	+	0.999825i	$0.494047\pi$
$314$	−13.7283	−0.774735
$315$	1.00000	0.0563436
$316$	9.98693	0.561809
$317$	−21.7022	−1.21892	−0.609458	−	0.792818i	$-0.708613\pi$
$317$	−21.7022	−1.21892	−0.609458	+	0.792818i	$0.708613\pi$
$318$	−7.98693	−0.447885
$319$	2.74178	0.153510
$320$	1.00000	0.0559017
$321$	14.6242	0.816246
$322$	1.00000	0.0557278
$323$	19.4759	1.08367
$324$	1.00000	0.0555556
$325$	4.80105	0.266314
$326$	−0.524145	−0.0290297
$327$	−16.6242	−0.919323
$328$	9.47586	0.523217
$329$	6.07707	0.335040
$330$	0.723979	0.0398537
$331$	12.9238	0.710357	0.355178	−	0.934799i	$-0.384420\pi$
$331$	12.9238	0.710357	0.355178	+	0.934799i	$0.384420\pi$
$332$	−4.97298	−0.272928
$333$	11.9869	0.656880
$334$	−1.65126	−0.0903532
$335$	−2.21290	−0.120904
$336$	1.00000	0.0545545
$337$	−2.72398	−0.148385	−0.0741923	−	0.997244i	$-0.523638\pi$
$337$	−2.72398	−0.148385	−0.0741923	+	0.997244i	$0.523638\pi$
$338$	10.0501	0.546651
$339$	−17.5890	−0.955305
$340$	−5.52503	−0.299637
$341$	−4.67828	−0.253343
$342$	−3.52503	−0.190612
$343$	1.00000	0.0539949
$344$	3.66086	0.197380
$345$	1.00000	0.0538382
$346$	18.0640	0.971127
$347$	−15.4759	−0.830787	−0.415394	−	0.909642i	$-0.636356\pi$
$347$	−15.4759	−0.830787	−0.415394	+	0.909642i	$0.636356\pi$
$348$	3.78710	0.203010
$349$	−16.6570	−0.891629	−0.445815	−	0.895125i	$-0.647086\pi$
$349$	−16.6570	−0.891629	−0.445815	+	0.895125i	$0.647086\pi$
$350$	1.00000	0.0534522
$351$	4.80105	0.256261
$352$	0.723979	0.0385882
$353$	−17.0910	−0.909663	−0.454832	−	0.890577i	$-0.650301\pi$
$353$	−17.0910	−0.909663	−0.454832	+	0.890577i	$0.650301\pi$
$354$	12.5390	0.666439
$355$	13.2630	0.703924
$356$	0.416209	0.0220590
$357$	−5.52503	−0.292415
$358$	−3.32172	−0.175558
$359$	−22.5669	−1.19103	−0.595517	−	0.803343i	$-0.703053\pi$
$359$	−22.5669	−1.19103	−0.595517	+	0.803343i	$0.703053\pi$
$360$	1.00000	0.0527046
$361$	−6.57420	−0.346010
$362$	23.5760	1.23912
$363$	−10.4759	−0.549840
$364$	4.80105	0.251643
$365$	−10.5390	−0.551635
$366$	−7.60209	−0.397368
$367$	13.3496	0.696844	0.348422	−	0.937338i	$-0.386718\pi$
$367$	13.3496	0.696844	0.348422	+	0.937338i	$0.386718\pi$
$368$	1.00000	0.0521286
$369$	9.47586	0.493293
$370$	11.9869	0.623171
$371$	−7.98693	−0.414661
$372$	−6.46191	−0.335034
$373$	−24.7566	−1.28185	−0.640924	−	0.767604i	$-0.721449\pi$
$373$	−24.7566	−1.28185	−0.640924	+	0.767604i	$0.721449\pi$
$374$	−4.00000	−0.206835
$375$	1.00000	0.0516398
$376$	6.07707	0.313401
$377$	18.1820	0.936422
$378$	1.00000	0.0514344
$379$	−22.9107	−1.17685	−0.588423	−	0.808553i	$-0.700251\pi$
$379$	−22.9107	−1.17685	−0.588423	+	0.808553i	$0.700251\pi$
$380$	−3.52503	−0.180830
$381$	−10.7109	−0.548737
$382$	−4.63732	−0.237266
$383$	−11.8825	−0.607166	−0.303583	−	0.952805i	$-0.598183\pi$
$383$	−11.8825	−0.607166	−0.303583	+	0.952805i	$0.598183\pi$
$384$	1.00000	0.0510310
$385$	0.723979	0.0368974
$386$	22.9960	1.17047
$387$	3.66086	0.186092
$388$	7.31212	0.371217
$389$	−3.79183	−0.192253	−0.0961267	−	0.995369i	$-0.530645\pi$
$389$	−3.79183	−0.192253	−0.0961267	+	0.995369i	$0.530645\pi$
$390$	4.80105	0.243110
$391$	−5.52503	−0.279413
$392$	1.00000	0.0505076
$393$	10.6652	0.537989
$394$	10.9238	0.550334
$395$	9.98693	0.502497
$396$	0.723979	0.0363813
$397$	−16.0244	−0.804243	−0.402121	−	0.915586i	$-0.631727\pi$
$397$	−16.0244	−0.804243	−0.402121	+	0.915586i	$0.631727\pi$
$398$	1.44796	0.0725795
$399$	−3.52503	−0.176472
$400$	1.00000	0.0500000
$401$	−16.7831	−0.838109	−0.419054	−	0.907961i	$-0.637638\pi$
$401$	−16.7831	−0.838109	−0.419054	+	0.907961i	$0.637638\pi$
$402$	−2.21290	−0.110370
$403$	−31.0239	−1.54541
$404$	−17.3400	−0.862698
$405$	1.00000	0.0496904
$406$	3.78710	0.187951
$407$	8.67828	0.430166
$408$	−5.52503	−0.273530
$409$	−31.9460	−1.57963	−0.789813	−	0.613348i	$-0.789823\pi$
$409$	−31.9460	−1.57963	−0.789813	+	0.613348i	$0.789823\pi$
$410$	9.47586	0.467979
$411$	−4.66521	−0.230118
$412$	−9.60209	−0.473061
$413$	12.5390	0.617003
$414$	1.00000	0.0491473
$415$	−4.97298	−0.244114
$416$	4.80105	0.235391
$417$	−5.83279	−0.285633
$418$	−2.55204	−0.124824
$419$	−25.6204	−1.25164	−0.625819	−	0.779968i	$-0.715235\pi$
$419$	−25.6204	−1.25164	−0.625819	+	0.779968i	$0.715235\pi$
$420$	1.00000	0.0487950
$421$	−32.4084	−1.57949	−0.789744	−	0.613437i	$-0.789787\pi$
$421$	−32.4084	−1.57949	−0.789744	+	0.613437i	$0.789787\pi$
$422$	1.52989	0.0744739
$423$	6.07707	0.295477
$424$	−7.98693	−0.387880
$425$	−5.52503	−0.268003
$426$	13.2630	0.642592
$427$	−7.60209	−0.367891
$428$	14.6242	0.706890
$429$	3.47586	0.167816
$430$	3.66086	0.176542
$431$	17.3086	0.833728	0.416864	−	0.908969i	$-0.363129\pi$
$431$	17.3086	0.833728	0.416864	+	0.908969i	$0.363129\pi$
$432$	1.00000	0.0481125
$433$	14.2638	0.685476	0.342738	−	0.939431i	$-0.388646\pi$
$433$	14.2638	0.685476	0.342738	+	0.939431i	$0.388646\pi$
$434$	−6.46191	−0.310181
$435$	3.78710	0.181577
$436$	−16.6242	−0.796157
$437$	−3.52503	−0.168625
$438$	−10.5390	−0.503572
$439$	−20.0640	−0.957602	−0.478801	−	0.877923i	$-0.658929\pi$
$439$	−20.0640	−0.957602	−0.478801	+	0.877923i	$0.658929\pi$
$440$	0.723979	0.0345143
$441$	1.00000	0.0476190
$442$	−26.5259	−1.26171
$443$	15.4759	0.735280	0.367640	−	0.929968i	$-0.380166\pi$
$443$	15.4759	0.735280	0.367640	+	0.929968i	$0.380166\pi$
$444$	11.9869	0.568875
$445$	0.416209	0.0197302
$446$	−24.6896	−1.16909
$447$	−3.44796	−0.163083
$448$	1.00000	0.0472456
$449$	30.6260	1.44533	0.722665	−	0.691198i	$-0.242917\pi$
$449$	30.6260	1.44533	0.722665	+	0.691198i	$0.242917\pi$
$450$	1.00000	0.0471405
$451$	6.86032	0.323040
$452$	−17.5890	−0.827318
$453$	−5.60209	−0.263209
$454$	0.547178	0.0256804
$455$	4.80105	0.225077
$456$	−3.52503	−0.165074
$457$	−12.0736	−0.564779	−0.282389	−	0.959300i	$-0.591127\pi$
$457$	−12.0736	−0.564779	−0.282389	+	0.959300i	$0.591127\pi$
$458$	−11.4480	−0.534928
$459$	−5.52503	−0.257886
$460$	1.00000	0.0466252
$461$	−3.23992	−0.150898	−0.0754490	−	0.997150i	$-0.524039\pi$
$461$	−3.23992	−0.150898	−0.0754490	+	0.997150i	$0.524039\pi$
$462$	0.723979	0.0336825
$463$	−21.3352	−0.991529	−0.495764	−	0.868457i	$-0.665112\pi$
$463$	−21.3352	−0.991529	−0.495764	+	0.868457i	$0.665112\pi$
$464$	3.78710	0.175812
$465$	−6.46191	−0.299664
$466$	8.62425	0.399511
$467$	37.2813	1.72517	0.862585	−	0.505912i	$-0.168844\pi$
$467$	37.2813	1.72517	0.862585	+	0.505912i	$0.168844\pi$
$468$	4.80105	0.221928
$469$	−2.21290	−0.102182
$470$	6.07707	0.280314
$471$	−13.7283	−0.632568
$472$	12.5390	0.577153
$473$	2.65038	0.121865
$474$	9.98693	0.458715
$475$	−3.52503	−0.161739
$476$	−5.52503	−0.253239
$477$	−7.98693	−0.365696
$478$	5.26295	0.240722
$479$	−15.4759	−0.707110	−0.353555	−	0.935414i	$-0.615027\pi$
$479$	−15.4759	−0.707110	−0.353555	+	0.935414i	$0.615027\pi$
$480$	1.00000	0.0456435
$481$	57.5498	2.62405
$482$	18.7013	0.851822
$483$	1.00000	0.0455016
$484$	−10.4759	−0.476175
$485$	7.31212	0.332026
$486$	1.00000	0.0453609
$487$	−14.1868	−0.642864	−0.321432	−	0.946933i	$-0.604164\pi$
$487$	−14.1868	−0.642864	−0.321432	+	0.946933i	$0.604164\pi$
$488$	−7.60209	−0.344131
$489$	−0.524145	−0.0237027
$490$	1.00000	0.0451754
$491$	−9.17629	−0.414120	−0.207060	−	0.978328i	$-0.566390\pi$
$491$	−9.17629	−0.414120	−0.207060	+	0.978328i	$0.566390\pi$
$492$	9.47586	0.427205
$493$	−20.9238	−0.942361
$494$	−16.9238	−0.761438
$495$	0.723979	0.0325404
$496$	−6.46191	−0.290148
$497$	13.2630	0.594925
$498$	−4.97298	−0.222845
$499$	−19.5742	−0.876261	−0.438131	−	0.898911i	$-0.644359\pi$
$499$	−19.5742	−0.876261	−0.438131	+	0.898911i	$0.644359\pi$
$500$	1.00000	0.0447214
$501$	−1.65126	−0.0737730
$502$	−3.61169	−0.161198
$503$	37.4584	1.67019	0.835094	−	0.550107i	$-0.185413\pi$
$503$	37.4584	1.67019	0.835094	+	0.550107i	$0.185413\pi$
$504$	1.00000	0.0445435
$505$	−17.3400	−0.771621
$506$	0.723979	0.0321848
$507$	10.0501	0.446338
$508$	−10.7109	−0.475220
$509$	−17.2581	−0.764951	−0.382476	−	0.923966i	$-0.624928\pi$
$509$	−17.2581	−0.764951	−0.382476	+	0.923966i	$0.624928\pi$
$510$	−5.52503	−0.244652
$511$	−10.5390	−0.466217
$512$	1.00000	0.0441942
$513$	−3.52503	−0.155634
$514$	4.78274	0.210958
$515$	−9.60209	−0.423119
$516$	3.66086	0.161160
$517$	4.39967	0.193497
$518$	11.9869	0.526676
$519$	18.0640	0.792922
$520$	4.80105	0.210540
$521$	−30.5355	−1.33778	−0.668892	−	0.743359i	$-0.733231\pi$
$521$	−30.5355	−1.33778	−0.668892	+	0.743359i	$0.733231\pi$
$522$	3.78710	0.165757
$523$	−31.0684	−1.35852	−0.679262	−	0.733896i	$-0.737700\pi$
$523$	−31.0684	−1.35852	−0.679262	+	0.733896i	$0.737700\pi$
$524$	10.6652	0.465912
$525$	1.00000	0.0436436
$526$	3.05005	0.132989
$527$	35.7022	1.55521
$528$	0.723979	0.0315071
$529$	1.00000	0.0434783
$530$	−7.98693	−0.346930
$531$	12.5390	0.544145
$532$	−3.52503	−0.152829
$533$	45.4940	1.97056
$534$	0.416209	0.0180111
$535$	14.6242	0.632261
$536$	−2.21290	−0.0955828
$537$	−3.32172	−0.143343
$538$	−18.0183	−0.776824
$539$	0.723979	0.0311840
$540$	1.00000	0.0430331
$541$	−37.6039	−1.61672	−0.808358	−	0.588691i	$-0.799643\pi$
$541$	−37.6039	−1.61672	−0.808358	+	0.588691i	$0.799643\pi$
$542$	20.7423	0.890957
$543$	23.5760	1.01174
$544$	−5.52503	−0.236884
$545$	−16.6242	−0.712104
$546$	4.80105	0.205466
$547$	34.9256	1.49331	0.746655	−	0.665212i	$-0.231659\pi$
$547$	34.9256	1.49331	0.746655	+	0.665212i	$0.231659\pi$
$548$	−4.66521	−0.199288
$549$	−7.60209	−0.324449
$550$	0.723979	0.0308705
$551$	−13.3496	−0.568713
$552$	1.00000	0.0425628
$553$	9.98693	0.424688
$554$	24.8650	1.05641
$555$	11.9869	0.508817
$556$	−5.83279	−0.247366
$557$	23.8886	1.01219	0.506096	−	0.862477i	$-0.331088\pi$
$557$	23.8886	1.01219	0.506096	+	0.862477i	$0.331088\pi$
$558$	−6.46191	−0.273554
$559$	17.5760	0.743384
$560$	1.00000	0.0422577
$561$	−4.00000	−0.168880
$562$	5.91334	0.249439
$563$	−24.7205	−1.04185	−0.520923	−	0.853604i	$-0.674412\pi$
$563$	−24.7205	−1.04185	−0.520923	+	0.853604i	$0.674412\pi$
$564$	6.07707	0.255891
$565$	−17.5890	−0.739976
$566$	7.34002	0.308524
$567$	1.00000	0.0419961
$568$	13.2630	0.556501
$569$	36.4131	1.52652	0.763258	−	0.646093i	$-0.223598\pi$
$569$	36.4131	1.52652	0.763258	+	0.646093i	$0.223598\pi$
$570$	−3.52503	−0.147647
$571$	17.9869	0.752730	0.376365	−	0.926472i	$-0.377174\pi$
$571$	17.9869	0.752730	0.376365	+	0.926472i	$0.377174\pi$
$572$	3.47586	0.145333
$573$	−4.63732	−0.193727
$574$	9.47586	0.395515
$575$	1.00000	0.0417029
$576$	1.00000	0.0416667
$577$	−4.78274	−0.199108	−0.0995541	−	0.995032i	$-0.531742\pi$
$577$	−4.78274	−0.199108	−0.0995541	+	0.995032i	$0.531742\pi$
$578$	13.5259	0.562604
$579$	22.9960	0.955682
$580$	3.78710	0.157251
$581$	−4.97298	−0.206314
$582$	7.31212	0.303097
$583$	−5.78237	−0.239481
$584$	−10.5390	−0.436106
$585$	4.80105	0.198499
$586$	−17.0501	−0.704331
$587$	−32.8785	−1.35704	−0.678520	−	0.734582i	$-0.737378\pi$
$587$	−32.8785	−1.35704	−0.678520	+	0.734582i	$0.737378\pi$
$588$	1.00000	0.0412393
$589$	22.7784	0.938567
$590$	12.5390	0.516221
$591$	10.9238	0.449346
$592$	11.9869	0.492660
$593$	4.01307	0.164797	0.0823985	−	0.996599i	$-0.473742\pi$
$593$	4.01307	0.164797	0.0823985	+	0.996599i	$0.473742\pi$
$594$	0.723979	0.0297052
$595$	−5.52503	−0.226504
$596$	−3.44796	−0.141234
$597$	1.44796	0.0592609
$598$	4.80105	0.196329
$599$	11.7167	0.478730	0.239365	−	0.970930i	$-0.423061\pi$
$599$	11.7167	0.478730	0.239365	+	0.970930i	$0.423061\pi$
$600$	1.00000	0.0408248
$601$	−33.1223	−1.35108	−0.675542	−	0.737321i	$-0.736091\pi$
$601$	−33.1223	−1.35108	−0.675542	+	0.737321i	$0.736091\pi$
$602$	3.66086	0.149205
$603$	−2.21290	−0.0901163
$604$	−5.60209	−0.227946
$605$	−10.4759	−0.425904
$606$	−17.3400	−0.704390
$607$	16.9777	0.689104	0.344552	−	0.938767i	$-0.388031\pi$
$607$	16.9777	0.689104	0.344552	+	0.938767i	$0.388031\pi$
$608$	−3.52503	−0.142959
$609$	3.78710	0.153461
$610$	−7.60209	−0.307800
$611$	29.1763	1.18035
$612$	−5.52503	−0.223336
$613$	31.6169	1.27700	0.638498	−	0.769624i	$-0.279556\pi$
$613$	31.6169	1.27700	0.638498	+	0.769624i	$0.279556\pi$
$614$	−24.4980	−0.988659
$615$	9.47586	0.382103
$616$	0.723979	0.0291699
$617$	−1.86069	−0.0749087	−0.0374543	−	0.999298i	$-0.511925\pi$
$617$	−1.86069	−0.0749087	−0.0374543	+	0.999298i	$0.511925\pi$
$618$	−9.60209	−0.386253
$619$	31.4170	1.26275	0.631377	−	0.775476i	$-0.282490\pi$
$619$	31.4170	1.26275	0.631377	+	0.775476i	$0.282490\pi$
$620$	−6.46191	−0.259516
$621$	1.00000	0.0401286
$622$	27.7249	1.11167
$623$	0.416209	0.0166751
$624$	4.80105	0.192196
$625$	1.00000	0.0400000
$626$	0.661740	0.0264484
$627$	−2.55204	−0.101919
$628$	−13.7283	−0.547820
$629$	−66.2281	−2.64069
$630$	1.00000	0.0398410
$631$	25.4436	1.01289	0.506447	−	0.862271i	$-0.330959\pi$
$631$	25.4436	1.01289	0.506447	+	0.862271i	$0.330959\pi$
$632$	9.98693	0.397259
$633$	1.52989	0.0608077
$634$	−21.7022	−0.861904
$635$	−10.7109	−0.425050
$636$	−7.98693	−0.316702
$637$	4.80105	0.190224
$638$	2.74178	0.108548
$639$	13.2630	0.524674
$640$	1.00000	0.0395285
$641$	−8.23904	−0.325422	−0.162711	−	0.986674i	$-0.552024\pi$
$641$	−8.23904	−0.325422	−0.162711	+	0.986674i	$0.552024\pi$
$642$	14.6242	0.577173
$643$	−37.8101	−1.49109	−0.745543	−	0.666458i	$-0.767810\pi$
$643$	−37.8101	−1.49109	−0.745543	+	0.666458i	$0.767810\pi$
$644$	1.00000	0.0394055
$645$	3.66086	0.144146
$646$	19.4759	0.766267
$647$	−1.05492	−0.0414730	−0.0207365	−	0.999785i	$-0.506601\pi$
$647$	−1.05492	−0.0414730	−0.0207365	+	0.999785i	$0.506601\pi$
$648$	1.00000	0.0392837
$649$	9.07795	0.356341
$650$	4.80105	0.188313
$651$	−6.46191	−0.253262
$652$	−0.524145	−0.0205271
$653$	−10.5963	−0.414667	−0.207334	−	0.978270i	$-0.566479\pi$
$653$	−10.5963	−0.414667	−0.207334	+	0.978270i	$0.566479\pi$
$654$	−16.6242	−0.650059
$655$	10.6652	0.416724
$656$	9.47586	0.369970
$657$	−10.5390	−0.411165
$658$	6.07707	0.236909
$659$	50.6996	1.97498	0.987488	−	0.157694i	$-0.0504059\pi$
$659$	50.6996	1.97498	0.987488	+	0.157694i	$0.0504059\pi$
$660$	0.723979	0.0281808
$661$	8.21763	0.319629	0.159814	−	0.987147i	$-0.448910\pi$
$661$	8.21763	0.319629	0.159814	+	0.987147i	$0.448910\pi$
$662$	12.9238	0.502298
$663$	−26.5259	−1.03018
$664$	−4.97298	−0.192989
$665$	−3.52503	−0.136695
$666$	11.9869	0.464484
$667$	3.78710	0.146637
$668$	−1.65126	−0.0638893
$669$	−24.6896	−0.954557
$670$	−2.21290	−0.0854919
$671$	−5.50375	−0.212470
$672$	1.00000	0.0385758
$673$	33.5219	1.29218	0.646088	−	0.763263i	$-0.276404\pi$
$673$	33.5219	1.29218	0.646088	+	0.763263i	$0.276404\pi$
$674$	−2.72398	−0.104924
$675$	1.00000	0.0384900
$676$	10.0501	0.386540
$677$	−19.0779	−0.733225	−0.366613	−	0.930374i	$-0.619483\pi$
$677$	−19.0779	−0.733225	−0.366613	+	0.930374i	$0.619483\pi$
$678$	−17.5890	−0.675502
$679$	7.31212	0.280614
$680$	−5.52503	−0.211875
$681$	0.547178	0.0209679
$682$	−4.67828	−0.179141
$683$	−14.6242	−0.559581	−0.279791	−	0.960061i	$-0.590265\pi$
$683$	−14.6242	−0.559581	−0.279791	+	0.960061i	$0.590265\pi$
$684$	−3.52503	−0.134783
$685$	−4.66521	−0.178249
$686$	1.00000	0.0381802
$687$	−11.4480	−0.436767
$688$	3.66086	0.139569
$689$	−38.3456	−1.46085
$690$	1.00000	0.0380693
$691$	4.48318	0.170548	0.0852741	−	0.996358i	$-0.472823\pi$
$691$	4.48318	0.170548	0.0852741	+	0.996358i	$0.472823\pi$
$692$	18.0640	0.686690
$693$	0.723979	0.0275017
$694$	−15.4759	−0.587455
$695$	−5.83279	−0.221251
$696$	3.78710	0.143550
$697$	−52.3543	−1.98306
$698$	−16.6570	−0.630477
$699$	8.62425	0.326199
$700$	1.00000	0.0377964
$701$	0.208171	0.00786253	0.00393126	−	0.999992i	$-0.498749\pi$
$701$	0.208171	0.00786253	0.00393126	+	0.999992i	$0.498749\pi$
$702$	4.80105	0.181204
$703$	−42.2542	−1.59365
$704$	0.723979	0.0272860
$705$	6.07707	0.228876
$706$	−17.0910	−0.643229
$707$	−17.3400	−0.652139
$708$	12.5390	0.471244
$709$	−49.8755	−1.87311	−0.936557	−	0.350515i	$-0.886007\pi$
$709$	−49.8755	−1.87311	−0.936557	+	0.350515i	$0.886007\pi$
$710$	13.2630	0.497750
$711$	9.98693	0.374539
$712$	0.416209	0.0155981
$713$	−6.46191	−0.242000
$714$	−5.52503	−0.206769
$715$	3.47586	0.129990
$716$	−3.32172	−0.124138
$717$	5.26295	0.196549
$718$	−22.5669	−0.842188
$719$	−8.82894	−0.329264	−0.164632	−	0.986355i	$-0.552644\pi$
$719$	−8.82894	−0.329264	−0.164632	+	0.986355i	$0.552644\pi$
$720$	1.00000	0.0372678
$721$	−9.60209	−0.357601
$722$	−6.57420	−0.244666
$723$	18.7013	0.695509
$724$	23.5760	0.876194
$725$	3.78710	0.140649
$726$	−10.4759	−0.388795
$727$	−38.6800	−1.43456	−0.717282	−	0.696783i	$-0.754614\pi$
$727$	−38.6800	−1.43456	−0.717282	+	0.696783i	$0.754614\pi$
$728$	4.80105	0.177939
$729$	1.00000	0.0370370
$730$	−10.5390	−0.390065
$731$	−20.2263	−0.748098
$732$	−7.60209	−0.280981
$733$	−31.6935	−1.17063	−0.585313	−	0.810808i	$-0.699028\pi$
$733$	−31.6935	−1.17063	−0.585313	+	0.810808i	$0.699028\pi$
$734$	13.3496	0.492743
$735$	1.00000	0.0368856
$736$	1.00000	0.0368605
$737$	−1.60209	−0.0590139
$738$	9.47586	0.348811
$739$	−5.34962	−0.196789	−0.0983944	−	0.995147i	$-0.531371\pi$
$739$	−5.34962	−0.196789	−0.0983944	+	0.995147i	$0.531371\pi$
$740$	11.9869	0.440648
$741$	−16.9238	−0.621712
$742$	−7.98693	−0.293209
$743$	−4.39967	−0.161408	−0.0807041	−	0.996738i	$-0.525717\pi$
$743$	−4.39967	−0.161408	−0.0807041	+	0.996738i	$0.525717\pi$
$744$	−6.46191	−0.236905
$745$	−3.44796	−0.126323
$746$	−24.7566	−0.906404
$747$	−4.97298	−0.181952
$748$	−4.00000	−0.146254
$749$	14.6242	0.534358
$750$	1.00000	0.0365148
$751$	−4.45704	−0.162640	−0.0813199	−	0.996688i	$-0.525914\pi$
$751$	−4.45704	−0.162640	−0.0813199	+	0.996688i	$0.525914\pi$
$752$	6.07707	0.221608
$753$	−3.61169	−0.131617
$754$	18.1820	0.662151
$755$	−5.60209	−0.203881
$756$	1.00000	0.0363696
$757$	36.4127	1.32344	0.661722	−	0.749750i	$-0.269826\pi$
$757$	36.4127	1.32344	0.661722	+	0.749750i	$0.269826\pi$
$758$	−22.9107	−0.832156
$759$	0.723979	0.0262788
$760$	−3.52503	−0.127866
$761$	−5.82667	−0.211217	−0.105608	−	0.994408i	$-0.533679\pi$
$761$	−5.82667	−0.211217	−0.105608	+	0.994408i	$0.533679\pi$
$762$	−10.7109	−0.388015
$763$	−16.6242	−0.601838
$764$	−4.63732	−0.167772
$765$	−5.52503	−0.199758
$766$	−11.8825	−0.429331
$767$	60.2002	2.17370
$768$	1.00000	0.0360844
$769$	−16.8729	−0.608452	−0.304226	−	0.952600i	$-0.598398\pi$
$769$	−16.8729	−0.608452	−0.304226	+	0.952600i	$0.598398\pi$
$770$	0.723979	0.0260904
$771$	4.78274	0.172246
$772$	22.9960	0.827645
$773$	47.0257	1.69140	0.845698	−	0.533662i	$-0.179184\pi$
$773$	47.0257	1.69140	0.845698	+	0.533662i	$0.179184\pi$
$774$	3.66086	0.131587
$775$	−6.46191	−0.232119
$776$	7.31212	0.262490
$777$	11.9869	0.430029
$778$	−3.79183	−0.135944
$779$	−33.4026	−1.19677
$780$	4.80105	0.171905
$781$	9.60209	0.343590
$782$	−5.52503	−0.197575
$783$	3.78710	0.135340
$784$	1.00000	0.0357143
$785$	−13.7283	−0.489985
$786$	10.6652	0.380416
$787$	36.4902	1.30073	0.650367	−	0.759620i	$-0.274615\pi$
$787$	36.4902	1.30073	0.650367	+	0.759620i	$0.274615\pi$
$788$	10.9238	0.389145
$789$	3.05005	0.108585
$790$	9.98693	0.355319
$791$	−17.5890	−0.625394
$792$	0.723979	0.0257255
$793$	−36.4980	−1.29608
$794$	−16.0244	−0.568686
$795$	−7.98693	−0.283267
$796$	1.44796	0.0513215
$797$	−35.7493	−1.26630	−0.633152	−	0.774027i	$-0.718239\pi$
$797$	−35.7493	−1.26630	−0.633152	+	0.774027i	$0.718239\pi$
$798$	−3.52503	−0.124785
$799$	−33.5760	−1.18783
$800$	1.00000	0.0353553
$801$	0.416209	0.0147060
$802$	−16.7831	−0.592632
$803$	−7.62999	−0.269257
$804$	−2.21290	−0.0780430
$805$	1.00000	0.0352454
$806$	−31.0239	−1.09277
$807$	−18.0183	−0.634274
$808$	−17.3400	−0.610020
$809$	32.9256	1.15760	0.578801	−	0.815469i	$-0.303521\pi$
$809$	32.9256	1.15760	0.578801	+	0.815469i	$0.303521\pi$
$810$	1.00000	0.0351364
$811$	−44.9195	−1.57734	−0.788668	−	0.614820i	$-0.789229\pi$
$811$	−44.9195	−1.57734	−0.788668	+	0.614820i	$0.789229\pi$
$812$	3.78710	0.132901
$813$	20.7423	0.727464
$814$	8.67828	0.304174
$815$	−0.524145	−0.0183600
$816$	−5.52503	−0.193415
$817$	−12.9046	−0.451476
$818$	−31.9460	−1.11696
$819$	4.80105	0.167762
$820$	9.47586	0.330911
$821$	34.3852	1.20005	0.600026	−	0.799980i	$-0.295157\pi$
$821$	34.3852	1.20005	0.600026	+	0.799980i	$0.295157\pi$
$822$	−4.66521	−0.162718
$823$	36.3852	1.26831	0.634154	−	0.773207i	$-0.281348\pi$
$823$	36.3852	1.26831	0.634154	+	0.773207i	$0.281348\pi$
$824$	−9.60209	−0.334505
$825$	0.723979	0.0252057
$826$	12.5390	0.436287
$827$	−26.6800	−0.927756	−0.463878	−	0.885899i	$-0.653542\pi$
$827$	−26.6800	−0.927756	−0.463878	+	0.885899i	$0.653542\pi$
$828$	1.00000	0.0347524
$829$	−36.7292	−1.27566	−0.637829	−	0.770178i	$-0.720167\pi$
$829$	−36.7292	−1.27566	−0.637829	+	0.770178i	$0.720167\pi$
$830$	−4.97298	−0.172615
$831$	24.8650	0.862559
$832$	4.80105	0.166446
$833$	−5.52503	−0.191431
$834$	−5.83279	−0.201973
$835$	−1.65126	−0.0571443
$836$	−2.55204	−0.0882642
$837$	−6.46191	−0.223356
$838$	−25.6204	−0.885042
$839$	7.89193	0.272460	0.136230	−	0.990677i	$-0.456501\pi$
$839$	7.89193	0.272460	0.136230	+	0.990677i	$0.456501\pi$
$840$	1.00000	0.0345033
$841$	−14.6579	−0.505444
$842$	−32.4084	−1.11687
$843$	5.91334	0.203666
$844$	1.52989	0.0526610
$845$	10.0501	0.345732
$846$	6.07707	0.208934
$847$	−10.4759	−0.359955
$848$	−7.98693	−0.274272
$849$	7.34002	0.251909
$850$	−5.52503	−0.189507
$851$	11.9869	0.410907
$852$	13.2630	0.454381
$853$	−28.2769	−0.968183	−0.484091	−	0.875017i	$-0.660850\pi$
$853$	−28.2769	−0.968183	−0.484091	+	0.875017i	$0.660850\pi$
$854$	−7.60209	−0.260138
$855$	−3.52503	−0.120553
$856$	14.6242	0.499846
$857$	−22.0312	−0.752573	−0.376286	−	0.926503i	$-0.622799\pi$
$857$	−22.0312	−0.752573	−0.376286	+	0.926503i	$0.622799\pi$
$858$	3.47586	0.118664
$859$	33.8433	1.15472	0.577359	−	0.816491i	$-0.304083\pi$
$859$	33.8433	1.15472	0.577359	+	0.816491i	$0.304083\pi$
$860$	3.66086	0.124834
$861$	9.47586	0.322936
$862$	17.3086	0.589535
$863$	−10.6242	−0.361654	−0.180827	−	0.983515i	$-0.557877\pi$
$863$	−10.6242	−0.361654	−0.180827	+	0.983515i	$0.557877\pi$
$864$	1.00000	0.0340207
$865$	18.0640	0.614194
$866$	14.2638	0.484705
$867$	13.5259	0.459364
$868$	−6.46191	−0.219331
$869$	7.23032	0.245272
$870$	3.78710	0.128395
$871$	−10.6242	−0.359989
$872$	−16.6242	−0.562968
$873$	7.31212	0.247478
$874$	−3.52503	−0.119236
$875$	1.00000	0.0338062
$876$	−10.5390	−0.356079
$877$	42.8929	1.44839	0.724196	−	0.689594i	$-0.242211\pi$
$877$	42.8929	1.44839	0.724196	+	0.689594i	$0.242211\pi$
$878$	−20.0640	−0.677127
$879$	−17.0501	−0.575084
$880$	0.723979	0.0244053
$881$	57.3958	1.93371	0.966857	−	0.255318i	$-0.0821802\pi$
$881$	57.3958	1.93371	0.966857	+	0.255318i	$0.0821802\pi$
$882$	1.00000	0.0336718
$883$	−30.4276	−1.02397	−0.511985	−	0.858995i	$-0.671090\pi$
$883$	−30.4276	−1.02397	−0.511985	+	0.858995i	$0.671090\pi$
$884$	−26.5259	−0.892163
$885$	12.5390	0.421493
$886$	15.4759	0.519922
$887$	43.0009	1.44383	0.721914	−	0.691983i	$-0.243263\pi$
$887$	43.0009	1.44383	0.721914	+	0.691983i	$0.243263\pi$
$888$	11.9869	0.402255
$889$	−10.7109	−0.359232
$890$	0.416209	0.0139514
$891$	0.723979	0.0242542
$892$	−24.6896	−0.826670
$893$	−21.4218	−0.716854
$894$	−3.44796	−0.115317
$895$	−3.32172	−0.111033
$896$	1.00000	0.0334077
$897$	4.80105	0.160302
$898$	30.6260	1.02200
$899$	−24.4719	−0.816183
$900$	1.00000	0.0333333
$901$	44.1280	1.47012
$902$	6.86032	0.228424
$903$	3.66086	0.121826
$904$	−17.5890	−0.585002
$905$	23.5760	0.783691
$906$	−5.60209	−0.186117
$907$	49.1193	1.63098	0.815490	−	0.578772i	$-0.196468\pi$
$907$	49.1193	1.63098	0.815490	+	0.578772i	$0.196468\pi$
$908$	0.547178	0.0181588
$909$	−17.3400	−0.575132
$910$	4.80105	0.159153
$911$	−17.2895	−0.572825	−0.286413	−	0.958106i	$-0.592463\pi$
$911$	−17.2895	−0.572825	−0.286413	+	0.958106i	$0.592463\pi$
$912$	−3.52503	−0.116725
$913$	−3.60033	−0.119154
$914$	−12.0736	−0.399359
$915$	−7.60209	−0.251317
$916$	−11.4480	−0.378251
$917$	10.6652	0.352196
$918$	−5.52503	−0.182353
$919$	1.28946	0.0425353	0.0212677	−	0.999774i	$-0.493230\pi$
$919$	1.28946	0.0425353	0.0212677	+	0.999774i	$0.493230\pi$
$920$	1.00000	0.0329690
$921$	−24.4980	−0.807237
$922$	−3.23992	−0.106701
$923$	63.6761	2.09592
$924$	0.723979	0.0238171
$925$	11.9869	0.394128
$926$	−21.3352	−0.701117
$927$	−9.60209	−0.315374
$928$	3.78710	0.124318
$929$	29.7936	0.977496	0.488748	−	0.872425i	$-0.337454\pi$
$929$	29.7936	0.977496	0.488748	+	0.872425i	$0.337454\pi$
$930$	−6.46191	−0.211894
$931$	−3.52503	−0.115528
$932$	8.62425	0.282497
$933$	27.7249	0.907671
$934$	37.2813	1.21988
$935$	−4.00000	−0.130814
$936$	4.80105	0.156927
$937$	−0.281263	−0.00918845	−0.00459423	−	0.999989i	$-0.501462\pi$
$937$	−0.281263	−0.00918845	−0.00459423	+	0.999989i	$0.501462\pi$
$938$	−2.21290	−0.0722538
$939$	0.661740	0.0215951
$940$	6.07707	0.198212
$941$	32.9256	1.07334	0.536672	−	0.843791i	$-0.319681\pi$
$941$	32.9256	1.07334	0.536672	+	0.843791i	$0.319681\pi$
$942$	−13.7283	−0.447293
$943$	9.47586	0.308576
$944$	12.5390	0.408109
$945$	1.00000	0.0325300
$946$	2.65038	0.0861714
$947$	−27.6039	−0.897005	−0.448502	−	0.893782i	$-0.648042\pi$
$947$	−27.6039	−0.897005	−0.448502	+	0.893782i	$0.648042\pi$
$948$	9.98693	0.324360
$949$	−50.5981	−1.64248
$950$	−3.52503	−0.114367
$951$	−21.7022	−0.703742
$952$	−5.52503	−0.179067
$953$	−42.1236	−1.36452	−0.682259	−	0.731110i	$-0.739002\pi$
$953$	−42.1236	−1.36452	−0.682259	+	0.731110i	$0.739002\pi$
$954$	−7.98693	−0.258586
$955$	−4.63732	−0.150060
$956$	5.26295	0.170216
$957$	2.74178	0.0886291
$958$	−15.4759	−0.500002
$959$	−4.66521	−0.150648
$960$	1.00000	0.0322749
$961$	10.7562	0.346975
$962$	57.5498	1.85548
$963$	14.6242	0.471260
$964$	18.7013	0.602329
$965$	22.9960	0.740268
$966$	1.00000	0.0321745
$967$	5.86903	0.188735	0.0943677	−	0.995537i	$-0.469917\pi$
$967$	5.86903	0.188735	0.0943677	+	0.995537i	$0.469917\pi$
$968$	−10.4759	−0.336707
$969$	19.4759	0.625655
$970$	7.31212	0.234778
$971$	−36.6077	−1.17480	−0.587399	−	0.809298i	$-0.699848\pi$
$971$	−36.6077	−1.17480	−0.587399	+	0.809298i	$0.699848\pi$
$972$	1.00000	0.0320750
$973$	−5.83279	−0.186991
$974$	−14.1868	−0.454573
$975$	4.80105	0.153757
$976$	−7.60209	−0.243337
$977$	18.3395	0.586733	0.293366	−	0.956000i	$-0.405224\pi$
$977$	18.3395	0.586733	0.293366	+	0.956000i	$0.405224\pi$
$978$	−0.524145	−0.0167603
$979$	0.301326	0.00963043
$980$	1.00000	0.0319438
$981$	−16.6242	−0.530771
$982$	−9.17629	−0.292827
$983$	−40.3177	−1.28594	−0.642968	−	0.765893i	$-0.722297\pi$
$983$	−40.3177	−1.28594	−0.642968	+	0.765893i	$0.722297\pi$
$984$	9.47586	0.302079
$985$	10.9238	0.348062
$986$	−20.9238	−0.666350
$987$	6.07707	0.193435
$988$	−16.9238	−0.538418
$989$	3.66086	0.116409
$990$	0.723979	0.0230095
$991$	−17.3496	−0.551129	−0.275564	−	0.961283i	$-0.588865\pi$
$991$	−17.3496	−0.551129	−0.275564	+	0.961283i	$0.588865\pi$
$992$	−6.46191	−0.205166
$993$	12.9238	0.410125
$994$	13.2630	0.420675
$995$	1.44796	0.0459033
$996$	−4.97298	−0.157575
$997$	−22.0949	−0.699751	−0.349876	−	0.936796i	$-0.613776\pi$
$997$	−22.0949	−0.699751	−0.349876	+	0.936796i	$0.613776\pi$
$998$	−19.5742	−0.619610
$999$	11.9869	0.379250

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4830.2.a.ce.1.3	✓	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4830.2.a.ce.1.3	✓	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)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{5} +1.00000 q^{6} +1.00000 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{5} +1.00000 q^{6} +1.00000 q^{7} +1.00000 q^{8} +1.00000 q^{9} +1.00000 q^{10} +0.723979 q^{11} +1.00000 q^{12} +4.80105 q^{13} +1.00000 q^{14} +1.00000 q^{15} +1.00000 q^{16} -5.52503 q^{17} +1.00000 q^{18} -3.52503 q^{19} +1.00000 q^{20} +1.00000 q^{21} +0.723979 q^{22} +1.00000 q^{23} +1.00000 q^{24} +1.00000 q^{25} +4.80105 q^{26} +1.00000 q^{27} +1.00000 q^{28} +3.78710 q^{29} +1.00000 q^{30} -6.46191 q^{31} +1.00000 q^{32} +0.723979 q^{33} -5.52503 q^{34} +1.00000 q^{35} +1.00000 q^{36} +11.9869 q^{37} -3.52503 q^{38} +4.80105 q^{39} +1.00000 q^{40} +9.47586 q^{41} +1.00000 q^{42} +3.66086 q^{43} +0.723979 q^{44} +1.00000 q^{45} +1.00000 q^{46} +6.07707 q^{47} +1.00000 q^{48} +1.00000 q^{49} +1.00000 q^{50} -5.52503 q^{51} +4.80105 q^{52} -7.98693 q^{53} +1.00000 q^{54} +0.723979 q^{55} +1.00000 q^{56} -3.52503 q^{57} +3.78710 q^{58} +12.5390 q^{59} +1.00000 q^{60} -7.60209 q^{61} -6.46191 q^{62} +1.00000 q^{63} +1.00000 q^{64} +4.80105 q^{65} +0.723979 q^{66} -2.21290 q^{67} -5.52503 q^{68} +1.00000 q^{69} +1.00000 q^{70} +13.2630 q^{71} +1.00000 q^{72} -10.5390 q^{73} +11.9869 q^{74} +1.00000 q^{75} -3.52503 q^{76} +0.723979 q^{77} +4.80105 q^{78} +9.98693 q^{79} +1.00000 q^{80} +1.00000 q^{81} +9.47586 q^{82} -4.97298 q^{83} +1.00000 q^{84} -5.52503 q^{85} +3.66086 q^{86} +3.78710 q^{87} +0.723979 q^{88} +0.416209 q^{89} +1.00000 q^{90} +4.80105 q^{91} +1.00000 q^{92} -6.46191 q^{93} +6.07707 q^{94} -3.52503 q^{95} +1.00000 q^{96} +7.31212 q^{97} +1.00000 q^{98} +0.723979 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 4 q^{2} + 4 q^{3} + 4 q^{4} + 4 q^{5} + 4 q^{6} + 4 q^{7} + 4 q^{8} + 4 q^{9}+O(q^{10}) \) 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	\( 4 q + 4 q^{2} + 4 q^{3} + 4 q^{4} + 4 q^{5} + 4 q^{6} + 4 q^{7} + 4 q^{8} + 4 q^{9} + 4 q^{10} + 4 q^{12} + 2 q^{13} + 4 q^{14} + 4 q^{15} + 4 q^{16} - 2 q^{17} + 4 q^{18} + 6 q^{19} + 4 q^{20} + 4 q^{21} + 4 q^{23} + 4 q^{24} + 4 q^{25} + 2 q^{26} + 4 q^{27} + 4 q^{28} + 14 q^{29} + 4 q^{30} - 4 q^{31} + 4 q^{32} - 2 q^{34} + 4 q^{35} + 4 q^{36} + 6 q^{37} + 6 q^{38} + 2 q^{39} + 4 q^{40} + 4 q^{42} + 10 q^{43} + 4 q^{45} + 4 q^{46} + 10 q^{47} + 4 q^{48} + 4 q^{49} + 4 q^{50} - 2 q^{51} + 2 q^{52} + 10 q^{53} + 4 q^{54} + 4 q^{56} + 6 q^{57} + 14 q^{58} + 14 q^{59} + 4 q^{60} + 4 q^{61} - 4 q^{62} + 4 q^{63} + 4 q^{64} + 2 q^{65} - 10 q^{67} - 2 q^{68} + 4 q^{69} + 4 q^{70} + 14 q^{71} + 4 q^{72} - 6 q^{73} + 6 q^{74} + 4 q^{75} + 6 q^{76} + 2 q^{78} - 2 q^{79} + 4 q^{80} + 4 q^{81} + 6 q^{83} + 4 q^{84} - 2 q^{85} + 10 q^{86} + 14 q^{87} - 8 q^{89} + 4 q^{90} + 2 q^{91} + 4 q^{92} - 4 q^{93} + 10 q^{94} + 6 q^{95} + 4 q^{96} + 8 q^{97} + 4 q^{98}+O(q^{100}) \) 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 + 4 * q^12 + 2 * q^13 + 4 * q^14 + 4 * q^15 + 4 * q^16 - 2 * q^17 + 4 * q^18 + 6 * q^19 + 4 * q^20 + 4 * q^21 + 4 * q^23 + 4 * q^24 + 4 * q^25 + 2 * q^26 + 4 * q^27 + 4 * q^28 + 14 * q^29 + 4 * q^30 - 4 * q^31 + 4 * q^32 - 2 * q^34 + 4 * q^35 + 4 * q^36 + 6 * q^37 + 6 * q^38 + 2 * q^39 + 4 * q^40 + 4 * q^42 + 10 * q^43 + 4 * q^45 + 4 * q^46 + 10 * q^47 + 4 * q^48 + 4 * q^49 + 4 * q^50 - 2 * q^51 + 2 * q^52 + 10 * q^53 + 4 * q^54 + 4 * q^56 + 6 * q^57 + 14 * q^58 + 14 * q^59 + 4 * q^60 + 4 * q^61 - 4 * q^62 + 4 * q^63 + 4 * q^64 + 2 * q^65 - 10 * q^67 - 2 * q^68 + 4 * q^69 + 4 * q^70 + 14 * q^71 + 4 * q^72 - 6 * q^73 + 6 * q^74 + 4 * q^75 + 6 * q^76 + 2 * q^78 - 2 * q^79 + 4 * q^80 + 4 * q^81 + 6 * q^83 + 4 * q^84 - 2 * q^85 + 10 * q^86 + 14 * q^87 - 8 * q^89 + 4 * q^90 + 2 * q^91 + 4 * q^92 - 4 * q^93 + 10 * q^94 + 6 * q^95 + 4 * q^96 + 8 * q^97 + 4 * q^98

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