LMFDB - Embedded newform 4830.2.a.ce.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:	4.4.6809.1
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			1.2
Root			$-0.582772$ 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)

$f(q)$	$=$	$q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{5} +1.00000 q^{6} +1.00000 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{5} +1.00000 q^{6} +1.00000 q^{7} +1.00000 q^{8} +1.00000 q^{9} +1.00000 q^{10} -1.16554 q^{11} +1.00000 q^{12} -2.26633 q^{13} +1.00000 q^{14} +1.00000 q^{15} +1.00000 q^{16} +3.43187 q^{17} +1.00000 q^{18} +5.43187 q^{19} +1.00000 q^{20} +1.00000 q^{21} -1.16554 q^{22} +1.00000 q^{23} +1.00000 q^{24} +1.00000 q^{25} -2.26633 q^{26} +1.00000 q^{27} +1.00000 q^{28} -4.75263 q^{29} +1.00000 q^{30} -4.15521 q^{31} +1.00000 q^{32} -1.16554 q^{33} +3.43187 q^{34} +1.00000 q^{35} +1.00000 q^{36} +0.723336 q^{37} +5.43187 q^{38} -2.26633 q^{39} +1.00000 q^{40} +8.64151 q^{41} +1.00000 q^{42} +8.42154 q^{43} -1.16554 q^{44} +1.00000 q^{45} +1.00000 q^{46} +0.899214 q^{47} +1.00000 q^{48} +1.00000 q^{49} +1.00000 q^{50} +3.43187 q^{51} -2.26633 q^{52} +3.27666 q^{53} +1.00000 q^{54} -1.16554 q^{55} +1.00000 q^{56} +5.43187 q^{57} -4.75263 q^{58} +5.05442 q^{59} +1.00000 q^{60} +6.53266 q^{61} -4.15521 q^{62} +1.00000 q^{63} +1.00000 q^{64} -2.26633 q^{65} -1.16554 q^{66} -10.7526 q^{67} +3.43187 q^{68} +1.00000 q^{69} +1.00000 q^{70} +3.88888 q^{71} +1.00000 q^{72} -3.05442 q^{73} +0.723336 q^{74} +1.00000 q^{75} +5.43187 q^{76} -1.16554 q^{77} -2.26633 q^{78} -1.27666 q^{79} +1.00000 q^{80} +1.00000 q^{81} +8.64151 q^{82} +7.76296 q^{83} +1.00000 q^{84} +3.43187 q^{85} +8.42154 q^{86} -4.75263 q^{87} -1.16554 q^{88} -9.52233 q^{89} +1.00000 q^{90} -2.26633 q^{91} +1.00000 q^{92} -4.15521 q^{93} +0.899214 q^{94} +5.43187 q^{95} +1.00000 q^{96} -10.1845 q^{97} +1.00000 q^{98} -1.16554 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$11$	−1.16554	−0.351425	−0.175712	−	0.984442i	$-0.556223\pi$
$11$	−1.16554	−0.351425	−0.175712	+	0.984442i	$0.556223\pi$
$12$	1.00000	0.288675
$13$	−2.26633	−0.628567	−0.314283	−	0.949329i	$-0.601764\pi$
$13$	−2.26633	−0.628567	−0.314283	+	0.949329i	$0.601764\pi$
$14$	1.00000	0.267261
$15$	1.00000	0.258199
$16$	1.00000	0.250000
$17$	3.43187	0.832352	0.416176	−	0.909284i	$-0.363370\pi$
$17$	3.43187	0.832352	0.416176	+	0.909284i	$0.363370\pi$
$18$	1.00000	0.235702
$19$	5.43187	1.24616	0.623079	−	0.782159i	$-0.285882\pi$
$19$	5.43187	1.24616	0.623079	+	0.782159i	$0.285882\pi$
$20$	1.00000	0.223607
$21$	1.00000	0.218218
$22$	−1.16554	−0.248495
$23$	1.00000	0.208514
$23$	1.00000	0.208514
$24$	1.00000	0.204124
$25$	1.00000	0.200000
$26$	−2.26633	−0.444464
$27$	1.00000	0.192450
$28$	1.00000	0.188982
$29$	−4.75263	−0.882541	−0.441270	−	0.897374i	$-0.645472\pi$
$29$	−4.75263	−0.882541	−0.441270	+	0.897374i	$0.645472\pi$
$30$	1.00000	0.182574
$31$	−4.15521	−0.746298	−0.373149	−	0.927771i	$-0.621722\pi$
$31$	−4.15521	−0.746298	−0.373149	+	0.927771i	$0.621722\pi$
$32$	1.00000	0.176777
$33$	−1.16554	−0.202895
$34$	3.43187	0.588562
$35$	1.00000	0.169031
$36$	1.00000	0.166667
$37$	0.723336	0.118916	0.0594578	−	0.998231i	$-0.481063\pi$
$37$	0.723336	0.118916	0.0594578	+	0.998231i	$0.481063\pi$
$38$	5.43187	0.881166
$39$	−2.26633	−0.362903
$40$	1.00000	0.158114
$41$	8.64151	1.34958	0.674788	−	0.738011i	$-0.264235\pi$
$41$	8.64151	1.34958	0.674788	+	0.738011i	$0.264235\pi$
$42$	1.00000	0.154303
$43$	8.42154	1.28427	0.642136	−	0.766590i	$-0.278048\pi$
$43$	8.42154	1.28427	0.642136	+	0.766590i	$0.278048\pi$
$44$	−1.16554	−0.175712
$45$	1.00000	0.149071
$46$	1.00000	0.147442
$47$	0.899214	0.131164	0.0655819	−	0.997847i	$-0.479110\pi$
$47$	0.899214	0.131164	0.0655819	+	0.997847i	$0.479110\pi$
$48$	1.00000	0.144338
$49$	1.00000	0.142857
$50$	1.00000	0.141421
$51$	3.43187	0.480558
$52$	−2.26633	−0.314283
$53$	3.27666	0.450084	0.225042	−	0.974349i	$-0.427748\pi$
$53$	3.27666	0.450084	0.225042	+	0.974349i	$0.427748\pi$
$54$	1.00000	0.136083
$55$	−1.16554	−0.157162
$56$	1.00000	0.133631
$57$	5.43187	0.719469
$58$	−4.75263	−0.624051
$59$	5.05442	0.658030	0.329015	−	0.944325i	$-0.393283\pi$
$59$	5.05442	0.658030	0.329015	+	0.944325i	$0.393283\pi$
$60$	1.00000	0.129099
$61$	6.53266	0.836421	0.418211	−	0.908350i	$-0.362657\pi$
$61$	6.53266	0.836421	0.418211	+	0.908350i	$0.362657\pi$
$62$	−4.15521	−0.527712
$63$	1.00000	0.125988
$64$	1.00000	0.125000
$65$	−2.26633	−0.281104
$66$	−1.16554	−0.143469
$67$	−10.7526	−1.31364	−0.656821	−	0.754046i	$-0.728099\pi$
$67$	−10.7526	−1.31364	−0.656821	+	0.754046i	$0.728099\pi$
$68$	3.43187	0.416176
$69$	1.00000	0.120386
$70$	1.00000	0.119523
$71$	3.88888	0.461525	0.230763	−	0.973010i	$-0.425878\pi$
$71$	3.88888	0.461525	0.230763	+	0.973010i	$0.425878\pi$
$72$	1.00000	0.117851
$73$	−3.05442	−0.357493	−0.178747	−	0.983895i	$-0.557204\pi$
$73$	−3.05442	−0.357493	−0.178747	+	0.983895i	$0.557204\pi$
$74$	0.723336	0.0840861
$75$	1.00000	0.115470
$76$	5.43187	0.623079
$77$	−1.16554	−0.132826
$78$	−2.26633	−0.256611
$79$	−1.27666	−0.143636	−0.0718180	−	0.997418i	$-0.522880\pi$
$79$	−1.27666	−0.143636	−0.0718180	+	0.997418i	$0.522880\pi$
$80$	1.00000	0.111803
$81$	1.00000	0.111111
$82$	8.64151	0.954295
$83$	7.76296	0.852096	0.426048	−	0.904701i	$-0.359906\pi$
$83$	7.76296	0.852096	0.426048	+	0.904701i	$0.359906\pi$
$84$	1.00000	0.109109
$85$	3.43187	0.372239
$86$	8.42154	0.908118
$87$	−4.75263	−0.509535
$88$	−1.16554	−0.124247
$89$	−9.52233	−1.00936	−0.504682	−	0.863305i	$-0.668390\pi$
$89$	−9.52233	−1.00936	−0.504682	+	0.863305i	$0.668390\pi$
$90$	1.00000	0.105409
$91$	−2.26633	−0.237576
$92$	1.00000	0.104257
$93$	−4.15521	−0.430875
$94$	0.899214	0.0927468
$95$	5.43187	0.557299
$96$	1.00000	0.102062
$97$	−10.1845	−1.03408	−0.517040	−	0.855961i	$-0.672966\pi$
$97$	−10.1845	−1.03408	−0.517040	+	0.855961i	$0.672966\pi$
$98$	1.00000	0.101015
$99$	−1.16554	−0.117142
$100$	1.00000	0.100000
$101$	−2.78809	−0.277426	−0.138713	−	0.990333i	$-0.544297\pi$
$101$	−2.78809	−0.277426	−0.138713	+	0.990333i	$0.544297\pi$
$102$	3.43187	0.339806
$103$	4.53266	0.446616	0.223308	−	0.974748i	$-0.428314\pi$
$103$	4.53266	0.446616	0.223308	+	0.974748i	$0.428314\pi$
$104$	−2.26633	−0.222232
$105$	1.00000	0.0975900
$106$	3.27666	0.318258
$107$	−20.3690	−1.96915	−0.984573	−	0.174975i	$-0.944016\pi$
$107$	−20.3690	−1.96915	−0.984573	+	0.174975i	$0.944016\pi$
$108$	1.00000	0.0962250
$109$	18.3690	1.75943	0.879716	−	0.475500i	$-0.157733\pi$
$109$	18.3690	1.75943	0.879716	+	0.475500i	$0.157733\pi$
$110$	−1.16554	−0.111130
$111$	0.723336	0.0686560
$112$	1.00000	0.0944911
$113$	7.80932	0.734639	0.367320	−	0.930095i	$-0.380275\pi$
$113$	7.80932	0.734639	0.367320	+	0.930095i	$0.380275\pi$
$114$	5.43187	0.508742
$115$	1.00000	0.0932505
$116$	−4.75263	−0.441270
$117$	−2.26633	−0.209522
$118$	5.05442	0.465297
$119$	3.43187	0.314599
$120$	1.00000	0.0912871
$121$	−9.64151	−0.876501
$122$	6.53266	0.591439
$123$	8.64151	0.779178
$124$	−4.15521	−0.373149
$125$	1.00000	0.0894427
$126$	1.00000	0.0890871
$127$	2.44221	0.216711	0.108355	−	0.994112i	$-0.465442\pi$
$127$	2.44221	0.216711	0.108355	+	0.994112i	$0.465442\pi$
$128$	1.00000	0.0883883
$129$	8.42154	0.741475
$130$	−2.26633	−0.198770
$131$	−10.1197	−0.884166	−0.442083	−	0.896974i	$-0.645760\pi$
$131$	−10.1197	−0.884166	−0.442083	+	0.896974i	$0.645760\pi$
$132$	−1.16554	−0.101448
$133$	5.43187	0.471003
$134$	−10.7526	−0.928886
$135$	1.00000	0.0860663
$136$	3.43187	0.294281
$137$	16.1197	1.37720	0.688601	−	0.725140i	$-0.258225\pi$
$137$	16.1197	1.37720	0.688601	+	0.725140i	$0.258225\pi$
$138$	1.00000	0.0851257
$139$	−4.92491	−0.417725	−0.208863	−	0.977945i	$-0.566976\pi$
$139$	−4.92491	−0.417725	−0.208863	+	0.977945i	$0.566976\pi$
$140$	1.00000	0.0845154
$141$	0.899214	0.0757275
$142$	3.88888	0.326348
$143$	2.64151	0.220894
$144$	1.00000	0.0833333
$145$	−4.75263	−0.394684
$146$	−3.05442	−0.252786
$147$	1.00000	0.0824786
$148$	0.723336	0.0594578
$149$	0.331088	0.0271238	0.0135619	−	0.999908i	$-0.495683\pi$
$149$	0.331088	0.0271238	0.0135619	+	0.999908i	$0.495683\pi$
$150$	1.00000	0.0816497
$151$	8.53266	0.694378	0.347189	−	0.937795i	$-0.387136\pi$
$151$	8.53266	0.694378	0.347189	+	0.937795i	$0.387136\pi$
$152$	5.43187	0.440583
$153$	3.43187	0.277451
$154$	−1.16554	−0.0939222
$155$	−4.15521	−0.333754
$156$	−2.26633	−0.181452
$157$	13.7068	1.09392	0.546962	−	0.837157i	$-0.315784\pi$
$157$	13.7068	1.09392	0.546962	+	0.837157i	$0.315784\pi$
$158$	−1.27666	−0.101566
$159$	3.27666	0.259856
$160$	1.00000	0.0790569
$161$	1.00000	0.0788110
$162$	1.00000	0.0785674
$163$	−1.35849	−0.106405	−0.0532027	−	0.998584i	$-0.516943\pi$
$163$	−1.35849	−0.106405	−0.0532027	+	0.998584i	$0.516943\pi$
$164$	8.64151	0.674788
$165$	−1.16554	−0.0907375
$166$	7.76296	0.602523
$167$	20.6060	1.59454	0.797272	−	0.603621i	$-0.206276\pi$
$167$	20.6060	1.59454	0.797272	+	0.603621i	$0.206276\pi$
$168$	1.00000	0.0771517
$169$	−7.86375	−0.604904
$170$	3.43187	0.263213
$171$	5.43187	0.415386
$172$	8.42154	0.642136
$173$	1.62255	0.123360	0.0616801	−	0.998096i	$-0.480354\pi$
$173$	1.62255	0.123360	0.0616801	+	0.998096i	$0.480354\pi$
$174$	−4.75263	−0.360296
$175$	1.00000	0.0755929
$176$	−1.16554	−0.0878562
$177$	5.05442	0.379914
$178$	−9.52233	−0.713728
$179$	−12.8431	−0.959937	−0.479968	−	0.877286i	$-0.659352\pi$
$179$	−12.8431	−0.959937	−0.479968	+	0.877286i	$0.659352\pi$
$180$	1.00000	0.0745356
$181$	−13.0860	−0.972674	−0.486337	−	0.873771i	$-0.661667\pi$
$181$	−13.0860	−0.972674	−0.486337	+	0.873771i	$0.661667\pi$
$182$	−2.26633	−0.167992
$183$	6.53266	0.482908
$184$	1.00000	0.0737210
$185$	0.723336	0.0531807
$186$	−4.15521	−0.304675
$187$	−4.00000	−0.292509
$188$	0.899214	0.0655819
$189$	1.00000	0.0727393
$190$	5.43187	0.394070
$191$	19.0923	1.38147	0.690737	−	0.723106i	$-0.257286\pi$
$191$	19.0923	1.38147	0.690737	+	0.723106i	$0.257286\pi$
$192$	1.00000	0.0721688
$193$	−20.3897	−1.46768	−0.733840	−	0.679322i	$-0.762274\pi$
$193$	−20.3897	−1.46768	−0.733840	+	0.679322i	$0.762274\pi$
$194$	−10.1845	−0.731205
$195$	−2.26633	−0.162295
$196$	1.00000	0.0714286
$197$	6.31042	0.449599	0.224799	−	0.974405i	$-0.427827\pi$
$197$	6.31042	0.449599	0.224799	+	0.974405i	$0.427827\pi$
$198$	−1.16554	−0.0828316
$199$	−2.33109	−0.165246	−0.0826232	−	0.996581i	$-0.526330\pi$
$199$	−2.33109	−0.165246	−0.0826232	+	0.996581i	$0.526330\pi$
$200$	1.00000	0.0707107
$201$	−10.7526	−0.758432
$202$	−2.78809	−0.196170
$203$	−4.75263	−0.333569
$204$	3.43187	0.240279
$205$	8.64151	0.603549
$206$	4.53266	0.315805
$207$	1.00000	0.0695048
$208$	−2.26633	−0.157142
$209$	−6.33109	−0.437931
$210$	1.00000	0.0690066
$211$	26.1674	1.80144	0.900720	−	0.434400i	$-0.143040\pi$
$211$	26.1674	1.80144	0.900720	+	0.434400i	$0.143040\pi$
$212$	3.27666	0.225042
$213$	3.88888	0.266462
$214$	−20.3690	−1.39240
$215$	8.42154	0.574344
$216$	1.00000	0.0680414
$217$	−4.15521	−0.282074
$218$	18.3690	1.24411
$219$	−3.05442	−0.206399
$220$	−1.16554	−0.0785810
$221$	−7.77776	−0.523189
$222$	0.723336	0.0485471
$223$	−22.6038	−1.51366	−0.756830	−	0.653612i	$-0.773253\pi$
$223$	−22.6038	−1.51366	−0.756830	+	0.653612i	$0.773253\pi$
$224$	1.00000	0.0668153
$225$	1.00000	0.0666667
$226$	7.80932	0.519469
$227$	−29.2682	−1.94260	−0.971300	−	0.237858i	$-0.923555\pi$
$227$	−29.2682	−1.94260	−0.971300	+	0.237858i	$0.923555\pi$
$228$	5.43187	0.359735
$229$	−7.66891	−0.506776	−0.253388	−	0.967365i	$-0.581545\pi$
$229$	−7.66891	−0.506776	−0.253388	+	0.967365i	$0.581545\pi$
$230$	1.00000	0.0659380
$231$	−1.16554	−0.0766872
$232$	−4.75263	−0.312025
$233$	−26.3690	−1.72749	−0.863745	−	0.503928i	$-0.831888\pi$
$233$	−26.3690	−1.72749	−0.863745	+	0.503928i	$0.831888\pi$
$234$	−2.26633	−0.148155
$235$	0.899214	0.0586582
$236$	5.05442	0.329015
$237$	−1.27666	−0.0829283
$238$	3.43187	0.222455
$239$	−4.11112	−0.265926	−0.132963	−	0.991121i	$-0.542449\pi$
$239$	−4.11112	−0.265926	−0.132963	+	0.991121i	$0.542449\pi$
$240$	1.00000	0.0645497
$241$	−21.4698	−1.38299	−0.691495	−	0.722381i	$-0.743048\pi$
$241$	−21.4698	−1.38299	−0.691495	+	0.722381i	$0.743048\pi$
$242$	−9.64151	−0.619780
$243$	1.00000	0.0641500
$244$	6.53266	0.418211
$245$	1.00000	0.0638877
$246$	8.64151	0.550962
$247$	−12.3104	−0.783293
$248$	−4.15521	−0.263856
$249$	7.76296	0.491958
$250$	1.00000	0.0632456
$251$	−16.4949	−1.04115	−0.520575	−	0.853816i	$-0.674282\pi$
$251$	−16.4949	−1.04115	−0.520575	+	0.853816i	$0.674282\pi$
$252$	1.00000	0.0629941
$253$	−1.16554	−0.0732771
$254$	2.44221	0.153238
$255$	3.43187	0.214912
$256$	1.00000	0.0625000
$257$	21.7887	1.35914	0.679570	−	0.733611i	$-0.262167\pi$
$257$	21.7887	1.35914	0.679570	+	0.733611i	$0.262167\pi$
$258$	8.42154	0.524302
$259$	0.723336	0.0449459
$260$	−2.26633	−0.140552
$261$	−4.75263	−0.294180
$262$	−10.1197	−0.625200
$263$	−14.8637	−0.916538	−0.458269	−	0.888814i	$-0.651530\pi$
$263$	−14.8637	−0.916538	−0.458269	+	0.888814i	$0.651530\pi$
$264$	−1.16554	−0.0717343
$265$	3.27666	0.201284
$266$	5.43187	0.333050
$267$	−9.52233	−0.582757
$268$	−10.7526	−0.656821
$269$	6.05499	0.369179	0.184590	−	0.982816i	$-0.440904\pi$
$269$	6.05499	0.369179	0.184590	+	0.982816i	$0.440904\pi$
$270$	1.00000	0.0608581
$271$	−5.22053	−0.317125	−0.158562	−	0.987349i	$-0.550686\pi$
$271$	−5.22053	−0.317125	−0.158562	+	0.987349i	$0.550686\pi$
$272$	3.43187	0.208088
$273$	−2.26633	−0.137165
$274$	16.1197	0.973829
$275$	−1.16554	−0.0702849
$276$	1.00000	0.0601929
$277$	1.35622	0.0814873	0.0407437	−	0.999170i	$-0.487027\pi$
$277$	1.35622	0.0814873	0.0407437	+	0.999170i	$0.487027\pi$
$278$	−4.92491	−0.295376
$279$	−4.15521	−0.248766
$280$	1.00000	0.0597614
$281$	−15.9268	−0.950113	−0.475056	−	0.879955i	$-0.657572\pi$
$281$	−15.9268	−0.950113	−0.475056	+	0.879955i	$0.657572\pi$
$282$	0.899214	0.0535474
$283$	−7.21191	−0.428703	−0.214352	−	0.976757i	$-0.568764\pi$
$283$	−7.21191	−0.428703	−0.214352	+	0.976757i	$0.568764\pi$
$284$	3.88888	0.230763
$285$	5.43187	0.321756
$286$	2.64151	0.156196
$287$	8.64151	0.510092
$288$	1.00000	0.0589256
$289$	−5.22224	−0.307191
$290$	−4.75263	−0.279084
$291$	−10.1845	−0.597026
$292$	−3.05442	−0.178747
$293$	0.863748	0.0504607	0.0252303	−	0.999682i	$-0.491968\pi$
$293$	0.863748	0.0504607	0.0252303	+	0.999682i	$0.491968\pi$
$294$	1.00000	0.0583212
$295$	5.05442	0.294280
$296$	0.723336	0.0420430
$297$	−1.16554	−0.0676317
$298$	0.331088	0.0191794
$299$	−2.26633	−0.131065
$300$	1.00000	0.0577350
$301$	8.42154	0.485409
$302$	8.53266	0.490999
$303$	−2.78809	−0.160172
$304$	5.43187	0.311539
$305$	6.53266	0.374059
$306$	3.43187	0.196187
$307$	−2.80516	−0.160099	−0.0800496	−	0.996791i	$-0.525508\pi$
$307$	−2.80516	−0.160099	−0.0800496	+	0.996791i	$0.525508\pi$
$308$	−1.16554	−0.0664130
$309$	4.53266	0.257854
$310$	−4.15521	−0.236000
$311$	16.0441	0.909777	0.454888	−	0.890548i	$-0.349679\pi$
$311$	16.0441	0.909777	0.454888	+	0.890548i	$0.349679\pi$
$312$	−2.26633	−0.128306
$313$	−4.36883	−0.246941	−0.123470	−	0.992348i	$-0.539402\pi$
$313$	−4.36883	−0.246941	−0.123470	+	0.992348i	$0.539402\pi$
$314$	13.7068	0.773521
$315$	1.00000	0.0563436
$316$	−1.27666	−0.0718180
$317$	28.2602	1.58725	0.793624	−	0.608408i	$-0.208192\pi$
$317$	28.2602	1.58725	0.793624	+	0.608408i	$0.208192\pi$
$318$	3.27666	0.183746
$319$	5.53940	0.310147
$320$	1.00000	0.0559017
$321$	−20.3690	−1.13689
$322$	1.00000	0.0557278
$323$	18.6415	1.03724
$324$	1.00000	0.0555556
$325$	−2.26633	−0.125713
$326$	−1.35849	−0.0752400
$327$	18.3690	1.01581
$328$	8.64151	0.477147
$329$	0.899214	0.0495753
$330$	−1.16554	−0.0641611
$331$	8.31042	0.456782	0.228391	−	0.973569i	$-0.426654\pi$
$331$	8.31042	0.456782	0.228391	+	0.973569i	$0.426654\pi$
$332$	7.76296	0.426048
$333$	0.723336	0.0396386
$334$	20.6060	1.12751
$335$	−10.7526	−0.587479
$336$	1.00000	0.0545545
$337$	−0.834456	−0.0454557	−0.0227279	−	0.999742i	$-0.507235\pi$
$337$	−0.834456	−0.0454557	−0.0227279	+	0.999742i	$0.507235\pi$
$338$	−7.86375	−0.427732
$339$	7.80932	0.424144
$340$	3.43187	0.186120
$341$	4.84308	0.262267
$342$	5.43187	0.293722
$343$	1.00000	0.0539949
$344$	8.42154	0.454059
$345$	1.00000	0.0538382
$346$	1.62255	0.0872288
$347$	−14.6415	−0.785997	−0.392999	−	0.919539i	$-0.628562\pi$
$347$	−14.6415	−0.785997	−0.392999	+	0.919539i	$0.628562\pi$
$348$	−4.75263	−0.254768
$349$	−18.2029	−0.974379	−0.487189	−	0.873296i	$-0.661978\pi$
$349$	−18.2029	−0.974379	−0.487189	+	0.873296i	$0.661978\pi$
$350$	1.00000	0.0534522
$351$	−2.26633	−0.120968
$352$	−1.16554	−0.0621237
$353$	−13.3855	−0.712439	−0.356219	−	0.934402i	$-0.615934\pi$
$353$	−13.3855	−0.712439	−0.356219	+	0.934402i	$0.615934\pi$
$354$	5.05442	0.268640
$355$	3.88888	0.206400
$356$	−9.52233	−0.504682
$357$	3.43187	0.181634
$358$	−12.8431	−0.678778
$359$	−18.0270	−0.951430	−0.475715	−	0.879600i	$-0.657811\pi$
$359$	−18.0270	−0.951430	−0.475715	+	0.879600i	$0.657811\pi$
$360$	1.00000	0.0527046
$361$	10.5053	0.552908
$362$	−13.0860	−0.687784
$363$	−9.64151	−0.506048
$364$	−2.26633	−0.118788
$365$	−3.05442	−0.159876
$366$	6.53266	0.341468
$367$	25.8157	1.34757	0.673784	−	0.738929i	$-0.264668\pi$
$367$	25.8157	1.34757	0.673784	+	0.738929i	$0.264668\pi$
$368$	1.00000	0.0521286
$369$	8.64151	0.449859
$370$	0.723336	0.0376044
$371$	3.27666	0.170116
$372$	−4.15521	−0.215438
$373$	−19.2353	−0.995967	−0.497984	−	0.867186i	$-0.665926\pi$
$373$	−19.2353	−0.995967	−0.497984	+	0.867186i	$0.665926\pi$
$374$	−4.00000	−0.206835
$375$	1.00000	0.0516398
$376$	0.899214	0.0463734
$377$	10.7710	0.554736
$378$	1.00000	0.0514344
$379$	−7.03376	−0.361300	−0.180650	−	0.983547i	$-0.557820\pi$
$379$	−7.03376	−0.361300	−0.180650	+	0.983547i	$0.557820\pi$
$380$	5.43187	0.278649
$381$	2.44221	0.125118
$382$	19.0923	0.976849
$383$	25.9084	1.32386	0.661929	−	0.749567i	$-0.269738\pi$
$383$	25.9084	1.32386	0.661929	+	0.749567i	$0.269738\pi$
$384$	1.00000	0.0510310
$385$	−1.16554	−0.0594016
$386$	−20.3897	−1.03781
$387$	8.42154	0.428091
$388$	−10.1845	−0.517040
$389$	11.3244	0.574167	0.287084	−	0.957905i	$-0.407314\pi$
$389$	11.3244	0.574167	0.287084	+	0.957905i	$0.407314\pi$
$390$	−2.26633	−0.114760
$391$	3.43187	0.173557
$392$	1.00000	0.0505076
$393$	−10.1197	−0.510474
$394$	6.31042	0.317914
$395$	−1.27666	−0.0642360
$396$	−1.16554	−0.0585708
$397$	−34.7235	−1.74272	−0.871362	−	0.490641i	$-0.836762\pi$
$397$	−34.7235	−1.74272	−0.871362	+	0.490641i	$0.836762\pi$
$398$	−2.33109	−0.116847
$399$	5.43187	0.271934
$400$	1.00000	0.0500000
$401$	35.1423	1.75492	0.877461	−	0.479647i	$-0.159235\pi$
$401$	35.1423	1.75492	0.877461	+	0.479647i	$0.159235\pi$
$402$	−10.7526	−0.536292
$403$	9.41708	0.469098
$404$	−2.78809	−0.138713
$405$	1.00000	0.0496904
$406$	−4.75263	−0.235869
$407$	−0.843080	−0.0417899
$408$	3.43187	0.169903
$409$	−6.47408	−0.320122	−0.160061	−	0.987107i	$-0.551169\pi$
$409$	−6.47408	−0.320122	−0.160061	+	0.987107i	$0.551169\pi$
$410$	8.64151	0.426774
$411$	16.1197	0.795128
$412$	4.53266	0.223308
$413$	5.05442	0.248712
$414$	1.00000	0.0491473
$415$	7.76296	0.381069
$416$	−2.26633	−0.111116
$417$	−4.92491	−0.241174
$418$	−6.33109	−0.309664
$419$	12.5876	0.614947	0.307473	−	0.951557i	$-0.400516\pi$
$419$	12.5876	0.614947	0.307473	+	0.951557i	$0.400516\pi$
$420$	1.00000	0.0487950
$421$	24.1306	1.17606	0.588028	−	0.808841i	$-0.299905\pi$
$421$	24.1306	1.17606	0.588028	+	0.808841i	$0.299905\pi$
$422$	26.1674	1.27381
$423$	0.899214	0.0437213
$424$	3.27666	0.159129
$425$	3.43187	0.166470
$426$	3.88888	0.188417
$427$	6.53266	0.316138
$428$	−20.3690	−0.984573
$429$	2.64151	0.127533
$430$	8.42154	0.406123
$431$	15.5664	0.749808	0.374904	−	0.927064i	$-0.377676\pi$
$431$	15.5664	0.749808	0.374904	+	0.927064i	$0.377676\pi$
$432$	1.00000	0.0481125
$433$	−4.90149	−0.235550	−0.117775	−	0.993040i	$-0.537576\pi$
$433$	−4.90149	−0.235550	−0.117775	+	0.993040i	$0.537576\pi$
$434$	−4.15521	−0.199456
$435$	−4.75263	−0.227871
$436$	18.3690	0.879716
$437$	5.43187	0.259842
$438$	−3.05442	−0.145946
$439$	−3.62255	−0.172895	−0.0864474	−	0.996256i	$-0.527551\pi$
$439$	−3.62255	−0.172895	−0.0864474	+	0.996256i	$0.527551\pi$
$440$	−1.16554	−0.0555651
$441$	1.00000	0.0476190
$442$	−7.77776	−0.369950
$443$	14.6415	0.695639	0.347820	−	0.937562i	$-0.386922\pi$
$443$	14.6415	0.695639	0.347820	+	0.937562i	$0.386922\pi$
$444$	0.723336	0.0343280
$445$	−9.52233	−0.451402
$446$	−22.6038	−1.07032
$447$	0.331088	0.0156599
$448$	1.00000	0.0472456
$449$	−23.9497	−1.13026	−0.565129	−	0.825003i	$-0.691174\pi$
$449$	−23.9497	−1.13026	−0.565129	+	0.825003i	$0.691174\pi$
$450$	1.00000	0.0471405
$451$	−10.0721	−0.474275
$452$	7.80932	0.367320
$453$	8.53266	0.400899
$454$	−29.2682	−1.37363
$455$	−2.26633	−0.106247
$456$	5.43187	0.254371
$457$	−22.6501	−1.05953	−0.529764	−	0.848145i	$-0.677720\pi$
$457$	−22.6501	−1.05953	−0.529764	+	0.848145i	$0.677720\pi$
$458$	−7.66891	−0.358345
$459$	3.43187	0.160186
$460$	1.00000	0.0466252
$461$	−24.5156	−1.14180	−0.570902	−	0.821018i	$-0.693407\pi$
$461$	−24.5156	−1.14180	−0.570902	+	0.821018i	$0.693407\pi$
$462$	−1.16554	−0.0542260
$463$	26.8112	1.24602	0.623011	−	0.782213i	$-0.285909\pi$
$463$	26.8112	1.24602	0.623011	+	0.782213i	$0.285909\pi$
$464$	−4.75263	−0.220635
$465$	−4.15521	−0.192693
$466$	−26.3690	−1.22152
$467$	3.83389	0.177411	0.0887057	−	0.996058i	$-0.471727\pi$
$467$	3.83389	0.177411	0.0887057	+	0.996058i	$0.471727\pi$
$468$	−2.26633	−0.104761
$469$	−10.7526	−0.496510
$470$	0.899214	0.0414776
$471$	13.7068	0.631577
$472$	5.05442	0.232649
$473$	−9.81567	−0.451325
$474$	−1.27666	−0.0586391
$475$	5.43187	0.249231
$476$	3.43187	0.157300
$477$	3.27666	0.150028
$478$	−4.11112	−0.188038
$479$	−14.6415	−0.668988	−0.334494	−	0.942398i	$-0.608565\pi$
$479$	−14.6415	−0.668988	−0.334494	+	0.942398i	$0.608565\pi$
$480$	1.00000	0.0456435
$481$	−1.63932	−0.0747464
$482$	−21.4698	−0.977922
$483$	1.00000	0.0455016
$484$	−9.64151	−0.438250
$485$	−10.1845	−0.462454
$486$	1.00000	0.0453609
$487$	−0.199299	−0.00903110	−0.00451555	−	0.999990i	$-0.501437\pi$
$487$	−0.199299	−0.00903110	−0.00451555	+	0.999990i	$0.501437\pi$
$488$	6.53266	0.295720
$489$	−1.35849	−0.0614332
$490$	1.00000	0.0451754
$491$	22.0379	0.994557	0.497279	−	0.867591i	$-0.334333\pi$
$491$	22.0379	0.994557	0.497279	+	0.867591i	$0.334333\pi$
$492$	8.64151	0.389589
$493$	−16.3104	−0.734584
$494$	−12.3104	−0.553872
$495$	−1.16554	−0.0523873
$496$	−4.15521	−0.186574
$497$	3.88888	0.174440
$498$	7.76296	0.347867
$499$	−2.49474	−0.111680	−0.0558401	−	0.998440i	$-0.517784\pi$
$499$	−2.49474	−0.111680	−0.0558401	+	0.998440i	$0.517784\pi$
$500$	1.00000	0.0447214
$501$	20.6060	0.920610
$502$	−16.4949	−0.736204
$503$	−36.9944	−1.64950	−0.824749	−	0.565499i	$-0.808684\pi$
$503$	−36.9944	−1.64950	−0.824749	+	0.565499i	$0.808684\pi$
$504$	1.00000	0.0445435
$505$	−2.78809	−0.124069
$506$	−1.16554	−0.0518147
$507$	−7.86375	−0.349241
$508$	2.44221	0.108355
$509$	25.7104	1.13959	0.569797	−	0.821785i	$-0.307022\pi$
$509$	25.7104	1.13959	0.569797	+	0.821785i	$0.307022\pi$
$510$	3.43187	0.151966
$511$	−3.05442	−0.135120
$512$	1.00000	0.0441942
$513$	5.43187	0.239823
$514$	21.7887	0.961056
$515$	4.53266	0.199733
$516$	8.42154	0.370738
$517$	−1.04807	−0.0460942
$518$	0.723336	0.0317815
$519$	1.62255	0.0712220
$520$	−2.26633	−0.0993851
$521$	−38.8053	−1.70009	−0.850046	−	0.526708i	$-0.823426\pi$
$521$	−38.8053	−1.70009	−0.850046	+	0.526708i	$0.823426\pi$
$522$	−4.75263	−0.208017
$523$	10.9187	0.477443	0.238721	−	0.971088i	$-0.423272\pi$
$523$	10.9187	0.477443	0.238721	+	0.971088i	$0.423272\pi$
$524$	−10.1197	−0.442083
$525$	1.00000	0.0436436
$526$	−14.8637	−0.648090
$527$	−14.2602	−0.621182
$528$	−1.16554	−0.0507238
$529$	1.00000	0.0434783
$530$	3.27666	0.142329
$531$	5.05442	0.219343
$532$	5.43187	0.235502
$533$	−19.5845	−0.848299
$534$	−9.52233	−0.412071
$535$	−20.3690	−0.880629
$536$	−10.7526	−0.464443
$537$	−12.8431	−0.554220
$538$	6.05499	0.261049
$539$	−1.16554	−0.0502035
$540$	1.00000	0.0430331
$541$	−3.88661	−0.167098	−0.0835491	−	0.996504i	$-0.526626\pi$
$541$	−3.88661	−0.167098	−0.0835491	+	0.996504i	$0.526626\pi$
$542$	−5.22053	−0.224241
$543$	−13.0860	−0.561574
$544$	3.43187	0.147140
$545$	18.3690	0.786842
$546$	−2.26633	−0.0969900
$547$	10.7297	0.458768	0.229384	−	0.973336i	$-0.426329\pi$
$547$	10.7297	0.458768	0.229384	+	0.973336i	$0.426329\pi$
$548$	16.1197	0.688601
$549$	6.53266	0.278807
$550$	−1.16554	−0.0496990
$551$	−25.8157	−1.09978
$552$	1.00000	0.0425628
$553$	−1.27666	−0.0542893
$554$	1.35622	0.0576202
$555$	0.723336	0.0307039
$556$	−4.92491	−0.208863
$557$	28.8701	1.22327	0.611633	−	0.791142i	$-0.290513\pi$
$557$	28.8701	1.22327	0.611633	+	0.791142i	$0.290513\pi$
$558$	−4.15521	−0.175904
$559$	−19.0860	−0.807251
$560$	1.00000	0.0422577
$561$	−4.00000	−0.168880
$562$	−15.9268	−0.671831
$563$	−38.5854	−1.62618	−0.813090	−	0.582138i	$-0.802216\pi$
$563$	−38.5854	−1.62618	−0.813090	+	0.582138i	$0.802216\pi$
$564$	0.899214	0.0378637
$565$	7.80932	0.328541
$566$	−7.21191	−0.303139
$567$	1.00000	0.0419961
$568$	3.88888	0.163174
$569$	−26.7024	−1.11942	−0.559711	−	0.828688i	$-0.689088\pi$
$569$	−26.7024	−1.11942	−0.559711	+	0.828688i	$0.689088\pi$
$570$	5.43187	0.227516
$571$	6.72334	0.281363	0.140681	−	0.990055i	$-0.455071\pi$
$571$	6.72334	0.281363	0.140681	+	0.990055i	$0.455071\pi$
$572$	2.64151	0.110447
$573$	19.0923	0.797594
$574$	8.64151	0.360690
$575$	1.00000	0.0417029
$576$	1.00000	0.0416667
$577$	−21.7887	−0.907074	−0.453537	−	0.891238i	$-0.649838\pi$
$577$	−21.7887	−0.907074	−0.453537	+	0.891238i	$0.649838\pi$
$578$	−5.22224	−0.217217
$579$	−20.3897	−0.847366
$580$	−4.75263	−0.197342
$581$	7.76296	0.322062
$582$	−10.1845	−0.422161
$583$	−3.81910	−0.158171
$584$	−3.05442	−0.126393
$585$	−2.26633	−0.0937012
$586$	0.863748	0.0356811
$587$	48.2981	1.99347	0.996737	−	0.0807131i	$-0.0257197\pi$
$587$	48.2981	1.99347	0.996737	+	0.0807131i	$0.0257197\pi$
$588$	1.00000	0.0412393
$589$	−22.5706	−0.930004
$590$	5.05442	0.208087
$591$	6.31042	0.259576
$592$	0.723336	0.0297289
$593$	15.2767	0.627337	0.313669	−	0.949532i	$-0.398442\pi$
$593$	15.2767	0.627337	0.313669	+	0.949532i	$0.398442\pi$
$594$	−1.16554	−0.0478228
$595$	3.43187	0.140693
$596$	0.331088	0.0135619
$597$	−2.33109	−0.0954051
$598$	−2.26633	−0.0926771
$599$	22.3667	0.913880	0.456940	−	0.889498i	$-0.348945\pi$
$599$	22.3667	0.913880	0.456940	+	0.889498i	$0.348945\pi$
$600$	1.00000	0.0408248
$601$	23.5638	0.961189	0.480595	−	0.876943i	$-0.340421\pi$
$601$	23.5638	0.961189	0.480595	+	0.876943i	$0.340421\pi$
$602$	8.42154	0.343236
$603$	−10.7526	−0.437881
$604$	8.53266	0.347189
$605$	−9.64151	−0.391983
$606$	−2.78809	−0.113259
$607$	−2.33469	−0.0947620	−0.0473810	−	0.998877i	$-0.515087\pi$
$607$	−2.33469	−0.0947620	−0.0473810	+	0.998877i	$0.515087\pi$
$608$	5.43187	0.220292
$609$	−4.75263	−0.192586
$610$	6.53266	0.264500
$611$	−2.03792	−0.0824452
$612$	3.43187	0.138725
$613$	9.16327	0.370101	0.185051	−	0.982729i	$-0.440755\pi$
$613$	9.16327	0.370101	0.185051	+	0.982729i	$0.440755\pi$
$614$	−2.80516	−0.113207
$615$	8.64151	0.348459
$616$	−1.16554	−0.0469611
$617$	−3.89750	−0.156908	−0.0784538	−	0.996918i	$-0.524998\pi$
$617$	−3.89750	−0.156908	−0.0784538	+	0.996918i	$0.524998\pi$
$618$	4.53266	0.182330
$619$	−28.4837	−1.14486	−0.572429	−	0.819954i	$-0.693999\pi$
$619$	−28.4837	−1.14486	−0.572429	+	0.819954i	$0.693999\pi$
$620$	−4.15521	−0.166877
$621$	1.00000	0.0401286
$622$	16.0441	0.643309
$623$	−9.52233	−0.381504
$624$	−2.26633	−0.0907258
$625$	1.00000	0.0400000
$626$	−4.36883	−0.174613
$627$	−6.33109	−0.252839
$628$	13.7068	0.546962
$629$	2.48240	0.0989796
$630$	1.00000	0.0398410
$631$	−40.6903	−1.61986	−0.809928	−	0.586529i	$-0.800494\pi$
$631$	−40.6903	−1.61986	−0.809928	+	0.586529i	$0.800494\pi$
$632$	−1.27666	−0.0507830
$633$	26.1674	1.04006
$634$	28.2602	1.12235
$635$	2.44221	0.0969161
$636$	3.27666	0.129928
$637$	−2.26633	−0.0897953
$638$	5.53940	0.219307
$639$	3.88888	0.153842
$640$	1.00000	0.0395285
$641$	−39.3060	−1.55249	−0.776246	−	0.630430i	$-0.782879\pi$
$641$	−39.3060	−1.55249	−0.776246	+	0.630430i	$0.782879\pi$
$642$	−20.3690	−0.803900
$643$	1.37934	0.0543958	0.0271979	−	0.999630i	$-0.491342\pi$
$643$	1.37934	0.0543958	0.0271979	+	0.999630i	$0.491342\pi$
$644$	1.00000	0.0394055
$645$	8.42154	0.331598
$646$	18.6415	0.733440
$647$	−16.7356	−0.657943	−0.328971	−	0.944340i	$-0.606702\pi$
$647$	−16.7356	−0.657943	−0.328971	+	0.944340i	$0.606702\pi$
$648$	1.00000	0.0392837
$649$	−5.89115	−0.231248
$650$	−2.26633	−0.0888928
$651$	−4.15521	−0.162856
$652$	−1.35849	−0.0532027
$653$	27.3416	1.06996	0.534980	−	0.844865i	$-0.320319\pi$
$653$	27.3416	1.06996	0.534980	+	0.844865i	$0.320319\pi$
$654$	18.3690	0.718285
$655$	−10.1197	−0.395411
$656$	8.64151	0.337394
$657$	−3.05442	−0.119164
$658$	0.899214	0.0350550
$659$	6.70039	0.261010	0.130505	−	0.991448i	$-0.458340\pi$
$659$	6.70039	0.261010	0.130505	+	0.991448i	$0.458340\pi$
$660$	−1.16554	−0.0453687
$661$	10.1809	0.395991	0.197996	−	0.980203i	$-0.436557\pi$
$661$	10.1809	0.395991	0.197996	+	0.980203i	$0.436557\pi$
$662$	8.31042	0.322994
$663$	−7.77776	−0.302063
$664$	7.76296	0.301261
$665$	5.43187	0.210639
$666$	0.723336	0.0280287
$667$	−4.75263	−0.184022
$668$	20.6060	0.797272
$669$	−22.6038	−0.873912
$670$	−10.7526	−0.415410
$671$	−7.61410	−0.293939
$672$	1.00000	0.0385758
$673$	−28.6119	−1.10291	−0.551454	−	0.834205i	$-0.685927\pi$
$673$	−28.6119	−1.10291	−0.551454	+	0.834205i	$0.685927\pi$
$674$	−0.834456	−0.0321420
$675$	1.00000	0.0384900
$676$	−7.86375	−0.302452
$677$	−4.10885	−0.157916	−0.0789579	−	0.996878i	$-0.525159\pi$
$677$	−4.10885	−0.157916	−0.0789579	+	0.996878i	$0.525159\pi$
$678$	7.80932	0.299915
$679$	−10.1845	−0.390845
$680$	3.43187	0.131606
$681$	−29.2682	−1.12156
$682$	4.84308	0.185451
$683$	20.3690	0.779398	0.389699	−	0.920942i	$-0.372579\pi$
$683$	20.3690	0.779398	0.389699	+	0.920942i	$0.372579\pi$
$684$	5.43187	0.207693
$685$	16.1197	0.615904
$686$	1.00000	0.0381802
$687$	−7.66891	−0.292587
$688$	8.42154	0.321068
$689$	−7.42600	−0.282908
$690$	1.00000	0.0380693
$691$	−8.89077	−0.338221	−0.169110	−	0.985597i	$-0.554089\pi$
$691$	−8.89077	−0.338221	−0.169110	+	0.985597i	$0.554089\pi$
$692$	1.62255	0.0616801
$693$	−1.16554	−0.0442754
$694$	−14.6415	−0.555784
$695$	−4.92491	−0.186812
$696$	−4.75263	−0.180148
$697$	29.6566	1.12332
$698$	−18.2029	−0.688990
$699$	−26.3690	−0.997367
$700$	1.00000	0.0377964
$701$	15.3244	0.578793	0.289396	−	0.957209i	$-0.406545\pi$
$701$	15.3244	0.578793	0.289396	+	0.957209i	$0.406545\pi$
$702$	−2.26633	−0.0855371
$703$	3.92907	0.148188
$704$	−1.16554	−0.0439281
$705$	0.899214	0.0338664
$706$	−13.3855	−0.503770
$707$	−2.78809	−0.104857
$708$	5.05442	0.189957
$709$	−43.5934	−1.63719	−0.818593	−	0.574374i	$-0.805245\pi$
$709$	−43.5934	−1.63719	−0.818593	+	0.574374i	$0.805245\pi$
$710$	3.88888	0.145947
$711$	−1.27666	−0.0478787
$712$	−9.52233	−0.356864
$713$	−4.15521	−0.155614
$714$	3.43187	0.128435
$715$	2.64151	0.0987868
$716$	−12.8431	−0.479968
$717$	−4.11112	−0.153533
$718$	−18.0270	−0.672762
$719$	−4.70627	−0.175514	−0.0877570	−	0.996142i	$-0.527970\pi$
$719$	−4.70627	−0.175514	−0.0877570	+	0.996142i	$0.527970\pi$
$720$	1.00000	0.0372678
$721$	4.53266	0.168805
$722$	10.5053	0.390965
$723$	−21.4698	−0.798470
$724$	−13.0860	−0.486337
$725$	−4.75263	−0.176508
$726$	−9.64151	−0.357830
$727$	−9.57619	−0.355161	−0.177581	−	0.984106i	$-0.556827\pi$
$727$	−9.57619	−0.355161	−0.177581	+	0.984106i	$0.556827\pi$
$728$	−2.26633	−0.0839958
$729$	1.00000	0.0370370
$730$	−3.05442	−0.113049
$731$	28.9017	1.06897
$732$	6.53266	0.241454
$733$	−32.8224	−1.21232	−0.606162	−	0.795341i	$-0.707292\pi$
$733$	−32.8224	−1.21232	−0.606162	+	0.795341i	$0.707292\pi$
$734$	25.8157	0.952874
$735$	1.00000	0.0368856
$736$	1.00000	0.0368605
$737$	12.5327	0.461646
$738$	8.64151	0.318098
$739$	−17.8157	−0.655360	−0.327680	−	0.944789i	$-0.606267\pi$
$739$	−17.8157	−0.655360	−0.327680	+	0.944789i	$0.606267\pi$
$740$	0.723336	0.0265903
$741$	−12.3104	−0.452235
$742$	3.27666	0.120290
$743$	1.04807	0.0384501	0.0192250	−	0.999815i	$-0.493880\pi$
$743$	1.04807	0.0384501	0.0192250	+	0.999815i	$0.493880\pi$
$744$	−4.15521	−0.152337
$745$	0.331088	0.0121301
$746$	−19.2353	−0.704255
$747$	7.76296	0.284032
$748$	−4.00000	−0.146254
$749$	−20.3690	−0.744267
$750$	1.00000	0.0365148
$751$	31.4441	1.14741	0.573706	−	0.819062i	$-0.305505\pi$
$751$	31.4441	1.14741	0.573706	+	0.819062i	$0.305505\pi$
$752$	0.899214	0.0327910
$753$	−16.4949	−0.601108
$754$	10.7710	0.392258
$755$	8.53266	0.310535
$756$	1.00000	0.0363696
$757$	42.2286	1.53482	0.767412	−	0.641154i	$-0.221544\pi$
$757$	42.2286	1.53482	0.767412	+	0.641154i	$0.221544\pi$
$758$	−7.03376	−0.255477
$759$	−1.16554	−0.0423066
$760$	5.43187	0.197035
$761$	37.8536	1.37219	0.686096	−	0.727511i	$-0.259323\pi$
$761$	37.8536	1.37219	0.686096	+	0.727511i	$0.259323\pi$
$762$	2.44221	0.0884719
$763$	18.3690	0.665003
$764$	19.0923	0.690737
$765$	3.43187	0.124080
$766$	25.9084	0.936109
$767$	−11.4550	−0.413616
$768$	1.00000	0.0360844
$769$	−39.9645	−1.44116	−0.720579	−	0.693373i	$-0.756124\pi$
$769$	−39.9645	−1.44116	−0.720579	+	0.693373i	$0.756124\pi$
$770$	−1.16554	−0.0420033
$771$	21.7887	0.784699
$772$	−20.3897	−0.733840
$773$	−12.9978	−0.467499	−0.233749	−	0.972297i	$-0.575100\pi$
$773$	−12.9978	−0.467499	−0.233749	+	0.972297i	$0.575100\pi$
$774$	8.42154	0.302706
$775$	−4.15521	−0.149260
$776$	−10.1845	−0.365602
$777$	0.723336	0.0259495
$778$	11.3244	0.405998
$779$	46.9396	1.68178
$780$	−2.26633	−0.0811476
$781$	−4.53266	−0.162191
$782$	3.43187	0.122724
$783$	−4.75263	−0.169845
$784$	1.00000	0.0357143
$785$	13.7068	0.489218
$786$	−10.1197	−0.360959
$787$	−31.8032	−1.13366	−0.566830	−	0.823835i	$-0.691830\pi$
$787$	−31.8032	−1.13366	−0.566830	+	0.823835i	$0.691830\pi$
$788$	6.31042	0.224799
$789$	−14.8637	−0.529163
$790$	−1.27666	−0.0454217
$791$	7.80932	0.277668
$792$	−1.16554	−0.0414158
$793$	−14.8052	−0.525747
$794$	−34.7235	−1.23229
$795$	3.27666	0.116211
$796$	−2.33109	−0.0826232
$797$	−42.7676	−1.51491	−0.757453	−	0.652890i	$-0.773557\pi$
$797$	−42.7676	−1.51491	−0.757453	+	0.652890i	$0.773557\pi$
$798$	5.43187	0.192286
$799$	3.08599	0.109174
$800$	1.00000	0.0353553
$801$	−9.52233	−0.336455
$802$	35.1423	1.24092
$803$	3.56006	0.125632
$804$	−10.7526	−0.379216
$805$	1.00000	0.0352454
$806$	9.41708	0.331702
$807$	6.05499	0.213146
$808$	−2.78809	−0.0980848
$809$	8.72969	0.306919	0.153460	−	0.988155i	$-0.450958\pi$
$809$	8.72969	0.306919	0.153460	+	0.988155i	$0.450958\pi$
$810$	1.00000	0.0351364
$811$	22.0488	0.774239	0.387119	−	0.922030i	$-0.373470\pi$
$811$	22.0488	0.774239	0.387119	+	0.922030i	$0.373470\pi$
$812$	−4.75263	−0.166785
$813$	−5.22053	−0.183092
$814$	−0.843080	−0.0295499
$815$	−1.35849	−0.0475859
$816$	3.43187	0.120140
$817$	45.7447	1.60041
$818$	−6.47408	−0.226361
$819$	−2.26633	−0.0791920
$820$	8.64151	0.301775
$821$	−31.6750	−1.10546	−0.552732	−	0.833359i	$-0.686415\pi$
$821$	−31.6750	−1.10546	−0.552732	+	0.833359i	$0.686415\pi$
$822$	16.1197	0.562241
$823$	−29.6750	−1.03440	−0.517202	−	0.855863i	$-0.673026\pi$
$823$	−29.6750	−1.03440	−0.517202	+	0.855863i	$0.673026\pi$
$824$	4.53266	0.157903
$825$	−1.16554	−0.0405790
$826$	5.05442	0.175866
$827$	2.42381	0.0842842	0.0421421	−	0.999112i	$-0.486582\pi$
$827$	2.42381	0.0842842	0.0421421	+	0.999112i	$0.486582\pi$
$828$	1.00000	0.0347524
$829$	0.497194	0.0172683	0.00863414	−	0.999963i	$-0.497252\pi$
$829$	0.497194	0.0172683	0.00863414	+	0.999963i	$0.497252\pi$
$830$	7.76296	0.269456
$831$	1.35622	0.0470467
$832$	−2.26633	−0.0785709
$833$	3.43187	0.118907
$834$	−4.92491	−0.170536
$835$	20.6060	0.713101
$836$	−6.33109	−0.218965
$837$	−4.15521	−0.143625
$838$	12.5876	0.434833
$839$	−43.0518	−1.48631	−0.743157	−	0.669117i	$-0.766673\pi$
$839$	−43.0518	−1.48631	−0.743157	+	0.669117i	$0.766673\pi$
$840$	1.00000	0.0345033
$841$	−6.41253	−0.221122
$842$	24.1306	0.831597
$843$	−15.9268	−0.548548
$844$	26.1674	0.900720
$845$	−7.86375	−0.270521
$846$	0.899214	0.0309156
$847$	−9.64151	−0.331286
$848$	3.27666	0.112521
$849$	−7.21191	−0.247512
$850$	3.43187	0.117712
$851$	0.723336	0.0247956
$852$	3.88888	0.133231
$853$	−20.3752	−0.697633	−0.348816	−	0.937191i	$-0.613416\pi$
$853$	−20.3752	−0.697633	−0.348816	+	0.937191i	$0.613416\pi$
$854$	6.53266	0.223543
$855$	5.43187	0.185766
$856$	−20.3690	−0.696198
$857$	30.9494	1.05721	0.528605	−	0.848868i	$-0.322715\pi$
$857$	30.9494	1.05721	0.528605	+	0.848868i	$0.322715\pi$
$858$	2.64151	0.0901796
$859$	−37.7384	−1.28762	−0.643809	−	0.765187i	$-0.722647\pi$
$859$	−37.7384	−1.28762	−0.643809	+	0.765187i	$0.722647\pi$
$860$	8.42154	0.287172
$861$	8.64151	0.294502
$862$	15.5664	0.530194
$863$	24.3690	0.829531	0.414765	−	0.909928i	$-0.363864\pi$
$863$	24.3690	0.829531	0.414765	+	0.909928i	$0.363864\pi$
$864$	1.00000	0.0340207
$865$	1.62255	0.0551683
$866$	−4.90149	−0.166559
$867$	−5.22224	−0.177357
$868$	−4.15521	−0.141037
$869$	1.48801	0.0504772
$870$	−4.75263	−0.161129
$871$	24.3690	0.825712
$872$	18.3690	0.622053
$873$	−10.1845	−0.344693
$874$	5.43187	0.183736
$875$	1.00000	0.0338062
$876$	−3.05442	−0.103199
$877$	22.3288	0.753990	0.376995	−	0.926215i	$-0.376957\pi$
$877$	22.3288	0.753990	0.376995	+	0.926215i	$0.376957\pi$
$878$	−3.62255	−0.122255
$879$	0.863748	0.0291335
$880$	−1.16554	−0.0392905
$881$	48.7333	1.64187	0.820933	−	0.571024i	$-0.193454\pi$
$881$	48.7333	1.64187	0.820933	+	0.571024i	$0.193454\pi$
$882$	1.00000	0.0336718
$883$	−27.9245	−0.939735	−0.469867	−	0.882737i	$-0.655698\pi$
$883$	−27.9245	−0.939735	−0.469867	+	0.882737i	$0.655698\pi$
$884$	−7.77776	−0.261594
$885$	5.05442	0.169903
$886$	14.6415	0.491891
$887$	33.2096	1.11507	0.557535	−	0.830153i	$-0.311747\pi$
$887$	33.2096	1.11507	0.557535	+	0.830153i	$0.311747\pi$
$888$	0.723336	0.0242736
$889$	2.44221	0.0819090
$890$	−9.52233	−0.319189
$891$	−1.16554	−0.0390472
$892$	−22.6038	−0.756830
$893$	4.88442	0.163451
$894$	0.331088	0.0110732
$895$	−12.8431	−0.429297
$896$	1.00000	0.0334077
$897$	−2.26633	−0.0756706
$898$	−23.9497	−0.799213
$899$	19.7482	0.658638
$900$	1.00000	0.0333333
$901$	11.2451	0.374629
$902$	−10.0721	−0.335363
$903$	8.42154	0.280251
$904$	7.80932	0.259734
$905$	−13.0860	−0.434993
$906$	8.53266	0.283479
$907$	−20.5728	−0.683110	−0.341555	−	0.939862i	$-0.610954\pi$
$907$	−20.5728	−0.683110	−0.341555	+	0.939862i	$0.610954\pi$
$908$	−29.2682	−0.971300
$909$	−2.78809	−0.0924752
$910$	−2.26633	−0.0751281
$911$	38.4887	1.27519	0.637595	−	0.770372i	$-0.279930\pi$
$911$	38.4887	1.27519	0.637595	+	0.770372i	$0.279930\pi$
$912$	5.43187	0.179867
$913$	−9.04807	−0.299448
$914$	−22.6501	−0.749200
$915$	6.53266	0.215963
$916$	−7.66891	−0.253388
$917$	−10.1197	−0.334183
$918$	3.43187	0.113269
$919$	−54.4887	−1.79742	−0.898709	−	0.438546i	$-0.855494\pi$
$919$	−54.4887	−1.79742	−0.898709	+	0.438546i	$0.855494\pi$
$920$	1.00000	0.0329690
$921$	−2.80516	−0.0924333
$922$	−24.5156	−0.807378
$923$	−8.81348	−0.290099
$924$	−1.16554	−0.0383436
$925$	0.723336	0.0237831
$926$	26.8112	0.881071
$927$	4.53266	0.148872
$928$	−4.75263	−0.156013
$929$	−4.90509	−0.160931	−0.0804653	−	0.996757i	$-0.525641\pi$
$929$	−4.90509	−0.160931	−0.0804653	+	0.996757i	$0.525641\pi$
$930$	−4.15521	−0.136255
$931$	5.43187	0.178022
$932$	−26.3690	−0.863745
$933$	16.0441	0.525260
$934$	3.83389	0.125449
$935$	−4.00000	−0.130814
$936$	−2.26633	−0.0740773
$937$	−54.7344	−1.78810	−0.894048	−	0.447972i	$-0.852146\pi$
$937$	−54.7344	−1.78810	−0.894048	+	0.447972i	$0.852146\pi$
$938$	−10.7526	−0.351086
$939$	−4.36883	−0.142571
$940$	0.899214	0.0293291
$941$	8.72969	0.284580	0.142290	−	0.989825i	$-0.454554\pi$
$941$	8.72969	0.284580	0.142290	+	0.989825i	$0.454554\pi$
$942$	13.7068	0.446593
$943$	8.64151	0.281406
$944$	5.05442	0.164507
$945$	1.00000	0.0325300
$946$	−9.81567	−0.319135
$947$	6.11339	0.198659	0.0993293	−	0.995055i	$-0.468330\pi$
$947$	6.11339	0.198659	0.0993293	+	0.995055i	$0.468330\pi$
$948$	−1.27666	−0.0414641
$949$	6.92233	0.224708
$950$	5.43187	0.176233
$951$	28.2602	0.916398
$952$	3.43187	0.111228
$953$	53.1141	1.72054	0.860268	−	0.509843i	$-0.170296\pi$
$953$	53.1141	1.72054	0.860268	+	0.509843i	$0.170296\pi$
$954$	3.27666	0.106086
$955$	19.0923	0.617814
$956$	−4.11112	−0.132963
$957$	5.53940	0.179063
$958$	−14.6415	−0.473046
$959$	16.1197	0.520534
$960$	1.00000	0.0322749
$961$	−13.7342	−0.443040
$962$	−1.63932	−0.0528537
$963$	−20.3690	−0.656382
$964$	−21.4698	−0.691495
$965$	−20.3897	−0.656367
$966$	1.00000	0.0321745
$967$	25.7459	0.827932	0.413966	−	0.910292i	$-0.364143\pi$
$967$	25.7459	0.827932	0.413966	+	0.910292i	$0.364143\pi$
$968$	−9.64151	−0.309890
$969$	18.6415	0.598851
$970$	−10.1845	−0.327005
$971$	−6.10525	−0.195927	−0.0979634	−	0.995190i	$-0.531233\pi$
$971$	−6.10525	−0.195927	−0.0979634	+	0.995190i	$0.531233\pi$
$972$	1.00000	0.0320750
$973$	−4.92491	−0.157885
$974$	−0.199299	−0.00638595
$975$	−2.26633	−0.0725806
$976$	6.53266	0.209105
$977$	−55.3525	−1.77088	−0.885442	−	0.464751i	$-0.846144\pi$
$977$	−55.3525	−1.77088	−0.885442	+	0.464751i	$0.846144\pi$
$978$	−1.35849	−0.0434398
$979$	11.0987	0.354716
$980$	1.00000	0.0319438
$981$	18.3690	0.586477
$982$	22.0379	0.703258
$983$	−6.45341	−0.205832	−0.102916	−	0.994690i	$-0.532817\pi$
$983$	−6.45341	−0.205832	−0.102916	+	0.994690i	$0.532817\pi$
$984$	8.64151	0.275481
$985$	6.31042	0.201067
$986$	−16.3104	−0.519430
$987$	0.899214	0.0286223
$988$	−12.3104	−0.391647
$989$	8.42154	0.267789
$990$	−1.16554	−0.0370434
$991$	−29.8157	−0.947126	−0.473563	−	0.880760i	$-0.657032\pi$
$991$	−29.8157	−0.947126	−0.473563	+	0.880760i	$0.657032\pi$
$992$	−4.15521	−0.131928
$993$	8.31042	0.263723
$994$	3.88888	0.123348
$995$	−2.33109	−0.0739005
$996$	7.76296	0.245979
$997$	−21.6042	−0.684210	−0.342105	−	0.939662i	$-0.611140\pi$
$997$	−21.6042	−0.684210	−0.342105	+	0.939662i	$0.611140\pi$
$998$	−2.49474	−0.0789698
$999$	0.723336	0.0228853

Twists

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

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

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{5} +1.00000 q^{6} +1.00000 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{5} +1.00000 q^{6} +1.00000 q^{7} +1.00000 q^{8} +1.00000 q^{9} +1.00000 q^{10} -1.16554 q^{11} +1.00000 q^{12} -2.26633 q^{13} +1.00000 q^{14} +1.00000 q^{15} +1.00000 q^{16} +3.43187 q^{17} +1.00000 q^{18} +5.43187 q^{19} +1.00000 q^{20} +1.00000 q^{21} -1.16554 q^{22} +1.00000 q^{23} +1.00000 q^{24} +1.00000 q^{25} -2.26633 q^{26} +1.00000 q^{27} +1.00000 q^{28} -4.75263 q^{29} +1.00000 q^{30} -4.15521 q^{31} +1.00000 q^{32} -1.16554 q^{33} +3.43187 q^{34} +1.00000 q^{35} +1.00000 q^{36} +0.723336 q^{37} +5.43187 q^{38} -2.26633 q^{39} +1.00000 q^{40} +8.64151 q^{41} +1.00000 q^{42} +8.42154 q^{43} -1.16554 q^{44} +1.00000 q^{45} +1.00000 q^{46} +0.899214 q^{47} +1.00000 q^{48} +1.00000 q^{49} +1.00000 q^{50} +3.43187 q^{51} -2.26633 q^{52} +3.27666 q^{53} +1.00000 q^{54} -1.16554 q^{55} +1.00000 q^{56} +5.43187 q^{57} -4.75263 q^{58} +5.05442 q^{59} +1.00000 q^{60} +6.53266 q^{61} -4.15521 q^{62} +1.00000 q^{63} +1.00000 q^{64} -2.26633 q^{65} -1.16554 q^{66} -10.7526 q^{67} +3.43187 q^{68} +1.00000 q^{69} +1.00000 q^{70} +3.88888 q^{71} +1.00000 q^{72} -3.05442 q^{73} +0.723336 q^{74} +1.00000 q^{75} +5.43187 q^{76} -1.16554 q^{77} -2.26633 q^{78} -1.27666 q^{79} +1.00000 q^{80} +1.00000 q^{81} +8.64151 q^{82} +7.76296 q^{83} +1.00000 q^{84} +3.43187 q^{85} +8.42154 q^{86} -4.75263 q^{87} -1.16554 q^{88} -9.52233 q^{89} +1.00000 q^{90} -2.26633 q^{91} +1.00000 q^{92} -4.15521 q^{93} +0.899214 q^{94} +5.43187 q^{95} +1.00000 q^{96} -10.1845 q^{97} +1.00000 q^{98} -1.16554 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 4 q^{2} + 4 q^{3} + 4 q^{4} + 4 q^{5} + 4 q^{6} + 4 q^{7} + 4 q^{8} + 4 q^{9}+O(q^{10}) \) 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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