LMFDB - Embedded newform 4970.2.a.z.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4970,2,Mod(1,4970)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4970, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("4970.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4970 = 2 \cdot 5 \cdot 7 \cdot 71 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4970.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:	$39.6856498046$
Analytic rank:	$0$
Dimension:	$9$
Coefficient field:	$\mathbb{Q}[x]/(x^{9} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{9} - 4x^{8} - 9x^{7} + 47x^{6} + 6x^{5} - 151x^{4} + 80x^{3} + 79x^{2} - 54x + 8 $ x^9 - 4x^8 - 9x^7 + 47x^6 + 6x^5 - 151x^4 + 80x^3 + 79x^2 - 54x + 8
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$-0.848518$ of defining polynomial
Character	$\chi$	$=$	4970.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -0.848518 q^{3} +1.00000 q^{4} -1.00000 q^{5} -0.848518 q^{6} +1.00000 q^{7} +1.00000 q^{8} -2.28002 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -0.848518 q^{3} +1.00000 q^{4} -1.00000 q^{5} -0.848518 q^{6} +1.00000 q^{7} +1.00000 q^{8} -2.28002 q^{9} -1.00000 q^{10} -0.0601583 q^{11} -0.848518 q^{12} -3.29182 q^{13} +1.00000 q^{14} +0.848518 q^{15} +1.00000 q^{16} -4.37496 q^{17} -2.28002 q^{18} -0.385243 q^{19} -1.00000 q^{20} -0.848518 q^{21} -0.0601583 q^{22} +0.919272 q^{23} -0.848518 q^{24} +1.00000 q^{25} -3.29182 q^{26} +4.48019 q^{27} +1.00000 q^{28} -10.1389 q^{29} +0.848518 q^{30} +5.32136 q^{31} +1.00000 q^{32} +0.0510455 q^{33} -4.37496 q^{34} -1.00000 q^{35} -2.28002 q^{36} +2.57238 q^{37} -0.385243 q^{38} +2.79317 q^{39} -1.00000 q^{40} +11.9572 q^{41} -0.848518 q^{42} +9.91694 q^{43} -0.0601583 q^{44} +2.28002 q^{45} +0.919272 q^{46} +11.2393 q^{47} -0.848518 q^{48} +1.00000 q^{49} +1.00000 q^{50} +3.71224 q^{51} -3.29182 q^{52} -3.23020 q^{53} +4.48019 q^{54} +0.0601583 q^{55} +1.00000 q^{56} +0.326886 q^{57} -10.1389 q^{58} +7.97185 q^{59} +0.848518 q^{60} +3.46597 q^{61} +5.32136 q^{62} -2.28002 q^{63} +1.00000 q^{64} +3.29182 q^{65} +0.0510455 q^{66} -9.42843 q^{67} -4.37496 q^{68} -0.780019 q^{69} -1.00000 q^{70} +1.00000 q^{71} -2.28002 q^{72} +10.4874 q^{73} +2.57238 q^{74} -0.848518 q^{75} -0.385243 q^{76} -0.0601583 q^{77} +2.79317 q^{78} +2.91927 q^{79} -1.00000 q^{80} +3.03853 q^{81} +11.9572 q^{82} +7.10510 q^{83} -0.848518 q^{84} +4.37496 q^{85} +9.91694 q^{86} +8.60304 q^{87} -0.0601583 q^{88} -10.2511 q^{89} +2.28002 q^{90} -3.29182 q^{91} +0.919272 q^{92} -4.51527 q^{93} +11.2393 q^{94} +0.385243 q^{95} -0.848518 q^{96} -12.1998 q^{97} +1.00000 q^{98} +0.137162 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 9 q + 9 q^{2} + 4 q^{3} + 9 q^{4} - 9 q^{5} + 4 q^{6} + 9 q^{7} + 9 q^{8} + 7 q^{9}+O(q^{10}) $ 9 * q + 9 * q^2 + 4 * q^3 + 9 * q^4 - 9 * q^5 + 4 * q^6 + 9 * q^7 + 9 * q^8 + 7 * q^9	\( 9 q + 9 q^{2} + 4 q^{3} + 9 q^{4} - 9 q^{5} + 4 q^{6} + 9 q^{7} + 9 q^{8} + 7 q^{9} - 9 q^{10} - 2 q^{11} + 4 q^{12} + 11 q^{13} + 9 q^{14} - 4 q^{15} + 9 q^{16} + 9 q^{17} + 7 q^{18} + 9 q^{19} - 9 q^{20} + 4 q^{21} - 2 q^{22} + 2 q^{23} + 4 q^{24} + 9 q^{25} + 11 q^{26} + 7 q^{27} + 9 q^{28} + 2 q^{29} - 4 q^{30} + 18 q^{31} + 9 q^{32} + 8 q^{33} + 9 q^{34} - 9 q^{35} + 7 q^{36} + 15 q^{37} + 9 q^{38} - 7 q^{39} - 9 q^{40} + 15 q^{41} + 4 q^{42} + 7 q^{43} - 2 q^{44} - 7 q^{45} + 2 q^{46} + 12 q^{47} + 4 q^{48} + 9 q^{49} + 9 q^{50} + 4 q^{51} + 11 q^{52} + 3 q^{53} + 7 q^{54} + 2 q^{55} + 9 q^{56} + 9 q^{57} + 2 q^{58} + 24 q^{59} - 4 q^{60} + 25 q^{61} + 18 q^{62} + 7 q^{63} + 9 q^{64} - 11 q^{65} + 8 q^{66} - 4 q^{67} + 9 q^{68} + 3 q^{69} - 9 q^{70} + 9 q^{71} + 7 q^{72} + 32 q^{73} + 15 q^{74} + 4 q^{75} + 9 q^{76} - 2 q^{77} - 7 q^{78} + 20 q^{79} - 9 q^{80} - 7 q^{81} + 15 q^{82} + 11 q^{83} + 4 q^{84} - 9 q^{85} + 7 q^{86} + 26 q^{87} - 2 q^{88} + 10 q^{89} - 7 q^{90} + 11 q^{91} + 2 q^{92} + 32 q^{93} + 12 q^{94} - 9 q^{95} + 4 q^{96} + 19 q^{97} + 9 q^{98} - 7 q^{99}+O(q^{100}) \) 9 * q + 9 * q^2 + 4 * q^3 + 9 * q^4 - 9 * q^5 + 4 * q^6 + 9 * q^7 + 9 * q^8 + 7 * q^9 - 9 * q^10 - 2 * q^11 + 4 * q^12 + 11 * q^13 + 9 * q^14 - 4 * q^15 + 9 * q^16 + 9 * q^17 + 7 * q^18 + 9 * q^19 - 9 * q^20 + 4 * q^21 - 2 * q^22 + 2 * q^23 + 4 * q^24 + 9 * q^25 + 11 * q^26 + 7 * q^27 + 9 * q^28 + 2 * q^29 - 4 * q^30 + 18 * q^31 + 9 * q^32 + 8 * q^33 + 9 * q^34 - 9 * q^35 + 7 * q^36 + 15 * q^37 + 9 * q^38 - 7 * q^39 - 9 * q^40 + 15 * q^41 + 4 * q^42 + 7 * q^43 - 2 * q^44 - 7 * q^45 + 2 * q^46 + 12 * q^47 + 4 * q^48 + 9 * q^49 + 9 * q^50 + 4 * q^51 + 11 * q^52 + 3 * q^53 + 7 * q^54 + 2 * q^55 + 9 * q^56 + 9 * q^57 + 2 * q^58 + 24 * q^59 - 4 * q^60 + 25 * q^61 + 18 * q^62 + 7 * q^63 + 9 * q^64 - 11 * q^65 + 8 * q^66 - 4 * q^67 + 9 * q^68 + 3 * q^69 - 9 * q^70 + 9 * q^71 + 7 * q^72 + 32 * q^73 + 15 * q^74 + 4 * q^75 + 9 * q^76 - 2 * q^77 - 7 * q^78 + 20 * q^79 - 9 * q^80 - 7 * q^81 + 15 * q^82 + 11 * q^83 + 4 * q^84 - 9 * q^85 + 7 * q^86 + 26 * q^87 - 2 * q^88 + 10 * q^89 - 7 * q^90 + 11 * q^91 + 2 * q^92 + 32 * q^93 + 12 * q^94 - 9 * q^95 + 4 * q^96 + 19 * q^97 + 9 * q^98 - 7 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	1.00000	0.707107
$2$	1.00000	0.707107
$3$	−0.848518	−0.489892	−0.244946	−	0.969537i	$-0.578770\pi$
$3$	−0.848518	−0.489892	−0.244946	+	0.969537i	$0.578770\pi$
$4$	1.00000	0.500000
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	−0.848518	−0.346406
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	1.00000	0.353553
$9$	−2.28002	−0.760006
$10$	−1.00000	−0.316228
$11$	−0.0601583	−0.0181384	−0.00906921	−	0.999959i	$-0.502887\pi$
$11$	−0.0601583	−0.0181384	−0.00906921	+	0.999959i	$0.502887\pi$
$12$	−0.848518	−0.244946
$13$	−3.29182	−0.912988	−0.456494	−	0.889727i	$-0.650895\pi$
$13$	−3.29182	−0.912988	−0.456494	+	0.889727i	$0.650895\pi$
$14$	1.00000	0.267261
$15$	0.848518	0.219086
$16$	1.00000	0.250000
$17$	−4.37496	−1.06108	−0.530542	−	0.847658i	$-0.678012\pi$
$17$	−4.37496	−1.06108	−0.530542	+	0.847658i	$0.678012\pi$
$18$	−2.28002	−0.537405
$19$	−0.385243	−0.0883807	−0.0441904	−	0.999023i	$-0.514071\pi$
$19$	−0.385243	−0.0883807	−0.0441904	+	0.999023i	$0.514071\pi$
$20$	−1.00000	−0.223607
$21$	−0.848518	−0.185162
$22$	−0.0601583	−0.0128258
$23$	0.919272	0.191681	0.0958407	−	0.995397i	$-0.469446\pi$
$23$	0.919272	0.191681	0.0958407	+	0.995397i	$0.469446\pi$
$24$	−0.848518	−0.173203
$25$	1.00000	0.200000
$26$	−3.29182	−0.645580
$27$	4.48019	0.862213
$28$	1.00000	0.188982
$29$	−10.1389	−1.88275	−0.941373	−	0.337368i	$-0.890463\pi$
$29$	−10.1389	−1.88275	−0.941373	+	0.337368i	$0.890463\pi$
$30$	0.848518	0.154918
$31$	5.32136	0.955744	0.477872	−	0.878429i	$-0.341408\pi$
$31$	5.32136	0.955744	0.477872	+	0.878429i	$0.341408\pi$
$32$	1.00000	0.176777
$33$	0.0510455	0.00888587
$34$	−4.37496	−0.750300
$35$	−1.00000	−0.169031
$36$	−2.28002	−0.380003
$37$	2.57238	0.422897	0.211449	−	0.977389i	$-0.432182\pi$
$37$	2.57238	0.422897	0.211449	+	0.977389i	$0.432182\pi$
$38$	−0.385243	−0.0624946
$39$	2.79317	0.447266
$40$	−1.00000	−0.158114
$41$	11.9572	1.86741	0.933703	−	0.358049i	$-0.116558\pi$
$41$	11.9572	1.86741	0.933703	+	0.358049i	$0.116558\pi$
$42$	−0.848518	−0.130929
$43$	9.91694	1.51232	0.756160	−	0.654387i	$-0.227073\pi$
$43$	9.91694	1.51232	0.756160	+	0.654387i	$0.227073\pi$
$44$	−0.0601583	−0.00906921
$45$	2.28002	0.339885
$46$	0.919272	0.135539
$47$	11.2393	1.63943	0.819713	−	0.572775i	$-0.194133\pi$
$47$	11.2393	1.63943	0.819713	+	0.572775i	$0.194133\pi$
$48$	−0.848518	−0.122473
$49$	1.00000	0.142857
$50$	1.00000	0.141421
$51$	3.71224	0.519817
$52$	−3.29182	−0.456494
$53$	−3.23020	−0.443701	−0.221851	−	0.975081i	$-0.571210\pi$
$53$	−3.23020	−0.443701	−0.221851	+	0.975081i	$0.571210\pi$
$54$	4.48019	0.609677
$55$	0.0601583	0.00811175
$56$	1.00000	0.133631
$57$	0.326886	0.0432970
$58$	−10.1389	−1.33130
$59$	7.97185	1.03785	0.518923	−	0.854821i	$-0.326333\pi$
$59$	7.97185	1.03785	0.518923	+	0.854821i	$0.326333\pi$
$60$	0.848518	0.109543
$61$	3.46597	0.443772	0.221886	−	0.975073i	$-0.428779\pi$
$61$	3.46597	0.443772	0.221886	+	0.975073i	$0.428779\pi$
$62$	5.32136	0.675813
$63$	−2.28002	−0.287255
$64$	1.00000	0.125000
$65$	3.29182	0.408301
$66$	0.0510455	0.00628326
$67$	−9.42843	−1.15187	−0.575933	−	0.817497i	$-0.695361\pi$
$67$	−9.42843	−1.15187	−0.575933	+	0.817497i	$0.695361\pi$
$68$	−4.37496	−0.530542
$69$	−0.780019	−0.0939033
$70$	−1.00000	−0.119523
$71$	1.00000	0.118678
$71$	1.00000	0.118678
$72$	−2.28002	−0.268703
$73$	10.4874	1.22745	0.613727	−	0.789518i	$-0.289669\pi$
$73$	10.4874	1.22745	0.613727	+	0.789518i	$0.289669\pi$
$74$	2.57238	0.299034
$75$	−0.848518	−0.0979785
$76$	−0.385243	−0.0441904
$77$	−0.0601583	−0.00685568
$78$	2.79317	0.316265
$79$	2.91927	0.328444	0.164222	−	0.986423i	$-0.447489\pi$
$79$	2.91927	0.328444	0.164222	+	0.986423i	$0.447489\pi$
$80$	−1.00000	−0.111803
$81$	3.03853	0.337614
$82$	11.9572	1.32046
$83$	7.10510	0.779886	0.389943	−	0.920839i	$-0.372495\pi$
$83$	7.10510	0.779886	0.389943	+	0.920839i	$0.372495\pi$
$84$	−0.848518	−0.0925809
$85$	4.37496	0.474532
$86$	9.91694	1.06937
$87$	8.60304	0.922343
$88$	−0.0601583	−0.00641290
$89$	−10.2511	−1.08662	−0.543309	−	0.839533i	$-0.682829\pi$
$89$	−10.2511	−1.08662	−0.543309	+	0.839533i	$0.682829\pi$
$90$	2.28002	0.240335
$91$	−3.29182	−0.345077
$92$	0.919272	0.0958407
$93$	−4.51527	−0.468212
$94$	11.2393	1.15925
$95$	0.385243	0.0395251
$96$	−0.848518	−0.0866015
$97$	−12.1998	−1.23870	−0.619351	−	0.785114i	$-0.712604\pi$
$97$	−12.1998	−1.23870	−0.619351	+	0.785114i	$0.712604\pi$
$98$	1.00000	0.101015
$99$	0.137162	0.0137853
$100$	1.00000	0.100000
$101$	−4.94735	−0.492280	−0.246140	−	0.969234i	$-0.579162\pi$
$101$	−4.94735	−0.492280	−0.246140	+	0.969234i	$0.579162\pi$
$102$	3.71224	0.367566
$103$	12.5874	1.24027	0.620136	−	0.784494i	$-0.287077\pi$
$103$	12.5874	1.24027	0.620136	+	0.784494i	$0.287077\pi$
$104$	−3.29182	−0.322790
$105$	0.848518	0.0828069
$106$	−3.23020	−0.313744
$107$	−15.9559	−1.54252	−0.771260	−	0.636521i	$-0.780373\pi$
$107$	−15.9559	−1.54252	−0.771260	+	0.636521i	$0.780373\pi$
$108$	4.48019	0.431107
$109$	−3.14511	−0.301247	−0.150623	−	0.988591i	$-0.548128\pi$
$109$	−3.14511	−0.301247	−0.150623	+	0.988591i	$0.548128\pi$
$110$	0.0601583	0.00573587
$111$	−2.18272	−0.207174
$112$	1.00000	0.0944911
$113$	2.74348	0.258085	0.129043	−	0.991639i	$-0.458810\pi$
$113$	2.74348	0.258085	0.129043	+	0.991639i	$0.458810\pi$
$114$	0.326886	0.0306156
$115$	−0.919272	−0.0857225
$116$	−10.1389	−0.941373
$117$	7.50541	0.693876
$118$	7.97185	0.733868
$119$	−4.37496	−0.401052
$120$	0.848518	0.0774588
$121$	−10.9964	−0.999671
$122$	3.46597	0.313794
$123$	−10.1459	−0.914828
$124$	5.32136	0.477872
$125$	−1.00000	−0.0894427
$126$	−2.28002	−0.203120
$127$	9.61932	0.853577	0.426788	−	0.904352i	$-0.359645\pi$
$127$	9.61932	0.853577	0.426788	+	0.904352i	$0.359645\pi$
$128$	1.00000	0.0883883
$129$	−8.41471	−0.740874
$130$	3.29182	0.288712
$131$	17.7180	1.54803	0.774016	−	0.633167i	$-0.218245\pi$
$131$	17.7180	1.54803	0.774016	+	0.633167i	$0.218245\pi$
$132$	0.0510455	0.00444294
$133$	−0.385243	−0.0334048
$134$	−9.42843	−0.814492
$135$	−4.48019	−0.385593
$136$	−4.37496	−0.375150
$137$	−3.74702	−0.320130	−0.160065	−	0.987107i	$-0.551170\pi$
$137$	−3.74702	−0.320130	−0.160065	+	0.987107i	$0.551170\pi$
$138$	−0.780019	−0.0663996
$139$	8.82364	0.748411	0.374206	−	0.927346i	$-0.377915\pi$
$139$	8.82364	0.748411	0.374206	+	0.927346i	$0.377915\pi$
$140$	−1.00000	−0.0845154
$141$	−9.53678	−0.803142
$142$	1.00000	0.0839181
$143$	0.198031	0.0165602
$144$	−2.28002	−0.190001
$145$	10.1389	0.841990
$146$	10.4874	0.867942
$147$	−0.848518	−0.0699846
$148$	2.57238	0.211449
$149$	10.7714	0.882431	0.441215	−	0.897401i	$-0.354547\pi$
$149$	10.7714	0.882431	0.441215	+	0.897401i	$0.354547\pi$
$150$	−0.848518	−0.0692812
$151$	13.9038	1.13148	0.565738	−	0.824585i	$-0.308591\pi$
$151$	13.9038	1.13148	0.565738	+	0.824585i	$0.308591\pi$
$152$	−0.385243	−0.0312473
$153$	9.97499	0.806430
$154$	−0.0601583	−0.00484770
$155$	−5.32136	−0.427422
$156$	2.79317	0.223633
$157$	−10.5261	−0.840071	−0.420036	−	0.907508i	$-0.637982\pi$
$157$	−10.5261	−0.840071	−0.420036	+	0.907508i	$0.637982\pi$
$158$	2.91927	0.232245
$159$	2.74088	0.217366
$160$	−1.00000	−0.0790569
$161$	0.919272	0.0724488
$162$	3.03853	0.238729
$163$	10.6043	0.830590	0.415295	−	0.909687i	$-0.363678\pi$
$163$	10.6043	0.830590	0.415295	+	0.909687i	$0.363678\pi$
$164$	11.9572	0.933703
$165$	−0.0510455	−0.00397388
$166$	7.10510	0.551463
$167$	−0.828797	−0.0641342	−0.0320671	−	0.999486i	$-0.510209\pi$
$167$	−0.828797	−0.0641342	−0.0320671	+	0.999486i	$0.510209\pi$
$168$	−0.848518	−0.0654646
$169$	−2.16389	−0.166453
$170$	4.37496	0.335544
$171$	0.878360	0.0671699
$172$	9.91694	0.756160
$173$	−9.77499	−0.743179	−0.371589	−	0.928397i	$-0.621187\pi$
$173$	−9.77499	−0.743179	−0.371589	+	0.928397i	$0.621187\pi$
$174$	8.60304	0.652195
$175$	1.00000	0.0755929
$176$	−0.0601583	−0.00453461
$177$	−6.76426	−0.508433
$178$	−10.2511	−0.768356
$179$	20.9571	1.56640	0.783202	−	0.621767i	$-0.213585\pi$
$179$	20.9571	1.56640	0.783202	+	0.621767i	$0.213585\pi$
$180$	2.28002	0.169942
$181$	25.7972	1.91749	0.958744	−	0.284270i	$-0.0917512\pi$
$181$	25.7972	1.91749	0.958744	+	0.284270i	$0.0917512\pi$
$182$	−3.29182	−0.244006
$183$	−2.94094	−0.217401
$184$	0.919272	0.0677696
$185$	−2.57238	−0.189125
$186$	−4.51527	−0.331076
$187$	0.263191	0.0192464
$188$	11.2393	0.819713
$189$	4.48019	0.325886
$190$	0.385243	0.0279484
$191$	1.91777	0.138765	0.0693824	−	0.997590i	$-0.477897\pi$
$191$	1.91777	0.138765	0.0693824	+	0.997590i	$0.477897\pi$
$192$	−0.848518	−0.0612365
$193$	4.64300	0.334211	0.167105	−	0.985939i	$-0.446558\pi$
$193$	4.64300	0.334211	0.167105	+	0.985939i	$0.446558\pi$
$194$	−12.1998	−0.875895
$195$	−2.79317	−0.200023
$196$	1.00000	0.0714286
$197$	−15.8100	−1.12642	−0.563208	−	0.826315i	$-0.690433\pi$
$197$	−15.8100	−1.12642	−0.563208	+	0.826315i	$0.690433\pi$
$198$	0.137162	0.00974768
$199$	16.3658	1.16014	0.580070	−	0.814567i	$-0.303025\pi$
$199$	16.3658	1.16014	0.580070	+	0.814567i	$0.303025\pi$
$200$	1.00000	0.0707107
$201$	8.00020	0.564290
$202$	−4.94735	−0.348094
$203$	−10.1389	−0.711611
$204$	3.71224	0.259909
$205$	−11.9572	−0.835129
$206$	12.5874	0.877005
$207$	−2.09596	−0.145679
$208$	−3.29182	−0.228247
$209$	0.0231756	0.00160309
$210$	0.848518	0.0585533
$211$	−7.25810	−0.499668	−0.249834	−	0.968289i	$-0.580376\pi$
$211$	−7.25810	−0.499668	−0.249834	+	0.968289i	$0.580376\pi$
$212$	−3.23020	−0.221851
$213$	−0.848518	−0.0581395
$214$	−15.9559	−1.09073
$215$	−9.91694	−0.676330
$216$	4.48019	0.304838
$217$	5.32136	0.361237
$218$	−3.14511	−0.213014
$219$	−8.89873	−0.601321
$220$	0.0601583	0.00405587
$221$	14.4016	0.968758
$222$	−2.18272	−0.146494
$223$	19.4863	1.30490	0.652448	−	0.757833i	$-0.273742\pi$
$223$	19.4863	1.30490	0.652448	+	0.757833i	$0.273742\pi$
$224$	1.00000	0.0668153
$225$	−2.28002	−0.152001
$226$	2.74348	0.182494
$227$	−5.88978	−0.390919	−0.195459	−	0.980712i	$-0.562620\pi$
$227$	−5.88978	−0.390919	−0.195459	+	0.980712i	$0.562620\pi$
$228$	0.326886	0.0216485
$229$	11.5299	0.761918	0.380959	−	0.924592i	$-0.375594\pi$
$229$	11.5299	0.761918	0.380959	+	0.924592i	$0.375594\pi$
$230$	−0.919272	−0.0606150
$231$	0.0510455	0.00335854
$232$	−10.1389	−0.665651
$233$	18.2626	1.19642	0.598211	−	0.801339i	$-0.295879\pi$
$233$	18.2626	1.19642	0.598211	+	0.801339i	$0.295879\pi$
$234$	7.50541	0.490644
$235$	−11.2393	−0.733173
$236$	7.97185	0.518923
$237$	−2.47706	−0.160902
$238$	−4.37496	−0.283587
$239$	−20.6743	−1.33731	−0.668656	−	0.743572i	$-0.733130\pi$
$239$	−20.6743	−1.33731	−0.668656	+	0.743572i	$0.733130\pi$
$240$	0.848518	0.0547716
$241$	−5.72347	−0.368681	−0.184341	−	0.982862i	$-0.559015\pi$
$241$	−5.72347	−0.368681	−0.184341	+	0.982862i	$0.559015\pi$
$242$	−10.9964	−0.706874
$243$	−16.0188	−1.02761
$244$	3.46597	0.221886
$245$	−1.00000	−0.0638877
$246$	−10.1459	−0.646881
$247$	1.26815	0.0806906
$248$	5.32136	0.337907
$249$	−6.02881	−0.382060
$250$	−1.00000	−0.0632456
$251$	−17.1379	−1.08173	−0.540866	−	0.841109i	$-0.681903\pi$
$251$	−17.1379	−1.08173	−0.540866	+	0.841109i	$0.681903\pi$
$252$	−2.28002	−0.143628
$253$	−0.0553019	−0.00347680
$254$	9.61932	0.603570
$255$	−3.71224	−0.232469
$256$	1.00000	0.0625000
$257$	9.20127	0.573960	0.286980	−	0.957937i	$-0.407349\pi$
$257$	9.20127	0.573960	0.286980	+	0.957937i	$0.407349\pi$
$258$	−8.41471	−0.523877
$259$	2.57238	0.159840
$260$	3.29182	0.204150
$261$	23.1169	1.43090
$262$	17.7180	1.09462
$263$	−6.78208	−0.418201	−0.209100	−	0.977894i	$-0.567054\pi$
$263$	−6.78208	−0.418201	−0.209100	+	0.977894i	$0.567054\pi$
$264$	0.0510455	0.00314163
$265$	3.23020	0.198429
$266$	−0.385243	−0.0236207
$267$	8.69828	0.532326
$268$	−9.42843	−0.575933
$269$	−11.1147	−0.677678	−0.338839	−	0.940844i	$-0.610034\pi$
$269$	−11.1147	−0.677678	−0.338839	+	0.940844i	$0.610034\pi$
$270$	−4.48019	−0.272656
$271$	24.1485	1.46691	0.733457	−	0.679736i	$-0.237905\pi$
$271$	24.1485	1.46691	0.733457	+	0.679736i	$0.237905\pi$
$272$	−4.37496	−0.265271
$273$	2.79317	0.169051
$274$	−3.74702	−0.226366
$275$	−0.0601583	−0.00362768
$276$	−0.780019	−0.0469516
$277$	1.02641	0.0616709	0.0308355	−	0.999524i	$-0.490183\pi$
$277$	1.02641	0.0616709	0.0308355	+	0.999524i	$0.490183\pi$
$278$	8.82364	0.529207
$279$	−12.1328	−0.726371
$280$	−1.00000	−0.0597614
$281$	2.38509	0.142282	0.0711412	−	0.997466i	$-0.477336\pi$
$281$	2.38509	0.142282	0.0711412	+	0.997466i	$0.477336\pi$
$282$	−9.53678	−0.567907
$283$	−11.3104	−0.672334	−0.336167	−	0.941802i	$-0.609131\pi$
$283$	−11.3104	−0.672334	−0.336167	+	0.941802i	$0.609131\pi$
$284$	1.00000	0.0593391
$285$	−0.326886	−0.0193630
$286$	0.198031	0.0117098
$287$	11.9572	0.705813
$288$	−2.28002	−0.134351
$289$	2.14032	0.125901
$290$	10.1389	0.595377
$291$	10.3518	0.606831
$292$	10.4874	0.613727
$293$	19.0169	1.11098	0.555489	−	0.831524i	$-0.312531\pi$
$293$	19.0169	1.11098	0.555489	+	0.831524i	$0.312531\pi$
$294$	−0.848518	−0.0494866
$295$	−7.97185	−0.464139
$296$	2.57238	0.149517
$297$	−0.269521	−0.0156392
$298$	10.7714	0.623973
$299$	−3.02608	−0.175003
$300$	−0.848518	−0.0489892
$301$	9.91694	0.571603
$302$	13.9038	0.800074
$303$	4.19792	0.241164
$304$	−0.385243	−0.0220952
$305$	−3.46597	−0.198461
$306$	9.97499	0.570232
$307$	6.26873	0.357775	0.178888	−	0.983870i	$-0.442750\pi$
$307$	6.26873	0.357775	0.178888	+	0.983870i	$0.442750\pi$
$308$	−0.0601583	−0.00342784
$309$	−10.6806	−0.607600
$310$	−5.32136	−0.302233
$311$	−3.93053	−0.222880	−0.111440	−	0.993771i	$-0.535546\pi$
$311$	−3.93053	−0.222880	−0.111440	+	0.993771i	$0.535546\pi$
$312$	2.79317	0.158132
$313$	16.6959	0.943709	0.471855	−	0.881676i	$-0.343585\pi$
$313$	16.6959	0.943709	0.471855	+	0.881676i	$0.343585\pi$
$314$	−10.5261	−0.594020
$315$	2.28002	0.128464
$316$	2.91927	0.164222
$317$	5.43286	0.305140	0.152570	−	0.988293i	$-0.451245\pi$
$317$	5.43286	0.305140	0.152570	+	0.988293i	$0.451245\pi$
$318$	2.74088	0.153701
$319$	0.609939	0.0341500
$320$	−1.00000	−0.0559017
$321$	13.5389	0.755668
$322$	0.919272	0.0512290
$323$	1.68542	0.0937795
$324$	3.03853	0.168807
$325$	−3.29182	−0.182598
$326$	10.6043	0.587316
$327$	2.66868	0.147578
$328$	11.9572	0.660228
$329$	11.2393	0.619644
$330$	−0.0510455	−0.00280996
$331$	−28.1447	−1.54697	−0.773487	−	0.633812i	$-0.781489\pi$
$331$	−28.1447	−1.54697	−0.773487	+	0.633812i	$0.781489\pi$
$332$	7.10510	0.389943
$333$	−5.86508	−0.321404
$334$	−0.828797	−0.0453497
$335$	9.42843	0.515130
$336$	−0.848518	−0.0462905
$337$	3.23763	0.176365	0.0881826	−	0.996104i	$-0.471894\pi$
$337$	3.23763	0.176365	0.0881826	+	0.996104i	$0.471894\pi$
$338$	−2.16389	−0.117700
$339$	−2.32790	−0.126434
$340$	4.37496	0.237266
$341$	−0.320124	−0.0173357
$342$	0.878360	0.0474963
$343$	1.00000	0.0539949
$344$	9.91694	0.534686
$345$	0.780019	0.0419948
$346$	−9.77499	−0.525507
$347$	−8.46433	−0.454389	−0.227195	−	0.973849i	$-0.572955\pi$
$347$	−8.46433	−0.454389	−0.227195	+	0.973849i	$0.572955\pi$
$348$	8.60304	0.461171
$349$	−29.8163	−1.59603	−0.798016	−	0.602636i	$-0.794117\pi$
$349$	−29.8163	−1.59603	−0.798016	+	0.602636i	$0.794117\pi$
$350$	1.00000	0.0534522
$351$	−14.7480	−0.787190
$352$	−0.0601583	−0.00320645
$353$	−1.36810	−0.0728164	−0.0364082	−	0.999337i	$-0.511592\pi$
$353$	−1.36810	−0.0728164	−0.0364082	+	0.999337i	$0.511592\pi$
$354$	−6.76426	−0.359516
$355$	−1.00000	−0.0530745
$356$	−10.2511	−0.543309
$357$	3.71224	0.196472
$358$	20.9571	1.10762
$359$	29.6041	1.56245	0.781223	−	0.624252i	$-0.214596\pi$
$359$	29.6041	1.56245	0.781223	+	0.624252i	$0.214596\pi$
$360$	2.28002	0.120167
$361$	−18.8516	−0.992189
$362$	25.7972	1.35587
$363$	9.33063	0.489731
$364$	−3.29182	−0.172538
$365$	−10.4874	−0.548934
$366$	−2.94094	−0.153725
$367$	−2.65704	−0.138696	−0.0693482	−	0.997593i	$-0.522092\pi$
$367$	−2.65704	−0.138696	−0.0693482	+	0.997593i	$0.522092\pi$
$368$	0.919272	0.0479204
$369$	−27.2627	−1.41924
$370$	−2.57238	−0.133732
$371$	−3.23020	−0.167703
$372$	−4.51527	−0.234106
$373$	−16.5102	−0.854868	−0.427434	−	0.904046i	$-0.640582\pi$
$373$	−16.5102	−0.854868	−0.427434	+	0.904046i	$0.640582\pi$
$374$	0.263191	0.0136093
$375$	0.848518	0.0438173
$376$	11.2393	0.579624
$377$	33.3755	1.71892
$378$	4.48019	0.230436
$379$	15.0792	0.774564	0.387282	−	0.921961i	$-0.373414\pi$
$379$	15.0792	0.774564	0.387282	+	0.921961i	$0.373414\pi$
$380$	0.385243	0.0197625
$381$	−8.16217	−0.418161
$382$	1.91777	0.0981215
$383$	−17.4852	−0.893450	−0.446725	−	0.894671i	$-0.647410\pi$
$383$	−17.4852	−0.893450	−0.446725	+	0.894671i	$0.647410\pi$
$384$	−0.848518	−0.0433008
$385$	0.0601583	0.00306595
$386$	4.64300	0.236323
$387$	−22.6108	−1.14937
$388$	−12.1998	−0.619351
$389$	20.6593	1.04747	0.523735	−	0.851881i	$-0.324538\pi$
$389$	20.6593	1.04747	0.523735	+	0.851881i	$0.324538\pi$
$390$	−2.79317	−0.141438
$391$	−4.02178	−0.203390
$392$	1.00000	0.0505076
$393$	−15.0341	−0.758368
$394$	−15.8100	−0.796496
$395$	−2.91927	−0.146885
$396$	0.137162	0.00689265
$397$	19.8432	0.995900	0.497950	−	0.867206i	$-0.334086\pi$
$397$	19.8432	0.995900	0.497950	+	0.867206i	$0.334086\pi$
$398$	16.3658	0.820342
$399$	0.326886	0.0163647
$400$	1.00000	0.0500000
$401$	24.5556	1.22625	0.613124	−	0.789986i	$-0.289912\pi$
$401$	24.5556	1.22625	0.613124	+	0.789986i	$0.289912\pi$
$402$	8.00020	0.399014
$403$	−17.5170	−0.872583
$404$	−4.94735	−0.246140
$405$	−3.03853	−0.150986
$406$	−10.1389	−0.503185
$407$	−0.154750	−0.00767069
$408$	3.71224	0.183783
$409$	−25.2092	−1.24651	−0.623257	−	0.782017i	$-0.714191\pi$
$409$	−25.2092	−1.24651	−0.623257	+	0.782017i	$0.714191\pi$
$410$	−11.9572	−0.590526
$411$	3.17942	0.156829
$412$	12.5874	0.620136
$413$	7.97185	0.392269
$414$	−2.09596	−0.103011
$415$	−7.10510	−0.348776
$416$	−3.29182	−0.161395
$417$	−7.48702	−0.366641
$418$	0.0231756	0.00113355
$419$	−3.71153	−0.181320	−0.0906602	−	0.995882i	$-0.528898\pi$
$419$	−3.71153	−0.181320	−0.0906602	+	0.995882i	$0.528898\pi$
$420$	0.848518	0.0414035
$421$	29.2183	1.42401	0.712006	−	0.702174i	$-0.247787\pi$
$421$	29.2183	1.42401	0.712006	+	0.702174i	$0.247787\pi$
$422$	−7.25810	−0.353319
$423$	−25.6259	−1.24597
$424$	−3.23020	−0.156872
$425$	−4.37496	−0.212217
$426$	−0.848518	−0.0411108
$427$	3.46597	0.167730
$428$	−15.9559	−0.771260
$429$	−0.168033	−0.00811270
$430$	−9.91694	−0.478238
$431$	13.0370	0.627970	0.313985	−	0.949428i	$-0.398336\pi$
$431$	13.0370	0.627970	0.313985	+	0.949428i	$0.398336\pi$
$432$	4.48019	0.215553
$433$	8.92811	0.429058	0.214529	−	0.976718i	$-0.431178\pi$
$433$	8.92811	0.429058	0.214529	+	0.976718i	$0.431178\pi$
$434$	5.32136	0.255433
$435$	−8.60304	−0.412484
$436$	−3.14511	−0.150623
$437$	−0.354143	−0.0169409
$438$	−8.89873	−0.425198
$439$	3.00167	0.143262	0.0716309	−	0.997431i	$-0.477180\pi$
$439$	3.00167	0.143262	0.0716309	+	0.997431i	$0.477180\pi$
$440$	0.0601583	0.00286794
$441$	−2.28002	−0.108572
$442$	14.4016	0.685015
$443$	26.3209	1.25054	0.625271	−	0.780408i	$-0.284988\pi$
$443$	26.3209	1.25054	0.625271	+	0.780408i	$0.284988\pi$
$444$	−2.18272	−0.103587
$445$	10.2511	0.485951
$446$	19.4863	0.922701
$447$	−9.13976	−0.432296
$448$	1.00000	0.0472456
$449$	6.36785	0.300517	0.150259	−	0.988647i	$-0.451989\pi$
$449$	6.36785	0.300517	0.150259	+	0.988647i	$0.451989\pi$
$450$	−2.28002	−0.107481
$451$	−0.719327	−0.0338718
$452$	2.74348	0.129043
$453$	−11.7976	−0.554301
$454$	−5.88978	−0.276421
$455$	3.29182	0.154323
$456$	0.326886	0.0153078
$457$	11.8180	0.552822	0.276411	−	0.961039i	$-0.410855\pi$
$457$	11.8180	0.552822	0.276411	+	0.961039i	$0.410855\pi$
$458$	11.5299	0.538757
$459$	−19.6007	−0.914881
$460$	−0.919272	−0.0428613
$461$	−17.4220	−0.811424	−0.405712	−	0.914001i	$-0.632976\pi$
$461$	−17.4220	−0.811424	−0.405712	+	0.914001i	$0.632976\pi$
$462$	0.0510455	0.00237485
$463$	−22.7745	−1.05842	−0.529210	−	0.848491i	$-0.677511\pi$
$463$	−22.7745	−1.05842	−0.529210	+	0.848491i	$0.677511\pi$
$464$	−10.1389	−0.470686
$465$	4.51527	0.209391
$466$	18.2626	0.845998
$467$	−32.9232	−1.52350	−0.761751	−	0.647870i	$-0.775660\pi$
$467$	−32.9232	−1.52350	−0.761751	+	0.647870i	$0.775660\pi$
$468$	7.50541	0.346938
$469$	−9.42843	−0.435365
$470$	−11.2393	−0.518432
$471$	8.93156	0.411544
$472$	7.97185	0.366934
$473$	−0.596587	−0.0274311
$474$	−2.47706	−0.113775
$475$	−0.385243	−0.0176761
$476$	−4.37496	−0.200526
$477$	7.36490	0.337216
$478$	−20.6743	−0.945622
$479$	0.143090	0.00653795	0.00326897	−	0.999995i	$-0.498959\pi$
$479$	0.143090	0.00653795	0.00326897	+	0.999995i	$0.498959\pi$
$480$	0.848518	0.0387294
$481$	−8.46784	−0.386100
$482$	−5.72347	−0.260697
$483$	−0.780019	−0.0354921
$484$	−10.9964	−0.499835
$485$	12.1998	0.553965
$486$	−16.0188	−0.726628
$487$	2.14399	0.0971535	0.0485768	−	0.998819i	$-0.484531\pi$
$487$	2.14399	0.0971535	0.0485768	+	0.998819i	$0.484531\pi$
$488$	3.46597	0.156897
$489$	−8.99792	−0.406900
$490$	−1.00000	−0.0451754
$491$	13.9126	0.627868	0.313934	−	0.949445i	$-0.398353\pi$
$491$	13.9126	0.627868	0.313934	+	0.949445i	$0.398353\pi$
$492$	−10.1459	−0.457414
$493$	44.3573	1.99775
$494$	1.26815	0.0570568
$495$	−0.137162	−0.00616497
$496$	5.32136	0.238936
$497$	1.00000	0.0448561
$498$	−6.02881	−0.270157
$499$	5.53421	0.247745	0.123873	−	0.992298i	$-0.460469\pi$
$499$	5.53421	0.247745	0.123873	+	0.992298i	$0.460469\pi$
$500$	−1.00000	−0.0447214
$501$	0.703249	0.0314189
$502$	−17.1379	−0.764900
$503$	−16.6805	−0.743745	−0.371873	−	0.928284i	$-0.621284\pi$
$503$	−16.6805	−0.743745	−0.371873	+	0.928284i	$0.621284\pi$
$504$	−2.28002	−0.101560
$505$	4.94735	0.220154
$506$	−0.0553019	−0.00245847
$507$	1.83610	0.0815441
$508$	9.61932	0.426788
$509$	9.92626	0.439974	0.219987	−	0.975503i	$-0.429399\pi$
$509$	9.92626	0.439974	0.219987	+	0.975503i	$0.429399\pi$
$510$	−3.71224	−0.164381
$511$	10.4874	0.463934
$512$	1.00000	0.0441942
$513$	−1.72596	−0.0762030
$514$	9.20127	0.405851
$515$	−12.5874	−0.554666
$516$	−8.41471	−0.370437
$517$	−0.676140	−0.0297366
$518$	2.57238	0.113024
$519$	8.29426	0.364078
$520$	3.29182	0.144356
$521$	7.02393	0.307724	0.153862	−	0.988092i	$-0.450829\pi$
$521$	7.02393	0.307724	0.153862	+	0.988092i	$0.450829\pi$
$522$	23.1169	1.01180
$523$	35.7787	1.56449	0.782246	−	0.622970i	$-0.214074\pi$
$523$	35.7787	1.56449	0.782246	+	0.622970i	$0.214074\pi$
$524$	17.7180	0.774016
$525$	−0.848518	−0.0370324
$526$	−6.78208	−0.295713
$527$	−23.2808	−1.01413
$528$	0.0510455	0.00222147
$529$	−22.1549	−0.963258
$530$	3.23020	0.140311
$531$	−18.1759	−0.788769
$532$	−0.385243	−0.0167024
$533$	−39.3611	−1.70492
$534$	8.69828	0.376411
$535$	15.9559	0.689836
$536$	−9.42843	−0.407246
$537$	−17.7825	−0.767370
$538$	−11.1147	−0.479190
$539$	−0.0601583	−0.00259120
$540$	−4.48019	−0.192797
$541$	−11.8029	−0.507447	−0.253724	−	0.967277i	$-0.581655\pi$
$541$	−11.8029	−0.507447	−0.253724	+	0.967277i	$0.581655\pi$
$542$	24.1485	1.03727
$543$	−21.8894	−0.939363
$544$	−4.37496	−0.187575
$545$	3.14511	0.134722
$546$	2.79317	0.119537
$547$	−29.9893	−1.28225	−0.641124	−	0.767437i	$-0.721532\pi$
$547$	−29.9893	−1.28225	−0.641124	+	0.767437i	$0.721532\pi$
$548$	−3.74702	−0.160065
$549$	−7.90247	−0.337269
$550$	−0.0601583	−0.00256516
$551$	3.90594	0.166398
$552$	−0.780019	−0.0331998
$553$	2.91927	0.124140
$554$	1.02641	0.0436079
$555$	2.18272	0.0926511
$556$	8.82364	0.374206
$557$	7.17146	0.303865	0.151932	−	0.988391i	$-0.451450\pi$
$557$	7.17146	0.303865	0.151932	+	0.988391i	$0.451450\pi$
$558$	−12.1328	−0.513622
$559$	−32.6448	−1.38073
$560$	−1.00000	−0.0422577
$561$	−0.223322	−0.00942867
$562$	2.38509	0.100609
$563$	6.88495	0.290166	0.145083	−	0.989419i	$-0.453655\pi$
$563$	6.88495	0.290166	0.145083	+	0.989419i	$0.453655\pi$
$564$	−9.53678	−0.401571
$565$	−2.74348	−0.115419
$566$	−11.3104	−0.475412
$567$	3.03853	0.127606
$568$	1.00000	0.0419591
$569$	29.1894	1.22368	0.611841	−	0.790981i	$-0.290429\pi$
$569$	29.1894	1.22368	0.611841	+	0.790981i	$0.290429\pi$
$570$	−0.326886	−0.0136917
$571$	25.7675	1.07834	0.539168	−	0.842198i	$-0.318739\pi$
$571$	25.7675	1.07834	0.539168	+	0.842198i	$0.318739\pi$
$572$	0.198031	0.00828008
$573$	−1.62726	−0.0679798
$574$	11.9572	0.499085
$575$	0.919272	0.0383363
$576$	−2.28002	−0.0950007
$577$	7.33549	0.305381	0.152690	−	0.988274i	$-0.451206\pi$
$577$	7.33549	0.305381	0.152690	+	0.988274i	$0.451206\pi$
$578$	2.14032	0.0890255
$579$	−3.93967	−0.163727
$580$	10.1389	0.420995
$581$	7.10510	0.294769
$582$	10.3518	0.429094
$583$	0.194323	0.00804805
$584$	10.4874	0.433971
$585$	−7.50541	−0.310311
$586$	19.0169	0.785580
$587$	11.1712	0.461084	0.230542	−	0.973062i	$-0.425950\pi$
$587$	11.1712	0.461084	0.230542	+	0.973062i	$0.425950\pi$
$588$	−0.848518	−0.0349923
$589$	−2.05002	−0.0844694
$590$	−7.97185	−0.328196
$591$	13.4151	0.551822
$592$	2.57238	0.105724
$593$	35.3130	1.45013	0.725066	−	0.688680i	$-0.241809\pi$
$593$	35.3130	1.45013	0.725066	+	0.688680i	$0.241809\pi$
$594$	−0.269521	−0.0110586
$595$	4.37496	0.179356
$596$	10.7714	0.441215
$597$	−13.8867	−0.568343
$598$	−3.02608	−0.123746
$599$	−25.0178	−1.02220	−0.511100	−	0.859521i	$-0.670762\pi$
$599$	−25.0178	−1.02220	−0.511100	+	0.859521i	$0.670762\pi$
$600$	−0.848518	−0.0346406
$601$	12.5966	0.513827	0.256914	−	0.966434i	$-0.417294\pi$
$601$	12.5966	0.513827	0.256914	+	0.966434i	$0.417294\pi$
$602$	9.91694	0.404184
$603$	21.4970	0.875425
$604$	13.9038	0.565738
$605$	10.9964	0.447066
$606$	4.19792	0.170529
$607$	−22.6048	−0.917502	−0.458751	−	0.888565i	$-0.651703\pi$
$607$	−22.6048	−0.917502	−0.458751	+	0.888565i	$0.651703\pi$
$608$	−0.385243	−0.0156237
$609$	8.60304	0.348613
$610$	−3.46597	−0.140333
$611$	−36.9979	−1.49678
$612$	9.97499	0.403215
$613$	−33.8271	−1.36626	−0.683132	−	0.730295i	$-0.739383\pi$
$613$	−33.8271	−1.36626	−0.683132	+	0.730295i	$0.739383\pi$
$614$	6.26873	0.252985
$615$	10.1459	0.409123
$616$	−0.0601583	−0.00242385
$617$	−36.3901	−1.46501	−0.732505	−	0.680761i	$-0.761649\pi$
$617$	−36.3901	−1.46501	−0.732505	+	0.680761i	$0.761649\pi$
$618$	−10.6806	−0.429638
$619$	5.37777	0.216151	0.108075	−	0.994143i	$-0.465531\pi$
$619$	5.37777	0.216151	0.108075	+	0.994143i	$0.465531\pi$
$620$	−5.32136	−0.213711
$621$	4.11851	0.165270
$622$	−3.93053	−0.157600
$623$	−10.2511	−0.410703
$624$	2.79317	0.111816
$625$	1.00000	0.0400000
$626$	16.6959	0.667303
$627$	−0.0196649	−0.000785340 0
$628$	−10.5261	−0.420036
$629$	−11.2541	−0.448730
$630$	2.28002	0.0908380
$631$	38.9722	1.55146	0.775729	−	0.631067i	$-0.217383\pi$
$631$	38.9722	1.55146	0.775729	+	0.631067i	$0.217383\pi$
$632$	2.91927	0.116122
$633$	6.15863	0.244784
$634$	5.43286	0.215766
$635$	−9.61932	−0.381731
$636$	2.74088	0.108683
$637$	−3.29182	−0.130427
$638$	0.609939	0.0241477
$639$	−2.28002	−0.0901961
$640$	−1.00000	−0.0395285
$641$	−19.1269	−0.755466	−0.377733	−	0.925915i	$-0.623296\pi$
$641$	−19.1269	−0.755466	−0.377733	+	0.925915i	$0.623296\pi$
$642$	13.5389	0.534338
$643$	13.8291	0.545368	0.272684	−	0.962104i	$-0.412089\pi$
$643$	13.8291	0.545368	0.272684	+	0.962104i	$0.412089\pi$
$644$	0.919272	0.0362244
$645$	8.41471	0.331329
$646$	1.68542	0.0663121
$647$	−32.5629	−1.28018	−0.640089	−	0.768301i	$-0.721103\pi$
$647$	−32.5629	−1.28018	−0.640089	+	0.768301i	$0.721103\pi$
$648$	3.03853	0.119365
$649$	−0.479573	−0.0188249
$650$	−3.29182	−0.129116
$651$	−4.51527	−0.176967
$652$	10.6043	0.415295
$653$	−37.0187	−1.44865	−0.724326	−	0.689458i	$-0.757849\pi$
$653$	−37.0187	−1.44865	−0.724326	+	0.689458i	$0.757849\pi$
$654$	2.66868	0.104354
$655$	−17.7180	−0.692301
$656$	11.9572	0.466851
$657$	−23.9114	−0.932872
$658$	11.2393	0.438155
$659$	10.8414	0.422321	0.211160	−	0.977451i	$-0.432276\pi$
$659$	10.8414	0.422321	0.211160	+	0.977451i	$0.432276\pi$
$660$	−0.0510455	−0.00198694
$661$	38.6253	1.50235	0.751175	−	0.660103i	$-0.229487\pi$
$661$	38.6253	1.50235	0.751175	+	0.660103i	$0.229487\pi$
$662$	−28.1447	−1.09388
$663$	−12.2200	−0.474587
$664$	7.10510	0.275731
$665$	0.385243	0.0149391
$666$	−5.86508	−0.227267
$667$	−9.32040	−0.360887
$668$	−0.828797	−0.0320671
$669$	−16.5345	−0.639259
$670$	9.42843	0.364252
$671$	−0.208507	−0.00804933
$672$	−0.848518	−0.0327323
$673$	−16.6914	−0.643405	−0.321702	−	0.946841i	$-0.604255\pi$
$673$	−16.6914	−0.643405	−0.321702	+	0.946841i	$0.604255\pi$
$674$	3.23763	0.124709
$675$	4.48019	0.172443
$676$	−2.16389	−0.0832265
$677$	−36.1098	−1.38781	−0.693906	−	0.720066i	$-0.744111\pi$
$677$	−36.1098	−1.38781	−0.693906	+	0.720066i	$0.744111\pi$
$678$	−2.32790	−0.0894024
$679$	−12.1998	−0.468185
$680$	4.37496	0.167772
$681$	4.99759	0.191508
$682$	−0.320124	−0.0122582
$683$	−23.9000	−0.914507	−0.457254	−	0.889336i	$-0.651167\pi$
$683$	−23.9000	−0.914507	−0.457254	+	0.889336i	$0.651167\pi$
$684$	0.878360	0.0335849
$685$	3.74702	0.143166
$686$	1.00000	0.0381802
$687$	−9.78334	−0.373258
$688$	9.91694	0.378080
$689$	10.6332	0.405094
$690$	0.780019	0.0296948
$691$	−34.0143	−1.29397	−0.646983	−	0.762505i	$-0.723969\pi$
$691$	−34.0143	−1.29397	−0.646983	+	0.762505i	$0.723969\pi$
$692$	−9.77499	−0.371589
$693$	0.137162	0.00521035
$694$	−8.46433	−0.321302
$695$	−8.82364	−0.334700
$696$	8.60304	0.326097
$697$	−52.3125	−1.98148
$698$	−29.8163	−1.12856
$699$	−15.4961	−0.586118
$700$	1.00000	0.0377964
$701$	1.26664	0.0478403	0.0239202	−	0.999714i	$-0.492385\pi$
$701$	1.26664	0.0478403	0.0239202	+	0.999714i	$0.492385\pi$
$702$	−14.7480	−0.556628
$703$	−0.990993	−0.0373760
$704$	−0.0601583	−0.00226730
$705$	9.53678	0.359176
$706$	−1.36810	−0.0514890
$707$	−4.94735	−0.186064
$708$	−6.76426	−0.254216
$709$	20.9940	0.788445	0.394223	−	0.919015i	$-0.371014\pi$
$709$	20.9940	0.788445	0.394223	+	0.919015i	$0.371014\pi$
$710$	−1.00000	−0.0375293
$711$	−6.65599	−0.249619
$712$	−10.2511	−0.384178
$713$	4.89178	0.183198
$714$	3.71224	0.138927
$715$	−0.198031	−0.00740593
$716$	20.9571	0.783202
$717$	17.5425	0.655138
$718$	29.6041	1.10482
$719$	−23.0148	−0.858307	−0.429154	−	0.903232i	$-0.641188\pi$
$719$	−23.0148	−0.858307	−0.429154	+	0.903232i	$0.641188\pi$
$720$	2.28002	0.0849712
$721$	12.5874	0.468779
$722$	−18.8516	−0.701583
$723$	4.85647	0.180614
$724$	25.7972	0.958744
$725$	−10.1389	−0.376549
$726$	9.33063	0.346292
$727$	25.0154	0.927772	0.463886	−	0.885895i	$-0.346455\pi$
$727$	25.0154	0.927772	0.463886	+	0.885895i	$0.346455\pi$
$728$	−3.29182	−0.122003
$729$	4.47668	0.165803
$730$	−10.4874	−0.388155
$731$	−43.3863	−1.60470
$732$	−2.94094	−0.108700
$733$	−18.0738	−0.667572	−0.333786	−	0.942649i	$-0.608326\pi$
$733$	−18.0738	−0.667572	−0.333786	+	0.942649i	$0.608326\pi$
$734$	−2.65704	−0.0980732
$735$	0.848518	0.0312981
$736$	0.919272	0.0338848
$737$	0.567199	0.0208930
$738$	−27.2627	−1.00355
$739$	5.23562	0.192595	0.0962976	−	0.995353i	$-0.469300\pi$
$739$	5.23562	0.192595	0.0962976	+	0.995353i	$0.469300\pi$
$740$	−2.57238	−0.0945627
$741$	−1.07605	−0.0395297
$742$	−3.23020	−0.118584
$743$	15.8180	0.580306	0.290153	−	0.956980i	$-0.406294\pi$
$743$	15.8180	0.580306	0.290153	+	0.956980i	$0.406294\pi$
$744$	−4.51527	−0.165538
$745$	−10.7714	−0.394635
$746$	−16.5102	−0.604483
$747$	−16.1998	−0.592718
$748$	0.263191	0.00962320
$749$	−15.9559	−0.583018
$750$	0.848518	0.0309835
$751$	17.5069	0.638835	0.319418	−	0.947614i	$-0.396513\pi$
$751$	17.5069	0.638835	0.319418	+	0.947614i	$0.396513\pi$
$752$	11.2393	0.409856
$753$	14.5418	0.529932
$754$	33.3755	1.21546
$755$	−13.9038	−0.506011
$756$	4.48019	0.162943
$757$	8.04065	0.292243	0.146121	−	0.989267i	$-0.453321\pi$
$757$	8.04065	0.292243	0.146121	+	0.989267i	$0.453321\pi$
$758$	15.0792	0.547699
$759$	0.0469247	0.00170326
$760$	0.385243	0.0139742
$761$	−17.2291	−0.624556	−0.312278	−	0.949991i	$-0.601092\pi$
$761$	−17.2291	−0.624556	−0.312278	+	0.949991i	$0.601092\pi$
$762$	−8.16217	−0.295684
$763$	−3.14511	−0.113861
$764$	1.91777	0.0693824
$765$	−9.97499	−0.360647
$766$	−17.4852	−0.631765
$767$	−26.2419	−0.947541
$768$	−0.848518	−0.0306183
$769$	30.3157	1.09321	0.546606	−	0.837390i	$-0.315919\pi$
$769$	30.3157	1.09321	0.546606	+	0.837390i	$0.315919\pi$
$770$	0.0601583	0.00216796
$771$	−7.80745	−0.281178
$772$	4.64300	0.167105
$773$	−30.4669	−1.09582	−0.547908	−	0.836538i	$-0.684576\pi$
$773$	−30.4669	−1.09582	−0.547908	+	0.836538i	$0.684576\pi$
$774$	−22.6108	−0.812728
$775$	5.32136	0.191149
$776$	−12.1998	−0.437947
$777$	−2.18272	−0.0783045
$778$	20.6593	0.740673
$779$	−4.60644	−0.165043
$780$	−2.79317	−0.100012
$781$	−0.0601583	−0.00215263
$782$	−4.02178	−0.143819
$783$	−45.4242	−1.62333
$784$	1.00000	0.0357143
$785$	10.5261	0.375691
$786$	−15.0341	−0.536248
$787$	−24.2387	−0.864017	−0.432008	−	0.901870i	$-0.642195\pi$
$787$	−24.2387	−0.864017	−0.432008	+	0.901870i	$0.642195\pi$
$788$	−15.8100	−0.563208
$789$	5.75472	0.204873
$790$	−2.91927	−0.103863
$791$	2.74348	0.0975471
$792$	0.137162	0.00487384
$793$	−11.4094	−0.405159
$794$	19.8432	0.704207
$795$	−2.74088	−0.0972090
$796$	16.3658	0.580070
$797$	2.83727	0.100501	0.0502506	−	0.998737i	$-0.483998\pi$
$797$	2.83727	0.100501	0.0502506	+	0.998737i	$0.483998\pi$
$798$	0.326886	0.0115716
$799$	−49.1717	−1.73957
$800$	1.00000	0.0353553
$801$	23.3728	0.825836
$802$	24.5556	0.867089
$803$	−0.630903	−0.0222641
$804$	8.00020	0.282145
$805$	−0.919272	−0.0324001
$806$	−17.5170	−0.617009
$807$	9.43106	0.331989
$808$	−4.94735	−0.174047
$809$	22.2779	0.783248	0.391624	−	0.920125i	$-0.371913\pi$
$809$	22.2779	0.783248	0.391624	+	0.920125i	$0.371913\pi$
$810$	−3.03853	−0.106763
$811$	49.2426	1.72914	0.864571	−	0.502511i	$-0.167590\pi$
$811$	49.2426	1.72914	0.864571	+	0.502511i	$0.167590\pi$
$812$	−10.1389	−0.355806
$813$	−20.4904	−0.718630
$814$	−0.154750	−0.00542400
$815$	−10.6043	−0.371451
$816$	3.71224	0.129954
$817$	−3.82043	−0.133660
$818$	−25.2092	−0.881419
$819$	7.50541	0.262260
$820$	−11.9572	−0.417565
$821$	12.3109	0.429654	0.214827	−	0.976652i	$-0.431081\pi$
$821$	12.3109	0.429654	0.214827	+	0.976652i	$0.431081\pi$
$822$	3.17942	0.110895
$823$	−33.1726	−1.15632	−0.578162	−	0.815922i	$-0.696230\pi$
$823$	−33.1726	−1.15632	−0.578162	+	0.815922i	$0.696230\pi$
$824$	12.5874	0.438502
$825$	0.0510455	0.00177717
$826$	7.97185	0.277376
$827$	44.8132	1.55831	0.779154	−	0.626832i	$-0.215649\pi$
$827$	44.8132	1.55831	0.779154	+	0.626832i	$0.215649\pi$
$828$	−2.09596	−0.0728395
$829$	−48.6872	−1.69098	−0.845488	−	0.533995i	$-0.820690\pi$
$829$	−48.6872	−1.69098	−0.845488	+	0.533995i	$0.820690\pi$
$830$	−7.10510	−0.246622
$831$	−0.870927	−0.0302121
$832$	−3.29182	−0.114123
$833$	−4.37496	−0.151584
$834$	−7.48702	−0.259254
$835$	0.828797	0.0286817
$836$	0.0231756	0.000801544 0
$837$	23.8407	0.824055
$838$	−3.71153	−0.128213
$839$	47.9871	1.65670	0.828349	−	0.560213i	$-0.189281\pi$
$839$	47.9871	1.65670	0.828349	+	0.560213i	$0.189281\pi$
$840$	0.848518	0.0292767
$841$	73.7972	2.54473
$842$	29.2183	1.00693
$843$	−2.02379	−0.0697030
$844$	−7.25810	−0.249834
$845$	2.16389	0.0744401
$846$	−25.6259	−0.881035
$847$	−10.9964	−0.377840
$848$	−3.23020	−0.110925
$849$	9.59708	0.329371
$850$	−4.37496	−0.150060
$851$	2.36472	0.0810616
$852$	−0.848518	−0.0290698
$853$	19.3267	0.661733	0.330866	−	0.943678i	$-0.392659\pi$
$853$	19.3267	0.661733	0.330866	+	0.943678i	$0.392659\pi$
$854$	3.46597	0.118603
$855$	−0.878360	−0.0300393
$856$	−15.9559	−0.545363
$857$	−36.1125	−1.23358	−0.616791	−	0.787127i	$-0.711567\pi$
$857$	−36.1125	−1.23358	−0.616791	+	0.787127i	$0.711567\pi$
$858$	−0.168033	−0.00573654
$859$	32.5469	1.11049	0.555243	−	0.831688i	$-0.312625\pi$
$859$	32.5469	1.11049	0.555243	+	0.831688i	$0.312625\pi$
$860$	−9.91694	−0.338165
$861$	−10.1459	−0.345772
$862$	13.0370	0.444041
$863$	−6.63825	−0.225969	−0.112984	−	0.993597i	$-0.536041\pi$
$863$	−6.63825	−0.225969	−0.112984	+	0.993597i	$0.536041\pi$
$864$	4.48019	0.152419
$865$	9.77499	0.332360
$866$	8.92811	0.303390
$867$	−1.81610	−0.0616779
$868$	5.32136	0.180619
$869$	−0.175619	−0.00595745
$870$	−8.60304	−0.291670
$871$	31.0367	1.05164
$872$	−3.14511	−0.106507
$873$	27.8158	0.941421
$874$	−0.354143	−0.0119791
$875$	−1.00000	−0.0338062
$876$	−8.89873	−0.300660
$877$	43.2785	1.46141	0.730706	−	0.682692i	$-0.239191\pi$
$877$	43.2785	1.46141	0.730706	+	0.682692i	$0.239191\pi$
$878$	3.00167	0.101301
$879$	−16.1362	−0.544259
$880$	0.0601583	0.00202794
$881$	11.2603	0.379369	0.189685	−	0.981845i	$-0.439253\pi$
$881$	11.2603	0.379369	0.189685	+	0.981845i	$0.439253\pi$
$882$	−2.28002	−0.0767722
$883$	−48.7595	−1.64089	−0.820443	−	0.571728i	$-0.806273\pi$
$883$	−48.7595	−1.64089	−0.820443	+	0.571728i	$0.806273\pi$
$884$	14.4016	0.484379
$885$	6.76426	0.227378
$886$	26.3209	0.884267
$887$	9.89688	0.332305	0.166152	−	0.986100i	$-0.446866\pi$
$887$	9.89688	0.332305	0.166152	+	0.986100i	$0.446866\pi$
$888$	−2.18272	−0.0732471
$889$	9.61932	0.322622
$890$	10.2511	0.343619
$891$	−0.182793	−0.00612378
$892$	19.4863	0.652448
$893$	−4.32987	−0.144894
$894$	−9.13976	−0.305679
$895$	−20.9571	−0.700517
$896$	1.00000	0.0334077
$897$	2.56769	0.0857325
$898$	6.36785	0.212498
$899$	−53.9527	−1.79942
$900$	−2.28002	−0.0760006
$901$	14.1320	0.470805
$902$	−0.719327	−0.0239510
$903$	−8.41471	−0.280024
$904$	2.74348	0.0912470
$905$	−25.7972	−0.857527
$906$	−11.7976	−0.391950
$907$	0.354484	0.0117705	0.00588523	−	0.999983i	$-0.498127\pi$
$907$	0.354484	0.0117705	0.00588523	+	0.999983i	$0.498127\pi$
$908$	−5.88978	−0.195459
$909$	11.2800	0.374135
$910$	3.29182	0.109123
$911$	−3.29390	−0.109132	−0.0545659	−	0.998510i	$-0.517378\pi$
$911$	−3.29390	−0.109132	−0.0545659	+	0.998510i	$0.517378\pi$
$912$	0.326886	0.0108243
$913$	−0.427431	−0.0141459
$914$	11.8180	0.390904
$915$	2.94094	0.0972245
$916$	11.5299	0.380959
$917$	17.7180	0.585101
$918$	−19.6007	−0.646919
$919$	−0.282219	−0.00930955	−0.00465477	−	0.999989i	$-0.501482\pi$
$919$	−0.282219	−0.00930955	−0.00465477	+	0.999989i	$0.501482\pi$
$920$	−0.919272	−0.0303075
$921$	−5.31913	−0.175271
$922$	−17.4220	−0.573763
$923$	−3.29182	−0.108352
$924$	0.0510455	0.00167927
$925$	2.57238	0.0845795
$926$	−22.7745	−0.748415
$927$	−28.6994	−0.942613
$928$	−10.1389	−0.332826
$929$	−26.4731	−0.868554	−0.434277	−	0.900779i	$-0.642996\pi$
$929$	−26.4731	−0.868554	−0.434277	+	0.900779i	$0.642996\pi$
$930$	4.51527	0.148062
$931$	−0.385243	−0.0126258
$932$	18.2626	0.598211
$933$	3.33512	0.109187
$934$	−32.9232	−1.07728
$935$	−0.263191	−0.00860725
$936$	7.50541	0.245322
$937$	54.8428	1.79164	0.895819	−	0.444420i	$-0.146590\pi$
$937$	54.8428	1.79164	0.895819	+	0.444420i	$0.146590\pi$
$938$	−9.42843	−0.307849
$939$	−14.1668	−0.462316
$940$	−11.2393	−0.366587
$941$	0.890406	0.0290264	0.0145132	−	0.999895i	$-0.495380\pi$
$941$	0.890406	0.0290264	0.0145132	+	0.999895i	$0.495380\pi$
$942$	8.93156	0.291006
$943$	10.9919	0.357947
$944$	7.97185	0.259462
$945$	−4.48019	−0.145741
$946$	−0.596587	−0.0193967
$947$	10.3411	0.336040	0.168020	−	0.985784i	$-0.446263\pi$
$947$	10.3411	0.336040	0.168020	+	0.985784i	$0.446263\pi$
$948$	−2.47706	−0.0804510
$949$	−34.5226	−1.12065
$950$	−0.385243	−0.0124989
$951$	−4.60988	−0.149486
$952$	−4.37496	−0.141793
$953$	−38.5823	−1.24980	−0.624902	−	0.780703i	$-0.714861\pi$
$953$	−38.5823	−1.24980	−0.624902	+	0.780703i	$0.714861\pi$
$954$	7.36490	0.238447
$955$	−1.91777	−0.0620575
$956$	−20.6743	−0.668656
$957$	−0.517545	−0.0167298
$958$	0.143090	0.00462303
$959$	−3.74702	−0.120998
$960$	0.848518	0.0273858
$961$	−2.68313	−0.0865525
$962$	−8.46784	−0.273014
$963$	36.3798	1.17232
$964$	−5.72347	−0.184341
$965$	−4.64300	−0.149464
$966$	−0.780019	−0.0250967
$967$	−59.7004	−1.91983	−0.959917	−	0.280283i	$-0.909572\pi$
$967$	−59.7004	−1.91983	−0.959917	+	0.280283i	$0.909572\pi$
$968$	−10.9964	−0.353437
$969$	−1.43011	−0.0459418
$970$	12.1998	0.391712
$971$	48.0503	1.54201	0.771004	−	0.636831i	$-0.219755\pi$
$971$	48.0503	1.54201	0.771004	+	0.636831i	$0.219755\pi$
$972$	−16.0188	−0.513804
$973$	8.82364	0.282873
$974$	2.14399	0.0686979
$975$	2.79317	0.0894531
$976$	3.46597	0.110943
$977$	16.5789	0.530407	0.265204	−	0.964192i	$-0.414561\pi$
$977$	16.5789	0.530407	0.265204	+	0.964192i	$0.414561\pi$
$978$	−8.99792	−0.287722
$979$	0.616692	0.0197096
$980$	−1.00000	−0.0319438
$981$	7.17090	0.228949
$982$	13.9126	0.443970
$983$	−46.1830	−1.47301	−0.736504	−	0.676433i	$-0.763525\pi$
$983$	−46.1830	−1.47301	−0.736504	+	0.676433i	$0.763525\pi$
$984$	−10.1459	−0.323440
$985$	15.8100	0.503748
$986$	44.3573	1.41262
$987$	−9.53678	−0.303559
$988$	1.26815	0.0403453
$989$	9.11637	0.289884
$990$	−0.137162	−0.00435930
$991$	−23.6966	−0.752746	−0.376373	−	0.926468i	$-0.622829\pi$
$991$	−23.6966	−0.752746	−0.376373	+	0.926468i	$0.622829\pi$
$992$	5.32136	0.168953
$993$	23.8813	0.757850
$994$	1.00000	0.0317181
$995$	−16.3658	−0.518830
$996$	−6.02881	−0.191030
$997$	6.12290	0.193914	0.0969571	−	0.995289i	$-0.469089\pi$
$997$	6.12290	0.193914	0.0969571	+	0.995289i	$0.469089\pi$
$998$	5.53421	0.175182
$999$	11.5248	0.364628

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4970.2.a.z.1.3	✓	9

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4970.2.a.z.1.3	✓	9	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:	\( N \)	\(=\)	\( 4970 = 2 \cdot 5 \cdot 7 \cdot 71 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4970.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -0.848518 q^{3} +1.00000 q^{4} -1.00000 q^{5} -0.848518 q^{6} +1.00000 q^{7} +1.00000 q^{8} -2.28002 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -0.848518 q^{3} +1.00000 q^{4} -1.00000 q^{5} -0.848518 q^{6} +1.00000 q^{7} +1.00000 q^{8} -2.28002 q^{9} -1.00000 q^{10} -0.0601583 q^{11} -0.848518 q^{12} -3.29182 q^{13} +1.00000 q^{14} +0.848518 q^{15} +1.00000 q^{16} -4.37496 q^{17} -2.28002 q^{18} -0.385243 q^{19} -1.00000 q^{20} -0.848518 q^{21} -0.0601583 q^{22} +0.919272 q^{23} -0.848518 q^{24} +1.00000 q^{25} -3.29182 q^{26} +4.48019 q^{27} +1.00000 q^{28} -10.1389 q^{29} +0.848518 q^{30} +5.32136 q^{31} +1.00000 q^{32} +0.0510455 q^{33} -4.37496 q^{34} -1.00000 q^{35} -2.28002 q^{36} +2.57238 q^{37} -0.385243 q^{38} +2.79317 q^{39} -1.00000 q^{40} +11.9572 q^{41} -0.848518 q^{42} +9.91694 q^{43} -0.0601583 q^{44} +2.28002 q^{45} +0.919272 q^{46} +11.2393 q^{47} -0.848518 q^{48} +1.00000 q^{49} +1.00000 q^{50} +3.71224 q^{51} -3.29182 q^{52} -3.23020 q^{53} +4.48019 q^{54} +0.0601583 q^{55} +1.00000 q^{56} +0.326886 q^{57} -10.1389 q^{58} +7.97185 q^{59} +0.848518 q^{60} +3.46597 q^{61} +5.32136 q^{62} -2.28002 q^{63} +1.00000 q^{64} +3.29182 q^{65} +0.0510455 q^{66} -9.42843 q^{67} -4.37496 q^{68} -0.780019 q^{69} -1.00000 q^{70} +1.00000 q^{71} -2.28002 q^{72} +10.4874 q^{73} +2.57238 q^{74} -0.848518 q^{75} -0.385243 q^{76} -0.0601583 q^{77} +2.79317 q^{78} +2.91927 q^{79} -1.00000 q^{80} +3.03853 q^{81} +11.9572 q^{82} +7.10510 q^{83} -0.848518 q^{84} +4.37496 q^{85} +9.91694 q^{86} +8.60304 q^{87} -0.0601583 q^{88} -10.2511 q^{89} +2.28002 q^{90} -3.29182 q^{91} +0.919272 q^{92} -4.51527 q^{93} +11.2393 q^{94} +0.385243 q^{95} -0.848518 q^{96} -12.1998 q^{97} +1.00000 q^{98} +0.137162 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 9 q + 9 q^{2} + 4 q^{3} + 9 q^{4} - 9 q^{5} + 4 q^{6} + 9 q^{7} + 9 q^{8} + 7 q^{9}+O(q^{10}) \) 9 * q + 9 * q^2 + 4 * q^3 + 9 * q^4 - 9 * q^5 + 4 * q^6 + 9 * q^7 + 9 * q^8 + 7 * q^9	\( 9 q + 9 q^{2} + 4 q^{3} + 9 q^{4} - 9 q^{5} + 4 q^{6} + 9 q^{7} + 9 q^{8} + 7 q^{9} - 9 q^{10} - 2 q^{11} + 4 q^{12} + 11 q^{13} + 9 q^{14} - 4 q^{15} + 9 q^{16} + 9 q^{17} + 7 q^{18} + 9 q^{19} - 9 q^{20} + 4 q^{21} - 2 q^{22} + 2 q^{23} + 4 q^{24} + 9 q^{25} + 11 q^{26} + 7 q^{27} + 9 q^{28} + 2 q^{29} - 4 q^{30} + 18 q^{31} + 9 q^{32} + 8 q^{33} + 9 q^{34} - 9 q^{35} + 7 q^{36} + 15 q^{37} + 9 q^{38} - 7 q^{39} - 9 q^{40} + 15 q^{41} + 4 q^{42} + 7 q^{43} - 2 q^{44} - 7 q^{45} + 2 q^{46} + 12 q^{47} + 4 q^{48} + 9 q^{49} + 9 q^{50} + 4 q^{51} + 11 q^{52} + 3 q^{53} + 7 q^{54} + 2 q^{55} + 9 q^{56} + 9 q^{57} + 2 q^{58} + 24 q^{59} - 4 q^{60} + 25 q^{61} + 18 q^{62} + 7 q^{63} + 9 q^{64} - 11 q^{65} + 8 q^{66} - 4 q^{67} + 9 q^{68} + 3 q^{69} - 9 q^{70} + 9 q^{71} + 7 q^{72} + 32 q^{73} + 15 q^{74} + 4 q^{75} + 9 q^{76} - 2 q^{77} - 7 q^{78} + 20 q^{79} - 9 q^{80} - 7 q^{81} + 15 q^{82} + 11 q^{83} + 4 q^{84} - 9 q^{85} + 7 q^{86} + 26 q^{87} - 2 q^{88} + 10 q^{89} - 7 q^{90} + 11 q^{91} + 2 q^{92} + 32 q^{93} + 12 q^{94} - 9 q^{95} + 4 q^{96} + 19 q^{97} + 9 q^{98} - 7 q^{99}+O(q^{100}) \) 9 * q + 9 * q^2 + 4 * q^3 + 9 * q^4 - 9 * q^5 + 4 * q^6 + 9 * q^7 + 9 * q^8 + 7 * q^9 - 9 * q^10 - 2 * q^11 + 4 * q^12 + 11 * q^13 + 9 * q^14 - 4 * q^15 + 9 * q^16 + 9 * q^17 + 7 * q^18 + 9 * q^19 - 9 * q^20 + 4 * q^21 - 2 * q^22 + 2 * q^23 + 4 * q^24 + 9 * q^25 + 11 * q^26 + 7 * q^27 + 9 * q^28 + 2 * q^29 - 4 * q^30 + 18 * q^31 + 9 * q^32 + 8 * q^33 + 9 * q^34 - 9 * q^35 + 7 * q^36 + 15 * q^37 + 9 * q^38 - 7 * q^39 - 9 * q^40 + 15 * q^41 + 4 * q^42 + 7 * q^43 - 2 * q^44 - 7 * q^45 + 2 * q^46 + 12 * q^47 + 4 * q^48 + 9 * q^49 + 9 * q^50 + 4 * q^51 + 11 * q^52 + 3 * q^53 + 7 * q^54 + 2 * q^55 + 9 * q^56 + 9 * q^57 + 2 * q^58 + 24 * q^59 - 4 * q^60 + 25 * q^61 + 18 * q^62 + 7 * q^63 + 9 * q^64 - 11 * q^65 + 8 * q^66 - 4 * q^67 + 9 * q^68 + 3 * q^69 - 9 * q^70 + 9 * q^71 + 7 * q^72 + 32 * q^73 + 15 * q^74 + 4 * q^75 + 9 * q^76 - 2 * q^77 - 7 * q^78 + 20 * q^79 - 9 * q^80 - 7 * q^81 + 15 * q^82 + 11 * q^83 + 4 * q^84 - 9 * q^85 + 7 * q^86 + 26 * q^87 - 2 * q^88 + 10 * q^89 - 7 * q^90 + 11 * q^91 + 2 * q^92 + 32 * q^93 + 12 * q^94 - 9 * q^95 + 4 * q^96 + 19 * q^97 + 9 * q^98 - 7 * q^99

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