LMFDB - Embedded newform 4029.2.a.k.1.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4029,2,Mod(1,4029)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4029, 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("4029.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4029 = 3 \cdot 17 \cdot 79 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4029.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:	$32.1717269744$
Analytic rank:	$0$
Dimension:	$31$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Character	$\chi$	$=$	4029.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.28064 q^{2} +1.00000 q^{3} +3.20133 q^{4} +2.67486 q^{5} -2.28064 q^{6} -3.60745 q^{7} -2.73981 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-2.28064 q^{2} +1.00000 q^{3} +3.20133 q^{4} +2.67486 q^{5} -2.28064 q^{6} -3.60745 q^{7} -2.73981 q^{8} +1.00000 q^{9} -6.10039 q^{10} -4.75294 q^{11} +3.20133 q^{12} -2.82803 q^{13} +8.22732 q^{14} +2.67486 q^{15} -0.154140 q^{16} +1.00000 q^{17} -2.28064 q^{18} +7.19726 q^{19} +8.56310 q^{20} -3.60745 q^{21} +10.8398 q^{22} -7.90378 q^{23} -2.73981 q^{24} +2.15485 q^{25} +6.44974 q^{26} +1.00000 q^{27} -11.5487 q^{28} +3.76541 q^{29} -6.10039 q^{30} +10.2473 q^{31} +5.83115 q^{32} -4.75294 q^{33} -2.28064 q^{34} -9.64942 q^{35} +3.20133 q^{36} -11.2301 q^{37} -16.4144 q^{38} -2.82803 q^{39} -7.32859 q^{40} +3.99765 q^{41} +8.22732 q^{42} -2.71838 q^{43} -15.2158 q^{44} +2.67486 q^{45} +18.0257 q^{46} +7.28191 q^{47} -0.154140 q^{48} +6.01373 q^{49} -4.91444 q^{50} +1.00000 q^{51} -9.05348 q^{52} -10.1934 q^{53} -2.28064 q^{54} -12.7134 q^{55} +9.88373 q^{56} +7.19726 q^{57} -8.58756 q^{58} +1.09614 q^{59} +8.56310 q^{60} +8.22066 q^{61} -23.3703 q^{62} -3.60745 q^{63} -12.9905 q^{64} -7.56458 q^{65} +10.8398 q^{66} -1.58454 q^{67} +3.20133 q^{68} -7.90378 q^{69} +22.0069 q^{70} +12.1262 q^{71} -2.73981 q^{72} -11.5812 q^{73} +25.6118 q^{74} +2.15485 q^{75} +23.0408 q^{76} +17.1460 q^{77} +6.44974 q^{78} +1.00000 q^{79} -0.412301 q^{80} +1.00000 q^{81} -9.11721 q^{82} +14.9668 q^{83} -11.5487 q^{84} +2.67486 q^{85} +6.19965 q^{86} +3.76541 q^{87} +13.0222 q^{88} +5.52915 q^{89} -6.10039 q^{90} +10.2020 q^{91} -25.3026 q^{92} +10.2473 q^{93} -16.6074 q^{94} +19.2516 q^{95} +5.83115 q^{96} +9.40808 q^{97} -13.7152 q^{98} -4.75294 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 31 q + 4 q^{2} + 31 q^{3} + 34 q^{4} + 11 q^{5} + 4 q^{6} + 4 q^{7} + 12 q^{8} + 31 q^{9}+O(q^{10}) $ 31 * q + 4 * q^2 + 31 * q^3 + 34 * q^4 + 11 * q^5 + 4 * q^6 + 4 * q^7 + 12 * q^8 + 31 * q^9	\( 31 q + 4 q^{2} + 31 q^{3} + 34 q^{4} + 11 q^{5} + 4 q^{6} + 4 q^{7} + 12 q^{8} + 31 q^{9} + 5 q^{10} + 26 q^{11} + 34 q^{12} + 7 q^{13} + 19 q^{14} + 11 q^{15} + 40 q^{16} + 31 q^{17} + 4 q^{18} + 32 q^{19} + 23 q^{20} + 4 q^{21} + 2 q^{22} + 29 q^{23} + 12 q^{24} + 32 q^{25} + 13 q^{26} + 31 q^{27} - 13 q^{28} + 25 q^{29} + 5 q^{30} + 22 q^{31} + 28 q^{32} + 26 q^{33} + 4 q^{34} + 20 q^{35} + 34 q^{36} - 4 q^{37} + 19 q^{38} + 7 q^{39} - 3 q^{40} + 33 q^{41} + 19 q^{42} + 6 q^{43} + 30 q^{44} + 11 q^{45} - 11 q^{46} + 23 q^{47} + 40 q^{48} + 31 q^{49} + 6 q^{50} + 31 q^{51} - 7 q^{52} + 12 q^{53} + 4 q^{54} + 40 q^{56} + 32 q^{57} + 9 q^{58} + 27 q^{59} + 23 q^{60} - 4 q^{61} + 25 q^{62} + 4 q^{63} + 10 q^{64} + 54 q^{65} + 2 q^{66} + 34 q^{68} + 29 q^{69} - 59 q^{70} + 35 q^{71} + 12 q^{72} + 5 q^{73} + 48 q^{74} + 32 q^{75} + 32 q^{76} + 42 q^{77} + 13 q^{78} + 31 q^{79} + 24 q^{80} + 31 q^{81} + 5 q^{82} + 67 q^{83} - 13 q^{84} + 11 q^{85} - 20 q^{86} + 25 q^{87} - 7 q^{88} + 22 q^{89} + 5 q^{90} + 16 q^{91} + 57 q^{92} + 22 q^{93} + 45 q^{94} + 73 q^{95} + 28 q^{96} - 13 q^{97} - 19 q^{98} + 26 q^{99}+O(q^{100}) \) 31 * q + 4 * q^2 + 31 * q^3 + 34 * q^4 + 11 * q^5 + 4 * q^6 + 4 * q^7 + 12 * q^8 + 31 * q^9 + 5 * q^10 + 26 * q^11 + 34 * q^12 + 7 * q^13 + 19 * q^14 + 11 * q^15 + 40 * q^16 + 31 * q^17 + 4 * q^18 + 32 * q^19 + 23 * q^20 + 4 * q^21 + 2 * q^22 + 29 * q^23 + 12 * q^24 + 32 * q^25 + 13 * q^26 + 31 * q^27 - 13 * q^28 + 25 * q^29 + 5 * q^30 + 22 * q^31 + 28 * q^32 + 26 * q^33 + 4 * q^34 + 20 * q^35 + 34 * q^36 - 4 * q^37 + 19 * q^38 + 7 * q^39 - 3 * q^40 + 33 * q^41 + 19 * q^42 + 6 * q^43 + 30 * q^44 + 11 * q^45 - 11 * q^46 + 23 * q^47 + 40 * q^48 + 31 * q^49 + 6 * q^50 + 31 * q^51 - 7 * q^52 + 12 * q^53 + 4 * q^54 + 40 * q^56 + 32 * q^57 + 9 * q^58 + 27 * q^59 + 23 * q^60 - 4 * q^61 + 25 * q^62 + 4 * q^63 + 10 * q^64 + 54 * q^65 + 2 * q^66 + 34 * q^68 + 29 * q^69 - 59 * q^70 + 35 * q^71 + 12 * q^72 + 5 * q^73 + 48 * q^74 + 32 * q^75 + 32 * q^76 + 42 * q^77 + 13 * q^78 + 31 * q^79 + 24 * q^80 + 31 * q^81 + 5 * q^82 + 67 * q^83 - 13 * q^84 + 11 * q^85 - 20 * q^86 + 25 * q^87 - 7 * q^88 + 22 * q^89 + 5 * q^90 + 16 * q^91 + 57 * q^92 + 22 * q^93 + 45 * q^94 + 73 * q^95 + 28 * q^96 - 13 * q^97 - 19 * q^98 + 26 * 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 $

$2$	−2.28064	−1.61266	−0.806329	−	0.591467i	$-0.798549\pi$
$2$	−2.28064	−1.61266	−0.806329	+	0.591467i	$0.798549\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	3.20133	1.60067
$5$	2.67486	1.19623	0.598116	−	0.801410i	$-0.295916\pi$
$5$	2.67486	1.19623	0.598116	+	0.801410i	$0.295916\pi$
$6$	−2.28064	−0.931069
$7$	−3.60745	−1.36349	−0.681745	−	0.731590i	$-0.738779\pi$
$7$	−3.60745	−1.36349	−0.681745	+	0.731590i	$0.738779\pi$
$8$	−2.73981	−0.968668
$9$	1.00000	0.333333
$10$	−6.10039	−1.92911
$11$	−4.75294	−1.43307	−0.716533	−	0.697553i	$-0.754272\pi$
$11$	−4.75294	−1.43307	−0.716533	+	0.697553i	$0.754272\pi$
$12$	3.20133	0.924145
$13$	−2.82803	−0.784356	−0.392178	−	0.919889i	$-0.628278\pi$
$13$	−2.82803	−0.784356	−0.392178	+	0.919889i	$0.628278\pi$
$14$	8.22732	2.19884
$15$	2.67486	0.690645
$16$	−0.154140	−0.0385349
$17$	1.00000	0.242536
$17$	1.00000	0.242536
$18$	−2.28064	−0.537553
$19$	7.19726	1.65117	0.825583	−	0.564281i	$-0.190846\pi$
$19$	7.19726	1.65117	0.825583	+	0.564281i	$0.190846\pi$
$20$	8.56310	1.91477
$21$	−3.60745	−0.787211
$22$	10.8398	2.31105
$23$	−7.90378	−1.64805	−0.824026	−	0.566552i	$-0.808277\pi$
$23$	−7.90378	−1.64805	−0.824026	+	0.566552i	$0.808277\pi$
$24$	−2.73981	−0.559261
$25$	2.15485	0.430970
$26$	6.44974	1.26490
$27$	1.00000	0.192450
$28$	−11.5487	−2.18249
$29$	3.76541	0.699220	0.349610	−	0.936895i	$-0.386314\pi$
$29$	3.76541	0.699220	0.349610	+	0.936895i	$0.386314\pi$
$30$	−6.10039	−1.11377
$31$	10.2473	1.84046	0.920231	−	0.391376i	$-0.128001\pi$
$31$	10.2473	1.84046	0.920231	+	0.391376i	$0.128001\pi$
$32$	5.83115	1.03081
$33$	−4.75294	−0.827381
$34$	−2.28064	−0.391127
$35$	−9.64942	−1.63105
$36$	3.20133	0.533555
$37$	−11.2301	−1.84621	−0.923107	−	0.384543i	$-0.874359\pi$
$37$	−11.2301	−1.84621	−0.923107	+	0.384543i	$0.874359\pi$
$38$	−16.4144	−2.66277
$39$	−2.82803	−0.452848
$40$	−7.32859	−1.15875
$41$	3.99765	0.624328	0.312164	−	0.950028i	$-0.398946\pi$
$41$	3.99765	0.624328	0.312164	+	0.950028i	$0.398946\pi$
$42$	8.22732	1.26950
$43$	−2.71838	−0.414549	−0.207274	−	0.978283i	$-0.566459\pi$
$43$	−2.71838	−0.414549	−0.207274	+	0.978283i	$0.566459\pi$
$44$	−15.2158	−2.29386
$45$	2.67486	0.398744
$46$	18.0257	2.65774
$47$	7.28191	1.06218	0.531088	−	0.847317i	$-0.321783\pi$
$47$	7.28191	1.06218	0.531088	+	0.847317i	$0.321783\pi$
$48$	−0.154140	−0.0222481
$49$	6.01373	0.859104
$50$	−4.91444	−0.695007
$51$	1.00000	0.140028
$52$	−9.05348	−1.25549
$53$	−10.1934	−1.40017	−0.700087	−	0.714057i	$-0.746856\pi$
$53$	−10.1934	−1.40017	−0.700087	+	0.714057i	$0.746856\pi$
$54$	−2.28064	−0.310356
$55$	−12.7134	−1.71428
$56$	9.88373	1.32077
$57$	7.19726	0.953301
$58$	−8.58756	−1.12760
$59$	1.09614	0.142706	0.0713529	−	0.997451i	$-0.477268\pi$
$59$	1.09614	0.142706	0.0713529	+	0.997451i	$0.477268\pi$
$60$	8.56310	1.10549
$61$	8.22066	1.05255	0.526274	−	0.850315i	$-0.323589\pi$
$61$	8.22066	1.05255	0.526274	+	0.850315i	$0.323589\pi$
$62$	−23.3703	−2.96803
$63$	−3.60745	−0.454497
$64$	−12.9905	−1.62381
$65$	−7.56458	−0.938271
$66$	10.8398	1.33428
$67$	−1.58454	−0.193582	−0.0967912	−	0.995305i	$-0.530858\pi$
$67$	−1.58454	−0.193582	−0.0967912	+	0.995305i	$0.530858\pi$
$68$	3.20133	0.388218
$69$	−7.90378	−0.951503
$70$	22.0069	2.63032
$71$	12.1262	1.43912	0.719560	−	0.694430i	$-0.244343\pi$
$71$	12.1262	1.43912	0.719560	+	0.694430i	$0.244343\pi$
$72$	−2.73981	−0.322889
$73$	−11.5812	−1.35548	−0.677741	−	0.735301i	$-0.737041\pi$
$73$	−11.5812	−1.35548	−0.677741	+	0.735301i	$0.737041\pi$
$74$	25.6118	2.97731
$75$	2.15485	0.248821
$76$	23.0408	2.64296
$77$	17.1460	1.95397
$78$	6.44974	0.730289
$79$	1.00000	0.112509
$79$	1.00000	0.112509
$80$	−0.412301	−0.0460967
$81$	1.00000	0.111111
$82$	−9.11721	−1.00683
$83$	14.9668	1.64282	0.821412	−	0.570336i	$-0.193187\pi$
$83$	14.9668	1.64282	0.821412	+	0.570336i	$0.193187\pi$
$84$	−11.5487	−1.26006
$85$	2.67486	0.290129
$86$	6.19965	0.668526
$87$	3.76541	0.403695
$88$	13.0222	1.38817
$89$	5.52915	0.586089	0.293045	−	0.956099i	$-0.405332\pi$
$89$	5.52915	0.586089	0.293045	+	0.956099i	$0.405332\pi$
$90$	−6.10039	−0.643037
$91$	10.2020	1.06946
$92$	−25.3026	−2.63798
$93$	10.2473	1.06259
$94$	−16.6074	−1.71293
$95$	19.2516	1.97518
$96$	5.83115	0.595140
$97$	9.40808	0.955245	0.477623	−	0.878565i	$-0.341499\pi$
$97$	9.40808	0.955245	0.477623	+	0.878565i	$0.341499\pi$
$98$	−13.7152	−1.38544
$99$	−4.75294	−0.477689
$100$	6.89839	0.689839
$101$	−1.63157	−0.162347	−0.0811735	−	0.996700i	$-0.525867\pi$
$101$	−1.63157	−0.162347	−0.0811735	+	0.996700i	$0.525867\pi$
$102$	−2.28064	−0.225817
$103$	3.45584	0.340514	0.170257	−	0.985400i	$-0.445540\pi$
$103$	3.45584	0.340514	0.170257	+	0.985400i	$0.445540\pi$
$104$	7.74827	0.759781
$105$	−9.64942	−0.941687
$106$	23.2476	2.25800
$107$	4.86976	0.470778	0.235389	−	0.971901i	$-0.424364\pi$
$107$	4.86976	0.470778	0.235389	+	0.971901i	$0.424364\pi$
$108$	3.20133	0.308048
$109$	−4.34182	−0.415871	−0.207936	−	0.978143i	$-0.566674\pi$
$109$	−4.34182	−0.415871	−0.207936	+	0.978143i	$0.566674\pi$
$110$	28.9948	2.76455
$111$	−11.2301	−1.06591
$112$	0.556052	0.0525420
$113$	14.8190	1.39405	0.697026	−	0.717046i	$-0.254506\pi$
$113$	14.8190	1.39405	0.697026	+	0.717046i	$0.254506\pi$
$114$	−16.4144	−1.53735
$115$	−21.1415	−1.97145
$116$	12.0543	1.11922
$117$	−2.82803	−0.261452
$118$	−2.49991	−0.230136
$119$	−3.60745	−0.330695
$120$	−7.32859	−0.669006
$121$	11.5905	1.05368
$122$	−18.7484	−1.69740
$123$	3.99765	0.360456
$124$	32.8049	2.94596
$125$	−7.61036	−0.680692
$126$	8.22732	0.732948
$127$	1.09995	0.0976048	0.0488024	−	0.998808i	$-0.484460\pi$
$127$	1.09995	0.0976048	0.0488024	+	0.998808i	$0.484460\pi$
$128$	17.9644	1.58784
$129$	−2.71838	−0.239340
$130$	17.2521	1.51311
$131$	18.1027	1.58164	0.790820	−	0.612049i	$-0.209655\pi$
$131$	18.1027	1.58164	0.790820	+	0.612049i	$0.209655\pi$
$132$	−15.2158	−1.32436
$133$	−25.9638	−2.25135
$134$	3.61377	0.312182
$135$	2.67486	0.230215
$136$	−2.73981	−0.234937
$137$	2.48460	0.212273	0.106137	−	0.994352i	$-0.466152\pi$
$137$	2.48460	0.212273	0.106137	+	0.994352i	$0.466152\pi$
$138$	18.0257	1.53445
$139$	14.2415	1.20795	0.603973	−	0.797005i	$-0.293584\pi$
$139$	14.2415	1.20795	0.603973	+	0.797005i	$0.293584\pi$
$140$	−30.8910	−2.61076
$141$	7.28191	0.613248
$142$	−27.6556	−2.32081
$143$	13.4415	1.12403
$144$	−0.154140	−0.0128450
$145$	10.0719	0.836429
$146$	26.4127	2.18593
$147$	6.01373	0.496004
$148$	−35.9512	−2.95517
$149$	−4.21059	−0.344945	−0.172472	−	0.985014i	$-0.555176\pi$
$149$	−4.21059	−0.344945	−0.172472	+	0.985014i	$0.555176\pi$
$150$	−4.91444	−0.401263
$151$	4.14682	0.337464	0.168732	−	0.985662i	$-0.446033\pi$
$151$	4.14682	0.337464	0.168732	+	0.985662i	$0.446033\pi$
$152$	−19.7191	−1.59943
$153$	1.00000	0.0808452
$154$	−39.1040	−3.15109
$155$	27.4099	2.20162
$156$	−9.05348	−0.724858
$157$	19.3117	1.54124	0.770620	−	0.637294i	$-0.219946\pi$
$157$	19.3117	1.54124	0.770620	+	0.637294i	$0.219946\pi$
$158$	−2.28064	−0.181438
$159$	−10.1934	−0.808391
$160$	15.5975	1.23309
$161$	28.5125	2.24710
$162$	−2.28064	−0.179184
$163$	−10.7248	−0.840031	−0.420016	−	0.907517i	$-0.637975\pi$
$163$	−10.7248	−0.840031	−0.420016	+	0.907517i	$0.637975\pi$
$164$	12.7978	0.999340
$165$	−12.7134	−0.989740
$166$	−34.1340	−2.64931
$167$	8.79439	0.680530	0.340265	−	0.940330i	$-0.389483\pi$
$167$	8.79439	0.680530	0.340265	+	0.940330i	$0.389483\pi$
$168$	9.88373	0.762547
$169$	−5.00222	−0.384786
$170$	−6.10039	−0.467878
$171$	7.19726	0.550389
$172$	−8.70243	−0.663554
$173$	15.6994	1.19360	0.596802	−	0.802388i	$-0.296438\pi$
$173$	15.6994	1.19360	0.596802	+	0.802388i	$0.296438\pi$
$174$	−8.58756	−0.651022
$175$	−7.77352	−0.587623
$176$	0.732617	0.0552231
$177$	1.09614	0.0823912
$178$	−12.6100	−0.945161
$179$	14.1097	1.05461	0.527305	−	0.849676i	$-0.323202\pi$
$179$	14.1097	1.05461	0.527305	+	0.849676i	$0.323202\pi$
$180$	8.56310	0.638256
$181$	−9.59645	−0.713299	−0.356649	−	0.934238i	$-0.616081\pi$
$181$	−9.59645	−0.713299	−0.356649	+	0.934238i	$0.616081\pi$
$182$	−23.2671	−1.72467
$183$	8.22066	0.607689
$184$	21.6548	1.59642
$185$	−30.0388	−2.20850
$186$	−23.3703	−1.71360
$187$	−4.75294	−0.347570
$188$	23.3118	1.70019
$189$	−3.60745	−0.262404
$190$	−43.9061	−3.18528
$191$	−16.8447	−1.21884	−0.609421	−	0.792847i	$-0.708598\pi$
$191$	−16.8447	−1.21884	−0.609421	+	0.792847i	$0.708598\pi$
$192$	−12.9905	−0.937508
$193$	−12.2947	−0.884995	−0.442497	−	0.896770i	$-0.645907\pi$
$193$	−12.2947	−0.884995	−0.442497	+	0.896770i	$0.645907\pi$
$194$	−21.4565	−1.54048
$195$	−7.56458	−0.541711
$196$	19.2519	1.37514
$197$	0.733843	0.0522841	0.0261421	−	0.999658i	$-0.491678\pi$
$197$	0.733843	0.0522841	0.0261421	+	0.999658i	$0.491678\pi$
$198$	10.8398	0.770349
$199$	2.02286	0.143397	0.0716984	−	0.997426i	$-0.477158\pi$
$199$	2.02286	0.143397	0.0716984	+	0.997426i	$0.477158\pi$
$200$	−5.90388	−0.417467
$201$	−1.58454	−0.111765
$202$	3.72102	0.261810
$203$	−13.5836	−0.953379
$204$	3.20133	0.224138
$205$	10.6931	0.746841
$206$	−7.88155	−0.549133
$207$	−7.90378	−0.549351
$208$	0.435912	0.0302251
$209$	−34.2082	−2.36623
$210$	22.0069	1.51862
$211$	−27.1196	−1.86699	−0.933496	−	0.358588i	$-0.883258\pi$
$211$	−27.1196	−1.86699	−0.933496	+	0.358588i	$0.883258\pi$
$212$	−32.6325	−2.24121
$213$	12.1262	0.830877
$214$	−11.1062	−0.759203
$215$	−7.27127	−0.495896
$216$	−2.73981	−0.186420
$217$	−36.9665	−2.50945
$218$	9.90215	0.670658
$219$	−11.5812	−0.782588
$220$	−40.6999	−2.74399
$221$	−2.82803	−0.190234
$222$	25.6118	1.71895
$223$	−10.2494	−0.686351	−0.343175	−	0.939271i	$-0.611502\pi$
$223$	−10.2494	−0.686351	−0.343175	+	0.939271i	$0.611502\pi$
$224$	−21.0356	−1.40550
$225$	2.15485	0.143657
$226$	−33.7968	−2.24813
$227$	16.4170	1.08964	0.544819	−	0.838554i	$-0.316599\pi$
$227$	16.4170	1.08964	0.544819	+	0.838554i	$0.316599\pi$
$228$	23.0408	1.52592
$229$	10.9550	0.723927	0.361963	−	0.932192i	$-0.382107\pi$
$229$	10.9550	0.723927	0.361963	+	0.932192i	$0.382107\pi$
$230$	48.2161	3.17928
$231$	17.1460	1.12813
$232$	−10.3165	−0.677312
$233$	27.2344	1.78419	0.892093	−	0.451852i	$-0.149237\pi$
$233$	27.2344	1.78419	0.892093	+	0.451852i	$0.149237\pi$
$234$	6.44974	0.421632
$235$	19.4781	1.27061
$236$	3.50912	0.228424
$237$	1.00000	0.0649570
$238$	8.22732	0.533298
$239$	11.1314	0.720031	0.360016	−	0.932946i	$-0.382771\pi$
$239$	11.1314	0.720031	0.360016	+	0.932946i	$0.382771\pi$
$240$	−0.412301	−0.0266139
$241$	−6.97632	−0.449384	−0.224692	−	0.974430i	$-0.572138\pi$
$241$	−6.97632	−0.449384	−0.224692	+	0.974430i	$0.572138\pi$
$242$	−26.4338	−1.69923
$243$	1.00000	0.0641500
$244$	26.3171	1.68478
$245$	16.0859	1.02769
$246$	−9.11721	−0.581292
$247$	−20.3541	−1.29510
$248$	−28.0755	−1.78280
$249$	14.9668	0.948485
$250$	17.3565	1.09772
$251$	12.5102	0.789638	0.394819	−	0.918759i	$-0.370807\pi$
$251$	12.5102	0.789638	0.394819	+	0.918759i	$0.370807\pi$
$252$	−11.5487	−0.727497
$253$	37.5662	2.36177
$254$	−2.50859	−0.157403
$255$	2.67486	0.167506
$256$	−14.9893	−0.936834
$257$	−19.8944	−1.24098	−0.620488	−	0.784216i	$-0.713065\pi$
$257$	−19.8944	−1.24098	−0.620488	+	0.784216i	$0.713065\pi$
$258$	6.19965	0.385973
$259$	40.5120	2.51729
$260$	−24.2167	−1.50186
$261$	3.76541	0.233073
$262$	−41.2858	−2.55064
$263$	5.61631	0.346316	0.173158	−	0.984894i	$-0.444603\pi$
$263$	5.61631	0.346316	0.173158	+	0.984894i	$0.444603\pi$
$264$	13.0222	0.801458
$265$	−27.2659	−1.67493
$266$	59.2142	3.63065
$267$	5.52915	0.338379
$268$	−5.07264	−0.309861
$269$	−4.67648	−0.285130	−0.142565	−	0.989785i	$-0.545535\pi$
$269$	−4.67648	−0.285130	−0.142565	+	0.989785i	$0.545535\pi$
$270$	−6.10039	−0.371258
$271$	−5.49377	−0.333723	−0.166861	−	0.985980i	$-0.553363\pi$
$271$	−5.49377	−0.333723	−0.166861	+	0.985980i	$0.553363\pi$
$272$	−0.154140	−0.00934609
$273$	10.2020	0.617454
$274$	−5.66647	−0.342324
$275$	−10.2419	−0.617609
$276$	−25.3026	−1.52304
$277$	−4.86185	−0.292120	−0.146060	−	0.989276i	$-0.546659\pi$
$277$	−4.86185	−0.292120	−0.146060	+	0.989276i	$0.546659\pi$
$278$	−32.4797	−1.94800
$279$	10.2473	0.613487
$280$	26.4376	1.57995
$281$	−19.5207	−1.16451	−0.582254	−	0.813007i	$-0.697829\pi$
$281$	−19.5207	−1.16451	−0.582254	+	0.813007i	$0.697829\pi$
$282$	−16.6074	−0.988959
$283$	11.3990	0.677602	0.338801	−	0.940858i	$-0.389979\pi$
$283$	11.3990	0.677602	0.338801	+	0.940858i	$0.389979\pi$
$284$	38.8201	2.30355
$285$	19.2516	1.14037
$286$	−30.6552	−1.81268
$287$	−14.4213	−0.851265
$288$	5.83115	0.343604
$289$	1.00000	0.0588235
$290$	−22.9705	−1.34887
$291$	9.40808	0.551511
$292$	−37.0754	−2.16967
$293$	28.0156	1.63669	0.818343	−	0.574730i	$-0.194893\pi$
$293$	28.0156	1.63669	0.818343	+	0.574730i	$0.194893\pi$
$294$	−13.7152	−0.799885
$295$	2.93203	0.170709
$296$	30.7683	1.78837
$297$	−4.75294	−0.275794
$298$	9.60285	0.556278
$299$	22.3522	1.29266
$300$	6.89839	0.398279
$301$	9.80643	0.565233
$302$	−9.45742	−0.544213
$303$	−1.63157	−0.0937311
$304$	−1.10938	−0.0636275
$305$	21.9891	1.25909
$306$	−2.28064	−0.130376
$307$	24.2347	1.38315	0.691573	−	0.722306i	$-0.256918\pi$
$307$	24.2347	1.38315	0.691573	+	0.722306i	$0.256918\pi$
$308$	54.8901	3.12766
$309$	3.45584	0.196596
$310$	−62.5122	−3.55046
$311$	7.00815	0.397396	0.198698	−	0.980061i	$-0.436329\pi$
$311$	7.00815	0.397396	0.198698	+	0.980061i	$0.436329\pi$
$312$	7.74827	0.438659
$313$	9.00979	0.509263	0.254632	−	0.967038i	$-0.418046\pi$
$313$	9.00979	0.509263	0.254632	+	0.967038i	$0.418046\pi$
$314$	−44.0431	−2.48549
$315$	−9.64942	−0.543683
$316$	3.20133	0.180089
$317$	−7.95241	−0.446652	−0.223326	−	0.974744i	$-0.571691\pi$
$317$	−7.95241	−0.446652	−0.223326	+	0.974744i	$0.571691\pi$
$318$	23.2476	1.30366
$319$	−17.8968	−1.00203
$320$	−34.7477	−1.94246
$321$	4.86976	0.271804
$322$	−65.0269	−3.62381
$323$	7.19726	0.400467
$324$	3.20133	0.177852
$325$	−6.09399	−0.338034
$326$	24.4594	1.35468
$327$	−4.34182	−0.240103
$328$	−10.9528	−0.604767
$329$	−26.2692	−1.44827
$330$	28.9948	1.59611
$331$	−31.3687	−1.72418	−0.862091	−	0.506754i	$-0.830845\pi$
$331$	−31.3687	−1.72418	−0.862091	+	0.506754i	$0.830845\pi$
$332$	47.9138	2.62961
$333$	−11.2301	−0.615405
$334$	−20.0569	−1.09746
$335$	−4.23841	−0.231569
$336$	0.556052	0.0303351
$337$	0.391866	0.0213463	0.0106731	−	0.999943i	$-0.496603\pi$
$337$	0.391866	0.0213463	0.0106731	+	0.999943i	$0.496603\pi$
$338$	11.4083	0.620529
$339$	14.8190	0.804856
$340$	8.56310	0.464399
$341$	−48.7046	−2.63750
$342$	−16.4144	−0.887589
$343$	3.55793	0.192110
$344$	7.44784	0.401560
$345$	−21.1415	−1.13822
$346$	−35.8048	−1.92488
$347$	31.2815	1.67928	0.839639	−	0.543145i	$-0.182767\pi$
$347$	31.2815	1.67928	0.839639	+	0.543145i	$0.182767\pi$
$348$	12.0543	0.646180
$349$	34.3713	1.83985	0.919927	−	0.392091i	$-0.128248\pi$
$349$	34.3713	1.83985	0.919927	+	0.392091i	$0.128248\pi$
$350$	17.7286	0.947635
$351$	−2.82803	−0.150949
$352$	−27.7151	−1.47722
$353$	5.00856	0.266579	0.133289	−	0.991077i	$-0.457446\pi$
$353$	5.00856	0.266579	0.133289	+	0.991077i	$0.457446\pi$
$354$	−2.49991	−0.132869
$355$	32.4359	1.72152
$356$	17.7007	0.938133
$357$	−3.60745	−0.190927
$358$	−32.1793	−1.70073
$359$	−17.6801	−0.933119	−0.466560	−	0.884490i	$-0.654507\pi$
$359$	−17.6801	−0.933119	−0.466560	+	0.884490i	$0.654507\pi$
$360$	−7.32859	−0.386251
$361$	32.8006	1.72635
$362$	21.8861	1.15031
$363$	11.5905	0.608343
$364$	32.6600	1.71185
$365$	−30.9782	−1.62147
$366$	−18.7484	−0.979994
$367$	0.783792	0.0409136	0.0204568	−	0.999791i	$-0.493488\pi$
$367$	0.783792	0.0409136	0.0204568	+	0.999791i	$0.493488\pi$
$368$	1.21829	0.0635075
$369$	3.99765	0.208109
$370$	68.5079	3.56155
$371$	36.7723	1.90912
$372$	32.8049	1.70085
$373$	−12.0319	−0.622986	−0.311493	−	0.950248i	$-0.600829\pi$
$373$	−12.0319	−0.622986	−0.311493	+	0.950248i	$0.600829\pi$
$374$	10.8398	0.560511
$375$	−7.61036	−0.392998
$376$	−19.9510	−1.02890
$377$	−10.6487	−0.548437
$378$	8.22732	0.423167
$379$	−11.2666	−0.578725	−0.289362	−	0.957220i	$-0.593443\pi$
$379$	−11.2666	−0.578725	−0.289362	+	0.957220i	$0.593443\pi$
$380$	61.6309	3.16160
$381$	1.09995	0.0563522
$382$	38.4168	1.96558
$383$	−24.0861	−1.23074	−0.615370	−	0.788238i	$-0.710993\pi$
$383$	−24.0861	−1.23074	−0.615370	+	0.788238i	$0.710993\pi$
$384$	17.9644	0.916741
$385$	45.8632	2.33740
$386$	28.0399	1.42719
$387$	−2.71838	−0.138183
$388$	30.1184	1.52903
$389$	−19.6932	−0.998486	−0.499243	−	0.866462i	$-0.666389\pi$
$389$	−19.6932	−0.998486	−0.499243	+	0.866462i	$0.666389\pi$
$390$	17.2521	0.873595
$391$	−7.90378	−0.399711
$392$	−16.4765	−0.832187
$393$	18.1027	0.913160
$394$	−1.67363	−0.0843164
$395$	2.67486	0.134587
$396$	−15.2158	−0.764620
$397$	−24.9800	−1.25371	−0.626854	−	0.779137i	$-0.715658\pi$
$397$	−24.9800	−1.25371	−0.626854	+	0.779137i	$0.715658\pi$
$398$	−4.61342	−0.231250
$399$	−25.9638	−1.29982
$400$	−0.332148	−0.0166074
$401$	22.8544	1.14129	0.570646	−	0.821196i	$-0.306693\pi$
$401$	22.8544	1.14129	0.570646	+	0.821196i	$0.306693\pi$
$402$	3.61377	0.180238
$403$	−28.9796	−1.44358
$404$	−5.22319	−0.259863
$405$	2.67486	0.132915
$406$	30.9793	1.53747
$407$	53.3760	2.64575
$408$	−2.73981	−0.135641
$409$	−10.5353	−0.520939	−0.260470	−	0.965482i	$-0.583877\pi$
$409$	−10.5353	−0.520939	−0.260470	+	0.965482i	$0.583877\pi$
$410$	−24.3872	−1.20440
$411$	2.48460	0.122556
$412$	11.0633	0.545050
$413$	−3.95429	−0.194578
$414$	18.0257	0.885915
$415$	40.0341	1.96520
$416$	−16.4907	−0.808523
$417$	14.2415	0.697407
$418$	78.0167	3.81592
$419$	19.7915	0.966878	0.483439	−	0.875378i	$-0.339387\pi$
$419$	19.7915	0.966878	0.483439	+	0.875378i	$0.339387\pi$
$420$	−30.8910	−1.50733
$421$	4.49625	0.219134	0.109567	−	0.993979i	$-0.465054\pi$
$421$	4.49625	0.219134	0.109567	+	0.993979i	$0.465054\pi$
$422$	61.8502	3.01082
$423$	7.28191	0.354059
$424$	27.9280	1.35631
$425$	2.15485	0.104526
$426$	−27.6556	−1.33992
$427$	−29.6557	−1.43514
$428$	15.5897	0.753558
$429$	13.4415	0.648961
$430$	16.5832	0.799711
$431$	20.0253	0.964585	0.482292	−	0.876010i	$-0.339804\pi$
$431$	20.0253	0.964585	0.482292	+	0.876010i	$0.339804\pi$
$432$	−0.154140	−0.00741605
$433$	−15.5180	−0.745746	−0.372873	−	0.927882i	$-0.621627\pi$
$433$	−15.5180	−0.745746	−0.372873	+	0.927882i	$0.621627\pi$
$434$	84.3074	4.04689
$435$	10.0719	0.482912
$436$	−13.8996	−0.665671
$437$	−56.8856	−2.72121
$438$	26.4127	1.26205
$439$	−10.3652	−0.494703	−0.247351	−	0.968926i	$-0.579560\pi$
$439$	−10.3652	−0.494703	−0.247351	+	0.968926i	$0.579560\pi$
$440$	34.8324	1.66057
$441$	6.01373	0.286368
$442$	6.44974	0.306783
$443$	17.7311	0.842428	0.421214	−	0.906961i	$-0.361604\pi$
$443$	17.7311	0.842428	0.421214	+	0.906961i	$0.361604\pi$
$444$	−35.9512	−1.70617
$445$	14.7897	0.701098
$446$	23.3752	1.10685
$447$	−4.21059	−0.199154
$448$	46.8626	2.21405
$449$	7.17495	0.338607	0.169303	−	0.985564i	$-0.445848\pi$
$449$	7.17495	0.338607	0.169303	+	0.985564i	$0.445848\pi$
$450$	−4.91444	−0.231669
$451$	−19.0006	−0.894704
$452$	47.4404	2.23141
$453$	4.14682	0.194835
$454$	−37.4414	−1.75721
$455$	27.2889	1.27932
$456$	−19.7191	−0.923433
$457$	23.3766	1.09351	0.546756	−	0.837292i	$-0.315863\pi$
$457$	23.3766	1.09351	0.546756	+	0.837292i	$0.315863\pi$
$458$	−24.9844	−1.16745
$459$	1.00000	0.0466760
$460$	−67.6808	−3.15564
$461$	−20.8454	−0.970866	−0.485433	−	0.874274i	$-0.661338\pi$
$461$	−20.8454	−0.970866	−0.485433	+	0.874274i	$0.661338\pi$
$462$	−39.1040	−1.81928
$463$	19.5630	0.909168	0.454584	−	0.890704i	$-0.349788\pi$
$463$	19.5630	0.909168	0.454584	+	0.890704i	$0.349788\pi$
$464$	−0.580400	−0.0269444
$465$	27.4099	1.27110
$466$	−62.1120	−2.87728
$467$	−32.1144	−1.48608	−0.743038	−	0.669250i	$-0.766616\pi$
$467$	−32.1144	−1.48608	−0.743038	+	0.669250i	$0.766616\pi$
$468$	−9.05348	−0.418497
$469$	5.71616	0.263948
$470$	−44.4225	−2.04906
$471$	19.3117	0.889836
$472$	−3.00322	−0.138235
$473$	12.9203	0.594076
$474$	−2.28064	−0.104753
$475$	15.5090	0.711603
$476$	−11.5487	−0.529332
$477$	−10.1934	−0.466725
$478$	−25.3868	−1.16116
$479$	28.6345	1.30834	0.654172	−	0.756346i	$-0.273017\pi$
$479$	28.6345	1.30834	0.654172	+	0.756346i	$0.273017\pi$
$480$	15.5975	0.711925
$481$	31.7591	1.44809
$482$	15.9105	0.724703
$483$	28.5125	1.29737
$484$	37.1050	1.68659
$485$	25.1652	1.14269
$486$	−2.28064	−0.103452
$487$	11.3785	0.515609	0.257804	−	0.966197i	$-0.417001\pi$
$487$	11.3785	0.515609	0.257804	+	0.966197i	$0.417001\pi$
$488$	−22.5230	−1.01957
$489$	−10.7248	−0.484992
$490$	−36.6861	−1.65731
$491$	−1.47855	−0.0667258	−0.0333629	−	0.999443i	$-0.510622\pi$
$491$	−1.47855	−0.0667258	−0.0333629	+	0.999443i	$0.510622\pi$
$492$	12.7978	0.576969
$493$	3.76541	0.169586
$494$	46.4205	2.08856
$495$	−12.7134	−0.571427
$496$	−1.57951	−0.0709220
$497$	−43.7449	−1.96223
$498$	−34.1340	−1.52958
$499$	10.6851	0.478332	0.239166	−	0.970979i	$-0.423126\pi$
$499$	10.6851	0.478332	0.239166	+	0.970979i	$0.423126\pi$
$500$	−24.3633	−1.08956
$501$	8.79439	0.392904
$502$	−28.5314	−1.27342
$503$	15.3226	0.683200	0.341600	−	0.939845i	$-0.389031\pi$
$503$	15.3226	0.683200	0.341600	+	0.939845i	$0.389031\pi$
$504$	9.88373	0.440256
$505$	−4.36421	−0.194205
$506$	−85.6752	−3.80873
$507$	−5.00222	−0.222156
$508$	3.52131	0.156233
$509$	−9.58075	−0.424659	−0.212330	−	0.977198i	$-0.568105\pi$
$509$	−9.58075	−0.424659	−0.212330	+	0.977198i	$0.568105\pi$
$510$	−6.10039	−0.270130
$511$	41.7788	1.84819
$512$	−1.74344	−0.0770498
$513$	7.19726	0.317767
$514$	45.3719	2.00127
$515$	9.24388	0.407334
$516$	−8.70243	−0.383103
$517$	−34.6105	−1.52217
$518$	−92.3934	−4.05953
$519$	15.6994	0.689128
$520$	20.7255	0.908873
$521$	−25.6248	−1.12264	−0.561322	−	0.827597i	$-0.689707\pi$
$521$	−25.6248	−1.12264	−0.561322	+	0.827597i	$0.689707\pi$
$522$	−8.58756	−0.375868
$523$	19.2731	0.842755	0.421377	−	0.906885i	$-0.361547\pi$
$523$	19.2731	0.842755	0.421377	+	0.906885i	$0.361547\pi$
$524$	57.9527	2.53168
$525$	−7.77352	−0.339264
$526$	−12.8088	−0.558490
$527$	10.2473	0.446377
$528$	0.732617	0.0318831
$529$	39.4697	1.71608
$530$	62.1839	2.70109
$531$	1.09614	0.0475686
$532$	−83.1188	−3.60365
$533$	−11.3055	−0.489695
$534$	−12.6100	−0.545689
$535$	13.0259	0.563159
$536$	4.34133	0.187517
$537$	14.1097	0.608880
$538$	10.6654	0.459817
$539$	−28.5829	−1.23115
$540$	8.56310	0.368497
$541$	34.2905	1.47426	0.737131	−	0.675750i	$-0.236180\pi$
$541$	34.2905	1.47426	0.737131	+	0.675750i	$0.236180\pi$
$542$	12.5293	0.538181
$543$	−9.59645	−0.411823
$544$	5.83115	0.250009
$545$	−11.6138	−0.497478
$546$	−23.2671	−0.995741
$547$	23.4414	1.00228	0.501142	−	0.865365i	$-0.332914\pi$
$547$	23.4414	1.00228	0.501142	+	0.865365i	$0.332914\pi$
$548$	7.95401	0.339779
$549$	8.22066	0.350849
$550$	23.3581	0.995992
$551$	27.1007	1.15453
$552$	21.6548	0.921691
$553$	−3.60745	−0.153405
$554$	11.0881	0.471090
$555$	−30.0388	−1.27508
$556$	45.5916	1.93352
$557$	−13.8969	−0.588829	−0.294414	−	0.955678i	$-0.595125\pi$
$557$	−13.8969	−0.588829	−0.294414	+	0.955678i	$0.595125\pi$
$558$	−23.3703	−0.989345
$559$	7.68767	0.325154
$560$	1.48736	0.0628523
$561$	−4.75294	−0.200669
$562$	44.5198	1.87795
$563$	37.6222	1.58559	0.792794	−	0.609489i	$-0.208626\pi$
$563$	37.6222	1.58559	0.792794	+	0.609489i	$0.208626\pi$
$564$	23.3118	0.981604
$565$	39.6386	1.66761
$566$	−25.9971	−1.09274
$567$	−3.60745	−0.151499
$568$	−33.2236	−1.39403
$569$	17.1420	0.718631	0.359316	−	0.933216i	$-0.383010\pi$
$569$	17.1420	0.718631	0.359316	+	0.933216i	$0.383010\pi$
$570$	−43.9061	−1.83902
$571$	−22.0795	−0.923999	−0.461999	−	0.886880i	$-0.652868\pi$
$571$	−22.0795	−0.923999	−0.461999	+	0.886880i	$0.652868\pi$
$572$	43.0307	1.79920
$573$	−16.8447	−0.703699
$574$	32.8899	1.37280
$575$	−17.0315	−0.710261
$576$	−12.9905	−0.541271
$577$	7.95890	0.331333	0.165667	−	0.986182i	$-0.447022\pi$
$577$	7.95890	0.331333	0.165667	+	0.986182i	$0.447022\pi$
$578$	−2.28064	−0.0948622
$579$	−12.2947	−0.510952
$580$	32.2436	1.33884
$581$	−53.9922	−2.23997
$582$	−21.4565	−0.889399
$583$	48.4488	2.00654
$584$	31.7304	1.31301
$585$	−7.56458	−0.312757
$586$	−63.8935	−2.63942
$587$	−41.2626	−1.70309	−0.851545	−	0.524282i	$-0.824334\pi$
$587$	−41.2626	−1.70309	−0.851545	+	0.524282i	$0.824334\pi$
$588$	19.2519	0.793937
$589$	73.7522	3.03891
$590$	−6.68691	−0.275296
$591$	0.733843	0.0301863
$592$	1.73100	0.0711437
$593$	−1.56993	−0.0644692	−0.0322346	−	0.999480i	$-0.510262\pi$
$593$	−1.56993	−0.0644692	−0.0322346	+	0.999480i	$0.510262\pi$
$594$	10.8398	0.444761
$595$	−9.64942	−0.395588
$596$	−13.4795	−0.552141
$597$	2.02286	0.0827902
$598$	−50.9773	−2.08462
$599$	−4.24121	−0.173291	−0.0866455	−	0.996239i	$-0.527615\pi$
$599$	−4.24121	−0.173291	−0.0866455	+	0.996239i	$0.527615\pi$
$600$	−5.90388	−0.241025
$601$	1.90328	0.0776363	0.0388182	−	0.999246i	$-0.487641\pi$
$601$	1.90328	0.0776363	0.0388182	+	0.999246i	$0.487641\pi$
$602$	−22.3650	−0.911528
$603$	−1.58454	−0.0645274
$604$	13.2754	0.540166
$605$	31.0029	1.26045
$606$	3.72102	0.151156
$607$	−11.0660	−0.449154	−0.224577	−	0.974456i	$-0.572100\pi$
$607$	−11.0660	−0.449154	−0.224577	+	0.974456i	$0.572100\pi$
$608$	41.9684	1.70204
$609$	−13.5836	−0.550434
$610$	−50.1492	−2.03048
$611$	−20.5935	−0.833124
$612$	3.20133	0.129406
$613$	−22.9468	−0.926812	−0.463406	−	0.886146i	$-0.653373\pi$
$613$	−22.9468	−0.926812	−0.463406	+	0.886146i	$0.653373\pi$
$614$	−55.2707	−2.23054
$615$	10.6931	0.431189
$616$	−46.9768	−1.89275
$617$	16.6111	0.668736	0.334368	−	0.942443i	$-0.391477\pi$
$617$	16.6111	0.668736	0.334368	+	0.942443i	$0.391477\pi$
$618$	−7.88155	−0.317042
$619$	36.1536	1.45314	0.726568	−	0.687095i	$-0.241114\pi$
$619$	36.1536	1.45314	0.726568	+	0.687095i	$0.241114\pi$
$620$	87.7483	3.52405
$621$	−7.90378	−0.317168
$622$	−15.9831	−0.640863
$623$	−19.9462	−0.799126
$624$	0.435912	0.0174505
$625$	−31.1309	−1.24523
$626$	−20.5481	−0.821268
$627$	−34.2082	−1.36614
$628$	61.8231	2.46701
$629$	−11.2301	−0.447773
$630$	22.0069	0.876775
$631$	19.5470	0.778154	0.389077	−	0.921205i	$-0.372794\pi$
$631$	19.5470	0.778154	0.389077	+	0.921205i	$0.372794\pi$
$632$	−2.73981	−0.108984
$633$	−27.1196	−1.07791
$634$	18.1366	0.720297
$635$	2.94221	0.116758
$636$	−32.6325	−1.29396
$637$	−17.0070	−0.673843
$638$	40.8162	1.61593
$639$	12.1262	0.479707
$640$	48.0521	1.89943
$641$	−3.41916	−0.135049	−0.0675243	−	0.997718i	$-0.521510\pi$
$641$	−3.41916	−0.135049	−0.0675243	+	0.997718i	$0.521510\pi$
$642$	−11.1062	−0.438326
$643$	−6.95943	−0.274453	−0.137227	−	0.990540i	$-0.543819\pi$
$643$	−6.95943	−0.274453	−0.137227	+	0.990540i	$0.543819\pi$
$644$	91.2781	3.59686
$645$	−7.27127	−0.286306
$646$	−16.4144	−0.645816
$647$	36.9986	1.45456	0.727282	−	0.686338i	$-0.240783\pi$
$647$	36.9986	1.45456	0.727282	+	0.686338i	$0.240783\pi$
$648$	−2.73981	−0.107630
$649$	−5.20991	−0.204507
$650$	13.8982	0.545133
$651$	−36.9665	−1.44883
$652$	−34.3336	−1.34461
$653$	−2.59348	−0.101491	−0.0507454	−	0.998712i	$-0.516160\pi$
$653$	−2.59348	−0.101491	−0.0507454	+	0.998712i	$0.516160\pi$
$654$	9.90215	0.387205
$655$	48.4221	1.89201
$656$	−0.616196	−0.0240584
$657$	−11.5812	−0.451827
$658$	59.9106	2.33556
$659$	−8.26032	−0.321776	−0.160888	−	0.986973i	$-0.551436\pi$
$659$	−8.26032	−0.321776	−0.160888	+	0.986973i	$0.551436\pi$
$660$	−40.6999	−1.58424
$661$	−15.3132	−0.595613	−0.297807	−	0.954626i	$-0.596255\pi$
$661$	−15.3132	−0.595613	−0.297807	+	0.954626i	$0.596255\pi$
$662$	71.5409	2.78051
$663$	−2.82803	−0.109832
$664$	−41.0063	−1.59135
$665$	−69.4494	−2.69313
$666$	25.6118	0.992437
$667$	−29.7610	−1.15235
$668$	28.1537	1.08930
$669$	−10.2494	−0.396265
$670$	9.66631	0.373442
$671$	−39.0723	−1.50837
$672$	−21.0356	−0.811467
$673$	−46.0965	−1.77689	−0.888444	−	0.458985i	$-0.848213\pi$
$673$	−46.0965	−1.77689	−0.888444	+	0.458985i	$0.848213\pi$
$674$	−0.893706	−0.0344243
$675$	2.15485	0.0829402
$676$	−16.0138	−0.615914
$677$	8.43950	0.324356	0.162178	−	0.986761i	$-0.448148\pi$
$677$	8.43950	0.324356	0.162178	+	0.986761i	$0.448148\pi$
$678$	−33.7968	−1.29796
$679$	−33.9392	−1.30247
$680$	−7.32859	−0.281039
$681$	16.4170	0.629102
$682$	111.078	4.25339
$683$	18.2588	0.698652	0.349326	−	0.937001i	$-0.386411\pi$
$683$	18.2588	0.698652	0.349326	+	0.937001i	$0.386411\pi$
$684$	23.0408	0.880988
$685$	6.64593	0.253928
$686$	−8.11436	−0.309808
$687$	10.9550	0.417959
$688$	0.419010	0.0159746
$689$	28.8274	1.09823
$690$	48.2161	1.83556
$691$	22.9533	0.873184	0.436592	−	0.899660i	$-0.356185\pi$
$691$	22.9533	0.873184	0.436592	+	0.899660i	$0.356185\pi$
$692$	50.2590	1.91056
$693$	17.1460	0.651324
$694$	−71.3419	−2.70810
$695$	38.0938	1.44498
$696$	−10.3165	−0.391046
$697$	3.99765	0.151422
$698$	−78.3886	−2.96705
$699$	27.2344	1.03010
$700$	−24.8856	−0.940588
$701$	1.00287	0.0378780	0.0189390	−	0.999821i	$-0.493971\pi$
$701$	1.00287	0.0378780	0.0189390	+	0.999821i	$0.493971\pi$
$702$	6.44974	0.243430
$703$	−80.8259	−3.04841
$704$	61.7431	2.32703
$705$	19.4781	0.733586
$706$	−11.4227	−0.429900
$707$	5.88580	0.221358
$708$	3.50912	0.131881
$709$	35.9356	1.34959	0.674795	−	0.738005i	$-0.264232\pi$
$709$	35.9356	1.34959	0.674795	+	0.738005i	$0.264232\pi$
$710$	−73.9748	−2.77623
$711$	1.00000	0.0375029
$712$	−15.1488	−0.567726
$713$	−80.9921	−3.03318
$714$	8.22732	0.307900
$715$	35.9540	1.34460
$716$	45.1699	1.68808
$717$	11.1314	0.415710
$718$	40.3220	1.50480
$719$	−52.1302	−1.94413	−0.972065	−	0.234713i	$-0.924585\pi$
$719$	−52.1302	−1.94413	−0.972065	+	0.234713i	$0.924585\pi$
$720$	−0.412301	−0.0153656
$721$	−12.4668	−0.464288
$722$	−74.8065	−2.78401
$723$	−6.97632	−0.259452
$724$	−30.7214	−1.14175
$725$	8.11390	0.301343
$726$	−26.4338	−0.981049
$727$	29.6731	1.10052	0.550258	−	0.834995i	$-0.314530\pi$
$727$	29.6731	1.10052	0.550258	+	0.834995i	$0.314530\pi$
$728$	−27.9515	−1.03595
$729$	1.00000	0.0370370
$730$	70.6501	2.61488
$731$	−2.71838	−0.100543
$732$	26.3171	0.972706
$733$	34.1023	1.25960	0.629798	−	0.776759i	$-0.283138\pi$
$733$	34.1023	1.25960	0.629798	+	0.776759i	$0.283138\pi$
$734$	−1.78755	−0.0659796
$735$	16.0859	0.593336
$736$	−46.0882	−1.69883
$737$	7.53123	0.277416
$738$	−9.11721	−0.335609
$739$	−47.1048	−1.73278	−0.866389	−	0.499369i	$-0.833565\pi$
$739$	−47.1048	−1.73278	−0.866389	+	0.499369i	$0.833565\pi$
$740$	−96.1643	−3.53507
$741$	−20.3541	−0.747727
$742$	−83.8645	−3.07876
$743$	−18.7353	−0.687333	−0.343666	−	0.939092i	$-0.611669\pi$
$743$	−18.7353	−0.687333	−0.343666	+	0.939092i	$0.611669\pi$
$744$	−28.0755	−1.02930
$745$	−11.2627	−0.412634
$746$	27.4404	1.00466
$747$	14.9668	0.547608
$748$	−15.2158	−0.556343
$749$	−17.5674	−0.641901
$750$	17.3565	0.633771
$751$	29.1066	1.06211	0.531057	−	0.847336i	$-0.321795\pi$
$751$	29.1066	1.06211	0.531057	+	0.847336i	$0.321795\pi$
$752$	−1.12243	−0.0409309
$753$	12.5102	0.455898
$754$	24.2859	0.884441
$755$	11.0921	0.403685
$756$	−11.5487	−0.420021
$757$	−38.3125	−1.39249	−0.696245	−	0.717804i	$-0.745147\pi$
$757$	−38.3125	−1.39249	−0.696245	+	0.717804i	$0.745147\pi$
$758$	25.6950	0.933285
$759$	37.5662	1.36357
$760$	−52.7458	−1.91329
$761$	−15.3461	−0.556295	−0.278147	−	0.960538i	$-0.589720\pi$
$761$	−15.3461	−0.556295	−0.278147	+	0.960538i	$0.589720\pi$
$762$	−2.50859	−0.0908768
$763$	15.6629	0.567036
$764$	−53.9256	−1.95096
$765$	2.67486	0.0967096
$766$	54.9317	1.98476
$767$	−3.09993	−0.111932
$768$	−14.9893	−0.540881
$769$	−34.5021	−1.24418	−0.622089	−	0.782946i	$-0.713716\pi$
$769$	−34.5021	−1.24418	−0.622089	+	0.782946i	$0.713716\pi$
$770$	−104.597	−3.76943
$771$	−19.8944	−0.716478
$772$	−39.3595	−1.41658
$773$	−30.9623	−1.11364	−0.556819	−	0.830634i	$-0.687978\pi$
$773$	−30.9623	−1.11364	−0.556819	+	0.830634i	$0.687978\pi$
$774$	6.19965	0.222842
$775$	22.0813	0.793184
$776$	−25.7763	−0.925316
$777$	40.5120	1.45336
$778$	44.9132	1.61022
$779$	28.7721	1.03087
$780$	−24.2167	−0.867098
$781$	−57.6354	−2.06236
$782$	18.0257	0.644598
$783$	3.76541	0.134565
$784$	−0.926954	−0.0331055
$785$	51.6560	1.84368
$786$	−41.2858	−1.47261
$787$	−5.77261	−0.205771	−0.102886	−	0.994693i	$-0.532808\pi$
$787$	−5.77261	−0.205771	−0.102886	+	0.994693i	$0.532808\pi$
$788$	2.34927	0.0836894
$789$	5.61631	0.199946
$790$	−6.10039	−0.217042
$791$	−53.4587	−1.90077
$792$	13.0222	0.462722
$793$	−23.2483	−0.825572
$794$	56.9704	2.02180
$795$	−27.2659	−0.967023
$796$	6.47585	0.229530
$797$	−27.9204	−0.988992	−0.494496	−	0.869180i	$-0.664647\pi$
$797$	−27.9204	−0.988992	−0.494496	+	0.869180i	$0.664647\pi$
$798$	59.2142	2.09616
$799$	7.28191	0.257616
$800$	12.5653	0.444249
$801$	5.52915	0.195363
$802$	−52.1226	−1.84051
$803$	55.0450	1.94250
$804$	−5.07264	−0.178898
$805$	76.2669	2.68805
$806$	66.0921	2.32799
$807$	−4.67648	−0.164620
$808$	4.47018	0.157260
$809$	−5.24753	−0.184493	−0.0922466	−	0.995736i	$-0.529405\pi$
$809$	−5.24753	−0.184493	−0.0922466	+	0.995736i	$0.529405\pi$
$810$	−6.10039	−0.214346
$811$	17.8684	0.627444	0.313722	−	0.949515i	$-0.398424\pi$
$811$	17.8684	0.627444	0.313722	+	0.949515i	$0.398424\pi$
$812$	−43.4855	−1.52604
$813$	−5.49377	−0.192675
$814$	−121.731	−4.26669
$815$	−28.6873	−1.00487
$816$	−0.154140	−0.00539597
$817$	−19.5649	−0.684489
$818$	24.0274	0.840097
$819$	10.2020	0.356487
$820$	34.2323	1.19544
$821$	−17.9143	−0.625214	−0.312607	−	0.949883i	$-0.601202\pi$
$821$	−17.9143	−0.625214	−0.312607	+	0.949883i	$0.601202\pi$
$822$	−5.66647	−0.197641
$823$	−34.9092	−1.21686	−0.608428	−	0.793609i	$-0.708200\pi$
$823$	−34.9092	−1.21686	−0.608428	+	0.793609i	$0.708200\pi$
$824$	−9.46835	−0.329846
$825$	−10.2419	−0.356577
$826$	9.01832	0.313788
$827$	−8.52974	−0.296608	−0.148304	−	0.988942i	$-0.547381\pi$
$827$	−8.52974	−0.296608	−0.148304	+	0.988942i	$0.547381\pi$
$828$	−25.3026	−0.879327
$829$	−44.8678	−1.55832	−0.779161	−	0.626823i	$-0.784355\pi$
$829$	−44.8678	−1.55832	−0.779161	+	0.626823i	$0.784355\pi$
$830$	−91.3035	−3.16919
$831$	−4.86185	−0.168656
$832$	36.7376	1.27365
$833$	6.01373	0.208363
$834$	−32.4797	−1.12468
$835$	23.5237	0.814072
$836$	−109.512	−3.78754
$837$	10.2473	0.354197
$838$	−45.1373	−1.55924
$839$	−36.0127	−1.24330	−0.621649	−	0.783296i	$-0.713537\pi$
$839$	−36.0127	−1.24330	−0.621649	+	0.783296i	$0.713537\pi$
$840$	26.4376	0.912182
$841$	−14.8217	−0.511092
$842$	−10.2543	−0.353388
$843$	−19.5207	−0.672329
$844$	−86.8189	−2.98843
$845$	−13.3802	−0.460293
$846$	−16.6074	−0.570976
$847$	−41.8121	−1.43668
$848$	1.57121	0.0539556
$849$	11.3990	0.391214
$850$	−4.91444	−0.168564
$851$	88.7601	3.04266
$852$	38.8201	1.32996
$853$	−25.4854	−0.872603	−0.436302	−	0.899800i	$-0.643712\pi$
$853$	−25.4854	−0.872603	−0.436302	+	0.899800i	$0.643712\pi$
$854$	67.6339	2.31439
$855$	19.2516	0.658392
$856$	−13.3422	−0.456027
$857$	−1.34025	−0.0457819	−0.0228910	−	0.999738i	$-0.507287\pi$
$857$	−1.34025	−0.0457819	−0.0228910	+	0.999738i	$0.507287\pi$
$858$	−30.6552	−1.04655
$859$	−0.493425	−0.0168355	−0.00841773	−	0.999965i	$-0.502679\pi$
$859$	−0.493425	−0.0168355	−0.00841773	+	0.999965i	$0.502679\pi$
$860$	−23.2777	−0.793764
$861$	−14.4213	−0.491478
$862$	−45.6706	−1.55555
$863$	−26.2936	−0.895044	−0.447522	−	0.894273i	$-0.647693\pi$
$863$	−26.2936	−0.895044	−0.447522	+	0.894273i	$0.647693\pi$
$864$	5.83115	0.198380
$865$	41.9937	1.42783
$866$	35.3909	1.20263
$867$	1.00000	0.0339618
$868$	−118.342	−4.01679
$869$	−4.75294	−0.161233
$870$	−22.9705	−0.778773
$871$	4.48113	0.151837
$872$	11.8958	0.402841
$873$	9.40808	0.318415
$874$	129.736	4.38838
$875$	27.4540	0.928116
$876$	−37.0754	−1.25266
$877$	37.1018	1.25284	0.626420	−	0.779486i	$-0.284519\pi$
$877$	37.1018	1.25284	0.626420	+	0.779486i	$0.284519\pi$
$878$	23.6393	0.797787
$879$	28.0156	0.944941
$880$	1.95964	0.0660596
$881$	23.6374	0.796365	0.398183	−	0.917306i	$-0.369641\pi$
$881$	23.6374	0.796365	0.398183	+	0.917306i	$0.369641\pi$
$882$	−13.7152	−0.461814
$883$	23.3225	0.784865	0.392433	−	0.919781i	$-0.371634\pi$
$883$	23.3225	0.784865	0.392433	+	0.919781i	$0.371634\pi$
$884$	−9.05348	−0.304501
$885$	2.93203	0.0985590
$886$	−40.4382	−1.35855
$887$	39.9203	1.34039	0.670196	−	0.742184i	$-0.266210\pi$
$887$	39.9203	1.34039	0.670196	+	0.742184i	$0.266210\pi$
$888$	30.7683	1.03252
$889$	−3.96802	−0.133083
$890$	−33.7300	−1.13063
$891$	−4.75294	−0.159230
$892$	−32.8117	−1.09862
$893$	52.4099	1.75383
$894$	9.60285	0.321167
$895$	37.7415	1.26156
$896$	−64.8057	−2.16501
$897$	22.3522	0.746317
$898$	−16.3635	−0.546057
$899$	38.5852	1.28689
$900$	6.89839	0.229946
$901$	−10.1934	−0.339592
$902$	43.3336	1.44285
$903$	9.80643	0.326338
$904$	−40.6011	−1.35037
$905$	−25.6691	−0.853270
$906$	−9.45742	−0.314202
$907$	51.1793	1.69938	0.849691	−	0.527281i	$-0.176789\pi$
$907$	51.1793	1.69938	0.849691	+	0.527281i	$0.176789\pi$
$908$	52.5564	1.74414
$909$	−1.63157	−0.0541157
$910$	−62.2362	−2.06311
$911$	8.16327	0.270461	0.135231	−	0.990814i	$-0.456822\pi$
$911$	8.16327	0.270461	0.135231	+	0.990814i	$0.456822\pi$
$912$	−1.10938	−0.0367354
$913$	−71.1365	−2.35428
$914$	−53.3137	−1.76346
$915$	21.9891	0.726936
$916$	35.0706	1.15877
$917$	−65.3046	−2.15655
$918$	−2.28064	−0.0752724
$919$	−39.4561	−1.30154	−0.650768	−	0.759277i	$-0.725553\pi$
$919$	−39.4561	−1.30154	−0.650768	+	0.759277i	$0.725553\pi$
$920$	57.9236	1.90968
$921$	24.2347	0.798560
$922$	47.5409	1.56568
$923$	−34.2934	−1.12878
$924$	54.8901	1.80575
$925$	−24.1991	−0.795663
$926$	−44.6161	−1.46618
$927$	3.45584	0.113505
$928$	21.9567	0.720764
$929$	−2.23502	−0.0733287	−0.0366643	−	0.999328i	$-0.511673\pi$
$929$	−2.23502	−0.0733287	−0.0366643	+	0.999328i	$0.511673\pi$
$930$	−62.5122	−2.04986
$931$	43.2824	1.41852
$932$	87.1864	2.85588
$933$	7.00815	0.229437
$934$	73.2414	2.39653
$935$	−12.7134	−0.415774
$936$	7.74827	0.253260
$937$	−2.39393	−0.0782064	−0.0391032	−	0.999235i	$-0.512450\pi$
$937$	−2.39393	−0.0782064	−0.0391032	+	0.999235i	$0.512450\pi$
$938$	−13.0365	−0.425657
$939$	9.00979	0.294023
$940$	62.3557	2.03382
$941$	34.1571	1.11349	0.556745	−	0.830683i	$-0.312050\pi$
$941$	34.1571	1.11349	0.556745	+	0.830683i	$0.312050\pi$
$942$	−44.0431	−1.43500
$943$	−31.5965	−1.02892
$944$	−0.168959	−0.00549916
$945$	−9.64942	−0.313896
$946$	−29.4666	−0.958042
$947$	3.25604	0.105807	0.0529036	−	0.998600i	$-0.483152\pi$
$947$	3.25604	0.105807	0.0529036	+	0.998600i	$0.483152\pi$
$948$	3.20133	0.103974
$949$	32.7522	1.06318
$950$	−35.3705	−1.14757
$951$	−7.95241	−0.257875
$952$	9.88373	0.320334
$953$	47.3449	1.53365	0.766825	−	0.641856i	$-0.221835\pi$
$953$	47.3449	1.53365	0.766825	+	0.641856i	$0.221835\pi$
$954$	23.2476	0.752668
$955$	−45.0572	−1.45802
$956$	35.6353	1.15253
$957$	−17.8968	−0.578522
$958$	−65.3051	−2.10991
$959$	−8.96306	−0.289432
$960$	−34.7477	−1.12148
$961$	74.0063	2.38730
$962$	−72.4311	−2.33527
$963$	4.86976	0.156926
$964$	−22.3335	−0.719314
$965$	−32.8867	−1.05866
$966$	−65.0269	−2.09221
$967$	−18.8957	−0.607646	−0.303823	−	0.952729i	$-0.598263\pi$
$967$	−18.8957	−0.607646	−0.303823	+	0.952729i	$0.598263\pi$
$968$	−31.7557	−1.02067
$969$	7.19726	0.231209
$970$	−57.3929	−1.84278
$971$	59.1280	1.89751	0.948755	−	0.316014i	$-0.102345\pi$
$971$	59.1280	1.89751	0.948755	+	0.316014i	$0.102345\pi$
$972$	3.20133	0.102683
$973$	−51.3754	−1.64702
$974$	−25.9503	−0.831501
$975$	−6.09399	−0.195164
$976$	−1.26713	−0.0405598
$977$	−18.3485	−0.587021	−0.293510	−	0.955956i	$-0.594823\pi$
$977$	−18.3485	−0.587021	−0.293510	+	0.955956i	$0.594823\pi$
$978$	24.4594	0.782127
$979$	−26.2798	−0.839905
$980$	51.4962	1.64498
$981$	−4.34182	−0.138624
$982$	3.37203	0.107606
$983$	−40.5263	−1.29259	−0.646294	−	0.763088i	$-0.723682\pi$
$983$	−40.5263	−1.29259	−0.646294	+	0.763088i	$0.723682\pi$
$984$	−10.9528	−0.349162
$985$	1.96292	0.0625439
$986$	−8.58756	−0.273484
$987$	−26.2692	−0.836157
$988$	−65.1603	−2.07302
$989$	21.4855	0.683198
$990$	28.9948	0.921516
$991$	4.68239	0.148741	0.0743706	−	0.997231i	$-0.476305\pi$
$991$	4.68239	0.148741	0.0743706	+	0.997231i	$0.476305\pi$
$992$	59.7533	1.89717
$993$	−31.3687	−0.995456
$994$	99.7664	3.16440
$995$	5.41086	0.171536
$996$	47.9138	1.51821
$997$	45.3096	1.43497	0.717485	−	0.696574i	$-0.245293\pi$
$997$	45.3096	1.43497	0.717485	+	0.696574i	$0.245293\pi$
$998$	−24.3690	−0.771386
$999$	−11.2301	−0.355304

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4029.2.a.k.1.4	✓	31

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4029.2.a.k.1.4	✓	31	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:	\( N \)	\(=\)	\( 4029 = 3 \cdot 17 \cdot 79 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4029.a (trivial)

\(f(q)\)	\(=\)	\(q-2.28064 q^{2} +1.00000 q^{3} +3.20133 q^{4} +2.67486 q^{5} -2.28064 q^{6} -3.60745 q^{7} -2.73981 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-2.28064 q^{2} +1.00000 q^{3} +3.20133 q^{4} +2.67486 q^{5} -2.28064 q^{6} -3.60745 q^{7} -2.73981 q^{8} +1.00000 q^{9} -6.10039 q^{10} -4.75294 q^{11} +3.20133 q^{12} -2.82803 q^{13} +8.22732 q^{14} +2.67486 q^{15} -0.154140 q^{16} +1.00000 q^{17} -2.28064 q^{18} +7.19726 q^{19} +8.56310 q^{20} -3.60745 q^{21} +10.8398 q^{22} -7.90378 q^{23} -2.73981 q^{24} +2.15485 q^{25} +6.44974 q^{26} +1.00000 q^{27} -11.5487 q^{28} +3.76541 q^{29} -6.10039 q^{30} +10.2473 q^{31} +5.83115 q^{32} -4.75294 q^{33} -2.28064 q^{34} -9.64942 q^{35} +3.20133 q^{36} -11.2301 q^{37} -16.4144 q^{38} -2.82803 q^{39} -7.32859 q^{40} +3.99765 q^{41} +8.22732 q^{42} -2.71838 q^{43} -15.2158 q^{44} +2.67486 q^{45} +18.0257 q^{46} +7.28191 q^{47} -0.154140 q^{48} +6.01373 q^{49} -4.91444 q^{50} +1.00000 q^{51} -9.05348 q^{52} -10.1934 q^{53} -2.28064 q^{54} -12.7134 q^{55} +9.88373 q^{56} +7.19726 q^{57} -8.58756 q^{58} +1.09614 q^{59} +8.56310 q^{60} +8.22066 q^{61} -23.3703 q^{62} -3.60745 q^{63} -12.9905 q^{64} -7.56458 q^{65} +10.8398 q^{66} -1.58454 q^{67} +3.20133 q^{68} -7.90378 q^{69} +22.0069 q^{70} +12.1262 q^{71} -2.73981 q^{72} -11.5812 q^{73} +25.6118 q^{74} +2.15485 q^{75} +23.0408 q^{76} +17.1460 q^{77} +6.44974 q^{78} +1.00000 q^{79} -0.412301 q^{80} +1.00000 q^{81} -9.11721 q^{82} +14.9668 q^{83} -11.5487 q^{84} +2.67486 q^{85} +6.19965 q^{86} +3.76541 q^{87} +13.0222 q^{88} +5.52915 q^{89} -6.10039 q^{90} +10.2020 q^{91} -25.3026 q^{92} +10.2473 q^{93} -16.6074 q^{94} +19.2516 q^{95} +5.83115 q^{96} +9.40808 q^{97} -13.7152 q^{98} -4.75294 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 31 q + 4 q^{2} + 31 q^{3} + 34 q^{4} + 11 q^{5} + 4 q^{6} + 4 q^{7} + 12 q^{8} + 31 q^{9}+O(q^{10}) \) 31 * q + 4 * q^2 + 31 * q^3 + 34 * q^4 + 11 * q^5 + 4 * q^6 + 4 * q^7 + 12 * q^8 + 31 * q^9	\( 31 q + 4 q^{2} + 31 q^{3} + 34 q^{4} + 11 q^{5} + 4 q^{6} + 4 q^{7} + 12 q^{8} + 31 q^{9} + 5 q^{10} + 26 q^{11} + 34 q^{12} + 7 q^{13} + 19 q^{14} + 11 q^{15} + 40 q^{16} + 31 q^{17} + 4 q^{18} + 32 q^{19} + 23 q^{20} + 4 q^{21} + 2 q^{22} + 29 q^{23} + 12 q^{24} + 32 q^{25} + 13 q^{26} + 31 q^{27} - 13 q^{28} + 25 q^{29} + 5 q^{30} + 22 q^{31} + 28 q^{32} + 26 q^{33} + 4 q^{34} + 20 q^{35} + 34 q^{36} - 4 q^{37} + 19 q^{38} + 7 q^{39} - 3 q^{40} + 33 q^{41} + 19 q^{42} + 6 q^{43} + 30 q^{44} + 11 q^{45} - 11 q^{46} + 23 q^{47} + 40 q^{48} + 31 q^{49} + 6 q^{50} + 31 q^{51} - 7 q^{52} + 12 q^{53} + 4 q^{54} + 40 q^{56} + 32 q^{57} + 9 q^{58} + 27 q^{59} + 23 q^{60} - 4 q^{61} + 25 q^{62} + 4 q^{63} + 10 q^{64} + 54 q^{65} + 2 q^{66} + 34 q^{68} + 29 q^{69} - 59 q^{70} + 35 q^{71} + 12 q^{72} + 5 q^{73} + 48 q^{74} + 32 q^{75} + 32 q^{76} + 42 q^{77} + 13 q^{78} + 31 q^{79} + 24 q^{80} + 31 q^{81} + 5 q^{82} + 67 q^{83} - 13 q^{84} + 11 q^{85} - 20 q^{86} + 25 q^{87} - 7 q^{88} + 22 q^{89} + 5 q^{90} + 16 q^{91} + 57 q^{92} + 22 q^{93} + 45 q^{94} + 73 q^{95} + 28 q^{96} - 13 q^{97} - 19 q^{98} + 26 q^{99}+O(q^{100}) \) 31 * q + 4 * q^2 + 31 * q^3 + 34 * q^4 + 11 * q^5 + 4 * q^6 + 4 * q^7 + 12 * q^8 + 31 * q^9 + 5 * q^10 + 26 * q^11 + 34 * q^12 + 7 * q^13 + 19 * q^14 + 11 * q^15 + 40 * q^16 + 31 * q^17 + 4 * q^18 + 32 * q^19 + 23 * q^20 + 4 * q^21 + 2 * q^22 + 29 * q^23 + 12 * q^24 + 32 * q^25 + 13 * q^26 + 31 * q^27 - 13 * q^28 + 25 * q^29 + 5 * q^30 + 22 * q^31 + 28 * q^32 + 26 * q^33 + 4 * q^34 + 20 * q^35 + 34 * q^36 - 4 * q^37 + 19 * q^38 + 7 * q^39 - 3 * q^40 + 33 * q^41 + 19 * q^42 + 6 * q^43 + 30 * q^44 + 11 * q^45 - 11 * q^46 + 23 * q^47 + 40 * q^48 + 31 * q^49 + 6 * q^50 + 31 * q^51 - 7 * q^52 + 12 * q^53 + 4 * q^54 + 40 * q^56 + 32 * q^57 + 9 * q^58 + 27 * q^59 + 23 * q^60 - 4 * q^61 + 25 * q^62 + 4 * q^63 + 10 * q^64 + 54 * q^65 + 2 * q^66 + 34 * q^68 + 29 * q^69 - 59 * q^70 + 35 * q^71 + 12 * q^72 + 5 * q^73 + 48 * q^74 + 32 * q^75 + 32 * q^76 + 42 * q^77 + 13 * q^78 + 31 * q^79 + 24 * q^80 + 31 * q^81 + 5 * q^82 + 67 * q^83 - 13 * q^84 + 11 * q^85 - 20 * q^86 + 25 * q^87 - 7 * q^88 + 22 * q^89 + 5 * q^90 + 16 * q^91 + 57 * q^92 + 22 * q^93 + 45 * q^94 + 73 * q^95 + 28 * q^96 - 13 * q^97 - 19 * q^98 + 26 * q^99

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