LMFDB - Embedded newform 4029.2.a.l.1.25

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:	$32$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.25
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)

$f(q)$	$=$	$q+1.48854 q^{2} -1.00000 q^{3} +0.215757 q^{4} +4.37211 q^{5} -1.48854 q^{6} -4.26225 q^{7} -2.65592 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.48854 q^{2} -1.00000 q^{3} +0.215757 q^{4} +4.37211 q^{5} -1.48854 q^{6} -4.26225 q^{7} -2.65592 q^{8} +1.00000 q^{9} +6.50806 q^{10} +2.03389 q^{11} -0.215757 q^{12} -1.63370 q^{13} -6.34454 q^{14} -4.37211 q^{15} -4.38496 q^{16} -1.00000 q^{17} +1.48854 q^{18} +6.68857 q^{19} +0.943312 q^{20} +4.26225 q^{21} +3.02754 q^{22} +0.998569 q^{23} +2.65592 q^{24} +14.1153 q^{25} -2.43184 q^{26} -1.00000 q^{27} -0.919610 q^{28} -5.55421 q^{29} -6.50806 q^{30} +4.45619 q^{31} -1.21536 q^{32} -2.03389 q^{33} -1.48854 q^{34} -18.6350 q^{35} +0.215757 q^{36} -9.01736 q^{37} +9.95622 q^{38} +1.63370 q^{39} -11.6120 q^{40} +4.65058 q^{41} +6.34454 q^{42} +10.6556 q^{43} +0.438827 q^{44} +4.37211 q^{45} +1.48641 q^{46} +5.93059 q^{47} +4.38496 q^{48} +11.1668 q^{49} +21.0112 q^{50} +1.00000 q^{51} -0.352483 q^{52} -1.83041 q^{53} -1.48854 q^{54} +8.89240 q^{55} +11.3202 q^{56} -6.68857 q^{57} -8.26767 q^{58} +9.08592 q^{59} -0.943312 q^{60} +2.34574 q^{61} +6.63322 q^{62} -4.26225 q^{63} +6.96081 q^{64} -7.14273 q^{65} -3.02754 q^{66} +6.16936 q^{67} -0.215757 q^{68} -0.998569 q^{69} -27.7390 q^{70} +11.6032 q^{71} -2.65592 q^{72} -3.88003 q^{73} -13.4227 q^{74} -14.1153 q^{75} +1.44311 q^{76} -8.66896 q^{77} +2.43184 q^{78} +1.00000 q^{79} -19.1715 q^{80} +1.00000 q^{81} +6.92259 q^{82} -13.1498 q^{83} +0.919610 q^{84} -4.37211 q^{85} +15.8613 q^{86} +5.55421 q^{87} -5.40186 q^{88} +10.2926 q^{89} +6.50806 q^{90} +6.96325 q^{91} +0.215448 q^{92} -4.45619 q^{93} +8.82793 q^{94} +29.2431 q^{95} +1.21536 q^{96} -11.2327 q^{97} +16.6222 q^{98} +2.03389 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - q^{2} - 32 q^{3} + 41 q^{4} - q^{5} + q^{6} + 4 q^{7} - 3 q^{8} + 32 q^{9}+O(q^{10}) $ 32 * q - q^2 - 32 * q^3 + 41 * q^4 - q^5 + q^6 + 4 * q^7 - 3 * q^8 + 32 * q^9	\( 32 q - q^{2} - 32 q^{3} + 41 q^{4} - q^{5} + q^{6} + 4 q^{7} - 3 q^{8} + 32 q^{9} + 17 q^{10} + 8 q^{11} - 41 q^{12} + 17 q^{13} + q^{14} + q^{15} + 55 q^{16} - 32 q^{17} - q^{18} + 48 q^{19} - 7 q^{20} - 4 q^{21} - 4 q^{22} - 19 q^{23} + 3 q^{24} + 63 q^{25} + 27 q^{26} - 32 q^{27} + 17 q^{28} - 15 q^{29} - 17 q^{30} + 20 q^{31} + 13 q^{32} - 8 q^{33} + q^{34} + 22 q^{35} + 41 q^{36} + 6 q^{37} + 11 q^{38} - 17 q^{39} + 47 q^{40} + q^{41} - q^{42} + 40 q^{43} + 22 q^{44} - q^{45} + 5 q^{46} - 5 q^{47} - 55 q^{48} + 88 q^{49} + 17 q^{50} + 32 q^{51} + 23 q^{52} - 34 q^{53} + q^{54} + 48 q^{55} - 48 q^{57} - 9 q^{58} + 41 q^{59} + 7 q^{60} + 20 q^{61} + 15 q^{62} + 4 q^{63} + 93 q^{64} - 58 q^{65} + 4 q^{66} + 52 q^{67} - 41 q^{68} + 19 q^{69} + 25 q^{70} + q^{71} - 3 q^{72} + 19 q^{73} + 12 q^{74} - 63 q^{75} + 128 q^{76} - 20 q^{77} - 27 q^{78} + 32 q^{79} - 16 q^{80} + 32 q^{81} - 5 q^{82} + 31 q^{83} - 17 q^{84} + q^{85} - 62 q^{86} + 15 q^{87} + 35 q^{88} + 18 q^{89} + 17 q^{90} + 48 q^{91} - 75 q^{92} - 20 q^{93} + 29 q^{94} + 5 q^{95} - 13 q^{96} + 17 q^{97} + 30 q^{98} + 8 q^{99}+O(q^{100}) \) 32 * q - q^2 - 32 * q^3 + 41 * q^4 - q^5 + q^6 + 4 * q^7 - 3 * q^8 + 32 * q^9 + 17 * q^10 + 8 * q^11 - 41 * q^12 + 17 * q^13 + q^14 + q^15 + 55 * q^16 - 32 * q^17 - q^18 + 48 * q^19 - 7 * q^20 - 4 * q^21 - 4 * q^22 - 19 * q^23 + 3 * q^24 + 63 * q^25 + 27 * q^26 - 32 * q^27 + 17 * q^28 - 15 * q^29 - 17 * q^30 + 20 * q^31 + 13 * q^32 - 8 * q^33 + q^34 + 22 * q^35 + 41 * q^36 + 6 * q^37 + 11 * q^38 - 17 * q^39 + 47 * q^40 + q^41 - q^42 + 40 * q^43 + 22 * q^44 - q^45 + 5 * q^46 - 5 * q^47 - 55 * q^48 + 88 * q^49 + 17 * q^50 + 32 * q^51 + 23 * q^52 - 34 * q^53 + q^54 + 48 * q^55 - 48 * q^57 - 9 * q^58 + 41 * q^59 + 7 * q^60 + 20 * q^61 + 15 * q^62 + 4 * q^63 + 93 * q^64 - 58 * q^65 + 4 * q^66 + 52 * q^67 - 41 * q^68 + 19 * q^69 + 25 * q^70 + q^71 - 3 * q^72 + 19 * q^73 + 12 * q^74 - 63 * q^75 + 128 * q^76 - 20 * q^77 - 27 * q^78 + 32 * q^79 - 16 * q^80 + 32 * q^81 - 5 * q^82 + 31 * q^83 - 17 * q^84 + q^85 - 62 * q^86 + 15 * q^87 + 35 * q^88 + 18 * q^89 + 17 * q^90 + 48 * q^91 - 75 * q^92 - 20 * q^93 + 29 * q^94 + 5 * q^95 - 13 * q^96 + 17 * q^97 + 30 * q^98 + 8 * 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 $

$2$	1.48854	1.05256	0.526279	−	0.850312i	$-0.323587\pi$
$2$	1.48854	1.05256	0.526279	+	0.850312i	$0.323587\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	0.215757	0.107878
$5$	4.37211	1.95527	0.977633	−	0.210319i	$-0.0674503\pi$
$5$	4.37211	1.95527	0.977633	+	0.210319i	$0.0674503\pi$
$6$	−1.48854	−0.607695
$7$	−4.26225	−1.61098	−0.805489	−	0.592610i	$-0.798098\pi$
$7$	−4.26225	−1.61098	−0.805489	+	0.592610i	$0.798098\pi$
$8$	−2.65592	−0.939010
$9$	1.00000	0.333333
$10$	6.50806	2.05803
$11$	2.03389	0.613242	0.306621	−	0.951832i	$-0.400802\pi$
$11$	2.03389	0.613242	0.306621	+	0.951832i	$0.400802\pi$
$12$	−0.215757	−0.0622837
$13$	−1.63370	−0.453108	−0.226554	−	0.973999i	$-0.572746\pi$
$13$	−1.63370	−0.453108	−0.226554	+	0.973999i	$0.572746\pi$
$14$	−6.34454	−1.69565
$15$	−4.37211	−1.12887
$16$	−4.38496	−1.09624
$17$	−1.00000	−0.242536
$17$	−1.00000	−0.242536
$18$	1.48854	0.350853
$19$	6.68857	1.53446	0.767232	−	0.641370i	$-0.221634\pi$
$19$	6.68857	1.53446	0.767232	+	0.641370i	$0.221634\pi$
$20$	0.943312	0.210931
$21$	4.26225	0.930099
$22$	3.02754	0.645473
$23$	0.998569	0.208216	0.104108	−	0.994566i	$-0.466801\pi$
$23$	0.998569	0.208216	0.104108	+	0.994566i	$0.466801\pi$
$24$	2.65592	0.542138
$25$	14.1153	2.82306
$26$	−2.43184	−0.476922
$27$	−1.00000	−0.192450
$28$	−0.919610	−0.173790
$29$	−5.55421	−1.03139	−0.515695	−	0.856772i	$-0.672466\pi$
$29$	−5.55421	−1.03139	−0.515695	+	0.856772i	$0.672466\pi$
$30$	−6.50806	−1.18820
$31$	4.45619	0.800355	0.400178	−	0.916438i	$-0.368948\pi$
$31$	4.45619	0.800355	0.400178	+	0.916438i	$0.368948\pi$
$32$	−1.21536	−0.214847
$33$	−2.03389	−0.354055
$34$	−1.48854	−0.255283
$35$	−18.6350	−3.14989
$36$	0.215757	0.0359595
$37$	−9.01736	−1.48244	−0.741222	−	0.671260i	$-0.765754\pi$
$37$	−9.01736	−1.48244	−0.741222	+	0.671260i	$0.765754\pi$
$38$	9.95622	1.61511
$39$	1.63370	0.261602
$40$	−11.6120	−1.83601
$41$	4.65058	0.726299	0.363150	−	0.931731i	$-0.381701\pi$
$41$	4.65058	0.726299	0.363150	+	0.931731i	$0.381701\pi$
$42$	6.34454	0.978983
$43$	10.6556	1.62496	0.812480	−	0.582989i	$-0.198117\pi$
$43$	10.6556	1.62496	0.812480	+	0.582989i	$0.198117\pi$
$44$	0.438827	0.0661556
$45$	4.37211	0.651755
$46$	1.48641	0.219159
$47$	5.93059	0.865065	0.432533	−	0.901618i	$-0.357620\pi$
$47$	5.93059	0.865065	0.432533	+	0.901618i	$0.357620\pi$
$48$	4.38496	0.632915
$49$	11.1668	1.59525
$50$	21.0112	2.97144
$51$	1.00000	0.140028
$52$	−0.352483	−0.0488806
$53$	−1.83041	−0.251426	−0.125713	−	0.992067i	$-0.540122\pi$
$53$	−1.83041	−0.251426	−0.125713	+	0.992067i	$0.540122\pi$
$54$	−1.48854	−0.202565
$55$	8.89240	1.19905
$56$	11.3202	1.51272
$57$	−6.68857	−0.885923
$58$	−8.26767	−1.08560
$59$	9.08592	1.18289	0.591443	−	0.806347i	$-0.298558\pi$
$59$	9.08592	1.18289	0.591443	+	0.806347i	$0.298558\pi$
$60$	−0.943312	−0.121781
$61$	2.34574	0.300341	0.150171	−	0.988660i	$-0.452018\pi$
$61$	2.34574	0.300341	0.150171	+	0.988660i	$0.452018\pi$
$62$	6.63322	0.842420
$63$	−4.26225	−0.536993
$64$	6.96081	0.870101
$65$	−7.14273	−0.885946
$66$	−3.02754	−0.372664
$67$	6.16936	0.753708	0.376854	−	0.926273i	$-0.377006\pi$
$67$	6.16936	0.753708	0.376854	+	0.926273i	$0.377006\pi$
$68$	−0.215757	−0.0261644
$69$	−0.998569	−0.120214
$70$	−27.7390	−3.31544
$71$	11.6032	1.37705	0.688524	−	0.725213i	$-0.258259\pi$
$71$	11.6032	1.37705	0.688524	+	0.725213i	$0.258259\pi$
$72$	−2.65592	−0.313003
$73$	−3.88003	−0.454124	−0.227062	−	0.973880i	$-0.572912\pi$
$73$	−3.88003	−0.454124	−0.227062	+	0.973880i	$0.572912\pi$
$74$	−13.4227	−1.56036
$75$	−14.1153	−1.62990
$76$	1.44311	0.165536
$77$	−8.66896	−0.987920
$78$	2.43184	0.275351
$79$	1.00000	0.112509
$79$	1.00000	0.112509
$80$	−19.1715	−2.14344
$81$	1.00000	0.111111
$82$	6.92259	0.764472
$83$	−13.1498	−1.44337	−0.721687	−	0.692219i	$-0.756633\pi$
$83$	−13.1498	−1.44337	−0.721687	+	0.692219i	$0.756633\pi$
$84$	0.919610	0.100338
$85$	−4.37211	−0.474222
$86$	15.8613	1.71036
$87$	5.55421	0.595474
$88$	−5.40186	−0.575840
$89$	10.2926	1.09102	0.545508	−	0.838105i	$-0.316337\pi$
$89$	10.2926	1.09102	0.545508	+	0.838105i	$0.316337\pi$
$90$	6.50806	0.686010
$91$	6.96325	0.729947
$92$	0.215448	0.0224620
$93$	−4.45619	−0.462085
$94$	8.82793	0.910531
$95$	29.2431	3.00028
$96$	1.21536	0.124042
$97$	−11.2327	−1.14051	−0.570254	−	0.821468i	$-0.693155\pi$
$97$	−11.2327	−1.14051	−0.570254	+	0.821468i	$0.693155\pi$
$98$	16.6222	1.67910
$99$	2.03389	0.204414
$100$	3.04548	0.304548
$101$	13.1560	1.30907	0.654533	−	0.756033i	$-0.272865\pi$
$101$	13.1560	1.30907	0.654533	+	0.756033i	$0.272865\pi$
$102$	1.48854	0.147388
$103$	−16.9290	−1.66806	−0.834032	−	0.551716i	$-0.813973\pi$
$103$	−16.9290	−1.66806	−0.834032	+	0.551716i	$0.813973\pi$
$104$	4.33899	0.425473
$105$	18.6350	1.81859
$106$	−2.72464	−0.264640
$107$	9.67039	0.934872	0.467436	−	0.884027i	$-0.345178\pi$
$107$	9.67039	0.934872	0.467436	+	0.884027i	$0.345178\pi$
$108$	−0.215757	−0.0207612
$109$	13.8973	1.33112	0.665558	−	0.746346i	$-0.268194\pi$
$109$	13.8973	1.33112	0.665558	+	0.746346i	$0.268194\pi$
$110$	13.2367	1.26207
$111$	9.01736	0.855890
$112$	18.6898	1.76602
$113$	−10.7115	−1.00766	−0.503829	−	0.863804i	$-0.668076\pi$
$113$	−10.7115	−1.00766	−0.503829	+	0.863804i	$0.668076\pi$
$114$	−9.95622	−0.932485
$115$	4.36585	0.407117
$116$	−1.19836	−0.111265
$117$	−1.63370	−0.151036
$118$	13.5248	1.24506
$119$	4.26225	0.390720
$120$	11.6120	1.06002
$121$	−6.86328	−0.623934
$122$	3.49173	0.316126
$123$	−4.65058	−0.419329
$124$	0.961454	0.0863411
$125$	39.8531	3.56457
$126$	−6.34454	−0.565216
$127$	14.3452	1.27293	0.636464	−	0.771307i	$-0.280396\pi$
$127$	14.3452	1.27293	0.636464	+	0.771307i	$0.280396\pi$
$128$	12.7922	1.13068
$129$	−10.6556	−0.938171
$130$	−10.6323	−0.932510
$131$	18.3959	1.60726	0.803628	−	0.595132i	$-0.202900\pi$
$131$	18.3959	1.60726	0.803628	+	0.595132i	$0.202900\pi$
$132$	−0.438827	−0.0381950
$133$	−28.5084	−2.47199
$134$	9.18336	0.793321
$135$	−4.37211	−0.376291
$136$	2.65592	0.227743
$137$	−10.7640	−0.919629	−0.459815	−	0.888015i	$-0.652084\pi$
$137$	−10.7640	−0.919629	−0.459815	+	0.888015i	$0.652084\pi$
$138$	−1.48641	−0.126532
$139$	10.7831	0.914611	0.457306	−	0.889310i	$-0.348815\pi$
$139$	10.7831	0.914611	0.457306	+	0.889310i	$0.348815\pi$
$140$	−4.02063	−0.339805
$141$	−5.93059	−0.499446
$142$	17.2719	1.44942
$143$	−3.32278	−0.277865
$144$	−4.38496	−0.365414
$145$	−24.2836	−2.01664
$146$	−5.77559	−0.477992
$147$	−11.1668	−0.921020
$148$	−1.94556	−0.159924
$149$	5.89568	0.482993	0.241497	−	0.970402i	$-0.422362\pi$
$149$	5.89568	0.482993	0.241497	+	0.970402i	$0.422362\pi$
$150$	−21.0112	−1.71556
$151$	−5.98716	−0.487228	−0.243614	−	0.969872i	$-0.578333\pi$
$151$	−5.98716	−0.487228	−0.243614	+	0.969872i	$0.578333\pi$
$152$	−17.7643	−1.44088
$153$	−1.00000	−0.0808452
$154$	−12.9041	−1.03984
$155$	19.4829	1.56491
$156$	0.352483	0.0282212
$157$	−17.7437	−1.41610	−0.708050	−	0.706163i	$-0.750425\pi$
$157$	−17.7437	−1.41610	−0.708050	+	0.706163i	$0.750425\pi$
$158$	1.48854	0.118422
$159$	1.83041	0.145161
$160$	−5.31368	−0.420084
$161$	−4.25615	−0.335431
$162$	1.48854	0.116951
$163$	15.5489	1.21789	0.608943	−	0.793214i	$-0.291594\pi$
$163$	15.5489	1.21789	0.608943	+	0.793214i	$0.291594\pi$
$164$	1.00340	0.0783520
$165$	−8.89240	−0.692272
$166$	−19.5740	−1.51924
$167$	9.74451	0.754053	0.377026	−	0.926203i	$-0.376947\pi$
$167$	9.74451	0.754053	0.377026	+	0.926203i	$0.376947\pi$
$168$	−11.3202	−0.873372
$169$	−10.3310	−0.794693
$170$	−6.50806	−0.499146
$171$	6.68857	0.511488
$172$	2.29901	0.175298
$173$	−12.5863	−0.956918	−0.478459	−	0.878110i	$-0.658804\pi$
$173$	−12.5863	−0.956918	−0.478459	+	0.878110i	$0.658804\pi$
$174$	8.26767	0.626770
$175$	−60.1630	−4.54790
$176$	−8.91855	−0.672261
$177$	−9.08592	−0.682940
$178$	15.3210	1.14836
$179$	−17.0568	−1.27488	−0.637441	−	0.770499i	$-0.720007\pi$
$179$	−17.0568	−1.27488	−0.637441	+	0.770499i	$0.720007\pi$
$180$	0.943312	0.0703104
$181$	6.89535	0.512527	0.256264	−	0.966607i	$-0.417508\pi$
$181$	6.89535	0.512527	0.256264	+	0.966607i	$0.417508\pi$
$182$	10.3651	0.768312
$183$	−2.34574	−0.173402
$184$	−2.65212	−0.195517
$185$	−39.4249	−2.89857
$186$	−6.63322	−0.486372
$187$	−2.03389	−0.148733
$188$	1.27957	0.0933219
$189$	4.26225	0.310033
$190$	43.5296	3.15797
$191$	16.5129	1.19483	0.597417	−	0.801931i	$-0.296194\pi$
$191$	16.5129	1.19483	0.597417	+	0.801931i	$0.296194\pi$
$192$	−6.96081	−0.502353
$193$	19.3237	1.39095	0.695474	−	0.718551i	$-0.255194\pi$
$193$	19.3237	1.39095	0.695474	+	0.718551i	$0.255194\pi$
$194$	−16.7203	−1.20045
$195$	7.14273	0.511501
$196$	2.40931	0.172093
$197$	6.60253	0.470411	0.235206	−	0.971946i	$-0.424424\pi$
$197$	6.60253	0.470411	0.235206	+	0.971946i	$0.424424\pi$
$198$	3.02754	0.215158
$199$	−14.2347	−1.00907	−0.504537	−	0.863390i	$-0.668337\pi$
$199$	−14.2347	−1.00907	−0.504537	+	0.863390i	$0.668337\pi$
$200$	−37.4892	−2.65088
$201$	−6.16936	−0.435153
$202$	19.5832	1.37787
$203$	23.6734	1.66155
$204$	0.215757	0.0151060
$205$	20.3328	1.42011
$206$	−25.1995	−1.75573
$207$	0.998569	0.0694053
$208$	7.16373	0.496715
$209$	13.6038	0.940997
$210$	27.7390	1.91417
$211$	−16.4718	−1.13396	−0.566981	−	0.823731i	$-0.691889\pi$
$211$	−16.4718	−1.13396	−0.566981	+	0.823731i	$0.691889\pi$
$212$	−0.394923	−0.0271234
$213$	−11.6032	−0.795040
$214$	14.3948	0.984007
$215$	46.5873	3.17723
$216$	2.65592	0.180713
$217$	−18.9934	−1.28936
$218$	20.6867	1.40108
$219$	3.88003	0.262188
$220$	1.91860	0.129352
$221$	1.63370	0.109895
$222$	13.4227	0.900874
$223$	11.8605	0.794237	0.397119	−	0.917767i	$-0.370010\pi$
$223$	11.8605	0.794237	0.397119	+	0.917767i	$0.370010\pi$
$224$	5.18017	0.346114
$225$	14.1153	0.941021
$226$	−15.9446	−1.06062
$227$	−20.5934	−1.36683	−0.683415	−	0.730030i	$-0.739506\pi$
$227$	−20.5934	−1.36683	−0.683415	+	0.730030i	$0.739506\pi$
$228$	−1.44311	−0.0955720
$229$	6.58986	0.435470	0.217735	−	0.976008i	$-0.430133\pi$
$229$	6.58986	0.435470	0.217735	+	0.976008i	$0.430133\pi$
$230$	6.49875	0.428515
$231$	8.66896	0.570376
$232$	14.7515	0.968486
$233$	−10.9470	−0.717164	−0.358582	−	0.933498i	$-0.616740\pi$
$233$	−10.9470	−0.717164	−0.358582	+	0.933498i	$0.616740\pi$
$234$	−2.43184	−0.158974
$235$	25.9292	1.69143
$236$	1.96035	0.127608
$237$	−1.00000	−0.0649570
$238$	6.34454	0.411255
$239$	−2.57884	−0.166811	−0.0834057	−	0.996516i	$-0.526580\pi$
$239$	−2.57884	−0.166811	−0.0834057	+	0.996516i	$0.526580\pi$
$240$	19.1715	1.23752
$241$	−20.4299	−1.31601	−0.658003	−	0.753015i	$-0.728599\pi$
$241$	−20.4299	−1.31601	−0.658003	+	0.753015i	$0.728599\pi$
$242$	−10.2163	−0.656727
$243$	−1.00000	−0.0641500
$244$	0.506109	0.0324003
$245$	48.8223	3.11914
$246$	−6.92259	−0.441368
$247$	−10.9271	−0.695277
$248$	−11.8353	−0.751541
$249$	13.1498	0.833333
$250$	59.3231	3.75192
$251$	−18.8090	−1.18721	−0.593606	−	0.804756i	$-0.702296\pi$
$251$	−18.8090	−1.18721	−0.593606	+	0.804756i	$0.702296\pi$
$252$	−0.919610	−0.0579300
$253$	2.03098	0.127687
$254$	21.3534	1.33983
$255$	4.37211	0.273792
$256$	5.12007	0.320004
$257$	20.0246	1.24910	0.624551	−	0.780984i	$-0.285282\pi$
$257$	20.0246	1.24910	0.624551	+	0.780984i	$0.285282\pi$
$258$	−15.8613	−0.987479
$259$	38.4342	2.38819
$260$	−1.54109	−0.0955745
$261$	−5.55421	−0.343797
$262$	27.3831	1.69173
$263$	−7.55330	−0.465757	−0.232878	−	0.972506i	$-0.574814\pi$
$263$	−7.55330	−0.465757	−0.232878	+	0.972506i	$0.574814\pi$
$264$	5.40186	0.332461
$265$	−8.00273	−0.491604
$266$	−42.4359	−2.60191
$267$	−10.2926	−0.629899
$268$	1.33108	0.0813088
$269$	−8.08725	−0.493088	−0.246544	−	0.969132i	$-0.579295\pi$
$269$	−8.08725	−0.493088	−0.246544	+	0.969132i	$0.579295\pi$
$270$	−6.50806	−0.396068
$271$	−21.4142	−1.30082	−0.650409	−	0.759584i	$-0.725403\pi$
$271$	−21.4142	−1.30082	−0.650409	+	0.759584i	$0.725403\pi$
$272$	4.38496	0.265877
$273$	−6.96325	−0.421435
$274$	−16.0226	−0.967963
$275$	28.7091	1.73122
$276$	−0.215448	−0.0129685
$277$	−10.7909	−0.648361	−0.324180	−	0.945995i	$-0.605088\pi$
$277$	−10.7909	−0.648361	−0.324180	+	0.945995i	$0.605088\pi$
$278$	16.0511	0.962682
$279$	4.45619	0.266785
$280$	49.4931	2.95778
$281$	18.6319	1.11149	0.555743	−	0.831354i	$-0.312434\pi$
$281$	18.6319	1.11149	0.555743	+	0.831354i	$0.312434\pi$
$282$	−8.82793	−0.525696
$283$	9.15058	0.543945	0.271973	−	0.962305i	$-0.412324\pi$
$283$	9.15058	0.543945	0.271973	+	0.962305i	$0.412324\pi$
$284$	2.50348	0.148554
$285$	−29.2431	−1.73221
$286$	−4.94610	−0.292469
$287$	−19.8219	−1.17005
$288$	−1.21536	−0.0716158
$289$	1.00000	0.0588235
$290$	−36.1471	−2.12263
$291$	11.2327	0.658473
$292$	−0.837144	−0.0489902
$293$	30.7650	1.79731	0.898655	−	0.438656i	$-0.144545\pi$
$293$	30.7650	1.79731	0.898655	+	0.438656i	$0.144545\pi$
$294$	−16.6222	−0.969427
$295$	39.7246	2.31286
$296$	23.9494	1.39203
$297$	−2.03389	−0.118018
$298$	8.77597	0.508378
$299$	−1.63137	−0.0943443
$300$	−3.04548	−0.175831
$301$	−45.4167	−2.61778
$302$	−8.91214	−0.512836
$303$	−13.1560	−0.755790
$304$	−29.3291	−1.68214
$305$	10.2558	0.587247
$306$	−1.48854	−0.0850943
$307$	23.6726	1.35107	0.675534	−	0.737328i	$-0.263913\pi$
$307$	23.6726	1.35107	0.675534	+	0.737328i	$0.263913\pi$
$308$	−1.87039	−0.106575
$309$	16.9290	0.963058
$310$	29.0012	1.64716
$311$	−9.87271	−0.559830	−0.279915	−	0.960025i	$-0.590306\pi$
$311$	−9.87271	−0.559830	−0.279915	+	0.960025i	$0.590306\pi$
$312$	−4.33899	−0.245647
$313$	−4.06634	−0.229843	−0.114921	−	0.993375i	$-0.536662\pi$
$313$	−4.06634	−0.229843	−0.114921	+	0.993375i	$0.536662\pi$
$314$	−26.4122	−1.49053
$315$	−18.6350	−1.04996
$316$	0.215757	0.0121373
$317$	−12.5844	−0.706809	−0.353404	−	0.935471i	$-0.614976\pi$
$317$	−12.5844	−0.706809	−0.353404	+	0.935471i	$0.614976\pi$
$318$	2.72464	0.152790
$319$	−11.2967	−0.632492
$320$	30.4334	1.70128
$321$	−9.67039	−0.539749
$322$	−6.33546	−0.353061
$323$	−6.68857	−0.372162
$324$	0.215757	0.0119865
$325$	−23.0603	−1.27915
$326$	23.1452	1.28190
$327$	−13.8973	−0.768520
$328$	−12.3516	−0.682002
$329$	−25.2777	−1.39360
$330$	−13.2367	−0.728657
$331$	14.8331	0.815301	0.407650	−	0.913138i	$-0.366348\pi$
$331$	14.8331	0.815301	0.407650	+	0.913138i	$0.366348\pi$
$332$	−2.83715	−0.155709
$333$	−9.01736	−0.494148
$334$	14.5051	0.793684
$335$	26.9731	1.47370
$336$	−18.6898	−1.01961
$337$	20.3053	1.10610	0.553050	−	0.833148i	$-0.313464\pi$
$337$	20.3053	1.10610	0.553050	+	0.833148i	$0.313464\pi$
$338$	−15.3781	−0.836461
$339$	10.7115	0.581771
$340$	−0.943312	−0.0511583
$341$	9.06341	0.490811
$342$	9.95622	0.538371
$343$	−17.7598	−0.958940
$344$	−28.3004	−1.52585
$345$	−4.36585	−0.235049
$346$	−18.7352	−1.00721
$347$	19.7515	1.06032	0.530159	−	0.847898i	$-0.322132\pi$
$347$	19.7515	1.06032	0.530159	+	0.847898i	$0.322132\pi$
$348$	1.19836	0.0642388
$349$	−11.4869	−0.614880	−0.307440	−	0.951567i	$-0.599472\pi$
$349$	−11.4869	−0.614880	−0.307440	+	0.951567i	$0.599472\pi$
$350$	−89.5552	−4.78692
$351$	1.63370	0.0872007
$352$	−2.47191	−0.131753
$353$	16.3374	0.869553	0.434776	−	0.900538i	$-0.356827\pi$
$353$	16.3374	0.869553	0.434776	+	0.900538i	$0.356827\pi$
$354$	−13.5248	−0.718834
$355$	50.7305	2.69250
$356$	2.22071	0.117697
$357$	−4.26225	−0.225582
$358$	−25.3897	−1.34189
$359$	19.8664	1.04851	0.524255	−	0.851561i	$-0.324344\pi$
$359$	19.8664	1.04851	0.524255	+	0.851561i	$0.324344\pi$
$360$	−11.6120	−0.612004
$361$	25.7370	1.35458
$362$	10.2640	0.539465
$363$	6.86328	0.360229
$364$	1.50237	0.0787456
$365$	−16.9639	−0.887932
$366$	−3.49173	−0.182516
$367$	−19.9673	−1.04229	−0.521143	−	0.853469i	$-0.674494\pi$
$367$	−19.9673	−1.04229	−0.521143	+	0.853469i	$0.674494\pi$
$368$	−4.37869	−0.228255
$369$	4.65058	0.242100
$370$	−58.6856	−3.05092
$371$	7.80164	0.405041
$372$	−0.961454	−0.0498491
$373$	−14.8113	−0.766901	−0.383451	−	0.923561i	$-0.625264\pi$
$373$	−14.8113	−0.766901	−0.383451	+	0.923561i	$0.625264\pi$
$374$	−3.02754	−0.156550
$375$	−39.8531	−2.05801
$376$	−15.7512	−0.812305
$377$	9.07393	0.467331
$378$	6.34454	0.326328
$379$	−28.8805	−1.48349	−0.741747	−	0.670680i	$-0.766002\pi$
$379$	−28.8805	−1.48349	−0.741747	+	0.670680i	$0.766002\pi$
$380$	6.30941	0.323666
$381$	−14.3452	−0.734925
$382$	24.5802	1.25763
$383$	−11.2363	−0.574146	−0.287073	−	0.957909i	$-0.592682\pi$
$383$	−11.2363	−0.574146	−0.287073	+	0.957909i	$0.592682\pi$
$384$	−12.7922	−0.652798
$385$	−37.9016	−1.93165
$386$	28.7641	1.46405
$387$	10.6556	0.541653
$388$	−2.42353	−0.123036
$389$	−23.0179	−1.16705	−0.583526	−	0.812094i	$-0.698328\pi$
$389$	−23.0179	−1.16705	−0.583526	+	0.812094i	$0.698328\pi$
$390$	10.6323	0.538385
$391$	−0.998569	−0.0504998
$392$	−29.6581	−1.49796
$393$	−18.3959	−0.927950
$394$	9.82815	0.495135
$395$	4.37211	0.219985
$396$	0.438827	0.0220519
$397$	−8.64321	−0.433790	−0.216895	−	0.976195i	$-0.569593\pi$
$397$	−8.64321	−0.433790	−0.216895	+	0.976195i	$0.569593\pi$
$398$	−21.1890	−1.06211
$399$	28.5084	1.42720
$400$	−61.8951	−3.09476
$401$	16.2738	0.812677	0.406339	−	0.913723i	$-0.366805\pi$
$401$	16.2738	0.812677	0.406339	+	0.913723i	$0.366805\pi$
$402$	−9.18336	−0.458024
$403$	−7.28009	−0.362647
$404$	2.83849	0.141220
$405$	4.37211	0.217252
$406$	35.2389	1.74888
$407$	−18.3404	−0.909097
$408$	−2.65592	−0.131488
$409$	−32.7633	−1.62004	−0.810021	−	0.586401i	$-0.800544\pi$
$409$	−32.7633	−1.62004	−0.810021	+	0.586401i	$0.800544\pi$
$410$	30.2663	1.49475
$411$	10.7640	0.530948
$412$	−3.65255	−0.179948
$413$	−38.7265	−1.90560
$414$	1.48641	0.0730531
$415$	−57.4922	−2.82218
$416$	1.98554	0.0973490
$417$	−10.7831	−0.528051
$418$	20.2499	0.990454
$419$	27.9409	1.36500	0.682502	−	0.730883i	$-0.260892\pi$
$419$	27.9409	1.36500	0.682502	+	0.730883i	$0.260892\pi$
$420$	4.02063	0.196187
$421$	29.1181	1.41913	0.709566	−	0.704639i	$-0.248891\pi$
$421$	29.1181	1.41913	0.709566	+	0.704639i	$0.248891\pi$
$422$	−24.5189	−1.19356
$423$	5.93059	0.288355
$424$	4.86141	0.236091
$425$	−14.1153	−0.684693
$426$	−17.2719	−0.836825
$427$	−9.99812	−0.483843
$428$	2.08645	0.100853
$429$	3.32278	0.160425
$430$	69.3471	3.34422
$431$	19.6495	0.946482	0.473241	−	0.880933i	$-0.343084\pi$
$431$	19.6495	0.946482	0.473241	+	0.880933i	$0.343084\pi$
$432$	4.38496	0.210972
$433$	20.4105	0.980864	0.490432	−	0.871479i	$-0.336839\pi$
$433$	20.4105	0.980864	0.490432	+	0.871479i	$0.336839\pi$
$434$	−28.2725	−1.35712
$435$	24.2836	1.16431
$436$	2.99843	0.143599
$437$	6.67900	0.319500
$438$	5.77559	0.275969
$439$	28.7047	1.37000	0.685000	−	0.728543i	$-0.259802\pi$
$439$	28.7047	1.37000	0.685000	+	0.728543i	$0.259802\pi$
$440$	−23.6175	−1.12592
$441$	11.1668	0.531751
$442$	2.43184	0.115671
$443$	−23.9165	−1.13631	−0.568154	−	0.822922i	$-0.692342\pi$
$443$	−23.9165	−1.13631	−0.568154	+	0.822922i	$0.692342\pi$
$444$	1.94556	0.0923321
$445$	45.0005	2.13323
$446$	17.6548	0.835981
$447$	−5.89568	−0.278856
$448$	−29.6687	−1.40172
$449$	−18.5959	−0.877596	−0.438798	−	0.898586i	$-0.644596\pi$
$449$	−18.5959	−0.877596	−0.438798	+	0.898586i	$0.644596\pi$
$450$	21.0112	0.990479
$451$	9.45879	0.445397
$452$	−2.31109	−0.108705
$453$	5.98716	0.281301
$454$	−30.6541	−1.43867
$455$	30.4441	1.42724
$456$	17.7643	0.831890
$457$	32.6017	1.52504	0.762522	−	0.646962i	$-0.223961\pi$
$457$	32.6017	1.52504	0.762522	+	0.646962i	$0.223961\pi$
$458$	9.80928	0.458357
$459$	1.00000	0.0466760
$460$	0.941962	0.0439192
$461$	7.76827	0.361804	0.180902	−	0.983501i	$-0.442098\pi$
$461$	7.76827	0.361804	0.180902	+	0.983501i	$0.442098\pi$
$462$	12.9041	0.600354
$463$	−0.554177	−0.0257548	−0.0128774	−	0.999917i	$-0.504099\pi$
$463$	−0.554177	−0.0257548	−0.0128774	+	0.999917i	$0.504099\pi$
$464$	24.3550	1.13065
$465$	−19.4829	−0.903499
$466$	−16.2951	−0.754857
$467$	−14.3934	−0.666045	−0.333023	−	0.942919i	$-0.608069\pi$
$467$	−14.3934	−0.666045	−0.333023	+	0.942919i	$0.608069\pi$
$468$	−0.352483	−0.0162935
$469$	−26.2954	−1.21421
$470$	38.5967	1.78033
$471$	17.7437	0.817585
$472$	−24.1315	−1.11074
$473$	21.6723	0.996493
$474$	−1.48854	−0.0683710
$475$	94.4113	4.33189
$476$	0.919610	0.0421503
$477$	−1.83041	−0.0838085
$478$	−3.83872	−0.175579
$479$	−4.86346	−0.222217	−0.111109	−	0.993808i	$-0.535440\pi$
$479$	−4.86346	−0.222217	−0.111109	+	0.993808i	$0.535440\pi$
$480$	5.31368	0.242535
$481$	14.7317	0.671708
$482$	−30.4108	−1.38517
$483$	4.25615	0.193661
$484$	−1.48080	−0.0673091
$485$	−49.1106	−2.23000
$486$	−1.48854	−0.0675216
$487$	−22.2245	−1.00709	−0.503544	−	0.863969i	$-0.667971\pi$
$487$	−22.2245	−1.00709	−0.503544	+	0.863969i	$0.667971\pi$
$488$	−6.23010	−0.282023
$489$	−15.5489	−0.703147
$490$	72.6741	3.28308
$491$	−2.24279	−0.101216	−0.0506078	−	0.998719i	$-0.516116\pi$
$491$	−2.24279	−0.101216	−0.0506078	+	0.998719i	$0.516116\pi$
$492$	−1.00340	−0.0452366
$493$	5.55421	0.250149
$494$	−16.2655	−0.731820
$495$	8.89240	0.399684
$496$	−19.5402	−0.877382
$497$	−49.4558	−2.21840
$498$	19.5740	0.877131
$499$	−17.5265	−0.784595	−0.392298	−	0.919838i	$-0.628320\pi$
$499$	−17.5265	−0.784595	−0.392298	+	0.919838i	$0.628320\pi$
$500$	8.59859	0.384541
$501$	−9.74451	−0.435353
$502$	−27.9979	−1.24961
$503$	−14.8822	−0.663563	−0.331781	−	0.943356i	$-0.607650\pi$
$503$	−14.8822	−0.663563	−0.331781	+	0.943356i	$0.607650\pi$
$504$	11.3202	0.504242
$505$	57.5192	2.55957
$506$	3.02320	0.134398
$507$	10.3310	0.458816
$508$	3.09507	0.137321
$509$	−0.166599	−0.00738439	−0.00369219	−	0.999993i	$-0.501175\pi$
$509$	−0.166599	−0.00738439	−0.00369219	+	0.999993i	$0.501175\pi$
$510$	6.50806	0.288182
$511$	16.5377	0.731584
$512$	−17.9629	−0.793856
$513$	−6.68857	−0.295308
$514$	29.8075	1.31475
$515$	−74.0154	−3.26151
$516$	−2.29901	−0.101208
$517$	12.0622	0.530494
$518$	57.2110	2.51371
$519$	12.5863	0.552477
$520$	18.9705	0.831912
$521$	−8.54658	−0.374432	−0.187216	−	0.982319i	$-0.559946\pi$
$521$	−8.54658	−0.374432	−0.187216	+	0.982319i	$0.559946\pi$
$522$	−8.26767	−0.361866
$523$	−1.14699	−0.0501542	−0.0250771	−	0.999686i	$-0.507983\pi$
$523$	−1.14699	−0.0501542	−0.0250771	+	0.999686i	$0.507983\pi$
$524$	3.96904	0.173388
$525$	60.1630	2.62573
$526$	−11.2434	−0.490236
$527$	−4.45619	−0.194115
$528$	8.91855	0.388130
$529$	−22.0029	−0.956646
$530$	−11.9124	−0.517441
$531$	9.08592	0.394295
$532$	−6.15088	−0.266674
$533$	−7.59768	−0.329092
$534$	−15.3210	−0.663005
$535$	42.2800	1.82792
$536$	−16.3853	−0.707739
$537$	17.0568	0.736054
$538$	−12.0382	−0.519004
$539$	22.7120	0.978276
$540$	−0.943312	−0.0405937
$541$	−37.5097	−1.61267	−0.806334	−	0.591460i	$-0.798552\pi$
$541$	−37.5097	−1.61267	−0.806334	+	0.591460i	$0.798552\pi$
$542$	−31.8759	−1.36919
$543$	−6.89535	−0.295908
$544$	1.21536	0.0521081
$545$	60.7603	2.60269
$546$	−10.3651	−0.443585
$547$	−18.0587	−0.772135	−0.386067	−	0.922471i	$-0.626167\pi$
$547$	−18.0587	−0.772135	−0.386067	+	0.922471i	$0.626167\pi$
$548$	−2.32240	−0.0992082
$549$	2.34574	0.100114
$550$	42.7346	1.82221
$551$	−37.1497	−1.58263
$552$	2.65212	0.112882
$553$	−4.26225	−0.181249
$554$	−16.0627	−0.682437
$555$	39.4249	1.67349
$556$	2.32653	0.0986669
$557$	18.8959	0.800643	0.400322	−	0.916375i	$-0.368898\pi$
$557$	18.8959	0.800643	0.400322	+	0.916375i	$0.368898\pi$
$558$	6.63322	0.280807
$559$	−17.4081	−0.736282
$560$	81.7138	3.45304
$561$	2.03389	0.0858711
$562$	27.7344	1.16990
$563$	27.4252	1.15583	0.577917	−	0.816096i	$-0.303866\pi$
$563$	27.4252	1.15583	0.577917	+	0.816096i	$0.303866\pi$
$564$	−1.27957	−0.0538794
$565$	−46.8320	−1.97024
$566$	13.6210	0.572534
$567$	−4.26225	−0.178998
$568$	−30.8172	−1.29306
$569$	−44.3118	−1.85765	−0.928824	−	0.370522i	$-0.879179\pi$
$569$	−44.3118	−1.85765	−0.928824	+	0.370522i	$0.879179\pi$
$570$	−43.5296	−1.82326
$571$	−27.1184	−1.13487	−0.567435	−	0.823418i	$-0.692064\pi$
$571$	−27.1184	−1.13487	−0.567435	+	0.823418i	$0.692064\pi$
$572$	−0.716913	−0.0299756
$573$	−16.5129	−0.689837
$574$	−29.5058	−1.23155
$575$	14.0951	0.587807
$576$	6.96081	0.290034
$577$	30.2358	1.25873	0.629367	−	0.777108i	$-0.283314\pi$
$577$	30.2358	1.25873	0.629367	+	0.777108i	$0.283314\pi$
$578$	1.48854	0.0619152
$579$	−19.3237	−0.803065
$580$	−5.23935	−0.217552
$581$	56.0476	2.32525
$582$	16.7203	0.693081
$583$	−3.72285	−0.154185
$584$	10.3051	0.426427
$585$	−7.14273	−0.295315
$586$	45.7950	1.89177
$587$	−10.9601	−0.452371	−0.226185	−	0.974084i	$-0.572625\pi$
$587$	−10.9601	−0.452371	−0.226185	+	0.974084i	$0.572625\pi$
$588$	−2.40931	−0.0993582
$589$	29.8055	1.22812
$590$	59.1318	2.43442
$591$	−6.60253	−0.271592
$592$	39.5408	1.62512
$593$	−10.9568	−0.449940	−0.224970	−	0.974366i	$-0.572228\pi$
$593$	−10.9568	−0.449940	−0.224970	+	0.974366i	$0.572228\pi$
$594$	−3.02754	−0.124221
$595$	18.6350	0.763961
$596$	1.27203	0.0521046
$597$	14.2347	0.582589
$598$	−2.42836	−0.0993029
$599$	12.4959	0.510568	0.255284	−	0.966866i	$-0.417831\pi$
$599$	12.4959	0.510568	0.255284	+	0.966866i	$0.417831\pi$
$600$	37.4892	1.53049
$601$	−29.2012	−1.19114	−0.595572	−	0.803302i	$-0.703074\pi$
$601$	−29.2012	−1.19114	−0.595572	+	0.803302i	$0.703074\pi$
$602$	−67.6047	−2.75536
$603$	6.16936	0.251236
$604$	−1.29177	−0.0525614
$605$	−30.0070	−1.21996
$606$	−19.5832	−0.795513
$607$	−20.2117	−0.820366	−0.410183	−	0.912003i	$-0.634535\pi$
$607$	−20.2117	−0.820366	−0.410183	+	0.912003i	$0.634535\pi$
$608$	−8.12902	−0.329675
$609$	−23.6734	−0.959295
$610$	15.2662	0.618111
$611$	−9.68883	−0.391968
$612$	−0.215757	−0.00872146
$613$	19.8214	0.800580	0.400290	−	0.916388i	$-0.368909\pi$
$613$	19.8214	0.800580	0.400290	+	0.916388i	$0.368909\pi$
$614$	35.2377	1.42208
$615$	−20.3328	−0.819900
$616$	23.0241	0.927666
$617$	−9.48632	−0.381905	−0.190952	−	0.981599i	$-0.561158\pi$
$617$	−9.48632	−0.381905	−0.190952	+	0.981599i	$0.561158\pi$
$618$	25.1995	1.01367
$619$	−14.5485	−0.584753	−0.292376	−	0.956303i	$-0.594446\pi$
$619$	−14.5485	−0.584753	−0.292376	+	0.956303i	$0.594446\pi$
$620$	4.20358	0.168820
$621$	−0.998569	−0.0400712
$622$	−14.6959	−0.589253
$623$	−43.8698	−1.75760
$624$	−7.16373	−0.286779
$625$	103.666	4.14662
$626$	−6.05291	−0.241923
$627$	−13.6038	−0.543285
$628$	−3.82832	−0.152767
$629$	9.01736	0.359546
$630$	−27.7390	−1.10515
$631$	24.5247	0.976314	0.488157	−	0.872756i	$-0.337669\pi$
$631$	24.5247	0.976314	0.488157	+	0.872756i	$0.337669\pi$
$632$	−2.65592	−0.105647
$633$	16.4718	0.654694
$634$	−18.7324	−0.743957
$635$	62.7186	2.48891
$636$	0.394923	0.0156597
$637$	−18.2432	−0.722822
$638$	−16.8156	−0.665734
$639$	11.6032	0.459016
$640$	55.9288	2.21078
$641$	34.2860	1.35422	0.677109	−	0.735883i	$-0.263233\pi$
$641$	34.2860	1.35422	0.677109	+	0.735883i	$0.263233\pi$
$642$	−14.3948	−0.568117
$643$	8.91494	0.351571	0.175785	−	0.984429i	$-0.443754\pi$
$643$	8.91494	0.351571	0.175785	+	0.984429i	$0.443754\pi$
$644$	−0.918294	−0.0361858
$645$	−46.5873	−1.83437
$646$	−9.95622	−0.391722
$647$	−41.7439	−1.64112	−0.820561	−	0.571559i	$-0.806339\pi$
$647$	−41.7439	−1.64112	−0.820561	+	0.571559i	$0.806339\pi$
$648$	−2.65592	−0.104334
$649$	18.4798	0.725396
$650$	−34.3262	−1.34638
$651$	18.9934	0.744410
$652$	3.35479	0.131384
$653$	−20.3352	−0.795779	−0.397889	−	0.917433i	$-0.630257\pi$
$653$	−20.3352	−0.795779	−0.397889	+	0.917433i	$0.630257\pi$
$654$	−20.6867	−0.808912
$655$	80.4288	3.14261
$656$	−20.3926	−0.796199
$657$	−3.88003	−0.151375
$658$	−37.6268	−1.46685
$659$	0.906652	0.0353181	0.0176591	−	0.999844i	$-0.494379\pi$
$659$	0.906652	0.0353181	0.0176591	+	0.999844i	$0.494379\pi$
$660$	−1.91860	−0.0746813
$661$	−14.7947	−0.575447	−0.287723	−	0.957714i	$-0.592898\pi$
$661$	−14.7947	−0.575447	−0.287723	+	0.957714i	$0.592898\pi$
$662$	22.0797	0.858152
$663$	−1.63370	−0.0634478
$664$	34.9247	1.35534
$665$	−124.642	−4.83339
$666$	−13.4227	−0.520120
$667$	−5.54626	−0.214752
$668$	2.10245	0.0813460
$669$	−11.8605	−0.458553
$670$	40.1506	1.55115
$671$	4.77098	0.184182
$672$	−5.18017	−0.199829
$673$	3.43645	0.132465	0.0662327	−	0.997804i	$-0.478902\pi$
$673$	3.43645	0.132465	0.0662327	+	0.997804i	$0.478902\pi$
$674$	30.2253	1.16424
$675$	−14.1153	−0.543299
$676$	−2.22899	−0.0857303
$677$	−10.3765	−0.398801	−0.199400	−	0.979918i	$-0.563899\pi$
$677$	−10.3765	−0.398801	−0.199400	+	0.979918i	$0.563899\pi$
$678$	15.9446	0.612348
$679$	47.8766	1.83733
$680$	11.6120	0.445299
$681$	20.5934	0.789140
$682$	13.4913	0.516608
$683$	11.3733	0.435189	0.217594	−	0.976039i	$-0.430179\pi$
$683$	11.3733	0.435189	0.217594	+	0.976039i	$0.430179\pi$
$684$	1.44311	0.0551785
$685$	−47.0613	−1.79812
$686$	−26.4362	−1.00934
$687$	−6.58986	−0.251419
$688$	−46.7243	−1.78135
$689$	2.99034	0.113923
$690$	−6.49875	−0.247403
$691$	−50.8638	−1.93495	−0.967475	−	0.252966i	$-0.918594\pi$
$691$	−50.8638	−1.93495	−0.967475	+	0.252966i	$0.918594\pi$
$692$	−2.71558	−0.103231
$693$	−8.66896	−0.329307
$694$	29.4010	1.11605
$695$	47.1449	1.78831
$696$	−14.7515	−0.559155
$697$	−4.65058	−0.176153
$698$	−17.0988	−0.647197
$699$	10.9470	0.414055
$700$	−12.9806	−0.490620
$701$	17.2765	0.652526	0.326263	−	0.945279i	$-0.394210\pi$
$701$	17.2765	0.652526	0.326263	+	0.945279i	$0.394210\pi$
$702$	2.43184	0.0917838
$703$	−60.3132	−2.27476
$704$	14.1576	0.533583
$705$	−25.9292	−0.976549
$706$	24.3189	0.915255
$707$	−56.0740	−2.10888
$708$	−1.96035	−0.0736745
$709$	−49.1993	−1.84772	−0.923860	−	0.382730i	$-0.874984\pi$
$709$	−49.1993	−1.84772	−0.923860	+	0.382730i	$0.874984\pi$
$710$	75.5145	2.83401
$711$	1.00000	0.0375029
$712$	−27.3364	−1.02448
$713$	4.44981	0.166647
$714$	−6.34454	−0.237438
$715$	−14.5276	−0.543300
$716$	−3.68012	−0.137532
$717$	2.57884	0.0963086
$718$	29.5720	1.10362
$719$	−50.4107	−1.88000	−0.940001	−	0.341171i	$-0.889176\pi$
$719$	−50.4107	−1.88000	−0.940001	+	0.341171i	$0.889176\pi$
$720$	−19.1715	−0.714481
$721$	72.1557	2.68722
$722$	38.3106	1.42577
$723$	20.4299	0.759797
$724$	1.48772	0.0552907
$725$	−78.3994	−2.91168
$726$	10.2163	0.379162
$727$	−22.0292	−0.817019	−0.408509	−	0.912754i	$-0.633951\pi$
$727$	−22.0292	−0.817019	−0.408509	+	0.912754i	$0.633951\pi$
$728$	−18.4938	−0.685428
$729$	1.00000	0.0370370
$730$	−25.2515	−0.934600
$731$	−10.6556	−0.394111
$732$	−0.506109	−0.0187063
$733$	26.6003	0.982505	0.491253	−	0.871017i	$-0.336539\pi$
$733$	26.6003	0.982505	0.491253	+	0.871017i	$0.336539\pi$
$734$	−29.7222	−1.09707
$735$	−48.8223	−1.80084
$736$	−1.21362	−0.0447346
$737$	12.5478	0.462205
$738$	6.92259	0.254824
$739$	−33.8249	−1.24427	−0.622134	−	0.782911i	$-0.713734\pi$
$739$	−33.8249	−1.24427	−0.622134	+	0.782911i	$0.713734\pi$
$740$	−8.50619	−0.312694
$741$	10.9271	0.401419
$742$	11.6131	0.426329
$743$	−16.7000	−0.612663	−0.306331	−	0.951925i	$-0.599102\pi$
$743$	−16.7000	−0.612663	−0.306331	+	0.951925i	$0.599102\pi$
$744$	11.8353	0.433903
$745$	25.7766	0.944380
$746$	−22.0473	−0.807208
$747$	−13.1498	−0.481125
$748$	−0.438827	−0.0160451
$749$	−41.2176	−1.50606
$750$	−59.3231	−2.16617
$751$	37.1143	1.35432	0.677160	−	0.735835i	$-0.263210\pi$
$751$	37.1143	1.35432	0.677160	+	0.735835i	$0.263210\pi$
$752$	−26.0054	−0.948320
$753$	18.8090	0.685437
$754$	13.5069	0.491893
$755$	−26.1765	−0.952661
$756$	0.919610	0.0334459
$757$	−10.7124	−0.389350	−0.194675	−	0.980868i	$-0.562365\pi$
$757$	−10.7124	−0.389350	−0.194675	+	0.980868i	$0.562365\pi$
$758$	−42.9899	−1.56146
$759$	−2.03098	−0.0737200
$760$	−77.6675	−2.81729
$761$	7.13159	0.258520	0.129260	−	0.991611i	$-0.458740\pi$
$761$	7.13159	0.258520	0.129260	+	0.991611i	$0.458740\pi$
$762$	−21.3534	−0.773551
$763$	−59.2336	−2.14440
$764$	3.56278	0.128897
$765$	−4.37211	−0.158074
$766$	−16.7257	−0.604322
$767$	−14.8437	−0.535975
$768$	−5.12007	−0.184755
$769$	−2.51498	−0.0906923	−0.0453462	−	0.998971i	$-0.514439\pi$
$769$	−2.51498	−0.0906923	−0.0453462	+	0.998971i	$0.514439\pi$
$770$	−56.4182	−2.03317
$771$	−20.0246	−0.721170
$772$	4.16922	0.150053
$773$	−31.0747	−1.11768	−0.558840	−	0.829275i	$-0.688753\pi$
$773$	−31.0747	−1.11768	−0.558840	+	0.829275i	$0.688753\pi$
$774$	15.8613	0.570121
$775$	62.9005	2.25945
$776$	29.8332	1.07095
$777$	−38.4342	−1.37882
$778$	−34.2631	−1.22839
$779$	31.1058	1.11448
$780$	1.54109	0.0551800
$781$	23.5997	0.844464
$782$	−1.48641	−0.0531540
$783$	5.55421	0.198491
$784$	−48.9659	−1.74878
$785$	−77.5772	−2.76885
$786$	−27.3831	−0.976721
$787$	−34.3376	−1.22400	−0.612002	−	0.790856i	$-0.709635\pi$
$787$	−34.3376	−1.22400	−0.612002	+	0.790856i	$0.709635\pi$
$788$	1.42454	0.0507472
$789$	7.55330	0.268905
$790$	6.50806	0.231547
$791$	45.6553	1.62331
$792$	−5.40186	−0.191947
$793$	−3.83224	−0.136087
$794$	−12.8658	−0.456589
$795$	8.00273	0.283828
$796$	−3.07124	−0.108857
$797$	−47.9034	−1.69682	−0.848412	−	0.529336i	$-0.822441\pi$
$797$	−47.9034	−1.69682	−0.848412	+	0.529336i	$0.822441\pi$
$798$	42.4359	1.50221
$799$	−5.93059	−0.209809
$800$	−17.1552	−0.606528
$801$	10.2926	0.363672
$802$	24.2243	0.855390
$803$	−7.89158	−0.278488
$804$	−1.33108	−0.0469437
$805$	−18.6083	−0.655858
$806$	−10.8367	−0.381707
$807$	8.08725	0.284685
$808$	−34.9412	−1.22923
$809$	−19.7738	−0.695211	−0.347606	−	0.937641i	$-0.613005\pi$
$809$	−19.7738	−0.695211	−0.347606	+	0.937641i	$0.613005\pi$
$810$	6.50806	0.228670
$811$	−6.80477	−0.238948	−0.119474	−	0.992837i	$-0.538121\pi$
$811$	−6.80477	−0.238948	−0.119474	+	0.992837i	$0.538121\pi$
$812$	5.10770	0.179245
$813$	21.4142	0.751028
$814$	−27.3004	−0.956878
$815$	67.9816	2.38129
$816$	−4.38496	−0.153504
$817$	71.2705	2.49344
$818$	−48.7696	−1.70519
$819$	6.96325	0.243316
$820$	4.38695	0.153199
$821$	−11.1537	−0.389268	−0.194634	−	0.980876i	$-0.562352\pi$
$821$	−11.1537	−0.389268	−0.194634	+	0.980876i	$0.562352\pi$
$822$	16.0226	0.558854
$823$	8.62351	0.300597	0.150298	−	0.988641i	$-0.451977\pi$
$823$	8.62351	0.300597	0.150298	+	0.988641i	$0.451977\pi$
$824$	44.9621	1.56633
$825$	−28.7091	−0.999521
$826$	−57.6460	−2.00576
$827$	43.4953	1.51248	0.756240	−	0.654295i	$-0.227034\pi$
$827$	43.4953	1.51248	0.756240	+	0.654295i	$0.227034\pi$
$828$	0.215448	0.00748734
$829$	−36.6167	−1.27175	−0.635876	−	0.771791i	$-0.719361\pi$
$829$	−36.6167	−1.27175	−0.635876	+	0.771791i	$0.719361\pi$
$830$	−85.5795	−2.97051
$831$	10.7909	0.374331
$832$	−11.3719	−0.394250
$833$	−11.1668	−0.386906
$834$	−16.0511	−0.555805
$835$	42.6040	1.47437
$836$	2.93512	0.101513
$837$	−4.45619	−0.154028
$838$	41.5913	1.43675
$839$	−10.9246	−0.377160	−0.188580	−	0.982058i	$-0.560389\pi$
$839$	−10.9246	−0.377160	−0.188580	+	0.982058i	$0.560389\pi$
$840$	−49.4931	−1.70767
$841$	1.84922	0.0637661
$842$	43.3436	1.49372
$843$	−18.6319	−0.641717
$844$	−3.55390	−0.122330
$845$	−45.1683	−1.55384
$846$	8.82793	0.303510
$847$	29.2530	1.00514
$848$	8.02626	0.275623
$849$	−9.15058	−0.314047
$850$	−21.0112	−0.720680
$851$	−9.00445	−0.308669
$852$	−2.50348	−0.0857676
$853$	−18.3246	−0.627423	−0.313712	−	0.949518i	$-0.601573\pi$
$853$	−18.3246	−0.627423	−0.313712	+	0.949518i	$0.601573\pi$
$854$	−14.8826	−0.509273
$855$	29.2431	1.00009
$856$	−25.6838	−0.877854
$857$	28.7715	0.982816	0.491408	−	0.870930i	$-0.336482\pi$
$857$	28.7715	0.982816	0.491408	+	0.870930i	$0.336482\pi$
$858$	4.94610	0.168857
$859$	21.5565	0.735499	0.367750	−	0.929925i	$-0.380128\pi$
$859$	21.5565	0.735499	0.367750	+	0.929925i	$0.380128\pi$
$860$	10.0515	0.342754
$861$	19.8219	0.675530
$862$	29.2491	0.996228
$863$	23.6158	0.803893	0.401946	−	0.915663i	$-0.368334\pi$
$863$	23.6158	0.803893	0.401946	+	0.915663i	$0.368334\pi$
$864$	1.21536	0.0413474
$865$	−55.0286	−1.87103
$866$	30.3818	1.03242
$867$	−1.00000	−0.0339618
$868$	−4.09796	−0.139094
$869$	2.03389	0.0689951
$870$	36.1471	1.22550
$871$	−10.0789	−0.341511
$872$	−36.9100	−1.24993
$873$	−11.2327	−0.380169
$874$	9.94196	0.336292
$875$	−169.864	−5.74245
$876$	0.837144	0.0282845
$877$	−21.1916	−0.715591	−0.357795	−	0.933800i	$-0.616471\pi$
$877$	−21.1916	−0.715591	−0.357795	+	0.933800i	$0.616471\pi$
$878$	42.7281	1.44200
$879$	−30.7650	−1.03768
$880$	−38.9928	−1.31445
$881$	−21.0275	−0.708433	−0.354217	−	0.935163i	$-0.615252\pi$
$881$	−21.0275	−0.708433	−0.354217	+	0.935163i	$0.615252\pi$
$882$	16.6222	0.559699
$883$	40.5202	1.36361	0.681806	−	0.731533i	$-0.261195\pi$
$883$	40.5202	1.36361	0.681806	+	0.731533i	$0.261195\pi$
$884$	0.352483	0.0118553
$885$	−39.7246	−1.33533
$886$	−35.6007	−1.19603
$887$	32.6887	1.09758	0.548790	−	0.835961i	$-0.315089\pi$
$887$	32.6887	1.09758	0.548790	+	0.835961i	$0.315089\pi$
$888$	−23.9494	−0.803689
$889$	−61.1427	−2.05066
$890$	66.9851	2.24535
$891$	2.03389	0.0681380
$892$	2.55898	0.0856811
$893$	39.6672	1.32741
$894$	−8.77597	−0.293512
$895$	−74.5740	−2.49273
$896$	−54.5235	−1.82150
$897$	1.63137	0.0544697
$898$	−27.6808	−0.923720
$899$	−24.7506	−0.825479
$900$	3.04548	0.101516
$901$	1.83041	0.0609796
$902$	14.0798	0.468806
$903$	45.4167	1.51137
$904$	28.4490	0.946200
$905$	30.1472	1.00213
$906$	8.91214	0.296086
$907$	−20.6964	−0.687214	−0.343607	−	0.939114i	$-0.611649\pi$
$907$	−20.6964	−0.687214	−0.343607	+	0.939114i	$0.611649\pi$
$908$	−4.44316	−0.147452
$909$	13.1560	0.436355
$910$	45.3173	1.50225
$911$	4.27776	0.141728	0.0708642	−	0.997486i	$-0.477424\pi$
$911$	4.27776	0.141728	0.0708642	+	0.997486i	$0.477424\pi$
$912$	29.3291	0.971185
$913$	−26.7452	−0.885138
$914$	48.5290	1.60520
$915$	−10.2558	−0.339047
$916$	1.42181	0.0469778
$917$	−78.4079	−2.58926
$918$	1.48854	0.0491292
$919$	−4.35570	−0.143681	−0.0718407	−	0.997416i	$-0.522887\pi$
$919$	−4.35570	−0.143681	−0.0718407	+	0.997416i	$0.522887\pi$
$920$	−11.5953	−0.382287
$921$	−23.6726	−0.780040
$922$	11.5634	0.380820
$923$	−18.9562	−0.623952
$924$	1.87039	0.0615313
$925$	−127.283	−4.18504
$926$	−0.824916	−0.0271084
$927$	−16.9290	−0.556022
$928$	6.75036	0.221591
$929$	8.42852	0.276531	0.138265	−	0.990395i	$-0.455847\pi$
$929$	8.42852	0.276531	0.138265	+	0.990395i	$0.455847\pi$
$930$	−29.0012	−0.950986
$931$	74.6897	2.44786
$932$	−2.36190	−0.0773666
$933$	9.87271	0.323218
$934$	−21.4251	−0.701051
$935$	−8.89240	−0.290813
$936$	4.33899	0.141824
$937$	−53.4904	−1.74746	−0.873728	−	0.486414i	$-0.838305\pi$
$937$	−53.4904	−1.74746	−0.873728	+	0.486414i	$0.838305\pi$
$938$	−39.1418	−1.27802
$939$	4.06634	0.132700
$940$	5.59440	0.182469
$941$	−17.9973	−0.586696	−0.293348	−	0.956006i	$-0.594769\pi$
$941$	−17.9973	−0.586696	−0.293348	+	0.956006i	$0.594769\pi$
$942$	26.4122	0.860556
$943$	4.64393	0.151227
$944$	−39.8414	−1.29673
$945$	18.6350	0.606197
$946$	32.2601	1.04887
$947$	6.06354	0.197039	0.0985193	−	0.995135i	$-0.468589\pi$
$947$	6.06354	0.197039	0.0985193	+	0.995135i	$0.468589\pi$
$948$	−0.215757	−0.00700746
$949$	6.33883	0.205767
$950$	140.535	4.55956
$951$	12.5844	0.408076
$952$	−11.3202	−0.366890
$953$	25.8534	0.837475	0.418737	−	0.908107i	$-0.362473\pi$
$953$	25.8534	0.837475	0.418737	+	0.908107i	$0.362473\pi$
$954$	−2.72464	−0.0882133
$955$	72.1963	2.33622
$956$	−0.556403	−0.0179954
$957$	11.2967	0.365169
$958$	−7.23946	−0.233896
$959$	45.8788	1.48150
$960$	−30.4334	−0.982234
$961$	−11.1424	−0.359432
$962$	21.9287	0.707011
$963$	9.67039	0.311624
$964$	−4.40790	−0.141969
$965$	84.4852	2.71967
$966$	6.33546	0.203840
$967$	5.38668	0.173224	0.0866119	−	0.996242i	$-0.472396\pi$
$967$	5.38668	0.173224	0.0866119	+	0.996242i	$0.472396\pi$
$968$	18.2283	0.585880
$969$	6.68857	0.214868
$970$	−73.1031	−2.34720
$971$	37.2466	1.19530	0.597651	−	0.801757i	$-0.296101\pi$
$971$	37.2466	1.19530	0.597651	+	0.801757i	$0.296101\pi$
$972$	−0.215757	−0.00692041
$973$	−45.9603	−1.47342
$974$	−33.0821	−1.06002
$975$	23.0603	0.738519
$976$	−10.2860	−0.329246
$977$	56.3656	1.80329	0.901647	−	0.432472i	$-0.142359\pi$
$977$	56.3656	1.80329	0.901647	+	0.432472i	$0.142359\pi$
$978$	−23.1452	−0.740103
$979$	20.9341	0.669057
$980$	10.5338	0.336488
$981$	13.8973	0.443705
$982$	−3.33848	−0.106535
$983$	14.1691	0.451923	0.225962	−	0.974136i	$-0.427448\pi$
$983$	14.1691	0.451923	0.225962	+	0.974136i	$0.427448\pi$
$984$	12.3516	0.393754
$985$	28.8670	0.919778
$986$	8.26767	0.263296
$987$	25.2777	0.804596
$988$	−2.35761	−0.0750055
$989$	10.6403	0.338342
$990$	13.2367	0.420690
$991$	10.1680	0.322997	0.161499	−	0.986873i	$-0.448367\pi$
$991$	10.1680	0.322997	0.161499	+	0.986873i	$0.448367\pi$
$992$	−5.41587	−0.171954
$993$	−14.8331	−0.470714
$994$	−73.6171	−2.33499
$995$	−62.2358	−1.97301
$996$	2.83715	0.0898987
$997$	5.74776	0.182033	0.0910166	−	0.995849i	$-0.470988\pi$
$997$	5.74776	0.182033	0.0910166	+	0.995849i	$0.470988\pi$
$998$	−26.0890	−0.825832
$999$	9.01736	0.285297

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4029.2.a.l.1.25	✓	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4029.2.a.l.1.25	✓	32	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)

\(f(q)\)	\(=\)	\(q+1.48854 q^{2} -1.00000 q^{3} +0.215757 q^{4} +4.37211 q^{5} -1.48854 q^{6} -4.26225 q^{7} -2.65592 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.48854 q^{2} -1.00000 q^{3} +0.215757 q^{4} +4.37211 q^{5} -1.48854 q^{6} -4.26225 q^{7} -2.65592 q^{8} +1.00000 q^{9} +6.50806 q^{10} +2.03389 q^{11} -0.215757 q^{12} -1.63370 q^{13} -6.34454 q^{14} -4.37211 q^{15} -4.38496 q^{16} -1.00000 q^{17} +1.48854 q^{18} +6.68857 q^{19} +0.943312 q^{20} +4.26225 q^{21} +3.02754 q^{22} +0.998569 q^{23} +2.65592 q^{24} +14.1153 q^{25} -2.43184 q^{26} -1.00000 q^{27} -0.919610 q^{28} -5.55421 q^{29} -6.50806 q^{30} +4.45619 q^{31} -1.21536 q^{32} -2.03389 q^{33} -1.48854 q^{34} -18.6350 q^{35} +0.215757 q^{36} -9.01736 q^{37} +9.95622 q^{38} +1.63370 q^{39} -11.6120 q^{40} +4.65058 q^{41} +6.34454 q^{42} +10.6556 q^{43} +0.438827 q^{44} +4.37211 q^{45} +1.48641 q^{46} +5.93059 q^{47} +4.38496 q^{48} +11.1668 q^{49} +21.0112 q^{50} +1.00000 q^{51} -0.352483 q^{52} -1.83041 q^{53} -1.48854 q^{54} +8.89240 q^{55} +11.3202 q^{56} -6.68857 q^{57} -8.26767 q^{58} +9.08592 q^{59} -0.943312 q^{60} +2.34574 q^{61} +6.63322 q^{62} -4.26225 q^{63} +6.96081 q^{64} -7.14273 q^{65} -3.02754 q^{66} +6.16936 q^{67} -0.215757 q^{68} -0.998569 q^{69} -27.7390 q^{70} +11.6032 q^{71} -2.65592 q^{72} -3.88003 q^{73} -13.4227 q^{74} -14.1153 q^{75} +1.44311 q^{76} -8.66896 q^{77} +2.43184 q^{78} +1.00000 q^{79} -19.1715 q^{80} +1.00000 q^{81} +6.92259 q^{82} -13.1498 q^{83} +0.919610 q^{84} -4.37211 q^{85} +15.8613 q^{86} +5.55421 q^{87} -5.40186 q^{88} +10.2926 q^{89} +6.50806 q^{90} +6.96325 q^{91} +0.215448 q^{92} -4.45619 q^{93} +8.82793 q^{94} +29.2431 q^{95} +1.21536 q^{96} -11.2327 q^{97} +16.6222 q^{98} +2.03389 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - q^{2} - 32 q^{3} + 41 q^{4} - q^{5} + q^{6} + 4 q^{7} - 3 q^{8} + 32 q^{9}+O(q^{10}) \) 32 * q - q^2 - 32 * q^3 + 41 * q^4 - q^5 + q^6 + 4 * q^7 - 3 * q^8 + 32 * q^9	\( 32 q - q^{2} - 32 q^{3} + 41 q^{4} - q^{5} + q^{6} + 4 q^{7} - 3 q^{8} + 32 q^{9} + 17 q^{10} + 8 q^{11} - 41 q^{12} + 17 q^{13} + q^{14} + q^{15} + 55 q^{16} - 32 q^{17} - q^{18} + 48 q^{19} - 7 q^{20} - 4 q^{21} - 4 q^{22} - 19 q^{23} + 3 q^{24} + 63 q^{25} + 27 q^{26} - 32 q^{27} + 17 q^{28} - 15 q^{29} - 17 q^{30} + 20 q^{31} + 13 q^{32} - 8 q^{33} + q^{34} + 22 q^{35} + 41 q^{36} + 6 q^{37} + 11 q^{38} - 17 q^{39} + 47 q^{40} + q^{41} - q^{42} + 40 q^{43} + 22 q^{44} - q^{45} + 5 q^{46} - 5 q^{47} - 55 q^{48} + 88 q^{49} + 17 q^{50} + 32 q^{51} + 23 q^{52} - 34 q^{53} + q^{54} + 48 q^{55} - 48 q^{57} - 9 q^{58} + 41 q^{59} + 7 q^{60} + 20 q^{61} + 15 q^{62} + 4 q^{63} + 93 q^{64} - 58 q^{65} + 4 q^{66} + 52 q^{67} - 41 q^{68} + 19 q^{69} + 25 q^{70} + q^{71} - 3 q^{72} + 19 q^{73} + 12 q^{74} - 63 q^{75} + 128 q^{76} - 20 q^{77} - 27 q^{78} + 32 q^{79} - 16 q^{80} + 32 q^{81} - 5 q^{82} + 31 q^{83} - 17 q^{84} + q^{85} - 62 q^{86} + 15 q^{87} + 35 q^{88} + 18 q^{89} + 17 q^{90} + 48 q^{91} - 75 q^{92} - 20 q^{93} + 29 q^{94} + 5 q^{95} - 13 q^{96} + 17 q^{97} + 30 q^{98} + 8 q^{99}+O(q^{100}) \) 32 * q - q^2 - 32 * q^3 + 41 * q^4 - q^5 + q^6 + 4 * q^7 - 3 * q^8 + 32 * q^9 + 17 * q^10 + 8 * q^11 - 41 * q^12 + 17 * q^13 + q^14 + q^15 + 55 * q^16 - 32 * q^17 - q^18 + 48 * q^19 - 7 * q^20 - 4 * q^21 - 4 * q^22 - 19 * q^23 + 3 * q^24 + 63 * q^25 + 27 * q^26 - 32 * q^27 + 17 * q^28 - 15 * q^29 - 17 * q^30 + 20 * q^31 + 13 * q^32 - 8 * q^33 + q^34 + 22 * q^35 + 41 * q^36 + 6 * q^37 + 11 * q^38 - 17 * q^39 + 47 * q^40 + q^41 - q^42 + 40 * q^43 + 22 * q^44 - q^45 + 5 * q^46 - 5 * q^47 - 55 * q^48 + 88 * q^49 + 17 * q^50 + 32 * q^51 + 23 * q^52 - 34 * q^53 + q^54 + 48 * q^55 - 48 * q^57 - 9 * q^58 + 41 * q^59 + 7 * q^60 + 20 * q^61 + 15 * q^62 + 4 * q^63 + 93 * q^64 - 58 * q^65 + 4 * q^66 + 52 * q^67 - 41 * q^68 + 19 * q^69 + 25 * q^70 + q^71 - 3 * q^72 + 19 * q^73 + 12 * q^74 - 63 * q^75 + 128 * q^76 - 20 * q^77 - 27 * q^78 + 32 * q^79 - 16 * q^80 + 32 * q^81 - 5 * q^82 + 31 * q^83 - 17 * q^84 + q^85 - 62 * q^86 + 15 * q^87 + 35 * q^88 + 18 * q^89 + 17 * q^90 + 48 * q^91 - 75 * q^92 - 20 * q^93 + 29 * q^94 + 5 * q^95 - 13 * q^96 + 17 * q^97 + 30 * q^98 + 8 * q^99

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