LMFDB - Embedded newform 8041.2.a.e.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8041,2,Mod(1,8041)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8041, 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("8041.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8041 = 11 \cdot 17 \cdot 43 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8041.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:	$64.2077082653$
Analytic rank:	$0$
Dimension:	$66$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Character	$\chi$	$=$	8041.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.55220 q^{2} +1.68778 q^{3} +4.51375 q^{4} -1.92240 q^{5} -4.30756 q^{6} -1.71256 q^{7} -6.41560 q^{8} -0.151402 q^{9} +O(q^{10})$	\(q-2.55220 q^{2} +1.68778 q^{3} +4.51375 q^{4} -1.92240 q^{5} -4.30756 q^{6} -1.71256 q^{7} -6.41560 q^{8} -0.151402 q^{9} +4.90636 q^{10} -1.00000 q^{11} +7.61821 q^{12} -6.40187 q^{13} +4.37081 q^{14} -3.24458 q^{15} +7.34642 q^{16} -1.00000 q^{17} +0.386408 q^{18} +1.89269 q^{19} -8.67722 q^{20} -2.89043 q^{21} +2.55220 q^{22} -6.96741 q^{23} -10.8281 q^{24} -1.30438 q^{25} +16.3389 q^{26} -5.31887 q^{27} -7.73007 q^{28} +6.96156 q^{29} +8.28084 q^{30} +0.551084 q^{31} -5.91838 q^{32} -1.68778 q^{33} +2.55220 q^{34} +3.29223 q^{35} -0.683389 q^{36} -7.68935 q^{37} -4.83054 q^{38} -10.8049 q^{39} +12.3333 q^{40} -5.85830 q^{41} +7.37696 q^{42} +1.00000 q^{43} -4.51375 q^{44} +0.291054 q^{45} +17.7823 q^{46} +5.71529 q^{47} +12.3991 q^{48} -4.06713 q^{49} +3.32905 q^{50} -1.68778 q^{51} -28.8964 q^{52} -0.301009 q^{53} +13.5748 q^{54} +1.92240 q^{55} +10.9871 q^{56} +3.19445 q^{57} -17.7673 q^{58} -11.4720 q^{59} -14.6452 q^{60} -6.65328 q^{61} -1.40648 q^{62} +0.259285 q^{63} +0.412065 q^{64} +12.3070 q^{65} +4.30756 q^{66} -4.27401 q^{67} -4.51375 q^{68} -11.7594 q^{69} -8.40244 q^{70} +10.3487 q^{71} +0.971332 q^{72} +6.78711 q^{73} +19.6248 q^{74} -2.20151 q^{75} +8.54315 q^{76} +1.71256 q^{77} +27.5764 q^{78} +0.235653 q^{79} -14.1228 q^{80} -8.52287 q^{81} +14.9516 q^{82} -1.89469 q^{83} -13.0467 q^{84} +1.92240 q^{85} -2.55220 q^{86} +11.7496 q^{87} +6.41560 q^{88} -3.86590 q^{89} -0.742830 q^{90} +10.9636 q^{91} -31.4491 q^{92} +0.930108 q^{93} -14.5866 q^{94} -3.63851 q^{95} -9.98892 q^{96} -16.1511 q^{97} +10.3801 q^{98} +0.151402 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 66 q + 7 q^{2} + 3 q^{3} + 61 q^{4} + 4 q^{5} + 10 q^{6} + 14 q^{7} + 21 q^{8} + 65 q^{9}+O(q^{10}) $ 66 * q + 7 * q^2 + 3 * q^3 + 61 * q^4 + 4 * q^5 + 10 * q^6 + 14 * q^7 + 21 * q^8 + 65 * q^9	\( 66 q + 7 q^{2} + 3 q^{3} + 61 q^{4} + 4 q^{5} + 10 q^{6} + 14 q^{7} + 21 q^{8} + 65 q^{9} + 13 q^{10} - 66 q^{11} + 9 q^{12} - 12 q^{13} + 25 q^{14} + 13 q^{15} + 47 q^{16} - 66 q^{17} + 37 q^{18} + 19 q^{20} + 26 q^{21} - 7 q^{22} + 47 q^{23} + 15 q^{24} + 52 q^{25} + 16 q^{26} + 9 q^{27} + 3 q^{28} + 57 q^{29} + 2 q^{30} + 31 q^{31} + 39 q^{32} - 3 q^{33} - 7 q^{34} + 36 q^{35} + 39 q^{36} - 14 q^{37} + 18 q^{38} + 71 q^{39} + 29 q^{40} + 62 q^{41} - 3 q^{42} + 66 q^{43} - 61 q^{44} - 2 q^{45} + 19 q^{46} + 32 q^{47} + 26 q^{48} + 42 q^{49} + 10 q^{50} - 3 q^{51} - 7 q^{52} + 33 q^{53} + 100 q^{54} - 4 q^{55} + 61 q^{56} + 35 q^{57} - 16 q^{58} + 59 q^{59} + 50 q^{60} + 26 q^{61} + 29 q^{62} + 62 q^{63} + 29 q^{64} + 55 q^{65} - 10 q^{66} + 5 q^{67} - 61 q^{68} - 36 q^{69} - 35 q^{70} + 128 q^{71} + 87 q^{72} + 23 q^{73} + 64 q^{74} - 11 q^{75} + 74 q^{76} - 14 q^{77} + 45 q^{78} + 39 q^{79} + 95 q^{80} + 54 q^{81} - 6 q^{82} + 48 q^{83} + 38 q^{84} - 4 q^{85} + 7 q^{86} + 14 q^{87} - 21 q^{88} + 28 q^{89} + 135 q^{90} - 18 q^{91} + 108 q^{92} - 9 q^{93} + 37 q^{94} + 149 q^{95} + 104 q^{96} + 19 q^{97} + 30 q^{98} - 65 q^{99}+O(q^{100}) \) 66 * q + 7 * q^2 + 3 * q^3 + 61 * q^4 + 4 * q^5 + 10 * q^6 + 14 * q^7 + 21 * q^8 + 65 * q^9 + 13 * q^10 - 66 * q^11 + 9 * q^12 - 12 * q^13 + 25 * q^14 + 13 * q^15 + 47 * q^16 - 66 * q^17 + 37 * q^18 + 19 * q^20 + 26 * q^21 - 7 * q^22 + 47 * q^23 + 15 * q^24 + 52 * q^25 + 16 * q^26 + 9 * q^27 + 3 * q^28 + 57 * q^29 + 2 * q^30 + 31 * q^31 + 39 * q^32 - 3 * q^33 - 7 * q^34 + 36 * q^35 + 39 * q^36 - 14 * q^37 + 18 * q^38 + 71 * q^39 + 29 * q^40 + 62 * q^41 - 3 * q^42 + 66 * q^43 - 61 * q^44 - 2 * q^45 + 19 * q^46 + 32 * q^47 + 26 * q^48 + 42 * q^49 + 10 * q^50 - 3 * q^51 - 7 * q^52 + 33 * q^53 + 100 * q^54 - 4 * q^55 + 61 * q^56 + 35 * q^57 - 16 * q^58 + 59 * q^59 + 50 * q^60 + 26 * q^61 + 29 * q^62 + 62 * q^63 + 29 * q^64 + 55 * q^65 - 10 * q^66 + 5 * q^67 - 61 * q^68 - 36 * q^69 - 35 * q^70 + 128 * q^71 + 87 * q^72 + 23 * q^73 + 64 * q^74 - 11 * q^75 + 74 * q^76 - 14 * q^77 + 45 * q^78 + 39 * q^79 + 95 * q^80 + 54 * q^81 - 6 * q^82 + 48 * q^83 + 38 * q^84 - 4 * q^85 + 7 * q^86 + 14 * q^87 - 21 * q^88 + 28 * q^89 + 135 * q^90 - 18 * q^91 + 108 * q^92 - 9 * q^93 + 37 * q^94 + 149 * q^95 + 104 * q^96 + 19 * q^97 + 30 * q^98 - 65 * 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 $

$2$	−2.55220	−1.80468	−0.902341	−	0.431024i	$-0.858152\pi$
$2$	−2.55220	−1.80468	−0.902341	+	0.431024i	$0.858152\pi$
$3$	1.68778	0.974440	0.487220	−	0.873279i	$-0.338011\pi$
$3$	1.68778	0.974440	0.487220	+	0.873279i	$0.338011\pi$
$4$	4.51375	2.25687
$5$	−1.92240	−0.859723	−0.429861	−	0.902895i	$-0.641438\pi$
$5$	−1.92240	−0.859723	−0.429861	+	0.902895i	$0.641438\pi$
$6$	−4.30756	−1.75855
$7$	−1.71256	−0.647288	−0.323644	−	0.946179i	$-0.604908\pi$
$7$	−1.71256	−0.647288	−0.323644	+	0.946179i	$0.604908\pi$
$8$	−6.41560	−2.26826
$9$	−0.151402	−0.0504672
$10$	4.90636	1.55153
$11$	−1.00000	−0.301511
$11$	−1.00000	−0.301511
$12$	7.61821	2.19919
$13$	−6.40187	−1.77556	−0.887780	−	0.460268i	$-0.847753\pi$
$13$	−6.40187	−1.77556	−0.887780	+	0.460268i	$0.847753\pi$
$14$	4.37081	1.16815
$15$	−3.24458	−0.837748
$16$	7.34642	1.83661
$17$	−1.00000	−0.242536
$17$	−1.00000	−0.242536
$18$	0.386408	0.0910773
$19$	1.89269	0.434214	0.217107	−	0.976148i	$-0.430338\pi$
$19$	1.89269	0.434214	0.217107	+	0.976148i	$0.430338\pi$
$20$	−8.67722	−1.94029
$21$	−2.89043	−0.630743
$22$	2.55220	0.544132
$23$	−6.96741	−1.45281	−0.726403	−	0.687269i	$-0.758809\pi$
$23$	−6.96741	−1.45281	−0.726403	+	0.687269i	$0.758809\pi$
$24$	−10.8281	−2.21028
$25$	−1.30438	−0.260877
$26$	16.3389	3.20432
$27$	−5.31887	−1.02362
$28$	−7.73007	−1.46085
$29$	6.96156	1.29273	0.646364	−	0.763029i	$-0.276289\pi$
$29$	6.96156	1.29273	0.646364	+	0.763029i	$0.276289\pi$
$30$	8.28084	1.51187
$31$	0.551084	0.0989776	0.0494888	−	0.998775i	$-0.484241\pi$
$31$	0.551084	0.0989776	0.0494888	+	0.998775i	$0.484241\pi$
$32$	−5.91838	−1.04623
$33$	−1.68778	−0.293805
$34$	2.55220	0.437699
$35$	3.29223	0.556488
$36$	−0.683389	−0.113898
$37$	−7.68935	−1.26412	−0.632061	−	0.774919i	$-0.717791\pi$
$37$	−7.68935	−1.26412	−0.632061	+	0.774919i	$0.717791\pi$
$38$	−4.83054	−0.783618
$39$	−10.8049	−1.73018
$40$	12.3333	1.95007
$41$	−5.85830	−0.914913	−0.457456	−	0.889232i	$-0.651239\pi$
$41$	−5.85830	−0.914913	−0.457456	+	0.889232i	$0.651239\pi$
$42$	7.37696	1.13829
$43$	1.00000	0.152499
$43$	1.00000	0.152499
$44$	−4.51375	−0.680473
$45$	0.291054	0.0433878
$46$	17.7823	2.62185
$47$	5.71529	0.833661	0.416831	−	0.908984i	$-0.363141\pi$
$47$	5.71529	0.833661	0.416831	+	0.908984i	$0.363141\pi$
$48$	12.3991	1.78966
$49$	−4.06713	−0.581019
$50$	3.32905	0.470799
$51$	−1.68778	−0.236336
$52$	−28.8964	−4.00721
$53$	−0.301009	−0.0413468	−0.0206734	−	0.999786i	$-0.506581\pi$
$53$	−0.301009	−0.0413468	−0.0206734	+	0.999786i	$0.506581\pi$
$54$	13.5748	1.84730
$55$	1.92240	0.259216
$56$	10.9871	1.46821
$57$	3.19445	0.423115
$58$	−17.7673	−2.33296
$59$	−11.4720	−1.49353	−0.746764	−	0.665089i	$-0.768394\pi$
$59$	−11.4720	−1.49353	−0.746764	+	0.665089i	$0.768394\pi$
$60$	−14.6452	−1.89069
$61$	−6.65328	−0.851866	−0.425933	−	0.904755i	$-0.640054\pi$
$61$	−6.65328	−0.851866	−0.425933	+	0.904755i	$0.640054\pi$
$62$	−1.40648	−0.178623
$63$	0.259285	0.0326668
$64$	0.412065	0.0515081
$65$	12.3070	1.52649
$66$	4.30756	0.530224
$67$	−4.27401	−0.522154	−0.261077	−	0.965318i	$-0.584078\pi$
$67$	−4.27401	−0.522154	−0.261077	+	0.965318i	$0.584078\pi$
$68$	−4.51375	−0.547372
$69$	−11.7594	−1.41567
$70$	−8.40244	−1.00428
$71$	10.3487	1.22816	0.614080	−	0.789243i	$-0.289527\pi$
$71$	10.3487	1.22816	0.614080	+	0.789243i	$0.289527\pi$
$72$	0.971332	0.114473
$73$	6.78711	0.794371	0.397186	−	0.917738i	$-0.369987\pi$
$73$	6.78711	0.794371	0.397186	+	0.917738i	$0.369987\pi$
$74$	19.6248	2.28134
$75$	−2.20151	−0.254208
$76$	8.54315	0.979966
$77$	1.71256	0.195165
$78$	27.5764	3.12242
$79$	0.235653	0.0265131	0.0132565	−	0.999912i	$-0.495780\pi$
$79$	0.235653	0.0265131	0.0132565	+	0.999912i	$0.495780\pi$
$80$	−14.1228	−1.57897
$81$	−8.52287	−0.946986
$82$	14.9516	1.65113
$83$	−1.89469	−0.207969	−0.103985	−	0.994579i	$-0.533159\pi$
$83$	−1.89469	−0.207969	−0.103985	+	0.994579i	$0.533159\pi$
$84$	−13.0467	−1.42351
$85$	1.92240	0.208513
$86$	−2.55220	−0.275211
$87$	11.7496	1.25969
$88$	6.41560	0.683905
$89$	−3.86590	−0.409785	−0.204892	−	0.978785i	$-0.565684\pi$
$89$	−3.86590	−0.409785	−0.204892	+	0.978785i	$0.565684\pi$
$90$	−0.742830	−0.0783012
$91$	10.9636	1.14930
$92$	−31.4491	−3.27880
$93$	0.930108	0.0964477
$94$	−14.5866	−1.50449
$95$	−3.63851	−0.373304
$96$	−9.98892	−1.01949
$97$	−16.1511	−1.63990	−0.819950	−	0.572435i	$-0.805999\pi$
$97$	−16.1511	−1.63990	−0.819950	+	0.572435i	$0.805999\pi$
$98$	10.3801	1.04855
$99$	0.151402	0.0152164
$100$	−5.88765	−0.588765
$101$	−2.07002	−0.205975	−0.102987	−	0.994683i	$-0.532840\pi$
$101$	−2.07002	−0.205975	−0.102987	+	0.994683i	$0.532840\pi$
$102$	4.30756	0.426512
$103$	−14.9127	−1.46939	−0.734694	−	0.678399i	$-0.762674\pi$
$103$	−14.9127	−1.46939	−0.734694	+	0.678399i	$0.762674\pi$
$104$	41.0718	4.02742
$105$	5.55655	0.542264
$106$	0.768237	0.0746178
$107$	−1.95233	−0.188739	−0.0943695	−	0.995537i	$-0.530083\pi$
$107$	−1.95233	−0.188739	−0.0943695	+	0.995537i	$0.530083\pi$
$108$	−24.0080	−2.31017
$109$	17.8985	1.71436	0.857181	−	0.515015i	$-0.172214\pi$
$109$	17.8985	1.71436	0.857181	+	0.515015i	$0.172214\pi$
$110$	−4.90636	−0.467803
$111$	−12.9779	−1.23181
$112$	−12.5812	−1.18881
$113$	−15.0834	−1.41892	−0.709462	−	0.704744i	$-0.751062\pi$
$113$	−15.0834	−1.41892	−0.709462	+	0.704744i	$0.751062\pi$
$114$	−8.15289	−0.763588
$115$	13.3941	1.24901
$116$	31.4227	2.91753
$117$	0.969254	0.0896076
$118$	29.2789	2.69534
$119$	1.71256	0.156990
$120$	20.8160	1.90023
$121$	1.00000	0.0909091
$122$	16.9805	1.53735
$123$	−9.88752	−0.891528
$124$	2.48745	0.223380
$125$	12.1195	1.08400
$126$	−0.661748	−0.0589532
$127$	−5.60771	−0.497604	−0.248802	−	0.968554i	$-0.580037\pi$
$127$	−5.60771	−0.497604	−0.248802	+	0.968554i	$0.580037\pi$
$128$	10.7851	0.953276
$129$	1.68778	0.148601
$130$	−31.4099	−2.75483
$131$	12.2234	1.06796	0.533981	−	0.845497i	$-0.320695\pi$
$131$	12.2234	1.06796	0.533981	+	0.845497i	$0.320695\pi$
$132$	−7.61821	−0.663080
$133$	−3.24136	−0.281061
$134$	10.9082	0.942321
$135$	10.2250	0.880027
$136$	6.41560	0.550133
$137$	−15.9971	−1.36672	−0.683362	−	0.730080i	$-0.739483\pi$
$137$	−15.9971	−1.36672	−0.683362	+	0.730080i	$0.739483\pi$
$138$	30.0125	2.55483
$139$	−16.2289	−1.37652	−0.688260	−	0.725464i	$-0.741625\pi$
$139$	−16.2289	−1.37652	−0.688260	+	0.725464i	$0.741625\pi$
$140$	14.8603	1.25592
$141$	9.64616	0.812353
$142$	−26.4119	−2.21644
$143$	6.40187	0.535351
$144$	−1.11226	−0.0926884
$145$	−13.3829	−1.11139
$146$	−17.3221	−1.43359
$147$	−6.86442	−0.566168
$148$	−34.7078	−2.85296
$149$	3.35518	0.274867	0.137433	−	0.990511i	$-0.456115\pi$
$149$	3.35518	0.274867	0.137433	+	0.990511i	$0.456115\pi$
$150$	5.61870	0.458765
$151$	−14.4532	−1.17618	−0.588092	−	0.808794i	$-0.700121\pi$
$151$	−14.4532	−1.17618	−0.588092	+	0.808794i	$0.700121\pi$
$152$	−12.1428	−0.984909
$153$	0.151402	0.0122401
$154$	−4.37081	−0.352210
$155$	−1.05940	−0.0850933
$156$	−48.7708	−3.90479
$157$	9.18243	0.732838	0.366419	−	0.930450i	$-0.380584\pi$
$157$	9.18243	0.732838	0.366419	+	0.930450i	$0.380584\pi$
$158$	−0.601436	−0.0478477
$159$	−0.508037	−0.0402900
$160$	11.3775	0.899469
$161$	11.9321	0.940383
$162$	21.7521	1.70901
$163$	3.19517	0.250265	0.125132	−	0.992140i	$-0.460064\pi$
$163$	3.19517	0.250265	0.125132	+	0.992140i	$0.460064\pi$
$164$	−26.4429	−2.06484
$165$	3.24458	0.252591
$166$	4.83564	0.375319
$167$	−22.9659	−1.77715	−0.888577	−	0.458728i	$-0.848305\pi$
$167$	−22.9659	−1.77715	−0.888577	+	0.458728i	$0.848305\pi$
$168$	18.5438	1.43069
$169$	27.9840	2.15261
$170$	−4.90636	−0.376300
$171$	−0.286557	−0.0219136
$172$	4.51375	0.344170
$173$	12.2167	0.928819	0.464410	−	0.885620i	$-0.346267\pi$
$173$	12.2167	0.928819	0.464410	+	0.885620i	$0.346267\pi$
$174$	−29.9873	−2.27333
$175$	2.23384	0.168862
$176$	−7.34642	−0.553758
$177$	−19.3622	−1.45535
$178$	9.86657	0.739531
$179$	20.6365	1.54244	0.771221	−	0.636568i	$-0.219647\pi$
$179$	20.6365	1.54244	0.771221	+	0.636568i	$0.219647\pi$
$180$	1.31375	0.0979209
$181$	−20.6164	−1.53241	−0.766203	−	0.642599i	$-0.777856\pi$
$181$	−20.6164	−1.53241	−0.766203	+	0.642599i	$0.777856\pi$
$182$	−27.9814	−2.07412
$183$	−11.2293	−0.830092
$184$	44.7001	3.29533
$185$	14.7820	1.08679
$186$	−2.37383	−0.174057
$187$	1.00000	0.0731272
$188$	25.7974	1.88147
$189$	9.10890	0.662575
$190$	9.28623	0.673694
$191$	−7.64041	−0.552840	−0.276420	−	0.961037i	$-0.589148\pi$
$191$	−7.64041	−0.552840	−0.276420	+	0.961037i	$0.589148\pi$
$192$	0.695474	0.0501915
$193$	−3.15747	−0.227280	−0.113640	−	0.993522i	$-0.536251\pi$
$193$	−3.15747	−0.227280	−0.113640	+	0.993522i	$0.536251\pi$
$194$	41.2210	2.95950
$195$	20.7714	1.48747
$196$	−18.3580	−1.31129
$197$	13.9627	0.994803	0.497401	−	0.867520i	$-0.334288\pi$
$197$	13.9627	0.994803	0.497401	+	0.867520i	$0.334288\pi$
$198$	−0.386408	−0.0274608
$199$	−4.46228	−0.316323	−0.158161	−	0.987413i	$-0.550557\pi$
$199$	−4.46228	−0.316323	−0.158161	+	0.987413i	$0.550557\pi$
$200$	8.36840	0.591735
$201$	−7.21359	−0.508808
$202$	5.28312	0.371719
$203$	−11.9221	−0.836767
$204$	−7.61821	−0.533381
$205$	11.2620	0.786572
$206$	38.0602	2.65178
$207$	1.05488	0.0733191
$208$	−47.0309	−3.26100
$209$	−1.89269	−0.130920
$210$	−14.1815	−0.978614
$211$	8.19721	0.564319	0.282160	−	0.959367i	$-0.408949\pi$
$211$	8.19721	0.564319	0.282160	+	0.959367i	$0.408949\pi$
$212$	−1.35868	−0.0933145
$213$	17.4663	1.19677
$214$	4.98275	0.340614
$215$	−1.92240	−0.131107
$216$	34.1237	2.32183
$217$	−0.943766	−0.0640670
$218$	−45.6805	−3.09388
$219$	11.4551	0.774067
$220$	8.67722	0.585018
$221$	6.40187	0.430636
$222$	33.1223	2.22303
$223$	7.44534	0.498577	0.249288	−	0.968429i	$-0.419803\pi$
$223$	7.44534	0.498577	0.249288	+	0.968429i	$0.419803\pi$
$224$	10.1356	0.677213
$225$	0.197486	0.0131657
$226$	38.4958	2.56070
$227$	6.52721	0.433226	0.216613	−	0.976258i	$-0.430499\pi$
$227$	6.52721	0.433226	0.216613	+	0.976258i	$0.430499\pi$
$228$	14.4189	0.954918
$229$	1.53271	0.101285	0.0506423	−	0.998717i	$-0.483873\pi$
$229$	1.53271	0.101285	0.0506423	+	0.998717i	$0.483873\pi$
$230$	−34.1846	−2.25406
$231$	2.89043	0.190176
$232$	−44.6626	−2.93224
$233$	5.42224	0.355222	0.177611	−	0.984101i	$-0.443163\pi$
$233$	5.42224	0.355222	0.177611	+	0.984101i	$0.443163\pi$
$234$	−2.47373	−0.161713
$235$	−10.9871	−0.716718
$236$	−51.7818	−3.37071
$237$	0.397731	0.0258354
$238$	−4.37081	−0.283317
$239$	4.43750	0.287038	0.143519	−	0.989648i	$-0.454158\pi$
$239$	4.43750	0.287038	0.143519	+	0.989648i	$0.454158\pi$
$240$	−23.8361	−1.53861
$241$	−17.5467	−1.13029	−0.565143	−	0.824993i	$-0.691179\pi$
$241$	−17.5467	−1.13029	−0.565143	+	0.824993i	$0.691179\pi$
$242$	−2.55220	−0.164062
$243$	1.57188	0.100836
$244$	−30.0312	−1.92255
$245$	7.81865	0.499515
$246$	25.2350	1.60892
$247$	−12.1168	−0.770973
$248$	−3.53553	−0.224507
$249$	−3.19782	−0.202654
$250$	−30.9315	−1.95628
$251$	−4.11194	−0.259543	−0.129772	−	0.991544i	$-0.541424\pi$
$251$	−4.11194	−0.259543	−0.129772	+	0.991544i	$0.541424\pi$
$252$	1.17035	0.0737249
$253$	6.96741	0.438037
$254$	14.3120	0.898016
$255$	3.24458	0.203184
$256$	−28.3499	−1.77187
$257$	23.8685	1.48887	0.744437	−	0.667692i	$-0.232718\pi$
$257$	23.8685	1.48887	0.744437	+	0.667692i	$0.232718\pi$
$258$	−4.30756	−0.268177
$259$	13.1685	0.818251
$260$	55.5505	3.44509
$261$	−1.05399	−0.0652404
$262$	−31.1966	−1.92733
$263$	10.9249	0.673657	0.336828	−	0.941566i	$-0.390646\pi$
$263$	10.9249	0.673657	0.336828	+	0.941566i	$0.390646\pi$
$264$	10.8281	0.666424
$265$	0.578660	0.0355468
$266$	8.27261	0.507226
$267$	−6.52479	−0.399311
$268$	−19.2918	−1.17844
$269$	17.8740	1.08980	0.544898	−	0.838503i	$-0.316569\pi$
$269$	17.8740	1.08980	0.544898	+	0.838503i	$0.316569\pi$
$270$	−26.0963	−1.58817
$271$	13.8827	0.843315	0.421658	−	0.906755i	$-0.361448\pi$
$271$	13.8827	0.843315	0.421658	+	0.906755i	$0.361448\pi$
$272$	−7.34642	−0.445442
$273$	18.5041	1.11992
$274$	40.8278	2.46650
$275$	1.30438	0.0786572
$276$	−53.0792	−3.19499
$277$	−31.2867	−1.87984	−0.939918	−	0.341399i	$-0.889099\pi$
$277$	−31.2867	−1.87984	−0.939918	+	0.341399i	$0.889099\pi$
$278$	41.4196	2.48418
$279$	−0.0834351	−0.00499513
$280$	−21.1216	−1.26226
$281$	25.6949	1.53283	0.766415	−	0.642346i	$-0.222039\pi$
$281$	25.6949	1.53283	0.766415	+	0.642346i	$0.222039\pi$
$282$	−24.6190	−1.46604
$283$	5.36402	0.318858	0.159429	−	0.987209i	$-0.449035\pi$
$283$	5.36402	0.318858	0.159429	+	0.987209i	$0.449035\pi$
$284$	46.7113	2.77180
$285$	−6.14101	−0.363762
$286$	−16.3389	−0.966139
$287$	10.0327	0.592212
$288$	0.896052	0.0528004
$289$	1.00000	0.0588235
$290$	34.1559	2.00570
$291$	−27.2596	−1.59798
$292$	30.6353	1.79280
$293$	21.9399	1.28174	0.640870	−	0.767649i	$-0.278574\pi$
$293$	21.9399	1.28174	0.640870	+	0.767649i	$0.278574\pi$
$294$	17.5194	1.02175
$295$	22.0538	1.28402
$296$	49.3318	2.86735
$297$	5.31887	0.308632
$298$	−8.56310	−0.496047
$299$	44.6045	2.57954
$300$	−9.93706	−0.573716
$301$	−1.71256	−0.0987104
$302$	36.8875	2.12264
$303$	−3.49374	−0.200710
$304$	13.9045	0.797480
$305$	12.7903	0.732369
$306$	−0.386408	−0.0220895
$307$	23.2245	1.32549	0.662745	−	0.748845i	$-0.269391\pi$
$307$	23.2245	1.32549	0.662745	+	0.748845i	$0.269391\pi$
$308$	7.73007	0.440462
$309$	−25.1693	−1.43183
$310$	2.70381	0.153566
$311$	10.8561	0.615596	0.307798	−	0.951452i	$-0.400408\pi$
$311$	10.8561	0.615596	0.307798	+	0.951452i	$0.400408\pi$
$312$	69.3202	3.92448
$313$	−7.73472	−0.437192	−0.218596	−	0.975815i	$-0.570148\pi$
$313$	−7.73472	−0.437192	−0.218596	+	0.975815i	$0.570148\pi$
$314$	−23.4354	−1.32254
$315$	−0.498449	−0.0280844
$316$	1.06368	0.0598367
$317$	−5.07509	−0.285046	−0.142523	−	0.989792i	$-0.545521\pi$
$317$	−5.07509	−0.285046	−0.142523	+	0.989792i	$0.545521\pi$
$318$	1.29661	0.0727105
$319$	−6.96156	−0.389772
$320$	−0.792153	−0.0442827
$321$	−3.29510	−0.183915
$322$	−30.4532	−1.69709
$323$	−1.89269	−0.105312
$324$	−38.4701	−2.13723
$325$	8.35049	0.463202
$326$	−8.15471	−0.451648
$327$	30.2087	1.67054
$328$	37.5845	2.07526
$329$	−9.78780	−0.539619
$330$	−8.28084	−0.455845
$331$	35.8776	1.97201	0.986004	−	0.166719i	$-0.0533173\pi$
$331$	35.8776	1.97201	0.986004	+	0.166719i	$0.0533173\pi$
$332$	−8.55216	−0.469361
$333$	1.16418	0.0637967
$334$	58.6136	3.20720
$335$	8.21636	0.448908
$336$	−21.2343	−1.15843
$337$	14.5541	0.792814	0.396407	−	0.918075i	$-0.370257\pi$
$337$	14.5541	0.792814	0.396407	+	0.918075i	$0.370257\pi$
$338$	−71.4208	−3.88478
$339$	−25.4574	−1.38266
$340$	8.67722	0.470589
$341$	−0.551084	−0.0298429
$342$	0.731352	0.0395470
$343$	18.9531	1.02337
$344$	−6.41560	−0.345906
$345$	22.6063	1.21708
$346$	−31.1795	−1.67622
$347$	−19.1165	−1.02623	−0.513113	−	0.858321i	$-0.671508\pi$
$347$	−19.1165	−1.02623	−0.513113	+	0.858321i	$0.671508\pi$
$348$	53.0346	2.84295
$349$	20.0039	1.07078	0.535392	−	0.844604i	$-0.320164\pi$
$349$	20.0039	1.07078	0.535392	+	0.844604i	$0.320164\pi$
$350$	−5.70121	−0.304742
$351$	34.0507	1.81749
$352$	5.91838	0.315451
$353$	−1.86843	−0.0994465	−0.0497233	−	0.998763i	$-0.515834\pi$
$353$	−1.86843	−0.0994465	−0.0497233	+	0.998763i	$0.515834\pi$
$354$	49.4163	2.62645
$355$	−19.8943	−1.05588
$356$	−17.4497	−0.924833
$357$	2.89043	0.152978
$358$	−52.6685	−2.78361
$359$	6.51806	0.344010	0.172005	−	0.985096i	$-0.444976\pi$
$359$	6.51806	0.344010	0.172005	+	0.985096i	$0.444976\pi$
$360$	−1.86729	−0.0984147
$361$	−15.4177	−0.811458
$362$	52.6173	2.76550
$363$	1.68778	0.0885854
$364$	49.4869	2.59382
$365$	−13.0475	−0.682939
$366$	28.6594	1.49805
$367$	−22.5368	−1.17641	−0.588205	−	0.808712i	$-0.700165\pi$
$367$	−22.5368	−1.17641	−0.588205	+	0.808712i	$0.700165\pi$
$368$	−51.1855	−2.66823
$369$	0.886957	0.0461731
$370$	−37.7267	−1.96132
$371$	0.515497	0.0267633
$372$	4.19827	0.217670
$373$	−33.4475	−1.73184	−0.865922	−	0.500179i	$-0.833268\pi$
$373$	−33.4475	−1.73184	−0.865922	+	0.500179i	$0.833268\pi$
$374$	−2.55220	−0.131971
$375$	20.4551	1.05630
$376$	−36.6670	−1.89096
$377$	−44.5670	−2.29532
$378$	−23.2478	−1.19574
$379$	32.2903	1.65864	0.829322	−	0.558772i	$-0.188727\pi$
$379$	32.2903	1.65864	0.829322	+	0.558772i	$0.188727\pi$
$380$	−16.4233	−0.842499
$381$	−9.46458	−0.484885
$382$	19.4999	0.997701
$383$	−11.8352	−0.604751	−0.302376	−	0.953189i	$-0.597780\pi$
$383$	−11.8352	−0.604751	−0.302376	+	0.953189i	$0.597780\pi$
$384$	18.2028	0.928910
$385$	−3.29223	−0.167787
$386$	8.05851	0.410167
$387$	−0.151402	−0.00769618
$388$	−72.9022	−3.70105
$389$	−5.24028	−0.265693	−0.132846	−	0.991137i	$-0.542412\pi$
$389$	−5.24028	−0.265693	−0.132846	+	0.991137i	$0.542412\pi$
$390$	−53.0129	−2.68441
$391$	6.96741	0.352357
$392$	26.0931	1.31790
$393$	20.6304	1.04066
$394$	−35.6357	−1.79530
$395$	−0.453020	−0.0227939
$396$	0.683389	0.0343416
$397$	30.6811	1.53984	0.769921	−	0.638140i	$-0.220296\pi$
$397$	30.6811	1.53984	0.769921	+	0.638140i	$0.220296\pi$
$398$	11.3887	0.570862
$399$	−5.47070	−0.273877
$400$	−9.58255	−0.479127
$401$	36.4597	1.82071	0.910355	−	0.413827i	$-0.135808\pi$
$401$	36.4597	1.82071	0.910355	+	0.413827i	$0.135808\pi$
$402$	18.4106	0.918235
$403$	−3.52797	−0.175741
$404$	−9.34356	−0.464859
$405$	16.3844	0.814145
$406$	30.4276	1.51010
$407$	7.68935	0.381147
$408$	10.8281	0.536071
$409$	−31.4341	−1.55432	−0.777158	−	0.629305i	$-0.783340\pi$
$409$	−31.4341	−1.55432	−0.777158	+	0.629305i	$0.783340\pi$
$410$	−28.7429	−1.41951
$411$	−26.9995	−1.33179
$412$	−67.3120	−3.31622
$413$	19.6465	0.966743
$414$	−2.69226	−0.132318
$415$	3.64235	0.178796
$416$	37.8887	1.85765
$417$	−27.3909	−1.34134
$418$	4.83054	0.236270
$419$	−23.8544	−1.16536	−0.582681	−	0.812701i	$-0.697996\pi$
$419$	−23.8544	−1.16536	−0.582681	+	0.812701i	$0.697996\pi$
$420$	25.0809	1.22382
$421$	−32.9763	−1.60717	−0.803584	−	0.595191i	$-0.797076\pi$
$421$	−32.9763	−1.60717	−0.803584	+	0.595191i	$0.797076\pi$
$422$	−20.9210	−1.01842
$423$	−0.865305	−0.0420726
$424$	1.93115	0.0937851
$425$	1.30438	0.0632719
$426$	−44.5775	−2.15979
$427$	11.3942	0.551402
$428$	−8.81233	−0.425960
$429$	10.8049	0.521668
$430$	4.90636	0.236605
$431$	−1.94724	−0.0937954	−0.0468977	−	0.998900i	$-0.514933\pi$
$431$	−1.94724	−0.0937954	−0.0468977	+	0.998900i	$0.514933\pi$
$432$	−39.0747	−1.87998
$433$	−14.8348	−0.712917	−0.356459	−	0.934311i	$-0.616016\pi$
$433$	−14.8348	−0.712917	−0.356459	+	0.934311i	$0.616016\pi$
$434$	2.40868	0.115620
$435$	−22.5874	−1.08298
$436$	80.7891	3.86910
$437$	−13.1872	−0.630828
$438$	−29.2359	−1.39694
$439$	−7.15444	−0.341463	−0.170731	−	0.985318i	$-0.554613\pi$
$439$	−7.15444	−0.341463	−0.170731	+	0.985318i	$0.554613\pi$
$440$	−12.3333	−0.587969
$441$	0.615770	0.0293224
$442$	−16.3389	−0.777161
$443$	38.4837	1.82841	0.914207	−	0.405247i	$-0.132815\pi$
$443$	38.4837	1.82841	0.914207	+	0.405247i	$0.132815\pi$
$444$	−58.5791	−2.78004
$445$	7.43181	0.352301
$446$	−19.0020	−0.899772
$447$	5.66280	0.267841
$448$	−0.705687	−0.0333406
$449$	25.9163	1.22307	0.611534	−	0.791218i	$-0.290553\pi$
$449$	25.9163	1.22307	0.611534	+	0.791218i	$0.290553\pi$
$450$	−0.504024	−0.0237599
$451$	5.85830	0.275857
$452$	−68.0825	−3.20233
$453$	−24.3938	−1.14612
$454$	−16.6588	−0.781836
$455$	−21.0764	−0.988078
$456$	−20.4943	−0.959734
$457$	−5.90871	−0.276398	−0.138199	−	0.990404i	$-0.544131\pi$
$457$	−5.90871	−0.276398	−0.138199	+	0.990404i	$0.544131\pi$
$458$	−3.91180	−0.182786
$459$	5.31887	0.248264
$460$	60.4578	2.81886
$461$	5.02210	0.233902	0.116951	−	0.993138i	$-0.462688\pi$
$461$	5.02210	0.233902	0.116951	+	0.993138i	$0.462688\pi$
$462$	−7.37696	−0.343207
$463$	27.7142	1.28799	0.643995	−	0.765030i	$-0.277276\pi$
$463$	27.7142	1.28799	0.643995	+	0.765030i	$0.277276\pi$
$464$	51.1426	2.37423
$465$	−1.78804	−0.0829183
$466$	−13.8387	−0.641063
$467$	−21.0998	−0.976383	−0.488192	−	0.872737i	$-0.662343\pi$
$467$	−21.0998	−0.976383	−0.488192	+	0.872737i	$0.662343\pi$
$468$	4.37497	0.202233
$469$	7.31951	0.337984
$470$	28.0413	1.29345
$471$	15.4979	0.714106
$472$	73.5998	3.38771
$473$	−1.00000	−0.0459800
$474$	−1.01509	−0.0466247
$475$	−2.46880	−0.113276
$476$	7.73007	0.354307
$477$	0.0455733	0.00208666
$478$	−11.3254	−0.518012
$479$	−20.2569	−0.925560	−0.462780	−	0.886473i	$-0.653148\pi$
$479$	−20.2569	−0.925560	−0.462780	+	0.886473i	$0.653148\pi$
$480$	19.2027	0.876478
$481$	49.2263	2.24452
$482$	44.7829	2.03980
$483$	20.1388	0.916346
$484$	4.51375	0.205170
$485$	31.0489	1.40986
$486$	−4.01177	−0.181978
$487$	−36.8996	−1.67208	−0.836040	−	0.548668i	$-0.815135\pi$
$487$	−36.8996	−1.67208	−0.836040	+	0.548668i	$0.815135\pi$
$488$	42.6848	1.93225
$489$	5.39273	0.243868
$490$	−19.9548	−0.901465
$491$	−20.5684	−0.928239	−0.464119	−	0.885773i	$-0.653629\pi$
$491$	−20.5684	−0.928239	−0.464119	+	0.885773i	$0.653629\pi$
$492$	−44.6298	−2.01207
$493$	−6.96156	−0.313533
$494$	30.9245	1.39136
$495$	−0.291054	−0.0130819
$496$	4.04850	0.181783
$497$	−17.7227	−0.794973
$498$	8.16149	0.365725
$499$	−44.6401	−1.99837	−0.999183	−	0.0404211i	$-0.987130\pi$
$499$	−44.6401	−1.99837	−0.999183	+	0.0404211i	$0.987130\pi$
$500$	54.7045	2.44646
$501$	−38.7613	−1.73173
$502$	10.4945	0.468393
$503$	−14.1099	−0.629130	−0.314565	−	0.949236i	$-0.601859\pi$
$503$	−14.1099	−0.629130	−0.314565	+	0.949236i	$0.601859\pi$
$504$	−1.66347	−0.0740967
$505$	3.97941	0.177081
$506$	−17.7823	−0.790518
$507$	47.2307	2.09759
$508$	−25.3118	−1.12303
$509$	8.10193	0.359112	0.179556	−	0.983748i	$-0.442534\pi$
$509$	8.10193	0.359112	0.179556	+	0.983748i	$0.442534\pi$
$510$	−8.28084	−0.366682
$511$	−11.6234	−0.514187
$512$	50.7845	2.24438
$513$	−10.0670	−0.444469
$514$	−60.9172	−2.68694
$515$	28.6681	1.26327
$516$	7.61821	0.335373
$517$	−5.71529	−0.251358
$518$	−33.6087	−1.47668
$519$	20.6191	0.905078
$520$	−78.9564	−3.46247
$521$	−6.85285	−0.300229	−0.150114	−	0.988669i	$-0.547964\pi$
$521$	−6.85285	−0.300229	−0.150114	+	0.988669i	$0.547964\pi$
$522$	2.69000	0.117738
$523$	3.66908	0.160437	0.0802187	−	0.996777i	$-0.474438\pi$
$523$	3.66908	0.160437	0.0802187	+	0.996777i	$0.474438\pi$
$524$	55.1732	2.41025
$525$	3.77022	0.164546
$526$	−27.8825	−1.21574
$527$	−0.551084	−0.0240056
$528$	−12.3991	−0.539603
$529$	25.5448	1.11064
$530$	−1.47686	−0.0641506
$531$	1.73688	0.0753743
$532$	−14.6307	−0.634320
$533$	37.5041	1.62448
$534$	16.6526	0.720628
$535$	3.75316	0.162263
$536$	27.4204	1.18438
$537$	34.8298	1.50302
$538$	−45.6180	−1.96673
$539$	4.06713	0.175184
$540$	46.1530	1.98611
$541$	−5.31845	−0.228658	−0.114329	−	0.993443i	$-0.536472\pi$
$541$	−5.31845	−0.228658	−0.114329	+	0.993443i	$0.536472\pi$
$542$	−35.4315	−1.52191
$543$	−34.7959	−1.49324
$544$	5.91838	0.253748
$545$	−34.4080	−1.47388
$546$	−47.2263	−2.02110
$547$	12.4208	0.531073	0.265537	−	0.964101i	$-0.414451\pi$
$547$	12.4208	0.531073	0.265537	+	0.964101i	$0.414451\pi$
$548$	−72.2068	−3.08452
$549$	1.00732	0.0429913
$550$	−3.32905	−0.141951
$551$	13.1761	0.561321
$552$	75.4439	3.21111
$553$	−0.403571	−0.0171616
$554$	79.8501	3.39251
$555$	24.9488	1.05902
$556$	−73.2533	−3.10663
$557$	−15.8086	−0.669831	−0.334916	−	0.942248i	$-0.608708\pi$
$557$	−15.8086	−0.669831	−0.334916	+	0.942248i	$0.608708\pi$
$558$	0.212943	0.00901461
$559$	−6.40187	−0.270770
$560$	24.1861	1.02205
$561$	1.68778	0.0712581
$562$	−65.5786	−2.76627
$563$	−34.8260	−1.46774	−0.733870	−	0.679290i	$-0.762288\pi$
$563$	−34.8260	−1.46774	−0.733870	+	0.679290i	$0.762288\pi$
$564$	43.5403	1.83338
$565$	28.9962	1.21988
$566$	−13.6901	−0.575437
$567$	14.5959	0.612972
$568$	−66.3929	−2.78578
$569$	33.1339	1.38904	0.694522	−	0.719472i	$-0.255616\pi$
$569$	33.1339	1.38904	0.694522	+	0.719472i	$0.255616\pi$
$570$	15.6731	0.656474
$571$	−25.3751	−1.06192	−0.530958	−	0.847398i	$-0.678168\pi$
$571$	−25.3751	−1.06192	−0.530958	+	0.847398i	$0.678168\pi$
$572$	28.8964	1.20822
$573$	−12.8953	−0.538710
$574$	−25.6055	−1.06875
$575$	9.08817	0.379003
$576$	−0.0623873	−0.00259947
$577$	−22.7286	−0.946205	−0.473102	−	0.881007i	$-0.656866\pi$
$577$	−22.7286	−0.946205	−0.473102	+	0.881007i	$0.656866\pi$
$578$	−2.55220	−0.106158
$579$	−5.32911	−0.221470
$580$	−60.4070	−2.50826
$581$	3.24478	0.134616
$582$	69.5720	2.88385
$583$	0.301009	0.0124665
$584$	−43.5434	−1.80184
$585$	−1.86329	−0.0770377
$586$	−55.9950	−2.31313
$587$	16.3772	0.675957	0.337979	−	0.941154i	$-0.390257\pi$
$587$	16.3772	0.675957	0.337979	+	0.941154i	$0.390257\pi$
$588$	−30.9843	−1.27777
$589$	1.04303	0.0429775
$590$	−56.2858	−2.31725
$591$	23.5660	0.969376
$592$	−56.4893	−2.32169
$593$	−24.0978	−0.989578	−0.494789	−	0.869013i	$-0.664755\pi$
$593$	−24.0978	−0.989578	−0.494789	+	0.869013i	$0.664755\pi$
$594$	−13.5748	−0.556983
$595$	−3.29223	−0.134968
$596$	15.1444	0.620340
$597$	−7.53135	−0.308237
$598$	−113.840	−4.65525
$599$	19.6342	0.802233	0.401117	−	0.916027i	$-0.368622\pi$
$599$	19.6342	0.802233	0.401117	+	0.916027i	$0.368622\pi$
$600$	14.1240	0.576610
$601$	29.0284	1.18409	0.592046	−	0.805904i	$-0.298320\pi$
$601$	29.0284	1.18409	0.592046	+	0.805904i	$0.298320\pi$
$602$	4.37081	0.178141
$603$	0.647093	0.0263517
$604$	−65.2381	−2.65450
$605$	−1.92240	−0.0781566
$606$	8.91674	0.362218
$607$	−1.92859	−0.0782793	−0.0391396	−	0.999234i	$-0.512462\pi$
$607$	−1.92859	−0.0782793	−0.0391396	+	0.999234i	$0.512462\pi$
$608$	−11.2017	−0.454288
$609$	−20.1219	−0.815379
$610$	−32.6434	−1.32169
$611$	−36.5886	−1.48022
$612$	0.683389	0.0276244
$613$	−10.2465	−0.413851	−0.206925	−	0.978357i	$-0.566346\pi$
$613$	−10.2465	−0.413851	−0.206925	+	0.978357i	$0.566346\pi$
$614$	−59.2736	−2.39209
$615$	19.0078	0.766467
$616$	−10.9871	−0.442683
$617$	−7.72994	−0.311196	−0.155598	−	0.987820i	$-0.549730\pi$
$617$	−7.72994	−0.311196	−0.155598	+	0.987820i	$0.549730\pi$
$618$	64.2371	2.58400
$619$	−28.6980	−1.15347	−0.576735	−	0.816931i	$-0.695674\pi$
$619$	−28.6980	−1.15347	−0.576735	+	0.816931i	$0.695674\pi$
$620$	−4.78188	−0.192045
$621$	37.0587	1.48712
$622$	−27.7071	−1.11095
$623$	6.62060	0.265249
$624$	−79.3777	−3.17765
$625$	−16.7767	−0.671067
$626$	19.7406	0.788993
$627$	−3.19445	−0.127574
$628$	41.4472	1.65392
$629$	7.68935	0.306595
$630$	1.27214	0.0506834
$631$	36.8160	1.46562	0.732812	−	0.680431i	$-0.238208\pi$
$631$	36.8160	1.46562	0.732812	+	0.680431i	$0.238208\pi$
$632$	−1.51186	−0.0601385
$633$	13.8351	0.549895
$634$	12.9527	0.514416
$635$	10.7803	0.427801
$636$	−2.29315	−0.0909293
$637$	26.0372	1.03163
$638$	17.7673	0.703415
$639$	−1.56681	−0.0619819
$640$	−20.7332	−0.819553
$641$	−10.6373	−0.420150	−0.210075	−	0.977685i	$-0.567371\pi$
$641$	−10.6373	−0.420150	−0.210075	+	0.977685i	$0.567371\pi$
$642$	8.40978	0.331907
$643$	0.744933	0.0293773	0.0146886	−	0.999892i	$-0.495324\pi$
$643$	0.744933	0.0293773	0.0146886	+	0.999892i	$0.495324\pi$
$644$	53.8586	2.12233
$645$	−3.24458	−0.127755
$646$	4.83054	0.190055
$647$	−38.0417	−1.49557	−0.747786	−	0.663940i	$-0.768883\pi$
$647$	−38.0417	−1.49557	−0.747786	+	0.663940i	$0.768883\pi$
$648$	54.6793	2.14801
$649$	11.4720	0.450316
$650$	−21.3122	−0.835932
$651$	−1.59287	−0.0624294
$652$	14.4222	0.564816
$653$	27.3891	1.07182	0.535910	−	0.844275i	$-0.319969\pi$
$653$	27.3891	1.07182	0.535910	+	0.844275i	$0.319969\pi$
$654$	−77.0987	−3.01480
$655$	−23.4982	−0.918151
$656$	−43.0376	−1.68033
$657$	−1.02758	−0.0400897
$658$	24.9805	0.973840
$659$	−50.5459	−1.96899	−0.984494	−	0.175419i	$-0.943872\pi$
$659$	−50.5459	−1.96899	−0.984494	+	0.175419i	$0.943872\pi$
$660$	14.6452	0.570065
$661$	1.64168	0.0638540	0.0319270	−	0.999490i	$-0.489836\pi$
$661$	1.64168	0.0638540	0.0319270	+	0.999490i	$0.489836\pi$
$662$	−91.5669	−3.55885
$663$	10.8049	0.419629
$664$	12.1556	0.471728
$665$	6.23118	0.241635
$666$	−2.97123	−0.115133
$667$	−48.5040	−1.87808
$668$	−103.662	−4.01081
$669$	12.5661	0.485833
$670$	−20.9698	−0.810135
$671$	6.65328	0.256847
$672$	17.1066	0.659903
$673$	42.7226	1.64683	0.823417	−	0.567436i	$-0.192065\pi$
$673$	42.7226	1.64683	0.823417	+	0.567436i	$0.192065\pi$
$674$	−37.1451	−1.43078
$675$	6.93784	0.267038
$676$	126.313	4.85817
$677$	19.8067	0.761234	0.380617	−	0.924733i	$-0.375712\pi$
$677$	19.8067	0.761234	0.380617	+	0.924733i	$0.375712\pi$
$678$	64.9725	2.49525
$679$	27.6598	1.06149
$680$	−12.3333	−0.472962
$681$	11.0165	0.422153
$682$	1.40648	0.0538569
$683$	−17.8280	−0.682168	−0.341084	−	0.940033i	$-0.610794\pi$
$683$	−17.8280	−0.682168	−0.341084	+	0.940033i	$0.610794\pi$
$684$	−1.29345	−0.0494562
$685$	30.7528	1.17500
$686$	−48.3723	−1.84686
$687$	2.58688	0.0986957
$688$	7.34642	0.280080
$689$	1.92702	0.0734137
$690$	−57.6960	−2.19645
$691$	−33.1667	−1.26172	−0.630861	−	0.775896i	$-0.717298\pi$
$691$	−33.1667	−1.26172	−0.630861	+	0.775896i	$0.717298\pi$
$692$	55.1432	2.09623
$693$	−0.259285	−0.00984942
$694$	48.7892	1.85201
$695$	31.1985	1.18343
$696$	−75.3805	−2.85729
$697$	5.85830	0.221899
$698$	−51.0541	−1.93242
$699$	9.15154	0.346143
$700$	10.0830	0.381101
$701$	−33.4233	−1.26238	−0.631191	−	0.775628i	$-0.717433\pi$
$701$	−33.4233	−1.26238	−0.631191	+	0.775628i	$0.717433\pi$
$702$	−86.9044	−3.28000
$703$	−14.5536	−0.548899
$704$	−0.412065	−0.0155303
$705$	−18.5438	−0.698398
$706$	4.76862	0.179469
$707$	3.54504	0.133325
$708$	−87.3962	−3.28455
$709$	22.9348	0.861333	0.430667	−	0.902511i	$-0.358278\pi$
$709$	22.9348	0.861333	0.430667	+	0.902511i	$0.358278\pi$
$710$	50.7742	1.90552
$711$	−0.0356783	−0.00133804
$712$	24.8021	0.929497
$713$	−3.83963	−0.143795
$714$	−7.37696	−0.276076
$715$	−12.3070	−0.460254
$716$	93.1478	3.48109
$717$	7.48951	0.279701
$718$	−16.6354	−0.620828
$719$	−13.2992	−0.495976	−0.247988	−	0.968763i	$-0.579769\pi$
$719$	−13.2992	−0.495976	−0.247988	+	0.968763i	$0.579769\pi$
$720$	2.13821	0.0796864
$721$	25.5389	0.951117
$722$	39.3491	1.46442
$723$	−29.6150	−1.10139
$724$	−93.0573	−3.45845
$725$	−9.08054	−0.337243
$726$	−4.30756	−0.159868
$727$	3.96447	0.147034	0.0735170	−	0.997294i	$-0.476578\pi$
$727$	3.96447	0.147034	0.0735170	+	0.997294i	$0.476578\pi$
$728$	−70.3381	−2.60690
$729$	28.2216	1.04524
$730$	33.3000	1.23249
$731$	−1.00000	−0.0369863
$732$	−50.6861	−1.87341
$733$	−44.2946	−1.63606	−0.818029	−	0.575177i	$-0.804933\pi$
$733$	−44.2946	−1.63606	−0.818029	+	0.575177i	$0.804933\pi$
$734$	57.5184	2.12304
$735$	13.1961	0.486747
$736$	41.2358	1.51997
$737$	4.27401	0.157435
$738$	−2.26369	−0.0833278
$739$	37.4410	1.37729	0.688645	−	0.725099i	$-0.258206\pi$
$739$	37.4410	1.37729	0.688645	+	0.725099i	$0.258206\pi$
$740$	66.7222	2.45276
$741$	−20.4505	−0.751266
$742$	−1.31565	−0.0482992
$743$	47.3360	1.73659	0.868295	−	0.496048i	$-0.165216\pi$
$743$	47.3360	1.73659	0.868295	+	0.496048i	$0.165216\pi$
$744$	−5.96720	−0.218768
$745$	−6.44999	−0.236309
$746$	85.3648	3.12543
$747$	0.286860	0.0104956
$748$	4.51375	0.165039
$749$	3.34349	0.122168
$750$	−52.2056	−1.90628
$751$	−0.493717	−0.0180160	−0.00900800	−	0.999959i	$-0.502867\pi$
$751$	−0.493717	−0.0180160	−0.00900800	+	0.999959i	$0.502867\pi$
$752$	41.9870	1.53111
$753$	−6.94005	−0.252909
$754$	113.744	4.14232
$755$	27.7848	1.01119
$756$	41.1153	1.49535
$757$	−5.54369	−0.201489	−0.100744	−	0.994912i	$-0.532122\pi$
$757$	−5.54369	−0.201489	−0.100744	+	0.994912i	$0.532122\pi$
$758$	−82.4115	−2.99332
$759$	11.7594	0.426841
$760$	23.3432	0.846748
$761$	−17.8368	−0.646583	−0.323291	−	0.946299i	$-0.604789\pi$
$761$	−17.8368	−0.646583	−0.323291	+	0.946299i	$0.604789\pi$
$762$	24.1555	0.875063
$763$	−30.6522	−1.10969
$764$	−34.4869	−1.24769
$765$	−0.291054	−0.0105231
$766$	30.2059	1.09138
$767$	73.4423	2.65185
$768$	−47.8483	−1.72658
$769$	−7.40911	−0.267180	−0.133590	−	0.991037i	$-0.542650\pi$
$769$	−7.40911	−0.267180	−0.133590	+	0.991037i	$0.542650\pi$
$770$	8.40244	0.302803
$771$	40.2847	1.45082
$772$	−14.2520	−0.512941
$773$	17.0296	0.612514	0.306257	−	0.951949i	$-0.400923\pi$
$773$	17.0296	0.612514	0.306257	+	0.951949i	$0.400923\pi$
$774$	0.386408	0.0138892
$775$	−0.718824	−0.0258209
$776$	103.619	3.71971
$777$	22.2255	0.797336
$778$	13.3743	0.479491
$779$	−11.0880	−0.397268
$780$	93.7569	3.35704
$781$	−10.3487	−0.370304
$782$	−17.7823	−0.635892
$783$	−37.0276	−1.32326
$784$	−29.8789	−1.06710
$785$	−17.6523	−0.630037
$786$	−52.6529	−1.87807
$787$	55.3472	1.97292	0.986458	−	0.164015i	$-0.0524445\pi$
$787$	55.3472	1.97292	0.986458	+	0.164015i	$0.0524445\pi$
$788$	63.0242	2.24514
$789$	18.4388	0.656438
$790$	1.15620	0.0411357
$791$	25.8312	0.918452
$792$	−0.971332	−0.0345148
$793$	42.5935	1.51254
$794$	−78.3045	−2.77892
$795$	0.976650	0.0346382
$796$	−20.1416	−0.713901
$797$	36.8661	1.30586	0.652932	−	0.757416i	$-0.273539\pi$
$797$	36.8661	1.30586	0.652932	+	0.757416i	$0.273539\pi$
$798$	13.9623	0.494261
$799$	−5.71529	−0.202193
$800$	7.71983	0.272937
$801$	0.585304	0.0206807
$802$	−93.0526	−3.28580
$803$	−6.78711	−0.239512
$804$	−32.5603	−1.14831
$805$	−22.9383	−0.808469
$806$	9.00410	0.317156
$807$	30.1673	1.06194
$808$	13.2804	0.467204
$809$	11.3903	0.400463	0.200232	−	0.979749i	$-0.435831\pi$
$809$	11.3903	0.400463	0.200232	+	0.979749i	$0.435831\pi$
$810$	−41.8162	−1.46927
$811$	−13.9114	−0.488496	−0.244248	−	0.969713i	$-0.578541\pi$
$811$	−13.9114	−0.488496	−0.244248	+	0.969713i	$0.578541\pi$
$812$	−53.8134	−1.88848
$813$	23.4310	0.821760
$814$	−19.6248	−0.687849
$815$	−6.14238	−0.215158
$816$	−12.3991	−0.434057
$817$	1.89269	0.0662170
$818$	80.2263	2.80505
$819$	−1.65991	−0.0580019
$820$	50.8338	1.77519
$821$	−38.3873	−1.33973	−0.669863	−	0.742485i	$-0.733647\pi$
$821$	−38.3873	−1.33973	−0.669863	+	0.742485i	$0.733647\pi$
$822$	68.9084	2.40346
$823$	27.6049	0.962246	0.481123	−	0.876653i	$-0.340229\pi$
$823$	27.6049	0.962246	0.481123	+	0.876653i	$0.340229\pi$
$824$	95.6736	3.33295
$825$	2.20151	0.0766467
$826$	−50.1420	−1.74466
$827$	−36.7997	−1.27965	−0.639826	−	0.768520i	$-0.720994\pi$
$827$	−36.7997	−1.27965	−0.639826	+	0.768520i	$0.720994\pi$
$828$	4.76145	0.165472
$829$	42.4605	1.47472	0.737358	−	0.675503i	$-0.236073\pi$
$829$	42.4605	1.47472	0.737358	+	0.675503i	$0.236073\pi$
$830$	−9.29603	−0.322670
$831$	−52.8051	−1.83179
$832$	−2.63799	−0.0914557
$833$	4.06713	0.140918
$834$	69.9071	2.42068
$835$	44.1496	1.52786
$836$	−8.54315	−0.295471
$837$	−2.93114	−0.101315
$838$	60.8813	2.10311
$839$	−31.0246	−1.07109	−0.535544	−	0.844507i	$-0.679893\pi$
$839$	−31.0246	−1.07109	−0.535544	+	0.844507i	$0.679893\pi$
$840$	−35.6486	−1.22999
$841$	19.4633	0.671148
$842$	84.1623	2.90043
$843$	43.3673	1.49365
$844$	37.0002	1.27360
$845$	−53.7963	−1.85065
$846$	2.20844	0.0759276
$847$	−1.71256	−0.0588443
$848$	−2.21134	−0.0759378
$849$	9.05328	0.310708
$850$	−3.32905	−0.114186
$851$	53.5749	1.83652
$852$	78.8383	2.70096
$853$	19.8013	0.677982	0.338991	−	0.940790i	$-0.389914\pi$
$853$	19.8013	0.677982	0.338991	+	0.940790i	$0.389914\pi$
$854$	−29.0802	−0.995105
$855$	0.550877	0.0188396
$856$	12.5254	0.428108
$857$	21.5636	0.736599	0.368300	−	0.929707i	$-0.379940\pi$
$857$	21.5636	0.736599	0.368300	+	0.929707i	$0.379940\pi$
$858$	−27.5764	−0.941444
$859$	−19.8998	−0.678973	−0.339487	−	0.940611i	$-0.610253\pi$
$859$	−19.8998	−0.678973	−0.339487	+	0.940611i	$0.610253\pi$
$860$	−8.67722	−0.295891
$861$	16.9330	0.577075
$862$	4.96976	0.169271
$863$	−49.9189	−1.69926	−0.849629	−	0.527380i	$-0.823174\pi$
$863$	−49.9189	−1.69926	−0.849629	+	0.527380i	$0.823174\pi$
$864$	31.4791	1.07094
$865$	−23.4854	−0.798527
$866$	37.8616	1.28659
$867$	1.68778	0.0573200
$868$	−4.25992	−0.144591
$869$	−0.235653	−0.00799399
$870$	57.6476	1.95444
$871$	27.3617	0.927115
$872$	−114.829	−3.88861
$873$	2.44531	0.0827612
$874$	33.6564	1.13844
$875$	−20.7555	−0.701663
$876$	51.7056	1.74697
$877$	38.1124	1.28696	0.643482	−	0.765462i	$-0.277489\pi$
$877$	38.1124	1.28696	0.643482	+	0.765462i	$0.277489\pi$
$878$	18.2596	0.616232
$879$	37.0296	1.24898
$880$	14.1228	0.476078
$881$	−2.15368	−0.0725592	−0.0362796	−	0.999342i	$-0.511551\pi$
$881$	−2.15368	−0.0725592	−0.0362796	+	0.999342i	$0.511551\pi$
$882$	−1.57157	−0.0529176
$883$	−31.7600	−1.06881	−0.534405	−	0.845229i	$-0.679464\pi$
$883$	−31.7600	−1.06881	−0.534405	+	0.845229i	$0.679464\pi$
$884$	28.8964	0.971892
$885$	37.2219	1.25120
$886$	−98.2182	−3.29970
$887$	55.8958	1.87680	0.938398	−	0.345557i	$-0.112310\pi$
$887$	55.8958	1.87680	0.938398	+	0.345557i	$0.112310\pi$
$888$	83.2612	2.79406
$889$	9.60355	0.322093
$890$	−18.9675	−0.635792
$891$	8.52287	0.285527
$892$	33.6064	1.12523
$893$	10.8173	0.361987
$894$	−14.4526	−0.483368
$895$	−39.6715	−1.32607
$896$	−18.4701	−0.617044
$897$	75.2825	2.51361
$898$	−66.1438	−2.20725
$899$	3.83640	0.127951
$900$	0.891401	0.0297134
$901$	0.301009	0.0100281
$902$	−14.9516	−0.497833
$903$	−2.89043	−0.0961874
$904$	96.7688	3.21848
$905$	39.6330	1.31744
$906$	62.2580	2.06838
$907$	−59.5305	−1.97668	−0.988340	−	0.152265i	$-0.951343\pi$
$907$	−59.5305	−1.97668	−0.988340	+	0.152265i	$0.951343\pi$
$908$	29.4622	0.977737
$909$	0.313405	0.0103950
$910$	53.7913	1.78317
$911$	−6.10300	−0.202202	−0.101101	−	0.994876i	$-0.532236\pi$
$911$	−6.10300	−0.202202	−0.101101	+	0.994876i	$0.532236\pi$
$912$	23.4678	0.777096
$913$	1.89469	0.0627051
$914$	15.0802	0.498810
$915$	21.5871	0.713649
$916$	6.91829	0.228587
$917$	−20.9333	−0.691278
$918$	−13.5748	−0.448037
$919$	36.6128	1.20775	0.603873	−	0.797081i	$-0.293623\pi$
$919$	36.6128	1.20775	0.603873	+	0.797081i	$0.293623\pi$
$920$	−85.9314	−2.83307
$921$	39.1978	1.29161
$922$	−12.8174	−0.422119
$923$	−66.2508	−2.18067
$924$	13.0467	0.429204
$925$	10.0299	0.329780
$926$	−70.7324	−2.32441
$927$	2.25780	0.0741559
$928$	−41.2011	−1.35249
$929$	33.9011	1.11226	0.556130	−	0.831096i	$-0.312286\pi$
$929$	33.9011	1.11226	0.556130	+	0.831096i	$0.312286\pi$
$930$	4.56344	0.149641
$931$	−7.69784	−0.252286
$932$	24.4746	0.801692
$933$	18.3228	0.599861
$934$	53.8510	1.76206
$935$	−1.92240	−0.0628692
$936$	−6.21835	−0.203253
$937$	6.77711	0.221399	0.110699	−	0.993854i	$-0.464691\pi$
$937$	6.77711	0.221399	0.110699	+	0.993854i	$0.464691\pi$
$938$	−18.6809	−0.609953
$939$	−13.0545	−0.426018
$940$	−49.5929	−1.61754
$941$	−18.2739	−0.595711	−0.297855	−	0.954611i	$-0.596271\pi$
$941$	−18.2739	−0.595711	−0.297855	+	0.954611i	$0.596271\pi$
$942$	−39.5538	−1.28873
$943$	40.8172	1.32919
$944$	−84.2782	−2.74302
$945$	−17.5109	−0.569631
$946$	2.55220	0.0829793
$947$	21.8039	0.708531	0.354265	−	0.935145i	$-0.384731\pi$
$947$	21.8039	0.708531	0.354265	+	0.935145i	$0.384731\pi$
$948$	1.79526	0.0583072
$949$	−43.4502	−1.41045
$950$	6.30088	0.204427
$951$	−8.56564	−0.277760
$952$	−10.9871	−0.356094
$953$	−36.8291	−1.19301	−0.596506	−	0.802608i	$-0.703445\pi$
$953$	−36.8291	−1.19301	−0.596506	+	0.802608i	$0.703445\pi$
$954$	−0.116312	−0.00376575
$955$	14.6879	0.475290
$956$	20.0297	0.647808
$957$	−11.7496	−0.379810
$958$	51.6997	1.67034
$959$	27.3960	0.884663
$960$	−1.33698	−0.0431508
$961$	−30.6963	−0.990203
$962$	−125.635	−4.05065
$963$	0.295586	0.00952513
$964$	−79.2016	−2.55091
$965$	6.06992	0.195397
$966$	−51.3983	−1.65371
$967$	23.6308	0.759914	0.379957	−	0.925004i	$-0.375939\pi$
$967$	23.6308	0.759914	0.379957	+	0.925004i	$0.375939\pi$
$968$	−6.41560	−0.206205
$969$	−3.19445	−0.102621
$970$	−79.2432	−2.54435
$971$	−35.4549	−1.13780	−0.568900	−	0.822406i	$-0.692631\pi$
$971$	−35.4549	−1.13780	−0.568900	+	0.822406i	$0.692631\pi$
$972$	7.09509	0.227575
$973$	27.7931	0.891005
$974$	94.1753	3.01757
$975$	14.0938	0.451362
$976$	−48.8778	−1.56454
$977$	24.5124	0.784222	0.392111	−	0.919918i	$-0.371745\pi$
$977$	24.5124	0.784222	0.392111	+	0.919918i	$0.371745\pi$
$978$	−13.7634	−0.440104
$979$	3.86590	0.123555
$980$	35.2914	1.12734
$981$	−2.70986	−0.0865191
$982$	52.4948	1.67517
$983$	23.3273	0.744024	0.372012	−	0.928228i	$-0.378668\pi$
$983$	23.3273	0.744024	0.372012	+	0.928228i	$0.378668\pi$
$984$	63.4343	2.02221
$985$	−26.8419	−0.855255
$986$	17.7673	0.565827
$987$	−16.5196	−0.525826
$988$	−54.6921	−1.73999
$989$	−6.96741	−0.221551
$990$	0.742830	0.0236087
$991$	13.8501	0.439962	0.219981	−	0.975504i	$-0.429400\pi$
$991$	13.8501	0.439962	0.219981	+	0.975504i	$0.429400\pi$
$992$	−3.26152	−0.103553
$993$	60.5534	1.92160
$994$	45.2320	1.43467
$995$	8.57828	0.271950
$996$	−14.4342	−0.457364
$997$	13.1697	0.417088	0.208544	−	0.978013i	$-0.433128\pi$
$997$	13.1697	0.417088	0.208544	+	0.978013i	$0.433128\pi$
$998$	113.931	3.60641
$999$	40.8987	1.29398

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8041.2.a.e.1.2	✓	66

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8041.2.a.e.1.2	✓	66	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:	\( N \)	\(=\)	\( 8041 = 11 \cdot 17 \cdot 43 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8041.a (trivial)

\(f(q)\)	\(=\)	\(q-2.55220 q^{2} +1.68778 q^{3} +4.51375 q^{4} -1.92240 q^{5} -4.30756 q^{6} -1.71256 q^{7} -6.41560 q^{8} -0.151402 q^{9} +O(q^{10})\)	\(q-2.55220 q^{2} +1.68778 q^{3} +4.51375 q^{4} -1.92240 q^{5} -4.30756 q^{6} -1.71256 q^{7} -6.41560 q^{8} -0.151402 q^{9} +4.90636 q^{10} -1.00000 q^{11} +7.61821 q^{12} -6.40187 q^{13} +4.37081 q^{14} -3.24458 q^{15} +7.34642 q^{16} -1.00000 q^{17} +0.386408 q^{18} +1.89269 q^{19} -8.67722 q^{20} -2.89043 q^{21} +2.55220 q^{22} -6.96741 q^{23} -10.8281 q^{24} -1.30438 q^{25} +16.3389 q^{26} -5.31887 q^{27} -7.73007 q^{28} +6.96156 q^{29} +8.28084 q^{30} +0.551084 q^{31} -5.91838 q^{32} -1.68778 q^{33} +2.55220 q^{34} +3.29223 q^{35} -0.683389 q^{36} -7.68935 q^{37} -4.83054 q^{38} -10.8049 q^{39} +12.3333 q^{40} -5.85830 q^{41} +7.37696 q^{42} +1.00000 q^{43} -4.51375 q^{44} +0.291054 q^{45} +17.7823 q^{46} +5.71529 q^{47} +12.3991 q^{48} -4.06713 q^{49} +3.32905 q^{50} -1.68778 q^{51} -28.8964 q^{52} -0.301009 q^{53} +13.5748 q^{54} +1.92240 q^{55} +10.9871 q^{56} +3.19445 q^{57} -17.7673 q^{58} -11.4720 q^{59} -14.6452 q^{60} -6.65328 q^{61} -1.40648 q^{62} +0.259285 q^{63} +0.412065 q^{64} +12.3070 q^{65} +4.30756 q^{66} -4.27401 q^{67} -4.51375 q^{68} -11.7594 q^{69} -8.40244 q^{70} +10.3487 q^{71} +0.971332 q^{72} +6.78711 q^{73} +19.6248 q^{74} -2.20151 q^{75} +8.54315 q^{76} +1.71256 q^{77} +27.5764 q^{78} +0.235653 q^{79} -14.1228 q^{80} -8.52287 q^{81} +14.9516 q^{82} -1.89469 q^{83} -13.0467 q^{84} +1.92240 q^{85} -2.55220 q^{86} +11.7496 q^{87} +6.41560 q^{88} -3.86590 q^{89} -0.742830 q^{90} +10.9636 q^{91} -31.4491 q^{92} +0.930108 q^{93} -14.5866 q^{94} -3.63851 q^{95} -9.98892 q^{96} -16.1511 q^{97} +10.3801 q^{98} +0.151402 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 66 q + 7 q^{2} + 3 q^{3} + 61 q^{4} + 4 q^{5} + 10 q^{6} + 14 q^{7} + 21 q^{8} + 65 q^{9}+O(q^{10}) \) 66 * q + 7 * q^2 + 3 * q^3 + 61 * q^4 + 4 * q^5 + 10 * q^6 + 14 * q^7 + 21 * q^8 + 65 * q^9	\( 66 q + 7 q^{2} + 3 q^{3} + 61 q^{4} + 4 q^{5} + 10 q^{6} + 14 q^{7} + 21 q^{8} + 65 q^{9} + 13 q^{10} - 66 q^{11} + 9 q^{12} - 12 q^{13} + 25 q^{14} + 13 q^{15} + 47 q^{16} - 66 q^{17} + 37 q^{18} + 19 q^{20} + 26 q^{21} - 7 q^{22} + 47 q^{23} + 15 q^{24} + 52 q^{25} + 16 q^{26} + 9 q^{27} + 3 q^{28} + 57 q^{29} + 2 q^{30} + 31 q^{31} + 39 q^{32} - 3 q^{33} - 7 q^{34} + 36 q^{35} + 39 q^{36} - 14 q^{37} + 18 q^{38} + 71 q^{39} + 29 q^{40} + 62 q^{41} - 3 q^{42} + 66 q^{43} - 61 q^{44} - 2 q^{45} + 19 q^{46} + 32 q^{47} + 26 q^{48} + 42 q^{49} + 10 q^{50} - 3 q^{51} - 7 q^{52} + 33 q^{53} + 100 q^{54} - 4 q^{55} + 61 q^{56} + 35 q^{57} - 16 q^{58} + 59 q^{59} + 50 q^{60} + 26 q^{61} + 29 q^{62} + 62 q^{63} + 29 q^{64} + 55 q^{65} - 10 q^{66} + 5 q^{67} - 61 q^{68} - 36 q^{69} - 35 q^{70} + 128 q^{71} + 87 q^{72} + 23 q^{73} + 64 q^{74} - 11 q^{75} + 74 q^{76} - 14 q^{77} + 45 q^{78} + 39 q^{79} + 95 q^{80} + 54 q^{81} - 6 q^{82} + 48 q^{83} + 38 q^{84} - 4 q^{85} + 7 q^{86} + 14 q^{87} - 21 q^{88} + 28 q^{89} + 135 q^{90} - 18 q^{91} + 108 q^{92} - 9 q^{93} + 37 q^{94} + 149 q^{95} + 104 q^{96} + 19 q^{97} + 30 q^{98} - 65 q^{99}+O(q^{100}) \) 66 * q + 7 * q^2 + 3 * q^3 + 61 * q^4 + 4 * q^5 + 10 * q^6 + 14 * q^7 + 21 * q^8 + 65 * q^9 + 13 * q^10 - 66 * q^11 + 9 * q^12 - 12 * q^13 + 25 * q^14 + 13 * q^15 + 47 * q^16 - 66 * q^17 + 37 * q^18 + 19 * q^20 + 26 * q^21 - 7 * q^22 + 47 * q^23 + 15 * q^24 + 52 * q^25 + 16 * q^26 + 9 * q^27 + 3 * q^28 + 57 * q^29 + 2 * q^30 + 31 * q^31 + 39 * q^32 - 3 * q^33 - 7 * q^34 + 36 * q^35 + 39 * q^36 - 14 * q^37 + 18 * q^38 + 71 * q^39 + 29 * q^40 + 62 * q^41 - 3 * q^42 + 66 * q^43 - 61 * q^44 - 2 * q^45 + 19 * q^46 + 32 * q^47 + 26 * q^48 + 42 * q^49 + 10 * q^50 - 3 * q^51 - 7 * q^52 + 33 * q^53 + 100 * q^54 - 4 * q^55 + 61 * q^56 + 35 * q^57 - 16 * q^58 + 59 * q^59 + 50 * q^60 + 26 * q^61 + 29 * q^62 + 62 * q^63 + 29 * q^64 + 55 * q^65 - 10 * q^66 + 5 * q^67 - 61 * q^68 - 36 * q^69 - 35 * q^70 + 128 * q^71 + 87 * q^72 + 23 * q^73 + 64 * q^74 - 11 * q^75 + 74 * q^76 - 14 * q^77 + 45 * q^78 + 39 * q^79 + 95 * q^80 + 54 * q^81 - 6 * q^82 + 48 * q^83 + 38 * q^84 - 4 * q^85 + 7 * q^86 + 14 * q^87 - 21 * q^88 + 28 * q^89 + 135 * q^90 - 18 * q^91 + 108 * q^92 - 9 * q^93 + 37 * q^94 + 149 * q^95 + 104 * q^96 + 19 * q^97 + 30 * q^98 - 65 * q^99

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