LMFDB - Embedded newform 8049.2.a.d.1.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8049,2,Mod(1,8049)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8049, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([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("8049.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8049 = 3 \cdot 2683 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8049.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:	$64.2715885869$
Analytic rank:	$0$
Dimension:	$129$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.10
Character	$\chi$	$=$	8049.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.58791 q^{2} +1.00000 q^{3} +4.69728 q^{4} +1.64365 q^{5} -2.58791 q^{6} -4.45906 q^{7} -6.98031 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-2.58791 q^{2} +1.00000 q^{3} +4.69728 q^{4} +1.64365 q^{5} -2.58791 q^{6} -4.45906 q^{7} -6.98031 q^{8} +1.00000 q^{9} -4.25362 q^{10} +2.49097 q^{11} +4.69728 q^{12} -4.42988 q^{13} +11.5396 q^{14} +1.64365 q^{15} +8.66985 q^{16} +3.68494 q^{17} -2.58791 q^{18} +1.67976 q^{19} +7.72068 q^{20} -4.45906 q^{21} -6.44641 q^{22} -8.01851 q^{23} -6.98031 q^{24} -2.29841 q^{25} +11.4641 q^{26} +1.00000 q^{27} -20.9454 q^{28} +8.58996 q^{29} -4.25362 q^{30} +0.269083 q^{31} -8.47617 q^{32} +2.49097 q^{33} -9.53628 q^{34} -7.32913 q^{35} +4.69728 q^{36} +2.67698 q^{37} -4.34706 q^{38} -4.42988 q^{39} -11.4732 q^{40} -9.79932 q^{41} +11.5396 q^{42} -5.50504 q^{43} +11.7008 q^{44} +1.64365 q^{45} +20.7512 q^{46} +2.26880 q^{47} +8.66985 q^{48} +12.8832 q^{49} +5.94808 q^{50} +3.68494 q^{51} -20.8084 q^{52} +1.89625 q^{53} -2.58791 q^{54} +4.09428 q^{55} +31.1256 q^{56} +1.67976 q^{57} -22.2300 q^{58} +2.44327 q^{59} +7.72068 q^{60} +0.459247 q^{61} -0.696362 q^{62} -4.45906 q^{63} +4.59587 q^{64} -7.28118 q^{65} -6.44641 q^{66} +15.9709 q^{67} +17.3092 q^{68} -8.01851 q^{69} +18.9671 q^{70} +6.75553 q^{71} -6.98031 q^{72} -9.34843 q^{73} -6.92777 q^{74} -2.29841 q^{75} +7.89029 q^{76} -11.1074 q^{77} +11.4641 q^{78} -0.123274 q^{79} +14.2502 q^{80} +1.00000 q^{81} +25.3597 q^{82} -6.25601 q^{83} -20.9454 q^{84} +6.05675 q^{85} +14.2466 q^{86} +8.58996 q^{87} -17.3877 q^{88} +5.82588 q^{89} -4.25362 q^{90} +19.7531 q^{91} -37.6652 q^{92} +0.269083 q^{93} -5.87146 q^{94} +2.76093 q^{95} -8.47617 q^{96} +13.4076 q^{97} -33.3405 q^{98} +2.49097 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 129 q + 8 q^{2} + 129 q^{3} + 158 q^{4} + 11 q^{5} + 8 q^{6} + 40 q^{7} + 18 q^{8} + 129 q^{9}+O(q^{10}) $ 129 * q + 8 * q^2 + 129 * q^3 + 158 * q^4 + 11 * q^5 + 8 * q^6 + 40 * q^7 + 18 * q^8 + 129 * q^9	\( 129 q + 8 q^{2} + 129 q^{3} + 158 q^{4} + 11 q^{5} + 8 q^{6} + 40 q^{7} + 18 q^{8} + 129 q^{9} + 20 q^{10} + 48 q^{11} + 158 q^{12} + 77 q^{13} + 13 q^{14} + 11 q^{15} + 212 q^{16} + 9 q^{17} + 8 q^{18} + 68 q^{19} + 19 q^{20} + 40 q^{21} + 45 q^{22} + 64 q^{23} + 18 q^{24} + 188 q^{25} + 19 q^{26} + 129 q^{27} + 69 q^{28} + 23 q^{29} + 20 q^{30} + 133 q^{31} + 24 q^{32} + 48 q^{33} + 63 q^{34} + 26 q^{35} + 158 q^{36} + 147 q^{37} + 9 q^{38} + 77 q^{39} + 58 q^{40} + 21 q^{41} + 13 q^{42} + 76 q^{43} + 110 q^{44} + 11 q^{45} + 48 q^{46} + 85 q^{47} + 212 q^{48} + 213 q^{49} + 17 q^{50} + 9 q^{51} + 139 q^{52} + 30 q^{53} + 8 q^{54} + 103 q^{55} + 19 q^{56} + 68 q^{57} + 94 q^{58} + 64 q^{59} + 19 q^{60} + 110 q^{61} - 10 q^{62} + 40 q^{63} + 288 q^{64} - 8 q^{65} + 45 q^{66} + 118 q^{67} - 15 q^{68} + 64 q^{69} + 75 q^{70} + 154 q^{71} + 18 q^{72} + 137 q^{73} + 28 q^{74} + 188 q^{75} + 156 q^{76} + 17 q^{77} + 19 q^{78} + 157 q^{79} + 2 q^{80} + 129 q^{81} + 72 q^{82} + 39 q^{83} + 69 q^{84} + 127 q^{85} + 54 q^{86} + 23 q^{87} + 97 q^{88} + 31 q^{89} + 20 q^{90} + 137 q^{91} + 82 q^{92} + 133 q^{93} + 40 q^{94} + 68 q^{95} + 24 q^{96} + 170 q^{97} - 21 q^{98} + 48 q^{99}+O(q^{100}) \) 129 * q + 8 * q^2 + 129 * q^3 + 158 * q^4 + 11 * q^5 + 8 * q^6 + 40 * q^7 + 18 * q^8 + 129 * q^9 + 20 * q^10 + 48 * q^11 + 158 * q^12 + 77 * q^13 + 13 * q^14 + 11 * q^15 + 212 * q^16 + 9 * q^17 + 8 * q^18 + 68 * q^19 + 19 * q^20 + 40 * q^21 + 45 * q^22 + 64 * q^23 + 18 * q^24 + 188 * q^25 + 19 * q^26 + 129 * q^27 + 69 * q^28 + 23 * q^29 + 20 * q^30 + 133 * q^31 + 24 * q^32 + 48 * q^33 + 63 * q^34 + 26 * q^35 + 158 * q^36 + 147 * q^37 + 9 * q^38 + 77 * q^39 + 58 * q^40 + 21 * q^41 + 13 * q^42 + 76 * q^43 + 110 * q^44 + 11 * q^45 + 48 * q^46 + 85 * q^47 + 212 * q^48 + 213 * q^49 + 17 * q^50 + 9 * q^51 + 139 * q^52 + 30 * q^53 + 8 * q^54 + 103 * q^55 + 19 * q^56 + 68 * q^57 + 94 * q^58 + 64 * q^59 + 19 * q^60 + 110 * q^61 - 10 * q^62 + 40 * q^63 + 288 * q^64 - 8 * q^65 + 45 * q^66 + 118 * q^67 - 15 * q^68 + 64 * q^69 + 75 * q^70 + 154 * q^71 + 18 * q^72 + 137 * q^73 + 28 * q^74 + 188 * q^75 + 156 * q^76 + 17 * q^77 + 19 * q^78 + 157 * q^79 + 2 * q^80 + 129 * q^81 + 72 * q^82 + 39 * q^83 + 69 * q^84 + 127 * q^85 + 54 * q^86 + 23 * q^87 + 97 * q^88 + 31 * q^89 + 20 * q^90 + 137 * q^91 + 82 * q^92 + 133 * q^93 + 40 * q^94 + 68 * q^95 + 24 * q^96 + 170 * q^97 - 21 * q^98 + 48 * 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 $

$2$	−2.58791	−1.82993	−0.914964	−	0.403535i	$-0.867781\pi$
$2$	−2.58791	−1.82993	−0.914964	+	0.403535i	$0.867781\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	4.69728	2.34864
$5$	1.64365	0.735063	0.367531	−	0.930011i	$-0.380203\pi$
$5$	1.64365	0.735063	0.367531	+	0.930011i	$0.380203\pi$
$6$	−2.58791	−1.05651
$7$	−4.45906	−1.68537	−0.842683	−	0.538411i	$-0.819025\pi$
$7$	−4.45906	−1.68537	−0.842683	+	0.538411i	$0.819025\pi$
$8$	−6.98031	−2.46791
$9$	1.00000	0.333333
$10$	−4.25362	−1.34511
$11$	2.49097	0.751056	0.375528	−	0.926811i	$-0.377461\pi$
$11$	2.49097	0.751056	0.375528	+	0.926811i	$0.377461\pi$
$12$	4.69728	1.35599
$13$	−4.42988	−1.22863	−0.614314	−	0.789061i	$-0.710567\pi$
$13$	−4.42988	−1.22863	−0.614314	+	0.789061i	$0.710567\pi$
$14$	11.5396	3.08410
$15$	1.64365	0.424389
$16$	8.66985	2.16746
$17$	3.68494	0.893728	0.446864	−	0.894602i	$-0.352541\pi$
$17$	3.68494	0.893728	0.446864	+	0.894602i	$0.352541\pi$
$18$	−2.58791	−0.609976
$19$	1.67976	0.385363	0.192681	−	0.981261i	$-0.438282\pi$
$19$	1.67976	0.385363	0.192681	+	0.981261i	$0.438282\pi$
$20$	7.72068	1.72640
$21$	−4.45906	−0.973046
$22$	−6.44641	−1.37438
$23$	−8.01851	−1.67197	−0.835987	−	0.548749i	$-0.815104\pi$
$23$	−8.01851	−1.67197	−0.835987	+	0.548749i	$0.815104\pi$
$24$	−6.98031	−1.42485
$25$	−2.29841	−0.459683
$26$	11.4641	2.24830
$27$	1.00000	0.192450
$28$	−20.9454	−3.95831
$29$	8.58996	1.59512	0.797558	−	0.603243i	$-0.206125\pi$
$29$	8.58996	1.59512	0.797558	+	0.603243i	$0.206125\pi$
$30$	−4.25362	−0.776601
$31$	0.269083	0.0483287	0.0241644	−	0.999708i	$-0.492307\pi$
$31$	0.269083	0.0483287	0.0241644	+	0.999708i	$0.492307\pi$
$32$	−8.47617	−1.49839
$33$	2.49097	0.433622
$34$	−9.53628	−1.63546
$35$	−7.32913	−1.23885
$36$	4.69728	0.782879
$37$	2.67698	0.440092	0.220046	−	0.975489i	$-0.429379\pi$
$37$	2.67698	0.440092	0.220046	+	0.975489i	$0.429379\pi$
$38$	−4.34706	−0.705186
$39$	−4.42988	−0.709349
$40$	−11.4732	−1.81407
$41$	−9.79932	−1.53040	−0.765198	−	0.643795i	$-0.777359\pi$
$41$	−9.79932	−1.53040	−0.765198	+	0.643795i	$0.777359\pi$
$42$	11.5396	1.78060
$43$	−5.50504	−0.839511	−0.419756	−	0.907637i	$-0.637884\pi$
$43$	−5.50504	−0.839511	−0.419756	+	0.907637i	$0.637884\pi$
$44$	11.7008	1.76396
$45$	1.64365	0.245021
$46$	20.7512	3.05959
$47$	2.26880	0.330939	0.165469	−	0.986215i	$-0.447086\pi$
$47$	2.26880	0.330939	0.165469	+	0.986215i	$0.447086\pi$
$48$	8.66985	1.25138
$49$	12.8832	1.84046
$50$	5.94808	0.841186
$51$	3.68494	0.515994
$52$	−20.8084	−2.88560
$53$	1.89625	0.260470	0.130235	−	0.991483i	$-0.458427\pi$
$53$	1.89625	0.260470	0.130235	+	0.991483i	$0.458427\pi$
$54$	−2.58791	−0.352170
$55$	4.09428	0.552073
$56$	31.1256	4.15933
$57$	1.67976	0.222489
$58$	−22.2300	−2.91895
$59$	2.44327	0.318087	0.159043	−	0.987272i	$-0.449159\pi$
$59$	2.44327	0.318087	0.159043	+	0.987272i	$0.449159\pi$
$60$	7.72068	0.996736
$61$	0.459247	0.0588005	0.0294003	−	0.999568i	$-0.490640\pi$
$61$	0.459247	0.0588005	0.0294003	+	0.999568i	$0.490640\pi$
$62$	−0.696362	−0.0884381
$63$	−4.45906	−0.561788
$64$	4.59587	0.574484
$65$	−7.28118	−0.903119
$66$	−6.44641	−0.793498
$67$	15.9709	1.95116	0.975580	−	0.219645i	$-0.0704898\pi$
$67$	15.9709	1.95116	0.975580	+	0.219645i	$0.0704898\pi$
$68$	17.3092	2.09904
$69$	−8.01851	−0.965315
$70$	18.9671	2.26701
$71$	6.75553	0.801733	0.400867	−	0.916136i	$-0.368709\pi$
$71$	6.75553	0.801733	0.400867	+	0.916136i	$0.368709\pi$
$72$	−6.98031	−0.822637
$73$	−9.34843	−1.09415	−0.547076	−	0.837083i	$-0.684259\pi$
$73$	−9.34843	−1.09415	−0.547076	+	0.837083i	$0.684259\pi$
$74$	−6.92777	−0.805337
$75$	−2.29841	−0.265398
$76$	7.89029	0.905078
$77$	−11.1074	−1.26580
$78$	11.4641	1.29806
$79$	−0.123274	−0.0138694	−0.00693469	−	0.999976i	$-0.502207\pi$
$79$	−0.123274	−0.0138694	−0.00693469	+	0.999976i	$0.502207\pi$
$80$	14.2502	1.59322
$81$	1.00000	0.111111
$82$	25.3597	2.80052
$83$	−6.25601	−0.686686	−0.343343	−	0.939210i	$-0.611559\pi$
$83$	−6.25601	−0.686686	−0.343343	+	0.939210i	$0.611559\pi$
$84$	−20.9454	−2.28533
$85$	6.05675	0.656946
$86$	14.2466	1.53625
$87$	8.58996	0.920940
$88$	−17.3877	−1.85354
$89$	5.82588	0.617542	0.308771	−	0.951136i	$-0.400082\pi$
$89$	5.82588	0.617542	0.308771	+	0.951136i	$0.400082\pi$
$90$	−4.25362	−0.448371
$91$	19.7531	2.07069
$92$	−37.6652	−3.92686
$93$	0.269083	0.0279026
$94$	−5.87146	−0.605595
$95$	2.76093	0.283266
$96$	−8.47617	−0.865096
$97$	13.4076	1.36133	0.680667	−	0.732593i	$-0.261690\pi$
$97$	13.4076	1.36133	0.680667	+	0.732593i	$0.261690\pi$
$98$	−33.3405	−3.36790
$99$	2.49097	0.250352
$100$	−10.7963	−1.07963
$101$	−11.9003	−1.18412	−0.592061	−	0.805893i	$-0.701685\pi$
$101$	−11.9003	−1.18412	−0.592061	+	0.805893i	$0.701685\pi$
$102$	−9.53628	−0.944232
$103$	1.08080	0.106494	0.0532472	−	0.998581i	$-0.483043\pi$
$103$	1.08080	0.106494	0.0532472	+	0.998581i	$0.483043\pi$
$104$	30.9219	3.03215
$105$	−7.32913	−0.715250
$106$	−4.90733	−0.476642
$107$	−12.7661	−1.23414	−0.617071	−	0.786908i	$-0.711681\pi$
$107$	−12.7661	−1.23414	−0.617071	+	0.786908i	$0.711681\pi$
$108$	4.69728	0.451996
$109$	8.81828	0.844638	0.422319	−	0.906447i	$-0.361216\pi$
$109$	8.81828	0.844638	0.422319	+	0.906447i	$0.361216\pi$
$110$	−10.5956	−1.01025
$111$	2.67698	0.254087
$112$	−38.6594	−3.65297
$113$	−10.7739	−1.01352	−0.506761	−	0.862086i	$-0.669157\pi$
$113$	−10.7739	−1.01352	−0.506761	+	0.862086i	$0.669157\pi$
$114$	−4.34706	−0.407140
$115$	−13.1796	−1.22901
$116$	40.3494	3.74635
$117$	−4.42988	−0.409543
$118$	−6.32297	−0.582076
$119$	−16.4313	−1.50626
$120$	−11.4732	−1.04735
$121$	−4.79507	−0.435915
$122$	−1.18849	−0.107601
$123$	−9.79932	−0.883575
$124$	1.26396	0.113507
$125$	−11.9960	−1.07296
$126$	11.5396	1.02803
$127$	11.4703	1.01782	0.508912	−	0.860818i	$-0.330048\pi$
$127$	11.4703	1.01782	0.508912	+	0.860818i	$0.330048\pi$
$128$	5.05865	0.447125
$129$	−5.50504	−0.484692
$130$	18.8430	1.65264
$131$	−8.24277	−0.720174	−0.360087	−	0.932919i	$-0.617253\pi$
$131$	−8.24277	−0.720174	−0.360087	+	0.932919i	$0.617253\pi$
$132$	11.7008	1.01842
$133$	−7.49014	−0.649477
$134$	−41.3313	−3.57048
$135$	1.64365	0.141463
$136$	−25.7220	−2.20564
$137$	−2.81004	−0.240078	−0.120039	−	0.992769i	$-0.538302\pi$
$137$	−2.81004	−0.240078	−0.120039	+	0.992769i	$0.538302\pi$
$138$	20.7512	1.76646
$139$	10.1626	0.861981	0.430990	−	0.902357i	$-0.358164\pi$
$139$	10.1626	0.861981	0.430990	+	0.902357i	$0.358164\pi$
$140$	−34.4270	−2.90961
$141$	2.26880	0.191068
$142$	−17.4827	−1.46711
$143$	−11.0347	−0.922768
$144$	8.66985	0.722487
$145$	14.1189	1.17251
$146$	24.1929	2.00222
$147$	12.8832	1.06259
$148$	12.5745	1.03362
$149$	−12.3139	−1.00879	−0.504396	−	0.863472i	$-0.668285\pi$
$149$	−12.3139	−1.00879	−0.504396	+	0.863472i	$0.668285\pi$
$150$	5.94808	0.485659
$151$	0.560558	0.0456176	0.0228088	−	0.999740i	$-0.492739\pi$
$151$	0.560558	0.0456176	0.0228088	+	0.999740i	$0.492739\pi$
$152$	−11.7252	−0.951041
$153$	3.68494	0.297909
$154$	28.7449	2.31633
$155$	0.442278	0.0355246
$156$	−20.8084	−1.66600
$157$	17.1298	1.36711	0.683554	−	0.729900i	$-0.260433\pi$
$157$	17.1298	1.36711	0.683554	+	0.729900i	$0.260433\pi$
$158$	0.319022	0.0253800
$159$	1.89625	0.150383
$160$	−13.9319	−1.10141
$161$	35.7550	2.81789
$162$	−2.58791	−0.203325
$163$	−22.4954	−1.76197	−0.880987	−	0.473140i	$-0.843120\pi$
$163$	−22.4954	−1.76197	−0.880987	+	0.473140i	$0.843120\pi$
$164$	−46.0301	−3.59435
$165$	4.09428	0.318740
$166$	16.1900	1.25659
$167$	7.24752	0.560830	0.280415	−	0.959879i	$-0.409528\pi$
$167$	7.24752	0.560830	0.280415	+	0.959879i	$0.409528\pi$
$168$	31.1256	2.40139
$169$	6.62386	0.509528
$170$	−15.6743	−1.20216
$171$	1.67976	0.128454
$172$	−25.8587	−1.97171
$173$	18.9913	1.44388	0.721941	−	0.691955i	$-0.243250\pi$
$173$	18.9913	1.44388	0.721941	+	0.691955i	$0.243250\pi$
$174$	−22.2300	−1.68525
$175$	10.2488	0.774733
$176$	21.5963	1.62788
$177$	2.44327	0.183648
$178$	−15.0769	−1.13006
$179$	10.1372	0.757693	0.378846	−	0.925460i	$-0.376321\pi$
$179$	10.1372	0.757693	0.378846	+	0.925460i	$0.376321\pi$
$180$	7.72068	0.575466
$181$	−7.95875	−0.591569	−0.295785	−	0.955255i	$-0.595581\pi$
$181$	−7.95875	−0.591569	−0.295785	+	0.955255i	$0.595581\pi$
$182$	−51.1192	−3.78921
$183$	0.459247	0.0339485
$184$	55.9716	4.12628
$185$	4.40001	0.323495
$186$	−0.696362	−0.0510598
$187$	9.17906	0.671240
$188$	10.6572	0.777256
$189$	−4.45906	−0.324349
$190$	−7.14505	−0.518356
$191$	18.6897	1.35234	0.676168	−	0.736747i	$-0.263639\pi$
$191$	18.6897	1.35234	0.676168	+	0.736747i	$0.263639\pi$
$192$	4.59587	0.331678
$193$	−24.7112	−1.77875	−0.889377	−	0.457175i	$-0.848861\pi$
$193$	−24.7112	−1.77875	−0.889377	+	0.457175i	$0.848861\pi$
$194$	−34.6976	−2.49115
$195$	−7.28118	−0.521416
$196$	60.5159	4.32256
$197$	3.57610	0.254787	0.127393	−	0.991852i	$-0.459339\pi$
$197$	3.57610	0.254787	0.127393	+	0.991852i	$0.459339\pi$
$198$	−6.44641	−0.458126
$199$	27.2853	1.93420	0.967100	−	0.254396i	$-0.0818765\pi$
$199$	27.2853	1.93420	0.967100	+	0.254396i	$0.0818765\pi$
$200$	16.0436	1.13446
$201$	15.9709	1.12650
$202$	30.7968	2.16686
$203$	−38.3031	−2.68835
$204$	17.3092	1.21188
$205$	−16.1067	−1.12494
$206$	−2.79701	−0.194877
$207$	−8.01851	−0.557325
$208$	−38.4064	−2.66301
$209$	4.18423	0.289429
$210$	18.9671	1.30886
$211$	12.5117	0.861341	0.430671	−	0.902509i	$-0.358277\pi$
$211$	12.5117	0.861341	0.430671	+	0.902509i	$0.358277\pi$
$212$	8.90722	0.611751
$213$	6.75553	0.462881
$214$	33.0374	2.25839
$215$	−9.04837	−0.617093
$216$	−6.98031	−0.474950
$217$	−1.19986	−0.0814515
$218$	−22.8209	−1.54563
$219$	−9.34843	−0.631708
$220$	19.2320	1.29662
$221$	−16.3238	−1.09806
$222$	−6.92777	−0.464962
$223$	29.1095	1.94932	0.974659	−	0.223694i	$-0.0718115\pi$
$223$	29.1095	1.94932	0.974659	+	0.223694i	$0.0718115\pi$
$224$	37.7957	2.52533
$225$	−2.29841	−0.153228
$226$	27.8819	1.85467
$227$	28.4704	1.88965	0.944824	−	0.327579i	$-0.106233\pi$
$227$	28.4704	1.88965	0.944824	+	0.327579i	$0.106233\pi$
$228$	7.89029	0.522547
$229$	−2.44463	−0.161546	−0.0807728	−	0.996733i	$-0.525739\pi$
$229$	−2.44463	−0.161546	−0.0807728	+	0.996733i	$0.525739\pi$
$230$	34.1077	2.24899
$231$	−11.1074	−0.730812
$232$	−59.9605	−3.93660
$233$	−19.2229	−1.25934	−0.629668	−	0.776864i	$-0.716809\pi$
$233$	−19.2229	−1.25934	−0.629668	+	0.776864i	$0.716809\pi$
$234$	11.4641	0.749434
$235$	3.72912	0.243261
$236$	11.4767	0.747071
$237$	−0.123274	−0.00800750
$238$	42.5228	2.75634
$239$	14.3637	0.929111	0.464556	−	0.885544i	$-0.346214\pi$
$239$	14.3637	0.929111	0.464556	+	0.885544i	$0.346214\pi$
$240$	14.2502	0.919847
$241$	−9.14953	−0.589373	−0.294687	−	0.955594i	$-0.595215\pi$
$241$	−9.14953	−0.589373	−0.294687	+	0.955594i	$0.595215\pi$
$242$	12.4092	0.797694
$243$	1.00000	0.0641500
$244$	2.15721	0.138101
$245$	21.1755	1.35285
$246$	25.3597	1.61688
$247$	−7.44113	−0.473468
$248$	−1.87828	−0.119271
$249$	−6.25601	−0.396458
$250$	31.0447	1.96344
$251$	3.20202	0.202110	0.101055	−	0.994881i	$-0.467778\pi$
$251$	3.20202	0.202110	0.101055	+	0.994881i	$0.467778\pi$
$252$	−20.9454	−1.31944
$253$	−19.9739	−1.25575
$254$	−29.6841	−1.86255
$255$	6.05675	0.379288
$256$	−22.2831	−1.39269
$257$	−9.95883	−0.621215	−0.310607	−	0.950538i	$-0.600532\pi$
$257$	−9.95883	−0.621215	−0.310607	+	0.950538i	$0.600532\pi$
$258$	14.2466	0.886952
$259$	−11.9368	−0.741716
$260$	−34.2017	−2.12110
$261$	8.58996	0.531705
$262$	21.3315	1.31787
$263$	23.5587	1.45269	0.726347	−	0.687328i	$-0.241216\pi$
$263$	23.5587	1.45269	0.726347	+	0.687328i	$0.241216\pi$
$264$	−17.3877	−1.07014
$265$	3.11678	0.191462
$266$	19.3838	1.18850
$267$	5.82588	0.356538
$268$	75.0199	4.58257
$269$	11.5299	0.702993	0.351497	−	0.936189i	$-0.385673\pi$
$269$	11.5299	0.702993	0.351497	+	0.936189i	$0.385673\pi$
$270$	−4.25362	−0.258867
$271$	13.9797	0.849205	0.424602	−	0.905380i	$-0.360414\pi$
$271$	13.9797	0.849205	0.424602	+	0.905380i	$0.360414\pi$
$272$	31.9478	1.93712
$273$	19.7531	1.19551
$274$	7.27213	0.439325
$275$	−5.72528	−0.345247
$276$	−37.6652	−2.26718
$277$	17.5738	1.05591	0.527955	−	0.849273i	$-0.322959\pi$
$277$	17.5738	1.05591	0.527955	+	0.849273i	$0.322959\pi$
$278$	−26.2999	−1.57736
$279$	0.269083	0.0161096
$280$	51.1596	3.05737
$281$	23.7152	1.41473	0.707364	−	0.706849i	$-0.249884\pi$
$281$	23.7152	1.41473	0.707364	+	0.706849i	$0.249884\pi$
$282$	−5.87146	−0.349640
$283$	11.0975	0.659679	0.329839	−	0.944037i	$-0.393005\pi$
$283$	11.0975	0.659679	0.329839	+	0.944037i	$0.393005\pi$
$284$	31.7326	1.88298
$285$	2.76093	0.163544
$286$	28.5568	1.68860
$287$	43.6957	2.57928
$288$	−8.47617	−0.499463
$289$	−3.42125	−0.201250
$290$	−36.5384	−2.14561
$291$	13.4076	0.785967
$292$	−43.9122	−2.56976
$293$	5.57049	0.325432	0.162716	−	0.986673i	$-0.447975\pi$
$293$	5.57049	0.325432	0.162716	+	0.986673i	$0.447975\pi$
$294$	−33.3405	−1.94446
$295$	4.01588	0.233814
$296$	−18.6861	−1.08611
$297$	2.49097	0.144541
$298$	31.8672	1.84602
$299$	35.5211	2.05424
$300$	−10.7963	−0.623323
$301$	24.5473	1.41488
$302$	−1.45067	−0.0834769
$303$	−11.9003	−0.683653
$304$	14.5632	0.835259
$305$	0.754842	0.0432221
$306$	−9.53628	−0.545153
$307$	13.7439	0.784404	0.392202	−	0.919879i	$-0.371713\pi$
$307$	13.7439	0.784404	0.392202	+	0.919879i	$0.371713\pi$
$308$	−52.1744	−2.97291
$309$	1.08080	0.0614845
$310$	−1.14458	−0.0650076
$311$	−19.9412	−1.13076	−0.565381	−	0.824830i	$-0.691271\pi$
$311$	−19.9412	−1.13076	−0.565381	+	0.824830i	$0.691271\pi$
$312$	30.9219	1.75061
$313$	16.1943	0.915357	0.457678	−	0.889118i	$-0.348681\pi$
$313$	16.1943	0.915357	0.457678	+	0.889118i	$0.348681\pi$
$314$	−44.3304	−2.50171
$315$	−7.32913	−0.412950
$316$	−0.579051	−0.0325742
$317$	1.20768	0.0678303	0.0339151	−	0.999425i	$-0.489202\pi$
$317$	1.20768	0.0678303	0.0339151	+	0.999425i	$0.489202\pi$
$318$	−4.90733	−0.275190
$319$	21.3973	1.19802
$320$	7.55401	0.422282
$321$	−12.7661	−0.712532
$322$	−92.5307	−5.15653
$323$	6.18980	0.344410
$324$	4.69728	0.260960
$325$	10.1817	0.564779
$326$	58.2160	3.22429
$327$	8.81828	0.487652
$328$	68.4022	3.77688
$329$	−10.1167	−0.557753
$330$	−10.5956	−0.583271
$331$	5.18567	0.285030	0.142515	−	0.989793i	$-0.454481\pi$
$331$	5.18567	0.285030	0.142515	+	0.989793i	$0.454481\pi$
$332$	−29.3862	−1.61278
$333$	2.67698	0.146697
$334$	−18.7559	−1.02628
$335$	26.2506	1.43423
$336$	−38.6594	−2.10904
$337$	−11.4017	−0.621092	−0.310546	−	0.950558i	$-0.600512\pi$
$337$	−11.4017	−0.621092	−0.310546	+	0.950558i	$0.600512\pi$
$338$	−17.1420	−0.932399
$339$	−10.7739	−0.585158
$340$	28.4502	1.54293
$341$	0.670278	0.0362976
$342$	−4.34706	−0.235062
$343$	−26.2335	−1.41647
$344$	38.4269	2.07184
$345$	−13.1796	−0.709567
$346$	−49.1477	−2.64220
$347$	−16.0928	−0.863906	−0.431953	−	0.901896i	$-0.642175\pi$
$347$	−16.0928	−0.863906	−0.431953	+	0.901896i	$0.642175\pi$
$348$	40.3494	2.16295
$349$	21.6975	1.16144	0.580720	−	0.814103i	$-0.302771\pi$
$349$	21.6975	1.16144	0.580720	+	0.814103i	$0.302771\pi$
$350$	−26.5228	−1.41771
$351$	−4.42988	−0.236450
$352$	−21.1139	−1.12537
$353$	−8.25795	−0.439526	−0.219763	−	0.975553i	$-0.570528\pi$
$353$	−8.25795	−0.439526	−0.219763	+	0.975553i	$0.570528\pi$
$354$	−6.32297	−0.336062
$355$	11.1037	0.589324
$356$	27.3658	1.45038
$357$	−16.4313	−0.869639
$358$	−26.2343	−1.38652
$359$	5.22381	0.275702	0.137851	−	0.990453i	$-0.455980\pi$
$359$	5.22381	0.275702	0.137851	+	0.990453i	$0.455980\pi$
$360$	−11.4732	−0.604690
$361$	−16.1784	−0.851495
$362$	20.5965	1.08253
$363$	−4.79507	−0.251676
$364$	92.7858	4.86330
$365$	−15.3656	−0.804270
$366$	−1.18849	−0.0621233
$367$	5.99639	0.313009	0.156504	−	0.987677i	$-0.449977\pi$
$367$	5.99639	0.313009	0.156504	+	0.987677i	$0.449977\pi$
$368$	−69.5193	−3.62394
$369$	−9.79932	−0.510132
$370$	−11.3868	−0.591973
$371$	−8.45550	−0.438988
$372$	1.26396	0.0655331
$373$	−14.6707	−0.759621	−0.379810	−	0.925064i	$-0.624011\pi$
$373$	−14.6707	−0.759621	−0.379810	+	0.925064i	$0.624011\pi$
$374$	−23.7546	−1.22832
$375$	−11.9960	−0.619473
$376$	−15.8369	−0.816728
$377$	−38.0525	−1.95980
$378$	11.5396	0.593535
$379$	−2.01569	−0.103539	−0.0517695	−	0.998659i	$-0.516486\pi$
$379$	−2.01569	−0.103539	−0.0517695	+	0.998659i	$0.516486\pi$
$380$	12.9689	0.665289
$381$	11.4703	0.587641
$382$	−48.3672	−2.47468
$383$	−30.9188	−1.57988	−0.789939	−	0.613185i	$-0.789888\pi$
$383$	−30.9188	−1.57988	−0.789939	+	0.613185i	$0.789888\pi$
$384$	5.05865	0.258148
$385$	−18.2566	−0.930445
$386$	63.9504	3.25499
$387$	−5.50504	−0.279837
$388$	62.9792	3.19728
$389$	−13.4491	−0.681895	−0.340948	−	0.940082i	$-0.610748\pi$
$389$	−13.4491	−0.681895	−0.340948	+	0.940082i	$0.610748\pi$
$390$	18.8430	0.954154
$391$	−29.5477	−1.49429
$392$	−89.9286	−4.54208
$393$	−8.24277	−0.415793
$394$	−9.25462	−0.466241
$395$	−0.202619	−0.0101949
$396$	11.7008	0.587986
$397$	3.97227	0.199362	0.0996812	−	0.995019i	$-0.468218\pi$
$397$	3.97227	0.199362	0.0996812	+	0.995019i	$0.468218\pi$
$398$	−70.6118	−3.53945
$399$	−7.49014	−0.374976
$400$	−19.9269	−0.996345
$401$	28.7736	1.43688	0.718442	−	0.695587i	$-0.244856\pi$
$401$	28.7736	1.43688	0.718442	+	0.695587i	$0.244856\pi$
$402$	−41.3313	−2.06142
$403$	−1.19201	−0.0593780
$404$	−55.8989	−2.78107
$405$	1.64365	0.0816737
$406$	99.1250	4.91949
$407$	6.66827	0.330534
$408$	−25.7220	−1.27343
$409$	11.9263	0.589716	0.294858	−	0.955541i	$-0.404728\pi$
$409$	11.9263	0.589716	0.294858	+	0.955541i	$0.404728\pi$
$410$	41.6826	2.05856
$411$	−2.81004	−0.138609
$412$	5.07681	0.250117
$413$	−10.8947	−0.536093
$414$	20.7512	1.01986
$415$	−10.2827	−0.504757
$416$	37.5485	1.84096
$417$	10.1626	0.497665
$418$	−10.8284	−0.529634
$419$	−4.52096	−0.220863	−0.110432	−	0.993884i	$-0.535223\pi$
$419$	−4.52096	−0.220863	−0.110432	+	0.993884i	$0.535223\pi$
$420$	−34.4270	−1.67986
$421$	11.1731	0.544545	0.272272	−	0.962220i	$-0.412225\pi$
$421$	11.1731	0.544545	0.272272	+	0.962220i	$0.412225\pi$
$422$	−32.3792	−1.57619
$423$	2.26880	0.110313
$424$	−13.2364	−0.642818
$425$	−8.46950	−0.410831
$426$	−17.4827	−0.847039
$427$	−2.04781	−0.0991004
$428$	−59.9657	−2.89855
$429$	−11.0347	−0.532761
$430$	23.4164	1.12924
$431$	−37.0197	−1.78318	−0.891588	−	0.452848i	$-0.850408\pi$
$431$	−37.0197	−1.78318	−0.891588	+	0.452848i	$0.850408\pi$
$432$	8.66985	0.417128
$433$	20.3746	0.979142	0.489571	−	0.871963i	$-0.337153\pi$
$433$	20.3746	0.979142	0.489571	+	0.871963i	$0.337153\pi$
$434$	3.10512	0.149050
$435$	14.1189	0.676949
$436$	41.4219	1.98375
$437$	−13.4692	−0.644317
$438$	24.1929	1.15598
$439$	28.4654	1.35858	0.679290	−	0.733870i	$-0.262288\pi$
$439$	28.4654	1.35858	0.679290	+	0.733870i	$0.262288\pi$
$440$	−28.5794	−1.36247
$441$	12.8832	0.613485
$442$	42.2446	2.00937
$443$	2.37095	0.112647	0.0563236	−	0.998413i	$-0.482062\pi$
$443$	2.37095	0.112647	0.0563236	+	0.998413i	$0.482062\pi$
$444$	12.5745	0.596759
$445$	9.57571	0.453932
$446$	−75.3329	−3.56711
$447$	−12.3139	−0.582427
$448$	−20.4933	−0.968215
$449$	−26.2152	−1.23717	−0.618586	−	0.785717i	$-0.712294\pi$
$449$	−26.2152	−1.23717	−0.618586	+	0.785717i	$0.712294\pi$
$450$	5.94808	0.280395
$451$	−24.4098	−1.14941
$452$	−50.6080	−2.38040
$453$	0.560558	0.0263373
$454$	−73.6789	−3.45792
$455$	32.4672	1.52209
$456$	−11.7252	−0.549084
$457$	−13.9718	−0.653574	−0.326787	−	0.945098i	$-0.605966\pi$
$457$	−13.9718	−0.653574	−0.326787	+	0.945098i	$0.605966\pi$
$458$	6.32648	0.295617
$459$	3.68494	0.171998
$460$	−61.9083	−2.88649
$461$	−11.4466	−0.533119	−0.266560	−	0.963818i	$-0.585887\pi$
$461$	−11.4466	−0.533119	−0.266560	+	0.963818i	$0.585887\pi$
$462$	28.7449	1.33733
$463$	6.92009	0.321604	0.160802	−	0.986987i	$-0.448592\pi$
$463$	6.92009	0.321604	0.160802	+	0.986987i	$0.448592\pi$
$464$	74.4736	3.45735
$465$	0.442278	0.0205102
$466$	49.7472	2.30449
$467$	11.8254	0.547215	0.273608	−	0.961841i	$-0.411783\pi$
$467$	11.8254	0.547215	0.273608	+	0.961841i	$0.411783\pi$
$468$	−20.8084	−0.961868
$469$	−71.2153	−3.28842
$470$	−9.65062	−0.445150
$471$	17.1298	0.789301
$472$	−17.0548	−0.785010
$473$	−13.7129	−0.630520
$474$	0.319022	0.0146531
$475$	−3.86078	−0.177145
$476$	−77.1825	−3.53765
$477$	1.89625	0.0868235
$478$	−37.1720	−1.70021
$479$	−0.362937	−0.0165830	−0.00829150	−	0.999966i	$-0.502639\pi$
$479$	−0.362937	−0.0165830	−0.00829150	+	0.999966i	$0.502639\pi$
$480$	−13.9319	−0.635900
$481$	−11.8587	−0.540710
$482$	23.6782	1.07851
$483$	35.7550	1.62691
$484$	−22.5238	−1.02381
$485$	22.0374	1.00067
$486$	−2.58791	−0.117390
$487$	12.6203	0.571881	0.285940	−	0.958247i	$-0.407694\pi$
$487$	12.6203	0.571881	0.285940	+	0.958247i	$0.407694\pi$
$488$	−3.20568	−0.145115
$489$	−22.4954	−1.01728
$490$	−54.8002	−2.47562
$491$	20.5254	0.926299	0.463149	−	0.886280i	$-0.346719\pi$
$491$	20.5254	0.926299	0.463149	+	0.886280i	$0.346719\pi$
$492$	−46.0301	−2.07520
$493$	31.6534	1.42560
$494$	19.2570	0.866412
$495$	4.09428	0.184024
$496$	2.33291	0.104751
$497$	−30.1233	−1.35121
$498$	16.1900	0.725490
$499$	27.4936	1.23078	0.615391	−	0.788222i	$-0.288998\pi$
$499$	27.4936	1.23078	0.615391	+	0.788222i	$0.288998\pi$
$500$	−56.3487	−2.51999
$501$	7.24752	0.323795
$502$	−8.28653	−0.369846
$503$	−1.58386	−0.0706207	−0.0353103	−	0.999376i	$-0.511242\pi$
$503$	−1.58386	−0.0706207	−0.0353103	+	0.999376i	$0.511242\pi$
$504$	31.1256	1.38644
$505$	−19.5599	−0.870404
$506$	51.6906	2.29793
$507$	6.62386	0.294176
$508$	53.8792	2.39050
$509$	4.03127	0.178683	0.0893414	−	0.996001i	$-0.471524\pi$
$509$	4.03127	0.178683	0.0893414	+	0.996001i	$0.471524\pi$
$510$	−15.6743	−0.694070
$511$	41.6852	1.84404
$512$	47.5493	2.10140
$513$	1.67976	0.0741631
$514$	25.7726	1.13678
$515$	1.77646	0.0782800
$516$	−25.8587	−1.13837
$517$	5.65152	0.248554
$518$	30.8913	1.35729
$519$	18.9913	0.833625
$520$	50.8249	2.22882
$521$	15.0174	0.657924	0.328962	−	0.944343i	$-0.393301\pi$
$521$	15.0174	0.657924	0.328962	+	0.944343i	$0.393301\pi$
$522$	−22.2300	−0.972982
$523$	−11.2390	−0.491448	−0.245724	−	0.969340i	$-0.579026\pi$
$523$	−11.2390	−0.491448	−0.245724	+	0.969340i	$0.579026\pi$
$524$	−38.7186	−1.69143
$525$	10.2488	0.447292
$526$	−60.9679	−2.65833
$527$	0.991553	0.0431927
$528$	21.5963	0.939860
$529$	41.2965	1.79550
$530$	−8.06594	−0.350362
$531$	2.44327	0.106029
$532$	−35.1832	−1.52539
$533$	43.4098	1.88029
$534$	−15.0769	−0.652439
$535$	−20.9829	−0.907172
$536$	−111.482	−4.81529
$537$	10.1372	0.437454
$538$	−29.8385	−1.28643
$539$	32.0916	1.38228
$540$	7.72068	0.332245
$541$	3.68200	0.158302	0.0791508	−	0.996863i	$-0.474779\pi$
$541$	3.68200	0.158302	0.0791508	+	0.996863i	$0.474779\pi$
$542$	−36.1781	−1.55398
$543$	−7.95875	−0.341543
$544$	−31.2341	−1.33915
$545$	14.4942	0.620862
$546$	−51.1192	−2.18770
$547$	−6.61734	−0.282937	−0.141469	−	0.989943i	$-0.545182\pi$
$547$	−6.61734	−0.282937	−0.141469	+	0.989943i	$0.545182\pi$
$548$	−13.1995	−0.563856
$549$	0.459247	0.0196002
$550$	14.8165	0.631778
$551$	14.4290	0.614698
$552$	55.9716	2.38231
$553$	0.549685	0.0233750
$554$	−45.4795	−1.93224
$555$	4.40001	0.186770
$556$	47.7365	2.02448
$557$	18.5490	0.785945	0.392973	−	0.919550i	$-0.371447\pi$
$557$	18.5490	0.785945	0.392973	+	0.919550i	$0.371447\pi$
$558$	−0.696362	−0.0294794
$559$	24.3867	1.03145
$560$	−63.5425	−2.68516
$561$	9.17906	0.387540
$562$	−61.3727	−2.58885
$563$	43.9994	1.85435	0.927177	−	0.374625i	$-0.122228\pi$
$563$	43.9994	1.85435	0.927177	+	0.374625i	$0.122228\pi$
$564$	10.6572	0.448749
$565$	−17.7085	−0.745003
$566$	−28.7194	−1.20716
$567$	−4.45906	−0.187263
$568$	−47.1556	−1.97861
$569$	−10.7050	−0.448778	−0.224389	−	0.974500i	$-0.572039\pi$
$569$	−10.7050	−0.448778	−0.224389	+	0.974500i	$0.572039\pi$
$570$	−7.14505	−0.299273
$571$	−13.8862	−0.581118	−0.290559	−	0.956857i	$-0.593841\pi$
$571$	−13.8862	−0.581118	−0.290559	+	0.956857i	$0.593841\pi$
$572$	−51.8331	−2.16725
$573$	18.6897	0.780772
$574$	−113.081	−4.71989
$575$	18.4298	0.768578
$576$	4.59587	0.191495
$577$	−7.19390	−0.299486	−0.149743	−	0.988725i	$-0.547845\pi$
$577$	−7.19390	−0.299486	−0.149743	+	0.988725i	$0.547845\pi$
$578$	8.85389	0.368273
$579$	−24.7112	−1.02696
$580$	66.3203	2.75380
$581$	27.8959	1.15732
$582$	−34.6976	−1.43826
$583$	4.72351	0.195628
$584$	65.2549	2.70027
$585$	−7.28118	−0.301040
$586$	−14.4159	−0.595516
$587$	19.0052	0.784428	0.392214	−	0.919874i	$-0.371709\pi$
$587$	19.0052	0.784428	0.392214	+	0.919874i	$0.371709\pi$
$588$	60.5159	2.49563
$589$	0.451994	0.0186241
$590$	−10.3927	−0.427863
$591$	3.57610	0.147101
$592$	23.2090	0.953883
$593$	−18.3943	−0.755361	−0.377681	−	0.925936i	$-0.623278\pi$
$593$	−18.3943	−0.755361	−0.377681	+	0.925936i	$0.623278\pi$
$594$	−6.44641	−0.264499
$595$	−27.0074	−1.10719
$596$	−57.8417	−2.36929
$597$	27.2853	1.11671
$598$	−91.9253	−3.75910
$599$	4.19395	0.171360	0.0856800	−	0.996323i	$-0.472694\pi$
$599$	4.19395	0.171360	0.0856800	+	0.996323i	$0.472694\pi$
$600$	16.0436	0.654978
$601$	0.431456	0.0175994	0.00879972	−	0.999961i	$-0.497199\pi$
$601$	0.431456	0.0175994	0.00879972	+	0.999961i	$0.497199\pi$
$602$	−63.5262	−2.58913
$603$	15.9709	0.650387
$604$	2.63310	0.107139
$605$	−7.88142	−0.320425
$606$	30.7968	1.25104
$607$	−40.9765	−1.66318	−0.831592	−	0.555387i	$-0.812570\pi$
$607$	−40.9765	−1.66318	−0.831592	+	0.555387i	$0.812570\pi$
$608$	−14.2379	−0.577424
$609$	−38.3031	−1.55212
$610$	−1.95346	−0.0790934
$611$	−10.0505	−0.406601
$612$	17.3092	0.699681
$613$	23.0671	0.931673	0.465836	−	0.884871i	$-0.345754\pi$
$613$	23.0671	0.931673	0.465836	+	0.884871i	$0.345754\pi$
$614$	−35.5679	−1.43540
$615$	−16.1067	−0.649483
$616$	77.5329	3.12389
$617$	9.38468	0.377813	0.188906	−	0.981995i	$-0.439506\pi$
$617$	9.38468	0.377813	0.188906	+	0.981995i	$0.439506\pi$
$618$	−2.79701	−0.112512
$619$	−7.81656	−0.314174	−0.157087	−	0.987585i	$-0.550210\pi$
$619$	−7.81656	−0.314174	−0.157087	+	0.987585i	$0.550210\pi$
$620$	2.07750	0.0834345
$621$	−8.01851	−0.321772
$622$	51.6061	2.06921
$623$	−25.9779	−1.04078
$624$	−38.4064	−1.53749
$625$	−8.22524	−0.329009
$626$	−41.9094	−1.67504
$627$	4.18423	0.167102
$628$	80.4635	3.21084
$629$	9.86448	0.393323
$630$	18.9671	0.755669
$631$	45.5585	1.81366	0.906828	−	0.421501i	$-0.138497\pi$
$631$	45.5585	1.81366	0.906828	+	0.421501i	$0.138497\pi$
$632$	0.860489	0.0342284
$633$	12.5117	0.497296
$634$	−3.12538	−0.124125
$635$	18.8532	0.748165
$636$	8.90722	0.353194
$637$	−57.0710	−2.26124
$638$	−55.3743	−2.19229
$639$	6.75553	0.267244
$640$	8.31465	0.328665
$641$	39.3655	1.55485	0.777423	−	0.628978i	$-0.216527\pi$
$641$	39.3655	1.55485	0.777423	+	0.628978i	$0.216527\pi$
$642$	33.0374	1.30388
$643$	5.79186	0.228409	0.114204	−	0.993457i	$-0.463568\pi$
$643$	5.79186	0.228409	0.114204	+	0.993457i	$0.463568\pi$
$644$	167.951	6.61820
$645$	−9.04837	−0.356279
$646$	−16.0186	−0.630245
$647$	−31.1287	−1.22380	−0.611898	−	0.790937i	$-0.709594\pi$
$647$	−31.1287	−1.22380	−0.611898	+	0.790937i	$0.709594\pi$
$648$	−6.98031	−0.274212
$649$	6.08612	0.238901
$650$	−26.3493	−1.03351
$651$	−1.19986	−0.0470261
$652$	−105.667	−4.13824
$653$	−35.9759	−1.40785	−0.703923	−	0.710276i	$-0.748570\pi$
$653$	−35.9759	−1.40785	−0.703923	+	0.710276i	$0.748570\pi$
$654$	−22.8209	−0.892369
$655$	−13.5482	−0.529373
$656$	−84.9586	−3.31708
$657$	−9.34843	−0.364717
$658$	26.1812	1.02065
$659$	−6.91906	−0.269528	−0.134764	−	0.990878i	$-0.543028\pi$
$659$	−6.91906	−0.269528	−0.134764	+	0.990878i	$0.543028\pi$
$660$	19.2320	0.748604
$661$	−6.06569	−0.235928	−0.117964	−	0.993018i	$-0.537637\pi$
$661$	−6.06569	−0.235928	−0.117964	+	0.993018i	$0.537637\pi$
$662$	−13.4201	−0.521585
$663$	−16.3238	−0.633965
$664$	43.6688	1.69468
$665$	−12.3112	−0.477407
$666$	−6.92777	−0.268446
$667$	−68.8787	−2.66699
$668$	34.0436	1.31719
$669$	29.1095	1.12544
$670$	−67.9343	−2.62453
$671$	1.14397	0.0441625
$672$	37.7957	1.45800
$673$	−35.3078	−1.36102	−0.680509	−	0.732740i	$-0.738241\pi$
$673$	−35.3078	−1.36102	−0.680509	+	0.732740i	$0.738241\pi$
$674$	29.5067	1.13655
$675$	−2.29841	−0.0884659
$676$	31.1141	1.19670
$677$	40.2373	1.54645	0.773223	−	0.634134i	$-0.218643\pi$
$677$	40.2373	1.54645	0.773223	+	0.634134i	$0.218643\pi$
$678$	27.8819	1.07080
$679$	−59.7852	−2.29435
$680$	−42.2779	−1.62128
$681$	28.4704	1.09099
$682$	−1.73462	−0.0664219
$683$	−4.21106	−0.161132	−0.0805659	−	0.996749i	$-0.525673\pi$
$683$	−4.21106	−0.161132	−0.0805659	+	0.996749i	$0.525673\pi$
$684$	7.89029	0.301693
$685$	−4.61872	−0.176472
$686$	67.8899	2.59205
$687$	−2.44463	−0.0932684
$688$	−47.7279	−1.81961
$689$	−8.40018	−0.320021
$690$	34.1077	1.29846
$691$	7.65761	0.291309	0.145655	−	0.989336i	$-0.453471\pi$
$691$	7.65761	0.291309	0.145655	+	0.989336i	$0.453471\pi$
$692$	89.2073	3.39115
$693$	−11.1074	−0.421934
$694$	41.6467	1.58089
$695$	16.7038	0.633610
$696$	−59.9605	−2.27280
$697$	−36.1099	−1.36776
$698$	−56.1512	−2.12535
$699$	−19.2229	−0.727078
$700$	48.1412	1.81957
$701$	43.3430	1.63704	0.818521	−	0.574476i	$-0.194794\pi$
$701$	43.3430	1.63704	0.818521	+	0.574476i	$0.194794\pi$
$702$	11.4641	0.432686
$703$	4.49667	0.169595
$704$	11.4482	0.431469
$705$	3.72912	0.140447
$706$	21.3708	0.804301
$707$	53.0640	1.99568
$708$	11.4767	0.431322
$709$	4.11582	0.154573	0.0772865	−	0.997009i	$-0.475374\pi$
$709$	4.11582	0.154573	0.0772865	+	0.997009i	$0.475374\pi$
$710$	−28.7354	−1.07842
$711$	−0.123274	−0.00462313
$712$	−40.6664	−1.52404
$713$	−2.15764	−0.0808044
$714$	42.5228	1.59138
$715$	−18.1372	−0.678293
$716$	47.6174	1.77955
$717$	14.3637	0.536423
$718$	−13.5187	−0.504515
$719$	−36.4236	−1.35837	−0.679186	−	0.733966i	$-0.737667\pi$
$719$	−36.4236	−1.35837	−0.679186	+	0.733966i	$0.737667\pi$
$720$	14.2502	0.531074
$721$	−4.81935	−0.179482
$722$	41.8683	1.55818
$723$	−9.14953	−0.340275
$724$	−37.3844	−1.38938
$725$	−19.7433	−0.733247
$726$	12.4092	0.460549
$727$	47.1339	1.74810	0.874050	−	0.485836i	$-0.161485\pi$
$727$	47.1339	1.74810	0.874050	+	0.485836i	$0.161485\pi$
$728$	−137.883	−5.11027
$729$	1.00000	0.0370370
$730$	39.7647	1.47176
$731$	−20.2857	−0.750295
$732$	2.15721	0.0797328
$733$	29.2624	1.08083	0.540416	−	0.841398i	$-0.318267\pi$
$733$	29.2624	1.08083	0.540416	+	0.841398i	$0.318267\pi$
$734$	−15.5181	−0.572784
$735$	21.1755	0.781069
$736$	67.9663	2.50527
$737$	39.7831	1.46543
$738$	25.3597	0.933505
$739$	10.5785	0.389135	0.194568	−	0.980889i	$-0.437670\pi$
$739$	10.5785	0.389135	0.194568	+	0.980889i	$0.437670\pi$
$740$	20.6681	0.759773
$741$	−7.44113	−0.273357
$742$	21.8821	0.803316
$743$	21.0907	0.773744	0.386872	−	0.922133i	$-0.373555\pi$
$743$	21.0907	0.773744	0.386872	+	0.922133i	$0.373555\pi$
$744$	−1.87828	−0.0688611
$745$	−20.2397	−0.741526
$746$	37.9665	1.39005
$747$	−6.25601	−0.228895
$748$	43.1166	1.57650
$749$	56.9246	2.07998
$750$	31.0447	1.13359
$751$	−13.0586	−0.476517	−0.238258	−	0.971202i	$-0.576577\pi$
$751$	−13.0586	−0.476517	−0.238258	+	0.971202i	$0.576577\pi$
$752$	19.6702	0.717298
$753$	3.20202	0.116688
$754$	98.4764	3.58630
$755$	0.921362	0.0335318
$756$	−20.9454	−0.761778
$757$	−0.269806	−0.00980627	−0.00490313	−	0.999988i	$-0.501561\pi$
$757$	−0.269806	−0.00980627	−0.00490313	+	0.999988i	$0.501561\pi$
$758$	5.21643	0.189469
$759$	−19.9739	−0.725005
$760$	−19.2722	−0.699075
$761$	−40.0633	−1.45229	−0.726147	−	0.687540i	$-0.758691\pi$
$761$	−40.0633	−1.45229	−0.726147	+	0.687540i	$0.758691\pi$
$762$	−29.6841	−1.07534
$763$	−39.3212	−1.42352
$764$	87.7905	3.17615
$765$	6.05675	0.218982
$766$	80.0151	2.89106
$767$	−10.8234	−0.390811
$768$	−22.2831	−0.804071
$769$	14.6233	0.527331	0.263666	−	0.964614i	$-0.415068\pi$
$769$	14.6233	0.527331	0.263666	+	0.964614i	$0.415068\pi$
$770$	47.2466	1.70265
$771$	−9.95883	−0.358659
$772$	−116.075	−4.17765
$773$	48.4800	1.74371	0.871853	−	0.489768i	$-0.162919\pi$
$773$	48.4800	1.74371	0.871853	+	0.489768i	$0.162919\pi$
$774$	14.2466	0.512082
$775$	−0.618464	−0.0222159
$776$	−93.5891	−3.35965
$777$	−11.9368	−0.428230
$778$	34.8050	1.24782
$779$	−16.4605	−0.589758
$780$	−34.2017	−1.22462
$781$	16.8278	0.602146
$782$	76.4667	2.73445
$783$	8.58996	0.306980
$784$	111.695	3.98912
$785$	28.1554	1.00491
$786$	21.3315	0.760871
$787$	54.9594	1.95909	0.979545	−	0.201226i	$-0.0644924\pi$
$787$	54.9594	1.95909	0.979545	+	0.201226i	$0.0644924\pi$
$788$	16.7979	0.598402
$789$	23.5587	0.838713
$790$	0.524360	0.0186559
$791$	48.0414	1.70816
$792$	−17.3877	−0.617846
$793$	−2.03441	−0.0722440
$794$	−10.2799	−0.364819
$795$	3.11678	0.110541
$796$	128.166	4.54274
$797$	19.9847	0.707896	0.353948	−	0.935265i	$-0.384839\pi$
$797$	19.9847	0.707896	0.353948	+	0.935265i	$0.384839\pi$
$798$	19.3838	0.686179
$799$	8.36039	0.295769
$800$	19.4817	0.688784
$801$	5.82588	0.205847
$802$	−74.4634	−2.62939
$803$	−23.2867	−0.821768
$804$	75.0199	2.64575
$805$	58.7687	2.07132
$806$	3.08480	0.108658
$807$	11.5299	0.405873
$808$	83.0676	2.92231
$809$	−17.0216	−0.598446	−0.299223	−	0.954183i	$-0.596727\pi$
$809$	−17.0216	−0.598446	−0.299223	+	0.954183i	$0.596727\pi$
$810$	−4.25362	−0.149457
$811$	−7.30573	−0.256539	−0.128270	−	0.991739i	$-0.540942\pi$
$811$	−7.30573	−0.256539	−0.128270	+	0.991739i	$0.540942\pi$
$812$	−179.920	−6.31396
$813$	13.9797	0.490289
$814$	−17.2569	−0.604853
$815$	−36.9745	−1.29516
$816$	31.9478	1.11840
$817$	−9.24714	−0.323516
$818$	−30.8641	−1.07914
$819$	19.7531	0.690229
$820$	−75.6574	−2.64207
$821$	42.0969	1.46919	0.734596	−	0.678504i	$-0.237372\pi$
$821$	42.0969	1.46919	0.734596	+	0.678504i	$0.237372\pi$
$822$	7.27213	0.253645
$823$	−3.57296	−0.124546	−0.0622728	−	0.998059i	$-0.519835\pi$
$823$	−3.57296	−0.124546	−0.0622728	+	0.998059i	$0.519835\pi$
$824$	−7.54431	−0.262819
$825$	−5.72528	−0.199329
$826$	28.1945	0.981011
$827$	−20.2668	−0.704747	−0.352373	−	0.935860i	$-0.614625\pi$
$827$	−20.2668	−0.704747	−0.352373	+	0.935860i	$0.614625\pi$
$828$	−37.6652	−1.30895
$829$	40.0825	1.39212	0.696061	−	0.717982i	$-0.254934\pi$
$829$	40.0825	1.39212	0.696061	+	0.717982i	$0.254934\pi$
$830$	26.6107	0.923670
$831$	17.5738	0.609629
$832$	−20.3592	−0.705827
$833$	47.4737	1.64487
$834$	−26.2999	−0.910691
$835$	11.9124	0.412245
$836$	19.6545	0.679764
$837$	0.269083	0.00930087
$838$	11.6998	0.404164
$839$	11.8039	0.407517	0.203758	−	0.979021i	$-0.434684\pi$
$839$	11.8039	0.407517	0.203758	+	0.979021i	$0.434684\pi$
$840$	51.1596	1.76517
$841$	44.7874	1.54439
$842$	−28.9150	−0.996478
$843$	23.7152	0.816794
$844$	58.7709	2.02298
$845$	10.8873	0.374535
$846$	−5.87146	−0.201865
$847$	21.3815	0.734676
$848$	16.4402	0.564560
$849$	11.0975	0.380866
$850$	21.9183	0.751792
$851$	−21.4654	−0.735823
$852$	31.7326	1.08714
$853$	−53.0177	−1.81529	−0.907645	−	0.419739i	$-0.862122\pi$
$853$	−53.0177	−1.81529	−0.907645	+	0.419739i	$0.862122\pi$
$854$	5.29954	0.181347
$855$	2.76093	0.0944220
$856$	89.1110	3.04575
$857$	−26.5785	−0.907903	−0.453952	−	0.891026i	$-0.649986\pi$
$857$	−26.5785	−0.907903	−0.453952	+	0.891026i	$0.649986\pi$
$858$	28.5568	0.974914
$859$	−15.5321	−0.529948	−0.264974	−	0.964256i	$-0.585363\pi$
$859$	−15.5321	−0.529948	−0.264974	+	0.964256i	$0.585363\pi$
$860$	−42.5027	−1.44933
$861$	43.6957	1.48915
$862$	95.8036	3.26308
$863$	13.6851	0.465846	0.232923	−	0.972495i	$-0.425171\pi$
$863$	13.6851	0.465846	0.232923	+	0.972495i	$0.425171\pi$
$864$	−8.47617	−0.288365
$865$	31.2150	1.06134
$866$	−52.7277	−1.79176
$867$	−3.42125	−0.116192
$868$	−5.63606	−0.191300
$869$	−0.307071	−0.0104167
$870$	−36.5384	−1.23877
$871$	−70.7494	−2.39725
$872$	−61.5543	−2.08449
$873$	13.4076	0.453778
$874$	34.8569	1.17905
$875$	53.4910	1.80833
$876$	−43.9122	−1.48365
$877$	−3.55973	−0.120203	−0.0601017	−	0.998192i	$-0.519143\pi$
$877$	−3.55973	−0.120203	−0.0601017	+	0.998192i	$0.519143\pi$
$878$	−73.6659	−2.48610
$879$	5.57049	0.187888
$880$	35.4968	1.19660
$881$	19.6813	0.663080	0.331540	−	0.943441i	$-0.392432\pi$
$881$	19.6813	0.663080	0.331540	+	0.943441i	$0.392432\pi$
$882$	−33.3405	−1.12263
$883$	47.7012	1.60527	0.802636	−	0.596469i	$-0.203430\pi$
$883$	47.7012	1.60527	0.802636	+	0.596469i	$0.203430\pi$
$884$	−76.6775	−2.57894
$885$	4.01588	0.134992
$886$	−6.13580	−0.206136
$887$	−54.0745	−1.81564	−0.907822	−	0.419355i	$-0.862256\pi$
$887$	−54.0745	−1.81564	−0.907822	+	0.419355i	$0.862256\pi$
$888$	−18.6861	−0.627065
$889$	−51.1467	−1.71541
$890$	−24.7811	−0.830664
$891$	2.49097	0.0834506
$892$	136.736	4.57824
$893$	3.81104	0.127532
$894$	31.8672	1.06580
$895$	16.6621	0.556952
$896$	−22.5568	−0.753570
$897$	35.5211	1.18601
$898$	67.8426	2.26394
$899$	2.31141	0.0770899
$900$	−10.7963	−0.359876
$901$	6.98757	0.232790
$902$	63.1704	2.10334
$903$	24.5473	0.816883
$904$	75.2051	2.50128
$905$	−13.0814	−0.434841
$906$	−1.45067	−0.0481954
$907$	47.3241	1.57137	0.785685	−	0.618626i	$-0.212310\pi$
$907$	47.3241	1.57137	0.785685	+	0.618626i	$0.212310\pi$
$908$	133.733	4.43810
$909$	−11.9003	−0.394707
$910$	−84.0222	−2.78531
$911$	−28.6788	−0.950171	−0.475085	−	0.879940i	$-0.657583\pi$
$911$	−28.6788	−0.950171	−0.475085	+	0.879940i	$0.657583\pi$
$912$	14.5632	0.482237
$913$	−15.5835	−0.515739
$914$	36.1578	1.19599
$915$	0.754842	0.0249543
$916$	−11.4831	−0.379412
$917$	36.7550	1.21376
$918$	−9.53628	−0.314744
$919$	−15.1178	−0.498691	−0.249345	−	0.968415i	$-0.580215\pi$
$919$	−15.1178	−0.498691	−0.249345	+	0.968415i	$0.580215\pi$
$920$	91.9978	3.03308
$921$	13.7439	0.452876
$922$	29.6227	0.975570
$923$	−29.9262	−0.985032
$924$	−52.1744	−1.71641
$925$	−6.15279	−0.202303
$926$	−17.9086	−0.588512
$927$	1.08080	0.0354981
$928$	−72.8100	−2.39010
$929$	11.0826	0.363607	0.181803	−	0.983335i	$-0.441807\pi$
$929$	11.0826	0.363607	0.181803	+	0.983335i	$0.441807\pi$
$930$	−1.14458	−0.0375321
$931$	21.6406	0.709243
$932$	−90.2954	−2.95772
$933$	−19.9412	−0.652846
$934$	−30.6031	−1.00136
$935$	15.0872	0.493403
$936$	30.9219	1.01072
$937$	−15.7682	−0.515124	−0.257562	−	0.966262i	$-0.582919\pi$
$937$	−15.7682	−0.515124	−0.257562	+	0.966262i	$0.582919\pi$
$938$	184.299	6.01757
$939$	16.1943	0.528481
$940$	17.5167	0.571332
$941$	−37.2958	−1.21581	−0.607905	−	0.794010i	$-0.707990\pi$
$941$	−37.2958	−1.21581	−0.607905	+	0.794010i	$0.707990\pi$
$942$	−44.3304	−1.44436
$943$	78.5759	2.55878
$944$	21.1828	0.689441
$945$	−7.32913	−0.238417
$946$	35.4877	1.15381
$947$	−51.9565	−1.68836	−0.844180	−	0.536060i	$-0.819912\pi$
$947$	−51.9565	−1.68836	−0.844180	+	0.536060i	$0.819912\pi$
$948$	−0.579051	−0.0188067
$949$	41.4125	1.34431
$950$	9.99134	0.324162
$951$	1.20768	0.0391618
$952$	114.696	3.71731
$953$	58.6216	1.89894	0.949470	−	0.313857i	$-0.101621\pi$
$953$	58.6216	1.89894	0.949470	+	0.313857i	$0.101621\pi$
$954$	−4.90733	−0.158881
$955$	30.7193	0.994052
$956$	67.4703	2.18215
$957$	21.3973	0.691677
$958$	0.939247	0.0303457
$959$	12.5301	0.404619
$960$	7.55401	0.243805
$961$	−30.9276	−0.997664
$962$	30.6892	0.989460
$963$	−12.7661	−0.411381
$964$	−42.9779	−1.38422
$965$	−40.6166	−1.30750
$966$	−92.5307	−2.97713
$967$	3.54180	0.113897	0.0569483	−	0.998377i	$-0.481863\pi$
$967$	3.54180	0.113897	0.0569483	+	0.998377i	$0.481863\pi$
$968$	33.4710	1.07580
$969$	6.18980	0.198845
$970$	−57.0308	−1.83115
$971$	−15.6837	−0.503315	−0.251657	−	0.967816i	$-0.580976\pi$
$971$	−15.6837	−0.503315	−0.251657	+	0.967816i	$0.580976\pi$
$972$	4.69728	0.150665
$973$	−45.3156	−1.45275
$974$	−32.6602	−1.04650
$975$	10.1817	0.326075
$976$	3.98160	0.127448
$977$	27.5349	0.880920	0.440460	−	0.897772i	$-0.354815\pi$
$977$	27.5349	0.880920	0.440460	+	0.897772i	$0.354815\pi$
$978$	58.2160	1.86154
$979$	14.5121	0.463808
$980$	99.4670	3.17736
$981$	8.81828	0.281546
$982$	−53.1179	−1.69506
$983$	23.2602	0.741884	0.370942	−	0.928656i	$-0.379035\pi$
$983$	23.2602	0.741884	0.370942	+	0.928656i	$0.379035\pi$
$984$	68.4022	2.18058
$985$	5.87786	0.187284
$986$	−81.9162	−2.60874
$987$	−10.1167	−0.322019
$988$	−34.9530	−1.11200
$989$	44.1422	1.40364
$990$	−10.5956	−0.336751
$991$	33.4461	1.06245	0.531226	−	0.847230i	$-0.321732\pi$
$991$	33.4461	1.06245	0.531226	+	0.847230i	$0.321732\pi$
$992$	−2.28079	−0.0724153
$993$	5.18567	0.164562
$994$	77.9563	2.47262
$995$	44.8474	1.42176
$996$	−29.3862	−0.931137
$997$	−32.8669	−1.04090	−0.520452	−	0.853891i	$-0.674236\pi$
$997$	−32.8669	−1.04090	−0.520452	+	0.853891i	$0.674236\pi$
$998$	−71.1510	−2.25224
$999$	2.67698	0.0846958

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8049.2.a.d.1.10	✓	129

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8049.2.a.d.1.10	✓	129	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:	\( N \)	\(=\)	\( 8049 = 3 \cdot 2683 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8049.a (trivial)

\(f(q)\)	\(=\)	\(q-2.58791 q^{2} +1.00000 q^{3} +4.69728 q^{4} +1.64365 q^{5} -2.58791 q^{6} -4.45906 q^{7} -6.98031 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-2.58791 q^{2} +1.00000 q^{3} +4.69728 q^{4} +1.64365 q^{5} -2.58791 q^{6} -4.45906 q^{7} -6.98031 q^{8} +1.00000 q^{9} -4.25362 q^{10} +2.49097 q^{11} +4.69728 q^{12} -4.42988 q^{13} +11.5396 q^{14} +1.64365 q^{15} +8.66985 q^{16} +3.68494 q^{17} -2.58791 q^{18} +1.67976 q^{19} +7.72068 q^{20} -4.45906 q^{21} -6.44641 q^{22} -8.01851 q^{23} -6.98031 q^{24} -2.29841 q^{25} +11.4641 q^{26} +1.00000 q^{27} -20.9454 q^{28} +8.58996 q^{29} -4.25362 q^{30} +0.269083 q^{31} -8.47617 q^{32} +2.49097 q^{33} -9.53628 q^{34} -7.32913 q^{35} +4.69728 q^{36} +2.67698 q^{37} -4.34706 q^{38} -4.42988 q^{39} -11.4732 q^{40} -9.79932 q^{41} +11.5396 q^{42} -5.50504 q^{43} +11.7008 q^{44} +1.64365 q^{45} +20.7512 q^{46} +2.26880 q^{47} +8.66985 q^{48} +12.8832 q^{49} +5.94808 q^{50} +3.68494 q^{51} -20.8084 q^{52} +1.89625 q^{53} -2.58791 q^{54} +4.09428 q^{55} +31.1256 q^{56} +1.67976 q^{57} -22.2300 q^{58} +2.44327 q^{59} +7.72068 q^{60} +0.459247 q^{61} -0.696362 q^{62} -4.45906 q^{63} +4.59587 q^{64} -7.28118 q^{65} -6.44641 q^{66} +15.9709 q^{67} +17.3092 q^{68} -8.01851 q^{69} +18.9671 q^{70} +6.75553 q^{71} -6.98031 q^{72} -9.34843 q^{73} -6.92777 q^{74} -2.29841 q^{75} +7.89029 q^{76} -11.1074 q^{77} +11.4641 q^{78} -0.123274 q^{79} +14.2502 q^{80} +1.00000 q^{81} +25.3597 q^{82} -6.25601 q^{83} -20.9454 q^{84} +6.05675 q^{85} +14.2466 q^{86} +8.58996 q^{87} -17.3877 q^{88} +5.82588 q^{89} -4.25362 q^{90} +19.7531 q^{91} -37.6652 q^{92} +0.269083 q^{93} -5.87146 q^{94} +2.76093 q^{95} -8.47617 q^{96} +13.4076 q^{97} -33.3405 q^{98} +2.49097 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 129 q + 8 q^{2} + 129 q^{3} + 158 q^{4} + 11 q^{5} + 8 q^{6} + 40 q^{7} + 18 q^{8} + 129 q^{9}+O(q^{10}) \) 129 * q + 8 * q^2 + 129 * q^3 + 158 * q^4 + 11 * q^5 + 8 * q^6 + 40 * q^7 + 18 * q^8 + 129 * q^9	\( 129 q + 8 q^{2} + 129 q^{3} + 158 q^{4} + 11 q^{5} + 8 q^{6} + 40 q^{7} + 18 q^{8} + 129 q^{9} + 20 q^{10} + 48 q^{11} + 158 q^{12} + 77 q^{13} + 13 q^{14} + 11 q^{15} + 212 q^{16} + 9 q^{17} + 8 q^{18} + 68 q^{19} + 19 q^{20} + 40 q^{21} + 45 q^{22} + 64 q^{23} + 18 q^{24} + 188 q^{25} + 19 q^{26} + 129 q^{27} + 69 q^{28} + 23 q^{29} + 20 q^{30} + 133 q^{31} + 24 q^{32} + 48 q^{33} + 63 q^{34} + 26 q^{35} + 158 q^{36} + 147 q^{37} + 9 q^{38} + 77 q^{39} + 58 q^{40} + 21 q^{41} + 13 q^{42} + 76 q^{43} + 110 q^{44} + 11 q^{45} + 48 q^{46} + 85 q^{47} + 212 q^{48} + 213 q^{49} + 17 q^{50} + 9 q^{51} + 139 q^{52} + 30 q^{53} + 8 q^{54} + 103 q^{55} + 19 q^{56} + 68 q^{57} + 94 q^{58} + 64 q^{59} + 19 q^{60} + 110 q^{61} - 10 q^{62} + 40 q^{63} + 288 q^{64} - 8 q^{65} + 45 q^{66} + 118 q^{67} - 15 q^{68} + 64 q^{69} + 75 q^{70} + 154 q^{71} + 18 q^{72} + 137 q^{73} + 28 q^{74} + 188 q^{75} + 156 q^{76} + 17 q^{77} + 19 q^{78} + 157 q^{79} + 2 q^{80} + 129 q^{81} + 72 q^{82} + 39 q^{83} + 69 q^{84} + 127 q^{85} + 54 q^{86} + 23 q^{87} + 97 q^{88} + 31 q^{89} + 20 q^{90} + 137 q^{91} + 82 q^{92} + 133 q^{93} + 40 q^{94} + 68 q^{95} + 24 q^{96} + 170 q^{97} - 21 q^{98} + 48 q^{99}+O(q^{100}) \) 129 * q + 8 * q^2 + 129 * q^3 + 158 * q^4 + 11 * q^5 + 8 * q^6 + 40 * q^7 + 18 * q^8 + 129 * q^9 + 20 * q^10 + 48 * q^11 + 158 * q^12 + 77 * q^13 + 13 * q^14 + 11 * q^15 + 212 * q^16 + 9 * q^17 + 8 * q^18 + 68 * q^19 + 19 * q^20 + 40 * q^21 + 45 * q^22 + 64 * q^23 + 18 * q^24 + 188 * q^25 + 19 * q^26 + 129 * q^27 + 69 * q^28 + 23 * q^29 + 20 * q^30 + 133 * q^31 + 24 * q^32 + 48 * q^33 + 63 * q^34 + 26 * q^35 + 158 * q^36 + 147 * q^37 + 9 * q^38 + 77 * q^39 + 58 * q^40 + 21 * q^41 + 13 * q^42 + 76 * q^43 + 110 * q^44 + 11 * q^45 + 48 * q^46 + 85 * q^47 + 212 * q^48 + 213 * q^49 + 17 * q^50 + 9 * q^51 + 139 * q^52 + 30 * q^53 + 8 * q^54 + 103 * q^55 + 19 * q^56 + 68 * q^57 + 94 * q^58 + 64 * q^59 + 19 * q^60 + 110 * q^61 - 10 * q^62 + 40 * q^63 + 288 * q^64 - 8 * q^65 + 45 * q^66 + 118 * q^67 - 15 * q^68 + 64 * q^69 + 75 * q^70 + 154 * q^71 + 18 * q^72 + 137 * q^73 + 28 * q^74 + 188 * q^75 + 156 * q^76 + 17 * q^77 + 19 * q^78 + 157 * q^79 + 2 * q^80 + 129 * q^81 + 72 * q^82 + 39 * q^83 + 69 * q^84 + 127 * q^85 + 54 * q^86 + 23 * q^87 + 97 * q^88 + 31 * q^89 + 20 * q^90 + 137 * q^91 + 82 * q^92 + 133 * q^93 + 40 * q^94 + 68 * q^95 + 24 * q^96 + 170 * q^97 - 21 * q^98 + 48 * q^99

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