LMFDB - Embedded newform 8018.2.a.k.1.17

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8018,2,Mod(1,8018)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8018, 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("8018.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8018 = 2 \cdot 19 \cdot 211 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8018.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:	$64.0240523407$
Analytic rank:	$0$
Dimension:	$49$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.17
Character	$\chi$	$=$	8018.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -0.823102 q^{3} +1.00000 q^{4} +1.30158 q^{5} -0.823102 q^{6} +0.990463 q^{7} +1.00000 q^{8} -2.32250 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -0.823102 q^{3} +1.00000 q^{4} +1.30158 q^{5} -0.823102 q^{6} +0.990463 q^{7} +1.00000 q^{8} -2.32250 q^{9} +1.30158 q^{10} +2.45467 q^{11} -0.823102 q^{12} -1.10552 q^{13} +0.990463 q^{14} -1.07133 q^{15} +1.00000 q^{16} +3.67462 q^{17} -2.32250 q^{18} +1.00000 q^{19} +1.30158 q^{20} -0.815252 q^{21} +2.45467 q^{22} +3.34514 q^{23} -0.823102 q^{24} -3.30590 q^{25} -1.10552 q^{26} +4.38096 q^{27} +0.990463 q^{28} +7.61236 q^{29} -1.07133 q^{30} +10.3859 q^{31} +1.00000 q^{32} -2.02044 q^{33} +3.67462 q^{34} +1.28916 q^{35} -2.32250 q^{36} -9.71734 q^{37} +1.00000 q^{38} +0.909957 q^{39} +1.30158 q^{40} +5.28007 q^{41} -0.815252 q^{42} -9.78927 q^{43} +2.45467 q^{44} -3.02292 q^{45} +3.34514 q^{46} +5.93027 q^{47} -0.823102 q^{48} -6.01898 q^{49} -3.30590 q^{50} -3.02459 q^{51} -1.10552 q^{52} -9.49673 q^{53} +4.38096 q^{54} +3.19495 q^{55} +0.990463 q^{56} -0.823102 q^{57} +7.61236 q^{58} +1.08798 q^{59} -1.07133 q^{60} +1.69520 q^{61} +10.3859 q^{62} -2.30035 q^{63} +1.00000 q^{64} -1.43892 q^{65} -2.02044 q^{66} +3.25797 q^{67} +3.67462 q^{68} -2.75339 q^{69} +1.28916 q^{70} -11.1222 q^{71} -2.32250 q^{72} -0.759106 q^{73} -9.71734 q^{74} +2.72109 q^{75} +1.00000 q^{76} +2.43126 q^{77} +0.909957 q^{78} -2.36945 q^{79} +1.30158 q^{80} +3.36153 q^{81} +5.28007 q^{82} +14.6925 q^{83} -0.815252 q^{84} +4.78281 q^{85} -9.78927 q^{86} -6.26575 q^{87} +2.45467 q^{88} -2.99331 q^{89} -3.02292 q^{90} -1.09498 q^{91} +3.34514 q^{92} -8.54866 q^{93} +5.93027 q^{94} +1.30158 q^{95} -0.823102 q^{96} +4.59458 q^{97} -6.01898 q^{98} -5.70098 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 49 q + 49 q^{2} + 13 q^{3} + 49 q^{4} + 17 q^{5} + 13 q^{6} + 22 q^{7} + 49 q^{8} + 66 q^{9}+O(q^{10}) $ 49 * q + 49 * q^2 + 13 * q^3 + 49 * q^4 + 17 * q^5 + 13 * q^6 + 22 * q^7 + 49 * q^8 + 66 * q^9	\( 49 q + 49 q^{2} + 13 q^{3} + 49 q^{4} + 17 q^{5} + 13 q^{6} + 22 q^{7} + 49 q^{8} + 66 q^{9} + 17 q^{10} + 21 q^{11} + 13 q^{12} + 13 q^{13} + 22 q^{14} + 8 q^{15} + 49 q^{16} + 24 q^{17} + 66 q^{18} + 49 q^{19} + 17 q^{20} + 6 q^{21} + 21 q^{22} + 22 q^{23} + 13 q^{24} + 96 q^{25} + 13 q^{26} + 31 q^{27} + 22 q^{28} + 33 q^{29} + 8 q^{30} + 21 q^{31} + 49 q^{32} + 20 q^{33} + 24 q^{34} + 18 q^{35} + 66 q^{36} + 48 q^{37} + 49 q^{38} + 4 q^{39} + 17 q^{40} + 37 q^{41} + 6 q^{42} + 43 q^{43} + 21 q^{44} + 47 q^{45} + 22 q^{46} + 7 q^{47} + 13 q^{48} + 87 q^{49} + 96 q^{50} + 12 q^{51} + 13 q^{52} + 23 q^{53} + 31 q^{54} + 31 q^{55} + 22 q^{56} + 13 q^{57} + 33 q^{58} + 37 q^{59} + 8 q^{60} + 61 q^{61} + 21 q^{62} + 45 q^{63} + 49 q^{64} + 36 q^{65} + 20 q^{66} + 43 q^{67} + 24 q^{68} + 18 q^{69} + 18 q^{70} + 14 q^{71} + 66 q^{72} + 90 q^{73} + 48 q^{74} + 53 q^{75} + 49 q^{76} + 46 q^{77} + 4 q^{78} + 16 q^{79} + 17 q^{80} + 97 q^{81} + 37 q^{82} + 11 q^{83} + 6 q^{84} + 88 q^{85} + 43 q^{86} - 35 q^{87} + 21 q^{88} + 46 q^{89} + 47 q^{90} + 27 q^{91} + 22 q^{92} + 9 q^{93} + 7 q^{94} + 17 q^{95} + 13 q^{96} + 34 q^{97} + 87 q^{98} + 84 q^{99}+O(q^{100}) \) 49 * q + 49 * q^2 + 13 * q^3 + 49 * q^4 + 17 * q^5 + 13 * q^6 + 22 * q^7 + 49 * q^8 + 66 * q^9 + 17 * q^10 + 21 * q^11 + 13 * q^12 + 13 * q^13 + 22 * q^14 + 8 * q^15 + 49 * q^16 + 24 * q^17 + 66 * q^18 + 49 * q^19 + 17 * q^20 + 6 * q^21 + 21 * q^22 + 22 * q^23 + 13 * q^24 + 96 * q^25 + 13 * q^26 + 31 * q^27 + 22 * q^28 + 33 * q^29 + 8 * q^30 + 21 * q^31 + 49 * q^32 + 20 * q^33 + 24 * q^34 + 18 * q^35 + 66 * q^36 + 48 * q^37 + 49 * q^38 + 4 * q^39 + 17 * q^40 + 37 * q^41 + 6 * q^42 + 43 * q^43 + 21 * q^44 + 47 * q^45 + 22 * q^46 + 7 * q^47 + 13 * q^48 + 87 * q^49 + 96 * q^50 + 12 * q^51 + 13 * q^52 + 23 * q^53 + 31 * q^54 + 31 * q^55 + 22 * q^56 + 13 * q^57 + 33 * q^58 + 37 * q^59 + 8 * q^60 + 61 * q^61 + 21 * q^62 + 45 * q^63 + 49 * q^64 + 36 * q^65 + 20 * q^66 + 43 * q^67 + 24 * q^68 + 18 * q^69 + 18 * q^70 + 14 * q^71 + 66 * q^72 + 90 * q^73 + 48 * q^74 + 53 * q^75 + 49 * q^76 + 46 * q^77 + 4 * q^78 + 16 * q^79 + 17 * q^80 + 97 * q^81 + 37 * q^82 + 11 * q^83 + 6 * q^84 + 88 * q^85 + 43 * q^86 - 35 * q^87 + 21 * q^88 + 46 * q^89 + 47 * q^90 + 27 * q^91 + 22 * q^92 + 9 * q^93 + 7 * q^94 + 17 * q^95 + 13 * q^96 + 34 * q^97 + 87 * q^98 + 84 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	1.00000	0.707107
$2$	1.00000	0.707107
$3$	−0.823102	−0.475218	−0.237609	−	0.971361i	$-0.576364\pi$
$3$	−0.823102	−0.475218	−0.237609	+	0.971361i	$0.576364\pi$
$4$	1.00000	0.500000
$5$	1.30158	0.582083	0.291042	−	0.956710i	$-0.405998\pi$
$5$	1.30158	0.582083	0.291042	+	0.956710i	$0.405998\pi$
$6$	−0.823102	−0.336030
$7$	0.990463	0.374360	0.187180	−	0.982326i	$-0.440065\pi$
$7$	0.990463	0.374360	0.187180	+	0.982326i	$0.440065\pi$
$8$	1.00000	0.353553
$9$	−2.32250	−0.774168
$10$	1.30158	0.411595
$11$	2.45467	0.740111	0.370056	−	0.929010i	$-0.379339\pi$
$11$	2.45467	0.740111	0.370056	+	0.929010i	$0.379339\pi$
$12$	−0.823102	−0.237609
$13$	−1.10552	−0.306616	−0.153308	−	0.988178i	$-0.548993\pi$
$13$	−1.10552	−0.306616	−0.153308	+	0.988178i	$0.548993\pi$
$14$	0.990463	0.264712
$15$	−1.07133	−0.276616
$16$	1.00000	0.250000
$17$	3.67462	0.891227	0.445613	−	0.895226i	$-0.352986\pi$
$17$	3.67462	0.891227	0.445613	+	0.895226i	$0.352986\pi$
$18$	−2.32250	−0.547419
$19$	1.00000	0.229416
$19$	1.00000	0.229416
$20$	1.30158	0.291042
$21$	−0.815252	−0.177903
$22$	2.45467	0.523338
$23$	3.34514	0.697509	0.348755	−	0.937214i	$-0.386605\pi$
$23$	3.34514	0.697509	0.348755	+	0.937214i	$0.386605\pi$
$24$	−0.823102	−0.168015
$25$	−3.30590	−0.661179
$26$	−1.10552	−0.216811
$27$	4.38096	0.843117
$28$	0.990463	0.187180
$29$	7.61236	1.41358	0.706790	−	0.707424i	$-0.250143\pi$
$29$	7.61236	1.41358	0.706790	+	0.707424i	$0.250143\pi$
$30$	−1.07133	−0.195597
$31$	10.3859	1.86536	0.932682	−	0.360700i	$-0.117462\pi$
$31$	10.3859	1.86536	0.932682	+	0.360700i	$0.117462\pi$
$32$	1.00000	0.176777
$33$	−2.02044	−0.351714
$34$	3.67462	0.630192
$35$	1.28916	0.217909
$36$	−2.32250	−0.387084
$37$	−9.71734	−1.59752	−0.798761	−	0.601649i	$-0.794511\pi$
$37$	−9.71734	−1.59752	−0.798761	+	0.601649i	$0.794511\pi$
$38$	1.00000	0.162221
$39$	0.909957	0.145710
$40$	1.30158	0.205798
$41$	5.28007	0.824609	0.412305	−	0.911046i	$-0.364724\pi$
$41$	5.28007	0.824609	0.412305	+	0.911046i	$0.364724\pi$
$42$	−0.815252	−0.125796
$43$	−9.78927	−1.49285	−0.746425	−	0.665470i	$-0.768231\pi$
$43$	−9.78927	−1.49285	−0.746425	+	0.665470i	$0.768231\pi$
$44$	2.45467	0.370056
$45$	−3.02292	−0.450630
$46$	3.34514	0.493214
$47$	5.93027	0.865019	0.432509	−	0.901629i	$-0.357628\pi$
$47$	5.93027	0.865019	0.432509	+	0.901629i	$0.357628\pi$
$48$	−0.823102	−0.118805
$49$	−6.01898	−0.859855
$50$	−3.30590	−0.467524
$51$	−3.02459	−0.423527
$52$	−1.10552	−0.153308
$53$	−9.49673	−1.30448	−0.652238	−	0.758014i	$-0.726170\pi$
$53$	−9.49673	−1.30448	−0.652238	+	0.758014i	$0.726170\pi$
$54$	4.38096	0.596173
$55$	3.19495	0.430807
$56$	0.990463	0.132356
$57$	−0.823102	−0.109022
$58$	7.61236	0.999552
$59$	1.08798	0.141643	0.0708214	−	0.997489i	$-0.477438\pi$
$59$	1.08798	0.141643	0.0708214	+	0.997489i	$0.477438\pi$
$60$	−1.07133	−0.138308
$61$	1.69520	0.217048	0.108524	−	0.994094i	$-0.465388\pi$
$61$	1.69520	0.217048	0.108524	+	0.994094i	$0.465388\pi$
$62$	10.3859	1.31901
$63$	−2.30035	−0.289817
$64$	1.00000	0.125000
$65$	−1.43892	−0.178476
$66$	−2.02044	−0.248700
$67$	3.25797	0.398025	0.199012	−	0.979997i	$-0.436227\pi$
$67$	3.25797	0.398025	0.199012	+	0.979997i	$0.436227\pi$
$68$	3.67462	0.445613
$69$	−2.75339	−0.331469
$70$	1.28916	0.154085
$71$	−11.1222	−1.31997	−0.659983	−	0.751280i	$-0.729437\pi$
$71$	−11.1222	−1.31997	−0.659983	+	0.751280i	$0.729437\pi$
$72$	−2.32250	−0.273710
$73$	−0.759106	−0.0888467	−0.0444233	−	0.999013i	$-0.514145\pi$
$73$	−0.759106	−0.0888467	−0.0444233	+	0.999013i	$0.514145\pi$
$74$	−9.71734	−1.12962
$75$	2.72109	0.314204
$76$	1.00000	0.114708
$77$	2.43126	0.277068
$78$	0.909957	0.103032
$79$	−2.36945	−0.266584	−0.133292	−	0.991077i	$-0.542555\pi$
$79$	−2.36945	−0.266584	−0.133292	+	0.991077i	$0.542555\pi$
$80$	1.30158	0.145521
$81$	3.36153	0.373504
$82$	5.28007	0.583087
$83$	14.6925	1.61272	0.806358	−	0.591428i	$-0.201435\pi$
$83$	14.6925	1.61272	0.806358	+	0.591428i	$0.201435\pi$
$84$	−0.815252	−0.0889513
$85$	4.78281	0.518768
$86$	−9.78927	−1.05560
$87$	−6.26575	−0.671759
$88$	2.45467	0.261669
$89$	−2.99331	−0.317290	−0.158645	−	0.987336i	$-0.550713\pi$
$89$	−2.99331	−0.317290	−0.158645	+	0.987336i	$0.550713\pi$
$90$	−3.02292	−0.318644
$91$	−1.09498	−0.114785
$92$	3.34514	0.348755
$93$	−8.54866	−0.886454
$94$	5.93027	0.611661
$95$	1.30158	0.133539
$96$	−0.823102	−0.0840075
$97$	4.59458	0.466509	0.233254	−	0.972416i	$-0.425063\pi$
$97$	4.59458	0.466509	0.233254	+	0.972416i	$0.425063\pi$
$98$	−6.01898	−0.608009
$99$	−5.70098	−0.572970
$100$	−3.30590	−0.330590
$101$	17.6299	1.75424	0.877122	−	0.480268i	$-0.159461\pi$
$101$	17.6299	1.75424	0.877122	+	0.480268i	$0.159461\pi$
$102$	−3.02459	−0.299479
$103$	0.995805	0.0981196	0.0490598	−	0.998796i	$-0.484378\pi$
$103$	0.995805	0.0981196	0.0490598	+	0.998796i	$0.484378\pi$
$104$	−1.10552	−0.108405
$105$	−1.06111	−0.103554
$106$	−9.49673	−0.922404
$107$	−1.05357	−0.101853	−0.0509263	−	0.998702i	$-0.516217\pi$
$107$	−1.05357	−0.101853	−0.0509263	+	0.998702i	$0.516217\pi$
$108$	4.38096	0.421558
$109$	2.49532	0.239009	0.119504	−	0.992834i	$-0.461869\pi$
$109$	2.49532	0.239009	0.119504	+	0.992834i	$0.461869\pi$
$110$	3.19495	0.304626
$111$	7.99836	0.759171
$112$	0.990463	0.0935900
$113$	11.6593	1.09681	0.548407	−	0.836212i	$-0.315235\pi$
$113$	11.6593	1.09681	0.548407	+	0.836212i	$0.315235\pi$
$114$	−0.823102	−0.0770905
$115$	4.35396	0.406009
$116$	7.61236	0.706790
$117$	2.56758	0.237373
$118$	1.08798	0.100157
$119$	3.63958	0.333640
$120$	−1.07133	−0.0977987
$121$	−4.97459	−0.452235
$122$	1.69520	0.153476
$123$	−4.34604	−0.391869
$124$	10.3859	0.932682
$125$	−10.8108	−0.966945
$126$	−2.30035	−0.204932
$127$	−2.36180	−0.209575	−0.104788	−	0.994495i	$-0.533416\pi$
$127$	−2.36180	−0.209575	−0.104788	+	0.994495i	$0.533416\pi$
$128$	1.00000	0.0883883
$129$	8.05757	0.709429
$130$	−1.43892	−0.126202
$131$	19.7744	1.72769	0.863847	−	0.503755i	$-0.168049\pi$
$131$	19.7744	1.72769	0.863847	+	0.503755i	$0.168049\pi$
$132$	−2.02044	−0.175857
$133$	0.990463	0.0858840
$134$	3.25797	0.281446
$135$	5.70216	0.490764
$136$	3.67462	0.315096
$137$	11.6676	0.996830	0.498415	−	0.866939i	$-0.333916\pi$
$137$	11.6676	0.996830	0.498415	+	0.866939i	$0.333916\pi$
$138$	−2.75339	−0.234384
$139$	1.55905	0.132237	0.0661183	−	0.997812i	$-0.478939\pi$
$139$	1.55905	0.132237	0.0661183	+	0.997812i	$0.478939\pi$
$140$	1.28916	0.108954
$141$	−4.88122	−0.411072
$142$	−11.1222	−0.933357
$143$	−2.71369	−0.226930
$144$	−2.32250	−0.193542
$145$	9.90808	0.822821
$146$	−0.759106	−0.0628241
$147$	4.95424	0.408618
$148$	−9.71734	−0.798761
$149$	−17.2533	−1.41345	−0.706723	−	0.707491i	$-0.749827\pi$
$149$	−17.2533	−1.41345	−0.706723	+	0.707491i	$0.749827\pi$
$150$	2.72109	0.222176
$151$	−23.5957	−1.92019	−0.960093	−	0.279679i	$-0.909772\pi$
$151$	−23.5957	−1.92019	−0.960093	+	0.279679i	$0.909772\pi$
$152$	1.00000	0.0811107
$153$	−8.53432	−0.689959
$154$	2.43126	0.195917
$155$	13.5181	1.08580
$156$	0.909957	0.0728548
$157$	14.3219	1.14302	0.571508	−	0.820597i	$-0.306359\pi$
$157$	14.3219	1.14302	0.571508	+	0.820597i	$0.306359\pi$
$158$	−2.36945	−0.188504
$159$	7.81677	0.619911
$160$	1.30158	0.102899
$161$	3.31324	0.261120
$162$	3.36153	0.264107
$163$	22.0877	1.73004	0.865022	−	0.501733i	$-0.167304\pi$
$163$	22.0877	1.73004	0.865022	+	0.501733i	$0.167304\pi$
$164$	5.28007	0.412305
$165$	−2.62977	−0.204727
$166$	14.6925	1.14036
$167$	22.1856	1.71677	0.858386	−	0.513005i	$-0.171468\pi$
$167$	22.1856	1.71677	0.858386	+	0.513005i	$0.171468\pi$
$168$	−0.815252	−0.0628981
$169$	−11.7778	−0.905986
$170$	4.78281	0.366825
$171$	−2.32250	−0.177606
$172$	−9.78927	−0.746425
$173$	3.25953	0.247818	0.123909	−	0.992294i	$-0.460457\pi$
$173$	3.25953	0.247818	0.123909	+	0.992294i	$0.460457\pi$
$174$	−6.26575	−0.475005
$175$	−3.27437	−0.247519
$176$	2.45467	0.185028
$177$	−0.895517	−0.0673112
$178$	−2.99331	−0.224358
$179$	5.84560	0.436921	0.218460	−	0.975846i	$-0.429897\pi$
$179$	5.84560	0.436921	0.218460	+	0.975846i	$0.429897\pi$
$180$	−3.02292	−0.225315
$181$	9.62521	0.715436	0.357718	−	0.933830i	$-0.383555\pi$
$181$	9.62521	0.715436	0.357718	+	0.933830i	$0.383555\pi$
$182$	−1.09498	−0.0811652
$183$	−1.39532	−0.103145
$184$	3.34514	0.246607
$185$	−12.6479	−0.929890
$186$	−8.54866	−0.626818
$187$	9.01999	0.659607
$188$	5.93027	0.432509
$189$	4.33918	0.315629
$190$	1.30158	0.0944264
$191$	20.3329	1.47123	0.735617	−	0.677398i	$-0.236892\pi$
$191$	20.3329	1.47123	0.735617	+	0.677398i	$0.236892\pi$
$192$	−0.823102	−0.0594023
$193$	−16.9746	−1.22186	−0.610931	−	0.791684i	$-0.709205\pi$
$193$	−16.9746	−1.22186	−0.610931	+	0.791684i	$0.709205\pi$
$194$	4.59458	0.329871
$195$	1.18438	0.0848152
$196$	−6.01898	−0.429927
$197$	11.9042	0.848138	0.424069	−	0.905630i	$-0.360601\pi$
$197$	11.9042	0.848138	0.424069	+	0.905630i	$0.360601\pi$
$198$	−5.70098	−0.405151
$199$	11.3615	0.805395	0.402697	−	0.915333i	$-0.368073\pi$
$199$	11.3615	0.805395	0.402697	+	0.915333i	$0.368073\pi$
$200$	−3.30590	−0.233762
$201$	−2.68164	−0.189149
$202$	17.6299	1.24044
$203$	7.53976	0.529188
$204$	−3.02459	−0.211764
$205$	6.87243	0.479991
$206$	0.995805	0.0693810
$207$	−7.76909	−0.539989
$208$	−1.10552	−0.0766541
$209$	2.45467	0.169793
$210$	−1.06111	−0.0732238
$211$	1.00000	0.0688428
$211$	1.00000	0.0688428
$212$	−9.49673	−0.652238
$213$	9.15473	0.627272
$214$	−1.05357	−0.0720206
$215$	−12.7415	−0.868963
$216$	4.38096	0.298087
$217$	10.2869	0.698317
$218$	2.49532	0.169005
$219$	0.624822	0.0422215
$220$	3.19495	0.215403
$221$	−4.06237	−0.273265
$222$	7.99836	0.536815
$223$	2.00991	0.134594	0.0672968	−	0.997733i	$-0.478563\pi$
$223$	2.00991	0.134594	0.0672968	+	0.997733i	$0.478563\pi$
$224$	0.990463	0.0661781
$225$	7.67795	0.511864
$226$	11.6593	0.775564
$227$	−17.3215	−1.14967	−0.574833	−	0.818271i	$-0.694933\pi$
$227$	−17.3215	−1.14967	−0.574833	+	0.818271i	$0.694933\pi$
$228$	−0.823102	−0.0545112
$229$	−19.6320	−1.29732	−0.648659	−	0.761079i	$-0.724670\pi$
$229$	−19.6320	−1.29732	−0.648659	+	0.761079i	$0.724670\pi$
$230$	4.35396	0.287091
$231$	−2.00118	−0.131668
$232$	7.61236	0.499776
$233$	−2.25864	−0.147969	−0.0739844	−	0.997259i	$-0.523571\pi$
$233$	−2.25864	−0.147969	−0.0739844	+	0.997259i	$0.523571\pi$
$234$	2.56758	0.167848
$235$	7.71871	0.503513
$236$	1.08798	0.0708214
$237$	1.95030	0.126686
$238$	3.63958	0.235919
$239$	−14.1710	−0.916647	−0.458323	−	0.888786i	$-0.651550\pi$
$239$	−14.1710	−0.916647	−0.458323	+	0.888786i	$0.651550\pi$
$240$	−1.07133	−0.0691541
$241$	−5.20525	−0.335300	−0.167650	−	0.985847i	$-0.553618\pi$
$241$	−5.20525	−0.335300	−0.167650	+	0.985847i	$0.553618\pi$
$242$	−4.97459	−0.319778
$243$	−15.9098	−1.02061
$244$	1.69520	0.108524
$245$	−7.83417	−0.500507
$246$	−4.34604	−0.277093
$247$	−1.10552	−0.0703426
$248$	10.3859	0.659506
$249$	−12.0935	−0.766392
$250$	−10.8108	−0.683733
$251$	−16.0634	−1.01391	−0.506956	−	0.861972i	$-0.669229\pi$
$251$	−16.0634	−1.01391	−0.506956	+	0.861972i	$0.669229\pi$
$252$	−2.30035	−0.144909
$253$	8.21122	0.516235
$254$	−2.36180	−0.148192
$255$	−3.93674	−0.246528
$256$	1.00000	0.0625000
$257$	22.8553	1.42567	0.712837	−	0.701329i	$-0.247410\pi$
$257$	22.8553	1.42567	0.712837	+	0.701329i	$0.247410\pi$
$258$	8.05757	0.501642
$259$	−9.62467	−0.598048
$260$	−1.43892	−0.0892382
$261$	−17.6797	−1.09435
$262$	19.7744	1.22166
$263$	27.4556	1.69298	0.846492	−	0.532402i	$-0.178710\pi$
$263$	27.4556	1.69298	0.846492	+	0.532402i	$0.178710\pi$
$264$	−2.02044	−0.124350
$265$	−12.3607	−0.759314
$266$	0.990463	0.0607292
$267$	2.46380	0.150782
$268$	3.25797	0.199012
$269$	28.4626	1.73539	0.867697	−	0.497093i	$-0.165599\pi$
$269$	28.4626	1.73539	0.867697	+	0.497093i	$0.165599\pi$
$270$	5.70216	0.347023
$271$	−23.9987	−1.45781	−0.728907	−	0.684613i	$-0.759971\pi$
$271$	−23.9987	−1.45781	−0.728907	+	0.684613i	$0.759971\pi$
$272$	3.67462	0.222807
$273$	0.901279	0.0545479
$274$	11.6676	0.704865
$275$	−8.11489	−0.489346
$276$	−2.75339	−0.165735
$277$	−12.7451	−0.765777	−0.382889	−	0.923795i	$-0.625071\pi$
$277$	−12.7451	−0.765777	−0.382889	+	0.923795i	$0.625071\pi$
$278$	1.55905	0.0935054
$279$	−24.1213	−1.44410
$280$	1.28916	0.0770423
$281$	6.98507	0.416694	0.208347	−	0.978055i	$-0.433192\pi$
$281$	6.98507	0.416694	0.208347	+	0.978055i	$0.433192\pi$
$282$	−4.88122	−0.290672
$283$	−9.04760	−0.537824	−0.268912	−	0.963165i	$-0.586664\pi$
$283$	−9.04760	−0.537824	−0.268912	+	0.963165i	$0.586664\pi$
$284$	−11.1222	−0.659983
$285$	−1.07133	−0.0634602
$286$	−2.71369	−0.160464
$287$	5.22972	0.308701
$288$	−2.32250	−0.136855
$289$	−3.49715	−0.205715
$290$	9.90808	0.581822
$291$	−3.78181	−0.221693
$292$	−0.759106	−0.0444233
$293$	8.00190	0.467476	0.233738	−	0.972300i	$-0.424904\pi$
$293$	8.00190	0.467476	0.233738	+	0.972300i	$0.424904\pi$
$294$	4.95424	0.288937
$295$	1.41609	0.0824479
$296$	−9.71734	−0.564809
$297$	10.7538	0.624000
$298$	−17.2533	−0.999457
$299$	−3.69812	−0.213868
$300$	2.72109	0.157102
$301$	−9.69591	−0.558863
$302$	−23.5957	−1.35778
$303$	−14.5112	−0.833648
$304$	1.00000	0.0573539
$305$	2.20643	0.126340
$306$	−8.53432	−0.487875
$307$	−18.7802	−1.07184	−0.535921	−	0.844268i	$-0.680035\pi$
$307$	−18.7802	−1.07184	−0.535921	+	0.844268i	$0.680035\pi$
$308$	2.43126	0.138534
$309$	−0.819649	−0.0466282
$310$	13.5181	0.767774
$311$	32.2570	1.82912	0.914562	−	0.404446i	$-0.132535\pi$
$311$	32.2570	1.82912	0.914562	+	0.404446i	$0.132535\pi$
$312$	0.909957	0.0515162
$313$	−12.8346	−0.725453	−0.362727	−	0.931896i	$-0.618154\pi$
$313$	−12.8346	−0.725453	−0.362727	+	0.931896i	$0.618154\pi$
$314$	14.3219	0.808234
$315$	−2.99409	−0.168698
$316$	−2.36945	−0.133292
$317$	−20.2583	−1.13782	−0.568910	−	0.822400i	$-0.692635\pi$
$317$	−20.2583	−1.13782	−0.568910	+	0.822400i	$0.692635\pi$
$318$	7.81677	0.438343
$319$	18.6858	1.04621
$320$	1.30158	0.0727604
$321$	0.867196	0.0484021
$322$	3.31324	0.184639
$323$	3.67462	0.204461
$324$	3.36153	0.186752
$325$	3.65474	0.202728
$326$	22.0877	1.22333
$327$	−2.05391	−0.113581
$328$	5.28007	0.291543
$329$	5.87371	0.323828
$330$	−2.62977	−0.144764
$331$	0.634126	0.0348547	0.0174274	−	0.999848i	$-0.494452\pi$
$331$	0.634126	0.0348547	0.0174274	+	0.999848i	$0.494452\pi$
$332$	14.6925	0.806358
$333$	22.5686	1.23675
$334$	22.1856	1.21394
$335$	4.24051	0.231684
$336$	−0.815252	−0.0444756
$337$	29.2498	1.59334	0.796670	−	0.604414i	$-0.206593\pi$
$337$	29.2498	1.59334	0.796670	+	0.604414i	$0.206593\pi$
$338$	−11.7778	−0.640629
$339$	−9.59678	−0.521225
$340$	4.78281	0.259384
$341$	25.4940	1.38058
$342$	−2.32250	−0.125587
$343$	−12.8948	−0.696255
$344$	−9.78927	−0.527802
$345$	−3.58375	−0.192943
$346$	3.25953	0.175233
$347$	22.2271	1.19321	0.596607	−	0.802534i	$-0.296515\pi$
$347$	22.2271	1.19321	0.596607	+	0.802534i	$0.296515\pi$
$348$	−6.26575	−0.335879
$349$	17.7781	0.951639	0.475820	−	0.879543i	$-0.342151\pi$
$349$	17.7781	0.951639	0.475820	+	0.879543i	$0.342151\pi$
$350$	−3.27437	−0.175022
$351$	−4.84325	−0.258513
$352$	2.45467	0.130834
$353$	−15.5345	−0.826817	−0.413409	−	0.910546i	$-0.635662\pi$
$353$	−15.5345	−0.826817	−0.413409	+	0.910546i	$0.635662\pi$
$354$	−0.895517	−0.0475962
$355$	−14.4765	−0.768331
$356$	−2.99331	−0.158645
$357$	−2.99574	−0.158552
$358$	5.84560	0.308949
$359$	−32.3574	−1.70776	−0.853880	−	0.520470i	$-0.825757\pi$
$359$	−32.3574	−1.70776	−0.853880	+	0.520470i	$0.825757\pi$
$360$	−3.02292	−0.159322
$361$	1.00000	0.0526316
$362$	9.62521	0.505890
$363$	4.09459	0.214910
$364$	−1.09498	−0.0573925
$365$	−0.988036	−0.0517162
$366$	−1.39532	−0.0729346
$367$	8.87086	0.463055	0.231528	−	0.972828i	$-0.425628\pi$
$367$	8.87086	0.463055	0.231528	+	0.972828i	$0.425628\pi$
$368$	3.34514	0.174377
$369$	−12.2630	−0.638386
$370$	−12.6479	−0.657532
$371$	−9.40616	−0.488344
$372$	−8.54866	−0.443227
$373$	19.4261	1.00584	0.502922	−	0.864332i	$-0.332258\pi$
$373$	19.4261	1.00584	0.502922	+	0.864332i	$0.332258\pi$
$374$	9.01999	0.466413
$375$	8.89836	0.459510
$376$	5.93027	0.305830
$377$	−8.41563	−0.433427
$378$	4.33918	0.223183
$379$	−15.2291	−0.782267	−0.391134	−	0.920334i	$-0.627917\pi$
$379$	−15.2291	−0.782267	−0.391134	+	0.920334i	$0.627917\pi$
$380$	1.30158	0.0667695
$381$	1.94400	0.0995940
$382$	20.3329	1.04032
$383$	1.77884	0.0908947	0.0454473	−	0.998967i	$-0.485529\pi$
$383$	1.77884	0.0908947	0.0454473	+	0.998967i	$0.485529\pi$
$384$	−0.823102	−0.0420037
$385$	3.16448	0.161277
$386$	−16.9746	−0.863986
$387$	22.7356	1.15572
$388$	4.59458	0.233254
$389$	28.3218	1.43597	0.717985	−	0.696058i	$-0.245064\pi$
$389$	28.3218	1.43597	0.717985	+	0.696058i	$0.245064\pi$
$390$	1.18438	0.0599734
$391$	12.2921	0.621639
$392$	−6.01898	−0.304005
$393$	−16.2763	−0.821031
$394$	11.9042	0.599724
$395$	−3.08403	−0.155174
$396$	−5.70098	−0.286485
$397$	−5.42842	−0.272445	−0.136222	−	0.990678i	$-0.543496\pi$
$397$	−5.42842	−0.272445	−0.136222	+	0.990678i	$0.543496\pi$
$398$	11.3615	0.569500
$399$	−0.815252	−0.0408136
$400$	−3.30590	−0.165295
$401$	21.2579	1.06157	0.530785	−	0.847506i	$-0.321897\pi$
$401$	21.2579	1.06157	0.530785	+	0.847506i	$0.321897\pi$
$402$	−2.68164	−0.133748
$403$	−11.4818	−0.571951
$404$	17.6299	0.877122
$405$	4.37530	0.217410
$406$	7.53976	0.374192
$407$	−23.8529	−1.18234
$408$	−3.02459	−0.149739
$409$	12.6817	0.627070	0.313535	−	0.949577i	$-0.398487\pi$
$409$	12.6817	0.627070	0.313535	+	0.949577i	$0.398487\pi$
$410$	6.87243	0.339405
$411$	−9.60362	−0.473712
$412$	0.995805	0.0490598
$413$	1.07760	0.0530254
$414$	−7.76909	−0.381830
$415$	19.1235	0.938735
$416$	−1.10552	−0.0542026
$417$	−1.28325	−0.0628412
$418$	2.45467	0.120062
$419$	−9.72388	−0.475043	−0.237521	−	0.971382i	$-0.576335\pi$
$419$	−9.72388	−0.475043	−0.237521	+	0.971382i	$0.576335\pi$
$420$	−1.06111	−0.0517771
$421$	8.21672	0.400458	0.200229	−	0.979749i	$-0.435831\pi$
$421$	8.21672	0.400458	0.200229	+	0.979749i	$0.435831\pi$
$422$	1.00000	0.0486792
$423$	−13.7731	−0.669670
$424$	−9.49673	−0.461202
$425$	−12.1479	−0.589260
$426$	9.15473	0.443548
$427$	1.67903	0.0812541
$428$	−1.05357	−0.0509263
$429$	2.23364	0.107841
$430$	−12.7415	−0.614450
$431$	1.14589	0.0551957	0.0275978	−	0.999619i	$-0.491214\pi$
$431$	1.14589	0.0551957	0.0275978	+	0.999619i	$0.491214\pi$
$432$	4.38096	0.210779
$433$	38.8787	1.86839	0.934196	−	0.356761i	$-0.116119\pi$
$433$	38.8787	1.86839	0.934196	+	0.356761i	$0.116119\pi$
$434$	10.2869	0.493785
$435$	−8.15536	−0.391019
$436$	2.49532	0.119504
$437$	3.34514	0.160020
$438$	0.624822	0.0298551
$439$	−17.0705	−0.814730	−0.407365	−	0.913265i	$-0.633552\pi$
$439$	−17.0705	−0.814730	−0.407365	+	0.913265i	$0.633552\pi$
$440$	3.19495	0.152313
$441$	13.9791	0.665672
$442$	−4.06237	−0.193227
$443$	−5.09960	−0.242289	−0.121145	−	0.992635i	$-0.538656\pi$
$443$	−5.09960	−0.242289	−0.121145	+	0.992635i	$0.538656\pi$
$444$	7.99836	0.379585
$445$	−3.89602	−0.184689
$446$	2.00991	0.0951720
$447$	14.2012	0.671695
$448$	0.990463	0.0467950
$449$	−30.0034	−1.41595	−0.707973	−	0.706239i	$-0.750390\pi$
$449$	−30.0034	−1.41595	−0.707973	+	0.706239i	$0.750390\pi$
$450$	7.67795	0.361942
$451$	12.9609	0.610303
$452$	11.6593	0.548407
$453$	19.4216	0.912507
$454$	−17.3215	−0.812936
$455$	−1.42520	−0.0668144
$456$	−0.823102	−0.0385453
$457$	−0.703292	−0.0328986	−0.0164493	−	0.999865i	$-0.505236\pi$
$457$	−0.703292	−0.0328986	−0.0164493	+	0.999865i	$0.505236\pi$
$458$	−19.6320	−0.917342
$459$	16.0984	0.751408
$460$	4.35396	0.203004
$461$	28.1362	1.31043	0.655216	−	0.755442i	$-0.272578\pi$
$461$	28.1362	1.31043	0.655216	+	0.755442i	$0.272578\pi$
$462$	−2.00118	−0.0931031
$463$	−0.502800	−0.0233671	−0.0116835	−	0.999932i	$-0.503719\pi$
$463$	−0.502800	−0.0233671	−0.0116835	+	0.999932i	$0.503719\pi$
$464$	7.61236	0.353395
$465$	−11.1267	−0.515990
$466$	−2.25864	−0.104630
$467$	7.69508	0.356086	0.178043	−	0.984023i	$-0.443023\pi$
$467$	7.69508	0.356086	0.178043	+	0.984023i	$0.443023\pi$
$468$	2.56758	0.118686
$469$	3.22690	0.149005
$470$	7.71871	0.356037
$471$	−11.7884	−0.543182
$472$	1.08798	0.0500783
$473$	−24.0294	−1.10488
$474$	1.95030	0.0895803
$475$	−3.30590	−0.151685
$476$	3.63958	0.166820
$477$	22.0562	1.00988
$478$	−14.1710	−0.648167
$479$	−31.8086	−1.45337	−0.726686	−	0.686969i	$-0.758941\pi$
$479$	−31.8086	−1.45337	−0.726686	+	0.686969i	$0.758941\pi$
$480$	−1.07133	−0.0488993
$481$	10.7427	0.489826
$482$	−5.20525	−0.237093
$483$	−2.72713	−0.124089
$484$	−4.97459	−0.226118
$485$	5.98020	0.271547
$486$	−15.9098	−0.721682
$487$	−12.9825	−0.588292	−0.294146	−	0.955760i	$-0.595035\pi$
$487$	−12.9825	−0.588292	−0.294146	+	0.955760i	$0.595035\pi$
$488$	1.69520	0.0767381
$489$	−18.1804	−0.822148
$490$	−7.83417	−0.353912
$491$	−1.04813	−0.0473015	−0.0236508	−	0.999720i	$-0.507529\pi$
$491$	−1.04813	−0.0473015	−0.0236508	+	0.999720i	$0.507529\pi$
$492$	−4.34604	−0.195935
$493$	27.9725	1.25982
$494$	−1.10552	−0.0497398
$495$	−7.42027	−0.333517
$496$	10.3859	0.466341
$497$	−11.0162	−0.494143
$498$	−12.0935	−0.541921
$499$	20.5024	0.917813	0.458907	−	0.888485i	$-0.348241\pi$
$499$	20.5024	0.917813	0.458907	+	0.888485i	$0.348241\pi$
$500$	−10.8108	−0.483472
$501$	−18.2610	−0.815841
$502$	−16.0634	−0.716945
$503$	9.23472	0.411756	0.205878	−	0.978578i	$-0.433995\pi$
$503$	9.23472	0.411756	0.205878	+	0.978578i	$0.433995\pi$
$504$	−2.30035	−0.102466
$505$	22.9467	1.02112
$506$	8.21122	0.365033
$507$	9.69435	0.430541
$508$	−2.36180	−0.104788
$509$	−3.85875	−0.171036	−0.0855181	−	0.996337i	$-0.527255\pi$
$509$	−3.85875	−0.171036	−0.0855181	+	0.996337i	$0.527255\pi$
$510$	−3.93674	−0.174322
$511$	−0.751867	−0.0332606
$512$	1.00000	0.0441942
$513$	4.38096	0.193424
$514$	22.8553	1.00810
$515$	1.29612	0.0571138
$516$	8.05757	0.354715
$517$	14.5569	0.640210
$518$	−9.62467	−0.422884
$519$	−2.68293	−0.117767
$520$	−1.43892	−0.0631009
$521$	−21.2678	−0.931757	−0.465879	−	0.884849i	$-0.654262\pi$
$521$	−21.2678	−0.931757	−0.465879	+	0.884849i	$0.654262\pi$
$522$	−17.6797	−0.773821
$523$	28.3532	1.23980	0.619901	−	0.784680i	$-0.287173\pi$
$523$	28.3532	1.23980	0.619901	+	0.784680i	$0.287173\pi$
$524$	19.7744	0.863847
$525$	2.69514	0.117625
$526$	27.4556	1.19712
$527$	38.1643	1.66246
$528$	−2.02044	−0.0879286
$529$	−11.8101	−0.513481
$530$	−12.3607	−0.536916
$531$	−2.52683	−0.109655
$532$	0.990463	0.0429420
$533$	−5.83724	−0.252839
$534$	2.46380	0.106619
$535$	−1.37130	−0.0592866
$536$	3.25797	0.140723
$537$	−4.81152	−0.207633
$538$	28.4626	1.22711
$539$	−14.7746	−0.636388
$540$	5.70216	0.245382
$541$	−12.4631	−0.535829	−0.267915	−	0.963443i	$-0.586335\pi$
$541$	−12.4631	−0.535829	−0.267915	+	0.963443i	$0.586335\pi$
$542$	−23.9987	−1.03083
$543$	−7.92253	−0.339988
$544$	3.67462	0.157548
$545$	3.24786	0.139123
$546$	0.901279	0.0385712
$547$	15.6395	0.668696	0.334348	−	0.942450i	$-0.391484\pi$
$547$	15.6395	0.668696	0.334348	+	0.942450i	$0.391484\pi$
$548$	11.6676	0.498415
$549$	−3.93711	−0.168032
$550$	−8.11489	−0.346020
$551$	7.61236	0.324297
$552$	−2.75339	−0.117192
$553$	−2.34686	−0.0997985
$554$	−12.7451	−0.541486
$555$	10.4105	0.441901
$556$	1.55905	0.0661183
$557$	−19.5744	−0.829396	−0.414698	−	0.909959i	$-0.636113\pi$
$557$	−19.5744	−0.829396	−0.414698	+	0.909959i	$0.636113\pi$
$558$	−24.1213	−1.02114
$559$	10.8222	0.457732
$560$	1.28916	0.0544772
$561$	−7.42437	−0.313457
$562$	6.98507	0.294647
$563$	−37.7246	−1.58990	−0.794950	−	0.606675i	$-0.792503\pi$
$563$	−37.7246	−1.58990	−0.794950	+	0.606675i	$0.792503\pi$
$564$	−4.88122	−0.205536
$565$	15.1755	0.638437
$566$	−9.04760	−0.380299
$567$	3.32947	0.139825
$568$	−11.1222	−0.466679
$569$	−16.0056	−0.670991	−0.335495	−	0.942042i	$-0.608904\pi$
$569$	−16.0056	−0.670991	−0.335495	+	0.942042i	$0.608904\pi$
$570$	−1.07133	−0.0448731
$571$	−8.76030	−0.366607	−0.183304	−	0.983056i	$-0.558679\pi$
$571$	−8.76030	−0.366607	−0.183304	+	0.983056i	$0.558679\pi$
$572$	−2.71369	−0.113465
$573$	−16.7360	−0.699157
$574$	5.22972	0.218284
$575$	−11.0587	−0.461179
$576$	−2.32250	−0.0967710
$577$	−6.27247	−0.261126	−0.130563	−	0.991440i	$-0.541679\pi$
$577$	−6.27247	−0.261126	−0.130563	+	0.991440i	$0.541679\pi$
$578$	−3.49715	−0.145462
$579$	13.9719	0.580650
$580$	9.90808	0.411411
$581$	14.5524	0.603736
$582$	−3.78181	−0.156761
$583$	−23.3114	−0.965458
$584$	−0.759106	−0.0314120
$585$	3.34190	0.138171
$586$	8.00190	0.330555
$587$	39.5709	1.63327	0.816634	−	0.577157i	$-0.195838\pi$
$587$	39.5709	1.63327	0.816634	+	0.577157i	$0.195838\pi$
$588$	4.95424	0.204309
$589$	10.3859	0.427944
$590$	1.41609	0.0582994
$591$	−9.79835	−0.403050
$592$	−9.71734	−0.399380
$593$	−16.0131	−0.657580	−0.328790	−	0.944403i	$-0.606641\pi$
$593$	−16.0131	−0.657580	−0.328790	+	0.944403i	$0.606641\pi$
$594$	10.7538	0.441235
$595$	4.73719	0.194206
$596$	−17.2533	−0.706723
$597$	−9.35166	−0.382738
$598$	−3.69812	−0.151227
$599$	36.3399	1.48481	0.742404	−	0.669953i	$-0.233686\pi$
$599$	36.3399	1.48481	0.742404	+	0.669953i	$0.233686\pi$
$600$	2.72109	0.111088
$601$	−48.4907	−1.97798	−0.988988	−	0.147997i	$-0.952717\pi$
$601$	−48.4907	−1.97798	−0.988988	+	0.147997i	$0.952717\pi$
$602$	−9.69591	−0.395176
$603$	−7.56666	−0.308138
$604$	−23.5957	−0.960093
$605$	−6.47481	−0.263238
$606$	−14.5112	−0.589478
$607$	0.933385	0.0378849	0.0189425	−	0.999821i	$-0.493970\pi$
$607$	0.933385	0.0378849	0.0189425	+	0.999821i	$0.493970\pi$
$608$	1.00000	0.0405554
$609$	−6.20599	−0.251479
$610$	2.20643	0.0893359
$611$	−6.55604	−0.265229
$612$	−8.53432	−0.344980
$613$	−8.79606	−0.355270	−0.177635	−	0.984096i	$-0.556845\pi$
$613$	−8.79606	−0.355270	−0.177635	+	0.984096i	$0.556845\pi$
$614$	−18.7802	−0.757906
$615$	−5.65671	−0.228100
$616$	2.43126	0.0979583
$617$	40.7482	1.64046	0.820230	−	0.572034i	$-0.193846\pi$
$617$	40.7482	1.64046	0.820230	+	0.572034i	$0.193846\pi$
$618$	−0.819649	−0.0329711
$619$	−36.1498	−1.45298	−0.726492	−	0.687175i	$-0.758851\pi$
$619$	−36.1498	−1.45298	−0.726492	+	0.687175i	$0.758851\pi$
$620$	13.5181	0.542899
$621$	14.6549	0.588082
$622$	32.2570	1.29339
$623$	−2.96476	−0.118781
$624$	0.909957	0.0364274
$625$	2.45842	0.0983367
$626$	−12.8346	−0.512973
$627$	−2.02044	−0.0806888
$628$	14.3219	0.571508
$629$	−35.7076	−1.42375
$630$	−2.99409	−0.119287
$631$	−20.9995	−0.835978	−0.417989	−	0.908452i	$-0.637265\pi$
$631$	−20.9995	−0.835978	−0.417989	+	0.908452i	$0.637265\pi$
$632$	−2.36945	−0.0942518
$633$	−0.823102	−0.0327154
$634$	−20.2583	−0.804560
$635$	−3.07406	−0.121990
$636$	7.81677	0.309955
$637$	6.65411	0.263646
$638$	18.6858	0.739780
$639$	25.8314	1.02188
$640$	1.30158	0.0514494
$641$	−15.3925	−0.607969	−0.303985	−	0.952677i	$-0.598317\pi$
$641$	−15.3925	−0.607969	−0.303985	+	0.952677i	$0.598317\pi$
$642$	0.867196	0.0342255
$643$	−11.1360	−0.439160	−0.219580	−	0.975594i	$-0.570469\pi$
$643$	−11.1360	−0.439160	−0.219580	+	0.975594i	$0.570469\pi$
$644$	3.31324	0.130560
$645$	10.4875	0.412947
$646$	3.67462	0.144576
$647$	−20.6066	−0.810129	−0.405064	−	0.914288i	$-0.632751\pi$
$647$	−20.6066	−0.810129	−0.405064	+	0.914288i	$0.632751\pi$
$648$	3.36153	0.132053
$649$	2.67063	0.104831
$650$	3.65474	0.143351
$651$	−8.46713	−0.331853
$652$	22.0877	0.865022
$653$	−3.45733	−0.135296	−0.0676479	−	0.997709i	$-0.521549\pi$
$653$	−3.45733	−0.135296	−0.0676479	+	0.997709i	$0.521549\pi$
$654$	−2.05391	−0.0803141
$655$	25.7379	1.00566
$656$	5.28007	0.206152
$657$	1.76303	0.0687822
$658$	5.87371	0.228981
$659$	24.2797	0.945802	0.472901	−	0.881116i	$-0.343207\pi$
$659$	24.2797	0.945802	0.472901	+	0.881116i	$0.343207\pi$
$660$	−2.62977	−0.102364
$661$	38.7833	1.50849	0.754247	−	0.656591i	$-0.228002\pi$
$661$	38.7833	1.50849	0.754247	+	0.656591i	$0.228002\pi$
$662$	0.634126	0.0246460
$663$	3.34375	0.129860
$664$	14.6925	0.570181
$665$	1.28916	0.0499917
$666$	22.5686	0.874514
$667$	25.4644	0.985985
$668$	22.1856	0.858386
$669$	−1.65436	−0.0639613
$670$	4.24051	0.163825
$671$	4.16116	0.160640
$672$	−0.815252	−0.0314490
$673$	23.9539	0.923354	0.461677	−	0.887048i	$-0.347248\pi$
$673$	23.9539	0.923354	0.461677	+	0.887048i	$0.347248\pi$
$674$	29.2498	1.12666
$675$	−14.4830	−0.557451
$676$	−11.7778	−0.452993
$677$	1.75186	0.0673295	0.0336647	−	0.999433i	$-0.489282\pi$
$677$	1.75186	0.0673295	0.0336647	+	0.999433i	$0.489282\pi$
$678$	−9.59678	−0.368562
$679$	4.55076	0.174642
$680$	4.78281	0.183412
$681$	14.2573	0.546342
$682$	25.4940	0.976215
$683$	−18.7191	−0.716267	−0.358134	−	0.933670i	$-0.616587\pi$
$683$	−18.7191	−0.716267	−0.358134	+	0.933670i	$0.616587\pi$
$684$	−2.32250	−0.0888031
$685$	15.1863	0.580238
$686$	−12.8948	−0.492327
$687$	16.1591	0.616509
$688$	−9.78927	−0.373212
$689$	10.4988	0.399974
$690$	−3.58375	−0.136431
$691$	−18.5817	−0.706880	−0.353440	−	0.935457i	$-0.614988\pi$
$691$	−18.5817	−0.706880	−0.353440	+	0.935457i	$0.614988\pi$
$692$	3.25953	0.123909
$693$	−5.64661	−0.214497
$694$	22.2271	0.843729
$695$	2.02922	0.0769727
$696$	−6.26575	−0.237503
$697$	19.4023	0.734914
$698$	17.7781	0.672911
$699$	1.85909	0.0703174
$700$	−3.27437	−0.123759
$701$	16.8886	0.637872	0.318936	−	0.947776i	$-0.396674\pi$
$701$	16.8886	0.637872	0.318936	+	0.947776i	$0.396674\pi$
$702$	−4.84325	−0.182797
$703$	−9.71734	−0.366496
$704$	2.45467	0.0925139
$705$	−6.35328	−0.239278
$706$	−15.5345	−0.584648
$707$	17.4618	0.656718
$708$	−0.895517	−0.0336556
$709$	−18.0512	−0.677928	−0.338964	−	0.940799i	$-0.610077\pi$
$709$	−18.0512	−0.677928	−0.338964	+	0.940799i	$0.610077\pi$
$710$	−14.4765	−0.543292
$711$	5.50307	0.206381
$712$	−2.99331	−0.112179
$713$	34.7423	1.30111
$714$	−2.99574	−0.112113
$715$	−3.53208	−0.132092
$716$	5.84560	0.218460
$717$	11.6642	0.435607
$718$	−32.3574	−1.20757
$719$	23.8745	0.890368	0.445184	−	0.895439i	$-0.353138\pi$
$719$	23.8745	0.890368	0.445184	+	0.895439i	$0.353138\pi$
$720$	−3.02292	−0.112658
$721$	0.986308	0.0367320
$722$	1.00000	0.0372161
$723$	4.28445	0.159340
$724$	9.62521	0.357718
$725$	−25.1657	−0.934629
$726$	4.09459	0.151965
$727$	−18.0715	−0.670233	−0.335117	−	0.942177i	$-0.608776\pi$
$727$	−18.0715	−0.670233	−0.335117	+	0.942177i	$0.608776\pi$
$728$	−1.09498	−0.0405826
$729$	3.01076	0.111510
$730$	−0.988036	−0.0365688
$731$	−35.9719	−1.33047
$732$	−1.39532	−0.0515726
$733$	−20.0152	−0.739277	−0.369638	−	0.929176i	$-0.620518\pi$
$733$	−20.0152	−0.739277	−0.369638	+	0.929176i	$0.620518\pi$
$734$	8.87086	0.327430
$735$	6.44832	0.237850
$736$	3.34514	0.123303
$737$	7.99726	0.294583
$738$	−12.2630	−0.451407
$739$	−14.0861	−0.518165	−0.259082	−	0.965855i	$-0.583420\pi$
$739$	−14.0861	−0.518165	−0.259082	+	0.965855i	$0.583420\pi$
$740$	−12.6479	−0.464945
$741$	0.909957	0.0334281
$742$	−9.40616	−0.345311
$743$	30.8652	1.13234	0.566168	−	0.824290i	$-0.308425\pi$
$743$	30.8652	1.13234	0.566168	+	0.824290i	$0.308425\pi$
$744$	−8.54866	−0.313409
$745$	−22.4565	−0.822743
$746$	19.4261	0.711238
$747$	−34.1235	−1.24851
$748$	9.01999	0.329804
$749$	−1.04352	−0.0381295
$750$	8.89836	0.324922
$751$	−45.4430	−1.65824	−0.829120	−	0.559071i	$-0.811158\pi$
$751$	−45.4430	−1.65824	−0.829120	+	0.559071i	$0.811158\pi$
$752$	5.93027	0.216255
$753$	13.2218	0.481830
$754$	−8.41563	−0.306479
$755$	−30.7116	−1.11771
$756$	4.33918	0.157815
$757$	14.2040	0.516253	0.258127	−	0.966111i	$-0.416895\pi$
$757$	14.2040	0.516253	0.258127	+	0.966111i	$0.416895\pi$
$758$	−15.2291	−0.553146
$759$	−6.75867	−0.245324
$760$	1.30158	0.0472132
$761$	19.5288	0.707919	0.353960	−	0.935261i	$-0.384835\pi$
$761$	19.5288	0.707919	0.353960	+	0.935261i	$0.384835\pi$
$762$	1.94400	0.0704236
$763$	2.47153	0.0894753
$764$	20.3329	0.735617
$765$	−11.1081	−0.401614
$766$	1.77884	0.0642722
$767$	−1.20278	−0.0434300
$768$	−0.823102	−0.0297011
$769$	−11.9381	−0.430501	−0.215250	−	0.976559i	$-0.569057\pi$
$769$	−11.9381	−0.430501	−0.215250	+	0.976559i	$0.569057\pi$
$770$	3.16448	0.114040
$771$	−18.8122	−0.677506
$772$	−16.9746	−0.610931
$773$	−14.5860	−0.524621	−0.262310	−	0.964984i	$-0.584484\pi$
$773$	−14.5860	−0.524621	−0.262310	+	0.964984i	$0.584484\pi$
$774$	22.7356	0.817215
$775$	−34.3347	−1.23334
$776$	4.59458	0.164936
$777$	7.92208	0.284203
$778$	28.3218	1.01538
$779$	5.28007	0.189178
$780$	1.18438	0.0424076
$781$	−27.3014	−0.976922
$782$	12.2921	0.439565
$783$	33.3495	1.19181
$784$	−6.01898	−0.214964
$785$	18.6411	0.665330
$786$	−16.2763	−0.580557
$787$	−0.209749	−0.00747675	−0.00373838	−	0.999993i	$-0.501190\pi$
$787$	−0.209749	−0.00747675	−0.00373838	+	0.999993i	$0.501190\pi$
$788$	11.9042	0.424069
$789$	−22.5987	−0.804536
$790$	−3.08403	−0.109725
$791$	11.5481	0.410603
$792$	−5.70098	−0.202576
$793$	−1.87408	−0.0665505
$794$	−5.42842	−0.192648
$795$	10.1741	0.360840
$796$	11.3615	0.402697
$797$	−29.9325	−1.06026	−0.530132	−	0.847915i	$-0.677858\pi$
$797$	−29.9325	−1.06026	−0.530132	+	0.847915i	$0.677858\pi$
$798$	−0.815252	−0.0288596
$799$	21.7915	0.770928
$800$	−3.30590	−0.116881
$801$	6.95197	0.245636
$802$	21.2579	0.750644
$803$	−1.86336	−0.0657564
$804$	−2.68164	−0.0945743
$805$	4.31243	0.151993
$806$	−11.4818	−0.404431
$807$	−23.4276	−0.824691
$808$	17.6299	0.620219
$809$	42.1762	1.48284	0.741418	−	0.671044i	$-0.234154\pi$
$809$	42.1762	1.48284	0.741418	+	0.671044i	$0.234154\pi$
$810$	4.37530	0.153732
$811$	−0.736708	−0.0258693	−0.0129347	−	0.999916i	$-0.504117\pi$
$811$	−0.736708	−0.0258693	−0.0129347	+	0.999916i	$0.504117\pi$
$812$	7.53976	0.264594
$813$	19.7533	0.692780
$814$	−23.8529	−0.836043
$815$	28.7489	1.00703
$816$	−3.02459	−0.105882
$817$	−9.78927	−0.342483
$818$	12.6817	0.443406
$819$	2.54309	0.0888628
$820$	6.87243	0.239996
$821$	53.7569	1.87613	0.938064	−	0.346463i	$-0.112617\pi$
$821$	53.7569	1.87613	0.938064	+	0.346463i	$0.112617\pi$
$822$	−9.60362	−0.334965
$823$	32.4059	1.12960	0.564799	−	0.825229i	$-0.308954\pi$
$823$	32.4059	1.12960	0.564799	+	0.825229i	$0.308954\pi$
$824$	0.995805	0.0346905
$825$	6.67938	0.232546
$826$	1.07760	0.0374946
$827$	−40.9921	−1.42544	−0.712718	−	0.701451i	$-0.752536\pi$
$827$	−40.9921	−1.42544	−0.712718	+	0.701451i	$0.752536\pi$
$828$	−7.76909	−0.269995
$829$	−19.9797	−0.693925	−0.346963	−	0.937879i	$-0.612787\pi$
$829$	−19.9797	−0.693925	−0.346963	+	0.937879i	$0.612787\pi$
$830$	19.1235	0.663786
$831$	10.4905	0.363911
$832$	−1.10552	−0.0383271
$833$	−22.1175	−0.766325
$834$	−1.28325	−0.0444355
$835$	28.8762	0.999304
$836$	2.45467	0.0848966
$837$	45.5003	1.57272
$838$	−9.72388	−0.335906
$839$	−50.8793	−1.75655	−0.878274	−	0.478157i	$-0.841305\pi$
$839$	−50.8793	−1.75655	−0.878274	+	0.478157i	$0.841305\pi$
$840$	−1.06111	−0.0366119
$841$	28.9480	0.998208
$842$	8.21672	0.283167
$843$	−5.74942	−0.198021
$844$	1.00000	0.0344214
$845$	−15.3298	−0.527360
$846$	−13.7731	−0.473528
$847$	−4.92714	−0.169299
$848$	−9.49673	−0.326119
$849$	7.44709	0.255584
$850$	−12.1479	−0.416670
$851$	−32.5058	−1.11429
$852$	9.15473	0.313636
$853$	−8.47192	−0.290073	−0.145037	−	0.989426i	$-0.546330\pi$
$853$	−8.47192	−0.290073	−0.145037	+	0.989426i	$0.546330\pi$
$854$	1.67903	0.0574553
$855$	−3.02292	−0.103382
$856$	−1.05357	−0.0360103
$857$	−38.4107	−1.31208	−0.656042	−	0.754725i	$-0.727771\pi$
$857$	−38.4107	−1.31208	−0.656042	+	0.754725i	$0.727771\pi$
$858$	2.23364	0.0762554
$859$	−39.2963	−1.34077	−0.670386	−	0.742013i	$-0.733871\pi$
$859$	−39.2963	−1.34077	−0.670386	+	0.742013i	$0.733871\pi$
$860$	−12.7415	−0.434481
$861$	−4.30459	−0.146700
$862$	1.14589	0.0390292
$863$	−50.6909	−1.72554	−0.862769	−	0.505598i	$-0.831272\pi$
$863$	−50.6909	−1.72554	−0.862769	+	0.505598i	$0.831272\pi$
$864$	4.38096	0.149043
$865$	4.24253	0.144250
$866$	38.8787	1.32115
$867$	2.87851	0.0977595
$868$	10.2869	0.349159
$869$	−5.81623	−0.197302
$870$	−8.15536	−0.276493
$871$	−3.60176	−0.122041
$872$	2.49532	0.0845023
$873$	−10.6709	−0.361156
$874$	3.34514	0.113151
$875$	−10.7077	−0.361985
$876$	0.624822	0.0211108
$877$	−33.7643	−1.14014	−0.570070	−	0.821596i	$-0.693084\pi$
$877$	−33.7643	−1.14014	−0.570070	+	0.821596i	$0.693084\pi$
$878$	−17.0705	−0.576101
$879$	−6.58638	−0.222153
$880$	3.19495	0.107702
$881$	−31.7337	−1.06914	−0.534568	−	0.845126i	$-0.679526\pi$
$881$	−31.7337	−1.06914	−0.534568	+	0.845126i	$0.679526\pi$
$882$	13.9791	0.470701
$883$	−22.4714	−0.756222	−0.378111	−	0.925760i	$-0.623426\pi$
$883$	−22.4714	−0.756222	−0.378111	+	0.925760i	$0.623426\pi$
$884$	−4.06237	−0.136632
$885$	−1.16558	−0.0391807
$886$	−5.09960	−0.171324
$887$	21.6572	0.727179	0.363589	−	0.931559i	$-0.381551\pi$
$887$	21.6572	0.727179	0.363589	+	0.931559i	$0.381551\pi$
$888$	7.99836	0.268407
$889$	−2.33927	−0.0784566
$890$	−3.89602	−0.130595
$891$	8.25146	0.276434
$892$	2.00991	0.0672968
$893$	5.93027	0.198449
$894$	14.2012	0.474960
$895$	7.60850	0.254324
$896$	0.990463	0.0330891
$897$	3.04393	0.101634
$898$	−30.0034	−1.00123
$899$	79.0613	2.63684
$900$	7.67795	0.255932
$901$	−34.8969	−1.16258
$902$	12.9609	0.431549
$903$	7.98072	0.265582
$904$	11.6593	0.387782
$905$	12.5280	0.416444
$906$	19.4216	0.645240
$907$	−4.41317	−0.146537	−0.0732685	−	0.997312i	$-0.523343\pi$
$907$	−4.41317	−0.146537	−0.0732685	+	0.997312i	$0.523343\pi$
$908$	−17.3215	−0.574833
$909$	−40.9456	−1.35808
$910$	−1.42520	−0.0472449
$911$	3.62749	0.120184	0.0600920	−	0.998193i	$-0.480861\pi$
$911$	3.62749	0.120184	0.0600920	+	0.998193i	$0.480861\pi$
$912$	−0.823102	−0.0272556
$913$	36.0654	1.19359
$914$	−0.703292	−0.0232628
$915$	−1.81612	−0.0600391
$916$	−19.6320	−0.648659
$917$	19.5858	0.646779
$918$	16.0984	0.531326
$919$	−58.4499	−1.92808	−0.964042	−	0.265748i	$-0.914381\pi$
$919$	−58.4499	−1.92808	−0.964042	+	0.265748i	$0.914381\pi$
$920$	4.35396	0.143546
$921$	15.4580	0.509358
$922$	28.1362	0.926615
$923$	12.2959	0.404724
$924$	−2.00118	−0.0658339
$925$	32.1245	1.05625
$926$	−0.502800	−0.0165230
$927$	−2.31276	−0.0759610
$928$	7.61236	0.249888
$929$	−10.7638	−0.353150	−0.176575	−	0.984287i	$-0.556502\pi$
$929$	−10.7638	−0.353150	−0.176575	+	0.984287i	$0.556502\pi$
$930$	−11.1267	−0.364860
$931$	−6.01898	−0.197264
$932$	−2.25864	−0.0739844
$933$	−26.5508	−0.869233
$934$	7.69508	0.251791
$935$	11.7402	0.383946
$936$	2.56758	0.0839239
$937$	6.63233	0.216669	0.108334	−	0.994115i	$-0.465448\pi$
$937$	6.63233	0.216669	0.108334	+	0.994115i	$0.465448\pi$
$938$	3.22690	0.105362
$939$	10.5642	0.344748
$940$	7.71871	0.251756
$941$	18.4225	0.600555	0.300278	−	0.953852i	$-0.402921\pi$
$941$	18.4225	0.600555	0.300278	+	0.953852i	$0.402921\pi$
$942$	−11.7884	−0.384087
$943$	17.6626	0.575173
$944$	1.08798	0.0354107
$945$	5.64778	0.183722
$946$	−24.0294	−0.781265
$947$	−35.5913	−1.15656	−0.578282	−	0.815837i	$-0.696277\pi$
$947$	−35.5913	−1.15656	−0.578282	+	0.815837i	$0.696277\pi$
$948$	1.95030	0.0633429
$949$	0.839208	0.0272418
$950$	−3.30590	−0.107257
$951$	16.6746	0.540712
$952$	3.63958	0.117959
$953$	−2.74352	−0.0888713	−0.0444356	−	0.999012i	$-0.514149\pi$
$953$	−2.74352	−0.0888713	−0.0444356	+	0.999012i	$0.514149\pi$
$954$	22.0562	0.714095
$955$	26.4648	0.856381
$956$	−14.1710	−0.458323
$957$	−15.3804	−0.497176
$958$	−31.8086	−1.02769
$959$	11.5563	0.373173
$960$	−1.07133	−0.0345771
$961$	76.8670	2.47958
$962$	10.7427	0.346359
$963$	2.44692	0.0788509
$964$	−5.20525	−0.167650
$965$	−22.0938	−0.711225
$966$	−2.72713	−0.0877440
$967$	−6.86099	−0.220635	−0.110317	−	0.993896i	$-0.535187\pi$
$967$	−6.86099	−0.220635	−0.110317	+	0.993896i	$0.535187\pi$
$968$	−4.97459	−0.159889
$969$	−3.02459	−0.0971638
$970$	5.98020	0.192013
$971$	−17.4422	−0.559745	−0.279873	−	0.960037i	$-0.590292\pi$
$971$	−17.4422	−0.559745	−0.279873	+	0.960037i	$0.590292\pi$
$972$	−15.9098	−0.510306
$973$	1.54418	0.0495041
$974$	−12.9825	−0.415985
$975$	−3.00822	−0.0963402
$976$	1.69520	0.0542620
$977$	−39.1590	−1.25281	−0.626403	−	0.779499i	$-0.715474\pi$
$977$	−39.1590	−1.25281	−0.626403	+	0.779499i	$0.715474\pi$
$978$	−18.1804	−0.581347
$979$	−7.34759	−0.234830
$980$	−7.83417	−0.250254
$981$	−5.79540	−0.185033
$982$	−1.04813	−0.0334472
$983$	−52.1873	−1.66452	−0.832258	−	0.554389i	$-0.812952\pi$
$983$	−52.1873	−1.66452	−0.832258	+	0.554389i	$0.812952\pi$
$984$	−4.34604	−0.138547
$985$	15.4942	0.493687
$986$	27.9725	0.890827
$987$	−4.83466	−0.153889
$988$	−1.10552	−0.0351713
$989$	−32.7465	−1.04128
$990$	−7.42027	−0.235832
$991$	−8.12260	−0.258023	−0.129011	−	0.991643i	$-0.541180\pi$
$991$	−8.12260	−0.258023	−0.129011	+	0.991643i	$0.541180\pi$
$992$	10.3859	0.329753
$993$	−0.521950	−0.0165636
$994$	−11.0162	−0.349412
$995$	14.7879	0.468807
$996$	−12.0935	−0.383196
$997$	22.0808	0.699307	0.349653	−	0.936879i	$-0.386299\pi$
$997$	22.0808	0.699307	0.349653	+	0.936879i	$0.386299\pi$
$998$	20.5024	0.648992
$999$	−42.5713	−1.34690

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8018.2.a.k.1.17	✓	49

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8018.2.a.k.1.17	✓	49	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:	\( N \)	\(=\)	\( 8018 = 2 \cdot 19 \cdot 211 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8018.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -0.823102 q^{3} +1.00000 q^{4} +1.30158 q^{5} -0.823102 q^{6} +0.990463 q^{7} +1.00000 q^{8} -2.32250 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -0.823102 q^{3} +1.00000 q^{4} +1.30158 q^{5} -0.823102 q^{6} +0.990463 q^{7} +1.00000 q^{8} -2.32250 q^{9} +1.30158 q^{10} +2.45467 q^{11} -0.823102 q^{12} -1.10552 q^{13} +0.990463 q^{14} -1.07133 q^{15} +1.00000 q^{16} +3.67462 q^{17} -2.32250 q^{18} +1.00000 q^{19} +1.30158 q^{20} -0.815252 q^{21} +2.45467 q^{22} +3.34514 q^{23} -0.823102 q^{24} -3.30590 q^{25} -1.10552 q^{26} +4.38096 q^{27} +0.990463 q^{28} +7.61236 q^{29} -1.07133 q^{30} +10.3859 q^{31} +1.00000 q^{32} -2.02044 q^{33} +3.67462 q^{34} +1.28916 q^{35} -2.32250 q^{36} -9.71734 q^{37} +1.00000 q^{38} +0.909957 q^{39} +1.30158 q^{40} +5.28007 q^{41} -0.815252 q^{42} -9.78927 q^{43} +2.45467 q^{44} -3.02292 q^{45} +3.34514 q^{46} +5.93027 q^{47} -0.823102 q^{48} -6.01898 q^{49} -3.30590 q^{50} -3.02459 q^{51} -1.10552 q^{52} -9.49673 q^{53} +4.38096 q^{54} +3.19495 q^{55} +0.990463 q^{56} -0.823102 q^{57} +7.61236 q^{58} +1.08798 q^{59} -1.07133 q^{60} +1.69520 q^{61} +10.3859 q^{62} -2.30035 q^{63} +1.00000 q^{64} -1.43892 q^{65} -2.02044 q^{66} +3.25797 q^{67} +3.67462 q^{68} -2.75339 q^{69} +1.28916 q^{70} -11.1222 q^{71} -2.32250 q^{72} -0.759106 q^{73} -9.71734 q^{74} +2.72109 q^{75} +1.00000 q^{76} +2.43126 q^{77} +0.909957 q^{78} -2.36945 q^{79} +1.30158 q^{80} +3.36153 q^{81} +5.28007 q^{82} +14.6925 q^{83} -0.815252 q^{84} +4.78281 q^{85} -9.78927 q^{86} -6.26575 q^{87} +2.45467 q^{88} -2.99331 q^{89} -3.02292 q^{90} -1.09498 q^{91} +3.34514 q^{92} -8.54866 q^{93} +5.93027 q^{94} +1.30158 q^{95} -0.823102 q^{96} +4.59458 q^{97} -6.01898 q^{98} -5.70098 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 49 q + 49 q^{2} + 13 q^{3} + 49 q^{4} + 17 q^{5} + 13 q^{6} + 22 q^{7} + 49 q^{8} + 66 q^{9}+O(q^{10}) \) 49 * q + 49 * q^2 + 13 * q^3 + 49 * q^4 + 17 * q^5 + 13 * q^6 + 22 * q^7 + 49 * q^8 + 66 * q^9	\( 49 q + 49 q^{2} + 13 q^{3} + 49 q^{4} + 17 q^{5} + 13 q^{6} + 22 q^{7} + 49 q^{8} + 66 q^{9} + 17 q^{10} + 21 q^{11} + 13 q^{12} + 13 q^{13} + 22 q^{14} + 8 q^{15} + 49 q^{16} + 24 q^{17} + 66 q^{18} + 49 q^{19} + 17 q^{20} + 6 q^{21} + 21 q^{22} + 22 q^{23} + 13 q^{24} + 96 q^{25} + 13 q^{26} + 31 q^{27} + 22 q^{28} + 33 q^{29} + 8 q^{30} + 21 q^{31} + 49 q^{32} + 20 q^{33} + 24 q^{34} + 18 q^{35} + 66 q^{36} + 48 q^{37} + 49 q^{38} + 4 q^{39} + 17 q^{40} + 37 q^{41} + 6 q^{42} + 43 q^{43} + 21 q^{44} + 47 q^{45} + 22 q^{46} + 7 q^{47} + 13 q^{48} + 87 q^{49} + 96 q^{50} + 12 q^{51} + 13 q^{52} + 23 q^{53} + 31 q^{54} + 31 q^{55} + 22 q^{56} + 13 q^{57} + 33 q^{58} + 37 q^{59} + 8 q^{60} + 61 q^{61} + 21 q^{62} + 45 q^{63} + 49 q^{64} + 36 q^{65} + 20 q^{66} + 43 q^{67} + 24 q^{68} + 18 q^{69} + 18 q^{70} + 14 q^{71} + 66 q^{72} + 90 q^{73} + 48 q^{74} + 53 q^{75} + 49 q^{76} + 46 q^{77} + 4 q^{78} + 16 q^{79} + 17 q^{80} + 97 q^{81} + 37 q^{82} + 11 q^{83} + 6 q^{84} + 88 q^{85} + 43 q^{86} - 35 q^{87} + 21 q^{88} + 46 q^{89} + 47 q^{90} + 27 q^{91} + 22 q^{92} + 9 q^{93} + 7 q^{94} + 17 q^{95} + 13 q^{96} + 34 q^{97} + 87 q^{98} + 84 q^{99}+O(q^{100}) \) 49 * q + 49 * q^2 + 13 * q^3 + 49 * q^4 + 17 * q^5 + 13 * q^6 + 22 * q^7 + 49 * q^8 + 66 * q^9 + 17 * q^10 + 21 * q^11 + 13 * q^12 + 13 * q^13 + 22 * q^14 + 8 * q^15 + 49 * q^16 + 24 * q^17 + 66 * q^18 + 49 * q^19 + 17 * q^20 + 6 * q^21 + 21 * q^22 + 22 * q^23 + 13 * q^24 + 96 * q^25 + 13 * q^26 + 31 * q^27 + 22 * q^28 + 33 * q^29 + 8 * q^30 + 21 * q^31 + 49 * q^32 + 20 * q^33 + 24 * q^34 + 18 * q^35 + 66 * q^36 + 48 * q^37 + 49 * q^38 + 4 * q^39 + 17 * q^40 + 37 * q^41 + 6 * q^42 + 43 * q^43 + 21 * q^44 + 47 * q^45 + 22 * q^46 + 7 * q^47 + 13 * q^48 + 87 * q^49 + 96 * q^50 + 12 * q^51 + 13 * q^52 + 23 * q^53 + 31 * q^54 + 31 * q^55 + 22 * q^56 + 13 * q^57 + 33 * q^58 + 37 * q^59 + 8 * q^60 + 61 * q^61 + 21 * q^62 + 45 * q^63 + 49 * q^64 + 36 * q^65 + 20 * q^66 + 43 * q^67 + 24 * q^68 + 18 * q^69 + 18 * q^70 + 14 * q^71 + 66 * q^72 + 90 * q^73 + 48 * q^74 + 53 * q^75 + 49 * q^76 + 46 * q^77 + 4 * q^78 + 16 * q^79 + 17 * q^80 + 97 * q^81 + 37 * q^82 + 11 * q^83 + 6 * q^84 + 88 * q^85 + 43 * q^86 - 35 * q^87 + 21 * q^88 + 46 * q^89 + 47 * q^90 + 27 * q^91 + 22 * q^92 + 9 * q^93 + 7 * q^94 + 17 * q^95 + 13 * q^96 + 34 * q^97 + 87 * q^98 + 84 * q^99

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