LMFDB - Embedded newform 2669.2.a.b.1.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2669,2,Mod(1,2669)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2669, 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("2669.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2669 = 17 \cdot 157 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2669.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:	$21.3120722995$
Analytic rank:	$1$
Dimension:	$45$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.9
Character	$\chi$	$=$	2669.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.83672 q^{2} +2.17585 q^{3} +1.37355 q^{4} -2.57891 q^{5} -3.99644 q^{6} -3.01876 q^{7} +1.15062 q^{8} +1.73434 q^{9} +O(q^{10})$	\(q-1.83672 q^{2} +2.17585 q^{3} +1.37355 q^{4} -2.57891 q^{5} -3.99644 q^{6} -3.01876 q^{7} +1.15062 q^{8} +1.73434 q^{9} +4.73675 q^{10} -2.28353 q^{11} +2.98864 q^{12} +3.95068 q^{13} +5.54462 q^{14} -5.61134 q^{15} -4.86046 q^{16} +1.00000 q^{17} -3.18550 q^{18} +5.32502 q^{19} -3.54226 q^{20} -6.56838 q^{21} +4.19420 q^{22} +4.64730 q^{23} +2.50358 q^{24} +1.65080 q^{25} -7.25630 q^{26} -2.75389 q^{27} -4.14641 q^{28} +1.70149 q^{29} +10.3065 q^{30} -1.59766 q^{31} +6.62608 q^{32} -4.96862 q^{33} -1.83672 q^{34} +7.78512 q^{35} +2.38220 q^{36} -1.16913 q^{37} -9.78059 q^{38} +8.59610 q^{39} -2.96734 q^{40} +4.58959 q^{41} +12.0643 q^{42} -12.4478 q^{43} -3.13653 q^{44} -4.47271 q^{45} -8.53579 q^{46} +7.55382 q^{47} -10.5757 q^{48} +2.11291 q^{49} -3.03205 q^{50} +2.17585 q^{51} +5.42645 q^{52} -0.945668 q^{53} +5.05813 q^{54} +5.88901 q^{55} -3.47344 q^{56} +11.5865 q^{57} -3.12517 q^{58} +1.38811 q^{59} -7.70745 q^{60} -9.35274 q^{61} +2.93446 q^{62} -5.23556 q^{63} -2.44935 q^{64} -10.1885 q^{65} +9.12597 q^{66} +8.64931 q^{67} +1.37355 q^{68} +10.1118 q^{69} -14.2991 q^{70} -3.54199 q^{71} +1.99556 q^{72} -3.52236 q^{73} +2.14737 q^{74} +3.59189 q^{75} +7.31417 q^{76} +6.89342 q^{77} -15.7886 q^{78} +6.37385 q^{79} +12.5347 q^{80} -11.1951 q^{81} -8.42981 q^{82} -9.50432 q^{83} -9.02199 q^{84} -2.57891 q^{85} +22.8631 q^{86} +3.70220 q^{87} -2.62746 q^{88} -6.46929 q^{89} +8.21513 q^{90} -11.9262 q^{91} +6.38329 q^{92} -3.47628 q^{93} -13.8743 q^{94} -13.7328 q^{95} +14.4174 q^{96} -1.25433 q^{97} -3.88084 q^{98} -3.96041 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 45 q - 2 q^{2} - 20 q^{3} + 34 q^{4} - 10 q^{5} - 14 q^{6} - 20 q^{7} - 9 q^{8} + 39 q^{9}+O(q^{10}) $ 45 * q - 2 * q^2 - 20 * q^3 + 34 * q^4 - 10 * q^5 - 14 * q^6 - 20 * q^7 - 9 * q^8 + 39 * q^9	\( 45 q - 2 q^{2} - 20 q^{3} + 34 q^{4} - 10 q^{5} - 14 q^{6} - 20 q^{7} - 9 q^{8} + 39 q^{9} - 21 q^{10} - 26 q^{11} - 23 q^{12} - 6 q^{13} - 7 q^{14} - 10 q^{15} + 20 q^{16} + 45 q^{17} - 3 q^{18} - 56 q^{19} - 26 q^{20} + 2 q^{21} - 23 q^{22} - 38 q^{23} - 35 q^{24} + 27 q^{25} - 10 q^{26} - 71 q^{27} - 29 q^{28} - 29 q^{29} + 9 q^{30} - 57 q^{31} + 4 q^{33} - 2 q^{34} - 16 q^{35} + 44 q^{36} - 14 q^{37} - 6 q^{38} - 25 q^{39} - 48 q^{40} - 23 q^{41} - q^{42} - 43 q^{43} - 29 q^{44} - 63 q^{45} - 42 q^{46} + 11 q^{47} - 6 q^{48} - 9 q^{49} + 14 q^{50} - 20 q^{51} - 27 q^{52} + 7 q^{53} + 10 q^{54} - 41 q^{55} - 14 q^{56} - 5 q^{57} - 58 q^{58} - 59 q^{59} + q^{60} - 40 q^{61} - 34 q^{62} - 56 q^{63} - 67 q^{64} - 3 q^{65} - 53 q^{66} - 44 q^{67} + 34 q^{68} - 17 q^{69} + 14 q^{70} - 18 q^{71} - 25 q^{72} - 2 q^{73} - 5 q^{74} - 85 q^{75} - 123 q^{76} - 4 q^{77} + 33 q^{78} - 119 q^{79} - 17 q^{80} + 21 q^{81} - 6 q^{82} - 32 q^{83} + 54 q^{84} - 10 q^{85} - 14 q^{86} - 3 q^{87} - 33 q^{88} - 25 q^{89} - 23 q^{90} - 177 q^{91} - 62 q^{92} + 36 q^{93} - 64 q^{94} - 47 q^{95} - 153 q^{96} - 82 q^{97} + 13 q^{98} - 45 q^{99}+O(q^{100}) \) 45 * q - 2 * q^2 - 20 * q^3 + 34 * q^4 - 10 * q^5 - 14 * q^6 - 20 * q^7 - 9 * q^8 + 39 * q^9 - 21 * q^10 - 26 * q^11 - 23 * q^12 - 6 * q^13 - 7 * q^14 - 10 * q^15 + 20 * q^16 + 45 * q^17 - 3 * q^18 - 56 * q^19 - 26 * q^20 + 2 * q^21 - 23 * q^22 - 38 * q^23 - 35 * q^24 + 27 * q^25 - 10 * q^26 - 71 * q^27 - 29 * q^28 - 29 * q^29 + 9 * q^30 - 57 * q^31 + 4 * q^33 - 2 * q^34 - 16 * q^35 + 44 * q^36 - 14 * q^37 - 6 * q^38 - 25 * q^39 - 48 * q^40 - 23 * q^41 - q^42 - 43 * q^43 - 29 * q^44 - 63 * q^45 - 42 * q^46 + 11 * q^47 - 6 * q^48 - 9 * q^49 + 14 * q^50 - 20 * q^51 - 27 * q^52 + 7 * q^53 + 10 * q^54 - 41 * q^55 - 14 * q^56 - 5 * q^57 - 58 * q^58 - 59 * q^59 + q^60 - 40 * q^61 - 34 * q^62 - 56 * q^63 - 67 * q^64 - 3 * q^65 - 53 * q^66 - 44 * q^67 + 34 * q^68 - 17 * q^69 + 14 * q^70 - 18 * q^71 - 25 * q^72 - 2 * q^73 - 5 * q^74 - 85 * q^75 - 123 * q^76 - 4 * q^77 + 33 * q^78 - 119 * q^79 - 17 * q^80 + 21 * q^81 - 6 * q^82 - 32 * q^83 + 54 * q^84 - 10 * q^85 - 14 * q^86 - 3 * q^87 - 33 * q^88 - 25 * q^89 - 23 * q^90 - 177 * q^91 - 62 * q^92 + 36 * q^93 - 64 * q^94 - 47 * q^95 - 153 * q^96 - 82 * q^97 + 13 * q^98 - 45 * 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 $

$2$	−1.83672	−1.29876	−0.649379	−	0.760465i	$-0.724971\pi$
$2$	−1.83672	−1.29876	−0.649379	+	0.760465i	$0.724971\pi$
$3$	2.17585	1.25623	0.628115	−	0.778121i	$-0.283827\pi$
$3$	2.17585	1.25623	0.628115	+	0.778121i	$0.283827\pi$
$4$	1.37355	0.686774
$5$	−2.57891	−1.15333	−0.576663	−	0.816982i	$-0.695645\pi$
$5$	−2.57891	−1.15333	−0.576663	+	0.816982i	$0.695645\pi$
$6$	−3.99644	−1.63154
$7$	−3.01876	−1.14098	−0.570492	−	0.821303i	$-0.693247\pi$
$7$	−3.01876	−1.14098	−0.570492	+	0.821303i	$0.693247\pi$
$8$	1.15062	0.406805
$9$	1.73434	0.578113
$10$	4.73675	1.49789
$11$	−2.28353	−0.688509	−0.344254	−	0.938876i	$-0.611868\pi$
$11$	−2.28353	−0.688509	−0.344254	+	0.938876i	$0.611868\pi$
$12$	2.98864	0.862746
$13$	3.95068	1.09572	0.547861	−	0.836570i	$-0.315442\pi$
$13$	3.95068	1.09572	0.547861	+	0.836570i	$0.315442\pi$
$14$	5.54462	1.48186
$15$	−5.61134	−1.44884
$16$	−4.86046	−1.21512
$17$	1.00000	0.242536
$17$	1.00000	0.242536
$18$	−3.18550	−0.750830
$19$	5.32502	1.22164	0.610822	−	0.791768i	$-0.290839\pi$
$19$	5.32502	1.22164	0.610822	+	0.791768i	$0.290839\pi$
$20$	−3.54226	−0.792074
$21$	−6.56838	−1.43334
$22$	4.19420	0.894207
$23$	4.64730	0.969028	0.484514	−	0.874783i	$-0.338996\pi$
$23$	4.64730	0.969028	0.484514	+	0.874783i	$0.338996\pi$
$24$	2.50358	0.511040
$25$	1.65080	0.330159
$26$	−7.25630	−1.42308
$27$	−2.75389	−0.529987
$28$	−4.14641	−0.783598
$29$	1.70149	0.315959	0.157980	−	0.987442i	$-0.449502\pi$
$29$	1.70149	0.315959	0.157980	+	0.987442i	$0.449502\pi$
$30$	10.3065	1.88170
$31$	−1.59766	−0.286949	−0.143474	−	0.989654i	$-0.545827\pi$
$31$	−1.59766	−0.286949	−0.143474	+	0.989654i	$0.545827\pi$
$32$	6.62608	1.17134
$33$	−4.96862	−0.864925
$34$	−1.83672	−0.314995
$35$	7.78512	1.31593
$36$	2.38220	0.397033
$37$	−1.16913	−0.192204	−0.0961019	−	0.995372i	$-0.530637\pi$
$37$	−1.16913	−0.192204	−0.0961019	+	0.995372i	$0.530637\pi$
$38$	−9.78059	−1.58662
$39$	8.59610	1.37648
$40$	−2.96734	−0.469178
$41$	4.58959	0.716774	0.358387	−	0.933573i	$-0.383327\pi$
$41$	4.58959	0.716774	0.358387	+	0.933573i	$0.383327\pi$
$42$	12.0643	1.86156
$43$	−12.4478	−1.89827	−0.949135	−	0.314869i	$-0.898039\pi$
$43$	−12.4478	−1.89827	−0.949135	+	0.314869i	$0.898039\pi$
$44$	−3.13653	−0.472850
$45$	−4.47271	−0.666753
$46$	−8.53579	−1.25853
$47$	7.55382	1.10184	0.550919	−	0.834559i	$-0.314277\pi$
$47$	7.55382	1.10184	0.550919	+	0.834559i	$0.314277\pi$
$48$	−10.5757	−1.52646
$49$	2.11291	0.301845
$50$	−3.03205	−0.428797
$51$	2.17585	0.304680
$52$	5.42645	0.752513
$53$	−0.945668	−0.129897	−0.0649487	−	0.997889i	$-0.520688\pi$
$53$	−0.945668	−0.129897	−0.0649487	+	0.997889i	$0.520688\pi$
$54$	5.05813	0.688325
$55$	5.88901	0.794075
$56$	−3.47344	−0.464158
$57$	11.5865	1.53467
$58$	−3.12517	−0.410355
$59$	1.38811	0.180716	0.0903582	−	0.995909i	$-0.471199\pi$
$59$	1.38811	0.180716	0.0903582	+	0.995909i	$0.471199\pi$
$60$	−7.70745	−0.995027
$61$	−9.35274	−1.19750	−0.598748	−	0.800938i	$-0.704335\pi$
$61$	−9.35274	−1.19750	−0.598748	+	0.800938i	$0.704335\pi$
$62$	2.93446	0.372677
$63$	−5.23556	−0.659618
$64$	−2.44935	−0.306169
$65$	−10.1885	−1.26372
$66$	9.12597	1.12333
$67$	8.64931	1.05668	0.528341	−	0.849032i	$-0.322814\pi$
$67$	8.64931	1.05668	0.528341	+	0.849032i	$0.322814\pi$
$68$	1.37355	0.166567
$69$	10.1118	1.21732
$70$	−14.2991	−1.70907
$71$	−3.54199	−0.420357	−0.210178	−	0.977663i	$-0.567404\pi$
$71$	−3.54199	−0.420357	−0.210178	+	0.977663i	$0.567404\pi$
$72$	1.99556	0.235179
$73$	−3.52236	−0.412261	−0.206131	−	0.978524i	$-0.566087\pi$
$73$	−3.52236	−0.412261	−0.206131	+	0.978524i	$0.566087\pi$
$74$	2.14737	0.249626
$75$	3.59189	0.414756
$76$	7.31417	0.838993
$77$	6.89342	0.785578
$78$	−15.7886	−1.78771
$79$	6.37385	0.717114	0.358557	−	0.933508i	$-0.383269\pi$
$79$	6.37385	0.717114	0.358557	+	0.933508i	$0.383269\pi$
$80$	12.5347	1.40142
$81$	−11.1951	−1.24390
$82$	−8.42981	−0.930916
$83$	−9.50432	−1.04324	−0.521618	−	0.853179i	$-0.674671\pi$
$83$	−9.50432	−1.04324	−0.521618	+	0.853179i	$0.674671\pi$
$84$	−9.02199	−0.984380
$85$	−2.57891	−0.279722
$86$	22.8631	2.46540
$87$	3.70220	0.396917
$88$	−2.62746	−0.280089
$89$	−6.46929	−0.685743	−0.342872	−	0.939382i	$-0.611400\pi$
$89$	−6.46929	−0.685743	−0.342872	+	0.939382i	$0.611400\pi$
$90$	8.21513	0.865951
$91$	−11.9262	−1.25020
$92$	6.38329	0.665504
$93$	−3.47628	−0.360474
$94$	−13.8743	−1.43102
$95$	−13.7328	−1.40895
$96$	14.4174	1.47147
$97$	−1.25433	−0.127358	−0.0636791	−	0.997970i	$-0.520283\pi$
$97$	−1.25433	−0.127358	−0.0636791	+	0.997970i	$0.520283\pi$
$98$	−3.88084	−0.392024
$99$	−3.96041	−0.398036
$100$	2.26745	0.226745
$101$	−2.49503	−0.248265	−0.124132	−	0.992266i	$-0.539615\pi$
$101$	−2.49503	−0.248265	−0.124132	+	0.992266i	$0.539615\pi$
$102$	−3.99644	−0.395706
$103$	−11.4320	−1.12643	−0.563213	−	0.826312i	$-0.690435\pi$
$103$	−11.4320	−1.12643	−0.563213	+	0.826312i	$0.690435\pi$
$104$	4.54572	0.445745
$105$	16.9393	1.65311
$106$	1.73693	0.168705
$107$	−15.8360	−1.53092	−0.765462	−	0.643481i	$-0.777489\pi$
$107$	−15.8360	−1.53092	−0.765462	+	0.643481i	$0.777489\pi$
$108$	−3.78260	−0.363981
$109$	−15.0195	−1.43861	−0.719305	−	0.694695i	$-0.755539\pi$
$109$	−15.0195	−1.43861	−0.719305	+	0.694695i	$0.755539\pi$
$110$	−10.8165	−1.03131
$111$	−2.54386	−0.241452
$112$	14.6726	1.38643
$113$	−7.81134	−0.734829	−0.367414	−	0.930057i	$-0.619757\pi$
$113$	−7.81134	−0.734829	−0.367414	+	0.930057i	$0.619757\pi$
$114$	−21.2811	−1.99316
$115$	−11.9850	−1.11760
$116$	2.33708	0.216992
$117$	6.85182	0.633451
$118$	−2.54957	−0.234707
$119$	−3.01876	−0.276729
$120$	−6.45651	−0.589396
$121$	−5.78551	−0.525956
$122$	17.1784	1.55526
$123$	9.98628	0.900433
$124$	−2.19447	−0.197069
$125$	8.63731	0.772544
$126$	9.61626	0.856685
$127$	−18.8182	−1.66984	−0.834922	−	0.550368i	$-0.814487\pi$
$127$	−18.8182	−1.66984	−0.834922	+	0.550368i	$0.814487\pi$
$128$	−8.75339	−0.773698
$129$	−27.0846	−2.38466
$130$	18.7134	1.64127
$131$	12.9573	1.13208	0.566042	−	0.824376i	$-0.308474\pi$
$131$	12.9573	1.13208	0.566042	+	0.824376i	$0.308474\pi$
$132$	−6.82464	−0.594008
$133$	−16.0750	−1.39388
$134$	−15.8864	−1.37237
$135$	7.10205	0.611247
$136$	1.15062	0.0986647
$137$	2.98392	0.254933	0.127467	−	0.991843i	$-0.459315\pi$
$137$	2.98392	0.254933	0.127467	+	0.991843i	$0.459315\pi$
$138$	−18.5726	−1.58101
$139$	−1.40158	−0.118881	−0.0594403	−	0.998232i	$-0.518932\pi$
$139$	−1.40158	−0.118881	−0.0594403	+	0.998232i	$0.518932\pi$
$140$	10.6932	0.903744
$141$	16.4360	1.38416
$142$	6.50565	0.545942
$143$	−9.02148	−0.754414
$144$	−8.42969	−0.702474
$145$	−4.38800	−0.364404
$146$	6.46960	0.535428
$147$	4.59739	0.379186
$148$	−1.60586	−0.132001
$149$	1.15711	0.0947942	0.0473971	−	0.998876i	$-0.484907\pi$
$149$	1.15711	0.0947942	0.0473971	+	0.998876i	$0.484907\pi$
$150$	−6.59730	−0.538668
$151$	−15.0252	−1.22274	−0.611368	−	0.791346i	$-0.709381\pi$
$151$	−15.0252	−1.22274	−0.611368	+	0.791346i	$0.709381\pi$
$152$	6.12707	0.496971
$153$	1.73434	0.140213
$154$	−12.6613	−1.02028
$155$	4.12024	0.330945
$156$	11.8072	0.945329
$157$	1.00000	0.0798087
$157$	1.00000	0.0798087
$158$	−11.7070	−0.931358
$159$	−2.05763	−0.163181
$160$	−17.0881	−1.35093
$161$	−14.0291	−1.10565
$162$	20.5623	1.61552
$163$	−5.45730	−0.427448	−0.213724	−	0.976894i	$-0.568559\pi$
$163$	−5.45730	−0.427448	−0.213724	+	0.976894i	$0.568559\pi$
$164$	6.30403	0.492262
$165$	12.8136	0.997540
$166$	17.4568	1.35491
$167$	2.69628	0.208644	0.104322	−	0.994544i	$-0.466733\pi$
$167$	2.69628	0.208644	0.104322	+	0.994544i	$0.466733\pi$
$168$	−7.55770	−0.583089
$169$	2.60786	0.200605
$170$	4.73675	0.363292
$171$	9.23540	0.706249
$172$	−17.0976	−1.30368
$173$	19.1837	1.45851	0.729253	−	0.684244i	$-0.239868\pi$
$173$	19.1837	1.45851	0.729253	+	0.684244i	$0.239868\pi$
$174$	−6.79991	−0.515500
$175$	−4.98336	−0.376706
$176$	11.0990	0.836618
$177$	3.02032	0.227021
$178$	11.8823	0.890615
$179$	−2.46266	−0.184068	−0.0920340	−	0.995756i	$-0.529337\pi$
$179$	−2.46266	−0.184068	−0.0920340	+	0.995756i	$0.529337\pi$
$180$	−6.14349	−0.457908
$181$	2.76921	0.205834	0.102917	−	0.994690i	$-0.467182\pi$
$181$	2.76921	0.205834	0.102917	+	0.994690i	$0.467182\pi$
$182$	21.9050	1.62371
$183$	−20.3502	−1.50433
$184$	5.34726	0.394205
$185$	3.01509	0.221673
$186$	6.38496	0.468168
$187$	−2.28353	−0.166988
$188$	10.3755	0.756713
$189$	8.31334	0.604706
$190$	25.2233	1.82989
$191$	17.4554	1.26303	0.631515	−	0.775364i	$-0.282434\pi$
$191$	17.4554	1.26303	0.631515	+	0.775364i	$0.282434\pi$
$192$	−5.32942	−0.384618
$193$	22.0023	1.58376	0.791880	−	0.610677i	$-0.209102\pi$
$193$	22.0023	1.58376	0.791880	+	0.610677i	$0.209102\pi$
$194$	2.30386	0.165407
$195$	−22.1686	−1.58753
$196$	2.90219	0.207299
$197$	−22.8931	−1.63106	−0.815532	−	0.578712i	$-0.803556\pi$
$197$	−22.8931	−1.63106	−0.815532	+	0.578712i	$0.803556\pi$
$198$	7.27417	0.516953
$199$	2.67925	0.189927	0.0949633	−	0.995481i	$-0.469727\pi$
$199$	2.67925	0.189927	0.0949633	+	0.995481i	$0.469727\pi$
$200$	1.89943	0.134310
$201$	18.8196	1.32743
$202$	4.58267	0.322436
$203$	−5.13640	−0.360504
$204$	2.98864	0.209247
$205$	−11.8362	−0.826673
$206$	20.9974	1.46296
$207$	8.05999	0.560208
$208$	−19.2021	−1.33143
$209$	−12.1598	−0.841113
$210$	−31.1128	−2.14698
$211$	−19.3849	−1.33451	−0.667256	−	0.744828i	$-0.732531\pi$
$211$	−19.3849	−1.33451	−0.667256	+	0.744828i	$0.732531\pi$
$212$	−1.29892	−0.0892102
$213$	−7.70685	−0.528065
$214$	29.0863	1.98830
$215$	32.1018	2.18932
$216$	−3.16868	−0.215601
$217$	4.82296	0.327404
$218$	27.5867	1.86841
$219$	−7.66415	−0.517895
$220$	8.08885	0.545350
$221$	3.95068	0.265751
$222$	4.67236	0.313588
$223$	1.43520	0.0961081	0.0480540	−	0.998845i	$-0.484698\pi$
$223$	1.43520	0.0961081	0.0480540	+	0.998845i	$0.484698\pi$
$224$	−20.0026	−1.33648
$225$	2.86304	0.190869
$226$	14.3473	0.954366
$227$	−24.0646	−1.59722	−0.798611	−	0.601847i	$-0.794432\pi$
$227$	−24.0646	−1.59722	−0.798611	+	0.601847i	$0.794432\pi$
$228$	15.9146	1.05397
$229$	3.90480	0.258036	0.129018	−	0.991642i	$-0.458817\pi$
$229$	3.90480	0.258036	0.129018	+	0.991642i	$0.458817\pi$
$230$	22.0131	1.45150
$231$	14.9991	0.986866
$232$	1.95777	0.128534
$233$	−4.29556	−0.281411	−0.140706	−	0.990051i	$-0.544937\pi$
$233$	−4.29556	−0.281411	−0.140706	+	0.990051i	$0.544937\pi$
$234$	−12.5849	−0.822700
$235$	−19.4806	−1.27078
$236$	1.90663	0.124111
$237$	13.8686	0.900860
$238$	5.54462	0.359405
$239$	8.25098	0.533712	0.266856	−	0.963736i	$-0.414015\pi$
$239$	8.25098	0.533712	0.266856	+	0.963736i	$0.414015\pi$
$240$	27.2737	1.76051
$241$	−3.02050	−0.194567	−0.0972837	−	0.995257i	$-0.531015\pi$
$241$	−3.02050	−0.194567	−0.0972837	+	0.995257i	$0.531015\pi$
$242$	10.6264	0.683089
$243$	−16.0972	−1.03264
$244$	−12.8464	−0.822409
$245$	−5.44902	−0.348125
$246$	−18.3420	−1.16944
$247$	21.0375	1.33858
$248$	−1.83830	−0.116732
$249$	−20.6800	−1.31054
$250$	−15.8643	−1.00335
$251$	−23.0681	−1.45605	−0.728024	−	0.685551i	$-0.759561\pi$
$251$	−23.0681	−1.45605	−0.728024	+	0.685551i	$0.759561\pi$
$252$	−7.19129	−0.453009
$253$	−10.6122	−0.667184
$254$	34.5638	2.16872
$255$	−5.61134	−0.351396
$256$	20.9762	1.31102
$257$	9.38589	0.585476	0.292738	−	0.956193i	$-0.405434\pi$
$257$	9.38589	0.585476	0.292738	+	0.956193i	$0.405434\pi$
$258$	49.7468	3.09710
$259$	3.52932	0.219301
$260$	−13.9943	−0.867892
$261$	2.95096	0.182660
$262$	−23.7989	−1.47030
$263$	−2.79495	−0.172344	−0.0861720	−	0.996280i	$-0.527463\pi$
$263$	−2.79495	−0.172344	−0.0861720	+	0.996280i	$0.527463\pi$
$264$	−5.71698	−0.351856
$265$	2.43880	0.149814
$266$	29.5252	1.81031
$267$	−14.0762	−0.861451
$268$	11.8802	0.725701
$269$	6.03295	0.367835	0.183918	−	0.982942i	$-0.441122\pi$
$269$	6.03295	0.367835	0.183918	+	0.982942i	$0.441122\pi$
$270$	−13.0445	−0.793862
$271$	12.9881	0.788970	0.394485	−	0.918902i	$-0.370923\pi$
$271$	12.9881	0.788970	0.394485	+	0.918902i	$0.370923\pi$
$272$	−4.86046	−0.294709
$273$	−25.9496	−1.57054
$274$	−5.48063	−0.331097
$275$	−3.76963	−0.227317
$276$	13.8891	0.836025
$277$	6.72641	0.404151	0.202076	−	0.979370i	$-0.435231\pi$
$277$	6.72641	0.404151	0.202076	+	0.979370i	$0.435231\pi$
$278$	2.57432	0.154397
$279$	−2.77089	−0.165889
$280$	8.95770	0.535325
$281$	23.8540	1.42301	0.711504	−	0.702682i	$-0.248014\pi$
$281$	23.8540	1.42301	0.711504	+	0.702682i	$0.248014\pi$
$282$	−30.1884	−1.79769
$283$	6.30539	0.374817	0.187408	−	0.982282i	$-0.439991\pi$
$283$	6.30539	0.374817	0.187408	+	0.982282i	$0.439991\pi$
$284$	−4.86509	−0.288690
$285$	−29.8805	−1.76997
$286$	16.5699	0.979801
$287$	−13.8549	−0.817828
$288$	11.4919	0.677165
$289$	1.00000	0.0588235
$290$	8.05954	0.473272
$291$	−2.72924	−0.159991
$292$	−4.83813	−0.283130
$293$	−18.3381	−1.07132	−0.535661	−	0.844433i	$-0.679937\pi$
$293$	−18.3381	−1.07132	−0.535661	+	0.844433i	$0.679937\pi$
$294$	−8.44413	−0.492472
$295$	−3.57981	−0.208425
$296$	−1.34522	−0.0781894
$297$	6.28858	0.364900
$298$	−2.12529	−0.123115
$299$	18.3600	1.06178
$300$	4.93363	0.284843
$301$	37.5769	2.16590
$302$	27.5972	1.58804
$303$	−5.42882	−0.311877
$304$	−25.8821	−1.48444
$305$	24.1199	1.38110
$306$	−3.18550	−0.182103
$307$	−28.8965	−1.64921	−0.824604	−	0.565710i	$-0.808602\pi$
$307$	−28.8965	−1.64921	−0.824604	+	0.565710i	$0.808602\pi$
$308$	9.46844	0.539514
$309$	−24.8743	−1.41505
$310$	−7.56773	−0.429818
$311$	−8.95010	−0.507513	−0.253757	−	0.967268i	$-0.581666\pi$
$311$	−8.95010	−0.507513	−0.253757	+	0.967268i	$0.581666\pi$
$312$	9.89083	0.559958
$313$	−8.21855	−0.464540	−0.232270	−	0.972651i	$-0.574615\pi$
$313$	−8.21855	−0.464540	−0.232270	+	0.972651i	$0.574615\pi$
$314$	−1.83672	−0.103652
$315$	13.5020	0.760754
$316$	8.75479	0.492495
$317$	−3.66115	−0.205631	−0.102815	−	0.994700i	$-0.532785\pi$
$317$	−3.66115	−0.205631	−0.102815	+	0.994700i	$0.532785\pi$
$318$	3.77930	0.211933
$319$	−3.88540	−0.217541
$320$	6.31666	0.353112
$321$	−34.4568	−1.92319
$322$	25.7675	1.43597
$323$	5.32502	0.296292
$324$	−15.3770	−0.854277
$325$	6.52176	0.361762
$326$	10.0235	0.555152
$327$	−32.6803	−1.80722
$328$	5.28087	0.291587
$329$	−22.8032	−1.25718
$330$	−23.5351	−1.29556
$331$	8.49930	0.467164	0.233582	−	0.972337i	$-0.424955\pi$
$331$	8.49930	0.467164	0.233582	+	0.972337i	$0.424955\pi$
$332$	−13.0546	−0.716467
$333$	−2.02767	−0.111116
$334$	−4.95232	−0.270979
$335$	−22.3058	−1.21870
$336$	31.9254	1.74167
$337$	−21.7721	−1.18600	−0.593001	−	0.805201i	$-0.702057\pi$
$337$	−21.7721	−1.18600	−0.593001	+	0.805201i	$0.702057\pi$
$338$	−4.78992	−0.260537
$339$	−16.9963	−0.923114
$340$	−3.54226	−0.192106
$341$	3.64831	0.197567
$342$	−16.9629	−0.917246
$343$	14.7529	0.796584
$344$	−14.3227	−0.772226
$345$	−26.0776	−1.40397
$346$	−35.2351	−1.89425
$347$	13.9546	0.749124	0.374562	−	0.927202i	$-0.377793\pi$
$347$	13.9546	0.749124	0.374562	+	0.927202i	$0.377793\pi$
$348$	5.08515	0.272592
$349$	−1.60178	−0.0857412	−0.0428706	−	0.999081i	$-0.513650\pi$
$349$	−1.60178	−0.0857412	−0.0428706	+	0.999081i	$0.513650\pi$
$350$	9.15304	0.489251
$351$	−10.8797	−0.580718
$352$	−15.1308	−0.806476
$353$	29.5895	1.57489	0.787444	−	0.616386i	$-0.211404\pi$
$353$	29.5895	1.57489	0.787444	+	0.616386i	$0.211404\pi$
$354$	−5.54749	−0.294846
$355$	9.13448	0.484808
$356$	−8.88588	−0.470951
$357$	−6.56838	−0.347636
$358$	4.52322	0.239060
$359$	0.864835	0.0456443	0.0228221	−	0.999740i	$-0.492735\pi$
$359$	0.864835	0.0456443	0.0228221	+	0.999740i	$0.492735\pi$
$360$	−5.14638	−0.271238
$361$	9.35586	0.492414
$362$	−5.08628	−0.267329
$363$	−12.5884	−0.660721
$364$	−16.3811	−0.858605
$365$	9.08387	0.475471
$366$	37.3777	1.95376
$367$	−34.1115	−1.78061	−0.890304	−	0.455367i	$-0.849508\pi$
$367$	−34.1115	−1.78061	−0.890304	+	0.455367i	$0.849508\pi$
$368$	−22.5880	−1.17748
$369$	7.95991	0.414376
$370$	−5.53787	−0.287900
$371$	2.85474	0.148211
$372$	−4.77484	−0.247564
$373$	−11.8611	−0.614146	−0.307073	−	0.951686i	$-0.599350\pi$
$373$	−11.8611	−0.614146	−0.307073	+	0.951686i	$0.599350\pi$
$374$	4.19420	0.216877
$375$	18.7935	0.970493
$376$	8.69156	0.448233
$377$	6.72205	0.346203
$378$	−15.2693	−0.785368
$379$	−34.7255	−1.78373	−0.891864	−	0.452303i	$-0.850603\pi$
$379$	−34.7255	−1.78373	−0.891864	+	0.452303i	$0.850603\pi$
$380$	−18.8626	−0.967632
$381$	−40.9456	−2.09771
$382$	−32.0607	−1.64037
$383$	−5.69983	−0.291248	−0.145624	−	0.989340i	$-0.546519\pi$
$383$	−5.69983	−0.291248	−0.145624	+	0.989340i	$0.546519\pi$
$384$	−19.0461	−0.971942
$385$	−17.7775	−0.906026
$386$	−40.4121	−2.05692
$387$	−21.5887	−1.09742
$388$	−1.72289	−0.0874663
$389$	−32.4475	−1.64515	−0.822576	−	0.568655i	$-0.807464\pi$
$389$	−32.4475	−1.64515	−0.822576	+	0.568655i	$0.807464\pi$
$390$	40.7176	2.06181
$391$	4.64730	0.235024
$392$	2.43116	0.122792
$393$	28.1932	1.42216
$394$	42.0482	2.11836
$395$	−16.4376	−0.827065
$396$	−5.43981	−0.273361
$397$	14.4018	0.722806	0.361403	−	0.932410i	$-0.382298\pi$
$397$	14.4018	0.722806	0.361403	+	0.932410i	$0.382298\pi$
$398$	−4.92103	−0.246669
$399$	−34.9768	−1.75103
$400$	−8.02363	−0.401181
$401$	−38.7322	−1.93419	−0.967096	−	0.254412i	$-0.918118\pi$
$401$	−38.7322	−1.93419	−0.967096	+	0.254412i	$0.918118\pi$
$402$	−34.5664	−1.72402
$403$	−6.31186	−0.314416
$404$	−3.42704	−0.170502
$405$	28.8712	1.43462
$406$	9.43413	0.468208
$407$	2.66974	0.132334
$408$	2.50358	0.123945
$409$	1.51145	0.0747363	0.0373681	−	0.999302i	$-0.488103\pi$
$409$	1.51145	0.0747363	0.0373681	+	0.999302i	$0.488103\pi$
$410$	21.7397	1.07365
$411$	6.49257	0.320255
$412$	−15.7024	−0.773600
$413$	−4.19037	−0.206194
$414$	−14.8040	−0.727575
$415$	24.5108	1.20319
$416$	26.1775	1.28346
$417$	−3.04964	−0.149341
$418$	22.3342	1.09240
$419$	14.9185	0.728819	0.364409	−	0.931239i	$-0.381271\pi$
$419$	14.9185	0.728819	0.364409	+	0.931239i	$0.381271\pi$
$420$	23.2669	1.13531
$421$	−5.96882	−0.290902	−0.145451	−	0.989365i	$-0.546463\pi$
$421$	−5.96882	−0.290902	−0.145451	+	0.989365i	$0.546463\pi$
$422$	35.6047	1.73321
$423$	13.1009	0.636987
$424$	−1.08810	−0.0528429
$425$	1.65080	0.0800753
$426$	14.1553	0.685829
$427$	28.2337	1.36632
$428$	−21.7515	−1.05140
$429$	−19.6294	−0.947717
$430$	−58.9620	−2.84340
$431$	12.0737	0.581569	0.290785	−	0.956788i	$-0.406084\pi$
$431$	12.0737	0.581569	0.290785	+	0.956788i	$0.406084\pi$
$432$	13.3852	0.643995
$433$	−27.6233	−1.32749	−0.663746	−	0.747958i	$-0.731034\pi$
$433$	−27.6233	−1.32749	−0.663746	+	0.747958i	$0.731034\pi$
$434$	−8.85844	−0.425219
$435$	−9.54765	−0.457775
$436$	−20.6300	−0.988000
$437$	24.7470	1.18381
$438$	14.0769	0.672621
$439$	22.0895	1.05428	0.527138	−	0.849780i	$-0.323265\pi$
$439$	22.0895	1.05428	0.527138	+	0.849780i	$0.323265\pi$
$440$	6.77600	0.323033
$441$	3.66451	0.174500
$442$	−7.25630	−0.345147
$443$	−3.91284	−0.185905	−0.0929524	−	0.995671i	$-0.529630\pi$
$443$	−3.91284	−0.185905	−0.0929524	+	0.995671i	$0.529630\pi$
$444$	−3.49411	−0.165823
$445$	16.6837	0.790885
$446$	−2.63606	−0.124821
$447$	2.51770	0.119083
$448$	7.39400	0.349333
$449$	−16.5287	−0.780036	−0.390018	−	0.920807i	$-0.627531\pi$
$449$	−16.5287	−0.780036	−0.390018	+	0.920807i	$0.627531\pi$
$450$	−5.25861	−0.247893
$451$	−10.4804	−0.493505
$452$	−10.7293	−0.504662
$453$	−32.6927	−1.53604
$454$	44.1999	2.07441
$455$	30.7565	1.44189
$456$	13.3316	0.624309
$457$	6.59754	0.308620	0.154310	−	0.988022i	$-0.450685\pi$
$457$	6.59754	0.308620	0.154310	+	0.988022i	$0.450685\pi$
$458$	−7.17203	−0.335127
$459$	−2.75389	−0.128541
$460$	−16.4619	−0.767542
$461$	27.1580	1.26487	0.632437	−	0.774612i	$-0.282055\pi$
$461$	27.1580	1.26487	0.632437	+	0.774612i	$0.282055\pi$
$462$	−27.5491	−1.28170
$463$	12.6929	0.589890	0.294945	−	0.955514i	$-0.404699\pi$
$463$	12.6929	0.589890	0.294945	+	0.955514i	$0.404699\pi$
$464$	−8.27003	−0.383927
$465$	8.96503	0.415743
$466$	7.88975	0.365485
$467$	16.9480	0.784262	0.392131	−	0.919909i	$-0.371738\pi$
$467$	16.9480	0.784262	0.392131	+	0.919909i	$0.371738\pi$
$468$	9.41131	0.435038
$469$	−26.1102	−1.20566
$470$	35.7805	1.65043
$471$	2.17585	0.100258
$472$	1.59718	0.0735163
$473$	28.4248	1.30698
$474$	−25.4727	−1.17000
$475$	8.79052	0.403337
$476$	−4.14641	−0.190051
$477$	−1.64011	−0.0750954
$478$	−15.1548	−0.693163
$479$	−2.92777	−0.133773	−0.0668865	−	0.997761i	$-0.521307\pi$
$479$	−2.92777	−0.133773	−0.0668865	+	0.997761i	$0.521307\pi$
$480$	−37.1812	−1.69708
$481$	−4.61886	−0.210602
$482$	5.54782	0.252696
$483$	−30.5252	−1.38895
$484$	−7.94668	−0.361213
$485$	3.23481	0.146885
$486$	29.5661	1.34114
$487$	21.5221	0.975259	0.487630	−	0.873051i	$-0.337862\pi$
$487$	21.5221	0.975259	0.487630	+	0.873051i	$0.337862\pi$
$488$	−10.7614	−0.487147
$489$	−11.8743	−0.536973
$490$	10.0083	0.452131
$491$	30.4310	1.37333	0.686666	−	0.726973i	$-0.259074\pi$
$491$	30.4310	1.37333	0.686666	+	0.726973i	$0.259074\pi$
$492$	13.7166	0.618394
$493$	1.70149	0.0766313
$494$	−38.6400	−1.73849
$495$	10.2136	0.459065
$496$	7.76538	0.348676
$497$	10.6924	0.479620
$498$	37.9834	1.70208
$499$	−36.1377	−1.61775	−0.808873	−	0.587983i	$-0.799922\pi$
$499$	−36.1377	−1.61775	−0.808873	+	0.587983i	$0.799922\pi$
$500$	11.8638	0.530564
$501$	5.86671	0.262105
$502$	42.3698	1.89106
$503$	−24.6977	−1.10121	−0.550607	−	0.834765i	$-0.685604\pi$
$503$	−24.6977	−1.10121	−0.550607	+	0.834765i	$0.685604\pi$
$504$	−6.02412	−0.268336
$505$	6.43446	0.286330
$506$	19.4917	0.866512
$507$	5.67433	0.252006
$508$	−25.8477	−1.14681
$509$	−16.6608	−0.738478	−0.369239	−	0.929334i	$-0.620382\pi$
$509$	−16.6608	−0.738478	−0.369239	+	0.929334i	$0.620382\pi$
$510$	10.3065	0.456378
$511$	10.6332	0.470384
$512$	−21.0208	−0.928995
$513$	−14.6645	−0.647455
$514$	−17.2393	−0.760391
$515$	29.4821	1.29914
$516$	−37.2020	−1.63773
$517$	−17.2493	−0.758625
$518$	−6.48239	−0.284820
$519$	41.7408	1.83222
$520$	−11.7230	−0.514089
$521$	−21.5220	−0.942897	−0.471448	−	0.881894i	$-0.656269\pi$
$521$	−21.5220	−0.942897	−0.471448	+	0.881894i	$0.656269\pi$
$522$	−5.42010	−0.237231
$523$	−8.18145	−0.357750	−0.178875	−	0.983872i	$-0.557246\pi$
$523$	−8.18145	−0.357750	−0.178875	+	0.983872i	$0.557246\pi$
$524$	17.7975	0.777486
$525$	−10.8431	−0.473230
$526$	5.13355	0.223833
$527$	−1.59766	−0.0695953
$528$	24.1498	1.05098
$529$	−1.40264	−0.0609842
$530$	−4.47939	−0.194572
$531$	2.40745	0.104475
$532$	−22.0797	−0.957278
$533$	18.1320	0.785384
$534$	25.8541	1.11882
$535$	40.8397	1.76565
$536$	9.95205	0.429863
$537$	−5.35839	−0.231232
$538$	−11.0809	−0.477729
$539$	−4.82489	−0.207823
$540$	9.75501	0.419789
$541$	10.8024	0.464432	0.232216	−	0.972664i	$-0.425402\pi$
$541$	10.8024	0.464432	0.232216	+	0.972664i	$0.425402\pi$
$542$	−23.8555	−1.02468
$543$	6.02540	0.258575
$544$	6.62608	0.284091
$545$	38.7340	1.65918
$546$	47.6621	2.03975
$547$	−44.4077	−1.89874	−0.949368	−	0.314165i	$-0.898276\pi$
$547$	−44.4077	−1.89874	−0.949368	+	0.314165i	$0.898276\pi$
$548$	4.09856	0.175082
$549$	−16.2208	−0.692288
$550$	6.92377	0.295231
$551$	9.06048	0.385989
$552$	11.6349	0.495213
$553$	−19.2411	−0.818215
$554$	−12.3546	−0.524895
$555$	6.56038	0.278473
$556$	−1.92514	−0.0816441
$557$	43.2647	1.83318	0.916592	−	0.399823i	$-0.130929\pi$
$557$	43.2647	1.83318	0.916592	+	0.399823i	$0.130929\pi$
$558$	5.08936	0.215450
$559$	−49.1772	−2.07998
$560$	−37.8393	−1.59900
$561$	−4.96862	−0.209775
$562$	−43.8131	−1.84815
$563$	10.3736	0.437194	0.218597	−	0.975815i	$-0.429852\pi$
$563$	10.3736	0.437194	0.218597	+	0.975815i	$0.429852\pi$
$564$	22.5756	0.950606
$565$	20.1448	0.847497
$566$	−11.5813	−0.486796
$567$	33.7953	1.41927
$568$	−4.07548	−0.171003
$569$	11.1983	0.469457	0.234728	−	0.972061i	$-0.424580\pi$
$569$	11.1983	0.469457	0.234728	+	0.972061i	$0.424580\pi$
$570$	54.8822	2.29876
$571$	−18.4778	−0.773270	−0.386635	−	0.922233i	$-0.626363\pi$
$571$	−18.4778	−0.773270	−0.386635	+	0.922233i	$0.626363\pi$
$572$	−12.3914	−0.518112
$573$	37.9804	1.58665
$574$	25.4476	1.06216
$575$	7.67174	0.319933
$576$	−4.24800	−0.177000
$577$	23.1866	0.965270	0.482635	−	0.875821i	$-0.339680\pi$
$577$	23.1866	0.965270	0.482635	+	0.875821i	$0.339680\pi$
$578$	−1.83672	−0.0763976
$579$	47.8738	1.98957
$580$	−6.02713	−0.250263
$581$	28.6913	1.19031
$582$	5.01286	0.207790
$583$	2.15946	0.0894355
$584$	−4.05289	−0.167710
$585$	−17.6703	−0.730575
$586$	33.6819	1.39139
$587$	42.0217	1.73442	0.867211	−	0.497941i	$-0.165910\pi$
$587$	42.0217	1.73442	0.867211	+	0.497941i	$0.165910\pi$
$588$	6.31474	0.260415
$589$	−8.50759	−0.350549
$590$	6.57512	0.270693
$591$	−49.8120	−2.04899
$592$	5.68251	0.233550
$593$	14.7027	0.603767	0.301883	−	0.953345i	$-0.402385\pi$
$593$	14.7027	0.603767	0.301883	+	0.953345i	$0.402385\pi$
$594$	−11.5504	−0.473918
$595$	7.78512	0.319159
$596$	1.58935	0.0651022
$597$	5.82965	0.238592
$598$	−33.7222	−1.37900
$599$	2.91165	0.118967	0.0594835	−	0.998229i	$-0.481055\pi$
$599$	2.91165	0.118967	0.0594835	+	0.998229i	$0.481055\pi$
$600$	4.13289	0.168725
$601$	−9.64178	−0.393297	−0.196648	−	0.980474i	$-0.563006\pi$
$601$	−9.64178	−0.393297	−0.196648	+	0.980474i	$0.563006\pi$
$602$	−69.0183	−2.81298
$603$	15.0008	0.610881
$604$	−20.6379	−0.839744
$605$	14.9203	0.606598
$606$	9.97123	0.405053
$607$	26.8560	1.09005	0.545025	−	0.838420i	$-0.316520\pi$
$607$	26.8560	1.09005	0.545025	+	0.838420i	$0.316520\pi$
$608$	35.2840	1.43096
$609$	−11.1760	−0.452876
$610$	−44.3016	−1.79372
$611$	29.8427	1.20731
$612$	2.38220	0.0962947
$613$	46.7242	1.88717	0.943586	−	0.331127i	$-0.107429\pi$
$613$	46.7242	1.88717	0.943586	+	0.331127i	$0.107429\pi$
$614$	53.0748	2.14192
$615$	−25.7538	−1.03849
$616$	7.93169	0.319577
$617$	−7.98675	−0.321535	−0.160767	−	0.986992i	$-0.551397\pi$
$617$	−7.98675	−0.321535	−0.160767	+	0.986992i	$0.551397\pi$
$618$	45.6872	1.83781
$619$	−21.6978	−0.872108	−0.436054	−	0.899920i	$-0.643624\pi$
$619$	−21.6978	−0.872108	−0.436054	+	0.899920i	$0.643624\pi$
$620$	5.65934	0.227285
$621$	−12.7981	−0.513572
$622$	16.4388	0.659137
$623$	19.5292	0.782422
$624$	−41.7810	−1.67258
$625$	−30.5289	−1.22115
$626$	15.0952	0.603325
$627$	−26.4580	−1.05663
$628$	1.37355	0.0548105
$629$	−1.16913	−0.0466163
$630$	−24.7995	−0.988036
$631$	−30.5452	−1.21599	−0.607993	−	0.793942i	$-0.708025\pi$
$631$	−30.5452	−1.21599	−0.607993	+	0.793942i	$0.708025\pi$
$632$	7.33386	0.291725
$633$	−42.1787	−1.67645
$634$	6.72452	0.267065
$635$	48.5305	1.92587
$636$	−2.82626	−0.112069
$637$	8.34744	0.330738
$638$	7.13640	0.282533
$639$	−6.14301	−0.243014
$640$	22.5742	0.892325
$641$	−6.13980	−0.242508	−0.121254	−	0.992622i	$-0.538691\pi$
$641$	−6.13980	−0.242508	−0.121254	+	0.992622i	$0.538691\pi$
$642$	63.2876	2.49776
$643$	7.71227	0.304142	0.152071	−	0.988370i	$-0.451406\pi$
$643$	7.71227	0.304142	0.152071	+	0.988370i	$0.451406\pi$
$644$	−19.2696	−0.759329
$645$	69.8488	2.75029
$646$	−9.78059	−0.384812
$647$	50.0485	1.96761	0.983804	−	0.179245i	$-0.0573655\pi$
$647$	50.0485	1.96761	0.983804	+	0.179245i	$0.0573655\pi$
$648$	−12.8813	−0.506024
$649$	−3.16978	−0.124425
$650$	−11.9787	−0.469842
$651$	10.4941	0.411295
$652$	−7.49586	−0.293560
$653$	15.0061	0.587234	0.293617	−	0.955923i	$-0.405141\pi$
$653$	15.0061	0.587234	0.293617	+	0.955923i	$0.405141\pi$
$654$	60.0246	2.34715
$655$	−33.4157	−1.30566
$656$	−22.3075	−0.870963
$657$	−6.10897	−0.238334
$658$	41.8831	1.63277
$659$	8.74511	0.340661	0.170331	−	0.985387i	$-0.445516\pi$
$659$	8.74511	0.340661	0.170331	+	0.985387i	$0.445516\pi$
$660$	17.6001	0.685085
$661$	−22.7703	−0.885662	−0.442831	−	0.896605i	$-0.646026\pi$
$661$	−22.7703	−0.885662	−0.442831	+	0.896605i	$0.646026\pi$
$662$	−15.6108	−0.606733
$663$	8.59610	0.333845
$664$	−10.9358	−0.424393
$665$	41.4559	1.60759
$666$	3.72426	0.144312
$667$	7.90734	0.306173
$668$	3.70347	0.143292
$669$	3.12279	0.120734
$670$	40.9696	1.58279
$671$	21.3572	0.824486
$672$	−43.5226	−1.67892
$673$	−46.8619	−1.80639	−0.903196	−	0.429228i	$-0.858786\pi$
$673$	−46.8619	−1.80639	−0.903196	+	0.429228i	$0.858786\pi$
$674$	39.9893	1.54033
$675$	−4.54611	−0.174980
$676$	3.58203	0.137770
$677$	−24.2331	−0.931352	−0.465676	−	0.884955i	$-0.654189\pi$
$677$	−24.2331	−0.931352	−0.465676	+	0.884955i	$0.654189\pi$
$678$	31.2175	1.19890
$679$	3.78653	0.145314
$680$	−2.96734	−0.113792
$681$	−52.3610	−2.00648
$682$	−6.70092	−0.256592
$683$	−23.6699	−0.905705	−0.452852	−	0.891586i	$-0.649594\pi$
$683$	−23.6699	−0.905705	−0.452852	+	0.891586i	$0.649594\pi$
$684$	12.6853	0.485033
$685$	−7.69527	−0.294021
$686$	−27.0971	−1.03457
$687$	8.49627	0.324153
$688$	60.5020	2.30662
$689$	−3.73603	−0.142331
$690$	47.8972	1.82342
$691$	−15.4009	−0.585878	−0.292939	−	0.956131i	$-0.594633\pi$
$691$	−15.4009	−0.585878	−0.292939	+	0.956131i	$0.594633\pi$
$692$	26.3497	1.00166
$693$	11.9555	0.454153
$694$	−25.6308	−0.972931
$695$	3.61456	0.137108
$696$	4.25981	0.161468
$697$	4.58959	0.173843
$698$	2.94202	0.111357
$699$	−9.34651	−0.353517
$700$	−6.84488	−0.258712
$701$	−6.10988	−0.230767	−0.115384	−	0.993321i	$-0.536810\pi$
$701$	−6.10988	−0.230767	−0.115384	+	0.993321i	$0.536810\pi$
$702$	19.9831	0.754212
$703$	−6.22564	−0.234805
$704$	5.59315	0.210800
$705$	−42.3870	−1.59639
$706$	−54.3476	−2.04540
$707$	7.53189	0.283266
$708$	4.14856	0.155912
$709$	39.0317	1.46587	0.732934	−	0.680300i	$-0.238150\pi$
$709$	39.0317	1.46587	0.732934	+	0.680300i	$0.238150\pi$
$710$	−16.7775	−0.629649
$711$	11.0544	0.414573
$712$	−7.44368	−0.278964
$713$	−7.42482	−0.278062
$714$	12.0643	0.451495
$715$	23.2656	0.870084
$716$	−3.38258	−0.126413
$717$	17.9529	0.670464
$718$	−1.58846	−0.0592809
$719$	4.02571	0.150134	0.0750668	−	0.997179i	$-0.476083\pi$
$719$	4.02571	0.150134	0.0750668	+	0.997179i	$0.476083\pi$
$720$	21.7394	0.810181
$721$	34.5104	1.28523
$722$	−17.1841	−0.639527
$723$	−6.57216	−0.244421
$724$	3.80365	0.141361
$725$	2.80881	0.104317
$726$	23.1214	0.858117
$727$	42.3571	1.57094	0.785470	−	0.618900i	$-0.212421\pi$
$727$	42.3571	1.57094	0.785470	+	0.618900i	$0.212421\pi$
$728$	−13.7224	−0.508588
$729$	−1.43989	−0.0533291
$730$	−16.6845	−0.617523
$731$	−12.4478	−0.460398
$732$	−27.9520	−1.03313
$733$	30.1325	1.11297	0.556485	−	0.830858i	$-0.312150\pi$
$733$	30.1325	1.11297	0.556485	+	0.830858i	$0.312150\pi$
$734$	62.6534	2.31258
$735$	−11.8563	−0.437325
$736$	30.7934	1.13506
$737$	−19.7509	−0.727534
$738$	−14.6201	−0.538175
$739$	9.93611	0.365506	0.182753	−	0.983159i	$-0.441499\pi$
$739$	9.93611	0.365506	0.182753	+	0.983159i	$0.441499\pi$
$740$	4.14136	0.152240
$741$	45.7744	1.68157
$742$	−5.24337	−0.192490
$743$	4.81688	0.176714	0.0883572	−	0.996089i	$-0.471838\pi$
$743$	4.81688	0.176714	0.0883572	+	0.996089i	$0.471838\pi$
$744$	−3.99987	−0.146642
$745$	−2.98409	−0.109328
$746$	21.7856	0.797628
$747$	−16.4837	−0.603108
$748$	−3.13653	−0.114683
$749$	47.8051	1.74676
$750$	−34.5185	−1.26044
$751$	−18.4567	−0.673493	−0.336747	−	0.941595i	$-0.609327\pi$
$751$	−18.4567	−0.673493	−0.336747	+	0.941595i	$0.609327\pi$
$752$	−36.7150	−1.33886
$753$	−50.1929	−1.82913
$754$	−12.3465	−0.449634
$755$	38.7488	1.41021
$756$	11.4188	0.415297
$757$	−5.22771	−0.190004	−0.0950022	−	0.995477i	$-0.530286\pi$
$757$	−5.22771	−0.190004	−0.0950022	+	0.995477i	$0.530286\pi$
$758$	63.7811	2.31663
$759$	−23.0906	−0.838137
$760$	−15.8012	−0.573169
$761$	25.6719	0.930604	0.465302	−	0.885152i	$-0.345946\pi$
$761$	25.6719	0.930604	0.465302	+	0.885152i	$0.345946\pi$
$762$	75.2057	2.72442
$763$	45.3403	1.64143
$764$	23.9759	0.867416
$765$	−4.47271	−0.161711
$766$	10.4690	0.378260
$767$	5.48397	0.198015
$768$	45.6412	1.64694
$769$	42.4952	1.53241	0.766207	−	0.642593i	$-0.222142\pi$
$769$	42.4952	1.53241	0.766207	+	0.642593i	$0.222142\pi$
$770$	32.6524	1.17671
$771$	20.4223	0.735492
$772$	30.2212	1.08769
$773$	−4.27947	−0.153922	−0.0769609	−	0.997034i	$-0.524522\pi$
$773$	−4.27947	−0.153922	−0.0769609	+	0.997034i	$0.524522\pi$
$774$	39.6524	1.42528
$775$	−2.63742	−0.0947388
$776$	−1.44326	−0.0518099
$777$	7.67929	0.275493
$778$	59.5970	2.13666
$779$	24.4397	0.875642
$780$	−30.4496	−1.09027
$781$	8.08822	0.289419
$782$	−8.53579	−0.305239
$783$	−4.68572	−0.167454
$784$	−10.2697	−0.366776
$785$	−2.57891	−0.0920454
$786$	−51.7830	−1.84704
$787$	−1.73559	−0.0618672	−0.0309336	−	0.999521i	$-0.509848\pi$
$787$	−1.73559	−0.0618672	−0.0309336	+	0.999521i	$0.509848\pi$
$788$	−31.4447	−1.12017
$789$	−6.08140	−0.216504
$790$	30.1913	1.07416
$791$	23.5806	0.838428
$792$	−4.55692	−0.161923
$793$	−36.9497	−1.31212
$794$	−26.4521	−0.938750
$795$	5.30646	0.188201
$796$	3.68007	0.130437
$797$	0.617912	0.0218876	0.0109438	−	0.999940i	$-0.496516\pi$
$797$	0.617912	0.0218876	0.0109438	+	0.999940i	$0.496516\pi$
$798$	64.2426	2.27416
$799$	7.55382	0.267235
$800$	10.9383	0.386728
$801$	−11.2199	−0.396437
$802$	71.1402	2.51205
$803$	8.04340	0.283846
$804$	25.8497	0.911648
$805$	36.1798	1.27517
$806$	11.5931	0.408350
$807$	13.1268	0.462086
$808$	−2.87082	−0.100995
$809$	−28.7460	−1.01065	−0.505327	−	0.862928i	$-0.668628\pi$
$809$	−28.7460	−1.01065	−0.505327	+	0.862928i	$0.668628\pi$
$810$	−53.0283	−1.86322
$811$	16.7748	0.589043	0.294522	−	0.955645i	$-0.404840\pi$
$811$	16.7748	0.589043	0.294522	+	0.955645i	$0.404840\pi$
$812$	−7.05509	−0.247585
$813$	28.2602	0.991127
$814$	−4.90357	−0.171870
$815$	14.0739	0.492987
$816$	−10.5757	−0.370222
$817$	−66.2848	−2.31901
$818$	−2.77611	−0.0970644
$819$	−20.6840	−0.722757
$820$	−16.2575	−0.567738
$821$	−0.777606	−0.0271386	−0.0135693	−	0.999908i	$-0.504319\pi$
$821$	−0.777606	−0.0271386	−0.0135693	+	0.999908i	$0.504319\pi$
$822$	−11.9250	−0.415934
$823$	−40.0778	−1.39702	−0.698511	−	0.715599i	$-0.746154\pi$
$823$	−40.0778	−1.39702	−0.698511	+	0.715599i	$0.746154\pi$
$824$	−13.1538	−0.458236
$825$	−8.20217	−0.285563
$826$	7.69654	0.267797
$827$	−2.42978	−0.0844916	−0.0422458	−	0.999107i	$-0.513451\pi$
$827$	−2.42978	−0.0844916	−0.0422458	+	0.999107i	$0.513451\pi$
$828$	11.0708	0.384736
$829$	48.1683	1.67295	0.836477	−	0.548002i	$-0.184611\pi$
$829$	48.1683	1.67295	0.836477	+	0.548002i	$0.184611\pi$
$830$	−45.0196	−1.56265
$831$	14.6357	0.507707
$832$	−9.67659	−0.335475
$833$	2.11291	0.0732081
$834$	5.60133	0.193958
$835$	−6.95347	−0.240635
$836$	−16.7021	−0.577654
$837$	4.39979	0.152079
$838$	−27.4012	−0.946560
$839$	12.6492	0.436699	0.218350	−	0.975871i	$-0.429933\pi$
$839$	12.6492	0.436699	0.218350	+	0.975871i	$0.429933\pi$
$840$	19.4906	0.672491
$841$	−26.1049	−0.900170
$842$	10.9631	0.377812
$843$	51.9028	1.78763
$844$	−26.6261	−0.916508
$845$	−6.72546	−0.231363
$846$	−24.0627	−0.827292
$847$	17.4651	0.600107
$848$	4.59638	0.157840
$849$	13.7196	0.470856
$850$	−3.03205	−0.103999
$851$	−5.43329	−0.186251
$852$	−10.5857	−0.362661
$853$	−21.3683	−0.731636	−0.365818	−	0.930686i	$-0.619211\pi$
$853$	−21.3683	−0.731636	−0.365818	+	0.930686i	$0.619211\pi$
$854$	−51.8574	−1.77452
$855$	−23.8173	−0.814534
$856$	−18.2212	−0.622787
$857$	−55.1768	−1.88480	−0.942402	−	0.334483i	$-0.891438\pi$
$857$	−55.1768	−1.88480	−0.942402	+	0.334483i	$0.891438\pi$
$858$	36.0538	1.23086
$859$	−5.04691	−0.172198	−0.0860991	−	0.996287i	$-0.527440\pi$
$859$	−5.04691	−0.172198	−0.0860991	+	0.996287i	$0.527440\pi$
$860$	44.0933	1.50357
$861$	−30.1462	−1.02738
$862$	−22.1760	−0.755318
$863$	−30.4127	−1.03526	−0.517629	−	0.855605i	$-0.673185\pi$
$863$	−30.4127	−1.03526	−0.517629	+	0.855605i	$0.673185\pi$
$864$	−18.2475	−0.620793
$865$	−49.4730	−1.68213
$866$	50.7363	1.72409
$867$	2.17585	0.0738959
$868$	6.62457	0.224853
$869$	−14.5548	−0.493739
$870$	17.5364	0.594539
$871$	34.1706	1.15783
$872$	−17.2817	−0.585233
$873$	−2.17544	−0.0736274
$874$	−45.4533	−1.53748
$875$	−26.0740	−0.881461
$876$	−10.5271	−0.355677
$877$	19.1961	0.648206	0.324103	−	0.946022i	$-0.394938\pi$
$877$	19.1961	0.648206	0.324103	+	0.946022i	$0.394938\pi$
$878$	−40.5723	−1.36925
$879$	−39.9010	−1.34583
$880$	−28.6233	−0.964892
$881$	−39.5294	−1.33178	−0.665889	−	0.746051i	$-0.731948\pi$
$881$	−39.5294	−1.33178	−0.665889	+	0.746051i	$0.731948\pi$
$882$	−6.73069	−0.226634
$883$	−38.6919	−1.30209	−0.651044	−	0.759040i	$-0.725669\pi$
$883$	−38.6919	−1.30209	−0.651044	+	0.759040i	$0.725669\pi$
$884$	5.42645	0.182511
$885$	−7.78915	−0.261829
$886$	7.18680	0.241445
$887$	6.81243	0.228739	0.114369	−	0.993438i	$-0.463515\pi$
$887$	6.81243	0.228739	0.114369	+	0.993438i	$0.463515\pi$
$888$	−2.92701	−0.0982239
$889$	56.8076	1.90527
$890$	−30.6434	−1.02717
$891$	25.5643	0.856435
$892$	1.97132	0.0660045
$893$	40.2242	1.34605
$894$	−4.62432	−0.154660
$895$	6.35099	0.212290
$896$	26.4244	0.882777
$897$	39.9486	1.33385
$898$	30.3586	1.01308
$899$	−2.71841	−0.0906641
$900$	3.93252	0.131084
$901$	−0.945668	−0.0315048
$902$	19.2497	0.640944
$903$	81.7618	2.72086
$904$	−8.98787	−0.298932
$905$	−7.14156	−0.237394
$906$	60.0474	1.99494
$907$	−2.39037	−0.0793711	−0.0396855	−	0.999212i	$-0.512636\pi$
$907$	−2.39037	−0.0793711	−0.0396855	+	0.999212i	$0.512636\pi$
$908$	−33.0539	−1.09693
$909$	−4.32723	−0.143525
$910$	−56.4912	−1.87266
$911$	−4.74627	−0.157251	−0.0786255	−	0.996904i	$-0.525053\pi$
$911$	−4.74627	−0.157251	−0.0786255	+	0.996904i	$0.525053\pi$
$912$	−56.3156	−1.86480
$913$	21.7034	0.718277
$914$	−12.1179	−0.400823
$915$	52.4814	1.73498
$916$	5.36343	0.177213
$917$	−39.1150	−1.29169
$918$	5.05813	0.166943
$919$	44.9597	1.48308	0.741541	−	0.670907i	$-0.234095\pi$
$919$	44.9597	1.48308	0.741541	+	0.670907i	$0.234095\pi$
$920$	−13.7901	−0.454647
$921$	−62.8745	−2.07178
$922$	−49.8817	−1.64277
$923$	−13.9933	−0.460594
$924$	20.6019	0.677754
$925$	−1.92999	−0.0634578
$926$	−23.3134	−0.766124
$927$	−19.8269	−0.651202
$928$	11.2742	0.370094
$929$	−14.6130	−0.479438	−0.239719	−	0.970842i	$-0.577055\pi$
$929$	−14.6130	−0.479438	−0.239719	+	0.970842i	$0.577055\pi$
$930$	−16.4663	−0.539950
$931$	11.2513	0.368747
$932$	−5.90016	−0.193266
$933$	−19.4741	−0.637553
$934$	−31.1288	−1.01857
$935$	5.88901	0.192591
$936$	7.88383	0.257691
$937$	43.1069	1.40824	0.704121	−	0.710080i	$-0.251341\pi$
$937$	43.1069	1.40824	0.704121	+	0.710080i	$0.251341\pi$
$938$	47.9572	1.56586
$939$	−17.8824	−0.583569
$940$	−26.7576	−0.872737
$941$	−26.6010	−0.867167	−0.433584	−	0.901113i	$-0.642751\pi$
$941$	−26.6010	−0.867167	−0.433584	+	0.901113i	$0.642751\pi$
$942$	−3.99644	−0.130211
$943$	21.3292	0.694574
$944$	−6.74685	−0.219591
$945$	−21.4394	−0.697423
$946$	−52.2085	−1.69745
$947$	14.8830	0.483631	0.241816	−	0.970322i	$-0.422257\pi$
$947$	14.8830	0.483631	0.241816	+	0.970322i	$0.422257\pi$
$948$	19.0491	0.618687
$949$	−13.9157	−0.451723
$950$	−16.1457	−0.523837
$951$	−7.96613	−0.258319
$952$	−3.47344	−0.112575
$953$	−56.2397	−1.82178	−0.910892	−	0.412645i	$-0.864605\pi$
$953$	−56.2397	−1.82178	−0.910892	+	0.412645i	$0.864605\pi$
$954$	3.01242	0.0975308
$955$	−45.0160	−1.45668
$956$	11.3331	0.366539
$957$	−8.45406	−0.273281
$958$	5.37749	0.173739
$959$	−9.00774	−0.290875
$960$	13.7441	0.443590
$961$	−28.4475	−0.917660
$962$	8.48356	0.273521
$963$	−27.4650	−0.885047
$964$	−4.14880	−0.133624
$965$	−56.7420	−1.82659
$966$	56.0663	1.80390
$967$	45.4798	1.46253	0.731266	−	0.682092i	$-0.238930\pi$
$967$	45.4798	1.46253	0.731266	+	0.682092i	$0.238930\pi$
$968$	−6.65691	−0.213961
$969$	11.5865	0.372211
$970$	−5.94145	−0.190769
$971$	40.7354	1.30726	0.653631	−	0.756813i	$-0.273245\pi$
$971$	40.7354	1.30726	0.653631	+	0.756813i	$0.273245\pi$
$972$	−22.1103	−0.709187
$973$	4.23104	0.135641
$974$	−39.5301	−1.26663
$975$	14.1904	0.454457
$976$	45.4586	1.45510
$977$	27.5600	0.881722	0.440861	−	0.897575i	$-0.354673\pi$
$977$	27.5600	0.881722	0.440861	+	0.897575i	$0.354673\pi$
$978$	21.8097	0.697399
$979$	14.7728	0.472140
$980$	−7.48449	−0.239083
$981$	−26.0490	−0.831679
$982$	−55.8933	−1.78363
$983$	44.6643	1.42457	0.712284	−	0.701891i	$-0.247661\pi$
$983$	44.6643	1.42457	0.712284	+	0.701891i	$0.247661\pi$
$984$	11.4904	0.366300
$985$	59.0393	1.88115
$986$	−3.12517	−0.0995256
$987$	−49.6163	−1.57931
$988$	28.8960	0.919303
$989$	−57.8486	−1.83948
$990$	−18.7595	−0.596215
$991$	−55.0404	−1.74842	−0.874209	−	0.485550i	$-0.838619\pi$
$991$	−55.0404	−1.74842	−0.874209	+	0.485550i	$0.838619\pi$
$992$	−10.5863	−0.336114
$993$	18.4932	0.586865
$994$	−19.6390	−0.622911
$995$	−6.90954	−0.219047
$996$	−28.4050	−0.900047
$997$	19.5380	0.618776	0.309388	−	0.950936i	$-0.399876\pi$
$997$	19.5380	0.618776	0.309388	+	0.950936i	$0.399876\pi$
$998$	66.3749	2.10106
$999$	3.21966	0.101865

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2669.2.a.b.1.9	✓	45

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2669.2.a.b.1.9	✓	45	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:	\( N \)	\(=\)	\( 2669 = 17 \cdot 157 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2669.a (trivial)

\(f(q)\)	\(=\)	\(q-1.83672 q^{2} +2.17585 q^{3} +1.37355 q^{4} -2.57891 q^{5} -3.99644 q^{6} -3.01876 q^{7} +1.15062 q^{8} +1.73434 q^{9} +O(q^{10})\)	\(q-1.83672 q^{2} +2.17585 q^{3} +1.37355 q^{4} -2.57891 q^{5} -3.99644 q^{6} -3.01876 q^{7} +1.15062 q^{8} +1.73434 q^{9} +4.73675 q^{10} -2.28353 q^{11} +2.98864 q^{12} +3.95068 q^{13} +5.54462 q^{14} -5.61134 q^{15} -4.86046 q^{16} +1.00000 q^{17} -3.18550 q^{18} +5.32502 q^{19} -3.54226 q^{20} -6.56838 q^{21} +4.19420 q^{22} +4.64730 q^{23} +2.50358 q^{24} +1.65080 q^{25} -7.25630 q^{26} -2.75389 q^{27} -4.14641 q^{28} +1.70149 q^{29} +10.3065 q^{30} -1.59766 q^{31} +6.62608 q^{32} -4.96862 q^{33} -1.83672 q^{34} +7.78512 q^{35} +2.38220 q^{36} -1.16913 q^{37} -9.78059 q^{38} +8.59610 q^{39} -2.96734 q^{40} +4.58959 q^{41} +12.0643 q^{42} -12.4478 q^{43} -3.13653 q^{44} -4.47271 q^{45} -8.53579 q^{46} +7.55382 q^{47} -10.5757 q^{48} +2.11291 q^{49} -3.03205 q^{50} +2.17585 q^{51} +5.42645 q^{52} -0.945668 q^{53} +5.05813 q^{54} +5.88901 q^{55} -3.47344 q^{56} +11.5865 q^{57} -3.12517 q^{58} +1.38811 q^{59} -7.70745 q^{60} -9.35274 q^{61} +2.93446 q^{62} -5.23556 q^{63} -2.44935 q^{64} -10.1885 q^{65} +9.12597 q^{66} +8.64931 q^{67} +1.37355 q^{68} +10.1118 q^{69} -14.2991 q^{70} -3.54199 q^{71} +1.99556 q^{72} -3.52236 q^{73} +2.14737 q^{74} +3.59189 q^{75} +7.31417 q^{76} +6.89342 q^{77} -15.7886 q^{78} +6.37385 q^{79} +12.5347 q^{80} -11.1951 q^{81} -8.42981 q^{82} -9.50432 q^{83} -9.02199 q^{84} -2.57891 q^{85} +22.8631 q^{86} +3.70220 q^{87} -2.62746 q^{88} -6.46929 q^{89} +8.21513 q^{90} -11.9262 q^{91} +6.38329 q^{92} -3.47628 q^{93} -13.8743 q^{94} -13.7328 q^{95} +14.4174 q^{96} -1.25433 q^{97} -3.88084 q^{98} -3.96041 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 45 q - 2 q^{2} - 20 q^{3} + 34 q^{4} - 10 q^{5} - 14 q^{6} - 20 q^{7} - 9 q^{8} + 39 q^{9}+O(q^{10}) \) 45 * q - 2 * q^2 - 20 * q^3 + 34 * q^4 - 10 * q^5 - 14 * q^6 - 20 * q^7 - 9 * q^8 + 39 * q^9	\( 45 q - 2 q^{2} - 20 q^{3} + 34 q^{4} - 10 q^{5} - 14 q^{6} - 20 q^{7} - 9 q^{8} + 39 q^{9} - 21 q^{10} - 26 q^{11} - 23 q^{12} - 6 q^{13} - 7 q^{14} - 10 q^{15} + 20 q^{16} + 45 q^{17} - 3 q^{18} - 56 q^{19} - 26 q^{20} + 2 q^{21} - 23 q^{22} - 38 q^{23} - 35 q^{24} + 27 q^{25} - 10 q^{26} - 71 q^{27} - 29 q^{28} - 29 q^{29} + 9 q^{30} - 57 q^{31} + 4 q^{33} - 2 q^{34} - 16 q^{35} + 44 q^{36} - 14 q^{37} - 6 q^{38} - 25 q^{39} - 48 q^{40} - 23 q^{41} - q^{42} - 43 q^{43} - 29 q^{44} - 63 q^{45} - 42 q^{46} + 11 q^{47} - 6 q^{48} - 9 q^{49} + 14 q^{50} - 20 q^{51} - 27 q^{52} + 7 q^{53} + 10 q^{54} - 41 q^{55} - 14 q^{56} - 5 q^{57} - 58 q^{58} - 59 q^{59} + q^{60} - 40 q^{61} - 34 q^{62} - 56 q^{63} - 67 q^{64} - 3 q^{65} - 53 q^{66} - 44 q^{67} + 34 q^{68} - 17 q^{69} + 14 q^{70} - 18 q^{71} - 25 q^{72} - 2 q^{73} - 5 q^{74} - 85 q^{75} - 123 q^{76} - 4 q^{77} + 33 q^{78} - 119 q^{79} - 17 q^{80} + 21 q^{81} - 6 q^{82} - 32 q^{83} + 54 q^{84} - 10 q^{85} - 14 q^{86} - 3 q^{87} - 33 q^{88} - 25 q^{89} - 23 q^{90} - 177 q^{91} - 62 q^{92} + 36 q^{93} - 64 q^{94} - 47 q^{95} - 153 q^{96} - 82 q^{97} + 13 q^{98} - 45 q^{99}+O(q^{100}) \) 45 * q - 2 * q^2 - 20 * q^3 + 34 * q^4 - 10 * q^5 - 14 * q^6 - 20 * q^7 - 9 * q^8 + 39 * q^9 - 21 * q^10 - 26 * q^11 - 23 * q^12 - 6 * q^13 - 7 * q^14 - 10 * q^15 + 20 * q^16 + 45 * q^17 - 3 * q^18 - 56 * q^19 - 26 * q^20 + 2 * q^21 - 23 * q^22 - 38 * q^23 - 35 * q^24 + 27 * q^25 - 10 * q^26 - 71 * q^27 - 29 * q^28 - 29 * q^29 + 9 * q^30 - 57 * q^31 + 4 * q^33 - 2 * q^34 - 16 * q^35 + 44 * q^36 - 14 * q^37 - 6 * q^38 - 25 * q^39 - 48 * q^40 - 23 * q^41 - q^42 - 43 * q^43 - 29 * q^44 - 63 * q^45 - 42 * q^46 + 11 * q^47 - 6 * q^48 - 9 * q^49 + 14 * q^50 - 20 * q^51 - 27 * q^52 + 7 * q^53 + 10 * q^54 - 41 * q^55 - 14 * q^56 - 5 * q^57 - 58 * q^58 - 59 * q^59 + q^60 - 40 * q^61 - 34 * q^62 - 56 * q^63 - 67 * q^64 - 3 * q^65 - 53 * q^66 - 44 * q^67 + 34 * q^68 - 17 * q^69 + 14 * q^70 - 18 * q^71 - 25 * q^72 - 2 * q^73 - 5 * q^74 - 85 * q^75 - 123 * q^76 - 4 * q^77 + 33 * q^78 - 119 * q^79 - 17 * q^80 + 21 * q^81 - 6 * q^82 - 32 * q^83 + 54 * q^84 - 10 * q^85 - 14 * q^86 - 3 * q^87 - 33 * q^88 - 25 * q^89 - 23 * q^90 - 177 * q^91 - 62 * q^92 + 36 * q^93 - 64 * q^94 - 47 * q^95 - 153 * q^96 - 82 * q^97 + 13 * q^98 - 45 * q^99

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