LMFDB - Embedded newform 2671.2.a.b.1.50

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2671,2,Mod(1,2671)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2671, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("2671.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2671 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2671.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:	$21.3280423799$
Analytic rank:	$0$
Dimension:	$122$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.50
Character	$\chi$	$=$	2671.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.509370 q^{2} -0.885422 q^{3} -1.74054 q^{4} +0.504334 q^{5} +0.451007 q^{6} -3.65254 q^{7} +1.90532 q^{8} -2.21603 q^{9} +O(q^{10})$	\(q-0.509370 q^{2} -0.885422 q^{3} -1.74054 q^{4} +0.504334 q^{5} +0.451007 q^{6} -3.65254 q^{7} +1.90532 q^{8} -2.21603 q^{9} -0.256893 q^{10} -6.04584 q^{11} +1.54111 q^{12} +3.96193 q^{13} +1.86049 q^{14} -0.446549 q^{15} +2.51057 q^{16} +4.52663 q^{17} +1.12878 q^{18} -4.95465 q^{19} -0.877815 q^{20} +3.23404 q^{21} +3.07957 q^{22} -8.25605 q^{23} -1.68701 q^{24} -4.74565 q^{25} -2.01809 q^{26} +4.61839 q^{27} +6.35740 q^{28} -6.63563 q^{29} +0.227458 q^{30} -3.12824 q^{31} -5.08945 q^{32} +5.35312 q^{33} -2.30573 q^{34} -1.84210 q^{35} +3.85709 q^{36} -8.78745 q^{37} +2.52375 q^{38} -3.50798 q^{39} +0.960918 q^{40} -2.32573 q^{41} -1.64732 q^{42} -8.13127 q^{43} +10.5230 q^{44} -1.11762 q^{45} +4.20538 q^{46} +4.33187 q^{47} -2.22292 q^{48} +6.34104 q^{49} +2.41729 q^{50} -4.00798 q^{51} -6.89590 q^{52} +3.07080 q^{53} -2.35246 q^{54} -3.04913 q^{55} -6.95925 q^{56} +4.38695 q^{57} +3.37999 q^{58} +7.63472 q^{59} +0.777237 q^{60} -7.33160 q^{61} +1.59343 q^{62} +8.09413 q^{63} -2.42874 q^{64} +1.99814 q^{65} -2.72672 q^{66} +16.1404 q^{67} -7.87879 q^{68} +7.31009 q^{69} +0.938310 q^{70} -15.5563 q^{71} -4.22224 q^{72} +13.7880 q^{73} +4.47606 q^{74} +4.20190 q^{75} +8.62378 q^{76} +22.0827 q^{77} +1.78686 q^{78} -6.91854 q^{79} +1.26617 q^{80} +2.55887 q^{81} +1.18466 q^{82} -0.611787 q^{83} -5.62898 q^{84} +2.28293 q^{85} +4.14182 q^{86} +5.87533 q^{87} -11.5193 q^{88} -2.19980 q^{89} +0.569281 q^{90} -14.4711 q^{91} +14.3700 q^{92} +2.76981 q^{93} -2.20652 q^{94} -2.49880 q^{95} +4.50631 q^{96} -5.20264 q^{97} -3.22993 q^{98} +13.3978 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 122 q + 14 q^{2} + 10 q^{3} + 128 q^{4} + 33 q^{5} + 22 q^{6} + 6 q^{7} + 36 q^{8} + 162 q^{9}+O(q^{10}) $ 122 * q + 14 * q^2 + 10 * q^3 + 128 * q^4 + 33 * q^5 + 22 * q^6 + 6 * q^7 + 36 * q^8 + 162 * q^9	\( 122 q + 14 q^{2} + 10 q^{3} + 128 q^{4} + 33 q^{5} + 22 q^{6} + 6 q^{7} + 36 q^{8} + 162 q^{9} + 16 q^{10} + 43 q^{11} + 23 q^{12} + 25 q^{13} + 45 q^{14} + 12 q^{15} + 132 q^{16} + 103 q^{17} + 30 q^{18} + 37 q^{19} + 63 q^{20} + 81 q^{21} + 15 q^{23} + 60 q^{24} + 151 q^{25} + 59 q^{26} + 22 q^{27} - 3 q^{28} + 80 q^{29} - 9 q^{30} + 15 q^{31} + 66 q^{32} + 93 q^{33} + 30 q^{34} + 23 q^{35} + 162 q^{36} + 18 q^{37} + 41 q^{38} + 10 q^{39} + 29 q^{40} + 249 q^{41} - 8 q^{42} + 14 q^{43} + 100 q^{44} + 59 q^{45} + 11 q^{46} + 57 q^{47} + 33 q^{48} + 180 q^{49} + 63 q^{50} + 26 q^{51} + 31 q^{52} + 65 q^{53} + 65 q^{54} - 8 q^{55} + 120 q^{56} + 57 q^{57} - 31 q^{58} + 108 q^{59} - q^{60} + 70 q^{61} + 25 q^{62} - 7 q^{63} + 100 q^{64} + 171 q^{65} + 12 q^{66} - 6 q^{67} + 184 q^{68} + 64 q^{69} - 24 q^{70} + 47 q^{71} + 53 q^{72} + 76 q^{73} + 66 q^{74} + 40 q^{75} + 32 q^{76} + 73 q^{77} - 19 q^{78} + 8 q^{79} + 115 q^{80} + 250 q^{81} - 13 q^{82} + 116 q^{83} + 159 q^{84} + 31 q^{85} + 91 q^{86} + 25 q^{87} - 43 q^{88} + 361 q^{89} + 32 q^{90} + 7 q^{91} + 5 q^{92} + 18 q^{93} + 23 q^{94} + 42 q^{95} + 77 q^{96} + 79 q^{97} + 56 q^{98} + 74 q^{99}+O(q^{100}) \) 122 * q + 14 * q^2 + 10 * q^3 + 128 * q^4 + 33 * q^5 + 22 * q^6 + 6 * q^7 + 36 * q^8 + 162 * q^9 + 16 * q^10 + 43 * q^11 + 23 * q^12 + 25 * q^13 + 45 * q^14 + 12 * q^15 + 132 * q^16 + 103 * q^17 + 30 * q^18 + 37 * q^19 + 63 * q^20 + 81 * q^21 + 15 * q^23 + 60 * q^24 + 151 * q^25 + 59 * q^26 + 22 * q^27 - 3 * q^28 + 80 * q^29 - 9 * q^30 + 15 * q^31 + 66 * q^32 + 93 * q^33 + 30 * q^34 + 23 * q^35 + 162 * q^36 + 18 * q^37 + 41 * q^38 + 10 * q^39 + 29 * q^40 + 249 * q^41 - 8 * q^42 + 14 * q^43 + 100 * q^44 + 59 * q^45 + 11 * q^46 + 57 * q^47 + 33 * q^48 + 180 * q^49 + 63 * q^50 + 26 * q^51 + 31 * q^52 + 65 * q^53 + 65 * q^54 - 8 * q^55 + 120 * q^56 + 57 * q^57 - 31 * q^58 + 108 * q^59 - q^60 + 70 * q^61 + 25 * q^62 - 7 * q^63 + 100 * q^64 + 171 * q^65 + 12 * q^66 - 6 * q^67 + 184 * q^68 + 64 * q^69 - 24 * q^70 + 47 * q^71 + 53 * q^72 + 76 * q^73 + 66 * q^74 + 40 * q^75 + 32 * q^76 + 73 * q^77 - 19 * q^78 + 8 * q^79 + 115 * q^80 + 250 * q^81 - 13 * q^82 + 116 * q^83 + 159 * q^84 + 31 * q^85 + 91 * q^86 + 25 * q^87 - 43 * q^88 + 361 * q^89 + 32 * q^90 + 7 * q^91 + 5 * q^92 + 18 * q^93 + 23 * q^94 + 42 * q^95 + 77 * q^96 + 79 * q^97 + 56 * q^98 + 74 * 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 $

$2$	−0.509370	−0.360179	−0.180089	−	0.983650i	$-0.557639\pi$
$2$	−0.509370	−0.360179	−0.180089	+	0.983650i	$0.557639\pi$
$3$	−0.885422	−0.511199	−0.255599	−	0.966783i	$-0.582273\pi$
$3$	−0.885422	−0.511199	−0.255599	+	0.966783i	$0.582273\pi$
$4$	−1.74054	−0.870271
$5$	0.504334	0.225545	0.112773	−	0.993621i	$-0.464027\pi$
$5$	0.504334	0.225545	0.112773	+	0.993621i	$0.464027\pi$
$6$	0.451007	0.184123
$7$	−3.65254	−1.38053	−0.690265	−	0.723557i	$-0.742506\pi$
$7$	−3.65254	−1.38053	−0.690265	+	0.723557i	$0.742506\pi$
$8$	1.90532	0.673632
$9$	−2.21603	−0.738676
$10$	−0.256893	−0.0812366
$11$	−6.04584	−1.82289	−0.911445	−	0.411422i	$-0.865032\pi$
$11$	−6.04584	−1.82289	−0.911445	+	0.411422i	$0.865032\pi$
$12$	1.54111	0.444881
$13$	3.96193	1.09884	0.549421	−	0.835546i	$-0.314849\pi$
$13$	3.96193	1.09884	0.549421	+	0.835546i	$0.314849\pi$
$14$	1.86049	0.497237
$15$	−0.446549	−0.115298
$16$	2.51057	0.627644
$17$	4.52663	1.09787	0.548934	−	0.835865i	$-0.315034\pi$
$17$	4.52663	1.09787	0.548934	+	0.835865i	$0.315034\pi$
$18$	1.12878	0.266055
$19$	−4.95465	−1.13667	−0.568337	−	0.822796i	$-0.692413\pi$
$19$	−4.95465	−1.13667	−0.568337	+	0.822796i	$0.692413\pi$
$20$	−0.877815	−0.196286
$21$	3.23404	0.705725
$22$	3.07957	0.656566
$23$	−8.25605	−1.72151	−0.860753	−	0.509023i	$-0.830007\pi$
$23$	−8.25605	−1.72151	−0.860753	+	0.509023i	$0.830007\pi$
$24$	−1.68701	−0.344360
$25$	−4.74565	−0.949129
$26$	−2.01809	−0.395779
$27$	4.61839	0.888809
$28$	6.35740	1.20144
$29$	−6.63563	−1.23221	−0.616103	−	0.787666i	$-0.711289\pi$
$29$	−6.63563	−1.23221	−0.616103	+	0.787666i	$0.711289\pi$
$30$	0.227458	0.0415280
$31$	−3.12824	−0.561848	−0.280924	−	0.959730i	$-0.590641\pi$
$31$	−3.12824	−0.561848	−0.280924	+	0.959730i	$0.590641\pi$
$32$	−5.08945	−0.899696
$33$	5.35312	0.931859
$34$	−2.30573	−0.395429
$35$	−1.84210	−0.311372
$36$	3.85709	0.642849
$37$	−8.78745	−1.44465	−0.722324	−	0.691554i	$-0.756926\pi$
$37$	−8.78745	−1.44465	−0.722324	+	0.691554i	$0.756926\pi$
$38$	2.52375	0.409406
$39$	−3.50798	−0.561726
$40$	0.960918	0.151934
$41$	−2.32573	−0.363218	−0.181609	−	0.983371i	$-0.558130\pi$
$41$	−2.32573	−0.363218	−0.181609	+	0.983371i	$0.558130\pi$
$42$	−1.64732	−0.254187
$43$	−8.13127	−1.24001	−0.620004	−	0.784599i	$-0.712869\pi$
$43$	−8.13127	−1.24001	−0.620004	+	0.784599i	$0.712869\pi$
$44$	10.5230	1.58641
$45$	−1.11762	−0.166605
$46$	4.20538	0.620049
$47$	4.33187	0.631868	0.315934	−	0.948781i	$-0.397682\pi$
$47$	4.33187	0.631868	0.315934	+	0.948781i	$0.397682\pi$
$48$	−2.22292	−0.320850
$49$	6.34104	0.905862
$50$	2.41729	0.341856
$51$	−4.00798	−0.561229
$52$	−6.89590	−0.956290
$53$	3.07080	0.421806	0.210903	−	0.977507i	$-0.432360\pi$
$53$	3.07080	0.421806	0.210903	+	0.977507i	$0.432360\pi$
$54$	−2.35246	−0.320130
$55$	−3.04913	−0.411144
$56$	−6.95925	−0.929969
$57$	4.38695	0.581066
$58$	3.37999	0.443814
$59$	7.63472	0.993956	0.496978	−	0.867763i	$-0.334443\pi$
$59$	7.63472	0.993956	0.496978	+	0.867763i	$0.334443\pi$
$60$	0.777237	0.100341
$61$	−7.33160	−0.938715	−0.469357	−	0.883008i	$-0.655514\pi$
$61$	−7.33160	−0.938715	−0.469357	+	0.883008i	$0.655514\pi$
$62$	1.59343	0.202366
$63$	8.09413	1.01976
$64$	−2.42874	−0.303592
$65$	1.99814	0.247838
$66$	−2.72672	−0.335636
$67$	16.1404	1.97186	0.985929	−	0.167164i	$-0.0534611\pi$
$67$	16.1404	1.97186	0.985929	+	0.167164i	$0.0534611\pi$
$68$	−7.87879	−0.955444
$69$	7.31009	0.880031
$70$	0.938310	0.112149
$71$	−15.5563	−1.84620	−0.923098	−	0.384564i	$-0.874352\pi$
$71$	−15.5563	−1.84620	−0.923098	+	0.384564i	$0.874352\pi$
$72$	−4.22224	−0.497596
$73$	13.7880	1.61376	0.806881	−	0.590714i	$-0.201154\pi$
$73$	13.7880	1.61376	0.806881	+	0.590714i	$0.201154\pi$
$74$	4.47606	0.520332
$75$	4.20190	0.485194
$76$	8.62378	0.989215
$77$	22.0827	2.51655
$78$	1.78686	0.202322
$79$	−6.91854	−0.778397	−0.389198	−	0.921154i	$-0.627248\pi$
$79$	−6.91854	−0.778397	−0.389198	+	0.921154i	$0.627248\pi$
$80$	1.26617	0.141562
$81$	2.55887	0.284318
$82$	1.18466	0.130823
$83$	−0.611787	−0.0671524	−0.0335762	−	0.999436i	$-0.510690\pi$
$83$	−0.611787	−0.0671524	−0.0335762	+	0.999436i	$0.510690\pi$
$84$	−5.62898	−0.614172
$85$	2.28293	0.247619
$86$	4.14182	0.446624
$87$	5.87533	0.629901
$88$	−11.5193	−1.22796
$89$	−2.19980	−0.233178	−0.116589	−	0.993180i	$-0.537196\pi$
$89$	−2.19980	−0.233178	−0.116589	+	0.993180i	$0.537196\pi$
$90$	0.569281	0.0600075
$91$	−14.4711	−1.51698
$92$	14.3700	1.49818
$93$	2.76981	0.287216
$94$	−2.20652	−0.227585
$95$	−2.49880	−0.256371
$96$	4.50631	0.459923
$97$	−5.20264	−0.528248	−0.264124	−	0.964489i	$-0.585083\pi$
$97$	−5.20264	−0.528248	−0.264124	+	0.964489i	$0.585083\pi$
$98$	−3.22993	−0.326272
$99$	13.3978	1.34653
$100$	8.26000	0.826000
$101$	3.78052	0.376176	0.188088	−	0.982152i	$-0.439771\pi$
$101$	3.78052	0.376176	0.188088	+	0.982152i	$0.439771\pi$
$102$	2.04154	0.202143
$103$	0.747200	0.0736238	0.0368119	−	0.999322i	$-0.488280\pi$
$103$	0.747200	0.0736238	0.0368119	+	0.999322i	$0.488280\pi$
$104$	7.54873	0.740214
$105$	1.63104	0.159173
$106$	−1.56417	−0.151926
$107$	7.82917	0.756875	0.378437	−	0.925627i	$-0.376462\pi$
$107$	7.82917	0.756875	0.378437	+	0.925627i	$0.376462\pi$
$108$	−8.03850	−0.773505
$109$	7.66678	0.734344	0.367172	−	0.930153i	$-0.380326\pi$
$109$	7.66678	0.734344	0.367172	+	0.930153i	$0.380326\pi$
$110$	1.55313	0.148085
$111$	7.78060	0.738502
$112$	−9.16997	−0.866481
$113$	9.84678	0.926307	0.463154	−	0.886278i	$-0.346718\pi$
$113$	9.84678	0.926307	0.463154	+	0.886278i	$0.346718\pi$
$114$	−2.23458	−0.209288
$115$	−4.16381	−0.388277
$116$	11.5496	1.07235
$117$	−8.77974	−0.811688
$118$	−3.88890	−0.358002
$119$	−16.5337	−1.51564
$120$	−0.850817	−0.0776686
$121$	25.5522	2.32293
$122$	3.73449	0.338105
$123$	2.05925	0.185676
$124$	5.44483	0.488960
$125$	−4.91506	−0.439617
$126$	−4.12290	−0.367297
$127$	3.57549	0.317274	0.158637	−	0.987337i	$-0.449290\pi$
$127$	3.57549	0.317274	0.158637	+	0.987337i	$0.449290\pi$
$128$	11.4160	1.00904
$129$	7.19961	0.633890
$130$	−1.01779	−0.0892661
$131$	−8.98499	−0.785023	−0.392511	−	0.919747i	$-0.628394\pi$
$131$	−8.98499	−0.785023	−0.392511	+	0.919747i	$0.628394\pi$
$132$	−9.31733	−0.810970
$133$	18.0970	1.56921
$134$	−8.22140	−0.710221
$135$	2.32921	0.200467
$136$	8.62467	0.739559
$137$	−12.6789	−1.08323	−0.541614	−	0.840627i	$-0.682187\pi$
$137$	−12.6789	−1.08323	−0.541614	+	0.840627i	$0.682187\pi$
$138$	−3.72354	−0.316968
$139$	−18.1677	−1.54096	−0.770482	−	0.637462i	$-0.779984\pi$
$139$	−18.1677	−1.54096	−0.770482	+	0.637462i	$0.779984\pi$
$140$	3.20625	0.270978
$141$	−3.83553	−0.323010
$142$	7.92392	0.664961
$143$	−23.9532	−2.00307
$144$	−5.56350	−0.463625
$145$	−3.34657	−0.277918
$146$	−7.02318	−0.581243
$147$	−5.61449	−0.463075
$148$	15.2949	1.25724
$149$	−10.5929	−0.867803	−0.433902	−	0.900960i	$-0.642863\pi$
$149$	−10.5929	−0.867803	−0.433902	+	0.900960i	$0.642863\pi$
$150$	−2.14032	−0.174756
$151$	4.51324	0.367282	0.183641	−	0.982993i	$-0.441212\pi$
$151$	4.51324	0.367282	0.183641	+	0.982993i	$0.441212\pi$
$152$	−9.44018	−0.765700
$153$	−10.0311	−0.810969
$154$	−11.2482	−0.906409
$155$	−1.57768	−0.126722
$156$	6.10578	0.488854
$157$	−8.96466	−0.715458	−0.357729	−	0.933825i	$-0.616449\pi$
$157$	−8.96466	−0.715458	−0.357729	+	0.933825i	$0.616449\pi$
$158$	3.52409	0.280362
$159$	−2.71895	−0.215627
$160$	−2.56678	−0.202922
$161$	30.1555	2.37659
$162$	−1.30341	−0.102405
$163$	20.7358	1.62415	0.812076	−	0.583552i	$-0.198338\pi$
$163$	20.7358	1.62415	0.812076	+	0.583552i	$0.198338\pi$
$164$	4.04803	0.316098
$165$	2.69976	0.210176
$166$	0.311626	0.0241868
$167$	4.60429	0.356290	0.178145	−	0.984004i	$-0.442990\pi$
$167$	4.60429	0.356290	0.178145	+	0.984004i	$0.442990\pi$
$168$	6.16187	0.475399
$169$	2.69687	0.207452
$170$	−1.16286	−0.0891871
$171$	10.9796	0.839634
$172$	14.1528	1.07914
$173$	9.62939	0.732109	0.366054	−	0.930593i	$-0.380708\pi$
$173$	9.62939	0.732109	0.366054	+	0.930593i	$0.380708\pi$
$174$	−2.99271	−0.226877
$175$	17.3337	1.31030
$176$	−15.1785	−1.14412
$177$	−6.75995	−0.508109
$178$	1.12051	0.0839858
$179$	5.77891	0.431936	0.215968	−	0.976400i	$-0.430709\pi$
$179$	5.77891	0.431936	0.215968	+	0.976400i	$0.430709\pi$
$180$	1.94526	0.144991
$181$	13.8677	1.03078	0.515390	−	0.856956i	$-0.327647\pi$
$181$	13.8677	1.03078	0.515390	+	0.856956i	$0.327647\pi$
$182$	7.37113	0.546385
$183$	6.49155	0.479870
$184$	−15.7304	−1.15966
$185$	−4.43182	−0.325834
$186$	−1.41086	−0.103449
$187$	−27.3673	−2.00129
$188$	−7.53980	−0.549897
$189$	−16.8688	−1.22703
$190$	1.27281	0.0923395
$191$	−14.0014	−1.01311	−0.506553	−	0.862209i	$-0.669081\pi$
$191$	−14.0014	−1.01311	−0.506553	+	0.862209i	$0.669081\pi$
$192$	2.15046	0.155196
$193$	25.4644	1.83297	0.916484	−	0.400071i	$-0.131014\pi$
$193$	25.4644	1.83297	0.916484	+	0.400071i	$0.131014\pi$
$194$	2.65007	0.190264
$195$	−1.76919	−0.126695
$196$	−11.0368	−0.788346
$197$	−15.1490	−1.07932	−0.539660	−	0.841883i	$-0.681447\pi$
$197$	−15.1490	−1.07932	−0.539660	+	0.841883i	$0.681447\pi$
$198$	−6.82441	−0.484990
$199$	−22.3512	−1.58444	−0.792219	−	0.610237i	$-0.791074\pi$
$199$	−22.3512	−1.58444	−0.792219	+	0.610237i	$0.791074\pi$
$200$	−9.04197	−0.639364
$201$	−14.2910	−1.00801
$202$	−1.92568	−0.135490
$203$	24.2369	1.70110
$204$	6.97605	0.488421
$205$	−1.17295	−0.0819220
$206$	−0.380601	−0.0265177
$207$	18.2956	1.27163
$208$	9.94671	0.689681
$209$	29.9550	2.07203
$210$	−0.830800	−0.0573307
$211$	−0.766111	−0.0527412	−0.0263706	−	0.999652i	$-0.508395\pi$
$211$	−0.766111	−0.0527412	−0.0263706	+	0.999652i	$0.508395\pi$
$212$	−5.34485	−0.367086
$213$	13.7739	0.943773
$214$	−3.98794	−0.272610
$215$	−4.10088	−0.279678
$216$	8.79949	0.598730
$217$	11.4260	0.775648
$218$	−3.90522	−0.264495
$219$	−12.2082	−0.824953
$220$	5.30713	0.357807
$221$	17.9342	1.20638
$222$	−3.96320	−0.265993
$223$	15.5303	1.03999	0.519993	−	0.854171i	$-0.325935\pi$
$223$	15.5303	1.03999	0.519993	+	0.854171i	$0.325935\pi$
$224$	18.5894	1.24206
$225$	10.5165	0.701099
$226$	−5.01565	−0.333636
$227$	2.69150	0.178641	0.0893204	−	0.996003i	$-0.471530\pi$
$227$	2.69150	0.178641	0.0893204	+	0.996003i	$0.471530\pi$
$228$	−7.63568	−0.505685
$229$	12.9600	0.856424	0.428212	−	0.903678i	$-0.359144\pi$
$229$	12.9600	0.856424	0.428212	+	0.903678i	$0.359144\pi$
$230$	2.12092	0.139849
$231$	−19.5525	−1.28646
$232$	−12.6430	−0.830053
$233$	8.78412	0.575467	0.287733	−	0.957711i	$-0.407098\pi$
$233$	8.78412	0.575467	0.287733	+	0.957711i	$0.407098\pi$
$234$	4.47213	0.292353
$235$	2.18471	0.142515
$236$	−13.2886	−0.865012
$237$	6.12583	0.397915
$238$	8.42176	0.545901
$239$	−3.99381	−0.258338	−0.129169	−	0.991623i	$-0.541231\pi$
$239$	−3.99381	−0.258338	−0.129169	+	0.991623i	$0.541231\pi$
$240$	−1.12109	−0.0723663
$241$	−8.14326	−0.524554	−0.262277	−	0.964993i	$-0.584473\pi$
$241$	−8.14326	−0.524554	−0.262277	+	0.964993i	$0.584473\pi$
$242$	−13.0155	−0.836669
$243$	−16.1208	−1.03415
$244$	12.7610	0.816936
$245$	3.19800	0.204313
$246$	−1.04892	−0.0668767
$247$	−19.6300	−1.24902
$248$	−5.96029	−0.378479
$249$	0.541690	0.0343282
$250$	2.50358	0.158341
$251$	−27.1969	−1.71666	−0.858328	−	0.513102i	$-0.828496\pi$
$251$	−27.1969	−1.71666	−0.858328	+	0.513102i	$0.828496\pi$
$252$	−14.0882	−0.887472
$253$	49.9148	3.13811
$254$	−1.82125	−0.114275
$255$	−2.02136	−0.126582
$256$	−0.957495	−0.0598434
$257$	14.0915	0.879003	0.439501	−	0.898242i	$-0.355155\pi$
$257$	14.0915	0.879003	0.439501	+	0.898242i	$0.355155\pi$
$258$	−3.66726	−0.228314
$259$	32.0965	1.99438
$260$	−3.47784	−0.215687
$261$	14.7047	0.910200
$262$	4.57668	0.282748
$263$	29.0849	1.79345	0.896727	−	0.442585i	$-0.145938\pi$
$263$	29.0849	1.79345	0.896727	+	0.442585i	$0.145938\pi$
$264$	10.1994	0.627730
$265$	1.54871	0.0951364
$266$	−9.21808	−0.565197
$267$	1.94775	0.119200
$268$	−28.0930	−1.71605
$269$	3.95740	0.241287	0.120644	−	0.992696i	$-0.461504\pi$
$269$	3.95740	0.241287	0.120644	+	0.992696i	$0.461504\pi$
$270$	−1.18643	−0.0722038
$271$	−24.5048	−1.48856	−0.744280	−	0.667868i	$-0.767207\pi$
$271$	−24.5048	−1.48856	−0.744280	+	0.667868i	$0.767207\pi$
$272$	11.3644	0.689070
$273$	12.8130	0.775479
$274$	6.45822	0.390156
$275$	28.6914	1.73016
$276$	−12.7235	−0.765866
$277$	2.69045	0.161653	0.0808266	−	0.996728i	$-0.474244\pi$
$277$	2.69045	0.161653	0.0808266	+	0.996728i	$0.474244\pi$
$278$	9.25407	0.555022
$279$	6.93226	0.415024
$280$	−3.50979	−0.209750
$281$	25.3438	1.51189	0.755943	−	0.654638i	$-0.227179\pi$
$281$	25.3438	1.51189	0.755943	+	0.654638i	$0.227179\pi$
$282$	1.95370	0.116341
$283$	29.3786	1.74638	0.873189	−	0.487382i	$-0.162048\pi$
$283$	29.3786	1.74638	0.873189	+	0.487382i	$0.162048\pi$
$284$	27.0765	1.60669
$285$	2.21249	0.131057
$286$	12.2010	0.721462
$287$	8.49481	0.501433
$288$	11.2784	0.664584
$289$	3.49037	0.205316
$290$	1.70464	0.100100
$291$	4.60653	0.270040
$292$	−23.9986	−1.40441
$293$	−9.06177	−0.529394	−0.264697	−	0.964332i	$-0.585272\pi$
$293$	−9.06177	−0.529394	−0.264697	+	0.964332i	$0.585272\pi$
$294$	2.85985	0.166790
$295$	3.85045	0.224182
$296$	−16.7429	−0.973161
$297$	−27.9220	−1.62020
$298$	5.39570	0.312564
$299$	−32.7099	−1.89166
$300$	−7.31358	−0.422250
$301$	29.6998	1.71187
$302$	−2.29891	−0.132287
$303$	−3.34735	−0.192300
$304$	−12.4390	−0.713426
$305$	−3.69758	−0.211723
$306$	5.10956	0.292094
$307$	−20.5940	−1.17536	−0.587682	−	0.809092i	$-0.699959\pi$
$307$	−20.5940	−1.17536	−0.587682	+	0.809092i	$0.699959\pi$
$308$	−38.4358	−2.19008
$309$	−0.661587	−0.0376364
$310$	0.803621	0.0456426
$311$	12.3134	0.698227	0.349114	−	0.937080i	$-0.386483\pi$
$311$	12.3134	0.698227	0.349114	+	0.937080i	$0.386483\pi$
$312$	−6.68381	−0.378396
$313$	−19.6832	−1.11256	−0.556279	−	0.830996i	$-0.687771\pi$
$313$	−19.6832	−1.11256	−0.556279	+	0.830996i	$0.687771\pi$
$314$	4.56633	0.257693
$315$	4.08215	0.230003
$316$	12.0420	0.677416
$317$	−8.27558	−0.464803	−0.232402	−	0.972620i	$-0.574658\pi$
$317$	−8.27558	−0.464803	−0.232402	+	0.972620i	$0.574658\pi$
$318$	1.38495	0.0776642
$319$	40.1179	2.24617
$320$	−1.22490	−0.0684738
$321$	−6.93212	−0.386913
$322$	−15.3603	−0.855997
$323$	−22.4279	−1.24792
$324$	−4.45381	−0.247434
$325$	−18.8019	−1.04294
$326$	−10.5622	−0.584985
$327$	−6.78833	−0.375396
$328$	−4.43125	−0.244675
$329$	−15.8223	−0.872313
$330$	−1.37518	−0.0757010
$331$	−3.00359	−0.165092	−0.0825461	−	0.996587i	$-0.526305\pi$
$331$	−3.00359	−0.165092	−0.0825461	+	0.996587i	$0.526305\pi$
$332$	1.06484	0.0584408
$333$	19.4732	1.06713
$334$	−2.34528	−0.128328
$335$	8.14014	0.444743
$336$	8.11929	0.442944
$337$	−12.9143	−0.703487	−0.351744	−	0.936096i	$-0.614411\pi$
$337$	−12.9143	−0.703487	−0.351744	+	0.936096i	$0.614411\pi$
$338$	−1.37371	−0.0747197
$339$	−8.71856	−0.473527
$340$	−3.97355	−0.215496
$341$	18.9128	1.02419
$342$	−5.59270	−0.302418
$343$	2.40689	0.129960
$344$	−15.4927	−0.835309
$345$	3.68673	0.198487
$346$	−4.90492	−0.263690
$347$	−14.6340	−0.785595	−0.392798	−	0.919625i	$-0.628493\pi$
$347$	−14.6340	−0.785595	−0.392798	+	0.919625i	$0.628493\pi$
$348$	−10.2263	−0.548185
$349$	−7.88944	−0.422312	−0.211156	−	0.977452i	$-0.567723\pi$
$349$	−7.88944	−0.422312	−0.211156	+	0.977452i	$0.567723\pi$
$350$	−8.82924	−0.471943
$351$	18.2977	0.976659
$352$	30.7700	1.64005
$353$	−15.6493	−0.832928	−0.416464	−	0.909152i	$-0.636731\pi$
$353$	−15.6493	−0.832928	−0.416464	+	0.909152i	$0.636731\pi$
$354$	3.44331	0.183010
$355$	−7.84559	−0.416401
$356$	3.82884	0.202928
$357$	14.6393	0.774793
$358$	−2.94360	−0.155574
$359$	−9.81401	−0.517964	−0.258982	−	0.965882i	$-0.583387\pi$
$359$	−9.81401	−0.517964	−0.258982	+	0.965882i	$0.583387\pi$
$360$	−2.12942	−0.112230
$361$	5.54855	0.292029
$362$	−7.06379	−0.371265
$363$	−22.6245	−1.18748
$364$	25.1876	1.32019
$365$	6.95376	0.363976
$366$	−3.30660	−0.172839
$367$	1.96032	0.102328	0.0511639	−	0.998690i	$-0.483707\pi$
$367$	1.96032	0.102328	0.0511639	+	0.998690i	$0.483707\pi$
$368$	−20.7274	−1.08049
$369$	5.15388	0.268300
$370$	2.25743	0.117358
$371$	−11.2162	−0.582316
$372$	−4.82097	−0.249956
$373$	−9.73155	−0.503881	−0.251940	−	0.967743i	$-0.581069\pi$
$373$	−9.73155	−0.503881	−0.251940	+	0.967743i	$0.581069\pi$
$374$	13.9401	0.720823
$375$	4.35191	0.224731
$376$	8.25359	0.425646
$377$	−26.2899	−1.35400
$378$	8.59247	0.441949
$379$	−31.9738	−1.64239	−0.821193	−	0.570651i	$-0.806691\pi$
$379$	−31.9738	−1.64239	−0.821193	+	0.570651i	$0.806691\pi$
$380$	4.34927	0.223113
$381$	−3.16582	−0.162190
$382$	7.13189	0.364899
$383$	−6.14814	−0.314155	−0.157078	−	0.987586i	$-0.550207\pi$
$383$	−6.14814	−0.314155	−0.157078	+	0.987586i	$0.550207\pi$
$384$	−10.1080	−0.515821
$385$	11.1370	0.567597
$386$	−12.9708	−0.660196
$387$	18.0191	0.915964
$388$	9.05542	0.459719
$389$	−29.5570	−1.49860	−0.749299	−	0.662232i	$-0.769609\pi$
$389$	−29.5570	−1.49860	−0.749299	+	0.662232i	$0.769609\pi$
$390$	0.901173	0.0456327
$391$	−37.3721	−1.88999
$392$	12.0817	0.610218
$393$	7.95551	0.401302
$394$	7.71642	0.388748
$395$	−3.48926	−0.175564
$396$	−23.3194	−1.17184
$397$	−30.2945	−1.52044	−0.760218	−	0.649668i	$-0.774908\pi$
$397$	−30.2945	−1.52044	−0.760218	+	0.649668i	$0.774908\pi$
$398$	11.3850	0.570680
$399$	−16.0235	−0.802179
$400$	−11.9143	−0.595715
$401$	−9.39302	−0.469065	−0.234532	−	0.972108i	$-0.575356\pi$
$401$	−9.39302	−0.469065	−0.234532	+	0.972108i	$0.575356\pi$
$402$	7.27941	0.363064
$403$	−12.3938	−0.617382
$404$	−6.58015	−0.327375
$405$	1.29052	0.0641266
$406$	−12.3455	−0.612698
$407$	53.1276	2.63344
$408$	−7.63647	−0.378062
$409$	−1.27121	−0.0628573	−0.0314287	−	0.999506i	$-0.510006\pi$
$409$	−1.27121	−0.0628573	−0.0314287	+	0.999506i	$0.510006\pi$
$410$	0.597462	0.0295066
$411$	11.2261	0.553745
$412$	−1.30053	−0.0640727
$413$	−27.8861	−1.37219
$414$	−9.31924	−0.458016
$415$	−0.308545	−0.0151459
$416$	−20.1640	−0.988623
$417$	16.0861	0.787738
$418$	−15.2582	−0.746302
$419$	13.8195	0.675127	0.337563	−	0.941303i	$-0.390397\pi$
$419$	13.8195	0.675127	0.337563	+	0.941303i	$0.390397\pi$
$420$	−2.83889	−0.138524
$421$	−8.48219	−0.413397	−0.206698	−	0.978405i	$-0.566272\pi$
$421$	−8.48219	−0.413397	−0.206698	+	0.978405i	$0.566272\pi$
$422$	0.390234	0.0189963
$423$	−9.59954	−0.466746
$424$	5.85085	0.284142
$425$	−21.4818	−1.04202
$426$	−7.01601	−0.339927
$427$	26.7789	1.29592
$428$	−13.6270	−0.658686
$429$	21.2087	1.02396
$430$	2.08886	0.100734
$431$	−4.76794	−0.229664	−0.114832	−	0.993385i	$-0.536633\pi$
$431$	−4.76794	−0.229664	−0.114832	+	0.993385i	$0.536633\pi$
$432$	11.5948	0.557855
$433$	24.5546	1.18002	0.590010	−	0.807396i	$-0.299124\pi$
$433$	24.5546	1.18002	0.590010	+	0.807396i	$0.299124\pi$
$434$	−5.82006	−0.279372
$435$	2.96313	0.142071
$436$	−13.3444	−0.639079
$437$	40.9058	1.95679
$438$	6.21848	0.297130
$439$	−27.6665	−1.32045	−0.660225	−	0.751068i	$-0.729539\pi$
$439$	−27.6665	−1.32045	−0.660225	+	0.751068i	$0.729539\pi$
$440$	−5.80956	−0.276960
$441$	−14.0519	−0.669139
$442$	−9.13512	−0.434514
$443$	13.6620	0.649100	0.324550	−	0.945869i	$-0.394787\pi$
$443$	13.6620	0.649100	0.324550	+	0.945869i	$0.394787\pi$
$444$	−13.5425	−0.642697
$445$	−1.10943	−0.0525922
$446$	−7.91066	−0.374580
$447$	9.37918	0.443620
$448$	8.87106	0.419118
$449$	−6.26558	−0.295691	−0.147845	−	0.989010i	$-0.547234\pi$
$449$	−6.26558	−0.295691	−0.147845	+	0.989010i	$0.547234\pi$
$450$	−5.35678	−0.252521
$451$	14.0610	0.662106
$452$	−17.1387	−0.806139
$453$	−3.99612	−0.187754
$454$	−1.37097	−0.0643426
$455$	−7.29827	−0.342148
$456$	8.35855	0.391425
$457$	−12.8054	−0.599010	−0.299505	−	0.954095i	$-0.596822\pi$
$457$	−12.8054	−0.599010	−0.299505	+	0.954095i	$0.596822\pi$
$458$	−6.60145	−0.308466
$459$	20.9057	0.975795
$460$	7.24729	0.337907
$461$	28.9513	1.34839	0.674197	−	0.738551i	$-0.264490\pi$
$461$	28.9513	1.34839	0.674197	+	0.738551i	$0.264490\pi$
$462$	9.95944	0.463355
$463$	−23.9440	−1.11277	−0.556387	−	0.830923i	$-0.687813\pi$
$463$	−23.9440	−1.11277	−0.556387	+	0.830923i	$0.687813\pi$
$464$	−16.6592	−0.773386
$465$	1.39691	0.0647802
$466$	−4.47436	−0.207271
$467$	26.5152	1.22698	0.613489	−	0.789703i	$-0.289766\pi$
$467$	26.5152	1.22698	0.613489	+	0.789703i	$0.289766\pi$
$468$	15.2815	0.706388
$469$	−58.9533	−2.72221
$470$	−1.11283	−0.0513308
$471$	7.93751	0.365741
$472$	14.5466	0.669561
$473$	49.1604	2.26040
$474$	−3.12031	−0.143321
$475$	23.5130	1.07885
$476$	28.7776	1.31902
$477$	−6.80497	−0.311578
$478$	2.03433	0.0930480
$479$	5.50181	0.251384	0.125692	−	0.992069i	$-0.459885\pi$
$479$	5.50181	0.251384	0.125692	+	0.992069i	$0.459885\pi$
$480$	2.27269	0.103733
$481$	−34.8153	−1.58744
$482$	4.14793	0.188933
$483$	−26.7004	−1.21491
$484$	−44.4747	−2.02158
$485$	−2.62387	−0.119144
$486$	8.21146	0.372479
$487$	22.1140	1.00208	0.501040	−	0.865424i	$-0.332951\pi$
$487$	22.1140	1.00208	0.501040	+	0.865424i	$0.332951\pi$
$488$	−13.9690	−0.632348
$489$	−18.3599	−0.830264
$490$	−1.62896	−0.0735891
$491$	12.7871	0.577074	0.288537	−	0.957469i	$-0.406831\pi$
$491$	12.7871	0.577074	0.288537	+	0.957469i	$0.406831\pi$
$492$	−3.58421	−0.161589
$493$	−30.0370	−1.35280
$494$	9.99891	0.449872
$495$	6.75695	0.303702
$496$	−7.85367	−0.352640
$497$	56.8201	2.54873
$498$	−0.275920	−0.0123643
$499$	4.95851	0.221974	0.110987	−	0.993822i	$-0.464599\pi$
$499$	4.95851	0.221974	0.110987	+	0.993822i	$0.464599\pi$
$500$	8.55488	0.382586
$501$	−4.07674	−0.182135
$502$	13.8533	0.618303
$503$	19.4049	0.865220	0.432610	−	0.901581i	$-0.357593\pi$
$503$	19.4049	0.865220	0.432610	+	0.901581i	$0.357593\pi$
$504$	15.4219	0.686946
$505$	1.90664	0.0848446
$506$	−25.4251	−1.13028
$507$	−2.38787	−0.106049
$508$	−6.22330	−0.276114
$509$	6.51072	0.288582	0.144291	−	0.989535i	$-0.453910\pi$
$509$	6.51072	0.288582	0.144291	+	0.989535i	$0.453910\pi$
$510$	1.02962	0.0455923
$511$	−50.3612	−2.22785
$512$	−22.3443	−0.987489
$513$	−22.8825	−1.01029
$514$	−7.17777	−0.316598
$515$	0.376839	0.0166055
$516$	−12.5312	−0.551656
$517$	−26.1898	−1.15183
$518$	−16.3490	−0.718333
$519$	−8.52607	−0.374253
$520$	3.80709	0.166952
$521$	8.12457	0.355944	0.177972	−	0.984036i	$-0.443046\pi$
$521$	8.12457	0.355944	0.177972	+	0.984036i	$0.443046\pi$
$522$	−7.49015	−0.327835
$523$	9.25723	0.404790	0.202395	−	0.979304i	$-0.435127\pi$
$523$	9.25723	0.404790	0.202395	+	0.979304i	$0.435127\pi$
$524$	15.6388	0.683183
$525$	−15.3476	−0.669824
$526$	−14.8150	−0.645964
$527$	−14.1604	−0.616835
$528$	13.4394	0.584875
$529$	45.1623	1.96358
$530$	−0.788865	−0.0342661
$531$	−16.9188	−0.734212
$532$	−31.4987	−1.36564
$533$	−9.21437	−0.399119
$534$	−0.992124	−0.0429334
$535$	3.94852	0.170709
$536$	30.7525	1.32831
$537$	−5.11677	−0.220805
$538$	−2.01578	−0.0869065
$539$	−38.3369	−1.65129
$540$	−4.05409	−0.174460
$541$	−5.02224	−0.215923	−0.107962	−	0.994155i	$-0.534432\pi$
$541$	−5.02224	−0.215923	−0.107962	+	0.994155i	$0.534432\pi$
$542$	12.4820	0.536147
$543$	−12.2788	−0.526933
$544$	−23.0380	−0.987748
$545$	3.86662	0.165628
$546$	−6.52656	−0.279311
$547$	−39.9798	−1.70941	−0.854707	−	0.519110i	$-0.826263\pi$
$547$	−39.9798	−1.70941	−0.854707	+	0.519110i	$0.826263\pi$
$548$	22.0681	0.942702
$549$	16.2470	0.693406
$550$	−14.6145	−0.623166
$551$	32.8772	1.40062
$552$	13.9280	0.592817
$553$	25.2702	1.07460
$554$	−1.37043	−0.0582240
$555$	3.92403	0.166566
$556$	31.6216	1.34106
$557$	−14.6985	−0.622797	−0.311399	−	0.950279i	$-0.600797\pi$
$557$	−14.6985	−0.622797	−0.311399	+	0.950279i	$0.600797\pi$
$558$	−3.53108	−0.149483
$559$	−32.2155	−1.36257
$560$	−4.62473	−0.195431
$561$	24.2316	1.02306
$562$	−12.9094	−0.544549
$563$	1.23807	0.0521786	0.0260893	−	0.999660i	$-0.491695\pi$
$563$	1.23807	0.0521786	0.0260893	+	0.999660i	$0.491695\pi$
$564$	6.67591	0.281106
$565$	4.96607	0.208924
$566$	−14.9646	−0.629008
$567$	−9.34635	−0.392510
$568$	−29.6398	−1.24366
$569$	34.6816	1.45393	0.726963	−	0.686676i	$-0.240931\pi$
$569$	34.6816	1.45393	0.726963	+	0.686676i	$0.240931\pi$
$570$	−1.12698	−0.0472038
$571$	−3.34629	−0.140038	−0.0700190	−	0.997546i	$-0.522306\pi$
$571$	−3.34629	−0.140038	−0.0700190	+	0.997546i	$0.522306\pi$
$572$	41.6915	1.74321
$573$	12.3972	0.517899
$574$	−4.32700	−0.180605
$575$	39.1803	1.63393
$576$	5.38215	0.224256
$577$	−27.3260	−1.13760	−0.568798	−	0.822477i	$-0.692591\pi$
$577$	−27.3260	−1.13760	−0.568798	+	0.822477i	$0.692591\pi$
$578$	−1.77789	−0.0739505
$579$	−22.5467	−0.937011
$580$	5.82486	0.241864
$581$	2.23458	0.0927058
$582$	−2.34643	−0.0972625
$583$	−18.5656	−0.768907
$584$	26.2705	1.08708
$585$	−4.42793	−0.183072
$586$	4.61579	0.190677
$587$	−21.4996	−0.887385	−0.443693	−	0.896179i	$-0.646332\pi$
$587$	−21.4996	−0.887385	−0.443693	+	0.896179i	$0.646332\pi$
$588$	9.77226	0.403001
$589$	15.4993	0.638638
$590$	−1.96130	−0.0807456
$591$	13.4132	0.551746
$592$	−22.0616	−0.906724
$593$	−43.5965	−1.79029	−0.895146	−	0.445772i	$-0.852929\pi$
$593$	−43.5965	−1.79029	−0.895146	+	0.445772i	$0.852929\pi$
$594$	14.2226	0.583562
$595$	−8.33851	−0.341845
$596$	18.4374	0.755224
$597$	19.7903	0.809962
$598$	16.6614	0.681336
$599$	6.99466	0.285794	0.142897	−	0.989738i	$-0.454358\pi$
$599$	6.99466	0.285794	0.142897	+	0.989738i	$0.454358\pi$
$600$	8.00596	0.326842
$601$	15.6622	0.638875	0.319437	−	0.947607i	$-0.396506\pi$
$601$	15.6622	0.638875	0.319437	+	0.947607i	$0.396506\pi$
$602$	−15.1282	−0.616578
$603$	−35.7675	−1.45656
$604$	−7.85548	−0.319635
$605$	12.8869	0.523925
$606$	1.70504	0.0692625
$607$	−32.5494	−1.32114	−0.660569	−	0.750766i	$-0.729685\pi$
$607$	−32.5494	−1.32114	−0.660569	+	0.750766i	$0.729685\pi$
$608$	25.2164	1.02266
$609$	−21.4599	−0.869598
$610$	1.88343	0.0762579
$611$	17.1626	0.694323
$612$	17.4596	0.705764
$613$	32.3876	1.30812	0.654061	−	0.756441i	$-0.273064\pi$
$613$	32.3876	1.30812	0.654061	+	0.756441i	$0.273064\pi$
$614$	10.4900	0.423341
$615$	1.03855	0.0418784
$616$	42.0745	1.69523
$617$	−46.1696	−1.85872	−0.929359	−	0.369178i	$-0.879639\pi$
$617$	−46.1696	−1.85872	−0.929359	+	0.369178i	$0.879639\pi$
$618$	0.336992	0.0135558
$619$	38.0861	1.53081	0.765405	−	0.643549i	$-0.222539\pi$
$619$	38.0861	1.53081	0.765405	+	0.643549i	$0.222539\pi$
$620$	2.74601	0.110283
$621$	−38.1296	−1.53009
$622$	−6.27206	−0.251487
$623$	8.03484	0.321909
$624$	−8.80704	−0.352564
$625$	21.2494	0.849976
$626$	10.0260	0.400720
$627$	−26.5228	−1.05922
$628$	15.6034	0.622643
$629$	−39.7776	−1.58603
$630$	−2.07932	−0.0828421
$631$	−15.6089	−0.621379	−0.310690	−	0.950511i	$-0.600560\pi$
$631$	−15.6089	−0.621379	−0.310690	+	0.950511i	$0.600560\pi$
$632$	−13.1820	−0.524353
$633$	0.678331	0.0269612
$634$	4.21533	0.167412
$635$	1.80324	0.0715596
$636$	4.73245	0.187654
$637$	25.1227	0.995399
$638$	−20.4349	−0.809024
$639$	34.4733	1.36374
$640$	5.75749	0.227585
$641$	−8.96424	−0.354066	−0.177033	−	0.984205i	$-0.556650\pi$
$641$	−8.96424	−0.354066	−0.177033	+	0.984205i	$0.556650\pi$
$642$	3.53101	0.139358
$643$	44.7822	1.76604	0.883019	−	0.469338i	$-0.155507\pi$
$643$	44.7822	1.76604	0.883019	+	0.469338i	$0.155507\pi$
$644$	−52.4870	−2.06828
$645$	3.63101	0.142971
$646$	11.4241	0.449474
$647$	4.32620	0.170080	0.0850402	−	0.996378i	$-0.472898\pi$
$647$	4.32620	0.170080	0.0850402	+	0.996378i	$0.472898\pi$
$648$	4.87545	0.191526
$649$	−46.1583	−1.81187
$650$	9.57712	0.375646
$651$	−10.1168	−0.396510
$652$	−36.0915	−1.41345
$653$	16.3445	0.639610	0.319805	−	0.947483i	$-0.396383\pi$
$653$	16.3445	0.639610	0.319805	+	0.947483i	$0.396383\pi$
$654$	3.45777	0.135209
$655$	−4.53144	−0.177058
$656$	−5.83892	−0.227971
$657$	−30.5546	−1.19205
$658$	8.05941	0.314188
$659$	34.0249	1.32542	0.662712	−	0.748875i	$-0.269406\pi$
$659$	34.0249	1.32542	0.662712	+	0.748875i	$0.269406\pi$
$660$	−4.69905	−0.182910
$661$	−37.0094	−1.43950	−0.719749	−	0.694234i	$-0.755743\pi$
$661$	−37.0094	−1.43950	−0.719749	+	0.694234i	$0.755743\pi$
$662$	1.52994	0.0594627
$663$	−15.8793	−0.616701
$664$	−1.16565	−0.0452360
$665$	9.12696	0.353928
$666$	−9.91908	−0.384357
$667$	54.7841	2.12125
$668$	−8.01396	−0.310069
$669$	−13.7509	−0.531639
$670$	−4.14634	−0.160187
$671$	44.3257	1.71117
$672$	−16.4595	−0.634937
$673$	−46.4570	−1.79079	−0.895394	−	0.445275i	$-0.853106\pi$
$673$	−46.4570	−1.79079	−0.895394	+	0.445275i	$0.853106\pi$
$674$	6.57815	0.253381
$675$	−21.9172	−0.843594
$676$	−4.69402	−0.180539
$677$	−26.1106	−1.00351	−0.501757	−	0.865009i	$-0.667313\pi$
$677$	−26.1106	−1.00351	−0.501757	+	0.865009i	$0.667313\pi$
$678$	4.44097	0.170554
$679$	19.0028	0.729262
$680$	4.34972	0.166804
$681$	−2.38311	−0.0913210
$682$	−9.63362	−0.368890
$683$	−37.3234	−1.42814	−0.714069	−	0.700075i	$-0.753150\pi$
$683$	−37.3234	−1.42814	−0.714069	+	0.700075i	$0.753150\pi$
$684$	−19.1105	−0.730710
$685$	−6.39438	−0.244317
$686$	−1.22600	−0.0468088
$687$	−11.4751	−0.437803
$688$	−20.4142	−0.778283
$689$	12.1663	0.463498
$690$	−1.87791	−0.0714907
$691$	37.7208	1.43497	0.717483	−	0.696576i	$-0.245294\pi$
$691$	37.7208	1.43497	0.717483	+	0.696576i	$0.245294\pi$
$692$	−16.7604	−0.637133
$693$	−48.9358	−1.85892
$694$	7.45412	0.282955
$695$	−9.16259	−0.347557
$696$	11.1944	0.424322
$697$	−10.5277	−0.398766
$698$	4.01864	0.152108
$699$	−7.77765	−0.294178
$700$	−30.1700	−1.14032
$701$	40.4368	1.52728	0.763639	−	0.645643i	$-0.223411\pi$
$701$	40.4368	1.52728	0.763639	+	0.645643i	$0.223411\pi$
$702$	−9.32030	−0.351772
$703$	43.5388	1.64210
$704$	14.6838	0.553415
$705$	−1.93439	−0.0728534
$706$	7.97128	0.300003
$707$	−13.8085	−0.519322
$708$	11.7660	0.442193
$709$	−1.63923	−0.0615627	−0.0307814	−	0.999526i	$-0.509800\pi$
$709$	−1.63923	−0.0615627	−0.0307814	+	0.999526i	$0.509800\pi$
$710$	3.99631	0.149979
$711$	15.3317	0.574983
$712$	−4.19131	−0.157076
$713$	25.8269	0.967224
$714$	−7.45681	−0.279064
$715$	−12.0804	−0.451782
$716$	−10.0584	−0.375902
$717$	3.53621	0.132062
$718$	4.99896	0.186559
$719$	24.8782	0.927802	0.463901	−	0.885887i	$-0.346449\pi$
$719$	24.8782	0.927802	0.463901	+	0.885887i	$0.346449\pi$
$720$	−2.80587	−0.104568
$721$	−2.72918	−0.101640
$722$	−2.82626	−0.105183
$723$	7.21022	0.268151
$724$	−24.1374	−0.897058
$725$	31.4903	1.16952
$726$	11.5242	0.427704
$727$	43.4490	1.61143	0.805716	−	0.592301i	$-0.201781\pi$
$727$	43.4490	1.61143	0.805716	+	0.592301i	$0.201781\pi$
$728$	−27.5720	−1.02189
$729$	6.59714	0.244338
$730$	−3.54203	−0.131097
$731$	−36.8073	−1.36137
$732$	−11.2988	−0.417617
$733$	−35.1877	−1.29969	−0.649844	−	0.760067i	$-0.725166\pi$
$733$	−35.1877	−1.29969	−0.649844	+	0.760067i	$0.725166\pi$
$734$	−0.998526	−0.0368563
$735$	−2.83158	−0.104444
$736$	42.0187	1.54883
$737$	−97.5820	−3.59448
$738$	−2.62523	−0.0966361
$739$	−22.1568	−0.815052	−0.407526	−	0.913194i	$-0.633608\pi$
$739$	−22.1568	−0.815052	−0.407526	+	0.913194i	$0.633608\pi$
$740$	7.71376	0.283564
$741$	17.3808	0.638500
$742$	5.71319	0.209738
$743$	−5.27471	−0.193510	−0.0967551	−	0.995308i	$-0.530846\pi$
$743$	−5.27471	−0.193510	−0.0967551	+	0.995308i	$0.530846\pi$
$744$	5.27737	0.193478
$745$	−5.34236	−0.195729
$746$	4.95696	0.181487
$747$	1.35574	0.0496038
$748$	47.6339	1.74167
$749$	−28.5964	−1.04489
$750$	−2.21673	−0.0809435
$751$	−23.0730	−0.841946	−0.420973	−	0.907073i	$-0.638311\pi$
$751$	−23.0730	−0.841946	−0.420973	+	0.907073i	$0.638311\pi$
$752$	10.8755	0.396588
$753$	24.0808	0.877552
$754$	13.3913	0.487681
$755$	2.27618	0.0828387
$756$	29.3609	1.06785
$757$	13.0390	0.473909	0.236955	−	0.971521i	$-0.423851\pi$
$757$	13.0390	0.473909	0.236955	+	0.971521i	$0.423851\pi$
$758$	16.2865	0.591552
$759$	−44.1956	−1.60420
$760$	−4.76101	−0.172700
$761$	−16.9312	−0.613755	−0.306878	−	0.951749i	$-0.599284\pi$
$761$	−16.9312	−0.613755	−0.306878	+	0.951749i	$0.599284\pi$
$762$	1.61257	0.0584174
$763$	−28.0032	−1.01378
$764$	24.3701	0.881678
$765$	−5.05905	−0.182910
$766$	3.13167	0.113152
$767$	30.2482	1.09220
$768$	0.847787	0.0305919
$769$	−16.0238	−0.577833	−0.288916	−	0.957354i	$-0.593295\pi$
$769$	−16.0238	−0.577833	−0.288916	+	0.957354i	$0.593295\pi$
$770$	−5.67287	−0.204436
$771$	−12.4769	−0.449345
$772$	−44.3219	−1.59518
$773$	42.5786	1.53145	0.765723	−	0.643171i	$-0.222381\pi$
$773$	42.5786	1.53145	0.765723	+	0.643171i	$0.222381\pi$
$774$	−9.17840	−0.329911
$775$	14.8455	0.533266
$776$	−9.91269	−0.355845
$777$	−28.4190	−1.01952
$778$	15.0554	0.539763
$779$	11.5232	0.412860
$780$	3.07936	0.110259
$781$	94.0511	3.36541
$782$	19.0362	0.680733
$783$	−30.6459	−1.09519
$784$	15.9196	0.568559
$785$	−4.52119	−0.161368
$786$	−4.05229	−0.144541
$787$	−13.8683	−0.494351	−0.247175	−	0.968971i	$-0.579502\pi$
$787$	−13.8683	−0.494351	−0.247175	+	0.968971i	$0.579502\pi$
$788$	26.3674	0.939301
$789$	−25.7524	−0.916811
$790$	1.77732	0.0632343
$791$	−35.9657	−1.27879
$792$	25.5270	0.907062
$793$	−29.0473	−1.03150
$794$	15.4311	0.547629
$795$	−1.37126	−0.0486336
$796$	38.9033	1.37889
$797$	53.2938	1.88776	0.943881	−	0.330286i	$-0.107145\pi$
$797$	53.2938	1.88776	0.943881	+	0.330286i	$0.107145\pi$
$798$	8.16189	0.288928
$799$	19.6088	0.693708
$800$	24.1527	0.853928
$801$	4.87481	0.172243
$802$	4.78452	0.168947
$803$	−83.3600	−2.94171
$804$	24.8741	0.877243
$805$	15.2085	0.536028
$806$	6.31305	0.222368
$807$	−3.50397	−0.123346
$808$	7.20309	0.253404
$809$	14.4701	0.508740	0.254370	−	0.967107i	$-0.418132\pi$
$809$	14.4701	0.508740	0.254370	+	0.967107i	$0.418132\pi$
$810$	−0.657354	−0.0230971
$811$	−22.2019	−0.779613	−0.389807	−	0.920897i	$-0.627458\pi$
$811$	−22.2019	−0.779613	−0.389807	+	0.920897i	$0.627458\pi$
$812$	−42.1853	−1.48041
$813$	21.6971	0.760949
$814$	−27.0616	−0.948507
$815$	10.4578	0.366319
$816$	−10.0623	−0.352252
$817$	40.2876	1.40949
$818$	0.647516	0.0226399
$819$	32.0684	1.12056
$820$	2.04156	0.0712944
$821$	−11.7746	−0.410938	−0.205469	−	0.978664i	$-0.565872\pi$
$821$	−11.7746	−0.410938	−0.205469	+	0.978664i	$0.565872\pi$
$822$	−5.71825	−0.199447
$823$	−10.8460	−0.378069	−0.189034	−	0.981970i	$-0.560536\pi$
$823$	−10.8460	−0.378069	−0.189034	+	0.981970i	$0.560536\pi$
$824$	1.42365	0.0495953
$825$	−25.4040	−0.884454
$826$	14.2043	0.494232
$827$	6.14483	0.213677	0.106838	−	0.994276i	$-0.465927\pi$
$827$	6.14483	0.213677	0.106838	+	0.994276i	$0.465927\pi$
$828$	−31.8443	−1.10667
$829$	−32.1145	−1.11538	−0.557692	−	0.830048i	$-0.688313\pi$
$829$	−32.1145	−1.11538	−0.557692	+	0.830048i	$0.688313\pi$
$830$	0.157164	0.00545523
$831$	−2.38218	−0.0826369
$832$	−9.62249	−0.333600
$833$	28.7035	0.994518
$834$	−8.19375	−0.283726
$835$	2.32210	0.0803596
$836$	−52.1380	−1.80323
$837$	−14.4474	−0.499375
$838$	−7.03923	−0.243166
$839$	38.8625	1.34168	0.670841	−	0.741601i	$-0.265933\pi$
$839$	38.8625	1.34168	0.670841	+	0.741601i	$0.265933\pi$
$840$	3.10764	0.107224
$841$	15.0315	0.518329
$842$	4.32057	0.148897
$843$	−22.4400	−0.772874
$844$	1.33345	0.0458992
$845$	1.36013	0.0467898
$846$	4.88972	0.168112
$847$	−93.3304	−3.20687
$848$	7.70946	0.264744
$849$	−26.0125	−0.892746
$850$	10.9422	0.375313
$851$	72.5497	2.48697
$852$	−23.9741	−0.821339
$853$	−44.9191	−1.53800	−0.769000	−	0.639249i	$-0.779245\pi$
$853$	−44.9191	−1.53800	−0.769000	+	0.639249i	$0.779245\pi$
$854$	−13.6404	−0.466764
$855$	5.53741	0.189375
$856$	14.9171	0.509855
$857$	−34.2256	−1.16913	−0.584563	−	0.811348i	$-0.698734\pi$
$857$	−34.2256	−1.16913	−0.584563	+	0.811348i	$0.698734\pi$
$858$	−10.8031	−0.368810
$859$	16.6905	0.569473	0.284736	−	0.958606i	$-0.408094\pi$
$859$	16.6905	0.569473	0.284736	+	0.958606i	$0.408094\pi$
$860$	7.13776	0.243396
$861$	−7.52149	−0.256332
$862$	2.42864	0.0827200
$863$	4.62616	0.157476	0.0787382	−	0.996895i	$-0.474911\pi$
$863$	4.62616	0.157476	0.0787382	+	0.996895i	$0.474911\pi$
$864$	−23.5050	−0.799657
$865$	4.85643	0.165124
$866$	−12.5074	−0.425018
$867$	−3.09045	−0.104957
$868$	−19.8875	−0.675024
$869$	41.8284	1.41893
$870$	−1.50933	−0.0511710
$871$	63.9469	2.16676
$872$	14.6077	0.494677
$873$	11.5292	0.390204
$874$	−20.8362	−0.704794
$875$	17.9525	0.606904
$876$	21.2489	0.717933
$877$	40.3576	1.36278	0.681390	−	0.731920i	$-0.261376\pi$
$877$	40.3576	1.36278	0.681390	+	0.731920i	$0.261376\pi$
$878$	14.0925	0.475598
$879$	8.02349	0.270626
$880$	−7.65506	−0.258052
$881$	28.8958	0.973523	0.486762	−	0.873535i	$-0.338178\pi$
$881$	28.8958	0.973523	0.486762	+	0.873535i	$0.338178\pi$
$882$	7.15762	0.241010
$883$	4.49301	0.151202	0.0756008	−	0.997138i	$-0.475913\pi$
$883$	4.49301	0.151202	0.0756008	+	0.997138i	$0.475913\pi$
$884$	−31.2152	−1.04988
$885$	−3.40928	−0.114602
$886$	−6.95900	−0.233792
$887$	−39.2704	−1.31857	−0.659285	−	0.751893i	$-0.729141\pi$
$887$	−39.2704	−1.31857	−0.659285	+	0.751893i	$0.729141\pi$
$888$	14.8245	0.497479
$889$	−13.0596	−0.438006
$890$	0.565112	0.0189426
$891$	−15.4705	−0.518281
$892$	−27.0311	−0.905069
$893$	−21.4629	−0.718228
$894$	−4.77747	−0.159782
$895$	2.91450	0.0974211
$896$	−41.6974	−1.39301
$897$	28.9620	0.967014
$898$	3.19150	0.106502
$899$	20.7578	0.692312
$900$	−18.3044	−0.610146
$901$	13.9004	0.463088
$902$	−7.16224	−0.238476
$903$	−26.2968	−0.875104
$904$	18.7613	0.623990
$905$	6.99397	0.232487
$906$	2.03550	0.0676250
$907$	−29.0800	−0.965584	−0.482792	−	0.875735i	$-0.660377\pi$
$907$	−29.0800	−0.965584	−0.482792	+	0.875735i	$0.660377\pi$
$908$	−4.68466	−0.155466
$909$	−8.37773	−0.277872
$910$	3.71752	0.123234
$911$	48.4746	1.60603	0.803017	−	0.595956i	$-0.203227\pi$
$911$	48.4746	1.60603	0.803017	+	0.595956i	$0.203227\pi$
$912$	11.0138	0.364703
$913$	3.69877	0.122411
$914$	6.52267	0.215751
$915$	3.27391	0.108232
$916$	−22.5575	−0.745321
$917$	32.8180	1.08375
$918$	−10.6487	−0.351461
$919$	−10.4807	−0.345727	−0.172864	−	0.984946i	$-0.555302\pi$
$919$	−10.4807	−0.345727	−0.172864	+	0.984946i	$0.555302\pi$
$920$	−7.93338	−0.261556
$921$	18.2344	0.600844
$922$	−14.7469	−0.485663
$923$	−61.6331	−2.02868
$924$	34.0319	1.11957
$925$	41.7022	1.37116
$926$	12.1964	0.400797
$927$	−1.65582	−0.0543841
$928$	33.7717	1.10861
$929$	−21.9895	−0.721451	−0.360726	−	0.932672i	$-0.617471\pi$
$929$	−21.9895	−0.721451	−0.360726	+	0.932672i	$0.617471\pi$
$930$	−0.711543	−0.0233324
$931$	−31.4176	−1.02967
$932$	−15.2891	−0.500812
$933$	−10.9025	−0.356933
$934$	−13.5060	−0.441931
$935$	−13.8023	−0.451382
$936$	−16.7282	−0.546779
$937$	−24.8054	−0.810357	−0.405178	−	0.914238i	$-0.632791\pi$
$937$	−24.8054	−0.810357	−0.405178	+	0.914238i	$0.632791\pi$
$938$	30.0290	0.980481
$939$	17.4279	0.568738
$940$	−3.80258	−0.124027
$941$	44.6735	1.45632	0.728158	−	0.685409i	$-0.240377\pi$
$941$	44.6735	1.45632	0.728158	+	0.685409i	$0.240377\pi$
$942$	−4.04313	−0.131732
$943$	19.2013	0.625281
$944$	19.1675	0.623850
$945$	−8.50753	−0.276750
$946$	−25.0408	−0.814147
$947$	10.6798	0.347046	0.173523	−	0.984830i	$-0.444485\pi$
$947$	10.6798	0.347046	0.173523	+	0.984830i	$0.444485\pi$
$948$	−10.6623	−0.346294
$949$	54.6270	1.77327
$950$	−11.9768	−0.388579
$951$	7.32738	0.237607
$952$	−31.5019	−1.02098
$953$	1.69119	0.0547830	0.0273915	−	0.999625i	$-0.491280\pi$
$953$	1.69119	0.0547830	0.0273915	+	0.999625i	$0.491280\pi$
$954$	3.46625	0.112224
$955$	−7.06140	−0.228501
$956$	6.95140	0.224824
$957$	−35.5213	−1.14824
$958$	−2.80246	−0.0905433
$959$	46.3100	1.49543
$960$	1.08455	0.0350037
$961$	−21.2141	−0.684327
$962$	17.7338	0.571762
$963$	−17.3497	−0.559085
$964$	14.1737	0.456504
$965$	12.8426	0.413417
$966$	13.6004	0.437584
$967$	−8.31289	−0.267325	−0.133662	−	0.991027i	$-0.542674\pi$
$967$	−8.31289	−0.267325	−0.133662	+	0.991027i	$0.542674\pi$
$968$	48.6851	1.56480
$969$	19.8581	0.637935
$970$	1.33652	0.0429131
$971$	29.4449	0.944932	0.472466	−	0.881349i	$-0.343364\pi$
$971$	29.4449	0.944932	0.472466	+	0.881349i	$0.343364\pi$
$972$	28.0590	0.899993
$973$	66.3582	2.12735
$974$	−11.2642	−0.360928
$975$	16.6476	0.533151
$976$	−18.4065	−0.589178
$977$	−25.6923	−0.821970	−0.410985	−	0.911642i	$-0.634815\pi$
$977$	−25.6923	−0.821970	−0.410985	+	0.911642i	$0.634815\pi$
$978$	9.35198	0.299043
$979$	13.2996	0.425058
$980$	−5.56626	−0.177808
$981$	−16.9898	−0.542442
$982$	−6.51337	−0.207850
$983$	32.7537	1.04468	0.522340	−	0.852737i	$-0.325059\pi$
$983$	32.7537	1.04468	0.522340	+	0.852737i	$0.325059\pi$
$984$	3.92353	0.125078
$985$	−7.64015	−0.243435
$986$	15.2999	0.487250
$987$	14.0094	0.445925
$988$	34.1668	1.08699
$989$	67.1322	2.13468
$990$	−3.44178	−0.109387
$991$	−2.07756	−0.0659960	−0.0329980	−	0.999455i	$-0.510506\pi$
$991$	−2.07756	−0.0659960	−0.0329980	+	0.999455i	$0.510506\pi$
$992$	15.9210	0.505492
$993$	2.65944	0.0843949
$994$	−28.9424	−0.917998
$995$	−11.2725	−0.357362
$996$	−0.942834	−0.0298748
$997$	−33.4383	−1.05900	−0.529501	−	0.848309i	$-0.677621\pi$
$997$	−33.4383	−1.05900	−0.529501	+	0.848309i	$0.677621\pi$
$998$	−2.52572	−0.0799501
$999$	−40.5838	−1.28402

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2671.2.a.b.1.50	✓	122

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2671.2.a.b.1.50	✓	122	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:	\( N \)	\(=\)	\( 2671 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2671.a (trivial)

\(f(q)\)	\(=\)	\(q-0.509370 q^{2} -0.885422 q^{3} -1.74054 q^{4} +0.504334 q^{5} +0.451007 q^{6} -3.65254 q^{7} +1.90532 q^{8} -2.21603 q^{9} +O(q^{10})\)	\(q-0.509370 q^{2} -0.885422 q^{3} -1.74054 q^{4} +0.504334 q^{5} +0.451007 q^{6} -3.65254 q^{7} +1.90532 q^{8} -2.21603 q^{9} -0.256893 q^{10} -6.04584 q^{11} +1.54111 q^{12} +3.96193 q^{13} +1.86049 q^{14} -0.446549 q^{15} +2.51057 q^{16} +4.52663 q^{17} +1.12878 q^{18} -4.95465 q^{19} -0.877815 q^{20} +3.23404 q^{21} +3.07957 q^{22} -8.25605 q^{23} -1.68701 q^{24} -4.74565 q^{25} -2.01809 q^{26} +4.61839 q^{27} +6.35740 q^{28} -6.63563 q^{29} +0.227458 q^{30} -3.12824 q^{31} -5.08945 q^{32} +5.35312 q^{33} -2.30573 q^{34} -1.84210 q^{35} +3.85709 q^{36} -8.78745 q^{37} +2.52375 q^{38} -3.50798 q^{39} +0.960918 q^{40} -2.32573 q^{41} -1.64732 q^{42} -8.13127 q^{43} +10.5230 q^{44} -1.11762 q^{45} +4.20538 q^{46} +4.33187 q^{47} -2.22292 q^{48} +6.34104 q^{49} +2.41729 q^{50} -4.00798 q^{51} -6.89590 q^{52} +3.07080 q^{53} -2.35246 q^{54} -3.04913 q^{55} -6.95925 q^{56} +4.38695 q^{57} +3.37999 q^{58} +7.63472 q^{59} +0.777237 q^{60} -7.33160 q^{61} +1.59343 q^{62} +8.09413 q^{63} -2.42874 q^{64} +1.99814 q^{65} -2.72672 q^{66} +16.1404 q^{67} -7.87879 q^{68} +7.31009 q^{69} +0.938310 q^{70} -15.5563 q^{71} -4.22224 q^{72} +13.7880 q^{73} +4.47606 q^{74} +4.20190 q^{75} +8.62378 q^{76} +22.0827 q^{77} +1.78686 q^{78} -6.91854 q^{79} +1.26617 q^{80} +2.55887 q^{81} +1.18466 q^{82} -0.611787 q^{83} -5.62898 q^{84} +2.28293 q^{85} +4.14182 q^{86} +5.87533 q^{87} -11.5193 q^{88} -2.19980 q^{89} +0.569281 q^{90} -14.4711 q^{91} +14.3700 q^{92} +2.76981 q^{93} -2.20652 q^{94} -2.49880 q^{95} +4.50631 q^{96} -5.20264 q^{97} -3.22993 q^{98} +13.3978 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 122 q + 14 q^{2} + 10 q^{3} + 128 q^{4} + 33 q^{5} + 22 q^{6} + 6 q^{7} + 36 q^{8} + 162 q^{9}+O(q^{10}) \) 122 * q + 14 * q^2 + 10 * q^3 + 128 * q^4 + 33 * q^5 + 22 * q^6 + 6 * q^7 + 36 * q^8 + 162 * q^9	\( 122 q + 14 q^{2} + 10 q^{3} + 128 q^{4} + 33 q^{5} + 22 q^{6} + 6 q^{7} + 36 q^{8} + 162 q^{9} + 16 q^{10} + 43 q^{11} + 23 q^{12} + 25 q^{13} + 45 q^{14} + 12 q^{15} + 132 q^{16} + 103 q^{17} + 30 q^{18} + 37 q^{19} + 63 q^{20} + 81 q^{21} + 15 q^{23} + 60 q^{24} + 151 q^{25} + 59 q^{26} + 22 q^{27} - 3 q^{28} + 80 q^{29} - 9 q^{30} + 15 q^{31} + 66 q^{32} + 93 q^{33} + 30 q^{34} + 23 q^{35} + 162 q^{36} + 18 q^{37} + 41 q^{38} + 10 q^{39} + 29 q^{40} + 249 q^{41} - 8 q^{42} + 14 q^{43} + 100 q^{44} + 59 q^{45} + 11 q^{46} + 57 q^{47} + 33 q^{48} + 180 q^{49} + 63 q^{50} + 26 q^{51} + 31 q^{52} + 65 q^{53} + 65 q^{54} - 8 q^{55} + 120 q^{56} + 57 q^{57} - 31 q^{58} + 108 q^{59} - q^{60} + 70 q^{61} + 25 q^{62} - 7 q^{63} + 100 q^{64} + 171 q^{65} + 12 q^{66} - 6 q^{67} + 184 q^{68} + 64 q^{69} - 24 q^{70} + 47 q^{71} + 53 q^{72} + 76 q^{73} + 66 q^{74} + 40 q^{75} + 32 q^{76} + 73 q^{77} - 19 q^{78} + 8 q^{79} + 115 q^{80} + 250 q^{81} - 13 q^{82} + 116 q^{83} + 159 q^{84} + 31 q^{85} + 91 q^{86} + 25 q^{87} - 43 q^{88} + 361 q^{89} + 32 q^{90} + 7 q^{91} + 5 q^{92} + 18 q^{93} + 23 q^{94} + 42 q^{95} + 77 q^{96} + 79 q^{97} + 56 q^{98} + 74 q^{99}+O(q^{100}) \) 122 * q + 14 * q^2 + 10 * q^3 + 128 * q^4 + 33 * q^5 + 22 * q^6 + 6 * q^7 + 36 * q^8 + 162 * q^9 + 16 * q^10 + 43 * q^11 + 23 * q^12 + 25 * q^13 + 45 * q^14 + 12 * q^15 + 132 * q^16 + 103 * q^17 + 30 * q^18 + 37 * q^19 + 63 * q^20 + 81 * q^21 + 15 * q^23 + 60 * q^24 + 151 * q^25 + 59 * q^26 + 22 * q^27 - 3 * q^28 + 80 * q^29 - 9 * q^30 + 15 * q^31 + 66 * q^32 + 93 * q^33 + 30 * q^34 + 23 * q^35 + 162 * q^36 + 18 * q^37 + 41 * q^38 + 10 * q^39 + 29 * q^40 + 249 * q^41 - 8 * q^42 + 14 * q^43 + 100 * q^44 + 59 * q^45 + 11 * q^46 + 57 * q^47 + 33 * q^48 + 180 * q^49 + 63 * q^50 + 26 * q^51 + 31 * q^52 + 65 * q^53 + 65 * q^54 - 8 * q^55 + 120 * q^56 + 57 * q^57 - 31 * q^58 + 108 * q^59 - q^60 + 70 * q^61 + 25 * q^62 - 7 * q^63 + 100 * q^64 + 171 * q^65 + 12 * q^66 - 6 * q^67 + 184 * q^68 + 64 * q^69 - 24 * q^70 + 47 * q^71 + 53 * q^72 + 76 * q^73 + 66 * q^74 + 40 * q^75 + 32 * q^76 + 73 * q^77 - 19 * q^78 + 8 * q^79 + 115 * q^80 + 250 * q^81 - 13 * q^82 + 116 * q^83 + 159 * q^84 + 31 * q^85 + 91 * q^86 + 25 * q^87 - 43 * q^88 + 361 * q^89 + 32 * q^90 + 7 * q^91 + 5 * q^92 + 18 * q^93 + 23 * q^94 + 42 * q^95 + 77 * q^96 + 79 * q^97 + 56 * q^98 + 74 * q^99

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