LMFDB - Embedded newform 2671.2.a.b.1.81

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			1.81
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)

$f(q)$	$=$	$q+1.22132 q^{2} +3.27998 q^{3} -0.508366 q^{4} -2.67260 q^{5} +4.00592 q^{6} -2.35950 q^{7} -3.06353 q^{8} +7.75829 q^{9} +O(q^{10})$	\(q+1.22132 q^{2} +3.27998 q^{3} -0.508366 q^{4} -2.67260 q^{5} +4.00592 q^{6} -2.35950 q^{7} -3.06353 q^{8} +7.75829 q^{9} -3.26411 q^{10} +1.94534 q^{11} -1.66743 q^{12} +4.41343 q^{13} -2.88172 q^{14} -8.76607 q^{15} -2.72483 q^{16} +3.92079 q^{17} +9.47539 q^{18} +4.10965 q^{19} +1.35866 q^{20} -7.73913 q^{21} +2.37589 q^{22} -1.66090 q^{23} -10.0483 q^{24} +2.14277 q^{25} +5.39023 q^{26} +15.6071 q^{27} +1.19949 q^{28} +2.60316 q^{29} -10.7062 q^{30} -4.24119 q^{31} +2.79915 q^{32} +6.38068 q^{33} +4.78856 q^{34} +6.30600 q^{35} -3.94405 q^{36} +9.89737 q^{37} +5.01922 q^{38} +14.4760 q^{39} +8.18758 q^{40} +8.30439 q^{41} -9.45200 q^{42} +1.86772 q^{43} -0.988945 q^{44} -20.7348 q^{45} -2.02849 q^{46} -1.06890 q^{47} -8.93740 q^{48} -1.43274 q^{49} +2.61702 q^{50} +12.8601 q^{51} -2.24364 q^{52} +2.13791 q^{53} +19.0613 q^{54} -5.19911 q^{55} +7.22841 q^{56} +13.4796 q^{57} +3.17931 q^{58} +0.757159 q^{59} +4.45637 q^{60} +1.65253 q^{61} -5.17987 q^{62} -18.3057 q^{63} +8.86834 q^{64} -11.7953 q^{65} +7.79288 q^{66} +0.348893 q^{67} -1.99320 q^{68} -5.44771 q^{69} +7.70168 q^{70} -0.645299 q^{71} -23.7677 q^{72} +0.955846 q^{73} +12.0879 q^{74} +7.02826 q^{75} -2.08921 q^{76} -4.59004 q^{77} +17.6798 q^{78} -6.36556 q^{79} +7.28238 q^{80} +27.9161 q^{81} +10.1424 q^{82} -3.56250 q^{83} +3.93431 q^{84} -10.4787 q^{85} +2.28109 q^{86} +8.53833 q^{87} -5.95961 q^{88} -11.3485 q^{89} -25.3239 q^{90} -10.4135 q^{91} +0.844344 q^{92} -13.9110 q^{93} -1.30548 q^{94} -10.9834 q^{95} +9.18118 q^{96} +8.90186 q^{97} -1.74984 q^{98} +15.0925 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	1.22132	0.863607	0.431803	−	0.901968i	$-0.357877\pi$
$2$	1.22132	0.863607	0.431803	+	0.901968i	$0.357877\pi$
$3$	3.27998	1.89370	0.946849	−	0.321677i	$-0.104247\pi$
$3$	3.27998	1.89370	0.946849	+	0.321677i	$0.104247\pi$
$4$	−0.508366	−0.254183
$5$	−2.67260	−1.19522	−0.597611	−	0.801786i	$-0.703883\pi$
$5$	−2.67260	−1.19522	−0.597611	+	0.801786i	$0.703883\pi$
$6$	4.00592	1.63541
$7$	−2.35950	−0.891809	−0.445904	−	0.895081i	$-0.647118\pi$
$7$	−2.35950	−0.891809	−0.445904	+	0.895081i	$0.647118\pi$
$8$	−3.06353	−1.08312
$9$	7.75829	2.58610
$10$	−3.26411	−1.03220
$11$	1.94534	0.586542	0.293271	−	0.956029i	$-0.405256\pi$
$11$	1.94534	0.586542	0.293271	+	0.956029i	$0.405256\pi$
$12$	−1.66743	−0.481346
$13$	4.41343	1.22406	0.612032	−	0.790833i	$-0.290352\pi$
$13$	4.41343	1.22406	0.612032	+	0.790833i	$0.290352\pi$
$14$	−2.88172	−0.770172
$15$	−8.76607	−2.26339
$16$	−2.72483	−0.681208
$17$	3.92079	0.950931	0.475466	−	0.879734i	$-0.342280\pi$
$17$	3.92079	0.950931	0.475466	+	0.879734i	$0.342280\pi$
$18$	9.47539	2.23337
$19$	4.10965	0.942819	0.471409	−	0.881915i	$-0.343745\pi$
$19$	4.10965	0.942819	0.471409	+	0.881915i	$0.343745\pi$
$20$	1.35866	0.303805
$21$	−7.73913	−1.68882
$22$	2.37589	0.506542
$23$	−1.66090	−0.346321	−0.173160	−	0.984894i	$-0.555398\pi$
$23$	−1.66090	−0.346321	−0.173160	+	0.984894i	$0.555398\pi$
$24$	−10.0483	−2.05111
$25$	2.14277	0.428555
$26$	5.39023	1.05711
$27$	15.6071	3.00359
$28$	1.19949	0.226683
$29$	2.60316	0.483395	0.241698	−	0.970352i	$-0.422296\pi$
$29$	2.60316	0.483395	0.241698	+	0.970352i	$0.422296\pi$
$30$	−10.7062	−1.95468
$31$	−4.24119	−0.761740	−0.380870	−	0.924629i	$-0.624375\pi$
$31$	−4.24119	−0.761740	−0.380870	+	0.924629i	$0.624375\pi$
$32$	2.79915	0.494825
$33$	6.38068	1.11073
$34$	4.78856	0.821231
$35$	6.30600	1.06591
$36$	−3.94405	−0.657342
$37$	9.89737	1.62712	0.813558	−	0.581483i	$-0.197527\pi$
$37$	9.89737	1.62712	0.813558	+	0.581483i	$0.197527\pi$
$38$	5.01922	0.814225
$39$	14.4760	2.31801
$40$	8.18758	1.29457
$41$	8.30439	1.29693	0.648464	−	0.761245i	$-0.275412\pi$
$41$	8.30439	1.29693	0.648464	+	0.761245i	$0.275412\pi$
$42$	−9.45200	−1.45847
$43$	1.86772	0.284824	0.142412	−	0.989807i	$-0.454514\pi$
$43$	1.86772	0.284824	0.142412	+	0.989807i	$0.454514\pi$
$44$	−0.988945	−0.149089
$45$	−20.7348	−3.09096
$46$	−2.02849	−0.299085
$47$	−1.06890	−0.155916	−0.0779578	−	0.996957i	$-0.524840\pi$
$47$	−1.06890	−0.155916	−0.0779578	+	0.996957i	$0.524840\pi$
$48$	−8.93740	−1.29000
$49$	−1.43274	−0.204677
$50$	2.61702	0.370103
$51$	12.8601	1.80078
$52$	−2.24364	−0.311136
$53$	2.13791	0.293665	0.146833	−	0.989161i	$-0.453092\pi$
$53$	2.13791	0.293665	0.146833	+	0.989161i	$0.453092\pi$
$54$	19.0613	2.59392
$55$	−5.19911	−0.701048
$56$	7.22841	0.965937
$57$	13.4796	1.78541
$58$	3.17931	0.417464
$59$	0.757159	0.0985737	0.0492868	−	0.998785i	$-0.484305\pi$
$59$	0.757159	0.0985737	0.0492868	+	0.998785i	$0.484305\pi$
$60$	4.45637	0.575315
$61$	1.65253	0.211585	0.105792	−	0.994388i	$-0.466262\pi$
$61$	1.65253	0.211585	0.105792	+	0.994388i	$0.466262\pi$
$62$	−5.17987	−0.657844
$63$	−18.3057	−2.30630
$64$	8.86834	1.10854
$65$	−11.7953	−1.46303
$66$	7.79288	0.959238
$67$	0.348893	0.0426241	0.0213120	−	0.999773i	$-0.493216\pi$
$67$	0.348893	0.0426241	0.0213120	+	0.999773i	$0.493216\pi$
$68$	−1.99320	−0.241711
$69$	−5.44771	−0.655828
$70$	7.70168	0.920527
$71$	−0.645299	−0.0765830	−0.0382915	−	0.999267i	$-0.512192\pi$
$71$	−0.645299	−0.0765830	−0.0382915	+	0.999267i	$0.512192\pi$
$72$	−23.7677	−2.80105
$73$	0.955846	0.111873	0.0559366	−	0.998434i	$-0.482186\pi$
$73$	0.955846	0.111873	0.0559366	+	0.998434i	$0.482186\pi$
$74$	12.0879	1.40519
$75$	7.02826	0.811553
$76$	−2.08921	−0.239649
$77$	−4.59004	−0.523083
$78$	17.6798	2.00185
$79$	−6.36556	−0.716181	−0.358091	−	0.933687i	$-0.616572\pi$
$79$	−6.36556	−0.716181	−0.358091	+	0.933687i	$0.616572\pi$
$80$	7.28238	0.814194
$81$	27.9161	3.10179
$82$	10.1424	1.12004
$83$	−3.56250	−0.391035	−0.195517	−	0.980700i	$-0.562639\pi$
$83$	−3.56250	−0.391035	−0.195517	+	0.980700i	$0.562639\pi$
$84$	3.93431	0.429269
$85$	−10.4787	−1.13657
$86$	2.28109	0.245976
$87$	8.53833	0.915405
$88$	−5.95961	−0.635296
$89$	−11.3485	−1.20294	−0.601471	−	0.798894i	$-0.705419\pi$
$89$	−11.3485	−1.20294	−0.601471	+	0.798894i	$0.705419\pi$
$90$	−25.3239	−2.66937
$91$	−10.4135	−1.09163
$92$	0.844344	0.0880289
$93$	−13.9110	−1.44251
$94$	−1.30548	−0.134650
$95$	−10.9834	−1.12688
$96$	9.18118	0.937050
$97$	8.90186	0.903847	0.451924	−	0.892057i	$-0.350738\pi$
$97$	8.90186	0.903847	0.451924	+	0.892057i	$0.350738\pi$
$98$	−1.74984	−0.176760
$99$	15.0925	1.51685
$100$	−1.08931	−0.108931
$101$	−7.81113	−0.777236	−0.388618	−	0.921399i	$-0.627047\pi$
$101$	−7.81113	−0.777236	−0.388618	+	0.921399i	$0.627047\pi$
$102$	15.7064	1.55516
$103$	−0.869054	−0.0856305	−0.0428152	−	0.999083i	$-0.513633\pi$
$103$	−0.869054	−0.0856305	−0.0428152	+	0.999083i	$0.513633\pi$
$104$	−13.5207	−1.32581
$105$	20.6836	2.01851
$106$	2.61109	0.253611
$107$	−16.4402	−1.58934	−0.794668	−	0.607045i	$-0.792355\pi$
$107$	−16.4402	−1.58934	−0.794668	+	0.607045i	$0.792355\pi$
$108$	−7.93412	−0.763461
$109$	−11.3738	−1.08941	−0.544706	−	0.838627i	$-0.683359\pi$
$109$	−11.3738	−1.08941	−0.544706	+	0.838627i	$0.683359\pi$
$110$	−6.34980	−0.605430
$111$	32.4632	3.08127
$112$	6.42925	0.607507
$113$	10.8276	1.01858	0.509289	−	0.860596i	$-0.329908\pi$
$113$	10.8276	1.01858	0.509289	+	0.860596i	$0.329908\pi$
$114$	16.4630	1.54190
$115$	4.43891	0.413930
$116$	−1.32336	−0.122871
$117$	34.2406	3.16555
$118$	0.924737	0.0851289
$119$	−9.25112	−0.848049
$120$	26.8551	2.45153
$121$	−7.21565	−0.655968
$122$	2.01827	0.182726
$123$	27.2383	2.45599
$124$	2.15608	0.193621
$125$	7.63621	0.683004
$126$	−22.3572	−1.99174
$127$	−16.0485	−1.42408	−0.712039	−	0.702140i	$-0.752228\pi$
$127$	−16.0485	−1.42408	−0.712039	+	0.702140i	$0.752228\pi$
$128$	5.23281	0.462520
$129$	6.12608	0.539371
$130$	−14.4059	−1.26348
$131$	14.7887	1.29209	0.646045	−	0.763299i	$-0.276422\pi$
$131$	14.7887	1.29209	0.646045	+	0.763299i	$0.276422\pi$
$132$	−3.24372	−0.282330
$133$	−9.69674	−0.840814
$134$	0.426112	0.0368105
$135$	−41.7115	−3.58995
$136$	−12.0115	−1.02997
$137$	20.1035	1.71756	0.858781	−	0.512343i	$-0.171222\pi$
$137$	20.1035	1.71756	0.858781	+	0.512343i	$0.171222\pi$
$138$	−6.65343	−0.566377
$139$	−16.3401	−1.38595	−0.692975	−	0.720961i	$-0.743701\pi$
$139$	−16.3401	−1.38595	−0.692975	+	0.720961i	$0.743701\pi$
$140$	−3.20576	−0.270936
$141$	−3.50598	−0.295257
$142$	−0.788120	−0.0661376
$143$	8.58561	0.717965
$144$	−21.1400	−1.76167
$145$	−6.95721	−0.577765
$146$	1.16740	0.0966146
$147$	−4.69936	−0.387596
$148$	−5.03148	−0.413585
$149$	−4.56471	−0.373956	−0.186978	−	0.982364i	$-0.559869\pi$
$149$	−4.56471	−0.373956	−0.186978	+	0.982364i	$0.559869\pi$
$150$	8.58379	0.700863
$151$	1.89733	0.154403	0.0772013	−	0.997016i	$-0.475402\pi$
$151$	1.89733	0.154403	0.0772013	+	0.997016i	$0.475402\pi$
$152$	−12.5900	−1.02119
$153$	30.4186	2.45920
$154$	−5.60593	−0.451739
$155$	11.3350	0.910448
$156$	−7.35909	−0.589198
$157$	8.60839	0.687025	0.343512	−	0.939148i	$-0.388383\pi$
$157$	8.60839	0.687025	0.343512	+	0.939148i	$0.388383\pi$
$158$	−7.77442	−0.618499
$159$	7.01232	0.556113
$160$	−7.48101	−0.591426
$161$	3.91889	0.308852
$162$	34.0947	2.67873
$163$	9.99929	0.783205	0.391603	−	0.920134i	$-0.371921\pi$
$163$	9.99929	0.783205	0.391603	+	0.920134i	$0.371921\pi$
$164$	−4.22167	−0.329657
$165$	−17.0530	−1.32757
$166$	−4.35097	−0.337701
$167$	−19.9646	−1.54491	−0.772454	−	0.635071i	$-0.780971\pi$
$167$	−19.9646	−1.54491	−0.772454	+	0.635071i	$0.780971\pi$
$168$	23.7091	1.82919
$169$	6.47832	0.498333
$170$	−12.7979	−0.981553
$171$	31.8839	2.43822
$172$	−0.949484	−0.0723975
$173$	13.8636	1.05403	0.527015	−	0.849856i	$-0.323311\pi$
$173$	13.8636	1.05403	0.527015	+	0.849856i	$0.323311\pi$
$174$	10.4281	0.790550
$175$	−5.05588	−0.382189
$176$	−5.30072	−0.399557
$177$	2.48347	0.186669
$178$	−13.8603	−1.03887
$179$	−12.8817	−0.962826	−0.481413	−	0.876494i	$-0.659876\pi$
$179$	−12.8817	−0.962826	−0.481413	+	0.876494i	$0.659876\pi$
$180$	10.5409	0.785669
$181$	−9.22923	−0.686003	−0.343002	−	0.939335i	$-0.611444\pi$
$181$	−9.22923	−0.686003	−0.343002	+	0.939335i	$0.611444\pi$
$182$	−12.7183	−0.942740
$183$	5.42026	0.400677
$184$	5.08821	0.375108
$185$	−26.4517	−1.94477
$186$	−16.9899	−1.24576
$187$	7.62727	0.557761
$188$	0.543394	0.0396311
$189$	−36.8250	−2.67863
$190$	−13.4143	−0.973179
$191$	−5.60568	−0.405613	−0.202806	−	0.979219i	$-0.565006\pi$
$191$	−5.60568	−0.405613	−0.202806	+	0.979219i	$0.565006\pi$
$192$	29.0880	2.09925
$193$	2.47792	0.178365	0.0891824	−	0.996015i	$-0.471575\pi$
$193$	2.47792	0.178365	0.0891824	+	0.996015i	$0.471575\pi$
$194$	10.8721	0.780569
$195$	−38.6884	−2.77053
$196$	0.728356	0.0520254
$197$	24.3084	1.73190	0.865950	−	0.500131i	$-0.166715\pi$
$197$	24.3084	1.73190	0.865950	+	0.500131i	$0.166715\pi$
$198$	18.4329	1.30997
$199$	0.942622	0.0668207	0.0334104	−	0.999442i	$-0.489363\pi$
$199$	0.942622	0.0668207	0.0334104	+	0.999442i	$0.489363\pi$
$200$	−6.56445	−0.464177
$201$	1.14436	0.0807172
$202$	−9.53992	−0.671227
$203$	−6.14218	−0.431096
$204$	−6.53765	−0.457727
$205$	−22.1943	−1.55012
$206$	−1.06140	−0.0739511
$207$	−12.8857	−0.895619
$208$	−12.0258	−0.833842
$209$	7.99467	0.553003
$210$	25.2614	1.74320
$211$	10.8898	0.749687	0.374843	−	0.927088i	$-0.377696\pi$
$211$	10.8898	0.749687	0.374843	+	0.927088i	$0.377696\pi$
$212$	−1.08684	−0.0746447
$213$	−2.11657	−0.145025
$214$	−20.0788	−1.37256
$215$	−4.99165	−0.340428
$216$	−47.8128	−3.25325
$217$	10.0071	0.679326
$218$	−13.8911	−0.940824
$219$	3.13516	0.211854
$220$	2.64305	0.178194
$221$	17.3041	1.16400
$222$	39.6481	2.66101
$223$	−17.7240	−1.18688	−0.593442	−	0.804877i	$-0.702231\pi$
$223$	−17.7240	−1.18688	−0.593442	+	0.804877i	$0.702231\pi$
$224$	−6.60462	−0.441290
$225$	16.6242	1.10828
$226$	13.2241	0.879651
$227$	5.08396	0.337434	0.168717	−	0.985665i	$-0.446038\pi$
$227$	5.08396	0.337434	0.168717	+	0.985665i	$0.446038\pi$
$228$	−6.85256	−0.453822
$229$	17.2844	1.14219	0.571094	−	0.820885i	$-0.306519\pi$
$229$	17.2844	1.14219	0.571094	+	0.820885i	$0.306519\pi$
$230$	5.42135	0.357473
$231$	−15.0552	−0.990563
$232$	−7.97487	−0.523576
$233$	15.7046	1.02884	0.514422	−	0.857537i	$-0.328007\pi$
$233$	15.7046	1.02884	0.514422	+	0.857537i	$0.328007\pi$
$234$	41.8189	2.73379
$235$	2.85675	0.186354
$236$	−0.384914	−0.0250558
$237$	−20.8789	−1.35623
$238$	−11.2986	−0.732381
$239$	−12.3237	−0.797153	−0.398576	−	0.917135i	$-0.630496\pi$
$239$	−12.3237	−0.797153	−0.398576	+	0.917135i	$0.630496\pi$
$240$	23.8861	1.54184
$241$	24.2310	1.56085	0.780427	−	0.625247i	$-0.215002\pi$
$241$	24.2310	1.56085	0.780427	+	0.625247i	$0.215002\pi$
$242$	−8.81265	−0.566499
$243$	44.7432	2.87028
$244$	−0.840089	−0.0537812
$245$	3.82913	0.244634
$246$	33.2667	2.12101
$247$	18.1376	1.15407
$248$	12.9930	0.825057
$249$	−11.6849	−0.740502
$250$	9.32630	0.589847
$251$	−27.1528	−1.71387	−0.856936	−	0.515422i	$-0.827635\pi$
$251$	−27.1528	−1.71387	−0.856936	+	0.515422i	$0.827635\pi$
$252$	9.30600	0.586223
$253$	−3.23101	−0.203132
$254$	−19.6005	−1.22984
$255$	−34.3699	−2.15233
$256$	−11.3457	−0.709107
$257$	−7.47712	−0.466410	−0.233205	−	0.972428i	$-0.574921\pi$
$257$	−7.47712	−0.466410	−0.233205	+	0.972428i	$0.574921\pi$
$258$	7.48193	0.465805
$259$	−23.3529	−1.45108
$260$	5.99633	0.371877
$261$	20.1961	1.25011
$262$	18.0618	1.11586
$263$	29.8918	1.84321	0.921604	−	0.388131i	$-0.126879\pi$
$263$	29.8918	1.84321	0.921604	+	0.388131i	$0.126879\pi$
$264$	−19.5474	−1.20306
$265$	−5.71378	−0.350995
$266$	−11.8429	−0.726133
$267$	−37.2230	−2.27801
$268$	−0.177365	−0.0108343
$269$	−18.3251	−1.11730	−0.558651	−	0.829403i	$-0.688681\pi$
$269$	−18.3251	−1.11730	−0.558651	+	0.829403i	$0.688681\pi$
$270$	−50.9433	−3.10031
$271$	−21.6484	−1.31504	−0.657522	−	0.753435i	$-0.728395\pi$
$271$	−21.6484	−1.31504	−0.657522	+	0.753435i	$0.728395\pi$
$272$	−10.6835	−0.647782
$273$	−34.1561	−2.06722
$274$	24.5530	1.48330
$275$	4.16842	0.251365
$276$	2.76943	0.166700
$277$	−14.2887	−0.858522	−0.429261	−	0.903180i	$-0.641226\pi$
$277$	−14.2887	−0.858522	−0.429261	+	0.903180i	$0.641226\pi$
$278$	−19.9566	−1.19692
$279$	−32.9044	−1.96993
$280$	−19.3186	−1.15451
$281$	−32.5383	−1.94107	−0.970535	−	0.240959i	$-0.922538\pi$
$281$	−32.5383	−1.94107	−0.970535	+	0.240959i	$0.922538\pi$
$282$	−4.28195	−0.254986
$283$	−10.6521	−0.633199	−0.316600	−	0.948559i	$-0.602541\pi$
$283$	−10.6521	−0.633199	−0.316600	+	0.948559i	$0.602541\pi$
$284$	0.328048	0.0194661
$285$	−36.0255	−2.13397
$286$	10.4858	0.620040
$287$	−19.5942	−1.15661
$288$	21.7166	1.27967
$289$	−1.62741	−0.0957301
$290$	−8.49701	−0.498962
$291$	29.1980	1.71161
$292$	−0.485920	−0.0284363
$293$	25.0642	1.46427	0.732134	−	0.681161i	$-0.238524\pi$
$293$	25.0642	1.46427	0.732134	+	0.681161i	$0.238524\pi$
$294$	−5.73944	−0.334731
$295$	−2.02358	−0.117817
$296$	−30.3209	−1.76236
$297$	30.3611	1.76173
$298$	−5.57499	−0.322951
$299$	−7.33025	−0.423919
$300$	−3.57293	−0.206283
$301$	−4.40689	−0.254009
$302$	2.31726	0.133343
$303$	−25.6204	−1.47185
$304$	−11.1981	−0.642256
$305$	−4.41654	−0.252890
$306$	37.1510	2.12378
$307$	−2.26599	−0.129327	−0.0646635	−	0.997907i	$-0.520597\pi$
$307$	−2.26599	−0.129327	−0.0646635	+	0.997907i	$0.520597\pi$
$308$	2.33342	0.132959
$309$	−2.85048	−0.162158
$310$	13.8437	0.786269
$311$	−20.2837	−1.15019	−0.575093	−	0.818088i	$-0.695034\pi$
$311$	−20.2837	−1.15019	−0.575093	+	0.818088i	$0.695034\pi$
$312$	−44.3475	−2.51068
$313$	−22.5747	−1.27600	−0.637998	−	0.770038i	$-0.720237\pi$
$313$	−22.5747	−1.27600	−0.637998	+	0.770038i	$0.720237\pi$
$314$	10.5136	0.593319
$315$	48.9238	2.75654
$316$	3.23603	0.182041
$317$	−0.103980	−0.00584009	−0.00292004	−	0.999996i	$-0.500929\pi$
$317$	−0.103980	−0.00584009	−0.00292004	+	0.999996i	$0.500929\pi$
$318$	8.56432	0.480263
$319$	5.06404	0.283532
$320$	−23.7015	−1.32495
$321$	−53.9236	−3.00972
$322$	4.78624	0.266727
$323$	16.1131	0.896556
$324$	−14.1916	−0.788423
$325$	9.45697	0.524578
$326$	12.2124	0.676381
$327$	−37.3059	−2.06302
$328$	−25.4407	−1.40473
$329$	2.52208	0.139047
$330$	−20.8272	−1.14650
$331$	7.85280	0.431629	0.215814	−	0.976434i	$-0.430759\pi$
$331$	7.85280	0.431629	0.215814	+	0.976434i	$0.430759\pi$
$332$	1.81105	0.0993945
$333$	76.7866	4.20788
$334$	−24.3833	−1.33419
$335$	−0.932451	−0.0509452
$336$	21.0878	1.15044
$337$	−30.2791	−1.64941	−0.824704	−	0.565564i	$-0.808658\pi$
$337$	−30.2791	−1.64941	−0.824704	+	0.565564i	$0.808658\pi$
$338$	7.91214	0.430363
$339$	35.5144	1.92888
$340$	5.32701	0.288898
$341$	−8.25055	−0.446793
$342$	38.9405	2.10566
$343$	19.8971	1.07434
$344$	−5.72181	−0.308499
$345$	14.5595	0.783859
$346$	16.9320	0.910268
$347$	−12.0283	−0.645710	−0.322855	−	0.946448i	$-0.604643\pi$
$347$	−12.0283	−0.645710	−0.322855	+	0.946448i	$0.604643\pi$
$348$	−4.34060	−0.232680
$349$	20.3049	1.08690	0.543449	−	0.839442i	$-0.317118\pi$
$349$	20.3049	1.08690	0.543449	+	0.839442i	$0.317118\pi$
$350$	−6.17487	−0.330061
$351$	68.8808	3.67658
$352$	5.44531	0.290236
$353$	28.7411	1.52973	0.764867	−	0.644188i	$-0.222805\pi$
$353$	28.7411	1.52973	0.764867	+	0.644188i	$0.222805\pi$
$354$	3.03312	0.161209
$355$	1.72463	0.0915336
$356$	5.76921	0.305768
$357$	−30.3435	−1.60595
$358$	−15.7328	−0.831503
$359$	4.58676	0.242080	0.121040	−	0.992648i	$-0.461377\pi$
$359$	4.58676	0.242080	0.121040	+	0.992648i	$0.461377\pi$
$360$	63.5216	3.34788
$361$	−2.11076	−0.111093
$362$	−11.2719	−0.592437
$363$	−23.6672	−1.24221
$364$	5.29387	0.277474
$365$	−2.55459	−0.133713
$366$	6.61990	0.346028
$367$	−27.2921	−1.42464	−0.712318	−	0.701857i	$-0.752354\pi$
$367$	−27.2921	−1.42464	−0.712318	+	0.701857i	$0.752354\pi$
$368$	4.52567	0.235917
$369$	64.4278	3.35398
$370$	−32.3061	−1.67951
$371$	−5.04442	−0.261893
$372$	7.07189	0.366661
$373$	13.3013	0.688716	0.344358	−	0.938838i	$-0.388097\pi$
$373$	13.3013	0.688716	0.344358	+	0.938838i	$0.388097\pi$
$374$	9.31537	0.481686
$375$	25.0467	1.29340
$376$	3.27462	0.168875
$377$	11.4889	0.591707
$378$	−44.9753	−2.31328
$379$	10.2720	0.527636	0.263818	−	0.964572i	$-0.415018\pi$
$379$	10.2720	0.527636	0.263818	+	0.964572i	$0.415018\pi$
$380$	5.58361	0.286433
$381$	−52.6389	−2.69677
$382$	−6.84635	−0.350290
$383$	0.964287	0.0492727	0.0246364	−	0.999696i	$-0.492157\pi$
$383$	0.964287	0.0492727	0.0246364	+	0.999696i	$0.492157\pi$
$384$	17.1635	0.875873
$385$	12.2673	0.625201
$386$	3.02635	0.154037
$387$	14.4903	0.736583
$388$	−4.52541	−0.229743
$389$	−4.11770	−0.208775	−0.104388	−	0.994537i	$-0.533288\pi$
$389$	−4.11770	−0.208775	−0.104388	+	0.994537i	$0.533288\pi$
$390$	−47.2511	−2.39265
$391$	−6.51203	−0.329327
$392$	4.38924	0.221690
$393$	48.5065	2.44683
$394$	29.6884	1.49568
$395$	17.0126	0.855996
$396$	−7.67252	−0.385559
$397$	9.86304	0.495012	0.247506	−	0.968886i	$-0.420389\pi$
$397$	9.86304	0.495012	0.247506	+	0.968886i	$0.420389\pi$
$398$	1.15125	0.0577068
$399$	−31.8051	−1.59225
$400$	−5.83870	−0.291935
$401$	14.2244	0.710331	0.355166	−	0.934803i	$-0.384424\pi$
$401$	14.2244	0.710331	0.355166	+	0.934803i	$0.384424\pi$
$402$	1.39764	0.0697079
$403$	−18.7182	−0.932418
$404$	3.97091	0.197560
$405$	−74.6086	−3.70733
$406$	−7.50159	−0.372298
$407$	19.2537	0.954373
$408$	−39.3974	−1.95046
$409$	−25.5888	−1.26529	−0.632643	−	0.774444i	$-0.718030\pi$
$409$	−25.5888	−1.26529	−0.632643	+	0.774444i	$0.718030\pi$
$410$	−27.1064	−1.33869
$411$	65.9393	3.25255
$412$	0.441798	0.0217658
$413$	−1.78652	−0.0879089
$414$	−15.7376	−0.773463
$415$	9.52112	0.467373
$416$	12.3539	0.605698
$417$	−53.5953	−2.62457
$418$	9.76409	0.477577
$419$	3.58942	0.175354	0.0876772	−	0.996149i	$-0.472056\pi$
$419$	3.58942	0.175354	0.0876772	+	0.996149i	$0.472056\pi$
$420$	−10.5148	−0.513071
$421$	34.6326	1.68789	0.843946	−	0.536429i	$-0.180227\pi$
$421$	34.6326	1.68789	0.843946	+	0.536429i	$0.180227\pi$
$422$	13.3000	0.647435
$423$	−8.29286	−0.403213
$424$	−6.54956	−0.318075
$425$	8.40136	0.407526
$426$	−2.58502	−0.125245
$427$	−3.89915	−0.188693
$428$	8.35765	0.403982
$429$	28.1607	1.35961
$430$	−6.09643	−0.293996
$431$	−39.3812	−1.89693	−0.948463	−	0.316888i	$-0.897362\pi$
$431$	−39.3812	−1.89693	−0.948463	+	0.316888i	$0.897362\pi$
$432$	−42.5267	−2.04607
$433$	−31.6291	−1.52000	−0.759998	−	0.649925i	$-0.774800\pi$
$433$	−31.6291	−1.52000	−0.759998	+	0.649925i	$0.774800\pi$
$434$	12.2219	0.586671
$435$	−22.8195	−1.09411
$436$	5.78205	0.276910
$437$	−6.82571	−0.326518
$438$	3.82905	0.182959
$439$	−9.89603	−0.472312	−0.236156	−	0.971715i	$-0.575888\pi$
$439$	−9.89603	−0.472312	−0.236156	+	0.971715i	$0.575888\pi$
$440$	15.9276	0.759320
$441$	−11.1156	−0.529314
$442$	21.1339	1.00524
$443$	−0.300559	−0.0142800	−0.00714000	−	0.999975i	$-0.502273\pi$
$443$	−0.300559	−0.0142800	−0.00714000	+	0.999975i	$0.502273\pi$
$444$	−16.5032	−0.783206
$445$	30.3301	1.43778
$446$	−21.6467	−1.02500
$447$	−14.9722	−0.708159
$448$	−20.9249	−0.988608
$449$	25.6057	1.20841	0.604203	−	0.796830i	$-0.293492\pi$
$449$	25.6057	1.20841	0.604203	+	0.796830i	$0.293492\pi$
$450$	20.3036	0.957121
$451$	16.1549	0.760703
$452$	−5.50440	−0.258905
$453$	6.22322	0.292392
$454$	6.20916	0.291410
$455$	27.8311	1.30474
$456$	−41.2951	−1.93382
$457$	−39.0442	−1.82641	−0.913206	−	0.407497i	$-0.866402\pi$
$457$	−39.0442	−1.82641	−0.913206	+	0.407497i	$0.866402\pi$
$458$	21.1099	0.986401
$459$	61.1921	2.85620
$460$	−2.25659	−0.105214
$461$	18.9191	0.881149	0.440575	−	0.897716i	$-0.354775\pi$
$461$	18.9191	0.881149	0.440575	+	0.897716i	$0.354775\pi$
$462$	−18.3873	−0.855457
$463$	14.7642	0.686149	0.343075	−	0.939308i	$-0.388532\pi$
$463$	14.7642	0.686149	0.343075	+	0.939308i	$0.388532\pi$
$464$	−7.09318	−0.329293
$465$	37.1786	1.72411
$466$	19.1804	0.888516
$467$	22.7781	1.05404	0.527021	−	0.849852i	$-0.323309\pi$
$467$	22.7781	1.05404	0.527021	+	0.849852i	$0.323309\pi$
$468$	−17.4068	−0.804628
$469$	−0.823215	−0.0380125
$470$	3.48902	0.160936
$471$	28.2354	1.30102
$472$	−2.31958	−0.106767
$473$	3.63335	0.167061
$474$	−25.4999	−1.17125
$475$	8.80605	0.404049
$476$	4.70296	0.215560
$477$	16.5866	0.759446
$478$	−15.0512	−0.688427
$479$	7.79200	0.356026	0.178013	−	0.984028i	$-0.443033\pi$
$479$	7.79200	0.356026	0.178013	+	0.984028i	$0.443033\pi$
$480$	−24.5376	−1.11998
$481$	43.6813	1.99170
$482$	29.5939	1.34796
$483$	12.8539	0.584873
$484$	3.66819	0.166736
$485$	−23.7911	−1.08030
$486$	54.6460	2.47879
$487$	30.6173	1.38740	0.693701	−	0.720263i	$-0.255979\pi$
$487$	30.6173	1.38740	0.693701	+	0.720263i	$0.255979\pi$
$488$	−5.06257	−0.229172
$489$	32.7975	1.48315
$490$	4.67661	0.211268
$491$	31.5750	1.42496	0.712481	−	0.701692i	$-0.247572\pi$
$491$	31.5750	1.42496	0.712481	+	0.701692i	$0.247572\pi$
$492$	−13.8470	−0.624271
$493$	10.2065	0.459676
$494$	22.1519	0.996663
$495$	−40.3362	−1.81298
$496$	11.5565	0.518903
$497$	1.52259	0.0682974
$498$	−14.2711	−0.639503
$499$	25.4696	1.14018	0.570088	−	0.821584i	$-0.306909\pi$
$499$	25.4696	1.14018	0.570088	+	0.821584i	$0.306909\pi$
$500$	−3.88199	−0.173608
$501$	−65.4836	−2.92559
$502$	−33.1624	−1.48011
$503$	−10.0595	−0.448532	−0.224266	−	0.974528i	$-0.571998\pi$
$503$	−10.0595	−0.448532	−0.224266	+	0.974528i	$0.571998\pi$
$504$	56.0801	2.49801
$505$	20.8760	0.928970
$506$	−3.94611	−0.175426
$507$	21.2488	0.943692
$508$	8.15853	0.361976
$509$	−22.8682	−1.01362	−0.506808	−	0.862059i	$-0.669175\pi$
$509$	−22.8682	−1.01362	−0.506808	+	0.862059i	$0.669175\pi$
$510$	−41.9768	−1.85877
$511$	−2.25532	−0.0997696
$512$	−24.3224	−1.07491
$513$	64.1397	2.83184
$514$	−9.13200	−0.402795
$515$	2.32263	0.102347
$516$	−3.11429	−0.137099
$517$	−2.07938	−0.0914511
$518$	−28.5214	−1.25316
$519$	45.4724	1.99602
$520$	36.1353	1.58464
$521$	17.5150	0.767346	0.383673	−	0.923469i	$-0.374659\pi$
$521$	17.5150	0.767346	0.383673	+	0.923469i	$0.374659\pi$
$522$	24.6660	1.07960
$523$	31.7698	1.38920	0.694599	−	0.719397i	$-0.255582\pi$
$523$	31.7698	1.38920	0.694599	+	0.719397i	$0.255582\pi$
$524$	−7.51805	−0.328428
$525$	−16.5832	−0.723751
$526$	36.5076	1.59181
$527$	−16.6288	−0.724362
$528$	−17.3863	−0.756641
$529$	−20.2414	−0.880062
$530$	−6.97839	−0.303122
$531$	5.87426	0.254921
$532$	4.92949	0.213721
$533$	36.6508	1.58752
$534$	−45.4614	−1.96731
$535$	43.9381	1.89961
$536$	−1.06884	−0.0461671
$537$	−42.2519	−1.82330
$538$	−22.3809	−0.964910
$539$	−2.78716	−0.120052
$540$	21.2047	0.912505
$541$	−27.7449	−1.19285	−0.596424	−	0.802670i	$-0.703412\pi$
$541$	−27.7449	−1.19285	−0.596424	+	0.802670i	$0.703412\pi$
$542$	−26.4397	−1.13568
$543$	−30.2717	−1.29908
$544$	10.9749	0.470545
$545$	30.3976	1.30209
$546$	−41.7157	−1.78527
$547$	−25.2885	−1.08126	−0.540629	−	0.841261i	$-0.681814\pi$
$547$	−25.2885	−1.08126	−0.540629	+	0.841261i	$0.681814\pi$
$548$	−10.2200	−0.436575
$549$	12.8208	0.547178
$550$	5.09100	0.217081
$551$	10.6981	0.455754
$552$	16.6892	0.710341
$553$	15.0196	0.638697
$554$	−17.4511	−0.741426
$555$	−86.7610	−3.68280
$556$	8.30676	0.352285
$557$	−0.313325	−0.0132760	−0.00663801	−	0.999978i	$-0.502113\pi$
$557$	−0.313325	−0.0132760	−0.00663801	+	0.999978i	$0.502113\pi$
$558$	−40.1869	−1.70125
$559$	8.24303	0.348643
$560$	−17.1828	−0.726106
$561$	25.0173	1.05623
$562$	−39.7398	−1.67632
$563$	−37.5178	−1.58119	−0.790594	−	0.612341i	$-0.790228\pi$
$563$	−37.5178	−1.58119	−0.790594	+	0.612341i	$0.790228\pi$
$564$	1.78232	0.0750494
$565$	−28.9379	−1.21743
$566$	−13.0096	−0.546835
$567$	−65.8683	−2.76621
$568$	1.97689	0.0829486
$569$	38.9162	1.63145	0.815725	−	0.578439i	$-0.196338\pi$
$569$	38.9162	1.63145	0.815725	+	0.578439i	$0.196338\pi$
$570$	−43.9988	−1.84291
$571$	18.0234	0.754257	0.377128	−	0.926161i	$-0.376912\pi$
$571$	18.0234	0.754257	0.377128	+	0.926161i	$0.376912\pi$
$572$	−4.36463	−0.182495
$573$	−18.3865	−0.768108
$574$	−23.9309	−0.998858
$575$	−3.55893	−0.148417
$576$	68.8031	2.86680
$577$	−15.2014	−0.632844	−0.316422	−	0.948618i	$-0.602482\pi$
$577$	−15.2014	−0.632844	−0.316422	+	0.948618i	$0.602482\pi$
$578$	−1.98760	−0.0826732
$579$	8.12755	0.337769
$580$	3.53681	0.146858
$581$	8.40573	0.348728
$582$	35.6602	1.47816
$583$	4.15897	0.172247
$584$	−2.92826	−0.121172
$585$	−91.5114	−3.78353
$586$	30.6116	1.26455
$587$	−18.0156	−0.743585	−0.371793	−	0.928316i	$-0.621257\pi$
$587$	−18.0156	−0.743585	−0.371793	+	0.928316i	$0.621257\pi$
$588$	2.38899	0.0985204
$589$	−17.4298	−0.718183
$590$	−2.47145	−0.101748
$591$	79.7310	3.27970
$592$	−26.9687	−1.10840
$593$	−32.8144	−1.34752	−0.673762	−	0.738948i	$-0.735323\pi$
$593$	−32.8144	−1.34752	−0.673762	+	0.738948i	$0.735323\pi$
$594$	37.0808	1.52144
$595$	24.7245	1.01361
$596$	2.32054	0.0950532
$597$	3.09178	0.126538
$598$	−8.95261	−0.366099
$599$	7.05665	0.288327	0.144163	−	0.989554i	$-0.453951\pi$
$599$	7.05665	0.288327	0.144163	+	0.989554i	$0.453951\pi$
$600$	−21.5313	−0.879011
$601$	−4.62617	−0.188705	−0.0943527	−	0.995539i	$-0.530078\pi$
$601$	−4.62617	−0.188705	−0.0943527	+	0.995539i	$0.530078\pi$
$602$	−5.38224	−0.219364
$603$	2.70681	0.110230
$604$	−0.964539	−0.0392465
$605$	19.2845	0.784027
$606$	−31.2908	−1.27110
$607$	10.4655	0.424783	0.212391	−	0.977185i	$-0.431875\pi$
$607$	10.4655	0.424783	0.212391	+	0.977185i	$0.431875\pi$
$608$	11.5035	0.466531
$609$	−20.1462	−0.816367
$610$	−5.39403	−0.218398
$611$	−4.71753	−0.190851
$612$	−15.4638	−0.625087
$613$	3.26989	0.132070	0.0660348	−	0.997817i	$-0.478965\pi$
$613$	3.26989	0.132070	0.0660348	+	0.997817i	$0.478965\pi$
$614$	−2.76751	−0.111688
$615$	−72.7969	−2.93545
$616$	14.0617	0.566563
$617$	1.17113	0.0471479	0.0235740	−	0.999722i	$-0.492495\pi$
$617$	1.17113	0.0471479	0.0235740	+	0.999722i	$0.492495\pi$
$618$	−3.48137	−0.140041
$619$	19.3983	0.779683	0.389841	−	0.920882i	$-0.372530\pi$
$619$	19.3983	0.779683	0.389841	+	0.920882i	$0.372530\pi$
$620$	−5.76232	−0.231420
$621$	−25.9218	−1.04021
$622$	−24.7730	−0.993308
$623$	26.7769	1.07280
$624$	−39.4446	−1.57905
$625$	−31.1224	−1.24490
$626$	−27.5710	−1.10196
$627$	26.2224	1.04722
$628$	−4.37621	−0.174630
$629$	38.8055	1.54728
$630$	59.7518	2.38057
$631$	1.49519	0.0595227	0.0297613	−	0.999557i	$-0.490525\pi$
$631$	1.49519	0.0595227	0.0297613	+	0.999557i	$0.490525\pi$
$632$	19.5011	0.775711
$633$	35.7185	1.41968
$634$	−0.126993	−0.00504354
$635$	42.8913	1.70209
$636$	−3.56483	−0.141355
$637$	−6.32328	−0.250538
$638$	6.18484	0.244860
$639$	−5.00642	−0.198051
$640$	−13.9852	−0.552814
$641$	−11.0291	−0.435625	−0.217813	−	0.975991i	$-0.569892\pi$
$641$	−11.0291	−0.435625	−0.217813	+	0.975991i	$0.569892\pi$
$642$	−65.8582	−2.59922
$643$	−6.73072	−0.265434	−0.132717	−	0.991154i	$-0.542370\pi$
$643$	−6.73072	−0.265434	−0.132717	+	0.991154i	$0.542370\pi$
$644$	−1.99223	−0.0785050
$645$	−16.3725	−0.644668
$646$	19.6793	0.774272
$647$	−48.6114	−1.91111	−0.955557	−	0.294808i	$-0.904744\pi$
$647$	−48.6114	−1.91111	−0.955557	+	0.294808i	$0.904744\pi$
$648$	−85.5219	−3.35962
$649$	1.47293	0.0578176
$650$	11.5500	0.453029
$651$	32.8231	1.28644
$652$	−5.08330	−0.199077
$653$	−39.2922	−1.53762	−0.768811	−	0.639476i	$-0.779151\pi$
$653$	−39.2922	−1.53762	−0.768811	+	0.639476i	$0.779151\pi$
$654$	−45.5626	−1.78164
$655$	−39.5241	−1.54433
$656$	−22.6281	−0.883477
$657$	7.41573	0.289315
$658$	3.08028	0.120082
$659$	37.5709	1.46355	0.731777	−	0.681544i	$-0.238691\pi$
$659$	37.5709	1.46355	0.731777	+	0.681544i	$0.238691\pi$
$660$	8.66916	0.337447
$661$	−10.8036	−0.420213	−0.210106	−	0.977679i	$-0.567381\pi$
$661$	−10.8036	−0.420213	−0.210106	+	0.977679i	$0.567381\pi$
$662$	9.59082	0.372758
$663$	56.7572	2.20427
$664$	10.9138	0.423538
$665$	25.9155	1.00496
$666$	93.7814	3.63395
$667$	−4.32359	−0.167410
$668$	10.1493	0.392689
$669$	−58.1342	−2.24760
$670$	−1.13883	−0.0439967
$671$	3.21473	0.124103
$672$	−21.6630	−0.835670
$673$	−49.8936	−1.92326	−0.961629	−	0.274353i	$-0.911536\pi$
$673$	−49.8936	−1.92326	−0.961629	+	0.274353i	$0.911536\pi$
$674$	−36.9806	−1.42444
$675$	33.4425	1.28720
$676$	−3.29336	−0.126668
$677$	−5.52315	−0.212272	−0.106136	−	0.994352i	$-0.533848\pi$
$677$	−5.52315	−0.212272	−0.106136	+	0.994352i	$0.533848\pi$
$678$	43.3747	1.66579
$679$	−21.0040	−0.806059
$680$	32.1018	1.23105
$681$	16.6753	0.638998
$682$	−10.0766	−0.385853
$683$	29.6416	1.13420	0.567102	−	0.823648i	$-0.308065\pi$
$683$	29.6416	1.13420	0.567102	+	0.823648i	$0.308065\pi$
$684$	−16.2087	−0.619754
$685$	−53.7287	−2.05287
$686$	24.3008	0.927809
$687$	56.6926	2.16296
$688$	−5.08921	−0.194025
$689$	9.43553	0.359465
$690$	17.7819	0.676946
$691$	24.4341	0.929517	0.464759	−	0.885437i	$-0.346141\pi$
$691$	24.4341	0.929517	0.464759	+	0.885437i	$0.346141\pi$
$692$	−7.04779	−0.267917
$693$	−35.6108	−1.35274
$694$	−14.6904	−0.557640
$695$	43.6705	1.65652
$696$	−26.1574	−0.991495
$697$	32.5598	1.23329
$698$	24.7989	0.938653
$699$	51.5109	1.94832
$700$	2.57024	0.0971459
$701$	24.9247	0.941392	0.470696	−	0.882295i	$-0.344003\pi$
$701$	24.9247	0.941392	0.470696	+	0.882295i	$0.344003\pi$
$702$	84.1258	3.17512
$703$	40.6747	1.53408
$704$	17.2519	0.650207
$705$	9.37008	0.352898
$706$	35.1022	1.32109
$707$	18.4304	0.693146
$708$	−1.26251	−0.0474481
$709$	−20.8942	−0.784697	−0.392348	−	0.919817i	$-0.628337\pi$
$709$	−20.8942	−0.784697	−0.392348	+	0.919817i	$0.628337\pi$
$710$	2.10633	0.0790491
$711$	−49.3858	−1.85211
$712$	34.7666	1.30293
$713$	7.04418	0.263807
$714$	−37.0593	−1.38691
$715$	−22.9459	−0.858127
$716$	6.54863	0.244734
$717$	−40.4215	−1.50957
$718$	5.60193	0.209062
$719$	−3.61693	−0.134889	−0.0674443	−	0.997723i	$-0.521485\pi$
$719$	−3.61693	−0.134889	−0.0674443	+	0.997723i	$0.521485\pi$
$720$	56.4988	2.10558
$721$	2.05054	0.0763660
$722$	−2.57793	−0.0959405
$723$	79.4772	2.95579
$724$	4.69183	0.174370
$725$	5.57799	0.207161
$726$	−28.9053	−1.07278
$727$	26.0808	0.967282	0.483641	−	0.875266i	$-0.339314\pi$
$727$	26.0808	0.967282	0.483641	+	0.875266i	$0.339314\pi$
$728$	31.9021	1.18237
$729$	63.0085	2.33365
$730$	−3.11998	−0.115476
$731$	7.32293	0.270848
$732$	−2.75548	−0.101845
$733$	24.8036	0.916140	0.458070	−	0.888916i	$-0.348541\pi$
$733$	24.8036	0.916140	0.458070	+	0.888916i	$0.348541\pi$
$734$	−33.3325	−1.23033
$735$	12.5595	0.463264
$736$	−4.64911	−0.171368
$737$	0.678716	0.0250008
$738$	78.6873	2.89652
$739$	−16.6600	−0.612848	−0.306424	−	0.951895i	$-0.599133\pi$
$739$	−16.6600	−0.612848	−0.306424	+	0.951895i	$0.599133\pi$
$740$	13.4471	0.494326
$741$	59.4911	2.18546
$742$	−6.16087	−0.226173
$743$	11.5857	0.425039	0.212520	−	0.977157i	$-0.431833\pi$
$743$	11.5857	0.425039	0.212520	+	0.977157i	$0.431833\pi$
$744$	42.6168	1.56241
$745$	12.1996	0.446960
$746$	16.2452	0.594780
$747$	−27.6389	−1.01125
$748$	−3.87744	−0.141773
$749$	38.7908	1.41738
$750$	30.5901	1.11699
$751$	−41.3596	−1.50923	−0.754617	−	0.656166i	$-0.772177\pi$
$751$	−41.3596	−1.50923	−0.754617	+	0.656166i	$0.772177\pi$
$752$	2.91258	0.106211
$753$	−89.0609	−3.24556
$754$	14.0316	0.511002
$755$	−5.07080	−0.184545
$756$	18.7206	0.680861
$757$	41.0575	1.49226	0.746130	−	0.665800i	$-0.231910\pi$
$757$	41.0575	1.49226	0.746130	+	0.665800i	$0.231910\pi$
$758$	12.5454	0.455670
$759$	−10.5977	−0.384671
$760$	33.6481	1.22054
$761$	−42.3315	−1.53451	−0.767257	−	0.641340i	$-0.778379\pi$
$761$	−42.3315	−1.53451	−0.767257	+	0.641340i	$0.778379\pi$
$762$	−64.2892	−2.32895
$763$	26.8365	0.971547
$764$	2.84974	0.103100
$765$	−81.2967	−2.93929
$766$	1.17771	0.0425523
$767$	3.34166	0.120661
$768$	−37.2138	−1.34284
$769$	0.0562227	0.00202744	0.00101372	−	0.999999i	$-0.499677\pi$
$769$	0.0562227	0.00202744	0.00101372	+	0.999999i	$0.499677\pi$
$770$	14.9824	0.539928
$771$	−24.5248	−0.883241
$772$	−1.25969	−0.0453373
$773$	−2.39070	−0.0859875	−0.0429938	−	0.999075i	$-0.513690\pi$
$773$	−2.39070	−0.0859875	−0.0429938	+	0.999075i	$0.513690\pi$
$774$	17.6973	0.636118
$775$	−9.08790	−0.326447
$776$	−27.2711	−0.978976
$777$	−76.5970	−2.74790
$778$	−5.02904	−0.180300
$779$	34.1281	1.22277
$780$	19.6679	0.704223
$781$	−1.25533	−0.0449191
$782$	−7.95330	−0.284409
$783$	40.6278	1.45192
$784$	3.90397	0.139428
$785$	−23.0068	−0.821147
$786$	59.2422	2.11310
$787$	−41.1283	−1.46607	−0.733033	−	0.680193i	$-0.761896\pi$
$787$	−41.1283	−1.46607	−0.733033	+	0.680193i	$0.761896\pi$
$788$	−12.3575	−0.440219
$789$	98.0446	3.49048
$790$	20.7779	0.739244
$791$	−25.5478	−0.908377
$792$	−46.2363	−1.64294
$793$	7.29331	0.258993
$794$	12.0460	0.427495
$795$	−18.7411	−0.664679
$796$	−0.479197	−0.0169847
$797$	4.89717	0.173467	0.0867333	−	0.996232i	$-0.472357\pi$
$797$	4.89717	0.173467	0.0867333	+	0.996232i	$0.472357\pi$
$798$	−38.8444	−1.37508
$799$	−4.19095	−0.148265
$800$	5.99795	0.212060
$801$	−88.0452	−3.11093
$802$	17.3726	0.613447
$803$	1.85945	0.0656184
$804$	−0.581756	−0.0205169
$805$	−10.4736	−0.369147
$806$	−22.8610	−0.805243
$807$	−60.1061	−2.11583
$808$	23.9296	0.841841
$809$	−21.1417	−0.743303	−0.371652	−	0.928372i	$-0.621208\pi$
$809$	−21.1417	−0.743303	−0.371652	+	0.928372i	$0.621208\pi$
$810$	−91.1213	−3.20168
$811$	35.4113	1.24346	0.621730	−	0.783232i	$-0.286430\pi$
$811$	35.4113	1.24346	0.621730	+	0.783232i	$0.286430\pi$
$812$	3.12247	0.109577
$813$	−71.0062	−2.49030
$814$	23.5151	0.824203
$815$	−26.7241	−0.936104
$816$	−35.0417	−1.22670
$817$	7.67567	0.268538
$818$	−31.2523	−1.09271
$819$	−80.7909	−2.82306
$820$	11.2828	0.394013
$821$	37.0558	1.29325	0.646627	−	0.762806i	$-0.276179\pi$
$821$	37.0558	1.29325	0.646627	+	0.762806i	$0.276179\pi$
$822$	80.5333	2.80892
$823$	−55.1635	−1.92288	−0.961439	−	0.275017i	$-0.911316\pi$
$823$	−55.1635	−1.92288	−0.961439	+	0.275017i	$0.911316\pi$
$824$	2.66237	0.0927482
$825$	13.6724	0.476010
$826$	−2.18192	−0.0759187
$827$	−7.18303	−0.249778	−0.124889	−	0.992171i	$-0.539858\pi$
$827$	−7.18303	−0.249778	−0.124889	+	0.992171i	$0.539858\pi$
$828$	6.55066	0.227651
$829$	−27.5273	−0.956064	−0.478032	−	0.878343i	$-0.658650\pi$
$829$	−27.5273	−0.956064	−0.478032	+	0.878343i	$0.658650\pi$
$830$	11.6284	0.403627
$831$	−46.8666	−1.62578
$832$	39.1398	1.35693
$833$	−5.61747	−0.194634
$834$	−65.4573	−2.26660
$835$	53.3573	1.84651
$836$	−4.06422	−0.140564
$837$	−66.1926	−2.28795
$838$	4.38384	0.151437
$839$	11.7086	0.404225	0.202113	−	0.979362i	$-0.435219\pi$
$839$	11.7086	0.404225	0.202113	+	0.979362i	$0.435219\pi$
$840$	−63.3648	−2.18629
$841$	−22.2235	−0.766329
$842$	42.2977	1.45767
$843$	−106.725	−3.67580
$844$	−5.53602	−0.190558
$845$	−17.3139	−0.595618
$846$	−10.1283	−0.348217
$847$	17.0254	0.584998
$848$	−5.82546	−0.200047
$849$	−34.9386	−1.19909
$850$	10.2608	0.351942
$851$	−16.4385	−0.563505
$852$	1.07599	0.0368629
$853$	6.08399	0.208312	0.104156	−	0.994561i	$-0.466786\pi$
$853$	6.08399	0.208312	0.104156	+	0.994561i	$0.466786\pi$
$854$	−4.76213	−0.162957
$855$	−85.2127	−2.91421
$856$	50.3651	1.72144
$857$	14.9701	0.511368	0.255684	−	0.966760i	$-0.417699\pi$
$857$	14.9701	0.511368	0.255684	+	0.966760i	$0.417699\pi$
$858$	34.3933	1.17417
$859$	48.1987	1.64452	0.822260	−	0.569112i	$-0.192713\pi$
$859$	48.1987	1.64452	0.822260	+	0.569112i	$0.192713\pi$
$860$	2.53759	0.0865310
$861$	−64.2688	−2.19027
$862$	−48.0972	−1.63820
$863$	−0.845347	−0.0287759	−0.0143880	−	0.999896i	$-0.504580\pi$
$863$	−0.845347	−0.0287759	−0.0143880	+	0.999896i	$0.504580\pi$
$864$	43.6867	1.48625
$865$	−37.0518	−1.25980
$866$	−38.6294	−1.31268
$867$	−5.33788	−0.181284
$868$	−5.08727	−0.172673
$869$	−12.3832	−0.420071
$870$	−27.8700	−0.944883
$871$	1.53981	0.0521746
$872$	34.8440	1.17997
$873$	69.0632	2.33744
$874$	−8.33641	−0.281983
$875$	−18.0177	−0.609109
$876$	−1.59381	−0.0538498
$877$	−13.1675	−0.444635	−0.222318	−	0.974974i	$-0.571362\pi$
$877$	−13.1675	−0.444635	−0.222318	+	0.974974i	$0.571362\pi$
$878$	−12.0863	−0.407892
$879$	82.2103	2.77288
$880$	14.1667	0.477559
$881$	8.42209	0.283747	0.141874	−	0.989885i	$-0.454687\pi$
$881$	8.42209	0.283747	0.141874	+	0.989885i	$0.454687\pi$
$882$	−13.5757	−0.457119
$883$	−22.0601	−0.742380	−0.371190	−	0.928557i	$-0.621050\pi$
$883$	−22.0601	−0.742380	−0.371190	+	0.928557i	$0.621050\pi$
$884$	−8.79682	−0.295869
$885$	−6.63731	−0.223111
$886$	−0.367080	−0.0123323
$887$	−18.0363	−0.605601	−0.302800	−	0.953054i	$-0.597922\pi$
$887$	−18.0363	−0.605601	−0.302800	+	0.953054i	$0.597922\pi$
$888$	−99.4519	−3.33739
$889$	37.8666	1.27001
$890$	37.0429	1.24168
$891$	54.3064	1.81933
$892$	9.01025	0.301686
$893$	−4.39282	−0.147000
$894$	−18.2859	−0.611571
$895$	34.4277	1.15079
$896$	−12.3468	−0.412479
$897$	−24.0431	−0.802775
$898$	31.2728	1.04359
$899$	−11.0405	−0.368222
$900$	−8.45120	−0.281707
$901$	8.38231	0.279255
$902$	19.7303	0.656948
$903$	−14.4545	−0.481016
$904$	−33.1708	−1.10324
$905$	24.6660	0.819926
$906$	7.60057	0.252512
$907$	30.5709	1.01509	0.507545	−	0.861625i	$-0.330553\pi$
$907$	30.5709	1.01509	0.507545	+	0.861625i	$0.330553\pi$
$908$	−2.58451	−0.0857700
$909$	−60.6010	−2.01001
$910$	33.9908	1.12678
$911$	47.9027	1.58709	0.793543	−	0.608514i	$-0.208234\pi$
$911$	47.9027	1.58709	0.793543	+	0.608514i	$0.208234\pi$
$912$	−36.7296	−1.21624
$913$	−6.93027	−0.229358
$914$	−47.6857	−1.57730
$915$	−14.4862	−0.478898
$916$	−8.78682	−0.290325
$917$	−34.8939	−1.15230
$918$	74.7355	2.46664
$919$	−54.8038	−1.80781	−0.903906	−	0.427731i	$-0.859313\pi$
$919$	−54.8038	−1.80781	−0.903906	+	0.427731i	$0.859313\pi$
$920$	−13.5987	−0.448337
$921$	−7.43241	−0.244906
$922$	23.1063	0.760967
$923$	−2.84798	−0.0937424
$924$	7.65358	0.251784
$925$	21.2078	0.697308
$926$	18.0319	0.592563
$927$	−6.74237	−0.221449
$928$	7.28666	0.239196
$929$	−1.18181	−0.0387741	−0.0193870	−	0.999812i	$-0.506171\pi$
$929$	−1.18181	−0.0387741	−0.0193870	+	0.999812i	$0.506171\pi$
$930$	45.4071	1.48896
$931$	−5.88806	−0.192973
$932$	−7.98369	−0.261515
$933$	−66.5303	−2.17811
$934$	27.8194	0.910279
$935$	−20.3846	−0.666648
$936$	−104.897	−3.42867
$937$	36.8255	1.20304	0.601518	−	0.798859i	$-0.294563\pi$
$937$	36.8255	1.20304	0.601518	+	0.798859i	$0.294563\pi$
$938$	−1.00541	−0.0328279
$939$	−74.0445	−2.41635
$940$	−1.45227	−0.0473679
$941$	−36.7062	−1.19659	−0.598293	−	0.801277i	$-0.704154\pi$
$941$	−36.7062	−1.19659	−0.598293	+	0.801277i	$0.704154\pi$
$942$	34.4846	1.12357
$943$	−13.7927	−0.449153
$944$	−2.06313	−0.0671492
$945$	98.4184	3.20155
$946$	4.43749	0.144275
$947$	−15.8165	−0.513966	−0.256983	−	0.966416i	$-0.582729\pi$
$947$	−15.8165	−0.513966	−0.256983	+	0.966416i	$0.582729\pi$
$948$	10.6141	0.344731
$949$	4.21855	0.136940
$950$	10.7550	0.348940
$951$	−0.341052	−0.0110594
$952$	28.3411	0.918540
$953$	−44.6157	−1.44525	−0.722623	−	0.691243i	$-0.757064\pi$
$953$	−44.6157	−1.44525	−0.722623	+	0.691243i	$0.757064\pi$
$954$	20.2576	0.655863
$955$	14.9817	0.484797
$956$	6.26494	0.202623
$957$	16.6100	0.536924
$958$	9.51656	0.307466
$959$	−47.4344	−1.53174
$960$	−77.7405	−2.50906
$961$	−13.0123	−0.419752
$962$	53.3490	1.72004
$963$	−127.548	−4.11017
$964$	−12.3182	−0.396743
$965$	−6.62249	−0.213186
$966$	15.6988	0.505100
$967$	−43.7993	−1.40849	−0.704246	−	0.709956i	$-0.748715\pi$
$967$	−43.7993	−1.40849	−0.704246	+	0.709956i	$0.748715\pi$
$968$	22.1054	0.710493
$969$	52.8506	1.69781
$970$	−29.0567	−0.932953
$971$	−26.0054	−0.834554	−0.417277	−	0.908779i	$-0.637016\pi$
$971$	−26.0054	−0.834554	−0.417277	+	0.908779i	$0.637016\pi$
$972$	−22.7459	−0.729576
$973$	38.5546	1.23600
$974$	37.3937	1.19817
$975$	31.0187	0.993393
$976$	−4.50286	−0.144133
$977$	−28.0688	−0.898000	−0.449000	−	0.893532i	$-0.648220\pi$
$977$	−28.0688	−0.898000	−0.449000	+	0.893532i	$0.648220\pi$
$978$	40.0564	1.28086
$979$	−22.0768	−0.705577
$980$	−1.94660	−0.0621819
$981$	−88.2412	−2.81732
$982$	38.5634	1.23061
$983$	18.3838	0.586353	0.293177	−	0.956058i	$-0.405288\pi$
$983$	18.3838	0.586353	0.293177	+	0.956058i	$0.405288\pi$
$984$	−83.4452	−2.66014
$985$	−64.9665	−2.07000
$986$	12.4654	0.396979
$987$	8.27239	0.263313
$988$	−9.22056	−0.293345
$989$	−3.10209	−0.0986406
$990$	−49.2636	−1.56570
$991$	5.72738	0.181936	0.0909681	−	0.995854i	$-0.471004\pi$
$991$	5.72738	0.181936	0.0909681	+	0.995854i	$0.471004\pi$
$992$	−11.8717	−0.376928
$993$	25.7570	0.817375
$994$	1.85957	0.0589821
$995$	−2.51925	−0.0798656
$996$	5.94022	0.188223
$997$	−21.0257	−0.665892	−0.332946	−	0.942946i	$-0.608043\pi$
$997$	−21.0257	−0.665892	−0.332946	+	0.942946i	$0.608043\pi$
$998$	31.1066	0.984664
$999$	154.469	4.88719

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2671.2.a.b.1.81	✓	122

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2671.2.a.b.1.81	✓	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)

\(f(q)\)	\(=\)	\(q+1.22132 q^{2} +3.27998 q^{3} -0.508366 q^{4} -2.67260 q^{5} +4.00592 q^{6} -2.35950 q^{7} -3.06353 q^{8} +7.75829 q^{9} +O(q^{10})\)	\(q+1.22132 q^{2} +3.27998 q^{3} -0.508366 q^{4} -2.67260 q^{5} +4.00592 q^{6} -2.35950 q^{7} -3.06353 q^{8} +7.75829 q^{9} -3.26411 q^{10} +1.94534 q^{11} -1.66743 q^{12} +4.41343 q^{13} -2.88172 q^{14} -8.76607 q^{15} -2.72483 q^{16} +3.92079 q^{17} +9.47539 q^{18} +4.10965 q^{19} +1.35866 q^{20} -7.73913 q^{21} +2.37589 q^{22} -1.66090 q^{23} -10.0483 q^{24} +2.14277 q^{25} +5.39023 q^{26} +15.6071 q^{27} +1.19949 q^{28} +2.60316 q^{29} -10.7062 q^{30} -4.24119 q^{31} +2.79915 q^{32} +6.38068 q^{33} +4.78856 q^{34} +6.30600 q^{35} -3.94405 q^{36} +9.89737 q^{37} +5.01922 q^{38} +14.4760 q^{39} +8.18758 q^{40} +8.30439 q^{41} -9.45200 q^{42} +1.86772 q^{43} -0.988945 q^{44} -20.7348 q^{45} -2.02849 q^{46} -1.06890 q^{47} -8.93740 q^{48} -1.43274 q^{49} +2.61702 q^{50} +12.8601 q^{51} -2.24364 q^{52} +2.13791 q^{53} +19.0613 q^{54} -5.19911 q^{55} +7.22841 q^{56} +13.4796 q^{57} +3.17931 q^{58} +0.757159 q^{59} +4.45637 q^{60} +1.65253 q^{61} -5.17987 q^{62} -18.3057 q^{63} +8.86834 q^{64} -11.7953 q^{65} +7.79288 q^{66} +0.348893 q^{67} -1.99320 q^{68} -5.44771 q^{69} +7.70168 q^{70} -0.645299 q^{71} -23.7677 q^{72} +0.955846 q^{73} +12.0879 q^{74} +7.02826 q^{75} -2.08921 q^{76} -4.59004 q^{77} +17.6798 q^{78} -6.36556 q^{79} +7.28238 q^{80} +27.9161 q^{81} +10.1424 q^{82} -3.56250 q^{83} +3.93431 q^{84} -10.4787 q^{85} +2.28109 q^{86} +8.53833 q^{87} -5.95961 q^{88} -11.3485 q^{89} -25.3239 q^{90} -10.4135 q^{91} +0.844344 q^{92} -13.9110 q^{93} -1.30548 q^{94} -10.9834 q^{95} +9.18118 q^{96} +8.90186 q^{97} -1.74984 q^{98} +15.0925 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 122 q + 14 q^{2} + 10 q^{3} + 128 q^{4} + 33 q^{5} + 22 q^{6} + 6 q^{7} + 36 q^{8} + 162 q^{9}+O(q^{10}) \) 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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