LMFDB - Embedded newform 671.2.a.b.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [671,2,Mod(1,671)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(671, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("671.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 671 = 11 \cdot 61 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	671.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:	$5.35796197563$
Analytic rank:	$1$
Dimension:	$6$
Coefficient field:	6.6.2661761.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{5} - 6x^{4} + 3x^{3} + 9x^{2} - x - 1 $ x^6 - x^5 - 6x^4 + 3x^3 + 9*x^2 - x - 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$1.58234$ of defining polynomial
Character	$\chi$	$=$	671.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.28896 q^{2} -1.58234 q^{3} +3.23932 q^{4} +0.631975 q^{5} +3.62191 q^{6} +0.582341 q^{7} -2.83675 q^{8} -0.496198 q^{9} +O(q^{10})$	\(q-2.28896 q^{2} -1.58234 q^{3} +3.23932 q^{4} +0.631975 q^{5} +3.62191 q^{6} +0.582341 q^{7} -2.83675 q^{8} -0.496198 q^{9} -1.44656 q^{10} -1.00000 q^{11} -5.12571 q^{12} -2.96493 q^{13} -1.33295 q^{14} -1.00000 q^{15} +0.0145620 q^{16} +5.10302 q^{17} +1.13578 q^{18} -0.695952 q^{19} +2.04717 q^{20} -0.921461 q^{21} +2.28896 q^{22} +5.73306 q^{23} +4.48871 q^{24} -4.60061 q^{25} +6.78659 q^{26} +5.53218 q^{27} +1.88639 q^{28} +0.254413 q^{29} +2.28896 q^{30} -1.80785 q^{31} +5.64018 q^{32} +1.58234 q^{33} -11.6806 q^{34} +0.368025 q^{35} -1.60735 q^{36} -0.222199 q^{37} +1.59300 q^{38} +4.69152 q^{39} -1.79276 q^{40} -0.991271 q^{41} +2.10918 q^{42} -1.31668 q^{43} -3.23932 q^{44} -0.313585 q^{45} -13.1227 q^{46} -8.61673 q^{47} -0.0230421 q^{48} -6.66088 q^{49} +10.5306 q^{50} -8.07471 q^{51} -9.60435 q^{52} -2.36824 q^{53} -12.6629 q^{54} -0.631975 q^{55} -1.65196 q^{56} +1.10123 q^{57} -0.582341 q^{58} -2.31861 q^{59} -3.23932 q^{60} -1.00000 q^{61} +4.13809 q^{62} -0.288956 q^{63} -12.9392 q^{64} -1.87376 q^{65} -3.62191 q^{66} -1.88308 q^{67} +16.5303 q^{68} -9.07165 q^{69} -0.842393 q^{70} -6.30661 q^{71} +1.40759 q^{72} -11.7573 q^{73} +0.508603 q^{74} +7.27973 q^{75} -2.25441 q^{76} -0.582341 q^{77} -10.7387 q^{78} -7.48096 q^{79} +0.00920284 q^{80} -7.26519 q^{81} +2.26898 q^{82} +14.3012 q^{83} -2.98491 q^{84} +3.22498 q^{85} +3.01381 q^{86} -0.402568 q^{87} +2.83675 q^{88} -18.4863 q^{89} +0.717783 q^{90} -1.72660 q^{91} +18.5712 q^{92} +2.86063 q^{93} +19.7233 q^{94} -0.439825 q^{95} -8.92468 q^{96} -1.52260 q^{97} +15.2465 q^{98} +0.496198 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - q^{3} + 2 q^{4} - q^{5} - q^{6} - 5 q^{7} - 6 q^{8} - 5 q^{9}+O(q^{10}) $ 6 * q - q^3 + 2 * q^4 - q^5 - q^6 - 5 * q^7 - 6 * q^8 - 5 * q^9	\( 6 q - q^{3} + 2 q^{4} - q^{5} - q^{6} - 5 q^{7} - 6 q^{8} - 5 q^{9} - 7 q^{10} - 6 q^{11} - 6 q^{12} - 4 q^{13} + q^{14} - 6 q^{15} - 10 q^{16} - 5 q^{17} - 3 q^{19} - 6 q^{20} - 12 q^{21} - 3 q^{23} + 10 q^{24} - 11 q^{25} + q^{26} - 4 q^{27} + 4 q^{28} - q^{29} - 10 q^{31} + 3 q^{32} + q^{33} - 19 q^{34} + 7 q^{35} + 3 q^{36} - 19 q^{37} - 3 q^{38} + 8 q^{39} + 5 q^{40} - 7 q^{41} + q^{42} - 2 q^{43} - 2 q^{44} + 4 q^{45} - 7 q^{46} + 5 q^{47} + q^{48} - 25 q^{49} + 17 q^{50} - q^{51} + 2 q^{52} - 9 q^{53} - 11 q^{54} + q^{55} - 4 q^{56} + 11 q^{57} + 5 q^{58} - 5 q^{59} - 2 q^{60} - 6 q^{61} + 3 q^{62} + 12 q^{63} - 6 q^{64} - 11 q^{65} + q^{66} - 14 q^{67} + 18 q^{68} - 7 q^{69} + 7 q^{70} - 14 q^{71} - q^{72} - 14 q^{73} + 6 q^{74} + 6 q^{75} - 11 q^{76} + 5 q^{77} - 26 q^{78} + 5 q^{79} + 26 q^{80} - 14 q^{81} + q^{82} + 17 q^{83} - 3 q^{84} + 2 q^{85} - 7 q^{86} + 4 q^{87} + 6 q^{88} - 25 q^{89} + 22 q^{90} - 4 q^{91} + 35 q^{92} - q^{93} + 30 q^{94} + 3 q^{95} + 8 q^{96} - 24 q^{97} - 2 q^{98} + 5 q^{99}+O(q^{100}) \) 6 * q - q^3 + 2 * q^4 - q^5 - q^6 - 5 * q^7 - 6 * q^8 - 5 * q^9 - 7 * q^10 - 6 * q^11 - 6 * q^12 - 4 * q^13 + q^14 - 6 * q^15 - 10 * q^16 - 5 * q^17 - 3 * q^19 - 6 * q^20 - 12 * q^21 - 3 * q^23 + 10 * q^24 - 11 * q^25 + q^26 - 4 * q^27 + 4 * q^28 - q^29 - 10 * q^31 + 3 * q^32 + q^33 - 19 * q^34 + 7 * q^35 + 3 * q^36 - 19 * q^37 - 3 * q^38 + 8 * q^39 + 5 * q^40 - 7 * q^41 + q^42 - 2 * q^43 - 2 * q^44 + 4 * q^45 - 7 * q^46 + 5 * q^47 + q^48 - 25 * q^49 + 17 * q^50 - q^51 + 2 * q^52 - 9 * q^53 - 11 * q^54 + q^55 - 4 * q^56 + 11 * q^57 + 5 * q^58 - 5 * q^59 - 2 * q^60 - 6 * q^61 + 3 * q^62 + 12 * q^63 - 6 * q^64 - 11 * q^65 + q^66 - 14 * q^67 + 18 * q^68 - 7 * q^69 + 7 * q^70 - 14 * q^71 - q^72 - 14 * q^73 + 6 * q^74 + 6 * q^75 - 11 * q^76 + 5 * q^77 - 26 * q^78 + 5 * q^79 + 26 * q^80 - 14 * q^81 + q^82 + 17 * q^83 - 3 * q^84 + 2 * q^85 - 7 * q^86 + 4 * q^87 + 6 * q^88 - 25 * q^89 + 22 * q^90 - 4 * q^91 + 35 * q^92 - q^93 + 30 * q^94 + 3 * q^95 + 8 * q^96 - 24 * q^97 - 2 * q^98 + 5 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−2.28896	−1.61854	−0.809268	−	0.587439i	$-0.800136\pi$
$2$	−2.28896	−1.61854	−0.809268	+	0.587439i	$0.800136\pi$
$3$	−1.58234	−0.913565	−0.456782	−	0.889578i	$-0.650998\pi$
$3$	−1.58234	−0.913565	−0.456782	+	0.889578i	$0.650998\pi$
$4$	3.23932	1.61966
$5$	0.631975	0.282628	0.141314	−	0.989965i	$-0.454867\pi$
$5$	0.631975	0.282628	0.141314	+	0.989965i	$0.454867\pi$
$6$	3.62191	1.47864
$7$	0.582341	0.220104	0.110052	−	0.993926i	$-0.464898\pi$
$7$	0.582341	0.220104	0.110052	+	0.993926i	$0.464898\pi$
$8$	−2.83675	−1.00294
$9$	−0.496198	−0.165399
$10$	−1.44656	−0.457444
$11$	−1.00000	−0.301511
$11$	−1.00000	−0.301511
$12$	−5.12571	−1.47967
$13$	−2.96493	−0.822323	−0.411161	−	0.911563i	$-0.634877\pi$
$13$	−2.96493	−0.822323	−0.411161	+	0.911563i	$0.634877\pi$
$14$	−1.33295	−0.356246
$15$	−1.00000	−0.258199
$16$	0.0145620	0.00364051
$17$	5.10302	1.23766	0.618832	−	0.785524i	$-0.287606\pi$
$17$	5.10302	1.23766	0.618832	+	0.785524i	$0.287606\pi$
$18$	1.13578	0.267705
$19$	−0.695952	−0.159662	−0.0798312	−	0.996808i	$-0.525438\pi$
$19$	−0.695952	−0.159662	−0.0798312	+	0.996808i	$0.525438\pi$
$20$	2.04717	0.457761
$21$	−0.921461	−0.201079
$22$	2.28896	0.488007
$23$	5.73306	1.19542	0.597712	−	0.801711i	$-0.296076\pi$
$23$	5.73306	1.19542	0.597712	+	0.801711i	$0.296076\pi$
$24$	4.48871	0.916254
$25$	−4.60061	−0.920121
$26$	6.78659	1.33096
$27$	5.53218	1.06467
$28$	1.88639	0.356494
$29$	0.254413	0.0472433	0.0236217	−	0.999721i	$-0.492480\pi$
$29$	0.254413	0.0472433	0.0236217	+	0.999721i	$0.492480\pi$
$30$	2.28896	0.417904
$31$	−1.80785	−0.324699	−0.162350	−	0.986733i	$-0.551907\pi$
$31$	−1.80785	−0.324699	−0.162350	+	0.986733i	$0.551907\pi$
$32$	5.64018	0.997052
$33$	1.58234	0.275450
$34$	−11.6806	−2.00320
$35$	0.368025	0.0622075
$36$	−1.60735	−0.267891
$37$	−0.222199	−0.0365292	−0.0182646	−	0.999833i	$-0.505814\pi$
$37$	−0.222199	−0.0365292	−0.0182646	+	0.999833i	$0.505814\pi$
$38$	1.59300	0.258419
$39$	4.69152	0.751245
$40$	−1.79276	−0.283460
$41$	−0.991271	−0.154810	−0.0774052	−	0.997000i	$-0.524664\pi$
$41$	−0.991271	−0.154810	−0.0774052	+	0.997000i	$0.524664\pi$
$42$	2.10918	0.325454
$43$	−1.31668	−0.200791	−0.100396	−	0.994948i	$-0.532011\pi$
$43$	−1.31668	−0.200791	−0.100396	+	0.994948i	$0.532011\pi$
$44$	−3.23932	−0.488346
$45$	−0.313585	−0.0467465
$46$	−13.1227	−1.93484
$47$	−8.61673	−1.25688	−0.628440	−	0.777858i	$-0.716306\pi$
$47$	−8.61673	−1.25688	−0.628440	+	0.777858i	$0.716306\pi$
$48$	−0.0230421	−0.00332584
$49$	−6.66088	−0.951554
$50$	10.5306	1.48925
$51$	−8.07471	−1.13069
$52$	−9.60435	−1.33188
$53$	−2.36824	−0.325303	−0.162652	−	0.986684i	$-0.552005\pi$
$53$	−2.36824	−0.325303	−0.162652	+	0.986684i	$0.552005\pi$
$54$	−12.6629	−1.72320
$55$	−0.631975	−0.0852155
$56$	−1.65196	−0.220752
$57$	1.10123	0.145862
$58$	−0.582341	−0.0764651
$59$	−2.31861	−0.301857	−0.150929	−	0.988545i	$-0.548226\pi$
$59$	−2.31861	−0.301857	−0.150929	+	0.988545i	$0.548226\pi$
$60$	−3.23932	−0.418195
$61$	−1.00000	−0.128037
$61$	−1.00000	−0.128037
$62$	4.13809	0.525538
$63$	−0.288956	−0.0364051
$64$	−12.9392	−1.61741
$65$	−1.87376	−0.232411
$66$	−3.62191	−0.445826
$67$	−1.88308	−0.230055	−0.115027	−	0.993362i	$-0.536696\pi$
$67$	−1.88308	−0.230055	−0.115027	+	0.993362i	$0.536696\pi$
$68$	16.5303	2.00459
$69$	−9.07165	−1.09210
$70$	−0.842393	−0.100685
$71$	−6.30661	−0.748457	−0.374228	−	0.927337i	$-0.622092\pi$
$71$	−6.30661	−0.748457	−0.374228	+	0.927337i	$0.622092\pi$
$72$	1.40759	0.165886
$73$	−11.7573	−1.37609	−0.688043	−	0.725670i	$-0.741530\pi$
$73$	−11.7573	−1.37609	−0.688043	+	0.725670i	$0.741530\pi$
$74$	0.508603	0.0591239
$75$	7.27973	0.840591
$76$	−2.25441	−0.258599
$77$	−0.582341	−0.0663639
$78$	−10.7387	−1.21592
$79$	−7.48096	−0.841673	−0.420837	−	0.907136i	$-0.638263\pi$
$79$	−7.48096	−0.841673	−0.420837	+	0.907136i	$0.638263\pi$
$80$	0.00920284	0.00102891
$81$	−7.26519	−0.807244
$82$	2.26898	0.250566
$83$	14.3012	1.56976	0.784879	−	0.619649i	$-0.212725\pi$
$83$	14.3012	1.56976	0.784879	+	0.619649i	$0.212725\pi$
$84$	−2.98491	−0.325680
$85$	3.22498	0.349798
$86$	3.01381	0.324988
$87$	−0.402568	−0.0431598
$88$	2.83675	0.302399
$89$	−18.4863	−1.95955	−0.979773	−	0.200114i	$-0.935869\pi$
$89$	−18.4863	−1.95955	−0.979773	+	0.200114i	$0.935869\pi$
$90$	0.717783	0.0756609
$91$	−1.72660	−0.180997
$92$	18.5712	1.93618
$93$	2.86063	0.296634
$94$	19.7233	2.03431
$95$	−0.439825	−0.0451250
$96$	−8.92468	−0.910871
$97$	−1.52260	−0.154596	−0.0772982	−	0.997008i	$-0.524629\pi$
$97$	−1.52260	−0.154596	−0.0772982	+	0.997008i	$0.524629\pi$
$98$	15.2465	1.54013
$99$	0.496198	0.0498698
$100$	−14.9028	−1.49028
$101$	−2.12268	−0.211214	−0.105607	−	0.994408i	$-0.533679\pi$
$101$	−2.12268	−0.211214	−0.105607	+	0.994408i	$0.533679\pi$
$102$	18.4827	1.83006
$103$	−7.37006	−0.726193	−0.363097	−	0.931751i	$-0.618281\pi$
$103$	−7.37006	−0.726193	−0.363097	+	0.931751i	$0.618281\pi$
$104$	8.41077	0.824744
$105$	−0.582341	−0.0568306
$106$	5.42081	0.526515
$107$	6.08107	0.587879	0.293940	−	0.955824i	$-0.405034\pi$
$107$	6.08107	0.587879	0.293940	+	0.955824i	$0.405034\pi$
$108$	17.9205	1.72440
$109$	−7.11386	−0.681384	−0.340692	−	0.940175i	$-0.610661\pi$
$109$	−7.11386	−0.681384	−0.340692	+	0.940175i	$0.610661\pi$
$110$	1.44656	0.137924
$111$	0.351594	0.0333718
$112$	0.00848006	0.000801290 0
$113$	−14.9398	−1.40542	−0.702711	−	0.711476i	$-0.748027\pi$
$113$	−14.9398	−1.40542	−0.702711	+	0.711476i	$0.748027\pi$
$114$	−2.52068	−0.236083
$115$	3.62315	0.337860
$116$	0.824126	0.0765182
$117$	1.47119	0.136012
$118$	5.30720	0.488567
$119$	2.97169	0.272415
$120$	2.83675	0.258959
$121$	1.00000	0.0909091
$122$	2.28896	0.207232
$123$	1.56853	0.141429
$124$	−5.85621	−0.525903
$125$	−6.06735	−0.542680
$126$	0.661409	0.0589230
$127$	6.68796	0.593461	0.296730	−	0.954961i	$-0.404104\pi$
$127$	6.68796	0.593461	0.296730	+	0.954961i	$0.404104\pi$
$128$	18.3370	1.62078
$129$	2.08343	0.183436
$130$	4.28896	0.376166
$131$	−4.92739	−0.430508	−0.215254	−	0.976558i	$-0.569058\pi$
$131$	−4.92739	−0.430508	−0.215254	+	0.976558i	$0.569058\pi$
$132$	5.12571	0.446136
$133$	−0.405281	−0.0351423
$134$	4.31028	0.372352
$135$	3.49620	0.300905
$136$	−14.4760	−1.24131
$137$	−9.50506	−0.812072	−0.406036	−	0.913857i	$-0.633089\pi$
$137$	−9.50506	−0.812072	−0.406036	+	0.913857i	$0.633089\pi$
$138$	20.7646	1.76760
$139$	9.79756	0.831018	0.415509	−	0.909589i	$-0.363603\pi$
$139$	9.79756	0.831018	0.415509	+	0.909589i	$0.363603\pi$
$140$	1.19215	0.100755
$141$	13.6346	1.14824
$142$	14.4356	1.21140
$143$	2.96493	0.247940
$144$	−0.00722566	−0.000602138 0
$145$	0.160783	0.0133523
$146$	26.9119	2.22725
$147$	10.5398	0.869306
$148$	−0.719773	−0.0591650
$149$	1.66396	0.136317	0.0681584	−	0.997675i	$-0.478288\pi$
$149$	1.66396	0.136317	0.0681584	+	0.997675i	$0.478288\pi$
$150$	−16.6630	−1.36053
$151$	−6.66835	−0.542662	−0.271331	−	0.962486i	$-0.587464\pi$
$151$	−6.66835	−0.542662	−0.271331	+	0.962486i	$0.587464\pi$
$152$	1.97424	0.160132
$153$	−2.53211	−0.204709
$154$	1.33295	0.107412
$155$	−1.14252	−0.0917691
$156$	15.1974	1.21676
$157$	23.7735	1.89733	0.948667	−	0.316276i	$-0.102433\pi$
$157$	23.7735	1.89733	0.948667	+	0.316276i	$0.102433\pi$
$158$	17.1236	1.36228
$159$	3.74737	0.297186
$160$	3.56445	0.281795
$161$	3.33859	0.263118
$162$	16.6297	1.30655
$163$	−3.87511	−0.303522	−0.151761	−	0.988417i	$-0.548494\pi$
$163$	−3.87511	−0.303522	−0.151761	+	0.988417i	$0.548494\pi$
$164$	−3.21104	−0.250740
$165$	1.00000	0.0778499
$166$	−32.7348	−2.54071
$167$	7.90494	0.611702	0.305851	−	0.952079i	$-0.401059\pi$
$167$	7.90494	0.611702	0.305851	+	0.952079i	$0.401059\pi$
$168$	2.61396	0.201671
$169$	−4.20921	−0.323785
$170$	−7.38184	−0.566161
$171$	0.345330	0.0264081
$172$	−4.26514	−0.325214
$173$	−18.6659	−1.41914	−0.709572	−	0.704633i	$-0.751112\pi$
$173$	−18.6659	−1.41914	−0.709572	+	0.704633i	$0.751112\pi$
$174$	0.921461	0.0698558
$175$	−2.67912	−0.202522
$176$	−0.0145620	−0.00109765
$177$	3.66883	0.275766
$178$	42.3144	3.17160
$179$	18.2615	1.36493	0.682465	−	0.730918i	$-0.260908\pi$
$179$	18.2615	1.36493	0.682465	+	0.730918i	$0.260908\pi$
$180$	−1.01580	−0.0757135
$181$	−16.5313	−1.22876	−0.614380	−	0.789010i	$-0.710594\pi$
$181$	−16.5313	−1.22876	−0.614380	+	0.789010i	$0.710594\pi$
$182$	3.95211	0.292950
$183$	1.58234	0.116970
$184$	−16.2633	−1.19894
$185$	−0.140424	−0.0103242
$186$	−6.54786	−0.480113
$187$	−5.10302	−0.373169
$188$	−27.9124	−2.03572
$189$	3.22161	0.234338
$190$	1.00674	0.0730365
$191$	−11.8576	−0.857987	−0.428993	−	0.903308i	$-0.641132\pi$
$191$	−11.8576	−0.857987	−0.428993	+	0.903308i	$0.641132\pi$
$192$	20.4743	1.47760
$193$	15.8354	1.13986	0.569930	−	0.821693i	$-0.306970\pi$
$193$	15.8354	1.13986	0.569930	+	0.821693i	$0.306970\pi$
$194$	3.48516	0.250220
$195$	2.96493	0.212323
$196$	−21.5767	−1.54120
$197$	8.49439	0.605200	0.302600	−	0.953118i	$-0.402145\pi$
$197$	8.49439	0.605200	0.302600	+	0.953118i	$0.402145\pi$
$198$	−1.13578	−0.0807161
$199$	−2.21225	−0.156822	−0.0784112	−	0.996921i	$-0.524985\pi$
$199$	−2.21225	−0.156822	−0.0784112	+	0.996921i	$0.524985\pi$
$200$	13.0508	0.922830
$201$	2.97967	0.210170
$202$	4.85871	0.341858
$203$	0.148155	0.0103984
$204$	−26.1566	−1.83133
$205$	−0.626458	−0.0437538
$206$	16.8697	1.17537
$207$	−2.84473	−0.197723
$208$	−0.0431754	−0.00299367
$209$	0.695952	0.0481400
$210$	1.33295	0.0919824
$211$	−16.3121	−1.12297	−0.561487	−	0.827486i	$-0.689771\pi$
$211$	−16.3121	−1.12297	−0.561487	+	0.827486i	$0.689771\pi$
$212$	−7.67151	−0.526881
$213$	9.97920	0.683764
$214$	−13.9193	−0.951504
$215$	−0.832106	−0.0567492
$216$	−15.6934	−1.06780
$217$	−1.05278	−0.0714676
$218$	16.2833	1.10285
$219$	18.6040	1.25714
$220$	−2.04717	−0.138020
$221$	−15.1301	−1.01776
$222$	−0.804783	−0.0540135
$223$	−6.12017	−0.409837	−0.204919	−	0.978779i	$-0.565693\pi$
$223$	−6.12017	−0.409837	−0.204919	+	0.978779i	$0.565693\pi$
$224$	3.28450	0.219455
$225$	2.28281	0.152188
$226$	34.1966	2.27473
$227$	−20.5936	−1.36684	−0.683422	−	0.730023i	$-0.739509\pi$
$227$	−20.5936	−1.36684	−0.683422	+	0.730023i	$0.739509\pi$
$228$	3.56725	0.236247
$229$	−25.8604	−1.70890	−0.854450	−	0.519533i	$-0.826106\pi$
$229$	−25.8604	−1.70890	−0.854450	+	0.519533i	$0.826106\pi$
$230$	−8.29323	−0.546840
$231$	0.921461	0.0606277
$232$	−0.721707	−0.0473824
$233$	0.182692	0.0119686	0.00598428	−	0.999982i	$-0.498095\pi$
$233$	0.182692	0.0119686	0.00598428	+	0.999982i	$0.498095\pi$
$234$	−3.36750	−0.220140
$235$	−5.44556	−0.355229
$236$	−7.51072	−0.488906
$237$	11.8374	0.768923
$238$	−6.80208	−0.440913
$239$	28.7839	1.86187	0.930937	−	0.365179i	$-0.118992\pi$
$239$	28.7839	1.86187	0.930937	+	0.365179i	$0.118992\pi$
$240$	−0.0145620	−0.000939975 0
$241$	4.41084	0.284127	0.142063	−	0.989858i	$-0.454626\pi$
$241$	4.41084	0.284127	0.142063	+	0.989858i	$0.454626\pi$
$242$	−2.28896	−0.147140
$243$	−5.10052	−0.327199
$244$	−3.23932	−0.207376
$245$	−4.20951	−0.268936
$246$	−3.59029	−0.228909
$247$	2.06345	0.131294
$248$	5.12842	0.325655
$249$	−22.6293	−1.43407
$250$	13.8879	0.878347
$251$	7.87551	0.497098	0.248549	−	0.968619i	$-0.420046\pi$
$251$	7.87551	0.497098	0.248549	+	0.968619i	$0.420046\pi$
$252$	−0.936023	−0.0589639
$253$	−5.73306	−0.360434
$254$	−15.3085	−0.960538
$255$	−5.10302	−0.319563
$256$	−16.0941	−1.00588
$257$	6.84911	0.427236	0.213618	−	0.976917i	$-0.431475\pi$
$257$	6.84911	0.427236	0.213618	+	0.976917i	$0.431475\pi$
$258$	−4.76888	−0.296897
$259$	−0.129395	−0.00804023
$260$	−6.06971	−0.376428
$261$	−0.126239	−0.00781402
$262$	11.2786	0.696793
$263$	6.90261	0.425633	0.212816	−	0.977092i	$-0.431736\pi$
$263$	6.90261	0.425633	0.212816	+	0.977092i	$0.431736\pi$
$264$	−4.48871	−0.276261
$265$	−1.49667	−0.0919398
$266$	0.927671	0.0568792
$267$	29.2516	1.79017
$268$	−6.09990	−0.372610
$269$	29.7708	1.81516	0.907580	−	0.419879i	$-0.137927\pi$
$269$	29.7708	1.81516	0.907580	+	0.419879i	$0.137927\pi$
$270$	−8.00265	−0.487026
$271$	3.21433	0.195257	0.0976283	−	0.995223i	$-0.468874\pi$
$271$	3.21433	0.195257	0.0976283	+	0.995223i	$0.468874\pi$
$272$	0.0743103	0.00450572
$273$	2.73206	0.165352
$274$	21.7567	1.31437
$275$	4.60061	0.277427
$276$	−29.3860	−1.76883
$277$	−9.28022	−0.557594	−0.278797	−	0.960350i	$-0.589936\pi$
$277$	−9.28022	−0.557594	−0.278797	+	0.960350i	$0.589936\pi$
$278$	−22.4262	−1.34503
$279$	0.897052	0.0537051
$280$	−1.04400	−0.0623907
$281$	−20.2625	−1.20876	−0.604381	−	0.796695i	$-0.706580\pi$
$281$	−20.2625	−1.20876	−0.604381	+	0.796695i	$0.706580\pi$
$282$	−31.2090	−1.85847
$283$	19.4223	1.15454	0.577269	−	0.816554i	$-0.304118\pi$
$283$	19.4223	1.15454	0.577269	+	0.816554i	$0.304118\pi$
$284$	−20.4291	−1.21225
$285$	0.695952	0.0412247
$286$	−6.78659	−0.401299
$287$	−0.577257	−0.0340744
$288$	−2.79865	−0.164912
$289$	9.04077	0.531810
$290$	−0.368025	−0.0216112
$291$	2.40927	0.141234
$292$	−38.0856	−2.22879
$293$	0.344618	0.0201328	0.0100664	−	0.999949i	$-0.496796\pi$
$293$	0.344618	0.0201328	0.0100664	+	0.999949i	$0.496796\pi$
$294$	−24.1251	−1.40700
$295$	−1.46530	−0.0853133
$296$	0.630323	0.0366368
$297$	−5.53218	−0.321009
$298$	−3.80873	−0.220634
$299$	−16.9981	−0.983025
$300$	23.5814	1.36147
$301$	−0.766754	−0.0441949
$302$	15.2636	0.878319
$303$	3.35880	0.192958
$304$	−0.0101345	−0.000581252 0
$305$	−0.631975	−0.0361868
$306$	5.79589	0.331329
$307$	−5.34124	−0.304841	−0.152420	−	0.988316i	$-0.548707\pi$
$307$	−5.34124	−0.304841	−0.152420	+	0.988316i	$0.548707\pi$
$308$	−1.88639	−0.107487
$309$	11.6619	0.663425
$310$	2.61517	0.148532
$311$	6.86593	0.389331	0.194666	−	0.980870i	$-0.437638\pi$
$311$	6.86593	0.389331	0.194666	+	0.980870i	$0.437638\pi$
$312$	−13.3087	−0.753457
$313$	−17.7485	−1.00320	−0.501601	−	0.865099i	$-0.667256\pi$
$313$	−17.7485	−1.00320	−0.501601	+	0.865099i	$0.667256\pi$
$314$	−54.4166	−3.07091
$315$	−0.182613	−0.0102891
$316$	−24.2332	−1.36323
$317$	−28.5005	−1.60075	−0.800373	−	0.599502i	$-0.795365\pi$
$317$	−28.5005	−1.60075	−0.800373	+	0.599502i	$0.795365\pi$
$318$	−8.57757	−0.481006
$319$	−0.254413	−0.0142444
$320$	−8.17728	−0.457124
$321$	−9.62232	−0.537066
$322$	−7.64189	−0.425866
$323$	−3.55146	−0.197608
$324$	−23.5343	−1.30746
$325$	13.6405	0.756637
$326$	8.86995	0.491261
$327$	11.2566	0.622489
$328$	2.81199	0.155266
$329$	−5.01787	−0.276644
$330$	−2.28896	−0.126003
$331$	16.0363	0.881434	0.440717	−	0.897646i	$-0.354724\pi$
$331$	16.0363	0.881434	0.440717	+	0.897646i	$0.354724\pi$
$332$	46.3261	2.54247
$333$	0.110255	0.00604192
$334$	−18.0941	−0.990062
$335$	−1.19006	−0.0650199
$336$	−0.0134183	−0.000732031 0
$337$	−12.6301	−0.688006	−0.344003	−	0.938969i	$-0.611783\pi$
$337$	−12.6301	−0.688006	−0.344003	+	0.938969i	$0.611783\pi$
$338$	9.63469	0.524058
$339$	23.6399	1.28394
$340$	10.4467	0.566554
$341$	1.80785	0.0979005
$342$	−0.790446	−0.0427424
$343$	−7.95528	−0.429545
$344$	3.73508	0.201382
$345$	−5.73306	−0.308657
$346$	42.7255	2.29694
$347$	12.7039	0.681982	0.340991	−	0.940067i	$-0.389238\pi$
$347$	12.7039	0.681982	0.340991	+	0.940067i	$0.389238\pi$
$348$	−1.30405	−0.0699043
$349$	6.93661	0.371308	0.185654	−	0.982615i	$-0.440560\pi$
$349$	6.93661	0.371308	0.185654	+	0.982615i	$0.440560\pi$
$350$	6.13239	0.327790
$351$	−16.4025	−0.875501
$352$	−5.64018	−0.300622
$353$	17.3457	0.923217	0.461608	−	0.887084i	$-0.347273\pi$
$353$	17.3457	0.923217	0.461608	+	0.887084i	$0.347273\pi$
$354$	−8.39779	−0.446338
$355$	−3.98562	−0.211535
$356$	−59.8831	−3.17380
$357$	−4.70223	−0.248868
$358$	−41.7998	−2.20919
$359$	19.5004	1.02919	0.514595	−	0.857433i	$-0.327942\pi$
$359$	19.5004	1.02919	0.514595	+	0.857433i	$0.327942\pi$
$360$	0.889564	0.0468841
$361$	−18.5157	−0.974508
$362$	37.8394	1.98879
$363$	−1.58234	−0.0830513
$364$	−5.59300	−0.293153
$365$	−7.43031	−0.388920
$366$	−3.62191	−0.189320
$367$	6.69675	0.349567	0.174784	−	0.984607i	$-0.444077\pi$
$367$	6.69675	0.349567	0.174784	+	0.984607i	$0.444077\pi$
$368$	0.0834849	0.00435195
$369$	0.491867	0.0256056
$370$	0.321425	0.0167101
$371$	−1.37912	−0.0716006
$372$	9.26651	0.480446
$373$	−21.3505	−1.10549	−0.552743	−	0.833352i	$-0.686419\pi$
$373$	−21.3505	−1.10549	−0.552743	+	0.833352i	$0.686419\pi$
$374$	11.6806	0.603988
$375$	9.60061	0.495773
$376$	24.4435	1.26058
$377$	−0.754316	−0.0388493
$378$	−7.37413	−0.379284
$379$	17.1048	0.878615	0.439308	−	0.898337i	$-0.355224\pi$
$379$	17.1048	0.878615	0.439308	+	0.898337i	$0.355224\pi$
$380$	−1.42473	−0.0730873
$381$	−10.5826	−0.542165
$382$	27.1416	1.38868
$383$	−9.94970	−0.508406	−0.254203	−	0.967151i	$-0.581813\pi$
$383$	−9.94970	−0.508406	−0.254203	+	0.967151i	$0.581813\pi$
$384$	−29.0154	−1.48069
$385$	−0.368025	−0.0187563
$386$	−36.2466	−1.84490
$387$	0.653332	0.0332108
$388$	−4.93218	−0.250394
$389$	15.8874	0.805523	0.402761	−	0.915305i	$-0.368050\pi$
$389$	15.8874	0.805523	0.402761	+	0.915305i	$0.368050\pi$
$390$	−6.78659	−0.343652
$391$	29.2559	1.47953
$392$	18.8953	0.954355
$393$	7.79681	0.393297
$394$	−19.4433	−0.979539
$395$	−4.72778	−0.237880
$396$	1.60735	0.0807722
$397$	15.8021	0.793083	0.396542	−	0.918017i	$-0.370210\pi$
$397$	15.8021	0.793083	0.396542	+	0.918017i	$0.370210\pi$
$398$	5.06375	0.253823
$399$	0.641293	0.0321048
$400$	−0.0669942	−0.00334971
$401$	13.0008	0.649231	0.324615	−	0.945846i	$-0.394765\pi$
$401$	13.0008	0.649231	0.324615	+	0.945846i	$0.394765\pi$
$402$	−6.82034	−0.340167
$403$	5.36014	0.267008
$404$	−6.87603	−0.342095
$405$	−4.59142	−0.228150
$406$	−0.339120	−0.0168303
$407$	0.222199	0.0110140
$408$	22.9060	1.13401
$409$	37.0532	1.83216	0.916080	−	0.400995i	$-0.131335\pi$
$409$	37.0532	1.83216	0.916080	+	0.400995i	$0.131335\pi$
$410$	1.43394	0.0708171
$411$	15.0402	0.741880
$412$	−23.8740	−1.17619
$413$	−1.35022	−0.0664400
$414$	6.51147	0.320021
$415$	9.03798	0.443657
$416$	−16.7227	−0.819898
$417$	−15.5031	−0.759189
$418$	−1.59300	−0.0779164
$419$	16.2608	0.794393	0.397196	−	0.917734i	$-0.369983\pi$
$419$	16.2608	0.794393	0.397196	+	0.917734i	$0.369983\pi$
$420$	−1.88639	−0.0920463
$421$	16.6819	0.813028	0.406514	−	0.913645i	$-0.366744\pi$
$421$	16.6819	0.813028	0.406514	+	0.913645i	$0.366744\pi$
$422$	37.3378	1.81757
$423$	4.27561	0.207887
$424$	6.71813	0.326261
$425$	−23.4770	−1.13880
$426$	−22.8420	−1.10670
$427$	−0.582341	−0.0281814
$428$	19.6985	0.952165
$429$	−4.69152	−0.226509
$430$	1.90466	0.0918506
$431$	−16.2191	−0.781249	−0.390624	−	0.920550i	$-0.627741\pi$
$431$	−16.2191	−0.781249	−0.390624	+	0.920550i	$0.627741\pi$
$432$	0.0805597	0.00387593
$433$	11.7728	0.565763	0.282882	−	0.959155i	$-0.408710\pi$
$433$	11.7728	0.565763	0.282882	+	0.959155i	$0.408710\pi$
$434$	2.40978	0.115673
$435$	−0.254413	−0.0121982
$436$	−23.0441	−1.10361
$437$	−3.98993	−0.190864
$438$	−42.5838	−2.03473
$439$	−19.8101	−0.945483	−0.472741	−	0.881201i	$-0.656735\pi$
$439$	−19.8101	−0.945483	−0.472741	+	0.881201i	$0.656735\pi$
$440$	1.79276	0.0854664
$441$	3.30512	0.157387
$442$	34.6321	1.64728
$443$	−16.8573	−0.800912	−0.400456	−	0.916316i	$-0.631148\pi$
$443$	−16.8573	−0.800912	−0.400456	+	0.916316i	$0.631148\pi$
$444$	1.13893	0.0540510
$445$	−11.6829	−0.553822
$446$	14.0088	0.663336
$447$	−2.63295	−0.124534
$448$	−7.53504	−0.355997
$449$	7.39461	0.348973	0.174487	−	0.984660i	$-0.444173\pi$
$449$	7.39461	0.348973	0.174487	+	0.984660i	$0.444173\pi$
$450$	−5.22526	−0.246321
$451$	0.991271	0.0466771
$452$	−48.3949	−2.27631
$453$	10.5516	0.495757
$454$	47.1378	2.21229
$455$	−1.09117	−0.0511547
$456$	−3.12393	−0.146291
$457$	4.70610	0.220142	0.110071	−	0.993924i	$-0.464892\pi$
$457$	4.70610	0.220142	0.110071	+	0.993924i	$0.464892\pi$
$458$	59.1932	2.76592
$459$	28.2308	1.31770
$460$	11.7365	0.547219
$461$	6.98323	0.325241	0.162621	−	0.986689i	$-0.448005\pi$
$461$	6.98323	0.325241	0.162621	+	0.986689i	$0.448005\pi$
$462$	−2.10918	−0.0981281
$463$	4.53115	0.210580	0.105290	−	0.994442i	$-0.466423\pi$
$463$	4.53115	0.210580	0.105290	+	0.994442i	$0.466423\pi$
$464$	0.00370477	0.000171990 0
$465$	1.80785	0.0838370
$466$	−0.418174	−0.0193715
$467$	−0.774924	−0.0358592	−0.0179296	−	0.999839i	$-0.505707\pi$
$467$	−0.774924	−0.0358592	−0.0179296	+	0.999839i	$0.505707\pi$
$468$	4.76567	0.220293
$469$	−1.09659	−0.0506359
$470$	12.4647	0.574952
$471$	−37.6178	−1.73334
$472$	6.57732	0.302746
$473$	1.31668	0.0605408
$474$	−27.0953	−1.24453
$475$	3.20180	0.146909
$476$	9.62627	0.441219
$477$	1.17512	0.0538050
$478$	−65.8850	−3.01351
$479$	−16.0849	−0.734938	−0.367469	−	0.930036i	$-0.619776\pi$
$479$	−16.0849	−0.734938	−0.367469	+	0.930036i	$0.619776\pi$
$480$	−5.64018	−0.257438
$481$	0.658803	0.0300388
$482$	−10.0962	−0.459870
$483$	−5.28279	−0.240375
$484$	3.23932	0.147242
$485$	−0.962244	−0.0436932
$486$	11.6749	0.529583
$487$	−9.99516	−0.452924	−0.226462	−	0.974020i	$-0.572716\pi$
$487$	−9.99516	−0.452924	−0.226462	+	0.974020i	$0.572716\pi$
$488$	2.83675	0.128414
$489$	6.13174	0.277287
$490$	9.63539	0.435282
$491$	16.4464	0.742216	0.371108	−	0.928590i	$-0.378978\pi$
$491$	16.4464	0.742216	0.371108	+	0.928590i	$0.378978\pi$
$492$	5.08097	0.229068
$493$	1.29827	0.0584713
$494$	−4.72314	−0.212504
$495$	0.313585	0.0140946
$496$	−0.0263260	−0.00118207
$497$	−3.67259	−0.164738
$498$	51.7975	2.32110
$499$	−0.665213	−0.0297790	−0.0148895	−	0.999889i	$-0.504740\pi$
$499$	−0.665213	−0.0297790	−0.0148895	+	0.999889i	$0.504740\pi$
$500$	−19.6541	−0.878957
$501$	−12.5083	−0.558830
$502$	−18.0267	−0.804571
$503$	8.22706	0.366827	0.183413	−	0.983036i	$-0.441285\pi$
$503$	8.22706	0.366827	0.183413	+	0.983036i	$0.441285\pi$
$504$	0.819698	0.0365123
$505$	−1.34148	−0.0596950
$506$	13.1227	0.583376
$507$	6.66040	0.295799
$508$	21.6645	0.961205
$509$	−24.0070	−1.06409	−0.532046	−	0.846716i	$-0.678577\pi$
$509$	−24.0070	−1.06409	−0.532046	+	0.846716i	$0.678577\pi$
$510$	11.6806	0.517225
$511$	−6.84674	−0.302882
$512$	0.164750	0.00728100
$513$	−3.85013	−0.169987
$514$	−15.6773	−0.691497
$515$	−4.65769	−0.205242
$516$	6.74890	0.297104
$517$	8.61673	0.378963
$518$	0.296180	0.0130134
$519$	29.5359	1.29648
$520$	5.31540	0.233096
$521$	−22.8045	−0.999082	−0.499541	−	0.866290i	$-0.666498\pi$
$521$	−22.8045	−0.999082	−0.499541	+	0.866290i	$0.666498\pi$
$522$	0.288956	0.0126473
$523$	8.18415	0.357868	0.178934	−	0.983861i	$-0.442735\pi$
$523$	8.18415	0.357868	0.178934	+	0.983861i	$0.442735\pi$
$524$	−15.9614	−0.697277
$525$	4.23928	0.185017
$526$	−15.7998	−0.688902
$527$	−9.22548	−0.401868
$528$	0.0230421	0.00100278
$529$	9.86794	0.429041
$530$	3.42582	0.148808
$531$	1.15049	0.0499270
$532$	−1.31284	−0.0569187
$533$	2.93905	0.127304
$534$	−66.9557	−2.89746
$535$	3.84309	0.166151
$536$	5.34183	0.230732
$537$	−28.8960	−1.24695
$538$	−68.1442	−2.93790
$539$	6.66088	0.286904
$540$	11.3253	0.487364
$541$	−14.0330	−0.603327	−0.301664	−	0.953414i	$-0.597542\pi$
$541$	−14.0330	−0.603327	−0.301664	+	0.953414i	$0.597542\pi$
$542$	−7.35746	−0.316030
$543$	26.1581	1.12255
$544$	28.7819	1.23401
$545$	−4.49578	−0.192578
$546$	−6.25358	−0.267628
$547$	20.8299	0.890623	0.445311	−	0.895376i	$-0.353093\pi$
$547$	20.8299	0.890623	0.445311	+	0.895376i	$0.353093\pi$
$548$	−30.7899	−1.31528
$549$	0.496198	0.0211772
$550$	−10.5306	−0.449026
$551$	−0.177059	−0.00754298
$552$	25.7340	1.09531
$553$	−4.35646	−0.185256
$554$	21.2420	0.902487
$555$	0.222199	0.00943181
$556$	31.7375	1.34597
$557$	32.2724	1.36743	0.683713	−	0.729751i	$-0.260364\pi$
$557$	32.2724	1.36743	0.683713	+	0.729751i	$0.260364\pi$
$558$	−2.05331	−0.0869237
$559$	3.90385	0.165115
$560$	0.00535919	0.000226467 0
$561$	8.07471	0.340914
$562$	46.3801	1.95643
$563$	−9.65561	−0.406936	−0.203468	−	0.979082i	$-0.565221\pi$
$563$	−9.65561	−0.406936	−0.203468	+	0.979082i	$0.565221\pi$
$564$	44.1669	1.85976
$565$	−9.44161	−0.397211
$566$	−44.4569	−1.86866
$567$	−4.23082	−0.177678
$568$	17.8903	0.750660
$569$	37.8090	1.58503	0.792517	−	0.609849i	$-0.208770\pi$
$569$	37.8090	1.58503	0.792517	+	0.609849i	$0.208770\pi$
$570$	−1.59300	−0.0667236
$571$	−16.2933	−0.681855	−0.340928	−	0.940090i	$-0.610741\pi$
$571$	−16.2933	−0.681855	−0.340928	+	0.940090i	$0.610741\pi$
$572$	9.60435	0.401578
$573$	18.7628	0.783827
$574$	1.32132	0.0551507
$575$	−26.3755	−1.09994
$576$	6.42043	0.267518
$577$	35.5990	1.48201	0.741003	−	0.671501i	$-0.234350\pi$
$577$	35.5990	1.48201	0.741003	+	0.671501i	$0.234350\pi$
$578$	−20.6939	−0.860754
$579$	−25.0570	−1.04134
$580$	0.520827	0.0216262
$581$	8.32815	0.345510
$582$	−5.51471	−0.228592
$583$	2.36824	0.0980827
$584$	33.3525	1.38014
$585$	0.929757	0.0384407
$586$	−0.788815	−0.0325856
$587$	22.6721	0.935778	0.467889	−	0.883787i	$-0.345015\pi$
$587$	22.6721	0.935778	0.467889	+	0.883787i	$0.345015\pi$
$588$	34.1417	1.40798
$589$	1.25818	0.0518423
$590$	3.35402	0.138083
$591$	−13.4410	−0.552889
$592$	−0.00323566	−0.000132985 0
$593$	−35.1948	−1.44528	−0.722638	−	0.691226i	$-0.757071\pi$
$593$	−35.1948	−1.44528	−0.722638	+	0.691226i	$0.757071\pi$
$594$	12.6629	0.519566
$595$	1.87804	0.0769920
$596$	5.39009	0.220787
$597$	3.50054	0.143267
$598$	38.9079	1.59106
$599$	−17.9038	−0.731529	−0.365765	−	0.930707i	$-0.619193\pi$
$599$	−17.9038	−0.731529	−0.365765	+	0.930707i	$0.619193\pi$
$600$	−20.6508	−0.843065
$601$	−11.7102	−0.477670	−0.238835	−	0.971060i	$-0.576766\pi$
$601$	−11.7102	−0.477670	−0.238835	+	0.971060i	$0.576766\pi$
$602$	1.75507	0.0715311
$603$	0.934381	0.0380509
$604$	−21.6009	−0.878929
$605$	0.631975	0.0256934
$606$	−7.68814	−0.312309
$607$	15.8385	0.642866	0.321433	−	0.946932i	$-0.395836\pi$
$607$	15.8385	0.642866	0.321433	+	0.946932i	$0.395836\pi$
$608$	−3.92529	−0.159192
$609$	−0.234432	−0.00949965
$610$	1.44656	0.0585697
$611$	25.5480	1.03356
$612$	−8.20231	−0.331559
$613$	−35.9280	−1.45112	−0.725559	−	0.688160i	$-0.758419\pi$
$613$	−35.9280	−1.45112	−0.725559	+	0.688160i	$0.758419\pi$
$614$	12.2259	0.493396
$615$	0.991271	0.0399719
$616$	1.65196	0.0665592
$617$	19.6177	0.789780	0.394890	−	0.918728i	$-0.370783\pi$
$617$	19.6177	0.789780	0.394890	+	0.918728i	$0.370783\pi$
$618$	−26.6937	−1.07378
$619$	37.3241	1.50018	0.750091	−	0.661334i	$-0.230010\pi$
$619$	37.3241	1.50018	0.750091	+	0.661334i	$0.230010\pi$
$620$	−3.70098	−0.148635
$621$	31.7163	1.27273
$622$	−15.7158	−0.630147
$623$	−10.7653	−0.431304
$624$	0.0683181	0.00273491
$625$	19.1686	0.766745
$626$	40.6255	1.62372
$627$	−1.10123	−0.0439790
$628$	77.0101	3.07304
$629$	−1.13388	−0.0452109
$630$	0.417994	0.0166533
$631$	−15.8027	−0.629096	−0.314548	−	0.949242i	$-0.601853\pi$
$631$	−15.8027	−0.629096	−0.314548	+	0.949242i	$0.601853\pi$
$632$	21.2216	0.844151
$633$	25.8114	1.02591
$634$	65.2364	2.59087
$635$	4.22663	0.167729
$636$	12.1389	0.481340
$637$	19.7490	0.782485
$638$	0.582341	0.0230551
$639$	3.12933	0.123794
$640$	11.5885	0.458077
$641$	−39.2060	−1.54854	−0.774271	−	0.632854i	$-0.781883\pi$
$641$	−39.2060	−1.54854	−0.774271	+	0.632854i	$0.781883\pi$
$642$	22.0251	0.869261
$643$	−3.83243	−0.151136	−0.0755682	−	0.997141i	$-0.524077\pi$
$643$	−3.83243	−0.151136	−0.0755682	+	0.997141i	$0.524077\pi$
$644$	10.8148	0.426162
$645$	1.31668	0.0518440
$646$	8.12913	0.319836
$647$	−43.7648	−1.72057	−0.860287	−	0.509810i	$-0.829716\pi$
$647$	−43.7648	−1.72057	−0.860287	+	0.509810i	$0.829716\pi$
$648$	20.6096	0.809620
$649$	2.31861	0.0910134
$650$	−31.2224	−1.22464
$651$	1.66586	0.0652903
$652$	−12.5527	−0.491602
$653$	23.3030	0.911915	0.455957	−	0.890002i	$-0.349297\pi$
$653$	23.3030	0.911915	0.455957	+	0.890002i	$0.349297\pi$
$654$	−25.7658	−1.00752
$655$	−3.11399	−0.121674
$656$	−0.0144349	−0.000563589 0
$657$	5.83395	0.227604
$658$	11.4857	0.447759
$659$	−15.7880	−0.615013	−0.307506	−	0.951546i	$-0.599495\pi$
$659$	−15.7880	−0.615013	−0.307506	+	0.951546i	$0.599495\pi$
$660$	3.23932	0.126090
$661$	49.2630	1.91611	0.958054	−	0.286588i	$-0.0925210\pi$
$661$	49.2630	1.91611	0.958054	+	0.286588i	$0.0925210\pi$
$662$	−36.7064	−1.42663
$663$	23.9409	0.929788
$664$	−40.5689	−1.57438
$665$	−0.256128	−0.00993220
$666$	−0.252368	−0.00977906
$667$	1.45856	0.0564759
$668$	25.6066	0.990750
$669$	9.68420	0.374413
$670$	2.72399	0.105237
$671$	1.00000	0.0386046
$672$	−5.19720	−0.200486
$673$	4.69808	0.181098	0.0905488	−	0.995892i	$-0.471138\pi$
$673$	4.69808	0.181098	0.0905488	+	0.995892i	$0.471138\pi$
$674$	28.9098	1.11356
$675$	−25.4514	−0.979624
$676$	−13.6350	−0.524422
$677$	8.37423	0.321848	0.160924	−	0.986967i	$-0.448553\pi$
$677$	8.37423	0.321848	0.160924	+	0.986967i	$0.448553\pi$
$678$	−54.1107	−2.07811
$679$	−0.886670	−0.0340273
$680$	−9.14847	−0.350828
$681$	32.5861	1.24870
$682$	−4.13809	−0.158456
$683$	−37.8468	−1.44817	−0.724084	−	0.689712i	$-0.757737\pi$
$683$	−37.8468	−1.44817	−0.724084	+	0.689712i	$0.757737\pi$
$684$	1.11864	0.0427721
$685$	−6.00696	−0.229514
$686$	18.2093	0.695234
$687$	40.9199	1.56119
$688$	−0.0191735	−0.000730982 0
$689$	7.02167	0.267504
$690$	13.1227	0.499573
$691$	−43.3860	−1.65048	−0.825240	−	0.564782i	$-0.808960\pi$
$691$	−43.3860	−1.65048	−0.825240	+	0.564782i	$0.808960\pi$
$692$	−60.4650	−2.29853
$693$	0.288956	0.0109765
$694$	−29.0787	−1.10381
$695$	6.19182	0.234869
$696$	1.14199	0.0432869
$697$	−5.05847	−0.191603
$698$	−15.8776	−0.600976
$699$	−0.289081	−0.0109341
$700$	−8.67853	−0.328018
$701$	−35.5759	−1.34368	−0.671841	−	0.740695i	$-0.734496\pi$
$701$	−35.5759	−1.34368	−0.671841	+	0.740695i	$0.734496\pi$
$702$	37.5446	1.41703
$703$	0.154640	0.00583234
$704$	12.9392	0.487666
$705$	8.61673	0.324525
$706$	−39.7035	−1.49426
$707$	−1.23612	−0.0464891
$708$	11.8845	0.446648
$709$	−24.9173	−0.935788	−0.467894	−	0.883785i	$-0.654987\pi$
$709$	−24.9173	−0.935788	−0.467894	+	0.883785i	$0.654987\pi$
$710$	9.12291	0.342377
$711$	3.71204	0.139212
$712$	52.4411	1.96531
$713$	−10.3645	−0.388154
$714$	10.7632	0.402803
$715$	1.87376	0.0700747
$716$	59.1550	2.21072
$717$	−45.5459	−1.70094
$718$	−44.6355	−1.66578
$719$	32.4932	1.21179	0.605895	−	0.795545i	$-0.292815\pi$
$719$	32.4932	1.21179	0.605895	+	0.795545i	$0.292815\pi$
$720$	−0.00456644	−0.000170181 0
$721$	−4.29188	−0.159838
$722$	42.3815	1.57728
$723$	−6.97944	−0.259568
$724$	−53.5501	−1.99017
$725$	−1.17045	−0.0434696
$726$	3.62191	0.134422
$727$	39.3124	1.45802	0.729008	−	0.684505i	$-0.239982\pi$
$727$	39.3124	1.45802	0.729008	+	0.684505i	$0.239982\pi$
$728$	4.89793	0.181529
$729$	29.8663	1.10616
$730$	17.0077	0.629482
$731$	−6.71902	−0.248512
$732$	5.12571	0.189452
$733$	−20.3084	−0.750106	−0.375053	−	0.927003i	$-0.622376\pi$
$733$	−20.3084	−0.750106	−0.375053	+	0.927003i	$0.622376\pi$
$734$	−15.3286	−0.565787
$735$	6.66088	0.245690
$736$	32.3354	1.19190
$737$	1.88308	0.0693641
$738$	−1.12586	−0.0414436
$739$	−7.59236	−0.279290	−0.139645	−	0.990202i	$-0.544596\pi$
$739$	−7.59236	−0.279290	−0.139645	+	0.990202i	$0.544596\pi$
$740$	−0.454879	−0.0167217
$741$	−3.26508	−0.119946
$742$	3.15676	0.115888
$743$	−23.5740	−0.864847	−0.432423	−	0.901671i	$-0.642341\pi$
$743$	−23.5740	−0.864847	−0.432423	+	0.901671i	$0.642341\pi$
$744$	−8.11491	−0.297507
$745$	1.05158	0.0385269
$746$	48.8703	1.78927
$747$	−7.09622	−0.259637
$748$	−16.5303	−0.604408
$749$	3.54125	0.129395
$750$	−21.9754	−0.802427
$751$	−35.9528	−1.31194	−0.655968	−	0.754788i	$-0.727740\pi$
$751$	−35.9528	−1.31194	−0.655968	+	0.754788i	$0.727740\pi$
$752$	−0.125477	−0.00457568
$753$	−12.4617	−0.454131
$754$	1.72660	0.0628790
$755$	−4.21423	−0.153372
$756$	10.4358	0.379548
$757$	16.2079	0.589087	0.294544	−	0.955638i	$-0.404832\pi$
$757$	16.2079	0.589087	0.294544	+	0.955638i	$0.404832\pi$
$758$	−39.1522	−1.42207
$759$	9.07165	0.329280
$760$	1.24767	0.0452579
$761$	−23.7682	−0.861595	−0.430798	−	0.902449i	$-0.641768\pi$
$761$	−23.7682	−0.861595	−0.430798	+	0.902449i	$0.641768\pi$
$762$	24.2232	0.877513
$763$	−4.14269	−0.149975
$764$	−38.4106	−1.38965
$765$	−1.60023	−0.0578564
$766$	22.7744	0.822874
$767$	6.87451	0.248224
$768$	25.4664	0.918939
$769$	−30.8233	−1.11152	−0.555759	−	0.831344i	$-0.687572\pi$
$769$	−30.8233	−1.11152	−0.555759	+	0.831344i	$0.687572\pi$
$770$	0.842393	0.0303577
$771$	−10.8376	−0.390308
$772$	51.2961	1.84619
$773$	−23.7044	−0.852588	−0.426294	−	0.904585i	$-0.640181\pi$
$773$	−23.7044	−0.852588	−0.426294	+	0.904585i	$0.640181\pi$
$774$	−1.49545	−0.0537528
$775$	8.31720	0.298763
$776$	4.31923	0.155051
$777$	0.204747	0.00734527
$778$	−36.3656	−1.30377
$779$	0.689877	0.0247174
$780$	9.60435	0.343891
$781$	6.30661	0.225668
$782$	−66.9654	−2.39468
$783$	1.40746	0.0502985
$784$	−0.0969959	−0.00346414
$785$	15.0243	0.536240
$786$	−17.8466	−0.636566
$787$	6.44674	0.229802	0.114901	−	0.993377i	$-0.463345\pi$
$787$	6.44674	0.229802	0.114901	+	0.993377i	$0.463345\pi$
$788$	27.5161	0.980219
$789$	−10.9223	−0.388843
$790$	10.8217	0.385018
$791$	−8.70007	−0.309339
$792$	−1.40759	−0.0500166
$793$	2.96493	0.105288
$794$	−36.1703	−1.28363
$795$	2.36824	0.0839930
$796$	−7.16620	−0.253999
$797$	13.5260	0.479116	0.239558	−	0.970882i	$-0.422997\pi$
$797$	13.5260	0.479116	0.239558	+	0.970882i	$0.422997\pi$
$798$	−1.46789	−0.0519628
$799$	−43.9713	−1.55559
$800$	−25.9482	−0.917409
$801$	9.17288	0.324108
$802$	−29.7583	−1.05080
$803$	11.7573	0.414906
$804$	9.65211	0.340404
$805$	2.10991	0.0743644
$806$	−12.2691	−0.432162
$807$	−47.1076	−1.65827
$808$	6.02151	0.211836
$809$	4.66134	0.163884	0.0819420	−	0.996637i	$-0.473888\pi$
$809$	4.66134	0.163884	0.0819420	+	0.996637i	$0.473888\pi$
$810$	10.5096	0.369268
$811$	−42.2122	−1.48227	−0.741136	−	0.671355i	$-0.765712\pi$
$811$	−42.2122	−1.48227	−0.741136	+	0.671355i	$0.765712\pi$
$812$	0.479922	0.0168420
$813$	−5.08616	−0.178379
$814$	−0.508603	−0.0178265
$815$	−2.44897	−0.0857837
$816$	−0.117584	−0.00411627
$817$	0.916343	0.0320588
$818$	−84.8131	−2.96542
$819$	0.856735	0.0299367
$820$	−2.02930	−0.0708662
$821$	−18.8859	−0.659121	−0.329561	−	0.944134i	$-0.606901\pi$
$821$	−18.8859	−0.659121	−0.329561	+	0.944134i	$0.606901\pi$
$822$	−34.4265	−1.20076
$823$	−2.21205	−0.0771070	−0.0385535	−	0.999257i	$-0.512275\pi$
$823$	−2.21205	−0.0771070	−0.0385535	+	0.999257i	$0.512275\pi$
$824$	20.9070	0.728331
$825$	−7.27973	−0.253448
$826$	3.09060	0.107536
$827$	1.76595	0.0614083	0.0307041	−	0.999529i	$-0.490225\pi$
$827$	1.76595	0.0614083	0.0307041	+	0.999529i	$0.490225\pi$
$828$	−9.21501	−0.320244
$829$	−27.9768	−0.971674	−0.485837	−	0.874049i	$-0.661485\pi$
$829$	−27.9768	−0.971674	−0.485837	+	0.874049i	$0.661485\pi$
$830$	−20.6876	−0.718075
$831$	14.6845	0.509399
$832$	38.3639	1.33003
$833$	−33.9906	−1.17770
$834$	35.4859	1.22878
$835$	4.99572	0.172884
$836$	2.25441	0.0779705
$837$	−10.0013	−0.345697
$838$	−37.2203	−1.28575
$839$	−17.4889	−0.603785	−0.301893	−	0.953342i	$-0.597618\pi$
$839$	−17.4889	−0.603785	−0.301893	+	0.953342i	$0.597618\pi$
$840$	1.65196	0.0569979
$841$	−28.9353	−0.997768
$842$	−38.1842	−1.31592
$843$	32.0623	1.10428
$844$	−52.8403	−1.81884
$845$	−2.66011	−0.0915107
$846$	−9.78668	−0.336473
$847$	0.582341	0.0200095
$848$	−0.0344864	−0.00118427
$849$	−30.7327	−1.05474
$850$	53.7378	1.84319
$851$	−1.27388	−0.0436680
$852$	32.3258	1.10747
$853$	20.4425	0.699939	0.349970	−	0.936761i	$-0.386192\pi$
$853$	20.4425	0.699939	0.349970	+	0.936761i	$0.386192\pi$
$854$	1.33295	0.0456127
$855$	0.218240	0.00746366
$856$	−17.2505	−0.589610
$857$	−27.2147	−0.929638	−0.464819	−	0.885406i	$-0.653881\pi$
$857$	−27.2147	−0.929638	−0.464819	+	0.885406i	$0.653881\pi$
$858$	10.7387	0.366613
$859$	18.8806	0.644198	0.322099	−	0.946706i	$-0.395612\pi$
$859$	18.8806	0.644198	0.322099	+	0.946706i	$0.395612\pi$
$860$	−2.69546	−0.0919144
$861$	0.913417	0.0311292
$862$	37.1249	1.26448
$863$	−39.4565	−1.34311	−0.671557	−	0.740953i	$-0.734374\pi$
$863$	−39.4565	−1.34311	−0.671557	+	0.740953i	$0.734374\pi$
$864$	31.2024	1.06153
$865$	−11.7964	−0.401090
$866$	−26.9474	−0.915709
$867$	−14.3056	−0.485843
$868$	−3.41031	−0.115753
$869$	7.48096	0.253774
$870$	0.582341	0.0197432
$871$	5.58319	0.189179
$872$	20.1803	0.683390
$873$	0.755511	0.0255702
$874$	9.13278	0.308921
$875$	−3.53326	−0.119446
$876$	60.2644	2.03615
$877$	−19.3187	−0.652345	−0.326172	−	0.945310i	$-0.605759\pi$
$877$	−19.3187	−0.652345	−0.326172	+	0.945310i	$0.605759\pi$
$878$	45.3444	1.53030
$879$	−0.545303	−0.0183926
$880$	−0.00920284	−0.000310228 0
$881$	49.9142	1.68165	0.840827	−	0.541305i	$-0.182069\pi$
$881$	49.9142	1.68165	0.840827	+	0.541305i	$0.182069\pi$
$882$	−7.56527	−0.254736
$883$	−14.1185	−0.475126	−0.237563	−	0.971372i	$-0.576349\pi$
$883$	−14.1185	−0.475126	−0.237563	+	0.971372i	$0.576349\pi$
$884$	−49.0112	−1.64842
$885$	2.31861	0.0779392
$886$	38.5855	1.29631
$887$	20.8636	0.700530	0.350265	−	0.936651i	$-0.386091\pi$
$887$	20.8636	0.700530	0.350265	+	0.936651i	$0.386091\pi$
$888$	−0.997385	−0.0334701
$889$	3.89467	0.130623
$890$	26.7416	0.896382
$891$	7.26519	0.243393
$892$	−19.8252	−0.663797
$893$	5.99683	0.200676
$894$	6.02670	0.201563
$895$	11.5408	0.385768
$896$	10.6784	0.356740
$897$	26.8968	0.898057
$898$	−16.9259	−0.564826
$899$	−0.459941	−0.0153399
$900$	7.39477	0.246492
$901$	−12.0852	−0.402616
$902$	−2.26898	−0.0755486
$903$	1.21327	0.0403749
$904$	42.3806	1.40956
$905$	−10.4474	−0.347282
$906$	−24.1521	−0.802401
$907$	−3.79367	−0.125967	−0.0629833	−	0.998015i	$-0.520061\pi$
$907$	−3.79367	−0.125967	−0.0629833	+	0.998015i	$0.520061\pi$
$908$	−66.7093	−2.21382
$909$	1.05327	0.0349347
$910$	2.49763	0.0827957
$911$	12.7670	0.422988	0.211494	−	0.977379i	$-0.432167\pi$
$911$	12.7670	0.422988	0.211494	+	0.977379i	$0.432167\pi$
$912$	0.0160362	0.000531011 0
$913$	−14.3012	−0.473300
$914$	−10.7721	−0.356308
$915$	1.00000	0.0330590
$916$	−83.7700	−2.76784
$917$	−2.86942	−0.0947566
$918$	−64.6190	−2.13275
$919$	−23.8147	−0.785574	−0.392787	−	0.919629i	$-0.628489\pi$
$919$	−23.8147	−0.785574	−0.392787	+	0.919629i	$0.628489\pi$
$920$	−10.2780	−0.338855
$921$	8.45167	0.278492
$922$	−15.9843	−0.526415
$923$	18.6986	0.615473
$924$	2.98491	0.0981963
$925$	1.02225	0.0336113
$926$	−10.3716	−0.340832
$927$	3.65701	0.120112
$928$	1.43493	0.0471040
$929$	−32.9099	−1.07974	−0.539870	−	0.841749i	$-0.681526\pi$
$929$	−32.9099	−1.07974	−0.539870	+	0.841749i	$0.681526\pi$
$930$	−4.13809	−0.135693
$931$	4.63565	0.151927
$932$	0.591798	0.0193850
$933$	−10.8642	−0.355679
$934$	1.77377	0.0580394
$935$	−3.22498	−0.105468
$936$	−4.17341	−0.136412
$937$	23.5691	0.769968	0.384984	−	0.922923i	$-0.374207\pi$
$937$	23.5691	0.769968	0.384984	+	0.922923i	$0.374207\pi$
$938$	2.51005	0.0819561
$939$	28.0841	0.916490
$940$	−17.6399	−0.575351
$941$	−49.2539	−1.60563	−0.802816	−	0.596227i	$-0.796666\pi$
$941$	−49.2539	−1.60563	−0.802816	+	0.596227i	$0.796666\pi$
$942$	86.1056	2.80547
$943$	−5.68301	−0.185064
$944$	−0.0337637	−0.00109891
$945$	2.03598	0.0662304
$946$	−3.01381	−0.0979875
$947$	−26.4718	−0.860218	−0.430109	−	0.902777i	$-0.641525\pi$
$947$	−26.4718	−0.860218	−0.430109	+	0.902777i	$0.641525\pi$
$948$	38.3452	1.24539
$949$	34.8595	1.13159
$950$	−7.32879	−0.237777
$951$	45.0975	1.46239
$952$	−8.42996	−0.273217
$953$	−34.6781	−1.12333	−0.561667	−	0.827363i	$-0.689840\pi$
$953$	−34.6781	−1.12333	−0.561667	+	0.827363i	$0.689840\pi$
$954$	−2.68980	−0.0870854
$955$	−7.49372	−0.242491
$956$	93.2402	3.01560
$957$	0.402568	0.0130132
$958$	36.8177	1.18952
$959$	−5.53518	−0.178740
$960$	12.9392	0.417612
$961$	−27.7317	−0.894570
$962$	−1.50797	−0.0486189
$963$	−3.01742	−0.0972349
$964$	14.2881	0.460189
$965$	10.0076	0.322156
$966$	12.0921	0.389056
$967$	51.5173	1.65668	0.828342	−	0.560223i	$-0.189285\pi$
$967$	51.5173	1.65668	0.828342	+	0.560223i	$0.189285\pi$
$968$	−2.83675	−0.0911767
$969$	5.61961	0.180528
$970$	2.20253	0.0707191
$971$	31.5466	1.01238	0.506190	−	0.862422i	$-0.331054\pi$
$971$	31.5466	1.01238	0.506190	+	0.862422i	$0.331054\pi$
$972$	−16.5222	−0.529951
$973$	5.70552	0.182910
$974$	22.8785	0.733074
$975$	−21.5839	−0.691237
$976$	−0.0145620	−0.000466119 0
$977$	44.5042	1.42381	0.711907	−	0.702274i	$-0.247832\pi$
$977$	44.5042	1.42381	0.711907	+	0.702274i	$0.247832\pi$
$978$	−14.0353	−0.448799
$979$	18.4863	0.590825
$980$	−13.6360	−0.435585
$981$	3.52989	0.112701
$982$	−37.6451	−1.20130
$983$	41.3591	1.31915	0.659575	−	0.751638i	$-0.270736\pi$
$983$	41.3591	1.31915	0.659575	+	0.751638i	$0.270736\pi$
$984$	−4.44953	−0.141846
$985$	5.36824	0.171046
$986$	−2.97169	−0.0946380
$987$	7.93998	0.252732
$988$	6.68417	0.212652
$989$	−7.54858	−0.240031
$990$	−0.717783	−0.0228126
$991$	44.1798	1.40342	0.701709	−	0.712463i	$-0.252420\pi$
$991$	44.1798	1.40342	0.701709	+	0.712463i	$0.252420\pi$
$992$	−10.1966	−0.323742
$993$	−25.3749	−0.805247
$994$	8.40641	0.266635
$995$	−1.39809	−0.0443224
$996$	−73.3036	−2.32272
$997$	24.4086	0.773028	0.386514	−	0.922284i	$-0.373679\pi$
$997$	24.4086	0.773028	0.386514	+	0.922284i	$0.373679\pi$
$998$	1.52264	0.0481984
$999$	−1.22924	−0.0388915

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	671.2.a.b.1.1	✓	6
3.2	odd	2		6039.2.a.b.1.6		6
11.10	odd	2		7381.2.a.h.1.6		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
671.2.a.b.1.1	✓	6	1.1	even	1	trivial
6039.2.a.b.1.6		6	3.2	odd	2
7381.2.a.h.1.6		6	11.10	odd	2

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:	\( N \)	\(=\)	\( 671 = 11 \cdot 61 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	671.a (trivial)

\(f(q)\)	\(=\)	\(q-2.28896 q^{2} -1.58234 q^{3} +3.23932 q^{4} +0.631975 q^{5} +3.62191 q^{6} +0.582341 q^{7} -2.83675 q^{8} -0.496198 q^{9} +O(q^{10})\)	\(q-2.28896 q^{2} -1.58234 q^{3} +3.23932 q^{4} +0.631975 q^{5} +3.62191 q^{6} +0.582341 q^{7} -2.83675 q^{8} -0.496198 q^{9} -1.44656 q^{10} -1.00000 q^{11} -5.12571 q^{12} -2.96493 q^{13} -1.33295 q^{14} -1.00000 q^{15} +0.0145620 q^{16} +5.10302 q^{17} +1.13578 q^{18} -0.695952 q^{19} +2.04717 q^{20} -0.921461 q^{21} +2.28896 q^{22} +5.73306 q^{23} +4.48871 q^{24} -4.60061 q^{25} +6.78659 q^{26} +5.53218 q^{27} +1.88639 q^{28} +0.254413 q^{29} +2.28896 q^{30} -1.80785 q^{31} +5.64018 q^{32} +1.58234 q^{33} -11.6806 q^{34} +0.368025 q^{35} -1.60735 q^{36} -0.222199 q^{37} +1.59300 q^{38} +4.69152 q^{39} -1.79276 q^{40} -0.991271 q^{41} +2.10918 q^{42} -1.31668 q^{43} -3.23932 q^{44} -0.313585 q^{45} -13.1227 q^{46} -8.61673 q^{47} -0.0230421 q^{48} -6.66088 q^{49} +10.5306 q^{50} -8.07471 q^{51} -9.60435 q^{52} -2.36824 q^{53} -12.6629 q^{54} -0.631975 q^{55} -1.65196 q^{56} +1.10123 q^{57} -0.582341 q^{58} -2.31861 q^{59} -3.23932 q^{60} -1.00000 q^{61} +4.13809 q^{62} -0.288956 q^{63} -12.9392 q^{64} -1.87376 q^{65} -3.62191 q^{66} -1.88308 q^{67} +16.5303 q^{68} -9.07165 q^{69} -0.842393 q^{70} -6.30661 q^{71} +1.40759 q^{72} -11.7573 q^{73} +0.508603 q^{74} +7.27973 q^{75} -2.25441 q^{76} -0.582341 q^{77} -10.7387 q^{78} -7.48096 q^{79} +0.00920284 q^{80} -7.26519 q^{81} +2.26898 q^{82} +14.3012 q^{83} -2.98491 q^{84} +3.22498 q^{85} +3.01381 q^{86} -0.402568 q^{87} +2.83675 q^{88} -18.4863 q^{89} +0.717783 q^{90} -1.72660 q^{91} +18.5712 q^{92} +2.86063 q^{93} +19.7233 q^{94} -0.439825 q^{95} -8.92468 q^{96} -1.52260 q^{97} +15.2465 q^{98} +0.496198 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - q^{3} + 2 q^{4} - q^{5} - q^{6} - 5 q^{7} - 6 q^{8} - 5 q^{9}+O(q^{10}) \) 6 * q - q^3 + 2 * q^4 - q^5 - q^6 - 5 * q^7 - 6 * q^8 - 5 * q^9	\( 6 q - q^{3} + 2 q^{4} - q^{5} - q^{6} - 5 q^{7} - 6 q^{8} - 5 q^{9} - 7 q^{10} - 6 q^{11} - 6 q^{12} - 4 q^{13} + q^{14} - 6 q^{15} - 10 q^{16} - 5 q^{17} - 3 q^{19} - 6 q^{20} - 12 q^{21} - 3 q^{23} + 10 q^{24} - 11 q^{25} + q^{26} - 4 q^{27} + 4 q^{28} - q^{29} - 10 q^{31} + 3 q^{32} + q^{33} - 19 q^{34} + 7 q^{35} + 3 q^{36} - 19 q^{37} - 3 q^{38} + 8 q^{39} + 5 q^{40} - 7 q^{41} + q^{42} - 2 q^{43} - 2 q^{44} + 4 q^{45} - 7 q^{46} + 5 q^{47} + q^{48} - 25 q^{49} + 17 q^{50} - q^{51} + 2 q^{52} - 9 q^{53} - 11 q^{54} + q^{55} - 4 q^{56} + 11 q^{57} + 5 q^{58} - 5 q^{59} - 2 q^{60} - 6 q^{61} + 3 q^{62} + 12 q^{63} - 6 q^{64} - 11 q^{65} + q^{66} - 14 q^{67} + 18 q^{68} - 7 q^{69} + 7 q^{70} - 14 q^{71} - q^{72} - 14 q^{73} + 6 q^{74} + 6 q^{75} - 11 q^{76} + 5 q^{77} - 26 q^{78} + 5 q^{79} + 26 q^{80} - 14 q^{81} + q^{82} + 17 q^{83} - 3 q^{84} + 2 q^{85} - 7 q^{86} + 4 q^{87} + 6 q^{88} - 25 q^{89} + 22 q^{90} - 4 q^{91} + 35 q^{92} - q^{93} + 30 q^{94} + 3 q^{95} + 8 q^{96} - 24 q^{97} - 2 q^{98} + 5 q^{99}+O(q^{100}) \) 6 * q - q^3 + 2 * q^4 - q^5 - q^6 - 5 * q^7 - 6 * q^8 - 5 * q^9 - 7 * q^10 - 6 * q^11 - 6 * q^12 - 4 * q^13 + q^14 - 6 * q^15 - 10 * q^16 - 5 * q^17 - 3 * q^19 - 6 * q^20 - 12 * q^21 - 3 * q^23 + 10 * q^24 - 11 * q^25 + q^26 - 4 * q^27 + 4 * q^28 - q^29 - 10 * q^31 + 3 * q^32 + q^33 - 19 * q^34 + 7 * q^35 + 3 * q^36 - 19 * q^37 - 3 * q^38 + 8 * q^39 + 5 * q^40 - 7 * q^41 + q^42 - 2 * q^43 - 2 * q^44 + 4 * q^45 - 7 * q^46 + 5 * q^47 + q^48 - 25 * q^49 + 17 * q^50 - q^51 + 2 * q^52 - 9 * q^53 - 11 * q^54 + q^55 - 4 * q^56 + 11 * q^57 + 5 * q^58 - 5 * q^59 - 2 * q^60 - 6 * q^61 + 3 * q^62 + 12 * q^63 - 6 * q^64 - 11 * q^65 + q^66 - 14 * q^67 + 18 * q^68 - 7 * q^69 + 7 * q^70 - 14 * q^71 - q^72 - 14 * q^73 + 6 * q^74 + 6 * q^75 - 11 * q^76 + 5 * q^77 - 26 * q^78 + 5 * q^79 + 26 * q^80 - 14 * q^81 + q^82 + 17 * q^83 - 3 * q^84 + 2 * q^85 - 7 * q^86 + 4 * q^87 + 6 * q^88 - 25 * q^89 + 22 * q^90 - 4 * q^91 + 35 * q^92 - q^93 + 30 * q^94 + 3 * q^95 + 8 * q^96 - 24 * q^97 - 2 * q^98 + 5 * q^99

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