LMFDB - Embedded newform 8002.2.a.f.1.17

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8002,2,Mod(1,8002)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8002, 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("8002.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8002 = 2 \cdot 4001 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8002.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:	$63.8962916974$
Analytic rank:	$1$
Dimension:	$89$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.17
Character	$\chi$	$=$	8002.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -2.23021 q^{3} +1.00000 q^{4} -2.99176 q^{5} +2.23021 q^{6} +3.17674 q^{7} -1.00000 q^{8} +1.97381 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -2.23021 q^{3} +1.00000 q^{4} -2.99176 q^{5} +2.23021 q^{6} +3.17674 q^{7} -1.00000 q^{8} +1.97381 q^{9} +2.99176 q^{10} +2.87644 q^{11} -2.23021 q^{12} +5.87782 q^{13} -3.17674 q^{14} +6.67223 q^{15} +1.00000 q^{16} +0.409644 q^{17} -1.97381 q^{18} -0.0449398 q^{19} -2.99176 q^{20} -7.08478 q^{21} -2.87644 q^{22} -4.10744 q^{23} +2.23021 q^{24} +3.95061 q^{25} -5.87782 q^{26} +2.28860 q^{27} +3.17674 q^{28} -10.4606 q^{29} -6.67223 q^{30} +4.37339 q^{31} -1.00000 q^{32} -6.41505 q^{33} -0.409644 q^{34} -9.50403 q^{35} +1.97381 q^{36} +7.53981 q^{37} +0.0449398 q^{38} -13.1088 q^{39} +2.99176 q^{40} +1.77017 q^{41} +7.08478 q^{42} -7.38674 q^{43} +2.87644 q^{44} -5.90517 q^{45} +4.10744 q^{46} +6.07955 q^{47} -2.23021 q^{48} +3.09168 q^{49} -3.95061 q^{50} -0.913590 q^{51} +5.87782 q^{52} -3.32573 q^{53} -2.28860 q^{54} -8.60561 q^{55} -3.17674 q^{56} +0.100225 q^{57} +10.4606 q^{58} -13.4768 q^{59} +6.67223 q^{60} +4.65279 q^{61} -4.37339 q^{62} +6.27030 q^{63} +1.00000 q^{64} -17.5850 q^{65} +6.41505 q^{66} -10.4253 q^{67} +0.409644 q^{68} +9.16043 q^{69} +9.50403 q^{70} -1.94198 q^{71} -1.97381 q^{72} -12.5206 q^{73} -7.53981 q^{74} -8.81067 q^{75} -0.0449398 q^{76} +9.13770 q^{77} +13.1088 q^{78} -3.79632 q^{79} -2.99176 q^{80} -11.0255 q^{81} -1.77017 q^{82} +10.3901 q^{83} -7.08478 q^{84} -1.22556 q^{85} +7.38674 q^{86} +23.3292 q^{87} -2.87644 q^{88} -14.2382 q^{89} +5.90517 q^{90} +18.6723 q^{91} -4.10744 q^{92} -9.75355 q^{93} -6.07955 q^{94} +0.134449 q^{95} +2.23021 q^{96} -7.45318 q^{97} -3.09168 q^{98} +5.67756 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 89 q - 89 q^{2} - 12 q^{3} + 89 q^{4} - 18 q^{5} + 12 q^{6} - 27 q^{7} - 89 q^{8} + 95 q^{9}+O(q^{10}) $ 89 * q - 89 * q^2 - 12 * q^3 + 89 * q^4 - 18 * q^5 + 12 * q^6 - 27 * q^7 - 89 * q^8 + 95 * q^9	\( 89 q - 89 q^{2} - 12 q^{3} + 89 q^{4} - 18 q^{5} + 12 q^{6} - 27 q^{7} - 89 q^{8} + 95 q^{9} + 18 q^{10} - 26 q^{11} - 12 q^{12} + 2 q^{13} + 27 q^{14} - 21 q^{15} + 89 q^{16} - 60 q^{17} - 95 q^{18} + q^{19} - 18 q^{20} - 6 q^{21} + 26 q^{22} - 45 q^{23} + 12 q^{24} + 107 q^{25} - 2 q^{26} - 45 q^{27} - 27 q^{28} - 18 q^{29} + 21 q^{30} - 38 q^{31} - 89 q^{32} - 29 q^{33} + 60 q^{34} - 47 q^{35} + 95 q^{36} - 15 q^{37} - q^{38} - 38 q^{39} + 18 q^{40} - 50 q^{41} + 6 q^{42} - 15 q^{43} - 26 q^{44} - 35 q^{45} + 45 q^{46} - 121 q^{47} - 12 q^{48} + 132 q^{49} - 107 q^{50} + 6 q^{51} + 2 q^{52} - 46 q^{53} + 45 q^{54} - 37 q^{55} + 27 q^{56} - 42 q^{57} + 18 q^{58} - 34 q^{59} - 21 q^{60} + 41 q^{61} + 38 q^{62} - 131 q^{63} + 89 q^{64} - 57 q^{65} + 29 q^{66} - 11 q^{67} - 60 q^{68} + 15 q^{69} + 47 q^{70} - 66 q^{71} - 95 q^{72} - 47 q^{73} + 15 q^{74} - 46 q^{75} + q^{76} - 106 q^{77} + 38 q^{78} - 51 q^{79} - 18 q^{80} + 113 q^{81} + 50 q^{82} - 141 q^{83} - 6 q^{84} - 7 q^{85} + 15 q^{86} - 110 q^{87} + 26 q^{88} - 30 q^{89} + 35 q^{90} + 37 q^{91} - 45 q^{92} - 44 q^{93} + 121 q^{94} - 98 q^{95} + 12 q^{96} + 3 q^{97} - 132 q^{98} - 71 q^{99}+O(q^{100}) \) 89 * q - 89 * q^2 - 12 * q^3 + 89 * q^4 - 18 * q^5 + 12 * q^6 - 27 * q^7 - 89 * q^8 + 95 * q^9 + 18 * q^10 - 26 * q^11 - 12 * q^12 + 2 * q^13 + 27 * q^14 - 21 * q^15 + 89 * q^16 - 60 * q^17 - 95 * q^18 + q^19 - 18 * q^20 - 6 * q^21 + 26 * q^22 - 45 * q^23 + 12 * q^24 + 107 * q^25 - 2 * q^26 - 45 * q^27 - 27 * q^28 - 18 * q^29 + 21 * q^30 - 38 * q^31 - 89 * q^32 - 29 * q^33 + 60 * q^34 - 47 * q^35 + 95 * q^36 - 15 * q^37 - q^38 - 38 * q^39 + 18 * q^40 - 50 * q^41 + 6 * q^42 - 15 * q^43 - 26 * q^44 - 35 * q^45 + 45 * q^46 - 121 * q^47 - 12 * q^48 + 132 * q^49 - 107 * q^50 + 6 * q^51 + 2 * q^52 - 46 * q^53 + 45 * q^54 - 37 * q^55 + 27 * q^56 - 42 * q^57 + 18 * q^58 - 34 * q^59 - 21 * q^60 + 41 * q^61 + 38 * q^62 - 131 * q^63 + 89 * q^64 - 57 * q^65 + 29 * q^66 - 11 * q^67 - 60 * q^68 + 15 * q^69 + 47 * q^70 - 66 * q^71 - 95 * q^72 - 47 * q^73 + 15 * q^74 - 46 * q^75 + q^76 - 106 * q^77 + 38 * q^78 - 51 * q^79 - 18 * q^80 + 113 * q^81 + 50 * q^82 - 141 * q^83 - 6 * q^84 - 7 * q^85 + 15 * q^86 - 110 * q^87 + 26 * q^88 - 30 * q^89 + 35 * q^90 + 37 * q^91 - 45 * q^92 - 44 * q^93 + 121 * q^94 - 98 * q^95 + 12 * q^96 + 3 * q^97 - 132 * q^98 - 71 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	−2.23021	−1.28761	−0.643805	−	0.765190i	$-0.722645\pi$
$3$	−2.23021	−1.28761	−0.643805	+	0.765190i	$0.722645\pi$
$4$	1.00000	0.500000
$5$	−2.99176	−1.33795	−0.668977	−	0.743283i	$-0.733268\pi$
$5$	−2.99176	−1.33795	−0.668977	+	0.743283i	$0.733268\pi$
$6$	2.23021	0.910477
$7$	3.17674	1.20069	0.600347	−	0.799739i	$-0.295029\pi$
$7$	3.17674	1.20069	0.600347	+	0.799739i	$0.295029\pi$
$8$	−1.00000	−0.353553
$9$	1.97381	0.657938
$10$	2.99176	0.946077
$11$	2.87644	0.867279	0.433640	−	0.901086i	$-0.357229\pi$
$11$	2.87644	0.867279	0.433640	+	0.901086i	$0.357229\pi$
$12$	−2.23021	−0.643805
$13$	5.87782	1.63022	0.815108	−	0.579310i	$-0.196678\pi$
$13$	5.87782	1.63022	0.815108	+	0.579310i	$0.196678\pi$
$14$	−3.17674	−0.849019
$15$	6.67223	1.72276
$16$	1.00000	0.250000
$17$	0.409644	0.0993533	0.0496766	−	0.998765i	$-0.484181\pi$
$17$	0.409644	0.0993533	0.0496766	+	0.998765i	$0.484181\pi$
$18$	−1.97381	−0.465233
$19$	−0.0449398	−0.0103099	−0.00515495	−	0.999987i	$-0.501641\pi$
$19$	−0.0449398	−0.0103099	−0.00515495	+	0.999987i	$0.501641\pi$
$20$	−2.99176	−0.668977
$21$	−7.08478	−1.54603
$22$	−2.87644	−0.613259
$23$	−4.10744	−0.856460	−0.428230	−	0.903670i	$-0.640863\pi$
$23$	−4.10744	−0.856460	−0.428230	+	0.903670i	$0.640863\pi$
$24$	2.23021	0.455239
$25$	3.95061	0.790122
$26$	−5.87782	−1.15274
$27$	2.28860	0.440442
$28$	3.17674	0.600347
$29$	−10.4606	−1.94248	−0.971239	−	0.238105i	$-0.923474\pi$
$29$	−10.4606	−1.94248	−0.971239	+	0.238105i	$0.923474\pi$
$30$	−6.67223	−1.21818
$31$	4.37339	0.785484	0.392742	−	0.919649i	$-0.371527\pi$
$31$	4.37339	0.785484	0.392742	+	0.919649i	$0.371527\pi$
$32$	−1.00000	−0.176777
$33$	−6.41505	−1.11672
$34$	−0.409644	−0.0702534
$35$	−9.50403	−1.60647
$36$	1.97381	0.328969
$37$	7.53981	1.23954	0.619768	−	0.784785i	$-0.287226\pi$
$37$	7.53981	1.23954	0.619768	+	0.784785i	$0.287226\pi$
$38$	0.0449398	0.00729020
$39$	−13.1088	−2.09908
$40$	2.99176	0.473038
$41$	1.77017	0.276455	0.138227	−	0.990401i	$-0.455860\pi$
$41$	1.77017	0.276455	0.138227	+	0.990401i	$0.455860\pi$
$42$	7.08478	1.09321
$43$	−7.38674	−1.12647	−0.563233	−	0.826298i	$-0.690443\pi$
$43$	−7.38674	−1.12647	−0.563233	+	0.826298i	$0.690443\pi$
$44$	2.87644	0.433640
$45$	−5.90517	−0.880291
$46$	4.10744	0.605609
$47$	6.07955	0.886793	0.443397	−	0.896325i	$-0.353773\pi$
$47$	6.07955	0.886793	0.443397	+	0.896325i	$0.353773\pi$
$48$	−2.23021	−0.321902
$49$	3.09168	0.441668
$50$	−3.95061	−0.558701
$51$	−0.913590	−0.127928
$52$	5.87782	0.815108
$53$	−3.32573	−0.456824	−0.228412	−	0.973565i	$-0.573353\pi$
$53$	−3.32573	−0.456824	−0.228412	+	0.973565i	$0.573353\pi$
$54$	−2.28860	−0.311440
$55$	−8.60561	−1.16038
$56$	−3.17674	−0.424510
$57$	0.100225	0.0132751
$58$	10.4606	1.37354
$59$	−13.4768	−1.75453	−0.877267	−	0.480002i	$-0.840636\pi$
$59$	−13.4768	−1.75453	−0.877267	+	0.480002i	$0.840636\pi$
$60$	6.67223	0.861381
$61$	4.65279	0.595729	0.297864	−	0.954608i	$-0.403726\pi$
$61$	4.65279	0.595729	0.297864	+	0.954608i	$0.403726\pi$
$62$	−4.37339	−0.555421
$63$	6.27030	0.789983
$64$	1.00000	0.125000
$65$	−17.5850	−2.18115
$66$	6.41505	0.789638
$67$	−10.4253	−1.27365	−0.636827	−	0.771007i	$-0.719753\pi$
$67$	−10.4253	−1.27365	−0.636827	+	0.771007i	$0.719753\pi$
$68$	0.409644	0.0496766
$69$	9.16043	1.10279
$70$	9.50403	1.13595
$71$	−1.94198	−0.230471	−0.115236	−	0.993338i	$-0.536762\pi$
$71$	−1.94198	−0.230471	−0.115236	+	0.993338i	$0.536762\pi$
$72$	−1.97381	−0.232616
$73$	−12.5206	−1.46543	−0.732715	−	0.680536i	$-0.761747\pi$
$73$	−12.5206	−1.46543	−0.732715	+	0.680536i	$0.761747\pi$
$74$	−7.53981	−0.876485
$75$	−8.81067	−1.01737
$76$	−0.0449398	−0.00515495
$77$	9.13770	1.04134
$78$	13.1088	1.48427
$79$	−3.79632	−0.427119	−0.213559	−	0.976930i	$-0.568506\pi$
$79$	−3.79632	−0.427119	−0.213559	+	0.976930i	$0.568506\pi$
$80$	−2.99176	−0.334489
$81$	−11.0255	−1.22506
$82$	−1.77017	−0.195483
$83$	10.3901	1.14047	0.570233	−	0.821483i	$-0.306853\pi$
$83$	10.3901	1.14047	0.570233	+	0.821483i	$0.306853\pi$
$84$	−7.08478	−0.773013
$85$	−1.22556	−0.132930
$86$	7.38674	0.796532
$87$	23.3292	2.50115
$88$	−2.87644	−0.306630
$89$	−14.2382	−1.50925	−0.754624	−	0.656157i	$-0.772181\pi$
$89$	−14.2382	−1.50925	−0.754624	+	0.656157i	$0.772181\pi$
$90$	5.90517	0.622460
$91$	18.6723	1.95739
$92$	−4.10744	−0.428230
$93$	−9.75355	−1.01140
$94$	−6.07955	−0.627058
$95$	0.134449	0.0137942
$96$	2.23021	0.227619
$97$	−7.45318	−0.756756	−0.378378	−	0.925651i	$-0.623518\pi$
$97$	−7.45318	−0.756756	−0.378378	+	0.925651i	$0.623518\pi$
$98$	−3.09168	−0.312306
$99$	5.67756	0.570616
$100$	3.95061	0.395061
$101$	−7.46779	−0.743073	−0.371537	−	0.928418i	$-0.621169\pi$
$101$	−7.46779	−0.743073	−0.371537	+	0.928418i	$0.621169\pi$
$102$	0.913590	0.0904589
$103$	−1.64935	−0.162515	−0.0812576	−	0.996693i	$-0.525894\pi$
$103$	−1.64935	−0.162515	−0.0812576	+	0.996693i	$0.525894\pi$
$104$	−5.87782	−0.576368
$105$	21.1959	2.06851
$106$	3.32573	0.323023
$107$	7.60858	0.735550	0.367775	−	0.929915i	$-0.380120\pi$
$107$	7.60858	0.735550	0.367775	+	0.929915i	$0.380120\pi$
$108$	2.28860	0.220221
$109$	17.6382	1.68943	0.844716	−	0.535214i	$-0.179769\pi$
$109$	17.6382	1.68943	0.844716	+	0.535214i	$0.179769\pi$
$110$	8.60561	0.820513
$111$	−16.8153	−1.59604
$112$	3.17674	0.300174
$113$	−3.80999	−0.358414	−0.179207	−	0.983811i	$-0.557353\pi$
$113$	−3.80999	−0.358414	−0.179207	+	0.983811i	$0.557353\pi$
$114$	−0.100225	−0.00938693
$115$	12.2885	1.14590
$116$	−10.4606	−0.971239
$117$	11.6017	1.07258
$118$	13.4768	1.24064
$119$	1.30133	0.119293
$120$	−6.67223	−0.609089
$121$	−2.72609	−0.247827
$122$	−4.65279	−0.421244
$123$	−3.94785	−0.355966
$124$	4.37339	0.392742
$125$	3.13952	0.280807
$126$	−6.27030	−0.558602
$127$	−0.903805	−0.0801997	−0.0400999	−	0.999196i	$-0.512768\pi$
$127$	−0.903805	−0.0801997	−0.0400999	+	0.999196i	$0.512768\pi$
$128$	−1.00000	−0.0883883
$129$	16.4739	1.45045
$130$	17.5850	1.54231
$131$	5.64914	0.493567	0.246784	−	0.969071i	$-0.420626\pi$
$131$	5.64914	0.493567	0.246784	+	0.969071i	$0.420626\pi$
$132$	−6.41505	−0.558359
$133$	−0.142762	−0.0123790
$134$	10.4253	0.900609
$135$	−6.84695	−0.589291
$136$	−0.409644	−0.0351267
$137$	−15.3763	−1.31369	−0.656844	−	0.754026i	$-0.728109\pi$
$137$	−15.3763	−1.31369	−0.656844	+	0.754026i	$0.728109\pi$
$138$	−9.16043	−0.779787
$139$	4.48707	0.380589	0.190294	−	0.981727i	$-0.439056\pi$
$139$	4.48707	0.380589	0.190294	+	0.981727i	$0.439056\pi$
$140$	−9.50403	−0.803237
$141$	−13.5586	−1.14184
$142$	1.94198	0.162968
$143$	16.9072	1.41385
$144$	1.97381	0.164485
$145$	31.2955	2.59895
$146$	12.5206	1.03622
$147$	−6.89507	−0.568696
$148$	7.53981	0.619768
$149$	12.8310	1.05115	0.525576	−	0.850746i	$-0.323850\pi$
$149$	12.8310	1.05115	0.525576	+	0.850746i	$0.323850\pi$
$150$	8.81067	0.719388
$151$	10.6126	0.863642	0.431821	−	0.901959i	$-0.357871\pi$
$151$	10.6126	0.863642	0.431821	+	0.901959i	$0.357871\pi$
$152$	0.0449398	0.00364510
$153$	0.808561	0.0653683
$154$	−9.13770	−0.736337
$155$	−13.0841	−1.05094
$156$	−13.1088	−1.04954
$157$	6.53432	0.521496	0.260748	−	0.965407i	$-0.416031\pi$
$157$	6.53432	0.521496	0.260748	+	0.965407i	$0.416031\pi$
$158$	3.79632	0.302019
$159$	7.41706	0.588211
$160$	2.99176	0.236519
$161$	−13.0483	−1.02835
$162$	11.0255	0.866245
$163$	0.0662900	0.00519223	0.00259612	−	0.999997i	$-0.499174\pi$
$163$	0.0662900	0.00519223	0.00259612	+	0.999997i	$0.499174\pi$
$164$	1.77017	0.138227
$165$	19.1923	1.49412
$166$	−10.3901	−0.806431
$167$	24.0806	1.86341	0.931707	−	0.363210i	$-0.118319\pi$
$167$	24.0806	1.86341	0.931707	+	0.363210i	$0.118319\pi$
$168$	7.08478	0.546603
$169$	21.5488	1.65760
$170$	1.22556	0.0939958
$171$	−0.0887028	−0.00678327
$172$	−7.38674	−0.563233
$173$	6.47747	0.492473	0.246236	−	0.969210i	$-0.420806\pi$
$173$	6.47747	0.492473	0.246236	+	0.969210i	$0.420806\pi$
$174$	−23.3292	−1.76858
$175$	12.5501	0.948696
$176$	2.87644	0.216820
$177$	30.0561	2.25916
$178$	14.2382	1.06720
$179$	15.6680	1.17108	0.585540	−	0.810644i	$-0.300883\pi$
$179$	15.6680	1.17108	0.585540	+	0.810644i	$0.300883\pi$
$180$	−5.90517	−0.440146
$181$	−8.63524	−0.641852	−0.320926	−	0.947104i	$-0.603994\pi$
$181$	−8.63524	−0.641852	−0.320926	+	0.947104i	$0.603994\pi$
$182$	−18.6723	−1.38408
$183$	−10.3767	−0.767066
$184$	4.10744	0.302804
$185$	−22.5573	−1.65844
$186$	9.75355	0.715165
$187$	1.17832	0.0861670
$188$	6.07955	0.443397
$189$	7.27030	0.528836
$190$	−0.134449	−0.00975395
$191$	−26.8480	−1.94265	−0.971325	−	0.237756i	$-0.923588\pi$
$191$	−26.8480	−1.94265	−0.971325	+	0.237756i	$0.923588\pi$
$192$	−2.23021	−0.160951
$193$	−6.76640	−0.487056	−0.243528	−	0.969894i	$-0.578305\pi$
$193$	−6.76640	−0.487056	−0.243528	+	0.969894i	$0.578305\pi$
$194$	7.45318	0.535107
$195$	39.2182	2.80847
$196$	3.09168	0.220834
$197$	10.2037	0.726983	0.363491	−	0.931598i	$-0.381585\pi$
$197$	10.2037	0.726983	0.363491	+	0.931598i	$0.381585\pi$
$198$	−5.67756	−0.403487
$199$	22.7961	1.61597	0.807986	−	0.589202i	$-0.200558\pi$
$199$	22.7961	1.61597	0.807986	+	0.589202i	$0.200558\pi$
$200$	−3.95061	−0.279350
$201$	23.2506	1.63997
$202$	7.46779	0.525432
$203$	−33.2305	−2.33232
$204$	−0.913590	−0.0639641
$205$	−5.29593	−0.369884
$206$	1.64935	0.114916
$207$	−8.10732	−0.563498
$208$	5.87782	0.407554
$209$	−0.129267	−0.00894156
$210$	−21.1959	−1.46266
$211$	−19.4376	−1.33814	−0.669069	−	0.743200i	$-0.733307\pi$
$211$	−19.4376	−1.33814	−0.669069	+	0.743200i	$0.733307\pi$
$212$	−3.32573	−0.228412
$213$	4.33102	0.296757
$214$	−7.60858	−0.520112
$215$	22.0993	1.50716
$216$	−2.28860	−0.155720
$217$	13.8931	0.943126
$218$	−17.6382	−1.19461
$219$	27.9236	1.88690
$220$	−8.60561	−0.580190
$221$	2.40782	0.161967
$222$	16.8153	1.12857
$223$	−17.7609	−1.18936	−0.594678	−	0.803964i	$-0.702721\pi$
$223$	−17.7609	−1.18936	−0.594678	+	0.803964i	$0.702721\pi$
$224$	−3.17674	−0.212255
$225$	7.79777	0.519852
$226$	3.80999	0.253437
$227$	−17.8611	−1.18548	−0.592740	−	0.805394i	$-0.701954\pi$
$227$	−17.8611	−1.18548	−0.592740	+	0.805394i	$0.701954\pi$
$228$	0.100225	0.00663756
$229$	10.7868	0.712811	0.356405	−	0.934331i	$-0.384002\pi$
$229$	10.7868	0.712811	0.356405	+	0.934331i	$0.384002\pi$
$230$	−12.2885	−0.810277
$231$	−20.3789	−1.34084
$232$	10.4606	0.686770
$233$	−18.3195	−1.20015	−0.600076	−	0.799943i	$-0.704863\pi$
$233$	−18.3195	−1.20015	−0.600076	+	0.799943i	$0.704863\pi$
$234$	−11.6017	−0.758429
$235$	−18.1885	−1.18649
$236$	−13.4768	−0.877267
$237$	8.46656	0.549962
$238$	−1.30133	−0.0843529
$239$	−6.69475	−0.433047	−0.216524	−	0.976277i	$-0.569472\pi$
$239$	−6.69475	−0.433047	−0.216524	+	0.976277i	$0.569472\pi$
$240$	6.67223	0.430691
$241$	9.54019	0.614537	0.307269	−	0.951623i	$-0.400585\pi$
$241$	9.54019	0.614537	0.307269	+	0.951623i	$0.400585\pi$
$242$	2.72609	0.175240
$243$	17.7233	1.13695
$244$	4.65279	0.297864
$245$	−9.24954	−0.590932
$246$	3.94785	0.251706
$247$	−0.264148	−0.0168073
$248$	−4.37339	−0.277710
$249$	−23.1721	−1.46848
$250$	−3.13952	−0.198561
$251$	−10.2226	−0.645245	−0.322623	−	0.946528i	$-0.604564\pi$
$251$	−10.2226	−0.645245	−0.322623	+	0.946528i	$0.604564\pi$
$252$	6.27030	0.394991
$253$	−11.8148	−0.742790
$254$	0.903805	0.0567098
$255$	2.73324	0.171162
$256$	1.00000	0.0625000
$257$	−5.82950	−0.363634	−0.181817	−	0.983332i	$-0.558198\pi$
$257$	−5.82950	−0.363634	−0.181817	+	0.983332i	$0.558198\pi$
$258$	−16.4739	−1.02562
$259$	23.9520	1.48831
$260$	−17.5850	−1.09058
$261$	−20.6472	−1.27803
$262$	−5.64914	−0.349005
$263$	19.8703	1.22525	0.612627	−	0.790372i	$-0.290113\pi$
$263$	19.8703	1.22525	0.612627	+	0.790372i	$0.290113\pi$
$264$	6.41505	0.394819
$265$	9.94977	0.611210
$266$	0.142762	0.00875330
$267$	31.7542	1.94332
$268$	−10.4253	−0.636827
$269$	10.7343	0.654482	0.327241	−	0.944941i	$-0.393881\pi$
$269$	10.7343	0.654482	0.327241	+	0.944941i	$0.393881\pi$
$270$	6.84695	0.416692
$271$	−29.8320	−1.81216	−0.906081	−	0.423104i	$-0.860941\pi$
$271$	−29.8320	−1.81216	−0.906081	+	0.423104i	$0.860941\pi$
$272$	0.409644	0.0248383
$273$	−41.6431	−2.52036
$274$	15.3763	0.928918
$275$	11.3637	0.685257
$276$	9.16043	0.551393
$277$	−11.1578	−0.670405	−0.335202	−	0.942146i	$-0.608805\pi$
$277$	−11.1578	−0.670405	−0.335202	+	0.942146i	$0.608805\pi$
$278$	−4.48707	−0.269117
$279$	8.63226	0.516800
$280$	9.50403	0.567975
$281$	−15.9649	−0.952385	−0.476193	−	0.879341i	$-0.657983\pi$
$281$	−15.9649	−0.952385	−0.476193	+	0.879341i	$0.657983\pi$
$282$	13.5586	0.807405
$283$	14.5326	0.863875	0.431938	−	0.901903i	$-0.357830\pi$
$283$	14.5326	0.863875	0.431938	+	0.901903i	$0.357830\pi$
$284$	−1.94198	−0.115236
$285$	−0.299849	−0.0177615
$286$	−16.9072	−0.999744
$287$	5.62338	0.331938
$288$	−1.97381	−0.116308
$289$	−16.8322	−0.990129
$290$	−31.2955	−1.83773
$291$	16.6221	0.974406
$292$	−12.5206	−0.732715
$293$	−11.1568	−0.651788	−0.325894	−	0.945406i	$-0.605665\pi$
$293$	−11.1568	−0.651788	−0.325894	+	0.945406i	$0.605665\pi$
$294$	6.89507	0.402129
$295$	40.3194	2.34749
$296$	−7.53981	−0.438243
$297$	6.58303	0.381986
$298$	−12.8310	−0.743277
$299$	−24.1428	−1.39621
$300$	−8.81067	−0.508684
$301$	−23.4657	−1.35254
$302$	−10.6126	−0.610687
$303$	16.6547	0.956788
$304$	−0.0449398	−0.00257747
$305$	−13.9200	−0.797058
$306$	−0.808561	−0.0462224
$307$	−2.77770	−0.158532	−0.0792660	−	0.996854i	$-0.525258\pi$
$307$	−2.77770	−0.158532	−0.0792660	+	0.996854i	$0.525258\pi$
$308$	9.13770	0.520669
$309$	3.67839	0.209256
$310$	13.0841	0.743128
$311$	0.615059	0.0348768	0.0174384	−	0.999848i	$-0.494449\pi$
$311$	0.615059	0.0348768	0.0174384	+	0.999848i	$0.494449\pi$
$312$	13.1088	0.742137
$313$	−3.77072	−0.213134	−0.106567	−	0.994306i	$-0.533986\pi$
$313$	−3.77072	−0.213134	−0.106567	+	0.994306i	$0.533986\pi$
$314$	−6.53432	−0.368753
$315$	−18.7592	−1.05696
$316$	−3.79632	−0.213559
$317$	7.51989	0.422359	0.211180	−	0.977447i	$-0.432270\pi$
$317$	7.51989	0.422359	0.211180	+	0.977447i	$0.432270\pi$
$318$	−7.41706	−0.415928
$319$	−30.0892	−1.68467
$320$	−2.99176	−0.167244
$321$	−16.9687	−0.947101
$322$	13.0483	0.727151
$323$	−0.0184093	−0.00102432
$324$	−11.0255	−0.612528
$325$	23.2210	1.28807
$326$	−0.0662900	−0.00367146
$327$	−39.3368	−2.17533
$328$	−1.77017	−0.0977415
$329$	19.3131	1.06477
$330$	−19.1923	−1.05650
$331$	−1.96516	−0.108015	−0.0540075	−	0.998541i	$-0.517199\pi$
$331$	−1.96516	−0.108015	−0.0540075	+	0.998541i	$0.517199\pi$
$332$	10.3901	0.570233
$333$	14.8822	0.815539
$334$	−24.0806	−1.31763
$335$	31.1900	1.70409
$336$	−7.08478	−0.386506
$337$	29.4778	1.60576	0.802879	−	0.596142i	$-0.203301\pi$
$337$	29.4778	1.60576	0.802879	+	0.596142i	$0.203301\pi$
$338$	−21.5488	−1.17210
$339$	8.49706	0.461497
$340$	−1.22556	−0.0664651
$341$	12.5798	0.681234
$342$	0.0887028	0.00479650
$343$	−12.4157	−0.670386
$344$	7.38674	0.398266
$345$	−27.4058	−1.47548
$346$	−6.47747	−0.348231
$347$	−3.59165	−0.192810	−0.0964048	−	0.995342i	$-0.530734\pi$
$347$	−3.59165	−0.192810	−0.0964048	+	0.995342i	$0.530734\pi$
$348$	23.3292	1.25058
$349$	−18.2249	−0.975555	−0.487777	−	0.872968i	$-0.662192\pi$
$349$	−18.2249	−0.975555	−0.487777	+	0.872968i	$0.662192\pi$
$350$	−12.5501	−0.670829
$351$	13.4520	0.718015
$352$	−2.87644	−0.153315
$353$	−2.82457	−0.150336	−0.0751682	−	0.997171i	$-0.523949\pi$
$353$	−2.82457	−0.150336	−0.0751682	+	0.997171i	$0.523949\pi$
$354$	−30.0561	−1.59746
$355$	5.80995	0.308360
$356$	−14.2382	−0.754624
$357$	−2.90224	−0.153603
$358$	−15.6680	−0.828078
$359$	4.07627	0.215138	0.107569	−	0.994198i	$-0.465693\pi$
$359$	4.07627	0.215138	0.107569	+	0.994198i	$0.465693\pi$
$360$	5.90517	0.311230
$361$	−18.9980	−0.999894
$362$	8.63524	0.453858
$363$	6.07974	0.319104
$364$	18.6723	0.978695
$365$	37.4587	1.96068
$366$	10.3767	0.542398
$367$	1.32069	0.0689393	0.0344696	−	0.999406i	$-0.489026\pi$
$367$	1.32069	0.0689393	0.0344696	+	0.999406i	$0.489026\pi$
$368$	−4.10744	−0.214115
$369$	3.49400	0.181890
$370$	22.5573	1.17270
$371$	−10.5650	−0.548506
$372$	−9.75355	−0.505698
$373$	−10.9340	−0.566142	−0.283071	−	0.959099i	$-0.591353\pi$
$373$	−10.9340	−0.566142	−0.283071	+	0.959099i	$0.591353\pi$
$374$	−1.17832	−0.0609293
$375$	−7.00177	−0.361570
$376$	−6.07955	−0.313529
$377$	−61.4854	−3.16666
$378$	−7.27030	−0.373944
$379$	−12.8845	−0.661830	−0.330915	−	0.943660i	$-0.607357\pi$
$379$	−12.8845	−0.661830	−0.330915	+	0.943660i	$0.607357\pi$
$380$	0.134449	0.00689709
$381$	2.01567	0.103266
$382$	26.8480	1.37366
$383$	23.0787	1.17927	0.589634	−	0.807671i	$-0.299272\pi$
$383$	23.0787	1.17927	0.589634	+	0.807671i	$0.299272\pi$
$384$	2.23021	0.113810
$385$	−27.3378	−1.39326
$386$	6.76640	0.344401
$387$	−14.5801	−0.741146
$388$	−7.45318	−0.378378
$389$	−3.13297	−0.158848	−0.0794239	−	0.996841i	$-0.525308\pi$
$389$	−3.13297	−0.158848	−0.0794239	+	0.996841i	$0.525308\pi$
$390$	−39.2182	−1.98589
$391$	−1.68259	−0.0850921
$392$	−3.09168	−0.156153
$393$	−12.5987	−0.635522
$394$	−10.2037	−0.514055
$395$	11.3577	0.571466
$396$	5.67756	0.285308
$397$	−17.8372	−0.895222	−0.447611	−	0.894228i	$-0.647725\pi$
$397$	−17.8372	−0.895222	−0.447611	+	0.894228i	$0.647725\pi$
$398$	−22.7961	−1.14266
$399$	0.318389	0.0159394
$400$	3.95061	0.197531
$401$	−19.1171	−0.954665	−0.477332	−	0.878723i	$-0.658396\pi$
$401$	−19.1171	−0.954665	−0.477332	+	0.878723i	$0.658396\pi$
$402$	−23.2506	−1.15963
$403$	25.7060	1.28051
$404$	−7.46779	−0.371537
$405$	32.9856	1.63907
$406$	33.2305	1.64920
$407$	21.6878	1.07502
$408$	0.913590	0.0452295
$409$	10.5904	0.523661	0.261830	−	0.965114i	$-0.415674\pi$
$409$	10.5904	0.523661	0.261830	+	0.965114i	$0.415674\pi$
$410$	5.29593	0.261547
$411$	34.2924	1.69152
$412$	−1.64935	−0.0812576
$413$	−42.8124	−2.10666
$414$	8.10732	0.398453
$415$	−31.0848	−1.52589
$416$	−5.87782	−0.288184
$417$	−10.0071	−0.490049
$418$	0.129267	0.00632264
$419$	0.178290	0.00871006	0.00435503	−	0.999991i	$-0.498614\pi$
$419$	0.178290	0.00871006	0.00435503	+	0.999991i	$0.498614\pi$
$420$	21.1959	1.03426
$421$	17.8254	0.868759	0.434379	−	0.900730i	$-0.356968\pi$
$421$	17.8254	0.868759	0.434379	+	0.900730i	$0.356968\pi$
$422$	19.4376	0.946207
$423$	11.9999	0.583455
$424$	3.32573	0.161512
$425$	1.61834	0.0785012
$426$	−4.33102	−0.209839
$427$	14.7807	0.715289
$428$	7.60858	0.367775
$429$	−37.7065	−1.82049
$430$	−22.0993	−1.06572
$431$	30.2650	1.45782	0.728908	−	0.684612i	$-0.240028\pi$
$431$	30.2650	1.45782	0.728908	+	0.684612i	$0.240028\pi$
$432$	2.28860	0.110111
$433$	−17.9349	−0.861895	−0.430947	−	0.902377i	$-0.641821\pi$
$433$	−17.9349	−0.861895	−0.430947	+	0.902377i	$0.641821\pi$
$434$	−13.8931	−0.666891
$435$	−69.7953	−3.34643
$436$	17.6382	0.844716
$437$	0.184587	0.00883001
$438$	−27.9236	−1.33424
$439$	−30.4663	−1.45408	−0.727038	−	0.686597i	$-0.759104\pi$
$439$	−30.4663	−1.45408	−0.727038	+	0.686597i	$0.759104\pi$
$440$	8.60561	0.410256
$441$	6.10239	0.290590
$442$	−2.40782	−0.114528
$443$	−9.86679	−0.468786	−0.234393	−	0.972142i	$-0.575310\pi$
$443$	−9.86679	−0.468786	−0.234393	+	0.972142i	$0.575310\pi$
$444$	−16.8153	−0.798020
$445$	42.5973	2.01931
$446$	17.7609	0.841002
$447$	−28.6157	−1.35347
$448$	3.17674	0.150087
$449$	20.0101	0.944333	0.472166	−	0.881509i	$-0.343472\pi$
$449$	20.0101	0.944333	0.472166	+	0.881509i	$0.343472\pi$
$450$	−7.79777	−0.367591
$451$	5.09180	0.239764
$452$	−3.80999	−0.179207
$453$	−23.6683	−1.11203
$454$	17.8611	0.838262
$455$	−55.8630	−2.61890
$456$	−0.100225	−0.00469346
$457$	−15.3149	−0.716402	−0.358201	−	0.933644i	$-0.616610\pi$
$457$	−15.3149	−0.716402	−0.358201	+	0.933644i	$0.616610\pi$
$458$	−10.7868	−0.504033
$459$	0.937513	0.0437594
$460$	12.2885	0.572952
$461$	11.3234	0.527384	0.263692	−	0.964607i	$-0.415060\pi$
$461$	11.3234	0.527384	0.263692	+	0.964607i	$0.415060\pi$
$462$	20.3789	0.948115
$463$	10.2140	0.474685	0.237343	−	0.971426i	$-0.423724\pi$
$463$	10.2140	0.474685	0.237343	+	0.971426i	$0.423724\pi$
$464$	−10.4606	−0.485620
$465$	29.1803	1.35320
$466$	18.3195	0.848636
$467$	−33.7918	−1.56370	−0.781850	−	0.623467i	$-0.785724\pi$
$467$	−33.7918	−1.56370	−0.781850	+	0.623467i	$0.785724\pi$
$468$	11.6017	0.536290
$469$	−33.1185	−1.52927
$470$	18.1885	0.838974
$471$	−14.5729	−0.671483
$472$	13.4768	0.620322
$473$	−21.2475	−0.976962
$474$	−8.46656	−0.388882
$475$	−0.177540	−0.00814608
$476$	1.30133	0.0596465
$477$	−6.56437	−0.300562
$478$	6.69475	0.306211
$479$	13.1188	0.599412	0.299706	−	0.954032i	$-0.403111\pi$
$479$	13.1188	0.599412	0.299706	+	0.954032i	$0.403111\pi$
$480$	−6.67223	−0.304544
$481$	44.3177	2.02071
$482$	−9.54019	−0.434544
$483$	29.1003	1.32411
$484$	−2.72609	−0.123913
$485$	22.2981	1.01251
$486$	−17.7233	−0.803946
$487$	16.6755	0.755641	0.377820	−	0.925879i	$-0.376674\pi$
$487$	16.6755	0.755641	0.377820	+	0.925879i	$0.376674\pi$
$488$	−4.65279	−0.210622
$489$	−0.147840	−0.00668557
$490$	9.24954	0.417852
$491$	1.49758	0.0675848	0.0337924	−	0.999429i	$-0.489242\pi$
$491$	1.49758	0.0675848	0.0337924	+	0.999429i	$0.489242\pi$
$492$	−3.94785	−0.177983
$493$	−4.28511	−0.192992
$494$	0.264148	0.0118846
$495$	−16.9859	−0.763458
$496$	4.37339	0.196371
$497$	−6.16918	−0.276726
$498$	23.1721	1.03837
$499$	−3.29467	−0.147490	−0.0737448	−	0.997277i	$-0.523495\pi$
$499$	−3.29467	−0.147490	−0.0737448	+	0.997277i	$0.523495\pi$
$500$	3.13952	0.140403
$501$	−53.7047	−2.39935
$502$	10.2226	0.456257
$503$	−15.1707	−0.676428	−0.338214	−	0.941069i	$-0.609823\pi$
$503$	−15.1707	−0.676428	−0.338214	+	0.941069i	$0.609823\pi$
$504$	−6.27030	−0.279301
$505$	22.3418	0.994198
$506$	11.8148	0.525232
$507$	−48.0583	−2.13434
$508$	−0.903805	−0.0400999
$509$	−18.9804	−0.841290	−0.420645	−	0.907225i	$-0.638196\pi$
$509$	−18.9804	−0.841290	−0.420645	+	0.907225i	$0.638196\pi$
$510$	−2.73324	−0.121030
$511$	−39.7748	−1.75953
$512$	−1.00000	−0.0441942
$513$	−0.102849	−0.00454091
$514$	5.82950	0.257128
$515$	4.93445	0.217438
$516$	16.4739	0.725225
$517$	17.4875	0.769098
$518$	−23.9520	−1.05239
$519$	−14.4461	−0.634113
$520$	17.5850	0.771154
$521$	1.71889	0.0753061	0.0376530	−	0.999291i	$-0.488012\pi$
$521$	1.71889	0.0753061	0.0376530	+	0.999291i	$0.488012\pi$
$522$	20.6472	0.903704
$523$	−7.11361	−0.311057	−0.155528	−	0.987831i	$-0.549708\pi$
$523$	−7.11361	−0.311057	−0.155528	+	0.987831i	$0.549708\pi$
$524$	5.64914	0.246784
$525$	−27.9892	−1.22155
$526$	−19.8703	−0.866386
$527$	1.79153	0.0780404
$528$	−6.41505	−0.279179
$529$	−6.12896	−0.266476
$530$	−9.94977	−0.432191
$531$	−26.6008	−1.15438
$532$	−0.142762	−0.00618952
$533$	10.4048	0.450681
$534$	−31.7542	−1.37414
$535$	−22.7630	−0.984132
$536$	10.4253	0.450304
$537$	−34.9428	−1.50789
$538$	−10.7343	−0.462789
$539$	8.89302	0.383050
$540$	−6.84695	−0.294646
$541$	3.96026	0.170265	0.0851325	−	0.996370i	$-0.472869\pi$
$541$	3.96026	0.170265	0.0851325	+	0.996370i	$0.472869\pi$
$542$	29.8320	1.28139
$543$	19.2584	0.826455
$544$	−0.409644	−0.0175633
$545$	−52.7692	−2.26038
$546$	41.6431	1.78216
$547$	−28.7228	−1.22810	−0.614050	−	0.789267i	$-0.710461\pi$
$547$	−28.7228	−1.22810	−0.614050	+	0.789267i	$0.710461\pi$
$548$	−15.3763	−0.656844
$549$	9.18375	0.391953
$550$	−11.3637	−0.484550
$551$	0.470096	0.0200268
$552$	−9.16043	−0.389894
$553$	−12.0599	−0.512839
$554$	11.1578	0.474048
$555$	50.3074	2.13543
$556$	4.48707	0.190294
$557$	25.2730	1.07085	0.535425	−	0.844582i	$-0.320151\pi$
$557$	25.2730	1.07085	0.535425	+	0.844582i	$0.320151\pi$
$558$	−8.63226	−0.365433
$559$	−43.4179	−1.83638
$560$	−9.50403	−0.401619
$561$	−2.62789	−0.110950
$562$	15.9649	0.673438
$563$	2.64723	0.111568	0.0557838	−	0.998443i	$-0.482234\pi$
$563$	2.64723	0.111568	0.0557838	+	0.998443i	$0.482234\pi$
$564$	−13.5586	−0.570922
$565$	11.3986	0.479541
$566$	−14.5326	−0.610852
$567$	−35.0251	−1.47092
$568$	1.94198	0.0814839
$569$	40.9857	1.71821	0.859104	−	0.511801i	$-0.171021\pi$
$569$	40.9857	1.71821	0.859104	+	0.511801i	$0.171021\pi$
$570$	0.299849	0.0125593
$571$	5.39212	0.225653	0.112827	−	0.993615i	$-0.464010\pi$
$571$	5.39212	0.225653	0.112827	+	0.993615i	$0.464010\pi$
$572$	16.9072	0.706926
$573$	59.8764	2.50137
$574$	−5.62338	−0.234716
$575$	−16.2269	−0.676708
$576$	1.97381	0.0822423
$577$	21.1188	0.879186	0.439593	−	0.898197i	$-0.355123\pi$
$577$	21.1188	0.879186	0.439593	+	0.898197i	$0.355123\pi$
$578$	16.8322	0.700127
$579$	15.0905	0.627138
$580$	31.2955	1.29947
$581$	33.0068	1.36935
$582$	−16.6221	−0.689009
$583$	−9.56626	−0.396194
$584$	12.5206	0.518108
$585$	−34.7096	−1.43506
$586$	11.1568	0.460883
$587$	29.9092	1.23449	0.617243	−	0.786773i	$-0.288250\pi$
$587$	29.9092	1.23449	0.617243	+	0.786773i	$0.288250\pi$
$588$	−6.89507	−0.284348
$589$	−0.196539	−0.00809825
$590$	−40.3194	−1.65992
$591$	−22.7563	−0.936070
$592$	7.53981	0.309884
$593$	−33.8666	−1.39074	−0.695368	−	0.718654i	$-0.744758\pi$
$593$	−33.8666	−1.39074	−0.695368	+	0.718654i	$0.744758\pi$
$594$	−6.58303	−0.270105
$595$	−3.89327	−0.159609
$596$	12.8310	0.525576
$597$	−50.8399	−2.08074
$598$	24.1428	0.987272
$599$	−8.68011	−0.354660	−0.177330	−	0.984151i	$-0.556746\pi$
$599$	−8.68011	−0.354660	−0.177330	+	0.984151i	$0.556746\pi$
$600$	8.81067	0.359694
$601$	−9.43732	−0.384956	−0.192478	−	0.981301i	$-0.561652\pi$
$601$	−9.43732	−0.384956	−0.192478	+	0.981301i	$0.561652\pi$
$602$	23.4657	0.956392
$603$	−20.5776	−0.837985
$604$	10.6126	0.431821
$605$	8.15580	0.331581
$606$	−16.6547	−0.676551
$607$	−47.4223	−1.92481	−0.962407	−	0.271612i	$-0.912443\pi$
$607$	−47.4223	−1.92481	−0.962407	+	0.271612i	$0.912443\pi$
$608$	0.0449398	0.00182255
$609$	74.1108	3.00312
$610$	13.9200	0.563605
$611$	35.7345	1.44566
$612$	0.808561	0.0326842
$613$	6.64719	0.268478	0.134239	−	0.990949i	$-0.457141\pi$
$613$	6.64719	0.268478	0.134239	+	0.990949i	$0.457141\pi$
$614$	2.77770	0.112099
$615$	11.8110	0.476266
$616$	−9.13770	−0.368169
$617$	17.6597	0.710952	0.355476	−	0.934685i	$-0.384319\pi$
$617$	17.6597	0.710952	0.355476	+	0.934685i	$0.384319\pi$
$618$	−3.67839	−0.147966
$619$	−8.26016	−0.332004	−0.166002	−	0.986125i	$-0.553086\pi$
$619$	−8.26016	−0.332004	−0.166002	+	0.986125i	$0.553086\pi$
$620$	−13.0841	−0.525471
$621$	−9.40030	−0.377221
$622$	−0.615059	−0.0246616
$623$	−45.2311	−1.81215
$624$	−13.1088	−0.524770
$625$	−29.1457	−1.16583
$626$	3.77072	0.150708
$627$	0.288291	0.0115132
$628$	6.53432	0.260748
$629$	3.08864	0.123152
$630$	18.7592	0.747384
$631$	35.3130	1.40579	0.702894	−	0.711295i	$-0.251891\pi$
$631$	35.3130	1.40579	0.702894	+	0.711295i	$0.251891\pi$
$632$	3.79632	0.151009
$633$	43.3498	1.72300
$634$	−7.51989	−0.298653
$635$	2.70396	0.107304
$636$	7.41706	0.294105
$637$	18.1723	0.720014
$638$	30.0892	1.19124
$639$	−3.83312	−0.151636
$640$	2.99176	0.118260
$641$	8.04189	0.317636	0.158818	−	0.987308i	$-0.449232\pi$
$641$	8.04189	0.317636	0.158818	+	0.987308i	$0.449232\pi$
$642$	16.9687	0.669701
$643$	−49.0753	−1.93534	−0.967670	−	0.252219i	$-0.918840\pi$
$643$	−49.0753	−1.93534	−0.967670	+	0.252219i	$0.918840\pi$
$644$	−13.0483	−0.514173
$645$	−49.2860	−1.94064
$646$	0.0184093	0.000724305 0
$647$	−29.6011	−1.16374	−0.581870	−	0.813282i	$-0.697679\pi$
$647$	−29.6011	−1.16374	−0.581870	+	0.813282i	$0.697679\pi$
$648$	11.0255	0.433123
$649$	−38.7653	−1.52167
$650$	−23.2210	−0.910802
$651$	−30.9845	−1.21438
$652$	0.0662900	0.00259612
$653$	−32.4370	−1.26936	−0.634678	−	0.772777i	$-0.718867\pi$
$653$	−32.4370	−1.26936	−0.634678	+	0.772777i	$0.718867\pi$
$654$	39.3368	1.53819
$655$	−16.9008	−0.660371
$656$	1.77017	0.0691137
$657$	−24.7134	−0.964162
$658$	−19.3131	−0.752905
$659$	13.9037	0.541613	0.270806	−	0.962634i	$-0.412710\pi$
$659$	13.9037	0.541613	0.270806	+	0.962634i	$0.412710\pi$
$660$	19.1923	0.747058
$661$	−11.8673	−0.461583	−0.230792	−	0.973003i	$-0.574132\pi$
$661$	−11.8673	−0.461583	−0.230792	+	0.973003i	$0.574132\pi$
$662$	1.96516	0.0763781
$663$	−5.36992	−0.208551
$664$	−10.3901	−0.403216
$665$	0.427109	0.0165626
$666$	−14.8822	−0.576673
$667$	42.9661	1.66366
$668$	24.0806	0.931707
$669$	39.6104	1.53143
$670$	−31.1900	−1.20497
$671$	13.3835	0.516663
$672$	7.08478	0.273301
$673$	36.4468	1.40492	0.702461	−	0.711722i	$-0.252085\pi$
$673$	36.4468	1.40492	0.702461	+	0.711722i	$0.252085\pi$
$674$	−29.4778	−1.13544
$675$	9.04138	0.348003
$676$	21.5488	0.828801
$677$	−38.0433	−1.46212	−0.731061	−	0.682313i	$-0.760974\pi$
$677$	−38.0433	−1.46212	−0.731061	+	0.682313i	$0.760974\pi$
$678$	−8.49706	−0.326328
$679$	−23.6768	−0.908633
$680$	1.22556	0.0469979
$681$	39.8339	1.52644
$682$	−12.5798	−0.481705
$683$	−22.9866	−0.879556	−0.439778	−	0.898106i	$-0.644943\pi$
$683$	−22.9866	−0.879556	−0.439778	+	0.898106i	$0.644943\pi$
$684$	−0.0887028	−0.00339164
$685$	46.0022	1.75766
$686$	12.4157	0.474035
$687$	−24.0567	−0.917822
$688$	−7.38674	−0.281617
$689$	−19.5480	−0.744721
$690$	27.4058	1.04332
$691$	0.544416	0.0207106	0.0103553	−	0.999946i	$-0.496704\pi$
$691$	0.544416	0.0207106	0.0103553	+	0.999946i	$0.496704\pi$
$692$	6.47747	0.246236
$693$	18.0361	0.685136
$694$	3.59165	0.136337
$695$	−13.4242	−0.509210
$696$	−23.3292	−0.884291
$697$	0.725142	0.0274667
$698$	18.2249	0.689822
$699$	40.8563	1.54533
$700$	12.5501	0.474348
$701$	−17.9420	−0.677661	−0.338831	−	0.940847i	$-0.610031\pi$
$701$	−17.9420	−0.677661	−0.338831	+	0.940847i	$0.610031\pi$
$702$	−13.4520	−0.507713
$703$	−0.338837	−0.0127795
$704$	2.87644	0.108410
$705$	40.5642	1.52773
$706$	2.82457	0.106304
$707$	−23.7232	−0.892204
$708$	30.0561	1.12958
$709$	40.0237	1.50312	0.751561	−	0.659664i	$-0.229301\pi$
$709$	40.0237	1.50312	0.751561	+	0.659664i	$0.229301\pi$
$710$	−5.80995	−0.218043
$711$	−7.49322	−0.281018
$712$	14.2382	0.533600
$713$	−17.9634	−0.672735
$714$	2.90224	0.108614
$715$	−50.5823	−1.89167
$716$	15.6680	0.585540
$717$	14.9307	0.557596
$718$	−4.07627	−0.152125
$719$	−5.16033	−0.192448	−0.0962238	−	0.995360i	$-0.530676\pi$
$719$	−5.16033	−0.192448	−0.0962238	+	0.995360i	$0.530676\pi$
$720$	−5.90517	−0.220073
$721$	−5.23955	−0.195131
$722$	18.9980	0.707032
$723$	−21.2766	−0.791284
$724$	−8.63524	−0.320926
$725$	−41.3256	−1.53480
$726$	−6.07974	−0.225640
$727$	−37.3998	−1.38708	−0.693540	−	0.720418i	$-0.743950\pi$
$727$	−37.3998	−1.38708	−0.693540	+	0.720418i	$0.743950\pi$
$728$	−18.6723	−0.692042
$729$	−6.45012	−0.238893
$730$	−37.4587	−1.38641
$731$	−3.02593	−0.111918
$732$	−10.3767	−0.383533
$733$	−24.3292	−0.898619	−0.449310	−	0.893376i	$-0.648330\pi$
$733$	−24.3292	−0.898619	−0.449310	+	0.893376i	$0.648330\pi$
$734$	−1.32069	−0.0487474
$735$	20.6284	0.760889
$736$	4.10744	0.151402
$737$	−29.9878	−1.10461
$738$	−3.49400	−0.128616
$739$	47.5423	1.74887	0.874437	−	0.485140i	$-0.161231\pi$
$739$	47.5423	1.74887	0.874437	+	0.485140i	$0.161231\pi$
$740$	−22.5573	−0.829222
$741$	0.589105	0.0216413
$742$	10.5650	0.387852
$743$	−9.29169	−0.340879	−0.170439	−	0.985368i	$-0.554519\pi$
$743$	−9.29169	−0.340879	−0.170439	+	0.985368i	$0.554519\pi$
$744$	9.75355	0.357583
$745$	−38.3871	−1.40639
$746$	10.9340	0.400323
$747$	20.5082	0.750356
$748$	1.17832	0.0430835
$749$	24.1705	0.883171
$750$	7.00177	0.255668
$751$	−48.4294	−1.76721	−0.883606	−	0.468231i	$-0.844892\pi$
$751$	−48.4294	−1.76721	−0.883606	+	0.468231i	$0.844892\pi$
$752$	6.07955	0.221698
$753$	22.7985	0.830824
$754$	61.4854	2.23917
$755$	−31.7504	−1.15551
$756$	7.27030	0.264418
$757$	2.54987	0.0926767	0.0463383	−	0.998926i	$-0.485245\pi$
$757$	2.54987	0.0926767	0.0463383	+	0.998926i	$0.485245\pi$
$758$	12.8845	0.467985
$759$	26.3494	0.956423
$760$	−0.134449	−0.00487698
$761$	1.67142	0.0605889	0.0302945	−	0.999541i	$-0.490355\pi$
$761$	1.67142	0.0605889	0.0302945	+	0.999541i	$0.490355\pi$
$762$	−2.01567	−0.0730200
$763$	56.0319	2.02849
$764$	−26.8480	−0.971325
$765$	−2.41902	−0.0874598
$766$	−23.0787	−0.833868
$767$	−79.2145	−2.86027
$768$	−2.23021	−0.0804756
$769$	−41.7056	−1.50394	−0.751971	−	0.659197i	$-0.770896\pi$
$769$	−41.7056	−1.50394	−0.751971	+	0.659197i	$0.770896\pi$
$770$	27.3378	0.985185
$771$	13.0010	0.468219
$772$	−6.76640	−0.243528
$773$	7.22538	0.259879	0.129939	−	0.991522i	$-0.458522\pi$
$773$	7.22538	0.259879	0.129939	+	0.991522i	$0.458522\pi$
$774$	14.5801	0.524069
$775$	17.2776	0.620628
$776$	7.45318	0.267554
$777$	−53.4179	−1.91636
$778$	3.13297	0.112322
$779$	−0.0795513	−0.00285022
$780$	39.2182	1.40424
$781$	−5.58600	−0.199883
$782$	1.68259	0.0601692
$783$	−23.9401	−0.855549
$784$	3.09168	0.110417
$785$	−19.5491	−0.697737
$786$	12.5987	0.449382
$787$	−4.32145	−0.154043	−0.0770216	−	0.997029i	$-0.524541\pi$
$787$	−4.32145	−0.154043	−0.0770216	+	0.997029i	$0.524541\pi$
$788$	10.2037	0.363491
$789$	−44.3148	−1.57765
$790$	−11.3577	−0.404087
$791$	−12.1033	−0.430346
$792$	−5.67756	−0.201743
$793$	27.3483	0.971166
$794$	17.8372	0.633017
$795$	−22.1900	−0.786999
$796$	22.7961	0.807986
$797$	18.0545	0.639524	0.319762	−	0.947498i	$-0.396397\pi$
$797$	18.0545	0.639524	0.319762	+	0.947498i	$0.396397\pi$
$798$	−0.318389	−0.0112708
$799$	2.49045	0.0881058
$800$	−3.95061	−0.139675
$801$	−28.1036	−0.992992
$802$	19.1171	0.675050
$803$	−36.0149	−1.27094
$804$	23.2506	0.819984
$805$	39.0372	1.37588
$806$	−25.7060	−0.905455
$807$	−23.9397	−0.842717
$808$	7.46779	0.262716
$809$	37.1388	1.30573	0.652865	−	0.757475i	$-0.273567\pi$
$809$	37.1388	1.30573	0.652865	+	0.757475i	$0.273567\pi$
$810$	−32.9856	−1.15900
$811$	42.8300	1.50397	0.751983	−	0.659183i	$-0.229098\pi$
$811$	42.8300	1.50397	0.751983	+	0.659183i	$0.229098\pi$
$812$	−33.2305	−1.16616
$813$	66.5314	2.33336
$814$	−21.6878	−0.760157
$815$	−0.198324	−0.00694697
$816$	−0.913590	−0.0319821
$817$	0.331958	0.0116138
$818$	−10.5904	−0.370284
$819$	36.8557	1.28784
$820$	−5.29593	−0.184942
$821$	28.2632	0.986392	0.493196	−	0.869918i	$-0.335829\pi$
$821$	28.2632	0.986392	0.493196	+	0.869918i	$0.335829\pi$
$822$	−34.2924	−1.19608
$823$	−41.7146	−1.45408	−0.727040	−	0.686595i	$-0.759105\pi$
$823$	−41.7146	−1.45408	−0.727040	+	0.686595i	$0.759105\pi$
$824$	1.64935	0.0574578
$825$	−25.3434	−0.882343
$826$	42.8124	1.48963
$827$	25.4331	0.884396	0.442198	−	0.896917i	$-0.354199\pi$
$827$	25.4331	0.884396	0.442198	+	0.896917i	$0.354199\pi$
$828$	−8.10732	−0.281749
$829$	36.2266	1.25820	0.629101	−	0.777323i	$-0.283423\pi$
$829$	36.2266	1.25820	0.629101	+	0.777323i	$0.283423\pi$
$830$	31.0848	1.07897
$831$	24.8841	0.863219
$832$	5.87782	0.203777
$833$	1.26649	0.0438812
$834$	10.0071	0.346517
$835$	−72.0434	−2.49316
$836$	−0.129267	−0.00447078
$837$	10.0090	0.345960
$838$	−0.178290	−0.00615894
$839$	−47.2793	−1.63226	−0.816131	−	0.577867i	$-0.803885\pi$
$839$	−47.2793	−1.63226	−0.816131	+	0.577867i	$0.803885\pi$
$840$	−21.1959	−0.731330
$841$	80.4235	2.77322
$842$	−17.8254	−0.614305
$843$	35.6050	1.22630
$844$	−19.4376	−0.669069
$845$	−64.4688	−2.21780
$846$	−11.9999	−0.412565
$847$	−8.66008	−0.297564
$848$	−3.32573	−0.114206
$849$	−32.4108	−1.11233
$850$	−1.61834	−0.0555087
$851$	−30.9693	−1.06161
$852$	4.33102	0.148378
$853$	13.7714	0.471525	0.235763	−	0.971811i	$-0.424241\pi$
$853$	13.7714	0.471525	0.235763	+	0.971811i	$0.424241\pi$
$854$	−14.7807	−0.505785
$855$	0.265377	0.00907571
$856$	−7.60858	−0.260056
$857$	−1.29834	−0.0443505	−0.0221752	−	0.999754i	$-0.507059\pi$
$857$	−1.29834	−0.0443505	−0.0221752	+	0.999754i	$0.507059\pi$
$858$	37.7065	1.28728
$859$	8.77784	0.299496	0.149748	−	0.988724i	$-0.452154\pi$
$859$	8.77784	0.299496	0.149748	+	0.988724i	$0.452154\pi$
$860$	22.0993	0.753581
$861$	−12.5413	−0.427406
$862$	−30.2650	−1.03083
$863$	−16.3484	−0.556506	−0.278253	−	0.960508i	$-0.589755\pi$
$863$	−16.3484	−0.556506	−0.278253	+	0.960508i	$0.589755\pi$
$864$	−2.28860	−0.0778599
$865$	−19.3790	−0.658906
$866$	17.9349	0.609452
$867$	37.5392	1.27490
$868$	13.8931	0.471563
$869$	−10.9199	−0.370431
$870$	69.7953	2.36628
$871$	−61.2781	−2.07633
$872$	−17.6382	−0.597305
$873$	−14.7112	−0.497899
$874$	−0.184587	−0.00624376
$875$	9.97343	0.337163
$876$	27.9236	0.943451
$877$	−9.17037	−0.309661	−0.154831	−	0.987941i	$-0.549483\pi$
$877$	−9.17037	−0.309661	−0.154831	+	0.987941i	$0.549483\pi$
$878$	30.4663	1.02819
$879$	24.8820	0.839248
$880$	−8.60561	−0.290095
$881$	−8.18227	−0.275668	−0.137834	−	0.990455i	$-0.544014\pi$
$881$	−8.18227	−0.275668	−0.137834	+	0.990455i	$0.544014\pi$
$882$	−6.10239	−0.205478
$883$	−32.2369	−1.08486	−0.542429	−	0.840102i	$-0.682495\pi$
$883$	−32.2369	−1.08486	−0.542429	+	0.840102i	$0.682495\pi$
$884$	2.40782	0.0809836
$885$	−89.9206	−3.02265
$886$	9.86679	0.331481
$887$	−26.2001	−0.879713	−0.439856	−	0.898068i	$-0.644971\pi$
$887$	−26.2001	−0.879713	−0.439856	+	0.898068i	$0.644971\pi$
$888$	16.8153	0.564285
$889$	−2.87115	−0.0962954
$890$	−42.5973	−1.42786
$891$	−31.7142	−1.06247
$892$	−17.7609	−0.594678
$893$	−0.273214	−0.00914275
$894$	28.6157	0.957051
$895$	−46.8748	−1.56685
$896$	−3.17674	−0.106127
$897$	53.8434	1.79778
$898$	−20.0101	−0.667744
$899$	−45.7481	−1.52579
$900$	7.79777	0.259926
$901$	−1.36236	−0.0453870
$902$	−5.09180	−0.169538
$903$	52.3334	1.74155
$904$	3.80999	0.126718
$905$	25.8345	0.858769
$906$	23.6683	0.786327
$907$	−31.9990	−1.06251	−0.531255	−	0.847212i	$-0.678279\pi$
$907$	−31.9990	−1.06251	−0.531255	+	0.847212i	$0.678279\pi$
$908$	−17.8611	−0.592740
$909$	−14.7400	−0.488896
$910$	55.8630	1.85184
$911$	9.51394	0.315211	0.157605	−	0.987502i	$-0.449623\pi$
$911$	9.51394	0.315211	0.157605	+	0.987502i	$0.449623\pi$
$912$	0.100225	0.00331878
$913$	29.8866	0.989103
$914$	15.3149	0.506573
$915$	31.0445	1.02630
$916$	10.7868	0.356405
$917$	17.9458	0.592624
$918$	−0.937513	−0.0309425
$919$	12.1447	0.400615	0.200308	−	0.979733i	$-0.435806\pi$
$919$	12.1447	0.400615	0.200308	+	0.979733i	$0.435806\pi$
$920$	−12.2885	−0.405138
$921$	6.19485	0.204127
$922$	−11.3234	−0.372917
$923$	−11.4146	−0.375718
$924$	−20.3789	−0.670418
$925$	29.7869	0.979386
$926$	−10.2140	−0.335653
$927$	−3.25551	−0.106925
$928$	10.4606	0.343385
$929$	26.7624	0.878046	0.439023	−	0.898476i	$-0.355325\pi$
$929$	26.7624	0.878046	0.439023	+	0.898476i	$0.355325\pi$
$930$	−29.1803	−0.956858
$931$	−0.138939	−0.00455355
$932$	−18.3195	−0.600076
$933$	−1.37171	−0.0449077
$934$	33.7918	1.10570
$935$	−3.52524	−0.115288
$936$	−11.6017	−0.379215
$937$	−35.5309	−1.16074	−0.580371	−	0.814352i	$-0.697093\pi$
$937$	−35.5309	−1.16074	−0.580371	+	0.814352i	$0.697093\pi$
$938$	33.1185	1.08136
$939$	8.40948	0.274433
$940$	−18.1885	−0.593245
$941$	35.9899	1.17324	0.586618	−	0.809864i	$-0.300459\pi$
$941$	35.9899	1.17324	0.586618	+	0.809864i	$0.300459\pi$
$942$	14.5729	0.474810
$943$	−7.27088	−0.236772
$944$	−13.4768	−0.438634
$945$	−21.7510	−0.707559
$946$	21.2475	0.690816
$947$	32.2511	1.04802	0.524010	−	0.851712i	$-0.324436\pi$
$947$	32.2511	1.04802	0.524010	+	0.851712i	$0.324436\pi$
$948$	8.46656	0.274981
$949$	−73.5941	−2.38897
$950$	0.177540	0.00576015
$951$	−16.7709	−0.543834
$952$	−1.30133	−0.0421764
$953$	−57.1235	−1.85041	−0.925206	−	0.379464i	$-0.876108\pi$
$953$	−57.1235	−1.85041	−0.925206	+	0.379464i	$0.876108\pi$
$954$	6.56437	0.212529
$955$	80.3226	2.59918
$956$	−6.69475	−0.216524
$957$	67.1051	2.16920
$958$	−13.1188	−0.423848
$959$	−48.8466	−1.57734
$960$	6.67223	0.215345
$961$	−11.8735	−0.383015
$962$	−44.3177	−1.42886
$963$	15.0179	0.483946
$964$	9.54019	0.307269
$965$	20.2434	0.651659
$966$	−29.1003	−0.936287
$967$	48.1762	1.54924	0.774621	−	0.632426i	$-0.217941\pi$
$967$	48.1762	1.54924	0.774621	+	0.632426i	$0.217941\pi$
$968$	2.72609	0.0876199
$969$	0.0410566	0.00131893
$970$	−22.2981	−0.715949
$971$	13.7406	0.440958	0.220479	−	0.975392i	$-0.429238\pi$
$971$	13.7406	0.440958	0.220479	+	0.975392i	$0.429238\pi$
$972$	17.7233	0.568476
$973$	14.2543	0.456971
$974$	−16.6755	−0.534319
$975$	−51.7876	−1.65853
$976$	4.65279	0.148932
$977$	14.7892	0.473149	0.236574	−	0.971613i	$-0.423975\pi$
$977$	14.7892	0.473149	0.236574	+	0.971613i	$0.423975\pi$
$978$	0.147840	0.00472741
$979$	−40.9554	−1.30894
$980$	−9.24954	−0.295466
$981$	34.8145	1.11154
$982$	−1.49758	−0.0477897
$983$	−36.9679	−1.17909	−0.589546	−	0.807735i	$-0.700693\pi$
$983$	−36.9679	−1.17909	−0.589546	+	0.807735i	$0.700693\pi$
$984$	3.94785	0.125853
$985$	−30.5270	−0.972670
$986$	4.28511	0.136466
$987$	−43.0723	−1.37101
$988$	−0.264148	−0.00840367
$989$	30.3406	0.964774
$990$	16.9859	0.539847
$991$	−37.2459	−1.18315	−0.591577	−	0.806249i	$-0.701494\pi$
$991$	−37.2459	−1.18315	−0.591577	+	0.806249i	$0.701494\pi$
$992$	−4.37339	−0.138855
$993$	4.38271	0.139081
$994$	6.16918	0.195675
$995$	−68.2003	−2.16210
$996$	−23.1721	−0.734238
$997$	31.2610	0.990046	0.495023	−	0.868880i	$-0.335160\pi$
$997$	31.2610	0.990046	0.495023	+	0.868880i	$0.335160\pi$
$998$	3.29467	0.104291
$999$	17.2556	0.545944

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8002.2.a.f.1.17	✓	89

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8002.2.a.f.1.17	✓	89	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:	\( N \)	\(=\)	\( 8002 = 2 \cdot 4001 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8002.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -2.23021 q^{3} +1.00000 q^{4} -2.99176 q^{5} +2.23021 q^{6} +3.17674 q^{7} -1.00000 q^{8} +1.97381 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -2.23021 q^{3} +1.00000 q^{4} -2.99176 q^{5} +2.23021 q^{6} +3.17674 q^{7} -1.00000 q^{8} +1.97381 q^{9} +2.99176 q^{10} +2.87644 q^{11} -2.23021 q^{12} +5.87782 q^{13} -3.17674 q^{14} +6.67223 q^{15} +1.00000 q^{16} +0.409644 q^{17} -1.97381 q^{18} -0.0449398 q^{19} -2.99176 q^{20} -7.08478 q^{21} -2.87644 q^{22} -4.10744 q^{23} +2.23021 q^{24} +3.95061 q^{25} -5.87782 q^{26} +2.28860 q^{27} +3.17674 q^{28} -10.4606 q^{29} -6.67223 q^{30} +4.37339 q^{31} -1.00000 q^{32} -6.41505 q^{33} -0.409644 q^{34} -9.50403 q^{35} +1.97381 q^{36} +7.53981 q^{37} +0.0449398 q^{38} -13.1088 q^{39} +2.99176 q^{40} +1.77017 q^{41} +7.08478 q^{42} -7.38674 q^{43} +2.87644 q^{44} -5.90517 q^{45} +4.10744 q^{46} +6.07955 q^{47} -2.23021 q^{48} +3.09168 q^{49} -3.95061 q^{50} -0.913590 q^{51} +5.87782 q^{52} -3.32573 q^{53} -2.28860 q^{54} -8.60561 q^{55} -3.17674 q^{56} +0.100225 q^{57} +10.4606 q^{58} -13.4768 q^{59} +6.67223 q^{60} +4.65279 q^{61} -4.37339 q^{62} +6.27030 q^{63} +1.00000 q^{64} -17.5850 q^{65} +6.41505 q^{66} -10.4253 q^{67} +0.409644 q^{68} +9.16043 q^{69} +9.50403 q^{70} -1.94198 q^{71} -1.97381 q^{72} -12.5206 q^{73} -7.53981 q^{74} -8.81067 q^{75} -0.0449398 q^{76} +9.13770 q^{77} +13.1088 q^{78} -3.79632 q^{79} -2.99176 q^{80} -11.0255 q^{81} -1.77017 q^{82} +10.3901 q^{83} -7.08478 q^{84} -1.22556 q^{85} +7.38674 q^{86} +23.3292 q^{87} -2.87644 q^{88} -14.2382 q^{89} +5.90517 q^{90} +18.6723 q^{91} -4.10744 q^{92} -9.75355 q^{93} -6.07955 q^{94} +0.134449 q^{95} +2.23021 q^{96} -7.45318 q^{97} -3.09168 q^{98} +5.67756 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 89 q - 89 q^{2} - 12 q^{3} + 89 q^{4} - 18 q^{5} + 12 q^{6} - 27 q^{7} - 89 q^{8} + 95 q^{9}+O(q^{10}) \) 89 * q - 89 * q^2 - 12 * q^3 + 89 * q^4 - 18 * q^5 + 12 * q^6 - 27 * q^7 - 89 * q^8 + 95 * q^9	\( 89 q - 89 q^{2} - 12 q^{3} + 89 q^{4} - 18 q^{5} + 12 q^{6} - 27 q^{7} - 89 q^{8} + 95 q^{9} + 18 q^{10} - 26 q^{11} - 12 q^{12} + 2 q^{13} + 27 q^{14} - 21 q^{15} + 89 q^{16} - 60 q^{17} - 95 q^{18} + q^{19} - 18 q^{20} - 6 q^{21} + 26 q^{22} - 45 q^{23} + 12 q^{24} + 107 q^{25} - 2 q^{26} - 45 q^{27} - 27 q^{28} - 18 q^{29} + 21 q^{30} - 38 q^{31} - 89 q^{32} - 29 q^{33} + 60 q^{34} - 47 q^{35} + 95 q^{36} - 15 q^{37} - q^{38} - 38 q^{39} + 18 q^{40} - 50 q^{41} + 6 q^{42} - 15 q^{43} - 26 q^{44} - 35 q^{45} + 45 q^{46} - 121 q^{47} - 12 q^{48} + 132 q^{49} - 107 q^{50} + 6 q^{51} + 2 q^{52} - 46 q^{53} + 45 q^{54} - 37 q^{55} + 27 q^{56} - 42 q^{57} + 18 q^{58} - 34 q^{59} - 21 q^{60} + 41 q^{61} + 38 q^{62} - 131 q^{63} + 89 q^{64} - 57 q^{65} + 29 q^{66} - 11 q^{67} - 60 q^{68} + 15 q^{69} + 47 q^{70} - 66 q^{71} - 95 q^{72} - 47 q^{73} + 15 q^{74} - 46 q^{75} + q^{76} - 106 q^{77} + 38 q^{78} - 51 q^{79} - 18 q^{80} + 113 q^{81} + 50 q^{82} - 141 q^{83} - 6 q^{84} - 7 q^{85} + 15 q^{86} - 110 q^{87} + 26 q^{88} - 30 q^{89} + 35 q^{90} + 37 q^{91} - 45 q^{92} - 44 q^{93} + 121 q^{94} - 98 q^{95} + 12 q^{96} + 3 q^{97} - 132 q^{98} - 71 q^{99}+O(q^{100}) \) 89 * q - 89 * q^2 - 12 * q^3 + 89 * q^4 - 18 * q^5 + 12 * q^6 - 27 * q^7 - 89 * q^8 + 95 * q^9 + 18 * q^10 - 26 * q^11 - 12 * q^12 + 2 * q^13 + 27 * q^14 - 21 * q^15 + 89 * q^16 - 60 * q^17 - 95 * q^18 + q^19 - 18 * q^20 - 6 * q^21 + 26 * q^22 - 45 * q^23 + 12 * q^24 + 107 * q^25 - 2 * q^26 - 45 * q^27 - 27 * q^28 - 18 * q^29 + 21 * q^30 - 38 * q^31 - 89 * q^32 - 29 * q^33 + 60 * q^34 - 47 * q^35 + 95 * q^36 - 15 * q^37 - q^38 - 38 * q^39 + 18 * q^40 - 50 * q^41 + 6 * q^42 - 15 * q^43 - 26 * q^44 - 35 * q^45 + 45 * q^46 - 121 * q^47 - 12 * q^48 + 132 * q^49 - 107 * q^50 + 6 * q^51 + 2 * q^52 - 46 * q^53 + 45 * q^54 - 37 * q^55 + 27 * q^56 - 42 * q^57 + 18 * q^58 - 34 * q^59 - 21 * q^60 + 41 * q^61 + 38 * q^62 - 131 * q^63 + 89 * q^64 - 57 * q^65 + 29 * q^66 - 11 * q^67 - 60 * q^68 + 15 * q^69 + 47 * q^70 - 66 * q^71 - 95 * q^72 - 47 * q^73 + 15 * q^74 - 46 * q^75 + q^76 - 106 * q^77 + 38 * q^78 - 51 * q^79 - 18 * q^80 + 113 * q^81 + 50 * q^82 - 141 * q^83 - 6 * q^84 - 7 * q^85 + 15 * q^86 - 110 * q^87 + 26 * q^88 - 30 * q^89 + 35 * q^90 + 37 * q^91 - 45 * q^92 - 44 * q^93 + 121 * q^94 - 98 * q^95 + 12 * q^96 + 3 * q^97 - 132 * q^98 - 71 * q^99

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