LMFDB - Embedded newform 8031.2.a.b.1.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8031,2,Mod(1,8031)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8031, 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("8031.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8031 = 3 \cdot 2677 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8031.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:	$64.1278578633$
Analytic rank:	$1$
Dimension:	$102$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.14
Character	$\chi$	$=$	8031.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.29383 q^{2} -1.00000 q^{3} +3.26167 q^{4} +1.63510 q^{5} +2.29383 q^{6} +1.45930 q^{7} -2.89406 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-2.29383 q^{2} -1.00000 q^{3} +3.26167 q^{4} +1.63510 q^{5} +2.29383 q^{6} +1.45930 q^{7} -2.89406 q^{8} +1.00000 q^{9} -3.75066 q^{10} +3.29520 q^{11} -3.26167 q^{12} +2.79642 q^{13} -3.34740 q^{14} -1.63510 q^{15} +0.115145 q^{16} -2.74406 q^{17} -2.29383 q^{18} -5.12724 q^{19} +5.33317 q^{20} -1.45930 q^{21} -7.55864 q^{22} -5.67118 q^{23} +2.89406 q^{24} -2.32643 q^{25} -6.41453 q^{26} -1.00000 q^{27} +4.75976 q^{28} +4.58840 q^{29} +3.75066 q^{30} +2.05224 q^{31} +5.52399 q^{32} -3.29520 q^{33} +6.29441 q^{34} +2.38611 q^{35} +3.26167 q^{36} +4.34751 q^{37} +11.7610 q^{38} -2.79642 q^{39} -4.73208 q^{40} -3.36664 q^{41} +3.34740 q^{42} +6.80541 q^{43} +10.7478 q^{44} +1.63510 q^{45} +13.0087 q^{46} +7.53642 q^{47} -0.115145 q^{48} -4.87043 q^{49} +5.33645 q^{50} +2.74406 q^{51} +9.12101 q^{52} -4.53928 q^{53} +2.29383 q^{54} +5.38799 q^{55} -4.22331 q^{56} +5.12724 q^{57} -10.5250 q^{58} -8.19177 q^{59} -5.33317 q^{60} +3.71591 q^{61} -4.70749 q^{62} +1.45930 q^{63} -12.9014 q^{64} +4.57244 q^{65} +7.55864 q^{66} -12.7731 q^{67} -8.95021 q^{68} +5.67118 q^{69} -5.47334 q^{70} -10.7574 q^{71} -2.89406 q^{72} -11.3557 q^{73} -9.97246 q^{74} +2.32643 q^{75} -16.7234 q^{76} +4.80869 q^{77} +6.41453 q^{78} +12.3528 q^{79} +0.188274 q^{80} +1.00000 q^{81} +7.72252 q^{82} -1.81294 q^{83} -4.75976 q^{84} -4.48682 q^{85} -15.6105 q^{86} -4.58840 q^{87} -9.53649 q^{88} -15.4722 q^{89} -3.75066 q^{90} +4.08083 q^{91} -18.4975 q^{92} -2.05224 q^{93} -17.2873 q^{94} -8.38358 q^{95} -5.52399 q^{96} +13.3321 q^{97} +11.1720 q^{98} +3.29520 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 102 q - 6 q^{2} - 102 q^{3} + 96 q^{4} - 20 q^{5} + 6 q^{6} + 12 q^{7} - 21 q^{8} + 102 q^{9}+O(q^{10}) $ 102 * q - 6 * q^2 - 102 * q^3 + 96 * q^4 - 20 * q^5 + 6 * q^6 + 12 * q^7 - 21 * q^8 + 102 * q^9	\( 102 q - 6 q^{2} - 102 q^{3} + 96 q^{4} - 20 q^{5} + 6 q^{6} + 12 q^{7} - 21 q^{8} + 102 q^{9} - 16 q^{10} - 28 q^{11} - 96 q^{12} - 2 q^{13} - 41 q^{14} + 20 q^{15} + 88 q^{16} - 77 q^{17} - 6 q^{18} + 10 q^{19} - 50 q^{20} - 12 q^{21} + 24 q^{22} - 29 q^{23} + 21 q^{24} + 74 q^{25} - 45 q^{26} - 102 q^{27} + 19 q^{28} - 68 q^{29} + 16 q^{30} - 29 q^{31} - 48 q^{32} + 28 q^{33} - 19 q^{34} - 49 q^{35} + 96 q^{36} + 4 q^{37} - 44 q^{38} + 2 q^{39} - 41 q^{40} - 122 q^{41} + 41 q^{42} + 85 q^{43} - 86 q^{44} - 20 q^{45} - 28 q^{46} - 39 q^{47} - 88 q^{48} + 24 q^{49} - 37 q^{50} + 77 q^{51} + 8 q^{52} - 37 q^{53} + 6 q^{54} - 13 q^{55} - 130 q^{56} - 10 q^{57} + 17 q^{58} - 58 q^{59} + 50 q^{60} - 114 q^{61} - 64 q^{62} + 12 q^{63} + 47 q^{64} - 92 q^{65} - 24 q^{66} + 121 q^{67} - 138 q^{68} + 29 q^{69} - 2 q^{70} - 67 q^{71} - 21 q^{72} - 72 q^{73} - 111 q^{74} - 74 q^{75} - 17 q^{76} - 57 q^{77} + 45 q^{78} - 24 q^{79} - 97 q^{80} + 102 q^{81} - q^{82} - 78 q^{83} - 19 q^{84} - 24 q^{85} - 80 q^{86} + 68 q^{87} + 54 q^{88} - 176 q^{89} - 16 q^{90} - 3 q^{91} - 82 q^{92} + 29 q^{93} - 41 q^{94} - 90 q^{95} + 48 q^{96} - 77 q^{97} - 48 q^{98} - 28 q^{99}+O(q^{100}) \) 102 * q - 6 * q^2 - 102 * q^3 + 96 * q^4 - 20 * q^5 + 6 * q^6 + 12 * q^7 - 21 * q^8 + 102 * q^9 - 16 * q^10 - 28 * q^11 - 96 * q^12 - 2 * q^13 - 41 * q^14 + 20 * q^15 + 88 * q^16 - 77 * q^17 - 6 * q^18 + 10 * q^19 - 50 * q^20 - 12 * q^21 + 24 * q^22 - 29 * q^23 + 21 * q^24 + 74 * q^25 - 45 * q^26 - 102 * q^27 + 19 * q^28 - 68 * q^29 + 16 * q^30 - 29 * q^31 - 48 * q^32 + 28 * q^33 - 19 * q^34 - 49 * q^35 + 96 * q^36 + 4 * q^37 - 44 * q^38 + 2 * q^39 - 41 * q^40 - 122 * q^41 + 41 * q^42 + 85 * q^43 - 86 * q^44 - 20 * q^45 - 28 * q^46 - 39 * q^47 - 88 * q^48 + 24 * q^49 - 37 * q^50 + 77 * q^51 + 8 * q^52 - 37 * q^53 + 6 * q^54 - 13 * q^55 - 130 * q^56 - 10 * q^57 + 17 * q^58 - 58 * q^59 + 50 * q^60 - 114 * q^61 - 64 * q^62 + 12 * q^63 + 47 * q^64 - 92 * q^65 - 24 * q^66 + 121 * q^67 - 138 * q^68 + 29 * q^69 - 2 * q^70 - 67 * q^71 - 21 * q^72 - 72 * q^73 - 111 * q^74 - 74 * q^75 - 17 * q^76 - 57 * q^77 + 45 * q^78 - 24 * q^79 - 97 * q^80 + 102 * q^81 - q^82 - 78 * q^83 - 19 * q^84 - 24 * q^85 - 80 * q^86 + 68 * q^87 + 54 * q^88 - 176 * q^89 - 16 * q^90 - 3 * q^91 - 82 * q^92 + 29 * q^93 - 41 * q^94 - 90 * q^95 + 48 * q^96 - 77 * q^97 - 48 * q^98 - 28 * 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 $

$2$	−2.29383	−1.62198	−0.810992	−	0.585057i	$-0.801072\pi$
$2$	−2.29383	−1.62198	−0.810992	+	0.585057i	$0.801072\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	3.26167	1.63083
$5$	1.63510	0.731241	0.365620	−	0.930764i	$-0.380857\pi$
$5$	1.63510	0.731241	0.365620	+	0.930764i	$0.380857\pi$
$6$	2.29383	0.936453
$7$	1.45930	0.551565	0.275782	−	0.961220i	$-0.411063\pi$
$7$	1.45930	0.551565	0.275782	+	0.961220i	$0.411063\pi$
$8$	−2.89406	−1.02320
$9$	1.00000	0.333333
$10$	−3.75066	−1.18606
$11$	3.29520	0.993540	0.496770	−	0.867882i	$-0.334519\pi$
$11$	3.29520	0.993540	0.496770	+	0.867882i	$0.334519\pi$
$12$	−3.26167	−0.941563
$13$	2.79642	0.775588	0.387794	−	0.921746i	$-0.373237\pi$
$13$	2.79642	0.775588	0.387794	+	0.921746i	$0.373237\pi$
$14$	−3.34740	−0.894629
$15$	−1.63510	−0.422182
$16$	0.115145	0.0287862
$17$	−2.74406	−0.665532	−0.332766	−	0.943009i	$-0.607982\pi$
$17$	−2.74406	−0.665532	−0.332766	+	0.943009i	$0.607982\pi$
$18$	−2.29383	−0.540662
$19$	−5.12724	−1.17627	−0.588135	−	0.808763i	$-0.700138\pi$
$19$	−5.12724	−1.17627	−0.588135	+	0.808763i	$0.700138\pi$
$20$	5.33317	1.19253
$21$	−1.45930	−0.318446
$22$	−7.55864	−1.61151
$23$	−5.67118	−1.18252	−0.591262	−	0.806480i	$-0.701370\pi$
$23$	−5.67118	−1.18252	−0.591262	+	0.806480i	$0.701370\pi$
$24$	2.89406	0.590747
$25$	−2.32643	−0.465287
$26$	−6.41453	−1.25799
$27$	−1.00000	−0.192450
$28$	4.75976	0.899511
$29$	4.58840	0.852044	0.426022	−	0.904713i	$-0.359915\pi$
$29$	4.58840	0.852044	0.426022	+	0.904713i	$0.359915\pi$
$30$	3.75066	0.684773
$31$	2.05224	0.368593	0.184297	−	0.982871i	$-0.440999\pi$
$31$	2.05224	0.368593	0.184297	+	0.982871i	$0.440999\pi$
$32$	5.52399	0.976513
$33$	−3.29520	−0.573621
$34$	6.29441	1.07948
$35$	2.38611	0.403327
$36$	3.26167	0.543611
$37$	4.34751	0.714726	0.357363	−	0.933966i	$-0.383676\pi$
$37$	4.34751	0.714726	0.357363	+	0.933966i	$0.383676\pi$
$38$	11.7610	1.90789
$39$	−2.79642	−0.447786
$40$	−4.73208	−0.748208
$41$	−3.36664	−0.525781	−0.262891	−	0.964826i	$-0.584676\pi$
$41$	−3.36664	−0.525781	−0.262891	+	0.964826i	$0.584676\pi$
$42$	3.34740	0.516515
$43$	6.80541	1.03781	0.518907	−	0.854830i	$-0.326339\pi$
$43$	6.80541	1.03781	0.518907	+	0.854830i	$0.326339\pi$
$44$	10.7478	1.62030
$45$	1.63510	0.243747
$46$	13.0087	1.91804
$47$	7.53642	1.09930	0.549650	−	0.835395i	$-0.314761\pi$
$47$	7.53642	1.09930	0.549650	+	0.835395i	$0.314761\pi$
$48$	−0.115145	−0.0166197
$49$	−4.87043	−0.695776
$50$	5.33645	0.754688
$51$	2.74406	0.384245
$52$	9.12101	1.26486
$53$	−4.53928	−0.623517	−0.311759	−	0.950161i	$-0.600918\pi$
$53$	−4.53928	−0.623517	−0.311759	+	0.950161i	$0.600918\pi$
$54$	2.29383	0.312151
$55$	5.38799	0.726517
$56$	−4.22331	−0.564363
$57$	5.12724	0.679120
$58$	−10.5250	−1.38200
$59$	−8.19177	−1.06648	−0.533239	−	0.845965i	$-0.679025\pi$
$59$	−8.19177	−1.06648	−0.533239	+	0.845965i	$0.679025\pi$
$60$	−5.33317	−0.688509
$61$	3.71591	0.475773	0.237887	−	0.971293i	$-0.423545\pi$
$61$	3.71591	0.475773	0.237887	+	0.971293i	$0.423545\pi$
$62$	−4.70749	−0.597852
$63$	1.45930	0.183855
$64$	−12.9014	−1.61267
$65$	4.57244	0.567142
$66$	7.55864	0.930404
$67$	−12.7731	−1.56048	−0.780241	−	0.625479i	$-0.784904\pi$
$67$	−12.7731	−1.56048	−0.780241	+	0.625479i	$0.784904\pi$
$68$	−8.95021	−1.08537
$69$	5.67118	0.682730
$70$	−5.47334	−0.654190
$71$	−10.7574	−1.27667	−0.638337	−	0.769757i	$-0.720377\pi$
$71$	−10.7574	−1.27667	−0.638337	+	0.769757i	$0.720377\pi$
$72$	−2.89406	−0.341068
$73$	−11.3557	−1.32909	−0.664544	−	0.747249i	$-0.731374\pi$
$73$	−11.3557	−1.32909	−0.664544	+	0.747249i	$0.731374\pi$
$74$	−9.97246	−1.15927
$75$	2.32643	0.268633
$76$	−16.7234	−1.91830
$77$	4.80869	0.548001
$78$	6.41453	0.726302
$79$	12.3528	1.38980	0.694900	−	0.719107i	$-0.255449\pi$
$79$	12.3528	1.38980	0.694900	+	0.719107i	$0.255449\pi$
$80$	0.188274	0.0210497
$81$	1.00000	0.111111
$82$	7.72252	0.852809
$83$	−1.81294	−0.198996	−0.0994979	−	0.995038i	$-0.531724\pi$
$83$	−1.81294	−0.198996	−0.0994979	+	0.995038i	$0.531724\pi$
$84$	−4.75976	−0.519333
$85$	−4.48682	−0.486664
$86$	−15.6105	−1.68332
$87$	−4.58840	−0.491928
$88$	−9.53649	−1.01659
$89$	−15.4722	−1.64005	−0.820024	−	0.572329i	$-0.806040\pi$
$89$	−15.4722	−1.64005	−0.820024	+	0.572329i	$0.806040\pi$
$90$	−3.75066	−0.395354
$91$	4.08083	0.427787
$92$	−18.4975	−1.92850
$93$	−2.05224	−0.212807
$94$	−17.2873	−1.78305
$95$	−8.38358	−0.860137
$96$	−5.52399	−0.563790
$97$	13.3321	1.35367	0.676833	−	0.736137i	$-0.263352\pi$
$97$	13.3321	1.35367	0.676833	+	0.736137i	$0.263352\pi$
$98$	11.1720	1.12854
$99$	3.29520	0.331180
$100$	−7.58805	−0.758805
$101$	−3.78795	−0.376915	−0.188457	−	0.982081i	$-0.560349\pi$
$101$	−3.78795	−0.376915	−0.188457	+	0.982081i	$0.560349\pi$
$102$	−6.29441	−0.623240
$103$	−6.39463	−0.630082	−0.315041	−	0.949078i	$-0.602018\pi$
$103$	−6.39463	−0.630082	−0.315041	+	0.949078i	$0.602018\pi$
$104$	−8.09301	−0.793585
$105$	−2.38611	−0.232861
$106$	10.4123	1.01134
$107$	−16.1068	−1.55710	−0.778551	−	0.627582i	$-0.784045\pi$
$107$	−16.1068	−1.55710	−0.778551	+	0.627582i	$0.784045\pi$
$108$	−3.26167	−0.313854
$109$	4.89569	0.468922	0.234461	−	0.972126i	$-0.424668\pi$
$109$	4.89569	0.468922	0.234461	+	0.972126i	$0.424668\pi$
$110$	−12.3592	−1.17840
$111$	−4.34751	−0.412647
$112$	0.168031	0.0158775
$113$	−15.7059	−1.47749	−0.738745	−	0.673985i	$-0.764581\pi$
$113$	−15.7059	−1.47749	−0.738745	+	0.673985i	$0.764581\pi$
$114$	−11.7610	−1.10152
$115$	−9.27298	−0.864710
$116$	14.9658	1.38954
$117$	2.79642	0.258529
$118$	18.7905	1.72981
$119$	−4.00441	−0.367084
$120$	4.73208	0.431978
$121$	−0.141664	−0.0128786
$122$	−8.52367	−0.771697
$123$	3.36664	0.303560
$124$	6.69373	0.601114
$125$	−11.9795	−1.07148
$126$	−3.34740	−0.298210
$127$	11.4064	1.01215	0.506077	−	0.862488i	$-0.331095\pi$
$127$	11.4064	1.01215	0.506077	+	0.862488i	$0.331095\pi$
$128$	18.5457	1.63922
$129$	−6.80541	−0.599183
$130$	−10.4884	−0.919895
$131$	−7.53398	−0.658247	−0.329123	−	0.944287i	$-0.606753\pi$
$131$	−7.53398	−0.658247	−0.329123	+	0.944287i	$0.606753\pi$
$132$	−10.7478	−0.935480
$133$	−7.48220	−0.648789
$134$	29.2994	2.53108
$135$	−1.63510	−0.140727
$136$	7.94146	0.680975
$137$	−6.85613	−0.585759	−0.292880	−	0.956149i	$-0.594613\pi$
$137$	−6.85613	−0.585759	−0.292880	+	0.956149i	$0.594613\pi$
$138$	−13.0087	−1.10738
$139$	5.16447	0.438045	0.219022	−	0.975720i	$-0.429713\pi$
$139$	5.16447	0.438045	0.219022	+	0.975720i	$0.429713\pi$
$140$	7.78271	0.657759
$141$	−7.53642	−0.634681
$142$	24.6758	2.07074
$143$	9.21477	0.770578
$144$	0.115145	0.00959540
$145$	7.50251	0.623050
$146$	26.0481	2.15576
$147$	4.87043	0.401707
$148$	14.1801	1.16560
$149$	10.3874	0.850970	0.425485	−	0.904965i	$-0.360104\pi$
$149$	10.3874	0.850970	0.425485	+	0.904965i	$0.360104\pi$
$150$	−5.33645	−0.435719
$151$	−0.340609	−0.0277184	−0.0138592	−	0.999904i	$-0.504412\pi$
$151$	−0.340609	−0.0277184	−0.0138592	+	0.999904i	$0.504412\pi$
$152$	14.8385	1.20356
$153$	−2.74406	−0.221844
$154$	−11.0303	−0.888850
$155$	3.35563	0.269530
$156$	−9.12101	−0.730265
$157$	−7.12876	−0.568937	−0.284469	−	0.958685i	$-0.591817\pi$
$157$	−7.12876	−0.568937	−0.284469	+	0.958685i	$0.591817\pi$
$158$	−28.3353	−2.25423
$159$	4.53928	0.359988
$160$	9.03230	0.714066
$161$	−8.27598	−0.652238
$162$	−2.29383	−0.180221
$163$	10.1690	0.796501	0.398250	−	0.917277i	$-0.369617\pi$
$163$	10.1690	0.796501	0.398250	+	0.917277i	$0.369617\pi$
$164$	−10.9809	−0.857462
$165$	−5.38799	−0.419455
$166$	4.15858	0.322768
$167$	−0.920485	−0.0712293	−0.0356146	−	0.999366i	$-0.511339\pi$
$167$	−0.920485	−0.0712293	−0.0356146	+	0.999366i	$0.511339\pi$
$168$	4.22331	0.325835
$169$	−5.18002	−0.398463
$170$	10.2920	0.789362
$171$	−5.12724	−0.392090
$172$	22.1970	1.69250
$173$	−22.9025	−1.74124	−0.870621	−	0.491954i	$-0.836283\pi$
$173$	−22.9025	−1.74124	−0.870621	+	0.491954i	$0.836283\pi$
$174$	10.5250	0.797900
$175$	−3.39497	−0.256636
$176$	0.379425	0.0286002
$177$	8.19177	0.615731
$178$	35.4906	2.66013
$179$	5.41551	0.404774	0.202387	−	0.979306i	$-0.435130\pi$
$179$	5.41551	0.404774	0.202387	+	0.979306i	$0.435130\pi$
$180$	5.33317	0.397511
$181$	−14.4873	−1.07683	−0.538415	−	0.842680i	$-0.680977\pi$
$181$	−14.4873	−1.07683	−0.538415	+	0.842680i	$0.680977\pi$
$182$	−9.36074	−0.693864
$183$	−3.71591	−0.274688
$184$	16.4127	1.20996
$185$	7.10863	0.522637
$186$	4.70749	0.345170
$187$	−9.04222	−0.661233
$188$	24.5813	1.79278
$189$	−1.45930	−0.106149
$190$	19.2305	1.39513
$191$	11.1032	0.803396	0.401698	−	0.915772i	$-0.368420\pi$
$191$	11.1032	0.803396	0.401698	+	0.915772i	$0.368420\pi$
$192$	12.9014	0.931078
$193$	14.6996	1.05810	0.529050	−	0.848590i	$-0.322548\pi$
$193$	14.6996	1.05810	0.529050	+	0.848590i	$0.322548\pi$
$194$	−30.5815	−2.19562
$195$	−4.57244	−0.327440
$196$	−15.8857	−1.13470
$197$	0.594591	0.0423629	0.0211814	−	0.999776i	$-0.493257\pi$
$197$	0.594591	0.0423629	0.0211814	+	0.999776i	$0.493257\pi$
$198$	−7.55864	−0.537169
$199$	−17.2408	−1.22217	−0.611083	−	0.791566i	$-0.709266\pi$
$199$	−17.2408	−1.22217	−0.611083	+	0.791566i	$0.709266\pi$
$200$	6.73283	0.476083
$201$	12.7731	0.900945
$202$	8.68892	0.611350
$203$	6.69587	0.469958
$204$	8.95021	0.626640
$205$	−5.50481	−0.384473
$206$	14.6682	1.02198
$207$	−5.67118	−0.394175
$208$	0.321994	0.0223262
$209$	−16.8953	−1.16867
$210$	5.47334	0.377697
$211$	−2.85611	−0.196623	−0.0983114	−	0.995156i	$-0.531344\pi$
$211$	−2.85611	−0.196623	−0.0983114	+	0.995156i	$0.531344\pi$
$212$	−14.8056	−1.01685
$213$	10.7574	0.737088
$214$	36.9463	2.52560
$215$	11.1276	0.758893
$216$	2.89406	0.196916
$217$	2.99484	0.203303
$218$	−11.2299	−0.760584
$219$	11.3557	0.767349
$220$	17.5739	1.18483
$221$	−7.67355	−0.516179
$222$	9.97246	0.669308
$223$	0.591499	0.0396097	0.0198049	−	0.999804i	$-0.493696\pi$
$223$	0.591499	0.0396097	0.0198049	+	0.999804i	$0.493696\pi$
$224$	8.06118	0.538610
$225$	−2.32643	−0.155096
$226$	36.0268	2.39647
$227$	1.84153	0.122227	0.0611134	−	0.998131i	$-0.480535\pi$
$227$	1.84153	0.122227	0.0611134	+	0.998131i	$0.480535\pi$
$228$	16.7234	1.10753
$229$	−23.0556	−1.52355	−0.761777	−	0.647839i	$-0.775673\pi$
$229$	−23.0556	−1.52355	−0.761777	+	0.647839i	$0.775673\pi$
$230$	21.2707	1.40255
$231$	−4.80869	−0.316389
$232$	−13.2791	−0.871815
$233$	9.92134	0.649968	0.324984	−	0.945719i	$-0.394641\pi$
$233$	9.92134	0.649968	0.324984	+	0.945719i	$0.394641\pi$
$234$	−6.41453	−0.419331
$235$	12.3228	0.803853
$236$	−26.7188	−1.73925
$237$	−12.3528	−0.802401
$238$	9.18546	0.595405
$239$	15.9249	1.03010	0.515049	−	0.857161i	$-0.327774\pi$
$239$	15.9249	1.03010	0.515049	+	0.857161i	$0.327774\pi$
$240$	−0.188274	−0.0121530
$241$	−19.6550	−1.26609	−0.633045	−	0.774115i	$-0.718195\pi$
$241$	−19.6550	−1.26609	−0.633045	+	0.774115i	$0.718195\pi$
$242$	0.324954	0.0208888
$243$	−1.00000	−0.0641500
$244$	12.1201	0.775907
$245$	−7.96367	−0.508780
$246$	−7.72252	−0.492370
$247$	−14.3379	−0.912301
$248$	−5.93930	−0.377146
$249$	1.81294	0.114890
$250$	27.4789	1.73792
$251$	−0.0401549	−0.00253455	−0.00126728	−	0.999999i	$-0.500403\pi$
$251$	−0.0401549	−0.00253455	−0.00126728	+	0.999999i	$0.500403\pi$
$252$	4.75976	0.299837
$253$	−18.6877	−1.17488
$254$	−26.1644	−1.64170
$255$	4.48682	0.280976
$256$	−16.7379	−1.04612
$257$	15.4134	0.961462	0.480731	−	0.876868i	$-0.340371\pi$
$257$	15.4134	0.961462	0.480731	+	0.876868i	$0.340371\pi$
$258$	15.6105	0.971865
$259$	6.34433	0.394218
$260$	14.9138	0.924914
$261$	4.58840	0.284015
$262$	17.2817	1.06767
$263$	−10.5196	−0.648666	−0.324333	−	0.945943i	$-0.605140\pi$
$263$	−10.5196	−0.648666	−0.324333	+	0.945943i	$0.605140\pi$
$264$	9.53649	0.586931
$265$	−7.42219	−0.455941
$266$	17.1629	1.05233
$267$	15.4722	0.946883
$268$	−41.6616	−2.54489
$269$	−26.2426	−1.60004	−0.800020	−	0.599974i	$-0.795178\pi$
$269$	−26.2426	−1.60004	−0.800020	+	0.599974i	$0.795178\pi$
$270$	3.75066	0.228258
$271$	−0.602327	−0.0365888	−0.0182944	−	0.999833i	$-0.505824\pi$
$271$	−0.602327	−0.0365888	−0.0182944	+	0.999833i	$0.505824\pi$
$272$	−0.315964	−0.0191581
$273$	−4.08083	−0.246983
$274$	15.7268	0.950092
$275$	−7.66606	−0.462281
$276$	18.4975	1.11342
$277$	17.5266	1.05307	0.526536	−	0.850153i	$-0.323490\pi$
$277$	17.5266	1.05307	0.526536	+	0.850153i	$0.323490\pi$
$278$	−11.8464	−0.710502
$279$	2.05224	0.122864
$280$	−6.90555	−0.412685
$281$	27.9883	1.66964	0.834820	−	0.550524i	$-0.185572\pi$
$281$	27.9883	1.66964	0.834820	+	0.550524i	$0.185572\pi$
$282$	17.2873	1.02944
$283$	−2.47652	−0.147214	−0.0736070	−	0.997287i	$-0.523451\pi$
$283$	−2.47652	−0.147214	−0.0736070	+	0.997287i	$0.523451\pi$
$284$	−35.0872	−2.08204
$285$	8.38358	0.496600
$286$	−21.1371	−1.24987
$287$	−4.91295	−0.290002
$288$	5.52399	0.325504
$289$	−9.47014	−0.557067
$290$	−17.2095	−1.01058
$291$	−13.3321	−0.781539
$292$	−37.0386	−2.16752
$293$	4.43068	0.258843	0.129421	−	0.991590i	$-0.458688\pi$
$293$	4.43068	0.258843	0.129421	+	0.991590i	$0.458688\pi$
$294$	−11.1720	−0.651562
$295$	−13.3944	−0.779852
$296$	−12.5819	−0.731310
$297$	−3.29520	−0.191207
$298$	−23.8270	−1.38026
$299$	−15.8590	−0.917152
$300$	7.58805	0.438097
$301$	9.93115	0.572422
$302$	0.781300	0.0449587
$303$	3.78795	0.217612
$304$	−0.590375	−0.0338604
$305$	6.07589	0.347905
$306$	6.29441	0.359828
$307$	1.90247	0.108580	0.0542898	−	0.998525i	$-0.482711\pi$
$307$	1.90247	0.108580	0.0542898	+	0.998525i	$0.482711\pi$
$308$	15.6844	0.893700
$309$	6.39463	0.363778
$310$	−7.69725	−0.437174
$311$	−31.3911	−1.78002	−0.890012	−	0.455937i	$-0.849304\pi$
$311$	−31.3911	−1.78002	−0.890012	+	0.455937i	$0.849304\pi$
$312$	8.09301	0.458176
$313$	24.5781	1.38924	0.694618	−	0.719379i	$-0.255573\pi$
$313$	24.5781	1.38924	0.694618	+	0.719379i	$0.255573\pi$
$314$	16.3522	0.922807
$315$	2.38611	0.134442
$316$	40.2908	2.26653
$317$	−29.7125	−1.66882	−0.834409	−	0.551146i	$-0.814191\pi$
$317$	−29.7125	−1.66882	−0.834409	+	0.551146i	$0.814191\pi$
$318$	−10.4123	−0.583895
$319$	15.1197	0.846540
$320$	−21.0951	−1.17925
$321$	16.1068	0.898993
$322$	18.9837	1.05792
$323$	14.0695	0.782846
$324$	3.26167	0.181204
$325$	−6.50569	−0.360871
$326$	−23.3261	−1.29191
$327$	−4.89569	−0.270732
$328$	9.74326	0.537981
$329$	10.9979	0.606335
$330$	12.3592	0.680349
$331$	19.4426	1.06866	0.534332	−	0.845275i	$-0.320563\pi$
$331$	19.4426	1.06866	0.534332	+	0.845275i	$0.320563\pi$
$332$	−5.91321	−0.324529
$333$	4.34751	0.238242
$334$	2.11144	0.115533
$335$	−20.8854	−1.14109
$336$	−0.168031	−0.00916685
$337$	−1.44576	−0.0787554	−0.0393777	−	0.999224i	$-0.512538\pi$
$337$	−1.44576	−0.0787554	−0.0393777	+	0.999224i	$0.512538\pi$
$338$	11.8821	0.646301
$339$	15.7059	0.853029
$340$	−14.6345	−0.793669
$341$	6.76254	0.366212
$342$	11.7610	0.635964
$343$	−17.3226	−0.935330
$344$	−19.6952	−1.06190
$345$	9.27298	0.499240
$346$	52.5344	2.82427
$347$	−17.9466	−0.963425	−0.481713	−	0.876329i	$-0.659985\pi$
$347$	−17.9466	−0.963425	−0.481713	+	0.876329i	$0.659985\pi$
$348$	−14.9658	−0.802253
$349$	14.7099	0.787402	0.393701	−	0.919238i	$-0.371194\pi$
$349$	14.7099	0.787402	0.393701	+	0.919238i	$0.371194\pi$
$350$	7.78750	0.416259
$351$	−2.79642	−0.149262
$352$	18.2026	0.970204
$353$	−16.7100	−0.889385	−0.444693	−	0.895683i	$-0.646687\pi$
$353$	−16.7100	−0.889385	−0.444693	+	0.895683i	$0.646687\pi$
$354$	−18.7905	−0.998706
$355$	−17.5895	−0.933556
$356$	−50.4652	−2.67465
$357$	4.00441	0.211936
$358$	−12.4223	−0.656538
$359$	−1.61393	−0.0851800	−0.0425900	−	0.999093i	$-0.513561\pi$
$359$	−1.61393	−0.0851800	−0.0425900	+	0.999093i	$0.513561\pi$
$360$	−4.73208	−0.249403
$361$	7.28862	0.383611
$362$	33.2314	1.74660
$363$	0.141664	0.00743544
$364$	13.3103	0.697650
$365$	−18.5678	−0.971883
$366$	8.52367	0.445539
$367$	20.6140	1.07604	0.538021	−	0.842931i	$-0.319172\pi$
$367$	20.6140	1.07604	0.538021	+	0.842931i	$0.319172\pi$
$368$	−0.653007	−0.0340404
$369$	−3.36664	−0.175260
$370$	−16.3060	−0.847709
$371$	−6.62418	−0.343910
$372$	−6.69373	−0.347054
$373$	27.6771	1.43307	0.716533	−	0.697553i	$-0.245728\pi$
$373$	27.6771	1.43307	0.716533	+	0.697553i	$0.245728\pi$
$374$	20.7413	1.07251
$375$	11.9795	0.618618
$376$	−21.8108	−1.12481
$377$	12.8311	0.660836
$378$	3.34740	0.172172
$379$	12.3404	0.633883	0.316942	−	0.948445i	$-0.397344\pi$
$379$	12.3404	0.633883	0.316942	+	0.948445i	$0.397344\pi$
$380$	−27.3445	−1.40274
$381$	−11.4064	−0.584367
$382$	−25.4688	−1.30310
$383$	20.1112	1.02763	0.513816	−	0.857900i	$-0.328231\pi$
$383$	20.1112	1.02763	0.513816	+	0.857900i	$0.328231\pi$
$384$	−18.5457	−0.946405
$385$	7.86272	0.400721
$386$	−33.7184	−1.71622
$387$	6.80541	0.345938
$388$	43.4847	2.20760
$389$	−15.0650	−0.763826	−0.381913	−	0.924198i	$-0.624735\pi$
$389$	−15.0650	−0.763826	−0.381913	+	0.924198i	$0.624735\pi$
$390$	10.4884	0.531102
$391$	15.5621	0.787008
$392$	14.0953	0.711921
$393$	7.53398	0.380039
$394$	−1.36389	−0.0687120
$395$	20.1981	1.01628
$396$	10.7478	0.540100
$397$	26.1095	1.31040	0.655199	−	0.755456i	$-0.272585\pi$
$397$	26.1095	1.31040	0.655199	+	0.755456i	$0.272585\pi$
$398$	39.5475	1.98233
$399$	7.48220	0.374579
$400$	−0.267877	−0.0133938
$401$	35.5709	1.77633	0.888164	−	0.459527i	$-0.151981\pi$
$401$	35.5709	1.77633	0.888164	+	0.459527i	$0.151981\pi$
$402$	−29.2994	−1.46132
$403$	5.73893	0.285877
$404$	−12.3550	−0.614686
$405$	1.63510	0.0812490
$406$	−15.3592	−0.762264
$407$	14.3259	0.710109
$408$	−7.94146	−0.393161
$409$	5.34481	0.264284	0.132142	−	0.991231i	$-0.457815\pi$
$409$	5.34481	0.264284	0.132142	+	0.991231i	$0.457815\pi$
$410$	12.6271	0.623609
$411$	6.85613	0.338188
$412$	−20.8572	−1.02756
$413$	−11.9543	−0.588231
$414$	13.0087	0.639345
$415$	−2.96434	−0.145514
$416$	15.4474	0.757372
$417$	−5.16447	−0.252905
$418$	38.7550	1.89557
$419$	−30.6124	−1.49551	−0.747756	−	0.663973i	$-0.768869\pi$
$419$	−30.6124	−1.49551	−0.747756	+	0.663973i	$0.768869\pi$
$420$	−7.78271	−0.379757
$421$	−11.3047	−0.550958	−0.275479	−	0.961307i	$-0.588836\pi$
$421$	−11.3047	−0.550958	−0.275479	+	0.961307i	$0.588836\pi$
$422$	6.55144	0.318919
$423$	7.53642	0.366433
$424$	13.1369	0.637985
$425$	6.38387	0.309663
$426$	−24.6758	−1.19555
$427$	5.42263	0.262420
$428$	−52.5350	−2.53937
$429$	−9.21477	−0.444893
$430$	−25.5247	−1.23091
$431$	−36.1048	−1.73911	−0.869554	−	0.493838i	$-0.835594\pi$
$431$	−36.1048	−1.73911	−0.869554	+	0.493838i	$0.835594\pi$
$432$	−0.115145	−0.00553991
$433$	−0.451585	−0.0217018	−0.0108509	−	0.999941i	$-0.503454\pi$
$433$	−0.451585	−0.0217018	−0.0108509	+	0.999941i	$0.503454\pi$
$434$	−6.86966	−0.329754
$435$	−7.50251	−0.359718
$436$	15.9681	0.764734
$437$	29.0775	1.39097
$438$	−26.0481	−1.24463
$439$	23.3480	1.11434	0.557169	−	0.830399i	$-0.311888\pi$
$439$	23.3480	1.11434	0.557169	+	0.830399i	$0.311888\pi$
$440$	−15.5932	−0.743375
$441$	−4.87043	−0.231925
$442$	17.6018	0.837234
$443$	36.6643	1.74197	0.870986	−	0.491308i	$-0.163481\pi$
$443$	36.6643	1.74197	0.870986	+	0.491308i	$0.163481\pi$
$444$	−14.1801	−0.672959
$445$	−25.2986	−1.19927
$446$	−1.35680	−0.0642464
$447$	−10.3874	−0.491308
$448$	−18.8271	−0.889495
$449$	−24.6052	−1.16119	−0.580596	−	0.814192i	$-0.697180\pi$
$449$	−24.6052	−1.16119	−0.580596	+	0.814192i	$0.697180\pi$
$450$	5.33645	0.251563
$451$	−11.0938	−0.522385
$452$	−51.2275	−2.40954
$453$	0.340609	0.0160032
$454$	−4.22416	−0.198250
$455$	6.67258	0.312815
$456$	−14.8385	−0.694878
$457$	28.4499	1.33083	0.665415	−	0.746474i	$-0.268255\pi$
$457$	28.4499	1.33083	0.665415	+	0.746474i	$0.268255\pi$
$458$	52.8856	2.47118
$459$	2.74406	0.128082
$460$	−30.2454	−1.41020
$461$	−33.1385	−1.54341	−0.771706	−	0.635979i	$-0.780597\pi$
$461$	−33.1385	−1.54341	−0.771706	+	0.635979i	$0.780597\pi$
$462$	11.0303	0.513178
$463$	−38.5357	−1.79091	−0.895454	−	0.445154i	$-0.853149\pi$
$463$	−38.5357	−1.79091	−0.895454	+	0.445154i	$0.853149\pi$
$464$	0.528330	0.0245271
$465$	−3.35563	−0.155613
$466$	−22.7579	−1.05424
$467$	41.5662	1.92346	0.961728	−	0.274005i	$-0.0883486\pi$
$467$	41.5662	1.92346	0.961728	+	0.274005i	$0.0883486\pi$
$468$	9.12101	0.421619
$469$	−18.6398	−0.860707
$470$	−28.2665	−1.30384
$471$	7.12876	0.328476
$472$	23.7074	1.09122
$473$	22.4252	1.03111
$474$	28.3353	1.30148
$475$	11.9282	0.547303
$476$	−13.0611	−0.598653
$477$	−4.53928	−0.207839
$478$	−36.5291	−1.67080
$479$	3.38386	0.154613	0.0773063	−	0.997007i	$-0.475368\pi$
$479$	3.38386	0.154613	0.0773063	+	0.997007i	$0.475368\pi$
$480$	−9.03230	−0.412266
$481$	12.1575	0.554333
$482$	45.0853	2.05358
$483$	8.27598	0.376570
$484$	−0.462061	−0.0210028
$485$	21.7993	0.989855
$486$	2.29383	0.104050
$487$	27.4399	1.24342	0.621711	−	0.783246i	$-0.286438\pi$
$487$	27.4399	1.24342	0.621711	+	0.783246i	$0.286438\pi$
$488$	−10.7540	−0.486813
$489$	−10.1690	−0.459860
$490$	18.2673	0.825234
$491$	−26.5336	−1.19745	−0.598723	−	0.800956i	$-0.704325\pi$
$491$	−26.5336	−1.19745	−0.598723	+	0.800956i	$0.704325\pi$
$492$	10.9809	0.495056
$493$	−12.5908	−0.567063
$494$	32.8888	1.47974
$495$	5.38799	0.242172
$496$	0.236305	0.0106104
$497$	−15.6984	−0.704168
$498$	−4.15858	−0.186350
$499$	34.4481	1.54211	0.771053	−	0.636770i	$-0.219730\pi$
$499$	34.4481	1.54211	0.771053	+	0.636770i	$0.219730\pi$
$500$	−39.0731	−1.74740
$501$	0.920485	0.0411242
$502$	0.0921085	0.00411100
$503$	0.229284	0.0102233	0.00511163	−	0.999987i	$-0.498373\pi$
$503$	0.229284	0.0102233	0.00511163	+	0.999987i	$0.498373\pi$
$504$	−4.22331	−0.188121
$505$	−6.19369	−0.275616
$506$	42.8664	1.90564
$507$	5.18002	0.230053
$508$	37.2039	1.65066
$509$	2.26307	0.100309	0.0501543	−	0.998741i	$-0.484029\pi$
$509$	2.26307	0.100309	0.0501543	+	0.998741i	$0.484029\pi$
$510$	−10.2920	−0.455738
$511$	−16.5714	−0.733078
$512$	1.30253	0.0575642
$513$	5.12724	0.226373
$514$	−35.3558	−1.55948
$515$	−10.4559	−0.460742
$516$	−22.1970	−0.977168
$517$	24.8340	1.09220
$518$	−14.5528	−0.639415
$519$	22.9025	1.00531
$520$	−13.2329	−0.580302
$521$	−29.6477	−1.29889	−0.649445	−	0.760408i	$-0.724999\pi$
$521$	−29.6477	−1.29889	−0.649445	+	0.760408i	$0.724999\pi$
$522$	−10.5250	−0.460668
$523$	0.195036	0.00852835	0.00426417	−	0.999991i	$-0.498643\pi$
$523$	0.195036	0.00852835	0.00426417	+	0.999991i	$0.498643\pi$
$524$	−24.5733	−1.07349
$525$	3.39497	0.148169
$526$	24.1302	1.05213
$527$	−5.63147	−0.245311
$528$	−0.379425	−0.0165124
$529$	9.16234	0.398362
$530$	17.0253	0.739530
$531$	−8.19177	−0.355492
$532$	−24.4045	−1.05807
$533$	−9.41456	−0.407790
$534$	−35.4906	−1.53583
$535$	−26.3363	−1.13862
$536$	36.9661	1.59669
$537$	−5.41551	−0.233697
$538$	60.1961	2.59524
$539$	−16.0491	−0.691282
$540$	−5.33317	−0.229503
$541$	−19.7210	−0.847871	−0.423936	−	0.905692i	$-0.639352\pi$
$541$	−19.7210	−0.847871	−0.423936	+	0.905692i	$0.639352\pi$
$542$	1.38164	0.0593464
$543$	14.4873	0.621708
$544$	−15.1582	−0.649901
$545$	8.00496	0.342895
$546$	9.36074	0.400603
$547$	−15.3058	−0.654427	−0.327214	−	0.944950i	$-0.606110\pi$
$547$	−15.3058	−0.654427	−0.327214	+	0.944950i	$0.606110\pi$
$548$	−22.3624	−0.955276
$549$	3.71591	0.158591
$550$	17.5847	0.749812
$551$	−23.5258	−1.00223
$552$	−16.4127	−0.698572
$553$	18.0265	0.766564
$554$	−40.2031	−1.70807
$555$	−7.10863	−0.301745
$556$	16.8448	0.714378
$557$	−45.0946	−1.91072	−0.955359	−	0.295448i	$-0.904531\pi$
$557$	−45.0946	−1.91072	−0.955359	+	0.295448i	$0.904531\pi$
$558$	−4.70749	−0.199284
$559$	19.0308	0.804917
$560$	0.274749	0.0116102
$561$	9.04222	0.381763
$562$	−64.2004	−2.70813
$563$	−1.46010	−0.0615357	−0.0307679	−	0.999527i	$-0.509795\pi$
$563$	−1.46010	−0.0615357	−0.0307679	+	0.999527i	$0.509795\pi$
$564$	−24.5813	−1.03506
$565$	−25.6808	−1.08040
$566$	5.68073	0.238779
$567$	1.45930	0.0612850
$568$	31.1326	1.30630
$569$	39.3380	1.64913	0.824566	−	0.565765i	$-0.191419\pi$
$569$	39.3380	1.64913	0.824566	+	0.565765i	$0.191419\pi$
$570$	−19.2305	−0.805478
$571$	−40.0272	−1.67509	−0.837543	−	0.546371i	$-0.816009\pi$
$571$	−40.0272	−1.67509	−0.837543	+	0.546371i	$0.816009\pi$
$572$	30.0555	1.25668
$573$	−11.1032	−0.463841
$574$	11.2695	0.470379
$575$	13.1936	0.550213
$576$	−12.9014	−0.537558
$577$	34.9653	1.45563	0.727813	−	0.685776i	$-0.240537\pi$
$577$	34.9653	1.45563	0.727813	+	0.685776i	$0.240537\pi$
$578$	21.7229	0.903554
$579$	−14.6996	−0.610895
$580$	24.4707	1.01609
$581$	−2.64563	−0.109759
$582$	30.5815	1.26764
$583$	−14.9578	−0.619489
$584$	32.8641	1.35993
$585$	4.57244	0.189047
$586$	−10.1632	−0.419839
$587$	3.39366	0.140071	0.0700356	−	0.997544i	$-0.477689\pi$
$587$	3.39366	0.140071	0.0700356	+	0.997544i	$0.477689\pi$
$588$	15.8857	0.655117
$589$	−10.5223	−0.433565
$590$	30.7245	1.26491
$591$	−0.594591	−0.0244582
$592$	0.500593	0.0205743
$593$	−16.9102	−0.694419	−0.347209	−	0.937788i	$-0.612871\pi$
$593$	−16.9102	−0.694419	−0.347209	+	0.937788i	$0.612871\pi$
$594$	7.55864	0.310135
$595$	−6.54764	−0.268427
$596$	33.8803	1.38779
$597$	17.2408	0.705618
$598$	36.3780	1.48761
$599$	5.41345	0.221188	0.110594	−	0.993866i	$-0.464725\pi$
$599$	5.41345	0.221188	0.110594	+	0.993866i	$0.464725\pi$
$600$	−6.73283	−0.274867
$601$	−12.3660	−0.504418	−0.252209	−	0.967673i	$-0.581157\pi$
$601$	−12.3660	−0.504418	−0.252209	+	0.967673i	$0.581157\pi$
$602$	−22.7804	−0.928460
$603$	−12.7731	−0.520161
$604$	−1.11095	−0.0452040
$605$	−0.231636	−0.00941733
$606$	−8.68892	−0.352963
$607$	14.8036	0.600859	0.300429	−	0.953804i	$-0.402870\pi$
$607$	14.8036	0.600859	0.300429	+	0.953804i	$0.402870\pi$
$608$	−28.3228	−1.14864
$609$	−6.69587	−0.271330
$610$	−13.9371	−0.564296
$611$	21.0750	0.852604
$612$	−8.95021	−0.361791
$613$	−18.6909	−0.754920	−0.377460	−	0.926026i	$-0.623202\pi$
$613$	−18.6909	−0.754920	−0.377460	+	0.926026i	$0.623202\pi$
$614$	−4.36394	−0.176114
$615$	5.50481	0.221976
$616$	−13.9166	−0.560717
$617$	−12.5533	−0.505377	−0.252689	−	0.967548i	$-0.581315\pi$
$617$	−12.5533	−0.505377	−0.252689	+	0.967548i	$0.581315\pi$
$618$	−14.6682	−0.590042
$619$	17.9978	0.723392	0.361696	−	0.932296i	$-0.382198\pi$
$619$	17.9978	0.723392	0.361696	+	0.932296i	$0.382198\pi$
$620$	10.9449	0.439559
$621$	5.67118	0.227577
$622$	72.0058	2.88717
$623$	−22.5786	−0.904593
$624$	−0.321994	−0.0128901
$625$	−7.95554	−0.318222
$626$	−56.3780	−2.25332
$627$	16.8953	0.674733
$628$	−23.2517	−0.927842
$629$	−11.9298	−0.475673
$630$	−5.47334	−0.218063
$631$	−7.27906	−0.289775	−0.144887	−	0.989448i	$-0.546282\pi$
$631$	−7.27906	−0.289775	−0.144887	+	0.989448i	$0.546282\pi$
$632$	−35.7497	−1.42205
$633$	2.85611	0.113520
$634$	68.1554	2.70680
$635$	18.6506	0.740128
$636$	14.8056	0.587081
$637$	−13.6198	−0.539636
$638$	−34.6820	−1.37308
$639$	−10.7574	−0.425558
$640$	30.3241	1.19867
$641$	27.5486	1.08811	0.544053	−	0.839051i	$-0.316889\pi$
$641$	27.5486	1.08811	0.544053	+	0.839051i	$0.316889\pi$
$642$	−36.9463	−1.45815
$643$	35.2023	1.38824	0.694122	−	0.719857i	$-0.255793\pi$
$643$	35.2023	1.38824	0.694122	+	0.719857i	$0.255793\pi$
$644$	−26.9935	−1.06369
$645$	−11.1276	−0.438147
$646$	−32.2730	−1.26976
$647$	24.1134	0.947994	0.473997	−	0.880526i	$-0.342811\pi$
$647$	24.1134	0.947994	0.473997	+	0.880526i	$0.342811\pi$
$648$	−2.89406	−0.113689
$649$	−26.9935	−1.05959
$650$	14.9230	0.585327
$651$	−2.99484	−0.117377
$652$	33.1680	1.29896
$653$	−22.5651	−0.883042	−0.441521	−	0.897251i	$-0.645561\pi$
$653$	−22.5651	−0.883042	−0.441521	+	0.897251i	$0.645561\pi$
$654$	11.2299	0.439123
$655$	−12.3188	−0.481337
$656$	−0.387652	−0.0151352
$657$	−11.3557	−0.443029
$658$	−25.2274	−0.983466
$659$	11.6431	0.453549	0.226775	−	0.973947i	$-0.427182\pi$
$659$	11.6431	0.453549	0.226775	+	0.973947i	$0.427182\pi$
$660$	−17.5739	−0.684061
$661$	5.13205	0.199614	0.0998068	−	0.995007i	$-0.468178\pi$
$661$	5.13205	0.199614	0.0998068	+	0.995007i	$0.468178\pi$
$662$	−44.5981	−1.73336
$663$	7.67355	0.298016
$664$	5.24675	0.203613
$665$	−12.2342	−0.474421
$666$	−9.97246	−0.386425
$667$	−26.0217	−1.00756
$668$	−3.00232	−0.116163
$669$	−0.591499	−0.0228687
$670$	47.9075	1.85083
$671$	12.2446	0.472699
$672$	−8.06118	−0.310967
$673$	−40.6652	−1.56753	−0.783764	−	0.621059i	$-0.786703\pi$
$673$	−40.6652	−1.56753	−0.783764	+	0.621059i	$0.786703\pi$
$674$	3.31633	0.127740
$675$	2.32643	0.0895445
$676$	−16.8955	−0.649827
$677$	−6.20114	−0.238329	−0.119165	−	0.992875i	$-0.538022\pi$
$677$	−6.20114	−0.238329	−0.119165	+	0.992875i	$0.538022\pi$
$678$	−36.0268	−1.38360
$679$	19.4555	0.746634
$680$	12.9851	0.497957
$681$	−1.84153	−0.0705676
$682$	−15.5121	−0.593990
$683$	37.3989	1.43103	0.715515	−	0.698597i	$-0.246192\pi$
$683$	37.3989	1.43103	0.715515	+	0.698597i	$0.246192\pi$
$684$	−16.7234	−0.639434
$685$	−11.2105	−0.428331
$686$	39.7351	1.51709
$687$	23.0556	0.879624
$688$	0.783607	0.0298747
$689$	−12.6937	−0.483593
$690$	−21.2707	−0.809760
$691$	−31.1146	−1.18366	−0.591828	−	0.806064i	$-0.701594\pi$
$691$	−31.1146	−1.18366	−0.591828	+	0.806064i	$0.701594\pi$
$692$	−74.7003	−2.83968
$693$	4.80869	0.182667
$694$	41.1666	1.56266
$695$	8.44445	0.320316
$696$	13.2791	0.503343
$697$	9.23827	0.349924
$698$	−33.7420	−1.27715
$699$	−9.92134	−0.375259
$700$	−11.0733	−0.418530
$701$	17.3918	0.656878	0.328439	−	0.944525i	$-0.393478\pi$
$701$	17.3918	0.656878	0.328439	+	0.944525i	$0.393478\pi$
$702$	6.41453	0.242101
$703$	−22.2907	−0.840711
$704$	−42.5127	−1.60226
$705$	−12.3228	−0.464105
$706$	38.3300	1.44257
$707$	−5.52776	−0.207893
$708$	26.7188	1.00415
$709$	−19.5886	−0.735664	−0.367832	−	0.929892i	$-0.619900\pi$
$709$	−19.5886	−0.735664	−0.367832	+	0.929892i	$0.619900\pi$
$710$	40.3475	1.51421
$711$	12.3528	0.463267
$712$	44.7774	1.67810
$713$	−11.6386	−0.435870
$714$	−9.18546	−0.343757
$715$	15.0671	0.563478
$716$	17.6636	0.660120
$717$	−15.9249	−0.594727
$718$	3.70209	0.138161
$719$	17.1618	0.640029	0.320014	−	0.947413i	$-0.396312\pi$
$719$	17.1618	0.640029	0.320014	+	0.947413i	$0.396312\pi$
$720$	0.188274	0.00701655
$721$	−9.33171	−0.347531
$722$	−16.7189	−0.622212
$723$	19.6550	0.730977
$724$	−47.2527	−1.75613
$725$	−10.6746	−0.396445
$726$	−0.324954	−0.0120602
$727$	0.944382	0.0350252	0.0175126	−	0.999847i	$-0.494425\pi$
$727$	0.944382	0.0350252	0.0175126	+	0.999847i	$0.494425\pi$
$728$	−11.8101	−0.437713
$729$	1.00000	0.0370370
$730$	42.5914	1.57638
$731$	−18.6744	−0.690699
$732$	−12.1201	−0.447970
$733$	−18.0405	−0.666343	−0.333171	−	0.942866i	$-0.608119\pi$
$733$	−18.0405	−0.666343	−0.333171	+	0.942866i	$0.608119\pi$
$734$	−47.2851	−1.74532
$735$	7.96367	0.293744
$736$	−31.3276	−1.15475
$737$	−42.0899	−1.55040
$738$	7.72252	0.284270
$739$	14.5953	0.536895	0.268448	−	0.963294i	$-0.413489\pi$
$739$	14.5953	0.536895	0.268448	+	0.963294i	$0.413489\pi$
$740$	23.1860	0.852334
$741$	14.3379	0.526717
$742$	15.1948	0.557817
$743$	7.88536	0.289286	0.144643	−	0.989484i	$-0.453797\pi$
$743$	7.88536	0.289286	0.144643	+	0.989484i	$0.453797\pi$
$744$	5.93930	0.217745
$745$	16.9845	0.622264
$746$	−63.4867	−2.32441
$747$	−1.81294	−0.0663320
$748$	−29.4927	−1.07836
$749$	−23.5047	−0.858842
$750$	−27.4789	−1.00339
$751$	−31.5602	−1.15165	−0.575823	−	0.817574i	$-0.695318\pi$
$751$	−31.5602	−1.15165	−0.575823	+	0.817574i	$0.695318\pi$
$752$	0.867779	0.0316447
$753$	0.0401549	0.00146332
$754$	−29.4324	−1.07187
$755$	−0.556931	−0.0202688
$756$	−4.75976	−0.173111
$757$	8.87908	0.322716	0.161358	−	0.986896i	$-0.448413\pi$
$757$	8.87908	0.322716	0.161358	+	0.986896i	$0.448413\pi$
$758$	−28.3068	−1.02815
$759$	18.6877	0.678320
$760$	24.2625	0.880095
$761$	−40.5285	−1.46916	−0.734579	−	0.678523i	$-0.762620\pi$
$761$	−40.5285	−1.46916	−0.734579	+	0.678523i	$0.762620\pi$
$762$	26.1644	0.947835
$763$	7.14429	0.258641
$764$	36.2148	1.31021
$765$	−4.48682	−0.162221
$766$	−46.1316	−1.66680
$767$	−22.9076	−0.827147
$768$	16.7379	0.603976
$769$	15.4497	0.557132	0.278566	−	0.960417i	$-0.410141\pi$
$769$	15.4497	0.557132	0.278566	+	0.960417i	$0.410141\pi$
$770$	−18.0358	−0.649964
$771$	−15.4134	−0.555100
$772$	47.9452	1.72559
$773$	−14.1593	−0.509275	−0.254638	−	0.967037i	$-0.581956\pi$
$773$	−14.1593	−0.509275	−0.254638	+	0.967037i	$0.581956\pi$
$774$	−15.6105	−0.561107
$775$	−4.77440	−0.171501
$776$	−38.5837	−1.38507
$777$	−6.34433	−0.227602
$778$	34.5566	1.23891
$779$	17.2616	0.618461
$780$	−14.9138	−0.534000
$781$	−35.4479	−1.26843
$782$	−35.6968	−1.27651
$783$	−4.58840	−0.163976
$784$	−0.560805	−0.0200288
$785$	−11.6563	−0.416030
$786$	−17.2817	−0.616417
$787$	−25.7081	−0.916393	−0.458197	−	0.888851i	$-0.651504\pi$
$787$	−25.7081	−0.916393	−0.458197	+	0.888851i	$0.651504\pi$
$788$	1.93936	0.0690869
$789$	10.5196	0.374508
$790$	−46.3311	−1.64839
$791$	−22.9197	−0.814931
$792$	−9.53649	−0.338865
$793$	10.3912	0.369004
$794$	−59.8908	−2.12545
$795$	7.42219	0.263238
$796$	−56.2337	−1.99315
$797$	31.5798	1.11862	0.559308	−	0.828960i	$-0.311067\pi$
$797$	31.5798	1.11862	0.559308	+	0.828960i	$0.311067\pi$
$798$	−17.1629	−0.607561
$799$	−20.6804	−0.731619
$800$	−12.8512	−0.454358
$801$	−15.4722	−0.546683
$802$	−81.5938	−2.88118
$803$	−37.4194	−1.32050
$804$	41.6616	1.46929
$805$	−13.5321	−0.476943
$806$	−13.1641	−0.463687
$807$	26.2426	0.923783
$808$	10.9625	0.385661
$809$	1.33329	0.0468760	0.0234380	−	0.999725i	$-0.492539\pi$
$809$	1.33329	0.0468760	0.0234380	+	0.999725i	$0.492539\pi$
$810$	−3.75066	−0.131785
$811$	−35.8729	−1.25967	−0.629835	−	0.776729i	$-0.716877\pi$
$811$	−35.8729	−1.25967	−0.629835	+	0.776729i	$0.716877\pi$
$812$	21.8397	0.766423
$813$	0.602327	0.0211245
$814$	−32.8612	−1.15179
$815$	16.6274	0.582434
$816$	0.315964	0.0110610
$817$	−34.8930	−1.22075
$818$	−12.2601	−0.428665
$819$	4.08083	0.142596
$820$	−17.9549	−0.627012
$821$	−7.42635	−0.259181	−0.129591	−	0.991568i	$-0.541366\pi$
$821$	−7.42635	−0.259181	−0.129591	+	0.991568i	$0.541366\pi$
$822$	−15.7268	−0.548536
$823$	4.06016	0.141528	0.0707641	−	0.997493i	$-0.477456\pi$
$823$	4.06016	0.141528	0.0707641	+	0.997493i	$0.477456\pi$
$824$	18.5064	0.644702
$825$	7.66606	0.266898
$826$	27.4211	0.954102
$827$	−27.0448	−0.940440	−0.470220	−	0.882549i	$-0.655826\pi$
$827$	−27.0448	−0.940440	−0.470220	+	0.882549i	$0.655826\pi$
$828$	−18.4975	−0.642833
$829$	−19.8926	−0.690897	−0.345448	−	0.938438i	$-0.612273\pi$
$829$	−19.8926	−0.690897	−0.345448	+	0.938438i	$0.612273\pi$
$830$	6.79971	0.236021
$831$	−17.5266	−0.607992
$832$	−36.0778	−1.25077
$833$	13.3648	0.463062
$834$	11.8464	0.410208
$835$	−1.50509	−0.0520858
$836$	−55.1068	−1.90591
$837$	−2.05224	−0.0709358
$838$	70.2197	2.42570
$839$	−38.0688	−1.31428	−0.657141	−	0.753767i	$-0.728235\pi$
$839$	−38.0688	−1.31428	−0.657141	+	0.753767i	$0.728235\pi$
$840$	6.90555	0.238264
$841$	−7.94659	−0.274020
$842$	25.9311	0.893645
$843$	−27.9883	−0.963967
$844$	−9.31569	−0.320659
$845$	−8.46987	−0.291372
$846$	−17.2873	−0.594349
$847$	−0.206731	−0.00710336
$848$	−0.522674	−0.0179487
$849$	2.47652	0.0849940
$850$	−14.6435	−0.502269
$851$	−24.6555	−0.845181
$852$	35.0872	1.20207
$853$	−24.6652	−0.844521	−0.422261	−	0.906474i	$-0.638763\pi$
$853$	−24.6652	−0.844521	−0.422261	+	0.906474i	$0.638763\pi$
$854$	−12.4386	−0.425641
$855$	−8.38358	−0.286712
$856$	46.6139	1.59323
$857$	51.1871	1.74852	0.874259	−	0.485461i	$-0.161348\pi$
$857$	51.1871	1.74852	0.874259	+	0.485461i	$0.161348\pi$
$858$	21.1371	0.721610
$859$	14.9035	0.508501	0.254251	−	0.967138i	$-0.418171\pi$
$859$	14.9035	0.508501	0.254251	+	0.967138i	$0.418171\pi$
$860$	36.2944	1.23763
$861$	4.91295	0.167433
$862$	82.8184	2.82081
$863$	28.7458	0.978519	0.489260	−	0.872138i	$-0.337267\pi$
$863$	28.7458	0.978519	0.489260	+	0.872138i	$0.337267\pi$
$864$	−5.52399	−0.187930
$865$	−37.4479	−1.27327
$866$	1.03586	0.0352000
$867$	9.47014	0.321623
$868$	9.76817	0.331553
$869$	40.7050	1.38082
$870$	17.2095	0.583457
$871$	−35.7190	−1.21029
$872$	−14.1684	−0.479802
$873$	13.3321	0.451222
$874$	−66.6990	−2.25613
$875$	−17.4817	−0.590989
$876$	37.0386	1.25142
$877$	5.34954	0.180641	0.0903206	−	0.995913i	$-0.471211\pi$
$877$	5.34954	0.180641	0.0903206	+	0.995913i	$0.471211\pi$
$878$	−53.5563	−1.80744
$879$	−4.43068	−0.149443
$880$	0.620400	0.0209137
$881$	43.9802	1.48173	0.740866	−	0.671653i	$-0.234415\pi$
$881$	43.9802	1.48173	0.740866	+	0.671653i	$0.234415\pi$
$882$	11.1720	0.376180
$883$	8.50876	0.286343	0.143171	−	0.989698i	$-0.454270\pi$
$883$	8.50876	0.286343	0.143171	+	0.989698i	$0.454270\pi$
$884$	−25.0286	−0.841802
$885$	13.3944	0.450248
$886$	−84.1017	−2.82545
$887$	−0.192473	−0.00646260	−0.00323130	−	0.999995i	$-0.501029\pi$
$887$	−0.192473	−0.00646260	−0.00323130	+	0.999995i	$0.501029\pi$
$888$	12.5819	0.422222
$889$	16.6454	0.558268
$890$	58.0309	1.94520
$891$	3.29520	0.110393
$892$	1.92927	0.0645969
$893$	−38.6410	−1.29307
$894$	23.8270	0.796894
$895$	8.85493	0.295988
$896$	27.0638	0.904137
$897$	15.8590	0.529518
$898$	56.4403	1.88344
$899$	9.41650	0.314058
$900$	−7.58805	−0.252935
$901$	12.4560	0.414971
$902$	25.4472	0.847300
$903$	−9.93115	−0.330488
$904$	45.4538	1.51177
$905$	−23.6882	−0.787422
$906$	−0.781300	−0.0259569
$907$	25.3240	0.840869	0.420434	−	0.907323i	$-0.361878\pi$
$907$	25.3240	0.840869	0.420434	+	0.907323i	$0.361878\pi$
$908$	6.00646	0.199332
$909$	−3.78795	−0.125638
$910$	−15.3058	−0.507382
$911$	−18.5250	−0.613760	−0.306880	−	0.951748i	$-0.599285\pi$
$911$	−18.5250	−0.613760	−0.306880	+	0.951748i	$0.599285\pi$
$912$	0.590375	0.0195493
$913$	−5.97399	−0.197710
$914$	−65.2593	−2.15858
$915$	−6.07589	−0.200863
$916$	−75.1996	−2.48466
$917$	−10.9944	−0.363066
$918$	−6.29441	−0.207747
$919$	−4.19021	−0.138222	−0.0691111	−	0.997609i	$-0.522016\pi$
$919$	−4.19021	−0.138222	−0.0691111	+	0.997609i	$0.522016\pi$
$920$	26.8365	0.884774
$921$	−1.90247	−0.0626884
$922$	76.0141	2.50339
$923$	−30.0824	−0.990173
$924$	−15.6844	−0.515978
$925$	−10.1142	−0.332553
$926$	88.3945	2.90483
$927$	−6.39463	−0.210027
$928$	25.3463	0.832032
$929$	56.0010	1.83733	0.918666	−	0.395036i	$-0.129268\pi$
$929$	56.0010	1.83733	0.918666	+	0.395036i	$0.129268\pi$
$930$	7.69725	0.252403
$931$	24.9719	0.818421
$932$	32.3601	1.05999
$933$	31.3911	1.02770
$934$	−95.3460	−3.11982
$935$	−14.7850	−0.483520
$936$	−8.09301	−0.264528
$937$	−45.2635	−1.47869	−0.739347	−	0.673324i	$-0.764866\pi$
$937$	−45.2635	−1.47869	−0.739347	+	0.673324i	$0.764866\pi$
$938$	42.7566	1.39605
$939$	−24.5781	−0.802076
$940$	40.1930	1.31095
$941$	5.84905	0.190674	0.0953368	−	0.995445i	$-0.469607\pi$
$941$	5.84905	0.190674	0.0953368	+	0.995445i	$0.469607\pi$
$942$	−16.3522	−0.532783
$943$	19.0929	0.621749
$944$	−0.943239	−0.0306998
$945$	−2.38611	−0.0776203
$946$	−51.4396	−1.67245
$947$	−5.69233	−0.184976	−0.0924879	−	0.995714i	$-0.529482\pi$
$947$	−5.69233	−0.184976	−0.0924879	+	0.995714i	$0.529482\pi$
$948$	−40.2908	−1.30858
$949$	−31.7554	−1.03082
$950$	−27.3613	−0.887717
$951$	29.7125	0.963492
$952$	11.5890	0.375602
$953$	23.2962	0.754638	0.377319	−	0.926083i	$-0.376846\pi$
$953$	23.2962	0.754638	0.377319	+	0.926083i	$0.376846\pi$
$954$	10.4123	0.337112
$955$	18.1548	0.587476
$956$	51.9418	1.67992
$957$	−15.1197	−0.488750
$958$	−7.76202	−0.250779
$959$	−10.0052	−0.323084
$960$	21.0951	0.680843
$961$	−26.7883	−0.864139
$962$	−27.8872	−0.899120
$963$	−16.1068	−0.519034
$964$	−64.1081	−2.06478
$965$	24.0354	0.773727
$966$	−18.9837	−0.610791
$967$	49.6210	1.59570	0.797852	−	0.602854i	$-0.205970\pi$
$967$	49.6210	1.59570	0.797852	+	0.602854i	$0.205970\pi$
$968$	0.409984	0.0131774
$969$	−14.0695	−0.451976
$970$	−50.0040	−1.60553
$971$	26.2452	0.842248	0.421124	−	0.907003i	$-0.361636\pi$
$971$	26.2452	0.842248	0.421124	+	0.907003i	$0.361636\pi$
$972$	−3.26167	−0.104618
$973$	7.53653	0.241610
$974$	−62.9426	−2.01681
$975$	6.50569	0.208349
$976$	0.427867	0.0136957
$977$	−40.8040	−1.30544	−0.652718	−	0.757601i	$-0.726371\pi$
$977$	−40.8040	−1.30544	−0.652718	+	0.757601i	$0.726371\pi$
$978$	23.3261	0.745886
$979$	−50.9839	−1.62945
$980$	−25.9749	−0.829736
$981$	4.89569	0.156307
$982$	60.8637	1.94224
$983$	−15.2711	−0.487072	−0.243536	−	0.969892i	$-0.578307\pi$
$983$	−15.2711	−0.487072	−0.243536	+	0.969892i	$0.578307\pi$
$984$	−9.74326	−0.310604
$985$	0.972219	0.0309775
$986$	28.8813	0.919767
$987$	−10.9979	−0.350068
$988$	−46.7656	−1.48781
$989$	−38.5947	−1.22724
$990$	−12.3592	−0.392800
$991$	−10.9621	−0.348223	−0.174112	−	0.984726i	$-0.555705\pi$
$991$	−10.9621	−0.348223	−0.174112	+	0.984726i	$0.555705\pi$
$992$	11.3366	0.359936
$993$	−19.4426	−0.616993
$994$	36.0094	1.14215
$995$	−28.1905	−0.893698
$996$	5.91321	0.187367
$997$	16.2787	0.515551	0.257775	−	0.966205i	$-0.417011\pi$
$997$	16.2787	0.515551	0.257775	+	0.966205i	$0.417011\pi$
$998$	−79.0181	−2.50127
$999$	−4.34751	−0.137549

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8031.2.a.b.1.14	✓	102

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8031.2.a.b.1.14	✓	102	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:	\( N \)	\(=\)	\( 8031 = 3 \cdot 2677 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8031.a (trivial)

\(f(q)\)	\(=\)	\(q-2.29383 q^{2} -1.00000 q^{3} +3.26167 q^{4} +1.63510 q^{5} +2.29383 q^{6} +1.45930 q^{7} -2.89406 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-2.29383 q^{2} -1.00000 q^{3} +3.26167 q^{4} +1.63510 q^{5} +2.29383 q^{6} +1.45930 q^{7} -2.89406 q^{8} +1.00000 q^{9} -3.75066 q^{10} +3.29520 q^{11} -3.26167 q^{12} +2.79642 q^{13} -3.34740 q^{14} -1.63510 q^{15} +0.115145 q^{16} -2.74406 q^{17} -2.29383 q^{18} -5.12724 q^{19} +5.33317 q^{20} -1.45930 q^{21} -7.55864 q^{22} -5.67118 q^{23} +2.89406 q^{24} -2.32643 q^{25} -6.41453 q^{26} -1.00000 q^{27} +4.75976 q^{28} +4.58840 q^{29} +3.75066 q^{30} +2.05224 q^{31} +5.52399 q^{32} -3.29520 q^{33} +6.29441 q^{34} +2.38611 q^{35} +3.26167 q^{36} +4.34751 q^{37} +11.7610 q^{38} -2.79642 q^{39} -4.73208 q^{40} -3.36664 q^{41} +3.34740 q^{42} +6.80541 q^{43} +10.7478 q^{44} +1.63510 q^{45} +13.0087 q^{46} +7.53642 q^{47} -0.115145 q^{48} -4.87043 q^{49} +5.33645 q^{50} +2.74406 q^{51} +9.12101 q^{52} -4.53928 q^{53} +2.29383 q^{54} +5.38799 q^{55} -4.22331 q^{56} +5.12724 q^{57} -10.5250 q^{58} -8.19177 q^{59} -5.33317 q^{60} +3.71591 q^{61} -4.70749 q^{62} +1.45930 q^{63} -12.9014 q^{64} +4.57244 q^{65} +7.55864 q^{66} -12.7731 q^{67} -8.95021 q^{68} +5.67118 q^{69} -5.47334 q^{70} -10.7574 q^{71} -2.89406 q^{72} -11.3557 q^{73} -9.97246 q^{74} +2.32643 q^{75} -16.7234 q^{76} +4.80869 q^{77} +6.41453 q^{78} +12.3528 q^{79} +0.188274 q^{80} +1.00000 q^{81} +7.72252 q^{82} -1.81294 q^{83} -4.75976 q^{84} -4.48682 q^{85} -15.6105 q^{86} -4.58840 q^{87} -9.53649 q^{88} -15.4722 q^{89} -3.75066 q^{90} +4.08083 q^{91} -18.4975 q^{92} -2.05224 q^{93} -17.2873 q^{94} -8.38358 q^{95} -5.52399 q^{96} +13.3321 q^{97} +11.1720 q^{98} +3.29520 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 102 q - 6 q^{2} - 102 q^{3} + 96 q^{4} - 20 q^{5} + 6 q^{6} + 12 q^{7} - 21 q^{8} + 102 q^{9}+O(q^{10}) \) 102 * q - 6 * q^2 - 102 * q^3 + 96 * q^4 - 20 * q^5 + 6 * q^6 + 12 * q^7 - 21 * q^8 + 102 * q^9	\( 102 q - 6 q^{2} - 102 q^{3} + 96 q^{4} - 20 q^{5} + 6 q^{6} + 12 q^{7} - 21 q^{8} + 102 q^{9} - 16 q^{10} - 28 q^{11} - 96 q^{12} - 2 q^{13} - 41 q^{14} + 20 q^{15} + 88 q^{16} - 77 q^{17} - 6 q^{18} + 10 q^{19} - 50 q^{20} - 12 q^{21} + 24 q^{22} - 29 q^{23} + 21 q^{24} + 74 q^{25} - 45 q^{26} - 102 q^{27} + 19 q^{28} - 68 q^{29} + 16 q^{30} - 29 q^{31} - 48 q^{32} + 28 q^{33} - 19 q^{34} - 49 q^{35} + 96 q^{36} + 4 q^{37} - 44 q^{38} + 2 q^{39} - 41 q^{40} - 122 q^{41} + 41 q^{42} + 85 q^{43} - 86 q^{44} - 20 q^{45} - 28 q^{46} - 39 q^{47} - 88 q^{48} + 24 q^{49} - 37 q^{50} + 77 q^{51} + 8 q^{52} - 37 q^{53} + 6 q^{54} - 13 q^{55} - 130 q^{56} - 10 q^{57} + 17 q^{58} - 58 q^{59} + 50 q^{60} - 114 q^{61} - 64 q^{62} + 12 q^{63} + 47 q^{64} - 92 q^{65} - 24 q^{66} + 121 q^{67} - 138 q^{68} + 29 q^{69} - 2 q^{70} - 67 q^{71} - 21 q^{72} - 72 q^{73} - 111 q^{74} - 74 q^{75} - 17 q^{76} - 57 q^{77} + 45 q^{78} - 24 q^{79} - 97 q^{80} + 102 q^{81} - q^{82} - 78 q^{83} - 19 q^{84} - 24 q^{85} - 80 q^{86} + 68 q^{87} + 54 q^{88} - 176 q^{89} - 16 q^{90} - 3 q^{91} - 82 q^{92} + 29 q^{93} - 41 q^{94} - 90 q^{95} + 48 q^{96} - 77 q^{97} - 48 q^{98} - 28 q^{99}+O(q^{100}) \) 102 * q - 6 * q^2 - 102 * q^3 + 96 * q^4 - 20 * q^5 + 6 * q^6 + 12 * q^7 - 21 * q^8 + 102 * q^9 - 16 * q^10 - 28 * q^11 - 96 * q^12 - 2 * q^13 - 41 * q^14 + 20 * q^15 + 88 * q^16 - 77 * q^17 - 6 * q^18 + 10 * q^19 - 50 * q^20 - 12 * q^21 + 24 * q^22 - 29 * q^23 + 21 * q^24 + 74 * q^25 - 45 * q^26 - 102 * q^27 + 19 * q^28 - 68 * q^29 + 16 * q^30 - 29 * q^31 - 48 * q^32 + 28 * q^33 - 19 * q^34 - 49 * q^35 + 96 * q^36 + 4 * q^37 - 44 * q^38 + 2 * q^39 - 41 * q^40 - 122 * q^41 + 41 * q^42 + 85 * q^43 - 86 * q^44 - 20 * q^45 - 28 * q^46 - 39 * q^47 - 88 * q^48 + 24 * q^49 - 37 * q^50 + 77 * q^51 + 8 * q^52 - 37 * q^53 + 6 * q^54 - 13 * q^55 - 130 * q^56 - 10 * q^57 + 17 * q^58 - 58 * q^59 + 50 * q^60 - 114 * q^61 - 64 * q^62 + 12 * q^63 + 47 * q^64 - 92 * q^65 - 24 * q^66 + 121 * q^67 - 138 * q^68 + 29 * q^69 - 2 * q^70 - 67 * q^71 - 21 * q^72 - 72 * q^73 - 111 * q^74 - 74 * q^75 - 17 * q^76 - 57 * q^77 + 45 * q^78 - 24 * q^79 - 97 * q^80 + 102 * q^81 - q^82 - 78 * q^83 - 19 * q^84 - 24 * q^85 - 80 * q^86 + 68 * q^87 + 54 * q^88 - 176 * q^89 - 16 * q^90 - 3 * q^91 - 82 * q^92 + 29 * q^93 - 41 * q^94 - 90 * q^95 + 48 * q^96 - 77 * q^97 - 48 * q^98 - 28 * q^99

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