LMFDB - Embedded newform 8027.2.a.c.1.18

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8027,2,Mod(1,8027)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8027, 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("8027.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8027 = 23 \cdot 349 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8027.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:	$64.0959177025$
Analytic rank:	$1$
Dimension:	$143$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.18
Character	$\chi$	$=$	8027.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.31697 q^{2} -3.13483 q^{3} +3.36836 q^{4} -3.69960 q^{5} +7.26332 q^{6} +1.63548 q^{7} -3.17044 q^{8} +6.82718 q^{9} +O(q^{10})$	\(q-2.31697 q^{2} -3.13483 q^{3} +3.36836 q^{4} -3.69960 q^{5} +7.26332 q^{6} +1.63548 q^{7} -3.17044 q^{8} +6.82718 q^{9} +8.57187 q^{10} +1.46100 q^{11} -10.5592 q^{12} -1.63554 q^{13} -3.78937 q^{14} +11.5976 q^{15} +0.609109 q^{16} +6.37807 q^{17} -15.8184 q^{18} -2.34717 q^{19} -12.4616 q^{20} -5.12697 q^{21} -3.38509 q^{22} +1.00000 q^{23} +9.93881 q^{24} +8.68705 q^{25} +3.78951 q^{26} -11.9976 q^{27} +5.50889 q^{28} +6.92609 q^{29} -26.8714 q^{30} +9.09327 q^{31} +4.92959 q^{32} -4.57999 q^{33} -14.7778 q^{34} -6.05064 q^{35} +22.9964 q^{36} -2.60267 q^{37} +5.43832 q^{38} +5.12716 q^{39} +11.7294 q^{40} +0.194612 q^{41} +11.8790 q^{42} -8.00007 q^{43} +4.92116 q^{44} -25.2579 q^{45} -2.31697 q^{46} +10.8974 q^{47} -1.90946 q^{48} -4.32519 q^{49} -20.1277 q^{50} -19.9942 q^{51} -5.50909 q^{52} -6.06919 q^{53} +27.7981 q^{54} -5.40511 q^{55} -5.18521 q^{56} +7.35799 q^{57} -16.0476 q^{58} -13.9975 q^{59} +39.0650 q^{60} +11.5625 q^{61} -21.0688 q^{62} +11.1658 q^{63} -12.6399 q^{64} +6.05086 q^{65} +10.6117 q^{66} -6.26033 q^{67} +21.4836 q^{68} -3.13483 q^{69} +14.0192 q^{70} +8.59773 q^{71} -21.6452 q^{72} -9.08281 q^{73} +6.03031 q^{74} -27.2325 q^{75} -7.90610 q^{76} +2.38944 q^{77} -11.8795 q^{78} +1.54628 q^{79} -2.25346 q^{80} +17.1289 q^{81} -0.450910 q^{82} +0.631008 q^{83} -17.2695 q^{84} -23.5963 q^{85} +18.5359 q^{86} -21.7121 q^{87} -4.63201 q^{88} -2.16226 q^{89} +58.5217 q^{90} -2.67491 q^{91} +3.36836 q^{92} -28.5059 q^{93} -25.2490 q^{94} +8.68359 q^{95} -15.4535 q^{96} -14.6512 q^{97} +10.0213 q^{98} +9.97450 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 143 q - 17 q^{2} - 17 q^{3} + 121 q^{4} - 22 q^{5} - 11 q^{6} - 33 q^{7} - 45 q^{8} + 104 q^{9}+O(q^{10}) $ 143 * q - 17 * q^2 - 17 * q^3 + 121 * q^4 - 22 * q^5 - 11 * q^6 - 33 * q^7 - 45 * q^8 + 104 * q^9	\( 143 q - 17 q^{2} - 17 q^{3} + 121 q^{4} - 22 q^{5} - 11 q^{6} - 33 q^{7} - 45 q^{8} + 104 q^{9} - 22 q^{10} - 14 q^{11} - 36 q^{12} - 87 q^{13} - 18 q^{14} - 19 q^{15} + 81 q^{16} - 14 q^{17} - 60 q^{18} - 18 q^{19} - 25 q^{20} - 26 q^{21} - 62 q^{22} + 143 q^{23} - 21 q^{24} + 67 q^{25} - 5 q^{26} - 47 q^{27} - 76 q^{28} - 54 q^{29} - 22 q^{30} - 62 q^{31} - 117 q^{32} - 59 q^{33} - 35 q^{34} - 52 q^{35} + 52 q^{36} - 190 q^{37} - 19 q^{38} - 43 q^{39} - 41 q^{40} - 50 q^{41} + 8 q^{42} - 50 q^{43} - 18 q^{44} - 75 q^{45} - 17 q^{46} - 63 q^{47} - 35 q^{48} + 74 q^{49} - 53 q^{50} - 33 q^{51} - 124 q^{52} - 100 q^{53} - 46 q^{54} - 61 q^{55} - 3 q^{56} - 80 q^{57} - 112 q^{58} - 109 q^{59} - 55 q^{60} - 76 q^{61} - 6 q^{62} - 93 q^{63} + 57 q^{64} - 17 q^{65} + 50 q^{66} - 120 q^{67} + 26 q^{68} - 17 q^{69} - 109 q^{71} - 153 q^{72} - 94 q^{73} + 35 q^{74} - 105 q^{75} - 16 q^{76} - 52 q^{77} - 59 q^{78} - 29 q^{79} - 30 q^{80} + 39 q^{81} - 65 q^{82} + 8 q^{83} + 11 q^{84} - 155 q^{85} - 15 q^{86} - 25 q^{87} - 139 q^{88} + 6 q^{89} + 82 q^{90} - 34 q^{91} + 121 q^{92} - 151 q^{93} - 3 q^{94} - 70 q^{95} - 23 q^{96} - 203 q^{97} - 18 q^{98} - 49 q^{99}+O(q^{100}) \) 143 * q - 17 * q^2 - 17 * q^3 + 121 * q^4 - 22 * q^5 - 11 * q^6 - 33 * q^7 - 45 * q^8 + 104 * q^9 - 22 * q^10 - 14 * q^11 - 36 * q^12 - 87 * q^13 - 18 * q^14 - 19 * q^15 + 81 * q^16 - 14 * q^17 - 60 * q^18 - 18 * q^19 - 25 * q^20 - 26 * q^21 - 62 * q^22 + 143 * q^23 - 21 * q^24 + 67 * q^25 - 5 * q^26 - 47 * q^27 - 76 * q^28 - 54 * q^29 - 22 * q^30 - 62 * q^31 - 117 * q^32 - 59 * q^33 - 35 * q^34 - 52 * q^35 + 52 * q^36 - 190 * q^37 - 19 * q^38 - 43 * q^39 - 41 * q^40 - 50 * q^41 + 8 * q^42 - 50 * q^43 - 18 * q^44 - 75 * q^45 - 17 * q^46 - 63 * q^47 - 35 * q^48 + 74 * q^49 - 53 * q^50 - 33 * q^51 - 124 * q^52 - 100 * q^53 - 46 * q^54 - 61 * q^55 - 3 * q^56 - 80 * q^57 - 112 * q^58 - 109 * q^59 - 55 * q^60 - 76 * q^61 - 6 * q^62 - 93 * q^63 + 57 * q^64 - 17 * q^65 + 50 * q^66 - 120 * q^67 + 26 * q^68 - 17 * q^69 - 109 * q^71 - 153 * q^72 - 94 * q^73 + 35 * q^74 - 105 * q^75 - 16 * q^76 - 52 * q^77 - 59 * q^78 - 29 * q^79 - 30 * q^80 + 39 * q^81 - 65 * q^82 + 8 * q^83 + 11 * q^84 - 155 * q^85 - 15 * q^86 - 25 * q^87 - 139 * q^88 + 6 * q^89 + 82 * q^90 - 34 * q^91 + 121 * q^92 - 151 * q^93 - 3 * q^94 - 70 * q^95 - 23 * q^96 - 203 * q^97 - 18 * q^98 - 49 * 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 $

$2$	−2.31697	−1.63835	−0.819173	−	0.573546i	$-0.805567\pi$
$2$	−2.31697	−1.63835	−0.819173	+	0.573546i	$0.805567\pi$
$3$	−3.13483	−1.80990	−0.904949	−	0.425521i	$-0.860091\pi$
$3$	−3.13483	−1.80990	−0.904949	+	0.425521i	$0.860091\pi$
$4$	3.36836	1.68418
$5$	−3.69960	−1.65451	−0.827256	−	0.561825i	$-0.810099\pi$
$5$	−3.69960	−1.65451	−0.827256	+	0.561825i	$0.810099\pi$
$6$	7.26332	2.96524
$7$	1.63548	0.618155	0.309077	−	0.951037i	$-0.399980\pi$
$7$	1.63548	0.618155	0.309077	+	0.951037i	$0.399980\pi$
$8$	−3.17044	−1.12092
$9$	6.82718	2.27573
$10$	8.57187	2.71066
$11$	1.46100	0.440507	0.220254	−	0.975443i	$-0.429311\pi$
$11$	1.46100	0.440507	0.220254	+	0.975443i	$0.429311\pi$
$12$	−10.5592	−3.04819
$13$	−1.63554	−0.453618	−0.226809	−	0.973939i	$-0.572829\pi$
$13$	−1.63554	−0.453618	−0.226809	+	0.973939i	$0.572829\pi$
$14$	−3.78937	−1.01275
$15$	11.5976	2.99450
$16$	0.609109	0.152277
$17$	6.37807	1.54691	0.773454	−	0.633852i	$-0.218527\pi$
$17$	6.37807	1.54691	0.773454	+	0.633852i	$0.218527\pi$
$18$	−15.8184	−3.72843
$19$	−2.34717	−0.538478	−0.269239	−	0.963073i	$-0.586772\pi$
$19$	−2.34717	−0.538478	−0.269239	+	0.963073i	$0.586772\pi$
$20$	−12.4616	−2.78649
$21$	−5.12697	−1.11880
$22$	−3.38509	−0.721704
$23$	1.00000	0.208514
$23$	1.00000	0.208514
$24$	9.93881	2.02875
$25$	8.68705	1.73741
$26$	3.78951	0.743184
$27$	−11.9976	−2.30894
$28$	5.50889	1.04108
$29$	6.92609	1.28614	0.643071	−	0.765806i	$-0.277660\pi$
$29$	6.92609	1.28614	0.643071	+	0.765806i	$0.277660\pi$
$30$	−26.8714	−4.90602
$31$	9.09327	1.63320	0.816599	−	0.577205i	$-0.195857\pi$
$31$	9.09327	1.63320	0.816599	+	0.577205i	$0.195857\pi$
$32$	4.92959	0.871437
$33$	−4.57999	−0.797273
$34$	−14.7778	−2.53437
$35$	−6.05064	−1.02274
$36$	22.9964	3.83273
$37$	−2.60267	−0.427876	−0.213938	−	0.976847i	$-0.568629\pi$
$37$	−2.60267	−0.427876	−0.213938	+	0.976847i	$0.568629\pi$
$38$	5.43832	0.882213
$39$	5.12716	0.821002
$40$	11.7294	1.85458
$41$	0.194612	0.0303932	0.0151966	−	0.999885i	$-0.495163\pi$
$41$	0.194612	0.0303932	0.0151966	+	0.999885i	$0.495163\pi$
$42$	11.8790	1.83298
$43$	−8.00007	−1.22000	−0.610000	−	0.792402i	$-0.708830\pi$
$43$	−8.00007	−1.22000	−0.610000	+	0.792402i	$0.708830\pi$
$44$	4.92116	0.741893
$45$	−25.2579	−3.76522
$46$	−2.31697	−0.341619
$47$	10.8974	1.58955	0.794775	−	0.606904i	$-0.207589\pi$
$47$	10.8974	1.58955	0.794775	+	0.606904i	$0.207589\pi$
$48$	−1.90946	−0.275606
$49$	−4.32519	−0.617885
$50$	−20.1277	−2.84648
$51$	−19.9942	−2.79975
$52$	−5.50909	−0.763974
$53$	−6.06919	−0.833668	−0.416834	−	0.908983i	$-0.636860\pi$
$53$	−6.06919	−0.833668	−0.416834	+	0.908983i	$0.636860\pi$
$54$	27.7981	3.78284
$55$	−5.40511	−0.728825
$56$	−5.18521	−0.692902
$57$	7.35799	0.974589
$58$	−16.0476	−2.10715
$59$	−13.9975	−1.82232	−0.911161	−	0.412049i	$-0.864813\pi$
$59$	−13.9975	−1.82232	−0.911161	+	0.412049i	$0.864813\pi$
$60$	39.0650	5.04327
$61$	11.5625	1.48042	0.740211	−	0.672375i	$-0.234726\pi$
$61$	11.5625	1.48042	0.740211	+	0.672375i	$0.234726\pi$
$62$	−21.0688	−2.67574
$63$	11.1658	1.40675
$64$	−12.6399	−1.57999
$65$	6.05086	0.750517
$66$	10.6117	1.30621
$67$	−6.26033	−0.764821	−0.382411	−	0.923992i	$-0.624906\pi$
$67$	−6.26033	−0.764821	−0.382411	+	0.923992i	$0.624906\pi$
$68$	21.4836	2.60527
$69$	−3.13483	−0.377390
$70$	14.0192	1.67561
$71$	8.59773	1.02036	0.510181	−	0.860067i	$-0.329578\pi$
$71$	8.59773	1.02036	0.510181	+	0.860067i	$0.329578\pi$
$72$	−21.6452	−2.55091
$73$	−9.08281	−1.06306	−0.531531	−	0.847039i	$-0.678383\pi$
$73$	−9.08281	−1.06306	−0.531531	+	0.847039i	$0.678383\pi$
$74$	6.03031	0.701009
$75$	−27.2325	−3.14454
$76$	−7.90610	−0.906892
$77$	2.38944	0.272302
$78$	−11.8795	−1.34509
$79$	1.54628	0.173970	0.0869849	−	0.996210i	$-0.472277\pi$
$79$	1.54628	0.173970	0.0869849	+	0.996210i	$0.472277\pi$
$80$	−2.25346	−0.251945
$81$	17.1289	1.90321
$82$	−0.450910	−0.0497947
$83$	0.631008	0.0692621	0.0346310	−	0.999400i	$-0.488974\pi$
$83$	0.631008	0.0692621	0.0346310	+	0.999400i	$0.488974\pi$
$84$	−17.2695	−1.88425
$85$	−23.5963	−2.55938
$86$	18.5359	1.99878
$87$	−21.7121	−2.32779
$88$	−4.63201	−0.493774
$89$	−2.16226	−0.229199	−0.114599	−	0.993412i	$-0.536558\pi$
$89$	−2.16226	−0.229199	−0.114599	+	0.993412i	$0.536558\pi$
$90$	58.5217	6.16873
$91$	−2.67491	−0.280406
$92$	3.36836	0.351175
$93$	−28.5059	−2.95592
$94$	−25.2490	−2.60423
$95$	8.68359	0.890918
$96$	−15.4535	−1.57721
$97$	−14.6512	−1.48760	−0.743801	−	0.668401i	$-0.766979\pi$
$97$	−14.6512	−1.48760	−0.743801	+	0.668401i	$0.766979\pi$
$98$	10.0213	1.01231
$99$	9.97450	1.00248
$100$	29.2611	2.92611
$101$	−16.9575	−1.68734	−0.843669	−	0.536864i	$-0.819609\pi$
$101$	−16.9575	−1.68734	−0.843669	+	0.536864i	$0.819609\pi$
$102$	46.3259	4.58695
$103$	9.52559	0.938585	0.469292	−	0.883043i	$-0.344509\pi$
$103$	9.52559	0.938585	0.469292	+	0.883043i	$0.344509\pi$
$104$	5.18539	0.508470
$105$	18.9678	1.85106
$106$	14.0621	1.36584
$107$	−18.9766	−1.83454	−0.917269	−	0.398268i	$-0.869611\pi$
$107$	−18.9766	−1.83454	−0.917269	+	0.398268i	$0.869611\pi$
$108$	−40.4121	−3.88866
$109$	−0.689248	−0.0660180	−0.0330090	−	0.999455i	$-0.510509\pi$
$109$	−0.689248	−0.0660180	−0.0330090	+	0.999455i	$0.510509\pi$
$110$	12.5235	1.19407
$111$	8.15894	0.774412
$112$	0.996189	0.0941310
$113$	2.48315	0.233595	0.116798	−	0.993156i	$-0.462737\pi$
$113$	2.48315	0.233595	0.116798	+	0.993156i	$0.462737\pi$
$114$	−17.0482	−1.59671
$115$	−3.69960	−0.344990
$116$	23.3295	2.16609
$117$	−11.1662	−1.03231
$118$	32.4319	2.98560
$119$	10.4312	0.956229
$120$	−36.7696	−3.35659
$121$	−8.86549	−0.805953
$122$	−26.7899	−2.42544
$123$	−0.610075	−0.0550086
$124$	30.6294	2.75060
$125$	−13.6406	−1.22006
$126$	−25.8707	−2.30475
$127$	−17.5808	−1.56004	−0.780022	−	0.625752i	$-0.784792\pi$
$127$	−17.5808	−1.56004	−0.780022	+	0.625752i	$0.784792\pi$
$128$	19.4272	1.71714
$129$	25.0789	2.20807
$130$	−14.0197	−1.22961
$131$	3.32080	0.290139	0.145070	−	0.989421i	$-0.453659\pi$
$131$	3.32080	0.290139	0.145070	+	0.989421i	$0.453659\pi$
$132$	−15.4270	−1.34275
$133$	−3.83876	−0.332863
$134$	14.5050	1.25304
$135$	44.3863	3.82016
$136$	−20.2213	−1.73396
$137$	−13.9689	−1.19344	−0.596721	−	0.802449i	$-0.703530\pi$
$137$	−13.9689	−1.19344	−0.596721	+	0.802449i	$0.703530\pi$
$138$	7.26332	0.618295
$139$	21.7122	1.84161	0.920804	−	0.390026i	$-0.127534\pi$
$139$	21.7122	1.84161	0.920804	+	0.390026i	$0.127534\pi$
$140$	−20.3807	−1.72248
$141$	−34.1616	−2.87692
$142$	−19.9207	−1.67171
$143$	−2.38953	−0.199822
$144$	4.15850	0.346542
$145$	−25.6238	−2.12794
$146$	21.0446	1.74166
$147$	13.5588	1.11831
$148$	−8.76672	−0.720620
$149$	11.6500	0.954402	0.477201	−	0.878794i	$-0.341651\pi$
$149$	11.6500	0.954402	0.477201	+	0.878794i	$0.341651\pi$
$150$	63.0969	5.15184
$151$	−9.31249	−0.757840	−0.378920	−	0.925430i	$-0.623704\pi$
$151$	−9.31249	−0.757840	−0.378920	+	0.925430i	$0.623704\pi$
$152$	7.44156	0.603590
$153$	43.5442	3.52034
$154$	−5.53626	−0.446125
$155$	−33.6415	−2.70215
$156$	17.2701	1.38271
$157$	7.15760	0.571239	0.285619	−	0.958343i	$-0.407801\pi$
$157$	7.15760	0.571239	0.285619	+	0.958343i	$0.407801\pi$
$158$	−3.58268	−0.285023
$159$	19.0259	1.50885
$160$	−18.2375	−1.44180
$161$	1.63548	0.128894
$162$	−39.6871	−3.11812
$163$	−23.1891	−1.81631	−0.908156	−	0.418632i	$-0.862510\pi$
$163$	−23.1891	−1.81631	−0.908156	+	0.418632i	$0.862510\pi$
$164$	0.655522	0.0511876
$165$	16.9441	1.31910
$166$	−1.46203	−0.113475
$167$	20.3594	1.57545	0.787727	−	0.616024i	$-0.211258\pi$
$167$	20.3594	1.57545	0.787727	+	0.616024i	$0.211258\pi$
$168$	16.2548	1.25408
$169$	−10.3250	−0.794231
$170$	54.6720	4.19315
$171$	−16.0246	−1.22543
$172$	−26.9471	−2.05470
$173$	20.2166	1.53704	0.768521	−	0.639825i	$-0.220993\pi$
$173$	20.2166	1.53704	0.768521	+	0.639825i	$0.220993\pi$
$174$	50.3064	3.81372
$175$	14.2075	1.07399
$176$	0.889908	0.0670793
$177$	43.8799	3.29822
$178$	5.00988	0.375507
$179$	9.41263	0.703533	0.351766	−	0.936088i	$-0.385581\pi$
$179$	9.41263	0.703533	0.351766	+	0.936088i	$0.385581\pi$
$180$	−85.0775	−6.34130
$181$	10.5949	0.787511	0.393756	−	0.919215i	$-0.371176\pi$
$181$	10.5949	0.787511	0.393756	+	0.919215i	$0.371176\pi$
$182$	6.19768	0.459403
$183$	−36.2464	−2.67941
$184$	−3.17044	−0.233728
$185$	9.62884	0.707926
$186$	66.0473	4.84282
$187$	9.31834	0.681425
$188$	36.7064	2.67709
$189$	−19.6219	−1.42728
$190$	−20.1196	−1.45963
$191$	16.2993	1.17938	0.589689	−	0.807631i	$-0.299251\pi$
$191$	16.2993	1.17938	0.589689	+	0.807631i	$0.299251\pi$
$192$	39.6241	2.85963
$193$	11.9397	0.859439	0.429720	−	0.902962i	$-0.358612\pi$
$193$	11.9397	0.859439	0.429720	+	0.902962i	$0.358612\pi$
$194$	33.9464	2.43721
$195$	−18.9684	−1.35836
$196$	−14.5688	−1.04063
$197$	16.5016	1.17569	0.587845	−	0.808974i	$-0.299976\pi$
$197$	16.5016	1.17569	0.587845	+	0.808974i	$0.299976\pi$
$198$	−23.1106	−1.64240
$199$	13.2419	0.938693	0.469346	−	0.883014i	$-0.344490\pi$
$199$	13.2419	0.938693	0.469346	+	0.883014i	$0.344490\pi$
$200$	−27.5418	−1.94750
$201$	19.6251	1.38425
$202$	39.2901	2.76444
$203$	11.3275	0.795035
$204$	−67.3475	−4.71527
$205$	−0.719986	−0.0502860
$206$	−22.0705	−1.53773
$207$	6.82718	0.474522
$208$	−0.996225	−0.0690758
$209$	−3.42921	−0.237203
$210$	−43.9477	−3.03268
$211$	7.01061	0.482630	0.241315	−	0.970447i	$-0.422421\pi$
$211$	7.01061	0.482630	0.241315	+	0.970447i	$0.422421\pi$
$212$	−20.4432	−1.40404
$213$	−26.9525	−1.84675
$214$	43.9683	3.00561
$215$	29.5971	2.01850
$216$	38.0376	2.58813
$217$	14.8719	1.00957
$218$	1.59697	0.108160
$219$	28.4731	1.92403
$220$	−18.2063	−1.22747
$221$	−10.4316	−0.701706
$222$	−18.9040	−1.26875
$223$	−16.4987	−1.10483	−0.552416	−	0.833568i	$-0.686294\pi$
$223$	−16.4987	−1.10483	−0.552416	+	0.833568i	$0.686294\pi$
$224$	8.06227	0.538683
$225$	59.3081	3.95387
$226$	−5.75339	−0.382710
$227$	11.5795	0.768561	0.384280	−	0.923216i	$-0.374450\pi$
$227$	11.5795	0.768561	0.384280	+	0.923216i	$0.374450\pi$
$228$	24.7843	1.64138
$229$	4.65447	0.307576	0.153788	−	0.988104i	$-0.450853\pi$
$229$	4.65447	0.307576	0.153788	+	0.988104i	$0.450853\pi$
$230$	8.57187	0.565212
$231$	−7.49049	−0.492838
$232$	−21.9588	−1.44166
$233$	−1.11195	−0.0728463	−0.0364231	−	0.999336i	$-0.511596\pi$
$233$	−1.11195	−0.0728463	−0.0364231	+	0.999336i	$0.511596\pi$
$234$	25.8717	1.69128
$235$	−40.3161	−2.62993
$236$	−47.1487	−3.06912
$237$	−4.84732	−0.314868
$238$	−24.1689	−1.56663
$239$	−28.9512	−1.87270	−0.936349	−	0.351072i	$-0.885817\pi$
$239$	−28.9512	−1.87270	−0.936349	+	0.351072i	$0.885817\pi$
$240$	7.06423	0.455994
$241$	−24.4403	−1.57434	−0.787169	−	0.616738i	$-0.788454\pi$
$241$	−24.4403	−1.57434	−0.787169	+	0.616738i	$0.788454\pi$
$242$	20.5411	1.32043
$243$	−17.7035	−1.13568
$244$	38.9465	2.49329
$245$	16.0015	1.02230
$246$	1.41353	0.0901232
$247$	3.83890	0.244263
$248$	−28.8297	−1.83069
$249$	−1.97810	−0.125357
$250$	31.6050	1.99887
$251$	−8.35218	−0.527185	−0.263592	−	0.964634i	$-0.584907\pi$
$251$	−8.35218	−0.527185	−0.263592	+	0.964634i	$0.584907\pi$
$252$	37.6102	2.36922
$253$	1.46100	0.0918522
$254$	40.7342	2.55589
$255$	73.9705	4.63221
$256$	−19.7324	−1.23327
$257$	22.9800	1.43345	0.716725	−	0.697356i	$-0.245640\pi$
$257$	22.9800	1.43345	0.716725	+	0.697356i	$0.245640\pi$
$258$	−58.1071	−3.61759
$259$	−4.25662	−0.264494
$260$	20.3815	1.26400
$261$	47.2857	2.92691
$262$	−7.69419	−0.475349
$263$	3.39665	0.209446	0.104723	−	0.994501i	$-0.466604\pi$
$263$	3.39665	0.209446	0.104723	+	0.994501i	$0.466604\pi$
$264$	14.5206	0.893680
$265$	22.4536	1.37931
$266$	8.89429	0.545344
$267$	6.77831	0.414826
$268$	−21.0870	−1.28810
$269$	6.81361	0.415433	0.207717	−	0.978189i	$-0.433397\pi$
$269$	6.81361	0.415433	0.207717	+	0.978189i	$0.433397\pi$
$270$	−102.842	−6.25875
$271$	−4.19001	−0.254525	−0.127262	−	0.991869i	$-0.540619\pi$
$271$	−4.19001	−0.254525	−0.127262	+	0.991869i	$0.540619\pi$
$272$	3.88494	0.235559
$273$	8.38539	0.507507
$274$	32.3655	1.95527
$275$	12.6918	0.765342
$276$	−10.5592	−0.635591
$277$	−3.98995	−0.239733	−0.119866	−	0.992790i	$-0.538247\pi$
$277$	−3.98995	−0.239733	−0.119866	+	0.992790i	$0.538247\pi$
$278$	−50.3066	−3.01719
$279$	62.0814	3.71672
$280$	19.1832	1.14642
$281$	−19.3118	−1.15204	−0.576022	−	0.817434i	$-0.695396\pi$
$281$	−19.3118	−1.15204	−0.576022	+	0.817434i	$0.695396\pi$
$282$	79.1514	4.71340
$283$	−21.2597	−1.26376	−0.631880	−	0.775067i	$-0.717716\pi$
$283$	−21.2597	−1.26376	−0.631880	+	0.775067i	$0.717716\pi$
$284$	28.9602	1.71847
$285$	−27.2216	−1.61247
$286$	5.53646	0.327378
$287$	0.318284	0.0187877
$288$	33.6552	1.98315
$289$	23.6797	1.39293
$290$	59.3696	3.48630
$291$	45.9290	2.69241
$292$	−30.5941	−1.79039
$293$	−29.2209	−1.70711	−0.853553	−	0.521006i	$-0.825557\pi$
$293$	−29.2209	−1.70711	−0.853553	+	0.521006i	$0.825557\pi$
$294$	−31.4153	−1.83217
$295$	51.7853	3.01506
$296$	8.25161	0.479615
$297$	−17.5284	−1.01710
$298$	−26.9926	−1.56364
$299$	−1.63554	−0.0945859
$300$	−91.7287	−5.29596
$301$	−13.0840	−0.754149
$302$	21.5768	1.24160
$303$	53.1591	3.05391
$304$	−1.42968	−0.0819980
$305$	−42.7765	−2.44938
$306$	−100.891	−5.76754
$307$	−17.7221	−1.01145	−0.505727	−	0.862694i	$-0.668776\pi$
$307$	−17.7221	−1.01145	−0.505727	+	0.862694i	$0.668776\pi$
$308$	8.04848	0.458605
$309$	−29.8612	−1.69874
$310$	77.9463	4.42705
$311$	1.03772	0.0588439	0.0294219	−	0.999567i	$-0.490633\pi$
$311$	1.03772	0.0588439	0.0294219	+	0.999567i	$0.490633\pi$
$312$	−16.2554	−0.920278
$313$	6.20187	0.350551	0.175275	−	0.984519i	$-0.443918\pi$
$313$	6.20187	0.350551	0.175275	+	0.984519i	$0.443918\pi$
$314$	−16.5840	−0.935887
$315$	−41.3088	−2.32749
$316$	5.20841	0.292996
$317$	−17.0773	−0.959155	−0.479578	−	0.877499i	$-0.659210\pi$
$317$	−17.0773	−0.959155	−0.479578	+	0.877499i	$0.659210\pi$
$318$	−44.0825	−2.47202
$319$	10.1190	0.566555
$320$	46.7628	2.61412
$321$	59.4885	3.32033
$322$	−3.78937	−0.211173
$323$	−14.9704	−0.832976
$324$	57.6962	3.20534
$325$	−14.2081	−0.788121
$326$	53.7285	2.97575
$327$	2.16068	0.119486
$328$	−0.617005	−0.0340684
$329$	17.8225	0.982589
$330$	−39.2591	−2.16114
$331$	16.2592	0.893688	0.446844	−	0.894612i	$-0.352548\pi$
$331$	16.2592	0.893688	0.446844	+	0.894612i	$0.352548\pi$
$332$	2.12546	0.116650
$333$	−17.7689	−0.973730
$334$	−47.1720	−2.58114
$335$	23.1607	1.26541
$336$	−3.12289	−0.170367
$337$	6.51025	0.354636	0.177318	−	0.984154i	$-0.443258\pi$
$337$	6.51025	0.354636	0.177318	+	0.984154i	$0.443258\pi$
$338$	23.9227	1.30122
$339$	−7.78427	−0.422784
$340$	−79.4808	−4.31045
$341$	13.2852	0.719436
$342$	37.1284	2.00768
$343$	−18.5222	−1.00010
$344$	25.3638	1.36752
$345$	11.5976	0.624396
$346$	−46.8413	−2.51821
$347$	14.3626	0.771027	0.385514	−	0.922702i	$-0.374024\pi$
$347$	14.3626	0.771027	0.385514	+	0.922702i	$0.374024\pi$
$348$	−73.1342	−3.92041
$349$	1.00000	0.0535288
$349$	1.00000	0.0535288
$350$	−32.9185	−1.75957
$351$	19.6226	1.04738
$352$	7.20213	0.383875
$353$	−25.6198	−1.36360	−0.681802	−	0.731537i	$-0.738803\pi$
$353$	−25.6198	−1.36360	−0.681802	+	0.731537i	$0.738803\pi$
$354$	−101.669	−5.40362
$355$	−31.8082	−1.68820
$356$	−7.28325	−0.386011
$357$	−32.7002	−1.73068
$358$	−21.8088	−1.15263
$359$	−8.22623	−0.434164	−0.217082	−	0.976153i	$-0.569654\pi$
$359$	−8.22623	−0.434164	−0.217082	+	0.976153i	$0.569654\pi$
$360$	80.0786	4.22051
$361$	−13.4908	−0.710042
$362$	−24.5480	−1.29022
$363$	27.7918	1.45869
$364$	−9.01003	−0.472254
$365$	33.6028	1.75885
$366$	83.9819	4.38980
$367$	−16.2383	−0.847632	−0.423816	−	0.905748i	$-0.639310\pi$
$367$	−16.2383	−0.847632	−0.423816	+	0.905748i	$0.639310\pi$
$368$	0.609109	0.0317520
$369$	1.32865	0.0691668
$370$	−22.3097	−1.15983
$371$	−9.92607	−0.515336
$372$	−96.0179	−4.97830
$373$	−14.3221	−0.741572	−0.370786	−	0.928718i	$-0.620912\pi$
$373$	−14.3221	−0.741572	−0.370786	+	0.928718i	$0.620912\pi$
$374$	−21.5903	−1.11641
$375$	42.7611	2.20817
$376$	−34.5496	−1.78176
$377$	−11.3279	−0.583418
$378$	45.4633	2.33838
$379$	27.7354	1.42467	0.712337	−	0.701838i	$-0.247637\pi$
$379$	27.7354	1.42467	0.712337	+	0.701838i	$0.247637\pi$
$380$	29.2494	1.50046
$381$	55.1129	2.82352
$382$	−37.7650	−1.93223
$383$	8.92323	0.455956	0.227978	−	0.973666i	$-0.426789\pi$
$383$	8.92323	0.455956	0.227978	+	0.973666i	$0.426789\pi$
$384$	−60.9011	−3.10784
$385$	−8.83997	−0.450527
$386$	−27.6640	−1.40806
$387$	−54.6180	−2.77639
$388$	−49.3504	−2.50539
$389$	20.8259	1.05591	0.527956	−	0.849271i	$-0.322958\pi$
$389$	20.8259	1.05591	0.527956	+	0.849271i	$0.322958\pi$
$390$	43.9493	2.22546
$391$	6.37807	0.322553
$392$	13.7128	0.692599
$393$	−10.4101	−0.525122
$394$	−38.2337	−1.92619
$395$	−5.72061	−0.287835
$396$	33.5977	1.68835
$397$	1.11228	0.0558239	0.0279119	−	0.999610i	$-0.491114\pi$
$397$	1.11228	0.0558239	0.0279119	+	0.999610i	$0.491114\pi$
$398$	−30.6811	−1.53790
$399$	12.0339	0.602447
$400$	5.29137	0.264568
$401$	6.99132	0.349130	0.174565	−	0.984646i	$-0.444148\pi$
$401$	6.99132	0.349130	0.174565	+	0.984646i	$0.444148\pi$
$402$	−45.4708	−2.26788
$403$	−14.8724	−0.740849
$404$	−57.1190	−2.84178
$405$	−63.3701	−3.14888
$406$	−26.2455	−1.30254
$407$	−3.80249	−0.188483
$408$	63.3904	3.13829
$409$	3.08543	0.152565	0.0762825	−	0.997086i	$-0.475695\pi$
$409$	3.08543	0.152565	0.0762825	+	0.997086i	$0.475695\pi$
$410$	1.66819	0.0823859
$411$	43.7901	2.16001
$412$	32.0856	1.58074
$413$	−22.8927	−1.12648
$414$	−15.8184	−0.777431
$415$	−2.33448	−0.114595
$416$	−8.06256	−0.395300
$417$	−68.0642	−3.33312
$418$	7.94538	0.388621
$419$	6.93010	0.338557	0.169279	−	0.985568i	$-0.445856\pi$
$419$	6.93010	0.338557	0.169279	+	0.985568i	$0.445856\pi$
$420$	63.8901	3.11752
$421$	−19.9450	−0.972061	−0.486030	−	0.873942i	$-0.661556\pi$
$421$	−19.9450	−0.972061	−0.486030	+	0.873942i	$0.661556\pi$
$422$	−16.2434	−0.790715
$423$	74.3986	3.61738
$424$	19.2420	0.934475
$425$	55.4066	2.68762
$426$	62.4481	3.02562
$427$	18.9102	0.915130
$428$	−63.9200	−3.08969
$429$	7.49077	0.361658
$430$	−68.5756	−3.30701
$431$	21.4770	1.03451	0.517254	−	0.855832i	$-0.326954\pi$
$431$	21.4770	1.03451	0.517254	+	0.855832i	$0.326954\pi$
$432$	−7.30784	−0.351599
$433$	−39.9983	−1.92220	−0.961099	−	0.276205i	$-0.910923\pi$
$433$	−39.9983	−1.92220	−0.961099	+	0.276205i	$0.910923\pi$
$434$	−34.4577	−1.65402
$435$	80.3263	3.85135
$436$	−2.32163	−0.111186
$437$	−2.34717	−0.112280
$438$	−65.9713	−3.15223
$439$	−29.1489	−1.39120	−0.695600	−	0.718429i	$-0.744862\pi$
$439$	−29.1489	−1.39120	−0.695600	+	0.718429i	$0.744862\pi$
$440$	17.1366	0.816955
$441$	−29.5289	−1.40614
$442$	24.1697	1.14964
$443$	−17.6363	−0.837924	−0.418962	−	0.908004i	$-0.637606\pi$
$443$	−17.6363	−0.837924	−0.418962	+	0.908004i	$0.637606\pi$
$444$	27.4822	1.30425
$445$	7.99949	0.379212
$446$	38.2269	1.81010
$447$	−36.5207	−1.72737
$448$	−20.6724	−0.976680
$449$	−5.44459	−0.256946	−0.128473	−	0.991713i	$-0.541008\pi$
$449$	−5.44459	−0.256946	−0.128473	+	0.991713i	$0.541008\pi$
$450$	−137.415	−6.47782
$451$	0.284327	0.0133885
$452$	8.36414	0.393416
$453$	29.1931	1.37161
$454$	−26.8294	−1.25917
$455$	9.89609	0.463936
$456$	−23.3281	−1.09244
$457$	32.9985	1.54361	0.771803	−	0.635861i	$-0.219355\pi$
$457$	32.9985	1.54361	0.771803	+	0.635861i	$0.219355\pi$
$458$	−10.7843	−0.503916
$459$	−76.5214	−3.57171
$460$	−12.4616	−0.581024
$461$	36.7811	1.71307	0.856534	−	0.516091i	$-0.172613\pi$
$461$	36.7811	1.71307	0.856534	+	0.516091i	$0.172613\pi$
$462$	17.3553	0.807440
$463$	−22.6307	−1.05174	−0.525868	−	0.850566i	$-0.676259\pi$
$463$	−22.6307	−1.05174	−0.525868	+	0.850566i	$0.676259\pi$
$464$	4.21875	0.195850
$465$	105.460	4.89061
$466$	2.57636	0.119347
$467$	−1.12540	−0.0520774	−0.0260387	−	0.999661i	$-0.508289\pi$
$467$	−1.12540	−0.0520774	−0.0260387	+	0.999661i	$0.508289\pi$
$468$	−37.6116	−1.73860
$469$	−10.2387	−0.472778
$470$	93.4112	4.30874
$471$	−22.4379	−1.03388
$472$	44.3783	2.04268
$473$	−11.6881	−0.537419
$474$	11.2311	0.515862
$475$	−20.3900	−0.935557
$476$	35.1361	1.61046
$477$	−41.4355	−1.89720
$478$	67.0791	3.06813
$479$	20.8286	0.951684	0.475842	−	0.879531i	$-0.342143\pi$
$479$	20.8286	0.951684	0.475842	+	0.879531i	$0.342143\pi$
$480$	57.1716	2.60952
$481$	4.25678	0.194092
$482$	56.6274	2.57931
$483$	−5.12697	−0.233285
$484$	−29.8621	−1.35737
$485$	54.2035	2.46126
$486$	41.0184	1.86063
$487$	−15.5027	−0.702496	−0.351248	−	0.936283i	$-0.614243\pi$
$487$	−15.5027	−0.702496	−0.351248	+	0.936283i	$0.614243\pi$
$488$	−36.6581	−1.65944
$489$	72.6940	3.28734
$490$	−37.0750	−1.67488
$491$	−0.658225	−0.0297053	−0.0148526	−	0.999890i	$-0.504728\pi$
$491$	−0.658225	−0.0297053	−0.0148526	+	0.999890i	$0.504728\pi$
$492$	−2.05495	−0.0926444
$493$	44.1751	1.98955
$494$	−8.89462	−0.400188
$495$	−36.9017	−1.65861
$496$	5.53879	0.248699
$497$	14.0615	0.630742
$498$	4.58321	0.205379
$499$	11.6270	0.520497	0.260249	−	0.965542i	$-0.416195\pi$
$499$	11.6270	0.520497	0.260249	+	0.965542i	$0.416195\pi$
$500$	−45.9465	−2.05479
$501$	−63.8232	−2.85141
$502$	19.3518	0.863711
$503$	36.3842	1.62229	0.811145	−	0.584845i	$-0.198845\pi$
$503$	36.3842	1.62229	0.811145	+	0.584845i	$0.198845\pi$
$504$	−35.4004	−1.57686
$505$	62.7361	2.79172
$506$	−3.38509	−0.150486
$507$	32.3672	1.43748
$508$	−59.2184	−2.62739
$509$	30.3244	1.34411	0.672053	−	0.740503i	$-0.265413\pi$
$509$	30.3244	1.34411	0.672053	+	0.740503i	$0.265413\pi$
$510$	−171.388	−7.58917
$511$	−14.8548	−0.657137
$512$	6.86495	0.303391
$513$	28.1604	1.24331
$514$	−53.2439	−2.34849
$515$	−35.2409	−1.55290
$516$	84.4746	3.71879
$517$	15.9211	0.700209
$518$	9.86248	0.433332
$519$	−63.3757	−2.78189
$520$	−19.1839	−0.841270
$521$	23.8135	1.04329	0.521643	−	0.853164i	$-0.325319\pi$
$521$	23.8135	1.04329	0.521643	+	0.853164i	$0.325319\pi$
$522$	−109.560	−4.79529
$523$	42.3170	1.85039	0.925196	−	0.379488i	$-0.123900\pi$
$523$	42.3170	1.85039	0.925196	+	0.379488i	$0.123900\pi$
$524$	11.1856	0.488646
$525$	−44.5383	−1.94381
$526$	−7.86994	−0.343146
$527$	57.9975	2.52641
$528$	−2.78971	−0.121407
$529$	1.00000	0.0434783
$530$	−52.0243	−2.25979
$531$	−95.5637	−4.14711
$532$	−12.9303	−0.560600
$533$	−0.318296	−0.0137869
$534$	−15.7052	−0.679629
$535$	70.2059	3.03527
$536$	19.8480	0.857304
$537$	−29.5070	−1.27332
$538$	−15.7869	−0.680623
$539$	−6.31910	−0.272183
$540$	149.509	6.43384
$541$	14.1737	0.609374	0.304687	−	0.952453i	$-0.401448\pi$
$541$	14.1737	0.609374	0.304687	+	0.952453i	$0.401448\pi$
$542$	9.70813	0.417000
$543$	−33.2132	−1.42531
$544$	31.4413	1.34803
$545$	2.54994	0.109228
$546$	−19.4287	−0.831471
$547$	6.62152	0.283116	0.141558	−	0.989930i	$-0.454789\pi$
$547$	6.62152	0.283116	0.141558	+	0.989930i	$0.454789\pi$
$548$	−47.0521	−2.00997
$549$	78.9391	3.36904
$550$	−29.4065	−1.25390
$551$	−16.2567	−0.692559
$552$	9.93881	0.423024
$553$	2.52891	0.107540
$554$	9.24460	0.392766
$555$	−30.1848	−1.28127
$556$	73.1345	3.10159
$557$	25.9238	1.09843	0.549213	−	0.835682i	$-0.314927\pi$
$557$	25.9238	1.09843	0.549213	+	0.835682i	$0.314927\pi$
$558$	−143.841	−6.08927
$559$	13.0845	0.553414
$560$	−3.68550	−0.155741
$561$	−29.2115	−1.23331
$562$	44.7448	1.88745
$563$	−19.8028	−0.834590	−0.417295	−	0.908771i	$-0.637022\pi$
$563$	−19.8028	−0.834590	−0.417295	+	0.908771i	$0.637022\pi$
$564$	−115.068	−4.84525
$565$	−9.18668	−0.386486
$566$	49.2582	2.07047
$567$	28.0140	1.17648
$568$	−27.2586	−1.14375
$569$	−41.7835	−1.75166	−0.875828	−	0.482623i	$-0.839684\pi$
$569$	−41.7835	−1.75166	−0.875828	+	0.482623i	$0.839684\pi$
$570$	63.0717	2.64178
$571$	30.6214	1.28146	0.640732	−	0.767765i	$-0.278631\pi$
$571$	30.6214	1.28146	0.640732	+	0.767765i	$0.278631\pi$
$572$	−8.04877	−0.336536
$573$	−51.0956	−2.13455
$574$	−0.737456	−0.0307808
$575$	8.68705	0.362275
$576$	−86.2952	−3.59563
$577$	18.2136	0.758242	0.379121	−	0.925347i	$-0.376226\pi$
$577$	18.2136	0.758242	0.379121	+	0.925347i	$0.376226\pi$
$578$	−54.8653	−2.28209
$579$	−37.4290	−1.55550
$580$	−86.3100	−3.58383
$581$	1.03200	0.0428147
$582$	−106.416	−4.41109
$583$	−8.86708	−0.367237
$584$	28.7965	1.19161
$585$	41.3103	1.70797
$586$	67.7041	2.79683
$587$	−23.1275	−0.954575	−0.477288	−	0.878747i	$-0.658380\pi$
$587$	−23.1275	−0.954575	−0.477288	+	0.878747i	$0.658380\pi$
$588$	45.6707	1.88343
$589$	−21.3434	−0.879441
$590$	−119.985	−4.93970
$591$	−51.7298	−2.12788
$592$	−1.58531	−0.0651559
$593$	23.6819	0.972499	0.486249	−	0.873820i	$-0.338365\pi$
$593$	23.6819	0.972499	0.486249	+	0.873820i	$0.338365\pi$
$594$	40.6129	1.66637
$595$	−38.5914	−1.58209
$596$	39.2412	1.60738
$597$	−41.5111	−1.69894
$598$	3.78951	0.154964
$599$	−21.9811	−0.898124	−0.449062	−	0.893501i	$-0.648242\pi$
$599$	−21.9811	−0.898124	−0.449062	+	0.893501i	$0.648242\pi$
$600$	86.3390	3.52477
$601$	−25.5998	−1.04424	−0.522120	−	0.852872i	$-0.674859\pi$
$601$	−25.5998	−1.04424	−0.522120	+	0.852872i	$0.674859\pi$
$602$	30.3152	1.23556
$603$	−42.7404	−1.74053
$604$	−31.3678	−1.27634
$605$	32.7988	1.33346
$606$	−123.168	−5.00336
$607$	−45.5288	−1.84796	−0.923978	−	0.382447i	$-0.875082\pi$
$607$	−45.5288	−1.84796	−0.923978	+	0.382447i	$0.875082\pi$
$608$	−11.5706	−0.469249
$609$	−35.5099	−1.43893
$610$	99.1120	4.01293
$611$	−17.8232	−0.721049
$612$	146.672	5.92888
$613$	−15.8394	−0.639747	−0.319873	−	0.947460i	$-0.603640\pi$
$613$	−15.8394	−0.639747	−0.319873	+	0.947460i	$0.603640\pi$
$614$	41.0616	1.65711
$615$	2.25704	0.0910125
$616$	−7.57558	−0.305229
$617$	−9.79847	−0.394471	−0.197236	−	0.980356i	$-0.563196\pi$
$617$	−9.79847	−0.394471	−0.197236	+	0.980356i	$0.563196\pi$
$618$	69.1874	2.78313
$619$	−4.85778	−0.195251	−0.0976254	−	0.995223i	$-0.531125\pi$
$619$	−4.85778	−0.195251	−0.0976254	+	0.995223i	$0.531125\pi$
$620$	−113.316	−4.55090
$621$	−11.9976	−0.481447
$622$	−2.40437	−0.0964066
$623$	−3.53634	−0.141680
$624$	3.12300	0.125020
$625$	7.02964	0.281186
$626$	−14.3696	−0.574323
$627$	10.7500	0.429314
$628$	24.1094	0.962068
$629$	−16.6000	−0.661885
$630$	95.7114	3.81323
$631$	−0.652463	−0.0259742	−0.0129871	−	0.999916i	$-0.504134\pi$
$631$	−0.652463	−0.0259742	−0.0129871	+	0.999916i	$0.504134\pi$
$632$	−4.90238	−0.195006
$633$	−21.9771	−0.873511
$634$	39.5676	1.57143
$635$	65.0420	2.58111
$636$	64.0860	2.54118
$637$	7.07404	0.280284
$638$	−23.4454	−0.928214
$639$	58.6983	2.32207
$640$	−71.8729	−2.84103
$641$	−39.6978	−1.56797	−0.783984	−	0.620781i	$-0.786815\pi$
$641$	−39.6978	−1.56797	−0.783984	+	0.620781i	$0.786815\pi$
$642$	−137.833	−5.43984
$643$	−18.6396	−0.735076	−0.367538	−	0.930009i	$-0.619799\pi$
$643$	−18.6396	−0.735076	−0.367538	+	0.930009i	$0.619799\pi$
$644$	5.50889	0.217081
$645$	−92.7819	−3.65328
$646$	34.6860	1.36470
$647$	29.5024	1.15986	0.579930	−	0.814666i	$-0.303080\pi$
$647$	29.5024	1.15986	0.579930	+	0.814666i	$0.303080\pi$
$648$	−54.3061	−2.13335
$649$	−20.4504	−0.802747
$650$	32.9197	1.29122
$651$	−46.6209	−1.82722
$652$	−78.1092	−3.05899
$653$	−9.08656	−0.355585	−0.177792	−	0.984068i	$-0.556896\pi$
$653$	−9.08656	−0.355585	−0.177792	+	0.984068i	$0.556896\pi$
$654$	−5.00623	−0.195759
$655$	−12.2856	−0.480039
$656$	0.118540	0.00462820
$657$	−62.0100	−2.41924
$658$	−41.2943	−1.60982
$659$	14.5148	0.565416	0.282708	−	0.959206i	$-0.408767\pi$
$659$	14.5148	0.565416	0.282708	+	0.959206i	$0.408767\pi$
$660$	57.0738	2.22160
$661$	−37.4743	−1.45758	−0.728791	−	0.684737i	$-0.759917\pi$
$661$	−37.4743	−1.45758	−0.728791	+	0.684737i	$0.759917\pi$
$662$	−37.6721	−1.46417
$663$	32.7014	1.27002
$664$	−2.00057	−0.0776373
$665$	14.2019	0.550725
$666$	41.1700	1.59531
$667$	6.92609	0.268179
$668$	68.5776	2.65335
$669$	51.7206	1.99963
$670$	−53.6628	−2.07317
$671$	16.8927	0.652137
$672$	−25.2739	−0.974961
$673$	−11.8317	−0.456078	−0.228039	−	0.973652i	$-0.573231\pi$
$673$	−11.8317	−0.456078	−0.228039	+	0.973652i	$0.573231\pi$
$674$	−15.0841	−0.581016
$675$	−104.224	−4.01157
$676$	−34.7783	−1.33763
$677$	−37.5647	−1.44373	−0.721864	−	0.692035i	$-0.756714\pi$
$677$	−37.5647	−1.44373	−0.721864	+	0.692035i	$0.756714\pi$
$678$	18.0359	0.692666
$679$	−23.9618	−0.919568
$680$	74.8107	2.86886
$681$	−36.2999	−1.39102
$682$	−30.7815	−1.17869
$683$	−47.1611	−1.80457	−0.902286	−	0.431139i	$-0.858112\pi$
$683$	−47.1611	−1.80457	−0.902286	+	0.431139i	$0.858112\pi$
$684$	−53.9764	−2.06384
$685$	51.6793	1.97456
$686$	42.9153	1.63852
$687$	−14.5910	−0.556681
$688$	−4.87292	−0.185778
$689$	9.92643	0.378167
$690$	−26.8714	−1.02298
$691$	25.2895	0.962058	0.481029	−	0.876705i	$-0.340263\pi$
$691$	25.2895	0.962058	0.481029	+	0.876705i	$0.340263\pi$
$692$	68.0968	2.58865
$693$	16.3131	0.619685
$694$	−33.2778	−1.26321
$695$	−80.3266	−3.04696
$696$	68.8371	2.60926
$697$	1.24125	0.0470156
$698$	−2.31697	−0.0876987
$699$	3.48578	0.131844
$700$	47.8560	1.80879
$701$	−27.9509	−1.05569	−0.527845	−	0.849341i	$-0.677000\pi$
$701$	−27.9509	−1.05569	−0.527845	+	0.849341i	$0.677000\pi$
$702$	−45.4649	−1.71596
$703$	6.10891	0.230402
$704$	−18.4669	−0.695999
$705$	126.384	4.75990
$706$	59.3603	2.23406
$707$	−27.7338	−1.04304
$708$	147.803	5.55478
$709$	−0.196989	−0.00739806	−0.00369903	−	0.999993i	$-0.501177\pi$
$709$	−0.196989	−0.00739806	−0.00369903	+	0.999993i	$0.501177\pi$
$710$	73.6986	2.76586
$711$	10.5567	0.395908
$712$	6.85531	0.256913
$713$	9.09327	0.340545
$714$	75.7653	2.83545
$715$	8.84029	0.330608
$716$	31.7051	1.18487
$717$	90.7572	3.38939
$718$	19.0599	0.711311
$719$	−22.7014	−0.846621	−0.423311	−	0.905985i	$-0.639132\pi$
$719$	−22.7014	−0.846621	−0.423311	+	0.905985i	$0.639132\pi$
$720$	−15.3848	−0.573358
$721$	15.5790	0.580191
$722$	31.2578	1.16329
$723$	76.6162	2.84939
$724$	35.6873	1.32631
$725$	60.1673	2.23456
$726$	−64.3929	−2.38984
$727$	−21.0827	−0.781912	−0.390956	−	0.920409i	$-0.627856\pi$
$727$	−21.0827	−0.781912	−0.390956	+	0.920409i	$0.627856\pi$
$728$	8.48063	0.314313
$729$	4.11076	0.152250
$730$	−77.8566	−2.88160
$731$	−51.0250	−1.88723
$732$	−122.091	−4.51261
$733$	30.4537	1.12483	0.562416	−	0.826854i	$-0.309872\pi$
$733$	30.4537	1.12483	0.562416	+	0.826854i	$0.309872\pi$
$734$	37.6237	1.38871
$735$	−50.1620	−1.85025
$736$	4.92959	0.181707
$737$	−9.14633	−0.336910
$738$	−3.07844	−0.113319
$739$	6.37661	0.234567	0.117284	−	0.993098i	$-0.462581\pi$
$739$	6.37661	0.234567	0.117284	+	0.993098i	$0.462581\pi$
$740$	32.4334	1.19227
$741$	−12.0343	−0.442091
$742$	22.9984	0.844298
$743$	−24.9023	−0.913576	−0.456788	−	0.889576i	$-0.651000\pi$
$743$	−24.9023	−0.913576	−0.456788	+	0.889576i	$0.651000\pi$
$744$	90.3762	3.31335
$745$	−43.1002	−1.57907
$746$	33.1840	1.21495
$747$	4.30801	0.157622
$748$	31.3875	1.14764
$749$	−31.0359	−1.13403
$750$	−99.0763	−3.61775
$751$	27.7775	1.01362	0.506808	−	0.862059i	$-0.330825\pi$
$751$	27.7775	1.01362	0.506808	+	0.862059i	$0.330825\pi$
$752$	6.63772	0.242053
$753$	26.1827	0.954151
$754$	26.2465	0.955840
$755$	34.4525	1.25385
$756$	−66.0934	−2.40379
$757$	1.44328	0.0524567	0.0262284	−	0.999656i	$-0.491650\pi$
$757$	1.44328	0.0524567	0.0262284	+	0.999656i	$0.491650\pi$
$758$	−64.2622	−2.33411
$759$	−4.57999	−0.166243
$760$	−27.5308	−0.998648
$761$	−2.28953	−0.0829955	−0.0414977	−	0.999139i	$-0.513213\pi$
$761$	−2.28953	−0.0829955	−0.0414977	+	0.999139i	$0.513213\pi$
$762$	−127.695	−4.62590
$763$	−1.12725	−0.0408094
$764$	54.9019	1.98628
$765$	−161.096	−5.82445
$766$	−20.6749	−0.747013
$767$	22.8936	0.826639
$768$	61.8577	2.23210
$769$	−17.2672	−0.622670	−0.311335	−	0.950300i	$-0.600776\pi$
$769$	−17.2672	−0.622670	−0.311335	+	0.950300i	$0.600776\pi$
$770$	20.4820	0.738119
$771$	−72.0383	−2.59440
$772$	40.2172	1.44745
$773$	−1.64284	−0.0590889	−0.0295445	−	0.999563i	$-0.509406\pi$
$773$	−1.64284	−0.0590889	−0.0295445	+	0.999563i	$0.509406\pi$
$774$	126.548	4.54868
$775$	78.9937	2.83754
$776$	46.4507	1.66748
$777$	13.3438	0.478707
$778$	−48.2529	−1.72995
$779$	−0.456787	−0.0163661
$780$	−63.8925	−2.28772
$781$	12.5613	0.449477
$782$	−14.7778	−0.528453
$783$	−83.0964	−2.96962
$784$	−2.63452	−0.0940898
$785$	−26.4803	−0.945122
$786$	24.1200	0.860332
$787$	−49.2289	−1.75482	−0.877410	−	0.479741i	$-0.840731\pi$
$787$	−49.2289	−1.75482	−0.877410	+	0.479741i	$0.840731\pi$
$788$	55.5833	1.98007
$789$	−10.6479	−0.379077
$790$	13.2545	0.471574
$791$	4.06116	0.144398
$792$	−31.6236	−1.12369
$793$	−18.9109	−0.671546
$794$	−2.57713	−0.0914588
$795$	−70.3883	−2.49642
$796$	44.6034	1.58093
$797$	36.3750	1.28847	0.644235	−	0.764828i	$-0.277176\pi$
$797$	36.3750	1.28847	0.644235	+	0.764828i	$0.277176\pi$
$798$	−27.8821	−0.987017
$799$	69.5044	2.45889
$800$	42.8236	1.51404
$801$	−14.7621	−0.521594
$802$	−16.1987	−0.571995
$803$	−13.2700	−0.468287
$804$	66.1043	2.33132
$805$	−6.05064	−0.213257
$806$	34.4590	1.21377
$807$	−21.3595	−0.751891
$808$	53.7629	1.89137
$809$	−16.1645	−0.568313	−0.284156	−	0.958778i	$-0.591714\pi$
$809$	−16.1645	−0.568313	−0.284156	+	0.958778i	$0.591714\pi$
$810$	146.827	5.15896
$811$	16.1921	0.568581	0.284290	−	0.958738i	$-0.408242\pi$
$811$	16.1921	0.568581	0.284290	+	0.958738i	$0.408242\pi$
$812$	38.1551	1.33898
$813$	13.1350	0.460664
$814$	8.81027	0.308800
$815$	85.7905	3.00511
$816$	−12.1786	−0.426338
$817$	18.7775	0.656942
$818$	−7.14886	−0.249954
$819$	−18.2621	−0.638128
$820$	−2.42517	−0.0846906
$821$	−39.8061	−1.38924	−0.694622	−	0.719375i	$-0.744428\pi$
$821$	−39.8061	−1.38924	−0.694622	+	0.719375i	$0.744428\pi$
$822$	−101.460	−3.53884
$823$	−15.5790	−0.543050	−0.271525	−	0.962431i	$-0.587528\pi$
$823$	−15.5790	−0.543050	−0.271525	+	0.962431i	$0.587528\pi$
$824$	−30.2003	−1.05208
$825$	−39.7866	−1.38519
$826$	53.0418	1.84556
$827$	29.5353	1.02704	0.513522	−	0.858076i	$-0.328340\pi$
$827$	29.5353	1.02704	0.513522	+	0.858076i	$0.328340\pi$
$828$	22.9964	0.799180
$829$	0.277913	0.00965233	0.00482616	−	0.999988i	$-0.498464\pi$
$829$	0.277913	0.00965233	0.00482616	+	0.999988i	$0.498464\pi$
$830$	5.40892	0.187746
$831$	12.5078	0.433892
$832$	20.6732	0.716714
$833$	−27.5864	−0.955811
$834$	157.703	5.46080
$835$	−75.3215	−2.60661
$836$	−11.5508	−0.399493
$837$	−109.097	−3.77095
$838$	−16.0568	−0.554674
$839$	46.6796	1.61156	0.805779	−	0.592216i	$-0.201747\pi$
$839$	46.6796	1.61156	0.805779	+	0.592216i	$0.201747\pi$
$840$	−60.1361	−2.07489
$841$	18.9707	0.654163
$842$	46.2120	1.59257
$843$	60.5392	2.08508
$844$	23.6142	0.812835
$845$	38.1984	1.31406
$846$	−172.379	−5.92653
$847$	−14.4994	−0.498204
$848$	−3.69680	−0.126949
$849$	66.6457	2.28727
$850$	−128.376	−4.40324
$851$	−2.60267	−0.0892184
$852$	−90.7855	−3.11026
$853$	−35.8235	−1.22657	−0.613287	−	0.789860i	$-0.710153\pi$
$853$	−35.8235	−1.22657	−0.613287	+	0.789860i	$0.710153\pi$
$854$	−43.8145	−1.49930
$855$	59.2845	2.02749
$856$	60.1642	2.05637
$857$	−15.5462	−0.531047	−0.265524	−	0.964104i	$-0.585545\pi$
$857$	−15.5462	−0.531047	−0.265524	+	0.964104i	$0.585545\pi$
$858$	−17.3559	−0.592520
$859$	−6.40678	−0.218597	−0.109298	−	0.994009i	$-0.534860\pi$
$859$	−6.40678	−0.218597	−0.109298	+	0.994009i	$0.534860\pi$
$860$	99.6935	3.39952
$861$	−0.997769	−0.0340039
$862$	−49.7615	−1.69488
$863$	−1.08754	−0.0370204	−0.0185102	−	0.999829i	$-0.505892\pi$
$863$	−1.08754	−0.0370204	−0.0185102	+	0.999829i	$0.505892\pi$
$864$	−59.1432	−2.01209
$865$	−74.7934	−2.54305
$866$	92.6750	3.14922
$867$	−74.2321	−2.52105
$868$	50.0938	1.70030
$869$	2.25911	0.0766350
$870$	−186.114	−6.30985
$871$	10.2390	0.346937
$872$	2.18522	0.0740009
$873$	−100.026	−3.38538
$874$	5.43832	0.183954
$875$	−22.3090	−0.754183
$876$	95.9075	3.24041
$877$	12.7651	0.431046	0.215523	−	0.976499i	$-0.430854\pi$
$877$	12.7651	0.431046	0.215523	+	0.976499i	$0.430854\pi$
$878$	67.5372	2.27927
$879$	91.6028	3.08969
$880$	−3.29230	−0.110984
$881$	32.2421	1.08626	0.543132	−	0.839648i	$-0.317238\pi$
$881$	32.2421	1.08626	0.543132	+	0.839648i	$0.317238\pi$
$882$	68.4176	2.30374
$883$	−25.3393	−0.852735	−0.426367	−	0.904550i	$-0.640207\pi$
$883$	−25.3393	−0.852735	−0.426367	+	0.904550i	$0.640207\pi$
$884$	−35.1374	−1.18180
$885$	−162.338	−5.45694
$886$	40.8627	1.37281
$887$	0.378305	0.0127022	0.00635112	−	0.999980i	$-0.497978\pi$
$887$	0.378305	0.0127022	0.00635112	+	0.999980i	$0.497978\pi$
$888$	−25.8674	−0.868054
$889$	−28.7531	−0.964349
$890$	−18.5346	−0.621280
$891$	25.0253	0.838378
$892$	−55.5734	−1.86073
$893$	−25.5781	−0.855937
$894$	84.6174	2.83003
$895$	−34.8230	−1.16400
$896$	31.7729	1.06146
$897$	5.12716	0.171191
$898$	12.6150	0.420967
$899$	62.9808	2.10053
$900$	199.771	6.65903
$901$	−38.7097	−1.28961
$902$	−0.658778	−0.0219349
$903$	41.0161	1.36493
$904$	−7.87269	−0.261842
$905$	−39.1968	−1.30295
$906$	−67.6396	−2.24717
$907$	−49.6725	−1.64935	−0.824675	−	0.565607i	$-0.808642\pi$
$907$	−49.6725	−1.64935	−0.824675	+	0.565607i	$0.808642\pi$
$908$	39.0040	1.29439
$909$	−115.772	−3.83992
$910$	−22.9289	−0.760087
$911$	1.71676	0.0568788	0.0284394	−	0.999596i	$-0.490946\pi$
$911$	1.71676	0.0568788	0.0284394	+	0.999596i	$0.490946\pi$
$912$	4.48182	0.148408
$913$	0.921901	0.0305105
$914$	−76.4567	−2.52896
$915$	134.097	4.43312
$916$	15.6779	0.518013
$917$	5.43111	0.179351
$918$	177.298	5.85170
$919$	40.2573	1.32796	0.663982	−	0.747748i	$-0.268865\pi$
$919$	40.2573	1.32796	0.663982	+	0.747748i	$0.268865\pi$
$920$	11.7294	0.386706
$921$	55.5558	1.83063
$922$	−85.2208	−2.80660
$923$	−14.0620	−0.462855
$924$	−25.2307	−0.830027
$925$	−22.6095	−0.743397
$926$	52.4346	1.72311
$927$	65.0330	2.13596
$928$	34.1428	1.12079
$929$	−53.0820	−1.74156	−0.870782	−	0.491669i	$-0.836387\pi$
$929$	−53.0820	−1.74156	−0.870782	+	0.491669i	$0.836387\pi$
$930$	−244.349	−8.01251
$931$	10.1520	0.332717
$932$	−3.74544	−0.122686
$933$	−3.25309	−0.106501
$934$	2.60752	0.0853208
$935$	−34.4742	−1.12743
$936$	35.4016	1.15714
$937$	19.8165	0.647376	0.323688	−	0.946164i	$-0.395077\pi$
$937$	19.8165	0.647376	0.323688	+	0.946164i	$0.395077\pi$
$938$	23.7227	0.774574
$939$	−19.4418	−0.634461
$940$	−135.799	−4.42927
$941$	−2.58321	−0.0842104	−0.0421052	−	0.999113i	$-0.513406\pi$
$941$	−2.58321	−0.0842104	−0.0421052	+	0.999113i	$0.513406\pi$
$942$	51.9880	1.69386
$943$	0.194612	0.00633743
$944$	−8.52603	−0.277499
$945$	72.5931	2.36145
$946$	27.0810	0.880478
$947$	33.3740	1.08451	0.542254	−	0.840214i	$-0.317571\pi$
$947$	33.3740	1.08451	0.542254	+	0.840214i	$0.317571\pi$
$948$	−16.3275	−0.530293
$949$	14.8553	0.482224
$950$	47.2430	1.53277
$951$	53.5344	1.73597
$952$	−33.0716	−1.07186
$953$	−9.46599	−0.306633	−0.153317	−	0.988177i	$-0.548995\pi$
$953$	−9.46599	−0.306633	−0.153317	+	0.988177i	$0.548995\pi$
$954$	96.0048	3.10827
$955$	−60.3010	−1.95129
$956$	−97.5179	−3.15396
$957$	−31.7214	−1.02541
$958$	−48.2593	−1.55919
$959$	−22.8459	−0.737732
$960$	−146.594	−4.73128
$961$	51.6875	1.66734
$962$	−9.86284	−0.317991
$963$	−129.557	−4.17491
$964$	−82.3236	−2.65146
$965$	−44.1722	−1.42195
$966$	11.8790	0.382202
$967$	29.4128	0.945852	0.472926	−	0.881102i	$-0.343198\pi$
$967$	29.4128	0.945852	0.472926	+	0.881102i	$0.343198\pi$
$968$	28.1075	0.903409
$969$	46.9297	1.50760
$970$	−125.588	−4.03239
$971$	−4.03704	−0.129555	−0.0647773	−	0.997900i	$-0.520634\pi$
$971$	−4.03704	−0.129555	−0.0647773	+	0.997900i	$0.520634\pi$
$972$	−59.6316	−1.91268
$973$	35.5100	1.13840
$974$	35.9194	1.15093
$975$	44.5399	1.42642
$976$	7.04281	0.225435
$977$	19.1715	0.613351	0.306676	−	0.951814i	$-0.400783\pi$
$977$	19.1715	0.613351	0.306676	+	0.951814i	$0.400783\pi$
$978$	−168.430	−5.38580
$979$	−3.15905	−0.100964
$980$	53.8987	1.72173
$981$	−4.70562	−0.150239
$982$	1.52509	0.0486675
$983$	43.7056	1.39399	0.696996	−	0.717075i	$-0.254519\pi$
$983$	43.7056	1.39399	0.696996	+	0.717075i	$0.254519\pi$
$984$	1.93421	0.0616603
$985$	−61.0493	−1.94519
$986$	−102.352	−3.25956
$987$	−55.8707	−1.77838
$988$	12.9308	0.411383
$989$	−8.00007	−0.254387
$990$	85.5001	2.71737
$991$	−29.7368	−0.944622	−0.472311	−	0.881432i	$-0.656580\pi$
$991$	−29.7368	−0.944622	−0.472311	+	0.881432i	$0.656580\pi$
$992$	44.8261	1.42323
$993$	−50.9700	−1.61748
$994$	−32.5800	−1.03337
$995$	−48.9897	−1.55308
$996$	−6.66296	−0.211124
$997$	34.1468	1.08144	0.540720	−	0.841202i	$-0.318152\pi$
$997$	34.1468	1.08144	0.540720	+	0.841202i	$0.318152\pi$
$998$	−26.9395	−0.852754
$999$	31.2258	0.987939

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8027.2.a.c.1.18	✓	143

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8027.2.a.c.1.18	✓	143	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:	\( N \)	\(=\)	\( 8027 = 23 \cdot 349 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8027.a (trivial)

\(f(q)\)	\(=\)	\(q-2.31697 q^{2} -3.13483 q^{3} +3.36836 q^{4} -3.69960 q^{5} +7.26332 q^{6} +1.63548 q^{7} -3.17044 q^{8} +6.82718 q^{9} +O(q^{10})\)	\(q-2.31697 q^{2} -3.13483 q^{3} +3.36836 q^{4} -3.69960 q^{5} +7.26332 q^{6} +1.63548 q^{7} -3.17044 q^{8} +6.82718 q^{9} +8.57187 q^{10} +1.46100 q^{11} -10.5592 q^{12} -1.63554 q^{13} -3.78937 q^{14} +11.5976 q^{15} +0.609109 q^{16} +6.37807 q^{17} -15.8184 q^{18} -2.34717 q^{19} -12.4616 q^{20} -5.12697 q^{21} -3.38509 q^{22} +1.00000 q^{23} +9.93881 q^{24} +8.68705 q^{25} +3.78951 q^{26} -11.9976 q^{27} +5.50889 q^{28} +6.92609 q^{29} -26.8714 q^{30} +9.09327 q^{31} +4.92959 q^{32} -4.57999 q^{33} -14.7778 q^{34} -6.05064 q^{35} +22.9964 q^{36} -2.60267 q^{37} +5.43832 q^{38} +5.12716 q^{39} +11.7294 q^{40} +0.194612 q^{41} +11.8790 q^{42} -8.00007 q^{43} +4.92116 q^{44} -25.2579 q^{45} -2.31697 q^{46} +10.8974 q^{47} -1.90946 q^{48} -4.32519 q^{49} -20.1277 q^{50} -19.9942 q^{51} -5.50909 q^{52} -6.06919 q^{53} +27.7981 q^{54} -5.40511 q^{55} -5.18521 q^{56} +7.35799 q^{57} -16.0476 q^{58} -13.9975 q^{59} +39.0650 q^{60} +11.5625 q^{61} -21.0688 q^{62} +11.1658 q^{63} -12.6399 q^{64} +6.05086 q^{65} +10.6117 q^{66} -6.26033 q^{67} +21.4836 q^{68} -3.13483 q^{69} +14.0192 q^{70} +8.59773 q^{71} -21.6452 q^{72} -9.08281 q^{73} +6.03031 q^{74} -27.2325 q^{75} -7.90610 q^{76} +2.38944 q^{77} -11.8795 q^{78} +1.54628 q^{79} -2.25346 q^{80} +17.1289 q^{81} -0.450910 q^{82} +0.631008 q^{83} -17.2695 q^{84} -23.5963 q^{85} +18.5359 q^{86} -21.7121 q^{87} -4.63201 q^{88} -2.16226 q^{89} +58.5217 q^{90} -2.67491 q^{91} +3.36836 q^{92} -28.5059 q^{93} -25.2490 q^{94} +8.68359 q^{95} -15.4535 q^{96} -14.6512 q^{97} +10.0213 q^{98} +9.97450 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 143 q - 17 q^{2} - 17 q^{3} + 121 q^{4} - 22 q^{5} - 11 q^{6} - 33 q^{7} - 45 q^{8} + 104 q^{9}+O(q^{10}) \) 143 * q - 17 * q^2 - 17 * q^3 + 121 * q^4 - 22 * q^5 - 11 * q^6 - 33 * q^7 - 45 * q^8 + 104 * q^9	\( 143 q - 17 q^{2} - 17 q^{3} + 121 q^{4} - 22 q^{5} - 11 q^{6} - 33 q^{7} - 45 q^{8} + 104 q^{9} - 22 q^{10} - 14 q^{11} - 36 q^{12} - 87 q^{13} - 18 q^{14} - 19 q^{15} + 81 q^{16} - 14 q^{17} - 60 q^{18} - 18 q^{19} - 25 q^{20} - 26 q^{21} - 62 q^{22} + 143 q^{23} - 21 q^{24} + 67 q^{25} - 5 q^{26} - 47 q^{27} - 76 q^{28} - 54 q^{29} - 22 q^{30} - 62 q^{31} - 117 q^{32} - 59 q^{33} - 35 q^{34} - 52 q^{35} + 52 q^{36} - 190 q^{37} - 19 q^{38} - 43 q^{39} - 41 q^{40} - 50 q^{41} + 8 q^{42} - 50 q^{43} - 18 q^{44} - 75 q^{45} - 17 q^{46} - 63 q^{47} - 35 q^{48} + 74 q^{49} - 53 q^{50} - 33 q^{51} - 124 q^{52} - 100 q^{53} - 46 q^{54} - 61 q^{55} - 3 q^{56} - 80 q^{57} - 112 q^{58} - 109 q^{59} - 55 q^{60} - 76 q^{61} - 6 q^{62} - 93 q^{63} + 57 q^{64} - 17 q^{65} + 50 q^{66} - 120 q^{67} + 26 q^{68} - 17 q^{69} - 109 q^{71} - 153 q^{72} - 94 q^{73} + 35 q^{74} - 105 q^{75} - 16 q^{76} - 52 q^{77} - 59 q^{78} - 29 q^{79} - 30 q^{80} + 39 q^{81} - 65 q^{82} + 8 q^{83} + 11 q^{84} - 155 q^{85} - 15 q^{86} - 25 q^{87} - 139 q^{88} + 6 q^{89} + 82 q^{90} - 34 q^{91} + 121 q^{92} - 151 q^{93} - 3 q^{94} - 70 q^{95} - 23 q^{96} - 203 q^{97} - 18 q^{98} - 49 q^{99}+O(q^{100}) \) 143 * q - 17 * q^2 - 17 * q^3 + 121 * q^4 - 22 * q^5 - 11 * q^6 - 33 * q^7 - 45 * q^8 + 104 * q^9 - 22 * q^10 - 14 * q^11 - 36 * q^12 - 87 * q^13 - 18 * q^14 - 19 * q^15 + 81 * q^16 - 14 * q^17 - 60 * q^18 - 18 * q^19 - 25 * q^20 - 26 * q^21 - 62 * q^22 + 143 * q^23 - 21 * q^24 + 67 * q^25 - 5 * q^26 - 47 * q^27 - 76 * q^28 - 54 * q^29 - 22 * q^30 - 62 * q^31 - 117 * q^32 - 59 * q^33 - 35 * q^34 - 52 * q^35 + 52 * q^36 - 190 * q^37 - 19 * q^38 - 43 * q^39 - 41 * q^40 - 50 * q^41 + 8 * q^42 - 50 * q^43 - 18 * q^44 - 75 * q^45 - 17 * q^46 - 63 * q^47 - 35 * q^48 + 74 * q^49 - 53 * q^50 - 33 * q^51 - 124 * q^52 - 100 * q^53 - 46 * q^54 - 61 * q^55 - 3 * q^56 - 80 * q^57 - 112 * q^58 - 109 * q^59 - 55 * q^60 - 76 * q^61 - 6 * q^62 - 93 * q^63 + 57 * q^64 - 17 * q^65 + 50 * q^66 - 120 * q^67 + 26 * q^68 - 17 * q^69 - 109 * q^71 - 153 * q^72 - 94 * q^73 + 35 * q^74 - 105 * q^75 - 16 * q^76 - 52 * q^77 - 59 * q^78 - 29 * q^79 - 30 * q^80 + 39 * q^81 - 65 * q^82 + 8 * q^83 + 11 * q^84 - 155 * q^85 - 15 * q^86 - 25 * q^87 - 139 * q^88 + 6 * q^89 + 82 * q^90 - 34 * q^91 + 121 * q^92 - 151 * q^93 - 3 * q^94 - 70 * q^95 - 23 * q^96 - 203 * q^97 - 18 * q^98 - 49 * q^99

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