LMFDB - Embedded newform 8018.2.a.f.1.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8018,2,Mod(1,8018)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8018, 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("8018.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8018 = 2 \cdot 19 \cdot 211 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8018.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:	$64.0240523407$
Analytic rank:	$1$
Dimension:	$34$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.6
Character	$\chi$	$=$	8018.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -2.52151 q^{3} +1.00000 q^{4} -1.30481 q^{5} +2.52151 q^{6} +0.799571 q^{7} -1.00000 q^{8} +3.35801 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -2.52151 q^{3} +1.00000 q^{4} -1.30481 q^{5} +2.52151 q^{6} +0.799571 q^{7} -1.00000 q^{8} +3.35801 q^{9} +1.30481 q^{10} -2.77863 q^{11} -2.52151 q^{12} +3.89576 q^{13} -0.799571 q^{14} +3.29008 q^{15} +1.00000 q^{16} +7.65293 q^{17} -3.35801 q^{18} -1.00000 q^{19} -1.30481 q^{20} -2.01613 q^{21} +2.77863 q^{22} -0.364205 q^{23} +2.52151 q^{24} -3.29748 q^{25} -3.89576 q^{26} -0.902726 q^{27} +0.799571 q^{28} +1.06453 q^{29} -3.29008 q^{30} -6.08375 q^{31} -1.00000 q^{32} +7.00634 q^{33} -7.65293 q^{34} -1.04329 q^{35} +3.35801 q^{36} -0.605400 q^{37} +1.00000 q^{38} -9.82319 q^{39} +1.30481 q^{40} -6.71543 q^{41} +2.01613 q^{42} -8.72098 q^{43} -2.77863 q^{44} -4.38156 q^{45} +0.364205 q^{46} +4.28942 q^{47} -2.52151 q^{48} -6.36069 q^{49} +3.29748 q^{50} -19.2969 q^{51} +3.89576 q^{52} +4.28026 q^{53} +0.902726 q^{54} +3.62558 q^{55} -0.799571 q^{56} +2.52151 q^{57} -1.06453 q^{58} +3.47311 q^{59} +3.29008 q^{60} +0.0120131 q^{61} +6.08375 q^{62} +2.68497 q^{63} +1.00000 q^{64} -5.08322 q^{65} -7.00634 q^{66} +7.73505 q^{67} +7.65293 q^{68} +0.918346 q^{69} +1.04329 q^{70} +1.35383 q^{71} -3.35801 q^{72} +14.5653 q^{73} +0.605400 q^{74} +8.31462 q^{75} -1.00000 q^{76} -2.22171 q^{77} +9.82319 q^{78} -5.61430 q^{79} -1.30481 q^{80} -7.79780 q^{81} +6.71543 q^{82} -11.4959 q^{83} -2.01613 q^{84} -9.98560 q^{85} +8.72098 q^{86} -2.68422 q^{87} +2.77863 q^{88} -14.4300 q^{89} +4.38156 q^{90} +3.11493 q^{91} -0.364205 q^{92} +15.3402 q^{93} -4.28942 q^{94} +1.30481 q^{95} +2.52151 q^{96} -5.00978 q^{97} +6.36069 q^{98} -9.33067 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 34 q - 34 q^{2} - 10 q^{3} + 34 q^{4} + 7 q^{5} + 10 q^{6} - 6 q^{7} - 34 q^{8} + 38 q^{9}+O(q^{10}) $ 34 * q - 34 * q^2 - 10 * q^3 + 34 * q^4 + 7 * q^5 + 10 * q^6 - 6 * q^7 - 34 * q^8 + 38 * q^9	\( 34 q - 34 q^{2} - 10 q^{3} + 34 q^{4} + 7 q^{5} + 10 q^{6} - 6 q^{7} - 34 q^{8} + 38 q^{9} - 7 q^{10} + 4 q^{11} - 10 q^{12} - 5 q^{13} + 6 q^{14} - 17 q^{15} + 34 q^{16} + 8 q^{17} - 38 q^{18} - 34 q^{19} + 7 q^{20} - 4 q^{22} - 24 q^{23} + 10 q^{24} + 5 q^{25} + 5 q^{26} - 31 q^{27} - 6 q^{28} + 24 q^{29} + 17 q^{30} - 28 q^{31} - 34 q^{32} - 16 q^{33} - 8 q^{34} + 2 q^{35} + 38 q^{36} - 36 q^{37} + 34 q^{38} - 9 q^{39} - 7 q^{40} + 9 q^{41} - 24 q^{43} + 4 q^{44} + 22 q^{45} + 24 q^{46} - 29 q^{47} - 10 q^{48} + 22 q^{49} - 5 q^{50} - 21 q^{51} - 5 q^{52} - 9 q^{53} + 31 q^{54} - 28 q^{55} + 6 q^{56} + 10 q^{57} - 24 q^{58} - 28 q^{59} - 17 q^{60} + 23 q^{61} + 28 q^{62} - 27 q^{63} + 34 q^{64} - 6 q^{65} + 16 q^{66} - 51 q^{67} + 8 q^{68} - 17 q^{69} - 2 q^{70} - 31 q^{71} - 38 q^{72} - 26 q^{73} + 36 q^{74} - 109 q^{75} - 34 q^{76} - 28 q^{77} + 9 q^{78} - 36 q^{79} + 7 q^{80} + 6 q^{81} - 9 q^{82} - 10 q^{83} - 32 q^{85} + 24 q^{86} - 8 q^{87} - 4 q^{88} - 34 q^{89} - 22 q^{90} - 41 q^{91} - 24 q^{92} - 33 q^{93} + 29 q^{94} - 7 q^{95} + 10 q^{96} - 56 q^{97} - 22 q^{98} - 28 q^{99}+O(q^{100}) \) 34 * q - 34 * q^2 - 10 * q^3 + 34 * q^4 + 7 * q^5 + 10 * q^6 - 6 * q^7 - 34 * q^8 + 38 * q^9 - 7 * q^10 + 4 * q^11 - 10 * q^12 - 5 * q^13 + 6 * q^14 - 17 * q^15 + 34 * q^16 + 8 * q^17 - 38 * q^18 - 34 * q^19 + 7 * q^20 - 4 * q^22 - 24 * q^23 + 10 * q^24 + 5 * q^25 + 5 * q^26 - 31 * q^27 - 6 * q^28 + 24 * q^29 + 17 * q^30 - 28 * q^31 - 34 * q^32 - 16 * q^33 - 8 * q^34 + 2 * q^35 + 38 * q^36 - 36 * q^37 + 34 * q^38 - 9 * q^39 - 7 * q^40 + 9 * q^41 - 24 * q^43 + 4 * q^44 + 22 * q^45 + 24 * q^46 - 29 * q^47 - 10 * q^48 + 22 * q^49 - 5 * q^50 - 21 * q^51 - 5 * q^52 - 9 * q^53 + 31 * q^54 - 28 * q^55 + 6 * q^56 + 10 * q^57 - 24 * q^58 - 28 * q^59 - 17 * q^60 + 23 * q^61 + 28 * q^62 - 27 * q^63 + 34 * q^64 - 6 * q^65 + 16 * q^66 - 51 * q^67 + 8 * q^68 - 17 * q^69 - 2 * q^70 - 31 * q^71 - 38 * q^72 - 26 * q^73 + 36 * q^74 - 109 * q^75 - 34 * q^76 - 28 * q^77 + 9 * q^78 - 36 * q^79 + 7 * q^80 + 6 * q^81 - 9 * q^82 - 10 * q^83 - 32 * q^85 + 24 * q^86 - 8 * q^87 - 4 * q^88 - 34 * q^89 - 22 * q^90 - 41 * q^91 - 24 * q^92 - 33 * q^93 + 29 * q^94 - 7 * q^95 + 10 * q^96 - 56 * q^97 - 22 * 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 $

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	−2.52151	−1.45579	−0.727897	−	0.685686i	$-0.759502\pi$
$3$	−2.52151	−1.45579	−0.727897	+	0.685686i	$0.759502\pi$
$4$	1.00000	0.500000
$5$	−1.30481	−0.583528	−0.291764	−	0.956490i	$-0.594242\pi$
$5$	−1.30481	−0.583528	−0.291764	+	0.956490i	$0.594242\pi$
$6$	2.52151	1.02940
$7$	0.799571	0.302209	0.151105	−	0.988518i	$-0.451717\pi$
$7$	0.799571	0.302209	0.151105	+	0.988518i	$0.451717\pi$
$8$	−1.00000	−0.353553
$9$	3.35801	1.11934
$10$	1.30481	0.412616
$11$	−2.77863	−0.837788	−0.418894	−	0.908035i	$-0.637582\pi$
$11$	−2.77863	−0.837788	−0.418894	+	0.908035i	$0.637582\pi$
$12$	−2.52151	−0.727897
$13$	3.89576	1.08049	0.540245	−	0.841508i	$-0.318332\pi$
$13$	3.89576	1.08049	0.540245	+	0.841508i	$0.318332\pi$
$14$	−0.799571	−0.213694
$15$	3.29008	0.849496
$16$	1.00000	0.250000
$17$	7.65293	1.85611	0.928054	−	0.372446i	$-0.121481\pi$
$17$	7.65293	1.85611	0.928054	+	0.372446i	$0.121481\pi$
$18$	−3.35801	−0.791491
$19$	−1.00000	−0.229416
$19$	−1.00000	−0.229416
$20$	−1.30481	−0.291764
$21$	−2.01613	−0.439955
$22$	2.77863	0.592406
$23$	−0.364205	−0.0759420	−0.0379710	−	0.999279i	$-0.512089\pi$
$23$	−0.364205	−0.0759420	−0.0379710	+	0.999279i	$0.512089\pi$
$24$	2.52151	0.514701
$25$	−3.29748	−0.659495
$26$	−3.89576	−0.764021
$27$	−0.902726	−0.173730
$28$	0.799571	0.151105
$29$	1.06453	0.197678	0.0988391	−	0.995103i	$-0.468487\pi$
$29$	1.06453	0.197678	0.0988391	+	0.995103i	$0.468487\pi$
$30$	−3.29008	−0.600685
$31$	−6.08375	−1.09267	−0.546337	−	0.837565i	$-0.683978\pi$
$31$	−6.08375	−1.09267	−0.546337	+	0.837565i	$0.683978\pi$
$32$	−1.00000	−0.176777
$33$	7.00634	1.21965
$34$	−7.65293	−1.31247
$35$	−1.04329	−0.176348
$36$	3.35801	0.559668
$37$	−0.605400	−0.0995272	−0.0497636	−	0.998761i	$-0.515847\pi$
$37$	−0.605400	−0.0995272	−0.0497636	+	0.998761i	$0.515847\pi$
$38$	1.00000	0.162221
$39$	−9.82319	−1.57297
$40$	1.30481	0.206308
$41$	−6.71543	−1.04877	−0.524387	−	0.851480i	$-0.675706\pi$
$41$	−6.71543	−1.04877	−0.524387	+	0.851480i	$0.675706\pi$
$42$	2.01613	0.311095
$43$	−8.72098	−1.32994	−0.664968	−	0.746872i	$-0.731555\pi$
$43$	−8.72098	−1.32994	−0.664968	+	0.746872i	$0.731555\pi$
$44$	−2.77863	−0.418894
$45$	−4.38156	−0.653164
$46$	0.364205	0.0536991
$47$	4.28942	0.625677	0.312838	−	0.949806i	$-0.398720\pi$
$47$	4.28942	0.625677	0.312838	+	0.949806i	$0.398720\pi$
$48$	−2.52151	−0.363949
$49$	−6.36069	−0.908670
$50$	3.29748	0.466334
$51$	−19.2969	−2.70211
$52$	3.89576	0.540245
$53$	4.28026	0.587938	0.293969	−	0.955815i	$-0.405024\pi$
$53$	4.28026	0.587938	0.293969	+	0.955815i	$0.405024\pi$
$54$	0.902726	0.122845
$55$	3.62558	0.488873
$56$	−0.799571	−0.106847
$57$	2.52151	0.333982
$58$	−1.06453	−0.139780
$59$	3.47311	0.452160	0.226080	−	0.974109i	$-0.427409\pi$
$59$	3.47311	0.452160	0.226080	+	0.974109i	$0.427409\pi$
$60$	3.29008	0.424748
$61$	0.0120131	0.00153812	0.000769059	−	1.00000i	$-0.499755\pi$
$61$	0.0120131	0.00153812	0.000769059		1.00000i	$0.499755\pi$
$62$	6.08375	0.772637
$63$	2.68497	0.338274
$64$	1.00000	0.125000
$65$	−5.08322	−0.630495
$66$	−7.00634	−0.862421
$67$	7.73505	0.944987	0.472494	−	0.881334i	$-0.343354\pi$
$67$	7.73505	0.944987	0.472494	+	0.881334i	$0.343354\pi$
$68$	7.65293	0.928054
$69$	0.918346	0.110556
$70$	1.04329	0.124697
$71$	1.35383	0.160671	0.0803353	−	0.996768i	$-0.474401\pi$
$71$	1.35383	0.160671	0.0803353	+	0.996768i	$0.474401\pi$
$72$	−3.35801	−0.395745
$73$	14.5653	1.70474	0.852368	−	0.522943i	$-0.175166\pi$
$73$	14.5653	1.70474	0.852368	+	0.522943i	$0.175166\pi$
$74$	0.605400	0.0703763
$75$	8.31462	0.960090
$76$	−1.00000	−0.114708
$77$	−2.22171	−0.253187
$78$	9.82319	1.11226
$79$	−5.61430	−0.631659	−0.315829	−	0.948816i	$-0.602283\pi$
$79$	−5.61430	−0.631659	−0.315829	+	0.948816i	$0.602283\pi$
$80$	−1.30481	−0.145882
$81$	−7.79780	−0.866422
$82$	6.71543	0.741595
$83$	−11.4959	−1.26184	−0.630919	−	0.775848i	$-0.717322\pi$
$83$	−11.4959	−1.26184	−0.630919	+	0.775848i	$0.717322\pi$
$84$	−2.01613	−0.219977
$85$	−9.98560	−1.08309
$86$	8.72098	0.940407
$87$	−2.68422	−0.287779
$88$	2.77863	0.296203
$89$	−14.4300	−1.52958	−0.764791	−	0.644279i	$-0.777158\pi$
$89$	−14.4300	−1.52958	−0.764791	+	0.644279i	$0.777158\pi$
$90$	4.38156	0.461857
$91$	3.11493	0.326534
$92$	−0.364205	−0.0379710
$93$	15.3402	1.59071
$94$	−4.28942	−0.442420
$95$	1.30481	0.133870
$96$	2.52151	0.257350
$97$	−5.00978	−0.508666	−0.254333	−	0.967117i	$-0.581856\pi$
$97$	−5.00978	−0.508666	−0.254333	+	0.967117i	$0.581856\pi$
$98$	6.36069	0.642526
$99$	−9.33067	−0.937767
$100$	−3.29748	−0.329748
$101$	9.81176	0.976306	0.488153	−	0.872758i	$-0.337671\pi$
$101$	9.81176	0.976306	0.488153	+	0.872758i	$0.337671\pi$
$102$	19.2969	1.91068
$103$	−7.28866	−0.718173	−0.359087	−	0.933304i	$-0.616912\pi$
$103$	−7.28866	−0.718173	−0.359087	+	0.933304i	$0.616912\pi$
$104$	−3.89576	−0.382011
$105$	2.63066	0.256726
$106$	−4.28026	−0.415735
$107$	2.44780	0.236637	0.118319	−	0.992976i	$-0.462250\pi$
$107$	2.44780	0.236637	0.118319	+	0.992976i	$0.462250\pi$
$108$	−0.902726	−0.0868649
$109$	19.9143	1.90745	0.953724	−	0.300682i	$-0.0972144\pi$
$109$	19.9143	1.90745	0.953724	+	0.300682i	$0.0972144\pi$
$110$	−3.62558	−0.345685
$111$	1.52652	0.144891
$112$	0.799571	0.0755523
$113$	7.64216	0.718913	0.359457	−	0.933162i	$-0.382962\pi$
$113$	7.64216	0.718913	0.359457	+	0.933162i	$0.382962\pi$
$114$	−2.52151	−0.236161
$115$	0.475217	0.0443142
$116$	1.06453	0.0988391
$117$	13.0820	1.20943
$118$	−3.47311	−0.319726
$119$	6.11906	0.560933
$120$	−3.29008	−0.300342
$121$	−3.27922	−0.298111
$122$	−0.0120131	−0.00108761
$123$	16.9330	1.52680
$124$	−6.08375	−0.546337
$125$	10.8266	0.968362
$126$	−2.68497	−0.239196
$127$	5.82058	0.516493	0.258247	−	0.966079i	$-0.416855\pi$
$127$	5.82058	0.516493	0.258247	+	0.966079i	$0.416855\pi$
$128$	−1.00000	−0.0883883
$129$	21.9900	1.93611
$130$	5.08322	0.445827
$131$	12.9111	1.12805	0.564025	−	0.825757i	$-0.309252\pi$
$131$	12.9111	1.12805	0.564025	+	0.825757i	$0.309252\pi$
$132$	7.00634	0.609824
$133$	−0.799571	−0.0693316
$134$	−7.73505	−0.668207
$135$	1.17788	0.101376
$136$	−7.65293	−0.656233
$137$	7.54807	0.644875	0.322438	−	0.946591i	$-0.395498\pi$
$137$	7.54807	0.644875	0.322438	+	0.946591i	$0.395498\pi$
$138$	−0.918346	−0.0781748
$139$	−7.83970	−0.664955	−0.332477	−	0.943111i	$-0.607885\pi$
$139$	−7.83970	−0.664955	−0.332477	+	0.943111i	$0.607885\pi$
$140$	−1.04329	−0.0881738
$141$	−10.8158	−0.910856
$142$	−1.35383	−0.113611
$143$	−10.8249	−0.905221
$144$	3.35801	0.279834
$145$	−1.38901	−0.115351
$146$	−14.5653	−1.20543
$147$	16.0385	1.32284
$148$	−0.605400	−0.0497636
$149$	19.3930	1.58874	0.794368	−	0.607437i	$-0.207802\pi$
$149$	19.3930	1.58874	0.794368	+	0.607437i	$0.207802\pi$
$150$	−8.31462	−0.678886
$151$	3.42356	0.278605	0.139303	−	0.990250i	$-0.455514\pi$
$151$	3.42356	0.278605	0.139303	+	0.990250i	$0.455514\pi$
$152$	1.00000	0.0811107
$153$	25.6986	2.07761
$154$	2.22171	0.179031
$155$	7.93813	0.637606
$156$	−9.82319	−0.786485
$157$	−11.5698	−0.923371	−0.461686	−	0.887044i	$-0.652755\pi$
$157$	−11.5698	−0.923371	−0.461686	+	0.887044i	$0.652755\pi$
$158$	5.61430	0.446650
$159$	−10.7927	−0.855917
$160$	1.30481	0.103154
$161$	−0.291208	−0.0229504
$162$	7.79780	0.612653
$163$	−1.05270	−0.0824536	−0.0412268	−	0.999150i	$-0.513127\pi$
$163$	−1.05270	−0.0824536	−0.0412268	+	0.999150i	$0.513127\pi$
$164$	−6.71543	−0.524387
$165$	−9.14193	−0.711698
$166$	11.4959	0.892255
$167$	−20.7095	−1.60255	−0.801275	−	0.598297i	$-0.795844\pi$
$167$	−20.7095	−1.60255	−0.801275	+	0.598297i	$0.795844\pi$
$168$	2.01613	0.155547
$169$	2.17694	0.167457
$170$	9.98560	0.765861
$171$	−3.35801	−0.256793
$172$	−8.72098	−0.664968
$173$	−11.1231	−0.845677	−0.422839	−	0.906205i	$-0.638966\pi$
$173$	−11.1231	−0.845677	−0.422839	+	0.906205i	$0.638966\pi$
$174$	2.68422	0.203490
$175$	−2.63657	−0.199306
$176$	−2.77863	−0.209447
$177$	−8.75748	−0.658252
$178$	14.4300	1.08158
$179$	−18.2322	−1.36274	−0.681371	−	0.731939i	$-0.738616\pi$
$179$	−18.2322	−1.36274	−0.681371	+	0.731939i	$0.738616\pi$
$180$	−4.38156	−0.326582
$181$	2.80685	0.208631	0.104316	−	0.994544i	$-0.466735\pi$
$181$	2.80685	0.208631	0.104316	+	0.994544i	$0.466735\pi$
$182$	−3.11493	−0.230894
$183$	−0.0302911	−0.00223918
$184$	0.364205	0.0268495
$185$	0.789931	0.0580768
$186$	−15.3402	−1.12480
$187$	−21.2647	−1.55503
$188$	4.28942	0.312838
$189$	−0.721793	−0.0525027
$190$	−1.30481	−0.0946607
$191$	−7.64346	−0.553061	−0.276531	−	0.961005i	$-0.589185\pi$
$191$	−7.64346	−0.553061	−0.276531	+	0.961005i	$0.589185\pi$
$192$	−2.52151	−0.181974
$193$	16.5009	1.18776	0.593879	−	0.804554i	$-0.297596\pi$
$193$	16.5009	1.18776	0.593879	+	0.804554i	$0.297596\pi$
$194$	5.00978	0.359681
$195$	12.8174	0.917871
$196$	−6.36069	−0.454335
$197$	3.98120	0.283648	0.141824	−	0.989892i	$-0.454703\pi$
$197$	3.98120	0.283648	0.141824	+	0.989892i	$0.454703\pi$
$198$	9.33067	0.663102
$199$	5.48861	0.389077	0.194538	−	0.980895i	$-0.437679\pi$
$199$	5.48861	0.389077	0.194538	+	0.980895i	$0.437679\pi$
$200$	3.29748	0.233167
$201$	−19.5040	−1.37571
$202$	−9.81176	−0.690353
$203$	0.851167	0.0597402
$204$	−19.2969	−1.35106
$205$	8.76235	0.611989
$206$	7.28866	0.507825
$207$	−1.22300	−0.0850046
$208$	3.89576	0.270122
$209$	2.77863	0.192202
$210$	−2.63066	−0.181532
$211$	−1.00000	−0.0688428
$211$	−1.00000	−0.0688428
$212$	4.28026	0.293969
$213$	−3.41371	−0.233903
$214$	−2.44780	−0.167328
$215$	11.3792	0.776055
$216$	0.902726	0.0614227
$217$	−4.86439	−0.330216
$218$	−19.9143	−1.34877
$219$	−36.7265	−2.48174
$220$	3.62558	0.244436
$221$	29.8140	2.00550
$222$	−1.52652	−0.102453
$223$	−6.84314	−0.458251	−0.229125	−	0.973397i	$-0.573587\pi$
$223$	−6.84314	−0.458251	−0.229125	+	0.973397i	$0.573587\pi$
$224$	−0.799571	−0.0534236
$225$	−11.0730	−0.738198
$226$	−7.64216	−0.508349
$227$	3.01964	0.200421	0.100210	−	0.994966i	$-0.468048\pi$
$227$	3.01964	0.200421	0.100210	+	0.994966i	$0.468048\pi$
$228$	2.52151	0.166991
$229$	17.5925	1.16255	0.581273	−	0.813709i	$-0.302555\pi$
$229$	17.5925	1.16255	0.581273	+	0.813709i	$0.302555\pi$
$230$	−0.475217	−0.0313349
$231$	5.60207	0.368589
$232$	−1.06453	−0.0698898
$233$	18.3348	1.20115	0.600576	−	0.799568i	$-0.294938\pi$
$233$	18.3348	1.20115	0.600576	+	0.799568i	$0.294938\pi$
$234$	−13.0820	−0.855197
$235$	−5.59687	−0.365100
$236$	3.47311	0.226080
$237$	14.1565	0.919565
$238$	−6.11906	−0.396640
$239$	22.9250	1.48290	0.741449	−	0.671010i	$-0.234139\pi$
$239$	22.9250	1.48290	0.741449	+	0.671010i	$0.234139\pi$
$240$	3.29008	0.212374
$241$	−28.4679	−1.83378	−0.916890	−	0.399141i	$-0.869308\pi$
$241$	−28.4679	−1.83378	−0.916890	+	0.399141i	$0.869308\pi$
$242$	3.27922	0.210796
$243$	22.3704	1.43506
$244$	0.0120131	0.000769059 0
$245$	8.29947	0.530234
$246$	−16.9330	−1.07961
$247$	−3.89576	−0.247881
$248$	6.08375	0.386319
$249$	28.9870	1.83698
$250$	−10.8266	−0.684735
$251$	1.11181	0.0701770	0.0350885	−	0.999384i	$-0.488829\pi$
$251$	1.11181	0.0701770	0.0350885	+	0.999384i	$0.488829\pi$
$252$	2.68497	0.169137
$253$	1.01199	0.0636233
$254$	−5.82058	−0.365216
$255$	25.1788	1.57676
$256$	1.00000	0.0625000
$257$	2.54796	0.158937	0.0794686	−	0.996837i	$-0.474678\pi$
$257$	2.54796	0.158937	0.0794686	+	0.996837i	$0.474678\pi$
$258$	−21.9900	−1.36904
$259$	−0.484060	−0.0300780
$260$	−5.08322	−0.315248
$261$	3.57470	0.221268
$262$	−12.9111	−0.797652
$263$	−8.20479	−0.505929	−0.252964	−	0.967476i	$-0.581406\pi$
$263$	−8.20479	−0.505929	−0.252964	+	0.967476i	$0.581406\pi$
$264$	−7.00634	−0.431211
$265$	−5.58491	−0.343078
$266$	0.799571	0.0490248
$267$	36.3855	2.22676
$268$	7.73505	0.472494
$269$	−4.08601	−0.249129	−0.124564	−	0.992212i	$-0.539753\pi$
$269$	−4.08601	−0.249129	−0.124564	+	0.992212i	$0.539753\pi$
$270$	−1.17788	−0.0716837
$271$	10.9546	0.665442	0.332721	−	0.943025i	$-0.392033\pi$
$271$	10.9546	0.665442	0.332721	+	0.943025i	$0.392033\pi$
$272$	7.65293	0.464027
$273$	−7.85434	−0.475366
$274$	−7.54807	−0.455996
$275$	9.16247	0.552518
$276$	0.918346	0.0552779
$277$	−12.7817	−0.767979	−0.383990	−	0.923337i	$-0.625450\pi$
$277$	−12.7817	−0.767979	−0.383990	+	0.923337i	$0.625450\pi$
$278$	7.83970	0.470194
$279$	−20.4293	−1.22307
$280$	1.04329	0.0623483
$281$	−11.1853	−0.667261	−0.333631	−	0.942704i	$-0.608274\pi$
$281$	−11.1853	−0.667261	−0.333631	+	0.942704i	$0.608274\pi$
$282$	10.8158	0.644073
$283$	−23.3188	−1.38616	−0.693080	−	0.720861i	$-0.743747\pi$
$283$	−23.3188	−1.38616	−0.693080	+	0.720861i	$0.743747\pi$
$284$	1.35383	0.0803353
$285$	−3.29008	−0.194888
$286$	10.8249	0.640088
$287$	−5.36946	−0.316949
$288$	−3.35801	−0.197873
$289$	41.5673	2.44514
$290$	1.38901	0.0815653
$291$	12.6322	0.740513
$292$	14.5653	0.852368
$293$	31.1003	1.81690	0.908448	−	0.417997i	$-0.137268\pi$
$293$	31.1003	1.81690	0.908448	+	0.417997i	$0.137268\pi$
$294$	−16.0385	−0.935386
$295$	−4.53174	−0.263848
$296$	0.605400	0.0351882
$297$	2.50834	0.145549
$298$	−19.3930	−1.12341
$299$	−1.41885	−0.0820545
$300$	8.31462	0.480045
$301$	−6.97304	−0.401919
$302$	−3.42356	−0.197004
$303$	−24.7404	−1.42130
$304$	−1.00000	−0.0573539
$305$	−0.0156748	−0.000897534 0
$306$	−25.6986	−1.46909
$307$	−0.0218889	−0.00124927	−0.000624634	−	1.00000i	$-0.500199\pi$
$307$	−0.0218889	−0.00124927	−0.000624634		1.00000i	$0.500199\pi$
$308$	−2.22171	−0.126594
$309$	18.3784	1.04551
$310$	−7.93813	−0.450855
$311$	13.2602	0.751915	0.375958	−	0.926637i	$-0.377314\pi$
$311$	13.2602	0.751915	0.375958	+	0.926637i	$0.377314\pi$
$312$	9.82319	0.556129
$313$	10.0382	0.567395	0.283697	−	0.958914i	$-0.408439\pi$
$313$	10.0382	0.567395	0.283697	+	0.958914i	$0.408439\pi$
$314$	11.5698	0.652922
$315$	−3.50336	−0.197392
$316$	−5.61430	−0.315829
$317$	−4.97697	−0.279534	−0.139767	−	0.990184i	$-0.544635\pi$
$317$	−4.97697	−0.279534	−0.139767	+	0.990184i	$0.544635\pi$
$318$	10.7927	0.605225
$319$	−2.95793	−0.165613
$320$	−1.30481	−0.0729410
$321$	−6.17214	−0.344495
$322$	0.291208	0.0162284
$323$	−7.65293	−0.425820
$324$	−7.79780	−0.433211
$325$	−12.8462	−0.712578
$326$	1.05270	0.0583035
$327$	−50.2142	−2.77685
$328$	6.71543	0.370798
$329$	3.42970	0.189085
$330$	9.14193	0.503247
$331$	−7.36237	−0.404672	−0.202336	−	0.979316i	$-0.564853\pi$
$331$	−7.36237	−0.404672	−0.202336	+	0.979316i	$0.564853\pi$
$332$	−11.4959	−0.630919
$333$	−2.03294	−0.111404
$334$	20.7095	1.13317
$335$	−10.0928	−0.551426
$336$	−2.01613	−0.109989
$337$	−32.7350	−1.78319	−0.891594	−	0.452836i	$-0.850412\pi$
$337$	−32.7350	−1.78319	−0.891594	+	0.452836i	$0.850412\pi$
$338$	−2.17694	−0.118410
$339$	−19.2698	−1.04659
$340$	−9.98560	−0.541545
$341$	16.9045	0.915430
$342$	3.35801	0.181580
$343$	−10.6828	−0.576818
$344$	8.72098	0.470204
$345$	−1.19826	−0.0645124
$346$	11.1231	0.597984
$347$	−5.23535	−0.281048	−0.140524	−	0.990077i	$-0.544879\pi$
$347$	−5.23535	−0.281048	−0.140524	+	0.990077i	$0.544879\pi$
$348$	−2.68422	−0.143889
$349$	4.59594	0.246015	0.123008	−	0.992406i	$-0.460746\pi$
$349$	4.59594	0.246015	0.123008	+	0.992406i	$0.460746\pi$
$350$	2.63657	0.140930
$351$	−3.51680	−0.187713
$352$	2.77863	0.148101
$353$	−12.7713	−0.679749	−0.339874	−	0.940471i	$-0.610385\pi$
$353$	−12.7713	−0.679749	−0.339874	+	0.940471i	$0.610385\pi$
$354$	8.75748	0.465455
$355$	−1.76649	−0.0937557
$356$	−14.4300	−0.764791
$357$	−15.4293	−0.816603
$358$	18.2322	0.963604
$359$	26.1923	1.38238	0.691189	−	0.722674i	$-0.257087\pi$
$359$	26.1923	1.38238	0.691189	+	0.722674i	$0.257087\pi$
$360$	4.38156	0.230928
$361$	1.00000	0.0526316
$362$	−2.80685	−0.147525
$363$	8.26857	0.433988
$364$	3.11493	0.163267
$365$	−19.0049	−0.994761
$366$	0.0302911	0.00158334
$367$	−2.59280	−0.135343	−0.0676715	−	0.997708i	$-0.521557\pi$
$367$	−2.59280	−0.135343	−0.0676715	+	0.997708i	$0.521557\pi$
$368$	−0.364205	−0.0189855
$369$	−22.5505	−1.17393
$370$	−0.789931	−0.0410665
$371$	3.42237	0.177680
$372$	15.3402	0.795354
$373$	−14.7986	−0.766242	−0.383121	−	0.923698i	$-0.625151\pi$
$373$	−14.7986	−0.766242	−0.383121	+	0.923698i	$0.625151\pi$
$374$	21.2647	1.09957
$375$	−27.2994	−1.40974
$376$	−4.28942	−0.221210
$377$	4.14715	0.213589
$378$	0.721793	0.0371250
$379$	−1.85860	−0.0954697	−0.0477348	−	0.998860i	$-0.515200\pi$
$379$	−1.85860	−0.0954697	−0.0477348	+	0.998860i	$0.515200\pi$
$380$	1.30481	0.0669352
$381$	−14.6767	−0.751908
$382$	7.64346	0.391073
$383$	4.34636	0.222089	0.111044	−	0.993815i	$-0.464580\pi$
$383$	4.34636	0.222089	0.111044	+	0.993815i	$0.464580\pi$
$384$	2.52151	0.128675
$385$	2.89891	0.147742
$386$	−16.5009	−0.839872
$387$	−29.2851	−1.48865
$388$	−5.00978	−0.254333
$389$	17.5666	0.890664	0.445332	−	0.895366i	$-0.353086\pi$
$389$	17.5666	0.890664	0.445332	+	0.895366i	$0.353086\pi$
$390$	−12.8174	−0.649033
$391$	−2.78723	−0.140957
$392$	6.36069	0.321263
$393$	−32.5555	−1.64221
$394$	−3.98120	−0.200570
$395$	7.32559	0.368590
$396$	−9.33067	−0.468884
$397$	−19.4283	−0.975080	−0.487540	−	0.873101i	$-0.662106\pi$
$397$	−19.4283	−0.975080	−0.487540	+	0.873101i	$0.662106\pi$
$398$	−5.48861	−0.275119
$399$	2.01613	0.100933
$400$	−3.29748	−0.164874
$401$	0.725569	0.0362332	0.0181166	−	0.999836i	$-0.494233\pi$
$401$	0.725569	0.0362332	0.0181166	+	0.999836i	$0.494233\pi$
$402$	19.5040	0.972772
$403$	−23.7008	−1.18062
$404$	9.81176	0.488153
$405$	10.1746	0.505581
$406$	−0.851167	−0.0422427
$407$	1.68218	0.0833827
$408$	19.2969	0.955341
$409$	−31.2019	−1.54283	−0.771417	−	0.636330i	$-0.780452\pi$
$409$	−31.2019	−1.54283	−0.771417	+	0.636330i	$0.780452\pi$
$410$	−8.76235	−0.432741
$411$	−19.0325	−0.938806
$412$	−7.28866	−0.359087
$413$	2.77700	0.136647
$414$	1.22300	0.0601074
$415$	14.9999	0.736318
$416$	−3.89576	−0.191005
$417$	19.7679	0.968037
$418$	−2.77863	−0.135907
$419$	25.3211	1.23702	0.618508	−	0.785778i	$-0.287737\pi$
$419$	25.3211	1.23702	0.618508	+	0.785778i	$0.287737\pi$
$420$	2.63066	0.128363
$421$	0.00367721	0.000179216 0	8.96081e−5	−	1.00000i	$-0.499971\pi$
$421$	0.00367721	0.000179216 0	8.96081e−5		1.00000i	$0.499971\pi$
$422$	1.00000	0.0486792
$423$	14.4039	0.700343
$424$	−4.28026	−0.207868
$425$	−25.2354	−1.22409
$426$	3.41371	0.165395
$427$	0.00960531	0.000464834 0
$428$	2.44780	0.118319
$429$	27.2950	1.31782
$430$	−11.3792	−0.548754
$431$	0.218352	0.0105177	0.00525883	−	0.999986i	$-0.498326\pi$
$431$	0.218352	0.0105177	0.00525883	+	0.999986i	$0.498326\pi$
$432$	−0.902726	−0.0434324
$433$	−4.43807	−0.213280	−0.106640	−	0.994298i	$-0.534009\pi$
$433$	−4.43807	−0.213280	−0.106640	+	0.994298i	$0.534009\pi$
$434$	4.86439	0.233498
$435$	3.50239	0.167927
$436$	19.9143	0.953724
$437$	0.364205	0.0174223
$438$	36.7265	1.75486
$439$	21.9720	1.04867	0.524333	−	0.851513i	$-0.324315\pi$
$439$	21.9720	1.04867	0.524333	+	0.851513i	$0.324315\pi$
$440$	−3.62558	−0.172843
$441$	−21.3593	−1.01711
$442$	−29.8140	−1.41811
$443$	12.8136	0.608794	0.304397	−	0.952545i	$-0.401545\pi$
$443$	12.8136	0.608794	0.304397	+	0.952545i	$0.401545\pi$
$444$	1.52652	0.0724455
$445$	18.8284	0.892553
$446$	6.84314	0.324032
$447$	−48.8996	−2.31287
$448$	0.799571	0.0377762
$449$	−18.5901	−0.877321	−0.438660	−	0.898653i	$-0.644547\pi$
$449$	−18.5901	−0.877321	−0.438660	+	0.898653i	$0.644547\pi$
$450$	11.0730	0.521984
$451$	18.6597	0.878651
$452$	7.64216	0.359457
$453$	−8.63253	−0.405592
$454$	−3.01964	−0.141719
$455$	−4.06439	−0.190542
$456$	−2.52151	−0.118081
$457$	−1.73739	−0.0812718	−0.0406359	−	0.999174i	$-0.512938\pi$
$457$	−1.73739	−0.0812718	−0.0406359	+	0.999174i	$0.512938\pi$
$458$	−17.5925	−0.822044
$459$	−6.90850	−0.322461
$460$	0.475217	0.0221571
$461$	−7.11700	−0.331472	−0.165736	−	0.986170i	$-0.553000\pi$
$461$	−7.11700	−0.331472	−0.165736	+	0.986170i	$0.553000\pi$
$462$	−5.60207	−0.260632
$463$	−13.3969	−0.622605	−0.311302	−	0.950311i	$-0.600765\pi$
$463$	−13.3969	−0.622605	−0.311302	+	0.950311i	$0.600765\pi$
$464$	1.06453	0.0494196
$465$	−20.0161	−0.928222
$466$	−18.3348	−0.849342
$467$	39.7771	1.84067	0.920333	−	0.391136i	$-0.127918\pi$
$467$	39.7771	1.84067	0.920333	+	0.391136i	$0.127918\pi$
$468$	13.0820	0.604716
$469$	6.18472	0.285584
$470$	5.59687	0.258164
$471$	29.1734	1.34424
$472$	−3.47311	−0.159863
$473$	24.2324	1.11421
$474$	−14.1565	−0.650231
$475$	3.29748	0.151299
$476$	6.11906	0.280467
$477$	14.3731	0.658101
$478$	−22.9250	−1.04857
$479$	−38.3005	−1.74999	−0.874997	−	0.484128i	$-0.839137\pi$
$479$	−38.3005	−1.74999	−0.874997	+	0.484128i	$0.839137\pi$
$480$	−3.29008	−0.150171
$481$	−2.35849	−0.107538
$482$	28.4679	1.29668
$483$	0.734283	0.0334110
$484$	−3.27922	−0.149055
$485$	6.53679	0.296821
$486$	−22.3704	−1.01474
$487$	−7.61033	−0.344857	−0.172429	−	0.985022i	$-0.555161\pi$
$487$	−7.61033	−0.344857	−0.172429	+	0.985022i	$0.555161\pi$
$488$	−0.0120131	−0.000543807 0
$489$	2.65438	0.120035
$490$	−8.29947	−0.374932
$491$	−19.0040	−0.857637	−0.428819	−	0.903391i	$-0.641070\pi$
$491$	−19.0040	−0.857637	−0.428819	+	0.903391i	$0.641070\pi$
$492$	16.9330	0.763400
$493$	8.14677	0.366912
$494$	3.89576	0.175278
$495$	12.1747	0.547213
$496$	−6.08375	−0.273169
$497$	1.08249	0.0485562
$498$	−28.9870	−1.29894
$499$	−21.3594	−0.956179	−0.478089	−	0.878311i	$-0.658671\pi$
$499$	−21.3594	−0.956179	−0.478089	+	0.878311i	$0.658671\pi$
$500$	10.8266	0.484181
$501$	52.2192	2.33298
$502$	−1.11181	−0.0496226
$503$	2.46112	0.109736	0.0548680	−	0.998494i	$-0.482526\pi$
$503$	2.46112	0.109736	0.0548680	+	0.998494i	$0.482526\pi$
$504$	−2.68497	−0.119598
$505$	−12.8025	−0.569702
$506$	−1.01199	−0.0449885
$507$	−5.48917	−0.243782
$508$	5.82058	0.258247
$509$	12.1939	0.540486	0.270243	−	0.962792i	$-0.412896\pi$
$509$	12.1939	0.540486	0.270243	+	0.962792i	$0.412896\pi$
$510$	−25.1788	−1.11494
$511$	11.6460	0.515187
$512$	−1.00000	−0.0441942
$513$	0.902726	0.0398563
$514$	−2.54796	−0.112386
$515$	9.51030	0.419074
$516$	21.9900	0.968057
$517$	−11.9187	−0.524185
$518$	0.484060	0.0212684
$519$	28.0471	1.23113
$520$	5.08322	0.222914
$521$	−42.8254	−1.87622	−0.938108	−	0.346343i	$-0.887423\pi$
$521$	−42.8254	−1.87622	−0.938108	+	0.346343i	$0.887423\pi$
$522$	−3.57470	−0.156460
$523$	−31.0624	−1.35826	−0.679131	−	0.734017i	$-0.737643\pi$
$523$	−31.0624	−1.35826	−0.679131	+	0.734017i	$0.737643\pi$
$524$	12.9111	0.564025
$525$	6.64813	0.290148
$526$	8.20479	0.357746
$527$	−46.5585	−2.02812
$528$	7.00634	0.304912
$529$	−22.8674	−0.994233
$530$	5.58491	0.242593
$531$	11.6627	0.506120
$532$	−0.799571	−0.0346658
$533$	−26.1617	−1.13319
$534$	−36.3855	−1.57455
$535$	−3.19390	−0.138084
$536$	−7.73505	−0.334103
$537$	45.9728	1.98387
$538$	4.08601	0.176161
$539$	17.6740	0.761273
$540$	1.17788	0.0506880
$541$	−17.4481	−0.750152	−0.375076	−	0.926994i	$-0.622383\pi$
$541$	−17.4481	−0.750152	−0.375076	+	0.926994i	$0.622383\pi$
$542$	−10.9546	−0.470539
$543$	−7.07750	−0.303724
$544$	−7.65293	−0.328117
$545$	−25.9844	−1.11305
$546$	7.85434	0.336135
$547$	−4.97551	−0.212737	−0.106369	−	0.994327i	$-0.533922\pi$
$547$	−4.97551	−0.212737	−0.106369	+	0.994327i	$0.533922\pi$
$548$	7.54807	0.322438
$549$	0.0403401	0.00172167
$550$	−9.16247	−0.390689
$551$	−1.06453	−0.0453505
$552$	−0.918346	−0.0390874
$553$	−4.48903	−0.190893
$554$	12.7817	0.543043
$555$	−1.99182	−0.0845479
$556$	−7.83970	−0.332477
$557$	−15.1663	−0.642618	−0.321309	−	0.946974i	$-0.604123\pi$
$557$	−15.1663	−0.642618	−0.321309	+	0.946974i	$0.604123\pi$
$558$	20.4293	0.864841
$559$	−33.9748	−1.43698
$560$	−1.04329	−0.0440869
$561$	53.6190	2.26380
$562$	11.1853	0.471825
$563$	16.6395	0.701273	0.350636	−	0.936512i	$-0.385965\pi$
$563$	16.6395	0.701273	0.350636	+	0.936512i	$0.385965\pi$
$564$	−10.8158	−0.455428
$565$	−9.97154	−0.419506
$566$	23.3188	0.980163
$567$	−6.23489	−0.261841
$568$	−1.35383	−0.0568056
$569$	38.3381	1.60722	0.803609	−	0.595158i	$-0.202911\pi$
$569$	38.3381	1.60722	0.803609	+	0.595158i	$0.202911\pi$
$570$	3.29008	0.137806
$571$	11.3271	0.474024	0.237012	−	0.971507i	$-0.423832\pi$
$571$	11.3271	0.474024	0.237012	+	0.971507i	$0.423832\pi$
$572$	−10.8249	−0.452611
$573$	19.2730	0.805143
$574$	5.36946	0.224117
$575$	1.20096	0.0500834
$576$	3.35801	0.139917
$577$	−31.4533	−1.30942	−0.654709	−	0.755881i	$-0.727209\pi$
$577$	−31.4533	−1.30942	−0.654709	+	0.755881i	$0.727209\pi$
$578$	−41.5673	−1.72897
$579$	−41.6071	−1.72913
$580$	−1.38901	−0.0576754
$581$	−9.19178	−0.381339
$582$	−12.6322	−0.523621
$583$	−11.8932	−0.492568
$584$	−14.5653	−0.602715
$585$	−17.0695	−0.705737
$586$	−31.1003	−1.28474
$587$	24.4135	1.00765	0.503827	−	0.863804i	$-0.331925\pi$
$587$	24.4135	1.00765	0.503827	+	0.863804i	$0.331925\pi$
$588$	16.0385	0.661418
$589$	6.08375	0.250677
$590$	4.53174	0.186569
$591$	−10.0386	−0.412934
$592$	−0.605400	−0.0248818
$593$	−8.45840	−0.347345	−0.173672	−	0.984803i	$-0.555563\pi$
$593$	−8.45840	−0.347345	−0.173672	+	0.984803i	$0.555563\pi$
$594$	−2.50834	−0.102919
$595$	−7.98419	−0.327320
$596$	19.3930	0.794368
$597$	−13.8396	−0.566416
$598$	1.41885	0.0580213
$599$	−30.2801	−1.23721	−0.618606	−	0.785701i	$-0.712302\pi$
$599$	−30.2801	−1.23721	−0.618606	+	0.785701i	$0.712302\pi$
$600$	−8.31462	−0.339443
$601$	−40.5590	−1.65444	−0.827219	−	0.561880i	$-0.810078\pi$
$601$	−40.5590	−1.65444	−0.827219	+	0.561880i	$0.810078\pi$
$602$	6.97304	0.284200
$603$	25.9744	1.05776
$604$	3.42356	0.139303
$605$	4.27875	0.173956
$606$	24.7404	1.00501
$607$	−2.93615	−0.119175	−0.0595873	−	0.998223i	$-0.518978\pi$
$607$	−2.93615	−0.119175	−0.0595873	+	0.998223i	$0.518978\pi$
$608$	1.00000	0.0405554
$609$	−2.14623	−0.0869694
$610$	0.0156748	0.000634652 0
$611$	16.7106	0.676037
$612$	25.6986	1.03880
$613$	−47.2433	−1.90814	−0.954070	−	0.299585i	$-0.903152\pi$
$613$	−47.2433	−1.90814	−0.954070	+	0.299585i	$0.903152\pi$
$614$	0.0218889	0.000883366 0
$615$	−22.0943	−0.890930
$616$	2.22171	0.0895153
$617$	−27.4424	−1.10479	−0.552395	−	0.833582i	$-0.686286\pi$
$617$	−27.4424	−1.10479	−0.552395	+	0.833582i	$0.686286\pi$
$618$	−18.3784	−0.739289
$619$	−6.34495	−0.255025	−0.127513	−	0.991837i	$-0.540699\pi$
$619$	−6.34495	−0.255025	−0.127513	+	0.991837i	$0.540699\pi$
$620$	7.93813	0.318803
$621$	0.328777	0.0131934
$622$	−13.2602	−0.531684
$623$	−11.5378	−0.462254
$624$	−9.82319	−0.393242
$625$	2.36074	0.0944297
$626$	−10.0382	−0.401209
$627$	−7.00634	−0.279806
$628$	−11.5698	−0.461686
$629$	−4.63308	−0.184733
$630$	3.50336	0.139577
$631$	−19.8874	−0.791704	−0.395852	−	0.918314i	$-0.629551\pi$
$631$	−19.8874	−0.791704	−0.395852	+	0.918314i	$0.629551\pi$
$632$	5.61430	0.223325
$633$	2.52151	0.100221
$634$	4.97697	0.197661
$635$	−7.59474	−0.301388
$636$	−10.7927	−0.427959
$637$	−24.7797	−0.981807
$638$	2.95793	0.117106
$639$	4.54619	0.179844
$640$	1.30481	0.0515770
$641$	7.16636	0.283054	0.141527	−	0.989934i	$-0.454799\pi$
$641$	7.16636	0.283054	0.141527	+	0.989934i	$0.454799\pi$
$642$	6.17214	0.243595
$643$	−3.07420	−0.121235	−0.0606174	−	0.998161i	$-0.519307\pi$
$643$	−3.07420	−0.121235	−0.0606174	+	0.998161i	$0.519307\pi$
$644$	−0.291208	−0.0114752
$645$	−28.6928	−1.12978
$646$	7.65293	0.301100
$647$	−1.15299	−0.0453288	−0.0226644	−	0.999743i	$-0.507215\pi$
$647$	−1.15299	−0.0453288	−0.0226644	+	0.999743i	$0.507215\pi$
$648$	7.79780	0.306326
$649$	−9.65048	−0.378815
$650$	12.8462	0.503868
$651$	12.2656	0.480727
$652$	−1.05270	−0.0412268
$653$	31.1948	1.22075	0.610373	−	0.792114i	$-0.291019\pi$
$653$	31.1948	1.22075	0.610373	+	0.792114i	$0.291019\pi$
$654$	50.2142	1.96353
$655$	−16.8465	−0.658249
$656$	−6.71543	−0.262194
$657$	48.9103	1.90817
$658$	−3.42970	−0.133704
$659$	5.82510	0.226914	0.113457	−	0.993543i	$-0.463808\pi$
$659$	5.82510	0.226914	0.113457	+	0.993543i	$0.463808\pi$
$660$	−9.14193	−0.355849
$661$	−22.7631	−0.885382	−0.442691	−	0.896674i	$-0.645976\pi$
$661$	−22.7631	−0.885382	−0.442691	+	0.896674i	$0.645976\pi$
$662$	7.36237	0.286146
$663$	−75.1762	−2.91960
$664$	11.4959	0.446127
$665$	1.04329	0.0404569
$666$	2.03294	0.0787748
$667$	−0.387707	−0.0150121
$668$	−20.7095	−0.801275
$669$	17.2550	0.667119
$670$	10.0928	0.389917
$671$	−0.0333799	−0.00128862
$672$	2.01613	0.0777737
$673$	8.63759	0.332954	0.166477	−	0.986045i	$-0.446761\pi$
$673$	8.63759	0.332954	0.166477	+	0.986045i	$0.446761\pi$
$674$	32.7350	1.26090
$675$	2.97672	0.114574
$676$	2.17694	0.0837283
$677$	−6.76957	−0.260176	−0.130088	−	0.991502i	$-0.541526\pi$
$677$	−6.76957	−0.260176	−0.130088	+	0.991502i	$0.541526\pi$
$678$	19.2698	0.740051
$679$	−4.00567	−0.153724
$680$	9.98560	0.382930
$681$	−7.61405	−0.291771
$682$	−16.9045	−0.647307
$683$	−43.9246	−1.68073	−0.840365	−	0.542022i	$-0.817659\pi$
$683$	−43.9246	−1.68073	−0.840365	+	0.542022i	$0.817659\pi$
$684$	−3.35801	−0.128397
$685$	−9.84878	−0.376303
$686$	10.6828	0.407872
$687$	−44.3597	−1.69243
$688$	−8.72098	−0.332484
$689$	16.6748	0.635261
$690$	1.19826	0.0456172
$691$	−5.49773	−0.209144	−0.104572	−	0.994517i	$-0.533347\pi$
$691$	−5.49773	−0.209144	−0.104572	+	0.994517i	$0.533347\pi$
$692$	−11.1231	−0.422839
$693$	−7.46053	−0.283402
$694$	5.23535	0.198731
$695$	10.2293	0.388020
$696$	2.68422	0.101745
$697$	−51.3927	−1.94664
$698$	−4.59594	−0.173959
$699$	−46.2313	−1.74863
$700$	−2.63657	−0.0996528
$701$	25.6821	0.969998	0.484999	−	0.874515i	$-0.338820\pi$
$701$	25.6821	0.969998	0.484999	+	0.874515i	$0.338820\pi$
$702$	3.51680	0.132733
$703$	0.605400	0.0228331
$704$	−2.77863	−0.104724
$705$	14.1126	0.531510
$706$	12.7713	0.480655
$707$	7.84519	0.295049
$708$	−8.75748	−0.329126
$709$	29.3132	1.10088	0.550441	−	0.834874i	$-0.314460\pi$
$709$	29.3132	1.10088	0.550441	+	0.834874i	$0.314460\pi$
$710$	1.76649	0.0662953
$711$	−18.8529	−0.707039
$712$	14.4300	0.540789
$713$	2.21573	0.0829798
$714$	15.4293	0.577426
$715$	14.1244	0.528222
$716$	−18.2322	−0.681371
$717$	−57.8057	−2.15879
$718$	−26.1923	−0.977489
$719$	7.09606	0.264639	0.132319	−	0.991207i	$-0.457758\pi$
$719$	7.09606	0.264639	0.132319	+	0.991207i	$0.457758\pi$
$720$	−4.38156	−0.163291
$721$	−5.82780	−0.217039
$722$	−1.00000	−0.0372161
$723$	71.7821	2.66961
$724$	2.80685	0.104316
$725$	−3.51026	−0.130368
$726$	−8.26857	−0.306876
$727$	−53.0524	−1.96760	−0.983802	−	0.179260i	$-0.942630\pi$
$727$	−53.0524	−1.96760	−0.983802	+	0.179260i	$0.942630\pi$
$728$	−3.11493	−0.115447
$729$	−33.0138	−1.22273
$730$	19.0049	0.703402
$731$	−66.7410	−2.46851
$732$	−0.0302911	−0.00111959
$733$	2.07510	0.0766455	0.0383228	−	0.999265i	$-0.487798\pi$
$733$	2.07510	0.0766455	0.0383228	+	0.999265i	$0.487798\pi$
$734$	2.59280	0.0957019
$735$	−20.9272	−0.771911
$736$	0.364205	0.0134248
$737$	−21.4929	−0.791699
$738$	22.5505	0.830095
$739$	5.31092	0.195365	0.0976826	−	0.995218i	$-0.468857\pi$
$739$	5.31092	0.195365	0.0976826	+	0.995218i	$0.468857\pi$
$740$	0.789931	0.0290384
$741$	9.82319	0.360864
$742$	−3.42237	−0.125639
$743$	−38.3062	−1.40532	−0.702658	−	0.711527i	$-0.748004\pi$
$743$	−38.3062	−1.40532	−0.702658	+	0.711527i	$0.748004\pi$
$744$	−15.3402	−0.562400
$745$	−25.3041	−0.927072
$746$	14.7986	0.541815
$747$	−38.6033	−1.41242
$748$	−21.2647	−0.777513
$749$	1.95719	0.0715141
$750$	27.2994	0.996833
$751$	−27.6236	−1.00800	−0.504000	−	0.863704i	$-0.668139\pi$
$751$	−27.6236	−1.00800	−0.504000	+	0.863704i	$0.668139\pi$
$752$	4.28942	0.156419
$753$	−2.80344	−0.102163
$754$	−4.14715	−0.151030
$755$	−4.46708	−0.162574
$756$	−0.721793	−0.0262514
$757$	21.0354	0.764545	0.382272	−	0.924050i	$-0.375142\pi$
$757$	21.0354	0.764545	0.382272	+	0.924050i	$0.375142\pi$
$758$	1.85860	0.0675073
$759$	−2.55174	−0.0926224
$760$	−1.30481	−0.0473303
$761$	2.24554	0.0814009	0.0407005	−	0.999171i	$-0.487041\pi$
$761$	2.24554	0.0814009	0.0407005	+	0.999171i	$0.487041\pi$
$762$	14.6767	0.531679
$763$	15.9229	0.576449
$764$	−7.64346	−0.276531
$765$	−33.5317	−1.21234
$766$	−4.34636	−0.157040
$767$	13.5304	0.488554
$768$	−2.52151	−0.0909871
$769$	1.21029	0.0436443	0.0218222	−	0.999762i	$-0.493053\pi$
$769$	1.21029	0.0436443	0.0218222	+	0.999762i	$0.493053\pi$
$770$	−2.89891	−0.104469
$771$	−6.42470	−0.231380
$772$	16.5009	0.593879
$773$	−26.0181	−0.935805	−0.467902	−	0.883780i	$-0.654990\pi$
$773$	−26.0181	−0.935805	−0.467902	+	0.883780i	$0.654990\pi$
$774$	29.2851	1.05263
$775$	20.0610	0.720614
$776$	5.00978	0.179840
$777$	1.22056	0.0437874
$778$	−17.5666	−0.629794
$779$	6.71543	0.240605
$780$	12.8174	0.458936
$781$	−3.76180	−0.134608
$782$	2.78723	0.0996713
$783$	−0.960979	−0.0343426
$784$	−6.36069	−0.227167
$785$	15.0964	0.538813
$786$	32.5555	1.16122
$787$	46.2025	1.64694	0.823471	−	0.567358i	$-0.192034\pi$
$787$	46.2025	1.64694	0.823471	+	0.567358i	$0.192034\pi$
$788$	3.98120	0.141824
$789$	20.6885	0.736528
$790$	−7.32559	−0.260633
$791$	6.11044	0.217262
$792$	9.33067	0.331551
$793$	0.0468001	0.00166192
$794$	19.4283	0.689486
$795$	14.0824	0.499451
$796$	5.48861	0.194538
$797$	23.9577	0.848626	0.424313	−	0.905515i	$-0.360516\pi$
$797$	23.9577	0.848626	0.424313	+	0.905515i	$0.360516\pi$
$798$	−2.01613	−0.0713701
$799$	32.8267	1.16132
$800$	3.29748	0.116583
$801$	−48.4562	−1.71212
$802$	−0.725569	−0.0256207
$803$	−40.4715	−1.42821
$804$	−19.5040	−0.687853
$805$	0.379970	0.0133922
$806$	23.7008	0.834826
$807$	10.3029	0.362680
$808$	−9.81176	−0.345176
$809$	8.90368	0.313037	0.156518	−	0.987675i	$-0.449973\pi$
$809$	8.90368	0.313037	0.156518	+	0.987675i	$0.449973\pi$
$810$	−10.1746	−0.357500
$811$	23.9080	0.839524	0.419762	−	0.907634i	$-0.362113\pi$
$811$	23.9080	0.839524	0.419762	+	0.907634i	$0.362113\pi$
$812$	0.851167	0.0298701
$813$	−27.6220	−0.968747
$814$	−1.68218	−0.0589605
$815$	1.37357	0.0481139
$816$	−19.2969	−0.675528
$817$	8.72098	0.305108
$818$	31.2019	1.09095
$819$	10.4600	0.365501
$820$	8.76235	0.305994
$821$	−10.6105	−0.370308	−0.185154	−	0.982710i	$-0.559278\pi$
$821$	−10.6105	−0.370308	−0.185154	+	0.982710i	$0.559278\pi$
$822$	19.0325	0.663836
$823$	−13.9862	−0.487528	−0.243764	−	0.969835i	$-0.578382\pi$
$823$	−13.9862	−0.487528	−0.243764	+	0.969835i	$0.578382\pi$
$824$	7.28866	0.253913
$825$	−23.1033	−0.804352
$826$	−2.77700	−0.0966241
$827$	−18.1663	−0.631706	−0.315853	−	0.948808i	$-0.602291\pi$
$827$	−18.1663	−0.631706	−0.315853	+	0.948808i	$0.602291\pi$
$828$	−1.22300	−0.0425023
$829$	−13.3080	−0.462205	−0.231103	−	0.972929i	$-0.574233\pi$
$829$	−13.3080	−0.462205	−0.231103	+	0.972929i	$0.574233\pi$
$830$	−14.9999	−0.520655
$831$	32.2292	1.11802
$832$	3.89576	0.135061
$833$	−48.6779	−1.68659
$834$	−19.7679	−0.684506
$835$	27.0219	0.935132
$836$	2.77863	0.0961009
$837$	5.49196	0.189830
$838$	−25.3211	−0.874702
$839$	27.2650	0.941291	0.470646	−	0.882322i	$-0.344021\pi$
$839$	27.2650	0.941291	0.470646	+	0.882322i	$0.344021\pi$
$840$	−2.63066	−0.0907662
$841$	−27.8668	−0.960923
$842$	−0.00367721	−0.000126725 0
$843$	28.2039	0.971395
$844$	−1.00000	−0.0344214
$845$	−2.84048	−0.0977156
$846$	−14.4039	−0.495217
$847$	−2.62197	−0.0900918
$848$	4.28026	0.146985
$849$	58.7986	2.01796
$850$	25.2354	0.865566
$851$	0.220490	0.00755829
$852$	−3.41371	−0.116952
$853$	16.2075	0.554934	0.277467	−	0.960735i	$-0.410505\pi$
$853$	16.2075	0.554934	0.277467	+	0.960735i	$0.410505\pi$
$854$	−0.00960531	−0.000328687 0
$855$	4.38156	0.149846
$856$	−2.44780	−0.0836640
$857$	−50.3412	−1.71962	−0.859811	−	0.510613i	$-0.829419\pi$
$857$	−50.3412	−1.71962	−0.859811	+	0.510613i	$0.829419\pi$
$858$	−27.2950	−0.931837
$859$	−19.5488	−0.666996	−0.333498	−	0.942751i	$-0.608229\pi$
$859$	−19.5488	−0.666996	−0.333498	+	0.942751i	$0.608229\pi$
$860$	11.3792	0.388027
$861$	13.5392	0.461413
$862$	−0.218352	−0.00743711
$863$	−15.3137	−0.521283	−0.260642	−	0.965436i	$-0.583934\pi$
$863$	−15.3137	−0.521283	−0.260642	+	0.965436i	$0.583934\pi$
$864$	0.902726	0.0307114
$865$	14.5136	0.493476
$866$	4.43807	0.150812
$867$	−104.812	−3.55962
$868$	−4.86439	−0.165108
$869$	15.6001	0.529196
$870$	−3.50239	−0.118742
$871$	30.1339	1.02105
$872$	−19.9143	−0.674385
$873$	−16.8229	−0.569368
$874$	−0.364205	−0.0123194
$875$	8.65664	0.292648
$876$	−36.7265	−1.24087
$877$	48.7290	1.64546	0.822731	−	0.568431i	$-0.192450\pi$
$877$	48.7290	1.64546	0.822731	+	0.568431i	$0.192450\pi$
$878$	−21.9720	−0.741519
$879$	−78.4196	−2.64503
$880$	3.62558	0.122218
$881$	−0.668036	−0.0225067	−0.0112533	−	0.999937i	$-0.503582\pi$
$881$	−0.668036	−0.0225067	−0.0112533	+	0.999937i	$0.503582\pi$
$882$	21.3593	0.719203
$883$	−10.2464	−0.344819	−0.172410	−	0.985025i	$-0.555155\pi$
$883$	−10.2464	−0.344819	−0.172410	+	0.985025i	$0.555155\pi$
$884$	29.8140	1.00275
$885$	11.4268	0.384108
$886$	−12.8136	−0.430482
$887$	−34.8610	−1.17052	−0.585259	−	0.810846i	$-0.699007\pi$
$887$	−34.8610	−1.17052	−0.585259	+	0.810846i	$0.699007\pi$
$888$	−1.52652	−0.0512267
$889$	4.65397	0.156089
$890$	−18.8284	−0.631130
$891$	21.6672	0.725878
$892$	−6.84314	−0.229125
$893$	−4.28942	−0.143540
$894$	48.8996	1.63545
$895$	23.7896	0.795197
$896$	−0.799571	−0.0267118
$897$	3.57766	0.119454
$898$	18.5901	0.620359
$899$	−6.47634	−0.215998
$900$	−11.0730	−0.369099
$901$	32.7565	1.09128
$902$	−18.6597	−0.621300
$903$	17.5826	0.585112
$904$	−7.64216	−0.254174
$905$	−3.66240	−0.121742
$906$	8.63253	0.286797
$907$	−54.8683	−1.82187	−0.910937	−	0.412546i	$-0.864639\pi$
$907$	−54.8683	−1.82187	−0.910937	+	0.412546i	$0.864639\pi$
$908$	3.01964	0.100210
$909$	32.9480	1.09282
$910$	4.06439	0.134733
$911$	−27.5250	−0.911943	−0.455971	−	0.889994i	$-0.650708\pi$
$911$	−27.5250	−0.911943	−0.455971	+	0.889994i	$0.650708\pi$
$912$	2.52151	0.0834955
$913$	31.9428	1.05715
$914$	1.73739	0.0574679
$915$	0.0395241	0.00130663
$916$	17.5925	0.581273
$917$	10.3234	0.340907
$918$	6.90850	0.228014
$919$	9.70911	0.320274	0.160137	−	0.987095i	$-0.448806\pi$
$919$	9.70911	0.320274	0.160137	+	0.987095i	$0.448806\pi$
$920$	−0.475217	−0.0156675
$921$	0.0551932	0.00181868
$922$	7.11700	0.234386
$923$	5.27421	0.173603
$924$	5.60207	0.184294
$925$	1.99629	0.0656377
$926$	13.3969	0.440248
$927$	−24.4754	−0.803878
$928$	−1.06453	−0.0349449
$929$	19.0467	0.624901	0.312450	−	0.949934i	$-0.398850\pi$
$929$	19.0467	0.624901	0.312450	+	0.949934i	$0.398850\pi$
$930$	20.0161	0.656352
$931$	6.36069	0.208463
$932$	18.3348	0.600576
$933$	−33.4356	−1.09463
$934$	−39.7771	−1.30155
$935$	27.7463	0.907401
$936$	−13.0820	−0.427598
$937$	33.5339	1.09550	0.547752	−	0.836641i	$-0.315484\pi$
$937$	33.5339	1.09550	0.547752	+	0.836641i	$0.315484\pi$
$938$	−6.18472	−0.201938
$939$	−25.3115	−0.826010
$940$	−5.59687	−0.182550
$941$	10.4020	0.339095	0.169548	−	0.985522i	$-0.445769\pi$
$941$	10.4020	0.339095	0.169548	+	0.985522i	$0.445769\pi$
$942$	−29.1734	−0.950520
$943$	2.44579	0.0796460
$944$	3.47311	0.113040
$945$	0.941801	0.0306368
$946$	−24.2324	−0.787862
$947$	−41.5978	−1.35175	−0.675873	−	0.737018i	$-0.736233\pi$
$947$	−41.5978	−1.35175	−0.675873	+	0.737018i	$0.736233\pi$
$948$	14.1565	0.459782
$949$	56.7428	1.84195
$950$	−3.29748	−0.106984
$951$	12.5495	0.406944
$952$	−6.11906	−0.198320
$953$	−2.75552	−0.0892601	−0.0446300	−	0.999004i	$-0.514211\pi$
$953$	−2.75552	−0.0892601	−0.0446300	+	0.999004i	$0.514211\pi$
$954$	−14.3731	−0.465348
$955$	9.97324	0.322726
$956$	22.9250	0.741449
$957$	7.45846	0.241098
$958$	38.3005	1.23743
$959$	6.03522	0.194887
$960$	3.29008	0.106187
$961$	6.01204	0.193937
$962$	2.35849	0.0760409
$963$	8.21973	0.264877
$964$	−28.4679	−0.916890
$965$	−21.5304	−0.693090
$966$	−0.734283	−0.0236252
$967$	−27.2955	−0.877765	−0.438883	−	0.898544i	$-0.644626\pi$
$967$	−27.2955	−0.877765	−0.438883	+	0.898544i	$0.644626\pi$
$968$	3.27922	0.105398
$969$	19.2969	0.619907
$970$	−6.53679	−0.209884
$971$	−1.20939	−0.0388112	−0.0194056	−	0.999812i	$-0.506177\pi$
$971$	−1.20939	−0.0388112	−0.0194056	+	0.999812i	$0.506177\pi$
$972$	22.3704	0.717531
$973$	−6.26840	−0.200956
$974$	7.61033	0.243851
$975$	32.3918	1.03737
$976$	0.0120131	0.000384529 0
$977$	27.2591	0.872095	0.436047	−	0.899924i	$-0.356378\pi$
$977$	27.2591	0.872095	0.436047	+	0.899924i	$0.356378\pi$
$978$	−2.65438	−0.0848779
$979$	40.0957	1.28147
$980$	8.29947	0.265117
$981$	66.8726	2.13508
$982$	19.0040	0.606441
$983$	−44.2827	−1.41240	−0.706199	−	0.708013i	$-0.749592\pi$
$983$	−44.2827	−1.41240	−0.706199	+	0.708013i	$0.749592\pi$
$984$	−16.9330	−0.539805
$985$	−5.19469	−0.165517
$986$	−8.14677	−0.259446
$987$	−8.64801	−0.275269
$988$	−3.89576	−0.123941
$989$	3.17622	0.100998
$990$	−12.1747	−0.386938
$991$	−23.6487	−0.751224	−0.375612	−	0.926777i	$-0.622568\pi$
$991$	−23.6487	−0.751224	−0.375612	+	0.926777i	$0.622568\pi$
$992$	6.08375	0.193159
$993$	18.5643	0.589119
$994$	−1.08249	−0.0343344
$995$	−7.16157	−0.227037
$996$	28.9870	0.918489
$997$	−25.7276	−0.814802	−0.407401	−	0.913249i	$-0.633565\pi$
$997$	−25.7276	−0.814802	−0.407401	+	0.913249i	$0.633565\pi$
$998$	21.3594	0.676120
$999$	0.546510	0.0172908

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8018.2.a.f.1.6	✓	34

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8018.2.a.f.1.6	✓	34	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:	\( N \)	\(=\)	\( 8018 = 2 \cdot 19 \cdot 211 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8018.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -2.52151 q^{3} +1.00000 q^{4} -1.30481 q^{5} +2.52151 q^{6} +0.799571 q^{7} -1.00000 q^{8} +3.35801 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -2.52151 q^{3} +1.00000 q^{4} -1.30481 q^{5} +2.52151 q^{6} +0.799571 q^{7} -1.00000 q^{8} +3.35801 q^{9} +1.30481 q^{10} -2.77863 q^{11} -2.52151 q^{12} +3.89576 q^{13} -0.799571 q^{14} +3.29008 q^{15} +1.00000 q^{16} +7.65293 q^{17} -3.35801 q^{18} -1.00000 q^{19} -1.30481 q^{20} -2.01613 q^{21} +2.77863 q^{22} -0.364205 q^{23} +2.52151 q^{24} -3.29748 q^{25} -3.89576 q^{26} -0.902726 q^{27} +0.799571 q^{28} +1.06453 q^{29} -3.29008 q^{30} -6.08375 q^{31} -1.00000 q^{32} +7.00634 q^{33} -7.65293 q^{34} -1.04329 q^{35} +3.35801 q^{36} -0.605400 q^{37} +1.00000 q^{38} -9.82319 q^{39} +1.30481 q^{40} -6.71543 q^{41} +2.01613 q^{42} -8.72098 q^{43} -2.77863 q^{44} -4.38156 q^{45} +0.364205 q^{46} +4.28942 q^{47} -2.52151 q^{48} -6.36069 q^{49} +3.29748 q^{50} -19.2969 q^{51} +3.89576 q^{52} +4.28026 q^{53} +0.902726 q^{54} +3.62558 q^{55} -0.799571 q^{56} +2.52151 q^{57} -1.06453 q^{58} +3.47311 q^{59} +3.29008 q^{60} +0.0120131 q^{61} +6.08375 q^{62} +2.68497 q^{63} +1.00000 q^{64} -5.08322 q^{65} -7.00634 q^{66} +7.73505 q^{67} +7.65293 q^{68} +0.918346 q^{69} +1.04329 q^{70} +1.35383 q^{71} -3.35801 q^{72} +14.5653 q^{73} +0.605400 q^{74} +8.31462 q^{75} -1.00000 q^{76} -2.22171 q^{77} +9.82319 q^{78} -5.61430 q^{79} -1.30481 q^{80} -7.79780 q^{81} +6.71543 q^{82} -11.4959 q^{83} -2.01613 q^{84} -9.98560 q^{85} +8.72098 q^{86} -2.68422 q^{87} +2.77863 q^{88} -14.4300 q^{89} +4.38156 q^{90} +3.11493 q^{91} -0.364205 q^{92} +15.3402 q^{93} -4.28942 q^{94} +1.30481 q^{95} +2.52151 q^{96} -5.00978 q^{97} +6.36069 q^{98} -9.33067 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 34 q - 34 q^{2} - 10 q^{3} + 34 q^{4} + 7 q^{5} + 10 q^{6} - 6 q^{7} - 34 q^{8} + 38 q^{9}+O(q^{10}) \) 34 * q - 34 * q^2 - 10 * q^3 + 34 * q^4 + 7 * q^5 + 10 * q^6 - 6 * q^7 - 34 * q^8 + 38 * q^9	\( 34 q - 34 q^{2} - 10 q^{3} + 34 q^{4} + 7 q^{5} + 10 q^{6} - 6 q^{7} - 34 q^{8} + 38 q^{9} - 7 q^{10} + 4 q^{11} - 10 q^{12} - 5 q^{13} + 6 q^{14} - 17 q^{15} + 34 q^{16} + 8 q^{17} - 38 q^{18} - 34 q^{19} + 7 q^{20} - 4 q^{22} - 24 q^{23} + 10 q^{24} + 5 q^{25} + 5 q^{26} - 31 q^{27} - 6 q^{28} + 24 q^{29} + 17 q^{30} - 28 q^{31} - 34 q^{32} - 16 q^{33} - 8 q^{34} + 2 q^{35} + 38 q^{36} - 36 q^{37} + 34 q^{38} - 9 q^{39} - 7 q^{40} + 9 q^{41} - 24 q^{43} + 4 q^{44} + 22 q^{45} + 24 q^{46} - 29 q^{47} - 10 q^{48} + 22 q^{49} - 5 q^{50} - 21 q^{51} - 5 q^{52} - 9 q^{53} + 31 q^{54} - 28 q^{55} + 6 q^{56} + 10 q^{57} - 24 q^{58} - 28 q^{59} - 17 q^{60} + 23 q^{61} + 28 q^{62} - 27 q^{63} + 34 q^{64} - 6 q^{65} + 16 q^{66} - 51 q^{67} + 8 q^{68} - 17 q^{69} - 2 q^{70} - 31 q^{71} - 38 q^{72} - 26 q^{73} + 36 q^{74} - 109 q^{75} - 34 q^{76} - 28 q^{77} + 9 q^{78} - 36 q^{79} + 7 q^{80} + 6 q^{81} - 9 q^{82} - 10 q^{83} - 32 q^{85} + 24 q^{86} - 8 q^{87} - 4 q^{88} - 34 q^{89} - 22 q^{90} - 41 q^{91} - 24 q^{92} - 33 q^{93} + 29 q^{94} - 7 q^{95} + 10 q^{96} - 56 q^{97} - 22 q^{98} - 28 q^{99}+O(q^{100}) \) 34 * q - 34 * q^2 - 10 * q^3 + 34 * q^4 + 7 * q^5 + 10 * q^6 - 6 * q^7 - 34 * q^8 + 38 * q^9 - 7 * q^10 + 4 * q^11 - 10 * q^12 - 5 * q^13 + 6 * q^14 - 17 * q^15 + 34 * q^16 + 8 * q^17 - 38 * q^18 - 34 * q^19 + 7 * q^20 - 4 * q^22 - 24 * q^23 + 10 * q^24 + 5 * q^25 + 5 * q^26 - 31 * q^27 - 6 * q^28 + 24 * q^29 + 17 * q^30 - 28 * q^31 - 34 * q^32 - 16 * q^33 - 8 * q^34 + 2 * q^35 + 38 * q^36 - 36 * q^37 + 34 * q^38 - 9 * q^39 - 7 * q^40 + 9 * q^41 - 24 * q^43 + 4 * q^44 + 22 * q^45 + 24 * q^46 - 29 * q^47 - 10 * q^48 + 22 * q^49 - 5 * q^50 - 21 * q^51 - 5 * q^52 - 9 * q^53 + 31 * q^54 - 28 * q^55 + 6 * q^56 + 10 * q^57 - 24 * q^58 - 28 * q^59 - 17 * q^60 + 23 * q^61 + 28 * q^62 - 27 * q^63 + 34 * q^64 - 6 * q^65 + 16 * q^66 - 51 * q^67 + 8 * q^68 - 17 * q^69 - 2 * q^70 - 31 * q^71 - 38 * q^72 - 26 * q^73 + 36 * q^74 - 109 * q^75 - 34 * q^76 - 28 * q^77 + 9 * q^78 - 36 * q^79 + 7 * q^80 + 6 * q^81 - 9 * q^82 - 10 * q^83 - 32 * q^85 + 24 * q^86 - 8 * q^87 - 4 * q^88 - 34 * q^89 - 22 * q^90 - 41 * q^91 - 24 * q^92 - 33 * q^93 + 29 * q^94 - 7 * q^95 + 10 * q^96 - 56 * q^97 - 22 * q^98 - 28 * q^99

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