LMFDB - Embedded newform 8018.2.a.d.1.9

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:	$30$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.9
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)

$f(q)$	$=$	$q+1.00000 q^{2} -1.51420 q^{3} +1.00000 q^{4} -2.91196 q^{5} -1.51420 q^{6} -3.75064 q^{7} +1.00000 q^{8} -0.707195 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -1.51420 q^{3} +1.00000 q^{4} -2.91196 q^{5} -1.51420 q^{6} -3.75064 q^{7} +1.00000 q^{8} -0.707195 q^{9} -2.91196 q^{10} -1.07783 q^{11} -1.51420 q^{12} +3.84825 q^{13} -3.75064 q^{14} +4.40929 q^{15} +1.00000 q^{16} +1.46263 q^{17} -0.707195 q^{18} +1.00000 q^{19} -2.91196 q^{20} +5.67922 q^{21} -1.07783 q^{22} -1.57188 q^{23} -1.51420 q^{24} +3.47950 q^{25} +3.84825 q^{26} +5.61344 q^{27} -3.75064 q^{28} +2.48697 q^{29} +4.40929 q^{30} -5.80679 q^{31} +1.00000 q^{32} +1.63205 q^{33} +1.46263 q^{34} +10.9217 q^{35} -0.707195 q^{36} +8.92851 q^{37} +1.00000 q^{38} -5.82702 q^{39} -2.91196 q^{40} -3.70538 q^{41} +5.67922 q^{42} +2.26373 q^{43} -1.07783 q^{44} +2.05932 q^{45} -1.57188 q^{46} +3.11736 q^{47} -1.51420 q^{48} +7.06728 q^{49} +3.47950 q^{50} -2.21472 q^{51} +3.84825 q^{52} -4.03335 q^{53} +5.61344 q^{54} +3.13859 q^{55} -3.75064 q^{56} -1.51420 q^{57} +2.48697 q^{58} +15.0431 q^{59} +4.40929 q^{60} +6.86485 q^{61} -5.80679 q^{62} +2.65243 q^{63} +1.00000 q^{64} -11.2059 q^{65} +1.63205 q^{66} +7.13230 q^{67} +1.46263 q^{68} +2.38015 q^{69} +10.9217 q^{70} +4.01635 q^{71} -0.707195 q^{72} -15.5522 q^{73} +8.92851 q^{74} -5.26867 q^{75} +1.00000 q^{76} +4.04254 q^{77} -5.82702 q^{78} -11.9353 q^{79} -2.91196 q^{80} -6.37829 q^{81} -3.70538 q^{82} -0.410968 q^{83} +5.67922 q^{84} -4.25913 q^{85} +2.26373 q^{86} -3.76577 q^{87} -1.07783 q^{88} -1.42947 q^{89} +2.05932 q^{90} -14.4334 q^{91} -1.57188 q^{92} +8.79265 q^{93} +3.11736 q^{94} -2.91196 q^{95} -1.51420 q^{96} -7.18019 q^{97} +7.06728 q^{98} +0.762233 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 30 q + 30 q^{2} - 10 q^{3} + 30 q^{4} - 12 q^{5} - 10 q^{6} - 15 q^{7} + 30 q^{8} + 10 q^{9}+O(q^{10}) $ 30 * q + 30 * q^2 - 10 * q^3 + 30 * q^4 - 12 * q^5 - 10 * q^6 - 15 * q^7 + 30 * q^8 + 10 * q^9	\( 30 q + 30 q^{2} - 10 q^{3} + 30 q^{4} - 12 q^{5} - 10 q^{6} - 15 q^{7} + 30 q^{8} + 10 q^{9} - 12 q^{10} - 17 q^{11} - 10 q^{12} - 19 q^{13} - 15 q^{14} - 8 q^{15} + 30 q^{16} - 18 q^{17} + 10 q^{18} + 30 q^{19} - 12 q^{20} - 14 q^{21} - 17 q^{22} - 15 q^{23} - 10 q^{24} - 4 q^{25} - 19 q^{26} - 37 q^{27} - 15 q^{28} - 37 q^{29} - 8 q^{30} - 11 q^{31} + 30 q^{32} + 6 q^{33} - 18 q^{34} - 4 q^{35} + 10 q^{36} - 46 q^{37} + 30 q^{38} - 12 q^{40} - 28 q^{41} - 14 q^{42} - 61 q^{43} - 17 q^{44} - 14 q^{45} - 15 q^{46} - 4 q^{47} - 10 q^{48} - q^{49} - 4 q^{50} - 8 q^{51} - 19 q^{52} - 19 q^{53} - 37 q^{54} - 17 q^{55} - 15 q^{56} - 10 q^{57} - 37 q^{58} - 6 q^{59} - 8 q^{60} - 32 q^{61} - 11 q^{62} - 24 q^{63} + 30 q^{64} - 24 q^{65} + 6 q^{66} - 44 q^{67} - 18 q^{68} - 2 q^{69} - 4 q^{70} + 10 q^{71} + 10 q^{72} - 58 q^{73} - 46 q^{74} - 42 q^{75} + 30 q^{76} - 32 q^{77} - 42 q^{79} - 12 q^{80} - 38 q^{81} - 28 q^{82} - 25 q^{83} - 14 q^{84} - 48 q^{85} - 61 q^{86} - 15 q^{87} - 17 q^{88} - 39 q^{89} - 14 q^{90} - 21 q^{91} - 15 q^{92} - 45 q^{93} - 4 q^{94} - 12 q^{95} - 10 q^{96} - 33 q^{97} - q^{98} - 38 q^{99}+O(q^{100}) \) 30 * q + 30 * q^2 - 10 * q^3 + 30 * q^4 - 12 * q^5 - 10 * q^6 - 15 * q^7 + 30 * q^8 + 10 * q^9 - 12 * q^10 - 17 * q^11 - 10 * q^12 - 19 * q^13 - 15 * q^14 - 8 * q^15 + 30 * q^16 - 18 * q^17 + 10 * q^18 + 30 * q^19 - 12 * q^20 - 14 * q^21 - 17 * q^22 - 15 * q^23 - 10 * q^24 - 4 * q^25 - 19 * q^26 - 37 * q^27 - 15 * q^28 - 37 * q^29 - 8 * q^30 - 11 * q^31 + 30 * q^32 + 6 * q^33 - 18 * q^34 - 4 * q^35 + 10 * q^36 - 46 * q^37 + 30 * q^38 - 12 * q^40 - 28 * q^41 - 14 * q^42 - 61 * q^43 - 17 * q^44 - 14 * q^45 - 15 * q^46 - 4 * q^47 - 10 * q^48 - q^49 - 4 * q^50 - 8 * q^51 - 19 * q^52 - 19 * q^53 - 37 * q^54 - 17 * q^55 - 15 * q^56 - 10 * q^57 - 37 * q^58 - 6 * q^59 - 8 * q^60 - 32 * q^61 - 11 * q^62 - 24 * q^63 + 30 * q^64 - 24 * q^65 + 6 * q^66 - 44 * q^67 - 18 * q^68 - 2 * q^69 - 4 * q^70 + 10 * q^71 + 10 * q^72 - 58 * q^73 - 46 * q^74 - 42 * q^75 + 30 * q^76 - 32 * q^77 - 42 * q^79 - 12 * q^80 - 38 * q^81 - 28 * q^82 - 25 * q^83 - 14 * q^84 - 48 * q^85 - 61 * q^86 - 15 * q^87 - 17 * q^88 - 39 * q^89 - 14 * q^90 - 21 * q^91 - 15 * q^92 - 45 * q^93 - 4 * q^94 - 12 * q^95 - 10 * q^96 - 33 * q^97 - q^98 - 38 * 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
$3$	−1.51420	−0.874224	−0.437112	−	0.899407i	$-0.643999\pi$
$3$	−1.51420	−0.874224	−0.437112	+	0.899407i	$0.643999\pi$
$4$	1.00000	0.500000
$5$	−2.91196	−1.30227	−0.651134	−	0.758963i	$-0.725706\pi$
$5$	−2.91196	−1.30227	−0.651134	+	0.758963i	$0.725706\pi$
$6$	−1.51420	−0.618170
$7$	−3.75064	−1.41761	−0.708804	−	0.705406i	$-0.750765\pi$
$7$	−3.75064	−1.41761	−0.708804	+	0.705406i	$0.750765\pi$
$8$	1.00000	0.353553
$9$	−0.707195	−0.235732
$10$	−2.91196	−0.920842
$11$	−1.07783	−0.324977	−0.162488	−	0.986710i	$-0.551952\pi$
$11$	−1.07783	−0.324977	−0.162488	+	0.986710i	$0.551952\pi$
$12$	−1.51420	−0.437112
$13$	3.84825	1.06731	0.533656	−	0.845702i	$-0.320818\pi$
$13$	3.84825	1.06731	0.533656	+	0.845702i	$0.320818\pi$
$14$	−3.75064	−1.00240
$15$	4.40929	1.13847
$16$	1.00000	0.250000
$17$	1.46263	0.354741	0.177370	−	0.984144i	$-0.443241\pi$
$17$	1.46263	0.354741	0.177370	+	0.984144i	$0.443241\pi$
$18$	−0.707195	−0.166687
$19$	1.00000	0.229416
$19$	1.00000	0.229416
$20$	−2.91196	−0.651134
$21$	5.67922	1.23931
$22$	−1.07783	−0.229793
$23$	−1.57188	−0.327760	−0.163880	−	0.986480i	$-0.552401\pi$
$23$	−1.57188	−0.327760	−0.163880	+	0.986480i	$0.552401\pi$
$24$	−1.51420	−0.309085
$25$	3.47950	0.695901
$26$	3.84825	0.754703
$27$	5.61344	1.08031
$28$	−3.75064	−0.708804
$29$	2.48697	0.461818	0.230909	−	0.972975i	$-0.425830\pi$
$29$	2.48697	0.461818	0.230909	+	0.972975i	$0.425830\pi$
$30$	4.40929	0.805023
$31$	−5.80679	−1.04293	−0.521465	−	0.853273i	$-0.674614\pi$
$31$	−5.80679	−1.04293	−0.521465	+	0.853273i	$0.674614\pi$
$32$	1.00000	0.176777
$33$	1.63205	0.284103
$34$	1.46263	0.250840
$35$	10.9217	1.84610
$36$	−0.707195	−0.117866
$37$	8.92851	1.46784	0.733919	−	0.679237i	$-0.237689\pi$
$37$	8.92851	1.46784	0.733919	+	0.679237i	$0.237689\pi$
$38$	1.00000	0.162221
$39$	−5.82702	−0.933070
$40$	−2.91196	−0.460421
$41$	−3.70538	−0.578683	−0.289341	−	0.957226i	$-0.593436\pi$
$41$	−3.70538	−0.578683	−0.289341	+	0.957226i	$0.593436\pi$
$42$	5.67922	0.876322
$43$	2.26373	0.345216	0.172608	−	0.984991i	$-0.444781\pi$
$43$	2.26373	0.345216	0.172608	+	0.984991i	$0.444781\pi$
$44$	−1.07783	−0.162488
$45$	2.05932	0.306986
$46$	−1.57188	−0.231762
$47$	3.11736	0.454713	0.227357	−	0.973812i	$-0.426992\pi$
$47$	3.11736	0.454713	0.227357	+	0.973812i	$0.426992\pi$
$48$	−1.51420	−0.218556
$49$	7.06728	1.00961
$50$	3.47950	0.492076
$51$	−2.21472	−0.310123
$52$	3.84825	0.533656
$53$	−4.03335	−0.554023	−0.277012	−	0.960867i	$-0.589344\pi$
$53$	−4.03335	−0.554023	−0.277012	+	0.960867i	$0.589344\pi$
$54$	5.61344	0.763892
$55$	3.13859	0.423207
$56$	−3.75064	−0.501200
$57$	−1.51420	−0.200561
$58$	2.48697	0.326555
$59$	15.0431	1.95844	0.979222	−	0.202791i	$-0.0650011\pi$
$59$	15.0431	1.95844	0.979222	+	0.202791i	$0.0650011\pi$
$60$	4.40929	0.569237
$61$	6.86485	0.878954	0.439477	−	0.898254i	$-0.355164\pi$
$61$	6.86485	0.878954	0.439477	+	0.898254i	$0.355164\pi$
$62$	−5.80679	−0.737463
$63$	2.65243	0.334175
$64$	1.00000	0.125000
$65$	−11.2059	−1.38992
$66$	1.63205	0.200891
$67$	7.13230	0.871349	0.435675	−	0.900104i	$-0.356510\pi$
$67$	7.13230	0.871349	0.435675	+	0.900104i	$0.356510\pi$
$68$	1.46263	0.177370
$69$	2.38015	0.286536
$70$	10.9217	1.30539
$71$	4.01635	0.476653	0.238326	−	0.971185i	$-0.423401\pi$
$71$	4.01635	0.476653	0.238326	+	0.971185i	$0.423401\pi$
$72$	−0.707195	−0.0833437
$73$	−15.5522	−1.82025	−0.910125	−	0.414333i	$-0.864015\pi$
$73$	−15.5522	−1.82025	−0.910125	+	0.414333i	$0.864015\pi$
$74$	8.92851	1.03792
$75$	−5.26867	−0.608374
$76$	1.00000	0.114708
$77$	4.04254	0.460690
$78$	−5.82702	−0.659780
$79$	−11.9353	−1.34283	−0.671415	−	0.741081i	$-0.734313\pi$
$79$	−11.9353	−1.34283	−0.671415	+	0.741081i	$0.734313\pi$
$80$	−2.91196	−0.325567
$81$	−6.37829	−0.708699
$82$	−3.70538	−0.409190
$83$	−0.410968	−0.0451095	−0.0225548	−	0.999746i	$-0.507180\pi$
$83$	−0.410968	−0.0451095	−0.0225548	+	0.999746i	$0.507180\pi$
$84$	5.67922	0.619654
$85$	−4.25913	−0.461967
$86$	2.26373	0.244104
$87$	−3.76577	−0.403733
$88$	−1.07783	−0.114897
$89$	−1.42947	−0.151523	−0.0757617	−	0.997126i	$-0.524139\pi$
$89$	−1.42947	−0.151523	−0.0757617	+	0.997126i	$0.524139\pi$
$90$	2.05932	0.217072
$91$	−14.4334	−1.51303
$92$	−1.57188	−0.163880
$93$	8.79265	0.911755
$94$	3.11736	0.321531
$95$	−2.91196	−0.298761
$96$	−1.51420	−0.154543
$97$	−7.18019	−0.729038	−0.364519	−	0.931196i	$-0.618767\pi$
$97$	−7.18019	−0.729038	−0.364519	+	0.931196i	$0.618767\pi$
$98$	7.06728	0.713903
$99$	0.762233	0.0766073
$100$	3.47950	0.347950
$101$	−15.3214	−1.52454	−0.762270	−	0.647260i	$-0.775915\pi$
$101$	−15.3214	−1.52454	−0.762270	+	0.647260i	$0.775915\pi$
$102$	−2.21472	−0.219290
$103$	17.0428	1.67928	0.839640	−	0.543143i	$-0.182766\pi$
$103$	17.0428	1.67928	0.839640	+	0.543143i	$0.182766\pi$
$104$	3.84825	0.377352
$105$	−16.5377	−1.61391
$106$	−4.03335	−0.391754
$107$	5.51478	0.533134	0.266567	−	0.963816i	$-0.414111\pi$
$107$	5.51478	0.533134	0.266567	+	0.963816i	$0.414111\pi$
$108$	5.61344	0.540153
$109$	5.98523	0.573281	0.286641	−	0.958038i	$-0.407461\pi$
$109$	5.98523	0.573281	0.286641	+	0.958038i	$0.407461\pi$
$110$	3.13859	0.299252
$111$	−13.5196	−1.28322
$112$	−3.75064	−0.354402
$113$	−12.7751	−1.20178	−0.600892	−	0.799331i	$-0.705188\pi$
$113$	−12.7751	−1.20178	−0.600892	+	0.799331i	$0.705188\pi$
$114$	−1.51420	−0.141818
$115$	4.57726	0.426832
$116$	2.48697	0.230909
$117$	−2.72146	−0.251599
$118$	15.0431	1.38483
$119$	−5.48581	−0.502883
$120$	4.40929	0.402511
$121$	−9.83829	−0.894390
$122$	6.86485	0.621514
$123$	5.61069	0.505899
$124$	−5.80679	−0.521465
$125$	4.42762	0.396018
$126$	2.65243	0.236297
$127$	12.7818	1.13420	0.567100	−	0.823649i	$-0.308065\pi$
$127$	12.7818	1.13420	0.567100	+	0.823649i	$0.308065\pi$
$128$	1.00000	0.0883883
$129$	−3.42775	−0.301796
$130$	−11.2059	−0.982825
$131$	7.49553	0.654888	0.327444	−	0.944871i	$-0.393813\pi$
$131$	7.49553	0.654888	0.327444	+	0.944871i	$0.393813\pi$
$132$	1.63205	0.142051
$133$	−3.75064	−0.325221
$134$	7.13230	0.616137
$135$	−16.3461	−1.40685
$136$	1.46263	0.125420
$137$	13.2190	1.12937	0.564687	−	0.825305i	$-0.308997\pi$
$137$	13.2190	1.12937	0.564687	+	0.825305i	$0.308997\pi$
$138$	2.38015	0.202612
$139$	6.65074	0.564108	0.282054	−	0.959399i	$-0.408984\pi$
$139$	6.65074	0.564108	0.282054	+	0.959399i	$0.408984\pi$
$140$	10.9217	0.923052
$141$	−4.72031	−0.397522
$142$	4.01635	0.337045
$143$	−4.14774	−0.346852
$144$	−0.707195	−0.0589329
$145$	−7.24195	−0.601411
$146$	−15.5522	−1.28711
$147$	−10.7013	−0.882626
$148$	8.92851	0.733919
$149$	1.10176	0.0902598	0.0451299	−	0.998981i	$-0.485630\pi$
$149$	1.10176	0.0902598	0.0451299	+	0.998981i	$0.485630\pi$
$150$	−5.26867	−0.430185
$151$	−18.1525	−1.47723	−0.738616	−	0.674126i	$-0.764520\pi$
$151$	−18.1525	−1.47723	−0.738616	+	0.674126i	$0.764520\pi$
$152$	1.00000	0.0811107
$153$	−1.03437	−0.0836236
$154$	4.04254	0.325757
$155$	16.9091	1.35817
$156$	−5.82702	−0.466535
$157$	−12.2033	−0.973932	−0.486966	−	0.873421i	$-0.661896\pi$
$157$	−12.2033	−0.973932	−0.486966	+	0.873421i	$0.661896\pi$
$158$	−11.9353	−0.949525
$159$	6.10731	0.484341
$160$	−2.91196	−0.230211
$161$	5.89557	0.464636
$162$	−6.37829	−0.501126
$163$	−12.8855	−1.00927	−0.504634	−	0.863333i	$-0.668373\pi$
$163$	−12.8855	−1.00927	−0.504634	+	0.863333i	$0.668373\pi$
$164$	−3.70538	−0.289341
$165$	−4.75245	−0.369978
$166$	−0.410968	−0.0318973
$167$	16.3595	1.26594	0.632968	−	0.774178i	$-0.281837\pi$
$167$	16.3595	1.26594	0.632968	+	0.774178i	$0.281837\pi$
$168$	5.67922	0.438161
$169$	1.80900	0.139153
$170$	−4.25913	−0.326660
$171$	−0.707195	−0.0540805
$172$	2.26373	0.172608
$173$	8.11338	0.616849	0.308424	−	0.951249i	$-0.400198\pi$
$173$	8.11338	0.616849	0.308424	+	0.951249i	$0.400198\pi$
$174$	−3.76577	−0.285482
$175$	−13.0504	−0.986514
$176$	−1.07783	−0.0812442
$177$	−22.7783	−1.71212
$178$	−1.42947	−0.107143
$179$	15.2583	1.14046	0.570231	−	0.821484i	$-0.306854\pi$
$179$	15.2583	1.14046	0.570231	+	0.821484i	$0.306854\pi$
$180$	2.05932	0.153493
$181$	−7.21792	−0.536504	−0.268252	−	0.963349i	$-0.586446\pi$
$181$	−7.21792	−0.536504	−0.268252	+	0.963349i	$0.586446\pi$
$182$	−14.4334	−1.06987
$183$	−10.3948	−0.768403
$184$	−1.57188	−0.115881
$185$	−25.9995	−1.91152
$186$	8.79265	0.644708
$187$	−1.57646	−0.115283
$188$	3.11736	0.227357
$189$	−21.0540	−1.53145
$190$	−2.91196	−0.211256
$191$	−8.88480	−0.642882	−0.321441	−	0.946930i	$-0.604167\pi$
$191$	−8.88480	−0.642882	−0.321441	+	0.946930i	$0.604167\pi$
$192$	−1.51420	−0.109278
$193$	−13.7683	−0.991065	−0.495533	−	0.868589i	$-0.665027\pi$
$193$	−13.7683	−0.991065	−0.495533	+	0.868589i	$0.665027\pi$
$194$	−7.18019	−0.515508
$195$	16.9680	1.21511
$196$	7.06728	0.504805
$197$	−22.4145	−1.59697	−0.798483	−	0.602017i	$-0.794364\pi$
$197$	−22.4145	−1.59697	−0.798483	+	0.602017i	$0.794364\pi$
$198$	0.762233	0.0541695
$199$	−9.43267	−0.668664	−0.334332	−	0.942455i	$-0.608511\pi$
$199$	−9.43267	−0.668664	−0.334332	+	0.942455i	$0.608511\pi$
$200$	3.47950	0.246038
$201$	−10.7997	−0.761755
$202$	−15.3214	−1.07801
$203$	−9.32771	−0.654677
$204$	−2.21472	−0.155061
$205$	10.7899	0.753600
$206$	17.0428	1.18743
$207$	1.11163	0.0772635
$208$	3.84825	0.266828
$209$	−1.07783	−0.0745548
$210$	−16.5377	−1.14121
$211$	−1.00000	−0.0688428
$211$	−1.00000	−0.0688428
$212$	−4.03335	−0.277012
$213$	−6.08156	−0.416702
$214$	5.51478	0.376983
$215$	−6.59189	−0.449563
$216$	5.61344	0.381946
$217$	21.7792	1.47847
$218$	5.98523	0.405371
$219$	23.5492	1.59131
$220$	3.13859	0.211603
$221$	5.62857	0.378619
$222$	−13.5196	−0.907374
$223$	−16.7954	−1.12470	−0.562352	−	0.826898i	$-0.690103\pi$
$223$	−16.7954	−1.12470	−0.562352	+	0.826898i	$0.690103\pi$
$224$	−3.75064	−0.250600
$225$	−2.46069	−0.164046
$226$	−12.7751	−0.849789
$227$	−20.7288	−1.37582	−0.687910	−	0.725796i	$-0.741472\pi$
$227$	−20.7288	−1.37582	−0.687910	+	0.725796i	$0.741472\pi$
$228$	−1.51420	−0.100280
$229$	11.3130	0.747584	0.373792	−	0.927512i	$-0.378057\pi$
$229$	11.3130	0.747584	0.373792	+	0.927512i	$0.378057\pi$
$230$	4.57726	0.301816
$231$	−6.12121	−0.402746
$232$	2.48697	0.163277
$233$	−9.25379	−0.606236	−0.303118	−	0.952953i	$-0.598028\pi$
$233$	−9.25379	−0.606236	−0.303118	+	0.952953i	$0.598028\pi$
$234$	−2.72146	−0.177907
$235$	−9.07762	−0.592159
$236$	15.0431	0.979222
$237$	18.0725	1.17394
$238$	−5.48581	−0.355592
$239$	−17.7783	−1.14998	−0.574992	−	0.818159i	$-0.694995\pi$
$239$	−17.7783	−1.14998	−0.574992	+	0.818159i	$0.694995\pi$
$240$	4.40929	0.284619
$241$	−26.5501	−1.71024	−0.855122	−	0.518427i	$-0.826518\pi$
$241$	−26.5501	−1.71024	−0.855122	+	0.518427i	$0.826518\pi$
$242$	−9.83829	−0.632429
$243$	−7.18230	−0.460745
$244$	6.86485	0.439477
$245$	−20.5796	−1.31478
$246$	5.61069	0.357724
$247$	3.84825	0.244858
$248$	−5.80679	−0.368732
$249$	0.622287	0.0394359
$250$	4.42762	0.280027
$251$	−12.9230	−0.815693	−0.407846	−	0.913051i	$-0.633720\pi$
$251$	−12.9230	−0.815693	−0.407846	+	0.913051i	$0.633720\pi$
$252$	2.65243	0.167087
$253$	1.69422	0.106515
$254$	12.7818	0.802001
$255$	6.44918	0.403863
$256$	1.00000	0.0625000
$257$	−8.73531	−0.544894	−0.272447	−	0.962171i	$-0.587833\pi$
$257$	−8.73531	−0.544894	−0.272447	+	0.962171i	$0.587833\pi$
$258$	−3.42775	−0.213402
$259$	−33.4876	−2.08082
$260$	−11.2059	−0.694962
$261$	−1.75877	−0.108865
$262$	7.49553	0.463075
$263$	3.79962	0.234295	0.117147	−	0.993115i	$-0.462625\pi$
$263$	3.79962	0.234295	0.117147	+	0.993115i	$0.462625\pi$
$264$	1.63205	0.100445
$265$	11.7450	0.721487
$266$	−3.75064	−0.229966
$267$	2.16450	0.132465
$268$	7.13230	0.435675
$269$	−25.0708	−1.52859	−0.764297	−	0.644865i	$-0.776914\pi$
$269$	−25.0708	−1.52859	−0.764297	+	0.644865i	$0.776914\pi$
$270$	−16.3461	−0.994792
$271$	15.6996	0.953686	0.476843	−	0.878989i	$-0.341781\pi$
$271$	15.6996	0.953686	0.476843	+	0.878989i	$0.341781\pi$
$272$	1.46263	0.0886852
$273$	21.8550	1.32273
$274$	13.2190	0.798588
$275$	−3.75030	−0.226152
$276$	2.38015	0.143268
$277$	3.43748	0.206538	0.103269	−	0.994653i	$-0.467070\pi$
$277$	3.43748	0.206538	0.103269	+	0.994653i	$0.467070\pi$
$278$	6.65074	0.398885
$279$	4.10653	0.245852
$280$	10.9217	0.652696
$281$	18.6736	1.11398	0.556988	−	0.830520i	$-0.311957\pi$
$281$	18.6736	1.11398	0.556988	+	0.830520i	$0.311957\pi$
$282$	−4.72031	−0.281090
$283$	29.7132	1.76627	0.883133	−	0.469123i	$-0.155430\pi$
$283$	29.7132	1.76627	0.883133	+	0.469123i	$0.155430\pi$
$284$	4.01635	0.238326
$285$	4.40929	0.261184
$286$	−4.14774	−0.245261
$287$	13.8975	0.820345
$288$	−0.707195	−0.0416718
$289$	−14.8607	−0.874159
$290$	−7.24195	−0.425262
$291$	10.8723	0.637343
$292$	−15.5522	−0.910125
$293$	−16.6447	−0.972392	−0.486196	−	0.873850i	$-0.661616\pi$
$293$	−16.6447	−0.972392	−0.486196	+	0.873850i	$0.661616\pi$
$294$	−10.7013	−0.624111
$295$	−43.8049	−2.55042
$296$	8.92851	0.518959
$297$	−6.05031	−0.351075
$298$	1.10176	0.0638233
$299$	−6.04900	−0.349822
$300$	−5.26867	−0.304187
$301$	−8.49044	−0.489381
$302$	−18.1525	−1.04456
$303$	23.1997	1.33279
$304$	1.00000	0.0573539
$305$	−19.9902	−1.14463
$306$	−1.03437	−0.0591308
$307$	−21.8723	−1.24832	−0.624158	−	0.781298i	$-0.714558\pi$
$307$	−21.8723	−1.24832	−0.624158	+	0.781298i	$0.714558\pi$
$308$	4.04254	0.230345
$309$	−25.8063	−1.46807
$310$	16.9091	0.960375
$311$	14.2577	0.808479	0.404239	−	0.914653i	$-0.367536\pi$
$311$	14.2577	0.808479	0.404239	+	0.914653i	$0.367536\pi$
$312$	−5.82702	−0.329890
$313$	1.50800	0.0852373	0.0426187	−	0.999091i	$-0.486430\pi$
$313$	1.50800	0.0852373	0.0426187	+	0.999091i	$0.486430\pi$
$314$	−12.2033	−0.688674
$315$	−7.72377	−0.435185
$316$	−11.9353	−0.671415
$317$	7.27695	0.408714	0.204357	−	0.978896i	$-0.434490\pi$
$317$	7.27695	0.408714	0.204357	+	0.978896i	$0.434490\pi$
$318$	6.10731	0.342481
$319$	−2.68052	−0.150080
$320$	−2.91196	−0.162783
$321$	−8.35049	−0.466079
$322$	5.89557	0.328547
$323$	1.46263	0.0813831
$324$	−6.37829	−0.354350
$325$	13.3900	0.742743
$326$	−12.8855	−0.713661
$327$	−9.06285	−0.501177
$328$	−3.70538	−0.204595
$329$	−11.6921	−0.644605
$330$	−4.75245	−0.261614
$331$	22.6267	1.24368	0.621838	−	0.783146i	$-0.286386\pi$
$331$	22.6267	1.24368	0.621838	+	0.783146i	$0.286386\pi$
$332$	−0.410968	−0.0225548
$333$	−6.31419	−0.346016
$334$	16.3595	0.895152
$335$	−20.7690	−1.13473
$336$	5.67922	0.309827
$337$	0.650779	0.0354502	0.0177251	−	0.999843i	$-0.494358\pi$
$337$	0.650779	0.0354502	0.0177251	+	0.999843i	$0.494358\pi$
$338$	1.80900	0.0983964
$339$	19.3441	1.05063
$340$	−4.25913	−0.230984
$341$	6.25871	0.338928
$342$	−0.707195	−0.0382407
$343$	−0.252324	−0.0136242
$344$	2.26373	0.122052
$345$	−6.93090	−0.373147
$346$	8.11338	0.436178
$347$	9.25992	0.497098	0.248549	−	0.968619i	$-0.420046\pi$
$347$	9.25992	0.497098	0.248549	+	0.968619i	$0.420046\pi$
$348$	−3.76577	−0.201866
$349$	−10.2506	−0.548704	−0.274352	−	0.961629i	$-0.588463\pi$
$349$	−10.2506	−0.548704	−0.274352	+	0.961629i	$0.588463\pi$
$350$	−13.0504	−0.697571
$351$	21.6019	1.15302
$352$	−1.07783	−0.0574483
$353$	16.8906	0.898993	0.449497	−	0.893282i	$-0.351603\pi$
$353$	16.8906	0.898993	0.449497	+	0.893282i	$0.351603\pi$
$354$	−22.7783	−1.21065
$355$	−11.6954	−0.620730
$356$	−1.42947	−0.0757617
$357$	8.30661	0.439633
$358$	15.2583	0.806429
$359$	−15.9866	−0.843743	−0.421872	−	0.906656i	$-0.638627\pi$
$359$	−15.9866	−0.843743	−0.421872	+	0.906656i	$0.638627\pi$
$360$	2.05932	0.108536
$361$	1.00000	0.0526316
$362$	−7.21792	−0.379365
$363$	14.8972	0.781898
$364$	−14.4334	−0.756514
$365$	45.2875	2.37045
$366$	−10.3948	−0.543343
$367$	−25.4157	−1.32669	−0.663346	−	0.748313i	$-0.730864\pi$
$367$	−25.4157	−1.32669	−0.663346	+	0.748313i	$0.730864\pi$
$368$	−1.57188	−0.0819401
$369$	2.62042	0.136414
$370$	−25.9995	−1.35165
$371$	15.1276	0.785388
$372$	8.79265	0.455878
$373$	−8.15582	−0.422293	−0.211146	−	0.977454i	$-0.567720\pi$
$373$	−8.15582	−0.422293	−0.211146	+	0.977454i	$0.567720\pi$
$374$	−1.57646	−0.0815171
$375$	−6.70431	−0.346209
$376$	3.11736	0.160765
$377$	9.57046	0.492904
$378$	−21.0540	−1.08290
$379$	−25.6554	−1.31783	−0.658915	−	0.752217i	$-0.728984\pi$
$379$	−25.6554	−1.31783	−0.658915	+	0.752217i	$0.728984\pi$
$380$	−2.91196	−0.149380
$381$	−19.3542	−0.991546
$382$	−8.88480	−0.454586
$383$	−8.78453	−0.448869	−0.224434	−	0.974489i	$-0.572053\pi$
$383$	−8.78453	−0.448869	−0.224434	+	0.974489i	$0.572053\pi$
$384$	−1.51420	−0.0772713
$385$	−11.7717	−0.599941
$386$	−13.7683	−0.700789
$387$	−1.60090	−0.0813783
$388$	−7.18019	−0.364519
$389$	18.6271	0.944429	0.472215	−	0.881484i	$-0.343455\pi$
$389$	18.6271	0.944429	0.472215	+	0.881484i	$0.343455\pi$
$390$	16.9680	0.859210
$391$	−2.29909	−0.116270
$392$	7.06728	0.356951
$393$	−11.3497	−0.572519
$394$	−22.4145	−1.12923
$395$	34.7552	1.74872
$396$	0.762233	0.0383037
$397$	6.46399	0.324418	0.162209	−	0.986756i	$-0.448138\pi$
$397$	6.46399	0.324418	0.162209	+	0.986756i	$0.448138\pi$
$398$	−9.43267	−0.472817
$399$	5.67922	0.284317
$400$	3.47950	0.173975
$401$	−23.6505	−1.18105	−0.590524	−	0.807020i	$-0.701079\pi$
$401$	−23.6505	−1.18105	−0.590524	+	0.807020i	$0.701079\pi$
$402$	−10.7997	−0.538642
$403$	−22.3460	−1.11313
$404$	−15.3214	−0.762270
$405$	18.5733	0.922916
$406$	−9.32771	−0.462927
$407$	−9.62338	−0.477013
$408$	−2.21472	−0.109645
$409$	0.663992	0.0328323	0.0164161	−	0.999865i	$-0.494774\pi$
$409$	0.663992	0.0328323	0.0164161	+	0.999865i	$0.494774\pi$
$410$	10.7899	0.532875
$411$	−20.0162	−0.987326
$412$	17.0428	0.839640
$413$	−56.4212	−2.77630
$414$	1.11163	0.0546335
$415$	1.19672	0.0587447
$416$	3.84825	0.188676
$417$	−10.0706	−0.493157
$418$	−1.07783	−0.0527182
$419$	29.2325	1.42810	0.714050	−	0.700095i	$-0.246859\pi$
$419$	29.2325	1.42810	0.714050	+	0.700095i	$0.246859\pi$
$420$	−16.5377	−0.806955
$421$	12.7450	0.621154	0.310577	−	0.950548i	$-0.399478\pi$
$421$	12.7450	0.621154	0.310577	+	0.950548i	$0.399478\pi$
$422$	−1.00000	−0.0486792
$423$	−2.20458	−0.107190
$424$	−4.03335	−0.195877
$425$	5.08924	0.246864
$426$	−6.08156	−0.294653
$427$	−25.7476	−1.24601
$428$	5.51478	0.266567
$429$	6.28051	0.303226
$430$	−6.59189	−0.317889
$431$	10.6344	0.512241	0.256121	−	0.966645i	$-0.417556\pi$
$431$	10.6344	0.512241	0.256121	+	0.966645i	$0.417556\pi$
$432$	5.61344	0.270077
$433$	34.3350	1.65004	0.825018	−	0.565107i	$-0.191165\pi$
$433$	34.3350	1.65004	0.825018	+	0.565107i	$0.191165\pi$
$434$	21.7792	1.04543
$435$	10.9658	0.525768
$436$	5.98523	0.286641
$437$	−1.57188	−0.0751934
$438$	23.5492	1.12522
$439$	3.35608	0.160177	0.0800885	−	0.996788i	$-0.474480\pi$
$439$	3.35608	0.160177	0.0800885	+	0.996788i	$0.474480\pi$
$440$	3.13859	0.149626
$441$	−4.99794	−0.237997
$442$	5.62857	0.267724
$443$	17.8153	0.846431	0.423216	−	0.906029i	$-0.360901\pi$
$443$	17.8153	0.846431	0.423216	+	0.906029i	$0.360901\pi$
$444$	−13.5196	−0.641610
$445$	4.16255	0.197324
$446$	−16.7954	−0.795285
$447$	−1.66829	−0.0789073
$448$	−3.75064	−0.177201
$449$	12.0352	0.567978	0.283989	−	0.958828i	$-0.408342\pi$
$449$	12.0352	0.567978	0.283989	+	0.958828i	$0.408342\pi$
$450$	−2.46069	−0.115998
$451$	3.99375	0.188058
$452$	−12.7751	−0.600892
$453$	27.4866	1.29143
$454$	−20.7288	−0.972851
$455$	42.0294	1.97037
$456$	−1.51420	−0.0709090
$457$	−26.3704	−1.23355	−0.616777	−	0.787138i	$-0.711562\pi$
$457$	−26.3704	−1.23355	−0.616777	+	0.787138i	$0.711562\pi$
$458$	11.3130	0.528622
$459$	8.21040	0.383229
$460$	4.57726	0.213416
$461$	41.5856	1.93684	0.968418	−	0.249333i	$-0.0802112\pi$
$461$	41.5856	1.93684	0.968418	+	0.249333i	$0.0802112\pi$
$462$	−6.12121	−0.284785
$463$	−7.69812	−0.357762	−0.178881	−	0.983871i	$-0.557248\pi$
$463$	−7.69812	−0.357762	−0.178881	+	0.983871i	$0.557248\pi$
$464$	2.48697	0.115455
$465$	−25.6038	−1.18735
$466$	−9.25379	−0.428673
$467$	−8.83687	−0.408922	−0.204461	−	0.978875i	$-0.565544\pi$
$467$	−8.83687	−0.408922	−0.204461	+	0.978875i	$0.565544\pi$
$468$	−2.72146	−0.125799
$469$	−26.7507	−1.23523
$470$	−9.07762	−0.418719
$471$	18.4783	0.851435
$472$	15.0431	0.692415
$473$	−2.43991	−0.112187
$474$	18.0725	0.830098
$475$	3.47950	0.159651
$476$	−5.48581	−0.251441
$477$	2.85236	0.130601
$478$	−17.7783	−0.813161
$479$	1.71555	0.0783854	0.0391927	−	0.999232i	$-0.487521\pi$
$479$	1.71555	0.0783854	0.0391927	+	0.999232i	$0.487521\pi$
$480$	4.40929	0.201256
$481$	34.3591	1.56664
$482$	−26.5501	−1.20932
$483$	−8.92707	−0.406196
$484$	−9.83829	−0.447195
$485$	20.9084	0.949403
$486$	−7.18230	−0.325796
$487$	36.7555	1.66555	0.832775	−	0.553612i	$-0.186751\pi$
$487$	36.7555	1.66555	0.832775	+	0.553612i	$0.186751\pi$
$488$	6.86485	0.310757
$489$	19.5112	0.882327
$490$	−20.5796	−0.929692
$491$	−27.6658	−1.24854	−0.624270	−	0.781208i	$-0.714604\pi$
$491$	−27.6658	−1.24854	−0.624270	+	0.781208i	$0.714604\pi$
$492$	5.61069	0.252949
$493$	3.63752	0.163826
$494$	3.84825	0.173141
$495$	−2.21959	−0.0997632
$496$	−5.80679	−0.260733
$497$	−15.0639	−0.675707
$498$	0.622287	0.0278854
$499$	10.8003	0.483489	0.241744	−	0.970340i	$-0.422280\pi$
$499$	10.8003	0.483489	0.241744	+	0.970340i	$0.422280\pi$
$500$	4.42762	0.198009
$501$	−24.7716	−1.10671
$502$	−12.9230	−0.576782
$503$	35.5294	1.58418	0.792090	−	0.610405i	$-0.208993\pi$
$503$	35.5294	1.58418	0.792090	+	0.610405i	$0.208993\pi$
$504$	2.65243	0.118149
$505$	44.6154	1.98536
$506$	1.69422	0.0753172
$507$	−2.73918	−0.121651
$508$	12.7818	0.567100
$509$	12.3705	0.548313	0.274156	−	0.961685i	$-0.411601\pi$
$509$	12.3705	0.548313	0.274156	+	0.961685i	$0.411601\pi$
$510$	6.44918	0.285574
$511$	58.3308	2.58040
$512$	1.00000	0.0441942
$513$	5.61344	0.247839
$514$	−8.73531	−0.385298
$515$	−49.6280	−2.18687
$516$	−3.42775	−0.150898
$517$	−3.35997	−0.147771
$518$	−33.4876	−1.47136
$519$	−12.2853	−0.539264
$520$	−11.2059	−0.491413
$521$	2.85190	0.124944	0.0624720	−	0.998047i	$-0.480102\pi$
$521$	2.85190	0.124944	0.0624720	+	0.998047i	$0.480102\pi$
$522$	−1.75877	−0.0769793
$523$	−38.7923	−1.69627	−0.848135	−	0.529780i	$-0.822274\pi$
$523$	−38.7923	−1.69627	−0.848135	+	0.529780i	$0.822274\pi$
$524$	7.49553	0.327444
$525$	19.7609	0.862435
$526$	3.79962	0.165671
$527$	−8.49321	−0.369970
$528$	1.63205	0.0710257
$529$	−20.5292	−0.892573
$530$	11.7450	0.510168
$531$	−10.6384	−0.461667
$532$	−3.75064	−0.162611
$533$	−14.2592	−0.617634
$534$	2.16450	0.0936672
$535$	−16.0588	−0.694283
$536$	7.13230	0.308068
$537$	−23.1042	−0.997020
$538$	−25.0708	−1.08088
$539$	−7.61730	−0.328100
$540$	−16.3461	−0.703424
$541$	12.1375	0.521832	0.260916	−	0.965362i	$-0.415975\pi$
$541$	12.1375	0.521832	0.260916	+	0.965362i	$0.415975\pi$
$542$	15.6996	0.674357
$543$	10.9294	0.469025
$544$	1.46263	0.0627099
$545$	−17.4288	−0.746566
$546$	21.8550	0.935309
$547$	−22.8269	−0.976008	−0.488004	−	0.872841i	$-0.662275\pi$
$547$	−22.8269	−0.976008	−0.488004	+	0.872841i	$0.662275\pi$
$548$	13.2190	0.564687
$549$	−4.85478	−0.207197
$550$	−3.75030	−0.159913
$551$	2.48697	0.105948
$552$	2.38015	0.101306
$553$	44.7651	1.90361
$554$	3.43748	0.146045
$555$	39.3684	1.67110
$556$	6.65074	0.282054
$557$	−25.2863	−1.07142	−0.535708	−	0.844403i	$-0.679955\pi$
$557$	−25.2863	−1.07142	−0.535708	+	0.844403i	$0.679955\pi$
$558$	4.10653	0.173843
$559$	8.71140	0.368453
$560$	10.9217	0.461526
$561$	2.38708	0.100783
$562$	18.6736	0.787700
$563$	−15.2668	−0.643419	−0.321709	−	0.946838i	$-0.604257\pi$
$563$	−15.2668	−0.643419	−0.321709	+	0.946838i	$0.604257\pi$
$564$	−4.72031	−0.198761
$565$	37.2007	1.56504
$566$	29.7132	1.24894
$567$	23.9227	1.00466
$568$	4.01635	0.168522
$569$	10.3893	0.435542	0.217771	−	0.976000i	$-0.430121\pi$
$569$	10.3893	0.435542	0.217771	+	0.976000i	$0.430121\pi$
$570$	4.40929	0.184685
$571$	43.2802	1.81122	0.905610	−	0.424111i	$-0.139413\pi$
$571$	43.2802	1.81122	0.905610	+	0.424111i	$0.139413\pi$
$572$	−4.14774	−0.173426
$573$	13.4534	0.562023
$574$	13.8975	0.580071
$575$	−5.46938	−0.228089
$576$	−0.707195	−0.0294664
$577$	−0.0509341	−0.00212042	−0.00106021	−	0.999999i	$-0.500337\pi$
$577$	−0.0509341	−0.00212042	−0.00106021	+	0.999999i	$0.500337\pi$
$578$	−14.8607	−0.618124
$579$	20.8480	0.866413
$580$	−7.24195	−0.300705
$581$	1.54139	0.0639476
$582$	10.8723	0.450670
$583$	4.34725	0.180045
$584$	−15.5522	−0.643556
$585$	7.92478	0.327649
$586$	−16.6447	−0.687585
$587$	35.4468	1.46305	0.731523	−	0.681816i	$-0.238810\pi$
$587$	35.4468	1.46305	0.731523	+	0.681816i	$0.238810\pi$
$588$	−10.7013	−0.441313
$589$	−5.80679	−0.239265
$590$	−43.8049	−1.80342
$591$	33.9401	1.39611
$592$	8.92851	0.366960
$593$	42.7870	1.75705	0.878527	−	0.477693i	$-0.158527\pi$
$593$	42.7870	1.75705	0.878527	+	0.477693i	$0.158527\pi$
$594$	−6.05031	−0.248247
$595$	15.9744	0.654888
$596$	1.10176	0.0451299
$597$	14.2830	0.584562
$598$	−6.04900	−0.247362
$599$	−9.99719	−0.408474	−0.204237	−	0.978921i	$-0.565471\pi$
$599$	−9.99719	−0.408474	−0.204237	+	0.978921i	$0.565471\pi$
$600$	−5.26867	−0.215093
$601$	−33.2591	−1.35667	−0.678334	−	0.734754i	$-0.737298\pi$
$601$	−33.2591	−1.35667	−0.678334	+	0.734754i	$0.737298\pi$
$602$	−8.49044	−0.346044
$603$	−5.04392	−0.205404
$604$	−18.1525	−0.738616
$605$	28.6487	1.16474
$606$	23.1997	0.942425
$607$	−36.1194	−1.46604	−0.733020	−	0.680207i	$-0.761890\pi$
$607$	−36.1194	−1.46604	−0.733020	+	0.680207i	$0.761890\pi$
$608$	1.00000	0.0405554
$609$	14.1240	0.572335
$610$	−19.9902	−0.809378
$611$	11.9964	0.485321
$612$	−1.03437	−0.0418118
$613$	−6.76126	−0.273085	−0.136542	−	0.990634i	$-0.543599\pi$
$613$	−6.76126	−0.273085	−0.136542	+	0.990634i	$0.543599\pi$
$614$	−21.8723	−0.882693
$615$	−16.3381	−0.658815
$616$	4.04254	0.162878
$617$	7.78351	0.313352	0.156676	−	0.987650i	$-0.449922\pi$
$617$	7.78351	0.313352	0.156676	+	0.987650i	$0.449922\pi$
$618$	−25.8063	−1.03808
$619$	−38.9974	−1.56744	−0.783718	−	0.621116i	$-0.786679\pi$
$619$	−38.9974	−1.56744	−0.783718	+	0.621116i	$0.786679\pi$
$620$	16.9091	0.679087
$621$	−8.82368	−0.354082
$622$	14.2577	0.571681
$623$	5.36142	0.214801
$624$	−5.82702	−0.233267
$625$	−30.2906	−1.21162
$626$	1.50800	0.0602719
$627$	1.63205	0.0651776
$628$	−12.2033	−0.486966
$629$	13.0591	0.520702
$630$	−7.72377	−0.307722
$631$	4.37505	0.174168	0.0870840	−	0.996201i	$-0.472245\pi$
$631$	4.37505	0.174168	0.0870840	+	0.996201i	$0.472245\pi$
$632$	−11.9353	−0.474762
$633$	1.51420	0.0601841
$634$	7.27695	0.289005
$635$	−37.2200	−1.47703
$636$	6.10731	0.242170
$637$	27.1966	1.07757
$638$	−2.68052	−0.106123
$639$	−2.84034	−0.112362
$640$	−2.91196	−0.115105
$641$	−37.2885	−1.47281	−0.736403	−	0.676543i	$-0.763477\pi$
$641$	−37.2885	−1.47281	−0.736403	+	0.676543i	$0.763477\pi$
$642$	−8.35049	−0.329567
$643$	8.12265	0.320326	0.160163	−	0.987091i	$-0.448798\pi$
$643$	8.12265	0.320326	0.160163	+	0.987091i	$0.448798\pi$
$644$	5.89557	0.232318
$645$	9.98145	0.393019
$646$	1.46263	0.0575465
$647$	−11.0717	−0.435273	−0.217637	−	0.976030i	$-0.569835\pi$
$647$	−11.0717	−0.435273	−0.217637	+	0.976030i	$0.569835\pi$
$648$	−6.37829	−0.250563
$649$	−16.2138	−0.636449
$650$	13.3900	0.525199
$651$	−32.9780	−1.29251
$652$	−12.8855	−0.504634
$653$	−18.4963	−0.723818	−0.361909	−	0.932213i	$-0.617875\pi$
$653$	−18.4963	−0.723818	−0.361909	+	0.932213i	$0.617875\pi$
$654$	−9.06285	−0.354385
$655$	−21.8267	−0.852839
$656$	−3.70538	−0.144671
$657$	10.9985	0.429091
$658$	−11.6921	−0.455805
$659$	5.55865	0.216534	0.108267	−	0.994122i	$-0.465470\pi$
$659$	5.55865	0.216534	0.108267	+	0.994122i	$0.465470\pi$
$660$	−4.75245	−0.184989
$661$	31.7288	1.23411	0.617053	−	0.786921i	$-0.288326\pi$
$661$	31.7288	1.23411	0.617053	+	0.786921i	$0.288326\pi$
$662$	22.6267	0.879412
$663$	−8.52279	−0.330998
$664$	−0.410968	−0.0159486
$665$	10.9217	0.423525
$666$	−6.31419	−0.244670
$667$	−3.90922	−0.151366
$668$	16.3595	0.632968
$669$	25.4316	0.983243
$670$	−20.7690	−0.802375
$671$	−7.39912	−0.285640
$672$	5.67922	0.219081
$673$	−9.09724	−0.350673	−0.175336	−	0.984509i	$-0.556101\pi$
$673$	−9.09724	−0.350673	−0.175336	+	0.984509i	$0.556101\pi$
$674$	0.650779	0.0250671
$675$	19.5320	0.751787
$676$	1.80900	0.0695767
$677$	−22.6646	−0.871073	−0.435537	−	0.900171i	$-0.643441\pi$
$677$	−22.6646	−0.871073	−0.435537	+	0.900171i	$0.643441\pi$
$678$	19.3441	0.742906
$679$	26.9303	1.03349
$680$	−4.25913	−0.163330
$681$	31.3876	1.20278
$682$	6.25871	0.239659
$683$	−43.6585	−1.67055	−0.835273	−	0.549836i	$-0.814690\pi$
$683$	−43.6585	−1.67055	−0.835273	+	0.549836i	$0.814690\pi$
$684$	−0.707195	−0.0270403
$685$	−38.4931	−1.47075
$686$	−0.252324	−0.00963379
$687$	−17.1302	−0.653557
$688$	2.26373	0.0863040
$689$	−15.5213	−0.591316
$690$	−6.93090	−0.263855
$691$	11.2109	0.426481	0.213241	−	0.977000i	$-0.431598\pi$
$691$	11.2109	0.426481	0.213241	+	0.977000i	$0.431598\pi$
$692$	8.11338	0.308424
$693$	−2.85886	−0.108599
$694$	9.25992	0.351502
$695$	−19.3667	−0.734620
$696$	−3.76577	−0.142741
$697$	−5.41961	−0.205282
$698$	−10.2506	−0.387992
$699$	14.0121	0.529986
$700$	−13.0504	−0.493257
$701$	−3.58061	−0.135238	−0.0676188	−	0.997711i	$-0.521540\pi$
$701$	−3.58061	−0.135238	−0.0676188	+	0.997711i	$0.521540\pi$
$702$	21.6019	0.815311
$703$	8.92851	0.336745
$704$	−1.07783	−0.0406221
$705$	13.7453	0.517679
$706$	16.8906	0.635684
$707$	57.4651	2.16120
$708$	−22.7783	−0.856060
$709$	−2.67917	−0.100618	−0.0503091	−	0.998734i	$-0.516021\pi$
$709$	−2.67917	−0.100618	−0.0503091	+	0.998734i	$0.516021\pi$
$710$	−11.6954	−0.438922
$711$	8.44061	0.316548
$712$	−1.42947	−0.0535716
$713$	9.12760	0.341831
$714$	8.30661	0.310867
$715$	12.0781	0.451694
$716$	15.2583	0.570231
$717$	26.9199	1.00534
$718$	−15.9866	−0.596616
$719$	14.8596	0.554170	0.277085	−	0.960845i	$-0.410632\pi$
$719$	14.8596	0.554170	0.277085	+	0.960845i	$0.410632\pi$
$720$	2.05932	0.0767464
$721$	−63.9215	−2.38056
$722$	1.00000	0.0372161
$723$	40.2022	1.49514
$724$	−7.21792	−0.268252
$725$	8.65341	0.321380
$726$	14.8972	0.552885
$727$	9.59031	0.355685	0.177842	−	0.984059i	$-0.443088\pi$
$727$	9.59031	0.355685	0.177842	+	0.984059i	$0.443088\pi$
$728$	−14.4334	−0.534936
$729$	30.0103	1.11149
$730$	45.2875	1.67616
$731$	3.31101	0.122462
$732$	−10.3948	−0.384201
$733$	23.0869	0.852733	0.426367	−	0.904550i	$-0.359793\pi$
$733$	23.0869	0.852733	0.426367	+	0.904550i	$0.359793\pi$
$734$	−25.4157	−0.938112
$735$	31.1617	1.14942
$736$	−1.57188	−0.0579404
$737$	−7.68738	−0.283168
$738$	2.62042	0.0964591
$739$	−13.6708	−0.502889	−0.251444	−	0.967872i	$-0.580906\pi$
$739$	−13.6708	−0.502889	−0.251444	+	0.967872i	$0.580906\pi$
$740$	−25.9995	−0.955759
$741$	−5.82702	−0.214061
$742$	15.1276	0.555353
$743$	33.5068	1.22925	0.614623	−	0.788821i	$-0.289308\pi$
$743$	33.5068	1.22925	0.614623	+	0.788821i	$0.289308\pi$
$744$	8.79265	0.322354
$745$	−3.20828	−0.117542
$746$	−8.15582	−0.298606
$747$	0.290634	0.0106337
$748$	−1.57646	−0.0576413
$749$	−20.6839	−0.755774
$750$	−6.70431	−0.244807
$751$	−41.6802	−1.52093	−0.760466	−	0.649377i	$-0.775030\pi$
$751$	−41.6802	−1.52093	−0.760466	+	0.649377i	$0.775030\pi$
$752$	3.11736	0.113678
$753$	19.5680	0.713098
$754$	9.57046	0.348536
$755$	52.8594	1.92375
$756$	−21.0540	−0.765725
$757$	−17.9851	−0.653678	−0.326839	−	0.945080i	$-0.605984\pi$
$757$	−17.9851	−0.653678	−0.326839	+	0.945080i	$0.605984\pi$
$758$	−25.6554	−0.931846
$759$	−2.56539	−0.0931177
$760$	−2.91196	−0.105628
$761$	−4.58948	−0.166369	−0.0831843	−	0.996534i	$-0.526509\pi$
$761$	−4.58948	−0.166369	−0.0831843	+	0.996534i	$0.526509\pi$
$762$	−19.3542	−0.701129
$763$	−22.4484	−0.812688
$764$	−8.88480	−0.321441
$765$	3.01203	0.108900
$766$	−8.78453	−0.317398
$767$	57.8895	2.09027
$768$	−1.51420	−0.0546390
$769$	37.8200	1.36382	0.681911	−	0.731435i	$-0.261149\pi$
$769$	37.8200	1.36382	0.681911	+	0.731435i	$0.261149\pi$
$770$	−11.7717	−0.424223
$771$	13.2270	0.476360
$772$	−13.7683	−0.495533
$773$	−28.6396	−1.03009	−0.515047	−	0.857162i	$-0.672226\pi$
$773$	−28.6396	−1.03009	−0.515047	+	0.857162i	$0.672226\pi$
$774$	−1.60090	−0.0575431
$775$	−20.2048	−0.725776
$776$	−7.18019	−0.257754
$777$	50.7070	1.81910
$778$	18.6271	0.667812
$779$	−3.70538	−0.132759
$780$	16.9680	0.607553
$781$	−4.32893	−0.154901
$782$	−2.29909	−0.0822153
$783$	13.9604	0.498905
$784$	7.06728	0.252403
$785$	35.5356	1.26832
$786$	−11.3497	−0.404832
$787$	10.9807	0.391419	0.195710	−	0.980662i	$-0.437299\pi$
$787$	10.9807	0.391419	0.195710	+	0.980662i	$0.437299\pi$
$788$	−22.4145	−0.798483
$789$	−5.75339	−0.204826
$790$	34.7552	1.23654
$791$	47.9149	1.70366
$792$	0.762233	0.0270848
$793$	26.4176	0.938117
$794$	6.46399	0.229398
$795$	−17.7842	−0.630741
$796$	−9.43267	−0.334332
$797$	−51.9536	−1.84029	−0.920145	−	0.391578i	$-0.871929\pi$
$797$	−51.9536	−1.84029	−0.920145	+	0.391578i	$0.871929\pi$
$798$	5.67922	0.201042
$799$	4.55955	0.161305
$800$	3.47950	0.123019
$801$	1.01091	0.0357188
$802$	−23.6505	−0.835127
$803$	16.7626	0.591539
$804$	−10.7997	−0.380877
$805$	−17.1676	−0.605080
$806$	−22.3460	−0.787103
$807$	37.9622	1.33633
$808$	−15.3214	−0.539006
$809$	−44.5391	−1.56591	−0.782955	−	0.622078i	$-0.786289\pi$
$809$	−44.5391	−1.56591	−0.782955	+	0.622078i	$0.786289\pi$
$810$	18.5733	0.652600
$811$	−14.9982	−0.526657	−0.263329	−	0.964706i	$-0.584820\pi$
$811$	−14.9982	−0.526657	−0.263329	+	0.964706i	$0.584820\pi$
$812$	−9.32771	−0.327338
$813$	−23.7724	−0.833735
$814$	−9.62338	−0.337299
$815$	37.5220	1.31434
$816$	−2.21472	−0.0775307
$817$	2.26373	0.0791980
$818$	0.663992	0.0232159
$819$	10.2072	0.356669
$820$	10.7899	0.376800
$821$	2.08865	0.0728946	0.0364473	−	0.999336i	$-0.488396\pi$
$821$	2.08865	0.0728946	0.0364473	+	0.999336i	$0.488396\pi$
$822$	−20.0162	−0.698145
$823$	−41.4810	−1.44594	−0.722969	−	0.690881i	$-0.757223\pi$
$823$	−41.4810	−1.44594	−0.722969	+	0.690881i	$0.757223\pi$
$824$	17.0428	0.593715
$825$	5.67871	0.197707
$826$	−56.4212	−1.96314
$827$	8.40067	0.292120	0.146060	−	0.989276i	$-0.453341\pi$
$827$	8.40067	0.292120	0.146060	+	0.989276i	$0.453341\pi$
$828$	1.11163	0.0386317
$829$	19.8866	0.690690	0.345345	−	0.938476i	$-0.387762\pi$
$829$	19.8866	0.690690	0.345345	+	0.938476i	$0.387762\pi$
$830$	1.19672	0.0415388
$831$	−5.20504	−0.180561
$832$	3.84825	0.133414
$833$	10.3368	0.358150
$834$	−10.0706	−0.348715
$835$	−47.6382	−1.64859
$836$	−1.07783	−0.0372774
$837$	−32.5961	−1.12668
$838$	29.2325	1.00982
$839$	−11.3724	−0.392619	−0.196309	−	0.980542i	$-0.562896\pi$
$839$	−11.3724	−0.392619	−0.196309	+	0.980542i	$0.562896\pi$
$840$	−16.5377	−0.570603
$841$	−22.8150	−0.786724
$842$	12.7450	0.439222
$843$	−28.2757	−0.973865
$844$	−1.00000	−0.0344214
$845$	−5.26772	−0.181215
$846$	−2.20458	−0.0757950
$847$	36.8999	1.26789
$848$	−4.03335	−0.138506
$849$	−44.9917	−1.54411
$850$	5.08924	0.174559
$851$	−14.0346	−0.481099
$852$	−6.08156	−0.208351
$853$	41.3708	1.41651	0.708255	−	0.705957i	$-0.249483\pi$
$853$	41.3708	1.41651	0.708255	+	0.705957i	$0.249483\pi$
$854$	−25.7476	−0.881063
$855$	2.05932	0.0704273
$856$	5.51478	0.188491
$857$	−2.40091	−0.0820134	−0.0410067	−	0.999159i	$-0.513057\pi$
$857$	−2.40091	−0.0820134	−0.0410067	+	0.999159i	$0.513057\pi$
$858$	6.28051	0.214413
$859$	−26.9831	−0.920651	−0.460326	−	0.887750i	$-0.652267\pi$
$859$	−26.9831	−0.920651	−0.460326	+	0.887750i	$0.652267\pi$
$860$	−6.59189	−0.224782
$861$	−21.0436	−0.717165
$862$	10.6344	0.362209
$863$	−30.0776	−1.02385	−0.511926	−	0.859029i	$-0.671068\pi$
$863$	−30.0776	−1.02385	−0.511926	+	0.859029i	$0.671068\pi$
$864$	5.61344	0.190973
$865$	−23.6258	−0.803302
$866$	34.3350	1.16675
$867$	22.5021	0.764211
$868$	21.7792	0.739233
$869$	12.8642	0.436389
$870$	10.9658	0.371774
$871$	27.4468	0.930001
$872$	5.98523	0.202686
$873$	5.07779	0.171857
$874$	−1.57188	−0.0531698
$875$	−16.6064	−0.561398
$876$	23.5492	0.795654
$877$	34.9447	1.18000	0.589999	−	0.807404i	$-0.299128\pi$
$877$	34.9447	1.18000	0.589999	+	0.807404i	$0.299128\pi$
$878$	3.35608	0.113262
$879$	25.2034	0.850089
$880$	3.13859	0.105802
$881$	−18.7866	−0.632936	−0.316468	−	0.948603i	$-0.602497\pi$
$881$	−18.7866	−0.632936	−0.316468	+	0.948603i	$0.602497\pi$
$882$	−4.99794	−0.168289
$883$	−7.55279	−0.254172	−0.127086	−	0.991892i	$-0.540562\pi$
$883$	−7.55279	−0.254172	−0.127086	+	0.991892i	$0.540562\pi$
$884$	5.62857	0.189309
$885$	66.3294	2.22964
$886$	17.8153	0.598517
$887$	50.9029	1.70915	0.854576	−	0.519327i	$-0.173817\pi$
$887$	50.9029	1.70915	0.854576	+	0.519327i	$0.173817\pi$
$888$	−13.5196	−0.453687
$889$	−47.9398	−1.60785
$890$	4.16255	0.139529
$891$	6.87469	0.230311
$892$	−16.7954	−0.562352
$893$	3.11736	0.104318
$894$	−1.66829	−0.0557959
$895$	−44.4317	−1.48519
$896$	−3.75064	−0.125300
$897$	9.15940	0.305823
$898$	12.0352	0.401621
$899$	−14.4413	−0.481644
$900$	−2.46069	−0.0820229
$901$	−5.89931	−0.196535
$902$	3.99375	0.132977
$903$	12.8562	0.427828
$904$	−12.7751	−0.424894
$905$	21.0183	0.698671
$906$	27.4866	0.913181
$907$	−49.9273	−1.65781	−0.828904	−	0.559391i	$-0.811035\pi$
$907$	−49.9273	−1.65781	−0.828904	+	0.559391i	$0.811035\pi$
$908$	−20.7288	−0.687910
$909$	10.8352	0.359382
$910$	42.0294	1.39326
$911$	17.5228	0.580557	0.290278	−	0.956942i	$-0.406252\pi$
$911$	17.5228	0.580557	0.290278	+	0.956942i	$0.406252\pi$
$912$	−1.51420	−0.0501402
$913$	0.442952	0.0146596
$914$	−26.3704	−0.872255
$915$	30.2691	1.00067
$916$	11.3130	0.373792
$917$	−28.1130	−0.928373
$918$	8.21040	0.270984
$919$	45.3792	1.49692	0.748461	−	0.663179i	$-0.230793\pi$
$919$	45.3792	1.49692	0.748461	+	0.663179i	$0.230793\pi$
$920$	4.57726	0.150908
$921$	33.1190	1.09131
$922$	41.5856	1.36955
$923$	15.4559	0.508737
$924$	−6.12121	−0.201373
$925$	31.0668	1.02147
$926$	−7.69812	−0.252976
$927$	−12.0526	−0.395859
$928$	2.48697	0.0816387
$929$	−12.7024	−0.416753	−0.208376	−	0.978049i	$-0.566818\pi$
$929$	−12.7024	−0.416753	−0.208376	+	0.978049i	$0.566818\pi$
$930$	−25.6038	−0.839583
$931$	7.06728	0.231621
$932$	−9.25379	−0.303118
$933$	−21.5890	−0.706792
$934$	−8.83687	−0.289151
$935$	4.59060	0.150129
$936$	−2.72146	−0.0889537
$937$	−14.7613	−0.482230	−0.241115	−	0.970497i	$-0.577513\pi$
$937$	−14.7613	−0.482230	−0.241115	+	0.970497i	$0.577513\pi$
$938$	−26.7507	−0.873440
$939$	−2.28342	−0.0745166
$940$	−9.07762	−0.296079
$941$	−41.3244	−1.34714	−0.673569	−	0.739124i	$-0.735240\pi$
$941$	−41.3244	−1.34714	−0.673569	+	0.739124i	$0.735240\pi$
$942$	18.4783	0.602055
$943$	5.82442	0.189669
$944$	15.0431	0.489611
$945$	61.3083	1.99436
$946$	−2.43991	−0.0793283
$947$	−13.6375	−0.443161	−0.221580	−	0.975142i	$-0.571121\pi$
$947$	−13.6375	−0.443161	−0.221580	+	0.975142i	$0.571121\pi$
$948$	18.0725	0.586968
$949$	−59.8488	−1.94277
$950$	3.47950	0.112890
$951$	−11.0188	−0.357308
$952$	−5.48581	−0.177796
$953$	−36.7962	−1.19195	−0.595974	−	0.803004i	$-0.703234\pi$
$953$	−36.7962	−1.19195	−0.595974	+	0.803004i	$0.703234\pi$
$954$	2.85236	0.0923487
$955$	25.8722	0.837204
$956$	−17.7783	−0.574992
$957$	4.05885	0.131204
$958$	1.71555	0.0554268
$959$	−49.5796	−1.60101
$960$	4.40929	0.142309
$961$	2.71883	0.0877041
$962$	34.3591	1.10778
$963$	−3.90002	−0.125676
$964$	−26.5501	−0.855122
$965$	40.0928	1.29063
$966$	−8.92707	−0.287224
$967$	−58.2120	−1.87197	−0.935986	−	0.352037i	$-0.885489\pi$
$967$	−58.2120	−1.87197	−0.935986	+	0.352037i	$0.885489\pi$
$968$	−9.83829	−0.316215
$969$	−2.21472	−0.0711471
$970$	20.9084	0.671329
$971$	37.8708	1.21533	0.607666	−	0.794193i	$-0.292106\pi$
$971$	37.8708	1.21533	0.607666	+	0.794193i	$0.292106\pi$
$972$	−7.18230	−0.230372
$973$	−24.9445	−0.799684
$974$	36.7555	1.17772
$975$	−20.2751	−0.649324
$976$	6.86485	0.219738
$977$	−12.9466	−0.414197	−0.207099	−	0.978320i	$-0.566402\pi$
$977$	−12.9466	−0.414197	−0.207099	+	0.978320i	$0.566402\pi$
$978$	19.5112	0.623900
$979$	1.54072	0.0492416
$980$	−20.5796	−0.657392
$981$	−4.23273	−0.135141
$982$	−27.6658	−0.882852
$983$	32.3229	1.03094	0.515471	−	0.856907i	$-0.327617\pi$
$983$	32.3229	1.03094	0.515471	+	0.856907i	$0.327617\pi$
$984$	5.61069	0.178862
$985$	65.2701	2.07968
$986$	3.63752	0.115842
$987$	17.7042	0.563530
$988$	3.84825	0.122429
$989$	−3.55832	−0.113148
$990$	−2.21959	−0.0705432
$991$	−5.15566	−0.163775	−0.0818875	−	0.996642i	$-0.526095\pi$
$991$	−5.15566	−0.163775	−0.0818875	+	0.996642i	$0.526095\pi$
$992$	−5.80679	−0.184366
$993$	−34.2614	−1.08725
$994$	−15.0639	−0.477797
$995$	27.4675	0.870779
$996$	0.622287	0.0197179
$997$	44.7018	1.41572	0.707861	−	0.706352i	$-0.249661\pi$
$997$	44.7018	1.41572	0.707861	+	0.706352i	$0.249661\pi$
$998$	10.8003	0.341878
$999$	50.1196	1.58572

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8018.2.a.d.1.9	✓	30

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8018.2.a.d.1.9	✓	30	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)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -1.51420 q^{3} +1.00000 q^{4} -2.91196 q^{5} -1.51420 q^{6} -3.75064 q^{7} +1.00000 q^{8} -0.707195 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -1.51420 q^{3} +1.00000 q^{4} -2.91196 q^{5} -1.51420 q^{6} -3.75064 q^{7} +1.00000 q^{8} -0.707195 q^{9} -2.91196 q^{10} -1.07783 q^{11} -1.51420 q^{12} +3.84825 q^{13} -3.75064 q^{14} +4.40929 q^{15} +1.00000 q^{16} +1.46263 q^{17} -0.707195 q^{18} +1.00000 q^{19} -2.91196 q^{20} +5.67922 q^{21} -1.07783 q^{22} -1.57188 q^{23} -1.51420 q^{24} +3.47950 q^{25} +3.84825 q^{26} +5.61344 q^{27} -3.75064 q^{28} +2.48697 q^{29} +4.40929 q^{30} -5.80679 q^{31} +1.00000 q^{32} +1.63205 q^{33} +1.46263 q^{34} +10.9217 q^{35} -0.707195 q^{36} +8.92851 q^{37} +1.00000 q^{38} -5.82702 q^{39} -2.91196 q^{40} -3.70538 q^{41} +5.67922 q^{42} +2.26373 q^{43} -1.07783 q^{44} +2.05932 q^{45} -1.57188 q^{46} +3.11736 q^{47} -1.51420 q^{48} +7.06728 q^{49} +3.47950 q^{50} -2.21472 q^{51} +3.84825 q^{52} -4.03335 q^{53} +5.61344 q^{54} +3.13859 q^{55} -3.75064 q^{56} -1.51420 q^{57} +2.48697 q^{58} +15.0431 q^{59} +4.40929 q^{60} +6.86485 q^{61} -5.80679 q^{62} +2.65243 q^{63} +1.00000 q^{64} -11.2059 q^{65} +1.63205 q^{66} +7.13230 q^{67} +1.46263 q^{68} +2.38015 q^{69} +10.9217 q^{70} +4.01635 q^{71} -0.707195 q^{72} -15.5522 q^{73} +8.92851 q^{74} -5.26867 q^{75} +1.00000 q^{76} +4.04254 q^{77} -5.82702 q^{78} -11.9353 q^{79} -2.91196 q^{80} -6.37829 q^{81} -3.70538 q^{82} -0.410968 q^{83} +5.67922 q^{84} -4.25913 q^{85} +2.26373 q^{86} -3.76577 q^{87} -1.07783 q^{88} -1.42947 q^{89} +2.05932 q^{90} -14.4334 q^{91} -1.57188 q^{92} +8.79265 q^{93} +3.11736 q^{94} -2.91196 q^{95} -1.51420 q^{96} -7.18019 q^{97} +7.06728 q^{98} +0.762233 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 30 q + 30 q^{2} - 10 q^{3} + 30 q^{4} - 12 q^{5} - 10 q^{6} - 15 q^{7} + 30 q^{8} + 10 q^{9}+O(q^{10}) \) 30 * q + 30 * q^2 - 10 * q^3 + 30 * q^4 - 12 * q^5 - 10 * q^6 - 15 * q^7 + 30 * q^8 + 10 * q^9	\( 30 q + 30 q^{2} - 10 q^{3} + 30 q^{4} - 12 q^{5} - 10 q^{6} - 15 q^{7} + 30 q^{8} + 10 q^{9} - 12 q^{10} - 17 q^{11} - 10 q^{12} - 19 q^{13} - 15 q^{14} - 8 q^{15} + 30 q^{16} - 18 q^{17} + 10 q^{18} + 30 q^{19} - 12 q^{20} - 14 q^{21} - 17 q^{22} - 15 q^{23} - 10 q^{24} - 4 q^{25} - 19 q^{26} - 37 q^{27} - 15 q^{28} - 37 q^{29} - 8 q^{30} - 11 q^{31} + 30 q^{32} + 6 q^{33} - 18 q^{34} - 4 q^{35} + 10 q^{36} - 46 q^{37} + 30 q^{38} - 12 q^{40} - 28 q^{41} - 14 q^{42} - 61 q^{43} - 17 q^{44} - 14 q^{45} - 15 q^{46} - 4 q^{47} - 10 q^{48} - q^{49} - 4 q^{50} - 8 q^{51} - 19 q^{52} - 19 q^{53} - 37 q^{54} - 17 q^{55} - 15 q^{56} - 10 q^{57} - 37 q^{58} - 6 q^{59} - 8 q^{60} - 32 q^{61} - 11 q^{62} - 24 q^{63} + 30 q^{64} - 24 q^{65} + 6 q^{66} - 44 q^{67} - 18 q^{68} - 2 q^{69} - 4 q^{70} + 10 q^{71} + 10 q^{72} - 58 q^{73} - 46 q^{74} - 42 q^{75} + 30 q^{76} - 32 q^{77} - 42 q^{79} - 12 q^{80} - 38 q^{81} - 28 q^{82} - 25 q^{83} - 14 q^{84} - 48 q^{85} - 61 q^{86} - 15 q^{87} - 17 q^{88} - 39 q^{89} - 14 q^{90} - 21 q^{91} - 15 q^{92} - 45 q^{93} - 4 q^{94} - 12 q^{95} - 10 q^{96} - 33 q^{97} - q^{98} - 38 q^{99}+O(q^{100}) \) 30 * q + 30 * q^2 - 10 * q^3 + 30 * q^4 - 12 * q^5 - 10 * q^6 - 15 * q^7 + 30 * q^8 + 10 * q^9 - 12 * q^10 - 17 * q^11 - 10 * q^12 - 19 * q^13 - 15 * q^14 - 8 * q^15 + 30 * q^16 - 18 * q^17 + 10 * q^18 + 30 * q^19 - 12 * q^20 - 14 * q^21 - 17 * q^22 - 15 * q^23 - 10 * q^24 - 4 * q^25 - 19 * q^26 - 37 * q^27 - 15 * q^28 - 37 * q^29 - 8 * q^30 - 11 * q^31 + 30 * q^32 + 6 * q^33 - 18 * q^34 - 4 * q^35 + 10 * q^36 - 46 * q^37 + 30 * q^38 - 12 * q^40 - 28 * q^41 - 14 * q^42 - 61 * q^43 - 17 * q^44 - 14 * q^45 - 15 * q^46 - 4 * q^47 - 10 * q^48 - q^49 - 4 * q^50 - 8 * q^51 - 19 * q^52 - 19 * q^53 - 37 * q^54 - 17 * q^55 - 15 * q^56 - 10 * q^57 - 37 * q^58 - 6 * q^59 - 8 * q^60 - 32 * q^61 - 11 * q^62 - 24 * q^63 + 30 * q^64 - 24 * q^65 + 6 * q^66 - 44 * q^67 - 18 * q^68 - 2 * q^69 - 4 * q^70 + 10 * q^71 + 10 * q^72 - 58 * q^73 - 46 * q^74 - 42 * q^75 + 30 * q^76 - 32 * q^77 - 42 * q^79 - 12 * q^80 - 38 * q^81 - 28 * q^82 - 25 * q^83 - 14 * q^84 - 48 * q^85 - 61 * q^86 - 15 * q^87 - 17 * q^88 - 39 * q^89 - 14 * q^90 - 21 * q^91 - 15 * q^92 - 45 * q^93 - 4 * q^94 - 12 * q^95 - 10 * q^96 - 33 * q^97 - q^98 - 38 * q^99

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