LMFDB - Embedded newform 4017.2.a.i.1.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4017,2,Mod(1,4017)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4017, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 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("4017.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4017 = 3 \cdot 13 \cdot 103 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4017.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:	$32.0759064919$
Analytic rank:	$1$
Dimension:	$25$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.10
Character	$\chi$	$=$	4017.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.726163 q^{2} -1.00000 q^{3} -1.47269 q^{4} +0.449507 q^{5} +0.726163 q^{6} +4.04793 q^{7} +2.52174 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-0.726163 q^{2} -1.00000 q^{3} -1.47269 q^{4} +0.449507 q^{5} +0.726163 q^{6} +4.04793 q^{7} +2.52174 q^{8} +1.00000 q^{9} -0.326416 q^{10} -1.83576 q^{11} +1.47269 q^{12} -1.00000 q^{13} -2.93946 q^{14} -0.449507 q^{15} +1.11418 q^{16} -4.56755 q^{17} -0.726163 q^{18} +6.19810 q^{19} -0.661983 q^{20} -4.04793 q^{21} +1.33306 q^{22} -0.193684 q^{23} -2.52174 q^{24} -4.79794 q^{25} +0.726163 q^{26} -1.00000 q^{27} -5.96133 q^{28} -0.219801 q^{29} +0.326416 q^{30} +3.13759 q^{31} -5.85255 q^{32} +1.83576 q^{33} +3.31679 q^{34} +1.81957 q^{35} -1.47269 q^{36} -6.01294 q^{37} -4.50084 q^{38} +1.00000 q^{39} +1.13354 q^{40} -7.72240 q^{41} +2.93946 q^{42} -5.53476 q^{43} +2.70350 q^{44} +0.449507 q^{45} +0.140646 q^{46} -3.39733 q^{47} -1.11418 q^{48} +9.38575 q^{49} +3.48409 q^{50} +4.56755 q^{51} +1.47269 q^{52} -11.1548 q^{53} +0.726163 q^{54} -0.825186 q^{55} +10.2078 q^{56} -6.19810 q^{57} +0.159611 q^{58} +0.305246 q^{59} +0.661983 q^{60} +5.70984 q^{61} -2.27840 q^{62} +4.04793 q^{63} +2.02155 q^{64} -0.449507 q^{65} -1.33306 q^{66} +9.16637 q^{67} +6.72657 q^{68} +0.193684 q^{69} -1.32131 q^{70} +10.5331 q^{71} +2.52174 q^{72} -2.59666 q^{73} +4.36638 q^{74} +4.79794 q^{75} -9.12787 q^{76} -7.43102 q^{77} -0.726163 q^{78} -7.52846 q^{79} +0.500832 q^{80} +1.00000 q^{81} +5.60773 q^{82} -13.7682 q^{83} +5.96133 q^{84} -2.05315 q^{85} +4.01914 q^{86} +0.219801 q^{87} -4.62930 q^{88} +8.73068 q^{89} -0.326416 q^{90} -4.04793 q^{91} +0.285236 q^{92} -3.13759 q^{93} +2.46702 q^{94} +2.78609 q^{95} +5.85255 q^{96} +5.76986 q^{97} -6.81559 q^{98} -1.83576 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 25 q - 2 q^{2} - 25 q^{3} + 28 q^{4} - 3 q^{5} + 2 q^{6} - 11 q^{7} - 15 q^{8} + 25 q^{9}+O(q^{10}) $ 25 * q - 2 * q^2 - 25 * q^3 + 28 * q^4 - 3 * q^5 + 2 * q^6 - 11 * q^7 - 15 * q^8 + 25 * q^9	\( 25 q - 2 q^{2} - 25 q^{3} + 28 q^{4} - 3 q^{5} + 2 q^{6} - 11 q^{7} - 15 q^{8} + 25 q^{9} + 2 q^{10} - q^{11} - 28 q^{12} - 25 q^{13} - 12 q^{14} + 3 q^{15} + 26 q^{16} - 10 q^{17} - 2 q^{18} + 22 q^{19} - 2 q^{20} + 11 q^{21} - 5 q^{22} - 49 q^{23} + 15 q^{24} + 22 q^{25} + 2 q^{26} - 25 q^{27} - 30 q^{28} - 22 q^{29} - 2 q^{30} + 8 q^{31} - 12 q^{32} + q^{33} - q^{34} - 2 q^{35} + 28 q^{36} - 26 q^{38} + 25 q^{39} - 22 q^{40} - 5 q^{41} + 12 q^{42} - 13 q^{43} - 25 q^{44} - 3 q^{45} + 13 q^{46} - 56 q^{47} - 26 q^{48} + 28 q^{49} - 31 q^{50} + 10 q^{51} - 28 q^{52} - 20 q^{53} + 2 q^{54} - 14 q^{55} - 22 q^{56} - 22 q^{57} - 21 q^{58} + 2 q^{59} + 2 q^{60} + 29 q^{61} - 39 q^{62} - 11 q^{63} + 21 q^{64} + 3 q^{65} + 5 q^{66} - 14 q^{67} - 60 q^{68} + 49 q^{69} - 31 q^{70} - 36 q^{71} - 15 q^{72} - 30 q^{73} - 64 q^{74} - 22 q^{75} + 38 q^{76} - 37 q^{77} - 2 q^{78} - 29 q^{79} + 25 q^{81} - 6 q^{82} - 17 q^{83} + 30 q^{84} + 3 q^{85} - 27 q^{86} + 22 q^{87} - 81 q^{88} - 38 q^{89} + 2 q^{90} + 11 q^{91} - 85 q^{92} - 8 q^{93} + 26 q^{94} - 71 q^{95} + 12 q^{96} + 19 q^{98} - q^{99}+O(q^{100}) \) 25 * q - 2 * q^2 - 25 * q^3 + 28 * q^4 - 3 * q^5 + 2 * q^6 - 11 * q^7 - 15 * q^8 + 25 * q^9 + 2 * q^10 - q^11 - 28 * q^12 - 25 * q^13 - 12 * q^14 + 3 * q^15 + 26 * q^16 - 10 * q^17 - 2 * q^18 + 22 * q^19 - 2 * q^20 + 11 * q^21 - 5 * q^22 - 49 * q^23 + 15 * q^24 + 22 * q^25 + 2 * q^26 - 25 * q^27 - 30 * q^28 - 22 * q^29 - 2 * q^30 + 8 * q^31 - 12 * q^32 + q^33 - q^34 - 2 * q^35 + 28 * q^36 - 26 * q^38 + 25 * q^39 - 22 * q^40 - 5 * q^41 + 12 * q^42 - 13 * q^43 - 25 * q^44 - 3 * q^45 + 13 * q^46 - 56 * q^47 - 26 * q^48 + 28 * q^49 - 31 * q^50 + 10 * q^51 - 28 * q^52 - 20 * q^53 + 2 * q^54 - 14 * q^55 - 22 * q^56 - 22 * q^57 - 21 * q^58 + 2 * q^59 + 2 * q^60 + 29 * q^61 - 39 * q^62 - 11 * q^63 + 21 * q^64 + 3 * q^65 + 5 * q^66 - 14 * q^67 - 60 * q^68 + 49 * q^69 - 31 * q^70 - 36 * q^71 - 15 * q^72 - 30 * q^73 - 64 * q^74 - 22 * q^75 + 38 * q^76 - 37 * q^77 - 2 * q^78 - 29 * q^79 + 25 * q^81 - 6 * q^82 - 17 * q^83 + 30 * q^84 + 3 * q^85 - 27 * q^86 + 22 * q^87 - 81 * q^88 - 38 * q^89 + 2 * q^90 + 11 * q^91 - 85 * q^92 - 8 * q^93 + 26 * q^94 - 71 * q^95 + 12 * q^96 + 19 * q^98 - 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 $

$2$	−0.726163	−0.513475	−0.256738	−	0.966481i	$-0.582648\pi$
$2$	−0.726163	−0.513475	−0.256738	+	0.966481i	$0.582648\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	−1.47269	−0.736343
$5$	0.449507	0.201026	0.100513	−	0.994936i	$-0.467952\pi$
$5$	0.449507	0.201026	0.100513	+	0.994936i	$0.467952\pi$
$6$	0.726163	0.296455
$7$	4.04793	1.52997	0.764987	−	0.644046i	$-0.222745\pi$
$7$	4.04793	1.52997	0.764987	+	0.644046i	$0.222745\pi$
$8$	2.52174	0.891569
$9$	1.00000	0.333333
$10$	−0.326416	−0.103222
$11$	−1.83576	−0.553502	−0.276751	−	0.960942i	$-0.589258\pi$
$11$	−1.83576	−0.553502	−0.276751	+	0.960942i	$0.589258\pi$
$12$	1.47269	0.425128
$13$	−1.00000	−0.277350
$13$	−1.00000	−0.277350
$14$	−2.93946	−0.785604
$15$	−0.449507	−0.116062
$16$	1.11418	0.278545
$17$	−4.56755	−1.10779	−0.553897	−	0.832585i	$-0.686860\pi$
$17$	−4.56755	−1.10779	−0.553897	+	0.832585i	$0.686860\pi$
$18$	−0.726163	−0.171158
$19$	6.19810	1.42194	0.710971	−	0.703221i	$-0.248256\pi$
$19$	6.19810	1.42194	0.710971	+	0.703221i	$0.248256\pi$
$20$	−0.661983	−0.148024
$21$	−4.04793	−0.883331
$22$	1.33306	0.284209
$23$	−0.193684	−0.0403860	−0.0201930	−	0.999796i	$-0.506428\pi$
$23$	−0.193684	−0.0403860	−0.0201930	+	0.999796i	$0.506428\pi$
$24$	−2.52174	−0.514748
$25$	−4.79794	−0.959589
$26$	0.726163	0.142412
$27$	−1.00000	−0.192450
$28$	−5.96133	−1.12659
$29$	−0.219801	−0.0408160	−0.0204080	−	0.999792i	$-0.506497\pi$
$29$	−0.219801	−0.0408160	−0.0204080	+	0.999792i	$0.506497\pi$
$30$	0.326416	0.0595950
$31$	3.13759	0.563527	0.281764	−	0.959484i	$-0.409081\pi$
$31$	3.13759	0.563527	0.281764	+	0.959484i	$0.409081\pi$
$32$	−5.85255	−1.03459
$33$	1.83576	0.319564
$34$	3.31679	0.568825
$35$	1.81957	0.307564
$36$	−1.47269	−0.245448
$37$	−6.01294	−0.988521	−0.494261	−	0.869314i	$-0.664561\pi$
$37$	−6.01294	−0.988521	−0.494261	+	0.869314i	$0.664561\pi$
$38$	−4.50084	−0.730132
$39$	1.00000	0.160128
$40$	1.13354	0.179228
$41$	−7.72240	−1.20604	−0.603018	−	0.797727i	$-0.706035\pi$
$41$	−7.72240	−1.20604	−0.603018	+	0.797727i	$0.706035\pi$
$42$	2.93946	0.453568
$43$	−5.53476	−0.844044	−0.422022	−	0.906586i	$-0.638679\pi$
$43$	−5.53476	−0.844044	−0.422022	+	0.906586i	$0.638679\pi$
$44$	2.70350	0.407567
$45$	0.449507	0.0670085
$46$	0.140646	0.0207372
$47$	−3.39733	−0.495552	−0.247776	−	0.968817i	$-0.579700\pi$
$47$	−3.39733	−0.495552	−0.247776	+	0.968817i	$0.579700\pi$
$48$	−1.11418	−0.160818
$49$	9.38575	1.34082
$50$	3.48409	0.492725
$51$	4.56755	0.639585
$52$	1.47269	0.204225
$53$	−11.1548	−1.53223	−0.766113	−	0.642706i	$-0.777812\pi$
$53$	−11.1548	−1.53223	−0.766113	+	0.642706i	$0.777812\pi$
$54$	0.726163	0.0988183
$55$	−0.825186	−0.111268
$56$	10.2078	1.36408
$57$	−6.19810	−0.820959
$58$	0.159611	0.0209580
$59$	0.305246	0.0397396	0.0198698	−	0.999803i	$-0.493675\pi$
$59$	0.305246	0.0397396	0.0198698	+	0.999803i	$0.493675\pi$
$60$	0.661983	0.0854616
$61$	5.70984	0.731070	0.365535	−	0.930798i	$-0.380886\pi$
$61$	5.70984	0.731070	0.365535	+	0.930798i	$0.380886\pi$
$62$	−2.27840	−0.289357
$63$	4.04793	0.509991
$64$	2.02155	0.252694
$65$	−0.449507	−0.0557545
$66$	−1.33306	−0.164088
$67$	9.16637	1.11985	0.559925	−	0.828543i	$-0.310830\pi$
$67$	9.16637	1.11985	0.559925	+	0.828543i	$0.310830\pi$
$68$	6.72657	0.815717
$69$	0.193684	0.0233169
$70$	−1.32131	−0.157926
$71$	10.5331	1.25005	0.625023	−	0.780607i	$-0.285090\pi$
$71$	10.5331	1.25005	0.625023	+	0.780607i	$0.285090\pi$
$72$	2.52174	0.297190
$73$	−2.59666	−0.303916	−0.151958	−	0.988387i	$-0.548558\pi$
$73$	−2.59666	−0.303916	−0.151958	+	0.988387i	$0.548558\pi$
$74$	4.36638	0.507581
$75$	4.79794	0.554019
$76$	−9.12787	−1.04704
$77$	−7.43102	−0.846844
$78$	−0.726163	−0.0822218
$79$	−7.52846	−0.847018	−0.423509	−	0.905892i	$-0.639202\pi$
$79$	−7.52846	−0.847018	−0.423509	+	0.905892i	$0.639202\pi$
$80$	0.500832	0.0559947
$81$	1.00000	0.111111
$82$	5.60773	0.619270
$83$	−13.7682	−1.51125	−0.755626	−	0.655003i	$-0.772667\pi$
$83$	−13.7682	−1.51125	−0.755626	+	0.655003i	$0.772667\pi$
$84$	5.96133	0.650435
$85$	−2.05315	−0.222695
$86$	4.01914	0.433395
$87$	0.219801	0.0235651
$88$	−4.62930	−0.493485
$89$	8.73068	0.925451	0.462725	−	0.886502i	$-0.346872\pi$
$89$	8.73068	0.925451	0.462725	+	0.886502i	$0.346872\pi$
$90$	−0.326416	−0.0344072
$91$	−4.04793	−0.424339
$92$	0.285236	0.0297379
$93$	−3.13759	−0.325353
$94$	2.46702	0.254454
$95$	2.78609	0.285847
$96$	5.85255	0.597324
$97$	5.76986	0.585841	0.292920	−	0.956137i	$-0.405373\pi$
$97$	5.76986	0.585841	0.292920	+	0.956137i	$0.405373\pi$
$98$	−6.81559	−0.688478
$99$	−1.83576	−0.184501
$100$	7.06587	0.706587
$101$	9.22329	0.917752	0.458876	−	0.888500i	$-0.348252\pi$
$101$	9.22329	0.917752	0.458876	+	0.888500i	$0.348252\pi$
$102$	−3.31679	−0.328411
$103$	−1.00000	−0.0985329
$103$	−1.00000	−0.0985329
$104$	−2.52174	−0.247277
$105$	−1.81957	−0.177572
$106$	8.10019	0.786760
$107$	5.81416	0.562076	0.281038	−	0.959697i	$-0.409321\pi$
$107$	5.81416	0.562076	0.281038	+	0.959697i	$0.409321\pi$
$108$	1.47269	0.141709
$109$	−9.22702	−0.883788	−0.441894	−	0.897067i	$-0.645693\pi$
$109$	−9.22702	−0.883788	−0.441894	+	0.897067i	$0.645693\pi$
$110$	0.599220	0.0571334
$111$	6.01294	0.570723
$112$	4.51012	0.426167
$113$	−5.98157	−0.562699	−0.281349	−	0.959605i	$-0.590782\pi$
$113$	−5.98157	−0.562699	−0.281349	+	0.959605i	$0.590782\pi$
$114$	4.50084	0.421542
$115$	−0.0870625	−0.00811862
$116$	0.323698	0.0300546
$117$	−1.00000	−0.0924500
$118$	−0.221658	−0.0204053
$119$	−18.4891	−1.69490
$120$	−1.13354	−0.103477
$121$	−7.62999	−0.693636
$122$	−4.14628	−0.375386
$123$	7.72240	0.696306
$124$	−4.62068	−0.414950
$125$	−4.40424	−0.393928
$126$	−2.93946	−0.261868
$127$	7.53066	0.668238	0.334119	−	0.942531i	$-0.391561\pi$
$127$	7.53066	0.668238	0.334119	+	0.942531i	$0.391561\pi$
$128$	10.2371	0.904843
$129$	5.53476	0.487309
$130$	0.326416	0.0286285
$131$	19.6796	1.71941	0.859707	−	0.510787i	$-0.170646\pi$
$131$	19.6796	1.71941	0.859707	+	0.510787i	$0.170646\pi$
$132$	−2.70350	−0.235309
$133$	25.0895	2.17554
$134$	−6.65628	−0.575015
$135$	−0.449507	−0.0386874
$136$	−11.5182	−0.987675
$137$	−12.7131	−1.08615	−0.543075	−	0.839684i	$-0.682740\pi$
$137$	−12.7131	−1.08615	−0.543075	+	0.839684i	$0.682740\pi$
$138$	−0.140646	−0.0119726
$139$	−7.46446	−0.633128	−0.316564	−	0.948571i	$-0.602529\pi$
$139$	−7.46446	−0.633128	−0.316564	+	0.948571i	$0.602529\pi$
$140$	−2.67966	−0.226473
$141$	3.39733	0.286107
$142$	−7.64873	−0.641867
$143$	1.83576	0.153514
$144$	1.11418	0.0928483
$145$	−0.0988020	−0.00820506
$146$	1.88560	0.156053
$147$	−9.38575	−0.774124
$148$	8.85518	0.727891
$149$	−1.51141	−0.123820	−0.0619098	−	0.998082i	$-0.519719\pi$
$149$	−1.51141	−0.123820	−0.0619098	+	0.998082i	$0.519719\pi$
$150$	−3.48409	−0.284475
$151$	16.5916	1.35021	0.675104	−	0.737723i	$-0.264099\pi$
$151$	16.5916	1.35021	0.675104	+	0.737723i	$0.264099\pi$
$152$	15.6300	1.26776
$153$	−4.56755	−0.369265
$154$	5.39614	0.434833
$155$	1.41037	0.113283
$156$	−1.47269	−0.117909
$157$	−5.39029	−0.430192	−0.215096	−	0.976593i	$-0.569006\pi$
$157$	−5.39029	−0.430192	−0.215096	+	0.976593i	$0.569006\pi$
$158$	5.46689	0.434922
$159$	11.1548	0.884631
$160$	−2.63076	−0.207980
$161$	−0.784021	−0.0617895
$162$	−0.726163	−0.0570528
$163$	0.390742	0.0306053	0.0153027	−	0.999883i	$-0.495129\pi$
$163$	0.390742	0.0306053	0.0153027	+	0.999883i	$0.495129\pi$
$164$	11.3727	0.888057
$165$	0.825186	0.0642407
$166$	9.99794	0.775991
$167$	−17.2653	−1.33603	−0.668015	−	0.744148i	$-0.732856\pi$
$167$	−17.2653	−1.33603	−0.668015	+	0.744148i	$0.732856\pi$
$168$	−10.2078	−0.787551
$169$	1.00000	0.0769231
$170$	1.49092	0.114348
$171$	6.19810	0.473981
$172$	8.15097	0.621506
$173$	−16.3530	−1.24330	−0.621650	−	0.783295i	$-0.713537\pi$
$173$	−16.3530	−1.24330	−0.621650	+	0.783295i	$0.713537\pi$
$174$	−0.159611	−0.0121001
$175$	−19.4217	−1.46815
$176$	−2.04536	−0.154175
$177$	−0.305246	−0.0229437
$178$	−6.33990	−0.475196
$179$	−0.665028	−0.0497066	−0.0248533	−	0.999691i	$-0.507912\pi$
$179$	−0.665028	−0.0497066	−0.0248533	+	0.999691i	$0.507912\pi$
$180$	−0.661983	−0.0493413
$181$	−10.9789	−0.816058	−0.408029	−	0.912969i	$-0.633784\pi$
$181$	−10.9789	−0.816058	−0.408029	+	0.912969i	$0.633784\pi$
$182$	2.93946	0.217887
$183$	−5.70984	−0.422084
$184$	−0.488421	−0.0360069
$185$	−2.70286	−0.198718
$186$	2.27840	0.167060
$187$	8.38492	0.613166
$188$	5.00321	0.364897
$189$	−4.04793	−0.294444
$190$	−2.02316	−0.146775
$191$	12.1602	0.879880	0.439940	−	0.898027i	$-0.355000\pi$
$191$	12.1602	0.879880	0.439940	+	0.898027i	$0.355000\pi$
$192$	−2.02155	−0.145893
$193$	−16.1298	−1.16105	−0.580524	−	0.814243i	$-0.697152\pi$
$193$	−16.1298	−1.16105	−0.580524	+	0.814243i	$0.697152\pi$
$194$	−4.18986	−0.300815
$195$	0.449507	0.0321899
$196$	−13.8223	−0.987305
$197$	−9.84554	−0.701466	−0.350733	−	0.936476i	$-0.614067\pi$
$197$	−9.84554	−0.701466	−0.350733	+	0.936476i	$0.614067\pi$
$198$	1.33306	0.0947365
$199$	−17.0686	−1.20996	−0.604979	−	0.796241i	$-0.706818\pi$
$199$	−17.0686	−1.20996	−0.604979	+	0.796241i	$0.706818\pi$
$200$	−12.0992	−0.855540
$201$	−9.16637	−0.646546
$202$	−6.69762	−0.471243
$203$	−0.889739	−0.0624474
$204$	−6.72657	−0.470954
$205$	−3.47127	−0.242444
$206$	0.726163	0.0505942
$207$	−0.193684	−0.0134620
$208$	−1.11418	−0.0772545
$209$	−11.3782	−0.787048
$210$	1.32131	0.0911789
$211$	21.3810	1.47193	0.735966	−	0.677019i	$-0.236728\pi$
$211$	21.3810	1.47193	0.735966	+	0.677019i	$0.236728\pi$
$212$	16.4275	1.12824
$213$	−10.5331	−0.721714
$214$	−4.22203	−0.288612
$215$	−2.48792	−0.169674
$216$	−2.52174	−0.171583
$217$	12.7007	0.862182
$218$	6.70032	0.453803
$219$	2.59666	0.175466
$220$	1.21524	0.0819315
$221$	4.56755	0.307247
$222$	−4.36638	−0.293052
$223$	−5.03447	−0.337133	−0.168566	−	0.985690i	$-0.553914\pi$
$223$	−5.03447	−0.337133	−0.168566	+	0.985690i	$0.553914\pi$
$224$	−23.6907	−1.58290
$225$	−4.79794	−0.319863
$226$	4.34360	0.288932
$227$	−16.7210	−1.10981	−0.554907	−	0.831912i	$-0.687246\pi$
$227$	−16.7210	−1.10981	−0.554907	+	0.831912i	$0.687246\pi$
$228$	9.12787	0.604508
$229$	−11.1561	−0.737216	−0.368608	−	0.929585i	$-0.620166\pi$
$229$	−11.1561	−0.737216	−0.368608	+	0.929585i	$0.620166\pi$
$230$	0.0632216	0.00416871
$231$	7.43102	0.488925
$232$	−0.554280	−0.0363903
$233$	19.3763	1.26938	0.634692	−	0.772765i	$-0.281127\pi$
$233$	19.3763	1.26938	0.634692	+	0.772765i	$0.281127\pi$
$234$	0.726163	0.0474708
$235$	−1.52713	−0.0996187
$236$	−0.449531	−0.0292620
$237$	7.52846	0.489026
$238$	13.4261	0.870287
$239$	−3.94247	−0.255017	−0.127509	−	0.991837i	$-0.540698\pi$
$239$	−3.94247	−0.255017	−0.127509	+	0.991837i	$0.540698\pi$
$240$	−0.500832	−0.0323285
$241$	−27.6869	−1.78347	−0.891736	−	0.452556i	$-0.850512\pi$
$241$	−27.6869	−1.78347	−0.891736	+	0.452556i	$0.850512\pi$
$242$	5.54062	0.356165
$243$	−1.00000	−0.0641500
$244$	−8.40881	−0.538319
$245$	4.21896	0.269539
$246$	−5.60773	−0.357536
$247$	−6.19810	−0.394376
$248$	7.91217	0.502423
$249$	13.7682	0.872522
$250$	3.19820	0.202272
$251$	−18.8315	−1.18863	−0.594315	−	0.804232i	$-0.702577\pi$
$251$	−18.8315	−1.18863	−0.594315	+	0.804232i	$0.702577\pi$
$252$	−5.96133	−0.375529
$253$	0.355558	0.0223537
$254$	−5.46849	−0.343124
$255$	2.05315	0.128573
$256$	−11.4769	−0.717308
$257$	−27.1805	−1.69547	−0.847736	−	0.530418i	$-0.822035\pi$
$257$	−27.1805	−1.69547	−0.847736	+	0.530418i	$0.822035\pi$
$258$	−4.01914	−0.250221
$259$	−24.3400	−1.51241
$260$	0.661983	0.0410544
$261$	−0.219801	−0.0136053
$262$	−14.2906	−0.882876
$263$	−8.26876	−0.509874	−0.254937	−	0.966958i	$-0.582055\pi$
$263$	−8.26876	−0.509874	−0.254937	+	0.966958i	$0.582055\pi$
$264$	4.62930	0.284914
$265$	−5.01415	−0.308017
$266$	−18.2191	−1.11708
$267$	−8.73068	−0.534309
$268$	−13.4992	−0.824595
$269$	20.6467	1.25885	0.629426	−	0.777061i	$-0.283290\pi$
$269$	20.6467	1.25885	0.629426	+	0.777061i	$0.283290\pi$
$270$	0.326416	0.0198650
$271$	−2.38739	−0.145024	−0.0725119	−	0.997368i	$-0.523102\pi$
$271$	−2.38739	−0.145024	−0.0725119	+	0.997368i	$0.523102\pi$
$272$	−5.08907	−0.308570
$273$	4.04793	0.244992
$274$	9.23175	0.557711
$275$	8.80786	0.531134
$276$	−0.285236	−0.0171692
$277$	28.2581	1.69786	0.848931	−	0.528504i	$-0.177247\pi$
$277$	28.2581	1.69786	0.848931	+	0.528504i	$0.177247\pi$
$278$	5.42042	0.325095
$279$	3.13759	0.187842
$280$	4.58849	0.274215
$281$	−13.8469	−0.826036	−0.413018	−	0.910723i	$-0.635525\pi$
$281$	−13.8469	−0.826036	−0.413018	+	0.910723i	$0.635525\pi$
$282$	−2.46702	−0.146909
$283$	18.9929	1.12901	0.564505	−	0.825429i	$-0.309067\pi$
$283$	18.9929	1.12901	0.564505	+	0.825429i	$0.309067\pi$
$284$	−15.5119	−0.920463
$285$	−2.78609	−0.165034
$286$	−1.33306	−0.0788255
$287$	−31.2598	−1.84520
$288$	−5.85255	−0.344865
$289$	3.86253	0.227208
$290$	0.0717464	0.00421310
$291$	−5.76986	−0.338235
$292$	3.82407	0.223787
$293$	−2.79108	−0.163057	−0.0815283	−	0.996671i	$-0.525980\pi$
$293$	−2.79108	−0.163057	−0.0815283	+	0.996671i	$0.525980\pi$
$294$	6.81559	0.397493
$295$	0.137210	0.00798868
$296$	−15.1631	−0.881335
$297$	1.83576	0.106521
$298$	1.09753	0.0635783
$299$	0.193684	0.0112011
$300$	−7.06587	−0.407948
$301$	−22.4043	−1.29137
$302$	−12.0482	−0.693298
$303$	−9.22329	−0.529864
$304$	6.90580	0.396075
$305$	2.56661	0.146964
$306$	3.31679	0.189608
$307$	−17.4139	−0.993865	−0.496932	−	0.867789i	$-0.665540\pi$
$307$	−17.4139	−0.993865	−0.496932	+	0.867789i	$0.665540\pi$
$308$	10.9436	0.623568
$309$	1.00000	0.0568880
$310$	−1.02416	−0.0581682
$311$	−31.6882	−1.79687	−0.898436	−	0.439105i	$-0.855296\pi$
$311$	−31.6882	−1.79687	−0.898436	+	0.439105i	$0.855296\pi$
$312$	2.52174	0.142765
$313$	−31.1372	−1.75998	−0.879990	−	0.474992i	$-0.842451\pi$
$313$	−31.1372	−1.75998	−0.879990	+	0.474992i	$0.842451\pi$
$314$	3.91423	0.220893
$315$	1.81957	0.102521
$316$	11.0871	0.623696
$317$	−13.3439	−0.749469	−0.374735	−	0.927132i	$-0.622266\pi$
$317$	−13.3439	−0.749469	−0.374735	+	0.927132i	$0.622266\pi$
$318$	−8.10019	−0.454236
$319$	0.403501	0.0225917
$320$	0.908701	0.0507979
$321$	−5.81416	−0.324515
$322$	0.569327	0.0317274
$323$	−28.3102	−1.57522
$324$	−1.47269	−0.0818159
$325$	4.79794	0.266142
$326$	−0.283743	−0.0157151
$327$	9.22702	0.510255
$328$	−19.4739	−1.07526
$329$	−13.7522	−0.758182
$330$	−0.599220	−0.0329860
$331$	−11.4062	−0.626942	−0.313471	−	0.949598i	$-0.601492\pi$
$331$	−11.4062	−0.626942	−0.313471	+	0.949598i	$0.601492\pi$
$332$	20.2762	1.11280
$333$	−6.01294	−0.329507
$334$	12.5374	0.686018
$335$	4.12035	0.225119
$336$	−4.51012	−0.246047
$337$	6.31156	0.343813	0.171906	−	0.985113i	$-0.445007\pi$
$337$	6.31156	0.343813	0.171906	+	0.985113i	$0.445007\pi$
$338$	−0.726163	−0.0394981
$339$	5.98157	0.324874
$340$	3.02364	0.163980
$341$	−5.75985	−0.311913
$342$	−4.50084	−0.243377
$343$	9.65735	0.521448
$344$	−13.9572	−0.752523
$345$	0.0870625	0.00468728
$346$	11.8750	0.638403
$347$	−2.91384	−0.156423	−0.0782115	−	0.996937i	$-0.524921\pi$
$347$	−2.91384	−0.156423	−0.0782115	+	0.996937i	$0.524921\pi$
$348$	−0.323698	−0.0173520
$349$	7.22031	0.386494	0.193247	−	0.981150i	$-0.438098\pi$
$349$	7.22031	0.386494	0.193247	+	0.981150i	$0.438098\pi$
$350$	14.1034	0.753856
$351$	1.00000	0.0533761
$352$	10.7439	0.572650
$353$	8.38347	0.446207	0.223103	−	0.974795i	$-0.428381\pi$
$353$	8.38347	0.446207	0.223103	+	0.974795i	$0.428381\pi$
$354$	0.221658	0.0117810
$355$	4.73469	0.251291
$356$	−12.8576	−0.681450
$357$	18.4891	0.978549
$358$	0.482919	0.0255231
$359$	−22.6114	−1.19338	−0.596692	−	0.802471i	$-0.703518\pi$
$359$	−22.6114	−1.19338	−0.596692	+	0.802471i	$0.703518\pi$
$360$	1.13354	0.0597427
$361$	19.4165	1.02192
$362$	7.97251	0.419026
$363$	7.62999	0.400471
$364$	5.96133	0.312459
$365$	−1.16722	−0.0610950
$366$	4.14628	0.216729
$367$	−8.91713	−0.465470	−0.232735	−	0.972540i	$-0.574768\pi$
$367$	−8.91713	−0.465470	−0.232735	+	0.972540i	$0.574768\pi$
$368$	−0.215799	−0.0112493
$369$	−7.72240	−0.402012
$370$	1.96272	0.102037
$371$	−45.1538	−2.34427
$372$	4.62068	0.239571
$373$	17.1187	0.886372	0.443186	−	0.896430i	$-0.353848\pi$
$373$	17.1187	0.886372	0.443186	+	0.896430i	$0.353848\pi$
$374$	−6.08882	−0.314846
$375$	4.40424	0.227434
$376$	−8.56719	−0.441819
$377$	0.219801	0.0113203
$378$	2.93946	0.151189
$379$	16.9272	0.869492	0.434746	−	0.900553i	$-0.356838\pi$
$379$	16.9272	0.869492	0.434746	+	0.900553i	$0.356838\pi$
$380$	−4.10304	−0.210481
$381$	−7.53066	−0.385807
$382$	−8.83028	−0.451797
$383$	−13.5861	−0.694216	−0.347108	−	0.937825i	$-0.612836\pi$
$383$	−13.5861	−0.694216	−0.347108	+	0.937825i	$0.612836\pi$
$384$	−10.2371	−0.522411
$385$	−3.34030	−0.170237
$386$	11.7129	0.596169
$387$	−5.53476	−0.281348
$388$	−8.49720	−0.431380
$389$	−0.912461	−0.0462636	−0.0231318	−	0.999732i	$-0.507364\pi$
$389$	−0.912461	−0.0462636	−0.0231318	+	0.999732i	$0.507364\pi$
$390$	−0.326416	−0.0165287
$391$	0.884663	0.0447393
$392$	23.6684	1.19543
$393$	−19.6796	−0.992704
$394$	7.14947	0.360185
$395$	−3.38409	−0.170272
$396$	2.70350	0.135856
$397$	14.7038	0.737960	0.368980	−	0.929437i	$-0.379707\pi$
$397$	14.7038	0.737960	0.368980	+	0.929437i	$0.379707\pi$
$398$	12.3946	0.621283
$399$	−25.0895	−1.25605
$400$	−5.34577	−0.267289
$401$	−9.42144	−0.470484	−0.235242	−	0.971937i	$-0.575588\pi$
$401$	−9.42144	−0.470484	−0.235242	+	0.971937i	$0.575588\pi$
$402$	6.65628	0.331985
$403$	−3.13759	−0.156294
$404$	−13.5830	−0.675780
$405$	0.449507	0.0223362
$406$	0.646096	0.0320652
$407$	11.0383	0.547148
$408$	11.5182	0.570234
$409$	30.5647	1.51133	0.755663	−	0.654961i	$-0.227315\pi$
$409$	30.5647	1.51133	0.755663	+	0.654961i	$0.227315\pi$
$410$	2.52071	0.124489
$411$	12.7131	0.627089
$412$	1.47269	0.0725541
$413$	1.23561	0.0608006
$414$	0.140646	0.00691240
$415$	−6.18889	−0.303801
$416$	5.85255	0.286945
$417$	7.46446	0.365536
$418$	8.26245	0.404130
$419$	5.01487	0.244992	0.122496	−	0.992469i	$-0.460910\pi$
$419$	5.01487	0.244992	0.122496	+	0.992469i	$0.460910\pi$
$420$	2.67966	0.130754
$421$	−28.8584	−1.40647	−0.703236	−	0.710957i	$-0.748262\pi$
$421$	−28.8584	−1.40647	−0.703236	+	0.710957i	$0.748262\pi$
$422$	−15.5261	−0.755800
$423$	−3.39733	−0.165184
$424$	−28.1294	−1.36609
$425$	21.9149	1.06303
$426$	7.64873	0.370582
$427$	23.1130	1.11852
$428$	−8.56244	−0.413881
$429$	−1.83576	−0.0886312
$430$	1.80663	0.0871236
$431$	−12.8075	−0.616916	−0.308458	−	0.951238i	$-0.599813\pi$
$431$	−12.8075	−0.616916	−0.308458	+	0.951238i	$0.599813\pi$
$432$	−1.11418	−0.0536060
$433$	18.6710	0.897272	0.448636	−	0.893715i	$-0.351910\pi$
$433$	18.6710	0.897272	0.448636	+	0.893715i	$0.351910\pi$
$434$	−9.22281	−0.442709
$435$	0.0988020	0.00473720
$436$	13.5885	0.650772
$437$	−1.20048	−0.0574265
$438$	−1.88560	−0.0900975
$439$	13.3163	0.635551	0.317775	−	0.948166i	$-0.397064\pi$
$439$	13.3163	0.635551	0.317775	+	0.948166i	$0.397064\pi$
$440$	−2.08090	−0.0992032
$441$	9.38575	0.446940
$442$	−3.31679	−0.157764
$443$	−0.548587	−0.0260641	−0.0130321	−	0.999915i	$-0.504148\pi$
$443$	−0.548587	−0.0260641	−0.0130321	+	0.999915i	$0.504148\pi$
$444$	−8.85518	−0.420248
$445$	3.92450	0.186039
$446$	3.65585	0.173109
$447$	1.51141	0.0714873
$448$	8.18310	0.386615
$449$	−30.4801	−1.43845	−0.719223	−	0.694779i	$-0.755502\pi$
$449$	−30.4801	−1.43845	−0.719223	+	0.694779i	$0.755502\pi$
$450$	3.48409	0.164242
$451$	14.1765	0.667544
$452$	8.80898	0.414339
$453$	−16.5916	−0.779543
$454$	12.1422	0.569862
$455$	−1.81957	−0.0853029
$456$	−15.6300	−0.731942
$457$	5.39575	0.252402	0.126201	−	0.992005i	$-0.459722\pi$
$457$	5.39575	0.252402	0.126201	+	0.992005i	$0.459722\pi$
$458$	8.10116	0.378542
$459$	4.56755	0.213195
$460$	0.128216	0.00597809
$461$	−2.56494	−0.119461	−0.0597305	−	0.998215i	$-0.519024\pi$
$461$	−2.56494	−0.119461	−0.0597305	+	0.998215i	$0.519024\pi$
$462$	−5.39614	−0.251051
$463$	20.9632	0.974243	0.487122	−	0.873334i	$-0.338047\pi$
$463$	20.9632	0.974243	0.487122	+	0.873334i	$0.338047\pi$
$464$	−0.244898	−0.0113691
$465$	−1.41037	−0.0654042
$466$	−14.0704	−0.651797
$467$	21.8937	1.01312	0.506560	−	0.862205i	$-0.330917\pi$
$467$	21.8937	1.01312	0.506560	+	0.862205i	$0.330917\pi$
$468$	1.47269	0.0680750
$469$	37.1048	1.71334
$470$	1.10894	0.0511517
$471$	5.39029	0.248371
$472$	0.769749	0.0354306
$473$	10.1605	0.467180
$474$	−5.46689	−0.251103
$475$	−29.7382	−1.36448
$476$	27.2287	1.24803
$477$	−11.1548	−0.510742
$478$	2.86288	0.130945
$479$	−15.8112	−0.722432	−0.361216	−	0.932482i	$-0.617638\pi$
$479$	−15.8112	−0.722432	−0.361216	+	0.932482i	$0.617638\pi$
$480$	2.63076	0.120077
$481$	6.01294	0.274166
$482$	20.1052	0.915768
$483$	0.784021	0.0356742
$484$	11.2366	0.510754
$485$	2.59359	0.117769
$486$	0.726163	0.0329394
$487$	42.0271	1.90443	0.952215	−	0.305429i	$-0.0987997\pi$
$487$	42.0271	1.90443	0.952215	+	0.305429i	$0.0987997\pi$
$488$	14.3987	0.651800
$489$	−0.390742	−0.0176700
$490$	−3.06365	−0.138402
$491$	−22.1109	−0.997850	−0.498925	−	0.866645i	$-0.666272\pi$
$491$	−22.1109	−0.997850	−0.498925	+	0.866645i	$0.666272\pi$
$492$	−11.3727	−0.512720
$493$	1.00395	0.0452157
$494$	4.50084	0.202502
$495$	−0.825186	−0.0370894
$496$	3.49584	0.156968
$497$	42.6371	1.91254
$498$	−9.99794	−0.448018
$499$	32.9041	1.47299	0.736495	−	0.676443i	$-0.236480\pi$
$499$	32.9041	1.47299	0.736495	+	0.676443i	$0.236480\pi$
$500$	6.48607	0.290066
$501$	17.2653	0.771358
$502$	13.6747	0.610332
$503$	30.4556	1.35795	0.678975	−	0.734162i	$-0.262425\pi$
$503$	30.4556	1.35795	0.678975	+	0.734162i	$0.262425\pi$
$504$	10.2078	0.454693
$505$	4.14593	0.184492
$506$	−0.258193	−0.0114781
$507$	−1.00000	−0.0444116
$508$	−11.0903	−0.492053
$509$	15.5928	0.691138	0.345569	−	0.938393i	$-0.387686\pi$
$509$	15.5928	0.691138	0.345569	+	0.938393i	$0.387686\pi$
$510$	−1.49092	−0.0660190
$511$	−10.5111	−0.464984
$512$	−12.1401	−0.536523
$513$	−6.19810	−0.273653
$514$	19.7375	0.870583
$515$	−0.449507	−0.0198076
$516$	−8.15097	−0.358827
$517$	6.23668	0.274289
$518$	17.6748	0.776586
$519$	16.3530	0.717819
$520$	−1.13354	−0.0497090
$521$	41.3769	1.81276	0.906378	−	0.422467i	$-0.138836\pi$
$521$	41.3769	1.81276	0.906378	+	0.422467i	$0.138836\pi$
$522$	0.159611	0.00698600
$523$	37.8137	1.65348	0.826739	−	0.562585i	$-0.190193\pi$
$523$	37.8137	1.65348	0.826739	+	0.562585i	$0.190193\pi$
$524$	−28.9819	−1.26608
$525$	19.4217	0.847634
$526$	6.00447	0.261807
$527$	−14.3311	−0.624272
$528$	2.04536	0.0890131
$529$	−22.9625	−0.998369
$530$	3.64109	0.158159
$531$	0.305246	0.0132465
$532$	−36.9490	−1.60194
$533$	7.72240	0.334494
$534$	6.33990	0.274354
$535$	2.61351	0.112992
$536$	23.1152	0.998424
$537$	0.665028	0.0286981
$538$	−14.9929	−0.646389
$539$	−17.2300	−0.742147
$540$	0.661983	0.0284872
$541$	18.7174	0.804722	0.402361	−	0.915481i	$-0.368190\pi$
$541$	18.7174	0.804722	0.402361	+	0.915481i	$0.368190\pi$
$542$	1.73364	0.0744661
$543$	10.9789	0.471152
$544$	26.7318	1.14612
$545$	−4.14761	−0.177664
$546$	−2.93946	−0.125797
$547$	−23.9429	−1.02372	−0.511862	−	0.859068i	$-0.671044\pi$
$547$	−23.9429	−1.02372	−0.511862	+	0.859068i	$0.671044\pi$
$548$	18.7223	0.799779
$549$	5.70984	0.243690
$550$	−6.39595	−0.272724
$551$	−1.36235	−0.0580380
$552$	0.488421	0.0207886
$553$	−30.4747	−1.29592
$554$	−20.5200	−0.871810
$555$	2.70286	0.114730
$556$	10.9928	0.466199
$557$	11.3657	0.481581	0.240791	−	0.970577i	$-0.422593\pi$
$557$	11.3657	0.481581	0.240791	+	0.970577i	$0.422593\pi$
$558$	−2.27840	−0.0964524
$559$	5.53476	0.234096
$560$	2.02733	0.0856704
$561$	−8.38492	−0.354012
$562$	10.0551	0.424149
$563$	−22.3685	−0.942720	−0.471360	−	0.881941i	$-0.656237\pi$
$563$	−22.3685	−0.942720	−0.471360	+	0.881941i	$0.656237\pi$
$564$	−5.00321	−0.210673
$565$	−2.68876	−0.113117
$566$	−13.7920	−0.579719
$567$	4.04793	0.169997
$568$	26.5616	1.11450
$569$	−17.4611	−0.732005	−0.366003	−	0.930614i	$-0.619274\pi$
$569$	−17.4611	−0.732005	−0.366003	+	0.930614i	$0.619274\pi$
$570$	2.02316	0.0847407
$571$	−32.0728	−1.34221	−0.671103	−	0.741364i	$-0.734179\pi$
$571$	−32.0728	−1.34221	−0.671103	+	0.741364i	$0.734179\pi$
$572$	−2.70350	−0.113039
$573$	−12.1602	−0.507999
$574$	22.6997	0.947467
$575$	0.929286	0.0387539
$576$	2.02155	0.0842313
$577$	32.7405	1.36301	0.681503	−	0.731815i	$-0.261327\pi$
$577$	32.7405	1.36301	0.681503	+	0.731815i	$0.261327\pi$
$578$	−2.80483	−0.116666
$579$	16.1298	0.670332
$580$	0.145504	0.00604174
$581$	−55.7326	−2.31218
$582$	4.18986	0.173675
$583$	20.4775	0.848090
$584$	−6.54810	−0.270962
$585$	−0.449507	−0.0185848
$586$	2.02678	0.0837255
$587$	−15.7763	−0.651156	−0.325578	−	0.945515i	$-0.605559\pi$
$587$	−15.7763	−0.651156	−0.325578	+	0.945515i	$0.605559\pi$
$588$	13.8223	0.570021
$589$	19.4471	0.801303
$590$	−0.0996369	−0.00410199
$591$	9.84554	0.404991
$592$	−6.69950	−0.275348
$593$	−21.8852	−0.898719	−0.449360	−	0.893351i	$-0.648348\pi$
$593$	−21.8852	−0.898719	−0.449360	+	0.893351i	$0.648348\pi$
$594$	−1.33306	−0.0546961
$595$	−8.31100	−0.340718
$596$	2.22583	0.0911737
$597$	17.0686	0.698569
$598$	−0.140646	−0.00575146
$599$	−20.1444	−0.823078	−0.411539	−	0.911392i	$-0.635009\pi$
$599$	−20.1444	−0.823078	−0.411539	+	0.911392i	$0.635009\pi$
$600$	12.0992	0.493946
$601$	−31.9331	−1.30258	−0.651289	−	0.758830i	$-0.725771\pi$
$601$	−31.9331	−1.30258	−0.651289	+	0.758830i	$0.725771\pi$
$602$	16.2692	0.663084
$603$	9.16637	0.373284
$604$	−24.4343	−0.994216
$605$	−3.42973	−0.139439
$606$	6.69762	0.272072
$607$	−35.7522	−1.45114	−0.725568	−	0.688150i	$-0.758423\pi$
$607$	−35.7522	−1.45114	−0.725568	+	0.688150i	$0.758423\pi$
$608$	−36.2747	−1.47113
$609$	0.889739	0.0360540
$610$	−1.86378	−0.0754623
$611$	3.39733	0.137441
$612$	6.72657	0.271906
$613$	16.7771	0.677622	0.338811	−	0.940854i	$-0.389975\pi$
$613$	16.7771	0.677622	0.338811	+	0.940854i	$0.389975\pi$
$614$	12.6454	0.510325
$615$	3.47127	0.139975
$616$	−18.7391	−0.755020
$617$	15.7815	0.635338	0.317669	−	0.948202i	$-0.397100\pi$
$617$	15.7815	0.635338	0.317669	+	0.948202i	$0.397100\pi$
$618$	−0.726163	−0.0292106
$619$	−14.5542	−0.584984	−0.292492	−	0.956268i	$-0.594484\pi$
$619$	−14.5542	−0.584984	−0.292492	+	0.956268i	$0.594484\pi$
$620$	−2.07703	−0.0834155
$621$	0.193684	0.00777228
$622$	23.0108	0.922649
$623$	35.3412	1.41592
$624$	1.11418	0.0446029
$625$	22.0100	0.880399
$626$	22.6107	0.903706
$627$	11.3782	0.454402
$628$	7.93821	0.316769
$629$	27.4644	1.09508
$630$	−1.32131	−0.0526422
$631$	−22.6551	−0.901886	−0.450943	−	0.892553i	$-0.648912\pi$
$631$	−22.6551	−0.901886	−0.450943	+	0.892553i	$0.648912\pi$
$632$	−18.9848	−0.755175
$633$	−21.3810	−0.849820
$634$	9.68987	0.384834
$635$	3.38508	0.134333
$636$	−16.4275	−0.651392
$637$	−9.38575	−0.371877
$638$	−0.293008	−0.0116003
$639$	10.5331	0.416682
$640$	4.60166	0.181897
$641$	19.9667	0.788639	0.394319	−	0.918973i	$-0.370980\pi$
$641$	19.9667	0.788639	0.394319	+	0.918973i	$0.370980\pi$
$642$	4.22203	0.166630
$643$	−10.1556	−0.400496	−0.200248	−	0.979745i	$-0.564175\pi$
$643$	−10.1556	−0.400496	−0.200248	+	0.979745i	$0.564175\pi$
$644$	1.15462	0.0454983
$645$	2.48792	0.0979616
$646$	20.5578	0.808836
$647$	−17.2004	−0.676217	−0.338108	−	0.941107i	$-0.609787\pi$
$647$	−17.2004	−0.676217	−0.338108	+	0.941107i	$0.609787\pi$
$648$	2.52174	0.0990632
$649$	−0.560357	−0.0219959
$650$	−3.48409	−0.136657
$651$	−12.7007	−0.497781
$652$	−0.575441	−0.0225360
$653$	4.69964	0.183911	0.0919555	−	0.995763i	$-0.470688\pi$
$653$	4.69964	0.183911	0.0919555	+	0.995763i	$0.470688\pi$
$654$	−6.70032	−0.262003
$655$	8.84612	0.345646
$656$	−8.60414	−0.335935
$657$	−2.59666	−0.101305
$658$	9.98633	0.389308
$659$	−7.07348	−0.275544	−0.137772	−	0.990464i	$-0.543994\pi$
$659$	−7.07348	−0.275544	−0.137772	+	0.990464i	$0.543994\pi$
$660$	−1.21524	−0.0473032
$661$	−39.3301	−1.52976	−0.764882	−	0.644171i	$-0.777203\pi$
$661$	−39.3301	−1.52976	−0.764882	+	0.644171i	$0.777203\pi$
$662$	8.28277	0.321919
$663$	−4.56755	−0.177389
$664$	−34.7197	−1.34739
$665$	11.2779	0.437338
$666$	4.36638	0.169194
$667$	0.0425720	0.00164839
$668$	25.4264	0.983777
$669$	5.03447	0.194644
$670$	−2.99205	−0.115593
$671$	−10.4819	−0.404649
$672$	23.6907	0.913890
$673$	−46.1131	−1.77753	−0.888765	−	0.458362i	$-0.848436\pi$
$673$	−46.1131	−1.77753	−0.888765	+	0.458362i	$0.848436\pi$
$674$	−4.58322	−0.176539
$675$	4.79794	0.184673
$676$	−1.47269	−0.0566418
$677$	41.5308	1.59616	0.798079	−	0.602553i	$-0.205850\pi$
$677$	41.5308	1.59616	0.798079	+	0.602553i	$0.205850\pi$
$678$	−4.34360	−0.166815
$679$	23.3560	0.896322
$680$	−5.17750	−0.198548
$681$	16.7210	0.640752
$682$	4.18259	0.160160
$683$	−39.5906	−1.51489	−0.757446	−	0.652898i	$-0.773553\pi$
$683$	−39.5906	−1.51489	−0.757446	+	0.652898i	$0.773553\pi$
$684$	−9.12787	−0.349013
$685$	−5.71461	−0.218344
$686$	−7.01281	−0.267750
$687$	11.1561	0.425632
$688$	−6.16672	−0.235104
$689$	11.1548	0.424963
$690$	−0.0632216	−0.00240680
$691$	10.8852	0.414094	0.207047	−	0.978331i	$-0.433615\pi$
$691$	10.8852	0.414094	0.207047	+	0.978331i	$0.433615\pi$
$692$	24.0829	0.915495
$693$	−7.43102	−0.282281
$694$	2.11592	0.0803194
$695$	−3.35533	−0.127275
$696$	0.554280	0.0210099
$697$	35.2725	1.33604
$698$	−5.24313	−0.198455
$699$	−19.3763	−0.732879
$700$	28.6021	1.08106
$701$	12.5868	0.475396	0.237698	−	0.971339i	$-0.423607\pi$
$701$	12.5868	0.475396	0.237698	+	0.971339i	$0.423607\pi$
$702$	−0.726163	−0.0274073
$703$	−37.2688	−1.40562
$704$	−3.71108	−0.139866
$705$	1.52713	0.0575149
$706$	−6.08777	−0.229116
$707$	37.3353	1.40414
$708$	0.449531	0.0168944
$709$	28.7620	1.08018	0.540091	−	0.841607i	$-0.318390\pi$
$709$	28.7620	1.08018	0.540091	+	0.841607i	$0.318390\pi$
$710$	−3.43816	−0.129032
$711$	−7.52846	−0.282339
$712$	22.0165	0.825103
$713$	−0.607701	−0.0227586
$714$	−13.4261	−0.502460
$715$	0.825186	0.0308602
$716$	0.979379	0.0366011
$717$	3.94247	0.147234
$718$	16.4196	0.612773
$719$	−18.0932	−0.674762	−0.337381	−	0.941368i	$-0.609541\pi$
$719$	−18.0932	−0.674762	−0.337381	+	0.941368i	$0.609541\pi$
$720$	0.500832	0.0186649
$721$	−4.04793	−0.150753
$722$	−14.0996	−0.524731
$723$	27.6869	1.02969
$724$	16.1685	0.600899
$725$	1.05459	0.0391666
$726$	−5.54062	−0.205632
$727$	4.36550	0.161907	0.0809537	−	0.996718i	$-0.474203\pi$
$727$	4.36550	0.161907	0.0809537	+	0.996718i	$0.474203\pi$
$728$	−10.2078	−0.378327
$729$	1.00000	0.0370370
$730$	0.847591	0.0313707
$731$	25.2803	0.935027
$732$	8.40881	0.310798
$733$	−47.9217	−1.77003	−0.885014	−	0.465564i	$-0.845851\pi$
$733$	−47.9217	−1.77003	−0.885014	+	0.465564i	$0.845851\pi$
$734$	6.47529	0.239007
$735$	−4.21896	−0.155619
$736$	1.13355	0.0417831
$737$	−16.8272	−0.619840
$738$	5.60773	0.206423
$739$	33.8538	1.24533	0.622667	−	0.782487i	$-0.286049\pi$
$739$	33.8538	1.24533	0.622667	+	0.782487i	$0.286049\pi$
$740$	3.98046	0.146325
$741$	6.19810	0.227693
$742$	32.7890	1.20372
$743$	12.7913	0.469269	0.234634	−	0.972084i	$-0.424611\pi$
$743$	12.7913	0.469269	0.234634	+	0.972084i	$0.424611\pi$
$744$	−7.91217	−0.290074
$745$	−0.679390	−0.0248909
$746$	−12.4310	−0.455130
$747$	−13.7682	−0.503751
$748$	−12.3484	−0.451501
$749$	23.5353	0.859962
$750$	−3.19820	−0.116782
$751$	−3.25388	−0.118736	−0.0593678	−	0.998236i	$-0.518908\pi$
$751$	−3.25388	−0.118736	−0.0593678	+	0.998236i	$0.518908\pi$
$752$	−3.78524	−0.138034
$753$	18.8315	0.686256
$754$	−0.159611	−0.00581270
$755$	7.45805	0.271426
$756$	5.96133	0.216812
$757$	46.8217	1.70176	0.850882	−	0.525356i	$-0.176068\pi$
$757$	46.8217	1.70176	0.850882	+	0.525356i	$0.176068\pi$
$758$	−12.2919	−0.446463
$759$	−0.355558	−0.0129059
$760$	7.02579	0.254852
$761$	1.94615	0.0705477	0.0352739	−	0.999378i	$-0.488770\pi$
$761$	1.94615	0.0705477	0.0352739	+	0.999378i	$0.488770\pi$
$762$	5.46849	0.198103
$763$	−37.3503	−1.35217
$764$	−17.9081	−0.647894
$765$	−2.05315	−0.0742317
$766$	9.86571	0.356463
$767$	−0.305246	−0.0110218
$768$	11.4769	0.414138
$769$	26.4749	0.954708	0.477354	−	0.878711i	$-0.341596\pi$
$769$	26.4749	0.954708	0.477354	+	0.878711i	$0.341596\pi$
$770$	2.42560	0.0874126
$771$	27.1805	0.978881
$772$	23.7541	0.854930
$773$	15.6403	0.562543	0.281272	−	0.959628i	$-0.409244\pi$
$773$	15.6403	0.562543	0.281272	+	0.959628i	$0.409244\pi$
$774$	4.01914	0.144465
$775$	−15.0540	−0.540754
$776$	14.5501	0.522318
$777$	24.3400	0.873192
$778$	0.662596	0.0237552
$779$	−47.8643	−1.71491
$780$	−0.661983	−0.0237028
$781$	−19.3362	−0.691902
$782$	−0.642410	−0.0229725
$783$	0.219801	0.00785504
$784$	10.4574	0.373479
$785$	−2.42297	−0.0864796
$786$	14.2906	0.509729
$787$	−3.05167	−0.108780	−0.0543902	−	0.998520i	$-0.517321\pi$
$787$	−3.05167	−0.108780	−0.0543902	+	0.998520i	$0.517321\pi$
$788$	14.4994	0.516520
$789$	8.26876	0.294376
$790$	2.45741	0.0874306
$791$	−24.2130	−0.860915
$792$	−4.62930	−0.164495
$793$	−5.70984	−0.202762
$794$	−10.6773	−0.378924
$795$	5.01415	0.177834
$796$	25.1366	0.890944
$797$	−25.2691	−0.895076	−0.447538	−	0.894265i	$-0.647699\pi$
$797$	−25.2691	−0.895076	−0.447538	+	0.894265i	$0.647699\pi$
$798$	18.2191	0.644948
$799$	15.5175	0.548970
$800$	28.0802	0.992786
$801$	8.73068	0.308484
$802$	6.84151	0.241582
$803$	4.76684	0.168218
$804$	13.4992	0.476080
$805$	−0.352423	−0.0124213
$806$	2.27840	0.0802532
$807$	−20.6467	−0.726798
$808$	23.2587	0.818239
$809$	44.7885	1.57468	0.787340	−	0.616518i	$-0.211457\pi$
$809$	44.7885	1.57468	0.787340	+	0.616518i	$0.211457\pi$
$810$	−0.326416	−0.0114691
$811$	−41.7988	−1.46775	−0.733877	−	0.679282i	$-0.762291\pi$
$811$	−41.7988	−1.46775	−0.733877	+	0.679282i	$0.762291\pi$
$812$	1.31031	0.0459828
$813$	2.38739	0.0837296
$814$	−8.01561	−0.280947
$815$	0.175641	0.00615245
$816$	5.08907	0.178153
$817$	−34.3051	−1.20018
$818$	−22.1949	−0.776028
$819$	−4.04793	−0.141446
$820$	5.11210	0.178522
$821$	−16.8810	−0.589153	−0.294576	−	0.955628i	$-0.595179\pi$
$821$	−16.8810	−0.589153	−0.294576	+	0.955628i	$0.595179\pi$
$822$	−9.23175	−0.321994
$823$	−14.5320	−0.506553	−0.253276	−	0.967394i	$-0.581508\pi$
$823$	−14.5320	−0.506553	−0.253276	+	0.967394i	$0.581508\pi$
$824$	−2.52174	−0.0878489
$825$	−8.80786	−0.306650
$826$	−0.897257	−0.0312196
$827$	−14.0135	−0.487297	−0.243648	−	0.969864i	$-0.578344\pi$
$827$	−14.0135	−0.487297	−0.243648	+	0.969864i	$0.578344\pi$
$828$	0.285236	0.00991265
$829$	14.9139	0.517980	0.258990	−	0.965880i	$-0.416610\pi$
$829$	14.9139	0.517980	0.258990	+	0.965880i	$0.416610\pi$
$830$	4.49414	0.155994
$831$	−28.2581	−0.980261
$832$	−2.02155	−0.0700846
$833$	−42.8699	−1.48535
$834$	−5.42042	−0.187694
$835$	−7.76088	−0.268576
$836$	16.7566	0.579538
$837$	−3.13759	−0.108451
$838$	−3.64161	−0.125797
$839$	18.5252	0.639561	0.319781	−	0.947492i	$-0.396391\pi$
$839$	18.5252	0.639561	0.319781	+	0.947492i	$0.396391\pi$
$840$	−4.58849	−0.158318
$841$	−28.9517	−0.998334
$842$	20.9559	0.722188
$843$	13.8469	0.476912
$844$	−31.4876	−1.08385
$845$	0.449507	0.0154635
$846$	2.46702	0.0848179
$847$	−30.8857	−1.06124
$848$	−12.4284	−0.426794
$849$	−18.9929	−0.651835
$850$	−15.9138	−0.545838
$851$	1.16461	0.0399224
$852$	15.5119	0.531429
$853$	−41.5317	−1.42202	−0.711009	−	0.703183i	$-0.751761\pi$
$853$	−41.5317	−1.42202	−0.711009	+	0.703183i	$0.751761\pi$
$854$	−16.7838	−0.574331
$855$	2.78609	0.0952823
$856$	14.6618	0.501130
$857$	41.3161	1.41133	0.705666	−	0.708545i	$-0.250648\pi$
$857$	41.3161	1.41133	0.705666	+	0.708545i	$0.250648\pi$
$858$	1.33306	0.0455099
$859$	4.15132	0.141641	0.0708206	−	0.997489i	$-0.477438\pi$
$859$	4.15132	0.141641	0.0708206	+	0.997489i	$0.477438\pi$
$860$	3.66392	0.124939
$861$	31.2598	1.06533
$862$	9.30034	0.316771
$863$	−49.9792	−1.70131	−0.850656	−	0.525723i	$-0.823795\pi$
$863$	−49.9792	−1.70131	−0.850656	+	0.525723i	$0.823795\pi$
$864$	5.85255	0.199108
$865$	−7.35081	−0.249935
$866$	−13.5582	−0.460727
$867$	−3.86253	−0.131179
$868$	−18.7042	−0.634862
$869$	13.8204	0.468826
$870$	−0.0717464	−0.00243243
$871$	−9.16637	−0.310591
$872$	−23.2681	−0.787958
$873$	5.76986	0.195280
$874$	0.871741	0.0294871
$875$	−17.8281	−0.602699
$876$	−3.82407	−0.129203
$877$	−20.5684	−0.694545	−0.347272	−	0.937764i	$-0.612892\pi$
$877$	−20.5684	−0.694545	−0.347272	+	0.937764i	$0.612892\pi$
$878$	−9.66978	−0.326339
$879$	2.79108	0.0941408
$880$	−0.919406	−0.0309932
$881$	−41.4951	−1.39800	−0.699002	−	0.715119i	$-0.746372\pi$
$881$	−41.4951	−1.39800	−0.699002	+	0.715119i	$0.746372\pi$
$882$	−6.81559	−0.229493
$883$	−14.8059	−0.498259	−0.249129	−	0.968470i	$-0.580144\pi$
$883$	−14.8059	−0.498259	−0.249129	+	0.968470i	$0.580144\pi$
$884$	−6.72657	−0.226239
$885$	−0.137210	−0.00461226
$886$	0.398364	0.0133833
$887$	15.5878	0.523388	0.261694	−	0.965151i	$-0.415719\pi$
$887$	15.5878	0.523388	0.261694	+	0.965151i	$0.415719\pi$
$888$	15.1631	0.508839
$889$	30.4836	1.02239
$890$	−2.84983	−0.0955266
$891$	−1.83576	−0.0615002
$892$	7.41419	0.248246
$893$	−21.0570	−0.704647
$894$	−1.09753	−0.0367069
$895$	−0.298935	−0.00999229
$896$	41.4392	1.38439
$897$	−0.193684	−0.00646693
$898$	22.1336	0.738606
$899$	−0.689644	−0.0230009
$900$	7.06587	0.235529
$901$	50.9500	1.69739
$902$	−10.2944	−0.342767
$903$	22.4043	0.745570
$904$	−15.0839	−0.501685
$905$	−4.93511	−0.164049
$906$	12.0482	0.400276
$907$	−29.4269	−0.977103	−0.488552	−	0.872535i	$-0.662475\pi$
$907$	−29.4269	−0.977103	−0.488552	+	0.872535i	$0.662475\pi$
$908$	24.6249	0.817204
$909$	9.22329	0.305917
$910$	1.32131	0.0438009
$911$	33.5567	1.11178	0.555892	−	0.831254i	$-0.312377\pi$
$911$	33.5567	1.11178	0.555892	+	0.831254i	$0.312377\pi$
$912$	−6.90580	−0.228674
$913$	25.2750	0.836481
$914$	−3.91819	−0.129602
$915$	−2.56661	−0.0848496
$916$	16.4294	0.542844
$917$	79.6617	2.63066
$918$	−3.31679	−0.109470
$919$	37.8144	1.24738	0.623691	−	0.781671i	$-0.285632\pi$
$919$	37.8144	1.24738	0.623691	+	0.781671i	$0.285632\pi$
$920$	−0.219549	−0.00723831
$921$	17.4139	0.573808
$922$	1.86256	0.0613403
$923$	−10.5331	−0.346700
$924$	−10.9436	−0.360017
$925$	28.8497	0.948574
$926$	−15.2227	−0.500250
$927$	−1.00000	−0.0328443
$928$	1.28640	0.0422280
$929$	−14.1607	−0.464599	−0.232299	−	0.972644i	$-0.574625\pi$
$929$	−14.1607	−0.464599	−0.232299	+	0.972644i	$0.574625\pi$
$930$	1.02416	0.0335834
$931$	58.1739	1.90657
$932$	−28.5352	−0.934703
$933$	31.6882	1.03742
$934$	−15.8984	−0.520212
$935$	3.76908	0.123262
$936$	−2.52174	−0.0824256
$937$	9.77669	0.319391	0.159695	−	0.987166i	$-0.448949\pi$
$937$	9.77669	0.319391	0.159695	+	0.987166i	$0.448949\pi$
$938$	−26.9442	−0.879759
$939$	31.1372	1.01612
$940$	2.24898	0.0733536
$941$	−51.2898	−1.67200	−0.836000	−	0.548730i	$-0.815111\pi$
$941$	−51.2898	−1.67200	−0.836000	+	0.548730i	$0.815111\pi$
$942$	−3.91423	−0.127533
$943$	1.49571	0.0487070
$944$	0.340098	0.0110693
$945$	−1.81957	−0.0591907
$946$	−7.37818	−0.239885
$947$	−26.9483	−0.875701	−0.437851	−	0.899048i	$-0.644260\pi$
$947$	−26.9483	−0.875701	−0.437851	+	0.899048i	$0.644260\pi$
$948$	−11.0871	−0.360091
$949$	2.59666	0.0842912
$950$	21.5948	0.700627
$951$	13.3439	0.432706
$952$	−46.6248	−1.51112
$953$	30.5343	0.989103	0.494551	−	0.869148i	$-0.335332\pi$
$953$	30.5343	0.989103	0.494551	+	0.869148i	$0.335332\pi$
$954$	8.10019	0.262253
$955$	5.46609	0.176878
$956$	5.80603	0.187780
$957$	−0.403501	−0.0130433
$958$	11.4815	0.370951
$959$	−51.4616	−1.66178
$960$	−0.908701	−0.0293282
$961$	−21.1555	−0.682437
$962$	−4.36638	−0.140778
$963$	5.81416	0.187359
$964$	40.7742	1.31325
$965$	−7.25046	−0.233401
$966$	−0.569327	−0.0183178
$967$	12.6099	0.405507	0.202754	−	0.979230i	$-0.435011\pi$
$967$	12.6099	0.405507	0.202754	+	0.979230i	$0.435011\pi$
$968$	−19.2408	−0.618424
$969$	28.3102	0.909454
$970$	−1.88337	−0.0604715
$971$	−11.5278	−0.369946	−0.184973	−	0.982744i	$-0.559220\pi$
$971$	−11.5278	−0.369946	−0.184973	+	0.982744i	$0.559220\pi$
$972$	1.47269	0.0472364
$973$	−30.2156	−0.968669
$974$	−30.5185	−0.977877
$975$	−4.79794	−0.153657
$976$	6.36179	0.203636
$977$	−17.6886	−0.565907	−0.282954	−	0.959134i	$-0.591314\pi$
$977$	−17.6886	−0.565907	−0.282954	+	0.959134i	$0.591314\pi$
$978$	0.283743	0.00907310
$979$	−16.0274	−0.512239
$980$	−6.21321	−0.198474
$981$	−9.22702	−0.294596
$982$	16.0561	0.512371
$983$	−21.6903	−0.691814	−0.345907	−	0.938269i	$-0.612429\pi$
$983$	−21.6903	−0.691814	−0.345907	+	0.938269i	$0.612429\pi$
$984$	19.4739	0.620804
$985$	−4.42564	−0.141013
$986$	−0.729033	−0.0232171
$987$	13.7522	0.437737
$988$	9.12787	0.290396
$989$	1.07200	0.0340875
$990$	0.599220	0.0190445
$991$	57.9191	1.83986	0.919930	−	0.392083i	$-0.128246\pi$
$991$	57.9191	1.83986	0.919930	+	0.392083i	$0.128246\pi$
$992$	−18.3629	−0.583022
$993$	11.4062	0.361965
$994$	−30.9615	−0.982040
$995$	−7.67243	−0.243233
$996$	−20.2762	−0.642476
$997$	−45.1151	−1.42881	−0.714405	−	0.699732i	$-0.753303\pi$
$997$	−45.1151	−1.42881	−0.714405	+	0.699732i	$0.753303\pi$
$998$	−23.8937	−0.756343
$999$	6.01294	0.190241

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4017.2.a.i.1.10	✓	25

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4017.2.a.i.1.10	✓	25	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:	\( N \)	\(=\)	\( 4017 = 3 \cdot 13 \cdot 103 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4017.a (trivial)

\(f(q)\)	\(=\)	\(q-0.726163 q^{2} -1.00000 q^{3} -1.47269 q^{4} +0.449507 q^{5} +0.726163 q^{6} +4.04793 q^{7} +2.52174 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-0.726163 q^{2} -1.00000 q^{3} -1.47269 q^{4} +0.449507 q^{5} +0.726163 q^{6} +4.04793 q^{7} +2.52174 q^{8} +1.00000 q^{9} -0.326416 q^{10} -1.83576 q^{11} +1.47269 q^{12} -1.00000 q^{13} -2.93946 q^{14} -0.449507 q^{15} +1.11418 q^{16} -4.56755 q^{17} -0.726163 q^{18} +6.19810 q^{19} -0.661983 q^{20} -4.04793 q^{21} +1.33306 q^{22} -0.193684 q^{23} -2.52174 q^{24} -4.79794 q^{25} +0.726163 q^{26} -1.00000 q^{27} -5.96133 q^{28} -0.219801 q^{29} +0.326416 q^{30} +3.13759 q^{31} -5.85255 q^{32} +1.83576 q^{33} +3.31679 q^{34} +1.81957 q^{35} -1.47269 q^{36} -6.01294 q^{37} -4.50084 q^{38} +1.00000 q^{39} +1.13354 q^{40} -7.72240 q^{41} +2.93946 q^{42} -5.53476 q^{43} +2.70350 q^{44} +0.449507 q^{45} +0.140646 q^{46} -3.39733 q^{47} -1.11418 q^{48} +9.38575 q^{49} +3.48409 q^{50} +4.56755 q^{51} +1.47269 q^{52} -11.1548 q^{53} +0.726163 q^{54} -0.825186 q^{55} +10.2078 q^{56} -6.19810 q^{57} +0.159611 q^{58} +0.305246 q^{59} +0.661983 q^{60} +5.70984 q^{61} -2.27840 q^{62} +4.04793 q^{63} +2.02155 q^{64} -0.449507 q^{65} -1.33306 q^{66} +9.16637 q^{67} +6.72657 q^{68} +0.193684 q^{69} -1.32131 q^{70} +10.5331 q^{71} +2.52174 q^{72} -2.59666 q^{73} +4.36638 q^{74} +4.79794 q^{75} -9.12787 q^{76} -7.43102 q^{77} -0.726163 q^{78} -7.52846 q^{79} +0.500832 q^{80} +1.00000 q^{81} +5.60773 q^{82} -13.7682 q^{83} +5.96133 q^{84} -2.05315 q^{85} +4.01914 q^{86} +0.219801 q^{87} -4.62930 q^{88} +8.73068 q^{89} -0.326416 q^{90} -4.04793 q^{91} +0.285236 q^{92} -3.13759 q^{93} +2.46702 q^{94} +2.78609 q^{95} +5.85255 q^{96} +5.76986 q^{97} -6.81559 q^{98} -1.83576 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 25 q - 2 q^{2} - 25 q^{3} + 28 q^{4} - 3 q^{5} + 2 q^{6} - 11 q^{7} - 15 q^{8} + 25 q^{9}+O(q^{10}) \) 25 * q - 2 * q^2 - 25 * q^3 + 28 * q^4 - 3 * q^5 + 2 * q^6 - 11 * q^7 - 15 * q^8 + 25 * q^9	\( 25 q - 2 q^{2} - 25 q^{3} + 28 q^{4} - 3 q^{5} + 2 q^{6} - 11 q^{7} - 15 q^{8} + 25 q^{9} + 2 q^{10} - q^{11} - 28 q^{12} - 25 q^{13} - 12 q^{14} + 3 q^{15} + 26 q^{16} - 10 q^{17} - 2 q^{18} + 22 q^{19} - 2 q^{20} + 11 q^{21} - 5 q^{22} - 49 q^{23} + 15 q^{24} + 22 q^{25} + 2 q^{26} - 25 q^{27} - 30 q^{28} - 22 q^{29} - 2 q^{30} + 8 q^{31} - 12 q^{32} + q^{33} - q^{34} - 2 q^{35} + 28 q^{36} - 26 q^{38} + 25 q^{39} - 22 q^{40} - 5 q^{41} + 12 q^{42} - 13 q^{43} - 25 q^{44} - 3 q^{45} + 13 q^{46} - 56 q^{47} - 26 q^{48} + 28 q^{49} - 31 q^{50} + 10 q^{51} - 28 q^{52} - 20 q^{53} + 2 q^{54} - 14 q^{55} - 22 q^{56} - 22 q^{57} - 21 q^{58} + 2 q^{59} + 2 q^{60} + 29 q^{61} - 39 q^{62} - 11 q^{63} + 21 q^{64} + 3 q^{65} + 5 q^{66} - 14 q^{67} - 60 q^{68} + 49 q^{69} - 31 q^{70} - 36 q^{71} - 15 q^{72} - 30 q^{73} - 64 q^{74} - 22 q^{75} + 38 q^{76} - 37 q^{77} - 2 q^{78} - 29 q^{79} + 25 q^{81} - 6 q^{82} - 17 q^{83} + 30 q^{84} + 3 q^{85} - 27 q^{86} + 22 q^{87} - 81 q^{88} - 38 q^{89} + 2 q^{90} + 11 q^{91} - 85 q^{92} - 8 q^{93} + 26 q^{94} - 71 q^{95} + 12 q^{96} + 19 q^{98} - q^{99}+O(q^{100}) \) 25 * q - 2 * q^2 - 25 * q^3 + 28 * q^4 - 3 * q^5 + 2 * q^6 - 11 * q^7 - 15 * q^8 + 25 * q^9 + 2 * q^10 - q^11 - 28 * q^12 - 25 * q^13 - 12 * q^14 + 3 * q^15 + 26 * q^16 - 10 * q^17 - 2 * q^18 + 22 * q^19 - 2 * q^20 + 11 * q^21 - 5 * q^22 - 49 * q^23 + 15 * q^24 + 22 * q^25 + 2 * q^26 - 25 * q^27 - 30 * q^28 - 22 * q^29 - 2 * q^30 + 8 * q^31 - 12 * q^32 + q^33 - q^34 - 2 * q^35 + 28 * q^36 - 26 * q^38 + 25 * q^39 - 22 * q^40 - 5 * q^41 + 12 * q^42 - 13 * q^43 - 25 * q^44 - 3 * q^45 + 13 * q^46 - 56 * q^47 - 26 * q^48 + 28 * q^49 - 31 * q^50 + 10 * q^51 - 28 * q^52 - 20 * q^53 + 2 * q^54 - 14 * q^55 - 22 * q^56 - 22 * q^57 - 21 * q^58 + 2 * q^59 + 2 * q^60 + 29 * q^61 - 39 * q^62 - 11 * q^63 + 21 * q^64 + 3 * q^65 + 5 * q^66 - 14 * q^67 - 60 * q^68 + 49 * q^69 - 31 * q^70 - 36 * q^71 - 15 * q^72 - 30 * q^73 - 64 * q^74 - 22 * q^75 + 38 * q^76 - 37 * q^77 - 2 * q^78 - 29 * q^79 + 25 * q^81 - 6 * q^82 - 17 * q^83 + 30 * q^84 + 3 * q^85 - 27 * q^86 + 22 * q^87 - 81 * q^88 - 38 * q^89 + 2 * q^90 + 11 * q^91 - 85 * q^92 - 8 * q^93 + 26 * q^94 - 71 * q^95 + 12 * q^96 + 19 * q^98 - q^99

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