LMFDB - Embedded newform 4017.2.a.e.1.3

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:	$16$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 21 x^{14} - 3 x^{13} + 177 x^{12} + 45 x^{11} - 763 x^{10} - 251 x^{9} + 1771 x^{8} + 639 x^{7} + \cdots + 7 $ x^16 - 21x^14 - 3x^13 + 177x^12 + 45x^11 - 763x^10 - 251x^9 + 1771x^8 + 639x^7 - 2118x^6 - 710x^5 + 1113x^4 + 243x^3 - 183x^2 - 10x + 7
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$1.91188$ of defining polynomial
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)

$f(q)$	$=$	$q-1.91188 q^{2} +1.00000 q^{3} +1.65528 q^{4} -0.339131 q^{5} -1.91188 q^{6} -3.26096 q^{7} +0.659059 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.91188 q^{2} +1.00000 q^{3} +1.65528 q^{4} -0.339131 q^{5} -1.91188 q^{6} -3.26096 q^{7} +0.659059 q^{8} +1.00000 q^{9} +0.648377 q^{10} -2.68706 q^{11} +1.65528 q^{12} -1.00000 q^{13} +6.23456 q^{14} -0.339131 q^{15} -4.57061 q^{16} +0.748890 q^{17} -1.91188 q^{18} +5.50928 q^{19} -0.561357 q^{20} -3.26096 q^{21} +5.13733 q^{22} -4.13710 q^{23} +0.659059 q^{24} -4.88499 q^{25} +1.91188 q^{26} +1.00000 q^{27} -5.39780 q^{28} +8.25016 q^{29} +0.648377 q^{30} +9.77678 q^{31} +7.42033 q^{32} -2.68706 q^{33} -1.43179 q^{34} +1.10589 q^{35} +1.65528 q^{36} +6.92649 q^{37} -10.5331 q^{38} -1.00000 q^{39} -0.223507 q^{40} +0.230971 q^{41} +6.23456 q^{42} -9.67061 q^{43} -4.44784 q^{44} -0.339131 q^{45} +7.90964 q^{46} -6.78381 q^{47} -4.57061 q^{48} +3.63384 q^{49} +9.33951 q^{50} +0.748890 q^{51} -1.65528 q^{52} -0.371784 q^{53} -1.91188 q^{54} +0.911264 q^{55} -2.14916 q^{56} +5.50928 q^{57} -15.7733 q^{58} +12.4298 q^{59} -0.561357 q^{60} +15.3501 q^{61} -18.6920 q^{62} -3.26096 q^{63} -5.04556 q^{64} +0.339131 q^{65} +5.13733 q^{66} -14.0463 q^{67} +1.23962 q^{68} -4.13710 q^{69} -2.11433 q^{70} +4.52536 q^{71} +0.659059 q^{72} -9.39560 q^{73} -13.2426 q^{74} -4.88499 q^{75} +9.11941 q^{76} +8.76239 q^{77} +1.91188 q^{78} -16.1319 q^{79} +1.55003 q^{80} +1.00000 q^{81} -0.441589 q^{82} -5.28253 q^{83} -5.39780 q^{84} -0.253971 q^{85} +18.4890 q^{86} +8.25016 q^{87} -1.77093 q^{88} +15.9556 q^{89} +0.648377 q^{90} +3.26096 q^{91} -6.84807 q^{92} +9.77678 q^{93} +12.9698 q^{94} -1.86837 q^{95} +7.42033 q^{96} -7.29669 q^{97} -6.94747 q^{98} -2.68706 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 16 q^{3} + 10 q^{4} - 6 q^{5} - 13 q^{7} - 9 q^{8} + 16 q^{9}+O(q^{10}) $ 16 * q + 16 * q^3 + 10 * q^4 - 6 * q^5 - 13 * q^7 - 9 * q^8 + 16 * q^9	\( 16 q + 16 q^{3} + 10 q^{4} - 6 q^{5} - 13 q^{7} - 9 q^{8} + 16 q^{9} - 8 q^{10} - 5 q^{11} + 10 q^{12} - 16 q^{13} - 8 q^{14} - 6 q^{15} - 14 q^{16} - q^{17} + 6 q^{19} - 4 q^{20} - 13 q^{21} - 11 q^{22} - 21 q^{23} - 9 q^{24} - 10 q^{25} + 16 q^{27} - 10 q^{28} - 17 q^{29} - 8 q^{30} - 33 q^{31} - 18 q^{32} - 5 q^{33} - 5 q^{34} - 4 q^{35} + 10 q^{36} - 23 q^{37} - 28 q^{38} - 16 q^{39} - 12 q^{40} + 7 q^{41} - 8 q^{42} - 33 q^{43} + 11 q^{44} - 6 q^{45} - 15 q^{46} - 13 q^{47} - 14 q^{48} - 17 q^{49} + 35 q^{50} - q^{51} - 10 q^{52} - 20 q^{53} - 54 q^{55} + 12 q^{56} + 6 q^{57} - 33 q^{58} + 6 q^{59} - 4 q^{60} - 49 q^{61} - 13 q^{62} - 13 q^{63} - 35 q^{64} + 6 q^{65} - 11 q^{66} - 4 q^{67} - 14 q^{68} - 21 q^{69} - 33 q^{70} - 29 q^{71} - 9 q^{72} - 21 q^{73} + 22 q^{74} - 10 q^{75} + 10 q^{76} - 21 q^{77} - 70 q^{79} - 8 q^{80} + 16 q^{81} - 10 q^{82} + 5 q^{83} - 10 q^{84} + 14 q^{85} + 29 q^{86} - 17 q^{87} - 45 q^{88} - 8 q^{89} - 8 q^{90} + 13 q^{91} - 29 q^{92} - 33 q^{93} + 12 q^{94} - 45 q^{95} - 18 q^{96} - 30 q^{97} + 15 q^{98} - 5 q^{99}+O(q^{100}) \) 16 * q + 16 * q^3 + 10 * q^4 - 6 * q^5 - 13 * q^7 - 9 * q^8 + 16 * q^9 - 8 * q^10 - 5 * q^11 + 10 * q^12 - 16 * q^13 - 8 * q^14 - 6 * q^15 - 14 * q^16 - q^17 + 6 * q^19 - 4 * q^20 - 13 * q^21 - 11 * q^22 - 21 * q^23 - 9 * q^24 - 10 * q^25 + 16 * q^27 - 10 * q^28 - 17 * q^29 - 8 * q^30 - 33 * q^31 - 18 * q^32 - 5 * q^33 - 5 * q^34 - 4 * q^35 + 10 * q^36 - 23 * q^37 - 28 * q^38 - 16 * q^39 - 12 * q^40 + 7 * q^41 - 8 * q^42 - 33 * q^43 + 11 * q^44 - 6 * q^45 - 15 * q^46 - 13 * q^47 - 14 * q^48 - 17 * q^49 + 35 * q^50 - q^51 - 10 * q^52 - 20 * q^53 - 54 * q^55 + 12 * q^56 + 6 * q^57 - 33 * q^58 + 6 * q^59 - 4 * q^60 - 49 * q^61 - 13 * q^62 - 13 * q^63 - 35 * q^64 + 6 * q^65 - 11 * q^66 - 4 * q^67 - 14 * q^68 - 21 * q^69 - 33 * q^70 - 29 * q^71 - 9 * q^72 - 21 * q^73 + 22 * q^74 - 10 * q^75 + 10 * q^76 - 21 * q^77 - 70 * q^79 - 8 * q^80 + 16 * q^81 - 10 * q^82 + 5 * q^83 - 10 * q^84 + 14 * q^85 + 29 * q^86 - 17 * q^87 - 45 * q^88 - 8 * q^89 - 8 * q^90 + 13 * q^91 - 29 * q^92 - 33 * q^93 + 12 * q^94 - 45 * q^95 - 18 * q^96 - 30 * q^97 + 15 * q^98 - 5 * 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 $

$2$	−1.91188	−1.35190	−0.675951	−	0.736946i	$-0.736267\pi$
$2$	−1.91188	−1.35190	−0.675951	+	0.736946i	$0.736267\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	1.65528	0.827641
$5$	−0.339131	−0.151664	−0.0758319	−	0.997121i	$-0.524161\pi$
$5$	−0.339131	−0.151664	−0.0758319	+	0.997121i	$0.524161\pi$
$6$	−1.91188	−0.780521
$7$	−3.26096	−1.23253	−0.616263	−	0.787540i	$-0.711354\pi$
$7$	−3.26096	−1.23253	−0.616263	+	0.787540i	$0.711354\pi$
$8$	0.659059	0.233013
$9$	1.00000	0.333333
$10$	0.648377	0.205035
$11$	−2.68706	−0.810179	−0.405090	−	0.914277i	$-0.632760\pi$
$11$	−2.68706	−0.810179	−0.405090	+	0.914277i	$0.632760\pi$
$12$	1.65528	0.477839
$13$	−1.00000	−0.277350
$13$	−1.00000	−0.277350
$14$	6.23456	1.66626
$15$	−0.339131	−0.0875631
$16$	−4.57061	−1.14265
$17$	0.748890	0.181632	0.0908162	−	0.995868i	$-0.471052\pi$
$17$	0.748890	0.181632	0.0908162	+	0.995868i	$0.471052\pi$
$18$	−1.91188	−0.450634
$19$	5.50928	1.26392	0.631958	−	0.775003i	$-0.282252\pi$
$19$	5.50928	1.26392	0.631958	+	0.775003i	$0.282252\pi$
$20$	−0.561357	−0.125523
$21$	−3.26096	−0.711599
$22$	5.13733	1.09528
$23$	−4.13710	−0.862646	−0.431323	−	0.902198i	$-0.641953\pi$
$23$	−4.13710	−0.862646	−0.431323	+	0.902198i	$0.641953\pi$
$24$	0.659059	0.134530
$25$	−4.88499	−0.976998
$26$	1.91188	0.374950
$27$	1.00000	0.192450
$28$	−5.39780	−1.02009
$29$	8.25016	1.53202	0.766008	−	0.642831i	$-0.222240\pi$
$29$	8.25016	1.53202	0.766008	+	0.642831i	$0.222240\pi$
$30$	0.648377	0.118377
$31$	9.77678	1.75596	0.877981	−	0.478696i	$-0.158890\pi$
$31$	9.77678	1.75596	0.877981	+	0.478696i	$0.158890\pi$
$32$	7.42033	1.31174
$33$	−2.68706	−0.467757
$34$	−1.43179	−0.245549
$35$	1.10589	0.186930
$36$	1.65528	0.275880
$37$	6.92649	1.13871	0.569354	−	0.822093i	$-0.307194\pi$
$37$	6.92649	1.13871	0.569354	+	0.822093i	$0.307194\pi$
$38$	−10.5331	−1.70869
$39$	−1.00000	−0.160128
$40$	−0.223507	−0.0353396
$41$	0.230971	0.0360716	0.0180358	−	0.999837i	$-0.494259\pi$
$41$	0.230971	0.0360716	0.0180358	+	0.999837i	$0.494259\pi$
$42$	6.23456	0.962013
$43$	−9.67061	−1.47475	−0.737377	−	0.675481i	$-0.763936\pi$
$43$	−9.67061	−1.47475	−0.737377	+	0.675481i	$0.763936\pi$
$44$	−4.44784	−0.670537
$45$	−0.339131	−0.0505546
$46$	7.90964	1.16621
$47$	−6.78381	−0.989521	−0.494760	−	0.869029i	$-0.664744\pi$
$47$	−6.78381	−0.989521	−0.494760	+	0.869029i	$0.664744\pi$
$48$	−4.57061	−0.659710
$49$	3.63384	0.519121
$50$	9.33951	1.32081
$51$	0.748890	0.104866
$52$	−1.65528	−0.229546
$53$	−0.371784	−0.0510684	−0.0255342	−	0.999674i	$-0.508129\pi$
$53$	−0.371784	−0.0510684	−0.0255342	+	0.999674i	$0.508129\pi$
$54$	−1.91188	−0.260174
$55$	0.911264	0.122875
$56$	−2.14916	−0.287194
$57$	5.50928	0.729722
$58$	−15.7733	−2.07114
$59$	12.4298	1.61823	0.809113	−	0.587654i	$-0.199948\pi$
$59$	12.4298	1.61823	0.809113	+	0.587654i	$0.199948\pi$
$60$	−0.561357	−0.0724708
$61$	15.3501	1.96538	0.982692	−	0.185249i	$-0.0593093\pi$
$61$	15.3501	1.96538	0.982692	+	0.185249i	$0.0593093\pi$
$62$	−18.6920	−2.37389
$63$	−3.26096	−0.410842
$64$	−5.04556	−0.630695
$65$	0.339131	0.0420640
$66$	5.13733	0.632362
$67$	−14.0463	−1.71603	−0.858014	−	0.513626i	$-0.828302\pi$
$67$	−14.0463	−1.71603	−0.858014	+	0.513626i	$0.828302\pi$
$68$	1.23962	0.150326
$69$	−4.13710	−0.498049
$70$	−2.11433	−0.252711
$71$	4.52536	0.537062	0.268531	−	0.963271i	$-0.413462\pi$
$71$	4.52536	0.537062	0.268531	+	0.963271i	$0.413462\pi$
$72$	0.659059	0.0776709
$73$	−9.39560	−1.09967	−0.549836	−	0.835273i	$-0.685310\pi$
$73$	−9.39560	−1.09967	−0.549836	+	0.835273i	$0.685310\pi$
$74$	−13.2426	−1.53942
$75$	−4.88499	−0.564070
$76$	9.11941	1.04607
$77$	8.76239	0.998567
$78$	1.91188	0.216478
$79$	−16.1319	−1.81498	−0.907491	−	0.420072i	$-0.862005\pi$
$79$	−16.1319	−1.81498	−0.907491	+	0.420072i	$0.862005\pi$
$80$	1.55003	0.173299
$81$	1.00000	0.111111
$82$	−0.441589	−0.0487653
$83$	−5.28253	−0.579833	−0.289917	−	0.957052i	$-0.593628\pi$
$83$	−5.28253	−0.579833	−0.289917	+	0.957052i	$0.593628\pi$
$84$	−5.39780	−0.588949
$85$	−0.253971	−0.0275471
$86$	18.4890	1.99372
$87$	8.25016	0.884510
$88$	−1.77093	−0.188782
$89$	15.9556	1.69129	0.845643	−	0.533749i	$-0.179217\pi$
$89$	15.9556	1.69129	0.845643	+	0.533749i	$0.179217\pi$
$90$	0.648377	0.0683449
$91$	3.26096	0.341841
$92$	−6.84807	−0.713961
$93$	9.77678	1.01380
$94$	12.9698	1.33774
$95$	−1.86837	−0.191690
$96$	7.42033	0.757334
$97$	−7.29669	−0.740867	−0.370434	−	0.928859i	$-0.620791\pi$
$97$	−7.29669	−0.740867	−0.370434	+	0.928859i	$0.620791\pi$
$98$	−6.94747	−0.701800
$99$	−2.68706	−0.270060
$100$	−8.08604	−0.808604
$101$	−14.5754	−1.45031	−0.725153	−	0.688587i	$-0.758231\pi$
$101$	−14.5754	−1.45031	−0.725153	+	0.688587i	$0.758231\pi$
$102$	−1.43179	−0.141768
$103$	1.00000	0.0985329
$103$	1.00000	0.0985329
$104$	−0.659059	−0.0646261
$105$	1.10589	0.107924
$106$	0.710806	0.0690395
$107$	9.87991	0.955127	0.477564	−	0.878597i	$-0.341520\pi$
$107$	9.87991	0.955127	0.477564	+	0.878597i	$0.341520\pi$
$108$	1.65528	0.159280
$109$	1.96075	0.187806	0.0939028	−	0.995581i	$-0.470066\pi$
$109$	1.96075	0.187806	0.0939028	+	0.995581i	$0.470066\pi$
$110$	−1.74223	−0.166115
$111$	6.92649	0.657433
$112$	14.9046	1.40835
$113$	−11.8952	−1.11901	−0.559504	−	0.828828i	$-0.689008\pi$
$113$	−11.8952	−1.11901	−0.559504	+	0.828828i	$0.689008\pi$
$114$	−10.5331	−0.986513
$115$	1.40302	0.130832
$116$	13.6563	1.26796
$117$	−1.00000	−0.0924500
$118$	−23.7643	−2.18768
$119$	−2.44210	−0.223867
$120$	−0.223507	−0.0204033
$121$	−3.77971	−0.343610
$122$	−29.3476	−2.65701
$123$	0.230971	0.0208260
$124$	16.1833	1.45331
$125$	3.35230	0.299839
$126$	6.23456	0.555418
$127$	−2.73798	−0.242956	−0.121478	−	0.992594i	$-0.538763\pi$
$127$	−2.73798	−0.242956	−0.121478	+	0.992594i	$0.538763\pi$
$128$	−5.19416	−0.459103
$129$	−9.67061	−0.851450
$130$	−0.648377	−0.0568664
$131$	−8.61479	−0.752678	−0.376339	−	0.926482i	$-0.622817\pi$
$131$	−8.61479	−0.752678	−0.376339	+	0.926482i	$0.622817\pi$
$132$	−4.44784	−0.387135
$133$	−17.9655	−1.55781
$134$	26.8548	2.31990
$135$	−0.339131	−0.0291877
$136$	0.493563	0.0423226
$137$	10.4946	0.896614	0.448307	−	0.893880i	$-0.352027\pi$
$137$	10.4946	0.896614	0.448307	+	0.893880i	$0.352027\pi$
$138$	7.90964	0.673314
$139$	−14.9527	−1.26827	−0.634136	−	0.773221i	$-0.718644\pi$
$139$	−14.9527	−1.26827	−0.634136	+	0.773221i	$0.718644\pi$
$140$	1.83056	0.154711
$141$	−6.78381	−0.571300
$142$	−8.65195	−0.726056
$143$	2.68706	0.224703
$144$	−4.57061	−0.380884
$145$	−2.79788	−0.232352
$146$	17.9632	1.48665
$147$	3.63384	0.299714
$148$	11.4653	0.942441
$149$	−14.2852	−1.17029	−0.585146	−	0.810928i	$-0.698963\pi$
$149$	−14.2852	−1.17029	−0.585146	+	0.810928i	$0.698963\pi$
$150$	9.33951	0.762568
$151$	−16.9683	−1.38086	−0.690430	−	0.723399i	$-0.742579\pi$
$151$	−16.9683	−1.38086	−0.690430	+	0.723399i	$0.742579\pi$
$152$	3.63094	0.294508
$153$	0.748890	0.0605441
$154$	−16.7526	−1.34997
$155$	−3.31561	−0.266316
$156$	−1.65528	−0.132529
$157$	−5.89868	−0.470766	−0.235383	−	0.971903i	$-0.575634\pi$
$157$	−5.89868	−0.470766	−0.235383	+	0.971903i	$0.575634\pi$
$158$	30.8423	2.45368
$159$	−0.371784	−0.0294844
$160$	−2.51646	−0.198944
$161$	13.4909	1.06323
$162$	−1.91188	−0.150211
$163$	−19.9483	−1.56247	−0.781234	−	0.624238i	$-0.785409\pi$
$163$	−19.9483	−1.56247	−0.781234	+	0.624238i	$0.785409\pi$
$164$	0.382322	0.0298544
$165$	0.911264	0.0709418
$166$	10.0996	0.783878
$167$	11.6242	0.899504	0.449752	−	0.893153i	$-0.351512\pi$
$167$	11.6242	0.899504	0.449752	+	0.893153i	$0.351512\pi$
$168$	−2.14916	−0.165812
$169$	1.00000	0.0769231
$170$	0.485563	0.0372409
$171$	5.50928	0.421305
$172$	−16.0076	−1.22057
$173$	−3.68599	−0.280241	−0.140120	−	0.990134i	$-0.544749\pi$
$173$	−3.68599	−0.280241	−0.140120	+	0.990134i	$0.544749\pi$
$174$	−15.7733	−1.19577
$175$	15.9297	1.20418
$176$	12.2815	0.925752
$177$	12.4298	0.934283
$178$	−30.5051	−2.28645
$179$	18.1415	1.35596	0.677981	−	0.735079i	$-0.262855\pi$
$179$	18.1415	1.35596	0.677981	+	0.735079i	$0.262855\pi$
$180$	−0.561357	−0.0418411
$181$	−19.2544	−1.43117	−0.715584	−	0.698527i	$-0.753839\pi$
$181$	−19.2544	−1.43117	−0.715584	+	0.698527i	$0.753839\pi$
$182$	−6.23456	−0.462136
$183$	15.3501	1.13471
$184$	−2.72660	−0.201007
$185$	−2.34898	−0.172701
$186$	−18.6920	−1.37057
$187$	−2.01231	−0.147155
$188$	−11.2291	−0.818968
$189$	−3.26096	−0.237200
$190$	3.57209	0.259147
$191$	−5.51366	−0.398954	−0.199477	−	0.979902i	$-0.563924\pi$
$191$	−5.51366	−0.398954	−0.199477	+	0.979902i	$0.563924\pi$
$192$	−5.04556	−0.364132
$193$	13.2714	0.955298	0.477649	−	0.878551i	$-0.341489\pi$
$193$	13.2714	0.955298	0.477649	+	0.878551i	$0.341489\pi$
$194$	13.9504	1.00158
$195$	0.339131	0.0242856
$196$	6.01504	0.429645
$197$	14.9455	1.06483	0.532413	−	0.846485i	$-0.321286\pi$
$197$	14.9455	1.06483	0.532413	+	0.846485i	$0.321286\pi$
$198$	5.13733	0.365094
$199$	−12.6831	−0.899078	−0.449539	−	0.893261i	$-0.648412\pi$
$199$	−12.6831	−0.899078	−0.449539	+	0.893261i	$0.648412\pi$
$200$	−3.21950	−0.227653
$201$	−14.0463	−0.990749
$202$	27.8664	1.96067
$203$	−26.9034	−1.88825
$204$	1.23962	0.0867910
$205$	−0.0783294	−0.00547076
$206$	−1.91188	−0.133207
$207$	−4.13710	−0.287549
$208$	4.57061	0.316914
$209$	−14.8038	−1.02400
$210$	−2.11433	−0.145903
$211$	2.55811	0.176108	0.0880539	−	0.996116i	$-0.471935\pi$
$211$	2.55811	0.176108	0.0880539	+	0.996116i	$0.471935\pi$
$212$	−0.615407	−0.0422663
$213$	4.52536	0.310073
$214$	−18.8892	−1.29124
$215$	3.27960	0.223667
$216$	0.659059	0.0448433
$217$	−31.8817	−2.16427
$218$	−3.74871	−0.253895
$219$	−9.39560	−0.634896
$220$	1.50840	0.101696
$221$	−0.748890	−0.0503758
$222$	−13.2426	−0.888785
$223$	15.9499	1.06808	0.534041	−	0.845459i	$-0.320673\pi$
$223$	15.9499	1.06808	0.534041	+	0.845459i	$0.320673\pi$
$224$	−24.1974	−1.61675
$225$	−4.88499	−0.325666
$226$	22.7422	1.51279
$227$	1.26450	0.0839276	0.0419638	−	0.999119i	$-0.486639\pi$
$227$	1.26450	0.0839276	0.0419638	+	0.999119i	$0.486639\pi$
$228$	9.11941	0.603948
$229$	−24.7677	−1.63669	−0.818347	−	0.574724i	$-0.805109\pi$
$229$	−24.7677	−1.63669	−0.818347	+	0.574724i	$0.805109\pi$
$230$	−2.68240	−0.176872
$231$	8.76239	0.576523
$232$	5.43735	0.356979
$233$	12.9749	0.850014	0.425007	−	0.905190i	$-0.360272\pi$
$233$	12.9749	0.850014	0.425007	+	0.905190i	$0.360272\pi$
$234$	1.91188	0.124983
$235$	2.30060	0.150075
$236$	20.5749	1.33931
$237$	−16.1319	−1.04788
$238$	4.66899	0.302646
$239$	8.39490	0.543021	0.271510	−	0.962436i	$-0.412477\pi$
$239$	8.39490	0.543021	0.271510	+	0.962436i	$0.412477\pi$
$240$	1.55003	0.100054
$241$	2.96402	0.190929	0.0954647	−	0.995433i	$-0.469566\pi$
$241$	2.96402	0.190929	0.0954647	+	0.995433i	$0.469566\pi$
$242$	7.22635	0.464527
$243$	1.00000	0.0641500
$244$	25.4088	1.62663
$245$	−1.23235	−0.0787318
$246$	−0.441589	−0.0281547
$247$	−5.50928	−0.350547
$248$	6.44348	0.409161
$249$	−5.28253	−0.334767
$250$	−6.40920	−0.405353
$251$	−22.8747	−1.44384	−0.721919	−	0.691978i	$-0.756740\pi$
$251$	−22.8747	−1.44384	−0.721919	+	0.691978i	$0.756740\pi$
$252$	−5.39780	−0.340030
$253$	11.1166	0.698898
$254$	5.23468	0.328453
$255$	−0.253971	−0.0159043
$256$	20.0217	1.25136
$257$	−23.7852	−1.48368	−0.741841	−	0.670575i	$-0.766047\pi$
$257$	−23.7852	−1.48368	−0.741841	+	0.670575i	$0.766047\pi$
$258$	18.4890	1.15108
$259$	−22.5870	−1.40349
$260$	0.561357	0.0348139
$261$	8.25016	0.510672
$262$	16.4704	1.01755
$263$	6.83158	0.421253	0.210627	−	0.977567i	$-0.432450\pi$
$263$	6.83158	0.421253	0.210627	+	0.977567i	$0.432450\pi$
$264$	−1.77093	−0.108993
$265$	0.126083	0.00774523
$266$	34.3479	2.10601
$267$	15.9556	0.976465
$268$	−23.2506	−1.42026
$269$	10.5663	0.644239	0.322120	−	0.946699i	$-0.395605\pi$
$269$	10.5663	0.644239	0.322120	+	0.946699i	$0.395605\pi$
$270$	0.648377	0.0394590
$271$	2.27089	0.137947	0.0689734	−	0.997619i	$-0.478028\pi$
$271$	2.27089	0.137947	0.0689734	+	0.997619i	$0.478028\pi$
$272$	−3.42288	−0.207543
$273$	3.26096	0.197362
$274$	−20.0644	−1.21213
$275$	13.1263	0.791543
$276$	−6.84807	−0.412206
$277$	2.44144	0.146692	0.0733459	−	0.997307i	$-0.476632\pi$
$277$	2.44144	0.146692	0.0733459	+	0.997307i	$0.476632\pi$
$278$	28.5878	1.71458
$279$	9.77678	0.585320
$280$	0.728847	0.0435570
$281$	18.2237	1.08713	0.543566	−	0.839366i	$-0.317074\pi$
$281$	18.2237	1.08713	0.543566	+	0.839366i	$0.317074\pi$
$282$	12.9698	0.772342
$283$	13.5467	0.805268	0.402634	−	0.915361i	$-0.368095\pi$
$283$	13.5467	0.805268	0.402634	+	0.915361i	$0.368095\pi$
$284$	7.49075	0.444495
$285$	−1.86837	−0.110672
$286$	−5.13733	−0.303777
$287$	−0.753187	−0.0444592
$288$	7.42033	0.437247
$289$	−16.4392	−0.967010
$290$	5.34921	0.314117
$291$	−7.29669	−0.427740
$292$	−15.5524	−0.910133
$293$	−16.4415	−0.960521	−0.480261	−	0.877126i	$-0.659458\pi$
$293$	−16.4415	−0.960521	−0.480261	+	0.877126i	$0.659458\pi$
$294$	−6.94747	−0.405185
$295$	−4.21533	−0.245426
$296$	4.56496	0.265333
$297$	−2.68706	−0.155919
$298$	27.3116	1.58212
$299$	4.13710	0.239255
$300$	−8.08604	−0.466848
$301$	31.5355	1.81767
$302$	32.4413	1.86679
$303$	−14.5754	−0.837335
$304$	−25.1808	−1.44422
$305$	−5.20570	−0.298078
$306$	−1.43179	−0.0818498
$307$	−8.43708	−0.481529	−0.240765	−	0.970584i	$-0.577398\pi$
$307$	−8.43708	−0.481529	−0.240765	+	0.970584i	$0.577398\pi$
$308$	14.5042	0.826455
$309$	1.00000	0.0568880
$310$	6.33904	0.360033
$311$	−13.7627	−0.780409	−0.390205	−	0.920728i	$-0.627596\pi$
$311$	−13.7627	−0.780409	−0.390205	+	0.920728i	$0.627596\pi$
$312$	−0.659059	−0.0373119
$313$	26.4319	1.49402	0.747010	−	0.664812i	$-0.231489\pi$
$313$	26.4319	1.49402	0.747010	+	0.664812i	$0.231489\pi$
$314$	11.2776	0.636430
$315$	1.10589	0.0623099
$316$	−26.7029	−1.50215
$317$	−16.8478	−0.946269	−0.473135	−	0.880990i	$-0.656878\pi$
$317$	−16.8478	−0.946269	−0.473135	+	0.880990i	$0.656878\pi$
$318$	0.710806	0.0398600
$319$	−22.1687	−1.24121
$320$	1.71110	0.0956536
$321$	9.87991	0.551443
$322$	−25.7930	−1.43739
$323$	4.12584	0.229568
$324$	1.65528	0.0919601
$325$	4.88499	0.270971
$326$	38.1387	2.11230
$327$	1.96075	0.108430
$328$	0.152224	0.00840515
$329$	22.1217	1.21961
$330$	−1.74223	−0.0959065
$331$	−2.75348	−0.151345	−0.0756724	−	0.997133i	$-0.524110\pi$
$331$	−2.75348	−0.151345	−0.0756724	+	0.997133i	$0.524110\pi$
$332$	−8.74408	−0.479894
$333$	6.92649	0.379569
$334$	−22.2240	−1.21604
$335$	4.76353	0.260259
$336$	14.9046	0.813110
$337$	−2.52497	−0.137544	−0.0687720	−	0.997632i	$-0.521908\pi$
$337$	−2.52497	−0.137544	−0.0687720	+	0.997632i	$0.521908\pi$
$338$	−1.91188	−0.103993
$339$	−11.8952	−0.646059
$340$	−0.420394	−0.0227991
$341$	−26.2708	−1.42264
$342$	−10.5331	−0.569564
$343$	10.9769	0.592696
$344$	−6.37351	−0.343636
$345$	1.40302	0.0755360
$346$	7.04716	0.378858
$347$	−17.6787	−0.949040	−0.474520	−	0.880245i	$-0.657378\pi$
$347$	−17.6787	−0.949040	−0.474520	+	0.880245i	$0.657378\pi$
$348$	13.6563	0.732057
$349$	−9.72071	−0.520338	−0.260169	−	0.965563i	$-0.583778\pi$
$349$	−9.72071	−0.520338	−0.260169	+	0.965563i	$0.583778\pi$
$350$	−30.4557	−1.62793
$351$	−1.00000	−0.0533761
$352$	−19.9389	−1.06275
$353$	−10.3378	−0.550227	−0.275114	−	0.961412i	$-0.588715\pi$
$353$	−10.3378	−0.550227	−0.275114	+	0.961412i	$0.588715\pi$
$354$	−23.7643	−1.26306
$355$	−1.53469	−0.0814529
$356$	26.4110	1.39978
$357$	−2.44210	−0.129249
$358$	−34.6844	−1.83313
$359$	−22.0762	−1.16514	−0.582568	−	0.812782i	$-0.697952\pi$
$359$	−22.0762	−1.16514	−0.582568	+	0.812782i	$0.697952\pi$
$360$	−0.223507	−0.0117799
$361$	11.3522	0.597484
$362$	36.8121	1.93480
$363$	−3.77971	−0.198383
$364$	5.39780	0.282922
$365$	3.18633	0.166780
$366$	−29.3476	−1.53402
$367$	−1.51616	−0.0791430	−0.0395715	−	0.999217i	$-0.512599\pi$
$367$	−1.51616	−0.0791430	−0.0395715	+	0.999217i	$0.512599\pi$
$368$	18.9091	0.985703
$369$	0.230971	0.0120239
$370$	4.49097	0.233475
$371$	1.21237	0.0629432
$372$	16.1833	0.839066
$373$	−24.7957	−1.28387	−0.641937	−	0.766757i	$-0.721869\pi$
$373$	−24.7957	−1.28387	−0.641937	+	0.766757i	$0.721869\pi$
$374$	3.84730	0.198939
$375$	3.35230	0.173112
$376$	−4.47094	−0.230571
$377$	−8.25016	−0.424905
$378$	6.23456	0.320671
$379$	−8.61000	−0.442266	−0.221133	−	0.975244i	$-0.570976\pi$
$379$	−8.61000	−0.442266	−0.221133	+	0.975244i	$0.570976\pi$
$380$	−3.09267	−0.158651
$381$	−2.73798	−0.140271
$382$	10.5414	0.539347
$383$	−4.86420	−0.248549	−0.124275	−	0.992248i	$-0.539660\pi$
$383$	−4.86420	−0.248549	−0.124275	+	0.992248i	$0.539660\pi$
$384$	−5.19416	−0.265063
$385$	−2.97159	−0.151446
$386$	−25.3734	−1.29147
$387$	−9.67061	−0.491585
$388$	−12.0781	−0.613172
$389$	−16.4152	−0.832286	−0.416143	−	0.909299i	$-0.636618\pi$
$389$	−16.4152	−0.832286	−0.416143	+	0.909299i	$0.636618\pi$
$390$	−0.648377	−0.0328318
$391$	−3.09823	−0.156684
$392$	2.39492	0.120962
$393$	−8.61479	−0.434559
$394$	−28.5741	−1.43954
$395$	5.47083	0.275267
$396$	−4.44784	−0.223512
$397$	−13.9378	−0.699518	−0.349759	−	0.936840i	$-0.613736\pi$
$397$	−13.9378	−0.699518	−0.349759	+	0.936840i	$0.613736\pi$
$398$	24.2485	1.21547
$399$	−17.9655	−0.899402
$400$	22.3274	1.11637
$401$	29.9653	1.49639	0.748197	−	0.663477i	$-0.230920\pi$
$401$	29.9653	1.49639	0.748197	+	0.663477i	$0.230920\pi$
$402$	26.8548	1.33940
$403$	−9.77678	−0.487016
$404$	−24.1264	−1.20033
$405$	−0.339131	−0.0168515
$406$	51.4361	2.55273
$407$	−18.6119	−0.922557
$408$	0.493563	0.0244350
$409$	14.1269	0.698532	0.349266	−	0.937024i	$-0.386431\pi$
$409$	14.1269	0.698532	0.349266	+	0.937024i	$0.386431\pi$
$410$	0.149756	0.00739594
$411$	10.4946	0.517660
$412$	1.65528	0.0815499
$413$	−40.5331	−1.99450
$414$	7.90964	0.388738
$415$	1.79147	0.0879397
$416$	−7.42033	−0.363811
$417$	−14.9527	−0.732238
$418$	28.3030	1.38435
$419$	17.8331	0.871204	0.435602	−	0.900139i	$-0.356536\pi$
$419$	17.8331	0.871204	0.435602	+	0.900139i	$0.356536\pi$
$420$	1.83056	0.0893222
$421$	−10.5637	−0.514841	−0.257421	−	0.966299i	$-0.582873\pi$
$421$	−10.5637	−0.514841	−0.257421	+	0.966299i	$0.582873\pi$
$422$	−4.89080	−0.238080
$423$	−6.78381	−0.329840
$424$	−0.245028	−0.0118996
$425$	−3.65832	−0.177454
$426$	−8.65195	−0.419188
$427$	−50.0561	−2.42239
$428$	16.3540	0.790502
$429$	2.68706	0.129732
$430$	−6.27020	−0.302376
$431$	31.0413	1.49521	0.747603	−	0.664146i	$-0.231205\pi$
$431$	31.0413	1.49521	0.747603	+	0.664146i	$0.231205\pi$
$432$	−4.57061	−0.219903
$433$	−6.05009	−0.290749	−0.145374	−	0.989377i	$-0.546439\pi$
$433$	−6.05009	−0.290749	−0.145374	+	0.989377i	$0.546439\pi$
$434$	60.9539	2.92588
$435$	−2.79788	−0.134148
$436$	3.24559	0.155436
$437$	−22.7925	−1.09031
$438$	17.9632	0.858317
$439$	−36.5690	−1.74534	−0.872672	−	0.488307i	$-0.837615\pi$
$439$	−36.5690	−1.74534	−0.872672	+	0.488307i	$0.837615\pi$
$440$	0.600577	0.0286314
$441$	3.63384	0.173040
$442$	1.43179	0.0681031
$443$	24.9882	1.18722	0.593612	−	0.804751i	$-0.297701\pi$
$443$	24.9882	1.18722	0.593612	+	0.804751i	$0.297701\pi$
$444$	11.4653	0.544118
$445$	−5.41102	−0.256507
$446$	−30.4942	−1.44394
$447$	−14.2852	−0.675668
$448$	16.4533	0.777348
$449$	−7.98943	−0.377044	−0.188522	−	0.982069i	$-0.560370\pi$
$449$	−7.98943	−0.377044	−0.188522	+	0.982069i	$0.560370\pi$
$450$	9.33951	0.440269
$451$	−0.620633	−0.0292245
$452$	−19.6899	−0.926136
$453$	−16.9683	−0.797240
$454$	−2.41757	−0.113462
$455$	−1.10589	−0.0518449
$456$	3.63094	0.170035
$457$	15.7968	0.738944	0.369472	−	0.929242i	$-0.379539\pi$
$457$	15.7968	0.738944	0.369472	+	0.929242i	$0.379539\pi$
$458$	47.3528	2.21265
$459$	0.748890	0.0349552
$460$	2.32239	0.108282
$461$	3.19126	0.148632	0.0743159	−	0.997235i	$-0.476323\pi$
$461$	3.19126	0.148632	0.0743159	+	0.997235i	$0.476323\pi$
$462$	−16.7526	−0.779403
$463$	−15.7929	−0.733956	−0.366978	−	0.930230i	$-0.619608\pi$
$463$	−15.7929	−0.733956	−0.366978	+	0.930230i	$0.619608\pi$
$464$	−37.7082	−1.75056
$465$	−3.31561	−0.153758
$466$	−24.8064	−1.14914
$467$	−32.7546	−1.51570	−0.757851	−	0.652428i	$-0.773751\pi$
$467$	−32.7546	−1.51570	−0.757851	+	0.652428i	$0.773751\pi$
$468$	−1.65528	−0.0765154
$469$	45.8044	2.11505
$470$	−4.39847	−0.202886
$471$	−5.89868	−0.271797
$472$	8.19199	0.377067
$473$	25.9855	1.19482
$474$	30.8423	1.41663
$475$	−26.9128	−1.23484
$476$	−4.04236	−0.185281
$477$	−0.371784	−0.0170228
$478$	−16.0500	−0.734111
$479$	−14.0255	−0.640843	−0.320421	−	0.947275i	$-0.603824\pi$
$479$	−14.0255	−0.640843	−0.320421	+	0.947275i	$0.603824\pi$
$480$	−2.51646	−0.114860
$481$	−6.92649	−0.315821
$482$	−5.66685	−0.258118
$483$	13.4909	0.613858
$484$	−6.25648	−0.284386
$485$	2.47453	0.112363
$486$	−1.91188	−0.0867246
$487$	2.25892	0.102361	0.0511807	−	0.998689i	$-0.483702\pi$
$487$	2.25892	0.102361	0.0511807	+	0.998689i	$0.483702\pi$
$488$	10.1166	0.457959
$489$	−19.9483	−0.902091
$490$	2.35610	0.106438
$491$	−10.0520	−0.453640	−0.226820	−	0.973937i	$-0.572833\pi$
$491$	−10.0520	−0.453640	−0.226820	+	0.973937i	$0.572833\pi$
$492$	0.382322	0.0172364
$493$	6.17846	0.278264
$494$	10.5331	0.473906
$495$	0.911264	0.0409583
$496$	−44.6858	−2.00645
$497$	−14.7570	−0.661943
$498$	10.0996	0.452572
$499$	−30.2036	−1.35210	−0.676049	−	0.736857i	$-0.736309\pi$
$499$	−30.2036	−1.35210	−0.676049	+	0.736857i	$0.736309\pi$
$500$	5.54901	0.248159
$501$	11.6242	0.519329
$502$	43.7337	1.95193
$503$	−5.87640	−0.262016	−0.131008	−	0.991381i	$-0.541821\pi$
$503$	−5.87640	−0.262016	−0.131008	+	0.991381i	$0.541821\pi$
$504$	−2.14916	−0.0957314
$505$	4.94297	0.219959
$506$	−21.2537	−0.944842
$507$	1.00000	0.0444116
$508$	−4.53212	−0.201080
$509$	22.9543	1.01743	0.508716	−	0.860935i	$-0.330120\pi$
$509$	22.9543	1.01743	0.508716	+	0.860935i	$0.330120\pi$
$510$	0.485563	0.0215011
$511$	30.6386	1.35537
$512$	−27.8908	−1.23261
$513$	5.50928	0.243241
$514$	45.4745	2.00579
$515$	−0.339131	−0.0149439
$516$	−16.0076	−0.704695
$517$	18.2285	0.801689
$518$	43.1836	1.89738
$519$	−3.68599	−0.161797
$520$	0.223507	0.00980144
$521$	−1.95330	−0.0855755	−0.0427877	−	0.999084i	$-0.513624\pi$
$521$	−1.95330	−0.0855755	−0.0427877	+	0.999084i	$0.513624\pi$
$522$	−15.7733	−0.690379
$523$	−14.5162	−0.634750	−0.317375	−	0.948300i	$-0.602801\pi$
$523$	−14.5162	−0.634750	−0.317375	+	0.948300i	$0.602801\pi$
$524$	−14.2599	−0.622947
$525$	15.9297	0.695231
$526$	−13.0611	−0.569493
$527$	7.32173	0.318939
$528$	12.2815	0.534483
$529$	−5.88437	−0.255842
$530$	−0.241056	−0.0104708
$531$	12.4298	0.539408
$532$	−29.7380	−1.28931
$533$	−0.230971	−0.0100045
$534$	−30.5051	−1.32009
$535$	−3.35058	−0.144858
$536$	−9.25734	−0.399856
$537$	18.1415	0.782866
$538$	−20.2015	−0.870949
$539$	−9.76436	−0.420581
$540$	−0.561357	−0.0241569
$541$	−16.4493	−0.707209	−0.353604	−	0.935395i	$-0.615044\pi$
$541$	−16.4493	−0.707209	−0.353604	+	0.935395i	$0.615044\pi$
$542$	−4.34167	−0.186491
$543$	−19.2544	−0.826285
$544$	5.55701	0.238255
$545$	−0.664949	−0.0284833
$546$	−6.23456	−0.266814
$547$	−13.2213	−0.565302	−0.282651	−	0.959223i	$-0.591214\pi$
$547$	−13.2213	−0.565302	−0.282651	+	0.959223i	$0.591214\pi$
$548$	17.3715	0.742074
$549$	15.3501	0.655128
$550$	−25.0958	−1.07009
$551$	45.4525	1.93634
$552$	−2.72660	−0.116052
$553$	52.6055	2.23701
$554$	−4.66774	−0.198313
$555$	−2.34898	−0.0997088
$556$	−24.7510	−1.04967
$557$	−22.9489	−0.972374	−0.486187	−	0.873855i	$-0.661613\pi$
$557$	−22.9489	−0.972374	−0.486187	+	0.873855i	$0.661613\pi$
$558$	−18.6920	−0.791296
$559$	9.67061	0.409023
$560$	−5.05459	−0.213595
$561$	−2.01231	−0.0849598
$562$	−34.8414	−1.46970
$563$	−22.2245	−0.936651	−0.468326	−	0.883556i	$-0.655143\pi$
$563$	−22.2245	−0.936651	−0.468326	+	0.883556i	$0.655143\pi$
$564$	−11.2291	−0.472831
$565$	4.03403	0.169713
$566$	−25.8997	−1.08864
$567$	−3.26096	−0.136947
$568$	2.98248	0.125142
$569$	−14.8122	−0.620960	−0.310480	−	0.950580i	$-0.600490\pi$
$569$	−14.8122	−0.620960	−0.310480	+	0.950580i	$0.600490\pi$
$570$	3.57209	0.149618
$571$	15.1521	0.634096	0.317048	−	0.948409i	$-0.397308\pi$
$571$	15.1521	0.634096	0.317048	+	0.948409i	$0.397308\pi$
$572$	4.44784	0.185974
$573$	−5.51366	−0.230336
$574$	1.44000	0.0601046
$575$	20.2097	0.842803
$576$	−5.04556	−0.210232
$577$	−9.40360	−0.391477	−0.195739	−	0.980656i	$-0.562710\pi$
$577$	−9.40360	−0.391477	−0.195739	+	0.980656i	$0.562710\pi$
$578$	31.4297	1.30730
$579$	13.2714	0.551541
$580$	−4.63128	−0.192304
$581$	17.2261	0.714659
$582$	13.9504	0.578263
$583$	0.999005	0.0413746
$584$	−6.19226	−0.256237
$585$	0.339131	0.0140213
$586$	31.4341	1.29853
$587$	−37.6843	−1.55540	−0.777699	−	0.628637i	$-0.783613\pi$
$587$	−37.6843	−1.55540	−0.777699	+	0.628637i	$0.783613\pi$
$588$	6.01504	0.248056
$589$	53.8630	2.21939
$590$	8.05921	0.331792
$591$	14.9455	0.614777
$592$	−31.6582	−1.30115
$593$	−31.1766	−1.28027	−0.640135	−	0.768263i	$-0.721121\pi$
$593$	−31.1766	−1.28027	−0.640135	+	0.768263i	$0.721121\pi$
$594$	5.13733	0.210787
$595$	0.828190	0.0339525
$596$	−23.6461	−0.968581
$597$	−12.6831	−0.519083
$598$	−7.90964	−0.323449
$599$	−29.1091	−1.18937	−0.594683	−	0.803960i	$-0.702722\pi$
$599$	−29.1091	−1.18937	−0.594683	+	0.803960i	$0.702722\pi$
$600$	−3.21950	−0.131435
$601$	11.4337	0.466389	0.233194	−	0.972430i	$-0.425082\pi$
$601$	11.4337	0.466389	0.233194	+	0.972430i	$0.425082\pi$
$602$	−60.2920	−2.45732
$603$	−14.0463	−0.572009
$604$	−28.0873	−1.14286
$605$	1.28181	0.0521132
$606$	27.8664	1.13200
$607$	−22.3170	−0.905817	−0.452909	−	0.891557i	$-0.649614\pi$
$607$	−22.3170	−0.905817	−0.452909	+	0.891557i	$0.649614\pi$
$608$	40.8807	1.65793
$609$	−26.9034	−1.09018
$610$	9.95267	0.402972
$611$	6.78381	0.274444
$612$	1.23962	0.0501088
$613$	−5.65742	−0.228501	−0.114251	−	0.993452i	$-0.536447\pi$
$613$	−5.65742	−0.228501	−0.114251	+	0.993452i	$0.536447\pi$
$614$	16.1307	0.650981
$615$	−0.0783294	−0.00315855
$616$	5.77493	0.232679
$617$	41.8073	1.68310	0.841548	−	0.540182i	$-0.181644\pi$
$617$	41.8073	1.68310	0.841548	+	0.540182i	$0.181644\pi$
$618$	−1.91188	−0.0769071
$619$	43.3309	1.74162	0.870809	−	0.491622i	$-0.163596\pi$
$619$	43.3309	1.74162	0.870809	+	0.491622i	$0.163596\pi$
$620$	−5.48826	−0.220414
$621$	−4.13710	−0.166016
$622$	26.3125	1.05504
$623$	−52.0304	−2.08455
$624$	4.57061	0.182971
$625$	23.2881	0.931523
$626$	−50.5346	−2.01977
$627$	−14.8038	−0.591206
$628$	−9.76398	−0.389625
$629$	5.18717	0.206826
$630$	−2.11433	−0.0842369
$631$	−23.3554	−0.929764	−0.464882	−	0.885373i	$-0.653903\pi$
$631$	−23.3554	−0.929764	−0.464882	+	0.885373i	$0.653903\pi$
$632$	−10.6319	−0.422914
$633$	2.55811	0.101676
$634$	32.2111	1.27926
$635$	0.928532	0.0368477
$636$	−0.615407	−0.0244025
$637$	−3.63384	−0.143978
$638$	42.3838	1.67799
$639$	4.52536	0.179021
$640$	1.76150	0.0696293
$641$	0.0713964	0.00281999	0.00140999	−	0.999999i	$-0.499551\pi$
$641$	0.0713964	0.00281999	0.00140999	+	0.999999i	$0.499551\pi$
$642$	−18.8892	−0.745497
$643$	−26.1570	−1.03153	−0.515765	−	0.856730i	$-0.672492\pi$
$643$	−26.1570	−1.03153	−0.515765	+	0.856730i	$0.672492\pi$
$644$	22.3313	0.879976
$645$	3.27960	0.129134
$646$	−7.88811	−0.310354
$647$	−43.6715	−1.71690	−0.858452	−	0.512893i	$-0.828574\pi$
$647$	−43.6715	−1.71690	−0.858452	+	0.512893i	$0.828574\pi$
$648$	0.659059	0.0258903
$649$	−33.3997	−1.31105
$650$	−9.33951	−0.366326
$651$	−31.8817	−1.24954
$652$	−33.0200	−1.29316
$653$	8.38496	0.328129	0.164064	−	0.986450i	$-0.447539\pi$
$653$	8.38496	0.328129	0.164064	+	0.986450i	$0.447539\pi$
$654$	−3.74871	−0.146586
$655$	2.92154	0.114154
$656$	−1.05568	−0.0412173
$657$	−9.39560	−0.366557
$658$	−42.2941	−1.64879
$659$	−2.70837	−0.105503	−0.0527515	−	0.998608i	$-0.516799\pi$
$659$	−2.70837	−0.105503	−0.0527515	+	0.998608i	$0.516799\pi$
$660$	1.50840	0.0587144
$661$	−50.8828	−1.97911	−0.989556	−	0.144147i	$-0.953956\pi$
$661$	−50.8828	−1.97911	−0.989556	+	0.144147i	$0.953956\pi$
$662$	5.26432	0.204603
$663$	−0.748890	−0.0290845
$664$	−3.48150	−0.135108
$665$	6.09266	0.236263
$666$	−13.2426	−0.513140
$667$	−34.1318	−1.32159
$668$	19.2413	0.744467
$669$	15.9499	0.616657
$670$	−9.10729	−0.351845
$671$	−41.2467	−1.59231
$672$	−24.1974	−0.933434
$673$	36.2860	1.39872	0.699361	−	0.714769i	$-0.253468\pi$
$673$	36.2860	1.39872	0.699361	+	0.714769i	$0.253468\pi$
$674$	4.82744	0.185946
$675$	−4.88499	−0.188023
$676$	1.65528	0.0636647
$677$	−12.1473	−0.466860	−0.233430	−	0.972374i	$-0.574995\pi$
$677$	−12.1473	−0.466860	−0.233430	+	0.972374i	$0.574995\pi$
$678$	22.7422	0.873409
$679$	23.7942	0.913138
$680$	−0.167382	−0.00641881
$681$	1.26450	0.0484556
$682$	50.2266	1.92328
$683$	18.1221	0.693423	0.346711	−	0.937972i	$-0.387298\pi$
$683$	18.1221	0.693423	0.346711	+	0.937972i	$0.387298\pi$
$684$	9.11941	0.348690
$685$	−3.55904	−0.135984
$686$	−20.9865	−0.801268
$687$	−24.7677	−0.944946
$688$	44.2005	1.68513
$689$	0.371784	0.0141638
$690$	−2.68240	−0.102117
$691$	−29.9315	−1.13865	−0.569323	−	0.822114i	$-0.692795\pi$
$691$	−29.9315	−1.13865	−0.569323	+	0.822114i	$0.692795\pi$
$692$	−6.10135	−0.231939
$693$	8.76239	0.332856
$694$	33.7995	1.28301
$695$	5.07092	0.192351
$696$	5.43735	0.206102
$697$	0.172972	0.00655178
$698$	18.5848	0.703446
$699$	12.9749	0.490756
$700$	26.3682	0.996625
$701$	42.0586	1.58853	0.794266	−	0.607571i	$-0.207856\pi$
$701$	42.0586	1.58853	0.794266	+	0.607571i	$0.207856\pi$
$702$	1.91188	0.0721592
$703$	38.1600	1.43923
$704$	13.5577	0.510976
$705$	2.30060	0.0866456
$706$	19.7647	0.743854
$707$	47.5298	1.78754
$708$	20.5749	0.773251
$709$	3.86883	0.145297	0.0726484	−	0.997358i	$-0.476855\pi$
$709$	3.86883	0.145297	0.0726484	+	0.997358i	$0.476855\pi$
$710$	2.93414	0.110116
$711$	−16.1319	−0.604994
$712$	10.5157	0.394091
$713$	−40.4476	−1.51477
$714$	4.66899	0.174733
$715$	−0.911264	−0.0340794
$716$	30.0294	1.12225
$717$	8.39490	0.313513
$718$	42.2070	1.57515
$719$	17.2105	0.641842	0.320921	−	0.947106i	$-0.396008\pi$
$719$	17.2105	0.641842	0.320921	+	0.947106i	$0.396008\pi$
$720$	1.55003	0.0577663
$721$	−3.26096	−0.121444
$722$	−21.7040	−0.807740
$723$	2.96402	0.110233
$724$	−31.8715	−1.18449
$725$	−40.3020	−1.49678
$726$	7.22635	0.268195
$727$	17.5206	0.649802	0.324901	−	0.945748i	$-0.394669\pi$
$727$	17.5206	0.649802	0.324901	+	0.945748i	$0.394669\pi$
$728$	2.14916	0.0796533
$729$	1.00000	0.0370370
$730$	−6.09189	−0.225471
$731$	−7.24222	−0.267863
$732$	25.4088	0.939136
$733$	30.8238	1.13850	0.569251	−	0.822164i	$-0.307233\pi$
$733$	30.8238	1.13850	0.569251	+	0.822164i	$0.307233\pi$
$734$	2.89872	0.106994
$735$	−1.23235	−0.0454558
$736$	−30.6987	−1.13157
$737$	37.7432	1.39029
$738$	−0.441589	−0.0162551
$739$	24.1346	0.887804	0.443902	−	0.896075i	$-0.353594\pi$
$739$	24.1346	0.887804	0.443902	+	0.896075i	$0.353594\pi$
$740$	−3.88823	−0.142934
$741$	−5.50928	−0.202389
$742$	−2.31791	−0.0850930
$743$	−11.1931	−0.410635	−0.205318	−	0.978695i	$-0.565823\pi$
$743$	−11.1931	−0.410635	−0.205318	+	0.978695i	$0.565823\pi$
$744$	6.44348	0.236229
$745$	4.84456	0.177491
$746$	47.4064	1.73567
$747$	−5.28253	−0.193278
$748$	−3.33094	−0.121791
$749$	−32.2180	−1.17722
$750$	−6.40920	−0.234031
$751$	19.9359	0.727473	0.363736	−	0.931502i	$-0.381501\pi$
$751$	19.9359	0.727473	0.363736	+	0.931502i	$0.381501\pi$
$752$	31.0061	1.13068
$753$	−22.8747	−0.833600
$754$	15.7733	0.574430
$755$	5.75447	0.209427
$756$	−5.39780	−0.196316
$757$	36.5316	1.32777	0.663883	−	0.747837i	$-0.268907\pi$
$757$	36.5316	1.32777	0.663883	+	0.747837i	$0.268907\pi$
$758$	16.4613	0.597901
$759$	11.1166	0.403509
$760$	−1.23136	−0.0446663
$761$	−5.50282	−0.199477	−0.0997386	−	0.995014i	$-0.531801\pi$
$761$	−5.50282	−0.199477	−0.0997386	+	0.995014i	$0.531801\pi$
$762$	5.23468	0.189632
$763$	−6.39391	−0.231475
$764$	−9.12666	−0.330191
$765$	−0.253971	−0.00918235
$766$	9.29977	0.336014
$767$	−12.4298	−0.448815
$768$	20.0217	0.722471
$769$	−17.5846	−0.634118	−0.317059	−	0.948406i	$-0.602695\pi$
$769$	−17.5846	−0.634118	−0.317059	+	0.948406i	$0.602695\pi$
$770$	5.68133	0.204741
$771$	−23.7852	−0.856605
$772$	21.9679	0.790644
$773$	−20.4202	−0.734463	−0.367231	−	0.930130i	$-0.619694\pi$
$773$	−20.4202	−0.734463	−0.367231	+	0.930130i	$0.619694\pi$
$774$	18.4890	0.664575
$775$	−47.7595	−1.71557
$776$	−4.80895	−0.172631
$777$	−22.5870	−0.810303
$778$	31.3840	1.12517
$779$	1.27249	0.0455915
$780$	0.561357	0.0200998
$781$	−12.1599	−0.435116
$782$	5.92345	0.211822
$783$	8.25016	0.294837
$784$	−16.6089	−0.593174
$785$	2.00042	0.0713982
$786$	16.4704	0.587481
$787$	5.96136	0.212500	0.106250	−	0.994339i	$-0.466116\pi$
$787$	5.96136	0.212500	0.106250	+	0.994339i	$0.466116\pi$
$788$	24.7391	0.881293
$789$	6.83158	0.243211
$790$	−10.4596	−0.372134
$791$	38.7898	1.37921
$792$	−1.77093	−0.0629273
$793$	−15.3501	−0.545099
$794$	26.6474	0.945680
$795$	0.126083	0.00447171
$796$	−20.9940	−0.744114
$797$	24.0798	0.852951	0.426475	−	0.904499i	$-0.359755\pi$
$797$	24.0798	0.852951	0.426475	+	0.904499i	$0.359755\pi$
$798$	34.3479	1.21590
$799$	−5.08033	−0.179729
$800$	−36.2482	−1.28157
$801$	15.9556	0.563762
$802$	−57.2900	−2.02298
$803$	25.2465	0.890931
$804$	−23.2506	−0.819985
$805$	−4.57518	−0.161254
$806$	18.6920	0.658398
$807$	10.5663	0.371952
$808$	−9.60606	−0.337940
$809$	12.6357	0.444248	0.222124	−	0.975018i	$-0.428701\pi$
$809$	12.6357	0.444248	0.222124	+	0.975018i	$0.428701\pi$
$810$	0.648377	0.0227816
$811$	26.2028	0.920105	0.460052	−	0.887892i	$-0.347831\pi$
$811$	26.2028	0.920105	0.460052	+	0.887892i	$0.347831\pi$
$812$	−44.5328	−1.56279
$813$	2.27089	0.0796436
$814$	35.5837	1.24721
$815$	6.76506	0.236970
$816$	−3.42288	−0.119825
$817$	−53.2781	−1.86397
$818$	−27.0090	−0.944348
$819$	3.26096	0.113947
$820$	−0.129657	−0.00452783
$821$	−35.8376	−1.25074	−0.625371	−	0.780328i	$-0.715052\pi$
$821$	−35.8376	−1.25074	−0.625371	+	0.780328i	$0.715052\pi$
$822$	−20.0644	−0.699826
$823$	−42.0427	−1.46552	−0.732759	−	0.680488i	$-0.761768\pi$
$823$	−42.0427	−1.46552	−0.732759	+	0.680488i	$0.761768\pi$
$824$	0.659059	0.0229594
$825$	13.1263	0.456998
$826$	77.4944	2.69638
$827$	49.1720	1.70988	0.854940	−	0.518728i	$-0.173594\pi$
$827$	49.1720	1.70988	0.854940	+	0.518728i	$0.173594\pi$
$828$	−6.84807	−0.237987
$829$	−2.25607	−0.0783567	−0.0391784	−	0.999232i	$-0.512474\pi$
$829$	−2.25607	−0.0783567	−0.0391784	+	0.999232i	$0.512474\pi$
$830$	−3.42507	−0.118886
$831$	2.44144	0.0846926
$832$	5.04556	0.174923
$833$	2.72135	0.0942891
$834$	28.5878	0.989914
$835$	−3.94211	−0.136422
$836$	−24.5044	−0.847503
$837$	9.77678	0.337935
$838$	−34.0947	−1.17778
$839$	39.4428	1.36172	0.680858	−	0.732415i	$-0.261607\pi$
$839$	39.4428	1.36172	0.680858	+	0.732415i	$0.261607\pi$
$840$	0.728847	0.0251476
$841$	39.0652	1.34708
$842$	20.1964	0.696015
$843$	18.2237	0.627656
$844$	4.23440	0.145754
$845$	−0.339131	−0.0116664
$846$	12.9698	0.445912
$847$	12.3255	0.423508
$848$	1.69928	0.0583534
$849$	13.5467	0.464922
$850$	6.99426	0.239901
$851$	−28.6556	−0.982301
$852$	7.49075	0.256629
$853$	17.5886	0.602222	0.301111	−	0.953589i	$-0.402642\pi$
$853$	17.5886	0.602222	0.301111	+	0.953589i	$0.402642\pi$
$854$	95.7013	3.27483
$855$	−1.86837	−0.0638968
$856$	6.51145	0.222557
$857$	0.840966	0.0287269	0.0143634	−	0.999897i	$-0.495428\pi$
$857$	0.840966	0.0287269	0.0143634	+	0.999897i	$0.495428\pi$
$858$	−5.13733	−0.175386
$859$	42.5458	1.45164	0.725822	−	0.687882i	$-0.241459\pi$
$859$	42.5458	1.45164	0.725822	+	0.687882i	$0.241459\pi$
$860$	5.42866	0.185116
$861$	−0.753187	−0.0256686
$862$	−59.3472	−2.02137
$863$	−22.3988	−0.762465	−0.381233	−	0.924479i	$-0.624500\pi$
$863$	−22.3988	−0.762465	−0.381233	+	0.924479i	$0.624500\pi$
$864$	7.42033	0.252445
$865$	1.25003	0.0425023
$866$	11.5670	0.393064
$867$	−16.4392	−0.558303
$868$	−52.7731	−1.79124
$869$	43.3474	1.47046
$870$	5.34921	0.181355
$871$	14.0463	0.475941
$872$	1.29225	0.0437611
$873$	−7.29669	−0.246956
$874$	43.5765	1.47400
$875$	−10.9317	−0.369559
$876$	−15.5524	−0.525466
$877$	−28.8905	−0.975563	−0.487782	−	0.872966i	$-0.662194\pi$
$877$	−28.8905	−0.975563	−0.487782	+	0.872966i	$0.662194\pi$
$878$	69.9155	2.35953
$879$	−16.4415	−0.554557
$880$	−4.16503	−0.140403
$881$	17.5375	0.590852	0.295426	−	0.955366i	$-0.404538\pi$
$881$	17.5375	0.590852	0.295426	+	0.955366i	$0.404538\pi$
$882$	−6.94747	−0.233933
$883$	49.5778	1.66842	0.834212	−	0.551444i	$-0.185923\pi$
$883$	49.5778	1.66842	0.834212	+	0.551444i	$0.185923\pi$
$884$	−1.23962	−0.0416930
$885$	−4.21533	−0.141697
$886$	−47.7744	−1.60501
$887$	−29.3606	−0.985832	−0.492916	−	0.870077i	$-0.664069\pi$
$887$	−29.3606	−0.985832	−0.492916	+	0.870077i	$0.664069\pi$
$888$	4.56496	0.153190
$889$	8.92843	0.299450
$890$	10.3452	0.346772
$891$	−2.68706	−0.0900199
$892$	26.4015	0.883988
$893$	−37.3739	−1.25067
$894$	27.3116	0.913437
$895$	−6.15235	−0.205651
$896$	16.9379	0.565856
$897$	4.13710	0.138134
$898$	15.2748	0.509727
$899$	80.6600	2.69016
$900$	−8.08604	−0.269535
$901$	−0.278425	−0.00927568
$902$	1.18658	0.0395087
$903$	31.5355	1.04943
$904$	−7.83965	−0.260743
$905$	6.52976	0.217056
$906$	32.4413	1.07779
$907$	55.6622	1.84823	0.924117	−	0.382110i	$-0.124803\pi$
$907$	55.6622	1.84823	0.924117	+	0.382110i	$0.124803\pi$
$908$	2.09310	0.0694620
$909$	−14.5754	−0.483436
$910$	2.11433	0.0700893
$911$	−26.5302	−0.878985	−0.439492	−	0.898246i	$-0.644842\pi$
$911$	−26.5302	−0.878985	−0.439492	+	0.898246i	$0.644842\pi$
$912$	−25.1808	−0.833818
$913$	14.1945	0.469769
$914$	−30.2016	−0.998980
$915$	−5.20570	−0.172095
$916$	−40.9975	−1.35460
$917$	28.0925	0.927695
$918$	−1.43179	−0.0472560
$919$	−43.7588	−1.44347	−0.721735	−	0.692170i	$-0.756655\pi$
$919$	−43.7588	−1.44347	−0.721735	+	0.692170i	$0.756655\pi$
$920$	0.924672	0.0304855
$921$	−8.43708	−0.278011
$922$	−6.10130	−0.200936
$923$	−4.52536	−0.148954
$924$	14.5042	0.477154
$925$	−33.8358	−1.11251
$926$	30.1940	0.992237
$927$	1.00000	0.0328443
$928$	61.2189	2.00961
$929$	10.3023	0.338007	0.169003	−	0.985615i	$-0.445945\pi$
$929$	10.3023	0.338007	0.169003	+	0.985615i	$0.445945\pi$
$930$	6.33904	0.207865
$931$	20.0199	0.656125
$932$	21.4771	0.703507
$933$	−13.7627	−0.450569
$934$	62.6228	2.04908
$935$	0.682436	0.0223181
$936$	−0.659059	−0.0215420
$937$	−27.4931	−0.898159	−0.449080	−	0.893492i	$-0.648248\pi$
$937$	−27.4931	−0.898159	−0.449080	+	0.893492i	$0.648248\pi$
$938$	−87.5724	−2.85934
$939$	26.4319	0.862573
$940$	3.80814	0.124208
$941$	−1.82371	−0.0594512	−0.0297256	−	0.999558i	$-0.509463\pi$
$941$	−1.82371	−0.0594512	−0.0297256	+	0.999558i	$0.509463\pi$
$942$	11.2776	0.367443
$943$	−0.955552	−0.0311170
$944$	−56.8118	−1.84907
$945$	1.10589	0.0359746
$946$	−49.6812	−1.61527
$947$	11.2175	0.364521	0.182260	−	0.983250i	$-0.441659\pi$
$947$	11.2175	0.364521	0.182260	+	0.983250i	$0.441659\pi$
$948$	−26.7029	−0.867269
$949$	9.39560	0.304994
$950$	51.4540	1.66939
$951$	−16.8478	−0.546329
$952$	−1.60949	−0.0521638
$953$	57.4783	1.86191	0.930953	−	0.365139i	$-0.118978\pi$
$953$	57.4783	1.86191	0.930953	+	0.365139i	$0.118978\pi$
$954$	0.710806	0.0230132
$955$	1.86985	0.0605069
$956$	13.8959	0.449426
$957$	−22.1687	−0.716612
$958$	26.8151	0.866357
$959$	−34.2224	−1.10510
$960$	1.71110	0.0552256
$961$	64.5854	2.08340
$962$	13.2426	0.426959
$963$	9.87991	0.318376
$964$	4.90629	0.158021
$965$	−4.50075	−0.144884
$966$	−25.7930	−0.829876
$967$	17.3102	0.556659	0.278329	−	0.960486i	$-0.410219\pi$
$967$	17.3102	0.556659	0.278329	+	0.960486i	$0.410219\pi$
$968$	−2.49105	−0.0800654
$969$	4.12584	0.132541
$970$	−4.73101	−0.151903
$971$	22.3197	0.716275	0.358137	−	0.933669i	$-0.383412\pi$
$971$	22.3197	0.716275	0.358137	+	0.933669i	$0.383412\pi$
$972$	1.65528	0.0530932
$973$	48.7602	1.56318
$974$	−4.31878	−0.138383
$975$	4.88499	0.156445
$976$	−70.1594	−2.24575
$977$	−48.9788	−1.56697	−0.783485	−	0.621411i	$-0.786560\pi$
$977$	−48.9788	−1.56697	−0.783485	+	0.621411i	$0.786560\pi$
$978$	38.1387	1.21954
$979$	−42.8736	−1.37024
$980$	−2.03988	−0.0651617
$981$	1.96075	0.0626018
$982$	19.2182	0.613277
$983$	−47.3676	−1.51079	−0.755396	−	0.655269i	$-0.772555\pi$
$983$	−47.3676	−1.51079	−0.755396	+	0.655269i	$0.772555\pi$
$984$	0.152224	0.00485271
$985$	−5.06849	−0.161495
$986$	−11.8125	−0.376186
$987$	22.1217	0.704142
$988$	−9.11941	−0.290127
$989$	40.0083	1.27219
$990$	−1.74223	−0.0553716
$991$	20.0520	0.636971	0.318486	−	0.947928i	$-0.396826\pi$
$991$	20.0520	0.636971	0.318486	+	0.947928i	$0.396826\pi$
$992$	72.5469	2.30337
$993$	−2.75348	−0.0873790
$994$	28.2136	0.894882
$995$	4.30121	0.136358
$996$	−8.74408	−0.277067
$997$	−39.8125	−1.26087	−0.630437	−	0.776240i	$-0.717124\pi$
$997$	−39.8125	−1.26087	−0.630437	+	0.776240i	$0.717124\pi$
$998$	57.7456	1.82791
$999$	6.92649	0.219144

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4017.2.a.e.1.3	✓	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4017.2.a.e.1.3	✓	16	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)

\(f(q)\)	\(=\)	\(q-1.91188 q^{2} +1.00000 q^{3} +1.65528 q^{4} -0.339131 q^{5} -1.91188 q^{6} -3.26096 q^{7} +0.659059 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.91188 q^{2} +1.00000 q^{3} +1.65528 q^{4} -0.339131 q^{5} -1.91188 q^{6} -3.26096 q^{7} +0.659059 q^{8} +1.00000 q^{9} +0.648377 q^{10} -2.68706 q^{11} +1.65528 q^{12} -1.00000 q^{13} +6.23456 q^{14} -0.339131 q^{15} -4.57061 q^{16} +0.748890 q^{17} -1.91188 q^{18} +5.50928 q^{19} -0.561357 q^{20} -3.26096 q^{21} +5.13733 q^{22} -4.13710 q^{23} +0.659059 q^{24} -4.88499 q^{25} +1.91188 q^{26} +1.00000 q^{27} -5.39780 q^{28} +8.25016 q^{29} +0.648377 q^{30} +9.77678 q^{31} +7.42033 q^{32} -2.68706 q^{33} -1.43179 q^{34} +1.10589 q^{35} +1.65528 q^{36} +6.92649 q^{37} -10.5331 q^{38} -1.00000 q^{39} -0.223507 q^{40} +0.230971 q^{41} +6.23456 q^{42} -9.67061 q^{43} -4.44784 q^{44} -0.339131 q^{45} +7.90964 q^{46} -6.78381 q^{47} -4.57061 q^{48} +3.63384 q^{49} +9.33951 q^{50} +0.748890 q^{51} -1.65528 q^{52} -0.371784 q^{53} -1.91188 q^{54} +0.911264 q^{55} -2.14916 q^{56} +5.50928 q^{57} -15.7733 q^{58} +12.4298 q^{59} -0.561357 q^{60} +15.3501 q^{61} -18.6920 q^{62} -3.26096 q^{63} -5.04556 q^{64} +0.339131 q^{65} +5.13733 q^{66} -14.0463 q^{67} +1.23962 q^{68} -4.13710 q^{69} -2.11433 q^{70} +4.52536 q^{71} +0.659059 q^{72} -9.39560 q^{73} -13.2426 q^{74} -4.88499 q^{75} +9.11941 q^{76} +8.76239 q^{77} +1.91188 q^{78} -16.1319 q^{79} +1.55003 q^{80} +1.00000 q^{81} -0.441589 q^{82} -5.28253 q^{83} -5.39780 q^{84} -0.253971 q^{85} +18.4890 q^{86} +8.25016 q^{87} -1.77093 q^{88} +15.9556 q^{89} +0.648377 q^{90} +3.26096 q^{91} -6.84807 q^{92} +9.77678 q^{93} +12.9698 q^{94} -1.86837 q^{95} +7.42033 q^{96} -7.29669 q^{97} -6.94747 q^{98} -2.68706 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 16 q^{3} + 10 q^{4} - 6 q^{5} - 13 q^{7} - 9 q^{8} + 16 q^{9}+O(q^{10}) \) 16 * q + 16 * q^3 + 10 * q^4 - 6 * q^5 - 13 * q^7 - 9 * q^8 + 16 * q^9	\( 16 q + 16 q^{3} + 10 q^{4} - 6 q^{5} - 13 q^{7} - 9 q^{8} + 16 q^{9} - 8 q^{10} - 5 q^{11} + 10 q^{12} - 16 q^{13} - 8 q^{14} - 6 q^{15} - 14 q^{16} - q^{17} + 6 q^{19} - 4 q^{20} - 13 q^{21} - 11 q^{22} - 21 q^{23} - 9 q^{24} - 10 q^{25} + 16 q^{27} - 10 q^{28} - 17 q^{29} - 8 q^{30} - 33 q^{31} - 18 q^{32} - 5 q^{33} - 5 q^{34} - 4 q^{35} + 10 q^{36} - 23 q^{37} - 28 q^{38} - 16 q^{39} - 12 q^{40} + 7 q^{41} - 8 q^{42} - 33 q^{43} + 11 q^{44} - 6 q^{45} - 15 q^{46} - 13 q^{47} - 14 q^{48} - 17 q^{49} + 35 q^{50} - q^{51} - 10 q^{52} - 20 q^{53} - 54 q^{55} + 12 q^{56} + 6 q^{57} - 33 q^{58} + 6 q^{59} - 4 q^{60} - 49 q^{61} - 13 q^{62} - 13 q^{63} - 35 q^{64} + 6 q^{65} - 11 q^{66} - 4 q^{67} - 14 q^{68} - 21 q^{69} - 33 q^{70} - 29 q^{71} - 9 q^{72} - 21 q^{73} + 22 q^{74} - 10 q^{75} + 10 q^{76} - 21 q^{77} - 70 q^{79} - 8 q^{80} + 16 q^{81} - 10 q^{82} + 5 q^{83} - 10 q^{84} + 14 q^{85} + 29 q^{86} - 17 q^{87} - 45 q^{88} - 8 q^{89} - 8 q^{90} + 13 q^{91} - 29 q^{92} - 33 q^{93} + 12 q^{94} - 45 q^{95} - 18 q^{96} - 30 q^{97} + 15 q^{98} - 5 q^{99}+O(q^{100}) \) 16 * q + 16 * q^3 + 10 * q^4 - 6 * q^5 - 13 * q^7 - 9 * q^8 + 16 * q^9 - 8 * q^10 - 5 * q^11 + 10 * q^12 - 16 * q^13 - 8 * q^14 - 6 * q^15 - 14 * q^16 - q^17 + 6 * q^19 - 4 * q^20 - 13 * q^21 - 11 * q^22 - 21 * q^23 - 9 * q^24 - 10 * q^25 + 16 * q^27 - 10 * q^28 - 17 * q^29 - 8 * q^30 - 33 * q^31 - 18 * q^32 - 5 * q^33 - 5 * q^34 - 4 * q^35 + 10 * q^36 - 23 * q^37 - 28 * q^38 - 16 * q^39 - 12 * q^40 + 7 * q^41 - 8 * q^42 - 33 * q^43 + 11 * q^44 - 6 * q^45 - 15 * q^46 - 13 * q^47 - 14 * q^48 - 17 * q^49 + 35 * q^50 - q^51 - 10 * q^52 - 20 * q^53 - 54 * q^55 + 12 * q^56 + 6 * q^57 - 33 * q^58 + 6 * q^59 - 4 * q^60 - 49 * q^61 - 13 * q^62 - 13 * q^63 - 35 * q^64 + 6 * q^65 - 11 * q^66 - 4 * q^67 - 14 * q^68 - 21 * q^69 - 33 * q^70 - 29 * q^71 - 9 * q^72 - 21 * q^73 + 22 * q^74 - 10 * q^75 + 10 * q^76 - 21 * q^77 - 70 * q^79 - 8 * q^80 + 16 * q^81 - 10 * q^82 + 5 * q^83 - 10 * q^84 + 14 * q^85 + 29 * q^86 - 17 * q^87 - 45 * q^88 - 8 * q^89 - 8 * q^90 + 13 * q^91 - 29 * q^92 - 33 * q^93 + 12 * q^94 - 45 * q^95 - 18 * q^96 - 30 * q^97 + 15 * q^98 - 5 * q^99

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