LMFDB - Embedded newform 6045.2.a.bh.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6045,2,Mod(1,6045)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6045, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 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("6045.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6045 = 3 \cdot 5 \cdot 13 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6045.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:	$48.2695680219$
Analytic rank:	$0$
Dimension:	$17$
Coefficient field:	$\mathbb{Q}[x]/(x^{17} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{17} - 2 x^{16} - 25 x^{15} + 47 x^{14} + 252 x^{13} - 437 x^{12} - 1319 x^{11} + 2056 x^{10} + \cdots + 8 $ x^17 - 2x^16 - 25x^15 + 47x^14 + 252x^13 - 437x^12 - 1319x^11 + 2056x^10 + 3854x^9 - 5201x^8 - 6304x^7 + 6915x^6 + 5469x^5 - 4238x^4 - 2198x^3 + 760x^2 + 306x + 8
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{3} $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$-2.18223$ of defining polynomial
Character	$\chi$	$=$	6045.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.18223 q^{2} -1.00000 q^{3} +2.76211 q^{4} +1.00000 q^{5} +2.18223 q^{6} -1.44741 q^{7} -1.66310 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-2.18223 q^{2} -1.00000 q^{3} +2.76211 q^{4} +1.00000 q^{5} +2.18223 q^{6} -1.44741 q^{7} -1.66310 q^{8} +1.00000 q^{9} -2.18223 q^{10} -3.50873 q^{11} -2.76211 q^{12} +1.00000 q^{13} +3.15859 q^{14} -1.00000 q^{15} -1.89496 q^{16} +3.69558 q^{17} -2.18223 q^{18} +3.16614 q^{19} +2.76211 q^{20} +1.44741 q^{21} +7.65684 q^{22} -2.36003 q^{23} +1.66310 q^{24} +1.00000 q^{25} -2.18223 q^{26} -1.00000 q^{27} -3.99792 q^{28} -2.80811 q^{29} +2.18223 q^{30} +1.00000 q^{31} +7.46143 q^{32} +3.50873 q^{33} -8.06459 q^{34} -1.44741 q^{35} +2.76211 q^{36} -3.36666 q^{37} -6.90924 q^{38} -1.00000 q^{39} -1.66310 q^{40} -2.08360 q^{41} -3.15859 q^{42} +11.7269 q^{43} -9.69150 q^{44} +1.00000 q^{45} +5.15013 q^{46} +2.96698 q^{47} +1.89496 q^{48} -4.90499 q^{49} -2.18223 q^{50} -3.69558 q^{51} +2.76211 q^{52} -6.88615 q^{53} +2.18223 q^{54} -3.50873 q^{55} +2.40720 q^{56} -3.16614 q^{57} +6.12794 q^{58} +12.8901 q^{59} -2.76211 q^{60} -0.163939 q^{61} -2.18223 q^{62} -1.44741 q^{63} -12.4926 q^{64} +1.00000 q^{65} -7.65684 q^{66} +1.56955 q^{67} +10.2076 q^{68} +2.36003 q^{69} +3.15859 q^{70} -8.10448 q^{71} -1.66310 q^{72} -4.95058 q^{73} +7.34681 q^{74} -1.00000 q^{75} +8.74525 q^{76} +5.07858 q^{77} +2.18223 q^{78} -7.77624 q^{79} -1.89496 q^{80} +1.00000 q^{81} +4.54689 q^{82} -10.2095 q^{83} +3.99792 q^{84} +3.69558 q^{85} -25.5908 q^{86} +2.80811 q^{87} +5.83538 q^{88} +3.52692 q^{89} -2.18223 q^{90} -1.44741 q^{91} -6.51868 q^{92} -1.00000 q^{93} -6.47463 q^{94} +3.16614 q^{95} -7.46143 q^{96} +7.93248 q^{97} +10.7038 q^{98} -3.50873 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 17 q + 2 q^{2} - 17 q^{3} + 20 q^{4} + 17 q^{5} - 2 q^{6} + 18 q^{7} + 9 q^{8} + 17 q^{9}+O(q^{10}) $ 17 * q + 2 * q^2 - 17 * q^3 + 20 * q^4 + 17 * q^5 - 2 * q^6 + 18 * q^7 + 9 * q^8 + 17 * q^9	\( 17 q + 2 q^{2} - 17 q^{3} + 20 q^{4} + 17 q^{5} - 2 q^{6} + 18 q^{7} + 9 q^{8} + 17 q^{9} + 2 q^{10} + 3 q^{11} - 20 q^{12} + 17 q^{13} + q^{14} - 17 q^{15} + 26 q^{16} + 2 q^{18} + 10 q^{19} + 20 q^{20} - 18 q^{21} + 5 q^{22} + 16 q^{23} - 9 q^{24} + 17 q^{25} + 2 q^{26} - 17 q^{27} + 36 q^{28} - 3 q^{29} - 2 q^{30} + 17 q^{31} + 20 q^{32} - 3 q^{33} + q^{34} + 18 q^{35} + 20 q^{36} + 14 q^{37} + 22 q^{38} - 17 q^{39} + 9 q^{40} - 6 q^{41} - q^{42} + 24 q^{43} - 15 q^{44} + 17 q^{45} + 6 q^{46} + 25 q^{47} - 26 q^{48} + 31 q^{49} + 2 q^{50} + 20 q^{52} - 15 q^{53} - 2 q^{54} + 3 q^{55} + 31 q^{56} - 10 q^{57} + 44 q^{58} + 16 q^{59} - 20 q^{60} - 5 q^{61} + 2 q^{62} + 18 q^{63} + 35 q^{64} + 17 q^{65} - 5 q^{66} + 50 q^{67} + 13 q^{68} - 16 q^{69} + q^{70} + 16 q^{71} + 9 q^{72} + 33 q^{73} + 2 q^{74} - 17 q^{75} + 9 q^{77} - 2 q^{78} - 10 q^{79} + 26 q^{80} + 17 q^{81} + 61 q^{82} + 27 q^{83} - 36 q^{84} - 12 q^{86} + 3 q^{87} + 23 q^{88} - 24 q^{89} + 2 q^{90} + 18 q^{91} - 21 q^{92} - 17 q^{93} + 6 q^{94} + 10 q^{95} - 20 q^{96} + 48 q^{97} + 14 q^{98} + 3 q^{99}+O(q^{100}) \) 17 * q + 2 * q^2 - 17 * q^3 + 20 * q^4 + 17 * q^5 - 2 * q^6 + 18 * q^7 + 9 * q^8 + 17 * q^9 + 2 * q^10 + 3 * q^11 - 20 * q^12 + 17 * q^13 + q^14 - 17 * q^15 + 26 * q^16 + 2 * q^18 + 10 * q^19 + 20 * q^20 - 18 * q^21 + 5 * q^22 + 16 * q^23 - 9 * q^24 + 17 * q^25 + 2 * q^26 - 17 * q^27 + 36 * q^28 - 3 * q^29 - 2 * q^30 + 17 * q^31 + 20 * q^32 - 3 * q^33 + q^34 + 18 * q^35 + 20 * q^36 + 14 * q^37 + 22 * q^38 - 17 * q^39 + 9 * q^40 - 6 * q^41 - q^42 + 24 * q^43 - 15 * q^44 + 17 * q^45 + 6 * q^46 + 25 * q^47 - 26 * q^48 + 31 * q^49 + 2 * q^50 + 20 * q^52 - 15 * q^53 - 2 * q^54 + 3 * q^55 + 31 * q^56 - 10 * q^57 + 44 * q^58 + 16 * q^59 - 20 * q^60 - 5 * q^61 + 2 * q^62 + 18 * q^63 + 35 * q^64 + 17 * q^65 - 5 * q^66 + 50 * q^67 + 13 * q^68 - 16 * q^69 + q^70 + 16 * q^71 + 9 * q^72 + 33 * q^73 + 2 * q^74 - 17 * q^75 + 9 * q^77 - 2 * q^78 - 10 * q^79 + 26 * q^80 + 17 * q^81 + 61 * q^82 + 27 * q^83 - 36 * q^84 - 12 * q^86 + 3 * q^87 + 23 * q^88 - 24 * q^89 + 2 * q^90 + 18 * q^91 - 21 * q^92 - 17 * q^93 + 6 * q^94 + 10 * q^95 - 20 * q^96 + 48 * q^97 + 14 * q^98 + 3 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	−2.18223	−1.54307	−0.771534	−	0.636189i	$-0.780510\pi$
$2$	−2.18223	−1.54307	−0.771534	+	0.636189i	$0.780510\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	2.76211	1.38106
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	2.18223	0.890890
$7$	−1.44741	−0.547071	−0.273536	−	0.961862i	$-0.588193\pi$
$7$	−1.44741	−0.547071	−0.273536	+	0.961862i	$0.588193\pi$
$8$	−1.66310	−0.587996
$9$	1.00000	0.333333
$10$	−2.18223	−0.690081
$11$	−3.50873	−1.05792	−0.528961	−	0.848646i	$-0.677418\pi$
$11$	−3.50873	−1.05792	−0.528961	+	0.848646i	$0.677418\pi$
$12$	−2.76211	−0.797353
$13$	1.00000	0.277350
$13$	1.00000	0.277350
$14$	3.15859	0.844168
$15$	−1.00000	−0.258199
$16$	−1.89496	−0.473739
$17$	3.69558	0.896309	0.448155	−	0.893956i	$-0.352081\pi$
$17$	3.69558	0.896309	0.448155	+	0.893956i	$0.352081\pi$
$18$	−2.18223	−0.514356
$19$	3.16614	0.726363	0.363182	−	0.931718i	$-0.381690\pi$
$19$	3.16614	0.726363	0.363182	+	0.931718i	$0.381690\pi$
$20$	2.76211	0.617627
$21$	1.44741	0.315852
$22$	7.65684	1.63244
$23$	−2.36003	−0.492101	−0.246051	−	0.969257i	$-0.579133\pi$
$23$	−2.36003	−0.492101	−0.246051	+	0.969257i	$0.579133\pi$
$24$	1.66310	0.339480
$25$	1.00000	0.200000
$26$	−2.18223	−0.427970
$27$	−1.00000	−0.192450
$28$	−3.99792	−0.755536
$29$	−2.80811	−0.521454	−0.260727	−	0.965413i	$-0.583962\pi$
$29$	−2.80811	−0.521454	−0.260727	+	0.965413i	$0.583962\pi$
$30$	2.18223	0.398418
$31$	1.00000	0.179605
$31$	1.00000	0.179605
$32$	7.46143	1.31901
$33$	3.50873	0.610791
$34$	−8.06459	−1.38307
$35$	−1.44741	−0.244658
$36$	2.76211	0.460352
$37$	−3.36666	−0.553475	−0.276738	−	0.960946i	$-0.589253\pi$
$37$	−3.36666	−0.553475	−0.276738	+	0.960946i	$0.589253\pi$
$38$	−6.90924	−1.12083
$39$	−1.00000	−0.160128
$40$	−1.66310	−0.262960
$41$	−2.08360	−0.325404	−0.162702	−	0.986675i	$-0.552021\pi$
$41$	−2.08360	−0.325404	−0.162702	+	0.986675i	$0.552021\pi$
$42$	−3.15859	−0.487380
$43$	11.7269	1.78834	0.894171	−	0.447727i	$-0.147766\pi$
$43$	11.7269	1.78834	0.894171	+	0.447727i	$0.147766\pi$
$44$	−9.69150	−1.46105
$45$	1.00000	0.149071
$46$	5.15013	0.759345
$47$	2.96698	0.432779	0.216389	−	0.976307i	$-0.430572\pi$
$47$	2.96698	0.432779	0.216389	+	0.976307i	$0.430572\pi$
$48$	1.89496	0.273513
$49$	−4.90499	−0.700713
$50$	−2.18223	−0.308613
$51$	−3.69558	−0.517484
$52$	2.76211	0.383036
$53$	−6.88615	−0.945885	−0.472943	−	0.881093i	$-0.656808\pi$
$53$	−6.88615	−0.945885	−0.472943	+	0.881093i	$0.656808\pi$
$54$	2.18223	0.296963
$55$	−3.50873	−0.473117
$56$	2.40720	0.321676
$57$	−3.16614	−0.419366
$58$	6.12794	0.804638
$59$	12.8901	1.67815	0.839073	−	0.544018i	$-0.183098\pi$
$59$	12.8901	1.67815	0.839073	+	0.544018i	$0.183098\pi$
$60$	−2.76211	−0.356587
$61$	−0.163939	−0.0209903	−0.0104951	−	0.999945i	$-0.503341\pi$
$61$	−0.163939	−0.0209903	−0.0104951	+	0.999945i	$0.503341\pi$
$62$	−2.18223	−0.277143
$63$	−1.44741	−0.182357
$64$	−12.4926	−1.56158
$65$	1.00000	0.124035
$66$	−7.65684	−0.942492
$67$	1.56955	0.191751	0.0958755	−	0.995393i	$-0.469435\pi$
$67$	1.56955	0.191751	0.0958755	+	0.995393i	$0.469435\pi$
$68$	10.2076	1.23785
$69$	2.36003	0.284115
$70$	3.15859	0.377523
$71$	−8.10448	−0.961825	−0.480913	−	0.876769i	$-0.659695\pi$
$71$	−8.10448	−0.961825	−0.480913	+	0.876769i	$0.659695\pi$
$72$	−1.66310	−0.195999
$73$	−4.95058	−0.579422	−0.289711	−	0.957114i	$-0.593559\pi$
$73$	−4.95058	−0.579422	−0.289711	+	0.957114i	$0.593559\pi$
$74$	7.34681	0.854050
$75$	−1.00000	−0.115470
$76$	8.74525	1.00315
$77$	5.07858	0.578758
$78$	2.18223	0.247089
$79$	−7.77624	−0.874896	−0.437448	−	0.899244i	$-0.644118\pi$
$79$	−7.77624	−0.874896	−0.437448	+	0.899244i	$0.644118\pi$
$80$	−1.89496	−0.211863
$81$	1.00000	0.111111
$82$	4.54689	0.502120
$83$	−10.2095	−1.12064	−0.560322	−	0.828275i	$-0.689322\pi$
$83$	−10.2095	−1.12064	−0.560322	+	0.828275i	$0.689322\pi$
$84$	3.99792	0.436209
$85$	3.69558	0.400842
$86$	−25.5908	−2.75953
$87$	2.80811	0.301061
$88$	5.83538	0.622054
$89$	3.52692	0.373852	0.186926	−	0.982374i	$-0.440147\pi$
$89$	3.52692	0.373852	0.186926	+	0.982374i	$0.440147\pi$
$90$	−2.18223	−0.230027
$91$	−1.44741	−0.151730
$92$	−6.51868	−0.679619
$93$	−1.00000	−0.103695
$94$	−6.47463	−0.667807
$95$	3.16614	0.324839
$96$	−7.46143	−0.761529
$97$	7.93248	0.805422	0.402711	−	0.915327i	$-0.368068\pi$
$97$	7.93248	0.805422	0.402711	+	0.915327i	$0.368068\pi$
$98$	10.7038	1.08125
$99$	−3.50873	−0.352640
$100$	2.76211	0.276211
$101$	−16.6954	−1.66125	−0.830625	−	0.556832i	$-0.812017\pi$
$101$	−16.6954	−1.66125	−0.830625	+	0.556832i	$0.812017\pi$
$102$	8.06459	0.798513
$103$	12.5956	1.24108	0.620542	−	0.784173i	$-0.286912\pi$
$103$	12.5956	1.24108	0.620542	+	0.784173i	$0.286912\pi$
$104$	−1.66310	−0.163081
$105$	1.44741	0.141253
$106$	15.0271	1.45956
$107$	9.36723	0.905564	0.452782	−	0.891621i	$-0.350432\pi$
$107$	9.36723	0.905564	0.452782	+	0.891621i	$0.350432\pi$
$108$	−2.76211	−0.265784
$109$	14.5447	1.39313	0.696565	−	0.717494i	$-0.254711\pi$
$109$	14.5447	1.39313	0.696565	+	0.717494i	$0.254711\pi$
$110$	7.65684	0.730051
$111$	3.36666	0.319549
$112$	2.74279	0.259169
$113$	4.37389	0.411461	0.205730	−	0.978609i	$-0.434043\pi$
$113$	4.37389	0.411461	0.205730	+	0.978609i	$0.434043\pi$
$114$	6.90924	0.647110
$115$	−2.36003	−0.220074
$116$	−7.75633	−0.720157
$117$	1.00000	0.0924500
$118$	−28.1291	−2.58949
$119$	−5.34903	−0.490345
$120$	1.66310	0.151820
$121$	1.31117	0.119197
$122$	0.357753	0.0323894
$123$	2.08360	0.187872
$124$	2.76211	0.248045
$125$	1.00000	0.0894427
$126$	3.15859	0.281389
$127$	9.00778	0.799312	0.399656	−	0.916665i	$-0.369130\pi$
$127$	9.00778	0.799312	0.399656	+	0.916665i	$0.369130\pi$
$128$	12.3389	1.09061
$129$	−11.7269	−1.03250
$130$	−2.18223	−0.191394
$131$	12.4051	1.08384	0.541920	−	0.840430i	$-0.317698\pi$
$131$	12.4051	1.08384	0.541920	+	0.840430i	$0.317698\pi$
$132$	9.69150	0.843537
$133$	−4.58272	−0.397372
$134$	−3.42511	−0.295885
$135$	−1.00000	−0.0860663
$136$	−6.14613	−0.527026
$137$	−12.6101	−1.07736	−0.538678	−	0.842512i	$-0.681076\pi$
$137$	−12.6101	−1.07736	−0.538678	+	0.842512i	$0.681076\pi$
$138$	−5.15013	−0.438408
$139$	−8.34714	−0.707995	−0.353997	−	0.935246i	$-0.615178\pi$
$139$	−8.34714	−0.707995	−0.353997	+	0.935246i	$0.615178\pi$
$140$	−3.99792	−0.337886
$141$	−2.96698	−0.249865
$142$	17.6858	1.48416
$143$	−3.50873	−0.293415
$144$	−1.89496	−0.157913
$145$	−2.80811	−0.233201
$146$	10.8033	0.894087
$147$	4.90499	0.404557
$148$	−9.29909	−0.764381
$149$	−19.9341	−1.63307	−0.816534	−	0.577297i	$-0.804107\pi$
$149$	−19.9341	−1.63307	−0.816534	+	0.577297i	$0.804107\pi$
$150$	2.18223	0.178178
$151$	14.8064	1.20493	0.602465	−	0.798146i	$-0.294185\pi$
$151$	14.8064	1.20493	0.602465	+	0.798146i	$0.294185\pi$
$152$	−5.26563	−0.427099
$153$	3.69558	0.298770
$154$	−11.0826	−0.893063
$155$	1.00000	0.0803219
$156$	−2.76211	−0.221146
$157$	12.1149	0.966872	0.483436	−	0.875380i	$-0.339389\pi$
$157$	12.1149	0.966872	0.483436	+	0.875380i	$0.339389\pi$
$158$	16.9695	1.35002
$159$	6.88615	0.546107
$160$	7.46143	0.589878
$161$	3.41595	0.269214
$162$	−2.18223	−0.171452
$163$	18.2708	1.43108	0.715540	−	0.698572i	$-0.246181\pi$
$163$	18.2708	1.43108	0.715540	+	0.698572i	$0.246181\pi$
$164$	−5.75514	−0.449401
$165$	3.50873	0.273154
$166$	22.2795	1.72923
$167$	21.1899	1.63973	0.819863	−	0.572559i	$-0.194049\pi$
$167$	21.1899	1.63973	0.819863	+	0.572559i	$0.194049\pi$
$168$	−2.40720	−0.185720
$169$	1.00000	0.0769231
$170$	−8.06459	−0.618526
$171$	3.16614	0.242121
$172$	32.3911	2.46980
$173$	9.17024	0.697201	0.348600	−	0.937271i	$-0.386657\pi$
$173$	9.17024	0.697201	0.348600	+	0.937271i	$0.386657\pi$
$174$	−6.12794	−0.464558
$175$	−1.44741	−0.109414
$176$	6.64888	0.501179
$177$	−12.8901	−0.968878
$178$	−7.69653	−0.576880
$179$	−20.6771	−1.54548	−0.772740	−	0.634723i	$-0.781114\pi$
$179$	−20.6771	−1.54548	−0.772740	+	0.634723i	$0.781114\pi$
$180$	2.76211	0.205876
$181$	−24.5437	−1.82432	−0.912159	−	0.409836i	$-0.865586\pi$
$181$	−24.5437	−1.82432	−0.912159	+	0.409836i	$0.865586\pi$
$182$	3.15859	0.234130
$183$	0.163939	0.0121187
$184$	3.92498	0.289354
$185$	−3.36666	−0.247522
$186$	2.18223	0.160009
$187$	−12.9668	−0.948225
$188$	8.19514	0.597692
$189$	1.44741	0.105284
$190$	−6.90924	−0.501249
$191$	−8.39824	−0.607675	−0.303838	−	0.952724i	$-0.598268\pi$
$191$	−8.39824	−0.607675	−0.303838	+	0.952724i	$0.598268\pi$
$192$	12.4926	0.901578
$193$	4.26129	0.306735	0.153367	−	0.988169i	$-0.450988\pi$
$193$	4.26129	0.306735	0.153367	+	0.988169i	$0.450988\pi$
$194$	−17.3105	−1.24282
$195$	−1.00000	−0.0716115
$196$	−13.5481	−0.967724
$197$	12.8581	0.916101	0.458050	−	0.888926i	$-0.348548\pi$
$197$	12.8581	0.916101	0.458050	+	0.888926i	$0.348548\pi$
$198$	7.65684	0.544148
$199$	2.40700	0.170628	0.0853139	−	0.996354i	$-0.472811\pi$
$199$	2.40700	0.170628	0.0853139	+	0.996354i	$0.472811\pi$
$200$	−1.66310	−0.117599
$201$	−1.56955	−0.110707
$202$	36.4331	2.56342
$203$	4.06451	0.285272
$204$	−10.2076	−0.714675
$205$	−2.08360	−0.145525
$206$	−27.4865	−1.91508
$207$	−2.36003	−0.164034
$208$	−1.89496	−0.131392
$209$	−11.1091	−0.768435
$210$	−3.15859	−0.217963
$211$	9.42265	0.648682	0.324341	−	0.945940i	$-0.394857\pi$
$211$	9.42265	0.648682	0.324341	+	0.945940i	$0.394857\pi$
$212$	−19.0203	−1.30632
$213$	8.10448	0.555310
$214$	−20.4414	−1.39735
$215$	11.7269	0.799770
$216$	1.66310	0.113160
$217$	−1.44741	−0.0982569
$218$	−31.7398	−2.14969
$219$	4.95058	0.334529
$220$	−9.69150	−0.653401
$221$	3.69558	0.248591
$222$	−7.34681	−0.493086
$223$	−17.1240	−1.14671	−0.573354	−	0.819308i	$-0.694358\pi$
$223$	−17.1240	−1.14671	−0.573354	+	0.819308i	$0.694358\pi$
$224$	−10.7998	−0.721591
$225$	1.00000	0.0666667
$226$	−9.54482	−0.634912
$227$	−13.7045	−0.909597	−0.454798	−	0.890594i	$-0.650289\pi$
$227$	−13.7045	−0.909597	−0.454798	+	0.890594i	$0.650289\pi$
$228$	−8.74525	−0.579168
$229$	−9.68295	−0.639867	−0.319934	−	0.947440i	$-0.603661\pi$
$229$	−9.68295	−0.639867	−0.319934	+	0.947440i	$0.603661\pi$
$230$	5.15013	0.339589
$231$	−5.07858	−0.334146
$232$	4.67019	0.306613
$233$	−16.2522	−1.06472	−0.532359	−	0.846518i	$-0.678694\pi$
$233$	−16.2522	−1.06472	−0.532359	+	0.846518i	$0.678694\pi$
$234$	−2.18223	−0.142657
$235$	2.96698	0.193545
$236$	35.6039	2.31762
$237$	7.77624	0.505121
$238$	11.6728	0.756635
$239$	2.18844	0.141558	0.0707792	−	0.997492i	$-0.477451\pi$
$239$	2.18844	0.141558	0.0707792	+	0.997492i	$0.477451\pi$
$240$	1.89496	0.122319
$241$	12.9326	0.833063	0.416531	−	0.909121i	$-0.363246\pi$
$241$	12.9326	0.833063	0.416531	+	0.909121i	$0.363246\pi$
$242$	−2.86127	−0.183929
$243$	−1.00000	−0.0641500
$244$	−0.452819	−0.0289888
$245$	−4.90499	−0.313368
$246$	−4.54689	−0.289899
$247$	3.16614	0.201457
$248$	−1.66310	−0.105607
$249$	10.2095	0.647004
$250$	−2.18223	−0.138016
$251$	−17.3278	−1.09372	−0.546859	−	0.837225i	$-0.684177\pi$
$251$	−17.3278	−1.09372	−0.546859	+	0.837225i	$0.684177\pi$
$252$	−3.99792	−0.251845
$253$	8.28072	0.520604
$254$	−19.6570	−1.23339
$255$	−3.69558	−0.231426
$256$	−1.94097	−0.121311
$257$	−11.3457	−0.707728	−0.353864	−	0.935297i	$-0.615132\pi$
$257$	−11.3457	−0.707728	−0.353864	+	0.935297i	$0.615132\pi$
$258$	25.5908	1.59322
$259$	4.87295	0.302790
$260$	2.76211	0.171299
$261$	−2.80811	−0.173818
$262$	−27.0708	−1.67244
$263$	−15.6878	−0.967349	−0.483674	−	0.875248i	$-0.660698\pi$
$263$	−15.6878	−0.967349	−0.483674	+	0.875248i	$0.660698\pi$
$264$	−5.83538	−0.359143
$265$	−6.88615	−0.423013
$266$	10.0005	0.613172
$267$	−3.52692	−0.215844
$268$	4.33527	0.264819
$269$	−30.5894	−1.86507	−0.932534	−	0.361082i	$-0.882407\pi$
$269$	−30.5894	−1.86507	−0.932534	+	0.361082i	$0.882407\pi$
$270$	2.18223	0.132806
$271$	1.37669	0.0836282	0.0418141	−	0.999125i	$-0.486686\pi$
$271$	1.37669	0.0836282	0.0418141	+	0.999125i	$0.486686\pi$
$272$	−7.00296	−0.424617
$273$	1.44741	0.0876015
$274$	27.5182	1.66243
$275$	−3.50873	−0.211584
$276$	6.51868	0.392378
$277$	−6.02608	−0.362072	−0.181036	−	0.983476i	$-0.557945\pi$
$277$	−6.02608	−0.362072	−0.181036	+	0.983476i	$0.557945\pi$
$278$	18.2153	1.09248
$279$	1.00000	0.0598684
$280$	2.40720	0.143858
$281$	5.94771	0.354811	0.177405	−	0.984138i	$-0.443230\pi$
$281$	5.94771	0.354811	0.177405	+	0.984138i	$0.443230\pi$
$282$	6.47463	0.385558
$283$	22.5003	1.33750	0.668752	−	0.743485i	$-0.266829\pi$
$283$	22.5003	1.33750	0.668752	+	0.743485i	$0.266829\pi$
$284$	−22.3855	−1.32834
$285$	−3.16614	−0.187546
$286$	7.65684	0.452758
$287$	3.01583	0.178019
$288$	7.46143	0.439669
$289$	−3.34270	−0.196630
$290$	6.12794	0.359845
$291$	−7.93248	−0.465010
$292$	−13.6741	−0.800214
$293$	−21.8643	−1.27732	−0.638662	−	0.769488i	$-0.720512\pi$
$293$	−21.8643	−1.27732	−0.638662	+	0.769488i	$0.720512\pi$
$294$	−10.7038	−0.624258
$295$	12.8901	0.750490
$296$	5.59910	0.325441
$297$	3.50873	0.203597
$298$	43.5008	2.51993
$299$	−2.36003	−0.136484
$300$	−2.76211	−0.159471
$301$	−16.9737	−0.978350
$302$	−32.3110	−1.85929
$303$	16.6954	0.959124
$304$	−5.99970	−0.344107
$305$	−0.163939	−0.00938714
$306$	−8.06459	−0.461022
$307$	26.5752	1.51673	0.758364	−	0.651831i	$-0.225999\pi$
$307$	26.5752	1.51673	0.758364	+	0.651831i	$0.225999\pi$
$308$	14.0276	0.799298
$309$	−12.5956	−0.716541
$310$	−2.18223	−0.123942
$311$	11.4393	0.648662	0.324331	−	0.945944i	$-0.394861\pi$
$311$	11.4393	0.648662	0.324331	+	0.945944i	$0.394861\pi$
$312$	1.66310	0.0941547
$313$	21.3085	1.20443	0.602214	−	0.798335i	$-0.294285\pi$
$313$	21.3085	1.20443	0.602214	+	0.798335i	$0.294285\pi$
$314$	−26.4374	−1.49195
$315$	−1.44741	−0.0815526
$316$	−21.4789	−1.20828
$317$	2.38756	0.134098	0.0670492	−	0.997750i	$-0.478642\pi$
$317$	2.38756	0.134098	0.0670492	+	0.997750i	$0.478642\pi$
$318$	−15.0271	−0.842680
$319$	9.85291	0.551657
$320$	−12.4926	−0.698359
$321$	−9.36723	−0.522828
$322$	−7.45437	−0.415416
$323$	11.7007	0.651046
$324$	2.76211	0.153451
$325$	1.00000	0.0554700
$326$	−39.8710	−2.20825
$327$	−14.5447	−0.804324
$328$	3.46525	0.191336
$329$	−4.29445	−0.236761
$330$	−7.65684	−0.421495
$331$	7.09190	0.389806	0.194903	−	0.980823i	$-0.437561\pi$
$331$	7.09190	0.389806	0.194903	+	0.980823i	$0.437561\pi$
$332$	−28.1999	−1.54767
$333$	−3.36666	−0.184492
$334$	−46.2412	−2.53021
$335$	1.56955	0.0857537
$336$	−2.74279	−0.149631
$337$	−12.1141	−0.659896	−0.329948	−	0.943999i	$-0.607031\pi$
$337$	−12.1141	−0.659896	−0.329948	+	0.943999i	$0.607031\pi$
$338$	−2.18223	−0.118697
$339$	−4.37389	−0.237557
$340$	10.2076	0.553585
$341$	−3.50873	−0.190008
$342$	−6.90924	−0.373609
$343$	17.2315	0.930411
$344$	−19.5031	−1.05154
$345$	2.36003	0.127060
$346$	−20.0115	−1.07583
$347$	−8.73949	−0.469160	−0.234580	−	0.972097i	$-0.575372\pi$
$347$	−8.73949	−0.469160	−0.234580	+	0.972097i	$0.575372\pi$
$348$	7.75633	0.415783
$349$	15.4725	0.828223	0.414112	−	0.910226i	$-0.364092\pi$
$349$	15.4725	0.828223	0.414112	+	0.910226i	$0.364092\pi$
$350$	3.15859	0.168834
$351$	−1.00000	−0.0533761
$352$	−26.1801	−1.39541
$353$	21.3769	1.13778	0.568888	−	0.822415i	$-0.307374\pi$
$353$	21.3769	1.13778	0.568888	+	0.822415i	$0.307374\pi$
$354$	28.1291	1.49504
$355$	−8.10448	−0.430141
$356$	9.74175	0.516312
$357$	5.34903	0.283101
$358$	45.1222	2.38478
$359$	−8.05133	−0.424933	−0.212467	−	0.977168i	$-0.568150\pi$
$359$	−8.05133	−0.424933	−0.212467	+	0.977168i	$0.568150\pi$
$360$	−1.66310	−0.0876533
$361$	−8.97553	−0.472397
$362$	53.5599	2.81505
$363$	−1.31117	−0.0688185
$364$	−3.99792	−0.209548
$365$	−4.95058	−0.259125
$366$	−0.357753	−0.0187000
$367$	19.0589	0.994868	0.497434	−	0.867502i	$-0.334276\pi$
$367$	19.0589	0.994868	0.497434	+	0.867502i	$0.334276\pi$
$368$	4.47216	0.233127
$369$	−2.08360	−0.108468
$370$	7.34681	0.381943
$371$	9.96711	0.517467
$372$	−2.76211	−0.143209
$373$	1.57981	0.0817995	0.0408998	−	0.999163i	$-0.486978\pi$
$373$	1.57981	0.0817995	0.0408998	+	0.999163i	$0.486978\pi$
$374$	28.2964	1.46317
$375$	−1.00000	−0.0516398
$376$	−4.93440	−0.254472
$377$	−2.80811	−0.144625
$378$	−3.15859	−0.162460
$379$	35.3795	1.81732	0.908661	−	0.417534i	$-0.137106\pi$
$379$	35.3795	1.81732	0.908661	+	0.417534i	$0.137106\pi$
$380$	8.74525	0.448622
$381$	−9.00778	−0.461483
$382$	18.3269	0.937684
$383$	1.45149	0.0741675	0.0370838	−	0.999312i	$-0.488193\pi$
$383$	1.45149	0.0741675	0.0370838	+	0.999312i	$0.488193\pi$
$384$	−12.3389	−0.629666
$385$	5.07858	0.258829
$386$	−9.29911	−0.473312
$387$	11.7269	0.596114
$388$	21.9104	1.11233
$389$	30.5755	1.55024	0.775118	−	0.631816i	$-0.217690\pi$
$389$	30.5755	1.55024	0.775118	+	0.631816i	$0.217690\pi$
$390$	2.18223	0.110501
$391$	−8.72169	−0.441075
$392$	8.15751	0.412017
$393$	−12.4051	−0.625755
$394$	−28.0593	−1.41361
$395$	−7.77624	−0.391265
$396$	−9.69150	−0.487016
$397$	−33.4567	−1.67914	−0.839572	−	0.543248i	$-0.817194\pi$
$397$	−33.4567	−1.67914	−0.839572	+	0.543248i	$0.817194\pi$
$398$	−5.25262	−0.263290
$399$	4.58272	0.229423
$400$	−1.89496	−0.0947478
$401$	30.6088	1.52853	0.764265	−	0.644903i	$-0.223102\pi$
$401$	30.6088	1.52853	0.764265	+	0.644903i	$0.223102\pi$
$402$	3.42511	0.170829
$403$	1.00000	0.0498135
$404$	−46.1145	−2.29428
$405$	1.00000	0.0496904
$406$	−8.86967	−0.440194
$407$	11.8127	0.585533
$408$	6.14613	0.304279
$409$	−8.65524	−0.427974	−0.213987	−	0.976836i	$-0.568645\pi$
$409$	−8.65524	−0.427974	−0.213987	+	0.976836i	$0.568645\pi$
$410$	4.54689	0.224555
$411$	12.6101	0.622012
$412$	34.7906	1.71401
$413$	−18.6573	−0.918066
$414$	5.15013	0.253115
$415$	−10.2095	−0.501167
$416$	7.46143	0.365827
$417$	8.34714	0.408761
$418$	24.2427	1.18575
$419$	16.4556	0.803909	0.401954	−	0.915660i	$-0.368331\pi$
$419$	16.4556	0.803909	0.401954	+	0.915660i	$0.368331\pi$
$420$	3.99792	0.195079
$421$	1.70286	0.0829922	0.0414961	−	0.999139i	$-0.486788\pi$
$421$	1.70286	0.0829922	0.0414961	+	0.999139i	$0.486788\pi$
$422$	−20.5624	−1.00096
$423$	2.96698	0.144260
$424$	11.4524	0.556177
$425$	3.69558	0.179262
$426$	−17.6858	−0.856881
$427$	0.237288	0.0114832
$428$	25.8734	1.25064
$429$	3.50873	0.169403
$430$	−25.5908	−1.23410
$431$	−34.1210	−1.64355	−0.821775	−	0.569812i	$-0.807016\pi$
$431$	−34.1210	−1.64355	−0.821775	+	0.569812i	$0.807016\pi$
$432$	1.89496	0.0911711
$433$	19.3996	0.932288	0.466144	−	0.884709i	$-0.345643\pi$
$433$	19.3996	0.932288	0.466144	+	0.884709i	$0.345643\pi$
$434$	3.15859	0.151617
$435$	2.80811	0.134639
$436$	40.1741	1.92399
$437$	−7.47221	−0.357444
$438$	−10.8033	−0.516201
$439$	−18.1176	−0.864708	−0.432354	−	0.901704i	$-0.642317\pi$
$439$	−18.1176	−0.864708	−0.432354	+	0.901704i	$0.642317\pi$
$440$	5.83538	0.278191
$441$	−4.90499	−0.233571
$442$	−8.06459	−0.383593
$443$	30.5445	1.45121	0.725607	−	0.688109i	$-0.241559\pi$
$443$	30.5445	1.45121	0.725607	+	0.688109i	$0.241559\pi$
$444$	9.29909	0.441315
$445$	3.52692	0.167192
$446$	37.3685	1.76945
$447$	19.9341	0.942853
$448$	18.0820	0.854295
$449$	33.2933	1.57121	0.785603	−	0.618731i	$-0.212353\pi$
$449$	33.2933	1.57121	0.785603	+	0.618731i	$0.212353\pi$
$450$	−2.18223	−0.102871
$451$	7.31079	0.344251
$452$	12.0812	0.568251
$453$	−14.8064	−0.695666
$454$	29.9062	1.40357
$455$	−1.44741	−0.0678558
$456$	5.26563	0.246586
$457$	34.7073	1.62354	0.811769	−	0.583979i	$-0.198505\pi$
$457$	34.7073	1.62354	0.811769	+	0.583979i	$0.198505\pi$
$458$	21.1304	0.987358
$459$	−3.69558	−0.172495
$460$	−6.51868	−0.303935
$461$	14.8252	0.690479	0.345239	−	0.938515i	$-0.387798\pi$
$461$	14.8252	0.690479	0.345239	+	0.938515i	$0.387798\pi$
$462$	11.0826	0.515610
$463$	−18.2863	−0.849835	−0.424917	−	0.905232i	$-0.639697\pi$
$463$	−18.2863	−0.849835	−0.424917	+	0.905232i	$0.639697\pi$
$464$	5.32125	0.247033
$465$	−1.00000	−0.0463739
$466$	35.4660	1.64293
$467$	−33.9967	−1.57318	−0.786591	−	0.617475i	$-0.788156\pi$
$467$	−33.9967	−1.57318	−0.786591	+	0.617475i	$0.788156\pi$
$468$	2.76211	0.127679
$469$	−2.27179	−0.104901
$470$	−6.47463	−0.298652
$471$	−12.1149	−0.558224
$472$	−21.4376	−0.986744
$473$	−41.1466	−1.89192
$474$	−16.9695	−0.779436
$475$	3.16614	0.145273
$476$	−14.7746	−0.677194
$477$	−6.88615	−0.315295
$478$	−4.77567	−0.218434
$479$	18.0730	0.825776	0.412888	−	0.910782i	$-0.364520\pi$
$479$	18.0730	0.825776	0.412888	+	0.910782i	$0.364520\pi$
$480$	−7.46143	−0.340566
$481$	−3.36666	−0.153506
$482$	−28.2219	−1.28547
$483$	−3.41595	−0.155431
$484$	3.62160	0.164618
$485$	7.93248	0.360196
$486$	2.18223	0.0989878
$487$	−4.08990	−0.185331	−0.0926654	−	0.995697i	$-0.529539\pi$
$487$	−4.08990	−0.185331	−0.0926654	+	0.995697i	$0.529539\pi$
$488$	0.272648	0.0123422
$489$	−18.2708	−0.826234
$490$	10.7038	0.483549
$491$	28.2433	1.27460	0.637301	−	0.770615i	$-0.280051\pi$
$491$	28.2433	1.27460	0.637301	+	0.770615i	$0.280051\pi$
$492$	5.75514	0.259462
$493$	−10.3776	−0.467384
$494$	−6.90924	−0.310862
$495$	−3.50873	−0.157706
$496$	−1.89496	−0.0850860
$497$	11.7305	0.526187
$498$	−22.2795	−0.998370
$499$	18.5202	0.829079	0.414539	−	0.910031i	$-0.363943\pi$
$499$	18.5202	0.829079	0.414539	+	0.910031i	$0.363943\pi$
$500$	2.76211	0.123525
$501$	−21.1899	−0.946697
$502$	37.8131	1.68768
$503$	36.2192	1.61494	0.807468	−	0.589911i	$-0.200837\pi$
$503$	36.2192	1.61494	0.807468	+	0.589911i	$0.200837\pi$
$504$	2.40720	0.107225
$505$	−16.6954	−0.742934
$506$	−18.0704	−0.803327
$507$	−1.00000	−0.0444116
$508$	24.8805	1.10389
$509$	−28.1671	−1.24848	−0.624242	−	0.781231i	$-0.714592\pi$
$509$	−28.1671	−1.24848	−0.624242	+	0.781231i	$0.714592\pi$
$510$	8.06459	0.357106
$511$	7.16554	0.316985
$512$	−20.4421	−0.903422
$513$	−3.16614	−0.139789
$514$	24.7590	1.09207
$515$	12.5956	0.555030
$516$	−32.3911	−1.42594
$517$	−10.4103	−0.457846
$518$	−10.6339	−0.467226
$519$	−9.17024	−0.402529
$520$	−1.66310	−0.0729320
$521$	36.0454	1.57918	0.789590	−	0.613635i	$-0.210293\pi$
$521$	36.0454	1.57918	0.789590	+	0.613635i	$0.210293\pi$
$522$	6.12794	0.268213
$523$	31.1951	1.36407	0.682033	−	0.731321i	$-0.261096\pi$
$523$	31.1951	1.36407	0.682033	+	0.731321i	$0.261096\pi$
$524$	34.2643	1.49684
$525$	1.44741	0.0631703
$526$	34.2342	1.49268
$527$	3.69558	0.160982
$528$	−6.64888	−0.289356
$529$	−17.4302	−0.757837
$530$	15.0271	0.652737
$531$	12.8901	0.559382
$532$	−12.6580	−0.548794
$533$	−2.08360	−0.0902508
$534$	7.69653	0.333062
$535$	9.36723	0.404981
$536$	−2.61032	−0.112749
$537$	20.6771	0.892283
$538$	66.7530	2.87793
$539$	17.2103	0.741299
$540$	−2.76211	−0.118862
$541$	20.3342	0.874234	0.437117	−	0.899405i	$-0.356000\pi$
$541$	20.3342	0.874234	0.437117	+	0.899405i	$0.356000\pi$
$542$	−3.00426	−0.129044
$543$	24.5437	1.05327
$544$	27.5743	1.18224
$545$	14.5447	0.623027
$546$	−3.15859	−0.135175
$547$	14.1337	0.604312	0.302156	−	0.953258i	$-0.402294\pi$
$547$	14.1337	0.604312	0.302156	+	0.953258i	$0.402294\pi$
$548$	−34.8306	−1.48789
$549$	−0.163939	−0.00699676
$550$	7.65684	0.326489
$551$	−8.89089	−0.378765
$552$	−3.92498	−0.167058
$553$	11.2554	0.478630
$554$	13.1503	0.558701
$555$	3.36666	0.142907
$556$	−23.0557	−0.977781
$557$	5.57737	0.236321	0.118160	−	0.992995i	$-0.462300\pi$
$557$	5.57737	0.236321	0.118160	+	0.992995i	$0.462300\pi$
$558$	−2.18223	−0.0923810
$559$	11.7269	0.495997
$560$	2.74279	0.115904
$561$	12.9668	0.547458
$562$	−12.9792	−0.547497
$563$	3.10992	0.131068	0.0655338	−	0.997850i	$-0.479125\pi$
$563$	3.10992	0.131068	0.0655338	+	0.997850i	$0.479125\pi$
$564$	−8.19514	−0.345078
$565$	4.37389	0.184011
$566$	−49.1008	−2.06386
$567$	−1.44741	−0.0607857
$568$	13.4786	0.565550
$569$	−20.6565	−0.865965	−0.432983	−	0.901402i	$-0.642539\pi$
$569$	−20.6565	−0.865965	−0.432983	+	0.901402i	$0.642539\pi$
$570$	6.90924	0.289396
$571$	29.4267	1.23147	0.615734	−	0.787954i	$-0.288860\pi$
$571$	29.4267	1.23147	0.615734	+	0.787954i	$0.288860\pi$
$572$	−9.69150	−0.405222
$573$	8.39824	0.350841
$574$	−6.58123	−0.274695
$575$	−2.36003	−0.0984202
$576$	−12.4926	−0.520526
$577$	−25.6489	−1.06778	−0.533888	−	0.845555i	$-0.679270\pi$
$577$	−25.6489	−1.06778	−0.533888	+	0.845555i	$0.679270\pi$
$578$	7.29453	0.303413
$579$	−4.26129	−0.177093
$580$	−7.75633	−0.322064
$581$	14.7774	0.613072
$582$	17.3105	0.717542
$583$	24.1616	1.00067
$584$	8.23333	0.340698
$585$	1.00000	0.0413449
$586$	47.7128	1.97100
$587$	16.7777	0.692489	0.346244	−	0.938144i	$-0.387457\pi$
$587$	16.7777	0.692489	0.346244	+	0.938144i	$0.387457\pi$
$588$	13.5481	0.558716
$589$	3.16614	0.130459
$590$	−28.1291	−1.15806
$591$	−12.8581	−0.528911
$592$	6.37967	0.262203
$593$	−14.6247	−0.600564	−0.300282	−	0.953851i	$-0.597081\pi$
$593$	−14.6247	−0.600564	−0.300282	+	0.953851i	$0.597081\pi$
$594$	−7.65684	−0.314164
$595$	−5.34903	−0.219289
$596$	−55.0604	−2.25536
$597$	−2.40700	−0.0985120
$598$	5.15013	0.210604
$599$	31.8486	1.30130	0.650649	−	0.759379i	$-0.274497\pi$
$599$	31.8486	1.30130	0.650649	+	0.759379i	$0.274497\pi$
$600$	1.66310	0.0678960
$601$	−3.12692	−0.127550	−0.0637750	−	0.997964i	$-0.520314\pi$
$601$	−3.12692	−0.127550	−0.0637750	+	0.997964i	$0.520314\pi$
$602$	37.0405	1.50966
$603$	1.56955	0.0639170
$604$	40.8970	1.66408
$605$	1.31117	0.0533066
$606$	−36.4331	−1.47999
$607$	40.0015	1.62361	0.811805	−	0.583928i	$-0.198485\pi$
$607$	40.0015	1.62361	0.811805	+	0.583928i	$0.198485\pi$
$608$	23.6240	0.958078
$609$	−4.06451	−0.164702
$610$	0.357753	0.0144850
$611$	2.96698	0.120031
$612$	10.2076	0.412618
$613$	−24.4658	−0.988162	−0.494081	−	0.869416i	$-0.664495\pi$
$613$	−24.4658	−0.988162	−0.494081	+	0.869416i	$0.664495\pi$
$614$	−57.9931	−2.34041
$615$	2.08360	0.0840189
$616$	−8.44621	−0.340308
$617$	38.5218	1.55083	0.775414	−	0.631454i	$-0.217541\pi$
$617$	38.5218	1.55083	0.775414	+	0.631454i	$0.217541\pi$
$618$	27.4865	1.10567
$619$	5.52293	0.221985	0.110993	−	0.993821i	$-0.464597\pi$
$619$	5.52293	0.221985	0.110993	+	0.993821i	$0.464597\pi$
$620$	2.76211	0.110929
$621$	2.36003	0.0947049
$622$	−24.9631	−1.00093
$623$	−5.10491	−0.204524
$624$	1.89496	0.0758590
$625$	1.00000	0.0400000
$626$	−46.5000	−1.85851
$627$	11.1091	0.443656
$628$	33.4627	1.33531
$629$	−12.4418	−0.496085
$630$	3.15859	0.125841
$631$	47.5630	1.89345	0.946726	−	0.322041i	$-0.104369\pi$
$631$	47.5630	1.89345	0.946726	+	0.322041i	$0.104369\pi$
$632$	12.9327	0.514435
$633$	−9.42265	−0.374517
$634$	−5.21019	−0.206923
$635$	9.00778	0.357463
$636$	19.0203	0.754205
$637$	−4.90499	−0.194343
$638$	−21.5013	−0.851244
$639$	−8.10448	−0.320608
$640$	12.3389	0.487737
$641$	11.9011	0.470066	0.235033	−	0.971987i	$-0.424480\pi$
$641$	11.9011	0.470066	0.235033	+	0.971987i	$0.424480\pi$
$642$	20.4414	0.806759
$643$	8.58116	0.338408	0.169204	−	0.985581i	$-0.445880\pi$
$643$	8.58116	0.338408	0.169204	+	0.985581i	$0.445880\pi$
$644$	9.43523	0.371800
$645$	−11.7269	−0.461748
$646$	−25.5336	−1.00461
$647$	−16.4291	−0.645893	−0.322947	−	0.946417i	$-0.604673\pi$
$647$	−16.4291	−0.645893	−0.322947	+	0.946417i	$0.604673\pi$
$648$	−1.66310	−0.0653329
$649$	−45.2278	−1.77535
$650$	−2.18223	−0.0855940
$651$	1.44741	0.0567286
$652$	50.4660	1.97640
$653$	5.14682	0.201411	0.100705	−	0.994916i	$-0.467890\pi$
$653$	5.14682	0.201411	0.100705	+	0.994916i	$0.467890\pi$
$654$	31.7398	1.24113
$655$	12.4051	0.484708
$656$	3.94833	0.154156
$657$	−4.95058	−0.193141
$658$	9.37147	0.365338
$659$	0.524148	0.0204179	0.0102089	−	0.999948i	$-0.496750\pi$
$659$	0.524148	0.0204179	0.0102089	+	0.999948i	$0.496750\pi$
$660$	9.69150	0.377241
$661$	−17.2031	−0.669124	−0.334562	−	0.942374i	$-0.608588\pi$
$661$	−17.2031	−0.669124	−0.334562	+	0.942374i	$0.608588\pi$
$662$	−15.4761	−0.601497
$663$	−3.69558	−0.143524
$664$	16.9795	0.658934
$665$	−4.58272	−0.177710
$666$	7.34681	0.284683
$667$	6.62724	0.256608
$668$	58.5290	2.26456
$669$	17.1240	0.662052
$670$	−3.42511	−0.132324
$671$	0.575219	0.0222061
$672$	10.7998	0.416611
$673$	9.35088	0.360450	0.180225	−	0.983625i	$-0.442317\pi$
$673$	9.35088	0.360450	0.180225	+	0.983625i	$0.442317\pi$
$674$	26.4357	1.01826
$675$	−1.00000	−0.0384900
$676$	2.76211	0.106235
$677$	−47.5505	−1.82751	−0.913756	−	0.406262i	$-0.866832\pi$
$677$	−47.5505	−1.82751	−0.913756	+	0.406262i	$0.866832\pi$
$678$	9.54482	0.366566
$679$	−11.4816	−0.440623
$680$	−6.14613	−0.235693
$681$	13.7045	0.525156
$682$	7.65684	0.293196
$683$	43.9171	1.68044	0.840220	−	0.542245i	$-0.182426\pi$
$683$	43.9171	1.68044	0.840220	+	0.542245i	$0.182426\pi$
$684$	8.74525	0.334383
$685$	−12.6101	−0.481808
$686$	−37.6029	−1.43569
$687$	9.68295	0.369427
$688$	−22.2220	−0.847207
$689$	−6.88615	−0.262341
$690$	−5.15013	−0.196062
$691$	−7.80594	−0.296952	−0.148476	−	0.988916i	$-0.547437\pi$
$691$	−7.80594	−0.296952	−0.148476	+	0.988916i	$0.547437\pi$
$692$	25.3292	0.962874
$693$	5.07858	0.192919
$694$	19.0715	0.723946
$695$	−8.34714	−0.316625
$696$	−4.67019	−0.177023
$697$	−7.70011	−0.291662
$698$	−33.7645	−1.27800
$699$	16.2522	0.614716
$700$	−3.99792	−0.151107
$701$	15.7375	0.594398	0.297199	−	0.954816i	$-0.403947\pi$
$701$	15.7375	0.594398	0.297199	+	0.954816i	$0.403947\pi$
$702$	2.18223	0.0823628
$703$	−10.6593	−0.402024
$704$	43.8332	1.65203
$705$	−2.96698	−0.111743
$706$	−46.6492	−1.75567
$707$	24.1651	0.908823
$708$	−35.6039	−1.33808
$709$	−16.5617	−0.621989	−0.310994	−	0.950412i	$-0.600662\pi$
$709$	−16.5617	−0.621989	−0.310994	+	0.950412i	$0.600662\pi$
$710$	17.6858	0.663737
$711$	−7.77624	−0.291632
$712$	−5.86563	−0.219824
$713$	−2.36003	−0.0883840
$714$	−11.6728	−0.436844
$715$	−3.50873	−0.131219
$716$	−57.1125	−2.13440
$717$	−2.18844	−0.0817288
$718$	17.5698	0.655700
$719$	−8.92328	−0.332782	−0.166391	−	0.986060i	$-0.553211\pi$
$719$	−8.92328	−0.332782	−0.166391	+	0.986060i	$0.553211\pi$
$720$	−1.89496	−0.0706208
$721$	−18.2311	−0.678962
$722$	19.5866	0.728940
$723$	−12.9326	−0.480969
$724$	−67.7925	−2.51949
$725$	−2.80811	−0.104291
$726$	2.86127	0.106192
$727$	−14.1721	−0.525612	−0.262806	−	0.964849i	$-0.584648\pi$
$727$	−14.1721	−0.525612	−0.262806	+	0.964849i	$0.584648\pi$
$728$	2.40720	0.0892168
$729$	1.00000	0.0370370
$730$	10.8033	0.399848
$731$	43.3378	1.60291
$732$	0.452819	0.0167367
$733$	33.7826	1.24779	0.623894	−	0.781509i	$-0.285550\pi$
$733$	33.7826	1.24779	0.623894	+	0.781509i	$0.285550\pi$
$734$	−41.5909	−1.53515
$735$	4.90499	0.180923
$736$	−17.6092	−0.649085
$737$	−5.50712	−0.202857
$738$	4.54689	0.167373
$739$	30.1376	1.10863	0.554315	−	0.832307i	$-0.312980\pi$
$739$	30.1376	1.10863	0.554315	+	0.832307i	$0.312980\pi$
$740$	−9.29909	−0.341841
$741$	−3.16614	−0.116311
$742$	−21.7505	−0.798486
$743$	33.9109	1.24407	0.622035	−	0.782989i	$-0.286306\pi$
$743$	33.9109	1.24407	0.622035	+	0.782989i	$0.286306\pi$
$744$	1.66310	0.0609724
$745$	−19.9341	−0.730330
$746$	−3.44751	−0.126222
$747$	−10.2095	−0.373548
$748$	−35.8157	−1.30955
$749$	−13.5583	−0.495408
$750$	2.18223	0.0796837
$751$	17.0848	0.623434	0.311717	−	0.950175i	$-0.399096\pi$
$751$	17.0848	0.623434	0.311717	+	0.950175i	$0.399096\pi$
$752$	−5.62230	−0.205024
$753$	17.3278	0.631459
$754$	6.12794	0.223166
$755$	14.8064	0.538861
$756$	3.99792	0.145403
$757$	11.5220	0.418776	0.209388	−	0.977833i	$-0.432853\pi$
$757$	11.5220	0.418776	0.209388	+	0.977833i	$0.432853\pi$
$758$	−77.2061	−2.80425
$759$	−8.28072	−0.300571
$760$	−5.26563	−0.191004
$761$	33.0431	1.19781	0.598907	−	0.800819i	$-0.295602\pi$
$761$	33.0431	1.19781	0.598907	+	0.800819i	$0.295602\pi$
$762$	19.6570	0.712099
$763$	−21.0522	−0.762141
$764$	−23.1969	−0.839234
$765$	3.69558	0.133614
$766$	−3.16747	−0.114446
$767$	12.8901	0.465434
$768$	1.94097	0.0700389
$769$	−6.63781	−0.239366	−0.119683	−	0.992812i	$-0.538188\pi$
$769$	−6.63781	−0.239366	−0.119683	+	0.992812i	$0.538188\pi$
$770$	−11.0826	−0.399390
$771$	11.3457	0.408607
$772$	11.7702	0.423618
$773$	−1.51609	−0.0545300	−0.0272650	−	0.999628i	$-0.508680\pi$
$773$	−1.51609	−0.0545300	−0.0272650	+	0.999628i	$0.508680\pi$
$774$	−25.5908	−0.919844
$775$	1.00000	0.0359211
$776$	−13.1925	−0.473585
$777$	−4.87295	−0.174816
$778$	−66.7226	−2.39212
$779$	−6.59698	−0.236361
$780$	−2.76211	−0.0988995
$781$	28.4364	1.01754
$782$	19.0327	0.680608
$783$	2.80811	0.100354
$784$	9.29474	0.331955
$785$	12.1149	0.432399
$786$	27.0708	0.965582
$787$	−12.7013	−0.452752	−0.226376	−	0.974040i	$-0.572688\pi$
$787$	−12.7013	−0.452752	−0.226376	+	0.974040i	$0.572688\pi$
$788$	35.5155	1.26519
$789$	15.6878	0.558499
$790$	16.9695	0.603749
$791$	−6.33083	−0.225098
$792$	5.83538	0.207351
$793$	−0.163939	−0.00582166
$794$	73.0101	2.59103
$795$	6.88615	0.244226
$796$	6.64841	0.235647
$797$	49.1058	1.73942	0.869709	−	0.493565i	$-0.164306\pi$
$797$	49.1058	1.73942	0.869709	+	0.493565i	$0.164306\pi$
$798$	−10.0005	−0.354015
$799$	10.9647	0.387904
$800$	7.46143	0.263801
$801$	3.52692	0.124617
$802$	−66.7953	−2.35862
$803$	17.3702	0.612983
$804$	−4.33527	−0.152893
$805$	3.41595	0.120396
$806$	−2.18223	−0.0768657
$807$	30.5894	1.07680
$808$	27.7661	0.976809
$809$	8.15958	0.286876	0.143438	−	0.989659i	$-0.454184\pi$
$809$	8.15958	0.286876	0.143438	+	0.989659i	$0.454184\pi$
$810$	−2.18223	−0.0766756
$811$	15.4091	0.541088	0.270544	−	0.962708i	$-0.412796\pi$
$811$	15.4091	0.541088	0.270544	+	0.962708i	$0.412796\pi$
$812$	11.2266	0.393977
$813$	−1.37669	−0.0482828
$814$	−25.7780	−0.903517
$815$	18.2708	0.639998
$816$	7.00296	0.245153
$817$	37.1292	1.29899
$818$	18.8877	0.660393
$819$	−1.44741	−0.0505768
$820$	−5.75514	−0.200978
$821$	37.4388	1.30662	0.653312	−	0.757089i	$-0.273379\pi$
$821$	37.4388	1.30662	0.653312	+	0.757089i	$0.273379\pi$
$822$	−27.5182	−0.959806
$823$	42.3430	1.47598	0.737992	−	0.674809i	$-0.235774\pi$
$823$	42.3430	1.47598	0.737992	+	0.674809i	$0.235774\pi$
$824$	−20.9479	−0.729753
$825$	3.50873	0.122158
$826$	40.7145	1.41664
$827$	−40.1503	−1.39616	−0.698082	−	0.716018i	$-0.745963\pi$
$827$	−40.1503	−1.39616	−0.698082	+	0.716018i	$0.745963\pi$
$828$	−6.51868	−0.226540
$829$	5.04541	0.175234	0.0876172	−	0.996154i	$-0.472075\pi$
$829$	5.04541	0.175234	0.0876172	+	0.996154i	$0.472075\pi$
$830$	22.2795	0.773334
$831$	6.02608	0.209042
$832$	−12.4926	−0.433104
$833$	−18.1268	−0.628056
$834$	−18.2153	−0.630746
$835$	21.1899	0.733308
$836$	−30.6847	−1.06125
$837$	−1.00000	−0.0345651
$838$	−35.9099	−1.24049
$839$	−11.9995	−0.414269	−0.207134	−	0.978313i	$-0.566414\pi$
$839$	−11.9995	−0.414269	−0.207134	+	0.978313i	$0.566414\pi$
$840$	−2.40720	−0.0830563
$841$	−21.1145	−0.728086
$842$	−3.71602	−0.128063
$843$	−5.94771	−0.204850
$844$	26.0264	0.895867
$845$	1.00000	0.0344010
$846$	−6.47463	−0.222602
$847$	−1.89780	−0.0652093
$848$	13.0489	0.448103
$849$	−22.5003	−0.772209
$850$	−8.06459	−0.276613
$851$	7.94543	0.272366
$852$	22.3855	0.766915
$853$	27.5908	0.944692	0.472346	−	0.881413i	$-0.343407\pi$
$853$	27.5908	0.944692	0.472346	+	0.881413i	$0.343407\pi$
$854$	−0.517817	−0.0177193
$855$	3.16614	0.108280
$856$	−15.5787	−0.532468
$857$	20.5732	0.702768	0.351384	−	0.936231i	$-0.385711\pi$
$857$	20.5732	0.702768	0.351384	+	0.936231i	$0.385711\pi$
$858$	−7.65684	−0.261400
$859$	−26.5290	−0.905159	−0.452580	−	0.891724i	$-0.649496\pi$
$859$	−26.5290	−0.905159	−0.452580	+	0.891724i	$0.649496\pi$
$860$	32.3911	1.10453
$861$	−3.01583	−0.102779
$862$	74.4598	2.53611
$863$	3.64506	0.124079	0.0620396	−	0.998074i	$-0.480239\pi$
$863$	3.64506	0.124079	0.0620396	+	0.998074i	$0.480239\pi$
$864$	−7.46143	−0.253843
$865$	9.17024	0.311798
$866$	−42.3344	−1.43858
$867$	3.34270	0.113524
$868$	−3.99792	−0.135698
$869$	27.2847	0.925571
$870$	−6.12794	−0.207757
$871$	1.56955	0.0531822
$872$	−24.1894	−0.819155
$873$	7.93248	0.268474
$874$	16.3060	0.551560
$875$	−1.44741	−0.0489315
$876$	13.6741	0.462004
$877$	32.7498	1.10588	0.552941	−	0.833221i	$-0.313506\pi$
$877$	32.7498	1.10588	0.552941	+	0.833221i	$0.313506\pi$
$878$	39.5368	1.33430
$879$	21.8643	0.737463
$880$	6.64888	0.224134
$881$	32.2950	1.08805	0.544023	−	0.839070i	$-0.316901\pi$
$881$	32.2950	1.08805	0.544023	+	0.839070i	$0.316901\pi$
$882$	10.7038	0.360416
$883$	−3.55078	−0.119493	−0.0597465	−	0.998214i	$-0.519029\pi$
$883$	−3.55078	−0.119493	−0.0597465	+	0.998214i	$0.519029\pi$
$884$	10.2076	0.343319
$885$	−12.8901	−0.433296
$886$	−66.6551	−2.23932
$887$	−25.2495	−0.847796	−0.423898	−	0.905710i	$-0.639339\pi$
$887$	−25.2495	−0.847796	−0.423898	+	0.905710i	$0.639339\pi$
$888$	−5.59910	−0.187894
$889$	−13.0380	−0.437280
$890$	−7.69653	−0.257988
$891$	−3.50873	−0.117547
$892$	−47.2985	−1.58367
$893$	9.39389	0.314355
$894$	−43.5008	−1.45488
$895$	−20.6771	−0.691160
$896$	−17.8595	−0.596643
$897$	2.36003	0.0787992
$898$	−72.6534	−2.42448
$899$	−2.80811	−0.0936559
$900$	2.76211	0.0920704
$901$	−25.4483	−0.847806
$902$	−15.9538	−0.531203
$903$	16.9737	0.564851
$904$	−7.27423	−0.241937
$905$	−24.5437	−0.815860
$906$	32.3110	1.07346
$907$	−47.4438	−1.57534	−0.787672	−	0.616094i	$-0.788714\pi$
$907$	−47.4438	−1.57534	−0.787672	+	0.616094i	$0.788714\pi$
$908$	−37.8533	−1.25620
$909$	−16.6954	−0.553750
$910$	3.15859	0.104706
$911$	−33.7437	−1.11798	−0.558990	−	0.829174i	$-0.688811\pi$
$911$	−33.7437	−1.11798	−0.558990	+	0.829174i	$0.688811\pi$
$912$	5.99970	0.198670
$913$	35.8225	1.18555
$914$	−75.7391	−2.50523
$915$	0.163939	0.00541967
$916$	−26.7454	−0.883693
$917$	−17.9553	−0.592938
$918$	8.06459	0.266171
$919$	−15.2929	−0.504466	−0.252233	−	0.967667i	$-0.581165\pi$
$919$	−15.2929	−0.504466	−0.252233	+	0.967667i	$0.581165\pi$
$920$	3.92498	0.129403
$921$	−26.5752	−0.875683
$922$	−32.3520	−1.06546
$923$	−8.10448	−0.266762
$924$	−14.0276	−0.461475
$925$	−3.36666	−0.110695
$926$	39.9048	1.31135
$927$	12.5956	0.413695
$928$	−20.9526	−0.687801
$929$	−29.4940	−0.967665	−0.483833	−	0.875161i	$-0.660756\pi$
$929$	−29.4940	−0.967665	−0.483833	+	0.875161i	$0.660756\pi$
$930$	2.18223	0.0715580
$931$	−15.5299	−0.508972
$932$	−44.8905	−1.47044
$933$	−11.4393	−0.374505
$934$	74.1886	2.42752
$935$	−12.9668	−0.424059
$936$	−1.66310	−0.0543603
$937$	9.06827	0.296247	0.148124	−	0.988969i	$-0.452677\pi$
$937$	9.06827	0.296247	0.148124	+	0.988969i	$0.452677\pi$
$938$	4.95756	0.161870
$939$	−21.3085	−0.695377
$940$	8.19514	0.267296
$941$	47.5161	1.54898	0.774490	−	0.632586i	$-0.218006\pi$
$941$	47.5161	1.54898	0.774490	+	0.632586i	$0.218006\pi$
$942$	26.4374	0.861377
$943$	4.91737	0.160132
$944$	−24.4262	−0.795004
$945$	1.44741	0.0470844
$946$	89.7913	2.91937
$947$	−40.7413	−1.32391	−0.661957	−	0.749541i	$-0.730274\pi$
$947$	−40.7413	−1.32391	−0.661957	+	0.749541i	$0.730274\pi$
$948$	21.4789	0.697601
$949$	−4.95058	−0.160703
$950$	−6.90924	−0.224165
$951$	−2.38756	−0.0774218
$952$	8.89600	0.288321
$953$	−0.132147	−0.00428068	−0.00214034	−	0.999998i	$-0.500681\pi$
$953$	−0.132147	−0.00428068	−0.00214034	+	0.999998i	$0.500681\pi$
$954$	15.0271	0.486521
$955$	−8.39824	−0.271761
$956$	6.04472	0.195500
$957$	−9.85291	−0.318499
$958$	−39.4394	−1.27423
$959$	18.2521	0.589390
$960$	12.4926	0.403198
$961$	1.00000	0.0322581
$962$	7.34681	0.236871
$963$	9.36723	0.301855
$964$	35.7213	1.15051
$965$	4.26129	0.137176
$966$	7.45437	0.239840
$967$	−19.3295	−0.621594	−0.310797	−	0.950476i	$-0.600596\pi$
$967$	−19.3295	−0.621594	−0.310797	+	0.950476i	$0.600596\pi$
$968$	−2.18061	−0.0700875
$969$	−11.7007	−0.375882
$970$	−17.3105	−0.555806
$971$	5.74625	0.184406	0.0922029	−	0.995740i	$-0.470609\pi$
$971$	5.74625	0.184406	0.0922029	+	0.995740i	$0.470609\pi$
$972$	−2.76211	−0.0885948
$973$	12.0818	0.387324
$974$	8.92508	0.285978
$975$	−1.00000	−0.0320256
$976$	0.310658	0.00994392
$977$	43.4758	1.39092	0.695458	−	0.718567i	$-0.255202\pi$
$977$	43.4758	1.39092	0.695458	+	0.718567i	$0.255202\pi$
$978$	39.8710	1.27493
$979$	−12.3750	−0.395506
$980$	−13.5481	−0.432780
$981$	14.5447	0.464377
$982$	−61.6333	−1.96680
$983$	−18.7968	−0.599525	−0.299763	−	0.954014i	$-0.596908\pi$
$983$	−18.7968	−0.599525	−0.299763	+	0.954014i	$0.596908\pi$
$984$	−3.46525	−0.110468
$985$	12.8581	0.409693
$986$	22.6463	0.721205
$987$	4.29445	0.136694
$988$	8.74525	0.278223
$989$	−27.6760	−0.880044
$990$	7.65684	0.243350
$991$	−49.9037	−1.58524	−0.792622	−	0.609713i	$-0.791285\pi$
$991$	−49.9037	−1.58524	−0.792622	+	0.609713i	$0.791285\pi$
$992$	7.46143	0.236901
$993$	−7.09190	−0.225055
$994$	−25.5987	−0.811942
$995$	2.40700	0.0763071
$996$	28.1999	0.893549
$997$	15.7185	0.497810	0.248905	−	0.968528i	$-0.419929\pi$
$997$	15.7185	0.497810	0.248905	+	0.968528i	$0.419929\pi$
$998$	−40.4153	−1.27932
$999$	3.36666	0.106516

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6045.2.a.bh.1.3	✓	17

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6045.2.a.bh.1.3	✓	17	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:	\( N \)	\(=\)	\( 6045 = 3 \cdot 5 \cdot 13 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6045.a (trivial)

\(f(q)\)	\(=\)	\(q-2.18223 q^{2} -1.00000 q^{3} +2.76211 q^{4} +1.00000 q^{5} +2.18223 q^{6} -1.44741 q^{7} -1.66310 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-2.18223 q^{2} -1.00000 q^{3} +2.76211 q^{4} +1.00000 q^{5} +2.18223 q^{6} -1.44741 q^{7} -1.66310 q^{8} +1.00000 q^{9} -2.18223 q^{10} -3.50873 q^{11} -2.76211 q^{12} +1.00000 q^{13} +3.15859 q^{14} -1.00000 q^{15} -1.89496 q^{16} +3.69558 q^{17} -2.18223 q^{18} +3.16614 q^{19} +2.76211 q^{20} +1.44741 q^{21} +7.65684 q^{22} -2.36003 q^{23} +1.66310 q^{24} +1.00000 q^{25} -2.18223 q^{26} -1.00000 q^{27} -3.99792 q^{28} -2.80811 q^{29} +2.18223 q^{30} +1.00000 q^{31} +7.46143 q^{32} +3.50873 q^{33} -8.06459 q^{34} -1.44741 q^{35} +2.76211 q^{36} -3.36666 q^{37} -6.90924 q^{38} -1.00000 q^{39} -1.66310 q^{40} -2.08360 q^{41} -3.15859 q^{42} +11.7269 q^{43} -9.69150 q^{44} +1.00000 q^{45} +5.15013 q^{46} +2.96698 q^{47} +1.89496 q^{48} -4.90499 q^{49} -2.18223 q^{50} -3.69558 q^{51} +2.76211 q^{52} -6.88615 q^{53} +2.18223 q^{54} -3.50873 q^{55} +2.40720 q^{56} -3.16614 q^{57} +6.12794 q^{58} +12.8901 q^{59} -2.76211 q^{60} -0.163939 q^{61} -2.18223 q^{62} -1.44741 q^{63} -12.4926 q^{64} +1.00000 q^{65} -7.65684 q^{66} +1.56955 q^{67} +10.2076 q^{68} +2.36003 q^{69} +3.15859 q^{70} -8.10448 q^{71} -1.66310 q^{72} -4.95058 q^{73} +7.34681 q^{74} -1.00000 q^{75} +8.74525 q^{76} +5.07858 q^{77} +2.18223 q^{78} -7.77624 q^{79} -1.89496 q^{80} +1.00000 q^{81} +4.54689 q^{82} -10.2095 q^{83} +3.99792 q^{84} +3.69558 q^{85} -25.5908 q^{86} +2.80811 q^{87} +5.83538 q^{88} +3.52692 q^{89} -2.18223 q^{90} -1.44741 q^{91} -6.51868 q^{92} -1.00000 q^{93} -6.47463 q^{94} +3.16614 q^{95} -7.46143 q^{96} +7.93248 q^{97} +10.7038 q^{98} -3.50873 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 17 q + 2 q^{2} - 17 q^{3} + 20 q^{4} + 17 q^{5} - 2 q^{6} + 18 q^{7} + 9 q^{8} + 17 q^{9}+O(q^{10}) \) 17 * q + 2 * q^2 - 17 * q^3 + 20 * q^4 + 17 * q^5 - 2 * q^6 + 18 * q^7 + 9 * q^8 + 17 * q^9	\( 17 q + 2 q^{2} - 17 q^{3} + 20 q^{4} + 17 q^{5} - 2 q^{6} + 18 q^{7} + 9 q^{8} + 17 q^{9} + 2 q^{10} + 3 q^{11} - 20 q^{12} + 17 q^{13} + q^{14} - 17 q^{15} + 26 q^{16} + 2 q^{18} + 10 q^{19} + 20 q^{20} - 18 q^{21} + 5 q^{22} + 16 q^{23} - 9 q^{24} + 17 q^{25} + 2 q^{26} - 17 q^{27} + 36 q^{28} - 3 q^{29} - 2 q^{30} + 17 q^{31} + 20 q^{32} - 3 q^{33} + q^{34} + 18 q^{35} + 20 q^{36} + 14 q^{37} + 22 q^{38} - 17 q^{39} + 9 q^{40} - 6 q^{41} - q^{42} + 24 q^{43} - 15 q^{44} + 17 q^{45} + 6 q^{46} + 25 q^{47} - 26 q^{48} + 31 q^{49} + 2 q^{50} + 20 q^{52} - 15 q^{53} - 2 q^{54} + 3 q^{55} + 31 q^{56} - 10 q^{57} + 44 q^{58} + 16 q^{59} - 20 q^{60} - 5 q^{61} + 2 q^{62} + 18 q^{63} + 35 q^{64} + 17 q^{65} - 5 q^{66} + 50 q^{67} + 13 q^{68} - 16 q^{69} + q^{70} + 16 q^{71} + 9 q^{72} + 33 q^{73} + 2 q^{74} - 17 q^{75} + 9 q^{77} - 2 q^{78} - 10 q^{79} + 26 q^{80} + 17 q^{81} + 61 q^{82} + 27 q^{83} - 36 q^{84} - 12 q^{86} + 3 q^{87} + 23 q^{88} - 24 q^{89} + 2 q^{90} + 18 q^{91} - 21 q^{92} - 17 q^{93} + 6 q^{94} + 10 q^{95} - 20 q^{96} + 48 q^{97} + 14 q^{98} + 3 q^{99}+O(q^{100}) \) 17 * q + 2 * q^2 - 17 * q^3 + 20 * q^4 + 17 * q^5 - 2 * q^6 + 18 * q^7 + 9 * q^8 + 17 * q^9 + 2 * q^10 + 3 * q^11 - 20 * q^12 + 17 * q^13 + q^14 - 17 * q^15 + 26 * q^16 + 2 * q^18 + 10 * q^19 + 20 * q^20 - 18 * q^21 + 5 * q^22 + 16 * q^23 - 9 * q^24 + 17 * q^25 + 2 * q^26 - 17 * q^27 + 36 * q^28 - 3 * q^29 - 2 * q^30 + 17 * q^31 + 20 * q^32 - 3 * q^33 + q^34 + 18 * q^35 + 20 * q^36 + 14 * q^37 + 22 * q^38 - 17 * q^39 + 9 * q^40 - 6 * q^41 - q^42 + 24 * q^43 - 15 * q^44 + 17 * q^45 + 6 * q^46 + 25 * q^47 - 26 * q^48 + 31 * q^49 + 2 * q^50 + 20 * q^52 - 15 * q^53 - 2 * q^54 + 3 * q^55 + 31 * q^56 - 10 * q^57 + 44 * q^58 + 16 * q^59 - 20 * q^60 - 5 * q^61 + 2 * q^62 + 18 * q^63 + 35 * q^64 + 17 * q^65 - 5 * q^66 + 50 * q^67 + 13 * q^68 - 16 * q^69 + q^70 + 16 * q^71 + 9 * q^72 + 33 * q^73 + 2 * q^74 - 17 * q^75 + 9 * q^77 - 2 * q^78 - 10 * q^79 + 26 * q^80 + 17 * q^81 + 61 * q^82 + 27 * q^83 - 36 * q^84 - 12 * q^86 + 3 * q^87 + 23 * q^88 - 24 * q^89 + 2 * q^90 + 18 * q^91 - 21 * q^92 - 17 * q^93 + 6 * q^94 + 10 * q^95 - 20 * q^96 + 48 * q^97 + 14 * q^98 + 3 * q^99

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