LMFDB - Embedded newform 9251.2.a.t.1.18

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [9251,2,Mod(1,9251)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(9251, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("9251.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 9251 = 11 \cdot 29^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	9251.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:	$73.8696069099$
Analytic rank:	$1$
Dimension:	$18$
Coefficient field:	$\mathbb{Q}[x]/(x^{18} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{18} - 24 x^{16} - x^{15} + 233 x^{14} + 24 x^{13} - 1184 x^{12} - 207 x^{11} + 3413 x^{10} + \cdots - 41 $ x^18 - 24x^16 - x^15 + 233x^14 + 24x^13 - 1184x^12 - 207x^11 + 3413x^10 + 820x^9 - 5661x^8 - 1595x^7 + 5262x^6 + 1498x^5 - 2567x^4 - 605x^3 + 583x^2 + 80*x - 41
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.18
Root			$-2.63004$ of defining polynomial
Character	$\chi$	$=$	9251.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.63004 q^{2} -1.94297 q^{3} +4.91711 q^{4} +1.09435 q^{5} -5.11009 q^{6} +1.26974 q^{7} +7.67212 q^{8} +0.775130 q^{9} +O(q^{10})$	\(q+2.63004 q^{2} -1.94297 q^{3} +4.91711 q^{4} +1.09435 q^{5} -5.11009 q^{6} +1.26974 q^{7} +7.67212 q^{8} +0.775130 q^{9} +2.87818 q^{10} -1.00000 q^{11} -9.55380 q^{12} -3.69578 q^{13} +3.33946 q^{14} -2.12629 q^{15} +10.3438 q^{16} -2.57992 q^{17} +2.03862 q^{18} -0.269398 q^{19} +5.38104 q^{20} -2.46706 q^{21} -2.63004 q^{22} -6.80128 q^{23} -14.9067 q^{24} -3.80240 q^{25} -9.72006 q^{26} +4.32285 q^{27} +6.24344 q^{28} -5.59222 q^{30} -2.38168 q^{31} +11.8603 q^{32} +1.94297 q^{33} -6.78528 q^{34} +1.38954 q^{35} +3.81140 q^{36} +7.13754 q^{37} -0.708528 q^{38} +7.18079 q^{39} +8.39598 q^{40} -11.8922 q^{41} -6.48847 q^{42} -9.98237 q^{43} -4.91711 q^{44} +0.848263 q^{45} -17.8876 q^{46} +1.22043 q^{47} -20.0976 q^{48} -5.38777 q^{49} -10.0005 q^{50} +5.01270 q^{51} -18.1726 q^{52} -2.44507 q^{53} +11.3693 q^{54} -1.09435 q^{55} +9.74157 q^{56} +0.523432 q^{57} -4.34619 q^{59} -10.4552 q^{60} +9.65118 q^{61} -6.26392 q^{62} +0.984212 q^{63} +10.5054 q^{64} -4.04448 q^{65} +5.11009 q^{66} +11.7749 q^{67} -12.6857 q^{68} +13.2147 q^{69} +3.65454 q^{70} -15.2531 q^{71} +5.94689 q^{72} +7.49764 q^{73} +18.7720 q^{74} +7.38795 q^{75} -1.32466 q^{76} -1.26974 q^{77} +18.8858 q^{78} -0.916642 q^{79} +11.3197 q^{80} -10.7246 q^{81} -31.2771 q^{82} -0.114200 q^{83} -12.1308 q^{84} -2.82333 q^{85} -26.2540 q^{86} -7.67212 q^{88} -1.64850 q^{89} +2.23097 q^{90} -4.69267 q^{91} -33.4426 q^{92} +4.62754 q^{93} +3.20979 q^{94} -0.294816 q^{95} -23.0441 q^{96} -14.8211 q^{97} -14.1700 q^{98} -0.775130 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 18 q + 3 q^{3} + 12 q^{4} - 6 q^{5} - q^{6} - 5 q^{7} - 3 q^{8} + 9 q^{9}+O(q^{10}) $ 18 * q + 3 * q^3 + 12 * q^4 - 6 * q^5 - q^6 - 5 * q^7 - 3 * q^8 + 9 * q^9	\( 18 q + 3 q^{3} + 12 q^{4} - 6 q^{5} - q^{6} - 5 q^{7} - 3 q^{8} + 9 q^{9} + 5 q^{10} - 18 q^{11} + 3 q^{12} - 15 q^{13} - 12 q^{14} + 27 q^{15} + 4 q^{16} - 6 q^{17} + 12 q^{18} - 11 q^{19} - 18 q^{20} - 6 q^{21} - 20 q^{23} - 3 q^{24} - 4 q^{25} + 10 q^{26} - 6 q^{27} - 6 q^{28} - 19 q^{30} + 8 q^{31} + 24 q^{32} - 3 q^{33} - 22 q^{34} + 22 q^{35} + 17 q^{36} - 9 q^{37} - 3 q^{38} + 8 q^{39} + 36 q^{40} - 3 q^{41} + 28 q^{42} - 13 q^{43} - 12 q^{44} - q^{45} - 37 q^{46} + q^{47} - 46 q^{48} - 23 q^{49} - 34 q^{50} + 4 q^{51} - 33 q^{52} - 6 q^{53} - 56 q^{54} + 6 q^{55} - 10 q^{56} + 14 q^{57} - 16 q^{59} - 3 q^{60} + 2 q^{61} - 24 q^{62} - 67 q^{63} + 11 q^{64} - 35 q^{65} + q^{66} + 9 q^{67} - 5 q^{68} + 47 q^{69} + 69 q^{70} - 13 q^{71} - 22 q^{72} + 57 q^{73} + 33 q^{74} + q^{75} + 26 q^{76} + 5 q^{77} + 5 q^{78} - 27 q^{79} - 10 q^{80} - 34 q^{81} - 55 q^{82} + 10 q^{83} - 35 q^{84} - 40 q^{85} + 4 q^{86} + 3 q^{88} + 80 q^{89} - 64 q^{90} - 38 q^{91} - 58 q^{92} + 17 q^{93} + 8 q^{94} - 7 q^{95} + 8 q^{96} - 20 q^{97} + 78 q^{98} - 9 q^{99}+O(q^{100}) \) 18 * q + 3 * q^3 + 12 * q^4 - 6 * q^5 - q^6 - 5 * q^7 - 3 * q^8 + 9 * q^9 + 5 * q^10 - 18 * q^11 + 3 * q^12 - 15 * q^13 - 12 * q^14 + 27 * q^15 + 4 * q^16 - 6 * q^17 + 12 * q^18 - 11 * q^19 - 18 * q^20 - 6 * q^21 - 20 * q^23 - 3 * q^24 - 4 * q^25 + 10 * q^26 - 6 * q^27 - 6 * q^28 - 19 * q^30 + 8 * q^31 + 24 * q^32 - 3 * q^33 - 22 * q^34 + 22 * q^35 + 17 * q^36 - 9 * q^37 - 3 * q^38 + 8 * q^39 + 36 * q^40 - 3 * q^41 + 28 * q^42 - 13 * q^43 - 12 * q^44 - q^45 - 37 * q^46 + q^47 - 46 * q^48 - 23 * q^49 - 34 * q^50 + 4 * q^51 - 33 * q^52 - 6 * q^53 - 56 * q^54 + 6 * q^55 - 10 * q^56 + 14 * q^57 - 16 * q^59 - 3 * q^60 + 2 * q^61 - 24 * q^62 - 67 * q^63 + 11 * q^64 - 35 * q^65 + q^66 + 9 * q^67 - 5 * q^68 + 47 * q^69 + 69 * q^70 - 13 * q^71 - 22 * q^72 + 57 * q^73 + 33 * q^74 + q^75 + 26 * q^76 + 5 * q^77 + 5 * q^78 - 27 * q^79 - 10 * q^80 - 34 * q^81 - 55 * q^82 + 10 * q^83 - 35 * q^84 - 40 * q^85 + 4 * q^86 + 3 * q^88 + 80 * q^89 - 64 * q^90 - 38 * q^91 - 58 * q^92 + 17 * q^93 + 8 * q^94 - 7 * q^95 + 8 * q^96 - 20 * q^97 + 78 * q^98 - 9 * 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 $

$2$	2.63004	1.85972	0.929860	−	0.367915i	$-0.119928\pi$
$2$	2.63004	1.85972	0.929860	+	0.367915i	$0.119928\pi$
$3$	−1.94297	−1.12177	−0.560887	−	0.827892i	$-0.689540\pi$
$3$	−1.94297	−1.12177	−0.560887	+	0.827892i	$0.689540\pi$
$4$	4.91711	2.45856
$5$	1.09435	0.489408	0.244704	−	0.969598i	$-0.421309\pi$
$5$	1.09435	0.489408	0.244704	+	0.969598i	$0.421309\pi$
$6$	−5.11009	−2.08618
$7$	1.26974	0.479916	0.239958	−	0.970783i	$-0.422866\pi$
$7$	1.26974	0.479916	0.239958	+	0.970783i	$0.422866\pi$
$8$	7.67212	2.71250
$9$	0.775130	0.258377
$10$	2.87818	0.910161
$11$	−1.00000	−0.301511
$11$	−1.00000	−0.301511
$12$	−9.55380	−2.75794
$13$	−3.69578	−1.02503	−0.512513	−	0.858680i	$-0.671285\pi$
$13$	−3.69578	−1.02503	−0.512513	+	0.858680i	$0.671285\pi$
$14$	3.33946	0.892508
$15$	−2.12629	−0.549005
$16$	10.3438	2.58594
$17$	−2.57992	−0.625722	−0.312861	−	0.949799i	$-0.601287\pi$
$17$	−2.57992	−0.625722	−0.312861	+	0.949799i	$0.601287\pi$
$18$	2.03862	0.480508
$19$	−0.269398	−0.0618042	−0.0309021	−	0.999522i	$-0.509838\pi$
$19$	−0.269398	−0.0618042	−0.0309021	+	0.999522i	$0.509838\pi$
$20$	5.38104	1.20324
$21$	−2.46706	−0.538357
$22$	−2.63004	−0.560726
$23$	−6.80128	−1.41816	−0.709082	−	0.705126i	$-0.750890\pi$
$23$	−6.80128	−1.41816	−0.709082	+	0.705126i	$0.750890\pi$
$24$	−14.9067	−3.04282
$25$	−3.80240	−0.760480
$26$	−9.72006	−1.90626
$27$	4.32285	0.831934
$28$	6.24344	1.17990
$29$	0	0
$29$	0	0
$30$	−5.59222	−1.02100
$31$	−2.38168	−0.427763	−0.213881	−	0.976860i	$-0.568611\pi$
$31$	−2.38168	−0.427763	−0.213881	+	0.976860i	$0.568611\pi$
$32$	11.8603	2.09662
$33$	1.94297	0.338228
$34$	−6.78528	−1.16367
$35$	1.38954	0.234874
$36$	3.81140	0.635234
$37$	7.13754	1.17341	0.586703	−	0.809803i	$-0.300426\pi$
$37$	7.13754	1.17341	0.586703	+	0.809803i	$0.300426\pi$
$38$	−0.708528	−0.114938
$39$	7.18079	1.14985
$40$	8.39598	1.32752
$41$	−11.8922	−1.85726	−0.928628	−	0.371012i	$-0.879011\pi$
$41$	−11.8922	−1.85726	−0.928628	+	0.371012i	$0.879011\pi$
$42$	−6.48847	−1.00119
$43$	−9.98237	−1.52230	−0.761148	−	0.648578i	$-0.775364\pi$
$43$	−9.98237	−1.52230	−0.761148	+	0.648578i	$0.775364\pi$
$44$	−4.91711	−0.741282
$45$	0.848263	0.126452
$46$	−17.8876	−2.63739
$47$	1.22043	0.178018	0.0890092	−	0.996031i	$-0.471630\pi$
$47$	1.22043	0.178018	0.0890092	+	0.996031i	$0.471630\pi$
$48$	−20.0976	−2.90084
$49$	−5.38777	−0.769681
$50$	−10.0005	−1.41428
$51$	5.01270	0.701918
$52$	−18.1726	−2.52008
$53$	−2.44507	−0.335856	−0.167928	−	0.985799i	$-0.553708\pi$
$53$	−2.44507	−0.335856	−0.167928	+	0.985799i	$0.553708\pi$
$54$	11.3693	1.54716
$55$	−1.09435	−0.147562
$56$	9.74157	1.30177
$57$	0.523432	0.0693303
$58$	0	0
$59$	−4.34619	−0.565825	−0.282913	−	0.959146i	$-0.591301\pi$
$59$	−4.34619	−0.565825	−0.282913	+	0.959146i	$0.591301\pi$
$60$	−10.4552	−1.34976
$61$	9.65118	1.23571	0.617853	−	0.786293i	$-0.288003\pi$
$61$	9.65118	1.23571	0.617853	+	0.786293i	$0.288003\pi$
$62$	−6.26392	−0.795519
$63$	0.984212	0.123999
$64$	10.5054	1.31318
$65$	−4.04448	−0.501656
$66$	5.11009	0.629008
$67$	11.7749	1.43853	0.719265	−	0.694736i	$-0.244479\pi$
$67$	11.7749	1.43853	0.719265	+	0.694736i	$0.244479\pi$
$68$	−12.6857	−1.53837
$69$	13.2147	1.59086
$70$	3.65454	0.436801
$71$	−15.2531	−1.81021	−0.905103	−	0.425192i	$-0.860207\pi$
$71$	−15.2531	−1.81021	−0.905103	+	0.425192i	$0.860207\pi$
$72$	5.94689	0.700848
$73$	7.49764	0.877533	0.438766	−	0.898601i	$-0.355416\pi$
$73$	7.49764	0.877533	0.438766	+	0.898601i	$0.355416\pi$
$74$	18.7720	2.18220
$75$	7.38795	0.853087
$76$	−1.32466	−0.151949
$77$	−1.26974	−0.144700
$78$	18.8858	2.13839
$79$	−0.916642	−0.103130	−0.0515651	−	0.998670i	$-0.516421\pi$
$79$	−0.916642	−0.103130	−0.0515651	+	0.998670i	$0.516421\pi$
$80$	11.3197	1.26558
$81$	−10.7246	−1.19162
$82$	−31.2771	−3.45397
$83$	−0.114200	−0.0125350	−0.00626752	−	0.999980i	$-0.501995\pi$
$83$	−0.114200	−0.0125350	−0.00626752	+	0.999980i	$0.501995\pi$
$84$	−12.1308	−1.32358
$85$	−2.82333	−0.306233
$86$	−26.2540	−2.83104
$87$	0	0
$88$	−7.67212	−0.817850
$89$	−1.64850	−0.174740	−0.0873701	−	0.996176i	$-0.527846\pi$
$89$	−1.64850	−0.174740	−0.0873701	+	0.996176i	$0.527846\pi$
$90$	2.23097	0.235164
$91$	−4.69267	−0.491926
$92$	−33.4426	−3.48664
$93$	4.62754	0.479853
$94$	3.20979	0.331064
$95$	−0.294816	−0.0302474
$96$	−23.0441	−2.35193
$97$	−14.8211	−1.50485	−0.752426	−	0.658677i	$-0.771116\pi$
$97$	−14.8211	−1.50485	−0.752426	+	0.658677i	$0.771116\pi$
$98$	−14.1700	−1.43139
$99$	−0.775130	−0.0779035
$100$	−18.6968	−1.86968
$101$	4.22213	0.420118	0.210059	−	0.977689i	$-0.432634\pi$
$101$	4.22213	0.420118	0.210059	+	0.977689i	$0.432634\pi$
$102$	13.1836	1.30537
$103$	−8.17641	−0.805646	−0.402823	−	0.915278i	$-0.631971\pi$
$103$	−8.17641	−0.805646	−0.402823	+	0.915278i	$0.631971\pi$
$104$	−28.3545	−2.78038
$105$	−2.69983	−0.263476
$106$	−6.43063	−0.624598
$107$	15.9501	1.54196	0.770978	−	0.636862i	$-0.219768\pi$
$107$	15.9501	1.54196	0.770978	+	0.636862i	$0.219768\pi$
$108$	21.2559	2.04535
$109$	−4.25260	−0.407325	−0.203663	−	0.979041i	$-0.565285\pi$
$109$	−4.25260	−0.407325	−0.203663	+	0.979041i	$0.565285\pi$
$110$	−2.87818	−0.274424
$111$	−13.8680	−1.31630
$112$	13.1338	1.24103
$113$	−7.91563	−0.744640	−0.372320	−	0.928104i	$-0.621438\pi$
$113$	−7.91563	−0.744640	−0.372320	+	0.928104i	$0.621438\pi$
$114$	1.37665	0.128935
$115$	−7.44297	−0.694061
$116$	0	0
$117$	−2.86471	−0.264843
$118$	−11.4306	−1.05228
$119$	−3.27582	−0.300294
$120$	−16.3131	−1.48918
$121$	1.00000	0.0909091
$122$	25.3830	2.29807
$123$	23.1063	2.08342
$124$	−11.7110	−1.05168
$125$	−9.63290	−0.861593
$126$	2.58852	0.230603
$127$	6.48707	0.575635	0.287817	−	0.957685i	$-0.407070\pi$
$127$	6.48707	0.575635	0.287817	+	0.957685i	$0.407070\pi$
$128$	3.90920	0.345527
$129$	19.3954	1.70767
$130$	−10.6371	−0.932939
$131$	14.4429	1.26188	0.630941	−	0.775831i	$-0.282669\pi$
$131$	14.4429	1.26188	0.630941	+	0.775831i	$0.282669\pi$
$132$	9.55380	0.831551
$133$	−0.342065	−0.0296608
$134$	30.9684	2.67526
$135$	4.73071	0.407155
$136$	−19.7934	−1.69727
$137$	11.8010	1.00823	0.504115	−	0.863637i	$-0.331819\pi$
$137$	11.8010	1.00823	0.504115	+	0.863637i	$0.331819\pi$
$138$	34.7551	2.95855
$139$	2.77478	0.235354	0.117677	−	0.993052i	$-0.462455\pi$
$139$	2.77478	0.235354	0.117677	+	0.993052i	$0.462455\pi$
$140$	6.83250	0.577452
$141$	−2.37126	−0.199696
$142$	−40.1162	−3.36648
$143$	3.69578	0.309057
$144$	8.01776	0.668146
$145$	0	0
$146$	19.7191	1.63196
$147$	10.4683	0.863408
$148$	35.0961	2.88488
$149$	23.6557	1.93795	0.968974	−	0.247163i	$-0.0794982\pi$
$149$	23.6557	1.93795	0.968974	+	0.247163i	$0.0794982\pi$
$150$	19.4306	1.58650
$151$	−7.73738	−0.629659	−0.314830	−	0.949148i	$-0.601947\pi$
$151$	−7.73738	−0.629659	−0.314830	+	0.949148i	$0.601947\pi$
$152$	−2.06685	−0.167644
$153$	−1.99977	−0.161672
$154$	−3.33946	−0.269101
$155$	−2.60639	−0.209350
$156$	35.3087	2.82696
$157$	−0.787207	−0.0628259	−0.0314130	−	0.999506i	$-0.510001\pi$
$157$	−0.787207	−0.0628259	−0.0314130	+	0.999506i	$0.510001\pi$
$158$	−2.41080	−0.191793
$159$	4.75070	0.376755
$160$	12.9793	1.02610
$161$	−8.63584	−0.680599
$162$	−28.2060	−2.21608
$163$	−18.2609	−1.43030	−0.715152	−	0.698969i	$-0.753642\pi$
$163$	−18.2609	−1.43030	−0.715152	+	0.698969i	$0.753642\pi$
$164$	−58.4755	−4.56617
$165$	2.12629	0.165531
$166$	−0.300350	−0.0233117
$167$	−25.2573	−1.95446	−0.977232	−	0.212172i	$-0.931946\pi$
$167$	−25.2573	−1.95446	−0.977232	+	0.212172i	$0.931946\pi$
$168$	−18.9276	−1.46029
$169$	0.658807	0.0506775
$170$	−7.42547	−0.569507
$171$	−0.208819	−0.0159688
$172$	−49.0844	−3.74265
$173$	2.56544	0.195046	0.0975232	−	0.995233i	$-0.468908\pi$
$173$	2.56544	0.195046	0.0975232	+	0.995233i	$0.468908\pi$
$174$	0	0
$175$	−4.82805	−0.364966
$176$	−10.3438	−0.779690
$177$	8.44451	0.634728
$178$	−4.33561	−0.324968
$179$	21.7011	1.62202	0.811008	−	0.585035i	$-0.198919\pi$
$179$	21.7011	1.62202	0.811008	+	0.585035i	$0.198919\pi$
$180$	4.17100	0.310888
$181$	−8.68091	−0.645247	−0.322624	−	0.946527i	$-0.604565\pi$
$181$	−8.68091	−0.645247	−0.322624	+	0.946527i	$0.604565\pi$
$182$	−12.3419	−0.914844
$183$	−18.7519	−1.38618
$184$	−52.1802	−3.84678
$185$	7.81097	0.574274
$186$	12.1706	0.892392
$187$	2.57992	0.188662
$188$	6.00100	0.437668
$189$	5.48889	0.399258
$190$	−0.775377	−0.0562517
$191$	24.9437	1.80486	0.902432	−	0.430833i	$-0.141780\pi$
$191$	24.9437	1.80486	0.902432	+	0.430833i	$0.141780\pi$
$192$	−20.4117	−1.47309
$193$	22.5682	1.62449	0.812247	−	0.583313i	$-0.198244\pi$
$193$	22.5682	1.62449	0.812247	+	0.583313i	$0.198244\pi$
$194$	−38.9800	−2.79860
$195$	7.85829	0.562744
$196$	−26.4922	−1.89230
$197$	14.4869	1.03215	0.516075	−	0.856544i	$-0.327393\pi$
$197$	14.4869	1.03215	0.516075	+	0.856544i	$0.327393\pi$
$198$	−2.03862	−0.144879
$199$	−15.7427	−1.11597	−0.557987	−	0.829850i	$-0.688426\pi$
$199$	−15.7427	−1.11597	−0.557987	+	0.829850i	$0.688426\pi$
$200$	−29.1725	−2.06280
$201$	−22.8782	−1.61371
$202$	11.1044	0.781301
$203$	0	0
$204$	24.6480	1.72570
$205$	−13.0143	−0.908956
$206$	−21.5043	−1.49827
$207$	−5.27188	−0.366421
$208$	−38.2283	−2.65065
$209$	0.269398	0.0186347
$210$	−7.10065	−0.489991
$211$	11.5330	0.793963	0.396981	−	0.917827i	$-0.370058\pi$
$211$	11.5330	0.793963	0.396981	+	0.917827i	$0.370058\pi$
$212$	−12.0227	−0.825721
$213$	29.6363	2.03064
$214$	41.9494	2.86760
$215$	−10.9242	−0.745024
$216$	33.1654	2.25662
$217$	−3.02411	−0.205290
$218$	−11.1845	−0.757511
$219$	−14.5677	−0.984393
$220$	−5.38104	−0.362789
$221$	9.53481	0.641381
$222$	−36.4735	−2.44794
$223$	−24.5074	−1.64114	−0.820570	−	0.571546i	$-0.806344\pi$
$223$	−24.5074	−1.64114	−0.820570	+	0.571546i	$0.806344\pi$
$224$	15.0594	1.00620
$225$	−2.94736	−0.196490
$226$	−20.8184	−1.38482
$227$	2.36805	0.157173	0.0785864	−	0.996907i	$-0.474959\pi$
$227$	2.36805	0.157173	0.0785864	+	0.996907i	$0.474959\pi$
$228$	2.57377	0.170452
$229$	19.8461	1.31147	0.655735	−	0.754991i	$-0.272359\pi$
$229$	19.8461	1.31147	0.655735	+	0.754991i	$0.272359\pi$
$230$	−19.5753	−1.29076
$231$	2.46706	0.162321
$232$	0	0
$233$	18.1775	1.19085	0.595424	−	0.803411i	$-0.296984\pi$
$233$	18.1775	1.19085	0.595424	+	0.803411i	$0.296984\pi$
$234$	−7.53431	−0.492533
$235$	1.33558	0.0871236
$236$	−21.3707	−1.39111
$237$	1.78101	0.115689
$238$	−8.61553	−0.558462
$239$	−16.1630	−1.04549	−0.522747	−	0.852488i	$-0.675093\pi$
$239$	−16.1630	−1.04549	−0.522747	+	0.852488i	$0.675093\pi$
$240$	−21.9938	−1.41969
$241$	2.63452	0.169705	0.0848523	−	0.996394i	$-0.472958\pi$
$241$	2.63452	0.169705	0.0848523	+	0.996394i	$0.472958\pi$
$242$	2.63004	0.169065
$243$	7.86894	0.504793
$244$	47.4559	3.03805
$245$	−5.89610	−0.376688
$246$	60.7704	3.87458
$247$	0.995637	0.0633508
$248$	−18.2725	−1.16031
$249$	0.221887	0.0140615
$250$	−25.3349	−1.60232
$251$	−9.42849	−0.595121	−0.297560	−	0.954703i	$-0.596173\pi$
$251$	−9.42849	−0.595121	−0.297560	+	0.954703i	$0.596173\pi$
$252$	4.83948	0.304858
$253$	6.80128	0.427593
$254$	17.0613	1.07052
$255$	5.48564	0.343524
$256$	−10.7295	−0.670595
$257$	−5.69662	−0.355346	−0.177673	−	0.984090i	$-0.556857\pi$
$257$	−5.69662	−0.355346	−0.177673	+	0.984090i	$0.556857\pi$
$258$	51.0108	3.17579
$259$	9.06281	0.563135
$260$	−19.8871	−1.23335
$261$	0	0
$262$	37.9854	2.34675
$263$	−12.1320	−0.748093	−0.374047	−	0.927410i	$-0.622030\pi$
$263$	−12.1320	−0.748093	−0.374047	+	0.927410i	$0.622030\pi$
$264$	14.9067	0.917443
$265$	−2.67576	−0.164371
$266$	−0.899644	−0.0551607
$267$	3.20298	0.196019
$268$	57.8984	3.53671
$269$	12.3180	0.751044	0.375522	−	0.926814i	$-0.377463\pi$
$269$	12.3180	0.751044	0.375522	+	0.926814i	$0.377463\pi$
$270$	12.4420	0.757194
$271$	29.3582	1.78339	0.891693	−	0.452642i	$-0.149518\pi$
$271$	29.3582	1.78339	0.891693	+	0.452642i	$0.149518\pi$
$272$	−26.6860	−1.61808
$273$	9.11772	0.551830
$274$	31.0372	1.87502
$275$	3.80240	0.229293
$276$	64.9780	3.91122
$277$	−9.59940	−0.576772	−0.288386	−	0.957514i	$-0.593119\pi$
$277$	−9.59940	−0.576772	−0.288386	+	0.957514i	$0.593119\pi$
$278$	7.29778	0.437692
$279$	−1.84611	−0.110524
$280$	10.6607	0.637098
$281$	−17.5224	−1.04530	−0.522651	−	0.852547i	$-0.675057\pi$
$281$	−17.5224	−1.04530	−0.522651	+	0.852547i	$0.675057\pi$
$282$	−6.23652	−0.371379
$283$	−22.9751	−1.36573	−0.682865	−	0.730545i	$-0.739266\pi$
$283$	−22.9751	−1.36573	−0.682865	+	0.730545i	$0.739266\pi$
$284$	−75.0010	−4.45049
$285$	0.572818	0.0339308
$286$	9.72006	0.574759
$287$	−15.1000	−0.891326
$288$	9.19324	0.541717
$289$	−10.3440	−0.608473
$290$	0	0
$291$	28.7969	1.68810
$292$	36.8667	2.15746
$293$	−24.6305	−1.43893	−0.719465	−	0.694529i	$-0.755613\pi$
$293$	−24.6305	−1.43893	−0.719465	+	0.694529i	$0.755613\pi$
$294$	27.5320	1.60570
$295$	−4.75625	−0.276919
$296$	54.7601	3.18286
$297$	−4.32285	−0.250837
$298$	62.2154	3.60404
$299$	25.1360	1.45365
$300$	36.3273	2.09736
$301$	−12.6750	−0.730574
$302$	−20.3496	−1.17099
$303$	−8.20348	−0.471277
$304$	−2.78659	−0.159822
$305$	10.5618	0.604765
$306$	−5.25948	−0.300664
$307$	17.8980	1.02149	0.510746	−	0.859732i	$-0.329369\pi$
$307$	17.8980	1.02149	0.510746	+	0.859732i	$0.329369\pi$
$308$	−6.24344	−0.355753
$309$	15.8865	0.903752
$310$	−6.85492	−0.389333
$311$	13.0912	0.742336	0.371168	−	0.928566i	$-0.378957\pi$
$311$	13.0912	0.742336	0.371168	+	0.928566i	$0.378957\pi$
$312$	55.0919	3.11896
$313$	−28.8939	−1.63318	−0.816590	−	0.577218i	$-0.804138\pi$
$313$	−28.8939	−1.63318	−0.816590	+	0.577218i	$0.804138\pi$
$314$	−2.07038	−0.116839
$315$	1.07707	0.0606861
$316$	−4.50723	−0.253551
$317$	−20.2673	−1.13832	−0.569161	−	0.822226i	$-0.692732\pi$
$317$	−20.2673	−1.13832	−0.569161	+	0.822226i	$0.692732\pi$
$318$	12.4945	0.700658
$319$	0	0
$320$	11.4966	0.642680
$321$	−30.9906	−1.72973
$322$	−22.7126	−1.26572
$323$	0.695024	0.0386722
$324$	−52.7339	−2.92966
$325$	14.0528	0.779511
$326$	−48.0269	−2.65996
$327$	8.26267	0.456927
$328$	−91.2387	−5.03781
$329$	1.54963	0.0854338
$330$	5.59222	0.307842
$331$	−11.5815	−0.636577	−0.318289	−	0.947994i	$-0.603108\pi$
$331$	−11.5815	−0.636577	−0.318289	+	0.947994i	$0.603108\pi$
$332$	−0.561532	−0.0308181
$333$	5.53253	0.303181
$334$	−66.4276	−3.63476
$335$	12.8858	0.704028
$336$	−25.5187	−1.39216
$337$	−15.4614	−0.842237	−0.421118	−	0.907006i	$-0.638362\pi$
$337$	−15.4614	−0.842237	−0.421118	+	0.907006i	$0.638362\pi$
$338$	1.73269	0.0942459
$339$	15.3798	0.835318
$340$	−13.8826	−0.752891
$341$	2.38168	0.128975
$342$	−0.549201	−0.0296974
$343$	−15.7292	−0.849298
$344$	−76.5859	−4.12923
$345$	14.4615	0.778579
$346$	6.74720	0.362732
$347$	18.1484	0.974256	0.487128	−	0.873331i	$-0.338044\pi$
$347$	18.1484	0.974256	0.487128	+	0.873331i	$0.338044\pi$
$348$	0	0
$349$	−32.1067	−1.71863	−0.859317	−	0.511444i	$-0.829111\pi$
$349$	−32.1067	−1.71863	−0.859317	+	0.511444i	$0.829111\pi$
$350$	−12.6980	−0.678735
$351$	−15.9763	−0.852753
$352$	−11.8603	−0.632154
$353$	−2.39400	−0.127420	−0.0637098	−	0.997968i	$-0.520293\pi$
$353$	−2.39400	−0.127420	−0.0637098	+	0.997968i	$0.520293\pi$
$354$	22.2094	1.18042
$355$	−16.6922	−0.885929
$356$	−8.10584	−0.429609
$357$	6.36481	0.336861
$358$	57.0747	3.01649
$359$	4.44937	0.234829	0.117414	−	0.993083i	$-0.462539\pi$
$359$	4.44937	0.234829	0.117414	+	0.993083i	$0.462539\pi$
$360$	6.50797	0.343000
$361$	−18.9274	−0.996180
$362$	−22.8312	−1.19998
$363$	−1.94297	−0.101979
$364$	−23.0744	−1.20943
$365$	8.20504	0.429471
$366$	−49.3184	−2.57791
$367$	22.6247	1.18100	0.590500	−	0.807038i	$-0.298931\pi$
$367$	22.6247	1.18100	0.590500	+	0.807038i	$0.298931\pi$
$368$	−70.3507	−3.66729
$369$	−9.21804	−0.479872
$370$	20.5432	1.06799
$371$	−3.10460	−0.161183
$372$	22.7541	1.17975
$373$	7.80426	0.404089	0.202045	−	0.979376i	$-0.435241\pi$
$373$	7.80426	0.404089	0.202045	+	0.979376i	$0.435241\pi$
$374$	6.78528	0.350859
$375$	18.7164	0.966512
$376$	9.36331	0.482876
$377$	0	0
$378$	14.4360	0.742508
$379$	−18.4271	−0.946538	−0.473269	−	0.880918i	$-0.656926\pi$
$379$	−18.4271	−0.946538	−0.473269	+	0.880918i	$0.656926\pi$
$380$	−1.44964	−0.0743650
$381$	−12.6042	−0.645732
$382$	65.6030	3.35654
$383$	13.1264	0.670727	0.335363	−	0.942089i	$-0.391141\pi$
$383$	13.1264	0.670727	0.335363	+	0.942089i	$0.391141\pi$
$384$	−7.59545	−0.387604
$385$	−1.38954	−0.0708173
$386$	59.3553	3.02110
$387$	−7.73763	−0.393326
$388$	−72.8769	−3.69976
$389$	14.7934	0.750056	0.375028	−	0.927013i	$-0.377633\pi$
$389$	14.7934	0.750056	0.375028	+	0.927013i	$0.377633\pi$
$390$	20.6676	1.04655
$391$	17.5467	0.887376
$392$	−41.3356	−2.08776
$393$	−28.0621	−1.41555
$394$	38.1011	1.91951
$395$	−1.00313	−0.0504728
$396$	−3.81140	−0.191530
$397$	−16.9772	−0.852059	−0.426029	−	0.904709i	$-0.640088\pi$
$397$	−16.9772	−0.852059	−0.426029	+	0.904709i	$0.640088\pi$
$398$	−41.4040	−2.07540
$399$	0.664621	0.0332727
$400$	−39.3311	−1.96655
$401$	21.3775	1.06754	0.533772	−	0.845629i	$-0.320774\pi$
$401$	21.3775	1.06754	0.533772	+	0.845629i	$0.320774\pi$
$402$	−60.1706	−3.00104
$403$	8.80218	0.438468
$404$	20.7607	1.03288
$405$	−11.7364	−0.583187
$406$	0	0
$407$	−7.13754	−0.353795
$408$	38.4580	1.90395
$409$	−8.43445	−0.417056	−0.208528	−	0.978016i	$-0.566867\pi$
$409$	−8.43445	−0.417056	−0.208528	+	0.978016i	$0.566867\pi$
$410$	−34.2280	−1.69040
$411$	−22.9290	−1.13101
$412$	−40.2043	−1.98072
$413$	−5.51851	−0.271548
$414$	−13.8652	−0.681440
$415$	−0.124974	−0.00613475
$416$	−43.8329	−2.14909
$417$	−5.39131	−0.264014
$418$	0.708528	0.0346552
$419$	18.0735	0.882949	0.441475	−	0.897274i	$-0.354456\pi$
$419$	18.0735	0.882949	0.441475	+	0.897274i	$0.354456\pi$
$420$	−13.2753	−0.647770
$421$	−6.27051	−0.305606	−0.152803	−	0.988257i	$-0.548830\pi$
$421$	−6.27051	−0.305606	−0.152803	+	0.988257i	$0.548830\pi$
$422$	30.3322	1.47655
$423$	0.945995	0.0459958
$424$	−18.7589	−0.911011
$425$	9.80987	0.475849
$426$	77.9445	3.77643
$427$	12.2545	0.593035
$428$	78.4285	3.79098
$429$	−7.18079	−0.346692
$430$	−28.7311	−1.38554
$431$	−0.0961437	−0.00463108	−0.00231554	−	0.999997i	$-0.500737\pi$
$431$	−0.0961437	−0.00463108	−0.00231554	+	0.999997i	$0.500737\pi$
$432$	44.7145	2.15133
$433$	−17.7748	−0.854201	−0.427100	−	0.904204i	$-0.640465\pi$
$433$	−17.7748	−0.854201	−0.427100	+	0.904204i	$0.640465\pi$
$434$	−7.95353	−0.381782
$435$	0	0
$436$	−20.9105	−1.00143
$437$	1.83225	0.0876484
$438$	−38.3136	−1.83070
$439$	−7.21112	−0.344168	−0.172084	−	0.985082i	$-0.555050\pi$
$439$	−7.21112	−0.344168	−0.172084	+	0.985082i	$0.555050\pi$
$440$	−8.39598	−0.400262
$441$	−4.17622	−0.198868
$442$	25.0769	1.19279
$443$	−10.4748	−0.497673	−0.248837	−	0.968545i	$-0.580048\pi$
$443$	−10.4748	−0.497673	−0.248837	+	0.968545i	$0.580048\pi$
$444$	−68.1906	−3.23618
$445$	−1.80403	−0.0855193
$446$	−64.4556	−3.05206
$447$	−45.9622	−2.17394
$448$	13.3391	0.630215
$449$	32.3082	1.52472	0.762359	−	0.647155i	$-0.224041\pi$
$449$	32.3082	1.52472	0.762359	+	0.647155i	$0.224041\pi$
$450$	−7.75166	−0.365417
$451$	11.8922	0.559984
$452$	−38.9220	−1.83074
$453$	15.0335	0.706335
$454$	6.22806	0.292297
$455$	−5.13542	−0.240752
$456$	4.01583	0.188059
$457$	16.9656	0.793615	0.396808	−	0.917902i	$-0.370118\pi$
$457$	16.9656	0.793615	0.396808	+	0.917902i	$0.370118\pi$
$458$	52.1961	2.43897
$459$	−11.1526	−0.520559
$460$	−36.5979	−1.70639
$461$	−11.8684	−0.552768	−0.276384	−	0.961047i	$-0.589136\pi$
$461$	−11.8684	−0.552768	−0.276384	+	0.961047i	$0.589136\pi$
$462$	6.48847	0.301871
$463$	40.1293	1.86497	0.932484	−	0.361212i	$-0.117637\pi$
$463$	40.1293	1.86497	0.932484	+	0.361212i	$0.117637\pi$
$464$	0	0
$465$	5.06414	0.234844
$466$	47.8076	2.21464
$467$	2.53162	0.117149	0.0585746	−	0.998283i	$-0.481344\pi$
$467$	2.53162	0.117149	0.0585746	+	0.998283i	$0.481344\pi$
$468$	−14.0861	−0.651131
$469$	14.9510	0.690373
$470$	3.51263	0.162026
$471$	1.52952	0.0704765
$472$	−33.3444	−1.53480
$473$	9.98237	0.458990
$474$	4.68412	0.215149
$475$	1.02436	0.0470008
$476$	−16.1075	−0.738288
$477$	−1.89525	−0.0867775
$478$	−42.5092	−1.94433
$479$	1.17720	0.0537877	0.0268939	−	0.999638i	$-0.491438\pi$
$479$	1.17720	0.0537877	0.0268939	+	0.999638i	$0.491438\pi$
$480$	−25.2183	−1.15105
$481$	−26.3788	−1.20277
$482$	6.92890	0.315603
$483$	16.7792	0.763478
$484$	4.91711	0.223505
$485$	−16.2194	−0.736486
$486$	20.6956	0.938772
$487$	16.8572	0.763871	0.381936	−	0.924189i	$-0.375258\pi$
$487$	16.8572	0.763871	0.381936	+	0.924189i	$0.375258\pi$
$488$	74.0450	3.35186
$489$	35.4804	1.60448
$490$	−15.5070	−0.700534
$491$	−13.9123	−0.627855	−0.313927	−	0.949447i	$-0.601645\pi$
$491$	−13.9123	−0.627855	−0.313927	+	0.949447i	$0.601645\pi$
$492$	113.616	5.12221
$493$	0	0
$494$	2.61856	0.117815
$495$	−0.848263	−0.0381266
$496$	−24.6355	−1.10617
$497$	−19.3674	−0.868746
$498$	0.583570	0.0261504
$499$	10.5963	0.474357	0.237179	−	0.971466i	$-0.423777\pi$
$499$	10.5963	0.474357	0.237179	+	0.971466i	$0.423777\pi$
$500$	−47.3660	−2.11827
$501$	49.0741	2.19247
$502$	−24.7973	−1.10676
$503$	−36.1345	−1.61116	−0.805578	−	0.592490i	$-0.798145\pi$
$503$	−36.1345	−1.61116	−0.805578	+	0.592490i	$0.798145\pi$
$504$	7.55099	0.336348
$505$	4.62049	0.205609
$506$	17.8876	0.795202
$507$	−1.28004	−0.0568487
$508$	31.8977	1.41523
$509$	−33.2864	−1.47539	−0.737696	−	0.675133i	$-0.764086\pi$
$509$	−33.2864	−1.47539	−0.737696	+	0.675133i	$0.764086\pi$
$510$	14.4275	0.638859
$511$	9.52004	0.421142
$512$	−36.0375	−1.59265
$513$	−1.16457	−0.0514170
$514$	−14.9823	−0.660843
$515$	−8.94785	−0.394289
$516$	95.3695	4.19841
$517$	−1.22043	−0.0536746
$518$	23.8355	1.04727
$519$	−4.98456	−0.218798
$520$	−31.0297	−1.36074
$521$	−33.3750	−1.46218	−0.731092	−	0.682279i	$-0.760989\pi$
$521$	−33.3750	−1.46218	−0.731092	+	0.682279i	$0.760989\pi$
$522$	0	0
$523$	−35.5447	−1.55426	−0.777131	−	0.629339i	$-0.783326\pi$
$523$	−35.5447	−1.55426	−0.777131	+	0.629339i	$0.783326\pi$
$524$	71.0174	3.10241
$525$	9.38075	0.409410
$526$	−31.9077	−1.39124
$527$	6.14454	0.267660
$528$	20.0976	0.874636
$529$	23.2574	1.01119
$530$	−7.03736	−0.305683
$531$	−3.36886	−0.146196
$532$	−1.68197	−0.0729227
$533$	43.9511	1.90373
$534$	8.42396	0.364540
$535$	17.4550	0.754645
$536$	90.3382	3.90202
$537$	−42.1646	−1.81953
$538$	32.3969	1.39673
$539$	5.38777	0.232068
$540$	23.2614	1.00101
$541$	12.0536	0.518224	0.259112	−	0.965847i	$-0.416570\pi$
$541$	12.0536	0.518224	0.259112	+	0.965847i	$0.416570\pi$
$542$	77.2133	3.31660
$543$	16.8668	0.723822
$544$	−30.5985	−1.31190
$545$	−4.65383	−0.199348
$546$	23.9800	1.02625
$547$	7.20691	0.308145	0.154073	−	0.988060i	$-0.450761\pi$
$547$	7.20691	0.308145	0.154073	+	0.988060i	$0.450761\pi$
$548$	58.0269	2.47879
$549$	7.48092	0.319278
$550$	10.0005	0.426421
$551$	0	0
$552$	101.385	4.31521
$553$	−1.16389	−0.0494938
$554$	−25.2468	−1.07263
$555$	−15.1765	−0.644205
$556$	13.6439	0.578630
$557$	8.75714	0.371052	0.185526	−	0.982639i	$-0.440601\pi$
$557$	8.75714	0.371052	0.185526	+	0.982639i	$0.440601\pi$
$558$	−4.85535	−0.205544
$559$	36.8926	1.56039
$560$	14.3730	0.607371
$561$	−5.01270	−0.211636
$562$	−46.0847	−1.94397
$563$	38.1309	1.60702	0.803512	−	0.595288i	$-0.202962\pi$
$563$	38.1309	1.60702	0.803512	+	0.595288i	$0.202962\pi$
$564$	−11.6598	−0.490965
$565$	−8.66246	−0.364433
$566$	−60.4255	−2.53987
$567$	−13.6174	−0.571876
$568$	−117.023	−4.91019
$569$	−1.46170	−0.0612775	−0.0306388	−	0.999531i	$-0.509754\pi$
$569$	−1.46170	−0.0612775	−0.0306388	+	0.999531i	$0.509754\pi$
$570$	1.50653	0.0631017
$571$	−28.7352	−1.20253	−0.601266	−	0.799049i	$-0.705337\pi$
$571$	−28.7352	−1.20253	−0.601266	+	0.799049i	$0.705337\pi$
$572$	18.1726	0.759833
$573$	−48.4649	−2.02465
$574$	−39.7137	−1.65762
$575$	25.8612	1.07849
$576$	8.14308	0.339295
$577$	−26.2111	−1.09118	−0.545591	−	0.838052i	$-0.683695\pi$
$577$	−26.2111	−1.09118	−0.545591	+	0.838052i	$0.683695\pi$
$578$	−27.2052	−1.13159
$579$	−43.8493	−1.82232
$580$	0	0
$581$	−0.145004	−0.00601576
$582$	75.7370	3.13940
$583$	2.44507	0.101264
$584$	57.5228	2.38031
$585$	−3.13500	−0.129616
$586$	−64.7792	−2.67601
$587$	9.60542	0.396458	0.198229	−	0.980156i	$-0.436481\pi$
$587$	9.60542	0.396458	0.198229	+	0.980156i	$0.436481\pi$
$588$	51.4736	2.12274
$589$	0.641621	0.0264375
$590$	−12.5091	−0.514992
$591$	−28.1476	−1.15784
$592$	73.8290	3.03435
$593$	−22.5880	−0.927577	−0.463788	−	0.885946i	$-0.653510\pi$
$593$	−22.5880	−0.927577	−0.463788	+	0.885946i	$0.653510\pi$
$594$	−11.3693	−0.466487
$595$	−3.58489	−0.146966
$596$	116.318	4.76455
$597$	30.5877	1.25187
$598$	66.1088	2.70339
$599$	−13.4573	−0.549852	−0.274926	−	0.961465i	$-0.588653\pi$
$599$	−13.4573	−0.549852	−0.274926	+	0.961465i	$0.588653\pi$
$600$	56.6812	2.31400
$601$	0.709481	0.0289404	0.0144702	−	0.999895i	$-0.495394\pi$
$601$	0.709481	0.0289404	0.0144702	+	0.999895i	$0.495394\pi$
$602$	−33.3357	−1.35866
$603$	9.12706	0.371683
$604$	−38.0456	−1.54805
$605$	1.09435	0.0444916
$606$	−21.5755	−0.876444
$607$	30.9004	1.25421	0.627104	−	0.778935i	$-0.284240\pi$
$607$	30.9004	1.25421	0.627104	+	0.778935i	$0.284240\pi$
$608$	−3.19513	−0.129580
$609$	0	0
$610$	27.7779	1.12469
$611$	−4.51046	−0.182474
$612$	−9.83309	−0.397479
$613$	−13.7778	−0.556481	−0.278240	−	0.960511i	$-0.589751\pi$
$613$	−13.7778	−0.556481	−0.278240	+	0.960511i	$0.589751\pi$
$614$	47.0724	1.89969
$615$	25.2863	1.01964
$616$	−9.74157	−0.392499
$617$	37.6446	1.51551	0.757757	−	0.652537i	$-0.226295\pi$
$617$	37.6446	1.51551	0.757757	+	0.652537i	$0.226295\pi$
$618$	41.7822	1.68073
$619$	8.72451	0.350668	0.175334	−	0.984509i	$-0.443900\pi$
$619$	8.72451	0.350668	0.175334	+	0.984509i	$0.443900\pi$
$620$	−12.8159	−0.514700
$621$	−29.4009	−1.17982
$622$	34.4305	1.38054
$623$	−2.09316	−0.0838606
$624$	74.2763	2.97343
$625$	8.47024	0.338810
$626$	−75.9921	−3.03726
$627$	−0.523432	−0.0209039
$628$	−3.87078	−0.154461
$629$	−18.4143	−0.734225
$630$	2.83274	0.112859
$631$	14.8662	0.591814	0.295907	−	0.955217i	$-0.404378\pi$
$631$	14.8662	0.591814	0.295907	+	0.955217i	$0.404378\pi$
$632$	−7.03258	−0.279741
$633$	−22.4082	−0.890647
$634$	−53.3037	−2.11696
$635$	7.09912	0.281720
$636$	23.3597	0.926272
$637$	19.9120	0.788943
$638$	0	0
$639$	−11.8231	−0.467715
$640$	4.27802	0.169104
$641$	−30.7088	−1.21293	−0.606463	−	0.795112i	$-0.707412\pi$
$641$	−30.7088	−1.21293	−0.606463	+	0.795112i	$0.707412\pi$
$642$	−81.5065	−3.21680
$643$	16.0992	0.634889	0.317444	−	0.948277i	$-0.397175\pi$
$643$	16.0992	0.634889	0.317444	+	0.948277i	$0.397175\pi$
$644$	−42.4634	−1.67329
$645$	21.2254	0.835748
$646$	1.82794	0.0719194
$647$	6.67293	0.262340	0.131170	−	0.991360i	$-0.458127\pi$
$647$	6.67293	0.262340	0.131170	+	0.991360i	$0.458127\pi$
$648$	−82.2801	−3.23227
$649$	4.34619	0.170603
$650$	36.9595	1.44967
$651$	5.87575	0.230289
$652$	−89.7908	−3.51648
$653$	−14.7352	−0.576634	−0.288317	−	0.957535i	$-0.593096\pi$
$653$	−14.7352	−0.576634	−0.288317	+	0.957535i	$0.593096\pi$
$654$	21.7312	0.849756
$655$	15.8056	0.617575
$656$	−123.010	−4.80275
$657$	5.81165	0.226734
$658$	4.07559	0.158883
$659$	−24.4889	−0.953952	−0.476976	−	0.878916i	$-0.658267\pi$
$659$	−24.4889	−0.953952	−0.476976	+	0.878916i	$0.658267\pi$
$660$	10.4552	0.406968
$661$	−0.828280	−0.0322164	−0.0161082	−	0.999870i	$-0.505128\pi$
$661$	−0.828280	−0.0322164	−0.0161082	+	0.999870i	$0.505128\pi$
$662$	−30.4598	−1.18386
$663$	−18.5258	−0.719484
$664$	−0.876153	−0.0340013
$665$	−0.374338	−0.0145162
$666$	14.5508	0.563831
$667$	0	0
$668$	−124.193	−4.80516
$669$	47.6172	1.84099
$670$	33.8902	1.30929
$671$	−9.65118	−0.372580
$672$	−29.2600	−1.12873
$673$	35.6257	1.37327	0.686635	−	0.727002i	$-0.259087\pi$
$673$	35.6257	1.37327	0.686635	+	0.727002i	$0.259087\pi$
$674$	−40.6641	−1.56632
$675$	−16.4372	−0.632669
$676$	3.23943	0.124593
$677$	27.1156	1.04214	0.521068	−	0.853515i	$-0.325534\pi$
$677$	27.1156	1.04214	0.521068	+	0.853515i	$0.325534\pi$
$678$	40.4496	1.55346
$679$	−18.8189	−0.722202
$680$	−21.6609	−0.830658
$681$	−4.60104	−0.176312
$682$	6.26392	0.239858
$683$	−29.2757	−1.12021	−0.560103	−	0.828423i	$-0.689238\pi$
$683$	−29.2757	−1.12021	−0.560103	+	0.828423i	$0.689238\pi$
$684$	−1.02678	−0.0392601
$685$	12.9144	0.493435
$686$	−41.3685	−1.57945
$687$	−38.5604	−1.47117
$688$	−103.255	−3.93656
$689$	9.03645	0.344261
$690$	38.0342	1.44794
$691$	6.77129	0.257592	0.128796	−	0.991671i	$-0.458889\pi$
$691$	6.77129	0.257592	0.128796	+	0.991671i	$0.458889\pi$
$692$	12.6145	0.479532
$693$	−0.984212	−0.0373871
$694$	47.7310	1.81184
$695$	3.03658	0.115184
$696$	0	0
$697$	30.6810	1.16212
$698$	−84.4420	−3.19618
$699$	−35.3184	−1.33586
$700$	−23.7400	−0.897289
$701$	19.9688	0.754210	0.377105	−	0.926171i	$-0.376920\pi$
$701$	19.9688	0.754210	0.377105	+	0.926171i	$0.376920\pi$
$702$	−42.0184	−1.58588
$703$	−1.92284	−0.0725213
$704$	−10.5054	−0.395938
$705$	−2.59499	−0.0977330
$706$	−6.29631	−0.236965
$707$	5.36100	0.201621
$708$	41.5226	1.56051
$709$	38.3150	1.43895	0.719475	−	0.694519i	$-0.244383\pi$
$709$	38.3150	1.43895	0.719475	+	0.694519i	$0.244383\pi$
$710$	−43.9011	−1.64758
$711$	−0.710517	−0.0266465
$712$	−12.6475	−0.473983
$713$	16.1985	0.606638
$714$	16.7397	0.626468
$715$	4.04448	0.151255
$716$	106.707	3.98782
$717$	31.4041	1.17281
$718$	11.7020	0.436715
$719$	40.7824	1.52093	0.760463	−	0.649382i	$-0.224972\pi$
$719$	40.7824	1.52093	0.760463	+	0.649382i	$0.224972\pi$
$720$	8.77423	0.326996
$721$	−10.3819	−0.386642
$722$	−49.7799	−1.85262
$723$	−5.11880	−0.190370
$724$	−42.6850	−1.58638
$725$	0	0
$726$	−5.11009	−0.189653
$727$	−2.63133	−0.0975906	−0.0487953	−	0.998809i	$-0.515538\pi$
$727$	−2.63133	−0.0975906	−0.0487953	+	0.998809i	$0.515538\pi$
$728$	−36.0027	−1.33435
$729$	16.8846	0.625355
$730$	21.5796	0.798696
$731$	25.7537	0.952534
$732$	−92.2054	−3.40801
$733$	−32.5001	−1.20042	−0.600210	−	0.799843i	$-0.704916\pi$
$733$	−32.5001	−1.20042	−0.600210	+	0.799843i	$0.704916\pi$
$734$	59.5039	2.19633
$735$	11.4559	0.422559
$736$	−80.6649	−2.97335
$737$	−11.7749	−0.433733
$738$	−24.2438	−0.892427
$739$	−36.8029	−1.35382	−0.676908	−	0.736067i	$-0.736681\pi$
$739$	−36.8029	−1.35382	−0.676908	+	0.736067i	$0.736681\pi$
$740$	38.4074	1.41188
$741$	−1.93449	−0.0710653
$742$	−8.16522	−0.299754
$743$	−19.6588	−0.721212	−0.360606	−	0.932718i	$-0.617430\pi$
$743$	−19.6588	−0.721212	−0.360606	+	0.932718i	$0.617430\pi$
$744$	35.5030	1.30160
$745$	25.8876	0.948447
$746$	20.5255	0.751492
$747$	−0.0885196	−0.00323876
$748$	12.6857	0.463836
$749$	20.2525	0.740009
$750$	49.2250	1.79744
$751$	13.5456	0.494286	0.247143	−	0.968979i	$-0.420508\pi$
$751$	13.5456	0.494286	0.247143	+	0.968979i	$0.420508\pi$
$752$	12.6239	0.460345
$753$	18.3193	0.667591
$754$	0	0
$755$	−8.46740	−0.308160
$756$	26.9895	0.981598
$757$	−9.88113	−0.359136	−0.179568	−	0.983746i	$-0.557470\pi$
$757$	−9.88113	−0.359136	−0.179568	+	0.983746i	$0.557470\pi$
$758$	−48.4641	−1.76030
$759$	−13.2147	−0.479662
$760$	−2.26186	−0.0820463
$761$	−31.8041	−1.15290	−0.576450	−	0.817133i	$-0.695562\pi$
$761$	−31.8041	−1.15290	−0.576450	+	0.817133i	$0.695562\pi$
$762$	−33.1495	−1.20088
$763$	−5.39969	−0.195482
$764$	122.651	4.43736
$765$	−2.18845	−0.0791235
$766$	34.5229	1.24736
$767$	16.0626	0.579985
$768$	20.8471	0.752256
$769$	13.6812	0.493357	0.246679	−	0.969097i	$-0.420661\pi$
$769$	13.6812	0.493357	0.246679	+	0.969097i	$0.420661\pi$
$770$	−3.65454	−0.131700
$771$	11.0684	0.398617
$772$	110.970	3.99391
$773$	−36.7460	−1.32166	−0.660832	−	0.750534i	$-0.729796\pi$
$773$	−36.7460	−1.32166	−0.660832	+	0.750534i	$0.729796\pi$
$774$	−20.3503	−0.731476
$775$	9.05611	0.325305
$776$	−113.709	−4.08192
$777$	−17.6088	−0.631711
$778$	38.9073	1.39489
$779$	3.20375	0.114786
$780$	38.6401	1.38354
$781$	15.2531	0.545798
$782$	46.1486	1.65027
$783$	0	0
$784$	−55.7297	−1.99035
$785$	−0.861479	−0.0307475
$786$	−73.8045	−2.63252
$787$	11.6966	0.416940	0.208470	−	0.978029i	$-0.433152\pi$
$787$	11.6966	0.416940	0.208470	+	0.978029i	$0.433152\pi$
$788$	71.2337	2.53760
$789$	23.5722	0.839192
$790$	−2.63826	−0.0938652
$791$	−10.0508	−0.357364
$792$	−5.94689	−0.211314
$793$	−35.6687	−1.26663
$794$	−44.6506	−1.58459
$795$	5.19892	0.184387
$796$	−77.4088	−2.74368
$797$	−33.7962	−1.19712	−0.598561	−	0.801077i	$-0.704261\pi$
$797$	−33.7962	−1.19712	−0.598561	+	0.801077i	$0.704261\pi$
$798$	1.74798	0.0618779
$799$	−3.14862	−0.111390
$800$	−45.0974	−1.59443
$801$	−1.27780	−0.0451488
$802$	56.2238	1.98533
$803$	−7.49764	−0.264586
$804$	−112.495	−3.96738
$805$	−9.45062	−0.333091
$806$	23.1501	0.815427
$807$	−23.9336	−0.842501
$808$	32.3927	1.13957
$809$	−8.66379	−0.304603	−0.152301	−	0.988334i	$-0.548668\pi$
$809$	−8.66379	−0.304603	−0.152301	+	0.988334i	$0.548668\pi$
$810$	−30.8673	−1.08456
$811$	−32.7006	−1.14827	−0.574136	−	0.818760i	$-0.694662\pi$
$811$	−32.7006	−1.14827	−0.574136	+	0.818760i	$0.694662\pi$
$812$	0	0
$813$	−57.0421	−2.00055
$814$	−18.7720	−0.657959
$815$	−19.9838	−0.700002
$816$	51.8501	1.81512
$817$	2.68923	0.0940842
$818$	−22.1829	−0.775608
$819$	−3.63743	−0.127102
$820$	−63.9926	−2.23472
$821$	29.3276	1.02354	0.511771	−	0.859122i	$-0.328990\pi$
$821$	29.3276	1.02354	0.511771	+	0.859122i	$0.328990\pi$
$822$	−60.3043	−2.10335
$823$	5.36839	0.187130	0.0935651	−	0.995613i	$-0.470174\pi$
$823$	5.36839	0.187130	0.0935651	+	0.995613i	$0.470174\pi$
$824$	−62.7304	−2.18532
$825$	−7.38795	−0.257215
$826$	−14.5139	−0.505004
$827$	−10.8454	−0.377130	−0.188565	−	0.982061i	$-0.560384\pi$
$827$	−10.8454	−0.377130	−0.188565	+	0.982061i	$0.560384\pi$
$828$	−25.9224	−0.900866
$829$	14.5867	0.506617	0.253308	−	0.967386i	$-0.418481\pi$
$829$	14.5867	0.506617	0.253308	+	0.967386i	$0.418481\pi$
$830$	−0.328688	−0.0114089
$831$	18.6513	0.647008
$832$	−38.8258	−1.34604
$833$	13.9000	0.481606
$834$	−14.1794	−0.490991
$835$	−27.6403	−0.956530
$836$	1.32466	0.0458143
$837$	−10.2957	−0.355870
$838$	47.5341	1.64204
$839$	−1.97130	−0.0680567	−0.0340284	−	0.999421i	$-0.510834\pi$
$839$	−1.97130	−0.0680567	−0.0340284	+	0.999421i	$0.510834\pi$
$840$	−20.7134	−0.714680
$841$	0	0
$842$	−16.4917	−0.568341
$843$	34.0456	1.17259
$844$	56.7089	1.95200
$845$	0.720965	0.0248020
$846$	2.48800	0.0855393
$847$	1.26974	0.0436287
$848$	−25.2912	−0.868504
$849$	44.6400	1.53204
$850$	25.8004	0.884945
$851$	−48.5444	−1.66408
$852$	145.725	4.99245
$853$	−13.7434	−0.470564	−0.235282	−	0.971927i	$-0.575601\pi$
$853$	−13.7434	−0.470564	−0.235282	+	0.971927i	$0.575601\pi$
$854$	32.2297	1.10288
$855$	−0.228520	−0.00781524
$856$	122.371	4.18256
$857$	16.8371	0.575145	0.287573	−	0.957759i	$-0.407152\pi$
$857$	16.8371	0.575145	0.287573	+	0.957759i	$0.407152\pi$
$858$	−18.8858	−0.644750
$859$	5.62271	0.191844	0.0959222	−	0.995389i	$-0.469420\pi$
$859$	5.62271	0.191844	0.0959222	+	0.995389i	$0.469420\pi$
$860$	−53.7155	−1.83168
$861$	29.3389	0.999866
$862$	−0.252862	−0.00861251
$863$	−26.9450	−0.917218	−0.458609	−	0.888638i	$-0.651652\pi$
$863$	−26.9450	−0.917218	−0.458609	+	0.888638i	$0.651652\pi$
$864$	51.2701	1.74425
$865$	2.80748	0.0954573
$866$	−46.7484	−1.58857
$867$	20.0981	0.682569
$868$	−14.8699	−0.504717
$869$	0.916642	0.0310949
$870$	0	0
$871$	−43.5174	−1.47453
$872$	−32.6264	−1.10487
$873$	−11.4883	−0.388819
$874$	4.81889	0.163001
$875$	−12.2313	−0.413492
$876$	−71.6309	−2.42019
$877$	2.85191	0.0963022	0.0481511	−	0.998840i	$-0.484667\pi$
$877$	2.85191	0.0963022	0.0481511	+	0.998840i	$0.484667\pi$
$878$	−18.9655	−0.640056
$879$	47.8563	1.61415
$880$	−11.3197	−0.381586
$881$	−18.5065	−0.623500	−0.311750	−	0.950164i	$-0.600915\pi$
$881$	−18.5065	−0.623500	−0.311750	+	0.950164i	$0.600915\pi$
$882$	−10.9836	−0.369838
$883$	6.39380	0.215168	0.107584	−	0.994196i	$-0.465688\pi$
$883$	6.39380	0.215168	0.107584	+	0.994196i	$0.465688\pi$
$884$	46.8837	1.57687
$885$	9.24124	0.310641
$886$	−27.5492	−0.925533
$887$	35.7495	1.20035	0.600176	−	0.799868i	$-0.295097\pi$
$887$	35.7495	1.20035	0.600176	+	0.799868i	$0.295097\pi$
$888$	−106.397	−3.57045
$889$	8.23688	0.276256
$890$	−4.74467	−0.159042
$891$	10.7246	0.359286
$892$	−120.506	−4.03483
$893$	−0.328782	−0.0110023
$894$	−120.883	−4.04292
$895$	23.7486	0.793827
$896$	4.96365	0.165824
$897$	−48.8386	−1.63067
$898$	84.9718	2.83555
$899$	0	0
$900$	−14.4925	−0.483082
$901$	6.30808	0.210152
$902$	31.2771	1.04141
$903$	24.6271	0.819539
$904$	−60.7296	−2.01984
$905$	−9.49995	−0.315789
$906$	39.5387	1.31359
$907$	−0.390242	−0.0129578	−0.00647889	−	0.999979i	$-0.502062\pi$
$907$	−0.390242	−0.0129578	−0.00647889	+	0.999979i	$0.502062\pi$
$908$	11.6440	0.386418
$909$	3.27270	0.108549
$910$	−13.5064	−0.447732
$911$	−11.8250	−0.391781	−0.195891	−	0.980626i	$-0.562760\pi$
$911$	−11.8250	−0.391781	−0.195891	+	0.980626i	$0.562760\pi$
$912$	5.41425	0.179284
$913$	0.114200	0.00377946
$914$	44.6201	1.47590
$915$	−20.5212	−0.678409
$916$	97.5857	3.22432
$917$	18.3387	0.605597
$918$	−29.3318	−0.968093
$919$	43.5697	1.43723	0.718617	−	0.695407i	$-0.244776\pi$
$919$	43.5697	1.43723	0.718617	+	0.695407i	$0.244776\pi$
$920$	−57.1034	−1.88264
$921$	−34.7752	−1.14588
$922$	−31.2145	−1.02799
$923$	56.3720	1.85551
$924$	12.1308	0.399074
$925$	−27.1398	−0.892351
$926$	105.542	3.46832
$927$	−6.33778	−0.208160
$928$	0	0
$929$	−14.0306	−0.460330	−0.230165	−	0.973152i	$-0.573927\pi$
$929$	−14.0306	−0.460330	−0.230165	+	0.973152i	$0.573927\pi$
$930$	13.3189	0.436744
$931$	1.45145	0.0475695
$932$	89.3808	2.92777
$933$	−25.4359	−0.832733
$934$	6.65825	0.217865
$935$	2.82333	0.0923327
$936$	−21.9784	−0.718387
$937$	−36.4689	−1.19139	−0.595694	−	0.803211i	$-0.703123\pi$
$937$	−36.4689	−1.19139	−0.595694	+	0.803211i	$0.703123\pi$
$938$	39.3217	1.28390
$939$	56.1400	1.83206
$940$	6.56720	0.214198
$941$	−13.1905	−0.429997	−0.214999	−	0.976614i	$-0.568975\pi$
$941$	−13.1905	−0.429997	−0.214999	+	0.976614i	$0.568975\pi$
$942$	4.02269	0.131066
$943$	80.8824	2.63389
$944$	−44.9559	−1.46319
$945$	6.00676	0.195400
$946$	26.2540	0.853592
$947$	22.6383	0.735645	0.367822	−	0.929896i	$-0.380103\pi$
$947$	22.6383	0.735645	0.367822	+	0.929896i	$0.380103\pi$
$948$	8.75741	0.284427
$949$	−27.7097	−0.899494
$950$	2.69411	0.0874083
$951$	39.3787	1.27694
$952$	−25.1324	−0.814547
$953$	11.9511	0.387133	0.193566	−	0.981087i	$-0.437995\pi$
$953$	11.9511	0.387133	0.193566	+	0.981087i	$0.437995\pi$
$954$	−4.98458	−0.161382
$955$	27.2971	0.883314
$956$	−79.4750	−2.57041
$957$	0	0
$958$	3.09609	0.100030
$959$	14.9842	0.483865
$960$	−22.3376	−0.720942
$961$	−25.3276	−0.817019
$962$	−69.3773	−2.23681
$963$	12.3634	0.398406
$964$	12.9542	0.417228
$965$	24.6975	0.795040
$966$	44.1299	1.41986
$967$	−10.6821	−0.343514	−0.171757	−	0.985139i	$-0.554944\pi$
$967$	−10.6821	−0.343514	−0.171757	+	0.985139i	$0.554944\pi$
$968$	7.67212	0.246591
$969$	−1.35041	−0.0433815
$970$	−42.6578	−1.36966
$971$	38.3044	1.22925	0.614623	−	0.788821i	$-0.289308\pi$
$971$	38.3044	1.22925	0.614623	+	0.788821i	$0.289308\pi$
$972$	38.6924	1.24106
$973$	3.52324	0.112950
$974$	44.3350	1.42059
$975$	−27.3042	−0.874436
$976$	99.8294	3.19546
$977$	−11.2636	−0.360353	−0.180177	−	0.983634i	$-0.557667\pi$
$977$	−11.2636	−0.360353	−0.180177	+	0.983634i	$0.557667\pi$
$978$	93.3148	2.98388
$979$	1.64850	0.0526862
$980$	−28.9918	−0.926108
$981$	−3.29632	−0.105243
$982$	−36.5900	−1.16763
$983$	46.2354	1.47468	0.737340	−	0.675522i	$-0.236082\pi$
$983$	46.2354	1.47468	0.737340	+	0.675522i	$0.236082\pi$
$984$	177.274	5.65129
$985$	15.8537	0.505142
$986$	0	0
$987$	−3.01088	−0.0958375
$988$	4.89565	0.155752
$989$	67.8928	2.15887
$990$	−2.23097	−0.0709048
$991$	−2.32717	−0.0739251	−0.0369625	−	0.999317i	$-0.511768\pi$
$991$	−2.32717	−0.0739251	−0.0369625	+	0.999317i	$0.511768\pi$
$992$	−28.2474	−0.896854
$993$	22.5025	0.714096
$994$	−50.9370	−1.61562
$995$	−17.2281	−0.546166
$996$	1.09104	0.0345709
$997$	−40.5161	−1.28316	−0.641579	−	0.767057i	$-0.721720\pi$
$997$	−40.5161	−1.28316	−0.641579	+	0.767057i	$0.721720\pi$
$998$	27.8688	0.882171
$999$	30.8546	0.976195

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	9251.2.a.t.1.18	yes	18
29.28	even	2		9251.2.a.s.1.1	✓	18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
9251.2.a.s.1.1	✓	18	29.28	even	2
9251.2.a.t.1.18	yes	18	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:	\( N \)	\(=\)	\( 9251 = 11 \cdot 29^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	9251.a (trivial)

\(f(q)\)	\(=\)	\(q+2.63004 q^{2} -1.94297 q^{3} +4.91711 q^{4} +1.09435 q^{5} -5.11009 q^{6} +1.26974 q^{7} +7.67212 q^{8} +0.775130 q^{9} +O(q^{10})\)	\(q+2.63004 q^{2} -1.94297 q^{3} +4.91711 q^{4} +1.09435 q^{5} -5.11009 q^{6} +1.26974 q^{7} +7.67212 q^{8} +0.775130 q^{9} +2.87818 q^{10} -1.00000 q^{11} -9.55380 q^{12} -3.69578 q^{13} +3.33946 q^{14} -2.12629 q^{15} +10.3438 q^{16} -2.57992 q^{17} +2.03862 q^{18} -0.269398 q^{19} +5.38104 q^{20} -2.46706 q^{21} -2.63004 q^{22} -6.80128 q^{23} -14.9067 q^{24} -3.80240 q^{25} -9.72006 q^{26} +4.32285 q^{27} +6.24344 q^{28} -5.59222 q^{30} -2.38168 q^{31} +11.8603 q^{32} +1.94297 q^{33} -6.78528 q^{34} +1.38954 q^{35} +3.81140 q^{36} +7.13754 q^{37} -0.708528 q^{38} +7.18079 q^{39} +8.39598 q^{40} -11.8922 q^{41} -6.48847 q^{42} -9.98237 q^{43} -4.91711 q^{44} +0.848263 q^{45} -17.8876 q^{46} +1.22043 q^{47} -20.0976 q^{48} -5.38777 q^{49} -10.0005 q^{50} +5.01270 q^{51} -18.1726 q^{52} -2.44507 q^{53} +11.3693 q^{54} -1.09435 q^{55} +9.74157 q^{56} +0.523432 q^{57} -4.34619 q^{59} -10.4552 q^{60} +9.65118 q^{61} -6.26392 q^{62} +0.984212 q^{63} +10.5054 q^{64} -4.04448 q^{65} +5.11009 q^{66} +11.7749 q^{67} -12.6857 q^{68} +13.2147 q^{69} +3.65454 q^{70} -15.2531 q^{71} +5.94689 q^{72} +7.49764 q^{73} +18.7720 q^{74} +7.38795 q^{75} -1.32466 q^{76} -1.26974 q^{77} +18.8858 q^{78} -0.916642 q^{79} +11.3197 q^{80} -10.7246 q^{81} -31.2771 q^{82} -0.114200 q^{83} -12.1308 q^{84} -2.82333 q^{85} -26.2540 q^{86} -7.67212 q^{88} -1.64850 q^{89} +2.23097 q^{90} -4.69267 q^{91} -33.4426 q^{92} +4.62754 q^{93} +3.20979 q^{94} -0.294816 q^{95} -23.0441 q^{96} -14.8211 q^{97} -14.1700 q^{98} -0.775130 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q + 3 q^{3} + 12 q^{4} - 6 q^{5} - q^{6} - 5 q^{7} - 3 q^{8} + 9 q^{9}+O(q^{10}) \) 18 * q + 3 * q^3 + 12 * q^4 - 6 * q^5 - q^6 - 5 * q^7 - 3 * q^8 + 9 * q^9	\( 18 q + 3 q^{3} + 12 q^{4} - 6 q^{5} - q^{6} - 5 q^{7} - 3 q^{8} + 9 q^{9} + 5 q^{10} - 18 q^{11} + 3 q^{12} - 15 q^{13} - 12 q^{14} + 27 q^{15} + 4 q^{16} - 6 q^{17} + 12 q^{18} - 11 q^{19} - 18 q^{20} - 6 q^{21} - 20 q^{23} - 3 q^{24} - 4 q^{25} + 10 q^{26} - 6 q^{27} - 6 q^{28} - 19 q^{30} + 8 q^{31} + 24 q^{32} - 3 q^{33} - 22 q^{34} + 22 q^{35} + 17 q^{36} - 9 q^{37} - 3 q^{38} + 8 q^{39} + 36 q^{40} - 3 q^{41} + 28 q^{42} - 13 q^{43} - 12 q^{44} - q^{45} - 37 q^{46} + q^{47} - 46 q^{48} - 23 q^{49} - 34 q^{50} + 4 q^{51} - 33 q^{52} - 6 q^{53} - 56 q^{54} + 6 q^{55} - 10 q^{56} + 14 q^{57} - 16 q^{59} - 3 q^{60} + 2 q^{61} - 24 q^{62} - 67 q^{63} + 11 q^{64} - 35 q^{65} + q^{66} + 9 q^{67} - 5 q^{68} + 47 q^{69} + 69 q^{70} - 13 q^{71} - 22 q^{72} + 57 q^{73} + 33 q^{74} + q^{75} + 26 q^{76} + 5 q^{77} + 5 q^{78} - 27 q^{79} - 10 q^{80} - 34 q^{81} - 55 q^{82} + 10 q^{83} - 35 q^{84} - 40 q^{85} + 4 q^{86} + 3 q^{88} + 80 q^{89} - 64 q^{90} - 38 q^{91} - 58 q^{92} + 17 q^{93} + 8 q^{94} - 7 q^{95} + 8 q^{96} - 20 q^{97} + 78 q^{98} - 9 q^{99}+O(q^{100}) \) 18 * q + 3 * q^3 + 12 * q^4 - 6 * q^5 - q^6 - 5 * q^7 - 3 * q^8 + 9 * q^9 + 5 * q^10 - 18 * q^11 + 3 * q^12 - 15 * q^13 - 12 * q^14 + 27 * q^15 + 4 * q^16 - 6 * q^17 + 12 * q^18 - 11 * q^19 - 18 * q^20 - 6 * q^21 - 20 * q^23 - 3 * q^24 - 4 * q^25 + 10 * q^26 - 6 * q^27 - 6 * q^28 - 19 * q^30 + 8 * q^31 + 24 * q^32 - 3 * q^33 - 22 * q^34 + 22 * q^35 + 17 * q^36 - 9 * q^37 - 3 * q^38 + 8 * q^39 + 36 * q^40 - 3 * q^41 + 28 * q^42 - 13 * q^43 - 12 * q^44 - q^45 - 37 * q^46 + q^47 - 46 * q^48 - 23 * q^49 - 34 * q^50 + 4 * q^51 - 33 * q^52 - 6 * q^53 - 56 * q^54 + 6 * q^55 - 10 * q^56 + 14 * q^57 - 16 * q^59 - 3 * q^60 + 2 * q^61 - 24 * q^62 - 67 * q^63 + 11 * q^64 - 35 * q^65 + q^66 + 9 * q^67 - 5 * q^68 + 47 * q^69 + 69 * q^70 - 13 * q^71 - 22 * q^72 + 57 * q^73 + 33 * q^74 + q^75 + 26 * q^76 + 5 * q^77 + 5 * q^78 - 27 * q^79 - 10 * q^80 - 34 * q^81 - 55 * q^82 + 10 * q^83 - 35 * q^84 - 40 * q^85 + 4 * q^86 + 3 * q^88 + 80 * q^89 - 64 * q^90 - 38 * q^91 - 58 * q^92 + 17 * q^93 + 8 * q^94 - 7 * q^95 + 8 * q^96 - 20 * q^97 + 78 * q^98 - 9 * q^99

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