LMFDB - Embedded newform 9251.2.a.s.1.14

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			1.14
Root			$1.38618$ 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)

$f(q)$	$=$	$q+1.38618 q^{2} -1.15136 q^{3} -0.0785084 q^{4} +2.40583 q^{5} -1.59599 q^{6} -1.37301 q^{7} -2.88118 q^{8} -1.67437 q^{9} +O(q^{10})$	\(q+1.38618 q^{2} -1.15136 q^{3} -0.0785084 q^{4} +2.40583 q^{5} -1.59599 q^{6} -1.37301 q^{7} -2.88118 q^{8} -1.67437 q^{9} +3.33491 q^{10} +1.00000 q^{11} +0.0903913 q^{12} +0.978832 q^{13} -1.90324 q^{14} -2.76997 q^{15} -3.83682 q^{16} +6.03897 q^{17} -2.32098 q^{18} -1.73115 q^{19} -0.188878 q^{20} +1.58083 q^{21} +1.38618 q^{22} +1.70303 q^{23} +3.31728 q^{24} +0.788002 q^{25} +1.35684 q^{26} +5.38188 q^{27} +0.107793 q^{28} -3.83967 q^{30} -0.510010 q^{31} +0.443850 q^{32} -1.15136 q^{33} +8.37109 q^{34} -3.30323 q^{35} +0.131452 q^{36} -2.72551 q^{37} -2.39968 q^{38} -1.12699 q^{39} -6.93163 q^{40} -9.73132 q^{41} +2.19131 q^{42} -5.38229 q^{43} -0.0785084 q^{44} -4.02825 q^{45} +2.36070 q^{46} -1.69424 q^{47} +4.41756 q^{48} -5.11484 q^{49} +1.09231 q^{50} -6.95302 q^{51} -0.0768466 q^{52} +2.36898 q^{53} +7.46025 q^{54} +2.40583 q^{55} +3.95590 q^{56} +1.99317 q^{57} +5.54331 q^{59} +0.217466 q^{60} -0.0301060 q^{61} -0.706965 q^{62} +2.29893 q^{63} +8.28890 q^{64} +2.35490 q^{65} -1.59599 q^{66} +3.93290 q^{67} -0.474110 q^{68} -1.96079 q^{69} -4.57886 q^{70} +2.34073 q^{71} +4.82418 q^{72} +7.86190 q^{73} -3.77805 q^{74} -0.907273 q^{75} +0.135910 q^{76} -1.37301 q^{77} -1.56221 q^{78} +0.986518 q^{79} -9.23072 q^{80} -1.17335 q^{81} -13.4893 q^{82} -0.874924 q^{83} -0.124108 q^{84} +14.5287 q^{85} -7.46081 q^{86} -2.88118 q^{88} +17.7543 q^{89} -5.58388 q^{90} -1.34395 q^{91} -0.133702 q^{92} +0.587204 q^{93} -2.34852 q^{94} -4.16484 q^{95} -0.511031 q^{96} -11.0680 q^{97} -7.09009 q^{98} -1.67437 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	1.38618	0.980176	0.490088	−	0.871673i	$-0.336965\pi$
$2$	1.38618	0.980176	0.490088	+	0.871673i	$0.336965\pi$
$3$	−1.15136	−0.664737	−0.332369	−	0.943150i	$-0.607848\pi$
$3$	−1.15136	−0.664737	−0.332369	+	0.943150i	$0.607848\pi$
$4$	−0.0785084	−0.0392542
$5$	2.40583	1.07592	0.537959	−	0.842971i	$-0.319195\pi$
$5$	2.40583	1.07592	0.537959	+	0.842971i	$0.319195\pi$
$6$	−1.59599	−0.651560
$7$	−1.37301	−0.518949	−0.259475	−	0.965750i	$-0.583549\pi$
$7$	−1.37301	−0.518949	−0.259475	+	0.965750i	$0.583549\pi$
$8$	−2.88118	−1.01865
$9$	−1.67437	−0.558124
$10$	3.33491	1.05459
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	0.0903913	0.0260937
$13$	0.978832	0.271479	0.135740	−	0.990745i	$-0.456659\pi$
$13$	0.978832	0.271479	0.135740	+	0.990745i	$0.456659\pi$
$14$	−1.90324	−0.508662
$15$	−2.76997	−0.715203
$16$	−3.83682	−0.959205
$17$	6.03897	1.46466	0.732332	−	0.680947i	$-0.238432\pi$
$17$	6.03897	1.46466	0.732332	+	0.680947i	$0.238432\pi$
$18$	−2.32098	−0.547060
$19$	−1.73115	−0.397153	−0.198576	−	0.980085i	$-0.563632\pi$
$19$	−1.73115	−0.397153	−0.198576	+	0.980085i	$0.563632\pi$
$20$	−0.188878	−0.0422343
$21$	1.58083	0.344965
$22$	1.38618	0.295534
$23$	1.70303	0.355105	0.177553	−	0.984111i	$-0.443182\pi$
$23$	1.70303	0.355105	0.177553	+	0.984111i	$0.443182\pi$
$24$	3.31728	0.677136
$25$	0.788002	0.157600
$26$	1.35684	0.266098
$27$	5.38188	1.03574
$28$	0.107793	0.0203709
$29$	0	0
$29$	0	0
$30$	−3.83967	−0.701025
$31$	−0.510010	−0.0916005	−0.0458002	−	0.998951i	$-0.514584\pi$
$31$	−0.510010	−0.0916005	−0.0458002	+	0.998951i	$0.514584\pi$
$32$	0.443850	0.0784624
$33$	−1.15136	−0.200426
$34$	8.37109	1.43563
$35$	−3.30323	−0.558347
$36$	0.131452	0.0219087
$37$	−2.72551	−0.448072	−0.224036	−	0.974581i	$-0.571923\pi$
$37$	−2.72551	−0.448072	−0.224036	+	0.974581i	$0.571923\pi$
$38$	−2.39968	−0.389280
$39$	−1.12699	−0.180462
$40$	−6.93163	−1.09599
$41$	−9.73132	−1.51978	−0.759888	−	0.650054i	$-0.774746\pi$
$41$	−9.73132	−1.51978	−0.759888	+	0.650054i	$0.774746\pi$
$42$	2.19131	0.338126
$43$	−5.38229	−0.820791	−0.410396	−	0.911908i	$-0.634609\pi$
$43$	−5.38229	−0.820791	−0.410396	+	0.911908i	$0.634609\pi$
$44$	−0.0785084	−0.0118356
$45$	−4.02825	−0.600496
$46$	2.36070	0.348066
$47$	−1.69424	−0.247130	−0.123565	−	0.992336i	$-0.539433\pi$
$47$	−1.69424	−0.247130	−0.123565	+	0.992336i	$0.539433\pi$
$48$	4.41756	0.637619
$49$	−5.11484	−0.730692
$50$	1.09231	0.154476
$51$	−6.95302	−0.973617
$52$	−0.0768466	−0.0106567
$53$	2.36898	0.325404	0.162702	−	0.986675i	$-0.447979\pi$
$53$	2.36898	0.325404	0.162702	+	0.986675i	$0.447979\pi$
$54$	7.46025	1.01521
$55$	2.40583	0.324402
$56$	3.95590	0.528629
$57$	1.99317	0.264002
$58$	0	0
$59$	5.54331	0.721678	0.360839	−	0.932628i	$-0.382490\pi$
$59$	5.54331	0.721678	0.360839	+	0.932628i	$0.382490\pi$
$60$	0.217466	0.0280747
$61$	−0.0301060	−0.00385467	−0.00192734	−	0.999998i	$-0.500613\pi$
$61$	−0.0301060	−0.00385467	−0.00192734	+	0.999998i	$0.500613\pi$
$62$	−0.706965	−0.0897846
$63$	2.29893	0.289638
$64$	8.28890	1.03611
$65$	2.35490	0.292090
$66$	−1.59599	−0.196453
$67$	3.93290	0.480481	0.240240	−	0.970713i	$-0.422774\pi$
$67$	3.93290	0.480481	0.240240	+	0.970713i	$0.422774\pi$
$68$	−0.474110	−0.0574942
$69$	−1.96079	−0.236052
$70$	−4.57886	−0.547279
$71$	2.34073	0.277794	0.138897	−	0.990307i	$-0.455644\pi$
$71$	2.34073	0.277794	0.138897	+	0.990307i	$0.455644\pi$
$72$	4.82418	0.568535
$73$	7.86190	0.920166	0.460083	−	0.887876i	$-0.347820\pi$
$73$	7.86190	0.920166	0.460083	+	0.887876i	$0.347820\pi$
$74$	−3.77805	−0.439189
$75$	−0.907273	−0.104763
$76$	0.135910	0.0155899
$77$	−1.37301	−0.156469
$78$	−1.56221	−0.176885
$79$	0.986518	0.110992	0.0554960	−	0.998459i	$-0.482326\pi$
$79$	0.986518	0.110992	0.0554960	+	0.998459i	$0.482326\pi$
$80$	−9.23072	−1.03203
$81$	−1.17335	−0.130373
$82$	−13.4893	−1.48965
$83$	−0.874924	−0.0960354	−0.0480177	−	0.998846i	$-0.515290\pi$
$83$	−0.874924	−0.0960354	−0.0480177	+	0.998846i	$0.515290\pi$
$84$	−0.124108	−0.0135413
$85$	14.5287	1.57586
$86$	−7.46081	−0.804520
$87$	0	0
$88$	−2.88118	−0.307135
$89$	17.7543	1.88195	0.940976	−	0.338473i	$-0.109910\pi$
$89$	17.7543	1.88195	0.940976	+	0.338473i	$0.109910\pi$
$90$	−5.58388	−0.588592
$91$	−1.34395	−0.140884
$92$	−0.133702	−0.0139394
$93$	0.587204	0.0608902
$94$	−2.34852	−0.242231
$95$	−4.16484	−0.427304
$96$	−0.511031	−0.0521569
$97$	−11.0680	−1.12378	−0.561892	−	0.827211i	$-0.689926\pi$
$97$	−11.0680	−1.12378	−0.561892	+	0.827211i	$0.689926\pi$
$98$	−7.09009	−0.716207
$99$	−1.67437	−0.168281
$100$	−0.0618648	−0.00618648
$101$	−19.6093	−1.95119	−0.975597	−	0.219567i	$-0.929536\pi$
$101$	−19.6093	−1.95119	−0.975597	+	0.219567i	$0.929536\pi$
$102$	−9.63813	−0.954317
$103$	−8.74595	−0.861764	−0.430882	−	0.902408i	$-0.641798\pi$
$103$	−8.74595	−0.861764	−0.430882	+	0.902408i	$0.641798\pi$
$104$	−2.82020	−0.276543
$105$	3.80320	0.371154
$106$	3.28383	0.318953
$107$	−7.31471	−0.707140	−0.353570	−	0.935408i	$-0.615032\pi$
$107$	−7.31471	−0.707140	−0.353570	+	0.935408i	$0.615032\pi$
$108$	−0.422523	−0.0406573
$109$	−8.76619	−0.839649	−0.419824	−	0.907605i	$-0.637908\pi$
$109$	−8.76619	−0.839649	−0.419824	+	0.907605i	$0.637908\pi$
$110$	3.33491	0.317971
$111$	3.13804	0.297850
$112$	5.26799	0.497779
$113$	5.63932	0.530503	0.265251	−	0.964179i	$-0.414545\pi$
$113$	5.63932	0.530503	0.265251	+	0.964179i	$0.414545\pi$
$114$	2.76289	0.258769
$115$	4.09718	0.382064
$116$	0	0
$117$	−1.63893	−0.151519
$118$	7.68402	0.707372
$119$	−8.29157	−0.760087
$120$	7.98079	0.728543
$121$	1.00000	0.0909091
$122$	−0.0417322	−0.00377826
$123$	11.2042	1.01025
$124$	0.0400400	0.00359570
$125$	−10.1333	−0.906353
$126$	3.18673	0.283897
$127$	9.00860	0.799384	0.399692	−	0.916649i	$-0.369117\pi$
$127$	9.00860	0.799384	0.399692	+	0.916649i	$0.369117\pi$
$128$	10.6022	0.937110
$129$	6.19694	0.545610
$130$	3.26431	0.286299
$131$	21.6200	1.88895	0.944475	−	0.328583i	$-0.106571\pi$
$131$	21.6200	1.88895	0.944475	+	0.328583i	$0.106571\pi$
$132$	0.0903913	0.00786755
$133$	2.37689	0.206102
$134$	5.45171	0.470956
$135$	12.9479	1.11438
$136$	−17.3994	−1.49198
$137$	−9.51545	−0.812959	−0.406480	−	0.913660i	$-0.633244\pi$
$137$	−9.51545	−0.812959	−0.406480	+	0.913660i	$0.633244\pi$
$138$	−2.71801	−0.231372
$139$	−5.96618	−0.506045	−0.253022	−	0.967460i	$-0.581425\pi$
$139$	−5.96618	−0.506045	−0.253022	+	0.967460i	$0.581425\pi$
$140$	0.259331	0.0219175
$141$	1.95068	0.164277
$142$	3.24468	0.272287
$143$	0.978832	0.0818541
$144$	6.42427	0.535356
$145$	0	0
$146$	10.8980	0.901925
$147$	5.88902	0.485718
$148$	0.213976	0.0175887
$149$	−5.10379	−0.418119	−0.209059	−	0.977903i	$-0.567040\pi$
$149$	−5.10379	−0.418119	−0.209059	+	0.977903i	$0.567040\pi$
$150$	−1.25764	−0.102686
$151$	−5.22780	−0.425433	−0.212716	−	0.977114i	$-0.568231\pi$
$151$	−5.22780	−0.425433	−0.212716	+	0.977114i	$0.568231\pi$
$152$	4.98776	0.404561
$153$	−10.1115	−0.817465
$154$	−1.90324	−0.153367
$155$	−1.22700	−0.0985546
$156$	0.0884779	0.00708390
$157$	−18.4404	−1.47170	−0.735852	−	0.677142i	$-0.763218\pi$
$157$	−18.4404	−1.47170	−0.735852	+	0.677142i	$0.763218\pi$
$158$	1.36749	0.108792
$159$	−2.72754	−0.216308
$160$	1.06783	0.0844192
$161$	−2.33827	−0.184282
$162$	−1.62648	−0.127788
$163$	0.201130	0.0157537	0.00787686	−	0.999969i	$-0.497493\pi$
$163$	0.201130	0.0157537	0.00787686	+	0.999969i	$0.497493\pi$
$164$	0.763990	0.0596576
$165$	−2.76997	−0.215642
$166$	−1.21280	−0.0941317
$167$	−19.4303	−1.50356	−0.751779	−	0.659415i	$-0.770804\pi$
$167$	−19.4303	−1.50356	−0.751779	+	0.659415i	$0.770804\pi$
$168$	−4.55466	−0.351399
$169$	−12.0419	−0.926299
$170$	20.1394	1.54462
$171$	2.89859	0.221661
$172$	0.422555	0.0322195
$173$	6.40876	0.487249	0.243624	−	0.969870i	$-0.421664\pi$
$173$	6.40876	0.487249	0.243624	+	0.969870i	$0.421664\pi$
$174$	0	0
$175$	−1.08194	−0.0817866
$176$	−3.83682	−0.289211
$177$	−6.38234	−0.479726
$178$	24.6106	1.84465
$179$	−14.4016	−1.07643	−0.538213	−	0.842809i	$-0.680900\pi$
$179$	−14.4016	−1.07643	−0.538213	+	0.842809i	$0.680900\pi$
$180$	0.316252	0.0235720
$181$	−13.2600	−0.985609	−0.492805	−	0.870140i	$-0.664028\pi$
$181$	−13.2600	−0.985609	−0.492805	+	0.870140i	$0.664028\pi$
$182$	−1.86295	−0.138091
$183$	0.0346628	0.00256234
$184$	−4.90673	−0.361729
$185$	−6.55711	−0.482088
$186$	0.813970	0.0596832
$187$	6.03897	0.441613
$188$	0.133012	0.00970089
$189$	−7.38938	−0.537498
$190$	−5.77322	−0.418833
$191$	−23.3106	−1.68669	−0.843347	−	0.537370i	$-0.819418\pi$
$191$	−23.3106	−1.68669	−0.843347	+	0.537370i	$0.819418\pi$
$192$	−9.54349	−0.688742
$193$	4.68407	0.337167	0.168583	−	0.985687i	$-0.446081\pi$
$193$	4.68407	0.337167	0.168583	+	0.985687i	$0.446081\pi$
$194$	−15.3422	−1.10151
$195$	−2.71134	−0.194163
$196$	0.401558	0.0286827
$197$	−20.1189	−1.43341	−0.716707	−	0.697375i	$-0.754351\pi$
$197$	−20.1189	−1.43341	−0.716707	+	0.697375i	$0.754351\pi$
$198$	−2.32098	−0.164945
$199$	0.326498	0.0231449	0.0115724	−	0.999933i	$-0.496316\pi$
$199$	0.326498	0.0231449	0.0115724	+	0.999933i	$0.496316\pi$
$200$	−2.27038	−0.160540
$201$	−4.52818	−0.319393
$202$	−27.1819	−1.91252
$203$	0	0
$204$	0.545870	0.0382186
$205$	−23.4119	−1.63516
$206$	−12.1235	−0.844681
$207$	−2.85150	−0.198193
$208$	−3.75560	−0.260404
$209$	−1.73115	−0.119746
$210$	5.27191	0.363796
$211$	22.0141	1.51551	0.757756	−	0.652538i	$-0.226296\pi$
$211$	22.0141	1.51551	0.757756	+	0.652538i	$0.226296\pi$
$212$	−0.185985	−0.0127735
$213$	−2.69502	−0.184660
$214$	−10.1395	−0.693122
$215$	−12.9489	−0.883104
$216$	−15.5062	−1.05506
$217$	0.700249	0.0475360
$218$	−12.1515	−0.823004
$219$	−9.05187	−0.611669
$220$	−0.188878	−0.0127341
$221$	5.91114	0.397626
$222$	4.34989	0.291945
$223$	−20.8540	−1.39649	−0.698244	−	0.715860i	$-0.746035\pi$
$223$	−20.8540	−1.39649	−0.698244	+	0.715860i	$0.746035\pi$
$224$	−0.609411	−0.0407180
$225$	−1.31941	−0.0879607
$226$	7.81711	0.519986
$227$	−13.7794	−0.914571	−0.457285	−	0.889320i	$-0.651178\pi$
$227$	−13.7794	−0.914571	−0.457285	+	0.889320i	$0.651178\pi$
$228$	−0.156481	−0.0103632
$229$	−15.0470	−0.994335	−0.497167	−	0.867655i	$-0.665627\pi$
$229$	−15.0470	−0.994335	−0.497167	+	0.867655i	$0.665627\pi$
$230$	5.67943	0.374491
$231$	1.58083	0.104011
$232$	0	0
$233$	4.06961	0.266609	0.133305	−	0.991075i	$-0.457441\pi$
$233$	4.06961	0.266609	0.133305	+	0.991075i	$0.457441\pi$
$234$	−2.27185	−0.148516
$235$	−4.07604	−0.265892
$236$	−0.435197	−0.0283289
$237$	−1.13584	−0.0737805
$238$	−11.4936	−0.745019
$239$	1.73006	0.111908	0.0559542	−	0.998433i	$-0.482180\pi$
$239$	1.73006	0.111908	0.0559542	+	0.998433i	$0.482180\pi$
$240$	10.6279	0.686026
$241$	17.1026	1.10167	0.550837	−	0.834613i	$-0.314309\pi$
$241$	17.1026	1.10167	0.550837	+	0.834613i	$0.314309\pi$
$242$	1.38618	0.0891069
$243$	−14.7947	−0.949080
$244$	0.00236357	0.000151312 0
$245$	−12.3054	−0.786165
$246$	15.5311	0.990225
$247$	−1.69450	−0.107819
$248$	1.46943	0.0933090
$249$	1.00735	0.0638383
$250$	−14.0466	−0.888386
$251$	22.2588	1.40497	0.702483	−	0.711700i	$-0.252075\pi$
$251$	22.2588	1.40497	0.702483	+	0.711700i	$0.252075\pi$
$252$	−0.180486	−0.0113695
$253$	1.70303	0.107068
$254$	12.4875	0.783538
$255$	−16.7278	−1.04753
$256$	−1.88126	−0.117579
$257$	−29.1433	−1.81791	−0.908955	−	0.416894i	$-0.863119\pi$
$257$	−29.1433	−1.81791	−0.908955	+	0.416894i	$0.863119\pi$
$258$	8.59007	0.534795
$259$	3.74216	0.232526
$260$	−0.184879	−0.0114657
$261$	0	0
$262$	29.9692	1.85150
$263$	−1.03168	−0.0636164	−0.0318082	−	0.999494i	$-0.510127\pi$
$263$	−1.03168	−0.0636164	−0.0318082	+	0.999494i	$0.510127\pi$
$264$	3.31728	0.204164
$265$	5.69935	0.350108
$266$	3.29479	0.202016
$267$	−20.4416	−1.25100
$268$	−0.308766	−0.0188609
$269$	−1.45315	−0.0886001	−0.0443000	−	0.999018i	$-0.514106\pi$
$269$	−1.45315	−0.0886001	−0.0443000	+	0.999018i	$0.514106\pi$
$270$	17.9481	1.09228
$271$	25.2038	1.53102	0.765512	−	0.643421i	$-0.222486\pi$
$271$	25.2038	1.53102	0.765512	+	0.643421i	$0.222486\pi$
$272$	−23.1704	−1.40491
$273$	1.54737	0.0936508
$274$	−13.1901	−0.796844
$275$	0.788002	0.0475183
$276$	0.153939	0.00926602
$277$	−32.1096	−1.92928	−0.964641	−	0.263569i	$-0.915100\pi$
$277$	−32.1096	−1.92928	−0.964641	+	0.263569i	$0.915100\pi$
$278$	−8.27019	−0.496013
$279$	0.853947	0.0511245
$280$	9.51720	0.568762
$281$	−32.8742	−1.96111	−0.980556	−	0.196240i	$-0.937127\pi$
$281$	−32.8742	−1.96111	−0.980556	+	0.196240i	$0.937127\pi$
$282$	2.70399	0.161020
$283$	7.57643	0.450372	0.225186	−	0.974316i	$-0.427701\pi$
$283$	7.57643	0.450372	0.225186	+	0.974316i	$0.427701\pi$
$284$	−0.183767	−0.0109046
$285$	4.79523	0.284045
$286$	1.35684	0.0802314
$287$	13.3612	0.788687
$288$	−0.743171	−0.0437918
$289$	19.4691	1.14524
$290$	0	0
$291$	12.7432	0.747021
$292$	−0.617225	−0.0361204
$293$	7.65880	0.447432	0.223716	−	0.974654i	$-0.428181\pi$
$293$	7.65880	0.447432	0.223716	+	0.974654i	$0.428181\pi$
$294$	8.16323	0.476089
$295$	13.3363	0.776467
$296$	7.85270	0.456429
$297$	5.38188	0.312288
$298$	−7.07476	−0.409830
$299$	1.66698	0.0964037
$300$	0.0712286	0.00411238
$301$	7.38994	0.425949
$302$	−7.24667	−0.416999
$303$	22.5773	1.29703
$304$	6.64211	0.380951
$305$	−0.0724297	−0.00414731
$306$	−14.0163	−0.801260
$307$	−24.1799	−1.38002	−0.690009	−	0.723801i	$-0.742394\pi$
$307$	−24.1799	−1.38002	−0.690009	+	0.723801i	$0.742394\pi$
$308$	0.107793	0.00614207
$309$	10.0697	0.572847
$310$	−1.70083	−0.0966009
$311$	27.6672	1.56886	0.784431	−	0.620216i	$-0.212955\pi$
$311$	27.6672	1.56886	0.784431	+	0.620216i	$0.212955\pi$
$312$	3.24706	0.183828
$313$	9.85395	0.556978	0.278489	−	0.960439i	$-0.410166\pi$
$313$	9.85395	0.556978	0.278489	+	0.960439i	$0.410166\pi$
$314$	−25.5617	−1.44253
$315$	5.53083	0.311627
$316$	−0.0774499	−0.00435690
$317$	−8.10460	−0.455200	−0.227600	−	0.973755i	$-0.573088\pi$
$317$	−8.10460	−0.455200	−0.227600	+	0.973755i	$0.573088\pi$
$318$	−3.78086	−0.212020
$319$	0	0
$320$	19.9416	1.11477
$321$	8.42185	0.470062
$322$	−3.24126	−0.180629
$323$	−10.4544	−0.581696
$324$	0.0921181	0.00511767
$325$	0.771322	0.0427853
$326$	0.278802	0.0154414
$327$	10.0930	0.558146
$328$	28.0377	1.54812
$329$	2.32621	0.128248
$330$	−3.83967	−0.211367
$331$	−15.5132	−0.852682	−0.426341	−	0.904563i	$-0.640198\pi$
$331$	−15.5132	−0.852682	−0.426341	+	0.904563i	$0.640198\pi$
$332$	0.0686889	0.00376979
$333$	4.56353	0.250080
$334$	−26.9338	−1.47375
$335$	9.46188	0.516958
$336$	−6.06535	−0.330892
$337$	14.2869	0.778258	0.389129	−	0.921183i	$-0.372776\pi$
$337$	14.2869	0.778258	0.389129	+	0.921183i	$0.372776\pi$
$338$	−16.6922	−0.907936
$339$	−6.49288	−0.352645
$340$	−1.14063	−0.0618591
$341$	−0.510010	−0.0276186
$342$	4.01796	0.217267
$343$	16.6338	0.898141
$344$	15.5074	0.836101
$345$	−4.71733	−0.253972
$346$	8.88368	0.477590
$347$	−6.64037	−0.356474	−0.178237	−	0.983988i	$-0.557039\pi$
$347$	−6.64037	−0.356474	−0.178237	+	0.983988i	$0.557039\pi$
$348$	0	0
$349$	3.01142	0.161198	0.0805988	−	0.996747i	$-0.474317\pi$
$349$	3.01142	0.161198	0.0805988	+	0.996747i	$0.474317\pi$
$350$	−1.49976	−0.0801653
$351$	5.26796	0.281183
$352$	0.443850	0.0236573
$353$	7.26831	0.386853	0.193427	−	0.981115i	$-0.438040\pi$
$353$	7.26831	0.386853	0.193427	+	0.981115i	$0.438040\pi$
$354$	−8.84707	−0.470216
$355$	5.63140	0.298884
$356$	−1.39386	−0.0738745
$357$	9.54657	0.505258
$358$	−19.9632	−1.05509
$359$	−19.7929	−1.04463	−0.522314	−	0.852753i	$-0.674931\pi$
$359$	−19.7929	−1.04463	−0.522314	+	0.852753i	$0.674931\pi$
$360$	11.6061	0.611697
$361$	−16.0031	−0.842270
$362$	−18.3808	−0.966071
$363$	−1.15136	−0.0604307
$364$	0.105511	0.00553029
$365$	18.9144	0.990024
$366$	0.0480488	0.00251155
$367$	−9.91892	−0.517764	−0.258882	−	0.965909i	$-0.583354\pi$
$367$	−9.91892	−0.517764	−0.258882	+	0.965909i	$0.583354\pi$
$368$	−6.53420	−0.340619
$369$	16.2939	0.848224
$370$	−9.08933	−0.472532
$371$	−3.25263	−0.168868
$372$	−0.0461004	−0.00239020
$373$	9.31223	0.482169	0.241085	−	0.970504i	$-0.422497\pi$
$373$	9.31223	0.482169	0.241085	+	0.970504i	$0.422497\pi$
$374$	8.37109	0.432859
$375$	11.6671	0.602487
$376$	4.88141	0.251740
$377$	0	0
$378$	−10.2430	−0.526843
$379$	−14.5896	−0.749418	−0.374709	−	0.927143i	$-0.622257\pi$
$379$	−14.5896	−0.749418	−0.374709	+	0.927143i	$0.622257\pi$
$380$	0.326975	0.0167735
$381$	−10.3721	−0.531380
$382$	−32.3126	−1.65326
$383$	14.9973	0.766325	0.383163	−	0.923681i	$-0.374835\pi$
$383$	14.9973	0.766325	0.383163	+	0.923681i	$0.374835\pi$
$384$	−12.2069	−0.622932
$385$	−3.30323	−0.168348
$386$	6.49295	0.330483
$387$	9.01196	0.458104
$388$	0.868930	0.0441132
$389$	−26.4560	−1.34137	−0.670686	−	0.741741i	$-0.734000\pi$
$389$	−26.4560	−1.34137	−0.670686	+	0.741741i	$0.734000\pi$
$390$	−3.75840	−0.190314
$391$	10.2845	0.520110
$392$	14.7368	0.744321
$393$	−24.8924	−1.25566
$394$	−27.8884	−1.40500
$395$	2.37339	0.119418
$396$	0.131452	0.00660573
$397$	6.57905	0.330193	0.165097	−	0.986277i	$-0.447206\pi$
$397$	6.57905	0.330193	0.165097	+	0.986277i	$0.447206\pi$
$398$	0.452585	0.0226860
$399$	−2.73665	−0.137004
$400$	−3.02342	−0.151171
$401$	−25.1993	−1.25839	−0.629197	−	0.777246i	$-0.716616\pi$
$401$	−25.1993	−1.25839	−0.629197	+	0.777246i	$0.716616\pi$
$402$	−6.27687	−0.313062
$403$	−0.499214	−0.0248676
$404$	1.53949	0.0765926
$405$	−2.82288	−0.140270
$406$	0	0
$407$	−2.72551	−0.135099
$408$	20.0329	0.991778
$409$	25.8318	1.27730	0.638651	−	0.769497i	$-0.279493\pi$
$409$	25.8318	1.27730	0.638651	+	0.769497i	$0.279493\pi$
$410$	−32.4530	−1.60274
$411$	10.9557	0.540404
$412$	0.686631	0.0338279
$413$	−7.61103	−0.374514
$414$	−3.95269	−0.194264
$415$	−2.10492	−0.103326
$416$	0.434455	0.0213009
$417$	6.86921	0.336387
$418$	−2.39968	−0.117372
$419$	18.4012	0.898956	0.449478	−	0.893291i	$-0.351610\pi$
$419$	18.4012	0.898956	0.449478	+	0.893291i	$0.351610\pi$
$420$	−0.298583	−0.0145694
$421$	−7.80236	−0.380264	−0.190132	−	0.981759i	$-0.560892\pi$
$421$	−7.80236	−0.380264	−0.190132	+	0.981759i	$0.560892\pi$
$422$	30.5154	1.48547
$423$	2.83679	0.137929
$424$	−6.82546	−0.331474
$425$	4.75872	0.230832
$426$	−3.73579	−0.180999
$427$	0.0413358	0.00200038
$428$	0.574266	0.0277582
$429$	−1.12699	−0.0544114
$430$	−17.9494	−0.865598
$431$	−33.6877	−1.62268	−0.811340	−	0.584574i	$-0.801262\pi$
$431$	−33.6877	−1.62268	−0.811340	+	0.584574i	$0.801262\pi$
$432$	−20.6493	−0.993490
$433$	22.7526	1.09342	0.546711	−	0.837321i	$-0.315880\pi$
$433$	22.7526	1.09342	0.546711	+	0.837321i	$0.315880\pi$
$434$	0.970670	0.0465937
$435$	0	0
$436$	0.688220	0.0329597
$437$	−2.94819	−0.141031
$438$	−12.5475	−0.599543
$439$	5.56846	0.265768	0.132884	−	0.991132i	$-0.457576\pi$
$439$	5.56846	0.265768	0.132884	+	0.991132i	$0.457576\pi$
$440$	−6.93163	−0.330452
$441$	8.56416	0.407817
$442$	8.19389	0.389744
$443$	27.5811	1.31042	0.655208	−	0.755448i	$-0.272581\pi$
$443$	27.5811	1.31042	0.655208	+	0.755448i	$0.272581\pi$
$444$	−0.246363	−0.0116919
$445$	42.7138	2.02483
$446$	−28.9074	−1.36880
$447$	5.87629	0.277939
$448$	−11.3807	−0.537689
$449$	−35.9110	−1.69474	−0.847372	−	0.531000i	$-0.821816\pi$
$449$	−35.9110	−1.69474	−0.847372	+	0.531000i	$0.821816\pi$
$450$	−1.82894	−0.0862170
$451$	−9.73132	−0.458230
$452$	−0.442734	−0.0208245
$453$	6.01908	0.282801
$454$	−19.1007	−0.896441
$455$	−3.23330	−0.151580
$456$	−5.74270	−0.268927
$457$	−4.39904	−0.205778	−0.102889	−	0.994693i	$-0.532809\pi$
$457$	−4.39904	−0.205778	−0.102889	+	0.994693i	$0.532809\pi$
$458$	−20.8579	−0.974623
$459$	32.5010	1.51702
$460$	−0.321663	−0.0149976
$461$	35.9918	1.67630	0.838152	−	0.545437i	$-0.183636\pi$
$461$	35.9918	1.67630	0.838152	+	0.545437i	$0.183636\pi$
$462$	2.19131	0.101949
$463$	−2.33790	−0.108651	−0.0543257	−	0.998523i	$-0.517301\pi$
$463$	−2.33790	−0.108651	−0.0543257	+	0.998523i	$0.517301\pi$
$464$	0	0
$465$	1.41271	0.0655129
$466$	5.64121	0.261324
$467$	13.9840	0.647102	0.323551	−	0.946211i	$-0.395123\pi$
$467$	13.9840	0.647102	0.323551	+	0.946211i	$0.395123\pi$
$468$	0.128670	0.00594776
$469$	−5.39992	−0.249345
$470$	−5.65013	−0.260621
$471$	21.2315	0.978296
$472$	−15.9713	−0.735139
$473$	−5.38229	−0.247478
$474$	−1.57447	−0.0723179
$475$	−1.36415	−0.0625915
$476$	0.650958	0.0298366
$477$	−3.96655	−0.181616
$478$	2.39817	0.109690
$479$	−31.8489	−1.45521	−0.727607	−	0.685994i	$-0.759368\pi$
$479$	−31.8489	−1.45521	−0.727607	+	0.685994i	$0.759368\pi$
$480$	−1.22945	−0.0561166
$481$	−2.66782	−0.121642
$482$	23.7072	1.07983
$483$	2.69219	0.122499
$484$	−0.0785084	−0.00356856
$485$	−26.6277	−1.20910
$486$	−20.5081	−0.930266
$487$	−8.89056	−0.402870	−0.201435	−	0.979502i	$-0.564560\pi$
$487$	−8.89056	−0.402870	−0.201435	+	0.979502i	$0.564560\pi$
$488$	0.0867408	0.00392657
$489$	−0.231573	−0.0104721
$490$	−17.0575	−0.770580
$491$	33.1387	1.49553	0.747764	−	0.663964i	$-0.231127\pi$
$491$	33.1387	1.49553	0.747764	+	0.663964i	$0.231127\pi$
$492$	−0.879626	−0.0396566
$493$	0	0
$494$	−2.34889	−0.105681
$495$	−4.02825	−0.181056
$496$	1.95682	0.0878636
$497$	−3.21385	−0.144161
$498$	1.39637	0.0625728
$499$	35.5794	1.59275	0.796377	−	0.604800i	$-0.206747\pi$
$499$	35.5794	1.59275	0.796377	+	0.604800i	$0.206747\pi$
$500$	0.795552	0.0355782
$501$	22.3712	0.999471
$502$	30.8547	1.37711
$503$	−28.5383	−1.27246	−0.636231	−	0.771499i	$-0.719507\pi$
$503$	−28.5383	−1.27246	−0.636231	+	0.771499i	$0.719507\pi$
$504$	−6.62365	−0.295041
$505$	−47.1765	−2.09933
$506$	2.36070	0.104946
$507$	13.8645	0.615745
$508$	−0.707251	−0.0313792
$509$	18.0845	0.801581	0.400790	−	0.916170i	$-0.368736\pi$
$509$	18.0845	0.801581	0.400790	+	0.916170i	$0.368736\pi$
$510$	−23.1877	−1.02677
$511$	−10.7945	−0.477519
$512$	−23.8121	−1.05236
$513$	−9.31684	−0.411348
$514$	−40.3979	−1.78187
$515$	−21.0412	−0.927188
$516$	−0.486512	−0.0214175
$517$	−1.69424	−0.0745125
$518$	5.18730	0.227917
$519$	−7.37878	−0.323892
$520$	−6.78490	−0.297538
$521$	27.5896	1.20872	0.604360	−	0.796711i	$-0.293429\pi$
$521$	27.5896	1.20872	0.604360	+	0.796711i	$0.293429\pi$
$522$	0	0
$523$	−23.1634	−1.01286	−0.506432	−	0.862280i	$-0.669036\pi$
$523$	−23.1634	−1.01286	−0.506432	+	0.862280i	$0.669036\pi$
$524$	−1.69735	−0.0741492
$525$	1.24570	0.0543666
$526$	−1.43010	−0.0623553
$527$	−3.07993	−0.134164
$528$	4.41756	0.192249
$529$	−20.0997	−0.873900
$530$	7.90032	0.343168
$531$	−9.28158	−0.402786
$532$	−0.186605	−0.00809037
$533$	−9.52533	−0.412588
$534$	−28.3357	−1.22620
$535$	−17.5979	−0.760825
$536$	−11.3314	−0.489443
$537$	16.5814	0.715541
$538$	−2.01432	−0.0868437
$539$	−5.11484	−0.220312
$540$	−1.01652	−0.0437439
$541$	−38.3283	−1.64786	−0.823932	−	0.566688i	$-0.808224\pi$
$541$	−38.3283	−1.64786	−0.823932	+	0.566688i	$0.808224\pi$
$542$	34.9370	1.50067
$543$	15.2670	0.655171
$544$	2.68040	0.114921
$545$	−21.0899	−0.903394
$546$	2.14492	0.0917943
$547$	−1.52875	−0.0653645	−0.0326823	−	0.999466i	$-0.510405\pi$
$547$	−1.52875	−0.0653645	−0.0326823	+	0.999466i	$0.510405\pi$
$548$	0.747042	0.0319121
$549$	0.0504086	0.00215139
$550$	1.09231	0.0465763
$551$	0	0
$552$	5.64941	0.240455
$553$	−1.35450	−0.0575992
$554$	−44.5097	−1.89104
$555$	7.54959	0.320462
$556$	0.468395	0.0198644
$557$	−20.0398	−0.849115	−0.424558	−	0.905401i	$-0.639570\pi$
$557$	−20.0398	−0.849115	−0.424558	+	0.905401i	$0.639570\pi$
$558$	1.18372	0.0501110
$559$	−5.26836	−0.222828
$560$	12.6739	0.535569
$561$	−6.95302	−0.293557
$562$	−45.5696	−1.92224
$563$	−0.565111	−0.0238166	−0.0119083	−	0.999929i	$-0.503791\pi$
$563$	−0.565111	−0.0238166	−0.0119083	+	0.999929i	$0.503791\pi$
$564$	−0.153144	−0.00644854
$565$	13.5672	0.570777
$566$	10.5023	0.441444
$567$	1.61103	0.0676568
$568$	−6.74409	−0.282976
$569$	10.8737	0.455849	0.227924	−	0.973679i	$-0.426806\pi$
$569$	10.8737	0.455849	0.227924	+	0.973679i	$0.426806\pi$
$570$	6.64705	0.278414
$571$	18.4657	0.772763	0.386382	−	0.922339i	$-0.373725\pi$
$571$	18.4657	0.772763	0.386382	+	0.922339i	$0.373725\pi$
$572$	−0.0768466	−0.00321312
$573$	26.8388	1.12121
$574$	18.5210	0.773052
$575$	1.34199	0.0559648
$576$	−13.8787	−0.578279
$577$	−33.2202	−1.38297	−0.691487	−	0.722388i	$-0.743044\pi$
$577$	−33.2202	−1.38297	−0.691487	+	0.722388i	$0.743044\pi$
$578$	26.9877	1.12254
$579$	−5.39304	−0.224127
$580$	0	0
$581$	1.20128	0.0498375
$582$	17.6644	0.732212
$583$	2.36898	0.0981130
$584$	−22.6516	−0.937329
$585$	−3.94298	−0.163022
$586$	10.6165	0.438562
$587$	−19.4978	−0.804761	−0.402380	−	0.915473i	$-0.631817\pi$
$587$	−19.4978	−0.804761	−0.402380	+	0.915473i	$0.631817\pi$
$588$	−0.462337	−0.0190665
$589$	0.882903	0.0363794
$590$	18.4864	0.761074
$591$	23.1641	0.952843
$592$	10.4573	0.429792
$593$	6.38642	0.262259	0.131129	−	0.991365i	$-0.458140\pi$
$593$	6.38642	0.262259	0.131129	+	0.991365i	$0.458140\pi$
$594$	7.46025	0.306098
$595$	−19.9481	−0.817791
$596$	0.400690	0.0164129
$597$	−0.375917	−0.0153852
$598$	2.31073	0.0944927
$599$	−24.4472	−0.998884	−0.499442	−	0.866347i	$-0.666462\pi$
$599$	−24.4472	−0.998884	−0.499442	+	0.866347i	$0.666462\pi$
$600$	2.61402	0.106717
$601$	8.78275	0.358256	0.179128	−	0.983826i	$-0.442672\pi$
$601$	8.78275	0.358256	0.179128	+	0.983826i	$0.442672\pi$
$602$	10.2438	0.417505
$603$	−6.58515	−0.268168
$604$	0.410426	0.0167000
$605$	2.40583	0.0978108
$606$	31.2962	1.27132
$607$	−5.14176	−0.208698	−0.104349	−	0.994541i	$-0.533276\pi$
$607$	−5.14176	−0.208698	−0.104349	+	0.994541i	$0.533276\pi$
$608$	−0.768371	−0.0311616
$609$	0	0
$610$	−0.100401	−0.00406510
$611$	−1.65838	−0.0670907
$612$	0.793837	0.0320889
$613$	19.3485	0.781481	0.390740	−	0.920501i	$-0.372219\pi$
$613$	19.3485	0.781481	0.390740	+	0.920501i	$0.372219\pi$
$614$	−33.5176	−1.35266
$615$	26.9554	1.08695
$616$	3.95590	0.159388
$617$	10.5571	0.425013	0.212507	−	0.977160i	$-0.431837\pi$
$617$	10.5571	0.425013	0.212507	+	0.977160i	$0.431837\pi$
$618$	13.9584	0.561491
$619$	37.8121	1.51980	0.759898	−	0.650042i	$-0.225249\pi$
$619$	37.8121	1.51980	0.759898	+	0.650042i	$0.225249\pi$
$620$	0.0963294	0.00386868
$621$	9.16548	0.367798
$622$	38.3517	1.53776
$623$	−24.3768	−0.976638
$624$	4.32405	0.173100
$625$	−28.3191	−1.13276
$626$	13.6593	0.545937
$627$	1.99317	0.0795997
$628$	1.44773	0.0577706
$629$	−16.4593	−0.656275
$630$	7.66672	0.305450
$631$	−14.1837	−0.564646	−0.282323	−	0.959319i	$-0.591105\pi$
$631$	−14.1837	−0.564646	−0.282323	+	0.959319i	$0.591105\pi$
$632$	−2.84234	−0.113062
$633$	−25.3461	−1.00742
$634$	−11.2344	−0.446176
$635$	21.6731	0.860072
$636$	0.214135	0.00849100
$637$	−5.00657	−0.198368
$638$	0	0
$639$	−3.91926	−0.155044
$640$	25.5070	1.00825
$641$	24.6087	0.971984	0.485992	−	0.873963i	$-0.338458\pi$
$641$	24.6087	0.971984	0.485992	+	0.873963i	$0.338458\pi$
$642$	11.6742	0.460744
$643$	−19.5738	−0.771917	−0.385959	−	0.922516i	$-0.626129\pi$
$643$	−19.5738	−0.771917	−0.385959	+	0.922516i	$0.626129\pi$
$644$	0.183574	0.00723383
$645$	14.9088	0.587032
$646$	−14.4916	−0.570165
$647$	49.3416	1.93982	0.969909	−	0.243468i	$-0.0782851\pi$
$647$	49.3416	1.93982	0.969909	+	0.243468i	$0.0782851\pi$
$648$	3.38065	0.132804
$649$	5.54331	0.217594
$650$	1.06919	0.0419371
$651$	−0.806237	−0.0315989
$652$	−0.0157904	−0.000618400 0
$653$	−40.0710	−1.56810	−0.784050	−	0.620697i	$-0.786850\pi$
$653$	−40.0710	−1.56810	−0.784050	+	0.620697i	$0.786850\pi$
$654$	13.9907	0.547081
$655$	52.0140	2.03236
$656$	37.3373	1.45778
$657$	−13.1638	−0.513567
$658$	3.22454	0.125706
$659$	17.3687	0.676588	0.338294	−	0.941040i	$-0.390150\pi$
$659$	17.3687	0.676588	0.338294	+	0.941040i	$0.390150\pi$
$660$	0.217466	0.00846485
$661$	25.2687	0.982838	0.491419	−	0.870923i	$-0.336478\pi$
$661$	25.2687	0.982838	0.491419	+	0.870923i	$0.336478\pi$
$662$	−21.5040	−0.835778
$663$	−6.80584	−0.264317
$664$	2.52082	0.0978267
$665$	5.71838	0.221749
$666$	6.32586	0.245122
$667$	0	0
$668$	1.52544	0.0590210
$669$	24.0104	0.928297
$670$	13.1159	0.506710
$671$	−0.0301060	−0.00116223
$672$	0.701651	0.0270668
$673$	−28.9810	−1.11714	−0.558568	−	0.829459i	$-0.688649\pi$
$673$	−28.9810	−1.11714	−0.558568	+	0.829459i	$0.688649\pi$
$674$	19.8042	0.762830
$675$	4.24093	0.163234
$676$	0.945389	0.0363611
$677$	19.6424	0.754919	0.377459	−	0.926026i	$-0.376798\pi$
$677$	19.6424	0.754919	0.377459	+	0.926026i	$0.376798\pi$
$678$	−9.00029	−0.345654
$679$	15.1965	0.583187
$680$	−41.8599	−1.60525
$681$	15.8650	0.607949
$682$	−0.706965	−0.0270711
$683$	1.90661	0.0729545	0.0364772	−	0.999334i	$-0.488386\pi$
$683$	1.90661	0.0729545	0.0364772	+	0.999334i	$0.488386\pi$
$684$	−0.227564	−0.00870111
$685$	−22.8925	−0.874678
$686$	23.0574	0.880337
$687$	17.3245	0.660971
$688$	20.6509	0.787307
$689$	2.31883	0.0883405
$690$	−6.53906	−0.248938
$691$	13.0690	0.497168	0.248584	−	0.968610i	$-0.420035\pi$
$691$	13.0690	0.497168	0.248584	+	0.968610i	$0.420035\pi$
$692$	−0.503141	−0.0191266
$693$	2.29893	0.0873292
$694$	−9.20474	−0.349407
$695$	−14.3536	−0.544463
$696$	0	0
$697$	−58.7671	−2.22596
$698$	4.17437	0.158002
$699$	−4.68558	−0.177225
$700$	0.0849410	0.00321047
$701$	−32.3309	−1.22112	−0.610561	−	0.791969i	$-0.709056\pi$
$701$	−32.3309	−1.22112	−0.610561	+	0.791969i	$0.709056\pi$
$702$	7.30233	0.275609
$703$	4.71827	0.177953
$704$	8.28890	0.312400
$705$	4.69299	0.176748
$706$	10.0752	0.379185
$707$	26.9237	1.01257
$708$	0.501067	0.0188313
$709$	29.2032	1.09675	0.548375	−	0.836232i	$-0.315246\pi$
$709$	29.2032	1.09675	0.548375	+	0.836232i	$0.315246\pi$
$710$	7.80613	0.292959
$711$	−1.65180	−0.0619473
$712$	−51.1534	−1.91706
$713$	−0.868560	−0.0325278
$714$	13.2332	0.495242
$715$	2.35490	0.0880683
$716$	1.13065	0.0422542
$717$	−1.99192	−0.0743896
$718$	−27.4365	−1.02392
$719$	−45.6533	−1.70258	−0.851290	−	0.524696i	$-0.824179\pi$
$719$	−45.6533	−1.70258	−0.851290	+	0.524696i	$0.824179\pi$
$720$	15.4557	0.575999
$721$	12.0083	0.447212
$722$	−22.1832	−0.825573
$723$	−19.6912	−0.732324
$724$	1.04102	0.0386893
$725$	0	0
$726$	−1.59599	−0.0592327
$727$	40.1294	1.48832	0.744159	−	0.668003i	$-0.232851\pi$
$727$	40.1294	1.48832	0.744159	+	0.668003i	$0.232851\pi$
$728$	3.87216	0.143512
$729$	20.5541	0.761261
$730$	26.2187	0.970398
$731$	−32.5035	−1.20218
$732$	−0.00272132	−0.000100583 0
$733$	−11.8996	−0.439522	−0.219761	−	0.975554i	$-0.570528\pi$
$733$	−11.8996	−0.439522	−0.219761	+	0.975554i	$0.570528\pi$
$734$	−13.7494	−0.507500
$735$	14.1680	0.522593
$736$	0.755889	0.0278624
$737$	3.93290	0.144870
$738$	22.5862	0.831409
$739$	−25.8235	−0.949934	−0.474967	−	0.880004i	$-0.657540\pi$
$739$	−25.8235	−0.949934	−0.474967	+	0.880004i	$0.657540\pi$
$740$	0.514788	0.0189240
$741$	1.95098	0.0716711
$742$	−4.50873	−0.165521
$743$	−46.2434	−1.69651	−0.848253	−	0.529592i	$-0.822345\pi$
$743$	−46.2434	−1.69651	−0.848253	+	0.529592i	$0.822345\pi$
$744$	−1.69184	−0.0620260
$745$	−12.2788	−0.449861
$746$	12.9084	0.472611
$747$	1.46495	0.0535997
$748$	−0.474110	−0.0173352
$749$	10.0432	0.366970
$750$	16.1727	0.590543
$751$	30.9977	1.13112	0.565561	−	0.824707i	$-0.308660\pi$
$751$	30.9977	1.13112	0.565561	+	0.824707i	$0.308660\pi$
$752$	6.50049	0.237048
$753$	−25.6279	−0.933933
$754$	0	0
$755$	−12.5772	−0.457731
$756$	0.580128	0.0210991
$757$	3.59958	0.130829	0.0654146	−	0.997858i	$-0.479163\pi$
$757$	3.59958	0.130829	0.0654146	+	0.997858i	$0.479163\pi$
$758$	−20.2238	−0.734561
$759$	−1.96079	−0.0711723
$760$	11.9997	0.435274
$761$	9.95606	0.360907	0.180454	−	0.983584i	$-0.442243\pi$
$761$	9.95606	0.360907	0.180454	+	0.983584i	$0.442243\pi$
$762$	−14.3776	−0.520847
$763$	12.0361	0.435735
$764$	1.83008	0.0662098
$765$	−24.3265	−0.879526
$766$	20.7889	0.751134
$767$	5.42597	0.195921
$768$	2.16600	0.0781590
$769$	18.7115	0.674754	0.337377	−	0.941370i	$-0.390460\pi$
$769$	18.7115	0.674754	0.337377	+	0.941370i	$0.390460\pi$
$770$	−4.57886	−0.165011
$771$	33.5544	1.20843
$772$	−0.367739	−0.0132352
$773$	−6.91095	−0.248569	−0.124285	−	0.992247i	$-0.539664\pi$
$773$	−6.91095	−0.248569	−0.124285	+	0.992247i	$0.539664\pi$
$774$	12.4922	0.449022
$775$	−0.401889	−0.0144363
$776$	31.8889	1.14475
$777$	−4.30857	−0.154569
$778$	−36.6727	−1.31478
$779$	16.8464	0.603583
$780$	0.212863	0.00762170
$781$	2.34073	0.0837581
$782$	14.2562	0.509800
$783$	0	0
$784$	19.6247	0.700883
$785$	−44.3644	−1.58343
$786$	−34.5053	−1.23076
$787$	−18.8405	−0.671593	−0.335796	−	0.941935i	$-0.609005\pi$
$787$	−18.8405	−0.671593	−0.335796	+	0.941935i	$0.609005\pi$
$788$	1.57950	0.0562675
$789$	1.18784	0.0422882
$790$	3.28994	0.117051
$791$	−7.74285	−0.275304
$792$	4.82418	0.171420
$793$	−0.0294687	−0.00104646
$794$	9.11974	0.323647
$795$	−6.56200	−0.232730
$796$	−0.0256329	−0.000908533 0
$797$	9.39864	0.332917	0.166458	−	0.986048i	$-0.446767\pi$
$797$	9.39864	0.332917	0.166458	+	0.986048i	$0.446767\pi$
$798$	−3.79348	−0.134288
$799$	−10.2315	−0.361963
$800$	0.349755	0.0123657
$801$	−29.7273	−1.05036
$802$	−34.9308	−1.23345
$803$	7.86190	0.277440
$804$	0.355500	0.0125375
$805$	−5.62548	−0.198272
$806$	−0.692000	−0.0243747
$807$	1.67310	0.0588958
$808$	56.4979	1.98759
$809$	20.9584	0.736857	0.368428	−	0.929656i	$-0.379896\pi$
$809$	20.9584	0.736857	0.368428	+	0.929656i	$0.379896\pi$
$810$	−3.91302	−0.137490
$811$	−7.78372	−0.273323	−0.136662	−	0.990618i	$-0.543637\pi$
$811$	−7.78372	−0.273323	−0.136662	+	0.990618i	$0.543637\pi$
$812$	0	0
$813$	−29.0187	−1.01773
$814$	−3.77805	−0.132421
$815$	0.483884	0.0169497
$816$	26.6775	0.933898
$817$	9.31754	0.325980
$818$	35.8075	1.25198
$819$	2.25027	0.0786308
$820$	1.83803	0.0641867
$821$	−26.5331	−0.926013	−0.463007	−	0.886355i	$-0.653229\pi$
$821$	−26.5331	−0.926013	−0.463007	+	0.886355i	$0.653229\pi$
$822$	15.1865	0.529692
$823$	40.3289	1.40578	0.702888	−	0.711300i	$-0.251893\pi$
$823$	40.3289	1.40578	0.702888	+	0.711300i	$0.251893\pi$
$824$	25.1987	0.877838
$825$	−0.907273	−0.0315872
$826$	−10.5502	−0.367090
$827$	−22.7206	−0.790074	−0.395037	−	0.918665i	$-0.629268\pi$
$827$	−22.7206	−0.790074	−0.395037	+	0.918665i	$0.629268\pi$
$828$	0.223867	0.00777991
$829$	14.0061	0.486451	0.243225	−	0.969970i	$-0.421795\pi$
$829$	14.0061	0.486451	0.243225	+	0.969970i	$0.421795\pi$
$830$	−2.91779	−0.101278
$831$	36.9697	1.28246
$832$	8.11344	0.281283
$833$	−30.8884	−1.07022
$834$	9.52196	0.329718
$835$	−46.7458	−1.61771
$836$	0.135910	0.00470054
$837$	−2.74481	−0.0948746
$838$	25.5073	0.881136
$839$	−37.4586	−1.29321	−0.646607	−	0.762824i	$-0.723812\pi$
$839$	−37.4586	−1.29321	−0.646607	+	0.762824i	$0.723812\pi$
$840$	−10.9577	−0.378077
$841$	0	0
$842$	−10.8155	−0.372726
$843$	37.8500	1.30362
$844$	−1.72829	−0.0594902
$845$	−28.9707	−0.996622
$846$	3.93230	0.135195
$847$	−1.37301	−0.0471772
$848$	−9.08934	−0.312129
$849$	−8.72318	−0.299379
$850$	6.59644	0.226256
$851$	−4.64162	−0.159113
$852$	0.211582	0.00724868
$853$	−8.05331	−0.275740	−0.137870	−	0.990450i	$-0.544026\pi$
$853$	−8.05331	−0.275740	−0.137870	+	0.990450i	$0.544026\pi$
$854$	0.0572988	0.00196073
$855$	6.97350	0.238489
$856$	21.0750	0.720330
$857$	−41.1675	−1.40626	−0.703128	−	0.711063i	$-0.748214\pi$
$857$	−41.1675	−1.40626	−0.703128	+	0.711063i	$0.748214\pi$
$858$	−1.56221	−0.0533328
$859$	−42.9519	−1.46550	−0.732750	−	0.680498i	$-0.761763\pi$
$859$	−42.9519	−1.46550	−0.732750	+	0.680498i	$0.761763\pi$
$860$	1.01659	0.0346656
$861$	−15.3835	−0.524269
$862$	−46.6972	−1.59051
$863$	41.0241	1.39648	0.698239	−	0.715865i	$-0.253967\pi$
$863$	41.0241	1.39648	0.698239	+	0.715865i	$0.253967\pi$
$864$	2.38875	0.0812669
$865$	15.4184	0.524240
$866$	31.5392	1.07175
$867$	−22.4160	−0.761286
$868$	−0.0549754	−0.00186599
$869$	0.986518	0.0334653
$870$	0	0
$871$	3.84965	0.130440
$872$	25.2570	0.855310
$873$	18.5319	0.627211
$874$	−4.08672	−0.138235
$875$	13.9132	0.470351
$876$	0.710648	0.0240106
$877$	14.3160	0.483417	0.241708	−	0.970349i	$-0.422292\pi$
$877$	14.3160	0.483417	0.241708	+	0.970349i	$0.422292\pi$
$878$	7.71888	0.260499
$879$	−8.81803	−0.297425
$880$	−9.23072	−0.311168
$881$	−20.0196	−0.674477	−0.337239	−	0.941419i	$-0.609493\pi$
$881$	−20.0196	−0.674477	−0.337239	+	0.941419i	$0.609493\pi$
$882$	11.8715	0.399733
$883$	19.8955	0.669537	0.334768	−	0.942300i	$-0.391342\pi$
$883$	19.8955	0.669537	0.334768	+	0.942300i	$0.391342\pi$
$884$	−0.464074	−0.0156085
$885$	−15.3548	−0.516146
$886$	38.2323	1.28444
$887$	33.0589	1.11001	0.555005	−	0.831847i	$-0.312716\pi$
$887$	33.0589	1.11001	0.555005	+	0.831847i	$0.312716\pi$
$888$	−9.04128	−0.303405
$889$	−12.3689	−0.414840
$890$	59.2089	1.98469
$891$	−1.17335	−0.0393088
$892$	1.63721	0.0548180
$893$	2.93298	0.0981484
$894$	8.14559	0.272429
$895$	−34.6478	−1.15815
$896$	−14.5569	−0.486313
$897$	−1.91929	−0.0640831
$898$	−49.7790	−1.66115
$899$	0	0
$900$	0.103585	0.00345283
$901$	14.3062	0.476608
$902$	−13.4893	−0.449146
$903$	−8.50847	−0.283144
$904$	−16.2479	−0.540398
$905$	−31.9013	−1.06044
$906$	8.34352	0.277195
$907$	32.3582	1.07444	0.537218	−	0.843443i	$-0.319475\pi$
$907$	32.3582	1.07444	0.537218	+	0.843443i	$0.319475\pi$
$908$	1.08180	0.0359007
$909$	32.8332	1.08901
$910$	−4.48194	−0.148575
$911$	55.9071	1.85229	0.926143	−	0.377173i	$-0.123104\pi$
$911$	55.9071	1.85229	0.926143	+	0.377173i	$0.123104\pi$
$912$	−7.64745	−0.253232
$913$	−0.874924	−0.0289558
$914$	−6.09785	−0.201699
$915$	0.0833926	0.00275687
$916$	1.18132	0.0390318
$917$	−29.6845	−0.980269
$918$	45.0522	1.48694
$919$	25.1783	0.830557	0.415278	−	0.909694i	$-0.363684\pi$
$919$	25.1783	0.830557	0.415278	+	0.909694i	$0.363684\pi$
$920$	−11.8047	−0.389191
$921$	27.8397	0.917350
$922$	49.8910	1.64307
$923$	2.29119	0.0754153
$924$	−0.124108	−0.00408286
$925$	−2.14771	−0.0706163
$926$	−3.24075	−0.106498
$927$	14.6440	0.480972
$928$	0	0
$929$	55.7948	1.83057	0.915284	−	0.402809i	$-0.131966\pi$
$929$	55.7948	1.83057	0.915284	+	0.402809i	$0.131966\pi$
$930$	1.95827	0.0642142
$931$	8.85455	0.290196
$932$	−0.319499	−0.0104655
$933$	−31.8549	−1.04288
$934$	19.3843	0.634274
$935$	14.5287	0.475140
$936$	4.72206	0.154345
$937$	−4.41681	−0.144291	−0.0721455	−	0.997394i	$-0.522985\pi$
$937$	−4.41681	−0.144291	−0.0721455	+	0.997394i	$0.522985\pi$
$938$	−7.48525	−0.244402
$939$	−11.3454	−0.370244
$940$	0.320004	0.0104374
$941$	5.05296	0.164722	0.0823610	−	0.996603i	$-0.473754\pi$
$941$	5.05296	0.164722	0.0823610	+	0.996603i	$0.473754\pi$
$942$	29.4307	0.958903
$943$	−16.5727	−0.539681
$944$	−21.2687	−0.692237
$945$	−17.7776	−0.578304
$946$	−7.46081	−0.242572
$947$	−10.6695	−0.346712	−0.173356	−	0.984859i	$-0.555461\pi$
$947$	−10.6695	−0.346712	−0.173356	+	0.984859i	$0.555461\pi$
$948$	0.0891726	0.00289619
$949$	7.69548	0.249806
$950$	−1.89095	−0.0613507
$951$	9.33130	0.302588
$952$	23.8895	0.774264
$953$	−26.3519	−0.853622	−0.426811	−	0.904341i	$-0.640363\pi$
$953$	−26.3519	−0.853622	−0.426811	+	0.904341i	$0.640363\pi$
$954$	−5.49835	−0.178016
$955$	−56.0812	−1.81474
$956$	−0.135824	−0.00439287
$957$	0	0
$958$	−44.1483	−1.42637
$959$	13.0648	0.421885
$960$	−22.9600	−0.741030
$961$	−30.7399	−0.991609
$962$	−3.69808	−0.119231
$963$	12.2476	0.394672
$964$	−1.34270	−0.0432453
$965$	11.2691	0.362764
$966$	3.73186	0.120071
$967$	−2.49199	−0.0801369	−0.0400684	−	0.999197i	$-0.512758\pi$
$967$	−2.49199	−0.0801369	−0.0400684	+	0.999197i	$0.512758\pi$
$968$	−2.88118	−0.0926048
$969$	12.0367	0.386675
$970$	−36.9107	−1.18513
$971$	1.67478	0.0537461	0.0268731	−	0.999639i	$-0.491445\pi$
$971$	1.67478	0.0537461	0.0268731	+	0.999639i	$0.491445\pi$
$972$	1.16151	0.0372554
$973$	8.19163	0.262612
$974$	−12.3239	−0.394883
$975$	−0.888068	−0.0284409
$976$	0.115511	0.00369742
$977$	−7.92507	−0.253545	−0.126773	−	0.991932i	$-0.540462\pi$
$977$	−7.92507	−0.253545	−0.126773	+	0.991932i	$0.540462\pi$
$978$	−0.321001	−0.0102645
$979$	17.7543	0.567430
$980$	0.966079	0.0308603
$981$	14.6779	0.468629
$982$	45.9362	1.46588
$983$	43.6234	1.39137	0.695685	−	0.718347i	$-0.255101\pi$
$983$	43.6234	1.39137	0.695685	+	0.718347i	$0.255101\pi$
$984$	−32.2815	−1.02910
$985$	−48.4026	−1.54224
$986$	0	0
$987$	−2.67830	−0.0852512
$988$	0.133033	0.00423234
$989$	−9.16617	−0.291467
$990$	−5.58388	−0.177467
$991$	15.7381	0.499937	0.249968	−	0.968254i	$-0.419580\pi$
$991$	15.7381	0.499937	0.249968	+	0.968254i	$0.419580\pi$
$992$	−0.226368	−0.00718719
$993$	17.8612	0.566809
$994$	−4.45498	−0.141303
$995$	0.785498	0.0249020
$996$	−0.0790856	−0.00250592
$997$	56.3878	1.78582	0.892910	−	0.450236i	$-0.148660\pi$
$997$	56.3878	1.78582	0.892910	+	0.450236i	$0.148660\pi$
$998$	49.3195	1.56118
$999$	−14.6684	−0.464087

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	9251.2.a.s.1.14	✓	18
29.28	even	2		9251.2.a.t.1.5	yes	18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
9251.2.a.s.1.14	✓	18	1.1	even	1	trivial
9251.2.a.t.1.5	yes	18	29.28	even	2

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)

\(f(q)\)	\(=\)	\(q+1.38618 q^{2} -1.15136 q^{3} -0.0785084 q^{4} +2.40583 q^{5} -1.59599 q^{6} -1.37301 q^{7} -2.88118 q^{8} -1.67437 q^{9} +O(q^{10})\)	\(q+1.38618 q^{2} -1.15136 q^{3} -0.0785084 q^{4} +2.40583 q^{5} -1.59599 q^{6} -1.37301 q^{7} -2.88118 q^{8} -1.67437 q^{9} +3.33491 q^{10} +1.00000 q^{11} +0.0903913 q^{12} +0.978832 q^{13} -1.90324 q^{14} -2.76997 q^{15} -3.83682 q^{16} +6.03897 q^{17} -2.32098 q^{18} -1.73115 q^{19} -0.188878 q^{20} +1.58083 q^{21} +1.38618 q^{22} +1.70303 q^{23} +3.31728 q^{24} +0.788002 q^{25} +1.35684 q^{26} +5.38188 q^{27} +0.107793 q^{28} -3.83967 q^{30} -0.510010 q^{31} +0.443850 q^{32} -1.15136 q^{33} +8.37109 q^{34} -3.30323 q^{35} +0.131452 q^{36} -2.72551 q^{37} -2.39968 q^{38} -1.12699 q^{39} -6.93163 q^{40} -9.73132 q^{41} +2.19131 q^{42} -5.38229 q^{43} -0.0785084 q^{44} -4.02825 q^{45} +2.36070 q^{46} -1.69424 q^{47} +4.41756 q^{48} -5.11484 q^{49} +1.09231 q^{50} -6.95302 q^{51} -0.0768466 q^{52} +2.36898 q^{53} +7.46025 q^{54} +2.40583 q^{55} +3.95590 q^{56} +1.99317 q^{57} +5.54331 q^{59} +0.217466 q^{60} -0.0301060 q^{61} -0.706965 q^{62} +2.29893 q^{63} +8.28890 q^{64} +2.35490 q^{65} -1.59599 q^{66} +3.93290 q^{67} -0.474110 q^{68} -1.96079 q^{69} -4.57886 q^{70} +2.34073 q^{71} +4.82418 q^{72} +7.86190 q^{73} -3.77805 q^{74} -0.907273 q^{75} +0.135910 q^{76} -1.37301 q^{77} -1.56221 q^{78} +0.986518 q^{79} -9.23072 q^{80} -1.17335 q^{81} -13.4893 q^{82} -0.874924 q^{83} -0.124108 q^{84} +14.5287 q^{85} -7.46081 q^{86} -2.88118 q^{88} +17.7543 q^{89} -5.58388 q^{90} -1.34395 q^{91} -0.133702 q^{92} +0.587204 q^{93} -2.34852 q^{94} -4.16484 q^{95} -0.511031 q^{96} -11.0680 q^{97} -7.09009 q^{98} -1.67437 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q - 3 q^{3} + 12 q^{4} - 6 q^{5} - q^{6} - 5 q^{7} + 3 q^{8} + 9 q^{9}+O(q^{10}) \) 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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