LMFDB - Embedded newform 421.2.a.b.1.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [421,2,Mod(1,421)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(421, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("421.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 421 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	421.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:	$3.36170192510$
Analytic rank:	$0$
Dimension:	$19$
Coefficient field:	$\mathbb{Q}[x]/(x^{19} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{19} - 4 x^{18} - 20 x^{17} + 93 x^{16} + 145 x^{15} - 874 x^{14} - 402 x^{13} + 4263 x^{12} + \cdots + 89 $ x^19 - 4x^18 - 20x^17 + 93x^16 + 145x^15 - 874x^14 - 402x^13 + 4263x^12 - 159x^11 - 11551x^10 + 3133x^9 + 17375x^8 - 5935x^7 - 14018x^6 + 4016x^5 + 5896x^4 - 1088x^3 - 1185x^2 + 101x + 89
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.11
Root			$0.519563$ of defining polynomial
Character	$\chi$	$=$	421.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.519563 q^{2} +3.06388 q^{3} -1.73005 q^{4} +0.568897 q^{5} +1.59188 q^{6} +0.332804 q^{7} -1.93800 q^{8} +6.38734 q^{9} +O(q^{10})$	\(q+0.519563 q^{2} +3.06388 q^{3} -1.73005 q^{4} +0.568897 q^{5} +1.59188 q^{6} +0.332804 q^{7} -1.93800 q^{8} +6.38734 q^{9} +0.295577 q^{10} +0.119783 q^{11} -5.30067 q^{12} +3.43037 q^{13} +0.172913 q^{14} +1.74303 q^{15} +2.45320 q^{16} +1.24801 q^{17} +3.31862 q^{18} -3.95007 q^{19} -0.984222 q^{20} +1.01967 q^{21} +0.0622347 q^{22} +3.97665 q^{23} -5.93778 q^{24} -4.67636 q^{25} +1.78229 q^{26} +10.3784 q^{27} -0.575770 q^{28} -6.63096 q^{29} +0.905613 q^{30} -1.80775 q^{31} +5.15058 q^{32} +0.367000 q^{33} +0.648417 q^{34} +0.189331 q^{35} -11.0504 q^{36} -4.17540 q^{37} -2.05231 q^{38} +10.5102 q^{39} -1.10252 q^{40} -3.33421 q^{41} +0.529783 q^{42} -1.55944 q^{43} -0.207231 q^{44} +3.63374 q^{45} +2.06612 q^{46} -8.32996 q^{47} +7.51630 q^{48} -6.88924 q^{49} -2.42966 q^{50} +3.82374 q^{51} -5.93472 q^{52} -7.88496 q^{53} +5.39222 q^{54} +0.0681441 q^{55} -0.644974 q^{56} -12.1025 q^{57} -3.44520 q^{58} -2.86921 q^{59} -3.01554 q^{60} +9.75064 q^{61} -0.939240 q^{62} +2.12573 q^{63} -2.23035 q^{64} +1.95152 q^{65} +0.190680 q^{66} +6.25043 q^{67} -2.15912 q^{68} +12.1840 q^{69} +0.0983694 q^{70} +9.94622 q^{71} -12.3786 q^{72} +13.3346 q^{73} -2.16938 q^{74} -14.3278 q^{75} +6.83383 q^{76} +0.0398643 q^{77} +5.46071 q^{78} -5.45859 q^{79} +1.39562 q^{80} +12.6361 q^{81} -1.73233 q^{82} +9.38546 q^{83} -1.76409 q^{84} +0.709987 q^{85} -0.810225 q^{86} -20.3164 q^{87} -0.232139 q^{88} +2.03454 q^{89} +1.88795 q^{90} +1.14164 q^{91} -6.87982 q^{92} -5.53873 q^{93} -4.32794 q^{94} -2.24718 q^{95} +15.7808 q^{96} +2.03203 q^{97} -3.57939 q^{98} +0.765094 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 19 q + 4 q^{2} + 7 q^{3} + 18 q^{4} + 7 q^{5} + 8 q^{6} + 3 q^{7} + 9 q^{8} + 20 q^{9}+O(q^{10}) $ 19 * q + 4 * q^2 + 7 * q^3 + 18 * q^4 + 7 * q^5 + 8 * q^6 + 3 * q^7 + 9 * q^8 + 20 * q^9	\( 19 q + 4 q^{2} + 7 q^{3} + 18 q^{4} + 7 q^{5} + 8 q^{6} + 3 q^{7} + 9 q^{8} + 20 q^{9} - 4 q^{10} + 31 q^{11} + 7 q^{12} - 2 q^{13} + 5 q^{14} + q^{15} + 8 q^{16} + 16 q^{17} + 2 q^{18} + 24 q^{19} + 5 q^{20} - 2 q^{21} - 11 q^{22} + 13 q^{23} + 23 q^{24} + 8 q^{25} + 14 q^{26} + 16 q^{27} - 12 q^{28} + 9 q^{29} - 15 q^{30} + 9 q^{31} + 2 q^{32} - 5 q^{33} - 8 q^{34} + 38 q^{35} - 8 q^{36} - 25 q^{37} + 9 q^{38} - 6 q^{39} - 23 q^{40} + 34 q^{41} - 39 q^{42} + 15 q^{43} + 29 q^{44} - 15 q^{45} - 25 q^{46} + 19 q^{47} - 17 q^{48} + 8 q^{49} - 21 q^{50} + 16 q^{51} - 19 q^{52} - 9 q^{53} + 2 q^{54} + 2 q^{55} - 7 q^{56} - 3 q^{57} - 18 q^{58} + 90 q^{59} - 67 q^{60} - 6 q^{61} - 27 q^{62} + 2 q^{63} - 49 q^{64} + 3 q^{65} - 3 q^{66} - 18 q^{67} + 22 q^{68} - 26 q^{69} - 55 q^{70} + 18 q^{71} - 51 q^{72} - 6 q^{73} + 12 q^{74} + 11 q^{75} - 23 q^{76} - 11 q^{77} - 49 q^{78} - 14 q^{79} - 15 q^{80} - 17 q^{81} - 55 q^{82} + 66 q^{83} - 68 q^{84} - 44 q^{85} - 26 q^{86} + q^{87} - 75 q^{88} + 19 q^{89} - 97 q^{90} - 22 q^{91} - 3 q^{92} - 44 q^{93} - 24 q^{94} + 8 q^{95} - 2 q^{96} - 29 q^{97} - 20 q^{98} + 38 q^{99}+O(q^{100}) \) 19 * q + 4 * q^2 + 7 * q^3 + 18 * q^4 + 7 * q^5 + 8 * q^6 + 3 * q^7 + 9 * q^8 + 20 * q^9 - 4 * q^10 + 31 * q^11 + 7 * q^12 - 2 * q^13 + 5 * q^14 + q^15 + 8 * q^16 + 16 * q^17 + 2 * q^18 + 24 * q^19 + 5 * q^20 - 2 * q^21 - 11 * q^22 + 13 * q^23 + 23 * q^24 + 8 * q^25 + 14 * q^26 + 16 * q^27 - 12 * q^28 + 9 * q^29 - 15 * q^30 + 9 * q^31 + 2 * q^32 - 5 * q^33 - 8 * q^34 + 38 * q^35 - 8 * q^36 - 25 * q^37 + 9 * q^38 - 6 * q^39 - 23 * q^40 + 34 * q^41 - 39 * q^42 + 15 * q^43 + 29 * q^44 - 15 * q^45 - 25 * q^46 + 19 * q^47 - 17 * q^48 + 8 * q^49 - 21 * q^50 + 16 * q^51 - 19 * q^52 - 9 * q^53 + 2 * q^54 + 2 * q^55 - 7 * q^56 - 3 * q^57 - 18 * q^58 + 90 * q^59 - 67 * q^60 - 6 * q^61 - 27 * q^62 + 2 * q^63 - 49 * q^64 + 3 * q^65 - 3 * q^66 - 18 * q^67 + 22 * q^68 - 26 * q^69 - 55 * q^70 + 18 * q^71 - 51 * q^72 - 6 * q^73 + 12 * q^74 + 11 * q^75 - 23 * q^76 - 11 * q^77 - 49 * q^78 - 14 * q^79 - 15 * q^80 - 17 * q^81 - 55 * q^82 + 66 * q^83 - 68 * q^84 - 44 * q^85 - 26 * q^86 + q^87 - 75 * q^88 + 19 * q^89 - 97 * q^90 - 22 * q^91 - 3 * q^92 - 44 * q^93 - 24 * q^94 + 8 * q^95 - 2 * q^96 - 29 * q^97 - 20 * q^98 + 38 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	0.519563	0.367386	0.183693	−	0.982984i	$-0.441195\pi$
$2$	0.519563	0.367386	0.183693	+	0.982984i	$0.441195\pi$
$3$	3.06388	1.76893	0.884465	−	0.466607i	$-0.154524\pi$
$3$	3.06388	1.76893	0.884465	+	0.466607i	$0.154524\pi$
$4$	−1.73005	−0.865027
$5$	0.568897	0.254418	0.127209	−	0.991876i	$-0.459398\pi$
$5$	0.568897	0.254418	0.127209	+	0.991876i	$0.459398\pi$
$6$	1.59188	0.649880
$7$	0.332804	0.125788	0.0628941	−	0.998020i	$-0.479967\pi$
$7$	0.332804	0.125788	0.0628941	+	0.998020i	$0.479967\pi$
$8$	−1.93800	−0.685185
$9$	6.38734	2.12911
$10$	0.295577	0.0934698
$11$	0.119783	0.0361159	0.0180580	−	0.999837i	$-0.494252\pi$
$11$	0.119783	0.0361159	0.0180580	+	0.999837i	$0.494252\pi$
$12$	−5.30067	−1.53017
$13$	3.43037	0.951412	0.475706	−	0.879604i	$-0.342193\pi$
$13$	3.43037	0.951412	0.475706	+	0.879604i	$0.342193\pi$
$14$	0.172913	0.0462129
$15$	1.74303	0.450048
$16$	2.45320	0.613300
$17$	1.24801	0.302686	0.151343	−	0.988481i	$-0.451640\pi$
$17$	1.24801	0.302686	0.151343	+	0.988481i	$0.451640\pi$
$18$	3.31862	0.782207
$19$	−3.95007	−0.906207	−0.453104	−	0.891458i	$-0.649683\pi$
$19$	−3.95007	−0.906207	−0.453104	+	0.891458i	$0.649683\pi$
$20$	−0.984222	−0.220079
$21$	1.01967	0.222511
$22$	0.0622347	0.0132685
$23$	3.97665	0.829188	0.414594	−	0.910006i	$-0.363924\pi$
$23$	3.97665	0.829188	0.414594	+	0.910006i	$0.363924\pi$
$24$	−5.93778	−1.21204
$25$	−4.67636	−0.935271
$26$	1.78229	0.349536
$27$	10.3784	1.99732
$28$	−0.575770	−0.108810
$29$	−6.63096	−1.23134	−0.615669	−	0.788005i	$-0.711114\pi$
$29$	−6.63096	−1.23134	−0.615669	+	0.788005i	$0.711114\pi$
$30$	0.905613	0.165341
$31$	−1.80775	−0.324682	−0.162341	−	0.986735i	$-0.551904\pi$
$31$	−1.80775	−0.324682	−0.162341	+	0.986735i	$0.551904\pi$
$32$	5.15058	0.910503
$33$	0.367000	0.0638865
$34$	0.648417	0.111203
$35$	0.189331	0.0320028
$36$	−11.0504	−1.84174
$37$	−4.17540	−0.686431	−0.343216	−	0.939257i	$-0.611516\pi$
$37$	−4.17540	−0.686431	−0.343216	+	0.939257i	$0.611516\pi$
$38$	−2.05231	−0.332928
$39$	10.5102	1.68298
$40$	−1.10252	−0.174324
$41$	−3.33421	−0.520716	−0.260358	−	0.965512i	$-0.583841\pi$
$41$	−3.33421	−0.520716	−0.260358	+	0.965512i	$0.583841\pi$
$42$	0.529783	0.0817473
$43$	−1.55944	−0.237812	−0.118906	−	0.992906i	$-0.537939\pi$
$43$	−1.55944	−0.237812	−0.118906	+	0.992906i	$0.537939\pi$
$44$	−0.207231	−0.0312413
$45$	3.63374	0.541685
$46$	2.06612	0.304632
$47$	−8.32996	−1.21505	−0.607525	−	0.794301i	$-0.707838\pi$
$47$	−8.32996	−1.21505	−0.607525	+	0.794301i	$0.707838\pi$
$48$	7.51630	1.08488
$49$	−6.88924	−0.984177
$50$	−2.42966	−0.343606
$51$	3.82374	0.535430
$52$	−5.93472	−0.822998
$53$	−7.88496	−1.08308	−0.541541	−	0.840674i	$-0.682159\pi$
$53$	−7.88496	−1.08308	−0.541541	+	0.840674i	$0.682159\pi$
$54$	5.39222	0.733788
$55$	0.0681441	0.00918855
$56$	−0.644974	−0.0861882
$57$	−12.1025	−1.60302
$58$	−3.44520	−0.452377
$59$	−2.86921	−0.373539	−0.186770	−	0.982404i	$-0.559802\pi$
$59$	−2.86921	−0.373539	−0.186770	+	0.982404i	$0.559802\pi$
$60$	−3.01554	−0.389304
$61$	9.75064	1.24844	0.624221	−	0.781248i	$-0.285417\pi$
$61$	9.75064	1.24844	0.624221	+	0.781248i	$0.285417\pi$
$62$	−0.939240	−0.119284
$63$	2.12573	0.267817
$64$	−2.23035	−0.278793
$65$	1.95152	0.242057
$66$	0.190680	0.0234710
$67$	6.25043	0.763612	0.381806	−	0.924242i	$-0.375302\pi$
$67$	6.25043	0.763612	0.381806	+	0.924242i	$0.375302\pi$
$68$	−2.15912	−0.261832
$69$	12.1840	1.46678
$70$	0.0983694	0.0117574
$71$	9.94622	1.18040	0.590199	−	0.807258i	$-0.299049\pi$
$71$	9.94622	1.18040	0.590199	+	0.807258i	$0.299049\pi$
$72$	−12.3786	−1.45884
$73$	13.3346	1.56070	0.780350	−	0.625343i	$-0.215041\pi$
$73$	13.3346	1.56070	0.780350	+	0.625343i	$0.215041\pi$
$74$	−2.16938	−0.252185
$75$	−14.3278	−1.65443
$76$	6.83383	0.783894
$77$	0.0398643	0.00454296
$78$	5.46071	0.618304
$79$	−5.45859	−0.614140	−0.307070	−	0.951687i	$-0.599349\pi$
$79$	−5.45859	−0.614140	−0.307070	+	0.951687i	$0.599349\pi$
$80$	1.39562	0.156035
$81$	12.6361	1.40401
$82$	−1.73233	−0.191304
$83$	9.38546	1.03019	0.515094	−	0.857134i	$-0.327757\pi$
$83$	9.38546	1.03019	0.515094	+	0.857134i	$0.327757\pi$
$84$	−1.76409	−0.192478
$85$	0.709987	0.0770089
$86$	−0.810225	−0.0873688
$87$	−20.3164	−2.17815
$88$	−0.232139	−0.0247461
$89$	2.03454	0.215660	0.107830	−	0.994169i	$-0.465610\pi$
$89$	2.03454	0.215660	0.107830	+	0.994169i	$0.465610\pi$
$90$	1.88795	0.199008
$91$	1.14164	0.119676
$92$	−6.87982	−0.717270
$93$	−5.53873	−0.574339
$94$	−4.32794	−0.446393
$95$	−2.24718	−0.230556
$96$	15.7808	1.61062
$97$	2.03203	0.206321	0.103160	−	0.994665i	$-0.467104\pi$
$97$	2.03203	0.206321	0.103160	+	0.994665i	$0.467104\pi$
$98$	−3.57939	−0.361573
$99$	0.765094	0.0768949
$100$	8.09035	0.809035
$101$	−8.02476	−0.798494	−0.399247	−	0.916844i	$-0.630728\pi$
$101$	−8.02476	−0.798494	−0.399247	+	0.916844i	$0.630728\pi$
$102$	1.98667	0.196710
$103$	−12.4831	−1.23000	−0.614999	−	0.788528i	$-0.710844\pi$
$103$	−12.4831	−1.23000	−0.614999	+	0.788528i	$0.710844\pi$
$104$	−6.64804	−0.651894
$105$	0.580088	0.0566108
$106$	−4.09673	−0.397910
$107$	6.13874	0.593454	0.296727	−	0.954962i	$-0.404105\pi$
$107$	6.13874	0.593454	0.296727	+	0.954962i	$0.404105\pi$
$108$	−17.9552	−1.72774
$109$	−3.17955	−0.304546	−0.152273	−	0.988338i	$-0.548659\pi$
$109$	−3.17955	−0.304546	−0.152273	+	0.988338i	$0.548659\pi$
$110$	0.0354051	0.00337575
$111$	−12.7929	−1.21425
$112$	0.816435	0.0771459
$113$	11.7573	1.10603	0.553017	−	0.833170i	$-0.313476\pi$
$113$	11.7573	1.10603	0.553017	+	0.833170i	$0.313476\pi$
$114$	−6.28801	−0.588926
$115$	2.26230	0.210961
$116$	11.4719	1.06514
$117$	21.9109	2.02566
$118$	−1.49073	−0.137233
$119$	0.415342	0.0380743
$120$	−3.37798	−0.308366
$121$	−10.9857	−0.998696
$122$	5.06607	0.458660
$123$	−10.2156	−0.921109
$124$	3.12751	0.280859
$125$	−5.50485	−0.492369
$126$	1.10445	0.0983924
$127$	−11.5158	−1.02187	−0.510933	−	0.859621i	$-0.670700\pi$
$127$	−11.5158	−1.02187	−0.510933	+	0.859621i	$0.670700\pi$
$128$	−11.4600	−1.01293
$129$	−4.77792	−0.420672
$130$	1.01394	0.0889283
$131$	5.33632	0.466237	0.233118	−	0.972448i	$-0.425107\pi$
$131$	5.33632	0.466237	0.233118	+	0.972448i	$0.425107\pi$
$132$	−0.634930	−0.0552636
$133$	−1.31460	−0.113990
$134$	3.24749	0.280541
$135$	5.90423	0.508155
$136$	−2.41863	−0.207396
$137$	20.8851	1.78434	0.892169	−	0.451702i	$-0.149183\pi$
$137$	20.8851	1.78434	0.892169	+	0.451702i	$0.149183\pi$
$138$	6.33033	0.538873
$139$	12.3073	1.04390	0.521948	−	0.852978i	$-0.325206\pi$
$139$	12.3073	1.04390	0.521948	+	0.852978i	$0.325206\pi$
$140$	−0.327553	−0.0276833
$141$	−25.5220	−2.14934
$142$	5.16768	0.433662
$143$	0.410899	0.0343611
$144$	15.6694	1.30578
$145$	−3.77233	−0.313275
$146$	6.92818	0.573380
$147$	−21.1078	−1.74094
$148$	7.22367	0.593782
$149$	−1.56010	−0.127809	−0.0639043	−	0.997956i	$-0.520355\pi$
$149$	−1.56010	−0.127809	−0.0639043	+	0.997956i	$0.520355\pi$
$150$	−7.44418	−0.607814
$151$	−19.3622	−1.57568	−0.787838	−	0.615882i	$-0.788800\pi$
$151$	−19.3622	−1.57568	−0.787838	+	0.615882i	$0.788800\pi$
$152$	7.65521	0.620920
$153$	7.97144	0.644452
$154$	0.0207120	0.00166902
$155$	−1.02842	−0.0826050
$156$	−18.1832	−1.45582
$157$	−13.4243	−1.07138	−0.535688	−	0.844416i	$-0.679948\pi$
$157$	−13.4243	−1.07138	−0.535688	+	0.844416i	$0.679948\pi$
$158$	−2.83608	−0.225626
$159$	−24.1585	−1.91590
$160$	2.93015	0.231649
$161$	1.32345	0.104302
$162$	6.56523	0.515813
$163$	11.7744	0.922243	0.461121	−	0.887337i	$-0.347447\pi$
$163$	11.7744	0.922243	0.461121	+	0.887337i	$0.347447\pi$
$164$	5.76836	0.450433
$165$	0.208785	0.0162539
$166$	4.87633	0.378477
$167$	4.26349	0.329919	0.164959	−	0.986300i	$-0.447251\pi$
$167$	4.26349	0.329919	0.164959	+	0.986300i	$0.447251\pi$
$168$	−1.97612	−0.152461
$169$	−1.23259	−0.0948148
$170$	0.368882	0.0282920
$171$	−25.2304	−1.92942
$172$	2.69791	0.205714
$173$	15.5222	1.18013	0.590064	−	0.807357i	$-0.299103\pi$
$173$	15.5222	1.18013	0.590064	+	0.807357i	$0.299103\pi$
$174$	−10.5557	−0.800223
$175$	−1.55631	−0.117646
$176$	0.293851	0.0221499
$177$	−8.79090	−0.660765
$178$	1.05707	0.0792306
$179$	9.56537	0.714949	0.357475	−	0.933923i	$-0.383638\pi$
$179$	9.56537	0.714949	0.357475	+	0.933923i	$0.383638\pi$
$180$	−6.28656	−0.468573
$181$	−19.4684	−1.44707	−0.723536	−	0.690287i	$-0.757484\pi$
$181$	−19.4684	−1.44707	−0.723536	+	0.690287i	$0.757484\pi$
$182$	0.593154	0.0439675
$183$	29.8748	2.20841
$184$	−7.70673	−0.568148
$185$	−2.37537	−0.174641
$186$	−2.87772	−0.211004
$187$	0.149490	0.0109318
$188$	14.4113	1.05105
$189$	3.45397	0.251239
$190$	−1.16755	−0.0847030
$191$	12.0662	0.873080	0.436540	−	0.899685i	$-0.356204\pi$
$191$	12.0662	0.873080	0.436540	+	0.899685i	$0.356204\pi$
$192$	−6.83351	−0.493166
$193$	16.7340	1.20454	0.602270	−	0.798293i	$-0.294263\pi$
$193$	16.7340	1.20454	0.602270	+	0.798293i	$0.294263\pi$
$194$	1.05576	0.0757995
$195$	5.97923	0.428181
$196$	11.9188	0.851340
$197$	15.5652	1.10898	0.554488	−	0.832192i	$-0.312914\pi$
$197$	15.5652	1.10898	0.554488	+	0.832192i	$0.312914\pi$
$198$	0.397514	0.0282501
$199$	−19.7161	−1.39764	−0.698818	−	0.715300i	$-0.746290\pi$
$199$	−19.7161	−1.39764	−0.698818	+	0.715300i	$0.746290\pi$
$200$	9.06276	0.640834
$201$	19.1506	1.35078
$202$	−4.16937	−0.293356
$203$	−2.20681	−0.154888
$204$	−6.61527	−0.463162
$205$	−1.89682	−0.132480
$206$	−6.48576	−0.451884
$207$	25.4002	1.76543
$208$	8.41537	0.583501
$209$	−0.473150	−0.0327285
$210$	0.301392	0.0207980
$211$	15.3251	1.05502	0.527511	−	0.849548i	$-0.323125\pi$
$211$	15.3251	1.05502	0.527511	+	0.849548i	$0.323125\pi$
$212$	13.6414	0.936896
$213$	30.4740	2.08804
$214$	3.18946	0.218027
$215$	−0.887158	−0.0605037
$216$	−20.1133	−1.36853
$217$	−0.601628	−0.0408412
$218$	−1.65198	−0.111886
$219$	40.8557	2.76077
$220$	−0.117893	−0.00794835
$221$	4.28112	0.287979
$222$	−6.64672	−0.446098
$223$	21.7199	1.45447	0.727237	−	0.686387i	$-0.240804\pi$
$223$	21.7199	1.45447	0.727237	+	0.686387i	$0.240804\pi$
$224$	1.71414	0.114531
$225$	−29.8695	−1.99130
$226$	6.10866	0.406342
$227$	14.6981	0.975549	0.487775	−	0.872970i	$-0.337809\pi$
$227$	14.6981	0.975549	0.487775	+	0.872970i	$0.337809\pi$
$228$	20.9380	1.38665
$229$	1.32253	0.0873953	0.0436977	−	0.999045i	$-0.486086\pi$
$229$	1.32253	0.0873953	0.0436977	+	0.999045i	$0.486086\pi$
$230$	1.17541	0.0775040
$231$	0.122139	0.00803617
$232$	12.8508	0.843695
$233$	13.0703	0.856266	0.428133	−	0.903716i	$-0.359171\pi$
$233$	13.0703	0.856266	0.428133	+	0.903716i	$0.359171\pi$
$234$	11.3841	0.744201
$235$	−4.73889	−0.309131
$236$	4.96389	0.323122
$237$	−16.7245	−1.08637
$238$	0.215796	0.0139880
$239$	11.8654	0.767507	0.383754	−	0.923436i	$-0.374631\pi$
$239$	11.8654	0.767507	0.383754	+	0.923436i	$0.374631\pi$
$240$	4.27600	0.276014
$241$	3.03740	0.195656	0.0978281	−	0.995203i	$-0.468810\pi$
$241$	3.03740	0.195656	0.0978281	+	0.995203i	$0.468810\pi$
$242$	−5.70773	−0.366907
$243$	7.58020	0.486270
$244$	−16.8691	−1.07994
$245$	−3.91927	−0.250393
$246$	−5.30764	−0.338403
$247$	−13.5502	−0.862177
$248$	3.50342	0.222467
$249$	28.7559	1.82233
$250$	−2.86011	−0.180889
$251$	−17.4787	−1.10325	−0.551623	−	0.834094i	$-0.685991\pi$
$251$	−17.4787	−1.10325	−0.551623	+	0.834094i	$0.685991\pi$
$252$	−3.67764	−0.231669
$253$	0.476334	0.0299469
$254$	−5.98320	−0.375419
$255$	2.17531	0.136223
$256$	−1.49348	−0.0933424
$257$	−27.4119	−1.70991	−0.854953	−	0.518705i	$-0.826414\pi$
$257$	−27.4119	−1.70991	−0.854953	+	0.518705i	$0.826414\pi$
$258$	−2.48243	−0.154549
$259$	−1.38959	−0.0863450
$260$	−3.37624	−0.209386
$261$	−42.3542	−2.62166
$262$	2.77255	0.171289
$263$	31.5064	1.94277	0.971384	−	0.237513i	$-0.0763322\pi$
$263$	31.5064	1.94277	0.971384	+	0.237513i	$0.0763322\pi$
$264$	−0.711245	−0.0437741
$265$	−4.48573	−0.275556
$266$	−0.683016	−0.0418784
$267$	6.23357	0.381488
$268$	−10.8136	−0.660545
$269$	13.1396	0.801138	0.400569	−	0.916267i	$-0.368813\pi$
$269$	13.1396	0.801138	0.400569	+	0.916267i	$0.368813\pi$
$270$	3.06762	0.186689
$271$	1.40657	0.0854428	0.0427214	−	0.999087i	$-0.486397\pi$
$271$	1.40657	0.0854428	0.0427214	+	0.999087i	$0.486397\pi$
$272$	3.06161	0.185637
$273$	3.49785	0.211699
$274$	10.8511	0.655541
$275$	−0.560148	−0.0337782
$276$	−21.0789	−1.26880
$277$	−11.2899	−0.678344	−0.339172	−	0.940724i	$-0.610147\pi$
$277$	−11.2899	−0.678344	−0.339172	+	0.940724i	$0.610147\pi$
$278$	6.39443	0.383513
$279$	−11.5467	−0.691284
$280$	−0.366923	−0.0219279
$281$	−22.5521	−1.34534	−0.672672	−	0.739941i	$-0.734853\pi$
$281$	−22.5521	−1.34534	−0.672672	+	0.739941i	$0.734853\pi$
$282$	−13.2603	−0.789637
$283$	12.7415	0.757406	0.378703	−	0.925518i	$-0.376370\pi$
$283$	12.7415	0.757406	0.378703	+	0.925518i	$0.376370\pi$
$284$	−17.2075	−1.02108
$285$	−6.88508	−0.407837
$286$	0.213488	0.0126238
$287$	−1.10964	−0.0654999
$288$	32.8985	1.93856
$289$	−15.4425	−0.908381
$290$	−1.95996	−0.115093
$291$	6.22587	0.364967
$292$	−23.0696	−1.35005
$293$	−18.9807	−1.10887	−0.554433	−	0.832228i	$-0.687065\pi$
$293$	−18.9807	−1.10887	−0.554433	+	0.832228i	$0.687065\pi$
$294$	−10.9668	−0.639598
$295$	−1.63228	−0.0950352
$296$	8.09191	0.470333
$297$	1.24315	0.0721351
$298$	−0.810571	−0.0469551
$299$	13.6414	0.788900
$300$	24.7878	1.43113
$301$	−0.518987	−0.0299139
$302$	−10.0599	−0.578882
$303$	−24.5869	−1.41248
$304$	−9.69030	−0.555777
$305$	5.54711	0.317626
$306$	4.14166	0.236763
$307$	−17.1952	−0.981381	−0.490691	−	0.871334i	$-0.663255\pi$
$307$	−17.1952	−0.981381	−0.490691	+	0.871334i	$0.663255\pi$
$308$	−0.0689674	−0.00392978
$309$	−38.2467	−2.17578
$310$	−0.534331	−0.0303479
$311$	5.25277	0.297857	0.148929	−	0.988848i	$-0.452417\pi$
$311$	5.25277	0.297857	0.148929	+	0.988848i	$0.452417\pi$
$312$	−20.3688	−1.15315
$313$	2.95015	0.166752	0.0833761	−	0.996518i	$-0.473430\pi$
$313$	2.95015	0.166752	0.0833761	+	0.996518i	$0.473430\pi$
$314$	−6.97476	−0.393608
$315$	1.20932	0.0681376
$316$	9.44367	0.531248
$317$	23.8317	1.33852	0.669261	−	0.743028i	$-0.266611\pi$
$317$	23.8317	1.33852	0.669261	+	0.743028i	$0.266611\pi$
$318$	−12.5519	−0.703874
$319$	−0.794276	−0.0444709
$320$	−1.26884	−0.0709302
$321$	18.8083	1.04978
$322$	0.687613	0.0383191
$323$	−4.92971	−0.274296
$324$	−21.8611	−1.21451
$325$	−16.0416	−0.889829
$326$	6.11754	0.338819
$327$	−9.74175	−0.538720
$328$	6.46168	0.356787
$329$	−2.77225	−0.152839
$330$	0.108477	0.00597146
$331$	15.2002	0.835476	0.417738	−	0.908567i	$-0.362823\pi$
$331$	15.2002	0.835476	0.417738	+	0.908567i	$0.362823\pi$
$332$	−16.2374	−0.891141
$333$	−26.6697	−1.46149
$334$	2.21515	0.121208
$335$	3.55585	0.194277
$336$	2.50146	0.136466
$337$	32.1540	1.75154	0.875771	−	0.482728i	$-0.160354\pi$
$337$	32.1540	1.75154	0.875771	+	0.482728i	$0.160354\pi$
$338$	−0.640409	−0.0348336
$339$	36.0229	1.95650
$340$	−1.22832	−0.0666148
$341$	−0.216538	−0.0117262
$342$	−13.1088	−0.708841
$343$	−4.62240	−0.249586
$344$	3.02218	0.162945
$345$	6.93141	0.373175
$346$	8.06473	0.433563
$347$	−12.1840	−0.654074	−0.327037	−	0.945012i	$-0.606050\pi$
$347$	−12.1840	−0.654074	−0.327037	+	0.945012i	$0.606050\pi$
$348$	35.1486	1.88416
$349$	29.0635	1.55573	0.777866	−	0.628430i	$-0.216302\pi$
$349$	29.0635	1.55573	0.777866	+	0.628430i	$0.216302\pi$
$350$	−0.808601	−0.0432216
$351$	35.6016	1.90028
$352$	0.616952	0.0328837
$353$	10.8957	0.579922	0.289961	−	0.957039i	$-0.406358\pi$
$353$	10.8957	0.579922	0.289961	+	0.957039i	$0.406358\pi$
$354$	−4.56742	−0.242756
$355$	5.65837	0.300315
$356$	−3.51986	−0.186552
$357$	1.27256	0.0673508
$358$	4.96981	0.262662
$359$	25.1394	1.32680	0.663402	−	0.748263i	$-0.269112\pi$
$359$	25.1394	1.32680	0.663402	+	0.748263i	$0.269112\pi$
$360$	−7.04217	−0.371155
$361$	−3.39698	−0.178789
$362$	−10.1150	−0.531634
$363$	−33.6587	−1.76662
$364$	−1.97510	−0.103523
$365$	7.58603	0.397071
$366$	15.5218	0.811338
$367$	−31.0367	−1.62010	−0.810052	−	0.586358i	$-0.800561\pi$
$367$	−31.0367	−1.62010	−0.810052	+	0.586358i	$0.800561\pi$
$368$	9.75551	0.508541
$369$	−21.2967	−1.10866
$370$	−1.23415	−0.0641606
$371$	−2.62415	−0.136239
$372$	9.58231	0.496819
$373$	−14.4144	−0.746347	−0.373173	−	0.927762i	$-0.621730\pi$
$373$	−14.4144	−0.746347	−0.373173	+	0.927762i	$0.621730\pi$
$374$	0.0776693	0.00401619
$375$	−16.8662	−0.870965
$376$	16.1434	0.832534
$377$	−22.7466	−1.17151
$378$	1.79455	0.0923019
$379$	−31.1931	−1.60228	−0.801142	−	0.598474i	$-0.795774\pi$
$379$	−31.1931	−1.60228	−0.801142	+	0.598474i	$0.795774\pi$
$380$	3.88774	0.199437
$381$	−35.2831	−1.80761
$382$	6.26915	0.320757
$383$	−1.18702	−0.0606540	−0.0303270	−	0.999540i	$-0.509655\pi$
$383$	−1.18702	−0.0606540	−0.0303270	+	0.999540i	$0.509655\pi$
$384$	−35.1119	−1.79180
$385$	0.0226787	0.00115581
$386$	8.69436	0.442531
$387$	−9.96065	−0.506328
$388$	−3.51551	−0.178473
$389$	−38.3493	−1.94439	−0.972193	−	0.234180i	$-0.924760\pi$
$389$	−38.3493	−1.94439	−0.972193	+	0.234180i	$0.924760\pi$
$390$	3.10658	0.157308
$391$	4.96288	0.250984
$392$	13.3513	0.674344
$393$	16.3498	0.824740
$394$	8.08711	0.407422
$395$	−3.10538	−0.156248
$396$	−1.32365	−0.0665162
$397$	−32.4578	−1.62901	−0.814504	−	0.580158i	$-0.802991\pi$
$397$	−32.4578	−1.62901	−0.814504	+	0.580158i	$0.802991\pi$
$398$	−10.2437	−0.513472
$399$	−4.02777	−0.201641
$400$	−11.4720	−0.573602
$401$	4.75218	0.237313	0.118656	−	0.992935i	$-0.462141\pi$
$401$	4.75218	0.237313	0.118656	+	0.992935i	$0.462141\pi$
$402$	9.94991	0.496256
$403$	−6.20125	−0.308906
$404$	13.8833	0.690719
$405$	7.18862	0.357205
$406$	−1.14658	−0.0569037
$407$	−0.500142	−0.0247911
$408$	−7.41039	−0.366869
$409$	−20.1680	−0.997244	−0.498622	−	0.866820i	$-0.666160\pi$
$409$	−20.1680	−0.997244	−0.498622	+	0.866820i	$0.666160\pi$
$410$	−0.985516	−0.0486712
$411$	63.9895	3.15637
$412$	21.5965	1.06398
$413$	−0.954885	−0.0469868
$414$	13.1970	0.648596
$415$	5.33936	0.262099
$416$	17.6684	0.866264
$417$	37.7082	1.84658
$418$	−0.245831	−0.0120240
$419$	19.4994	0.952608	0.476304	−	0.879281i	$-0.341976\pi$
$419$	19.4994	0.952608	0.476304	+	0.879281i	$0.341976\pi$
$420$	−1.00358	−0.0489699
$421$	1.00000	0.0487370
$421$	1.00000	0.0487370
$422$	7.96233	0.387600
$423$	−53.2063	−2.58698
$424$	15.2810	0.742112
$425$	−5.83612	−0.283093
$426$	15.8331	0.767118
$427$	3.24506	0.157039
$428$	−10.6203	−0.513354
$429$	1.25894	0.0607824
$430$	−0.460934	−0.0222282
$431$	2.34197	0.112809	0.0564045	−	0.998408i	$-0.482036\pi$
$431$	2.34197	0.112809	0.0564045	+	0.998408i	$0.482036\pi$
$432$	25.4602	1.22496
$433$	−13.3092	−0.639597	−0.319799	−	0.947486i	$-0.603615\pi$
$433$	−13.3092	−0.639597	−0.319799	+	0.947486i	$0.603615\pi$
$434$	−0.312583	−0.0150045
$435$	−11.5580	−0.554162
$436$	5.50080	0.263440
$437$	−15.7080	−0.751416
$438$	21.2271	1.01427
$439$	29.7316	1.41901	0.709505	−	0.704700i	$-0.248919\pi$
$439$	29.7316	1.41901	0.709505	+	0.704700i	$0.248919\pi$
$440$	−0.132063	−0.00629586
$441$	−44.0039	−2.09542
$442$	2.22431	0.105800
$443$	22.7054	1.07877	0.539383	−	0.842061i	$-0.318658\pi$
$443$	22.7054	1.07877	0.539383	+	0.842061i	$0.318658\pi$
$444$	22.1324	1.05036
$445$	1.15744	0.0548680
$446$	11.2849	0.534353
$447$	−4.77996	−0.226084
$448$	−0.742269	−0.0350689
$449$	−4.19552	−0.197999	−0.0989993	−	0.995088i	$-0.531564\pi$
$449$	−4.19552	−0.197999	−0.0989993	+	0.995088i	$0.531564\pi$
$450$	−15.5191	−0.731575
$451$	−0.399381	−0.0188061
$452$	−20.3408	−0.956750
$453$	−59.3235	−2.78726
$454$	7.63660	0.358403
$455$	0.649475	0.0304479
$456$	23.4546	1.09836
$457$	18.4457	0.862852	0.431426	−	0.902148i	$-0.358011\pi$
$457$	18.4457	0.862852	0.431426	+	0.902148i	$0.358011\pi$
$458$	0.687138	0.0321078
$459$	12.9523	0.604561
$460$	−3.91390	−0.182487
$461$	−26.9335	−1.25442	−0.627208	−	0.778851i	$-0.715803\pi$
$461$	−26.9335	−1.25442	−0.627208	+	0.778851i	$0.715803\pi$
$462$	0.0634590	0.00295238
$463$	26.3867	1.22629	0.613147	−	0.789969i	$-0.289903\pi$
$463$	26.3867	1.22629	0.613147	+	0.789969i	$0.289903\pi$
$464$	−16.2671	−0.755180
$465$	−3.15096	−0.146123
$466$	6.79086	0.314580
$467$	30.9172	1.43068	0.715340	−	0.698777i	$-0.246272\pi$
$467$	30.9172	1.43068	0.715340	+	0.698777i	$0.246272\pi$
$468$	−37.9071	−1.75225
$469$	2.08017	0.0960534
$470$	−2.46215	−0.113570
$471$	−41.1304	−1.89519
$472$	5.56052	0.255944
$473$	−0.186794	−0.00858879
$474$	−8.68940	−0.399117
$475$	18.4719	0.847550
$476$	−0.718564	−0.0329353
$477$	−50.3639	−2.30600
$478$	6.16480	0.281972
$479$	−20.6462	−0.943350	−0.471675	−	0.881773i	$-0.656350\pi$
$479$	−20.6462	−0.943350	−0.471675	+	0.881773i	$0.656350\pi$
$480$	8.97762	0.409770
$481$	−14.3231	−0.653079
$482$	1.57812	0.0718814
$483$	4.05487	0.184503
$484$	19.0058	0.863899
$485$	1.15601	0.0524918
$486$	3.93839	0.178649
$487$	7.88291	0.357209	0.178604	−	0.983921i	$-0.442842\pi$
$487$	7.88291	0.357209	0.178604	+	0.983921i	$0.442842\pi$
$488$	−18.8967	−0.855414
$489$	36.0753	1.63138
$490$	−2.03630	−0.0919908
$491$	4.92405	0.222219	0.111110	−	0.993808i	$-0.464560\pi$
$491$	4.92405	0.222219	0.111110	+	0.993808i	$0.464560\pi$
$492$	17.6735	0.796785
$493$	−8.27548	−0.372709
$494$	−7.04016	−0.316752
$495$	0.435260	0.0195635
$496$	−4.43478	−0.199127
$497$	3.31014	0.148480
$498$	14.9405	0.669499
$499$	−16.5509	−0.740920	−0.370460	−	0.928848i	$-0.620800\pi$
$499$	−16.5509	−0.740920	−0.370460	+	0.928848i	$0.620800\pi$
$500$	9.52369	0.425912
$501$	13.0628	0.583603
$502$	−9.08127	−0.405317
$503$	−33.3163	−1.48550	−0.742751	−	0.669568i	$-0.766479\pi$
$503$	−33.3163	−1.48550	−0.742751	+	0.669568i	$0.766479\pi$
$504$	−4.11966	−0.183504
$505$	−4.56526	−0.203151
$506$	0.247486	0.0110021
$507$	−3.77651	−0.167721
$508$	19.9230	0.883942
$509$	19.3864	0.859285	0.429642	−	0.902999i	$-0.358640\pi$
$509$	19.3864	0.859285	0.429642	+	0.902999i	$0.358640\pi$
$510$	1.13021	0.0500465
$511$	4.43782	0.196318
$512$	22.1440	0.978635
$513$	−40.9953	−1.80999
$514$	−14.2422	−0.628196
$515$	−7.10161	−0.312934
$516$	8.26606	0.363893
$517$	−0.997787	−0.0438826
$518$	−0.721979	−0.0317220
$519$	47.5580	2.08756
$520$	−3.78205	−0.165854
$521$	−18.2918	−0.801378	−0.400689	−	0.916214i	$-0.631229\pi$
$521$	−18.2918	−0.801378	−0.400689	+	0.916214i	$0.631229\pi$
$522$	−22.0057	−0.963161
$523$	−9.60945	−0.420192	−0.210096	−	0.977681i	$-0.567378\pi$
$523$	−9.60945	−0.420192	−0.210096	+	0.977681i	$0.567378\pi$
$524$	−9.23213	−0.403308
$525$	−4.76835	−0.208108
$526$	16.3696	0.713746
$527$	−2.25609	−0.0982766
$528$	0.900324	0.0391816
$529$	−7.18628	−0.312447
$530$	−2.33062	−0.101235
$531$	−18.3266	−0.795307
$532$	2.27433	0.0986046
$533$	−11.4375	−0.495415
$534$	3.23873	0.140153
$535$	3.49231	0.150986
$536$	−12.1133	−0.523216
$537$	29.3071	1.26469
$538$	6.82686	0.294327
$539$	−0.825214	−0.0355445
$540$	−10.2146	−0.439568
$541$	−9.90204	−0.425722	−0.212861	−	0.977082i	$-0.568278\pi$
$541$	−9.90204	−0.425722	−0.212861	+	0.977082i	$0.568278\pi$
$542$	0.730799	0.0313905
$543$	−59.6486	−2.55977
$544$	6.42796	0.275597
$545$	−1.80884	−0.0774820
$546$	1.81735	0.0777754
$547$	7.04543	0.301241	0.150620	−	0.988592i	$-0.451873\pi$
$547$	7.04543	0.301241	0.150620	+	0.988592i	$0.451873\pi$
$548$	−36.1324	−1.54350
$549$	62.2806	2.65807
$550$	−0.291032	−0.0124096
$551$	26.1927	1.11585
$552$	−23.6125	−1.00501
$553$	−1.81664	−0.0772515
$554$	−5.86581	−0.249214
$555$	−7.27784	−0.308927
$556$	−21.2924	−0.902998
$557$	−32.6105	−1.38175	−0.690875	−	0.722974i	$-0.742775\pi$
$557$	−32.6105	−1.38175	−0.690875	+	0.722974i	$0.742775\pi$
$558$	−5.99925	−0.253968
$559$	−5.34944	−0.226257
$560$	0.464467	0.0196273
$561$	0.458018	0.0193376
$562$	−11.7172	−0.494261
$563$	−27.4268	−1.15590	−0.577951	−	0.816071i	$-0.696148\pi$
$563$	−27.4268	−1.15590	−0.577951	+	0.816071i	$0.696148\pi$
$564$	44.1544	1.85924
$565$	6.68869	0.281395
$566$	6.62003	0.278260
$567$	4.20534	0.176608
$568$	−19.2757	−0.808792
$569$	−31.1285	−1.30498	−0.652488	−	0.757799i	$-0.726275\pi$
$569$	−31.1285	−1.30498	−0.652488	+	0.757799i	$0.726275\pi$
$570$	−3.57723	−0.149834
$571$	22.9963	0.962366	0.481183	−	0.876620i	$-0.340207\pi$
$571$	22.9963	0.962366	0.481183	+	0.876620i	$0.340207\pi$
$572$	−0.710878	−0.0297233
$573$	36.9694	1.54442
$574$	−0.576527	−0.0240638
$575$	−18.5962	−0.775516
$576$	−14.2460	−0.593583
$577$	−39.9303	−1.66232	−0.831161	−	0.556032i	$-0.812323\pi$
$577$	−39.9303	−1.66232	−0.831161	+	0.556032i	$0.812323\pi$
$578$	−8.02333	−0.333727
$579$	51.2709	2.13075
$580$	6.52634	0.270992
$581$	3.12352	0.129586
$582$	3.23473	0.134084
$583$	−0.944484	−0.0391165
$584$	−25.8425	−1.06937
$585$	12.4650	0.515366
$586$	−9.86167	−0.407382
$587$	34.7814	1.43558	0.717791	−	0.696259i	$-0.245153\pi$
$587$	34.7814	1.43558	0.717791	+	0.696259i	$0.245153\pi$
$588$	36.5176	1.50596
$589$	7.14074	0.294229
$590$	−0.848073	−0.0349146
$591$	47.6899	1.96170
$592$	−10.2431	−0.420988
$593$	31.6935	1.30149	0.650747	−	0.759294i	$-0.274456\pi$
$593$	31.6935	1.30149	0.650747	+	0.759294i	$0.274456\pi$
$594$	0.645896	0.0265014
$595$	0.236287	0.00968681
$596$	2.69906	0.110558
$597$	−60.4076	−2.47232
$598$	7.08754	0.289831
$599$	14.2508	0.582274	0.291137	−	0.956681i	$-0.405966\pi$
$599$	14.2508	0.582274	0.291137	+	0.956681i	$0.405966\pi$
$600$	27.7672	1.13359
$601$	−5.81473	−0.237188	−0.118594	−	0.992943i	$-0.537839\pi$
$601$	−5.81473	−0.237188	−0.118594	+	0.992943i	$0.537839\pi$
$602$	−0.269646	−0.0109900
$603$	39.9236	1.62582
$604$	33.4977	1.36300
$605$	−6.24970	−0.254086
$606$	−12.7744	−0.518925
$607$	4.34955	0.176543	0.0882715	−	0.996096i	$-0.471866\pi$
$607$	4.34955	0.176543	0.0882715	+	0.996096i	$0.471866\pi$
$608$	−20.3451	−0.825104
$609$	−6.76140	−0.273986
$610$	2.88207	0.116692
$611$	−28.5748	−1.15601
$612$	−13.7910	−0.557469
$613$	−33.5224	−1.35396	−0.676978	−	0.736003i	$-0.736711\pi$
$613$	−33.5224	−1.35396	−0.676978	+	0.736003i	$0.736711\pi$
$614$	−8.93398	−0.360546
$615$	−5.81162	−0.234347
$616$	−0.0772568	−0.00311277
$617$	−0.444143	−0.0178805	−0.00894026	−	0.999960i	$-0.502846\pi$
$617$	−0.444143	−0.0178805	−0.00894026	+	0.999960i	$0.502846\pi$
$618$	−19.8716	−0.799352
$619$	16.4372	0.660667	0.330334	−	0.943864i	$-0.392839\pi$
$619$	16.4372	0.660667	0.330334	+	0.943864i	$0.392839\pi$
$620$	1.77923	0.0714556
$621$	41.2712	1.65615
$622$	2.72914	0.109429
$623$	0.677102	0.0271275
$624$	25.7836	1.03217
$625$	20.2501	0.810004
$626$	1.53279	0.0612625
$627$	−1.44967	−0.0578944
$628$	23.2248	0.926769
$629$	−5.21092	−0.207773
$630$	0.628319	0.0250328
$631$	8.47166	0.337252	0.168626	−	0.985680i	$-0.446067\pi$
$631$	8.47166	0.337252	0.168626	+	0.985680i	$0.446067\pi$
$632$	10.5787	0.420800
$633$	46.9541	1.86626
$634$	12.3821	0.491754
$635$	−6.55132	−0.259981
$636$	41.7956	1.65730
$637$	−23.6326	−0.936358
$638$	−0.412676	−0.0163380
$639$	63.5298	2.51320
$640$	−6.51954	−0.257707
$641$	20.5073	0.809991	0.404995	−	0.914319i	$-0.367273\pi$
$641$	20.5073	0.809991	0.404995	+	0.914319i	$0.367273\pi$
$642$	9.77210	0.385674
$643$	21.8571	0.861960	0.430980	−	0.902362i	$-0.358168\pi$
$643$	21.8571	0.861960	0.430980	+	0.902362i	$0.358168\pi$
$644$	−2.28963	−0.0902242
$645$	−2.71814	−0.107027
$646$	−2.56129	−0.100773
$647$	32.3864	1.27324	0.636620	−	0.771178i	$-0.280332\pi$
$647$	32.3864	1.27324	0.636620	+	0.771178i	$0.280332\pi$
$648$	−24.4887	−0.962006
$649$	−0.343682	−0.0134907
$650$	−8.33462	−0.326911
$651$	−1.84331	−0.0722451
$652$	−20.3704	−0.797765
$653$	14.4920	0.567116	0.283558	−	0.958955i	$-0.408485\pi$
$653$	14.4920	0.567116	0.283558	+	0.958955i	$0.408485\pi$
$654$	−5.06145	−0.197918
$655$	3.03582	0.118619
$656$	−8.17947	−0.319355
$657$	85.1728	3.32291
$658$	−1.44036	−0.0561509
$659$	−38.8837	−1.51469	−0.757346	−	0.653014i	$-0.773504\pi$
$659$	−38.8837	−1.51469	−0.757346	+	0.653014i	$0.773504\pi$
$660$	−0.361210	−0.0140601
$661$	2.92684	0.113841	0.0569205	−	0.998379i	$-0.481872\pi$
$661$	2.92684	0.113841	0.0569205	+	0.998379i	$0.481872\pi$
$662$	7.89743	0.306943
$663$	13.1168	0.509415
$664$	−18.1890	−0.705870
$665$	−0.747871	−0.0290012
$666$	−13.8566	−0.536931
$667$	−26.3690	−1.02101
$668$	−7.37607	−0.285389
$669$	66.5471	2.57286
$670$	1.84749	0.0713747
$671$	1.16796	0.0450886
$672$	5.25190	0.202597
$673$	−27.6671	−1.06649	−0.533244	−	0.845961i	$-0.679027\pi$
$673$	−27.6671	−1.06649	−0.533244	+	0.845961i	$0.679027\pi$
$674$	16.7060	0.643492
$675$	−48.5330	−1.86804
$676$	2.13245	0.0820174
$677$	14.6827	0.564303	0.282151	−	0.959370i	$-0.408952\pi$
$677$	14.6827	0.564303	0.282151	+	0.959370i	$0.408952\pi$
$678$	18.7162	0.718790
$679$	0.676267	0.0259527
$680$	−1.37595	−0.0527653
$681$	45.0333	1.72568
$682$	−0.112505	−0.00430804
$683$	−11.6284	−0.444948	−0.222474	−	0.974939i	$-0.571413\pi$
$683$	−11.6284	−0.444948	−0.222474	+	0.974939i	$0.571413\pi$
$684$	43.6500	1.66900
$685$	11.8815	0.453968
$686$	−2.40163	−0.0916945
$687$	4.05207	0.154596
$688$	−3.82561	−0.145850
$689$	−27.0483	−1.03046
$690$	3.60130	0.137099
$691$	−47.4567	−1.80534	−0.902669	−	0.430335i	$-0.858395\pi$
$691$	−47.4567	−1.80534	−0.902669	+	0.430335i	$0.858395\pi$
$692$	−26.8542	−1.02084
$693$	0.254627	0.00967247
$694$	−6.33037	−0.240298
$695$	7.00161	0.265586
$696$	39.3732	1.49244
$697$	−4.16111	−0.157613
$698$	15.1003	0.571554
$699$	40.0459	1.51468
$700$	2.69250	0.101767
$701$	14.6550	0.553512	0.276756	−	0.960940i	$-0.410741\pi$
$701$	14.6550	0.553512	0.276756	+	0.960940i	$0.410741\pi$
$702$	18.4973	0.698135
$703$	16.4931	0.622049
$704$	−0.267158	−0.0100689
$705$	−14.5194	−0.546831
$706$	5.66102	0.213055
$707$	−2.67068	−0.100441
$708$	15.2087	0.571579
$709$	11.0264	0.414104	0.207052	−	0.978330i	$-0.433613\pi$
$709$	11.0264	0.414104	0.207052	+	0.978330i	$0.433613\pi$
$710$	2.93988	0.110332
$711$	−34.8659	−1.30757
$712$	−3.94292	−0.147767
$713$	−7.18879	−0.269222
$714$	0.661172	0.0247438
$715$	0.233759	0.00874210
$716$	−16.5486	−0.618451
$717$	36.3540	1.35767
$718$	13.0615	0.487450
$719$	36.9806	1.37914	0.689571	−	0.724218i	$-0.257799\pi$
$719$	36.9806	1.37914	0.689571	+	0.724218i	$0.257799\pi$
$720$	8.91428	0.332215
$721$	−4.15444	−0.154719
$722$	−1.76495	−0.0656845
$723$	9.30622	0.346102
$724$	33.6813	1.25176
$725$	31.0087	1.15164
$726$	−17.4878	−0.649033
$727$	31.5293	1.16936	0.584678	−	0.811265i	$-0.301221\pi$
$727$	31.5293	1.16936	0.584678	+	0.811265i	$0.301221\pi$
$728$	−2.21250	−0.0820005
$729$	−14.6834	−0.543830
$730$	3.94142	0.145878
$731$	−1.94619	−0.0719823
$732$	−51.6850	−1.91033
$733$	−22.0466	−0.814311	−0.407156	−	0.913359i	$-0.633479\pi$
$733$	−22.0466	−0.814311	−0.407156	+	0.913359i	$0.633479\pi$
$734$	−16.1255	−0.595204
$735$	−12.0081	−0.442927
$736$	20.4821	0.754978
$737$	0.748695	0.0275785
$738$	−11.0650	−0.407307
$739$	−12.1150	−0.445659	−0.222829	−	0.974857i	$-0.571529\pi$
$739$	−12.1150	−0.445659	−0.222829	+	0.974857i	$0.571529\pi$
$740$	4.10952	0.151069
$741$	−41.5160	−1.52513
$742$	−1.36341	−0.0500523
$743$	−22.4478	−0.823531	−0.411766	−	0.911290i	$-0.635088\pi$
$743$	−22.4478	−0.823531	−0.411766	+	0.911290i	$0.635088\pi$
$744$	10.7340	0.393529
$745$	−0.887537	−0.0325169
$746$	−7.48916	−0.274198
$747$	59.9481	2.19339
$748$	−0.258626	−0.00945629
$749$	2.04300	0.0746495
$750$	−8.76303	−0.319981
$751$	2.16267	0.0789170	0.0394585	−	0.999221i	$-0.487437\pi$
$751$	2.16267	0.0789170	0.0394585	+	0.999221i	$0.487437\pi$
$752$	−20.4351	−0.745190
$753$	−53.5525	−1.95156
$754$	−11.8183	−0.430397
$755$	−11.0151	−0.400881
$756$	−5.97556	−0.217329
$757$	−21.4285	−0.778832	−0.389416	−	0.921062i	$-0.627323\pi$
$757$	−21.4285	−0.778832	−0.389416	+	0.921062i	$0.627323\pi$
$758$	−16.2068	−0.588657
$759$	1.45943	0.0529739
$760$	4.35503	0.157973
$761$	39.9350	1.44764	0.723821	−	0.689988i	$-0.242384\pi$
$761$	39.9350	1.44764	0.723821	+	0.689988i	$0.242384\pi$
$762$	−18.3318	−0.664090
$763$	−1.05817	−0.0383083
$764$	−20.8752	−0.755238
$765$	4.53492	0.163961
$766$	−0.616732	−0.0222834
$767$	−9.84243	−0.355390
$768$	−4.57583	−0.165116
$769$	2.60549	0.0939564	0.0469782	−	0.998896i	$-0.485041\pi$
$769$	2.60549	0.0939564	0.0469782	+	0.998896i	$0.485041\pi$
$770$	0.0117830	0.000424629 0
$771$	−83.9866	−3.02470
$772$	−28.9507	−1.04196
$773$	−5.14230	−0.184956	−0.0924778	−	0.995715i	$-0.529479\pi$
$773$	−5.14230	−0.184956	−0.0924778	+	0.995715i	$0.529479\pi$
$774$	−5.17518	−0.186018
$775$	8.45369	0.303666
$776$	−3.93806	−0.141368
$777$	−4.25753	−0.152738
$778$	−19.9249	−0.714341
$779$	13.1703	0.471876
$780$	−10.3444	−0.370389
$781$	1.19139	0.0426312
$782$	2.57853	0.0922079
$783$	−68.8187	−2.45938
$784$	−16.9007	−0.603596
$785$	−7.63704	−0.272577
$786$	8.49476	0.302998
$787$	−47.2584	−1.68458	−0.842289	−	0.539026i	$-0.818792\pi$
$787$	−47.2584	−1.68458	−0.842289	+	0.539026i	$0.818792\pi$
$788$	−26.9287	−0.959295
$789$	96.5318	3.43662
$790$	−1.61344	−0.0574035
$791$	3.91288	0.139126
$792$	−1.48275	−0.0526872
$793$	33.4483	1.18778
$794$	−16.8638	−0.598475
$795$	−13.7437	−0.487439
$796$	34.1099	1.20899
$797$	−50.3286	−1.78273	−0.891365	−	0.453287i	$-0.850251\pi$
$797$	−50.3286	−1.78273	−0.891365	+	0.453287i	$0.850251\pi$
$798$	−2.09268	−0.0740800
$799$	−10.3958	−0.367779
$800$	−24.0860	−0.851568
$801$	12.9953	0.459165
$802$	2.46905	0.0871853
$803$	1.59726	0.0563661
$804$	−33.1315	−1.16846
$805$	0.752904	0.0265364
$806$	−3.22194	−0.113488
$807$	40.2582	1.41716
$808$	15.5520	0.547116
$809$	−20.1175	−0.707293	−0.353646	−	0.935379i	$-0.615058\pi$
$809$	−20.1175	−0.707293	−0.353646	+	0.935379i	$0.615058\pi$
$810$	3.73494	0.131232
$811$	50.1635	1.76148	0.880739	−	0.473601i	$-0.157046\pi$
$811$	50.1635	1.76148	0.880739	+	0.473601i	$0.157046\pi$
$812$	3.81791	0.133982
$813$	4.30955	0.151142
$814$	−0.259855	−0.00910791
$815$	6.69842	0.234636
$816$	9.38039	0.328379
$817$	6.15988	0.215507
$818$	−10.4785	−0.366374
$819$	7.29204	0.254805
$820$	3.28160	0.114598
$821$	8.64252	0.301626	0.150813	−	0.988562i	$-0.451811\pi$
$821$	8.64252	0.301626	0.150813	+	0.988562i	$0.451811\pi$
$822$	33.2465	1.15961
$823$	−39.4937	−1.37667	−0.688333	−	0.725395i	$-0.741657\pi$
$823$	−39.4937	−1.37667	−0.688333	+	0.725395i	$0.741657\pi$
$824$	24.1922	0.842777
$825$	−1.71622	−0.0597512
$826$	−0.496123	−0.0172623
$827$	52.4408	1.82354	0.911772	−	0.410697i	$-0.134715\pi$
$827$	52.4408	1.82354	0.911772	+	0.410697i	$0.134715\pi$
$828$	−43.9437	−1.52715
$829$	−20.1771	−0.700779	−0.350390	−	0.936604i	$-0.613951\pi$
$829$	−20.1771	−0.700779	−0.350390	+	0.936604i	$0.613951\pi$
$830$	2.77413	0.0962915
$831$	−34.5908	−1.19994
$832$	−7.65091	−0.265247
$833$	−8.59782	−0.297897
$834$	19.5918	0.678407
$835$	2.42549	0.0839374
$836$	0.818576	0.0283111
$837$	−18.7615	−0.648494
$838$	10.1312	0.349975
$839$	−0.346581	−0.0119653	−0.00598266	−	0.999982i	$-0.501904\pi$
$839$	−0.346581	−0.0119653	−0.00598266	+	0.999982i	$0.501904\pi$
$840$	−1.12421	−0.0387889
$841$	14.9697	0.516195
$842$	0.519563	0.0179053
$843$	−69.0968	−2.37982
$844$	−26.5132	−0.912622
$845$	−0.701218	−0.0241226
$846$	−27.6440	−0.950420
$847$	−3.65607	−0.125624
$848$	−19.3434	−0.664254
$849$	39.0385	1.33980
$850$	−3.03223	−0.104005
$851$	−16.6041	−0.569181
$852$	−52.7217	−1.80621
$853$	30.0380	1.02848	0.514240	−	0.857646i	$-0.328074\pi$
$853$	30.0380	1.02848	0.514240	+	0.857646i	$0.328074\pi$
$854$	1.68601	0.0576941
$855$	−14.3535	−0.490879
$856$	−11.8968	−0.406626
$857$	39.5053	1.34948	0.674738	−	0.738057i	$-0.264256\pi$
$857$	39.5053	1.34948	0.674738	+	0.738057i	$0.264256\pi$
$858$	0.654100	0.0223306
$859$	41.4913	1.41566	0.707832	−	0.706381i	$-0.249673\pi$
$859$	41.4913	1.41566	0.707832	+	0.706381i	$0.249673\pi$
$860$	1.53483	0.0523373
$861$	−3.39979	−0.115865
$862$	1.21680	0.0414444
$863$	−32.8502	−1.11823	−0.559116	−	0.829089i	$-0.688859\pi$
$863$	−32.8502	−1.11823	−0.559116	+	0.829089i	$0.688859\pi$
$864$	53.4547	1.81857
$865$	8.83050	0.300246
$866$	−6.91494	−0.234979
$867$	−47.3138	−1.60686
$868$	1.04085	0.0353287
$869$	−0.653846	−0.0221802
$870$	−6.00508	−0.203591
$871$	21.4413	0.726510
$872$	6.16196	0.208670
$873$	12.9792	0.439280
$874$	−8.16130	−0.276060
$875$	−1.83204	−0.0619342
$876$	−70.6825	−2.38814
$877$	−31.8505	−1.07551	−0.537757	−	0.843100i	$-0.680728\pi$
$877$	−31.8505	−1.07551	−0.537757	+	0.843100i	$0.680728\pi$
$878$	15.4474	0.521325
$879$	−58.1546	−1.96151
$880$	0.167171	0.00563534
$881$	−4.80585	−0.161913	−0.0809566	−	0.996718i	$-0.525798\pi$
$881$	−4.80585	−0.161913	−0.0809566	+	0.996718i	$0.525798\pi$
$882$	−22.8628	−0.769830
$883$	−23.5595	−0.792840	−0.396420	−	0.918069i	$-0.629748\pi$
$883$	−23.5595	−0.792840	−0.396420	+	0.918069i	$0.629748\pi$
$884$	−7.40657	−0.249110
$885$	−5.00111	−0.168111
$886$	11.7969	0.396323
$887$	42.0417	1.41162	0.705810	−	0.708401i	$-0.250583\pi$
$887$	42.0417	1.41162	0.705810	+	0.708401i	$0.250583\pi$
$888$	24.7926	0.831986
$889$	−3.83252	−0.128539
$890$	0.601363	0.0201577
$891$	1.51359	0.0507070
$892$	−37.5766	−1.25816
$893$	32.9039	1.10109
$894$	−2.48349	−0.0830603
$895$	5.44171	0.181896
$896$	−3.81393	−0.127414
$897$	41.7954	1.39551
$898$	−2.17983	−0.0727420
$899$	11.9871	0.399793
$900$	51.6758	1.72253
$901$	−9.84048	−0.327834
$902$	−0.207503	−0.00690911
$903$	−1.59011	−0.0529156
$904$	−22.7856	−0.757839
$905$	−11.0755	−0.368162
$906$	−30.8223	−1.02400
$907$	27.8960	0.926272	0.463136	−	0.886287i	$-0.346724\pi$
$907$	27.8960	0.926272	0.463136	+	0.886287i	$0.346724\pi$
$908$	−25.4286	−0.843877
$909$	−51.2569	−1.70008
$910$	0.337443	0.0111861
$911$	0.128708	0.00426429	0.00213214	−	0.999998i	$-0.499321\pi$
$911$	0.128708	0.00426429	0.00213214	+	0.999998i	$0.499321\pi$
$912$	−29.6899	−0.983130
$913$	1.12422	0.0372062
$914$	9.58367	0.317000
$915$	16.9957	0.561859
$916$	−2.28805	−0.0755993
$917$	1.77595	0.0586471
$918$	6.72952	0.222107
$919$	22.7822	0.751515	0.375757	−	0.926718i	$-0.377383\pi$
$919$	22.7822	0.751515	0.375757	+	0.926718i	$0.377383\pi$
$920$	−4.38433	−0.144547
$921$	−52.6839	−1.73599
$922$	−13.9936	−0.460855
$923$	34.1192	1.12305
$924$	−0.211308	−0.00695151
$925$	19.5257	0.642000
$926$	13.7095	0.450524
$927$	−79.7339	−2.61881
$928$	−34.1533	−1.12114
$929$	10.8534	0.356088	0.178044	−	0.984023i	$-0.443023\pi$
$929$	10.8534	0.356088	0.178044	+	0.984023i	$0.443023\pi$
$930$	−1.63712	−0.0536834
$931$	27.2130	0.891869
$932$	−22.6124	−0.740694
$933$	16.0938	0.526889
$934$	16.0634	0.525612
$935$	0.0850443	0.00278125
$936$	−42.4633	−1.38796
$937$	25.1643	0.822083	0.411041	−	0.911617i	$-0.365165\pi$
$937$	25.1643	0.822083	0.411041	+	0.911617i	$0.365165\pi$
$938$	1.08078	0.0352887
$939$	9.03889	0.294973
$940$	8.19854	0.267407
$941$	11.2017	0.365163	0.182582	−	0.983191i	$-0.441555\pi$
$941$	11.2017	0.365163	0.182582	+	0.983191i	$0.441555\pi$
$942$	−21.3698	−0.696266
$943$	−13.2590	−0.431771
$944$	−7.03874	−0.229091
$945$	1.96495	0.0639199
$946$	−0.0970511	−0.00315540
$947$	−12.4027	−0.403034	−0.201517	−	0.979485i	$-0.564587\pi$
$947$	−12.4027	−0.403034	−0.201517	+	0.979485i	$0.564587\pi$
$948$	28.9342	0.939740
$949$	45.7427	1.48487
$950$	9.59731	0.311378
$951$	73.0174	2.36775
$952$	−0.804931	−0.0260880
$953$	−15.3583	−0.497505	−0.248752	−	0.968567i	$-0.580021\pi$
$953$	−15.3583	−0.497505	−0.248752	+	0.968567i	$0.580021\pi$
$954$	−26.1672	−0.847194
$955$	6.86442	0.222128
$956$	−20.5277	−0.663915
$957$	−2.43356	−0.0786659
$958$	−10.7270	−0.346574
$959$	6.95066	0.224449
$960$	−3.88756	−0.125470
$961$	−27.7320	−0.894582
$962$	−7.44177	−0.239932
$963$	39.2102	1.26353
$964$	−5.25487	−0.169248
$965$	9.51992	0.306457
$966$	2.10676	0.0677839
$967$	−4.05602	−0.130433	−0.0652165	−	0.997871i	$-0.520774\pi$
$967$	−4.05602	−0.130433	−0.0652165	+	0.997871i	$0.520774\pi$
$968$	21.2902	0.684292
$969$	−15.1040	−0.485211
$970$	0.600621	0.0192848
$971$	−52.1485	−1.67352	−0.836762	−	0.547567i	$-0.815554\pi$
$971$	−52.1485	−1.67352	−0.836762	+	0.547567i	$0.815554\pi$
$972$	−13.1142	−0.420637
$973$	4.09594	0.131310
$974$	4.09566	0.131233
$975$	−49.1495	−1.57404
$976$	23.9203	0.765669
$977$	−55.4696	−1.77463	−0.887315	−	0.461163i	$-0.847432\pi$
$977$	−55.4696	−1.77463	−0.887315	+	0.461163i	$0.847432\pi$
$978$	18.7434	0.599348
$979$	0.243703	0.00778877
$980$	6.78055	0.216597
$981$	−20.3089	−0.648412
$982$	2.55835	0.0816403
$983$	−37.8121	−1.20602	−0.603009	−	0.797734i	$-0.706032\pi$
$983$	−37.8121	−1.20602	−0.603009	+	0.797734i	$0.706032\pi$
$984$	19.7978	0.631131
$985$	8.85500	0.282144
$986$	−4.29963	−0.136928
$987$	−8.49382	−0.270361
$988$	23.4425	0.745806
$989$	−6.20133	−0.197191
$990$	0.226145	0.00718735
$991$	−31.3483	−0.995810	−0.497905	−	0.867232i	$-0.665897\pi$
$991$	−31.3483	−0.995810	−0.497905	+	0.867232i	$0.665897\pi$
$992$	−9.31098	−0.295624
$993$	46.5714	1.47790
$994$	1.71983	0.0545496
$995$	−11.2164	−0.355584
$996$	−49.7493	−1.57637
$997$	8.40911	0.266319	0.133160	−	0.991095i	$-0.457488\pi$
$997$	8.40911	0.266319	0.133160	+	0.991095i	$0.457488\pi$
$998$	−8.59923	−0.272204
$999$	−43.3339	−1.37102

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	421.2.a.b.1.11	✓	19
3.2	odd	2		3789.2.a.g.1.9		19
4.3	odd	2		6736.2.a.k.1.2		19

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
421.2.a.b.1.11	✓	19	1.1	even	1	trivial
3789.2.a.g.1.9		19	3.2	odd	2
6736.2.a.k.1.2		19	4.3	odd	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:	\( N \)	\(=\)	\( 421 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	421.a (trivial)

\(f(q)\)	\(=\)	\(q+0.519563 q^{2} +3.06388 q^{3} -1.73005 q^{4} +0.568897 q^{5} +1.59188 q^{6} +0.332804 q^{7} -1.93800 q^{8} +6.38734 q^{9} +O(q^{10})\)	\(q+0.519563 q^{2} +3.06388 q^{3} -1.73005 q^{4} +0.568897 q^{5} +1.59188 q^{6} +0.332804 q^{7} -1.93800 q^{8} +6.38734 q^{9} +0.295577 q^{10} +0.119783 q^{11} -5.30067 q^{12} +3.43037 q^{13} +0.172913 q^{14} +1.74303 q^{15} +2.45320 q^{16} +1.24801 q^{17} +3.31862 q^{18} -3.95007 q^{19} -0.984222 q^{20} +1.01967 q^{21} +0.0622347 q^{22} +3.97665 q^{23} -5.93778 q^{24} -4.67636 q^{25} +1.78229 q^{26} +10.3784 q^{27} -0.575770 q^{28} -6.63096 q^{29} +0.905613 q^{30} -1.80775 q^{31} +5.15058 q^{32} +0.367000 q^{33} +0.648417 q^{34} +0.189331 q^{35} -11.0504 q^{36} -4.17540 q^{37} -2.05231 q^{38} +10.5102 q^{39} -1.10252 q^{40} -3.33421 q^{41} +0.529783 q^{42} -1.55944 q^{43} -0.207231 q^{44} +3.63374 q^{45} +2.06612 q^{46} -8.32996 q^{47} +7.51630 q^{48} -6.88924 q^{49} -2.42966 q^{50} +3.82374 q^{51} -5.93472 q^{52} -7.88496 q^{53} +5.39222 q^{54} +0.0681441 q^{55} -0.644974 q^{56} -12.1025 q^{57} -3.44520 q^{58} -2.86921 q^{59} -3.01554 q^{60} +9.75064 q^{61} -0.939240 q^{62} +2.12573 q^{63} -2.23035 q^{64} +1.95152 q^{65} +0.190680 q^{66} +6.25043 q^{67} -2.15912 q^{68} +12.1840 q^{69} +0.0983694 q^{70} +9.94622 q^{71} -12.3786 q^{72} +13.3346 q^{73} -2.16938 q^{74} -14.3278 q^{75} +6.83383 q^{76} +0.0398643 q^{77} +5.46071 q^{78} -5.45859 q^{79} +1.39562 q^{80} +12.6361 q^{81} -1.73233 q^{82} +9.38546 q^{83} -1.76409 q^{84} +0.709987 q^{85} -0.810225 q^{86} -20.3164 q^{87} -0.232139 q^{88} +2.03454 q^{89} +1.88795 q^{90} +1.14164 q^{91} -6.87982 q^{92} -5.53873 q^{93} -4.32794 q^{94} -2.24718 q^{95} +15.7808 q^{96} +2.03203 q^{97} -3.57939 q^{98} +0.765094 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 19 q + 4 q^{2} + 7 q^{3} + 18 q^{4} + 7 q^{5} + 8 q^{6} + 3 q^{7} + 9 q^{8} + 20 q^{9}+O(q^{10}) \) 19 * q + 4 * q^2 + 7 * q^3 + 18 * q^4 + 7 * q^5 + 8 * q^6 + 3 * q^7 + 9 * q^8 + 20 * q^9	\( 19 q + 4 q^{2} + 7 q^{3} + 18 q^{4} + 7 q^{5} + 8 q^{6} + 3 q^{7} + 9 q^{8} + 20 q^{9} - 4 q^{10} + 31 q^{11} + 7 q^{12} - 2 q^{13} + 5 q^{14} + q^{15} + 8 q^{16} + 16 q^{17} + 2 q^{18} + 24 q^{19} + 5 q^{20} - 2 q^{21} - 11 q^{22} + 13 q^{23} + 23 q^{24} + 8 q^{25} + 14 q^{26} + 16 q^{27} - 12 q^{28} + 9 q^{29} - 15 q^{30} + 9 q^{31} + 2 q^{32} - 5 q^{33} - 8 q^{34} + 38 q^{35} - 8 q^{36} - 25 q^{37} + 9 q^{38} - 6 q^{39} - 23 q^{40} + 34 q^{41} - 39 q^{42} + 15 q^{43} + 29 q^{44} - 15 q^{45} - 25 q^{46} + 19 q^{47} - 17 q^{48} + 8 q^{49} - 21 q^{50} + 16 q^{51} - 19 q^{52} - 9 q^{53} + 2 q^{54} + 2 q^{55} - 7 q^{56} - 3 q^{57} - 18 q^{58} + 90 q^{59} - 67 q^{60} - 6 q^{61} - 27 q^{62} + 2 q^{63} - 49 q^{64} + 3 q^{65} - 3 q^{66} - 18 q^{67} + 22 q^{68} - 26 q^{69} - 55 q^{70} + 18 q^{71} - 51 q^{72} - 6 q^{73} + 12 q^{74} + 11 q^{75} - 23 q^{76} - 11 q^{77} - 49 q^{78} - 14 q^{79} - 15 q^{80} - 17 q^{81} - 55 q^{82} + 66 q^{83} - 68 q^{84} - 44 q^{85} - 26 q^{86} + q^{87} - 75 q^{88} + 19 q^{89} - 97 q^{90} - 22 q^{91} - 3 q^{92} - 44 q^{93} - 24 q^{94} + 8 q^{95} - 2 q^{96} - 29 q^{97} - 20 q^{98} + 38 q^{99}+O(q^{100}) \) 19 * q + 4 * q^2 + 7 * q^3 + 18 * q^4 + 7 * q^5 + 8 * q^6 + 3 * q^7 + 9 * q^8 + 20 * q^9 - 4 * q^10 + 31 * q^11 + 7 * q^12 - 2 * q^13 + 5 * q^14 + q^15 + 8 * q^16 + 16 * q^17 + 2 * q^18 + 24 * q^19 + 5 * q^20 - 2 * q^21 - 11 * q^22 + 13 * q^23 + 23 * q^24 + 8 * q^25 + 14 * q^26 + 16 * q^27 - 12 * q^28 + 9 * q^29 - 15 * q^30 + 9 * q^31 + 2 * q^32 - 5 * q^33 - 8 * q^34 + 38 * q^35 - 8 * q^36 - 25 * q^37 + 9 * q^38 - 6 * q^39 - 23 * q^40 + 34 * q^41 - 39 * q^42 + 15 * q^43 + 29 * q^44 - 15 * q^45 - 25 * q^46 + 19 * q^47 - 17 * q^48 + 8 * q^49 - 21 * q^50 + 16 * q^51 - 19 * q^52 - 9 * q^53 + 2 * q^54 + 2 * q^55 - 7 * q^56 - 3 * q^57 - 18 * q^58 + 90 * q^59 - 67 * q^60 - 6 * q^61 - 27 * q^62 + 2 * q^63 - 49 * q^64 + 3 * q^65 - 3 * q^66 - 18 * q^67 + 22 * q^68 - 26 * q^69 - 55 * q^70 + 18 * q^71 - 51 * q^72 - 6 * q^73 + 12 * q^74 + 11 * q^75 - 23 * q^76 - 11 * q^77 - 49 * q^78 - 14 * q^79 - 15 * q^80 - 17 * q^81 - 55 * q^82 + 66 * q^83 - 68 * q^84 - 44 * q^85 - 26 * q^86 + q^87 - 75 * q^88 + 19 * q^89 - 97 * q^90 - 22 * q^91 - 3 * q^92 - 44 * q^93 - 24 * q^94 + 8 * q^95 - 2 * q^96 - 29 * q^97 - 20 * q^98 + 38 * q^99

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