LMFDB - Embedded newform 667.2.a.a.1.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [667,2,Mod(1,667)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(667, 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("667.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 667 = 23 \cdot 29 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	667.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:	$5.32602181482$
Analytic rank:	$1$
Dimension:	$10$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - 3x^{9} - 10x^{8} + 32x^{7} + 32x^{6} - 118x^{5} - 29x^{4} + 182x^{3} - 28x^{2} - 101x + 43 $ x^10 - 3x^9 - 10x^8 + 32x^7 + 32x^6 - 118x^5 - 29x^4 + 182x^3 - 28x^2 - 101*x + 43
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.8
Root			$-1.35371$ of defining polynomial
Character	$\chi$	$=$	667.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.35371 q^{2} -1.32895 q^{3} -0.167476 q^{4} +1.38626 q^{5} -1.79900 q^{6} -1.97610 q^{7} -2.93413 q^{8} -1.23390 q^{9} +O(q^{10})$	\(q+1.35371 q^{2} -1.32895 q^{3} -0.167476 q^{4} +1.38626 q^{5} -1.79900 q^{6} -1.97610 q^{7} -2.93413 q^{8} -1.23390 q^{9} +1.87659 q^{10} +3.53607 q^{11} +0.222567 q^{12} -2.23412 q^{13} -2.67506 q^{14} -1.84226 q^{15} -3.63700 q^{16} -2.50101 q^{17} -1.67034 q^{18} -8.35998 q^{19} -0.232165 q^{20} +2.62613 q^{21} +4.78680 q^{22} +1.00000 q^{23} +3.89930 q^{24} -3.07829 q^{25} -3.02434 q^{26} +5.62663 q^{27} +0.330950 q^{28} +1.00000 q^{29} -2.49388 q^{30} -4.77146 q^{31} +0.944826 q^{32} -4.69924 q^{33} -3.38563 q^{34} -2.73938 q^{35} +0.206650 q^{36} -3.65039 q^{37} -11.3170 q^{38} +2.96902 q^{39} -4.06746 q^{40} -7.41237 q^{41} +3.55501 q^{42} +0.277753 q^{43} -0.592208 q^{44} -1.71051 q^{45} +1.35371 q^{46} +13.6939 q^{47} +4.83337 q^{48} -3.09503 q^{49} -4.16711 q^{50} +3.32370 q^{51} +0.374162 q^{52} +0.801772 q^{53} +7.61681 q^{54} +4.90190 q^{55} +5.79813 q^{56} +11.1100 q^{57} +1.35371 q^{58} +1.41698 q^{59} +0.308535 q^{60} +0.569427 q^{61} -6.45916 q^{62} +2.43831 q^{63} +8.55302 q^{64} -3.09706 q^{65} -6.36140 q^{66} -1.69709 q^{67} +0.418860 q^{68} -1.32895 q^{69} -3.70832 q^{70} +6.09579 q^{71} +3.62043 q^{72} -3.10503 q^{73} -4.94157 q^{74} +4.09088 q^{75} +1.40010 q^{76} -6.98762 q^{77} +4.01919 q^{78} +2.74032 q^{79} -5.04181 q^{80} -3.77577 q^{81} -10.0342 q^{82} -1.75206 q^{83} -0.439815 q^{84} -3.46704 q^{85} +0.375996 q^{86} -1.32895 q^{87} -10.3753 q^{88} +6.56562 q^{89} -2.31553 q^{90} +4.41484 q^{91} -0.167476 q^{92} +6.34101 q^{93} +18.5375 q^{94} -11.5891 q^{95} -1.25562 q^{96} -11.7642 q^{97} -4.18977 q^{98} -4.36317 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q - 3 q^{2} - 9 q^{3} + 9 q^{4} - 10 q^{5} + 4 q^{6} + q^{7} - 9 q^{8} + 7 q^{9}+O(q^{10}) $ 10 * q - 3 * q^2 - 9 * q^3 + 9 * q^4 - 10 * q^5 + 4 * q^6 + q^7 - 9 * q^8 + 7 * q^9	\( 10 q - 3 q^{2} - 9 q^{3} + 9 q^{4} - 10 q^{5} + 4 q^{6} + q^{7} - 9 q^{8} + 7 q^{9} - 6 q^{10} - 17 q^{12} - 13 q^{13} - 12 q^{14} + 2 q^{15} - 5 q^{16} - 22 q^{17} + 12 q^{18} - 2 q^{19} + 3 q^{20} - 7 q^{21} + 3 q^{22} + 10 q^{23} - 6 q^{24} + 10 q^{25} - 25 q^{26} - 24 q^{27} + 19 q^{28} + 10 q^{29} - 3 q^{30} - 22 q^{31} - 31 q^{32} - 9 q^{33} + 13 q^{34} - 15 q^{35} + 19 q^{36} - 9 q^{37} - 10 q^{38} + 4 q^{39} - 6 q^{40} - 25 q^{41} - 34 q^{42} + 3 q^{43} - 27 q^{44} - 28 q^{45} - 3 q^{46} - 17 q^{47} - 3 q^{48} + 17 q^{49} + 2 q^{50} + 38 q^{51} - 18 q^{52} - 43 q^{53} - 47 q^{54} - 11 q^{55} - 7 q^{56} + 18 q^{57} - 3 q^{58} - 7 q^{59} - 21 q^{60} - 6 q^{61} + 3 q^{62} + 11 q^{63} + 33 q^{64} + 11 q^{65} + 55 q^{66} + 11 q^{67} - 51 q^{68} - 9 q^{69} + 34 q^{70} - 17 q^{71} + 34 q^{72} - 44 q^{73} + 9 q^{74} + q^{75} + 24 q^{76} - 71 q^{77} + 38 q^{78} + 5 q^{79} + 38 q^{80} + 18 q^{81} + 33 q^{82} - 32 q^{83} + 14 q^{84} + 16 q^{85} - 9 q^{86} - 9 q^{87} + 18 q^{88} - 10 q^{89} - 9 q^{90} - 3 q^{91} + 9 q^{92} - 8 q^{93} + 47 q^{94} - 8 q^{95} + 60 q^{96} + 6 q^{97} - 73 q^{98} + 26 q^{99}+O(q^{100}) \) 10 * q - 3 * q^2 - 9 * q^3 + 9 * q^4 - 10 * q^5 + 4 * q^6 + q^7 - 9 * q^8 + 7 * q^9 - 6 * q^10 - 17 * q^12 - 13 * q^13 - 12 * q^14 + 2 * q^15 - 5 * q^16 - 22 * q^17 + 12 * q^18 - 2 * q^19 + 3 * q^20 - 7 * q^21 + 3 * q^22 + 10 * q^23 - 6 * q^24 + 10 * q^25 - 25 * q^26 - 24 * q^27 + 19 * q^28 + 10 * q^29 - 3 * q^30 - 22 * q^31 - 31 * q^32 - 9 * q^33 + 13 * q^34 - 15 * q^35 + 19 * q^36 - 9 * q^37 - 10 * q^38 + 4 * q^39 - 6 * q^40 - 25 * q^41 - 34 * q^42 + 3 * q^43 - 27 * q^44 - 28 * q^45 - 3 * q^46 - 17 * q^47 - 3 * q^48 + 17 * q^49 + 2 * q^50 + 38 * q^51 - 18 * q^52 - 43 * q^53 - 47 * q^54 - 11 * q^55 - 7 * q^56 + 18 * q^57 - 3 * q^58 - 7 * q^59 - 21 * q^60 - 6 * q^61 + 3 * q^62 + 11 * q^63 + 33 * q^64 + 11 * q^65 + 55 * q^66 + 11 * q^67 - 51 * q^68 - 9 * q^69 + 34 * q^70 - 17 * q^71 + 34 * q^72 - 44 * q^73 + 9 * q^74 + q^75 + 24 * q^76 - 71 * q^77 + 38 * q^78 + 5 * q^79 + 38 * q^80 + 18 * q^81 + 33 * q^82 - 32 * q^83 + 14 * q^84 + 16 * q^85 - 9 * q^86 - 9 * q^87 + 18 * q^88 - 10 * q^89 - 9 * q^90 - 3 * q^91 + 9 * q^92 - 8 * q^93 + 47 * q^94 - 8 * q^95 + 60 * q^96 + 6 * q^97 - 73 * q^98 + 26 * 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 $

$2$	1.35371	0.957216	0.478608	−	0.878029i	$-0.341142\pi$
$2$	1.35371	0.957216	0.478608	+	0.878029i	$0.341142\pi$
$3$	−1.32895	−0.767267	−0.383634	−	0.923485i	$-0.625327\pi$
$3$	−1.32895	−0.767267	−0.383634	+	0.923485i	$0.625327\pi$
$4$	−0.167476	−0.0837382
$5$	1.38626	0.619953	0.309976	−	0.950744i	$-0.399679\pi$
$5$	1.38626	0.619953	0.309976	+	0.950744i	$0.399679\pi$
$6$	−1.79900	−0.734440
$7$	−1.97610	−0.746895	−0.373448	−	0.927651i	$-0.621824\pi$
$7$	−1.97610	−0.746895	−0.373448	+	0.927651i	$0.621824\pi$
$8$	−2.93413	−1.03737
$9$	−1.23390	−0.411301
$10$	1.87659	0.593428
$11$	3.53607	1.06616	0.533082	−	0.846063i	$-0.321034\pi$
$11$	3.53607	1.06616	0.533082	+	0.846063i	$0.321034\pi$
$12$	0.222567	0.0642496
$13$	−2.23412	−0.619633	−0.309816	−	0.950796i	$-0.600268\pi$
$13$	−2.23412	−0.619633	−0.309816	+	0.950796i	$0.600268\pi$
$14$	−2.67506	−0.714940
$15$	−1.84226	−0.475669
$16$	−3.63700	−0.909250
$17$	−2.50101	−0.606583	−0.303291	−	0.952898i	$-0.598086\pi$
$17$	−2.50101	−0.606583	−0.303291	+	0.952898i	$0.598086\pi$
$18$	−1.67034	−0.393704
$19$	−8.35998	−1.91791	−0.958955	−	0.283557i	$-0.908486\pi$
$19$	−8.35998	−1.91791	−0.958955	+	0.283557i	$0.908486\pi$
$20$	−0.232165	−0.0519138
$21$	2.62613	0.573068
$22$	4.78680	1.02055
$23$	1.00000	0.208514
$23$	1.00000	0.208514
$24$	3.89930	0.795941
$25$	−3.07829	−0.615659
$26$	−3.02434	−0.593122
$27$	5.62663	1.08284
$28$	0.330950	0.0625437
$29$	1.00000	0.185695
$29$	1.00000	0.185695
$30$	−2.49388	−0.455318
$31$	−4.77146	−0.856980	−0.428490	−	0.903547i	$-0.640954\pi$
$31$	−4.77146	−0.856980	−0.428490	+	0.903547i	$0.640954\pi$
$32$	0.944826	0.167023
$33$	−4.69924	−0.818033
$34$	−3.38563	−0.580631
$35$	−2.73938	−0.463040
$36$	0.206650	0.0344416
$37$	−3.65039	−0.600121	−0.300061	−	0.953920i	$-0.597007\pi$
$37$	−3.65039	−0.600121	−0.300061	+	0.953920i	$0.597007\pi$
$38$	−11.3170	−1.83585
$39$	2.96902	0.475424
$40$	−4.06746	−0.643121
$41$	−7.41237	−1.15762	−0.578809	−	0.815463i	$-0.696482\pi$
$41$	−7.41237	−1.15762	−0.578809	+	0.815463i	$0.696482\pi$
$42$	3.55501	0.548550
$43$	0.277753	0.0423570	0.0211785	−	0.999776i	$-0.493258\pi$
$43$	0.277753	0.0423570	0.0211785	+	0.999776i	$0.493258\pi$
$44$	−0.592208	−0.0892788
$45$	−1.71051	−0.254987
$46$	1.35371	0.199593
$47$	13.6939	1.99746	0.998728	−	0.0504206i	$-0.0160562\pi$
$47$	13.6939	1.99746	0.998728	+	0.0504206i	$0.0160562\pi$
$48$	4.83337	0.697637
$49$	−3.09503	−0.442148
$50$	−4.16711	−0.589318
$51$	3.32370	0.465411
$52$	0.374162	0.0518870
$53$	0.801772	0.110132	0.0550659	−	0.998483i	$-0.482463\pi$
$53$	0.801772	0.110132	0.0550659	+	0.998483i	$0.482463\pi$
$54$	7.61681	1.03652
$55$	4.90190	0.660972
$56$	5.79813	0.774807
$57$	11.1100	1.47155
$58$	1.35371	0.177750
$59$	1.41698	0.184475	0.0922374	−	0.995737i	$-0.470598\pi$
$59$	1.41698	0.184475	0.0922374	+	0.995737i	$0.470598\pi$
$60$	0.308535	0.0398317
$61$	0.569427	0.0729077	0.0364538	−	0.999335i	$-0.488394\pi$
$61$	0.569427	0.0729077	0.0364538	+	0.999335i	$0.488394\pi$
$62$	−6.45916	−0.820314
$63$	2.43831	0.307199
$64$	8.55302	1.06913
$65$	−3.09706	−0.384143
$66$	−6.36140	−0.783034
$67$	−1.69709	−0.207333	−0.103666	−	0.994612i	$-0.533057\pi$
$67$	−1.69709	−0.207333	−0.103666	+	0.994612i	$0.533057\pi$
$68$	0.418860	0.0507942
$69$	−1.32895	−0.159986
$70$	−3.70832	−0.443229
$71$	6.09579	0.723437	0.361719	−	0.932287i	$-0.382190\pi$
$71$	6.09579	0.723437	0.361719	+	0.932287i	$0.382190\pi$
$72$	3.62043	0.426672
$73$	−3.10503	−0.363416	−0.181708	−	0.983352i	$-0.558163\pi$
$73$	−3.10503	−0.363416	−0.181708	+	0.983352i	$0.558163\pi$
$74$	−4.94157	−0.574445
$75$	4.09088	0.472375
$76$	1.40010	0.160602
$77$	−6.98762	−0.796313
$78$	4.01919	0.455083
$79$	2.74032	0.308310	0.154155	−	0.988047i	$-0.450735\pi$
$79$	2.74032	0.308310	0.154155	+	0.988047i	$0.450735\pi$
$80$	−5.04181	−0.563692
$81$	−3.77577	−0.419530
$82$	−10.0342	−1.10809
$83$	−1.75206	−0.192313	−0.0961567	−	0.995366i	$-0.530655\pi$
$83$	−1.75206	−0.192313	−0.0961567	+	0.995366i	$0.530655\pi$
$84$	−0.439815	−0.0479877
$85$	−3.46704	−0.376053
$86$	0.375996	0.0405447
$87$	−1.32895	−0.142478
$88$	−10.3753	−1.10601
$89$	6.56562	0.695954	0.347977	−	0.937503i	$-0.386869\pi$
$89$	6.56562	0.695954	0.347977	+	0.937503i	$0.386869\pi$
$90$	−2.31553	−0.244078
$91$	4.41484	0.462801
$92$	−0.167476	−0.0174606
$93$	6.34101	0.657532
$94$	18.5375	1.91200
$95$	−11.5891	−1.18901
$96$	−1.25562	−0.128151
$97$	−11.7642	−1.19448	−0.597239	−	0.802064i	$-0.703735\pi$
$97$	−11.7642	−1.19448	−0.597239	+	0.802064i	$0.703735\pi$
$98$	−4.18977	−0.423231
$99$	−4.36317	−0.438515
$100$	0.515542	0.0515542
$101$	15.5678	1.54905	0.774526	−	0.632542i	$-0.217989\pi$
$101$	15.5678	1.54905	0.774526	+	0.632542i	$0.217989\pi$
$102$	4.49932	0.445499
$103$	−10.3717	−1.02195	−0.510977	−	0.859594i	$-0.670716\pi$
$103$	−10.3717	−1.02195	−0.510977	+	0.859594i	$0.670716\pi$
$104$	6.55519	0.642789
$105$	3.64049	0.355275
$106$	1.08536	0.105420
$107$	6.18308	0.597741	0.298870	−	0.954294i	$-0.403390\pi$
$107$	6.18308	0.597741	0.298870	+	0.954294i	$0.403390\pi$
$108$	−0.942328	−0.0906755
$109$	7.79821	0.746933	0.373466	−	0.927644i	$-0.378169\pi$
$109$	7.79821	0.746933	0.373466	+	0.927644i	$0.378169\pi$
$110$	6.63573	0.632692
$111$	4.85118	0.460453
$112$	7.18707	0.679114
$113$	−7.72800	−0.726989	−0.363495	−	0.931596i	$-0.618417\pi$
$113$	−7.72800	−0.726989	−0.363495	+	0.931596i	$0.618417\pi$
$114$	15.0396	1.40859
$115$	1.38626	0.129269
$116$	−0.167476	−0.0155498
$117$	2.75669	0.254856
$118$	1.91817	0.176582
$119$	4.94223	0.453054
$120$	5.40543	0.493446
$121$	1.50378	0.136707
$122$	0.770838	0.0697884
$123$	9.85064	0.888202
$124$	0.799107	0.0717620
$125$	−11.1986	−1.00163
$126$	3.30076	0.294055
$127$	3.60158	0.319589	0.159794	−	0.987150i	$-0.448917\pi$
$127$	3.60158	0.319589	0.159794	+	0.987150i	$0.448917\pi$
$128$	9.68863	0.856362
$129$	−0.369119	−0.0324991
$130$	−4.19251	−0.367708
$131$	6.24120	0.545296	0.272648	−	0.962114i	$-0.412101\pi$
$131$	6.24120	0.545296	0.272648	+	0.962114i	$0.412101\pi$
$132$	0.787013	0.0685007
$133$	16.5201	1.43248
$134$	−2.29737	−0.198462
$135$	7.79995	0.671313
$136$	7.33827	0.629252
$137$	3.58759	0.306509	0.153254	−	0.988187i	$-0.451025\pi$
$137$	3.58759	0.306509	0.153254	+	0.988187i	$0.451025\pi$
$138$	−1.79900	−0.153141
$139$	5.49794	0.466329	0.233164	−	0.972437i	$-0.425092\pi$
$139$	5.49794	0.466329	0.233164	+	0.972437i	$0.425092\pi$
$140$	0.458782	0.0387741
$141$	−18.1984	−1.53258
$142$	8.25191	0.692485
$143$	−7.89999	−0.660631
$144$	4.48770	0.373975
$145$	1.38626	0.115122
$146$	−4.20330	−0.347868
$147$	4.11313	0.339245
$148$	0.611355	0.0502531
$149$	−4.76557	−0.390411	−0.195205	−	0.980762i	$-0.562537\pi$
$149$	−4.76557	−0.390411	−0.195205	+	0.980762i	$0.562537\pi$
$150$	5.53786	0.452164
$151$	−3.44453	−0.280312	−0.140156	−	0.990129i	$-0.544760\pi$
$151$	−3.44453	−0.280312	−0.140156	+	0.990129i	$0.544760\pi$
$152$	24.5293	1.98959
$153$	3.08600	0.249488
$154$	−9.45919	−0.762243
$155$	−6.61447	−0.531287
$156$	−0.497241	−0.0398112
$157$	−19.6206	−1.56589	−0.782946	−	0.622089i	$-0.786284\pi$
$157$	−19.6206	−1.56589	−0.782946	+	0.622089i	$0.786284\pi$
$158$	3.70958	0.295119
$159$	−1.06551	−0.0845006
$160$	1.30977	0.103546
$161$	−1.97610	−0.155738
$162$	−5.11129	−0.401581
$163$	−9.93977	−0.778543	−0.389272	−	0.921123i	$-0.627273\pi$
$163$	−9.93977	−0.778543	−0.389272	+	0.921123i	$0.627273\pi$
$164$	1.24140	0.0969369
$165$	−6.51436	−0.507142
$166$	−2.37177	−0.184085
$167$	−5.46701	−0.423050	−0.211525	−	0.977373i	$-0.567843\pi$
$167$	−5.46701	−0.423050	−0.211525	+	0.977373i	$0.567843\pi$
$168$	−7.70540	−0.594484
$169$	−8.00872	−0.616055
$170$	−4.69335	−0.359964
$171$	10.3154	0.788839
$172$	−0.0465171	−0.00354690
$173$	−11.8184	−0.898533	−0.449266	−	0.893398i	$-0.648315\pi$
$173$	−11.8184	−0.898533	−0.449266	+	0.893398i	$0.648315\pi$
$174$	−1.79900	−0.136382
$175$	6.08301	0.459832
$176$	−12.8607	−0.969410
$177$	−1.88309	−0.141541
$178$	8.88792	0.666178
$179$	22.7795	1.70262	0.851309	−	0.524665i	$-0.175809\pi$
$179$	22.7795	1.70262	0.851309	+	0.524665i	$0.175809\pi$
$180$	0.286470	0.0213522
$181$	24.5845	1.82735	0.913677	−	0.406440i	$-0.133230\pi$
$181$	24.5845	1.82735	0.913677	+	0.406440i	$0.133230\pi$
$182$	5.97640	0.443000
$183$	−0.756738	−0.0559397
$184$	−2.93413	−0.216307
$185$	−5.06038	−0.372047
$186$	8.58387	0.629400
$187$	−8.84373	−0.646717
$188$	−2.29340	−0.167263
$189$	−11.1188	−0.808772
$190$	−15.6882	−1.13814
$191$	9.68145	0.700525	0.350263	−	0.936652i	$-0.386092\pi$
$191$	9.68145	0.700525	0.350263	+	0.936652i	$0.386092\pi$
$192$	−11.3665	−0.820306
$193$	−19.2097	−1.38274	−0.691371	−	0.722500i	$-0.742993\pi$
$193$	−19.2097	−1.38274	−0.691371	+	0.722500i	$0.742993\pi$
$194$	−15.9253	−1.14337
$195$	4.11583	0.294740
$196$	0.518345	0.0370247
$197$	−4.97710	−0.354604	−0.177302	−	0.984157i	$-0.556737\pi$
$197$	−4.97710	−0.354604	−0.177302	+	0.984157i	$0.556737\pi$
$198$	−5.90645	−0.419753
$199$	−24.7441	−1.75406	−0.877030	−	0.480435i	$-0.840479\pi$
$199$	−24.7441	−1.75406	−0.877030	+	0.480435i	$0.840479\pi$
$200$	9.03211	0.638666
$201$	2.25534	0.159080
$202$	21.0742	1.48278
$203$	−1.97610	−0.138695
$204$	−0.556642	−0.0389727
$205$	−10.2755	−0.717669
$206$	−14.0402	−0.978231
$207$	−1.23390	−0.0857622
$208$	8.12548	0.563401
$209$	−29.5615	−2.04481
$210$	4.92815	0.340075
$211$	1.71186	0.117850	0.0589248	−	0.998262i	$-0.481233\pi$
$211$	1.71186	0.117850	0.0589248	+	0.998262i	$0.481233\pi$
$212$	−0.134278	−0.00922225
$213$	−8.10097	−0.555070
$214$	8.37008	0.572167
$215$	0.385037	0.0262593
$216$	−16.5093	−1.12331
$217$	9.42888	0.640074
$218$	10.5565	0.714976
$219$	4.12642	0.278838
$220$	−0.820953	−0.0553486
$221$	5.58754	0.375859
$222$	6.56707	0.440753
$223$	−20.8620	−1.39702	−0.698512	−	0.715599i	$-0.746154\pi$
$223$	−20.8620	−1.39702	−0.698512	+	0.715599i	$0.746154\pi$
$224$	−1.86707	−0.124749
$225$	3.79832	0.253221
$226$	−10.4615	−0.695886
$227$	16.3626	1.08602	0.543011	−	0.839726i	$-0.317284\pi$
$227$	16.3626	1.08602	0.543011	+	0.839726i	$0.317284\pi$
$228$	−1.86066	−0.123225
$229$	2.76859	0.182954	0.0914768	−	0.995807i	$-0.470841\pi$
$229$	2.76859	0.182954	0.0914768	+	0.995807i	$0.470841\pi$
$230$	1.87659	0.123738
$231$	9.28617	0.610985
$232$	−2.93413	−0.192635
$233$	−25.0315	−1.63987	−0.819935	−	0.572456i	$-0.805991\pi$
$233$	−25.0315	−1.63987	−0.819935	+	0.572456i	$0.805991\pi$
$234$	3.73175	0.243952
$235$	18.9832	1.23833
$236$	−0.237310	−0.0154476
$237$	−3.64173	−0.236556
$238$	6.69034	0.433670
$239$	−9.98095	−0.645614	−0.322807	−	0.946465i	$-0.604626\pi$
$239$	−9.98095	−0.645614	−0.322807	+	0.946465i	$0.604626\pi$
$240$	6.70030	0.432502
$241$	20.1062	1.29516	0.647578	−	0.761999i	$-0.275782\pi$
$241$	20.1062	1.29516	0.647578	+	0.761999i	$0.275782\pi$
$242$	2.03567	0.130858
$243$	−11.8621	−0.760953
$244$	−0.0953657	−0.00610516
$245$	−4.29051	−0.274111
$246$	13.3349	0.850201
$247$	18.6772	1.18840
$248$	14.0001	0.889006
$249$	2.32839	0.147556
$250$	−15.1596	−0.958778
$251$	−21.7410	−1.37228	−0.686141	−	0.727468i	$-0.740697\pi$
$251$	−21.7410	−1.37228	−0.686141	+	0.727468i	$0.740697\pi$
$252$	−0.408360	−0.0257243
$253$	3.53607	0.222311
$254$	4.87549	0.305915
$255$	4.60750	0.288533
$256$	−3.99046	−0.249404
$257$	−23.8033	−1.48481	−0.742406	−	0.669951i	$-0.766315\pi$
$257$	−23.8033	−1.48481	−0.742406	+	0.669951i	$0.766315\pi$
$258$	−0.499679	−0.0311086
$259$	7.21354	0.448228
$260$	0.518685	0.0321675
$261$	−1.23390	−0.0763767
$262$	8.44876	0.521966
$263$	7.09655	0.437592	0.218796	−	0.975771i	$-0.429787\pi$
$263$	7.09655	0.437592	0.218796	+	0.975771i	$0.429787\pi$
$264$	13.7882	0.848604
$265$	1.11146	0.0682766
$266$	22.3634	1.37119
$267$	−8.72535	−0.533983
$268$	0.284223	0.0173617
$269$	−15.7201	−0.958473	−0.479236	−	0.877686i	$-0.659086\pi$
$269$	−15.7201	−0.958473	−0.479236	+	0.877686i	$0.659086\pi$
$270$	10.5588	0.642591
$271$	24.5666	1.49232	0.746158	−	0.665769i	$-0.231896\pi$
$271$	24.5666	1.49232	0.746158	+	0.665769i	$0.231896\pi$
$272$	9.09615	0.551535
$273$	−5.86708	−0.355092
$274$	4.85655	0.293395
$275$	−10.8851	−0.656393
$276$	0.222567	0.0133970
$277$	−17.0540	−1.02468	−0.512339	−	0.858783i	$-0.671221\pi$
$277$	−17.0540	−1.02468	−0.512339	+	0.858783i	$0.671221\pi$
$278$	7.44260	0.446377
$279$	5.88752	0.352477
$280$	8.03769	0.480344
$281$	13.3960	0.799138	0.399569	−	0.916703i	$-0.369160\pi$
$281$	13.3960	0.799138	0.399569	+	0.916703i	$0.369160\pi$
$282$	−24.6353	−1.46701
$283$	−6.05871	−0.360153	−0.180076	−	0.983653i	$-0.557634\pi$
$283$	−6.05871	−0.360153	−0.180076	+	0.983653i	$0.557634\pi$
$284$	−1.02090	−0.0605793
$285$	15.4013	0.912292
$286$	−10.6943	−0.632366
$287$	14.6476	0.864619
$288$	−1.16582	−0.0686968
$289$	−10.7450	−0.632057
$290$	1.87659	0.110197
$291$	15.6340	0.916483
$292$	0.520020	0.0304319
$293$	−26.6645	−1.55776	−0.778879	−	0.627174i	$-0.784211\pi$
$293$	−26.6645	−1.55776	−0.778879	+	0.627174i	$0.784211\pi$
$294$	5.56798	0.324731
$295$	1.96429	0.114366
$296$	10.7107	0.622548
$297$	19.8961	1.15449
$298$	−6.45119	−0.373707
$299$	−2.23412	−0.129202
$300$	−0.685127	−0.0395558
$301$	−0.548868	−0.0316362
$302$	−4.66288	−0.268319
$303$	−20.6887	−1.18854
$304$	30.4052	1.74386
$305$	0.789372	0.0451993
$306$	4.17754	0.238814
$307$	0.711442	0.0406041	0.0203021	−	0.999794i	$-0.493537\pi$
$307$	0.711442	0.0406041	0.0203021	+	0.999794i	$0.493537\pi$
$308$	1.17026	0.0666819
$309$	13.7834	0.784112
$310$	−8.95405	−0.508556
$311$	−16.3241	−0.925652	−0.462826	−	0.886449i	$-0.653165\pi$
$311$	−16.3241	−0.925652	−0.462826	+	0.886449i	$0.653165\pi$
$312$	−8.71149	−0.493191
$313$	−23.5100	−1.32887	−0.664433	−	0.747348i	$-0.731327\pi$
$313$	−23.5100	−1.32887	−0.664433	+	0.747348i	$0.731327\pi$
$314$	−26.5605	−1.49890
$315$	3.38013	0.190449
$316$	−0.458938	−0.0258173
$317$	−20.3834	−1.14485	−0.572423	−	0.819959i	$-0.693996\pi$
$317$	−20.3834	−1.14485	−0.572423	+	0.819959i	$0.693996\pi$
$318$	−1.44239	−0.0808853
$319$	3.53607	0.197982
$320$	11.8567	0.662808
$321$	−8.21698	−0.458627
$322$	−2.67506	−0.149075
$323$	20.9084	1.16337
$324$	0.632353	0.0351307
$325$	6.87727	0.381482
$326$	−13.4555	−0.745234
$327$	−10.3634	−0.573097
$328$	21.7489	1.20088
$329$	−27.0604	−1.49189
$330$	−8.81853	−0.485444
$331$	−16.5383	−0.909027	−0.454514	−	0.890740i	$-0.650187\pi$
$331$	−16.5383	−0.909027	−0.454514	+	0.890740i	$0.650187\pi$
$332$	0.293428	0.0161040
$333$	4.50423	0.246830
$334$	−7.40074	−0.404950
$335$	−2.35261	−0.128537
$336$	−9.55122	−0.521062
$337$	12.5533	0.683822	0.341911	−	0.939732i	$-0.388926\pi$
$337$	12.5533	0.683822	0.341911	+	0.939732i	$0.388926\pi$
$338$	−10.8415	−0.589698
$339$	10.2701	0.557795
$340$	0.580647	0.0314900
$341$	−16.8722	−0.913681
$342$	13.9640	0.755089
$343$	19.9488	1.07713
$344$	−0.814963	−0.0439399
$345$	−1.84226	−0.0991839
$346$	−15.9986	−0.860090
$347$	14.1627	0.760292	0.380146	−	0.924927i	$-0.375874\pi$
$347$	14.1627	0.760292	0.380146	+	0.924927i	$0.375874\pi$
$348$	0.222567	0.0119309
$349$	−16.2032	−0.867337	−0.433669	−	0.901072i	$-0.642781\pi$
$349$	−16.2032	−0.867337	−0.433669	+	0.901072i	$0.642781\pi$
$350$	8.23462	0.440159
$351$	−12.5706	−0.670966
$352$	3.34097	0.178074
$353$	24.3378	1.29537	0.647685	−	0.761908i	$-0.275737\pi$
$353$	24.3378	1.29537	0.647685	+	0.761908i	$0.275737\pi$
$354$	−2.54915	−0.135486
$355$	8.45033	0.448497
$356$	−1.09959	−0.0582780
$357$	−6.56796	−0.347613
$358$	30.8367	1.62977
$359$	−6.58491	−0.347538	−0.173769	−	0.984786i	$-0.555595\pi$
$359$	−6.58491	−0.347538	−0.173769	+	0.984786i	$0.555595\pi$
$360$	5.01885	0.264516
$361$	50.8893	2.67838
$362$	33.2803	1.74917
$363$	−1.99844	−0.104891
$364$	−0.739382	−0.0387541
$365$	−4.30437	−0.225301
$366$	−1.02440	−0.0535463
$367$	7.12298	0.371816	0.185908	−	0.982567i	$-0.440477\pi$
$367$	7.12298	0.371816	0.185908	+	0.982567i	$0.440477\pi$
$368$	−3.63700	−0.189592
$369$	9.14615	0.476130
$370$	−6.85028	−0.356129
$371$	−1.58438	−0.0822570
$372$	−1.06197	−0.0550606
$373$	18.6082	0.963494	0.481747	−	0.876310i	$-0.340002\pi$
$373$	18.6082	0.963494	0.481747	+	0.876310i	$0.340002\pi$
$374$	−11.9718	−0.619048
$375$	14.8823	0.768519
$376$	−40.1796	−2.07210
$377$	−2.23412	−0.115063
$378$	−15.0516	−0.774169
$379$	−20.7459	−1.06565	−0.532823	−	0.846227i	$-0.678869\pi$
$379$	−20.7459	−1.06565	−0.532823	+	0.846227i	$0.678869\pi$
$380$	1.94090	0.0995660
$381$	−4.78631	−0.245210
$382$	13.1059	0.670554
$383$	14.6697	0.749586	0.374793	−	0.927109i	$-0.377714\pi$
$383$	14.6697	0.749586	0.374793	+	0.927109i	$0.377714\pi$
$384$	−12.8757	−0.657058
$385$	−9.68663	−0.493677
$386$	−26.0042	−1.32358
$387$	−0.342720	−0.0174215
$388$	1.97023	0.100023
$389$	18.7510	0.950714	0.475357	−	0.879793i	$-0.342319\pi$
$389$	18.7510	0.950714	0.475357	+	0.879793i	$0.342319\pi$
$390$	5.57162	0.282130
$391$	−2.50101	−0.126481
$392$	9.08123	0.458671
$393$	−8.29422	−0.418388
$394$	−6.73754	−0.339432
$395$	3.79878	0.191137
$396$	0.730728	0.0367204
$397$	−4.15830	−0.208699	−0.104350	−	0.994541i	$-0.533276\pi$
$397$	−4.15830	−0.208699	−0.104350	+	0.994541i	$0.533276\pi$
$398$	−33.4962	−1.67901
$399$	−21.9544	−1.09909
$400$	11.1957	0.559787
$401$	34.4267	1.71919	0.859594	−	0.510977i	$-0.170716\pi$
$401$	34.4267	1.71919	0.859594	+	0.510977i	$0.170716\pi$
$402$	3.05308	0.152274
$403$	10.6600	0.531013
$404$	−2.60724	−0.129715
$405$	−5.23419	−0.260089
$406$	−2.67506	−0.132761
$407$	−12.9080	−0.639828
$408$	−9.75217	−0.482804
$409$	31.0883	1.53722	0.768608	−	0.639720i	$-0.220950\pi$
$409$	31.0883	1.53722	0.768608	+	0.639720i	$0.220950\pi$
$410$	−13.9100	−0.686964
$411$	−4.76771	−0.235174
$412$	1.73702	0.0855766
$413$	−2.80009	−0.137783
$414$	−1.67034	−0.0820929
$415$	−2.42880	−0.119225
$416$	−2.11085	−0.103493
$417$	−7.30646	−0.357799
$418$	−40.0176	−1.95732
$419$	−34.0627	−1.66407	−0.832035	−	0.554723i	$-0.812824\pi$
$419$	−34.0627	−1.66407	−0.832035	+	0.554723i	$0.812824\pi$
$420$	−0.609696	−0.0297501
$421$	−0.342300	−0.0166827	−0.00834133	−	0.999965i	$-0.502655\pi$
$421$	−0.342300	−0.0166827	−0.00834133	+	0.999965i	$0.502655\pi$
$422$	2.31736	0.112807
$423$	−16.8969	−0.821556
$424$	−2.35250	−0.114248
$425$	7.69883	0.373448
$426$	−10.9663	−0.531321
$427$	−1.12524	−0.0544544
$428$	−1.03552	−0.0500538
$429$	10.4987	0.506880
$430$	0.521227	0.0251358
$431$	−0.178594	−0.00860259	−0.00430130	−	0.999991i	$-0.501369\pi$
$431$	−0.178594	−0.00860259	−0.00430130	+	0.999991i	$0.501369\pi$
$432$	−20.4640	−0.984576
$433$	−23.1627	−1.11313	−0.556564	−	0.830805i	$-0.687880\pi$
$433$	−23.1627	−1.11313	−0.556564	+	0.830805i	$0.687880\pi$
$434$	12.7639	0.612689
$435$	−1.84226	−0.0883296
$436$	−1.30602	−0.0625468
$437$	−8.35998	−0.399912
$438$	5.58596	0.266908
$439$	40.1969	1.91849	0.959247	−	0.282568i	$-0.0911864\pi$
$439$	40.1969	1.91849	0.959247	+	0.282568i	$0.0911864\pi$
$440$	−14.3828	−0.685673
$441$	3.81897	0.181856
$442$	7.56390	0.359778
$443$	−29.6990	−1.41104	−0.705522	−	0.708688i	$-0.749287\pi$
$443$	−29.6990	−1.41104	−0.705522	+	0.708688i	$0.749287\pi$
$444$	−0.812458	−0.0385575
$445$	9.10163	0.431459
$446$	−28.2411	−1.33725
$447$	6.33319	0.299549
$448$	−16.9016	−0.798526
$449$	14.3122	0.675433	0.337717	−	0.941248i	$-0.390345\pi$
$449$	14.3122	0.675433	0.337717	+	0.941248i	$0.390345\pi$
$450$	5.14181	0.242387
$451$	−26.2107	−1.23421
$452$	1.29426	0.0608768
$453$	4.57759	0.215074
$454$	22.1501	1.03956
$455$	6.12010	0.286915
$456$	−32.5981	−1.52654
$457$	21.6423	1.01238	0.506192	−	0.862421i	$-0.331053\pi$
$457$	21.6423	1.01238	0.506192	+	0.862421i	$0.331053\pi$
$458$	3.74786	0.175126
$459$	−14.0722	−0.656835
$460$	−0.232165	−0.0108248
$461$	−29.6270	−1.37987	−0.689934	−	0.723873i	$-0.742360\pi$
$461$	−29.6270	−1.37987	−0.689934	+	0.723873i	$0.742360\pi$
$462$	12.5708	0.584844
$463$	5.35831	0.249022	0.124511	−	0.992218i	$-0.460264\pi$
$463$	5.35831	0.249022	0.124511	+	0.992218i	$0.460264\pi$
$464$	−3.63700	−0.168843
$465$	8.79027	0.407639
$466$	−33.8854	−1.56971
$467$	−37.0339	−1.71372	−0.856862	−	0.515546i	$-0.827589\pi$
$467$	−37.0339	−1.71372	−0.856862	+	0.515546i	$0.827589\pi$
$468$	−0.461680	−0.0213412
$469$	3.35362	0.154856
$470$	25.6977	1.18535
$471$	26.0747	1.20146
$472$	−4.15759	−0.191369
$473$	0.982154	0.0451595
$474$	−4.92984	−0.226435
$475$	25.7345	1.18078
$476$	−0.827708	−0.0379379
$477$	−0.989309	−0.0452974
$478$	−13.5113	−0.617992
$479$	−17.8727	−0.816624	−0.408312	−	0.912842i	$-0.633882\pi$
$479$	−17.8727	−0.816624	−0.408312	+	0.912842i	$0.633882\pi$
$480$	−1.74061	−0.0794478
$481$	8.15541	0.371855
$482$	27.2179	1.23974
$483$	2.62613	0.119493
$484$	−0.251847	−0.0114476
$485$	−16.3083	−0.740520
$486$	−16.0578	−0.728396
$487$	12.2062	0.553117	0.276558	−	0.960997i	$-0.410806\pi$
$487$	12.2062	0.553117	0.276558	+	0.960997i	$0.410806\pi$
$488$	−1.67077	−0.0756323
$489$	13.2094	0.597351
$490$	−5.80810	−0.262383
$491$	24.7304	1.11607	0.558035	−	0.829818i	$-0.311556\pi$
$491$	24.7304	1.11607	0.558035	+	0.829818i	$0.311556\pi$
$492$	−1.64975	−0.0743765
$493$	−2.50101	−0.112640
$494$	25.2834	1.13756
$495$	−6.04847	−0.271858
$496$	17.3538	0.779208
$497$	−12.0459	−0.540332
$498$	3.15196	0.141243
$499$	10.8831	0.487194	0.243597	−	0.969877i	$-0.421673\pi$
$499$	10.8831	0.487194	0.243597	+	0.969877i	$0.421673\pi$
$500$	1.87550	0.0838749
$501$	7.26537	0.324593
$502$	−29.4310	−1.31357
$503$	20.3508	0.907397	0.453699	−	0.891155i	$-0.350104\pi$
$503$	20.3508	0.907397	0.453699	+	0.891155i	$0.350104\pi$
$504$	−7.15433	−0.318679
$505$	21.5809	0.960339
$506$	4.78680	0.212799
$507$	10.6431	0.472679
$508$	−0.603180	−0.0267618
$509$	−19.9141	−0.882675	−0.441337	−	0.897341i	$-0.645496\pi$
$509$	−19.9141	−0.882675	−0.441337	+	0.897341i	$0.645496\pi$
$510$	6.23721	0.276188
$511$	6.13585	0.271434
$512$	−24.7792	−1.09510
$513$	−47.0385	−2.07680
$514$	−32.2228	−1.42128
$515$	−14.3778	−0.633563
$516$	0.0618187	0.00272142
$517$	48.4225	2.12962
$518$	9.76502	0.429050
$519$	15.7060	0.689415
$520$	9.08718	0.398499
$521$	4.37040	0.191471	0.0957354	−	0.995407i	$-0.469480\pi$
$521$	4.37040	0.191471	0.0957354	+	0.995407i	$0.469480\pi$
$522$	−1.67034	−0.0731090
$523$	11.0065	0.481282	0.240641	−	0.970614i	$-0.422642\pi$
$523$	11.0065	0.481282	0.240641	+	0.970614i	$0.422642\pi$
$524$	−1.04525	−0.0456621
$525$	−8.08399	−0.352814
$526$	9.60666	0.418870
$527$	11.9334	0.519829
$528$	17.0911	0.743796
$529$	1.00000	0.0434783
$530$	1.50459	0.0653554
$531$	−1.74841	−0.0758747
$532$	−2.76674	−0.119953
$533$	16.5601	0.717298
$534$	−11.8116	−0.511136
$535$	8.57134	0.370571
$536$	4.97949	0.215081
$537$	−30.2727	−1.30636
$538$	−21.2804	−0.917465
$539$	−10.9443	−0.471402
$540$	−1.30631	−0.0562145
$541$	−26.3156	−1.13140	−0.565698	−	0.824612i	$-0.691393\pi$
$541$	−26.3156	−1.13140	−0.565698	+	0.824612i	$0.691393\pi$
$542$	33.2560	1.42847
$543$	−32.6715	−1.40207
$544$	−2.36301	−0.101313
$545$	10.8103	0.463063
$546$	−7.94231	−0.339899
$547$	−13.0388	−0.557498	−0.278749	−	0.960364i	$-0.589920\pi$
$547$	−13.0388	−0.557498	−0.278749	+	0.960364i	$0.589920\pi$
$548$	−0.600837	−0.0256665
$549$	−0.702618	−0.0299870
$550$	−14.7352	−0.628310
$551$	−8.35998	−0.356147
$552$	3.89930	0.165965
$553$	−5.41513	−0.230275
$554$	−23.0862	−0.980838
$555$	6.72497	0.285459
$556$	−0.920775	−0.0390496
$557$	33.6743	1.42683	0.713413	−	0.700744i	$-0.247148\pi$
$557$	33.6743	1.42683	0.713413	+	0.700744i	$0.247148\pi$
$558$	7.96998	0.337396
$559$	−0.620533	−0.0262458
$560$	9.96312	0.421019
$561$	11.7528	0.496205
$562$	18.1342	0.764947
$563$	0.665558	0.0280499	0.0140250	−	0.999902i	$-0.495536\pi$
$563$	0.665558	0.0280499	0.0140250	+	0.999902i	$0.495536\pi$
$564$	3.04781	0.128336
$565$	−10.7130	−0.450699
$566$	−8.20172	−0.344744
$567$	7.46130	0.313345
$568$	−17.8858	−0.750473
$569$	27.3469	1.14644	0.573220	−	0.819402i	$-0.305694\pi$
$569$	27.3469	1.14644	0.573220	+	0.819402i	$0.305694\pi$
$570$	20.8488	0.873260
$571$	37.0483	1.55042	0.775211	−	0.631703i	$-0.217644\pi$
$571$	37.0483	1.55042	0.775211	+	0.631703i	$0.217644\pi$
$572$	1.32306	0.0553201
$573$	−12.8661	−0.537490
$574$	19.8285	0.827627
$575$	−3.07829	−0.128374
$576$	−10.5536	−0.439733
$577$	−36.6980	−1.52776	−0.763878	−	0.645361i	$-0.776707\pi$
$577$	−36.6980	−1.52776	−0.763878	+	0.645361i	$0.776707\pi$
$578$	−14.5455	−0.605015
$579$	25.5286	1.06093
$580$	−0.232165	−0.00964014
$581$	3.46224	0.143638
$582$	21.1639	0.877272
$583$	2.83512	0.117419
$584$	9.11056	0.376998
$585$	3.82147	0.157998
$586$	−36.0959	−1.49111
$587$	44.2025	1.82443	0.912217	−	0.409708i	$-0.134369\pi$
$587$	44.2025	1.82443	0.912217	+	0.409708i	$0.134369\pi$
$588$	−0.688853	−0.0284078
$589$	39.8893	1.64361
$590$	2.65908	0.109473
$591$	6.61429	0.272076
$592$	13.2765	0.545660
$593$	10.9158	0.448260	0.224130	−	0.974559i	$-0.428046\pi$
$593$	10.9158	0.448260	0.224130	+	0.974559i	$0.428046\pi$
$594$	26.9335	1.10510
$595$	6.85120	0.280872
$596$	0.798121	0.0326923
$597$	32.8835	1.34583
$598$	−3.02434	−0.123675
$599$	33.8617	1.38355	0.691775	−	0.722113i	$-0.256829\pi$
$599$	33.8617	1.38355	0.691775	+	0.722113i	$0.256829\pi$
$600$	−12.0032	−0.490028
$601$	11.0861	0.452212	0.226106	−	0.974103i	$-0.427400\pi$
$601$	11.0861	0.452212	0.226106	+	0.974103i	$0.427400\pi$
$602$	−0.743006	−0.0302827
$603$	2.09405	0.0852763
$604$	0.576877	0.0234728
$605$	2.08462	0.0847519
$606$	−28.0065	−1.13769
$607$	−48.9042	−1.98496	−0.992480	−	0.122409i	$-0.960938\pi$
$607$	−48.9042	−1.98496	−0.992480	+	0.122409i	$0.960938\pi$
$608$	−7.89873	−0.320336
$609$	2.62613	0.106416
$610$	1.06858	0.0432655
$611$	−30.5937	−1.23769
$612$	−0.516832	−0.0208917
$613$	42.8587	1.73105	0.865524	−	0.500868i	$-0.166986\pi$
$613$	42.8587	1.73105	0.865524	+	0.500868i	$0.166986\pi$
$614$	0.963084	0.0388669
$615$	13.6555	0.550644
$616$	20.5026	0.826072
$617$	4.57435	0.184157	0.0920783	−	0.995752i	$-0.470649\pi$
$617$	4.57435	0.184157	0.0920783	+	0.995752i	$0.470649\pi$
$618$	18.6587	0.750564
$619$	−20.1899	−0.811500	−0.405750	−	0.913984i	$-0.632990\pi$
$619$	−20.1899	−0.811500	−0.405750	+	0.913984i	$0.632990\pi$
$620$	1.10777	0.0444890
$621$	5.62663	0.225789
$622$	−22.0980	−0.886049
$623$	−12.9743	−0.519805
$624$	−10.7983	−0.432279
$625$	−0.132649	−0.00530596
$626$	−31.8257	−1.27201
$627$	39.2856	1.56891
$628$	3.28598	0.131125
$629$	9.12966	0.364023
$630$	4.57571	0.182300
$631$	−23.7334	−0.944810	−0.472405	−	0.881382i	$-0.656614\pi$
$631$	−23.7334	−0.944810	−0.472405	+	0.881382i	$0.656614\pi$
$632$	−8.04044	−0.319831
$633$	−2.27497	−0.0904221
$634$	−27.5931	−1.09586
$635$	4.99272	0.198130
$636$	0.178448	0.00707593
$637$	6.91467	0.273969
$638$	4.78680	0.189511
$639$	−7.52161	−0.297550
$640$	13.4309	0.530904
$641$	−4.65245	−0.183761	−0.0918804	−	0.995770i	$-0.529288\pi$
$641$	−4.65245	−0.183761	−0.0918804	+	0.995770i	$0.529288\pi$
$642$	−11.1234	−0.439005
$643$	37.8681	1.49337	0.746686	−	0.665177i	$-0.231644\pi$
$643$	37.8681	1.49337	0.746686	+	0.665177i	$0.231644\pi$
$644$	0.330950	0.0130413
$645$	−0.511693	−0.0201479
$646$	28.3038	1.11360
$647$	−3.45426	−0.135801	−0.0679005	−	0.997692i	$-0.521630\pi$
$647$	−3.45426	−0.135801	−0.0679005	+	0.997692i	$0.521630\pi$
$648$	11.0786	0.435209
$649$	5.01053	0.196680
$650$	9.30981	0.365161
$651$	−12.5305	−0.491108
$652$	1.66468	0.0651938
$653$	−19.7131	−0.771434	−0.385717	−	0.922617i	$-0.626046\pi$
$653$	−19.7131	−0.771434	−0.385717	+	0.922617i	$0.626046\pi$
$654$	−14.0290	−0.548577
$655$	8.65190	0.338058
$656$	26.9588	1.05256
$657$	3.83131	0.149474
$658$	−36.6319	−1.42806
$659$	14.8667	0.579123	0.289561	−	0.957159i	$-0.406491\pi$
$659$	14.8667	0.579123	0.289561	+	0.957159i	$0.406491\pi$
$660$	1.09100	0.0424672
$661$	−4.32998	−0.168417	−0.0842083	−	0.996448i	$-0.526836\pi$
$661$	−4.32998	−0.168417	−0.0842083	+	0.996448i	$0.526836\pi$
$662$	−22.3880	−0.870135
$663$	−7.42554	−0.288384
$664$	5.14076	0.199500
$665$	22.9012	0.888069
$666$	6.09741	0.236270
$667$	1.00000	0.0387202
$668$	0.915596	0.0354255
$669$	27.7245	1.07189
$670$	−3.18474	−0.123037
$671$	2.01353	0.0777316
$672$	2.48123	0.0957157
$673$	7.67405	0.295813	0.147906	−	0.989001i	$-0.452747\pi$
$673$	7.67405	0.295813	0.147906	+	0.989001i	$0.452747\pi$
$674$	16.9935	0.654565
$675$	−17.3204	−0.666663
$676$	1.34127	0.0515874
$677$	−0.0107641	−0.000413699 0	−0.000206850	−	1.00000i	$-0.500066\pi$
$677$	−0.0107641	−0.000413699 0	−0.000206850		1.00000i	$0.500066\pi$
$678$	13.9027	0.533930
$679$	23.2473	0.892149
$680$	10.1727	0.390106
$681$	−21.7450	−0.833269
$682$	−22.8400	−0.874590
$683$	−35.4181	−1.35523	−0.677617	−	0.735415i	$-0.736987\pi$
$683$	−35.4181	−1.35523	−0.677617	+	0.735415i	$0.736987\pi$
$684$	−1.72759	−0.0660560
$685$	4.97332	0.190021
$686$	27.0048	1.03105
$687$	−3.67931	−0.140374
$688$	−1.01019	−0.0385130
$689$	−1.79125	−0.0682413
$690$	−2.49388	−0.0949404
$691$	−36.0660	−1.37201	−0.686007	−	0.727595i	$-0.740638\pi$
$691$	−36.0660	−1.37201	−0.686007	+	0.727595i	$0.740638\pi$
$692$	1.97930	0.0752416
$693$	8.62205	0.327524
$694$	19.1721	0.727763
$695$	7.62155	0.289102
$696$	3.89930	0.147803
$697$	18.5384	0.702192
$698$	−21.9344	−0.830229
$699$	33.2656	1.25822
$700$	−1.01876	−0.0385056
$701$	14.9498	0.564646	0.282323	−	0.959319i	$-0.408895\pi$
$701$	14.9498	0.564646	0.282323	+	0.959319i	$0.408895\pi$
$702$	−17.0168	−0.642260
$703$	30.5172	1.15098
$704$	30.2440	1.13987
$705$	−25.2277	−0.950129
$706$	32.9463	1.23995
$707$	−30.7635	−1.15698
$708$	0.315373	0.0118524
$709$	10.8489	0.407441	0.203720	−	0.979029i	$-0.434697\pi$
$709$	10.8489	0.407441	0.203720	+	0.979029i	$0.434697\pi$
$710$	11.4393	0.429308
$711$	−3.38128	−0.126808
$712$	−19.2644	−0.721963
$713$	−4.77146	−0.178693
$714$	−8.89110	−0.332741
$715$	−10.9514	−0.409560
$716$	−3.81503	−0.142574
$717$	13.2641	0.495358
$718$	−8.91404	−0.332669
$719$	−25.3040	−0.943681	−0.471840	−	0.881684i	$-0.656410\pi$
$719$	−25.3040	−0.943681	−0.471840	+	0.881684i	$0.656410\pi$
$720$	6.22111	0.231847
$721$	20.4955	0.763293
$722$	68.8892	2.56379
$723$	−26.7201	−0.993730
$724$	−4.11733	−0.153019
$725$	−3.07829	−0.114325
$726$	−2.70530	−0.100403
$727$	4.00939	0.148700	0.0743500	−	0.997232i	$-0.476312\pi$
$727$	4.00939	0.148700	0.0743500	+	0.997232i	$0.476312\pi$
$728$	−12.9537	−0.480096
$729$	27.0914	1.00338
$730$	−5.82686	−0.215662
$731$	−0.694662	−0.0256930
$732$	0.126736	0.00468429
$733$	−18.3318	−0.677100	−0.338550	−	0.940948i	$-0.609936\pi$
$733$	−18.3318	−0.677100	−0.338550	+	0.940948i	$0.609936\pi$
$734$	9.64243	0.355908
$735$	5.70186	0.210316
$736$	0.944826	0.0348267
$737$	−6.00104	−0.221051
$738$	12.3812	0.455759
$739$	46.6945	1.71768	0.858842	−	0.512241i	$-0.171184\pi$
$739$	46.6945	1.71768	0.858842	+	0.512241i	$0.171184\pi$
$740$	0.847495	0.0311545
$741$	−24.8210	−0.911821
$742$	−2.14479	−0.0787377
$743$	17.4041	0.638495	0.319247	−	0.947671i	$-0.396570\pi$
$743$	17.4041	0.638495	0.319247	+	0.947671i	$0.396570\pi$
$744$	−18.6053	−0.682105
$745$	−6.60631	−0.242036
$746$	25.1900	0.922271
$747$	2.16187	0.0790987
$748$	1.48112	0.0541550
$749$	−12.2184	−0.446450
$750$	20.1463	0.735639
$751$	30.4335	1.11053	0.555267	−	0.831672i	$-0.312616\pi$
$751$	30.4335	1.11053	0.555267	+	0.831672i	$0.312616\pi$
$752$	−49.8046	−1.81619
$753$	28.8927	1.05291
$754$	−3.02434	−0.110140
$755$	−4.77500	−0.173780
$756$	1.86213	0.0677251
$757$	8.03379	0.291993	0.145997	−	0.989285i	$-0.453361\pi$
$757$	8.03379	0.291993	0.145997	+	0.989285i	$0.453361\pi$
$758$	−28.0839	−1.02005
$759$	−4.69924	−0.170572
$760$	34.0038	1.23345
$761$	−2.47383	−0.0896762	−0.0448381	−	0.998994i	$-0.514277\pi$
$761$	−2.47383	−0.0896762	−0.0448381	+	0.998994i	$0.514277\pi$
$762$	−6.47926	−0.234719
$763$	−15.4100	−0.557880
$764$	−1.62142	−0.0586608
$765$	4.27799	0.154671
$766$	19.8585	0.717515
$767$	−3.16569	−0.114307
$768$	5.30311	0.191360
$769$	−19.9681	−0.720070	−0.360035	−	0.932939i	$-0.617235\pi$
$769$	−19.9681	−0.720070	−0.360035	+	0.932939i	$0.617235\pi$
$770$	−13.1129	−0.472555
$771$	31.6333	1.13925
$772$	3.21717	0.115788
$773$	−50.0938	−1.80175	−0.900875	−	0.434079i	$-0.857074\pi$
$773$	−50.0938	−1.80175	−0.900875	+	0.434079i	$0.857074\pi$
$774$	−0.463943	−0.0166761
$775$	14.6880	0.527607
$776$	34.5178	1.23912
$777$	−9.58640	−0.343910
$778$	25.3834	0.910038
$779$	61.9673	2.22021
$780$	−0.689304	−0.0246810
$781$	21.5551	0.771303
$782$	−3.38563	−0.121070
$783$	5.62663	0.201079
$784$	11.2566	0.402023
$785$	−27.1991	−0.970779
$786$	−11.2279	−0.400487
$787$	19.3697	0.690455	0.345228	−	0.938519i	$-0.387802\pi$
$787$	19.3697	0.690455	0.345228	+	0.938519i	$0.387802\pi$
$788$	0.833547	0.0296939
$789$	−9.43093	−0.335750
$790$	5.14244	0.182960
$791$	15.2713	0.542985
$792$	12.8021	0.454902
$793$	−1.27217	−0.0451760
$794$	−5.62912	−0.199770
$795$	−1.47707	−0.0523864
$796$	4.14405	0.146882
$797$	−0.609345	−0.0215841	−0.0107920	−	0.999942i	$-0.503435\pi$
$797$	−0.609345	−0.0215841	−0.0107920	+	0.999942i	$0.503435\pi$
$798$	−29.7198	−1.05207
$799$	−34.2484	−1.21162
$800$	−2.90845	−0.102829
$801$	−8.10133	−0.286247
$802$	46.6037	1.64563
$803$	−10.9796	−0.387462
$804$	−0.377717	−0.0133211
$805$	−2.73938	−0.0965504
$806$	14.4305	0.508294
$807$	20.8912	0.735405
$808$	−45.6779	−1.60694
$809$	−16.5080	−0.580390	−0.290195	−	0.956968i	$-0.593720\pi$
$809$	−16.5080	−0.580390	−0.290195	+	0.956968i	$0.593720\pi$
$810$	−7.08556	−0.248961
$811$	−6.48787	−0.227820	−0.113910	−	0.993491i	$-0.536338\pi$
$811$	−6.48787	−0.227820	−0.113910	+	0.993491i	$0.536338\pi$
$812$	0.330950	0.0116141
$813$	−32.6477	−1.14500
$814$	−17.4737	−0.612453
$815$	−13.7791	−0.482660
$816$	−12.0883	−0.423175
$817$	−2.32201	−0.0812369
$818$	42.0844	1.47145
$819$	−5.44748	−0.190350
$820$	1.72090	0.0600963
$821$	−34.0168	−1.18719	−0.593597	−	0.804762i	$-0.702293\pi$
$821$	−34.0168	−1.18719	−0.593597	+	0.804762i	$0.702293\pi$
$822$	−6.45409	−0.225112
$823$	9.97377	0.347664	0.173832	−	0.984775i	$-0.444385\pi$
$823$	9.97377	0.347664	0.173832	+	0.984775i	$0.444385\pi$
$824$	30.4319	1.06015
$825$	14.4656	0.503629
$826$	−3.79050	−0.131888
$827$	−9.94112	−0.345686	−0.172843	−	0.984949i	$-0.555295\pi$
$827$	−9.94112	−0.345686	−0.172843	+	0.984949i	$0.555295\pi$
$828$	0.206650	0.00718158
$829$	−13.7684	−0.478196	−0.239098	−	0.970995i	$-0.576852\pi$
$829$	−13.7684	−0.478196	−0.239098	+	0.970995i	$0.576852\pi$
$830$	−3.28789	−0.114124
$831$	22.6639	0.786202
$832$	−19.1084	−0.662466
$833$	7.74070	0.268199
$834$	−9.89081	−0.342491
$835$	−7.57868	−0.262271
$836$	4.95085	0.171229
$837$	−26.8472	−0.927976
$838$	−46.1109	−1.59287
$839$	31.4440	1.08557	0.542785	−	0.839872i	$-0.317370\pi$
$839$	31.4440	1.08557	0.542785	+	0.839872i	$0.317370\pi$
$840$	−10.6817	−0.368552
$841$	1.00000	0.0344828
$842$	−0.463373	−0.0159689
$843$	−17.8025	−0.613152
$844$	−0.286697	−0.00986851
$845$	−11.1021	−0.381925
$846$	−22.8735	−0.786406
$847$	−2.97161	−0.102106
$848$	−2.91604	−0.100137
$849$	8.05169	0.276333
$850$	10.4220	0.357470
$851$	−3.65039	−0.125134
$852$	1.35672	0.0464805
$853$	41.3479	1.41573	0.707863	−	0.706350i	$-0.249659\pi$
$853$	41.3479	1.41573	0.707863	+	0.706350i	$0.249659\pi$
$854$	−1.52325	−0.0521246
$855$	14.2998	0.489043
$856$	−18.1420	−0.620079
$857$	16.0797	0.549273	0.274636	−	0.961548i	$-0.411443\pi$
$857$	16.0797	0.549273	0.274636	+	0.961548i	$0.411443\pi$
$858$	14.2121	0.485194
$859$	−53.5923	−1.82854	−0.914272	−	0.405101i	$-0.867236\pi$
$859$	−53.5923	−1.82854	−0.914272	+	0.405101i	$0.867236\pi$
$860$	−0.0644847	−0.00219891
$861$	−19.4658	−0.663394
$862$	−0.241765	−0.00823454
$863$	51.1249	1.74031	0.870156	−	0.492777i	$-0.164018\pi$
$863$	51.1249	1.74031	0.870156	+	0.492777i	$0.164018\pi$
$864$	5.31618	0.180860
$865$	−16.3833	−0.557048
$866$	−31.3555	−1.06550
$867$	14.2795	0.484957
$868$	−1.57911	−0.0535987
$869$	9.68994	0.328709
$870$	−2.49388	−0.0845505
$871$	3.79151	0.128470
$872$	−22.8809	−0.774847
$873$	14.5159	0.491290
$874$	−11.3170	−0.382802
$875$	22.1295	0.748114
$876$	−0.691078	−0.0233494
$877$	−40.5681	−1.36989	−0.684944	−	0.728595i	$-0.740174\pi$
$877$	−40.5681	−1.36989	−0.684944	+	0.728595i	$0.740174\pi$
$878$	54.4149	1.83641
$879$	35.4357	1.19522
$880$	−17.8282	−0.600988
$881$	0.946046	0.0318731	0.0159365	−	0.999873i	$-0.494927\pi$
$881$	0.946046	0.0318731	0.0159365	+	0.999873i	$0.494927\pi$
$882$	5.16977	0.174075
$883$	−23.3935	−0.787254	−0.393627	−	0.919270i	$-0.628780\pi$
$883$	−23.3935	−0.787254	−0.393627	+	0.919270i	$0.628780\pi$
$884$	−0.935782	−0.0314738
$885$	−2.61044	−0.0877490
$886$	−40.2038	−1.35067
$887$	−5.42208	−0.182055	−0.0910277	−	0.995848i	$-0.529015\pi$
$887$	−5.42208	−0.182055	−0.0910277	+	0.995848i	$0.529015\pi$
$888$	−14.2340	−0.477661
$889$	−7.11708	−0.238699
$890$	12.3209	0.412999
$891$	−13.3514	−0.447288
$892$	3.49390	0.116984
$893$	−114.480	−3.83094
$894$	8.57328	0.286733
$895$	31.5782	1.05554
$896$	−19.1457	−0.639612
$897$	2.96902	0.0991328
$898$	19.3745	0.646535
$899$	−4.77146	−0.159137
$900$	−0.636129	−0.0212043
$901$	−2.00524	−0.0668041
$902$	−35.4816	−1.18141
$903$	0.729415	0.0242734
$904$	22.6750	0.754158
$905$	34.0805	1.13287
$906$	6.19672	0.205872
$907$	11.8758	0.394330	0.197165	−	0.980370i	$-0.436827\pi$
$907$	11.8758	0.394330	0.197165	+	0.980370i	$0.436827\pi$
$908$	−2.74035	−0.0909415
$909$	−19.2091	−0.637127
$910$	8.28482	0.274639
$911$	−36.5576	−1.21121	−0.605604	−	0.795767i	$-0.707068\pi$
$911$	−36.5576	−1.21121	−0.605604	+	0.795767i	$0.707068\pi$
$912$	−40.4069	−1.33801
$913$	−6.19540	−0.205038
$914$	29.2974	0.969071
$915$	−1.04903	−0.0346800
$916$	−0.463674	−0.0153202
$917$	−12.3332	−0.407279
$918$	−19.0497	−0.628733
$919$	−13.2115	−0.435806	−0.217903	−	0.975970i	$-0.569922\pi$
$919$	−13.2115	−0.435806	−0.217903	+	0.975970i	$0.569922\pi$
$920$	−4.06746	−0.134100
$921$	−0.945468	−0.0311542
$922$	−40.1063	−1.32083
$923$	−13.6187	−0.448265
$924$	−1.55521	−0.0511628
$925$	11.2370	0.369470
$926$	7.25358	0.238367
$927$	12.7977	0.420331
$928$	0.944826	0.0310154
$929$	17.6973	0.580630	0.290315	−	0.956931i	$-0.406240\pi$
$929$	17.6973	0.580630	0.290315	+	0.956931i	$0.406240\pi$
$930$	11.8995	0.390198
$931$	25.8744	0.848000
$932$	4.19219	0.137320
$933$	21.6938	0.710223
$934$	−50.1330	−1.64040
$935$	−12.2597	−0.400934
$936$	−8.08847	−0.264380
$937$	−36.5078	−1.19266	−0.596330	−	0.802740i	$-0.703375\pi$
$937$	−36.5078	−1.19266	−0.596330	+	0.802740i	$0.703375\pi$
$938$	4.53983	0.148231
$939$	31.2436	1.01960
$940$	−3.17924	−0.103695
$941$	−2.99313	−0.0975731	−0.0487865	−	0.998809i	$-0.515535\pi$
$941$	−2.99313	−0.0975731	−0.0487865	+	0.998809i	$0.515535\pi$
$942$	35.2975	1.15005
$943$	−7.41237	−0.241380
$944$	−5.15354	−0.167734
$945$	−15.4135	−0.501400
$946$	1.32955	0.0432274
$947$	−16.7084	−0.542951	−0.271475	−	0.962445i	$-0.587512\pi$
$947$	−16.7084	−0.542951	−0.271475	+	0.962445i	$0.587512\pi$
$948$	0.609904	0.0198088
$949$	6.93701	0.225185
$950$	34.8369	1.13026
$951$	27.0884	0.878402
$952$	−14.5012	−0.469985
$953$	−8.65425	−0.280339	−0.140169	−	0.990128i	$-0.544765\pi$
$953$	−8.65425	−0.280339	−0.140169	+	0.990128i	$0.544765\pi$
$954$	−1.33924	−0.0433593
$955$	13.4210	0.434293
$956$	1.67157	0.0540626
$957$	−4.69924	−0.151905
$958$	−24.1944	−0.781685
$959$	−7.08943	−0.228930
$960$	−15.7569	−0.508551
$961$	−8.23317	−0.265586
$962$	11.0400	0.355945
$963$	−7.62932	−0.245851
$964$	−3.36732	−0.108454
$965$	−26.6295	−0.857234
$966$	3.55501	0.114381
$967$	−34.3926	−1.10599	−0.552996	−	0.833184i	$-0.686515\pi$
$967$	−34.3926	−1.10599	−0.552996	+	0.833184i	$0.686515\pi$
$968$	−4.41228	−0.141816
$969$	−27.7861	−0.892617
$970$	−22.0766	−0.708837
$971$	−45.9840	−1.47570	−0.737848	−	0.674967i	$-0.764158\pi$
$971$	−45.9840	−1.47570	−0.737848	+	0.674967i	$0.764158\pi$
$972$	1.98662	0.0637209
$973$	−10.8645	−0.348299
$974$	16.5237	0.529452
$975$	−9.13952	−0.292699
$976$	−2.07101	−0.0662913
$977$	−53.5312	−1.71262	−0.856308	−	0.516466i	$-0.827247\pi$
$977$	−53.5312	−1.71262	−0.856308	+	0.516466i	$0.827247\pi$
$978$	17.8817	0.571793
$979$	23.2165	0.742001
$980$	0.718560	0.0229536
$981$	−9.62223	−0.307214
$982$	33.4778	1.06832
$983$	−52.8683	−1.68624	−0.843118	−	0.537729i	$-0.819282\pi$
$983$	−52.8683	−1.68624	−0.843118	+	0.537729i	$0.819282\pi$
$984$	−28.9031	−0.921396
$985$	−6.89954	−0.219838
$986$	−3.38563	−0.107820
$987$	35.9619	1.14468
$988$	−3.12799	−0.0995146
$989$	0.277753	0.00883203
$990$	−8.18785	−0.260227
$991$	−7.11177	−0.225913	−0.112956	−	0.993600i	$-0.536032\pi$
$991$	−7.11177	−0.225913	−0.112956	+	0.993600i	$0.536032\pi$
$992$	−4.50820	−0.143135
$993$	21.9785	0.697467
$994$	−16.3066	−0.517214
$995$	−34.3016	−1.08743
$996$	−0.389951	−0.0123561
$997$	−32.4973	−1.02920	−0.514601	−	0.857430i	$-0.672060\pi$
$997$	−32.4973	−1.02920	−0.514601	+	0.857430i	$0.672060\pi$
$998$	14.7325	0.466349
$999$	−20.5394	−0.649838

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	667.2.a.a.1.8	✓	10
3.2	odd	2		6003.2.a.l.1.3		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
667.2.a.a.1.8	✓	10	1.1	even	1	trivial
6003.2.a.l.1.3		10	3.2	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:	\( N \)	\(=\)	\( 667 = 23 \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	667.a (trivial)

\(f(q)\)	\(=\)	\(q+1.35371 q^{2} -1.32895 q^{3} -0.167476 q^{4} +1.38626 q^{5} -1.79900 q^{6} -1.97610 q^{7} -2.93413 q^{8} -1.23390 q^{9} +O(q^{10})\)	\(q+1.35371 q^{2} -1.32895 q^{3} -0.167476 q^{4} +1.38626 q^{5} -1.79900 q^{6} -1.97610 q^{7} -2.93413 q^{8} -1.23390 q^{9} +1.87659 q^{10} +3.53607 q^{11} +0.222567 q^{12} -2.23412 q^{13} -2.67506 q^{14} -1.84226 q^{15} -3.63700 q^{16} -2.50101 q^{17} -1.67034 q^{18} -8.35998 q^{19} -0.232165 q^{20} +2.62613 q^{21} +4.78680 q^{22} +1.00000 q^{23} +3.89930 q^{24} -3.07829 q^{25} -3.02434 q^{26} +5.62663 q^{27} +0.330950 q^{28} +1.00000 q^{29} -2.49388 q^{30} -4.77146 q^{31} +0.944826 q^{32} -4.69924 q^{33} -3.38563 q^{34} -2.73938 q^{35} +0.206650 q^{36} -3.65039 q^{37} -11.3170 q^{38} +2.96902 q^{39} -4.06746 q^{40} -7.41237 q^{41} +3.55501 q^{42} +0.277753 q^{43} -0.592208 q^{44} -1.71051 q^{45} +1.35371 q^{46} +13.6939 q^{47} +4.83337 q^{48} -3.09503 q^{49} -4.16711 q^{50} +3.32370 q^{51} +0.374162 q^{52} +0.801772 q^{53} +7.61681 q^{54} +4.90190 q^{55} +5.79813 q^{56} +11.1100 q^{57} +1.35371 q^{58} +1.41698 q^{59} +0.308535 q^{60} +0.569427 q^{61} -6.45916 q^{62} +2.43831 q^{63} +8.55302 q^{64} -3.09706 q^{65} -6.36140 q^{66} -1.69709 q^{67} +0.418860 q^{68} -1.32895 q^{69} -3.70832 q^{70} +6.09579 q^{71} +3.62043 q^{72} -3.10503 q^{73} -4.94157 q^{74} +4.09088 q^{75} +1.40010 q^{76} -6.98762 q^{77} +4.01919 q^{78} +2.74032 q^{79} -5.04181 q^{80} -3.77577 q^{81} -10.0342 q^{82} -1.75206 q^{83} -0.439815 q^{84} -3.46704 q^{85} +0.375996 q^{86} -1.32895 q^{87} -10.3753 q^{88} +6.56562 q^{89} -2.31553 q^{90} +4.41484 q^{91} -0.167476 q^{92} +6.34101 q^{93} +18.5375 q^{94} -11.5891 q^{95} -1.25562 q^{96} -11.7642 q^{97} -4.18977 q^{98} -4.36317 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - 3 q^{2} - 9 q^{3} + 9 q^{4} - 10 q^{5} + 4 q^{6} + q^{7} - 9 q^{8} + 7 q^{9}+O(q^{10}) \) 10 * q - 3 * q^2 - 9 * q^3 + 9 * q^4 - 10 * q^5 + 4 * q^6 + q^7 - 9 * q^8 + 7 * q^9	\( 10 q - 3 q^{2} - 9 q^{3} + 9 q^{4} - 10 q^{5} + 4 q^{6} + q^{7} - 9 q^{8} + 7 q^{9} - 6 q^{10} - 17 q^{12} - 13 q^{13} - 12 q^{14} + 2 q^{15} - 5 q^{16} - 22 q^{17} + 12 q^{18} - 2 q^{19} + 3 q^{20} - 7 q^{21} + 3 q^{22} + 10 q^{23} - 6 q^{24} + 10 q^{25} - 25 q^{26} - 24 q^{27} + 19 q^{28} + 10 q^{29} - 3 q^{30} - 22 q^{31} - 31 q^{32} - 9 q^{33} + 13 q^{34} - 15 q^{35} + 19 q^{36} - 9 q^{37} - 10 q^{38} + 4 q^{39} - 6 q^{40} - 25 q^{41} - 34 q^{42} + 3 q^{43} - 27 q^{44} - 28 q^{45} - 3 q^{46} - 17 q^{47} - 3 q^{48} + 17 q^{49} + 2 q^{50} + 38 q^{51} - 18 q^{52} - 43 q^{53} - 47 q^{54} - 11 q^{55} - 7 q^{56} + 18 q^{57} - 3 q^{58} - 7 q^{59} - 21 q^{60} - 6 q^{61} + 3 q^{62} + 11 q^{63} + 33 q^{64} + 11 q^{65} + 55 q^{66} + 11 q^{67} - 51 q^{68} - 9 q^{69} + 34 q^{70} - 17 q^{71} + 34 q^{72} - 44 q^{73} + 9 q^{74} + q^{75} + 24 q^{76} - 71 q^{77} + 38 q^{78} + 5 q^{79} + 38 q^{80} + 18 q^{81} + 33 q^{82} - 32 q^{83} + 14 q^{84} + 16 q^{85} - 9 q^{86} - 9 q^{87} + 18 q^{88} - 10 q^{89} - 9 q^{90} - 3 q^{91} + 9 q^{92} - 8 q^{93} + 47 q^{94} - 8 q^{95} + 60 q^{96} + 6 q^{97} - 73 q^{98} + 26 q^{99}+O(q^{100}) \) 10 * q - 3 * q^2 - 9 * q^3 + 9 * q^4 - 10 * q^5 + 4 * q^6 + q^7 - 9 * q^8 + 7 * q^9 - 6 * q^10 - 17 * q^12 - 13 * q^13 - 12 * q^14 + 2 * q^15 - 5 * q^16 - 22 * q^17 + 12 * q^18 - 2 * q^19 + 3 * q^20 - 7 * q^21 + 3 * q^22 + 10 * q^23 - 6 * q^24 + 10 * q^25 - 25 * q^26 - 24 * q^27 + 19 * q^28 + 10 * q^29 - 3 * q^30 - 22 * q^31 - 31 * q^32 - 9 * q^33 + 13 * q^34 - 15 * q^35 + 19 * q^36 - 9 * q^37 - 10 * q^38 + 4 * q^39 - 6 * q^40 - 25 * q^41 - 34 * q^42 + 3 * q^43 - 27 * q^44 - 28 * q^45 - 3 * q^46 - 17 * q^47 - 3 * q^48 + 17 * q^49 + 2 * q^50 + 38 * q^51 - 18 * q^52 - 43 * q^53 - 47 * q^54 - 11 * q^55 - 7 * q^56 + 18 * q^57 - 3 * q^58 - 7 * q^59 - 21 * q^60 - 6 * q^61 + 3 * q^62 + 11 * q^63 + 33 * q^64 + 11 * q^65 + 55 * q^66 + 11 * q^67 - 51 * q^68 - 9 * q^69 + 34 * q^70 - 17 * q^71 + 34 * q^72 - 44 * q^73 + 9 * q^74 + q^75 + 24 * q^76 - 71 * q^77 + 38 * q^78 + 5 * q^79 + 38 * q^80 + 18 * q^81 + 33 * q^82 - 32 * q^83 + 14 * q^84 + 16 * q^85 - 9 * q^86 - 9 * q^87 + 18 * q^88 - 10 * q^89 - 9 * q^90 - 3 * q^91 + 9 * q^92 - 8 * q^93 + 47 * q^94 - 8 * q^95 + 60 * q^96 + 6 * q^97 - 73 * q^98 + 26 * q^99

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