LMFDB - Embedded newform 6009.2.a.d.1.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6009,2,Mod(1,6009)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6009, 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("6009.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6009 = 3 \cdot 2003 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6009.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:	$47.9821065746$
Analytic rank:	$0$
Dimension:	$93$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.9
Character	$\chi$	$=$	6009.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.46607 q^{2} -1.00000 q^{3} +4.08152 q^{4} -3.84806 q^{5} +2.46607 q^{6} +3.41335 q^{7} -5.13317 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-2.46607 q^{2} -1.00000 q^{3} +4.08152 q^{4} -3.84806 q^{5} +2.46607 q^{6} +3.41335 q^{7} -5.13317 q^{8} +1.00000 q^{9} +9.48961 q^{10} +1.67484 q^{11} -4.08152 q^{12} -2.42723 q^{13} -8.41756 q^{14} +3.84806 q^{15} +4.49575 q^{16} +4.57233 q^{17} -2.46607 q^{18} -0.245173 q^{19} -15.7059 q^{20} -3.41335 q^{21} -4.13029 q^{22} +1.31671 q^{23} +5.13317 q^{24} +9.80759 q^{25} +5.98573 q^{26} -1.00000 q^{27} +13.9316 q^{28} -9.24802 q^{29} -9.48961 q^{30} +9.01678 q^{31} -0.820499 q^{32} -1.67484 q^{33} -11.2757 q^{34} -13.1348 q^{35} +4.08152 q^{36} +5.56630 q^{37} +0.604614 q^{38} +2.42723 q^{39} +19.7528 q^{40} +1.45438 q^{41} +8.41756 q^{42} -0.474047 q^{43} +6.83590 q^{44} -3.84806 q^{45} -3.24710 q^{46} +3.18066 q^{47} -4.49575 q^{48} +4.65094 q^{49} -24.1862 q^{50} -4.57233 q^{51} -9.90679 q^{52} -0.846545 q^{53} +2.46607 q^{54} -6.44490 q^{55} -17.5213 q^{56} +0.245173 q^{57} +22.8063 q^{58} +3.59681 q^{59} +15.7059 q^{60} +8.23733 q^{61} -22.2360 q^{62} +3.41335 q^{63} -6.96809 q^{64} +9.34014 q^{65} +4.13029 q^{66} +4.25556 q^{67} +18.6621 q^{68} -1.31671 q^{69} +32.3913 q^{70} +5.35996 q^{71} -5.13317 q^{72} -2.79293 q^{73} -13.7269 q^{74} -9.80759 q^{75} -1.00068 q^{76} +5.71682 q^{77} -5.98573 q^{78} +8.71703 q^{79} -17.2999 q^{80} +1.00000 q^{81} -3.58660 q^{82} -6.19718 q^{83} -13.9316 q^{84} -17.5946 q^{85} +1.16904 q^{86} +9.24802 q^{87} -8.59726 q^{88} +0.0916925 q^{89} +9.48961 q^{90} -8.28498 q^{91} +5.37417 q^{92} -9.01678 q^{93} -7.84375 q^{94} +0.943440 q^{95} +0.820499 q^{96} -0.264994 q^{97} -11.4695 q^{98} +1.67484 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 93 q + 2 q^{2} - 93 q^{3} + 114 q^{4} - 20 q^{5} - 2 q^{6} + 28 q^{7} + 6 q^{8} + 93 q^{9}+O(q^{10}) $ 93 * q + 2 * q^2 - 93 * q^3 + 114 * q^4 - 20 * q^5 - 2 * q^6 + 28 * q^7 + 6 * q^8 + 93 * q^9	\( 93 q + 2 q^{2} - 93 q^{3} + 114 q^{4} - 20 q^{5} - 2 q^{6} + 28 q^{7} + 6 q^{8} + 93 q^{9} + 19 q^{10} + 10 q^{11} - 114 q^{12} + 20 q^{13} + 13 q^{14} + 20 q^{15} + 148 q^{16} - 43 q^{17} + 2 q^{18} + 50 q^{19} - 31 q^{20} - 28 q^{21} + 36 q^{22} + 21 q^{23} - 6 q^{24} + 137 q^{25} + 2 q^{26} - 93 q^{27} + 62 q^{28} - q^{29} - 19 q^{30} + 58 q^{31} + 19 q^{32} - 10 q^{33} + 30 q^{34} + 30 q^{35} + 114 q^{36} + 42 q^{37} - 6 q^{38} - 20 q^{39} + 53 q^{40} - 7 q^{41} - 13 q^{42} + 60 q^{43} + 25 q^{44} - 20 q^{45} + 57 q^{46} + 9 q^{47} - 148 q^{48} + 145 q^{49} + 41 q^{50} + 43 q^{51} + 71 q^{52} - 45 q^{53} - 2 q^{54} + 78 q^{55} + 44 q^{56} - 50 q^{57} + 40 q^{58} + 42 q^{59} + 31 q^{60} + 69 q^{61} - 42 q^{62} + 28 q^{63} + 230 q^{64} - 4 q^{65} - 36 q^{66} + 76 q^{67} - 91 q^{68} - 21 q^{69} + 57 q^{70} + 92 q^{71} + 6 q^{72} + 29 q^{73} + 59 q^{74} - 137 q^{75} + 131 q^{76} - 98 q^{77} - 2 q^{78} + 215 q^{79} - 37 q^{80} + 93 q^{81} + 50 q^{82} - 27 q^{83} - 62 q^{84} + 52 q^{85} + 82 q^{86} + q^{87} + 136 q^{88} - 14 q^{89} + 19 q^{90} + 101 q^{91} - 14 q^{92} - 58 q^{93} + 112 q^{94} + 59 q^{95} - 19 q^{96} + 38 q^{97} - 16 q^{98} + 10 q^{99}+O(q^{100}) \) 93 * q + 2 * q^2 - 93 * q^3 + 114 * q^4 - 20 * q^5 - 2 * q^6 + 28 * q^7 + 6 * q^8 + 93 * q^9 + 19 * q^10 + 10 * q^11 - 114 * q^12 + 20 * q^13 + 13 * q^14 + 20 * q^15 + 148 * q^16 - 43 * q^17 + 2 * q^18 + 50 * q^19 - 31 * q^20 - 28 * q^21 + 36 * q^22 + 21 * q^23 - 6 * q^24 + 137 * q^25 + 2 * q^26 - 93 * q^27 + 62 * q^28 - q^29 - 19 * q^30 + 58 * q^31 + 19 * q^32 - 10 * q^33 + 30 * q^34 + 30 * q^35 + 114 * q^36 + 42 * q^37 - 6 * q^38 - 20 * q^39 + 53 * q^40 - 7 * q^41 - 13 * q^42 + 60 * q^43 + 25 * q^44 - 20 * q^45 + 57 * q^46 + 9 * q^47 - 148 * q^48 + 145 * q^49 + 41 * q^50 + 43 * q^51 + 71 * q^52 - 45 * q^53 - 2 * q^54 + 78 * q^55 + 44 * q^56 - 50 * q^57 + 40 * q^58 + 42 * q^59 + 31 * q^60 + 69 * q^61 - 42 * q^62 + 28 * q^63 + 230 * q^64 - 4 * q^65 - 36 * q^66 + 76 * q^67 - 91 * q^68 - 21 * q^69 + 57 * q^70 + 92 * q^71 + 6 * q^72 + 29 * q^73 + 59 * q^74 - 137 * q^75 + 131 * q^76 - 98 * q^77 - 2 * q^78 + 215 * q^79 - 37 * q^80 + 93 * q^81 + 50 * q^82 - 27 * q^83 - 62 * q^84 + 52 * q^85 + 82 * q^86 + q^87 + 136 * q^88 - 14 * q^89 + 19 * q^90 + 101 * q^91 - 14 * q^92 - 58 * q^93 + 112 * q^94 + 59 * q^95 - 19 * q^96 + 38 * q^97 - 16 * q^98 + 10 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−2.46607	−1.74378	−0.871889	−	0.489704i	$-0.837105\pi$
$2$	−2.46607	−1.74378	−0.871889	+	0.489704i	$0.837105\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	4.08152	2.04076
$5$	−3.84806	−1.72091	−0.860453	−	0.509530i	$-0.829819\pi$
$5$	−3.84806	−1.72091	−0.860453	+	0.509530i	$0.829819\pi$
$6$	2.46607	1.00677
$7$	3.41335	1.29012	0.645062	−	0.764130i	$-0.276832\pi$
$7$	3.41335	1.29012	0.645062	+	0.764130i	$0.276832\pi$
$8$	−5.13317	−1.81485
$9$	1.00000	0.333333
$10$	9.48961	3.00088
$11$	1.67484	0.504984	0.252492	−	0.967599i	$-0.418750\pi$
$11$	1.67484	0.504984	0.252492	+	0.967599i	$0.418750\pi$
$12$	−4.08152	−1.17823
$13$	−2.42723	−0.673193	−0.336596	−	0.941649i	$-0.609276\pi$
$13$	−2.42723	−0.673193	−0.336596	+	0.941649i	$0.609276\pi$
$14$	−8.41756	−2.24969
$15$	3.84806	0.993566
$16$	4.49575	1.12394
$17$	4.57233	1.10895	0.554477	−	0.832199i	$-0.312918\pi$
$17$	4.57233	1.10895	0.554477	+	0.832199i	$0.312918\pi$
$18$	−2.46607	−0.581259
$19$	−0.245173	−0.0562464	−0.0281232	−	0.999604i	$-0.508953\pi$
$19$	−0.245173	−0.0562464	−0.0281232	+	0.999604i	$0.508953\pi$
$20$	−15.7059	−3.51195
$21$	−3.41335	−0.744853
$22$	−4.13029	−0.880580
$23$	1.31671	0.274553	0.137276	−	0.990533i	$-0.456165\pi$
$23$	1.31671	0.274553	0.137276	+	0.990533i	$0.456165\pi$
$24$	5.13317	1.04780
$25$	9.80759	1.96152
$26$	5.98573	1.17390
$27$	−1.00000	−0.192450
$28$	13.9316	2.63283
$29$	−9.24802	−1.71731	−0.858657	−	0.512550i	$-0.828701\pi$
$29$	−9.24802	−1.71731	−0.858657	+	0.512550i	$0.828701\pi$
$30$	−9.48961	−1.73256
$31$	9.01678	1.61946	0.809730	−	0.586802i	$-0.199613\pi$
$31$	9.01678	1.61946	0.809730	+	0.586802i	$0.199613\pi$
$32$	−0.820499	−0.145045
$33$	−1.67484	−0.291553
$34$	−11.2757	−1.93377
$35$	−13.1348	−2.22018
$36$	4.08152	0.680253
$37$	5.56630	0.915094	0.457547	−	0.889185i	$-0.348728\pi$
$37$	5.56630	0.915094	0.457547	+	0.889185i	$0.348728\pi$
$38$	0.604614	0.0980813
$39$	2.42723	0.388668
$40$	19.7528	3.12319
$41$	1.45438	0.227136	0.113568	−	0.993530i	$-0.463772\pi$
$41$	1.45438	0.227136	0.113568	+	0.993530i	$0.463772\pi$
$42$	8.41756	1.29886
$43$	−0.474047	−0.0722915	−0.0361458	−	0.999347i	$-0.511508\pi$
$43$	−0.474047	−0.0722915	−0.0361458	+	0.999347i	$0.511508\pi$
$44$	6.83590	1.03055
$45$	−3.84806	−0.573635
$46$	−3.24710	−0.478759
$47$	3.18066	0.463948	0.231974	−	0.972722i	$-0.425482\pi$
$47$	3.18066	0.463948	0.231974	+	0.972722i	$0.425482\pi$
$48$	−4.49575	−0.648906
$49$	4.65094	0.664419
$50$	−24.1862	−3.42045
$51$	−4.57233	−0.640255
$52$	−9.90679	−1.37382
$53$	−0.846545	−0.116282	−0.0581410	−	0.998308i	$-0.518517\pi$
$53$	−0.846545	−0.116282	−0.0581410	+	0.998308i	$0.518517\pi$
$54$	2.46607	0.335590
$55$	−6.44490	−0.869031
$56$	−17.5213	−2.34138
$57$	0.245173	0.0324739
$58$	22.8063	2.99461
$59$	3.59681	0.468265	0.234132	−	0.972205i	$-0.424775\pi$
$59$	3.59681	0.468265	0.234132	+	0.972205i	$0.424775\pi$
$60$	15.7059	2.02763
$61$	8.23733	1.05468	0.527341	−	0.849654i	$-0.323189\pi$
$61$	8.23733	1.05468	0.527341	+	0.849654i	$0.323189\pi$
$62$	−22.2360	−2.82398
$63$	3.41335	0.430041
$64$	−6.96809	−0.871011
$65$	9.34014	1.15850
$66$	4.13029	0.508403
$67$	4.25556	0.519899	0.259950	−	0.965622i	$-0.416294\pi$
$67$	4.25556	0.519899	0.259950	+	0.965622i	$0.416294\pi$
$68$	18.6621	2.26311
$69$	−1.31671	−0.158513
$70$	32.3913	3.87150
$71$	5.35996	0.636110	0.318055	−	0.948072i	$-0.396970\pi$
$71$	5.35996	0.636110	0.318055	+	0.948072i	$0.396970\pi$
$72$	−5.13317	−0.604950
$73$	−2.79293	−0.326888	−0.163444	−	0.986553i	$-0.552260\pi$
$73$	−2.79293	−0.326888	−0.163444	+	0.986553i	$0.552260\pi$
$74$	−13.7269	−1.59572
$75$	−9.80759	−1.13248
$76$	−1.00068	−0.114785
$77$	5.71682	0.651492
$78$	−5.98573	−0.677751
$79$	8.71703	0.980743	0.490371	−	0.871514i	$-0.336861\pi$
$79$	8.71703	0.980743	0.490371	+	0.871514i	$0.336861\pi$
$80$	−17.2999	−1.93419
$81$	1.00000	0.111111
$82$	−3.58660	−0.396074
$83$	−6.19718	−0.680229	−0.340115	−	0.940384i	$-0.610466\pi$
$83$	−6.19718	−0.680229	−0.340115	+	0.940384i	$0.610466\pi$
$84$	−13.9316	−1.52007
$85$	−17.5946	−1.90840
$86$	1.16904	0.126060
$87$	9.24802	0.991492
$88$	−8.59726	−0.916471
$89$	0.0916925	0.00971939	0.00485969	−	0.999988i	$-0.498453\pi$
$89$	0.0916925	0.00971939	0.00485969	+	0.999988i	$0.498453\pi$
$90$	9.48961	1.00029
$91$	−8.28498	−0.868502
$92$	5.37417	0.560296
$93$	−9.01678	−0.934996
$94$	−7.84375	−0.809021
$95$	0.943440	0.0967949
$96$	0.820499	0.0837418
$97$	−0.264994	−0.0269060	−0.0134530	−	0.999910i	$-0.504282\pi$
$97$	−0.264994	−0.0269060	−0.0134530	+	0.999910i	$0.504282\pi$
$98$	−11.4695	−1.15860
$99$	1.67484	0.168328
$100$	40.0298	4.00298
$101$	0.384941	0.0383031	0.0191515	−	0.999817i	$-0.493904\pi$
$101$	0.384941	0.0383031	0.0191515	+	0.999817i	$0.493904\pi$
$102$	11.2757	1.11646
$103$	−3.15777	−0.311144	−0.155572	−	0.987825i	$-0.549722\pi$
$103$	−3.15777	−0.311144	−0.155572	+	0.987825i	$0.549722\pi$
$104$	12.4594	1.22175
$105$	13.1348	1.28182
$106$	2.08764	0.202770
$107$	9.84400	0.951656	0.475828	−	0.879538i	$-0.342149\pi$
$107$	9.84400	0.951656	0.475828	+	0.879538i	$0.342149\pi$
$108$	−4.08152	−0.392744
$109$	19.4043	1.85859	0.929296	−	0.369335i	$-0.120415\pi$
$109$	19.4043	1.85859	0.929296	+	0.369335i	$0.120415\pi$
$110$	15.8936	1.51540
$111$	−5.56630	−0.528330
$112$	15.3456	1.45002
$113$	−7.16595	−0.674116	−0.337058	−	0.941484i	$-0.609432\pi$
$113$	−7.16595	−0.674116	−0.337058	+	0.941484i	$0.609432\pi$
$114$	−0.604614	−0.0566272
$115$	−5.06678	−0.472480
$116$	−37.7460	−3.50463
$117$	−2.42723	−0.224398
$118$	−8.87000	−0.816550
$119$	15.6070	1.43069
$120$	−19.7528	−1.80317
$121$	−8.19490	−0.744991
$122$	−20.3139	−1.83913
$123$	−1.45438	−0.131137
$124$	36.8021	3.30493
$125$	−18.4999	−1.65468
$126$	−8.41756	−0.749896
$127$	−1.01380	−0.0899604	−0.0449802	−	0.998988i	$-0.514322\pi$
$127$	−1.01380	−0.0899604	−0.0449802	+	0.998988i	$0.514322\pi$
$128$	18.8248	1.66389
$129$	0.474047	0.0417375
$130$	−23.0335	−2.02017
$131$	0.550663	0.0481117	0.0240558	−	0.999711i	$-0.492342\pi$
$131$	0.550663	0.0481117	0.0240558	+	0.999711i	$0.492342\pi$
$132$	−6.83590	−0.594989
$133$	−0.836859	−0.0725649
$134$	−10.4945	−0.906588
$135$	3.84806	0.331189
$136$	−23.4706	−2.01259
$137$	7.32757	0.626037	0.313018	−	0.949747i	$-0.398660\pi$
$137$	7.32757	0.626037	0.313018	+	0.949747i	$0.398660\pi$
$138$	3.24710	0.276412
$139$	−5.59180	−0.474291	−0.237145	−	0.971474i	$-0.576212\pi$
$139$	−5.59180	−0.474291	−0.237145	+	0.971474i	$0.576212\pi$
$140$	−53.6098	−4.53086
$141$	−3.18066	−0.267860
$142$	−13.2180	−1.10923
$143$	−4.06523	−0.339952
$144$	4.49575	0.374646
$145$	35.5870	2.95534
$146$	6.88758	0.570020
$147$	−4.65094	−0.383603
$148$	22.7190	1.86749
$149$	−4.85321	−0.397590	−0.198795	−	0.980041i	$-0.563703\pi$
$149$	−4.85321	−0.397590	−0.198795	+	0.980041i	$0.563703\pi$
$150$	24.1862	1.97480
$151$	−18.2057	−1.48156	−0.740778	−	0.671750i	$-0.765543\pi$
$151$	−18.2057	−1.48156	−0.740778	+	0.671750i	$0.765543\pi$
$152$	1.25851	0.102079
$153$	4.57233	0.369651
$154$	−14.0981	−1.13606
$155$	−34.6971	−2.78694
$156$	9.90679	0.793178
$157$	13.5006	1.07747	0.538733	−	0.842476i	$-0.318903\pi$
$157$	13.5006	1.07747	0.538733	+	0.842476i	$0.318903\pi$
$158$	−21.4968	−1.71020
$159$	0.846545	0.0671354
$160$	3.15733	0.249609
$161$	4.49438	0.354207
$162$	−2.46607	−0.193753
$163$	−14.1383	−1.10740	−0.553698	−	0.832718i	$-0.686784\pi$
$163$	−14.1383	−1.10740	−0.553698	+	0.832718i	$0.686784\pi$
$164$	5.93607	0.463529
$165$	6.44490	0.501735
$166$	15.2827	1.18617
$167$	−8.52493	−0.659679	−0.329840	−	0.944037i	$-0.606995\pi$
$167$	−8.52493	−0.659679	−0.329840	+	0.944037i	$0.606995\pi$
$168$	17.5213	1.35180
$169$	−7.10855	−0.546811
$170$	43.3896	3.32783
$171$	−0.245173	−0.0187488
$172$	−1.93483	−0.147530
$173$	−6.75735	−0.513752	−0.256876	−	0.966444i	$-0.582693\pi$
$173$	−6.75735	−0.513752	−0.256876	+	0.966444i	$0.582693\pi$
$174$	−22.8063	−1.72894
$175$	33.4767	2.53060
$176$	7.52968	0.567571
$177$	−3.59681	−0.270353
$178$	−0.226120	−0.0169484
$179$	0.0276308	0.00206523	0.00103261	−	0.999999i	$-0.499671\pi$
$179$	0.0276308	0.00206523	0.00103261	+	0.999999i	$0.499671\pi$
$180$	−15.7059	−1.17065
$181$	2.32207	0.172598	0.0862992	−	0.996269i	$-0.472496\pi$
$181$	2.32207	0.172598	0.0862992	+	0.996269i	$0.472496\pi$
$182$	20.4314	1.51447
$183$	−8.23733	−0.608921
$184$	−6.75890	−0.498272
$185$	−21.4195	−1.57479
$186$	22.2360	1.63042
$187$	7.65794	0.560004
$188$	12.9819	0.946805
$189$	−3.41335	−0.248284
$190$	−2.32659	−0.168789
$191$	−17.8384	−1.29074	−0.645371	−	0.763869i	$-0.723297\pi$
$191$	−17.8384	−1.29074	−0.645371	+	0.763869i	$0.723297\pi$
$192$	6.96809	0.502878
$193$	−11.1786	−0.804651	−0.402326	−	0.915497i	$-0.631798\pi$
$193$	−11.1786	−0.804651	−0.402326	+	0.915497i	$0.631798\pi$
$194$	0.653494	0.0469181
$195$	−9.34014	−0.668861
$196$	18.9829	1.35592
$197$	−11.9847	−0.853872	−0.426936	−	0.904282i	$-0.640407\pi$
$197$	−11.9847	−0.853872	−0.426936	+	0.904282i	$0.640407\pi$
$198$	−4.13029	−0.293527
$199$	11.6698	0.827247	0.413623	−	0.910448i	$-0.364263\pi$
$199$	11.6698	0.827247	0.413623	+	0.910448i	$0.364263\pi$
$200$	−50.3441	−3.55986
$201$	−4.25556	−0.300164
$202$	−0.949293	−0.0667920
$203$	−31.5667	−2.21555
$204$	−18.6621	−1.30661
$205$	−5.59654	−0.390879
$206$	7.78728	0.542566
$207$	1.31671	0.0915176
$208$	−10.9122	−0.756627
$209$	−0.410626	−0.0284036
$210$	−32.3913	−2.23521
$211$	0.716316	0.0493132	0.0246566	−	0.999696i	$-0.492151\pi$
$211$	0.716316	0.0493132	0.0246566	+	0.999696i	$0.492151\pi$
$212$	−3.45519	−0.237303
$213$	−5.35996	−0.367258
$214$	−24.2760	−1.65948
$215$	1.82416	0.124407
$216$	5.13317	0.349268
$217$	30.7774	2.08931
$218$	−47.8524	−3.24097
$219$	2.79293	0.188729
$220$	−26.3050	−1.77348
$221$	−11.0981	−0.746540
$222$	13.7269	0.921290
$223$	−25.2345	−1.68983	−0.844915	−	0.534901i	$-0.820349\pi$
$223$	−25.2345	−1.68983	−0.844915	+	0.534901i	$0.820349\pi$
$224$	−2.80065	−0.187126
$225$	9.80759	0.653839
$226$	17.6718	1.17551
$227$	−7.45447	−0.494770	−0.247385	−	0.968917i	$-0.579571\pi$
$227$	−7.45447	−0.494770	−0.247385	+	0.968917i	$0.579571\pi$
$228$	1.00068	0.0662714
$229$	−10.2872	−0.679799	−0.339899	−	0.940462i	$-0.610393\pi$
$229$	−10.2872	−0.679799	−0.339899	+	0.940462i	$0.610393\pi$
$230$	12.4950	0.823899
$231$	−5.71682	−0.376139
$232$	47.4717	3.11667
$233$	8.09007	0.529998	0.264999	−	0.964249i	$-0.414628\pi$
$233$	8.09007	0.529998	0.264999	+	0.964249i	$0.414628\pi$
$234$	5.98573	0.391300
$235$	−12.2394	−0.798410
$236$	14.6804	0.955616
$237$	−8.71703	−0.566232
$238$	−38.4879	−2.49480
$239$	−6.69491	−0.433058	−0.216529	−	0.976276i	$-0.569474\pi$
$239$	−6.69491	−0.433058	−0.216529	+	0.976276i	$0.569474\pi$
$240$	17.2999	1.11671
$241$	24.1937	1.55845	0.779226	−	0.626744i	$-0.215613\pi$
$241$	24.1937	1.55845	0.779226	+	0.626744i	$0.215613\pi$
$242$	20.2092	1.29910
$243$	−1.00000	−0.0641500
$244$	33.6208	2.15235
$245$	−17.8971	−1.14340
$246$	3.58660	0.228673
$247$	0.595091	0.0378647
$248$	−46.2847	−2.93908
$249$	6.19718	0.392730
$250$	45.6221	2.88540
$251$	19.4746	1.22922	0.614612	−	0.788829i	$-0.289312\pi$
$251$	19.4746	1.22922	0.614612	+	0.788829i	$0.289312\pi$
$252$	13.9316	0.877610
$253$	2.20528	0.138645
$254$	2.50011	0.156871
$255$	17.5946	1.10182
$256$	−32.4872	−2.03045
$257$	−2.36658	−0.147623	−0.0738117	−	0.997272i	$-0.523516\pi$
$257$	−2.36658	−0.147623	−0.0738117	+	0.997272i	$0.523516\pi$
$258$	−1.16904	−0.0727809
$259$	18.9997	1.18058
$260$	38.1219	2.36422
$261$	−9.24802	−0.572438
$262$	−1.35798	−0.0838961
$263$	21.5728	1.33023	0.665117	−	0.746739i	$-0.268382\pi$
$263$	21.5728	1.33023	0.665117	+	0.746739i	$0.268382\pi$
$264$	8.59726	0.529125
$265$	3.25756	0.200110
$266$	2.06376	0.126537
$267$	−0.0916925	−0.00561149
$268$	17.3691	1.06099
$269$	17.7387	1.08155	0.540775	−	0.841168i	$-0.318131\pi$
$269$	17.7387	1.08155	0.540775	+	0.841168i	$0.318131\pi$
$270$	−9.48961	−0.577519
$271$	22.2670	1.35262	0.676312	−	0.736615i	$-0.263577\pi$
$271$	22.2670	1.35262	0.676312	+	0.736615i	$0.263577\pi$
$272$	20.5561	1.24639
$273$	8.28498	0.501430
$274$	−18.0703	−1.09167
$275$	16.4262	0.990536
$276$	−5.37417	−0.323487
$277$	−16.0078	−0.961815	−0.480908	−	0.876771i	$-0.659693\pi$
$277$	−16.0078	−0.961815	−0.480908	+	0.876771i	$0.659693\pi$
$278$	13.7898	0.827057
$279$	9.01678	0.539820
$280$	67.4231	4.02930
$281$	31.4669	1.87716	0.938578	−	0.345068i	$-0.112144\pi$
$281$	31.4669	1.87716	0.938578	+	0.345068i	$0.112144\pi$
$282$	7.84375	0.467089
$283$	−21.7110	−1.29059	−0.645294	−	0.763934i	$-0.723265\pi$
$283$	−21.7110	−1.29059	−0.645294	+	0.763934i	$0.723265\pi$
$284$	21.8768	1.29815
$285$	−0.943440	−0.0558845
$286$	10.0252	0.592800
$287$	4.96430	0.293033
$288$	−0.820499	−0.0483484
$289$	3.90622	0.229778
$290$	−87.7601	−5.15345
$291$	0.264994	0.0155342
$292$	−11.3994	−0.667100
$293$	18.6266	1.08818	0.544089	−	0.839027i	$-0.316875\pi$
$293$	18.6266	1.08818	0.544089	+	0.839027i	$0.316875\pi$
$294$	11.4695	0.668918
$295$	−13.8408	−0.805840
$296$	−28.5728	−1.66076
$297$	−1.67484	−0.0971843
$298$	11.9684	0.693309
$299$	−3.19596	−0.184827
$300$	−40.0298	−2.31112
$301$	−1.61809	−0.0932650
$302$	44.8965	2.58350
$303$	−0.384941	−0.0221143
$304$	−1.10223	−0.0632175
$305$	−31.6978	−1.81501
$306$	−11.2757	−0.644589
$307$	−5.61066	−0.320217	−0.160109	−	0.987099i	$-0.551184\pi$
$307$	−5.61066	−0.320217	−0.160109	+	0.987099i	$0.551184\pi$
$308$	23.3333	1.32954
$309$	3.15777	0.179639
$310$	85.5657	4.85980
$311$	14.4310	0.818306	0.409153	−	0.912466i	$-0.365824\pi$
$311$	14.4310	0.818306	0.409153	+	0.912466i	$0.365824\pi$
$312$	−12.4594	−0.705375
$313$	−21.2379	−1.20043	−0.600217	−	0.799837i	$-0.704919\pi$
$313$	−21.2379	−1.20043	−0.600217	+	0.799837i	$0.704919\pi$
$314$	−33.2935	−1.87886
$315$	−13.1348	−0.740061
$316$	35.5787	2.00146
$317$	−19.9068	−1.11808	−0.559040	−	0.829141i	$-0.688830\pi$
$317$	−19.9068	−1.11808	−0.559040	+	0.829141i	$0.688830\pi$
$318$	−2.08764	−0.117069
$319$	−15.4890	−0.867217
$320$	26.8136	1.49893
$321$	−9.84400	−0.549439
$322$	−11.0835	−0.617658
$323$	−1.12101	−0.0623747
$324$	4.08152	0.226751
$325$	−23.8053	−1.32048
$326$	34.8660	1.93105
$327$	−19.4043	−1.07306
$328$	−7.46558	−0.412218
$329$	10.8567	0.598550
$330$	−15.8936	−0.874914
$331$	17.0942	0.939583	0.469792	−	0.882777i	$-0.344329\pi$
$331$	17.0942	0.939583	0.469792	+	0.882777i	$0.344329\pi$
$332$	−25.2939	−1.38818
$333$	5.56630	0.305031
$334$	21.0231	1.15033
$335$	−16.3757	−0.894697
$336$	−15.3456	−0.837169
$337$	34.7921	1.89525	0.947624	−	0.319387i	$-0.103477\pi$
$337$	34.7921	1.89525	0.947624	+	0.319387i	$0.103477\pi$
$338$	17.5302	0.953517
$339$	7.16595	0.389201
$340$	−71.8128	−3.89459
$341$	15.1017	0.817802
$342$	0.604614	0.0326938
$343$	−8.01817	−0.432940
$344$	2.43337	0.131198
$345$	5.06678	0.272786
$346$	16.6641	0.895869
$347$	19.2708	1.03451	0.517256	−	0.855831i	$-0.326953\pi$
$347$	19.2708	1.03451	0.517256	+	0.855831i	$0.326953\pi$
$348$	37.7460	2.02340
$349$	−27.2052	−1.45626	−0.728130	−	0.685439i	$-0.759610\pi$
$349$	−27.2052	−1.45626	−0.728130	+	0.685439i	$0.759610\pi$
$350$	−82.5560	−4.41280
$351$	2.42723	0.129556
$352$	−1.37421	−0.0732455
$353$	−14.8752	−0.791726	−0.395863	−	0.918310i	$-0.629554\pi$
$353$	−14.8752	−0.791726	−0.395863	+	0.918310i	$0.629554\pi$
$354$	8.87000	0.471435
$355$	−20.6255	−1.09469
$356$	0.374245	0.0198349
$357$	−15.6070	−0.826008
$358$	−0.0681397	−0.00360129
$359$	4.77123	0.251816	0.125908	−	0.992042i	$-0.459816\pi$
$359$	4.77123	0.251816	0.125908	+	0.992042i	$0.459816\pi$
$360$	19.7528	1.04106
$361$	−18.9399	−0.996836
$362$	−5.72640	−0.300973
$363$	8.19490	0.430121
$364$	−33.8153	−1.77240
$365$	10.7474	0.562544
$366$	20.3139	1.06182
$367$	−20.4517	−1.06757	−0.533786	−	0.845620i	$-0.679231\pi$
$367$	−20.4517	−1.06757	−0.533786	+	0.845620i	$0.679231\pi$
$368$	5.91959	0.308580
$369$	1.45438	0.0757119
$370$	52.8220	2.74609
$371$	−2.88955	−0.150018
$372$	−36.8021	−1.90810
$373$	−17.6437	−0.913554	−0.456777	−	0.889581i	$-0.650996\pi$
$373$	−17.6437	−0.913554	−0.456777	+	0.889581i	$0.650996\pi$
$374$	−18.8850	−0.976522
$375$	18.4999	0.955331
$376$	−16.3269	−0.841996
$377$	22.4471	1.15608
$378$	8.41756	0.432953
$379$	−15.4565	−0.793949	−0.396974	−	0.917830i	$-0.629940\pi$
$379$	−15.4565	−0.793949	−0.396974	+	0.917830i	$0.629940\pi$
$380$	3.85067	0.197535
$381$	1.01380	0.0519387
$382$	43.9909	2.25077
$383$	−23.0301	−1.17678	−0.588392	−	0.808576i	$-0.700239\pi$
$383$	−23.0301	−1.17678	−0.588392	+	0.808576i	$0.700239\pi$
$384$	−18.8248	−0.960650
$385$	−21.9987	−1.12116
$386$	27.5672	1.40313
$387$	−0.474047	−0.0240972
$388$	−1.08158	−0.0549087
$389$	23.6117	1.19716	0.598581	−	0.801062i	$-0.295731\pi$
$389$	23.6117	1.19716	0.598581	+	0.801062i	$0.295731\pi$
$390$	23.0335	1.16635
$391$	6.02043	0.304466
$392$	−23.8741	−1.20582
$393$	−0.550663	−0.0277773
$394$	29.5551	1.48896
$395$	−33.5437	−1.68777
$396$	6.83590	0.343517
$397$	−4.18707	−0.210143	−0.105072	−	0.994465i	$-0.533507\pi$
$397$	−4.18707	−0.210143	−0.105072	+	0.994465i	$0.533507\pi$
$398$	−28.7785	−1.44253
$399$	0.836859	0.0418954
$400$	44.0925	2.20462
$401$	14.2172	0.709971	0.354986	−	0.934872i	$-0.384486\pi$
$401$	14.2172	0.709971	0.354986	+	0.934872i	$0.384486\pi$
$402$	10.4945	0.523419
$403$	−21.8858	−1.09021
$404$	1.57114	0.0781673
$405$	−3.84806	−0.191212
$406$	77.8458	3.86342
$407$	9.32268	0.462108
$408$	23.4706	1.16197
$409$	24.1447	1.19388	0.596939	−	0.802287i	$-0.296384\pi$
$409$	24.1447	1.19388	0.596939	+	0.802287i	$0.296384\pi$
$410$	13.8015	0.681606
$411$	−7.32757	−0.361443
$412$	−12.8885	−0.634970
$413$	12.2772	0.604120
$414$	−3.24710	−0.159586
$415$	23.8472	1.17061
$416$	1.99154	0.0976433
$417$	5.59180	0.273832
$418$	1.01263	0.0495295
$419$	−5.48280	−0.267852	−0.133926	−	0.990991i	$-0.542759\pi$
$419$	−5.48280	−0.267852	−0.133926	+	0.990991i	$0.542759\pi$
$420$	53.6098	2.61589
$421$	−4.33215	−0.211136	−0.105568	−	0.994412i	$-0.533666\pi$
$421$	−4.33215	−0.211136	−0.105568	+	0.994412i	$0.533666\pi$
$422$	−1.76649	−0.0859912
$423$	3.18066	0.154649
$424$	4.34546	0.211034
$425$	44.8436	2.17523
$426$	13.2180	0.640416
$427$	28.1169	1.36067
$428$	40.1785	1.94210
$429$	4.06523	0.196271
$430$	−4.49852	−0.216938
$431$	−36.0507	−1.73650	−0.868250	−	0.496127i	$-0.834755\pi$
$431$	−36.0507	−1.73650	−0.868250	+	0.496127i	$0.834755\pi$
$432$	−4.49575	−0.216302
$433$	−4.87505	−0.234280	−0.117140	−	0.993115i	$-0.537373\pi$
$433$	−4.87505	−0.234280	−0.117140	+	0.993115i	$0.537373\pi$
$434$	−75.8993	−3.64328
$435$	−35.5870	−1.70627
$436$	79.1989	3.79294
$437$	−0.322821	−0.0154426
$438$	−6.88758	−0.329101
$439$	−0.217420	−0.0103769	−0.00518844	−	0.999987i	$-0.501652\pi$
$439$	−0.217420	−0.0103769	−0.00518844	+	0.999987i	$0.501652\pi$
$440$	33.0828	1.57716
$441$	4.65094	0.221473
$442$	27.3688	1.30180
$443$	−1.98263	−0.0941978	−0.0470989	−	0.998890i	$-0.514998\pi$
$443$	−1.98263	−0.0941978	−0.0470989	+	0.998890i	$0.514998\pi$
$444$	−22.7190	−1.07819
$445$	−0.352839	−0.0167262
$446$	62.2302	2.94669
$447$	4.85321	0.229549
$448$	−23.7845	−1.12371
$449$	26.8767	1.26839	0.634194	−	0.773174i	$-0.281332\pi$
$449$	26.8767	1.26839	0.634194	+	0.773174i	$0.281332\pi$
$450$	−24.1862	−1.14015
$451$	2.43586	0.114700
$452$	−29.2479	−1.37571
$453$	18.2057	0.855376
$454$	18.3833	0.862769
$455$	31.8811	1.49461
$456$	−1.25851	−0.0589353
$457$	−4.53340	−0.212063	−0.106032	−	0.994363i	$-0.533815\pi$
$457$	−4.53340	−0.212063	−0.106032	+	0.994363i	$0.533815\pi$
$458$	25.3690	1.18542
$459$	−4.57233	−0.213418
$460$	−20.6801	−0.964217
$461$	4.03542	0.187948	0.0939741	−	0.995575i	$-0.470043\pi$
$461$	4.03542	0.187948	0.0939741	+	0.995575i	$0.470043\pi$
$462$	14.0981	0.655903
$463$	28.9099	1.34356	0.671778	−	0.740753i	$-0.265531\pi$
$463$	28.9099	1.34356	0.671778	+	0.740753i	$0.265531\pi$
$464$	−41.5768	−1.93015
$465$	34.6971	1.60904
$466$	−19.9507	−0.924199
$467$	0.477078	0.0220765	0.0110383	−	0.999939i	$-0.496486\pi$
$467$	0.477078	0.0220765	0.0110383	+	0.999939i	$0.496486\pi$
$468$	−9.90679	−0.457941
$469$	14.5257	0.670734
$470$	30.1832	1.39225
$471$	−13.5006	−0.622076
$472$	−18.4631	−0.849831
$473$	−0.793955	−0.0365061
$474$	21.4968	0.987383
$475$	−2.40455	−0.110328
$476$	63.7001	2.91969
$477$	−0.846545	−0.0387606
$478$	16.5101	0.755157
$479$	25.7366	1.17594	0.587969	−	0.808884i	$-0.299928\pi$
$479$	25.7366	1.17594	0.587969	+	0.808884i	$0.299928\pi$
$480$	−3.15733	−0.144112
$481$	−13.5107	−0.616035
$482$	−59.6634	−2.71759
$483$	−4.49438	−0.204502
$484$	−33.4476	−1.52035
$485$	1.01971	0.0463028
$486$	2.46607	0.111863
$487$	33.9909	1.54027	0.770136	−	0.637879i	$-0.220188\pi$
$487$	33.9909	1.54027	0.770136	+	0.637879i	$0.220188\pi$
$488$	−42.2836	−1.91409
$489$	14.1383	0.639355
$490$	44.1355	1.99384
$491$	1.53387	0.0692224	0.0346112	−	0.999401i	$-0.488981\pi$
$491$	1.53387	0.0692224	0.0346112	+	0.999401i	$0.488981\pi$
$492$	−5.93607	−0.267619
$493$	−42.2850	−1.90442
$494$	−1.46754	−0.0660276
$495$	−6.44490	−0.289677
$496$	40.5372	1.82017
$497$	18.2954	0.820660
$498$	−15.2827	−0.684834
$499$	−25.0587	−1.12178	−0.560890	−	0.827890i	$-0.689541\pi$
$499$	−25.0587	−1.12178	−0.560890	+	0.827890i	$0.689541\pi$
$500$	−75.5077	−3.37681
$501$	8.52493	0.380866
$502$	−48.0257	−2.14349
$503$	−26.0393	−1.16104	−0.580518	−	0.814247i	$-0.697150\pi$
$503$	−26.0393	−1.16104	−0.580518	+	0.814247i	$0.697150\pi$
$504$	−17.5213	−0.780461
$505$	−1.48128	−0.0659160
$506$	−5.43838	−0.241766
$507$	7.10855	0.315702
$508$	−4.13785	−0.183588
$509$	21.2368	0.941304	0.470652	−	0.882319i	$-0.344019\pi$
$509$	21.2368	0.941304	0.470652	+	0.882319i	$0.344019\pi$
$510$	−43.3896	−1.92133
$511$	−9.53325	−0.421726
$512$	42.4662	1.87676
$513$	0.245173	0.0108246
$514$	5.83617	0.257422
$515$	12.1513	0.535450
$516$	1.93483	0.0851762
$517$	5.32711	0.234286
$518$	−46.8547	−2.05868
$519$	6.75735	0.296615
$520$	−47.9446	−2.10251
$521$	3.97447	0.174125	0.0870624	−	0.996203i	$-0.472252\pi$
$521$	3.97447	0.174125	0.0870624	+	0.996203i	$0.472252\pi$
$522$	22.8063	0.998205
$523$	−9.10036	−0.397931	−0.198966	−	0.980006i	$-0.563758\pi$
$523$	−9.10036	−0.397931	−0.198966	+	0.980006i	$0.563758\pi$
$524$	2.24754	0.0981843
$525$	−33.4767	−1.46104
$526$	−53.2001	−2.31963
$527$	41.2277	1.79591
$528$	−7.52968	−0.327687
$529$	−21.2663	−0.924621
$530$	−8.03338	−0.348948
$531$	3.59681	0.156088
$532$	−3.41565	−0.148087
$533$	−3.53011	−0.152906
$534$	0.226120	0.00978519
$535$	−37.8803	−1.63771
$536$	−21.8445	−0.943539
$537$	−0.0276308	−0.00119236
$538$	−43.7450	−1.88598
$539$	7.78959	0.335521
$540$	15.7059	0.675876
$541$	16.7407	0.719740	0.359870	−	0.933003i	$-0.382821\pi$
$541$	16.7407	0.719740	0.359870	+	0.933003i	$0.382821\pi$
$542$	−54.9121	−2.35868
$543$	−2.32207	−0.0996497
$544$	−3.75159	−0.160848
$545$	−74.6689	−3.19846
$546$	−20.4314	−0.874382
$547$	−21.3898	−0.914563	−0.457281	−	0.889322i	$-0.651177\pi$
$547$	−21.3898	−0.914563	−0.457281	+	0.889322i	$0.651177\pi$
$548$	29.9076	1.27759
$549$	8.23733	0.351561
$550$	−40.5082	−1.72727
$551$	2.26736	0.0965929
$552$	6.75890	0.287678
$553$	29.7543	1.26528
$554$	39.4764	1.67719
$555$	21.4195	0.909206
$556$	−22.8230	−0.967913
$557$	43.4510	1.84108	0.920539	−	0.390651i	$-0.127750\pi$
$557$	43.4510	1.84108	0.920539	+	0.390651i	$0.127750\pi$
$558$	−22.2360	−0.941326
$559$	1.15062	0.0486661
$560$	−59.0507	−2.49535
$561$	−7.65794	−0.323318
$562$	−77.5996	−3.27334
$563$	2.32163	0.0978451	0.0489226	−	0.998803i	$-0.484421\pi$
$563$	2.32163	0.0978451	0.0489226	+	0.998803i	$0.484421\pi$
$564$	−12.9819	−0.546638
$565$	27.5750	1.16009
$566$	53.5410	2.25050
$567$	3.41335	0.143347
$568$	−27.5136	−1.15444
$569$	20.7574	0.870195	0.435097	−	0.900383i	$-0.356714\pi$
$569$	20.7574	0.870195	0.435097	+	0.900383i	$0.356714\pi$
$570$	2.32659	0.0974502
$571$	−15.2650	−0.638818	−0.319409	−	0.947617i	$-0.603484\pi$
$571$	−15.2650	−0.638818	−0.319409	+	0.947617i	$0.603484\pi$
$572$	−16.5923	−0.693760
$573$	17.8384	0.745211
$574$	−12.2423	−0.510985
$575$	12.9137	0.538540
$576$	−6.96809	−0.290337
$577$	23.6120	0.982982	0.491491	−	0.870883i	$-0.336452\pi$
$577$	23.6120	0.982982	0.491491	+	0.870883i	$0.336452\pi$
$578$	−9.63303	−0.400681
$579$	11.1786	0.464566
$580$	145.249	6.03113
$581$	−21.1531	−0.877580
$582$	−0.653494	−0.0270882
$583$	−1.41783	−0.0587205
$584$	14.3366	0.593253
$585$	9.34014	0.386167
$586$	−45.9346	−1.89754
$587$	−12.9187	−0.533210	−0.266605	−	0.963806i	$-0.585902\pi$
$587$	−12.9187	−0.533210	−0.266605	+	0.963806i	$0.585902\pi$
$588$	−18.9829	−0.782841
$589$	−2.21067	−0.0910889
$590$	34.1323	1.40521
$591$	11.9847	0.492983
$592$	25.0247	1.02851
$593$	10.5925	0.434980	0.217490	−	0.976063i	$-0.430213\pi$
$593$	10.5925	0.434980	0.217490	+	0.976063i	$0.430213\pi$
$594$	4.13029	0.169468
$595$	−60.0566	−2.46208
$596$	−19.8085	−0.811386
$597$	−11.6698	−0.477611
$598$	7.88146	0.322297
$599$	2.17401	0.0888275	0.0444137	−	0.999013i	$-0.485858\pi$
$599$	2.17401	0.0888275	0.0444137	+	0.999013i	$0.485858\pi$
$600$	50.3441	2.05529
$601$	21.8622	0.891780	0.445890	−	0.895088i	$-0.352887\pi$
$601$	21.8622	0.891780	0.445890	+	0.895088i	$0.352887\pi$
$602$	3.99032	0.162633
$603$	4.25556	0.173300
$604$	−74.3067	−3.02350
$605$	31.5345	1.28206
$606$	0.949293	0.0385624
$607$	22.7103	0.921784	0.460892	−	0.887456i	$-0.347530\pi$
$607$	22.7103	0.921784	0.460892	+	0.887456i	$0.347530\pi$
$608$	0.201164	0.00815827
$609$	31.5667	1.27915
$610$	78.1690	3.16497
$611$	−7.72021	−0.312326
$612$	18.6621	0.754369
$613$	29.4396	1.18905	0.594527	−	0.804075i	$-0.297339\pi$
$613$	29.4396	1.18905	0.594527	+	0.804075i	$0.297339\pi$
$614$	13.8363	0.558388
$615$	5.59654	0.225674
$616$	−29.3454	−1.18236
$617$	31.9810	1.28751	0.643754	−	0.765232i	$-0.277376\pi$
$617$	31.9810	1.28751	0.643754	+	0.765232i	$0.277376\pi$
$618$	−7.78728	−0.313250
$619$	−26.5780	−1.06826	−0.534130	−	0.845402i	$-0.679361\pi$
$619$	−26.5780	−1.06826	−0.534130	+	0.845402i	$0.679361\pi$
$620$	−141.617	−5.68747
$621$	−1.31671	−0.0528377
$622$	−35.5879	−1.42694
$623$	0.312978	0.0125392
$624$	10.9122	0.436839
$625$	22.1509	0.886035
$626$	52.3741	2.09329
$627$	0.410626	0.0163988
$628$	55.1030	2.19885
$629$	25.4510	1.01480
$630$	32.3913	1.29050
$631$	35.3766	1.40832	0.704160	−	0.710042i	$-0.251324\pi$
$631$	35.3766	1.40832	0.704160	+	0.710042i	$0.251324\pi$
$632$	−44.7460	−1.77990
$633$	−0.716316	−0.0284710
$634$	49.0917	1.94968
$635$	3.90118	0.154813
$636$	3.45519	0.137007
$637$	−11.2889	−0.447282
$638$	38.1970	1.51223
$639$	5.35996	0.212037
$640$	−72.4391	−2.86341
$641$	9.86428	0.389616	0.194808	−	0.980841i	$-0.437592\pi$
$641$	9.86428	0.389616	0.194808	+	0.980841i	$0.437592\pi$
$642$	24.2760	0.958098
$643$	−7.36611	−0.290491	−0.145245	−	0.989396i	$-0.546397\pi$
$643$	−7.36611	−0.290491	−0.145245	+	0.989396i	$0.546397\pi$
$644$	18.3439	0.722851
$645$	−1.82416	−0.0718264
$646$	2.76449	0.108768
$647$	−11.4312	−0.449409	−0.224704	−	0.974427i	$-0.572142\pi$
$647$	−11.4312	−0.449409	−0.224704	+	0.974427i	$0.572142\pi$
$648$	−5.13317	−0.201650
$649$	6.02409	0.236466
$650$	58.7056	2.30262
$651$	−30.7774	−1.20626
$652$	−57.7056	−2.25993
$653$	27.2386	1.06593	0.532964	−	0.846138i	$-0.321078\pi$
$653$	27.2386	1.06593	0.532964	+	0.846138i	$0.321078\pi$
$654$	47.8524	1.87118
$655$	−2.11899	−0.0827957
$656$	6.53852	0.255286
$657$	−2.79293	−0.108963
$658$	−26.7734	−1.04374
$659$	47.3694	1.84525	0.922625	−	0.385698i	$-0.126039\pi$
$659$	47.3694	1.84525	0.922625	+	0.385698i	$0.126039\pi$
$660$	26.3050	1.02392
$661$	47.1144	1.83254	0.916268	−	0.400566i	$-0.131186\pi$
$661$	47.1144	1.83254	0.916268	+	0.400566i	$0.131186\pi$
$662$	−42.1556	−1.63842
$663$	11.0981	0.431015
$664$	31.8112	1.23451
$665$	3.22029	0.124877
$666$	−13.7269	−0.531907
$667$	−12.1770	−0.471494
$668$	−34.7947	−1.34625
$669$	25.2345	0.975623
$670$	40.3836	1.56015
$671$	13.7962	0.532598
$672$	2.80065	0.108037
$673$	49.9342	1.92482	0.962411	−	0.271598i	$-0.0875523\pi$
$673$	49.9342	1.92482	0.962411	+	0.271598i	$0.0875523\pi$
$674$	−85.8000	−3.30489
$675$	−9.80759	−0.377494
$676$	−29.0137	−1.11591
$677$	5.15175	0.197998	0.0989989	−	0.995088i	$-0.468436\pi$
$677$	5.15175	0.197998	0.0989989	+	0.995088i	$0.468436\pi$
$678$	−17.6718	−0.678680
$679$	−0.904515	−0.0347121
$680$	90.3163	3.46347
$681$	7.45447	0.285656
$682$	−37.2419	−1.42606
$683$	40.2331	1.53948	0.769738	−	0.638360i	$-0.220387\pi$
$683$	40.2331	1.53948	0.769738	+	0.638360i	$0.220387\pi$
$684$	−1.00068	−0.0382618
$685$	−28.1970	−1.07735
$686$	19.7734	0.754952
$687$	10.2872	0.392482
$688$	−2.13120	−0.0812511
$689$	2.05476	0.0782802
$690$	−12.4950	−0.475678
$691$	−10.1693	−0.386857	−0.193429	−	0.981114i	$-0.561961\pi$
$691$	−10.1693	−0.386857	−0.193429	+	0.981114i	$0.561961\pi$
$692$	−27.5802	−1.04844
$693$	5.71682	0.217164
$694$	−47.5233	−1.80396
$695$	21.5176	0.816210
$696$	−47.4717	−1.79941
$697$	6.64990	0.251883
$698$	67.0900	2.53939
$699$	−8.09007	−0.305995
$700$	136.636	5.16435
$701$	19.1219	0.722223	0.361112	−	0.932523i	$-0.382397\pi$
$701$	19.1219	0.722223	0.361112	+	0.932523i	$0.382397\pi$
$702$	−5.98573	−0.225917
$703$	−1.36470	−0.0514708
$704$	−11.6705	−0.439847
$705$	12.2394	0.460962
$706$	36.6833	1.38059
$707$	1.31394	0.0494157
$708$	−14.6804	−0.551725
$709$	50.5005	1.89659	0.948293	−	0.317395i	$-0.102808\pi$
$709$	50.5005	1.89659	0.948293	+	0.317395i	$0.102808\pi$
$710$	50.8639	1.90889
$711$	8.71703	0.326914
$712$	−0.470674	−0.0176392
$713$	11.8725	0.444627
$714$	38.4879	1.44037
$715$	15.6433	0.585025
$716$	0.112776	0.00421463
$717$	6.69491	0.250026
$718$	−11.7662	−0.439110
$719$	36.4573	1.35963	0.679813	−	0.733385i	$-0.262061\pi$
$719$	36.4573	1.35963	0.679813	+	0.733385i	$0.262061\pi$
$720$	−17.2999	−0.644730
$721$	−10.7786	−0.401414
$722$	46.7072	1.73826
$723$	−24.1937	−0.899772
$724$	9.47758	0.352232
$725$	−90.7008	−3.36854
$726$	−20.2092	−0.750035
$727$	52.9717	1.96461	0.982306	−	0.187282i	$-0.0599677\pi$
$727$	52.9717	1.96461	0.982306	+	0.187282i	$0.0599677\pi$
$728$	42.5283	1.57620
$729$	1.00000	0.0370370
$730$	−26.5038	−0.980951
$731$	−2.16750	−0.0801679
$732$	−33.6208	−1.24266
$733$	−36.9346	−1.36421	−0.682106	−	0.731253i	$-0.738936\pi$
$733$	−36.9346	−1.36421	−0.682106	+	0.731253i	$0.738936\pi$
$734$	50.4354	1.86161
$735$	17.8971	0.660144
$736$	−1.08036	−0.0398225
$737$	7.12739	0.262541
$738$	−3.58660	−0.132025
$739$	12.7462	0.468877	0.234439	−	0.972131i	$-0.424675\pi$
$739$	12.7462	0.468877	0.234439	+	0.972131i	$0.424675\pi$
$740$	−87.4240	−3.21377
$741$	−0.595091	−0.0218612
$742$	7.12585	0.261598
$743$	23.2580	0.853253	0.426627	−	0.904428i	$-0.359702\pi$
$743$	23.2580	0.853253	0.426627	+	0.904428i	$0.359702\pi$
$744$	46.2847	1.69688
$745$	18.6754	0.684216
$746$	43.5106	1.59303
$747$	−6.19718	−0.226743
$748$	31.2560	1.14283
$749$	33.6010	1.22775
$750$	−45.6221	−1.66588
$751$	−50.1858	−1.83130	−0.915652	−	0.401972i	$-0.868325\pi$
$751$	−50.1858	−1.83130	−0.915652	+	0.401972i	$0.868325\pi$
$752$	14.2995	0.521448
$753$	−19.4746	−0.709693
$754$	−55.3562	−2.01595
$755$	70.0565	2.54962
$756$	−13.9316	−0.506689
$757$	−6.10817	−0.222005	−0.111003	−	0.993820i	$-0.535406\pi$
$757$	−6.10817	−0.222005	−0.111003	+	0.993820i	$0.535406\pi$
$758$	38.1169	1.38447
$759$	−2.20528	−0.0800466
$760$	−4.84284	−0.175668
$761$	−22.4576	−0.814089	−0.407044	−	0.913408i	$-0.633441\pi$
$761$	−22.4576	−0.814089	−0.407044	+	0.913408i	$0.633441\pi$
$762$	−2.50011	−0.0905695
$763$	66.2335	2.39781
$764$	−72.8078	−2.63409
$765$	−17.5946	−0.636135
$766$	56.7939	2.05205
$767$	−8.73029	−0.315233
$768$	32.4872	1.17228
$769$	−13.6076	−0.490703	−0.245351	−	0.969434i	$-0.578903\pi$
$769$	−13.6076	−0.490703	−0.245351	+	0.969434i	$0.578903\pi$
$770$	54.2504	1.95505
$771$	2.36658	0.0852304
$772$	−45.6255	−1.64210
$773$	−18.8017	−0.676249	−0.338125	−	0.941101i	$-0.609793\pi$
$773$	−18.8017	−0.676249	−0.338125	+	0.941101i	$0.609793\pi$
$774$	1.16904	0.0420201
$775$	88.4329	3.17660
$776$	1.36026	0.0488304
$777$	−18.9997	−0.681611
$778$	−58.2283	−2.08758
$779$	−0.356574	−0.0127756
$780$	−38.1219	−1.36498
$781$	8.97709	0.321225
$782$	−14.8468	−0.530921
$783$	9.24802	0.330497
$784$	20.9094	0.746766
$785$	−51.9512	−1.85422
$786$	1.35798	0.0484374
$787$	15.0561	0.536693	0.268347	−	0.963322i	$-0.413523\pi$
$787$	15.0561	0.536693	0.268347	+	0.963322i	$0.413523\pi$
$788$	−48.9156	−1.74255
$789$	−21.5728	−0.768011
$790$	82.7212	2.94309
$791$	−24.4599	−0.869693
$792$	−8.59726	−0.305490
$793$	−19.9939	−0.710004
$794$	10.3256	0.366443
$795$	−3.25756	−0.115534
$796$	47.6303	1.68821
$797$	−50.4196	−1.78596	−0.892978	−	0.450101i	$-0.851388\pi$
$797$	−50.4196	−1.78596	−0.892978	+	0.450101i	$0.851388\pi$
$798$	−2.06376	−0.0730562
$799$	14.5431	0.514496
$800$	−8.04712	−0.284509
$801$	0.0916925	0.00323980
$802$	−35.0606	−1.23803
$803$	−4.67772	−0.165073
$804$	−17.3691	−0.612562
$805$	−17.2947	−0.609557
$806$	53.9720	1.90108
$807$	−17.7387	−0.624433
$808$	−1.97597	−0.0695144
$809$	32.0201	1.12577	0.562884	−	0.826536i	$-0.309692\pi$
$809$	32.0201	1.12577	0.562884	+	0.826536i	$0.309692\pi$
$810$	9.48961	0.333431
$811$	25.6365	0.900220	0.450110	−	0.892973i	$-0.351385\pi$
$811$	25.6365	0.900220	0.450110	+	0.892973i	$0.351385\pi$
$812$	−128.840	−4.52140
$813$	−22.2670	−0.780938
$814$	−22.9904	−0.805814
$815$	54.4050	1.90572
$816$	−20.5561	−0.719606
$817$	0.116223	0.00406614
$818$	−59.5425	−2.08186
$819$	−8.28498	−0.289501
$820$	−22.8424	−0.797690
$821$	46.5533	1.62472	0.812361	−	0.583155i	$-0.198182\pi$
$821$	46.5533	1.62472	0.812361	+	0.583155i	$0.198182\pi$
$822$	18.0703	0.630275
$823$	14.4565	0.503922	0.251961	−	0.967737i	$-0.418925\pi$
$823$	14.4565	0.503922	0.251961	+	0.967737i	$0.418925\pi$
$824$	16.2094	0.564680
$825$	−16.4262	−0.571886
$826$	−30.2764	−1.05345
$827$	6.33790	0.220390	0.110195	−	0.993910i	$-0.464852\pi$
$827$	6.33790	0.220390	0.110195	+	0.993910i	$0.464852\pi$
$828$	5.37417	0.186765
$829$	5.24853	0.182289	0.0911445	−	0.995838i	$-0.470947\pi$
$829$	5.24853	0.182289	0.0911445	+	0.995838i	$0.470947\pi$
$830$	−58.8088	−2.04128
$831$	16.0078	0.555304
$832$	16.9132	0.586359
$833$	21.2656	0.736810
$834$	−13.7898	−0.477502
$835$	32.8045	1.13525
$836$	−1.67598	−0.0579648
$837$	−9.01678	−0.311665
$838$	13.5210	0.467075
$839$	1.50001	0.0517860	0.0258930	−	0.999665i	$-0.491757\pi$
$839$	1.50001	0.0517860	0.0258930	+	0.999665i	$0.491757\pi$
$840$	−67.4231	−2.32632
$841$	56.5259	1.94917
$842$	10.6834	0.368174
$843$	−31.4669	−1.08378
$844$	2.92365	0.100636
$845$	27.3541	0.941011
$846$	−7.84375	−0.269674
$847$	−27.9720	−0.961131
$848$	−3.80585	−0.130694
$849$	21.7110	0.745121
$850$	−110.588	−3.79312
$851$	7.32920	0.251242
$852$	−21.8768	−0.749485
$853$	12.6947	0.434659	0.217330	−	0.976098i	$-0.430265\pi$
$853$	12.6947	0.434659	0.217330	+	0.976098i	$0.430265\pi$
$854$	−69.3382	−2.37271
$855$	0.943440	0.0322650
$856$	−50.5310	−1.72711
$857$	−52.0134	−1.77675	−0.888373	−	0.459123i	$-0.848164\pi$
$857$	−52.0134	−1.77675	−0.888373	+	0.459123i	$0.848164\pi$
$858$	−10.0252	−0.342253
$859$	−42.8753	−1.46289	−0.731443	−	0.681902i	$-0.761153\pi$
$859$	−42.8753	−1.46289	−0.731443	+	0.681902i	$0.761153\pi$
$860$	7.44535	0.253884
$861$	−4.96430	−0.169183
$862$	88.9036	3.02807
$863$	−3.22177	−0.109670	−0.0548351	−	0.998495i	$-0.517463\pi$
$863$	−3.22177	−0.109670	−0.0548351	+	0.998495i	$0.517463\pi$
$864$	0.820499	0.0279139
$865$	26.0027	0.884119
$866$	12.0222	0.408532
$867$	−3.90622	−0.132662
$868$	125.618	4.26377
$869$	14.5997	0.495260
$870$	87.7601	2.97535
$871$	−10.3292	−0.349992
$872$	−99.6055	−3.37307
$873$	−0.264994	−0.00896868
$874$	0.796100	0.0269285
$875$	−63.1466	−2.13475
$876$	11.3994	0.385150
$877$	−3.66460	−0.123745	−0.0618724	−	0.998084i	$-0.519707\pi$
$877$	−3.66460	−0.123745	−0.0618724	+	0.998084i	$0.519707\pi$
$878$	0.536173	0.0180950
$879$	−18.6266	−0.628260
$880$	−28.9747	−0.976736
$881$	48.1465	1.62210	0.811049	−	0.584979i	$-0.198897\pi$
$881$	48.1465	1.62210	0.811049	+	0.584979i	$0.198897\pi$
$882$	−11.4695	−0.386200
$883$	−15.1638	−0.510302	−0.255151	−	0.966901i	$-0.582125\pi$
$883$	−15.1638	−0.510302	−0.255151	+	0.966901i	$0.582125\pi$
$884$	−45.2971	−1.52351
$885$	13.8408	0.465252
$886$	4.88932	0.164260
$887$	30.8764	1.03673	0.518365	−	0.855160i	$-0.326541\pi$
$887$	30.8764	1.03673	0.518365	+	0.855160i	$0.326541\pi$
$888$	28.5728	0.958840
$889$	−3.46046	−0.116060
$890$	0.870126	0.0291667
$891$	1.67484	0.0561094
$892$	−102.995	−3.44853
$893$	−0.779812	−0.0260954
$894$	−11.9684	−0.400282
$895$	−0.106325	−0.00355406
$896$	64.2556	2.14663
$897$	3.19596	0.106710
$898$	−66.2798	−2.21179
$899$	−83.3874	−2.78112
$900$	40.0298	1.33433
$901$	−3.87069	−0.128951
$902$	−6.00700	−0.200011
$903$	1.61809	0.0538466
$904$	36.7841	1.22342
$905$	−8.93548	−0.297026
$906$	−44.8965	−1.49159
$907$	−32.1040	−1.06600	−0.532998	−	0.846117i	$-0.678935\pi$
$907$	−32.1040	−1.06600	−0.532998	+	0.846117i	$0.678935\pi$
$908$	−30.4255	−1.00971
$909$	0.384941	0.0127677
$910$	−78.6212	−2.60627
$911$	15.2883	0.506524	0.253262	−	0.967398i	$-0.418496\pi$
$911$	15.2883	0.506524	0.253262	+	0.967398i	$0.418496\pi$
$912$	1.10223	0.0364986
$913$	−10.3793	−0.343505
$914$	11.1797	0.369791
$915$	31.6978	1.04790
$916$	−41.9875	−1.38731
$917$	1.87961	0.0620700
$918$	11.2757	0.372154
$919$	−30.9673	−1.02152	−0.510759	−	0.859724i	$-0.670635\pi$
$919$	−30.9673	−1.02152	−0.510759	+	0.859724i	$0.670635\pi$
$920$	26.0087	0.857480
$921$	5.61066	0.184878
$922$	−9.95164	−0.327740
$923$	−13.0099	−0.428225
$924$	−23.3333	−0.767609
$925$	54.5920	1.79497
$926$	−71.2938	−2.34286
$927$	−3.15777	−0.103715
$928$	7.58799	0.249088
$929$	−14.6171	−0.479571	−0.239785	−	0.970826i	$-0.577077\pi$
$929$	−14.6171	−0.479571	−0.239785	+	0.970826i	$0.577077\pi$
$930$	−85.5657	−2.80581
$931$	−1.14028	−0.0373712
$932$	33.0198	1.08160
$933$	−14.4310	−0.472449
$934$	−1.17651	−0.0384966
$935$	−29.4682	−0.963714
$936$	12.4594	0.407248
$937$	−8.21288	−0.268303	−0.134152	−	0.990961i	$-0.542831\pi$
$937$	−8.21288	−0.268303	−0.134152	+	0.990961i	$0.542831\pi$
$938$	−35.8214	−1.16961
$939$	21.2379	0.693071
$940$	−49.9553	−1.62936
$941$	−26.1396	−0.852125	−0.426063	−	0.904694i	$-0.640100\pi$
$941$	−26.1396	−0.852125	−0.426063	+	0.904694i	$0.640100\pi$
$942$	33.2935	1.08476
$943$	1.91499	0.0623607
$944$	16.1704	0.526300
$945$	13.1348	0.427274
$946$	1.95795	0.0636585
$947$	−56.4303	−1.83374	−0.916870	−	0.399187i	$-0.869293\pi$
$947$	−56.4303	−1.83374	−0.916870	+	0.399187i	$0.869293\pi$
$948$	−35.5787	−1.15554
$949$	6.77909	0.220059
$950$	5.92980	0.192388
$951$	19.9068	0.645523
$952$	−80.1132	−2.59648
$953$	39.7878	1.28885	0.644426	−	0.764666i	$-0.277096\pi$
$953$	39.7878	1.28885	0.644426	+	0.764666i	$0.277096\pi$
$954$	2.08764	0.0675899
$955$	68.6434	2.22125
$956$	−27.3254	−0.883767
$957$	15.4890	0.500688
$958$	−63.4685	−2.05057
$959$	25.0116	0.807665
$960$	−26.8136	−0.865407
$961$	50.3023	1.62265
$962$	33.3184	1.07423
$963$	9.84400	0.317219
$964$	98.7469	3.18042
$965$	43.0158	1.38473
$966$	11.0835	0.356605
$967$	27.1857	0.874233	0.437116	−	0.899405i	$-0.356000\pi$
$967$	27.1857	0.874233	0.437116	+	0.899405i	$0.356000\pi$
$968$	42.0659	1.35205
$969$	1.12101	0.0360120
$970$	−2.51469	−0.0807417
$971$	−8.50943	−0.273081	−0.136540	−	0.990635i	$-0.543598\pi$
$971$	−8.50943	−0.273081	−0.136540	+	0.990635i	$0.543598\pi$
$972$	−4.08152	−0.130915
$973$	−19.0868	−0.611894
$974$	−83.8240	−2.68589
$975$	23.8053	0.762380
$976$	37.0330	1.18540
$977$	−21.2811	−0.680841	−0.340421	−	0.940273i	$-0.610569\pi$
$977$	−21.2811	−0.680841	−0.340421	+	0.940273i	$0.610569\pi$
$978$	−34.8660	−1.11489
$979$	0.153571	0.00490814
$980$	−73.0473	−2.33341
$981$	19.4043	0.619531
$982$	−3.78262	−0.120708
$983$	13.8475	0.441667	0.220834	−	0.975311i	$-0.429122\pi$
$983$	13.8475	0.441667	0.220834	+	0.975311i	$0.429122\pi$
$984$	7.46558	0.237994
$985$	46.1177	1.46943
$986$	104.278	3.32089
$987$	−10.8567	−0.345573
$988$	2.42887	0.0772727
$989$	−0.624182	−0.0198478
$990$	15.8936	0.505132
$991$	49.2018	1.56295	0.781473	−	0.623938i	$-0.214468\pi$
$991$	49.2018	1.56295	0.781473	+	0.623938i	$0.214468\pi$
$992$	−7.39826	−0.234895
$993$	−17.0942	−0.542469
$994$	−45.1178	−1.43105
$995$	−44.9059	−1.42361
$996$	25.2939	0.801468
$997$	−40.4672	−1.28161	−0.640805	−	0.767704i	$-0.721399\pi$
$997$	−40.4672	−1.28161	−0.640805	+	0.767704i	$0.721399\pi$
$998$	61.7965	1.95613
$999$	−5.56630	−0.176110

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6009.2.a.d.1.9	✓	93

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6009.2.a.d.1.9	✓	93	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 6009 = 3 \cdot 2003 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6009.a (trivial)

\(f(q)\)	\(=\)	\(q-2.46607 q^{2} -1.00000 q^{3} +4.08152 q^{4} -3.84806 q^{5} +2.46607 q^{6} +3.41335 q^{7} -5.13317 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-2.46607 q^{2} -1.00000 q^{3} +4.08152 q^{4} -3.84806 q^{5} +2.46607 q^{6} +3.41335 q^{7} -5.13317 q^{8} +1.00000 q^{9} +9.48961 q^{10} +1.67484 q^{11} -4.08152 q^{12} -2.42723 q^{13} -8.41756 q^{14} +3.84806 q^{15} +4.49575 q^{16} +4.57233 q^{17} -2.46607 q^{18} -0.245173 q^{19} -15.7059 q^{20} -3.41335 q^{21} -4.13029 q^{22} +1.31671 q^{23} +5.13317 q^{24} +9.80759 q^{25} +5.98573 q^{26} -1.00000 q^{27} +13.9316 q^{28} -9.24802 q^{29} -9.48961 q^{30} +9.01678 q^{31} -0.820499 q^{32} -1.67484 q^{33} -11.2757 q^{34} -13.1348 q^{35} +4.08152 q^{36} +5.56630 q^{37} +0.604614 q^{38} +2.42723 q^{39} +19.7528 q^{40} +1.45438 q^{41} +8.41756 q^{42} -0.474047 q^{43} +6.83590 q^{44} -3.84806 q^{45} -3.24710 q^{46} +3.18066 q^{47} -4.49575 q^{48} +4.65094 q^{49} -24.1862 q^{50} -4.57233 q^{51} -9.90679 q^{52} -0.846545 q^{53} +2.46607 q^{54} -6.44490 q^{55} -17.5213 q^{56} +0.245173 q^{57} +22.8063 q^{58} +3.59681 q^{59} +15.7059 q^{60} +8.23733 q^{61} -22.2360 q^{62} +3.41335 q^{63} -6.96809 q^{64} +9.34014 q^{65} +4.13029 q^{66} +4.25556 q^{67} +18.6621 q^{68} -1.31671 q^{69} +32.3913 q^{70} +5.35996 q^{71} -5.13317 q^{72} -2.79293 q^{73} -13.7269 q^{74} -9.80759 q^{75} -1.00068 q^{76} +5.71682 q^{77} -5.98573 q^{78} +8.71703 q^{79} -17.2999 q^{80} +1.00000 q^{81} -3.58660 q^{82} -6.19718 q^{83} -13.9316 q^{84} -17.5946 q^{85} +1.16904 q^{86} +9.24802 q^{87} -8.59726 q^{88} +0.0916925 q^{89} +9.48961 q^{90} -8.28498 q^{91} +5.37417 q^{92} -9.01678 q^{93} -7.84375 q^{94} +0.943440 q^{95} +0.820499 q^{96} -0.264994 q^{97} -11.4695 q^{98} +1.67484 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 93 q + 2 q^{2} - 93 q^{3} + 114 q^{4} - 20 q^{5} - 2 q^{6} + 28 q^{7} + 6 q^{8} + 93 q^{9}+O(q^{10}) \) 93 * q + 2 * q^2 - 93 * q^3 + 114 * q^4 - 20 * q^5 - 2 * q^6 + 28 * q^7 + 6 * q^8 + 93 * q^9	\( 93 q + 2 q^{2} - 93 q^{3} + 114 q^{4} - 20 q^{5} - 2 q^{6} + 28 q^{7} + 6 q^{8} + 93 q^{9} + 19 q^{10} + 10 q^{11} - 114 q^{12} + 20 q^{13} + 13 q^{14} + 20 q^{15} + 148 q^{16} - 43 q^{17} + 2 q^{18} + 50 q^{19} - 31 q^{20} - 28 q^{21} + 36 q^{22} + 21 q^{23} - 6 q^{24} + 137 q^{25} + 2 q^{26} - 93 q^{27} + 62 q^{28} - q^{29} - 19 q^{30} + 58 q^{31} + 19 q^{32} - 10 q^{33} + 30 q^{34} + 30 q^{35} + 114 q^{36} + 42 q^{37} - 6 q^{38} - 20 q^{39} + 53 q^{40} - 7 q^{41} - 13 q^{42} + 60 q^{43} + 25 q^{44} - 20 q^{45} + 57 q^{46} + 9 q^{47} - 148 q^{48} + 145 q^{49} + 41 q^{50} + 43 q^{51} + 71 q^{52} - 45 q^{53} - 2 q^{54} + 78 q^{55} + 44 q^{56} - 50 q^{57} + 40 q^{58} + 42 q^{59} + 31 q^{60} + 69 q^{61} - 42 q^{62} + 28 q^{63} + 230 q^{64} - 4 q^{65} - 36 q^{66} + 76 q^{67} - 91 q^{68} - 21 q^{69} + 57 q^{70} + 92 q^{71} + 6 q^{72} + 29 q^{73} + 59 q^{74} - 137 q^{75} + 131 q^{76} - 98 q^{77} - 2 q^{78} + 215 q^{79} - 37 q^{80} + 93 q^{81} + 50 q^{82} - 27 q^{83} - 62 q^{84} + 52 q^{85} + 82 q^{86} + q^{87} + 136 q^{88} - 14 q^{89} + 19 q^{90} + 101 q^{91} - 14 q^{92} - 58 q^{93} + 112 q^{94} + 59 q^{95} - 19 q^{96} + 38 q^{97} - 16 q^{98} + 10 q^{99}+O(q^{100}) \) 93 * q + 2 * q^2 - 93 * q^3 + 114 * q^4 - 20 * q^5 - 2 * q^6 + 28 * q^7 + 6 * q^8 + 93 * q^9 + 19 * q^10 + 10 * q^11 - 114 * q^12 + 20 * q^13 + 13 * q^14 + 20 * q^15 + 148 * q^16 - 43 * q^17 + 2 * q^18 + 50 * q^19 - 31 * q^20 - 28 * q^21 + 36 * q^22 + 21 * q^23 - 6 * q^24 + 137 * q^25 + 2 * q^26 - 93 * q^27 + 62 * q^28 - q^29 - 19 * q^30 + 58 * q^31 + 19 * q^32 - 10 * q^33 + 30 * q^34 + 30 * q^35 + 114 * q^36 + 42 * q^37 - 6 * q^38 - 20 * q^39 + 53 * q^40 - 7 * q^41 - 13 * q^42 + 60 * q^43 + 25 * q^44 - 20 * q^45 + 57 * q^46 + 9 * q^47 - 148 * q^48 + 145 * q^49 + 41 * q^50 + 43 * q^51 + 71 * q^52 - 45 * q^53 - 2 * q^54 + 78 * q^55 + 44 * q^56 - 50 * q^57 + 40 * q^58 + 42 * q^59 + 31 * q^60 + 69 * q^61 - 42 * q^62 + 28 * q^63 + 230 * q^64 - 4 * q^65 - 36 * q^66 + 76 * q^67 - 91 * q^68 - 21 * q^69 + 57 * q^70 + 92 * q^71 + 6 * q^72 + 29 * q^73 + 59 * q^74 - 137 * q^75 + 131 * q^76 - 98 * q^77 - 2 * q^78 + 215 * q^79 - 37 * q^80 + 93 * q^81 + 50 * q^82 - 27 * q^83 - 62 * q^84 + 52 * q^85 + 82 * q^86 + q^87 + 136 * q^88 - 14 * q^89 + 19 * q^90 + 101 * q^91 - 14 * q^92 - 58 * q^93 + 112 * q^94 + 59 * q^95 - 19 * q^96 + 38 * q^97 - 16 * q^98 + 10 * q^99

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