LMFDB - Embedded newform 147.6.a.o.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [147,6,Mod(1,147)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(147, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 6, names="a")

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

chi := DirichletCharacter("147.1");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 147 = 3 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	147.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:	$23.5764215125$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	$\mathbb{Q}[x]/(x^{6} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 2x^{5} - 59x^{4} + 122x^{3} + 941x^{2} - 1856x - 2338 $ x^6 - 2x^5 - 59x^4 + 122x^3 + 941x^2 - 1856*x - 2338
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{4}\cdot 7^{3} $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$4.27213$ of defining polynomial
Character	$\chi$	$=$	147.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-3.09163 q^{2} +9.00000 q^{3} -22.4418 q^{4} +13.7926 q^{5} -27.8246 q^{6} +168.314 q^{8} +81.0000 q^{9} +O(q^{10})$	\(q-3.09163 q^{2} +9.00000 q^{3} -22.4418 q^{4} +13.7926 q^{5} -27.8246 q^{6} +168.314 q^{8} +81.0000 q^{9} -42.6416 q^{10} -3.66659 q^{11} -201.977 q^{12} -780.229 q^{13} +124.133 q^{15} +197.776 q^{16} +50.0832 q^{17} -250.422 q^{18} +1063.38 q^{19} -309.532 q^{20} +11.3357 q^{22} +4102.45 q^{23} +1514.82 q^{24} -2934.76 q^{25} +2412.18 q^{26} +729.000 q^{27} -1487.11 q^{29} -383.774 q^{30} +5519.97 q^{31} -5997.49 q^{32} -32.9993 q^{33} -154.838 q^{34} -1817.79 q^{36} +6143.27 q^{37} -3287.59 q^{38} -7022.06 q^{39} +2321.49 q^{40} +10757.9 q^{41} +17696.7 q^{43} +82.2850 q^{44} +1117.20 q^{45} -12683.3 q^{46} +29468.5 q^{47} +1779.98 q^{48} +9073.19 q^{50} +450.749 q^{51} +17509.8 q^{52} -19255.9 q^{53} -2253.80 q^{54} -50.5718 q^{55} +9570.46 q^{57} +4597.58 q^{58} +6619.18 q^{59} -2785.78 q^{60} +36750.3 q^{61} -17065.7 q^{62} +12213.2 q^{64} -10761.4 q^{65} +102.021 q^{66} +46909.2 q^{67} -1123.96 q^{68} +36922.1 q^{69} -41693.7 q^{71} +13633.4 q^{72} +29451.1 q^{73} -18992.7 q^{74} -26412.9 q^{75} -23864.3 q^{76} +21709.6 q^{78} +22124.4 q^{79} +2727.84 q^{80} +6561.00 q^{81} -33259.5 q^{82} -3896.35 q^{83} +690.778 q^{85} -54711.6 q^{86} -13384.0 q^{87} -617.138 q^{88} +20530.8 q^{89} -3453.97 q^{90} -92066.6 q^{92} +49679.7 q^{93} -91105.4 q^{94} +14666.8 q^{95} -53977.4 q^{96} +17742.9 q^{97} -296.994 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 2 q^{2} + 54 q^{3} + 150 q^{4} + 100 q^{5} + 18 q^{6} - 114 q^{8} + 486 q^{9}+O(q^{10}) $ 6 * q + 2 * q^2 + 54 * q^3 + 150 * q^4 + 100 * q^5 + 18 * q^6 - 114 * q^8 + 486 * q^9	\( 6 q + 2 q^{2} + 54 q^{3} + 150 q^{4} + 100 q^{5} + 18 q^{6} - 114 q^{8} + 486 q^{9} + 864 q^{10} + 604 q^{11} + 1350 q^{12} + 1352 q^{13} + 900 q^{15} + 4578 q^{16} + 3028 q^{17} + 162 q^{18} + 1728 q^{19} + 452 q^{20} - 4116 q^{22} - 4484 q^{23} - 1026 q^{24} + 4806 q^{25} + 14172 q^{26} + 4374 q^{27} - 5320 q^{29} + 7776 q^{30} + 3976 q^{31} - 37326 q^{32} + 5436 q^{33} - 16336 q^{34} + 12150 q^{36} + 22680 q^{37} + 52744 q^{38} + 12168 q^{39} + 100600 q^{40} + 28756 q^{41} - 6768 q^{43} - 64940 q^{44} + 8100 q^{45} + 540 q^{46} + 51552 q^{47} + 41202 q^{48} - 40622 q^{50} + 27252 q^{51} + 119296 q^{52} + 80884 q^{53} + 1458 q^{54} + 11656 q^{55} + 15552 q^{57} - 70464 q^{58} + 8872 q^{59} + 4068 q^{60} + 50896 q^{61} + 11824 q^{62} + 199590 q^{64} + 3492 q^{65} - 37044 q^{66} + 6480 q^{67} + 37348 q^{68} - 40356 q^{69} - 110852 q^{71} - 9234 q^{72} + 64232 q^{73} - 27464 q^{74} + 43254 q^{75} - 194864 q^{76} + 127548 q^{78} + 111696 q^{79} - 308940 q^{80} + 39366 q^{81} - 189640 q^{82} + 101128 q^{83} - 23292 q^{85} + 3824 q^{86} - 47880 q^{87} - 97788 q^{88} - 35012 q^{89} + 69984 q^{90} - 449260 q^{92} + 35784 q^{93} - 121016 q^{94} - 119080 q^{95} - 335934 q^{96} + 70952 q^{97} + 48924 q^{99}+O(q^{100}) \) 6 * q + 2 * q^2 + 54 * q^3 + 150 * q^4 + 100 * q^5 + 18 * q^6 - 114 * q^8 + 486 * q^9 + 864 * q^10 + 604 * q^11 + 1350 * q^12 + 1352 * q^13 + 900 * q^15 + 4578 * q^16 + 3028 * q^17 + 162 * q^18 + 1728 * q^19 + 452 * q^20 - 4116 * q^22 - 4484 * q^23 - 1026 * q^24 + 4806 * q^25 + 14172 * q^26 + 4374 * q^27 - 5320 * q^29 + 7776 * q^30 + 3976 * q^31 - 37326 * q^32 + 5436 * q^33 - 16336 * q^34 + 12150 * q^36 + 22680 * q^37 + 52744 * q^38 + 12168 * q^39 + 100600 * q^40 + 28756 * q^41 - 6768 * q^43 - 64940 * q^44 + 8100 * q^45 + 540 * q^46 + 51552 * q^47 + 41202 * q^48 - 40622 * q^50 + 27252 * q^51 + 119296 * q^52 + 80884 * q^53 + 1458 * q^54 + 11656 * q^55 + 15552 * q^57 - 70464 * q^58 + 8872 * q^59 + 4068 * q^60 + 50896 * q^61 + 11824 * q^62 + 199590 * q^64 + 3492 * q^65 - 37044 * q^66 + 6480 * q^67 + 37348 * q^68 - 40356 * q^69 - 110852 * q^71 - 9234 * q^72 + 64232 * q^73 - 27464 * q^74 + 43254 * q^75 - 194864 * q^76 + 127548 * q^78 + 111696 * q^79 - 308940 * q^80 + 39366 * q^81 - 189640 * q^82 + 101128 * q^83 - 23292 * q^85 + 3824 * q^86 - 47880 * q^87 - 97788 * q^88 - 35012 * q^89 + 69984 * q^90 - 449260 * q^92 + 35784 * q^93 - 121016 * q^94 - 119080 * q^95 - 335934 * q^96 + 70952 * q^97 + 48924 * 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 $

$2$	−3.09163	−0.546527	−0.273264	−	0.961939i	$-0.588103\pi$
$2$	−3.09163	−0.546527	−0.273264	+	0.961939i	$0.588103\pi$
$3$	9.00000	0.577350
$3$	9.00000	0.577350
$4$	−22.4418	−0.701308
$5$	13.7926	0.246730	0.123365	−	0.992361i	$-0.460631\pi$
$5$	13.7926	0.246730	0.123365	+	0.992361i	$0.460631\pi$
$6$	−27.8246	−0.315538
$7$	0	0
$7$	0	0
$8$	168.314	0.929811
$9$	81.0000	0.333333
$10$	−42.6416	−0.134845
$11$	−3.66659	−0.00913651	−0.00456826	−	0.999990i	$-0.501454\pi$
$11$	−3.66659	−0.00913651	−0.00456826	+	0.999990i	$0.501454\pi$
$12$	−201.977	−0.404900
$13$	−780.229	−1.28045	−0.640226	−	0.768186i	$-0.721159\pi$
$13$	−780.229	−1.28045	−0.640226	+	0.768186i	$0.721159\pi$
$14$	0	0
$15$	124.133	0.142449
$16$	197.776	0.193140
$17$	50.0832	0.0420310	0.0210155	−	0.999779i	$-0.493310\pi$
$17$	50.0832	0.0420310	0.0210155	+	0.999779i	$0.493310\pi$
$18$	−250.422	−0.182176
$19$	1063.38	0.675781	0.337891	−	0.941185i	$-0.390287\pi$
$19$	1063.38	0.675781	0.337891	+	0.941185i	$0.390287\pi$
$20$	−309.532	−0.173033
$21$	0	0
$22$	11.3357	0.00499336
$23$	4102.45	1.61705	0.808526	−	0.588460i	$-0.200266\pi$
$23$	4102.45	1.61705	0.808526	+	0.588460i	$0.200266\pi$
$24$	1514.82	0.536827
$25$	−2934.76	−0.939124
$26$	2412.18	0.699803
$27$	729.000	0.192450
$28$	0	0
$29$	−1487.11	−0.328358	−0.164179	−	0.986431i	$-0.552497\pi$
$29$	−1487.11	−0.328358	−0.164179	+	0.986431i	$0.552497\pi$
$30$	−383.774	−0.0778525
$31$	5519.97	1.03165	0.515825	−	0.856694i	$-0.327485\pi$
$31$	5519.97	1.03165	0.515825	+	0.856694i	$0.327485\pi$
$32$	−5997.49	−1.03537
$33$	−32.9993	−0.00527497
$34$	−154.838	−0.0229711
$35$	0	0
$36$	−1817.79	−0.233769
$37$	6143.27	0.737726	0.368863	−	0.929484i	$-0.379747\pi$
$37$	6143.27	0.737726	0.368863	+	0.929484i	$0.379747\pi$
$38$	−3287.59	−0.369333
$39$	−7022.06	−0.739270
$40$	2321.49	0.229412
$41$	10757.9	0.999468	0.499734	−	0.866179i	$-0.333431\pi$
$41$	10757.9	0.999468	0.499734	+	0.866179i	$0.333431\pi$
$42$	0	0
$43$	17696.7	1.45956	0.729779	−	0.683683i	$-0.239623\pi$
$43$	17696.7	1.45956	0.729779	+	0.683683i	$0.239623\pi$
$44$	82.2850	0.00640751
$45$	1117.20	0.0822432
$46$	−12683.3	−0.883763
$47$	29468.5	1.94587	0.972933	−	0.231089i	$-0.0742289\pi$
$47$	29468.5	1.94587	0.972933	+	0.231089i	$0.0742289\pi$
$48$	1779.98	0.111510
$49$	0	0
$50$	9073.19	0.513257
$51$	450.749	0.0242666
$52$	17509.8	0.897991
$53$	−19255.9	−0.941616	−0.470808	−	0.882236i	$-0.656038\pi$
$53$	−19255.9	−0.941616	−0.470808	+	0.882236i	$0.656038\pi$
$54$	−2253.80	−0.105179
$55$	−50.5718	−0.00225425
$56$	0	0
$57$	9570.46	0.390163
$58$	4597.58	0.179457
$59$	6619.18	0.247557	0.123778	−	0.992310i	$-0.460499\pi$
$59$	6619.18	0.247557	0.123778	+	0.992310i	$0.460499\pi$
$60$	−2785.78	−0.0999009
$61$	36750.3	1.26455	0.632275	−	0.774744i	$-0.282121\pi$
$61$	36750.3	1.26455	0.632275	+	0.774744i	$0.282121\pi$
$62$	−17065.7	−0.563825
$63$	0	0
$64$	12213.2	0.372717
$65$	−10761.4	−0.315926
$66$	102.021	0.00288292
$67$	46909.2	1.27665	0.638323	−	0.769768i	$-0.279628\pi$
$67$	46909.2	1.27665	0.638323	+	0.769768i	$0.279628\pi$
$68$	−1123.96	−0.0294767
$69$	36922.1	0.933606
$70$	0	0
$71$	−41693.7	−0.981577	−0.490789	−	0.871279i	$-0.663291\pi$
$71$	−41693.7	−0.981577	−0.490789	+	0.871279i	$0.663291\pi$
$72$	13633.4	0.309937
$73$	29451.1	0.646837	0.323418	−	0.946256i	$-0.395168\pi$
$73$	29451.1	0.646837	0.323418	+	0.946256i	$0.395168\pi$
$74$	−18992.7	−0.403188
$75$	−26412.9	−0.542204
$76$	−23864.3	−0.473931
$77$	0	0
$78$	21709.6	0.404031
$79$	22124.4	0.398844	0.199422	−	0.979914i	$-0.436094\pi$
$79$	22124.4	0.398844	0.199422	+	0.979914i	$0.436094\pi$
$80$	2727.84	0.0476535
$81$	6561.00	0.111111
$82$	−33259.5	−0.546237
$83$	−3896.35	−0.0620816	−0.0310408	−	0.999518i	$-0.509882\pi$
$83$	−3896.35	−0.0620816	−0.0310408	+	0.999518i	$0.509882\pi$
$84$	0	0
$85$	690.778	0.0103703
$86$	−54711.6	−0.797689
$87$	−13384.0	−0.189577
$88$	−617.138	−0.00849523
$89$	20530.8	0.274746	0.137373	−	0.990519i	$-0.456134\pi$
$89$	20530.8	0.274746	0.137373	+	0.990519i	$0.456134\pi$
$90$	−3453.97	−0.0449482
$91$	0	0
$92$	−92066.6	−1.13405
$93$	49679.7	0.595624
$94$	−91105.4	−1.06347
$95$	14666.8	0.166735
$96$	−53977.4	−0.597770
$97$	17742.9	0.191468	0.0957338	−	0.995407i	$-0.469480\pi$
$97$	17742.9	0.191468	0.0957338	+	0.995407i	$0.469480\pi$
$98$	0	0
$99$	−296.994	−0.00304550
$100$	65861.5	0.658615
$101$	−142085.	−1.38594	−0.692971	−	0.720965i	$-0.743699\pi$
$101$	−142085.	−1.38594	−0.692971	+	0.720965i	$0.743699\pi$
$102$	−1393.55	−0.0132624
$103$	−210538.	−1.95540	−0.977702	−	0.209996i	$-0.932655\pi$
$103$	−210538.	−1.95540	−0.977702	+	0.209996i	$0.932655\pi$
$104$	−131323.	−1.19058
$105$	0	0
$106$	59532.0	0.514619
$107$	−202671.	−1.71132	−0.855660	−	0.517538i	$-0.826849\pi$
$107$	−202671.	−1.71132	−0.855660	+	0.517538i	$0.826849\pi$
$108$	−16360.1	−0.134967
$109$	139538.	1.12493	0.562466	−	0.826821i	$-0.309853\pi$
$109$	139538.	1.12493	0.562466	+	0.826821i	$0.309853\pi$
$110$	156.349	0.00123201
$111$	55289.4	0.425926
$112$	0	0
$113$	−206316.	−1.51998	−0.759989	−	0.649936i	$-0.774796\pi$
$113$	−206316.	−1.51998	−0.759989	+	0.649936i	$0.774796\pi$
$114$	−29588.3	−0.213235
$115$	56583.5	0.398975
$116$	33373.4	0.230280
$117$	−63198.5	−0.426818
$118$	−20464.0	−0.135296
$119$	0	0
$120$	20893.4	0.132451
$121$	−161038.	−0.999917
$122$	−113618.	−0.691111
$123$	96821.4	0.577043
$124$	−123878.	−0.723504
$125$	−83580.0	−0.478440
$126$	0	0
$127$	89874.2	0.494454	0.247227	−	0.968958i	$-0.420481\pi$
$127$	89874.2	0.494454	0.247227	+	0.968958i	$0.420481\pi$
$128$	154161.	0.831668
$129$	159270.	0.842676
$130$	33270.2	0.172662
$131$	320115.	1.62978	0.814889	−	0.579617i	$-0.196798\pi$
$131$	320115.	1.62978	0.814889	+	0.579617i	$0.196798\pi$
$132$	740.565	0.00369938
$133$	0	0
$134$	−145026.	−0.697722
$135$	10054.8	0.0474832
$136$	8429.69	0.0390809
$137$	258971.	1.17883	0.589414	−	0.807831i	$-0.299359\pi$
$137$	258971.	1.17883	0.589414	+	0.807831i	$0.299359\pi$
$138$	−114149.	−0.510241
$139$	282366.	1.23958	0.619791	−	0.784767i	$-0.287217\pi$
$139$	282366.	1.23958	0.619791	+	0.784767i	$0.287217\pi$
$140$	0	0
$141$	265216.	1.12345
$142$	128901.	0.536459
$143$	2860.78	0.0116989
$144$	16019.8	0.0643801
$145$	−20511.1	−0.0810156
$146$	−91051.9	−0.353514
$147$	0	0
$148$	−137866.	−0.517373
$149$	−319669.	−1.17960	−0.589800	−	0.807549i	$-0.700793\pi$
$149$	−319669.	−1.17960	−0.589800	+	0.807549i	$0.700793\pi$
$150$	81658.7	0.296329
$151$	−84046.3	−0.299969	−0.149985	−	0.988688i	$-0.547922\pi$
$151$	−84046.3	−0.299969	−0.149985	+	0.988688i	$0.547922\pi$
$152$	178982.	0.628349
$153$	4056.74	0.0140103
$154$	0	0
$155$	76134.8	0.254539
$156$	157588.	0.518456
$157$	126195.	0.408596	0.204298	−	0.978909i	$-0.434509\pi$
$157$	126195.	0.408596	0.204298	+	0.978909i	$0.434509\pi$
$158$	−68400.2	−0.217979
$159$	−173303.	−0.543642
$160$	−82721.1	−0.255456
$161$	0	0
$162$	−20284.2	−0.0607253
$163$	−235790.	−0.695114	−0.347557	−	0.937659i	$-0.612989\pi$
$163$	−235790.	−0.695114	−0.347557	+	0.937659i	$0.612989\pi$
$164$	−241428.	−0.700935
$165$	−455.146	−0.00130149
$166$	12046.1	0.0339293
$167$	149843.	0.415761	0.207881	−	0.978154i	$-0.433343\pi$
$167$	149843.	0.415761	0.207881	+	0.978154i	$0.433343\pi$
$168$	0	0
$169$	237464.	0.639559
$170$	−2135.63	−0.00566765
$171$	86134.1	0.225260
$172$	−397147.	−1.02360
$173$	704460.	1.78954	0.894769	−	0.446530i	$-0.147340\pi$
$173$	704460.	1.78954	0.894769	+	0.446530i	$0.147340\pi$
$174$	41378.2	0.103609
$175$	0	0
$176$	−725.162	−0.00176463
$177$	59572.7	0.142927
$178$	−63473.6	−0.150156
$179$	−557573.	−1.30067	−0.650337	−	0.759645i	$-0.725373\pi$
$179$	−557573.	−1.30067	−0.650337	+	0.759645i	$0.725373\pi$
$180$	−25072.1	−0.0576778
$181$	443092.	1.00530	0.502652	−	0.864489i	$-0.332358\pi$
$181$	443092.	1.00530	0.502652	+	0.864489i	$0.332358\pi$
$182$	0	0
$183$	330752.	0.730088
$184$	690500.	1.50355
$185$	84731.7	0.182019
$186$	−153591.	−0.325525
$187$	−183.634	−0.000384017 0
$188$	−661327.	−1.36465
$189$	0	0
$190$	−45344.4	−0.0911254
$191$	157481.	0.312353	0.156177	−	0.987729i	$-0.450083\pi$
$191$	157481.	0.312353	0.156177	+	0.987729i	$0.450083\pi$
$192$	109919.	0.215188
$193$	−778040.	−1.50352	−0.751759	−	0.659437i	$-0.770795\pi$
$193$	−778040.	−1.50352	−0.751759	+	0.659437i	$0.770795\pi$
$194$	−54854.4	−0.104642
$195$	−96852.5	−0.182400
$196$	0	0
$197$	−340283.	−0.624704	−0.312352	−	0.949966i	$-0.601117\pi$
$197$	−340283.	−0.624704	−0.312352	+	0.949966i	$0.601117\pi$
$198$	918.193	0.00166445
$199$	296509.	0.530768	0.265384	−	0.964143i	$-0.414501\pi$
$199$	296509.	0.530768	0.265384	+	0.964143i	$0.414501\pi$
$200$	−493961.	−0.873209
$201$	422182.	0.737072
$202$	439274.	0.757456
$203$	0	0
$204$	−10115.6	−0.0170184
$205$	148380.	0.246599
$206$	650904.	1.06868
$207$	332299.	0.539017
$208$	−154310.	−0.247307
$209$	−3898.99	−0.00617429
$210$	0	0
$211$	506728.	0.783554	0.391777	−	0.920060i	$-0.371860\pi$
$211$	506728.	0.783554	0.391777	+	0.920060i	$0.371860\pi$
$212$	432138.	0.660363
$213$	−375243.	−0.566714
$214$	626582.	0.935283
$215$	244084.	0.360116
$216$	122701.	0.178942
$217$	0	0
$218$	−431399.	−0.614806
$219$	265060.	0.373451
$220$	1134.93	0.00158092
$221$	−39076.3	−0.0538187
$222$	−170934.	−0.232780
$223$	−462362.	−0.622615	−0.311308	−	0.950309i	$-0.600767\pi$
$223$	−462362.	−0.622615	−0.311308	+	0.950309i	$0.600767\pi$
$224$	0	0
$225$	−237716.	−0.313041
$226$	637852.	0.830709
$227$	−98226.6	−0.126521	−0.0632607	−	0.997997i	$-0.520150\pi$
$227$	−98226.6	−0.126521	−0.0632607	+	0.997997i	$0.520150\pi$
$228$	−214779.	−0.273624
$229$	501403.	0.631827	0.315914	−	0.948788i	$-0.397689\pi$
$229$	501403.	0.631827	0.315914	+	0.948788i	$0.397689\pi$
$230$	−174935.	−0.218051
$231$	0	0
$232$	−250301.	−0.305311
$233$	−613916.	−0.740831	−0.370415	−	0.928866i	$-0.620785\pi$
$233$	−613916.	−0.740831	−0.370415	+	0.928866i	$0.620785\pi$
$234$	195386.	0.233268
$235$	406447.	0.480103
$236$	−148547.	−0.173613
$237$	199119.	0.230273
$238$	0	0
$239$	1.10020e6	1.24588	0.622940	−	0.782269i	$-0.285938\pi$
$239$	1.10020e6	1.24588	0.622940	+	0.782269i	$0.285938\pi$
$240$	24550.6	0.0275127
$241$	89883.5	0.0996868	0.0498434	−	0.998757i	$-0.484128\pi$
$241$	89883.5	0.0996868	0.0498434	+	0.998757i	$0.484128\pi$
$242$	497868.	0.546482
$243$	59049.0	0.0641500
$244$	−824744.	−0.886839
$245$	0	0
$246$	−299335.	−0.315370
$247$	−829683.	−0.865306
$248$	929087.	0.959240
$249$	−35067.2	−0.0358429
$250$	258398.	0.261480
$251$	1.01050e6	1.01240	0.506202	−	0.862415i	$-0.331049\pi$
$251$	1.01050e6	1.01240	0.506202	+	0.862415i	$0.331049\pi$
$252$	0	0
$253$	−15042.0	−0.0147742
$254$	−277858.	−0.270233
$255$	6217.00	0.00598729
$256$	−867430.	−0.827246
$257$	−1.21233e6	−1.14495	−0.572475	−	0.819922i	$-0.694017\pi$
$257$	−1.21233e6	−1.14495	−0.572475	+	0.819922i	$0.694017\pi$
$258$	−492405.	−0.460546
$259$	0	0
$260$	241505.	0.221561
$261$	−120456.	−0.109453
$262$	−989677.	−0.890718
$263$	384901.	0.343131	0.171566	−	0.985173i	$-0.445117\pi$
$263$	384901.	0.343131	0.171566	+	0.985173i	$0.445117\pi$
$264$	−5554.24	−0.00490473
$265$	−265589.	−0.232325
$266$	0	0
$267$	184777.	0.158625
$268$	−1.05273e6	−0.895322
$269$	−1.57455e6	−1.32671	−0.663355	−	0.748305i	$-0.730868\pi$
$269$	−1.57455e6	−1.32671	−0.663355	+	0.748305i	$0.730868\pi$
$270$	−31085.7	−0.0259508
$271$	332270.	0.274832	0.137416	−	0.990513i	$-0.456120\pi$
$271$	332270.	0.274832	0.137416	+	0.990513i	$0.456120\pi$
$272$	9905.24	0.00811788
$273$	0	0
$274$	−800643.	−0.644262
$275$	10760.6	0.00858032
$276$	−828600.	−0.654745
$277$	2.23543e6	1.75050	0.875251	−	0.483669i	$-0.160696\pi$
$277$	2.23543e6	1.75050	0.875251	+	0.483669i	$0.160696\pi$
$278$	−872970.	−0.677465
$279$	447118.	0.343883
$280$	0	0
$281$	69723.6	0.0526761	0.0263381	−	0.999653i	$-0.491615\pi$
$281$	69723.6	0.0526761	0.0263381	+	0.999653i	$0.491615\pi$
$282$	−819949.	−0.613994
$283$	−476452.	−0.353633	−0.176817	−	0.984244i	$-0.556580\pi$
$283$	−476452.	−0.353633	−0.176817	+	0.984244i	$0.556580\pi$
$284$	935684.	0.688388
$285$	132002.	0.0962647
$286$	−8844.46	−0.00639376
$287$	0	0
$288$	−485797.	−0.345123
$289$	−1.41735e6	−0.998233
$290$	63412.6	0.0442773
$291$	159686.	0.110544
$292$	−660938.	−0.453632
$293$	2.27589e6	1.54875	0.774377	−	0.632724i	$-0.218063\pi$
$293$	2.27589e6	1.54875	0.774377	+	0.632724i	$0.218063\pi$
$294$	0	0
$295$	91295.8	0.0610796
$296$	1.03400e6	0.685946
$297$	−2672.94	−0.00175832
$298$	988297.	0.644684
$299$	−3.20085e6	−2.07056
$300$	592754.	0.380252
$301$	0	0
$302$	259840.	0.163941
$303$	−1.27877e6	−0.800174
$304$	210312.	0.130521
$305$	506882.	0.312002
$306$	−12541.9	−0.00765703
$307$	−1.61790e6	−0.979731	−0.489866	−	0.871798i	$-0.662954\pi$
$307$	−1.61790e6	−0.979731	−0.489866	+	0.871798i	$0.662954\pi$
$308$	0	0
$309$	−1.89484e6	−1.12895
$310$	−235380.	−0.139112
$311$	−1.02667e6	−0.601910	−0.300955	−	0.953638i	$-0.597305\pi$
$311$	−1.02667e6	−0.601910	−0.300955	+	0.953638i	$0.597305\pi$
$312$	−1.18191e6	−0.687381
$313$	317214.	0.183017	0.0915085	−	0.995804i	$-0.470831\pi$
$313$	317214.	0.183017	0.0915085	+	0.995804i	$0.470831\pi$
$314$	−390149.	−0.223309
$315$	0	0
$316$	−496512.	−0.279712
$317$	1.57126e6	0.878212	0.439106	−	0.898435i	$-0.355295\pi$
$317$	1.57126e6	0.878212	0.439106	+	0.898435i	$0.355295\pi$
$318$	535788.	0.297116
$319$	5452.61	0.00300005
$320$	168452.	0.0919602
$321$	−1.82404e6	−0.988031
$322$	0	0
$323$	53257.7	0.0284038
$324$	−147241.	−0.0779231
$325$	2.28979e6	1.20250
$326$	728974.	0.379899
$327$	1.25584e6	0.649479
$328$	1.81071e6	0.929317
$329$	0	0
$330$	1407.14	0.000711301 0
$331$	1.53832e6	0.771751	0.385875	−	0.922551i	$-0.373899\pi$
$331$	1.53832e6	0.771751	0.385875	+	0.922551i	$0.373899\pi$
$332$	87441.4	0.0435383
$333$	497605.	0.245909
$334$	−463257.	−0.227225
$335$	647000.	0.314987
$336$	0	0
$337$	−2.86811e6	−1.37569	−0.687846	−	0.725857i	$-0.741444\pi$
$337$	−2.86811e6	−1.37569	−0.687846	+	0.725857i	$0.741444\pi$
$338$	−734149.	−0.349537
$339$	−1.85685e6	−0.877559
$340$	−15502.3	−0.00727277
$341$	−20239.5	−0.00942569
$342$	−266295.	−0.123111
$343$	0	0
$344$	2.97860e6	1.35711
$345$	509252.	0.230348
$346$	−2.17793e6	−0.978031
$347$	−111966.	−0.0499185	−0.0249593	−	0.999688i	$-0.507946\pi$
$347$	−111966.	−0.0499185	−0.0249593	+	0.999688i	$0.507946\pi$
$348$	300361.	0.132952
$349$	−3.75314e6	−1.64942	−0.824711	−	0.565555i	$-0.808662\pi$
$349$	−3.75314e6	−1.64942	−0.824711	+	0.565555i	$0.808662\pi$
$350$	0	0
$351$	−568787.	−0.246423
$352$	21990.3	0.00945965
$353$	3.22923e6	1.37931	0.689655	−	0.724138i	$-0.257762\pi$
$353$	3.22923e6	1.37931	0.689655	+	0.724138i	$0.257762\pi$
$354$	−184176.	−0.0781134
$355$	−575065.	−0.242184
$356$	−460749.	−0.192681
$357$	0	0
$358$	1.72381e6	0.710855
$359$	1.83659e6	0.752100	0.376050	−	0.926599i	$-0.377282\pi$
$359$	1.83659e6	0.752100	0.376050	+	0.926599i	$0.377282\pi$
$360$	188040.	0.0764707
$361$	−1.34531e6	−0.543319
$362$	−1.36988e6	−0.549427
$363$	−1.44934e6	−0.577302
$364$	0	0
$365$	406208.	0.159594
$366$	−1.02256e6	−0.399013
$367$	−339025.	−0.131391	−0.0656957	−	0.997840i	$-0.520927\pi$
$367$	−339025.	−0.131391	−0.0656957	+	0.997840i	$0.520927\pi$
$368$	811366.	0.312318
$369$	871392.	0.333156
$370$	−261959.	−0.0994784
$371$	0	0
$372$	−1.11490e6	−0.417715
$373$	−706622.	−0.262975	−0.131488	−	0.991318i	$-0.541975\pi$
$373$	−706622.	−0.262975	−0.131488	+	0.991318i	$0.541975\pi$
$374$	567.729	0.000209876 0
$375$	−752220.	−0.276227
$376$	4.95995e6	1.80929
$377$	1.16028e6	0.420447
$378$	0	0
$379$	648296.	0.231833	0.115917	−	0.993259i	$-0.463019\pi$
$379$	648296.	0.231833	0.115917	+	0.993259i	$0.463019\pi$
$380$	−329151.	−0.116933
$381$	808868.	0.285473
$382$	−486873.	−0.170709
$383$	−3.07022e6	−1.06948	−0.534741	−	0.845016i	$-0.679591\pi$
$383$	−3.07022e6	−1.06948	−0.534741	+	0.845016i	$0.679591\pi$
$384$	1.38745e6	0.480164
$385$	0	0
$386$	2.40541e6	0.821714
$387$	1.43343e6	0.486519
$388$	−398183.	−0.134278
$389$	−4.59998e6	−1.54128	−0.770641	−	0.637270i	$-0.780064\pi$
$389$	−4.59998e6	−1.54128	−0.770641	+	0.637270i	$0.780064\pi$
$390$	299432.	0.0996865
$391$	205464.	0.0679663
$392$	0	0
$393$	2.88104e6	0.940953
$394$	1.05203e6	0.341418
$395$	305153.	0.0984066
$396$	6665.09	0.00213584
$397$	2.64159e6	0.841181	0.420590	−	0.907251i	$-0.361823\pi$
$397$	2.64159e6	0.841181	0.420590	+	0.907251i	$0.361823\pi$
$398$	−916694.	−0.290079
$399$	0	0
$400$	−580425.	−0.181383
$401$	4.89677e6	1.52072	0.760359	−	0.649503i	$-0.225023\pi$
$401$	4.89677e6	1.52072	0.760359	+	0.649503i	$0.225023\pi$
$402$	−1.30523e6	−0.402830
$403$	−4.30684e6	−1.32098
$404$	3.18865e6	0.971972
$405$	90493.3	0.0274144
$406$	0	0
$407$	−22524.8	−0.00674025
$408$	75867.2	0.0225634
$409$	96336.3	0.0284762	0.0142381	−	0.999899i	$-0.495468\pi$
$409$	96336.3	0.0284762	0.0142381	+	0.999899i	$0.495468\pi$
$410$	−458735.	−0.134773
$411$	2.33074e6	0.680597
$412$	4.72485e6	1.37134
$413$	0	0
$414$	−1.02734e6	−0.294588
$415$	−53740.9	−0.0153174
$416$	4.67941e6	1.32574
$417$	2.54129e6	0.715673
$418$	12054.2	0.00337442
$419$	1.09657e6	0.305142	0.152571	−	0.988292i	$-0.451245\pi$
$419$	1.09657e6	0.305142	0.152571	+	0.988292i	$0.451245\pi$
$420$	0	0
$421$	−1.93660e6	−0.532517	−0.266259	−	0.963902i	$-0.585788\pi$
$421$	−1.93660e6	−0.532517	−0.266259	+	0.963902i	$0.585788\pi$
$422$	−1.56661e6	−0.428234
$423$	2.38695e6	0.648622
$424$	−3.24103e6	−0.875526
$425$	−146982.	−0.0394723
$426$	1.16011e6	0.309725
$427$	0	0
$428$	4.54830e6	1.20016
$429$	25747.0	0.00675435
$430$	−754616.	−0.196813
$431$	−3.07330e6	−0.796914	−0.398457	−	0.917187i	$-0.630454\pi$
$431$	−3.07330e6	−0.796914	−0.398457	+	0.917187i	$0.630454\pi$
$432$	144179.	0.0371699
$433$	3.80919e6	0.976366	0.488183	−	0.872741i	$-0.337660\pi$
$433$	3.80919e6	0.976366	0.488183	+	0.872741i	$0.337660\pi$
$434$	0	0
$435$	−184600.	−0.0467744
$436$	−3.13149e6	−0.788923
$437$	4.36248e6	1.09277
$438$	−819467.	−0.204101
$439$	533019.	0.132002	0.0660011	−	0.997820i	$-0.478976\pi$
$439$	533019.	0.132002	0.0660011	+	0.997820i	$0.478976\pi$
$440$	−8511.94	−0.00209603
$441$	0	0
$442$	120809.	0.0294134
$443$	−4.66745e6	−1.12998	−0.564990	−	0.825098i	$-0.691120\pi$
$443$	−4.66745e6	−1.12998	−0.564990	+	0.825098i	$0.691120\pi$
$444$	−1.24080e6	−0.298706
$445$	283173.	0.0677879
$446$	1.42945e6	0.340276
$447$	−2.87702e6	−0.681042
$448$	0	0
$449$	−6.10134e6	−1.42827	−0.714133	−	0.700010i	$-0.753179\pi$
$449$	−6.10134e6	−1.42827	−0.714133	+	0.700010i	$0.753179\pi$
$450$	734929.	0.171086
$451$	−39444.9	−0.00913166
$452$	4.63012e6	1.06597
$453$	−756417.	−0.173187
$454$	303680.	0.0691475
$455$	0	0
$456$	1.61084e6	0.362778
$457$	5.94498e6	1.33156	0.665779	−	0.746149i	$-0.268099\pi$
$457$	5.94498e6	1.33156	0.665779	+	0.746149i	$0.268099\pi$
$458$	−1.55015e6	−0.345311
$459$	36510.6	0.00808887
$460$	−1.26984e6	−0.279804
$461$	2.09415e6	0.458940	0.229470	−	0.973316i	$-0.426301\pi$
$461$	2.09415e6	0.458940	0.229470	+	0.973316i	$0.426301\pi$
$462$	0	0
$463$	2.41123e6	0.522741	0.261371	−	0.965239i	$-0.415826\pi$
$463$	2.41123e6	0.522741	0.261371	+	0.965239i	$0.415826\pi$
$464$	−294114.	−0.0634191
$465$	685213.	0.146958
$466$	1.89800e6	0.404884
$467$	4.51833e6	0.958706	0.479353	−	0.877622i	$-0.340871\pi$
$467$	4.51833e6	0.958706	0.479353	+	0.877622i	$0.340871\pi$
$468$	1.41829e6	0.299330
$469$	0	0
$470$	−1.25658e6	−0.262389
$471$	1.13576e6	0.235903
$472$	1.11410e6	0.230181
$473$	−64886.6	−0.0133353
$474$	−615602.	−0.125850
$475$	−3.12078e6	−0.634643
$476$	0	0
$477$	−1.55973e6	−0.313872
$478$	−3.40140e6	−0.680908
$479$	−8.35928e6	−1.66468	−0.832339	−	0.554267i	$-0.812999\pi$
$479$	−8.35928e6	−1.66468	−0.832339	+	0.554267i	$0.812999\pi$
$480$	−744490.	−0.147488
$481$	−4.79315e6	−0.944624
$482$	−277886.	−0.0544815
$483$	0	0
$484$	3.61398e6	0.701249
$485$	244721.	0.0472407
$486$	−182557.	−0.0350598
$487$	598304.	0.114314	0.0571570	−	0.998365i	$-0.481796\pi$
$487$	598304.	0.114314	0.0571570	+	0.998365i	$0.481796\pi$
$488$	6.18558e6	1.17579
$489$	−2.12211e6	−0.401324
$490$	0	0
$491$	2.76760e6	0.518084	0.259042	−	0.965866i	$-0.416593\pi$
$491$	2.76760e6	0.518084	0.259042	+	0.965866i	$0.416593\pi$
$492$	−2.17285e6	−0.404685
$493$	−74479.1	−0.0138012
$494$	2.56507e6	0.472914
$495$	−4096.32	−0.000751416 0
$496$	1.09172e6	0.199253
$497$	0	0
$498$	108415.	0.0195891
$499$	3.03921e6	0.546398	0.273199	−	0.961958i	$-0.411918\pi$
$499$	3.03921e6	0.546398	0.273199	+	0.961958i	$0.411918\pi$
$500$	1.87569e6	0.335533
$501$	1.34858e6	0.240040
$502$	−3.12410e6	−0.553307
$503$	−9.37896e6	−1.65286	−0.826428	−	0.563043i	$-0.809631\pi$
$503$	−9.37896e6	−1.65286	−0.826428	+	0.563043i	$0.809631\pi$
$504$	0	0
$505$	−1.95973e6	−0.341953
$506$	46504.3	0.00807452
$507$	2.13717e6	0.369250
$508$	−2.01694e6	−0.346764
$509$	−5.90139e6	−1.00962	−0.504812	−	0.863229i	$-0.668438\pi$
$509$	−5.90139e6	−1.00962	−0.504812	+	0.863229i	$0.668438\pi$
$510$	−19220.6	−0.00327222
$511$	0	0
$512$	−2.25139e6	−0.379555
$513$	775207.	0.130054
$514$	3.74806e6	0.625747
$515$	−2.90386e6	−0.482456
$516$	−3.57432e6	−0.590975
$517$	−108049.	−0.0177784
$518$	0	0
$519$	6.34014e6	1.03319
$520$	−1.81129e6	−0.293751
$521$	−9.37426e6	−1.51301	−0.756506	−	0.653986i	$-0.773095\pi$
$521$	−9.37426e6	−1.51301	−0.756506	+	0.653986i	$0.773095\pi$
$522$	372404.	0.0598188
$523$	−6.46830e6	−1.03404	−0.517018	−	0.855975i	$-0.672958\pi$
$523$	−6.46830e6	−1.03404	−0.517018	+	0.855975i	$0.672958\pi$
$524$	−7.18398e6	−1.14298
$525$	0	0
$526$	−1.18997e6	−0.187531
$527$	276458.	0.0433613
$528$	−6526.46	−0.00101881
$529$	1.03938e7	1.61486
$530$	821102.	0.126972
$531$	536154.	0.0825188
$532$	0	0
$533$	−8.39364e6	−1.27977
$534$	−571262.	−0.0866927
$535$	−2.79536e6	−0.422234
$536$	7.89546e6	1.18704
$537$	−5.01815e6	−0.750945
$538$	4.86792e6	0.725083
$539$	0	0
$540$	−225649.	−0.0333003
$541$	−2.46089e6	−0.361492	−0.180746	−	0.983530i	$-0.557851\pi$
$541$	−2.46089e6	−0.361492	−0.180746	+	0.983530i	$0.557851\pi$
$542$	−1.02725e6	−0.150203
$543$	3.98783e6	0.580413
$544$	−300373.	−0.0435175
$545$	1.92459e6	0.277554
$546$	0	0
$547$	503726.	0.0719824	0.0359912	−	0.999352i	$-0.488541\pi$
$547$	503726.	0.0719824	0.0359912	+	0.999352i	$0.488541\pi$
$548$	−5.81180e6	−0.826721
$549$	2.97677e6	0.421517
$550$	−33267.7	−0.00468938
$551$	−1.58137e6	−0.221898
$552$	6.21450e6	0.868077
$553$	0	0
$554$	−6.91113e6	−0.956697
$555$	762585.	0.105089
$556$	−6.33681e6	−0.869328
$557$	632648.	0.0864021	0.0432011	−	0.999066i	$-0.486244\pi$
$557$	632648.	0.0864021	0.0432011	+	0.999066i	$0.486244\pi$
$558$	−1.38232e6	−0.187942
$559$	−1.38075e7	−1.86890
$560$	0	0
$561$	−1652.71	−0.000221712 0
$562$	−215559.	−0.0287889
$563$	−1.00780e7	−1.33999	−0.669995	−	0.742366i	$-0.733704\pi$
$563$	−1.00780e7	−1.33999	−0.669995	+	0.742366i	$0.733704\pi$
$564$	−5.95194e6	−0.787881
$565$	−2.84564e6	−0.375024
$566$	1.47301e6	0.193270
$567$	0	0
$568$	−7.01763e6	−0.912682
$569$	2.01685e6	0.261151	0.130576	−	0.991438i	$-0.458317\pi$
$569$	2.01685e6	0.261151	0.130576	+	0.991438i	$0.458317\pi$
$570$	−408100.	−0.0526113
$571$	4.09727e6	0.525902	0.262951	−	0.964809i	$-0.415304\pi$
$571$	4.09727e6	0.525902	0.262951	+	0.964809i	$0.415304\pi$
$572$	−64201.1	−0.00820451
$573$	1.41733e6	0.180337
$574$	0	0
$575$	−1.20397e7	−1.51861
$576$	989267.	0.124239
$577$	8.14322e6	1.01826	0.509128	−	0.860691i	$-0.329968\pi$
$577$	8.14322e6	1.01826	0.509128	+	0.860691i	$0.329968\pi$
$578$	4.38191e6	0.545562
$579$	−7.00236e6	−0.868057
$580$	460307.	0.0568169
$581$	0	0
$582$	−493689.	−0.0604152
$583$	70603.4	0.00860309
$584$	4.95703e6	0.601436
$585$	−871673.	−0.105309
$586$	−7.03621e6	−0.846437
$587$	8.81465e6	1.05587	0.527934	−	0.849285i	$-0.322967\pi$
$587$	8.81465e6	1.05587	0.527934	+	0.849285i	$0.322967\pi$
$588$	0	0
$589$	5.86985e6	0.697170
$590$	−282253.	−0.0333816
$591$	−3.06254e6	−0.360673
$592$	1.21499e6	0.142485
$593$	1.15739e7	1.35158	0.675792	−	0.737093i	$-0.263802\pi$
$593$	1.15739e7	1.35158	0.675792	+	0.737093i	$0.263802\pi$
$594$	8263.74	0.000960972 0
$595$	0	0
$596$	7.17396e6	0.827263
$597$	2.66858e6	0.306439
$598$	9.89584e6	1.13162
$599$	−1.23551e7	−1.40695	−0.703474	−	0.710721i	$-0.748369\pi$
$599$	−1.23551e7	−1.40695	−0.703474	+	0.710721i	$0.748369\pi$
$600$	−4.44565e6	−0.504147
$601$	8.33752e6	0.941566	0.470783	−	0.882249i	$-0.343971\pi$
$601$	8.33752e6	0.941566	0.470783	+	0.882249i	$0.343971\pi$
$602$	0	0
$603$	3.79964e6	0.425549
$604$	1.88616e6	0.210371
$605$	−2.22113e6	−0.246709
$606$	3.95347e6	0.437317
$607$	8.67189e6	0.955305	0.477653	−	0.878549i	$-0.341488\pi$
$607$	8.67189e6	0.955305	0.477653	+	0.878549i	$0.341488\pi$
$608$	−6.37764e6	−0.699682
$609$	0	0
$610$	−1.56709e6	−0.170518
$611$	−2.29921e7	−2.49159
$612$	−91040.7	−0.00982555
$613$	5.24031e6	0.563256	0.281628	−	0.959524i	$-0.409126\pi$
$613$	5.24031e6	0.563256	0.281628	+	0.959524i	$0.409126\pi$
$614$	5.00196e6	0.535450
$615$	1.33542e6	0.142374
$616$	0	0
$617$	−6.95644e6	−0.735655	−0.367828	−	0.929894i	$-0.619898\pi$
$617$	−6.95644e6	−0.735655	−0.367828	+	0.929894i	$0.619898\pi$
$618$	5.85813e6	0.617004
$619$	−1.82763e7	−1.91717	−0.958586	−	0.284802i	$-0.908072\pi$
$619$	−1.82763e7	−1.91717	−0.958586	+	0.284802i	$0.908072\pi$
$620$	−1.70861e6	−0.178510
$621$	2.99069e6	0.311202
$622$	3.17409e6	0.328960
$623$	0	0
$624$	−1.38879e6	−0.142783
$625$	8.01835e6	0.821079
$626$	−980707.	−0.100024
$627$	−35090.9	−0.00356473
$628$	−2.83205e6	−0.286551
$629$	307674.	0.0310074
$630$	0	0
$631$	1.90708e7	1.90676	0.953379	−	0.301777i	$-0.0975798\pi$
$631$	1.90708e7	1.90676	0.953379	+	0.301777i	$0.0975798\pi$
$632$	3.72384e6	0.370850
$633$	4.56055e6	0.452385
$634$	−4.85774e6	−0.479967
$635$	1.23960e6	0.121997
$636$	3.88924e6	0.381261
$637$	0	0
$638$	−16857.4	−0.00163961
$639$	−3.37719e6	−0.327192
$640$	2.12628e6	0.205197
$641$	3.20624e6	0.308213	0.154106	−	0.988054i	$-0.450750\pi$
$641$	3.20624e6	0.308213	0.154106	+	0.988054i	$0.450750\pi$
$642$	5.63923e6	0.539986
$643$	−4.35153e6	−0.415063	−0.207532	−	0.978228i	$-0.566543\pi$
$643$	−4.35153e6	−0.415063	−0.207532	+	0.978228i	$0.566543\pi$
$644$	0	0
$645$	2.19675e6	0.207913
$646$	−164653.	−0.0155234
$647$	5.59976e6	0.525907	0.262953	−	0.964809i	$-0.415303\pi$
$647$	5.59976e6	0.525907	0.262953	+	0.964809i	$0.415303\pi$
$648$	1.10431e6	0.103312
$649$	−24269.8	−0.00226180
$650$	−7.07917e6	−0.657202
$651$	0	0
$652$	5.29156e6	0.487489
$653$	−6.74495e6	−0.619007	−0.309504	−	0.950898i	$-0.600163\pi$
$653$	−6.74495e6	−0.619007	−0.309504	+	0.950898i	$0.600163\pi$
$654$	−3.88259e6	−0.354958
$655$	4.41523e6	0.402115
$656$	2.12766e6	0.193038
$657$	2.38554e6	0.215612
$658$	0	0
$659$	2.09622e6	0.188029	0.0940143	−	0.995571i	$-0.470030\pi$
$659$	2.09622e6	0.188029	0.0940143	+	0.995571i	$0.470030\pi$
$660$	10214.3	0.000912746 0
$661$	1.94185e7	1.72867	0.864335	−	0.502917i	$-0.167740\pi$
$661$	1.94185e7	1.72867	0.864335	+	0.502917i	$0.167740\pi$
$662$	−4.75591e6	−0.421783
$663$	−351687.	−0.0310722
$664$	−655810.	−0.0577242
$665$	0	0
$666$	−1.53841e6	−0.134396
$667$	−6.10079e6	−0.530972
$668$	−3.36274e6	−0.291577
$669$	−4.16126e6	−0.359467
$670$	−2.00028e6	−0.172149
$671$	−134748.	−0.0115536
$672$	0	0
$673$	1.27627e7	1.08619	0.543094	−	0.839672i	$-0.317253\pi$
$673$	1.27627e7	1.08619	0.543094	+	0.839672i	$0.317253\pi$
$674$	8.86713e6	0.751853
$675$	−2.13944e6	−0.180735
$676$	−5.32913e6	−0.448528
$677$	3.86502e6	0.324101	0.162050	−	0.986782i	$-0.448189\pi$
$677$	3.86502e6	0.324101	0.162050	+	0.986782i	$0.448189\pi$
$678$	5.74067e6	0.479610
$679$	0	0
$680$	116267.	0.00964241
$681$	−884039.	−0.0730472
$682$	62572.8	0.00515140
$683$	−2.06418e7	−1.69316	−0.846578	−	0.532265i	$-0.821341\pi$
$683$	−2.06418e7	−1.69316	−0.846578	+	0.532265i	$0.821341\pi$
$684$	−1.93301e6	−0.157977
$685$	3.57189e6	0.290852
$686$	0	0
$687$	4.51263e6	0.364786
$688$	3.49998e6	0.281900
$689$	1.50240e7	1.20570
$690$	−1.57442e6	−0.125892
$691$	1.62329e7	1.29330	0.646651	−	0.762786i	$-0.276169\pi$
$691$	1.62329e7	1.29330	0.646651	+	0.762786i	$0.276169\pi$
$692$	−1.58094e7	−1.25502
$693$	0	0
$694$	346156.	0.0272818
$695$	3.89456e6	0.305842
$696$	−2.25271e6	−0.176271
$697$	538791.	0.0420086
$698$	1.16033e7	0.901454
$699$	−5.52524e6	−0.427719
$700$	0	0
$701$	−8.27590e6	−0.636092	−0.318046	−	0.948075i	$-0.603027\pi$
$701$	−8.27590e6	−0.636092	−0.318046	+	0.948075i	$0.603027\pi$
$702$	1.75848e6	0.134677
$703$	6.53266e6	0.498542
$704$	−44780.7	−0.00340533
$705$	3.65802e6	0.277187
$706$	−9.98356e6	−0.753830
$707$	0	0
$708$	−1.33692e6	−0.100236
$709$	2.38973e7	1.78539	0.892696	−	0.450660i	$-0.148811\pi$
$709$	2.38973e7	1.78539	0.892696	+	0.450660i	$0.148811\pi$
$710$	1.77789e6	0.132360
$711$	1.79207e6	0.132948
$712$	3.45562e6	0.255462
$713$	2.26454e7	1.66823
$714$	0	0
$715$	39457.6	0.00288646
$716$	1.25130e7	0.912173
$717$	9.90179e6	0.719309
$718$	−5.67804e6	−0.411043
$719$	784349.	0.0565832	0.0282916	−	0.999600i	$-0.490993\pi$
$719$	784349.	0.0565832	0.0282916	+	0.999600i	$0.490993\pi$
$720$	220955.	0.0158845
$721$	0	0
$722$	4.15920e6	0.296939
$723$	808952.	0.0575542
$724$	−9.94381e6	−0.705028
$725$	4.36431e6	0.308369
$726$	4.48081e6	0.315511
$727$	1.61766e7	1.13514	0.567571	−	0.823324i	$-0.307883\pi$
$727$	1.61766e7	1.13514	0.567571	+	0.823324i	$0.307883\pi$
$728$	0	0
$729$	531441.	0.0370370
$730$	−1.25584e6	−0.0872224
$731$	886307.	0.0613467
$732$	−7.42270e6	−0.512017
$733$	1.36978e7	0.941654	0.470827	−	0.882226i	$-0.343956\pi$
$733$	1.36978e7	0.941654	0.470827	+	0.882226i	$0.343956\pi$
$734$	1.04814e6	0.0718090
$735$	0	0
$736$	−2.46044e7	−1.67424
$737$	−171997.	−0.0116641
$738$	−2.69402e6	−0.182079
$739$	−2.53712e7	−1.70895	−0.854477	−	0.519490i	$-0.826122\pi$
$739$	−2.53712e7	−1.70895	−0.854477	+	0.519490i	$0.826122\pi$
$740$	−1.90154e6	−0.127651
$741$	−7.46715e6	−0.499585
$742$	0	0
$743$	2.45336e7	1.63038	0.815192	−	0.579191i	$-0.196632\pi$
$743$	2.45336e7	1.63038	0.815192	+	0.579191i	$0.196632\pi$
$744$	8.36179e6	0.553818
$745$	−4.40907e6	−0.291042
$746$	2.18461e6	0.143723
$747$	−315605.	−0.0206939
$748$	4121.10	0.000269314 0
$749$	0	0
$750$	2.32558e6	0.150966
$751$	−1.84907e7	−1.19634	−0.598169	−	0.801370i	$-0.704105\pi$
$751$	−1.84907e7	−1.19634	−0.598169	+	0.801370i	$0.704105\pi$
$752$	5.82815e6	0.375825
$753$	9.09454e6	0.584512
$754$	−3.58716e6	−0.229786
$755$	−1.15922e6	−0.0740113
$756$	0	0
$757$	−2.94413e7	−1.86732	−0.933658	−	0.358166i	$-0.883402\pi$
$757$	−2.94413e7	−1.86732	−0.933658	+	0.358166i	$0.883402\pi$
$758$	−2.00429e6	−0.126703
$759$	−135378.	−0.00852990
$760$	2.46863e6	0.155032
$761$	−1.86236e7	−1.16574	−0.582870	−	0.812565i	$-0.698070\pi$
$761$	−1.86236e7	−1.16574	−0.582870	+	0.812565i	$0.698070\pi$
$762$	−2.50072e6	−0.156019
$763$	0	0
$764$	−3.53417e6	−0.219056
$765$	55953.0	0.00345676
$766$	9.49199e6	0.584501
$767$	−5.16448e6	−0.316984
$768$	−7.80687e6	−0.477611
$769$	−1.13326e7	−0.691056	−0.345528	−	0.938408i	$-0.612300\pi$
$769$	−1.13326e7	−0.691056	−0.345528	+	0.938408i	$0.612300\pi$
$770$	0	0
$771$	−1.09109e7	−0.661038
$772$	1.74607e7	1.05443
$773$	−8.22020e6	−0.494804	−0.247402	−	0.968913i	$-0.579577\pi$
$773$	−8.22020e6	−0.494804	−0.247402	+	0.968913i	$0.579577\pi$
$774$	−4.43164e6	−0.265896
$775$	−1.61998e7	−0.968848
$776$	2.98637e6	0.178029
$777$	0	0
$778$	1.42214e7	0.842352
$779$	1.14398e7	0.675422
$780$	2.17355e6	0.127918
$781$	152874.	0.00896819
$782$	−635217.	−0.0371454
$783$	−1.08410e6	−0.0631925
$784$	0	0
$785$	1.74056e6	0.100813
$786$	−8.90709e6	−0.514256
$787$	−5.43081e6	−0.312556	−0.156278	−	0.987713i	$-0.549950\pi$
$787$	−5.43081e6	−0.312556	−0.156278	+	0.987713i	$0.549950\pi$
$788$	7.63657e6	0.438110
$789$	3.46411e6	0.198107
$790$	−943418.	−0.0537819
$791$	0	0
$792$	−49988.1	−0.00283174
$793$	−2.86736e7	−1.61920
$794$	−8.16681e6	−0.459728
$795$	−2.39030e6	−0.134133
$796$	−6.65421e6	−0.372232
$797$	1.78388e7	0.994765	0.497382	−	0.867531i	$-0.334295\pi$
$797$	1.78388e7	0.994765	0.497382	+	0.867531i	$0.334295\pi$
$798$	0	0
$799$	1.47587e6	0.0817866
$800$	1.76012e7	0.972339
$801$	1.66300e6	0.0915819
$802$	−1.51390e7	−0.831115
$803$	−107985.	−0.00590983
$804$	−9.47455e6	−0.516914
$805$	0	0
$806$	1.33151e7	0.721951
$807$	−1.41709e7	−0.765976
$808$	−2.39149e7	−1.28867
$809$	1.18431e7	0.636199	0.318099	−	0.948057i	$-0.396955\pi$
$809$	1.18431e7	0.636199	0.318099	+	0.948057i	$0.396955\pi$
$810$	−279771.	−0.0149827
$811$	618053.	0.0329969	0.0164985	−	0.999864i	$-0.494748\pi$
$811$	618053.	0.0329969	0.0164985	+	0.999864i	$0.494748\pi$
$812$	0	0
$813$	2.99043e6	0.158674
$814$	69638.4	0.00368373
$815$	−3.25216e6	−0.171505
$816$	89147.1	0.00468686
$817$	1.88184e7	0.986342
$818$	−297836.	−0.0155630
$819$	0	0
$820$	−3.32992e6	−0.172941
$821$	4.31256e6	0.223294	0.111647	−	0.993748i	$-0.464387\pi$
$821$	4.31256e6	0.223294	0.111647	+	0.993748i	$0.464387\pi$
$822$	−7.20578e6	−0.371965
$823$	2.86620e7	1.47505	0.737524	−	0.675321i	$-0.235995\pi$
$823$	2.86620e7	1.47505	0.737524	+	0.675321i	$0.235995\pi$
$824$	−3.54364e7	−1.81816
$825$	96845.2	0.00495385
$826$	0	0
$827$	1.86894e7	0.950235	0.475117	−	0.879922i	$-0.342406\pi$
$827$	1.86894e7	0.950235	0.475117	+	0.879922i	$0.342406\pi$
$828$	−7.45740e6	−0.378017
$829$	1.32486e7	0.669550	0.334775	−	0.942298i	$-0.391340\pi$
$829$	1.32486e7	0.669550	0.334775	+	0.942298i	$0.391340\pi$
$830$	166147.	0.00837137
$831$	2.01189e7	1.01065
$832$	−9.52907e6	−0.477246
$833$	0	0
$834$	−7.85673e6	−0.391135
$835$	2.06672e6	0.102581
$836$	87500.6	0.00433007
$837$	4.02406e6	0.198541
$838$	−3.39019e6	−0.166769
$839$	−2.52930e7	−1.24049	−0.620247	−	0.784406i	$-0.712968\pi$
$839$	−2.52930e7	−1.24049	−0.620247	+	0.784406i	$0.712968\pi$
$840$	0	0
$841$	−1.82997e7	−0.892181
$842$	5.98723e6	0.291035
$843$	627512.	0.0304126
$844$	−1.13719e7	−0.549512
$845$	3.27525e6	0.157798
$846$	−7.37954e6	−0.354490
$847$	0	0
$848$	−3.80835e6	−0.181864
$849$	−4.28807e6	−0.204170
$850$	454414.	0.0215727
$851$	2.52025e7	1.19294
$852$	8.42115e6	0.397441
$853$	4.05806e7	1.90962	0.954808	−	0.297223i	$-0.0960605\pi$
$853$	4.05806e7	1.90962	0.954808	+	0.297223i	$0.0960605\pi$
$854$	0	0
$855$	1.18801e6	0.0555784
$856$	−3.41123e7	−1.59120
$857$	1.94469e7	0.904480	0.452240	−	0.891896i	$-0.350625\pi$
$857$	1.94469e7	0.904480	0.452240	+	0.891896i	$0.350625\pi$
$858$	−79600.1	−0.00369144
$859$	−2.03242e7	−0.939788	−0.469894	−	0.882723i	$-0.655708\pi$
$859$	−2.03242e7	−0.939788	−0.469894	+	0.882723i	$0.655708\pi$
$860$	−5.47769e6	−0.252552
$861$	0	0
$862$	9.50149e6	0.435536
$863$	−2.61202e7	−1.19385	−0.596926	−	0.802297i	$-0.703611\pi$
$863$	−2.61202e7	−1.19385	−0.596926	+	0.802297i	$0.703611\pi$
$864$	−4.37217e6	−0.199257
$865$	9.71634e6	0.441532
$866$	−1.17766e7	−0.533611
$867$	−1.27561e7	−0.576330
$868$	0	0
$869$	−81120.9	−0.00364404
$870$	570714.	0.0255635
$871$	−3.65999e7	−1.63469
$872$	2.34862e7	1.04597
$873$	1.43717e6	0.0638225
$874$	−1.34872e7	−0.597231
$875$	0	0
$876$	−5.94844e6	−0.261904
$877$	−1.62956e7	−0.715436	−0.357718	−	0.933830i	$-0.616445\pi$
$877$	−1.62956e7	−0.715436	−0.357718	+	0.933830i	$0.616445\pi$
$878$	−1.64789e6	−0.0721428
$879$	2.04830e7	0.894174
$880$	−10001.9	−0.000435387 0
$881$	2.93722e7	1.27496	0.637479	−	0.770467i	$-0.279977\pi$
$881$	2.93722e7	1.27496	0.637479	+	0.770467i	$0.279977\pi$
$882$	0	0
$883$	1.21821e7	0.525800	0.262900	−	0.964823i	$-0.415321\pi$
$883$	1.21821e7	0.525800	0.262900	+	0.964823i	$0.415321\pi$
$884$	876945.	0.0377435
$885$	821662.	0.0352643
$886$	1.44300e7	0.617565
$887$	−2.38021e7	−1.01579	−0.507897	−	0.861418i	$-0.669577\pi$
$887$	−2.38021e7	−1.01579	−0.507897	+	0.861418i	$0.669577\pi$
$888$	9.30597e6	0.396031
$889$	0	0
$890$	−875466.	−0.0370480
$891$	−24056.5	−0.00101517
$892$	1.03763e7	0.436645
$893$	3.13363e7	1.31498
$894$	8.89467e6	0.372208
$895$	−7.69038e6	−0.320915
$896$	0	0
$897$	−2.88077e7	−1.19544
$898$	1.88631e7	0.780587
$899$	−8.20879e6	−0.338750
$900$	5.33478e6	0.219538
$901$	−964396.	−0.0395771
$902$	121949.	0.00499070
$903$	0	0
$904$	−3.47259e7	−1.41329
$905$	6.11140e6	0.248039
$906$	2.33856e6	0.0946515
$907$	2.10870e7	0.851133	0.425566	−	0.904927i	$-0.360075\pi$
$907$	2.10870e7	0.851133	0.425566	+	0.904927i	$0.360075\pi$
$908$	2.20439e6	0.0887305
$909$	−1.15089e7	−0.461981
$910$	0	0
$911$	1.71528e7	0.684761	0.342381	−	0.939561i	$-0.388767\pi$
$911$	1.71528e7	0.684761	0.342381	+	0.939561i	$0.388767\pi$
$912$	1.89280e6	0.0753561
$913$	14286.3	0.000567210 0
$914$	−1.83797e7	−0.727733
$915$	4.56194e6	0.180134
$916$	−1.12524e7	−0.443105
$917$	0	0
$918$	−112877.	−0.00442079
$919$	7.35541e6	0.287289	0.143644	−	0.989629i	$-0.454118\pi$
$919$	7.35541e6	0.287289	0.143644	+	0.989629i	$0.454118\pi$
$920$	9.52379e6	0.370971
$921$	−1.45611e7	−0.565648
$922$	−6.47433e6	−0.250823
$923$	3.25306e7	1.25686
$924$	0	0
$925$	−1.80290e7	−0.692817
$926$	−7.45463e6	−0.285692
$927$	−1.70535e7	−0.651802
$928$	8.91891e6	0.339971
$929$	−3.34199e7	−1.27047	−0.635236	−	0.772318i	$-0.719097\pi$
$929$	−3.34199e7	−1.27047	−0.635236	+	0.772318i	$0.719097\pi$
$930$	−2.11842e6	−0.0803166
$931$	0	0
$932$	1.37774e7	0.519550
$933$	−9.24006e6	−0.347513
$934$	−1.39690e7	−0.523959
$935$	−2532.80	−9.47483e−5 0
$936$	−1.06372e7	−0.396860
$937$	−2.87696e7	−1.07049	−0.535247	−	0.844696i	$-0.679781\pi$
$937$	−2.87696e7	−1.07049	−0.535247	+	0.844696i	$0.679781\pi$
$938$	0	0
$939$	2.85493e6	0.105665
$940$	−9.12142e6	−0.336700
$941$	2.16379e7	0.796601	0.398300	−	0.917255i	$-0.369600\pi$
$941$	2.16379e7	0.796601	0.398300	+	0.917255i	$0.369600\pi$
$942$	−3.51134e6	−0.128927
$943$	4.41339e7	1.61619
$944$	1.30911e6	0.0478132
$945$	0	0
$946$	200605.	0.00728809
$947$	−6.31254e6	−0.228733	−0.114367	−	0.993439i	$-0.536484\pi$
$947$	−6.31254e6	−0.228733	−0.114367	+	0.993439i	$0.536484\pi$
$948$	−4.46860e6	−0.161492
$949$	−2.29786e7	−0.828244
$950$	9.64829e6	0.346850
$951$	1.41413e7	0.507036
$952$	0	0
$953$	−5.59599e6	−0.199593	−0.0997963	−	0.995008i	$-0.531819\pi$
$953$	−5.59599e6	−0.199593	−0.0997963	+	0.995008i	$0.531819\pi$
$954$	4.82209e6	0.171540
$955$	2.17208e6	0.0770668
$956$	−2.46905e7	−0.873746
$957$	49073.5	0.00173208
$958$	2.58438e7	0.909792
$959$	0	0
$960$	1.51606e6	0.0530933
$961$	1.84091e6	0.0643021
$962$	1.48186e7	0.516263
$963$	−1.64163e7	−0.570440
$964$	−2.01715e6	−0.0699111
$965$	−1.07312e7	−0.370963
$966$	0	0
$967$	1.33277e7	0.458340	0.229170	−	0.973386i	$-0.426399\pi$
$967$	1.33277e7	0.458340	0.229170	+	0.973386i	$0.426399\pi$
$968$	−2.71048e7	−0.929734
$969$	479319.	0.0163989
$970$	−756585.	−0.0258183
$971$	−3.63257e7	−1.23642	−0.618210	−	0.786013i	$-0.712142\pi$
$971$	−3.63257e7	−1.23642	−0.618210	+	0.786013i	$0.712142\pi$
$972$	−1.32517e6	−0.0449889
$973$	0	0
$974$	−1.84973e6	−0.0624758
$975$	2.06081e7	0.694266
$976$	7.26831e6	0.244236
$977$	−9.03739e6	−0.302905	−0.151453	−	0.988465i	$-0.548395\pi$
$977$	−9.03739e6	−0.302905	−0.151453	+	0.988465i	$0.548395\pi$
$978$	6.56077e6	0.219335
$979$	−75278.0	−0.00251022
$980$	0	0
$981$	1.13026e7	0.374977
$982$	−8.55639e6	−0.283147
$983$	1.98539e7	0.655332	0.327666	−	0.944794i	$-0.393738\pi$
$983$	1.98539e7	0.655332	0.327666	+	0.944794i	$0.393738\pi$
$984$	1.62964e7	0.536541
$985$	−4.69339e6	−0.154133
$986$	230261.	0.00754273
$987$	0	0
$988$	1.86196e7	0.606846
$989$	7.25999e7	2.36018
$990$	12664.3	0.000410670 0
$991$	−4.55557e7	−1.47353	−0.736764	−	0.676150i	$-0.763647\pi$
$991$	−4.55557e7	−1.47353	−0.736764	+	0.676150i	$0.763647\pi$
$992$	−3.31060e7	−1.06814
$993$	1.38449e7	0.445570
$994$	0	0
$995$	4.08963e6	0.130956
$996$	786973.	0.0251369
$997$	−4.51665e7	−1.43906	−0.719529	−	0.694462i	$-0.755642\pi$
$997$	−4.51665e7	−1.43906	−0.719529	+	0.694462i	$0.755642\pi$
$998$	−9.39610e6	−0.298622
$999$	4.47844e6	0.141975

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	147.6.a.o.1.3	yes	6
3.2	odd	2		441.6.a.ba.1.4		6
7.2	even	3		147.6.e.p.67.4		12
7.3	odd	6		147.6.e.q.79.4		12
7.4	even	3		147.6.e.p.79.4		12
7.5	odd	6		147.6.e.q.67.4		12
7.6	odd	2		147.6.a.n.1.3	✓	6
21.20	even	2		441.6.a.bb.1.4		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
147.6.a.n.1.3	✓	6	7.6	odd	2
147.6.a.o.1.3	yes	6	1.1	even	1	trivial
147.6.e.p.67.4		12	7.2	even	3
147.6.e.p.79.4		12	7.4	even	3
147.6.e.q.67.4		12	7.5	odd	6
147.6.e.q.79.4		12	7.3	odd	6
441.6.a.ba.1.4		6	3.2	odd	2
441.6.a.bb.1.4		6	21.20	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 147 = 3 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	147.a (trivial)

\(f(q)\)	\(=\)	\(q-3.09163 q^{2} +9.00000 q^{3} -22.4418 q^{4} +13.7926 q^{5} -27.8246 q^{6} +168.314 q^{8} +81.0000 q^{9} +O(q^{10})\)	\(q-3.09163 q^{2} +9.00000 q^{3} -22.4418 q^{4} +13.7926 q^{5} -27.8246 q^{6} +168.314 q^{8} +81.0000 q^{9} -42.6416 q^{10} -3.66659 q^{11} -201.977 q^{12} -780.229 q^{13} +124.133 q^{15} +197.776 q^{16} +50.0832 q^{17} -250.422 q^{18} +1063.38 q^{19} -309.532 q^{20} +11.3357 q^{22} +4102.45 q^{23} +1514.82 q^{24} -2934.76 q^{25} +2412.18 q^{26} +729.000 q^{27} -1487.11 q^{29} -383.774 q^{30} +5519.97 q^{31} -5997.49 q^{32} -32.9993 q^{33} -154.838 q^{34} -1817.79 q^{36} +6143.27 q^{37} -3287.59 q^{38} -7022.06 q^{39} +2321.49 q^{40} +10757.9 q^{41} +17696.7 q^{43} +82.2850 q^{44} +1117.20 q^{45} -12683.3 q^{46} +29468.5 q^{47} +1779.98 q^{48} +9073.19 q^{50} +450.749 q^{51} +17509.8 q^{52} -19255.9 q^{53} -2253.80 q^{54} -50.5718 q^{55} +9570.46 q^{57} +4597.58 q^{58} +6619.18 q^{59} -2785.78 q^{60} +36750.3 q^{61} -17065.7 q^{62} +12213.2 q^{64} -10761.4 q^{65} +102.021 q^{66} +46909.2 q^{67} -1123.96 q^{68} +36922.1 q^{69} -41693.7 q^{71} +13633.4 q^{72} +29451.1 q^{73} -18992.7 q^{74} -26412.9 q^{75} -23864.3 q^{76} +21709.6 q^{78} +22124.4 q^{79} +2727.84 q^{80} +6561.00 q^{81} -33259.5 q^{82} -3896.35 q^{83} +690.778 q^{85} -54711.6 q^{86} -13384.0 q^{87} -617.138 q^{88} +20530.8 q^{89} -3453.97 q^{90} -92066.6 q^{92} +49679.7 q^{93} -91105.4 q^{94} +14666.8 q^{95} -53977.4 q^{96} +17742.9 q^{97} -296.994 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 2 q^{2} + 54 q^{3} + 150 q^{4} + 100 q^{5} + 18 q^{6} - 114 q^{8} + 486 q^{9}+O(q^{10}) \) 6 * q + 2 * q^2 + 54 * q^3 + 150 * q^4 + 100 * q^5 + 18 * q^6 - 114 * q^8 + 486 * q^9	\( 6 q + 2 q^{2} + 54 q^{3} + 150 q^{4} + 100 q^{5} + 18 q^{6} - 114 q^{8} + 486 q^{9} + 864 q^{10} + 604 q^{11} + 1350 q^{12} + 1352 q^{13} + 900 q^{15} + 4578 q^{16} + 3028 q^{17} + 162 q^{18} + 1728 q^{19} + 452 q^{20} - 4116 q^{22} - 4484 q^{23} - 1026 q^{24} + 4806 q^{25} + 14172 q^{26} + 4374 q^{27} - 5320 q^{29} + 7776 q^{30} + 3976 q^{31} - 37326 q^{32} + 5436 q^{33} - 16336 q^{34} + 12150 q^{36} + 22680 q^{37} + 52744 q^{38} + 12168 q^{39} + 100600 q^{40} + 28756 q^{41} - 6768 q^{43} - 64940 q^{44} + 8100 q^{45} + 540 q^{46} + 51552 q^{47} + 41202 q^{48} - 40622 q^{50} + 27252 q^{51} + 119296 q^{52} + 80884 q^{53} + 1458 q^{54} + 11656 q^{55} + 15552 q^{57} - 70464 q^{58} + 8872 q^{59} + 4068 q^{60} + 50896 q^{61} + 11824 q^{62} + 199590 q^{64} + 3492 q^{65} - 37044 q^{66} + 6480 q^{67} + 37348 q^{68} - 40356 q^{69} - 110852 q^{71} - 9234 q^{72} + 64232 q^{73} - 27464 q^{74} + 43254 q^{75} - 194864 q^{76} + 127548 q^{78} + 111696 q^{79} - 308940 q^{80} + 39366 q^{81} - 189640 q^{82} + 101128 q^{83} - 23292 q^{85} + 3824 q^{86} - 47880 q^{87} - 97788 q^{88} - 35012 q^{89} + 69984 q^{90} - 449260 q^{92} + 35784 q^{93} - 121016 q^{94} - 119080 q^{95} - 335934 q^{96} + 70952 q^{97} + 48924 q^{99}+O(q^{100}) \) 6 * q + 2 * q^2 + 54 * q^3 + 150 * q^4 + 100 * q^5 + 18 * q^6 - 114 * q^8 + 486 * q^9 + 864 * q^10 + 604 * q^11 + 1350 * q^12 + 1352 * q^13 + 900 * q^15 + 4578 * q^16 + 3028 * q^17 + 162 * q^18 + 1728 * q^19 + 452 * q^20 - 4116 * q^22 - 4484 * q^23 - 1026 * q^24 + 4806 * q^25 + 14172 * q^26 + 4374 * q^27 - 5320 * q^29 + 7776 * q^30 + 3976 * q^31 - 37326 * q^32 + 5436 * q^33 - 16336 * q^34 + 12150 * q^36 + 22680 * q^37 + 52744 * q^38 + 12168 * q^39 + 100600 * q^40 + 28756 * q^41 - 6768 * q^43 - 64940 * q^44 + 8100 * q^45 + 540 * q^46 + 51552 * q^47 + 41202 * q^48 - 40622 * q^50 + 27252 * q^51 + 119296 * q^52 + 80884 * q^53 + 1458 * q^54 + 11656 * q^55 + 15552 * q^57 - 70464 * q^58 + 8872 * q^59 + 4068 * q^60 + 50896 * q^61 + 11824 * q^62 + 199590 * q^64 + 3492 * q^65 - 37044 * q^66 + 6480 * q^67 + 37348 * q^68 - 40356 * q^69 - 110852 * q^71 - 9234 * q^72 + 64232 * q^73 - 27464 * q^74 + 43254 * q^75 - 194864 * q^76 + 127548 * q^78 + 111696 * q^79 - 308940 * q^80 + 39366 * q^81 - 189640 * q^82 + 101128 * q^83 - 23292 * q^85 + 3824 * q^86 - 47880 * q^87 - 97788 * q^88 - 35012 * q^89 + 69984 * q^90 - 449260 * q^92 + 35784 * q^93 - 121016 * q^94 - 119080 * q^95 - 335934 * q^96 + 70952 * q^97 + 48924 * q^99

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