LMFDB - Embedded newform 147.6.a.n.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:	$1$
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	$-0.539369\pi$
$5$	−13.7926	−0.246730	−0.123365	+	0.992361i	$0.539369\pi$
$6$	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	$-0.278841\pi$
$13$	780.229	1.28045	0.640226	+	0.768186i	$0.278841\pi$
$14$	0	0
$15$	124.133	0.142449
$16$	197.776	0.193140
$17$	−50.0832	−0.0420310	−0.0210155	−	0.999779i	$-0.506690\pi$
$17$	−50.0832	−0.0420310	−0.0210155	+	0.999779i	$0.506690\pi$
$18$	−250.422	−0.182176
$19$	−1063.38	−0.675781	−0.337891	−	0.941185i	$-0.609713\pi$
$19$	−1063.38	−0.675781	−0.337891	+	0.941185i	$0.609713\pi$
$20$	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	$-0.672515\pi$
$31$	−5519.97	−1.03165	−0.515825	+	0.856694i	$0.672515\pi$
$32$	−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	$-0.666569\pi$
$41$	−10757.9	−0.999468	−0.499734	+	0.866179i	$0.666569\pi$
$42$	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	$-0.925771\pi$
$47$	−29468.5	−1.94587	−0.972933	+	0.231089i	$0.925771\pi$
$48$	−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	$-0.539501\pi$
$59$	−6619.18	−0.247557	−0.123778	+	0.992310i	$0.539501\pi$
$60$	−2785.78	−0.0999009
$61$	−36750.3	−1.26455	−0.632275	−	0.774744i	$-0.717879\pi$
$61$	−36750.3	−1.26455	−0.632275	+	0.774744i	$0.717879\pi$
$62$	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	$-0.604832\pi$
$73$	−29451.1	−0.646837	−0.323418	+	0.946256i	$0.604832\pi$
$74$	−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	$-0.490118\pi$
$83$	3896.35	0.0620816	0.0310408	+	0.999518i	$0.490118\pi$
$84$	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	$-0.543866\pi$
$89$	−20530.8	−0.274746	−0.137373	+	0.990519i	$0.543866\pi$
$90$	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	$-0.530520\pi$
$97$	−17742.9	−0.191468	−0.0957338	+	0.995407i	$0.530520\pi$
$98$	0	0
$99$	−296.994	−0.00304550
$100$	65861.5	0.658615
$101$	142085.	1.38594	0.692971	−	0.720965i	$-0.256301\pi$
$101$	142085.	1.38594	0.692971	+	0.720965i	$0.256301\pi$
$102$	−1393.55	−0.0132624
$103$	210538.	1.95540	0.977702	−	0.209996i	$-0.0673450\pi$
$103$	210538.	1.95540	0.977702	+	0.209996i	$0.0673450\pi$
$104$	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	$-0.803202\pi$
$131$	−320115.	−1.62978	−0.814889	+	0.579617i	$0.803202\pi$
$132$	−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	$-0.712783\pi$
$139$	−282366.	−1.23958	−0.619791	+	0.784767i	$0.712783\pi$
$140$	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	$-0.565491\pi$
$157$	−126195.	−0.408596	−0.204298	+	0.978909i	$0.565491\pi$
$158$	−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	$-0.566657\pi$
$167$	−149843.	−0.415761	−0.207881	+	0.978154i	$0.566657\pi$
$168$	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	$-0.852660\pi$
$173$	−704460.	−1.78954	−0.894769	+	0.446530i	$0.852660\pi$
$174$	−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	$-0.667642\pi$
$181$	−443092.	−1.00530	−0.502652	+	0.864489i	$0.667642\pi$
$182$	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	$-0.585499\pi$
$199$	−296509.	−0.530768	−0.265384	+	0.964143i	$0.585499\pi$
$200$	−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	$-0.399233\pi$
$223$	462362.	0.622615	0.311308	+	0.950309i	$0.399233\pi$
$224$	0	0
$225$	−237716.	−0.313041
$226$	637852.	0.830709
$227$	98226.6	0.126521	0.0632607	−	0.997997i	$-0.479850\pi$
$227$	98226.6	0.126521	0.0632607	+	0.997997i	$0.479850\pi$
$228$	−214779.	−0.273624
$229$	−501403.	−0.631827	−0.315914	−	0.948788i	$-0.602311\pi$
$229$	−501403.	−0.631827	−0.315914	+	0.948788i	$0.602311\pi$
$230$	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	$-0.515872\pi$
$241$	−89883.5	−0.0996868	−0.0498434	+	0.998757i	$0.515872\pi$
$242$	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	$-0.668951\pi$
$251$	−1.01050e6	−1.01240	−0.506202	+	0.862415i	$0.668951\pi$
$252$	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	$-0.305983\pi$
$257$	1.21233e6	1.14495	0.572475	+	0.819922i	$0.305983\pi$
$258$	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	$-0.269132\pi$
$269$	1.57455e6	1.32671	0.663355	+	0.748305i	$0.269132\pi$
$270$	−31085.7	−0.0259508
$271$	−332270.	−0.274832	−0.137416	−	0.990513i	$-0.543880\pi$
$271$	−332270.	−0.274832	−0.137416	+	0.990513i	$0.543880\pi$
$272$	−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	$-0.443420\pi$
$283$	476452.	0.353633	0.176817	+	0.984244i	$0.443420\pi$
$284$	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	$-0.781937\pi$
$293$	−2.27589e6	−1.54875	−0.774377	+	0.632724i	$0.781937\pi$
$294$	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	$-0.337046\pi$
$307$	1.61790e6	0.979731	0.489866	+	0.871798i	$0.337046\pi$
$308$	0	0
$309$	−1.89484e6	−1.12895
$310$	−235380.	−0.139112
$311$	1.02667e6	0.601910	0.300955	−	0.953638i	$-0.402695\pi$
$311$	1.02667e6	0.601910	0.300955	+	0.953638i	$0.402695\pi$
$312$	−1.18191e6	−0.687381
$313$	−317214.	−0.183017	−0.0915085	−	0.995804i	$-0.529169\pi$
$313$	−317214.	−0.183017	−0.0915085	+	0.995804i	$0.529169\pi$
$314$	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	$-0.191338\pi$
$349$	3.75314e6	1.64942	0.824711	+	0.565555i	$0.191338\pi$
$350$	0	0
$351$	−568787.	−0.246423
$352$	21990.3	0.00945965
$353$	−3.22923e6	−1.37931	−0.689655	−	0.724138i	$-0.742238\pi$
$353$	−3.22923e6	−1.37931	−0.689655	+	0.724138i	$0.742238\pi$
$354$	−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	$-0.479073\pi$
$367$	339025.	0.131391	0.0656957	+	0.997840i	$0.479073\pi$
$368$	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	$-0.320409\pi$
$383$	3.07022e6	1.06948	0.534741	+	0.845016i	$0.320409\pi$
$384$	−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	$-0.638177\pi$
$397$	−2.64159e6	−0.841181	−0.420590	+	0.907251i	$0.638177\pi$
$398$	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	$-0.504532\pi$
$409$	−96336.3	−0.0284762	−0.0142381	+	0.999899i	$0.504532\pi$
$410$	−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	$-0.548755\pi$
$419$	−1.09657e6	−0.305142	−0.152571	+	0.988292i	$0.548755\pi$
$420$	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	$-0.662340\pi$
$433$	−3.80919e6	−0.976366	−0.488183	+	0.872741i	$0.662340\pi$
$434$	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	$-0.521024\pi$
$439$	−533019.	−0.132002	−0.0660011	+	0.997820i	$0.521024\pi$
$440$	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	$-0.573699\pi$
$461$	−2.09415e6	−0.458940	−0.229470	+	0.973316i	$0.573699\pi$
$462$	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	$-0.659129\pi$
$467$	−4.51833e6	−0.958706	−0.479353	+	0.877622i	$0.659129\pi$
$468$	−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	$-0.187001\pi$
$479$	8.35928e6	1.66468	0.832339	+	0.554267i	$0.187001\pi$
$480$	−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	$-0.190369\pi$
$503$	9.37896e6	1.65286	0.826428	+	0.563043i	$0.190369\pi$
$504$	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	$-0.331562\pi$
$509$	5.90139e6	1.00962	0.504812	+	0.863229i	$0.331562\pi$
$510$	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	$-0.226905\pi$
$521$	9.37426e6	1.51301	0.756506	+	0.653986i	$0.226905\pi$
$522$	372404.	0.0598188
$523$	6.46830e6	1.03404	0.517018	−	0.855975i	$-0.327042\pi$
$523$	6.46830e6	1.03404	0.517018	+	0.855975i	$0.327042\pi$
$524$	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	$-0.266296\pi$
$563$	1.00780e7	1.33999	0.669995	+	0.742366i	$0.266296\pi$
$564$	−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	$-0.670032\pi$
$577$	−8.14322e6	−1.01826	−0.509128	+	0.860691i	$0.670032\pi$
$578$	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	$-0.677033\pi$
$587$	−8.81465e6	−1.05587	−0.527934	+	0.849285i	$0.677033\pi$
$588$	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	$-0.736198\pi$
$593$	−1.15739e7	−1.35158	−0.675792	+	0.737093i	$0.736198\pi$
$594$	−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	$-0.656029\pi$
$601$	−8.33752e6	−0.941566	−0.470783	+	0.882249i	$0.656029\pi$
$602$	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	$-0.658512\pi$
$607$	−8.67189e6	−0.955305	−0.477653	+	0.878549i	$0.658512\pi$
$608$	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	$-0.0919278\pi$
$619$	1.82763e7	1.91717	0.958586	+	0.284802i	$0.0919278\pi$
$620$	−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	$-0.433457\pi$
$643$	4.35153e6	0.415063	0.207532	+	0.978228i	$0.433457\pi$
$644$	0	0
$645$	2.19675e6	0.207913
$646$	−164653.	−0.0155234
$647$	−5.59976e6	−0.525907	−0.262953	−	0.964809i	$-0.584697\pi$
$647$	−5.59976e6	−0.525907	−0.262953	+	0.964809i	$0.584697\pi$
$648$	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	$-0.832260\pi$
$661$	−1.94185e7	−1.72867	−0.864335	+	0.502917i	$0.832260\pi$
$662$	−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	$-0.551811\pi$
$677$	−3.86502e6	−0.324101	−0.162050	+	0.986782i	$0.551811\pi$
$678$	−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	$-0.723831\pi$
$691$	−1.62329e7	−1.29330	−0.646651	+	0.762786i	$0.723831\pi$
$692$	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	$-0.509007\pi$
$719$	−784349.	−0.0565832	−0.0282916	+	0.999600i	$0.509007\pi$
$720$	−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	$-0.692117\pi$
$727$	−1.61766e7	−1.13514	−0.567571	+	0.823324i	$0.692117\pi$
$728$	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	$-0.656044\pi$
$733$	−1.36978e7	−0.941654	−0.470827	+	0.882226i	$0.656044\pi$
$734$	−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	$-0.301930\pi$
$761$	1.86236e7	1.16574	0.582870	+	0.812565i	$0.301930\pi$
$762$	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	$-0.387700\pi$
$769$	1.13326e7	0.691056	0.345528	+	0.938408i	$0.387700\pi$
$770$	0	0
$771$	−1.09109e7	−0.661038
$772$	1.74607e7	1.05443
$773$	8.22020e6	0.494804	0.247402	−	0.968913i	$-0.420423\pi$
$773$	8.22020e6	0.494804	0.247402	+	0.968913i	$0.420423\pi$
$774$	−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	$-0.450050\pi$
$787$	5.43081e6	0.312556	0.156278	+	0.987713i	$0.450050\pi$
$788$	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	$-0.665705\pi$
$797$	−1.78388e7	−0.994765	−0.497382	+	0.867531i	$0.665705\pi$
$798$	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	$-0.505252\pi$
$811$	−618053.	−0.0329969	−0.0164985	+	0.999864i	$0.505252\pi$
$812$	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	$-0.608660\pi$
$829$	−1.32486e7	−0.669550	−0.334775	+	0.942298i	$0.608660\pi$
$830$	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	$-0.287032\pi$
$839$	2.52930e7	1.24049	0.620247	+	0.784406i	$0.287032\pi$
$840$	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	$-0.903939\pi$
$853$	−4.05806e7	−1.90962	−0.954808	+	0.297223i	$0.903939\pi$
$854$	0	0
$855$	1.18801e6	0.0555784
$856$	−3.41123e7	−1.59120
$857$	−1.94469e7	−0.904480	−0.452240	−	0.891896i	$-0.649375\pi$
$857$	−1.94469e7	−0.904480	−0.452240	+	0.891896i	$0.649375\pi$
$858$	−79600.1	−0.00369144
$859$	2.03242e7	0.939788	0.469894	−	0.882723i	$-0.344292\pi$
$859$	2.03242e7	0.939788	0.469894	+	0.882723i	$0.344292\pi$
$860$	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	$-0.720023\pi$
$881$	−2.93722e7	−1.27496	−0.637479	+	0.770467i	$0.720023\pi$
$882$	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	$-0.330423\pi$
$887$	2.38021e7	1.01579	0.507897	+	0.861418i	$0.330423\pi$
$888$	−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	$-0.280903\pi$
$929$	3.34199e7	1.27047	0.635236	+	0.772318i	$0.280903\pi$
$930$	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	$-0.320219\pi$
$937$	2.87696e7	1.07049	0.535247	+	0.844696i	$0.320219\pi$
$938$	0	0
$939$	2.85493e6	0.105665
$940$	−9.12142e6	−0.336700
$941$	−2.16379e7	−0.796601	−0.398300	−	0.917255i	$-0.630400\pi$
$941$	−2.16379e7	−0.796601	−0.398300	+	0.917255i	$0.630400\pi$
$942$	−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	$-0.287858\pi$
$971$	3.63257e7	1.23642	0.618210	+	0.786013i	$0.287858\pi$
$972$	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	$-0.606262\pi$
$983$	−1.98539e7	−0.655332	−0.327666	+	0.944794i	$0.606262\pi$
$984$	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	$-0.244358\pi$
$997$	4.51665e7	1.43906	0.719529	+	0.694462i	$0.244358\pi$
$998$	−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.n.1.3	✓	6
3.2	odd	2		441.6.a.bb.1.4		6
7.2	even	3		147.6.e.q.67.4		12
7.3	odd	6		147.6.e.p.79.4		12
7.4	even	3		147.6.e.q.79.4		12
7.5	odd	6		147.6.e.p.67.4		12
7.6	odd	2		147.6.a.o.1.3	yes	6
21.20	even	2		441.6.a.ba.1.4		6

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

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 147 = 3 \cdot 7^{2} \)
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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