LMFDB - Embedded newform 147.6.a.i.1.1

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:	$2$
Coefficient field:	$\Q(\sqrt{249}) $
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x - 62 $ x^2 - x - 62
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 21)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$8.38987$ 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)

$f(q)$	$=$	$q-9.38987 q^{2} -9.00000 q^{3} +56.1696 q^{4} -71.7291 q^{5} +84.5088 q^{6} -226.949 q^{8} +81.0000 q^{9} +O(q^{10})$	\(q-9.38987 q^{2} -9.00000 q^{3} +56.1696 q^{4} -71.7291 q^{5} +84.5088 q^{6} -226.949 q^{8} +81.0000 q^{9} +673.526 q^{10} -560.610 q^{11} -505.526 q^{12} +533.509 q^{13} +645.562 q^{15} +333.597 q^{16} +1005.70 q^{17} -760.579 q^{18} +1368.53 q^{19} -4028.99 q^{20} +5264.05 q^{22} +3228.08 q^{23} +2042.54 q^{24} +2020.06 q^{25} -5009.58 q^{26} -729.000 q^{27} -753.456 q^{29} -6061.74 q^{30} +8206.42 q^{31} +4129.95 q^{32} +5045.49 q^{33} -9443.39 q^{34} +4549.74 q^{36} -2808.66 q^{37} -12850.3 q^{38} -4801.58 q^{39} +16278.9 q^{40} +245.827 q^{41} -17504.5 q^{43} -31489.2 q^{44} -5810.05 q^{45} -30311.2 q^{46} -16345.5 q^{47} -3002.37 q^{48} -18968.1 q^{50} -9051.30 q^{51} +29967.0 q^{52} -29641.7 q^{53} +6845.21 q^{54} +40212.0 q^{55} -12316.7 q^{57} +7074.85 q^{58} -10356.1 q^{59} +36260.9 q^{60} +954.179 q^{61} -77057.2 q^{62} -49454.8 q^{64} -38268.1 q^{65} -47376.5 q^{66} -19815.2 q^{67} +56489.8 q^{68} -29052.7 q^{69} +62125.4 q^{71} -18382.9 q^{72} +27109.6 q^{73} +26373.0 q^{74} -18180.5 q^{75} +76869.6 q^{76} +45086.2 q^{78} +44687.4 q^{79} -23928.6 q^{80} +6561.00 q^{81} -2308.29 q^{82} +15606.6 q^{83} -72137.9 q^{85} +164365. q^{86} +6781.10 q^{87} +127230. q^{88} +13635.3 q^{89} +54555.6 q^{90} +181320. q^{92} -73857.8 q^{93} +153482. q^{94} -98163.1 q^{95} -37169.5 q^{96} -12919.5 q^{97} -45409.4 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 3 q^{2} - 18 q^{3} + 65 q^{4} - 33 q^{5} + 27 q^{6} - 375 q^{8} + 162 q^{9}+O(q^{10}) $ 2 * q - 3 * q^2 - 18 * q^3 + 65 * q^4 - 33 * q^5 + 27 * q^6 - 375 * q^8 + 162 * q^9	\( 2 q - 3 q^{2} - 18 q^{3} + 65 q^{4} - 33 q^{5} + 27 q^{6} - 375 q^{8} + 162 q^{9} + 921 q^{10} - 1137 q^{11} - 585 q^{12} + 925 q^{13} + 297 q^{15} - 895 q^{16} - 324 q^{17} - 243 q^{18} + 2311 q^{19} - 3687 q^{20} + 1581 q^{22} + 1596 q^{23} + 3375 q^{24} + 395 q^{25} - 2508 q^{26} - 1458 q^{27} - 2217 q^{29} - 8289 q^{30} + 4294 q^{31} + 1017 q^{32} + 10233 q^{33} - 17940 q^{34} + 5265 q^{36} - 19109 q^{37} - 6828 q^{38} - 8325 q^{39} + 10545 q^{40} - 12858 q^{41} - 2771 q^{43} - 36579 q^{44} - 2673 q^{45} - 40740 q^{46} - 23160 q^{47} + 8055 q^{48} - 29352 q^{50} + 2916 q^{51} + 33424 q^{52} - 31653 q^{53} + 2187 q^{54} + 17889 q^{55} - 20799 q^{57} - 2277 q^{58} + 41097 q^{59} + 33183 q^{60} + 42052 q^{61} - 102057 q^{62} - 30031 q^{64} - 23106 q^{65} - 14229 q^{66} + 30763 q^{67} + 44748 q^{68} - 14364 q^{69} + 102096 q^{71} - 30375 q^{72} - 28577 q^{73} - 77784 q^{74} - 3555 q^{75} + 85192 q^{76} + 22572 q^{78} - 18464 q^{79} - 71511 q^{80} + 13122 q^{81} - 86040 q^{82} + 61179 q^{83} - 123636 q^{85} + 258510 q^{86} + 19953 q^{87} + 212565 q^{88} + 29322 q^{89} + 74601 q^{90} + 166908 q^{92} - 38646 q^{93} + 109938 q^{94} - 61662 q^{95} - 9153 q^{96} - 9791 q^{97} - 92097 q^{99}+O(q^{100}) \) 2 * q - 3 * q^2 - 18 * q^3 + 65 * q^4 - 33 * q^5 + 27 * q^6 - 375 * q^8 + 162 * q^9 + 921 * q^10 - 1137 * q^11 - 585 * q^12 + 925 * q^13 + 297 * q^15 - 895 * q^16 - 324 * q^17 - 243 * q^18 + 2311 * q^19 - 3687 * q^20 + 1581 * q^22 + 1596 * q^23 + 3375 * q^24 + 395 * q^25 - 2508 * q^26 - 1458 * q^27 - 2217 * q^29 - 8289 * q^30 + 4294 * q^31 + 1017 * q^32 + 10233 * q^33 - 17940 * q^34 + 5265 * q^36 - 19109 * q^37 - 6828 * q^38 - 8325 * q^39 + 10545 * q^40 - 12858 * q^41 - 2771 * q^43 - 36579 * q^44 - 2673 * q^45 - 40740 * q^46 - 23160 * q^47 + 8055 * q^48 - 29352 * q^50 + 2916 * q^51 + 33424 * q^52 - 31653 * q^53 + 2187 * q^54 + 17889 * q^55 - 20799 * q^57 - 2277 * q^58 + 41097 * q^59 + 33183 * q^60 + 42052 * q^61 - 102057 * q^62 - 30031 * q^64 - 23106 * q^65 - 14229 * q^66 + 30763 * q^67 + 44748 * q^68 - 14364 * q^69 + 102096 * q^71 - 30375 * q^72 - 28577 * q^73 - 77784 * q^74 - 3555 * q^75 + 85192 * q^76 + 22572 * q^78 - 18464 * q^79 - 71511 * q^80 + 13122 * q^81 - 86040 * q^82 + 61179 * q^83 - 123636 * q^85 + 258510 * q^86 + 19953 * q^87 + 212565 * q^88 + 29322 * q^89 + 74601 * q^90 + 166908 * q^92 - 38646 * q^93 + 109938 * q^94 - 61662 * q^95 - 9153 * q^96 - 9791 * q^97 - 92097 * 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 $

$2$	−9.38987	−1.65991	−0.829955	−	0.557831i	$-0.811634\pi$
$2$	−9.38987	−1.65991	−0.829955	+	0.557831i	$0.811634\pi$
$3$	−9.00000	−0.577350
$3$	−9.00000	−0.577350
$4$	56.1696	1.75530
$5$	−71.7291	−1.28313	−0.641564	−	0.767069i	$-0.721714\pi$
$5$	−71.7291	−1.28313	−0.641564	+	0.767069i	$0.721714\pi$
$6$	84.5088	0.958349
$7$	0	0
$7$	0	0
$8$	−226.949	−1.25373
$9$	81.0000	0.333333
$10$	673.526	2.12988
$11$	−560.610	−1.39694	−0.698472	−	0.715637i	$-0.746137\pi$
$11$	−560.610	−1.39694	−0.698472	+	0.715637i	$0.746137\pi$
$12$	−505.526	−1.01342
$13$	533.509	0.875555	0.437777	−	0.899083i	$-0.355766\pi$
$13$	533.509	0.875555	0.437777	+	0.899083i	$0.355766\pi$
$14$	0	0
$15$	645.562	0.740815
$16$	333.597	0.325778
$17$	1005.70	0.844007	0.422004	−	0.906594i	$-0.361327\pi$
$17$	1005.70	0.844007	0.422004	+	0.906594i	$0.361327\pi$
$18$	−760.579	−0.553303
$19$	1368.53	0.869699	0.434850	−	0.900503i	$-0.356801\pi$
$19$	1368.53	0.869699	0.434850	+	0.900503i	$0.356801\pi$
$20$	−4028.99	−2.25228
$21$	0	0
$22$	5264.05	2.31880
$23$	3228.08	1.27240	0.636201	−	0.771523i	$-0.280505\pi$
$23$	3228.08	1.27240	0.636201	+	0.771523i	$0.280505\pi$
$24$	2042.54	0.723841
$25$	2020.06	0.646419
$26$	−5009.58	−1.45334
$27$	−729.000	−0.192450
$28$	0	0
$29$	−753.456	−0.166365	−0.0831827	−	0.996534i	$-0.526508\pi$
$29$	−753.456	−0.166365	−0.0831827	+	0.996534i	$0.526508\pi$
$30$	−6061.74	−1.22969
$31$	8206.42	1.53373	0.766866	−	0.641807i	$-0.221815\pi$
$31$	8206.42	1.53373	0.766866	+	0.641807i	$0.221815\pi$
$32$	4129.95	0.712968
$33$	5045.49	0.806526
$34$	−9443.39	−1.40098
$35$	0	0
$36$	4549.74	0.585100
$37$	−2808.66	−0.337284	−0.168642	−	0.985677i	$-0.553938\pi$
$37$	−2808.66	−0.337284	−0.168642	+	0.985677i	$0.553938\pi$
$38$	−12850.3	−1.44362
$39$	−4801.58	−0.505502
$40$	16278.9	1.60870
$41$	245.827	0.0228387	0.0114193	−	0.999935i	$-0.496365\pi$
$41$	245.827	0.0228387	0.0114193	+	0.999935i	$0.496365\pi$
$42$	0	0
$43$	−17504.5	−1.44371	−0.721853	−	0.692047i	$-0.756709\pi$
$43$	−17504.5	−1.44371	−0.721853	+	0.692047i	$0.756709\pi$
$44$	−31489.2	−2.45206
$45$	−5810.05	−0.427710
$46$	−30311.2	−2.11207
$47$	−16345.5	−1.07933	−0.539663	−	0.841881i	$-0.681449\pi$
$47$	−16345.5	−1.07933	−0.539663	+	0.841881i	$0.681449\pi$
$48$	−3002.37	−0.188088
$49$	0	0
$50$	−18968.1	−1.07300
$51$	−9051.30	−0.487288
$52$	29967.0	1.53686
$53$	−29641.7	−1.44948	−0.724741	−	0.689021i	$-0.758041\pi$
$53$	−29641.7	−1.44948	−0.724741	+	0.689021i	$0.758041\pi$
$54$	6845.21	0.319450
$55$	40212.0	1.79246
$56$	0	0
$57$	−12316.7	−0.502121
$58$	7074.85	0.276151
$59$	−10356.1	−0.387317	−0.193659	−	0.981069i	$-0.562035\pi$
$59$	−10356.1	−0.387317	−0.193659	+	0.981069i	$0.562035\pi$
$60$	36260.9	1.30035
$61$	954.179	0.0328326	0.0164163	−	0.999865i	$-0.494774\pi$
$61$	954.179	0.0328326	0.0164163	+	0.999865i	$0.494774\pi$
$62$	−77057.2	−2.54586
$63$	0	0
$64$	−49454.8	−1.50924
$65$	−38268.1	−1.12345
$66$	−47376.5	−1.33876
$67$	−19815.2	−0.539276	−0.269638	−	0.962962i	$-0.586904\pi$
$67$	−19815.2	−0.539276	−0.269638	+	0.962962i	$0.586904\pi$
$68$	56489.8	1.48149
$69$	−29052.7	−0.734622
$70$	0	0
$71$	62125.4	1.46259	0.731296	−	0.682060i	$-0.238916\pi$
$71$	62125.4	1.46259	0.731296	+	0.682060i	$0.238916\pi$
$72$	−18382.9	−0.417910
$73$	27109.6	0.595410	0.297705	−	0.954658i	$-0.403779\pi$
$73$	27109.6	0.595410	0.297705	+	0.954658i	$0.403779\pi$
$74$	26373.0	0.559861
$75$	−18180.5	−0.373210
$76$	76869.6	1.52658
$77$	0	0
$78$	45086.2	0.839087
$79$	44687.4	0.805595	0.402798	−	0.915289i	$-0.368038\pi$
$79$	44687.4	0.805595	0.402798	+	0.915289i	$0.368038\pi$
$80$	−23928.6	−0.418015
$81$	6561.00	0.111111
$82$	−2308.29	−0.0379101
$83$	15606.6	0.248665	0.124332	−	0.992241i	$-0.460321\pi$
$83$	15606.6	0.248665	0.124332	+	0.992241i	$0.460321\pi$
$84$	0	0
$85$	−72137.9	−1.08297
$86$	164365.	2.39642
$87$	6781.10	0.0960511
$88$	127230.	1.75139
$89$	13635.3	0.182469	0.0912347	−	0.995829i	$-0.470919\pi$
$89$	13635.3	0.182469	0.0912347	+	0.995829i	$0.470919\pi$
$90$	54555.6	0.709959
$91$	0	0
$92$	181320.	2.23345
$93$	−73857.8	−0.885500
$94$	153482.	1.79159
$95$	−98163.1	−1.11594
$96$	−37169.5	−0.411632
$97$	−12919.5	−0.139417	−0.0697086	−	0.997567i	$-0.522207\pi$
$97$	−12919.5	−0.139417	−0.0697086	+	0.997567i	$0.522207\pi$
$98$	0	0
$99$	−45409.4	−0.465648
$100$	113466.	1.13466
$101$	25142.9	0.245252	0.122626	−	0.992453i	$-0.460868\pi$
$101$	25142.9	0.245252	0.122626	+	0.992453i	$0.460868\pi$
$102$	84990.5	0.808854
$103$	−160753.	−1.49302	−0.746511	−	0.665373i	$-0.768273\pi$
$103$	−160753.	−1.49302	−0.746511	+	0.665373i	$0.768273\pi$
$104$	−121079.	−1.09771
$105$	0	0
$106$	278331.	2.40601
$107$	−94375.5	−0.796893	−0.398446	−	0.917192i	$-0.630451\pi$
$107$	−94375.5	−0.796893	−0.398446	+	0.917192i	$0.630451\pi$
$108$	−40947.6	−0.337808
$109$	−83393.5	−0.672304	−0.336152	−	0.941808i	$-0.609126\pi$
$109$	−83393.5	−0.672304	−0.336152	+	0.941808i	$0.609126\pi$
$110$	−377586.	−2.97532
$111$	25278.0	0.194731
$112$	0	0
$113$	−179254.	−1.32060	−0.660301	−	0.751001i	$-0.729571\pi$
$113$	−179254.	−1.32060	−0.660301	+	0.751001i	$0.729571\pi$
$114$	115653.	0.833476
$115$	−231547.	−1.63266
$116$	−42321.3	−0.292021
$117$	43214.2	0.291852
$118$	97242.5	0.642911
$119$	0	0
$120$	−146510.	−0.928781
$121$	153233.	0.951455
$122$	−8959.61	−0.0544991
$123$	−2212.45	−0.0131859
$124$	460951.	2.69216
$125$	79256.4	0.453690
$126$	0	0
$127$	−143674.	−0.790440	−0.395220	−	0.918586i	$-0.629332\pi$
$127$	−143674.	−0.790440	−0.395220	+	0.918586i	$0.629332\pi$
$128$	332215.	1.79223
$129$	157540.	0.833524
$130$	359332.	1.86482
$131$	52289.9	0.266219	0.133110	−	0.991101i	$-0.457504\pi$
$131$	52289.9	0.266219	0.133110	+	0.991101i	$0.457504\pi$
$132$	283403.	1.41570
$133$	0	0
$134$	186062.	0.895150
$135$	52290.5	0.246938
$136$	−228243.	−1.05816
$137$	9410.10	0.0428344	0.0214172	−	0.999771i	$-0.493182\pi$
$137$	9410.10	0.0428344	0.0214172	+	0.999771i	$0.493182\pi$
$138$	272801.	1.21941
$139$	183094.	0.803781	0.401890	−	0.915688i	$-0.368353\pi$
$139$	183094.	0.803781	0.401890	+	0.915688i	$0.368353\pi$
$140$	0	0
$141$	147109.	0.623150
$142$	−583349.	−2.42777
$143$	−299090.	−1.22310
$144$	27021.3	0.108593
$145$	54044.7	0.213468
$146$	−254556.	−0.988328
$147$	0	0
$148$	−157762.	−0.592034
$149$	−167002.	−0.616247	−0.308123	−	0.951346i	$-0.599701\pi$
$149$	−167002.	−0.616247	−0.308123	+	0.951346i	$0.599701\pi$
$150$	170713.	0.619495
$151$	376264.	1.34292	0.671461	−	0.741040i	$-0.265667\pi$
$151$	376264.	1.34292	0.671461	+	0.741040i	$0.265667\pi$
$152$	−310586.	−1.09037
$153$	81461.7	0.281336
$154$	0	0
$155$	−588639.	−1.96797
$156$	−269703.	−0.887307
$157$	39075.0	0.126517	0.0632587	−	0.997997i	$-0.479851\pi$
$157$	39075.0	0.126517	0.0632587	+	0.997997i	$0.479851\pi$
$158$	−419608.	−1.33722
$159$	266775.	0.836859
$160$	−296237.	−0.914829
$161$	0	0
$162$	−61606.9	−0.184434
$163$	−477919.	−1.40892	−0.704458	−	0.709745i	$-0.748810\pi$
$163$	−477919.	−1.40892	−0.704458	+	0.709745i	$0.748810\pi$
$164$	13808.0	0.0400887
$165$	−361908.	−1.03488
$166$	−146544.	−0.412761
$167$	39793.4	0.110413	0.0552064	−	0.998475i	$-0.482418\pi$
$167$	39793.4	0.110413	0.0552064	+	0.998475i	$0.482418\pi$
$168$	0	0
$169$	−86661.4	−0.233404
$170$	677366.	1.79763
$171$	110851.	0.289900
$172$	−983221.	−2.53414
$173$	48338.2	0.122794	0.0613968	−	0.998113i	$-0.480445\pi$
$173$	48338.2	0.122794	0.0613968	+	0.998113i	$0.480445\pi$
$174$	−63673.7	−0.159436
$175$	0	0
$176$	−187018.	−0.455094
$177$	93205.0	0.223618
$178$	−128034.	−0.302883
$179$	−142911.	−0.333374	−0.166687	−	0.986010i	$-0.553307\pi$
$179$	−142911.	−0.333374	−0.166687	+	0.986010i	$0.553307\pi$
$180$	−326348.	−0.750759
$181$	−77245.3	−0.175257	−0.0876285	−	0.996153i	$-0.527929\pi$
$181$	−77245.3	−0.175257	−0.0876285	+	0.996153i	$0.527929\pi$
$182$	0	0
$183$	−8587.61	−0.0189559
$184$	−732610.	−1.59525
$185$	201463.	0.432778
$186$	693515.	1.46985
$187$	−563806.	−1.17903
$188$	−918119.	−1.89454
$189$	0	0
$190$	921739.	1.85235
$191$	272054.	0.539600	0.269800	−	0.962916i	$-0.413042\pi$
$191$	272054.	0.539600	0.269800	+	0.962916i	$0.413042\pi$
$192$	445093.	0.871360
$193$	−16033.8	−0.0309844	−0.0154922	−	0.999880i	$-0.504932\pi$
$193$	−16033.8	−0.0309844	−0.0154922	+	0.999880i	$0.504932\pi$
$194$	121312.	0.231420
$195$	344413.	0.648624
$196$	0	0
$197$	1.03228e6	1.89510	0.947552	−	0.319603i	$-0.103549\pi$
$197$	1.03228e6	1.89510	0.947552	+	0.319603i	$0.103549\pi$
$198$	426388.	0.772934
$199$	−881736.	−1.57836	−0.789180	−	0.614162i	$-0.789494\pi$
$199$	−881736.	−1.57836	−0.789180	+	0.614162i	$0.789494\pi$
$200$	−458451.	−0.810435
$201$	178337.	0.311351
$202$	−236089.	−0.407096
$203$	0	0
$204$	−508408.	−0.855337
$205$	−17633.0	−0.0293049
$206$	1.50945e6	2.47828
$207$	261474.	0.424134
$208$	177977.	0.285237
$209$	−767210.	−1.21492
$210$	0	0
$211$	−372813.	−0.576480	−0.288240	−	0.957558i	$-0.593070\pi$
$211$	−372813.	−0.576480	−0.288240	+	0.957558i	$0.593070\pi$
$212$	−1.66496e6	−2.54428
$213$	−559128.	−0.844428
$214$	886174.	1.32277
$215$	1.25558e6	1.85246
$216$	165446.	0.241280
$217$	0	0
$218$	783054.	1.11596
$219$	−243987.	−0.343760
$220$	2.25869e6	3.14630
$221$	536550.	0.738975
$222$	−237357.	−0.323236
$223$	−1.08205e6	−1.45708	−0.728541	−	0.685002i	$-0.759801\pi$
$223$	−1.08205e6	−1.45708	−0.728541	+	0.685002i	$0.759801\pi$
$224$	0	0
$225$	163625.	0.215473
$226$	1.68317e6	2.19208
$227$	553049.	0.712359	0.356179	−	0.934418i	$-0.384079\pi$
$227$	553049.	0.712359	0.356179	+	0.934418i	$0.384079\pi$
$228$	−691826.	−0.881373
$229$	523024.	0.659072	0.329536	−	0.944143i	$-0.393108\pi$
$229$	523024.	0.659072	0.329536	+	0.944143i	$0.393108\pi$
$230$	2.17420e6	2.71006
$231$	0	0
$232$	170996.	0.208577
$233$	−364181.	−0.439468	−0.219734	−	0.975560i	$-0.570519\pi$
$233$	−364181.	−0.439468	−0.219734	+	0.975560i	$0.570519\pi$
$234$	−405776.	−0.484447
$235$	1.17245e6	1.38492
$236$	−581698.	−0.679858
$237$	−402186.	−0.465111
$238$	0	0
$239$	371841.	0.421078	0.210539	−	0.977585i	$-0.432478\pi$
$239$	371841.	0.421078	0.210539	+	0.977585i	$0.432478\pi$
$240$	215357.	0.241341
$241$	−1.71147e6	−1.89814	−0.949069	−	0.315067i	$-0.897973\pi$
$241$	−1.71147e6	−1.89814	−0.949069	+	0.315067i	$0.897973\pi$
$242$	−1.43883e6	−1.57933
$243$	−59049.0	−0.0641500
$244$	53595.8	0.0576310
$245$	0	0
$246$	20774.6	0.0218874
$247$	730121.	0.761469
$248$	−1.86244e6	−1.92289
$249$	−140460.	−0.143567
$250$	−744207.	−0.753084
$251$	58134.1	0.0582434	0.0291217	−	0.999576i	$-0.490729\pi$
$251$	58134.1	0.0582434	0.0291217	+	0.999576i	$0.490729\pi$
$252$	0	0
$253$	−1.80969e6	−1.77748
$254$	1.34908e6	1.31206
$255$	649242.	0.625253
$256$	−1.53691e6	−1.46571
$257$	−311839.	−0.294509	−0.147254	−	0.989099i	$-0.547044\pi$
$257$	−311839.	−0.294509	−0.147254	+	0.989099i	$0.547044\pi$
$258$	−1.47928e6	−1.38357
$259$	0	0
$260$	−2.14950e6	−1.97199
$261$	−61029.9	−0.0554551
$262$	−490995.	−0.441900
$263$	863965.	0.770206	0.385103	−	0.922874i	$-0.374166\pi$
$263$	863965.	0.770206	0.385103	+	0.922874i	$0.374166\pi$
$264$	−1.14507e6	−1.01117
$265$	2.12617e6	1.85987
$266$	0	0
$267$	−122718.	−0.105349
$268$	−1.11301e6	−0.946592
$269$	−1.12069e6	−0.944290	−0.472145	−	0.881521i	$-0.656520\pi$
$269$	−1.12069e6	−0.944290	−0.472145	+	0.881521i	$0.656520\pi$
$270$	−491001.	−0.409895
$271$	1.14012e6	0.943030	0.471515	−	0.881858i	$-0.343707\pi$
$271$	1.14012e6	0.943030	0.471515	+	0.881858i	$0.343707\pi$
$272$	335498.	0.274959
$273$	0	0
$274$	−88359.6	−0.0711013
$275$	−1.13247e6	−0.903012
$276$	−1.63188e6	−1.28948
$277$	−1.98801e6	−1.55675	−0.778375	−	0.627799i	$-0.783956\pi$
$277$	−1.98801e6	−1.55675	−0.778375	+	0.627799i	$0.783956\pi$
$278$	−1.71923e6	−1.33420
$279$	664720.	0.511244
$280$	0	0
$281$	532321.	0.402168	0.201084	−	0.979574i	$-0.435554\pi$
$281$	532321.	0.402168	0.201084	+	0.979574i	$0.435554\pi$
$282$	−1.38134e6	−1.03437
$283$	2.62473e6	1.94813	0.974067	−	0.226259i	$-0.0726497\pi$
$283$	2.62473e6	1.94813	0.974067	+	0.226259i	$0.0726497\pi$
$284$	3.48956e6	2.56729
$285$	883468.	0.644286
$286$	2.80842e6	2.03024
$287$	0	0
$288$	334526.	0.237656
$289$	−408424.	−0.287651
$290$	−507473.	−0.354338
$291$	116275.	0.0804925
$292$	1.52274e6	1.04512
$293$	609962.	0.415082	0.207541	−	0.978226i	$-0.433454\pi$
$293$	609962.	0.415082	0.207541	+	0.978226i	$0.433454\pi$
$294$	0	0
$295$	742834.	0.496978
$296$	637424.	0.422863
$297$	408685.	0.268842
$298$	1.56812e6	1.02291
$299$	1.72221e6	1.11406
$300$	−1.02119e6	−0.655096
$301$	0	0
$302$	−3.53307e6	−2.22913
$303$	−226286.	−0.141596
$304$	456536.	0.283329
$305$	−68442.3	−0.0421284
$306$	−764915.	−0.466992
$307$	−1.34843e6	−0.816551	−0.408275	−	0.912859i	$-0.633870\pi$
$307$	−1.34843e6	−0.816551	−0.408275	+	0.912859i	$0.633870\pi$
$308$	0	0
$309$	1.44678e6	0.861997
$310$	5.52724e6	3.26666
$311$	−3.33061e6	−1.95264	−0.976320	−	0.216330i	$-0.930591\pi$
$311$	−3.33061e6	−1.95264	−0.976320	+	0.216330i	$0.930591\pi$
$312$	1.08972e6	0.633762
$313$	−2.83670e6	−1.63664	−0.818320	−	0.574763i	$-0.805094\pi$
$313$	−2.83670e6	−1.63664	−0.818320	+	0.574763i	$0.805094\pi$
$314$	−366909.	−0.210007
$315$	0	0
$316$	2.51007e6	1.41406
$317$	−1.08839e6	−0.608326	−0.304163	−	0.952620i	$-0.598377\pi$
$317$	−1.08839e6	−0.608326	−0.304163	+	0.952620i	$0.598377\pi$
$318$	−2.50498e6	−1.38911
$319$	422395.	0.232403
$320$	3.54734e6	1.93655
$321$	849380.	0.460086
$322$	0	0
$323$	1.37633e6	0.734033
$324$	368529.	0.195033
$325$	1.07772e6	0.565975
$326$	4.48760e6	2.33867
$327$	750541.	0.388155
$328$	−55790.4	−0.0286335
$329$	0	0
$330$	3.39827e6	1.71780
$331$	1.30555e6	0.654971	0.327485	−	0.944856i	$-0.393799\pi$
$331$	1.30555e6	0.654971	0.327485	+	0.944856i	$0.393799\pi$
$332$	876619.	0.436481
$333$	−227502.	−0.112428
$334$	−373654.	−0.183275
$335$	1.42133e6	0.691961
$336$	0	0
$337$	−3.17016e6	−1.52057	−0.760285	−	0.649590i	$-0.774941\pi$
$337$	−3.17016e6	−1.52057	−0.760285	+	0.649590i	$0.774941\pi$
$338$	813739.	0.387430
$339$	1.61328e6	0.762450
$340$	−4.05196e6	−1.90094
$341$	−4.60060e6	−2.14254
$342$	−1.04087e6	−0.481207
$343$	0	0
$344$	3.97263e6	1.81002
$345$	2.08392e6	0.942615
$346$	−453889.	−0.203826
$347$	−1.71592e6	−0.765019	−0.382510	−	0.923951i	$-0.624940\pi$
$347$	−1.71592e6	−0.765019	−0.382510	+	0.923951i	$0.624940\pi$
$348$	380892.	0.168598
$349$	−2.95822e6	−1.30007	−0.650034	−	0.759905i	$-0.725245\pi$
$349$	−2.95822e6	−1.30007	−0.650034	+	0.759905i	$0.725245\pi$
$350$	0	0
$351$	−388928.	−0.168501
$352$	−2.31529e6	−0.995976
$353$	3.76980e6	1.61021	0.805103	−	0.593135i	$-0.202110\pi$
$353$	3.76980e6	1.61021	0.805103	+	0.593135i	$0.202110\pi$
$354$	−875182.	−0.371185
$355$	−4.45620e6	−1.87669
$356$	765890.	0.320289
$357$	0	0
$358$	1.34191e6	0.553371
$359$	1.92987e6	0.790300	0.395150	−	0.918617i	$-0.370693\pi$
$359$	1.92987e6	0.790300	0.395150	+	0.918617i	$0.370693\pi$
$360$	1.31859e6	0.536232
$361$	−603234.	−0.243623
$362$	725323.	0.290911
$363$	−1.37909e6	−0.549323
$364$	0	0
$365$	−1.94455e6	−0.763988
$366$	80636.5	0.0314651
$367$	2.36742e6	0.917509	0.458754	−	0.888563i	$-0.348296\pi$
$367$	2.36742e6	0.917509	0.458754	+	0.888563i	$0.348296\pi$
$368$	1.07688e6	0.414521
$369$	19912.0	0.00761289
$370$	−1.89171e6	−0.718373
$371$	0	0
$372$	−4.14856e6	−1.55432
$373$	3.53829e6	1.31680	0.658402	−	0.752666i	$-0.271233\pi$
$373$	3.53829e6	1.31680	0.658402	+	0.752666i	$0.271233\pi$
$374$	5.29406e6	1.95709
$375$	−713307.	−0.261938
$376$	3.70960e6	1.35318
$377$	−401975.	−0.145662
$378$	0	0
$379$	1.79847e6	0.643139	0.321569	−	0.946886i	$-0.395790\pi$
$379$	1.79847e6	0.643139	0.321569	+	0.946886i	$0.395790\pi$
$380$	−5.51378e6	−1.95880
$381$	1.29307e6	0.456361
$382$	−2.55455e6	−0.895686
$383$	2.60815e6	0.908521	0.454261	−	0.890869i	$-0.349904\pi$
$383$	2.60815e6	0.908521	0.454261	+	0.890869i	$0.349904\pi$
$384$	−2.98994e6	−1.03475
$385$	0	0
$386$	150555.	0.0514313
$387$	−1.41786e6	−0.481235
$388$	−725683.	−0.244719
$389$	−2.82995e6	−0.948211	−0.474106	−	0.880468i	$-0.657228\pi$
$389$	−2.82995e6	−0.948211	−0.474106	+	0.880468i	$0.657228\pi$
$390$	−3.23399e6	−1.07666
$391$	3.24648e6	1.07392
$392$	0	0
$393$	−470609.	−0.153702
$394$	−9.69299e6	−3.14570
$395$	−3.20538e6	−1.03368
$396$	−2.55063e6	−0.817352
$397$	−2.43062e6	−0.773999	−0.387000	−	0.922080i	$-0.626489\pi$
$397$	−2.43062e6	−0.773999	−0.387000	+	0.922080i	$0.626489\pi$
$398$	8.27939e6	2.61993
$399$	0	0
$400$	673885.	0.210589
$401$	−2.43184e6	−0.755222	−0.377611	−	0.925964i	$-0.623254\pi$
$401$	−2.43184e6	−0.755222	−0.377611	+	0.925964i	$0.623254\pi$
$402$	−1.67456e6	−0.516815
$403$	4.37820e6	1.34287
$404$	1.41227e6	0.430491
$405$	−470614.	−0.142570
$406$	0	0
$407$	1.57457e6	0.471167
$408$	2.05419e6	0.610927
$409$	−4.77466e6	−1.41135	−0.705674	−	0.708537i	$-0.749356\pi$
$409$	−4.77466e6	−1.41135	−0.705674	+	0.708537i	$0.749356\pi$
$410$	165571.	0.0486436
$411$	−84690.9	−0.0247305
$412$	−9.02944e6	−2.62070
$413$	0	0
$414$	−2.45521e6	−0.704024
$415$	−1.11945e6	−0.319069
$416$	2.20336e6	0.624242
$417$	−1.64785e6	−0.464063
$418$	7.20400e6	2.01666
$419$	−457181.	−0.127219	−0.0636097	−	0.997975i	$-0.520261\pi$
$419$	−457181.	−0.127219	−0.0636097	+	0.997975i	$0.520261\pi$
$420$	0	0
$421$	−1.82396e6	−0.501545	−0.250773	−	0.968046i	$-0.580685\pi$
$421$	−1.82396e6	−0.501545	−0.250773	+	0.968046i	$0.580685\pi$
$422$	3.50066e6	0.956905
$423$	−1.32398e6	−0.359776
$424$	6.72715e6	1.81726
$425$	2.03157e6	0.545582
$426$	5.25014e6	1.40167
$427$	0	0
$428$	−5.30104e6	−1.39879
$429$	2.69181e6	0.706158
$430$	−1.17897e7	−3.07492
$431$	−3.38249e6	−0.877087	−0.438544	−	0.898710i	$-0.644506\pi$
$431$	−3.38249e6	−0.877087	−0.438544	+	0.898710i	$0.644506\pi$
$432$	−243192.	−0.0626960
$433$	−285266.	−0.0731190	−0.0365595	−	0.999331i	$-0.511640\pi$
$433$	−285266.	−0.0731190	−0.0365595	+	0.999331i	$0.511640\pi$
$434$	0	0
$435$	−486402.	−0.123246
$436$	−4.68418e6	−1.18010
$437$	4.41771e6	1.10661
$438$	2.29100e6	0.570611
$439$	4.35220e6	1.07782	0.538911	−	0.842363i	$-0.318836\pi$
$439$	4.35220e6	1.07782	0.538911	+	0.842363i	$0.318836\pi$
$440$	−9.12610e6	−2.24726
$441$	0	0
$442$	−5.03813e6	−1.22663
$443$	−5.10560e6	−1.23605	−0.618027	−	0.786157i	$-0.712068\pi$
$443$	−5.10560e6	−1.23605	−0.618027	+	0.786157i	$0.712068\pi$
$444$	1.41985e6	0.341811
$445$	−978049.	−0.234132
$446$	1.01603e7	2.41862
$447$	1.50301e6	0.355790
$448$	0	0
$449$	3.04163e6	0.712016	0.356008	−	0.934483i	$-0.384138\pi$
$449$	3.04163e6	0.712016	0.356008	+	0.934483i	$0.384138\pi$
$450$	−1.53642e6	−0.357666
$451$	−137813.	−0.0319043
$452$	−1.00686e7	−2.31805
$453$	−3.38638e6	−0.775336
$454$	−5.19305e6	−1.18245
$455$	0	0
$456$	2.79528e6	0.629524
$457$	−1.74432e6	−0.390694	−0.195347	−	0.980734i	$-0.562583\pi$
$457$	−1.74432e6	−0.390694	−0.195347	+	0.980734i	$0.562583\pi$
$458$	−4.91113e6	−1.09400
$459$	−733156.	−0.162429
$460$	−1.30059e7	−2.86580
$461$	−6.85701e6	−1.50273	−0.751367	−	0.659884i	$-0.770605\pi$
$461$	−6.85701e6	−1.50273	−0.751367	+	0.659884i	$0.770605\pi$
$462$	0	0
$463$	5.13844e6	1.11398	0.556992	−	0.830518i	$-0.311955\pi$
$463$	5.13844e6	1.11398	0.556992	+	0.830518i	$0.311955\pi$
$464$	−251351.	−0.0541982
$465$	5.29775e6	1.13621
$466$	3.41961e6	0.729477
$467$	−4.58171e6	−0.972154	−0.486077	−	0.873916i	$-0.661573\pi$
$467$	−4.58171e6	−0.972154	−0.486077	+	0.873916i	$0.661573\pi$
$468$	2.42733e6	0.512287
$469$	0	0
$470$	−1.10091e7	−2.29883
$471$	−351675.	−0.0730448
$472$	2.35031e6	0.485591
$473$	9.81320e6	2.01678
$474$	3.77647e6	0.772042
$475$	2.76450e6	0.562190
$476$	0	0
$477$	−2.40097e6	−0.483161
$478$	−3.49154e6	−0.698952
$479$	−288523.	−0.0574568	−0.0287284	−	0.999587i	$-0.509146\pi$
$479$	−288523.	−0.0574568	−0.0287284	+	0.999587i	$0.509146\pi$
$480$	2.66614e6	0.528177
$481$	−1.49845e6	−0.295310
$482$	1.60705e7	3.15074
$483$	0	0
$484$	8.60702e6	1.67009
$485$	926703.	0.178890
$486$	554462.	0.106483
$487$	−7.81685e6	−1.49351	−0.746757	−	0.665097i	$-0.768390\pi$
$487$	−7.81685e6	−1.49351	−0.746757	+	0.665097i	$0.768390\pi$
$488$	−216550.	−0.0411632
$489$	4.30127e6	0.813438
$490$	0	0
$491$	3.14467e6	0.588669	0.294335	−	0.955702i	$-0.404902\pi$
$491$	3.14467e6	0.588669	0.294335	+	0.955702i	$0.404902\pi$
$492$	−124272.	−0.0231452
$493$	−757751.	−0.140414
$494$	−6.85574e6	−1.26397
$495$	3.25718e6	0.597487
$496$	2.73763e6	0.499656
$497$	0	0
$498$	1.31890e6	0.238308
$499$	6.72563e6	1.20915	0.604577	−	0.796547i	$-0.293342\pi$
$499$	6.72563e6	1.20915	0.604577	+	0.796547i	$0.293342\pi$
$500$	4.45180e6	0.796362
$501$	−358140.	−0.0637469
$502$	−545871.	−0.0966787
$503$	−9.45056e6	−1.66547	−0.832737	−	0.553669i	$-0.813227\pi$
$503$	−9.45056e6	−1.66547	−0.832737	+	0.553669i	$0.813227\pi$
$504$	0	0
$505$	−1.80348e6	−0.314690
$506$	1.69928e7	2.95045
$507$	779952.	0.134756
$508$	−8.07011e6	−1.38746
$509$	−8.83702e6	−1.51186	−0.755930	−	0.654653i	$-0.772815\pi$
$509$	−8.83702e6	−1.51186	−0.755930	+	0.654653i	$0.772815\pi$
$510$	−6.09629e6	−1.03786
$511$	0	0
$512$	3.80044e6	0.640707
$513$	−997656.	−0.167374
$514$	2.92813e6	0.488858
$515$	1.15307e7	1.91574
$516$	8.84899e6	1.46308
$517$	9.16344e6	1.50776
$518$	0	0
$519$	−435044.	−0.0708949
$520$	8.68492e6	1.40850
$521$	694985.	0.112171	0.0560855	−	0.998426i	$-0.482138\pi$
$521$	694985.	0.112171	0.0560855	+	0.998426i	$0.482138\pi$
$522$	573063.	0.0920505
$523$	3.58210e6	0.572643	0.286321	−	0.958134i	$-0.407568\pi$
$523$	3.58210e6	0.572643	0.286321	+	0.958134i	$0.407568\pi$
$524$	2.93710e6	0.467294
$525$	0	0
$526$	−8.11252e6	−1.27847
$527$	8.25320e6	1.29448
$528$	1.68316e6	0.262749
$529$	3.98415e6	0.619009
$530$	−1.99644e7	−3.08722
$531$	−838845.	−0.129106
$532$	0	0
$533$	131151.	0.0199965
$534$	1.15230e6	0.174869
$535$	6.76947e6	1.02252
$536$	4.49705e6	0.676107
$537$	1.28620e6	0.192474
$538$	1.05231e7	1.56744
$539$	0	0
$540$	2.93714e6	0.433451
$541$	−5.16846e6	−0.759220	−0.379610	−	0.925147i	$-0.623942\pi$
$541$	−5.16846e6	−0.759220	−0.379610	+	0.925147i	$0.623942\pi$
$542$	−1.07055e7	−1.56535
$543$	695208.	0.101185
$544$	4.15349e6	0.601750
$545$	5.98174e6	0.862653
$546$	0	0
$547$	8.47489e6	1.21106	0.605530	−	0.795822i	$-0.292961\pi$
$547$	8.47489e6	1.21106	0.605530	+	0.795822i	$0.292961\pi$
$548$	528562.	0.0751873
$549$	77288.5	0.0109442
$550$	1.06337e7	1.49892
$551$	−1.03112e6	−0.144688
$552$	6.59349e6	0.921018
$553$	0	0
$554$	1.86671e7	2.58407
$555$	−1.81317e6	−0.249865
$556$	1.02843e7	1.41088
$557$	−1.04213e7	−1.42325	−0.711627	−	0.702557i	$-0.752041\pi$
$557$	−1.04213e7	−1.42325	−0.711627	+	0.702557i	$0.752041\pi$
$558$	−6.24163e6	−0.848619
$559$	−9.33880e6	−1.26404
$560$	0	0
$561$	5.07425e6	0.680714
$562$	−4.99842e6	−0.667562
$563$	−7.24077e6	−0.962751	−0.481375	−	0.876515i	$-0.659863\pi$
$563$	−7.24077e6	−0.962751	−0.481375	+	0.876515i	$0.659863\pi$
$564$	8.26307e6	1.09381
$565$	1.28577e7	1.69450
$566$	−2.46459e7	−3.23373
$567$	0	0
$568$	−1.40993e7	−1.83369
$569$	916536.	0.118678	0.0593388	−	0.998238i	$-0.481101\pi$
$569$	916536.	0.118678	0.0593388	+	0.998238i	$0.481101\pi$
$570$	−8.29565e6	−1.06946
$571$	1.00708e7	1.29262	0.646312	−	0.763073i	$-0.276311\pi$
$571$	1.00708e7	1.29262	0.646312	+	0.763073i	$0.276311\pi$
$572$	−1.67998e7	−2.14691
$573$	−2.44849e6	−0.311538
$574$	0	0
$575$	6.52091e6	0.822505
$576$	−4.00584e6	−0.503080
$577$	1.16997e7	1.46298	0.731488	−	0.681855i	$-0.238826\pi$
$577$	1.16997e7	1.46298	0.731488	+	0.681855i	$0.238826\pi$
$578$	3.83505e6	0.477475
$579$	144304.	0.0178888
$580$	3.03567e6	0.374701
$581$	0	0
$582$	−1.09181e6	−0.133610
$583$	1.66174e7	2.02485
$584$	−6.15251e6	−0.746484
$585$	−3.09972e6	−0.374483
$586$	−5.72747e6	−0.688999
$587$	−6.92367e6	−0.829357	−0.414678	−	0.909968i	$-0.636106\pi$
$587$	−6.92367e6	−0.829357	−0.414678	+	0.909968i	$0.636106\pi$
$588$	0	0
$589$	1.12307e7	1.33389
$590$	−6.97511e6	−0.824938
$591$	−9.29054e6	−1.09414
$592$	−936961.	−0.109880
$593$	1.57770e7	1.84242	0.921208	−	0.389069i	$-0.127203\pi$
$593$	1.57770e7	1.84242	0.921208	+	0.389069i	$0.127203\pi$
$594$	−3.83750e6	−0.446254
$595$	0	0
$596$	−9.38041e6	−1.08170
$597$	7.93563e6	0.911266
$598$	−1.61713e7	−1.84924
$599$	1.42708e7	1.62511	0.812553	−	0.582887i	$-0.198077\pi$
$599$	1.42708e7	1.62511	0.812553	+	0.582887i	$0.198077\pi$
$600$	4.12606e6	0.467905
$601$	7.63222e6	0.861916	0.430958	−	0.902372i	$-0.358176\pi$
$601$	7.63222e6	0.861916	0.430958	+	0.902372i	$0.358176\pi$
$602$	0	0
$603$	−1.60503e6	−0.179759
$604$	2.11346e7	2.35723
$605$	−1.09912e7	−1.22084
$606$	2.12480e6	0.235037
$607$	−3.56035e6	−0.392212	−0.196106	−	0.980583i	$-0.562830\pi$
$607$	−3.56035e6	−0.392212	−0.196106	+	0.980583i	$0.562830\pi$
$608$	5.65194e6	0.620067
$609$	0	0
$610$	642664.	0.0699294
$611$	−8.72046e6	−0.945010
$612$	4.57567e6	0.493829
$613$	−1.37284e7	−1.47560	−0.737800	−	0.675019i	$-0.764135\pi$
$613$	−1.37284e7	−1.47560	−0.737800	+	0.675019i	$0.764135\pi$
$614$	1.26616e7	1.35540
$615$	158697.	0.0169192
$616$	0	0
$617$	−6.51173e6	−0.688626	−0.344313	−	0.938855i	$-0.611888\pi$
$617$	−6.51173e6	−0.688626	−0.344313	+	0.938855i	$0.611888\pi$
$618$	−1.35851e7	−1.43084
$619$	8.85110e6	0.928476	0.464238	−	0.885711i	$-0.346328\pi$
$619$	8.85110e6	0.928476	0.464238	+	0.885711i	$0.346328\pi$
$620$	−3.30636e7	−3.45439
$621$	−2.35327e6	−0.244874
$622$	3.12739e7	3.24121
$623$	0	0
$624$	−1.60179e6	−0.164681
$625$	−1.19977e7	−1.22856
$626$	2.66363e7	2.71667
$627$	6.90489e6	0.701436
$628$	2.19483e6	0.222076
$629$	−2.82467e6	−0.284670
$630$	0	0
$631$	−6.89663e6	−0.689546	−0.344773	−	0.938686i	$-0.612044\pi$
$631$	−6.89663e6	−0.689546	−0.344773	+	0.938686i	$0.612044\pi$
$632$	−1.01418e7	−1.01000
$633$	3.35531e6	0.332831
$634$	1.02198e7	1.00977
$635$	1.03056e7	1.01424
$636$	1.49846e7	1.46894
$637$	0	0
$638$	−3.96623e6	−0.385768
$639$	5.03216e6	0.487531
$640$	−2.38295e7	−2.29967
$641$	−1.66695e7	−1.60242	−0.801210	−	0.598383i	$-0.795810\pi$
$641$	−1.66695e7	−1.60242	−0.801210	+	0.598383i	$0.795810\pi$
$642$	−7.97556e6	−0.763702
$643$	−1.28697e7	−1.22756	−0.613779	−	0.789478i	$-0.710351\pi$
$643$	−1.28697e7	−1.22756	−0.613779	+	0.789478i	$0.710351\pi$
$644$	0	0
$645$	−1.13002e7	−1.06952
$646$	−1.29235e7	−1.21843
$647$	−1.14731e7	−1.07751	−0.538754	−	0.842463i	$-0.681105\pi$
$647$	−1.14731e7	−1.07751	−0.538754	+	0.842463i	$0.681105\pi$
$648$	−1.48901e6	−0.139303
$649$	5.80574e6	0.541060
$650$	−1.01196e7	−0.939467
$651$	0	0
$652$	−2.68445e7	−2.47307
$653$	−1.31801e7	−1.20958	−0.604791	−	0.796384i	$-0.706743\pi$
$653$	−1.31801e7	−1.20958	−0.604791	+	0.796384i	$0.706743\pi$
$654$	−7.04748e6	−0.644302
$655$	−3.75070e6	−0.341593
$656$	82007.2	0.00744034
$657$	2.19588e6	0.198470
$658$	0	0
$659$	−1.13068e7	−1.01421	−0.507104	−	0.861885i	$-0.669284\pi$
$659$	−1.13068e7	−1.01421	−0.507104	+	0.861885i	$0.669284\pi$
$660$	−2.03282e7	−1.81652
$661$	2.20319e6	0.196132	0.0980661	−	0.995180i	$-0.468734\pi$
$661$	2.20319e6	0.196132	0.0980661	+	0.995180i	$0.468734\pi$
$662$	−1.22589e7	−1.08719
$663$	−4.82895e6	−0.426647
$664$	−3.54192e6	−0.311758
$665$	0	0
$666$	2.13621e6	0.186620
$667$	−2.43222e6	−0.211684
$668$	2.23518e6	0.193808
$669$	9.73843e6	0.841247
$670$	−1.33461e7	−1.14859
$671$	−534922.	−0.0458653
$672$	0	0
$673$	−1.89787e7	−1.61521	−0.807606	−	0.589723i	$-0.799237\pi$
$673$	−1.89787e7	−1.61521	−0.807606	+	0.589723i	$0.799237\pi$
$674$	2.97674e7	2.52401
$675$	−1.47262e6	−0.124403
$676$	−4.86773e6	−0.409694
$677$	−1.96475e7	−1.64754	−0.823771	−	0.566923i	$-0.808134\pi$
$677$	−1.96475e7	−1.64754	−0.823771	+	0.566923i	$0.808134\pi$
$678$	−1.51485e7	−1.26560
$679$	0	0
$680$	1.63717e7	1.35775
$681$	−4.97744e6	−0.411280
$682$	4.31990e7	3.55642
$683$	1.62705e7	1.33459	0.667295	−	0.744793i	$-0.267452\pi$
$683$	1.62705e7	1.33459	0.667295	+	0.744793i	$0.267452\pi$
$684$	6.22644e6	0.508861
$685$	−674978.	−0.0549621
$686$	0	0
$687$	−4.70722e6	−0.380515
$688$	−5.83944e6	−0.470328
$689$	−1.58141e7	−1.26910
$690$	−1.95678e7	−1.56465
$691$	1.94467e7	1.54935	0.774677	−	0.632357i	$-0.217912\pi$
$691$	1.94467e7	1.54935	0.774677	+	0.632357i	$0.217912\pi$
$692$	2.71514e6	0.215539
$693$	0	0
$694$	1.61122e7	1.26986
$695$	−1.31332e7	−1.03135
$696$	−1.53897e6	−0.120422
$697$	247229.	0.0192760
$698$	2.77772e7	2.15800
$699$	3.27763e6	0.253727
$700$	0	0
$701$	1.49625e7	1.15003	0.575014	−	0.818144i	$-0.304997\pi$
$701$	1.49625e7	1.15003	0.575014	+	0.818144i	$0.304997\pi$
$702$	3.65198e6	0.279696
$703$	−3.84373e6	−0.293335
$704$	2.77248e7	2.10832
$705$	−1.05520e7	−0.799581
$706$	−3.53979e7	−2.67280
$707$	0	0
$708$	5.23529e6	0.392516
$709$	1.58639e6	0.118521	0.0592603	−	0.998243i	$-0.481126\pi$
$709$	1.58639e6	0.118521	0.0592603	+	0.998243i	$0.481126\pi$
$710$	4.18431e7	3.11514
$711$	3.61968e6	0.268532
$712$	−3.09453e6	−0.228767
$713$	2.64910e7	1.95152
$714$	0	0
$715$	2.14535e7	1.56940
$716$	−8.02723e6	−0.585172
$717$	−3.34657e6	−0.243110
$718$	−1.81212e7	−1.31183
$719$	−1.81675e7	−1.31061	−0.655305	−	0.755364i	$-0.727460\pi$
$719$	−1.81675e7	−1.31061	−0.655305	+	0.755364i	$0.727460\pi$
$720$	−1.93822e6	−0.139338
$721$	0	0
$722$	5.66429e6	0.404392
$723$	1.54033e7	1.09589
$724$	−4.33884e6	−0.307629
$725$	−1.52203e6	−0.107542
$726$	1.29495e7	0.911826
$727$	1.26903e7	0.890506	0.445253	−	0.895405i	$-0.353114\pi$
$727$	1.26903e7	0.890506	0.445253	+	0.895405i	$0.353114\pi$
$728$	0	0
$729$	531441.	0.0370370
$730$	1.82591e7	1.26815
$731$	−1.76043e7	−1.21850
$732$	−482362.	−0.0332733
$733$	−3.11401e6	−0.214072	−0.107036	−	0.994255i	$-0.534136\pi$
$733$	−3.11401e6	−0.214072	−0.107036	+	0.994255i	$0.534136\pi$
$734$	−2.22298e7	−1.52298
$735$	0	0
$736$	1.33318e7	0.907182
$737$	1.11086e7	0.753339
$738$	−186971.	−0.0126367
$739$	9.09899e6	0.612890	0.306445	−	0.951888i	$-0.400861\pi$
$739$	9.09899e6	0.612890	0.306445	+	0.951888i	$0.400861\pi$
$740$	1.13161e7	0.759656
$741$	−6.57109e6	−0.439634
$742$	0	0
$743$	−8.79218e6	−0.584285	−0.292142	−	0.956375i	$-0.594368\pi$
$743$	−8.79218e6	−0.584285	−0.292142	+	0.956375i	$0.594368\pi$
$744$	1.67620e7	1.11018
$745$	1.19789e7	0.790724
$746$	−3.32241e7	−2.18578
$747$	1.26414e6	0.0828883
$748$	−3.16687e7	−2.06955
$749$	0	0
$750$	6.69786e6	0.434793
$751$	−2.80918e7	−1.81752	−0.908759	−	0.417320i	$-0.862969\pi$
$751$	−2.80918e7	−1.81752	−0.908759	+	0.417320i	$0.862969\pi$
$752$	−5.45280e6	−0.351621
$753$	−523207.	−0.0336268
$754$	3.77450e6	0.241786
$755$	−2.69891e7	−1.72314
$756$	0	0
$757$	−4.18815e6	−0.265634	−0.132817	−	0.991141i	$-0.542402\pi$
$757$	−4.18815e6	−0.265634	−0.132817	+	0.991141i	$0.542402\pi$
$758$	−1.68874e7	−1.06755
$759$	1.62872e7	1.02623
$760$	2.22781e7	1.39908
$761$	−393182.	−0.0246111	−0.0123056	−	0.999924i	$-0.503917\pi$
$761$	−393182.	−0.0246111	−0.0123056	+	0.999924i	$0.503917\pi$
$762$	−1.21417e7	−0.757518
$763$	0	0
$764$	1.52812e7	0.947159
$765$	−5.84317e6	−0.360990
$766$	−2.44901e7	−1.50806
$767$	−5.52508e6	−0.339117
$768$	1.38321e7	0.846226
$769$	1.57517e7	0.960530	0.480265	−	0.877124i	$-0.340541\pi$
$769$	1.57517e7	0.960530	0.480265	+	0.877124i	$0.340541\pi$
$770$	0	0
$771$	2.80655e6	0.170035
$772$	−900611.	−0.0543869
$773$	2.88472e6	0.173642	0.0868210	−	0.996224i	$-0.472329\pi$
$773$	2.88472e6	0.173642	0.0868210	+	0.996224i	$0.472329\pi$
$774$	1.33136e7	0.798807
$775$	1.65775e7	0.991433
$776$	2.93207e6	0.174791
$777$	0	0
$778$	2.65729e7	1.57394
$779$	336421.	0.0198628
$780$	1.93455e7	1.13853
$781$	−3.48281e7	−2.04316
$782$	−3.04840e7	−1.78261
$783$	549269.	0.0320170
$784$	0	0
$785$	−2.80281e6	−0.162338
$786$	4.41895e6	0.255131
$787$	−2.97866e7	−1.71429	−0.857145	−	0.515076i	$-0.827764\pi$
$787$	−2.97866e7	−1.71429	−0.857145	+	0.515076i	$0.827764\pi$
$788$	5.79829e7	3.32647
$789$	−7.77569e6	−0.444679
$790$	3.00981e7	1.71582
$791$	0	0
$792$	1.03056e7	0.583797
$793$	509063.	0.0287467
$794$	2.28232e7	1.28477
$795$	−1.91355e7	−1.07380
$796$	−4.95268e7	−2.77049
$797$	8.11321e6	0.452425	0.226213	−	0.974078i	$-0.427366\pi$
$797$	8.11321e6	0.452425	0.226213	+	0.974078i	$0.427366\pi$
$798$	0	0
$799$	−1.64387e7	−0.910960
$800$	8.34274e6	0.460876
$801$	1.10446e6	0.0608232
$802$	2.28347e7	1.25360
$803$	−1.51979e7	−0.831756
$804$	1.00171e7	0.546515
$805$	0	0
$806$	−4.11107e7	−2.22904
$807$	1.00862e7	0.545186
$808$	−5.70617e6	−0.307480
$809$	111597.	0.00599489	0.00299744	−	0.999996i	$-0.499046\pi$
$809$	111597.	0.00599489	0.00299744	+	0.999996i	$0.499046\pi$
$810$	4.41901e6	0.236653
$811$	−209250.	−0.0111716	−0.00558578	−	0.999984i	$-0.501778\pi$
$811$	−209250.	−0.0111716	−0.00558578	+	0.999984i	$0.501778\pi$
$812$	0	0
$813$	−1.02610e7	−0.544459
$814$	−1.47850e7	−0.782094
$815$	3.42807e7	1.80782
$816$	−3.01949e6	−0.158748
$817$	−2.39554e7	−1.25559
$818$	4.48334e7	2.34271
$819$	0	0
$820$	−990437.	−0.0514390
$821$	6.84614e6	0.354477	0.177238	−	0.984168i	$-0.443284\pi$
$821$	6.84614e6	0.354477	0.177238	+	0.984168i	$0.443284\pi$
$822$	795237.	0.0410503
$823$	−5.61210e6	−0.288819	−0.144409	−	0.989518i	$-0.546128\pi$
$823$	−5.61210e6	−0.288819	−0.144409	+	0.989518i	$0.546128\pi$
$824$	3.64828e7	1.87185
$825$	1.01922e7	0.521354
$826$	0	0
$827$	−2.15868e7	−1.09755	−0.548776	−	0.835969i	$-0.684906\pi$
$827$	−2.15868e7	−1.09755	−0.548776	+	0.835969i	$0.684906\pi$
$828$	1.46869e7	0.744483
$829$	1.92427e7	0.972478	0.486239	−	0.873826i	$-0.338368\pi$
$829$	1.92427e7	0.972478	0.486239	+	0.873826i	$0.338368\pi$
$830$	1.05115e7	0.529625
$831$	1.78921e7	0.898790
$832$	−2.63846e7	−1.32142
$833$	0	0
$834$	1.54731e7	0.770303
$835$	−2.85434e6	−0.141674
$836$	−4.30939e7	−2.13255
$837$	−5.98248e6	−0.295167
$838$	4.29287e6	0.211173
$839$	2.47678e7	1.21474	0.607369	−	0.794420i	$-0.292225\pi$
$839$	2.47678e7	1.21474	0.607369	+	0.794420i	$0.292225\pi$
$840$	0	0
$841$	−1.99435e7	−0.972323
$842$	1.71267e7	0.832520
$843$	−4.79089e6	−0.232192
$844$	−2.09407e7	−1.01190
$845$	6.21614e6	0.299488
$846$	1.24320e7	0.597195
$847$	0	0
$848$	−9.88836e6	−0.472210
$849$	−2.36226e7	−1.12476
$850$	−1.90762e7	−0.905618
$851$	−9.06659e6	−0.429161
$852$	−3.14060e7	−1.48222
$853$	−2.91267e7	−1.37062	−0.685312	−	0.728250i	$-0.740334\pi$
$853$	−2.91267e7	−1.37062	−0.685312	+	0.728250i	$0.740334\pi$
$854$	0	0
$855$	−7.95121e6	−0.371979
$856$	2.14185e7	0.999088
$857$	−3.22586e6	−0.150035	−0.0750175	−	0.997182i	$-0.523901\pi$
$857$	−3.22586e6	−0.150035	−0.0750175	+	0.997182i	$0.523901\pi$
$858$	−2.52758e7	−1.17216
$859$	2.64671e7	1.22384	0.611918	−	0.790921i	$-0.290398\pi$
$859$	2.64671e7	1.22384	0.611918	+	0.790921i	$0.290398\pi$
$860$	7.05255e7	3.25162
$861$	0	0
$862$	3.17611e7	1.45589
$863$	1.58510e7	0.724487	0.362243	−	0.932084i	$-0.382011\pi$
$863$	1.58510e7	0.724487	0.362243	+	0.932084i	$0.382011\pi$
$864$	−3.01073e6	−0.137211
$865$	−3.46726e6	−0.157560
$866$	2.67861e6	0.121371
$867$	3.67582e6	0.166076
$868$	0	0
$869$	−2.50522e7	−1.12537
$870$	4.56725e6	0.204577
$871$	−1.05716e7	−0.472166
$872$	1.89261e7	0.842888
$873$	−1.04648e6	−0.0464724
$874$	−4.14817e7	−1.83687
$875$	0	0
$876$	−1.37046e7	−0.603403
$877$	−1.49132e7	−0.654743	−0.327372	−	0.944896i	$-0.606163\pi$
$877$	−1.49132e7	−0.654743	−0.327372	+	0.944896i	$0.606163\pi$
$878$	−4.08665e7	−1.78909
$879$	−5.48966e6	−0.239648
$880$	1.34146e7	0.583944
$881$	−3.70679e7	−1.60901	−0.804504	−	0.593947i	$-0.797569\pi$
$881$	−3.70679e7	−1.60901	−0.804504	+	0.593947i	$0.797569\pi$
$882$	0	0
$883$	1.50440e7	0.649325	0.324663	−	0.945830i	$-0.394749\pi$
$883$	1.50440e7	0.649325	0.324663	+	0.945830i	$0.394749\pi$
$884$	3.01378e7	1.29712
$885$	−6.68551e6	−0.286930
$886$	4.79409e7	2.05174
$887$	1.78101e7	0.760075	0.380038	−	0.924971i	$-0.375911\pi$
$887$	1.78101e7	0.760075	0.380038	+	0.924971i	$0.375911\pi$
$888$	−5.73682e6	−0.244140
$889$	0	0
$890$	9.18375e6	0.388638
$891$	−3.67816e6	−0.155216
$892$	−6.07782e7	−2.55762
$893$	−2.23692e7	−0.938690
$894$	−1.41131e7	−0.590580
$895$	1.02508e7	0.427762
$896$	0	0
$897$	−1.54999e7	−0.643202
$898$	−2.85605e7	−1.18188
$899$	−6.18317e6	−0.255160
$900$	9.19074e6	0.378220
$901$	−2.98106e7	−1.22337
$902$	1.29405e6	0.0529583
$903$	0	0
$904$	4.06815e7	1.65568
$905$	5.54073e6	0.224877
$906$	3.17977e7	1.28699
$907$	−1.16936e6	−0.0471987	−0.0235993	−	0.999721i	$-0.507513\pi$
$907$	−1.16936e6	−0.0471987	−0.0235993	+	0.999721i	$0.507513\pi$
$908$	3.10645e7	1.25040
$909$	2.03658e6	0.0817506
$910$	0	0
$911$	2.74389e7	1.09539	0.547697	−	0.836677i	$-0.315505\pi$
$911$	2.74389e7	1.09539	0.547697	+	0.836677i	$0.315505\pi$
$912$	−4.10882e6	−0.163580
$913$	−8.74924e6	−0.347371
$914$	1.63790e7	0.648516
$915$	615981.	0.0243229
$916$	2.93781e7	1.15687
$917$	0	0
$918$	6.88423e6	0.269618
$919$	1.10218e7	0.430492	0.215246	−	0.976560i	$-0.430945\pi$
$919$	1.10218e7	0.430492	0.215246	+	0.976560i	$0.430945\pi$
$920$	5.25495e7	2.04691
$921$	1.21359e7	0.471436
$922$	6.43864e7	2.49440
$923$	3.31444e7	1.28058
$924$	0	0
$925$	−5.67367e6	−0.218027
$926$	−4.82493e7	−1.84911
$927$	−1.30210e7	−0.497674
$928$	−3.11173e6	−0.118613
$929$	4.25051e6	0.161585	0.0807927	−	0.996731i	$-0.474255\pi$
$929$	4.25051e6	0.161585	0.0807927	+	0.996731i	$0.474255\pi$
$930$	−4.97452e7	−1.88601
$931$	0	0
$932$	−2.04559e7	−0.771398
$933$	2.99755e7	1.12736
$934$	4.30216e7	1.61369
$935$	4.04413e7	1.51285
$936$	−9.80744e6	−0.365903
$937$	3.75738e7	1.39809	0.699046	−	0.715077i	$-0.253608\pi$
$937$	3.75738e7	1.39809	0.699046	+	0.715077i	$0.253608\pi$
$938$	0	0
$939$	2.55303e7	0.944915
$940$	6.58558e7	2.43094
$941$	6.87043e6	0.252936	0.126468	−	0.991971i	$-0.459636\pi$
$941$	6.87043e6	0.252936	0.126468	+	0.991971i	$0.459636\pi$
$942$	3.30218e6	0.121248
$943$	793550.	0.0290600
$944$	−3.45476e6	−0.126179
$945$	0	0
$946$	−9.21446e7	−3.34767
$947$	−2.30923e7	−0.836744	−0.418372	−	0.908276i	$-0.637399\pi$
$947$	−2.30923e7	−0.836744	−0.418372	+	0.908276i	$0.637399\pi$
$948$	−2.25906e7	−0.816409
$949$	1.44632e7	0.521314
$950$	−2.59583e7	−0.933185
$951$	9.79551e6	0.351217
$952$	0	0
$953$	−2.95399e7	−1.05360	−0.526802	−	0.849988i	$-0.676609\pi$
$953$	−2.95399e7	−1.05360	−0.526802	+	0.849988i	$0.676609\pi$
$954$	2.25448e7	0.802003
$955$	−1.95142e7	−0.692376
$956$	2.08862e7	0.739119
$957$	−3.80156e6	−0.134178
$958$	2.70919e6	0.0953730
$959$	0	0
$960$	−3.19261e7	−1.11807
$961$	3.87161e7	1.35233
$962$	1.40702e7	0.490188
$963$	−7.64442e6	−0.265631
$964$	−9.61329e7	−3.33180
$965$	1.15009e6	0.0397569
$966$	0	0
$967$	1.49151e7	0.512931	0.256466	−	0.966553i	$-0.417442\pi$
$967$	1.49151e7	0.512931	0.256466	+	0.966553i	$0.417442\pi$
$968$	−3.47761e7	−1.19287
$969$	−1.23869e7	−0.423794
$970$	−8.70162e6	−0.296941
$971$	1.54830e7	0.526995	0.263498	−	0.964660i	$-0.415124\pi$
$971$	1.54830e7	0.526995	0.263498	+	0.964660i	$0.415124\pi$
$972$	−3.31676e6	−0.112603
$973$	0	0
$974$	7.33992e7	2.47910
$975$	−9.69947e6	−0.326766
$976$	318311.	0.0106961
$977$	−2.83428e7	−0.949961	−0.474980	−	0.879996i	$-0.657545\pi$
$977$	−2.83428e7	−0.949961	−0.474980	+	0.879996i	$0.657545\pi$
$978$	−4.03884e7	−1.35023
$979$	−7.64410e6	−0.254900
$980$	0	0
$981$	−6.75487e6	−0.224101
$982$	−2.95280e7	−0.977138
$983$	2.56993e7	0.848278	0.424139	−	0.905597i	$-0.360577\pi$
$983$	2.56993e7	0.848278	0.424139	+	0.905597i	$0.360577\pi$
$984$	502113.	0.0165316
$985$	−7.40446e7	−2.43166
$986$	7.11518e6	0.233074
$987$	0	0
$988$	4.10106e7	1.33661
$989$	−5.65059e7	−1.83697
$990$	−3.05844e7	−0.991774
$991$	4.46405e7	1.44392	0.721962	−	0.691933i	$-0.243240\pi$
$991$	4.46405e7	1.44392	0.721962	+	0.691933i	$0.243240\pi$
$992$	3.38921e7	1.09350
$993$	−1.17499e7	−0.378148
$994$	0	0
$995$	6.32461e7	2.02524
$996$	−7.88957e6	−0.252003
$997$	2.30554e7	0.734572	0.367286	−	0.930108i	$-0.380287\pi$
$997$	2.30554e7	0.734572	0.367286	+	0.930108i	$0.380287\pi$
$998$	−6.31528e7	−2.00709
$999$	2.04752e6	0.0649103

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	147.6.a.i.1.1		2
3.2	odd	2		441.6.a.t.1.2		2
7.2	even	3		21.6.e.b.4.2	✓	4
7.3	odd	6		147.6.e.l.79.2		4
7.4	even	3		21.6.e.b.16.2	yes	4
7.5	odd	6		147.6.e.l.67.2		4
7.6	odd	2		147.6.a.k.1.1		2
21.2	odd	6		63.6.e.c.46.1		4
21.11	odd	6		63.6.e.c.37.1		4
21.20	even	2		441.6.a.s.1.2		2
28.11	odd	6		336.6.q.e.289.2		4
28.23	odd	6		336.6.q.e.193.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
21.6.e.b.4.2	✓	4	7.2	even	3
21.6.e.b.16.2	yes	4	7.4	even	3
63.6.e.c.37.1		4	21.11	odd	6
63.6.e.c.46.1		4	21.2	odd	6
147.6.a.i.1.1		2	1.1	even	1	trivial
147.6.a.k.1.1		2	7.6	odd	2
147.6.e.l.67.2		4	7.5	odd	6
147.6.e.l.79.2		4	7.3	odd	6
336.6.q.e.193.2		4	28.23	odd	6
336.6.q.e.289.2		4	28.11	odd	6
441.6.a.s.1.2		2	21.20	even	2
441.6.a.t.1.2		2	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)

\(f(q)\)	\(=\)	\(q-9.38987 q^{2} -9.00000 q^{3} +56.1696 q^{4} -71.7291 q^{5} +84.5088 q^{6} -226.949 q^{8} +81.0000 q^{9} +O(q^{10})\)	\(q-9.38987 q^{2} -9.00000 q^{3} +56.1696 q^{4} -71.7291 q^{5} +84.5088 q^{6} -226.949 q^{8} +81.0000 q^{9} +673.526 q^{10} -560.610 q^{11} -505.526 q^{12} +533.509 q^{13} +645.562 q^{15} +333.597 q^{16} +1005.70 q^{17} -760.579 q^{18} +1368.53 q^{19} -4028.99 q^{20} +5264.05 q^{22} +3228.08 q^{23} +2042.54 q^{24} +2020.06 q^{25} -5009.58 q^{26} -729.000 q^{27} -753.456 q^{29} -6061.74 q^{30} +8206.42 q^{31} +4129.95 q^{32} +5045.49 q^{33} -9443.39 q^{34} +4549.74 q^{36} -2808.66 q^{37} -12850.3 q^{38} -4801.58 q^{39} +16278.9 q^{40} +245.827 q^{41} -17504.5 q^{43} -31489.2 q^{44} -5810.05 q^{45} -30311.2 q^{46} -16345.5 q^{47} -3002.37 q^{48} -18968.1 q^{50} -9051.30 q^{51} +29967.0 q^{52} -29641.7 q^{53} +6845.21 q^{54} +40212.0 q^{55} -12316.7 q^{57} +7074.85 q^{58} -10356.1 q^{59} +36260.9 q^{60} +954.179 q^{61} -77057.2 q^{62} -49454.8 q^{64} -38268.1 q^{65} -47376.5 q^{66} -19815.2 q^{67} +56489.8 q^{68} -29052.7 q^{69} +62125.4 q^{71} -18382.9 q^{72} +27109.6 q^{73} +26373.0 q^{74} -18180.5 q^{75} +76869.6 q^{76} +45086.2 q^{78} +44687.4 q^{79} -23928.6 q^{80} +6561.00 q^{81} -2308.29 q^{82} +15606.6 q^{83} -72137.9 q^{85} +164365. q^{86} +6781.10 q^{87} +127230. q^{88} +13635.3 q^{89} +54555.6 q^{90} +181320. q^{92} -73857.8 q^{93} +153482. q^{94} -98163.1 q^{95} -37169.5 q^{96} -12919.5 q^{97} -45409.4 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 3 q^{2} - 18 q^{3} + 65 q^{4} - 33 q^{5} + 27 q^{6} - 375 q^{8} + 162 q^{9}+O(q^{10}) \) 2 * q - 3 * q^2 - 18 * q^3 + 65 * q^4 - 33 * q^5 + 27 * q^6 - 375 * q^8 + 162 * q^9	\( 2 q - 3 q^{2} - 18 q^{3} + 65 q^{4} - 33 q^{5} + 27 q^{6} - 375 q^{8} + 162 q^{9} + 921 q^{10} - 1137 q^{11} - 585 q^{12} + 925 q^{13} + 297 q^{15} - 895 q^{16} - 324 q^{17} - 243 q^{18} + 2311 q^{19} - 3687 q^{20} + 1581 q^{22} + 1596 q^{23} + 3375 q^{24} + 395 q^{25} - 2508 q^{26} - 1458 q^{27} - 2217 q^{29} - 8289 q^{30} + 4294 q^{31} + 1017 q^{32} + 10233 q^{33} - 17940 q^{34} + 5265 q^{36} - 19109 q^{37} - 6828 q^{38} - 8325 q^{39} + 10545 q^{40} - 12858 q^{41} - 2771 q^{43} - 36579 q^{44} - 2673 q^{45} - 40740 q^{46} - 23160 q^{47} + 8055 q^{48} - 29352 q^{50} + 2916 q^{51} + 33424 q^{52} - 31653 q^{53} + 2187 q^{54} + 17889 q^{55} - 20799 q^{57} - 2277 q^{58} + 41097 q^{59} + 33183 q^{60} + 42052 q^{61} - 102057 q^{62} - 30031 q^{64} - 23106 q^{65} - 14229 q^{66} + 30763 q^{67} + 44748 q^{68} - 14364 q^{69} + 102096 q^{71} - 30375 q^{72} - 28577 q^{73} - 77784 q^{74} - 3555 q^{75} + 85192 q^{76} + 22572 q^{78} - 18464 q^{79} - 71511 q^{80} + 13122 q^{81} - 86040 q^{82} + 61179 q^{83} - 123636 q^{85} + 258510 q^{86} + 19953 q^{87} + 212565 q^{88} + 29322 q^{89} + 74601 q^{90} + 166908 q^{92} - 38646 q^{93} + 109938 q^{94} - 61662 q^{95} - 9153 q^{96} - 9791 q^{97} - 92097 q^{99}+O(q^{100}) \) 2 * q - 3 * q^2 - 18 * q^3 + 65 * q^4 - 33 * q^5 + 27 * q^6 - 375 * q^8 + 162 * q^9 + 921 * q^10 - 1137 * q^11 - 585 * q^12 + 925 * q^13 + 297 * q^15 - 895 * q^16 - 324 * q^17 - 243 * q^18 + 2311 * q^19 - 3687 * q^20 + 1581 * q^22 + 1596 * q^23 + 3375 * q^24 + 395 * q^25 - 2508 * q^26 - 1458 * q^27 - 2217 * q^29 - 8289 * q^30 + 4294 * q^31 + 1017 * q^32 + 10233 * q^33 - 17940 * q^34 + 5265 * q^36 - 19109 * q^37 - 6828 * q^38 - 8325 * q^39 + 10545 * q^40 - 12858 * q^41 - 2771 * q^43 - 36579 * q^44 - 2673 * q^45 - 40740 * q^46 - 23160 * q^47 + 8055 * q^48 - 29352 * q^50 + 2916 * q^51 + 33424 * q^52 - 31653 * q^53 + 2187 * q^54 + 17889 * q^55 - 20799 * q^57 - 2277 * q^58 + 41097 * q^59 + 33183 * q^60 + 42052 * q^61 - 102057 * q^62 - 30031 * q^64 - 23106 * q^65 - 14229 * q^66 + 30763 * q^67 + 44748 * q^68 - 14364 * q^69 + 102096 * q^71 - 30375 * q^72 - 28577 * q^73 - 77784 * q^74 - 3555 * q^75 + 85192 * q^76 + 22572 * q^78 - 18464 * q^79 - 71511 * q^80 + 13122 * q^81 - 86040 * q^82 + 61179 * q^83 - 123636 * q^85 + 258510 * q^86 + 19953 * q^87 + 212565 * q^88 + 29322 * q^89 + 74601 * q^90 + 166908 * q^92 - 38646 * q^93 + 109938 * q^94 - 61662 * q^95 - 9153 * q^96 - 9791 * q^97 - 92097 * q^99

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