LMFDB - Embedded newform 387.8.a.a.1.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [387,8,Mod(1,387)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(387, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 8, names="a")

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

chi := DirichletCharacter("387.1");

S:= CuspForms(chi, 8);

N := Newforms(S);

Level:	$ N $	$=$	$ 387 = 3^{2} \cdot 43 $
Weight:	$ k $	$=$	$ 8 $
Character orbit:	$[\chi]$	$=$	387.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:	$120.893004862$
Analytic rank:	$1$
Dimension:	$10$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - x^{9} - 825 x^{8} + 431 x^{7} + 229838 x^{6} - 1804 x^{5} - 25242488 x^{4} - 2085744 x^{3} + \cdots - 5193030528 $ x^10 - x^9 - 825x^8 + 431x^7 + 229838x^6 - 1804x^5 - 25242488x^4 - 2085744x^3 + 933060896x^2 - 813446208x - 5193030528
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{5}\cdot 3^{2} $
Twist minimal:	no (minimal twist has level 129)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Root			$-10.1422$ of defining polynomial
Character	$\chi$	$=$	387.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-10.1422 q^{2} -25.1352 q^{4} -212.535 q^{5} -1278.88 q^{7} +1553.13 q^{8} +O(q^{10})$	\(q-10.1422 q^{2} -25.1352 q^{4} -212.535 q^{5} -1278.88 q^{7} +1553.13 q^{8} +2155.58 q^{10} -4362.71 q^{11} +1602.74 q^{13} +12970.7 q^{14} -12534.9 q^{16} +7659.58 q^{17} -52261.4 q^{19} +5342.12 q^{20} +44247.6 q^{22} +88943.8 q^{23} -32953.7 q^{25} -16255.4 q^{26} +32144.9 q^{28} +14383.9 q^{29} +28175.3 q^{31} -71668.9 q^{32} -77685.2 q^{34} +271808. q^{35} +260059. q^{37} +530047. q^{38} -330095. q^{40} +458326. q^{41} -79507.0 q^{43} +109657. q^{44} -902088. q^{46} +933763. q^{47} +811997. q^{49} +334224. q^{50} -40285.2 q^{52} +366609. q^{53} +927230. q^{55} -1.98627e6 q^{56} -145885. q^{58} -1.97834e6 q^{59} -701063. q^{61} -285761. q^{62} +2.33135e6 q^{64} -340640. q^{65} -392739. q^{67} -192525. q^{68} -2.75674e6 q^{70} +5.39266e6 q^{71} +2.17341e6 q^{73} -2.63758e6 q^{74} +1.31360e6 q^{76} +5.57939e6 q^{77} +826842. q^{79} +2.66411e6 q^{80} -4.64845e6 q^{82} +527990. q^{83} -1.62793e6 q^{85} +806378. q^{86} -6.77586e6 q^{88} -6.33239e6 q^{89} -2.04972e6 q^{91} -2.23562e6 q^{92} -9.47044e6 q^{94} +1.11074e7 q^{95} -1.17279e6 q^{97} -8.23546e6 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q + q^{2} + 371 q^{4} + 122 q^{5} - 2052 q^{7} + 927 q^{8}+O(q^{10}) $ 10 * q + q^2 + 371 * q^4 + 122 * q^5 - 2052 * q^7 + 927 * q^8	\( 10 q + q^{2} + 371 q^{4} + 122 q^{5} - 2052 q^{7} + 927 q^{8} - 10032 q^{10} + 8888 q^{11} - 16432 q^{13} + 28408 q^{14} - 26669 q^{16} + 48122 q^{17} - 56146 q^{19} + 88940 q^{20} - 100626 q^{22} + 236336 q^{23} - 135016 q^{25} + 166748 q^{26} - 259060 q^{28} + 248818 q^{29} - 430970 q^{31} - 69493 q^{32} + 445522 q^{34} - 298982 q^{35} - 261254 q^{37} - 257662 q^{38} - 671432 q^{40} + 126814 q^{41} - 795070 q^{43} + 620022 q^{44} - 809038 q^{46} - 627080 q^{47} - 1256116 q^{49} + 83117 q^{50} - 3674204 q^{52} + 1612384 q^{53} - 4732974 q^{55} + 4301484 q^{56} - 7268516 q^{58} + 3442492 q^{59} - 5217214 q^{61} + 2500324 q^{62} - 4657369 q^{64} + 1224166 q^{65} - 6810926 q^{67} + 3563486 q^{68} - 2745858 q^{70} + 13935120 q^{71} - 13743720 q^{73} + 1752692 q^{74} - 15817594 q^{76} + 7685750 q^{77} - 9007608 q^{79} + 13641024 q^{80} - 6329026 q^{82} + 21779128 q^{83} - 13177392 q^{85} - 79507 q^{86} - 13214750 q^{88} + 1895364 q^{89} - 16439838 q^{91} - 9614510 q^{92} + 3404276 q^{94} + 16861514 q^{95} - 20434472 q^{97} - 35731457 q^{98}+O(q^{100}) \) 10 * q + q^2 + 371 * q^4 + 122 * q^5 - 2052 * q^7 + 927 * q^8 - 10032 * q^10 + 8888 * q^11 - 16432 * q^13 + 28408 * q^14 - 26669 * q^16 + 48122 * q^17 - 56146 * q^19 + 88940 * q^20 - 100626 * q^22 + 236336 * q^23 - 135016 * q^25 + 166748 * q^26 - 259060 * q^28 + 248818 * q^29 - 430970 * q^31 - 69493 * q^32 + 445522 * q^34 - 298982 * q^35 - 261254 * q^37 - 257662 * q^38 - 671432 * q^40 + 126814 * q^41 - 795070 * q^43 + 620022 * q^44 - 809038 * q^46 - 627080 * q^47 - 1256116 * q^49 + 83117 * q^50 - 3674204 * q^52 + 1612384 * q^53 - 4732974 * q^55 + 4301484 * q^56 - 7268516 * q^58 + 3442492 * q^59 - 5217214 * q^61 + 2500324 * q^62 - 4657369 * q^64 + 1224166 * q^65 - 6810926 * q^67 + 3563486 * q^68 - 2745858 * q^70 + 13935120 * q^71 - 13743720 * q^73 + 1752692 * q^74 - 15817594 * q^76 + 7685750 * q^77 - 9007608 * q^79 + 13641024 * q^80 - 6329026 * q^82 + 21779128 * q^83 - 13177392 * q^85 - 79507 * q^86 - 13214750 * q^88 + 1895364 * q^89 - 16439838 * q^91 - 9614510 * q^92 + 3404276 * q^94 + 16861514 * q^95 - 20434472 * q^97 - 35731457 * q^98

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 $

$2$	−10.1422	−0.896455	−0.448227	−	0.893920i	$-0.647945\pi$
$2$	−10.1422	−0.896455	−0.448227	+	0.893920i	$0.647945\pi$
$3$	0	0
$3$	0	0
$4$	−25.1352	−0.196369
$5$	−212.535	−0.760390	−0.380195	−	0.924906i	$-0.624143\pi$
$5$	−212.535	−0.760390	−0.380195	+	0.924906i	$0.624143\pi$
$6$	0	0
$7$	−1278.88	−1.40925	−0.704624	−	0.709581i	$-0.748884\pi$
$7$	−1278.88	−1.40925	−0.704624	+	0.709581i	$0.748884\pi$
$8$	1553.13	1.07249
$9$	0	0
$10$	2155.58	0.681655
$11$	−4362.71	−0.988284	−0.494142	−	0.869381i	$-0.664518\pi$
$11$	−4362.71	−0.988284	−0.494142	+	0.869381i	$0.664518\pi$
$12$	0	0
$13$	1602.74	0.202331	0.101165	−	0.994870i	$-0.467743\pi$
$13$	1602.74	0.202331	0.101165	+	0.994870i	$0.467743\pi$
$14$	12970.7	1.26333
$15$	0	0
$16$	−12534.9	−0.765071
$17$	7659.58	0.378123	0.189062	−	0.981965i	$-0.439455\pi$
$17$	7659.58	0.378123	0.189062	+	0.981965i	$0.439455\pi$
$18$	0	0
$19$	−52261.4	−1.74801	−0.874004	−	0.485918i	$-0.838485\pi$
$19$	−52261.4	−1.74801	−0.874004	+	0.485918i	$0.838485\pi$
$20$	5342.12	0.149317
$21$	0	0
$22$	44247.6	0.885952
$23$	88943.8	1.52429	0.762146	−	0.647405i	$-0.224146\pi$
$23$	88943.8	1.52429	0.762146	+	0.647405i	$0.224146\pi$
$24$	0	0
$25$	−32953.7	−0.421808
$26$	−16255.4	−0.181380
$27$	0	0
$28$	32144.9	0.276732
$29$	14383.9	0.109517	0.0547587	−	0.998500i	$-0.482561\pi$
$29$	14383.9	0.109517	0.0547587	+	0.998500i	$0.482561\pi$
$30$	0	0
$31$	28175.3	0.169865	0.0849323	−	0.996387i	$-0.472933\pi$
$31$	28175.3	0.169865	0.0849323	+	0.996387i	$0.472933\pi$
$32$	−71668.9	−0.386639
$33$	0	0
$34$	−77685.2	−0.338971
$35$	271808.	1.07158
$36$	0	0
$37$	260059.	0.844046	0.422023	−	0.906585i	$-0.361320\pi$
$37$	260059.	0.844046	0.422023	+	0.906585i	$0.361320\pi$
$38$	530047.	1.56701
$39$	0	0
$40$	−330095.	−0.815511
$41$	458326.	1.03856	0.519280	−	0.854604i	$-0.326200\pi$
$41$	458326.	1.03856	0.519280	+	0.854604i	$0.326200\pi$
$42$	0	0
$43$	−79507.0	−0.152499
$43$	−79507.0	−0.152499
$44$	109657.	0.194068
$45$	0	0
$46$	−902088.	−1.36646
$47$	933763.	1.31188	0.655940	−	0.754813i	$-0.272272\pi$
$47$	933763.	1.31188	0.655940	+	0.754813i	$0.272272\pi$
$48$	0	0
$49$	811997.	0.985980
$50$	334224.	0.378132
$51$	0	0
$52$	−40285.2	−0.0397314
$53$	366609.	0.338250	0.169125	−	0.985595i	$-0.445906\pi$
$53$	366609.	0.338250	0.169125	+	0.985595i	$0.445906\pi$
$54$	0	0
$55$	927230.	0.751481
$56$	−1.98627e6	−1.51140
$57$	0	0
$58$	−145885.	−0.0981773
$59$	−1.97834e6	−1.25406	−0.627032	−	0.778994i	$-0.715730\pi$
$59$	−1.97834e6	−1.25406	−0.627032	+	0.778994i	$0.715730\pi$
$60$	0	0
$61$	−701063.	−0.395460	−0.197730	−	0.980257i	$-0.563357\pi$
$61$	−701063.	−0.395460	−0.197730	+	0.980257i	$0.563357\pi$
$62$	−285761.	−0.152276
$63$	0	0
$64$	2.33135e6	1.11168
$65$	−340640.	−0.153850
$66$	0	0
$67$	−392739.	−0.159530	−0.0797651	−	0.996814i	$-0.525417\pi$
$67$	−392739.	−0.159530	−0.0797651	+	0.996814i	$0.525417\pi$
$68$	−192525.	−0.0742516
$69$	0	0
$70$	−2.75674e6	−0.960621
$71$	5.39266e6	1.78813	0.894064	−	0.447938i	$-0.147842\pi$
$71$	5.39266e6	1.78813	0.894064	+	0.447938i	$0.147842\pi$
$72$	0	0
$73$	2.17341e6	0.653902	0.326951	−	0.945041i	$-0.393979\pi$
$73$	2.17341e6	0.653902	0.326951	+	0.945041i	$0.393979\pi$
$74$	−2.63758e6	−0.756649
$75$	0	0
$76$	1.31360e6	0.343254
$77$	5.57939e6	1.39274
$78$	0	0
$79$	826842.	0.188681	0.0943404	−	0.995540i	$-0.469926\pi$
$79$	826842.	0.188681	0.0943404	+	0.995540i	$0.469926\pi$
$80$	2.66411e6	0.581752
$81$	0	0
$82$	−4.64845e6	−0.931022
$83$	527990.	0.101357	0.0506784	−	0.998715i	$-0.483862\pi$
$83$	527990.	0.101357	0.0506784	+	0.998715i	$0.483862\pi$
$84$	0	0
$85$	−1.62793e6	−0.287521
$86$	806378.	0.136708
$87$	0	0
$88$	−6.77586e6	−1.05993
$89$	−6.33239e6	−0.952145	−0.476072	−	0.879406i	$-0.657940\pi$
$89$	−6.33239e6	−0.952145	−0.476072	+	0.879406i	$0.657940\pi$
$90$	0	0
$91$	−2.04972e6	−0.285134
$92$	−2.23562e6	−0.299323
$93$	0	0
$94$	−9.47044e6	−1.17604
$95$	1.11074e7	1.32917
$96$	0	0
$97$	−1.17279e6	−0.130473	−0.0652363	−	0.997870i	$-0.520780\pi$
$97$	−1.17279e6	−0.130473	−0.0652363	+	0.997870i	$0.520780\pi$
$98$	−8.23546e6	−0.883886
$99$	0	0
$100$	828298.	0.0828298
$101$	−6.14443e6	−0.593412	−0.296706	−	0.954969i	$-0.595888\pi$
$101$	−6.14443e6	−0.593412	−0.296706	+	0.954969i	$0.595888\pi$
$102$	0	0
$103$	1.80682e7	1.62924	0.814618	−	0.579998i	$-0.196947\pi$
$103$	1.80682e7	1.62924	0.814618	+	0.579998i	$0.196947\pi$
$104$	2.48927e6	0.216998
$105$	0	0
$106$	−3.71823e6	−0.303226
$107$	7.50566e6	0.592305	0.296153	−	0.955141i	$-0.404296\pi$
$107$	7.50566e6	0.592305	0.296153	+	0.955141i	$0.404296\pi$
$108$	0	0
$109$	1.48994e7	1.10199	0.550995	−	0.834509i	$-0.314249\pi$
$109$	1.48994e7	1.10199	0.550995	+	0.834509i	$0.314249\pi$
$110$	−9.40418e6	−0.673669
$111$	0	0
$112$	1.60307e7	1.07817
$113$	1.11635e7	0.727823	0.363912	−	0.931434i	$-0.381441\pi$
$113$	1.11635e7	0.727823	0.363912	+	0.931434i	$0.381441\pi$
$114$	0	0
$115$	−1.89037e7	−1.15906
$116$	−361541.	−0.0215058
$117$	0	0
$118$	2.00648e7	1.12421
$119$	−9.79570e6	−0.532870
$120$	0	0
$121$	−453949.	−0.0232948
$122$	7.11034e6	0.354512
$123$	0	0
$124$	−708192.	−0.0333561
$125$	2.36082e7	1.08113
$126$	0	0
$127$	1.32841e7	0.575466	0.287733	−	0.957711i	$-0.407098\pi$
$127$	1.32841e7	0.575466	0.287733	+	0.957711i	$0.407098\pi$
$128$	−1.44715e7	−0.609928
$129$	0	0
$130$	3.45484e6	0.137920
$131$	−1.64299e7	−0.638536	−0.319268	−	0.947664i	$-0.603437\pi$
$131$	−1.64299e7	−0.638536	−0.319268	+	0.947664i	$0.603437\pi$
$132$	0	0
$133$	6.68362e7	2.46338
$134$	3.98325e6	0.143012
$135$	0	0
$136$	1.18963e7	0.405534
$137$	−1.15697e7	−0.384415	−0.192207	−	0.981354i	$-0.561565\pi$
$137$	−1.15697e7	−0.384415	−0.192207	+	0.981354i	$0.561565\pi$
$138$	0	0
$139$	−1.75810e7	−0.555254	−0.277627	−	0.960689i	$-0.589548\pi$
$139$	−1.75810e7	−0.555254	−0.277627	+	0.960689i	$0.589548\pi$
$140$	−6.83194e6	−0.210424
$141$	0	0
$142$	−5.46936e7	−1.60298
$143$	−6.99230e6	−0.199960
$144$	0	0
$145$	−3.05708e6	−0.0832758
$146$	−2.20433e7	−0.586193
$147$	0	0
$148$	−6.53664e6	−0.165744
$149$	−6.09929e7	−1.51052	−0.755262	−	0.655423i	$-0.772490\pi$
$149$	−6.09929e7	−1.51052	−0.755262	+	0.655423i	$0.772490\pi$
$150$	0	0
$151$	7.13647e6	0.168680	0.0843402	−	0.996437i	$-0.473122\pi$
$151$	7.13647e6	0.168680	0.0843402	+	0.996437i	$0.473122\pi$
$152$	−8.11689e7	−1.87472
$153$	0	0
$154$	−5.65874e7	−1.24853
$155$	−5.98825e6	−0.129163
$156$	0	0
$157$	3.67969e7	0.758862	0.379431	−	0.925220i	$-0.376120\pi$
$157$	3.67969e7	0.758862	0.379431	+	0.925220i	$0.376120\pi$
$158$	−8.38602e6	−0.169144
$159$	0	0
$160$	1.52322e7	0.293996
$161$	−1.13749e8	−2.14810
$162$	0	0
$163$	−9.62797e6	−0.174132	−0.0870659	−	0.996203i	$-0.527749\pi$
$163$	−9.62797e6	−0.174132	−0.0870659	+	0.996203i	$0.527749\pi$
$164$	−1.15201e7	−0.203940
$165$	0	0
$166$	−5.35500e6	−0.0908617
$167$	9.86614e7	1.63923	0.819615	−	0.572915i	$-0.194188\pi$
$167$	9.86614e7	1.63923	0.819615	+	0.572915i	$0.194188\pi$
$168$	0	0
$169$	−6.01797e7	−0.959062
$170$	1.65109e7	0.257750
$171$	0	0
$172$	1.99842e6	0.0299459
$173$	−1.01964e8	−1.49722	−0.748610	−	0.663011i	$-0.769278\pi$
$173$	−1.01964e8	−1.49722	−0.748610	+	0.663011i	$0.769278\pi$
$174$	0	0
$175$	4.21439e7	0.594432
$176$	5.46862e7	0.756107
$177$	0	0
$178$	6.42246e7	0.853555
$179$	−4.61629e7	−0.601599	−0.300800	−	0.953687i	$-0.597254\pi$
$179$	−4.61629e7	−0.601599	−0.300800	+	0.953687i	$0.597254\pi$
$180$	0	0
$181$	−1.48493e8	−1.86136	−0.930681	−	0.365832i	$-0.880784\pi$
$181$	−1.48493e8	−1.86136	−0.930681	+	0.365832i	$0.880784\pi$
$182$	2.07887e7	0.255610
$183$	0	0
$184$	1.38141e8	1.63479
$185$	−5.52718e7	−0.641804
$186$	0	0
$187$	−3.34165e7	−0.373693
$188$	−2.34703e7	−0.257612
$189$	0	0
$190$	−1.12654e8	−1.19154
$191$	7.05108e7	0.732216	0.366108	−	0.930572i	$-0.380690\pi$
$191$	7.05108e7	0.732216	0.366108	+	0.930572i	$0.380690\pi$
$192$	0	0
$193$	1.35933e8	1.36105	0.680524	−	0.732726i	$-0.261752\pi$
$193$	1.35933e8	1.36105	0.680524	+	0.732726i	$0.261752\pi$
$194$	1.18947e7	0.116963
$195$	0	0
$196$	−2.04097e7	−0.193615
$197$	−1.27343e8	−1.18670	−0.593351	−	0.804944i	$-0.702196\pi$
$197$	−1.27343e8	−1.18670	−0.593351	+	0.804944i	$0.702196\pi$
$198$	0	0
$199$	−1.67647e8	−1.50803	−0.754014	−	0.656859i	$-0.771885\pi$
$199$	−1.67647e8	−1.50803	−0.754014	+	0.656859i	$0.771885\pi$
$200$	−5.11815e7	−0.452385
$201$	0	0
$202$	6.23182e7	0.531967
$203$	−1.83953e7	−0.154337
$204$	0	0
$205$	−9.74106e7	−0.789710
$206$	−1.83251e8	−1.46054
$207$	0	0
$208$	−2.00903e7	−0.154797
$209$	2.28001e8	1.72753
$210$	0	0
$211$	−1.67753e8	−1.22937	−0.614683	−	0.788774i	$-0.710716\pi$
$211$	−1.67753e8	−1.22937	−0.614683	+	0.788774i	$0.710716\pi$
$212$	−9.21479e6	−0.0664217
$213$	0	0
$214$	−7.61241e7	−0.530975
$215$	1.68980e7	0.115958
$216$	0	0
$217$	−3.60329e7	−0.239381
$218$	−1.51114e8	−0.987883
$219$	0	0
$220$	−2.33061e7	−0.147567
$221$	1.22763e7	0.0765061
$222$	0	0
$223$	5.08235e6	0.0306900	0.0153450	−	0.999882i	$-0.495115\pi$
$223$	5.08235e6	0.0306900	0.0153450	+	0.999882i	$0.495115\pi$
$224$	9.16561e7	0.544870
$225$	0	0
$226$	−1.13223e8	−0.652461
$227$	−1.20293e7	−0.0682576	−0.0341288	−	0.999417i	$-0.510866\pi$
$227$	−1.20293e7	−0.0682576	−0.0341288	+	0.999417i	$0.510866\pi$
$228$	0	0
$229$	−1.46652e8	−0.806983	−0.403491	−	0.914983i	$-0.632204\pi$
$229$	−1.46652e8	−0.806983	−0.403491	+	0.914983i	$0.632204\pi$
$230$	1.91726e8	1.03904
$231$	0	0
$232$	2.23401e7	0.117456
$233$	−1.80525e8	−0.934958	−0.467479	−	0.884004i	$-0.654838\pi$
$233$	−1.80525e8	−0.934958	−0.467479	+	0.884004i	$0.654838\pi$
$234$	0	0
$235$	−1.98458e8	−0.997540
$236$	4.97260e7	0.246259
$237$	0	0
$238$	9.93502e7	0.477694
$239$	1.62202e8	0.768534	0.384267	−	0.923222i	$-0.374454\pi$
$239$	1.62202e8	0.768534	0.384267	+	0.923222i	$0.374454\pi$
$240$	0	0
$241$	−3.28269e8	−1.51067	−0.755335	−	0.655339i	$-0.772526\pi$
$241$	−3.28269e8	−1.51067	−0.755335	+	0.655339i	$0.772526\pi$
$242$	4.60406e6	0.0208827
$243$	0	0
$244$	1.76214e7	0.0776560
$245$	−1.72578e8	−0.749729
$246$	0	0
$247$	−8.37616e7	−0.353676
$248$	4.37600e7	0.182178
$249$	0	0
$250$	−2.39439e8	−0.969182
$251$	3.89166e6	0.0155338	0.00776689	−	0.999970i	$-0.497528\pi$
$251$	3.89166e6	0.0155338	0.00776689	+	0.999970i	$0.497528\pi$
$252$	0	0
$253$	−3.88036e8	−1.50643
$254$	−1.34730e8	−0.515879
$255$	0	0
$256$	−1.51640e8	−0.564903
$257$	−1.51653e8	−0.557296	−0.278648	−	0.960393i	$-0.589886\pi$
$257$	−1.51653e8	−0.557296	−0.278648	+	0.960393i	$0.589886\pi$
$258$	0	0
$259$	−3.32585e8	−1.18947
$260$	8.56204e6	0.0302114
$261$	0	0
$262$	1.66636e8	0.572419
$263$	1.96116e8	0.664766	0.332383	−	0.943144i	$-0.392147\pi$
$263$	1.96116e8	0.664766	0.332383	+	0.943144i	$0.392147\pi$
$264$	0	0
$265$	−7.79174e7	−0.257202
$266$	−6.77868e8	−2.20831
$267$	0	0
$268$	9.87158e6	0.0313267
$269$	−4.36805e8	−1.36822	−0.684109	−	0.729380i	$-0.739809\pi$
$269$	−4.36805e8	−1.36822	−0.684109	+	0.729380i	$0.739809\pi$
$270$	0	0
$271$	5.31300e8	1.62161	0.810807	−	0.585314i	$-0.199029\pi$
$271$	5.31300e8	1.62161	0.810807	+	0.585314i	$0.199029\pi$
$272$	−9.60122e7	−0.289291
$273$	0	0
$274$	1.17343e8	0.344610
$275$	1.43767e8	0.416866
$276$	0	0
$277$	−3.49515e8	−0.988068	−0.494034	−	0.869443i	$-0.664478\pi$
$277$	−3.49515e8	−0.988068	−0.494034	+	0.869443i	$0.664478\pi$
$278$	1.78310e8	0.497760
$279$	0	0
$280$	4.22153e8	1.14926
$281$	1.00578e8	0.270416	0.135208	−	0.990817i	$-0.456830\pi$
$281$	1.00578e8	0.270416	0.135208	+	0.990817i	$0.456830\pi$
$282$	0	0
$283$	6.55233e8	1.71847	0.859237	−	0.511578i	$-0.170939\pi$
$283$	6.55233e8	1.71847	0.859237	+	0.511578i	$0.170939\pi$
$284$	−1.35546e8	−0.351132
$285$	0	0
$286$	7.09175e7	0.179255
$287$	−5.86145e8	−1.46359
$288$	0	0
$289$	−3.51670e8	−0.857023
$290$	3.10056e7	0.0746530
$291$	0	0
$292$	−5.46292e7	−0.128406
$293$	5.47004e8	1.27044	0.635220	−	0.772331i	$-0.280910\pi$
$293$	5.47004e8	1.27044	0.635220	+	0.772331i	$0.280910\pi$
$294$	0	0
$295$	4.20468e8	0.953577
$296$	4.03906e8	0.905231
$297$	0	0
$298$	6.18604e8	1.35412
$299$	1.42554e8	0.308411
$300$	0	0
$301$	1.01680e8	0.214908
$302$	−7.23798e7	−0.151214
$303$	0	0
$304$	6.55093e8	1.33735
$305$	1.49001e8	0.300704
$306$	0	0
$307$	1.08002e8	0.213034	0.106517	−	0.994311i	$-0.466030\pi$
$307$	1.08002e8	0.213034	0.106517	+	0.994311i	$0.466030\pi$
$308$	−1.40239e8	−0.273490
$309$	0	0
$310$	6.07342e7	0.115789
$311$	2.34744e8	0.442521	0.221260	−	0.975215i	$-0.428983\pi$
$311$	2.34744e8	0.442521	0.221260	+	0.975215i	$0.428983\pi$
$312$	0	0
$313$	−3.84354e8	−0.708478	−0.354239	−	0.935155i	$-0.615260\pi$
$313$	−3.84354e8	−0.708478	−0.354239	+	0.935155i	$0.615260\pi$
$314$	−3.73203e8	−0.680286
$315$	0	0
$316$	−2.07828e7	−0.0370510
$317$	1.08004e9	1.90429	0.952143	−	0.305652i	$-0.0988744\pi$
$317$	1.08004e9	1.90429	0.952143	+	0.305652i	$0.0988744\pi$
$318$	0	0
$319$	−6.27526e7	−0.108234
$320$	−4.95495e8	−0.845306
$321$	0	0
$322$	1.15366e9	1.92568
$323$	−4.00300e8	−0.660963
$324$	0	0
$325$	−5.28163e7	−0.0853447
$326$	9.76491e7	0.156101
$327$	0	0
$328$	7.11841e8	1.11385
$329$	−1.19417e9	−1.84876
$330$	0	0
$331$	−2.31094e7	−0.0350260	−0.0175130	−	0.999847i	$-0.505575\pi$
$331$	−2.31094e7	−0.0350260	−0.0175130	+	0.999847i	$0.505575\pi$
$332$	−1.32711e7	−0.0199033
$333$	0	0
$334$	−1.00065e9	−1.46949
$335$	8.34710e7	0.121305
$336$	0	0
$337$	−2.05616e8	−0.292653	−0.146326	−	0.989236i	$-0.546745\pi$
$337$	−2.05616e8	−0.292653	−0.146326	+	0.989236i	$0.546745\pi$
$338$	6.10357e8	0.859756
$339$	0	0
$340$	4.09184e7	0.0564601
$341$	−1.22921e8	−0.167875
$342$	0	0
$343$	1.47666e7	0.0197583
$344$	−1.23485e8	−0.163553
$345$	0	0
$346$	1.03414e9	1.34219
$347$	2.66053e8	0.341833	0.170917	−	0.985285i	$-0.445327\pi$
$347$	2.66053e8	0.341833	0.170917	+	0.985285i	$0.445327\pi$
$348$	0	0
$349$	−1.20392e9	−1.51604	−0.758019	−	0.652232i	$-0.773833\pi$
$349$	−1.20392e9	−1.51604	−0.758019	+	0.652232i	$0.773833\pi$
$350$	−4.27433e8	−0.532881
$351$	0	0
$352$	3.12670e8	0.382109
$353$	6.09355e8	0.737325	0.368663	−	0.929563i	$-0.379816\pi$
$353$	6.09355e8	0.737325	0.368663	+	0.929563i	$0.379816\pi$
$354$	0	0
$355$	−1.14613e9	−1.35967
$356$	1.59166e8	0.186971
$357$	0	0
$358$	4.68195e8	0.539307
$359$	7.91040e8	0.902336	0.451168	−	0.892439i	$-0.351008\pi$
$359$	7.91040e8	0.902336	0.451168	+	0.892439i	$0.351008\pi$
$360$	0	0
$361$	1.83738e9	2.05553
$362$	1.50605e9	1.66863
$363$	0	0
$364$	5.15201e7	0.0559914
$365$	−4.61927e8	−0.497220
$366$	0	0
$367$	−1.17856e9	−1.24458	−0.622288	−	0.782788i	$-0.713797\pi$
$367$	−1.17856e9	−1.24458	−0.622288	+	0.782788i	$0.713797\pi$
$368$	−1.11490e9	−1.16619
$369$	0	0
$370$	5.60579e8	0.575348
$371$	−4.68850e8	−0.476678
$372$	0	0
$373$	1.31480e9	1.31183	0.655915	−	0.754835i	$-0.272283\pi$
$373$	1.31480e9	1.31183	0.655915	+	0.754835i	$0.272283\pi$
$374$	3.38918e8	0.334999
$375$	0	0
$376$	1.45026e9	1.40698
$377$	2.30536e7	0.0221587
$378$	0	0
$379$	7.80611e8	0.736542	0.368271	−	0.929719i	$-0.379950\pi$
$379$	7.80611e8	0.736542	0.368271	+	0.929719i	$0.379950\pi$
$380$	−2.79187e8	−0.261007
$381$	0	0
$382$	−7.15137e8	−0.656398
$383$	5.04483e8	0.458829	0.229414	−	0.973329i	$-0.426319\pi$
$383$	5.04483e8	0.458829	0.229414	+	0.973329i	$0.426319\pi$
$384$	0	0
$385$	−1.18582e9	−1.05902
$386$	−1.37866e9	−1.22012
$387$	0	0
$388$	2.94783e7	0.0256207
$389$	1.45482e9	1.25310	0.626549	−	0.779382i	$-0.284467\pi$
$389$	1.45482e9	1.25310	0.626549	+	0.779382i	$0.284467\pi$
$390$	0	0
$391$	6.81272e8	0.576370
$392$	1.26114e9	1.05745
$393$	0	0
$394$	1.29154e9	1.06383
$395$	−1.75733e8	−0.143471
$396$	0	0
$397$	−2.35039e9	−1.88526	−0.942632	−	0.333833i	$-0.891658\pi$
$397$	−2.35039e9	−1.88526	−0.942632	+	0.333833i	$0.891658\pi$
$398$	1.70031e9	1.35188
$399$	0	0
$400$	4.13072e8	0.322713
$401$	1.18303e9	0.916199	0.458099	−	0.888901i	$-0.348530\pi$
$401$	1.18303e9	0.916199	0.458099	+	0.888901i	$0.348530\pi$
$402$	0	0
$403$	4.51578e7	0.0343689
$404$	1.54441e8	0.116528
$405$	0	0
$406$	1.86569e8	0.138356
$407$	−1.13456e9	−0.834157
$408$	0	0
$409$	−1.51454e9	−1.09459	−0.547294	−	0.836941i	$-0.684342\pi$
$409$	−1.51454e9	−1.09459	−0.547294	+	0.836941i	$0.684342\pi$
$410$	9.87960e8	0.707939
$411$	0	0
$412$	−4.54147e8	−0.319931
$413$	2.53007e9	1.76729
$414$	0	0
$415$	−1.12217e8	−0.0770706
$416$	−1.14867e8	−0.0782290
$417$	0	0
$418$	−2.31244e9	−1.54865
$419$	−3.42268e8	−0.227309	−0.113655	−	0.993520i	$-0.536256\pi$
$419$	−3.42268e8	−0.227309	−0.113655	+	0.993520i	$0.536256\pi$
$420$	0	0
$421$	−7.59253e8	−0.495905	−0.247953	−	0.968772i	$-0.579758\pi$
$421$	−7.59253e8	−0.495905	−0.247953	+	0.968772i	$0.579758\pi$
$422$	1.70139e9	1.10207
$423$	0	0
$424$	5.69392e8	0.362770
$425$	−2.52412e8	−0.159495
$426$	0	0
$427$	8.96577e8	0.557301
$428$	−1.88656e8	−0.116310
$429$	0	0
$430$	−1.71384e8	−0.103951
$431$	−1.10316e9	−0.663692	−0.331846	−	0.943334i	$-0.607671\pi$
$431$	−1.10316e9	−0.663692	−0.331846	+	0.943334i	$0.607671\pi$
$432$	0	0
$433$	2.13457e9	1.26358	0.631789	−	0.775140i	$-0.282321\pi$
$433$	2.13457e9	1.26358	0.631789	+	0.775140i	$0.282321\pi$
$434$	3.65454e8	0.214595
$435$	0	0
$436$	−3.74500e8	−0.216396
$437$	−4.64833e9	−2.66447
$438$	0	0
$439$	1.76912e9	0.998001	0.499000	−	0.866602i	$-0.333701\pi$
$439$	1.76912e9	0.998001	0.499000	+	0.866602i	$0.333701\pi$
$440$	1.44011e9	0.805956
$441$	0	0
$442$	−1.24509e8	−0.0685842
$443$	−2.21564e9	−1.21084	−0.605419	−	0.795907i	$-0.706995\pi$
$443$	−2.21564e9	−1.21084	−0.605419	+	0.795907i	$0.706995\pi$
$444$	0	0
$445$	1.34586e9	0.724001
$446$	−5.15463e7	−0.0275122
$447$	0	0
$448$	−2.98152e9	−1.56663
$449$	−1.52402e9	−0.794562	−0.397281	−	0.917697i	$-0.630046\pi$
$449$	−1.52402e9	−0.794562	−0.397281	+	0.917697i	$0.630046\pi$
$450$	0	0
$451$	−1.99954e9	−1.02639
$452$	−2.80597e8	−0.142922
$453$	0	0
$454$	1.22004e8	0.0611899
$455$	4.35638e8	0.216813
$456$	0	0
$457$	3.16906e9	1.55319	0.776594	−	0.630001i	$-0.216946\pi$
$457$	3.16906e9	1.55319	0.776594	+	0.630001i	$0.216946\pi$
$458$	1.48738e9	0.723424
$459$	0	0
$460$	4.75148e8	0.227602
$461$	3.51510e9	1.67103	0.835514	−	0.549468i	$-0.185170\pi$
$461$	3.51510e9	1.67103	0.835514	+	0.549468i	$0.185170\pi$
$462$	0	0
$463$	3.40997e9	1.59668	0.798340	−	0.602208i	$-0.205712\pi$
$463$	3.40997e9	1.59668	0.798340	+	0.602208i	$0.205712\pi$
$464$	−1.80301e8	−0.0837885
$465$	0	0
$466$	1.83093e9	0.838147
$467$	4.20511e9	1.91059	0.955297	−	0.295647i	$-0.0955351\pi$
$467$	4.20511e9	1.91059	0.955297	+	0.295647i	$0.0955351\pi$
$468$	0	0
$469$	5.02267e8	0.224818
$470$	2.01280e9	0.894250
$471$	0	0
$472$	−3.07263e9	−1.34497
$473$	3.46866e8	0.150712
$474$	0	0
$475$	1.72221e9	0.737323
$476$	2.46217e8	0.104639
$477$	0	0
$478$	−1.64509e9	−0.688956
$479$	−7.11589e7	−0.0295838	−0.0147919	−	0.999891i	$-0.504709\pi$
$479$	−7.11589e7	−0.0295838	−0.0147919	+	0.999891i	$0.504709\pi$
$480$	0	0
$481$	4.16808e8	0.170777
$482$	3.32937e9	1.35425
$483$	0	0
$484$	1.14101e7	0.00457436
$485$	2.49259e8	0.0992100
$486$	0	0
$487$	−3.85073e9	−1.51075	−0.755373	−	0.655296i	$-0.772544\pi$
$487$	−3.85073e9	−1.51075	−0.755373	+	0.655296i	$0.772544\pi$
$488$	−1.08884e9	−0.424127
$489$	0	0
$490$	1.75033e9	0.672098
$491$	2.26977e9	0.865361	0.432680	−	0.901547i	$-0.357568\pi$
$491$	2.26977e9	0.865361	0.432680	+	0.901547i	$0.357568\pi$
$492$	0	0
$493$	1.10174e8	0.0414111
$494$	8.49530e8	0.317055
$495$	0	0
$496$	−3.53175e8	−0.129958
$497$	−6.89658e9	−2.51992
$498$	0	0
$499$	−1.09105e9	−0.393090	−0.196545	−	0.980495i	$-0.562972\pi$
$499$	−1.09105e9	−0.393090	−0.196545	+	0.980495i	$0.562972\pi$
$500$	−5.93395e8	−0.212300
$501$	0	0
$502$	−3.94701e7	−0.0139253
$503$	4.03043e9	1.41209	0.706047	−	0.708165i	$-0.250477\pi$
$503$	4.03043e9	1.41209	0.706047	+	0.708165i	$0.250477\pi$
$504$	0	0
$505$	1.30591e9	0.451225
$506$	3.93555e9	1.35045
$507$	0	0
$508$	−3.33899e8	−0.113003
$509$	−2.28301e8	−0.0767355	−0.0383677	−	0.999264i	$-0.512216\pi$
$509$	−2.28301e8	−0.0767355	−0.0383677	+	0.999264i	$0.512216\pi$
$510$	0	0
$511$	−2.77954e9	−0.921509
$512$	3.39032e9	1.11634
$513$	0	0
$514$	1.53810e9	0.499591
$515$	−3.84012e9	−1.23885
$516$	0	0
$517$	−4.07374e9	−1.29651
$518$	3.37315e9	1.06631
$519$	0	0
$520$	−5.29058e8	−0.165003
$521$	−6.75488e8	−0.209260	−0.104630	−	0.994511i	$-0.533366\pi$
$521$	−6.75488e8	−0.209260	−0.104630	+	0.994511i	$0.533366\pi$
$522$	0	0
$523$	−6.38572e9	−1.95188	−0.975942	−	0.218031i	$-0.930037\pi$
$523$	−6.38572e9	−1.95188	−0.975942	+	0.218031i	$0.930037\pi$
$524$	4.12969e8	0.125389
$525$	0	0
$526$	−1.98906e9	−0.595933
$527$	2.15811e8	0.0642298
$528$	0	0
$529$	4.50617e9	1.32346
$530$	7.90256e8	0.230570
$531$	0	0
$532$	−1.67994e9	−0.483730
$533$	7.34579e8	0.210133
$534$	0	0
$535$	−1.59522e9	−0.450383
$536$	−6.09976e8	−0.171095
$537$	0	0
$538$	4.43018e9	1.22654
$539$	−3.54250e9	−0.974428
$540$	0	0
$541$	3.31299e8	0.0899560	0.0449780	−	0.998988i	$-0.485678\pi$
$541$	3.31299e8	0.0899560	0.0449780	+	0.998988i	$0.485678\pi$
$542$	−5.38857e9	−1.45370
$543$	0	0
$544$	−5.48954e8	−0.146197
$545$	−3.16666e9	−0.837941
$546$	0	0
$547$	−4.24571e9	−1.10916	−0.554581	−	0.832130i	$-0.687121\pi$
$547$	−4.24571e9	−1.10916	−0.554581	+	0.832130i	$0.687121\pi$
$548$	2.90806e8	0.0754870
$549$	0	0
$550$	−1.45812e9	−0.373701
$551$	−7.51721e8	−0.191437
$552$	0	0
$553$	−1.05743e9	−0.265898
$554$	3.54486e9	0.885758
$555$	0	0
$556$	4.41901e8	0.109034
$557$	−1.04050e9	−0.255123	−0.127562	−	0.991831i	$-0.540715\pi$
$557$	−1.04050e9	−0.255123	−0.127562	+	0.991831i	$0.540715\pi$
$558$	0	0
$559$	−1.27429e8	−0.0308552
$560$	−3.40709e9	−0.819832
$561$	0	0
$562$	−1.02009e9	−0.242416
$563$	1.47243e8	0.0347740	0.0173870	−	0.999849i	$-0.494465\pi$
$563$	1.47243e8	0.0347740	0.0173870	+	0.999849i	$0.494465\pi$
$564$	0	0
$565$	−2.37264e9	−0.553429
$566$	−6.64552e9	−1.54053
$567$	0	0
$568$	8.37551e9	1.91775
$569$	−7.78402e9	−1.77138	−0.885688	−	0.464281i	$-0.846313\pi$
$569$	−7.78402e9	−1.77138	−0.885688	+	0.464281i	$0.846313\pi$
$570$	0	0
$571$	1.03807e9	0.233346	0.116673	−	0.993170i	$-0.462777\pi$
$571$	1.03807e9	0.233346	0.116673	+	0.993170i	$0.462777\pi$
$572$	1.75753e8	0.0392659
$573$	0	0
$574$	5.94482e9	1.31204
$575$	−2.93103e9	−0.642958
$576$	0	0
$577$	−3.99469e9	−0.865700	−0.432850	−	0.901466i	$-0.642492\pi$
$577$	−3.99469e9	−0.865700	−0.432850	+	0.901466i	$0.642492\pi$
$578$	3.56671e9	0.768282
$579$	0	0
$580$	7.68403e7	0.0163528
$581$	−6.75237e8	−0.142837
$582$	0	0
$583$	−1.59941e9	−0.334287
$584$	3.37560e9	0.701303
$585$	0	0
$586$	−5.54784e9	−1.13889
$587$	−6.00546e9	−1.22550	−0.612750	−	0.790277i	$-0.709937\pi$
$587$	−6.00546e9	−1.22550	−0.612750	+	0.790277i	$0.709937\pi$
$588$	0	0
$589$	−1.47248e9	−0.296925
$590$	−4.26448e9	−0.854839
$591$	0	0
$592$	−3.25982e9	−0.645755
$593$	−5.07645e9	−0.999697	−0.499849	−	0.866113i	$-0.666611\pi$
$593$	−5.07645e9	−0.999697	−0.499849	+	0.866113i	$0.666611\pi$
$594$	0	0
$595$	2.08193e9	0.405189
$596$	1.53307e9	0.296619
$597$	0	0
$598$	−1.44582e9	−0.276477
$599$	5.03239e9	0.956710	0.478355	−	0.878166i	$-0.341233\pi$
$599$	5.03239e9	0.956710	0.478355	+	0.878166i	$0.341233\pi$
$600$	0	0
$601$	3.74243e9	0.703223	0.351612	−	0.936146i	$-0.385634\pi$
$601$	3.74243e9	0.703223	0.351612	+	0.936146i	$0.385634\pi$
$602$	−1.03126e9	−0.192656
$603$	0	0
$604$	−1.79377e8	−0.0331235
$605$	9.64803e7	0.0177131
$606$	0	0
$607$	6.76087e9	1.22699	0.613496	−	0.789697i	$-0.289763\pi$
$607$	6.76087e9	1.22699	0.613496	+	0.789697i	$0.289763\pi$
$608$	3.74552e9	0.675849
$609$	0	0
$610$	−1.51120e9	−0.269567
$611$	1.49658e9	0.265434
$612$	0	0
$613$	6.96736e9	1.22168	0.610838	−	0.791755i	$-0.290832\pi$
$613$	6.96736e9	1.22168	0.610838	+	0.791755i	$0.290832\pi$
$614$	−1.09538e9	−0.190975
$615$	0	0
$616$	8.66553e9	1.49370
$617$	−6.01635e9	−1.03118	−0.515590	−	0.856835i	$-0.672427\pi$
$617$	−6.01635e9	−1.03118	−0.515590	+	0.856835i	$0.672427\pi$
$618$	0	0
$619$	2.60861e9	0.442071	0.221036	−	0.975266i	$-0.429056\pi$
$619$	2.60861e9	0.442071	0.221036	+	0.975266i	$0.429056\pi$
$620$	1.50516e8	0.0253636
$621$	0	0
$622$	−2.38083e9	−0.396700
$623$	8.09839e9	1.34181
$624$	0	0
$625$	−2.44306e9	−0.400271
$626$	3.89821e9	0.635118
$627$	0	0
$628$	−9.24898e8	−0.149017
$629$	1.99194e9	0.319154
$630$	0	0
$631$	6.25938e9	0.991810	0.495905	−	0.868377i	$-0.334836\pi$
$631$	6.25938e9	0.991810	0.495905	+	0.868377i	$0.334836\pi$
$632$	1.28420e9	0.202358
$633$	0	0
$634$	−1.09540e10	−1.70711
$635$	−2.82334e9	−0.437578
$636$	0	0
$637$	1.30142e9	0.199494
$638$	6.36451e8	0.0970271
$639$	0	0
$640$	3.07570e9	0.463783
$641$	−3.91409e9	−0.586985	−0.293493	−	0.955961i	$-0.594818\pi$
$641$	−3.91409e9	−0.586985	−0.293493	+	0.955961i	$0.594818\pi$
$642$	0	0
$643$	−8.85118e9	−1.31299	−0.656497	−	0.754328i	$-0.727963\pi$
$643$	−8.85118e9	−1.31299	−0.656497	+	0.754328i	$0.727963\pi$
$644$	2.85909e9	0.421820
$645$	0	0
$646$	4.05994e9	0.592524
$647$	−6.30706e9	−0.915507	−0.457754	−	0.889079i	$-0.651346\pi$
$647$	−6.30706e9	−0.915507	−0.457754	+	0.889079i	$0.651346\pi$
$648$	0	0
$649$	8.63093e9	1.23937
$650$	5.35676e8	0.0765077
$651$	0	0
$652$	2.42001e8	0.0341940
$653$	−3.12342e9	−0.438970	−0.219485	−	0.975616i	$-0.570438\pi$
$653$	−3.12342e9	−0.438970	−0.219485	+	0.975616i	$0.570438\pi$
$654$	0	0
$655$	3.49194e9	0.485536
$656$	−5.74508e9	−0.794571
$657$	0	0
$658$	1.21116e10	1.65733
$659$	2.66144e9	0.362258	0.181129	−	0.983459i	$-0.442025\pi$
$659$	2.66144e9	0.362258	0.181129	+	0.983459i	$0.442025\pi$
$660$	0	0
$661$	−2.61269e9	−0.351871	−0.175935	−	0.984402i	$-0.556295\pi$
$661$	−2.61269e9	−0.351871	−0.175935	+	0.984402i	$0.556295\pi$
$662$	2.34381e8	0.0313993
$663$	0	0
$664$	8.20039e8	0.108704
$665$	−1.42051e10	−1.87313
$666$	0	0
$667$	1.27936e9	0.166936
$668$	−2.47987e9	−0.321893
$669$	0	0
$670$	−8.46582e8	−0.108745
$671$	3.05853e9	0.390827
$672$	0	0
$673$	1.41640e10	1.79116	0.895579	−	0.444903i	$-0.146762\pi$
$673$	1.41640e10	1.79116	0.895579	+	0.444903i	$0.146762\pi$
$674$	2.08541e9	0.262350
$675$	0	0
$676$	1.51263e9	0.188330
$677$	3.85547e9	0.477548	0.238774	−	0.971075i	$-0.423255\pi$
$677$	3.85547e9	0.477548	0.238774	+	0.971075i	$0.423255\pi$
$678$	0	0
$679$	1.49986e9	0.183868
$680$	−2.52839e9	−0.308364
$681$	0	0
$682$	1.24669e9	0.150492
$683$	−2.91278e9	−0.349812	−0.174906	−	0.984585i	$-0.555962\pi$
$683$	−2.91278e9	−0.349812	−0.174906	+	0.984585i	$0.555962\pi$
$684$	0	0
$685$	2.45897e9	0.292305
$686$	−1.49766e8	−0.0177124
$687$	0	0
$688$	9.96614e8	0.116672
$689$	5.87580e8	0.0684384
$690$	0	0
$691$	−8.24555e9	−0.950707	−0.475353	−	0.879795i	$-0.657680\pi$
$691$	−8.24555e9	−0.950707	−0.475353	+	0.879795i	$0.657680\pi$
$692$	2.56288e9	0.294007
$693$	0	0
$694$	−2.69837e9	−0.306438
$695$	3.73658e9	0.422209
$696$	0	0
$697$	3.51059e9	0.392704
$698$	1.22105e10	1.35906
$699$	0	0
$700$	−1.05930e9	−0.116728
$701$	5.32603e9	0.583970	0.291985	−	0.956423i	$-0.405684\pi$
$701$	5.32603e9	0.583970	0.291985	+	0.956423i	$0.405684\pi$
$702$	0	0
$703$	−1.35911e10	−1.47540
$704$	−1.01710e10	−1.09865
$705$	0	0
$706$	−6.18022e9	−0.660979
$707$	7.85800e9	0.836265
$708$	0	0
$709$	−3.66513e9	−0.386213	−0.193107	−	0.981178i	$-0.561856\pi$
$709$	−3.66513e9	−0.386213	−0.193107	+	0.981178i	$0.561856\pi$
$710$	1.16243e10	1.21889
$711$	0	0
$712$	−9.83505e9	−1.02117
$713$	2.50602e9	0.258923
$714$	0	0
$715$	1.48611e9	0.152048
$716$	1.16031e9	0.118135
$717$	0	0
$718$	−8.02291e9	−0.808903
$719$	−3.58135e9	−0.359332	−0.179666	−	0.983728i	$-0.557502\pi$
$719$	−3.58135e9	−0.359332	−0.179666	+	0.983728i	$0.557502\pi$
$720$	0	0
$721$	−2.31071e10	−2.29600
$722$	−1.86352e10	−1.84269
$723$	0	0
$724$	3.73240e9	0.365513
$725$	−4.74002e8	−0.0461952
$726$	0	0
$727$	1.35228e10	1.30525	0.652626	−	0.757680i	$-0.273667\pi$
$727$	1.35228e10	1.30525	0.652626	+	0.757680i	$0.273667\pi$
$728$	−3.18348e9	−0.305804
$729$	0	0
$730$	4.68497e9	0.445735
$731$	−6.08990e8	−0.0576633
$732$	0	0
$733$	6.62491e9	0.621321	0.310661	−	0.950521i	$-0.399450\pi$
$733$	6.62491e9	0.621321	0.310661	+	0.950521i	$0.399450\pi$
$734$	1.19533e10	1.11571
$735$	0	0
$736$	−6.37450e9	−0.589351
$737$	1.71341e9	0.157661
$738$	0	0
$739$	−1.68723e10	−1.53786	−0.768932	−	0.639330i	$-0.779212\pi$
$739$	−1.68723e10	−1.53786	−0.768932	+	0.639330i	$0.779212\pi$
$740$	1.38927e9	0.126030
$741$	0	0
$742$	4.75518e9	0.427320
$743$	4.54541e9	0.406549	0.203274	−	0.979122i	$-0.434842\pi$
$743$	4.54541e9	0.406549	0.203274	+	0.979122i	$0.434842\pi$
$744$	0	0
$745$	1.29632e10	1.14859
$746$	−1.33350e10	−1.17600
$747$	0	0
$748$	8.39930e8	0.0733817
$749$	−9.59885e9	−0.834705
$750$	0	0
$751$	−1.10181e10	−0.949223	−0.474612	−	0.880195i	$-0.657411\pi$
$751$	−1.10181e10	−0.949223	−0.474612	+	0.880195i	$0.657411\pi$
$752$	−1.17046e10	−1.00368
$753$	0	0
$754$	−2.33815e8	−0.0198643
$755$	−1.51675e9	−0.128263
$756$	0	0
$757$	−1.56446e10	−1.31078	−0.655389	−	0.755291i	$-0.727495\pi$
$757$	−1.56446e10	−1.31078	−0.655389	+	0.755291i	$0.727495\pi$
$758$	−7.91713e9	−0.660276
$759$	0	0
$760$	1.72513e10	1.42552
$761$	2.03531e10	1.67411	0.837055	−	0.547119i	$-0.184275\pi$
$761$	2.03531e10	1.67411	0.837055	+	0.547119i	$0.184275\pi$
$762$	0	0
$763$	−1.90546e10	−1.55298
$764$	−1.77230e9	−0.143784
$765$	0	0
$766$	−5.11658e9	−0.411319
$767$	−3.17078e9	−0.253736
$768$	0	0
$769$	1.54785e10	1.22740	0.613700	−	0.789539i	$-0.289680\pi$
$769$	1.54785e10	1.22740	0.613700	+	0.789539i	$0.289680\pi$
$770$	1.20268e10	0.949366
$771$	0	0
$772$	−3.41669e9	−0.267267
$773$	3.38582e9	0.263654	0.131827	−	0.991273i	$-0.457916\pi$
$773$	3.38582e9	0.263654	0.131827	+	0.991273i	$0.457916\pi$
$774$	0	0
$775$	−9.28482e8	−0.0716502
$776$	−1.82150e9	−0.139931
$777$	0	0
$778$	−1.47551e10	−1.12335
$779$	−2.39528e10	−1.81541
$780$	0	0
$781$	−2.35266e10	−1.76718
$782$	−6.90961e9	−0.516690
$783$	0	0
$784$	−1.01783e10	−0.754344
$785$	−7.82065e9	−0.577031
$786$	0	0
$787$	−2.62116e10	−1.91682	−0.958410	−	0.285395i	$-0.907875\pi$
$787$	−2.62116e10	−1.91682	−0.958410	+	0.285395i	$0.907875\pi$
$788$	3.20078e9	0.233031
$789$	0	0
$790$	1.78233e9	0.128615
$791$	−1.42768e10	−1.02568
$792$	0	0
$793$	−1.12362e9	−0.0800138
$794$	2.38381e10	1.69005
$795$	0	0
$796$	4.21383e9	0.296129
$797$	−2.46142e10	−1.72219	−0.861095	−	0.508444i	$-0.830221\pi$
$797$	−2.46142e10	−1.72219	−0.861095	+	0.508444i	$0.830221\pi$
$798$	0	0
$799$	7.15223e9	0.496053
$800$	2.36176e9	0.163087
$801$	0	0
$802$	−1.19985e10	−0.821331
$803$	−9.48197e9	−0.646240
$804$	0	0
$805$	2.41756e10	1.63340
$806$	−4.58001e8	−0.0308101
$807$	0	0
$808$	−9.54311e9	−0.636429
$809$	2.46053e9	0.163383	0.0816917	−	0.996658i	$-0.473968\pi$
$809$	2.46053e9	0.163383	0.0816917	+	0.996658i	$0.473968\pi$
$810$	0	0
$811$	−2.24117e9	−0.147537	−0.0737687	−	0.997275i	$-0.523503\pi$
$811$	−2.24117e9	−0.147537	−0.0737687	+	0.997275i	$0.523503\pi$
$812$	4.62369e8	0.0303070
$813$	0	0
$814$	1.15070e10	0.747784
$815$	2.04628e9	0.132408
$816$	0	0
$817$	4.15515e9	0.266569
$818$	1.53609e10	0.981248
$819$	0	0
$820$	2.44843e9	0.155074
$821$	−2.00024e10	−1.26148	−0.630741	−	0.775993i	$-0.717249\pi$
$821$	−2.00024e10	−1.26148	−0.630741	+	0.775993i	$0.717249\pi$
$822$	0	0
$823$	1.73819e10	1.08692	0.543461	−	0.839435i	$-0.317114\pi$
$823$	1.73819e10	1.08692	0.543461	+	0.839435i	$0.317114\pi$
$824$	2.80623e10	1.74734
$825$	0	0
$826$	−2.56605e10	−1.58429
$827$	3.83667e8	0.0235877	0.0117939	−	0.999930i	$-0.496246\pi$
$827$	3.83667e8	0.0235877	0.0117939	+	0.999930i	$0.496246\pi$
$828$	0	0
$829$	−2.02867e9	−0.123672	−0.0618358	−	0.998086i	$-0.519696\pi$
$829$	−2.02867e9	−0.123672	−0.0618358	+	0.998086i	$0.519696\pi$
$830$	1.13813e9	0.0690903
$831$	0	0
$832$	3.73656e9	0.224926
$833$	6.21955e9	0.372822
$834$	0	0
$835$	−2.09690e10	−1.24645
$836$	−5.73086e9	−0.339233
$837$	0	0
$838$	3.47136e9	0.203772
$839$	1.21514e10	0.710331	0.355165	−	0.934803i	$-0.384425\pi$
$839$	1.21514e10	0.710331	0.355165	+	0.934803i	$0.384425\pi$
$840$	0	0
$841$	−1.70430e10	−0.988006
$842$	7.70051e9	0.444557
$843$	0	0
$844$	4.21650e9	0.241409
$845$	1.27903e10	0.729261
$846$	0	0
$847$	5.80548e8	0.0328281
$848$	−4.59542e9	−0.258785
$849$	0	0
$850$	2.56002e9	0.142980
$851$	2.31306e10	1.28657
$852$	0	0
$853$	2.82461e10	1.55825	0.779125	−	0.626868i	$-0.215664\pi$
$853$	2.82461e10	1.55825	0.779125	+	0.626868i	$0.215664\pi$
$854$	−9.09329e9	−0.499596
$855$	0	0
$856$	1.16573e10	0.635242
$857$	2.30960e10	1.25344	0.626720	−	0.779245i	$-0.284397\pi$
$857$	2.30960e10	1.25344	0.626720	+	0.779245i	$0.284397\pi$
$858$	0	0
$859$	2.83702e10	1.52716	0.763582	−	0.645711i	$-0.223439\pi$
$859$	2.83702e10	1.52716	0.763582	+	0.645711i	$0.223439\pi$
$860$	−4.24736e8	−0.0227706
$861$	0	0
$862$	1.11885e10	0.594970
$863$	3.45326e10	1.82891	0.914453	−	0.404693i	$-0.132622\pi$
$863$	3.45326e10	1.82891	0.914453	+	0.404693i	$0.132622\pi$
$864$	0	0
$865$	2.16710e10	1.13847
$866$	−2.16493e10	−1.13274
$867$	0	0
$868$	9.05694e8	0.0470070
$869$	−3.60727e9	−0.186470
$870$	0	0
$871$	−6.29460e8	−0.0322779
$872$	2.31408e10	1.18187
$873$	0	0
$874$	4.71444e10	2.38858
$875$	−3.01920e10	−1.52358
$876$	0	0
$877$	3.55493e10	1.77964	0.889820	−	0.456312i	$-0.150830\pi$
$877$	3.55493e10	1.77964	0.889820	+	0.456312i	$0.150830\pi$
$878$	−1.79428e10	−0.894662
$879$	0	0
$880$	−1.16227e10	−0.574936
$881$	−1.39078e10	−0.685239	−0.342620	−	0.939474i	$-0.611314\pi$
$881$	−1.39078e10	−0.685239	−0.342620	+	0.939474i	$0.611314\pi$
$882$	0	0
$883$	−2.23686e10	−1.09339	−0.546697	−	0.837331i	$-0.684115\pi$
$883$	−2.23686e10	−1.09339	−0.546697	+	0.837331i	$0.684115\pi$
$884$	−3.08568e8	−0.0150234
$885$	0	0
$886$	2.24715e10	1.08546
$887$	−1.22809e10	−0.590876	−0.295438	−	0.955362i	$-0.595466\pi$
$887$	−1.22809e10	−0.590876	−0.295438	+	0.955362i	$0.595466\pi$
$888$	0	0
$889$	−1.69888e10	−0.810974
$890$	−1.36500e10	−0.649034
$891$	0	0
$892$	−1.27746e8	−0.00602656
$893$	−4.87998e10	−2.29318
$894$	0	0
$895$	9.81124e9	0.457450
$896$	1.85073e10	0.859539
$897$	0	0
$898$	1.54569e10	0.712289
$899$	4.05270e8	0.0186031
$900$	0	0
$901$	2.80807e9	0.127900
$902$	2.02798e10	0.920114
$903$	0	0
$904$	1.73384e10	0.780583
$905$	3.15600e10	1.41536
$906$	0	0
$907$	−6.60412e9	−0.293893	−0.146947	−	0.989144i	$-0.546945\pi$
$907$	−6.60412e9	−0.293893	−0.146947	+	0.989144i	$0.546945\pi$
$908$	3.02360e8	0.0134037
$909$	0	0
$910$	−4.41834e9	−0.194363
$911$	−6.88875e9	−0.301874	−0.150937	−	0.988543i	$-0.548229\pi$
$911$	−6.88875e9	−0.301874	−0.150937	+	0.988543i	$0.548229\pi$
$912$	0	0
$913$	−2.30347e9	−0.100169
$914$	−3.21414e10	−1.39236
$915$	0	0
$916$	3.68613e9	0.158466
$917$	2.10119e10	0.899856
$918$	0	0
$919$	−1.75565e10	−0.746164	−0.373082	−	0.927798i	$-0.621699\pi$
$919$	−1.75565e10	−0.746164	−0.373082	+	0.927798i	$0.621699\pi$
$920$	−2.93599e10	−1.24308
$921$	0	0
$922$	−3.56509e10	−1.49800
$923$	8.64305e9	0.361794
$924$	0	0
$925$	−8.56992e9	−0.356025
$926$	−3.45847e10	−1.43135
$927$	0	0
$928$	−1.03088e9	−0.0423437
$929$	−1.64473e10	−0.673039	−0.336520	−	0.941676i	$-0.609250\pi$
$929$	−1.64473e10	−0.673039	−0.336520	+	0.941676i	$0.609250\pi$
$930$	0	0
$931$	−4.24361e10	−1.72350
$932$	4.53753e9	0.183596
$933$	0	0
$934$	−4.26492e10	−1.71276
$935$	7.10219e9	0.284153
$936$	0	0
$937$	2.16939e10	0.861490	0.430745	−	0.902474i	$-0.358251\pi$
$937$	2.16939e10	0.861490	0.430745	+	0.902474i	$0.358251\pi$
$938$	−5.09411e9	−0.201539
$939$	0	0
$940$	4.98827e9	0.195886
$941$	1.79390e10	0.701835	0.350918	−	0.936406i	$-0.385870\pi$
$941$	1.79390e10	0.701835	0.350918	+	0.936406i	$0.385870\pi$
$942$	0	0
$943$	4.07653e10	1.58307
$944$	2.47984e10	0.959447
$945$	0	0
$946$	−3.51799e9	−0.135106
$947$	9.90160e8	0.0378862	0.0189431	−	0.999821i	$-0.493970\pi$
$947$	9.90160e8	0.0378862	0.0189431	+	0.999821i	$0.493970\pi$
$948$	0	0
$949$	3.48342e9	0.132304
$950$	−1.74670e10	−0.660977
$951$	0	0
$952$	−1.52140e10	−0.571498
$953$	−4.86532e10	−1.82090	−0.910450	−	0.413619i	$-0.864265\pi$
$953$	−4.86532e10	−1.82090	−0.910450	+	0.413619i	$0.864265\pi$
$954$	0	0
$955$	−1.49860e10	−0.556769
$956$	−4.07697e9	−0.150916
$957$	0	0
$958$	7.21709e8	0.0265206
$959$	1.47963e10	0.541736
$960$	0	0
$961$	−2.67188e10	−0.971146
$962$	−4.22736e9	−0.153093
$963$	0	0
$964$	8.25109e9	0.296648
$965$	−2.88905e10	−1.03493
$966$	0	0
$967$	−3.94567e10	−1.40323	−0.701613	−	0.712558i	$-0.747536\pi$
$967$	−3.94567e10	−1.40323	−0.701613	+	0.712558i	$0.747536\pi$
$968$	−7.05043e8	−0.0249834
$969$	0	0
$970$	−2.52805e9	−0.0889373
$971$	2.64064e9	0.0925638	0.0462819	−	0.998928i	$-0.485263\pi$
$971$	2.64064e9	0.0925638	0.0462819	+	0.998928i	$0.485263\pi$
$972$	0	0
$973$	2.24840e10	0.782490
$974$	3.90549e10	1.35431
$975$	0	0
$976$	8.78777e9	0.302555
$977$	3.16993e10	1.08747	0.543737	−	0.839255i	$-0.317009\pi$
$977$	3.16993e10	1.08747	0.543737	+	0.839255i	$0.317009\pi$
$978$	0	0
$979$	2.76264e10	0.940989
$980$	4.33778e9	0.147223
$981$	0	0
$982$	−2.30206e10	−0.775757
$983$	−3.22825e10	−1.08400	−0.542000	−	0.840379i	$-0.682333\pi$
$983$	−3.22825e10	−1.08400	−0.542000	+	0.840379i	$0.682333\pi$
$984$	0	0
$985$	2.70648e10	0.902356
$986$	−1.11741e9	−0.0371232
$987$	0	0
$988$	2.10536e9	0.0694509
$989$	−7.07165e9	−0.232452
$990$	0	0
$991$	−4.98001e10	−1.62544	−0.812722	−	0.582651i	$-0.802015\pi$
$991$	−4.98001e10	−1.62544	−0.812722	+	0.582651i	$0.802015\pi$
$992$	−2.01929e9	−0.0656763
$993$	0	0
$994$	6.99467e10	2.25899
$995$	3.56308e10	1.14669
$996$	0	0
$997$	−7.51788e8	−0.0240249	−0.0120125	−	0.999928i	$-0.503824\pi$
$997$	−7.51788e8	−0.0240249	−0.0120125	+	0.999928i	$0.503824\pi$
$998$	1.10656e10	0.352387
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	387.8.a.a.1.4		10
3.2	odd	2		129.8.a.a.1.7	✓	10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
129.8.a.a.1.7	✓	10	3.2	odd	2
387.8.a.a.1.4		10	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 387 = 3^{2} \cdot 43 \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	387.a (trivial)

\(f(q)\)	\(=\)	\(q-10.1422 q^{2} -25.1352 q^{4} -212.535 q^{5} -1278.88 q^{7} +1553.13 q^{8} +O(q^{10})\)	\(q-10.1422 q^{2} -25.1352 q^{4} -212.535 q^{5} -1278.88 q^{7} +1553.13 q^{8} +2155.58 q^{10} -4362.71 q^{11} +1602.74 q^{13} +12970.7 q^{14} -12534.9 q^{16} +7659.58 q^{17} -52261.4 q^{19} +5342.12 q^{20} +44247.6 q^{22} +88943.8 q^{23} -32953.7 q^{25} -16255.4 q^{26} +32144.9 q^{28} +14383.9 q^{29} +28175.3 q^{31} -71668.9 q^{32} -77685.2 q^{34} +271808. q^{35} +260059. q^{37} +530047. q^{38} -330095. q^{40} +458326. q^{41} -79507.0 q^{43} +109657. q^{44} -902088. q^{46} +933763. q^{47} +811997. q^{49} +334224. q^{50} -40285.2 q^{52} +366609. q^{53} +927230. q^{55} -1.98627e6 q^{56} -145885. q^{58} -1.97834e6 q^{59} -701063. q^{61} -285761. q^{62} +2.33135e6 q^{64} -340640. q^{65} -392739. q^{67} -192525. q^{68} -2.75674e6 q^{70} +5.39266e6 q^{71} +2.17341e6 q^{73} -2.63758e6 q^{74} +1.31360e6 q^{76} +5.57939e6 q^{77} +826842. q^{79} +2.66411e6 q^{80} -4.64845e6 q^{82} +527990. q^{83} -1.62793e6 q^{85} +806378. q^{86} -6.77586e6 q^{88} -6.33239e6 q^{89} -2.04972e6 q^{91} -2.23562e6 q^{92} -9.47044e6 q^{94} +1.11074e7 q^{95} -1.17279e6 q^{97} -8.23546e6 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + q^{2} + 371 q^{4} + 122 q^{5} - 2052 q^{7} + 927 q^{8}+O(q^{10}) \) 10 * q + q^2 + 371 * q^4 + 122 * q^5 - 2052 * q^7 + 927 * q^8	\( 10 q + q^{2} + 371 q^{4} + 122 q^{5} - 2052 q^{7} + 927 q^{8} - 10032 q^{10} + 8888 q^{11} - 16432 q^{13} + 28408 q^{14} - 26669 q^{16} + 48122 q^{17} - 56146 q^{19} + 88940 q^{20} - 100626 q^{22} + 236336 q^{23} - 135016 q^{25} + 166748 q^{26} - 259060 q^{28} + 248818 q^{29} - 430970 q^{31} - 69493 q^{32} + 445522 q^{34} - 298982 q^{35} - 261254 q^{37} - 257662 q^{38} - 671432 q^{40} + 126814 q^{41} - 795070 q^{43} + 620022 q^{44} - 809038 q^{46} - 627080 q^{47} - 1256116 q^{49} + 83117 q^{50} - 3674204 q^{52} + 1612384 q^{53} - 4732974 q^{55} + 4301484 q^{56} - 7268516 q^{58} + 3442492 q^{59} - 5217214 q^{61} + 2500324 q^{62} - 4657369 q^{64} + 1224166 q^{65} - 6810926 q^{67} + 3563486 q^{68} - 2745858 q^{70} + 13935120 q^{71} - 13743720 q^{73} + 1752692 q^{74} - 15817594 q^{76} + 7685750 q^{77} - 9007608 q^{79} + 13641024 q^{80} - 6329026 q^{82} + 21779128 q^{83} - 13177392 q^{85} - 79507 q^{86} - 13214750 q^{88} + 1895364 q^{89} - 16439838 q^{91} - 9614510 q^{92} + 3404276 q^{94} + 16861514 q^{95} - 20434472 q^{97} - 35731457 q^{98}+O(q^{100}) \) 10 * q + q^2 + 371 * q^4 + 122 * q^5 - 2052 * q^7 + 927 * q^8 - 10032 * q^10 + 8888 * q^11 - 16432 * q^13 + 28408 * q^14 - 26669 * q^16 + 48122 * q^17 - 56146 * q^19 + 88940 * q^20 - 100626 * q^22 + 236336 * q^23 - 135016 * q^25 + 166748 * q^26 - 259060 * q^28 + 248818 * q^29 - 430970 * q^31 - 69493 * q^32 + 445522 * q^34 - 298982 * q^35 - 261254 * q^37 - 257662 * q^38 - 671432 * q^40 + 126814 * q^41 - 795070 * q^43 + 620022 * q^44 - 809038 * q^46 - 627080 * q^47 - 1256116 * q^49 + 83117 * q^50 - 3674204 * q^52 + 1612384 * q^53 - 4732974 * q^55 + 4301484 * q^56 - 7268516 * q^58 + 3442492 * q^59 - 5217214 * q^61 + 2500324 * q^62 - 4657369 * q^64 + 1224166 * q^65 - 6810926 * q^67 + 3563486 * q^68 - 2745858 * q^70 + 13935120 * q^71 - 13743720 * q^73 + 1752692 * q^74 - 15817594 * q^76 + 7685750 * q^77 - 9007608 * q^79 + 13641024 * q^80 - 6329026 * q^82 + 21779128 * q^83 - 13177392 * q^85 - 79507 * q^86 - 13214750 * q^88 + 1895364 * q^89 - 16439838 * q^91 - 9614510 * q^92 + 3404276 * q^94 + 16861514 * q^95 - 20434472 * q^97 - 35731457 * q^98

Introduction

L-functions

Modular forms

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