LMFDB - Embedded newform 387.8.a.d.1.3

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:	$13$
Coefficient field:	$\mathbb{Q}[x]/(x^{13} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{13} - 3 x^{12} - 1279 x^{11} + 3765 x^{10} + 598742 x^{9} - 1518614 x^{8} - 124677082 x^{7} + \cdots + 1551032970660 $ x^13 - 3x^12 - 1279x^11 + 3765x^10 + 598742x^9 - 1518614x^8 - 124677082x^7 + 193428526x^6 + 11160446785x^5 + 1754605765x^4 - 349352939351x^3 - 481872751923x^2 + 2098464001560x + 1551032970660
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{6}\cdot 3^{3} $
Twist minimal:	no (minimal twist has level 43)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$16.3440$ 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)

$f(q)$	$=$	$q-17.3440 q^{2} +172.814 q^{4} +122.945 q^{5} +247.011 q^{7} -777.246 q^{8} +O(q^{10})$	\(q-17.3440 q^{2} +172.814 q^{4} +122.945 q^{5} +247.011 q^{7} -777.246 q^{8} -2132.35 q^{10} -2503.52 q^{11} +1376.69 q^{13} -4284.15 q^{14} -8639.60 q^{16} +32082.0 q^{17} +10245.1 q^{19} +21246.5 q^{20} +43421.0 q^{22} +21850.6 q^{23} -63009.6 q^{25} -23877.3 q^{26} +42686.8 q^{28} -173813. q^{29} +16044.0 q^{31} +249333. q^{32} -556429. q^{34} +30368.6 q^{35} -75677.9 q^{37} -177691. q^{38} -95558.2 q^{40} -452656. q^{41} -79507.0 q^{43} -432643. q^{44} -378977. q^{46} -113517. q^{47} -762529. q^{49} +1.09284e6 q^{50} +237911. q^{52} +1.42412e6 q^{53} -307794. q^{55} -191988. q^{56} +3.01460e6 q^{58} -1.48283e6 q^{59} -2.69078e6 q^{61} -278267. q^{62} -3.21855e6 q^{64} +169257. q^{65} +2.19036e6 q^{67} +5.54420e6 q^{68} -526713. q^{70} -4.77162e6 q^{71} +4.98637e6 q^{73} +1.31256e6 q^{74} +1.77049e6 q^{76} -618397. q^{77} +3.39256e6 q^{79} -1.06219e6 q^{80} +7.85086e6 q^{82} -8.35875e6 q^{83} +3.94431e6 q^{85} +1.37897e6 q^{86} +1.94585e6 q^{88} +7.83169e6 q^{89} +340058. q^{91} +3.77608e6 q^{92} +1.96883e6 q^{94} +1.25958e6 q^{95} +6.12777e6 q^{97} +1.32253e7 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 13 q - 16 q^{2} + 922 q^{4} - 998 q^{5} + 1360 q^{7} - 3870 q^{8}+O(q^{10}) $ 13 * q - 16 * q^2 + 922 * q^4 - 998 * q^5 + 1360 * q^7 - 3870 * q^8	\( 13 q - 16 q^{2} + 922 q^{4} - 998 q^{5} + 1360 q^{7} - 3870 q^{8} + 4667 q^{10} - 1620 q^{11} + 13550 q^{13} - 44160 q^{14} + 114026 q^{16} - 110880 q^{17} + 105058 q^{19} - 167251 q^{20} + 201504 q^{22} - 160184 q^{23} + 270149 q^{25} - 272104 q^{26} + 208172 q^{28} - 285546 q^{29} - 99616 q^{31} - 200126 q^{32} - 80941 q^{34} + 187104 q^{35} + 176038 q^{37} - 652165 q^{38} - 895387 q^{40} + 410260 q^{41} - 1033591 q^{43} + 2177076 q^{44} - 3975765 q^{46} + 424556 q^{47} - 1561359 q^{49} + 4063801 q^{50} - 4172312 q^{52} - 3992458 q^{53} + 406960 q^{55} - 1559556 q^{56} - 4052005 q^{58} - 2248836 q^{59} + 6210394 q^{61} - 885317 q^{62} - 3096318 q^{64} - 5600420 q^{65} - 1993648 q^{67} - 9327135 q^{68} - 1105098 q^{70} - 4978064 q^{71} + 8224814 q^{73} + 3613563 q^{74} + 10687121 q^{76} - 17261892 q^{77} + 6945708 q^{79} - 15822799 q^{80} - 508449 q^{82} - 22937328 q^{83} - 575532 q^{85} + 1272112 q^{86} + 11202656 q^{88} - 9291302 q^{89} + 25581108 q^{91} + 14388137 q^{92} - 24645805 q^{94} - 30750464 q^{95} + 10001852 q^{97} + 32304856 q^{98}+O(q^{100}) \) 13 * q - 16 * q^2 + 922 * q^4 - 998 * q^5 + 1360 * q^7 - 3870 * q^8 + 4667 * q^10 - 1620 * q^11 + 13550 * q^13 - 44160 * q^14 + 114026 * q^16 - 110880 * q^17 + 105058 * q^19 - 167251 * q^20 + 201504 * q^22 - 160184 * q^23 + 270149 * q^25 - 272104 * q^26 + 208172 * q^28 - 285546 * q^29 - 99616 * q^31 - 200126 * q^32 - 80941 * q^34 + 187104 * q^35 + 176038 * q^37 - 652165 * q^38 - 895387 * q^40 + 410260 * q^41 - 1033591 * q^43 + 2177076 * q^44 - 3975765 * q^46 + 424556 * q^47 - 1561359 * q^49 + 4063801 * q^50 - 4172312 * q^52 - 3992458 * q^53 + 406960 * q^55 - 1559556 * q^56 - 4052005 * q^58 - 2248836 * q^59 + 6210394 * q^61 - 885317 * q^62 - 3096318 * q^64 - 5600420 * q^65 - 1993648 * q^67 - 9327135 * q^68 - 1105098 * q^70 - 4978064 * q^71 + 8224814 * q^73 + 3613563 * q^74 + 10687121 * q^76 - 17261892 * q^77 + 6945708 * q^79 - 15822799 * q^80 - 508449 * q^82 - 22937328 * q^83 - 575532 * q^85 + 1272112 * q^86 + 11202656 * q^88 - 9291302 * q^89 + 25581108 * q^91 + 14388137 * q^92 - 24645805 * q^94 - 30750464 * q^95 + 10001852 * q^97 + 32304856 * 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 $

$2$	−17.3440	−1.53301	−0.766503	−	0.642241i	$-0.778005\pi$
$2$	−17.3440	−1.53301	−0.766503	+	0.642241i	$0.778005\pi$
$3$	0	0
$3$	0	0
$4$	172.814	1.35011
$5$	122.945	0.439860	0.219930	−	0.975516i	$-0.429417\pi$
$5$	122.945	0.439860	0.219930	+	0.975516i	$0.429417\pi$
$6$	0	0
$7$	247.011	0.272190	0.136095	−	0.990696i	$-0.456545\pi$
$7$	247.011	0.272190	0.136095	+	0.990696i	$0.456545\pi$
$8$	−777.246	−0.536715
$9$	0	0
$10$	−2132.35	−0.674308
$11$	−2503.52	−0.567123	−0.283561	−	0.958954i	$-0.591516\pi$
$11$	−2503.52	−0.567123	−0.283561	+	0.958954i	$0.591516\pi$
$12$	0	0
$13$	1376.69	0.173794	0.0868970	−	0.996217i	$-0.472305\pi$
$13$	1376.69	0.173794	0.0868970	+	0.996217i	$0.472305\pi$
$14$	−4284.15	−0.417269
$15$	0	0
$16$	−8639.60	−0.527320
$17$	32082.0	1.58376	0.791881	−	0.610675i	$-0.209102\pi$
$17$	32082.0	1.58376	0.791881	+	0.610675i	$0.209102\pi$
$18$	0	0
$19$	10245.1	0.342672	0.171336	−	0.985213i	$-0.445192\pi$
$19$	10245.1	0.342672	0.171336	+	0.985213i	$0.445192\pi$
$20$	21246.5	0.593858
$21$	0	0
$22$	43421.0	0.869402
$23$	21850.6	0.374469	0.187235	−	0.982315i	$-0.440048\pi$
$23$	21850.6	0.374469	0.187235	+	0.982315i	$0.440048\pi$
$24$	0	0
$25$	−63009.6	−0.806523
$26$	−23877.3	−0.266427
$27$	0	0
$28$	42686.8	0.367486
$29$	−173813.	−1.32339	−0.661696	−	0.749772i	$-0.730163\pi$
$29$	−173813.	−1.32339	−0.661696	+	0.749772i	$0.730163\pi$
$30$	0	0
$31$	16044.0	0.0967270	0.0483635	−	0.998830i	$-0.484599\pi$
$31$	16044.0	0.0967270	0.0483635	+	0.998830i	$0.484599\pi$
$32$	249333.	1.34510
$33$	0	0
$34$	−556429.	−2.42792
$35$	30368.6	0.119726
$36$	0	0
$37$	−75677.9	−0.245620	−0.122810	−	0.992430i	$-0.539191\pi$
$37$	−75677.9	−0.245620	−0.122810	+	0.992430i	$0.539191\pi$
$38$	−177691.	−0.525318
$39$	0	0
$40$	−95558.2	−0.236079
$41$	−452656.	−1.02571	−0.512855	−	0.858475i	$-0.671412\pi$
$41$	−452656.	−1.02571	−0.512855	+	0.858475i	$0.671412\pi$
$42$	0	0
$43$	−79507.0	−0.152499
$43$	−79507.0	−0.152499
$44$	−432643.	−0.765676
$45$	0	0
$46$	−378977.	−0.574063
$47$	−113517.	−0.159484	−0.0797420	−	0.996816i	$-0.525410\pi$
$47$	−113517.	−0.159484	−0.0797420	+	0.996816i	$0.525410\pi$
$48$	0	0
$49$	−762529.	−0.925912
$50$	1.09284e6	1.23640
$51$	0	0
$52$	237911.	0.234640
$53$	1.42412e6	1.31395	0.656976	−	0.753911i	$-0.271835\pi$
$53$	1.42412e6	1.31395	0.656976	+	0.753911i	$0.271835\pi$
$54$	0	0
$55$	−307794.	−0.249455
$56$	−191988.	−0.146089
$57$	0	0
$58$	3.01460e6	2.02877
$59$	−1.48283e6	−0.939960	−0.469980	−	0.882677i	$-0.655739\pi$
$59$	−1.48283e6	−0.939960	−0.469980	+	0.882677i	$0.655739\pi$
$60$	0	0
$61$	−2.69078e6	−1.51784	−0.758918	−	0.651187i	$-0.774271\pi$
$61$	−2.69078e6	−1.51784	−0.758918	+	0.651187i	$0.774271\pi$
$62$	−278267.	−0.148283
$63$	0	0
$64$	−3.21855e6	−1.53472
$65$	169257.	0.0764450
$66$	0	0
$67$	2.19036e6	0.889722	0.444861	−	0.895600i	$-0.353253\pi$
$67$	2.19036e6	0.889722	0.444861	+	0.895600i	$0.353253\pi$
$68$	5.54420e6	2.13825
$69$	0	0
$70$	−526713.	−0.183540
$71$	−4.77162e6	−1.58220	−0.791101	−	0.611685i	$-0.790492\pi$
$71$	−4.77162e6	−1.58220	−0.791101	+	0.611685i	$0.790492\pi$
$72$	0	0
$73$	4.98637e6	1.50022	0.750109	−	0.661314i	$-0.230001\pi$
$73$	4.98637e6	1.50022	0.750109	+	0.661314i	$0.230001\pi$
$74$	1.31256e6	0.376536
$75$	0	0
$76$	1.77049e6	0.462644
$77$	−618397.	−0.154365
$78$	0	0
$79$	3.39256e6	0.774163	0.387081	−	0.922046i	$-0.373483\pi$
$79$	3.39256e6	0.774163	0.387081	+	0.922046i	$0.373483\pi$
$80$	−1.06219e6	−0.231947
$81$	0	0
$82$	7.85086e6	1.57242
$83$	−8.35875e6	−1.60460	−0.802302	−	0.596918i	$-0.796392\pi$
$83$	−8.35875e6	−1.60460	−0.802302	+	0.596918i	$0.796392\pi$
$84$	0	0
$85$	3.94431e6	0.696634
$86$	1.37897e6	0.233781
$87$	0	0
$88$	1.94585e6	0.304383
$89$	7.83169e6	1.17758	0.588790	−	0.808286i	$-0.299604\pi$
$89$	7.83169e6	1.17758	0.588790	+	0.808286i	$0.299604\pi$
$90$	0	0
$91$	340058.	0.0473051
$92$	3.77608e6	0.505573
$93$	0	0
$94$	1.96883e6	0.244490
$95$	1.25958e6	0.150728
$96$	0	0
$97$	6.12777e6	0.681712	0.340856	−	0.940115i	$-0.389283\pi$
$97$	6.12777e6	0.681712	0.340856	+	0.940115i	$0.389283\pi$
$98$	1.32253e7	1.41943
$99$	0	0
$100$	−1.08889e7	−1.08889
$101$	1.48954e7	1.43856	0.719279	−	0.694721i	$-0.244472\pi$
$101$	1.48954e7	1.43856	0.719279	+	0.694721i	$0.244472\pi$
$102$	0	0
$103$	8.96048e6	0.807981	0.403990	−	0.914763i	$-0.367623\pi$
$103$	8.96048e6	0.807981	0.403990	+	0.914763i	$0.367623\pi$
$104$	−1.07003e6	−0.0932778
$105$	0	0
$106$	−2.46998e7	−2.01430
$107$	2.20290e6	0.173841	0.0869204	−	0.996215i	$-0.472297\pi$
$107$	2.20290e6	0.173841	0.0869204	+	0.996215i	$0.472297\pi$
$108$	0	0
$109$	1.43255e7	1.05954	0.529770	−	0.848141i	$-0.322278\pi$
$109$	1.43255e7	1.05954	0.529770	+	0.848141i	$0.322278\pi$
$110$	5.33838e6	0.382415
$111$	0	0
$112$	−2.13408e6	−0.143531
$113$	−5.69345e6	−0.371194	−0.185597	−	0.982626i	$-0.559422\pi$
$113$	−5.69345e6	−0.371194	−0.185597	+	0.982626i	$0.559422\pi$
$114$	0	0
$115$	2.68641e6	0.164714
$116$	−3.00372e7	−1.78672
$117$	0	0
$118$	2.57182e7	1.44096
$119$	7.92460e6	0.431085
$120$	0	0
$121$	−1.32196e7	−0.678372
$122$	4.66689e7	2.32685
$123$	0	0
$124$	2.77263e6	0.130592
$125$	−1.73517e7	−0.794617
$126$	0	0
$127$	2.89632e7	1.25468	0.627342	−	0.778744i	$-0.284143\pi$
$127$	2.89632e7	1.25468	0.627342	+	0.778744i	$0.284143\pi$
$128$	2.39079e7	1.00764
$129$	0	0
$130$	−2.93559e6	−0.117191
$131$	−1.30359e7	−0.506632	−0.253316	−	0.967384i	$-0.581521\pi$
$131$	−1.30359e7	−0.506632	−0.253316	+	0.967384i	$0.581521\pi$
$132$	0	0
$133$	2.53065e6	0.0932721
$134$	−3.79896e7	−1.36395
$135$	0	0
$136$	−2.49356e7	−0.850029
$137$	3.16388e7	1.05123	0.525615	−	0.850723i	$-0.323835\pi$
$137$	3.16388e7	1.05123	0.525615	+	0.850723i	$0.323835\pi$
$138$	0	0
$139$	−4.62889e7	−1.46193	−0.730963	−	0.682418i	$-0.760929\pi$
$139$	−4.62889e7	−1.46193	−0.730963	+	0.682418i	$0.760929\pi$
$140$	5.24811e6	0.161642
$141$	0	0
$142$	8.27589e7	2.42552
$143$	−3.44658e6	−0.0985625
$144$	0	0
$145$	−2.13693e7	−0.582107
$146$	−8.64835e7	−2.29984
$147$	0	0
$148$	−1.30782e7	−0.331613
$149$	−3.21433e7	−0.796048	−0.398024	−	0.917375i	$-0.630304\pi$
$149$	−3.21433e7	−0.796048	−0.398024	+	0.917375i	$0.630304\pi$
$150$	0	0
$151$	2.05927e7	0.486737	0.243369	−	0.969934i	$-0.421748\pi$
$151$	2.05927e7	0.486737	0.243369	+	0.969934i	$0.421748\pi$
$152$	−7.96296e6	−0.183917
$153$	0	0
$154$	1.07255e7	0.236643
$155$	1.97253e6	0.0425463
$156$	0	0
$157$	−2.11067e7	−0.435283	−0.217641	−	0.976029i	$-0.569836\pi$
$157$	−2.11067e7	−0.435283	−0.217641	+	0.976029i	$0.569836\pi$
$158$	−5.88404e7	−1.18680
$159$	0	0
$160$	3.06541e7	0.591655
$161$	5.39734e6	0.101927
$162$	0	0
$163$	983833.	0.0177936	0.00889682	−	0.999960i	$-0.497168\pi$
$163$	983833.	0.0177936	0.00889682	+	0.999960i	$0.497168\pi$
$164$	−7.82251e7	−1.38482
$165$	0	0
$166$	1.44974e8	2.45987
$167$	−9.39137e7	−1.56035	−0.780174	−	0.625563i	$-0.784869\pi$
$167$	−9.39137e7	−1.56035	−0.780174	+	0.625563i	$0.784869\pi$
$168$	0	0
$169$	−6.08532e7	−0.969796
$170$	−6.84100e7	−1.06794
$171$	0	0
$172$	−1.37399e7	−0.205889
$173$	−1.05361e8	−1.54710	−0.773551	−	0.633734i	$-0.781522\pi$
$173$	−1.05361e8	−1.54710	−0.773551	+	0.633734i	$0.781522\pi$
$174$	0	0
$175$	−1.55641e7	−0.219528
$176$	2.16294e7	0.299055
$177$	0	0
$178$	−1.35833e8	−1.80524
$179$	7.52808e7	0.981067	0.490533	−	0.871422i	$-0.336802\pi$
$179$	7.52808e7	0.981067	0.490533	+	0.871422i	$0.336802\pi$
$180$	0	0
$181$	−2.35542e7	−0.295253	−0.147626	−	0.989043i	$-0.547163\pi$
$181$	−2.35542e7	−0.295253	−0.147626	+	0.989043i	$0.547163\pi$
$182$	−5.89795e6	−0.0725189
$183$	0	0
$184$	−1.69833e7	−0.200983
$185$	−9.30419e6	−0.108038
$186$	0	0
$187$	−8.03180e7	−0.898188
$188$	−1.96172e7	−0.215320
$189$	0	0
$190$	−2.18461e7	−0.231066
$191$	−1.11671e8	−1.15964	−0.579820	−	0.814745i	$-0.696877\pi$
$191$	−1.11671e8	−1.15964	−0.579820	+	0.814745i	$0.696877\pi$
$192$	0	0
$193$	−1.17636e8	−1.17785	−0.588926	−	0.808187i	$-0.700449\pi$
$193$	−1.17636e8	−1.17785	−0.588926	+	0.808187i	$0.700449\pi$
$194$	−1.06280e8	−1.04507
$195$	0	0
$196$	−1.31775e8	−1.25008
$197$	5.42883e7	0.505912	0.252956	−	0.967478i	$-0.418597\pi$
$197$	5.42883e7	0.505912	0.252956	+	0.967478i	$0.418597\pi$
$198$	0	0
$199$	8.13364e7	0.731643	0.365822	−	0.930685i	$-0.380788\pi$
$199$	8.13364e7	0.731643	0.365822	+	0.930685i	$0.380788\pi$
$200$	4.89740e7	0.432873
$201$	0	0
$202$	−2.58346e8	−2.20532
$203$	−4.29336e7	−0.360215
$204$	0	0
$205$	−5.56516e7	−0.451169
$206$	−1.55410e8	−1.23864
$207$	0	0
$208$	−1.18941e7	−0.0916450
$209$	−2.56488e7	−0.194337
$210$	0	0
$211$	7.38401e7	0.541132	0.270566	−	0.962701i	$-0.412789\pi$
$211$	7.38401e7	0.541132	0.270566	+	0.962701i	$0.412789\pi$
$212$	2.46106e8	1.77397
$213$	0	0
$214$	−3.82071e7	−0.266499
$215$	−9.77496e6	−0.0670780
$216$	0	0
$217$	3.96305e6	0.0263282
$218$	−2.48461e8	−1.62428
$219$	0	0
$220$	−5.31911e7	−0.336790
$221$	4.41670e7	0.275248
$222$	0	0
$223$	−1.01645e8	−0.613790	−0.306895	−	0.951743i	$-0.599290\pi$
$223$	−1.01645e8	−0.613790	−0.306895	+	0.951743i	$0.599290\pi$
$224$	6.15878e7	0.366123
$225$	0	0
$226$	9.87471e7	0.569043
$227$	1.95225e8	1.10776	0.553880	−	0.832596i	$-0.313146\pi$
$227$	1.95225e8	1.10776	0.553880	+	0.832596i	$0.313146\pi$
$228$	0	0
$229$	−1.38246e8	−0.760727	−0.380363	−	0.924837i	$-0.624201\pi$
$229$	−1.38246e8	−0.760727	−0.380363	+	0.924837i	$0.624201\pi$
$230$	−4.65931e7	−0.252507
$231$	0	0
$232$	1.35095e8	0.710284
$233$	7.52341e7	0.389645	0.194822	−	0.980839i	$-0.437587\pi$
$233$	7.52341e7	0.389645	0.194822	+	0.980839i	$0.437587\pi$
$234$	0	0
$235$	−1.39563e7	−0.0701506
$236$	−2.56253e8	−1.26905
$237$	0	0
$238$	−1.37444e8	−0.660856
$239$	5.37584e7	0.254715	0.127357	−	0.991857i	$-0.459351\pi$
$239$	5.37584e7	0.254715	0.127357	+	0.991857i	$0.459351\pi$
$240$	0	0
$241$	−4.33242e8	−1.99375	−0.996876	−	0.0789843i	$-0.974832\pi$
$241$	−4.33242e8	−1.99375	−0.996876	+	0.0789843i	$0.974832\pi$
$242$	2.29280e8	1.03995
$243$	0	0
$244$	−4.65004e8	−2.04924
$245$	−9.37488e7	−0.407272
$246$	0	0
$247$	1.41043e7	0.0595544
$248$	−1.24702e7	−0.0519148
$249$	0	0
$250$	3.00948e8	1.21815
$251$	3.50742e8	1.40001	0.700003	−	0.714140i	$-0.253182\pi$
$251$	3.50742e8	1.40001	0.700003	+	0.714140i	$0.253182\pi$
$252$	0	0
$253$	−5.47035e7	−0.212370
$254$	−5.02338e8	−1.92344
$255$	0	0
$256$	−2.68346e6	−0.00999666
$257$	−3.82436e8	−1.40538	−0.702689	−	0.711497i	$-0.748017\pi$
$257$	−3.82436e8	−1.40538	−0.702689	+	0.711497i	$0.748017\pi$
$258$	0	0
$259$	−1.86933e7	−0.0668554
$260$	2.92499e7	0.103209
$261$	0	0
$262$	2.26095e8	0.776670
$263$	4.76819e8	1.61625	0.808125	−	0.589011i	$-0.200483\pi$
$263$	4.76819e8	1.61625	0.808125	+	0.589011i	$0.200483\pi$
$264$	0	0
$265$	1.75087e8	0.577955
$266$	−4.38916e7	−0.142987
$267$	0	0
$268$	3.78524e8	1.20122
$269$	−4.56754e8	−1.43070	−0.715352	−	0.698765i	$-0.753733\pi$
$269$	−4.56754e8	−1.43070	−0.715352	+	0.698765i	$0.753733\pi$
$270$	0	0
$271$	−3.80308e8	−1.16076	−0.580381	−	0.814345i	$-0.697096\pi$
$271$	−3.80308e8	−1.16076	−0.580381	+	0.814345i	$0.697096\pi$
$272$	−2.77176e8	−0.835149
$273$	0	0
$274$	−5.48742e8	−1.61154
$275$	1.57746e8	0.457398
$276$	0	0
$277$	−1.74969e8	−0.494632	−0.247316	−	0.968935i	$-0.579549\pi$
$277$	−1.74969e8	−0.494632	−0.247316	+	0.968935i	$0.579549\pi$
$278$	8.02834e8	2.24114
$279$	0	0
$280$	−2.36039e7	−0.0642585
$281$	9.23019e7	0.248164	0.124082	−	0.992272i	$-0.460401\pi$
$281$	9.23019e7	0.248164	0.124082	+	0.992272i	$0.460401\pi$
$282$	0	0
$283$	−6.07622e8	−1.59361	−0.796803	−	0.604239i	$-0.793477\pi$
$283$	−6.07622e8	−1.59361	−0.796803	+	0.604239i	$0.793477\pi$
$284$	−8.24601e8	−2.13614
$285$	0	0
$286$	5.97773e7	0.151097
$287$	−1.11811e8	−0.279189
$288$	0	0
$289$	6.18915e8	1.50830
$290$	3.70629e8	0.892373
$291$	0	0
$292$	8.61712e8	2.02545
$293$	4.12823e8	0.958798	0.479399	−	0.877597i	$-0.340855\pi$
$293$	4.12823e8	0.958798	0.479399	+	0.877597i	$0.340855\pi$
$294$	0	0
$295$	−1.82306e8	−0.413451
$296$	5.88204e7	0.131828
$297$	0	0
$298$	5.57493e8	1.22035
$299$	3.00815e7	0.0650805
$300$	0	0
$301$	−1.96391e7	−0.0415087
$302$	−3.57160e8	−0.746171
$303$	0	0
$304$	−8.85136e7	−0.180698
$305$	−3.30817e8	−0.667635
$306$	0	0
$307$	3.39020e8	0.668715	0.334358	−	0.942446i	$-0.391481\pi$
$307$	3.39020e8	0.668715	0.334358	+	0.942446i	$0.391481\pi$
$308$	−1.06867e8	−0.208410
$309$	0	0
$310$	−3.42115e7	−0.0652237
$311$	−3.14861e8	−0.593550	−0.296775	−	0.954947i	$-0.595911\pi$
$311$	−3.14861e8	−0.593550	−0.296775	+	0.954947i	$0.595911\pi$
$312$	0	0
$313$	−7.61170e7	−0.140306	−0.0701531	−	0.997536i	$-0.522349\pi$
$313$	−7.61170e7	−0.140306	−0.0701531	+	0.997536i	$0.522349\pi$
$314$	3.66074e8	0.667291
$315$	0	0
$316$	5.86280e8	1.04520
$317$	−3.04947e6	−0.00537671	−0.00268835	−	0.999996i	$-0.500856\pi$
$317$	−3.04947e6	−0.00537671	−0.00268835	+	0.999996i	$0.500856\pi$
$318$	0	0
$319$	4.35144e8	0.750525
$320$	−3.95703e8	−0.675064
$321$	0	0
$322$	−9.36113e7	−0.156255
$323$	3.28683e8	0.542711
$324$	0	0
$325$	−8.67448e7	−0.140169
$326$	−1.70636e7	−0.0272777
$327$	0	0
$328$	3.51825e8	0.550514
$329$	−2.80398e7	−0.0434100
$330$	0	0
$331$	−6.34097e8	−0.961076	−0.480538	−	0.876974i	$-0.659559\pi$
$331$	−6.34097e8	−0.961076	−0.480538	+	0.876974i	$0.659559\pi$
$332$	−1.44450e9	−2.16639
$333$	0	0
$334$	1.62884e9	2.39202
$335$	2.69293e8	0.391353
$336$	0	0
$337$	2.48720e8	0.354003	0.177001	−	0.984211i	$-0.443360\pi$
$337$	2.48720e8	0.354003	0.177001	+	0.984211i	$0.443360\pi$
$338$	1.05544e9	1.48670
$339$	0	0
$340$	6.81630e8	0.940529
$341$	−4.01666e7	−0.0548560
$342$	0	0
$343$	−3.91777e8	−0.524215
$344$	6.17965e7	0.0818482
$345$	0	0
$346$	1.82738e9	2.37172
$347$	−7.91060e8	−1.01638	−0.508190	−	0.861245i	$-0.669685\pi$
$347$	−7.91060e8	−1.01638	−0.508190	+	0.861245i	$0.669685\pi$
$348$	0	0
$349$	−5.53018e8	−0.696386	−0.348193	−	0.937423i	$-0.613205\pi$
$349$	−5.53018e8	−0.696386	−0.348193	+	0.937423i	$0.613205\pi$
$350$	2.69943e8	0.336538
$351$	0	0
$352$	−6.24209e8	−0.762836
$353$	−1.06776e9	−1.29200	−0.645999	−	0.763338i	$-0.723559\pi$
$353$	−1.06776e9	−1.29200	−0.645999	+	0.763338i	$0.723559\pi$
$354$	0	0
$355$	−5.86645e8	−0.695947
$356$	1.35342e9	1.58986
$357$	0	0
$358$	−1.30567e9	−1.50398
$359$	−1.46087e9	−1.66641	−0.833203	−	0.552967i	$-0.813496\pi$
$359$	−1.46087e9	−1.66641	−0.833203	+	0.552967i	$0.813496\pi$
$360$	0	0
$361$	−7.88910e8	−0.882576
$362$	4.08524e8	0.452624
$363$	0	0
$364$	5.87666e7	0.0638669
$365$	6.13047e8	0.659886
$366$	0	0
$367$	1.28374e9	1.35564	0.677822	−	0.735226i	$-0.262924\pi$
$367$	1.28374e9	1.35564	0.677822	+	0.735226i	$0.262924\pi$
$368$	−1.88781e8	−0.197465
$369$	0	0
$370$	1.61372e8	0.165623
$371$	3.51772e8	0.357645
$372$	0	0
$373$	−4.86215e8	−0.485118	−0.242559	−	0.970137i	$-0.577987\pi$
$373$	−4.86215e8	−0.485118	−0.242559	+	0.970137i	$0.577987\pi$
$374$	1.39303e9	1.37693
$375$	0	0
$376$	8.82303e7	0.0855974
$377$	−2.39286e8	−0.229998
$378$	0	0
$379$	−1.35199e9	−1.27567	−0.637834	−	0.770174i	$-0.720169\pi$
$379$	−1.35199e9	−1.27567	−0.637834	+	0.770174i	$0.720169\pi$
$380$	2.17673e8	0.203498
$381$	0	0
$382$	1.93682e9	1.77773
$383$	6.26582e8	0.569878	0.284939	−	0.958546i	$-0.408027\pi$
$383$	6.26582e8	0.569878	0.284939	+	0.958546i	$0.408027\pi$
$384$	0	0
$385$	−7.60286e7	−0.0678991
$386$	2.04028e9	1.80565
$387$	0	0
$388$	1.05896e9	0.920384
$389$	1.29391e9	1.11450	0.557250	−	0.830345i	$-0.311856\pi$
$389$	1.29391e9	1.11450	0.557250	+	0.830345i	$0.311856\pi$
$390$	0	0
$391$	7.01011e8	0.593070
$392$	5.92672e8	0.496951
$393$	0	0
$394$	−9.41575e8	−0.775565
$395$	4.17096e8	0.340523
$396$	0	0
$397$	2.44753e9	1.96319	0.981594	−	0.190981i	$-0.0611669\pi$
$397$	2.44753e9	1.96319	0.981594	+	0.190981i	$0.0611669\pi$
$398$	−1.41070e9	−1.12161
$399$	0	0
$400$	5.44378e8	0.425296
$401$	8.46869e8	0.655860	0.327930	−	0.944702i	$-0.393649\pi$
$401$	8.46869e8	0.655860	0.327930	+	0.944702i	$0.393649\pi$
$402$	0	0
$403$	2.20877e7	0.0168106
$404$	2.57413e9	1.94221
$405$	0	0
$406$	7.44640e8	0.552211
$407$	1.89461e8	0.139297
$408$	0	0
$409$	−1.06925e9	−0.772763	−0.386381	−	0.922339i	$-0.626275\pi$
$409$	−1.06925e9	−0.772763	−0.386381	+	0.922339i	$0.626275\pi$
$410$	9.65221e8	0.691645
$411$	0	0
$412$	1.54849e9	1.09086
$413$	−3.66275e8	−0.255848
$414$	0	0
$415$	−1.02766e9	−0.705801
$416$	3.43254e8	0.233770
$417$	0	0
$418$	4.44853e8	0.297920
$419$	−8.44198e8	−0.560654	−0.280327	−	0.959905i	$-0.590443\pi$
$419$	−8.44198e8	−0.560654	−0.280327	+	0.959905i	$0.590443\pi$
$420$	0	0
$421$	−8.77632e8	−0.573225	−0.286612	−	0.958047i	$-0.592529\pi$
$421$	−8.77632e8	−0.573225	−0.286612	+	0.958047i	$0.592529\pi$
$422$	−1.28068e9	−0.829559
$423$	0	0
$424$	−1.10689e9	−0.705217
$425$	−2.02147e9	−1.27734
$426$	0	0
$427$	−6.64653e8	−0.413140
$428$	3.80691e8	0.234704
$429$	0	0
$430$	1.69537e8	0.102831
$431$	4.03075e7	0.0242502	0.0121251	−	0.999926i	$-0.496140\pi$
$431$	4.03075e7	0.0242502	0.0121251	+	0.999926i	$0.496140\pi$
$432$	0	0
$433$	1.00411e9	0.594391	0.297196	−	0.954817i	$-0.403949\pi$
$433$	1.00411e9	0.594391	0.297196	+	0.954817i	$0.403949\pi$
$434$	−6.87351e7	−0.0403612
$435$	0	0
$436$	2.47564e9	1.43049
$437$	2.23862e8	0.128320
$438$	0	0
$439$	6.13553e8	0.346120	0.173060	−	0.984911i	$-0.444635\pi$
$439$	6.13553e8	0.346120	0.173060	+	0.984911i	$0.444635\pi$
$440$	2.39232e8	0.133886
$441$	0	0
$442$	−7.66031e8	−0.421957
$443$	1.76951e9	0.967028	0.483514	−	0.875337i	$-0.339360\pi$
$443$	1.76951e9	0.967028	0.483514	+	0.875337i	$0.339360\pi$
$444$	0	0
$445$	9.62864e8	0.517970
$446$	1.76293e9	0.940944
$447$	0	0
$448$	−7.95017e8	−0.417737
$449$	2.28688e9	1.19229	0.596145	−	0.802877i	$-0.296698\pi$
$449$	2.28688e9	1.19229	0.596145	+	0.802877i	$0.296698\pi$
$450$	0	0
$451$	1.13323e9	0.581704
$452$	−9.83906e8	−0.501152
$453$	0	0
$454$	−3.38599e9	−1.69820
$455$	4.18083e7	0.0208076
$456$	0	0
$457$	8.79369e8	0.430987	0.215494	−	0.976505i	$-0.430864\pi$
$457$	8.79369e8	0.430987	0.215494	+	0.976505i	$0.430864\pi$
$458$	2.39774e9	1.16620
$459$	0	0
$460$	4.64249e8	0.222381
$461$	−1.43825e9	−0.683724	−0.341862	−	0.939750i	$-0.611058\pi$
$461$	−1.43825e9	−0.683724	−0.341862	+	0.939750i	$0.611058\pi$
$462$	0	0
$463$	−3.40869e9	−1.59608	−0.798040	−	0.602605i	$-0.794130\pi$
$463$	−3.40869e9	−1.59608	−0.798040	+	0.602605i	$0.794130\pi$
$464$	1.50167e9	0.697850
$465$	0	0
$466$	−1.30486e9	−0.597327
$467$	−3.01086e9	−1.36798	−0.683992	−	0.729490i	$-0.739758\pi$
$467$	−3.01086e9	−1.36798	−0.683992	+	0.729490i	$0.739758\pi$
$468$	0	0
$469$	5.41043e8	0.242174
$470$	2.42057e8	0.107541
$471$	0	0
$472$	1.15252e9	0.504490
$473$	1.99047e8	0.0864854
$474$	0	0
$475$	−6.45540e8	−0.276373
$476$	1.36948e9	0.582011
$477$	0	0
$478$	−9.32385e8	−0.390479
$479$	−3.75213e7	−0.0155992	−0.00779961	−	0.999970i	$-0.502483\pi$
$479$	−3.75213e7	−0.0155992	−0.00779961	+	0.999970i	$0.502483\pi$
$480$	0	0
$481$	−1.04185e8	−0.0426872
$482$	7.51414e9	3.05643
$483$	0	0
$484$	−2.28452e9	−0.915874
$485$	7.53376e8	0.299858
$486$	0	0
$487$	1.34816e8	0.0528921	0.0264460	−	0.999650i	$-0.491581\pi$
$487$	1.34816e8	0.0528921	0.0264460	+	0.999650i	$0.491581\pi$
$488$	2.09140e9	0.814644
$489$	0	0
$490$	1.62598e9	0.624350
$491$	−1.26229e9	−0.481253	−0.240627	−	0.970618i	$-0.577353\pi$
$491$	−1.26229e9	−0.481253	−0.240627	+	0.970618i	$0.577353\pi$
$492$	0	0
$493$	−5.57626e9	−2.09594
$494$	−2.44625e8	−0.0912972
$495$	0	0
$496$	−1.38614e8	−0.0510060
$497$	−1.17864e9	−0.430660
$498$	0	0
$499$	−1.34095e9	−0.483128	−0.241564	−	0.970385i	$-0.577660\pi$
$499$	−1.34095e9	−0.483128	−0.241564	+	0.970385i	$0.577660\pi$
$500$	−2.99862e9	−1.07282
$501$	0	0
$502$	−6.08326e9	−2.14622
$503$	−5.65419e9	−1.98099	−0.990495	−	0.137546i	$-0.956078\pi$
$503$	−5.65419e9	−1.98099	−0.990495	+	0.137546i	$0.956078\pi$
$504$	0	0
$505$	1.83131e9	0.632764
$506$	9.48776e8	0.325564
$507$	0	0
$508$	5.00524e9	1.69396
$509$	−4.83455e9	−1.62497	−0.812483	−	0.582985i	$-0.801885\pi$
$509$	−4.83455e9	−1.62497	−0.812483	+	0.582985i	$0.801885\pi$
$510$	0	0
$511$	1.23169e9	0.408345
$512$	−3.01367e9	−0.992317
$513$	0	0
$514$	6.63297e9	2.15445
$515$	1.10164e9	0.355398
$516$	0	0
$517$	2.84191e8	0.0904470
$518$	3.24216e8	0.102490
$519$	0	0
$520$	−1.31554e8	−0.0410292
$521$	−1.47590e9	−0.457218	−0.228609	−	0.973518i	$-0.573418\pi$
$521$	−1.47590e9	−0.457218	−0.228609	+	0.973518i	$0.573418\pi$
$522$	0	0
$523$	−3.13778e9	−0.959106	−0.479553	−	0.877513i	$-0.659201\pi$
$523$	−3.13778e9	−0.959106	−0.479553	+	0.877513i	$0.659201\pi$
$524$	−2.25279e9	−0.684007
$525$	0	0
$526$	−8.26994e9	−2.47772
$527$	5.14724e8	0.153193
$528$	0	0
$529$	−2.92738e9	−0.859773
$530$	−3.03671e9	−0.886008
$531$	0	0
$532$	4.37331e8	0.125927
$533$	−6.23168e8	−0.178262
$534$	0	0
$535$	2.70835e8	0.0764656
$536$	−1.70245e9	−0.477527
$537$	0	0
$538$	7.92193e9	2.19328
$539$	1.90901e9	0.525106
$540$	0	0
$541$	−2.43519e9	−0.661214	−0.330607	−	0.943768i	$-0.607254\pi$
$541$	−2.43519e9	−0.661214	−0.330607	+	0.943768i	$0.607254\pi$
$542$	6.59606e9	1.77945
$543$	0	0
$544$	7.99909e9	2.13032
$545$	1.76124e9	0.466049
$546$	0	0
$547$	−4.11336e9	−1.07458	−0.537292	−	0.843396i	$-0.680553\pi$
$547$	−4.11336e9	−1.07458	−0.537292	+	0.843396i	$0.680553\pi$
$548$	5.46761e9	1.41927
$549$	0	0
$550$	−2.73594e9	−0.701193
$551$	−1.78073e9	−0.453489
$552$	0	0
$553$	8.37998e8	0.210720
$554$	3.03466e9	0.758274
$555$	0	0
$556$	−7.99935e9	−1.97375
$557$	−5.89179e9	−1.44462	−0.722311	−	0.691568i	$-0.756920\pi$
$557$	−5.89179e9	−1.44462	−0.722311	+	0.691568i	$0.756920\pi$
$558$	0	0
$559$	−1.09457e8	−0.0265033
$560$	−2.62373e8	−0.0631337
$561$	0	0
$562$	−1.60088e9	−0.380437
$563$	3.72337e9	0.879341	0.439671	−	0.898159i	$-0.355095\pi$
$563$	3.72337e9	0.879341	0.439671	+	0.898159i	$0.355095\pi$
$564$	0	0
$565$	−6.99979e8	−0.163273
$566$	1.05386e10	2.44301
$567$	0	0
$568$	3.70872e9	0.849191
$569$	−5.89440e9	−1.34136	−0.670682	−	0.741745i	$-0.733999\pi$
$569$	−5.89440e9	−1.34136	−0.670682	+	0.741745i	$0.733999\pi$
$570$	0	0
$571$	−4.09269e9	−0.919988	−0.459994	−	0.887922i	$-0.652148\pi$
$571$	−4.09269e9	−0.919988	−0.459994	+	0.887922i	$0.652148\pi$
$572$	−5.95615e8	−0.133070
$573$	0	0
$574$	1.93925e9	0.427998
$575$	−1.37680e9	−0.302018
$576$	0	0
$577$	6.73874e9	1.46037	0.730185	−	0.683249i	$-0.239434\pi$
$577$	6.73874e9	1.46037	0.730185	+	0.683249i	$0.239434\pi$
$578$	−1.07345e10	−2.31224
$579$	0	0
$580$	−3.69291e9	−0.785906
$581$	−2.06470e9	−0.436758
$582$	0	0
$583$	−3.56530e9	−0.745172
$584$	−3.87563e9	−0.805189
$585$	0	0
$586$	−7.15999e9	−1.46984
$587$	−6.12315e9	−1.24951	−0.624757	−	0.780819i	$-0.714802\pi$
$587$	−6.12315e9	−1.24951	−0.624757	+	0.780819i	$0.714802\pi$
$588$	0	0
$589$	1.64373e8	0.0331456
$590$	3.16191e9	0.633822
$591$	0	0
$592$	6.53827e8	0.129520
$593$	5.62188e9	1.10711	0.553554	−	0.832813i	$-0.313271\pi$
$593$	5.62188e9	1.10711	0.553554	+	0.832813i	$0.313271\pi$
$594$	0	0
$595$	9.74287e8	0.189617
$596$	−5.55481e9	−1.07475
$597$	0	0
$598$	−5.21734e8	−0.0997688
$599$	−2.62393e9	−0.498836	−0.249418	−	0.968396i	$-0.580239\pi$
$599$	−2.62393e9	−0.498836	−0.249418	+	0.968396i	$0.580239\pi$
$600$	0	0
$601$	5.85029e9	1.09930	0.549650	−	0.835395i	$-0.314761\pi$
$601$	5.85029e9	1.09930	0.549650	+	0.835395i	$0.314761\pi$
$602$	3.40620e8	0.0636330
$603$	0	0
$604$	3.55870e9	0.657147
$605$	−1.62527e9	−0.298389
$606$	0	0
$607$	3.51051e9	0.637103	0.318552	−	0.947905i	$-0.396804\pi$
$607$	3.51051e9	0.637103	0.318552	+	0.947905i	$0.396804\pi$
$608$	2.55444e9	0.460928
$609$	0	0
$610$	5.73769e9	1.02349
$611$	−1.56277e8	−0.0277174
$612$	0	0
$613$	−6.95815e9	−1.22006	−0.610032	−	0.792377i	$-0.708843\pi$
$613$	−6.95815e9	−1.22006	−0.610032	+	0.792377i	$0.708843\pi$
$614$	−5.87996e9	−1.02514
$615$	0	0
$616$	4.80646e8	0.0828501
$617$	7.18978e8	0.123230	0.0616151	−	0.998100i	$-0.480375\pi$
$617$	7.18978e8	0.123230	0.0616151	+	0.998100i	$0.480375\pi$
$618$	0	0
$619$	−1.57508e9	−0.266922	−0.133461	−	0.991054i	$-0.542609\pi$
$619$	−1.57508e9	−0.266922	−0.133461	+	0.991054i	$0.542609\pi$
$620$	3.40879e8	0.0574420
$621$	0	0
$622$	5.46094e9	0.909916
$623$	1.93451e9	0.320526
$624$	0	0
$625$	2.78932e9	0.457003
$626$	1.32017e9	0.215090
$627$	0	0
$628$	−3.64753e9	−0.587678
$629$	−2.42790e9	−0.389003
$630$	0	0
$631$	8.53967e9	1.35313	0.676564	−	0.736384i	$-0.263468\pi$
$631$	8.53967e9	1.35313	0.676564	+	0.736384i	$0.263468\pi$
$632$	−2.63685e9	−0.415504
$633$	0	0
$634$	5.28899e7	0.00824252
$635$	3.56087e9	0.551885
$636$	0	0
$637$	−1.04977e9	−0.160918
$638$	−7.54712e9	−1.15056
$639$	0	0
$640$	2.93934e9	0.443221
$641$	1.19699e9	0.179509	0.0897547	−	0.995964i	$-0.471392\pi$
$641$	1.19699e9	0.179509	0.0897547	+	0.995964i	$0.471392\pi$
$642$	0	0
$643$	1.19758e10	1.77651	0.888254	−	0.459353i	$-0.151919\pi$
$643$	1.19758e10	1.77651	0.888254	+	0.459353i	$0.151919\pi$
$644$	9.32733e8	0.137612
$645$	0	0
$646$	−5.70068e9	−0.831979
$647$	2.44410e9	0.354776	0.177388	−	0.984141i	$-0.443235\pi$
$647$	2.44410e9	0.354776	0.177388	+	0.984141i	$0.443235\pi$
$648$	0	0
$649$	3.71230e9	0.533072
$650$	1.50450e9	0.214880
$651$	0	0
$652$	1.70020e8	0.0240233
$653$	−1.08778e10	−1.52878	−0.764389	−	0.644755i	$-0.776959\pi$
$653$	−1.08778e10	−1.52878	−0.764389	+	0.644755i	$0.776959\pi$
$654$	0	0
$655$	−1.60270e9	−0.222847
$656$	3.91077e9	0.540877
$657$	0	0
$658$	4.86322e8	0.0665478
$659$	9.90053e9	1.34760	0.673798	−	0.738916i	$-0.264662\pi$
$659$	9.90053e9	1.34760	0.673798	+	0.738916i	$0.264662\pi$
$660$	0	0
$661$	−1.16773e9	−0.157267	−0.0786337	−	0.996904i	$-0.525056\pi$
$661$	−1.16773e9	−0.157267	−0.0786337	+	0.996904i	$0.525056\pi$
$662$	1.09978e10	1.47334
$663$	0	0
$664$	6.49680e9	0.861214
$665$	3.11130e8	0.0410266
$666$	0	0
$667$	−3.79791e9	−0.495570
$668$	−1.62296e10	−2.10664
$669$	0	0
$670$	−4.67062e9	−0.599946
$671$	6.73644e9	0.860799
$672$	0	0
$673$	−3.21526e9	−0.406596	−0.203298	−	0.979117i	$-0.565166\pi$
$673$	−3.21526e9	−0.406596	−0.203298	+	0.979117i	$0.565166\pi$
$674$	−4.31380e9	−0.542688
$675$	0	0
$676$	−1.05163e10	−1.30933
$677$	−1.11460e10	−1.38057	−0.690287	−	0.723536i	$-0.742516\pi$
$677$	−1.11460e10	−1.38057	−0.690287	+	0.723536i	$0.742516\pi$
$678$	0	0
$679$	1.51362e9	0.185556
$680$	−3.06570e9	−0.373894
$681$	0	0
$682$	6.96648e8	0.0840946
$683$	−1.36119e10	−1.63473	−0.817364	−	0.576121i	$-0.804566\pi$
$683$	−1.36119e10	−1.63473	−0.817364	+	0.576121i	$0.804566\pi$
$684$	0	0
$685$	3.88981e9	0.462394
$686$	6.79497e9	0.803624
$687$	0	0
$688$	6.86909e8	0.0804155
$689$	1.96057e9	0.228357
$690$	0	0
$691$	5.11725e9	0.590016	0.295008	−	0.955495i	$-0.404678\pi$
$691$	5.11725e9	0.590016	0.295008	+	0.955495i	$0.404678\pi$
$692$	−1.82078e10	−2.08875
$693$	0	0
$694$	1.37201e10	1.55812
$695$	−5.69097e9	−0.643042
$696$	0	0
$697$	−1.45221e10	−1.62448
$698$	9.59153e9	1.06756
$699$	0	0
$700$	−2.68968e9	−0.296386
$701$	5.39916e9	0.591988	0.295994	−	0.955190i	$-0.404349\pi$
$701$	5.39916e9	0.591988	0.295994	+	0.955190i	$0.404349\pi$
$702$	0	0
$703$	−7.75328e8	−0.0841670
$704$	8.05771e9	0.870377
$705$	0	0
$706$	1.85192e10	1.98064
$707$	3.67933e9	0.391562
$708$	0	0
$709$	−1.04570e9	−0.110191	−0.0550954	−	0.998481i	$-0.517546\pi$
$709$	−1.04570e9	−0.110191	−0.0550954	+	0.998481i	$0.517546\pi$
$710$	1.01748e10	1.06689
$711$	0	0
$712$	−6.08715e9	−0.632025
$713$	3.50572e8	0.0362213
$714$	0	0
$715$	−4.23738e8	−0.0433537
$716$	1.30095e10	1.32454
$717$	0	0
$718$	2.53373e10	2.55461
$719$	6.61572e8	0.0663783	0.0331892	−	0.999449i	$-0.489434\pi$
$719$	6.61572e8	0.0663783	0.0331892	+	0.999449i	$0.489434\pi$
$720$	0	0
$721$	2.21334e9	0.219925
$722$	1.36828e10	1.35299
$723$	0	0
$724$	−4.07049e9	−0.398623
$725$	1.09519e10	1.06735
$726$	0	0
$727$	1.73518e9	0.167484	0.0837421	−	0.996487i	$-0.473313\pi$
$727$	1.73518e9	0.167484	0.0837421	+	0.996487i	$0.473313\pi$
$728$	−2.64308e8	−0.0253893
$729$	0	0
$730$	−1.06327e10	−1.01161
$731$	−2.55074e9	−0.241522
$732$	0	0
$733$	−6.25015e9	−0.586174	−0.293087	−	0.956086i	$-0.594683\pi$
$733$	−6.25015e9	−0.586174	−0.293087	+	0.956086i	$0.594683\pi$
$734$	−2.22651e10	−2.07821
$735$	0	0
$736$	5.44807e9	0.503698
$737$	−5.48362e9	−0.504581
$738$	0	0
$739$	9.00137e9	0.820452	0.410226	−	0.911984i	$-0.365450\pi$
$739$	9.00137e9	0.820452	0.410226	+	0.911984i	$0.365450\pi$
$740$	−1.60789e9	−0.145863
$741$	0	0
$742$	−6.10112e9	−0.548272
$743$	1.37996e10	1.23426	0.617129	−	0.786862i	$-0.288296\pi$
$743$	1.37996e10	1.23426	0.617129	+	0.786862i	$0.288296\pi$
$744$	0	0
$745$	−3.95185e9	−0.350149
$746$	8.43290e9	0.743689
$747$	0	0
$748$	−1.38800e10	−1.21265
$749$	5.44141e8	0.0473178
$750$	0	0
$751$	2.50869e9	0.216126	0.108063	−	0.994144i	$-0.465535\pi$
$751$	2.50869e9	0.216126	0.108063	+	0.994144i	$0.465535\pi$
$752$	9.80739e8	0.0840990
$753$	0	0
$754$	4.15018e9	0.352588
$755$	2.53176e9	0.214096
$756$	0	0
$757$	−1.59957e10	−1.34020	−0.670099	−	0.742272i	$-0.733748\pi$
$757$	−1.59957e10	−1.34020	−0.670099	+	0.742272i	$0.733748\pi$
$758$	2.34490e10	1.95561
$759$	0	0
$760$	−9.79003e8	−0.0808978
$761$	1.66651e10	1.37076	0.685378	−	0.728187i	$-0.259637\pi$
$761$	1.66651e10	1.37076	0.685378	+	0.728187i	$0.259637\pi$
$762$	0	0
$763$	3.53856e9	0.288397
$764$	−1.92982e10	−1.56564
$765$	0	0
$766$	−1.08674e10	−0.873627
$767$	−2.04140e9	−0.163359
$768$	0	0
$769$	9.23584e9	0.732376	0.366188	−	0.930541i	$-0.380663\pi$
$769$	9.23584e9	0.732376	0.366188	+	0.930541i	$0.380663\pi$
$770$	1.31864e9	0.104090
$771$	0	0
$772$	−2.03291e10	−1.59022
$773$	2.96075e9	0.230554	0.115277	−	0.993333i	$-0.463224\pi$
$773$	2.96075e9	0.230554	0.115277	+	0.993333i	$0.463224\pi$
$774$	0	0
$775$	−1.01093e9	−0.0780126
$776$	−4.76278e9	−0.365885
$777$	0	0
$778$	−2.24415e10	−1.70854
$779$	−4.63751e9	−0.351482
$780$	0	0
$781$	1.19459e10	0.897303
$782$	−1.21583e10	−0.909180
$783$	0	0
$784$	6.58795e9	0.488252
$785$	−2.59496e9	−0.191464
$786$	0	0
$787$	9.32429e9	0.681874	0.340937	−	0.940086i	$-0.389256\pi$
$787$	9.32429e9	0.681874	0.340937	+	0.940086i	$0.389256\pi$
$788$	9.38176e9	0.683034
$789$	0	0
$790$	−7.23411e9	−0.522024
$791$	−1.40634e9	−0.101036
$792$	0	0
$793$	−3.70438e9	−0.263791
$794$	−4.24500e10	−3.00958
$795$	0	0
$796$	1.40560e10	0.987796
$797$	2.22955e10	1.55996	0.779978	−	0.625806i	$-0.215230\pi$
$797$	2.22955e10	1.55996	0.779978	+	0.625806i	$0.215230\pi$
$798$	0	0
$799$	−3.64184e9	−0.252585
$800$	−1.57104e10	−1.08485
$801$	0	0
$802$	−1.46881e10	−1.00544
$803$	−1.24835e10	−0.850808
$804$	0	0
$805$	6.63573e8	0.0448336
$806$	−3.83088e8	−0.0257707
$807$	0	0
$808$	−1.15774e10	−0.772096
$809$	5.80413e9	0.385405	0.192703	−	0.981257i	$-0.438275\pi$
$809$	5.80413e9	0.385405	0.192703	+	0.981257i	$0.438275\pi$
$810$	0	0
$811$	−1.62210e10	−1.06783	−0.533917	−	0.845537i	$-0.679280\pi$
$811$	−1.62210e10	−1.06783	−0.533917	+	0.845537i	$0.679280\pi$
$812$	−7.41951e9	−0.486328
$813$	0	0
$814$	−3.28601e9	−0.213542
$815$	1.20957e8	0.00782671
$816$	0	0
$817$	−8.14557e8	−0.0522570
$818$	1.85450e10	1.18465
$819$	0	0
$820$	−9.61736e9	−0.609126
$821$	−6.33227e9	−0.399354	−0.199677	−	0.979862i	$-0.563989\pi$
$821$	−6.33227e9	−0.399354	−0.199677	+	0.979862i	$0.563989\pi$
$822$	0	0
$823$	−2.22297e10	−1.39006	−0.695031	−	0.718980i	$-0.744609\pi$
$823$	−2.22297e10	−1.39006	−0.695031	+	0.718980i	$0.744609\pi$
$824$	−6.96450e9	−0.433655
$825$	0	0
$826$	6.35267e9	0.392216
$827$	4.64860e9	0.285794	0.142897	−	0.989738i	$-0.454358\pi$
$827$	4.64860e9	0.285794	0.142897	+	0.989738i	$0.454358\pi$
$828$	0	0
$829$	−8.14688e9	−0.496650	−0.248325	−	0.968677i	$-0.579880\pi$
$829$	−8.14688e9	−0.496650	−0.248325	+	0.968677i	$0.579880\pi$
$830$	1.78238e10	1.08200
$831$	0	0
$832$	−4.43095e9	−0.266726
$833$	−2.44634e10	−1.46643
$834$	0	0
$835$	−1.15462e10	−0.686335
$836$	−4.43247e9	−0.262376
$837$	0	0
$838$	1.46417e10	0.859486
$839$	−1.95604e10	−1.14343	−0.571715	−	0.820452i	$-0.693722\pi$
$839$	−1.95604e10	−1.14343	−0.571715	+	0.820452i	$0.693722\pi$
$840$	0	0
$841$	1.29610e10	0.751366
$842$	1.52216e10	0.878757
$843$	0	0
$844$	1.27606e10	0.730586
$845$	−7.48158e9	−0.426574
$846$	0	0
$847$	−3.26537e9	−0.184646
$848$	−1.23038e10	−0.692873
$849$	0	0
$850$	3.50604e10	1.95817
$851$	−1.65361e9	−0.0919770
$852$	0	0
$853$	1.58440e10	0.874061	0.437031	−	0.899447i	$-0.356030\pi$
$853$	1.58440e10	0.874061	0.437031	+	0.899447i	$0.356030\pi$
$854$	1.15277e10	0.633346
$855$	0	0
$856$	−1.71220e9	−0.0933029
$857$	−2.56284e10	−1.39088	−0.695438	−	0.718586i	$-0.744790\pi$
$857$	−2.56284e10	−1.39088	−0.695438	+	0.718586i	$0.744790\pi$
$858$	0	0
$859$	−3.28663e9	−0.176919	−0.0884596	−	0.996080i	$-0.528194\pi$
$859$	−3.28663e9	−0.176919	−0.0884596	+	0.996080i	$0.528194\pi$
$860$	−1.68925e9	−0.0905624
$861$	0	0
$862$	−6.99092e8	−0.0371757
$863$	−1.66288e10	−0.880688	−0.440344	−	0.897829i	$-0.645143\pi$
$863$	−1.66288e10	−0.880688	−0.440344	+	0.897829i	$0.645143\pi$
$864$	0	0
$865$	−1.29536e10	−0.680508
$866$	−1.74152e10	−0.911205
$867$	0	0
$868$	6.84869e8	0.0355458
$869$	−8.49334e9	−0.439045
$870$	0	0
$871$	3.01545e9	0.154628
$872$	−1.11344e10	−0.568671
$873$	0	0
$874$	−3.88265e9	−0.196715
$875$	−4.28607e9	−0.216287
$876$	0	0
$877$	−6.52780e9	−0.326790	−0.163395	−	0.986561i	$-0.552244\pi$
$877$	−6.52780e9	−0.326790	−0.163395	+	0.986561i	$0.552244\pi$
$878$	−1.06415e10	−0.530603
$879$	0	0
$880$	2.65922e9	0.131542
$881$	−2.61062e10	−1.28626	−0.643128	−	0.765759i	$-0.722364\pi$
$881$	−2.61062e10	−1.28626	−0.643128	+	0.765759i	$0.722364\pi$
$882$	0	0
$883$	9.02672e9	0.441232	0.220616	−	0.975361i	$-0.429193\pi$
$883$	9.02672e9	0.441232	0.220616	+	0.975361i	$0.429193\pi$
$884$	7.63266e9	0.371615
$885$	0	0
$886$	−3.06903e10	−1.48246
$887$	−2.03347e9	−0.0978372	−0.0489186	−	0.998803i	$-0.515577\pi$
$887$	−2.03347e9	−0.0978372	−0.0489186	+	0.998803i	$0.515577\pi$
$888$	0	0
$889$	7.15423e9	0.341513
$890$	−1.66999e10	−0.794051
$891$	0	0
$892$	−1.75657e10	−0.828682
$893$	−1.16299e9	−0.0546507
$894$	0	0
$895$	9.25537e9	0.431532
$896$	5.90551e9	0.274270
$897$	0	0
$898$	−3.96637e10	−1.82779
$899$	−2.78866e9	−0.128008
$900$	0	0
$901$	4.56884e10	2.08099
$902$	−1.96548e10	−0.891755
$903$	0	0
$904$	4.42521e9	0.199225
$905$	−2.89587e9	−0.129870
$906$	0	0
$907$	3.47024e10	1.54431	0.772155	−	0.635435i	$-0.219179\pi$
$907$	3.47024e10	1.54431	0.772155	+	0.635435i	$0.219179\pi$
$908$	3.37376e10	1.49559
$909$	0	0
$910$	−7.25121e8	−0.0318982
$911$	3.83459e10	1.68037	0.840183	−	0.542302i	$-0.182447\pi$
$911$	3.83459e10	1.68037	0.840183	+	0.542302i	$0.182447\pi$
$912$	0	0
$913$	2.09263e10	0.910007
$914$	−1.52518e10	−0.660706
$915$	0	0
$916$	−2.38908e10	−1.02706
$917$	−3.22002e9	−0.137900
$918$	0	0
$919$	7.63731e9	0.324591	0.162295	−	0.986742i	$-0.448110\pi$
$919$	7.63731e9	0.324591	0.162295	+	0.986742i	$0.448110\pi$
$920$	−2.08800e9	−0.0884044
$921$	0	0
$922$	2.49450e10	1.04815
$923$	−6.56905e9	−0.274977
$924$	0	0
$925$	4.76844e9	0.198098
$926$	5.91203e10	2.44680
$927$	0	0
$928$	−4.33372e10	−1.78009
$929$	1.44540e10	0.591469	0.295734	−	0.955270i	$-0.404436\pi$
$929$	1.44540e10	0.591469	0.295734	+	0.955270i	$0.404436\pi$
$930$	0	0
$931$	−7.81218e9	−0.317284
$932$	1.30015e10	0.526062
$933$	0	0
$934$	5.22202e10	2.09713
$935$	−9.87466e9	−0.395077
$936$	0	0
$937$	−2.76136e10	−1.09656	−0.548282	−	0.836293i	$-0.684718\pi$
$937$	−2.76136e10	−1.09656	−0.548282	+	0.836293i	$0.684718\pi$
$938$	−9.38384e9	−0.371254
$939$	0	0
$940$	−2.41183e9	−0.0947108
$941$	−1.88863e10	−0.738894	−0.369447	−	0.929252i	$-0.620453\pi$
$941$	−1.88863e10	−0.738894	−0.369447	+	0.929252i	$0.620453\pi$
$942$	0	0
$943$	−9.89081e9	−0.384097
$944$	1.28111e10	0.495659
$945$	0	0
$946$	−3.45228e9	−0.132583
$947$	1.55375e10	0.594506	0.297253	−	0.954799i	$-0.403930\pi$
$947$	1.55375e10	0.594506	0.297253	+	0.954799i	$0.403930\pi$
$948$	0	0
$949$	6.86469e9	0.260729
$950$	1.11962e10	0.423681
$951$	0	0
$952$	−6.15936e9	−0.231370
$953$	1.05814e10	0.396021	0.198011	−	0.980200i	$-0.436552\pi$
$953$	1.05814e10	0.396021	0.198011	+	0.980200i	$0.436552\pi$
$954$	0	0
$955$	−1.37293e10	−0.510079
$956$	9.29019e9	0.343892
$957$	0	0
$958$	6.50768e8	0.0239137
$959$	7.81511e9	0.286134
$960$	0	0
$961$	−2.72552e10	−0.990644
$962$	1.80699e9	0.0654398
$963$	0	0
$964$	−7.48701e10	−2.69178
$965$	−1.44627e10	−0.518090
$966$	0	0
$967$	−1.98827e9	−0.0707102	−0.0353551	−	0.999375i	$-0.511256\pi$
$967$	−1.98827e9	−0.0707102	−0.0353551	+	0.999375i	$0.511256\pi$
$968$	1.02748e10	0.364092
$969$	0	0
$970$	−1.30665e10	−0.459684
$971$	1.06982e10	0.375012	0.187506	−	0.982263i	$-0.439960\pi$
$971$	1.06982e10	0.375012	0.187506	+	0.982263i	$0.439960\pi$
$972$	0	0
$973$	−1.14339e10	−0.397922
$974$	−2.33825e9	−0.0810838
$975$	0	0
$976$	2.32473e10	0.800384
$977$	3.25937e10	1.11816	0.559078	−	0.829115i	$-0.311155\pi$
$977$	3.25937e10	1.11816	0.559078	+	0.829115i	$0.311155\pi$
$978$	0	0
$979$	−1.96068e10	−0.667832
$980$	−1.62011e10	−0.549860
$981$	0	0
$982$	2.18931e10	0.737764
$983$	3.26564e10	1.09656	0.548278	−	0.836296i	$-0.315284\pi$
$983$	3.26564e10	1.09656	0.548278	+	0.836296i	$0.315284\pi$
$984$	0	0
$985$	6.67446e9	0.222530
$986$	9.67145e10	3.21309
$987$	0	0
$988$	2.43742e9	0.0804047
$989$	−1.73728e9	−0.0571060
$990$	0	0
$991$	1.86068e10	0.607316	0.303658	−	0.952781i	$-0.401792\pi$
$991$	1.86068e10	0.607316	0.303658	+	0.952781i	$0.401792\pi$
$992$	4.00030e9	0.130107
$993$	0	0
$994$	2.04424e10	0.660205
$995$	9.99987e9	0.321821
$996$	0	0
$997$	5.77600e10	1.84584	0.922920	−	0.384993i	$-0.125796\pi$
$997$	5.77600e10	1.84584	0.922920	+	0.384993i	$0.125796\pi$
$998$	2.32575e10	0.740638
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	387.8.a.d.1.3		13
3.2	odd	2		43.8.a.b.1.11	✓	13

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
43.8.a.b.1.11	✓	13	3.2	odd	2
387.8.a.d.1.3		13	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)

\(f(q)\)	\(=\)	\(q-17.3440 q^{2} +172.814 q^{4} +122.945 q^{5} +247.011 q^{7} -777.246 q^{8} +O(q^{10})\)	\(q-17.3440 q^{2} +172.814 q^{4} +122.945 q^{5} +247.011 q^{7} -777.246 q^{8} -2132.35 q^{10} -2503.52 q^{11} +1376.69 q^{13} -4284.15 q^{14} -8639.60 q^{16} +32082.0 q^{17} +10245.1 q^{19} +21246.5 q^{20} +43421.0 q^{22} +21850.6 q^{23} -63009.6 q^{25} -23877.3 q^{26} +42686.8 q^{28} -173813. q^{29} +16044.0 q^{31} +249333. q^{32} -556429. q^{34} +30368.6 q^{35} -75677.9 q^{37} -177691. q^{38} -95558.2 q^{40} -452656. q^{41} -79507.0 q^{43} -432643. q^{44} -378977. q^{46} -113517. q^{47} -762529. q^{49} +1.09284e6 q^{50} +237911. q^{52} +1.42412e6 q^{53} -307794. q^{55} -191988. q^{56} +3.01460e6 q^{58} -1.48283e6 q^{59} -2.69078e6 q^{61} -278267. q^{62} -3.21855e6 q^{64} +169257. q^{65} +2.19036e6 q^{67} +5.54420e6 q^{68} -526713. q^{70} -4.77162e6 q^{71} +4.98637e6 q^{73} +1.31256e6 q^{74} +1.77049e6 q^{76} -618397. q^{77} +3.39256e6 q^{79} -1.06219e6 q^{80} +7.85086e6 q^{82} -8.35875e6 q^{83} +3.94431e6 q^{85} +1.37897e6 q^{86} +1.94585e6 q^{88} +7.83169e6 q^{89} +340058. q^{91} +3.77608e6 q^{92} +1.96883e6 q^{94} +1.25958e6 q^{95} +6.12777e6 q^{97} +1.32253e7 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 13 q - 16 q^{2} + 922 q^{4} - 998 q^{5} + 1360 q^{7} - 3870 q^{8}+O(q^{10}) \) 13 * q - 16 * q^2 + 922 * q^4 - 998 * q^5 + 1360 * q^7 - 3870 * q^8	\( 13 q - 16 q^{2} + 922 q^{4} - 998 q^{5} + 1360 q^{7} - 3870 q^{8} + 4667 q^{10} - 1620 q^{11} + 13550 q^{13} - 44160 q^{14} + 114026 q^{16} - 110880 q^{17} + 105058 q^{19} - 167251 q^{20} + 201504 q^{22} - 160184 q^{23} + 270149 q^{25} - 272104 q^{26} + 208172 q^{28} - 285546 q^{29} - 99616 q^{31} - 200126 q^{32} - 80941 q^{34} + 187104 q^{35} + 176038 q^{37} - 652165 q^{38} - 895387 q^{40} + 410260 q^{41} - 1033591 q^{43} + 2177076 q^{44} - 3975765 q^{46} + 424556 q^{47} - 1561359 q^{49} + 4063801 q^{50} - 4172312 q^{52} - 3992458 q^{53} + 406960 q^{55} - 1559556 q^{56} - 4052005 q^{58} - 2248836 q^{59} + 6210394 q^{61} - 885317 q^{62} - 3096318 q^{64} - 5600420 q^{65} - 1993648 q^{67} - 9327135 q^{68} - 1105098 q^{70} - 4978064 q^{71} + 8224814 q^{73} + 3613563 q^{74} + 10687121 q^{76} - 17261892 q^{77} + 6945708 q^{79} - 15822799 q^{80} - 508449 q^{82} - 22937328 q^{83} - 575532 q^{85} + 1272112 q^{86} + 11202656 q^{88} - 9291302 q^{89} + 25581108 q^{91} + 14388137 q^{92} - 24645805 q^{94} - 30750464 q^{95} + 10001852 q^{97} + 32304856 q^{98}+O(q^{100}) \) 13 * q - 16 * q^2 + 922 * q^4 - 998 * q^5 + 1360 * q^7 - 3870 * q^8 + 4667 * q^10 - 1620 * q^11 + 13550 * q^13 - 44160 * q^14 + 114026 * q^16 - 110880 * q^17 + 105058 * q^19 - 167251 * q^20 + 201504 * q^22 - 160184 * q^23 + 270149 * q^25 - 272104 * q^26 + 208172 * q^28 - 285546 * q^29 - 99616 * q^31 - 200126 * q^32 - 80941 * q^34 + 187104 * q^35 + 176038 * q^37 - 652165 * q^38 - 895387 * q^40 + 410260 * q^41 - 1033591 * q^43 + 2177076 * q^44 - 3975765 * q^46 + 424556 * q^47 - 1561359 * q^49 + 4063801 * q^50 - 4172312 * q^52 - 3992458 * q^53 + 406960 * q^55 - 1559556 * q^56 - 4052005 * q^58 - 2248836 * q^59 + 6210394 * q^61 - 885317 * q^62 - 3096318 * q^64 - 5600420 * q^65 - 1993648 * q^67 - 9327135 * q^68 - 1105098 * q^70 - 4978064 * q^71 + 8224814 * q^73 + 3613563 * q^74 + 10687121 * q^76 - 17261892 * q^77 + 6945708 * q^79 - 15822799 * q^80 - 508449 * q^82 - 22937328 * q^83 - 575532 * q^85 + 1272112 * q^86 + 11202656 * q^88 - 9291302 * q^89 + 25581108 * q^91 + 14388137 * q^92 - 24645805 * q^94 - 30750464 * q^95 + 10001852 * q^97 + 32304856 * q^98

Introduction

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