LMFDB - Embedded newform 387.8.a.d.1.10

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			1.10
Root			$-8.80627$ 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)

$f(q)$	$=$	$q+7.80627 q^{2} -67.0621 q^{4} +402.005 q^{5} -356.766 q^{7} -1522.71 q^{8} +O(q^{10})$	\(q+7.80627 q^{2} -67.0621 q^{4} +402.005 q^{5} -356.766 q^{7} -1522.71 q^{8} +3138.16 q^{10} -338.626 q^{11} -1901.99 q^{13} -2785.01 q^{14} -3302.71 q^{16} +13710.6 q^{17} +32375.1 q^{19} -26959.3 q^{20} -2643.41 q^{22} -103235. q^{23} +83482.7 q^{25} -14847.4 q^{26} +23925.5 q^{28} -97.3595 q^{29} -2919.43 q^{31} +169125. q^{32} +107029. q^{34} -143421. q^{35} -280235. q^{37} +252729. q^{38} -612136. q^{40} +68080.9 q^{41} -79507.0 q^{43} +22709.0 q^{44} -805883. q^{46} -145265. q^{47} -696261. q^{49} +651689. q^{50} +127551. q^{52} +450286. q^{53} -136129. q^{55} +543250. q^{56} -760.015 q^{58} -2.16940e6 q^{59} -240945. q^{61} -22789.9 q^{62} +1.74298e6 q^{64} -764608. q^{65} +763129. q^{67} -919465. q^{68} -1.11959e6 q^{70} -256406. q^{71} -4.25607e6 q^{73} -2.18759e6 q^{74} -2.17114e6 q^{76} +120810. q^{77} +6.60338e6 q^{79} -1.32771e6 q^{80} +531458. q^{82} -1.57834e6 q^{83} +5.51174e6 q^{85} -620653. q^{86} +515629. q^{88} -1.01079e7 q^{89} +678564. q^{91} +6.92319e6 q^{92} -1.13398e6 q^{94} +1.30149e7 q^{95} -1.90764e6 q^{97} -5.43520e6 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	7.80627	0.689983	0.344992	−	0.938606i	$-0.387882\pi$
$2$	7.80627	0.689983	0.344992	+	0.938606i	$0.387882\pi$
$3$	0	0
$3$	0	0
$4$	−67.0621	−0.523923
$5$	402.005	1.43826	0.719128	−	0.694878i	$-0.244542\pi$
$5$	402.005	1.43826	0.719128	+	0.694878i	$0.244542\pi$
$6$	0	0
$7$	−356.766	−0.393133	−0.196567	−	0.980490i	$-0.562979\pi$
$7$	−356.766	−0.393133	−0.196567	+	0.980490i	$0.562979\pi$
$8$	−1522.71	−1.05148
$9$	0	0
$10$	3138.16	0.992372
$11$	−338.626	−0.0767090	−0.0383545	−	0.999264i	$-0.512212\pi$
$11$	−338.626	−0.0767090	−0.0383545	+	0.999264i	$0.512212\pi$
$12$	0	0
$13$	−1901.99	−0.240108	−0.120054	−	0.992767i	$-0.538307\pi$
$13$	−1901.99	−0.240108	−0.120054	+	0.992767i	$0.538307\pi$
$14$	−2785.01	−0.271255
$15$	0	0
$16$	−3302.71	−0.201582
$17$	13710.6	0.676841	0.338421	−	0.940995i	$-0.390107\pi$
$17$	13710.6	0.676841	0.338421	+	0.940995i	$0.390107\pi$
$18$	0	0
$19$	32375.1	1.08286	0.541431	−	0.840745i	$-0.317883\pi$
$19$	32375.1	1.08286	0.541431	+	0.840745i	$0.317883\pi$
$20$	−26959.3	−0.753535
$21$	0	0
$22$	−2643.41	−0.0529279
$23$	−103235.	−1.76922	−0.884609	−	0.466334i	$-0.845574\pi$
$23$	−103235.	−1.76922	−0.884609	+	0.466334i	$0.845574\pi$
$24$	0	0
$25$	83482.7	1.06858
$26$	−14847.4	−0.165670
$27$	0	0
$28$	23925.5	0.205972
$29$	−97.3595	−0.000741285 0	−0.000370643	−	1.00000i	$-0.500118\pi$
$29$	−97.3595	−0.000741285 0	−0.000370643		1.00000i	$0.500118\pi$
$30$	0	0
$31$	−2919.43	−0.0176008	−0.00880039	−	0.999961i	$-0.502801\pi$
$31$	−2919.43	−0.0176008	−0.00880039	+	0.999961i	$0.502801\pi$
$32$	169125.	0.912394
$33$	0	0
$34$	107029.	0.467009
$35$	−143421.	−0.565426
$36$	0	0
$37$	−280235.	−0.909529	−0.454764	−	0.890612i	$-0.650277\pi$
$37$	−280235.	−0.909529	−0.454764	+	0.890612i	$0.650277\pi$
$38$	252729.	0.747157
$39$	0	0
$40$	−612136.	−1.51230
$41$	68080.9	0.154270	0.0771350	−	0.997021i	$-0.475423\pi$
$41$	68080.9	0.154270	0.0771350	+	0.997021i	$0.475423\pi$
$42$	0	0
$43$	−79507.0	−0.152499
$43$	−79507.0	−0.152499
$44$	22709.0	0.0401896
$45$	0	0
$46$	−805883.	−1.22073
$47$	−145265.	−0.204089	−0.102044	−	0.994780i	$-0.532538\pi$
$47$	−145265.	−0.204089	−0.102044	+	0.994780i	$0.532538\pi$
$48$	0	0
$49$	−696261.	−0.845446
$50$	651689.	0.737301
$51$	0	0
$52$	127551.	0.125798
$53$	450286.	0.415454	0.207727	−	0.978187i	$-0.433393\pi$
$53$	450286.	0.415454	0.207727	+	0.978187i	$0.433393\pi$
$54$	0	0
$55$	−136129.	−0.110327
$56$	543250.	0.413372
$57$	0	0
$58$	−760.015	−0.000511474 0
$59$	−2.16940e6	−1.37518	−0.687588	−	0.726101i	$-0.741330\pi$
$59$	−2.16940e6	−1.37518	−0.687588	+	0.726101i	$0.741330\pi$
$60$	0	0
$61$	−240945.	−0.135914	−0.0679570	−	0.997688i	$-0.521648\pi$
$61$	−240945.	−0.135914	−0.0679570	+	0.997688i	$0.521648\pi$
$62$	−22789.9	−0.0121442
$63$	0	0
$64$	1.74298e6	0.831118
$65$	−764608.	−0.345336
$66$	0	0
$67$	763129.	0.309982	0.154991	−	0.987916i	$-0.450465\pi$
$67$	763129.	0.309982	0.154991	+	0.987916i	$0.450465\pi$
$68$	−919465.	−0.354613
$69$	0	0
$70$	−1.11959e6	−0.390135
$71$	−256406.	−0.0850206	−0.0425103	−	0.999096i	$-0.513536\pi$
$71$	−256406.	−0.0850206	−0.0425103	+	0.999096i	$0.513536\pi$
$72$	0	0
$73$	−4.25607e6	−1.28050	−0.640249	−	0.768168i	$-0.721169\pi$
$73$	−4.25607e6	−1.28050	−0.640249	+	0.768168i	$0.721169\pi$
$74$	−2.18759e6	−0.627560
$75$	0	0
$76$	−2.17114e6	−0.567337
$77$	120810.	0.0301568
$78$	0	0
$79$	6.60338e6	1.50686	0.753428	−	0.657531i	$-0.228399\pi$
$79$	6.60338e6	1.50686	0.753428	+	0.657531i	$0.228399\pi$
$80$	−1.32771e6	−0.289926
$81$	0	0
$82$	531458.	0.106444
$83$	−1.57834e6	−0.302989	−0.151495	−	0.988458i	$-0.548409\pi$
$83$	−1.57834e6	−0.302989	−0.151495	+	0.988458i	$0.548409\pi$
$84$	0	0
$85$	5.51174e6	0.973470
$86$	−620653.	−0.105221
$87$	0	0
$88$	515629.	0.0806580
$89$	−1.01079e7	−1.51983	−0.759914	−	0.650024i	$-0.774759\pi$
$89$	−1.01079e7	−1.51983	−0.759914	+	0.650024i	$0.774759\pi$
$90$	0	0
$91$	678564.	0.0943944
$92$	6.92319e6	0.926934
$93$	0	0
$94$	−1.13398e6	−0.140818
$95$	1.30149e7	1.55743
$96$	0	0
$97$	−1.90764e6	−0.212224	−0.106112	−	0.994354i	$-0.533840\pi$
$97$	−1.90764e6	−0.212224	−0.106112	+	0.994354i	$0.533840\pi$
$98$	−5.43520e6	−0.583344
$99$	0	0
$100$	−5.59853e6	−0.559853
$101$	8.79838e6	0.849724	0.424862	−	0.905258i	$-0.360323\pi$
$101$	8.79838e6	0.849724	0.424862	+	0.905258i	$0.360323\pi$
$102$	0	0
$103$	1.98046e7	1.78581	0.892907	−	0.450242i	$-0.148662\pi$
$103$	1.98046e7	1.78581	0.892907	+	0.450242i	$0.148662\pi$
$104$	2.89617e6	0.252469
$105$	0	0
$106$	3.51506e6	0.286657
$107$	−1.19023e7	−0.939264	−0.469632	−	0.882862i	$-0.655613\pi$
$107$	−1.19023e7	−0.939264	−0.469632	+	0.882862i	$0.655613\pi$
$108$	0	0
$109$	−1.61101e7	−1.19153	−0.595766	−	0.803158i	$-0.703151\pi$
$109$	−1.61101e7	−1.19153	−0.595766	+	0.803158i	$0.703151\pi$
$110$	−1.06266e6	−0.0761238
$111$	0	0
$112$	1.17829e6	0.0792484
$113$	−7.15228e6	−0.466305	−0.233153	−	0.972440i	$-0.574904\pi$
$113$	−7.15228e6	−0.466305	−0.233153	+	0.972440i	$0.574904\pi$
$114$	0	0
$115$	−4.15011e7	−2.54459
$116$	6529.14	0.000388376 0
$117$	0	0
$118$	−1.69349e7	−0.948849
$119$	−4.89149e6	−0.266089
$120$	0	0
$121$	−1.93725e7	−0.994116
$122$	−1.88088e6	−0.0937784
$123$	0	0
$124$	195783.	0.00922146
$125$	2.15382e6	0.0986336
$126$	0	0
$127$	−1.95885e7	−0.848569	−0.424284	−	0.905529i	$-0.639474\pi$
$127$	−1.95885e7	−0.848569	−0.424284	+	0.905529i	$0.639474\pi$
$128$	−8.04179e6	−0.338936
$129$	0	0
$130$	−5.96874e6	−0.238276
$131$	−3.84474e7	−1.49423	−0.747115	−	0.664695i	$-0.768562\pi$
$131$	−3.84474e7	−1.49423	−0.747115	+	0.664695i	$0.768562\pi$
$132$	0	0
$133$	−1.15503e7	−0.425709
$134$	5.95719e6	0.213882
$135$	0	0
$136$	−2.08773e7	−0.711686
$137$	−5.35857e7	−1.78044	−0.890219	−	0.455533i	$-0.849449\pi$
$137$	−5.35857e7	−1.78044	−0.890219	+	0.455533i	$0.849449\pi$
$138$	0	0
$139$	−2.44467e7	−0.772091	−0.386046	−	0.922480i	$-0.626159\pi$
$139$	−2.44467e7	−0.772091	−0.386046	+	0.922480i	$0.626159\pi$
$140$	9.61815e6	0.296240
$141$	0	0
$142$	−2.00158e6	−0.0586628
$143$	644063.	0.0184184
$144$	0	0
$145$	−39139.0	−0.00106616
$146$	−3.32240e7	−0.883522
$147$	0	0
$148$	1.87932e7	0.476523
$149$	−6.83645e7	−1.69308	−0.846542	−	0.532321i	$-0.821320\pi$
$149$	−6.83645e7	−1.69308	−0.846542	+	0.532321i	$0.821320\pi$
$150$	0	0
$151$	4.48140e7	1.05924	0.529620	−	0.848235i	$-0.322335\pi$
$151$	4.48140e7	1.05924	0.529620	+	0.848235i	$0.322335\pi$
$152$	−4.92978e7	−1.13861
$153$	0	0
$154$	943077.	0.0208077
$155$	−1.17362e6	−0.0253144
$156$	0	0
$157$	4.45418e7	0.918585	0.459293	−	0.888285i	$-0.348103\pi$
$157$	4.45418e7	0.918585	0.459293	+	0.888285i	$0.348103\pi$
$158$	5.15478e7	1.03970
$159$	0	0
$160$	6.79889e7	1.31225
$161$	3.68308e7	0.695538
$162$	0	0
$163$	−2.04717e7	−0.370251	−0.185126	−	0.982715i	$-0.559269\pi$
$163$	−2.04717e7	−0.370251	−0.185126	+	0.982715i	$0.559269\pi$
$164$	−4.56565e6	−0.0808256
$165$	0	0
$166$	−1.23209e7	−0.209057
$167$	−9.99656e6	−0.166090	−0.0830449	−	0.996546i	$-0.526464\pi$
$167$	−9.99656e6	−0.166090	−0.0830449	+	0.996546i	$0.526464\pi$
$168$	0	0
$169$	−5.91310e7	−0.942348
$170$	4.30262e7	0.671678
$171$	0	0
$172$	5.33191e6	0.0798975
$173$	−9.15039e7	−1.34363	−0.671813	−	0.740721i	$-0.734484\pi$
$173$	−9.15039e7	−1.34363	−0.671813	+	0.740721i	$0.734484\pi$
$174$	0	0
$175$	−2.97838e7	−0.420094
$176$	1.11838e6	0.0154631
$177$	0	0
$178$	−7.89047e7	−1.04866
$179$	7.48516e7	0.975474	0.487737	−	0.872991i	$-0.337823\pi$
$179$	7.48516e7	0.975474	0.487737	+	0.872991i	$0.337823\pi$
$180$	0	0
$181$	−1.08411e7	−0.135894	−0.0679470	−	0.997689i	$-0.521645\pi$
$181$	−1.08411e7	−0.135894	−0.0679470	+	0.997689i	$0.521645\pi$
$182$	5.29706e6	0.0651305
$183$	0	0
$184$	1.57197e8	1.86030
$185$	−1.12656e8	−1.30813
$186$	0	0
$187$	−4.64278e6	−0.0519198
$188$	9.74179e6	0.106927
$189$	0	0
$190$	1.01598e8	1.07460
$191$	1.37400e8	1.42682	0.713410	−	0.700747i	$-0.247150\pi$
$191$	1.37400e8	1.42682	0.713410	+	0.700747i	$0.247150\pi$
$192$	0	0
$193$	−1.16548e8	−1.16695	−0.583477	−	0.812129i	$-0.698308\pi$
$193$	−1.16548e8	−1.16695	−0.583477	+	0.812129i	$0.698308\pi$
$194$	−1.48915e7	−0.146431
$195$	0	0
$196$	4.66928e7	0.442949
$197$	1.79080e8	1.66884	0.834422	−	0.551126i	$-0.185802\pi$
$197$	1.79080e8	1.66884	0.834422	+	0.551126i	$0.185802\pi$
$198$	0	0
$199$	−1.30708e8	−1.17575	−0.587875	−	0.808952i	$-0.700035\pi$
$199$	−1.30708e8	−1.17575	−0.587875	+	0.808952i	$0.700035\pi$
$200$	−1.27120e8	−1.12359
$201$	0	0
$202$	6.86825e7	0.586295
$203$	34734.5	0.000291424 0
$204$	0	0
$205$	2.73688e7	0.221880
$206$	1.54600e8	1.23218
$207$	0	0
$208$	6.28172e6	0.0484013
$209$	−1.09631e7	−0.0830653
$210$	0	0
$211$	3.03753e7	0.222604	0.111302	−	0.993787i	$-0.464498\pi$
$211$	3.03753e7	0.222604	0.111302	+	0.993787i	$0.464498\pi$
$212$	−3.01972e7	−0.217666
$213$	0	0
$214$	−9.29126e7	−0.648076
$215$	−3.19622e7	−0.219332
$216$	0	0
$217$	1.04155e6	0.00691945
$218$	−1.25760e8	−0.822137
$219$	0	0
$220$	9.12912e6	0.0578029
$221$	−2.60775e7	−0.162515
$222$	0	0
$223$	8.68403e7	0.524390	0.262195	−	0.965015i	$-0.415554\pi$
$223$	8.68403e7	0.524390	0.262195	+	0.965015i	$0.415554\pi$
$224$	−6.03379e7	−0.358692
$225$	0	0
$226$	−5.58326e7	−0.321743
$227$	−1.67604e8	−0.951028	−0.475514	−	0.879708i	$-0.657738\pi$
$227$	−1.67604e8	−0.951028	−0.475514	+	0.879708i	$0.657738\pi$
$228$	0	0
$229$	1.15619e8	0.636218	0.318109	−	0.948054i	$-0.396952\pi$
$229$	1.15619e8	0.636218	0.318109	+	0.948054i	$0.396952\pi$
$230$	−3.23969e8	−1.75572
$231$	0	0
$232$	148250.	0.000779448 0
$233$	−1.02835e8	−0.532592	−0.266296	−	0.963891i	$-0.585800\pi$
$233$	−1.02835e8	−0.532592	−0.266296	+	0.963891i	$0.585800\pi$
$234$	0	0
$235$	−5.83973e7	−0.293532
$236$	1.45485e8	0.720486
$237$	0	0
$238$	−3.81843e7	−0.183597
$239$	−2.55890e8	−1.21244	−0.606221	−	0.795296i	$-0.707315\pi$
$239$	−2.55890e8	−1.21244	−0.606221	+	0.795296i	$0.707315\pi$
$240$	0	0
$241$	−1.95565e6	−0.00899976	−0.00449988	−	0.999990i	$-0.501432\pi$
$241$	−1.95565e6	−0.00899976	−0.00449988	+	0.999990i	$0.501432\pi$
$242$	−1.51227e8	−0.685923
$243$	0	0
$244$	1.61583e7	0.0712085
$245$	−2.79900e8	−1.21597
$246$	0	0
$247$	−6.15771e7	−0.260004
$248$	4.44544e6	0.0185069
$249$	0	0
$250$	1.68133e7	0.0680556
$251$	2.99606e8	1.19589	0.597946	−	0.801536i	$-0.295984\pi$
$251$	2.99606e8	1.19589	0.597946	+	0.801536i	$0.295984\pi$
$252$	0	0
$253$	3.49582e7	0.135715
$254$	−1.52913e8	−0.585498
$255$	0	0
$256$	−2.85878e8	−1.06498
$257$	3.65657e8	1.34372	0.671859	−	0.740679i	$-0.265496\pi$
$257$	3.65657e8	1.34372	0.671859	+	0.740679i	$0.265496\pi$
$258$	0	0
$259$	9.99782e7	0.357566
$260$	5.12763e7	0.180930
$261$	0	0
$262$	−3.00131e8	−1.03099
$263$	−4.38062e8	−1.48488	−0.742438	−	0.669914i	$-0.766331\pi$
$263$	−4.38062e8	−1.48488	−0.742438	+	0.669914i	$0.766331\pi$
$264$	0	0
$265$	1.81017e8	0.597529
$266$	−9.01649e7	−0.293732
$267$	0	0
$268$	−5.11771e7	−0.162407
$269$	6.37770e7	0.199771	0.0998853	−	0.994999i	$-0.468152\pi$
$269$	6.37770e7	0.199771	0.0998853	+	0.994999i	$0.468152\pi$
$270$	0	0
$271$	3.49200e8	1.06582	0.532908	−	0.846173i	$-0.321099\pi$
$271$	3.49200e8	1.06582	0.532908	+	0.846173i	$0.321099\pi$
$272$	−4.52823e7	−0.136439
$273$	0	0
$274$	−4.18304e8	−1.22847
$275$	−2.82694e7	−0.0819695
$276$	0	0
$277$	2.62910e8	0.743238	0.371619	−	0.928385i	$-0.378803\pi$
$277$	2.62910e8	0.743238	0.371619	+	0.928385i	$0.378803\pi$
$278$	−1.90838e8	−0.532730
$279$	0	0
$280$	2.18389e8	0.594535
$281$	3.13673e8	0.843345	0.421673	−	0.906748i	$-0.361443\pi$
$281$	3.13673e8	0.843345	0.421673	+	0.906748i	$0.361443\pi$
$282$	0	0
$283$	3.05065e7	0.0800093	0.0400046	−	0.999199i	$-0.487263\pi$
$283$	3.05065e7	0.0800093	0.0400046	+	0.999199i	$0.487263\pi$
$284$	1.71951e7	0.0445442
$285$	0	0
$286$	5.02773e6	0.0127084
$287$	−2.42889e7	−0.0606487
$288$	0	0
$289$	−2.22357e8	−0.541886
$290$	−305529.	−0.000735631 0
$291$	0	0
$292$	2.85421e8	0.670882
$293$	−6.50794e8	−1.51149	−0.755747	−	0.654863i	$-0.772726\pi$
$293$	−6.50794e8	−1.51149	−0.755747	+	0.654863i	$0.772726\pi$
$294$	0	0
$295$	−8.72110e8	−1.97785
$296$	4.26716e8	0.956353
$297$	0	0
$298$	−5.33672e8	−1.16820
$299$	1.96353e8	0.424803
$300$	0	0
$301$	2.83654e7	0.0599523
$302$	3.49830e8	0.730858
$303$	0	0
$304$	−1.06926e8	−0.218285
$305$	−9.68611e7	−0.195479
$306$	0	0
$307$	−1.64397e8	−0.324273	−0.162136	−	0.986768i	$-0.551838\pi$
$307$	−1.64397e8	−0.324273	−0.162136	+	0.986768i	$0.551838\pi$
$308$	−8.10179e6	−0.0157999
$309$	0	0
$310$	−9.16163e6	−0.0174665
$311$	−6.67878e7	−0.125903	−0.0629515	−	0.998017i	$-0.520051\pi$
$311$	−6.67878e7	−0.125903	−0.0629515	+	0.998017i	$0.520051\pi$
$312$	0	0
$313$	3.66247e8	0.675101	0.337550	−	0.941307i	$-0.390402\pi$
$313$	3.66247e8	0.675101	0.337550	+	0.941307i	$0.390402\pi$
$314$	3.47706e8	0.633808
$315$	0	0
$316$	−4.42837e8	−0.789476
$317$	−8.45942e8	−1.49153	−0.745767	−	0.666206i	$-0.767917\pi$
$317$	−8.45942e8	−1.49153	−0.745767	+	0.666206i	$0.767917\pi$
$318$	0	0
$319$	32968.5	5.68632e−5 0
$320$	7.00686e8	1.19536
$321$	0	0
$322$	2.87511e8	0.479910
$323$	4.43883e8	0.732926
$324$	0	0
$325$	−1.58783e8	−0.256574
$326$	−1.59807e8	−0.255467
$327$	0	0
$328$	−1.03667e8	−0.162212
$329$	5.18256e7	0.0802341
$330$	0	0
$331$	−1.56474e8	−0.237162	−0.118581	−	0.992944i	$-0.537835\pi$
$331$	−1.56474e8	−0.237162	−0.118581	+	0.992944i	$0.537835\pi$
$332$	1.05847e8	0.158743
$333$	0	0
$334$	−7.80358e7	−0.114599
$335$	3.06781e8	0.445833
$336$	0	0
$337$	1.10367e9	1.57085	0.785424	−	0.618958i	$-0.212445\pi$
$337$	1.10367e9	1.57085	0.785424	+	0.618958i	$0.212445\pi$
$338$	−4.61592e8	−0.650205
$339$	0	0
$340$	−3.69629e8	−0.510024
$341$	988595.	0.00135014
$342$	0	0
$343$	5.42214e8	0.725506
$344$	1.21066e8	0.160349
$345$	0	0
$346$	−7.14304e8	−0.927079
$347$	7.51448e7	0.0965485	0.0482743	−	0.998834i	$-0.484628\pi$
$347$	7.51448e7	0.0965485	0.0482743	+	0.998834i	$0.484628\pi$
$348$	0	0
$349$	4.40370e8	0.554534	0.277267	−	0.960793i	$-0.410571\pi$
$349$	4.40370e8	0.554534	0.277267	+	0.960793i	$0.410571\pi$
$350$	−2.32500e8	−0.289858
$351$	0	0
$352$	−5.72701e7	−0.0699888
$353$	8.89528e7	0.107634	0.0538168	−	0.998551i	$-0.482861\pi$
$353$	8.89528e7	0.107634	0.0538168	+	0.998551i	$0.482861\pi$
$354$	0	0
$355$	−1.03076e8	−0.122281
$356$	6.77855e8	0.796273
$357$	0	0
$358$	5.84312e8	0.673061
$359$	1.09248e9	1.24619	0.623095	−	0.782146i	$-0.285875\pi$
$359$	1.09248e9	1.24619	0.623095	+	0.782146i	$0.285875\pi$
$360$	0	0
$361$	1.54275e8	0.172591
$362$	−8.46289e7	−0.0937645
$363$	0	0
$364$	−4.55060e7	−0.0494554
$365$	−1.71096e9	−1.84168
$366$	0	0
$367$	−5.91559e8	−0.624693	−0.312346	−	0.949968i	$-0.601115\pi$
$367$	−5.91559e8	−0.624693	−0.312346	+	0.949968i	$0.601115\pi$
$368$	3.40957e8	0.356642
$369$	0	0
$370$	−8.79422e8	−0.902591
$371$	−1.60647e8	−0.163329
$372$	0	0
$373$	1.17638e9	1.17373	0.586863	−	0.809686i	$-0.300363\pi$
$373$	1.17638e9	1.17373	0.586863	+	0.809686i	$0.300363\pi$
$374$	−3.62428e7	−0.0358238
$375$	0	0
$376$	2.21196e8	0.214595
$377$	185177.	0.000177988 0
$378$	0	0
$379$	1.58878e9	1.49908	0.749541	−	0.661958i	$-0.230274\pi$
$379$	1.58878e9	1.49908	0.749541	+	0.661958i	$0.230274\pi$
$380$	−8.72810e8	−0.815975
$381$	0	0
$382$	1.07258e9	0.984482
$383$	1.52083e9	1.38320	0.691599	−	0.722281i	$-0.256906\pi$
$383$	1.52083e9	1.38320	0.691599	+	0.722281i	$0.256906\pi$
$384$	0	0
$385$	4.85662e7	0.0433732
$386$	−9.09805e8	−0.805179
$387$	0	0
$388$	1.27930e8	0.111189
$389$	−1.81957e9	−1.56728	−0.783639	−	0.621217i	$-0.786639\pi$
$389$	−1.81957e9	−1.56728	−0.783639	+	0.621217i	$0.786639\pi$
$390$	0	0
$391$	−1.41542e9	−1.19748
$392$	1.06020e9	0.888971
$393$	0	0
$394$	1.39795e9	1.15147
$395$	2.65459e9	2.16724
$396$	0	0
$397$	2.11509e9	1.69653	0.848265	−	0.529571i	$-0.177647\pi$
$397$	2.11509e9	1.69653	0.848265	+	0.529571i	$0.177647\pi$
$398$	−1.02034e9	−0.811248
$399$	0	0
$400$	−2.75719e8	−0.215406
$401$	2.18744e9	1.69407	0.847034	−	0.531539i	$-0.178386\pi$
$401$	2.18744e9	1.69407	0.847034	+	0.531539i	$0.178386\pi$
$402$	0	0
$403$	5.55272e6	0.00422609
$404$	−5.90038e8	−0.445190
$405$	0	0
$406$	271147.	0.000201078 0
$407$	9.48949e7	0.0697690
$408$	0	0
$409$	−1.16511e9	−0.842045	−0.421022	−	0.907050i	$-0.638329\pi$
$409$	−1.16511e9	−0.842045	−0.421022	+	0.907050i	$0.638329\pi$
$410$	2.13648e8	0.153093
$411$	0	0
$412$	−1.32814e9	−0.935629
$413$	7.73968e8	0.540627
$414$	0	0
$415$	−6.34499e8	−0.435776
$416$	−3.21673e8	−0.219073
$417$	0	0
$418$	−8.55805e7	−0.0573136
$419$	9.59686e8	0.637353	0.318677	−	0.947864i	$-0.396762\pi$
$419$	9.59686e8	0.637353	0.318677	+	0.947864i	$0.396762\pi$
$420$	0	0
$421$	−1.02361e7	−0.00668572	−0.00334286	−	0.999994i	$-0.501064\pi$
$421$	−1.02361e7	−0.00668572	−0.00334286	+	0.999994i	$0.501064\pi$
$422$	2.37118e8	0.153593
$423$	0	0
$424$	−6.85655e8	−0.436843
$425$	1.14460e9	0.723258
$426$	0	0
$427$	8.59610e7	0.0534323
$428$	7.98194e8	0.492102
$429$	0	0
$430$	−2.49505e8	−0.151335
$431$	3.14206e9	1.89036	0.945179	−	0.326552i	$-0.105887\pi$
$431$	3.14206e9	1.89036	0.945179	+	0.326552i	$0.105887\pi$
$432$	0	0
$433$	−2.31364e9	−1.36958	−0.684792	−	0.728739i	$-0.740107\pi$
$433$	−2.31364e9	−1.36958	−0.684792	+	0.728739i	$0.740107\pi$
$434$	8.13063e6	0.00477431
$435$	0	0
$436$	1.08038e9	0.624271
$437$	−3.34225e9	−1.91582
$438$	0	0
$439$	1.64208e9	0.926337	0.463168	−	0.886270i	$-0.346713\pi$
$439$	1.64208e9	0.926337	0.463168	+	0.886270i	$0.346713\pi$
$440$	2.07285e8	0.116007
$441$	0	0
$442$	−2.03568e8	−0.112133
$443$	−7.12250e8	−0.389242	−0.194621	−	0.980879i	$-0.562348\pi$
$443$	−7.12250e8	−0.389242	−0.194621	+	0.980879i	$0.562348\pi$
$444$	0	0
$445$	−4.06341e9	−2.18590
$446$	6.77899e8	0.361820
$447$	0	0
$448$	−6.21835e8	−0.326740
$449$	−2.15899e9	−1.12561	−0.562805	−	0.826590i	$-0.690278\pi$
$449$	−2.15899e9	−1.12561	−0.562805	+	0.826590i	$0.690278\pi$
$450$	0	0
$451$	−2.30540e7	−0.0118339
$452$	4.79647e8	0.244308
$453$	0	0
$454$	−1.30836e9	−0.656193
$455$	2.72786e8	0.135763
$456$	0	0
$457$	−1.05753e9	−0.518308	−0.259154	−	0.965836i	$-0.583444\pi$
$457$	−1.05753e9	−0.518308	−0.259154	+	0.965836i	$0.583444\pi$
$458$	9.02555e8	0.438980
$459$	0	0
$460$	2.78315e9	1.33317
$461$	2.93548e9	1.39549	0.697743	−	0.716348i	$-0.254188\pi$
$461$	2.93548e9	1.39549	0.697743	+	0.716348i	$0.254188\pi$
$462$	0	0
$463$	2.80303e9	1.31248	0.656242	−	0.754550i	$-0.272145\pi$
$463$	2.80303e9	1.31248	0.656242	+	0.754550i	$0.272145\pi$
$464$	321551.	0.000149429 0
$465$	0	0
$466$	−8.02756e8	−0.367479
$467$	−1.35420e9	−0.615281	−0.307640	−	0.951503i	$-0.599539\pi$
$467$	−1.35420e9	−0.615281	−0.307640	+	0.951503i	$0.599539\pi$
$468$	0	0
$469$	−2.72258e8	−0.121864
$470$	−4.55865e8	−0.202532
$471$	0	0
$472$	3.30337e9	1.44597
$473$	2.69231e7	0.0116980
$474$	0	0
$475$	2.70276e9	1.15712
$476$	3.28034e8	0.139410
$477$	0	0
$478$	−1.99755e9	−0.836565
$479$	−1.17660e9	−0.489165	−0.244583	−	0.969628i	$-0.578651\pi$
$479$	−1.17660e9	−0.489165	−0.244583	+	0.969628i	$0.578651\pi$
$480$	0	0
$481$	5.33004e8	0.218385
$482$	−1.52663e7	−0.00620969
$483$	0	0
$484$	1.29916e9	0.520840
$485$	−7.66879e8	−0.305233
$486$	0	0
$487$	−1.73453e9	−0.680504	−0.340252	−	0.940334i	$-0.610512\pi$
$487$	−1.73453e9	−0.680504	−0.340252	+	0.940334i	$0.610512\pi$
$488$	3.66889e8	0.142911
$489$	0	0
$490$	−2.18498e9	−0.838997
$491$	−7.94788e8	−0.303016	−0.151508	−	0.988456i	$-0.548413\pi$
$491$	−7.94788e8	−0.303016	−0.151508	+	0.988456i	$0.548413\pi$
$492$	0	0
$493$	−1.33486e6	−0.000501732 0
$494$	−4.80687e8	−0.179398
$495$	0	0
$496$	9.64204e6	0.00354799
$497$	9.14769e7	0.0334244
$498$	0	0
$499$	−2.73492e8	−0.0985354	−0.0492677	−	0.998786i	$-0.515689\pi$
$499$	−2.73492e8	−0.0985354	−0.0492677	+	0.998786i	$0.515689\pi$
$500$	−1.44440e8	−0.0516764
$501$	0	0
$502$	2.33880e9	0.825146
$503$	−3.20927e9	−1.12439	−0.562197	−	0.827004i	$-0.690044\pi$
$503$	−3.20927e9	−1.12439	−0.562197	+	0.827004i	$0.690044\pi$
$504$	0	0
$505$	3.53699e9	1.22212
$506$	2.72893e8	0.0936409
$507$	0	0
$508$	1.31364e9	0.444585
$509$	2.06801e9	0.695090	0.347545	−	0.937663i	$-0.387015\pi$
$509$	2.06801e9	0.695090	0.347545	+	0.937663i	$0.387015\pi$
$510$	0	0
$511$	1.51842e9	0.503406
$512$	−1.20229e9	−0.395881
$513$	0	0
$514$	2.85442e9	0.927143
$515$	7.96155e9	2.56846
$516$	0	0
$517$	4.91906e7	0.0156554
$518$	7.80457e8	0.246715
$519$	0	0
$520$	1.16428e9	0.363115
$521$	3.73056e8	0.115569	0.0577846	−	0.998329i	$-0.481596\pi$
$521$	3.73056e8	0.115569	0.0577846	+	0.998329i	$0.481596\pi$
$522$	0	0
$523$	3.23366e9	0.988414	0.494207	−	0.869344i	$-0.335459\pi$
$523$	3.23366e9	0.988414	0.494207	+	0.869344i	$0.335459\pi$
$524$	2.57837e9	0.782862
$525$	0	0
$526$	−3.41963e9	−1.02454
$527$	−4.00273e7	−0.0119129
$528$	0	0
$529$	7.25272e9	2.13013
$530$	1.41307e9	0.412285
$531$	0	0
$532$	7.74589e8	0.223039
$533$	−1.29489e8	−0.0370414
$534$	0	0
$535$	−4.78478e9	−1.35090
$536$	−1.16202e9	−0.325940
$537$	0	0
$538$	4.97861e8	0.137838
$539$	2.35772e8	0.0648533
$540$	0	0
$541$	−6.33940e9	−1.72131	−0.860653	−	0.509192i	$-0.829944\pi$
$541$	−6.33940e9	−1.72131	−0.860653	+	0.509192i	$0.829944\pi$
$542$	2.72595e9	0.735395
$543$	0	0
$544$	2.31881e9	0.617545
$545$	−6.47633e9	−1.71373
$546$	0	0
$547$	2.18850e9	0.571731	0.285865	−	0.958270i	$-0.407719\pi$
$547$	2.18850e9	0.571731	0.285865	+	0.958270i	$0.407719\pi$
$548$	3.59357e9	0.932812
$549$	0	0
$550$	−2.20679e8	−0.0565576
$551$	−3.15202e6	−0.000802710 0
$552$	0	0
$553$	−2.35586e9	−0.592395
$554$	2.05235e9	0.512822
$555$	0	0
$556$	1.63945e9	0.404516
$557$	2.65106e9	0.650019	0.325009	−	0.945711i	$-0.394633\pi$
$557$	2.65106e9	0.650019	0.325009	+	0.945711i	$0.394633\pi$
$558$	0	0
$559$	1.51221e8	0.0366161
$560$	4.73680e8	0.113979
$561$	0	0
$562$	2.44862e9	0.581894
$563$	4.33945e9	1.02484	0.512419	−	0.858736i	$-0.328749\pi$
$563$	4.33945e9	1.02484	0.512419	+	0.858736i	$0.328749\pi$
$564$	0	0
$565$	−2.87525e9	−0.670666
$566$	2.38142e8	0.0552051
$567$	0	0
$568$	3.90432e8	0.0893976
$569$	−6.16980e8	−0.140404	−0.0702018	−	0.997533i	$-0.522364\pi$
$569$	−6.16980e8	−0.140404	−0.0702018	+	0.997533i	$0.522364\pi$
$570$	0	0
$571$	5.73913e9	1.29009	0.645045	−	0.764145i	$-0.276839\pi$
$571$	5.73913e9	1.29009	0.645045	+	0.764145i	$0.276839\pi$
$572$	−4.31923e7	−0.00964983
$573$	0	0
$574$	−1.89606e8	−0.0418466
$575$	−8.61837e9	−1.89055
$576$	0	0
$577$	5.29584e9	1.14768	0.573838	−	0.818969i	$-0.305454\pi$
$577$	5.29584e9	1.14768	0.573838	+	0.818969i	$0.305454\pi$
$578$	−1.73578e9	−0.373892
$579$	0	0
$580$	2.62474e6	0.000558585 0
$581$	5.63097e8	0.119115
$582$	0	0
$583$	−1.52479e8	−0.0318691
$584$	6.48075e9	1.34642
$585$	0	0
$586$	−5.08027e9	−1.04291
$587$	−4.99464e8	−0.101923	−0.0509613	−	0.998701i	$-0.516229\pi$
$587$	−4.99464e8	−0.101923	−0.0509613	+	0.998701i	$0.516229\pi$
$588$	0	0
$589$	−9.45168e7	−0.0190592
$590$	−6.80793e9	−1.36469
$591$	0	0
$592$	9.25536e8	0.183344
$593$	1.20268e9	0.236842	0.118421	−	0.992963i	$-0.462217\pi$
$593$	1.20268e9	0.236842	0.118421	+	0.992963i	$0.462217\pi$
$594$	0	0
$595$	−1.96640e9	−0.382704
$596$	4.58467e9	0.887046
$597$	0	0
$598$	1.53278e9	0.293107
$599$	5.47286e9	1.04045	0.520224	−	0.854030i	$-0.325849\pi$
$599$	5.47286e9	1.04045	0.520224	+	0.854030i	$0.325849\pi$
$600$	0	0
$601$	−4.60823e9	−0.865912	−0.432956	−	0.901415i	$-0.642529\pi$
$601$	−4.60823e9	−0.865912	−0.432956	+	0.901415i	$0.642529\pi$
$602$	2.21428e8	0.0413661
$603$	0	0
$604$	−3.00532e9	−0.554960
$605$	−7.78784e9	−1.42979
$606$	0	0
$607$	7.85259e9	1.42512	0.712562	−	0.701610i	$-0.247535\pi$
$607$	7.85259e9	1.42512	0.712562	+	0.701610i	$0.247535\pi$
$608$	5.47543e9	0.987997
$609$	0	0
$610$	−7.56124e8	−0.134877
$611$	2.76293e8	0.0490033
$612$	0	0
$613$	−1.04035e10	−1.82419	−0.912095	−	0.409980i	$-0.865536\pi$
$613$	−1.04035e10	−1.82419	−0.912095	+	0.409980i	$0.865536\pi$
$614$	−1.28333e9	−0.223743
$615$	0	0
$616$	−1.83959e8	−0.0317094
$617$	−2.89619e9	−0.496397	−0.248198	−	0.968709i	$-0.579838\pi$
$617$	−2.89619e9	−0.496397	−0.248198	+	0.968709i	$0.579838\pi$
$618$	0	0
$619$	−1.69036e9	−0.286458	−0.143229	−	0.989690i	$-0.545749\pi$
$619$	−1.69036e9	−0.286458	−0.143229	+	0.989690i	$0.545749\pi$
$620$	7.87057e7	0.0132628
$621$	0	0
$622$	−5.21364e8	−0.0868710
$623$	3.60614e9	0.597495
$624$	0	0
$625$	−5.65624e9	−0.926718
$626$	2.85902e9	0.465808
$627$	0	0
$628$	−2.98707e9	−0.481268
$629$	−3.84220e9	−0.615606
$630$	0	0
$631$	−3.25816e9	−0.516261	−0.258131	−	0.966110i	$-0.583106\pi$
$631$	−3.25816e9	−0.516261	−0.258131	+	0.966110i	$0.583106\pi$
$632$	−1.00550e10	−1.58443
$633$	0	0
$634$	−6.60366e9	−1.02913
$635$	−7.87465e9	−1.22046
$636$	0	0
$637$	1.32428e9	0.202998
$638$	257361.	3.92347e−5 0
$639$	0	0
$640$	−3.23284e9	−0.487477
$641$	−1.62115e9	−0.243119	−0.121560	−	0.992584i	$-0.538790\pi$
$641$	−1.62115e9	−0.243119	−0.121560	+	0.992584i	$0.538790\pi$
$642$	0	0
$643$	−4.87271e8	−0.0722823	−0.0361412	−	0.999347i	$-0.511507\pi$
$643$	−4.87271e8	−0.0722823	−0.0361412	+	0.999347i	$0.511507\pi$
$644$	−2.46995e9	−0.364408
$645$	0	0
$646$	3.46507e9	0.505707
$647$	−1.32422e10	−1.92219	−0.961095	−	0.276219i	$-0.910918\pi$
$647$	−1.32422e10	−1.92219	−0.961095	+	0.276219i	$0.910918\pi$
$648$	0	0
$649$	7.34617e8	0.105488
$650$	−1.23950e9	−0.177032
$651$	0	0
$652$	1.37287e9	0.193983
$653$	−1.05133e10	−1.47755	−0.738774	−	0.673953i	$-0.764595\pi$
$653$	−1.05133e10	−1.47755	−0.738774	+	0.673953i	$0.764595\pi$
$654$	0	0
$655$	−1.54560e10	−2.14908
$656$	−2.24852e8	−0.0310980
$657$	0	0
$658$	4.04565e8	0.0553602
$659$	−5.82980e9	−0.793514	−0.396757	−	0.917924i	$-0.629864\pi$
$659$	−5.82980e9	−0.793514	−0.396757	+	0.917924i	$0.629864\pi$
$660$	0	0
$661$	4.98936e9	0.671954	0.335977	−	0.941870i	$-0.390934\pi$
$661$	4.98936e9	0.671954	0.335977	+	0.941870i	$0.390934\pi$
$662$	−1.22148e9	−0.163638
$663$	0	0
$664$	2.40335e9	0.318587
$665$	−4.64328e9	−0.612279
$666$	0	0
$667$	1.00509e7	0.00131149
$668$	6.70391e8	0.0870183
$669$	0	0
$670$	2.39482e9	0.307617
$671$	8.15904e7	0.0104258
$672$	0	0
$673$	−9.45755e9	−1.19599	−0.597993	−	0.801502i	$-0.704035\pi$
$673$	−9.45755e9	−1.19599	−0.597993	+	0.801502i	$0.704035\pi$
$674$	8.61554e9	1.08386
$675$	0	0
$676$	3.96545e9	0.493718
$677$	1.17413e10	1.45431	0.727155	−	0.686474i	$-0.240842\pi$
$677$	1.17413e10	1.45431	0.727155	+	0.686474i	$0.240842\pi$
$678$	0	0
$679$	6.80579e8	0.0834324
$680$	−8.39277e9	−1.02359
$681$	0	0
$682$	7.71724e6	0.000931572 0
$683$	−8.01180e9	−0.962183	−0.481091	−	0.876670i	$-0.659759\pi$
$683$	−8.01180e9	−0.962183	−0.481091	+	0.876670i	$0.659759\pi$
$684$	0	0
$685$	−2.15417e10	−2.56072
$686$	4.23267e9	0.500587
$687$	0	0
$688$	2.62589e8	0.0307409
$689$	−8.56440e8	−0.0997538
$690$	0	0
$691$	9.40691e9	1.08461	0.542305	−	0.840181i	$-0.317552\pi$
$691$	9.40691e9	1.08461	0.542305	+	0.840181i	$0.317552\pi$
$692$	6.13645e9	0.703956
$693$	0	0
$694$	5.86600e8	0.0666169
$695$	−9.82769e9	−1.11046
$696$	0	0
$697$	9.33433e8	0.104416
$698$	3.43765e9	0.382619
$699$	0	0
$700$	1.99736e9	0.220097
$701$	−5.77903e9	−0.633639	−0.316819	−	0.948486i	$-0.602615\pi$
$701$	−5.77903e9	−0.633639	−0.316819	+	0.948486i	$0.602615\pi$
$702$	0	0
$703$	−9.07264e9	−0.984895
$704$	−5.90219e8	−0.0637542
$705$	0	0
$706$	6.94389e8	0.0742654
$707$	−3.13896e9	−0.334055
$708$	0	0
$709$	1.04068e10	1.09662	0.548311	−	0.836274i	$-0.315271\pi$
$709$	1.04068e10	1.09662	0.548311	+	0.836274i	$0.315271\pi$
$710$	−8.04642e8	−0.0843721
$711$	0	0
$712$	1.53913e10	1.59807
$713$	3.01388e8	0.0311396
$714$	0	0
$715$	2.58916e8	0.0264904
$716$	−5.01971e9	−0.511073
$717$	0	0
$718$	8.52822e9	0.859851
$719$	−1.83550e10	−1.84164	−0.920819	−	0.389991i	$-0.872478\pi$
$719$	−1.83550e10	−1.84164	−0.920819	+	0.389991i	$0.872478\pi$
$720$	0	0
$721$	−7.06560e9	−0.702063
$722$	1.20431e9	0.119085
$723$	0	0
$724$	7.27030e8	0.0711980
$725$	−8.12784e6	−0.000792122 0
$726$	0	0
$727$	1.38023e9	0.133223	0.0666116	−	0.997779i	$-0.478781\pi$
$727$	1.38023e9	0.133223	0.0666116	+	0.997779i	$0.478781\pi$
$728$	−1.03325e9	−0.0992539
$729$	0	0
$730$	−1.33562e10	−1.27073
$731$	−1.09009e9	−0.103217
$732$	0	0
$733$	2.24467e9	0.210518	0.105259	−	0.994445i	$-0.466433\pi$
$733$	2.24467e9	0.210518	0.105259	+	0.994445i	$0.466433\pi$
$734$	−4.61787e9	−0.431028
$735$	0	0
$736$	−1.74597e10	−1.61422
$737$	−2.58415e8	−0.0237784
$738$	0	0
$739$	4.41123e9	0.402072	0.201036	−	0.979584i	$-0.435569\pi$
$739$	4.41123e9	0.402072	0.201036	+	0.979584i	$0.435569\pi$
$740$	7.55494e9	0.685362
$741$	0	0
$742$	−1.25405e9	−0.112694
$743$	−1.31411e10	−1.17536	−0.587679	−	0.809094i	$-0.699958\pi$
$743$	−1.31411e10	−1.17536	−0.587679	+	0.809094i	$0.699958\pi$
$744$	0	0
$745$	−2.74828e10	−2.43509
$746$	9.18315e9	0.809852
$747$	0	0
$748$	3.11355e8	0.0272020
$749$	4.24633e9	0.369256
$750$	0	0
$751$	8.90398e9	0.767087	0.383543	−	0.923523i	$-0.374704\pi$
$751$	8.90398e9	0.767087	0.383543	+	0.923523i	$0.374704\pi$
$752$	4.79769e8	0.0411405
$753$	0	0
$754$	1.44554e6	0.000122809 0
$755$	1.80154e10	1.52346
$756$	0	0
$757$	−1.98575e10	−1.66375	−0.831877	−	0.554960i	$-0.812734\pi$
$757$	−1.98575e10	−1.66375	−0.831877	+	0.554960i	$0.812734\pi$
$758$	1.24024e10	1.03434
$759$	0	0
$760$	−1.98179e10	−1.63761
$761$	−4.10456e9	−0.337614	−0.168807	−	0.985649i	$-0.553991\pi$
$761$	−4.10456e9	−0.337614	−0.168807	+	0.985649i	$0.553991\pi$
$762$	0	0
$763$	5.74753e9	0.468431
$764$	−9.21432e9	−0.747544
$765$	0	0
$766$	1.18720e10	0.954384
$767$	4.12618e9	0.330190
$768$	0	0
$769$	1.69512e10	1.34418	0.672091	−	0.740468i	$-0.265396\pi$
$769$	1.69512e10	1.34418	0.672091	+	0.740468i	$0.265396\pi$
$770$	3.79121e8	0.0299268
$771$	0	0
$772$	7.81595e9	0.611394
$773$	−7.71790e8	−0.0600995	−0.0300498	−	0.999548i	$-0.509567\pi$
$773$	−7.71790e8	−0.0600995	−0.0300498	+	0.999548i	$0.509567\pi$
$774$	0	0
$775$	−2.43722e8	−0.0188078
$776$	2.90478e9	0.223150
$777$	0	0
$778$	−1.42041e10	−1.08140
$779$	2.20412e9	0.167053
$780$	0	0
$781$	8.68258e7	0.00652184
$782$	−1.10492e10	−0.826240
$783$	0	0
$784$	2.29955e9	0.170426
$785$	1.79060e10	1.32116
$786$	0	0
$787$	−1.55107e10	−1.13428	−0.567139	−	0.823622i	$-0.691950\pi$
$787$	−1.55107e10	−1.13428	−0.567139	+	0.823622i	$0.691950\pi$
$788$	−1.20095e10	−0.874346
$789$	0	0
$790$	2.07224e10	1.49536
$791$	2.55169e9	0.183320
$792$	0	0
$793$	4.58275e8	0.0326340
$794$	1.65110e10	1.17058
$795$	0	0
$796$	8.76553e9	0.616003
$797$	−1.44069e10	−1.00801	−0.504006	−	0.863700i	$-0.668141\pi$
$797$	−1.44069e10	−1.00801	−0.504006	+	0.863700i	$0.668141\pi$
$798$	0	0
$799$	−1.99168e9	−0.138136
$800$	1.41190e10	0.974964
$801$	0	0
$802$	1.70757e10	1.16888
$803$	1.44122e9	0.0982256
$804$	0	0
$805$	1.48062e10	1.00036
$806$	4.33460e7	0.00291593
$807$	0	0
$808$	−1.33974e10	−0.893469
$809$	1.32032e10	0.876714	0.438357	−	0.898801i	$-0.355560\pi$
$809$	1.32032e10	0.876714	0.438357	+	0.898801i	$0.355560\pi$
$810$	0	0
$811$	2.59038e10	1.70526	0.852629	−	0.522517i	$-0.175007\pi$
$811$	2.59038e10	1.70526	0.852629	+	0.522517i	$0.175007\pi$
$812$	−2.32937e6	−0.000152684 0
$813$	0	0
$814$	7.40775e8	0.0481394
$815$	−8.22971e9	−0.532516
$816$	0	0
$817$	−2.57405e9	−0.165135
$818$	−9.09516e9	−0.580997
$819$	0	0
$820$	−1.83541e9	−0.116248
$821$	1.80408e9	0.113777	0.0568885	−	0.998381i	$-0.481882\pi$
$821$	1.80408e9	0.113777	0.0568885	+	0.998381i	$0.481882\pi$
$822$	0	0
$823$	2.15004e10	1.34445	0.672227	−	0.740345i	$-0.265338\pi$
$823$	2.15004e10	1.34445	0.672227	+	0.740345i	$0.265338\pi$
$824$	−3.01566e10	−1.87775
$825$	0	0
$826$	6.04181e9	0.373024
$827$	−1.95017e10	−1.19895	−0.599477	−	0.800392i	$-0.704625\pi$
$827$	−1.95017e10	−1.19895	−0.599477	+	0.800392i	$0.704625\pi$
$828$	0	0
$829$	1.50758e10	0.919049	0.459524	−	0.888165i	$-0.348020\pi$
$829$	1.50758e10	0.919049	0.459524	+	0.888165i	$0.348020\pi$
$830$	−4.95307e9	−0.300678
$831$	0	0
$832$	−3.31513e9	−0.199558
$833$	−9.54619e9	−0.572233
$834$	0	0
$835$	−4.01866e9	−0.238880
$836$	7.35206e8	0.0435198
$837$	0	0
$838$	7.49157e9	0.439763
$839$	3.01700e10	1.76363	0.881816	−	0.471594i	$-0.156321\pi$
$839$	3.01700e10	1.76363	0.881816	+	0.471594i	$0.156321\pi$
$840$	0	0
$841$	−1.72499e10	−0.999999
$842$	−7.99060e7	−0.00461304
$843$	0	0
$844$	−2.03703e9	−0.116627
$845$	−2.37709e10	−1.35534
$846$	0	0
$847$	6.91144e9	0.390820
$848$	−1.48717e9	−0.0837480
$849$	0	0
$850$	8.93507e9	0.499036
$851$	2.89302e10	1.60915
$852$	0	0
$853$	−1.64145e9	−0.0905534	−0.0452767	−	0.998974i	$-0.514417\pi$
$853$	−1.64145e9	−0.0905534	−0.0452767	+	0.998974i	$0.514417\pi$
$854$	6.71035e8	0.0368674
$855$	0	0
$856$	1.81237e10	0.987619
$857$	2.57589e10	1.39796	0.698981	−	0.715141i	$-0.253637\pi$
$857$	2.57589e10	1.39796	0.698981	+	0.715141i	$0.253637\pi$
$858$	0	0
$859$	−2.14742e10	−1.15595	−0.577977	−	0.816053i	$-0.696158\pi$
$859$	−2.14742e10	−1.15595	−0.577977	+	0.816053i	$0.696158\pi$
$860$	2.14345e9	0.114913
$861$	0	0
$862$	2.45278e10	1.30432
$863$	3.38483e9	0.179266	0.0896332	−	0.995975i	$-0.471431\pi$
$863$	3.38483e9	0.179266	0.0896332	+	0.995975i	$0.471431\pi$
$864$	0	0
$865$	−3.67850e10	−1.93248
$866$	−1.80609e10	−0.944990
$867$	0	0
$868$	−6.98487e7	−0.00362526
$869$	−2.23608e9	−0.115589
$870$	0	0
$871$	−1.45146e9	−0.0744290
$872$	2.45310e10	1.25287
$873$	0	0
$874$	−2.60905e10	−1.32188
$875$	−7.68410e8	−0.0387762
$876$	0	0
$877$	−2.37382e10	−1.18836	−0.594182	−	0.804331i	$-0.702524\pi$
$877$	−2.37382e10	−1.18836	−0.594182	+	0.804331i	$0.702524\pi$
$878$	1.28185e10	0.639157
$879$	0	0
$880$	4.49596e8	0.0222399
$881$	1.49518e10	0.736678	0.368339	−	0.929692i	$-0.379927\pi$
$881$	1.49518e10	0.736678	0.368339	+	0.929692i	$0.379927\pi$
$882$	0	0
$883$	2.73527e10	1.33702	0.668510	−	0.743703i	$-0.266932\pi$
$883$	2.73527e10	1.33702	0.668510	+	0.743703i	$0.266932\pi$
$884$	1.74881e9	0.0851453
$885$	0	0
$886$	−5.56002e9	−0.268570
$887$	−3.74606e10	−1.80236	−0.901181	−	0.433443i	$-0.857299\pi$
$887$	−3.74606e10	−1.80236	−0.901181	+	0.433443i	$0.857299\pi$
$888$	0	0
$889$	6.98849e9	0.333601
$890$	−3.17201e10	−1.50823
$891$	0	0
$892$	−5.82370e9	−0.274740
$893$	−4.70297e9	−0.221000
$894$	0	0
$895$	3.00907e10	1.40298
$896$	2.86903e9	0.133247
$897$	0	0
$898$	−1.68536e10	−0.776652
$899$	284234.	1.30472e−5 0
$900$	0	0
$901$	6.17372e9	0.281197
$902$	−1.79965e8	−0.00816519
$903$	0	0
$904$	1.08908e10	0.490311
$905$	−4.35819e9	−0.195450
$906$	0	0
$907$	−4.76936e9	−0.212243	−0.106122	−	0.994353i	$-0.533843\pi$
$907$	−4.76936e9	−0.212243	−0.106122	+	0.994353i	$0.533843\pi$
$908$	1.12399e10	0.498265
$909$	0	0
$910$	2.12944e9	0.0936743
$911$	4.59972e9	0.201566	0.100783	−	0.994908i	$-0.467865\pi$
$911$	4.59972e9	0.201566	0.100783	+	0.994908i	$0.467865\pi$
$912$	0	0
$913$	5.34467e8	0.0232420
$914$	−8.25540e9	−0.357624
$915$	0	0
$916$	−7.75368e9	−0.333329
$917$	1.37167e10	0.587432
$918$	0	0
$919$	1.59138e10	0.676348	0.338174	−	0.941084i	$-0.390191\pi$
$919$	1.59138e10	0.676348	0.338174	+	0.941084i	$0.390191\pi$
$920$	6.31941e10	2.67559
$921$	0	0
$922$	2.29151e10	0.962862
$923$	4.87682e8	0.0204141
$924$	0	0
$925$	−2.33948e10	−0.971903
$926$	2.18812e10	0.905592
$927$	0	0
$928$	−1.64659e7	−0.000676344 0
$929$	2.22650e10	0.911102	0.455551	−	0.890210i	$-0.349442\pi$
$929$	2.22650e10	0.911102	0.455551	+	0.890210i	$0.349442\pi$
$930$	0	0
$931$	−2.25415e10	−0.915502
$932$	6.89632e9	0.279037
$933$	0	0
$934$	−1.05712e10	−0.424533
$935$	−1.86642e9	−0.0746739
$936$	0	0
$937$	−2.34525e10	−0.931322	−0.465661	−	0.884963i	$-0.654183\pi$
$937$	−2.34525e10	−0.931322	−0.465661	+	0.884963i	$0.654183\pi$
$938$	−2.12532e9	−0.0840842
$939$	0	0
$940$	3.91625e9	0.153788
$941$	−2.99250e10	−1.17077	−0.585383	−	0.810757i	$-0.699056\pi$
$941$	−2.99250e10	−1.17077	−0.585383	+	0.810757i	$0.699056\pi$
$942$	0	0
$943$	−7.02836e9	−0.272937
$944$	7.16492e9	0.277210
$945$	0	0
$946$	2.10169e8	0.00807143
$947$	2.94339e10	1.12622	0.563109	−	0.826383i	$-0.309605\pi$
$947$	2.94339e10	1.12622	0.563109	+	0.826383i	$0.309605\pi$
$948$	0	0
$949$	8.09500e9	0.307457
$950$	2.10985e10	0.798396
$951$	0	0
$952$	7.44830e9	0.279787
$953$	−3.72084e10	−1.39257	−0.696283	−	0.717767i	$-0.745164\pi$
$953$	−3.72084e10	−1.39257	−0.696283	+	0.717767i	$0.745164\pi$
$954$	0	0
$955$	5.52353e10	2.05213
$956$	1.71605e10	0.635226
$957$	0	0
$958$	−9.18488e9	−0.337516
$959$	1.91175e10	0.699949
$960$	0	0
$961$	−2.75041e10	−0.999690
$962$	4.16077e9	0.150682
$963$	0	0
$964$	1.31150e8	0.00471518
$965$	−4.68528e10	−1.67838
$966$	0	0
$967$	−1.49635e10	−0.532159	−0.266080	−	0.963951i	$-0.585728\pi$
$967$	−1.49635e10	−0.532159	−0.266080	+	0.963951i	$0.585728\pi$
$968$	2.94987e10	1.04529
$969$	0	0
$970$	−5.98647e9	−0.210605
$971$	−3.15367e10	−1.10548	−0.552738	−	0.833355i	$-0.686417\pi$
$971$	−3.15367e10	−1.10548	−0.552738	+	0.833355i	$0.686417\pi$
$972$	0	0
$973$	8.72174e9	0.303535
$974$	−1.35402e10	−0.469536
$975$	0	0
$976$	7.95773e8	0.0273978
$977$	−1.36797e10	−0.469295	−0.234648	−	0.972080i	$-0.575394\pi$
$977$	−1.36797e10	−0.469295	−0.234648	+	0.972080i	$0.575394\pi$
$978$	0	0
$979$	3.42279e9	0.116584
$980$	1.87707e10	0.637073
$981$	0	0
$982$	−6.20433e9	−0.209076
$983$	−1.28389e10	−0.431112	−0.215556	−	0.976491i	$-0.569156\pi$
$983$	−1.28389e10	−0.431112	−0.215556	+	0.976491i	$0.569156\pi$
$984$	0	0
$985$	7.19910e10	2.40022
$986$	−1.04203e7	−0.000346187 0
$987$	0	0
$988$	4.12949e9	0.136222
$989$	8.20794e9	0.269803
$990$	0	0
$991$	−5.51139e10	−1.79889	−0.899443	−	0.437038i	$-0.856028\pi$
$991$	−5.51139e10	−1.79889	−0.899443	+	0.437038i	$0.856028\pi$
$992$	−4.93748e8	−0.0160588
$993$	0	0
$994$	7.14093e8	0.0230623
$995$	−5.25451e10	−1.69103
$996$	0	0
$997$	5.87820e10	1.87850	0.939250	−	0.343234i	$-0.111522\pi$
$997$	5.87820e10	1.87850	0.939250	+	0.343234i	$0.111522\pi$
$998$	−2.13495e9	−0.0679878
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	387.8.a.d.1.10		13
3.2	odd	2		43.8.a.b.1.4	✓	13

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
43.8.a.b.1.4	✓	13	3.2	odd	2
387.8.a.d.1.10		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)

\(f(q)\)	\(=\)	\(q+7.80627 q^{2} -67.0621 q^{4} +402.005 q^{5} -356.766 q^{7} -1522.71 q^{8} +O(q^{10})\)	\(q+7.80627 q^{2} -67.0621 q^{4} +402.005 q^{5} -356.766 q^{7} -1522.71 q^{8} +3138.16 q^{10} -338.626 q^{11} -1901.99 q^{13} -2785.01 q^{14} -3302.71 q^{16} +13710.6 q^{17} +32375.1 q^{19} -26959.3 q^{20} -2643.41 q^{22} -103235. q^{23} +83482.7 q^{25} -14847.4 q^{26} +23925.5 q^{28} -97.3595 q^{29} -2919.43 q^{31} +169125. q^{32} +107029. q^{34} -143421. q^{35} -280235. q^{37} +252729. q^{38} -612136. q^{40} +68080.9 q^{41} -79507.0 q^{43} +22709.0 q^{44} -805883. q^{46} -145265. q^{47} -696261. q^{49} +651689. q^{50} +127551. q^{52} +450286. q^{53} -136129. q^{55} +543250. q^{56} -760.015 q^{58} -2.16940e6 q^{59} -240945. q^{61} -22789.9 q^{62} +1.74298e6 q^{64} -764608. q^{65} +763129. q^{67} -919465. q^{68} -1.11959e6 q^{70} -256406. q^{71} -4.25607e6 q^{73} -2.18759e6 q^{74} -2.17114e6 q^{76} +120810. q^{77} +6.60338e6 q^{79} -1.32771e6 q^{80} +531458. q^{82} -1.57834e6 q^{83} +5.51174e6 q^{85} -620653. q^{86} +515629. q^{88} -1.01079e7 q^{89} +678564. q^{91} +6.92319e6 q^{92} -1.13398e6 q^{94} +1.30149e7 q^{95} -1.90764e6 q^{97} -5.43520e6 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 13 q - 16 q^{2} + 922 q^{4} - 998 q^{5} + 1360 q^{7} - 3870 q^{8}+O(q^{10}) \) 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

L-functions

Modular forms

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Database

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