LMFDB - Embedded newform 387.8.a.a.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:	$10$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - x^{9} - 825 x^{8} + 431 x^{7} + 229838 x^{6} - 1804 x^{5} - 25242488 x^{4} - 2085744 x^{3} + \cdots - 5193030528 $ x^10 - x^9 - 825x^8 + 431x^7 + 229838x^6 - 1804x^5 - 25242488x^4 - 2085744x^3 + 933060896x^2 - 813446208x - 5193030528
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{5}\cdot 3^{2} $
Twist minimal:	no (minimal twist has level 129)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$-10.6558$ of defining polynomial
Character	$\chi$	$=$	387.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-10.6558 q^{2} -14.4536 q^{4} +201.175 q^{5} +957.575 q^{7} +1517.96 q^{8} +O(q^{10})$	\(q-10.6558 q^{2} -14.4536 q^{4} +201.175 q^{5} +957.575 q^{7} +1517.96 q^{8} -2143.69 q^{10} +2235.25 q^{11} +3574.02 q^{13} -10203.7 q^{14} -14325.0 q^{16} +17617.3 q^{17} -33052.0 q^{19} -2907.70 q^{20} -23818.4 q^{22} -44935.7 q^{23} -37653.4 q^{25} -38084.1 q^{26} -13840.4 q^{28} +125754. q^{29} -273077. q^{31} -41653.8 q^{32} -187727. q^{34} +192641. q^{35} -543163. q^{37} +352196. q^{38} +305376. q^{40} -128475. q^{41} -79507.0 q^{43} -32307.4 q^{44} +478826. q^{46} -69472.9 q^{47} +93407.3 q^{49} +401228. q^{50} -51657.3 q^{52} -1.44419e6 q^{53} +449678. q^{55} +1.45356e6 q^{56} -1.34002e6 q^{58} +539339. q^{59} +1.75799e6 q^{61} +2.90986e6 q^{62} +2.27746e6 q^{64} +719004. q^{65} -339734. q^{67} -254633. q^{68} -2.05274e6 q^{70} -829405. q^{71} -2.00855e6 q^{73} +5.78784e6 q^{74} +477719. q^{76} +2.14042e6 q^{77} -5.13808e6 q^{79} -2.88185e6 q^{80} +1.36900e6 q^{82} +2.37984e6 q^{83} +3.54416e6 q^{85} +847212. q^{86} +3.39302e6 q^{88} -5.20708e6 q^{89} +3.42239e6 q^{91} +649481. q^{92} +740291. q^{94} -6.64924e6 q^{95} +1.33459e6 q^{97} -995331. q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q + q^{2} + 371 q^{4} + 122 q^{5} - 2052 q^{7} + 927 q^{8}+O(q^{10}) $ 10 * q + q^2 + 371 * q^4 + 122 * q^5 - 2052 * q^7 + 927 * q^8	\( 10 q + q^{2} + 371 q^{4} + 122 q^{5} - 2052 q^{7} + 927 q^{8} - 10032 q^{10} + 8888 q^{11} - 16432 q^{13} + 28408 q^{14} - 26669 q^{16} + 48122 q^{17} - 56146 q^{19} + 88940 q^{20} - 100626 q^{22} + 236336 q^{23} - 135016 q^{25} + 166748 q^{26} - 259060 q^{28} + 248818 q^{29} - 430970 q^{31} - 69493 q^{32} + 445522 q^{34} - 298982 q^{35} - 261254 q^{37} - 257662 q^{38} - 671432 q^{40} + 126814 q^{41} - 795070 q^{43} + 620022 q^{44} - 809038 q^{46} - 627080 q^{47} - 1256116 q^{49} + 83117 q^{50} - 3674204 q^{52} + 1612384 q^{53} - 4732974 q^{55} + 4301484 q^{56} - 7268516 q^{58} + 3442492 q^{59} - 5217214 q^{61} + 2500324 q^{62} - 4657369 q^{64} + 1224166 q^{65} - 6810926 q^{67} + 3563486 q^{68} - 2745858 q^{70} + 13935120 q^{71} - 13743720 q^{73} + 1752692 q^{74} - 15817594 q^{76} + 7685750 q^{77} - 9007608 q^{79} + 13641024 q^{80} - 6329026 q^{82} + 21779128 q^{83} - 13177392 q^{85} - 79507 q^{86} - 13214750 q^{88} + 1895364 q^{89} - 16439838 q^{91} - 9614510 q^{92} + 3404276 q^{94} + 16861514 q^{95} - 20434472 q^{97} - 35731457 q^{98}+O(q^{100}) \) 10 * q + q^2 + 371 * q^4 + 122 * q^5 - 2052 * q^7 + 927 * q^8 - 10032 * q^10 + 8888 * q^11 - 16432 * q^13 + 28408 * q^14 - 26669 * q^16 + 48122 * q^17 - 56146 * q^19 + 88940 * q^20 - 100626 * q^22 + 236336 * q^23 - 135016 * q^25 + 166748 * q^26 - 259060 * q^28 + 248818 * q^29 - 430970 * q^31 - 69493 * q^32 + 445522 * q^34 - 298982 * q^35 - 261254 * q^37 - 257662 * q^38 - 671432 * q^40 + 126814 * q^41 - 795070 * q^43 + 620022 * q^44 - 809038 * q^46 - 627080 * q^47 - 1256116 * q^49 + 83117 * q^50 - 3674204 * q^52 + 1612384 * q^53 - 4732974 * q^55 + 4301484 * q^56 - 7268516 * q^58 + 3442492 * q^59 - 5217214 * q^61 + 2500324 * q^62 - 4657369 * q^64 + 1224166 * q^65 - 6810926 * q^67 + 3563486 * q^68 - 2745858 * q^70 + 13935120 * q^71 - 13743720 * q^73 + 1752692 * q^74 - 15817594 * q^76 + 7685750 * q^77 - 9007608 * q^79 + 13641024 * q^80 - 6329026 * q^82 + 21779128 * q^83 - 13177392 * q^85 - 79507 * q^86 - 13214750 * q^88 + 1895364 * q^89 - 16439838 * q^91 - 9614510 * q^92 + 3404276 * q^94 + 16861514 * q^95 - 20434472 * q^97 - 35731457 * q^98

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	−10.6558	−0.941850	−0.470925	−	0.882173i	$-0.656080\pi$
$2$	−10.6558	−0.941850	−0.470925	+	0.882173i	$0.656080\pi$
$3$	0	0
$3$	0	0
$4$	−14.4536	−0.112919
$5$	201.175	0.719747	0.359874	−	0.933001i	$-0.382820\pi$
$5$	201.175	0.719747	0.359874	+	0.933001i	$0.382820\pi$
$6$	0	0
$7$	957.575	1.05519	0.527594	−	0.849497i	$-0.323094\pi$
$7$	957.575	1.05519	0.527594	+	0.849497i	$0.323094\pi$
$8$	1517.96	1.04820
$9$	0	0
$10$	−2143.69	−0.677894
$11$	2235.25	0.506351	0.253176	−	0.967420i	$-0.418525\pi$
$11$	2235.25	0.506351	0.253176	+	0.967420i	$0.418525\pi$
$12$	0	0
$13$	3574.02	0.451185	0.225593	−	0.974222i	$-0.427568\pi$
$13$	3574.02	0.451185	0.225593	+	0.974222i	$0.427568\pi$
$14$	−10203.7	−0.993829
$15$	0	0
$16$	−14325.0	−0.874331
$17$	17617.3	0.869697	0.434848	−	0.900504i	$-0.356802\pi$
$17$	17617.3	0.869697	0.434848	+	0.900504i	$0.356802\pi$
$18$	0	0
$19$	−33052.0	−1.10550	−0.552751	−	0.833346i	$-0.686422\pi$
$19$	−33052.0	−1.10550	−0.552751	+	0.833346i	$0.686422\pi$
$20$	−2907.70	−0.0812728
$21$	0	0
$22$	−23818.4	−0.476907
$23$	−44935.7	−0.770094	−0.385047	−	0.922897i	$-0.625815\pi$
$23$	−44935.7	−0.770094	−0.385047	+	0.922897i	$0.625815\pi$
$24$	0	0
$25$	−37653.4	−0.481964
$26$	−38084.1	−0.424949
$27$	0	0
$28$	−13840.4	−0.119150
$29$	125754.	0.957481	0.478741	−	0.877956i	$-0.341093\pi$
$29$	125754.	0.957481	0.478741	+	0.877956i	$0.341093\pi$
$30$	0	0
$31$	−273077.	−1.64634	−0.823168	−	0.567797i	$-0.807796\pi$
$31$	−273077.	−1.64634	−0.823168	+	0.567797i	$0.807796\pi$
$32$	−41653.8	−0.224714
$33$	0	0
$34$	−187727.	−0.819124
$35$	192641.	0.759468
$36$	0	0
$37$	−543163.	−1.76289	−0.881443	−	0.472291i	$-0.843427\pi$
$37$	−543163.	−1.76289	−0.881443	+	0.472291i	$0.843427\pi$
$38$	352196.	1.04122
$39$	0	0
$40$	305376.	0.754441
$41$	−128475.	−0.291122	−0.145561	−	0.989349i	$-0.546499\pi$
$41$	−128475.	−0.291122	−0.145561	+	0.989349i	$0.546499\pi$
$42$	0	0
$43$	−79507.0	−0.152499
$43$	−79507.0	−0.152499
$44$	−32307.4	−0.0571764
$45$	0	0
$46$	478826.	0.725313
$47$	−69472.9	−0.0976052	−0.0488026	−	0.998808i	$-0.515541\pi$
$47$	−69472.9	−0.0976052	−0.0488026	+	0.998808i	$0.515541\pi$
$48$	0	0
$49$	93407.3	0.113421
$50$	401228.	0.453938
$51$	0	0
$52$	−51657.3	−0.0509472
$53$	−1.44419e6	−1.33247	−0.666237	−	0.745740i	$-0.732096\pi$
$53$	−1.44419e6	−1.33247	−0.666237	+	0.745740i	$0.732096\pi$
$54$	0	0
$55$	449678.	0.364445
$56$	1.45356e6	1.10605
$57$	0	0
$58$	−1.34002e6	−0.901804
$59$	539339.	0.341885	0.170942	−	0.985281i	$-0.445319\pi$
$59$	539339.	0.341885	0.170942	+	0.985281i	$0.445319\pi$
$60$	0	0
$61$	1.75799e6	0.991659	0.495830	−	0.868420i	$-0.334864\pi$
$61$	1.75799e6	0.991659	0.495830	+	0.868420i	$0.334864\pi$
$62$	2.90986e6	1.55060
$63$	0	0
$64$	2.27746e6	1.08598
$65$	719004.	0.324739
$66$	0	0
$67$	−339734.	−0.137999	−0.0689997	−	0.997617i	$-0.521981\pi$
$67$	−339734.	−0.137999	−0.0689997	+	0.997617i	$0.521981\pi$
$68$	−254633.	−0.0982049
$69$	0	0
$70$	−2.05274e6	−0.715305
$71$	−829405.	−0.275019	−0.137509	−	0.990500i	$-0.543910\pi$
$71$	−829405.	−0.275019	−0.137509	+	0.990500i	$0.543910\pi$
$72$	0	0
$73$	−2.00855e6	−0.604299	−0.302149	−	0.953261i	$-0.597704\pi$
$73$	−2.00855e6	−0.604299	−0.302149	+	0.953261i	$0.597704\pi$
$74$	5.78784e6	1.66037
$75$	0	0
$76$	477719.	0.124832
$77$	2.14042e6	0.534296
$78$	0	0
$79$	−5.13808e6	−1.17248	−0.586241	−	0.810137i	$-0.699393\pi$
$79$	−5.13808e6	−1.17248	−0.586241	+	0.810137i	$0.699393\pi$
$80$	−2.88185e6	−0.629297
$81$	0	0
$82$	1.36900e6	0.274193
$83$	2.37984e6	0.456851	0.228425	−	0.973561i	$-0.426642\pi$
$83$	2.37984e6	0.456851	0.228425	+	0.973561i	$0.426642\pi$
$84$	0	0
$85$	3.54416e6	0.625962
$86$	847212.	0.143631
$87$	0	0
$88$	3.39302e6	0.530759
$89$	−5.20708e6	−0.782941	−0.391471	−	0.920191i	$-0.628034\pi$
$89$	−5.20708e6	−0.782941	−0.391471	+	0.920191i	$0.628034\pi$
$90$	0	0
$91$	3.42239e6	0.476085
$92$	649481.	0.0869579
$93$	0	0
$94$	740291.	0.0919295
$95$	−6.64924e6	−0.795682
$96$	0	0
$97$	1.33459e6	0.148473	0.0742366	−	0.997241i	$-0.476348\pi$
$97$	1.33459e6	0.148473	0.0742366	+	0.997241i	$0.476348\pi$
$98$	−995331.	−0.106826
$99$	0	0
$100$	544227.	0.0544227
$101$	−3.27471e6	−0.316263	−0.158131	−	0.987418i	$-0.550547\pi$
$101$	−3.27471e6	−0.316263	−0.158131	+	0.987418i	$0.550547\pi$
$102$	0	0
$103$	5.84821e6	0.527342	0.263671	−	0.964613i	$-0.415067\pi$
$103$	5.84821e6	0.527342	0.263671	+	0.964613i	$0.415067\pi$
$104$	5.42521e6	0.472933
$105$	0	0
$106$	1.53890e7	1.25499
$107$	−6.88438e6	−0.543277	−0.271639	−	0.962399i	$-0.587566\pi$
$107$	−6.88438e6	−0.543277	−0.271639	+	0.962399i	$0.587566\pi$
$108$	0	0
$109$	−8.75413e6	−0.647471	−0.323735	−	0.946148i	$-0.604939\pi$
$109$	−8.75413e6	−0.647471	−0.323735	+	0.946148i	$0.604939\pi$
$110$	−4.79168e6	−0.343252
$111$	0	0
$112$	−1.37173e7	−0.922583
$113$	1.57494e7	1.02681	0.513405	−	0.858146i	$-0.328384\pi$
$113$	1.57494e7	1.02681	0.513405	+	0.858146i	$0.328384\pi$
$114$	0	0
$115$	−9.03996e6	−0.554273
$116$	−1.81760e6	−0.108117
$117$	0	0
$118$	−5.74710e6	−0.322004
$119$	1.68699e7	0.917693
$120$	0	0
$121$	−1.44908e7	−0.743608
$122$	−1.87328e7	−0.933994
$123$	0	0
$124$	3.94693e6	0.185902
$125$	−2.32918e7	−1.06664
$126$	0	0
$127$	4.27910e7	1.85370	0.926850	−	0.375433i	$-0.122506\pi$
$127$	4.27910e7	1.85370	0.926850	+	0.375433i	$0.122506\pi$
$128$	−1.89365e7	−0.798114
$129$	0	0
$130$	−7.66158e6	−0.305856
$131$	1.64516e7	0.639379	0.319690	−	0.947522i	$-0.396421\pi$
$131$	1.64516e7	0.639379	0.319690	+	0.947522i	$0.396421\pi$
$132$	0	0
$133$	−3.16497e7	−1.16651
$134$	3.62014e6	0.129975
$135$	0	0
$136$	2.67423e7	0.911618
$137$	−5.61407e6	−0.186533	−0.0932665	−	0.995641i	$-0.529731\pi$
$137$	−5.61407e6	−0.186533	−0.0932665	+	0.995641i	$0.529731\pi$
$138$	0	0
$139$	5.23441e7	1.65316	0.826582	−	0.562816i	$-0.190282\pi$
$139$	5.23441e7	1.65316	0.826582	+	0.562816i	$0.190282\pi$
$140$	−2.78434e6	−0.0857580
$141$	0	0
$142$	8.83799e6	0.259027
$143$	7.98882e6	0.228458
$144$	0	0
$145$	2.52987e7	0.689144
$146$	2.14027e7	0.569159
$147$	0	0
$148$	7.85064e6	0.199062
$149$	−4.58779e7	−1.13619	−0.568095	−	0.822963i	$-0.692320\pi$
$149$	−4.58779e7	−1.13619	−0.568095	+	0.822963i	$0.692320\pi$
$150$	0	0
$151$	−3.02051e7	−0.713938	−0.356969	−	0.934116i	$-0.616190\pi$
$151$	−3.02051e7	−0.713938	−0.356969	+	0.934116i	$0.616190\pi$
$152$	−5.01715e7	−1.15879
$153$	0	0
$154$	−2.28079e7	−0.503226
$155$	−5.49363e7	−1.18495
$156$	0	0
$157$	−1.89211e7	−0.390209	−0.195104	−	0.980782i	$-0.562505\pi$
$157$	−1.89211e7	−0.390209	−0.195104	+	0.980782i	$0.562505\pi$
$158$	5.47504e7	1.10430
$159$	0	0
$160$	−8.37972e6	−0.161737
$161$	−4.30293e7	−0.812594
$162$	0	0
$163$	7.78719e7	1.40839	0.704197	−	0.710005i	$-0.251307\pi$
$163$	7.78719e7	1.40839	0.704197	+	0.710005i	$0.251307\pi$
$164$	1.85692e6	0.0328730
$165$	0	0
$166$	−2.53591e7	−0.430285
$167$	−6.25720e7	−1.03961	−0.519807	−	0.854284i	$-0.673996\pi$
$167$	−6.25720e7	−1.03961	−0.519807	+	0.854284i	$0.673996\pi$
$168$	0	0
$169$	−4.99749e7	−0.796432
$170$	−3.77660e7	−0.589562
$171$	0	0
$172$	1.14916e6	0.0172199
$173$	6.06839e7	0.891070	0.445535	−	0.895265i	$-0.353013\pi$
$173$	6.06839e7	0.891070	0.445535	+	0.895265i	$0.353013\pi$
$174$	0	0
$175$	−3.60560e7	−0.508563
$176$	−3.20201e7	−0.442719
$177$	0	0
$178$	5.54857e7	0.737413
$179$	−1.16973e8	−1.52440	−0.762199	−	0.647343i	$-0.775880\pi$
$179$	−1.16973e8	−1.52440	−0.762199	+	0.647343i	$0.775880\pi$
$180$	0	0
$181$	−8.69808e7	−1.09031	−0.545153	−	0.838337i	$-0.683528\pi$
$181$	−8.69808e7	−1.09031	−0.545153	+	0.838337i	$0.683528\pi$
$182$	−3.64684e7	−0.448401
$183$	0	0
$184$	−6.82105e7	−0.807215
$185$	−1.09271e8	−1.26883
$186$	0	0
$187$	3.93791e7	0.440372
$188$	1.00413e6	0.0110214
$189$	0	0
$190$	7.08531e7	0.749413
$191$	−1.04904e8	−1.08937	−0.544684	−	0.838642i	$-0.683350\pi$
$191$	−1.04904e8	−1.08937	−0.544684	+	0.838642i	$0.683350\pi$
$192$	0	0
$193$	−1.49408e8	−1.49597	−0.747987	−	0.663713i	$-0.768979\pi$
$193$	−1.49408e8	−1.49597	−0.747987	+	0.663713i	$0.768979\pi$
$194$	−1.42212e7	−0.139839
$195$	0	0
$196$	−1.35007e6	−0.0128074
$197$	−2.58776e7	−0.241153	−0.120576	−	0.992704i	$-0.538474\pi$
$197$	−2.58776e7	−0.241153	−0.120576	+	0.992704i	$0.538474\pi$
$198$	0	0
$199$	−2.69723e7	−0.242623	−0.121311	−	0.992615i	$-0.538710\pi$
$199$	−2.69723e7	−0.242623	−0.121311	+	0.992615i	$0.538710\pi$
$200$	−5.71564e7	−0.505196
$201$	0	0
$202$	3.48947e7	0.297872
$203$	1.20419e8	1.01032
$204$	0	0
$205$	−2.58460e7	−0.209534
$206$	−6.23175e7	−0.496678
$207$	0	0
$208$	−5.11979e7	−0.394485
$209$	−7.38795e7	−0.559773
$210$	0	0
$211$	−2.24188e8	−1.64295	−0.821475	−	0.570244i	$-0.806849\pi$
$211$	−2.24188e8	−1.64295	−0.821475	+	0.570244i	$0.806849\pi$
$212$	2.08737e7	0.150461
$213$	0	0
$214$	7.33587e7	0.511686
$215$	−1.59949e7	−0.109760
$216$	0	0
$217$	−2.61491e8	−1.73719
$218$	9.32824e7	0.609820
$219$	0	0
$220$	−6.49945e6	−0.0411526
$221$	6.29645e7	0.392394
$222$	0	0
$223$	1.72437e7	0.104127	0.0520635	−	0.998644i	$-0.483420\pi$
$223$	1.72437e7	0.104127	0.0520635	+	0.998644i	$0.483420\pi$
$224$	−3.98866e7	−0.237115
$225$	0	0
$226$	−1.67823e8	−0.967101
$227$	1.93713e8	1.09918	0.549589	−	0.835435i	$-0.314784\pi$
$227$	1.93713e8	1.09918	0.549589	+	0.835435i	$0.314784\pi$
$228$	0	0
$229$	8.14401e7	0.448140	0.224070	−	0.974573i	$-0.428066\pi$
$229$	8.14401e7	0.448140	0.224070	+	0.974573i	$0.428066\pi$
$230$	9.63281e7	0.522042
$231$	0	0
$232$	1.90890e8	1.00363
$233$	2.58219e8	1.33734	0.668670	−	0.743559i	$-0.266864\pi$
$233$	2.58219e8	1.33734	0.668670	+	0.743559i	$0.266864\pi$
$234$	0	0
$235$	−1.39762e7	−0.0702511
$236$	−7.79538e6	−0.0386051
$237$	0	0
$238$	−1.79762e8	−0.864329
$239$	−3.21415e8	−1.52291	−0.761453	−	0.648220i	$-0.775514\pi$
$239$	−3.21415e8	−1.52291	−0.761453	+	0.648220i	$0.775514\pi$
$240$	0	0
$241$	−9.97805e7	−0.459183	−0.229592	−	0.973287i	$-0.573739\pi$
$241$	−9.97805e7	−0.459183	−0.229592	+	0.973287i	$0.573739\pi$
$242$	1.54412e8	0.700368
$243$	0	0
$244$	−2.54093e7	−0.111977
$245$	1.87913e7	0.0816347
$246$	0	0
$247$	−1.18128e8	−0.498786
$248$	−4.14519e8	−1.72569
$249$	0	0
$250$	2.48193e8	1.00461
$251$	4.35422e8	1.73801	0.869006	−	0.494802i	$-0.164759\pi$
$251$	4.35422e8	1.73801	0.869006	+	0.494802i	$0.164759\pi$
$252$	0	0
$253$	−1.00443e8	−0.389938
$254$	−4.55973e8	−1.74591
$255$	0	0
$256$	−8.97309e7	−0.334274
$257$	3.67243e8	1.34955	0.674773	−	0.738026i	$-0.264242\pi$
$257$	3.67243e8	1.34955	0.674773	+	0.738026i	$0.264242\pi$
$258$	0	0
$259$	−5.20119e8	−1.86018
$260$	−1.03922e7	−0.0366691
$261$	0	0
$262$	−1.75305e8	−0.602199
$263$	−3.92841e8	−1.33159	−0.665797	−	0.746133i	$-0.731908\pi$
$263$	−3.92841e8	−1.33159	−0.665797	+	0.746133i	$0.731908\pi$
$264$	0	0
$265$	−2.90536e8	−0.959045
$266$	3.37254e8	1.09868
$267$	0	0
$268$	4.91037e6	0.0155827
$269$	1.80892e7	0.0566613	0.0283307	−	0.999599i	$-0.490981\pi$
$269$	1.80892e7	0.0566613	0.0283307	+	0.999599i	$0.490981\pi$
$270$	0	0
$271$	−1.18934e8	−0.363006	−0.181503	−	0.983390i	$-0.558096\pi$
$271$	−1.18934e8	−0.363006	−0.181503	+	0.983390i	$0.558096\pi$
$272$	−2.52368e8	−0.760403
$273$	0	0
$274$	5.98225e7	0.175686
$275$	−8.41649e7	−0.244043
$276$	0	0
$277$	−2.40913e7	−0.0681053	−0.0340527	−	0.999420i	$-0.510841\pi$
$277$	−2.40913e7	−0.0681053	−0.0340527	+	0.999420i	$0.510841\pi$
$278$	−5.57769e8	−1.55703
$279$	0	0
$280$	2.92421e8	0.796076
$281$	3.12762e8	0.840894	0.420447	−	0.907317i	$-0.361873\pi$
$281$	3.12762e8	0.840894	0.420447	+	0.907317i	$0.361873\pi$
$282$	0	0
$283$	−5.59235e8	−1.46670	−0.733351	−	0.679850i	$-0.762045\pi$
$283$	−5.59235e8	−1.46670	−0.733351	+	0.679850i	$0.762045\pi$
$284$	1.19879e7	0.0310547
$285$	0	0
$286$	−8.51274e7	−0.215173
$287$	−1.23024e8	−0.307188
$288$	0	0
$289$	−9.99700e7	−0.243628
$290$	−2.69578e8	−0.649071
$291$	0	0
$292$	2.90307e7	0.0682365
$293$	−2.35214e8	−0.546294	−0.273147	−	0.961972i	$-0.588065\pi$
$293$	−2.35214e8	−0.546294	−0.273147	+	0.961972i	$0.588065\pi$
$294$	0	0
$295$	1.08502e8	0.246071
$296$	−8.24499e8	−1.84786
$297$	0	0
$298$	4.88866e8	1.07012
$299$	−1.60601e8	−0.347455
$300$	0	0
$301$	−7.61339e7	−0.160915
$302$	3.21859e8	0.672422
$303$	0	0
$304$	4.73471e8	0.966575
$305$	3.53665e8	0.713744
$306$	0	0
$307$	8.85429e8	1.74650	0.873252	−	0.487270i	$-0.162007\pi$
$307$	8.85429e8	1.74650	0.873252	+	0.487270i	$0.162007\pi$
$308$	−3.09367e7	−0.0603319
$309$	0	0
$310$	5.85391e8	1.11604
$311$	1.76021e7	0.0331821	0.0165910	−	0.999862i	$-0.494719\pi$
$311$	1.76021e7	0.0331821	0.0165910	+	0.999862i	$0.494719\pi$
$312$	0	0
$313$	4.96157e8	0.914563	0.457282	−	0.889322i	$-0.348823\pi$
$313$	4.96157e8	0.914563	0.457282	+	0.889322i	$0.348823\pi$
$314$	2.01620e8	0.367518
$315$	0	0
$316$	7.42636e7	0.132395
$317$	−1.86690e8	−0.329166	−0.164583	−	0.986363i	$-0.552628\pi$
$317$	−1.86690e8	−0.329166	−0.164583	+	0.986363i	$0.552628\pi$
$318$	0	0
$319$	2.81093e8	0.484822
$320$	4.58169e8	0.781629
$321$	0	0
$322$	4.58512e8	0.765342
$323$	−5.82286e8	−0.961452
$324$	0	0
$325$	−1.34574e8	−0.217455
$326$	−8.29789e8	−1.32650
$327$	0	0
$328$	−1.95020e8	−0.305155
$329$	−6.65255e7	−0.102992
$330$	0	0
$331$	2.27577e8	0.344930	0.172465	−	0.985016i	$-0.444827\pi$
$331$	2.27577e8	0.344930	0.172465	+	0.985016i	$0.444827\pi$
$332$	−3.43972e7	−0.0515869
$333$	0	0
$334$	6.66755e8	0.979161
$335$	−6.83461e7	−0.0993247
$336$	0	0
$337$	5.82154e8	0.828578	0.414289	−	0.910145i	$-0.364030\pi$
$337$	5.82154e8	0.828578	0.414289	+	0.910145i	$0.364030\pi$
$338$	5.32524e8	0.750119
$339$	0	0
$340$	−5.12258e7	−0.0706827
$341$	−6.10395e8	−0.833625
$342$	0	0
$343$	−6.99160e8	−0.935507
$344$	−1.20688e8	−0.159849
$345$	0	0
$346$	−6.46636e8	−0.839254
$347$	1.36939e9	1.75943	0.879717	−	0.475497i	$-0.157732\pi$
$347$	1.36939e9	1.75943	0.879717	+	0.475497i	$0.157732\pi$
$348$	0	0
$349$	5.85604e8	0.737420	0.368710	−	0.929544i	$-0.379799\pi$
$349$	5.85604e8	0.737420	0.368710	+	0.929544i	$0.379799\pi$
$350$	3.84206e8	0.478990
$351$	0	0
$352$	−9.31067e7	−0.113784
$353$	1.09719e9	1.32761	0.663807	−	0.747904i	$-0.268940\pi$
$353$	1.09719e9	1.32761	0.663807	+	0.747904i	$0.268940\pi$
$354$	0	0
$355$	−1.66856e8	−0.197944
$356$	7.52609e7	0.0884086
$357$	0	0
$358$	1.24644e9	1.43575
$359$	1.45245e9	1.65681	0.828403	−	0.560132i	$-0.189250\pi$
$359$	1.45245e9	1.65681	0.828403	+	0.560132i	$0.189250\pi$
$360$	0	0
$361$	1.98561e8	0.222136
$362$	9.26851e8	1.02690
$363$	0	0
$364$	−4.94657e7	−0.0537588
$365$	−4.04070e8	−0.434942
$366$	0	0
$367$	−1.00877e9	−1.06527	−0.532637	−	0.846344i	$-0.678799\pi$
$367$	−1.00877e9	−1.06527	−0.532637	+	0.846344i	$0.678799\pi$
$368$	6.43705e8	0.673317
$369$	0	0
$370$	1.16437e9	1.19505
$371$	−1.38292e9	−1.40601
$372$	0	0
$373$	7.06673e7	0.0705078	0.0352539	−	0.999378i	$-0.488776\pi$
$373$	7.06673e7	0.0705078	0.0352539	+	0.999378i	$0.488776\pi$
$374$	−4.19616e8	−0.414764
$375$	0	0
$376$	−1.05457e8	−0.102310
$377$	4.49448e8	0.432001
$378$	0	0
$379$	3.12820e8	0.295160	0.147580	−	0.989050i	$-0.452852\pi$
$379$	3.12820e8	0.295160	0.147580	+	0.989050i	$0.452852\pi$
$380$	9.61053e7	0.0898473
$381$	0	0
$382$	1.11784e9	1.02602
$383$	1.35474e9	1.23214	0.616072	−	0.787690i	$-0.288723\pi$
$383$	1.35474e9	1.23214	0.616072	+	0.787690i	$0.288723\pi$
$384$	0	0
$385$	4.30600e8	0.384558
$386$	1.59207e9	1.40898
$387$	0	0
$388$	−1.92896e7	−0.0167654
$389$	−1.44299e8	−0.124291	−0.0621455	−	0.998067i	$-0.519794\pi$
$389$	−1.44299e8	−0.124291	−0.0621455	+	0.998067i	$0.519794\pi$
$390$	0	0
$391$	−7.91645e8	−0.669748
$392$	1.41789e8	0.118888
$393$	0	0
$394$	2.75747e8	0.227130
$395$	−1.03366e9	−0.843890
$396$	0	0
$397$	−2.70306e8	−0.216815	−0.108407	−	0.994107i	$-0.534575\pi$
$397$	−2.70306e8	−0.216815	−0.108407	+	0.994107i	$0.534575\pi$
$398$	2.87411e8	0.228514
$399$	0	0
$400$	5.39387e8	0.421396
$401$	−2.48187e8	−0.192209	−0.0961045	−	0.995371i	$-0.530638\pi$
$401$	−2.48187e8	−0.192209	−0.0961045	+	0.995371i	$0.530638\pi$
$402$	0	0
$403$	−9.75980e8	−0.742803
$404$	4.73313e7	0.0357119
$405$	0	0
$406$	−1.28317e9	−0.951572
$407$	−1.21411e9	−0.892639
$408$	0	0
$409$	2.20584e9	1.59420	0.797099	−	0.603849i	$-0.206367\pi$
$409$	2.20584e9	1.59420	0.797099	+	0.603849i	$0.206367\pi$
$410$	2.75410e8	0.197350
$411$	0	0
$412$	−8.45275e7	−0.0595467
$413$	5.16458e8	0.360753
$414$	0	0
$415$	4.78765e8	0.328817
$416$	−1.48871e8	−0.101388
$417$	0	0
$418$	7.87246e8	0.527222
$419$	2.07809e8	0.138012	0.0690058	−	0.997616i	$-0.478017\pi$
$419$	2.07809e8	0.138012	0.0690058	+	0.997616i	$0.478017\pi$
$420$	0	0
$421$	6.53484e8	0.426823	0.213411	−	0.976962i	$-0.431543\pi$
$421$	6.53484e8	0.426823	0.213411	+	0.976962i	$0.431543\pi$
$422$	2.38891e9	1.54741
$423$	0	0
$424$	−2.19222e9	−1.39670
$425$	−6.63352e8	−0.419163
$426$	0	0
$427$	1.68341e9	1.04639
$428$	9.95039e7	0.0613461
$429$	0	0
$430$	1.70438e8	0.103378
$431$	−1.12074e9	−0.674272	−0.337136	−	0.941456i	$-0.609458\pi$
$431$	−1.12074e9	−0.674272	−0.337136	+	0.941456i	$0.609458\pi$
$432$	0	0
$433$	−3.10966e9	−1.84080	−0.920398	−	0.390983i	$-0.872135\pi$
$433$	−3.10966e9	−1.84080	−0.920398	+	0.390983i	$0.872135\pi$
$434$	2.78641e9	1.63618
$435$	0	0
$436$	1.26528e8	0.0731114
$437$	1.48521e9	0.851341
$438$	0	0
$439$	−1.69746e9	−0.957576	−0.478788	−	0.877931i	$-0.658924\pi$
$439$	−1.69746e9	−0.957576	−0.478788	+	0.877931i	$0.658924\pi$
$440$	6.82592e8	0.382012
$441$	0	0
$442$	−6.70938e8	−0.369576
$443$	1.17417e8	0.0641680	0.0320840	−	0.999485i	$-0.489786\pi$
$443$	1.17417e8	0.0641680	0.0320840	+	0.999485i	$0.489786\pi$
$444$	0	0
$445$	−1.04754e9	−0.563520
$446$	−1.83746e8	−0.0980720
$447$	0	0
$448$	2.18084e9	1.14591
$449$	5.66870e8	0.295544	0.147772	−	0.989021i	$-0.452790\pi$
$449$	5.66870e8	0.295544	0.147772	+	0.989021i	$0.452790\pi$
$450$	0	0
$451$	−2.87174e8	−0.147410
$452$	−2.27635e8	−0.115946
$453$	0	0
$454$	−2.06417e9	−1.03526
$455$	6.88501e8	0.342661
$456$	0	0
$457$	−1.74346e9	−0.854489	−0.427244	−	0.904136i	$-0.640516\pi$
$457$	−1.74346e9	−0.854489	−0.427244	+	0.904136i	$0.640516\pi$
$458$	−8.67811e8	−0.422081
$459$	0	0
$460$	1.30660e8	0.0625877
$461$	−6.90361e8	−0.328188	−0.164094	−	0.986445i	$-0.552470\pi$
$461$	−6.90361e8	−0.328188	−0.164094	+	0.986445i	$0.552470\pi$
$462$	0	0
$463$	2.51858e9	1.17929	0.589647	−	0.807661i	$-0.299267\pi$
$463$	2.51858e9	1.17929	0.589647	+	0.807661i	$0.299267\pi$
$464$	−1.80144e9	−0.837155
$465$	0	0
$466$	−2.75153e9	−1.25957
$467$	−2.86563e8	−0.130200	−0.0650999	−	0.997879i	$-0.520737\pi$
$467$	−2.86563e8	−0.130200	−0.0650999	+	0.997879i	$0.520737\pi$
$468$	0	0
$469$	−3.25321e8	−0.145615
$470$	1.48928e8	0.0661660
$471$	0	0
$472$	8.18695e8	0.358365
$473$	−1.77718e8	−0.0772179
$474$	0	0
$475$	1.24452e9	0.532813
$476$	−2.43830e8	−0.103625
$477$	0	0
$478$	3.42494e9	1.43435
$479$	−2.29304e9	−0.953317	−0.476659	−	0.879089i	$-0.658152\pi$
$479$	−2.29304e9	−0.953317	−0.476659	+	0.879089i	$0.658152\pi$
$480$	0	0
$481$	−1.94127e9	−0.795388
$482$	1.06324e9	0.432482
$483$	0	0
$484$	2.09444e8	0.0839672
$485$	2.68488e8	0.106863
$486$	0	0
$487$	−3.54210e9	−1.38966	−0.694831	−	0.719173i	$-0.744521\pi$
$487$	−3.54210e9	−1.38966	−0.694831	+	0.719173i	$0.744521\pi$
$488$	2.66856e9	1.03946
$489$	0	0
$490$	−2.00236e8	−0.0768876
$491$	−2.62430e9	−1.00052	−0.500262	−	0.865874i	$-0.666763\pi$
$491$	−2.62430e9	−1.00052	−0.500262	+	0.865874i	$0.666763\pi$
$492$	0	0
$493$	2.21545e9	0.832718
$494$	1.25875e9	0.469782
$495$	0	0
$496$	3.91183e9	1.43944
$497$	−7.94218e8	−0.290197
$498$	0	0
$499$	2.54642e9	0.917441	0.458720	−	0.888581i	$-0.348308\pi$
$499$	2.54642e9	0.917441	0.458720	+	0.888581i	$0.348308\pi$
$500$	3.36649e8	0.120443
$501$	0	0
$502$	−4.63978e9	−1.63695
$503$	2.19796e9	0.770072	0.385036	−	0.922901i	$-0.374189\pi$
$503$	2.19796e9	0.770072	0.385036	+	0.922901i	$0.374189\pi$
$504$	0	0
$505$	−6.58791e8	−0.227629
$506$	1.07030e9	0.367263
$507$	0	0
$508$	−6.18483e8	−0.209317
$509$	9.81851e8	0.330015	0.165007	−	0.986292i	$-0.447235\pi$
$509$	9.81851e8	0.330015	0.165007	+	0.986292i	$0.447235\pi$
$510$	0	0
$511$	−1.92333e9	−0.637649
$512$	3.38003e9	1.11295
$513$	0	0
$514$	−3.91327e9	−1.27107
$515$	1.17652e9	0.379553
$516$	0	0
$517$	−1.55289e8	−0.0494225
$518$	5.54230e9	1.75201
$519$	0	0
$520$	1.09142e9	0.340392
$521$	−1.51301e9	−0.468715	−0.234357	−	0.972151i	$-0.575299\pi$
$521$	−1.51301e9	−0.468715	−0.234357	+	0.972151i	$0.575299\pi$
$522$	0	0
$523$	3.88181e9	1.18653	0.593264	−	0.805008i	$-0.297839\pi$
$523$	3.88181e9	1.18653	0.593264	+	0.805008i	$0.297839\pi$
$524$	−2.37784e8	−0.0721977
$525$	0	0
$526$	4.18604e9	1.25416
$527$	−4.81087e9	−1.43181
$528$	0	0
$529$	−1.38561e9	−0.406955
$530$	3.09589e9	0.903276
$531$	0	0
$532$	4.57452e8	0.131721
$533$	−4.59171e8	−0.131350
$534$	0	0
$535$	−1.38497e9	−0.391022
$536$	−5.15702e8	−0.144651
$537$	0	0
$538$	−1.92755e8	−0.0533665
$539$	2.08789e8	0.0574310
$540$	0	0
$541$	−1.78344e9	−0.484248	−0.242124	−	0.970245i	$-0.577844\pi$
$541$	−1.78344e9	−0.484248	−0.242124	+	0.970245i	$0.577844\pi$
$542$	1.26734e9	0.341897
$543$	0	0
$544$	−7.33827e8	−0.195433
$545$	−1.76111e9	−0.466015
$546$	0	0
$547$	−5.88194e9	−1.53662	−0.768308	−	0.640081i	$-0.778901\pi$
$547$	−5.88194e9	−1.53662	−0.768308	+	0.640081i	$0.778901\pi$
$548$	8.11434e7	0.0210630
$549$	0	0
$550$	8.96846e8	0.229852
$551$	−4.15643e9	−1.05850
$552$	0	0
$553$	−4.92010e9	−1.23719
$554$	2.56713e8	0.0641450
$555$	0	0
$556$	−7.56559e8	−0.186673
$557$	−3.02826e9	−0.742507	−0.371253	−	0.928532i	$-0.621072\pi$
$557$	−3.02826e9	−0.742507	−0.371253	+	0.928532i	$0.621072\pi$
$558$	0	0
$559$	−2.84159e8	−0.0688051
$560$	−2.75958e9	−0.664027
$561$	0	0
$562$	−3.33273e9	−0.791996
$563$	−6.07272e9	−1.43418	−0.717091	−	0.696980i	$-0.754527\pi$
$563$	−6.07272e9	−1.43418	−0.717091	+	0.696980i	$0.754527\pi$
$564$	0	0
$565$	3.16840e9	0.739044
$566$	5.95911e9	1.38141
$567$	0	0
$568$	−1.25900e9	−0.288275
$569$	3.83940e8	0.0873717	0.0436859	−	0.999045i	$-0.486090\pi$
$569$	3.83940e8	0.0873717	0.0436859	+	0.999045i	$0.486090\pi$
$570$	0	0
$571$	5.08925e8	0.114400	0.0572001	−	0.998363i	$-0.481783\pi$
$571$	5.08925e8	0.114400	0.0572001	+	0.998363i	$0.481783\pi$
$572$	−1.15467e8	−0.0257972
$573$	0	0
$574$	1.31092e9	0.289325
$575$	1.69198e9	0.371158
$576$	0	0
$577$	5.99008e9	1.29813	0.649064	−	0.760734i	$-0.275161\pi$
$577$	5.99008e9	1.29813	0.649064	+	0.760734i	$0.275161\pi$
$578$	1.06526e9	0.229461
$579$	0	0
$580$	−3.65657e8	−0.0778172
$581$	2.27888e9	0.482064
$582$	0	0
$583$	−3.22813e9	−0.674700
$584$	−3.04889e9	−0.633427
$585$	0	0
$586$	2.50640e9	0.514527
$587$	6.48652e9	1.32367	0.661833	−	0.749651i	$-0.269779\pi$
$587$	6.48652e9	1.32367	0.661833	+	0.749651i	$0.269779\pi$
$588$	0	0
$589$	9.02572e9	1.82003
$590$	−1.15618e9	−0.231762
$591$	0	0
$592$	7.78083e9	1.54135
$593$	−7.74226e9	−1.52467	−0.762336	−	0.647182i	$-0.775947\pi$
$593$	−7.74226e9	−1.52467	−0.762336	+	0.647182i	$0.775947\pi$
$594$	0	0
$595$	3.39380e9	0.660507
$596$	6.63099e8	0.128297
$597$	0	0
$598$	1.71133e9	0.327251
$599$	−1.02919e9	−0.195660	−0.0978301	−	0.995203i	$-0.531190\pi$
$599$	−1.02919e9	−0.195660	−0.0978301	+	0.995203i	$0.531190\pi$
$600$	0	0
$601$	2.30557e9	0.433229	0.216614	−	0.976257i	$-0.430499\pi$
$601$	2.30557e9	0.433229	0.216614	+	0.976257i	$0.430499\pi$
$602$	8.11269e8	0.151557
$603$	0	0
$604$	4.36571e8	0.0806168
$605$	−2.91520e9	−0.535210
$606$	0	0
$607$	−2.36455e9	−0.429130	−0.214565	−	0.976710i	$-0.568833\pi$
$607$	−2.36455e9	−0.429130	−0.214565	+	0.976710i	$0.568833\pi$
$608$	1.37674e9	0.248422
$609$	0	0
$610$	−3.76859e9	−0.672240
$611$	−2.48297e8	−0.0440380
$612$	0	0
$613$	−4.21027e9	−0.738242	−0.369121	−	0.929381i	$-0.620341\pi$
$613$	−4.21027e9	−0.738242	−0.369121	+	0.929381i	$0.620341\pi$
$614$	−9.43497e9	−1.64494
$615$	0	0
$616$	3.24907e9	0.560050
$617$	7.09170e9	1.21549	0.607746	−	0.794132i	$-0.292074\pi$
$617$	7.09170e9	1.21549	0.607746	+	0.794132i	$0.292074\pi$
$618$	0	0
$619$	3.23665e9	0.548502	0.274251	−	0.961658i	$-0.411570\pi$
$619$	3.23665e9	0.548502	0.274251	+	0.961658i	$0.411570\pi$
$620$	7.94026e8	0.133802
$621$	0	0
$622$	−1.87565e8	−0.0312525
$623$	−4.98617e9	−0.826150
$624$	0	0
$625$	−1.74406e9	−0.285746
$626$	−5.28695e9	−0.861381
$627$	0	0
$628$	2.73477e8	0.0440618
$629$	−9.56906e9	−1.53318
$630$	0	0
$631$	−4.24096e9	−0.671988	−0.335994	−	0.941864i	$-0.609072\pi$
$631$	−4.24096e9	−0.671988	−0.335994	+	0.941864i	$0.609072\pi$
$632$	−7.79940e9	−1.22900
$633$	0	0
$634$	1.98934e9	0.310025
$635$	8.60849e9	1.33419
$636$	0	0
$637$	3.33839e8	0.0511740
$638$	−2.99527e9	−0.456630
$639$	0	0
$640$	−3.80956e9	−0.574440
$641$	−8.27507e9	−1.24099	−0.620495	−	0.784210i	$-0.713068\pi$
$641$	−8.27507e9	−1.24099	−0.620495	+	0.784210i	$0.713068\pi$
$642$	0	0
$643$	3.21955e9	0.477592	0.238796	−	0.971070i	$-0.423247\pi$
$643$	3.21955e9	0.477592	0.238796	+	0.971070i	$0.423247\pi$
$644$	6.21927e8	0.0917569
$645$	0	0
$646$	6.20473e9	0.905543
$647$	5.12587e9	0.744050	0.372025	−	0.928223i	$-0.378664\pi$
$647$	5.12587e9	0.744050	0.372025	+	0.928223i	$0.378664\pi$
$648$	0	0
$649$	1.20556e9	0.173114
$650$	1.43400e9	0.204810
$651$	0	0
$652$	−1.12553e9	−0.159034
$653$	8.03122e9	1.12872	0.564359	−	0.825530i	$-0.309124\pi$
$653$	8.03122e9	1.12872	0.564359	+	0.825530i	$0.309124\pi$
$654$	0	0
$655$	3.30966e9	0.460191
$656$	1.84041e9	0.254537
$657$	0	0
$658$	7.08884e8	0.0970029
$659$	−1.23759e10	−1.68452	−0.842261	−	0.539070i	$-0.818776\pi$
$659$	−1.23759e10	−1.68452	−0.842261	+	0.539070i	$0.818776\pi$
$660$	0	0
$661$	−6.26661e9	−0.843971	−0.421985	−	0.906603i	$-0.638667\pi$
$661$	−6.26661e9	−0.843971	−0.421985	+	0.906603i	$0.638667\pi$
$662$	−2.42502e9	−0.324872
$663$	0	0
$664$	3.61250e9	0.478872
$665$	−6.36715e9	−0.839594
$666$	0	0
$667$	−5.65086e9	−0.737351
$668$	9.04388e8	0.117392
$669$	0	0
$670$	7.28284e8	0.0935490
$671$	3.92955e9	0.502128
$672$	0	0
$673$	−1.35556e10	−1.71422	−0.857110	−	0.515134i	$-0.827742\pi$
$673$	−1.35556e10	−1.71422	−0.857110	+	0.515134i	$0.827742\pi$
$674$	−6.20333e9	−0.780397
$675$	0	0
$676$	7.22316e8	0.0899319
$677$	−7.09818e9	−0.879198	−0.439599	−	0.898194i	$-0.644879\pi$
$677$	−7.09818e9	−0.879198	−0.439599	+	0.898194i	$0.644879\pi$
$678$	0	0
$679$	1.27797e9	0.156667
$680$	5.37990e9	0.656134
$681$	0	0
$682$	6.50426e9	0.785150
$683$	−1.16617e10	−1.40052	−0.700260	−	0.713888i	$-0.746932\pi$
$683$	−1.16617e10	−1.40052	−0.700260	+	0.713888i	$0.746932\pi$
$684$	0	0
$685$	−1.12941e9	−0.134257
$686$	7.45012e9	0.881107
$687$	0	0
$688$	1.13894e9	0.133334
$689$	−5.16156e9	−0.601193
$690$	0	0
$691$	5.62825e9	0.648933	0.324467	−	0.945897i	$-0.394815\pi$
$691$	5.62825e9	0.648933	0.324467	+	0.945897i	$0.394815\pi$
$692$	−8.77098e8	−0.100618
$693$	0	0
$694$	−1.45919e10	−1.65712
$695$	1.05304e10	1.18986
$696$	0	0
$697$	−2.26338e9	−0.253188
$698$	−6.24009e9	−0.694539
$699$	0	0
$700$	5.21138e8	0.0574261
$701$	−3.78769e9	−0.415299	−0.207650	−	0.978203i	$-0.566581\pi$
$701$	−3.78769e9	−0.415299	−0.207650	+	0.978203i	$0.566581\pi$
$702$	0	0
$703$	1.79526e10	1.94887
$704$	5.09070e9	0.549886
$705$	0	0
$706$	−1.16915e10	−1.25041
$707$	−3.13578e9	−0.333717
$708$	0	0
$709$	1.25414e10	1.32155	0.660777	−	0.750582i	$-0.270227\pi$
$709$	1.25414e10	1.32155	0.660777	+	0.750582i	$0.270227\pi$
$710$	1.77799e9	0.186434
$711$	0	0
$712$	−7.90413e9	−0.820681
$713$	1.22709e10	1.26783
$714$	0	0
$715$	1.60716e9	0.164432
$716$	1.69067e9	0.172133
$717$	0	0
$718$	−1.54771e10	−1.56046
$719$	1.18698e10	1.19095	0.595473	−	0.803375i	$-0.296965\pi$
$719$	1.18698e10	1.19095	0.595473	+	0.803375i	$0.296965\pi$
$720$	0	0
$721$	5.60010e9	0.556445
$722$	−2.11583e9	−0.209219
$723$	0	0
$724$	1.25718e9	0.123116
$725$	−4.73509e9	−0.461472
$726$	0	0
$727$	−1.62657e10	−1.57001	−0.785007	−	0.619487i	$-0.787341\pi$
$727$	−1.62657e10	−1.57001	−0.785007	+	0.619487i	$0.787341\pi$
$728$	5.19505e9	0.499033
$729$	0	0
$730$	4.30570e9	0.409650
$731$	−1.40070e9	−0.132627
$732$	0	0
$733$	−5.57100e8	−0.0522480	−0.0261240	−	0.999659i	$-0.508316\pi$
$733$	−5.57100e8	−0.0522480	−0.0261240	+	0.999659i	$0.508316\pi$
$734$	1.07493e10	1.00333
$735$	0	0
$736$	1.87174e9	0.173051
$737$	−7.59391e8	−0.0698762
$738$	0	0
$739$	−4.42801e9	−0.403602	−0.201801	−	0.979427i	$-0.564679\pi$
$739$	−4.42801e9	−0.403602	−0.201801	+	0.979427i	$0.564679\pi$
$740$	1.57936e9	0.143275
$741$	0	0
$742$	1.47362e10	1.32425
$743$	1.80938e10	1.61834	0.809168	−	0.587577i	$-0.199918\pi$
$743$	1.80938e10	1.61834	0.809168	+	0.587577i	$0.199918\pi$
$744$	0	0
$745$	−9.22950e9	−0.817770
$746$	−7.53018e8	−0.0664078
$747$	0	0
$748$	−5.69168e8	−0.0497262
$749$	−6.59231e9	−0.573260
$750$	0	0
$751$	−2.03937e9	−0.175694	−0.0878468	−	0.996134i	$-0.527999\pi$
$751$	−2.03937e9	−0.175694	−0.0878468	+	0.996134i	$0.527999\pi$
$752$	9.95202e8	0.0853393
$753$	0	0
$754$	−4.78924e9	−0.406880
$755$	−6.07651e9	−0.513855
$756$	0	0
$757$	3.06993e9	0.257213	0.128606	−	0.991696i	$-0.458950\pi$
$757$	3.06993e9	0.257213	0.128606	+	0.991696i	$0.458950\pi$
$758$	−3.33336e9	−0.277997
$759$	0	0
$760$	−1.00933e10	−0.834036
$761$	−1.21229e8	−0.00997149	−0.00498575	−	0.999988i	$-0.501587\pi$
$761$	−1.21229e8	−0.00997149	−0.00498575	+	0.999988i	$0.501587\pi$
$762$	0	0
$763$	−8.38273e9	−0.683203
$764$	1.51623e9	0.123010
$765$	0	0
$766$	−1.44359e10	−1.16050
$767$	1.92761e9	0.154253
$768$	0	0
$769$	−1.56911e9	−0.124426	−0.0622129	−	0.998063i	$-0.519816\pi$
$769$	−1.56911e9	−0.124426	−0.0622129	+	0.998063i	$0.519816\pi$
$770$	−4.58840e9	−0.362196
$771$	0	0
$772$	2.15948e9	0.168923
$773$	−1.68087e10	−1.30890	−0.654450	−	0.756105i	$-0.727100\pi$
$773$	−1.68087e10	−1.30890	−0.654450	+	0.756105i	$0.727100\pi$
$774$	0	0
$775$	1.02823e10	0.793475
$776$	2.02586e9	0.155630
$777$	0	0
$778$	1.53762e9	0.117063
$779$	4.24635e9	0.321836
$780$	0	0
$781$	−1.85393e9	−0.139256
$782$	8.43562e9	0.630803
$783$	0	0
$784$	−1.33806e9	−0.0991678
$785$	−3.80646e9	−0.280852
$786$	0	0
$787$	−8.64981e9	−0.632550	−0.316275	−	0.948668i	$-0.602432\pi$
$787$	−8.64981e9	−0.632550	−0.316275	+	0.948668i	$0.602432\pi$
$788$	3.74023e8	0.0272306
$789$	0	0
$790$	1.10144e10	0.794818
$791$	1.50813e10	1.08348
$792$	0	0
$793$	6.28309e9	0.447422
$794$	2.88033e9	0.204207
$795$	0	0
$796$	3.89845e8	0.0273966
$797$	5.85964e9	0.409984	0.204992	−	0.978764i	$-0.434283\pi$
$797$	5.85964e9	0.409984	0.204992	+	0.978764i	$0.434283\pi$
$798$	0	0
$799$	−1.22392e9	−0.0848869
$800$	1.56841e9	0.108304
$801$	0	0
$802$	2.64464e9	0.181032
$803$	−4.48960e9	−0.305987
$804$	0	0
$805$	−8.65644e9	−0.584862
$806$	1.03999e10	0.699609
$807$	0	0
$808$	−4.97088e9	−0.331507
$809$	−1.88923e10	−1.25449	−0.627243	−	0.778824i	$-0.715817\pi$
$809$	−1.88923e10	−1.25449	−0.627243	+	0.778824i	$0.715817\pi$
$810$	0	0
$811$	−8.87161e8	−0.0584022	−0.0292011	−	0.999574i	$-0.509296\pi$
$811$	−8.87161e8	−0.0584022	−0.0292011	+	0.999574i	$0.509296\pi$
$812$	−1.74049e9	−0.114084
$813$	0	0
$814$	1.29373e10	0.840732
$815$	1.56659e10	1.01369
$816$	0	0
$817$	2.62786e9	0.168588
$818$	−2.35050e10	−1.50150
$819$	0	0
$820$	3.73567e8	0.0236603
$821$	−1.27653e10	−0.805060	−0.402530	−	0.915407i	$-0.631869\pi$
$821$	−1.27653e10	−0.805060	−0.402530	+	0.915407i	$0.631869\pi$
$822$	0	0
$823$	1.51004e10	0.944255	0.472128	−	0.881530i	$-0.343486\pi$
$823$	1.51004e10	0.944255	0.472128	+	0.881530i	$0.343486\pi$
$824$	8.87735e9	0.552762
$825$	0	0
$826$	−5.50328e9	−0.339775
$827$	−3.56843e8	−0.0219385	−0.0109693	−	0.999940i	$-0.503492\pi$
$827$	−3.56843e8	−0.0219385	−0.0109693	+	0.999940i	$0.503492\pi$
$828$	0	0
$829$	−5.73652e9	−0.349710	−0.174855	−	0.984594i	$-0.555946\pi$
$829$	−5.73652e9	−0.349710	−0.174855	+	0.984594i	$0.555946\pi$
$830$	−5.10164e9	−0.309696
$831$	0	0
$832$	8.13968e9	0.489977
$833$	1.64558e9	0.0986421
$834$	0	0
$835$	−1.25879e10	−0.748259
$836$	1.06782e9	0.0632087
$837$	0	0
$838$	−2.21437e9	−0.129986
$839$	−8.92027e9	−0.521448	−0.260724	−	0.965413i	$-0.583961\pi$
$839$	−8.92027e9	−0.521448	−0.260724	+	0.965413i	$0.583961\pi$
$840$	0	0
$841$	−1.43570e9	−0.0832297
$842$	−6.96340e9	−0.402003
$843$	0	0
$844$	3.24032e9	0.185520
$845$	−1.00537e10	−0.573230
$846$	0	0
$847$	−1.38761e10	−0.784646
$848$	2.06881e10	1.16502
$849$	0	0
$850$	7.06855e9	0.394788
$851$	2.44074e10	1.35759
$852$	0	0
$853$	−4.70918e8	−0.0259791	−0.0129895	−	0.999916i	$-0.504135\pi$
$853$	−4.70918e8	−0.0259791	−0.0129895	+	0.999916i	$0.504135\pi$
$854$	−1.79381e10	−0.985539
$855$	0	0
$856$	−1.04502e10	−0.569465
$857$	−1.57163e10	−0.852938	−0.426469	−	0.904502i	$-0.640243\pi$
$857$	−1.57163e10	−0.852938	−0.426469	+	0.904502i	$0.640243\pi$
$858$	0	0
$859$	1.61536e10	0.869550	0.434775	−	0.900539i	$-0.356828\pi$
$859$	1.61536e10	0.869550	0.434775	+	0.900539i	$0.356828\pi$
$860$	2.31183e8	0.0123940
$861$	0	0
$862$	1.19424e10	0.635063
$863$	−2.12356e10	−1.12467	−0.562337	−	0.826908i	$-0.690098\pi$
$863$	−2.12356e10	−1.12467	−0.562337	+	0.826908i	$0.690098\pi$
$864$	0	0
$865$	1.22081e10	0.641345
$866$	3.31360e10	1.73375
$867$	0	0
$868$	3.77949e9	0.196161
$869$	−1.14849e10	−0.593688
$870$	0	0
$871$	−1.21422e9	−0.0622633
$872$	−1.32884e10	−0.678680
$873$	0	0
$874$	−1.58262e10	−0.801836
$875$	−2.23036e10	−1.12550
$876$	0	0
$877$	−1.15277e10	−0.577090	−0.288545	−	0.957466i	$-0.593171\pi$
$877$	−1.15277e10	−0.577090	−0.288545	+	0.957466i	$0.593171\pi$
$878$	1.80878e10	0.901893
$879$	0	0
$880$	−6.44165e9	−0.318645
$881$	−3.38787e10	−1.66921	−0.834606	−	0.550848i	$-0.814304\pi$
$881$	−3.38787e10	−1.66921	−0.834606	+	0.550848i	$0.814304\pi$
$882$	0	0
$883$	−2.28998e10	−1.11936	−0.559679	−	0.828709i	$-0.689076\pi$
$883$	−2.28998e10	−1.11936	−0.559679	+	0.828709i	$0.689076\pi$
$884$	−9.10061e8	−0.0443086
$885$	0	0
$886$	−1.25118e9	−0.0604366
$887$	3.26496e10	1.57089	0.785445	−	0.618932i	$-0.212434\pi$
$887$	3.26496e10	1.57089	0.785445	+	0.618932i	$0.212434\pi$
$888$	0	0
$889$	4.09756e10	1.95600
$890$	1.11624e10	0.530751
$891$	0	0
$892$	−2.49233e8	−0.0117579
$893$	2.29622e9	0.107903
$894$	0	0
$895$	−2.35320e10	−1.09718
$896$	−1.81331e10	−0.842160
$897$	0	0
$898$	−6.04047e9	−0.278358
$899$	−3.43406e10	−1.57634
$900$	0	0
$901$	−2.54427e10	−1.15885
$902$	3.06007e9	0.138838
$903$	0	0
$904$	2.39070e10	1.07630
$905$	−1.74984e10	−0.784744
$906$	0	0
$907$	1.01088e10	0.449857	0.224929	−	0.974375i	$-0.427785\pi$
$907$	1.01088e10	0.449857	0.224929	+	0.974375i	$0.427785\pi$
$908$	−2.79984e9	−0.124117
$909$	0	0
$910$	−7.33654e9	−0.322735
$911$	−2.85664e10	−1.25182	−0.625910	−	0.779895i	$-0.715272\pi$
$911$	−2.85664e10	−1.25182	−0.625910	+	0.779895i	$0.715272\pi$
$912$	0	0
$913$	5.31954e9	0.231327
$914$	1.85780e10	0.804800
$915$	0	0
$916$	−1.17710e9	−0.0506034
$917$	1.57536e10	0.674665
$918$	0	0
$919$	2.52904e8	0.0107486	0.00537428	−	0.999986i	$-0.498289\pi$
$919$	2.52904e8	0.0107486	0.00537428	+	0.999986i	$0.498289\pi$
$920$	−1.37223e10	−0.580990
$921$	0	0
$922$	7.35636e9	0.309104
$923$	−2.96431e9	−0.124084
$924$	0	0
$925$	2.04520e10	0.849648
$926$	−2.68375e10	−1.11072
$927$	0	0
$928$	−5.23815e9	−0.215159
$929$	−1.83396e10	−0.750472	−0.375236	−	0.926929i	$-0.622438\pi$
$929$	−1.83396e10	−0.750472	−0.375236	+	0.926929i	$0.622438\pi$
$930$	0	0
$931$	−3.08730e9	−0.125388
$932$	−3.73218e9	−0.151011
$933$	0	0
$934$	3.05356e9	0.122629
$935$	7.92210e9	0.316956
$936$	0	0
$937$	−7.40480e9	−0.294052	−0.147026	−	0.989133i	$-0.546970\pi$
$937$	−7.40480e9	−0.294052	−0.147026	+	0.989133i	$0.546970\pi$
$938$	3.46656e9	0.137148
$939$	0	0
$940$	2.02007e8	0.00793265
$941$	2.48816e10	0.973451	0.486725	−	0.873555i	$-0.338191\pi$
$941$	2.48816e10	0.973451	0.486725	+	0.873555i	$0.338191\pi$
$942$	0	0
$943$	5.77311e9	0.224191
$944$	−7.72606e9	−0.298921
$945$	0	0
$946$	1.89373e9	0.0727276
$947$	−1.70907e9	−0.0653937	−0.0326968	−	0.999465i	$-0.510410\pi$
$947$	−1.70907e9	−0.0653937	−0.0326968	+	0.999465i	$0.510410\pi$
$948$	0	0
$949$	−7.17857e9	−0.272651
$950$	−1.32614e10	−0.501830
$951$	0	0
$952$	2.56078e10	0.961928
$953$	5.28096e10	1.97646	0.988229	−	0.152980i	$-0.0488870\pi$
$953$	5.28096e10	1.97646	0.988229	+	0.152980i	$0.0488870\pi$
$954$	0	0
$955$	−2.11041e10	−0.784069
$956$	4.64559e9	0.171964
$957$	0	0
$958$	2.44342e10	0.897882
$959$	−5.37590e9	−0.196827
$960$	0	0
$961$	4.70583e10	1.71042
$962$	2.06859e10	0.749136
$963$	0	0
$964$	1.44218e9	0.0518503
$965$	−3.00573e10	−1.07672
$966$	0	0
$967$	−2.51978e10	−0.896127	−0.448063	−	0.894002i	$-0.647886\pi$
$967$	−2.51978e10	−0.896127	−0.448063	+	0.894002i	$0.647886\pi$
$968$	−2.19965e10	−0.779452
$969$	0	0
$970$	−2.86095e9	−0.100649
$971$	4.38394e10	1.53673	0.768364	−	0.640013i	$-0.221071\pi$
$971$	4.38394e10	1.53673	0.768364	+	0.640013i	$0.221071\pi$
$972$	0	0
$973$	5.01234e10	1.74440
$974$	3.77439e10	1.30885
$975$	0	0
$976$	−2.51833e10	−0.867038
$977$	3.75464e10	1.28806	0.644032	−	0.764999i	$-0.277260\pi$
$977$	3.75464e10	1.28806	0.644032	+	0.764999i	$0.277260\pi$
$978$	0	0
$979$	−1.16391e10	−0.396443
$980$	−2.71601e8	−0.00921807
$981$	0	0
$982$	2.79640e10	0.942344
$983$	3.61128e10	1.21262	0.606309	−	0.795229i	$-0.292649\pi$
$983$	3.61128e10	1.21262	0.606309	+	0.795229i	$0.292649\pi$
$984$	0	0
$985$	−5.20593e9	−0.173569
$986$	−2.36074e10	−0.784296
$987$	0	0
$988$	1.70738e9	0.0563222
$989$	3.57270e9	0.117438
$990$	0	0
$991$	−4.43956e10	−1.44905	−0.724523	−	0.689250i	$-0.757940\pi$
$991$	−4.43956e10	−1.44905	−0.724523	+	0.689250i	$0.757940\pi$
$992$	1.13747e10	0.369955
$993$	0	0
$994$	8.46304e9	0.273322
$995$	−5.42616e9	−0.174627
$996$	0	0
$997$	7.69057e8	0.0245768	0.0122884	−	0.999924i	$-0.496088\pi$
$997$	7.69057e8	0.0245768	0.0122884	+	0.999924i	$0.496088\pi$
$998$	−2.71342e10	−0.864091
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	387.8.a.a.1.3		10
3.2	odd	2		129.8.a.a.1.8	✓	10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
129.8.a.a.1.8	✓	10	3.2	odd	2
387.8.a.a.1.3		10	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q-10.6558 q^{2} -14.4536 q^{4} +201.175 q^{5} +957.575 q^{7} +1517.96 q^{8} +O(q^{10})\)	\(q-10.6558 q^{2} -14.4536 q^{4} +201.175 q^{5} +957.575 q^{7} +1517.96 q^{8} -2143.69 q^{10} +2235.25 q^{11} +3574.02 q^{13} -10203.7 q^{14} -14325.0 q^{16} +17617.3 q^{17} -33052.0 q^{19} -2907.70 q^{20} -23818.4 q^{22} -44935.7 q^{23} -37653.4 q^{25} -38084.1 q^{26} -13840.4 q^{28} +125754. q^{29} -273077. q^{31} -41653.8 q^{32} -187727. q^{34} +192641. q^{35} -543163. q^{37} +352196. q^{38} +305376. q^{40} -128475. q^{41} -79507.0 q^{43} -32307.4 q^{44} +478826. q^{46} -69472.9 q^{47} +93407.3 q^{49} +401228. q^{50} -51657.3 q^{52} -1.44419e6 q^{53} +449678. q^{55} +1.45356e6 q^{56} -1.34002e6 q^{58} +539339. q^{59} +1.75799e6 q^{61} +2.90986e6 q^{62} +2.27746e6 q^{64} +719004. q^{65} -339734. q^{67} -254633. q^{68} -2.05274e6 q^{70} -829405. q^{71} -2.00855e6 q^{73} +5.78784e6 q^{74} +477719. q^{76} +2.14042e6 q^{77} -5.13808e6 q^{79} -2.88185e6 q^{80} +1.36900e6 q^{82} +2.37984e6 q^{83} +3.54416e6 q^{85} +847212. q^{86} +3.39302e6 q^{88} -5.20708e6 q^{89} +3.42239e6 q^{91} +649481. q^{92} +740291. q^{94} -6.64924e6 q^{95} +1.33459e6 q^{97} -995331. q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + q^{2} + 371 q^{4} + 122 q^{5} - 2052 q^{7} + 927 q^{8}+O(q^{10}) \) 10 * q + q^2 + 371 * q^4 + 122 * q^5 - 2052 * q^7 + 927 * q^8	\( 10 q + q^{2} + 371 q^{4} + 122 q^{5} - 2052 q^{7} + 927 q^{8} - 10032 q^{10} + 8888 q^{11} - 16432 q^{13} + 28408 q^{14} - 26669 q^{16} + 48122 q^{17} - 56146 q^{19} + 88940 q^{20} - 100626 q^{22} + 236336 q^{23} - 135016 q^{25} + 166748 q^{26} - 259060 q^{28} + 248818 q^{29} - 430970 q^{31} - 69493 q^{32} + 445522 q^{34} - 298982 q^{35} - 261254 q^{37} - 257662 q^{38} - 671432 q^{40} + 126814 q^{41} - 795070 q^{43} + 620022 q^{44} - 809038 q^{46} - 627080 q^{47} - 1256116 q^{49} + 83117 q^{50} - 3674204 q^{52} + 1612384 q^{53} - 4732974 q^{55} + 4301484 q^{56} - 7268516 q^{58} + 3442492 q^{59} - 5217214 q^{61} + 2500324 q^{62} - 4657369 q^{64} + 1224166 q^{65} - 6810926 q^{67} + 3563486 q^{68} - 2745858 q^{70} + 13935120 q^{71} - 13743720 q^{73} + 1752692 q^{74} - 15817594 q^{76} + 7685750 q^{77} - 9007608 q^{79} + 13641024 q^{80} - 6329026 q^{82} + 21779128 q^{83} - 13177392 q^{85} - 79507 q^{86} - 13214750 q^{88} + 1895364 q^{89} - 16439838 q^{91} - 9614510 q^{92} + 3404276 q^{94} + 16861514 q^{95} - 20434472 q^{97} - 35731457 q^{98}+O(q^{100}) \) 10 * q + q^2 + 371 * q^4 + 122 * q^5 - 2052 * q^7 + 927 * q^8 - 10032 * q^10 + 8888 * q^11 - 16432 * q^13 + 28408 * q^14 - 26669 * q^16 + 48122 * q^17 - 56146 * q^19 + 88940 * q^20 - 100626 * q^22 + 236336 * q^23 - 135016 * q^25 + 166748 * q^26 - 259060 * q^28 + 248818 * q^29 - 430970 * q^31 - 69493 * q^32 + 445522 * q^34 - 298982 * q^35 - 261254 * q^37 - 257662 * q^38 - 671432 * q^40 + 126814 * q^41 - 795070 * q^43 + 620022 * q^44 - 809038 * q^46 - 627080 * q^47 - 1256116 * q^49 + 83117 * q^50 - 3674204 * q^52 + 1612384 * q^53 - 4732974 * q^55 + 4301484 * q^56 - 7268516 * q^58 + 3442492 * q^59 - 5217214 * q^61 + 2500324 * q^62 - 4657369 * q^64 + 1224166 * q^65 - 6810926 * q^67 + 3563486 * q^68 - 2745858 * q^70 + 13935120 * q^71 - 13743720 * q^73 + 1752692 * q^74 - 15817594 * q^76 + 7685750 * q^77 - 9007608 * q^79 + 13641024 * q^80 - 6329026 * q^82 + 21779128 * q^83 - 13177392 * q^85 - 79507 * q^86 - 13214750 * q^88 + 1895364 * q^89 - 16439838 * q^91 - 9614510 * q^92 + 3404276 * q^94 + 16861514 * q^95 - 20434472 * q^97 - 35731457 * q^98

Introduction

L-functions

Modular forms

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Database

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