LMFDB - Embedded newform 9.24.a.b.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [9,24,Mod(1,9)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(9, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 24, names="a")

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

chi := DirichletCharacter("9.1");

S:= CuspForms(chi, 24);

N := Newforms(S);

Level:	$ N $	$=$	$ 9 = 3^{2} $
Weight:	$ k $	$=$	$ 24 $
Character orbit:	$[\chi]$	$=$	9.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:	$30.1683633611$
Analytic rank:	$1$
Dimension:	$2$
Coefficient field:	$\Q(\sqrt{144169}) $
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x - 36042 $ x^2 - x - 36042
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 2^{3}\cdot 3 $
Twist minimal:	no (minimal twist has level 1)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$190.348$ of defining polynomial
Character	$\chi$	$=$	9.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-5096.35 q^{2} +1.75842e7 q^{4} +3.19930e7 q^{5} -5.17135e9 q^{7} -4.68639e10 q^{8} +O(q^{10})$	\(q-5096.35 q^{2} +1.75842e7 q^{4} +3.19930e7 q^{5} -5.17135e9 q^{7} -4.68639e10 q^{8} -1.63048e11 q^{10} -6.04602e11 q^{11} +7.96710e12 q^{13} +2.63550e13 q^{14} +9.13280e13 q^{16} -1.98385e13 q^{17} +6.27346e14 q^{19} +5.62571e14 q^{20} +3.08127e15 q^{22} +4.55685e15 q^{23} -1.08974e16 q^{25} -4.06032e16 q^{26} -9.09340e16 q^{28} -4.14107e16 q^{29} +1.35683e15 q^{31} -7.23169e16 q^{32} +1.01104e17 q^{34} -1.65447e17 q^{35} +3.41258e17 q^{37} -3.19718e18 q^{38} -1.49932e18 q^{40} +3.69518e18 q^{41} -1.96955e18 q^{43} -1.06314e19 q^{44} -2.32233e19 q^{46} -2.44381e19 q^{47} -6.25860e17 q^{49} +5.55369e19 q^{50} +1.40095e20 q^{52} +6.39437e19 q^{53} -1.93431e19 q^{55} +2.42350e20 q^{56} +2.11044e20 q^{58} -2.81892e20 q^{59} -4.67790e20 q^{61} -6.91488e18 q^{62} -3.97563e20 q^{64} +2.54892e20 q^{65} +2.77406e20 q^{67} -3.48844e20 q^{68} +8.43177e20 q^{70} -2.29069e21 q^{71} -4.56908e21 q^{73} -1.73917e21 q^{74} +1.10314e22 q^{76} +3.12661e21 q^{77} -3.99005e21 q^{79} +2.92186e21 q^{80} -1.88319e22 q^{82} -1.45920e22 q^{83} -6.34694e20 q^{85} +1.00375e22 q^{86} +2.83340e22 q^{88} -1.80991e21 q^{89} -4.12007e22 q^{91} +8.01285e22 q^{92} +1.24545e23 q^{94} +2.00707e22 q^{95} +8.25561e22 q^{97} +3.18960e21 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 1080 q^{2} + 25326656 q^{4} - 73069020 q^{5} - 1359184400 q^{7} - 49459023360 q^{8}+O(q^{10}) $ 2 * q - 1080 * q^2 + 25326656 * q^4 - 73069020 * q^5 - 1359184400 * q^7 - 49459023360 * q^8	$ 2 q - 1080 q^{2} + 25326656 q^{4} - 73069020 q^{5} - 1359184400 q^{7} - 49459023360 q^{8} - 585013636080 q^{10} - 856801968264 q^{11} + 4376109322060 q^{13} + 41666034529728 q^{14} + 15956586401792 q^{16} - 254028147597540 q^{17} + 4260600979960 q^{19} - 250868387468160 q^{20} + 20\!\cdots\!60 q^{22}+ \cdots - 48\!\cdots\!40 q^{98}+O(q^{100}) $ 2 * q - 1080 * q^2 + 25326656 * q^4 - 73069020 * q^5 - 1359184400 * q^7 - 49459023360 * q^8 - 585013636080 * q^10 - 856801968264 * q^11 + 4376109322060 * q^13 + 41666034529728 * q^14 + 15956586401792 * q^16 - 254028147597540 * q^17 + 4260600979960 * q^19 - 250868387468160 * q^20 + 2068343882177760 * q^22 + 8144713079008560 * q^23 - 11780274628800850 * q^25 - 55025854658735184 * q^26 - 61418438819709440 * q^28 - 20818433601623340 * q^29 + 137714017177000384 * q^31 - 353265663781601280 * q^32 - 839483655961325328 * q^34 - 565961271250425120 * q^35 - 897721264408967780 * q^37 - 5699708971590961440 * q^38 - 1226668524414336000 * q^40 + 2294435477168314956 * q^41 - 1750760768619855800 * q^43 - 12584088840033038592 * q^44 - 8813206018050221376 * q^46 - 15759744217656780960 * q^47 - 13461981704376200814 * q^49 + 51990825483785316600 * q^50 + 112291883783912022400 * q^52 + 140287253401646796420 * q^53 + 7153550955060182640 * q^55 + 232456712054288117760 * q^56 + 293749486923568689360 * q^58 - 280872989971340771880 * q^59 - 180452892516502223636 * q^61 + 540743475843874103040 * q^62 - 893690254469352914944 * q^64 + 632168834809440380760 * q^65 + 1754233163431557625240 * q^67 - 2162050190142944330880 * q^68 - 765428657799921252480 * q^70 - 3055033510194143328624 * q^71 - 8063408253877606149260 * q^73 - 6715344283148807757072 * q^74 + 6207154294513080590080 * q^76 + 2165184764357449665600 * q^77 + 6244916814559639980640 * q^79 + 10840537585501794017280 * q^80 - 24457792891615712450640 * q^82 - 6875994082418498976120 * q^83 + 23969743087870314902520 * q^85 + 10916288812918999243296 * q^86 + 28988514668199273707520 * q^88 - 6395093086173070004820 * q^89 - 54890178162704560146016 * q^91 + 107907439017191756981760 * q^92 + 159400518006534931827072 * q^94 + 85533361066700858502000 * q^95 - 31147288846254030500540 * q^97 - 48364767616374671003640 * 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 $

$2$	−5096.35	−1.75960	−0.879801	−	0.475342i	$-0.842324\pi$
$2$	−5096.35	−1.75960	−0.879801	+	0.475342i	$0.842324\pi$
$3$	0	0
$3$	0	0
$4$	1.75842e7	2.09620
$5$	3.19930e7	0.293022	0.146511	−	0.989209i	$-0.453196\pi$
$5$	3.19930e7	0.293022	0.146511	+	0.989209i	$0.453196\pi$
$6$	0	0
$7$	−5.17135e9	−0.988500	−0.494250	−	0.869320i	$-0.664557\pi$
$7$	−5.17135e9	−0.988500	−0.494250	+	0.869320i	$0.664557\pi$
$8$	−4.68639e10	−1.92887
$9$	0	0
$10$	−1.63048e11	−0.515602
$11$	−6.04602e11	−0.638931	−0.319466	−	0.947598i	$-0.603503\pi$
$11$	−6.04602e11	−0.638931	−0.319466	+	0.947598i	$0.603503\pi$
$12$	0	0
$13$	7.96710e12	1.23297	0.616484	−	0.787367i	$-0.288556\pi$
$13$	7.96710e12	1.23297	0.616484	+	0.787367i	$0.288556\pi$
$14$	2.63550e13	1.73937
$15$	0	0
$16$	9.13280e13	1.29785
$17$	−1.98385e13	−0.140393	−0.0701967	−	0.997533i	$-0.522363\pi$
$17$	−1.98385e13	−0.140393	−0.0701967	+	0.997533i	$0.522363\pi$
$18$	0	0
$19$	6.27346e14	1.23550	0.617748	−	0.786377i	$-0.288045\pi$
$19$	6.27346e14	1.23550	0.617748	+	0.786377i	$0.288045\pi$
$20$	5.62571e14	0.614232
$21$	0	0
$22$	3.08127e15	1.12426
$23$	4.55685e15	0.997229	0.498614	−	0.866824i	$-0.333842\pi$
$23$	4.55685e15	0.997229	0.498614	+	0.866824i	$0.333842\pi$
$24$	0	0
$25$	−1.08974e16	−0.914138
$26$	−4.06032e16	−2.16953
$27$	0	0
$28$	−9.09340e16	−2.07209
$29$	−4.14107e16	−0.630283	−0.315142	−	0.949045i	$-0.602052\pi$
$29$	−4.14107e16	−0.630283	−0.315142	+	0.949045i	$0.602052\pi$
$30$	0	0
$31$	1.35683e15	0.00959104	0.00479552	−	0.999989i	$-0.498474\pi$
$31$	1.35683e15	0.00959104	0.00479552	+	0.999989i	$0.498474\pi$
$32$	−7.23169e16	−0.354826
$33$	0	0
$34$	1.01104e17	0.247037
$35$	−1.65447e17	−0.289652
$36$	0	0
$37$	3.41258e17	0.315328	0.157664	−	0.987493i	$-0.449604\pi$
$37$	3.41258e17	0.315328	0.157664	+	0.987493i	$0.449604\pi$
$38$	−3.19718e18	−2.17398
$39$	0	0
$40$	−1.49932e18	−0.565202
$41$	3.69518e18	1.04863	0.524313	−	0.851525i	$-0.324322\pi$
$41$	3.69518e18	1.04863	0.524313	+	0.851525i	$0.324322\pi$
$42$	0	0
$43$	−1.96955e18	−0.323207	−0.161603	−	0.986856i	$-0.551667\pi$
$43$	−1.96955e18	−0.323207	−0.161603	+	0.986856i	$0.551667\pi$
$44$	−1.06314e19	−1.33933
$45$	0	0
$46$	−2.32233e19	−1.75473
$47$	−2.44381e19	−1.44192	−0.720962	−	0.692975i	$-0.756300\pi$
$47$	−2.44381e19	−1.44192	−0.720962	+	0.692975i	$0.756300\pi$
$48$	0	0
$49$	−6.25860e17	−0.0228677
$50$	5.55369e19	1.60852
$51$	0	0
$52$	1.40095e20	2.58455
$53$	6.39437e19	0.947600	0.473800	−	0.880632i	$-0.342882\pi$
$53$	6.39437e19	0.947600	0.473800	+	0.880632i	$0.342882\pi$
$54$	0	0
$55$	−1.93431e19	−0.187221
$56$	2.42350e20	1.90669
$57$	0	0
$58$	2.11044e20	1.10905
$59$	−2.81892e20	−1.21698	−0.608491	−	0.793561i	$-0.708225\pi$
$59$	−2.81892e20	−1.21698	−0.608491	+	0.793561i	$0.708225\pi$
$60$	0	0
$61$	−4.67790e20	−1.37644	−0.688221	−	0.725501i	$-0.741608\pi$
$61$	−4.67790e20	−1.37644	−0.688221	+	0.725501i	$0.741608\pi$
$62$	−6.91488e18	−0.0168764
$63$	0	0
$64$	−3.97563e20	−0.673498
$65$	2.54892e20	0.361287
$66$	0	0
$67$	2.77406e20	0.277495	0.138747	−	0.990328i	$-0.455692\pi$
$67$	2.77406e20	0.277495	0.138747	+	0.990328i	$0.455692\pi$
$68$	−3.48844e20	−0.294293
$69$	0	0
$70$	8.43177e20	0.509672
$71$	−2.29069e21	−1.17624	−0.588119	−	0.808775i	$-0.700131\pi$
$71$	−2.29069e21	−1.17624	−0.588119	+	0.808775i	$0.700131\pi$
$72$	0	0
$73$	−4.56908e21	−1.70457	−0.852286	−	0.523075i	$-0.824785\pi$
$73$	−4.56908e21	−1.70457	−0.852286	+	0.523075i	$0.824785\pi$
$74$	−1.73917e21	−0.554852
$75$	0	0
$76$	1.10314e22	2.58984
$77$	3.12661e21	0.631583
$78$	0	0
$79$	−3.99005e21	−0.600160	−0.300080	−	0.953914i	$-0.597013\pi$
$79$	−3.99005e21	−0.600160	−0.300080	+	0.953914i	$0.597013\pi$
$80$	2.92186e21	0.380298
$81$	0	0
$82$	−1.88319e22	−1.84517
$83$	−1.45920e22	−1.24370	−0.621850	−	0.783136i	$-0.713619\pi$
$83$	−1.45920e22	−1.24370	−0.621850	+	0.783136i	$0.713619\pi$
$84$	0	0
$85$	−6.34694e20	−0.0411384
$86$	1.00375e22	0.568715
$87$	0	0
$88$	2.83340e22	1.23242
$89$	−1.80991e21	−0.0691310	−0.0345655	−	0.999402i	$-0.511005\pi$
$89$	−1.80991e21	−0.0691310	−0.0345655	+	0.999402i	$0.511005\pi$
$90$	0	0
$91$	−4.12007e22	−1.21879
$92$	8.01285e22	2.09039
$93$	0	0
$94$	1.24545e23	2.53721
$95$	2.00707e22	0.362027
$96$	0	0
$97$	8.25561e22	1.17186	0.585928	−	0.810363i	$-0.300730\pi$
$97$	8.25561e22	1.17186	0.585928	+	0.810363i	$0.300730\pi$
$98$	3.18960e21	0.0402380
$99$	0	0
$100$	−1.91622e23	−1.91622
$101$	−4.84234e22	−0.431877	−0.215938	−	0.976407i	$-0.569281\pi$
$101$	−4.84234e22	−0.431877	−0.215938	+	0.976407i	$0.569281\pi$
$102$	0	0
$103$	−3.23687e22	−0.230408	−0.115204	−	0.993342i	$-0.536752\pi$
$103$	−3.23687e22	−0.230408	−0.115204	+	0.993342i	$0.536752\pi$
$104$	−3.73370e23	−2.37824
$105$	0	0
$106$	−3.25880e23	−1.66740
$107$	5.92757e22	0.272247	0.136124	−	0.990692i	$-0.456536\pi$
$107$	5.92757e22	0.272247	0.136124	+	0.990692i	$0.456536\pi$
$108$	0	0
$109$	2.86887e23	1.06490	0.532448	−	0.846463i	$-0.321272\pi$
$109$	2.86887e23	1.06490	0.532448	+	0.846463i	$0.321272\pi$
$110$	9.85790e22	0.329434
$111$	0	0
$112$	−4.72290e23	−1.28292
$113$	4.87844e22	0.119641	0.0598204	−	0.998209i	$-0.480947\pi$
$113$	4.87844e22	0.119641	0.0598204	+	0.998209i	$0.480947\pi$
$114$	0	0
$115$	1.45787e23	0.292210
$116$	−7.28174e23	−1.32120
$117$	0	0
$118$	1.43662e24	2.14140
$119$	1.02592e23	0.138779
$120$	0	0
$121$	−5.29886e23	−0.591767
$122$	2.38402e24	2.42199
$123$	0	0
$124$	2.38587e22	0.0201047
$125$	−7.30026e23	−0.560884
$126$	0	0
$127$	1.36871e24	0.876131	0.438065	−	0.898943i	$-0.355664\pi$
$127$	1.36871e24	0.876131	0.438065	+	0.898943i	$0.355664\pi$
$128$	2.63276e24	1.53991
$129$	0	0
$130$	−1.29902e24	−0.635721
$131$	−2.63272e24	−1.17974	−0.589869	−	0.807499i	$-0.700820\pi$
$131$	−2.63272e24	−1.17974	−0.589869	+	0.807499i	$0.700820\pi$
$132$	0	0
$133$	−3.24423e24	−1.22129
$134$	−1.41376e24	−0.488280
$135$	0	0
$136$	9.29711e23	0.270801
$137$	1.21837e24	0.326207	0.163103	−	0.986609i	$-0.447850\pi$
$137$	1.21837e24	0.326207	0.163103	+	0.986609i	$0.447850\pi$
$138$	0	0
$139$	−3.72223e24	−0.843593	−0.421797	−	0.906690i	$-0.638600\pi$
$139$	−3.72223e24	−0.843593	−0.421797	+	0.906690i	$0.638600\pi$
$140$	−2.90925e24	−0.607168
$141$	0	0
$142$	1.16741e25	2.06971
$143$	−4.81693e24	−0.787782
$144$	0	0
$145$	−1.32485e24	−0.184687
$146$	2.32856e25	2.99937
$147$	0	0
$148$	6.00074e24	0.660990
$149$	−1.53044e25	−1.56018	−0.780088	−	0.625670i	$-0.784826\pi$
$149$	−1.53044e25	−1.56018	−0.780088	+	0.625670i	$0.784826\pi$
$150$	0	0
$151$	−1.25232e25	−1.09516	−0.547582	−	0.836752i	$-0.684452\pi$
$151$	−1.25232e25	−1.09516	−0.547582	+	0.836752i	$0.684452\pi$
$152$	−2.93999e25	−2.38311
$153$	0	0
$154$	−1.59343e25	−1.11134
$155$	4.34090e22	0.00281038
$156$	0	0
$157$	1.92166e23	0.0107357	0.00536785	−	0.999986i	$-0.498291\pi$
$157$	1.92166e23	0.0107357	0.00536785	+	0.999986i	$0.498291\pi$
$158$	2.03347e25	1.05604
$159$	0	0
$160$	−2.31363e24	−0.103972
$161$	−2.35651e25	−0.985761
$162$	0	0
$163$	−2.27639e25	−0.826206	−0.413103	−	0.910684i	$-0.635555\pi$
$163$	−2.27639e25	−0.826206	−0.413103	+	0.910684i	$0.635555\pi$
$164$	6.49767e25	2.19813
$165$	0	0
$166$	7.43657e25	2.18842
$167$	1.17984e25	0.324029	0.162015	−	0.986788i	$-0.448201\pi$
$167$	1.17984e25	0.324029	0.162015	+	0.986788i	$0.448201\pi$
$168$	0	0
$169$	2.17208e25	0.520211
$170$	3.23462e24	0.0723871
$171$	0	0
$172$	−3.46330e25	−0.677506
$173$	4.75865e25	0.870871	0.435435	−	0.900220i	$-0.356594\pi$
$173$	4.75865e25	0.870871	0.435435	+	0.900220i	$0.356594\pi$
$174$	0	0
$175$	5.63542e25	0.903626
$176$	−5.52172e25	−0.829236
$177$	0	0
$178$	9.22395e24	0.121643
$179$	−9.84804e25	−1.21770	−0.608850	−	0.793286i	$-0.708369\pi$
$179$	−9.84804e25	−1.21770	−0.608850	+	0.793286i	$0.708369\pi$
$180$	0	0
$181$	4.76456e25	0.518465	0.259233	−	0.965815i	$-0.416530\pi$
$181$	4.76456e25	0.518465	0.259233	+	0.965815i	$0.416530\pi$
$182$	2.09973e26	2.14458
$183$	0	0
$184$	−2.13552e26	−1.92353
$185$	1.09179e25	0.0923980
$186$	0	0
$187$	1.19944e25	0.0897017
$188$	−4.29724e26	−3.02256
$189$	0	0
$190$	−1.02287e26	−0.637024
$191$	8.54117e25	0.500765	0.250382	−	0.968147i	$-0.419444\pi$
$191$	8.54117e25	0.500765	0.250382	+	0.968147i	$0.419444\pi$
$192$	0	0
$193$	−2.66797e26	−1.38762	−0.693812	−	0.720156i	$-0.744070\pi$
$193$	−2.66797e26	−1.38762	−0.693812	+	0.720156i	$0.744070\pi$
$194$	−4.20735e26	−2.06200
$195$	0	0
$196$	−1.10052e25	−0.0479352
$197$	1.00070e26	0.411095	0.205547	−	0.978647i	$-0.434103\pi$
$197$	1.00070e26	0.411095	0.205547	+	0.978647i	$0.434103\pi$
$198$	0	0
$199$	4.46897e26	1.63454	0.817272	−	0.576251i	$-0.195485\pi$
$199$	4.46897e26	1.63454	0.817272	+	0.576251i	$0.195485\pi$
$200$	5.10694e26	1.76326
$201$	0	0
$202$	2.46783e26	0.759931
$203$	2.14149e26	0.623035
$204$	0	0
$205$	1.18220e26	0.307271
$206$	1.64962e26	0.405426
$207$	0	0
$208$	7.27620e26	1.60021
$209$	−3.79295e26	−0.789396
$210$	0	0
$211$	−7.96987e26	−1.48663	−0.743315	−	0.668941i	$-0.766748\pi$
$211$	−7.96987e26	−1.48663	−0.743315	+	0.668941i	$0.766748\pi$
$212$	1.12440e27	1.98636
$213$	0	0
$214$	−3.02090e26	−0.479047
$215$	−6.30120e25	−0.0947067
$216$	0	0
$217$	−7.01664e24	−0.00948074
$218$	−1.46208e27	−1.87379
$219$	0	0
$220$	−3.40132e26	−0.392452
$221$	−1.58056e26	−0.173101
$222$	0	0
$223$	−5.69004e26	−0.561836	−0.280918	−	0.959732i	$-0.590639\pi$
$223$	−5.69004e26	−0.561836	−0.280918	+	0.959732i	$0.590639\pi$
$224$	3.73976e26	0.350745
$225$	0	0
$226$	−2.48623e26	−0.210520
$227$	1.82165e27	1.46611	0.733056	−	0.680168i	$-0.238093\pi$
$227$	1.82165e27	1.46611	0.733056	+	0.680168i	$0.238093\pi$
$228$	0	0
$229$	1.11330e27	0.810032	0.405016	−	0.914310i	$-0.367266\pi$
$229$	1.11330e27	0.810032	0.405016	+	0.914310i	$0.367266\pi$
$230$	−7.42984e26	−0.514173
$231$	0	0
$232$	1.94067e27	1.21574
$233$	1.63214e27	0.973118	0.486559	−	0.873648i	$-0.338252\pi$
$233$	1.63214e27	0.973118	0.486559	+	0.873648i	$0.338252\pi$
$234$	0	0
$235$	−7.81849e26	−0.422515
$236$	−4.95683e27	−2.55104
$237$	0	0
$238$	−5.22845e26	−0.244196
$239$	−2.58550e27	−1.15072	−0.575358	−	0.817902i	$-0.695137\pi$
$239$	−2.58550e27	−1.15072	−0.575358	+	0.817902i	$0.695137\pi$
$240$	0	0
$241$	1.86784e27	0.755340	0.377670	−	0.925940i	$-0.376725\pi$
$241$	1.86784e27	0.755340	0.377670	+	0.925940i	$0.376725\pi$
$242$	2.70049e27	1.04127
$243$	0	0
$244$	−8.22571e27	−2.88530
$245$	−2.00232e25	−0.00670074
$246$	0	0
$247$	4.99813e27	1.52333
$248$	−6.35863e25	−0.0184999
$249$	0	0
$250$	3.72047e27	0.986933
$251$	4.11170e27	1.04177	0.520887	−	0.853626i	$-0.325601\pi$
$251$	4.11170e27	1.04177	0.520887	+	0.853626i	$0.325601\pi$
$252$	0	0
$253$	−2.75508e27	−0.637160
$254$	−6.97543e27	−1.54164
$255$	0	0
$256$	−1.00825e28	−2.03614
$257$	5.10426e27	0.985603	0.492802	−	0.870142i	$-0.335973\pi$
$257$	5.10426e27	0.985603	0.492802	+	0.870142i	$0.335973\pi$
$258$	0	0
$259$	−1.76476e27	−0.311702
$260$	4.48206e27	0.757329
$261$	0	0
$262$	1.34173e28	2.07587
$263$	−9.95433e27	−1.47408	−0.737040	−	0.675849i	$-0.763777\pi$
$263$	−9.95433e27	−1.47408	−0.737040	+	0.675849i	$0.763777\pi$
$264$	0	0
$265$	2.04575e27	0.277668
$266$	1.65337e28	2.14898
$267$	0	0
$268$	4.87795e27	0.581684
$269$	−6.42524e26	−0.0734071	−0.0367036	−	0.999326i	$-0.511686\pi$
$269$	−6.42524e26	−0.0734071	−0.0367036	+	0.999326i	$0.511686\pi$
$270$	0	0
$271$	1.19246e28	1.25111	0.625557	−	0.780178i	$-0.284872\pi$
$271$	1.19246e28	1.25111	0.625557	+	0.780178i	$0.284872\pi$
$272$	−1.81181e27	−0.182210
$273$	0	0
$274$	−6.20925e27	−0.573994
$275$	6.58858e27	0.584071
$276$	0	0
$277$	−5.29510e27	−0.431874	−0.215937	−	0.976407i	$-0.569281\pi$
$277$	−5.29510e27	−0.431874	−0.215937	+	0.976407i	$0.569281\pi$
$278$	1.89698e28	1.48439
$279$	0	0
$280$	7.75350e27	0.558702
$281$	−9.67433e27	−0.669111	−0.334556	−	0.942376i	$-0.608586\pi$
$281$	−9.67433e27	−0.669111	−0.334556	+	0.942376i	$0.608586\pi$
$282$	0	0
$283$	−2.62436e28	−1.67294	−0.836468	−	0.548016i	$-0.815383\pi$
$283$	−2.62436e28	−1.67294	−0.836468	+	0.548016i	$0.815383\pi$
$284$	−4.02799e28	−2.46563
$285$	0	0
$286$	2.45488e28	1.38618
$287$	−1.91091e28	−1.03657
$288$	0	0
$289$	−1.95740e28	−0.980290
$290$	6.75192e27	0.324975
$291$	0	0
$292$	−8.03435e28	−3.57312
$293$	−3.20151e28	−1.36892	−0.684458	−	0.729052i	$-0.739961\pi$
$293$	−3.20151e28	−1.36892	−0.684458	+	0.729052i	$0.739961\pi$
$294$	0	0
$295$	−9.01856e27	−0.356602
$296$	−1.59927e28	−0.608228
$297$	0	0
$298$	7.79965e28	2.74529
$299$	3.63049e28	1.22955
$300$	0	0
$301$	1.01853e28	0.319490
$302$	6.38225e28	1.92705
$303$	0	0
$304$	5.72943e28	1.60349
$305$	−1.49660e28	−0.403328
$306$	0	0
$307$	−1.15407e28	−0.288496	−0.144248	−	0.989542i	$-0.546076\pi$
$307$	−1.15407e28	−0.288496	−0.144248	+	0.989542i	$0.546076\pi$
$308$	5.49789e28	1.32392
$309$	0	0
$310$	−2.21228e26	−0.00494516
$311$	−3.62817e28	−0.781525	−0.390763	−	0.920491i	$-0.627789\pi$
$311$	−3.62817e28	−0.781525	−0.390763	+	0.920491i	$0.627789\pi$
$312$	0	0
$313$	2.56117e28	0.512481	0.256241	−	0.966613i	$-0.417516\pi$
$313$	2.56117e28	0.512481	0.256241	+	0.966613i	$0.417516\pi$
$314$	−9.79346e26	−0.0188906
$315$	0	0
$316$	−7.01618e28	−1.25805
$317$	2.91424e27	0.0503899	0.0251950	−	0.999683i	$-0.491979\pi$
$317$	2.91424e27	0.0503899	0.0251950	+	0.999683i	$0.491979\pi$
$318$	0	0
$319$	2.50370e28	0.402708
$320$	−1.27192e28	−0.197350
$321$	0	0
$322$	1.20096e29	1.73455
$323$	−1.24456e28	−0.173455
$324$	0	0
$325$	−8.68205e28	−1.12710
$326$	1.16013e29	1.45379
$327$	0	0
$328$	−1.73170e29	−2.02267
$329$	1.26378e29	1.42534
$330$	0	0
$331$	4.00537e28	0.421328	0.210664	−	0.977558i	$-0.432437\pi$
$331$	4.00537e28	0.421328	0.210664	+	0.977558i	$0.432437\pi$
$332$	−2.56588e29	−2.60704
$333$	0	0
$334$	−6.01289e28	−0.570163
$335$	8.87504e27	0.0813121
$336$	0	0
$337$	1.31131e29	1.12192	0.560959	−	0.827843i	$-0.310432\pi$
$337$	1.31131e29	1.12192	0.560959	+	0.827843i	$0.310432\pi$
$338$	−1.10697e29	−0.915364
$339$	0	0
$340$	−1.11606e28	−0.0862342
$341$	−8.20342e26	−0.00612801
$342$	0	0
$343$	1.44770e29	1.01110
$344$	9.23010e28	0.623425
$345$	0	0
$346$	−2.42518e29	−1.53239
$347$	−1.14051e29	−0.697126	−0.348563	−	0.937285i	$-0.613330\pi$
$347$	−1.14051e29	−0.697126	−0.348563	+	0.937285i	$0.613330\pi$
$348$	0	0
$349$	7.28518e28	0.416820	0.208410	−	0.978042i	$-0.433171\pi$
$349$	7.28518e28	0.416820	0.208410	+	0.978042i	$0.433171\pi$
$350$	−2.87201e29	−1.59002
$351$	0	0
$352$	4.37230e28	0.226709
$353$	3.68425e29	1.84902	0.924508	−	0.381164i	$-0.124477\pi$
$353$	3.68425e29	1.84902	0.924508	+	0.381164i	$0.124477\pi$
$354$	0	0
$355$	−7.32860e28	−0.344663
$356$	−3.18259e28	−0.144912
$357$	0	0
$358$	5.01891e29	2.14267
$359$	2.45802e29	1.01625	0.508123	−	0.861284i	$-0.330339\pi$
$359$	2.45802e29	1.01625	0.508123	+	0.861284i	$0.330339\pi$
$360$	0	0
$361$	1.35734e29	0.526448
$362$	−2.42819e29	−0.912292
$363$	0	0
$364$	−7.24481e29	−2.55482
$365$	−1.46179e29	−0.499477
$366$	0	0
$367$	−4.73025e29	−1.51783	−0.758917	−	0.651187i	$-0.774271\pi$
$367$	−4.73025e29	−1.51783	−0.758917	+	0.651187i	$0.774271\pi$
$368$	4.16168e29	1.29425
$369$	0	0
$370$	−5.56413e28	−0.162584
$371$	−3.30675e29	−0.936703
$372$	0	0
$373$	−2.90241e29	−0.772872	−0.386436	−	0.922316i	$-0.626294\pi$
$373$	−2.90241e29	−0.772872	−0.386436	+	0.922316i	$0.626294\pi$
$374$	−6.11278e28	−0.157839
$375$	0	0
$376$	1.14526e30	2.78129
$377$	−3.29924e29	−0.777120
$378$	0	0
$379$	2.72591e29	0.604172	0.302086	−	0.953281i	$-0.402317\pi$
$379$	2.72591e29	0.604172	0.302086	+	0.953281i	$0.402317\pi$
$380$	3.52927e29	0.758881
$381$	0	0
$382$	−4.35288e29	−0.881147
$383$	9.91721e29	1.94806	0.974032	−	0.226408i	$-0.0726984\pi$
$383$	9.91721e29	1.94806	0.974032	+	0.226408i	$0.0726984\pi$
$384$	0	0
$385$	1.00030e29	0.185068
$386$	1.35969e30	2.44166
$387$	0	0
$388$	1.45168e30	2.45644
$389$	−8.39840e29	−1.37967	−0.689836	−	0.723966i	$-0.742317\pi$
$389$	−8.39840e29	−1.37967	−0.689836	+	0.723966i	$0.742317\pi$
$390$	0	0
$391$	−9.04012e28	−0.140004
$392$	2.93303e28	0.0441089
$393$	0	0
$394$	−5.09992e29	−0.723363
$395$	−1.27654e29	−0.175860
$396$	0	0
$397$	9.94808e27	0.0129315	0.00646574	−	0.999979i	$-0.497942\pi$
$397$	9.94808e27	0.0129315	0.00646574	+	0.999979i	$0.497942\pi$
$398$	−2.27754e30	−2.87615
$399$	0	0
$400$	−9.95236e29	−1.18641
$401$	4.81480e29	0.557723	0.278861	−	0.960331i	$-0.410043\pi$
$401$	4.81480e29	0.557723	0.278861	+	0.960331i	$0.410043\pi$
$402$	0	0
$403$	1.08100e28	0.0118254
$404$	−8.51487e29	−0.905299
$405$	0	0
$406$	−1.09138e30	−1.09629
$407$	−2.06325e29	−0.201473
$408$	0	0
$409$	−8.22531e29	−0.759162	−0.379581	−	0.925159i	$-0.623932\pi$
$409$	−8.22531e29	−0.759162	−0.379581	+	0.925159i	$0.623932\pi$
$410$	−6.02490e29	−0.540674
$411$	0	0
$412$	−5.69178e29	−0.482981
$413$	1.45776e30	1.20299
$414$	0	0
$415$	−4.66841e29	−0.364431
$416$	−5.76156e29	−0.437489
$417$	0	0
$418$	1.93302e30	1.38902
$419$	−2.72055e30	−1.90194	−0.950969	−	0.309287i	$-0.899910\pi$
$419$	−2.72055e30	−1.90194	−0.950969	+	0.309287i	$0.899910\pi$
$420$	0	0
$421$	1.73534e30	1.14852	0.574261	−	0.818672i	$-0.305289\pi$
$421$	1.73534e30	1.14852	0.574261	+	0.818672i	$0.305289\pi$
$422$	4.06173e30	2.61588
$423$	0	0
$424$	−2.99665e30	−1.82780
$425$	2.16188e29	0.128339
$426$	0	0
$427$	2.41911e30	1.36061
$428$	1.04232e30	0.570684
$429$	0	0
$430$	3.21131e29	0.166646
$431$	−2.30954e30	−1.16691	−0.583455	−	0.812146i	$-0.698299\pi$
$431$	−2.30954e30	−1.16691	−0.583455	+	0.812146i	$0.698299\pi$
$432$	0	0
$433$	−4.49441e29	−0.215309	−0.107655	−	0.994188i	$-0.534334\pi$
$433$	−4.49441e29	−0.215309	−0.107655	+	0.994188i	$0.534334\pi$
$434$	3.57593e28	0.0166823
$435$	0	0
$436$	5.04468e30	2.23223
$437$	2.85872e30	1.23207
$438$	0	0
$439$	−1.98640e30	−0.812315	−0.406157	−	0.913803i	$-0.633132\pi$
$439$	−1.98640e30	−0.812315	−0.406157	+	0.913803i	$0.633132\pi$
$440$	9.06491e29	0.361125
$441$	0	0
$442$	8.05507e29	0.304588
$443$	2.09074e30	0.770294	0.385147	−	0.922855i	$-0.374151\pi$
$443$	2.09074e30	0.770294	0.385147	+	0.922855i	$0.374151\pi$
$444$	0	0
$445$	−5.79046e28	−0.0202569
$446$	2.89984e30	0.988607
$447$	0	0
$448$	2.05594e30	0.665753
$449$	−2.38796e30	−0.753694	−0.376847	−	0.926276i	$-0.622992\pi$
$449$	−2.38796e30	−0.753694	−0.376847	+	0.926276i	$0.622992\pi$
$450$	0	0
$451$	−2.23411e30	−0.670000
$452$	8.57834e29	0.250791
$453$	0	0
$454$	−9.28376e30	−2.57977
$455$	−1.31813e30	−0.357132
$456$	0	0
$457$	1.54921e30	0.399093	0.199547	−	0.979888i	$-0.436053\pi$
$457$	1.54921e30	0.399093	0.199547	+	0.979888i	$0.436053\pi$
$458$	−5.67374e30	−1.42533
$459$	0	0
$460$	2.56355e30	0.612530
$461$	−4.06665e30	−0.947711	−0.473855	−	0.880603i	$-0.657138\pi$
$461$	−4.06665e30	−0.947711	−0.473855	+	0.880603i	$0.657138\pi$
$462$	0	0
$463$	−6.37975e29	−0.141456	−0.0707282	−	0.997496i	$-0.522532\pi$
$463$	−6.37975e29	−0.141456	−0.0707282	+	0.997496i	$0.522532\pi$
$464$	−3.78196e30	−0.818013
$465$	0	0
$466$	−8.31798e30	−1.71230
$467$	−1.15365e30	−0.231701	−0.115851	−	0.993267i	$-0.536959\pi$
$467$	−1.15365e30	−0.231701	−0.115851	+	0.993267i	$0.536959\pi$
$468$	0	0
$469$	−1.43456e30	−0.274304
$470$	3.98458e30	0.743458
$471$	0	0
$472$	1.32105e31	2.34740
$473$	1.19080e30	0.206507
$474$	0	0
$475$	−6.83643e30	−1.12941
$476$	1.80400e30	0.290908
$477$	0	0
$478$	1.31766e31	2.02480
$479$	2.12936e30	0.319441	0.159721	−	0.987162i	$-0.448941\pi$
$479$	2.12936e30	0.319441	0.159721	+	0.987162i	$0.448941\pi$
$480$	0	0
$481$	2.71884e30	0.388790
$482$	−9.51914e30	−1.32910
$483$	0	0
$484$	−9.31762e30	−1.24046
$485$	2.64122e30	0.343380
$486$	0	0
$487$	4.84200e30	0.600401	0.300201	−	0.953876i	$-0.402946\pi$
$487$	4.84200e30	0.600401	0.300201	+	0.953876i	$0.402946\pi$
$488$	2.19225e31	2.65498
$489$	0	0
$490$	1.02045e29	0.0117906
$491$	3.44338e29	0.0388640	0.0194320	−	0.999811i	$-0.493814\pi$
$491$	3.44338e29	0.0388640	0.0194320	+	0.999811i	$0.493814\pi$
$492$	0	0
$493$	8.21528e29	0.0884877
$494$	−2.54722e31	−2.68045
$495$	0	0
$496$	1.23917e29	0.0124477
$497$	1.18460e31	1.16271
$498$	0	0
$499$	−1.27549e31	−1.19542	−0.597711	−	0.801711i	$-0.703923\pi$
$499$	−1.27549e31	−1.19542	−0.597711	+	0.801711i	$0.703923\pi$
$500$	−1.28369e31	−1.17573
$501$	0	0
$502$	−2.09546e31	−1.83311
$503$	−1.67840e31	−1.43504	−0.717520	−	0.696538i	$-0.754723\pi$
$503$	−1.67840e31	−1.43504	−0.717520	+	0.696538i	$0.754723\pi$
$504$	0	0
$505$	−1.54921e30	−0.126549
$506$	1.40409e31	1.12115
$507$	0	0
$508$	2.40677e31	1.83654
$509$	2.11935e31	1.58106	0.790529	−	0.612425i	$-0.209806\pi$
$509$	2.11935e31	1.58106	0.790529	+	0.612425i	$0.209806\pi$
$510$	0	0
$511$	2.36283e31	1.68497
$512$	2.92986e31	2.04288
$513$	0	0
$514$	−2.60131e31	−1.73427
$515$	−1.03557e30	−0.0675146
$516$	0	0
$517$	1.47753e31	0.921290
$518$	8.99386e30	0.548471
$519$	0	0
$520$	−1.19452e31	−0.696876
$521$	1.22820e30	0.0700869	0.0350434	−	0.999386i	$-0.488843\pi$
$521$	1.22820e30	0.0700869	0.0350434	+	0.999386i	$0.488843\pi$
$522$	0	0
$523$	7.24558e30	0.395643	0.197821	−	0.980238i	$-0.436613\pi$
$523$	7.24558e30	0.395643	0.197821	+	0.980238i	$0.436613\pi$
$524$	−4.62943e31	−2.47296
$525$	0	0
$526$	5.07308e31	2.59379
$527$	−2.69175e28	−0.00134652
$528$	0	0
$529$	−1.15570e29	−0.00553483
$530$	−1.04259e31	−0.488585
$531$	0	0
$532$	−5.70471e31	−2.56006
$533$	2.94399e31	1.29292
$534$	0	0
$535$	1.89641e30	0.0797744
$536$	−1.30003e31	−0.535252
$537$	0	0
$538$	3.27453e30	0.129167
$539$	3.78397e29	0.0146109
$540$	0	0
$541$	9.30820e30	0.344427	0.172214	−	0.985060i	$-0.444908\pi$
$541$	9.30820e30	0.344427	0.172214	+	0.985060i	$0.444908\pi$
$542$	−6.07719e31	−2.20146
$543$	0	0
$544$	1.43466e30	0.0498152
$545$	9.17839e30	0.312038
$546$	0	0
$547$	−2.67466e31	−0.871796	−0.435898	−	0.899996i	$-0.643569\pi$
$547$	−2.67466e31	−0.871796	−0.435898	+	0.899996i	$0.643569\pi$
$548$	2.14241e31	0.683794
$549$	0	0
$550$	−3.35777e31	−1.02773
$551$	−2.59789e31	−0.778712
$552$	0	0
$553$	2.06340e31	0.593258
$554$	2.69857e31	0.759926
$555$	0	0
$556$	−6.54524e31	−1.76834
$557$	−2.40510e31	−0.636501	−0.318250	−	0.948007i	$-0.603095\pi$
$557$	−2.40510e31	−0.636501	−0.318250	+	0.948007i	$0.603095\pi$
$558$	0	0
$559$	−1.56916e31	−0.398504
$560$	−1.51100e31	−0.375925
$561$	0	0
$562$	4.93038e31	1.17737
$563$	−2.15437e31	−0.504049	−0.252025	−	0.967721i	$-0.581096\pi$
$563$	−2.15437e31	−0.504049	−0.252025	+	0.967721i	$0.581096\pi$
$564$	0	0
$565$	1.56076e30	0.0350574
$566$	1.33747e32	2.94370
$567$	0	0
$568$	1.07351e32	2.26881
$569$	−1.70978e31	−0.354120	−0.177060	−	0.984200i	$-0.556659\pi$
$569$	−1.70978e31	−0.354120	−0.177060	+	0.984200i	$0.556659\pi$
$570$	0	0
$571$	−8.69138e31	−1.72891	−0.864457	−	0.502707i	$-0.832337\pi$
$571$	−8.69138e31	−1.72891	−0.864457	+	0.502707i	$0.832337\pi$
$572$	−8.47018e31	−1.65135
$573$	0	0
$574$	9.73865e31	1.82395
$575$	−4.96577e31	−0.911605
$576$	0	0
$577$	1.59167e31	0.280757	0.140378	−	0.990098i	$-0.455168\pi$
$577$	1.59167e31	0.280757	0.140378	+	0.990098i	$0.455168\pi$
$578$	9.97560e31	1.72492
$579$	0	0
$580$	−2.32965e31	−0.387140
$581$	7.54602e31	1.22940
$582$	0	0
$583$	−3.86605e31	−0.605451
$584$	2.14125e32	3.28790
$585$	0	0
$586$	1.63160e32	2.40875
$587$	−5.71080e31	−0.826721	−0.413361	−	0.910567i	$-0.635645\pi$
$587$	−5.71080e31	−0.826721	−0.413361	+	0.910567i	$0.635645\pi$
$588$	0	0
$589$	8.51202e29	0.0118497
$590$	4.59618e31	0.627478
$591$	0	0
$592$	3.11664e31	0.409248
$593$	−2.68653e31	−0.345989	−0.172995	−	0.984923i	$-0.555344\pi$
$593$	−2.68653e31	−0.345989	−0.172995	+	0.984923i	$0.555344\pi$
$594$	0	0
$595$	3.28223e30	0.0406653
$596$	−2.69115e32	−3.27044
$597$	0	0
$598$	−1.85023e32	−2.16352
$599$	−1.35452e30	−0.0155373	−0.00776867	−	0.999970i	$-0.502473\pi$
$599$	−1.35452e30	−0.0155373	−0.00776867	+	0.999970i	$0.502473\pi$
$600$	0	0
$601$	−7.37959e31	−0.814659	−0.407329	−	0.913281i	$-0.633540\pi$
$601$	−7.37959e31	−0.814659	−0.407329	+	0.913281i	$0.633540\pi$
$602$	−5.19077e31	−0.562175
$603$	0	0
$604$	−2.20210e32	−2.29568
$605$	−1.69527e31	−0.173401
$606$	0	0
$607$	−3.23323e31	−0.318395	−0.159198	−	0.987247i	$-0.550891\pi$
$607$	−3.23323e31	−0.318395	−0.159198	+	0.987247i	$0.550891\pi$
$608$	−4.53677e31	−0.438385
$609$	0	0
$610$	7.62721e31	0.709696
$611$	−1.94701e32	−1.77785
$612$	0	0
$613$	4.35574e31	0.383059	0.191530	−	0.981487i	$-0.438655\pi$
$613$	4.35574e31	0.383059	0.191530	+	0.981487i	$0.438655\pi$
$614$	5.88154e31	0.507639
$615$	0	0
$616$	−1.46525e32	−1.21824
$617$	2.29127e32	1.86981	0.934904	−	0.354902i	$-0.115486\pi$
$617$	2.29127e32	1.86981	0.934904	+	0.354902i	$0.115486\pi$
$618$	0	0
$619$	2.32366e32	1.82697	0.913484	−	0.406875i	$-0.133382\pi$
$619$	2.32366e32	1.82697	0.913484	+	0.406875i	$0.133382\pi$
$620$	7.63313e29	0.00589112
$621$	0	0
$622$	1.84904e32	1.37517
$623$	9.35970e30	0.0683360
$624$	0	0
$625$	1.06551e32	0.749787
$626$	−1.30526e32	−0.901763
$627$	0	0
$628$	3.37908e30	0.0225042
$629$	−6.77005e30	−0.0442700
$630$	0	0
$631$	−2.22944e32	−1.40559	−0.702793	−	0.711394i	$-0.748064\pi$
$631$	−2.22944e32	−1.40559	−0.702793	+	0.711394i	$0.748064\pi$
$632$	1.86989e32	1.15763
$633$	0	0
$634$	−1.48520e31	−0.0886662
$635$	4.37892e31	0.256726
$636$	0	0
$637$	−4.98629e30	−0.0281951
$638$	−1.27597e32	−0.708605
$639$	0	0
$640$	8.42299e31	0.451228
$641$	2.75021e32	1.44710	0.723550	−	0.690272i	$-0.242509\pi$
$641$	2.75021e32	1.44710	0.723550	+	0.690272i	$0.242509\pi$
$642$	0	0
$643$	1.47614e32	0.749377	0.374689	−	0.927151i	$-0.377750\pi$
$643$	1.47614e32	0.749377	0.374689	+	0.927151i	$0.377750\pi$
$644$	−4.14373e32	−2.06635
$645$	0	0
$646$	6.34273e31	0.305212
$647$	−1.82358e32	−0.862036	−0.431018	−	0.902343i	$-0.641846\pi$
$647$	−1.82358e32	−0.862036	−0.431018	+	0.902343i	$0.641846\pi$
$648$	0	0
$649$	1.70432e32	0.777567
$650$	4.42468e32	1.98325
$651$	0	0
$652$	−4.00284e32	−1.73189
$653$	4.35899e31	0.185304	0.0926519	−	0.995699i	$-0.470466\pi$
$653$	4.35899e31	0.185304	0.0926519	+	0.995699i	$0.470466\pi$
$654$	0	0
$655$	−8.42287e31	−0.345689
$656$	3.37473e32	1.36096
$657$	0	0
$658$	−6.44067e32	−2.50803
$659$	3.58880e31	0.137331	0.0686653	−	0.997640i	$-0.478126\pi$
$659$	3.58880e31	0.137331	0.0686653	+	0.997640i	$0.478126\pi$
$660$	0	0
$661$	2.78803e32	1.03034	0.515171	−	0.857088i	$-0.327729\pi$
$661$	2.78803e32	1.03034	0.515171	+	0.857088i	$0.327729\pi$
$662$	−2.04128e32	−0.741370
$663$	0	0
$664$	6.83836e32	2.39894
$665$	−1.03793e32	−0.357864
$666$	0	0
$667$	−1.88703e32	−0.628537
$668$	2.07466e32	0.679230
$669$	0	0
$670$	−4.52303e31	−0.143077
$671$	2.82827e32	0.879452
$672$	0	0
$673$	1.90131e31	0.0571320	0.0285660	−	0.999592i	$-0.490906\pi$
$673$	1.90131e31	0.0571320	0.0285660	+	0.999592i	$0.490906\pi$
$674$	−6.68289e32	−1.97413
$675$	0	0
$676$	3.81943e32	1.09047
$677$	3.87840e32	1.08864	0.544318	−	0.838879i	$-0.316788\pi$
$677$	3.87840e32	1.08864	0.544318	+	0.838879i	$0.316788\pi$
$678$	0	0
$679$	−4.26927e32	−1.15838
$680$	2.97442e31	0.0793507
$681$	0	0
$682$	4.18075e30	0.0107829
$683$	−6.51681e32	−1.65271	−0.826356	−	0.563148i	$-0.809590\pi$
$683$	−6.51681e32	−1.65271	−0.826356	+	0.563148i	$0.809590\pi$
$684$	0	0
$685$	3.89794e31	0.0955857
$686$	−7.37799e32	−1.77914
$687$	0	0
$688$	−1.79876e32	−0.419474
$689$	5.09446e32	1.16836
$690$	0	0
$691$	−6.18205e31	−0.137131	−0.0685654	−	0.997647i	$-0.521842\pi$
$691$	−6.18205e31	−0.137131	−0.0685654	+	0.997647i	$0.521842\pi$
$692$	8.36770e32	1.82552
$693$	0	0
$694$	5.81246e32	1.22666
$695$	−1.19085e32	−0.247191
$696$	0	0
$697$	−7.33069e31	−0.147220
$698$	−3.71278e32	−0.733436
$699$	0	0
$700$	9.90942e32	1.89418
$701$	−5.26483e32	−0.989982	−0.494991	−	0.868898i	$-0.664829\pi$
$701$	−5.26483e32	−0.989982	−0.494991	+	0.868898i	$0.664829\pi$
$702$	0	0
$703$	2.14087e32	0.389586
$704$	2.40367e32	0.430319
$705$	0	0
$706$	−1.87763e33	−3.25353
$707$	2.50415e32	0.426910
$708$	0	0
$709$	−7.09958e32	−1.17166	−0.585829	−	0.810435i	$-0.699231\pi$
$709$	−7.09958e32	−1.17166	−0.585829	+	0.810435i	$0.699231\pi$
$710$	3.73491e32	0.606470
$711$	0	0
$712$	8.48196e31	0.133345
$713$	6.18287e30	0.00956446
$714$	0	0
$715$	−1.54108e32	−0.230837
$716$	−1.73170e33	−2.55254
$717$	0	0
$718$	−1.25269e33	−1.78819
$719$	−4.58875e32	−0.644633	−0.322316	−	0.946632i	$-0.604461\pi$
$719$	−4.58875e32	−0.644633	−0.322316	+	0.946632i	$0.604461\pi$
$720$	0	0
$721$	1.67390e32	0.227758
$722$	−6.91748e32	−0.926339
$723$	0	0
$724$	8.37810e32	1.08681
$725$	4.51268e32	0.576166
$726$	0	0
$727$	1.25284e33	1.54970	0.774851	−	0.632144i	$-0.217825\pi$
$727$	1.25284e33	1.54970	0.774851	+	0.632144i	$0.217825\pi$
$728$	1.93083e33	2.35089
$729$	0	0
$730$	7.44977e32	0.878881
$731$	3.90730e31	0.0453761
$732$	0	0
$733$	−1.67809e30	−0.00188852	−0.000944258	−	1.00000i	$-0.500301\pi$
$733$	−1.67809e30	−0.00188852	−0.000944258		1.00000i	$0.500301\pi$
$734$	2.41070e33	2.67078
$735$	0	0
$736$	−3.29537e32	−0.353842
$737$	−1.67720e32	−0.177300
$738$	0	0
$739$	2.96573e32	0.303893	0.151946	−	0.988389i	$-0.451446\pi$
$739$	2.96573e32	0.303893	0.151946	+	0.988389i	$0.451446\pi$
$740$	1.91982e32	0.193685
$741$	0	0
$742$	1.68524e33	1.64822
$743$	4.48312e32	0.431727	0.215863	−	0.976424i	$-0.430743\pi$
$743$	4.48312e32	0.431727	0.215863	+	0.976424i	$0.430743\pi$
$744$	0	0
$745$	−4.89633e32	−0.457166
$746$	1.47917e33	1.35995
$747$	0	0
$748$	2.10912e32	0.188033
$749$	−3.06536e32	−0.269116
$750$	0	0
$751$	−3.50465e32	−0.298391	−0.149195	−	0.988808i	$-0.547668\pi$
$751$	−3.50465e32	−0.298391	−0.149195	+	0.988808i	$0.547668\pi$
$752$	−2.23188e33	−1.87140
$753$	0	0
$754$	1.68141e33	1.36742
$755$	−4.00654e32	−0.320907
$756$	0	0
$757$	4.37490e32	0.339911	0.169956	−	0.985452i	$-0.445638\pi$
$757$	4.37490e32	0.339911	0.169956	+	0.985452i	$0.445638\pi$
$758$	−1.38922e33	−1.06310
$759$	0	0
$760$	−9.40591e32	−0.698304
$761$	1.53089e31	0.0111949	0.00559744	−	0.999984i	$-0.498218\pi$
$761$	1.53089e31	0.0111949	0.00559744	+	0.999984i	$0.498218\pi$
$762$	0	0
$763$	−1.48360e33	−1.05265
$764$	1.50190e33	1.04970
$765$	0	0
$766$	−5.05416e33	−3.42782
$767$	−2.24586e33	−1.50050
$768$	0	0
$769$	2.67481e33	1.73436	0.867180	−	0.497995i	$-0.165930\pi$
$769$	2.67481e33	1.73436	0.867180	+	0.497995i	$0.165930\pi$
$770$	−5.09787e32	−0.325646
$771$	0	0
$772$	−4.69141e33	−2.90873
$773$	−8.38808e31	−0.0512387	−0.0256194	−	0.999672i	$-0.508156\pi$
$773$	−8.38808e31	−0.0512387	−0.0256194	+	0.999672i	$0.508156\pi$
$774$	0	0
$775$	−1.47859e31	−0.00876753
$776$	−3.86890e33	−2.26036
$777$	0	0
$778$	4.28012e33	2.42767
$779$	2.31816e33	1.29557
$780$	0	0
$781$	1.38496e33	0.751534
$782$	4.60716e32	0.246352
$783$	0	0
$784$	−5.71586e31	−0.0296788
$785$	6.14797e30	0.00314580
$786$	0	0
$787$	−3.07440e33	−1.52775	−0.763874	−	0.645366i	$-0.776705\pi$
$787$	−3.07440e33	−1.52775	−0.763874	+	0.645366i	$0.776705\pi$
$788$	1.75965e33	0.861737
$789$	0	0
$790$	6.50569e32	0.309444
$791$	−2.52281e32	−0.118265
$792$	0	0
$793$	−3.72693e33	−1.69711
$794$	−5.06989e31	−0.0227543
$795$	0	0
$796$	7.85832e33	3.42633
$797$	−2.31415e33	−0.994535	−0.497268	−	0.867597i	$-0.665663\pi$
$797$	−2.31415e33	−0.994535	−0.497268	+	0.867597i	$0.665663\pi$
$798$	0	0
$799$	4.84816e32	0.202437
$800$	7.88064e32	0.324360
$801$	0	0
$802$	−2.45379e33	−0.981370
$803$	2.76247e33	1.08910
$804$	0	0
$805$	−7.53918e32	−0.288849
$806$	−5.50915e31	−0.0208081
$807$	0	0
$808$	2.26931e33	0.833035
$809$	−3.80662e33	−1.37763	−0.688814	−	0.724938i	$-0.741868\pi$
$809$	−3.80662e33	−1.37763	−0.688814	+	0.724938i	$0.741868\pi$
$810$	0	0
$811$	4.24454e33	1.49311	0.746554	−	0.665325i	$-0.231707\pi$
$811$	4.24454e33	1.49311	0.746554	+	0.665325i	$0.231707\pi$
$812$	3.76564e33	1.30601
$813$	0	0
$814$	1.05151e33	0.354512
$815$	−7.28284e32	−0.242096
$816$	0	0
$817$	−1.23559e33	−0.399321
$818$	4.19191e33	1.33582
$819$	0	0
$820$	2.07880e33	0.644100
$821$	2.99736e33	0.915784	0.457892	−	0.889008i	$-0.348605\pi$
$821$	2.99736e33	0.915784	0.457892	+	0.889008i	$0.348605\pi$
$822$	0	0
$823$	−5.19319e32	−0.154289	−0.0771447	−	0.997020i	$-0.524580\pi$
$823$	−5.19319e32	−0.154289	−0.0771447	+	0.997020i	$0.524580\pi$
$824$	1.51692e33	0.444428
$825$	0	0
$826$	−7.42926e33	−2.11678
$827$	−4.81781e32	−0.135374	−0.0676872	−	0.997707i	$-0.521562\pi$
$827$	−4.81781e32	−0.135374	−0.0676872	+	0.997707i	$0.521562\pi$
$828$	0	0
$829$	−2.15627e33	−0.589287	−0.294644	−	0.955607i	$-0.595201\pi$
$829$	−2.15627e33	−0.589287	−0.294644	+	0.955607i	$0.595201\pi$
$830$	2.37918e33	0.641254
$831$	0	0
$832$	−3.16743e33	−0.830401
$833$	1.24161e31	0.00321048
$834$	0	0
$835$	3.77467e32	0.0949477
$836$	−6.66960e33	−1.65473
$837$	0	0
$838$	1.38649e34	3.34665
$839$	2.38371e32	0.0567532	0.0283766	−	0.999597i	$-0.490966\pi$
$839$	2.38371e32	0.0567532	0.0283766	+	0.999597i	$0.490966\pi$
$840$	0	0
$841$	−2.60187e33	−0.602743
$842$	−8.84388e33	−2.02094
$843$	0	0
$844$	−1.40144e34	−3.11627
$845$	6.94915e32	0.152433
$846$	0	0
$847$	2.74023e33	0.584962
$848$	5.83985e33	1.22984
$849$	0	0
$850$	−1.10177e33	−0.225826
$851$	1.55506e33	0.314454
$852$	0	0
$853$	−1.94872e32	−0.0383563	−0.0191781	−	0.999816i	$-0.506105\pi$
$853$	−1.94872e32	−0.0383563	−0.0191781	+	0.999816i	$0.506105\pi$
$854$	−1.23286e34	−2.39414
$855$	0	0
$856$	−2.77789e33	−0.525130
$857$	1.87495e33	0.349711	0.174855	−	0.984594i	$-0.444054\pi$
$857$	1.87495e33	0.349711	0.174855	+	0.984594i	$0.444054\pi$
$858$	0	0
$859$	6.46779e33	1.17445	0.587225	−	0.809424i	$-0.300220\pi$
$859$	6.46779e33	1.17445	0.587225	+	0.809424i	$0.300220\pi$
$860$	−1.10801e33	−0.198524
$861$	0	0
$862$	1.17702e34	2.05330
$863$	1.04050e34	1.79110	0.895550	−	0.444961i	$-0.146782\pi$
$863$	1.04050e34	1.79110	0.895550	+	0.444961i	$0.146782\pi$
$864$	0	0
$865$	1.52244e33	0.255184
$866$	2.29051e33	0.378858
$867$	0	0
$868$	−1.23382e32	−0.0198735
$869$	2.41239e33	0.383461
$870$	0	0
$871$	2.21012e33	0.342142
$872$	−1.34447e34	−2.05405
$873$	0	0
$874$	−1.45691e34	−2.16795
$875$	3.77522e33	0.554434
$876$	0	0
$877$	8.52438e33	1.21946	0.609730	−	0.792609i	$-0.291278\pi$
$877$	8.52438e33	1.21946	0.609730	+	0.792609i	$0.291278\pi$
$878$	1.01234e34	1.42935
$879$	0	0
$880$	−1.76656e33	−0.242984
$881$	−1.20706e34	−1.63872	−0.819362	−	0.573276i	$-0.805672\pi$
$881$	−1.20706e34	−1.63872	−0.819362	+	0.573276i	$0.805672\pi$
$882$	0	0
$883$	4.60310e33	0.608839	0.304420	−	0.952538i	$-0.401538\pi$
$883$	4.60310e33	0.608839	0.304420	+	0.952538i	$0.401538\pi$
$884$	−2.77928e33	−0.362853
$885$	0	0
$886$	−1.06551e34	−1.35541
$887$	7.25037e33	0.910413	0.455207	−	0.890386i	$-0.349565\pi$
$887$	7.25037e33	0.910413	0.455207	+	0.890386i	$0.349565\pi$
$888$	0	0
$889$	−7.07809e33	−0.866055
$890$	2.95102e32	0.0356441
$891$	0	0
$892$	−1.00055e34	−1.17772
$893$	−1.53312e34	−1.78149
$894$	0	0
$895$	−3.15069e33	−0.356813
$896$	−1.36149e34	−1.52220
$897$	0	0
$898$	1.21699e34	1.32620
$899$	−5.61873e31	−0.00604507
$900$	0	0
$901$	−1.26855e33	−0.133037
$902$	1.13858e34	1.17893
$903$	0	0
$904$	−2.28623e33	−0.230772
$905$	1.52433e33	0.151922
$906$	0	0
$907$	−3.03876e33	−0.295266	−0.147633	−	0.989042i	$-0.547165\pi$
$907$	−3.03876e33	−0.295266	−0.147633	+	0.989042i	$0.547165\pi$
$908$	3.20322e34	3.07326
$909$	0	0
$910$	6.71768e33	0.628410
$911$	1.60065e34	1.47855	0.739273	−	0.673406i	$-0.235169\pi$
$911$	1.60065e34	1.47855	0.739273	+	0.673406i	$0.235169\pi$
$912$	0	0
$913$	8.82233e33	0.794638
$914$	−7.89533e33	−0.702245
$915$	0	0
$916$	1.95764e34	1.69799
$917$	1.36147e34	1.16617
$918$	0	0
$919$	−1.54454e34	−1.29024	−0.645120	−	0.764081i	$-0.723193\pi$
$919$	−1.54454e34	−1.29024	−0.645120	+	0.764081i	$0.723193\pi$
$920$	−6.83217e33	−0.563636
$921$	0	0
$922$	2.07251e34	1.66759
$923$	−1.82501e34	−1.45026
$924$	0	0
$925$	−3.71881e33	−0.288253
$926$	3.25135e33	0.248907
$927$	0	0
$928$	2.99469e33	0.223641
$929$	−1.19786e34	−0.883535	−0.441768	−	0.897129i	$-0.645648\pi$
$929$	−1.19786e34	−0.883535	−0.441768	+	0.897129i	$0.645648\pi$
$930$	0	0
$931$	−3.92631e32	−0.0282529
$932$	2.86999e34	2.03985
$933$	0	0
$934$	5.87939e33	0.407702
$935$	3.83738e32	0.0262846
$936$	0	0
$937$	−2.83646e33	−0.189570	−0.0947852	−	0.995498i	$-0.530216\pi$
$937$	−2.83646e33	−0.189570	−0.0947852	+	0.995498i	$0.530216\pi$
$938$	7.31103e33	0.482665
$939$	0	0
$940$	−1.37482e34	−0.885676
$941$	−2.88589e34	−1.83653	−0.918267	−	0.395961i	$-0.870412\pi$
$941$	−2.88589e34	−1.83653	−0.918267	+	0.395961i	$0.870412\pi$
$942$	0	0
$943$	1.68384e34	1.04572
$944$	−2.57446e34	−1.57946
$945$	0	0
$946$	−6.06872e33	−0.363370
$947$	−2.29990e34	−1.36045	−0.680226	−	0.733002i	$-0.738118\pi$
$947$	−2.29990e34	−1.36045	−0.680226	+	0.733002i	$0.738118\pi$
$948$	0	0
$949$	−3.64023e34	−2.10168
$950$	3.48408e34	1.98732
$951$	0	0
$952$	−4.80786e33	−0.267687
$953$	2.39769e34	1.31894	0.659470	−	0.751731i	$-0.270781\pi$
$953$	2.39769e34	1.31894	0.659470	+	0.751731i	$0.270781\pi$
$954$	0	0
$955$	2.73258e33	0.146735
$956$	−4.54638e34	−2.41213
$957$	0	0
$958$	−1.08520e34	−0.562090
$959$	−6.30062e33	−0.322455
$960$	0	0
$961$	−2.00115e34	−0.999908
$962$	−1.38561e34	−0.684115
$963$	0	0
$964$	3.28444e34	1.58334
$965$	−8.53563e33	−0.406604
$966$	0	0
$967$	−6.66196e33	−0.309883	−0.154942	−	0.987924i	$-0.549519\pi$
$967$	−6.66196e33	−0.309883	−0.154942	+	0.987924i	$0.549519\pi$
$968$	2.48325e34	1.14144
$969$	0	0
$970$	−1.34606e34	−0.604211
$971$	3.35172e34	1.48678	0.743390	−	0.668858i	$-0.233217\pi$
$971$	3.35172e34	1.48678	0.743390	+	0.668858i	$0.233217\pi$
$972$	0	0
$973$	1.92490e34	0.833892
$974$	−2.46765e34	−1.05647
$975$	0	0
$976$	−4.27224e34	−1.78642
$977$	−1.17263e34	−0.484590	−0.242295	−	0.970203i	$-0.577900\pi$
$977$	−1.17263e34	−0.484590	−0.242295	+	0.970203i	$0.577900\pi$
$978$	0	0
$979$	1.09428e33	0.0441699
$980$	−3.52091e32	−0.0140461
$981$	0	0
$982$	−1.75487e33	−0.0683851
$983$	−1.51439e34	−0.583274	−0.291637	−	0.956529i	$-0.594200\pi$
$983$	−1.51439e34	−0.583274	−0.291637	+	0.956529i	$0.594200\pi$
$984$	0	0
$985$	3.20154e33	0.120460
$986$	−4.18679e33	−0.155703
$987$	0	0
$988$	8.78881e34	3.19319
$989$	−8.97497e33	−0.322311
$990$	0	0
$991$	2.60260e34	0.913187	0.456593	−	0.889675i	$-0.349069\pi$
$991$	2.60260e34	0.913187	0.456593	+	0.889675i	$0.349069\pi$
$992$	−9.81216e31	−0.00340315
$993$	0	0
$994$	−6.03711e34	−2.04591
$995$	1.42976e34	0.478957
$996$	0	0
$997$	−1.96863e34	−0.644422	−0.322211	−	0.946668i	$-0.604426\pi$
$997$	−1.96863e34	−0.644422	−0.322211	+	0.946668i	$0.604426\pi$
$998$	6.50036e34	2.10347
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	9.24.a.b.1.1		2
3.2	odd	2		1.24.a.a.1.2	✓	2
12.11	even	2		16.24.a.b.1.2		2
15.2	even	4		25.24.b.a.24.4		4
15.8	even	4		25.24.b.a.24.1		4
15.14	odd	2		25.24.a.a.1.1		2
21.20	even	2		49.24.a.b.1.2		2
24.5	odd	2		64.24.a.d.1.2		2
24.11	even	2		64.24.a.g.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1.24.a.a.1.2	✓	2	3.2	odd	2
9.24.a.b.1.1		2	1.1	even	1	trivial
16.24.a.b.1.2		2	12.11	even	2
25.24.a.a.1.1		2	15.14	odd	2
25.24.b.a.24.1		4	15.8	even	4
25.24.b.a.24.4		4	15.2	even	4
49.24.a.b.1.2		2	21.20	even	2
64.24.a.d.1.2		2	24.5	odd	2
64.24.a.g.1.1		2	24.11	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 9 = 3^{2} \)
Weight:	\( k \)	\(=\)	\( 24 \)
Character orbit:	\([\chi]\)	\(=\)	9.a (trivial)

\(f(q)\)	\(=\)	\(q-5096.35 q^{2} +1.75842e7 q^{4} +3.19930e7 q^{5} -5.17135e9 q^{7} -4.68639e10 q^{8} +O(q^{10})\)	\(q-5096.35 q^{2} +1.75842e7 q^{4} +3.19930e7 q^{5} -5.17135e9 q^{7} -4.68639e10 q^{8} -1.63048e11 q^{10} -6.04602e11 q^{11} +7.96710e12 q^{13} +2.63550e13 q^{14} +9.13280e13 q^{16} -1.98385e13 q^{17} +6.27346e14 q^{19} +5.62571e14 q^{20} +3.08127e15 q^{22} +4.55685e15 q^{23} -1.08974e16 q^{25} -4.06032e16 q^{26} -9.09340e16 q^{28} -4.14107e16 q^{29} +1.35683e15 q^{31} -7.23169e16 q^{32} +1.01104e17 q^{34} -1.65447e17 q^{35} +3.41258e17 q^{37} -3.19718e18 q^{38} -1.49932e18 q^{40} +3.69518e18 q^{41} -1.96955e18 q^{43} -1.06314e19 q^{44} -2.32233e19 q^{46} -2.44381e19 q^{47} -6.25860e17 q^{49} +5.55369e19 q^{50} +1.40095e20 q^{52} +6.39437e19 q^{53} -1.93431e19 q^{55} +2.42350e20 q^{56} +2.11044e20 q^{58} -2.81892e20 q^{59} -4.67790e20 q^{61} -6.91488e18 q^{62} -3.97563e20 q^{64} +2.54892e20 q^{65} +2.77406e20 q^{67} -3.48844e20 q^{68} +8.43177e20 q^{70} -2.29069e21 q^{71} -4.56908e21 q^{73} -1.73917e21 q^{74} +1.10314e22 q^{76} +3.12661e21 q^{77} -3.99005e21 q^{79} +2.92186e21 q^{80} -1.88319e22 q^{82} -1.45920e22 q^{83} -6.34694e20 q^{85} +1.00375e22 q^{86} +2.83340e22 q^{88} -1.80991e21 q^{89} -4.12007e22 q^{91} +8.01285e22 q^{92} +1.24545e23 q^{94} +2.00707e22 q^{95} +8.25561e22 q^{97} +3.18960e21 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 1080 q^{2} + 25326656 q^{4} - 73069020 q^{5} - 1359184400 q^{7} - 49459023360 q^{8}+O(q^{10}) \) 2 * q - 1080 * q^2 + 25326656 * q^4 - 73069020 * q^5 - 1359184400 * q^7 - 49459023360 * q^8	\( 2 q - 1080 q^{2} + 25326656 q^{4} - 73069020 q^{5} - 1359184400 q^{7} - 49459023360 q^{8} - 585013636080 q^{10} - 856801968264 q^{11} + 4376109322060 q^{13} + 41666034529728 q^{14} + 15956586401792 q^{16} - 254028147597540 q^{17} + 4260600979960 q^{19} - 250868387468160 q^{20} + 20\!\cdots\!60 q^{22}+ \cdots - 48\!\cdots\!40 q^{98}+O(q^{100}) \) 2 * q - 1080 * q^2 + 25326656 * q^4 - 73069020 * q^5 - 1359184400 * q^7 - 49459023360 * q^8 - 585013636080 * q^10 - 856801968264 * q^11 + 4376109322060 * q^13 + 41666034529728 * q^14 + 15956586401792 * q^16 - 254028147597540 * q^17 + 4260600979960 * q^19 - 250868387468160 * q^20 + 2068343882177760 * q^22 + 8144713079008560 * q^23 - 11780274628800850 * q^25 - 55025854658735184 * q^26 - 61418438819709440 * q^28 - 20818433601623340 * q^29 + 137714017177000384 * q^31 - 353265663781601280 * q^32 - 839483655961325328 * q^34 - 565961271250425120 * q^35 - 897721264408967780 * q^37 - 5699708971590961440 * q^38 - 1226668524414336000 * q^40 + 2294435477168314956 * q^41 - 1750760768619855800 * q^43 - 12584088840033038592 * q^44 - 8813206018050221376 * q^46 - 15759744217656780960 * q^47 - 13461981704376200814 * q^49 + 51990825483785316600 * q^50 + 112291883783912022400 * q^52 + 140287253401646796420 * q^53 + 7153550955060182640 * q^55 + 232456712054288117760 * q^56 + 293749486923568689360 * q^58 - 280872989971340771880 * q^59 - 180452892516502223636 * q^61 + 540743475843874103040 * q^62 - 893690254469352914944 * q^64 + 632168834809440380760 * q^65 + 1754233163431557625240 * q^67 - 2162050190142944330880 * q^68 - 765428657799921252480 * q^70 - 3055033510194143328624 * q^71 - 8063408253877606149260 * q^73 - 6715344283148807757072 * q^74 + 6207154294513080590080 * q^76 + 2165184764357449665600 * q^77 + 6244916814559639980640 * q^79 + 10840537585501794017280 * q^80 - 24457792891615712450640 * q^82 - 6875994082418498976120 * q^83 + 23969743087870314902520 * q^85 + 10916288812918999243296 * q^86 + 28988514668199273707520 * q^88 - 6395093086173070004820 * q^89 - 54890178162704560146016 * q^91 + 107907439017191756981760 * q^92 + 159400518006534931827072 * q^94 + 85533361066700858502000 * q^95 - 31147288846254030500540 * q^97 - 48364767616374671003640 * q^98

Introduction

L-functions

Modular forms

Varieties

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