LMFDB - Embedded newform 9.44.a.a.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [9,44,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, 44, names="a")

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

chi := DirichletCharacter("9.1");

S:= CuspForms(chi, 44);

N := Newforms(S);

Level:	$ N $	$=$	$ 9 = 3^{2} $
Weight:	$ k $	$=$	$ 44 $
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:	$105.399355811$
Analytic rank:	$1$
Dimension:	$3$
Coefficient field:	$\mathbb{Q}[x]/(x^{3} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - x^{2} - 908401710x + 974756489742 $ x^3 - x^2 - 908401710*x + 974756489742
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{13}\cdot 3^{5}\cdot 5\cdot 11 $
Twist minimal:	no (minimal twist has level 3)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$-30662.1$ 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)

$f(q)$	$=$	$q-4.56260e6 q^{2} +1.20212e13 q^{4} +1.29230e15 q^{5} -9.66721e17 q^{7} -1.47149e19 q^{8} +O(q^{10})$	\(q-4.56260e6 q^{2} +1.20212e13 q^{4} +1.29230e15 q^{5} -9.66721e17 q^{7} -1.47149e19 q^{8} -5.89624e21 q^{10} +4.14867e22 q^{11} +6.85476e23 q^{13} +4.41076e24 q^{14} -3.86016e25 q^{16} +1.87770e26 q^{17} -3.67577e27 q^{19} +1.55350e28 q^{20} -1.89287e29 q^{22} -2.38175e29 q^{23} +5.33166e29 q^{25} -3.12755e30 q^{26} -1.16211e31 q^{28} -4.15139e31 q^{29} -3.15649e31 q^{31} +3.05557e32 q^{32} -8.56717e32 q^{34} -1.24929e33 q^{35} -6.10581e32 q^{37} +1.67711e34 q^{38} -1.90160e34 q^{40} +4.47211e34 q^{41} -2.07163e35 q^{43} +4.98720e35 q^{44} +1.08670e36 q^{46} -1.73685e36 q^{47} -1.24926e36 q^{49} -2.43262e36 q^{50} +8.24025e36 q^{52} +1.34883e37 q^{53} +5.36132e37 q^{55} +1.42252e37 q^{56} +1.89411e38 q^{58} +7.90833e37 q^{59} +1.04129e38 q^{61} +1.44018e38 q^{62} -1.05459e39 q^{64} +8.85840e38 q^{65} +2.71441e39 q^{67} +2.25722e39 q^{68} +5.70002e39 q^{70} -6.41305e39 q^{71} +4.03967e39 q^{73} +2.78583e39 q^{74} -4.41872e40 q^{76} -4.01061e40 q^{77} -6.03727e40 q^{79} -4.98848e40 q^{80} -2.04044e41 q^{82} -2.83283e41 q^{83} +2.42654e41 q^{85} +9.45200e41 q^{86} -6.10471e41 q^{88} +7.96312e41 q^{89} -6.62665e41 q^{91} -2.86315e42 q^{92} +7.92454e42 q^{94} -4.75019e42 q^{95} -2.28074e41 q^{97} +5.69989e42 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q - 4857024 q^{2} - 1781058029568 q^{4} + 507753321105270 q^{5} - 16\!\cdots\!88 q^{7}+ \cdots - 11\!\cdots\!56 q^{8}+O(q^{10}) $ 3 * q - 4857024 * q^2 - 1781058029568 * q^4 + 507753321105270 * q^5 - 1633169303707089288 * q^7 - 11196260694472851456 * q^8	$ 3 q - 4857024 q^{2} - 1781058029568 q^{4} + 507753321105270 q^{5} - 16\!\cdots\!88 q^{7}+ \cdots + 20\!\cdots\!60 q^{98}+O(q^{100}) $ 3 * q - 4857024 * q^2 - 1781058029568 * q^4 + 507753321105270 * q^5 - 1633169303707089288 * q^7 - 11196260694472851456 * q^8 - 2286850690696789595520 * q^10 + 27750966261606959036820 * q^11 - 994786398159560287290750 * q^13 + 9473256819232835003171328 * q^14 + 23637690650696707825729536 * q^16 + 160517621023312837046953482 * q^17 - 3227133683900578441639486764 * q^19 + 19920520041146285724571791360 * q^20 - 172470540148626161048719521024 * q^22 - 114780279514038504224277444504 * q^23 + 1825420275602850437617559193525 * q^25 - 1775037275334840765729836075136 * q^26 - 8483554335441104836174737260544 * q^28 + 28241588775620253186792106789758 * q^29 - 56947467162250619768506214477136 * q^31 + 290372748061904590918491662450688 * q^32 - 1778246324363072918021693922216576 * q^34 + 3641689125493658442558484764497520 * q^35 - 7771759793894794226158134990367878 * q^37 + 11984574206649783949969526048471808 * q^38 - 75089135561625836440773237699379200 * q^40 + 150622420768399427659977962302801266 * q^41 - 503269829459862138385119574866599988 * q^43 + 589156491500651091472842134125289472 * q^44 + 1201666039209211956008162792803812864 * q^46 - 517590816657574666863303783889459536 * q^47 + 1183207682852736238558590379440977403 * q^49 - 5363972694460023429439963707950510400 * q^50 + 19510568225567423700598614061466308608 * q^52 - 3147649955233970731028729152905020634 * q^53 + 72798121427511388475535050768468313960 * q^55 - 64659225918940531158350848060065054720 * q^56 + 165860584701603780784654252956514011264 * q^58 + 178011039218636820023529236138863835076 * q^59 - 123533499732384273913895969461615945518 * q^61 + 685215538112102475249420816230843667456 * q^62 - 971015593402068342273570470768658087936 * q^64 + 2575578837917643212594035173081316043940 * q^65 + 1292774342372783673662410484960847098148 * q^67 + 2717789569206669919054906507790539296768 * q^68 + 1868357626946632141981582698458836116480 * q^70 - 22400468745595901369803420176388102887816 * q^71 + 31313509370447648548173493799361498480654 * q^73 - 12824367911381949889146580637796075349632 * q^74 - 45893435926810400921777338109031978491904 * q^76 - 15925552922292610065970442499593057720544 * q^77 - 43825544899857898915807551182364364018080 * q^79 - 51052771545930899482561003058120286535680 * q^80 - 207555016724016234735599639977066643719296 * q^82 - 89911369720242570860406785197345580904468 * q^83 - 609771200949453596987959942886782705526220 * q^85 + 1052084075872403200090705454196607607512320 * q^86 - 866229044996425850996432449444164589584384 * q^88 - 65289466052051143331840751197428752211806 * q^89 + 1361620777581018817929645459439738348447824 * q^91 - 3753917639661643691216268373890598977257472 * q^92 + 7862327422462694583153035384185107177477120 * q^94 - 9328236864095865156237338173319138974757400 * q^95 + 6130807410554375967448029821362307484893478 * q^97 + 2033290778553828878915746018754102329738560 * 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 $

$2$	−4.56260e6	−1.53839	−0.769196	−	0.639013i	$-0.779343\pi$
$2$	−4.56260e6	−1.53839	−0.769196	+	0.639013i	$0.779343\pi$
$3$	0	0
$3$	0	0
$4$	1.20212e13	1.36665
$5$	1.29230e15	1.21201	0.606007	−	0.795459i	$-0.292770\pi$
$5$	1.29230e15	1.21201	0.606007	+	0.795459i	$0.292770\pi$
$6$	0	0
$7$	−9.66721e17	−0.654174	−0.327087	−	0.944994i	$-0.606067\pi$
$7$	−9.66721e17	−0.654174	−0.327087	+	0.944994i	$0.606067\pi$
$8$	−1.47149e19	−0.564055
$9$	0	0
$10$	−5.89624e21	−1.86455
$11$	4.14867e22	1.69031	0.845155	−	0.534521i	$-0.179508\pi$
$11$	4.14867e22	1.69031	0.845155	+	0.534521i	$0.179508\pi$
$12$	0	0
$13$	6.85476e23	0.769503	0.384752	−	0.923020i	$-0.374287\pi$
$13$	6.85476e23	0.769503	0.384752	+	0.923020i	$0.374287\pi$
$14$	4.41076e24	1.00638
$15$	0	0
$16$	−3.86016e25	−0.498914
$17$	1.87770e26	0.659134	0.329567	−	0.944132i	$-0.393097\pi$
$17$	1.87770e26	0.659134	0.329567	+	0.944132i	$0.393097\pi$
$18$	0	0
$19$	−3.67577e27	−1.18072	−0.590359	−	0.807141i	$-0.701014\pi$
$19$	−3.67577e27	−1.18072	−0.590359	+	0.807141i	$0.701014\pi$
$20$	1.55350e28	1.65640
$21$	0	0
$22$	−1.89287e29	−2.60036
$23$	−2.38175e29	−1.25820	−0.629098	−	0.777326i	$-0.716576\pi$
$23$	−2.38175e29	−1.25820	−0.629098	+	0.777326i	$0.716576\pi$
$24$	0	0
$25$	5.33166e29	0.468978
$26$	−3.12755e30	−1.18380
$27$	0	0
$28$	−1.16211e31	−0.894028
$29$	−4.15139e31	−1.50188	−0.750942	−	0.660368i	$-0.770400\pi$
$29$	−4.15139e31	−1.50188	−0.750942	+	0.660368i	$0.770400\pi$
$30$	0	0
$31$	−3.15649e31	−0.272225	−0.136112	−	0.990693i	$-0.543461\pi$
$31$	−3.15649e31	−0.272225	−0.136112	+	0.990693i	$0.543461\pi$
$32$	3.05557e32	1.33158
$33$	0	0
$34$	−8.56717e32	−1.01401
$35$	−1.24929e33	−0.792868
$36$	0	0
$37$	−6.10581e32	−0.117329	−0.0586646	−	0.998278i	$-0.518684\pi$
$37$	−6.10581e32	−0.117329	−0.0586646	+	0.998278i	$0.518684\pi$
$38$	1.67711e34	1.81641
$39$	0	0
$40$	−1.90160e34	−0.683642
$41$	4.47211e34	0.945496	0.472748	−	0.881198i	$-0.343262\pi$
$41$	4.47211e34	0.945496	0.472748	+	0.881198i	$0.343262\pi$
$42$	0	0
$43$	−2.07163e35	−1.57304	−0.786520	−	0.617565i	$-0.788119\pi$
$43$	−2.07163e35	−1.57304	−0.786520	+	0.617565i	$0.788119\pi$
$44$	4.98720e35	2.31007
$45$	0	0
$46$	1.08670e36	1.93560
$47$	−1.73685e36	−1.94831	−0.974155	−	0.225883i	$-0.927473\pi$
$47$	−1.73685e36	−1.94831	−0.974155	+	0.225883i	$0.927473\pi$
$48$	0	0
$49$	−1.24926e36	−0.572056
$50$	−2.43262e36	−0.721472
$51$	0	0
$52$	8.24025e36	1.05164
$53$	1.34883e37	1.14294	0.571472	−	0.820622i	$-0.306373\pi$
$53$	1.34883e37	1.14294	0.571472	+	0.820622i	$0.306373\pi$
$54$	0	0
$55$	5.36132e37	2.04868
$56$	1.42252e37	0.368990
$57$	0	0
$58$	1.89411e38	2.31049
$59$	7.90833e37	0.667985	0.333992	−	0.942576i	$-0.391604\pi$
$59$	7.90833e37	0.667985	0.333992	+	0.942576i	$0.391604\pi$
$60$	0	0
$61$	1.04129e38	0.429517	0.214759	−	0.976667i	$-0.431103\pi$
$61$	1.04129e38	0.429517	0.214759	+	0.976667i	$0.431103\pi$
$62$	1.44018e38	0.418789
$63$	0	0
$64$	−1.05459e39	−1.54958
$65$	8.85840e38	0.932649
$66$	0	0
$67$	2.71441e39	1.48959	0.744796	−	0.667292i	$-0.232547\pi$
$67$	2.71441e39	1.48959	0.744796	+	0.667292i	$0.232547\pi$
$68$	2.25722e39	0.900806
$69$	0	0
$70$	5.70002e39	1.21974
$71$	−6.41305e39	−1.01160	−0.505801	−	0.862650i	$-0.668803\pi$
$71$	−6.41305e39	−1.01160	−0.505801	+	0.862650i	$0.668803\pi$
$72$	0	0
$73$	4.03967e39	0.350675	0.175337	−	0.984508i	$-0.443898\pi$
$73$	4.03967e39	0.350675	0.175337	+	0.984508i	$0.443898\pi$
$74$	2.78583e39	0.180498
$75$	0	0
$76$	−4.41872e40	−1.61363
$77$	−4.01061e40	−1.10576
$78$	0	0
$79$	−6.03727e40	−0.959087	−0.479543	−	0.877518i	$-0.659198\pi$
$79$	−6.03727e40	−0.959087	−0.479543	+	0.877518i	$0.659198\pi$
$80$	−4.98848e40	−0.604691
$81$	0	0
$82$	−2.04044e41	−1.45454
$83$	−2.83283e41	−1.55612	−0.778058	−	0.628193i	$-0.783795\pi$
$83$	−2.83283e41	−1.55612	−0.778058	+	0.628193i	$0.783795\pi$
$84$	0	0
$85$	2.42654e41	0.798879
$86$	9.45200e41	2.41995
$87$	0	0
$88$	−6.10471e41	−0.953427
$89$	7.96312e41	0.975434	0.487717	−	0.873002i	$-0.337830\pi$
$89$	7.96312e41	0.975434	0.487717	+	0.873002i	$0.337830\pi$
$90$	0	0
$91$	−6.62665e41	−0.503389
$92$	−2.86315e42	−1.71952
$93$	0	0
$94$	7.92454e42	2.99726
$95$	−4.75019e42	−1.43105
$96$	0	0
$97$	−2.28074e41	−0.0439018	−0.0219509	−	0.999759i	$-0.506988\pi$
$97$	−2.28074e41	−0.0439018	−0.0219509	+	0.999759i	$0.506988\pi$
$98$	5.69989e42	0.880047
$99$	0	0
$100$	6.40930e42	0.640930
$101$	1.22069e41	0.00985585	0.00492793	−	0.999988i	$-0.498431\pi$
$101$	1.22069e41	0.00985585	0.00492793	+	0.999988i	$0.498431\pi$
$102$	0	0
$103$	−1.54032e43	−0.815851	−0.407926	−	0.913015i	$-0.633748\pi$
$103$	−1.54032e43	−0.815851	−0.407926	+	0.913015i	$0.633748\pi$
$104$	−1.00867e43	−0.434042
$105$	0	0
$106$	−6.15415e43	−1.75830
$107$	3.88129e43	0.906201	0.453100	−	0.891459i	$-0.350318\pi$
$107$	3.88129e43	0.906201	0.453100	+	0.891459i	$0.350318\pi$
$108$	0	0
$109$	−6.58075e43	−1.03182	−0.515912	−	0.856642i	$-0.672547\pi$
$109$	−6.58075e43	−1.03182	−0.515912	+	0.856642i	$0.672547\pi$
$110$	−2.44616e44	−3.15167
$111$	0	0
$112$	3.73170e43	0.326377
$113$	−1.24527e43	−0.0899655	−0.0449828	−	0.998988i	$-0.514323\pi$
$113$	−1.24527e43	−0.0899655	−0.0449828	+	0.998988i	$0.514323\pi$
$114$	0	0
$115$	−3.07794e44	−1.52495
$116$	−4.99046e44	−2.05255
$117$	0	0
$118$	−3.60825e44	−1.02762
$119$	−1.81521e44	−0.431188
$120$	0	0
$121$	1.11875e45	1.85715
$122$	−4.75099e44	−0.660767
$123$	0	0
$124$	−3.79448e44	−0.372037
$125$	−7.80163e44	−0.643606
$126$	0	0
$127$	5.22881e44	0.306636	0.153318	−	0.988177i	$-0.451004\pi$
$127$	5.22881e44	0.306636	0.153318	+	0.988177i	$0.451004\pi$
$128$	2.12396e45	1.05228
$129$	0	0
$130$	−4.04173e45	−1.43478
$131$	1.97998e45	0.596112	0.298056	−	0.954548i	$-0.403662\pi$
$131$	1.97998e45	0.596112	0.298056	+	0.954548i	$0.403662\pi$
$132$	0	0
$133$	3.55345e45	0.772395
$134$	−1.23848e46	−2.29158
$135$	0	0
$136$	−2.76300e45	−0.371787
$137$	−7.04963e45	−0.810352	−0.405176	−	0.914239i	$-0.632790\pi$
$137$	−7.04963e45	−0.810352	−0.405176	+	0.914239i	$0.632790\pi$
$138$	0	0
$139$	−1.36482e46	−1.14884	−0.574419	−	0.818562i	$-0.694772\pi$
$139$	−1.36482e46	−1.14884	−0.574419	+	0.818562i	$0.694772\pi$
$140$	−1.50180e46	−1.08357
$141$	0	0
$142$	2.92601e46	1.55624
$143$	2.84382e46	1.30070
$144$	0	0
$145$	−5.36483e46	−1.82030
$146$	−1.84314e46	−0.539475
$147$	0	0
$148$	−7.33991e45	−0.160348
$149$	6.34924e46	1.20010	0.600049	−	0.799963i	$-0.295148\pi$
$149$	6.34924e46	1.20010	0.600049	+	0.799963i	$0.295148\pi$
$150$	0	0
$151$	7.57341e45	0.107470	0.0537350	−	0.998555i	$-0.482887\pi$
$151$	7.57341e45	0.107470	0.0537350	+	0.998555i	$0.482887\pi$
$152$	5.40884e46	0.665989
$153$	0	0
$154$	1.82988e47	1.70109
$155$	−4.07913e46	−0.329940
$156$	0	0
$157$	−1.59997e47	−0.982358	−0.491179	−	0.871059i	$-0.663434\pi$
$157$	−1.59997e47	−0.982358	−0.491179	+	0.871059i	$0.663434\pi$
$158$	2.75456e47	1.47545
$159$	0	0
$160$	3.94871e47	1.61389
$161$	2.30249e47	0.823080
$162$	0	0
$163$	2.01881e47	0.553430	0.276715	−	0.960952i	$-0.410754\pi$
$163$	2.01881e47	0.553430	0.276715	+	0.960952i	$0.410754\pi$
$164$	5.37601e47	1.29216
$165$	0	0
$166$	1.29251e48	2.39392
$167$	2.04593e47	0.333033	0.166517	−	0.986039i	$-0.446748\pi$
$167$	2.04593e47	0.333033	0.166517	+	0.986039i	$0.446748\pi$
$168$	0	0
$169$	−3.23653e47	−0.407865
$170$	−1.10713e48	−1.22899
$171$	0	0
$172$	−2.49034e48	−2.14980
$173$	−3.51004e47	−0.267498	−0.133749	−	0.991015i	$-0.542702\pi$
$173$	−3.51004e47	−0.267498	−0.133749	+	0.991015i	$0.542702\pi$
$174$	0	0
$175$	−5.15423e47	−0.306793
$176$	−1.60146e48	−0.843320
$177$	0	0
$178$	−3.63325e48	−1.50060
$179$	2.04481e48	0.748708	0.374354	−	0.927286i	$-0.377864\pi$
$179$	2.04481e48	0.748708	0.374354	+	0.927286i	$0.377864\pi$
$180$	0	0
$181$	−3.20223e48	−0.923345	−0.461672	−	0.887051i	$-0.652750\pi$
$181$	−3.20223e48	−0.923345	−0.461672	+	0.887051i	$0.652750\pi$
$182$	3.02347e48	0.774410
$183$	0	0
$184$	3.50472e48	0.709692
$185$	−7.89053e47	−0.142205
$186$	0	0
$187$	7.78995e48	1.11414
$188$	−2.08790e49	−2.66266
$189$	0	0
$190$	2.16732e49	2.20151
$191$	3.02200e48	0.274206	0.137103	−	0.990557i	$-0.456221\pi$
$191$	3.02200e48	0.274206	0.137103	+	0.990557i	$0.456221\pi$
$192$	0	0
$193$	−1.79481e49	−1.30178	−0.650888	−	0.759174i	$-0.725603\pi$
$193$	−1.79481e49	−1.30178	−0.650888	+	0.759174i	$0.725603\pi$
$194$	1.04061e48	0.0675383
$195$	0	0
$196$	−1.50177e49	−0.781802
$197$	−2.54943e49	−1.18965	−0.594825	−	0.803855i	$-0.702779\pi$
$197$	−2.54943e49	−1.18965	−0.594825	+	0.803855i	$0.702779\pi$
$198$	0	0
$199$	−2.22144e49	−0.834244	−0.417122	−	0.908851i	$-0.636961\pi$
$199$	−2.22144e49	−0.834244	−0.417122	+	0.908851i	$0.636961\pi$
$200$	−7.84546e48	−0.264529
$201$	0	0
$202$	−5.56950e47	−0.0151622
$203$	4.01323e49	0.982494
$204$	0	0
$205$	5.77930e49	1.14595
$206$	7.02786e49	1.25510
$207$	0	0
$208$	−2.64605e49	−0.383916
$209$	−1.52496e50	−1.99578
$210$	0	0
$211$	−1.11346e50	−1.18741	−0.593706	−	0.804682i	$-0.702336\pi$
$211$	−1.11346e50	−1.18741	−0.593706	+	0.804682i	$0.702336\pi$
$212$	1.62145e50	1.56201
$213$	0	0
$214$	−1.77087e50	−1.39409
$215$	−2.67716e50	−1.90655
$216$	0	0
$217$	3.05145e49	0.178083
$218$	3.00253e50	1.58735
$219$	0	0
$220$	6.44495e50	2.79983
$221$	1.28712e50	0.507206
$222$	0	0
$223$	8.11200e49	0.263374	0.131687	−	0.991291i	$-0.457961\pi$
$223$	8.11200e49	0.263374	0.131687	+	0.991291i	$0.457961\pi$
$224$	−2.95388e50	−0.871086
$225$	0	0
$226$	5.68165e49	0.138402
$227$	3.50053e50	0.775492	0.387746	−	0.921766i	$-0.373254\pi$
$227$	3.50053e50	0.775492	0.387746	+	0.921766i	$0.373254\pi$
$228$	0	0
$229$	5.91349e50	1.08488	0.542439	−	0.840095i	$-0.317501\pi$
$229$	5.91349e50	1.08488	0.542439	+	0.840095i	$0.317501\pi$
$230$	1.40434e51	2.34597
$231$	0	0
$232$	6.10870e50	0.847144
$233$	9.65662e50	1.22088	0.610440	−	0.792063i	$-0.290993\pi$
$233$	9.65662e50	1.22088	0.610440	+	0.792063i	$0.290993\pi$
$234$	0	0
$235$	−2.24453e51	−2.36138
$236$	9.50676e50	0.912902
$237$	0	0
$238$	8.28207e50	0.663337
$239$	−2.10427e51	−1.54009	−0.770047	−	0.637987i	$-0.779767\pi$
$239$	−2.10427e51	−1.54009	−0.770047	+	0.637987i	$0.779767\pi$
$240$	0	0
$241$	−1.35652e51	−0.829965	−0.414982	−	0.909829i	$-0.636212\pi$
$241$	−1.35652e51	−0.829965	−0.414982	+	0.909829i	$0.636212\pi$
$242$	−5.10440e51	−2.85702
$243$	0	0
$244$	1.25176e51	0.587001
$245$	−1.61442e51	−0.693340
$246$	0	0
$247$	−2.51965e51	−0.908566
$248$	4.64473e50	0.153550
$249$	0	0
$250$	3.55957e51	0.990119
$251$	−1.64213e51	−0.419201	−0.209601	−	0.977787i	$-0.567216\pi$
$251$	−1.64213e51	−0.419201	−0.209601	+	0.977787i	$0.567216\pi$
$252$	0	0
$253$	−9.88112e51	−2.12674
$254$	−2.38570e51	−0.471727
$255$	0	0
$256$	−4.14504e50	−0.0692420
$257$	6.10196e50	0.0937362	0.0468681	−	0.998901i	$-0.485076\pi$
$257$	6.10196e50	0.0937362	0.0468681	+	0.998901i	$0.485076\pi$
$258$	0	0
$259$	5.90262e50	0.0767537
$260$	1.06489e52	1.27461
$261$	0	0
$262$	−9.03384e51	−0.917054
$263$	−2.81731e51	−0.263504	−0.131752	−	0.991283i	$-0.542060\pi$
$263$	−2.81731e51	−0.263504	−0.131752	+	0.991283i	$0.542060\pi$
$264$	0	0
$265$	1.74309e52	1.38526
$266$	−1.62129e52	−1.18825
$267$	0	0
$268$	3.26305e52	2.03575
$269$	6.28193e51	0.361759	0.180880	−	0.983505i	$-0.442106\pi$
$269$	6.28193e51	0.361759	0.180880	+	0.983505i	$0.442106\pi$
$270$	0	0
$271$	−3.10633e52	−1.52549	−0.762743	−	0.646702i	$-0.776148\pi$
$271$	−3.10633e52	−1.52549	−0.762743	+	0.646702i	$0.776148\pi$
$272$	−7.24821e51	−0.328851
$273$	0	0
$274$	3.21646e52	1.24664
$275$	2.21193e52	0.792718
$276$	0	0
$277$	−3.49544e52	−1.07198	−0.535991	−	0.844224i	$-0.680062\pi$
$277$	−3.49544e52	−1.07198	−0.535991	+	0.844224i	$0.680062\pi$
$278$	6.22714e52	1.76736
$279$	0	0
$280$	1.83831e52	0.447221
$281$	−2.62712e52	−0.591962	−0.295981	−	0.955194i	$-0.595647\pi$
$281$	−2.62712e52	−0.591962	−0.295981	+	0.955194i	$0.595647\pi$
$282$	0	0
$283$	7.08487e52	1.37064	0.685320	−	0.728242i	$-0.259662\pi$
$283$	7.08487e52	1.37064	0.685320	+	0.728242i	$0.259662\pi$
$284$	−7.70925e52	−1.38251
$285$	0	0
$286$	−1.29752e53	−2.00099
$287$	−4.32328e52	−0.618519
$288$	0	0
$289$	−4.58954e52	−0.565543
$290$	2.44776e53	2.80034
$291$	0	0
$292$	4.85617e52	0.479250
$293$	9.78673e52	0.897395	0.448698	−	0.893684i	$-0.351888\pi$
$293$	9.78673e52	0.897395	0.448698	+	0.893684i	$0.351888\pi$
$294$	0	0
$295$	1.02199e53	0.809607
$296$	8.98461e51	0.0661801
$297$	0	0
$298$	−2.89690e53	−1.84622
$299$	−1.63264e53	−0.968186
$300$	0	0
$301$	2.00269e53	1.02904
$302$	−3.45544e52	−0.165331
$303$	0	0
$304$	1.41891e53	0.589077
$305$	1.34566e53	0.520581
$306$	0	0
$307$	3.49196e53	1.17380	0.586899	−	0.809660i	$-0.300348\pi$
$307$	3.49196e53	1.17380	0.586899	+	0.809660i	$0.300348\pi$
$308$	−4.82123e53	−1.51119
$309$	0	0
$310$	1.86114e53	0.507578
$311$	−1.85544e53	−0.472170	−0.236085	−	0.971732i	$-0.575864\pi$
$311$	−1.85544e53	−0.472170	−0.236085	+	0.971732i	$0.575864\pi$
$312$	0	0
$313$	7.17292e53	1.59035	0.795175	−	0.606380i	$-0.207379\pi$
$313$	7.17292e53	1.59035	0.795175	+	0.606380i	$0.207379\pi$
$314$	7.30002e53	1.51125
$315$	0	0
$316$	−7.25752e53	−1.31074
$317$	7.25321e52	0.122393	0.0611964	−	0.998126i	$-0.480508\pi$
$317$	7.25321e52	0.122393	0.0611964	+	0.998126i	$0.480508\pi$
$318$	0	0
$319$	−1.72227e54	−2.53865
$320$	−1.36284e54	−1.87811
$321$	0	0
$322$	−1.05053e54	−1.26622
$323$	−6.90198e53	−0.778251
$324$	0	0
$325$	3.65473e53	0.360880
$326$	−9.21103e53	−0.851393
$327$	0	0
$328$	−6.58064e53	−0.533311
$329$	1.67905e54	1.27453
$330$	0	0
$331$	−6.34311e53	−0.422669	−0.211334	−	0.977414i	$-0.567781\pi$
$331$	−6.34311e53	−0.422669	−0.211334	+	0.977414i	$0.567781\pi$
$332$	−3.40540e54	−2.12667
$333$	0	0
$334$	−9.33477e53	−0.512336
$335$	3.50783e54	1.80541
$336$	0	0
$337$	2.65467e54	1.20218	0.601088	−	0.799183i	$-0.294734\pi$
$337$	2.65467e54	1.20218	0.601088	+	0.799183i	$0.294734\pi$
$338$	1.47670e54	0.627456
$339$	0	0
$340$	2.91700e54	1.09179
$341$	−1.30952e54	−0.460145
$342$	0	0
$343$	3.31883e54	1.02840
$344$	3.04837e54	0.887280
$345$	0	0
$346$	1.60149e54	0.411518
$347$	3.14107e54	0.758567	0.379284	−	0.925280i	$-0.376170\pi$
$347$	3.14107e54	0.758567	0.379284	+	0.925280i	$0.376170\pi$
$348$	0	0
$349$	−1.66164e54	−0.354643	−0.177321	−	0.984153i	$-0.556743\pi$
$349$	−1.66164e54	−0.354643	−0.177321	+	0.984153i	$0.556743\pi$
$350$	2.35167e54	0.471969
$351$	0	0
$352$	1.26766e55	2.25079
$353$	−6.16284e54	−1.02950	−0.514748	−	0.857342i	$-0.672114\pi$
$353$	−6.16284e54	−1.02950	−0.514748	+	0.857342i	$0.672114\pi$
$354$	0	0
$355$	−8.28757e54	−1.22608
$356$	9.57262e54	1.33308
$357$	0	0
$358$	−9.32964e54	−1.15181
$359$	−5.63280e54	−0.654929	−0.327464	−	0.944864i	$-0.606194\pi$
$359$	−5.63280e54	−0.654929	−0.327464	+	0.944864i	$0.606194\pi$
$360$	0	0
$361$	3.81948e54	0.394094
$362$	1.46105e55	1.42047
$363$	0	0
$364$	−7.96602e54	−0.687958
$365$	5.22046e54	0.425023
$366$	0	0
$367$	−6.57731e54	−0.476132	−0.238066	−	0.971249i	$-0.576514\pi$
$367$	−6.57731e54	−0.476132	−0.238066	+	0.971249i	$0.576514\pi$
$368$	9.19396e54	0.627732
$369$	0	0
$370$	3.60013e54	0.218767
$371$	−1.30394e55	−0.747685
$372$	0	0
$373$	−1.12137e55	−0.572807	−0.286404	−	0.958109i	$-0.592460\pi$
$373$	−1.12137e55	−0.572807	−0.286404	+	0.958109i	$0.592460\pi$
$374$	−3.55424e55	−1.71399
$375$	0	0
$376$	2.55575e55	1.09895
$377$	−2.84568e55	−1.15570
$378$	0	0
$379$	3.17152e54	0.114954	0.0574771	−	0.998347i	$-0.481694\pi$
$379$	3.17152e54	0.114954	0.0574771	+	0.998347i	$0.481694\pi$
$380$	−5.71030e55	−1.95574
$381$	0	0
$382$	−1.37882e55	−0.421837
$383$	−2.67653e55	−0.774102	−0.387051	−	0.922058i	$-0.626506\pi$
$383$	−2.67653e55	−0.774102	−0.387051	+	0.922058i	$0.626506\pi$
$384$	0	0
$385$	−5.18290e55	−1.34019
$386$	8.18899e55	2.00264
$387$	0	0
$388$	−2.74172e54	−0.0599985
$389$	4.96399e55	1.02781	0.513907	−	0.857846i	$-0.328198\pi$
$389$	4.96399e55	1.02781	0.513907	+	0.857846i	$0.328198\pi$
$390$	0	0
$391$	−4.47221e55	−0.829320
$392$	1.83827e55	0.322671
$393$	0	0
$394$	1.16320e56	1.83015
$395$	−7.80195e55	−1.16243
$396$	0	0
$397$	1.17506e56	1.57060	0.785300	−	0.619116i	$-0.212509\pi$
$397$	1.17506e56	1.57060	0.785300	+	0.619116i	$0.212509\pi$
$398$	1.01355e56	1.28339
$399$	0	0
$400$	−2.05811e55	−0.233980
$401$	1.22312e54	0.0131785	0.00658926	−	0.999978i	$-0.497903\pi$
$401$	1.22312e54	0.0131785	0.00658926	+	0.999978i	$0.497903\pi$
$402$	0	0
$403$	−2.16370e55	−0.209478
$404$	1.46741e54	0.0134695
$405$	0	0
$406$	−1.83108e56	−1.51146
$407$	−2.53310e55	−0.198323
$408$	0	0
$409$	1.58299e56	1.11539	0.557696	−	0.830045i	$-0.311686\pi$
$409$	1.58299e56	1.11539	0.557696	+	0.830045i	$0.311686\pi$
$410$	−2.63686e56	−1.76293
$411$	0	0
$412$	−1.85165e56	−1.11498
$413$	−7.64515e55	−0.436978
$414$	0	0
$415$	−3.66086e56	−1.88603
$416$	2.09452e56	1.02466
$417$	0	0
$418$	6.95776e56	3.07029
$419$	−8.93668e55	−0.374606	−0.187303	−	0.982302i	$-0.559975\pi$
$419$	−8.93668e55	−0.374606	−0.187303	+	0.982302i	$0.559975\pi$
$420$	0	0
$421$	−2.19258e56	−0.829641	−0.414821	−	0.909903i	$-0.636156\pi$
$421$	−2.19258e56	−0.829641	−0.414821	+	0.909903i	$0.636156\pi$
$422$	5.08027e56	1.82671
$423$	0	0
$424$	−1.98478e56	−0.644683
$425$	1.00112e56	0.309119
$426$	0	0
$427$	−1.00664e56	−0.280979
$428$	4.66577e56	1.23846
$429$	0	0
$430$	1.22148e57	2.93302
$431$	−3.47761e55	−0.0794364	−0.0397182	−	0.999211i	$-0.512646\pi$
$431$	−3.47761e55	−0.0794364	−0.0397182	+	0.999211i	$0.512646\pi$
$432$	0	0
$433$	2.55606e56	0.528545	0.264272	−	0.964448i	$-0.414868\pi$
$433$	2.55606e56	0.528545	0.264272	+	0.964448i	$0.414868\pi$
$434$	−1.39225e56	−0.273961
$435$	0	0
$436$	−7.91085e56	−1.41014
$437$	8.75478e56	1.48557
$438$	0	0
$439$	−6.27063e56	−0.964548	−0.482274	−	0.876020i	$-0.660189\pi$
$439$	−6.27063e56	−0.964548	−0.482274	+	0.876020i	$0.660189\pi$
$440$	−7.88911e56	−1.15557
$441$	0	0
$442$	−5.87259e56	−0.780281
$443$	2.70311e55	0.0342124	0.0171062	−	0.999854i	$-0.494555\pi$
$443$	2.70311e55	0.0342124	0.0171062	+	0.999854i	$0.494555\pi$
$444$	0	0
$445$	1.02907e57	1.18224
$446$	−3.70118e56	−0.405173
$447$	0	0
$448$	1.01949e57	1.01370
$449$	−1.72989e57	−1.63954	−0.819768	−	0.572696i	$-0.805898\pi$
$449$	−1.72989e57	−1.63954	−0.819768	+	0.572696i	$0.805898\pi$
$450$	0	0
$451$	1.85533e57	1.59818
$452$	−1.49696e56	−0.122952
$453$	0	0
$454$	−1.59715e57	−1.19301
$455$	−8.56360e56	−0.610115
$456$	0	0
$457$	−9.95087e56	−0.645153	−0.322577	−	0.946543i	$-0.604549\pi$
$457$	−9.95087e56	−0.645153	−0.322577	+	0.946543i	$0.604549\pi$
$458$	−2.69809e57	−1.66897
$459$	0	0
$460$	−3.70005e57	−2.08408
$461$	1.80262e57	0.969025	0.484512	−	0.874784i	$-0.338997\pi$
$461$	1.80262e57	0.969025	0.484512	+	0.874784i	$0.338997\pi$
$462$	0	0
$463$	2.20081e57	1.07793	0.538965	−	0.842328i	$-0.318815\pi$
$463$	2.20081e57	1.07793	0.538965	+	0.842328i	$0.318815\pi$
$464$	1.60250e57	0.749311
$465$	0	0
$466$	−4.40593e57	−1.87819
$467$	−3.37955e57	−1.37577	−0.687885	−	0.725820i	$-0.741461\pi$
$467$	−3.37955e57	−1.37577	−0.687885	+	0.725820i	$0.741461\pi$
$468$	0	0
$469$	−2.62408e57	−0.974453
$470$	1.02409e58	3.63273
$471$	0	0
$472$	−1.16370e57	−0.376780
$473$	−8.59450e57	−2.65893
$474$	0	0
$475$	−1.95980e57	−0.553730
$476$	−2.18210e57	−0.589284
$477$	0	0
$478$	9.60095e57	2.36927
$479$	−1.37561e57	−0.324551	−0.162275	−	0.986746i	$-0.551883\pi$
$479$	−1.37561e57	−0.324551	−0.162275	+	0.986746i	$0.551883\pi$
$480$	0	0
$481$	−4.18539e56	−0.0902852
$482$	6.18925e57	1.27681
$483$	0	0
$484$	1.34487e58	2.53808
$485$	−2.94739e56	−0.0532096
$486$	0	0
$487$	4.03185e57	0.666242	0.333121	−	0.942884i	$-0.391898\pi$
$487$	4.03185e57	0.666242	0.333121	+	0.942884i	$0.391898\pi$
$488$	−1.53224e57	−0.242271
$489$	0	0
$490$	7.36596e57	1.06663
$491$	1.20430e58	1.66910	0.834552	−	0.550929i	$-0.185726\pi$
$491$	1.20430e58	1.66910	0.834552	+	0.550929i	$0.185726\pi$
$492$	0	0
$493$	−7.79504e57	−0.989942
$494$	1.14962e58	1.39773
$495$	0	0
$496$	1.21846e57	0.135817
$497$	6.19963e57	0.661764
$498$	0	0
$499$	−1.80912e58	−1.77135	−0.885675	−	0.464305i	$-0.846304\pi$
$499$	−1.80912e58	−1.77135	−0.885675	+	0.464305i	$0.846304\pi$
$500$	−9.37850e57	−0.879586
$501$	0	0
$502$	7.49238e57	0.644896
$503$	−1.83848e58	−1.51617	−0.758084	−	0.652157i	$-0.773864\pi$
$503$	−1.83848e58	−1.51617	−0.758084	+	0.652157i	$0.773864\pi$
$504$	0	0
$505$	1.57749e56	0.0119454
$506$	4.50836e58	3.27177
$507$	0	0
$508$	6.28566e57	0.419065
$509$	−2.58706e58	−1.65338	−0.826691	−	0.562656i	$-0.809780\pi$
$509$	−2.58706e58	−1.65338	−0.826691	+	0.562656i	$0.809780\pi$
$510$	0	0
$511$	−3.90523e57	−0.229402
$512$	−1.67913e58	−0.945760
$513$	0	0
$514$	−2.78408e57	−0.144203
$515$	−1.99055e58	−0.988823
$516$	0	0
$517$	−7.20561e58	−3.29325
$518$	−2.69313e57	−0.118077
$519$	0	0
$520$	−1.30350e58	−0.526065
$521$	1.15962e58	0.449059	0.224530	−	0.974467i	$-0.427915\pi$
$521$	1.15962e58	0.449059	0.224530	+	0.974467i	$0.427915\pi$
$522$	0	0
$523$	4.11381e58	1.46709	0.733547	−	0.679639i	$-0.237863\pi$
$523$	4.11381e58	1.46709	0.733547	+	0.679639i	$0.237863\pi$
$524$	2.38017e58	0.814677
$525$	0	0
$526$	1.28543e58	0.405372
$527$	−5.92693e57	−0.179433
$528$	0	0
$529$	2.08934e58	0.583059
$530$	−7.95300e58	−2.13108
$531$	0	0
$532$	4.27167e58	1.05559
$533$	3.06553e58	0.727562
$534$	0	0
$535$	5.01578e58	1.09833
$536$	−3.99422e58	−0.840211
$537$	0	0
$538$	−2.86619e58	−0.556527
$539$	−5.18279e58	−0.966952
$540$	0	0
$541$	−7.75327e58	−1.33581	−0.667903	−	0.744248i	$-0.732808\pi$
$541$	−7.75327e58	−1.33581	−0.667903	+	0.744248i	$0.732808\pi$
$542$	1.41729e59	2.34680
$543$	0	0
$544$	5.73743e58	0.877690
$545$	−8.50429e58	−1.25059
$546$	0	0
$547$	2.55610e58	0.347416	0.173708	−	0.984797i	$-0.444425\pi$
$547$	2.55610e58	0.347416	0.173708	+	0.984797i	$0.444425\pi$
$548$	−8.47449e58	−1.10747
$549$	0	0
$550$	−1.00922e59	−1.21951
$551$	1.52595e59	1.77330
$552$	0	0
$553$	5.83636e58	0.627410
$554$	1.59483e59	1.64913
$555$	0	0
$556$	−1.64068e59	−1.57006
$557$	−5.65846e58	−0.520969	−0.260484	−	0.965478i	$-0.583882\pi$
$557$	−5.65846e58	−0.520969	−0.260484	+	0.965478i	$0.583882\pi$
$558$	0	0
$559$	−1.42005e59	−1.21046
$560$	4.82247e58	0.395573
$561$	0	0
$562$	1.19865e59	0.910670
$563$	−1.84272e59	−1.34750	−0.673751	−	0.738958i	$-0.735318\pi$
$563$	−1.84272e59	−1.34750	−0.673751	+	0.738958i	$0.735318\pi$
$564$	0	0
$565$	−1.60926e58	−0.109039
$566$	−3.23254e59	−2.10858
$567$	0	0
$568$	9.43670e58	0.570599
$569$	2.36928e59	1.37944	0.689719	−	0.724077i	$-0.257734\pi$
$569$	2.36928e59	1.37944	0.689719	+	0.724077i	$0.257734\pi$
$570$	0	0
$571$	2.07972e59	1.12287	0.561433	−	0.827522i	$-0.310250\pi$
$571$	2.07972e59	1.12287	0.561433	+	0.827522i	$0.310250\pi$
$572$	3.41861e59	1.77760
$573$	0	0
$574$	1.97254e59	0.951525
$575$	−1.26987e59	−0.590066
$576$	0	0
$577$	2.08396e59	0.898688	0.449344	−	0.893359i	$-0.351658\pi$
$577$	2.08396e59	0.898688	0.449344	+	0.893359i	$0.351658\pi$
$578$	2.09402e59	0.870027
$579$	0	0
$580$	−6.44917e59	−2.48772
$581$	2.73856e59	1.01797
$582$	0	0
$583$	5.59584e59	1.93193
$584$	−5.94431e58	−0.197800
$585$	0	0
$586$	−4.46529e59	−1.38055
$587$	−2.73977e58	−0.0816574	−0.0408287	−	0.999166i	$-0.513000\pi$
$587$	−2.73977e58	−0.0816574	−0.0408287	+	0.999166i	$0.513000\pi$
$588$	0	0
$589$	1.16025e59	0.321421
$590$	−4.66294e59	−1.24549
$591$	0	0
$592$	2.35694e58	0.0585372
$593$	−2.35256e58	−0.0563462	−0.0281731	−	0.999603i	$-0.508969\pi$
$593$	−2.35256e58	−0.0563462	−0.0281731	+	0.999603i	$0.508969\pi$
$594$	0	0
$595$	−2.34579e59	−0.522606
$596$	7.63254e59	1.64012
$597$	0	0
$598$	7.44906e59	1.48945
$599$	1.14383e59	0.220641	0.110320	−	0.993896i	$-0.464812\pi$
$599$	1.14383e59	0.220641	0.110320	+	0.993896i	$0.464812\pi$
$600$	0	0
$601$	1.46354e59	0.262787	0.131393	−	0.991330i	$-0.458055\pi$
$601$	1.46354e59	0.262787	0.131393	+	0.991330i	$0.458055\pi$
$602$	−9.13745e59	−1.58307
$603$	0	0
$604$	9.10414e58	0.146874
$605$	1.44576e60	2.25089
$606$	0	0
$607$	−5.45219e59	−0.790705	−0.395352	−	0.918530i	$-0.629378\pi$
$607$	−5.45219e59	−0.790705	−0.395352	+	0.918530i	$0.629378\pi$
$608$	−1.12316e60	−1.57222
$609$	0	0
$610$	−6.13970e59	−0.800858
$611$	−1.19057e60	−1.49923
$612$	0	0
$613$	−1.00661e60	−1.18158	−0.590790	−	0.806826i	$-0.701184\pi$
$613$	−1.00661e60	−1.18158	−0.590790	+	0.806826i	$0.701184\pi$
$614$	−1.59324e60	−1.80576
$615$	0	0
$616$	5.90155e59	0.623708
$617$	1.26792e60	1.29408	0.647038	−	0.762458i	$-0.276008\pi$
$617$	1.26792e60	1.29408	0.647038	+	0.762458i	$0.276008\pi$
$618$	0	0
$619$	−8.28879e59	−0.789119	−0.394559	−	0.918870i	$-0.629103\pi$
$619$	−8.28879e59	−0.789119	−0.394559	+	0.918870i	$0.629103\pi$
$620$	−4.90360e59	−0.450914
$621$	0	0
$622$	8.46562e59	0.726382
$623$	−7.69811e59	−0.638104
$624$	0	0
$625$	−1.61434e60	−1.24904
$626$	−3.27271e60	−2.44658
$627$	0	0
$628$	−1.92336e60	−1.34254
$629$	−1.14649e59	−0.0773356
$630$	0	0
$631$	2.76062e60	1.73930	0.869650	−	0.493668i	$-0.164344\pi$
$631$	2.76062e60	1.73930	0.869650	+	0.493668i	$0.164344\pi$
$632$	8.88375e59	0.540977
$633$	0	0
$634$	−3.30935e59	−0.188288
$635$	6.75719e59	0.371647
$636$	0	0
$637$	−8.56341e59	−0.440199
$638$	7.85805e60	3.90544
$639$	0	0
$640$	2.74479e60	1.27538
$641$	2.57952e60	1.15902	0.579510	−	0.814965i	$-0.303244\pi$
$641$	2.57952e60	1.15902	0.579510	+	0.814965i	$0.303244\pi$
$642$	0	0
$643$	−9.94946e59	−0.418084	−0.209042	−	0.977907i	$-0.567035\pi$
$643$	−9.94946e59	−0.418084	−0.209042	+	0.977907i	$0.567035\pi$
$644$	2.76787e60	1.12486
$645$	0	0
$646$	3.14910e60	1.19726
$647$	9.07848e59	0.333865	0.166933	−	0.985968i	$-0.446614\pi$
$647$	9.07848e59	0.333865	0.166933	+	0.985968i	$0.446614\pi$
$648$	0	0
$649$	3.28091e60	1.12910
$650$	−1.66751e60	−0.555175
$651$	0	0
$652$	2.42686e60	0.756346
$653$	−3.98516e60	−1.20175	−0.600873	−	0.799344i	$-0.705180\pi$
$653$	−3.98516e60	−1.20175	−0.600873	+	0.799344i	$0.705180\pi$
$654$	0	0
$655$	2.55872e60	0.722496
$656$	−1.72631e60	−0.471722
$657$	0	0
$658$	−7.66082e60	−1.96073
$659$	−7.30688e60	−1.81007	−0.905035	−	0.425337i	$-0.860156\pi$
$659$	−7.30688e60	−1.81007	−0.905035	+	0.425337i	$0.860156\pi$
$660$	0	0
$661$	6.34402e59	0.147243	0.0736213	−	0.997286i	$-0.476544\pi$
$661$	6.34402e59	0.147243	0.0736213	+	0.997286i	$0.476544\pi$
$662$	2.89410e60	0.650231
$663$	0	0
$664$	4.16847e60	0.877734
$665$	4.59211e60	0.936153
$666$	0	0
$667$	9.88758e60	1.88966
$668$	2.45946e60	0.455140
$669$	0	0
$670$	−1.60048e61	−2.77742
$671$	4.31998e60	0.726018
$672$	0	0
$673$	−1.08068e61	−1.70363	−0.851814	−	0.523845i	$-0.824497\pi$
$673$	−1.08068e61	−1.70363	−0.851814	+	0.523845i	$0.824497\pi$
$674$	−1.21122e61	−1.84942
$675$	0	0
$676$	−3.89070e60	−0.557409
$677$	7.78512e60	1.08046	0.540230	−	0.841517i	$-0.318337\pi$
$677$	7.78512e60	1.08046	0.540230	+	0.841517i	$0.318337\pi$
$678$	0	0
$679$	2.20484e59	0.0287194
$680$	−3.57062e60	−0.450612
$681$	0	0
$682$	5.97483e60	0.707883
$683$	1.04731e61	1.20235	0.601174	−	0.799118i	$-0.294700\pi$
$683$	1.04731e61	1.20235	0.601174	+	0.799118i	$0.294700\pi$
$684$	0	0
$685$	−9.11022e60	−0.982158
$686$	−1.51425e61	−1.58208
$687$	0	0
$688$	7.99682e60	0.784812
$689$	9.24589e60	0.879499
$690$	0	0
$691$	9.34628e60	0.835335	0.417668	−	0.908600i	$-0.362848\pi$
$691$	9.34628e60	0.835335	0.417668	+	0.908600i	$0.362848\pi$
$692$	−4.21949e60	−0.365577
$693$	0	0
$694$	−1.43314e61	−1.16697
$695$	−1.76376e61	−1.39241
$696$	0	0
$697$	8.39727e60	0.623208
$698$	7.58141e60	0.545580
$699$	0	0
$700$	−6.19600e60	−0.419280
$701$	−1.17846e61	−0.773356	−0.386678	−	0.922215i	$-0.626377\pi$
$701$	−1.17846e61	−0.773356	−0.386678	+	0.922215i	$0.626377\pi$
$702$	0	0
$703$	2.24436e60	0.138533
$704$	−4.37515e61	−2.61927
$705$	0	0
$706$	2.81185e61	1.58377
$707$	−1.18006e59	−0.00644745
$708$	0	0
$709$	−2.12559e61	−1.09291	−0.546457	−	0.837487i	$-0.684024\pi$
$709$	−2.12559e61	−1.09291	−0.546457	+	0.837487i	$0.684024\pi$
$710$	3.78128e61	1.88619
$711$	0	0
$712$	−1.17176e61	−0.550198
$713$	7.51798e60	0.342512
$714$	0	0
$715$	3.67506e61	1.57647
$716$	2.45810e61	1.02322
$717$	0	0
$718$	2.57002e61	1.00754
$719$	2.58349e61	0.982960	0.491480	−	0.870889i	$-0.336456\pi$
$719$	2.58349e61	0.982960	0.491480	+	0.870889i	$0.336456\pi$
$720$	0	0
$721$	1.48906e61	0.533709
$722$	−1.74267e61	−0.606271
$723$	0	0
$724$	−3.84947e61	−1.26189
$725$	−2.21338e61	−0.704350
$726$	0	0
$727$	−7.14277e59	−0.0214228	−0.0107114	−	0.999943i	$-0.503410\pi$
$727$	−7.14277e59	−0.0214228	−0.0107114	+	0.999943i	$0.503410\pi$
$728$	9.75101e60	0.283939
$729$	0	0
$730$	−2.38188e61	−0.653852
$731$	−3.88988e61	−1.03684
$732$	0	0
$733$	−5.72283e61	−1.43839	−0.719193	−	0.694811i	$-0.755488\pi$
$733$	−5.72283e61	−1.43839	−0.719193	+	0.694811i	$0.755488\pi$
$734$	3.00096e61	0.732479
$735$	0	0
$736$	−7.27761e61	−1.67539
$737$	1.12612e62	2.51787
$738$	0	0
$739$	−5.83871e61	−1.23158	−0.615788	−	0.787912i	$-0.711162\pi$
$739$	−5.83871e61	−1.23158	−0.615788	+	0.787912i	$0.711162\pi$
$740$	−9.48536e60	−0.194344
$741$	0	0
$742$	5.94935e61	1.15023
$743$	−9.77520e61	−1.83597	−0.917987	−	0.396611i	$-0.870186\pi$
$743$	−9.77520e61	−1.83597	−0.917987	+	0.396611i	$0.870186\pi$
$744$	0	0
$745$	8.20510e61	1.45454
$746$	5.11635e61	0.881202
$747$	0	0
$748$	9.36445e61	1.52264
$749$	−3.75212e61	−0.592813
$750$	0	0
$751$	−2.27440e61	−0.339319	−0.169659	−	0.985503i	$-0.554267\pi$
$751$	−2.27440e61	−0.339319	−0.169659	+	0.985503i	$0.554267\pi$
$752$	6.70452e61	0.972040
$753$	0	0
$754$	1.29837e62	1.77793
$755$	9.78710e60	0.130255
$756$	0	0
$757$	−2.28350e61	−0.287104	−0.143552	−	0.989643i	$-0.545852\pi$
$757$	−2.28350e61	−0.287104	−0.143552	+	0.989643i	$0.545852\pi$
$758$	−1.44704e61	−0.176845
$759$	0	0
$760$	6.98984e61	0.807188
$761$	−8.53778e61	−0.958462	−0.479231	−	0.877689i	$-0.659084\pi$
$761$	−8.53778e61	−0.958462	−0.479231	+	0.877689i	$0.659084\pi$
$762$	0	0
$763$	6.36175e61	0.674993
$764$	3.63281e61	0.374745
$765$	0	0
$766$	1.22119e62	1.19087
$767$	5.42097e61	0.514016
$768$	0	0
$769$	−1.13257e62	−1.01542	−0.507712	−	0.861527i	$-0.669509\pi$
$769$	−1.13257e62	−1.01542	−0.507712	+	0.861527i	$0.669509\pi$
$770$	2.36475e62	2.06174
$771$	0	0
$772$	−2.15758e62	−1.77907
$773$	−2.18119e62	−1.74918	−0.874588	−	0.484866i	$-0.838868\pi$
$773$	−2.18119e62	−1.74918	−0.874588	+	0.484866i	$0.838868\pi$
$774$	0	0
$775$	−1.68293e61	−0.127667
$776$	3.35607e60	0.0247630
$777$	0	0
$778$	−2.26487e62	−1.58118
$779$	−1.64385e62	−1.11636
$780$	0	0
$781$	−2.66056e62	−1.70992
$782$	2.04049e62	1.27582
$783$	0	0
$784$	4.82236e61	0.285407
$785$	−2.06764e62	−1.19063
$786$	0	0
$787$	3.94168e61	0.214894	0.107447	−	0.994211i	$-0.465732\pi$
$787$	3.94168e61	0.214894	0.107447	+	0.994211i	$0.465732\pi$
$788$	−3.06472e62	−1.62584
$789$	0	0
$790$	3.55972e62	1.78827
$791$	1.20383e61	0.0588531
$792$	0	0
$793$	7.13781e61	0.330515
$794$	−5.36134e62	−2.41620
$795$	0	0
$796$	−2.67043e62	−1.14012
$797$	1.85308e62	0.770087	0.385043	−	0.922898i	$-0.374186\pi$
$797$	1.85308e62	0.770087	0.385043	+	0.922898i	$0.374186\pi$
$798$	0	0
$799$	−3.26127e62	−1.28420
$800$	1.62913e62	0.624482
$801$	0	0
$802$	−5.58062e60	−0.0202737
$803$	1.67593e62	0.592749
$804$	0	0
$805$	2.97551e62	0.997584
$806$	9.87209e61	0.322259
$807$	0	0
$808$	−1.79622e60	−0.00555924
$809$	−2.89492e62	−0.872455	−0.436228	−	0.899836i	$-0.643686\pi$
$809$	−2.89492e62	−0.872455	−0.436228	+	0.899836i	$0.643686\pi$
$810$	0	0
$811$	−3.86441e62	−1.10442	−0.552211	−	0.833704i	$-0.686216\pi$
$811$	−3.86441e62	−1.10442	−0.552211	+	0.833704i	$0.686216\pi$
$812$	4.82439e62	1.34273
$813$	0	0
$814$	1.15575e62	0.305098
$815$	2.60891e62	0.670765
$816$	0	0
$817$	7.61482e62	1.85732
$818$	−7.22255e62	−1.71591
$819$	0	0
$820$	6.94741e62	1.56612
$821$	7.00271e62	1.53776	0.768880	−	0.639394i	$-0.220815\pi$
$821$	7.00271e62	1.53776	0.768880	+	0.639394i	$0.220815\pi$
$822$	0	0
$823$	−6.16948e62	−1.28574	−0.642868	−	0.765977i	$-0.722256\pi$
$823$	−6.16948e62	−1.28574	−0.642868	+	0.765977i	$0.722256\pi$
$824$	2.26656e62	0.460185
$825$	0	0
$826$	3.48817e62	0.672244
$827$	1.18524e62	0.222555	0.111277	−	0.993789i	$-0.464506\pi$
$827$	1.18524e62	0.222555	0.111277	+	0.993789i	$0.464506\pi$
$828$	0	0
$829$	5.09313e62	0.907951	0.453976	−	0.891014i	$-0.350005\pi$
$829$	5.09313e62	0.907951	0.453976	+	0.891014i	$0.350005\pi$
$830$	1.67030e63	2.90146
$831$	0	0
$832$	−7.22896e62	−1.19241
$833$	−2.34574e62	−0.377061
$834$	0	0
$835$	2.64396e62	0.403641
$836$	−1.83318e63	−2.72754
$837$	0	0
$838$	4.07745e62	0.576291
$839$	1.03721e63	1.42884	0.714422	−	0.699715i	$-0.246690\pi$
$839$	1.03721e63	1.42884	0.714422	+	0.699715i	$0.246690\pi$
$840$	0	0
$841$	9.59365e62	1.25565
$842$	1.00039e63	1.27631
$843$	0	0
$844$	−1.33851e63	−1.62278
$845$	−4.18257e62	−0.494338
$846$	0	0
$847$	−1.08152e63	−1.21490
$848$	−5.20669e62	−0.570231
$849$	0	0
$850$	−4.56773e62	−0.475547
$851$	1.45425e62	0.147623
$852$	0	0
$853$	6.46285e62	0.623764	0.311882	−	0.950121i	$-0.399041\pi$
$853$	6.46285e62	0.623764	0.311882	+	0.950121i	$0.399041\pi$
$854$	4.59289e62	0.432256
$855$	0	0
$856$	−5.71126e62	−0.511147
$857$	3.89227e62	0.339715	0.169858	−	0.985469i	$-0.445669\pi$
$857$	3.89227e62	0.339715	0.169858	+	0.985469i	$0.445669\pi$
$858$	0	0
$859$	5.04634e62	0.418913	0.209456	−	0.977818i	$-0.432831\pi$
$859$	5.04634e62	0.418913	0.209456	+	0.977818i	$0.432831\pi$
$860$	−3.21827e63	−2.60558
$861$	0	0
$862$	1.58669e62	0.122204
$863$	−9.68552e62	−0.727597	−0.363799	−	0.931478i	$-0.618520\pi$
$863$	−9.68552e62	−0.727597	−0.363799	+	0.931478i	$0.618520\pi$
$864$	0	0
$865$	−4.53602e62	−0.324212
$866$	−1.16623e63	−0.813109
$867$	0	0
$868$	3.66820e62	0.243377
$869$	−2.50466e63	−1.62115
$870$	0	0
$871$	1.86066e63	1.14625
$872$	9.68348e62	0.582005
$873$	0	0
$874$	−3.99445e63	−2.28540
$875$	7.54200e62	0.421031
$876$	0	0
$877$	−6.26532e61	−0.0333006	−0.0166503	−	0.999861i	$-0.505300\pi$
$877$	−6.26532e61	−0.0333006	−0.0166503	+	0.999861i	$0.505300\pi$
$878$	2.86104e63	1.48385
$879$	0	0
$880$	−2.06956e63	−1.02212
$881$	3.44233e61	0.0165909	0.00829546	−	0.999966i	$-0.497359\pi$
$881$	3.44233e61	0.0165909	0.00829546	+	0.999966i	$0.497359\pi$
$882$	0	0
$883$	3.56652e62	0.163715	0.0818576	−	0.996644i	$-0.473915\pi$
$883$	3.56652e62	0.163715	0.0818576	+	0.996644i	$0.473915\pi$
$884$	1.54727e63	0.693173
$885$	0	0
$886$	−1.23332e62	−0.0526321
$887$	1.11406e63	0.464035	0.232017	−	0.972712i	$-0.425467\pi$
$887$	1.11406e63	0.464035	0.232017	+	0.972712i	$0.425467\pi$
$888$	0	0
$889$	−5.05481e62	−0.200593
$890$	−4.69524e63	−1.81875
$891$	0	0
$892$	9.75159e62	0.359941
$893$	6.38425e63	2.30040
$894$	0	0
$895$	2.64250e63	0.907445
$896$	−2.05328e63	−0.688375
$897$	0	0
$898$	7.89277e63	2.52225
$899$	1.31038e63	0.408850
$900$	0	0
$901$	2.53269e63	0.753353
$902$	−8.46513e63	−2.45863
$903$	0	0
$904$	1.83239e62	0.0507455
$905$	−4.13824e63	−1.11911
$906$	0	0
$907$	−4.75180e63	−1.22547	−0.612734	−	0.790289i	$-0.709930\pi$
$907$	−4.75180e63	−1.22547	−0.612734	+	0.790289i	$0.709930\pi$
$908$	4.20805e63	1.05983
$909$	0	0
$910$	3.90723e63	0.938596
$911$	4.95250e63	1.16193	0.580964	−	0.813929i	$-0.302676\pi$
$911$	4.95250e63	1.16193	0.580964	+	0.813929i	$0.302676\pi$
$912$	0	0
$913$	−1.17525e64	−2.63032
$914$	4.54018e63	0.992499
$915$	0	0
$916$	7.10873e63	1.48265
$917$	−1.91409e63	−0.389961
$918$	0	0
$919$	−2.19827e63	−0.427364	−0.213682	−	0.976903i	$-0.568546\pi$
$919$	−2.19827e63	−0.427364	−0.213682	+	0.976903i	$0.568546\pi$
$920$	4.52914e63	0.860156
$921$	0	0
$922$	−8.22464e63	−1.49074
$923$	−4.39599e63	−0.778431
$924$	0	0
$925$	−3.25541e62	−0.0550248
$926$	−1.00414e64	−1.65828
$927$	0	0
$928$	−1.26848e64	−1.99988
$929$	8.33744e62	0.128438	0.0642192	−	0.997936i	$-0.479544\pi$
$929$	8.33744e62	0.128438	0.0642192	+	0.997936i	$0.479544\pi$
$930$	0	0
$931$	4.59201e63	0.675437
$932$	1.16084e64	1.66852
$933$	0	0
$934$	1.54195e64	2.11647
$935$	1.00669e64	1.35035
$936$	0	0
$937$	1.31192e64	1.68077	0.840383	−	0.541993i	$-0.182330\pi$
$937$	1.31192e64	1.68077	0.840383	+	0.541993i	$0.182330\pi$
$938$	1.19726e64	1.49909
$939$	0	0
$940$	−2.69819e64	−3.22718
$941$	−1.09648e64	−1.28181	−0.640905	−	0.767620i	$-0.721441\pi$
$941$	−1.09648e64	−1.28181	−0.640905	+	0.767620i	$0.721441\pi$
$942$	0	0
$943$	−1.06515e64	−1.18962
$944$	−3.05274e63	−0.333267
$945$	0	0
$946$	3.92132e64	4.09047
$947$	−4.97351e62	−0.0507152	−0.0253576	−	0.999678i	$-0.508072\pi$
$947$	−4.97351e62	−0.0507152	−0.0253576	+	0.999678i	$0.508072\pi$
$948$	0	0
$949$	2.76910e63	0.269845
$950$	8.94176e63	0.851855
$951$	0	0
$952$	2.67105e63	0.243214
$953$	1.25621e64	1.11832	0.559160	−	0.829060i	$-0.311124\pi$
$953$	1.25621e64	1.11832	0.559160	+	0.829060i	$0.311124\pi$
$954$	0	0
$955$	3.90533e63	0.332342
$956$	−2.52959e64	−2.10477
$957$	0	0
$958$	6.27636e63	0.499286
$959$	6.81502e63	0.530112
$960$	0	0
$961$	−1.24484e64	−0.925894
$962$	1.90962e63	0.138894
$963$	0	0
$964$	−1.63070e64	−1.13427
$965$	−2.31943e64	−1.57777
$966$	0	0
$967$	−1.92657e63	−0.125347	−0.0626737	−	0.998034i	$-0.519963\pi$
$967$	−1.92657e63	−0.125347	−0.0626737	+	0.998034i	$0.519963\pi$
$968$	−1.64622e64	−1.04753
$969$	0	0
$970$	1.34478e63	0.0818573
$971$	−1.82399e64	−1.08595	−0.542973	−	0.839750i	$-0.682701\pi$
$971$	−1.82399e64	−1.08595	−0.542973	+	0.839750i	$0.682701\pi$
$972$	0	0
$973$	1.31940e64	0.751540
$974$	−1.83957e64	−1.02494
$975$	0	0
$976$	−4.01956e63	−0.214292
$977$	2.86004e64	1.49155	0.745776	−	0.666197i	$-0.232079\pi$
$977$	2.86004e64	1.49155	0.745776	+	0.666197i	$0.232079\pi$
$978$	0	0
$979$	3.30364e64	1.64879
$980$	−1.94073e64	−0.947554
$981$	0	0
$982$	−5.49475e64	−2.56774
$983$	−2.49132e64	−1.13901	−0.569507	−	0.821986i	$-0.692866\pi$
$983$	−2.49132e64	−1.13901	−0.569507	+	0.821986i	$0.692866\pi$
$984$	0	0
$985$	−3.29462e64	−1.44187
$986$	3.55656e64	1.52292
$987$	0	0
$988$	−3.02893e64	−1.24169
$989$	4.93411e64	1.97919
$990$	0	0
$991$	2.27461e63	0.0873620	0.0436810	−	0.999046i	$-0.486091\pi$
$991$	2.27461e63	0.0873620	0.0436810	+	0.999046i	$0.486091\pi$
$992$	−9.64487e63	−0.362490
$993$	0	0
$994$	−2.82864e64	−1.01805
$995$	−2.87076e64	−1.01111
$996$	0	0
$997$	3.04681e64	1.02778	0.513890	−	0.857856i	$-0.328204\pi$
$997$	3.04681e64	1.02778	0.513890	+	0.857856i	$0.328204\pi$
$998$	8.25426e64	2.72503
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	9.44.a.a.1.1		3
3.2	odd	2		3.44.a.a.1.3	✓	3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
3.44.a.a.1.3	✓	3	3.2	odd	2
9.44.a.a.1.1		3	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:	\( N \)	\(=\)	\( 9 = 3^{2} \)
Weight:	\( k \)	\(=\)	\( 44 \)
Character orbit:	\([\chi]\)	\(=\)	9.a (trivial)

\(f(q)\)	\(=\)	\(q-4.56260e6 q^{2} +1.20212e13 q^{4} +1.29230e15 q^{5} -9.66721e17 q^{7} -1.47149e19 q^{8} +O(q^{10})\)	\(q-4.56260e6 q^{2} +1.20212e13 q^{4} +1.29230e15 q^{5} -9.66721e17 q^{7} -1.47149e19 q^{8} -5.89624e21 q^{10} +4.14867e22 q^{11} +6.85476e23 q^{13} +4.41076e24 q^{14} -3.86016e25 q^{16} +1.87770e26 q^{17} -3.67577e27 q^{19} +1.55350e28 q^{20} -1.89287e29 q^{22} -2.38175e29 q^{23} +5.33166e29 q^{25} -3.12755e30 q^{26} -1.16211e31 q^{28} -4.15139e31 q^{29} -3.15649e31 q^{31} +3.05557e32 q^{32} -8.56717e32 q^{34} -1.24929e33 q^{35} -6.10581e32 q^{37} +1.67711e34 q^{38} -1.90160e34 q^{40} +4.47211e34 q^{41} -2.07163e35 q^{43} +4.98720e35 q^{44} +1.08670e36 q^{46} -1.73685e36 q^{47} -1.24926e36 q^{49} -2.43262e36 q^{50} +8.24025e36 q^{52} +1.34883e37 q^{53} +5.36132e37 q^{55} +1.42252e37 q^{56} +1.89411e38 q^{58} +7.90833e37 q^{59} +1.04129e38 q^{61} +1.44018e38 q^{62} -1.05459e39 q^{64} +8.85840e38 q^{65} +2.71441e39 q^{67} +2.25722e39 q^{68} +5.70002e39 q^{70} -6.41305e39 q^{71} +4.03967e39 q^{73} +2.78583e39 q^{74} -4.41872e40 q^{76} -4.01061e40 q^{77} -6.03727e40 q^{79} -4.98848e40 q^{80} -2.04044e41 q^{82} -2.83283e41 q^{83} +2.42654e41 q^{85} +9.45200e41 q^{86} -6.10471e41 q^{88} +7.96312e41 q^{89} -6.62665e41 q^{91} -2.86315e42 q^{92} +7.92454e42 q^{94} -4.75019e42 q^{95} -2.28074e41 q^{97} +5.69989e42 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q - 4857024 q^{2} - 1781058029568 q^{4} + 507753321105270 q^{5} - 16\!\cdots\!88 q^{7}+ \cdots - 11\!\cdots\!56 q^{8}+O(q^{10}) \) 3 * q - 4857024 * q^2 - 1781058029568 * q^4 + 507753321105270 * q^5 - 1633169303707089288 * q^7 - 11196260694472851456 * q^8	\( 3 q - 4857024 q^{2} - 1781058029568 q^{4} + 507753321105270 q^{5} - 16\!\cdots\!88 q^{7}+ \cdots + 20\!\cdots\!60 q^{98}+O(q^{100}) \) 3 * q - 4857024 * q^2 - 1781058029568 * q^4 + 507753321105270 * q^5 - 1633169303707089288 * q^7 - 11196260694472851456 * q^8 - 2286850690696789595520 * q^10 + 27750966261606959036820 * q^11 - 994786398159560287290750 * q^13 + 9473256819232835003171328 * q^14 + 23637690650696707825729536 * q^16 + 160517621023312837046953482 * q^17 - 3227133683900578441639486764 * q^19 + 19920520041146285724571791360 * q^20 - 172470540148626161048719521024 * q^22 - 114780279514038504224277444504 * q^23 + 1825420275602850437617559193525 * q^25 - 1775037275334840765729836075136 * q^26 - 8483554335441104836174737260544 * q^28 + 28241588775620253186792106789758 * q^29 - 56947467162250619768506214477136 * q^31 + 290372748061904590918491662450688 * q^32 - 1778246324363072918021693922216576 * q^34 + 3641689125493658442558484764497520 * q^35 - 7771759793894794226158134990367878 * q^37 + 11984574206649783949969526048471808 * q^38 - 75089135561625836440773237699379200 * q^40 + 150622420768399427659977962302801266 * q^41 - 503269829459862138385119574866599988 * q^43 + 589156491500651091472842134125289472 * q^44 + 1201666039209211956008162792803812864 * q^46 - 517590816657574666863303783889459536 * q^47 + 1183207682852736238558590379440977403 * q^49 - 5363972694460023429439963707950510400 * q^50 + 19510568225567423700598614061466308608 * q^52 - 3147649955233970731028729152905020634 * q^53 + 72798121427511388475535050768468313960 * q^55 - 64659225918940531158350848060065054720 * q^56 + 165860584701603780784654252956514011264 * q^58 + 178011039218636820023529236138863835076 * q^59 - 123533499732384273913895969461615945518 * q^61 + 685215538112102475249420816230843667456 * q^62 - 971015593402068342273570470768658087936 * q^64 + 2575578837917643212594035173081316043940 * q^65 + 1292774342372783673662410484960847098148 * q^67 + 2717789569206669919054906507790539296768 * q^68 + 1868357626946632141981582698458836116480 * q^70 - 22400468745595901369803420176388102887816 * q^71 + 31313509370447648548173493799361498480654 * q^73 - 12824367911381949889146580637796075349632 * q^74 - 45893435926810400921777338109031978491904 * q^76 - 15925552922292610065970442499593057720544 * q^77 - 43825544899857898915807551182364364018080 * q^79 - 51052771545930899482561003058120286535680 * q^80 - 207555016724016234735599639977066643719296 * q^82 - 89911369720242570860406785197345580904468 * q^83 - 609771200949453596987959942886782705526220 * q^85 + 1052084075872403200090705454196607607512320 * q^86 - 866229044996425850996432449444164589584384 * q^88 - 65289466052051143331840751197428752211806 * q^89 + 1361620777581018817929645459439738348447824 * q^91 - 3753917639661643691216268373890598977257472 * q^92 + 7862327422462694583153035384185107177477120 * q^94 - 9328236864095865156237338173319138974757400 * q^95 + 6130807410554375967448029821362307484893478 * q^97 + 2033290778553828878915746018754102329738560 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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