LMFDB - Embedded newform 9.42.a.c.1.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [9,42,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, 42, names="a")

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

chi := DirichletCharacter("9.1");

S:= CuspForms(chi, 42);

N := Newforms(S);

Level:	$ N $	$=$	$ 9 = 3^{2} $
Weight:	$ k $	$=$	$ 42 $
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:	$95.8245034108$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\mathbb{Q}[x]/(x^{4} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} - 196497525461x^{2} + 10360343667016365x + 6095744045744274504000 $ x^4 - x^3 - 196497525461x^2 + 10360343667016365x + 6095744045744274504000
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{13}\cdot 3^{10}\cdot 5^{2} $
Twist minimal:	no (minimal twist has level 3)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Root			$330995.$ 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)

$f(q)$	$=$	$q+2.00342e6 q^{2} +1.81468e12 q^{4} +3.43221e14 q^{5} -2.11939e17 q^{7} -7.69998e17 q^{8} +O(q^{10})$	\(q+2.00342e6 q^{2} +1.81468e12 q^{4} +3.43221e14 q^{5} -2.11939e17 q^{7} -7.69998e17 q^{8} +6.87617e20 q^{10} +2.68951e21 q^{11} -4.84491e22 q^{13} -4.24604e23 q^{14} -5.53316e24 q^{16} +2.66383e25 q^{17} +4.14274e24 q^{19} +6.22838e26 q^{20} +5.38824e27 q^{22} +6.80863e27 q^{23} +7.23261e28 q^{25} -9.70641e28 q^{26} -3.84602e29 q^{28} +1.53939e30 q^{29} -6.13330e29 q^{31} -9.39202e30 q^{32} +5.33678e31 q^{34} -7.27420e31 q^{35} +1.47726e32 q^{37} +8.29967e30 q^{38} -2.64280e32 q^{40} -1.43312e33 q^{41} +1.93562e33 q^{43} +4.88061e33 q^{44} +1.36406e34 q^{46} +1.54236e34 q^{47} +3.50578e32 q^{49} +1.44900e35 q^{50} -8.79197e34 q^{52} -2.77827e35 q^{53} +9.23098e35 q^{55} +1.63193e35 q^{56} +3.08404e36 q^{58} +2.82191e36 q^{59} +3.86057e36 q^{61} -1.22876e36 q^{62} -6.64865e36 q^{64} -1.66288e37 q^{65} -4.59962e36 q^{67} +4.83401e37 q^{68} -1.45733e38 q^{70} -9.12164e37 q^{71} -6.94314e36 q^{73} +2.95957e38 q^{74} +7.51776e36 q^{76} -5.70013e38 q^{77} +5.97141e38 q^{79} -1.89910e39 q^{80} -2.87114e39 q^{82} +3.36804e39 q^{83} +9.14284e39 q^{85} +3.87787e39 q^{86} -2.07092e39 q^{88} +1.32775e40 q^{89} +1.02683e40 q^{91} +1.23555e40 q^{92} +3.09000e40 q^{94} +1.42188e39 q^{95} -9.71560e40 q^{97} +7.02357e38 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 69822 q^{2} + 5352947588932 q^{4} - 118536963776280 q^{5} + 15\!\cdots\!36 q^{7}+ \cdots - 62\!\cdots\!84 q^{8}+O(q^{10}) $ 4 * q + 69822 * q^2 + 5352947588932 * q^4 - 118536963776280 * q^5 + 150256264888927136 * q^7 - 6279626248119395784 * q^8	$ 4 q + 69822 q^{2} + 5352947588932 q^{4} - 118536963776280 q^{5} + 15\!\cdots\!36 q^{7}+ \cdots + 68\!\cdots\!22 q^{98}+O(q^{100}) $ 4 * q + 69822 * q^2 + 5352947588932 * q^4 - 118536963776280 * q^5 + 150256264888927136 * q^7 - 6279626248119395784 * q^8 + 725751018728422700940 * q^10 - 724810647231440683056 * q^11 - 8843977274373065537608 * q^13 - 493449664223337937919568 * q^14 - 5962194966280197033033200 * q^16 + 38231582029295844707285688 * q^17 + 261842746845948075837831248 * q^19 - 785441926018305471679038360 * q^20 - 6322149663566345845522943976 * q^22 + 15395573913207335266380880032 * q^23 + 117350921958371528604086683900 * q^25 + 62942545095927728709970694052 * q^26 + 684437536459146482218511575712 * q^28 + 1036098964520685524199931325064 * q^29 + 9280613209905247622577480610304 * q^31 - 19645397922916950127447685511456 * q^32 + 92420157643501864091330064020004 * q^34 - 207436667553525639419383641992640 * q^35 + 200754880510048713109452091192856 * q^37 - 1146938682238729575315585266559528 * q^38 + 2565083222429486590317315499815600 * q^40 - 2357905268481965433001096926030504 * q^41 + 3943358618915609696106480688157360 * q^43 + 18494278585991583572852191821764304 * q^44 - 44252120640849956767942988241684816 * q^46 + 8890000412230234893665157147040320 * q^47 - 33104900387055220681685954563991580 * q^49 + 216323679312314207800001999371642050 * q^50 - 596234086188669794371774262733483208 * q^52 - 95704753827317216756019399314791128 * q^53 + 1291057043675253444545805475556816160 * q^55 - 1940580325939766339139469085046208320 * q^56 + 3859053206955865617315425524661917116 * q^58 + 1809289331104083090977131835906657808 * q^59 + 5381027332088000515346282395501157240 * q^61 - 14109494547714507002913033009898657152 * q^62 - 389844533130084697385386794140537792 * q^64 + 9754648834359651370261564655441346480 * q^65 - 73273159367285254897696664016673247728 * q^67 + 89019363361032581039655795923994746424 * q^68 - 127374089191018487217525315519713602080 * q^70 + 84396091414708989106237239330896374752 * q^71 - 44706579271813174655854382994714255832 * q^73 + 299692406925616462116506150539738813812 * q^74 + 1128262001217587654782588548338718696272 * q^76 - 833312137190144115784050615522845895552 * q^77 + 1416534390331633014953369475707893311680 * q^79 - 1539903590051088861086709486592809053280 * q^80 + 613971248288365719286532695984150451412 * q^82 - 1526205590962076227407755639349783073104 * q^83 - 285377453319367852617718519171747770960 * q^85 + 12934468921257599734617599325958640634024 * q^86 - 13219976774504188013705589441700285953696 * q^88 + 39593715237961905051969833281675978558872 * q^89 - 8845052344004724172694600210873108791616 * q^91 + 65206363053810587386463980322833360400544 * q^92 + 98582759073905793403791649187553312740832 * q^94 - 7880313586718908134850457997267850706400 * q^95 + 36750128325858234547252025624989137001352 * q^97 + 68350119771260167200829379908744318383822 * 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 $

$2$	2.00342e6	1.35101	0.675504	−	0.737356i	$-0.263926\pi$
$2$	2.00342e6	1.35101	0.675504	+	0.737356i	$0.263926\pi$
$3$	0	0
$3$	0	0
$4$	1.81468e12	0.825222
$5$	3.43221e14	1.60949	0.804746	−	0.593619i	$-0.202301\pi$
$5$	3.43221e14	1.60949	0.804746	+	0.593619i	$0.202301\pi$
$6$	0	0
$7$	−2.11939e17	−1.00393	−0.501963	−	0.864889i	$-0.667389\pi$
$7$	−2.11939e17	−1.00393	−0.501963	+	0.864889i	$0.667389\pi$
$8$	−7.69998e17	−0.236126
$9$	0	0
$10$	6.87617e20	2.17444
$11$	2.68951e21	1.20538	0.602690	−	0.797976i	$-0.294096\pi$
$11$	2.68951e21	1.20538	0.602690	+	0.797976i	$0.294096\pi$
$12$	0	0
$13$	−4.84491e22	−0.707045	−0.353522	−	0.935426i	$-0.615016\pi$
$13$	−4.84491e22	−0.707045	−0.353522	+	0.935426i	$0.615016\pi$
$14$	−4.24604e23	−1.35631
$15$	0	0
$16$	−5.53316e24	−1.14423
$17$	2.66383e25	1.58966	0.794830	−	0.606833i	$-0.207560\pi$
$17$	2.66383e25	1.58966	0.794830	+	0.606833i	$0.207560\pi$
$18$	0	0
$19$	4.14274e24	0.0252836	0.0126418	−	0.999920i	$-0.495976\pi$
$19$	4.14274e24	0.0252836	0.0126418	+	0.999920i	$0.495976\pi$
$20$	6.22838e26	1.32819
$21$	0	0
$22$	5.38824e27	1.62848
$23$	6.80863e27	0.827254	0.413627	−	0.910446i	$-0.364262\pi$
$23$	6.80863e27	0.827254	0.413627	+	0.910446i	$0.364262\pi$
$24$	0	0
$25$	7.23261e28	1.59047
$26$	−9.70641e28	−0.955223
$27$	0	0
$28$	−3.84602e29	−0.828461
$29$	1.53939e30	1.61506	0.807530	−	0.589827i	$-0.200804\pi$
$29$	1.53939e30	1.61506	0.807530	+	0.589827i	$0.200804\pi$
$30$	0	0
$31$	−6.13330e29	−0.163976	−0.0819878	−	0.996633i	$-0.526127\pi$
$31$	−6.13330e29	−0.163976	−0.0819878	+	0.996633i	$0.526127\pi$
$32$	−9.39202e30	−1.30974
$33$	0	0
$34$	5.33678e31	2.14764
$35$	−7.27420e31	−1.61581
$36$	0	0
$37$	1.47726e32	1.05032	0.525160	−	0.851004i	$-0.324006\pi$
$37$	1.47726e32	1.05032	0.525160	+	0.851004i	$0.324006\pi$
$38$	8.29967e30	0.0341584
$39$	0	0
$40$	−2.64280e32	−0.380044
$41$	−1.43312e33	−1.24226	−0.621131	−	0.783707i	$-0.713326\pi$
$41$	−1.43312e33	−1.24226	−0.621131	+	0.783707i	$0.713326\pi$
$42$	0	0
$43$	1.93562e33	0.632001	0.316000	−	0.948759i	$-0.397660\pi$
$43$	1.93562e33	0.632001	0.316000	+	0.948759i	$0.397660\pi$
$44$	4.88061e33	0.994706
$45$	0	0
$46$	1.36406e34	1.11763
$47$	1.54236e34	0.813168	0.406584	−	0.913614i	$-0.366720\pi$
$47$	1.54236e34	0.813168	0.406584	+	0.913614i	$0.366720\pi$
$48$	0	0
$49$	3.50578e32	0.00786621
$50$	1.44900e35	2.14873
$51$	0	0
$52$	−8.79197e34	−0.583469
$53$	−2.77827e35	−1.24773	−0.623863	−	0.781534i	$-0.714438\pi$
$53$	−2.77827e35	−1.24773	−0.623863	+	0.781534i	$0.714438\pi$
$54$	0	0
$55$	9.23098e35	1.94005
$56$	1.63193e35	0.237053
$57$	0	0
$58$	3.08404e36	2.18196
$59$	2.82191e36	1.40630	0.703148	−	0.711044i	$-0.251777\pi$
$59$	2.82191e36	1.40630	0.703148	+	0.711044i	$0.251777\pi$
$60$	0	0
$61$	3.86057e36	0.971382	0.485691	−	0.874130i	$-0.338568\pi$
$61$	3.86057e36	0.971382	0.485691	+	0.874130i	$0.338568\pi$
$62$	−1.22876e36	−0.221532
$63$	0	0
$64$	−6.64865e36	−0.625236
$65$	−1.66288e37	−1.13798
$66$	0	0
$67$	−4.59962e36	−0.169118	−0.0845588	−	0.996418i	$-0.526948\pi$
$67$	−4.59962e36	−0.169118	−0.0845588	+	0.996418i	$0.526948\pi$
$68$	4.83401e37	1.31182
$69$	0	0
$70$	−1.45733e38	−2.18297
$71$	−9.12164e37	−1.02159	−0.510795	−	0.859703i	$-0.670649\pi$
$71$	−9.12164e37	−1.02159	−0.510795	+	0.859703i	$0.670649\pi$
$72$	0	0
$73$	−6.94314e36	−0.0439985	−0.0219992	−	0.999758i	$-0.507003\pi$
$73$	−6.94314e36	−0.0439985	−0.0219992	+	0.999758i	$0.507003\pi$
$74$	2.95957e38	1.41899
$75$	0	0
$76$	7.51776e36	0.0208646
$77$	−5.70013e38	−1.21011
$78$	0	0
$79$	5.97141e38	0.749414	0.374707	−	0.927143i	$-0.377743\pi$
$79$	5.97141e38	0.749414	0.374707	+	0.927143i	$0.377743\pi$
$80$	−1.89910e39	−1.84163
$81$	0	0
$82$	−2.87114e39	−1.67830
$83$	3.36804e39	1.53559	0.767797	−	0.640694i	$-0.221353\pi$
$83$	3.36804e39	1.53559	0.767797	+	0.640694i	$0.221353\pi$
$84$	0	0
$85$	9.14284e39	2.55854
$86$	3.87787e39	0.853838
$87$	0	0
$88$	−2.07092e39	−0.284622
$89$	1.32775e40	1.44750	0.723752	−	0.690060i	$-0.242416\pi$
$89$	1.32775e40	1.44750	0.723752	+	0.690060i	$0.242416\pi$
$90$	0	0
$91$	1.02683e40	0.709820
$92$	1.23555e40	0.682668
$93$	0	0
$94$	3.09000e40	1.09860
$95$	1.42188e39	0.0406938
$96$	0	0
$97$	−9.71560e40	−1.81405	−0.907025	−	0.421077i	$-0.861652\pi$
$97$	−9.71560e40	−1.81405	−0.907025	+	0.421077i	$0.861652\pi$
$98$	7.02357e38	0.0106273
$99$	0	0
$100$	1.31249e41	1.31249
$101$	4.41832e40	0.360304	0.180152	−	0.983639i	$-0.442341\pi$
$101$	4.41832e40	0.360304	0.180152	+	0.983639i	$0.442341\pi$
$102$	0	0
$103$	2.87560e41	1.56879	0.784395	−	0.620262i	$-0.212974\pi$
$103$	2.87560e41	1.56879	0.784395	+	0.620262i	$0.212974\pi$
$104$	3.73057e40	0.166952
$105$	0	0
$106$	−5.56605e41	−1.68569
$107$	9.23802e40	0.230787	0.115394	−	0.993320i	$-0.463187\pi$
$107$	9.23802e40	0.230787	0.115394	+	0.993320i	$0.463187\pi$
$108$	0	0
$109$	−7.45590e41	−1.27426	−0.637128	−	0.770758i	$-0.719878\pi$
$109$	−7.45590e41	−1.27426	−0.637128	+	0.770758i	$0.719878\pi$
$110$	1.84936e42	2.62102
$111$	0	0
$112$	1.17269e42	1.14872
$113$	1.06665e42	0.870791	0.435396	−	0.900239i	$-0.356609\pi$
$113$	1.06665e42	0.870791	0.435396	+	0.900239i	$0.356609\pi$
$114$	0	0
$115$	2.33686e42	1.33146
$116$	2.79350e42	1.33278
$117$	0	0
$118$	5.65348e42	1.89992
$119$	−5.64570e42	−1.59590
$120$	0	0
$121$	2.25497e42	0.452939
$122$	7.73436e42	1.31235
$123$	0	0
$124$	−1.11300e42	−0.135316
$125$	9.21595e42	0.950353
$126$	0	0
$127$	3.83161e42	0.285368	0.142684	−	0.989768i	$-0.454427\pi$
$127$	3.83161e42	0.285368	0.142684	+	0.989768i	$0.454427\pi$
$128$	7.33322e42	0.465040
$129$	0	0
$130$	−3.33144e43	−1.53742
$131$	−2.73831e43	−1.07999	−0.539996	−	0.841667i	$-0.681574\pi$
$131$	−2.73831e43	−1.07999	−0.539996	+	0.841667i	$0.681574\pi$
$132$	0	0
$133$	−8.78010e41	−0.0253829
$134$	−9.21500e42	−0.228479
$135$	0	0
$136$	−2.05114e43	−0.375361
$137$	4.47383e42	0.0704544	0.0352272	−	0.999379i	$-0.488785\pi$
$137$	4.47383e42	0.0704544	0.0352272	+	0.999379i	$0.488785\pi$
$138$	0	0
$139$	−9.98093e43	−1.16780	−0.583899	−	0.811826i	$-0.698474\pi$
$139$	−9.98093e43	−1.16780	−0.583899	+	0.811826i	$0.698474\pi$
$140$	−1.32004e44	−1.33340
$141$	0	0
$142$	−1.82745e44	−1.38018
$143$	−1.30305e44	−0.852257
$144$	0	0
$145$	5.28350e44	2.59943
$146$	−1.39101e43	−0.0594423
$147$	0	0
$148$	2.68076e44	0.866746
$149$	−2.04820e44	−0.576837	−0.288419	−	0.957504i	$-0.593130\pi$
$149$	−2.04820e44	−0.576837	−0.288419	+	0.957504i	$0.593130\pi$
$150$	0	0
$151$	3.17569e43	0.0680472	0.0340236	−	0.999421i	$-0.489168\pi$
$151$	3.17569e43	0.0680472	0.0340236	+	0.999421i	$0.489168\pi$
$152$	−3.18990e42	−0.00597013
$153$	0	0
$154$	−1.14198e45	−1.63487
$155$	−2.10508e44	−0.263918
$156$	0	0
$157$	1.69451e44	0.163343	0.0816715	−	0.996659i	$-0.473974\pi$
$157$	1.69451e44	0.163343	0.0816715	+	0.996659i	$0.473974\pi$
$158$	1.19633e45	1.01246
$159$	0	0
$160$	−3.22354e45	−2.10801
$161$	−1.44301e45	−0.830501
$162$	0	0
$163$	4.18577e44	0.187038	0.0935189	−	0.995618i	$-0.470188\pi$
$163$	4.18577e44	0.187038	0.0935189	+	0.995618i	$0.470188\pi$
$164$	−2.60065e45	−1.02514
$165$	0	0
$166$	6.74761e45	2.07460
$167$	−4.36373e45	−1.18623	−0.593117	−	0.805117i	$-0.702103\pi$
$167$	−4.36373e45	−1.18623	−0.593117	+	0.805117i	$0.702103\pi$
$168$	0	0
$169$	−2.34814e45	−0.500088
$170$	1.83170e46	3.45661
$171$	0	0
$172$	3.51254e45	0.521541
$173$	4.54949e44	0.0599815	0.0299907	−	0.999550i	$-0.490452\pi$
$173$	4.54949e44	0.0599815	0.0299907	+	0.999550i	$0.490452\pi$
$174$	0	0
$175$	−1.53287e46	−1.59671
$176$	−1.48815e46	−1.37923
$177$	0	0
$178$	2.66004e46	1.95559
$179$	1.96397e46	1.28720	0.643601	−	0.765361i	$-0.277440\pi$
$179$	1.96397e46	1.28720	0.643601	+	0.765361i	$0.277440\pi$
$180$	0	0
$181$	2.64903e45	0.138254	0.0691268	−	0.997608i	$-0.477979\pi$
$181$	2.64903e45	0.138254	0.0691268	+	0.997608i	$0.477979\pi$
$182$	2.05717e46	0.958973
$183$	0	0
$184$	−5.24262e45	−0.195336
$185$	5.07027e46	1.69048
$186$	0	0
$187$	7.16441e46	1.91614
$188$	2.79890e46	0.671044
$189$	0	0
$190$	2.84862e45	0.0549777
$191$	−2.19040e46	−0.379612	−0.189806	−	0.981822i	$-0.560786\pi$
$191$	−2.19040e46	−0.379612	−0.189806	+	0.981822i	$0.560786\pi$
$192$	0	0
$193$	−1.09612e47	−1.53438	−0.767189	−	0.641421i	$-0.778345\pi$
$193$	−1.09612e47	−1.53438	−0.767189	+	0.641421i	$0.778345\pi$
$194$	−1.94645e47	−2.45080
$195$	0	0
$196$	6.36189e44	0.00649137
$197$	−6.57368e46	−0.604297	−0.302149	−	0.953261i	$-0.597704\pi$
$197$	−6.57368e46	−0.604297	−0.302149	+	0.953261i	$0.597704\pi$
$198$	0	0
$199$	−1.41080e47	−1.05433	−0.527166	−	0.849762i	$-0.676745\pi$
$199$	−1.41080e47	−1.05433	−0.527166	+	0.849762i	$0.676745\pi$
$200$	−5.56909e46	−0.375551
$201$	0	0
$202$	8.85177e46	0.486774
$203$	−3.26256e47	−1.62140
$204$	0	0
$205$	−4.91877e47	−1.99941
$206$	5.76104e47	2.11945
$207$	0	0
$208$	2.68077e47	0.809022
$209$	1.11420e46	0.0304764
$210$	0	0
$211$	−9.71826e46	−0.218675	−0.109337	−	0.994005i	$-0.534873\pi$
$211$	−9.71826e46	−0.218675	−0.109337	+	0.994005i	$0.534873\pi$
$212$	−5.04168e47	−1.02965
$213$	0	0
$214$	1.85077e47	0.311795
$215$	6.64347e47	1.01720
$216$	0	0
$217$	1.29989e47	0.164619
$218$	−1.49373e48	−1.72153
$219$	0	0
$220$	1.67513e48	1.60097
$221$	−1.29060e48	−1.12396
$222$	0	0
$223$	−1.08268e48	−0.783883	−0.391942	−	0.919990i	$-0.628197\pi$
$223$	−1.08268e48	−0.783883	−0.391942	+	0.919990i	$0.628197\pi$
$224$	1.99054e48	1.31488
$225$	0	0
$226$	2.13695e48	1.17645
$227$	7.22684e47	0.363428	0.181714	−	0.983351i	$-0.441835\pi$
$227$	7.22684e47	0.363428	0.181714	+	0.983351i	$0.441835\pi$
$228$	0	0
$229$	−3.57660e48	−1.50260	−0.751299	−	0.659962i	$-0.770572\pi$
$229$	−3.57660e48	−1.50260	−0.751299	+	0.659962i	$0.770572\pi$
$230$	4.68173e48	1.79881
$231$	0	0
$232$	−1.18532e48	−0.381358
$233$	−5.07597e48	−1.49528	−0.747640	−	0.664104i	$-0.768813\pi$
$233$	−5.07597e48	−1.49528	−0.747640	+	0.664104i	$0.768813\pi$
$234$	0	0
$235$	5.29371e48	1.30879
$236$	5.12087e48	1.16051
$237$	0	0
$238$	−1.13107e49	−2.15607
$239$	1.80945e48	0.316512	0.158256	−	0.987398i	$-0.449413\pi$
$239$	1.80945e48	0.316512	0.158256	+	0.987398i	$0.449413\pi$
$240$	0	0
$241$	2.18958e48	0.322858	0.161429	−	0.986884i	$-0.448390\pi$
$241$	2.18958e48	0.322858	0.161429	+	0.986884i	$0.448390\pi$
$242$	4.51765e48	0.611924
$243$	0	0
$244$	7.00571e48	0.801606
$245$	1.20326e47	0.0126606
$246$	0	0
$247$	−2.00712e47	−0.0178767
$248$	4.72262e47	0.0387190
$249$	0	0
$250$	1.84635e49	1.28393
$251$	−1.23621e49	−0.792100	−0.396050	−	0.918229i	$-0.629619\pi$
$251$	−1.23621e49	−0.792100	−0.396050	+	0.918229i	$0.629619\pi$
$252$	0	0
$253$	1.83119e49	0.997155
$254$	7.67635e48	0.385535
$255$	0	0
$256$	2.93121e49	1.25351
$257$	7.95215e48	0.313946	0.156973	−	0.987603i	$-0.449826\pi$
$257$	7.95215e48	0.313946	0.156973	+	0.987603i	$0.449826\pi$
$258$	0	0
$259$	−3.13089e49	−1.05444
$260$	−3.01759e49	−0.939089
$261$	0	0
$262$	−5.48599e49	−1.45908
$263$	1.51702e49	0.373162	0.186581	−	0.982440i	$-0.440259\pi$
$263$	1.51702e49	0.373162	0.186581	+	0.982440i	$0.440259\pi$
$264$	0	0
$265$	−9.53562e49	−2.00821
$266$	−1.75903e48	−0.0342925
$267$	0	0
$268$	−8.34686e48	−0.139560
$269$	−7.09419e49	−1.09896	−0.549479	−	0.835508i	$-0.685174\pi$
$269$	−7.09419e49	−1.09896	−0.549479	+	0.835508i	$0.685174\pi$
$270$	0	0
$271$	1.55633e49	0.207125	0.103563	−	0.994623i	$-0.466976\pi$
$271$	1.55633e49	0.207125	0.103563	+	0.994623i	$0.466976\pi$
$272$	−1.47394e50	−1.81894
$273$	0	0
$274$	8.96298e48	0.0951844
$275$	1.94522e50	1.91712
$276$	0	0
$277$	−3.47369e48	−0.0295091	−0.0147546	−	0.999891i	$-0.504697\pi$
$277$	−3.47369e48	−0.0295091	−0.0147546	+	0.999891i	$0.504697\pi$
$278$	−1.99960e50	−1.57770
$279$	0	0
$280$	5.60112e49	0.381536
$281$	−1.20363e50	−0.762104	−0.381052	−	0.924554i	$-0.624438\pi$
$281$	−1.20363e50	−0.762104	−0.381052	+	0.924554i	$0.624438\pi$
$282$	0	0
$283$	6.17804e49	0.338243	0.169121	−	0.985595i	$-0.445907\pi$
$283$	6.17804e49	0.338243	0.169121	+	0.985595i	$0.445907\pi$
$284$	−1.65529e50	−0.843039
$285$	0	0
$286$	−2.61055e50	−1.15141
$287$	3.03734e50	1.24714
$288$	0	0
$289$	4.28795e50	1.52702
$290$	1.05851e51	3.51185
$291$	0	0
$292$	−1.25996e49	−0.0363085
$293$	6.08165e49	0.163394	0.0816968	−	0.996657i	$-0.473966\pi$
$293$	6.08165e49	0.163394	0.0816968	+	0.996657i	$0.473966\pi$
$294$	0	0
$295$	9.68539e50	2.26342
$296$	−1.13749e50	−0.248008
$297$	0	0
$298$	−4.10341e50	−0.779312
$299$	−3.29872e50	−0.584906
$300$	0	0
$301$	−4.10234e50	−0.634481
$302$	6.36224e49	0.0919323
$303$	0	0
$304$	−2.29225e49	−0.0289303
$305$	1.32503e51	1.56343
$306$	0	0
$307$	−2.16833e50	−0.223763	−0.111882	−	0.993722i	$-0.535688\pi$
$307$	−2.16833e50	−0.223763	−0.111882	+	0.993722i	$0.535688\pi$
$308$	−1.03439e51	−0.998610
$309$	0	0
$310$	−4.21736e50	−0.356555
$311$	−4.74537e50	−0.375563	−0.187781	−	0.982211i	$-0.560130\pi$
$311$	−4.74537e50	−0.375563	−0.187781	+	0.982211i	$0.560130\pi$
$312$	0	0
$313$	−1.32823e51	−0.921749	−0.460875	−	0.887465i	$-0.652464\pi$
$313$	−1.32823e51	−0.921749	−0.460875	+	0.887465i	$0.652464\pi$
$314$	3.39481e50	0.220678
$315$	0	0
$316$	1.08362e51	0.618433
$317$	−8.98401e50	−0.480569	−0.240284	−	0.970703i	$-0.577241\pi$
$317$	−8.98401e50	−0.480569	−0.240284	+	0.970703i	$0.577241\pi$
$318$	0	0
$319$	4.14020e51	1.94676
$320$	−2.28196e51	−1.00631
$321$	0	0
$322$	−2.89097e51	−1.12201
$323$	1.10356e50	0.0401923
$324$	0	0
$325$	−3.50413e51	−1.12453
$326$	8.38587e50	0.252690
$327$	0	0
$328$	1.10350e51	0.293331
$329$	−3.26887e51	−0.816360
$330$	0	0
$331$	−1.36487e51	−0.301036	−0.150518	−	0.988607i	$-0.548094\pi$
$331$	−1.36487e51	−0.301036	−0.150518	+	0.988607i	$0.548094\pi$
$332$	6.11192e51	1.26721
$333$	0	0
$334$	−8.74240e51	−1.60261
$335$	−1.57869e51	−0.272194
$336$	0	0
$337$	4.08797e51	0.623871	0.311936	−	0.950103i	$-0.399023\pi$
$337$	4.08797e51	0.623871	0.311936	+	0.950103i	$0.399023\pi$
$338$	−4.70431e51	−0.675622
$339$	0	0
$340$	1.65913e52	2.11137
$341$	−1.64956e51	−0.197653
$342$	0	0
$343$	9.37133e51	0.996028
$344$	−1.49043e51	−0.149232
$345$	0	0
$346$	9.11455e50	0.0810354
$347$	9.67986e50	0.0811176	0.0405588	−	0.999177i	$-0.487086\pi$
$347$	9.67986e50	0.0811176	0.0405588	+	0.999177i	$0.487086\pi$
$348$	0	0
$349$	−1.20461e52	−0.897274	−0.448637	−	0.893714i	$-0.648090\pi$
$349$	−1.20461e52	−0.897274	−0.448637	+	0.893714i	$0.648090\pi$
$350$	−3.07099e52	−2.15717
$351$	0	0
$352$	−2.52600e52	−1.57873
$353$	1.65328e52	0.974912	0.487456	−	0.873147i	$-0.337925\pi$
$353$	1.65328e52	0.974912	0.487456	+	0.873147i	$0.337925\pi$
$354$	0	0
$355$	−3.13074e52	−1.64424
$356$	2.40944e52	1.19451
$357$	0	0
$358$	3.93465e52	1.73902
$359$	3.30801e52	1.38080	0.690399	−	0.723429i	$-0.257435\pi$
$359$	3.30801e52	1.38080	0.690399	+	0.723429i	$0.257435\pi$
$360$	0	0
$361$	−2.68300e52	−0.999361
$362$	5.30714e51	0.186782
$363$	0	0
$364$	1.86336e52	0.585759
$365$	−2.38303e51	−0.0708152
$366$	0	0
$367$	−5.27201e51	−0.140063	−0.0700313	−	0.997545i	$-0.522310\pi$
$367$	−5.27201e51	−0.140063	−0.0700313	+	0.997545i	$0.522310\pi$
$368$	−3.76732e52	−0.946569
$369$	0	0
$370$	1.01579e53	2.28385
$371$	5.88825e52	1.25262
$372$	0	0
$373$	2.13564e52	0.406909	0.203455	−	0.979084i	$-0.434783\pi$
$373$	2.13564e52	0.406909	0.203455	+	0.979084i	$0.434783\pi$
$374$	1.43534e53	2.58872
$375$	0	0
$376$	−1.18761e52	−0.192010
$377$	−7.45818e52	−1.14192
$378$	0	0
$379$	1.38114e53	1.89729	0.948643	−	0.316349i	$-0.102457\pi$
$379$	1.38114e53	1.89729	0.948643	+	0.316349i	$0.102457\pi$
$380$	2.58026e51	0.0335814
$381$	0	0
$382$	−4.38831e52	−0.512859
$383$	−1.09992e53	−1.21839	−0.609196	−	0.793020i	$-0.708508\pi$
$383$	−1.09992e53	−1.21839	−0.609196	+	0.793020i	$0.708508\pi$
$384$	0	0
$385$	−1.95641e53	−1.94766
$386$	−2.19599e53	−2.07296
$387$	0	0
$388$	−1.76307e53	−1.49699
$389$	6.95194e51	0.0559937	0.0279968	−	0.999608i	$-0.491087\pi$
$389$	6.95194e51	0.0559937	0.0279968	+	0.999608i	$0.491087\pi$
$390$	0	0
$391$	1.81370e53	1.31505
$392$	−2.69945e50	−0.00185742
$393$	0	0
$394$	−1.31699e53	−0.816410
$395$	2.04952e53	1.20618
$396$	0	0
$397$	1.86384e53	0.989015	0.494508	−	0.869173i	$-0.335348\pi$
$397$	1.86384e53	0.989015	0.494508	+	0.869173i	$0.335348\pi$
$398$	−2.82643e53	−1.42441
$399$	0	0
$400$	−4.00192e53	−1.81986
$401$	7.71907e52	0.333507	0.166754	−	0.985999i	$-0.446672\pi$
$401$	7.71907e52	0.333507	0.166754	+	0.985999i	$0.446672\pi$
$402$	0	0
$403$	2.97153e52	0.115938
$404$	8.01785e52	0.297331
$405$	0	0
$406$	−6.53629e53	−2.19052
$407$	3.97311e53	1.26603
$408$	0	0
$409$	−1.12970e52	−0.0325564	−0.0162782	−	0.999868i	$-0.505182\pi$
$409$	−1.12970e52	−0.0325564	−0.0162782	+	0.999868i	$0.505182\pi$
$410$	−9.85437e53	−2.70122
$411$	0	0
$412$	5.21829e53	1.29460
$413$	−5.98073e53	−1.41182
$414$	0	0
$415$	1.15598e54	2.47153
$416$	4.55035e53	0.926044
$417$	0	0
$418$	2.23221e52	0.0411738
$419$	2.36312e53	0.415049	0.207524	−	0.978230i	$-0.433459\pi$
$419$	2.36312e53	0.415049	0.207524	+	0.978230i	$0.433459\pi$
$420$	0	0
$421$	2.89686e53	0.461471	0.230736	−	0.973016i	$-0.425887\pi$
$421$	2.89686e53	0.461471	0.230736	+	0.973016i	$0.425887\pi$
$422$	−1.94698e53	−0.295431
$423$	0	0
$424$	2.13926e53	0.294621
$425$	1.92665e54	2.52830
$426$	0	0
$427$	−8.18207e53	−0.975195
$428$	1.67641e53	0.190451
$429$	0	0
$430$	1.33097e54	1.37425
$431$	1.78890e54	1.76118	0.880588	−	0.473883i	$-0.157148\pi$
$431$	1.78890e54	1.76118	0.880588	+	0.473883i	$0.157148\pi$
$432$	0	0
$433$	3.17218e53	0.284025	0.142012	−	0.989865i	$-0.454643\pi$
$433$	3.17218e53	0.284025	0.142012	+	0.989865i	$0.454643\pi$
$434$	2.60422e53	0.222402
$435$	0	0
$436$	−1.35301e54	−1.05154
$437$	2.82064e52	0.0209160
$438$	0	0
$439$	−2.40172e54	−1.62181	−0.810904	−	0.585180i	$-0.801024\pi$
$439$	−2.40172e54	−1.62181	−0.810904	+	0.585180i	$0.801024\pi$
$440$	−7.10783e53	−0.458097
$441$	0	0
$442$	−2.58562e54	−1.51848
$443$	−2.77202e54	−1.55425	−0.777124	−	0.629348i	$-0.783322\pi$
$443$	−2.77202e54	−1.55425	−0.777124	+	0.629348i	$0.783322\pi$
$444$	0	0
$445$	4.55710e54	2.32975
$446$	−2.16907e54	−1.05903
$447$	0	0
$448$	1.40911e54	0.627690
$449$	6.15902e53	0.262097	0.131048	−	0.991376i	$-0.458166\pi$
$449$	6.15902e53	0.262097	0.131048	+	0.991376i	$0.458166\pi$
$450$	0	0
$451$	−3.85439e54	−1.49740
$452$	1.93563e54	0.718596
$453$	0	0
$454$	1.44784e54	0.490994
$455$	3.52429e54	1.14245
$456$	0	0
$457$	−1.23275e53	−0.0365253	−0.0182626	−	0.999833i	$-0.505813\pi$
$457$	−1.23275e53	−0.0365253	−0.0182626	+	0.999833i	$0.505813\pi$
$458$	−7.16544e54	−2.03002
$459$	0	0
$460$	4.24067e54	1.09875
$461$	7.22256e54	1.78987	0.894936	−	0.446195i	$-0.147221\pi$
$461$	7.22256e54	1.78987	0.894936	+	0.446195i	$0.147221\pi$
$462$	0	0
$463$	4.66005e54	1.05677	0.528385	−	0.849005i	$-0.322798\pi$
$463$	4.66005e54	1.05677	0.528385	+	0.849005i	$0.322798\pi$
$464$	−8.51767e54	−1.84800
$465$	0	0
$466$	−1.01693e55	−2.02014
$467$	−9.30547e54	−1.76906	−0.884529	−	0.466485i	$-0.845520\pi$
$467$	−9.30547e54	−1.76906	−0.884529	+	0.466485i	$0.845520\pi$
$468$	0	0
$469$	9.74841e53	0.169781
$470$	1.06055e55	1.76818
$471$	0	0
$472$	−2.17286e54	−0.332064
$473$	5.20589e54	0.761800
$474$	0	0
$475$	2.99628e53	0.0402128
$476$	−1.02452e55	−1.31697
$477$	0	0
$478$	3.62510e54	0.427610
$479$	1.41559e55	1.59977	0.799887	−	0.600151i	$-0.204893\pi$
$479$	1.41559e55	1.59977	0.799887	+	0.600151i	$0.204893\pi$
$480$	0	0
$481$	−7.15718e54	−0.742623
$482$	4.38665e54	0.436183
$483$	0	0
$484$	4.09205e54	0.373775
$485$	−3.33460e55	−2.91970
$486$	0	0
$487$	−2.04972e55	−1.64949	−0.824746	−	0.565503i	$-0.808682\pi$
$487$	−2.04972e55	−1.64949	−0.824746	+	0.565503i	$0.808682\pi$
$488$	−2.97263e54	−0.229369
$489$	0	0
$490$	2.41064e53	0.0171046
$491$	4.95694e54	0.337321	0.168660	−	0.985674i	$-0.446056\pi$
$491$	4.95694e54	0.337321	0.168660	+	0.985674i	$0.446056\pi$
$492$	0	0
$493$	4.10067e55	2.56739
$494$	−4.02112e53	−0.0241515
$495$	0	0
$496$	3.39365e54	0.187626
$497$	1.93323e55	1.02560
$498$	0	0
$499$	−2.14720e55	−1.04909	−0.524543	−	0.851384i	$-0.675764\pi$
$499$	−2.14720e55	−1.04909	−0.524543	+	0.851384i	$0.675764\pi$
$500$	1.67240e55	0.784252
$501$	0	0
$502$	−2.47665e55	−1.07013
$503$	−2.45440e55	−1.01813	−0.509063	−	0.860729i	$-0.670008\pi$
$503$	−2.45440e55	−1.01813	−0.509063	+	0.860729i	$0.670008\pi$
$504$	0	0
$505$	1.51646e55	0.579907
$506$	3.66865e55	1.34716
$507$	0	0
$508$	6.95316e54	0.235492
$509$	−1.12858e55	−0.367130	−0.183565	−	0.983008i	$-0.558764\pi$
$509$	−1.12858e55	−0.367130	−0.183565	+	0.983008i	$0.558764\pi$
$510$	0	0
$511$	1.47152e54	0.0441712
$512$	4.25986e55	1.22846
$513$	0	0
$514$	1.59315e55	0.424144
$515$	9.86966e55	2.52496
$516$	0	0
$517$	4.14820e55	0.980175
$518$	−6.27250e55	−1.42456
$519$	0	0
$520$	1.28041e55	0.268708
$521$	3.43253e55	0.692534	0.346267	−	0.938136i	$-0.387449\pi$
$521$	3.43253e55	0.692534	0.346267	+	0.938136i	$0.387449\pi$
$522$	0	0
$523$	−2.52587e54	−0.0471114	−0.0235557	−	0.999723i	$-0.507499\pi$
$523$	−2.52587e54	−0.0471114	−0.0235557	+	0.999723i	$0.507499\pi$
$524$	−4.96916e55	−0.891234
$525$	0	0
$526$	3.03922e55	0.504144
$527$	−1.63381e55	−0.260665
$528$	0	0
$529$	−2.13820e55	−0.315651
$530$	−1.91039e56	−2.71310
$531$	0	0
$532$	−1.59331e54	−0.0209465
$533$	6.94333e55	0.878335
$534$	0	0
$535$	3.17069e55	0.371450
$536$	3.54170e54	0.0399331
$537$	0	0
$538$	−1.42127e56	−1.48470
$539$	9.42886e53	0.00948177
$540$	0	0
$541$	−1.02690e56	−0.957158	−0.478579	−	0.878045i	$-0.658848\pi$
$541$	−1.02690e56	−0.957158	−0.478579	+	0.878045i	$0.658848\pi$
$542$	3.11800e55	0.279827
$543$	0	0
$544$	−2.50188e56	−2.08204
$545$	−2.55902e56	−2.05091
$546$	0	0
$547$	6.01255e55	0.447011	0.223505	−	0.974703i	$-0.428250\pi$
$547$	6.01255e55	0.447011	0.223505	+	0.974703i	$0.428250\pi$
$548$	8.11858e54	0.0581405
$549$	0	0
$550$	3.89710e56	2.59004
$551$	6.37728e54	0.0408346
$552$	0	0
$553$	−1.26558e56	−0.752356
$554$	−6.95928e54	−0.0398671
$555$	0	0
$556$	−1.81122e56	−0.963693
$557$	−3.06039e56	−1.56944	−0.784721	−	0.619849i	$-0.787194\pi$
$557$	−3.06039e56	−1.56944	−0.784721	+	0.619849i	$0.787194\pi$
$558$	0	0
$559$	−9.37792e55	−0.446853
$560$	4.02493e56	1.84886
$561$	0	0
$562$	−2.41139e56	−1.02961
$563$	3.42167e56	1.40869	0.704346	−	0.709857i	$-0.251240\pi$
$563$	3.42167e56	1.40869	0.704346	+	0.709857i	$0.251240\pi$
$564$	0	0
$565$	3.66097e56	1.40153
$566$	1.23772e56	0.456969
$567$	0	0
$568$	7.02364e55	0.241224
$569$	−3.07296e56	−1.01802	−0.509008	−	0.860762i	$-0.669988\pi$
$569$	−3.07296e56	−1.01802	−0.509008	+	0.860762i	$0.669988\pi$
$570$	0	0
$571$	3.57289e56	1.10149	0.550743	−	0.834675i	$-0.314344\pi$
$571$	3.57289e56	1.10149	0.550743	+	0.834675i	$0.314344\pi$
$572$	−2.36461e56	−0.703301
$573$	0	0
$574$	6.08508e56	1.68489
$575$	4.92441e56	1.31572
$576$	0	0
$577$	−7.31817e55	−0.182095	−0.0910476	−	0.995847i	$-0.529022\pi$
$577$	−7.31817e55	−0.182095	−0.0910476	+	0.995847i	$0.529022\pi$
$578$	8.59057e56	2.06301
$579$	0	0
$580$	9.58787e56	2.14510
$581$	−7.13819e56	−1.54162
$582$	0	0
$583$	−7.47220e56	−1.50398
$584$	5.34620e54	0.0103892
$585$	0	0
$586$	1.21841e56	0.220746
$587$	−7.85589e56	−1.37440	−0.687202	−	0.726466i	$-0.741161\pi$
$587$	−7.85589e56	−1.37440	−0.687202	+	0.726466i	$0.741161\pi$
$588$	0	0
$589$	−2.54087e54	−0.00414590
$590$	1.94039e57	3.05790
$591$	0	0
$592$	−8.17391e56	−1.20181
$593$	−1.07054e57	−1.52048	−0.760240	−	0.649642i	$-0.774919\pi$
$593$	−1.07054e57	−1.52048	−0.760240	+	0.649642i	$0.774919\pi$
$594$	0	0
$595$	−1.93773e57	−2.56859
$596$	−3.71683e56	−0.476019
$597$	0	0
$598$	−6.60873e56	−0.790212
$599$	1.33866e57	1.54675	0.773374	−	0.633950i	$-0.218568\pi$
$599$	1.33866e57	1.54675	0.773374	+	0.633950i	$0.218568\pi$
$600$	0	0
$601$	−3.44829e55	−0.0372115	−0.0186058	−	0.999827i	$-0.505923\pi$
$601$	−3.44829e55	−0.0372115	−0.0186058	+	0.999827i	$0.505923\pi$
$602$	−8.21873e56	−0.857189
$603$	0	0
$604$	5.76286e55	0.0561540
$605$	7.73952e56	0.729003
$606$	0	0
$607$	1.12064e57	0.986505	0.493252	−	0.869886i	$-0.335808\pi$
$607$	1.12064e57	0.986505	0.493252	+	0.869886i	$0.335808\pi$
$608$	−3.89087e55	−0.0331149
$609$	0	0
$610$	2.65460e57	2.11221
$611$	−7.47260e56	−0.574946
$612$	0	0
$613$	7.02680e56	0.505612	0.252806	−	0.967517i	$-0.418646\pi$
$613$	7.02680e56	0.505612	0.252806	+	0.967517i	$0.418646\pi$
$614$	−4.34408e56	−0.302306
$615$	0	0
$616$	4.38909e56	0.285739
$617$	−1.57026e57	−0.988842	−0.494421	−	0.869223i	$-0.664620\pi$
$617$	−1.57026e57	−0.988842	−0.494421	+	0.869223i	$0.664620\pi$
$618$	0	0
$619$	−1.08061e57	−0.636813	−0.318406	−	0.947954i	$-0.603148\pi$
$619$	−1.08061e57	−0.636813	−0.318406	+	0.947954i	$0.603148\pi$
$620$	−3.82005e56	−0.217791
$621$	0	0
$622$	−9.50699e56	−0.507388
$623$	−2.81401e57	−1.45319
$624$	0	0
$625$	−1.25898e56	−0.0608807
$626$	−2.66100e57	−1.24529
$627$	0	0
$628$	3.07499e56	0.134794
$629$	3.93517e57	1.66965
$630$	0	0
$631$	−1.40291e57	−0.557736	−0.278868	−	0.960329i	$-0.589959\pi$
$631$	−1.40291e57	−0.557736	−0.278868	+	0.960329i	$0.589959\pi$
$632$	−4.59797e56	−0.176956
$633$	0	0
$634$	−1.79988e57	−0.649252
$635$	1.31509e57	0.459298
$636$	0	0
$637$	−1.69852e55	−0.00556176
$638$	8.29457e57	2.63009
$639$	0	0
$640$	2.51692e57	0.748478
$641$	−5.61783e57	−1.61800	−0.809001	−	0.587807i	$-0.799991\pi$
$641$	−5.61783e57	−1.61800	−0.809001	+	0.587807i	$0.799991\pi$
$642$	0	0
$643$	−4.94656e57	−1.33653	−0.668265	−	0.743923i	$-0.732963\pi$
$643$	−4.94656e57	−1.33653	−0.668265	+	0.743923i	$0.732963\pi$
$644$	−2.61861e57	−0.685348
$645$	0	0
$646$	2.21089e56	0.0543002
$647$	2.45422e57	0.583951	0.291976	−	0.956426i	$-0.405687\pi$
$647$	2.45422e57	0.583951	0.291976	+	0.956426i	$0.405687\pi$
$648$	0	0
$649$	7.58956e57	1.69512
$650$	−7.02026e57	−1.51925
$651$	0	0
$652$	7.59584e56	0.154348
$653$	3.19886e57	0.629906	0.314953	−	0.949107i	$-0.398011\pi$
$653$	3.19886e57	0.629906	0.314953	+	0.949107i	$0.398011\pi$
$654$	0	0
$655$	−9.39846e57	−1.73824
$656$	7.92967e57	1.42143
$657$	0	0
$658$	−6.54893e57	−1.10291
$659$	1.37754e57	0.224882	0.112441	−	0.993658i	$-0.464133\pi$
$659$	1.37754e57	0.224882	0.112441	+	0.993658i	$0.464133\pi$
$660$	0	0
$661$	7.48119e57	1.14773	0.573867	−	0.818949i	$-0.305443\pi$
$661$	7.48119e57	1.14773	0.573867	+	0.818949i	$0.305443\pi$
$662$	−2.73441e57	−0.406701
$663$	0	0
$664$	−2.59338e57	−0.362594
$665$	−3.01352e56	−0.0408536
$666$	0	0
$667$	1.04811e58	1.33606
$668$	−7.91878e57	−0.978906
$669$	0	0
$670$	−3.16278e57	−0.367736
$671$	1.03831e58	1.17088
$672$	0	0
$673$	1.60993e58	1.70804	0.854022	−	0.520237i	$-0.174156\pi$
$673$	1.60993e58	1.70804	0.854022	+	0.520237i	$0.174156\pi$
$674$	8.18994e57	0.842855
$675$	0	0
$676$	−4.26112e57	−0.412683
$677$	−5.61289e57	−0.527374	−0.263687	−	0.964608i	$-0.584939\pi$
$677$	−5.61289e57	−0.527374	−0.263687	+	0.964608i	$0.584939\pi$
$678$	0	0
$679$	2.05912e58	1.82117
$680$	−7.03996e57	−0.604140
$681$	0	0
$682$	−3.30476e57	−0.267030
$683$	2.16339e58	1.69633	0.848164	−	0.529733i	$-0.177708\pi$
$683$	2.16339e58	1.69633	0.848164	+	0.529733i	$0.177708\pi$
$684$	0	0
$685$	1.53551e57	0.113396
$686$	1.87747e58	1.34564
$687$	0	0
$688$	−1.07101e58	−0.723154
$689$	1.34605e58	0.882198
$690$	0	0
$691$	−9.86473e57	−0.609236	−0.304618	−	0.952475i	$-0.598529\pi$
$691$	−9.86473e57	−0.609236	−0.304618	+	0.952475i	$0.598529\pi$
$692$	8.25587e56	0.0494980
$693$	0	0
$694$	1.93929e57	0.109590
$695$	−3.42567e58	−1.87956
$696$	0	0
$697$	−3.81759e58	−1.97477
$698$	−2.41334e58	−1.21222
$699$	0	0
$700$	−2.78168e58	−1.31764
$701$	−2.34581e58	−1.07913	−0.539564	−	0.841944i	$-0.681411\pi$
$701$	−2.34581e58	−1.07913	−0.539564	+	0.841944i	$0.681411\pi$
$702$	0	0
$703$	6.11991e56	0.0265559
$704$	−1.78816e58	−0.753646
$705$	0	0
$706$	3.31222e58	1.31711
$707$	−9.36416e57	−0.361719
$708$	0	0
$709$	2.11154e58	0.769754	0.384877	−	0.922968i	$-0.374244\pi$
$709$	2.11154e58	0.769754	0.384877	+	0.922968i	$0.374244\pi$
$710$	−6.27220e58	−2.22138
$711$	0	0
$712$	−1.02236e58	−0.341794
$713$	−4.17593e57	−0.135649
$714$	0	0
$715$	−4.47233e58	−1.37170
$716$	3.56397e58	1.06223
$717$	0	0
$718$	6.62734e58	1.86547
$719$	3.21690e58	0.880024	0.440012	−	0.897992i	$-0.354974\pi$
$719$	3.21690e58	0.880024	0.440012	+	0.897992i	$0.354974\pi$
$720$	0	0
$721$	−6.09451e58	−1.57495
$722$	−5.37518e58	−1.35014
$723$	0	0
$724$	4.80715e57	0.114090
$725$	1.11338e59	2.56870
$726$	0	0
$727$	1.46981e58	0.320484	0.160242	−	0.987078i	$-0.448773\pi$
$727$	1.46981e58	0.320484	0.160242	+	0.987078i	$0.448773\pi$
$728$	−7.90654e57	−0.167607
$729$	0	0
$730$	−4.77423e57	−0.0956719
$731$	5.15618e58	1.00467
$732$	0	0
$733$	4.14987e58	0.764545	0.382273	−	0.924050i	$-0.375141\pi$
$733$	4.14987e58	0.764545	0.382273	+	0.924050i	$0.375141\pi$
$734$	−1.05621e58	−0.189226
$735$	0	0
$736$	−6.39467e58	−1.08349
$737$	−1.23708e58	−0.203851
$738$	0	0
$739$	4.59350e57	0.0716033	0.0358016	−	0.999359i	$-0.488602\pi$
$739$	4.59350e57	0.0716033	0.0358016	+	0.999359i	$0.488602\pi$
$740$	9.20092e58	1.39502
$741$	0	0
$742$	1.17966e59	1.69230
$743$	−8.66038e58	−1.20855	−0.604277	−	0.796774i	$-0.706538\pi$
$743$	−8.66038e58	−1.20855	−0.604277	+	0.796774i	$0.706538\pi$
$744$	0	0
$745$	−7.02985e58	−0.928416
$746$	4.27860e58	0.549738
$747$	0	0
$748$	1.30011e59	1.58124
$749$	−1.95790e58	−0.231693
$750$	0	0
$751$	1.41094e59	1.58085	0.790426	−	0.612557i	$-0.209859\pi$
$751$	1.41094e59	1.58085	0.790426	+	0.612557i	$0.209859\pi$
$752$	−8.53413e58	−0.930451
$753$	0	0
$754$	−1.49419e59	−1.54274
$755$	1.08996e58	0.109521
$756$	0	0
$757$	3.70705e58	0.352828	0.176414	−	0.984316i	$-0.443550\pi$
$757$	3.70705e58	0.352828	0.176414	+	0.984316i	$0.443550\pi$
$758$	2.76700e59	2.56325
$759$	0	0
$760$	−1.09484e57	−0.00960888
$761$	1.86135e59	1.59017	0.795084	−	0.606500i	$-0.207427\pi$
$761$	1.86135e59	1.59017	0.795084	+	0.606500i	$0.207427\pi$
$762$	0	0
$763$	1.58020e59	1.27926
$764$	−3.97489e58	−0.313264
$765$	0	0
$766$	−2.20361e59	−1.64606
$767$	−1.36719e59	−0.994314
$768$	0	0
$769$	−6.59899e58	−0.454975	−0.227487	−	0.973781i	$-0.573051\pi$
$769$	−6.59899e58	−0.454975	−0.227487	+	0.973781i	$0.573051\pi$
$770$	−3.91951e59	−2.63131
$771$	0	0
$772$	−1.98911e59	−1.26620
$773$	−1.95752e59	−1.21347	−0.606733	−	0.794906i	$-0.707520\pi$
$773$	−1.95752e59	−1.21347	−0.606733	+	0.794906i	$0.707520\pi$
$774$	0	0
$775$	−4.43597e58	−0.260798
$776$	7.48099e58	0.428345
$777$	0	0
$778$	1.39277e58	0.0756479
$779$	−5.93704e57	−0.0314089
$780$	0	0
$781$	−2.45328e59	−1.23140
$782$	3.63362e59	1.77664
$783$	0	0
$784$	−1.93981e57	−0.00900076
$785$	5.81591e58	0.262899
$786$	0	0
$787$	2.07905e59	0.892038	0.446019	−	0.895024i	$-0.352841\pi$
$787$	2.07905e59	0.892038	0.446019	+	0.895024i	$0.352841\pi$
$788$	−1.19291e59	−0.498679
$789$	0	0
$790$	4.10605e59	1.62955
$791$	−2.26065e59	−0.874209
$792$	0	0
$793$	−1.87041e59	−0.686811
$794$	3.73406e59	1.33617
$795$	0	0
$796$	−2.56015e59	−0.870058
$797$	−1.24780e58	−0.0413283	−0.0206642	−	0.999786i	$-0.506578\pi$
$797$	−1.24780e58	−0.0413283	−0.0206642	+	0.999786i	$0.506578\pi$
$798$	0	0
$799$	4.10859e59	1.29266
$800$	−6.79288e59	−2.08310
$801$	0	0
$802$	1.54646e59	0.450571
$803$	−1.86737e58	−0.0530348
$804$	0	0
$805$	−4.95273e59	−1.33669
$806$	5.95323e58	0.156633
$807$	0	0
$808$	−3.40210e58	−0.0850774
$809$	1.93365e58	0.0471448	0.0235724	−	0.999722i	$-0.492496\pi$
$809$	1.93365e58	0.0471448	0.0235724	+	0.999722i	$0.492496\pi$
$810$	0	0
$811$	6.76399e59	1.56775	0.783873	−	0.620921i	$-0.213241\pi$
$811$	6.76399e59	1.56775	0.783873	+	0.620921i	$0.213241\pi$
$812$	−5.92051e59	−1.33801
$813$	0	0
$814$	7.95982e59	1.71042
$815$	1.43665e59	0.301036
$816$	0	0
$817$	8.01879e57	0.0159793
$818$	−2.26327e58	−0.0439839
$819$	0	0
$820$	−8.92600e59	−1.64996
$821$	6.71492e59	1.21061	0.605307	−	0.795992i	$-0.293050\pi$
$821$	6.71492e59	1.21061	0.605307	+	0.795992i	$0.293050\pi$
$822$	0	0
$823$	−8.16687e59	−1.40074	−0.700372	−	0.713778i	$-0.746983\pi$
$823$	−8.16687e59	−1.40074	−0.700372	+	0.713778i	$0.746983\pi$
$824$	−2.21420e59	−0.370433
$825$	0	0
$826$	−1.19819e60	−1.90737
$827$	−6.61685e59	−1.02752	−0.513758	−	0.857935i	$-0.671747\pi$
$827$	−6.61685e59	−1.02752	−0.513758	+	0.857935i	$0.671747\pi$
$828$	0	0
$829$	8.11669e59	1.19953	0.599765	−	0.800176i	$-0.295261\pi$
$829$	8.11669e59	1.19953	0.599765	+	0.800176i	$0.295261\pi$
$830$	2.31592e60	3.33905
$831$	0	0
$832$	3.22121e59	0.442070
$833$	9.33882e57	0.0125046
$834$	0	0
$835$	−1.49772e60	−1.90923
$836$	2.02191e58	0.0251498
$837$	0	0
$838$	4.73434e59	0.560734
$839$	−8.50436e59	−0.982927	−0.491463	−	0.870898i	$-0.663538\pi$
$839$	−8.50436e59	−0.982927	−0.491463	+	0.870898i	$0.663538\pi$
$840$	0	0
$841$	1.46122e60	1.60842
$842$	5.80364e59	0.623451
$843$	0	0
$844$	−1.76356e59	−0.180455
$845$	−8.05931e59	−0.804888
$846$	0	0
$847$	−4.77916e59	−0.454717
$848$	1.53726e60	1.42769
$849$	0	0
$850$	3.85989e60	3.41575
$851$	1.00581e60	0.868880
$852$	0	0
$853$	−2.06137e60	−1.69708	−0.848538	−	0.529135i	$-0.822516\pi$
$853$	−2.06137e60	−1.69708	−0.848538	+	0.529135i	$0.822516\pi$
$854$	−1.63921e60	−1.31750
$855$	0	0
$856$	−7.11325e58	−0.0544949
$857$	−1.32928e60	−0.994285	−0.497142	−	0.867669i	$-0.665617\pi$
$857$	−1.32928e60	−0.994285	−0.497142	+	0.867669i	$0.665617\pi$
$858$	0	0
$859$	−1.38551e60	−0.987987	−0.493994	−	0.869466i	$-0.664463\pi$
$859$	−1.38551e60	−0.987987	−0.493994	+	0.869466i	$0.664463\pi$
$860$	1.20558e60	0.839416
$861$	0	0
$862$	3.58393e60	2.37936
$863$	7.45819e59	0.483517	0.241759	−	0.970336i	$-0.422276\pi$
$863$	7.45819e59	0.483517	0.241759	+	0.970336i	$0.422276\pi$
$864$	0	0
$865$	1.56148e59	0.0965398
$866$	6.35522e59	0.383719
$867$	0	0
$868$	2.35888e59	0.135847
$869$	1.60602e60	0.903328
$870$	0	0
$871$	2.22848e59	0.119574
$872$	5.74102e59	0.300885
$873$	0	0
$874$	5.65093e58	0.0282576
$875$	−1.95322e60	−0.954084
$876$	0	0
$877$	2.15621e60	1.00508	0.502538	−	0.864555i	$-0.332400\pi$
$877$	2.15621e60	1.00508	0.502538	+	0.864555i	$0.332400\pi$
$878$	−4.81166e60	−2.19107
$879$	0	0
$880$	−5.10765e60	−2.21986
$881$	−2.09977e60	−0.891589	−0.445795	−	0.895135i	$-0.647079\pi$
$881$	−2.09977e60	−0.891589	−0.445795	+	0.895135i	$0.647079\pi$
$882$	0	0
$883$	−2.55719e60	−1.03650	−0.518249	−	0.855230i	$-0.673416\pi$
$883$	−2.55719e60	−1.03650	−0.518249	+	0.855230i	$0.673416\pi$
$884$	−2.34203e60	−0.927517
$885$	0	0
$886$	−5.55353e60	−2.09980
$887$	−1.55710e60	−0.575285	−0.287642	−	0.957738i	$-0.592871\pi$
$887$	−1.55710e60	−0.575285	−0.287642	+	0.957738i	$0.592871\pi$
$888$	0	0
$889$	−8.12069e59	−0.286488
$890$	9.12981e60	3.14751
$891$	0	0
$892$	−1.96473e60	−0.646878
$893$	6.38961e58	0.0205598
$894$	0	0
$895$	6.74075e60	2.07174
$896$	−1.55420e60	−0.466865
$897$	0	0
$898$	1.23391e60	0.354095
$899$	−9.44151e59	−0.264830
$900$	0	0
$901$	−7.40085e60	−1.98346
$902$	−7.72198e60	−2.02299
$903$	0	0
$904$	−8.21318e59	−0.205617
$905$	9.09204e59	0.222518
$906$	0	0
$907$	−1.66650e60	−0.389814	−0.194907	−	0.980822i	$-0.562440\pi$
$907$	−1.66650e60	−0.389814	−0.194907	+	0.980822i	$0.562440\pi$
$908$	1.31144e60	0.299909
$909$	0	0
$910$	7.06064e60	1.54346
$911$	−3.26737e60	−0.698348	−0.349174	−	0.937058i	$-0.613538\pi$
$911$	−3.26737e60	−0.698348	−0.349174	+	0.937058i	$0.613538\pi$
$912$	0	0
$913$	9.05839e60	1.85097
$914$	−2.46972e59	−0.0493459
$915$	0	0
$916$	−6.49039e60	−1.23998
$917$	5.80355e60	1.08423
$918$	0	0
$919$	3.23443e60	0.577869	0.288934	−	0.957349i	$-0.406699\pi$
$919$	3.23443e60	0.577869	0.288934	+	0.957349i	$0.406699\pi$
$920$	−1.79938e60	−0.314393
$921$	0	0
$922$	1.44698e61	2.41813
$923$	4.41935e60	0.722310
$924$	0	0
$925$	1.06844e61	1.67050
$926$	9.33606e60	1.42770
$927$	0	0
$928$	−1.44579e61	−2.11530
$929$	−3.84037e60	−0.549606	−0.274803	−	0.961501i	$-0.588613\pi$
$929$	−3.84037e60	−0.549606	−0.274803	+	0.961501i	$0.588613\pi$
$930$	0	0
$931$	1.45236e57	0.000198886 0
$932$	−9.21127e60	−1.23394
$933$	0	0
$934$	−1.86428e61	−2.39001
$935$	2.45898e61	3.08402
$936$	0	0
$937$	2.56852e60	0.308334	0.154167	−	0.988045i	$-0.450731\pi$
$937$	2.56852e60	0.308334	0.154167	+	0.988045i	$0.450731\pi$
$938$	1.95302e60	0.229376
$939$	0	0
$940$	9.60641e60	1.08004
$941$	1.47165e61	1.61889	0.809444	−	0.587197i	$-0.199769\pi$
$941$	1.47165e61	1.61889	0.809444	+	0.587197i	$0.199769\pi$
$942$	0	0
$943$	−9.75757e60	−1.02767
$944$	−1.56141e61	−1.60913
$945$	0	0
$946$	1.04296e61	1.02920
$947$	1.41745e61	1.36878	0.684388	−	0.729118i	$-0.260070\pi$
$947$	1.41745e61	1.36878	0.684388	+	0.729118i	$0.260070\pi$
$948$	0	0
$949$	3.36389e59	0.0311089
$950$	6.00283e59	0.0543278
$951$	0	0
$952$	4.34718e60	0.376834
$953$	−1.56903e61	−1.33115	−0.665573	−	0.746332i	$-0.731813\pi$
$953$	−1.56903e61	−1.33115	−0.665573	+	0.746332i	$0.731813\pi$
$954$	0	0
$955$	−7.51793e60	−0.610983
$956$	3.28358e60	0.261193
$957$	0	0
$958$	2.83602e61	2.16131
$959$	−9.48180e59	−0.0707309
$960$	0	0
$961$	−1.36142e61	−0.973112
$962$	−1.43389e61	−1.00329
$963$	0	0
$964$	3.97339e60	0.266429
$965$	−3.76211e61	−2.46957
$966$	0	0
$967$	−8.55928e60	−0.538511	−0.269256	−	0.963069i	$-0.586778\pi$
$967$	−8.55928e60	−0.538511	−0.269256	+	0.963069i	$0.586778\pi$
$968$	−1.73632e60	−0.106951
$969$	0	0
$970$	−6.68062e61	−3.94454
$971$	1.94026e61	1.12167	0.560835	−	0.827928i	$-0.310480\pi$
$971$	1.94026e61	1.12167	0.560835	+	0.827928i	$0.310480\pi$
$972$	0	0
$973$	2.11535e61	1.17238
$974$	−4.10645e61	−2.22848
$975$	0	0
$976$	−2.13612e61	−1.11149
$977$	−6.21621e60	−0.316729	−0.158364	−	0.987381i	$-0.550622\pi$
$977$	−6.21621e60	−0.316729	−0.158364	+	0.987381i	$0.550622\pi$
$978$	0	0
$979$	3.57099e61	1.74479
$980$	2.18353e59	0.0104478
$981$	0	0
$982$	9.93085e60	0.455723
$983$	6.48229e60	0.291327	0.145664	−	0.989334i	$-0.453468\pi$
$983$	6.48229e60	0.291327	0.145664	+	0.989334i	$0.453468\pi$
$984$	0	0
$985$	−2.25623e61	−0.972612
$986$	8.21537e61	3.46857
$987$	0	0
$988$	−3.64229e59	−0.0147522
$989$	1.31789e61	0.522825
$990$	0	0
$991$	−2.42504e60	−0.0923016	−0.0461508	−	0.998934i	$-0.514695\pi$
$991$	−2.42504e60	−0.0923016	−0.0461508	+	0.998934i	$0.514695\pi$
$992$	5.76040e60	0.214765
$993$	0	0
$994$	3.87308e61	1.38559
$995$	−4.84217e61	−1.69694
$996$	0	0
$997$	2.46785e61	0.829979	0.414990	−	0.909826i	$-0.363785\pi$
$997$	2.46785e61	0.829979	0.414990	+	0.909826i	$0.363785\pi$
$998$	−4.30175e61	−1.41732
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	9.42.a.c.1.4		4
3.2	odd	2		3.42.a.b.1.1	✓	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
3.42.a.b.1.1	✓	4	3.2	odd	2
9.42.a.c.1.4		4	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:	\( k \)	\(=\)	\( 42 \)
Character orbit:	\([\chi]\)	\(=\)	9.a (trivial)

\(f(q)\)	\(=\)	\(q+2.00342e6 q^{2} +1.81468e12 q^{4} +3.43221e14 q^{5} -2.11939e17 q^{7} -7.69998e17 q^{8} +O(q^{10})\)	\(q+2.00342e6 q^{2} +1.81468e12 q^{4} +3.43221e14 q^{5} -2.11939e17 q^{7} -7.69998e17 q^{8} +6.87617e20 q^{10} +2.68951e21 q^{11} -4.84491e22 q^{13} -4.24604e23 q^{14} -5.53316e24 q^{16} +2.66383e25 q^{17} +4.14274e24 q^{19} +6.22838e26 q^{20} +5.38824e27 q^{22} +6.80863e27 q^{23} +7.23261e28 q^{25} -9.70641e28 q^{26} -3.84602e29 q^{28} +1.53939e30 q^{29} -6.13330e29 q^{31} -9.39202e30 q^{32} +5.33678e31 q^{34} -7.27420e31 q^{35} +1.47726e32 q^{37} +8.29967e30 q^{38} -2.64280e32 q^{40} -1.43312e33 q^{41} +1.93562e33 q^{43} +4.88061e33 q^{44} +1.36406e34 q^{46} +1.54236e34 q^{47} +3.50578e32 q^{49} +1.44900e35 q^{50} -8.79197e34 q^{52} -2.77827e35 q^{53} +9.23098e35 q^{55} +1.63193e35 q^{56} +3.08404e36 q^{58} +2.82191e36 q^{59} +3.86057e36 q^{61} -1.22876e36 q^{62} -6.64865e36 q^{64} -1.66288e37 q^{65} -4.59962e36 q^{67} +4.83401e37 q^{68} -1.45733e38 q^{70} -9.12164e37 q^{71} -6.94314e36 q^{73} +2.95957e38 q^{74} +7.51776e36 q^{76} -5.70013e38 q^{77} +5.97141e38 q^{79} -1.89910e39 q^{80} -2.87114e39 q^{82} +3.36804e39 q^{83} +9.14284e39 q^{85} +3.87787e39 q^{86} -2.07092e39 q^{88} +1.32775e40 q^{89} +1.02683e40 q^{91} +1.23555e40 q^{92} +3.09000e40 q^{94} +1.42188e39 q^{95} -9.71560e40 q^{97} +7.02357e38 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 69822 q^{2} + 5352947588932 q^{4} - 118536963776280 q^{5} + 15\!\cdots\!36 q^{7}+ \cdots - 62\!\cdots\!84 q^{8}+O(q^{10}) \) 4 * q + 69822 * q^2 + 5352947588932 * q^4 - 118536963776280 * q^5 + 150256264888927136 * q^7 - 6279626248119395784 * q^8	\( 4 q + 69822 q^{2} + 5352947588932 q^{4} - 118536963776280 q^{5} + 15\!\cdots\!36 q^{7}+ \cdots + 68\!\cdots\!22 q^{98}+O(q^{100}) \) 4 * q + 69822 * q^2 + 5352947588932 * q^4 - 118536963776280 * q^5 + 150256264888927136 * q^7 - 6279626248119395784 * q^8 + 725751018728422700940 * q^10 - 724810647231440683056 * q^11 - 8843977274373065537608 * q^13 - 493449664223337937919568 * q^14 - 5962194966280197033033200 * q^16 + 38231582029295844707285688 * q^17 + 261842746845948075837831248 * q^19 - 785441926018305471679038360 * q^20 - 6322149663566345845522943976 * q^22 + 15395573913207335266380880032 * q^23 + 117350921958371528604086683900 * q^25 + 62942545095927728709970694052 * q^26 + 684437536459146482218511575712 * q^28 + 1036098964520685524199931325064 * q^29 + 9280613209905247622577480610304 * q^31 - 19645397922916950127447685511456 * q^32 + 92420157643501864091330064020004 * q^34 - 207436667553525639419383641992640 * q^35 + 200754880510048713109452091192856 * q^37 - 1146938682238729575315585266559528 * q^38 + 2565083222429486590317315499815600 * q^40 - 2357905268481965433001096926030504 * q^41 + 3943358618915609696106480688157360 * q^43 + 18494278585991583572852191821764304 * q^44 - 44252120640849956767942988241684816 * q^46 + 8890000412230234893665157147040320 * q^47 - 33104900387055220681685954563991580 * q^49 + 216323679312314207800001999371642050 * q^50 - 596234086188669794371774262733483208 * q^52 - 95704753827317216756019399314791128 * q^53 + 1291057043675253444545805475556816160 * q^55 - 1940580325939766339139469085046208320 * q^56 + 3859053206955865617315425524661917116 * q^58 + 1809289331104083090977131835906657808 * q^59 + 5381027332088000515346282395501157240 * q^61 - 14109494547714507002913033009898657152 * q^62 - 389844533130084697385386794140537792 * q^64 + 9754648834359651370261564655441346480 * q^65 - 73273159367285254897696664016673247728 * q^67 + 89019363361032581039655795923994746424 * q^68 - 127374089191018487217525315519713602080 * q^70 + 84396091414708989106237239330896374752 * q^71 - 44706579271813174655854382994714255832 * q^73 + 299692406925616462116506150539738813812 * q^74 + 1128262001217587654782588548338718696272 * q^76 - 833312137190144115784050615522845895552 * q^77 + 1416534390331633014953369475707893311680 * q^79 - 1539903590051088861086709486592809053280 * q^80 + 613971248288365719286532695984150451412 * q^82 - 1526205590962076227407755639349783073104 * q^83 - 285377453319367852617718519171747770960 * q^85 + 12934468921257599734617599325958640634024 * q^86 - 13219976774504188013705589441700285953696 * q^88 + 39593715237961905051969833281675978558872 * q^89 - 8845052344004724172694600210873108791616 * q^91 + 65206363053810587386463980322833360400544 * q^92 + 98582759073905793403791649187553312740832 * q^94 - 7880313586718908134850457997267850706400 * q^95 + 36750128325858234547252025624989137001352 * q^97 + 68350119771260167200829379908744318383822 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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