LMFDB - Embedded newform 9.42.a.c.1.2

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			1.2
Root			$-161109.$ 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)

$f(q)$	$=$	$q-949201. q^{2} -1.29804e12 q^{4} +1.14706e14 q^{5} -7.22302e16 q^{7} +3.31942e18 q^{8} +O(q^{10})$	\(q-949201. q^{2} -1.29804e12 q^{4} +1.14706e14 q^{5} -7.22302e16 q^{7} +3.31942e18 q^{8} -1.08879e20 q^{10} -2.08542e21 q^{11} +1.02587e23 q^{13} +6.85610e22 q^{14} -2.96374e23 q^{16} -1.36112e25 q^{17} +1.23562e26 q^{19} -1.48892e26 q^{20} +1.97949e27 q^{22} +4.97896e27 q^{23} -3.23174e28 q^{25} -9.73760e28 q^{26} +9.37577e28 q^{28} -7.01030e29 q^{29} +1.80793e30 q^{31} -7.01816e30 q^{32} +1.29198e31 q^{34} -8.28521e30 q^{35} +2.23556e32 q^{37} -1.17286e32 q^{38} +3.80756e32 q^{40} -1.70393e33 q^{41} -2.72718e33 q^{43} +2.70696e33 q^{44} -4.72604e33 q^{46} +4.84907e33 q^{47} -3.93504e34 q^{49} +3.06757e34 q^{50} -1.33162e35 q^{52} +5.39056e33 q^{53} -2.39210e35 q^{55} -2.39762e35 q^{56} +6.65419e35 q^{58} -3.17087e36 q^{59} -1.06464e36 q^{61} -1.71609e36 q^{62} +7.31338e36 q^{64} +1.17673e37 q^{65} -3.93766e37 q^{67} +1.76679e37 q^{68} +7.86433e36 q^{70} +1.01810e38 q^{71} +2.40996e38 q^{73} -2.12200e38 q^{74} -1.60389e38 q^{76} +1.50630e38 q^{77} +3.87752e38 q^{79} -3.39958e37 q^{80} +1.61738e39 q^{82} -7.28847e38 q^{83} -1.56128e39 q^{85} +2.58864e39 q^{86} -6.92238e39 q^{88} +1.16027e40 q^{89} -7.40991e39 q^{91} -6.46289e39 q^{92} -4.60274e39 q^{94} +1.41733e40 q^{95} +9.69468e40 q^{97} +3.73515e40 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−949201.	−0.640093	−0.320047	−	0.947402i	$-0.603699\pi$
$2$	−949201.	−0.640093	−0.320047	+	0.947402i	$0.603699\pi$
$3$	0	0
$3$	0	0
$4$	−1.29804e12	−0.590280
$5$	1.14706e14	0.537897	0.268949	−	0.963154i	$-0.413324\pi$
$5$	1.14706e14	0.537897	0.268949	+	0.963154i	$0.413324\pi$
$6$	0	0
$7$	−7.22302e16	−0.342144	−0.171072	−	0.985259i	$-0.554723\pi$
$7$	−7.22302e16	−0.342144	−0.171072	+	0.985259i	$0.554723\pi$
$8$	3.31942e18	1.01793
$9$	0	0
$10$	−1.08879e20	−0.344305
$11$	−2.08542e21	−0.934639	−0.467319	−	0.884089i	$-0.654780\pi$
$11$	−2.08542e21	−0.934639	−0.467319	+	0.884089i	$0.654780\pi$
$12$	0	0
$13$	1.02587e23	1.49711	0.748557	−	0.663070i	$-0.230747\pi$
$13$	1.02587e23	1.49711	0.748557	+	0.663070i	$0.230747\pi$
$14$	6.85610e22	0.219004
$15$	0	0
$16$	−2.96374e23	−0.0612887
$17$	−1.36112e25	−0.812259	−0.406130	−	0.913815i	$-0.633122\pi$
$17$	−1.36112e25	−0.812259	−0.406130	+	0.913815i	$0.633122\pi$
$18$	0	0
$19$	1.23562e26	0.754115	0.377058	−	0.926190i	$-0.376936\pi$
$19$	1.23562e26	0.754115	0.377058	+	0.926190i	$0.376936\pi$
$20$	−1.48892e26	−0.317510
$21$	0	0
$22$	1.97949e27	0.598256
$23$	4.97896e27	0.604948	0.302474	−	0.953158i	$-0.402187\pi$
$23$	4.97896e27	0.604948	0.302474	+	0.953158i	$0.402187\pi$
$24$	0	0
$25$	−3.23174e28	−0.710666
$26$	−9.73760e28	−0.958293
$27$	0	0
$28$	9.37577e28	0.201961
$29$	−7.01030e29	−0.735492	−0.367746	−	0.929926i	$-0.619870\pi$
$29$	−7.01030e29	−0.735492	−0.367746	+	0.929926i	$0.619870\pi$
$30$	0	0
$31$	1.80793e30	0.483355	0.241677	−	0.970357i	$-0.422302\pi$
$31$	1.80793e30	0.483355	0.241677	+	0.970357i	$0.422302\pi$
$32$	−7.01816e30	−0.978698
$33$	0	0
$34$	1.29198e31	0.519922
$35$	−8.28521e30	−0.184038
$36$	0	0
$37$	2.23556e32	1.58947	0.794733	−	0.606959i	$-0.207611\pi$
$37$	2.23556e32	1.58947	0.794733	+	0.606959i	$0.207611\pi$
$38$	−1.17286e32	−0.482704
$39$	0	0
$40$	3.80756e32	0.547541
$41$	−1.70393e33	−1.47701	−0.738505	−	0.674248i	$-0.764468\pi$
$41$	−1.70393e33	−1.47701	−0.738505	+	0.674248i	$0.764468\pi$
$42$	0	0
$43$	−2.72718e33	−0.890451	−0.445226	−	0.895418i	$-0.646877\pi$
$43$	−2.72718e33	−0.890451	−0.445226	+	0.895418i	$0.646877\pi$
$44$	2.70696e33	0.551699
$45$	0	0
$46$	−4.72604e33	−0.387223
$47$	4.84907e33	0.255654	0.127827	−	0.991796i	$-0.459200\pi$
$47$	4.84907e33	0.255654	0.127827	+	0.991796i	$0.459200\pi$
$48$	0	0
$49$	−3.93504e34	−0.882937
$50$	3.06757e34	0.454893
$51$	0	0
$52$	−1.33162e35	−0.883717
$53$	5.39056e33	0.0242091	0.0121045	−	0.999927i	$-0.496147\pi$
$53$	5.39056e33	0.0242091	0.0121045	+	0.999927i	$0.496147\pi$
$54$	0	0
$55$	−2.39210e35	−0.502740
$56$	−2.39762e35	−0.348278
$57$	0	0
$58$	6.65419e35	0.470783
$59$	−3.17087e36	−1.58020	−0.790099	−	0.612979i	$-0.789971\pi$
$59$	−3.17087e36	−1.58020	−0.790099	+	0.612979i	$0.789971\pi$
$60$	0	0
$61$	−1.06464e36	−0.267882	−0.133941	−	0.990989i	$-0.542763\pi$
$61$	−1.06464e36	−0.267882	−0.133941	+	0.990989i	$0.542763\pi$
$62$	−1.71609e36	−0.309392
$63$	0	0
$64$	7.31338e36	0.687747
$65$	1.17673e37	0.805294
$66$	0	0
$67$	−3.93766e37	−1.44779	−0.723893	−	0.689912i	$-0.757649\pi$
$67$	−3.93766e37	−1.44779	−0.723893	+	0.689912i	$0.757649\pi$
$68$	1.76679e37	0.479461
$69$	0	0
$70$	7.86433e36	0.117802
$71$	1.01810e38	1.14023	0.570115	−	0.821565i	$-0.306898\pi$
$71$	1.01810e38	1.14023	0.570115	+	0.821565i	$0.306898\pi$
$72$	0	0
$73$	2.40996e38	1.52718	0.763591	−	0.645701i	$-0.223435\pi$
$73$	2.40996e38	1.52718	0.763591	+	0.645701i	$0.223435\pi$
$74$	−2.12200e38	−1.01741
$75$	0	0
$76$	−1.60389e38	−0.445140
$77$	1.50630e38	0.319781
$78$	0	0
$79$	3.87752e38	0.486630	0.243315	−	0.969947i	$-0.421765\pi$
$79$	3.87752e38	0.486630	0.243315	+	0.969947i	$0.421765\pi$
$80$	−3.39958e37	−0.0329671
$81$	0	0
$82$	1.61738e39	0.945425
$83$	−7.28847e38	−0.332304	−0.166152	−	0.986100i	$-0.553134\pi$
$83$	−7.28847e38	−0.332304	−0.166152	+	0.986100i	$0.553134\pi$
$84$	0	0
$85$	−1.56128e39	−0.436912
$86$	2.58864e39	0.569972
$87$	0	0
$88$	−6.92238e39	−0.951395
$89$	1.16027e40	1.26492	0.632459	−	0.774594i	$-0.282046\pi$
$89$	1.16027e40	1.26492	0.632459	+	0.774594i	$0.282046\pi$
$90$	0	0
$91$	−7.40991e39	−0.512229
$92$	−6.46289e39	−0.357089
$93$	0	0
$94$	−4.60274e39	−0.163642
$95$	1.41733e40	0.405637
$96$	0	0
$97$	9.69468e40	1.81014	0.905071	−	0.425260i	$-0.139817\pi$
$97$	9.69468e40	1.81014	0.905071	+	0.425260i	$0.139817\pi$
$98$	3.73515e40	0.565162
$99$	0	0
$100$	4.19492e40	0.419492
$101$	3.64422e40	0.297178	0.148589	−	0.988899i	$-0.452527\pi$
$101$	3.64422e40	0.297178	0.148589	+	0.988899i	$0.452527\pi$
$102$	0	0
$103$	2.48116e41	1.35360	0.676802	−	0.736165i	$-0.263365\pi$
$103$	2.48116e41	1.35360	0.676802	+	0.736165i	$0.263365\pi$
$104$	3.40530e41	1.52395
$105$	0	0
$106$	−5.11672e39	−0.0154961
$107$	3.56168e41	0.889791	0.444895	−	0.895583i	$-0.353241\pi$
$107$	3.56168e41	0.889791	0.444895	+	0.895583i	$0.353241\pi$
$108$	0	0
$109$	−1.67738e41	−0.286674	−0.143337	−	0.989674i	$-0.545783\pi$
$109$	−1.67738e41	−0.286674	−0.143337	+	0.989674i	$0.545783\pi$
$110$	2.27058e41	0.321801
$111$	0	0
$112$	2.14072e40	0.0209696
$113$	2.13093e42	1.73965	0.869825	−	0.493360i	$-0.164232\pi$
$113$	2.13093e42	1.73965	0.869825	+	0.493360i	$0.164232\pi$
$114$	0	0
$115$	5.71115e41	0.325400
$116$	9.09965e41	0.434146
$117$	0	0
$118$	3.00979e42	1.01147
$119$	9.83143e41	0.277910
$120$	0	0
$121$	−6.29534e41	−0.126450
$122$	1.01056e42	0.171469
$123$	0	0
$124$	−2.34676e42	−0.285315
$125$	−8.92319e42	−0.920163
$126$	0	0
$127$	1.48181e43	1.10361	0.551805	−	0.833973i	$-0.313939\pi$
$127$	1.48181e43	1.10361	0.551805	+	0.833973i	$0.313939\pi$
$128$	8.49122e42	0.538475
$129$	0	0
$130$	−1.11696e43	−0.515463
$131$	2.99812e43	1.18246	0.591232	−	0.806501i	$-0.298642\pi$
$131$	2.99812e43	1.18246	0.591232	+	0.806501i	$0.298642\pi$
$132$	0	0
$133$	−8.92495e42	−0.258016
$134$	3.73763e43	0.926718
$135$	0	0
$136$	−4.51814e43	−0.826822
$137$	−1.16632e44	−1.83674	−0.918369	−	0.395726i	$-0.870493\pi$
$137$	−1.16632e44	−1.83674	−0.918369	+	0.395726i	$0.870493\pi$
$138$	0	0
$139$	1.35351e44	1.58364	0.791822	−	0.610752i	$-0.209133\pi$
$139$	1.35351e44	1.58364	0.791822	+	0.610752i	$0.209133\pi$
$140$	1.07545e43	0.108634
$141$	0	0
$142$	−9.66379e43	−0.729854
$143$	−2.13938e44	−1.39926
$144$	0	0
$145$	−8.04121e43	−0.395619
$146$	−2.28753e44	−0.977539
$147$	0	0
$148$	−2.90185e44	−0.938231
$149$	−5.31972e44	−1.49820	−0.749100	−	0.662457i	$-0.769514\pi$
$149$	−5.31972e44	−1.49820	−0.749100	+	0.662457i	$0.769514\pi$
$150$	0	0
$151$	−7.04551e43	−0.150968	−0.0754840	−	0.997147i	$-0.524050\pi$
$151$	−7.04551e43	−0.150968	−0.0754840	+	0.997147i	$0.524050\pi$
$152$	4.10155e44	0.767635
$153$	0	0
$154$	−1.42979e44	−0.204690
$155$	2.07379e44	0.259995
$156$	0	0
$157$	−5.91730e44	−0.570401	−0.285201	−	0.958468i	$-0.592060\pi$
$157$	−5.91730e44	−0.570401	−0.285201	+	0.958468i	$0.592060\pi$
$158$	−3.68055e44	−0.311489
$159$	0	0
$160$	−8.05022e44	−0.526439
$161$	−3.59632e44	−0.206980
$162$	0	0
$163$	2.16790e45	0.968707	0.484354	−	0.874872i	$-0.339055\pi$
$163$	2.16790e45	0.968707	0.484354	+	0.874872i	$0.339055\pi$
$164$	2.21177e45	0.871850
$165$	0	0
$166$	6.91823e44	0.212706
$167$	−2.71432e45	−0.737858	−0.368929	−	0.929458i	$-0.620275\pi$
$167$	−2.71432e45	−0.737858	−0.368929	+	0.929458i	$0.620275\pi$
$168$	0	0
$169$	5.82871e45	1.24135
$170$	1.48197e45	0.279665
$171$	0	0
$172$	3.53999e45	0.525616
$173$	7.77679e45	1.02531	0.512655	−	0.858595i	$-0.328662\pi$
$173$	7.77679e45	1.02531	0.512655	+	0.858595i	$0.328662\pi$
$174$	0	0
$175$	2.33429e45	0.243150
$176$	6.18065e44	0.0572828
$177$	0	0
$178$	−1.10133e46	−0.809666
$179$	1.94084e46	1.27205	0.636023	−	0.771670i	$-0.280578\pi$
$179$	1.94084e46	1.27205	0.636023	+	0.771670i	$0.280578\pi$
$180$	0	0
$181$	−2.43655e46	−1.27164	−0.635822	−	0.771836i	$-0.719339\pi$
$181$	−2.43655e46	−1.27164	−0.635822	+	0.771836i	$0.719339\pi$
$182$	7.03349e45	0.327874
$183$	0	0
$184$	1.65273e46	0.615794
$185$	2.56432e46	0.854970
$186$	0	0
$187$	2.83852e46	0.759169
$188$	−6.29428e45	−0.150907
$189$	0	0
$190$	−1.34533e46	−0.259645
$191$	−6.56910e46	−1.13847	−0.569236	−	0.822174i	$-0.692761\pi$
$191$	−6.56910e46	−1.13847	−0.569236	+	0.822174i	$0.692761\pi$
$192$	0	0
$193$	2.17137e46	0.303954	0.151977	−	0.988384i	$-0.451436\pi$
$193$	2.17137e46	0.303954	0.151977	+	0.988384i	$0.451436\pi$
$194$	−9.20220e46	−1.15866
$195$	0	0
$196$	5.10784e46	0.521181
$197$	1.54064e47	1.41626	0.708132	−	0.706080i	$-0.249538\pi$
$197$	1.54064e47	1.41626	0.708132	+	0.706080i	$0.249538\pi$
$198$	0	0
$199$	2.19642e45	0.0164145	0.00820726	−	0.999966i	$-0.497388\pi$
$199$	2.19642e45	0.0164145	0.00820726	+	0.999966i	$0.497388\pi$
$200$	−1.07275e47	−0.723407
$201$	0	0
$202$	−3.45910e46	−0.190222
$203$	5.06356e46	0.251644
$204$	0	0
$205$	−1.95451e47	−0.794480
$206$	−2.35512e47	−0.866433
$207$	0	0
$208$	−3.04042e46	−0.0917563
$209$	−2.57680e47	−0.704826
$210$	0	0
$211$	−3.89810e47	−0.877127	−0.438564	−	0.898700i	$-0.644513\pi$
$211$	−3.89810e47	−0.877127	−0.438564	+	0.898700i	$0.644513\pi$
$212$	−6.99716e45	−0.0142901
$213$	0	0
$214$	−3.38075e47	−0.569549
$215$	−3.12823e47	−0.478971
$216$	0	0
$217$	−1.30587e47	−0.165377
$218$	1.59217e47	0.183498
$219$	0	0
$220$	3.10504e47	0.296757
$221$	−1.39634e48	−1.21605
$222$	0	0
$223$	1.89724e48	1.37364	0.686821	−	0.726827i	$-0.259006\pi$
$223$	1.89724e48	1.37364	0.686821	+	0.726827i	$0.259006\pi$
$224$	5.06923e47	0.334856
$225$	0	0
$226$	−2.02269e48	−1.11354
$227$	1.93755e48	0.974370	0.487185	−	0.873299i	$-0.338024\pi$
$227$	1.93755e48	0.974370	0.487185	+	0.873299i	$0.338024\pi$
$228$	0	0
$229$	4.36087e48	1.83209	0.916043	−	0.401080i	$-0.131365\pi$
$229$	4.36087e48	1.83209	0.916043	+	0.401080i	$0.131365\pi$
$230$	−5.42103e47	−0.208287
$231$	0	0
$232$	−2.32701e48	−0.748678
$233$	4.66734e48	1.37491	0.687453	−	0.726229i	$-0.258729\pi$
$233$	4.66734e48	1.37491	0.687453	+	0.726229i	$0.258729\pi$
$234$	0	0
$235$	5.56215e47	0.137515
$236$	4.11591e48	0.932760
$237$	0	0
$238$	−9.33200e47	−0.177888
$239$	3.69664e48	0.646622	0.323311	−	0.946293i	$-0.395204\pi$
$239$	3.69664e48	0.646622	0.323311	+	0.946293i	$0.395204\pi$
$240$	0	0
$241$	3.93114e46	0.00579654	0.00289827	−	0.999996i	$-0.499077\pi$
$241$	3.93114e46	0.00579654	0.00289827	+	0.999996i	$0.499077\pi$
$242$	5.97554e47	0.0809399
$243$	0	0
$244$	1.38195e48	0.158125
$245$	−4.51371e48	−0.474930
$246$	0	0
$247$	1.26759e49	1.12900
$248$	6.00126e48	0.492020
$249$	0	0
$250$	8.46990e48	0.588990
$251$	−1.04813e49	−0.671592	−0.335796	−	0.941935i	$-0.609005\pi$
$251$	−1.04813e49	−0.671592	−0.335796	+	0.941935i	$0.609005\pi$
$252$	0	0
$253$	−1.03832e49	−0.565408
$254$	−1.40653e49	−0.706414
$255$	0	0
$256$	−2.41422e49	−1.03242
$257$	−3.09114e48	−0.122036	−0.0610182	−	0.998137i	$-0.519435\pi$
$257$	−3.09114e48	−0.122036	−0.0610182	+	0.998137i	$0.519435\pi$
$258$	0	0
$259$	−1.61475e49	−0.543827
$260$	−1.52745e49	−0.475349
$261$	0	0
$262$	−2.84582e49	−0.756888
$263$	3.75357e47	0.00923318	0.00461659	−	0.999989i	$-0.498530\pi$
$263$	3.75357e47	0.00923318	0.00461659	+	0.999989i	$0.498530\pi$
$264$	0	0
$265$	6.18327e47	0.0130220
$266$	8.47157e48	0.165154
$267$	0	0
$268$	5.11124e49	0.854600
$269$	−4.83757e49	−0.749386	−0.374693	−	0.927149i	$-0.622252\pi$
$269$	−4.83757e49	−0.749386	−0.374693	+	0.927149i	$0.622252\pi$
$270$	0	0
$271$	−6.10803e49	−0.812888	−0.406444	−	0.913676i	$-0.633231\pi$
$271$	−6.10803e49	−0.812888	−0.406444	+	0.913676i	$0.633231\pi$
$272$	4.03402e48	0.0497823
$273$	0	0
$274$	1.10707e50	1.17568
$275$	6.73953e49	0.664216
$276$	0	0
$277$	−7.20270e49	−0.611871	−0.305936	−	0.952052i	$-0.598969\pi$
$277$	−7.20270e49	−0.611871	−0.305936	+	0.952052i	$0.598969\pi$
$278$	−1.28475e50	−1.01368
$279$	0	0
$280$	−2.75021e49	−0.187338
$281$	−7.49278e49	−0.474421	−0.237210	−	0.971458i	$-0.576233\pi$
$281$	−7.49278e49	−0.474421	−0.237210	+	0.971458i	$0.576233\pi$
$282$	0	0
$283$	6.15623e49	0.337049	0.168524	−	0.985697i	$-0.446100\pi$
$283$	6.15623e49	0.337049	0.168524	+	0.985697i	$0.446100\pi$
$284$	−1.32153e50	−0.673056
$285$	0	0
$286$	2.03070e50	0.895658
$287$	1.23075e50	0.505350
$288$	0	0
$289$	−9.55399e49	−0.340235
$290$	7.63272e49	0.253233
$291$	0	0
$292$	−3.12822e50	−0.901465
$293$	2.36755e50	0.636082	0.318041	−	0.948077i	$-0.396975\pi$
$293$	2.36755e50	0.636082	0.318041	+	0.948077i	$0.396975\pi$
$294$	0	0
$295$	−3.63716e50	−0.849985
$296$	7.42076e50	1.61796
$297$	0	0
$298$	5.04948e50	0.958988
$299$	5.10779e50	0.905677
$300$	0	0
$301$	1.96985e50	0.304663
$302$	6.68760e49	0.0966336
$303$	0	0
$304$	−3.66207e49	−0.0462188
$305$	−1.22121e50	−0.144093
$306$	0	0
$307$	1.27033e51	1.31094	0.655468	−	0.755223i	$-0.272472\pi$
$307$	1.27033e51	1.31094	0.655468	+	0.755223i	$0.272472\pi$
$308$	−1.95524e50	−0.188761
$309$	0	0
$310$	−1.96845e50	−0.166421
$311$	−1.73922e51	−1.37647	−0.688236	−	0.725487i	$-0.741615\pi$
$311$	−1.73922e51	−1.37647	−0.688236	+	0.725487i	$0.741615\pi$
$312$	0	0
$313$	3.53188e50	0.245102	0.122551	−	0.992462i	$-0.460893\pi$
$313$	3.53188e50	0.245102	0.122551	+	0.992462i	$0.460893\pi$
$314$	5.61670e50	0.365110
$315$	0	0
$316$	−5.03318e50	−0.287248
$317$	7.02233e50	0.375635	0.187818	−	0.982204i	$-0.439859\pi$
$317$	7.02233e50	0.375635	0.187818	+	0.982204i	$0.439859\pi$
$318$	0	0
$319$	1.46194e51	0.687419
$320$	8.38885e50	0.369937
$321$	0	0
$322$	3.41363e50	0.132486
$323$	−1.68184e51	−0.612537
$324$	0	0
$325$	−3.31535e51	−1.06395
$326$	−2.05777e51	−0.620063
$327$	0	0
$328$	−5.65606e51	−1.50349
$329$	−3.50249e50	−0.0874704
$330$	0	0
$331$	−3.92842e51	−0.866452	−0.433226	−	0.901285i	$-0.642625\pi$
$331$	−3.92842e51	−0.866452	−0.433226	+	0.901285i	$0.642625\pi$
$332$	9.46073e50	0.196153
$333$	0	0
$334$	2.57643e51	0.472298
$335$	−4.51671e51	−0.778760
$336$	0	0
$337$	−1.03514e51	−0.157975	−0.0789873	−	0.996876i	$-0.525169\pi$
$337$	−1.03514e51	−0.157975	−0.0789873	+	0.996876i	$0.525169\pi$
$338$	−5.53262e51	−0.794581
$339$	0	0
$340$	2.02661e51	0.257901
$341$	−3.77029e51	−0.451762
$342$	0	0
$343$	6.06142e51	0.644236
$344$	−9.05264e51	−0.906415
$345$	0	0
$346$	−7.38174e51	−0.656295
$347$	1.97747e52	1.65713	0.828565	−	0.559894i	$-0.189158\pi$
$347$	1.97747e52	1.65713	0.828565	+	0.559894i	$0.189158\pi$
$348$	0	0
$349$	1.12256e52	0.836158	0.418079	−	0.908411i	$-0.362704\pi$
$349$	1.12256e52	0.836158	0.418079	+	0.908411i	$0.362704\pi$
$350$	−2.21571e51	−0.155639
$351$	0	0
$352$	1.46358e52	0.914729
$353$	1.33863e52	0.789368	0.394684	−	0.918817i	$-0.370854\pi$
$353$	1.33863e52	0.789368	0.394684	+	0.918817i	$0.370854\pi$
$354$	0	0
$355$	1.16781e52	0.613327
$356$	−1.50607e52	−0.746657
$357$	0	0
$358$	−1.84225e52	−0.814229
$359$	3.81033e52	1.59047	0.795237	−	0.606298i	$-0.207346\pi$
$359$	3.81033e52	1.59047	0.795237	+	0.606298i	$0.207346\pi$
$360$	0	0
$361$	−1.15794e52	−0.431310
$362$	2.31278e52	0.813970
$363$	0	0
$364$	9.61836e51	0.302359
$365$	2.76435e52	0.821467
$366$	0	0
$367$	8.16575e51	0.216941	0.108470	−	0.994100i	$-0.465405\pi$
$367$	8.16575e51	0.216941	0.108470	+	0.994100i	$0.465405\pi$
$368$	−1.47564e51	−0.0370765
$369$	0	0
$370$	−2.43405e52	−0.547261
$371$	−3.89361e50	−0.00828300
$372$	0	0
$373$	−2.50717e51	−0.0477696	−0.0238848	−	0.999715i	$-0.507603\pi$
$373$	−2.50717e51	−0.0477696	−0.0238848	+	0.999715i	$0.507603\pi$
$374$	−2.69432e52	−0.485939
$375$	0	0
$376$	1.60961e52	0.260237
$377$	−7.19168e52	−1.10112
$378$	0	0
$379$	3.00144e52	0.412312	0.206156	−	0.978519i	$-0.433905\pi$
$379$	3.00144e52	0.412312	0.206156	+	0.978519i	$0.433905\pi$
$380$	−1.83975e52	−0.239439
$381$	0	0
$382$	6.23540e52	0.728728
$383$	4.77869e52	0.529340	0.264670	−	0.964339i	$-0.414737\pi$
$383$	4.77869e52	0.529340	0.264670	+	0.964339i	$0.414737\pi$
$384$	0	0
$385$	1.72782e52	0.172010
$386$	−2.06106e52	−0.194559
$387$	0	0
$388$	−1.25841e53	−1.06849
$389$	9.56063e51	0.0770052	0.0385026	−	0.999259i	$-0.487741\pi$
$389$	9.56063e51	0.0770052	0.0385026	+	0.999259i	$0.487741\pi$
$390$	0	0
$391$	−6.77698e52	−0.491375
$392$	−1.30621e53	−0.898767
$393$	0	0
$394$	−1.46238e53	−0.906542
$395$	4.44774e52	0.261757
$396$	0	0
$397$	5.70592e52	0.302775	0.151388	−	0.988474i	$-0.451626\pi$
$397$	5.70592e52	0.302775	0.151388	+	0.988474i	$0.451626\pi$
$398$	−2.08485e51	−0.0105068
$399$	0	0
$400$	9.57803e51	0.0435558
$401$	2.10266e52	0.0908469	0.0454234	−	0.998968i	$-0.485536\pi$
$401$	2.10266e52	0.0908469	0.0454234	+	0.998968i	$0.485536\pi$
$402$	0	0
$403$	1.85470e53	0.723637
$404$	−4.73035e52	−0.175418
$405$	0	0
$406$	−4.80633e52	−0.161076
$407$	−4.66209e53	−1.48558
$408$	0	0
$409$	−4.22684e51	−0.0121811	−0.00609056	−	0.999981i	$-0.501939\pi$
$409$	−4.22684e51	−0.0121811	−0.00609056	+	0.999981i	$0.501939\pi$
$410$	1.85522e53	0.508541
$411$	0	0
$412$	−3.22065e53	−0.799006
$413$	2.29032e53	0.540656
$414$	0	0
$415$	−8.36029e52	−0.178746
$416$	−7.19974e53	−1.46522
$417$	0	0
$418$	2.44590e53	0.451154
$419$	3.36354e53	0.590757	0.295379	−	0.955380i	$-0.404554\pi$
$419$	3.36354e53	0.590757	0.295379	+	0.955380i	$0.404554\pi$
$420$	0	0
$421$	5.17107e53	0.823755	0.411877	−	0.911239i	$-0.364873\pi$
$421$	5.17107e53	0.823755	0.411877	+	0.911239i	$0.364873\pi$
$422$	3.70008e53	0.561443
$423$	0	0
$424$	1.78935e52	0.0246431
$425$	4.39879e53	0.577245
$426$	0	0
$427$	7.68995e52	0.0916542
$428$	−4.62321e53	−0.525226
$429$	0	0
$430$	2.96932e53	0.306586
$431$	1.75749e54	1.73025	0.865124	−	0.501559i	$-0.167240\pi$
$431$	1.75749e54	1.73025	0.865124	+	0.501559i	$0.167240\pi$
$432$	0	0
$433$	−1.46349e54	−1.31035	−0.655176	−	0.755476i	$-0.727406\pi$
$433$	−1.46349e54	−1.31035	−0.655176	+	0.755476i	$0.727406\pi$
$434$	1.23953e53	0.105857
$435$	0	0
$436$	2.17731e53	0.169218
$437$	6.15213e53	0.456201
$438$	0	0
$439$	−1.27414e53	−0.0860387	−0.0430194	−	0.999074i	$-0.513698\pi$
$439$	−1.27414e53	−0.0860387	−0.0430194	+	0.999074i	$0.513698\pi$
$440$	−7.94036e53	−0.511753
$441$	0	0
$442$	1.32541e54	0.778383
$443$	2.79495e54	1.56710	0.783551	−	0.621328i	$-0.213406\pi$
$443$	2.79495e54	1.56710	0.783551	+	0.621328i	$0.213406\pi$
$444$	0	0
$445$	1.33089e54	0.680396
$446$	−1.80087e54	−0.879259
$447$	0	0
$448$	−5.28247e53	−0.235309
$449$	2.51902e54	1.07197	0.535985	−	0.844228i	$-0.319940\pi$
$449$	2.51902e54	1.07197	0.535985	+	0.844228i	$0.319940\pi$
$450$	0	0
$451$	3.55342e54	1.38047
$452$	−2.76604e54	−1.02688
$453$	0	0
$454$	−1.83913e54	−0.623688
$455$	−8.49958e53	−0.275527
$456$	0	0
$457$	1.55517e54	0.460782	0.230391	−	0.973098i	$-0.426000\pi$
$457$	1.55517e54	0.460782	0.230391	+	0.973098i	$0.426000\pi$
$458$	−4.13934e54	−1.17271
$459$	0	0
$460$	−7.41330e53	−0.192077
$461$	−6.49280e54	−1.60903	−0.804513	−	0.593935i	$-0.797574\pi$
$461$	−6.49280e54	−1.60903	−0.804513	+	0.593935i	$0.797574\pi$
$462$	0	0
$463$	−6.66332e54	−1.51106	−0.755528	−	0.655116i	$-0.772620\pi$
$463$	−6.66332e54	−1.51106	−0.755528	+	0.655116i	$0.772620\pi$
$464$	2.07767e53	0.0450774
$465$	0	0
$466$	−4.43024e54	−0.880068
$467$	3.67556e54	0.698759	0.349379	−	0.936981i	$-0.386392\pi$
$467$	3.67556e54	0.698759	0.349379	+	0.936981i	$0.386392\pi$
$468$	0	0
$469$	2.84418e54	0.495351
$470$	−5.27960e53	−0.0880228
$471$	0	0
$472$	−1.05254e55	−1.60853
$473$	5.68732e54	0.832250
$474$	0	0
$475$	−3.99321e54	−0.535924
$476$	−1.27616e54	−0.164045
$477$	0	0
$478$	−3.50886e54	−0.413899
$479$	−1.46454e55	−1.65510	−0.827550	−	0.561393i	$-0.810266\pi$
$479$	−1.46454e55	−1.65510	−0.827550	+	0.561393i	$0.810266\pi$
$480$	0	0
$481$	2.29340e55	2.37961
$482$	−3.73144e52	−0.00371033
$483$	0	0
$484$	8.17160e53	0.0746410
$485$	1.11203e55	0.973671
$486$	0	0
$487$	−5.71157e53	−0.0459633	−0.0229817	−	0.999736i	$-0.507316\pi$
$487$	−5.71157e53	−0.0459633	−0.0229817	+	0.999736i	$0.507316\pi$
$488$	−3.53400e54	−0.272684
$489$	0	0
$490$	4.28442e54	0.303999
$491$	1.22705e55	0.835013	0.417507	−	0.908674i	$-0.362904\pi$
$491$	1.22705e55	0.835013	0.417507	+	0.908674i	$0.362904\pi$
$492$	0	0
$493$	9.54189e54	0.597410
$494$	−1.20320e55	−0.722664
$495$	0	0
$496$	−5.35822e53	−0.0296242
$497$	−7.35373e54	−0.390123
$498$	0	0
$499$	2.84787e54	0.139142	0.0695711	−	0.997577i	$-0.477837\pi$
$499$	2.84787e54	0.139142	0.0695711	+	0.997577i	$0.477837\pi$
$500$	1.15827e55	0.543154
$501$	0	0
$502$	9.94890e54	0.429882
$503$	3.82363e55	1.58610	0.793052	−	0.609154i	$-0.208491\pi$
$503$	3.82363e55	1.58610	0.793052	+	0.609154i	$0.208491\pi$
$504$	0	0
$505$	4.18013e54	0.159851
$506$	9.85578e54	0.361914
$507$	0	0
$508$	−1.92345e55	−0.651439
$509$	−8.07505e54	−0.262682	−0.131341	−	0.991337i	$-0.541928\pi$
$509$	−8.07505e54	−0.262682	−0.131341	+	0.991337i	$0.541928\pi$
$510$	0	0
$511$	−1.74072e55	−0.522516
$512$	4.24338e54	0.122371
$513$	0	0
$514$	2.93411e54	0.0781146
$515$	2.84603e55	0.728100
$516$	0	0
$517$	−1.01124e55	−0.238944
$518$	1.53272e55	0.348100
$519$	0	0
$520$	3.90607e55	0.819731
$521$	2.48709e55	0.501785	0.250892	−	0.968015i	$-0.419276\pi$
$521$	2.48709e55	0.501785	0.250892	+	0.968015i	$0.419276\pi$
$522$	0	0
$523$	−2.78580e55	−0.519595	−0.259798	−	0.965663i	$-0.583656\pi$
$523$	−2.78580e55	−0.519595	−0.259798	+	0.965663i	$0.583656\pi$
$524$	−3.89169e55	−0.697985
$525$	0	0
$526$	−3.56289e53	−0.00591010
$527$	−2.46081e55	−0.392609
$528$	0	0
$529$	−4.29493e55	−0.634037
$530$	−5.86917e53	−0.00833530
$531$	0	0
$532$	1.15849e55	0.152302
$533$	−1.74802e56	−2.21125
$534$	0	0
$535$	4.08545e55	0.478616
$536$	−1.30707e56	−1.47374
$537$	0	0
$538$	4.59183e55	0.479677
$539$	8.20623e55	0.825228
$540$	0	0
$541$	−4.88133e55	−0.454982	−0.227491	−	0.973780i	$-0.573052\pi$
$541$	−4.88133e55	−0.454982	−0.227491	+	0.973780i	$0.573052\pi$
$542$	5.79775e55	0.520324
$543$	0	0
$544$	9.55258e55	0.794956
$545$	−1.92405e55	−0.154201
$546$	0	0
$547$	−4.27578e55	−0.317889	−0.158945	−	0.987288i	$-0.550809\pi$
$547$	−4.27578e55	−0.317889	−0.158945	+	0.987288i	$0.550809\pi$
$548$	1.51393e56	1.08419
$549$	0	0
$550$	−6.39717e55	−0.425161
$551$	−8.66210e55	−0.554646
$552$	0	0
$553$	−2.80074e55	−0.166498
$554$	6.83681e55	0.391655
$555$	0	0
$556$	−1.75691e56	−0.934794
$557$	−1.34558e56	−0.690047	−0.345024	−	0.938594i	$-0.612129\pi$
$557$	−1.34558e56	−0.690047	−0.345024	+	0.938594i	$0.612129\pi$
$558$	0	0
$559$	−2.79774e56	−1.33311
$560$	2.45552e54	0.0112795
$561$	0	0
$562$	7.11216e55	0.303674
$563$	1.26109e56	0.519189	0.259594	−	0.965718i	$-0.416411\pi$
$563$	1.26109e56	0.519189	0.259594	+	0.965718i	$0.416411\pi$
$564$	0	0
$565$	2.44430e56	0.935753
$566$	−5.84350e55	−0.215743
$567$	0	0
$568$	3.37949e56	1.16067
$569$	−3.82146e56	−1.26598	−0.632992	−	0.774159i	$-0.718173\pi$
$569$	−3.82146e56	−1.26598	−0.632992	+	0.774159i	$0.718173\pi$
$570$	0	0
$571$	−2.98561e56	−0.920434	−0.460217	−	0.887806i	$-0.652228\pi$
$571$	−2.98561e56	−0.920434	−0.460217	+	0.887806i	$0.652228\pi$
$572$	2.77700e56	0.825957
$573$	0	0
$574$	−1.16823e56	−0.323472
$575$	−1.60907e56	−0.429916
$576$	0	0
$577$	6.45520e56	1.60622	0.803111	−	0.595829i	$-0.203177\pi$
$577$	6.45520e56	1.60622	0.803111	+	0.595829i	$0.203177\pi$
$578$	9.06865e55	0.217782
$579$	0	0
$580$	1.04378e56	0.233526
$581$	5.26448e55	0.113696
$582$	0	0
$583$	−1.12416e55	−0.0226267
$584$	7.99965e56	1.55456
$585$	0	0
$586$	−2.24728e56	−0.407152
$587$	7.69679e56	1.34657	0.673285	−	0.739383i	$-0.264883\pi$
$587$	7.69679e56	1.34657	0.673285	+	0.739383i	$0.264883\pi$
$588$	0	0
$589$	2.23392e56	0.364505
$590$	3.45240e56	0.544070
$591$	0	0
$592$	−6.62563e55	−0.0974164
$593$	−9.29163e56	−1.31969	−0.659843	−	0.751404i	$-0.729377\pi$
$593$	−9.29163e56	−1.31969	−0.659843	+	0.751404i	$0.729377\pi$
$594$	0	0
$595$	1.12772e56	0.149487
$596$	6.90521e56	0.884358
$597$	0	0
$598$	−4.84832e56	−0.579718
$599$	2.79378e55	0.0322807	0.0161403	−	0.999870i	$-0.494862\pi$
$599$	2.79378e55	0.0322807	0.0161403	+	0.999870i	$0.494862\pi$
$600$	0	0
$601$	6.98610e56	0.753891	0.376945	−	0.926236i	$-0.376974\pi$
$601$	6.98610e56	0.753891	0.376945	+	0.926236i	$0.376974\pi$
$602$	−1.86978e56	−0.195013
$603$	0	0
$604$	9.14535e55	0.0891134
$605$	−7.22111e55	−0.0680172
$606$	0	0
$607$	−7.02909e56	−0.618772	−0.309386	−	0.950936i	$-0.600124\pi$
$607$	−7.02909e56	−0.618772	−0.309386	+	0.950936i	$0.600124\pi$
$608$	−8.67181e56	−0.738051
$609$	0	0
$610$	1.15917e56	0.0922329
$611$	4.97453e56	0.382743
$612$	0	0
$613$	−9.34826e56	−0.672653	−0.336327	−	0.941745i	$-0.609185\pi$
$613$	−9.34826e56	−0.672653	−0.336327	+	0.941745i	$0.609185\pi$
$614$	−1.20580e57	−0.839121
$615$	0	0
$616$	5.00005e56	0.325514
$617$	−1.77746e57	−1.11932	−0.559661	−	0.828722i	$-0.689069\pi$
$617$	−1.77746e57	−1.11932	−0.559661	+	0.828722i	$0.689069\pi$
$618$	0	0
$619$	−1.27117e57	−0.749111	−0.374555	−	0.927205i	$-0.622205\pi$
$619$	−1.27117e57	−0.749111	−0.374555	+	0.927205i	$0.622205\pi$
$620$	−2.69186e56	−0.153470
$621$	0	0
$622$	1.65087e57	0.881071
$623$	−8.38063e56	−0.432784
$624$	0	0
$625$	4.46084e56	0.215713
$626$	−3.35246e56	−0.156888
$627$	0	0
$628$	7.68089e56	0.336697
$629$	−3.04288e57	−1.29106
$630$	0	0
$631$	−3.85953e57	−1.53438	−0.767189	−	0.641421i	$-0.778345\pi$
$631$	−3.85953e57	−1.53438	−0.767189	+	0.641421i	$0.778345\pi$
$632$	1.28711e57	0.495355
$633$	0	0
$634$	−6.66560e56	−0.240442
$635$	1.69972e57	0.593629
$636$	0	0
$637$	−4.03686e57	−1.32186
$638$	−1.38768e57	−0.440013
$639$	0	0
$640$	9.73991e56	0.289645
$641$	3.96246e57	1.14124	0.570618	−	0.821215i	$-0.306704\pi$
$641$	3.96246e57	1.14124	0.570618	+	0.821215i	$0.306704\pi$
$642$	0	0
$643$	6.28846e56	0.169910	0.0849551	−	0.996385i	$-0.472925\pi$
$643$	6.28846e56	0.169910	0.0849551	+	0.996385i	$0.472925\pi$
$644$	4.66816e56	0.122176
$645$	0	0
$646$	1.59640e57	0.392081
$647$	1.90563e57	0.453420	0.226710	−	0.973962i	$-0.427203\pi$
$647$	1.90563e57	0.453420	0.226710	+	0.973962i	$0.427203\pi$
$648$	0	0
$649$	6.61259e57	1.47692
$650$	3.14694e57	0.681027
$651$	0	0
$652$	−2.81402e57	−0.571809
$653$	−2.23393e57	−0.439896	−0.219948	−	0.975512i	$-0.570589\pi$
$653$	−2.23393e57	−0.439896	−0.219948	+	0.975512i	$0.570589\pi$
$654$	0	0
$655$	3.43902e57	0.636045
$656$	5.05002e56	0.0905241
$657$	0	0
$658$	3.32457e56	0.0559893
$659$	−1.63351e57	−0.266668	−0.133334	−	0.991071i	$-0.542568\pi$
$659$	−1.63351e57	−0.266668	−0.133334	+	0.991071i	$0.542568\pi$
$660$	0	0
$661$	9.61694e57	1.47539	0.737695	−	0.675134i	$-0.235914\pi$
$661$	9.61694e57	1.47539	0.737695	+	0.675134i	$0.235914\pi$
$662$	3.72886e57	0.554610
$663$	0	0
$664$	−2.41935e57	−0.338262
$665$	−1.02374e57	−0.138786
$666$	0	0
$667$	−3.49040e57	−0.444934
$668$	3.52329e57	0.435543
$669$	0	0
$670$	4.28727e57	0.498479
$671$	2.22023e57	0.250373
$672$	0	0
$673$	3.39459e57	0.360146	0.180073	−	0.983653i	$-0.442367\pi$
$673$	3.39459e57	0.360146	0.180073	+	0.983653i	$0.442367\pi$
$674$	9.82558e56	0.101118
$675$	0	0
$676$	−7.56590e57	−0.732746
$677$	7.93301e57	0.745368	0.372684	−	0.927958i	$-0.378438\pi$
$677$	7.93301e57	0.745368	0.372684	+	0.927958i	$0.378438\pi$
$678$	0	0
$679$	−7.00249e57	−0.619330
$680$	−5.18256e57	−0.444745
$681$	0	0
$682$	3.57876e57	0.289170
$683$	1.09757e57	0.0860612	0.0430306	−	0.999074i	$-0.486299\pi$
$683$	1.09757e57	0.0860612	0.0430306	+	0.999074i	$0.486299\pi$
$684$	0	0
$685$	−1.33784e58	−0.987976
$686$	−5.75351e57	−0.412371
$687$	0	0
$688$	8.08265e56	0.0545746
$689$	5.53003e56	0.0362438
$690$	0	0
$691$	−7.67027e57	−0.473708	−0.236854	−	0.971545i	$-0.576116\pi$
$691$	−7.67027e57	−0.473708	−0.236854	+	0.971545i	$0.576116\pi$
$692$	−1.00946e58	−0.605221
$693$	0	0
$694$	−1.87702e58	−1.06072
$695$	1.55255e58	0.851838
$696$	0	0
$697$	2.31926e58	1.19972
$698$	−1.06554e58	−0.535219
$699$	0	0
$700$	−3.03000e57	−0.143527
$701$	−1.47954e58	−0.680623	−0.340312	−	0.940313i	$-0.610533\pi$
$701$	−1.47954e58	−0.680623	−0.340312	+	0.940313i	$0.610533\pi$
$702$	0	0
$703$	2.76232e58	1.19864
$704$	−1.52515e58	−0.642795
$705$	0	0
$706$	−1.27063e58	−0.505269
$707$	−2.63223e57	−0.101678
$708$	0	0
$709$	4.06301e57	0.148115	0.0740576	−	0.997254i	$-0.476405\pi$
$709$	4.06301e57	0.148115	0.0740576	+	0.997254i	$0.476405\pi$
$710$	−1.10849e58	−0.392587
$711$	0	0
$712$	3.85141e58	1.28760
$713$	9.00160e57	0.292405
$714$	0	0
$715$	−2.45399e58	−0.752659
$716$	−2.51929e58	−0.750864
$717$	0	0
$718$	−3.61677e58	−1.01805
$719$	−2.21575e58	−0.606148	−0.303074	−	0.952967i	$-0.598013\pi$
$719$	−2.21575e58	−0.606148	−0.303074	+	0.952967i	$0.598013\pi$
$720$	0	0
$721$	−1.79215e58	−0.463128
$722$	1.09912e58	0.276079
$723$	0	0
$724$	3.16275e58	0.750626
$725$	2.26554e58	0.522689
$726$	0	0
$727$	3.71059e58	0.809072	0.404536	−	0.914522i	$-0.367433\pi$
$727$	3.71059e58	0.809072	0.404536	+	0.914522i	$0.367433\pi$
$728$	−2.45966e58	−0.521412
$729$	0	0
$730$	−2.62393e58	−0.525816
$731$	3.71203e58	0.723277
$732$	0	0
$733$	−5.86816e58	−1.08111	−0.540556	−	0.841308i	$-0.681786\pi$
$733$	−5.86816e58	−1.08111	−0.540556	+	0.841308i	$0.681786\pi$
$734$	−7.75094e57	−0.138862
$735$	0	0
$736$	−3.49431e58	−0.592061
$737$	8.21167e58	1.35316
$738$	0	0
$739$	3.10061e58	0.483322	0.241661	−	0.970361i	$-0.422308\pi$
$739$	3.10061e58	0.483322	0.241661	+	0.970361i	$0.422308\pi$
$740$	−3.32858e58	−0.504672
$741$	0	0
$742$	3.69582e56	0.00530189
$743$	1.14471e59	1.59744	0.798722	−	0.601701i	$-0.205510\pi$
$743$	1.14471e59	1.59744	0.798722	+	0.601701i	$0.205510\pi$
$744$	0	0
$745$	−6.10201e58	−0.805878
$746$	2.37980e57	0.0305770
$747$	0	0
$748$	−3.68451e58	−0.448123
$749$	−2.57261e58	−0.304437
$750$	0	0
$751$	1.66331e59	1.86360	0.931802	−	0.362966i	$-0.118236\pi$
$751$	1.66331e59	1.86360	0.931802	+	0.362966i	$0.118236\pi$
$752$	−1.43714e57	−0.0156687
$753$	0	0
$754$	6.82635e58	0.704817
$755$	−8.08159e57	−0.0812053
$756$	0	0
$757$	1.61727e59	1.53927	0.769637	−	0.638482i	$-0.220437\pi$
$757$	1.61727e59	1.53927	0.769637	+	0.638482i	$0.220437\pi$
$758$	−2.84897e58	−0.263918
$759$	0	0
$760$	4.70471e58	0.412909
$761$	8.01236e58	0.684503	0.342251	−	0.939608i	$-0.388811\pi$
$761$	8.01236e58	0.684503	0.342251	+	0.939608i	$0.388811\pi$
$762$	0	0
$763$	1.21158e58	0.0980838
$764$	8.52696e58	0.672017
$765$	0	0
$766$	−4.53594e58	−0.338827
$767$	−3.25291e59	−2.36574
$768$	0	0
$769$	−1.30604e59	−0.900465	−0.450233	−	0.892911i	$-0.648659\pi$
$769$	−1.30604e59	−0.900465	−0.450233	+	0.892911i	$0.648659\pi$
$770$	−1.64004e58	−0.110102
$771$	0	0
$772$	−2.81852e58	−0.179418
$773$	2.04229e59	1.26601	0.633006	−	0.774147i	$-0.281821\pi$
$773$	2.04229e59	1.26601	0.633006	+	0.774147i	$0.281821\pi$
$774$	0	0
$775$	−5.84274e58	−0.343504
$776$	3.21807e59	1.84259
$777$	0	0
$778$	−9.07497e57	−0.0492905
$779$	−2.10542e59	−1.11384
$780$	0	0
$781$	−2.12316e59	−1.06570
$782$	6.43272e58	0.314526
$783$	0	0
$784$	1.16625e58	0.0541141
$785$	−6.78747e58	−0.306817
$786$	0	0
$787$	1.36195e59	0.584356	0.292178	−	0.956364i	$-0.405620\pi$
$787$	1.36195e59	0.584356	0.292178	+	0.956364i	$0.405620\pi$
$788$	−1.99982e59	−0.835993
$789$	0	0
$790$	−4.22180e58	−0.167549
$791$	−1.53918e59	−0.595211
$792$	0	0
$793$	−1.09219e59	−0.401050
$794$	−5.41607e58	−0.193805
$795$	0	0
$796$	−2.85105e57	−0.00968917
$797$	−1.40416e59	−0.465073	−0.232537	−	0.972588i	$-0.574703\pi$
$797$	−1.40416e59	−0.465073	−0.232537	+	0.972588i	$0.574703\pi$
$798$	0	0
$799$	−6.60018e58	−0.207657
$800$	2.26808e59	0.695527
$801$	0	0
$802$	−1.99585e58	−0.0581505
$803$	−5.02578e59	−1.42736
$804$	0	0
$805$	−4.12518e58	−0.111334
$806$	−1.76049e59	−0.463195
$807$	0	0
$808$	1.20967e59	0.302506
$809$	−5.07691e59	−1.23781	−0.618907	−	0.785465i	$-0.712424\pi$
$809$	−5.07691e59	−1.23781	−0.618907	+	0.785465i	$0.712424\pi$
$810$	0	0
$811$	−6.03203e59	−1.39809	−0.699047	−	0.715076i	$-0.746392\pi$
$811$	−6.03203e59	−1.39809	−0.699047	+	0.715076i	$0.746392\pi$
$812$	−6.57270e58	−0.148541
$813$	0	0
$814$	4.42526e59	0.950909
$815$	2.48670e59	0.521065
$816$	0	0
$817$	−3.36977e59	−0.671503
$818$	4.01212e57	0.00779706
$819$	0	0
$820$	2.53703e59	0.468966
$821$	3.15683e59	0.569136	0.284568	−	0.958656i	$-0.408150\pi$
$821$	3.15683e59	0.569136	0.284568	+	0.958656i	$0.408150\pi$
$822$	0	0
$823$	1.14484e60	1.96357	0.981785	−	0.189995i	$-0.0608471\pi$
$823$	1.14484e60	1.96357	0.981785	+	0.189995i	$0.0608471\pi$
$824$	8.23601e59	1.37787
$825$	0	0
$826$	−2.17398e59	−0.346070
$827$	8.01118e59	1.24404	0.622019	−	0.783002i	$-0.286313\pi$
$827$	8.01118e59	1.24404	0.622019	+	0.783002i	$0.286313\pi$
$828$	0	0
$829$	−3.02291e59	−0.446743	−0.223371	−	0.974733i	$-0.571706\pi$
$829$	−3.02291e59	−0.446743	−0.223371	+	0.974733i	$0.571706\pi$
$830$	7.93559e58	0.114414
$831$	0	0
$832$	7.50260e59	1.02964
$833$	5.35608e59	0.717174
$834$	0	0
$835$	−3.11347e59	−0.396892
$836$	3.34479e59	0.416045
$837$	0	0
$838$	−3.19268e59	−0.378140
$839$	−3.04705e59	−0.352175	−0.176088	−	0.984374i	$-0.556344\pi$
$839$	−3.04705e59	−0.352175	−0.176088	+	0.984374i	$0.556344\pi$
$840$	0	0
$841$	−4.17042e59	−0.459052
$842$	−4.90839e59	−0.527280
$843$	0	0
$844$	5.05989e59	0.517751
$845$	6.68586e59	0.667720
$846$	0	0
$847$	4.54714e58	0.0432642
$848$	−1.59762e57	−0.00148374
$849$	0	0
$850$	−4.17534e59	−0.369491
$851$	1.11308e60	0.961545
$852$	0	0
$853$	2.51869e59	0.207358	0.103679	−	0.994611i	$-0.466939\pi$
$853$	2.51869e59	0.207358	0.103679	+	0.994611i	$0.466939\pi$
$854$	−7.29931e58	−0.0586672
$855$	0	0
$856$	1.18227e60	0.905743
$857$	−2.02217e60	−1.51256	−0.756278	−	0.654250i	$-0.772984\pi$
$857$	−2.02217e60	−1.51256	−0.756278	+	0.654250i	$0.772984\pi$
$858$	0	0
$859$	1.10285e60	0.786423	0.393211	−	0.919448i	$-0.371364\pi$
$859$	1.10285e60	0.786423	0.393211	+	0.919448i	$0.371364\pi$
$860$	4.06056e59	0.282727
$861$	0	0
$862$	−1.66821e60	−1.10752
$863$	−2.89368e60	−1.87599	−0.937993	−	0.346653i	$-0.887318\pi$
$863$	−2.89368e60	−1.87599	−0.937993	+	0.346653i	$0.887318\pi$
$864$	0	0
$865$	8.92042e59	0.551512
$866$	1.38915e60	0.838748
$867$	0	0
$868$	1.69507e59	0.0976188
$869$	−8.08627e59	−0.454824
$870$	0	0
$871$	−4.03954e60	−2.16750
$872$	−5.56792e59	−0.291814
$873$	0	0
$874$	−5.83961e59	−0.292011
$875$	6.44524e59	0.314828
$876$	0	0
$877$	3.19678e60	1.49012	0.745060	−	0.666997i	$-0.232421\pi$
$877$	3.19678e60	1.49012	0.745060	+	0.666997i	$0.232421\pi$
$878$	1.20941e59	0.0550728
$879$	0	0
$880$	7.08955e58	0.0308123
$881$	2.79351e60	1.18616	0.593081	−	0.805143i	$-0.297911\pi$
$881$	2.79351e60	1.18616	0.593081	+	0.805143i	$0.297911\pi$
$882$	0	0
$883$	−4.93461e59	−0.200013	−0.100007	−	0.994987i	$-0.531886\pi$
$883$	−4.93461e59	−0.200013	−0.100007	+	0.994987i	$0.531886\pi$
$884$	1.81251e60	0.717808
$885$	0	0
$886$	−2.65297e60	−1.00309
$887$	−4.55196e60	−1.68176	−0.840881	−	0.541220i	$-0.817963\pi$
$887$	−4.55196e60	−1.68176	−0.840881	+	0.541220i	$0.817963\pi$
$888$	0	0
$889$	−1.07031e60	−0.377594
$890$	−1.26328e60	−0.435517
$891$	0	0
$892$	−2.46270e60	−0.810834
$893$	5.99163e59	0.192792
$894$	0	0
$895$	2.22625e60	0.684231
$896$	−6.13323e59	−0.184236
$897$	0	0
$898$	−2.39106e60	−0.686161
$899$	−1.26741e60	−0.355503
$900$	0	0
$901$	−7.33721e58	−0.0196641
$902$	−3.37291e60	−0.883631
$903$	0	0
$904$	7.07346e60	1.77084
$905$	−2.79486e60	−0.684014
$906$	0	0
$907$	4.67172e60	1.09277	0.546383	−	0.837535i	$-0.316004\pi$
$907$	4.67172e60	1.09277	0.546383	+	0.837535i	$0.316004\pi$
$908$	−2.51502e60	−0.575151
$909$	0	0
$910$	8.06781e59	0.176363
$911$	8.38645e60	1.79247	0.896235	−	0.443580i	$-0.146292\pi$
$911$	8.38645e60	1.79247	0.896235	+	0.443580i	$0.146292\pi$
$912$	0	0
$913$	1.51995e60	0.310584
$914$	−1.47617e60	−0.294943
$915$	0	0
$916$	−5.66059e60	−1.08144
$917$	−2.16555e60	−0.404573
$918$	0	0
$919$	−3.88394e60	−0.693912	−0.346956	−	0.937881i	$-0.612785\pi$
$919$	−3.88394e60	−0.693912	−0.346956	+	0.937881i	$0.612785\pi$
$920$	1.89577e60	0.331234
$921$	0	0
$922$	6.16297e60	1.02993
$923$	1.04444e61	1.70706
$924$	0	0
$925$	−7.22475e60	−1.12958
$926$	6.32484e60	0.967217
$927$	0	0
$928$	4.91994e60	0.719824
$929$	−2.93154e60	−0.419540	−0.209770	−	0.977751i	$-0.567272\pi$
$929$	−2.93154e60	−0.419540	−0.209770	+	0.977751i	$0.567272\pi$
$930$	0	0
$931$	−4.86224e60	−0.665837
$932$	−6.05839e60	−0.811580
$933$	0	0
$934$	−3.48884e60	−0.447271
$935$	3.25594e60	0.408355
$936$	0	0
$937$	5.93664e60	0.712655	0.356328	−	0.934361i	$-0.384029\pi$
$937$	5.93664e60	0.712655	0.356328	+	0.934361i	$0.384029\pi$
$938$	−2.69970e60	−0.317071
$939$	0	0
$940$	−7.21990e59	−0.0811727
$941$	7.34737e60	0.808248	0.404124	−	0.914704i	$-0.367576\pi$
$941$	7.34737e60	0.808248	0.404124	+	0.914704i	$0.367576\pi$
$942$	0	0
$943$	−8.48382e60	−0.893515
$944$	9.39763e59	0.0968484
$945$	0	0
$946$	−5.39841e60	−0.532718
$947$	1.09463e61	1.05704	0.528522	−	0.848920i	$-0.322747\pi$
$947$	1.09463e61	1.05704	0.528522	+	0.848920i	$0.322747\pi$
$948$	0	0
$949$	2.47231e61	2.28637
$950$	3.79036e60	0.343042
$951$	0	0
$952$	3.26346e60	0.282892
$953$	−1.58150e60	−0.134173	−0.0670864	−	0.997747i	$-0.521370\pi$
$953$	−1.58150e60	−0.134173	−0.0670864	+	0.997747i	$0.521370\pi$
$954$	0	0
$955$	−7.53513e60	−0.612381
$956$	−4.79839e60	−0.381688
$957$	0	0
$958$	1.39015e61	1.05942
$959$	8.42438e60	0.628429
$960$	0	0
$961$	−1.07218e61	−0.766368
$962$	−2.17690e61	−1.52318
$963$	0	0
$964$	−5.10278e58	−0.00342158
$965$	2.49068e60	0.163496
$966$	0	0
$967$	3.03716e61	1.91084	0.955421	−	0.295248i	$-0.0954023\pi$
$967$	3.03716e61	1.91084	0.955421	+	0.295248i	$0.0954023\pi$
$968$	−2.08969e60	−0.128717
$969$	0	0
$970$	−1.05554e61	−0.623240
$971$	−1.71562e61	−0.991809	−0.495904	−	0.868377i	$-0.665163\pi$
$971$	−1.71562e61	−0.991809	−0.495904	+	0.868377i	$0.665163\pi$
$972$	0	0
$973$	−9.77642e60	−0.541835
$974$	5.42143e59	0.0294208
$975$	0	0
$976$	3.15533e59	0.0164181
$977$	−2.61636e61	−1.33309	−0.666545	−	0.745465i	$-0.732228\pi$
$977$	−2.61636e61	−1.33309	−0.666545	+	0.745465i	$0.732228\pi$
$978$	0	0
$979$	−2.41964e61	−1.18224
$980$	5.85898e60	0.280342
$981$	0	0
$982$	−1.16472e61	−0.534486
$983$	2.15613e61	0.969007	0.484504	−	0.874789i	$-0.339000\pi$
$983$	2.15613e61	0.969007	0.484504	+	0.874789i	$0.339000\pi$
$984$	0	0
$985$	1.76720e61	0.761805
$986$	−9.05717e60	−0.382398
$987$	0	0
$988$	−1.64539e61	−0.666425
$989$	−1.35785e61	−0.538677
$990$	0	0
$991$	−2.71176e61	−1.03215	−0.516073	−	0.856545i	$-0.672607\pi$
$991$	−2.71176e61	−1.03215	−0.516073	+	0.856545i	$0.672607\pi$
$992$	−1.26883e61	−0.473058
$993$	0	0
$994$	6.98017e60	0.249715
$995$	2.51942e59	0.00882933
$996$	0	0
$997$	−2.74351e61	−0.922690	−0.461345	−	0.887221i	$-0.652633\pi$
$997$	−2.74351e61	−0.922690	−0.461345	+	0.887221i	$0.652633\pi$
$998$	−2.70320e60	−0.0890640
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	9.42.a.c.1.2		4
3.2	odd	2		3.42.a.b.1.3	✓	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
3.42.a.b.1.3	✓	4	3.2	odd	2
9.42.a.c.1.2		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)

\(f(q)\)	\(=\)	\(q-949201. q^{2} -1.29804e12 q^{4} +1.14706e14 q^{5} -7.22302e16 q^{7} +3.31942e18 q^{8} +O(q^{10})\)	\(q-949201. q^{2} -1.29804e12 q^{4} +1.14706e14 q^{5} -7.22302e16 q^{7} +3.31942e18 q^{8} -1.08879e20 q^{10} -2.08542e21 q^{11} +1.02587e23 q^{13} +6.85610e22 q^{14} -2.96374e23 q^{16} -1.36112e25 q^{17} +1.23562e26 q^{19} -1.48892e26 q^{20} +1.97949e27 q^{22} +4.97896e27 q^{23} -3.23174e28 q^{25} -9.73760e28 q^{26} +9.37577e28 q^{28} -7.01030e29 q^{29} +1.80793e30 q^{31} -7.01816e30 q^{32} +1.29198e31 q^{34} -8.28521e30 q^{35} +2.23556e32 q^{37} -1.17286e32 q^{38} +3.80756e32 q^{40} -1.70393e33 q^{41} -2.72718e33 q^{43} +2.70696e33 q^{44} -4.72604e33 q^{46} +4.84907e33 q^{47} -3.93504e34 q^{49} +3.06757e34 q^{50} -1.33162e35 q^{52} +5.39056e33 q^{53} -2.39210e35 q^{55} -2.39762e35 q^{56} +6.65419e35 q^{58} -3.17087e36 q^{59} -1.06464e36 q^{61} -1.71609e36 q^{62} +7.31338e36 q^{64} +1.17673e37 q^{65} -3.93766e37 q^{67} +1.76679e37 q^{68} +7.86433e36 q^{70} +1.01810e38 q^{71} +2.40996e38 q^{73} -2.12200e38 q^{74} -1.60389e38 q^{76} +1.50630e38 q^{77} +3.87752e38 q^{79} -3.39958e37 q^{80} +1.61738e39 q^{82} -7.28847e38 q^{83} -1.56128e39 q^{85} +2.58864e39 q^{86} -6.92238e39 q^{88} +1.16027e40 q^{89} -7.40991e39 q^{91} -6.46289e39 q^{92} -4.60274e39 q^{94} +1.41733e40 q^{95} +9.69468e40 q^{97} +3.73515e40 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 69822 q^{2} + 5352947588932 q^{4} - 118536963776280 q^{5} + 15\!\cdots\!36 q^{7}+ \cdots - 62\!\cdots\!84 q^{8}+O(q^{10}) \) 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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