LMFDB - Embedded newform 9.42.a.c.1.3

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			1.3
Root			$263663.$ 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)

$f(q)$	$=$	$q+1.59943e6 q^{2} +3.59152e11 q^{4} -3.20915e14 q^{5} +2.35480e17 q^{7} -2.94274e18 q^{8} +O(q^{10})$	\(q+1.59943e6 q^{2} +3.59152e11 q^{4} -3.20915e14 q^{5} +2.35480e17 q^{7} -2.94274e18 q^{8} -5.13282e20 q^{10} -4.09335e21 q^{11} +2.26252e22 q^{13} +3.76634e23 q^{14} -5.49650e24 q^{16} +2.18147e25 q^{17} -1.65269e26 q^{19} -1.15257e26 q^{20} -6.54702e27 q^{22} -1.04809e28 q^{23} +5.75119e28 q^{25} +3.61875e28 q^{26} +8.45732e28 q^{28} +1.48336e29 q^{29} +2.32552e30 q^{31} -2.32010e30 q^{32} +3.48911e31 q^{34} -7.55692e31 q^{35} -5.37090e31 q^{37} -2.64337e32 q^{38} +9.44372e32 q^{40} +9.27726e32 q^{41} +4.47072e33 q^{43} -1.47013e33 q^{44} -1.67634e34 q^{46} +1.02491e34 q^{47} +1.08833e34 q^{49} +9.19863e34 q^{50} +8.12590e33 q^{52} +2.32449e35 q^{53} +1.31362e36 q^{55} -6.92958e35 q^{56} +2.37253e35 q^{58} +1.00765e35 q^{59} +1.56573e36 q^{61} +3.71950e36 q^{62} +8.37609e36 q^{64} -7.26079e36 q^{65} -5.00920e36 q^{67} +7.83480e36 q^{68} -1.20868e38 q^{70} +7.95732e37 q^{71} -1.56377e38 q^{73} -8.59038e37 q^{74} -5.93568e37 q^{76} -9.63902e38 q^{77} +1.20235e39 q^{79} +1.76391e39 q^{80} +1.48383e39 q^{82} -2.45813e39 q^{83} -7.00068e39 q^{85} +7.15060e39 q^{86} +1.20457e40 q^{88} +1.06301e40 q^{89} +5.32780e39 q^{91} -3.76423e39 q^{92} +1.63927e40 q^{94} +5.30374e40 q^{95} +2.08674e40 q^{97} +1.74071e40 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	1.59943e6	1.07857	0.539287	−	0.842122i	$-0.318694\pi$
$2$	1.59943e6	1.07857	0.539287	+	0.842122i	$0.318694\pi$
$3$	0	0
$3$	0	0
$4$	3.59152e11	0.163323
$5$	−3.20915e14	−1.50489	−0.752446	−	0.658654i	$-0.771126\pi$
$5$	−3.20915e14	−1.50489	−0.752446	+	0.658654i	$0.771126\pi$
$6$	0	0
$7$	2.35480e17	1.11544	0.557718	−	0.830030i	$-0.311677\pi$
$7$	2.35480e17	1.11544	0.557718	+	0.830030i	$0.311677\pi$
$8$	−2.94274e18	−0.902418
$9$	0	0
$10$	−5.13282e20	−1.62314
$11$	−4.09335e21	−1.83455	−0.917273	−	0.398260i	$-0.869614\pi$
$11$	−4.09335e21	−1.83455	−0.917273	+	0.398260i	$0.869614\pi$
$12$	0	0
$13$	2.26252e22	0.330183	0.165091	−	0.986278i	$-0.447208\pi$
$13$	2.26252e22	0.330183	0.165091	+	0.986278i	$0.447208\pi$
$14$	3.76634e23	1.20308
$15$	0	0
$16$	−5.49650e24	−1.13665
$17$	2.18147e25	1.30181	0.650904	−	0.759160i	$-0.274390\pi$
$17$	2.18147e25	1.30181	0.650904	+	0.759160i	$0.274390\pi$
$18$	0	0
$19$	−1.65269e26	−1.00866	−0.504328	−	0.863512i	$-0.668260\pi$
$19$	−1.65269e26	−1.00866	−0.504328	+	0.863512i	$0.668260\pi$
$20$	−1.15257e26	−0.245784
$21$	0	0
$22$	−6.54702e27	−1.97869
$23$	−1.04809e28	−1.27344	−0.636718	−	0.771097i	$-0.719708\pi$
$23$	−1.04809e28	−1.27344	−0.636718	+	0.771097i	$0.719708\pi$
$24$	0	0
$25$	5.75119e28	1.26470
$26$	3.61875e28	0.356127
$27$	0	0
$28$	8.45732e28	0.182177
$29$	1.48336e29	0.155628	0.0778140	−	0.996968i	$-0.475206\pi$
$29$	1.48336e29	0.155628	0.0778140	+	0.996968i	$0.475206\pi$
$30$	0	0
$31$	2.32552e30	0.621734	0.310867	−	0.950453i	$-0.399381\pi$
$31$	2.32552e30	0.621734	0.310867	+	0.950453i	$0.399381\pi$
$32$	−2.32010e30	−0.323542
$33$	0	0
$34$	3.48911e31	1.40410
$35$	−7.55692e31	−1.67861
$36$	0	0
$37$	−5.37090e31	−0.381867	−0.190933	−	0.981603i	$-0.561151\pi$
$37$	−5.37090e31	−0.381867	−0.190933	+	0.981603i	$0.561151\pi$
$38$	−2.64337e32	−1.08791
$39$	0	0
$40$	9.44372e32	1.35804
$41$	9.27726e32	0.804176	0.402088	−	0.915601i	$-0.368285\pi$
$41$	9.27726e32	0.804176	0.402088	+	0.915601i	$0.368285\pi$
$42$	0	0
$43$	4.47072e33	1.45973	0.729867	−	0.683589i	$-0.239582\pi$
$43$	4.47072e33	1.45973	0.729867	+	0.683589i	$0.239582\pi$
$44$	−1.47013e33	−0.299624
$45$	0	0
$46$	−1.67634e34	−1.37350
$47$	1.02491e34	0.540355	0.270177	−	0.962811i	$-0.412918\pi$
$47$	1.02491e34	0.540355	0.270177	+	0.962811i	$0.412918\pi$
$48$	0	0
$49$	1.08833e34	0.244198
$50$	9.19863e34	1.36407
$51$	0	0
$52$	8.12590e33	0.0539266
$53$	2.32449e35	1.04393	0.521966	−	0.852966i	$-0.325199\pi$
$53$	2.32449e35	1.04393	0.521966	+	0.852966i	$0.325199\pi$
$54$	0	0
$55$	1.31362e36	2.76079
$56$	−6.92958e35	−1.00659
$57$	0	0
$58$	2.37253e35	0.167856
$59$	1.00765e35	0.0502159	0.0251080	−	0.999685i	$-0.492007\pi$
$59$	1.00765e35	0.0502159	0.0251080	+	0.999685i	$0.492007\pi$
$60$	0	0
$61$	1.56573e36	0.393964	0.196982	−	0.980407i	$-0.436886\pi$
$61$	1.56573e36	0.393964	0.196982	+	0.980407i	$0.436886\pi$
$62$	3.71950e36	0.670587
$63$	0	0
$64$	8.37609e36	0.787684
$65$	−7.26079e36	−0.496890
$66$	0	0
$67$	−5.00920e36	−0.184177	−0.0920883	−	0.995751i	$-0.529354\pi$
$67$	−5.00920e36	−0.184177	−0.0920883	+	0.995751i	$0.529354\pi$
$68$	7.83480e36	0.212616
$69$	0	0
$70$	−1.20868e38	−1.81051
$71$	7.95732e37	0.891191	0.445596	−	0.895234i	$-0.352992\pi$
$71$	7.95732e37	0.891191	0.445596	+	0.895234i	$0.352992\pi$
$72$	0	0
$73$	−1.56377e38	−0.990955	−0.495477	−	0.868621i	$-0.665007\pi$
$73$	−1.56377e38	−0.990955	−0.495477	+	0.868621i	$0.665007\pi$
$74$	−8.59038e37	−0.411872
$75$	0	0
$76$	−5.93568e37	−0.164737
$77$	−9.63902e38	−2.04632
$78$	0	0
$79$	1.20235e39	1.50895	0.754475	−	0.656329i	$-0.227892\pi$
$79$	1.20235e39	1.50895	0.754475	+	0.656329i	$0.227892\pi$
$80$	1.76391e39	1.71053
$81$	0	0
$82$	1.48383e39	0.867363
$83$	−2.45813e39	−1.12074	−0.560369	−	0.828243i	$-0.689341\pi$
$83$	−2.45813e39	−1.12074	−0.560369	+	0.828243i	$0.689341\pi$
$84$	0	0
$85$	−7.00068e39	−1.95908
$86$	7.15060e39	1.57443
$87$	0	0
$88$	1.20457e40	1.65553
$89$	1.06301e40	1.15889	0.579443	−	0.815012i	$-0.303270\pi$
$89$	1.06301e40	1.15889	0.579443	+	0.815012i	$0.303270\pi$
$90$	0	0
$91$	5.32780e39	0.368298
$92$	−3.76423e39	−0.207982
$93$	0	0
$94$	1.63927e40	0.582813
$95$	5.30374e40	1.51792
$96$	0	0
$97$	2.08674e40	0.389626	0.194813	−	0.980840i	$-0.437590\pi$
$97$	2.08674e40	0.389626	0.194813	+	0.980840i	$0.437590\pi$
$98$	1.74071e40	0.263386
$99$	0	0
$100$	2.06555e40	0.206555
$101$	−1.04865e41	−0.855146	−0.427573	−	0.903981i	$-0.640631\pi$
$101$	−1.04865e41	−0.855146	−0.427573	+	0.903981i	$0.640631\pi$
$102$	0	0
$103$	−2.03937e41	−1.11258	−0.556292	−	0.830987i	$-0.687777\pi$
$103$	−2.03937e41	−1.11258	−0.556292	+	0.830987i	$0.687777\pi$
$104$	−6.65803e40	−0.297963
$105$	0	0
$106$	3.71786e41	1.12596
$107$	7.60455e41	1.89979	0.949896	−	0.312567i	$-0.101189\pi$
$107$	7.60455e41	1.89979	0.949896	+	0.312567i	$0.101189\pi$
$108$	0	0
$109$	1.97252e41	0.337115	0.168557	−	0.985692i	$-0.446089\pi$
$109$	1.97252e41	0.337115	0.168557	+	0.985692i	$0.446089\pi$
$110$	2.10104e42	2.97772
$111$	0	0
$112$	−1.29432e42	−1.26786
$113$	−7.19758e41	−0.587595	−0.293798	−	0.955868i	$-0.594919\pi$
$113$	−7.19758e41	−0.587595	−0.293798	+	0.955868i	$0.594919\pi$
$114$	0	0
$115$	3.36347e42	1.91638
$116$	5.32752e40	0.0254177
$117$	0	0
$118$	1.61166e41	0.0541617
$119$	5.13694e42	1.45208
$120$	0	0
$121$	1.17770e43	2.36556
$122$	2.50428e42	0.424919
$123$	0	0
$124$	8.35214e41	0.101544
$125$	−3.86292e42	−0.398346
$126$	0	0
$127$	−7.84129e42	−0.583998	−0.291999	−	0.956419i	$-0.594320\pi$
$127$	−7.84129e42	−0.583998	−0.291999	+	0.956419i	$0.594320\pi$
$128$	1.84989e43	1.17312
$129$	0	0
$130$	−1.16131e43	−0.535933
$131$	−1.88589e43	−0.743799	−0.371899	−	0.928273i	$-0.621293\pi$
$131$	−1.88589e43	−0.743799	−0.371899	+	0.928273i	$0.621293\pi$
$132$	0	0
$133$	−3.89177e43	−1.12509
$134$	−8.01186e42	−0.198648
$135$	0	0
$136$	−6.41952e43	−1.17477
$137$	−4.38524e43	−0.690592	−0.345296	−	0.938494i	$-0.612221\pi$
$137$	−4.38524e43	−0.690592	−0.345296	+	0.938494i	$0.612221\pi$
$138$	0	0
$139$	2.01750e43	0.236054	0.118027	−	0.993010i	$-0.462343\pi$
$139$	2.01750e43	0.236054	0.118027	+	0.993010i	$0.462343\pi$
$140$	−2.71408e43	−0.274157
$141$	0	0
$142$	1.27272e44	0.961216
$143$	−9.26130e43	−0.605736
$144$	0	0
$145$	−4.76033e43	−0.234203
$146$	−2.50114e44	−1.06882
$147$	0	0
$148$	−1.92897e43	−0.0623677
$149$	−3.54704e44	−0.998958	−0.499479	−	0.866326i	$-0.666475\pi$
$149$	−3.54704e44	−0.998958	−0.499479	+	0.866326i	$0.666475\pi$
$150$	0	0
$151$	7.36078e44	1.57724	0.788618	−	0.614884i	$-0.210797\pi$
$151$	7.36078e44	1.57724	0.788618	+	0.614884i	$0.210797\pi$
$152$	4.86345e44	0.910230
$153$	0	0
$154$	−1.54169e45	−2.20711
$155$	−7.46294e44	−0.935643
$156$	0	0
$157$	−1.20760e45	−1.16407	−0.582036	−	0.813163i	$-0.697744\pi$
$157$	−1.20760e45	−1.16407	−0.582036	+	0.813163i	$0.697744\pi$
$158$	1.92307e45	1.62752
$159$	0	0
$160$	7.44554e44	0.486897
$161$	−2.46804e45	−1.42044
$162$	0	0
$163$	3.84692e45	1.71897	0.859484	−	0.511163i	$-0.170785\pi$
$163$	3.84692e45	1.71897	0.859484	+	0.511163i	$0.170785\pi$
$164$	3.33195e44	0.131341
$165$	0	0
$166$	−3.93160e45	−1.20880
$167$	1.57930e45	0.429316	0.214658	−	0.976689i	$-0.431136\pi$
$167$	1.57930e45	0.429316	0.214658	+	0.976689i	$0.431136\pi$
$168$	0	0
$169$	−4.18355e45	−0.890979
$170$	−1.11971e46	−2.11301
$171$	0	0
$172$	1.60567e45	0.238409
$173$	1.39579e46	1.84024	0.920122	−	0.391631i	$-0.128089\pi$
$173$	1.39579e46	1.84024	0.920122	+	0.391631i	$0.128089\pi$
$174$	0	0
$175$	1.35429e46	1.41069
$176$	2.24991e46	2.08523
$177$	0	0
$178$	1.70021e46	1.24995
$179$	4.81309e45	0.315454	0.157727	−	0.987483i	$-0.449583\pi$
$179$	4.81309e45	0.315454	0.157727	+	0.987483i	$0.449583\pi$
$180$	0	0
$181$	−1.02164e46	−0.533199	−0.266599	−	0.963807i	$-0.585900\pi$
$181$	−1.02164e46	−0.533199	−0.266599	+	0.963807i	$0.585900\pi$
$182$	8.52144e45	0.397237
$183$	0	0
$184$	3.08425e46	1.14917
$185$	1.72360e46	0.574668
$186$	0	0
$187$	−8.92952e46	−2.38822
$188$	3.68098e45	0.0882525
$189$	0	0
$190$	8.48297e46	1.63719
$191$	−3.42603e46	−0.593755	−0.296878	−	0.954916i	$-0.595945\pi$
$191$	−3.42603e46	−0.593755	−0.296878	+	0.954916i	$0.595945\pi$
$192$	0	0
$193$	1.60284e46	0.224370	0.112185	−	0.993687i	$-0.464215\pi$
$193$	1.60284e46	0.224370	0.112185	+	0.993687i	$0.464215\pi$
$194$	3.33759e46	0.420241
$195$	0	0
$196$	3.90877e45	0.0398833
$197$	−1.67914e47	−1.54358	−0.771792	−	0.635875i	$-0.780639\pi$
$197$	−1.67914e47	−1.54358	−0.771792	+	0.635875i	$0.780639\pi$
$198$	0	0
$199$	−5.27435e46	−0.394168	−0.197084	−	0.980387i	$-0.563147\pi$
$199$	−5.27435e46	−0.394168	−0.197084	+	0.980387i	$0.563147\pi$
$200$	−1.69243e47	−1.14129
$201$	0	0
$202$	−1.67723e47	−0.922339
$203$	3.49302e46	0.173593
$204$	0	0
$205$	−2.97722e47	−1.21020
$206$	−3.26183e47	−1.20001
$207$	0	0
$208$	−1.24360e47	−0.375302
$209$	6.76504e47	1.85043
$210$	0	0
$211$	−4.70265e47	−1.05816	−0.529081	−	0.848571i	$-0.677463\pi$
$211$	−4.70265e47	−1.05816	−0.529081	+	0.848571i	$0.677463\pi$
$212$	8.34844e46	0.170498
$213$	0	0
$214$	1.21629e48	2.04907
$215$	−1.43472e48	−2.19674
$216$	0	0
$217$	5.47614e47	0.693505
$218$	3.15490e47	0.363603
$219$	0	0
$220$	4.71788e47	0.450902
$221$	4.93564e47	0.429835
$222$	0	0
$223$	6.26777e47	0.453799	0.226899	−	0.973918i	$-0.427141\pi$
$223$	6.26777e47	0.453799	0.226899	+	0.973918i	$0.427141\pi$
$224$	−5.46337e47	−0.360891
$225$	0	0
$226$	−1.15120e48	−0.633766
$227$	−1.14299e48	−0.574794	−0.287397	−	0.957812i	$-0.592790\pi$
$227$	−1.14299e48	−0.574794	−0.287397	+	0.957812i	$0.592790\pi$
$228$	0	0
$229$	−2.06328e48	−0.866825	−0.433413	−	0.901196i	$-0.642691\pi$
$229$	−2.06328e48	−0.866825	−0.433413	+	0.901196i	$0.642691\pi$
$230$	5.37964e48	2.06696
$231$	0	0
$232$	−4.36515e47	−0.140442
$233$	7.30911e47	0.215312	0.107656	−	0.994188i	$-0.465665\pi$
$233$	7.30911e47	0.215312	0.107656	+	0.994188i	$0.465665\pi$
$234$	0	0
$235$	−3.28909e48	−0.813175
$236$	3.61898e46	0.00820144
$237$	0	0
$238$	8.21617e48	1.56618
$239$	−3.57354e48	−0.625089	−0.312545	−	0.949903i	$-0.601181\pi$
$239$	−3.57354e48	−0.625089	−0.312545	+	0.949903i	$0.601181\pi$
$240$	0	0
$241$	2.64837e47	0.0390507	0.0195254	−	0.999809i	$-0.493784\pi$
$241$	2.64837e47	0.0390507	0.0195254	+	0.999809i	$0.493784\pi$
$242$	1.88364e49	2.55143
$243$	0	0
$244$	5.62336e47	0.0643435
$245$	−3.49263e48	−0.367492
$246$	0	0
$247$	−3.73926e48	−0.333041
$248$	−6.84340e48	−0.561064
$249$	0	0
$250$	−6.17847e48	−0.429646
$251$	−1.94890e48	−0.124876	−0.0624380	−	0.998049i	$-0.519888\pi$
$251$	−1.94890e48	−0.124876	−0.0624380	+	0.998049i	$0.519888\pi$
$252$	0	0
$253$	4.29018e49	2.33617
$254$	−1.25416e49	−0.629886
$255$	0	0
$256$	1.11685e49	0.477612
$257$	−9.44017e48	−0.372692	−0.186346	−	0.982484i	$-0.559665\pi$
$257$	−9.44017e48	−0.372692	−0.186346	+	0.982484i	$0.559665\pi$
$258$	0	0
$259$	−1.26474e49	−0.425948
$260$	−2.60773e48	−0.0811537
$261$	0	0
$262$	−3.01635e49	−0.802243
$263$	5.72032e49	1.40711	0.703554	−	0.710641i	$-0.251595\pi$
$263$	5.72032e49	1.40711	0.703554	+	0.710641i	$0.251595\pi$
$264$	0	0
$265$	−7.45964e49	−1.57100
$266$	−6.22461e49	−1.21350
$267$	0	0
$268$	−1.79906e48	−0.0300804
$269$	2.68077e49	0.415278	0.207639	−	0.978206i	$-0.433422\pi$
$269$	2.68077e49	0.415278	0.207639	+	0.978206i	$0.433422\pi$
$270$	0	0
$271$	−8.22411e49	−1.09451	−0.547253	−	0.836967i	$-0.684327\pi$
$271$	−8.22411e49	−1.09451	−0.547253	+	0.836967i	$0.684327\pi$
$272$	−1.19905e50	−1.47970
$273$	0	0
$274$	−7.01388e49	−0.744855
$275$	−2.35416e50	−2.32015
$276$	0	0
$277$	2.17515e49	0.184780	0.0923898	−	0.995723i	$-0.470549\pi$
$277$	2.17515e49	0.184780	0.0923898	+	0.995723i	$0.470549\pi$
$278$	3.22685e49	0.254601
$279$	0	0
$280$	2.22381e50	1.51481
$281$	1.76875e50	1.11992	0.559961	−	0.828519i	$-0.310816\pi$
$281$	1.76875e50	1.11992	0.559961	+	0.828519i	$0.310816\pi$
$282$	0	0
$283$	1.98156e50	1.08489	0.542444	−	0.840092i	$-0.317499\pi$
$283$	1.98156e50	1.08489	0.542444	+	0.840092i	$0.317499\pi$
$284$	2.85789e49	0.145552
$285$	0	0
$286$	−1.48128e50	−0.653331
$287$	2.18461e50	0.897007
$288$	0	0
$289$	1.95077e50	0.694703
$290$	−7.61382e49	−0.252606
$291$	0	0
$292$	−5.61630e49	−0.161846
$293$	5.47637e50	1.47132	0.735659	−	0.677352i	$-0.236872\pi$
$293$	5.47637e50	1.47132	0.735659	+	0.677352i	$0.236872\pi$
$294$	0	0
$295$	−3.23369e49	−0.0755696
$296$	1.58052e50	0.344603
$297$	0	0
$298$	−5.67323e50	−1.07745
$299$	−2.37132e50	−0.420467
$300$	0	0
$301$	1.05277e51	1.62824
$302$	1.17731e51	1.70117
$303$	0	0
$304$	9.08402e50	1.14649
$305$	−5.02468e50	−0.592873
$306$	0	0
$307$	−1.15018e51	−1.18694	−0.593468	−	0.804857i	$-0.702242\pi$
$307$	−1.15018e51	−1.18694	−0.593468	+	0.804857i	$0.702242\pi$
$308$	−3.46187e50	−0.334212
$309$	0	0
$310$	−1.19365e51	−1.00916
$311$	9.25059e50	0.732119	0.366059	−	0.930592i	$-0.380707\pi$
$311$	9.25059e50	0.732119	0.366059	+	0.930592i	$0.380707\pi$
$312$	0	0
$313$	1.36691e51	0.948597	0.474299	−	0.880364i	$-0.342702\pi$
$313$	1.36691e51	0.948597	0.474299	+	0.880364i	$0.342702\pi$
$314$	−1.93147e51	−1.25554
$315$	0	0
$316$	4.31826e50	0.246447
$317$	−9.60481e49	−0.0513776	−0.0256888	−	0.999670i	$-0.508178\pi$
$317$	−9.60481e49	−0.0513776	−0.0256888	+	0.999670i	$0.508178\pi$
$318$	0	0
$319$	−6.07191e50	−0.285507
$320$	−2.68802e51	−1.18538
$321$	0	0
$322$	−3.94746e51	−1.53205
$323$	−3.60530e51	−1.31308
$324$	0	0
$325$	1.30122e51	0.417583
$326$	6.15288e51	1.85404
$327$	0	0
$328$	−2.73006e51	−0.725703
$329$	2.41346e51	0.602731
$330$	0	0
$331$	4.43023e51	0.977130	0.488565	−	0.872527i	$-0.337520\pi$
$331$	4.43023e51	0.977130	0.488565	+	0.872527i	$0.337520\pi$
$332$	−8.82842e50	−0.183043
$333$	0	0
$334$	2.52598e51	0.463050
$335$	1.60753e51	0.277166
$336$	0	0
$337$	−3.71004e50	−0.0566194	−0.0283097	−	0.999599i	$-0.509012\pi$
$337$	−3.71004e50	−0.0566194	−0.0283097	+	0.999599i	$0.509012\pi$
$338$	−6.69129e51	−0.960988
$339$	0	0
$340$	−2.51431e51	−0.319964
$341$	−9.51915e51	−1.14060
$342$	0	0
$343$	−7.93199e51	−0.843049
$344$	−1.31562e52	−1.31729
$345$	0	0
$346$	2.23247e52	1.98484
$347$	2.30793e51	0.193405	0.0967025	−	0.995313i	$-0.469170\pi$
$347$	2.30793e51	0.193405	0.0967025	+	0.995313i	$0.469170\pi$
$348$	0	0
$349$	−1.85442e52	−1.38129	−0.690647	−	0.723192i	$-0.742674\pi$
$349$	−1.85442e52	−1.38129	−0.690647	+	0.723192i	$0.742674\pi$
$350$	2.16610e52	1.52154
$351$	0	0
$352$	9.49695e51	0.593553
$353$	5.30734e51	0.312965	0.156482	−	0.987681i	$-0.449985\pi$
$353$	5.30734e51	0.312965	0.156482	+	0.987681i	$0.449985\pi$
$354$	0	0
$355$	−2.55363e52	−1.34115
$356$	3.81781e51	0.189273
$357$	0	0
$358$	7.69820e51	0.340241
$359$	6.85308e51	0.286055	0.143028	−	0.989719i	$-0.454316\pi$
$359$	6.85308e51	0.286055	0.143028	+	0.989719i	$0.454316\pi$
$360$	0	0
$361$	4.66809e50	0.0173877
$362$	−1.63405e52	−0.575095
$363$	0	0
$364$	1.91349e51	0.0601517
$365$	5.01837e52	1.49128
$366$	0	0
$367$	3.14343e51	0.0835120	0.0417560	−	0.999128i	$-0.486705\pi$
$367$	3.14343e51	0.0835120	0.0417560	+	0.999128i	$0.486705\pi$
$368$	5.76081e52	1.44745
$369$	0	0
$370$	2.75678e52	0.619822
$371$	5.47371e52	1.16444
$372$	0	0
$373$	9.77187e52	1.86186	0.930929	−	0.365199i	$-0.118999\pi$
$373$	9.77187e52	1.86186	0.930929	+	0.365199i	$0.118999\pi$
$374$	−1.42821e53	−2.57588
$375$	0	0
$376$	−3.01604e52	−0.487626
$377$	3.35614e51	0.0513857
$378$	0	0
$379$	−6.70476e52	−0.921042	−0.460521	−	0.887649i	$-0.652337\pi$
$379$	−6.70476e52	−0.921042	−0.460521	+	0.887649i	$0.652337\pi$
$380$	1.90485e52	0.247912
$381$	0	0
$382$	−5.47970e52	−0.640410
$383$	−2.82438e52	−0.312859	−0.156429	−	0.987689i	$-0.549998\pi$
$383$	−2.82438e52	−0.312859	−0.156429	+	0.987689i	$0.549998\pi$
$384$	0	0
$385$	3.09331e53	3.07949
$386$	2.56363e52	0.242000
$387$	0	0
$388$	7.49457e51	0.0636350
$389$	1.90072e52	0.153091	0.0765457	−	0.997066i	$-0.475611\pi$
$389$	1.90072e52	0.153091	0.0765457	+	0.997066i	$0.475611\pi$
$390$	0	0
$391$	−2.28637e53	−1.65777
$392$	−3.20269e52	−0.220369
$393$	0	0
$394$	−2.68567e53	−1.66487
$395$	−3.85852e53	−2.27081
$396$	0	0
$397$	−1.59987e53	−0.848947	−0.424474	−	0.905440i	$-0.639541\pi$
$397$	−1.59987e53	−0.848947	−0.424474	+	0.905440i	$0.639541\pi$
$398$	−8.43596e52	−0.425139
$399$	0	0
$400$	−3.16114e53	−1.43752
$401$	2.13645e53	0.923067	0.461534	−	0.887123i	$-0.347299\pi$
$401$	2.13645e53	0.923067	0.461534	+	0.887123i	$0.347299\pi$
$402$	0	0
$403$	5.26154e52	0.205286
$404$	−3.76623e52	−0.139665
$405$	0	0
$406$	5.58684e52	0.187233
$407$	2.19849e53	0.700551
$408$	0	0
$409$	2.66798e53	0.768872	0.384436	−	0.923152i	$-0.374396\pi$
$409$	2.66798e53	0.768872	0.384436	+	0.923152i	$0.374396\pi$
$410$	−4.76185e53	−1.30529
$411$	0	0
$412$	−7.32444e52	−0.181711
$413$	2.37281e52	0.0560127
$414$	0	0
$415$	7.88851e53	1.68659
$416$	−5.24927e52	−0.106828
$417$	0	0
$418$	1.08202e54	1.99582
$419$	4.29684e53	0.754678	0.377339	−	0.926075i	$-0.376839\pi$
$419$	4.29684e53	0.754678	0.377339	+	0.926075i	$0.376839\pi$
$420$	0	0
$421$	−2.09315e53	−0.333439	−0.166720	−	0.986004i	$-0.553317\pi$
$421$	−2.09315e53	−0.333439	−0.166720	+	0.986004i	$0.553317\pi$
$422$	−7.52156e53	−1.14131
$423$	0	0
$424$	−6.84038e53	−0.942063
$425$	1.25461e54	1.64640
$426$	0	0
$427$	3.68700e53	0.439442
$428$	2.73119e53	0.310280
$429$	0	0
$430$	−2.29474e54	−2.36935
$431$	1.17896e54	1.16069	0.580343	−	0.814372i	$-0.302919\pi$
$431$	1.17896e54	1.16069	0.580343	+	0.814372i	$0.302919\pi$
$432$	0	0
$433$	9.09513e53	0.814342	0.407171	−	0.913352i	$-0.366515\pi$
$433$	9.09513e53	0.814342	0.407171	+	0.913352i	$0.366515\pi$
$434$	8.75869e53	0.747997
$435$	0	0
$436$	7.08433e52	0.0550587
$437$	1.73217e54	1.28446
$438$	0	0
$439$	2.37938e54	1.60673	0.803363	−	0.595490i	$-0.203042\pi$
$439$	2.37938e54	1.60673	0.803363	+	0.595490i	$0.203042\pi$
$440$	−3.86564e54	−2.49139
$441$	0	0
$442$	7.89420e53	0.463609
$443$	2.17243e54	1.21806	0.609030	−	0.793147i	$-0.291559\pi$
$443$	2.17243e54	1.21806	0.609030	+	0.793147i	$0.291559\pi$
$444$	0	0
$445$	−3.41135e54	−1.74400
$446$	1.00249e54	0.489456
$447$	0	0
$448$	1.97241e54	0.878612
$449$	−4.64070e54	−1.97485	−0.987423	−	0.158100i	$-0.949463\pi$
$449$	−4.64070e54	−1.97485	−0.987423	+	0.158100i	$0.949463\pi$
$450$	0	0
$451$	−3.79751e54	−1.47530
$452$	−2.58502e53	−0.0959681
$453$	0	0
$454$	−1.82813e54	−0.619959
$455$	−1.70977e54	−0.554249
$456$	0	0
$457$	2.01271e54	0.596346	0.298173	−	0.954512i	$-0.403623\pi$
$457$	2.01271e54	0.596346	0.298173	+	0.954512i	$0.403623\pi$
$458$	−3.30008e54	−0.934936
$459$	0	0
$460$	1.20800e54	0.312990
$461$	4.15737e54	1.03027	0.515133	−	0.857110i	$-0.327742\pi$
$461$	4.15737e54	1.03027	0.515133	+	0.857110i	$0.327742\pi$
$462$	0	0
$463$	5.22768e54	1.18549	0.592746	−	0.805390i	$-0.298044\pi$
$463$	5.22768e54	1.18549	0.592746	+	0.805390i	$0.298044\pi$
$464$	−8.15329e53	−0.176894
$465$	0	0
$466$	1.16904e54	0.232230
$467$	9.76914e54	1.85721	0.928604	−	0.371073i	$-0.121010\pi$
$467$	9.76914e54	1.85721	0.928604	+	0.371073i	$0.121010\pi$
$468$	0	0
$469$	−1.17957e54	−0.205437
$470$	−5.26066e54	−0.877070
$471$	0	0
$472$	−2.96524e53	−0.0453158
$473$	−1.83002e55	−2.67795
$474$	0	0
$475$	−9.50495e54	−1.27565
$476$	1.84494e54	0.237159
$477$	0	0
$478$	−5.71563e54	−0.674205
$479$	1.65944e55	1.87536	0.937678	−	0.347505i	$-0.112971\pi$
$479$	1.65944e55	1.87536	0.937678	+	0.347505i	$0.112971\pi$
$480$	0	0
$481$	−1.21518e54	−0.126086
$482$	4.23588e53	0.0421191
$483$	0	0
$484$	4.22972e54	0.386351
$485$	−6.69667e54	−0.586345
$486$	0	0
$487$	4.75101e54	0.382333	0.191167	−	0.981558i	$-0.438773\pi$
$487$	4.75101e54	0.382333	0.191167	+	0.981558i	$0.438773\pi$
$488$	−4.60756e54	−0.355520
$489$	0	0
$490$	−5.58622e54	−0.396368
$491$	−1.29983e55	−0.884538	−0.442269	−	0.896883i	$-0.645826\pi$
$491$	−1.29983e55	−0.884538	−0.442269	+	0.896883i	$0.645826\pi$
$492$	0	0
$493$	3.23591e54	0.202598
$494$	−5.98068e54	−0.359210
$495$	0	0
$496$	−1.27822e55	−0.706694
$497$	1.87379e55	0.994067
$498$	0	0
$499$	3.12552e55	1.52708	0.763539	−	0.645762i	$-0.223460\pi$
$499$	3.12552e55	1.52708	0.763539	+	0.645762i	$0.223460\pi$
$500$	−1.38737e54	−0.0650592
$501$	0	0
$502$	−3.11713e54	−0.134688
$503$	−1.38978e55	−0.576504	−0.288252	−	0.957555i	$-0.593074\pi$
$503$	−1.38978e55	−0.576504	−0.288252	+	0.957555i	$0.593074\pi$
$504$	0	0
$505$	3.36526e55	1.28690
$506$	6.86185e55	2.51974
$507$	0	0
$508$	−2.81622e54	−0.0953806
$509$	4.24927e55	1.38229	0.691146	−	0.722715i	$-0.257106\pi$
$509$	4.24927e55	1.38229	0.691146	+	0.722715i	$0.257106\pi$
$510$	0	0
$511$	−3.68237e55	−1.10535
$512$	−2.28163e55	−0.657978
$513$	0	0
$514$	−1.50989e55	−0.401977
$515$	6.54465e55	1.67432
$516$	0	0
$517$	−4.19530e55	−0.991305
$518$	−2.02286e55	−0.459417
$519$	0	0
$520$	2.13666e55	0.448402
$521$	−7.63345e55	−1.54009	−0.770047	−	0.637987i	$-0.779767\pi$
$521$	−7.63345e55	−1.54009	−0.770047	+	0.637987i	$0.779767\pi$
$522$	0	0
$523$	8.49813e55	1.58504	0.792518	−	0.609849i	$-0.208770\pi$
$523$	8.49813e55	1.58504	0.792518	+	0.609849i	$0.208770\pi$
$524$	−6.77322e54	−0.121480
$525$	0	0
$526$	9.14925e55	1.51767
$527$	5.07305e55	0.809379
$528$	0	0
$529$	4.21094e55	0.621638
$530$	−1.19312e56	−1.69445
$531$	0	0
$532$	−1.39774e55	−0.183754
$533$	2.09900e55	0.265525
$534$	0	0
$535$	−2.44042e56	−2.85898
$536$	1.47408e55	0.166204
$537$	0	0
$538$	4.28771e55	0.447908
$539$	−4.45493e55	−0.447993
$540$	0	0
$541$	8.87529e54	0.0827254	0.0413627	−	0.999144i	$-0.486830\pi$
$541$	8.87529e54	0.0827254	0.0413627	+	0.999144i	$0.486830\pi$
$542$	−1.31539e56	−1.18051
$543$	0	0
$544$	−5.06122e55	−0.421190
$545$	−6.33011e55	−0.507321
$546$	0	0
$547$	−1.64997e56	−1.22669	−0.613345	−	0.789815i	$-0.710177\pi$
$547$	−1.64997e56	−1.22669	−0.613345	+	0.789815i	$0.710177\pi$
$548$	−1.57497e55	−0.112790
$549$	0	0
$550$	−3.76532e56	−2.50246
$551$	−2.45154e55	−0.156975
$552$	0	0
$553$	2.83129e56	1.68314
$554$	3.47900e55	0.199299
$555$	0	0
$556$	7.24590e54	0.0385531
$557$	−2.56239e56	−1.31405	−0.657027	−	0.753867i	$-0.728186\pi$
$557$	−2.56239e56	−1.31405	−0.657027	+	0.753867i	$0.728186\pi$
$558$	0	0
$559$	1.01151e56	0.481979
$560$	4.15366e56	1.90799
$561$	0	0
$562$	2.82900e56	1.20792
$563$	1.39228e55	0.0573196	0.0286598	−	0.999589i	$-0.490876\pi$
$563$	1.39228e55	0.0573196	0.0286598	+	0.999589i	$0.490876\pi$
$564$	0	0
$565$	2.30981e56	0.884268
$566$	3.16936e56	1.17013
$567$	0	0
$568$	−2.34164e56	−0.804227
$569$	2.49708e56	0.827239	0.413620	−	0.910450i	$-0.364264\pi$
$569$	2.49708e56	0.827239	0.413620	+	0.910450i	$0.364264\pi$
$570$	0	0
$571$	−1.43957e56	−0.443805	−0.221902	−	0.975069i	$-0.571227\pi$
$571$	−1.43957e56	−0.443805	−0.221902	+	0.975069i	$0.571227\pi$
$572$	−3.32621e55	−0.0989308
$573$	0	0
$574$	3.49414e56	0.967489
$575$	−6.02775e56	−1.61051
$576$	0	0
$577$	7.48240e56	1.86181	0.930907	−	0.365255i	$-0.119018\pi$
$577$	7.48240e56	1.86181	0.930907	+	0.365255i	$0.119018\pi$
$578$	3.12011e56	0.749289
$579$	0	0
$580$	−1.70968e55	−0.0382509
$581$	−5.78841e56	−1.25011
$582$	0	0
$583$	−9.51493e56	−1.91514
$584$	4.60177e56	0.894255
$585$	0	0
$586$	8.75907e56	1.58693
$587$	5.43255e56	0.950435	0.475217	−	0.879868i	$-0.342369\pi$
$587$	5.43255e56	0.950435	0.475217	+	0.879868i	$0.342369\pi$
$588$	0	0
$589$	−3.84337e56	−0.627116
$590$	−5.17206e55	−0.0815074
$591$	0	0
$592$	2.95211e56	0.434048
$593$	9.45252e56	1.34254	0.671269	−	0.741214i	$-0.265750\pi$
$593$	9.45252e56	1.34254	0.671269	+	0.741214i	$0.265750\pi$
$594$	0	0
$595$	−1.64852e57	−2.18523
$596$	−1.27392e56	−0.163153
$597$	0	0
$598$	−3.79277e56	−0.453505
$599$	3.47722e56	0.401775	0.200887	−	0.979614i	$-0.435617\pi$
$599$	3.47722e56	0.401775	0.200887	+	0.979614i	$0.435617\pi$
$600$	0	0
$601$	6.30772e56	0.680684	0.340342	−	0.940302i	$-0.389457\pi$
$601$	6.30772e56	0.680684	0.340342	+	0.940302i	$0.389457\pi$
$602$	1.68382e57	1.75618
$603$	0	0
$604$	2.64364e56	0.257599
$605$	−3.77941e57	−3.55991
$606$	0	0
$607$	−3.56157e56	−0.313526	−0.156763	−	0.987636i	$-0.550106\pi$
$607$	−3.56157e56	−0.313526	−0.156763	+	0.987636i	$0.550106\pi$
$608$	3.83440e56	0.326343
$609$	0	0
$610$	−8.03662e56	−0.639458
$611$	2.31888e56	0.178416
$612$	0	0
$613$	−4.16993e56	−0.300047	−0.150023	−	0.988682i	$-0.547935\pi$
$613$	−4.16993e56	−0.300047	−0.150023	+	0.988682i	$0.547935\pi$
$614$	−1.83963e57	−1.28020
$615$	0	0
$616$	2.83652e57	1.84663
$617$	−2.42342e57	−1.52610	−0.763051	−	0.646338i	$-0.776299\pi$
$617$	−2.42342e57	−1.52610	−0.763051	+	0.646338i	$0.776299\pi$
$618$	0	0
$619$	−1.32231e56	−0.0779246	−0.0389623	−	0.999241i	$-0.512405\pi$
$619$	−1.32231e56	−0.0779246	−0.0389623	+	0.999241i	$0.512405\pi$
$620$	−2.68033e56	−0.152812
$621$	0	0
$622$	1.47957e57	0.789645
$623$	2.50317e57	1.29266
$624$	0	0
$625$	−1.37567e57	−0.665233
$626$	2.18628e57	1.02313
$627$	0	0
$628$	−4.33711e56	−0.190120
$629$	−1.17165e57	−0.497117
$630$	0	0
$631$	1.32515e57	0.526822	0.263411	−	0.964684i	$-0.415153\pi$
$631$	1.32515e57	0.526822	0.263411	+	0.964684i	$0.415153\pi$
$632$	−3.53820e57	−1.36170
$633$	0	0
$634$	−1.53622e56	−0.0554146
$635$	2.51639e57	0.878854
$636$	0	0
$637$	2.46238e56	0.0806301
$638$	−9.71159e56	−0.307940
$639$	0	0
$640$	−5.93659e57	−1.76542
$641$	5.79020e56	0.166765	0.0833824	−	0.996518i	$-0.473428\pi$
$641$	5.79020e56	0.166765	0.0833824	+	0.996518i	$0.473428\pi$
$642$	0	0
$643$	9.70178e56	0.262136	0.131068	−	0.991373i	$-0.458159\pi$
$643$	9.70178e56	0.262136	0.131068	+	0.991373i	$0.458159\pi$
$644$	−8.86401e56	−0.231990
$645$	0	0
$646$	−5.76643e57	−1.41625
$647$	2.04507e57	0.486598	0.243299	−	0.969951i	$-0.421770\pi$
$647$	2.04507e57	0.486598	0.243299	+	0.969951i	$0.421770\pi$
$648$	0	0
$649$	−4.12464e56	−0.0921234
$650$	2.08121e57	0.450394
$651$	0	0
$652$	1.38163e57	0.280748
$653$	6.17960e56	0.121686	0.0608430	−	0.998147i	$-0.480621\pi$
$653$	6.17960e56	0.121686	0.0608430	+	0.998147i	$0.480621\pi$
$654$	0	0
$655$	6.05212e57	1.11934
$656$	−5.09925e57	−0.914065
$657$	0	0
$658$	3.86015e57	0.650091
$659$	−2.52320e57	−0.411909	−0.205955	−	0.978562i	$-0.566030\pi$
$659$	−2.52320e57	−0.411909	−0.205955	+	0.978562i	$0.566030\pi$
$660$	0	0
$661$	−4.49723e57	−0.689946	−0.344973	−	0.938613i	$-0.612112\pi$
$661$	−4.49723e57	−0.689946	−0.344973	+	0.938613i	$0.612112\pi$
$662$	7.08584e57	1.05391
$663$	0	0
$664$	7.23365e57	1.01137
$665$	1.24893e58	1.69314
$666$	0	0
$667$	−1.55469e57	−0.198182
$668$	5.67209e56	0.0701174
$669$	0	0
$670$	2.57113e57	0.298944
$671$	−6.40909e57	−0.722745
$672$	0	0
$673$	1.53837e58	1.63212	0.816061	−	0.577966i	$-0.196153\pi$
$673$	1.53837e58	1.63212	0.816061	+	0.577966i	$0.196153\pi$
$674$	−5.93395e56	−0.0610683
$675$	0	0
$676$	−1.50253e57	−0.145518
$677$	−1.37721e58	−1.29399	−0.646997	−	0.762492i	$-0.723976\pi$
$677$	−1.37721e58	−1.29399	−0.646997	+	0.762492i	$0.723976\pi$
$678$	0	0
$679$	4.91386e57	0.434603
$680$	2.06012e58	1.76791
$681$	0	0
$682$	−1.52252e58	−1.23022
$683$	1.94435e58	1.52458	0.762290	−	0.647236i	$-0.224075\pi$
$683$	1.94435e58	1.52458	0.762290	+	0.647236i	$0.224075\pi$
$684$	0	0
$685$	1.40729e58	1.03927
$686$	−1.26867e58	−0.909291
$687$	0	0
$688$	−2.45733e58	−1.65921
$689$	5.25921e57	0.344688
$690$	0	0
$691$	−2.44962e58	−1.51286	−0.756430	−	0.654074i	$-0.773058\pi$
$691$	−2.44962e58	−1.51286	−0.756430	+	0.654074i	$0.773058\pi$
$692$	5.01301e57	0.300555
$693$	0	0
$694$	3.69137e57	0.208602
$695$	−6.47447e57	−0.355235
$696$	0	0
$697$	2.02381e58	1.04688
$698$	−2.96601e58	−1.48983
$699$	0	0
$700$	4.86397e57	0.230399
$701$	1.67730e58	0.771599	0.385799	−	0.922583i	$-0.373926\pi$
$701$	1.67730e58	0.771599	0.385799	+	0.922583i	$0.373926\pi$
$702$	0	0
$703$	8.87644e57	0.385172
$704$	−3.42863e58	−1.44504
$705$	0	0
$706$	8.48872e57	0.337556
$707$	−2.46935e58	−0.953861
$708$	0	0
$709$	−4.58084e58	−1.66993	−0.834963	−	0.550306i	$-0.814511\pi$
$709$	−4.58084e58	−1.66993	−0.834963	+	0.550306i	$0.814511\pi$
$710$	−4.08435e58	−1.44653
$711$	0	0
$712$	−3.12816e58	−1.04580
$713$	−2.43735e58	−0.791739
$714$	0	0
$715$	2.97209e58	0.911567
$716$	1.72863e57	0.0515211
$717$	0	0
$718$	1.09610e58	0.308532
$719$	4.86766e58	1.33161	0.665807	−	0.746124i	$-0.268088\pi$
$719$	4.86766e58	1.33161	0.665807	+	0.746124i	$0.268088\pi$
$720$	0	0
$721$	−4.80232e58	−1.24102
$722$	7.46628e56	0.0187539
$723$	0	0
$724$	−3.66926e57	−0.0870838
$725$	8.53109e57	0.196823
$726$	0	0
$727$	−1.73618e58	−0.378563	−0.189282	−	0.981923i	$-0.560616\pi$
$727$	−1.73618e58	−0.378563	−0.189282	+	0.981923i	$0.560616\pi$
$728$	−1.56784e58	−0.332359
$729$	0	0
$730$	8.02653e58	1.60846
$731$	9.75274e58	1.90029
$732$	0	0
$733$	−2.87695e58	−0.530031	−0.265015	−	0.964244i	$-0.585377\pi$
$733$	−2.87695e58	−0.530031	−0.265015	+	0.964244i	$0.585377\pi$
$734$	5.02769e57	0.0900739
$735$	0	0
$736$	2.43166e58	0.412010
$737$	2.05044e58	0.337880
$738$	0	0
$739$	−9.32596e57	−0.145373	−0.0726863	−	0.997355i	$-0.523157\pi$
$739$	−9.32596e57	−0.145373	−0.0726863	+	0.997355i	$0.523157\pi$
$740$	6.19036e57	0.0938567
$741$	0	0
$742$	8.75482e58	1.25593
$743$	−6.98846e58	−0.975239	−0.487619	−	0.873056i	$-0.662135\pi$
$743$	−6.98846e58	−0.975239	−0.487619	+	0.873056i	$0.662135\pi$
$744$	0	0
$745$	1.13830e59	1.50332
$746$	1.56294e59	2.00815
$747$	0	0
$748$	−3.20705e58	−0.390053
$749$	1.79072e59	2.11910
$750$	0	0
$751$	1.15523e58	0.129434	0.0647172	−	0.997904i	$-0.479385\pi$
$751$	1.15523e58	0.129434	0.0647172	+	0.997904i	$0.479385\pi$
$752$	−5.63340e58	−0.614193
$753$	0	0
$754$	5.36791e57	0.0554233
$755$	−2.36219e59	−2.37357
$756$	0	0
$757$	−8.37064e58	−0.796697	−0.398348	−	0.917234i	$-0.630417\pi$
$757$	−8.37064e58	−0.796697	−0.398348	+	0.917234i	$0.630417\pi$
$758$	−1.07238e59	−0.993412
$759$	0	0
$760$	−1.56076e59	−1.36980
$761$	2.09392e58	0.178885	0.0894425	−	0.995992i	$-0.471491\pi$
$761$	2.09392e58	0.178885	0.0894425	+	0.995992i	$0.471491\pi$
$762$	0	0
$763$	4.64489e58	0.376030
$764$	−1.23047e58	−0.0969741
$765$	0	0
$766$	−4.51740e58	−0.337441
$767$	2.27982e57	0.0165805
$768$	0	0
$769$	1.28539e59	0.886229	0.443114	−	0.896465i	$-0.353874\pi$
$769$	1.28539e59	0.886229	0.443114	+	0.896465i	$0.353874\pi$
$770$	4.94753e59	3.32146
$771$	0	0
$772$	5.75663e57	0.0366449
$773$	−1.59781e59	−0.990478	−0.495239	−	0.868757i	$-0.664920\pi$
$773$	−1.59781e59	−0.990478	−0.495239	+	0.868757i	$0.664920\pi$
$774$	0	0
$775$	1.33745e59	0.786308
$776$	−6.14074e58	−0.351605
$777$	0	0
$778$	3.04006e58	0.165120
$779$	−1.53325e59	−0.811137
$780$	0	0
$781$	−3.25721e59	−1.63493
$782$	−3.65689e59	−1.78803
$783$	0	0
$784$	−5.98203e58	−0.277568
$785$	3.87537e59	1.75180
$786$	0	0
$787$	7.76783e58	0.333286	0.166643	−	0.986017i	$-0.446707\pi$
$787$	7.76783e58	0.333286	0.166643	+	0.986017i	$0.446707\pi$
$788$	−6.03068e58	−0.252103
$789$	0	0
$790$	−6.17143e59	−2.44923
$791$	−1.69489e59	−0.655425
$792$	0	0
$793$	3.54251e58	0.130080
$794$	−2.55889e59	−0.915653
$795$	0	0
$796$	−1.89429e58	−0.0643768
$797$	−1.52749e58	−0.0505920	−0.0252960	−	0.999680i	$-0.508053\pi$
$797$	−1.52749e58	−0.0505920	−0.0252960	+	0.999680i	$0.508053\pi$
$798$	0	0
$799$	2.23581e59	0.703438
$800$	−1.33433e59	−0.409184
$801$	0	0
$802$	3.41710e59	0.995597
$803$	6.40104e59	1.81795
$804$	0	0
$805$	7.92032e59	2.13760
$806$	8.41546e58	0.221416
$807$	0	0
$808$	3.08589e59	0.771699
$809$	−5.87620e59	−1.43269	−0.716345	−	0.697747i	$-0.754186\pi$
$809$	−5.87620e59	−1.43269	−0.716345	+	0.697747i	$0.754186\pi$
$810$	0	0
$811$	−2.60886e59	−0.604676	−0.302338	−	0.953201i	$-0.597767\pi$
$811$	−2.60886e59	−0.604676	−0.302338	+	0.953201i	$0.597767\pi$
$812$	1.25453e58	0.0283518
$813$	0	0
$814$	3.51634e59	0.755597
$815$	−1.23454e60	−2.58686
$816$	0	0
$817$	−7.38872e59	−1.47237
$818$	4.26724e59	0.829286
$819$	0	0
$820$	−1.06927e59	−0.197654
$821$	2.68738e59	0.484502	0.242251	−	0.970214i	$-0.422114\pi$
$821$	2.68738e59	0.484502	0.242251	+	0.970214i	$0.422114\pi$
$822$	0	0
$823$	−6.91646e59	−1.18628	−0.593140	−	0.805099i	$-0.702112\pi$
$823$	−6.91646e59	−1.18628	−0.593140	+	0.805099i	$0.702112\pi$
$824$	6.00135e59	1.00402
$825$	0	0
$826$	3.79514e58	0.0604139
$827$	1.66543e58	0.0258621	0.0129310	−	0.999916i	$-0.495884\pi$
$827$	1.66543e58	0.0258621	0.0129310	+	0.999916i	$0.495884\pi$
$828$	0	0
$829$	−8.91805e59	−1.31796	−0.658980	−	0.752161i	$-0.729012\pi$
$829$	−8.91805e59	−1.31796	−0.658980	+	0.752161i	$0.729012\pi$
$830$	1.26171e60	1.81911
$831$	0	0
$832$	1.89511e59	0.260080
$833$	2.37417e59	0.317899
$834$	0	0
$835$	−5.06822e59	−0.646075
$836$	2.42968e59	0.302218
$837$	0	0
$838$	6.87250e59	0.813977
$839$	−6.04271e59	−0.698411	−0.349206	−	0.937046i	$-0.613549\pi$
$839$	−6.04271e59	−0.698411	−0.349206	+	0.937046i	$0.613549\pi$
$840$	0	0
$841$	−8.86482e59	−0.975780
$842$	−3.34784e59	−0.359639
$843$	0	0
$844$	−1.68897e59	−0.172823
$845$	1.34257e60	1.34083
$846$	0	0
$847$	2.77324e60	2.63863
$848$	−1.27765e60	−1.18658
$849$	0	0
$850$	2.00666e60	1.77576
$851$	5.62917e59	0.486282
$852$	0	0
$853$	1.07100e60	0.881727	0.440863	−	0.897574i	$-0.354672\pi$
$853$	1.07100e60	0.881727	0.440863	+	0.897574i	$0.354672\pi$
$854$	5.89709e59	0.473971
$855$	0	0
$856$	−2.23782e60	−1.71441
$857$	1.09608e59	0.0819855	0.0409927	−	0.999159i	$-0.486948\pi$
$857$	1.09608e59	0.0819855	0.0409927	+	0.999159i	$0.486948\pi$
$858$	0	0
$859$	1.21084e60	0.863430	0.431715	−	0.902010i	$-0.357909\pi$
$859$	1.21084e60	0.863430	0.431715	+	0.902010i	$0.357909\pi$
$860$	−5.15283e59	−0.358779
$861$	0	0
$862$	1.88566e60	1.25189
$863$	1.35388e60	0.877728	0.438864	−	0.898554i	$-0.355381\pi$
$863$	1.35388e60	0.877728	0.438864	+	0.898554i	$0.355381\pi$
$864$	0	0
$865$	−4.47931e60	−2.76937
$866$	1.45470e60	0.878329
$867$	0	0
$868$	1.96676e59	0.113266
$869$	−4.92163e60	−2.76824
$870$	0	0
$871$	−1.13334e59	−0.0608120
$872$	−5.80462e59	−0.304218
$873$	0	0
$874$	2.77048e60	1.38538
$875$	−9.09641e59	−0.444329
$876$	0	0
$877$	1.82892e60	0.852517	0.426259	−	0.904601i	$-0.359831\pi$
$877$	1.82892e60	0.852517	0.426259	+	0.904601i	$0.359831\pi$
$878$	3.80566e60	1.73297
$879$	0	0
$880$	−7.22029e60	−3.13805
$881$	−9.73145e59	−0.413210	−0.206605	−	0.978424i	$-0.566242\pi$
$881$	−9.73145e59	−0.413210	−0.206605	+	0.978424i	$0.566242\pi$
$882$	0	0
$883$	−2.26914e60	−0.919742	−0.459871	−	0.887986i	$-0.652104\pi$
$883$	−2.26914e60	−0.919742	−0.459871	+	0.887986i	$0.652104\pi$
$884$	1.77264e59	0.0702021
$885$	0	0
$886$	3.47464e60	1.31377
$887$	−9.48427e59	−0.350404	−0.175202	−	0.984532i	$-0.556058\pi$
$887$	−9.48427e59	−0.350404	−0.175202	+	0.984532i	$0.556058\pi$
$888$	0	0
$889$	−1.84647e60	−0.651413
$890$	−5.45622e60	−1.88103
$891$	0	0
$892$	2.25108e59	0.0741160
$893$	−1.69386e60	−0.545032
$894$	0	0
$895$	−1.54459e60	−0.474725
$896$	4.35613e60	1.30854
$897$	0	0
$898$	−7.42247e60	−2.13002
$899$	3.44958e59	0.0967593
$900$	0	0
$901$	5.07081e60	1.35900
$902$	−6.07384e60	−1.59122
$903$	0	0
$904$	2.11806e60	0.530257
$905$	3.27862e60	0.802407
$906$	0	0
$907$	−6.87953e59	−0.160920	−0.0804599	−	0.996758i	$-0.525639\pi$
$907$	−6.87953e59	−0.160920	−0.0804599	+	0.996758i	$0.525639\pi$
$908$	−4.10507e59	−0.0938774
$909$	0	0
$910$	−2.73466e60	−0.597799
$911$	1.32323e60	0.282819	0.141409	−	0.989951i	$-0.454837\pi$
$911$	1.32323e60	0.282819	0.141409	+	0.989951i	$0.454837\pi$
$912$	0	0
$913$	1.00620e61	2.05604
$914$	3.21918e60	0.643204
$915$	0	0
$916$	−7.41032e59	−0.141573
$917$	−4.44091e60	−0.829660
$918$	0	0
$919$	−2.10890e60	−0.376780	−0.188390	−	0.982094i	$-0.560327\pi$
$919$	−2.10890e60	−0.376780	−0.188390	+	0.982094i	$0.560327\pi$
$920$	−9.89784e60	−1.72938
$921$	0	0
$922$	6.64942e60	1.11122
$923$	1.80036e60	0.294256
$924$	0	0
$925$	−3.08891e60	−0.482947
$926$	8.36130e60	1.27864
$927$	0	0
$928$	−3.44154e59	−0.0503523
$929$	8.23760e60	1.17890	0.589452	−	0.807803i	$-0.299344\pi$
$929$	8.23760e60	1.17890	0.589452	+	0.807803i	$0.299344\pi$
$930$	0	0
$931$	−1.79868e60	−0.246312
$932$	2.62508e59	0.0351655
$933$	0	0
$934$	1.56251e61	2.00314
$935$	2.86562e61	3.59402
$936$	0	0
$937$	1.44081e61	1.72960	0.864801	−	0.502115i	$-0.167445\pi$
$937$	1.44081e61	1.72960	0.864801	+	0.502115i	$0.167445\pi$
$938$	−1.88663e60	−0.221580
$939$	0	0
$940$	−1.18128e60	−0.132811
$941$	1.04517e61	1.14974	0.574870	−	0.818245i	$-0.305053\pi$
$941$	1.04517e61	1.14974	0.574870	+	0.818245i	$0.305053\pi$
$942$	0	0
$943$	−9.72339e60	−1.02407
$944$	−5.53852e59	−0.0570779
$945$	0	0
$946$	−2.92699e61	−2.88837
$947$	−9.09242e60	−0.878021	−0.439011	−	0.898482i	$-0.644671\pi$
$947$	−9.09242e60	−0.878021	−0.439011	+	0.898482i	$0.644671\pi$
$948$	0	0
$949$	−3.53806e60	−0.327196
$950$	−1.52025e61	−1.37588
$951$	0	0
$952$	−1.51167e61	−1.31039
$953$	−8.38627e60	−0.711483	−0.355742	−	0.934584i	$-0.615772\pi$
$953$	−8.38627e60	−0.711483	−0.355742	+	0.934584i	$0.615772\pi$
$954$	0	0
$955$	1.09947e61	0.893538
$956$	−1.28344e60	−0.102092
$957$	0	0
$958$	2.65416e61	2.02271
$959$	−1.03264e61	−0.770311
$960$	0	0
$961$	−8.58235e60	−0.613446
$962$	−1.94359e60	−0.135993
$963$	0	0
$964$	9.51167e58	0.00637790
$965$	−5.14376e60	−0.337653
$966$	0	0
$967$	2.28385e61	1.43689	0.718447	−	0.695581i	$-0.244853\pi$
$967$	2.28385e61	1.43689	0.718447	+	0.695581i	$0.244853\pi$
$968$	−3.46566e61	−2.13472
$969$	0	0
$970$	−1.07109e61	−0.632417
$971$	2.76347e61	1.59757	0.798786	−	0.601616i	$-0.205476\pi$
$971$	2.76347e61	1.59757	0.798786	+	0.601616i	$0.205476\pi$
$972$	0	0
$973$	4.75082e60	0.263303
$974$	7.59891e60	0.412375
$975$	0	0
$976$	−8.60605e60	−0.447799
$977$	2.22641e61	1.13440	0.567199	−	0.823581i	$-0.308027\pi$
$977$	2.22641e61	1.13440	0.567199	+	0.823581i	$0.308027\pi$
$978$	0	0
$979$	−4.35126e61	−2.12603
$980$	−1.25439e60	−0.0600201
$981$	0	0
$982$	−2.07899e61	−0.954040
$983$	−2.36280e61	−1.06189	−0.530945	−	0.847407i	$-0.678163\pi$
$983$	−2.36280e61	−1.06189	−0.530945	+	0.847407i	$0.678163\pi$
$984$	0	0
$985$	5.38863e61	2.32293
$986$	5.17561e60	0.218517
$987$	0	0
$988$	−1.34296e60	−0.0543934
$989$	−4.68570e61	−1.85888
$990$	0	0
$991$	−4.84850e61	−1.84543	−0.922716	−	0.385481i	$-0.874035\pi$
$991$	−4.84850e61	−1.84543	−0.922716	+	0.385481i	$0.874035\pi$
$992$	−5.39542e60	−0.201157
$993$	0	0
$994$	2.99700e61	1.07218
$995$	1.69262e61	0.593180
$996$	0	0
$997$	3.96621e60	0.133391	0.0666953	−	0.997773i	$-0.478754\pi$
$997$	3.96621e60	0.133391	0.0666953	+	0.997773i	$0.478754\pi$
$998$	4.99905e61	1.64707
$999$	0	0

Twists

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

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

\(f(q)\)	\(=\)	\(q+1.59943e6 q^{2} +3.59152e11 q^{4} -3.20915e14 q^{5} +2.35480e17 q^{7} -2.94274e18 q^{8} +O(q^{10})\)	\(q+1.59943e6 q^{2} +3.59152e11 q^{4} -3.20915e14 q^{5} +2.35480e17 q^{7} -2.94274e18 q^{8} -5.13282e20 q^{10} -4.09335e21 q^{11} +2.26252e22 q^{13} +3.76634e23 q^{14} -5.49650e24 q^{16} +2.18147e25 q^{17} -1.65269e26 q^{19} -1.15257e26 q^{20} -6.54702e27 q^{22} -1.04809e28 q^{23} +5.75119e28 q^{25} +3.61875e28 q^{26} +8.45732e28 q^{28} +1.48336e29 q^{29} +2.32552e30 q^{31} -2.32010e30 q^{32} +3.48911e31 q^{34} -7.55692e31 q^{35} -5.37090e31 q^{37} -2.64337e32 q^{38} +9.44372e32 q^{40} +9.27726e32 q^{41} +4.47072e33 q^{43} -1.47013e33 q^{44} -1.67634e34 q^{46} +1.02491e34 q^{47} +1.08833e34 q^{49} +9.19863e34 q^{50} +8.12590e33 q^{52} +2.32449e35 q^{53} +1.31362e36 q^{55} -6.92958e35 q^{56} +2.37253e35 q^{58} +1.00765e35 q^{59} +1.56573e36 q^{61} +3.71950e36 q^{62} +8.37609e36 q^{64} -7.26079e36 q^{65} -5.00920e36 q^{67} +7.83480e36 q^{68} -1.20868e38 q^{70} +7.95732e37 q^{71} -1.56377e38 q^{73} -8.59038e37 q^{74} -5.93568e37 q^{76} -9.63902e38 q^{77} +1.20235e39 q^{79} +1.76391e39 q^{80} +1.48383e39 q^{82} -2.45813e39 q^{83} -7.00068e39 q^{85} +7.15060e39 q^{86} +1.20457e40 q^{88} +1.06301e40 q^{89} +5.32780e39 q^{91} -3.76423e39 q^{92} +1.63927e40 q^{94} +5.30374e40 q^{95} +2.08674e40 q^{97} +1.74071e40 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 69822 q^{2} + 5352947588932 q^{4} - 118536963776280 q^{5} + 15\!\cdots\!36 q^{7}+ \cdots - 62\!\cdots\!84 q^{8}+O(q^{10}) \) 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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