LMFDB - Embedded newform 9.40.a.c.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [9,40,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, 40, names="a")

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

chi := DirichletCharacter("9.1");

S:= CuspForms(chi, 40);

N := Newforms(S);

Level:	$ N $	$=$	$ 9 = 3^{2} $
Weight:	$ k $	$=$	$ 40 $
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:	$86.7055962508$
Analytic rank:	$1$
Dimension:	$3$
Coefficient field:	$\mathbb{Q}[x]/(x^{3} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - 3876249523x - 18467420411022 $ x^3 - 3876249523*x - 18467420411022
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 2^{8}\cdot 3^{6}\cdot 5\cdot 7\cdot 13 $
Twist minimal:	no (minimal twist has level 3)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$-4792.65$ 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)

$f(q)$	$=$	$q-264126. q^{2} -4.79993e11 q^{4} +6.30487e13 q^{5} -4.59086e16 q^{7} +2.71983e17 q^{8} +O(q^{10})$	\(q-264126. q^{2} -4.79993e11 q^{4} +6.30487e13 q^{5} -4.59086e16 q^{7} +2.71983e17 q^{8} -1.66528e19 q^{10} +1.42816e20 q^{11} +2.23742e20 q^{13} +1.21256e22 q^{14} +1.92041e23 q^{16} -3.05051e23 q^{17} -1.47192e25 q^{19} -3.02629e25 q^{20} -3.77213e25 q^{22} +5.75448e26 q^{23} +2.15614e27 q^{25} -5.90959e25 q^{26} +2.20358e28 q^{28} -1.59256e28 q^{29} +2.90720e28 q^{31} -2.00247e29 q^{32} +8.05717e28 q^{34} -2.89448e30 q^{35} +4.49195e30 q^{37} +3.88772e30 q^{38} +1.71482e31 q^{40} +3.98145e31 q^{41} -1.13795e32 q^{43} -6.85506e31 q^{44} -1.51990e32 q^{46} +4.87913e32 q^{47} +1.19806e33 q^{49} -5.69493e32 q^{50} -1.07395e32 q^{52} +5.94518e32 q^{53} +9.00434e33 q^{55} -1.24864e34 q^{56} +4.20636e33 q^{58} +2.61158e34 q^{59} -4.20907e34 q^{61} -7.67866e33 q^{62} -5.26854e34 q^{64} +1.41066e34 q^{65} -4.97358e35 q^{67} +1.46422e35 q^{68} +7.64506e35 q^{70} -8.30261e35 q^{71} -5.71462e35 q^{73} -1.18644e36 q^{74} +7.06513e36 q^{76} -6.55647e36 q^{77} -1.34537e37 q^{79} +1.21080e37 q^{80} -1.05160e37 q^{82} -2.31025e37 q^{83} -1.92330e37 q^{85} +3.00563e37 q^{86} +3.88435e37 q^{88} -5.53932e37 q^{89} -1.02717e37 q^{91} -2.76211e38 q^{92} -1.28870e38 q^{94} -9.28027e38 q^{95} -5.58017e38 q^{97} -3.16438e38 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q - 533574 q^{2} + 957442653732 q^{4} + 53381973944430 q^{5} - 15\!\cdots\!28 q^{7}+ \cdots - 44\!\cdots\!96 q^{8}+O(q^{10}) $ 3 * q - 533574 * q^2 + 957442653732 * q^4 + 53381973944430 * q^5 - 1577312676222528 * q^7 - 447338335366356696 * q^8	$ 3 q - 533574 q^{2} + 957442653732 q^{4} + 53381973944430 q^{5} - 15\!\cdots\!28 q^{7}+ \cdots - 19\!\cdots\!10 q^{98}+O(q^{100}) $ 3 * q - 533574 * q^2 + 957442653732 * q^4 + 53381973944430 * q^5 - 1577312676222528 * q^7 - 447338335366356696 * q^8 - 39868781226579858780 * q^10 + 531160706905721914140 * q^11 + 5472528067017405393090 * q^13 - 31359570231859229549952 * q^14 + 12003837541695032587536 * q^16 - 723720005873980759323558 * q^17 - 10683569401487583427646724 * q^19 - 30604131461365012369119960 * q^20 - 101045594443676284003303224 * q^22 - 416442459750873750790818264 * q^23 - 1194715364288572543079384475 * q^25 - 9254747341970932587650915076 * q^26 + 64005281609518186278308249856 * q^28 - 72946887891838791172160902362 * q^29 - 3831507110009307505604788056 * q^31 - 378655322050508831885258466912 * q^32 + 3727087341552963400556140112844 * q^34 - 2740940042971075581743645973120 * q^35 + 2906927238124145306683518446922 * q^37 - 7416889079602877708972704812792 * q^38 + 15592183099728356300682924694800 * q^40 + 13833712444491609259076817725826 * q^41 - 241176797301842883739928662947228 * q^43 + 213525157746039384440606231602512 * q^44 - 104447080902359174134821948683856 * q^46 + 1086597674653689955742268879621504 * q^47 + 924338434806738131424394587158043 * q^49 + 118959783140473612655547453823350 * q^50 + 5952218540461015449104584358724888 * q^52 - 6299034091101274766075867439578034 * q^53 + 7235236907264709378202914522359640 * q^55 - 36130594637558190696891183124416000 * q^56 + 28134849555247756987293173039320884 * q^58 + 7558290777715899720301468980744156 * q^59 - 71826613334234103377163041195597598 * q^61 + 333393758003341216817271988077360816 * q^62 - 356382404098565729241928621083896256 * q^64 + 71965636207225251725741353420179060 * q^65 - 518823945846035691888588721831631172 * q^67 - 1121832034621182540659618925316456392 * q^68 + 381667128343527193098155020939403520 * q^70 - 849269787302723157596849576102980776 * q^71 + 637421615257246057146665571835045614 * q^73 - 8921405458543140139105593515161595412 * q^74 + 12865125362045862122037959358946857936 * q^76 + 2216532510892942434391561675975662336 * q^77 - 16306610864434983513399514618922802600 * q^79 + 18842531486692338792496997422435723680 * q^80 - 48904837208704969270795955453077116036 * q^82 - 59736269696761936146835722238132721148 * q^83 - 52409799455203108995417139125901789980 * q^85 - 8556959071360899197804948671059424200 * q^86 - 103087862263104555338872895329460381664 * q^88 - 181527336890478573173909838985501381086 * q^89 + 233409055536203220442569829829115229824 * q^91 - 965903931988757229715439967889497587232 * q^92 - 123012151365942572780176753392831409920 * q^94 - 842023600986663647572895848646980122600 * q^95 - 990533172774170511639359146813858429242 * q^97 - 1942548903376000593615944763865222165110 * 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 $

$2$	−264126.	−0.356226	−0.178113	−	0.984010i	$-0.556999\pi$
$2$	−264126.	−0.356226	−0.178113	+	0.984010i	$0.556999\pi$
$3$	0	0
$3$	0	0
$4$	−4.79993e11	−0.873103
$5$	6.30487e13	1.47829	0.739147	−	0.673544i	$-0.235229\pi$
$5$	6.30487e13	1.47829	0.739147	+	0.673544i	$0.235229\pi$
$6$	0	0
$7$	−4.59086e16	−1.52224	−0.761119	−	0.648613i	$-0.775350\pi$
$7$	−4.59086e16	−1.52224	−0.761119	+	0.648613i	$0.775350\pi$
$8$	2.71983e17	0.667248
$9$	0	0
$10$	−1.66528e19	−0.526607
$11$	1.42816e20	0.704075	0.352037	−	0.935986i	$-0.385489\pi$
$11$	1.42816e20	0.704075	0.352037	+	0.935986i	$0.385489\pi$
$12$	0	0
$13$	2.23742e20	0.0424474	0.0212237	−	0.999775i	$-0.493244\pi$
$13$	2.23742e20	0.0424474	0.0212237	+	0.999775i	$0.493244\pi$
$14$	1.21256e22	0.542261
$15$	0	0
$16$	1.92041e23	0.635412
$17$	−3.05051e23	−0.309470	−0.154735	−	0.987956i	$-0.549452\pi$
$17$	−3.05051e23	−0.309470	−0.154735	+	0.987956i	$0.549452\pi$
$18$	0	0
$19$	−1.47192e25	−1.70683	−0.853413	−	0.521235i	$-0.825472\pi$
$19$	−1.47192e25	−1.70683	−0.853413	+	0.521235i	$0.825472\pi$
$20$	−3.02629e25	−1.29070
$21$	0	0
$22$	−3.77213e25	−0.250810
$23$	5.75448e26	1.60810	0.804050	−	0.594562i	$-0.202675\pi$
$23$	5.75448e26	1.60810	0.804050	+	0.594562i	$0.202675\pi$
$24$	0	0
$25$	2.15614e27	1.18535
$26$	−5.90959e25	−0.0151209
$27$	0	0
$28$	2.20358e28	1.32907
$29$	−1.59256e28	−0.484546	−0.242273	−	0.970208i	$-0.577893\pi$
$29$	−1.59256e28	−0.484546	−0.242273	+	0.970208i	$0.577893\pi$
$30$	0	0
$31$	2.90720e28	0.240947	0.120474	−	0.992717i	$-0.461559\pi$
$31$	2.90720e28	0.240947	0.120474	+	0.992717i	$0.461559\pi$
$32$	−2.00247e29	−0.893598
$33$	0	0
$34$	8.05717e28	0.110241
$35$	−2.89448e30	−2.25031
$36$	0	0
$37$	4.49195e30	1.18168	0.590842	−	0.806787i	$-0.298796\pi$
$37$	4.49195e30	1.18168	0.590842	+	0.806787i	$0.298796\pi$
$38$	3.88772e30	0.608016
$39$	0	0
$40$	1.71482e31	0.986389
$41$	3.98145e31	1.41500	0.707499	−	0.706715i	$-0.249824\pi$
$41$	3.98145e31	1.41500	0.707499	+	0.706715i	$0.249824\pi$
$42$	0	0
$43$	−1.13795e32	−1.59768	−0.798840	−	0.601544i	$-0.794552\pi$
$43$	−1.13795e32	−1.59768	−0.798840	+	0.601544i	$0.794552\pi$
$44$	−6.85506e31	−0.614730
$45$	0	0
$46$	−1.51990e32	−0.572847
$47$	4.87913e32	1.20902	0.604511	−	0.796597i	$-0.293369\pi$
$47$	4.87913e32	1.20902	0.604511	+	0.796597i	$0.293369\pi$
$48$	0	0
$49$	1.19806e33	1.31721
$50$	−5.69493e32	−0.422253
$51$	0	0
$52$	−1.07395e32	−0.0370610
$53$	5.94518e32	0.141509	0.0707547	−	0.997494i	$-0.477459\pi$
$53$	5.94518e32	0.141509	0.0707547	+	0.997494i	$0.477459\pi$
$54$	0	0
$55$	9.00434e33	1.04083
$56$	−1.24864e34	−1.01571
$57$	0	0
$58$	4.20636e33	0.172608
$59$	2.61158e34	0.767872	0.383936	−	0.923360i	$-0.374568\pi$
$59$	2.61158e34	0.767872	0.383936	+	0.923360i	$0.374568\pi$
$60$	0	0
$61$	−4.20907e34	−0.646032	−0.323016	−	0.946393i	$-0.604697\pi$
$61$	−4.20907e34	−0.646032	−0.323016	+	0.946393i	$0.604697\pi$
$62$	−7.67866e33	−0.0858317
$63$	0	0
$64$	−5.26854e34	−0.317089
$65$	1.41066e34	0.0627498
$66$	0	0
$67$	−4.97358e35	−1.22521	−0.612605	−	0.790389i	$-0.709878\pi$
$67$	−4.97358e35	−1.22521	−0.612605	+	0.790389i	$0.709878\pi$
$68$	1.46422e35	0.270199
$69$	0	0
$70$	7.64506e35	0.801621
$71$	−8.30261e35	−0.660202	−0.330101	−	0.943946i	$-0.607083\pi$
$71$	−8.30261e35	−0.660202	−0.330101	+	0.943946i	$0.607083\pi$
$72$	0	0
$73$	−5.71462e35	−0.264358	−0.132179	−	0.991226i	$-0.542197\pi$
$73$	−5.71462e35	−0.264358	−0.132179	+	0.991226i	$0.542197\pi$
$74$	−1.18644e36	−0.420947
$75$	0	0
$76$	7.06513e36	1.49024
$77$	−6.55647e36	−1.07177
$78$	0	0
$79$	−1.34537e37	−1.33387	−0.666935	−	0.745116i	$-0.732394\pi$
$79$	−1.34537e37	−1.33387	−0.666935	+	0.745116i	$0.732394\pi$
$80$	1.21080e37	0.939325
$81$	0	0
$82$	−1.05160e37	−0.504059
$83$	−2.31025e37	−0.874252	−0.437126	−	0.899400i	$-0.644004\pi$
$83$	−2.31025e37	−0.874252	−0.437126	+	0.899400i	$0.644004\pi$
$84$	0	0
$85$	−1.92330e37	−0.457487
$86$	3.00563e37	0.569135
$87$	0	0
$88$	3.88435e37	0.469793
$89$	−5.53932e37	−0.537466	−0.268733	−	0.963215i	$-0.586605\pi$
$89$	−5.53932e37	−0.537466	−0.268733	+	0.963215i	$0.586605\pi$
$90$	0	0
$91$	−1.02717e37	−0.0646151
$92$	−2.76211e38	−1.40404
$93$	0	0
$94$	−1.28870e38	−0.430685
$95$	−9.28027e38	−2.52319
$96$	0	0
$97$	−5.58017e38	−1.01065	−0.505323	−	0.862930i	$-0.668627\pi$
$97$	−5.58017e38	−1.01065	−0.505323	+	0.862930i	$0.668627\pi$
$98$	−3.16438e38	−0.469224
$99$	0	0
$100$	−1.03493e39	−1.03493
$101$	8.58640e38	0.707203	0.353602	−	0.935396i	$-0.384957\pi$
$101$	8.58640e38	0.707203	0.353602	+	0.935396i	$0.384957\pi$
$102$	0	0
$103$	7.23179e38	0.406368	0.203184	−	0.979141i	$-0.434871\pi$
$103$	7.23179e38	0.406368	0.203184	+	0.979141i	$0.434871\pi$
$104$	6.08540e37	0.0283230
$105$	0	0
$106$	−1.57027e38	−0.0504094
$107$	−6.55460e39	−1.75211	−0.876057	−	0.482208i	$-0.839835\pi$
$107$	−6.55460e39	−1.75211	−0.876057	+	0.482208i	$0.839835\pi$
$108$	0	0
$109$	−5.87754e39	−1.09491	−0.547456	−	0.836835i	$-0.684403\pi$
$109$	−5.87754e39	−1.09491	−0.547456	+	0.836835i	$0.684403\pi$
$110$	−2.37828e39	−0.370771
$111$	0	0
$112$	−8.81636e39	−0.967248
$113$	−1.66536e40	−1.53631	−0.768154	−	0.640265i	$-0.778825\pi$
$113$	−1.66536e40	−1.53631	−0.768154	+	0.640265i	$0.778825\pi$
$114$	0	0
$115$	3.62812e40	2.37724
$116$	7.64418e39	0.423058
$117$	0	0
$118$	−6.89785e39	−0.273536
$119$	1.40045e40	0.471086
$120$	0	0
$121$	−2.07484e40	−0.504279
$122$	1.11172e40	0.230133
$123$	0	0
$124$	−1.39544e40	−0.210372
$125$	2.12571e40	0.274005
$126$	0	0
$127$	−1.17179e41	−1.10835	−0.554177	−	0.832399i	$-0.686967\pi$
$127$	−1.17179e41	−1.10835	−0.554177	+	0.832399i	$0.686967\pi$
$128$	1.24003e41	1.00655
$129$	0	0
$130$	−3.72592e39	−0.0223531
$131$	2.69471e40	0.139227	0.0696133	−	0.997574i	$-0.477823\pi$
$131$	2.69471e40	0.139227	0.0696133	+	0.997574i	$0.477823\pi$
$132$	0	0
$133$	6.75739e41	2.59820
$134$	1.31365e41	0.436452
$135$	0	0
$136$	−8.29687e40	−0.206493
$137$	−1.62934e41	−0.351528	−0.175764	−	0.984432i	$-0.556240\pi$
$137$	−1.62934e41	−0.351528	−0.175764	+	0.984432i	$0.556240\pi$
$138$	0	0
$139$	5.71049e41	0.928720	0.464360	−	0.885647i	$-0.346284\pi$
$139$	5.71049e41	0.928720	0.464360	+	0.885647i	$0.346284\pi$
$140$	1.38933e42	1.96476
$141$	0	0
$142$	2.19293e41	0.235181
$143$	3.19538e40	0.0298862
$144$	0	0
$145$	−1.00409e42	−0.716301
$146$	1.50938e41	0.0941711
$147$	0	0
$148$	−2.15611e42	−1.03173
$149$	4.00637e41	0.168120	0.0840598	−	0.996461i	$-0.473211\pi$
$149$	4.00637e41	0.168120	0.0840598	+	0.996461i	$0.473211\pi$
$150$	0	0
$151$	8.19755e41	0.265237	0.132618	−	0.991167i	$-0.457662\pi$
$151$	8.19755e41	0.265237	0.132618	+	0.991167i	$0.457662\pi$
$152$	−4.00338e42	−1.13888
$153$	0	0
$154$	1.73173e42	0.381792
$155$	1.83295e42	0.356191
$156$	0	0
$157$	2.75060e42	0.416279	0.208139	−	0.978099i	$-0.433259\pi$
$157$	2.75060e42	0.416279	0.208139	+	0.978099i	$0.433259\pi$
$158$	3.55347e42	0.475159
$159$	0	0
$160$	−1.26253e43	−1.32100
$161$	−2.64180e43	−2.44791
$162$	0	0
$163$	−3.05226e41	−0.0222313	−0.0111156	−	0.999938i	$-0.503538\pi$
$163$	−3.05226e41	−0.0222313	−0.0111156	+	0.999938i	$0.503538\pi$
$164$	−1.91107e43	−1.23544
$165$	0	0
$166$	6.10197e42	0.311431
$167$	8.60063e42	0.390444	0.195222	−	0.980759i	$-0.437457\pi$
$167$	8.60063e42	0.390444	0.195222	+	0.980759i	$0.437457\pi$
$168$	0	0
$169$	−2.77337e43	−0.998198
$170$	5.07994e42	0.162969
$171$	0	0
$172$	5.46210e43	1.39494
$173$	3.58571e43	0.817856	0.408928	−	0.912567i	$-0.365903\pi$
$173$	3.58571e43	0.817856	0.408928	+	0.912567i	$0.365903\pi$
$174$	0	0
$175$	−9.89856e43	−1.80439
$176$	2.74265e43	0.447377
$177$	0	0
$178$	1.46308e43	0.191459
$179$	−1.32734e44	−1.55721	−0.778606	−	0.627514i	$-0.784073\pi$
$179$	−1.32734e44	−1.55721	−0.778606	+	0.627514i	$0.784073\pi$
$180$	0	0
$181$	4.48145e43	0.423337	0.211668	−	0.977342i	$-0.432110\pi$
$181$	4.48145e43	0.423337	0.211668	+	0.977342i	$0.432110\pi$
$182$	2.71301e42	0.0230176
$183$	0	0
$184$	1.56512e44	1.07300
$185$	2.83211e44	1.74688
$186$	0	0
$187$	−4.35661e43	−0.217890
$188$	−2.34195e44	−1.05560
$189$	0	0
$190$	2.45116e44	0.898826
$191$	3.37653e44	1.11769	0.558843	−	0.829274i	$-0.311245\pi$
$191$	3.37653e44	1.11769	0.558843	+	0.829274i	$0.311245\pi$
$192$	0	0
$193$	−3.65762e43	−0.0988168	−0.0494084	−	0.998779i	$-0.515734\pi$
$193$	−3.65762e43	−0.0988168	−0.0494084	+	0.998779i	$0.515734\pi$
$194$	1.47387e44	0.360018
$195$	0	0
$196$	−5.75060e44	−1.15006
$197$	2.25016e44	0.407494	0.203747	−	0.979024i	$-0.434688\pi$
$197$	2.25016e44	0.407494	0.203747	+	0.979024i	$0.434688\pi$
$198$	0	0
$199$	4.01172e43	0.0596617	0.0298308	−	0.999555i	$-0.490503\pi$
$199$	4.01172e43	0.0596617	0.0298308	+	0.999555i	$0.490503\pi$
$200$	5.86435e44	0.790924
$201$	0	0
$202$	−2.26789e44	−0.251924
$203$	7.31122e44	0.737593
$204$	0	0
$205$	2.51025e45	2.09178
$206$	−1.91010e44	−0.144759
$207$	0	0
$208$	4.29677e43	0.0269716
$209$	−2.10214e45	−1.20173
$210$	0	0
$211$	−2.64355e45	−1.25510	−0.627552	−	0.778575i	$-0.715943\pi$
$211$	−2.64355e45	−1.25510	−0.627552	+	0.778575i	$0.715943\pi$
$212$	−2.85365e44	−0.123552
$213$	0	0
$214$	1.73124e45	0.624149
$215$	−7.17464e45	−2.36184
$216$	0	0
$217$	−1.33466e45	−0.366779
$218$	1.55241e45	0.390036
$219$	0	0
$220$	−4.32202e45	−0.908751
$221$	−6.82526e43	−0.0131362
$222$	0	0
$223$	−6.61885e45	−1.06866	−0.534328	−	0.845277i	$-0.679435\pi$
$223$	−6.61885e45	−1.06866	−0.534328	+	0.845277i	$0.679435\pi$
$224$	9.19308e45	1.36027
$225$	0	0
$226$	4.39864e45	0.547273
$227$	−1.14636e46	−1.30863	−0.654317	−	0.756220i	$-0.727044\pi$
$227$	−1.14636e46	−1.30863	−0.654317	+	0.756220i	$0.727044\pi$
$228$	0	0
$229$	−5.43505e45	−0.522892	−0.261446	−	0.965218i	$-0.584199\pi$
$229$	−5.43505e45	−0.522892	−0.261446	+	0.965218i	$0.584199\pi$
$230$	−9.58279e45	−0.846836
$231$	0	0
$232$	−4.33149e45	−0.323312
$233$	2.44861e46	1.68066	0.840328	−	0.542079i	$-0.182362\pi$
$233$	2.44861e46	1.68066	0.840328	+	0.542079i	$0.182362\pi$
$234$	0	0
$235$	3.07623e46	1.78729
$236$	−1.25354e46	−0.670432
$237$	0	0
$238$	−3.69894e45	−0.167813
$239$	−3.20935e46	−1.34171	−0.670855	−	0.741589i	$-0.734073\pi$
$239$	−3.20935e46	−1.34171	−0.670855	+	0.741589i	$0.734073\pi$
$240$	0	0
$241$	−4.03396e45	−0.143351	−0.0716753	−	0.997428i	$-0.522835\pi$
$241$	−4.03396e45	−0.143351	−0.0716753	+	0.997428i	$0.522835\pi$
$242$	5.48020e45	0.179637
$243$	0	0
$244$	2.02032e46	0.564053
$245$	7.55359e46	1.94722
$246$	0	0
$247$	−3.29330e45	−0.0724504
$248$	7.90710e45	0.160772
$249$	0	0
$250$	−5.61455e45	−0.0976079
$251$	9.02920e46	1.45215	0.726076	−	0.687615i	$-0.241342\pi$
$251$	9.02920e46	1.45215	0.726076	+	0.687615i	$0.241342\pi$
$252$	0	0
$253$	8.21830e46	1.13222
$254$	3.09501e46	0.394824
$255$	0	0
$256$	−3.78821e45	−0.0414720
$257$	−4.29725e45	−0.0436008	−0.0218004	−	0.999762i	$-0.506940\pi$
$257$	−4.29725e45	−0.0436008	−0.0218004	+	0.999762i	$0.506940\pi$
$258$	0	0
$259$	−2.06219e47	−1.79880
$260$	−6.77108e45	−0.0547870
$261$	0	0
$262$	−7.11742e45	−0.0495961
$263$	−1.26887e47	−0.820879	−0.410439	−	0.911888i	$-0.634625\pi$
$263$	−1.26887e47	−0.820879	−0.410439	+	0.911888i	$0.634625\pi$
$264$	0	0
$265$	3.74835e46	0.209193
$266$	−1.78480e47	−0.925545
$267$	0	0
$268$	2.38729e47	1.06973
$269$	−5.74667e46	−0.239468	−0.119734	−	0.992806i	$-0.538204\pi$
$269$	−5.74667e46	−0.239468	−0.119734	+	0.992806i	$0.538204\pi$
$270$	0	0
$271$	−3.95688e46	−0.142709	−0.0713546	−	0.997451i	$-0.522732\pi$
$271$	−3.95688e46	−0.142709	−0.0713546	+	0.997451i	$0.522732\pi$
$272$	−5.85824e46	−0.196641
$273$	0	0
$274$	4.30349e46	0.125223
$275$	3.07931e47	0.834577
$276$	0	0
$277$	4.47297e47	1.05254	0.526272	−	0.850316i	$-0.323589\pi$
$277$	4.47297e47	1.05254	0.526272	+	0.850316i	$0.323589\pi$
$278$	−1.50829e47	−0.330834
$279$	0	0
$280$	−7.87249e47	−1.50152
$281$	−3.99175e47	−0.710215	−0.355108	−	0.934825i	$-0.615556\pi$
$281$	−3.99175e47	−0.710215	−0.355108	+	0.934825i	$0.615556\pi$
$282$	0	0
$283$	−8.24030e47	−1.27675	−0.638377	−	0.769724i	$-0.720394\pi$
$283$	−8.24030e47	−1.27675	−0.638377	+	0.769724i	$0.720394\pi$
$284$	3.98520e47	0.576424
$285$	0	0
$286$	−8.43983e45	−0.0106462
$287$	−1.82783e48	−2.15396
$288$	0	0
$289$	−8.78590e47	−0.904228
$290$	2.65205e47	0.255165
$291$	0	0
$292$	2.74298e47	0.230811
$293$	6.28416e47	0.494685	0.247343	−	0.968928i	$-0.420443\pi$
$293$	6.28416e47	0.494685	0.247343	+	0.968928i	$0.420443\pi$
$294$	0	0
$295$	1.64657e48	1.13514
$296$	1.22174e48	0.788476
$297$	0	0
$298$	−1.05818e47	−0.0598886
$299$	1.28752e47	0.0682597
$300$	0	0
$301$	5.22419e48	2.43205
$302$	−2.16518e47	−0.0944842
$303$	0	0
$304$	−2.82670e48	−1.08454
$305$	−2.65376e48	−0.955025
$306$	0	0
$307$	−2.43683e48	−0.772018	−0.386009	−	0.922495i	$-0.626147\pi$
$307$	−2.43683e48	−0.772018	−0.386009	+	0.922495i	$0.626147\pi$
$308$	3.14706e48	0.935765
$309$	0	0
$310$	−4.84129e47	−0.126884
$311$	6.81462e48	1.67731	0.838657	−	0.544660i	$-0.183341\pi$
$311$	6.81462e48	1.67731	0.838657	+	0.544660i	$0.183341\pi$
$312$	0	0
$313$	−2.62388e48	−0.569941	−0.284970	−	0.958536i	$-0.591984\pi$
$313$	−2.62388e48	−0.569941	−0.284970	+	0.958536i	$0.591984\pi$
$314$	−7.26504e47	−0.148289
$315$	0	0
$316$	6.45769e48	1.16461
$317$	6.51955e48	1.10551	0.552754	−	0.833344i	$-0.313577\pi$
$317$	6.51955e48	1.10551	0.552754	+	0.833344i	$0.313577\pi$
$318$	0	0
$319$	−2.27443e48	−0.341156
$320$	−3.32174e48	−0.468750
$321$	0	0
$322$	6.97767e48	0.872009
$323$	4.49011e48	0.528211
$324$	0	0
$325$	4.82419e47	0.0503152
$326$	8.06181e46	0.00791935
$327$	0	0
$328$	1.08289e49	0.944154
$329$	−2.23994e49	−1.84042
$330$	0	0
$331$	−2.04347e49	−1.49184	−0.745919	−	0.666036i	$-0.767990\pi$
$331$	−2.04347e49	−1.49184	−0.745919	+	0.666036i	$0.767990\pi$
$332$	1.10891e49	0.763312
$333$	0	0
$334$	−2.27165e48	−0.139087
$335$	−3.13577e49	−1.81122
$336$	0	0
$337$	−1.34582e49	−0.692154	−0.346077	−	0.938206i	$-0.612486\pi$
$337$	−1.34582e49	−0.692154	−0.346077	+	0.938206i	$0.612486\pi$
$338$	7.32518e48	0.355584
$339$	0	0
$340$	9.23173e48	0.399433
$341$	4.15194e48	0.169645
$342$	0	0
$343$	−1.32453e49	−0.482865
$344$	−3.09504e49	−1.06605
$345$	0	0
$346$	−9.47079e48	−0.291342
$347$	−3.60982e49	−1.04969	−0.524844	−	0.851198i	$-0.675876\pi$
$347$	−3.60982e49	−1.04969	−0.524844	+	0.851198i	$0.675876\pi$
$348$	0	0
$349$	1.29981e49	0.337896	0.168948	−	0.985625i	$-0.445963\pi$
$349$	1.29981e49	0.337896	0.168948	+	0.985625i	$0.445963\pi$
$350$	2.61446e49	0.642770
$351$	0	0
$352$	−2.85985e49	−0.629160
$353$	7.99353e49	1.66392	0.831959	−	0.554837i	$-0.187219\pi$
$353$	7.99353e49	1.66392	0.831959	+	0.554837i	$0.187219\pi$
$354$	0	0
$355$	−5.23469e49	−0.975973
$356$	2.65884e49	0.469263
$357$	0	0
$358$	3.50584e49	0.554719
$359$	−7.75277e49	−1.16176	−0.580878	−	0.813990i	$-0.697291\pi$
$359$	−7.75277e49	−1.16176	−0.580878	+	0.813990i	$0.697291\pi$
$360$	0	0
$361$	1.42286e50	1.91326
$362$	−1.18367e49	−0.150804
$363$	0	0
$364$	4.93033e48	0.0564156
$365$	−3.60299e49	−0.390798
$366$	0	0
$367$	1.56697e49	0.152782	0.0763909	−	0.997078i	$-0.475660\pi$
$367$	1.56697e49	0.152782	0.0763909	+	0.997078i	$0.475660\pi$
$368$	1.10510e50	1.02181
$369$	0	0
$370$	−7.48034e49	−0.622283
$371$	−2.72935e49	−0.215411
$372$	0	0
$373$	5.67952e49	0.403636	0.201818	−	0.979423i	$-0.435315\pi$
$373$	5.67952e49	0.403636	0.201818	+	0.979423i	$0.435315\pi$
$374$	1.15069e49	0.0776180
$375$	0	0
$376$	1.32704e50	0.806718
$377$	−3.56322e48	−0.0205677
$378$	0	0
$379$	−3.40282e49	−0.177163	−0.0885817	−	0.996069i	$-0.528233\pi$
$379$	−3.40282e49	−0.177163	−0.0885817	+	0.996069i	$0.528233\pi$
$380$	4.45447e50	2.20301
$381$	0	0
$382$	−8.91828e49	−0.398149
$383$	1.51395e50	0.642295	0.321147	−	0.947029i	$-0.395932\pi$
$383$	1.51395e50	0.642295	0.321147	+	0.947029i	$0.395932\pi$
$384$	0	0
$385$	−4.13377e50	−1.58439
$386$	9.66071e48	0.0352011
$387$	0	0
$388$	2.67845e50	0.882398
$389$	−3.64065e50	−1.14068	−0.570338	−	0.821410i	$-0.693188\pi$
$389$	−3.64065e50	−1.14068	−0.570338	+	0.821410i	$0.693188\pi$
$390$	0	0
$391$	−1.75541e50	−0.497658
$392$	3.25852e50	0.878904
$393$	0	0
$394$	−5.94324e49	−0.145160
$395$	−8.48238e50	−1.97185
$396$	0	0
$397$	6.19440e50	1.30492	0.652461	−	0.757823i	$-0.273737\pi$
$397$	6.19440e50	1.30492	0.652461	+	0.757823i	$0.273737\pi$
$398$	−1.05960e49	−0.0212530
$399$	0	0
$400$	4.14069e50	0.753187
$401$	−1.98149e50	−0.343302	−0.171651	−	0.985158i	$-0.554910\pi$
$401$	−1.98149e50	−0.343302	−0.171651	+	0.985158i	$0.554910\pi$
$402$	0	0
$403$	6.50462e48	0.0102276
$404$	−4.12141e50	−0.617461
$405$	0	0
$406$	−1.93108e50	−0.262750
$407$	6.41521e50	0.831994
$408$	0	0
$409$	−8.18635e50	−0.964908	−0.482454	−	0.875921i	$-0.660254\pi$
$409$	−8.18635e50	−0.964908	−0.482454	+	0.875921i	$0.660254\pi$
$410$	−6.63021e50	−0.745147
$411$	0	0
$412$	−3.47121e50	−0.354802
$413$	−1.19894e51	−1.16888
$414$	0	0
$415$	−1.45658e51	−1.29240
$416$	−4.48037e49	−0.0379310
$417$	0	0
$418$	5.55228e50	0.428089
$419$	9.92910e50	0.730696	0.365348	−	0.930871i	$-0.380950\pi$
$419$	9.92910e50	0.730696	0.365348	+	0.930871i	$0.380950\pi$
$420$	0	0
$421$	−6.39132e50	−0.428637	−0.214319	−	0.976764i	$-0.568753\pi$
$421$	−6.39132e50	−0.428637	−0.214319	+	0.976764i	$0.568753\pi$
$422$	6.98230e50	0.447101
$423$	0	0
$424$	1.61699e50	0.0944219
$425$	−6.57733e50	−0.366831
$426$	0	0
$427$	1.93232e51	0.983414
$428$	3.14616e51	1.52978
$429$	0	0
$430$	1.89501e51	0.841349
$431$	−3.21896e50	−0.136587	−0.0682935	−	0.997665i	$-0.521755\pi$
$431$	−3.21896e50	−0.136587	−0.0682935	+	0.997665i	$0.521755\pi$
$432$	0	0
$433$	−4.43633e51	−1.71993	−0.859963	−	0.510356i	$-0.829514\pi$
$433$	−4.43633e51	−1.71993	−0.859963	+	0.510356i	$0.829514\pi$
$434$	3.52517e50	0.130656
$435$	0	0
$436$	2.82118e51	0.955970
$437$	−8.47013e51	−2.74475
$438$	0	0
$439$	3.25569e51	0.965128	0.482564	−	0.875861i	$-0.339706\pi$
$439$	3.25569e51	0.965128	0.482564	+	0.875861i	$0.339706\pi$
$440$	2.44903e51	0.694491
$441$	0	0
$442$	1.80273e49	0.00467946
$443$	4.09722e51	1.01769	0.508846	−	0.860858i	$-0.330072\pi$
$443$	4.09722e51	1.01769	0.508846	+	0.860858i	$0.330072\pi$
$444$	0	0
$445$	−3.49246e51	−0.794533
$446$	1.74821e51	0.380683
$447$	0	0
$448$	2.41871e51	0.482684
$449$	8.07315e51	1.54255	0.771275	−	0.636502i	$-0.219619\pi$
$449$	8.07315e51	1.54255	0.771275	+	0.636502i	$0.219619\pi$
$450$	0	0
$451$	5.68613e51	0.996264
$452$	7.99362e51	1.34136
$453$	0	0
$454$	3.02784e51	0.466170
$455$	−6.47615e50	−0.0955201
$456$	0	0
$457$	3.57503e51	0.484076	0.242038	−	0.970267i	$-0.422184\pi$
$457$	3.57503e51	0.484076	0.242038	+	0.970267i	$0.422184\pi$
$458$	1.43554e51	0.186268
$459$	0	0
$460$	−1.74147e52	−2.07558
$461$	−8.00610e51	−0.914645	−0.457323	−	0.889301i	$-0.651192\pi$
$461$	−8.00610e51	−0.914645	−0.457323	+	0.889301i	$0.651192\pi$
$462$	0	0
$463$	−8.57929e51	−0.900787	−0.450393	−	0.892830i	$-0.648716\pi$
$463$	−8.57929e51	−0.900787	−0.450393	+	0.892830i	$0.648716\pi$
$464$	−3.05837e51	−0.307886
$465$	0	0
$466$	−6.46740e51	−0.598693
$467$	−1.12846e52	−1.00186	−0.500932	−	0.865487i	$-0.667009\pi$
$467$	−1.12846e52	−1.00186	−0.500932	+	0.865487i	$0.667009\pi$
$468$	0	0
$469$	2.28330e52	1.86506
$470$	−8.12510e51	−0.636679
$471$	0	0
$472$	7.10306e51	0.512361
$473$	−1.62518e52	−1.12489
$474$	0	0
$475$	−3.17367e52	−2.02319
$476$	−6.72205e51	−0.411307
$477$	0	0
$478$	8.47673e51	0.477952
$479$	2.24291e52	1.21414	0.607071	−	0.794648i	$-0.292344\pi$
$479$	2.24291e52	1.21414	0.607071	+	0.794648i	$0.292344\pi$
$480$	0	0
$481$	1.00504e51	0.0501594
$482$	1.06547e51	0.0510652
$483$	0	0
$484$	9.95912e51	0.440287
$485$	−3.51822e52	−1.49403
$486$	0	0
$487$	6.05465e51	0.237287	0.118644	−	0.992937i	$-0.462145\pi$
$487$	6.05465e51	0.237287	0.118644	+	0.992937i	$0.462145\pi$
$488$	−1.14480e52	−0.431064
$489$	0	0
$490$	−1.99510e52	−0.693650
$491$	3.63912e52	1.21593	0.607963	−	0.793965i	$-0.291987\pi$
$491$	3.63912e52	1.21593	0.607963	+	0.793965i	$0.291987\pi$
$492$	0	0
$493$	4.85811e51	0.149952
$494$	8.69845e50	0.0258087
$495$	0	0
$496$	5.58303e51	0.153101
$497$	3.81161e52	1.00498
$498$	0	0
$499$	−5.72391e52	−1.39551	−0.697754	−	0.716337i	$-0.745817\pi$
$499$	−5.72391e52	−1.39551	−0.697754	+	0.716337i	$0.745817\pi$
$500$	−1.02033e52	−0.239235
$501$	0	0
$502$	−2.38484e52	−0.517294
$503$	−1.75324e52	−0.365818	−0.182909	−	0.983130i	$-0.558551\pi$
$503$	−1.75324e52	−0.365818	−0.182909	+	0.983130i	$0.558551\pi$
$504$	0	0
$505$	5.41361e52	1.04545
$506$	−2.17066e52	−0.403327
$507$	0	0
$508$	5.62453e52	0.967707
$509$	9.36160e52	1.55008	0.775039	−	0.631913i	$-0.217730\pi$
$509$	9.36160e52	1.55008	0.775039	+	0.631913i	$0.217730\pi$
$510$	0	0
$511$	2.62351e52	0.402415
$512$	−6.71707e52	−0.991780
$513$	0	0
$514$	1.13501e51	0.0155317
$515$	4.55955e52	0.600732
$516$	0	0
$517$	6.96817e52	0.851242
$518$	5.44678e52	0.640781
$519$	0	0
$520$	3.83676e51	0.0418697
$521$	6.14605e52	0.646042	0.323021	−	0.946392i	$-0.395302\pi$
$521$	6.14605e52	0.646042	0.323021	+	0.946392i	$0.395302\pi$
$522$	0	0
$523$	−2.50871e52	−0.244719	−0.122359	−	0.992486i	$-0.539046\pi$
$523$	−2.50871e52	−0.244719	−0.122359	+	0.992486i	$0.539046\pi$
$524$	−1.29344e52	−0.121559
$525$	0	0
$526$	3.35140e52	0.292418
$527$	−8.86844e51	−0.0745659
$528$	0	0
$529$	2.03088e53	1.58598
$530$	−9.90037e51	−0.0745198
$531$	0	0
$532$	−3.24350e53	−2.26849
$533$	8.90815e51	0.0600630
$534$	0	0
$535$	−4.13259e53	−2.59014
$536$	−1.35273e53	−0.817519
$537$	0	0
$538$	1.51784e52	0.0853046
$539$	1.71101e53	0.927412
$540$	0	0
$541$	2.37622e53	1.19823	0.599114	−	0.800664i	$-0.295520\pi$
$541$	2.37622e53	1.19823	0.599114	+	0.800664i	$0.295520\pi$
$542$	1.04511e52	0.0508368
$543$	0	0
$544$	6.10856e52	0.276542
$545$	−3.70571e53	−1.61860
$546$	0	0
$547$	1.01438e53	0.412524	0.206262	−	0.978497i	$-0.433870\pi$
$547$	1.01438e53	0.412524	0.206262	+	0.978497i	$0.433870\pi$
$548$	7.82071e52	0.306920
$549$	0	0
$550$	−8.13325e52	−0.297298
$551$	2.34412e53	0.827035
$552$	0	0
$553$	6.17641e53	2.03047
$554$	−1.18143e53	−0.374944
$555$	0	0
$556$	−2.74100e53	−0.810868
$557$	−3.06102e53	−0.874358	−0.437179	−	0.899374i	$-0.644022\pi$
$557$	−3.06102e53	−0.874358	−0.437179	+	0.899374i	$0.644022\pi$
$558$	0	0
$559$	−2.54608e52	−0.0678174
$560$	−5.55859e53	−1.42988
$561$	0	0
$562$	1.05432e53	0.252997
$563$	−1.09661e53	−0.254179	−0.127090	−	0.991891i	$-0.540564\pi$
$563$	−1.09661e53	−0.254179	−0.127090	+	0.991891i	$0.540564\pi$
$564$	0	0
$565$	−1.04999e54	−2.27111
$566$	2.17647e53	0.454813
$567$	0	0
$568$	−2.25817e53	−0.440519
$569$	−6.98263e53	−1.31622	−0.658112	−	0.752920i	$-0.728645\pi$
$569$	−6.98263e53	−1.31622	−0.658112	+	0.752920i	$0.728645\pi$
$570$	0	0
$571$	−2.15970e53	−0.380180	−0.190090	−	0.981767i	$-0.560878\pi$
$571$	−2.15970e53	−0.380180	−0.190090	+	0.981767i	$0.560878\pi$
$572$	−1.53376e52	−0.0260937
$573$	0	0
$574$	4.82776e53	0.767298
$575$	1.24075e54	1.90616
$576$	0	0
$577$	2.02592e53	0.290867	0.145433	−	0.989368i	$-0.453542\pi$
$577$	2.02592e53	0.290867	0.145433	+	0.989368i	$0.453542\pi$
$578$	2.32058e53	0.322110
$579$	0	0
$580$	4.81955e53	0.625404
$581$	1.06061e54	1.33082
$582$	0	0
$583$	8.49065e52	0.0996332
$584$	−1.55428e53	−0.176392
$585$	0	0
$586$	−1.65981e53	−0.176220
$587$	7.06852e53	0.725914	0.362957	−	0.931806i	$-0.381767\pi$
$587$	7.06852e53	0.725914	0.362957	+	0.931806i	$0.381767\pi$
$588$	0	0
$589$	−4.27917e53	−0.411255
$590$	−4.34900e53	−0.404367
$591$	0	0
$592$	8.62641e53	0.750856
$593$	1.68827e53	0.142192	0.0710959	−	0.997469i	$-0.477350\pi$
$593$	1.68827e53	0.142192	0.0710959	+	0.997469i	$0.477350\pi$
$594$	0	0
$595$	8.82962e53	0.696404
$596$	−1.92303e53	−0.146786
$597$	0	0
$598$	−3.40066e52	−0.0243159
$599$	8.66168e53	0.599486	0.299743	−	0.954020i	$-0.403099\pi$
$599$	8.66168e53	0.599486	0.299743	+	0.954020i	$0.403099\pi$
$600$	0	0
$601$	1.01881e54	0.660758	0.330379	−	0.943848i	$-0.392823\pi$
$601$	1.01881e54	0.660758	0.330379	+	0.943848i	$0.392823\pi$
$602$	−1.37984e54	−0.866359
$603$	0	0
$604$	−3.93477e53	−0.231579
$605$	−1.30816e54	−0.745472
$606$	0	0
$607$	−3.59220e53	−0.191947	−0.0959734	−	0.995384i	$-0.530596\pi$
$607$	−3.59220e53	−0.191947	−0.0959734	+	0.995384i	$0.530596\pi$
$608$	2.94748e54	1.52522
$609$	0	0
$610$	7.00926e53	0.340205
$611$	1.09166e53	0.0513199
$612$	0	0
$613$	9.11862e53	0.402207	0.201104	−	0.979570i	$-0.435547\pi$
$613$	9.11862e53	0.402207	0.201104	+	0.979570i	$0.435547\pi$
$614$	6.43631e53	0.275013
$615$	0	0
$616$	−1.78325e54	−0.715136
$617$	−2.52497e54	−0.981061	−0.490530	−	0.871424i	$-0.663197\pi$
$617$	−2.52497e54	−0.981061	−0.490530	+	0.871424i	$0.663197\pi$
$618$	0	0
$619$	3.13318e53	0.114292	0.0571462	−	0.998366i	$-0.481800\pi$
$619$	3.13318e53	0.114292	0.0571462	+	0.998366i	$0.481800\pi$
$620$	−8.79804e53	−0.310991
$621$	0	0
$622$	−1.79992e54	−0.597503
$623$	2.54302e54	0.818151
$624$	0	0
$625$	−2.58177e54	−0.780292
$626$	6.93035e53	0.203028
$627$	0	0
$628$	−1.32027e54	−0.363454
$629$	−1.37027e54	−0.365695
$630$	0	0
$631$	−3.45716e54	−0.867256	−0.433628	−	0.901092i	$-0.642767\pi$
$631$	−3.45716e54	−0.867256	−0.433628	+	0.901092i	$0.642767\pi$
$632$	−3.65918e54	−0.890022
$633$	0	0
$634$	−1.72198e54	−0.393811
$635$	−7.38800e54	−1.63847
$636$	0	0
$637$	2.68055e53	0.0559121
$638$	6.00734e53	0.121529
$639$	0	0
$640$	7.81821e54	1.48798
$641$	−3.85151e54	−0.711050	−0.355525	−	0.934667i	$-0.615698\pi$
$641$	−3.85151e54	−0.711050	−0.355525	+	0.934667i	$0.615698\pi$
$642$	0	0
$643$	1.53024e54	0.265855	0.132928	−	0.991126i	$-0.457562\pi$
$643$	1.53024e54	0.265855	0.132928	+	0.991126i	$0.457562\pi$
$644$	1.26805e55	2.13728
$645$	0	0
$646$	−1.18595e54	−0.188163
$647$	−1.27086e55	−1.95644	−0.978219	−	0.207577i	$-0.933442\pi$
$647$	−1.27086e55	−1.95644	−0.978219	+	0.207577i	$0.933442\pi$
$648$	0	0
$649$	3.72975e54	0.540639
$650$	−1.27419e53	−0.0179236
$651$	0	0
$652$	1.46507e53	0.0194102
$653$	−9.19237e54	−1.18201	−0.591004	−	0.806669i	$-0.701268\pi$
$653$	−9.19237e54	−1.18201	−0.591004	+	0.806669i	$0.701268\pi$
$654$	0	0
$655$	1.69898e54	0.205818
$656$	7.64603e54	0.899106
$657$	0	0
$658$	5.91626e54	0.655605
$659$	2.57996e54	0.277554	0.138777	−	0.990324i	$-0.455683\pi$
$659$	2.57996e54	0.277554	0.138777	+	0.990324i	$0.455683\pi$
$660$	0	0
$661$	−1.12332e55	−1.13914	−0.569568	−	0.821944i	$-0.692890\pi$
$661$	−1.12332e55	−1.13914	−0.569568	+	0.821944i	$0.692890\pi$
$662$	5.39732e54	0.531432
$663$	0	0
$664$	−6.28350e54	−0.583343
$665$	4.26044e55	3.84090
$666$	0	0
$667$	−9.16434e54	−0.779197
$668$	−4.12825e54	−0.340898
$669$	0	0
$670$	8.28239e54	0.645204
$671$	−6.01121e54	−0.454855
$672$	0	0
$673$	−1.50888e54	−0.107736	−0.0538681	−	0.998548i	$-0.517155\pi$
$673$	−1.50888e54	−0.107736	−0.0538681	+	0.998548i	$0.517155\pi$
$674$	3.55464e54	0.246563
$675$	0	0
$676$	1.33120e55	0.871530
$677$	−5.88105e54	−0.374090	−0.187045	−	0.982351i	$-0.559891\pi$
$677$	−5.88105e54	−0.374090	−0.187045	+	0.982351i	$0.559891\pi$
$678$	0	0
$679$	2.56178e55	1.53844
$680$	−5.23106e54	−0.305257
$681$	0	0
$682$	−1.09663e54	−0.0604319
$683$	−1.21018e55	−0.648109	−0.324054	−	0.946038i	$-0.605046\pi$
$683$	−1.21018e55	−0.648109	−0.324054	+	0.946038i	$0.605046\pi$
$684$	0	0
$685$	−1.02727e55	−0.519661
$686$	3.49842e54	0.172009
$687$	0	0
$688$	−2.18534e55	−1.01518
$689$	1.33018e53	0.00600671
$690$	0	0
$691$	1.62764e55	0.694601	0.347300	−	0.937754i	$-0.387098\pi$
$691$	1.62764e55	0.694601	0.347300	+	0.937754i	$0.387098\pi$
$692$	−1.72112e55	−0.714072
$693$	0	0
$694$	9.53445e54	0.373926
$695$	3.60039e55	1.37292
$696$	0	0
$697$	−1.21454e55	−0.437899
$698$	−3.43312e54	−0.120367
$699$	0	0
$700$	4.75124e55	1.57542
$701$	−1.79427e55	−0.578610	−0.289305	−	0.957237i	$-0.593424\pi$
$701$	−1.79427e55	−0.578610	−0.289305	+	0.957237i	$0.593424\pi$
$702$	0	0
$703$	−6.61180e55	−2.01693
$704$	−7.52430e54	−0.223254
$705$	0	0
$706$	−2.11130e55	−0.592731
$707$	−3.94190e55	−1.07653
$708$	0	0
$709$	1.14395e55	0.295669	0.147834	−	0.989012i	$-0.452770\pi$
$709$	1.14395e55	0.295669	0.147834	+	0.989012i	$0.452770\pi$
$710$	1.38261e55	0.347667
$711$	0	0
$712$	−1.50660e55	−0.358623
$713$	1.67294e55	0.387467
$714$	0	0
$715$	2.01465e54	0.0441805
$716$	6.37114e55	1.35961
$717$	0	0
$718$	2.04771e55	0.413848
$719$	−6.82369e55	−1.34216	−0.671082	−	0.741383i	$-0.734170\pi$
$719$	−6.82369e55	−1.34216	−0.671082	+	0.741383i	$0.734170\pi$
$720$	0	0
$721$	−3.32002e55	−0.618589
$722$	−3.75815e55	−0.681552
$723$	0	0
$724$	−2.15107e55	−0.369617
$725$	−3.43379e55	−0.574357
$726$	0	0
$727$	4.73186e55	0.750085	0.375043	−	0.927008i	$-0.377628\pi$
$727$	4.73186e55	0.750085	0.375043	+	0.927008i	$0.377628\pi$
$728$	−2.79372e54	−0.0431143
$729$	0	0
$730$	9.51643e54	0.139213
$731$	3.47134e55	0.494433
$732$	0	0
$733$	7.44240e54	0.100505	0.0502523	−	0.998737i	$-0.483997\pi$
$733$	7.44240e54	0.100505	0.0502523	+	0.998737i	$0.483997\pi$
$734$	−4.13876e54	−0.0544248
$735$	0	0
$736$	−1.15232e56	−1.43700
$737$	−7.10305e55	−0.862639
$738$	0	0
$739$	9.48337e55	1.09244	0.546218	−	0.837643i	$-0.316067\pi$
$739$	9.48337e55	1.09244	0.546218	+	0.837643i	$0.316067\pi$
$740$	−1.35940e56	−1.52520
$741$	0	0
$742$	7.20891e54	0.0767350
$743$	2.79365e55	0.289661	0.144830	−	0.989456i	$-0.453736\pi$
$743$	2.79365e55	0.289661	0.144830	+	0.989456i	$0.453736\pi$
$744$	0	0
$745$	2.52596e55	0.248530
$746$	−1.50011e55	−0.143786
$747$	0	0
$748$	2.09114e55	0.190240
$749$	3.00912e56	2.66713
$750$	0	0
$751$	−8.12653e55	−0.683796	−0.341898	−	0.939737i	$-0.611070\pi$
$751$	−8.12653e55	−0.683796	−0.341898	+	0.939737i	$0.611070\pi$
$752$	9.36995e55	0.768227
$753$	0	0
$754$	9.41137e53	0.00732676
$755$	5.16845e55	0.392098
$756$	0	0
$757$	2.71381e56	1.95528	0.977642	−	0.210277i	$-0.0674367\pi$
$757$	2.71381e56	1.95528	0.977642	+	0.210277i	$0.0674367\pi$
$758$	8.98771e54	0.0631102
$759$	0	0
$760$	−2.52408e56	−1.68359
$761$	2.53928e56	1.65086	0.825428	−	0.564507i	$-0.190934\pi$
$761$	2.53928e56	1.65086	0.825428	+	0.564507i	$0.190934\pi$
$762$	0	0
$763$	2.69830e56	1.66671
$764$	−1.62071e56	−0.975855
$765$	0	0
$766$	−3.99872e55	−0.228802
$767$	5.84319e54	0.0325942
$768$	0	0
$769$	−3.16540e56	−1.67828	−0.839140	−	0.543915i	$-0.816941\pi$
$769$	−3.16540e56	−1.67828	−0.839140	+	0.543915i	$0.816941\pi$
$770$	1.09183e56	0.564401
$771$	0	0
$772$	1.75563e55	0.0862773
$773$	8.83478e55	0.423346	0.211673	−	0.977341i	$-0.432109\pi$
$773$	8.83478e55	0.423346	0.211673	+	0.977341i	$0.432109\pi$
$774$	0	0
$775$	6.26834e55	0.285607
$776$	−1.51771e56	−0.674352
$777$	0	0
$778$	9.61590e55	0.406338
$779$	−5.86038e56	−2.41516
$780$	0	0
$781$	−1.18574e56	−0.464832
$782$	4.63648e55	0.177279
$783$	0	0
$784$	2.30077e56	0.836969
$785$	1.73422e56	0.615382
$786$	0	0
$787$	2.01468e56	0.680299	0.340149	−	0.940371i	$-0.389522\pi$
$787$	2.01468e56	0.680299	0.340149	+	0.940371i	$0.389522\pi$
$788$	−1.08006e56	−0.355784
$789$	0	0
$790$	2.24041e56	0.702425
$791$	7.64544e56	2.33863
$792$	0	0
$793$	−9.41744e54	−0.0274224
$794$	−1.63610e56	−0.464847
$795$	0	0
$796$	−1.92560e55	−0.0520908
$797$	−4.87383e56	−1.28657	−0.643285	−	0.765627i	$-0.722429\pi$
$797$	−4.87383e56	−1.28657	−0.643285	+	0.765627i	$0.722429\pi$
$798$	0	0
$799$	−1.48838e56	−0.374156
$800$	−4.31762e56	−1.05923
$801$	0	0
$802$	5.23362e55	0.122293
$803$	−8.16138e55	−0.186128
$804$	0	0
$805$	−1.66562e57	−3.61873
$806$	−1.71804e54	−0.00364333
$807$	0	0
$808$	2.33536e56	0.471880
$809$	−2.97630e56	−0.587057	−0.293529	−	0.955950i	$-0.594830\pi$
$809$	−2.97630e56	−0.587057	−0.293529	+	0.955950i	$0.594830\pi$
$810$	0	0
$811$	−7.70370e56	−1.44808	−0.724041	−	0.689757i	$-0.757717\pi$
$811$	−7.70370e56	−1.44808	−0.724041	+	0.689757i	$0.757717\pi$
$812$	−3.50934e56	−0.643995
$813$	0	0
$814$	−1.69442e56	−0.296378
$815$	−1.92441e55	−0.0328643
$816$	0	0
$817$	1.67498e57	2.72696
$818$	2.16223e56	0.343725
$819$	0	0
$820$	−1.20490e57	−1.82634
$821$	−4.31761e55	−0.0639075	−0.0319537	−	0.999489i	$-0.510173\pi$
$821$	−4.31761e55	−0.0639075	−0.0319537	+	0.999489i	$0.510173\pi$
$822$	0	0
$823$	4.12553e56	0.582348	0.291174	−	0.956670i	$-0.405954\pi$
$823$	4.12553e56	0.582348	0.291174	+	0.956670i	$0.405954\pi$
$824$	1.96693e56	0.271149
$825$	0	0
$826$	3.16671e56	0.416387
$827$	6.96480e56	0.894440	0.447220	−	0.894424i	$-0.352414\pi$
$827$	6.96480e56	0.894440	0.447220	+	0.894424i	$0.352414\pi$
$828$	0	0
$829$	1.42775e57	1.74920	0.874600	−	0.484845i	$-0.161124\pi$
$829$	1.42775e57	1.74920	0.874600	+	0.484845i	$0.161124\pi$
$830$	3.84721e56	0.460387
$831$	0	0
$832$	−1.17879e55	−0.0134596
$833$	−3.65468e56	−0.407636
$834$	0	0
$835$	5.42258e56	0.577192
$836$	1.00901e57	1.04924
$837$	0	0
$838$	−2.62253e56	−0.260293
$839$	−6.94535e56	−0.673497	−0.336749	−	0.941595i	$-0.609327\pi$
$839$	−6.94535e56	−0.673497	−0.336749	+	0.941595i	$0.609327\pi$
$840$	0	0
$841$	−8.26620e56	−0.765216
$842$	1.68811e56	0.152692
$843$	0	0
$844$	1.26889e57	1.09584
$845$	−1.74857e57	−1.47563
$846$	0	0
$847$	9.52532e56	0.767632
$848$	1.14172e56	0.0899168
$849$	0	0
$850$	1.73724e56	0.130675
$851$	2.58488e57	1.90027
$852$	0	0
$853$	−4.76945e56	−0.334936	−0.167468	−	0.985878i	$-0.553559\pi$
$853$	−4.76945e56	−0.334936	−0.167468	+	0.985878i	$0.553559\pi$
$854$	−5.10377e56	−0.350318
$855$	0	0
$856$	−1.78274e57	−1.16909
$857$	7.15190e56	0.458454	0.229227	−	0.973373i	$-0.426380\pi$
$857$	7.15190e56	0.458454	0.229227	+	0.973373i	$0.426380\pi$
$858$	0	0
$859$	−3.14874e57	−1.92872	−0.964362	−	0.264586i	$-0.914765\pi$
$859$	−3.14874e57	−1.92872	−0.964362	+	0.264586i	$0.914765\pi$
$860$	3.44378e57	2.06213
$861$	0	0
$862$	8.50211e55	0.0486558
$863$	−6.33719e56	−0.354557	−0.177279	−	0.984161i	$-0.556729\pi$
$863$	−6.33719e56	−0.354557	−0.177279	+	0.984161i	$0.556729\pi$
$864$	0	0
$865$	2.26074e57	1.20903
$866$	1.17175e57	0.612683
$867$	0	0
$868$	6.40626e56	0.320236
$869$	−1.92140e57	−0.939144
$870$	0	0
$871$	−1.11280e56	−0.0520070
$872$	−1.59859e57	−0.730577
$873$	0	0
$874$	2.23718e57	0.977750
$875$	−9.75885e56	−0.417101
$876$	0	0
$877$	−2.07724e57	−0.849171	−0.424585	−	0.905388i	$-0.639580\pi$
$877$	−2.07724e57	−0.849171	−0.424585	+	0.905388i	$0.639580\pi$
$878$	−8.59911e56	−0.343804
$879$	0	0
$880$	1.72921e57	0.661355
$881$	1.44068e57	0.538937	0.269468	−	0.963009i	$-0.413152\pi$
$881$	1.44068e57	0.538937	0.269468	+	0.963009i	$0.413152\pi$
$882$	0	0
$883$	−2.21527e57	−0.792852	−0.396426	−	0.918067i	$-0.629750\pi$
$883$	−2.21527e57	−0.792852	−0.396426	+	0.918067i	$0.629750\pi$
$884$	3.27608e55	0.0114693
$885$	0	0
$886$	−1.08218e57	−0.362528
$887$	−4.62524e56	−0.151574	−0.0757868	−	0.997124i	$-0.524147\pi$
$887$	−4.62524e56	−0.151574	−0.0757868	+	0.997124i	$0.524147\pi$
$888$	0	0
$889$	5.37954e57	1.68718
$890$	9.22450e56	0.283033
$891$	0	0
$892$	3.17700e57	0.933046
$893$	−7.18170e57	−2.06359
$894$	0	0
$895$	−8.36869e57	−2.30202
$896$	−5.69280e57	−1.53221
$897$	0	0
$898$	−2.13233e57	−0.549497
$899$	−4.62989e56	−0.116750
$900$	0	0
$901$	−1.81358e56	−0.0437929
$902$	−1.50185e57	−0.354895
$903$	0	0
$904$	−4.52950e57	−1.02510
$905$	2.82549e57	0.625816
$906$	0	0
$907$	5.47083e57	1.16068	0.580339	−	0.814375i	$-0.302920\pi$
$907$	5.47083e57	1.16068	0.580339	+	0.814375i	$0.302920\pi$
$908$	5.50247e57	1.14257
$909$	0	0
$910$	1.71052e56	0.0340267
$911$	5.88844e56	0.114655	0.0573274	−	0.998355i	$-0.481742\pi$
$911$	5.88844e56	0.114655	0.0573274	+	0.998355i	$0.481742\pi$
$912$	0	0
$913$	−3.29940e57	−0.615539
$914$	−9.44258e56	−0.172441
$915$	0	0
$916$	2.60879e57	0.456538
$917$	−1.23710e57	−0.211936
$918$	0	0
$919$	−3.41668e57	−0.560986	−0.280493	−	0.959856i	$-0.590498\pi$
$919$	−3.41668e57	−0.560986	−0.280493	+	0.959856i	$0.590498\pi$
$920$	9.86788e57	1.58621
$921$	0	0
$922$	2.11462e57	0.325821
$923$	−1.85764e56	−0.0280239
$924$	0	0
$925$	9.68529e57	1.40071
$926$	2.26601e57	0.320884
$927$	0	0
$928$	3.18906e57	0.432989
$929$	5.60274e57	0.744893	0.372447	−	0.928054i	$-0.378519\pi$
$929$	5.60274e57	0.744893	0.372447	+	0.928054i	$0.378519\pi$
$930$	0	0
$931$	−1.76345e58	−2.24824
$932$	−1.17532e58	−1.46739
$933$	0	0
$934$	2.98056e57	0.356890
$935$	−2.74678e57	−0.322105
$936$	0	0
$937$	2.84316e57	0.319800	0.159900	−	0.987133i	$-0.448883\pi$
$937$	2.84316e57	0.319800	0.159900	+	0.987133i	$0.448883\pi$
$938$	−6.03079e57	−0.664383
$939$	0	0
$940$	−1.47657e58	−1.56049
$941$	3.10342e57	0.321250	0.160625	−	0.987016i	$-0.448649\pi$
$941$	3.10342e57	0.321250	0.160625	+	0.987016i	$0.448649\pi$
$942$	0	0
$943$	2.29111e58	2.27546
$944$	5.01531e57	0.487915
$945$	0	0
$946$	4.29251e57	0.400714
$947$	−1.09739e58	−1.00354	−0.501771	−	0.865000i	$-0.667318\pi$
$947$	−1.09739e58	−1.00354	−0.501771	+	0.865000i	$0.667318\pi$
$948$	0	0
$949$	−1.27860e56	−0.0112213
$950$	8.38249e57	0.720713
$951$	0	0
$952$	3.80898e57	0.314332
$953$	1.56833e58	1.26802	0.634009	−	0.773326i	$-0.281408\pi$
$953$	1.56833e58	1.26802	0.634009	+	0.773326i	$0.281408\pi$
$954$	0	0
$955$	2.12886e58	1.65227
$956$	1.54047e58	1.17145
$957$	0	0
$958$	−5.92410e57	−0.432509
$959$	7.48006e57	0.535109
$960$	0	0
$961$	−1.37130e58	−0.941944
$962$	−2.65456e56	−0.0178681
$963$	0	0
$964$	1.93627e57	0.125160
$965$	−2.30608e57	−0.146080
$966$	0	0
$967$	−6.70320e57	−0.407817	−0.203909	−	0.978990i	$-0.565365\pi$
$967$	−6.70320e57	−0.407817	−0.203909	+	0.978990i	$0.565365\pi$
$968$	−5.64323e57	−0.336479
$969$	0	0
$970$	9.29254e57	0.532213
$971$	1.00902e57	0.0566405	0.0283202	−	0.999599i	$-0.490984\pi$
$971$	1.00902e57	0.0566405	0.0283202	+	0.999599i	$0.490984\pi$
$972$	0	0
$973$	−2.62161e58	−1.41373
$974$	−1.59919e57	−0.0845279
$975$	0	0
$976$	−8.08315e57	−0.410496
$977$	1.41653e58	0.705150	0.352575	−	0.935784i	$-0.385306\pi$
$977$	1.41653e58	0.705150	0.352575	+	0.935784i	$0.385306\pi$
$978$	0	0
$979$	−7.91101e57	−0.378416
$980$	−3.62567e58	−1.70012
$981$	0	0
$982$	−9.61185e57	−0.433145
$983$	8.83216e57	0.390187	0.195094	−	0.980785i	$-0.437499\pi$
$983$	8.83216e57	0.390187	0.195094	+	0.980785i	$0.437499\pi$
$984$	0	0
$985$	1.41869e58	0.602396
$986$	−1.28315e57	−0.0534169
$987$	0	0
$988$	1.58076e57	0.0632567
$989$	−6.54832e58	−2.56923
$990$	0	0
$991$	2.39176e58	0.902156	0.451078	−	0.892484i	$-0.351040\pi$
$991$	2.39176e58	0.902156	0.451078	+	0.892484i	$0.351040\pi$
$992$	−5.82159e57	−0.215310
$993$	0	0
$994$	−1.00675e58	−0.358002
$995$	2.52933e57	0.0881975
$996$	0	0
$997$	1.65650e58	0.555439	0.277719	−	0.960662i	$-0.410421\pi$
$997$	1.65650e58	0.555439	0.277719	+	0.960662i	$0.410421\pi$
$998$	1.51183e58	0.497116
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	9.40.a.c.1.2		3
3.2	odd	2		3.40.a.b.1.2	✓	3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
3.40.a.b.1.2	✓	3	3.2	odd	2
9.40.a.c.1.2		3	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 9 = 3^{2} \)
Weight:	\( k \)	\(=\)	\( 40 \)
Character orbit:	\([\chi]\)	\(=\)	9.a (trivial)

\(f(q)\)	\(=\)	\(q-264126. q^{2} -4.79993e11 q^{4} +6.30487e13 q^{5} -4.59086e16 q^{7} +2.71983e17 q^{8} +O(q^{10})\)	\(q-264126. q^{2} -4.79993e11 q^{4} +6.30487e13 q^{5} -4.59086e16 q^{7} +2.71983e17 q^{8} -1.66528e19 q^{10} +1.42816e20 q^{11} +2.23742e20 q^{13} +1.21256e22 q^{14} +1.92041e23 q^{16} -3.05051e23 q^{17} -1.47192e25 q^{19} -3.02629e25 q^{20} -3.77213e25 q^{22} +5.75448e26 q^{23} +2.15614e27 q^{25} -5.90959e25 q^{26} +2.20358e28 q^{28} -1.59256e28 q^{29} +2.90720e28 q^{31} -2.00247e29 q^{32} +8.05717e28 q^{34} -2.89448e30 q^{35} +4.49195e30 q^{37} +3.88772e30 q^{38} +1.71482e31 q^{40} +3.98145e31 q^{41} -1.13795e32 q^{43} -6.85506e31 q^{44} -1.51990e32 q^{46} +4.87913e32 q^{47} +1.19806e33 q^{49} -5.69493e32 q^{50} -1.07395e32 q^{52} +5.94518e32 q^{53} +9.00434e33 q^{55} -1.24864e34 q^{56} +4.20636e33 q^{58} +2.61158e34 q^{59} -4.20907e34 q^{61} -7.67866e33 q^{62} -5.26854e34 q^{64} +1.41066e34 q^{65} -4.97358e35 q^{67} +1.46422e35 q^{68} +7.64506e35 q^{70} -8.30261e35 q^{71} -5.71462e35 q^{73} -1.18644e36 q^{74} +7.06513e36 q^{76} -6.55647e36 q^{77} -1.34537e37 q^{79} +1.21080e37 q^{80} -1.05160e37 q^{82} -2.31025e37 q^{83} -1.92330e37 q^{85} +3.00563e37 q^{86} +3.88435e37 q^{88} -5.53932e37 q^{89} -1.02717e37 q^{91} -2.76211e38 q^{92} -1.28870e38 q^{94} -9.28027e38 q^{95} -5.58017e38 q^{97} -3.16438e38 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q - 533574 q^{2} + 957442653732 q^{4} + 53381973944430 q^{5} - 15\!\cdots\!28 q^{7}+ \cdots - 44\!\cdots\!96 q^{8}+O(q^{10}) \) 3 * q - 533574 * q^2 + 957442653732 * q^4 + 53381973944430 * q^5 - 1577312676222528 * q^7 - 447338335366356696 * q^8	\( 3 q - 533574 q^{2} + 957442653732 q^{4} + 53381973944430 q^{5} - 15\!\cdots\!28 q^{7}+ \cdots - 19\!\cdots\!10 q^{98}+O(q^{100}) \) 3 * q - 533574 * q^2 + 957442653732 * q^4 + 53381973944430 * q^5 - 1577312676222528 * q^7 - 447338335366356696 * q^8 - 39868781226579858780 * q^10 + 531160706905721914140 * q^11 + 5472528067017405393090 * q^13 - 31359570231859229549952 * q^14 + 12003837541695032587536 * q^16 - 723720005873980759323558 * q^17 - 10683569401487583427646724 * q^19 - 30604131461365012369119960 * q^20 - 101045594443676284003303224 * q^22 - 416442459750873750790818264 * q^23 - 1194715364288572543079384475 * q^25 - 9254747341970932587650915076 * q^26 + 64005281609518186278308249856 * q^28 - 72946887891838791172160902362 * q^29 - 3831507110009307505604788056 * q^31 - 378655322050508831885258466912 * q^32 + 3727087341552963400556140112844 * q^34 - 2740940042971075581743645973120 * q^35 + 2906927238124145306683518446922 * q^37 - 7416889079602877708972704812792 * q^38 + 15592183099728356300682924694800 * q^40 + 13833712444491609259076817725826 * q^41 - 241176797301842883739928662947228 * q^43 + 213525157746039384440606231602512 * q^44 - 104447080902359174134821948683856 * q^46 + 1086597674653689955742268879621504 * q^47 + 924338434806738131424394587158043 * q^49 + 118959783140473612655547453823350 * q^50 + 5952218540461015449104584358724888 * q^52 - 6299034091101274766075867439578034 * q^53 + 7235236907264709378202914522359640 * q^55 - 36130594637558190696891183124416000 * q^56 + 28134849555247756987293173039320884 * q^58 + 7558290777715899720301468980744156 * q^59 - 71826613334234103377163041195597598 * q^61 + 333393758003341216817271988077360816 * q^62 - 356382404098565729241928621083896256 * q^64 + 71965636207225251725741353420179060 * q^65 - 518823945846035691888588721831631172 * q^67 - 1121832034621182540659618925316456392 * q^68 + 381667128343527193098155020939403520 * q^70 - 849269787302723157596849576102980776 * q^71 + 637421615257246057146665571835045614 * q^73 - 8921405458543140139105593515161595412 * q^74 + 12865125362045862122037959358946857936 * q^76 + 2216532510892942434391561675975662336 * q^77 - 16306610864434983513399514618922802600 * q^79 + 18842531486692338792496997422435723680 * q^80 - 48904837208704969270795955453077116036 * q^82 - 59736269696761936146835722238132721148 * q^83 - 52409799455203108995417139125901789980 * q^85 - 8556959071360899197804948671059424200 * q^86 - 103087862263104555338872895329460381664 * q^88 - 181527336890478573173909838985501381086 * q^89 + 233409055536203220442569829829115229824 * q^91 - 965903931988757229715439967889497587232 * q^92 - 123012151365942572780176753392831409920 * q^94 - 842023600986663647572895848646980122600 * q^95 - 990533172774170511639359146813858429242 * q^97 - 1942548903376000593615944763865222165110 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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