LMFDB - Embedded newform 9.36.a.c.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [9,36,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, 36, names="a")

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

chi := DirichletCharacter("9.1");

S:= CuspForms(chi, 36);

N := Newforms(S);

Level:	$ N $	$=$	$ 9 = 3^{2} $
Weight:	$ k $	$=$	$ 36 $
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:	$69.8356175703$
Analytic rank:	$1$
Dimension:	$3$
Coefficient field:	$\mathbb{Q}[x]/(x^{3} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - x^{2} - 1847580440x + 20051963761200 $ x^3 - x^2 - 1847580440*x + 20051963761200
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{7}\cdot 3^{5}\cdot 5 $
Twist minimal:	no (minimal twist has level 3)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$-47629.1$ of defining polynomial
Character	$\chi$	$=$	9.1

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+314887. q^{2} +6.47940e10 q^{4} -2.58564e12 q^{5} +8.89060e14 q^{7} +9.58334e15 q^{8} +O(q^{10})$	\(q+314887. q^{2} +6.47940e10 q^{4} -2.58564e12 q^{5} +8.89060e14 q^{7} +9.58334e15 q^{8} -8.14184e17 q^{10} -2.05240e18 q^{11} -1.82090e19 q^{13} +2.79953e20 q^{14} +7.91364e20 q^{16} -3.53481e21 q^{17} +2.01653e22 q^{19} -1.67534e23 q^{20} -6.46272e23 q^{22} -2.51478e23 q^{23} +3.77515e24 q^{25} -5.73379e24 q^{26} +5.76057e25 q^{28} +8.93017e24 q^{29} -1.94629e26 q^{31} -8.00910e25 q^{32} -1.11307e27 q^{34} -2.29879e27 q^{35} -2.17467e27 q^{37} +6.34979e27 q^{38} -2.47791e28 q^{40} +7.70191e27 q^{41} -2.60169e28 q^{43} -1.32983e29 q^{44} -7.91871e28 q^{46} -3.33024e29 q^{47} +4.11609e29 q^{49} +1.18875e30 q^{50} -1.17984e30 q^{52} -1.01164e30 q^{53} +5.30676e30 q^{55} +8.52016e30 q^{56} +2.81199e30 q^{58} -1.91584e30 q^{59} +7.04823e30 q^{61} -6.12862e31 q^{62} -5.24107e31 q^{64} +4.70820e31 q^{65} +1.18905e32 q^{67} -2.29034e32 q^{68} -7.23859e32 q^{70} +2.78716e32 q^{71} -3.82719e32 q^{73} -6.84776e32 q^{74} +1.30659e33 q^{76} -1.82470e33 q^{77} -1.32234e33 q^{79} -2.04618e33 q^{80} +2.42523e33 q^{82} +5.69848e33 q^{83} +9.13975e33 q^{85} -8.19238e33 q^{86} -1.96688e34 q^{88} -1.72108e34 q^{89} -1.61889e34 q^{91} -1.62943e34 q^{92} -1.04865e35 q^{94} -5.21402e34 q^{95} +4.83801e34 q^{97} +1.29610e35 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q + 87330 q^{2} + 32488752900 q^{4} - 2768676235410 q^{5} + 488237848538064 q^{7} + 18\!\cdots\!52 q^{8}+O(q^{10}) $ 3 * q + 87330 * q^2 + 32488752900 * q^4 - 2768676235410 * q^5 + 488237848538064 * q^7 + 18683146678130952 * q^8	$ 3 q + 87330 q^{2} + 32488752900 q^{4} - 2768676235410 q^{5} + 488237848538064 q^{7} + 18\!\cdots\!52 q^{8}+ \cdots + 12\!\cdots\!86 q^{98}+O(q^{100}) $ 3 * q + 87330 * q^2 + 32488752900 * q^4 - 2768676235410 * q^5 + 488237848538064 * q^7 + 18683146678130952 * q^8 - 1127779626928867020 * q^10 - 3426356175124224804 * q^11 + 50087718431258539506 * q^13 + 217880362960444050144 * q^14 + 606906765664363747344 * q^16 - 2730709287864549111942 * q^17 + 28794251065778257727292 * q^19 - 88477655809138293889560 * q^20 - 122741766765729403865496 * q^22 - 1806983834691084779311608 * q^23 + 8598840806404444672708725 * q^25 - 12462234191474761114326516 * q^26 + 88582873604432535904569792 * q^28 - 78927943791269118086922714 * q^29 - 1597007179004406242679048 * q^31 - 212133152341134442715841504 * q^32 - 1031323232079473133177847620 * q^34 + 1159830211565676145196532000 * q^35 - 5102549932092597658956094086 * q^37 + 8724219045726720381610922664 * q^38 - 17377992868876213570860774960 * q^40 + 20208748955896036456754429058 * q^41 + 46721962642013867129638134372 * q^43 - 194349428414233101115805936688 * q^44 + 52087178478532028950981302192 * q^46 - 293197746513164578153478190816 * q^47 + 836105627836985614440420595707 * q^49 + 701125828082122697797800571950 * q^50 - 2520178249741268871517789030248 * q^52 + 108875909240521237104294715182 * q^53 - 6237008697722857733231584966440 * q^55 + 9347630291312236144016149603200 * q^56 + 11382186268398399744329433517572 * q^58 - 11320340569522247618095325505348 * q^59 + 12771547929195071355310409383218 * q^61 - 101447293741849863418951127675568 * q^62 - 41280658033851993168324127190976 * q^64 + 7709579158673152743776325663060 * q^65 + 175757710780078940305499908875612 * q^67 - 281442880096236379198382763169800 * q^68 - 1040498682940112273466514884936000 * q^70 + 27474747461715252213775775690424 * q^71 - 585184619829428568163757555870322 * q^73 - 134392541523566959843290841608516 * q^74 + 403477747366730076622590548780112 * q^76 - 5306726056931811905707525354511808 * q^77 - 2667396066634861458375845391576600 * q^79 - 7102490190805235743681469824979040 * q^80 + 917242845604400818117266629806188 * q^82 - 6578360642441675208543593208203580 * q^83 + 3560960065600250795485268792239140 * q^85 - 18773659018851120901851911340565224 * q^86 - 34961215155916125706150543997131872 * q^88 - 11419551912179244059325275346141822 * q^89 - 40541093249602611010364470781007648 * q^91 + 19232540048657476273178638696239456 * q^92 - 101336598951909608865466201817694528 * q^94 - 159588702835640097495158571410457960 * q^95 + 211792260572805448951439211684683142 * q^97 + 124471288129025507609829835395708786 * 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 $

$2$	314887.	1.69875	0.849375	−	0.527790i	$-0.176979\pi$
$2$	314887.	1.69875	0.849375	+	0.527790i	$0.176979\pi$
$3$	0	0
$3$	0	0
$4$	6.47940e10	1.88575
$5$	−2.58564e12	−1.51563	−0.757815	−	0.652470i	$-0.773733\pi$
$5$	−2.58564e12	−1.51563	−0.757815	+	0.652470i	$0.773733\pi$
$6$	0	0
$7$	8.89060e14	1.44449	0.722246	−	0.691636i	$-0.243110\pi$
$7$	8.89060e14	1.44449	0.722246	+	0.691636i	$0.243110\pi$
$8$	9.58334e15	1.50467
$9$	0	0
$10$	−8.14184e17	−2.57468
$11$	−2.05240e18	−1.22430	−0.612152	−	0.790740i	$-0.709696\pi$
$11$	−2.05240e18	−1.22430	−0.612152	+	0.790740i	$0.709696\pi$
$12$	0	0
$13$	−1.82090e19	−0.583819	−0.291910	−	0.956446i	$-0.594291\pi$
$13$	−1.82090e19	−0.583819	−0.291910	+	0.956446i	$0.594291\pi$
$14$	2.79953e20	2.45383
$15$	0	0
$16$	7.91364e20	0.670311
$17$	−3.53481e21	−1.03636	−0.518179	−	0.855272i	$-0.673390\pi$
$17$	−3.53481e21	−1.03636	−0.518179	+	0.855272i	$0.673390\pi$
$18$	0	0
$19$	2.01653e22	0.844144	0.422072	−	0.906562i	$-0.361303\pi$
$19$	2.01653e22	0.844144	0.422072	+	0.906562i	$0.361303\pi$
$20$	−1.67534e23	−2.85810
$21$	0	0
$22$	−6.46272e23	−2.07979
$23$	−2.51478e23	−0.371760	−0.185880	−	0.982572i	$-0.559514\pi$
$23$	−2.51478e23	−0.371760	−0.185880	+	0.982572i	$0.559514\pi$
$24$	0	0
$25$	3.77515e24	1.29713
$26$	−5.73379e24	−0.991763
$27$	0	0
$28$	5.76057e25	2.72396
$29$	8.93017e24	0.228505	0.114252	−	0.993452i	$-0.463553\pi$
$29$	8.93017e24	0.228505	0.114252	+	0.993452i	$0.463553\pi$
$30$	0	0
$31$	−1.94629e26	−1.55017	−0.775083	−	0.631859i	$-0.782292\pi$
$31$	−1.94629e26	−1.55017	−0.775083	+	0.631859i	$0.782292\pi$
$32$	−8.00910e25	−0.365982
$33$	0	0
$34$	−1.11307e27	−1.76051
$35$	−2.29879e27	−2.18932
$36$	0	0
$37$	−2.17467e27	−0.783184	−0.391592	−	0.920139i	$-0.628076\pi$
$37$	−2.17467e27	−0.783184	−0.391592	+	0.920139i	$0.628076\pi$
$38$	6.34979e27	1.43399
$39$	0	0
$40$	−2.47791e28	−2.28053
$41$	7.70191e27	0.460130	0.230065	−	0.973175i	$-0.426106\pi$
$41$	7.70191e27	0.460130	0.230065	+	0.973175i	$0.426106\pi$
$42$	0	0
$43$	−2.60169e28	−0.675394	−0.337697	−	0.941255i	$-0.609648\pi$
$43$	−2.60169e28	−0.675394	−0.337697	+	0.941255i	$0.609648\pi$
$44$	−1.32983e29	−2.30873
$45$	0	0
$46$	−7.91871e28	−0.631528
$47$	−3.33024e29	−1.82290	−0.911449	−	0.411412i	$-0.865036\pi$
$47$	−3.33024e29	−1.82290	−0.911449	+	0.411412i	$0.865036\pi$
$48$	0	0
$49$	4.11609e29	1.08656
$50$	1.18875e30	2.20351
$51$	0	0
$52$	−1.17984e30	−1.10094
$53$	−1.01164e30	−0.676390	−0.338195	−	0.941076i	$-0.609816\pi$
$53$	−1.01164e30	−0.676390	−0.338195	+	0.941076i	$0.609816\pi$
$54$	0	0
$55$	5.30676e30	1.85559
$56$	8.52016e30	2.17349
$57$	0	0
$58$	2.81199e30	0.388172
$59$	−1.91584e30	−0.196087	−0.0980435	−	0.995182i	$-0.531258\pi$
$59$	−1.91584e30	−0.196087	−0.0980435	+	0.995182i	$0.531258\pi$
$60$	0	0
$61$	7.04823e30	0.402539	0.201270	−	0.979536i	$-0.435493\pi$
$61$	7.04823e30	0.402539	0.201270	+	0.979536i	$0.435493\pi$
$62$	−6.12862e31	−2.63335
$63$	0	0
$64$	−5.24107e31	−1.29202
$65$	4.70820e31	0.884854
$66$	0	0
$67$	1.18905e32	1.31489	0.657445	−	0.753503i	$-0.271637\pi$
$67$	1.18905e32	1.31489	0.657445	+	0.753503i	$0.271637\pi$
$68$	−2.29034e32	−1.95432
$69$	0	0
$70$	−7.23859e32	−3.71910
$71$	2.78716e32	1.11723	0.558613	−	0.829428i	$-0.311334\pi$
$71$	2.78716e32	1.11723	0.558613	+	0.829428i	$0.311334\pi$
$72$	0	0
$73$	−3.82719e32	−0.943474	−0.471737	−	0.881739i	$-0.656373\pi$
$73$	−3.82719e32	−0.943474	−0.471737	+	0.881739i	$0.656373\pi$
$74$	−6.84776e32	−1.33043
$75$	0	0
$76$	1.30659e33	1.59185
$77$	−1.82470e33	−1.76850
$78$	0	0
$79$	−1.32234e33	−0.818218	−0.409109	−	0.912486i	$-0.634160\pi$
$79$	−1.32234e33	−0.818218	−0.409109	+	0.912486i	$0.634160\pi$
$80$	−2.04618e33	−1.01594
$81$	0	0
$82$	2.42523e33	0.781646
$83$	5.69848e33	1.48557	0.742783	−	0.669532i	$-0.233505\pi$
$83$	5.69848e33	1.48557	0.742783	+	0.669532i	$0.233505\pi$
$84$	0	0
$85$	9.13975e33	1.57074
$86$	−8.19238e33	−1.14733
$87$	0	0
$88$	−1.96688e34	−1.84218
$89$	−1.72108e34	−1.32274	−0.661371	−	0.750059i	$-0.730025\pi$
$89$	−1.72108e34	−1.32274	−0.661371	+	0.750059i	$0.730025\pi$
$90$	0	0
$91$	−1.61889e34	−0.843323
$92$	−1.62943e34	−0.701048
$93$	0	0
$94$	−1.04865e35	−3.09665
$95$	−5.21402e34	−1.27941
$96$	0	0
$97$	4.83801e34	0.824444	0.412222	−	0.911083i	$-0.364753\pi$
$97$	4.83801e34	0.824444	0.412222	+	0.911083i	$0.364753\pi$
$98$	1.29610e35	1.84579
$99$	0	0
$100$	2.44607e35	2.44607
$101$	−3.38688e34	−0.284561	−0.142281	−	0.989826i	$-0.545444\pi$
$101$	−3.38688e34	−0.284561	−0.142281	+	0.989826i	$0.545444\pi$
$102$	0	0
$103$	5.14533e34	0.306734	0.153367	−	0.988169i	$-0.450988\pi$
$103$	5.14533e34	0.306734	0.153367	+	0.988169i	$0.450988\pi$
$104$	−1.74503e35	−0.878457
$105$	0	0
$106$	−3.18551e35	−1.14902
$107$	2.18093e35	0.667461	0.333731	−	0.942668i	$-0.391692\pi$
$107$	2.18093e35	0.667461	0.333731	+	0.942668i	$0.391692\pi$
$108$	0	0
$109$	4.44389e35	0.983557	0.491778	−	0.870720i	$-0.336347\pi$
$109$	4.44389e35	0.983557	0.491778	+	0.870720i	$0.336347\pi$
$110$	1.67103e36	3.15218
$111$	0	0
$112$	7.03570e35	0.968260
$113$	3.31993e35	0.391071	0.195536	−	0.980697i	$-0.437355\pi$
$113$	3.31993e35	0.391071	0.195536	+	0.980697i	$0.437355\pi$
$114$	0	0
$115$	6.50232e35	0.563451
$116$	5.78621e35	0.430903
$117$	0	0
$118$	−6.03272e35	−0.333103
$119$	−3.14266e36	−1.49701
$120$	0	0
$121$	1.40208e36	0.498918
$122$	2.21940e36	0.683814
$123$	0	0
$124$	−1.26108e37	−2.92323
$125$	−2.23599e36	−0.450344
$126$	0	0
$127$	3.99299e35	0.0609162	0.0304581	−	0.999536i	$-0.490303\pi$
$127$	3.99299e35	0.0609162	0.0304581	+	0.999536i	$0.490303\pi$
$128$	−1.37515e37	−1.82884
$129$	0	0
$130$	1.48255e37	1.50315
$131$	8.23775e36	0.730400	0.365200	−	0.930929i	$-0.381001\pi$
$131$	8.23775e36	0.730400	0.365200	+	0.930929i	$0.381001\pi$
$132$	0	0
$133$	1.79282e37	1.21936
$134$	3.74415e37	2.23367
$135$	0	0
$136$	−3.38753e37	−1.55938
$137$	5.87550e36	0.237922	0.118961	−	0.992899i	$-0.462044\pi$
$137$	5.87550e36	0.237922	0.118961	+	0.992899i	$0.462044\pi$
$138$	0	0
$139$	−2.62173e37	−0.823813	−0.411907	−	0.911226i	$-0.635137\pi$
$139$	−2.62173e37	−0.823813	−0.411907	+	0.911226i	$0.635137\pi$
$140$	−1.48948e38	−4.12851
$141$	0	0
$142$	8.77641e37	1.89789
$143$	3.73721e37	0.714772
$144$	0	0
$145$	−2.30902e37	−0.346328
$146$	−1.20513e38	−1.60273
$147$	0	0
$148$	−1.40906e38	−1.47689
$149$	1.56999e37	0.146264	0.0731320	−	0.997322i	$-0.476701\pi$
$149$	1.56999e37	0.146264	0.0731320	+	0.997322i	$0.476701\pi$
$150$	0	0
$151$	8.16299e37	0.602217	0.301108	−	0.953590i	$-0.402643\pi$
$151$	8.16299e37	0.602217	0.301108	+	0.953590i	$0.402643\pi$
$152$	1.93251e38	1.27016
$153$	0	0
$154$	−5.74575e38	−3.00424
$155$	5.03241e38	2.34948
$156$	0	0
$157$	4.68779e38	1.74874	0.874369	−	0.485262i	$-0.161276\pi$
$157$	4.68779e38	1.74874	0.874369	+	0.485262i	$0.161276\pi$
$158$	−4.16387e38	−1.38995
$159$	0	0
$160$	2.07087e38	0.554693
$161$	−2.23579e38	−0.537005
$162$	0	0
$163$	5.22512e38	1.01114	0.505572	−	0.862784i	$-0.331281\pi$
$163$	5.22512e38	1.01114	0.505572	+	0.862784i	$0.331281\pi$
$164$	4.99037e38	0.867692
$165$	0	0
$166$	1.79437e39	2.52361
$167$	3.40776e38	0.431450	0.215725	−	0.976454i	$-0.430788\pi$
$167$	3.40776e38	0.431450	0.215725	+	0.976454i	$0.430788\pi$
$168$	0	0
$169$	−6.41217e38	−0.659155
$170$	2.87799e39	2.66829
$171$	0	0
$172$	−1.68574e39	−1.27363
$173$	−2.05298e39	−1.40145	−0.700725	−	0.713432i	$-0.747140\pi$
$173$	−2.05298e39	−1.40145	−0.700725	+	0.713432i	$0.747140\pi$
$174$	0	0
$175$	3.35634e39	1.87370
$176$	−1.62419e39	−0.820664
$177$	0	0
$178$	−5.41944e39	−2.24701
$179$	1.59660e39	0.600161	0.300081	−	0.953914i	$-0.402986\pi$
$179$	1.59660e39	0.600161	0.300081	+	0.953914i	$0.402986\pi$
$180$	0	0
$181$	−4.40686e39	−1.36381	−0.681906	−	0.731440i	$-0.738849\pi$
$181$	−4.40686e39	−1.36381	−0.681906	+	0.731440i	$0.738849\pi$
$182$	−5.09768e39	−1.43259
$183$	0	0
$184$	−2.41000e39	−0.559378
$185$	5.62293e39	1.18702
$186$	0	0
$187$	7.25483e39	1.26882
$188$	−2.15779e40	−3.43754
$189$	0	0
$190$	−1.64183e40	−2.17340
$191$	2.10798e38	0.0254555	0.0127278	−	0.999919i	$-0.495949\pi$
$191$	2.10798e38	0.0254555	0.0127278	+	0.999919i	$0.495949\pi$
$192$	0	0
$193$	1.90663e40	1.91873	0.959364	−	0.282170i	$-0.0910544\pi$
$193$	1.90663e40	1.91873	0.959364	+	0.282170i	$0.0910544\pi$
$194$	1.52342e40	1.40052
$195$	0	0
$196$	2.66698e40	2.04898
$197$	−1.95633e40	−1.37494	−0.687471	−	0.726212i	$-0.741279\pi$
$197$	−1.95633e40	−1.37494	−0.687471	+	0.726212i	$0.741279\pi$
$198$	0	0
$199$	−9.66419e39	−0.569163	−0.284582	−	0.958652i	$-0.591855\pi$
$199$	−9.66419e39	−0.569163	−0.284582	+	0.958652i	$0.591855\pi$
$200$	3.61786e40	1.95176
$201$	0	0
$202$	−1.06648e40	−0.483398
$203$	7.93946e39	0.330073
$204$	0	0
$205$	−1.99144e40	−0.697387
$206$	1.62020e40	0.521064
$207$	0	0
$208$	−1.44100e40	−0.391341
$209$	−4.13872e40	−1.03349
$210$	0	0
$211$	−6.88109e39	−0.145450	−0.0727251	−	0.997352i	$-0.523170\pi$
$211$	−6.88109e39	−0.145450	−0.0727251	+	0.997352i	$0.523170\pi$
$212$	−6.55481e40	−1.27551
$213$	0	0
$214$	6.86747e40	1.13385
$215$	6.72703e40	1.02365
$216$	0	0
$217$	−1.73037e41	−2.23920
$218$	1.39932e41	1.67082
$219$	0	0
$220$	3.43846e41	3.49918
$221$	6.43655e40	0.605046
$222$	0	0
$223$	−1.52790e41	−1.22676	−0.613378	−	0.789789i	$-0.710190\pi$
$223$	−1.52790e41	−1.22676	−0.613378	+	0.789789i	$0.710190\pi$
$224$	−7.12057e40	−0.528658
$225$	0	0
$226$	1.04540e41	0.664333
$227$	−1.54327e41	−0.907797	−0.453898	−	0.891053i	$-0.649967\pi$
$227$	−1.54327e41	−0.907797	−0.453898	+	0.891053i	$0.649967\pi$
$228$	0	0
$229$	−2.85667e41	−1.44125	−0.720625	−	0.693325i	$-0.756145\pi$
$229$	−2.85667e41	−1.44125	−0.720625	+	0.693325i	$0.756145\pi$
$230$	2.04749e41	0.957162
$231$	0	0
$232$	8.55809e40	0.343825
$233$	−2.74988e40	−0.102467	−0.0512337	−	0.998687i	$-0.516315\pi$
$233$	−2.74988e40	−0.102467	−0.0512337	+	0.998687i	$0.516315\pi$
$234$	0	0
$235$	8.61079e41	2.76284
$236$	−1.24135e41	−0.369772
$237$	0	0
$238$	−9.89582e41	−2.54305
$239$	−9.13574e39	−0.0218163	−0.0109081	−	0.999941i	$-0.503472\pi$
$239$	−9.13574e39	−0.0218163	−0.0109081	+	0.999941i	$0.503472\pi$
$240$	0	0
$241$	−1.74391e41	−0.359936	−0.179968	−	0.983672i	$-0.557599\pi$
$241$	−1.74391e41	−0.359936	−0.179968	+	0.983672i	$0.557599\pi$
$242$	4.41497e41	0.847538
$243$	0	0
$244$	4.56683e41	0.759089
$245$	−1.06427e42	−1.64682
$246$	0	0
$247$	−3.67191e41	−0.492827
$248$	−1.86520e42	−2.33249
$249$	0	0
$250$	−7.04083e41	−0.765021
$251$	9.25053e39	0.00937296	0.00468648	−	0.999989i	$-0.498508\pi$
$251$	9.25053e39	0.00937296	0.00468648	+	0.999989i	$0.498508\pi$
$252$	0	0
$253$	5.16132e41	0.455147
$254$	1.25734e41	0.103481
$255$	0	0
$256$	−2.52936e42	−1.81472
$257$	−8.65068e41	−0.579723	−0.289862	−	0.957069i	$-0.593609\pi$
$257$	−8.65068e41	−0.579723	−0.289862	+	0.957069i	$0.593609\pi$
$258$	0	0
$259$	−1.93342e42	−1.13130
$260$	3.05063e42	1.66862
$261$	0	0
$262$	2.59396e42	1.24077
$263$	1.58951e42	0.711277	0.355639	−	0.934624i	$-0.384263\pi$
$263$	1.58951e42	0.711277	0.355639	+	0.934624i	$0.384263\pi$
$264$	0	0
$265$	2.61573e42	1.02516
$266$	5.64534e42	2.07139
$267$	0	0
$268$	7.70430e42	2.47956
$269$	4.32299e42	1.30352	0.651762	−	0.758423i	$-0.274030\pi$
$269$	4.32299e42	1.30352	0.651762	+	0.758423i	$0.274030\pi$
$270$	0	0
$271$	6.45806e42	1.71056	0.855282	−	0.518163i	$-0.173384\pi$
$271$	6.45806e42	1.71056	0.855282	+	0.518163i	$0.173384\pi$
$272$	−2.79732e42	−0.694683
$273$	0	0
$274$	1.85012e42	0.404170
$275$	−7.74811e42	−1.58808
$276$	0	0
$277$	−1.05719e43	−1.90878	−0.954392	−	0.298555i	$-0.903495\pi$
$277$	−1.05719e43	−1.90878	−0.954392	+	0.298555i	$0.903495\pi$
$278$	−8.25548e42	−1.39945
$279$	0	0
$280$	−2.20301e43	−3.29420
$281$	1.01596e42	0.142730	0.0713652	−	0.997450i	$-0.477264\pi$
$281$	1.01596e42	0.142730	0.0713652	+	0.997450i	$0.477264\pi$
$282$	0	0
$283$	7.86611e42	0.976107	0.488054	−	0.872814i	$-0.337707\pi$
$283$	7.86611e42	0.976107	0.488054	+	0.872814i	$0.337707\pi$
$284$	1.80591e43	2.10681
$285$	0	0
$286$	1.17680e43	1.21422
$287$	6.84746e42	0.664655
$288$	0	0
$289$	8.61340e41	0.0740393
$290$	−7.27080e42	−0.588325
$291$	0	0
$292$	−2.47979e43	−1.77916
$293$	−1.69976e43	−1.14870	−0.574348	−	0.818611i	$-0.694744\pi$
$293$	−1.69976e43	−1.14870	−0.574348	+	0.818611i	$0.694744\pi$
$294$	0	0
$295$	4.95367e42	0.297195
$296$	−2.08406e43	−1.17844
$297$	0	0
$298$	4.94369e42	0.248466
$299$	4.57917e42	0.217041
$300$	0	0
$301$	−2.31306e43	−0.975602
$302$	2.57042e43	1.02302
$303$	0	0
$304$	1.59581e43	0.565839
$305$	−1.82242e43	−0.610100
$306$	0	0
$307$	−1.31155e43	−0.391619	−0.195810	−	0.980642i	$-0.562733\pi$
$307$	−1.31155e43	−0.391619	−0.195810	+	0.980642i	$0.562733\pi$
$308$	−1.18230e44	−3.33495
$309$	0	0
$310$	1.58464e44	3.99118
$311$	3.73438e43	0.889020	0.444510	−	0.895774i	$-0.353378\pi$
$311$	3.73438e43	0.889020	0.444510	+	0.895774i	$0.353378\pi$
$312$	0	0
$313$	−2.87704e43	−0.612238	−0.306119	−	0.951993i	$-0.599031\pi$
$313$	−2.87704e43	−0.612238	−0.306119	+	0.951993i	$0.599031\pi$
$314$	1.47612e44	2.97067
$315$	0	0
$316$	−8.56796e43	−1.54296
$317$	−9.00125e43	−1.53379	−0.766894	−	0.641773i	$-0.778199\pi$
$317$	−9.00125e43	−1.53379	−0.766894	+	0.641773i	$0.778199\pi$
$318$	0	0
$319$	−1.83282e43	−0.279759
$320$	1.35515e44	1.95823
$321$	0	0
$322$	−7.04021e43	−0.912237
$323$	−7.12805e43	−0.874836
$324$	0	0
$325$	−6.87419e43	−0.757291
$326$	1.64532e44	1.71768
$327$	0	0
$328$	7.38100e43	0.692346
$329$	−2.96078e44	−2.63316
$330$	0	0
$331$	−2.23808e44	−1.79014	−0.895068	−	0.445930i	$-0.852873\pi$
$331$	−2.23808e44	−1.79014	−0.895068	+	0.445930i	$0.852873\pi$
$332$	3.69227e44	2.80141
$333$	0	0
$334$	1.07306e44	0.732927
$335$	−3.07444e44	−1.99289
$336$	0	0
$337$	2.79105e44	1.63021	0.815106	−	0.579312i	$-0.196679\pi$
$337$	2.79105e44	1.63021	0.815106	+	0.579312i	$0.196679\pi$
$338$	−2.01911e44	−1.11974
$339$	0	0
$340$	5.92201e44	2.96202
$341$	3.99456e44	1.89787
$342$	0	0
$343$	2.91524e43	0.125034
$344$	−2.49329e44	−1.01625
$345$	0	0
$346$	−6.46456e44	−2.38071
$347$	5.39083e44	1.88751	0.943756	−	0.330643i	$-0.107266\pi$
$347$	5.39083e44	1.88751	0.943756	+	0.330643i	$0.107266\pi$
$348$	0	0
$349$	1.63788e44	0.518606	0.259303	−	0.965796i	$-0.416507\pi$
$349$	1.63788e44	0.518606	0.259303	+	0.965796i	$0.416507\pi$
$350$	1.05687e45	3.18295
$351$	0	0
$352$	1.64378e44	0.448073
$353$	−5.00187e44	−1.29740	−0.648702	−	0.761043i	$-0.724688\pi$
$353$	−5.00187e44	−1.29740	−0.648702	+	0.761043i	$0.724688\pi$
$354$	0	0
$355$	−7.20660e44	−1.69330
$356$	−1.11515e45	−2.49436
$357$	0	0
$358$	5.02748e44	1.01952
$359$	−6.16722e44	−1.19107	−0.595534	−	0.803330i	$-0.703060\pi$
$359$	−6.16722e44	−1.19107	−0.595534	+	0.803330i	$0.703060\pi$
$360$	0	0
$361$	−1.64019e44	−0.287421
$362$	−1.38766e45	−2.31678
$363$	0	0
$364$	−1.04895e45	−1.59030
$365$	9.89574e44	1.42996
$366$	0	0
$367$	−1.18610e45	−1.55764	−0.778818	−	0.627250i	$-0.784181\pi$
$367$	−1.18610e45	−1.55764	−0.778818	+	0.627250i	$0.784181\pi$
$368$	−1.99011e44	−0.249195
$369$	0	0
$370$	1.77059e45	2.01645
$371$	−8.99407e44	−0.977041
$372$	0	0
$373$	1.06538e45	1.05341	0.526706	−	0.850048i	$-0.323427\pi$
$373$	1.06538e45	1.05341	0.526706	+	0.850048i	$0.323427\pi$
$374$	2.28445e45	2.15540
$375$	0	0
$376$	−3.19148e45	−2.74287
$377$	−1.62610e44	−0.133405
$378$	0	0
$379$	1.24427e44	0.0930524	0.0465262	−	0.998917i	$-0.485185\pi$
$379$	1.24427e44	0.0930524	0.0465262	+	0.998917i	$0.485185\pi$
$380$	−3.37837e45	−2.41265
$381$	0	0
$382$	6.63774e43	0.0432425
$383$	2.30053e44	0.143169	0.0715846	−	0.997435i	$-0.477194\pi$
$383$	2.30053e44	0.143169	0.0715846	+	0.997435i	$0.477194\pi$
$384$	0	0
$385$	4.71802e45	2.68039
$386$	6.00373e45	3.25944
$387$	0	0
$388$	3.13474e45	1.55470
$389$	−1.23018e45	−0.583243	−0.291621	−	0.956534i	$-0.594195\pi$
$389$	−1.23018e45	−0.583243	−0.291621	+	0.956534i	$0.594195\pi$
$390$	0	0
$391$	8.88927e44	0.385277
$392$	3.94459e45	1.63492
$393$	0	0
$394$	−6.16024e45	−2.33568
$395$	3.41910e45	1.24012
$396$	0	0
$397$	−2.62258e45	−0.870752	−0.435376	−	0.900249i	$-0.643385\pi$
$397$	−2.62258e45	−0.870752	−0.435376	+	0.900249i	$0.643385\pi$
$398$	−3.04313e45	−0.966866
$399$	0	0
$400$	2.98752e45	0.869483
$401$	−2.22698e45	−0.620425	−0.310213	−	0.950667i	$-0.600400\pi$
$401$	−2.22698e45	−0.620425	−0.310213	+	0.950667i	$0.600400\pi$
$402$	0	0
$403$	3.54401e45	0.905017
$404$	−2.19449e45	−0.536612
$405$	0	0
$406$	2.50003e45	0.560712
$407$	4.46329e45	0.958855
$408$	0	0
$409$	2.77503e44	0.0547155	0.0273577	−	0.999626i	$-0.491291\pi$
$409$	2.77503e44	0.0547155	0.0273577	+	0.999626i	$0.491291\pi$
$410$	−6.27077e45	−1.18469
$411$	0	0
$412$	3.33386e45	0.578425
$413$	−1.70330e45	−0.283246
$414$	0	0
$415$	−1.47342e46	−2.25157
$416$	1.45838e45	0.213667
$417$	0	0
$418$	−1.30323e46	−1.75564
$419$	−2.74431e45	−0.354559	−0.177280	−	0.984161i	$-0.556730\pi$
$419$	−2.74431e45	−0.354559	−0.177280	+	0.984161i	$0.556730\pi$
$420$	0	0
$421$	5.30191e45	0.630225	0.315112	−	0.949054i	$-0.397958\pi$
$421$	5.30191e45	0.630225	0.315112	+	0.949054i	$0.397958\pi$
$422$	−2.16676e45	−0.247084
$423$	0	0
$424$	−9.69487e45	−1.01775
$425$	−1.33445e46	−1.34430
$426$	0	0
$427$	6.26630e45	0.581465
$428$	1.41311e46	1.25867
$429$	0	0
$430$	2.11825e46	1.73892
$431$	2.12281e46	1.67324	0.836621	−	0.547782i	$-0.184528\pi$
$431$	2.12281e46	1.67324	0.836621	+	0.547782i	$0.184528\pi$
$432$	0	0
$433$	−2.59717e46	−1.88782	−0.943912	−	0.330196i	$-0.892885\pi$
$433$	−2.59717e46	−1.88782	−0.943912	+	0.330196i	$0.892885\pi$
$434$	−5.44871e46	−3.80385
$435$	0	0
$436$	2.87937e46	1.85474
$437$	−5.07113e45	−0.313819
$438$	0	0
$439$	−1.14491e45	−0.0654099	−0.0327049	−	0.999465i	$-0.510412\pi$
$439$	−1.14491e45	−0.0654099	−0.0327049	+	0.999465i	$0.510412\pi$
$440$	5.08565e46	2.79206
$441$	0	0
$442$	2.02679e46	1.02782
$443$	3.09981e46	1.51102	0.755510	−	0.655137i	$-0.227389\pi$
$443$	3.09981e46	1.51102	0.755510	+	0.655137i	$0.227389\pi$
$444$	0	0
$445$	4.45008e46	2.00479
$446$	−4.81114e46	−2.08395
$447$	0	0
$448$	−4.65962e46	−1.86632
$449$	−2.02968e46	−0.781836	−0.390918	−	0.920425i	$-0.627842\pi$
$449$	−2.02968e46	−0.781836	−0.390918	+	0.920425i	$0.627842\pi$
$450$	0	0
$451$	−1.58074e46	−0.563339
$452$	2.15111e46	0.737464
$453$	0	0
$454$	−4.85955e46	−1.54212
$455$	4.18587e46	1.27816
$456$	0	0
$457$	−3.46406e46	−0.979607	−0.489803	−	0.871833i	$-0.662931\pi$
$457$	−3.46406e46	−0.979607	−0.489803	+	0.871833i	$0.662931\pi$
$458$	−8.99528e46	−2.44832
$459$	0	0
$460$	4.21311e46	1.06253
$461$	−1.41927e46	−0.344587	−0.172294	−	0.985046i	$-0.555118\pi$
$461$	−1.41927e46	−0.344587	−0.172294	+	0.985046i	$0.555118\pi$
$462$	0	0
$463$	−4.26132e46	−0.959129	−0.479565	−	0.877507i	$-0.659205\pi$
$463$	−4.26132e46	−0.959129	−0.479565	+	0.877507i	$0.659205\pi$
$464$	7.06702e45	0.153169
$465$	0	0
$466$	−8.65902e45	−0.174066
$467$	7.98255e46	1.54560	0.772798	−	0.634652i	$-0.218857\pi$
$467$	7.98255e46	1.54560	0.772798	+	0.634652i	$0.218857\pi$
$468$	0	0
$469$	1.05713e47	1.89935
$470$	2.71143e47	4.69337
$471$	0	0
$472$	−1.83601e46	−0.295047
$473$	5.33969e46	0.826888
$474$	0	0
$475$	7.61271e46	1.09497
$476$	−2.03625e47	−2.82300
$477$	0	0
$478$	−2.87672e45	−0.0370604
$479$	−8.93537e46	−1.10979	−0.554895	−	0.831920i	$-0.687242\pi$
$479$	−8.93537e46	−1.10979	−0.554895	+	0.831920i	$0.687242\pi$
$480$	0	0
$481$	3.95987e46	0.457238
$482$	−5.49133e46	−0.611441
$483$	0	0
$484$	9.08465e46	0.940837
$485$	−1.25093e47	−1.24955
$486$	0	0
$487$	1.97444e47	1.83522	0.917608	−	0.397486i	$-0.130117\pi$
$487$	1.97444e47	1.83522	0.917608	+	0.397486i	$0.130117\pi$
$488$	6.75456e46	0.605690
$489$	0	0
$490$	−3.35125e47	−2.79754
$491$	−4.10668e46	−0.330799	−0.165400	−	0.986227i	$-0.552891\pi$
$491$	−4.10668e46	−0.330799	−0.165400	+	0.986227i	$0.552891\pi$
$492$	0	0
$493$	−3.15665e46	−0.236813
$494$	−1.15623e47	−0.837191
$495$	0	0
$496$	−1.54022e47	−1.03909
$497$	2.47795e47	1.61383
$498$	0	0
$499$	−2.11891e47	−1.28633	−0.643167	−	0.765726i	$-0.722380\pi$
$499$	−2.11891e47	−1.28633	−0.643167	+	0.765726i	$0.722380\pi$
$500$	−1.44878e47	−0.849237
$501$	0	0
$502$	2.91287e45	0.0159223
$503$	−1.10572e47	−0.583720	−0.291860	−	0.956461i	$-0.594274\pi$
$503$	−1.10572e47	−0.583720	−0.291860	+	0.956461i	$0.594274\pi$
$504$	0	0
$505$	8.75725e46	0.431289
$506$	1.62523e47	0.773182
$507$	0	0
$508$	2.58721e46	0.114873
$509$	2.45677e47	1.05391	0.526954	−	0.849894i	$-0.323334\pi$
$509$	2.45677e47	1.05391	0.526954	+	0.849894i	$0.323334\pi$
$510$	0	0
$511$	−3.40260e47	−1.36284
$512$	−3.23962e47	−1.25392
$513$	0	0
$514$	−2.72399e47	−0.984805
$515$	−1.33040e47	−0.464895
$516$	0	0
$517$	6.83496e47	2.23178
$518$	−6.08807e47	−1.92180
$519$	0	0
$520$	4.51203e47	1.33142
$521$	−4.14045e47	−1.18137	−0.590686	−	0.806901i	$-0.701143\pi$
$521$	−4.14045e47	−1.18137	−0.590686	+	0.806901i	$0.701143\pi$
$522$	0	0
$523$	−5.96375e47	−1.59125	−0.795627	−	0.605787i	$-0.792858\pi$
$523$	−5.96375e47	−1.59125	−0.795627	+	0.605787i	$0.792858\pi$
$524$	5.33756e47	1.37735
$525$	0	0
$526$	5.00517e47	1.20828
$527$	6.87977e47	1.60653
$528$	0	0
$529$	−3.94346e47	−0.861794
$530$	8.23660e47	1.74149
$531$	0	0
$532$	1.16164e48	2.29941
$533$	−1.40244e47	−0.268633
$534$	0	0
$535$	−5.63911e47	−1.01162
$536$	1.13950e48	1.97848
$537$	0	0
$538$	1.36125e48	2.21436
$539$	−8.44784e47	−1.33028
$540$	0	0
$541$	−3.26439e47	−0.481781	−0.240891	−	0.970552i	$-0.577439\pi$
$541$	−3.26439e47	−0.481781	−0.240891	+	0.970552i	$0.577439\pi$
$542$	2.03356e48	2.90582
$543$	0	0
$544$	2.83107e47	0.379288
$545$	−1.14903e48	−1.49071
$546$	0	0
$547$	5.93281e47	0.721909	0.360955	−	0.932583i	$-0.382451\pi$
$547$	5.93281e47	0.721909	0.360955	+	0.932583i	$0.382451\pi$
$548$	3.80697e47	0.448662
$549$	0	0
$550$	−2.43978e48	−2.69776
$551$	1.80080e47	0.192891
$552$	0	0
$553$	−1.17564e48	−1.18191
$554$	−3.32895e48	−3.24255
$555$	0	0
$556$	−1.69872e48	−1.55351
$557$	6.26275e47	0.555008	0.277504	−	0.960724i	$-0.410493\pi$
$557$	6.26275e47	0.555008	0.277504	+	0.960724i	$0.410493\pi$
$558$	0	0
$559$	4.73743e47	0.394308
$560$	−1.81918e48	−1.46752
$561$	0	0
$562$	3.19913e47	0.242463
$563$	−1.90044e48	−1.39623	−0.698116	−	0.715985i	$-0.745978\pi$
$563$	−1.90044e48	−1.39623	−0.698116	+	0.715985i	$0.745978\pi$
$564$	0	0
$565$	−8.58414e47	−0.592719
$566$	2.47694e48	1.65816
$567$	0	0
$568$	2.67103e48	1.68106
$569$	−1.88708e48	−1.15166	−0.575832	−	0.817568i	$-0.695322\pi$
$569$	−1.88708e48	−1.15166	−0.575832	+	0.817568i	$0.695322\pi$
$570$	0	0
$571$	1.45610e48	0.835720	0.417860	−	0.908511i	$-0.362780\pi$
$571$	1.45610e48	0.835720	0.417860	+	0.908511i	$0.362780\pi$
$572$	2.42149e48	1.34788
$573$	0	0
$574$	2.15617e48	1.12908
$575$	−9.49368e47	−0.482223
$576$	0	0
$577$	−1.31602e48	−0.629051	−0.314526	−	0.949249i	$-0.601845\pi$
$577$	−1.31602e48	−0.629051	−0.314526	+	0.949249i	$0.601845\pi$
$578$	2.71225e47	0.125774
$579$	0	0
$580$	−1.49611e48	−0.653090
$581$	5.06629e48	2.14589
$582$	0	0
$583$	2.07628e48	0.828107
$584$	−3.66773e48	−1.41962
$585$	0	0
$586$	−5.35233e48	−1.95135
$587$	−3.36632e48	−1.19121	−0.595606	−	0.803277i	$-0.703088\pi$
$587$	−3.36632e48	−1.19121	−0.595606	+	0.803277i	$0.703088\pi$
$588$	0	0
$589$	−3.92475e48	−1.30856
$590$	1.55985e48	0.504861
$591$	0	0
$592$	−1.72096e48	−0.524977
$593$	1.31507e48	0.389486	0.194743	−	0.980854i	$-0.437613\pi$
$593$	1.31507e48	0.389486	0.194743	+	0.980854i	$0.437613\pi$
$594$	0	0
$595$	8.12579e48	2.26892
$596$	1.01726e48	0.275818
$597$	0	0
$598$	1.44192e48	0.368698
$599$	5.62894e48	1.39784	0.698919	−	0.715201i	$-0.253665\pi$
$599$	5.62894e48	1.39784	0.698919	+	0.715201i	$0.253665\pi$
$600$	0	0
$601$	6.95422e48	1.62909	0.814545	−	0.580101i	$-0.196987\pi$
$601$	6.95422e48	1.62909	0.814545	+	0.580101i	$0.196987\pi$
$602$	−7.28351e48	−1.65730
$603$	0	0
$604$	5.28913e48	1.13563
$605$	−3.62528e48	−0.756176
$606$	0	0
$607$	−3.70436e48	−0.729309	−0.364654	−	0.931143i	$-0.618813\pi$
$607$	−3.70436e48	−0.729309	−0.364654	+	0.931143i	$0.618813\pi$
$608$	−1.61506e48	−0.308941
$609$	0	0
$610$	−5.73856e48	−1.03641
$611$	6.06404e48	1.06424
$612$	0	0
$613$	−5.48390e48	−0.908932	−0.454466	−	0.890764i	$-0.650170\pi$
$613$	−5.48390e48	−0.908932	−0.454466	+	0.890764i	$0.650170\pi$
$614$	−4.12991e48	−0.665264
$615$	0	0
$616$	−1.74867e49	−2.66101
$617$	5.61348e48	0.830313	0.415156	−	0.909750i	$-0.363727\pi$
$617$	5.61348e48	0.830313	0.415156	+	0.909750i	$0.363727\pi$
$618$	0	0
$619$	2.35877e48	0.329684	0.164842	−	0.986320i	$-0.447289\pi$
$619$	2.35877e48	0.329684	0.164842	+	0.986320i	$0.447289\pi$
$620$	3.26070e49	4.43054
$621$	0	0
$622$	1.17591e49	1.51022
$623$	−1.53014e49	−1.91069
$624$	0	0
$625$	−5.20569e48	−0.614579
$626$	−9.05943e48	−1.04004
$627$	0	0
$628$	3.03741e49	3.29769
$629$	7.68706e48	0.811660
$630$	0	0
$631$	2.89336e48	0.288994	0.144497	−	0.989505i	$-0.453844\pi$
$631$	2.89336e48	0.288994	0.144497	+	0.989505i	$0.453844\pi$
$632$	−1.26724e49	−1.23115
$633$	0	0
$634$	−2.83437e49	−2.60552
$635$	−1.03244e48	−0.0923264
$636$	0	0
$637$	−7.49500e48	−0.634354
$638$	−5.77132e48	−0.475241
$639$	0	0
$640$	3.55565e49	2.77185
$641$	1.08872e49	0.825853	0.412926	−	0.910764i	$-0.364507\pi$
$641$	1.08872e49	0.825853	0.412926	+	0.910764i	$0.364507\pi$
$642$	0	0
$643$	5.30333e48	0.380940	0.190470	−	0.981693i	$-0.438999\pi$
$643$	5.30333e48	0.380940	0.190470	+	0.981693i	$0.438999\pi$
$644$	−1.44866e49	−1.01266
$645$	0	0
$646$	−2.24453e49	−1.48613
$647$	8.64507e48	0.557113	0.278557	−	0.960420i	$-0.410144\pi$
$647$	8.64507e48	0.557113	0.278557	+	0.960420i	$0.410144\pi$
$648$	0	0
$649$	3.93206e48	0.240070
$650$	−2.16459e49	−1.28645
$651$	0	0
$652$	3.38556e49	1.90677
$653$	2.69906e49	1.47990	0.739948	−	0.672664i	$-0.234850\pi$
$653$	2.69906e49	1.47990	0.739948	+	0.672664i	$0.234850\pi$
$654$	0	0
$655$	−2.12999e49	−1.10702
$656$	6.09501e48	0.308430
$657$	0	0
$658$	−9.32310e49	−4.47309
$659$	−6.87234e48	−0.321077	−0.160539	−	0.987030i	$-0.551323\pi$
$659$	−6.87234e48	−0.321077	−0.160539	+	0.987030i	$0.551323\pi$
$660$	0	0
$661$	3.16481e49	1.40224	0.701119	−	0.713045i	$-0.252684\pi$
$661$	3.16481e49	1.40224	0.701119	+	0.713045i	$0.252684\pi$
$662$	−7.04742e49	−3.04099
$663$	0	0
$664$	5.46104e49	2.23529
$665$	−4.63558e49	−1.84810
$666$	0	0
$667$	−2.24574e48	−0.0849489
$668$	2.20802e49	0.813609
$669$	0	0
$670$	−9.68102e49	−3.38542
$671$	−1.44658e49	−0.492830
$672$	0	0
$673$	−6.90752e48	−0.223387	−0.111694	−	0.993743i	$-0.535628\pi$
$673$	−6.90752e48	−0.223387	−0.111694	+	0.993743i	$0.535628\pi$
$674$	8.78864e49	2.76932
$675$	0	0
$676$	−4.15470e49	−1.24300
$677$	−3.65968e49	−1.06694	−0.533471	−	0.845818i	$-0.679113\pi$
$677$	−3.65968e49	−1.06694	−0.533471	+	0.845818i	$0.679113\pi$
$678$	0	0
$679$	4.30128e49	1.19090
$680$	8.75894e49	2.36344
$681$	0	0
$682$	1.25783e50	3.22401
$683$	4.27715e49	1.06854	0.534272	−	0.845312i	$-0.320586\pi$
$683$	4.27715e49	1.06854	0.534272	+	0.845312i	$0.320586\pi$
$684$	0	0
$685$	−1.51919e49	−0.360602
$686$	9.17972e48	0.212401
$687$	0	0
$688$	−2.05888e49	−0.452724
$689$	1.84210e49	0.394890
$690$	0	0
$691$	−4.11987e49	−0.839494	−0.419747	−	0.907641i	$-0.637881\pi$
$691$	−4.11987e49	−0.839494	−0.419747	+	0.907641i	$0.637881\pi$
$692$	−1.33021e50	−2.64279
$693$	0	0
$694$	1.69750e50	3.20641
$695$	6.77885e49	1.24860
$696$	0	0
$697$	−2.72248e49	−0.476860
$698$	5.15748e49	0.880982
$699$	0	0
$700$	2.17471e50	3.53333
$701$	−6.08013e48	−0.0963491	−0.0481745	−	0.998839i	$-0.515340\pi$
$701$	−6.08013e48	−0.0963491	−0.0481745	+	0.998839i	$0.515340\pi$
$702$	0	0
$703$	−4.38529e49	−0.661120
$704$	1.07567e50	1.58183
$705$	0	0
$706$	−1.57502e50	−2.20397
$707$	−3.01114e49	−0.411046
$708$	0	0
$709$	1.16393e50	1.51224	0.756118	−	0.654436i	$-0.227094\pi$
$709$	1.16393e50	1.51224	0.756118	+	0.654436i	$0.227094\pi$
$710$	−2.26926e50	−2.87650
$711$	0	0
$712$	−1.64937e50	−1.99029
$713$	4.89450e49	0.576290
$714$	0	0
$715$	−9.66309e49	−1.08333
$716$	1.03450e50	1.13176
$717$	0	0
$718$	−1.94198e50	−2.02333
$719$	1.15725e49	0.117672	0.0588360	−	0.998268i	$-0.481261\pi$
$719$	1.15725e49	0.117672	0.0588360	+	0.998268i	$0.481261\pi$
$720$	0	0
$721$	4.57451e49	0.443075
$722$	−5.16475e49	−0.488257
$723$	0	0
$724$	−2.85538e50	−2.57181
$725$	3.37128e49	0.296401
$726$	0	0
$727$	−3.49319e49	−0.292664	−0.146332	−	0.989236i	$-0.546747\pi$
$727$	−3.49319e49	−0.292664	−0.146332	+	0.989236i	$0.546747\pi$
$728$	−1.55144e50	−1.26892
$729$	0	0
$730$	3.11604e50	2.42914
$731$	9.19648e49	0.699951
$732$	0	0
$733$	2.27403e50	1.64997	0.824986	−	0.565153i	$-0.191183\pi$
$733$	2.27403e50	1.64997	0.824986	+	0.565153i	$0.191183\pi$
$734$	−3.73488e50	−2.64604
$735$	0	0
$736$	2.01411e49	0.136057
$737$	−2.44039e50	−1.60982
$738$	0	0
$739$	4.83328e49	0.304063	0.152032	−	0.988376i	$-0.451418\pi$
$739$	4.83328e49	0.304063	0.152032	+	0.988376i	$0.451418\pi$
$740$	3.64332e50	2.23842
$741$	0	0
$742$	−2.83211e50	−1.65975
$743$	−1.27541e50	−0.730040	−0.365020	−	0.931000i	$-0.618938\pi$
$743$	−1.27541e50	−0.730040	−0.365020	+	0.931000i	$0.618938\pi$
$744$	0	0
$745$	−4.05943e49	−0.221682
$746$	3.35473e50	1.78948
$747$	0	0
$748$	4.70069e50	2.39268
$749$	1.93898e50	0.964143
$750$	0	0
$751$	−7.89850e49	−0.374840	−0.187420	−	0.982280i	$-0.560012\pi$
$751$	−7.89850e49	−0.374840	−0.187420	+	0.982280i	$0.560012\pi$
$752$	−2.63543e50	−1.22191
$753$	0	0
$754$	−5.12037e49	−0.226622
$755$	−2.11066e50	−0.912738
$756$	0	0
$757$	6.60764e49	0.272815	0.136408	−	0.990653i	$-0.456444\pi$
$757$	6.60764e49	0.272815	0.136408	+	0.990653i	$0.456444\pi$
$758$	3.91804e49	0.158073
$759$	0	0
$760$	−4.99677e50	−1.92509
$761$	−3.99863e50	−1.50549	−0.752747	−	0.658310i	$-0.771272\pi$
$761$	−3.99863e50	−1.50549	−0.752747	+	0.658310i	$0.771272\pi$
$762$	0	0
$763$	3.95088e50	1.42074
$764$	1.36584e49	0.0480028
$765$	0	0
$766$	7.24407e49	0.243209
$767$	3.48856e49	0.114479
$768$	0	0
$769$	−3.41036e50	−1.06928	−0.534638	−	0.845081i	$-0.679552\pi$
$769$	−3.41036e50	−1.06928	−0.534638	+	0.845081i	$0.679552\pi$
$770$	1.48564e51	4.55331
$771$	0	0
$772$	1.23538e51	3.61825
$773$	5.59367e49	0.160160	0.0800802	−	0.996788i	$-0.474482\pi$
$773$	5.59367e49	0.160160	0.0800802	+	0.996788i	$0.474482\pi$
$774$	0	0
$775$	−7.34755e50	−2.01077
$776$	4.63643e50	1.24052
$777$	0	0
$778$	−3.87366e50	−0.990784
$779$	1.55311e50	0.388416
$780$	0	0
$781$	−5.72036e50	−1.36782
$782$	2.79912e50	0.654489
$783$	0	0
$784$	3.25732e50	0.728333
$785$	−1.21209e51	−2.65044
$786$	0	0
$787$	−5.37997e50	−1.12518	−0.562590	−	0.826736i	$-0.690195\pi$
$787$	−5.37997e50	−1.12518	−0.562590	+	0.826736i	$0.690195\pi$
$788$	−1.26759e51	−2.59280
$789$	0	0
$790$	1.07663e51	2.10665
$791$	2.95162e50	0.564900
$792$	0	0
$793$	−1.28342e50	−0.235010
$794$	−8.25815e50	−1.47919
$795$	0	0
$796$	−6.26181e50	−1.07330
$797$	2.56980e50	0.430902	0.215451	−	0.976515i	$-0.430878\pi$
$797$	2.56980e50	0.430902	0.215451	+	0.976515i	$0.430878\pi$
$798$	0	0
$799$	1.17718e51	1.88918
$800$	−3.02356e50	−0.474727
$801$	0	0
$802$	−7.01246e50	−1.05395
$803$	7.85491e50	1.15510
$804$	0	0
$805$	5.78095e50	0.813901
$806$	1.11596e51	1.53740
$807$	0	0
$808$	−3.24576e50	−0.428171
$809$	5.38460e50	0.695112	0.347556	−	0.937659i	$-0.387012\pi$
$809$	5.38460e50	0.695112	0.347556	+	0.937659i	$0.387012\pi$
$810$	0	0
$811$	1.74111e50	0.215259	0.107630	−	0.994191i	$-0.465674\pi$
$811$	1.74111e50	0.215259	0.107630	+	0.994191i	$0.465674\pi$
$812$	5.14429e50	0.622436
$813$	0	0
$814$	1.40543e51	1.62886
$815$	−1.35103e51	−1.53252
$816$	0	0
$817$	−5.24638e50	−0.570130
$818$	8.73821e49	0.0929479
$819$	0	0
$820$	−1.29033e51	−1.31510
$821$	1.66594e51	1.66209	0.831046	−	0.556204i	$-0.187743\pi$
$821$	1.66594e51	1.66209	0.831046	+	0.556204i	$0.187743\pi$
$822$	0	0
$823$	3.02282e50	0.289012	0.144506	−	0.989504i	$-0.453841\pi$
$823$	3.02282e50	0.289012	0.144506	+	0.989504i	$0.453841\pi$
$824$	4.93095e50	0.461534
$825$	0	0
$826$	−5.36345e50	−0.481165
$827$	4.63022e50	0.406682	0.203341	−	0.979108i	$-0.434820\pi$
$827$	4.63022e50	0.406682	0.203341	+	0.979108i	$0.434820\pi$
$828$	0	0
$829$	−3.82585e49	−0.0322124	−0.0161062	−	0.999870i	$-0.505127\pi$
$829$	−3.82585e49	−0.0322124	−0.0161062	+	0.999870i	$0.505127\pi$
$830$	−4.63961e51	−3.82485
$831$	0	0
$832$	9.54348e50	0.754308
$833$	−1.45496e51	−1.12606
$834$	0	0
$835$	−8.81124e50	−0.653919
$836$	−2.68164e51	−1.94890
$837$	0	0
$838$	−8.64149e50	−0.602307
$839$	−1.51079e51	−1.03127	−0.515633	−	0.856809i	$-0.672443\pi$
$839$	−1.51079e51	−1.03127	−0.515633	+	0.856809i	$0.672443\pi$
$840$	0	0
$841$	−1.44757e51	−0.947786
$842$	1.66950e51	1.07059
$843$	0	0
$844$	−4.45853e50	−0.274283
$845$	1.65796e51	0.999035
$846$	0	0
$847$	1.24654e51	0.720684
$848$	−8.00574e50	−0.453392
$849$	0	0
$850$	−4.20199e51	−2.28362
$851$	5.46883e50	0.291157
$852$	0	0
$853$	4.42362e50	0.226032	0.113016	−	0.993593i	$-0.463949\pi$
$853$	4.42362e50	0.226032	0.113016	+	0.993593i	$0.463949\pi$
$854$	1.97318e51	0.987764
$855$	0	0
$856$	2.09006e51	1.00431
$857$	4.10421e51	1.93226	0.966129	−	0.258059i	$-0.0830829\pi$
$857$	4.10421e51	1.93226	0.966129	+	0.258059i	$0.0830829\pi$
$858$	0	0
$859$	3.05622e51	1.38135	0.690675	−	0.723165i	$-0.257313\pi$
$859$	3.05622e51	1.38135	0.690675	+	0.723165i	$0.257313\pi$
$860$	4.35871e51	1.93035
$861$	0	0
$862$	6.68445e51	2.84242
$863$	2.21426e51	0.922657	0.461329	−	0.887229i	$-0.347373\pi$
$863$	2.21426e51	0.922657	0.461329	+	0.887229i	$0.347373\pi$
$864$	0	0
$865$	5.30826e51	2.12408
$866$	−8.17814e51	−3.20694
$867$	0	0
$868$	−1.12118e52	−4.22259
$869$	2.71396e51	1.00175
$870$	0	0
$871$	−2.16514e51	−0.767658
$872$	4.25873e51	1.47993
$873$	0	0
$874$	−1.59683e51	−0.533100
$875$	−1.98793e51	−0.650518
$876$	0	0
$877$	1.01208e51	0.318215	0.159108	−	0.987261i	$-0.449138\pi$
$877$	1.01208e51	0.318215	0.159108	+	0.987261i	$0.449138\pi$
$878$	−3.60518e50	−0.111115
$879$	0	0
$880$	4.19958e51	1.24382
$881$	−2.64312e51	−0.767430	−0.383715	−	0.923452i	$-0.625355\pi$
$881$	−2.64312e51	−0.767430	−0.383715	+	0.923452i	$0.625355\pi$
$882$	0	0
$883$	3.39738e51	0.948050	0.474025	−	0.880511i	$-0.342801\pi$
$883$	3.39738e51	0.948050	0.474025	+	0.880511i	$0.342801\pi$
$884$	4.17050e51	1.14097
$885$	0	0
$886$	9.76091e51	2.56685
$887$	−4.09378e51	−1.05551	−0.527754	−	0.849397i	$-0.676966\pi$
$887$	−4.09378e51	−1.05551	−0.527754	+	0.849397i	$0.676966\pi$
$888$	0	0
$889$	3.55000e50	0.0879930
$890$	1.40127e52	3.40563
$891$	0	0
$892$	−9.89984e51	−2.31336
$893$	−6.71552e51	−1.53879
$894$	0	0
$895$	−4.12823e51	−0.909622
$896$	−1.22259e52	−2.64175
$897$	0	0
$898$	−6.39118e51	−1.32814
$899$	−1.73807e51	−0.354220
$900$	0	0
$901$	3.57595e51	0.700983
$902$	−4.97753e51	−0.956972
$903$	0	0
$904$	3.18160e51	0.588435
$905$	1.13946e52	2.06703
$906$	0	0
$907$	6.74690e50	0.117754	0.0588771	−	0.998265i	$-0.481248\pi$
$907$	6.74690e50	0.117754	0.0588771	+	0.998265i	$0.481248\pi$
$908$	−9.99944e51	−1.71188
$909$	0	0
$910$	1.31808e52	2.17128
$911$	4.50163e51	0.727441	0.363720	−	0.931508i	$-0.381506\pi$
$911$	4.50163e51	0.727441	0.363720	+	0.931508i	$0.381506\pi$
$912$	0	0
$913$	−1.16955e52	−1.81878
$914$	−1.09079e52	−1.66411
$915$	0	0
$916$	−1.85095e52	−2.71784
$917$	7.32385e51	1.05506
$918$	0	0
$919$	−1.02476e52	−1.42102	−0.710511	−	0.703686i	$-0.751536\pi$
$919$	−1.02476e52	−1.42102	−0.710511	+	0.703686i	$0.751536\pi$
$920$	6.23139e51	0.847809
$921$	0	0
$922$	−4.46910e51	−0.585368
$923$	−5.07515e51	−0.652258
$924$	0	0
$925$	−8.20973e51	−1.01589
$926$	−1.34183e52	−1.62932
$927$	0	0
$928$	−7.15227e50	−0.0836285
$929$	4.03684e51	0.463198	0.231599	−	0.972811i	$-0.425604\pi$
$929$	4.03684e51	0.463198	0.231599	+	0.972811i	$0.425604\pi$
$930$	0	0
$931$	8.30021e51	0.917212
$932$	−1.78176e51	−0.193228
$933$	0	0
$934$	2.51360e52	2.62558
$935$	−1.87584e52	−1.92306
$936$	0	0
$937$	−1.56788e52	−1.54836	−0.774178	−	0.632968i	$-0.781836\pi$
$937$	−1.56788e52	−1.54836	−0.774178	+	0.632968i	$0.781836\pi$
$938$	3.32877e52	3.22652
$939$	0	0
$940$	5.57928e52	5.21003
$941$	−8.58654e50	−0.0787046	−0.0393523	−	0.999225i	$-0.512529\pi$
$941$	−8.58654e50	−0.0787046	−0.0393523	+	0.999225i	$0.512529\pi$
$942$	0	0
$943$	−1.93686e51	−0.171058
$944$	−1.51613e51	−0.131439
$945$	0	0
$946$	1.68140e52	1.40468
$947$	6.34472e51	0.520341	0.260170	−	0.965563i	$-0.416221\pi$
$947$	6.34472e51	0.520341	0.260170	+	0.965563i	$0.416221\pi$
$948$	0	0
$949$	6.96895e51	0.550818
$950$	2.39714e52	1.86008
$951$	0	0
$952$	−3.01172e52	−2.25251
$953$	−1.01401e52	−0.744587	−0.372293	−	0.928115i	$-0.621428\pi$
$953$	−1.01401e52	−0.744587	−0.372293	+	0.928115i	$0.621428\pi$
$954$	0	0
$955$	−5.45047e50	−0.0385811
$956$	−5.91941e50	−0.0411401
$957$	0	0
$958$	−2.81363e52	−1.88526
$959$	5.22367e51	0.343677
$960$	0	0
$961$	2.21168e52	1.40302
$962$	1.24691e52	0.776733
$963$	0	0
$964$	−1.12995e52	−0.678750
$965$	−4.92986e52	−2.90808
$966$	0	0
$967$	2.62715e50	0.0149459	0.00747294	−	0.999972i	$-0.497621\pi$
$967$	2.62715e50	0.0149459	0.00747294	+	0.999972i	$0.497621\pi$
$968$	1.34366e52	0.750709
$969$	0	0
$970$	−3.93903e52	−2.12268
$971$	1.35550e52	0.717405	0.358702	−	0.933452i	$-0.383219\pi$
$971$	1.35550e52	0.717405	0.358702	+	0.933452i	$0.383219\pi$
$972$	0	0
$973$	−2.33087e52	−1.18999
$974$	6.21725e52	3.11758
$975$	0	0
$976$	5.57772e51	0.269827
$977$	−1.04794e52	−0.497947	−0.248973	−	0.968510i	$-0.580093\pi$
$977$	−1.04794e52	−0.497947	−0.248973	+	0.968510i	$0.580093\pi$
$978$	0	0
$979$	3.53233e52	1.61944
$980$	−6.89585e52	−3.10550
$981$	0	0
$982$	−1.29314e52	−0.561945
$983$	1.08382e52	0.462668	0.231334	−	0.972874i	$-0.425691\pi$
$983$	1.08382e52	0.462668	0.231334	+	0.972874i	$0.425691\pi$
$984$	0	0
$985$	5.05838e52	2.08390
$986$	−9.93987e51	−0.402286
$987$	0	0
$988$	−2.37917e52	−0.929351
$989$	6.54268e51	0.251085
$990$	0	0
$991$	−4.54048e52	−1.68195	−0.840975	−	0.541074i	$-0.818018\pi$
$991$	−4.54048e52	−1.68195	−0.840975	+	0.541074i	$0.818018\pi$
$992$	1.55881e52	0.567333
$993$	0	0
$994$	7.80275e52	2.74149
$995$	2.49881e52	0.862640
$996$	0	0
$997$	−1.50067e52	−0.500174	−0.250087	−	0.968223i	$-0.580459\pi$
$997$	−1.50067e52	−0.500174	−0.250087	+	0.968223i	$0.580459\pi$
$998$	−6.67218e52	−2.18516
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	9.36.a.c.1.3		3
3.2	odd	2		3.36.a.b.1.1	✓	3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
3.36.a.b.1.1	✓	3	3.2	odd	2
9.36.a.c.1.3		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:	\( k \)	\(=\)	\( 36 \)
Character orbit:	\([\chi]\)	\(=\)	9.a (trivial)

\(f(q)\)	\(=\)	\(q+314887. q^{2} +6.47940e10 q^{4} -2.58564e12 q^{5} +8.89060e14 q^{7} +9.58334e15 q^{8} +O(q^{10})\)	\(q+314887. q^{2} +6.47940e10 q^{4} -2.58564e12 q^{5} +8.89060e14 q^{7} +9.58334e15 q^{8} -8.14184e17 q^{10} -2.05240e18 q^{11} -1.82090e19 q^{13} +2.79953e20 q^{14} +7.91364e20 q^{16} -3.53481e21 q^{17} +2.01653e22 q^{19} -1.67534e23 q^{20} -6.46272e23 q^{22} -2.51478e23 q^{23} +3.77515e24 q^{25} -5.73379e24 q^{26} +5.76057e25 q^{28} +8.93017e24 q^{29} -1.94629e26 q^{31} -8.00910e25 q^{32} -1.11307e27 q^{34} -2.29879e27 q^{35} -2.17467e27 q^{37} +6.34979e27 q^{38} -2.47791e28 q^{40} +7.70191e27 q^{41} -2.60169e28 q^{43} -1.32983e29 q^{44} -7.91871e28 q^{46} -3.33024e29 q^{47} +4.11609e29 q^{49} +1.18875e30 q^{50} -1.17984e30 q^{52} -1.01164e30 q^{53} +5.30676e30 q^{55} +8.52016e30 q^{56} +2.81199e30 q^{58} -1.91584e30 q^{59} +7.04823e30 q^{61} -6.12862e31 q^{62} -5.24107e31 q^{64} +4.70820e31 q^{65} +1.18905e32 q^{67} -2.29034e32 q^{68} -7.23859e32 q^{70} +2.78716e32 q^{71} -3.82719e32 q^{73} -6.84776e32 q^{74} +1.30659e33 q^{76} -1.82470e33 q^{77} -1.32234e33 q^{79} -2.04618e33 q^{80} +2.42523e33 q^{82} +5.69848e33 q^{83} +9.13975e33 q^{85} -8.19238e33 q^{86} -1.96688e34 q^{88} -1.72108e34 q^{89} -1.61889e34 q^{91} -1.62943e34 q^{92} -1.04865e35 q^{94} -5.21402e34 q^{95} +4.83801e34 q^{97} +1.29610e35 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q + 87330 q^{2} + 32488752900 q^{4} - 2768676235410 q^{5} + 488237848538064 q^{7} + 18\!\cdots\!52 q^{8}+O(q^{10}) \) 3 * q + 87330 * q^2 + 32488752900 * q^4 - 2768676235410 * q^5 + 488237848538064 * q^7 + 18683146678130952 * q^8	\( 3 q + 87330 q^{2} + 32488752900 q^{4} - 2768676235410 q^{5} + 488237848538064 q^{7} + 18\!\cdots\!52 q^{8}+ \cdots + 12\!\cdots\!86 q^{98}+O(q^{100}) \) 3 * q + 87330 * q^2 + 32488752900 * q^4 - 2768676235410 * q^5 + 488237848538064 * q^7 + 18683146678130952 * q^8 - 1127779626928867020 * q^10 - 3426356175124224804 * q^11 + 50087718431258539506 * q^13 + 217880362960444050144 * q^14 + 606906765664363747344 * q^16 - 2730709287864549111942 * q^17 + 28794251065778257727292 * q^19 - 88477655809138293889560 * q^20 - 122741766765729403865496 * q^22 - 1806983834691084779311608 * q^23 + 8598840806404444672708725 * q^25 - 12462234191474761114326516 * q^26 + 88582873604432535904569792 * q^28 - 78927943791269118086922714 * q^29 - 1597007179004406242679048 * q^31 - 212133152341134442715841504 * q^32 - 1031323232079473133177847620 * q^34 + 1159830211565676145196532000 * q^35 - 5102549932092597658956094086 * q^37 + 8724219045726720381610922664 * q^38 - 17377992868876213570860774960 * q^40 + 20208748955896036456754429058 * q^41 + 46721962642013867129638134372 * q^43 - 194349428414233101115805936688 * q^44 + 52087178478532028950981302192 * q^46 - 293197746513164578153478190816 * q^47 + 836105627836985614440420595707 * q^49 + 701125828082122697797800571950 * q^50 - 2520178249741268871517789030248 * q^52 + 108875909240521237104294715182 * q^53 - 6237008697722857733231584966440 * q^55 + 9347630291312236144016149603200 * q^56 + 11382186268398399744329433517572 * q^58 - 11320340569522247618095325505348 * q^59 + 12771547929195071355310409383218 * q^61 - 101447293741849863418951127675568 * q^62 - 41280658033851993168324127190976 * q^64 + 7709579158673152743776325663060 * q^65 + 175757710780078940305499908875612 * q^67 - 281442880096236379198382763169800 * q^68 - 1040498682940112273466514884936000 * q^70 + 27474747461715252213775775690424 * q^71 - 585184619829428568163757555870322 * q^73 - 134392541523566959843290841608516 * q^74 + 403477747366730076622590548780112 * q^76 - 5306726056931811905707525354511808 * q^77 - 2667396066634861458375845391576600 * q^79 - 7102490190805235743681469824979040 * q^80 + 917242845604400818117266629806188 * q^82 - 6578360642441675208543593208203580 * q^83 + 3560960065600250795485268792239140 * q^85 - 18773659018851120901851911340565224 * q^86 - 34961215155916125706150543997131872 * q^88 - 11419551912179244059325275346141822 * q^89 - 40541093249602611010364470781007648 * q^91 + 19232540048657476273178638696239456 * q^92 - 101336598951909608865466201817694528 * q^94 - 159588702835640097495158571410457960 * q^95 + 211792260572805448951439211684683142 * q^97 + 124471288129025507609829835395708786 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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