LMFDB - Embedded newform 9.46.a.b.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [9,46,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, 46, names="a")

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

chi := DirichletCharacter("9.1");

S:= CuspForms(chi, 46);

N := Newforms(S);

Level:	$ N $	$=$	$ 9 = 3^{2} $
Weight:	$ k $	$=$	$ 46 $
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:	$115.430153467$
Analytic rank:	$0$
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} - 148878150x + 389915850150 $ x^3 - x^2 - 148878150*x + 389915850150
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{14}\cdot 3^{7}\cdot 5 $
Twist minimal:	no (minimal twist has level 1)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$10585.6$ 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)

$f(q)$	$=$	$q-7.36851e6 q^{2} +1.91106e13 q^{4} -5.97253e15 q^{5} -1.35754e19 q^{7} +1.18440e20 q^{8} +O(q^{10})$	\(q-7.36851e6 q^{2} +1.91106e13 q^{4} -5.97253e15 q^{5} -1.35754e19 q^{7} +1.18440e20 q^{8} +4.40087e22 q^{10} +4.62684e23 q^{11} +1.84657e24 q^{13} +1.00031e26 q^{14} -1.54512e27 q^{16} -5.39007e27 q^{17} +2.04232e28 q^{19} -1.14139e29 q^{20} -3.40930e30 q^{22} +4.06607e30 q^{23} +7.24945e30 q^{25} -1.36065e31 q^{26} -2.59434e32 q^{28} -6.91615e32 q^{29} -4.29419e32 q^{31} +7.21801e33 q^{32} +3.97168e34 q^{34} +8.10796e34 q^{35} -1.38069e35 q^{37} -1.50489e35 q^{38} -7.07385e35 q^{40} -9.02413e35 q^{41} -2.22460e36 q^{43} +8.84218e36 q^{44} -2.99609e37 q^{46} +1.00563e37 q^{47} +7.72848e37 q^{49} -5.34177e37 q^{50} +3.52891e37 q^{52} +2.47477e38 q^{53} -2.76340e39 q^{55} -1.60787e39 q^{56} +5.09618e39 q^{58} -1.01841e40 q^{59} -2.35593e40 q^{61} +3.16418e39 q^{62} +1.17807e39 q^{64} -1.10287e40 q^{65} -2.39925e41 q^{67} -1.03008e41 q^{68} -5.97436e41 q^{70} -4.61674e40 q^{71} +6.89694e41 q^{73} +1.01736e42 q^{74} +3.90301e41 q^{76} -6.28113e42 q^{77} -1.80775e42 q^{79} +9.22828e42 q^{80} +6.64944e42 q^{82} -1.09933e42 q^{83} +3.21924e43 q^{85} +1.63920e43 q^{86} +5.48002e43 q^{88} +5.72005e43 q^{89} -2.50680e43 q^{91} +7.77051e43 q^{92} -7.41002e43 q^{94} -1.21978e44 q^{95} -2.85037e44 q^{97} -5.69474e44 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q - 3814272 q^{2} - 1915164893184 q^{4} + 912448458460350 q^{5} - 76\!\cdots\!08 q^{7}+ \cdots + 10\!\cdots\!60 q^{8}+O(q^{10}) $ 3 * q - 3814272 * q^2 - 1915164893184 * q^4 + 912448458460350 * q^5 - 7619710926638056008 * q^7 + 108947667758662287360 * q^8	$ 3 q - 3814272 q^{2} - 1915164893184 q^{4} + 912448458460350 q^{5} - 76\!\cdots\!08 q^{7}+ \cdots - 19\!\cdots\!04 q^{98}+O(q^{100}) $ 3 * q - 3814272 * q^2 - 1915164893184 * q^4 + 912448458460350 * q^5 - 7619710926638056008 * q^7 + 108947667758662287360 * q^8 + 1419132609182896876800 * q^10 + 292602117773160656797644 * q^11 - 24359353574857845965202054 * q^13 + 202717255077168503234024448 * q^14 - 2516639057595474468963090432 * q^16 - 1167342337360426664689201782 * q^17 + 139928385765722236845372310380 * q^19 - 381381185200730248341345484800 * q^20 - 3645081261141863565639576301056 * q^22 + 10673923189590823281275419815384 * q^23 + 43966129876780298643382415638125 * q^25 - 109857986164645419011108420802816 * q^26 + 5309187993026577435829326249984 * q^28 + 670860386246579691273176792023830 * q^29 - 4362750588615761992088215111558944 * q^31 - 2770584927822325193163626168451072 * q^32 + 53874322809182721932452359249215232 * q^34 - 15776204147695493575553971787662800 * q^35 - 389811033762613666259144433874550238 * q^37 + 298309080939187021552909089031242240 * q^38 + 1418999553421731071561941465300992000 * q^40 - 2715552056267791317916826925062933406 * q^41 + 1244478438653295151469201253707220756 * q^43 + 10866498414076105454653552938468999168 * q^44 - 29420915174298432781096019434857298944 * q^46 + 5368746178058366301880916464880208048 * q^47 + 78160841959900415140960388420190127371 * q^49 - 365636939507033508238037233476615120000 * q^50 + 134213023925843531561035140325636718592 * q^52 + 1852254617049027724838330153197946097774 * q^53 - 3433604438201040460840734686798586808200 * q^55 - 5263223929490768485344096600823148052480 * q^56 + 13570181249555445898814714558437144899840 * q^58 + 3587009869064273690797416085301514120060 * q^59 - 51762384161673790814764907347052617635894 * q^61 + 5676710491956141755174145478721599328256 * q^62 + 41050065173647728685920731234203689025536 * q^64 - 37939089079008549181090608539522846859900 * q^65 + 14148137855196379836825399018252188940732 * q^67 - 123753416143995711246382651604664796299264 * q^68 - 615758273709518152674920733006194538854400 * q^70 + 125388248998914140052658001286881482385544 * q^71 + 545662435246745842274304841909717562787966 * q^73 + 922589101552630918194661534146849410212608 * q^74 - 25740309904677479085695622290576752803840 * q^76 - 6645319565466313145724427222526529624900384 * q^77 + 906179897072215837642402032445458679683120 * q^79 + 16837014550545085717858942703269209282969600 * q^80 - 7077813252702994823298504428501096216345856 * q^82 - 1486742880234689875145309838364765216168236 * q^83 + 38251451691354483777201487197950382555147300 * q^85 - 49387084957597704283946327082198769274651136 * q^86 + 52989682432050008057661862219403039374049280 * q^88 + 157452314112877728949303270670086721758716690 * q^89 - 209450940191589584493053736413801309667114864 * q^91 - 31580552157061127996902171853509709970604032 * q^92 + 380017168558424107350771392050931198759503872 * q^94 - 11835463674693195649110972576862856536029000 * q^95 + 371229894708856356492851438771649466869172902 * q^97 - 19381455993535436564386424979420682870187904 * 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 $

$2$	−7.36851e6	−1.24224	−0.621119	−	0.783716i	$-0.713322\pi$
$2$	−7.36851e6	−1.24224	−0.621119	+	0.783716i	$0.713322\pi$
$3$	0	0
$3$	0	0
$4$	1.91106e13	0.543156
$5$	−5.97253e15	−1.12030	−0.560149	−	0.828392i	$-0.689256\pi$
$5$	−5.97253e15	−1.12030	−0.560149	+	0.828392i	$0.689256\pi$
$6$	0	0
$7$	−1.35754e19	−1.31234	−0.656171	−	0.754612i	$-0.727825\pi$
$7$	−1.35754e19	−1.31234	−0.656171	+	0.754612i	$0.727825\pi$
$8$	1.18440e20	0.567509
$9$	0	0
$10$	4.40087e22	1.39168
$11$	4.62684e23	1.71376	0.856879	−	0.515518i	$-0.172400\pi$
$11$	4.62684e23	1.71376	0.856879	+	0.515518i	$0.172400\pi$
$12$	0	0
$13$	1.84657e24	0.159456	0.0797280	−	0.996817i	$-0.474595\pi$
$13$	1.84657e24	0.159456	0.0797280	+	0.996817i	$0.474595\pi$
$14$	1.00031e26	1.63024
$15$	0	0
$16$	−1.54512e27	−1.24814
$17$	−5.39007e27	−1.11300	−0.556498	−	0.830849i	$-0.687855\pi$
$17$	−5.39007e27	−1.11300	−0.556498	+	0.830849i	$0.687855\pi$
$18$	0	0
$19$	2.04232e28	0.345278	0.172639	−	0.984985i	$-0.444771\pi$
$19$	2.04232e28	0.345278	0.172639	+	0.984985i	$0.444771\pi$
$20$	−1.14139e29	−0.608497
$21$	0	0
$22$	−3.40930e30	−2.12890
$23$	4.06607e30	0.933896	0.466948	−	0.884285i	$-0.345353\pi$
$23$	4.06607e30	0.933896	0.466948	+	0.884285i	$0.345353\pi$
$24$	0	0
$25$	7.24945e30	0.255067
$26$	−1.36065e31	−0.198082
$27$	0	0
$28$	−2.59434e32	−0.712807
$29$	−6.91615e32	−0.862799	−0.431400	−	0.902161i	$-0.641980\pi$
$29$	−6.91615e32	−0.862799	−0.431400	+	0.902161i	$0.641980\pi$
$30$	0	0
$31$	−4.29419e32	−0.119466	−0.0597329	−	0.998214i	$-0.519025\pi$
$31$	−4.29419e32	−0.119466	−0.0597329	+	0.998214i	$0.519025\pi$
$32$	7.21801e33	0.982976
$33$	0	0
$34$	3.97168e34	1.38261
$35$	8.10796e34	1.47021
$36$	0	0
$37$	−1.38069e35	−0.717062	−0.358531	−	0.933518i	$-0.616722\pi$
$37$	−1.38069e35	−0.717062	−0.358531	+	0.933518i	$0.616722\pi$
$38$	−1.50489e35	−0.428917
$39$	0	0
$40$	−7.07385e35	−0.635779
$41$	−9.02413e35	−0.465338	−0.232669	−	0.972556i	$-0.574746\pi$
$41$	−9.02413e35	−0.465338	−0.232669	+	0.972556i	$0.574746\pi$
$42$	0	0
$43$	−2.22460e36	−0.392837	−0.196418	−	0.980520i	$-0.562931\pi$
$43$	−2.22460e36	−0.392837	−0.196418	+	0.980520i	$0.562931\pi$
$44$	8.84218e36	0.930839
$45$	0	0
$46$	−2.99609e37	−1.16012
$47$	1.00563e37	0.240014	0.120007	−	0.992773i	$-0.461708\pi$
$47$	1.00563e37	0.240014	0.120007	+	0.992773i	$0.461708\pi$
$48$	0	0
$49$	7.72848e37	0.722241
$50$	−5.34177e37	−0.316855
$51$	0	0
$52$	3.52891e37	0.0866095
$53$	2.47477e38	0.395666	0.197833	−	0.980236i	$-0.436610\pi$
$53$	2.47477e38	0.395666	0.197833	+	0.980236i	$0.436610\pi$
$54$	0	0
$55$	−2.76340e39	−1.91992
$56$	−1.60787e39	−0.744765
$57$	0	0
$58$	5.09618e39	1.07180
$59$	−1.01841e40	−1.45798	−0.728991	−	0.684524i	$-0.760010\pi$
$59$	−1.01841e40	−1.45798	−0.728991	+	0.684524i	$0.760010\pi$
$60$	0	0
$61$	−2.35593e40	−1.59309	−0.796545	−	0.604580i	$-0.793341\pi$
$61$	−2.35593e40	−1.59309	−0.796545	+	0.604580i	$0.793341\pi$
$62$	3.16418e39	0.148405
$63$	0	0
$64$	1.17807e39	0.0270473
$65$	−1.10287e40	−0.178638
$66$	0	0
$67$	−2.39925e41	−1.96513	−0.982567	−	0.185910i	$-0.940477\pi$
$67$	−2.39925e41	−1.96513	−0.982567	+	0.185910i	$0.940477\pi$
$68$	−1.03008e41	−0.604531
$69$	0	0
$70$	−5.97436e41	−1.82636
$71$	−4.61674e40	−0.102570	−0.0512852	−	0.998684i	$-0.516332\pi$
$71$	−4.61674e40	−0.102570	−0.0512852	+	0.998684i	$0.516332\pi$
$72$	0	0
$73$	6.89694e41	0.820148	0.410074	−	0.912052i	$-0.365503\pi$
$73$	6.89694e41	0.820148	0.410074	+	0.912052i	$0.365503\pi$
$74$	1.01736e42	0.890762
$75$	0	0
$76$	3.90301e41	0.187540
$77$	−6.28113e42	−2.24904
$78$	0	0
$79$	−1.80775e42	−0.363520	−0.181760	−	0.983343i	$-0.558179\pi$
$79$	−1.80775e42	−0.363520	−0.181760	+	0.983343i	$0.558179\pi$
$80$	9.22828e42	1.39829
$81$	0	0
$82$	6.64944e42	0.578061
$83$	−1.09933e42	−0.0727566	−0.0363783	−	0.999338i	$-0.511582\pi$
$83$	−1.09933e42	−0.0727566	−0.0363783	+	0.999338i	$0.511582\pi$
$84$	0	0
$85$	3.21924e43	1.24689
$86$	1.63920e43	0.487997
$87$	0	0
$88$	5.48002e43	0.972573
$89$	5.72005e43	0.787272	0.393636	−	0.919266i	$-0.371217\pi$
$89$	5.72005e43	0.787272	0.393636	+	0.919266i	$0.371217\pi$
$90$	0	0
$91$	−2.50680e43	−0.209261
$92$	7.77051e43	0.507252
$93$	0	0
$94$	−7.41002e43	−0.298155
$95$	−1.21978e44	−0.386814
$96$	0	0
$97$	−2.85037e44	−0.565635	−0.282818	−	0.959174i	$-0.591269\pi$
$97$	−2.85037e44	−0.565635	−0.282818	+	0.959174i	$0.591269\pi$
$98$	−5.69474e44	−0.897196
$99$	0	0
$100$	1.38542e44	0.138542
$101$	1.12852e45	0.902146	0.451073	−	0.892487i	$-0.351041\pi$
$101$	1.12852e45	0.902146	0.451073	+	0.892487i	$0.351041\pi$
$102$	0	0
$103$	4.56079e44	0.234532	0.117266	−	0.993101i	$-0.462587\pi$
$103$	4.56079e44	0.234532	0.117266	+	0.993101i	$0.462587\pi$
$104$	2.18707e44	0.0904927
$105$	0	0
$106$	−1.82354e45	−0.491511
$107$	−7.56988e45	−1.65179	−0.825894	−	0.563826i	$-0.809329\pi$
$107$	−7.56988e45	−1.65179	−0.825894	+	0.563826i	$0.809329\pi$
$108$	0	0
$109$	−8.09431e45	−1.16435	−0.582175	−	0.813063i	$-0.697798\pi$
$109$	−8.09431e45	−1.16435	−0.582175	+	0.813063i	$0.697798\pi$
$110$	2.03621e46	2.38500
$111$	0	0
$112$	2.09756e46	1.63798
$113$	6.69178e45	0.427836	0.213918	−	0.976852i	$-0.431378\pi$
$113$	6.69178e45	0.427836	0.213918	+	0.976852i	$0.431378\pi$
$114$	0	0
$115$	−2.42847e46	−1.04624
$116$	−1.32172e46	−0.468635
$117$	0	0
$118$	7.50416e46	1.81116
$119$	7.31724e46	1.46063
$120$	0	0
$121$	1.41186e47	1.93697
$122$	1.73597e47	1.97900
$123$	0	0
$124$	−8.20647e45	−0.0648886
$125$	1.26452e47	0.834546
$126$	0	0
$127$	4.47769e46	0.206762	0.103381	−	0.994642i	$-0.467034\pi$
$127$	4.47769e46	0.206762	0.103381	+	0.994642i	$0.467034\pi$
$128$	−2.62642e47	−1.01657
$129$	0	0
$130$	8.12652e46	0.221911
$131$	−4.74426e46	−0.109035	−0.0545173	−	0.998513i	$-0.517362\pi$
$131$	−4.74426e46	−0.109035	−0.0545173	+	0.998513i	$0.517362\pi$
$132$	0	0
$133$	−2.77254e47	−0.453122
$134$	1.76789e48	2.44116
$135$	0	0
$136$	−6.38398e47	−0.631635
$137$	5.92244e47	0.496922	0.248461	−	0.968642i	$-0.420075\pi$
$137$	5.92244e47	0.496922	0.248461	+	0.968642i	$0.420075\pi$
$138$	0	0
$139$	1.01012e48	0.611701	0.305851	−	0.952080i	$-0.401059\pi$
$139$	1.01012e48	0.611701	0.305851	+	0.952080i	$0.401059\pi$
$140$	1.54948e48	0.798556
$141$	0	0
$142$	3.40185e47	0.127417
$143$	8.54380e47	0.273269
$144$	0	0
$145$	4.13070e48	0.966592
$146$	−5.08202e48	−1.01882
$147$	0	0
$148$	−2.63858e48	−0.389477
$149$	1.22411e49	1.55285	0.776426	−	0.630208i	$-0.217031\pi$
$149$	1.22411e49	1.55285	0.776426	+	0.630208i	$0.217031\pi$
$150$	0	0
$151$	1.39518e48	0.131114	0.0655572	−	0.997849i	$-0.479118\pi$
$151$	1.39518e48	0.131114	0.0655572	+	0.997849i	$0.479118\pi$
$152$	2.41892e48	0.195948
$153$	0	0
$154$	4.62826e49	2.79384
$155$	2.56472e48	0.133837
$156$	0	0
$157$	−1.81397e49	−0.709393	−0.354697	−	0.934981i	$-0.615416\pi$
$157$	−1.81397e49	−0.709393	−0.354697	+	0.934981i	$0.615416\pi$
$158$	1.33204e49	0.451578
$159$	0	0
$160$	−4.31098e49	−1.10123
$161$	−5.51986e49	−1.22559
$162$	0	0
$163$	−6.75472e49	−1.13602	−0.568010	−	0.823022i	$-0.692287\pi$
$163$	−6.75472e49	−1.13602	−0.568010	+	0.823022i	$0.692287\pi$
$164$	−1.72457e49	−0.252751
$165$	0	0
$166$	8.10045e48	0.0903810
$167$	−4.33548e49	−0.422587	−0.211294	−	0.977423i	$-0.567768\pi$
$167$	−4.33548e49	−0.422587	−0.211294	+	0.977423i	$0.567768\pi$
$168$	0	0
$169$	−1.30697e50	−0.974574
$170$	−2.37210e50	−1.54893
$171$	0	0
$172$	−4.25135e49	−0.213372
$173$	−1.27763e49	−0.0562816	−0.0281408	−	0.999604i	$-0.508959\pi$
$173$	−1.27763e49	−0.0562816	−0.0281408	+	0.999604i	$0.508959\pi$
$174$	0	0
$175$	−9.84143e49	−0.334736
$176$	−7.14903e50	−2.13901
$177$	0	0
$178$	−4.21483e50	−0.977980
$179$	1.84054e50	0.376489	0.188244	−	0.982122i	$-0.439720\pi$
$179$	1.84054e50	0.376489	0.188244	+	0.982122i	$0.439720\pi$
$180$	0	0
$181$	1.05925e51	1.68745	0.843725	−	0.536775i	$-0.180358\pi$
$181$	1.05925e51	1.68745	0.843725	+	0.536775i	$0.180358\pi$
$182$	1.84714e50	0.259952
$183$	0	0
$184$	4.81584e50	0.529994
$185$	8.24620e50	0.803323
$186$	0	0
$187$	−2.49390e51	−1.90741
$188$	1.92183e50	0.130365
$189$	0	0
$190$	8.98800e50	0.480515
$191$	−1.00828e51	−0.478992	−0.239496	−	0.970897i	$-0.576982\pi$
$191$	−1.00828e51	−0.478992	−0.239496	+	0.970897i	$0.576982\pi$
$192$	0	0
$193$	4.75247e51	1.78600	0.892998	−	0.450061i	$-0.148598\pi$
$193$	4.75247e51	1.78600	0.892998	+	0.450061i	$0.148598\pi$
$194$	2.10030e51	0.702654
$195$	0	0
$196$	1.47696e51	0.392290
$197$	−1.24255e51	−0.294324	−0.147162	−	0.989112i	$-0.547014\pi$
$197$	−1.24255e51	−0.294324	−0.147162	+	0.989112i	$0.547014\pi$
$198$	0	0
$199$	−3.30064e51	−0.622880	−0.311440	−	0.950266i	$-0.600811\pi$
$199$	−3.30064e51	−0.622880	−0.311440	+	0.950266i	$0.600811\pi$
$200$	8.58623e50	0.144753
$201$	0	0
$202$	−8.31549e51	−1.12068
$203$	9.38896e51	1.13229
$204$	0	0
$205$	5.38969e51	0.521317
$206$	−3.36062e51	−0.291345
$207$	0	0
$208$	−2.85317e51	−0.199023
$209$	9.44951e51	0.591722
$210$	0	0
$211$	−1.03587e52	−0.523540	−0.261770	−	0.965130i	$-0.584306\pi$
$211$	−1.03587e52	−0.523540	−0.261770	+	0.965130i	$0.584306\pi$
$212$	4.72945e51	0.214908
$213$	0	0
$214$	5.57788e52	2.05191
$215$	1.32865e52	0.440094
$216$	0	0
$217$	5.82954e51	0.156780
$218$	5.96430e52	1.44640
$219$	0	0
$220$	−5.28102e52	−1.04282
$221$	−9.95315e51	−0.177474
$222$	0	0
$223$	5.37304e52	0.782277	0.391139	−	0.920332i	$-0.372081\pi$
$223$	5.37304e52	0.782277	0.391139	+	0.920332i	$0.372081\pi$
$224$	−9.79874e52	−1.29000
$225$	0	0
$226$	−4.93085e52	−0.531474
$227$	−2.78314e52	−0.271615	−0.135807	−	0.990735i	$-0.543363\pi$
$227$	−2.78314e52	−0.271615	−0.135807	+	0.990735i	$0.543363\pi$
$228$	0	0
$229$	2.18798e53	1.75285	0.876425	−	0.481539i	$-0.159922\pi$
$229$	2.18798e53	1.75285	0.876425	+	0.481539i	$0.159922\pi$
$230$	1.78942e53	1.29968
$231$	0	0
$232$	−8.19147e52	−0.489646
$233$	−3.51723e53	−1.90850	−0.954252	−	0.299004i	$-0.903345\pi$
$233$	−3.51723e53	−1.90850	−0.954252	+	0.299004i	$0.903345\pi$
$234$	0	0
$235$	−6.00617e52	−0.268888
$236$	−1.94624e53	−0.791912
$237$	0	0
$238$	−5.39172e53	−1.81445
$239$	4.11764e53	1.26094	0.630472	−	0.776212i	$-0.282861\pi$
$239$	4.11764e53	1.26094	0.630472	+	0.776212i	$0.282861\pi$
$240$	0	0
$241$	−2.61521e53	−0.663931	−0.331966	−	0.943291i	$-0.607712\pi$
$241$	−2.61521e53	−0.663931	−0.331966	+	0.943291i	$0.607712\pi$
$242$	−1.04033e54	−2.40617
$243$	0	0
$244$	−4.50232e53	−0.865297
$245$	−4.61586e53	−0.809125
$246$	0	0
$247$	3.77130e52	0.0550566
$248$	−5.08603e52	−0.0677979
$249$	0	0
$250$	−9.31763e53	−1.03671
$251$	1.56252e54	1.58916	0.794581	−	0.607158i	$-0.207691\pi$
$251$	1.56252e54	1.58916	0.794581	+	0.607158i	$0.207691\pi$
$252$	0	0
$253$	1.88131e54	1.60047
$254$	−3.29939e53	−0.256847
$255$	0	0
$256$	1.89383e54	1.23578
$257$	−1.24463e53	−0.0743951	−0.0371975	−	0.999308i	$-0.511843\pi$
$257$	−1.24463e53	−0.0743951	−0.0371975	+	0.999308i	$0.511843\pi$
$258$	0	0
$259$	1.87434e54	0.941030
$260$	−2.10766e53	−0.0970285
$261$	0	0
$262$	3.49582e53	0.135447
$263$	2.80486e54	0.997487	0.498743	−	0.866750i	$-0.333795\pi$
$263$	2.80486e54	0.997487	0.498743	+	0.866750i	$0.333795\pi$
$264$	0	0
$265$	−1.47807e54	−0.443264
$266$	2.04295e54	0.562886
$267$	0	0
$268$	−4.58511e54	−1.06737
$269$	−1.28461e54	−0.275009	−0.137504	−	0.990501i	$-0.543908\pi$
$269$	−1.28461e54	−0.275009	−0.137504	+	0.990501i	$0.543908\pi$
$270$	0	0
$271$	9.12323e54	1.65325	0.826627	−	0.562750i	$-0.190257\pi$
$271$	9.12323e54	1.65325	0.826627	+	0.562750i	$0.190257\pi$
$272$	8.32830e54	1.38917
$273$	0	0
$274$	−4.36396e54	−0.617295
$275$	3.35421e54	0.437124
$276$	0	0
$277$	−8.28825e53	−0.0917630	−0.0458815	−	0.998947i	$-0.514610\pi$
$277$	−8.28825e53	−0.0917630	−0.0458815	+	0.998947i	$0.514610\pi$
$278$	−7.44307e54	−0.759879
$279$	0	0
$280$	9.60304e54	0.834359
$281$	5.88447e54	0.471862	0.235931	−	0.971770i	$-0.424186\pi$
$281$	5.88447e54	0.471862	0.235931	+	0.971770i	$0.424186\pi$
$282$	0	0
$283$	−2.28277e55	−1.56051	−0.780257	−	0.625458i	$-0.784912\pi$
$283$	−2.28277e55	−1.56051	−0.780257	+	0.625458i	$0.784912\pi$
$284$	−8.82287e53	−0.0557118
$285$	0	0
$286$	−6.29551e54	−0.339465
$287$	1.22506e55	0.610683
$288$	0	0
$289$	5.59968e54	0.238760
$290$	−3.04371e55	−1.20074
$291$	0	0
$292$	1.31805e55	0.445468
$293$	−2.32198e55	−0.726671	−0.363335	−	0.931658i	$-0.618362\pi$
$293$	−2.32198e55	−0.726671	−0.363335	+	0.931658i	$0.618362\pi$
$294$	0	0
$295$	6.08248e55	1.63337
$296$	−1.63528e55	−0.406939
$297$	0	0
$298$	−9.01988e55	−1.92901
$299$	7.50829e54	0.148915
$300$	0	0
$301$	3.01999e55	0.515536
$302$	−1.02804e55	−0.162875
$303$	0	0
$304$	−3.15563e55	−0.430954
$305$	1.40708e56	1.78473
$306$	0	0
$307$	1.19437e56	1.30775	0.653875	−	0.756603i	$-0.273142\pi$
$307$	1.19437e56	1.30775	0.653875	+	0.756603i	$0.273142\pi$
$308$	−1.20036e56	−1.22158
$309$	0	0
$310$	−1.88982e55	−0.166258
$311$	−1.65762e56	−1.35636	−0.678181	−	0.734895i	$-0.737232\pi$
$311$	−1.65762e56	−1.35636	−0.678181	+	0.734895i	$0.737232\pi$
$312$	0	0
$313$	−2.27179e56	−1.60924	−0.804619	−	0.593792i	$-0.797630\pi$
$313$	−2.27179e56	−1.60924	−0.804619	+	0.593792i	$0.797630\pi$
$314$	1.33662e56	0.881236
$315$	0	0
$316$	−3.45472e55	−0.197448
$317$	−3.49229e56	−1.85899	−0.929494	−	0.368836i	$-0.879756\pi$
$317$	−3.49229e56	−1.85899	−0.929494	+	0.368836i	$0.879756\pi$
$318$	0	0
$319$	−3.20000e56	−1.47863
$320$	−7.03609e54	−0.0303010
$321$	0	0
$322$	4.06731e56	1.52248
$323$	−1.10083e56	−0.384293
$324$	0	0
$325$	1.33866e55	0.0406720
$326$	4.97722e56	1.41121
$327$	0	0
$328$	−1.06882e56	−0.264083
$329$	−1.36519e56	−0.314981
$330$	0	0
$331$	1.49551e55	0.0301065	0.0150533	−	0.999887i	$-0.495208\pi$
$331$	1.49551e55	0.0301065	0.0150533	+	0.999887i	$0.495208\pi$
$332$	−2.10089e55	−0.0395182
$333$	0	0
$334$	3.19460e56	0.524954
$335$	1.43296e57	2.20154
$336$	0	0
$337$	3.73633e56	0.502080	0.251040	−	0.967977i	$-0.419227\pi$
$337$	3.73633e56	0.502080	0.251040	+	0.967977i	$0.419227\pi$
$338$	9.63043e56	1.21065
$339$	0	0
$340$	6.15216e56	0.677255
$341$	−1.98686e56	−0.204735
$342$	0	0
$343$	4.03490e56	0.364515
$344$	−2.63481e56	−0.222938
$345$	0	0
$346$	9.41420e55	0.0699151
$347$	−9.19083e56	−0.639649	−0.319824	−	0.947477i	$-0.603624\pi$
$347$	−9.19083e56	−0.639649	−0.319824	+	0.947477i	$0.603624\pi$
$348$	0	0
$349$	−1.53571e57	−0.939158	−0.469579	−	0.882891i	$-0.655594\pi$
$349$	−1.53571e57	−0.939158	−0.469579	+	0.882891i	$0.655594\pi$
$350$	7.25167e56	0.415822
$351$	0	0
$352$	3.33966e57	1.68458
$353$	1.08285e57	0.512435	0.256217	−	0.966619i	$-0.417524\pi$
$353$	1.08285e57	0.512435	0.256217	+	0.966619i	$0.417524\pi$
$354$	0	0
$355$	2.75736e56	0.114909
$356$	1.09314e57	0.427612
$357$	0	0
$358$	−1.35620e57	−0.467689
$359$	9.45652e56	0.306271	0.153136	−	0.988205i	$-0.451063\pi$
$359$	9.45652e56	0.306271	0.153136	+	0.988205i	$0.451063\pi$
$360$	0	0
$361$	−3.08163e57	−0.880783
$362$	−7.80511e57	−2.09622
$363$	0	0
$364$	−4.79064e56	−0.113661
$365$	−4.11922e57	−0.918810
$366$	0	0
$367$	−8.46364e57	−1.66944	−0.834719	−	0.550675i	$-0.814370\pi$
$367$	−8.46364e57	−1.66944	−0.834719	+	0.550675i	$0.814370\pi$
$368$	−6.28257e57	−1.16563
$369$	0	0
$370$	−6.07623e57	−0.997919
$371$	−3.35961e57	−0.519249
$372$	0	0
$373$	7.28034e57	0.997017	0.498509	−	0.866885i	$-0.333881\pi$
$373$	7.28034e57	0.997017	0.498509	+	0.866885i	$0.333881\pi$
$374$	1.83763e58	2.36945
$375$	0	0
$376$	1.19107e57	0.136210
$377$	−1.27712e57	−0.137578
$378$	0	0
$379$	−1.15746e58	−1.10694	−0.553471	−	0.832868i	$-0.686697\pi$
$379$	−1.15746e58	−1.10694	−0.553471	+	0.832868i	$0.686697\pi$
$380$	−2.33108e57	−0.210100
$381$	0	0
$382$	7.42949e57	0.595022
$383$	−1.13149e58	−0.854436	−0.427218	−	0.904149i	$-0.640506\pi$
$383$	−1.13149e58	−0.854436	−0.427218	+	0.904149i	$0.640506\pi$
$384$	0	0
$385$	3.75143e58	2.51959
$386$	−3.50187e58	−2.21863
$387$	0	0
$388$	−5.44723e57	−0.307229
$389$	3.09651e58	1.64819	0.824094	−	0.566453i	$-0.191685\pi$
$389$	3.09651e58	1.64819	0.824094	+	0.566453i	$0.191685\pi$
$390$	0	0
$391$	−2.19164e58	−1.03942
$392$	9.15359e57	0.409878
$393$	0	0
$394$	9.15577e57	0.365620
$395$	1.07968e58	0.407251
$396$	0	0
$397$	2.54438e58	0.856633	0.428317	−	0.903629i	$-0.359107\pi$
$397$	2.54438e58	0.856633	0.428317	+	0.903629i	$0.359107\pi$
$398$	2.43208e58	0.773766
$399$	0	0
$400$	−1.12013e58	−0.318359
$401$	2.41926e58	0.650031	0.325016	−	0.945709i	$-0.394630\pi$
$401$	2.41926e58	0.650031	0.325016	+	0.945709i	$0.394630\pi$
$402$	0	0
$403$	−7.92954e56	−0.0190495
$404$	2.15666e58	0.490007
$405$	0	0
$406$	−6.91827e58	−1.40657
$407$	−6.38823e58	−1.22887
$408$	0	0
$409$	4.68095e58	0.806418	0.403209	−	0.915108i	$-0.367895\pi$
$409$	4.68095e58	0.806418	0.403209	+	0.915108i	$0.367895\pi$
$410$	−3.97140e58	−0.647600
$411$	0	0
$412$	8.71595e57	0.127388
$413$	1.38253e59	1.91337
$414$	0	0
$415$	6.56581e57	0.0815091
$416$	1.33286e58	0.156741
$417$	0	0
$418$	−6.96288e58	−0.735060
$419$	−4.10143e58	−0.410317	−0.205158	−	0.978729i	$-0.565771\pi$
$419$	−4.10143e58	−0.410317	−0.205158	+	0.978729i	$0.565771\pi$
$420$	0	0
$421$	−5.12871e58	−0.460958	−0.230479	−	0.973077i	$-0.574029\pi$
$421$	−5.12871e58	−0.460958	−0.230479	+	0.973077i	$0.574029\pi$
$422$	7.63282e58	0.650362
$423$	0	0
$424$	2.93112e58	0.224544
$425$	−3.90751e58	−0.283889
$426$	0	0
$427$	3.19826e59	2.09068
$428$	−1.44665e59	−0.897179
$429$	0	0
$430$	−9.79019e58	−0.546702
$431$	1.63043e59	0.864100	0.432050	−	0.901850i	$-0.357790\pi$
$431$	1.63043e59	0.864100	0.432050	+	0.901850i	$0.357790\pi$
$432$	0	0
$433$	2.91636e59	1.39272	0.696360	−	0.717692i	$-0.254802\pi$
$433$	2.91636e59	1.39272	0.696360	+	0.717692i	$0.254802\pi$
$434$	−4.29551e58	−0.194758
$435$	0	0
$436$	−1.54687e59	−0.632424
$437$	8.30423e58	0.322453
$438$	0	0
$439$	−2.21702e59	−0.776816	−0.388408	−	0.921488i	$-0.626975\pi$
$439$	−2.21702e59	−0.776816	−0.388408	+	0.921488i	$0.626975\pi$
$440$	−3.27296e59	−1.08957
$441$	0	0
$442$	7.33399e58	0.220465
$443$	−3.23420e59	−0.924024	−0.462012	−	0.886874i	$-0.652872\pi$
$443$	−3.23420e59	−0.924024	−0.462012	+	0.886874i	$0.652872\pi$
$444$	0	0
$445$	−3.41632e59	−0.881980
$446$	−3.95913e59	−0.971775
$447$	0	0
$448$	−1.59928e58	−0.0354952
$449$	5.32736e59	1.12453	0.562263	−	0.826959i	$-0.309931\pi$
$449$	5.32736e59	1.12453	0.562263	+	0.826959i	$0.309931\pi$
$450$	0	0
$451$	−4.17532e59	−0.797477
$452$	1.27884e59	0.232382
$453$	0	0
$454$	2.05076e59	0.337410
$455$	1.49719e59	0.234434
$456$	0	0
$457$	−1.11648e60	−1.58393	−0.791967	−	0.610564i	$-0.790943\pi$
$457$	−1.11648e60	−1.58393	−0.791967	+	0.610564i	$0.790943\pi$
$458$	−1.61221e60	−2.17746
$459$	0	0
$460$	−4.64096e59	−0.568273
$461$	−8.63646e59	−1.00708	−0.503541	−	0.863971i	$-0.667970\pi$
$461$	−8.63646e59	−1.00708	−0.503541	+	0.863971i	$0.667970\pi$
$462$	0	0
$463$	−7.81313e59	−0.826519	−0.413260	−	0.910613i	$-0.635610\pi$
$463$	−7.81313e59	−0.826519	−0.413260	+	0.910613i	$0.635610\pi$
$464$	1.06863e60	1.07689
$465$	0	0
$466$	2.59168e60	2.37082
$467$	1.35783e60	1.18363	0.591816	−	0.806073i	$-0.298411\pi$
$467$	1.35783e60	1.18363	0.591816	+	0.806073i	$0.298411\pi$
$468$	0	0
$469$	3.25708e60	2.57893
$470$	4.42566e59	0.334023
$471$	0	0
$472$	−1.20620e60	−0.827417
$473$	−1.02929e60	−0.673227
$474$	0	0
$475$	1.48057e59	0.0880691
$476$	1.39837e60	0.793351
$477$	0	0
$478$	−3.03409e60	−1.56639
$479$	1.42047e60	0.699653	0.349827	−	0.936814i	$-0.386240\pi$
$479$	1.42047e60	0.699653	0.349827	+	0.936814i	$0.386240\pi$
$480$	0	0
$481$	−2.54954e59	−0.114340
$482$	1.92702e60	0.824761
$483$	0	0
$484$	2.69816e60	1.05208
$485$	1.70239e60	0.633680
$486$	0	0
$487$	5.47125e59	0.185646	0.0928229	−	0.995683i	$-0.470411\pi$
$487$	5.47125e59	0.185646	0.0928229	+	0.995683i	$0.470411\pi$
$488$	−2.79035e60	−0.904092
$489$	0	0
$490$	3.40120e60	1.00513
$491$	5.08915e60	1.43652	0.718260	−	0.695775i	$-0.244939\pi$
$491$	5.08915e60	1.43652	0.718260	+	0.695775i	$0.244939\pi$
$492$	0	0
$493$	3.72785e60	0.960292
$494$	−2.77888e59	−0.0683934
$495$	0	0
$496$	6.63504e59	0.149110
$497$	6.26741e59	0.134607
$498$	0	0
$499$	2.10435e59	0.0412910	0.0206455	−	0.999787i	$-0.493428\pi$
$499$	2.10435e59	0.0412910	0.0206455	+	0.999787i	$0.493428\pi$
$500$	2.41658e60	0.453289
$501$	0	0
$502$	−1.15135e61	−1.97412
$503$	−4.53975e60	−0.744307	−0.372153	−	0.928171i	$-0.621380\pi$
$503$	−4.53975e60	−0.744307	−0.372153	+	0.928171i	$0.621380\pi$
$504$	0	0
$505$	−6.74010e60	−1.01067
$506$	−1.38624e61	−1.98817
$507$	0	0
$508$	8.55714e59	0.112304
$509$	−2.61966e60	−0.328923	−0.164462	−	0.986383i	$-0.552589\pi$
$509$	−2.61966e60	−0.328923	−0.164462	+	0.986383i	$0.552589\pi$
$510$	0	0
$511$	−9.36288e60	−1.07631
$512$	−4.71382e60	−0.518560
$513$	0	0
$514$	9.17106e59	0.0924165
$515$	−2.72395e60	−0.262746
$516$	0	0
$517$	4.65290e60	0.411327
$518$	−1.38111e61	−1.16898
$519$	0	0
$520$	−1.30624e60	−0.101379
$521$	2.08020e61	1.54617	0.773083	−	0.634305i	$-0.218713\pi$
$521$	2.08020e61	1.54617	0.773083	+	0.634305i	$0.218713\pi$
$522$	0	0
$523$	2.10397e61	1.43467	0.717336	−	0.696728i	$-0.245361\pi$
$523$	2.10397e61	1.43467	0.717336	+	0.696728i	$0.245361\pi$
$524$	−9.06658e59	−0.0592229
$525$	0	0
$526$	−2.06677e61	−1.23912
$527$	2.31460e60	0.132965
$528$	0	0
$529$	−2.42332e60	−0.127838
$530$	1.08912e61	0.550639
$531$	0	0
$532$	−5.29849e60	−0.246116
$533$	−1.66637e60	−0.0742009
$534$	0	0
$535$	4.52114e61	1.85049
$536$	−2.84166e61	−1.11523
$537$	0	0
$538$	9.46570e60	0.341627
$539$	3.57585e61	1.23775
$540$	0	0
$541$	−2.45649e61	−0.782306	−0.391153	−	0.920326i	$-0.627924\pi$
$541$	−2.45649e61	−0.782306	−0.391153	+	0.920326i	$0.627924\pi$
$542$	−6.72246e61	−2.05374
$543$	0	0
$544$	−3.89056e61	−1.09405
$545$	4.83435e61	1.30442
$546$	0	0
$547$	4.92625e61	1.22406	0.612028	−	0.790836i	$-0.290354\pi$
$547$	4.92625e61	1.22406	0.612028	+	0.790836i	$0.290354\pi$
$548$	1.13182e61	0.269906
$549$	0	0
$550$	−2.47155e61	−0.543012
$551$	−1.41250e61	−0.297905
$552$	0	0
$553$	2.45409e61	0.477062
$554$	6.10721e60	0.113992
$555$	0	0
$556$	1.93040e61	0.332249
$557$	1.15656e62	1.91173	0.955863	−	0.293813i	$-0.0949242\pi$
$557$	1.15656e62	1.91173	0.955863	+	0.293813i	$0.0949242\pi$
$558$	0	0
$559$	−4.10789e60	−0.0626402
$560$	−1.25278e62	−1.83503
$561$	0	0
$562$	−4.33598e61	−0.586165
$563$	5.89709e61	0.765947	0.382974	−	0.923759i	$-0.374900\pi$
$563$	5.89709e61	0.765947	0.382974	+	0.923759i	$0.374900\pi$
$564$	0	0
$565$	−3.99669e61	−0.479303
$566$	1.68206e62	1.93853
$567$	0	0
$568$	−5.46805e60	−0.0582096
$569$	−7.93806e61	−0.812248	−0.406124	−	0.913818i	$-0.633120\pi$
$569$	−7.93806e61	−0.812248	−0.406124	+	0.913818i	$0.633120\pi$
$570$	0	0
$571$	7.67118e61	0.725354	0.362677	−	0.931915i	$-0.381863\pi$
$571$	7.67118e61	0.725354	0.362677	+	0.931915i	$0.381863\pi$
$572$	1.63277e61	0.148428
$573$	0	0
$574$	−9.02689e61	−0.758614
$575$	2.94768e61	0.238207
$576$	0	0
$577$	6.82798e60	0.0510313	0.0255156	−	0.999674i	$-0.491877\pi$
$577$	6.82798e60	0.0510313	0.0255156	+	0.999674i	$0.491877\pi$
$578$	−4.12613e61	−0.296597
$579$	0	0
$580$	7.89401e61	0.525011
$581$	1.49239e61	0.0954815
$582$	0	0
$583$	1.14504e62	0.678076
$584$	8.16871e61	0.465441
$585$	0	0
$586$	1.71096e62	0.902698
$587$	−1.68156e62	−0.853800	−0.426900	−	0.904299i	$-0.640394\pi$
$587$	−1.68156e62	−0.853800	−0.426900	+	0.904299i	$0.640394\pi$
$588$	0	0
$589$	−8.77013e60	−0.0412489
$590$	−4.48189e62	−2.02904
$591$	0	0
$592$	2.13333e62	0.894992
$593$	7.10812e61	0.287094	0.143547	−	0.989644i	$-0.454149\pi$
$593$	7.10812e61	0.287094	0.143547	+	0.989644i	$0.454149\pi$
$594$	0	0
$595$	−4.37025e62	−1.63634
$596$	2.33935e62	0.843441
$597$	0	0
$598$	−5.53250e61	−0.184988
$599$	3.72514e62	1.19961	0.599804	−	0.800147i	$-0.295245\pi$
$599$	3.72514e62	1.19961	0.599804	+	0.800147i	$0.295245\pi$
$600$	0	0
$601$	1.98326e61	0.0592520	0.0296260	−	0.999561i	$-0.490568\pi$
$601$	1.98326e61	0.0592520	0.0296260	+	0.999561i	$0.490568\pi$
$602$	−2.22528e62	−0.640419
$603$	0	0
$604$	2.66628e61	0.0712156
$605$	−8.43241e62	−2.16998
$606$	0	0
$607$	−3.31764e62	−0.792653	−0.396327	−	0.918110i	$-0.629715\pi$
$607$	−3.31764e62	−0.792653	−0.396327	+	0.918110i	$0.629715\pi$
$608$	1.47415e62	0.339400
$609$	0	0
$610$	−1.03681e63	−2.21707
$611$	1.85697e61	0.0382717
$612$	0	0
$613$	4.55123e62	0.871501	0.435750	−	0.900068i	$-0.356483\pi$
$613$	4.55123e62	0.871501	0.435750	+	0.900068i	$0.356483\pi$
$614$	−8.80072e62	−1.62454
$615$	0	0
$616$	−7.43935e62	−1.27635
$617$	4.88458e62	0.808000	0.404000	−	0.914759i	$-0.367620\pi$
$617$	4.88458e62	0.808000	0.404000	+	0.914759i	$0.367620\pi$
$618$	0	0
$619$	3.98061e62	0.612223	0.306111	−	0.951996i	$-0.400972\pi$
$619$	3.98061e62	0.612223	0.306111	+	0.951996i	$0.400972\pi$
$620$	4.90134e61	0.0726946
$621$	0	0
$622$	1.22142e63	1.68493
$623$	−7.76521e62	−1.03317
$624$	0	0
$625$	−9.61281e62	−1.19001
$626$	1.67397e63	1.99906
$627$	0	0
$628$	−3.46660e62	−0.385312
$629$	7.44200e62	0.798087
$630$	0	0
$631$	2.17238e62	0.216908	0.108454	−	0.994101i	$-0.465410\pi$
$631$	2.17238e62	0.216908	0.108454	+	0.994101i	$0.465410\pi$
$632$	−2.14109e62	−0.206301
$633$	0	0
$634$	2.57330e63	2.30931
$635$	−2.67432e62	−0.231635
$636$	0	0
$637$	1.42712e62	0.115166
$638$	2.35792e63	1.83681
$639$	0	0
$640$	1.56864e63	1.13887
$641$	−1.15093e63	−0.806757	−0.403379	−	0.915033i	$-0.632164\pi$
$641$	−1.15093e63	−0.806757	−0.403379	+	0.915033i	$0.632164\pi$
$642$	0	0
$643$	1.21311e63	0.792781	0.396391	−	0.918082i	$-0.370263\pi$
$643$	1.21311e63	0.792781	0.396391	+	0.918082i	$0.370263\pi$
$644$	−1.05488e63	−0.665688
$645$	0	0
$646$	8.11145e62	0.477383
$647$	2.91798e63	1.65858	0.829290	−	0.558818i	$-0.188745\pi$
$647$	2.91798e63	1.65858	0.829290	+	0.558818i	$0.188745\pi$
$648$	0	0
$649$	−4.71202e63	−2.49863
$650$	−9.86396e61	−0.0505244
$651$	0	0
$652$	−1.29087e63	−0.617037
$653$	9.80474e62	0.452782	0.226391	−	0.974036i	$-0.427307\pi$
$653$	9.80474e62	0.452782	0.226391	+	0.974036i	$0.427307\pi$
$654$	0	0
$655$	2.83353e62	0.122151
$656$	1.39434e63	0.580806
$657$	0	0
$658$	1.00594e63	0.391282
$659$	−1.71493e63	−0.644651	−0.322325	−	0.946629i	$-0.604465\pi$
$659$	−1.71493e63	−0.644651	−0.322325	+	0.946629i	$0.604465\pi$
$660$	0	0
$661$	4.68459e63	1.64490	0.822448	−	0.568840i	$-0.192608\pi$
$661$	4.68459e63	1.64490	0.822448	+	0.568840i	$0.192608\pi$
$662$	−1.10197e62	−0.0373995
$663$	0	0
$664$	−1.30205e62	−0.0412900
$665$	1.65591e63	0.507632
$666$	0	0
$667$	−2.81216e63	−0.805765
$668$	−8.28537e62	−0.229531
$669$	0	0
$670$	−1.05588e64	−2.73483
$671$	−1.09005e64	−2.73017
$672$	0	0
$673$	1.53030e63	0.358458	0.179229	−	0.983807i	$-0.442640\pi$
$673$	1.53030e63	0.358458	0.179229	+	0.983807i	$0.442640\pi$
$674$	−2.75312e63	−0.623703
$675$	0	0
$676$	−2.49770e63	−0.529346
$677$	2.15211e63	0.441184	0.220592	−	0.975366i	$-0.429201\pi$
$677$	2.15211e63	0.441184	0.220592	+	0.975366i	$0.429201\pi$
$678$	0	0
$679$	3.86949e63	0.742307
$680$	3.81285e63	0.707619
$681$	0	0
$682$	1.46402e63	0.254330
$683$	−5.70299e63	−0.958599	−0.479299	−	0.877651i	$-0.659109\pi$
$683$	−5.70299e63	−0.958599	−0.479299	+	0.877651i	$0.659109\pi$
$684$	0	0
$685$	−3.53720e63	−0.556700
$686$	−2.97312e63	−0.452814
$687$	0	0
$688$	3.43728e63	0.490315
$689$	4.56985e62	0.0630913
$690$	0	0
$691$	−8.52122e62	−0.110216	−0.0551081	−	0.998480i	$-0.517550\pi$
$691$	−8.52122e62	−0.110216	−0.0551081	+	0.998480i	$0.517550\pi$
$692$	−2.44162e62	−0.0305697
$693$	0	0
$694$	6.77227e63	0.794596
$695$	−6.03297e63	−0.685288
$696$	0	0
$697$	4.86407e63	0.517919
$698$	1.13159e64	1.16666
$699$	0	0
$700$	−1.88076e63	−0.181814
$701$	1.29219e64	1.20968	0.604842	−	0.796346i	$-0.293236\pi$
$701$	1.29219e64	1.20968	0.604842	+	0.796346i	$0.293236\pi$
$702$	0	0
$703$	−2.81981e63	−0.247585
$704$	5.45077e62	0.0463524
$705$	0	0
$706$	−7.97902e63	−0.636566
$707$	−1.53201e64	−1.18392
$708$	0	0
$709$	8.82566e63	0.640040	0.320020	−	0.947411i	$-0.396310\pi$
$709$	8.82566e63	0.640040	0.320020	+	0.947411i	$0.396310\pi$
$710$	−2.03176e63	−0.142745
$711$	0	0
$712$	6.77481e63	0.446784
$713$	−1.74605e63	−0.111569
$714$	0	0
$715$	−5.10281e63	−0.306143
$716$	3.51739e63	0.204492
$717$	0	0
$718$	−6.96805e63	−0.380462
$719$	1.32233e64	0.699747	0.349873	−	0.936797i	$-0.386225\pi$
$719$	1.32233e64	0.699747	0.349873	+	0.936797i	$0.386225\pi$
$720$	0	0
$721$	−6.19146e63	−0.307786
$722$	2.27071e64	1.09414
$723$	0	0
$724$	2.02429e64	0.916550
$725$	−5.01383e63	−0.220072
$726$	0	0
$727$	−3.36741e64	−1.38922	−0.694611	−	0.719386i	$-0.744423\pi$
$727$	−3.36741e64	−1.38922	−0.694611	+	0.719386i	$0.744423\pi$
$728$	−2.96904e63	−0.118757
$729$	0	0
$730$	3.03525e64	1.14138
$731$	1.19908e64	0.437226
$732$	0	0
$733$	−1.74069e64	−0.596873	−0.298437	−	0.954429i	$-0.596465\pi$
$733$	−1.74069e64	−0.596873	−0.298437	+	0.954429i	$0.596465\pi$
$734$	6.23644e64	2.07384
$735$	0	0
$736$	2.93489e64	0.917997
$737$	−1.11009e65	−3.36776
$738$	0	0
$739$	1.59709e64	0.455858	0.227929	−	0.973678i	$-0.426805\pi$
$739$	1.59709e64	0.455858	0.227929	+	0.973678i	$0.426805\pi$
$740$	1.57590e64	0.436330
$741$	0	0
$742$	2.47553e64	0.645031
$743$	1.55533e64	0.393164	0.196582	−	0.980487i	$-0.437016\pi$
$743$	1.55533e64	0.393164	0.196582	+	0.980487i	$0.437016\pi$
$744$	0	0
$745$	−7.31105e64	−1.73966
$746$	−5.36453e64	−1.23853
$747$	0	0
$748$	−4.76600e64	−1.03602
$749$	1.02764e65	2.16771
$750$	0	0
$751$	5.84568e64	1.16128	0.580639	−	0.814161i	$-0.302803\pi$
$751$	5.84568e64	1.16128	0.580639	+	0.814161i	$0.302803\pi$
$752$	−1.55382e64	−0.299571
$753$	0	0
$754$	9.41046e63	0.170905
$755$	−8.33279e63	−0.146887
$756$	0	0
$757$	−1.20065e64	−0.199416	−0.0997080	−	0.995017i	$-0.531791\pi$
$757$	−1.20065e64	−0.199416	−0.0997080	+	0.995017i	$0.531791\pi$
$758$	8.52879e64	1.37509
$759$	0	0
$760$	−1.44471e64	−0.219520
$761$	3.56581e64	0.526022	0.263011	−	0.964793i	$-0.415284\pi$
$761$	3.56581e64	0.526022	0.263011	+	0.964793i	$0.415284\pi$
$762$	0	0
$763$	1.09884e65	1.52803
$764$	−1.92688e64	−0.260168
$765$	0	0
$766$	8.33743e64	1.06141
$767$	−1.88057e64	−0.232484
$768$	0	0
$769$	−1.39554e65	−1.62704	−0.813521	−	0.581536i	$-0.802452\pi$
$769$	−1.39554e65	−1.62704	−0.813521	+	0.581536i	$0.802452\pi$
$770$	−2.76424e65	−3.12993
$771$	0	0
$772$	9.08227e64	0.970075
$773$	−1.32949e65	−1.37926	−0.689629	−	0.724163i	$-0.742227\pi$
$773$	−1.32949e65	−1.37926	−0.689629	+	0.724163i	$0.742227\pi$
$774$	0	0
$775$	−3.11305e63	−0.0304718
$776$	−3.37596e64	−0.321003
$777$	0	0
$778$	−2.28167e65	−2.04744
$779$	−1.84302e64	−0.160671
$780$	0	0
$781$	−2.13609e64	−0.175781
$782$	1.61491e65	1.29121
$783$	0	0
$784$	−1.19414e65	−0.901456
$785$	1.08340e65	0.794732
$786$	0	0
$787$	1.01514e65	0.703227	0.351613	−	0.936145i	$-0.385633\pi$
$787$	1.01514e65	0.703227	0.351613	+	0.936145i	$0.385633\pi$
$788$	−2.37460e64	−0.159864
$789$	0	0
$790$	−7.95566e64	−0.505902
$791$	−9.08437e64	−0.561466
$792$	0	0
$793$	−4.35039e64	−0.254028
$794$	−1.87483e65	−1.06414
$795$	0	0
$796$	−6.30773e64	−0.338321
$797$	−6.73597e64	−0.351227	−0.175613	−	0.984459i	$-0.556191\pi$
$797$	−6.73597e64	−0.351227	−0.175613	+	0.984459i	$0.556191\pi$
$798$	0	0
$799$	−5.42043e64	−0.267135
$800$	5.23266e64	0.250725
$801$	0	0
$802$	−1.78264e65	−0.807494
$803$	3.19111e65	1.40553
$804$	0	0
$805$	3.29675e65	1.37303
$806$	5.84289e63	0.0236641
$807$	0	0
$808$	1.33661e65	0.511976
$809$	2.59532e65	0.966829	0.483414	−	0.875392i	$-0.339396\pi$
$809$	2.59532e65	0.966829	0.483414	+	0.875392i	$0.339396\pi$
$810$	0	0
$811$	3.24133e65	1.14223	0.571115	−	0.820870i	$-0.306511\pi$
$811$	3.24133e65	1.14223	0.571115	+	0.820870i	$0.306511\pi$
$812$	1.79429e65	0.615009
$813$	0	0
$814$	4.70717e65	1.52655
$815$	4.03428e65	1.27268
$816$	0	0
$817$	−4.54336e64	−0.135638
$818$	−3.44917e65	−1.00176
$819$	0	0
$820$	1.03000e65	0.283157
$821$	6.22943e65	1.66620	0.833100	−	0.553123i	$-0.186564\pi$
$821$	6.22943e65	1.66620	0.833100	+	0.553123i	$0.186564\pi$
$822$	0	0
$823$	1.49111e65	0.377585	0.188792	−	0.982017i	$-0.439543\pi$
$823$	1.49111e65	0.377585	0.188792	+	0.982017i	$0.439543\pi$
$824$	5.40179e64	0.133099
$825$	0	0
$826$	−1.01872e66	−2.37686
$827$	−7.39891e65	−1.67994	−0.839970	−	0.542633i	$-0.817427\pi$
$827$	−7.39891e65	−1.67994	−0.839970	+	0.542633i	$0.817427\pi$
$828$	0	0
$829$	6.47384e65	1.39215	0.696073	−	0.717971i	$-0.254929\pi$
$829$	6.47384e65	1.39215	0.696073	+	0.717971i	$0.254929\pi$
$830$	−4.83802e64	−0.101254
$831$	0	0
$832$	2.17540e63	0.00431285
$833$	−4.16570e65	−0.803852
$834$	0	0
$835$	2.58938e65	0.473424
$836$	1.80586e65	0.321398
$837$	0	0
$838$	3.02214e65	0.509711
$839$	4.81442e65	0.790497	0.395248	−	0.918574i	$-0.370659\pi$
$839$	4.81442e65	0.790497	0.395248	+	0.918574i	$0.370659\pi$
$840$	0	0
$841$	−1.64223e65	−0.255578
$842$	3.77910e65	0.572619
$843$	0	0
$844$	−1.97961e65	−0.284364
$845$	7.80592e65	1.09181
$846$	0	0
$847$	−1.91666e66	−2.54196
$848$	−3.82382e65	−0.493845
$849$	0	0
$850$	2.87925e65	0.352658
$851$	−5.61397e65	−0.669661
$852$	0	0
$853$	1.52156e66	1.72162	0.860808	−	0.508929i	$-0.169959\pi$
$853$	1.52156e66	1.72162	0.860808	+	0.508929i	$0.169959\pi$
$854$	−2.35665e66	−2.59712
$855$	0	0
$856$	−8.96575e65	−0.937404
$857$	5.36235e63	0.00546118	0.00273059	−	0.999996i	$-0.499131\pi$
$857$	5.36235e63	0.00546118	0.00273059	+	0.999996i	$0.499131\pi$
$858$	0	0
$859$	−1.03735e66	−1.00249	−0.501243	−	0.865306i	$-0.667124\pi$
$859$	−1.03735e66	−1.00249	−0.501243	+	0.865306i	$0.667124\pi$
$860$	2.53914e65	0.239040
$861$	0	0
$862$	−1.20139e66	−1.07342
$863$	1.99751e66	1.73878	0.869391	−	0.494124i	$-0.164511\pi$
$863$	1.99751e66	1.73878	0.869391	+	0.494124i	$0.164511\pi$
$864$	0	0
$865$	7.63066e64	0.0630521
$866$	−2.14893e66	−1.73009
$867$	0	0
$868$	1.11406e65	0.0851560
$869$	−8.36417e65	−0.622985
$870$	0	0
$871$	−4.43038e65	−0.313352
$872$	−9.58687e65	−0.660779
$873$	0	0
$874$	−6.11898e65	−0.400564
$875$	−1.71664e66	−1.09521
$876$	0	0
$877$	−4.71670e65	−0.285856	−0.142928	−	0.989733i	$-0.545652\pi$
$877$	−4.71670e65	−0.285856	−0.142928	+	0.989733i	$0.545652\pi$
$878$	1.63361e66	0.964991
$879$	0	0
$880$	4.26978e66	2.39632
$881$	4.33691e65	0.237259	0.118629	−	0.992939i	$-0.462150\pi$
$881$	4.33691e65	0.237259	0.118629	+	0.992939i	$0.462150\pi$
$882$	0	0
$883$	2.23934e66	1.16413	0.582067	−	0.813141i	$-0.302244\pi$
$883$	2.23934e66	1.16413	0.582067	+	0.813141i	$0.302244\pi$
$884$	−1.90211e65	−0.0963961
$885$	0	0
$886$	2.38312e66	1.14786
$887$	4.37952e65	0.205658	0.102829	−	0.994699i	$-0.467211\pi$
$887$	4.37952e65	0.205658	0.102829	+	0.994699i	$0.467211\pi$
$888$	0	0
$889$	−6.07865e65	−0.271342
$890$	2.51732e66	1.09563
$891$	0	0
$892$	1.02682e66	0.424899
$893$	2.05383e65	0.0828716
$894$	0	0
$895$	−1.09927e66	−0.421780
$896$	3.56547e66	1.33409
$897$	0	0
$898$	−3.92547e66	−1.39693
$899$	2.96993e65	0.103075
$900$	0	0
$901$	−1.33392e66	−0.440375
$902$	3.07659e66	0.990656
$903$	0	0
$904$	7.92573e65	0.242800
$905$	−6.32641e66	−1.89045
$906$	0	0
$907$	−4.19442e66	−1.19264	−0.596319	−	0.802748i	$-0.703370\pi$
$907$	−4.19442e66	−1.19264	−0.596319	+	0.802748i	$0.703370\pi$
$908$	−5.31875e65	−0.147529
$909$	0	0
$910$	−1.10321e66	−0.291223
$911$	−3.79357e66	−0.976979	−0.488489	−	0.872570i	$-0.662452\pi$
$911$	−3.79357e66	−0.976979	−0.488489	+	0.872570i	$0.662452\pi$
$912$	0	0
$913$	−5.08645e65	−0.124687
$914$	8.22681e66	1.96762
$915$	0	0
$916$	4.18136e66	0.952071
$917$	6.44053e65	0.143091
$918$	0	0
$919$	2.48234e66	0.525125	0.262563	−	0.964915i	$-0.415432\pi$
$919$	2.48234e66	0.525125	0.262563	+	0.964915i	$0.415432\pi$
$920$	−2.87628e66	−0.593751
$921$	0	0
$922$	6.36379e66	1.25104
$923$	−8.52513e64	−0.0163555
$924$	0	0
$925$	−1.00092e66	−0.182899
$926$	5.75712e66	1.02673
$927$	0	0
$928$	−4.99208e66	−0.848111
$929$	3.46738e66	0.574974	0.287487	−	0.957784i	$-0.407180\pi$
$929$	3.46738e66	0.574974	0.287487	+	0.957784i	$0.407180\pi$
$930$	0	0
$931$	1.57841e66	0.249374
$932$	−6.72165e66	−1.03662
$933$	0	0
$934$	−1.00052e67	−1.47035
$935$	1.48949e67	2.13686
$936$	0	0
$937$	1.05128e67	1.43740	0.718701	−	0.695319i	$-0.244737\pi$
$937$	1.05128e67	1.43740	0.718701	+	0.695319i	$0.244737\pi$
$938$	−2.39998e67	−3.20364
$939$	0	0
$940$	−1.14782e66	−0.146048
$941$	−2.44367e66	−0.303582	−0.151791	−	0.988413i	$-0.548504\pi$
$941$	−2.44367e66	−0.303582	−0.151791	+	0.988413i	$0.548504\pi$
$942$	0	0
$943$	−3.66928e66	−0.434578
$944$	1.57356e67	1.81976
$945$	0	0
$946$	7.58433e66	0.836309
$947$	−7.28326e66	−0.784244	−0.392122	−	0.919913i	$-0.628259\pi$
$947$	−7.28326e66	−0.784244	−0.392122	+	0.919913i	$0.628259\pi$
$948$	0	0
$949$	1.27357e66	0.130777
$950$	−1.09096e66	−0.109403
$951$	0	0
$952$	8.66651e66	0.828921
$953$	1.42251e66	0.132882	0.0664410	−	0.997790i	$-0.478836\pi$
$953$	1.42251e66	0.132882	0.0664410	+	0.997790i	$0.478836\pi$
$954$	0	0
$955$	6.02196e66	0.536614
$956$	7.86907e66	0.684890
$957$	0	0
$958$	−1.04667e67	−0.869136
$959$	−8.03996e66	−0.652131
$960$	0	0
$961$	−1.27360e67	−0.985728
$962$	1.87863e66	0.142037
$963$	0	0
$964$	−4.99783e66	−0.360619
$965$	−2.83843e67	−2.00085
$966$	0	0
$967$	−8.11376e66	−0.545917	−0.272959	−	0.962026i	$-0.588002\pi$
$967$	−8.11376e66	−0.545917	−0.272959	+	0.962026i	$0.588002\pi$
$968$	1.67221e67	1.09925
$969$	0	0
$970$	−1.25441e67	−0.787182
$971$	−2.08461e67	−1.27818	−0.639090	−	0.769132i	$-0.720689\pi$
$971$	−2.08461e67	−1.27818	−0.639090	+	0.769132i	$0.720689\pi$
$972$	0	0
$973$	−1.37128e67	−0.802761
$974$	−4.03150e66	−0.230616
$975$	0	0
$976$	3.64019e67	1.98839
$977$	−1.98080e66	−0.105734	−0.0528668	−	0.998602i	$-0.516836\pi$
$977$	−1.98080e66	−0.105734	−0.0528668	+	0.998602i	$0.516836\pi$
$978$	0	0
$979$	2.64658e67	1.34919
$980$	−8.82119e66	−0.439482
$981$	0	0
$982$	−3.74995e67	−1.78450
$983$	3.93540e67	1.83035	0.915176	−	0.403055i	$-0.132052\pi$
$983$	3.93540e67	1.83035	0.915176	+	0.403055i	$0.132052\pi$
$984$	0	0
$985$	7.42119e66	0.329730
$986$	−2.74687e67	−1.19291
$987$	0	0
$988$	7.20718e65	0.0299043
$989$	−9.04539e66	−0.366869
$990$	0	0
$991$	−3.91335e67	−1.51667	−0.758336	−	0.651864i	$-0.773987\pi$
$991$	−3.91335e67	−1.51667	−0.758336	+	0.651864i	$0.773987\pi$
$992$	−3.09955e66	−0.117432
$993$	0	0
$994$	−4.61815e66	−0.167215
$995$	1.97132e67	0.697811
$996$	0	0
$997$	−2.80874e67	−0.950323	−0.475161	−	0.879899i	$-0.657610\pi$
$997$	−2.80874e67	−0.950323	−0.475161	+	0.879899i	$0.657610\pi$
$998$	−1.55059e66	−0.0512933
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	9.46.a.b.1.1		3
3.2	odd	2		1.46.a.a.1.3	✓	3
12.11	even	2		16.46.a.c.1.3		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1.46.a.a.1.3	✓	3	3.2	odd	2
9.46.a.b.1.1		3	1.1	even	1	trivial
16.46.a.c.1.3		3	12.11	even	2

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:	\( k \)	\(=\)	\( 46 \)
Character orbit:	\([\chi]\)	\(=\)	9.a (trivial)

\(f(q)\)	\(=\)	\(q-7.36851e6 q^{2} +1.91106e13 q^{4} -5.97253e15 q^{5} -1.35754e19 q^{7} +1.18440e20 q^{8} +O(q^{10})\)	\(q-7.36851e6 q^{2} +1.91106e13 q^{4} -5.97253e15 q^{5} -1.35754e19 q^{7} +1.18440e20 q^{8} +4.40087e22 q^{10} +4.62684e23 q^{11} +1.84657e24 q^{13} +1.00031e26 q^{14} -1.54512e27 q^{16} -5.39007e27 q^{17} +2.04232e28 q^{19} -1.14139e29 q^{20} -3.40930e30 q^{22} +4.06607e30 q^{23} +7.24945e30 q^{25} -1.36065e31 q^{26} -2.59434e32 q^{28} -6.91615e32 q^{29} -4.29419e32 q^{31} +7.21801e33 q^{32} +3.97168e34 q^{34} +8.10796e34 q^{35} -1.38069e35 q^{37} -1.50489e35 q^{38} -7.07385e35 q^{40} -9.02413e35 q^{41} -2.22460e36 q^{43} +8.84218e36 q^{44} -2.99609e37 q^{46} +1.00563e37 q^{47} +7.72848e37 q^{49} -5.34177e37 q^{50} +3.52891e37 q^{52} +2.47477e38 q^{53} -2.76340e39 q^{55} -1.60787e39 q^{56} +5.09618e39 q^{58} -1.01841e40 q^{59} -2.35593e40 q^{61} +3.16418e39 q^{62} +1.17807e39 q^{64} -1.10287e40 q^{65} -2.39925e41 q^{67} -1.03008e41 q^{68} -5.97436e41 q^{70} -4.61674e40 q^{71} +6.89694e41 q^{73} +1.01736e42 q^{74} +3.90301e41 q^{76} -6.28113e42 q^{77} -1.80775e42 q^{79} +9.22828e42 q^{80} +6.64944e42 q^{82} -1.09933e42 q^{83} +3.21924e43 q^{85} +1.63920e43 q^{86} +5.48002e43 q^{88} +5.72005e43 q^{89} -2.50680e43 q^{91} +7.77051e43 q^{92} -7.41002e43 q^{94} -1.21978e44 q^{95} -2.85037e44 q^{97} -5.69474e44 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q - 3814272 q^{2} - 1915164893184 q^{4} + 912448458460350 q^{5} - 76\!\cdots\!08 q^{7}+ \cdots + 10\!\cdots\!60 q^{8}+O(q^{10}) \) 3 * q - 3814272 * q^2 - 1915164893184 * q^4 + 912448458460350 * q^5 - 7619710926638056008 * q^7 + 108947667758662287360 * q^8	\( 3 q - 3814272 q^{2} - 1915164893184 q^{4} + 912448458460350 q^{5} - 76\!\cdots\!08 q^{7}+ \cdots - 19\!\cdots\!04 q^{98}+O(q^{100}) \) 3 * q - 3814272 * q^2 - 1915164893184 * q^4 + 912448458460350 * q^5 - 7619710926638056008 * q^7 + 108947667758662287360 * q^8 + 1419132609182896876800 * q^10 + 292602117773160656797644 * q^11 - 24359353574857845965202054 * q^13 + 202717255077168503234024448 * q^14 - 2516639057595474468963090432 * q^16 - 1167342337360426664689201782 * q^17 + 139928385765722236845372310380 * q^19 - 381381185200730248341345484800 * q^20 - 3645081261141863565639576301056 * q^22 + 10673923189590823281275419815384 * q^23 + 43966129876780298643382415638125 * q^25 - 109857986164645419011108420802816 * q^26 + 5309187993026577435829326249984 * q^28 + 670860386246579691273176792023830 * q^29 - 4362750588615761992088215111558944 * q^31 - 2770584927822325193163626168451072 * q^32 + 53874322809182721932452359249215232 * q^34 - 15776204147695493575553971787662800 * q^35 - 389811033762613666259144433874550238 * q^37 + 298309080939187021552909089031242240 * q^38 + 1418999553421731071561941465300992000 * q^40 - 2715552056267791317916826925062933406 * q^41 + 1244478438653295151469201253707220756 * q^43 + 10866498414076105454653552938468999168 * q^44 - 29420915174298432781096019434857298944 * q^46 + 5368746178058366301880916464880208048 * q^47 + 78160841959900415140960388420190127371 * q^49 - 365636939507033508238037233476615120000 * q^50 + 134213023925843531561035140325636718592 * q^52 + 1852254617049027724838330153197946097774 * q^53 - 3433604438201040460840734686798586808200 * q^55 - 5263223929490768485344096600823148052480 * q^56 + 13570181249555445898814714558437144899840 * q^58 + 3587009869064273690797416085301514120060 * q^59 - 51762384161673790814764907347052617635894 * q^61 + 5676710491956141755174145478721599328256 * q^62 + 41050065173647728685920731234203689025536 * q^64 - 37939089079008549181090608539522846859900 * q^65 + 14148137855196379836825399018252188940732 * q^67 - 123753416143995711246382651604664796299264 * q^68 - 615758273709518152674920733006194538854400 * q^70 + 125388248998914140052658001286881482385544 * q^71 + 545662435246745842274304841909717562787966 * q^73 + 922589101552630918194661534146849410212608 * q^74 - 25740309904677479085695622290576752803840 * q^76 - 6645319565466313145724427222526529624900384 * q^77 + 906179897072215837642402032445458679683120 * q^79 + 16837014550545085717858942703269209282969600 * q^80 - 7077813252702994823298504428501096216345856 * q^82 - 1486742880234689875145309838364765216168236 * q^83 + 38251451691354483777201487197950382555147300 * q^85 - 49387084957597704283946327082198769274651136 * q^86 + 52989682432050008057661862219403039374049280 * q^88 + 157452314112877728949303270670086721758716690 * q^89 - 209450940191589584493053736413801309667114864 * q^91 - 31580552157061127996902171853509709970604032 * q^92 + 380017168558424107350771392050931198759503872 * q^94 - 11835463674693195649110972576862856536029000 * q^95 + 371229894708856356492851438771649466869172902 * q^97 - 19381455993535436564386424979420682870187904 * q^98

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