LMFDB - Embedded newform 9.56.a.a.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [9,56,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, 56, names="a")

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

chi := DirichletCharacter("9.1");

S:= CuspForms(chi, 56);

N := Newforms(S);

Level:	$ N $	$=$	$ 9 = 3^{2} $
Weight:	$ k $	$=$	$ 56 $
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:	$172.423320917$
Analytic rank:	$1$
Dimension:	$4$
Coefficient field:	$\mathbb{Q}[x]/(x^{4} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} - 149272663100531x^{2} + 190291401428579434725x + 325546600176957146615614350 $ x^4 - x^3 - 149272663100531x^2 + 190291401428579434725x + 325546600176957146615614350
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{20}\cdot 3^{11}\cdot 5^{2}\cdot 7\cdot 11 $
Twist minimal:	no (minimal twist has level 1)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$1.14055e7$ 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)

$f(q)$	$=$	$q-3.25888e8 q^{2} +7.01743e16 q^{4} -2.73659e19 q^{5} -1.10303e23 q^{7} -1.11276e25 q^{8} +O(q^{10})$	\(q-3.25888e8 q^{2} +7.01743e16 q^{4} -2.73659e19 q^{5} -1.10303e23 q^{7} -1.11276e25 q^{8} +8.91821e27 q^{10} -4.91412e28 q^{11} -5.50498e30 q^{13} +3.59464e31 q^{14} +1.09807e33 q^{16} -6.74131e33 q^{17} +4.63069e34 q^{19} -1.92038e36 q^{20} +1.60146e37 q^{22} +2.33537e37 q^{23} +4.71335e38 q^{25} +1.79401e39 q^{26} -7.74043e39 q^{28} -8.29368e39 q^{29} -2.22670e40 q^{31} +4.30685e40 q^{32} +2.19691e42 q^{34} +3.01853e42 q^{35} -8.62039e42 q^{37} -1.50909e43 q^{38} +3.04517e44 q^{40} +1.28503e44 q^{41} -7.80265e44 q^{43} -3.44845e45 q^{44} -7.61071e45 q^{46} -2.24956e45 q^{47} -1.80601e46 q^{49} -1.53602e47 q^{50} -3.86308e47 q^{52} -6.54418e46 q^{53} +1.34479e48 q^{55} +1.22741e48 q^{56} +2.70281e48 q^{58} +4.81860e48 q^{59} -1.00856e48 q^{61} +7.25655e48 q^{62} -5.35975e49 q^{64} +1.50648e50 q^{65} +2.13547e50 q^{67} -4.73067e50 q^{68} -9.83705e50 q^{70} -9.56825e50 q^{71} +1.10863e51 q^{73} +2.80928e51 q^{74} +3.24956e51 q^{76} +5.42042e51 q^{77} +2.07492e52 q^{79} -3.00495e52 q^{80} -4.18778e52 q^{82} +1.06353e53 q^{83} +1.84482e53 q^{85} +2.54279e53 q^{86} +5.46825e53 q^{88} -7.48693e53 q^{89} +6.07215e53 q^{91} +1.63883e54 q^{92} +7.33106e53 q^{94} -1.26723e54 q^{95} -5.59692e53 q^{97} +5.88557e54 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 208622520 q^{2} + 38\!\cdots\!72 q^{4}+ \cdots - 45\!\cdots\!40 q^{8}+O(q^{10}) $ 4 * q - 208622520 * q^2 + 38727758778743872 * q^4 - 14396937963387167160 * q^5 - 205529376090660565972000 * q^7 - 4549274472651430619082240 * q^8	$ 4 q - 208622520 q^{2} + 38\!\cdots\!72 q^{4}+ \cdots - 43\!\cdots\!60 q^{98}+O(q^{100}) $ 4 * q - 208622520 * q^2 + 38727758778743872 * q^4 - 14396937963387167160 * q^5 - 205529376090660565972000 * q^7 - 4549274472651430619082240 * q^8 + 4648305821937663379975180560 * q^10 - 19492148713537948248062043408 * q^11 - 4449970852951030370486873382760 * q^13 + 28356223847864660359303625873856 * q^14 + 972748533533952319807553436258304 * q^16 - 8593971071724377583839140954773960 * q^17 + 339485321922051504109099704484079600 * q^19 - 2938981710383707492522432611899614080 * q^20 + 38006076575943531891094535037919254240 * q^22 - 49808560358713761517710452453445612960 * q^23 + 35720819629535961214417161732721803100 * q^25 + 2942801473325677064443328059884451887792 * q^26 - 14225688489857344137508473549032747368960 * q^28 + 18313921252535508838816178753292620581800 * q^29 + 228069689399145752868860523834729264526208 * q^31 - 633346612507316231430506989727883716689920 * q^32 + 896637942332031893460273084285964132034544 * q^34 + 4819663438502339394117495448236020975855040 * q^35 - 32137889117062584203203089731106089299166920 * q^37 + 4952027966320588944657713384757782381142240 * q^38 + 423453117316016459693780561000308646880691200 * q^40 - 246756563007211451240604479433521241061314408 * q^41 - 860266067148440101585711757682636198922476400 * q^43 + 486680632760661386186662626683912868907405056 * q^44 - 12358385464441662606619414449724307588901916992 * q^46 - 4275321492760062770492681289130578251551314240 * q^47 + 51896265177052512954332052101694146860214382372 * q^49 - 174698296445912937700335126041507926720149534600 * q^50 - 262201419493851260177411503538061050352769552000 * q^52 + 488469552022263686716757080744643106633189705480 * q^53 - 127591926326749967084952696035933816282025595680 * q^55 + 298136165704261759300184058675155027135738572800 * q^56 + 6079853356051584053436052229523762232408341938640 * q^58 - 8189687634125713603536212764174920044680103250000 * q^59 + 7023917261975601941077275556050474243839244469208 * q^61 + 30522733021551585983790682957575295692580599279360 * q^62 - 98185742120493275625308720675268779449265392713728 * q^64 + 96029582501479027321081622269423947602394832060080 * q^65 + 418567852430847740316243536772383918093566302547760 * q^67 - 627327947371921816104248533416688222149537051169920 * q^68 - 471522968288511321788110491009215619195633708224640 * q^70 - 997985577607888605538672501225224229003742837277408 * q^71 - 898993596628095916013292323795403905388680301942040 * q^73 + 7967044320232055682477818350544716808849477162563056 * q^74 - 60907940015267454915614913374117951647840510009600 * q^76 - 14299054939611075432133092801777785333545282382563200 * q^77 + 48721021140002244303635330301073120621076057627153600 * q^79 + 3558308494035098045228661758379879929555981454090240 * q^80 - 164154584875013842045822252535546173951453621276929360 * q^82 + 71840759606517399895238320212650236559070020961691920 * q^83 + 248899912487828257920888533066500872415304578192331760 * q^85 + 390961799675414150209662123589235297185712905683496992 * q^86 + 263660200754753376218335161392938332564087458967828480 * q^88 - 1567987214275383302209606514592359147814765036271890600 * q^89 + 1660326344231373069708515805926098978407334056523187008 * q^91 + 2737928811190126698927829997086921657569438136581219840 * q^92 - 4092215382133552783473757354682502518415689822573629056 * q^94 - 90834332415616009306267157723570331064559482078144800 * q^95 + 5113732531532480760212291157301231295251404057238280840 * q^97 - 4361266856004358769699597237924757031028912315048682360 * 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 $

$2$	−3.25888e8	−1.71690	−0.858448	−	0.512901i	$-0.828571\pi$
$2$	−3.25888e8	−1.71690	−0.858448	+	0.512901i	$0.828571\pi$
$3$	0	0
$3$	0	0
$4$	7.01743e16	1.94773
$5$	−2.73659e19	−1.64261	−0.821304	−	0.570490i	$-0.806753\pi$
$5$	−2.73659e19	−1.64261	−0.821304	+	0.570490i	$0.806753\pi$
$6$	0	0
$7$	−1.10303e23	−0.634440	−0.317220	−	0.948352i	$-0.602749\pi$
$7$	−1.10303e23	−0.634440	−0.317220	+	0.948352i	$0.602749\pi$
$8$	−1.11276e25	−1.62715
$9$	0	0
$10$	8.91821e27	2.82019
$11$	−4.91412e28	−1.13018	−0.565090	−	0.825030i	$-0.691158\pi$
$11$	−4.91412e28	−1.13018	−0.565090	+	0.825030i	$0.691158\pi$
$12$	0	0
$13$	−5.50498e30	−1.28030	−0.640152	−	0.768248i	$-0.721129\pi$
$13$	−5.50498e30	−1.28030	−0.640152	+	0.768248i	$0.721129\pi$
$14$	3.59464e31	1.08927
$15$	0	0
$16$	1.09807e33	0.845919
$17$	−6.74131e33	−0.980390	−0.490195	−	0.871613i	$-0.663074\pi$
$17$	−6.74131e33	−0.980390	−0.490195	+	0.871613i	$0.663074\pi$
$18$	0	0
$19$	4.63069e34	0.316171	0.158085	−	0.987425i	$-0.449468\pi$
$19$	4.63069e34	0.316171	0.158085	+	0.987425i	$0.449468\pi$
$20$	−1.92038e36	−3.19936
$21$	0	0
$22$	1.60146e37	1.94040
$23$	2.33537e37	0.833376	0.416688	−	0.909050i	$-0.363191\pi$
$23$	2.33537e37	0.833376	0.416688	+	0.909050i	$0.363191\pi$
$24$	0	0
$25$	4.71335e38	1.69816
$26$	1.79401e39	2.19815
$27$	0	0
$28$	−7.74043e39	−1.23572
$29$	−8.29368e39	−0.504431	−0.252216	−	0.967671i	$-0.581159\pi$
$29$	−8.29368e39	−0.504431	−0.252216	+	0.967671i	$0.581159\pi$
$30$	0	0
$31$	−2.22670e40	−0.216379	−0.108189	−	0.994130i	$-0.534505\pi$
$31$	−2.22670e40	−0.216379	−0.108189	+	0.994130i	$0.534505\pi$
$32$	4.30685e40	0.174797
$33$	0	0
$34$	2.19691e42	1.68323
$35$	3.01853e42	1.04214
$36$	0	0
$37$	−8.62039e42	−0.645624	−0.322812	−	0.946463i	$-0.604628\pi$
$37$	−8.62039e42	−0.645624	−0.322812	+	0.946463i	$0.604628\pi$
$38$	−1.50909e43	−0.542832
$39$	0	0
$40$	3.04517e44	2.67277
$41$	1.28503e44	0.571951	0.285975	−	0.958237i	$-0.407682\pi$
$41$	1.28503e44	0.571951	0.285975	+	0.958237i	$0.407682\pi$
$42$	0	0
$43$	−7.80265e44	−0.937259	−0.468629	−	0.883395i	$-0.655252\pi$
$43$	−7.80265e44	−0.937259	−0.468629	+	0.883395i	$0.655252\pi$
$44$	−3.44845e45	−2.20128
$45$	0	0
$46$	−7.61071e45	−1.43082
$47$	−2.24956e45	−0.234103	−0.117052	−	0.993126i	$-0.537344\pi$
$47$	−2.24956e45	−0.234103	−0.117052	+	0.993126i	$0.537344\pi$
$48$	0	0
$49$	−1.80601e46	−0.597486
$50$	−1.53602e47	−2.91557
$51$	0	0
$52$	−3.86308e47	−2.49369
$53$	−6.54418e46	−0.250189	−0.125095	−	0.992145i	$-0.539923\pi$
$53$	−6.54418e46	−0.250189	−0.125095	+	0.992145i	$0.539923\pi$
$54$	0	0
$55$	1.34479e48	1.85644
$56$	1.22741e48	1.03233
$57$	0	0
$58$	2.70281e48	0.866056
$59$	4.81860e48	0.964918	0.482459	−	0.875918i	$-0.339744\pi$
$59$	4.81860e48	0.964918	0.482459	+	0.875918i	$0.339744\pi$
$60$	0	0
$61$	−1.00856e48	−0.0807480	−0.0403740	−	0.999185i	$-0.512855\pi$
$61$	−1.00856e48	−0.0807480	−0.0403740	+	0.999185i	$0.512855\pi$
$62$	7.25655e48	0.371500
$63$	0	0
$64$	−5.35975e49	−1.14603
$65$	1.50648e50	2.10304
$66$	0	0
$67$	2.13547e50	1.29550	0.647749	−	0.761854i	$-0.275711\pi$
$67$	2.13547e50	1.29550	0.647749	+	0.761854i	$0.275711\pi$
$68$	−4.73067e50	−1.90953
$69$	0	0
$70$	−9.83705e50	−1.78924
$71$	−9.56825e50	−1.17822	−0.589112	−	0.808051i	$-0.700522\pi$
$71$	−9.56825e50	−1.17822	−0.589112	+	0.808051i	$0.700522\pi$
$72$	0	0
$73$	1.10863e51	0.635926	0.317963	−	0.948103i	$-0.397001\pi$
$73$	1.10863e51	0.635926	0.317963	+	0.948103i	$0.397001\pi$
$74$	2.80928e51	1.10847
$75$	0	0
$76$	3.24956e51	0.615815
$77$	5.42042e51	0.717031
$78$	0	0
$79$	2.07492e52	1.35599	0.677995	−	0.735067i	$-0.262849\pi$
$79$	2.07492e52	1.35599	0.677995	+	0.735067i	$0.262849\pi$
$80$	−3.00495e52	−1.38951
$81$	0	0
$82$	−4.18778e52	−0.981980
$83$	1.06353e53	1.78691	0.893456	−	0.449150i	$-0.148273\pi$
$83$	1.06353e53	1.78691	0.893456	+	0.449150i	$0.148273\pi$
$84$	0	0
$85$	1.84482e53	1.61040
$86$	2.54279e53	1.60917
$87$	0	0
$88$	5.46825e53	1.83897
$89$	−7.48693e53	−1.84535	−0.922675	−	0.385578i	$-0.874002\pi$
$89$	−7.48693e53	−1.84535	−0.922675	+	0.385578i	$0.874002\pi$
$90$	0	0
$91$	6.07215e53	0.812277
$92$	1.63883e54	1.62319
$93$	0	0
$94$	7.33106e53	0.401931
$95$	−1.26723e54	−0.519345
$96$	0	0
$97$	−5.59692e53	−0.129338	−0.0646691	−	0.997907i	$-0.520599\pi$
$97$	−5.59692e53	−0.129338	−0.0646691	+	0.997907i	$0.520599\pi$
$98$	5.88557e54	1.02582
$99$	0	0
$100$	3.30756e55	3.30756
$101$	1.15529e55	0.878729	0.439364	−	0.898309i	$-0.355204\pi$
$101$	1.15529e55	0.878729	0.439364	+	0.898309i	$0.355204\pi$
$102$	0	0
$103$	1.27447e55	0.565335	0.282667	−	0.959218i	$-0.408781\pi$
$103$	1.27447e55	0.565335	0.282667	+	0.959218i	$0.408781\pi$
$104$	6.12573e55	2.08325
$105$	0	0
$106$	2.13267e55	0.429549
$107$	3.18160e55	0.494984	0.247492	−	0.968890i	$-0.420394\pi$
$107$	3.18160e55	0.494984	0.247492	+	0.968890i	$0.420394\pi$
$108$	0	0
$109$	1.12821e56	1.05478	0.527388	−	0.849625i	$-0.323171\pi$
$109$	1.12821e56	1.05478	0.527388	+	0.849625i	$0.323171\pi$
$110$	−4.38252e56	−3.18732
$111$	0	0
$112$	−1.21120e56	−0.536685
$113$	2.75852e56	0.957238	0.478619	−	0.878023i	$-0.341138\pi$
$113$	2.75852e56	0.957238	0.478619	+	0.878023i	$0.341138\pi$
$114$	0	0
$115$	−6.39095e56	−1.36891
$116$	−5.82003e56	−0.982496
$117$	0	0
$118$	−1.57033e57	−1.65666
$119$	7.43586e56	0.621999
$120$	0	0
$121$	5.24270e56	0.277305
$122$	3.28678e56	0.138636
$123$	0	0
$124$	−1.56257e57	−0.421448
$125$	−5.30294e57	−1.14681
$126$	0	0
$127$	7.27512e57	1.01680	0.508402	−	0.861120i	$-0.330236\pi$
$127$	7.27512e57	1.01680	0.508402	+	0.861120i	$0.330236\pi$
$128$	1.59151e58	1.79281
$129$	0	0
$130$	−4.90946e58	−3.61070
$131$	−3.20710e58	−1.91052	−0.955261	−	0.295764i	$-0.904426\pi$
$131$	−3.20710e58	−1.91052	−0.955261	+	0.295764i	$0.904426\pi$
$132$	0	0
$133$	−5.10779e57	−0.200592
$134$	−6.95925e58	−2.22423
$135$	0	0
$136$	7.50148e58	1.59524
$137$	5.59686e58	0.973036	0.486518	−	0.873671i	$-0.338267\pi$
$137$	5.59686e58	0.973036	0.486518	+	0.873671i	$0.338267\pi$
$138$	0	0
$139$	6.10557e58	0.712556	0.356278	−	0.934380i	$-0.384046\pi$
$139$	6.10557e58	0.712556	0.356278	+	0.934380i	$0.384046\pi$
$140$	2.11824e59	2.02980
$141$	0	0
$142$	3.11818e59	2.02289
$143$	2.70521e59	1.44697
$144$	0	0
$145$	2.26964e59	0.828584
$146$	−3.61289e59	−1.09182
$147$	0	0
$148$	−6.04930e59	−1.25750
$149$	1.00005e59	0.172743	0.0863713	−	0.996263i	$-0.472473\pi$
$149$	1.00005e59	0.172743	0.0863713	+	0.996263i	$0.472473\pi$
$150$	0	0
$151$	8.74454e59	1.04682	0.523409	−	0.852082i	$-0.324660\pi$
$151$	8.74454e59	1.04682	0.523409	+	0.852082i	$0.324660\pi$
$152$	−5.15286e59	−0.514458
$153$	0	0
$154$	−1.76645e60	−1.23107
$155$	6.09356e59	0.355426
$156$	0	0
$157$	−2.34355e60	−0.960802	−0.480401	−	0.877049i	$-0.659509\pi$
$157$	−2.34355e60	−0.960802	−0.480401	+	0.877049i	$0.659509\pi$
$158$	−6.76192e60	−2.32809
$159$	0	0
$160$	−1.17861e60	−0.287124
$161$	−2.57598e60	−0.528727
$162$	0	0
$163$	9.54155e60	1.39463	0.697316	−	0.716763i	$-0.254377\pi$
$163$	9.54155e60	1.39463	0.697316	+	0.716763i	$0.254377\pi$
$164$	9.01764e60	1.11401
$165$	0	0
$166$	−3.46593e61	−3.06794
$167$	6.27360e60	0.470776	0.235388	−	0.971902i	$-0.424364\pi$
$167$	6.27360e60	0.470776	0.235388	+	0.971902i	$0.424364\pi$
$168$	0	0
$169$	1.18170e61	0.639179
$170$	−6.01204e61	−2.76488
$171$	0	0
$172$	−5.47546e61	−1.82553
$173$	−1.23980e61	−0.352439	−0.176219	−	0.984351i	$-0.556387\pi$
$173$	−1.23980e61	−0.352439	−0.176219	+	0.984351i	$0.556387\pi$
$174$	0	0
$175$	−5.19896e61	−1.07738
$176$	−5.39603e61	−0.956040
$177$	0	0
$178$	2.43990e62	3.16827
$179$	6.84198e61	0.761594	0.380797	−	0.924659i	$-0.375650\pi$
$179$	6.84198e61	0.761594	0.380797	+	0.924659i	$0.375650\pi$
$180$	0	0
$181$	−1.10035e61	−0.0902340	−0.0451170	−	0.998982i	$-0.514366\pi$
$181$	−1.10035e61	−0.0902340	−0.0451170	+	0.998982i	$0.514366\pi$
$182$	−1.97884e62	−1.39459
$183$	0	0
$184$	−2.59872e62	−1.35603
$185$	2.35905e62	1.06051
$186$	0	0
$187$	3.31276e62	1.10802
$188$	−1.57862e62	−0.455969
$189$	0	0
$190$	4.12975e62	0.891661
$191$	−7.90077e62	−1.47656	−0.738281	−	0.674493i	$-0.764362\pi$
$191$	−7.90077e62	−1.47656	−0.738281	+	0.674493i	$0.764362\pi$
$192$	0	0
$193$	−9.51922e62	−1.33590	−0.667952	−	0.744204i	$-0.732829\pi$
$193$	−9.51922e62	−1.33590	−0.667952	+	0.744204i	$0.732829\pi$
$194$	1.82397e62	0.222060
$195$	0	0
$196$	−1.26735e63	−1.16374
$197$	−1.86380e63	−1.48791	−0.743956	−	0.668229i	$-0.767053\pi$
$197$	−1.86380e63	−1.48791	−0.743956	+	0.668229i	$0.767053\pi$
$198$	0	0
$199$	−2.70172e62	−0.163373	−0.0816866	−	0.996658i	$-0.526031\pi$
$199$	−2.70172e62	−0.163373	−0.0816866	+	0.996658i	$0.526031\pi$
$200$	−5.24484e63	−2.76317
$201$	0	0
$202$	−3.76497e63	−1.50869
$203$	9.14817e62	0.320032
$204$	0	0
$205$	−3.51661e63	−0.939491
$206$	−4.15335e63	−0.970621
$207$	0	0
$208$	−6.04482e63	−1.08303
$209$	−2.27558e63	−0.357330
$210$	0	0
$211$	3.39112e63	0.409804	0.204902	−	0.978783i	$-0.434312\pi$
$211$	3.39112e63	0.409804	0.204902	+	0.978783i	$0.434312\pi$
$212$	−4.59233e63	−0.487301
$213$	0	0
$214$	−1.03685e64	−0.849836
$215$	2.13526e64	1.53955
$216$	0	0
$217$	2.45611e63	0.137280
$218$	−3.67669e64	−1.81094
$219$	0	0
$220$	9.43699e64	3.61585
$221$	3.71107e64	1.25520
$222$	0	0
$223$	−1.50393e64	−0.397049	−0.198524	−	0.980096i	$-0.563615\pi$
$223$	−1.50393e64	−0.397049	−0.198524	+	0.980096i	$0.563615\pi$
$224$	−4.75058e63	−0.110899
$225$	0	0
$226$	−8.98971e64	−1.64348
$227$	−6.25379e64	−1.01259	−0.506293	−	0.862361i	$-0.668985\pi$
$227$	−6.25379e64	−1.01259	−0.506293	+	0.862361i	$0.668985\pi$
$228$	0	0
$229$	9.72208e64	1.23675	0.618377	−	0.785882i	$-0.287791\pi$
$229$	9.72208e64	1.23675	0.618377	+	0.785882i	$0.287791\pi$
$230$	2.08274e65	2.35028
$231$	0	0
$232$	9.22889e64	0.820786
$233$	−1.58206e65	−1.25007	−0.625037	−	0.780595i	$-0.714916\pi$
$233$	−1.58206e65	−1.25007	−0.625037	+	0.780595i	$0.714916\pi$
$234$	0	0
$235$	6.15613e64	0.384540
$236$	3.38142e65	1.87940
$237$	0	0
$238$	−2.42326e65	−1.06791
$239$	1.73759e65	0.682346	0.341173	−	0.940000i	$-0.389176\pi$
$239$	1.73759e65	0.682346	0.341173	+	0.940000i	$0.389176\pi$
$240$	0	0
$241$	−8.77618e64	−0.274054	−0.137027	−	0.990567i	$-0.543755\pi$
$241$	−8.77618e64	−0.274054	−0.137027	+	0.990567i	$0.543755\pi$
$242$	−1.70854e65	−0.476103
$243$	0	0
$244$	−7.07751e64	−0.157275
$245$	4.94230e65	0.981435
$246$	0	0
$247$	−2.54918e65	−0.404795
$248$	2.47779e65	0.352081
$249$	0	0
$250$	1.72816e66	1.96895
$251$	−6.61756e63	−0.00675570	−0.00337785	−	0.999994i	$-0.501075\pi$
$251$	−6.61756e63	−0.00675570	−0.00337785	+	0.999994i	$0.501075\pi$
$252$	0	0
$253$	−1.14763e66	−0.941864
$254$	−2.37087e66	−1.74575
$255$	0	0
$256$	−3.25548e66	−1.93204
$257$	−2.05584e66	−1.09605	−0.548024	−	0.836463i	$-0.684620\pi$
$257$	−2.05584e66	−1.09605	−0.548024	+	0.836463i	$0.684620\pi$
$258$	0	0
$259$	9.50854e65	0.409610
$260$	1.05717e67	4.09615
$261$	0	0
$262$	1.04516e67	3.28017
$263$	5.76788e66	1.63017	0.815086	−	0.579340i	$-0.196690\pi$
$263$	5.76788e66	1.63017	0.815086	+	0.579340i	$0.196690\pi$
$264$	0	0
$265$	1.79087e66	0.410963
$266$	1.66457e66	0.344395
$267$	0	0
$268$	1.49855e67	2.52328
$269$	−3.84467e66	−0.584348	−0.292174	−	0.956365i	$-0.594379\pi$
$269$	−3.84467e66	−0.584348	−0.292174	+	0.956365i	$0.594379\pi$
$270$	0	0
$271$	−1.55611e67	−1.92923	−0.964615	−	0.263662i	$-0.915070\pi$
$271$	−1.55611e67	−1.92923	−0.964615	+	0.263662i	$0.915070\pi$
$272$	−7.40240e66	−0.829330
$273$	0	0
$274$	−1.82395e67	−1.67060
$275$	−2.31620e67	−1.91923
$276$	0	0
$277$	1.29112e65	0.00876541	0.00438271	−	0.999990i	$-0.498605\pi$
$277$	1.29112e65	0.00876541	0.00438271	+	0.999990i	$0.498605\pi$
$278$	−1.98973e67	−1.22338
$279$	0	0
$280$	−3.35891e67	−1.69571
$281$	4.05496e67	1.85594	0.927968	−	0.372661i	$-0.121554\pi$
$281$	4.05496e67	1.85594	0.927968	+	0.372661i	$0.121554\pi$
$282$	0	0
$283$	4.16122e67	1.56709	0.783545	−	0.621335i	$-0.213409\pi$
$283$	4.16122e67	1.56709	0.783545	+	0.621335i	$0.213409\pi$
$284$	−6.71445e67	−2.29486
$285$	0	0
$286$	−8.81597e67	−2.48430
$287$	−1.41743e67	−0.362869
$288$	0	0
$289$	−1.83619e66	−0.0388353
$290$	−7.39648e67	−1.42259
$291$	0	0
$292$	7.77972e67	1.23861
$293$	7.89264e67	1.14383	0.571917	−	0.820312i	$-0.306200\pi$
$293$	7.89264e67	1.14383	0.571917	+	0.820312i	$0.306200\pi$
$294$	0	0
$295$	−1.31865e68	−1.58498
$296$	9.59245e67	1.05053
$297$	0	0
$298$	−3.25905e67	−0.296581
$299$	−1.28562e68	−1.06697
$300$	0	0
$301$	8.60655e67	0.594635
$302$	−2.84974e68	−1.79728
$303$	0	0
$304$	5.08480e67	0.267455
$305$	2.76002e67	0.132637
$306$	0	0
$307$	1.91003e68	0.766893	0.383446	−	0.923563i	$-0.374737\pi$
$307$	1.91003e68	0.766893	0.383446	+	0.923563i	$0.374737\pi$
$308$	3.80374e68	1.39658
$309$	0	0
$310$	−1.98582e68	−0.610229
$311$	−3.42073e68	−0.962074	−0.481037	−	0.876700i	$-0.659740\pi$
$311$	−3.42073e68	−0.962074	−0.481037	+	0.876700i	$0.659740\pi$
$312$	0	0
$313$	7.31342e66	0.0172445	0.00862227	−	0.999963i	$-0.497255\pi$
$313$	7.31342e66	0.0172445	0.00862227	+	0.999963i	$0.497255\pi$
$314$	7.63735e68	1.64960
$315$	0	0
$316$	1.45606e69	2.64110
$317$	5.41902e68	0.901137	0.450569	−	0.892742i	$-0.351221\pi$
$317$	5.41902e68	0.901137	0.450569	+	0.892742i	$0.351221\pi$
$318$	0	0
$319$	4.07562e68	0.570098
$320$	1.46674e69	1.88247
$321$	0	0
$322$	8.39483e68	0.907769
$323$	−3.12169e68	−0.309971
$324$	0	0
$325$	−2.59469e69	−2.17417
$326$	−3.10948e69	−2.39444
$327$	0	0
$328$	−1.42994e69	−0.930650
$329$	2.48133e68	0.148524
$330$	0	0
$331$	−1.74335e69	−0.883315	−0.441658	−	0.897184i	$-0.645609\pi$
$331$	−1.74335e69	−0.883315	−0.441658	+	0.897184i	$0.645609\pi$
$332$	7.46327e69	3.48042
$333$	0	0
$334$	−2.04449e69	−0.808273
$335$	−5.84390e69	−2.12800
$336$	0	0
$337$	−3.48749e69	−1.07818	−0.539090	−	0.842248i	$-0.681232\pi$
$337$	−3.48749e69	−1.07818	−0.539090	+	0.842248i	$0.681232\pi$
$338$	−3.85102e69	−1.09740
$339$	0	0
$340$	1.29459e70	3.13662
$341$	1.09423e69	0.244547
$342$	0	0
$343$	5.32618e69	1.01351
$344$	8.68249e69	1.52506
$345$	0	0
$346$	4.04036e69	0.605101
$347$	3.19386e69	0.441830	0.220915	−	0.975293i	$-0.429096\pi$
$347$	3.19386e69	0.441830	0.220915	+	0.975293i	$0.429096\pi$
$348$	0	0
$349$	−1.03259e70	−1.21963	−0.609813	−	0.792545i	$-0.708755\pi$
$349$	−1.03259e70	−1.21963	−0.609813	+	0.792545i	$0.708755\pi$
$350$	1.69428e70	1.84975
$351$	0	0
$352$	−2.11644e69	−0.197552
$353$	6.47303e69	0.558860	0.279430	−	0.960166i	$-0.409855\pi$
$353$	6.47303e69	0.558860	0.279430	+	0.960166i	$0.409855\pi$
$354$	0	0
$355$	2.61843e70	1.93536
$356$	−5.25391e70	−3.59424
$357$	0	0
$358$	−2.22972e70	−1.30758
$359$	−1.06064e70	−0.576063	−0.288031	−	0.957621i	$-0.593001\pi$
$359$	−1.06064e70	−0.576063	−0.288031	+	0.957621i	$0.593001\pi$
$360$	0	0
$361$	−1.93067e70	−0.900036
$362$	3.58591e69	0.154922
$363$	0	0
$364$	4.26109e70	1.58209
$365$	−3.03385e70	−1.04458
$366$	0	0
$367$	5.03481e69	0.149165	0.0745824	−	0.997215i	$-0.476238\pi$
$367$	5.03481e69	0.149165	0.0745824	+	0.997215i	$0.476238\pi$
$368$	2.56439e70	0.704968
$369$	0	0
$370$	−7.68785e70	−1.82078
$371$	7.21842e69	0.158730
$372$	0	0
$373$	−9.67049e70	−1.83424	−0.917119	−	0.398613i	$-0.869492\pi$
$373$	−9.67049e70	−1.83424	−0.917119	+	0.398613i	$0.869492\pi$
$374$	−1.07959e71	−1.90235
$375$	0	0
$376$	2.50323e70	0.380921
$377$	4.56565e70	0.645826
$378$	0	0
$379$	−1.49089e71	−1.82333	−0.911667	−	0.410930i	$-0.865204\pi$
$379$	−1.49089e71	−1.82333	−0.911667	+	0.410930i	$0.865204\pi$
$380$	−8.89269e70	−1.01154
$381$	0	0
$382$	2.57477e71	2.53510
$383$	−1.32996e71	−1.21863	−0.609317	−	0.792927i	$-0.708556\pi$
$383$	−1.32996e71	−1.21863	−0.609317	+	0.792927i	$0.708556\pi$
$384$	0	0
$385$	−1.48335e71	−1.17780
$386$	3.10220e71	2.29361
$387$	0	0
$388$	−3.92760e70	−0.251916
$389$	−1.84119e70	−0.110023	−0.0550115	−	0.998486i	$-0.517520\pi$
$389$	−1.84119e70	−0.110023	−0.0550115	+	0.998486i	$0.517520\pi$
$390$	0	0
$391$	−1.57435e71	−0.817033
$392$	2.00966e71	0.972199
$393$	0	0
$394$	6.07389e71	2.55459
$395$	−5.67820e71	−2.22736
$396$	0	0
$397$	2.35772e70	0.0804922	0.0402461	−	0.999190i	$-0.487186\pi$
$397$	2.35772e70	0.0804922	0.0402461	+	0.999190i	$0.487186\pi$
$398$	8.80459e70	0.280495
$399$	0	0
$400$	5.17556e71	1.43651
$401$	5.55389e71	1.43922	0.719610	−	0.694378i	$-0.244321\pi$
$401$	5.55389e71	1.43922	0.719610	+	0.694378i	$0.244321\pi$
$402$	0	0
$403$	1.22579e71	0.277031
$404$	8.10720e71	1.71153
$405$	0	0
$406$	−2.98128e71	−0.549461
$407$	4.23617e71	0.729671
$408$	0	0
$409$	5.98705e71	0.901201	0.450600	−	0.892726i	$-0.351210\pi$
$409$	5.98705e71	0.901201	0.450600	+	0.892726i	$0.351210\pi$
$410$	1.14602e72	1.61301
$411$	0	0
$412$	8.94350e71	1.10112
$413$	−5.31506e71	−0.612183
$414$	0	0
$415$	−2.91045e72	−2.93520
$416$	−2.37091e71	−0.223794
$417$	0	0
$418$	7.41584e71	0.613498
$419$	−1.73387e71	−0.134317	−0.0671585	−	0.997742i	$-0.521393\pi$
$419$	−1.73387e71	−0.134317	−0.0671585	+	0.997742i	$0.521393\pi$
$420$	0	0
$421$	6.27129e71	0.426186	0.213093	−	0.977032i	$-0.431646\pi$
$421$	6.27129e71	0.426186	0.213093	+	0.977032i	$0.431646\pi$
$422$	−1.10513e72	−0.703590
$423$	0	0
$424$	7.28212e71	0.407096
$425$	−3.17741e72	−1.66486
$426$	0	0
$427$	1.11247e71	0.0512298
$428$	2.23267e72	0.964095
$429$	0	0
$430$	−6.95857e72	−2.64324
$431$	−3.86872e71	−0.137861	−0.0689306	−	0.997621i	$-0.521959\pi$
$431$	−3.86872e71	−0.137861	−0.0689306	+	0.997621i	$0.521959\pi$
$432$	0	0
$433$	−3.85260e72	−1.20875	−0.604376	−	0.796699i	$-0.706578\pi$
$433$	−3.85260e72	−1.20875	−0.604376	+	0.796699i	$0.706578\pi$
$434$	−8.00419e71	−0.235695
$435$	0	0
$436$	7.91712e72	2.05442
$437$	1.08144e72	0.263489
$438$	0	0
$439$	−7.04112e71	−0.151310	−0.0756550	−	0.997134i	$-0.524105\pi$
$439$	−7.04112e71	−0.151310	−0.0756550	+	0.997134i	$0.524105\pi$
$440$	−1.49643e73	−3.02071
$441$	0	0
$442$	−1.20940e73	−2.15504
$443$	1.05429e73	1.76545	0.882727	−	0.469887i	$-0.155705\pi$
$443$	1.05429e73	1.76545	0.882727	+	0.469887i	$0.155705\pi$
$444$	0	0
$445$	2.04886e73	3.03119
$446$	4.90113e72	0.681691
$447$	0	0
$448$	5.91196e72	0.727086
$449$	5.83745e71	0.0675226	0.0337613	−	0.999430i	$-0.489251\pi$
$449$	5.83745e71	0.0675226	0.0337613	+	0.999430i	$0.489251\pi$
$450$	0	0
$451$	−6.31482e72	−0.646407
$452$	1.93578e73	1.86444
$453$	0	0
$454$	2.03804e73	1.73850
$455$	−1.66170e73	−1.33425
$456$	0	0
$457$	−9.08985e72	−0.646936	−0.323468	−	0.946239i	$-0.604849\pi$
$457$	−9.08985e72	−0.646936	−0.323468	+	0.946239i	$0.604849\pi$
$458$	−3.16831e73	−2.12338
$459$	0	0
$460$	−4.48481e73	−2.66627
$461$	−1.94861e73	−1.09131	−0.545656	−	0.838009i	$-0.683719\pi$
$461$	−1.94861e73	−1.09131	−0.545656	+	0.838009i	$0.683719\pi$
$462$	0	0
$463$	−5.72642e72	−0.284712	−0.142356	−	0.989816i	$-0.545468\pi$
$463$	−5.72642e72	−0.284712	−0.142356	+	0.989816i	$0.545468\pi$
$464$	−9.10700e72	−0.426708
$465$	0	0
$466$	5.15575e73	2.14624
$467$	2.64935e73	1.03974	0.519871	−	0.854245i	$-0.325980\pi$
$467$	2.64935e73	1.03974	0.519871	+	0.854245i	$0.325980\pi$
$468$	0	0
$469$	−2.35549e73	−0.821916
$470$	−2.00621e73	−0.660215
$471$	0	0
$472$	−5.36196e73	−1.57007
$473$	3.83432e73	1.05927
$474$	0	0
$475$	2.18261e73	0.536910
$476$	5.21806e73	1.21149
$477$	0	0
$478$	−5.66260e73	−1.17152
$479$	−2.29697e73	−0.448672	−0.224336	−	0.974512i	$-0.572021\pi$
$479$	−2.29697e73	−0.448672	−0.224336	+	0.974512i	$0.572021\pi$
$480$	0	0
$481$	4.74551e73	0.826595
$482$	2.86005e73	0.470523
$483$	0	0
$484$	3.67903e73	0.540115
$485$	1.53165e73	0.212452
$486$	0	0
$487$	1.57576e74	1.95184	0.975920	−	0.218128i	$-0.0699951\pi$
$487$	1.57576e74	1.95184	0.975920	+	0.218128i	$0.0699951\pi$
$488$	1.12229e73	0.131389
$489$	0	0
$490$	−1.61064e74	−1.68502
$491$	9.33302e73	0.923168	0.461584	−	0.887096i	$-0.347281\pi$
$491$	9.33302e73	0.923168	0.461584	+	0.887096i	$0.347281\pi$
$492$	0	0
$493$	5.59102e73	0.494540
$494$	8.30749e73	0.694990
$495$	0	0
$496$	−2.44506e73	−0.183039
$497$	1.05541e74	0.747513
$498$	0	0
$499$	2.92720e74	1.85647	0.928235	−	0.371994i	$-0.121326\pi$
$499$	2.92720e74	1.85647	0.928235	+	0.371994i	$0.121326\pi$
$500$	−3.72130e74	−2.23367
$501$	0	0
$502$	2.15658e72	0.0115988
$503$	−1.72201e74	−0.876833	−0.438417	−	0.898772i	$-0.644461\pi$
$503$	−1.72201e74	−0.876833	−0.438417	+	0.898772i	$0.644461\pi$
$504$	0	0
$505$	−3.16156e74	−1.44341
$506$	3.74000e74	1.61708
$507$	0	0
$508$	5.10526e74	1.98046
$509$	3.58739e74	1.31838	0.659188	−	0.751978i	$-0.270900\pi$
$509$	3.58739e74	1.31838	0.659188	+	0.751978i	$0.270900\pi$
$510$	0	0
$511$	−1.22285e74	−0.403457
$512$	4.87523e74	1.52430
$513$	0	0
$514$	6.69975e74	1.88180
$515$	−3.48770e74	−0.928624
$516$	0	0
$517$	1.10546e74	0.264578
$518$	−3.09872e74	−0.703257
$519$	0	0
$520$	−1.67636e75	−3.42196
$521$	2.44717e74	0.473834	0.236917	−	0.971530i	$-0.423863\pi$
$521$	2.44717e74	0.473834	0.236917	+	0.971530i	$0.423863\pi$
$522$	0	0
$523$	4.08574e74	0.711990	0.355995	−	0.934488i	$-0.384142\pi$
$523$	4.08574e74	0.711990	0.355995	+	0.934488i	$0.384142\pi$
$524$	−2.25056e75	−3.72118
$525$	0	0
$526$	−1.87969e75	−2.79883
$527$	1.50109e74	0.212136
$528$	0	0
$529$	−2.39895e74	−0.305485
$530$	−5.83624e74	−0.705580
$531$	0	0
$532$	−3.58435e74	−0.390698
$533$	−7.07408e74	−0.732271
$534$	0	0
$535$	−8.70672e74	−0.813066
$536$	−2.37627e75	−2.10797
$537$	0	0
$538$	1.25293e75	1.00326
$539$	8.87495e74	0.675266
$540$	0	0
$541$	−1.21945e74	−0.0837988	−0.0418994	−	0.999122i	$-0.513341\pi$
$541$	−1.21945e74	−0.0837988	−0.0418994	+	0.999122i	$0.513341\pi$
$542$	5.07117e75	3.31229
$543$	0	0
$544$	−2.90338e74	−0.171370
$545$	−3.08744e75	−1.73258
$546$	0	0
$547$	1.44748e75	0.734446	0.367223	−	0.930133i	$-0.380309\pi$
$547$	1.44748e75	0.734446	0.367223	+	0.930133i	$0.380309\pi$
$548$	3.92756e75	1.89521
$549$	0	0
$550$	7.54822e75	3.29511
$551$	−3.84055e74	−0.159487
$552$	0	0
$553$	−2.28870e75	−0.860295
$554$	−4.20760e73	−0.0150493
$555$	0	0
$556$	4.28454e75	1.38787
$557$	−2.32271e74	−0.0716104	−0.0358052	−	0.999359i	$-0.511400\pi$
$557$	−2.32271e74	−0.0716104	−0.0358052	+	0.999359i	$0.511400\pi$
$558$	0	0
$559$	4.29534e75	1.19998
$560$	3.31455e75	0.881563
$561$	0	0
$562$	−1.32146e76	−3.18645
$563$	2.67933e75	0.615242	0.307621	−	0.951509i	$-0.400467\pi$
$563$	2.67933e75	0.615242	0.307621	+	0.951509i	$0.400467\pi$
$564$	0	0
$565$	−7.54894e75	−1.57237
$566$	−1.35609e76	−2.69053
$567$	0	0
$568$	1.06472e76	1.91715
$569$	−1.95670e75	−0.335688	−0.167844	−	0.985814i	$-0.553681\pi$
$569$	−1.95670e75	−0.335688	−0.167844	+	0.985814i	$0.553681\pi$
$570$	0	0
$571$	−6.00217e75	−0.935008	−0.467504	−	0.883991i	$-0.654847\pi$
$571$	−6.00217e75	−0.935008	−0.467504	+	0.883991i	$0.654847\pi$
$572$	1.89837e76	2.81831
$573$	0	0
$574$	4.61924e75	0.623007
$575$	1.10074e76	1.41521
$576$	0	0
$577$	−1.73805e75	−0.203108	−0.101554	−	0.994830i	$-0.532382\pi$
$577$	−1.73805e75	−0.203108	−0.101554	+	0.994830i	$0.532382\pi$
$578$	5.98393e74	0.0666762
$579$	0	0
$580$	1.59270e76	1.61386
$581$	−1.17311e76	−1.13369
$582$	0	0
$583$	3.21589e75	0.282759
$584$	−1.23364e76	−1.03475
$585$	0	0
$586$	−2.57212e76	−1.96384
$587$	2.45150e75	0.178601	0.0893006	−	0.996005i	$-0.471537\pi$
$587$	2.45150e75	0.178601	0.0893006	+	0.996005i	$0.471537\pi$
$588$	0	0
$589$	−1.03112e75	−0.0684127
$590$	4.29733e76	2.72125
$591$	0	0
$592$	−9.46575e75	−0.546145
$593$	−3.41502e76	−1.88100	−0.940500	−	0.339794i	$-0.889643\pi$
$593$	−3.41502e76	−1.88100	−0.940500	+	0.339794i	$0.889643\pi$
$594$	0	0
$595$	−2.03489e76	−1.02170
$596$	7.01779e75	0.336456
$597$	0	0
$598$	4.18968e76	1.83188
$599$	−4.74508e75	−0.198155	−0.0990777	−	0.995080i	$-0.531589\pi$
$599$	−4.74508e75	−0.198155	−0.0990777	+	0.995080i	$0.531589\pi$
$600$	0	0
$601$	−3.25978e76	−1.24205	−0.621027	−	0.783789i	$-0.713284\pi$
$601$	−3.25978e76	−1.24205	−0.621027	+	0.783789i	$0.713284\pi$
$602$	−2.80477e76	−1.02093
$603$	0	0
$604$	6.13642e76	2.03892
$605$	−1.43471e76	−0.455503
$606$	0	0
$607$	2.76963e76	0.803031	0.401515	−	0.915852i	$-0.368484\pi$
$607$	2.76963e76	0.803031	0.401515	+	0.915852i	$0.368484\pi$
$608$	1.99437e75	0.0552658
$609$	0	0
$610$	−8.99457e75	−0.227724
$611$	1.23838e76	0.299723
$612$	0	0
$613$	−7.08667e76	−1.56776	−0.783879	−	0.620913i	$-0.786762\pi$
$613$	−7.08667e76	−1.56776	−0.783879	+	0.620913i	$0.786762\pi$
$614$	−6.22456e76	−1.31667
$615$	0	0
$616$	−6.03164e76	−1.16672
$617$	5.00063e75	0.0925087	0.0462543	−	0.998930i	$-0.485272\pi$
$617$	5.00063e75	0.0925087	0.0462543	+	0.998930i	$0.485272\pi$
$618$	0	0
$619$	1.09383e77	1.85121	0.925604	−	0.378494i	$-0.123558\pi$
$619$	1.09383e77	1.85121	0.925604	+	0.378494i	$0.123558\pi$
$620$	4.27611e76	0.692273
$621$	0	0
$622$	1.11478e77	1.65178
$623$	8.25830e76	1.17076
$624$	0	0
$625$	1.42977e76	0.185595
$626$	−2.38336e75	−0.0296070
$627$	0	0
$628$	−1.64457e77	−1.87138
$629$	5.81127e76	0.632963
$630$	0	0
$631$	−6.03396e76	−0.602276	−0.301138	−	0.953581i	$-0.597366\pi$
$631$	−6.03396e76	−0.602276	−0.301138	+	0.953581i	$0.597366\pi$
$632$	−2.30889e77	−2.20640
$633$	0	0
$634$	−1.76599e77	−1.54716
$635$	−1.99090e77	−1.67021
$636$	0	0
$637$	9.94203e76	0.764963
$638$	−1.32820e77	−0.978798
$639$	0	0
$640$	−4.35530e77	−2.94489
$641$	1.24358e77	0.805522	0.402761	−	0.915305i	$-0.368051\pi$
$641$	1.24358e77	0.805522	0.402761	+	0.915305i	$0.368051\pi$
$642$	0	0
$643$	1.52782e77	0.908385	0.454192	−	0.890904i	$-0.349928\pi$
$643$	1.52782e77	0.908385	0.454192	+	0.890904i	$0.349928\pi$
$644$	−1.80768e77	−1.02982
$645$	0	0
$646$	1.01732e77	0.532187
$647$	8.10455e76	0.406313	0.203157	−	0.979146i	$-0.434880\pi$
$647$	8.10455e76	0.406313	0.203157	+	0.979146i	$0.434880\pi$
$648$	0	0
$649$	−2.36792e77	−1.09053
$650$	8.45578e77	3.73281
$651$	0	0
$652$	6.69572e77	2.71637
$653$	−2.22340e77	−0.864778	−0.432389	−	0.901687i	$-0.642329\pi$
$653$	−2.22340e77	−0.864778	−0.432389	+	0.901687i	$0.642329\pi$
$654$	0	0
$655$	8.77651e77	3.13824
$656$	1.41105e77	0.483824
$657$	0	0
$658$	−8.08637e76	−0.255001
$659$	−1.77062e77	−0.535520	−0.267760	−	0.963486i	$-0.586283\pi$
$659$	−1.77062e77	−0.535520	−0.267760	+	0.963486i	$0.586283\pi$
$660$	0	0
$661$	−3.47431e77	−0.966782	−0.483391	−	0.875405i	$-0.660595\pi$
$661$	−3.47431e77	−0.966782	−0.483391	+	0.875405i	$0.660595\pi$
$662$	5.68138e77	1.51656
$663$	0	0
$664$	−1.18346e78	−2.90758
$665$	1.39779e77	0.329493
$666$	0	0
$667$	−1.93688e77	−0.420381
$668$	4.40246e77	0.916943
$669$	0	0
$670$	1.90446e78	3.65355
$671$	4.95620e76	0.0912597
$672$	0	0
$673$	3.53476e77	0.599716	0.299858	−	0.953984i	$-0.403061\pi$
$673$	3.53476e77	0.599716	0.299858	+	0.953984i	$0.403061\pi$
$674$	1.13653e78	1.85112
$675$	0	0
$676$	8.29250e77	1.24495
$677$	−3.06962e77	−0.442482	−0.221241	−	0.975219i	$-0.571011\pi$
$677$	−3.06962e77	−0.442482	−0.221241	+	0.975219i	$0.571011\pi$
$678$	0	0
$679$	6.17357e76	0.0820573
$680$	−2.05284e78	−2.62036
$681$	0	0
$682$	−3.56596e77	−0.419862
$683$	6.23098e77	0.704672	0.352336	−	0.935874i	$-0.385388\pi$
$683$	6.23098e77	0.704672	0.352336	+	0.935874i	$0.385388\pi$
$684$	0	0
$685$	−1.53163e78	−1.59832
$686$	−1.73574e78	−1.74009
$687$	0	0
$688$	−8.56782e77	−0.792845
$689$	3.60255e77	0.320318
$690$	0	0
$691$	5.11269e77	0.419762	0.209881	−	0.977727i	$-0.432692\pi$
$691$	5.11269e77	0.419762	0.209881	+	0.977727i	$0.432692\pi$
$692$	−8.70021e77	−0.686455
$693$	0	0
$694$	−1.04084e78	−0.758575
$695$	−1.67084e78	−1.17045
$696$	0	0
$697$	−8.66282e77	−0.560735
$698$	3.36507e78	2.09397
$699$	0	0
$700$	−3.64834e78	−2.09845
$701$	−1.90874e78	−1.05561	−0.527804	−	0.849366i	$-0.676984\pi$
$701$	−1.90874e78	−1.05561	−0.527804	+	0.849366i	$0.676984\pi$
$702$	0	0
$703$	−3.99184e77	−0.204127
$704$	2.63385e78	1.29522
$705$	0	0
$706$	−2.10948e78	−0.959504
$707$	−1.27432e78	−0.557501
$708$	0	0
$709$	3.69220e78	1.49456	0.747280	−	0.664509i	$-0.231359\pi$
$709$	3.69220e78	1.49456	0.747280	+	0.664509i	$0.231359\pi$
$710$	−8.53317e78	−3.32281
$711$	0	0
$712$	8.33118e78	3.00266
$713$	−5.20018e77	−0.180325
$714$	0	0
$715$	−7.40305e78	−2.37681
$716$	4.80131e78	1.48338
$717$	0	0
$718$	3.45649e78	0.989039
$719$	8.48236e77	0.233600	0.116800	−	0.993155i	$-0.462736\pi$
$719$	8.48236e77	0.233600	0.116800	+	0.993155i	$0.462736\pi$
$720$	0	0
$721$	−1.40578e78	−0.358671
$722$	6.29182e78	1.54527
$723$	0	0
$724$	−7.72163e77	−0.175751
$725$	−3.90910e78	−0.856607
$726$	0	0
$727$	−1.05653e78	−0.214628	−0.107314	−	0.994225i	$-0.534225\pi$
$727$	−1.05653e78	−0.214628	−0.107314	+	0.994225i	$0.534225\pi$
$728$	−6.75686e78	−1.32170
$729$	0	0
$730$	9.88697e78	1.79343
$731$	5.26001e78	0.918879
$732$	0	0
$733$	7.22141e77	0.117021	0.0585104	−	0.998287i	$-0.481365\pi$
$733$	7.22141e77	0.117021	0.0585104	+	0.998287i	$0.481365\pi$
$734$	−1.64079e78	−0.256100
$735$	0	0
$736$	1.00581e78	0.145672
$737$	−1.04940e79	−1.46415
$738$	0	0
$739$	−6.27071e76	−0.00812073	−0.00406036	−	0.999992i	$-0.501292\pi$
$739$	−6.27071e76	−0.00812073	−0.00406036	+	0.999992i	$0.501292\pi$
$740$	1.65544e79	2.06558
$741$	0	0
$742$	−2.35240e78	−0.272523
$743$	−2.11611e77	−0.0236236	−0.0118118	−	0.999930i	$-0.503760\pi$
$743$	−2.11611e77	−0.0236236	−0.0118118	+	0.999930i	$0.503760\pi$
$744$	0	0
$745$	−2.73673e78	−0.283749
$746$	3.15150e79	3.14919
$747$	0	0
$748$	2.32471e79	2.15812
$749$	−3.50940e78	−0.314038
$750$	0	0
$751$	−1.43216e79	−1.19095	−0.595474	−	0.803374i	$-0.703036\pi$
$751$	−1.43216e79	−1.19095	−0.595474	+	0.803374i	$0.703036\pi$
$752$	−2.47017e78	−0.198032
$753$	0	0
$754$	−1.48789e79	−1.10882
$755$	−2.39302e79	−1.71951
$756$	0	0
$757$	−2.38175e79	−1.59132	−0.795662	−	0.605741i	$-0.792877\pi$
$757$	−2.38175e79	−1.59132	−0.795662	+	0.605741i	$0.792877\pi$
$758$	4.85862e79	3.13047
$759$	0	0
$760$	1.41012e79	0.845053
$761$	−1.24548e79	−0.719879	−0.359940	−	0.932976i	$-0.617203\pi$
$761$	−1.24548e79	−0.719879	−0.359940	+	0.932976i	$0.617203\pi$
$762$	0	0
$763$	−1.24445e79	−0.669192
$764$	−5.54431e79	−2.87594
$765$	0	0
$766$	4.33419e79	2.09227
$767$	−2.65263e79	−1.23539
$768$	0	0
$769$	1.10483e79	0.478984	0.239492	−	0.970898i	$-0.423019\pi$
$769$	1.10483e79	0.478984	0.239492	+	0.970898i	$0.423019\pi$
$770$	4.83405e79	2.02216
$771$	0	0
$772$	−6.68005e79	−2.60198
$773$	−1.34251e79	−0.504640	−0.252320	−	0.967644i	$-0.581194\pi$
$773$	−1.34251e79	−0.504640	−0.252320	+	0.967644i	$0.581194\pi$
$774$	0	0
$775$	−1.04952e79	−0.367447
$776$	6.22804e78	0.210453
$777$	0	0
$778$	6.00021e78	0.188898
$779$	5.95060e78	0.180834
$780$	0	0
$781$	4.70196e79	1.33160
$782$	5.13061e79	1.40276
$783$	0	0
$784$	−1.98311e79	−0.505424
$785$	6.41333e79	1.57822
$786$	0	0
$787$	−9.76349e78	−0.224027	−0.112013	−	0.993707i	$-0.535730\pi$
$787$	−9.76349e78	−0.224027	−0.112013	+	0.993707i	$0.535730\pi$
$788$	−1.30791e80	−2.89805
$789$	0	0
$790$	1.85046e80	3.82414
$791$	−3.04273e79	−0.607310
$792$	0	0
$793$	5.55211e78	0.103382
$794$	−7.68354e78	−0.138197
$795$	0	0
$796$	−1.89591e79	−0.318207
$797$	9.76352e79	1.58308	0.791539	−	0.611118i	$-0.209280\pi$
$797$	9.76352e79	1.58308	0.791539	+	0.611118i	$0.209280\pi$
$798$	0	0
$799$	1.51650e79	0.229512
$800$	2.02997e79	0.296834
$801$	0	0
$802$	−1.80995e80	−2.47099
$803$	−5.44793e79	−0.718711
$804$	0	0
$805$	7.04941e79	0.868492
$806$	−3.99471e79	−0.475633
$807$	0	0
$808$	−1.28557e80	−1.42982
$809$	−1.16511e80	−1.25252	−0.626259	−	0.779615i	$-0.715415\pi$
$809$	−1.16511e80	−1.25252	−0.626259	+	0.779615i	$0.715415\pi$
$810$	0	0
$811$	−4.92243e79	−0.494432	−0.247216	−	0.968960i	$-0.579516\pi$
$811$	−4.92243e79	−0.494432	−0.247216	+	0.968960i	$0.579516\pi$
$812$	6.41966e79	0.623335
$813$	0	0
$814$	−1.38052e80	−1.25277
$815$	−2.61113e80	−2.29084
$816$	0	0
$817$	−3.61317e79	−0.296334
$818$	−1.95111e80	−1.54727
$819$	0	0
$820$	−2.46776e80	−1.82987
$821$	6.21015e79	0.445313	0.222656	−	0.974897i	$-0.428527\pi$
$821$	6.21015e79	0.445313	0.222656	+	0.974897i	$0.428527\pi$
$822$	0	0
$823$	1.15377e80	0.773789	0.386894	−	0.922124i	$-0.373548\pi$
$823$	1.15377e80	0.773789	0.386894	+	0.922124i	$0.373548\pi$
$824$	−1.41818e80	−0.919885
$825$	0	0
$826$	1.73211e80	1.05105
$827$	−3.20884e79	−0.188342	−0.0941708	−	0.995556i	$-0.530020\pi$
$827$	−3.20884e79	−0.188342	−0.0941708	+	0.995556i	$0.530020\pi$
$828$	0	0
$829$	1.48156e80	0.813711	0.406855	−	0.913493i	$-0.366625\pi$
$829$	1.48156e80	0.813711	0.406855	+	0.913493i	$0.366625\pi$
$830$	9.48481e80	5.03943
$831$	0	0
$832$	2.95053e80	1.46726
$833$	1.21749e80	0.585769
$834$	0	0
$835$	−1.71683e80	−0.773300
$836$	−1.59687e80	−0.695981
$837$	0	0
$838$	5.65048e79	0.230608
$839$	4.75921e80	1.87967	0.939835	−	0.341630i	$-0.110979\pi$
$839$	4.75921e80	1.87967	0.939835	+	0.341630i	$0.110979\pi$
$840$	0	0
$841$	−2.01542e80	−0.745549
$842$	−2.04374e80	−0.731717
$843$	0	0
$844$	2.37970e80	0.798187
$845$	−3.23382e80	−1.04992
$846$	0	0
$847$	−5.78285e79	−0.175933
$848$	−7.18593e79	−0.211640
$849$	0	0
$850$	1.03548e81	2.85839
$851$	−2.01318e80	−0.538047
$852$	0	0
$853$	−4.08457e80	−1.02341	−0.511703	−	0.859162i	$-0.670985\pi$
$853$	−4.08457e80	−1.02341	−0.511703	+	0.859162i	$0.670985\pi$
$854$	−3.62542e79	−0.0879562
$855$	0	0
$856$	−3.54036e80	−0.805414
$857$	1.70584e80	0.375807	0.187904	−	0.982187i	$-0.439831\pi$
$857$	1.70584e80	0.375807	0.187904	+	0.982187i	$0.439831\pi$
$858$	0	0
$859$	3.33842e80	0.689809	0.344905	−	0.938638i	$-0.387911\pi$
$859$	3.33842e80	0.689809	0.344905	+	0.938638i	$0.387911\pi$
$860$	1.49841e81	2.99862
$861$	0	0
$862$	1.26077e80	0.236693
$863$	−4.33083e80	−0.787543	−0.393771	−	0.919208i	$-0.628830\pi$
$863$	−4.33083e80	−0.787543	−0.393771	+	0.919208i	$0.628830\pi$
$864$	0	0
$865$	3.39282e80	0.578919
$866$	1.25552e81	2.07530
$867$	0	0
$868$	1.72356e80	0.267383
$869$	−1.01964e81	−1.53251
$870$	0	0
$871$	−1.17557e81	−1.65863
$872$	−1.25543e81	−1.71628
$873$	0	0
$874$	−3.52428e80	−0.452383
$875$	5.84929e80	0.727582
$876$	0	0
$877$	6.55585e80	0.765844	0.382922	−	0.923781i	$-0.374918\pi$
$877$	6.55585e80	0.765844	0.382922	+	0.923781i	$0.374918\pi$
$878$	2.29462e80	0.259783
$879$	0	0
$880$	1.47667e81	1.57040
$881$	−9.94877e80	−1.02549	−0.512746	−	0.858541i	$-0.671372\pi$
$881$	−9.94877e80	−1.02549	−0.512746	+	0.858541i	$0.671372\pi$
$882$	0	0
$883$	7.57548e80	0.733653	0.366827	−	0.930289i	$-0.380444\pi$
$883$	7.57548e80	0.733653	0.366827	+	0.930289i	$0.380444\pi$
$884$	2.60422e81	2.44478
$885$	0	0
$886$	−3.43580e81	−3.03110
$887$	4.64982e80	0.397683	0.198841	−	0.980032i	$-0.436282\pi$
$887$	4.64982e80	0.397683	0.198841	+	0.980032i	$0.436282\pi$
$888$	0	0
$889$	−8.02466e80	−0.645102
$890$	−6.67701e81	−5.20423
$891$	0	0
$892$	−1.05537e81	−0.773343
$893$	−1.04170e80	−0.0740166
$894$	0	0
$895$	−1.87237e81	−1.25100
$896$	−1.75548e81	−1.13743
$897$	0	0
$898$	−1.90236e80	−0.115929
$899$	1.84675e80	0.109148
$900$	0	0
$901$	4.41163e80	0.245283
$902$	2.05793e81	1.10981
$903$	0	0
$904$	−3.06958e81	−1.55757
$905$	3.01120e80	0.148219
$906$	0	0
$907$	1.49725e81	0.693577	0.346788	−	0.937943i	$-0.387272\pi$
$907$	1.49725e81	0.693577	0.346788	+	0.937943i	$0.387272\pi$
$908$	−4.38855e81	−1.97224
$909$	0	0
$910$	5.41527e81	2.29077
$911$	−2.12167e81	−0.870807	−0.435404	−	0.900235i	$-0.643394\pi$
$911$	−2.12167e81	−0.870807	−0.435404	+	0.900235i	$0.643394\pi$
$912$	0	0
$913$	−5.22633e81	−2.01953
$914$	2.96227e81	1.11072
$915$	0	0
$916$	6.82240e81	2.40886
$917$	3.53753e81	1.21211
$918$	0	0
$919$	4.79467e81	1.54733	0.773664	−	0.633596i	$-0.218422\pi$
$919$	4.79467e81	1.54733	0.773664	+	0.633596i	$0.218422\pi$
$920$	7.11161e81	2.22742
$921$	0	0
$922$	6.35028e81	1.87367
$923$	5.26730e81	1.50849
$924$	0	0
$925$	−4.06309e81	−1.09637
$926$	1.86617e81	0.488821
$927$	0	0
$928$	−3.57196e80	−0.0881733
$929$	8.73325e80	0.209288	0.104644	−	0.994510i	$-0.466630\pi$
$929$	8.73325e80	0.209288	0.104644	+	0.994510i	$0.466630\pi$
$930$	0	0
$931$	−8.36306e80	−0.188907
$932$	−1.11020e82	−2.43480
$933$	0	0
$934$	−8.63393e81	−1.78513
$935$	−9.06566e81	−1.82004
$936$	0	0
$937$	2.20940e81	0.418250	0.209125	−	0.977889i	$-0.432938\pi$
$937$	2.20940e81	0.418250	0.209125	+	0.977889i	$0.432938\pi$
$938$	7.67626e81	1.41114
$939$	0	0
$940$	4.32002e81	0.748979
$941$	−7.24578e81	−1.22003	−0.610015	−	0.792390i	$-0.708837\pi$
$941$	−7.24578e81	−1.22003	−0.610015	+	0.792390i	$0.708837\pi$
$942$	0	0
$943$	3.00104e81	0.476650
$944$	5.29114e81	0.816242
$945$	0	0
$946$	−1.24956e82	−1.81866
$947$	1.07373e82	1.51800	0.759000	−	0.651090i	$-0.225688\pi$
$947$	1.07373e82	1.51800	0.759000	+	0.651090i	$0.225688\pi$
$948$	0	0
$949$	−6.10297e81	−0.814179
$950$	−7.11286e81	−0.921817
$951$	0	0
$952$	−8.27434e81	−1.01209
$953$	2.80192e81	0.332966	0.166483	−	0.986044i	$-0.446759\pi$
$953$	2.80192e81	0.332966	0.166483	+	0.986044i	$0.446759\pi$
$954$	0	0
$955$	2.16211e82	2.42541
$956$	1.21934e82	1.32903
$957$	0	0
$958$	7.48556e81	0.770322
$959$	−6.17350e81	−0.617333
$960$	0	0
$961$	−1.00941e82	−0.953180
$962$	−1.54650e82	−1.41918
$963$	0	0
$964$	−6.15862e81	−0.533784
$965$	2.60502e82	2.19437
$966$	0	0
$967$	6.52535e81	0.519249	0.259624	−	0.965710i	$-0.416401\pi$
$967$	6.52535e81	0.519249	0.259624	+	0.965710i	$0.416401\pi$
$968$	−5.83388e81	−0.451217
$969$	0	0
$970$	−4.99145e81	−0.364758
$971$	2.42379e82	1.72173	0.860866	−	0.508833i	$-0.169923\pi$
$971$	2.42379e82	1.72173	0.860866	+	0.508833i	$0.169923\pi$
$972$	0	0
$973$	−6.73462e81	−0.452074
$974$	−5.13522e82	−3.35110
$975$	0	0
$976$	−1.10747e81	−0.0683063
$977$	1.29199e82	0.774744	0.387372	−	0.921923i	$-0.373383\pi$
$977$	1.29199e82	0.774744	0.387372	+	0.921923i	$0.373383\pi$
$978$	0	0
$979$	3.67917e82	2.08558
$980$	3.46822e82	1.91157
$981$	0	0
$982$	−3.04152e82	−1.58498
$983$	1.06339e82	0.538854	0.269427	−	0.963021i	$-0.413166\pi$
$983$	1.06339e82	0.538854	0.269427	+	0.963021i	$0.413166\pi$
$984$	0	0
$985$	5.10044e82	2.44406
$986$	−1.82205e82	−0.849073
$987$	0	0
$988$	−1.78887e82	−0.788431
$989$	−1.82221e82	−0.781089
$990$	0	0
$991$	−2.78037e82	−1.12740	−0.563699	−	0.825980i	$-0.690622\pi$
$991$	−2.78037e82	−1.12740	−0.563699	+	0.825980i	$0.690622\pi$
$992$	−9.59005e80	−0.0378225
$993$	0	0
$994$	−3.43944e82	−1.28340
$995$	7.39349e81	0.268358
$996$	0	0
$997$	4.12474e82	1.41671	0.708353	−	0.705858i	$-0.249438\pi$
$997$	4.12474e82	1.41671	0.708353	+	0.705858i	$0.249438\pi$
$998$	−9.53941e82	−3.18736
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	9.56.a.a.1.1		4
3.2	odd	2		1.56.a.a.1.4	✓	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1.56.a.a.1.4	✓	4	3.2	odd	2
9.56.a.a.1.1		4	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 9 = 3^{2} \)
Weight:	\( k \)	\(=\)	\( 56 \)
Character orbit:	\([\chi]\)	\(=\)	9.a (trivial)

\(f(q)\)	\(=\)	\(q-3.25888e8 q^{2} +7.01743e16 q^{4} -2.73659e19 q^{5} -1.10303e23 q^{7} -1.11276e25 q^{8} +O(q^{10})\)	\(q-3.25888e8 q^{2} +7.01743e16 q^{4} -2.73659e19 q^{5} -1.10303e23 q^{7} -1.11276e25 q^{8} +8.91821e27 q^{10} -4.91412e28 q^{11} -5.50498e30 q^{13} +3.59464e31 q^{14} +1.09807e33 q^{16} -6.74131e33 q^{17} +4.63069e34 q^{19} -1.92038e36 q^{20} +1.60146e37 q^{22} +2.33537e37 q^{23} +4.71335e38 q^{25} +1.79401e39 q^{26} -7.74043e39 q^{28} -8.29368e39 q^{29} -2.22670e40 q^{31} +4.30685e40 q^{32} +2.19691e42 q^{34} +3.01853e42 q^{35} -8.62039e42 q^{37} -1.50909e43 q^{38} +3.04517e44 q^{40} +1.28503e44 q^{41} -7.80265e44 q^{43} -3.44845e45 q^{44} -7.61071e45 q^{46} -2.24956e45 q^{47} -1.80601e46 q^{49} -1.53602e47 q^{50} -3.86308e47 q^{52} -6.54418e46 q^{53} +1.34479e48 q^{55} +1.22741e48 q^{56} +2.70281e48 q^{58} +4.81860e48 q^{59} -1.00856e48 q^{61} +7.25655e48 q^{62} -5.35975e49 q^{64} +1.50648e50 q^{65} +2.13547e50 q^{67} -4.73067e50 q^{68} -9.83705e50 q^{70} -9.56825e50 q^{71} +1.10863e51 q^{73} +2.80928e51 q^{74} +3.24956e51 q^{76} +5.42042e51 q^{77} +2.07492e52 q^{79} -3.00495e52 q^{80} -4.18778e52 q^{82} +1.06353e53 q^{83} +1.84482e53 q^{85} +2.54279e53 q^{86} +5.46825e53 q^{88} -7.48693e53 q^{89} +6.07215e53 q^{91} +1.63883e54 q^{92} +7.33106e53 q^{94} -1.26723e54 q^{95} -5.59692e53 q^{97} +5.88557e54 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 208622520 q^{2} + 38\!\cdots\!72 q^{4}+ \cdots - 45\!\cdots\!40 q^{8}+O(q^{10}) \) 4 * q - 208622520 * q^2 + 38727758778743872 * q^4 - 14396937963387167160 * q^5 - 205529376090660565972000 * q^7 - 4549274472651430619082240 * q^8	\( 4 q - 208622520 q^{2} + 38\!\cdots\!72 q^{4}+ \cdots - 43\!\cdots\!60 q^{98}+O(q^{100}) \) 4 * q - 208622520 * q^2 + 38727758778743872 * q^4 - 14396937963387167160 * q^5 - 205529376090660565972000 * q^7 - 4549274472651430619082240 * q^8 + 4648305821937663379975180560 * q^10 - 19492148713537948248062043408 * q^11 - 4449970852951030370486873382760 * q^13 + 28356223847864660359303625873856 * q^14 + 972748533533952319807553436258304 * q^16 - 8593971071724377583839140954773960 * q^17 + 339485321922051504109099704484079600 * q^19 - 2938981710383707492522432611899614080 * q^20 + 38006076575943531891094535037919254240 * q^22 - 49808560358713761517710452453445612960 * q^23 + 35720819629535961214417161732721803100 * q^25 + 2942801473325677064443328059884451887792 * q^26 - 14225688489857344137508473549032747368960 * q^28 + 18313921252535508838816178753292620581800 * q^29 + 228069689399145752868860523834729264526208 * q^31 - 633346612507316231430506989727883716689920 * q^32 + 896637942332031893460273084285964132034544 * q^34 + 4819663438502339394117495448236020975855040 * q^35 - 32137889117062584203203089731106089299166920 * q^37 + 4952027966320588944657713384757782381142240 * q^38 + 423453117316016459693780561000308646880691200 * q^40 - 246756563007211451240604479433521241061314408 * q^41 - 860266067148440101585711757682636198922476400 * q^43 + 486680632760661386186662626683912868907405056 * q^44 - 12358385464441662606619414449724307588901916992 * q^46 - 4275321492760062770492681289130578251551314240 * q^47 + 51896265177052512954332052101694146860214382372 * q^49 - 174698296445912937700335126041507926720149534600 * q^50 - 262201419493851260177411503538061050352769552000 * q^52 + 488469552022263686716757080744643106633189705480 * q^53 - 127591926326749967084952696035933816282025595680 * q^55 + 298136165704261759300184058675155027135738572800 * q^56 + 6079853356051584053436052229523762232408341938640 * q^58 - 8189687634125713603536212764174920044680103250000 * q^59 + 7023917261975601941077275556050474243839244469208 * q^61 + 30522733021551585983790682957575295692580599279360 * q^62 - 98185742120493275625308720675268779449265392713728 * q^64 + 96029582501479027321081622269423947602394832060080 * q^65 + 418567852430847740316243536772383918093566302547760 * q^67 - 627327947371921816104248533416688222149537051169920 * q^68 - 471522968288511321788110491009215619195633708224640 * q^70 - 997985577607888605538672501225224229003742837277408 * q^71 - 898993596628095916013292323795403905388680301942040 * q^73 + 7967044320232055682477818350544716808849477162563056 * q^74 - 60907940015267454915614913374117951647840510009600 * q^76 - 14299054939611075432133092801777785333545282382563200 * q^77 + 48721021140002244303635330301073120621076057627153600 * q^79 + 3558308494035098045228661758379879929555981454090240 * q^80 - 164154584875013842045822252535546173951453621276929360 * q^82 + 71840759606517399895238320212650236559070020961691920 * q^83 + 248899912487828257920888533066500872415304578192331760 * q^85 + 390961799675414150209662123589235297185712905683496992 * q^86 + 263660200754753376218335161392938332564087458967828480 * q^88 - 1567987214275383302209606514592359147814765036271890600 * q^89 + 1660326344231373069708515805926098978407334056523187008 * q^91 + 2737928811190126698927829997086921657569438136581219840 * q^92 - 4092215382133552783473757354682502518415689822573629056 * q^94 - 90834332415616009306267157723570331064559482078144800 * q^95 + 5113732531532480760212291157301231295251404057238280840 * q^97 - 4361266856004358769699597237924757031028912315048682360 * q^98

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