LMFDB - Embedded newform 9.68.a.a.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [9,68,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, 68, names="a")

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

chi := DirichletCharacter("9.1");

S:= CuspForms(chi, 68);

N := Newforms(S);

Level:	$ N $	$=$	$ 9 = 3^{2} $
Weight:	$ k $	$=$	$ 68 $
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:	$255.861316737$
Analytic rank:	$1$
Dimension:	$5$
Coefficient field:	$\mathbb{Q}[x]/(x^{5} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{5} - x^{4} + \cdots + 20\!\cdots\!00 $ x^5 - x^4 - 939384011925257456x^3 + 31046449413968483513911200x^2 + 156793504704482691874379743265203200*x + 20916736226052669578405116700517591609696000
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{40}\cdot 3^{20}\cdot 5^{4}\cdot 7^{2}\cdot 11\cdot 13\cdot 17 $
Twist minimal:	no (minimal twist has level 1)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$-1.64845e8$ 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)

$f(q)$	$=$	$q-5.06726e9 q^{2} -1.21897e20 q^{4} +8.33551e22 q^{5} -1.15070e28 q^{7} +1.36548e30 q^{8} +O(q^{10})$	\(q-5.06726e9 q^{2} -1.21897e20 q^{4} +8.33551e22 q^{5} -1.15070e28 q^{7} +1.36548e30 q^{8} -4.22381e32 q^{10} +1.09259e35 q^{11} +1.54273e37 q^{13} +5.83087e37 q^{14} +1.10696e40 q^{16} -8.24456e40 q^{17} -5.93328e42 q^{19} -1.01607e43 q^{20} -5.53645e44 q^{22} -2.28489e45 q^{23} -6.08146e46 q^{25} -7.81738e46 q^{26} +1.40266e48 q^{28} -1.07438e49 q^{29} +1.32534e50 q^{31} -2.57601e50 q^{32} +4.17773e50 q^{34} -9.59164e50 q^{35} -5.20056e52 q^{37} +3.00655e52 q^{38} +1.13819e53 q^{40} +1.63973e54 q^{41} +5.64177e54 q^{43} -1.33184e55 q^{44} +1.15781e55 q^{46} -2.41027e55 q^{47} -2.85968e56 q^{49} +3.08163e56 q^{50} -1.88053e57 q^{52} -2.84898e57 q^{53} +9.10731e57 q^{55} -1.57125e58 q^{56} +5.44415e58 q^{58} +3.30680e59 q^{59} -6.89383e59 q^{61} -6.71583e59 q^{62} -3.28249e59 q^{64} +1.28594e60 q^{65} +2.58683e61 q^{67} +1.00499e61 q^{68} +4.86033e60 q^{70} +1.34953e62 q^{71} -1.11285e62 q^{73} +2.63526e62 q^{74} +7.23248e62 q^{76} -1.25724e63 q^{77} +1.23916e63 q^{79} +9.22705e62 q^{80} -8.30894e63 q^{82} -3.41100e63 q^{83} -6.87226e63 q^{85} -2.85883e64 q^{86} +1.49191e65 q^{88} -3.04246e65 q^{89} -1.77521e65 q^{91} +2.78521e65 q^{92} +1.22134e65 q^{94} -4.94569e65 q^{95} +2.29986e66 q^{97} +1.44907e66 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 5 q - 5554901256 q^{2} + 35\!\cdots\!40 q^{4}+ \cdots - 32\!\cdots\!80 q^{8}+O(q^{10}) $ 5 * q - 5554901256 * q^2 + 350472004382296600640 * q^4 - 330744836907160597528950 * q^5 + 33632726520317603069152899256 * q^7 - 3261706912683890613885787783680 * q^8	$ 5 q - 5554901256 q^{2} + 35\!\cdots\!40 q^{4}+ \cdots - 12\!\cdots\!08 q^{98}+O(q^{100}) $ 5 * q - 5554901256 * q^2 + 350472004382296600640 * q^4 - 330744836907160597528950 * q^5 + 33632726520317603069152899256 * q^7 - 3261706912683890613885787783680 * q^8 - 5287067006725590176865792208438800 * q^10 - 203006981551281631527218766884109060 * q^11 + 177822884499813229570219072356766702 * q^13 - 290753425875732621001638220329334092480 * q^14 + 18266362102387359184851236859301091348480 * q^16 - 75241497376497768433807587544150344102906 * q^17 + 3998884102997801557241177083441346393295100 * q^19 + 15074831378020267075078660994426474705846400 * q^20 + 1841247880573095918698534631505063585473750432 * q^22 + 419660874260151197180020017656265233426170968 * q^23 + 175279270003539476977813620578789764300129011875 * q^25 - 21416337629300654169124097666599354769371062960 * q^26 + 14982728306233364463143494158089725946900023694848 * q^28 - 18733547497571939101380180097730717676662894233950 * q^29 + 365849822471060800690376948081970588059264217288160 * q^31 - 1591165751988992347021834813546084975107380979204096 * q^32 + 7817592154883765712044327776251337623941567500782480 * q^34 - 4524513410554564733118320802153390591800073874285200 * q^35 - 56389392588768330454829645685931746748224606527380394 * q^37 + 311451303114725973135630000941921262878276604287141280 * q^38 - 1886768345048751997029226502271137564956948018338432000 * q^40 - 113555410342193387626817165052765483601006465327103010 * q^41 + 6508304671085340439704487085091235272293711787089861092 * q^43 - 49369449025916528958230735645862721892607029455332199680 * q^44 + 79552980744915855625545425031873854934595203714399466560 * q^46 + 128023594814179612806658270243785955024442659789917751344 * q^47 - 771329931628098140389185999842408514636676231229111640435 * q^49 + 3919481096957516748709549462396523762064894577356951885000 * q^50 + 672997930141532412373441872733517069231734104886640838016 * q^52 - 1046765637663599376128164919371991945530174947374966490822 * q^53 + 66942753107037791618627925698973654692865254681839842449400 * q^55 - 164746697572073652525116376573879338548073684495562965299200 * q^56 - 61137956327686914952144218440883774026433838412764071303120 * q^58 + 305790738450157663862297559072875409310668010528073986627500 * q^59 - 1137073938560830615075915586814815057732339483683661907261890 * q^61 + 2197846158587850633685459639420082896328263471188214086352128 * q^62 + 6319522016046144185339524760669817745425888834305772325437440 * q^64 - 17054811715744261908524663200762497384422620874171150779332900 * q^65 - 11903044989154510038048691316368615691989662189985228212145844 * q^67 - 81678078346863753465296539273887923556029130514802676363013248 * q^68 - 262230520857255225386866306600227822969034558447869634844476800 * q^70 + 112169920751076079402369696382938772997794660792753351047772040 * q^71 - 304061800126793465330511223999919410949872771539142074085150718 * q^73 - 921008183492866283853128598587548033201480125306857491530532080 * q^74 + 2076567511595431334156222539483464646991367936386801535927366400 * q^76 - 5018131462902473316385236580394702266689060843204393245422638432 * q^77 + 2994504004186984867153587379277397704940492543518650040519815600 * q^79 + 15198313539268031787508043655897930060910106707913153957798092800 * q^80 - 17699192859543411700126655967680257958811789647196784631772687408 * q^82 + 47352447490969920981134910324833485175129837165394254819464203588 * q^83 - 39334683419450918052255554891934302881190270223971152032299949300 * q^85 - 49699285824187070765304255878405188987409992188766856866277888160 * q^86 + 430257938373980762031490456670953174964896424231159472833711400960 * q^88 + 11988583288945008097106276879882407358382120120051430459779195150 * q^89 + 232376792470844928685229521265495056030669651812230900159714321360 * q^91 + 986292139147147043544160128863480288571347084605459783959415954944 * q^92 - 4927754861315037106505826725122767884474273389521981763161929704320 * q^94 + 2022377488008256909110920831467942087293430657450319294506545963000 * q^95 + 2897556354128426205551279700626881901316694084191208635967319112106 * q^97 - 12426885478574475523720488645206508880013087100212747539199689691208 * 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 $

$2$	−5.06726e9	−0.417127	−0.208563	−	0.978009i	$-0.566879\pi$
$2$	−5.06726e9	−0.417127	−0.208563	+	0.978009i	$0.566879\pi$
$3$	0	0
$3$	0	0
$4$	−1.21897e20	−0.826005
$5$	8.33551e22	0.320211	0.160106	−	0.987100i	$-0.448816\pi$
$5$	8.33551e22	0.320211	0.160106	+	0.987100i	$0.448816\pi$
$6$	0	0
$7$	−1.15070e28	−0.562570	−0.281285	−	0.959624i	$-0.590761\pi$
$7$	−1.15070e28	−0.562570	−0.281285	+	0.959624i	$0.590761\pi$
$8$	1.36548e30	0.761676
$9$	0	0
$10$	−4.22381e32	−0.133569
$11$	1.09259e35	1.41842	0.709208	−	0.705000i	$-0.249053\pi$
$11$	1.09259e35	1.41842	0.709208	+	0.705000i	$0.249053\pi$
$12$	0	0
$13$	1.54273e37	0.743338	0.371669	−	0.928365i	$-0.378786\pi$
$13$	1.54273e37	0.743338	0.371669	+	0.928365i	$0.378786\pi$
$14$	5.83087e37	0.234663
$15$	0	0
$16$	1.10696e40	0.508290
$17$	−8.24456e40	−0.496739	−0.248370	−	0.968665i	$-0.579895\pi$
$17$	−8.24456e40	−0.496739	−0.248370	+	0.968665i	$0.579895\pi$
$18$	0	0
$19$	−5.93328e42	−0.861091	−0.430546	−	0.902569i	$-0.641679\pi$
$19$	−5.93328e42	−0.861091	−0.430546	+	0.902569i	$0.641679\pi$
$20$	−1.01607e43	−0.264496
$21$	0	0
$22$	−5.53645e44	−0.591659
$23$	−2.28489e45	−0.550785	−0.275393	−	0.961332i	$-0.588808\pi$
$23$	−2.28489e45	−0.550785	−0.275393	+	0.961332i	$0.588808\pi$
$24$	0	0
$25$	−6.08146e46	−0.897465
$26$	−7.81738e46	−0.310066
$27$	0	0
$28$	1.40266e48	0.464686
$29$	−1.07438e49	−1.09856	−0.549281	−	0.835638i	$-0.685098\pi$
$29$	−1.07438e49	−1.09856	−0.549281	+	0.835638i	$0.685098\pi$
$30$	0	0
$31$	1.32534e50	1.45114	0.725572	−	0.688147i	$-0.241575\pi$
$31$	1.32534e50	1.45114	0.725572	+	0.688147i	$0.241575\pi$
$32$	−2.57601e50	−0.973697
$33$	0	0
$34$	4.17773e50	0.207203
$35$	−9.59164e50	−0.180141
$36$	0	0
$37$	−5.20056e52	−1.51807	−0.759037	−	0.651048i	$-0.774330\pi$
$37$	−5.20056e52	−1.51807	−0.759037	+	0.651048i	$0.774330\pi$
$38$	3.00655e52	0.359184
$39$	0	0
$40$	1.13819e53	0.243897
$41$	1.63973e54	1.53643	0.768217	−	0.640190i	$-0.221144\pi$
$41$	1.63973e54	1.53643	0.768217	+	0.640190i	$0.221144\pi$
$42$	0	0
$43$	5.64177e54	1.07207	0.536034	−	0.844197i	$-0.319922\pi$
$43$	5.64177e54	1.07207	0.536034	+	0.844197i	$0.319922\pi$
$44$	−1.33184e55	−1.17162
$45$	0	0
$46$	1.15781e55	0.229747
$47$	−2.41027e55	−0.232695	−0.116347	−	0.993209i	$-0.537119\pi$
$47$	−2.41027e55	−0.232695	−0.116347	+	0.993209i	$0.537119\pi$
$48$	0	0
$49$	−2.85968e56	−0.683515
$50$	3.08163e56	0.374356
$51$	0	0
$52$	−1.88053e57	−0.614001
$53$	−2.84898e57	−0.491414	−0.245707	−	0.969344i	$-0.579020\pi$
$53$	−2.84898e57	−0.491414	−0.245707	+	0.969344i	$0.579020\pi$
$54$	0	0
$55$	9.10731e57	0.454193
$56$	−1.57125e58	−0.428496
$57$	0	0
$58$	5.44415e58	0.458239
$59$	3.30680e59	1.56987	0.784937	−	0.619575i	$-0.212695\pi$
$59$	3.30680e59	1.56987	0.784937	+	0.619575i	$0.212695\pi$
$60$	0	0
$61$	−6.89383e59	−1.07130	−0.535650	−	0.844440i	$-0.679933\pi$
$61$	−6.89383e59	−1.07130	−0.535650	+	0.844440i	$0.679933\pi$
$62$	−6.71583e59	−0.605311
$63$	0	0
$64$	−3.28249e59	−0.102135
$65$	1.28594e60	0.238025
$66$	0	0
$67$	2.58683e61	1.73485	0.867424	−	0.497569i	$-0.165774\pi$
$67$	2.58683e61	1.73485	0.867424	+	0.497569i	$0.165774\pi$
$68$	1.00499e61	0.410309
$69$	0	0
$70$	4.86033e60	0.0751418
$71$	1.34953e62	1.29726	0.648630	−	0.761104i	$-0.275342\pi$
$71$	1.34953e62	1.29726	0.648630	+	0.761104i	$0.275342\pi$
$72$	0	0
$73$	−1.11285e62	−0.421814	−0.210907	−	0.977506i	$-0.567642\pi$
$73$	−1.11285e62	−0.421814	−0.210907	+	0.977506i	$0.567642\pi$
$74$	2.63526e62	0.633229
$75$	0	0
$76$	7.23248e62	0.711266
$77$	−1.25724e63	−0.797958
$78$	0	0
$79$	1.23916e63	0.333135	0.166568	−	0.986030i	$-0.446732\pi$
$79$	1.23916e63	0.333135	0.166568	+	0.986030i	$0.446732\pi$
$80$	9.22705e62	0.162760
$81$	0	0
$82$	−8.30894e63	−0.640887
$83$	−3.41100e63	−0.175294	−0.0876468	−	0.996152i	$-0.527935\pi$
$83$	−3.41100e63	−0.175294	−0.0876468	+	0.996152i	$0.527935\pi$
$84$	0	0
$85$	−6.87226e63	−0.159062
$86$	−2.85883e64	−0.447188
$87$	0	0
$88$	1.49191e65	1.08037
$89$	−3.04246e65	−1.50890	−0.754448	−	0.656360i	$-0.772095\pi$
$89$	−3.04246e65	−1.50890	−0.754448	+	0.656360i	$0.772095\pi$
$90$	0	0
$91$	−1.77521e65	−0.418180
$92$	2.78521e65	0.454951
$93$	0	0
$94$	1.22134e65	0.0970633
$95$	−4.94569e65	−0.275731
$96$	0	0
$97$	2.29986e66	0.638041	0.319021	−	0.947748i	$-0.396646\pi$
$97$	2.29986e66	0.638041	0.319021	+	0.947748i	$0.396646\pi$
$98$	1.44907e66	0.285112
$99$	0	0
$100$	7.41311e66	0.741311
$101$	−8.83103e66	−0.632769	−0.316385	−	0.948631i	$-0.602469\pi$
$101$	−8.83103e66	−0.632769	−0.316385	+	0.948631i	$0.602469\pi$
$102$	0	0
$103$	−1.08466e67	−0.402947	−0.201473	−	0.979494i	$-0.564573\pi$
$103$	−1.08466e67	−0.402947	−0.201473	+	0.979494i	$0.564573\pi$
$104$	2.10656e67	0.566182
$105$	0	0
$106$	1.44365e67	0.204982
$107$	2.87086e67	0.297616	0.148808	−	0.988866i	$-0.452456\pi$
$107$	2.87086e67	0.297616	0.148808	+	0.988866i	$0.452456\pi$
$108$	0	0
$109$	5.52911e66	0.0308225	0.0154112	−	0.999881i	$-0.495094\pi$
$109$	5.52911e66	0.0308225	0.0154112	+	0.999881i	$0.495094\pi$
$110$	−4.61491e67	−0.189456
$111$	0	0
$112$	−1.27377e68	−0.285949
$113$	−5.97000e68	−0.995054	−0.497527	−	0.867449i	$-0.665758\pi$
$113$	−5.97000e68	−0.995054	−0.497527	+	0.867449i	$0.665758\pi$
$114$	0	0
$115$	−1.90457e68	−0.176368
$116$	1.30963e69	0.907418
$117$	0	0
$118$	−1.67564e69	−0.654837
$119$	9.48698e68	0.279451
$120$	0	0
$121$	6.00410e69	1.01190
$122$	3.49328e69	0.446868
$123$	0	0
$124$	−1.61555e70	−1.19865
$125$	−1.07176e70	−0.607590
$126$	0	0
$127$	5.53532e70	1.84382	0.921909	−	0.387406i	$-0.126629\pi$
$127$	5.53532e70	1.84382	0.921909	+	0.387406i	$0.126629\pi$
$128$	3.96786e70	1.01630
$129$	0	0
$130$	−6.51619e69	−0.0992867
$131$	3.42212e70	0.403373	0.201687	−	0.979450i	$-0.435358\pi$
$131$	3.42212e70	0.403373	0.201687	+	0.979450i	$0.435358\pi$
$132$	0	0
$133$	6.82741e70	0.484424
$134$	−1.31081e71	−0.723652
$135$	0	0
$136$	−1.12578e71	−0.378354
$137$	−4.32164e71	−1.13634	−0.568171	−	0.822910i	$-0.692349\pi$
$137$	−4.32164e71	−1.13634	−0.568171	+	0.822910i	$0.692349\pi$
$138$	0	0
$139$	8.25204e71	1.33526	0.667629	−	0.744494i	$-0.267309\pi$
$139$	8.25204e71	1.33526	0.667629	+	0.744494i	$0.267309\pi$
$140$	1.16919e71	0.148798
$141$	0	0
$142$	−6.83840e71	−0.541122
$143$	1.68557e72	1.05436
$144$	0	0
$145$	−8.95549e71	−0.351772
$146$	5.63910e71	0.175950
$147$	0	0
$148$	6.33932e72	1.25394
$149$	6.68758e72	1.05567	0.527836	−	0.849346i	$-0.323003\pi$
$149$	6.68758e72	1.05567	0.527836	+	0.849346i	$0.323003\pi$
$150$	0	0
$151$	2.60779e72	0.263357	0.131679	−	0.991292i	$-0.457963\pi$
$151$	2.60779e72	0.263357	0.131679	+	0.991292i	$0.457963\pi$
$152$	−8.10176e72	−0.655872
$153$	0	0
$154$	6.37077e72	0.332849
$155$	1.10474e73	0.464673
$156$	0	0
$157$	−4.90233e73	−1.34204	−0.671018	−	0.741441i	$-0.734143\pi$
$157$	−4.90233e73	−1.34204	−0.671018	+	0.741441i	$0.734143\pi$
$158$	−6.27915e72	−0.138960
$159$	0	0
$160$	−2.14724e73	−0.311789
$161$	2.62921e73	0.309855
$162$	0	0
$163$	1.63101e74	1.27108	0.635538	−	0.772069i	$-0.280778\pi$
$163$	1.63101e74	1.27108	0.635538	+	0.772069i	$0.280778\pi$
$164$	−1.99878e74	−1.26910
$165$	0	0
$166$	1.72844e73	0.0731196
$167$	−8.02398e73	−0.277580	−0.138790	−	0.990322i	$-0.544321\pi$
$167$	−8.02398e73	−0.277580	−0.138790	+	0.990322i	$0.544321\pi$
$168$	0	0
$169$	−1.92729e74	−0.447449
$170$	3.48235e73	0.0663489
$171$	0	0
$172$	−6.87714e74	−0.885533
$173$	4.19257e74	0.444566	0.222283	−	0.974982i	$-0.428649\pi$
$173$	4.19257e74	0.444566	0.222283	+	0.974982i	$0.428649\pi$
$174$	0	0
$175$	6.99791e74	0.504887
$176$	1.20945e75	0.720966
$177$	0	0
$178$	1.54169e75	0.629401
$179$	−2.46277e75	−0.833389	−0.416695	−	0.909046i	$-0.636812\pi$
$179$	−2.46277e75	−0.833389	−0.416695	+	0.909046i	$0.636812\pi$
$180$	0	0
$181$	−5.01874e75	−1.17048	−0.585238	−	0.810862i	$-0.698999\pi$
$181$	−5.01874e75	−1.17048	−0.585238	+	0.810862i	$0.698999\pi$
$182$	8.99544e74	0.174434
$183$	0	0
$184$	−3.11996e75	−0.419520
$185$	−4.33493e75	−0.486104
$186$	0	0
$187$	−9.00795e75	−0.704583
$188$	2.93804e75	0.192207
$189$	0	0
$190$	2.50611e75	0.115015
$191$	1.28809e75	0.0495825	0.0247912	−	0.999693i	$-0.492108\pi$
$191$	1.28809e75	0.0495825	0.0247912	+	0.999693i	$0.492108\pi$
$192$	0	0
$193$	5.85943e76	1.59106	0.795528	−	0.605916i	$-0.207193\pi$
$193$	5.85943e76	1.59106	0.795528	+	0.605916i	$0.207193\pi$
$194$	−1.16540e76	−0.266144
$195$	0	0
$196$	3.48586e76	0.564587
$197$	6.37062e76	0.870087	0.435044	−	0.900409i	$-0.356733\pi$
$197$	6.37062e76	0.870087	0.435044	+	0.900409i	$0.356733\pi$
$198$	0	0
$199$	−9.92421e76	−0.966313	−0.483157	−	0.875534i	$-0.660510\pi$
$199$	−9.92421e76	−0.966313	−0.483157	+	0.875534i	$0.660510\pi$
$200$	−8.30409e76	−0.683577
$201$	0	0
$202$	4.47491e76	0.263945
$203$	1.23628e77	0.618018
$204$	0	0
$205$	1.36680e77	0.491984
$206$	5.49626e76	0.168080
$207$	0	0
$208$	1.70773e77	0.377831
$209$	−6.48266e77	−1.22139
$210$	0	0
$211$	−2.29628e77	−0.314459	−0.157229	−	0.987562i	$-0.550256\pi$
$211$	−2.29628e77	−0.314459	−0.157229	+	0.987562i	$0.550256\pi$
$212$	3.47282e77	0.405911
$213$	0	0
$214$	−1.45474e77	−0.124144
$215$	4.70270e77	0.343288
$216$	0	0
$217$	−1.52506e78	−0.816369
$218$	−2.80174e76	−0.0128569
$219$	0	0
$220$	−1.11015e78	−0.375166
$221$	−1.27191e78	−0.369245
$222$	0	0
$223$	−3.32066e77	−0.0712871	−0.0356436	−	0.999365i	$-0.511348\pi$
$223$	−3.32066e77	−0.0712871	−0.0356436	+	0.999365i	$0.511348\pi$
$224$	2.96421e78	0.547773
$225$	0	0
$226$	3.02515e78	0.415064
$227$	−1.36540e79	−1.61582	−0.807909	−	0.589307i	$-0.799401\pi$
$227$	−1.36540e79	−1.61582	−0.807909	+	0.589307i	$0.799401\pi$
$228$	0	0
$229$	4.64291e78	0.409545	0.204773	−	0.978810i	$-0.434354\pi$
$229$	4.64291e78	0.409545	0.204773	+	0.978810i	$0.434354\pi$
$230$	9.65094e77	0.0735677
$231$	0	0
$232$	−1.46704e79	−0.836747
$233$	2.73417e79	1.35021	0.675105	−	0.737721i	$-0.264098\pi$
$233$	2.73417e79	1.35021	0.675105	+	0.737721i	$0.264098\pi$
$234$	0	0
$235$	−2.00908e78	−0.0745116
$236$	−4.03088e79	−1.29672
$237$	0	0
$238$	−4.80730e78	−0.116566
$239$	−5.49826e79	−1.15850	−0.579249	−	0.815150i	$-0.696654\pi$
$239$	−5.49826e79	−1.15850	−0.579249	+	0.815150i	$0.696654\pi$
$240$	0	0
$241$	−3.38224e79	−0.539056	−0.269528	−	0.962993i	$-0.586868\pi$
$241$	−3.38224e79	−0.539056	−0.269528	+	0.962993i	$0.586868\pi$
$242$	−3.04243e79	−0.422091
$243$	0	0
$244$	8.40336e79	0.884900
$245$	−2.38368e79	−0.218869
$246$	0	0
$247$	−9.15342e79	−0.640082
$248$	1.80972e80	1.10530
$249$	0	0
$250$	5.43086e79	0.253442
$251$	8.54919e79	0.349024	0.174512	−	0.984655i	$-0.444165\pi$
$251$	8.54919e79	0.349024	0.174512	+	0.984655i	$0.444165\pi$
$252$	0	0
$253$	−2.49645e80	−0.781242
$254$	−2.80489e80	−0.769106
$255$	0	0
$256$	−1.52620e80	−0.321791
$257$	−7.14436e80	−1.32191	−0.660957	−	0.750423i	$-0.729850\pi$
$257$	−7.14436e80	−1.32191	−0.660957	+	0.750423i	$0.729850\pi$
$258$	0	0
$259$	5.98427e80	0.854022
$260$	−1.56752e80	−0.196610
$261$	0	0
$262$	−1.73408e80	−0.168258
$263$	−8.76506e80	−0.748578	−0.374289	−	0.927312i	$-0.622113\pi$
$263$	−8.76506e80	−0.748578	−0.374289	+	0.927312i	$0.622113\pi$
$264$	0	0
$265$	−2.37477e80	−0.157357
$266$	−3.45962e80	−0.202066
$267$	0	0
$268$	−3.15326e81	−1.43299
$269$	−4.76354e81	−1.91086	−0.955428	−	0.295223i	$-0.904606\pi$
$269$	−4.76354e81	−1.91086	−0.955428	+	0.295223i	$0.904606\pi$
$270$	0	0
$271$	−3.02040e81	−0.945352	−0.472676	−	0.881236i	$-0.656712\pi$
$271$	−3.02040e81	−0.945352	−0.472676	+	0.881236i	$0.656712\pi$
$272$	−9.12638e80	−0.252488
$273$	0	0
$274$	2.18988e81	0.473999
$275$	−6.64456e81	−1.27298
$276$	0	0
$277$	−3.30476e81	−0.496670	−0.248335	−	0.968674i	$-0.579883\pi$
$277$	−3.30476e81	−0.496670	−0.248335	+	0.968674i	$0.579883\pi$
$278$	−4.18152e81	−0.556972
$279$	0	0
$280$	−1.30972e81	−0.137209
$281$	9.67683e81	0.899645	0.449823	−	0.893118i	$-0.351487\pi$
$281$	9.67683e81	0.899645	0.449823	+	0.893118i	$0.351487\pi$
$282$	0	0
$283$	−1.18626e82	−0.869630	−0.434815	−	0.900520i	$-0.643186\pi$
$283$	−1.18626e82	−0.869630	−0.434815	+	0.900520i	$0.643186\pi$
$284$	−1.64503e82	−1.07154
$285$	0	0
$286$	−8.54122e81	−0.439802
$287$	−1.88683e82	−0.864351
$288$	0	0
$289$	−2.07499e82	−0.753250
$290$	4.53798e81	0.146733
$291$	0	0
$292$	1.35653e82	0.348421
$293$	−7.50510e82	−1.71906	−0.859530	−	0.511085i	$-0.829244\pi$
$293$	−7.50510e82	−1.71906	−0.859530	+	0.511085i	$0.829244\pi$
$294$	0	0
$295$	2.75638e82	0.502692
$296$	−7.10125e82	−1.15628
$297$	0	0
$298$	−3.38877e82	−0.440349
$299$	−3.52495e82	−0.409419
$300$	0	0
$301$	−6.49196e82	−0.603113
$302$	−1.32144e82	−0.109853
$303$	0	0
$304$	−6.56789e82	−0.437684
$305$	−5.74636e82	−0.343043
$306$	0	0
$307$	1.38135e83	0.662475	0.331237	−	0.943547i	$-0.392534\pi$
$307$	1.38135e83	0.662475	0.331237	+	0.943547i	$0.392534\pi$
$308$	1.53254e83	0.659117
$309$	0	0
$310$	−5.59799e82	−0.193827
$311$	−3.94064e83	−1.22488	−0.612441	−	0.790516i	$-0.709812\pi$
$311$	−3.94064e83	−1.22488	−0.612441	+	0.790516i	$0.709812\pi$
$312$	0	0
$313$	2.68725e83	0.673864	0.336932	−	0.941529i	$-0.390611\pi$
$313$	2.68725e83	0.673864	0.336932	+	0.941529i	$0.390611\pi$
$314$	2.48414e83	0.559799
$315$	0	0
$316$	−1.51050e83	−0.275171
$317$	−2.06813e83	−0.338917	−0.169458	−	0.985537i	$-0.554202\pi$
$317$	−2.06813e83	−0.338917	−0.169458	+	0.985537i	$0.554202\pi$
$318$	0	0
$319$	−1.17386e84	−1.55822
$320$	−2.73612e82	−0.0327048
$321$	0	0
$322$	−1.33229e83	−0.129249
$323$	4.89173e83	0.427738
$324$	0	0
$325$	−9.38202e83	−0.667120
$326$	−8.26474e83	−0.530200
$327$	0	0
$328$	2.23902e84	1.17026
$329$	2.77349e83	0.130907
$330$	0	0
$331$	5.77944e83	0.222663	0.111332	−	0.993783i	$-0.464488\pi$
$331$	5.77944e83	0.222663	0.111332	+	0.993783i	$0.464488\pi$
$332$	4.15791e83	0.144793
$333$	0	0
$334$	4.06596e83	0.115786
$335$	2.15625e84	0.555518
$336$	0	0
$337$	3.23409e84	0.682576	0.341288	−	0.939959i	$-0.389137\pi$
$337$	3.23409e84	0.682576	0.341288	+	0.939959i	$0.389137\pi$
$338$	9.76609e83	0.186643
$339$	0	0
$340$	8.37707e83	0.131386
$341$	1.44806e85	2.05832
$342$	0	0
$343$	8.10488e84	0.947095
$344$	7.70371e84	0.816568
$345$	0	0
$346$	−2.12448e84	−0.185440
$347$	−7.38268e84	−0.585028	−0.292514	−	0.956261i	$-0.594492\pi$
$347$	−7.38268e84	−0.585028	−0.292514	+	0.956261i	$0.594492\pi$
$348$	0	0
$349$	2.25397e85	1.47331	0.736657	−	0.676266i	$-0.236403\pi$
$349$	2.25397e85	1.47331	0.736657	+	0.676266i	$0.236403\pi$
$350$	−3.54602e84	−0.210602
$351$	0	0
$352$	−2.81453e85	−1.38111
$353$	2.28605e85	1.02008	0.510038	−	0.860152i	$-0.329631\pi$
$353$	2.28605e85	1.02008	0.510038	+	0.860152i	$0.329631\pi$
$354$	0	0
$355$	1.12490e85	0.415397
$356$	3.70866e85	1.24636
$357$	0	0
$358$	1.24795e85	0.347629
$359$	7.82216e84	0.198455	0.0992276	−	0.995065i	$-0.468363\pi$
$359$	7.82216e84	0.198455	0.0992276	+	0.995065i	$0.468363\pi$
$360$	0	0
$361$	−1.22740e85	−0.258521
$362$	2.54312e85	0.488237
$363$	0	0
$364$	2.16392e85	0.345418
$365$	−9.27618e84	−0.135070
$366$	0	0
$367$	6.12079e85	0.742155	0.371077	−	0.928602i	$-0.378988\pi$
$367$	6.12079e85	0.742155	0.371077	+	0.928602i	$0.378988\pi$
$368$	−2.52927e85	−0.279959
$369$	0	0
$370$	2.19662e85	0.202767
$371$	3.27831e85	0.276455
$372$	0	0
$373$	−1.28610e86	−0.905791	−0.452895	−	0.891564i	$-0.649609\pi$
$373$	−1.28610e86	−0.905791	−0.452895	+	0.891564i	$0.649609\pi$
$374$	4.56456e85	0.293900
$375$	0	0
$376$	−3.29117e85	−0.177238
$377$	−1.65747e86	−0.816602
$378$	0	0
$379$	5.21083e85	0.215027	0.107514	−	0.994204i	$-0.465711\pi$
$379$	5.21083e85	0.215027	0.107514	+	0.994204i	$0.465711\pi$
$380$	6.02864e85	0.227756
$381$	0	0
$382$	−6.52708e84	−0.0206822
$383$	1.33278e86	0.386901	0.193451	−	0.981110i	$-0.438032\pi$
$383$	1.33278e86	0.386901	0.193451	+	0.981110i	$0.438032\pi$
$384$	0	0
$385$	−1.04798e86	−0.255515
$386$	−2.96912e86	−0.663672
$387$	0	0
$388$	−2.80346e86	−0.527025
$389$	−9.94670e86	−1.71541	−0.857704	−	0.514144i	$-0.828110\pi$
$389$	−9.94670e86	−1.71541	−0.857704	+	0.514144i	$0.828110\pi$
$390$	0	0
$391$	1.88379e86	0.273597
$392$	−3.90482e86	−0.520617
$393$	0	0
$394$	−3.22815e86	−0.362937
$395$	1.03290e86	0.106674
$396$	0	0
$397$	−5.37440e86	−0.468649	−0.234325	−	0.972158i	$-0.575288\pi$
$397$	−5.37440e86	−0.468649	−0.234325	+	0.972158i	$0.575288\pi$
$398$	5.02885e86	0.403075
$399$	0	0
$400$	−6.73192e86	−0.456172
$401$	4.13165e86	0.257506	0.128753	−	0.991677i	$-0.458903\pi$
$401$	4.13165e86	0.257506	0.128753	+	0.991677i	$0.458903\pi$
$402$	0	0
$403$	2.04463e87	1.07869
$404$	1.07647e87	0.522671
$405$	0	0
$406$	−6.26456e86	−0.257792
$407$	−5.68210e87	−2.15326
$408$	0	0
$409$	−2.75139e87	−0.884753	−0.442376	−	0.896830i	$-0.645864\pi$
$409$	−2.75139e87	−0.884753	−0.442376	+	0.896830i	$0.645864\pi$
$410$	−6.92592e86	−0.205219
$411$	0	0
$412$	1.32217e87	0.332836
$413$	−3.80512e87	−0.883164
$414$	0	0
$415$	−2.84324e86	−0.0561310
$416$	−3.97408e87	−0.723786
$417$	0	0
$418$	3.28493e87	0.509472
$419$	1.09982e87	0.157454	0.0787268	−	0.996896i	$-0.474915\pi$
$419$	1.09982e87	0.157454	0.0787268	+	0.996896i	$0.474915\pi$
$420$	0	0
$421$	−1.24851e88	−1.52385	−0.761923	−	0.647668i	$-0.775744\pi$
$421$	−1.24851e88	−1.52385	−0.761923	+	0.647668i	$0.775744\pi$
$422$	1.16359e87	0.131169
$423$	0	0
$424$	−3.89022e87	−0.374298
$425$	5.01389e87	0.445806
$426$	0	0
$427$	7.93271e87	0.602681
$428$	−3.49949e87	−0.245832
$429$	0	0
$430$	−2.38298e87	−0.143195
$431$	2.68649e87	0.149347	0.0746736	−	0.997208i	$-0.476209\pi$
$431$	2.68649e87	0.149347	0.0746736	+	0.997208i	$0.476209\pi$
$432$	0	0
$433$	6.74157e87	0.320934	0.160467	−	0.987041i	$-0.448700\pi$
$433$	6.74157e87	0.320934	0.160467	+	0.987041i	$0.448700\pi$
$434$	7.72789e87	0.340530
$435$	0	0
$436$	−6.73981e86	−0.0254595
$437$	1.35569e88	0.474276
$438$	0	0
$439$	1.55673e88	0.467360	0.233680	−	0.972314i	$-0.424923\pi$
$439$	1.55673e88	0.467360	0.233680	+	0.972314i	$0.424923\pi$
$440$	1.24358e88	0.345948
$441$	0	0
$442$	6.44509e87	0.154022
$443$	7.64486e88	1.69373	0.846866	−	0.531806i	$-0.178487\pi$
$443$	7.64486e88	1.69373	0.846866	+	0.531806i	$0.178487\pi$
$444$	0	0
$445$	−2.53604e88	−0.483166
$446$	1.68266e87	0.0297358
$447$	0	0
$448$	3.77715e87	0.0574581
$449$	−3.05563e88	−0.431368	−0.215684	−	0.976463i	$-0.569198\pi$
$449$	−3.05563e88	−0.431368	−0.215684	+	0.976463i	$0.569198\pi$
$450$	0	0
$451$	1.79156e89	2.17930
$452$	7.27724e88	0.821920
$453$	0	0
$454$	6.91882e88	0.674001
$455$	−1.47973e88	−0.133906
$456$	0	0
$457$	−4.84706e88	−0.378692	−0.189346	−	0.981910i	$-0.560637\pi$
$457$	−4.84706e88	−0.378692	−0.189346	+	0.981910i	$0.560637\pi$
$458$	−2.35268e88	−0.170832
$459$	0	0
$460$	2.32161e88	0.145681
$461$	2.17512e89	1.26912	0.634560	−	0.772874i	$-0.281182\pi$
$461$	2.17512e89	1.26912	0.634560	+	0.772874i	$0.281182\pi$
$462$	0	0
$463$	−7.57996e88	−0.382564	−0.191282	−	0.981535i	$-0.561264\pi$
$463$	−7.57996e88	−0.382564	−0.191282	+	0.981535i	$0.561264\pi$
$464$	−1.18929e89	−0.558388
$465$	0	0
$466$	−1.38547e89	−0.563209
$467$	1.00599e89	0.380607	0.190304	−	0.981725i	$-0.439053\pi$
$467$	1.00599e89	0.380607	0.190304	+	0.981725i	$0.439053\pi$
$468$	0	0
$469$	−2.97665e89	−0.975973
$470$	1.01805e88	0.0310808
$471$	0	0
$472$	4.51536e89	1.19574
$473$	6.16416e89	1.52064
$474$	0	0
$475$	3.60830e89	0.772799
$476$	−1.15643e89	−0.230828
$477$	0	0
$478$	2.78611e89	0.483241
$479$	−9.96571e89	−1.61164	−0.805821	−	0.592159i	$-0.798276\pi$
$479$	−9.96571e89	−1.61164	−0.805821	+	0.592159i	$0.798276\pi$
$480$	0	0
$481$	−8.02304e89	−1.12844
$482$	1.71387e89	0.224855
$483$	0	0
$484$	−7.31881e89	−0.835836
$485$	1.91705e89	0.204308
$486$	0	0
$487$	−1.58587e90	−1.47247	−0.736236	−	0.676725i	$-0.763399\pi$
$487$	−1.58587e90	−1.47247	−0.736236	+	0.676725i	$0.763399\pi$
$488$	−9.41337e89	−0.815983
$489$	0	0
$490$	1.20787e89	0.0912963
$491$	−2.42050e90	−1.70874	−0.854369	−	0.519668i	$-0.826056\pi$
$491$	−2.42050e90	−1.70874	−0.854369	+	0.519668i	$0.826056\pi$
$492$	0	0
$493$	8.85778e89	0.545699
$494$	4.63827e89	0.266995
$495$	0	0
$496$	1.46709e90	0.737602
$497$	−1.55290e90	−0.729799
$498$	0	0
$499$	1.18042e90	0.484918	0.242459	−	0.970162i	$-0.422046\pi$
$499$	1.18042e90	0.484918	0.242459	+	0.970162i	$0.422046\pi$
$500$	1.30644e90	0.501872
$501$	0	0
$502$	−4.33210e89	−0.145587
$503$	−5.26757e90	−1.65609	−0.828043	−	0.560665i	$-0.810545\pi$
$503$	−5.26757e90	−1.65609	−0.828043	+	0.560665i	$0.810545\pi$
$504$	0	0
$505$	−7.36111e89	−0.202620
$506$	1.26502e90	0.325877
$507$	0	0
$508$	−6.74738e90	−1.52300
$509$	7.88037e90	1.66533	0.832666	−	0.553776i	$-0.186814\pi$
$509$	7.88037e90	1.66533	0.832666	+	0.553776i	$0.186814\pi$
$510$	0	0
$511$	1.28055e90	0.237300
$512$	−5.08216e90	−0.882073
$513$	0	0
$514$	3.62023e90	0.551406
$515$	−9.04121e89	−0.129028
$516$	0	0
$517$	−2.63344e90	−0.330058
$518$	−3.03238e90	−0.356235
$519$	0	0
$520$	1.75592e90	0.181298
$521$	1.48169e90	0.143448	0.0717239	−	0.997425i	$-0.477150\pi$
$521$	1.48169e90	0.143448	0.0717239	+	0.997425i	$0.477150\pi$
$522$	0	0
$523$	−1.36105e90	−0.115896	−0.0579481	−	0.998320i	$-0.518456\pi$
$523$	−1.36105e90	−0.115896	−0.0579481	+	0.998320i	$0.518456\pi$
$524$	−4.17146e90	−0.333188
$525$	0	0
$526$	4.44148e90	0.312252
$527$	−1.09268e91	−0.720840
$528$	0	0
$529$	−1.19887e91	−0.696636
$530$	1.20336e90	0.0656376
$531$	0	0
$532$	−8.32239e90	−0.400137
$533$	2.52966e91	1.14209
$534$	0	0
$535$	2.39301e90	0.0953000
$536$	3.53226e91	1.32139
$537$	0	0
$538$	2.41381e91	0.797069
$539$	−3.12446e91	−0.969508
$540$	0	0
$541$	−2.07523e90	−0.0568797	−0.0284399	−	0.999596i	$-0.509054\pi$
$541$	−2.07523e90	−0.0568797	−0.0284399	+	0.999596i	$0.509054\pi$
$542$	1.53052e91	0.394332
$543$	0	0
$544$	2.12381e91	0.483674
$545$	4.60879e89	0.00986971
$546$	0	0
$547$	5.89842e91	1.11728	0.558638	−	0.829412i	$-0.311324\pi$
$547$	5.89842e91	1.11728	0.558638	+	0.829412i	$0.311324\pi$
$548$	5.26794e91	0.938625
$549$	0	0
$550$	3.36697e91	0.530993
$551$	6.37459e91	0.945962
$552$	0	0
$553$	−1.42590e91	−0.187412
$554$	1.67461e91	0.207174
$555$	0	0
$556$	−1.00590e92	−1.10293
$557$	5.36319e91	0.553700	0.276850	−	0.960913i	$-0.410710\pi$
$557$	5.36319e91	0.553700	0.276850	+	0.960913i	$0.410710\pi$
$558$	0	0
$559$	8.70370e91	0.796908
$560$	−1.06175e91	−0.0915640
$561$	0	0
$562$	−4.90350e91	−0.375266
$563$	2.64660e91	0.190835	0.0954174	−	0.995437i	$-0.469581\pi$
$563$	2.64660e91	0.190835	0.0954174	+	0.995437i	$0.469581\pi$
$564$	0	0
$565$	−4.97630e91	−0.318628
$566$	6.01108e91	0.362746
$567$	0	0
$568$	1.84275e92	0.988091
$569$	−1.56640e92	−0.791848	−0.395924	−	0.918283i	$-0.629576\pi$
$569$	−1.56640e92	−0.791848	−0.395924	+	0.918283i	$0.629576\pi$
$570$	0	0
$571$	−1.15568e92	−0.519433	−0.259717	−	0.965685i	$-0.583629\pi$
$571$	−1.15568e92	−0.519433	−0.259717	+	0.965685i	$0.583629\pi$
$572$	−2.05466e92	−0.870908
$573$	0	0
$574$	9.56107e91	0.360544
$575$	1.38954e92	0.494310
$576$	0	0
$577$	−2.87114e90	−0.00909210	−0.00454605	−	0.999990i	$-0.501447\pi$
$577$	−2.87114e90	−0.00909210	−0.00454605	+	0.999990i	$0.501447\pi$
$578$	1.05145e92	0.314201
$579$	0	0
$580$	1.09165e92	0.290565
$581$	3.92503e91	0.0986149
$582$	0	0
$583$	−3.11278e92	−0.697030
$584$	−1.51957e92	−0.321286
$585$	0	0
$586$	3.80303e92	0.717066
$587$	−2.33816e92	−0.416387	−0.208194	−	0.978088i	$-0.566758\pi$
$587$	−2.33816e92	−0.416387	−0.208194	+	0.978088i	$0.566758\pi$
$588$	0	0
$589$	−7.86361e92	−1.24957
$590$	−1.39673e92	−0.209686
$591$	0	0
$592$	−5.75680e92	−0.771621
$593$	−1.19409e93	−1.51253	−0.756267	−	0.654263i	$-0.772979\pi$
$593$	−1.19409e93	−1.51253	−0.756267	+	0.654263i	$0.772979\pi$
$594$	0	0
$595$	7.90788e91	0.0894833
$596$	−8.15196e92	−0.871991
$597$	0	0
$598$	1.78618e92	0.170780
$599$	−1.02253e93	−0.924434	−0.462217	−	0.886767i	$-0.652946\pi$
$599$	−1.02253e93	−0.924434	−0.462217	+	0.886767i	$0.652946\pi$
$600$	0	0
$601$	−3.89386e92	−0.314837	−0.157418	−	0.987532i	$-0.550317\pi$
$601$	−3.89386e92	−0.314837	−0.157418	+	0.987532i	$0.550317\pi$
$602$	3.28964e92	0.251574
$603$	0	0
$604$	−3.17882e92	−0.217535
$605$	5.00472e92	0.324022
$606$	0	0
$607$	−2.57597e93	−1.49321	−0.746603	−	0.665270i	$-0.768317\pi$
$607$	−2.57597e93	−1.49321	−0.746603	+	0.665270i	$0.768317\pi$
$608$	1.52842e93	0.838442
$609$	0	0
$610$	2.91183e92	0.143092
$611$	−3.71838e92	−0.172971
$612$	0	0
$613$	4.23652e93	1.76638	0.883189	−	0.469017i	$-0.155392\pi$
$613$	4.23652e93	1.76638	0.883189	+	0.469017i	$0.155392\pi$
$614$	−6.99967e92	−0.276336
$615$	0	0
$616$	−1.71674e93	−0.607785
$617$	−8.17102e92	−0.273983	−0.136991	−	0.990572i	$-0.543743\pi$
$617$	−8.17102e92	−0.273983	−0.136991	+	0.990572i	$0.543743\pi$
$618$	0	0
$619$	−2.52814e92	−0.0760613	−0.0380306	−	0.999277i	$-0.512108\pi$
$619$	−2.52814e92	−0.0760613	−0.0380306	+	0.999277i	$0.512108\pi$
$620$	−1.34664e93	−0.383822
$621$	0	0
$622$	1.99683e93	0.510931
$623$	3.50095e93	0.848859
$624$	0	0
$625$	3.22759e93	0.702907
$626$	−1.36170e93	−0.281087
$627$	0	0
$628$	5.97579e93	1.10853
$629$	4.28764e93	0.754087
$630$	0	0
$631$	−7.14064e93	−1.12915	−0.564577	−	0.825380i	$-0.690961\pi$
$631$	−7.14064e93	−1.12915	−0.564577	+	0.825380i	$0.690961\pi$
$632$	1.69205e93	0.253741
$633$	0	0
$634$	1.04798e93	0.141371
$635$	4.61397e93	0.590412
$636$	0	0
$637$	−4.41169e93	−0.508083
$638$	5.94824e93	0.649974
$639$	0	0
$640$	3.30741e93	0.325431
$641$	−1.19515e94	−1.11603	−0.558017	−	0.829830i	$-0.688437\pi$
$641$	−1.19515e94	−1.11603	−0.558017	+	0.829830i	$0.688437\pi$
$642$	0	0
$643$	−3.95521e93	−0.332738	−0.166369	−	0.986064i	$-0.553204\pi$
$643$	−3.95521e93	−0.332738	−0.166369	+	0.986064i	$0.553204\pi$
$644$	−3.20493e93	−0.255942
$645$	0	0
$646$	−2.47876e93	−0.178421
$647$	9.68870e93	0.662174	0.331087	−	0.943600i	$-0.392585\pi$
$647$	9.68870e93	0.662174	0.331087	+	0.943600i	$0.392585\pi$
$648$	0	0
$649$	3.61298e94	2.22673
$650$	4.75411e93	0.278273
$651$	0	0
$652$	−1.98815e94	−1.04992
$653$	2.58186e94	1.29522	0.647608	−	0.761974i	$-0.275770\pi$
$653$	2.58186e94	1.29522	0.647608	+	0.761974i	$0.275770\pi$
$654$	0	0
$655$	2.85251e93	0.129165
$656$	1.81511e94	0.780954
$657$	0	0
$658$	−1.40540e93	−0.0546049
$659$	5.02240e92	0.0185460	0.00927300	−	0.999957i	$-0.497048\pi$
$659$	5.02240e92	0.0185460	0.00927300	+	0.999957i	$0.497048\pi$
$660$	0	0
$661$	−2.75448e94	−0.918948	−0.459474	−	0.888191i	$-0.651962\pi$
$661$	−2.75448e94	−0.918948	−0.459474	+	0.888191i	$0.651962\pi$
$662$	−2.92859e93	−0.0928787
$663$	0	0
$664$	−4.65765e93	−0.133517
$665$	5.69099e93	0.155118
$666$	0	0
$667$	2.45483e94	0.605071
$668$	9.78098e93	0.229282
$669$	0	0
$670$	−1.09263e94	−0.231722
$671$	−7.53215e94	−1.51955
$672$	0	0
$673$	7.54513e94	1.37772	0.688862	−	0.724893i	$-0.258111\pi$
$673$	7.54513e94	1.37772	0.688862	+	0.724893i	$0.258111\pi$
$674$	−1.63880e94	−0.284721
$675$	0	0
$676$	2.34931e94	0.369595
$677$	4.57696e94	0.685262	0.342631	−	0.939470i	$-0.388682\pi$
$677$	4.57696e94	0.685262	0.342631	+	0.939470i	$0.388682\pi$
$678$	0	0
$679$	−2.64644e94	−0.358943
$680$	−9.38391e93	−0.121153
$681$	0	0
$682$	−7.33767e94	−0.858582
$683$	−9.77094e94	−1.08854	−0.544268	−	0.838911i	$-0.683193\pi$
$683$	−9.77094e94	−1.08854	−0.544268	+	0.838911i	$0.683193\pi$
$684$	0	0
$685$	−3.60230e94	−0.363870
$686$	−4.10695e94	−0.395059
$687$	0	0
$688$	6.24520e94	0.544921
$689$	−4.39519e94	−0.365287
$690$	0	0
$691$	−1.14117e95	−0.860669	−0.430334	−	0.902670i	$-0.641604\pi$
$691$	−1.14117e95	−0.860669	−0.430334	+	0.902670i	$0.641604\pi$
$692$	−5.11061e94	−0.367214
$693$	0	0
$694$	3.74099e94	0.244031
$695$	6.87849e94	0.427565
$696$	0	0
$697$	−1.35189e95	−0.763207
$698$	−1.14214e95	−0.614559
$699$	0	0
$700$	−8.53023e94	−0.417039
$701$	7.36200e92	0.00343117	0.00171558	−	0.999999i	$-0.499454\pi$
$701$	7.36200e92	0.00343117	0.00171558	+	0.999999i	$0.499454\pi$
$702$	0	0
$703$	3.08564e95	1.30720
$704$	−3.58643e94	−0.144870
$705$	0	0
$706$	−1.15840e95	−0.425501
$707$	1.01618e95	0.355977
$708$	0	0
$709$	−2.42896e95	−0.774053	−0.387027	−	0.922069i	$-0.626498\pi$
$709$	−2.42896e95	−0.774053	−0.387027	+	0.922069i	$0.626498\pi$
$710$	−5.70015e94	−0.173273
$711$	0	0
$712$	−4.15441e95	−1.14929
$713$	−3.02825e95	−0.799268
$714$	0	0
$715$	1.40501e95	0.337619
$716$	3.00204e95	0.688384
$717$	0	0
$718$	−3.96369e94	−0.0827810
$719$	−6.97731e95	−1.39082	−0.695409	−	0.718614i	$-0.744777\pi$
$719$	−6.97731e95	−1.39082	−0.695409	+	0.718614i	$0.744777\pi$
$720$	0	0
$721$	1.24812e95	0.226686
$722$	6.21957e94	0.107836
$723$	0	0
$724$	6.11769e95	0.966819
$725$	6.53379e95	0.985920
$726$	0	0
$727$	5.00262e95	0.688327	0.344164	−	0.938910i	$-0.388162\pi$
$727$	5.00262e95	0.688327	0.344164	+	0.938910i	$0.388162\pi$
$728$	−2.42401e95	−0.318517
$729$	0	0
$730$	4.70048e94	0.0563412
$731$	−4.65139e95	−0.532538
$732$	0	0
$733$	−8.92678e95	−0.932634	−0.466317	−	0.884618i	$-0.654419\pi$
$733$	−8.92678e95	−0.932634	−0.466317	+	0.884618i	$0.654419\pi$
$734$	−3.10156e95	−0.309573
$735$	0	0
$736$	5.88590e95	0.536298
$737$	2.82635e96	2.46074
$738$	0	0
$739$	3.28768e95	0.261397	0.130699	−	0.991422i	$-0.458278\pi$
$739$	3.28768e95	0.261397	0.130699	+	0.991422i	$0.458278\pi$
$740$	5.28415e95	0.401525
$741$	0	0
$742$	−1.66120e95	−0.115317
$743$	1.93595e96	1.28460	0.642301	−	0.766453i	$-0.277980\pi$
$743$	1.93595e96	1.28460	0.642301	+	0.766453i	$0.277980\pi$
$744$	0	0
$745$	5.57444e95	0.338038
$746$	6.51698e95	0.377830
$747$	0	0
$748$	1.09804e96	0.581989
$749$	−3.30349e95	−0.167430
$750$	0	0
$751$	2.33056e96	1.08025	0.540123	−	0.841586i	$-0.318378\pi$
$751$	2.33056e96	1.08025	0.540123	+	0.841586i	$0.318378\pi$
$752$	−2.66806e95	−0.118277
$753$	0	0
$754$	8.39883e95	0.340627
$755$	2.17373e95	0.0843301
$756$	0	0
$757$	−3.90449e96	−1.38628	−0.693141	−	0.720802i	$-0.743774\pi$
$757$	−3.90449e96	−1.38628	−0.693141	+	0.720802i	$0.743774\pi$
$758$	−2.64046e95	−0.0896936
$759$	0	0
$760$	−6.75323e95	−0.210018
$761$	−4.58353e95	−0.136400	−0.0681999	−	0.997672i	$-0.521726\pi$
$761$	−4.58353e95	−0.136400	−0.0681999	+	0.997672i	$0.521726\pi$
$762$	0	0
$763$	−6.36232e94	−0.0173398
$764$	−1.57014e95	−0.0409554
$765$	0	0
$766$	−6.75355e95	−0.161387
$767$	5.10148e96	1.16695
$768$	0	0
$769$	6.37251e96	1.33591	0.667956	−	0.744201i	$-0.267169\pi$
$769$	6.37251e96	1.33591	0.667956	+	0.744201i	$0.267169\pi$
$770$	5.31036e95	0.106582
$771$	0	0
$772$	−7.14246e96	−1.31422
$773$	−1.01535e97	−1.78897	−0.894486	−	0.447096i	$-0.852458\pi$
$773$	−1.01535e97	−1.78897	−0.894486	+	0.447096i	$0.852458\pi$
$774$	0	0
$775$	−8.05999e96	−1.30235
$776$	3.14041e96	0.485980
$777$	0	0
$778$	5.04025e96	0.715542
$779$	−9.72899e96	−1.32301
$780$	0	0
$781$	1.47448e97	1.84005
$782$	−9.54564e95	−0.114124
$783$	0	0
$784$	−3.16554e96	−0.347424
$785$	−4.08634e96	−0.429735
$786$	0	0
$787$	−1.79495e97	−1.73340	−0.866699	−	0.498832i	$-0.833762\pi$
$787$	−1.79495e97	−1.73340	−0.866699	+	0.498832i	$0.833762\pi$
$788$	−7.76558e96	−0.718697
$789$	0	0
$790$	−5.23399e95	−0.0444964
$791$	6.86966e96	0.559787
$792$	0	0
$793$	−1.06353e97	−0.796338
$794$	2.72334e96	0.195486
$795$	0	0
$796$	1.20973e97	0.798180
$797$	2.24378e96	0.141947	0.0709737	−	0.997478i	$-0.477389\pi$
$797$	2.24378e96	0.141947	0.0709737	+	0.997478i	$0.477389\pi$
$798$	0	0
$799$	1.98716e96	0.115589
$800$	1.56659e97	0.873859
$801$	0	0
$802$	−2.09361e96	−0.107413
$803$	−1.21589e97	−0.598308
$804$	0	0
$805$	2.19158e96	0.0992191
$806$	−1.03607e97	−0.449950
$807$	0	0
$808$	−1.20586e97	−0.481965
$809$	−4.98406e97	−1.91121	−0.955603	−	0.294658i	$-0.904794\pi$
$809$	−4.98406e97	−1.91121	−0.955603	+	0.294658i	$0.904794\pi$
$810$	0	0
$811$	−6.56249e96	−0.231670	−0.115835	−	0.993268i	$-0.536954\pi$
$811$	−6.56249e96	−0.231670	−0.115835	+	0.993268i	$0.536954\pi$
$812$	−1.50699e97	−0.510486
$813$	0	0
$814$	2.87926e97	0.898181
$815$	1.35953e97	0.407013
$816$	0	0
$817$	−3.34742e97	−0.923148
$818$	1.39420e97	0.369054
$819$	0	0
$820$	−1.66609e97	−0.406381
$821$	1.14583e96	0.0268302	0.0134151	−	0.999910i	$-0.495730\pi$
$821$	1.14583e96	0.0268302	0.0134151	+	0.999910i	$0.495730\pi$
$822$	0	0
$823$	−4.59764e95	−0.00992295	−0.00496147	−	0.999988i	$-0.501579\pi$
$823$	−4.59764e95	−0.00992295	−0.00496147	+	0.999988i	$0.501579\pi$
$824$	−1.48108e97	−0.306915
$825$	0	0
$826$	1.92815e97	0.368391
$827$	7.95450e97	1.45941	0.729707	−	0.683760i	$-0.239657\pi$
$827$	7.95450e97	1.45941	0.729707	+	0.683760i	$0.239657\pi$
$828$	0	0
$829$	9.08914e97	1.53796	0.768982	−	0.639271i	$-0.220764\pi$
$829$	9.08914e97	1.53796	0.768982	+	0.639271i	$0.220764\pi$
$830$	1.44074e96	0.0234137
$831$	0	0
$832$	−5.06398e96	−0.0759208
$833$	2.35768e97	0.339529
$834$	0	0
$835$	−6.68839e96	−0.0888843
$836$	7.90216e97	1.00887
$837$	0	0
$838$	−5.57308e96	−0.0656781
$839$	−8.73266e97	−0.988828	−0.494414	−	0.869227i	$-0.664617\pi$
$839$	−8.73266e97	−0.988828	−0.494414	+	0.869227i	$0.664617\pi$
$840$	0	0
$841$	1.97831e97	0.206837
$842$	6.32651e97	0.635636
$843$	0	0
$844$	2.79910e97	0.259744
$845$	−1.60650e97	−0.143278
$846$	0	0
$847$	−6.90890e97	−0.569265
$848$	−3.15370e97	−0.249781
$849$	0	0
$850$	−2.54067e97	−0.185958
$851$	1.18827e98	0.836132
$852$	0	0
$853$	−5.65226e97	−0.367646	−0.183823	−	0.982959i	$-0.558847\pi$
$853$	−5.65226e97	−0.367646	−0.183823	+	0.982959i	$0.558847\pi$
$854$	−4.01971e97	−0.251394
$855$	0	0
$856$	3.92010e97	0.226687
$857$	3.44343e98	1.91484	0.957422	−	0.288692i	$-0.0932204\pi$
$857$	3.44343e98	1.91484	0.957422	+	0.288692i	$0.0932204\pi$
$858$	0	0
$859$	1.63520e97	0.0841008	0.0420504	−	0.999115i	$-0.486611\pi$
$859$	1.63520e97	0.0841008	0.0420504	+	0.999115i	$0.486611\pi$
$860$	−5.73244e97	−0.283558
$861$	0	0
$862$	−1.36131e97	−0.0622967
$863$	−1.28936e98	−0.567559	−0.283779	−	0.958890i	$-0.591588\pi$
$863$	−1.28936e98	−0.567559	−0.283779	+	0.958890i	$0.591588\pi$
$864$	0	0
$865$	3.49472e97	0.142355
$866$	−3.41612e97	−0.133870
$867$	0	0
$868$	1.85900e98	0.674326
$869$	1.35390e98	0.472524
$870$	0	0
$871$	3.99076e98	1.28958
$872$	7.54987e96	0.0234767
$873$	0	0
$874$	−6.86962e97	−0.197833
$875$	1.23327e98	0.341812
$876$	0	0
$877$	−3.61956e98	−0.929329	−0.464665	−	0.885487i	$-0.653825\pi$
$877$	−3.61956e98	−0.929329	−0.464665	+	0.885487i	$0.653825\pi$
$878$	−7.88834e97	−0.194948
$879$	0	0
$880$	1.00814e98	0.230862
$881$	−2.86429e98	−0.631428	−0.315714	−	0.948854i	$-0.602244\pi$
$881$	−2.86429e98	−0.631428	−0.315714	+	0.948854i	$0.602244\pi$
$882$	0	0
$883$	4.85729e98	0.992454	0.496227	−	0.868193i	$-0.334718\pi$
$883$	4.85729e98	0.992454	0.496227	+	0.868193i	$0.334718\pi$
$884$	1.55042e98	0.304998
$885$	0	0
$886$	−3.87385e98	−0.706501
$887$	−5.57320e98	−0.978730	−0.489365	−	0.872079i	$-0.662771\pi$
$887$	−5.57320e98	−0.978730	−0.489365	+	0.872079i	$0.662771\pi$
$888$	0	0
$889$	−6.36947e98	−1.03728
$890$	1.28508e98	0.201541
$891$	0	0
$892$	4.04778e97	0.0588835
$893$	1.43008e98	0.200372
$894$	0	0
$895$	−2.05285e98	−0.266861
$896$	−4.56580e98	−0.571740
$897$	0	0
$898$	1.54836e98	0.179935
$899$	−1.42392e99	−1.59417
$900$	0	0
$901$	2.34886e98	0.244105
$902$	−9.07829e98	−0.909044
$903$	0	0
$904$	−8.15190e98	−0.757908
$905$	−4.18337e98	−0.374800
$906$	0	0
$907$	−1.07550e99	−0.894882	−0.447441	−	0.894313i	$-0.647665\pi$
$907$	−1.07550e99	−0.894882	−0.447441	+	0.894313i	$0.647665\pi$
$908$	1.66438e99	1.33467
$909$	0	0
$910$	7.49815e97	0.0558557
$911$	−9.91254e98	−0.711737	−0.355868	−	0.934536i	$-0.615815\pi$
$911$	−9.91254e98	−0.711737	−0.355868	+	0.934536i	$0.615815\pi$
$912$	0	0
$913$	−3.72684e98	−0.248639
$914$	2.45613e98	0.157962
$915$	0	0
$916$	−5.65957e98	−0.338287
$917$	−3.93782e98	−0.226926
$918$	0	0
$919$	−1.32361e99	−0.709073	−0.354537	−	0.935042i	$-0.615361\pi$
$919$	−1.32361e99	−0.709073	−0.354537	+	0.935042i	$0.615361\pi$
$920$	−2.60065e98	−0.134335
$921$	0	0
$922$	−1.10219e99	−0.529383
$923$	2.08195e99	0.964302
$924$	0	0
$925$	3.16270e99	1.36242
$926$	3.84096e98	0.159578
$927$	0	0
$928$	2.76761e99	1.06967
$929$	1.24297e98	0.0463377	0.0231688	−	0.999732i	$-0.492624\pi$
$929$	1.24297e98	0.0463377	0.0231688	+	0.999732i	$0.492624\pi$
$930$	0	0
$931$	1.69673e99	0.588569
$932$	−3.33286e99	−1.11528
$933$	0	0
$934$	−5.09760e98	−0.158761
$935$	−7.50858e98	−0.225615
$936$	0	0
$937$	4.03865e99	1.12969	0.564846	−	0.825197i	$-0.308936\pi$
$937$	4.03865e99	1.12969	0.564846	+	0.825197i	$0.308936\pi$
$938$	1.50835e99	0.407105
$939$	0	0
$940$	2.44901e98	0.0615470
$941$	7.13430e99	1.73021	0.865105	−	0.501591i	$-0.167252\pi$
$941$	7.13430e99	1.73021	0.865105	+	0.501591i	$0.167252\pi$
$942$	0	0
$943$	−3.74660e99	−0.846244
$944$	3.66048e99	0.797952
$945$	0	0
$946$	−3.12354e99	−0.634298
$947$	−3.01348e99	−0.590668	−0.295334	−	0.955394i	$-0.595431\pi$
$947$	−3.01348e99	−0.590668	−0.295334	+	0.955394i	$0.595431\pi$
$948$	0	0
$949$	−1.71682e99	−0.313551
$950$	−1.82842e99	−0.322355
$951$	0	0
$952$	1.29543e99	0.212851
$953$	−4.15491e99	−0.659097	−0.329549	−	0.944139i	$-0.606897\pi$
$953$	−4.15491e99	−0.659097	−0.329549	+	0.944139i	$0.606897\pi$
$954$	0	0
$955$	1.07369e98	0.0158769
$956$	6.70220e99	0.956926
$957$	0	0
$958$	5.04988e99	0.672259
$959$	4.97289e99	0.639272
$960$	0	0
$961$	9.22395e99	1.10582
$962$	4.06548e99	0.470703
$963$	0	0
$964$	4.12285e99	0.445263
$965$	4.88413e99	0.509475
$966$	0	0
$967$	4.64253e99	0.451823	0.225911	−	0.974148i	$-0.427464\pi$
$967$	4.64253e99	0.451823	0.225911	+	0.974148i	$0.427464\pi$
$968$	8.19847e99	0.770741
$969$	0	0
$970$	−9.71419e98	−0.0852224
$971$	−1.49343e99	−0.126573	−0.0632863	−	0.997995i	$-0.520158\pi$
$971$	−1.49343e99	−0.126573	−0.0632863	+	0.997995i	$0.520158\pi$
$972$	0	0
$973$	−9.49559e99	−0.751176
$974$	8.03600e99	0.614207
$975$	0	0
$976$	−7.63118e99	−0.544531
$977$	−1.94135e100	−1.33855	−0.669275	−	0.743014i	$-0.733395\pi$
$977$	−1.94135e100	−1.33855	−0.669275	+	0.743014i	$0.733395\pi$
$978$	0	0
$979$	−3.32417e100	−2.14024
$980$	2.90564e99	0.180787
$981$	0	0
$982$	1.22653e100	0.712760
$983$	7.70721e99	0.432867	0.216433	−	0.976297i	$-0.430558\pi$
$983$	7.70721e99	0.432867	0.216433	+	0.976297i	$0.430558\pi$
$984$	0	0
$985$	5.31023e99	0.278612
$986$	−4.48846e99	−0.227625
$987$	0	0
$988$	1.11577e100	0.528711
$989$	−1.28908e100	−0.590479
$990$	0	0
$991$	4.23472e99	0.181283	0.0906415	−	0.995884i	$-0.471108\pi$
$991$	4.23472e99	0.181283	0.0906415	+	0.995884i	$0.471108\pi$
$992$	−3.41409e100	−1.41297
$993$	0	0
$994$	7.86892e99	0.304419
$995$	−8.27233e99	−0.309425
$996$	0	0
$997$	1.09542e100	0.383082	0.191541	−	0.981485i	$-0.438652\pi$
$997$	1.09542e100	0.383082	0.191541	+	0.981485i	$0.438652\pi$
$998$	−5.98149e99	−0.202272
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	9.68.a.a.1.3		5
3.2	odd	2		1.68.a.a.1.3	✓	5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1.68.a.a.1.3	✓	5	3.2	odd	2
9.68.a.a.1.3		5	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:	\( k \)	\(=\)	\( 68 \)
Character orbit:	\([\chi]\)	\(=\)	9.a (trivial)

\(f(q)\)	\(=\)	\(q-5.06726e9 q^{2} -1.21897e20 q^{4} +8.33551e22 q^{5} -1.15070e28 q^{7} +1.36548e30 q^{8} +O(q^{10})\)	\(q-5.06726e9 q^{2} -1.21897e20 q^{4} +8.33551e22 q^{5} -1.15070e28 q^{7} +1.36548e30 q^{8} -4.22381e32 q^{10} +1.09259e35 q^{11} +1.54273e37 q^{13} +5.83087e37 q^{14} +1.10696e40 q^{16} -8.24456e40 q^{17} -5.93328e42 q^{19} -1.01607e43 q^{20} -5.53645e44 q^{22} -2.28489e45 q^{23} -6.08146e46 q^{25} -7.81738e46 q^{26} +1.40266e48 q^{28} -1.07438e49 q^{29} +1.32534e50 q^{31} -2.57601e50 q^{32} +4.17773e50 q^{34} -9.59164e50 q^{35} -5.20056e52 q^{37} +3.00655e52 q^{38} +1.13819e53 q^{40} +1.63973e54 q^{41} +5.64177e54 q^{43} -1.33184e55 q^{44} +1.15781e55 q^{46} -2.41027e55 q^{47} -2.85968e56 q^{49} +3.08163e56 q^{50} -1.88053e57 q^{52} -2.84898e57 q^{53} +9.10731e57 q^{55} -1.57125e58 q^{56} +5.44415e58 q^{58} +3.30680e59 q^{59} -6.89383e59 q^{61} -6.71583e59 q^{62} -3.28249e59 q^{64} +1.28594e60 q^{65} +2.58683e61 q^{67} +1.00499e61 q^{68} +4.86033e60 q^{70} +1.34953e62 q^{71} -1.11285e62 q^{73} +2.63526e62 q^{74} +7.23248e62 q^{76} -1.25724e63 q^{77} +1.23916e63 q^{79} +9.22705e62 q^{80} -8.30894e63 q^{82} -3.41100e63 q^{83} -6.87226e63 q^{85} -2.85883e64 q^{86} +1.49191e65 q^{88} -3.04246e65 q^{89} -1.77521e65 q^{91} +2.78521e65 q^{92} +1.22134e65 q^{94} -4.94569e65 q^{95} +2.29986e66 q^{97} +1.44907e66 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 5 q - 5554901256 q^{2} + 35\!\cdots\!40 q^{4}+ \cdots - 32\!\cdots\!80 q^{8}+O(q^{10}) \) 5 * q - 5554901256 * q^2 + 350472004382296600640 * q^4 - 330744836907160597528950 * q^5 + 33632726520317603069152899256 * q^7 - 3261706912683890613885787783680 * q^8	\( 5 q - 5554901256 q^{2} + 35\!\cdots\!40 q^{4}+ \cdots - 12\!\cdots\!08 q^{98}+O(q^{100}) \) 5 * q - 5554901256 * q^2 + 350472004382296600640 * q^4 - 330744836907160597528950 * q^5 + 33632726520317603069152899256 * q^7 - 3261706912683890613885787783680 * q^8 - 5287067006725590176865792208438800 * q^10 - 203006981551281631527218766884109060 * q^11 + 177822884499813229570219072356766702 * q^13 - 290753425875732621001638220329334092480 * q^14 + 18266362102387359184851236859301091348480 * q^16 - 75241497376497768433807587544150344102906 * q^17 + 3998884102997801557241177083441346393295100 * q^19 + 15074831378020267075078660994426474705846400 * q^20 + 1841247880573095918698534631505063585473750432 * q^22 + 419660874260151197180020017656265233426170968 * q^23 + 175279270003539476977813620578789764300129011875 * q^25 - 21416337629300654169124097666599354769371062960 * q^26 + 14982728306233364463143494158089725946900023694848 * q^28 - 18733547497571939101380180097730717676662894233950 * q^29 + 365849822471060800690376948081970588059264217288160 * q^31 - 1591165751988992347021834813546084975107380979204096 * q^32 + 7817592154883765712044327776251337623941567500782480 * q^34 - 4524513410554564733118320802153390591800073874285200 * q^35 - 56389392588768330454829645685931746748224606527380394 * q^37 + 311451303114725973135630000941921262878276604287141280 * q^38 - 1886768345048751997029226502271137564956948018338432000 * q^40 - 113555410342193387626817165052765483601006465327103010 * q^41 + 6508304671085340439704487085091235272293711787089861092 * q^43 - 49369449025916528958230735645862721892607029455332199680 * q^44 + 79552980744915855625545425031873854934595203714399466560 * q^46 + 128023594814179612806658270243785955024442659789917751344 * q^47 - 771329931628098140389185999842408514636676231229111640435 * q^49 + 3919481096957516748709549462396523762064894577356951885000 * q^50 + 672997930141532412373441872733517069231734104886640838016 * q^52 - 1046765637663599376128164919371991945530174947374966490822 * q^53 + 66942753107037791618627925698973654692865254681839842449400 * q^55 - 164746697572073652525116376573879338548073684495562965299200 * q^56 - 61137956327686914952144218440883774026433838412764071303120 * q^58 + 305790738450157663862297559072875409310668010528073986627500 * q^59 - 1137073938560830615075915586814815057732339483683661907261890 * q^61 + 2197846158587850633685459639420082896328263471188214086352128 * q^62 + 6319522016046144185339524760669817745425888834305772325437440 * q^64 - 17054811715744261908524663200762497384422620874171150779332900 * q^65 - 11903044989154510038048691316368615691989662189985228212145844 * q^67 - 81678078346863753465296539273887923556029130514802676363013248 * q^68 - 262230520857255225386866306600227822969034558447869634844476800 * q^70 + 112169920751076079402369696382938772997794660792753351047772040 * q^71 - 304061800126793465330511223999919410949872771539142074085150718 * q^73 - 921008183492866283853128598587548033201480125306857491530532080 * q^74 + 2076567511595431334156222539483464646991367936386801535927366400 * q^76 - 5018131462902473316385236580394702266689060843204393245422638432 * q^77 + 2994504004186984867153587379277397704940492543518650040519815600 * q^79 + 15198313539268031787508043655897930060910106707913153957798092800 * q^80 - 17699192859543411700126655967680257958811789647196784631772687408 * q^82 + 47352447490969920981134910324833485175129837165394254819464203588 * q^83 - 39334683419450918052255554891934302881190270223971152032299949300 * q^85 - 49699285824187070765304255878405188987409992188766856866277888160 * q^86 + 430257938373980762031490456670953174964896424231159472833711400960 * q^88 + 11988583288945008097106276879882407358382120120051430459779195150 * q^89 + 232376792470844928685229521265495056030669651812230900159714321360 * q^91 + 986292139147147043544160128863480288571347084605459783959415954944 * q^92 - 4927754861315037106505826725122767884474273389521981763161929704320 * q^94 + 2022377488008256909110920831467942087293430657450319294506545963000 * q^95 + 2897556354128426205551279700626881901316694084191208635967319112106 * q^97 - 12426885478574475523720488645206508880013087100212747539199689691208 * q^98

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