LMFDB - Embedded newform 9.68.a.a.1.1

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			1.1
Root			$-8.99335e8$ 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)

$f(q)$	$=$	$q-2.26950e10 q^{2} +3.67490e20 q^{4} +1.61198e23 q^{5} +2.93806e28 q^{7} -4.99099e30 q^{8} +O(q^{10})$	\(q-2.26950e10 q^{2} +3.67490e20 q^{4} +1.61198e23 q^{5} +2.93806e28 q^{7} -4.99099e30 q^{8} -3.65838e33 q^{10} -1.03989e35 q^{11} -9.30624e35 q^{13} -6.66794e38 q^{14} +5.90387e40 q^{16} -2.52116e41 q^{17} -4.10720e41 q^{19} +5.92385e43 q^{20} +2.36002e45 q^{22} +7.28152e44 q^{23} -4.17779e46 q^{25} +2.11205e46 q^{26} +1.07971e49 q^{28} +8.66841e48 q^{29} +5.42697e49 q^{31} -6.03344e50 q^{32} +5.72177e51 q^{34} +4.73609e51 q^{35} +2.44090e52 q^{37} +9.32129e51 q^{38} -8.04536e53 q^{40} -8.84851e52 q^{41} -3.35174e54 q^{43} -3.82147e55 q^{44} -1.65254e55 q^{46} +1.34362e56 q^{47} +4.44845e56 q^{49} +9.48151e56 q^{50} -3.41995e56 q^{52} +3.87432e57 q^{53} -1.67627e58 q^{55} -1.46639e59 q^{56} -1.96730e59 q^{58} +2.62052e59 q^{59} -4.77635e59 q^{61} -1.23165e60 q^{62} +4.98032e60 q^{64} -1.50015e59 q^{65} -2.36430e61 q^{67} -9.26500e61 q^{68} -1.07486e62 q^{70} -2.36087e61 q^{71} +7.86035e61 q^{73} -5.53962e62 q^{74} -1.50935e62 q^{76} -3.05525e63 q^{77} -2.74602e63 q^{79} +9.51690e63 q^{80} +2.00817e63 q^{82} -9.16622e63 q^{83} -4.06405e64 q^{85} +7.60679e64 q^{86} +5.19006e65 q^{88} +3.36134e65 q^{89} -2.73423e64 q^{91} +2.67588e65 q^{92} -3.04935e66 q^{94} -6.62071e64 q^{95} +6.50306e66 q^{97} -1.00958e67 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−2.26950e10	−1.86821	−0.934105	−	0.356999i	$-0.883800\pi$
$2$	−2.26950e10	−1.86821	−0.934105	+	0.356999i	$0.883800\pi$
$3$	0	0
$3$	0	0
$4$	3.67490e20	2.49021
$5$	1.61198e23	0.619247	0.309623	−	0.950859i	$-0.399797\pi$
$5$	1.61198e23	0.619247	0.309623	+	0.950859i	$0.399797\pi$
$6$	0	0
$7$	2.93806e28	1.43641	0.718203	−	0.695834i	$-0.244965\pi$
$7$	2.93806e28	1.43641	0.718203	+	0.695834i	$0.244965\pi$
$8$	−4.99099e30	−2.78402
$9$	0	0
$10$	−3.65838e33	−1.15688
$11$	−1.03989e35	−1.34999	−0.674995	−	0.737822i	$-0.735854\pi$
$11$	−1.03989e35	−1.34999	−0.674995	+	0.737822i	$0.735854\pi$
$12$	0	0
$13$	−9.30624e35	−0.0448407	−0.0224203	−	0.999749i	$-0.507137\pi$
$13$	−9.30624e35	−0.0448407	−0.0224203	+	0.999749i	$0.507137\pi$
$14$	−6.66794e38	−2.68351
$15$	0	0
$16$	5.90387e40	2.71092
$17$	−2.52116e41	−1.51901	−0.759506	−	0.650500i	$-0.774559\pi$
$17$	−2.52116e41	−1.51901	−0.759506	+	0.650500i	$0.774559\pi$
$18$	0	0
$19$	−4.10720e41	−0.0596074	−0.0298037	−	0.999556i	$-0.509488\pi$
$19$	−4.10720e41	−0.0596074	−0.0298037	+	0.999556i	$0.509488\pi$
$20$	5.92385e43	1.54205
$21$	0	0
$22$	2.36002e45	2.52207
$23$	7.28152e44	0.175525	0.0877626	−	0.996141i	$-0.472028\pi$
$23$	7.28152e44	0.175525	0.0877626	+	0.996141i	$0.472028\pi$
$24$	0	0
$25$	−4.17779e46	−0.616533
$26$	2.11205e46	0.0837718
$27$	0	0
$28$	1.07971e49	3.57695
$29$	8.66841e48	0.886353	0.443176	−	0.896434i	$-0.353852\pi$
$29$	8.66841e48	0.886353	0.443176	+	0.896434i	$0.353852\pi$
$30$	0	0
$31$	5.42697e49	0.594211	0.297106	−	0.954845i	$-0.403979\pi$
$31$	5.42697e49	0.594211	0.297106	+	0.954845i	$0.403979\pi$
$32$	−6.03344e50	−2.28056
$33$	0	0
$34$	5.72177e51	2.83783
$35$	4.73609e51	0.889490
$36$	0	0
$37$	2.44090e52	0.712511	0.356255	−	0.934389i	$-0.384053\pi$
$37$	2.44090e52	0.712511	0.356255	+	0.934389i	$0.384053\pi$
$38$	9.32129e51	0.111359
$39$	0	0
$40$	−8.04536e53	−1.72399
$41$	−8.84851e52	−0.0829108	−0.0414554	−	0.999140i	$-0.513199\pi$
$41$	−8.84851e52	−0.0829108	−0.0414554	+	0.999140i	$0.513199\pi$
$42$	0	0
$43$	−3.35174e54	−0.636909	−0.318455	−	0.947938i	$-0.603164\pi$
$43$	−3.35174e54	−0.636909	−0.318455	+	0.947938i	$0.603164\pi$
$44$	−3.82147e55	−3.36176
$45$	0	0
$46$	−1.65254e55	−0.327918
$47$	1.34362e56	1.29718	0.648588	−	0.761140i	$-0.275360\pi$
$47$	1.34362e56	1.29718	0.648588	+	0.761140i	$0.275360\pi$
$48$	0	0
$49$	4.44845e56	1.06326
$50$	9.48151e56	1.15181
$51$	0	0
$52$	−3.41995e56	−0.111663
$53$	3.87432e57	0.668273	0.334136	−	0.942525i	$-0.391555\pi$
$53$	3.87432e57	0.668273	0.334136	+	0.942525i	$0.391555\pi$
$54$	0	0
$55$	−1.67627e58	−0.835977
$56$	−1.46639e59	−3.99898
$57$	0	0
$58$	−1.96730e59	−1.65589
$59$	2.62052e59	1.24407	0.622035	−	0.782989i	$-0.286306\pi$
$59$	2.62052e59	1.24407	0.622035	+	0.782989i	$0.286306\pi$
$60$	0	0
$61$	−4.77635e59	−0.742244	−0.371122	−	0.928584i	$-0.621027\pi$
$61$	−4.77635e59	−0.742244	−0.371122	+	0.928584i	$0.621027\pi$
$62$	−1.23165e60	−1.11011
$63$	0	0
$64$	4.98032e60	1.54963
$65$	−1.50015e59	−0.0277674
$66$	0	0
$67$	−2.36430e61	−1.58561	−0.792805	−	0.609476i	$-0.791380\pi$
$67$	−2.36430e61	−1.58561	−0.792805	+	0.609476i	$0.791380\pi$
$68$	−9.26500e61	−3.78265
$69$	0	0
$70$	−1.07486e62	−1.66175
$71$	−2.36087e61	−0.226943	−0.113471	−	0.993541i	$-0.536197\pi$
$71$	−2.36087e61	−0.226943	−0.113471	+	0.993541i	$0.536197\pi$
$72$	0	0
$73$	7.86035e61	0.297938	0.148969	−	0.988842i	$-0.452404\pi$
$73$	7.86035e61	0.297938	0.148969	+	0.988842i	$0.452404\pi$
$74$	−5.53962e62	−1.33112
$75$	0	0
$76$	−1.50935e62	−0.148435
$77$	−3.05525e63	−1.93913
$78$	0	0
$79$	−2.74602e63	−0.738237	−0.369118	−	0.929382i	$-0.620340\pi$
$79$	−2.74602e63	−0.738237	−0.369118	+	0.929382i	$0.620340\pi$
$80$	9.51690e63	1.67873
$81$	0	0
$82$	2.00817e63	0.154895
$83$	−9.16622e63	−0.471058	−0.235529	−	0.971867i	$-0.575682\pi$
$83$	−9.16622e63	−0.471058	−0.235529	+	0.971867i	$0.575682\pi$
$84$	0	0
$85$	−4.06405e64	−0.940643
$86$	7.60679e64	1.18988
$87$	0	0
$88$	5.19006e65	3.75840
$89$	3.36134e65	1.66704	0.833521	−	0.552488i	$-0.186321\pi$
$89$	3.36134e65	1.66704	0.833521	+	0.552488i	$0.186321\pi$
$90$	0	0
$91$	−2.73423e64	−0.0644094
$92$	2.67588e65	0.437094
$93$	0	0
$94$	−3.04935e66	−2.42340
$95$	−6.62071e64	−0.0369117
$96$	0	0
$97$	6.50306e66	1.80412	0.902059	−	0.431614i	$-0.142056\pi$
$97$	6.50306e66	1.80412	0.902059	+	0.431614i	$0.142056\pi$
$98$	−1.00958e67	−1.98639
$99$	0	0
$100$	−1.53530e67	−1.53530
$101$	−1.99950e67	−1.43270	−0.716352	−	0.697739i	$-0.754189\pi$
$101$	−1.99950e67	−1.43270	−0.716352	+	0.697739i	$0.754189\pi$
$102$	0	0
$103$	2.01461e67	0.748417	0.374209	−	0.927345i	$-0.377914\pi$
$103$	2.01461e67	0.748417	0.374209	+	0.927345i	$0.377914\pi$
$104$	4.64474e66	0.124837
$105$	0	0
$106$	−8.79277e67	−1.24847
$107$	3.65427e67	0.378830	0.189415	−	0.981897i	$-0.439341\pi$
$107$	3.65427e67	0.378830	0.189415	+	0.981897i	$0.439341\pi$
$108$	0	0
$109$	−5.60552e67	−0.312484	−0.156242	−	0.987719i	$-0.549938\pi$
$109$	−5.60552e67	−0.312484	−0.156242	+	0.987719i	$0.549938\pi$
$110$	3.80430e68	1.56178
$111$	0	0
$112$	1.73460e69	3.89399
$113$	9.31318e66	0.0155228	0.00776140	−	0.999970i	$-0.497529\pi$
$113$	9.31318e66	0.0155228	0.00776140	+	0.999970i	$0.497529\pi$
$114$	0	0
$115$	1.17376e68	0.108693
$116$	3.18555e69	2.20720
$117$	0	0
$118$	−5.94727e69	−2.32418
$119$	−7.40733e69	−2.18192
$120$	0	0
$121$	4.88014e69	0.822474
$122$	1.08399e70	1.38667
$123$	0	0
$124$	1.99436e70	1.47971
$125$	−1.76577e70	−1.00103
$126$	0	0
$127$	2.79868e70	0.932243	0.466121	−	0.884721i	$-0.345651\pi$
$127$	2.79868e70	0.932243	0.466121	+	0.884721i	$0.345651\pi$
$128$	−2.39907e70	−0.614480
$129$	0	0
$130$	3.40458e69	0.0518754
$131$	2.72280e70	0.320943	0.160471	−	0.987040i	$-0.448699\pi$
$131$	2.72280e70	0.320943	0.160471	+	0.987040i	$0.448699\pi$
$132$	0	0
$133$	−1.20672e70	−0.0856204
$134$	5.36578e71	2.96225
$135$	0	0
$136$	1.25831e72	4.22896
$137$	−3.57817e70	−0.0940853	−0.0470427	−	0.998893i	$-0.514980\pi$
$137$	−3.57817e70	−0.0940853	−0.0470427	+	0.998893i	$0.514980\pi$
$138$	0	0
$139$	7.45641e71	1.20652	0.603259	−	0.797545i	$-0.293869\pi$
$139$	7.45641e71	1.20652	0.603259	+	0.797545i	$0.293869\pi$
$140$	1.74047e72	2.21501
$141$	0	0
$142$	5.35799e71	0.423977
$143$	9.67743e70	0.0605345
$144$	0	0
$145$	1.39733e72	0.548871
$146$	−1.78391e72	−0.556611
$147$	0	0
$148$	8.97004e72	1.77430
$149$	−1.30102e72	−0.205373	−0.102686	−	0.994714i	$-0.532744\pi$
$149$	−1.30102e72	−0.205373	−0.102686	+	0.994714i	$0.532744\pi$
$150$	0	0
$151$	−1.36349e73	−1.37697	−0.688486	−	0.725250i	$-0.741724\pi$
$151$	−1.36349e73	−1.37697	−0.688486	+	0.725250i	$0.741724\pi$
$152$	2.04990e72	0.165948
$153$	0	0
$154$	6.93390e73	3.62271
$155$	8.74816e72	0.367963
$156$	0	0
$157$	−1.66635e73	−0.456171	−0.228085	−	0.973641i	$-0.573247\pi$
$157$	−1.66635e73	−0.456171	−0.228085	+	0.973641i	$0.573247\pi$
$158$	6.23209e73	1.37918
$159$	0	0
$160$	−9.72577e73	−1.41223
$161$	2.13936e73	0.252125
$162$	0	0
$163$	−9.35739e70	−0.000729239 0	−0.000364620	−	1.00000i	$-0.500116\pi$
$163$	−9.35739e70	−0.000729239 0	−0.000364620		1.00000i	$0.500116\pi$
$164$	−3.25174e73	−0.206465
$165$	0	0
$166$	2.08027e74	0.880035
$167$	−4.79288e74	−1.65804	−0.829019	−	0.559220i	$-0.811101\pi$
$167$	−4.79288e74	−1.65804	−0.829019	+	0.559220i	$0.811101\pi$
$168$	0	0
$169$	−4.29863e74	−0.997989
$170$	9.22337e74	1.75732
$171$	0	0
$172$	−1.23173e75	−1.58604
$173$	−1.22221e75	−1.29599	−0.647995	−	0.761645i	$-0.724392\pi$
$173$	−1.22221e75	−1.29599	−0.647995	+	0.761645i	$0.724392\pi$
$174$	0	0
$175$	−1.22746e75	−0.885592
$176$	−6.13935e75	−3.65972
$177$	0	0
$178$	−7.62856e75	−3.11438
$179$	1.85195e75	0.626689	0.313344	−	0.949640i	$-0.398551\pi$
$179$	1.85195e75	0.626689	0.313344	+	0.949640i	$0.398551\pi$
$180$	0	0
$181$	4.04550e75	0.943497	0.471748	−	0.881733i	$-0.343623\pi$
$181$	4.04550e75	0.943497	0.471748	+	0.881733i	$0.343623\pi$
$182$	6.20535e74	0.120330
$183$	0	0
$184$	−3.63420e75	−0.488666
$185$	3.93467e75	0.441220
$186$	0	0
$187$	2.62172e76	2.05065
$188$	4.93767e76	3.23024
$189$	0	0
$190$	1.50257e75	0.0689587
$191$	−8.00578e74	−0.0308167	−0.0154083	−	0.999881i	$-0.504905\pi$
$191$	−8.00578e74	−0.0308167	−0.0154083	+	0.999881i	$0.504905\pi$
$192$	0	0
$193$	−5.34503e76	−1.45138	−0.725688	−	0.688024i	$-0.758478\pi$
$193$	−5.34503e76	−1.45138	−0.725688	+	0.688024i	$0.758478\pi$
$194$	−1.47587e77	−3.37047
$195$	0	0
$196$	1.63476e77	2.64774
$197$	−2.95191e75	−0.0403166	−0.0201583	−	0.999797i	$-0.506417\pi$
$197$	−2.95191e75	−0.0403166	−0.0201583	+	0.999797i	$0.506417\pi$
$198$	0	0
$199$	−1.57308e77	−1.53170	−0.765850	−	0.643019i	$-0.777682\pi$
$199$	−1.57308e77	−1.53170	−0.765850	+	0.643019i	$0.777682\pi$
$200$	2.08513e77	1.71644
$201$	0	0
$202$	4.53788e77	2.67659
$203$	2.54684e77	1.27316
$204$	0	0
$205$	−1.42636e76	−0.0513422
$206$	−4.57216e77	−1.39820
$207$	0	0
$208$	−5.49428e76	−0.121560
$209$	4.27102e76	0.0804694
$210$	0	0
$211$	9.28985e77	1.27217	0.636087	−	0.771618i	$-0.280552\pi$
$211$	9.28985e77	1.27217	0.636087	+	0.771618i	$0.280552\pi$
$212$	1.42377e78	1.66414
$213$	0	0
$214$	−8.29337e77	−0.707734
$215$	−5.40294e77	−0.394404
$216$	0	0
$217$	1.59448e78	0.853528
$218$	1.27217e78	0.583786
$219$	0	0
$220$	−6.16013e78	−2.08176
$221$	2.34625e77	0.0681135
$222$	0	0
$223$	−6.42241e78	−1.37875	−0.689374	−	0.724406i	$-0.742114\pi$
$223$	−6.42241e78	−1.37875	−0.689374	+	0.724406i	$0.742114\pi$
$224$	−1.77266e79	−3.27580
$225$	0	0
$226$	−2.11363e77	−0.0289999
$227$	−1.17887e79	−1.39509	−0.697543	−	0.716543i	$-0.745723\pi$
$227$	−1.17887e79	−1.39509	−0.697543	+	0.716543i	$0.745723\pi$
$228$	0	0
$229$	−1.55534e79	−1.37194	−0.685972	−	0.727628i	$-0.740623\pi$
$229$	−1.55534e79	−1.37194	−0.685972	+	0.727628i	$0.740623\pi$
$230$	−2.66386e78	−0.203062
$231$	0	0
$232$	−4.32640e79	−2.46762
$233$	−1.81926e79	−0.898403	−0.449201	−	0.893431i	$-0.648291\pi$
$233$	−1.81926e79	−0.898403	−0.449201	+	0.893431i	$0.648291\pi$
$234$	0	0
$235$	2.16589e79	0.803272
$236$	9.63014e79	3.09799
$237$	0	0
$238$	1.68109e80	4.07628
$239$	2.13612e79	0.450087	0.225043	−	0.974349i	$-0.427748\pi$
$239$	2.13612e79	0.450087	0.225043	+	0.974349i	$0.427748\pi$
$240$	0	0
$241$	−3.27834e79	−0.522497	−0.261248	−	0.965272i	$-0.584134\pi$
$241$	−3.27834e79	−0.522497	−0.261248	+	0.965272i	$0.584134\pi$
$242$	−1.10755e80	−1.53655
$243$	0	0
$244$	−1.75526e80	−1.84834
$245$	7.17080e79	0.658421
$246$	0	0
$247$	3.82226e77	0.00267283
$248$	−2.70860e80	−1.65430
$249$	0	0
$250$	4.00742e80	1.87014
$251$	2.97257e80	1.21356	0.606782	−	0.794868i	$-0.292460\pi$
$251$	2.97257e80	1.21356	0.606782	+	0.794868i	$0.292460\pi$
$252$	0	0
$253$	−7.57195e79	−0.236957
$254$	−6.35161e80	−1.74162
$255$	0	0
$256$	−1.90498e80	−0.401653
$257$	−2.91395e80	−0.539166	−0.269583	−	0.962977i	$-0.586886\pi$
$257$	−2.91395e80	−0.539166	−0.269583	+	0.962977i	$0.586886\pi$
$258$	0	0
$259$	7.17151e80	1.02345
$260$	−5.51288e79	−0.0691467
$261$	0	0
$262$	−6.17940e80	−0.599588
$263$	−8.50029e79	−0.0725966	−0.0362983	−	0.999341i	$-0.511557\pi$
$263$	−8.50029e79	−0.0725966	−0.0362983	+	0.999341i	$0.511557\pi$
$264$	0	0
$265$	6.24531e80	0.413826
$266$	2.73866e80	0.159957
$267$	0	0
$268$	−8.68855e81	−3.94850
$269$	1.19177e81	0.478070	0.239035	−	0.971011i	$-0.423169\pi$
$269$	1.19177e81	0.478070	0.239035	+	0.971011i	$0.423169\pi$
$270$	0	0
$271$	3.56294e81	1.11516	0.557580	−	0.830123i	$-0.311730\pi$
$271$	3.56294e81	1.11516	0.557580	+	0.830123i	$0.311730\pi$
$272$	−1.48846e82	−4.11793
$273$	0	0
$274$	8.12066e80	0.175771
$275$	4.34443e81	0.832314
$276$	0	0
$277$	−1.14305e82	−1.71787	−0.858937	−	0.512081i	$-0.828875\pi$
$277$	−1.14305e82	−1.71787	−0.858937	+	0.512081i	$0.828875\pi$
$278$	−1.69223e82	−2.25403
$279$	0	0
$280$	−2.36378e82	−2.47636
$281$	−1.56122e82	−1.45145	−0.725727	−	0.687983i	$-0.758496\pi$
$281$	−1.56122e82	−1.45145	−0.725727	+	0.687983i	$0.758496\pi$
$282$	0	0
$283$	−9.49072e81	−0.695751	−0.347875	−	0.937541i	$-0.613097\pi$
$283$	−9.49072e81	−0.695751	−0.347875	+	0.937541i	$0.613097\pi$
$284$	−8.67594e81	−0.565135
$285$	0	0
$286$	−2.19629e81	−0.113091
$287$	−2.59975e81	−0.119094
$288$	0	0
$289$	3.60152e82	1.30740
$290$	−3.17124e82	−1.02541
$291$	0	0
$292$	2.88860e82	0.741928
$293$	8.72184e82	1.99776	0.998879	−	0.0473268i	$-0.0150702\pi$
$293$	8.72184e82	1.99776	0.998879	+	0.0473268i	$0.0150702\pi$
$294$	0	0
$295$	4.22422e82	0.770387
$296$	−1.21825e83	−1.98364
$297$	0	0
$298$	2.95266e82	0.383679
$299$	−6.77636e80	−0.00787067
$300$	0	0
$301$	−9.84764e82	−0.914860
$302$	3.09445e83	2.57247
$303$	0	0
$304$	−2.42484e82	−0.161591
$305$	−7.69937e82	−0.459632
$306$	0	0
$307$	1.53054e83	0.734021	0.367010	−	0.930217i	$-0.380381\pi$
$307$	1.53054e83	0.734021	0.367010	+	0.930217i	$0.380381\pi$
$308$	−1.12277e84	−4.82884
$309$	0	0
$310$	−1.98540e83	−0.687433
$311$	5.46579e82	0.169895	0.0849473	−	0.996385i	$-0.472928\pi$
$311$	5.46579e82	0.169895	0.0849473	+	0.996385i	$0.472928\pi$
$312$	0	0
$313$	3.36258e83	0.843214	0.421607	−	0.906779i	$-0.361466\pi$
$313$	3.36258e83	0.843214	0.421607	+	0.906779i	$0.361466\pi$
$314$	3.78178e83	0.852222
$315$	0	0
$316$	−1.00913e84	−1.83836
$317$	−6.50933e83	−1.06672	−0.533360	−	0.845888i	$-0.679071\pi$
$317$	−6.50933e83	−1.06672	−0.533360	+	0.845888i	$0.679071\pi$
$318$	0	0
$319$	−9.01416e83	−1.19657
$320$	8.02817e83	0.959604
$321$	0	0
$322$	−4.85528e83	−0.471023
$323$	1.03549e83	0.0905443
$324$	0	0
$325$	3.88796e82	0.0276458
$326$	2.12366e81	0.00136237
$327$	0	0
$328$	4.41628e83	0.230825
$329$	3.94765e84	1.86327
$330$	0	0
$331$	−2.75141e84	−1.06003	−0.530014	−	0.847989i	$-0.677813\pi$
$331$	−2.75141e84	−1.06003	−0.530014	+	0.847989i	$0.677813\pi$
$332$	−3.36849e84	−1.17303
$333$	0	0
$334$	1.08774e85	3.09756
$335$	−3.81119e84	−0.981883
$336$	0	0
$337$	8.52892e83	0.180008	0.0900041	−	0.995941i	$-0.471312\pi$
$337$	8.52892e83	0.180008	0.0900041	+	0.995941i	$0.471312\pi$
$338$	9.75576e84	1.86445
$339$	0	0
$340$	−1.49350e85	−2.34240
$341$	−5.64343e84	−0.802180
$342$	0	0
$343$	7.77614e83	0.0908681
$344$	1.67285e85	1.77317
$345$	0	0
$346$	2.77381e85	2.42118
$347$	−1.21189e84	−0.0960340	−0.0480170	−	0.998847i	$-0.515290\pi$
$347$	−1.21189e84	−0.0960340	−0.0480170	+	0.998847i	$0.515290\pi$
$348$	0	0
$349$	1.49172e85	0.975067	0.487534	−	0.873104i	$-0.337897\pi$
$349$	1.49172e85	0.975067	0.487534	+	0.873104i	$0.337897\pi$
$350$	2.78573e85	1.65447
$351$	0	0
$352$	6.27409e85	3.07873
$353$	−3.26597e84	−0.145734	−0.0728668	−	0.997342i	$-0.523215\pi$
$353$	−3.26597e84	−0.145734	−0.0728668	+	0.997342i	$0.523215\pi$
$354$	0	0
$355$	−3.80566e84	−0.140534
$356$	1.23526e86	4.15128
$357$	0	0
$358$	−4.20300e85	−1.17079
$359$	−2.09151e85	−0.530636	−0.265318	−	0.964161i	$-0.585477\pi$
$359$	−2.09151e85	−0.530636	−0.265318	+	0.964161i	$0.585477\pi$
$360$	0	0
$361$	−4.73092e85	−0.996447
$362$	−9.18128e85	−1.76265
$363$	0	0
$364$	−1.00480e85	−0.160393
$365$	1.26707e85	0.184497
$366$	0	0
$367$	7.55910e85	0.916552	0.458276	−	0.888810i	$-0.348467\pi$
$367$	7.55910e85	0.916552	0.458276	+	0.888810i	$0.348467\pi$
$368$	4.29892e85	0.475836
$369$	0	0
$370$	−8.92974e85	−0.824292
$371$	1.13830e86	0.959911
$372$	0	0
$373$	1.75561e86	1.23647	0.618233	−	0.785995i	$-0.287849\pi$
$373$	1.75561e86	1.23647	0.618233	+	0.785995i	$0.287849\pi$
$374$	−5.94999e86	−3.83105
$375$	0	0
$376$	−6.70600e86	−3.61136
$377$	−8.06703e84	−0.0397446
$378$	0	0
$379$	−2.06583e86	−0.852475	−0.426237	−	0.904611i	$-0.640161\pi$
$379$	−2.06583e86	−0.852475	−0.426237	+	0.904611i	$0.640161\pi$
$380$	−2.43304e85	−0.0919177
$381$	0	0
$382$	1.81691e85	0.0575720
$383$	−1.50230e86	−0.436111	−0.218055	−	0.975936i	$-0.569971\pi$
$383$	−1.50230e86	−0.436111	−0.218055	+	0.975936i	$0.569971\pi$
$384$	0	0
$385$	−4.92500e86	−1.20080
$386$	1.21305e87	2.71147
$387$	0	0
$388$	2.38981e87	4.49263
$389$	6.44644e86	1.11175	0.555876	−	0.831265i	$-0.312383\pi$
$389$	6.44644e86	1.11175	0.555876	+	0.831265i	$0.312383\pi$
$390$	0	0
$391$	−1.83579e86	−0.266625
$392$	−2.22022e87	−2.96014
$393$	0	0
$394$	6.69936e85	0.0753199
$395$	−4.42652e86	−0.457151
$396$	0	0
$397$	1.17131e87	1.02139	0.510694	−	0.859762i	$-0.329388\pi$
$397$	1.17131e87	1.02139	0.510694	+	0.859762i	$0.329388\pi$
$398$	3.57012e87	2.86154
$399$	0	0
$400$	−2.46651e87	−1.67138
$401$	−2.38898e87	−1.48894	−0.744469	−	0.667657i	$-0.767297\pi$
$401$	−2.38898e87	−1.48894	−0.744469	+	0.667657i	$0.767297\pi$
$402$	0	0
$403$	−5.05047e85	−0.0266448
$404$	−7.34797e87	−3.56773
$405$	0	0
$406$	−5.78005e87	−2.37853
$407$	−2.53825e87	−0.961883
$408$	0	0
$409$	2.85528e87	0.918159	0.459079	−	0.888395i	$-0.348179\pi$
$409$	2.85528e87	0.918159	0.459079	+	0.888395i	$0.348179\pi$
$410$	3.23713e86	0.0959181
$411$	0	0
$412$	7.40348e87	1.86371
$413$	7.69926e87	1.78699
$414$	0	0
$415$	−1.47757e87	−0.291701
$416$	5.61486e86	0.102262
$417$	0	0
$418$	−9.69308e86	−0.150334
$419$	3.71561e87	0.531937	0.265969	−	0.963982i	$-0.414308\pi$
$419$	3.71561e87	0.531937	0.265969	+	0.963982i	$0.414308\pi$
$420$	0	0
$421$	−8.25851e87	−1.00798	−0.503990	−	0.863710i	$-0.668135\pi$
$421$	−8.25851e87	−1.00798	−0.503990	+	0.863710i	$0.668135\pi$
$422$	−2.10833e88	−2.37669
$423$	0	0
$424$	−1.93367e88	−1.86048
$425$	1.05329e88	0.936522
$426$	0	0
$427$	−1.40332e88	−1.06616
$428$	1.34291e88	0.943365
$429$	0	0
$430$	1.22620e88	0.736830
$431$	−2.02458e88	−1.12550	−0.562750	−	0.826627i	$-0.690257\pi$
$431$	−2.02458e88	−1.12550	−0.562750	+	0.826627i	$0.690257\pi$
$432$	0	0
$433$	2.20914e88	1.05167	0.525835	−	0.850587i	$-0.323753\pi$
$433$	2.20914e88	1.05167	0.525835	+	0.850587i	$0.323753\pi$
$434$	−3.61867e88	−1.59457
$435$	0	0
$436$	−2.05997e88	−0.778151
$437$	−2.99067e86	−0.0104626
$438$	0	0
$439$	4.98644e86	0.0149703	0.00748513	−	0.999972i	$-0.497617\pi$
$439$	4.98644e86	0.0149703	0.00748513	+	0.999972i	$0.497617\pi$
$440$	8.36626e88	2.32738
$441$	0	0
$442$	−5.32482e87	−0.127250
$443$	−4.20816e88	−0.932324	−0.466162	−	0.884699i	$-0.654364\pi$
$443$	−4.20816e88	−0.932324	−0.466162	+	0.884699i	$0.654364\pi$
$444$	0	0
$445$	5.41840e88	1.03231
$446$	1.45757e89	2.57579
$447$	0	0
$448$	1.46325e89	2.22590
$449$	5.36803e88	0.757814	0.378907	−	0.925435i	$-0.376300\pi$
$449$	5.36803e88	0.757814	0.378907	+	0.925435i	$0.376300\pi$
$450$	0	0
$451$	9.20144e87	0.111929
$452$	3.42250e87	0.0386550
$453$	0	0
$454$	2.67546e89	2.60631
$455$	−4.40752e87	−0.0398853
$456$	0	0
$457$	−2.47901e89	−1.93680	−0.968401	−	0.249399i	$-0.919767\pi$
$457$	−2.47901e89	−1.93680	−0.968401	+	0.249399i	$0.919767\pi$
$458$	3.52984e89	2.56308
$459$	0	0
$460$	4.31347e88	0.270669
$461$	−1.39269e89	−0.812593	−0.406297	−	0.913741i	$-0.633180\pi$
$461$	−1.39269e89	−0.812593	−0.406297	+	0.913741i	$0.633180\pi$
$462$	0	0
$463$	2.69968e89	1.36254	0.681271	−	0.732032i	$-0.261428\pi$
$463$	2.69968e89	1.36254	0.681271	+	0.732032i	$0.261428\pi$
$464$	5.11772e89	2.40283
$465$	0	0
$466$	4.12881e89	1.67840
$467$	−3.76688e89	−1.42517	−0.712584	−	0.701586i	$-0.752475\pi$
$467$	−3.76688e89	−1.42517	−0.712584	+	0.701586i	$0.752475\pi$
$468$	0	0
$469$	−6.94646e89	−2.27758
$470$	−4.91549e89	−1.50068
$471$	0	0
$472$	−1.30790e90	−3.46352
$473$	3.48543e89	0.859822
$474$	0	0
$475$	1.71590e88	0.0367499
$476$	−2.72212e90	−5.43343
$477$	0	0
$478$	−4.84793e89	−0.840857
$479$	6.97444e89	1.12790	0.563949	−	0.825810i	$-0.309282\pi$
$479$	6.97444e89	1.12790	0.563949	+	0.825810i	$0.309282\pi$
$480$	0	0
$481$	−2.27156e88	−0.0319495
$482$	7.44020e89	0.976133
$483$	0	0
$484$	1.79340e90	2.04813
$485$	1.04828e90	1.11719
$486$	0	0
$487$	2.50021e89	0.232143	0.116072	−	0.993241i	$-0.462970\pi$
$487$	2.50021e89	0.232143	0.116072	+	0.993241i	$0.462970\pi$
$488$	2.38387e90	2.06642
$489$	0	0
$490$	−1.62741e90	−1.23007
$491$	−2.37132e90	−1.67402	−0.837009	−	0.547189i	$-0.815698\pi$
$491$	−2.37132e90	−1.67402	−0.837009	+	0.547189i	$0.815698\pi$
$492$	0	0
$493$	−2.18544e90	−1.34638
$494$	−8.67462e87	−0.00499341
$495$	0	0
$496$	3.20401e90	1.61086
$497$	−6.93638e89	−0.325982
$498$	0	0
$499$	3.70263e90	1.52104	0.760522	−	0.649312i	$-0.224943\pi$
$499$	3.70263e90	1.52104	0.760522	+	0.649312i	$0.224943\pi$
$500$	−6.48902e90	−2.49278
$501$	0	0
$502$	−6.74626e90	−2.26719
$503$	−3.39121e90	−1.06617	−0.533086	−	0.846061i	$-0.678968\pi$
$503$	−3.39121e90	−1.06617	−0.533086	+	0.846061i	$0.678968\pi$
$504$	0	0
$505$	−3.22316e90	−0.887197
$506$	1.71846e90	0.442686
$507$	0	0
$508$	1.02849e91	2.32148
$509$	6.34938e89	0.134179	0.0670897	−	0.997747i	$-0.478629\pi$
$509$	6.34938e89	0.134179	0.0670897	+	0.997747i	$0.478629\pi$
$510$	0	0
$511$	2.30942e90	0.427960
$512$	7.86374e90	1.36485
$513$	0	0
$514$	6.61321e90	1.00727
$515$	3.24750e90	0.463455
$516$	0	0
$517$	−1.39721e91	−1.75117
$518$	−1.62758e91	−1.91203
$519$	0	0
$520$	7.48721e89	0.0773051
$521$	6.72297e90	0.650874	0.325437	−	0.945564i	$-0.394489\pi$
$521$	6.72297e90	0.650874	0.325437	+	0.945564i	$0.394489\pi$
$522$	0	0
$523$	−3.61652e90	−0.307953	−0.153977	−	0.988075i	$-0.549208\pi$
$523$	−3.61652e90	−0.307953	−0.153977	+	0.988075i	$0.549208\pi$
$524$	1.00060e91	0.799214
$525$	0	0
$526$	1.92914e90	0.135626
$527$	−1.36823e91	−0.902614
$528$	0	0
$529$	−1.66792e91	−0.969191
$530$	−1.41738e91	−0.773113
$531$	0	0
$532$	−4.43458e90	−0.213212
$533$	8.23464e88	0.00371777
$534$	0	0
$535$	5.89060e90	0.234589
$536$	1.18002e92	4.41437
$537$	0	0
$538$	−2.70473e91	−0.893135
$539$	−4.62588e91	−1.43539
$540$	0	0
$541$	−5.31972e91	−1.45808	−0.729039	−	0.684472i	$-0.760033\pi$
$541$	−5.31972e91	−1.45808	−0.729039	+	0.684472i	$0.760033\pi$
$542$	−8.08610e91	−2.08335
$543$	0	0
$544$	1.52113e92	3.46419
$545$	−9.03597e90	−0.193505
$546$	0	0
$547$	−1.75688e90	−0.0332788	−0.0166394	−	0.999862i	$-0.505297\pi$
$547$	−1.75688e90	−0.0332788	−0.0166394	+	0.999862i	$0.505297\pi$
$548$	−1.31494e91	−0.234292
$549$	0	0
$550$	−9.85968e91	−1.55494
$551$	−3.56029e90	−0.0528331
$552$	0	0
$553$	−8.06798e91	−1.06041
$554$	2.59414e92	3.20935
$555$	0	0
$556$	2.74015e92	3.00448
$557$	−4.64449e91	−0.479500	−0.239750	−	0.970835i	$-0.577065\pi$
$557$	−4.64449e91	−0.479500	−0.239750	+	0.970835i	$0.577065\pi$
$558$	0	0
$559$	3.11921e90	0.0285594
$560$	2.79613e92	2.41134
$561$	0	0
$562$	3.54320e92	2.71162
$563$	−8.66238e90	−0.0624606	−0.0312303	−	0.999512i	$-0.509943\pi$
$563$	−8.66238e90	−0.0624606	−0.0312303	+	0.999512i	$0.509943\pi$
$564$	0	0
$565$	1.50126e90	0.00961245
$566$	2.15392e92	1.29981
$567$	0	0
$568$	1.17831e92	0.631813
$569$	−1.65010e92	−0.834162	−0.417081	−	0.908869i	$-0.636947\pi$
$569$	−1.65010e92	−0.834162	−0.417081	+	0.908869i	$0.636947\pi$
$570$	0	0
$571$	−3.09486e92	−1.39101	−0.695507	−	0.718519i	$-0.744820\pi$
$571$	−3.09486e92	−1.39101	−0.695507	+	0.718519i	$0.744820\pi$
$572$	3.55636e91	0.150743
$573$	0	0
$574$	5.90014e91	0.222492
$575$	−3.04207e91	−0.108217
$576$	0	0
$577$	−4.88740e92	−1.54771	−0.773853	−	0.633366i	$-0.781673\pi$
$577$	−4.88740e92	−1.54771	−0.773853	+	0.633366i	$0.781673\pi$
$578$	−8.17365e92	−2.44249
$579$	0	0
$580$	5.13504e92	1.36680
$581$	−2.69309e92	−0.676630
$582$	0	0
$583$	−4.02885e92	−0.902162
$584$	−3.92310e92	−0.829466
$585$	0	0
$586$	−1.97942e93	−3.73223
$587$	4.93586e92	0.878995	0.439498	−	0.898244i	$-0.355157\pi$
$587$	4.93586e92	0.878995	0.439498	+	0.898244i	$0.355157\pi$
$588$	0	0
$589$	−2.22896e91	−0.0354194
$590$	−9.58687e92	−1.43924
$591$	0	0
$592$	1.44107e93	1.93156
$593$	−8.91235e92	−1.12891	−0.564456	−	0.825463i	$-0.690914\pi$
$593$	−8.91235e92	−1.12891	−0.564456	+	0.825463i	$0.690914\pi$
$594$	0	0
$595$	−1.19404e93	−1.35115
$596$	−4.78110e92	−0.511420
$597$	0	0
$598$	1.53790e91	0.0147041
$599$	−1.27437e92	−0.115212	−0.0576059	−	0.998339i	$-0.518347\pi$
$599$	−1.27437e92	−0.115212	−0.0576059	+	0.998339i	$0.518347\pi$
$600$	0	0
$601$	1.93861e93	1.56746	0.783728	−	0.621104i	$-0.213316\pi$
$601$	1.93861e93	1.56746	0.783728	+	0.621104i	$0.213316\pi$
$602$	2.23492e93	1.70915
$603$	0	0
$604$	−5.01069e93	−3.42894
$605$	7.86668e92	0.509315
$606$	0	0
$607$	4.21833e92	0.244523	0.122261	−	0.992498i	$-0.460985\pi$
$607$	4.21833e92	0.244523	0.122261	+	0.992498i	$0.460985\pi$
$608$	2.47805e92	0.135938
$609$	0	0
$610$	1.74737e93	0.858690
$611$	−1.25041e92	−0.0581662
$612$	0	0
$613$	−8.48939e92	−0.353957	−0.176979	−	0.984215i	$-0.556632\pi$
$613$	−8.48939e92	−0.353957	−0.176979	+	0.984215i	$0.556632\pi$
$614$	−3.47356e93	−1.37130
$615$	0	0
$616$	1.52487e94	5.39859
$617$	−5.31064e93	−1.78071	−0.890357	−	0.455263i	$-0.849545\pi$
$617$	−5.31064e93	−1.78071	−0.890357	+	0.455263i	$0.849545\pi$
$618$	0	0
$619$	−5.93673e93	−1.78612	−0.893060	−	0.449937i	$-0.851446\pi$
$619$	−5.93673e93	−1.78612	−0.893060	+	0.449937i	$0.851446\pi$
$620$	3.21486e93	0.916305
$621$	0	0
$622$	−1.24046e93	−0.317399
$623$	9.87582e93	2.39455
$624$	0	0
$625$	−1.53972e91	−0.00335322
$626$	−7.63139e93	−1.57530
$627$	0	0
$628$	−6.12366e93	−1.13596
$629$	−6.15389e93	−1.08231
$630$	0	0
$631$	−4.19002e93	−0.662572	−0.331286	−	0.943530i	$-0.607482\pi$
$631$	−4.19002e93	−0.662572	−0.331286	+	0.943530i	$0.607482\pi$
$632$	1.37053e94	2.05527
$633$	0	0
$634$	1.47729e94	1.99286
$635$	4.51141e93	0.577288
$636$	0	0
$637$	−4.13983e92	−0.0476773
$638$	2.04576e94	2.23544
$639$	0	0
$640$	−3.86724e93	−0.380515
$641$	−1.17710e94	−1.09919	−0.549593	−	0.835433i	$-0.685217\pi$
$641$	−1.17710e94	−1.09919	−0.549593	+	0.835433i	$0.685217\pi$
$642$	0	0
$643$	2.15010e94	1.80880	0.904400	−	0.426686i	$-0.140319\pi$
$643$	2.15010e94	1.80880	0.904400	+	0.426686i	$0.140319\pi$
$644$	7.86192e93	0.627845
$645$	0	0
$646$	−2.35004e93	−0.169156
$647$	5.59785e93	0.382585	0.191292	−	0.981533i	$-0.438732\pi$
$647$	5.59785e93	0.382585	0.191292	+	0.981533i	$0.438732\pi$
$648$	0	0
$649$	−2.72504e94	−1.67948
$650$	−8.82372e92	−0.0516481
$651$	0	0
$652$	−3.43875e91	−0.00181596
$653$	−3.65193e94	−1.83202	−0.916012	−	0.401150i	$-0.868611\pi$
$653$	−3.65193e94	−1.83202	−0.916012	+	0.401150i	$0.868611\pi$
$654$	0	0
$655$	4.38909e93	0.198743
$656$	−5.22405e93	−0.224765
$657$	0	0
$658$	−8.95919e94	−3.48098
$659$	2.31946e94	0.856497	0.428249	−	0.903661i	$-0.359131\pi$
$659$	2.31946e94	0.856497	0.428249	+	0.903661i	$0.359131\pi$
$660$	0	0
$661$	1.29957e94	0.433563	0.216782	−	0.976220i	$-0.430444\pi$
$661$	1.29957e94	0.433563	0.216782	+	0.976220i	$0.430444\pi$
$662$	6.24433e94	1.98035
$663$	0	0
$664$	4.57485e94	1.31143
$665$	−1.94521e93	−0.0530201
$666$	0	0
$667$	6.31192e93	0.155577
$668$	−1.76133e95	−4.12886
$669$	0	0
$670$	8.64951e94	1.83436
$671$	4.96686e94	1.00202
$672$	0	0
$673$	3.32902e94	0.607872	0.303936	−	0.952693i	$-0.401699\pi$
$673$	3.32902e94	0.607872	0.303936	+	0.952693i	$0.401699\pi$
$674$	−1.93564e94	−0.336293
$675$	0	0
$676$	−1.57970e95	−2.48520
$677$	7.15153e94	1.07073	0.535364	−	0.844622i	$-0.320175\pi$
$677$	7.15153e94	1.07073	0.535364	+	0.844622i	$0.320175\pi$
$678$	0	0
$679$	1.91064e95	2.59144
$680$	2.02836e95	2.61877
$681$	0	0
$682$	1.28078e95	1.49864
$683$	4.63147e94	0.515971	0.257985	−	0.966149i	$-0.416941\pi$
$683$	4.63147e94	0.515971	0.257985	+	0.966149i	$0.416941\pi$
$684$	0	0
$685$	−5.76793e93	−0.0582620
$686$	−1.76480e94	−0.169761
$687$	0	0
$688$	−1.97883e95	−1.72661
$689$	−3.60554e93	−0.0299658
$690$	0	0
$691$	3.93163e94	0.296523	0.148261	−	0.988948i	$-0.452632\pi$
$691$	3.93163e94	0.296523	0.148261	+	0.988948i	$0.452632\pi$
$692$	−4.49150e95	−3.22728
$693$	0	0
$694$	2.75038e94	0.179412
$695$	1.20196e95	0.747132
$696$	0	0
$697$	2.23085e94	0.125942
$698$	−3.38545e95	−1.82163
$699$	0	0
$700$	−4.51080e95	−2.20531
$701$	2.12972e95	0.992588	0.496294	−	0.868154i	$-0.334694\pi$
$701$	2.12972e95	0.992588	0.496294	+	0.868154i	$0.334694\pi$
$702$	0	0
$703$	−1.00252e94	−0.0424709
$704$	−5.17897e95	−2.09199
$705$	0	0
$706$	7.41213e94	0.272261
$707$	−5.87467e95	−2.05794
$708$	0	0
$709$	−4.82912e94	−0.153893	−0.0769466	−	0.997035i	$-0.524517\pi$
$709$	−4.82912e94	−0.153893	−0.0769466	+	0.997035i	$0.524517\pi$
$710$	8.63695e94	0.262546
$711$	0	0
$712$	−1.67764e96	−4.64108
$713$	3.95166e94	0.104299
$714$	0	0
$715$	1.55998e94	0.0374858
$716$	6.80571e95	1.56059
$717$	0	0
$718$	4.74669e95	0.991339
$719$	3.57892e93	0.00713401	0.00356700	−	0.999994i	$-0.498865\pi$
$719$	3.57892e93	0.00713401	0.00356700	+	0.999994i	$0.498865\pi$
$720$	0	0
$721$	5.91905e95	1.07503
$722$	1.07368e96	1.86157
$723$	0	0
$724$	1.48668e96	2.34950
$725$	−3.62148e95	−0.546466
$726$	0	0
$727$	1.13472e96	1.56129	0.780646	−	0.624973i	$-0.214890\pi$
$727$	1.13472e96	1.56129	0.780646	+	0.624973i	$0.214890\pi$
$728$	1.36465e95	0.179317
$729$	0	0
$730$	−2.87562e95	−0.344680
$731$	8.45028e95	0.967473
$732$	0	0
$733$	−7.88530e95	−0.823826	−0.411913	−	0.911223i	$-0.635139\pi$
$733$	−7.88530e95	−0.823826	−0.411913	+	0.911223i	$0.635139\pi$
$734$	−1.71554e96	−1.71231
$735$	0	0
$736$	−4.39326e95	−0.400295
$737$	2.45860e96	2.14056
$738$	0	0
$739$	8.22688e95	0.654104	0.327052	−	0.945006i	$-0.393945\pi$
$739$	8.22688e95	0.654104	0.327052	+	0.945006i	$0.393945\pi$
$740$	1.44595e96	1.09873
$741$	0	0
$742$	−2.58337e96	−1.79331
$743$	−1.18799e96	−0.788293	−0.394147	−	0.919048i	$-0.628960\pi$
$743$	−1.18799e96	−0.788293	−0.394147	+	0.919048i	$0.628960\pi$
$744$	0	0
$745$	−2.09721e95	−0.127176
$746$	−3.98436e96	−2.30998
$747$	0	0
$748$	9.63454e96	5.10655
$749$	1.07365e96	0.544153
$750$	0	0
$751$	−2.90797e96	−1.34788	−0.673941	−	0.738785i	$-0.735400\pi$
$751$	−2.90797e96	−1.34788	−0.673941	+	0.738785i	$0.735400\pi$
$752$	7.93257e96	3.51654
$753$	0	0
$754$	1.83081e95	0.0742513
$755$	−2.19792e96	−0.852685
$756$	0	0
$757$	1.73071e96	0.614487	0.307244	−	0.951631i	$-0.400593\pi$
$757$	1.73071e96	0.614487	0.307244	+	0.951631i	$0.400593\pi$
$758$	4.68841e96	1.59260
$759$	0	0
$760$	3.30439e95	0.102763
$761$	−3.70707e96	−1.10318	−0.551588	−	0.834117i	$-0.685978\pi$
$761$	−3.70707e96	−1.10318	−0.551588	+	0.834117i	$0.685978\pi$
$762$	0	0
$763$	−1.64694e96	−0.448854
$764$	−2.94204e95	−0.0767399
$765$	0	0
$766$	3.40947e96	0.814746
$767$	−2.43872e95	−0.0557849
$768$	0	0
$769$	−9.72162e95	−0.203801	−0.101900	−	0.994795i	$-0.532492\pi$
$769$	−9.72162e95	−0.203801	−0.101900	+	0.994795i	$0.532492\pi$
$770$	1.11773e97	2.24335
$771$	0	0
$772$	−1.96424e97	−3.61423
$773$	7.27011e95	0.128094	0.0640469	−	0.997947i	$-0.479599\pi$
$773$	7.27011e95	0.128094	0.0640469	+	0.997947i	$0.479599\pi$
$774$	0	0
$775$	−2.26728e96	−0.366351
$776$	−3.24567e97	−5.02270
$777$	0	0
$778$	−1.46302e97	−2.07699
$779$	3.63426e94	0.00494209
$780$	0	0
$781$	2.45503e96	0.306371
$782$	4.16632e96	0.498111
$783$	0	0
$784$	2.62631e97	2.88242
$785$	−2.68611e96	−0.282482
$786$	0	0
$787$	−1.49904e96	−0.144764	−0.0723820	−	0.997377i	$-0.523060\pi$
$787$	−1.49904e96	−0.144764	−0.0723820	+	0.997377i	$0.523060\pi$
$788$	−1.08480e96	−0.100397
$789$	0	0
$790$	1.00460e97	0.854053
$791$	2.73627e95	0.0222970
$792$	0	0
$793$	4.44499e95	0.0332827
$794$	−2.65830e97	−1.90817
$795$	0	0
$796$	−5.78092e97	−3.81425
$797$	−1.40542e97	−0.889107	−0.444553	−	0.895752i	$-0.646638\pi$
$797$	−1.40542e97	−0.889107	−0.444553	+	0.895752i	$0.646638\pi$
$798$	0	0
$799$	−3.38748e97	−1.97043
$800$	2.52065e97	1.40604
$801$	0	0
$802$	5.42180e97	2.78165
$803$	−8.17387e96	−0.402214
$804$	0	0
$805$	3.44860e96	0.156128
$806$	1.14621e96	0.0497781
$807$	0	0
$808$	9.97951e97	3.98867
$809$	1.72375e97	0.660996	0.330498	−	0.943807i	$-0.392783\pi$
$809$	1.72375e97	0.660996	0.330498	+	0.943807i	$0.392783\pi$
$810$	0	0
$811$	−3.10291e97	−1.09540	−0.547698	−	0.836676i	$-0.684496\pi$
$811$	−3.10291e97	−1.09540	−0.547698	+	0.836676i	$0.684496\pi$
$812$	9.35936e97	3.17044
$813$	0	0
$814$	5.76057e97	1.79700
$815$	−1.50839e94	−0.000451579 0
$816$	0	0
$817$	1.37663e96	0.0379645
$818$	−6.48006e97	−1.71531
$819$	0	0
$820$	−5.24173e96	−0.127853
$821$	4.71160e97	1.10325	0.551623	−	0.834094i	$-0.314009\pi$
$821$	4.71160e97	1.10325	0.551623	+	0.834094i	$0.314009\pi$
$822$	0	0
$823$	−3.28396e97	−0.708766	−0.354383	−	0.935100i	$-0.615309\pi$
$823$	−3.28396e97	−0.708766	−0.354383	+	0.935100i	$0.615309\pi$
$824$	−1.00549e98	−2.08361
$825$	0	0
$826$	−1.74735e98	−3.33847
$827$	−1.14554e97	−0.210172	−0.105086	−	0.994463i	$-0.533512\pi$
$827$	−1.14554e97	−0.210172	−0.105086	+	0.994463i	$0.533512\pi$
$828$	0	0
$829$	5.31404e97	0.899183	0.449591	−	0.893234i	$-0.351570\pi$
$829$	5.31404e97	0.899183	0.449591	+	0.893234i	$0.351570\pi$
$830$	3.35336e97	0.544959
$831$	0	0
$832$	−4.63481e96	−0.0694865
$833$	−1.12152e98	−1.61511
$834$	0	0
$835$	−7.72601e97	−1.02673
$836$	1.56955e97	0.200385
$837$	0	0
$838$	−8.43258e97	−0.993770
$839$	−8.20510e97	−0.929091	−0.464545	−	0.885549i	$-0.653782\pi$
$839$	−8.20510e97	−0.929091	−0.464545	+	0.885549i	$0.653782\pi$
$840$	0	0
$841$	−2.05045e97	−0.214379
$842$	1.87427e98	1.88312
$843$	0	0
$844$	3.41392e98	3.16797
$845$	−6.92930e97	−0.618002
$846$	0	0
$847$	1.43382e98	1.18141
$848$	2.28735e98	1.81164
$849$	0	0
$850$	−2.39044e98	−1.74962
$851$	1.77734e97	0.125064
$852$	0	0
$853$	−2.75788e97	−0.179384	−0.0896918	−	0.995970i	$-0.528588\pi$
$853$	−2.75788e97	−0.179384	−0.0896918	+	0.995970i	$0.528588\pi$
$854$	3.18484e98	1.99182
$855$	0	0
$856$	−1.82384e98	−1.05467
$857$	2.49466e98	1.38725	0.693624	−	0.720337i	$-0.256013\pi$
$857$	2.49466e98	1.38725	0.693624	+	0.720337i	$0.256013\pi$
$858$	0	0
$859$	−5.28515e97	−0.271823	−0.135912	−	0.990721i	$-0.543396\pi$
$859$	−5.28515e97	−0.271823	−0.135912	+	0.990721i	$0.543396\pi$
$860$	−1.98552e98	−0.982148
$861$	0	0
$862$	4.59478e98	2.10267
$863$	1.41322e96	0.00622084	0.00311042	−	0.999995i	$-0.499010\pi$
$863$	1.41322e96	0.00622084	0.00311042	+	0.999995i	$0.499010\pi$
$864$	0	0
$865$	−1.97018e98	−0.802537
$866$	−5.01365e98	−1.96474
$867$	0	0
$868$	5.85955e98	2.12546
$869$	2.85554e98	0.996613
$870$	0	0
$871$	2.20027e97	0.0710998
$872$	2.79771e98	0.869962
$873$	0	0
$874$	6.78732e96	0.0195463
$875$	−5.18794e98	−1.43789
$876$	0	0
$877$	4.90704e98	1.25989	0.629946	−	0.776639i	$-0.283077\pi$
$877$	4.90704e98	1.25989	0.629946	+	0.776639i	$0.283077\pi$
$878$	−1.13167e97	−0.0279676
$879$	0	0
$880$	−9.89649e98	−2.26627
$881$	1.83004e98	0.403430	0.201715	−	0.979444i	$-0.435349\pi$
$881$	1.83004e98	0.403430	0.201715	+	0.979444i	$0.435349\pi$
$882$	0	0
$883$	1.47514e98	0.301404	0.150702	−	0.988579i	$-0.451847\pi$
$883$	1.47514e98	0.301404	0.150702	+	0.988579i	$0.451847\pi$
$884$	8.62223e97	0.169617
$885$	0	0
$886$	9.55042e98	1.74178
$887$	4.64176e98	0.815157	0.407579	−	0.913170i	$-0.366373\pi$
$887$	4.64176e98	0.815157	0.407579	+	0.913170i	$0.366373\pi$
$888$	0	0
$889$	8.22271e98	1.33908
$890$	−1.22971e99	−1.92857
$891$	0	0
$892$	−2.36017e99	−3.43337
$893$	−5.51852e97	−0.0773212
$894$	0	0
$895$	2.98530e98	0.388075
$896$	−7.04861e98	−0.882643
$897$	0	0
$898$	−1.21828e99	−1.41576
$899$	4.70432e98	0.526681
$900$	0	0
$901$	−9.76777e98	−1.01511
$902$	−2.08827e98	−0.209106
$903$	0	0
$904$	−4.64820e97	−0.0432158
$905$	6.52126e98	0.584257
$906$	0	0
$907$	8.33172e98	0.693251	0.346626	−	0.938004i	$-0.387327\pi$
$907$	8.33172e98	0.693251	0.346626	+	0.938004i	$0.387327\pi$
$908$	−4.33224e99	−3.47405
$909$	0	0
$910$	1.00029e98	0.0745141
$911$	−1.45347e99	−1.04362	−0.521809	−	0.853062i	$-0.674743\pi$
$911$	−1.45347e99	−1.04362	−0.521809	+	0.853062i	$0.674743\pi$
$912$	0	0
$913$	9.53182e98	0.635924
$914$	5.62611e99	3.61835
$915$	0	0
$916$	−5.71571e99	−3.41643
$917$	7.99977e98	0.461004
$918$	0	0
$919$	1.11251e99	0.595984	0.297992	−	0.954568i	$-0.403683\pi$
$919$	1.11251e99	0.595984	0.297992	+	0.954568i	$0.403683\pi$
$920$	−5.85825e98	−0.302605
$921$	0	0
$922$	3.16071e99	1.51809
$923$	2.19708e97	0.0101763
$924$	0	0
$925$	−1.01976e99	−0.439287
$926$	−6.12694e99	−2.54551
$927$	0	0
$928$	−5.23003e99	−2.02138
$929$	−3.66789e99	−1.36738	−0.683692	−	0.729771i	$-0.739627\pi$
$929$	−3.66789e99	−1.36738	−0.683692	+	0.729771i	$0.739627\pi$
$930$	0	0
$931$	−1.82707e98	−0.0633782
$932$	−6.68559e99	−2.23721
$933$	0	0
$934$	8.54894e99	2.66251
$935$	4.22615e99	1.26986
$936$	0	0
$937$	1.86027e98	0.0520354	0.0260177	−	0.999661i	$-0.491717\pi$
$937$	1.86027e98	0.0520354	0.0260177	+	0.999661i	$0.491717\pi$
$938$	1.57650e100	4.25499
$939$	0	0
$940$	7.95941e99	2.00031
$941$	−4.09124e99	−0.992208	−0.496104	−	0.868263i	$-0.665237\pi$
$941$	−4.09124e99	−0.992208	−0.496104	+	0.868263i	$0.665237\pi$
$942$	0	0
$943$	−6.44306e97	−0.0145529
$944$	1.54712e100	3.37258
$945$	0	0
$946$	−7.91019e99	−1.60633
$947$	4.63796e99	0.909082	0.454541	−	0.890726i	$-0.349803\pi$
$947$	4.63796e99	0.909082	0.454541	+	0.890726i	$0.349803\pi$
$948$	0	0
$949$	−7.31504e97	−0.0133598
$950$	−3.89424e98	−0.0686566
$951$	0	0
$952$	3.69699e100	6.07450
$953$	2.75137e99	0.436452	0.218226	−	0.975898i	$-0.429973\pi$
$953$	2.75137e99	0.436452	0.218226	+	0.975898i	$0.429973\pi$
$954$	0	0
$955$	−1.29051e98	−0.0190831
$956$	7.85003e99	1.12081
$957$	0	0
$958$	−1.58285e100	−2.10715
$959$	−1.05129e99	−0.135145
$960$	0	0
$961$	−5.39609e99	−0.646913
$962$	5.15530e98	0.0596883
$963$	0	0
$964$	−1.20476e100	−1.30112
$965$	−8.61606e99	−0.898760
$966$	0	0
$967$	4.36496e99	0.424809	0.212404	−	0.977182i	$-0.431871\pi$
$967$	4.36496e99	0.424809	0.212404	+	0.977182i	$0.431871\pi$
$968$	−2.43567e100	−2.28978
$969$	0	0
$970$	−2.37907e100	−2.08715
$971$	−6.33150e99	−0.536614	−0.268307	−	0.963333i	$-0.586464\pi$
$971$	−6.33150e99	−0.536614	−0.268307	+	0.963333i	$0.586464\pi$
$972$	0	0
$973$	2.19074e100	1.73305
$974$	−5.67423e99	−0.433692
$975$	0	0
$976$	−2.81990e100	−2.01217
$977$	−1.58929e100	−1.09581	−0.547905	−	0.836540i	$-0.684575\pi$
$977$	−1.58929e100	−1.09581	−0.547905	+	0.836540i	$0.684575\pi$
$978$	0	0
$979$	−3.49541e100	−2.25049
$980$	2.63519e100	1.63960
$981$	0	0
$982$	5.38171e100	3.12742
$983$	−4.62180e97	−0.00259578	−0.00129789	−	0.999999i	$-0.500413\pi$
$983$	−4.62180e97	−0.00259578	−0.00129789	+	0.999999i	$0.500413\pi$
$984$	0	0
$985$	−4.75841e98	−0.0249659
$986$	4.95987e100	2.51532
$987$	0	0
$988$	1.40464e98	0.00665591
$989$	−2.44058e99	−0.111794
$990$	0	0
$991$	−4.58345e100	−1.96212	−0.981059	−	0.193708i	$-0.937948\pi$
$991$	−4.58345e100	−1.96212	−0.981059	+	0.193708i	$0.937948\pi$
$992$	−3.27433e100	−1.35513
$993$	0	0
$994$	1.57421e100	0.609003
$995$	−2.53578e100	−0.948501
$996$	0	0
$997$	−4.49091e100	−1.57053	−0.785266	−	0.619159i	$-0.787474\pi$
$997$	−4.49091e100	−1.57053	−0.785266	+	0.619159i	$0.787474\pi$
$998$	−8.40312e100	−2.84163
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	9.68.a.a.1.1		5
3.2	odd	2		1.68.a.a.1.5	✓	5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1.68.a.a.1.5	✓	5	3.2	odd	2
9.68.a.a.1.1		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)

\(f(q)\)	\(=\)	\(q-2.26950e10 q^{2} +3.67490e20 q^{4} +1.61198e23 q^{5} +2.93806e28 q^{7} -4.99099e30 q^{8} +O(q^{10})\)	\(q-2.26950e10 q^{2} +3.67490e20 q^{4} +1.61198e23 q^{5} +2.93806e28 q^{7} -4.99099e30 q^{8} -3.65838e33 q^{10} -1.03989e35 q^{11} -9.30624e35 q^{13} -6.66794e38 q^{14} +5.90387e40 q^{16} -2.52116e41 q^{17} -4.10720e41 q^{19} +5.92385e43 q^{20} +2.36002e45 q^{22} +7.28152e44 q^{23} -4.17779e46 q^{25} +2.11205e46 q^{26} +1.07971e49 q^{28} +8.66841e48 q^{29} +5.42697e49 q^{31} -6.03344e50 q^{32} +5.72177e51 q^{34} +4.73609e51 q^{35} +2.44090e52 q^{37} +9.32129e51 q^{38} -8.04536e53 q^{40} -8.84851e52 q^{41} -3.35174e54 q^{43} -3.82147e55 q^{44} -1.65254e55 q^{46} +1.34362e56 q^{47} +4.44845e56 q^{49} +9.48151e56 q^{50} -3.41995e56 q^{52} +3.87432e57 q^{53} -1.67627e58 q^{55} -1.46639e59 q^{56} -1.96730e59 q^{58} +2.62052e59 q^{59} -4.77635e59 q^{61} -1.23165e60 q^{62} +4.98032e60 q^{64} -1.50015e59 q^{65} -2.36430e61 q^{67} -9.26500e61 q^{68} -1.07486e62 q^{70} -2.36087e61 q^{71} +7.86035e61 q^{73} -5.53962e62 q^{74} -1.50935e62 q^{76} -3.05525e63 q^{77} -2.74602e63 q^{79} +9.51690e63 q^{80} +2.00817e63 q^{82} -9.16622e63 q^{83} -4.06405e64 q^{85} +7.60679e64 q^{86} +5.19006e65 q^{88} +3.36134e65 q^{89} -2.73423e64 q^{91} +2.67588e65 q^{92} -3.04935e66 q^{94} -6.62071e64 q^{95} +6.50306e66 q^{97} -1.00958e67 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 5 q - 5554901256 q^{2} + 35\!\cdots\!40 q^{4}+ \cdots - 32\!\cdots\!80 q^{8}+O(q^{10}) \) 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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