LMFDB - Embedded newform 9.52.a.b.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [9,52,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, 52, names="a")

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

chi := DirichletCharacter("9.1");

S:= CuspForms(chi, 52);

N := Newforms(S);

Level:	$ N $	$=$	$ 9 = 3^{2} $
Weight:	$ k $	$=$	$ 52 $
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:	$148.258218073$
Analytic rank:	$1$
Dimension:	$4$
Coefficient field:	$\mathbb{Q}[x]/(x^{4} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - 2x^{3} - 495735060514x^{2} - 23954614981416598x + 48979992255622025570313 $ x^4 - 2x^3 - 495735060514x^2 - 23954614981416598*x + 48979992255622025570313
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{23}\cdot 3^{14}\cdot 5^{3}\cdot 7^{2}\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			$324949.$ 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)

$f(q)$	$=$	$q-8.12369e7 q^{2} +4.34763e15 q^{4} -2.42754e17 q^{5} +2.85586e21 q^{7} -1.70259e23 q^{8} +O(q^{10})$	\(q-8.12369e7 q^{2} +4.34763e15 q^{4} -2.42754e17 q^{5} +2.85586e21 q^{7} -1.70259e23 q^{8} +1.97206e25 q^{10} -3.52088e26 q^{11} +3.67432e28 q^{13} -2.32001e29 q^{14} +4.04130e30 q^{16} +6.54277e30 q^{17} +2.55736e32 q^{19} -1.05541e33 q^{20} +2.86025e34 q^{22} +1.69990e34 q^{23} -3.85160e35 q^{25} -2.98490e36 q^{26} +1.24162e37 q^{28} -3.94490e36 q^{29} +9.38800e37 q^{31} +5.50861e37 q^{32} -5.31514e38 q^{34} -6.93270e38 q^{35} -1.74413e40 q^{37} -2.07752e40 q^{38} +4.13310e40 q^{40} -2.14671e41 q^{41} -2.13159e41 q^{43} -1.53075e42 q^{44} -1.38095e42 q^{46} -4.04105e42 q^{47} -4.43335e42 q^{49} +3.12892e43 q^{50} +1.59746e44 q^{52} +4.94974e42 q^{53} +8.54708e43 q^{55} -4.86235e44 q^{56} +3.20472e44 q^{58} +1.20757e45 q^{59} +2.20569e45 q^{61} -7.62652e45 q^{62} -1.35752e46 q^{64} -8.91957e45 q^{65} +4.56801e46 q^{67} +2.84456e46 q^{68} +5.63191e46 q^{70} +1.91444e47 q^{71} -8.49448e46 q^{73} +1.41688e48 q^{74} +1.11185e48 q^{76} -1.00551e48 q^{77} +2.35655e48 q^{79} -9.81042e47 q^{80} +1.74392e49 q^{82} -5.38960e48 q^{83} -1.58828e48 q^{85} +1.73164e49 q^{86} +5.99461e49 q^{88} +7.58432e49 q^{89} +1.04933e50 q^{91} +7.39055e49 q^{92} +3.28282e50 q^{94} -6.20810e49 q^{95} -8.33376e50 q^{97} +3.60151e50 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 32756040 q^{2} + 79\!\cdots\!12 q^{4}+ \cdots + 13\!\cdots\!20 q^{8}+O(q^{10}) $ 4 * q - 32756040 * q^2 + 7978103470875712 * q^4 - 1214113112967557880 * q^5 + 6566332044151252469600 * q^7 + 139242173294665691205120 * q^8	$ 4 q - 32756040 q^{2} + 79\!\cdots\!12 q^{4}+ \cdots + 31\!\cdots\!80 q^{98}+O(q^{100}) $ 4 * q - 32756040 * q^2 + 7978103470875712 * q^4 - 1214113112967557880 * q^5 + 6566332044151252469600 * q^7 + 139242173294665691205120 * q^8 - 26338767422633182993407120 * q^10 - 352319730227217761184247248 * q^11 + 30737495492092678036022901080 * q^13 - 116878411871248994844784530624 * q^14 + 13655541308212814904424583532544 * q^16 - 48152025926602119975132578130120 * q^17 + 817578654717102241686587953106480 * q^19 - 6688106698568613691058684703008640 * q^20 - 34873949046188270313389204382330720 * q^22 + 54442545328795748403982512519744480 * q^23 - 577962011134461749109509927876368100 * q^25 - 1509847347916659653711306190553689648 * q^26 + 34411298173690719862562837156054996480 * q^28 - 24524817706178324469842039147126378520 * q^29 - 74015080632891216448581759119415494272 * q^31 + 698885110517892283834830116511622594560 * q^32 + 599176354190711613816800945566309634064 * q^34 - 5459558934032100428649177266758776617280 * q^35 + 9223299799194559520674909690367653437560 * q^37 - 42209741287618122996397532876280940717920 * q^38 - 260218563144774091908833544090781982745600 * q^40 - 146626572441904135431040424870320811649768 * q^41 - 383253403750663564628750277915860311246000 * q^43 - 3919911265019437916289330658643948094246144 * q^44 - 687622182810100175391810298681828635813312 * q^46 - 703242125794576181922406089648904926204480 * q^47 - 21525353693695885888621049774661370126875228 * q^49 + 65550763083377103476240548536052846777230600 * q^50 + 205575224727950383449569813934278240424406400 * q^52 + 46053881458574871528873628680364599519093960 * q^53 + 288271437023082169121432211103105268991934560 * q^55 + 718413197664523425962520880364481249783828480 * q^56 - 3260382815057328392932619475690091710393763920 * q^58 - 1119164779584192618652811959209270069996506640 * q^59 + 3426848506305498355799302542081826532801316248 * q^61 - 9652948821672246376570757837225648817671719680 * q^62 - 3410402571656263891001355509990182780636233728 * q^64 - 10662663070585071183633914150857043524084084560 * q^65 + 30875136607724238160818607702139418169238276720 * q^67 + 92264980123003683860202361552579885626636888960 * q^68 - 127365497175284237875848441551548839150619662720 * q^70 - 396890633217178572952249989093970445513163336288 * q^71 + 1093181650202404127682760092563948835468903177320 * q^73 + 2446722614206037598896806276944107193380656941456 * q^74 - 1930298057964975808050160660816178333985982024960 * q^76 - 1379856740595107958858322062475643650952236464000 * q^77 + 4057123342028363124154537966955503984273281629120 * q^79 - 6556705282035289158041818706914507044939664711680 * q^80 + 2672741123252406904410297531162443665031405248080 * q^82 - 10514534101014085301175610601927458547806407366960 * q^83 - 2214700921000481207852358003497850667551075883920 * q^85 + 43819383990098235110217468422860464230535375092832 * q^86 - 25053936600673669378312978656608794916631597373440 * q^88 + 90777724780188979543741952283884054816841444724440 * q^89 + 100567720661332633308233017957549269313038849882688 * q^91 - 192025202572015319809189966047000799088692638097920 * q^92 + 639818007616166555781273040037466169910601363859584 * q^94 + 418719878951800677902105757696028542296429654882400 * q^95 - 1321788056943507607869460465290134726019322989433720 * q^97 + 317844097908560926995320900303041587618753340105080 * 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 $

$2$	−8.12369e7	−1.71194	−0.855970	−	0.517026i	$-0.827039\pi$
$2$	−8.12369e7	−1.71194	−0.855970	+	0.517026i	$0.827039\pi$
$3$	0	0
$3$	0	0
$4$	4.34763e15	1.93074
$5$	−2.42754e17	−0.364277	−0.182138	−	0.983273i	$-0.558302\pi$
$5$	−2.42754e17	−0.364277	−0.182138	+	0.983273i	$0.558302\pi$
$6$	0	0
$7$	2.85586e21	0.804889	0.402445	−	0.915444i	$-0.368161\pi$
$7$	2.85586e21	0.804889	0.402445	+	0.915444i	$0.368161\pi$
$8$	−1.70259e23	−1.59336
$9$	0	0
$10$	1.97206e25	0.623620
$11$	−3.52088e26	−0.979801	−0.489900	−	0.871778i	$-0.662967\pi$
$11$	−3.52088e26	−0.979801	−0.489900	+	0.871778i	$0.662967\pi$
$12$	0	0
$13$	3.67432e28	1.44418	0.722091	−	0.691798i	$-0.243181\pi$
$13$	3.67432e28	1.44418	0.722091	+	0.691798i	$0.243181\pi$
$14$	−2.32001e29	−1.37792
$15$	0	0
$16$	4.04130e30	0.797006
$17$	6.54277e30	0.274988	0.137494	−	0.990503i	$-0.456095\pi$
$17$	6.54277e30	0.274988	0.137494	+	0.990503i	$0.456095\pi$
$18$	0	0
$19$	2.55736e32	0.630341	0.315170	−	0.949035i	$-0.397938\pi$
$19$	2.55736e32	0.630341	0.315170	+	0.949035i	$0.397938\pi$
$20$	−1.05541e33	−0.703322
$21$	0	0
$22$	2.86025e34	1.67736
$23$	1.69990e34	0.320896	0.160448	−	0.987044i	$-0.448706\pi$
$23$	1.69990e34	0.320896	0.160448	+	0.987044i	$0.448706\pi$
$24$	0	0
$25$	−3.85160e35	−0.867302
$26$	−2.98490e36	−2.47235
$27$	0	0
$28$	1.24162e37	1.55403
$29$	−3.94490e36	−0.201784	−0.100892	−	0.994897i	$-0.532170\pi$
$29$	−3.94490e36	−0.201784	−0.100892	+	0.994897i	$0.532170\pi$
$30$	0	0
$31$	9.38800e37	0.876698	0.438349	−	0.898805i	$-0.355563\pi$
$31$	9.38800e37	0.876698	0.438349	+	0.898805i	$0.355563\pi$
$32$	5.50861e37	0.228938
$33$	0	0
$34$	−5.31514e38	−0.470763
$35$	−6.93270e38	−0.293202
$36$	0	0
$37$	−1.74413e40	−1.78828	−0.894140	−	0.447787i	$-0.852212\pi$
$37$	−1.74413e40	−1.78828	−0.894140	+	0.447787i	$0.852212\pi$
$38$	−2.07752e40	−1.07911
$39$	0	0
$40$	4.13310e40	0.580425
$41$	−2.14671e41	−1.60615	−0.803074	−	0.595880i	$-0.796803\pi$
$41$	−2.14671e41	−1.60615	−0.803074	+	0.595880i	$0.796803\pi$
$42$	0	0
$43$	−2.13159e41	−0.473432	−0.236716	−	0.971579i	$-0.576071\pi$
$43$	−2.13159e41	−0.473432	−0.236716	+	0.971579i	$0.576071\pi$
$44$	−1.53075e42	−1.89174
$45$	0	0
$46$	−1.38095e42	−0.549354
$47$	−4.04105e42	−0.928963	−0.464481	−	0.885583i	$-0.653759\pi$
$47$	−4.04105e42	−0.928963	−0.464481	+	0.885583i	$0.653759\pi$
$48$	0	0
$49$	−4.43335e42	−0.352153
$50$	3.12892e43	1.48477
$51$	0	0
$52$	1.59746e44	2.78833
$53$	4.94974e42	0.0531555	0.0265777	−	0.999647i	$-0.491539\pi$
$53$	4.94974e42	0.0531555	0.0265777	+	0.999647i	$0.491539\pi$
$54$	0	0
$55$	8.54708e43	0.356919
$56$	−4.86235e44	−1.28248
$57$	0	0
$58$	3.20472e44	0.345443
$59$	1.20757e45	0.841752	0.420876	−	0.907118i	$-0.361723\pi$
$59$	1.20757e45	0.841752	0.420876	+	0.907118i	$0.361723\pi$
$60$	0	0
$61$	2.20569e45	0.657104	0.328552	−	0.944486i	$-0.393439\pi$
$61$	2.20569e45	0.657104	0.328552	+	0.944486i	$0.393439\pi$
$62$	−7.62652e45	−1.50085
$63$	0	0
$64$	−1.35752e46	−1.18893
$65$	−8.91957e45	−0.526082
$66$	0	0
$67$	4.56801e46	1.24400	0.621999	−	0.783018i	$-0.286321\pi$
$67$	4.56801e46	1.24400	0.621999	+	0.783018i	$0.286321\pi$
$68$	2.84456e46	0.530930
$69$	0	0
$70$	5.63191e46	0.501945
$71$	1.91444e47	1.18838	0.594189	−	0.804326i	$-0.297473\pi$
$71$	1.91444e47	1.18838	0.594189	+	0.804326i	$0.297473\pi$
$72$	0	0
$73$	−8.49448e46	−0.259659	−0.129830	−	0.991536i	$-0.541443\pi$
$73$	−8.49448e46	−0.259659	−0.129830	+	0.991536i	$0.541443\pi$
$74$	1.41688e48	3.06143
$75$	0	0
$76$	1.11185e48	1.21702
$77$	−1.00551e48	−0.788631
$78$	0	0
$79$	2.35655e48	0.961139	0.480570	−	0.876957i	$-0.340430\pi$
$79$	2.35655e48	0.961139	0.480570	+	0.876957i	$0.340430\pi$
$80$	−9.81042e47	−0.290331
$81$	0	0
$82$	1.74392e49	2.74963
$83$	−5.38960e48	−0.623828	−0.311914	−	0.950110i	$-0.600970\pi$
$83$	−5.38960e48	−0.623828	−0.311914	+	0.950110i	$0.600970\pi$
$84$	0	0
$85$	−1.58828e48	−0.100172
$86$	1.73164e49	0.810487
$87$	0	0
$88$	5.99461e49	1.56118
$89$	7.58432e49	1.48071	0.740357	−	0.672213i	$-0.234656\pi$
$89$	7.58432e49	1.48071	0.740357	+	0.672213i	$0.234656\pi$
$90$	0	0
$91$	1.04933e50	1.16241
$92$	7.39055e49	0.619565
$93$	0	0
$94$	3.28282e50	1.59033
$95$	−6.20810e49	−0.229619
$96$	0	0
$97$	−8.33376e50	−1.81201	−0.906007	−	0.423263i	$-0.860885\pi$
$97$	−8.33376e50	−1.81201	−0.906007	+	0.423263i	$0.860885\pi$
$98$	3.60151e50	0.602865
$99$	0	0
$100$	−1.67453e51	−1.67453
$101$	−3.60874e50	−0.280001	−0.140001	−	0.990151i	$-0.544710\pi$
$101$	−3.60874e50	−0.280001	−0.140001	+	0.990151i	$0.544710\pi$
$102$	0	0
$103$	−5.92261e50	−0.278717	−0.139359	−	0.990242i	$-0.544504\pi$
$103$	−5.92261e50	−0.278717	−0.139359	+	0.990242i	$0.544504\pi$
$104$	−6.25586e51	−2.30111
$105$	0	0
$106$	−4.02102e50	−0.0909989
$107$	2.68636e51	0.478495	0.239247	−	0.970959i	$-0.423099\pi$
$107$	2.68636e51	0.478495	0.239247	+	0.970959i	$0.423099\pi$
$108$	0	0
$109$	−1.08273e52	−1.20267	−0.601335	−	0.798997i	$-0.705364\pi$
$109$	−1.08273e52	−1.20267	−0.601335	+	0.798997i	$0.705364\pi$
$110$	−6.94338e51	−0.611023
$111$	0	0
$112$	1.15414e52	0.641502
$113$	1.18691e52	0.525915	0.262958	−	0.964807i	$-0.415302\pi$
$113$	1.18691e52	0.525915	0.262958	+	0.964807i	$0.415302\pi$
$114$	0	0
$115$	−4.12658e51	−0.116895
$116$	−1.71510e52	−0.389592
$117$	0	0
$118$	−9.80988e52	−1.44103
$119$	1.86852e52	0.221335
$120$	0	0
$121$	−5.16394e51	−0.0399903
$122$	−1.79184e53	−1.12492
$123$	0	0
$124$	4.08156e53	1.69267
$125$	2.01304e53	0.680215
$126$	0	0
$127$	2.91976e53	0.658190	0.329095	−	0.944297i	$-0.393256\pi$
$127$	2.91976e53	0.658190	0.329095	+	0.944297i	$0.393256\pi$
$128$	9.78766e53	1.80644
$129$	0	0
$130$	7.24598e53	0.900620
$131$	1.12031e54	1.14530	0.572651	−	0.819799i	$-0.305915\pi$
$131$	1.12031e54	1.14530	0.572651	+	0.819799i	$0.305915\pi$
$132$	0	0
$133$	7.30346e53	0.507355
$134$	−3.71091e54	−2.12965
$135$	0	0
$136$	−1.11396e54	−0.438156
$137$	−3.16309e54	−1.03214	−0.516068	−	0.856548i	$-0.672605\pi$
$137$	−3.16309e54	−1.03214	−0.516068	+	0.856548i	$0.672605\pi$
$138$	0	0
$139$	−8.65660e53	−0.195196	−0.0975978	−	0.995226i	$-0.531116\pi$
$139$	−8.65660e53	−0.195196	−0.0975978	+	0.995226i	$0.531116\pi$
$140$	−3.01408e54	−0.566097
$141$	0	0
$142$	−1.55523e55	−2.03443
$143$	−1.29368e55	−1.41501
$144$	0	0
$145$	9.57641e53	0.0735053
$146$	6.90065e54	0.444521
$147$	0	0
$148$	−7.58285e55	−3.45270
$149$	6.45813e54	0.247661	0.123830	−	0.992303i	$-0.460482\pi$
$149$	6.45813e54	0.247661	0.123830	+	0.992303i	$0.460482\pi$
$150$	0	0
$151$	2.64453e55	0.721832	0.360916	−	0.932598i	$-0.382464\pi$
$151$	2.64453e55	0.721832	0.360916	+	0.932598i	$0.382464\pi$
$152$	−4.35414e55	−1.00436
$153$	0	0
$154$	8.16847e55	1.35009
$155$	−2.27898e55	−0.319361
$156$	0	0
$157$	−1.74550e55	−0.176392	−0.0881962	−	0.996103i	$-0.528110\pi$
$157$	−1.74550e55	−0.176392	−0.0881962	+	0.996103i	$0.528110\pi$
$158$	−1.91439e56	−1.64541
$159$	0	0
$160$	−1.33724e55	−0.0833967
$161$	4.85467e55	0.258286
$162$	0	0
$163$	−2.44447e56	−0.949296	−0.474648	−	0.880176i	$-0.657425\pi$
$163$	−2.44447e56	−0.949296	−0.474648	+	0.880176i	$0.657425\pi$
$164$	−9.33311e56	−3.10105
$165$	0	0
$166$	4.37834e56	1.06796
$167$	7.65512e56	1.60207	0.801036	−	0.598616i	$-0.204282\pi$
$167$	7.65512e56	1.60207	0.801036	+	0.598616i	$0.204282\pi$
$168$	0	0
$169$	7.02756e56	1.08566
$170$	1.29027e56	0.171488
$171$	0	0
$172$	−9.26736e56	−0.914073
$173$	−6.79321e56	−0.577963	−0.288981	−	0.957335i	$-0.593317\pi$
$173$	−6.79321e56	−0.577963	−0.288981	+	0.957335i	$0.593317\pi$
$174$	0	0
$175$	−1.09996e57	−0.698082
$176$	−1.42289e57	−0.780907
$177$	0	0
$178$	−6.16126e57	−2.53489
$179$	−2.98876e57	−1.06596	−0.532978	−	0.846129i	$-0.678927\pi$
$179$	−2.98876e57	−1.06596	−0.532978	+	0.846129i	$0.678927\pi$
$180$	0	0
$181$	−1.29245e57	−0.347223	−0.173611	−	0.984814i	$-0.555544\pi$
$181$	−1.29245e57	−0.347223	−0.173611	+	0.984814i	$0.555544\pi$
$182$	−8.52446e57	−1.98997
$183$	0	0
$184$	−2.89423e57	−0.511304
$185$	4.23395e57	0.651429
$186$	0	0
$187$	−2.30363e57	−0.269434
$188$	−1.75690e58	−1.79358
$189$	0	0
$190$	5.04327e57	0.393093
$191$	−2.79327e58	−1.90442	−0.952209	−	0.305446i	$-0.901194\pi$
$191$	−2.79327e58	−1.90442	−0.952209	+	0.305446i	$0.901194\pi$
$192$	0	0
$193$	1.88817e58	0.987027	0.493514	−	0.869738i	$-0.335712\pi$
$193$	1.88817e58	0.987027	0.493514	+	0.869738i	$0.335712\pi$
$194$	6.77008e58	3.10206
$195$	0	0
$196$	−1.92746e58	−0.679915
$197$	3.18961e58	0.988209	0.494104	−	0.869403i	$-0.335496\pi$
$197$	3.18961e58	0.988209	0.494104	+	0.869403i	$0.335496\pi$
$198$	0	0
$199$	4.26943e58	1.02239	0.511195	−	0.859465i	$-0.329203\pi$
$199$	4.26943e58	1.02239	0.511195	+	0.859465i	$0.329203\pi$
$200$	6.55768e58	1.38193
$201$	0	0
$202$	2.93163e58	0.479346
$203$	−1.12661e58	−0.162414
$204$	0	0
$205$	5.21123e58	0.585082
$206$	4.81134e58	0.477147
$207$	0	0
$208$	1.48490e59	1.15102
$209$	−9.00417e58	−0.617609
$210$	0	0
$211$	−1.08128e59	−0.581748	−0.290874	−	0.956761i	$-0.593946\pi$
$211$	−1.08128e59	−0.581748	−0.290874	+	0.956761i	$0.593946\pi$
$212$	2.15197e58	0.102629
$213$	0	0
$214$	−2.18231e59	−0.819154
$215$	5.17452e58	0.172460
$216$	0	0
$217$	2.68108e59	0.705645
$218$	8.79580e59	2.05890
$219$	0	0
$220$	3.71596e59	0.689116
$221$	2.40402e59	0.397133
$222$	0	0
$223$	−6.98254e59	−0.916726	−0.458363	−	0.888765i	$-0.651564\pi$
$223$	−6.98254e59	−0.916726	−0.458363	+	0.888765i	$0.651564\pi$
$224$	1.57318e59	0.184270
$225$	0	0
$226$	−9.64205e59	−0.900335
$227$	−1.84393e60	−1.53846	−0.769228	−	0.638975i	$-0.779359\pi$
$227$	−1.84393e60	−1.53846	−0.769228	+	0.638975i	$0.779359\pi$
$228$	0	0
$229$	3.39685e59	0.226606	0.113303	−	0.993560i	$-0.463857\pi$
$229$	3.39685e59	0.226606	0.113303	+	0.993560i	$0.463857\pi$
$230$	3.35231e59	0.200117
$231$	0	0
$232$	6.71655e59	0.321516
$233$	1.17691e60	0.504854	0.252427	−	0.967616i	$-0.418771\pi$
$233$	1.17691e60	0.504854	0.252427	+	0.967616i	$0.418771\pi$
$234$	0	0
$235$	9.80980e59	0.338400
$236$	5.25005e60	1.62520
$237$	0	0
$238$	−1.51793e60	−0.378912
$239$	−5.07807e60	−1.13907	−0.569537	−	0.821966i	$-0.692878\pi$
$239$	−5.07807e60	−1.13907	−0.569537	+	0.821966i	$0.692878\pi$
$240$	0	0
$241$	4.94984e60	0.897752	0.448876	−	0.893594i	$-0.351824\pi$
$241$	4.94984e60	0.897752	0.448876	+	0.893594i	$0.351824\pi$
$242$	4.19503e59	0.0684609
$243$	0	0
$244$	9.58954e60	1.26870
$245$	1.07621e60	0.128281
$246$	0	0
$247$	9.39657e60	0.910327
$248$	−1.59839e61	−1.39690
$249$	0	0
$250$	−1.63533e61	−1.16449
$251$	1.18124e60	0.0759731	0.0379866	−	0.999278i	$-0.487906\pi$
$251$	1.18124e60	0.0759731	0.0379866	+	0.999278i	$0.487906\pi$
$252$	0	0
$253$	−5.98515e60	−0.314414
$254$	−2.37192e61	−1.12678
$255$	0	0
$256$	−4.89432e61	−1.90359
$257$	−2.72008e61	−0.957827	−0.478914	−	0.877862i	$-0.658969\pi$
$257$	−2.72008e61	−0.957827	−0.478914	+	0.877862i	$0.658969\pi$
$258$	0	0
$259$	−4.98099e61	−1.43937
$260$	−3.87790e61	−1.01572
$261$	0	0
$262$	−9.10105e61	−1.96069
$263$	2.48007e61	0.484834	0.242417	−	0.970172i	$-0.422060\pi$
$263$	2.48007e61	0.484834	0.242417	+	0.970172i	$0.422060\pi$
$264$	0	0
$265$	−1.20157e60	−0.0193633
$266$	−5.93310e61	−0.868560
$267$	0	0
$268$	1.98600e62	2.40183
$269$	6.54289e61	0.719592	0.359796	−	0.933031i	$-0.382846\pi$
$269$	6.54289e61	0.719592	0.359796	+	0.933031i	$0.382846\pi$
$270$	0	0
$271$	−6.85359e60	−0.0624024	−0.0312012	−	0.999513i	$-0.509933\pi$
$271$	−6.85359e60	−0.0624024	−0.0312012	+	0.999513i	$0.509933\pi$
$272$	2.64413e61	0.219167
$273$	0	0
$274$	2.56959e62	1.76695
$275$	1.35610e62	0.849784
$276$	0	0
$277$	−2.43203e62	−1.26688	−0.633438	−	0.773793i	$-0.718357\pi$
$277$	−2.43203e62	−1.26688	−0.633438	+	0.773793i	$0.718357\pi$
$278$	7.03235e61	0.334163
$279$	0	0
$280$	1.18035e62	0.467178
$281$	−2.21655e62	−0.801062	−0.400531	−	0.916283i	$-0.631174\pi$
$281$	−2.21655e62	−0.801062	−0.400531	+	0.916283i	$0.631174\pi$
$282$	0	0
$283$	1.63167e62	0.492127	0.246063	−	0.969254i	$-0.420863\pi$
$283$	1.63167e62	0.492127	0.246063	+	0.969254i	$0.420863\pi$
$284$	8.32329e62	2.29444
$285$	0	0
$286$	1.05095e63	2.42241
$287$	−6.13070e62	−1.29277
$288$	0	0
$289$	−5.23295e62	−0.924381
$290$	−7.77958e61	−0.125837
$291$	0	0
$292$	−3.69309e62	−0.501334
$293$	7.35742e62	0.915380	0.457690	−	0.889112i	$-0.348677\pi$
$293$	7.35742e62	0.915380	0.457690	+	0.889112i	$0.348677\pi$
$294$	0	0
$295$	−2.93141e62	−0.306631
$296$	2.96954e63	2.84938
$297$	0	0
$298$	−5.24638e62	−0.423980
$299$	6.24599e62	0.463432
$300$	0	0
$301$	−6.08751e62	−0.381060
$302$	−2.14833e63	−1.23573
$303$	0	0
$304$	1.03351e63	0.502386
$305$	−5.35441e62	−0.239368
$306$	0	0
$307$	−2.33959e63	−0.885341	−0.442671	−	0.896684i	$-0.645969\pi$
$307$	−2.33959e63	−0.885341	−0.442671	+	0.896684i	$0.645969\pi$
$308$	−4.37160e63	−1.52264
$309$	0	0
$310$	1.85137e63	0.546726
$311$	−5.85752e63	−1.59340	−0.796698	−	0.604378i	$-0.793422\pi$
$311$	−5.85752e63	−1.59340	−0.796698	+	0.604378i	$0.793422\pi$
$312$	0	0
$313$	−5.58306e63	−1.28971	−0.644855	−	0.764305i	$-0.723082\pi$
$313$	−5.58306e63	−1.28971	−0.644855	+	0.764305i	$0.723082\pi$
$314$	1.41799e63	0.301973
$315$	0	0
$316$	1.02454e64	1.85571
$317$	2.94076e63	0.491414	0.245707	−	0.969344i	$-0.420980\pi$
$317$	2.94076e63	0.491414	0.245707	+	0.969344i	$0.420980\pi$
$318$	0	0
$319$	1.38895e63	0.197708
$320$	3.29544e63	0.433101
$321$	0	0
$322$	−3.94379e63	−0.442169
$323$	1.67322e63	0.173336
$324$	0	0
$325$	−1.41520e64	−1.25254
$326$	1.98582e64	1.62514
$327$	0	0
$328$	3.65497e64	2.55918
$329$	−1.15406e64	−0.747712
$330$	0	0
$331$	8.27822e63	0.459540	0.229770	−	0.973245i	$-0.426203\pi$
$331$	8.27822e63	0.459540	0.229770	+	0.973245i	$0.426203\pi$
$332$	−2.34320e64	−1.20445
$333$	0	0
$334$	−6.21878e64	−2.74265
$335$	−1.10890e64	−0.453159
$336$	0	0
$337$	2.46670e63	0.0866070	0.0433035	−	0.999062i	$-0.486212\pi$
$337$	2.46670e63	0.0866070	0.0433035	+	0.999062i	$0.486212\pi$
$338$	−5.70897e64	−1.85858
$339$	0	0
$340$	−6.90527e63	−0.193405
$341$	−3.30540e64	−0.858989
$342$	0	0
$343$	−4.86141e64	−1.08833
$344$	3.62922e64	0.754350
$345$	0	0
$346$	5.51860e64	0.989437
$347$	−1.55920e64	−0.259717	−0.129858	−	0.991533i	$-0.541452\pi$
$347$	−1.55920e64	−0.259717	−0.129858	+	0.991533i	$0.541452\pi$
$348$	0	0
$349$	−5.23164e64	−0.752644	−0.376322	−	0.926489i	$-0.622811\pi$
$349$	−5.23164e64	−0.752644	−0.376322	+	0.926489i	$0.622811\pi$
$350$	8.93573e64	1.19507
$351$	0	0
$352$	−1.93951e64	−0.224313
$353$	−1.78259e65	−1.91777	−0.958885	−	0.283795i	$-0.908407\pi$
$353$	−1.78259e65	−1.91777	−0.958885	+	0.283795i	$0.908407\pi$
$354$	0	0
$355$	−4.64739e64	−0.432898
$356$	3.29738e65	2.85887
$357$	0	0
$358$	2.42798e65	1.82485
$359$	1.48533e65	1.03972	0.519858	−	0.854253i	$-0.325985\pi$
$359$	1.48533e65	1.03972	0.519858	+	0.854253i	$0.325985\pi$
$360$	0	0
$361$	−9.92004e64	−0.602670
$362$	1.04994e65	0.594425
$363$	0	0
$364$	4.56211e65	2.24430
$365$	2.06207e64	0.0945879
$366$	0	0
$367$	8.05130e64	0.321278	0.160639	−	0.987013i	$-0.448644\pi$
$367$	8.05130e64	0.321278	0.160639	+	0.987013i	$0.448644\pi$
$368$	6.86982e64	0.255756
$369$	0	0
$370$	−3.43953e65	−1.11521
$371$	1.41357e64	0.0427843
$372$	0	0
$373$	2.25234e64	0.0594372	0.0297186	−	0.999558i	$-0.490539\pi$
$373$	2.25234e64	0.0594372	0.0297186	+	0.999558i	$0.490539\pi$
$374$	1.87140e65	0.461254
$375$	0	0
$376$	6.88024e65	1.48018
$377$	−1.44948e65	−0.291413
$378$	0	0
$379$	−1.01382e66	−1.78098	−0.890491	−	0.455001i	$-0.849639\pi$
$379$	−1.01382e66	−1.78098	−0.890491	+	0.455001i	$0.849639\pi$
$380$	−2.69905e65	−0.443333
$381$	0	0
$382$	2.26917e66	3.26025
$383$	3.69389e65	0.496496	0.248248	−	0.968697i	$-0.420145\pi$
$383$	3.69389e65	0.496496	0.248248	+	0.968697i	$0.420145\pi$
$384$	0	0
$385$	2.44092e65	0.287280
$386$	−1.53389e66	−1.68973
$387$	0	0
$388$	−3.62321e66	−3.49852
$389$	1.20048e66	1.08552	0.542762	−	0.839887i	$-0.317379\pi$
$389$	1.20048e66	1.08552	0.542762	+	0.839887i	$0.317379\pi$
$390$	0	0
$391$	1.11221e65	0.0882426
$392$	7.54816e65	0.561108
$393$	0	0
$394$	−2.59114e66	−1.69175
$395$	−5.72063e65	−0.350121
$396$	0	0
$397$	−2.17708e66	−1.17143	−0.585714	−	0.810518i	$-0.699186\pi$
$397$	−2.17708e66	−1.17143	−0.585714	+	0.810518i	$0.699186\pi$
$398$	−3.46835e66	−1.75027
$399$	0	0
$400$	−1.55655e66	−0.691245
$401$	−4.28565e66	−1.78581	−0.892905	−	0.450245i	$-0.851337\pi$
$401$	−4.28565e66	−1.78581	−0.892905	+	0.450245i	$0.851337\pi$
$402$	0	0
$403$	3.44945e66	1.26611
$404$	−1.56895e66	−0.540609
$405$	0	0
$406$	9.15221e65	0.278043
$407$	6.14088e66	1.75216
$408$	0	0
$409$	7.61605e66	1.91772	0.958860	−	0.283878i	$-0.0916211\pi$
$409$	7.61605e66	1.91772	0.958860	+	0.283878i	$0.0916211\pi$
$410$	−4.23344e66	−1.00162
$411$	0	0
$412$	−2.57493e66	−0.538129
$413$	3.44863e66	0.677517
$414$	0	0
$415$	1.30835e66	0.227246
$416$	2.02404e66	0.330628
$417$	0	0
$418$	7.31471e66	1.05731
$419$	−3.51155e66	−0.477574	−0.238787	−	0.971072i	$-0.576750\pi$
$419$	−3.51155e66	−0.477574	−0.238787	+	0.971072i	$0.576750\pi$
$420$	0	0
$421$	−3.18883e66	−0.384094	−0.192047	−	0.981386i	$-0.561513\pi$
$421$	−3.18883e66	−0.384094	−0.192047	+	0.981386i	$0.561513\pi$
$422$	8.78397e66	0.995917
$423$	0	0
$424$	−8.42737e65	−0.0846960
$425$	−2.52001e66	−0.238498
$426$	0	0
$427$	6.29914e66	0.528896
$428$	1.16793e67	0.923847
$429$	0	0
$430$	−4.20362e66	−0.295242
$431$	2.27664e66	0.150704	0.0753519	−	0.997157i	$-0.475992\pi$
$431$	2.27664e66	0.150704	0.0753519	+	0.997157i	$0.475992\pi$
$432$	0	0
$433$	−2.96559e66	−0.174449	−0.0872247	−	0.996189i	$-0.527800\pi$
$433$	−2.96559e66	−0.174449	−0.0872247	+	0.996189i	$0.527800\pi$
$434$	−2.17802e67	−1.20802
$435$	0	0
$436$	−4.70733e67	−2.32204
$437$	4.34727e66	0.202274
$438$	0	0
$439$	3.03815e67	1.25824	0.629121	−	0.777307i	$-0.283415\pi$
$439$	3.03815e67	1.25824	0.629121	+	0.777307i	$0.283415\pi$
$440$	−1.45522e67	−0.568701
$441$	0	0
$442$	−1.95295e67	−0.679867
$443$	1.74549e67	0.573619	0.286810	−	0.957988i	$-0.407405\pi$
$443$	1.74549e67	0.573619	0.286810	+	0.957988i	$0.407405\pi$
$444$	0	0
$445$	−1.84112e67	−0.539390
$446$	5.67240e67	1.56938
$447$	0	0
$448$	−3.87689e67	−0.956960
$449$	2.54711e67	0.593972	0.296986	−	0.954882i	$-0.404019\pi$
$449$	2.54711e67	0.593972	0.296986	+	0.954882i	$0.404019\pi$
$450$	0	0
$451$	7.55832e67	1.57370
$452$	5.16023e67	1.01540
$453$	0	0
$454$	1.49795e68	2.63374
$455$	−2.54730e67	−0.423437
$456$	0	0
$457$	8.96015e67	1.33184	0.665920	−	0.746023i	$-0.268039\pi$
$457$	8.96015e67	1.33184	0.665920	+	0.746023i	$0.268039\pi$
$458$	−2.75949e67	−0.387935
$459$	0	0
$460$	−1.79409e67	−0.225693
$461$	−8.19688e67	−0.975607	−0.487804	−	0.872953i	$-0.662202\pi$
$461$	−8.19688e67	−0.975607	−0.487804	+	0.872953i	$0.662202\pi$
$462$	0	0
$463$	−1.13766e68	−1.21254	−0.606269	−	0.795259i	$-0.707335\pi$
$463$	−1.13766e68	−1.21254	−0.606269	+	0.795259i	$0.707335\pi$
$464$	−1.59425e67	−0.160823
$465$	0	0
$466$	−9.56082e67	−0.864280
$467$	−2.22344e67	−0.190303	−0.0951516	−	0.995463i	$-0.530334\pi$
$467$	−2.22344e67	−0.190303	−0.0951516	+	0.995463i	$0.530334\pi$
$468$	0	0
$469$	1.30456e68	1.00128
$470$	−7.96918e67	−0.579319
$471$	0	0
$472$	−2.05599e68	−1.34122
$473$	7.50507e67	0.463869
$474$	0	0
$475$	−9.84993e67	−0.546696
$476$	8.12364e67	0.427340
$477$	0	0
$478$	4.12527e68	1.95003
$479$	1.15577e68	0.517983	0.258992	−	0.965880i	$-0.416610\pi$
$479$	1.15577e68	0.517983	0.258992	+	0.965880i	$0.416610\pi$
$480$	0	0
$481$	−6.40851e68	−2.58260
$482$	−4.02110e68	−1.53690
$483$	0	0
$484$	−2.24509e67	−0.0772107
$485$	2.02305e68	0.660074
$486$	0	0
$487$	2.20619e66	0.00648118	0.00324059	−	0.999995i	$-0.498968\pi$
$487$	2.20619e66	0.00648118	0.00324059	+	0.999995i	$0.498968\pi$
$488$	−3.75539e68	−1.04701
$489$	0	0
$490$	−8.74282e67	−0.219610
$491$	−7.91071e68	−1.88642	−0.943208	−	0.332202i	$-0.892208\pi$
$491$	−7.91071e68	−1.88642	−0.943208	+	0.332202i	$0.892208\pi$
$492$	0	0
$493$	−2.58106e67	−0.0554883
$494$	−7.63348e68	−1.55842
$495$	0	0
$496$	3.79397e68	0.698734
$497$	5.46737e68	0.956512
$498$	0	0
$499$	−9.62285e68	−1.51964	−0.759819	−	0.650135i	$-0.774712\pi$
$499$	−9.62285e68	−1.51964	−0.759819	+	0.650135i	$0.774712\pi$
$500$	8.75194e68	1.31332
$501$	0	0
$502$	−9.59607e67	−0.130061
$503$	−5.82620e67	−0.0750588	−0.0375294	−	0.999296i	$-0.511949\pi$
$503$	−5.82620e67	−0.0750588	−0.0375294	+	0.999296i	$0.511949\pi$
$504$	0	0
$505$	8.76036e67	0.101998
$506$	4.86215e68	0.538258
$507$	0	0
$508$	1.26940e69	1.27079
$509$	−5.13252e68	−0.488683	−0.244342	−	0.969689i	$-0.578572\pi$
$509$	−5.13252e68	−0.488683	−0.244342	+	0.969689i	$0.578572\pi$
$510$	0	0
$511$	−2.42590e68	−0.208997
$512$	1.77201e69	1.45239
$513$	0	0
$514$	2.20971e69	1.63974
$515$	1.43774e68	0.101530
$516$	0	0
$517$	1.42280e69	0.910199
$518$	4.04640e69	2.46411
$519$	0	0
$520$	1.51863e69	0.838240
$521$	−1.75529e69	−0.922545	−0.461272	−	0.887259i	$-0.652607\pi$
$521$	−1.75529e69	−0.922545	−0.461272	+	0.887259i	$0.652607\pi$
$522$	0	0
$523$	3.31068e68	0.157806	0.0789032	−	0.996882i	$-0.474858\pi$
$523$	3.31068e68	0.157806	0.0789032	+	0.996882i	$0.474858\pi$
$524$	4.87069e69	2.21128
$525$	0	0
$526$	−2.01473e69	−0.830006
$527$	6.14235e68	0.241082
$528$	0	0
$529$	−2.51724e69	−0.897026
$530$	9.76118e67	0.0331488
$531$	0	0
$532$	3.17527e69	0.979568
$533$	−7.88771e69	−2.31957
$534$	0	0
$535$	−6.52124e68	−0.174304
$536$	−7.77744e69	−1.98214
$537$	0	0
$538$	−5.31524e69	−1.23190
$539$	1.56093e69	0.345040
$540$	0	0
$541$	−8.41369e69	−1.69222	−0.846109	−	0.533009i	$-0.821061\pi$
$541$	−8.41369e69	−1.69222	−0.846109	+	0.533009i	$0.821061\pi$
$542$	5.56764e68	0.106829
$543$	0	0
$544$	3.60415e68	0.0629552
$545$	2.62838e69	0.438104
$546$	0	0
$547$	1.11230e70	1.68867	0.844334	−	0.535817i	$-0.179996\pi$
$547$	1.11230e70	1.68867	0.844334	+	0.535817i	$0.179996\pi$
$548$	−1.37519e70	−1.99278
$549$	0	0
$550$	−1.10165e70	−1.45478
$551$	−1.00885e69	−0.127193
$552$	0	0
$553$	6.72997e69	0.773611
$554$	1.97570e70	2.16882
$555$	0	0
$556$	−3.76357e69	−0.376871
$557$	1.12523e70	1.07630	0.538152	−	0.842848i	$-0.319123\pi$
$557$	1.12523e70	1.07630	0.538152	+	0.842848i	$0.319123\pi$
$558$	0	0
$559$	−7.83214e69	−0.683722
$560$	−2.80171e69	−0.233684
$561$	0	0
$562$	1.80065e70	1.37137
$563$	2.06561e68	0.0150344	0.00751718	−	0.999972i	$-0.497607\pi$
$563$	2.06561e68	0.0150344	0.00751718	+	0.999972i	$0.497607\pi$
$564$	0	0
$565$	−2.88126e69	−0.191579
$566$	−1.32551e70	−0.842491
$567$	0	0
$568$	−3.25951e70	−1.89352
$569$	−1.15170e70	−0.639698	−0.319849	−	0.947469i	$-0.603632\pi$
$569$	−1.15170e70	−0.639698	−0.319849	+	0.947469i	$0.603632\pi$
$570$	0	0
$571$	2.10280e70	1.06801	0.534007	−	0.845480i	$-0.320686\pi$
$571$	2.10280e70	1.06801	0.534007	+	0.845480i	$0.320686\pi$
$572$	−5.62447e70	−2.73201
$573$	0	0
$574$	4.98039e70	2.21315
$575$	−6.54734e69	−0.278314
$576$	0	0
$577$	5.78798e68	0.0225187	0.0112594	−	0.999937i	$-0.496416\pi$
$577$	5.78798e68	0.0225187	0.0112594	+	0.999937i	$0.496416\pi$
$578$	4.25108e70	1.58248
$579$	0	0
$580$	4.16347e69	0.141919
$581$	−1.53919e70	−0.502113
$582$	0	0
$583$	−1.74274e69	−0.0520818
$584$	1.44626e70	0.413732
$585$	0	0
$586$	−5.97694e70	−1.56707
$587$	3.63201e70	0.911748	0.455874	−	0.890044i	$-0.349327\pi$
$587$	3.63201e70	0.911748	0.455874	+	0.890044i	$0.349327\pi$
$588$	0	0
$589$	2.40085e70	0.552619
$590$	2.38139e70	0.524933
$591$	0	0
$592$	−7.04857e70	−1.42527
$593$	2.80060e70	0.542447	0.271223	−	0.962516i	$-0.412572\pi$
$593$	2.80060e70	0.542447	0.271223	+	0.962516i	$0.412572\pi$
$594$	0	0
$595$	−4.53591e69	−0.0806272
$596$	2.80776e70	0.478167
$597$	0	0
$598$	−5.07405e70	−0.793367
$599$	−4.36080e70	−0.653404	−0.326702	−	0.945127i	$-0.605937\pi$
$599$	−4.36080e70	−0.653404	−0.326702	+	0.945127i	$0.605937\pi$
$600$	0	0
$601$	3.82831e70	0.526875	0.263437	−	0.964676i	$-0.415144\pi$
$601$	3.82831e70	0.526875	0.263437	+	0.964676i	$0.415144\pi$
$602$	4.94530e70	0.652352
$603$	0	0
$604$	1.14974e71	1.39367
$605$	1.25357e69	0.0145675
$606$	0	0
$607$	−2.49833e70	−0.266894	−0.133447	−	0.991056i	$-0.542605\pi$
$607$	−2.49833e70	−0.266894	−0.133447	+	0.991056i	$0.542605\pi$
$608$	1.40875e70	0.144309
$609$	0	0
$610$	4.34976e70	0.409783
$611$	−1.48481e71	−1.34159
$612$	0	0
$613$	−1.99012e71	−1.65439	−0.827193	−	0.561919i	$-0.810063\pi$
$613$	−1.99012e71	−1.65439	−0.827193	+	0.561919i	$0.810063\pi$
$614$	1.90061e71	1.51565
$615$	0	0
$616$	1.71197e71	1.25658
$617$	−5.04536e70	−0.355321	−0.177660	−	0.984092i	$-0.556853\pi$
$617$	−5.04536e70	−0.355321	−0.177660	+	0.984092i	$0.556853\pi$
$618$	0	0
$619$	−8.80938e70	−0.571260	−0.285630	−	0.958340i	$-0.592203\pi$
$619$	−8.80938e70	−0.571260	−0.285630	+	0.958340i	$0.592203\pi$
$620$	−9.90814e70	−0.616601
$621$	0	0
$622$	4.75846e71	2.72780
$623$	2.16597e71	1.19181
$624$	0	0
$625$	1.22178e71	0.619516
$626$	4.53551e71	2.20790
$627$	0	0
$628$	−7.58881e70	−0.340567
$629$	−1.14115e71	−0.491756
$630$	0	0
$631$	3.58339e71	1.42411	0.712057	−	0.702121i	$-0.247764\pi$
$631$	3.58339e71	1.42411	0.712057	+	0.702121i	$0.247764\pi$
$632$	−4.01224e71	−1.53144
$633$	0	0
$634$	−2.38898e71	−0.841271
$635$	−7.08782e70	−0.239763
$636$	0	0
$637$	−1.62895e71	−0.508573
$638$	−1.12834e71	−0.338465
$639$	0	0
$640$	−2.37599e71	−0.658046
$641$	−6.07769e71	−1.61755	−0.808777	−	0.588116i	$-0.799870\pi$
$641$	−6.07769e71	−1.61755	−0.808777	+	0.588116i	$0.799870\pi$
$642$	0	0
$643$	−7.85977e71	−1.93210	−0.966050	−	0.258353i	$-0.916820\pi$
$643$	−7.85977e71	−1.93210	−0.966050	+	0.258353i	$0.916820\pi$
$644$	2.11063e71	0.498681
$645$	0	0
$646$	−1.35927e71	−0.296741
$647$	−5.80462e71	−1.21819	−0.609095	−	0.793098i	$-0.708467\pi$
$647$	−5.80462e71	−1.21819	−0.609095	+	0.793098i	$0.708467\pi$
$648$	0	0
$649$	−4.25169e71	−0.824750
$650$	1.14966e72	2.14428
$651$	0	0
$652$	−1.06277e72	−1.83284
$653$	−9.50695e71	−1.57672	−0.788361	−	0.615213i	$-0.789070\pi$
$653$	−9.50695e71	−1.57672	−0.788361	+	0.615213i	$0.789070\pi$
$654$	0	0
$655$	−2.71960e71	−0.417207
$656$	−8.67551e71	−1.28011
$657$	0	0
$658$	9.37526e71	1.28004
$659$	−5.24300e71	−0.688655	−0.344327	−	0.938850i	$-0.611893\pi$
$659$	−5.24300e71	−0.688655	−0.344327	+	0.938850i	$0.611893\pi$
$660$	0	0
$661$	1.48904e71	0.181038	0.0905189	−	0.995895i	$-0.471147\pi$
$661$	1.48904e71	0.181038	0.0905189	+	0.995895i	$0.471147\pi$
$662$	−6.72497e71	−0.786704
$663$	0	0
$664$	9.17627e71	0.993986
$665$	−1.77294e71	−0.184817
$666$	0	0
$667$	−6.70595e70	−0.0647518
$668$	3.32817e72	3.09318
$669$	0	0
$670$	9.00838e71	0.775781
$671$	−7.76598e71	−0.643831
$672$	0	0
$673$	−5.12793e70	−0.0394056	−0.0197028	−	0.999806i	$-0.506272\pi$
$673$	−5.12793e70	−0.0394056	−0.0197028	+	0.999806i	$0.506272\pi$
$674$	−2.00387e71	−0.148266
$675$	0	0
$676$	3.05533e72	2.09612
$677$	2.88331e72	1.90494	0.952468	−	0.304639i	$-0.0985357\pi$
$677$	2.88331e72	1.90494	0.952468	+	0.304639i	$0.0985357\pi$
$678$	0	0
$679$	−2.38000e72	−1.45847
$680$	2.70419e71	0.159610
$681$	0	0
$682$	2.68521e72	1.47054
$683$	−1.21910e72	−0.643150	−0.321575	−	0.946884i	$-0.604212\pi$
$683$	−1.21910e72	−0.643150	−0.321575	+	0.946884i	$0.604212\pi$
$684$	0	0
$685$	7.67852e71	0.375983
$686$	3.94926e72	1.86316
$687$	0	0
$688$	−8.61439e71	−0.377328
$689$	1.81869e71	0.0767661
$690$	0	0
$691$	−1.39481e72	−0.546794	−0.273397	−	0.961901i	$-0.588147\pi$
$691$	−1.39481e72	−0.546794	−0.273397	+	0.961901i	$0.588147\pi$
$692$	−2.95344e72	−1.11589
$693$	0	0
$694$	1.26665e72	0.444619
$695$	2.10143e71	0.0711052
$696$	0	0
$697$	−1.40454e72	−0.441672
$698$	4.25002e72	1.28848
$699$	0	0
$700$	−4.78222e72	−1.34781
$701$	−5.63382e72	−1.53106	−0.765532	−	0.643397i	$-0.777524\pi$
$701$	−5.63382e72	−1.53106	−0.765532	+	0.643397i	$0.777524\pi$
$702$	0	0
$703$	−4.46038e72	−1.12723
$704$	4.77967e72	1.16492
$705$	0	0
$706$	1.44812e73	3.28311
$707$	−1.03060e72	−0.225370
$708$	0	0
$709$	3.78104e72	0.769365	0.384682	−	0.923049i	$-0.374311\pi$
$709$	3.78104e72	0.769365	0.384682	+	0.923049i	$0.374311\pi$
$710$	3.77539e72	0.741095
$711$	0	0
$712$	−1.29130e73	−2.35932
$713$	1.59587e72	0.281329
$714$	0	0
$715$	3.14047e72	0.515455
$716$	−1.29940e73	−2.05808
$717$	0	0
$718$	−1.20664e73	−1.77993
$719$	−6.26463e72	−0.891885	−0.445943	−	0.895062i	$-0.647131\pi$
$719$	−6.26463e72	−0.891885	−0.445943	+	0.895062i	$0.647131\pi$
$720$	0	0
$721$	−1.69141e72	−0.224336
$722$	8.05873e72	1.03173
$723$	0	0
$724$	−5.61907e72	−0.670396
$725$	1.51942e72	0.175008
$726$	0	0
$727$	1.48516e73	1.59457	0.797287	−	0.603600i	$-0.206267\pi$
$727$	1.48516e73	1.59457	0.797287	+	0.603600i	$0.206267\pi$
$728$	−1.78658e73	−1.85214
$729$	0	0
$730$	−1.67516e72	−0.161929
$731$	−1.39465e72	−0.130188
$732$	0	0
$733$	5.93373e72	0.516627	0.258313	−	0.966061i	$-0.416833\pi$
$733$	5.93373e72	0.516627	0.258313	+	0.966061i	$0.416833\pi$
$734$	−6.54063e72	−0.550009
$735$	0	0
$736$	9.36409e71	0.0734652
$737$	−1.60834e73	−1.21887
$738$	0	0
$739$	1.50074e72	0.106138	0.0530692	−	0.998591i	$-0.483100\pi$
$739$	1.50074e72	0.106138	0.0530692	+	0.998591i	$0.483100\pi$
$740$	1.84077e73	1.25774
$741$	0	0
$742$	−1.14834e72	−0.0732441
$743$	2.89489e73	1.78409	0.892047	−	0.451943i	$-0.149269\pi$
$743$	2.89489e73	1.78409	0.892047	+	0.451943i	$0.149269\pi$
$744$	0	0
$745$	−1.56774e72	−0.0902170
$746$	−1.82973e72	−0.101753
$747$	0	0
$748$	−1.00153e73	−0.520205
$749$	7.67184e72	0.385135
$750$	0	0
$751$	1.40821e73	0.660462	0.330231	−	0.943900i	$-0.392873\pi$
$751$	1.40821e73	0.660462	0.330231	+	0.943900i	$0.392873\pi$
$752$	−1.63311e73	−0.740389
$753$	0	0
$754$	1.17752e73	0.498882
$755$	−6.41970e72	−0.262946
$756$	0	0
$757$	−9.83514e72	−0.376561	−0.188281	−	0.982115i	$-0.560291\pi$
$757$	−9.83514e72	−0.376561	−0.188281	+	0.982115i	$0.560291\pi$
$758$	8.23593e73	3.04893
$759$	0	0
$760$	1.05698e73	0.365866
$761$	−4.56710e73	−1.52873	−0.764367	−	0.644782i	$-0.776948\pi$
$761$	−4.56710e73	−1.52873	−0.764367	+	0.644782i	$0.776948\pi$
$762$	0	0
$763$	−3.09213e73	−0.968016
$764$	−1.21441e74	−3.67693
$765$	0	0
$766$	−3.00081e73	−0.849971
$767$	4.43698e73	1.21564
$768$	0	0
$769$	3.75294e73	0.962167	0.481083	−	0.876675i	$-0.340243\pi$
$769$	3.75294e73	0.962167	0.481083	+	0.876675i	$0.340243\pi$
$770$	−1.98293e73	−0.491806
$771$	0	0
$772$	8.20906e73	1.90569
$773$	−3.47460e73	−0.780419	−0.390210	−	0.920726i	$-0.627597\pi$
$773$	−3.47460e73	−0.780419	−0.390210	+	0.920726i	$0.627597\pi$
$774$	0	0
$775$	−3.61588e73	−0.760362
$776$	1.41890e74	2.88720
$777$	0	0
$778$	−9.75230e73	−1.85835
$779$	−5.48992e73	−1.01242
$780$	0	0
$781$	−6.74052e73	−1.16437
$782$	−9.03522e72	−0.151066
$783$	0	0
$784$	−1.79165e73	−0.280668
$785$	4.23728e72	0.0642556
$786$	0	0
$787$	−5.13224e72	−0.0729376	−0.0364688	−	0.999335i	$-0.511611\pi$
$787$	−5.13224e72	−0.0729376	−0.0364688	+	0.999335i	$0.511611\pi$
$788$	1.38672e74	1.90797
$789$	0	0
$790$	4.64726e73	0.599385
$791$	3.38963e73	0.423304
$792$	0	0
$793$	8.10443e73	0.948978
$794$	1.76859e74	2.00541
$795$	0	0
$796$	1.85619e74	1.97397
$797$	5.49546e73	0.566001	0.283000	−	0.959120i	$-0.408670\pi$
$797$	5.49546e73	0.566001	0.283000	+	0.959120i	$0.408670\pi$
$798$	0	0
$799$	−2.64396e73	−0.255454
$800$	−2.12169e73	−0.198558
$801$	0	0
$802$	3.48153e74	3.05720
$803$	2.99081e73	0.254414
$804$	0	0
$805$	−1.17849e73	−0.0940874
$806$	−2.80223e74	−2.16750
$807$	0	0
$808$	6.14420e73	0.446144
$809$	−2.78397e73	−0.195874	−0.0979372	−	0.995193i	$-0.531224\pi$
$809$	−2.78397e73	−0.195874	−0.0979372	+	0.995193i	$0.531224\pi$
$810$	0	0
$811$	−2.13458e74	−1.41020	−0.705099	−	0.709109i	$-0.749098\pi$
$811$	−2.13458e74	−1.41020	−0.705099	+	0.709109i	$0.749098\pi$
$812$	−4.89807e73	−0.313579
$813$	0	0
$814$	−4.98866e74	−2.99959
$815$	5.93406e73	0.345806
$816$	0	0
$817$	−5.45124e73	−0.298424
$818$	−6.18704e74	−3.28302
$819$	0	0
$820$	2.26565e74	1.12964
$821$	1.21993e74	0.589639	0.294819	−	0.955553i	$-0.404741\pi$
$821$	1.21993e74	0.589639	0.294819	+	0.955553i	$0.404741\pi$
$822$	0	0
$823$	−9.32706e72	−0.0423691	−0.0211845	−	0.999776i	$-0.506744\pi$
$823$	−9.32706e72	−0.0423691	−0.0211845	+	0.999776i	$0.506744\pi$
$824$	1.00838e74	0.444098
$825$	0	0
$826$	−2.80156e74	−1.15987
$827$	−2.77630e73	−0.111449	−0.0557244	−	0.998446i	$-0.517747\pi$
$827$	−2.77630e73	−0.111449	−0.0557244	+	0.998446i	$0.517747\pi$
$828$	0	0
$829$	3.61616e74	1.36492	0.682461	−	0.730922i	$-0.260910\pi$
$829$	3.61616e74	1.36492	0.682461	+	0.730922i	$0.260910\pi$
$830$	−1.06286e74	−0.389032
$831$	0	0
$832$	−4.98797e74	−1.71704
$833$	−2.90064e73	−0.0968380
$834$	0	0
$835$	−1.85831e74	−0.583598
$836$	−3.91468e74	−1.19244
$837$	0	0
$838$	2.85267e74	0.817578
$839$	4.79920e74	1.33425	0.667127	−	0.744944i	$-0.267524\pi$
$839$	4.79920e74	1.33425	0.667127	+	0.744944i	$0.267524\pi$
$840$	0	0
$841$	−3.66644e74	−0.959283
$842$	2.59050e74	0.657546
$843$	0	0
$844$	−4.70100e74	−1.12320
$845$	−1.70597e74	−0.395481
$846$	0	0
$847$	−1.47475e73	−0.0321877
$848$	2.00034e73	0.0423652
$849$	0	0
$850$	2.04718e74	0.408294
$851$	−2.96486e74	−0.573852
$852$	0	0
$853$	6.60846e74	1.20476	0.602379	−	0.798210i	$-0.294220\pi$
$853$	6.60846e74	1.20476	0.602379	+	0.798210i	$0.294220\pi$
$854$	−5.11723e74	−0.905438
$855$	0	0
$856$	−4.57376e74	−0.762416
$857$	2.87199e74	0.464699	0.232349	−	0.972632i	$-0.425359\pi$
$857$	2.87199e74	0.464699	0.232349	+	0.972632i	$0.425359\pi$
$858$	0	0
$859$	7.69360e74	1.17302	0.586508	−	0.809944i	$-0.300502\pi$
$859$	7.69360e74	1.17302	0.586508	+	0.809944i	$0.300502\pi$
$860$	2.24969e74	0.332975
$861$	0	0
$862$	−1.84947e74	−0.257996
$863$	8.71585e74	1.18041	0.590207	−	0.807252i	$-0.299046\pi$
$863$	8.71585e74	1.18041	0.590207	+	0.807252i	$0.299046\pi$
$864$	0	0
$865$	1.64908e74	0.210538
$866$	2.40915e74	0.298647
$867$	0	0
$868$	1.16563e75	1.36241
$869$	−8.29714e74	−0.941725
$870$	0	0
$871$	1.67843e75	1.79656
$872$	1.84345e75	1.91629
$873$	0	0
$874$	−3.53158e74	−0.346280
$875$	5.74894e74	0.547498
$876$	0	0
$877$	1.44865e75	1.30159	0.650797	−	0.759252i	$-0.274435\pi$
$877$	1.44865e75	1.30159	0.650797	+	0.759252i	$0.274435\pi$
$878$	−2.46810e75	−2.15403
$879$	0	0
$880$	3.45413e74	0.284466
$881$	1.16519e75	0.932207	0.466103	−	0.884730i	$-0.345657\pi$
$881$	1.16519e75	0.932207	0.466103	+	0.884730i	$0.345657\pi$
$882$	0	0
$883$	−1.52991e75	−1.15523	−0.577615	−	0.816309i	$-0.696016\pi$
$883$	−1.52991e75	−1.15523	−0.577615	+	0.816309i	$0.696016\pi$
$884$	1.04518e75	0.766759
$885$	0	0
$886$	−1.41799e75	−0.982001
$887$	2.18618e75	1.47107	0.735535	−	0.677487i	$-0.236931\pi$
$887$	2.18618e75	1.47107	0.735535	+	0.677487i	$0.236931\pi$
$888$	0	0
$889$	8.33840e74	0.529770
$890$	1.49567e75	0.923403
$891$	0	0
$892$	−3.03575e75	−1.76996
$893$	−1.03344e75	−0.585563
$894$	0	0
$895$	7.25535e74	0.388303
$896$	2.79521e75	1.45399
$897$	0	0
$898$	−2.06919e75	−1.01684
$899$	−3.70348e74	−0.176904
$900$	0	0
$901$	3.23850e73	0.0146171
$902$	−6.14014e75	−2.69409
$903$	0	0
$904$	−2.02081e75	−0.837975
$905$	3.13746e74	0.126485
$906$	0	0
$907$	−3.40042e75	−1.29583	−0.647914	−	0.761714i	$-0.724358\pi$
$907$	−3.40042e75	−1.29583	−0.647914	+	0.761714i	$0.724358\pi$
$908$	−8.01672e75	−2.97035
$909$	0	0
$910$	2.06935e75	0.724899
$911$	4.11484e74	0.140163	0.0700817	−	0.997541i	$-0.477674\pi$
$911$	4.11484e74	0.140163	0.0700817	+	0.997541i	$0.477674\pi$
$912$	0	0
$913$	1.89761e75	0.611228
$914$	−7.27895e75	−2.28003
$915$	0	0
$916$	1.47682e75	0.437516
$917$	3.19944e75	0.921841
$918$	0	0
$919$	−4.75576e75	−1.29621	−0.648104	−	0.761552i	$-0.724438\pi$
$919$	−4.75576e75	−1.29621	−0.648104	+	0.761552i	$0.724438\pi$
$920$	7.02587e74	0.186256
$921$	0	0
$922$	6.65889e75	1.67018
$923$	7.03428e75	1.71623
$924$	0	0
$925$	6.71770e75	1.55098
$926$	9.24196e75	2.07579
$927$	0	0
$928$	−2.17309e74	−0.0461960
$929$	−7.98781e75	−1.65207	−0.826033	−	0.563622i	$-0.809407\pi$
$929$	−7.98781e75	−1.65207	−0.826033	+	0.563622i	$0.809407\pi$
$930$	0	0
$931$	−1.13377e75	−0.221977
$932$	5.11675e75	0.974740
$933$	0	0
$934$	1.80626e75	0.325787
$935$	5.59216e74	0.0981484
$936$	0	0
$937$	−3.77230e75	−0.626970	−0.313485	−	0.949593i	$-0.601497\pi$
$937$	−3.77230e75	−0.626970	−0.313485	+	0.949593i	$0.601497\pi$
$938$	−1.05978e76	−1.71413
$939$	0	0
$940$	4.26494e75	0.653360
$941$	1.08168e75	0.161274	0.0806371	−	0.996744i	$-0.474305\pi$
$941$	1.08168e75	0.161274	0.0806371	+	0.996744i	$0.474305\pi$
$942$	0	0
$943$	−3.64920e75	−0.515406
$944$	4.88014e75	0.670882
$945$	0	0
$946$	−6.09688e75	−0.794116
$947$	−2.23798e75	−0.283747	−0.141873	−	0.989885i	$-0.545313\pi$
$947$	−2.23798e75	−0.283747	−0.141873	+	0.989885i	$0.545313\pi$
$948$	0	0
$949$	−3.12115e75	−0.374995
$950$	8.00178e75	0.935911
$951$	0	0
$952$	−3.18132e75	−0.352667
$953$	−1.63024e76	−1.75947	−0.879737	−	0.475461i	$-0.842281\pi$
$953$	−1.63024e76	−1.75947	−0.879737	+	0.475461i	$0.842281\pi$
$954$	0	0
$955$	6.78078e75	0.693735
$956$	−2.20776e76	−2.19925
$957$	0	0
$958$	−9.38912e75	−0.886756
$959$	−9.03332e75	−0.830755
$960$	0	0
$961$	−2.65345e75	−0.231401
$962$	5.20607e76	4.42126
$963$	0	0
$964$	2.15201e76	1.73332
$965$	−4.58360e75	−0.359551
$966$	0	0
$967$	−1.19422e76	−0.888609	−0.444305	−	0.895876i	$-0.646549\pi$
$967$	−1.19422e76	−0.888609	−0.444305	+	0.895876i	$0.646549\pi$
$968$	8.79207e74	0.0637191
$969$	0	0
$970$	−1.64347e76	−1.13001
$971$	9.57238e75	0.641106	0.320553	−	0.947231i	$-0.396131\pi$
$971$	9.57238e75	0.641106	0.320553	+	0.947231i	$0.396131\pi$
$972$	0	0
$973$	−2.47220e75	−0.157111
$974$	−1.79224e74	−0.0110954
$975$	0	0
$976$	8.91387e75	0.523716
$977$	3.03295e75	0.173602	0.0868008	−	0.996226i	$-0.472336\pi$
$977$	3.03295e75	0.173602	0.0868008	+	0.996226i	$0.472336\pi$
$978$	0	0
$979$	−2.67035e76	−1.45081
$980$	4.67898e75	0.247677
$981$	0	0
$982$	6.42642e76	3.22943
$983$	−7.25776e75	−0.355376	−0.177688	−	0.984087i	$-0.556862\pi$
$983$	−7.25776e75	−0.355376	−0.177688	+	0.984087i	$0.556862\pi$
$984$	0	0
$985$	−7.74291e75	−0.359981
$986$	2.09677e75	0.0949926
$987$	0	0
$988$	4.08528e76	1.75760
$989$	−3.62349e75	−0.151922
$990$	0	0
$991$	−1.83886e74	−0.00732268	−0.00366134	−	0.999993i	$-0.501165\pi$
$991$	−1.83886e74	−0.00732268	−0.00366134	+	0.999993i	$0.501165\pi$
$992$	5.17148e75	0.200709
$993$	0	0
$994$	−4.44152e76	−1.63749
$995$	−1.03642e76	−0.372433
$996$	0	0
$997$	4.30923e76	1.47120	0.735602	−	0.677414i	$-0.236900\pi$
$997$	4.30923e76	1.47120	0.735602	+	0.677414i	$0.236900\pi$
$998$	7.81731e76	2.60153
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	9.52.a.b.1.1		4
3.2	odd	2		1.52.a.a.1.4	✓	4

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

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 9 = 3^{2} \)
Weight:	\( k \)	\(=\)	\( 52 \)
Character orbit:	\([\chi]\)	\(=\)	9.a (trivial)

\(f(q)\)	\(=\)	\(q-8.12369e7 q^{2} +4.34763e15 q^{4} -2.42754e17 q^{5} +2.85586e21 q^{7} -1.70259e23 q^{8} +O(q^{10})\)	\(q-8.12369e7 q^{2} +4.34763e15 q^{4} -2.42754e17 q^{5} +2.85586e21 q^{7} -1.70259e23 q^{8} +1.97206e25 q^{10} -3.52088e26 q^{11} +3.67432e28 q^{13} -2.32001e29 q^{14} +4.04130e30 q^{16} +6.54277e30 q^{17} +2.55736e32 q^{19} -1.05541e33 q^{20} +2.86025e34 q^{22} +1.69990e34 q^{23} -3.85160e35 q^{25} -2.98490e36 q^{26} +1.24162e37 q^{28} -3.94490e36 q^{29} +9.38800e37 q^{31} +5.50861e37 q^{32} -5.31514e38 q^{34} -6.93270e38 q^{35} -1.74413e40 q^{37} -2.07752e40 q^{38} +4.13310e40 q^{40} -2.14671e41 q^{41} -2.13159e41 q^{43} -1.53075e42 q^{44} -1.38095e42 q^{46} -4.04105e42 q^{47} -4.43335e42 q^{49} +3.12892e43 q^{50} +1.59746e44 q^{52} +4.94974e42 q^{53} +8.54708e43 q^{55} -4.86235e44 q^{56} +3.20472e44 q^{58} +1.20757e45 q^{59} +2.20569e45 q^{61} -7.62652e45 q^{62} -1.35752e46 q^{64} -8.91957e45 q^{65} +4.56801e46 q^{67} +2.84456e46 q^{68} +5.63191e46 q^{70} +1.91444e47 q^{71} -8.49448e46 q^{73} +1.41688e48 q^{74} +1.11185e48 q^{76} -1.00551e48 q^{77} +2.35655e48 q^{79} -9.81042e47 q^{80} +1.74392e49 q^{82} -5.38960e48 q^{83} -1.58828e48 q^{85} +1.73164e49 q^{86} +5.99461e49 q^{88} +7.58432e49 q^{89} +1.04933e50 q^{91} +7.39055e49 q^{92} +3.28282e50 q^{94} -6.20810e49 q^{95} -8.33376e50 q^{97} +3.60151e50 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 32756040 q^{2} + 79\!\cdots\!12 q^{4}+ \cdots + 13\!\cdots\!20 q^{8}+O(q^{10}) \) 4 * q - 32756040 * q^2 + 7978103470875712 * q^4 - 1214113112967557880 * q^5 + 6566332044151252469600 * q^7 + 139242173294665691205120 * q^8	\( 4 q - 32756040 q^{2} + 79\!\cdots\!12 q^{4}+ \cdots + 31\!\cdots\!80 q^{98}+O(q^{100}) \) 4 * q - 32756040 * q^2 + 7978103470875712 * q^4 - 1214113112967557880 * q^5 + 6566332044151252469600 * q^7 + 139242173294665691205120 * q^8 - 26338767422633182993407120 * q^10 - 352319730227217761184247248 * q^11 + 30737495492092678036022901080 * q^13 - 116878411871248994844784530624 * q^14 + 13655541308212814904424583532544 * q^16 - 48152025926602119975132578130120 * q^17 + 817578654717102241686587953106480 * q^19 - 6688106698568613691058684703008640 * q^20 - 34873949046188270313389204382330720 * q^22 + 54442545328795748403982512519744480 * q^23 - 577962011134461749109509927876368100 * q^25 - 1509847347916659653711306190553689648 * q^26 + 34411298173690719862562837156054996480 * q^28 - 24524817706178324469842039147126378520 * q^29 - 74015080632891216448581759119415494272 * q^31 + 698885110517892283834830116511622594560 * q^32 + 599176354190711613816800945566309634064 * q^34 - 5459558934032100428649177266758776617280 * q^35 + 9223299799194559520674909690367653437560 * q^37 - 42209741287618122996397532876280940717920 * q^38 - 260218563144774091908833544090781982745600 * q^40 - 146626572441904135431040424870320811649768 * q^41 - 383253403750663564628750277915860311246000 * q^43 - 3919911265019437916289330658643948094246144 * q^44 - 687622182810100175391810298681828635813312 * q^46 - 703242125794576181922406089648904926204480 * q^47 - 21525353693695885888621049774661370126875228 * q^49 + 65550763083377103476240548536052846777230600 * q^50 + 205575224727950383449569813934278240424406400 * q^52 + 46053881458574871528873628680364599519093960 * q^53 + 288271437023082169121432211103105268991934560 * q^55 + 718413197664523425962520880364481249783828480 * q^56 - 3260382815057328392932619475690091710393763920 * q^58 - 1119164779584192618652811959209270069996506640 * q^59 + 3426848506305498355799302542081826532801316248 * q^61 - 9652948821672246376570757837225648817671719680 * q^62 - 3410402571656263891001355509990182780636233728 * q^64 - 10662663070585071183633914150857043524084084560 * q^65 + 30875136607724238160818607702139418169238276720 * q^67 + 92264980123003683860202361552579885626636888960 * q^68 - 127365497175284237875848441551548839150619662720 * q^70 - 396890633217178572952249989093970445513163336288 * q^71 + 1093181650202404127682760092563948835468903177320 * q^73 + 2446722614206037598896806276944107193380656941456 * q^74 - 1930298057964975808050160660816178333985982024960 * q^76 - 1379856740595107958858322062475643650952236464000 * q^77 + 4057123342028363124154537966955503984273281629120 * q^79 - 6556705282035289158041818706914507044939664711680 * q^80 + 2672741123252406904410297531162443665031405248080 * q^82 - 10514534101014085301175610601927458547806407366960 * q^83 - 2214700921000481207852358003497850667551075883920 * q^85 + 43819383990098235110217468422860464230535375092832 * q^86 - 25053936600673669378312978656608794916631597373440 * q^88 + 90777724780188979543741952283884054816841444724440 * q^89 + 100567720661332633308233017957549269313038849882688 * q^91 - 192025202572015319809189966047000799088692638097920 * q^92 + 639818007616166555781273040037466169910601363859584 * q^94 + 418719878951800677902105757696028542296429654882400 * q^95 - 1321788056943507607869460465290134726019322989433720 * q^97 + 317844097908560926995320900303041587618753340105080 * q^98

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